Properties

Label 177.14.a.a.1.3
Level $177$
Weight $14$
Character 177.1
Self dual yes
Analytic conductor $189.799$
Analytic rank $1$
Dimension $30$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(189.798744245\)
Analytic rank: \(1\)
Dimension: \(30\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-153.212 q^{2} +729.000 q^{3} +15282.0 q^{4} +58431.3 q^{5} -111692. q^{6} +57012.1 q^{7} -1.08627e6 q^{8} +531441. q^{9} +O(q^{10})\) \(q-153.212 q^{2} +729.000 q^{3} +15282.0 q^{4} +58431.3 q^{5} -111692. q^{6} +57012.1 q^{7} -1.08627e6 q^{8} +531441. q^{9} -8.95239e6 q^{10} -8.87077e6 q^{11} +1.11405e7 q^{12} -4.66223e6 q^{13} -8.73495e6 q^{14} +4.25964e7 q^{15} +4.12395e7 q^{16} -9.15066e7 q^{17} -8.14232e7 q^{18} -1.77197e8 q^{19} +8.92945e8 q^{20} +4.15618e7 q^{21} +1.35911e9 q^{22} +7.81026e8 q^{23} -7.91889e8 q^{24} +2.19352e9 q^{25} +7.14310e8 q^{26} +3.87420e8 q^{27} +8.71257e8 q^{28} -3.99585e9 q^{29} -6.52629e9 q^{30} +5.30502e9 q^{31} +2.58031e9 q^{32} -6.46679e9 q^{33} +1.40199e10 q^{34} +3.33129e9 q^{35} +8.12146e9 q^{36} +1.42793e10 q^{37} +2.71487e10 q^{38} -3.39876e9 q^{39} -6.34720e10 q^{40} +3.50267e10 q^{41} -6.36778e9 q^{42} -2.93576e10 q^{43} -1.35563e11 q^{44} +3.10528e10 q^{45} -1.19663e11 q^{46} -4.10994e10 q^{47} +3.00636e10 q^{48} -9.36386e10 q^{49} -3.36073e11 q^{50} -6.67083e10 q^{51} -7.12480e10 q^{52} +2.99702e11 q^{53} -5.93575e10 q^{54} -5.18331e11 q^{55} -6.19304e10 q^{56} -1.29176e11 q^{57} +6.12212e11 q^{58} +4.21805e10 q^{59} +6.50957e11 q^{60} -6.54690e11 q^{61} -8.12793e11 q^{62} +3.02986e10 q^{63} -7.33168e11 q^{64} -2.72420e11 q^{65} +9.90791e11 q^{66} +1.22057e12 q^{67} -1.39840e12 q^{68} +5.69368e11 q^{69} -5.10395e11 q^{70} -1.52971e12 q^{71} -5.77287e11 q^{72} +1.65969e12 q^{73} -2.18776e12 q^{74} +1.59907e12 q^{75} -2.70791e12 q^{76} -5.05742e11 q^{77} +5.20732e11 q^{78} -2.59604e12 q^{79} +2.40968e12 q^{80} +2.82430e11 q^{81} -5.36651e12 q^{82} -2.52953e12 q^{83} +6.35146e11 q^{84} -5.34685e12 q^{85} +4.49794e12 q^{86} -2.91297e12 q^{87} +9.63603e12 q^{88} +6.85235e12 q^{89} -4.75766e12 q^{90} -2.65804e11 q^{91} +1.19356e13 q^{92} +3.86736e12 q^{93} +6.29692e12 q^{94} -1.03538e13 q^{95} +1.88104e12 q^{96} -5.66680e12 q^{97} +1.43466e13 q^{98} -4.71429e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} + O(q^{10}) \) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} - 5352519q^{10} - 13950782q^{11} + 83541942q^{12} - 17256988q^{13} + 33780109q^{14} - 100413918q^{15} + 499996762q^{16} - 317583695q^{17} - 73338858q^{18} - 863401469q^{19} - 1841280623q^{20} - 641113947q^{21} - 2723764842q^{22} - 3142075981q^{23} - 635907429q^{24} + 5435751692q^{25} - 6441414040q^{26} + 11622614670q^{27} - 7538400046q^{28} - 4604589283q^{29} - 3901986351q^{30} + 4308675373q^{31} + 6094556360q^{32} - 10170120078q^{33} + 38097713432q^{34} - 15447827315q^{35} + 60902075718q^{36} - 19633376949q^{37} - 18152222923q^{38} - 12580344252q^{39} + 14680384170q^{40} - 103644439493q^{41} + 24625699461q^{42} - 64494894924q^{43} - 199714496208q^{44} - 73201746222q^{45} - 265425792847q^{46} - 293365585139q^{47} + 364497639498q^{48} + 414396765797q^{49} - 126058522207q^{50} - 231518513655q^{51} + 156029960316q^{52} - 76747013118q^{53} - 53464027482q^{54} - 433465885754q^{55} - 502955241518q^{56} - 629419670901q^{57} - 1755031845830q^{58} + 1265416009230q^{59} - 1342293574167q^{60} - 2022612531219q^{61} - 3816005187046q^{62} - 467372067363q^{63} - 3570205594131q^{64} - 3889749040576q^{65} - 1985624569818q^{66} - 502618987776q^{67} - 8953998390517q^{68} - 2290573390149q^{69} - 6805178272420q^{70} - 1599540605456q^{71} - 463576515741q^{72} - 3826795087235q^{73} - 7573387813210q^{74} + 3962662983468q^{75} - 19498723328388q^{76} - 9088623115219q^{77} - 4695790835160q^{78} - 8595482172338q^{79} - 17452527463963q^{80} + 8472886094430q^{81} - 11181116792901q^{82} - 13548556984389q^{83} - 5495493633534q^{84} - 12851795888367q^{85} + 8539949468848q^{86} - 3356745587307q^{87} - 25134826741387q^{88} - 21826401667403q^{89} - 2844548049879q^{90} - 26577050621355q^{91} - 34908210763168q^{92} + 3141024346917q^{93} - 26426808959500q^{94} - 29105233533993q^{95} + 4442931586440q^{96} + 417815797414q^{97} + 29159956938360q^{98} - 7414017536862q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −153.212 −1.69277 −0.846385 0.532571i \(-0.821226\pi\)
−0.846385 + 0.532571i \(0.821226\pi\)
\(3\) 729.000 0.577350
\(4\) 15282.0 1.86547
\(5\) 58431.3 1.67240 0.836201 0.548423i \(-0.184772\pi\)
0.836201 + 0.548423i \(0.184772\pi\)
\(6\) −111692. −0.977322
\(7\) 57012.1 0.183160 0.0915799 0.995798i \(-0.470808\pi\)
0.0915799 + 0.995798i \(0.470808\pi\)
\(8\) −1.08627e6 −1.46505
\(9\) 531441. 0.333333
\(10\) −8.95239e6 −2.83099
\(11\) −8.87077e6 −1.50976 −0.754882 0.655861i \(-0.772306\pi\)
−0.754882 + 0.655861i \(0.772306\pi\)
\(12\) 1.11405e7 1.07703
\(13\) −4.66223e6 −0.267893 −0.133947 0.990989i \(-0.542765\pi\)
−0.133947 + 0.990989i \(0.542765\pi\)
\(14\) −8.73495e6 −0.310047
\(15\) 4.25964e7 0.965562
\(16\) 4.12395e7 0.614516
\(17\) −9.15066e7 −0.919464 −0.459732 0.888058i \(-0.652054\pi\)
−0.459732 + 0.888058i \(0.652054\pi\)
\(18\) −8.14232e7 −0.564257
\(19\) −1.77197e8 −0.864087 −0.432043 0.901853i \(-0.642207\pi\)
−0.432043 + 0.901853i \(0.642207\pi\)
\(20\) 8.92945e8 3.11982
\(21\) 4.15618e7 0.105747
\(22\) 1.35911e9 2.55568
\(23\) 7.81026e8 1.10011 0.550053 0.835130i \(-0.314608\pi\)
0.550053 + 0.835130i \(0.314608\pi\)
\(24\) −7.91889e8 −0.845845
\(25\) 2.19352e9 1.79693
\(26\) 7.14310e8 0.453482
\(27\) 3.87420e8 0.192450
\(28\) 8.71257e8 0.341680
\(29\) −3.99585e9 −1.24745 −0.623723 0.781645i \(-0.714381\pi\)
−0.623723 + 0.781645i \(0.714381\pi\)
\(30\) −6.52629e9 −1.63447
\(31\) 5.30502e9 1.07358 0.536792 0.843715i \(-0.319636\pi\)
0.536792 + 0.843715i \(0.319636\pi\)
\(32\) 2.58031e9 0.424812
\(33\) −6.46679e9 −0.871663
\(34\) 1.40199e10 1.55644
\(35\) 3.33129e9 0.306317
\(36\) 8.12146e9 0.621824
\(37\) 1.42793e10 0.914945 0.457473 0.889224i \(-0.348755\pi\)
0.457473 + 0.889224i \(0.348755\pi\)
\(38\) 2.71487e10 1.46270
\(39\) −3.39876e9 −0.154668
\(40\) −6.34720e10 −2.45015
\(41\) 3.50267e10 1.15161 0.575803 0.817588i \(-0.304689\pi\)
0.575803 + 0.817588i \(0.304689\pi\)
\(42\) −6.36778e9 −0.179006
\(43\) −2.93576e10 −0.708232 −0.354116 0.935202i \(-0.615218\pi\)
−0.354116 + 0.935202i \(0.615218\pi\)
\(44\) −1.35563e11 −2.81642
\(45\) 3.10528e10 0.557467
\(46\) −1.19663e11 −1.86223
\(47\) −4.10994e10 −0.556159 −0.278080 0.960558i \(-0.589698\pi\)
−0.278080 + 0.960558i \(0.589698\pi\)
\(48\) 3.00636e10 0.354791
\(49\) −9.36386e10 −0.966453
\(50\) −3.36073e11 −3.04179
\(51\) −6.67083e10 −0.530853
\(52\) −7.12480e10 −0.499748
\(53\) 2.99702e11 1.85736 0.928679 0.370883i \(-0.120945\pi\)
0.928679 + 0.370883i \(0.120945\pi\)
\(54\) −5.93575e10 −0.325774
\(55\) −5.18331e11 −2.52493
\(56\) −6.19304e10 −0.268338
\(57\) −1.29176e11 −0.498881
\(58\) 6.12212e11 2.11164
\(59\) 4.21805e10 0.130189
\(60\) 6.50957e11 1.80123
\(61\) −6.54690e11 −1.62702 −0.813508 0.581553i \(-0.802445\pi\)
−0.813508 + 0.581553i \(0.802445\pi\)
\(62\) −8.12793e11 −1.81733
\(63\) 3.02986e10 0.0610532
\(64\) −7.33168e11 −1.33363
\(65\) −2.72420e11 −0.448025
\(66\) 9.90791e11 1.47553
\(67\) 1.22057e12 1.64846 0.824228 0.566257i \(-0.191609\pi\)
0.824228 + 0.566257i \(0.191609\pi\)
\(68\) −1.39840e12 −1.71523
\(69\) 5.69368e11 0.635146
\(70\) −5.10395e11 −0.518524
\(71\) −1.52971e12 −1.41720 −0.708598 0.705612i \(-0.750672\pi\)
−0.708598 + 0.705612i \(0.750672\pi\)
\(72\) −5.77287e11 −0.488349
\(73\) 1.65969e12 1.28359 0.641797 0.766874i \(-0.278189\pi\)
0.641797 + 0.766874i \(0.278189\pi\)
\(74\) −2.18776e12 −1.54879
\(75\) 1.59907e12 1.03746
\(76\) −2.70791e12 −1.61193
\(77\) −5.05742e11 −0.276528
\(78\) 5.20732e11 0.261818
\(79\) −2.59604e12 −1.20153 −0.600766 0.799425i \(-0.705138\pi\)
−0.600766 + 0.799425i \(0.705138\pi\)
\(80\) 2.40968e12 1.02772
\(81\) 2.82430e11 0.111111
\(82\) −5.36651e12 −1.94941
\(83\) −2.52953e12 −0.849243 −0.424622 0.905371i \(-0.639593\pi\)
−0.424622 + 0.905371i \(0.639593\pi\)
\(84\) 6.35146e11 0.197269
\(85\) −5.34685e12 −1.53771
\(86\) 4.49794e12 1.19887
\(87\) −2.91297e12 −0.720213
\(88\) 9.63603e12 2.21188
\(89\) 6.85235e12 1.46152 0.730759 0.682635i \(-0.239166\pi\)
0.730759 + 0.682635i \(0.239166\pi\)
\(90\) −4.75766e12 −0.943664
\(91\) −2.65804e11 −0.0490673
\(92\) 1.19356e13 2.05222
\(93\) 3.86736e12 0.619833
\(94\) 6.29692e12 0.941450
\(95\) −1.03538e13 −1.44510
\(96\) 1.88104e12 0.245265
\(97\) −5.66680e12 −0.690752 −0.345376 0.938464i \(-0.612249\pi\)
−0.345376 + 0.938464i \(0.612249\pi\)
\(98\) 1.43466e13 1.63598
\(99\) −4.71429e12 −0.503255
\(100\) 3.35212e13 3.35212
\(101\) −8.69804e12 −0.815328 −0.407664 0.913132i \(-0.633657\pi\)
−0.407664 + 0.913132i \(0.633657\pi\)
\(102\) 1.02205e13 0.898612
\(103\) 1.24127e13 1.02429 0.512147 0.858898i \(-0.328850\pi\)
0.512147 + 0.858898i \(0.328850\pi\)
\(104\) 5.06442e12 0.392476
\(105\) 2.42851e12 0.176852
\(106\) −4.59179e13 −3.14408
\(107\) −4.89900e12 −0.315582 −0.157791 0.987472i \(-0.550437\pi\)
−0.157791 + 0.987472i \(0.550437\pi\)
\(108\) 5.92054e12 0.359010
\(109\) 1.80653e13 1.03175 0.515875 0.856664i \(-0.327467\pi\)
0.515875 + 0.856664i \(0.327467\pi\)
\(110\) 7.94146e13 4.27413
\(111\) 1.04096e13 0.528244
\(112\) 2.35115e12 0.112555
\(113\) −3.11508e13 −1.40754 −0.703768 0.710430i \(-0.748501\pi\)
−0.703768 + 0.710430i \(0.748501\pi\)
\(114\) 1.97914e13 0.844491
\(115\) 4.56364e13 1.83982
\(116\) −6.10643e13 −2.32708
\(117\) −2.47770e12 −0.0892977
\(118\) −6.46257e12 −0.220380
\(119\) −5.21699e12 −0.168409
\(120\) −4.62711e13 −1.41459
\(121\) 4.41679e13 1.27939
\(122\) 1.00306e14 2.75417
\(123\) 2.55345e13 0.664880
\(124\) 8.10710e13 2.00274
\(125\) 5.68427e13 1.33278
\(126\) −4.64211e12 −0.103349
\(127\) −3.45890e13 −0.731500 −0.365750 0.930713i \(-0.619187\pi\)
−0.365750 + 0.930713i \(0.619187\pi\)
\(128\) 9.11924e13 1.83271
\(129\) −2.14017e13 −0.408898
\(130\) 4.17381e13 0.758404
\(131\) −9.05081e13 −1.56467 −0.782337 0.622855i \(-0.785973\pi\)
−0.782337 + 0.622855i \(0.785973\pi\)
\(132\) −9.88253e13 −1.62606
\(133\) −1.01024e13 −0.158266
\(134\) −1.87007e14 −2.79046
\(135\) 2.26375e13 0.321854
\(136\) 9.94006e13 1.34706
\(137\) 6.91594e13 0.893650 0.446825 0.894621i \(-0.352555\pi\)
0.446825 + 0.894621i \(0.352555\pi\)
\(138\) −8.72341e13 −1.07516
\(139\) −4.61403e13 −0.542605 −0.271303 0.962494i \(-0.587454\pi\)
−0.271303 + 0.962494i \(0.587454\pi\)
\(140\) 5.09087e13 0.571425
\(141\) −2.99614e13 −0.321099
\(142\) 2.34370e14 2.39899
\(143\) 4.13576e13 0.404456
\(144\) 2.19164e13 0.204839
\(145\) −2.33483e14 −2.08623
\(146\) −2.54284e14 −2.17283
\(147\) −6.82626e13 −0.557982
\(148\) 2.18215e14 1.70681
\(149\) −1.48180e14 −1.10938 −0.554688 0.832059i \(-0.687162\pi\)
−0.554688 + 0.832059i \(0.687162\pi\)
\(150\) −2.44997e14 −1.75618
\(151\) 1.72056e14 1.18119 0.590596 0.806967i \(-0.298893\pi\)
0.590596 + 0.806967i \(0.298893\pi\)
\(152\) 1.92483e14 1.26593
\(153\) −4.86304e13 −0.306488
\(154\) 7.74858e13 0.468099
\(155\) 3.09979e14 1.79546
\(156\) −5.19398e13 −0.288529
\(157\) −1.31345e14 −0.699950 −0.349975 0.936759i \(-0.613810\pi\)
−0.349975 + 0.936759i \(0.613810\pi\)
\(158\) 3.97745e14 2.03392
\(159\) 2.18482e14 1.07235
\(160\) 1.50771e14 0.710456
\(161\) 4.45280e13 0.201495
\(162\) −4.32716e13 −0.188086
\(163\) −4.51031e13 −0.188359 −0.0941797 0.995555i \(-0.530023\pi\)
−0.0941797 + 0.995555i \(0.530023\pi\)
\(164\) 5.35276e14 2.14829
\(165\) −3.77863e14 −1.45777
\(166\) 3.87555e14 1.43757
\(167\) −9.10640e13 −0.324855 −0.162427 0.986720i \(-0.551932\pi\)
−0.162427 + 0.986720i \(0.551932\pi\)
\(168\) −4.51473e13 −0.154925
\(169\) −2.81139e14 −0.928233
\(170\) 8.19203e14 2.60299
\(171\) −9.41696e13 −0.288029
\(172\) −4.48641e14 −1.32119
\(173\) −4.89378e14 −1.38786 −0.693929 0.720044i \(-0.744122\pi\)
−0.693929 + 0.720044i \(0.744122\pi\)
\(174\) 4.46303e14 1.21916
\(175\) 1.25057e14 0.329125
\(176\) −3.65826e14 −0.927775
\(177\) 3.07496e13 0.0751646
\(178\) −1.04986e15 −2.47402
\(179\) −4.93063e14 −1.12036 −0.560180 0.828371i \(-0.689268\pi\)
−0.560180 + 0.828371i \(0.689268\pi\)
\(180\) 4.74547e14 1.03994
\(181\) −6.09433e14 −1.28830 −0.644148 0.764901i \(-0.722788\pi\)
−0.644148 + 0.764901i \(0.722788\pi\)
\(182\) 4.07243e13 0.0830596
\(183\) −4.77269e14 −0.939358
\(184\) −8.48403e14 −1.61171
\(185\) 8.34357e14 1.53016
\(186\) −5.92526e14 −1.04924
\(187\) 8.11735e14 1.38817
\(188\) −6.28079e14 −1.03750
\(189\) 2.20877e13 0.0352491
\(190\) 1.58633e15 2.44622
\(191\) −8.52949e14 −1.27118 −0.635589 0.772028i \(-0.719243\pi\)
−0.635589 + 0.772028i \(0.719243\pi\)
\(192\) −5.34480e14 −0.769969
\(193\) 4.00836e14 0.558270 0.279135 0.960252i \(-0.409952\pi\)
0.279135 + 0.960252i \(0.409952\pi\)
\(194\) 8.68223e14 1.16928
\(195\) −1.98594e14 −0.258667
\(196\) −1.43098e15 −1.80289
\(197\) −1.18643e15 −1.44615 −0.723074 0.690770i \(-0.757272\pi\)
−0.723074 + 0.690770i \(0.757272\pi\)
\(198\) 7.22287e14 0.851895
\(199\) −6.72887e14 −0.768064 −0.384032 0.923320i \(-0.625465\pi\)
−0.384032 + 0.923320i \(0.625465\pi\)
\(200\) −2.38274e15 −2.63258
\(201\) 8.89798e14 0.951737
\(202\) 1.33264e15 1.38016
\(203\) −2.27812e14 −0.228482
\(204\) −1.01943e15 −0.990291
\(205\) 2.04666e15 1.92595
\(206\) −1.90178e15 −1.73389
\(207\) 4.15069e14 0.366702
\(208\) −1.92268e14 −0.164625
\(209\) 1.57187e15 1.30457
\(210\) −3.72078e14 −0.299370
\(211\) −4.17827e13 −0.0325958 −0.0162979 0.999867i \(-0.505188\pi\)
−0.0162979 + 0.999867i \(0.505188\pi\)
\(212\) 4.58003e15 3.46485
\(213\) −1.11516e15 −0.818218
\(214\) 7.50586e14 0.534209
\(215\) −1.71540e15 −1.18445
\(216\) −4.20842e14 −0.281948
\(217\) 3.02450e14 0.196637
\(218\) −2.76783e15 −1.74651
\(219\) 1.20991e15 0.741084
\(220\) −7.92111e15 −4.71019
\(221\) 4.26625e14 0.246318
\(222\) −1.59488e15 −0.894196
\(223\) −2.33490e14 −0.127141 −0.0635706 0.997977i \(-0.520249\pi\)
−0.0635706 + 0.997977i \(0.520249\pi\)
\(224\) 1.47109e14 0.0778084
\(225\) 1.16572e15 0.598976
\(226\) 4.77268e15 2.38264
\(227\) −1.06554e15 −0.516893 −0.258447 0.966026i \(-0.583211\pi\)
−0.258447 + 0.966026i \(0.583211\pi\)
\(228\) −1.97407e15 −0.930649
\(229\) −3.34037e14 −0.153061 −0.0765303 0.997067i \(-0.524384\pi\)
−0.0765303 + 0.997067i \(0.524384\pi\)
\(230\) −6.99205e15 −3.11439
\(231\) −3.68686e14 −0.159654
\(232\) 4.34056e15 1.82757
\(233\) −3.54779e15 −1.45259 −0.726296 0.687382i \(-0.758760\pi\)
−0.726296 + 0.687382i \(0.758760\pi\)
\(234\) 3.79614e14 0.151161
\(235\) −2.40149e15 −0.930122
\(236\) 6.44601e14 0.242864
\(237\) −1.89251e15 −0.693705
\(238\) 7.99306e14 0.285077
\(239\) −1.34856e15 −0.468039 −0.234020 0.972232i \(-0.575188\pi\)
−0.234020 + 0.972232i \(0.575188\pi\)
\(240\) 1.75666e15 0.593353
\(241\) 3.35663e15 1.10355 0.551777 0.833992i \(-0.313950\pi\)
0.551777 + 0.833992i \(0.313950\pi\)
\(242\) −6.76706e15 −2.16571
\(243\) 2.05891e14 0.0641500
\(244\) −1.00049e16 −3.03516
\(245\) −5.47143e15 −1.61630
\(246\) −3.91219e15 −1.12549
\(247\) 8.26132e14 0.231483
\(248\) −5.76266e15 −1.57285
\(249\) −1.84403e15 −0.490311
\(250\) −8.70899e15 −2.25610
\(251\) −1.90252e13 −0.00480231 −0.00240115 0.999997i \(-0.500764\pi\)
−0.00240115 + 0.999997i \(0.500764\pi\)
\(252\) 4.63022e14 0.113893
\(253\) −6.92831e15 −1.66090
\(254\) 5.29946e15 1.23826
\(255\) −3.89785e15 −0.887799
\(256\) −7.96567e15 −1.76873
\(257\) −3.82535e15 −0.828143 −0.414072 0.910244i \(-0.635894\pi\)
−0.414072 + 0.910244i \(0.635894\pi\)
\(258\) 3.27900e15 0.692170
\(259\) 8.14092e14 0.167581
\(260\) −4.16311e15 −0.835779
\(261\) −2.12356e15 −0.415815
\(262\) 1.38669e16 2.64863
\(263\) −5.52965e15 −1.03035 −0.515176 0.857084i \(-0.672273\pi\)
−0.515176 + 0.857084i \(0.672273\pi\)
\(264\) 7.02467e15 1.27703
\(265\) 1.75120e16 3.10625
\(266\) 1.54780e15 0.267908
\(267\) 4.99536e15 0.843808
\(268\) 1.86527e16 3.07515
\(269\) 1.66099e15 0.267287 0.133644 0.991029i \(-0.457332\pi\)
0.133644 + 0.991029i \(0.457332\pi\)
\(270\) −3.46834e15 −0.544825
\(271\) −5.59072e14 −0.0857368 −0.0428684 0.999081i \(-0.513650\pi\)
−0.0428684 + 0.999081i \(0.513650\pi\)
\(272\) −3.77369e15 −0.565025
\(273\) −1.93771e14 −0.0283290
\(274\) −1.05961e16 −1.51275
\(275\) −1.94582e16 −2.71294
\(276\) 8.70105e15 1.18485
\(277\) −3.38679e15 −0.450475 −0.225237 0.974304i \(-0.572316\pi\)
−0.225237 + 0.974304i \(0.572316\pi\)
\(278\) 7.06925e15 0.918507
\(279\) 2.81930e15 0.357861
\(280\) −3.61867e15 −0.448768
\(281\) −4.65875e15 −0.564519 −0.282259 0.959338i \(-0.591084\pi\)
−0.282259 + 0.959338i \(0.591084\pi\)
\(282\) 4.59046e15 0.543547
\(283\) 1.19560e16 1.38349 0.691743 0.722144i \(-0.256843\pi\)
0.691743 + 0.722144i \(0.256843\pi\)
\(284\) −2.33770e16 −2.64374
\(285\) −7.54795e15 −0.834329
\(286\) −6.33648e15 −0.684651
\(287\) 1.99695e15 0.210928
\(288\) 1.37128e15 0.141604
\(289\) −1.53112e15 −0.154587
\(290\) 3.57724e16 3.53151
\(291\) −4.13110e15 −0.398806
\(292\) 2.53633e16 2.39451
\(293\) −9.27759e14 −0.0856635 −0.0428318 0.999082i \(-0.513638\pi\)
−0.0428318 + 0.999082i \(0.513638\pi\)
\(294\) 1.04587e16 0.944535
\(295\) 2.46466e15 0.217728
\(296\) −1.55111e16 −1.34044
\(297\) −3.43672e15 −0.290554
\(298\) 2.27030e16 1.87792
\(299\) −3.64132e15 −0.294711
\(300\) 2.44370e16 1.93535
\(301\) −1.67374e15 −0.129720
\(302\) −2.63611e16 −1.99949
\(303\) −6.34087e15 −0.470730
\(304\) −7.30751e15 −0.530996
\(305\) −3.82544e16 −2.72103
\(306\) 7.45076e15 0.518814
\(307\) 6.32361e15 0.431088 0.215544 0.976494i \(-0.430848\pi\)
0.215544 + 0.976494i \(0.430848\pi\)
\(308\) −7.72872e15 −0.515855
\(309\) 9.04886e15 0.591376
\(310\) −4.74925e16 −3.03931
\(311\) 1.71650e15 0.107573 0.0537864 0.998552i \(-0.482871\pi\)
0.0537864 + 0.998552i \(0.482871\pi\)
\(312\) 3.69197e15 0.226596
\(313\) 1.38424e16 0.832096 0.416048 0.909343i \(-0.363415\pi\)
0.416048 + 0.909343i \(0.363415\pi\)
\(314\) 2.01237e16 1.18486
\(315\) 1.77039e15 0.102106
\(316\) −3.96726e16 −2.24143
\(317\) 2.59932e16 1.43871 0.719357 0.694641i \(-0.244437\pi\)
0.719357 + 0.694641i \(0.244437\pi\)
\(318\) −3.34742e16 −1.81524
\(319\) 3.54463e16 1.88335
\(320\) −4.28400e16 −2.23036
\(321\) −3.57137e15 −0.182202
\(322\) −6.82222e15 −0.341085
\(323\) 1.62147e16 0.794496
\(324\) 4.31608e15 0.207275
\(325\) −1.02267e16 −0.481385
\(326\) 6.91035e15 0.318849
\(327\) 1.31696e16 0.595681
\(328\) −3.80483e16 −1.68716
\(329\) −2.34316e15 −0.101866
\(330\) 5.78932e16 2.46767
\(331\) −3.81986e16 −1.59649 −0.798243 0.602336i \(-0.794237\pi\)
−0.798243 + 0.602336i \(0.794237\pi\)
\(332\) −3.86561e16 −1.58424
\(333\) 7.58859e15 0.304982
\(334\) 1.39521e16 0.549905
\(335\) 7.13197e16 2.75688
\(336\) 1.71399e15 0.0649835
\(337\) 3.04057e16 1.13073 0.565367 0.824839i \(-0.308735\pi\)
0.565367 + 0.824839i \(0.308735\pi\)
\(338\) 4.30739e16 1.57129
\(339\) −2.27089e16 −0.812641
\(340\) −8.17103e16 −2.86856
\(341\) −4.70596e16 −1.62086
\(342\) 1.44279e16 0.487567
\(343\) −1.08624e16 −0.360175
\(344\) 3.18902e16 1.03759
\(345\) 3.32689e16 1.06222
\(346\) 7.49786e16 2.34932
\(347\) −6.75832e15 −0.207825 −0.103912 0.994586i \(-0.533136\pi\)
−0.103912 + 0.994586i \(0.533136\pi\)
\(348\) −4.45159e16 −1.34354
\(349\) −2.88294e16 −0.854025 −0.427013 0.904246i \(-0.640434\pi\)
−0.427013 + 0.904246i \(0.640434\pi\)
\(350\) −1.91602e16 −0.557133
\(351\) −1.80624e15 −0.0515561
\(352\) −2.28893e16 −0.641366
\(353\) 5.73974e16 1.57891 0.789454 0.613810i \(-0.210364\pi\)
0.789454 + 0.613810i \(0.210364\pi\)
\(354\) −4.71121e15 −0.127236
\(355\) −8.93830e16 −2.37012
\(356\) 1.04717e17 2.72642
\(357\) −3.80318e15 −0.0972308
\(358\) 7.55432e16 1.89651
\(359\) −2.48176e15 −0.0611852 −0.0305926 0.999532i \(-0.509739\pi\)
−0.0305926 + 0.999532i \(0.509739\pi\)
\(360\) −3.37316e16 −0.816716
\(361\) −1.06543e16 −0.253354
\(362\) 9.33726e16 2.18079
\(363\) 3.21984e16 0.738655
\(364\) −4.06200e15 −0.0915336
\(365\) 9.69778e16 2.14669
\(366\) 7.31234e16 1.59012
\(367\) 6.29557e16 1.34495 0.672474 0.740121i \(-0.265232\pi\)
0.672474 + 0.740121i \(0.265232\pi\)
\(368\) 3.22091e16 0.676033
\(369\) 1.86146e16 0.383869
\(370\) −1.27834e17 −2.59020
\(371\) 1.70866e16 0.340193
\(372\) 5.91008e16 1.15628
\(373\) 4.61935e16 0.888124 0.444062 0.895996i \(-0.353537\pi\)
0.444062 + 0.895996i \(0.353537\pi\)
\(374\) −1.24368e17 −2.34986
\(375\) 4.14383e16 0.769483
\(376\) 4.46449e16 0.814800
\(377\) 1.86295e16 0.334182
\(378\) −3.38410e15 −0.0596687
\(379\) 6.73317e16 1.16698 0.583492 0.812119i \(-0.301686\pi\)
0.583492 + 0.812119i \(0.301686\pi\)
\(380\) −1.58227e17 −2.69580
\(381\) −2.52154e16 −0.422332
\(382\) 1.30682e17 2.15181
\(383\) −3.33882e16 −0.540506 −0.270253 0.962789i \(-0.587107\pi\)
−0.270253 + 0.962789i \(0.587107\pi\)
\(384\) 6.64793e16 1.05812
\(385\) −2.95512e16 −0.462466
\(386\) −6.14130e16 −0.945023
\(387\) −1.56018e16 −0.236077
\(388\) −8.65998e16 −1.28858
\(389\) −1.12862e17 −1.65149 −0.825744 0.564045i \(-0.809245\pi\)
−0.825744 + 0.564045i \(0.809245\pi\)
\(390\) 3.04270e16 0.437865
\(391\) −7.14690e16 −1.01151
\(392\) 1.01717e17 1.41590
\(393\) −6.59804e16 −0.903365
\(394\) 1.81776e17 2.44800
\(395\) −1.51690e17 −2.00945
\(396\) −7.20436e16 −0.938808
\(397\) 1.19950e17 1.53767 0.768833 0.639450i \(-0.220838\pi\)
0.768833 + 0.639450i \(0.220838\pi\)
\(398\) 1.03094e17 1.30016
\(399\) −7.36462e15 −0.0913749
\(400\) 9.04595e16 1.10424
\(401\) −1.05944e17 −1.27244 −0.636218 0.771509i \(-0.719502\pi\)
−0.636218 + 0.771509i \(0.719502\pi\)
\(402\) −1.36328e17 −1.61107
\(403\) −2.47332e16 −0.287606
\(404\) −1.32923e17 −1.52097
\(405\) 1.65027e16 0.185822
\(406\) 3.49035e16 0.386768
\(407\) −1.26668e17 −1.38135
\(408\) 7.24631e16 0.777724
\(409\) 8.17113e16 0.863139 0.431569 0.902080i \(-0.357960\pi\)
0.431569 + 0.902080i \(0.357960\pi\)
\(410\) −3.13572e17 −3.26019
\(411\) 5.04172e16 0.515949
\(412\) 1.89690e17 1.91079
\(413\) 2.40480e15 0.0238454
\(414\) −6.35936e16 −0.620742
\(415\) −1.47804e17 −1.42028
\(416\) −1.20300e16 −0.113804
\(417\) −3.36363e16 −0.313273
\(418\) −2.40830e17 −2.20833
\(419\) 1.49815e17 1.35259 0.676294 0.736632i \(-0.263585\pi\)
0.676294 + 0.736632i \(0.263585\pi\)
\(420\) 3.71124e16 0.329913
\(421\) 1.82154e16 0.159443 0.0797216 0.996817i \(-0.474597\pi\)
0.0797216 + 0.996817i \(0.474597\pi\)
\(422\) 6.40162e15 0.0551771
\(423\) −2.18419e16 −0.185386
\(424\) −3.25556e17 −2.72112
\(425\) −2.00721e17 −1.65221
\(426\) 1.70856e17 1.38506
\(427\) −3.73253e16 −0.298004
\(428\) −7.48663e16 −0.588711
\(429\) 3.01497e16 0.233513
\(430\) 2.62820e17 2.00500
\(431\) −4.17536e16 −0.313756 −0.156878 0.987618i \(-0.550143\pi\)
−0.156878 + 0.987618i \(0.550143\pi\)
\(432\) 1.59770e16 0.118264
\(433\) −2.04882e17 −1.49394 −0.746968 0.664860i \(-0.768491\pi\)
−0.746968 + 0.664860i \(0.768491\pi\)
\(434\) −4.63390e16 −0.332862
\(435\) −1.70209e17 −1.20449
\(436\) 2.76074e17 1.92470
\(437\) −1.38395e17 −0.950587
\(438\) −1.85373e17 −1.25449
\(439\) −5.00437e16 −0.333680 −0.166840 0.985984i \(-0.553356\pi\)
−0.166840 + 0.985984i \(0.553356\pi\)
\(440\) 5.63046e17 3.69915
\(441\) −4.97634e16 −0.322151
\(442\) −6.53641e16 −0.416960
\(443\) −1.52884e17 −0.961029 −0.480515 0.876987i \(-0.659550\pi\)
−0.480515 + 0.876987i \(0.659550\pi\)
\(444\) 1.59079e17 0.985425
\(445\) 4.00392e17 2.44425
\(446\) 3.57735e16 0.215221
\(447\) −1.08023e17 −0.640498
\(448\) −4.17995e16 −0.244267
\(449\) −1.34269e17 −0.773347 −0.386674 0.922217i \(-0.626376\pi\)
−0.386674 + 0.922217i \(0.626376\pi\)
\(450\) −1.78603e17 −1.01393
\(451\) −3.10714e17 −1.73865
\(452\) −4.76045e17 −2.62572
\(453\) 1.25429e17 0.681962
\(454\) 1.63253e17 0.874982
\(455\) −1.55312e16 −0.0820602
\(456\) 1.40320e17 0.730884
\(457\) 5.54766e16 0.284875 0.142438 0.989804i \(-0.454506\pi\)
0.142438 + 0.989804i \(0.454506\pi\)
\(458\) 5.11785e16 0.259097
\(459\) −3.54515e16 −0.176951
\(460\) 6.97413e17 3.43213
\(461\) 6.60499e16 0.320491 0.160246 0.987077i \(-0.448771\pi\)
0.160246 + 0.987077i \(0.448771\pi\)
\(462\) 5.64871e16 0.270257
\(463\) −2.51121e17 −1.18469 −0.592346 0.805683i \(-0.701798\pi\)
−0.592346 + 0.805683i \(0.701798\pi\)
\(464\) −1.64787e17 −0.766576
\(465\) 2.25975e17 1.03661
\(466\) 5.43564e17 2.45891
\(467\) −3.50096e17 −1.56181 −0.780903 0.624652i \(-0.785241\pi\)
−0.780903 + 0.624652i \(0.785241\pi\)
\(468\) −3.78641e16 −0.166583
\(469\) 6.95875e16 0.301931
\(470\) 3.67938e17 1.57448
\(471\) −9.57508e16 −0.404116
\(472\) −4.58193e16 −0.190733
\(473\) 2.60425e17 1.06926
\(474\) 2.89956e17 1.17428
\(475\) −3.88684e17 −1.55270
\(476\) −7.97258e16 −0.314162
\(477\) 1.59274e17 0.619120
\(478\) 2.06615e17 0.792283
\(479\) 1.07914e16 0.0408224 0.0204112 0.999792i \(-0.493502\pi\)
0.0204112 + 0.999792i \(0.493502\pi\)
\(480\) 1.09912e17 0.410182
\(481\) −6.65733e16 −0.245108
\(482\) −5.14277e17 −1.86806
\(483\) 3.24609e16 0.116333
\(484\) 6.74972e17 2.38666
\(485\) −3.31119e17 −1.15521
\(486\) −3.15450e16 −0.108591
\(487\) −7.52372e16 −0.255561 −0.127781 0.991802i \(-0.540785\pi\)
−0.127781 + 0.991802i \(0.540785\pi\)
\(488\) 7.11168e17 2.38366
\(489\) −3.28802e16 −0.108749
\(490\) 8.38289e17 2.73602
\(491\) 4.39043e17 1.41409 0.707046 0.707168i \(-0.250027\pi\)
0.707046 + 0.707168i \(0.250027\pi\)
\(492\) 3.90216e17 1.24032
\(493\) 3.65646e17 1.14698
\(494\) −1.26573e17 −0.391848
\(495\) −2.75462e17 −0.841644
\(496\) 2.18776e17 0.659734
\(497\) −8.72120e16 −0.259573
\(498\) 2.82527e17 0.829984
\(499\) −4.51983e17 −1.31059 −0.655297 0.755371i \(-0.727456\pi\)
−0.655297 + 0.755371i \(0.727456\pi\)
\(500\) 8.68667e17 2.48627
\(501\) −6.63856e16 −0.187555
\(502\) 2.91489e15 0.00812921
\(503\) −5.56259e17 −1.53139 −0.765694 0.643205i \(-0.777604\pi\)
−0.765694 + 0.643205i \(0.777604\pi\)
\(504\) −3.29124e16 −0.0894459
\(505\) −5.08238e17 −1.36356
\(506\) 1.06150e18 2.81152
\(507\) −2.04950e17 −0.535916
\(508\) −5.28588e17 −1.36459
\(509\) −5.22554e16 −0.133188 −0.0665941 0.997780i \(-0.521213\pi\)
−0.0665941 + 0.997780i \(0.521213\pi\)
\(510\) 5.97199e17 1.50284
\(511\) 9.46224e16 0.235103
\(512\) 4.73388e17 1.16135
\(513\) −6.86497e16 −0.166294
\(514\) 5.86089e17 1.40186
\(515\) 7.25291e17 1.71303
\(516\) −3.27059e17 −0.762788
\(517\) 3.64583e17 0.839669
\(518\) −1.24729e17 −0.283676
\(519\) −3.56757e17 −0.801280
\(520\) 2.95921e17 0.656378
\(521\) −4.20569e17 −0.921281 −0.460641 0.887587i \(-0.652380\pi\)
−0.460641 + 0.887587i \(0.652380\pi\)
\(522\) 3.25355e17 0.703880
\(523\) 1.62460e17 0.347126 0.173563 0.984823i \(-0.444472\pi\)
0.173563 + 0.984823i \(0.444472\pi\)
\(524\) −1.38314e18 −2.91886
\(525\) 9.11665e16 0.190020
\(526\) 8.47210e17 1.74415
\(527\) −4.85444e17 −0.987120
\(528\) −2.66687e17 −0.535651
\(529\) 1.05965e17 0.210233
\(530\) −2.68304e18 −5.25817
\(531\) 2.24165e16 0.0433963
\(532\) −1.54384e17 −0.295241
\(533\) −1.63302e17 −0.308508
\(534\) −7.65350e17 −1.42837
\(535\) −2.86255e17 −0.527781
\(536\) −1.32587e18 −2.41507
\(537\) −3.59443e17 −0.646840
\(538\) −2.54484e17 −0.452456
\(539\) 8.30647e17 1.45912
\(540\) 3.45945e17 0.600410
\(541\) 1.04629e18 1.79420 0.897099 0.441829i \(-0.145670\pi\)
0.897099 + 0.441829i \(0.145670\pi\)
\(542\) 8.56566e16 0.145133
\(543\) −4.44277e17 −0.743798
\(544\) −2.36115e17 −0.390599
\(545\) 1.05558e18 1.72550
\(546\) 2.96880e16 0.0479545
\(547\) 2.72176e17 0.434442 0.217221 0.976122i \(-0.430301\pi\)
0.217221 + 0.976122i \(0.430301\pi\)
\(548\) 1.05689e18 1.66708
\(549\) −3.47929e17 −0.542339
\(550\) 2.98123e18 4.59238
\(551\) 7.08051e17 1.07790
\(552\) −6.18486e17 −0.930520
\(553\) −1.48006e17 −0.220072
\(554\) 5.18898e17 0.762550
\(555\) 6.08246e17 0.883436
\(556\) −7.05114e17 −1.01222
\(557\) 1.89819e17 0.269328 0.134664 0.990891i \(-0.457004\pi\)
0.134664 + 0.990891i \(0.457004\pi\)
\(558\) −4.31951e17 −0.605777
\(559\) 1.36872e17 0.189730
\(560\) 1.37381e17 0.188237
\(561\) 5.91755e17 0.801462
\(562\) 7.13777e17 0.955601
\(563\) 1.25172e18 1.65654 0.828269 0.560331i \(-0.189326\pi\)
0.828269 + 0.560331i \(0.189326\pi\)
\(564\) −4.57870e17 −0.599001
\(565\) −1.82018e18 −2.35397
\(566\) −1.83181e18 −2.34192
\(567\) 1.61019e16 0.0203511
\(568\) 1.66167e18 2.07626
\(569\) −9.61875e17 −1.18820 −0.594099 0.804392i \(-0.702491\pi\)
−0.594099 + 0.804392i \(0.702491\pi\)
\(570\) 1.15644e18 1.41233
\(571\) 9.77698e17 1.18051 0.590256 0.807216i \(-0.299027\pi\)
0.590256 + 0.807216i \(0.299027\pi\)
\(572\) 6.32025e17 0.754501
\(573\) −6.21800e17 −0.733915
\(574\) −3.05956e17 −0.357053
\(575\) 1.71319e18 1.97681
\(576\) −3.89636e17 −0.444542
\(577\) −8.76615e17 −0.988931 −0.494466 0.869197i \(-0.664636\pi\)
−0.494466 + 0.869197i \(0.664636\pi\)
\(578\) 2.34586e17 0.261680
\(579\) 2.92210e17 0.322317
\(580\) −3.56807e18 −3.89181
\(581\) −1.44214e17 −0.155547
\(582\) 6.32935e17 0.675086
\(583\) −2.65858e18 −2.80417
\(584\) −1.80286e18 −1.88053
\(585\) −1.44775e17 −0.149342
\(586\) 1.42144e17 0.145009
\(587\) −9.80311e17 −0.989045 −0.494523 0.869165i \(-0.664657\pi\)
−0.494523 + 0.869165i \(0.664657\pi\)
\(588\) −1.04319e18 −1.04090
\(589\) −9.40032e17 −0.927669
\(590\) −3.77616e17 −0.368564
\(591\) −8.64910e17 −0.834934
\(592\) 5.88870e17 0.562249
\(593\) 6.09093e17 0.575212 0.287606 0.957749i \(-0.407141\pi\)
0.287606 + 0.957749i \(0.407141\pi\)
\(594\) 5.26547e17 0.491842
\(595\) −3.04835e17 −0.281647
\(596\) −2.26448e18 −2.06951
\(597\) −4.90535e17 −0.443442
\(598\) 5.57895e17 0.498878
\(599\) −1.10894e18 −0.980920 −0.490460 0.871464i \(-0.663171\pi\)
−0.490460 + 0.871464i \(0.663171\pi\)
\(600\) −1.73702e18 −1.51992
\(601\) −9.40985e17 −0.814514 −0.407257 0.913314i \(-0.633515\pi\)
−0.407257 + 0.913314i \(0.633515\pi\)
\(602\) 2.56437e17 0.219585
\(603\) 6.48663e17 0.549486
\(604\) 2.62936e18 2.20348
\(605\) 2.58079e18 2.13965
\(606\) 9.71498e17 0.796838
\(607\) 1.11409e18 0.904054 0.452027 0.892004i \(-0.350701\pi\)
0.452027 + 0.892004i \(0.350701\pi\)
\(608\) −4.57222e17 −0.367074
\(609\) −1.66075e17 −0.131914
\(610\) 5.86104e18 4.60607
\(611\) 1.91615e17 0.148991
\(612\) −7.43167e17 −0.571745
\(613\) −8.90339e17 −0.677739 −0.338870 0.940833i \(-0.610045\pi\)
−0.338870 + 0.940833i \(0.610045\pi\)
\(614\) −9.68854e17 −0.729733
\(615\) 1.49201e18 1.11195
\(616\) 5.49371e17 0.405127
\(617\) −1.68253e18 −1.22775 −0.613876 0.789403i \(-0.710390\pi\)
−0.613876 + 0.789403i \(0.710390\pi\)
\(618\) −1.38640e18 −1.00106
\(619\) −2.41905e18 −1.72844 −0.864222 0.503110i \(-0.832189\pi\)
−0.864222 + 0.503110i \(0.832189\pi\)
\(620\) 4.73709e18 3.34939
\(621\) 3.02585e17 0.211715
\(622\) −2.62989e17 −0.182096
\(623\) 3.90667e17 0.267691
\(624\) −1.40163e17 −0.0950462
\(625\) 6.43762e17 0.432021
\(626\) −2.12082e18 −1.40855
\(627\) 1.14590e18 0.753192
\(628\) −2.00721e18 −1.30574
\(629\) −1.30665e18 −0.841259
\(630\) −2.71245e17 −0.172841
\(631\) 6.67951e16 0.0421263 0.0210632 0.999778i \(-0.493295\pi\)
0.0210632 + 0.999778i \(0.493295\pi\)
\(632\) 2.81999e18 1.76030
\(633\) −3.04596e16 −0.0188192
\(634\) −3.98247e18 −2.43541
\(635\) −2.02108e18 −1.22336
\(636\) 3.33884e18 2.00043
\(637\) 4.36565e17 0.258906
\(638\) −5.43080e18 −3.18808
\(639\) −8.12951e17 −0.472399
\(640\) 5.32849e18 3.06503
\(641\) 1.37427e18 0.782520 0.391260 0.920280i \(-0.372039\pi\)
0.391260 + 0.920280i \(0.372039\pi\)
\(642\) 5.47177e17 0.308426
\(643\) −1.38564e18 −0.773177 −0.386589 0.922252i \(-0.626347\pi\)
−0.386589 + 0.922252i \(0.626347\pi\)
\(644\) 6.80474e17 0.375884
\(645\) −1.25053e18 −0.683841
\(646\) −2.48429e18 −1.34490
\(647\) −1.84558e18 −0.989133 −0.494567 0.869140i \(-0.664673\pi\)
−0.494567 + 0.869140i \(0.664673\pi\)
\(648\) −3.06794e17 −0.162783
\(649\) −3.74174e17 −0.196555
\(650\) 1.56685e18 0.814874
\(651\) 2.20486e17 0.113529
\(652\) −6.89264e17 −0.351379
\(653\) 1.84638e18 0.931934 0.465967 0.884802i \(-0.345707\pi\)
0.465967 + 0.884802i \(0.345707\pi\)
\(654\) −2.01775e18 −1.00835
\(655\) −5.28851e18 −2.61676
\(656\) 1.44448e18 0.707681
\(657\) 8.82027e17 0.427865
\(658\) 3.59001e17 0.172436
\(659\) 2.20948e18 1.05084 0.525418 0.850844i \(-0.323909\pi\)
0.525418 + 0.850844i \(0.323909\pi\)
\(660\) −5.77449e18 −2.71943
\(661\) 1.56589e18 0.730218 0.365109 0.930965i \(-0.381032\pi\)
0.365109 + 0.930965i \(0.381032\pi\)
\(662\) 5.85248e18 2.70248
\(663\) 3.11009e17 0.142212
\(664\) 2.74774e18 1.24418
\(665\) −5.90294e17 −0.264684
\(666\) −1.16266e18 −0.516264
\(667\) −3.12086e18 −1.37232
\(668\) −1.39164e18 −0.606008
\(669\) −1.70214e17 −0.0734050
\(670\) −1.09270e19 −4.66677
\(671\) 5.80761e18 2.45641
\(672\) 1.07242e17 0.0449227
\(673\) 5.89216e17 0.244442 0.122221 0.992503i \(-0.460998\pi\)
0.122221 + 0.992503i \(0.460998\pi\)
\(674\) −4.65852e18 −1.91407
\(675\) 8.49813e17 0.345819
\(676\) −4.29635e18 −1.73159
\(677\) 3.48655e18 1.39178 0.695889 0.718150i \(-0.255011\pi\)
0.695889 + 0.718150i \(0.255011\pi\)
\(678\) 3.47929e18 1.37562
\(679\) −3.23077e17 −0.126518
\(680\) 5.80811e18 2.25282
\(681\) −7.76777e17 −0.298428
\(682\) 7.21010e18 2.74374
\(683\) 1.72730e18 0.651077 0.325539 0.945529i \(-0.394454\pi\)
0.325539 + 0.945529i \(0.394454\pi\)
\(684\) −1.43910e18 −0.537310
\(685\) 4.04108e18 1.49454
\(686\) 1.66425e18 0.609694
\(687\) −2.43513e17 −0.0883696
\(688\) −1.21069e18 −0.435220
\(689\) −1.39728e18 −0.497574
\(690\) −5.09720e18 −1.79810
\(691\) −2.01516e18 −0.704210 −0.352105 0.935960i \(-0.614534\pi\)
−0.352105 + 0.935960i \(0.614534\pi\)
\(692\) −7.47865e18 −2.58901
\(693\) −2.68772e17 −0.0921760
\(694\) 1.03546e18 0.351799
\(695\) −2.69604e18 −0.907454
\(696\) 3.16427e18 1.05515
\(697\) −3.20517e18 −1.05886
\(698\) 4.41702e18 1.44567
\(699\) −2.58634e18 −0.838655
\(700\) 1.91111e18 0.613973
\(701\) 9.53155e17 0.303387 0.151693 0.988428i \(-0.451527\pi\)
0.151693 + 0.988428i \(0.451527\pi\)
\(702\) 2.76738e17 0.0872726
\(703\) −2.53024e18 −0.790592
\(704\) 6.50377e18 2.01346
\(705\) −1.75069e18 −0.537006
\(706\) −8.79398e18 −2.67273
\(707\) −4.95894e17 −0.149335
\(708\) 4.69914e17 0.140218
\(709\) 3.49354e18 1.03292 0.516458 0.856312i \(-0.327250\pi\)
0.516458 + 0.856312i \(0.327250\pi\)
\(710\) 1.36946e19 4.01207
\(711\) −1.37964e18 −0.400511
\(712\) −7.44348e18 −2.14119
\(713\) 4.14335e18 1.18106
\(714\) 5.82694e17 0.164589
\(715\) 2.41658e18 0.676412
\(716\) −7.53496e18 −2.09000
\(717\) −9.83097e17 −0.270223
\(718\) 3.80236e17 0.103572
\(719\) −3.75865e18 −1.01460 −0.507299 0.861770i \(-0.669356\pi\)
−0.507299 + 0.861770i \(0.669356\pi\)
\(720\) 1.28060e18 0.342573
\(721\) 7.07675e17 0.187609
\(722\) 1.63237e18 0.428870
\(723\) 2.44699e18 0.637137
\(724\) −9.31333e18 −2.40328
\(725\) −8.76495e18 −2.24157
\(726\) −4.93319e18 −1.25037
\(727\) 5.59357e18 1.40513 0.702563 0.711621i \(-0.252039\pi\)
0.702563 + 0.711621i \(0.252039\pi\)
\(728\) 2.88734e17 0.0718858
\(729\) 1.50095e17 0.0370370
\(730\) −1.48582e19 −3.63385
\(731\) 2.68641e18 0.651193
\(732\) −7.29361e18 −1.75235
\(733\) −3.88978e18 −0.926295 −0.463148 0.886281i \(-0.653280\pi\)
−0.463148 + 0.886281i \(0.653280\pi\)
\(734\) −9.64558e18 −2.27669
\(735\) −3.98867e18 −0.933169
\(736\) 2.01529e18 0.467338
\(737\) −1.08274e19 −2.48878
\(738\) −2.85199e18 −0.649802
\(739\) −3.40683e18 −0.769417 −0.384708 0.923038i \(-0.625698\pi\)
−0.384708 + 0.923038i \(0.625698\pi\)
\(740\) 1.27506e19 2.85446
\(741\) 6.02250e17 0.133647
\(742\) −2.61788e18 −0.575869
\(743\) −3.77410e17 −0.0822973 −0.0411486 0.999153i \(-0.513102\pi\)
−0.0411486 + 0.999153i \(0.513102\pi\)
\(744\) −4.20098e18 −0.908085
\(745\) −8.65834e18 −1.85532
\(746\) −7.07740e18 −1.50339
\(747\) −1.34430e18 −0.283081
\(748\) 1.24049e19 2.58960
\(749\) −2.79302e17 −0.0578020
\(750\) −6.34885e18 −1.30256
\(751\) 3.65610e18 0.743633 0.371817 0.928306i \(-0.378735\pi\)
0.371817 + 0.928306i \(0.378735\pi\)
\(752\) −1.69492e18 −0.341769
\(753\) −1.38694e16 −0.00277261
\(754\) −2.85427e18 −0.565694
\(755\) 1.00535e19 1.97543
\(756\) 3.37543e17 0.0657563
\(757\) 1.20802e18 0.233320 0.116660 0.993172i \(-0.462781\pi\)
0.116660 + 0.993172i \(0.462781\pi\)
\(758\) −1.03160e19 −1.97544
\(759\) −5.05073e18 −0.958921
\(760\) 1.12470e19 2.11714
\(761\) 4.06658e18 0.758978 0.379489 0.925196i \(-0.376100\pi\)
0.379489 + 0.925196i \(0.376100\pi\)
\(762\) 3.86331e18 0.714911
\(763\) 1.02994e18 0.188975
\(764\) −1.30347e19 −2.37135
\(765\) −2.84154e18 −0.512571
\(766\) 5.11547e18 0.914953
\(767\) −1.96655e17 −0.0348767
\(768\) −5.80697e18 −1.02118
\(769\) −3.10739e18 −0.541844 −0.270922 0.962601i \(-0.587328\pi\)
−0.270922 + 0.962601i \(0.587328\pi\)
\(770\) 4.52760e18 0.782849
\(771\) −2.78868e18 −0.478129
\(772\) 6.12556e18 1.04144
\(773\) −3.80298e17 −0.0641146 −0.0320573 0.999486i \(-0.510206\pi\)
−0.0320573 + 0.999486i \(0.510206\pi\)
\(774\) 2.39039e18 0.399625
\(775\) 1.16366e19 1.92915
\(776\) 6.15566e18 1.01198
\(777\) 5.93473e17 0.0967530
\(778\) 1.72918e19 2.79559
\(779\) −6.20662e18 −0.995088
\(780\) −3.03491e18 −0.482537
\(781\) 1.35697e19 2.13963
\(782\) 1.09499e19 1.71225
\(783\) −1.54807e18 −0.240071
\(784\) −3.86161e18 −0.593901
\(785\) −7.67468e18 −1.17060
\(786\) 1.01090e19 1.52919
\(787\) 6.37155e18 0.955893 0.477947 0.878389i \(-0.341381\pi\)
0.477947 + 0.878389i \(0.341381\pi\)
\(788\) −1.81310e19 −2.69775
\(789\) −4.03112e18 −0.594874
\(790\) 2.32408e19 3.40153
\(791\) −1.77597e18 −0.257804
\(792\) 5.12098e18 0.737292
\(793\) 3.05232e18 0.435867
\(794\) −1.83778e19 −2.60291
\(795\) 1.27662e19 1.79339
\(796\) −1.02830e19 −1.43280
\(797\) 1.12213e19 1.55083 0.775416 0.631450i \(-0.217540\pi\)
0.775416 + 0.631450i \(0.217540\pi\)
\(798\) 1.12835e18 0.154677
\(799\) 3.76087e18 0.511368
\(800\) 5.65994e18 0.763356
\(801\) 3.64162e18 0.487173
\(802\) 1.62318e19 2.15394
\(803\) −1.47227e19 −1.93793
\(804\) 1.35978e19 1.77544
\(805\) 2.60183e18 0.336981
\(806\) 3.78942e18 0.486850
\(807\) 1.21086e18 0.154318
\(808\) 9.44839e18 1.19449
\(809\) 7.22737e18 0.906390 0.453195 0.891412i \(-0.350284\pi\)
0.453195 + 0.891412i \(0.350284\pi\)
\(810\) −2.52842e18 −0.314555
\(811\) 1.17677e19 1.45230 0.726148 0.687538i \(-0.241309\pi\)
0.726148 + 0.687538i \(0.241309\pi\)
\(812\) −3.48141e18 −0.426227
\(813\) −4.07563e17 −0.0495001
\(814\) 1.94071e19 2.33831
\(815\) −2.63544e18 −0.315013
\(816\) −2.75102e18 −0.326218
\(817\) 5.20207e18 0.611974
\(818\) −1.25192e19 −1.46110
\(819\) −1.41259e17 −0.0163558
\(820\) 3.12769e19 3.59281
\(821\) 1.60658e19 1.83093 0.915466 0.402396i \(-0.131823\pi\)
0.915466 + 0.402396i \(0.131823\pi\)
\(822\) −7.72453e18 −0.873384
\(823\) 2.19199e18 0.245889 0.122945 0.992414i \(-0.460766\pi\)
0.122945 + 0.992414i \(0.460766\pi\)
\(824\) −1.34835e19 −1.50064
\(825\) −1.41850e19 −1.56631
\(826\) −3.68445e17 −0.0403647
\(827\) −1.59480e19 −1.73349 −0.866744 0.498754i \(-0.833791\pi\)
−0.866744 + 0.498754i \(0.833791\pi\)
\(828\) 6.34307e18 0.684073
\(829\) 2.38520e18 0.255223 0.127611 0.991824i \(-0.459269\pi\)
0.127611 + 0.991824i \(0.459269\pi\)
\(830\) 2.26453e19 2.40420
\(831\) −2.46897e18 −0.260082
\(832\) 3.41820e18 0.357269
\(833\) 8.56855e18 0.888618
\(834\) 5.15349e18 0.530300
\(835\) −5.32099e18 −0.543288
\(836\) 2.40213e19 2.43364
\(837\) 2.05527e18 0.206611
\(838\) −2.29535e19 −2.28962
\(839\) 9.60090e18 0.950296 0.475148 0.879906i \(-0.342394\pi\)
0.475148 + 0.879906i \(0.342394\pi\)
\(840\) −2.63801e18 −0.259097
\(841\) 5.70616e18 0.556122
\(842\) −2.79083e18 −0.269901
\(843\) −3.39623e18 −0.325925
\(844\) −6.38522e17 −0.0608065
\(845\) −1.64273e19 −1.55238
\(846\) 3.34644e18 0.313817
\(847\) 2.51811e18 0.234332
\(848\) 1.23595e19 1.14138
\(849\) 8.71594e18 0.798756
\(850\) 3.07529e19 2.79681
\(851\) 1.11525e19 1.00654
\(852\) −1.70418e19 −1.52636
\(853\) 4.86237e18 0.432195 0.216097 0.976372i \(-0.430667\pi\)
0.216097 + 0.976372i \(0.430667\pi\)
\(854\) 5.71869e18 0.504452
\(855\) −5.50246e18 −0.481700
\(856\) 5.32162e18 0.462343
\(857\) 1.56370e19 1.34827 0.674137 0.738606i \(-0.264516\pi\)
0.674137 + 0.738606i \(0.264516\pi\)
\(858\) −4.61930e18 −0.395283
\(859\) −5.94500e18 −0.504890 −0.252445 0.967611i \(-0.581235\pi\)
−0.252445 + 0.967611i \(0.581235\pi\)
\(860\) −2.62147e19 −2.20956
\(861\) 1.45577e18 0.121779
\(862\) 6.39716e18 0.531117
\(863\) −1.26892e19 −1.04560 −0.522798 0.852456i \(-0.675112\pi\)
−0.522798 + 0.852456i \(0.675112\pi\)
\(864\) 9.99664e17 0.0817551
\(865\) −2.85950e19 −2.32105
\(866\) 3.13904e19 2.52889
\(867\) −1.11618e18 −0.0892507
\(868\) 4.62203e18 0.366821
\(869\) 2.30289e19 1.81403
\(870\) 2.60780e19 2.03892
\(871\) −5.69059e18 −0.441610
\(872\) −1.96238e19 −1.51156
\(873\) −3.01157e18 −0.230251
\(874\) 2.12038e19 1.60913
\(875\) 3.24072e18 0.244112
\(876\) 1.84898e19 1.38247
\(877\) 1.49793e19 1.11171 0.555857 0.831278i \(-0.312390\pi\)
0.555857 + 0.831278i \(0.312390\pi\)
\(878\) 7.66730e18 0.564843
\(879\) −6.76337e17 −0.0494578
\(880\) −2.13757e19 −1.55161
\(881\) 1.25429e19 0.903761 0.451881 0.892078i \(-0.350753\pi\)
0.451881 + 0.892078i \(0.350753\pi\)
\(882\) 7.62436e18 0.545328
\(883\) −1.17294e19 −0.832782 −0.416391 0.909186i \(-0.636705\pi\)
−0.416391 + 0.909186i \(0.636705\pi\)
\(884\) 6.51966e18 0.459500
\(885\) 1.79674e18 0.125705
\(886\) 2.34236e19 1.62680
\(887\) −1.51666e19 −1.04565 −0.522824 0.852440i \(-0.675122\pi\)
−0.522824 + 0.852440i \(0.675122\pi\)
\(888\) −1.13076e19 −0.773902
\(889\) −1.97199e18 −0.133981
\(890\) −6.13448e19 −4.13755
\(891\) −2.50537e18 −0.167752
\(892\) −3.56818e18 −0.237179
\(893\) 7.28268e18 0.480570
\(894\) 1.65505e19 1.08422
\(895\) −2.88103e19 −1.87369
\(896\) 5.19907e18 0.335679
\(897\) −2.65452e18 −0.170151
\(898\) 2.05716e19 1.30910
\(899\) −2.11980e19 −1.33924
\(900\) 1.78145e19 1.11737
\(901\) −2.74247e19 −1.70777
\(902\) 4.76051e19 2.94314
\(903\) −1.22016e18 −0.0748936
\(904\) 3.38381e19 2.06211
\(905\) −3.56100e19 −2.15455
\(906\) −1.92173e19 −1.15440
\(907\) 7.67289e18 0.457627 0.228814 0.973470i \(-0.426515\pi\)
0.228814 + 0.973470i \(0.426515\pi\)
\(908\) −1.62835e19 −0.964250
\(909\) −4.62249e18 −0.271776
\(910\) 2.37958e18 0.138909
\(911\) −2.63661e19 −1.52818 −0.764092 0.645107i \(-0.776813\pi\)
−0.764092 + 0.645107i \(0.776813\pi\)
\(912\) −5.32717e18 −0.306570
\(913\) 2.24389e19 1.28216
\(914\) −8.49969e18 −0.482229
\(915\) −2.78875e19 −1.57098
\(916\) −5.10473e18 −0.285531
\(917\) −5.16006e18 −0.286585
\(918\) 5.43161e18 0.299537
\(919\) −2.84367e19 −1.55714 −0.778572 0.627555i \(-0.784056\pi\)
−0.778572 + 0.627555i \(0.784056\pi\)
\(920\) −4.95733e19 −2.69542
\(921\) 4.60991e18 0.248889
\(922\) −1.01196e19 −0.542518
\(923\) 7.13186e18 0.379657
\(924\) −5.63424e18 −0.297829
\(925\) 3.13218e19 1.64409
\(926\) 3.84747e19 2.00541
\(927\) 6.59662e18 0.341431
\(928\) −1.03105e19 −0.529930
\(929\) 9.80405e18 0.500384 0.250192 0.968196i \(-0.419506\pi\)
0.250192 + 0.968196i \(0.419506\pi\)
\(930\) −3.46221e19 −1.75474
\(931\) 1.65925e19 0.835099
\(932\) −5.42171e19 −2.70977
\(933\) 1.25133e18 0.0621072
\(934\) 5.36389e19 2.64378
\(935\) 4.74307e19 2.32158
\(936\) 2.69144e18 0.130825
\(937\) −3.24278e19 −1.56535 −0.782673 0.622433i \(-0.786144\pi\)
−0.782673 + 0.622433i \(0.786144\pi\)
\(938\) −1.06616e19 −0.511100
\(939\) 1.00911e19 0.480411
\(940\) −3.66995e19 −1.73512
\(941\) −2.62189e19 −1.23107 −0.615533 0.788111i \(-0.711059\pi\)
−0.615533 + 0.788111i \(0.711059\pi\)
\(942\) 1.46702e19 0.684076
\(943\) 2.73568e19 1.26689
\(944\) 1.73950e18 0.0800032
\(945\) 1.29061e18 0.0589507
\(946\) −3.99002e19 −1.81002
\(947\) −1.67473e19 −0.754517 −0.377258 0.926108i \(-0.623133\pi\)
−0.377258 + 0.926108i \(0.623133\pi\)
\(948\) −2.89213e19 −1.29409
\(949\) −7.73785e18 −0.343866
\(950\) 5.95511e19 2.62837
\(951\) 1.89490e19 0.830641
\(952\) 5.66704e18 0.246727
\(953\) 2.46685e19 1.06669 0.533346 0.845897i \(-0.320935\pi\)
0.533346 + 0.845897i \(0.320935\pi\)
\(954\) −2.44027e19 −1.04803
\(955\) −4.98389e19 −2.12592
\(956\) −2.06086e19 −0.873115
\(957\) 2.58403e19 1.08735
\(958\) −1.65338e18 −0.0691029
\(959\) 3.94293e18 0.163681
\(960\) −3.12304e19 −1.28770
\(961\) 3.72564e18 0.152581
\(962\) 1.01998e19 0.414911
\(963\) −2.60353e18 −0.105194
\(964\) 5.12959e19 2.05865
\(965\) 2.34214e19 0.933652
\(966\) −4.97340e18 −0.196926
\(967\) 7.19705e18 0.283062 0.141531 0.989934i \(-0.454797\pi\)
0.141531 + 0.989934i \(0.454797\pi\)
\(968\) −4.79782e19 −1.87436
\(969\) 1.18205e19 0.458703
\(970\) 5.07314e19 1.95551
\(971\) −2.33356e19 −0.893497 −0.446749 0.894660i \(-0.647418\pi\)
−0.446749 + 0.894660i \(0.647418\pi\)
\(972\) 3.14642e18 0.119670
\(973\) −2.63056e18 −0.0993835
\(974\) 1.15273e19 0.432606
\(975\) −7.45524e18 −0.277928
\(976\) −2.69991e19 −0.999828
\(977\) 6.22648e18 0.229049 0.114524 0.993420i \(-0.463466\pi\)
0.114524 + 0.993420i \(0.463466\pi\)
\(978\) 5.03764e18 0.184088
\(979\) −6.07856e19 −2.20655
\(980\) −8.36141e19 −3.01516
\(981\) 9.60067e18 0.343916
\(982\) −6.72667e19 −2.39373
\(983\) −3.70282e19 −1.30898 −0.654492 0.756069i \(-0.727118\pi\)
−0.654492 + 0.756069i \(0.727118\pi\)
\(984\) −2.77372e19 −0.974081
\(985\) −6.93249e19 −2.41854
\(986\) −5.60215e19 −1.94158
\(987\) −1.70817e18 −0.0588124
\(988\) 1.26249e19 0.431825
\(989\) −2.29290e19 −0.779130
\(990\) 4.22042e19 1.42471
\(991\) 4.09604e19 1.37368 0.686840 0.726809i \(-0.258997\pi\)
0.686840 + 0.726809i \(0.258997\pi\)
\(992\) 1.36886e19 0.456071
\(993\) −2.78468e19 −0.921732
\(994\) 1.33619e19 0.439398
\(995\) −3.93177e19 −1.28451
\(996\) −2.81803e19 −0.914662
\(997\) 6.89215e18 0.222247 0.111124 0.993807i \(-0.464555\pi\)
0.111124 + 0.993807i \(0.464555\pi\)
\(998\) 6.92492e19 2.21853
\(999\) 5.53209e18 0.176081
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 177.14.a.a.1.3 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.a.1.3 30 1.1 even 1 trivial