Properties

Label 177.14.a.a.1.2
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 1.2
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-158.048 q^{2} +729.000 q^{3} +16787.0 q^{4} -61907.4 q^{5} -115217. q^{6} +140047. q^{7} -1.35842e6 q^{8} +531441. q^{9} +O(q^{10})\) \(q-158.048 q^{2} +729.000 q^{3} +16787.0 q^{4} -61907.4 q^{5} -115217. q^{6} +140047. q^{7} -1.35842e6 q^{8} +531441. q^{9} +9.78431e6 q^{10} +1.00908e7 q^{11} +1.22377e7 q^{12} +3.21335e7 q^{13} -2.21341e7 q^{14} -4.51305e7 q^{15} +7.71760e7 q^{16} -1.32468e8 q^{17} -8.39929e7 q^{18} +8.81457e7 q^{19} -1.03924e9 q^{20} +1.02094e8 q^{21} -1.59483e9 q^{22} -9.30531e8 q^{23} -9.90290e8 q^{24} +2.61183e9 q^{25} -5.07862e9 q^{26} +3.87420e8 q^{27} +2.35097e9 q^{28} -2.53556e9 q^{29} +7.13277e9 q^{30} -1.90332e9 q^{31} -1.06928e9 q^{32} +7.35619e9 q^{33} +2.09362e10 q^{34} -8.66995e9 q^{35} +8.92131e9 q^{36} -5.98250e9 q^{37} -1.39312e10 q^{38} +2.34253e10 q^{39} +8.40964e10 q^{40} -3.51635e10 q^{41} -1.61357e10 q^{42} -5.08079e9 q^{43} +1.69394e11 q^{44} -3.29001e10 q^{45} +1.47068e11 q^{46} +5.23615e10 q^{47} +5.62613e10 q^{48} -7.72759e10 q^{49} -4.12793e11 q^{50} -9.65690e10 q^{51} +5.39426e11 q^{52} +6.77282e10 q^{53} -6.12309e10 q^{54} -6.24695e11 q^{55} -1.90243e11 q^{56} +6.42582e10 q^{57} +4.00739e11 q^{58} +4.21805e10 q^{59} -7.57607e11 q^{60} -3.97617e11 q^{61} +3.00815e11 q^{62} +7.44267e10 q^{63} -4.63229e11 q^{64} -1.98930e12 q^{65} -1.16263e12 q^{66} +1.31939e12 q^{67} -2.22374e12 q^{68} -6.78357e11 q^{69} +1.37026e12 q^{70} +2.06032e12 q^{71} -7.21921e11 q^{72} -3.72820e11 q^{73} +9.45519e11 q^{74} +1.90402e12 q^{75} +1.47970e12 q^{76} +1.41319e12 q^{77} -3.70231e12 q^{78} -2.77004e12 q^{79} -4.77777e12 q^{80} +2.82430e11 q^{81} +5.55751e12 q^{82} +9.61094e11 q^{83} +1.71386e12 q^{84} +8.20074e12 q^{85} +8.03006e11 q^{86} -1.84842e12 q^{87} -1.37076e13 q^{88} -1.40040e12 q^{89} +5.19979e12 q^{90} +4.50020e12 q^{91} -1.56208e13 q^{92} -1.38752e12 q^{93} -8.27560e12 q^{94} -5.45687e12 q^{95} -7.79505e11 q^{96} -1.59667e12 q^{97} +1.22133e13 q^{98} +5.36266e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} + O(q^{10}) \) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} - 5352519q^{10} - 13950782q^{11} + 83541942q^{12} - 17256988q^{13} + 33780109q^{14} - 100413918q^{15} + 499996762q^{16} - 317583695q^{17} - 73338858q^{18} - 863401469q^{19} - 1841280623q^{20} - 641113947q^{21} - 2723764842q^{22} - 3142075981q^{23} - 635907429q^{24} + 5435751692q^{25} - 6441414040q^{26} + 11622614670q^{27} - 7538400046q^{28} - 4604589283q^{29} - 3901986351q^{30} + 4308675373q^{31} + 6094556360q^{32} - 10170120078q^{33} + 38097713432q^{34} - 15447827315q^{35} + 60902075718q^{36} - 19633376949q^{37} - 18152222923q^{38} - 12580344252q^{39} + 14680384170q^{40} - 103644439493q^{41} + 24625699461q^{42} - 64494894924q^{43} - 199714496208q^{44} - 73201746222q^{45} - 265425792847q^{46} - 293365585139q^{47} + 364497639498q^{48} + 414396765797q^{49} - 126058522207q^{50} - 231518513655q^{51} + 156029960316q^{52} - 76747013118q^{53} - 53464027482q^{54} - 433465885754q^{55} - 502955241518q^{56} - 629419670901q^{57} - 1755031845830q^{58} + 1265416009230q^{59} - 1342293574167q^{60} - 2022612531219q^{61} - 3816005187046q^{62} - 467372067363q^{63} - 3570205594131q^{64} - 3889749040576q^{65} - 1985624569818q^{66} - 502618987776q^{67} - 8953998390517q^{68} - 2290573390149q^{69} - 6805178272420q^{70} - 1599540605456q^{71} - 463576515741q^{72} - 3826795087235q^{73} - 7573387813210q^{74} + 3962662983468q^{75} - 19498723328388q^{76} - 9088623115219q^{77} - 4695790835160q^{78} - 8595482172338q^{79} - 17452527463963q^{80} + 8472886094430q^{81} - 11181116792901q^{82} - 13548556984389q^{83} - 5495493633534q^{84} - 12851795888367q^{85} + 8539949468848q^{86} - 3356745587307q^{87} - 25134826741387q^{88} - 21826401667403q^{89} - 2844548049879q^{90} - 26577050621355q^{91} - 34908210763168q^{92} + 3141024346917q^{93} - 26426808959500q^{94} - 29105233533993q^{95} + 4442931586440q^{96} + 417815797414q^{97} + 29159956938360q^{98} - 7414017536862q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −158.048 −1.74620 −0.873098 0.487546i \(-0.837892\pi\)
−0.873098 + 0.487546i \(0.837892\pi\)
\(3\) 729.000 0.577350
\(4\) 16787.0 2.04920
\(5\) −61907.4 −1.77189 −0.885947 0.463787i \(-0.846490\pi\)
−0.885947 + 0.463787i \(0.846490\pi\)
\(6\) −115217. −1.00817
\(7\) 140047. 0.449921 0.224961 0.974368i \(-0.427775\pi\)
0.224961 + 0.974368i \(0.427775\pi\)
\(8\) −1.35842e6 −1.83210
\(9\) 531441. 0.333333
\(10\) 9.78431e6 3.09407
\(11\) 1.00908e7 1.71741 0.858703 0.512473i \(-0.171271\pi\)
0.858703 + 0.512473i \(0.171271\pi\)
\(12\) 1.22377e7 1.18310
\(13\) 3.21335e7 1.84640 0.923201 0.384319i \(-0.125564\pi\)
0.923201 + 0.384319i \(0.125564\pi\)
\(14\) −2.21341e7 −0.785650
\(15\) −4.51305e7 −1.02300
\(16\) 7.71760e7 1.15001
\(17\) −1.32468e8 −1.33104 −0.665522 0.746379i \(-0.731791\pi\)
−0.665522 + 0.746379i \(0.731791\pi\)
\(18\) −8.39929e7 −0.582065
\(19\) 8.81457e7 0.429836 0.214918 0.976632i \(-0.431052\pi\)
0.214918 + 0.976632i \(0.431052\pi\)
\(20\) −1.03924e9 −3.63096
\(21\) 1.02094e8 0.259762
\(22\) −1.59483e9 −2.99893
\(23\) −9.30531e8 −1.31069 −0.655345 0.755330i \(-0.727477\pi\)
−0.655345 + 0.755330i \(0.727477\pi\)
\(24\) −9.90290e8 −1.05777
\(25\) 2.61183e9 2.13961
\(26\) −5.07862e9 −3.22418
\(27\) 3.87420e8 0.192450
\(28\) 2.35097e9 0.921977
\(29\) −2.53556e9 −0.791565 −0.395782 0.918344i \(-0.629527\pi\)
−0.395782 + 0.918344i \(0.629527\pi\)
\(30\) 7.13277e9 1.78636
\(31\) −1.90332e9 −0.385177 −0.192588 0.981280i \(-0.561688\pi\)
−0.192588 + 0.981280i \(0.561688\pi\)
\(32\) −1.06928e9 −0.176042
\(33\) 7.35619e9 0.991545
\(34\) 2.09362e10 2.32426
\(35\) −8.66995e9 −0.797213
\(36\) 8.92131e9 0.683066
\(37\) −5.98250e9 −0.383329 −0.191664 0.981461i \(-0.561388\pi\)
−0.191664 + 0.981461i \(0.561388\pi\)
\(38\) −1.39312e10 −0.750577
\(39\) 2.34253e10 1.06602
\(40\) 8.40964e10 3.24629
\(41\) −3.51635e10 −1.15611 −0.578053 0.816000i \(-0.696187\pi\)
−0.578053 + 0.816000i \(0.696187\pi\)
\(42\) −1.61357e10 −0.453595
\(43\) −5.08079e9 −0.122571 −0.0612853 0.998120i \(-0.519520\pi\)
−0.0612853 + 0.998120i \(0.519520\pi\)
\(44\) 1.69394e11 3.51930
\(45\) −3.29001e10 −0.590631
\(46\) 1.47068e11 2.28872
\(47\) 5.23615e10 0.708559 0.354279 0.935140i \(-0.384726\pi\)
0.354279 + 0.935140i \(0.384726\pi\)
\(48\) 5.62613e10 0.663960
\(49\) −7.72759e10 −0.797571
\(50\) −4.12793e11 −3.73617
\(51\) −9.65690e10 −0.768478
\(52\) 5.39426e11 3.78364
\(53\) 6.77282e10 0.419736 0.209868 0.977730i \(-0.432697\pi\)
0.209868 + 0.977730i \(0.432697\pi\)
\(54\) −6.12309e10 −0.336055
\(55\) −6.24695e11 −3.04306
\(56\) −1.90243e11 −0.824302
\(57\) 6.42582e10 0.248166
\(58\) 4.00739e11 1.38223
\(59\) 4.21805e10 0.130189
\(60\) −7.57607e11 −2.09634
\(61\) −3.97617e11 −0.988146 −0.494073 0.869421i \(-0.664492\pi\)
−0.494073 + 0.869421i \(0.664492\pi\)
\(62\) 3.00815e11 0.672594
\(63\) 7.44267e10 0.149974
\(64\) −4.63229e11 −0.842608
\(65\) −1.98930e12 −3.27163
\(66\) −1.16263e12 −1.73143
\(67\) 1.31939e12 1.78191 0.890957 0.454088i \(-0.150035\pi\)
0.890957 + 0.454088i \(0.150035\pi\)
\(68\) −2.22374e12 −2.72757
\(69\) −6.78357e11 −0.756727
\(70\) 1.37026e12 1.39209
\(71\) 2.06032e12 1.90878 0.954389 0.298566i \(-0.0965084\pi\)
0.954389 + 0.298566i \(0.0965084\pi\)
\(72\) −7.21921e11 −0.610701
\(73\) −3.72820e11 −0.288337 −0.144168 0.989553i \(-0.546051\pi\)
−0.144168 + 0.989553i \(0.546051\pi\)
\(74\) 9.45519e11 0.669366
\(75\) 1.90402e12 1.23530
\(76\) 1.47970e12 0.880818
\(77\) 1.41319e12 0.772698
\(78\) −3.70231e12 −1.86148
\(79\) −2.77004e12 −1.28207 −0.641034 0.767513i \(-0.721494\pi\)
−0.641034 + 0.767513i \(0.721494\pi\)
\(80\) −4.77777e12 −2.03770
\(81\) 2.82430e11 0.111111
\(82\) 5.55751e12 2.01878
\(83\) 9.61094e11 0.322670 0.161335 0.986900i \(-0.448420\pi\)
0.161335 + 0.986900i \(0.448420\pi\)
\(84\) 1.71386e12 0.532304
\(85\) 8.20074e12 2.35847
\(86\) 8.03006e11 0.214032
\(87\) −1.84842e12 −0.457010
\(88\) −1.37076e13 −3.14646
\(89\) −1.40040e12 −0.298687 −0.149344 0.988785i \(-0.547716\pi\)
−0.149344 + 0.988785i \(0.547716\pi\)
\(90\) 5.19979e12 1.03136
\(91\) 4.50020e12 0.830735
\(92\) −1.56208e13 −2.68586
\(93\) −1.38752e12 −0.222382
\(94\) −8.27560e12 −1.23728
\(95\) −5.45687e12 −0.761623
\(96\) −7.79505e11 −0.101638
\(97\) −1.59667e12 −0.194625 −0.0973127 0.995254i \(-0.531025\pi\)
−0.0973127 + 0.995254i \(0.531025\pi\)
\(98\) 1.22133e13 1.39271
\(99\) 5.36266e12 0.572469
\(100\) 4.38448e13 4.38448
\(101\) −3.16932e12 −0.297083 −0.148542 0.988906i \(-0.547458\pi\)
−0.148542 + 0.988906i \(0.547458\pi\)
\(102\) 1.52625e13 1.34191
\(103\) −2.30297e13 −1.90040 −0.950202 0.311636i \(-0.899123\pi\)
−0.950202 + 0.311636i \(0.899123\pi\)
\(104\) −4.36508e13 −3.38280
\(105\) −6.32039e12 −0.460271
\(106\) −1.07043e13 −0.732941
\(107\) −2.30047e13 −1.48191 −0.740957 0.671553i \(-0.765628\pi\)
−0.740957 + 0.671553i \(0.765628\pi\)
\(108\) 6.50364e12 0.394368
\(109\) 2.44685e13 1.39745 0.698723 0.715392i \(-0.253752\pi\)
0.698723 + 0.715392i \(0.253752\pi\)
\(110\) 9.87315e13 5.31378
\(111\) −4.36124e12 −0.221315
\(112\) 1.08083e13 0.517415
\(113\) 1.21901e13 0.550805 0.275402 0.961329i \(-0.411189\pi\)
0.275402 + 0.961329i \(0.411189\pi\)
\(114\) −1.01558e13 −0.433346
\(115\) 5.76068e13 2.32240
\(116\) −4.25645e13 −1.62207
\(117\) 1.70771e13 0.615467
\(118\) −6.66653e12 −0.227335
\(119\) −1.85517e13 −0.598865
\(120\) 6.13063e13 1.87425
\(121\) 6.73015e13 1.94948
\(122\) 6.28424e13 1.72549
\(123\) −2.56342e13 −0.667478
\(124\) −3.19510e13 −0.789303
\(125\) −8.61208e13 −2.01926
\(126\) −1.17630e13 −0.261883
\(127\) 3.93074e13 0.831286 0.415643 0.909528i \(-0.363557\pi\)
0.415643 + 0.909528i \(0.363557\pi\)
\(128\) 8.19717e13 1.64740
\(129\) −3.70390e12 −0.0707662
\(130\) 3.14404e14 5.71290
\(131\) −1.54608e13 −0.267281 −0.133641 0.991030i \(-0.542667\pi\)
−0.133641 + 0.991030i \(0.542667\pi\)
\(132\) 1.23489e14 2.03187
\(133\) 1.23445e13 0.193392
\(134\) −2.08526e14 −3.11157
\(135\) −2.39842e13 −0.341001
\(136\) 1.79947e14 2.43861
\(137\) 1.17132e14 1.51353 0.756765 0.653688i \(-0.226779\pi\)
0.756765 + 0.653688i \(0.226779\pi\)
\(138\) 1.07213e14 1.32139
\(139\) 8.88527e13 1.04490 0.522450 0.852670i \(-0.325018\pi\)
0.522450 + 0.852670i \(0.325018\pi\)
\(140\) −1.45543e14 −1.63365
\(141\) 3.81715e13 0.409087
\(142\) −3.25628e14 −3.33310
\(143\) 3.24252e14 3.17102
\(144\) 4.10145e13 0.383337
\(145\) 1.56970e14 1.40257
\(146\) 5.89232e13 0.503493
\(147\) −5.63341e13 −0.460478
\(148\) −1.00428e14 −0.785516
\(149\) 9.14953e13 0.684996 0.342498 0.939519i \(-0.388727\pi\)
0.342498 + 0.939519i \(0.388727\pi\)
\(150\) −3.00926e14 −2.15708
\(151\) −1.45208e14 −0.996872 −0.498436 0.866926i \(-0.666092\pi\)
−0.498436 + 0.866926i \(0.666092\pi\)
\(152\) −1.19739e14 −0.787503
\(153\) −7.03988e13 −0.443681
\(154\) −2.23351e14 −1.34928
\(155\) 1.17829e14 0.682492
\(156\) 3.93241e14 2.18449
\(157\) −1.15862e14 −0.617437 −0.308718 0.951154i \(-0.599900\pi\)
−0.308718 + 0.951154i \(0.599900\pi\)
\(158\) 4.37799e14 2.23874
\(159\) 4.93738e13 0.242335
\(160\) 6.61964e13 0.311928
\(161\) −1.30318e14 −0.589707
\(162\) −4.46373e13 −0.194022
\(163\) −2.91754e14 −1.21842 −0.609211 0.793008i \(-0.708514\pi\)
−0.609211 + 0.793008i \(0.708514\pi\)
\(164\) −5.90291e14 −2.36909
\(165\) −4.55403e14 −1.75691
\(166\) −1.51898e14 −0.563444
\(167\) −4.20713e14 −1.50082 −0.750410 0.660973i \(-0.770144\pi\)
−0.750410 + 0.660973i \(0.770144\pi\)
\(168\) −1.38687e14 −0.475911
\(169\) 7.29686e14 2.40920
\(170\) −1.29611e15 −4.11834
\(171\) 4.68442e13 0.143279
\(172\) −8.52913e13 −0.251171
\(173\) −5.29159e14 −1.50067 −0.750337 0.661056i \(-0.770109\pi\)
−0.750337 + 0.661056i \(0.770109\pi\)
\(174\) 2.92138e14 0.798029
\(175\) 3.65778e14 0.962655
\(176\) 7.78767e14 1.97504
\(177\) 3.07496e13 0.0751646
\(178\) 2.21330e14 0.521566
\(179\) −8.18391e14 −1.85959 −0.929793 0.368082i \(-0.880014\pi\)
−0.929793 + 0.368082i \(0.880014\pi\)
\(180\) −5.52295e14 −1.21032
\(181\) 6.63558e13 0.140271 0.0701355 0.997537i \(-0.477657\pi\)
0.0701355 + 0.997537i \(0.477657\pi\)
\(182\) −7.11245e14 −1.45063
\(183\) −2.89863e14 −0.570506
\(184\) 1.26405e15 2.40132
\(185\) 3.70361e14 0.679217
\(186\) 2.19294e14 0.388322
\(187\) −1.33671e15 −2.28594
\(188\) 8.78994e14 1.45198
\(189\) 5.42571e13 0.0865874
\(190\) 8.62445e14 1.32994
\(191\) 6.03349e14 0.899190 0.449595 0.893232i \(-0.351568\pi\)
0.449595 + 0.893232i \(0.351568\pi\)
\(192\) −3.37694e14 −0.486480
\(193\) 8.07855e14 1.12515 0.562575 0.826746i \(-0.309811\pi\)
0.562575 + 0.826746i \(0.309811\pi\)
\(194\) 2.52350e14 0.339854
\(195\) −1.45020e15 −1.88887
\(196\) −1.29723e15 −1.63438
\(197\) −5.05002e14 −0.615549 −0.307775 0.951459i \(-0.599584\pi\)
−0.307775 + 0.951459i \(0.599584\pi\)
\(198\) −8.47556e14 −0.999642
\(199\) 6.88300e14 0.785656 0.392828 0.919612i \(-0.371497\pi\)
0.392828 + 0.919612i \(0.371497\pi\)
\(200\) −3.54796e15 −3.91998
\(201\) 9.61835e14 1.02879
\(202\) 5.00904e14 0.518765
\(203\) −3.55097e14 −0.356142
\(204\) −1.62111e15 −1.57476
\(205\) 2.17688e15 2.04850
\(206\) 3.63978e15 3.31847
\(207\) −4.94522e14 −0.436897
\(208\) 2.47993e15 2.12338
\(209\) 8.89460e14 0.738203
\(210\) 9.98922e14 0.803723
\(211\) 9.51142e14 0.742009 0.371005 0.928631i \(-0.379013\pi\)
0.371005 + 0.928631i \(0.379013\pi\)
\(212\) 1.13695e15 0.860122
\(213\) 1.50197e15 1.10203
\(214\) 3.63584e15 2.58771
\(215\) 3.14539e14 0.217182
\(216\) −5.26281e14 −0.352588
\(217\) −2.66554e14 −0.173299
\(218\) −3.86719e15 −2.44021
\(219\) −2.71786e14 −0.166471
\(220\) −1.04868e16 −6.23583
\(221\) −4.25665e15 −2.45764
\(222\) 6.89283e14 0.386459
\(223\) −1.68205e15 −0.915919 −0.457959 0.888973i \(-0.651419\pi\)
−0.457959 + 0.888973i \(0.651419\pi\)
\(224\) −1.49749e14 −0.0792051
\(225\) 1.38803e15 0.713202
\(226\) −1.92662e15 −0.961813
\(227\) −4.72938e14 −0.229423 −0.114711 0.993399i \(-0.536594\pi\)
−0.114711 + 0.993399i \(0.536594\pi\)
\(228\) 1.07870e15 0.508541
\(229\) −4.56797e14 −0.209311 −0.104656 0.994509i \(-0.533374\pi\)
−0.104656 + 0.994509i \(0.533374\pi\)
\(230\) −9.10461e15 −4.05537
\(231\) 1.03021e15 0.446117
\(232\) 3.44436e15 1.45023
\(233\) −2.89061e15 −1.18352 −0.591760 0.806114i \(-0.701567\pi\)
−0.591760 + 0.806114i \(0.701567\pi\)
\(234\) −2.69899e15 −1.07473
\(235\) −3.24156e15 −1.25549
\(236\) 7.08086e14 0.266783
\(237\) −2.01936e15 −0.740202
\(238\) 2.93205e15 1.04573
\(239\) 8.89025e14 0.308552 0.154276 0.988028i \(-0.450696\pi\)
0.154276 + 0.988028i \(0.450696\pi\)
\(240\) −3.48299e15 −1.17647
\(241\) −1.22768e15 −0.403623 −0.201811 0.979424i \(-0.564683\pi\)
−0.201811 + 0.979424i \(0.564683\pi\)
\(242\) −1.06368e16 −3.40418
\(243\) 2.05891e14 0.0641500
\(244\) −6.67480e15 −2.02491
\(245\) 4.78395e15 1.41321
\(246\) 4.05142e15 1.16555
\(247\) 2.83243e15 0.793649
\(248\) 2.58551e15 0.705683
\(249\) 7.00637e14 0.186293
\(250\) 1.36112e16 3.52603
\(251\) 3.49950e15 0.883338 0.441669 0.897178i \(-0.354387\pi\)
0.441669 + 0.897178i \(0.354387\pi\)
\(252\) 1.24940e15 0.307326
\(253\) −9.38980e15 −2.25099
\(254\) −6.21244e15 −1.45159
\(255\) 5.97834e15 1.36166
\(256\) −9.16065e15 −2.03407
\(257\) −6.40028e14 −0.138559 −0.0692794 0.997597i \(-0.522070\pi\)
−0.0692794 + 0.997597i \(0.522070\pi\)
\(258\) 5.85392e14 0.123572
\(259\) −8.37830e14 −0.172468
\(260\) −3.33944e16 −6.70421
\(261\) −1.34750e15 −0.263855
\(262\) 2.44354e15 0.466725
\(263\) 9.02734e15 1.68208 0.841042 0.540970i \(-0.181943\pi\)
0.841042 + 0.540970i \(0.181943\pi\)
\(264\) −9.99281e15 −1.81661
\(265\) −4.19288e15 −0.743728
\(266\) −1.95102e15 −0.337701
\(267\) −1.02089e15 −0.172447
\(268\) 2.21486e16 3.65149
\(269\) 6.46851e15 1.04091 0.520457 0.853888i \(-0.325762\pi\)
0.520457 + 0.853888i \(0.325762\pi\)
\(270\) 3.79064e15 0.595454
\(271\) 5.40533e15 0.828937 0.414469 0.910064i \(-0.363967\pi\)
0.414469 + 0.910064i \(0.363967\pi\)
\(272\) −1.02233e16 −1.53072
\(273\) 3.28064e15 0.479625
\(274\) −1.85124e16 −2.64292
\(275\) 2.63554e16 3.67457
\(276\) −1.13876e16 −1.55068
\(277\) −4.86724e15 −0.647388 −0.323694 0.946162i \(-0.604925\pi\)
−0.323694 + 0.946162i \(0.604925\pi\)
\(278\) −1.40430e16 −1.82460
\(279\) −1.01150e15 −0.128392
\(280\) 1.17774e16 1.46058
\(281\) −9.80811e15 −1.18849 −0.594244 0.804285i \(-0.702548\pi\)
−0.594244 + 0.804285i \(0.702548\pi\)
\(282\) −6.03292e15 −0.714345
\(283\) 8.07718e15 0.934648 0.467324 0.884086i \(-0.345218\pi\)
0.467324 + 0.884086i \(0.345218\pi\)
\(284\) 3.45866e16 3.91146
\(285\) −3.97806e15 −0.439723
\(286\) −5.12473e16 −5.53722
\(287\) −4.92455e15 −0.520156
\(288\) −5.68259e14 −0.0586807
\(289\) 7.64313e15 0.771676
\(290\) −2.48087e16 −2.44916
\(291\) −1.16397e15 −0.112367
\(292\) −6.25853e15 −0.590859
\(293\) 5.49347e15 0.507233 0.253616 0.967305i \(-0.418380\pi\)
0.253616 + 0.967305i \(0.418380\pi\)
\(294\) 8.90347e15 0.804084
\(295\) −2.61129e15 −0.230681
\(296\) 8.12675e15 0.702297
\(297\) 3.90938e15 0.330515
\(298\) −1.44606e16 −1.19614
\(299\) −2.99012e16 −2.42006
\(300\) 3.19628e16 2.53138
\(301\) −7.11549e14 −0.0551471
\(302\) 2.29497e16 1.74073
\(303\) −2.31044e15 −0.171521
\(304\) 6.80273e15 0.494316
\(305\) 2.46154e16 1.75089
\(306\) 1.11264e16 0.774754
\(307\) −1.51216e16 −1.03086 −0.515429 0.856932i \(-0.672368\pi\)
−0.515429 + 0.856932i \(0.672368\pi\)
\(308\) 2.37232e16 1.58341
\(309\) −1.67886e16 −1.09720
\(310\) −1.86226e16 −1.19176
\(311\) 4.47789e15 0.280628 0.140314 0.990107i \(-0.455189\pi\)
0.140314 + 0.990107i \(0.455189\pi\)
\(312\) −3.18215e16 −1.95306
\(313\) −1.50670e16 −0.905708 −0.452854 0.891585i \(-0.649594\pi\)
−0.452854 + 0.891585i \(0.649594\pi\)
\(314\) 1.83117e16 1.07816
\(315\) −4.60757e15 −0.265738
\(316\) −4.65008e16 −2.62721
\(317\) 1.49652e16 0.828321 0.414160 0.910204i \(-0.364075\pi\)
0.414160 + 0.910204i \(0.364075\pi\)
\(318\) −7.80341e15 −0.423164
\(319\) −2.55858e16 −1.35944
\(320\) 2.86773e16 1.49301
\(321\) −1.67705e16 −0.855583
\(322\) 2.05965e16 1.02974
\(323\) −1.16765e16 −0.572130
\(324\) 4.74115e15 0.227689
\(325\) 8.39270e16 3.95057
\(326\) 4.61110e16 2.12760
\(327\) 1.78375e16 0.806816
\(328\) 4.77669e16 2.11810
\(329\) 7.33307e15 0.318796
\(330\) 7.19753e16 3.06791
\(331\) −5.41429e14 −0.0226287 −0.0113144 0.999936i \(-0.503602\pi\)
−0.0113144 + 0.999936i \(0.503602\pi\)
\(332\) 1.61339e16 0.661214
\(333\) −3.17934e15 −0.127776
\(334\) 6.64926e16 2.62072
\(335\) −8.16800e16 −3.15736
\(336\) 7.87922e15 0.298730
\(337\) −5.33197e15 −0.198287 −0.0991434 0.995073i \(-0.531610\pi\)
−0.0991434 + 0.995073i \(0.531610\pi\)
\(338\) −1.15325e17 −4.20693
\(339\) 8.88659e15 0.318007
\(340\) 1.37666e17 4.83296
\(341\) −1.92060e16 −0.661505
\(342\) −7.40361e15 −0.250192
\(343\) −2.43913e16 −0.808765
\(344\) 6.90186e15 0.224562
\(345\) 4.19953e16 1.34084
\(346\) 8.36322e16 2.62047
\(347\) 4.11371e16 1.26500 0.632502 0.774559i \(-0.282028\pi\)
0.632502 + 0.774559i \(0.282028\pi\)
\(348\) −3.10295e16 −0.936504
\(349\) −5.85757e16 −1.73521 −0.867606 0.497253i \(-0.834342\pi\)
−0.867606 + 0.497253i \(0.834342\pi\)
\(350\) −5.78104e16 −1.68098
\(351\) 1.24492e16 0.355340
\(352\) −1.07899e16 −0.302336
\(353\) −4.27597e16 −1.17625 −0.588124 0.808771i \(-0.700133\pi\)
−0.588124 + 0.808771i \(0.700133\pi\)
\(354\) −4.85990e15 −0.131252
\(355\) −1.27549e17 −3.38215
\(356\) −2.35085e16 −0.612069
\(357\) −1.35242e16 −0.345755
\(358\) 1.29345e17 3.24720
\(359\) 2.36312e16 0.582603 0.291301 0.956631i \(-0.405912\pi\)
0.291301 + 0.956631i \(0.405912\pi\)
\(360\) 4.46923e16 1.08210
\(361\) −3.42833e16 −0.815241
\(362\) −1.04874e16 −0.244941
\(363\) 4.90628e16 1.12554
\(364\) 7.55449e16 1.70234
\(365\) 2.30803e16 0.510902
\(366\) 4.58121e16 0.996215
\(367\) −8.56988e15 −0.183082 −0.0915409 0.995801i \(-0.529179\pi\)
−0.0915409 + 0.995801i \(0.529179\pi\)
\(368\) −7.18147e16 −1.50731
\(369\) −1.86873e16 −0.385368
\(370\) −5.85346e16 −1.18605
\(371\) 9.48513e15 0.188848
\(372\) −2.32923e16 −0.455704
\(373\) −5.52818e16 −1.06286 −0.531429 0.847103i \(-0.678345\pi\)
−0.531429 + 0.847103i \(0.678345\pi\)
\(374\) 2.11263e17 3.99170
\(375\) −6.27820e16 −1.16582
\(376\) −7.11290e16 −1.29815
\(377\) −8.14763e16 −1.46155
\(378\) −8.57520e15 −0.151198
\(379\) 5.37567e16 0.931704 0.465852 0.884863i \(-0.345748\pi\)
0.465852 + 0.884863i \(0.345748\pi\)
\(380\) −9.16046e16 −1.56072
\(381\) 2.86551e16 0.479943
\(382\) −9.53578e16 −1.57016
\(383\) −5.59865e16 −0.906340 −0.453170 0.891424i \(-0.649707\pi\)
−0.453170 + 0.891424i \(0.649707\pi\)
\(384\) 5.97574e16 0.951127
\(385\) −8.74867e16 −1.36914
\(386\) −1.27679e17 −1.96473
\(387\) −2.70014e15 −0.0408569
\(388\) −2.68034e16 −0.398826
\(389\) −7.95592e16 −1.16417 −0.582087 0.813126i \(-0.697764\pi\)
−0.582087 + 0.813126i \(0.697764\pi\)
\(390\) 2.29201e17 3.29834
\(391\) 1.23265e17 1.74459
\(392\) 1.04973e17 1.46123
\(393\) −1.12709e16 −0.154315
\(394\) 7.98143e16 1.07487
\(395\) 1.71486e17 2.27169
\(396\) 9.00232e16 1.17310
\(397\) −5.81774e16 −0.745789 −0.372895 0.927874i \(-0.621635\pi\)
−0.372895 + 0.927874i \(0.621635\pi\)
\(398\) −1.08784e17 −1.37191
\(399\) 8.99916e15 0.111655
\(400\) 2.01570e17 2.46057
\(401\) −5.08924e16 −0.611244 −0.305622 0.952153i \(-0.598864\pi\)
−0.305622 + 0.952153i \(0.598864\pi\)
\(402\) −1.52016e17 −1.79647
\(403\) −6.11602e16 −0.711191
\(404\) −5.32035e16 −0.608782
\(405\) −1.74845e16 −0.196877
\(406\) 5.61222e16 0.621893
\(407\) −6.03681e16 −0.658331
\(408\) 1.31181e17 1.40793
\(409\) 8.10710e16 0.856375 0.428187 0.903690i \(-0.359152\pi\)
0.428187 + 0.903690i \(0.359152\pi\)
\(410\) −3.44051e17 −3.57707
\(411\) 8.53890e16 0.873836
\(412\) −3.86600e17 −3.89430
\(413\) 5.90726e15 0.0585748
\(414\) 7.81580e16 0.762907
\(415\) −5.94988e16 −0.571736
\(416\) −3.43597e16 −0.325044
\(417\) 6.47736e16 0.603273
\(418\) −1.40577e17 −1.28905
\(419\) −1.51656e17 −1.36920 −0.684600 0.728919i \(-0.740023\pi\)
−0.684600 + 0.728919i \(0.740023\pi\)
\(420\) −1.06101e17 −0.943186
\(421\) −1.00481e17 −0.879531 −0.439765 0.898113i \(-0.644938\pi\)
−0.439765 + 0.898113i \(0.644938\pi\)
\(422\) −1.50326e17 −1.29569
\(423\) 2.78270e16 0.236186
\(424\) −9.20035e16 −0.769000
\(425\) −3.45983e17 −2.84791
\(426\) −2.37383e17 −1.92437
\(427\) −5.56851e16 −0.444588
\(428\) −3.86181e17 −3.03673
\(429\) 2.36380e17 1.83079
\(430\) −4.97120e16 −0.379242
\(431\) −1.90697e17 −1.43298 −0.716491 0.697596i \(-0.754253\pi\)
−0.716491 + 0.697596i \(0.754253\pi\)
\(432\) 2.98996e16 0.221320
\(433\) 1.32349e17 0.965047 0.482524 0.875883i \(-0.339720\pi\)
0.482524 + 0.875883i \(0.339720\pi\)
\(434\) 4.21282e16 0.302614
\(435\) 1.14431e17 0.809773
\(436\) 4.10753e17 2.86364
\(437\) −8.20223e16 −0.563381
\(438\) 4.29550e16 0.290692
\(439\) −8.19240e16 −0.546250 −0.273125 0.961978i \(-0.588057\pi\)
−0.273125 + 0.961978i \(0.588057\pi\)
\(440\) 8.48600e17 5.57520
\(441\) −4.10676e16 −0.265857
\(442\) 6.72753e17 4.29152
\(443\) −6.69174e16 −0.420644 −0.210322 0.977632i \(-0.567451\pi\)
−0.210322 + 0.977632i \(0.567451\pi\)
\(444\) −7.32122e16 −0.453518
\(445\) 8.66951e16 0.529242
\(446\) 2.65844e17 1.59937
\(447\) 6.67001e16 0.395483
\(448\) −6.48738e16 −0.379107
\(449\) 2.47874e17 1.42768 0.713838 0.700311i \(-0.246955\pi\)
0.713838 + 0.700311i \(0.246955\pi\)
\(450\) −2.19375e17 −1.24539
\(451\) −3.54828e17 −1.98550
\(452\) 2.04636e17 1.12871
\(453\) −1.05856e17 −0.575545
\(454\) 7.47467e16 0.400617
\(455\) −2.78596e17 −1.47197
\(456\) −8.72897e16 −0.454665
\(457\) −4.08041e16 −0.209531 −0.104765 0.994497i \(-0.533409\pi\)
−0.104765 + 0.994497i \(0.533409\pi\)
\(458\) 7.21956e16 0.365498
\(459\) −5.13207e16 −0.256159
\(460\) 9.67046e17 4.75906
\(461\) −2.20725e17 −1.07102 −0.535508 0.844530i \(-0.679880\pi\)
−0.535508 + 0.844530i \(0.679880\pi\)
\(462\) −1.62823e17 −0.779008
\(463\) 2.05707e17 0.970447 0.485224 0.874390i \(-0.338738\pi\)
0.485224 + 0.874390i \(0.338738\pi\)
\(464\) −1.95684e17 −0.910309
\(465\) 8.58976e16 0.394037
\(466\) 4.56853e17 2.06666
\(467\) −2.62262e17 −1.16997 −0.584987 0.811043i \(-0.698900\pi\)
−0.584987 + 0.811043i \(0.698900\pi\)
\(468\) 2.86673e17 1.26121
\(469\) 1.84776e17 0.801721
\(470\) 5.12321e17 2.19233
\(471\) −8.44632e16 −0.356477
\(472\) −5.72990e16 −0.238519
\(473\) −5.12692e16 −0.210503
\(474\) 3.19155e17 1.29254
\(475\) 2.30221e17 0.919680
\(476\) −3.11428e17 −1.22719
\(477\) 3.59935e16 0.139912
\(478\) −1.40508e17 −0.538791
\(479\) −1.65029e17 −0.624281 −0.312140 0.950036i \(-0.601046\pi\)
−0.312140 + 0.950036i \(0.601046\pi\)
\(480\) 4.82571e16 0.180092
\(481\) −1.92238e17 −0.707778
\(482\) 1.94032e17 0.704804
\(483\) −9.50019e16 −0.340468
\(484\) 1.12979e18 3.99488
\(485\) 9.88458e16 0.344855
\(486\) −3.25406e16 −0.112018
\(487\) 4.36977e17 1.48430 0.742148 0.670236i \(-0.233807\pi\)
0.742148 + 0.670236i \(0.233807\pi\)
\(488\) 5.40132e17 1.81038
\(489\) −2.12689e17 −0.703456
\(490\) −7.56091e17 −2.46774
\(491\) 4.17143e17 1.34356 0.671778 0.740753i \(-0.265531\pi\)
0.671778 + 0.740753i \(0.265531\pi\)
\(492\) −4.30322e17 −1.36779
\(493\) 3.35880e17 1.05361
\(494\) −4.47658e17 −1.38587
\(495\) −3.31989e17 −1.01435
\(496\) −1.46890e17 −0.442958
\(497\) 2.88542e17 0.858800
\(498\) −1.10734e17 −0.325305
\(499\) −2.22151e17 −0.644160 −0.322080 0.946712i \(-0.604382\pi\)
−0.322080 + 0.946712i \(0.604382\pi\)
\(500\) −1.44571e18 −4.13787
\(501\) −3.06700e17 −0.866499
\(502\) −5.53087e17 −1.54248
\(503\) −8.43217e16 −0.232139 −0.116069 0.993241i \(-0.537029\pi\)
−0.116069 + 0.993241i \(0.537029\pi\)
\(504\) −1.01103e17 −0.274767
\(505\) 1.96205e17 0.526400
\(506\) 1.48403e18 3.93066
\(507\) 5.31941e17 1.39095
\(508\) 6.59855e17 1.70347
\(509\) −5.29643e17 −1.34995 −0.674975 0.737841i \(-0.735846\pi\)
−0.674975 + 0.737841i \(0.735846\pi\)
\(510\) −9.44861e17 −2.37773
\(511\) −5.22123e16 −0.129729
\(512\) 7.76307e17 1.90449
\(513\) 3.41494e16 0.0827219
\(514\) 1.01155e17 0.241951
\(515\) 1.42571e18 3.36731
\(516\) −6.21774e16 −0.145014
\(517\) 5.28369e17 1.21688
\(518\) 1.32417e17 0.301162
\(519\) −3.85757e17 −0.866414
\(520\) 2.70231e18 5.99396
\(521\) −6.49432e17 −1.42262 −0.711309 0.702879i \(-0.751897\pi\)
−0.711309 + 0.702879i \(0.751897\pi\)
\(522\) 2.12969e17 0.460742
\(523\) −2.49874e17 −0.533899 −0.266950 0.963710i \(-0.586016\pi\)
−0.266950 + 0.963710i \(0.586016\pi\)
\(524\) −2.59541e17 −0.547712
\(525\) 2.66652e17 0.555789
\(526\) −1.42675e18 −2.93725
\(527\) 2.52128e17 0.512687
\(528\) 5.67721e17 1.14029
\(529\) 3.61852e17 0.717908
\(530\) 6.62674e17 1.29869
\(531\) 2.24165e16 0.0433963
\(532\) 2.07228e17 0.396299
\(533\) −1.12993e18 −2.13463
\(534\) 1.61349e17 0.301127
\(535\) 1.42416e18 2.62579
\(536\) −1.79229e18 −3.26465
\(537\) −5.96607e17 −1.07363
\(538\) −1.02233e18 −1.81764
\(539\) −7.79775e17 −1.36975
\(540\) −4.02623e17 −0.698778
\(541\) −4.65768e17 −0.798707 −0.399353 0.916797i \(-0.630765\pi\)
−0.399353 + 0.916797i \(0.630765\pi\)
\(542\) −8.54299e17 −1.44749
\(543\) 4.83734e16 0.0809855
\(544\) 1.41645e17 0.234320
\(545\) −1.51478e18 −2.47613
\(546\) −5.18498e17 −0.837519
\(547\) −4.11476e17 −0.656791 −0.328395 0.944540i \(-0.606508\pi\)
−0.328395 + 0.944540i \(0.606508\pi\)
\(548\) 1.96629e18 3.10152
\(549\) −2.11310e17 −0.329382
\(550\) −4.16541e18 −6.41652
\(551\) −2.23498e17 −0.340243
\(552\) 9.21496e17 1.38640
\(553\) −3.87936e17 −0.576829
\(554\) 7.69256e17 1.13047
\(555\) 2.69993e17 0.392146
\(556\) 1.49157e18 2.14121
\(557\) 7.85547e17 1.11459 0.557293 0.830316i \(-0.311840\pi\)
0.557293 + 0.830316i \(0.311840\pi\)
\(558\) 1.59865e17 0.224198
\(559\) −1.63263e17 −0.226314
\(560\) −6.69112e17 −0.916804
\(561\) −9.74458e17 −1.31979
\(562\) 1.55015e18 2.07533
\(563\) 2.41367e17 0.319429 0.159714 0.987163i \(-0.448943\pi\)
0.159714 + 0.987163i \(0.448943\pi\)
\(564\) 6.40786e17 0.838299
\(565\) −7.54658e17 −0.975967
\(566\) −1.27658e18 −1.63208
\(567\) 3.95534e16 0.0499912
\(568\) −2.79878e18 −3.49708
\(569\) −4.00958e17 −0.495300 −0.247650 0.968850i \(-0.579658\pi\)
−0.247650 + 0.968850i \(0.579658\pi\)
\(570\) 6.28722e17 0.767843
\(571\) 1.48605e18 1.79432 0.897159 0.441708i \(-0.145627\pi\)
0.897159 + 0.441708i \(0.145627\pi\)
\(572\) 5.44323e18 6.49805
\(573\) 4.39841e17 0.519148
\(574\) 7.78312e17 0.908294
\(575\) −2.43038e18 −2.80436
\(576\) −2.46179e17 −0.280869
\(577\) −9.51633e16 −0.107356 −0.0536780 0.998558i \(-0.517094\pi\)
−0.0536780 + 0.998558i \(0.517094\pi\)
\(578\) −1.20798e18 −1.34750
\(579\) 5.88926e17 0.649606
\(580\) 2.63506e18 2.87414
\(581\) 1.34598e17 0.145176
\(582\) 1.83963e17 0.196215
\(583\) 6.83431e17 0.720857
\(584\) 5.06447e17 0.528263
\(585\) −1.05720e18 −1.09054
\(586\) −8.68229e17 −0.885727
\(587\) 1.44895e18 1.46186 0.730931 0.682452i \(-0.239086\pi\)
0.730931 + 0.682452i \(0.239086\pi\)
\(588\) −9.45682e17 −0.943610
\(589\) −1.67769e17 −0.165563
\(590\) 4.12708e17 0.402814
\(591\) −3.68146e17 −0.355387
\(592\) −4.61705e17 −0.440832
\(593\) 3.21407e17 0.303529 0.151764 0.988417i \(-0.451504\pi\)
0.151764 + 0.988417i \(0.451504\pi\)
\(594\) −6.17868e17 −0.577144
\(595\) 1.14849e18 1.06112
\(596\) 1.53593e18 1.40369
\(597\) 5.01771e17 0.453599
\(598\) 4.72581e18 4.22590
\(599\) 1.09580e18 0.969299 0.484650 0.874708i \(-0.338947\pi\)
0.484650 + 0.874708i \(0.338947\pi\)
\(600\) −2.58646e18 −2.26320
\(601\) 1.71695e18 1.48619 0.743094 0.669187i \(-0.233358\pi\)
0.743094 + 0.669187i \(0.233358\pi\)
\(602\) 1.12459e17 0.0962976
\(603\) 7.01177e17 0.593971
\(604\) −2.43761e18 −2.04279
\(605\) −4.16646e18 −3.45428
\(606\) 3.65159e17 0.299509
\(607\) −2.14384e18 −1.73966 −0.869831 0.493349i \(-0.835772\pi\)
−0.869831 + 0.493349i \(0.835772\pi\)
\(608\) −9.42524e16 −0.0756692
\(609\) −2.58866e17 −0.205619
\(610\) −3.89041e18 −3.05739
\(611\) 1.68256e18 1.30828
\(612\) −1.18179e18 −0.909190
\(613\) −9.02440e17 −0.686950 −0.343475 0.939162i \(-0.611604\pi\)
−0.343475 + 0.939162i \(0.611604\pi\)
\(614\) 2.38994e18 1.80008
\(615\) 1.58695e18 1.18270
\(616\) −1.91970e18 −1.41566
\(617\) −6.39972e17 −0.466989 −0.233495 0.972358i \(-0.575016\pi\)
−0.233495 + 0.972358i \(0.575016\pi\)
\(618\) 2.65340e18 1.91592
\(619\) −1.18087e18 −0.843749 −0.421874 0.906654i \(-0.638628\pi\)
−0.421874 + 0.906654i \(0.638628\pi\)
\(620\) 1.97801e18 1.39856
\(621\) −3.60507e17 −0.252242
\(622\) −7.07720e17 −0.490031
\(623\) −1.96122e17 −0.134386
\(624\) 1.80787e18 1.22594
\(625\) 2.14325e18 1.43831
\(626\) 2.38130e18 1.58154
\(627\) 6.48416e17 0.426201
\(628\) −1.94497e18 −1.26525
\(629\) 7.92488e17 0.510227
\(630\) 7.28214e17 0.464030
\(631\) 2.10267e17 0.132611 0.0663057 0.997799i \(-0.478879\pi\)
0.0663057 + 0.997799i \(0.478879\pi\)
\(632\) 3.76289e18 2.34888
\(633\) 6.93382e17 0.428399
\(634\) −2.36522e18 −1.44641
\(635\) −2.43342e18 −1.47295
\(636\) 8.28840e17 0.496592
\(637\) −2.48314e18 −1.47264
\(638\) 4.04377e18 2.37384
\(639\) 1.09494e18 0.636259
\(640\) −5.07466e18 −2.91902
\(641\) 3.17673e17 0.180885 0.0904425 0.995902i \(-0.471172\pi\)
0.0904425 + 0.995902i \(0.471172\pi\)
\(642\) 2.65053e18 1.49401
\(643\) −1.20752e18 −0.673788 −0.336894 0.941543i \(-0.609376\pi\)
−0.336894 + 0.941543i \(0.609376\pi\)
\(644\) −2.18765e18 −1.20843
\(645\) 2.29299e17 0.125390
\(646\) 1.84544e18 0.999051
\(647\) 2.76485e18 1.48181 0.740906 0.671609i \(-0.234396\pi\)
0.740906 + 0.671609i \(0.234396\pi\)
\(648\) −3.83659e17 −0.203567
\(649\) 4.25635e17 0.223587
\(650\) −1.32645e19 −6.89847
\(651\) −1.94318e17 −0.100054
\(652\) −4.89768e18 −2.49679
\(653\) −7.10471e17 −0.358600 −0.179300 0.983794i \(-0.557383\pi\)
−0.179300 + 0.983794i \(0.557383\pi\)
\(654\) −2.81918e18 −1.40886
\(655\) 9.57137e17 0.473594
\(656\) −2.71378e18 −1.32953
\(657\) −1.98132e17 −0.0961123
\(658\) −1.15897e18 −0.556679
\(659\) 3.31791e18 1.57801 0.789004 0.614387i \(-0.210597\pi\)
0.789004 + 0.614387i \(0.210597\pi\)
\(660\) −7.64486e18 −3.60026
\(661\) 1.90290e18 0.887372 0.443686 0.896182i \(-0.353671\pi\)
0.443686 + 0.896182i \(0.353671\pi\)
\(662\) 8.55716e16 0.0395142
\(663\) −3.10310e18 −1.41892
\(664\) −1.30557e18 −0.591164
\(665\) −7.64218e17 −0.342670
\(666\) 5.02487e17 0.223122
\(667\) 2.35941e18 1.03750
\(668\) −7.06251e18 −3.07548
\(669\) −1.22621e18 −0.528806
\(670\) 1.29093e19 5.51337
\(671\) −4.01227e18 −1.69705
\(672\) −1.09167e17 −0.0457291
\(673\) 1.91544e18 0.794639 0.397319 0.917680i \(-0.369941\pi\)
0.397319 + 0.917680i \(0.369941\pi\)
\(674\) 8.42705e17 0.346247
\(675\) 1.01187e18 0.411768
\(676\) 1.22493e19 4.93692
\(677\) −3.03037e18 −1.20968 −0.604838 0.796348i \(-0.706762\pi\)
−0.604838 + 0.796348i \(0.706762\pi\)
\(678\) −1.40450e18 −0.555303
\(679\) −2.23609e17 −0.0875661
\(680\) −1.11401e19 −4.32095
\(681\) −3.44772e17 −0.132457
\(682\) 3.03546e18 1.15512
\(683\) 2.04409e18 0.770487 0.385243 0.922815i \(-0.374117\pi\)
0.385243 + 0.922815i \(0.374117\pi\)
\(684\) 7.86375e17 0.293606
\(685\) −7.25132e18 −2.68181
\(686\) 3.85498e18 1.41226
\(687\) −3.33005e17 −0.120846
\(688\) −3.92115e17 −0.140958
\(689\) 2.17634e18 0.775001
\(690\) −6.63726e18 −2.34137
\(691\) −6.90384e17 −0.241259 −0.120629 0.992698i \(-0.538491\pi\)
−0.120629 + 0.992698i \(0.538491\pi\)
\(692\) −8.88300e18 −3.07518
\(693\) 7.51025e17 0.257566
\(694\) −6.50162e18 −2.20894
\(695\) −5.50064e18 −1.85145
\(696\) 2.51094e18 0.837289
\(697\) 4.65803e18 1.53883
\(698\) 9.25775e18 3.03002
\(699\) −2.10725e18 −0.683306
\(700\) 6.14033e18 1.97267
\(701\) −1.85185e18 −0.589438 −0.294719 0.955584i \(-0.595226\pi\)
−0.294719 + 0.955584i \(0.595226\pi\)
\(702\) −1.96756e18 −0.620493
\(703\) −5.27331e17 −0.164768
\(704\) −4.67435e18 −1.44710
\(705\) −2.36310e18 −0.724858
\(706\) 6.75806e18 2.05396
\(707\) −4.43854e17 −0.133664
\(708\) 5.16194e17 0.154027
\(709\) −3.29092e18 −0.973008 −0.486504 0.873678i \(-0.661728\pi\)
−0.486504 + 0.873678i \(0.661728\pi\)
\(710\) 2.01588e19 5.90590
\(711\) −1.47212e18 −0.427356
\(712\) 1.90233e18 0.547226
\(713\) 1.77110e18 0.504847
\(714\) 2.13747e18 0.603755
\(715\) −2.00736e19 −5.61871
\(716\) −1.37384e19 −3.81066
\(717\) 6.48099e17 0.178142
\(718\) −3.73486e18 −1.01734
\(719\) 1.50005e18 0.404918 0.202459 0.979291i \(-0.435107\pi\)
0.202459 + 0.979291i \(0.435107\pi\)
\(720\) −2.53910e18 −0.679233
\(721\) −3.22524e18 −0.855032
\(722\) 5.41840e18 1.42357
\(723\) −8.94982e17 −0.233032
\(724\) 1.11392e18 0.287443
\(725\) −6.62243e18 −1.69364
\(726\) −7.75425e18 −1.96540
\(727\) 2.81316e18 0.706678 0.353339 0.935495i \(-0.385046\pi\)
0.353339 + 0.935495i \(0.385046\pi\)
\(728\) −6.11317e18 −1.52199
\(729\) 1.50095e17 0.0370370
\(730\) −3.64779e18 −0.892135
\(731\) 6.73041e17 0.163147
\(732\) −4.86593e18 −1.16908
\(733\) 2.45741e18 0.585197 0.292598 0.956235i \(-0.405480\pi\)
0.292598 + 0.956235i \(0.405480\pi\)
\(734\) 1.35445e18 0.319697
\(735\) 3.48750e18 0.815918
\(736\) 9.94998e17 0.230737
\(737\) 1.33137e19 3.06027
\(738\) 2.95349e18 0.672928
\(739\) −9.83537e17 −0.222127 −0.111064 0.993813i \(-0.535426\pi\)
−0.111064 + 0.993813i \(0.535426\pi\)
\(740\) 6.21726e18 1.39185
\(741\) 2.06484e18 0.458214
\(742\) −1.49910e18 −0.329766
\(743\) 2.68518e18 0.585527 0.292763 0.956185i \(-0.405425\pi\)
0.292763 + 0.956185i \(0.405425\pi\)
\(744\) 1.88484e18 0.407426
\(745\) −5.66424e18 −1.21374
\(746\) 8.73716e18 1.85596
\(747\) 5.10765e17 0.107557
\(748\) −2.24393e19 −4.68435
\(749\) −3.22174e18 −0.666744
\(750\) 9.92255e18 2.03575
\(751\) −4.88293e17 −0.0993164 −0.0496582 0.998766i \(-0.515813\pi\)
−0.0496582 + 0.998766i \(0.515813\pi\)
\(752\) 4.04105e18 0.814851
\(753\) 2.55114e18 0.509995
\(754\) 1.28771e19 2.55214
\(755\) 8.98944e18 1.76635
\(756\) 9.10815e17 0.177435
\(757\) −8.86885e18 −1.71295 −0.856474 0.516190i \(-0.827350\pi\)
−0.856474 + 0.516190i \(0.827350\pi\)
\(758\) −8.49611e18 −1.62694
\(759\) −6.84517e18 −1.29961
\(760\) 7.41273e18 1.39537
\(761\) 2.82019e18 0.526355 0.263177 0.964747i \(-0.415230\pi\)
0.263177 + 0.964747i \(0.415230\pi\)
\(762\) −4.52887e18 −0.838075
\(763\) 3.42674e18 0.628741
\(764\) 1.01284e19 1.84262
\(765\) 4.35821e18 0.786156
\(766\) 8.84853e18 1.58265
\(767\) 1.35541e18 0.240381
\(768\) −6.67812e18 −1.17437
\(769\) −1.02421e19 −1.78594 −0.892969 0.450119i \(-0.851382\pi\)
−0.892969 + 0.450119i \(0.851382\pi\)
\(770\) 1.38271e19 2.39078
\(771\) −4.66581e17 −0.0799969
\(772\) 1.35615e19 2.30566
\(773\) −4.56115e18 −0.768967 −0.384483 0.923132i \(-0.625620\pi\)
−0.384483 + 0.923132i \(0.625620\pi\)
\(774\) 4.26750e17 0.0713440
\(775\) −4.97113e18 −0.824127
\(776\) 2.16895e18 0.356574
\(777\) −6.10778e17 −0.0995743
\(778\) 1.25741e19 2.03287
\(779\) −3.09951e18 −0.496935
\(780\) −2.43445e19 −3.87068
\(781\) 2.07903e19 3.27815
\(782\) −1.94818e19 −3.04639
\(783\) −9.82327e17 −0.152337
\(784\) −5.96384e18 −0.917216
\(785\) 7.17270e18 1.09403
\(786\) 1.78134e18 0.269464
\(787\) −7.63075e18 −1.14481 −0.572403 0.819973i \(-0.693989\pi\)
−0.572403 + 0.819973i \(0.693989\pi\)
\(788\) −8.47748e18 −1.26138
\(789\) 6.58093e18 0.971151
\(790\) −2.71030e19 −3.96681
\(791\) 1.70719e18 0.247819
\(792\) −7.28476e18 −1.04882
\(793\) −1.27768e19 −1.82451
\(794\) 9.19480e18 1.30229
\(795\) −3.05661e18 −0.429391
\(796\) 1.15545e19 1.60996
\(797\) −3.81807e18 −0.527673 −0.263836 0.964567i \(-0.584988\pi\)
−0.263836 + 0.964567i \(0.584988\pi\)
\(798\) −1.42230e18 −0.194971
\(799\) −6.93621e18 −0.943122
\(800\) −2.79277e18 −0.376661
\(801\) −7.44230e17 −0.0995625
\(802\) 8.04342e18 1.06735
\(803\) −3.76205e18 −0.495192
\(804\) 1.61463e19 2.10819
\(805\) 8.06766e18 1.04490
\(806\) 9.66622e18 1.24188
\(807\) 4.71554e18 0.600971
\(808\) 4.30528e18 0.544287
\(809\) 5.86792e18 0.735900 0.367950 0.929846i \(-0.380060\pi\)
0.367950 + 0.929846i \(0.380060\pi\)
\(810\) 2.76338e18 0.343786
\(811\) 8.51285e18 1.05061 0.525303 0.850915i \(-0.323952\pi\)
0.525303 + 0.850915i \(0.323952\pi\)
\(812\) −5.96102e18 −0.729805
\(813\) 3.94048e18 0.478587
\(814\) 9.54104e18 1.14957
\(815\) 1.80617e19 2.15891
\(816\) −7.45281e18 −0.883759
\(817\) −4.47849e17 −0.0526852
\(818\) −1.28131e19 −1.49540
\(819\) 2.39159e18 0.276912
\(820\) 3.65434e19 4.19777
\(821\) −1.10664e19 −1.26118 −0.630589 0.776117i \(-0.717186\pi\)
−0.630589 + 0.776117i \(0.717186\pi\)
\(822\) −1.34955e19 −1.52589
\(823\) −1.39327e19 −1.56292 −0.781459 0.623956i \(-0.785524\pi\)
−0.781459 + 0.623956i \(0.785524\pi\)
\(824\) 3.12840e19 3.48173
\(825\) 1.92131e19 2.12152
\(826\) −9.33627e17 −0.102283
\(827\) 7.46655e18 0.811585 0.405793 0.913965i \(-0.366996\pi\)
0.405793 + 0.913965i \(0.366996\pi\)
\(828\) −8.30156e18 −0.895287
\(829\) −6.49135e18 −0.694593 −0.347297 0.937755i \(-0.612900\pi\)
−0.347297 + 0.937755i \(0.612900\pi\)
\(830\) 9.40364e18 0.998363
\(831\) −3.54822e18 −0.373770
\(832\) −1.48852e19 −1.55579
\(833\) 1.02366e19 1.06160
\(834\) −1.02373e19 −1.05343
\(835\) 2.60452e19 2.65929
\(836\) 1.49314e19 1.51272
\(837\) −7.37384e17 −0.0741273
\(838\) 2.39688e19 2.39089
\(839\) −1.24046e19 −1.22780 −0.613902 0.789382i \(-0.710401\pi\)
−0.613902 + 0.789382i \(0.710401\pi\)
\(840\) 8.58576e18 0.843264
\(841\) −3.83158e18 −0.373425
\(842\) 1.58808e19 1.53583
\(843\) −7.15012e18 −0.686173
\(844\) 1.59668e19 1.52052
\(845\) −4.51730e19 −4.26884
\(846\) −4.39800e18 −0.412427
\(847\) 9.42537e18 0.877114
\(848\) 5.22699e18 0.482701
\(849\) 5.88827e18 0.539619
\(850\) 5.46817e19 4.97301
\(851\) 5.56690e18 0.502425
\(852\) 2.52137e19 2.25828
\(853\) 7.66178e18 0.681022 0.340511 0.940241i \(-0.389400\pi\)
0.340511 + 0.940241i \(0.389400\pi\)
\(854\) 8.80088e18 0.776337
\(855\) −2.90000e18 −0.253874
\(856\) 3.12501e19 2.71502
\(857\) −2.80801e17 −0.0242116 −0.0121058 0.999927i \(-0.503853\pi\)
−0.0121058 + 0.999927i \(0.503853\pi\)
\(858\) −3.73593e19 −3.19692
\(859\) −5.71016e18 −0.484945 −0.242473 0.970158i \(-0.577958\pi\)
−0.242473 + 0.970158i \(0.577958\pi\)
\(860\) 5.28017e18 0.445049
\(861\) −3.58999e18 −0.300312
\(862\) 3.01391e19 2.50227
\(863\) −1.12092e19 −0.923643 −0.461821 0.886973i \(-0.652804\pi\)
−0.461821 + 0.886973i \(0.652804\pi\)
\(864\) −4.14261e17 −0.0338793
\(865\) 3.27589e19 2.65903
\(866\) −2.09174e19 −1.68516
\(867\) 5.57184e18 0.445528
\(868\) −4.47464e18 −0.355124
\(869\) −2.79520e19 −2.20183
\(870\) −1.80855e19 −1.41402
\(871\) 4.23966e19 3.29013
\(872\) −3.32386e19 −2.56027
\(873\) −8.48537e17 −0.0648751
\(874\) 1.29634e19 0.983774
\(875\) −1.20610e19 −0.908509
\(876\) −4.56247e18 −0.341133
\(877\) −8.32918e18 −0.618166 −0.309083 0.951035i \(-0.600022\pi\)
−0.309083 + 0.951035i \(0.600022\pi\)
\(878\) 1.29479e19 0.953860
\(879\) 4.00474e18 0.292851
\(880\) −4.82115e19 −3.49956
\(881\) 1.31768e19 0.949441 0.474720 0.880137i \(-0.342549\pi\)
0.474720 + 0.880137i \(0.342549\pi\)
\(882\) 6.49063e18 0.464238
\(883\) −1.76135e19 −1.25055 −0.625273 0.780406i \(-0.715013\pi\)
−0.625273 + 0.780406i \(0.715013\pi\)
\(884\) −7.14565e19 −5.03619
\(885\) −1.90363e18 −0.133184
\(886\) 1.05761e19 0.734527
\(887\) −3.24303e18 −0.223587 −0.111794 0.993731i \(-0.535660\pi\)
−0.111794 + 0.993731i \(0.535660\pi\)
\(888\) 5.92440e18 0.405472
\(889\) 5.50489e18 0.374013
\(890\) −1.37019e19 −0.924160
\(891\) 2.84994e18 0.190823
\(892\) −2.82366e19 −1.87690
\(893\) 4.61544e18 0.304564
\(894\) −1.05418e19 −0.690590
\(895\) 5.06645e19 3.29499
\(896\) 1.14799e19 0.741200
\(897\) −2.17980e19 −1.39722
\(898\) −3.91758e19 −2.49300
\(899\) 4.82597e18 0.304892
\(900\) 2.33009e19 1.46149
\(901\) −8.97180e18 −0.558687
\(902\) 5.60797e19 3.46707
\(903\) −5.18719e17 −0.0318392
\(904\) −1.65593e19 −1.00913
\(905\) −4.10792e18 −0.248545
\(906\) 1.67303e19 1.00501
\(907\) −2.96509e19 −1.76844 −0.884220 0.467071i \(-0.845309\pi\)
−0.884220 + 0.467071i \(0.845309\pi\)
\(908\) −7.93922e18 −0.470132
\(909\) −1.68431e18 −0.0990277
\(910\) 4.40313e19 2.57035
\(911\) 1.95371e19 1.13238 0.566188 0.824276i \(-0.308417\pi\)
0.566188 + 0.824276i \(0.308417\pi\)
\(912\) 4.95919e18 0.285394
\(913\) 9.69820e18 0.554155
\(914\) 6.44898e18 0.365882
\(915\) 1.79447e19 1.01088
\(916\) −7.66825e18 −0.428920
\(917\) −2.16524e18 −0.120255
\(918\) 8.11111e18 0.447304
\(919\) 7.82954e18 0.428731 0.214366 0.976753i \(-0.431232\pi\)
0.214366 + 0.976753i \(0.431232\pi\)
\(920\) −7.82543e19 −4.25488
\(921\) −1.10237e19 −0.595167
\(922\) 3.48851e19 1.87020
\(923\) 6.62053e19 3.52437
\(924\) 1.72942e19 0.914182
\(925\) −1.56252e19 −0.820173
\(926\) −3.25114e19 −1.69459
\(927\) −1.22389e19 −0.633468
\(928\) 2.71122e18 0.139349
\(929\) −3.21185e19 −1.63928 −0.819641 0.572878i \(-0.805827\pi\)
−0.819641 + 0.572878i \(0.805827\pi\)
\(930\) −1.35759e19 −0.688066
\(931\) −6.81153e18 −0.342824
\(932\) −4.85247e19 −2.42527
\(933\) 3.26438e18 0.162021
\(934\) 4.14499e19 2.04300
\(935\) 8.27520e19 4.05045
\(936\) −2.31978e19 −1.12760
\(937\) −3.54137e19 −1.70948 −0.854739 0.519058i \(-0.826283\pi\)
−0.854739 + 0.519058i \(0.826283\pi\)
\(938\) −2.92035e19 −1.39996
\(939\) −1.09838e19 −0.522911
\(940\) −5.44162e19 −2.57275
\(941\) 3.06493e19 1.43909 0.719545 0.694446i \(-0.244351\pi\)
0.719545 + 0.694446i \(0.244351\pi\)
\(942\) 1.33492e19 0.622479
\(943\) 3.27208e19 1.51530
\(944\) 3.25532e18 0.149719
\(945\) −3.35892e18 −0.153424
\(946\) 8.10297e18 0.367580
\(947\) −1.06457e18 −0.0479622 −0.0239811 0.999712i \(-0.507634\pi\)
−0.0239811 + 0.999712i \(0.507634\pi\)
\(948\) −3.38991e19 −1.51682
\(949\) −1.19800e19 −0.532386
\(950\) −3.63859e19 −1.60594
\(951\) 1.09097e19 0.478231
\(952\) 2.52011e19 1.09718
\(953\) −3.39355e19 −1.46740 −0.733702 0.679471i \(-0.762209\pi\)
−0.733702 + 0.679471i \(0.762209\pi\)
\(954\) −5.68869e18 −0.244314
\(955\) −3.73518e19 −1.59327
\(956\) 1.49241e19 0.632283
\(957\) −1.86520e19 −0.784872
\(958\) 2.60825e19 1.09012
\(959\) 1.64039e19 0.680969
\(960\) 2.09057e19 0.861991
\(961\) −2.07949e19 −0.851639
\(962\) 3.03828e19 1.23592
\(963\) −1.22257e19 −0.493971
\(964\) −2.06092e19 −0.827103
\(965\) −5.00122e19 −1.99365
\(966\) 1.50148e19 0.594523
\(967\) −7.03476e18 −0.276680 −0.138340 0.990385i \(-0.544177\pi\)
−0.138340 + 0.990385i \(0.544177\pi\)
\(968\) −9.14238e19 −3.57166
\(969\) −8.51214e18 −0.330319
\(970\) −1.56223e19 −0.602185
\(971\) 4.79224e19 1.83491 0.917453 0.397844i \(-0.130241\pi\)
0.917453 + 0.397844i \(0.130241\pi\)
\(972\) 3.45630e18 0.131456
\(973\) 1.24436e19 0.470123
\(974\) −6.90631e19 −2.59187
\(975\) 6.11828e19 2.28086
\(976\) −3.06865e19 −1.13638
\(977\) −4.27332e19 −1.57199 −0.785997 0.618230i \(-0.787850\pi\)
−0.785997 + 0.618230i \(0.787850\pi\)
\(978\) 3.36149e19 1.22837
\(979\) −1.41311e19 −0.512968
\(980\) 8.03083e19 2.89595
\(981\) 1.30036e19 0.465816
\(982\) −6.59285e19 −2.34611
\(983\) −1.24401e19 −0.439771 −0.219885 0.975526i \(-0.570568\pi\)
−0.219885 + 0.975526i \(0.570568\pi\)
\(984\) 3.48221e19 1.22289
\(985\) 3.12634e19 1.09069
\(986\) −5.30849e19 −1.83980
\(987\) 5.34581e18 0.184057
\(988\) 4.75480e19 1.62634
\(989\) 4.72783e18 0.160652
\(990\) 5.24700e19 1.77126
\(991\) 1.82236e19 0.611159 0.305580 0.952167i \(-0.401150\pi\)
0.305580 + 0.952167i \(0.401150\pi\)
\(992\) 2.03518e18 0.0678073
\(993\) −3.94702e17 −0.0130647
\(994\) −4.56033e19 −1.49963
\(995\) −4.26109e19 −1.39210
\(996\) 1.17616e19 0.381752
\(997\) 4.36946e18 0.140899 0.0704497 0.997515i \(-0.477557\pi\)
0.0704497 + 0.997515i \(0.477557\pi\)
\(998\) 3.51104e19 1.12483
\(999\) −2.31774e18 −0.0737716
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.1.2 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.a.1.2 30 1.1 even 1 trivial