Properties

Label 177.14.a.a.1.6
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 1.6
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-141.008 q^{2} +729.000 q^{3} +11691.3 q^{4} -32545.4 q^{5} -102795. q^{6} -339369. q^{7} -493432. q^{8} +531441. q^{9} +O(q^{10})\) \(q-141.008 q^{2} +729.000 q^{3} +11691.3 q^{4} -32545.4 q^{5} -102795. q^{6} -339369. q^{7} -493432. q^{8} +531441. q^{9} +4.58917e6 q^{10} +3.57384e6 q^{11} +8.52297e6 q^{12} -2.09171e7 q^{13} +4.78538e7 q^{14} -2.37256e7 q^{15} -2.61973e7 q^{16} +9.09292e6 q^{17} -7.49375e7 q^{18} +1.92711e8 q^{19} -3.80499e8 q^{20} -2.47400e8 q^{21} -5.03941e8 q^{22} -8.21298e8 q^{23} -3.59712e8 q^{24} -1.61499e8 q^{25} +2.94948e9 q^{26} +3.87420e8 q^{27} -3.96767e9 q^{28} -5.08788e8 q^{29} +3.34550e9 q^{30} +4.32040e9 q^{31} +7.73623e9 q^{32} +2.60533e9 q^{33} -1.28218e9 q^{34} +1.10449e10 q^{35} +6.21324e9 q^{36} -6.74260e9 q^{37} -2.71739e10 q^{38} -1.52486e10 q^{39} +1.60589e10 q^{40} +4.16817e10 q^{41} +3.48854e10 q^{42} +6.89112e10 q^{43} +4.17829e10 q^{44} -1.72960e10 q^{45} +1.15810e11 q^{46} -6.47713e10 q^{47} -1.90978e10 q^{48} +1.82821e10 q^{49} +2.27728e10 q^{50} +6.62874e9 q^{51} -2.44548e11 q^{52} +8.27456e10 q^{53} -5.46295e10 q^{54} -1.16312e11 q^{55} +1.67455e11 q^{56} +1.40486e11 q^{57} +7.17433e10 q^{58} +4.21805e10 q^{59} -2.77383e11 q^{60} -3.81752e11 q^{61} -6.09212e11 q^{62} -1.80354e11 q^{63} -8.76263e11 q^{64} +6.80755e11 q^{65} -3.67373e11 q^{66} -8.52576e11 q^{67} +1.06308e11 q^{68} -5.98726e11 q^{69} -1.55742e12 q^{70} -1.49429e12 q^{71} -2.62230e11 q^{72} +1.20889e11 q^{73} +9.50763e11 q^{74} -1.17733e11 q^{75} +2.25305e12 q^{76} -1.21285e12 q^{77} +2.15017e12 q^{78} +3.34434e12 q^{79} +8.52601e11 q^{80} +2.82430e11 q^{81} -5.87746e12 q^{82} +2.74183e12 q^{83} -2.89243e12 q^{84} -2.95933e11 q^{85} -9.71705e12 q^{86} -3.70906e11 q^{87} -1.76345e12 q^{88} +5.23866e12 q^{89} +2.43887e12 q^{90} +7.09861e12 q^{91} -9.60205e12 q^{92} +3.14957e12 q^{93} +9.13328e12 q^{94} -6.27186e12 q^{95} +5.63971e12 q^{96} +9.88927e12 q^{97} -2.57793e12 q^{98} +1.89929e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} + O(q^{10}) \) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} - 5352519q^{10} - 13950782q^{11} + 83541942q^{12} - 17256988q^{13} + 33780109q^{14} - 100413918q^{15} + 499996762q^{16} - 317583695q^{17} - 73338858q^{18} - 863401469q^{19} - 1841280623q^{20} - 641113947q^{21} - 2723764842q^{22} - 3142075981q^{23} - 635907429q^{24} + 5435751692q^{25} - 6441414040q^{26} + 11622614670q^{27} - 7538400046q^{28} - 4604589283q^{29} - 3901986351q^{30} + 4308675373q^{31} + 6094556360q^{32} - 10170120078q^{33} + 38097713432q^{34} - 15447827315q^{35} + 60902075718q^{36} - 19633376949q^{37} - 18152222923q^{38} - 12580344252q^{39} + 14680384170q^{40} - 103644439493q^{41} + 24625699461q^{42} - 64494894924q^{43} - 199714496208q^{44} - 73201746222q^{45} - 265425792847q^{46} - 293365585139q^{47} + 364497639498q^{48} + 414396765797q^{49} - 126058522207q^{50} - 231518513655q^{51} + 156029960316q^{52} - 76747013118q^{53} - 53464027482q^{54} - 433465885754q^{55} - 502955241518q^{56} - 629419670901q^{57} - 1755031845830q^{58} + 1265416009230q^{59} - 1342293574167q^{60} - 2022612531219q^{61} - 3816005187046q^{62} - 467372067363q^{63} - 3570205594131q^{64} - 3889749040576q^{65} - 1985624569818q^{66} - 502618987776q^{67} - 8953998390517q^{68} - 2290573390149q^{69} - 6805178272420q^{70} - 1599540605456q^{71} - 463576515741q^{72} - 3826795087235q^{73} - 7573387813210q^{74} + 3962662983468q^{75} - 19498723328388q^{76} - 9088623115219q^{77} - 4695790835160q^{78} - 8595482172338q^{79} - 17452527463963q^{80} + 8472886094430q^{81} - 11181116792901q^{82} - 13548556984389q^{83} - 5495493633534q^{84} - 12851795888367q^{85} + 8539949468848q^{86} - 3356745587307q^{87} - 25134826741387q^{88} - 21826401667403q^{89} - 2844548049879q^{90} - 26577050621355q^{91} - 34908210763168q^{92} + 3141024346917q^{93} - 26426808959500q^{94} - 29105233533993q^{95} + 4442931586440q^{96} + 417815797414q^{97} + 29159956938360q^{98} - 7414017536862q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −141.008 −1.55794 −0.778968 0.627064i \(-0.784256\pi\)
−0.778968 + 0.627064i \(0.784256\pi\)
\(3\) 729.000 0.577350
\(4\) 11691.3 1.42716
\(5\) −32545.4 −0.931504 −0.465752 0.884915i \(-0.654216\pi\)
−0.465752 + 0.884915i \(0.654216\pi\)
\(6\) −102795. −0.899474
\(7\) −339369. −1.09027 −0.545136 0.838348i \(-0.683522\pi\)
−0.545136 + 0.838348i \(0.683522\pi\)
\(8\) −493432. −0.665491
\(9\) 531441. 0.333333
\(10\) 4.58917e6 1.45122
\(11\) 3.57384e6 0.608251 0.304126 0.952632i \(-0.401636\pi\)
0.304126 + 0.952632i \(0.401636\pi\)
\(12\) 8.52297e6 0.823973
\(13\) −2.09171e7 −1.20190 −0.600952 0.799285i \(-0.705212\pi\)
−0.600952 + 0.799285i \(0.705212\pi\)
\(14\) 4.78538e7 1.69857
\(15\) −2.37256e7 −0.537804
\(16\) −2.61973e7 −0.390370
\(17\) 9.09292e6 0.0913662 0.0456831 0.998956i \(-0.485454\pi\)
0.0456831 + 0.998956i \(0.485454\pi\)
\(18\) −7.49375e7 −0.519312
\(19\) 1.92711e8 0.939742 0.469871 0.882735i \(-0.344300\pi\)
0.469871 + 0.882735i \(0.344300\pi\)
\(20\) −3.80499e8 −1.32941
\(21\) −2.47400e8 −0.629468
\(22\) −5.03941e8 −0.947616
\(23\) −8.21298e8 −1.15683 −0.578415 0.815742i \(-0.696329\pi\)
−0.578415 + 0.815742i \(0.696329\pi\)
\(24\) −3.59712e8 −0.384222
\(25\) −1.61499e8 −0.132300
\(26\) 2.94948e9 1.87249
\(27\) 3.87420e8 0.192450
\(28\) −3.96767e9 −1.55599
\(29\) −5.08788e8 −0.158836 −0.0794182 0.996841i \(-0.525306\pi\)
−0.0794182 + 0.996841i \(0.525306\pi\)
\(30\) 3.34550e9 0.837864
\(31\) 4.32040e9 0.874326 0.437163 0.899382i \(-0.355983\pi\)
0.437163 + 0.899382i \(0.355983\pi\)
\(32\) 7.73623e9 1.27366
\(33\) 2.60533e9 0.351174
\(34\) −1.28218e9 −0.142343
\(35\) 1.10449e10 1.01559
\(36\) 6.21324e9 0.475721
\(37\) −6.74260e9 −0.432033 −0.216016 0.976390i \(-0.569306\pi\)
−0.216016 + 0.976390i \(0.569306\pi\)
\(38\) −2.71739e10 −1.46406
\(39\) −1.52486e10 −0.693919
\(40\) 1.60589e10 0.619908
\(41\) 4.16817e10 1.37041 0.685204 0.728351i \(-0.259713\pi\)
0.685204 + 0.728351i \(0.259713\pi\)
\(42\) 3.48854e10 0.980671
\(43\) 6.89112e10 1.66244 0.831218 0.555947i \(-0.187644\pi\)
0.831218 + 0.555947i \(0.187644\pi\)
\(44\) 4.17829e10 0.868074
\(45\) −1.72960e10 −0.310501
\(46\) 1.15810e11 1.80227
\(47\) −6.47713e10 −0.876489 −0.438244 0.898856i \(-0.644400\pi\)
−0.438244 + 0.898856i \(0.644400\pi\)
\(48\) −1.90978e10 −0.225380
\(49\) 1.82821e10 0.188691
\(50\) 2.27728e10 0.206115
\(51\) 6.62874e9 0.0527503
\(52\) −2.44548e11 −1.71531
\(53\) 8.27456e10 0.512805 0.256402 0.966570i \(-0.417463\pi\)
0.256402 + 0.966570i \(0.417463\pi\)
\(54\) −5.46295e10 −0.299825
\(55\) −1.16312e11 −0.566589
\(56\) 1.67455e11 0.725566
\(57\) 1.40486e11 0.542560
\(58\) 7.17433e10 0.247457
\(59\) 4.21805e10 0.130189
\(60\) −2.77383e11 −0.767534
\(61\) −3.81752e11 −0.948719 −0.474360 0.880331i \(-0.657320\pi\)
−0.474360 + 0.880331i \(0.657320\pi\)
\(62\) −6.09212e11 −1.36214
\(63\) −1.80354e11 −0.363424
\(64\) −8.76263e11 −1.59391
\(65\) 6.80755e11 1.11958
\(66\) −3.67373e11 −0.547107
\(67\) −8.52576e11 −1.15146 −0.575728 0.817641i \(-0.695281\pi\)
−0.575728 + 0.817641i \(0.695281\pi\)
\(68\) 1.06308e11 0.130394
\(69\) −5.98726e11 −0.667896
\(70\) −1.55742e12 −1.58223
\(71\) −1.49429e12 −1.38438 −0.692188 0.721717i \(-0.743353\pi\)
−0.692188 + 0.721717i \(0.743353\pi\)
\(72\) −2.62230e11 −0.221830
\(73\) 1.20889e11 0.0934952 0.0467476 0.998907i \(-0.485114\pi\)
0.0467476 + 0.998907i \(0.485114\pi\)
\(74\) 9.50763e11 0.673079
\(75\) −1.17733e11 −0.0763837
\(76\) 2.25305e12 1.34116
\(77\) −1.21285e12 −0.663159
\(78\) 2.15017e12 1.08108
\(79\) 3.34434e12 1.54787 0.773936 0.633264i \(-0.218285\pi\)
0.773936 + 0.633264i \(0.218285\pi\)
\(80\) 8.52601e11 0.363631
\(81\) 2.82430e11 0.111111
\(82\) −5.87746e12 −2.13501
\(83\) 2.74183e12 0.920520 0.460260 0.887784i \(-0.347756\pi\)
0.460260 + 0.887784i \(0.347756\pi\)
\(84\) −2.89243e12 −0.898354
\(85\) −2.95933e11 −0.0851080
\(86\) −9.71705e12 −2.58997
\(87\) −3.70906e11 −0.0917042
\(88\) −1.76345e12 −0.404786
\(89\) 5.23866e12 1.11734 0.558670 0.829390i \(-0.311312\pi\)
0.558670 + 0.829390i \(0.311312\pi\)
\(90\) 2.43887e12 0.483741
\(91\) 7.09861e12 1.31040
\(92\) −9.60205e12 −1.65099
\(93\) 3.14957e12 0.504792
\(94\) 9.13328e12 1.36551
\(95\) −6.27186e12 −0.875373
\(96\) 5.63971e12 0.735349
\(97\) 9.88927e12 1.20545 0.602723 0.797950i \(-0.294082\pi\)
0.602723 + 0.797950i \(0.294082\pi\)
\(98\) −2.57793e12 −0.293969
\(99\) 1.89929e12 0.202750
\(100\) −1.88814e12 −0.188814
\(101\) 5.89937e12 0.552989 0.276495 0.961015i \(-0.410827\pi\)
0.276495 + 0.961015i \(0.410827\pi\)
\(102\) −9.34707e11 −0.0821816
\(103\) 2.03940e13 1.68291 0.841454 0.540328i \(-0.181700\pi\)
0.841454 + 0.540328i \(0.181700\pi\)
\(104\) 1.03212e13 0.799856
\(105\) 8.05173e12 0.586352
\(106\) −1.16678e13 −0.798916
\(107\) −1.02325e13 −0.659156 −0.329578 0.944128i \(-0.606906\pi\)
−0.329578 + 0.944128i \(0.606906\pi\)
\(108\) 4.52945e12 0.274658
\(109\) 2.01100e13 1.14852 0.574260 0.818673i \(-0.305290\pi\)
0.574260 + 0.818673i \(0.305290\pi\)
\(110\) 1.64010e13 0.882708
\(111\) −4.91536e12 −0.249434
\(112\) 8.89054e12 0.425609
\(113\) −4.04662e13 −1.82845 −0.914223 0.405211i \(-0.867198\pi\)
−0.914223 + 0.405211i \(0.867198\pi\)
\(114\) −1.98097e13 −0.845274
\(115\) 2.67295e13 1.07759
\(116\) −5.94840e12 −0.226685
\(117\) −1.11162e13 −0.400634
\(118\) −5.94780e12 −0.202826
\(119\) −3.08585e12 −0.0996139
\(120\) 1.17070e13 0.357904
\(121\) −2.17503e13 −0.630030
\(122\) 5.38302e13 1.47804
\(123\) 3.03859e13 0.791206
\(124\) 5.05112e13 1.24781
\(125\) 4.49843e13 1.05474
\(126\) 2.54315e13 0.566191
\(127\) 4.59756e13 0.972307 0.486154 0.873873i \(-0.338400\pi\)
0.486154 + 0.873873i \(0.338400\pi\)
\(128\) 6.01852e13 1.20955
\(129\) 5.02363e13 0.959808
\(130\) −9.59921e13 −1.74423
\(131\) 6.31090e13 1.09101 0.545504 0.838108i \(-0.316338\pi\)
0.545504 + 0.838108i \(0.316338\pi\)
\(132\) 3.04598e13 0.501183
\(133\) −6.54001e13 −1.02457
\(134\) 1.20220e14 1.79389
\(135\) −1.26088e13 −0.179268
\(136\) −4.48674e12 −0.0608034
\(137\) −5.15109e13 −0.665603 −0.332802 0.942997i \(-0.607994\pi\)
−0.332802 + 0.942997i \(0.607994\pi\)
\(138\) 8.44253e13 1.04054
\(139\) 2.20544e13 0.259358 0.129679 0.991556i \(-0.458605\pi\)
0.129679 + 0.991556i \(0.458605\pi\)
\(140\) 1.29129e14 1.44941
\(141\) −4.72183e13 −0.506041
\(142\) 2.10707e14 2.15677
\(143\) −7.47544e13 −0.731059
\(144\) −1.39223e13 −0.130123
\(145\) 1.65587e13 0.147957
\(146\) −1.70464e13 −0.145659
\(147\) 1.33277e13 0.108941
\(148\) −7.88299e13 −0.616581
\(149\) −5.03518e13 −0.376968 −0.188484 0.982076i \(-0.560357\pi\)
−0.188484 + 0.982076i \(0.560357\pi\)
\(150\) 1.66013e13 0.119001
\(151\) 1.20657e14 0.828327 0.414163 0.910203i \(-0.364074\pi\)
0.414163 + 0.910203i \(0.364074\pi\)
\(152\) −9.50899e13 −0.625390
\(153\) 4.83235e12 0.0304554
\(154\) 1.71022e14 1.03316
\(155\) −1.40609e14 −0.814438
\(156\) −1.78276e14 −0.990335
\(157\) −6.09316e13 −0.324710 −0.162355 0.986732i \(-0.551909\pi\)
−0.162355 + 0.986732i \(0.551909\pi\)
\(158\) −4.71580e14 −2.41148
\(159\) 6.03216e13 0.296068
\(160\) −2.51779e14 −1.18642
\(161\) 2.78723e14 1.26126
\(162\) −3.98249e13 −0.173104
\(163\) 1.45321e14 0.606890 0.303445 0.952849i \(-0.401863\pi\)
0.303445 + 0.952849i \(0.401863\pi\)
\(164\) 4.87314e14 1.95580
\(165\) −8.47916e13 −0.327120
\(166\) −3.86621e14 −1.43411
\(167\) −1.87744e14 −0.669743 −0.334872 0.942264i \(-0.608693\pi\)
−0.334872 + 0.942264i \(0.608693\pi\)
\(168\) 1.22075e14 0.418906
\(169\) 1.34650e14 0.444571
\(170\) 4.17290e13 0.132593
\(171\) 1.02415e14 0.313247
\(172\) 8.05663e14 2.37257
\(173\) −6.04115e14 −1.71325 −0.856623 0.515942i \(-0.827442\pi\)
−0.856623 + 0.515942i \(0.827442\pi\)
\(174\) 5.23009e13 0.142869
\(175\) 5.48079e13 0.144243
\(176\) −9.36250e13 −0.237443
\(177\) 3.07496e13 0.0751646
\(178\) −7.38694e14 −1.74074
\(179\) −6.12062e14 −1.39075 −0.695377 0.718645i \(-0.744763\pi\)
−0.695377 + 0.718645i \(0.744763\pi\)
\(180\) −2.02213e14 −0.443136
\(181\) 7.61474e14 1.60970 0.804849 0.593480i \(-0.202246\pi\)
0.804849 + 0.593480i \(0.202246\pi\)
\(182\) −1.00096e15 −2.04152
\(183\) −2.78297e14 −0.547743
\(184\) 4.05255e14 0.769861
\(185\) 2.19441e14 0.402440
\(186\) −4.44116e14 −0.786434
\(187\) 3.24967e13 0.0555736
\(188\) −7.57261e14 −1.25089
\(189\) −1.31478e14 −0.209823
\(190\) 8.84384e14 1.36377
\(191\) 5.67015e14 0.845041 0.422521 0.906353i \(-0.361145\pi\)
0.422521 + 0.906353i \(0.361145\pi\)
\(192\) −6.38796e14 −0.920247
\(193\) 5.03814e14 0.701694 0.350847 0.936433i \(-0.385894\pi\)
0.350847 + 0.936433i \(0.385894\pi\)
\(194\) −1.39447e15 −1.87801
\(195\) 4.96271e14 0.646388
\(196\) 2.13742e14 0.269293
\(197\) 1.05639e15 1.28764 0.643821 0.765176i \(-0.277348\pi\)
0.643821 + 0.765176i \(0.277348\pi\)
\(198\) −2.67815e14 −0.315872
\(199\) 1.18175e15 1.34891 0.674454 0.738317i \(-0.264379\pi\)
0.674454 + 0.738317i \(0.264379\pi\)
\(200\) 7.96890e13 0.0880448
\(201\) −6.21528e14 −0.664793
\(202\) −8.31859e14 −0.861521
\(203\) 1.72667e14 0.173175
\(204\) 7.74987e13 0.0752833
\(205\) −1.35655e15 −1.27654
\(206\) −2.87572e15 −2.62186
\(207\) −4.36471e14 −0.385610
\(208\) 5.47971e14 0.469187
\(209\) 6.88720e14 0.571599
\(210\) −1.13536e15 −0.913499
\(211\) 8.28907e14 0.646651 0.323326 0.946288i \(-0.395199\pi\)
0.323326 + 0.946288i \(0.395199\pi\)
\(212\) 9.67405e14 0.731855
\(213\) −1.08933e15 −0.799270
\(214\) 1.44287e15 1.02692
\(215\) −2.24274e15 −1.54857
\(216\) −1.91166e14 −0.128074
\(217\) −1.46621e15 −0.953252
\(218\) −2.83567e15 −1.78932
\(219\) 8.81283e13 0.0539795
\(220\) −1.35984e15 −0.808614
\(221\) −1.90198e14 −0.109813
\(222\) 6.93106e14 0.388602
\(223\) −2.60795e15 −1.42010 −0.710048 0.704153i \(-0.751327\pi\)
−0.710048 + 0.704153i \(0.751327\pi\)
\(224\) −2.62543e15 −1.38864
\(225\) −8.58275e13 −0.0441001
\(226\) 5.70606e15 2.84860
\(227\) 3.19516e15 1.54997 0.774987 0.631978i \(-0.217757\pi\)
0.774987 + 0.631978i \(0.217757\pi\)
\(228\) 1.64247e15 0.774321
\(229\) −2.26829e15 −1.03936 −0.519682 0.854360i \(-0.673950\pi\)
−0.519682 + 0.854360i \(0.673950\pi\)
\(230\) −3.76908e15 −1.67882
\(231\) −8.84168e14 −0.382875
\(232\) 2.51052e14 0.105704
\(233\) −3.28473e15 −1.34489 −0.672443 0.740149i \(-0.734755\pi\)
−0.672443 + 0.740149i \(0.734755\pi\)
\(234\) 1.56748e15 0.624162
\(235\) 2.10801e15 0.816453
\(236\) 4.93146e14 0.185801
\(237\) 2.43803e15 0.893664
\(238\) 4.35131e14 0.155192
\(239\) −8.22938e14 −0.285615 −0.142807 0.989751i \(-0.545613\pi\)
−0.142807 + 0.989751i \(0.545613\pi\)
\(240\) 6.21546e14 0.209942
\(241\) −3.01011e13 −0.00989626 −0.00494813 0.999988i \(-0.501575\pi\)
−0.00494813 + 0.999988i \(0.501575\pi\)
\(242\) 3.06698e15 0.981546
\(243\) 2.05891e14 0.0641500
\(244\) −4.46319e15 −1.35398
\(245\) −5.94999e14 −0.175767
\(246\) −4.28467e15 −1.23265
\(247\) −4.03096e15 −1.12948
\(248\) −2.13183e15 −0.581856
\(249\) 1.99880e15 0.531462
\(250\) −6.34316e15 −1.64322
\(251\) −5.39725e15 −1.36236 −0.681182 0.732114i \(-0.738534\pi\)
−0.681182 + 0.732114i \(0.738534\pi\)
\(252\) −2.10858e15 −0.518665
\(253\) −2.93519e15 −0.703644
\(254\) −6.48294e15 −1.51479
\(255\) −2.15735e14 −0.0491371
\(256\) −1.30825e15 −0.290490
\(257\) −2.41508e15 −0.522837 −0.261419 0.965226i \(-0.584190\pi\)
−0.261419 + 0.965226i \(0.584190\pi\)
\(258\) −7.08373e15 −1.49532
\(259\) 2.28823e15 0.471033
\(260\) 7.95892e15 1.59782
\(261\) −2.70391e14 −0.0529454
\(262\) −8.89888e15 −1.69972
\(263\) −6.62502e15 −1.23445 −0.617227 0.786785i \(-0.711744\pi\)
−0.617227 + 0.786785i \(0.711744\pi\)
\(264\) −1.28555e15 −0.233703
\(265\) −2.69299e15 −0.477679
\(266\) 9.22196e15 1.59622
\(267\) 3.81898e15 0.645096
\(268\) −9.96774e15 −1.64331
\(269\) −2.15137e15 −0.346199 −0.173100 0.984904i \(-0.555378\pi\)
−0.173100 + 0.984904i \(0.555378\pi\)
\(270\) 1.77794e15 0.279288
\(271\) −4.01545e15 −0.615792 −0.307896 0.951420i \(-0.599625\pi\)
−0.307896 + 0.951420i \(0.599625\pi\)
\(272\) −2.38210e14 −0.0356666
\(273\) 5.17488e15 0.756560
\(274\) 7.26346e15 1.03697
\(275\) −5.77174e14 −0.0804719
\(276\) −6.99990e15 −0.953197
\(277\) 1.33580e15 0.177674 0.0888369 0.996046i \(-0.471685\pi\)
0.0888369 + 0.996046i \(0.471685\pi\)
\(278\) −3.10986e15 −0.404063
\(279\) 2.29604e15 0.291442
\(280\) −5.44990e15 −0.675868
\(281\) 1.02666e16 1.24405 0.622024 0.782998i \(-0.286311\pi\)
0.622024 + 0.782998i \(0.286311\pi\)
\(282\) 6.65816e15 0.788379
\(283\) 5.11351e15 0.591708 0.295854 0.955233i \(-0.404396\pi\)
0.295854 + 0.955233i \(0.404396\pi\)
\(284\) −1.74702e16 −1.97573
\(285\) −4.57219e15 −0.505397
\(286\) 1.05410e16 1.13894
\(287\) −1.41455e16 −1.49412
\(288\) 4.11135e15 0.424554
\(289\) −9.82190e15 −0.991652
\(290\) −2.33491e15 −0.230507
\(291\) 7.20928e15 0.695965
\(292\) 1.41335e15 0.133433
\(293\) −1.05264e16 −0.971942 −0.485971 0.873975i \(-0.661534\pi\)
−0.485971 + 0.873975i \(0.661534\pi\)
\(294\) −1.87931e15 −0.169723
\(295\) −1.37278e15 −0.121271
\(296\) 3.32702e15 0.287514
\(297\) 1.38458e15 0.117058
\(298\) 7.10002e15 0.587292
\(299\) 1.71792e16 1.39040
\(300\) −1.37646e15 −0.109012
\(301\) −2.33863e16 −1.81251
\(302\) −1.70136e16 −1.29048
\(303\) 4.30064e15 0.319268
\(304\) −5.04851e15 −0.366847
\(305\) 1.24243e16 0.883736
\(306\) −6.81401e14 −0.0474475
\(307\) 1.98222e15 0.135130 0.0675651 0.997715i \(-0.478477\pi\)
0.0675651 + 0.997715i \(0.478477\pi\)
\(308\) −1.41798e16 −0.946436
\(309\) 1.48672e16 0.971628
\(310\) 1.98271e16 1.26884
\(311\) 1.40014e16 0.877461 0.438731 0.898619i \(-0.355428\pi\)
0.438731 + 0.898619i \(0.355428\pi\)
\(312\) 7.52413e15 0.461797
\(313\) 3.90874e15 0.234963 0.117481 0.993075i \(-0.462518\pi\)
0.117481 + 0.993075i \(0.462518\pi\)
\(314\) 8.59186e15 0.505877
\(315\) 5.86971e15 0.338531
\(316\) 3.90998e16 2.20906
\(317\) −2.27057e16 −1.25675 −0.628377 0.777909i \(-0.716281\pi\)
−0.628377 + 0.777909i \(0.716281\pi\)
\(318\) −8.50583e15 −0.461255
\(319\) −1.81833e15 −0.0966124
\(320\) 2.85183e16 1.48474
\(321\) −7.45950e15 −0.380564
\(322\) −3.93022e16 −1.96496
\(323\) 1.75231e15 0.0858606
\(324\) 3.30197e15 0.158574
\(325\) 3.37810e15 0.159012
\(326\) −2.04915e16 −0.945495
\(327\) 1.46602e16 0.663099
\(328\) −2.05671e16 −0.911995
\(329\) 2.19813e16 0.955610
\(330\) 1.19563e16 0.509632
\(331\) 2.83737e14 0.0118586 0.00592932 0.999982i \(-0.498113\pi\)
0.00592932 + 0.999982i \(0.498113\pi\)
\(332\) 3.20556e16 1.31373
\(333\) −3.58330e15 −0.144011
\(334\) 2.64734e16 1.04342
\(335\) 2.77474e16 1.07259
\(336\) 6.48120e15 0.245725
\(337\) −1.94267e16 −0.722445 −0.361222 0.932480i \(-0.617641\pi\)
−0.361222 + 0.932480i \(0.617641\pi\)
\(338\) −1.89867e16 −0.692613
\(339\) −2.94998e16 −1.05565
\(340\) −3.45985e15 −0.121463
\(341\) 1.54405e16 0.531810
\(342\) −1.44413e16 −0.488019
\(343\) 2.66767e16 0.884546
\(344\) −3.40030e16 −1.10634
\(345\) 1.94858e16 0.622148
\(346\) 8.51852e16 2.66913
\(347\) −9.23354e15 −0.283940 −0.141970 0.989871i \(-0.545344\pi\)
−0.141970 + 0.989871i \(0.545344\pi\)
\(348\) −4.33638e15 −0.130877
\(349\) −4.15080e16 −1.22961 −0.614803 0.788681i \(-0.710765\pi\)
−0.614803 + 0.788681i \(0.710765\pi\)
\(350\) −7.72836e15 −0.224722
\(351\) −8.10371e15 −0.231306
\(352\) 2.76481e16 0.774707
\(353\) 1.29564e15 0.0356410 0.0178205 0.999841i \(-0.494327\pi\)
0.0178205 + 0.999841i \(0.494327\pi\)
\(354\) −4.33595e15 −0.117102
\(355\) 4.86321e16 1.28955
\(356\) 6.12468e16 1.59463
\(357\) −2.24959e15 −0.0575121
\(358\) 8.63057e16 2.16671
\(359\) −4.33504e16 −1.06876 −0.534379 0.845245i \(-0.679454\pi\)
−0.534379 + 0.845245i \(0.679454\pi\)
\(360\) 8.53438e15 0.206636
\(361\) −4.91539e15 −0.116886
\(362\) −1.07374e17 −2.50780
\(363\) −1.58560e16 −0.363748
\(364\) 8.29920e16 1.87015
\(365\) −3.93439e15 −0.0870911
\(366\) 3.92422e16 0.853349
\(367\) −6.62560e16 −1.41545 −0.707727 0.706486i \(-0.750279\pi\)
−0.707727 + 0.706486i \(0.750279\pi\)
\(368\) 2.15158e16 0.451592
\(369\) 2.21513e16 0.456803
\(370\) −3.09430e16 −0.626976
\(371\) −2.80813e16 −0.559096
\(372\) 3.68227e16 0.720421
\(373\) −6.77688e16 −1.30293 −0.651467 0.758677i \(-0.725846\pi\)
−0.651467 + 0.758677i \(0.725846\pi\)
\(374\) −4.58230e15 −0.0865801
\(375\) 3.27936e16 0.608956
\(376\) 3.19602e16 0.583296
\(377\) 1.06424e16 0.190906
\(378\) 1.85395e16 0.326890
\(379\) 3.45510e15 0.0598834 0.0299417 0.999552i \(-0.490468\pi\)
0.0299417 + 0.999552i \(0.490468\pi\)
\(380\) −7.33263e16 −1.24930
\(381\) 3.35162e16 0.561362
\(382\) −7.99538e16 −1.31652
\(383\) −4.03416e16 −0.653072 −0.326536 0.945185i \(-0.605881\pi\)
−0.326536 + 0.945185i \(0.605881\pi\)
\(384\) 4.38750e16 0.698335
\(385\) 3.94727e16 0.617735
\(386\) −7.10419e16 −1.09319
\(387\) 3.66222e16 0.554145
\(388\) 1.15619e17 1.72037
\(389\) −4.77579e16 −0.698832 −0.349416 0.936968i \(-0.613620\pi\)
−0.349416 + 0.936968i \(0.613620\pi\)
\(390\) −6.99782e16 −1.00703
\(391\) −7.46800e15 −0.105695
\(392\) −9.02098e15 −0.125572
\(393\) 4.60064e16 0.629893
\(394\) −1.48960e17 −2.00606
\(395\) −1.08843e17 −1.44185
\(396\) 2.22052e16 0.289358
\(397\) −8.13622e16 −1.04300 −0.521500 0.853251i \(-0.674627\pi\)
−0.521500 + 0.853251i \(0.674627\pi\)
\(398\) −1.66637e17 −2.10151
\(399\) −4.76767e16 −0.591538
\(400\) 4.23085e15 0.0516461
\(401\) −6.34120e16 −0.761610 −0.380805 0.924655i \(-0.624353\pi\)
−0.380805 + 0.924655i \(0.624353\pi\)
\(402\) 8.76406e16 1.03570
\(403\) −9.03703e16 −1.05086
\(404\) 6.89714e16 0.789205
\(405\) −9.19178e15 −0.103500
\(406\) −2.43474e16 −0.269795
\(407\) −2.40970e16 −0.262784
\(408\) −3.27083e15 −0.0351049
\(409\) −1.46971e17 −1.55250 −0.776248 0.630427i \(-0.782880\pi\)
−0.776248 + 0.630427i \(0.782880\pi\)
\(410\) 1.91284e17 1.98877
\(411\) −3.75514e16 −0.384286
\(412\) 2.38433e17 2.40178
\(413\) −1.43148e16 −0.141941
\(414\) 6.15460e16 0.600756
\(415\) −8.92340e16 −0.857468
\(416\) −1.61819e17 −1.53082
\(417\) 1.60777e16 0.149740
\(418\) −9.71151e16 −0.890515
\(419\) −8.53034e16 −0.770150 −0.385075 0.922885i \(-0.625824\pi\)
−0.385075 + 0.922885i \(0.625824\pi\)
\(420\) 9.41353e16 0.836820
\(421\) 4.86032e16 0.425433 0.212716 0.977114i \(-0.431769\pi\)
0.212716 + 0.977114i \(0.431769\pi\)
\(422\) −1.16883e17 −1.00744
\(423\) −3.44221e16 −0.292163
\(424\) −4.08293e16 −0.341267
\(425\) −1.46850e15 −0.0120878
\(426\) 1.53605e17 1.24521
\(427\) 1.29555e17 1.03436
\(428\) −1.19632e17 −0.940722
\(429\) −5.44960e16 −0.422077
\(430\) 3.16245e17 2.41257
\(431\) 1.32000e17 0.991910 0.495955 0.868348i \(-0.334818\pi\)
0.495955 + 0.868348i \(0.334818\pi\)
\(432\) −1.01494e16 −0.0751267
\(433\) 9.75130e16 0.711036 0.355518 0.934670i \(-0.384305\pi\)
0.355518 + 0.934670i \(0.384305\pi\)
\(434\) 2.06748e17 1.48511
\(435\) 1.20713e16 0.0854228
\(436\) 2.35112e17 1.63913
\(437\) −1.58273e17 −1.08712
\(438\) −1.24268e16 −0.0840965
\(439\) 4.19591e16 0.279774 0.139887 0.990167i \(-0.455326\pi\)
0.139887 + 0.990167i \(0.455326\pi\)
\(440\) 5.73922e16 0.377060
\(441\) 9.71587e15 0.0628971
\(442\) 2.68194e16 0.171082
\(443\) −1.52350e17 −0.957677 −0.478839 0.877903i \(-0.658942\pi\)
−0.478839 + 0.877903i \(0.658942\pi\)
\(444\) −5.74670e16 −0.355983
\(445\) −1.70494e17 −1.04081
\(446\) 3.67742e17 2.21242
\(447\) −3.67065e16 −0.217643
\(448\) 2.97376e17 1.73780
\(449\) −2.14314e17 −1.23438 −0.617190 0.786814i \(-0.711729\pi\)
−0.617190 + 0.786814i \(0.711729\pi\)
\(450\) 1.21024e16 0.0687051
\(451\) 1.48964e17 0.833553
\(452\) −4.73103e17 −2.60949
\(453\) 8.79588e16 0.478235
\(454\) −4.50543e17 −2.41476
\(455\) −2.31027e17 −1.22064
\(456\) −6.93205e16 −0.361069
\(457\) 3.07100e17 1.57697 0.788486 0.615052i \(-0.210865\pi\)
0.788486 + 0.615052i \(0.210865\pi\)
\(458\) 3.19847e17 1.61926
\(459\) 3.52279e15 0.0175834
\(460\) 3.12503e17 1.53790
\(461\) −2.40168e17 −1.16536 −0.582678 0.812703i \(-0.697995\pi\)
−0.582678 + 0.812703i \(0.697995\pi\)
\(462\) 1.24675e17 0.596495
\(463\) −2.41166e17 −1.13773 −0.568865 0.822431i \(-0.692617\pi\)
−0.568865 + 0.822431i \(0.692617\pi\)
\(464\) 1.33289e16 0.0620049
\(465\) −1.02504e17 −0.470216
\(466\) 4.63173e17 2.09525
\(467\) 2.51988e17 1.12414 0.562070 0.827090i \(-0.310005\pi\)
0.562070 + 0.827090i \(0.310005\pi\)
\(468\) −1.29963e17 −0.571770
\(469\) 2.89338e17 1.25540
\(470\) −2.97246e17 −1.27198
\(471\) −4.44192e16 −0.187471
\(472\) −2.08132e16 −0.0866396
\(473\) 2.46278e17 1.01118
\(474\) −3.43782e17 −1.39227
\(475\) −3.11228e16 −0.124328
\(476\) −3.60777e16 −0.142165
\(477\) 4.39744e16 0.170935
\(478\) 1.16041e17 0.444969
\(479\) 6.98532e16 0.264244 0.132122 0.991233i \(-0.457821\pi\)
0.132122 + 0.991233i \(0.457821\pi\)
\(480\) −1.83547e17 −0.684981
\(481\) 1.41036e17 0.519261
\(482\) 4.24450e15 0.0154177
\(483\) 2.03189e17 0.728188
\(484\) −2.54290e17 −0.899155
\(485\) −3.21850e17 −1.12288
\(486\) −2.90323e16 −0.0999416
\(487\) −1.64688e16 −0.0559402 −0.0279701 0.999609i \(-0.508904\pi\)
−0.0279701 + 0.999609i \(0.508904\pi\)
\(488\) 1.88369e17 0.631365
\(489\) 1.05939e17 0.350388
\(490\) 8.38997e16 0.273833
\(491\) −1.43797e17 −0.463149 −0.231574 0.972817i \(-0.574388\pi\)
−0.231574 + 0.972817i \(0.574388\pi\)
\(492\) 3.55252e17 1.12918
\(493\) −4.62637e15 −0.0145123
\(494\) 5.68398e17 1.75965
\(495\) −6.18131e16 −0.188863
\(496\) −1.13183e17 −0.341310
\(497\) 5.07114e17 1.50935
\(498\) −2.81847e17 −0.827984
\(499\) 1.98943e17 0.576867 0.288434 0.957500i \(-0.406866\pi\)
0.288434 + 0.957500i \(0.406866\pi\)
\(500\) 5.25926e17 1.50529
\(501\) −1.36865e17 −0.386676
\(502\) 7.61056e17 2.12247
\(503\) −5.36371e17 −1.47664 −0.738318 0.674453i \(-0.764379\pi\)
−0.738318 + 0.674453i \(0.764379\pi\)
\(504\) 8.89927e16 0.241855
\(505\) −1.91997e17 −0.515112
\(506\) 4.13886e17 1.09623
\(507\) 9.81595e16 0.256673
\(508\) 5.37516e17 1.38764
\(509\) 2.34622e17 0.598002 0.299001 0.954253i \(-0.403347\pi\)
0.299001 + 0.954253i \(0.403347\pi\)
\(510\) 3.04204e16 0.0765524
\(511\) −4.10260e16 −0.101935
\(512\) −3.08563e17 −0.756987
\(513\) 7.46603e16 0.180853
\(514\) 3.40546e17 0.814546
\(515\) −6.63731e17 −1.56764
\(516\) 5.87328e17 1.36980
\(517\) −2.31482e17 −0.533126
\(518\) −3.22659e17 −0.733838
\(519\) −4.40400e17 −0.989143
\(520\) −3.35906e17 −0.745069
\(521\) 8.13954e17 1.78301 0.891507 0.453007i \(-0.149649\pi\)
0.891507 + 0.453007i \(0.149649\pi\)
\(522\) 3.81273e16 0.0824856
\(523\) 2.03568e17 0.434959 0.217480 0.976065i \(-0.430216\pi\)
0.217480 + 0.976065i \(0.430216\pi\)
\(524\) 7.37827e17 1.55704
\(525\) 3.99549e16 0.0832789
\(526\) 9.34182e17 1.92320
\(527\) 3.92851e16 0.0798838
\(528\) −6.82526e16 −0.137088
\(529\) 1.70494e17 0.338257
\(530\) 3.79734e17 0.744194
\(531\) 2.24165e16 0.0433963
\(532\) −7.64614e17 −1.46223
\(533\) −8.71859e17 −1.64710
\(534\) −5.38508e17 −1.00502
\(535\) 3.33021e17 0.614006
\(536\) 4.20689e17 0.766284
\(537\) −4.46193e17 −0.802953
\(538\) 3.03361e17 0.539356
\(539\) 6.53374e16 0.114772
\(540\) −1.47413e17 −0.255845
\(541\) −3.12937e17 −0.536629 −0.268315 0.963331i \(-0.586467\pi\)
−0.268315 + 0.963331i \(0.586467\pi\)
\(542\) 5.66211e17 0.959363
\(543\) 5.55114e17 0.929359
\(544\) 7.03449e16 0.116370
\(545\) −6.54487e17 −1.06985
\(546\) −7.29701e17 −1.17867
\(547\) 4.64466e16 0.0741372 0.0370686 0.999313i \(-0.488198\pi\)
0.0370686 + 0.999313i \(0.488198\pi\)
\(548\) −6.02230e17 −0.949924
\(549\) −2.02879e17 −0.316240
\(550\) 8.13863e16 0.125370
\(551\) −9.80491e16 −0.149265
\(552\) 2.95431e17 0.444479
\(553\) −1.13497e18 −1.68760
\(554\) −1.88359e17 −0.276804
\(555\) 1.59972e17 0.232349
\(556\) 2.57845e17 0.370146
\(557\) 4.79880e17 0.680885 0.340442 0.940265i \(-0.389423\pi\)
0.340442 + 0.940265i \(0.389423\pi\)
\(558\) −3.23760e17 −0.454048
\(559\) −1.44142e18 −1.99809
\(560\) −2.89346e17 −0.396456
\(561\) 2.36901e16 0.0320855
\(562\) −1.44768e18 −1.93815
\(563\) −1.23803e18 −1.63843 −0.819215 0.573486i \(-0.805591\pi\)
−0.819215 + 0.573486i \(0.805591\pi\)
\(564\) −5.52043e17 −0.722203
\(565\) 1.31699e18 1.70321
\(566\) −7.21047e17 −0.921843
\(567\) −9.58478e16 −0.121141
\(568\) 7.37328e17 0.921291
\(569\) −8.42942e17 −1.04128 −0.520641 0.853776i \(-0.674307\pi\)
−0.520641 + 0.853776i \(0.674307\pi\)
\(570\) 6.44716e17 0.787376
\(571\) 8.26813e16 0.0998326 0.0499163 0.998753i \(-0.484105\pi\)
0.0499163 + 0.998753i \(0.484105\pi\)
\(572\) −8.73977e17 −1.04334
\(573\) 4.13354e17 0.487885
\(574\) 1.99463e18 2.32774
\(575\) 1.32639e17 0.153049
\(576\) −4.65682e17 −0.531305
\(577\) 1.46434e17 0.165196 0.0825978 0.996583i \(-0.473678\pi\)
0.0825978 + 0.996583i \(0.473678\pi\)
\(578\) 1.38497e18 1.54493
\(579\) 3.67280e17 0.405123
\(580\) 1.93593e17 0.211158
\(581\) −9.30492e17 −1.00362
\(582\) −1.01657e18 −1.08427
\(583\) 2.95720e17 0.311914
\(584\) −5.96506e16 −0.0622202
\(585\) 3.61781e17 0.373193
\(586\) 1.48431e18 1.51422
\(587\) −2.12057e17 −0.213947 −0.106973 0.994262i \(-0.534116\pi\)
−0.106973 + 0.994262i \(0.534116\pi\)
\(588\) 1.55818e17 0.155477
\(589\) 8.32590e17 0.821640
\(590\) 1.93574e17 0.188933
\(591\) 7.70111e17 0.743420
\(592\) 1.76638e17 0.168652
\(593\) 4.33421e16 0.0409312 0.0204656 0.999791i \(-0.493485\pi\)
0.0204656 + 0.999791i \(0.493485\pi\)
\(594\) −1.95237e17 −0.182369
\(595\) 1.00430e17 0.0927908
\(596\) −5.88679e17 −0.537995
\(597\) 8.61499e17 0.778792
\(598\) −2.42240e18 −2.16615
\(599\) 7.59124e17 0.671489 0.335744 0.941953i \(-0.391012\pi\)
0.335744 + 0.941953i \(0.391012\pi\)
\(600\) 5.80933e16 0.0508327
\(601\) 7.45965e17 0.645705 0.322853 0.946449i \(-0.395358\pi\)
0.322853 + 0.946449i \(0.395358\pi\)
\(602\) 3.29766e18 2.82377
\(603\) −4.53094e17 −0.383818
\(604\) 1.41064e18 1.18216
\(605\) 7.07874e17 0.586876
\(606\) −6.06426e17 −0.497400
\(607\) 1.44337e18 1.17126 0.585629 0.810579i \(-0.300848\pi\)
0.585629 + 0.810579i \(0.300848\pi\)
\(608\) 1.49086e18 1.19691
\(609\) 1.25874e17 0.0999825
\(610\) −1.75193e18 −1.37680
\(611\) 1.35483e18 1.05345
\(612\) 5.64966e16 0.0434648
\(613\) −2.40464e18 −1.83044 −0.915221 0.402951i \(-0.867984\pi\)
−0.915221 + 0.402951i \(0.867984\pi\)
\(614\) −2.79509e17 −0.210524
\(615\) −9.88923e17 −0.737011
\(616\) 5.98460e17 0.441327
\(617\) 1.89253e17 0.138099 0.0690493 0.997613i \(-0.478003\pi\)
0.0690493 + 0.997613i \(0.478003\pi\)
\(618\) −2.09640e18 −1.51373
\(619\) 4.43390e17 0.316808 0.158404 0.987374i \(-0.449365\pi\)
0.158404 + 0.987374i \(0.449365\pi\)
\(620\) −1.64391e18 −1.16234
\(621\) −3.18188e17 −0.222632
\(622\) −1.97431e18 −1.36703
\(623\) −1.77784e18 −1.21820
\(624\) 3.99471e17 0.270885
\(625\) −1.26689e18 −0.850196
\(626\) −5.51165e17 −0.366057
\(627\) 5.02077e17 0.330013
\(628\) −7.12371e17 −0.463413
\(629\) −6.13100e16 −0.0394732
\(630\) −8.27677e17 −0.527409
\(631\) −2.89290e17 −0.182450 −0.0912248 0.995830i \(-0.529078\pi\)
−0.0912248 + 0.995830i \(0.529078\pi\)
\(632\) −1.65021e18 −1.03009
\(633\) 6.04273e17 0.373344
\(634\) 3.20170e18 1.95794
\(635\) −1.49630e18 −0.905708
\(636\) 7.05238e17 0.422537
\(637\) −3.82409e17 −0.226789
\(638\) 2.56399e17 0.150516
\(639\) −7.94125e17 −0.461459
\(640\) −1.95875e18 −1.12670
\(641\) 1.36610e17 0.0777868 0.0388934 0.999243i \(-0.487617\pi\)
0.0388934 + 0.999243i \(0.487617\pi\)
\(642\) 1.05185e18 0.592894
\(643\) 2.08256e17 0.116205 0.0581026 0.998311i \(-0.481495\pi\)
0.0581026 + 0.998311i \(0.481495\pi\)
\(644\) 3.25864e18 1.80002
\(645\) −1.63496e18 −0.894065
\(646\) −2.47090e17 −0.133765
\(647\) 1.55341e18 0.832548 0.416274 0.909239i \(-0.363336\pi\)
0.416274 + 0.909239i \(0.363336\pi\)
\(648\) −1.39360e17 −0.0739435
\(649\) 1.50747e17 0.0791876
\(650\) −4.76340e17 −0.247731
\(651\) −1.06887e18 −0.550361
\(652\) 1.69900e18 0.866131
\(653\) 2.82346e18 1.42510 0.712550 0.701621i \(-0.247540\pi\)
0.712550 + 0.701621i \(0.247540\pi\)
\(654\) −2.06720e18 −1.03306
\(655\) −2.05391e18 −1.01628
\(656\) −1.09195e18 −0.534966
\(657\) 6.42455e16 0.0311651
\(658\) −3.09955e18 −1.48878
\(659\) −1.08635e18 −0.516674 −0.258337 0.966055i \(-0.583174\pi\)
−0.258337 + 0.966055i \(0.583174\pi\)
\(660\) −9.91325e17 −0.466854
\(661\) −4.65670e17 −0.217154 −0.108577 0.994088i \(-0.534629\pi\)
−0.108577 + 0.994088i \(0.534629\pi\)
\(662\) −4.00093e16 −0.0184750
\(663\) −1.38654e17 −0.0634008
\(664\) −1.35291e18 −0.612598
\(665\) 2.12847e18 0.954394
\(666\) 5.05274e17 0.224360
\(667\) 4.17866e17 0.183747
\(668\) −2.19497e18 −0.955832
\(669\) −1.90120e18 −0.819893
\(670\) −3.91262e18 −1.67102
\(671\) −1.36432e18 −0.577060
\(672\) −1.91394e18 −0.801730
\(673\) 1.31869e18 0.547072 0.273536 0.961862i \(-0.411807\pi\)
0.273536 + 0.961862i \(0.411807\pi\)
\(674\) 2.73932e18 1.12552
\(675\) −6.25682e16 −0.0254612
\(676\) 1.57423e18 0.634475
\(677\) 4.38276e18 1.74953 0.874765 0.484547i \(-0.161015\pi\)
0.874765 + 0.484547i \(0.161015\pi\)
\(678\) 4.15972e18 1.64464
\(679\) −3.35611e18 −1.31426
\(680\) 1.46023e17 0.0566386
\(681\) 2.32927e18 0.894877
\(682\) −2.17723e18 −0.828526
\(683\) −2.95888e18 −1.11530 −0.557650 0.830076i \(-0.688297\pi\)
−0.557650 + 0.830076i \(0.688297\pi\)
\(684\) 1.19736e18 0.447055
\(685\) 1.67644e18 0.620012
\(686\) −3.76164e18 −1.37807
\(687\) −1.65358e18 −0.600077
\(688\) −1.80529e18 −0.648965
\(689\) −1.73080e18 −0.616341
\(690\) −2.74766e18 −0.969267
\(691\) 1.39667e18 0.488073 0.244037 0.969766i \(-0.421528\pi\)
0.244037 + 0.969766i \(0.421528\pi\)
\(692\) −7.06290e18 −2.44508
\(693\) −6.44559e17 −0.221053
\(694\) 1.30201e18 0.442360
\(695\) −7.17771e17 −0.241593
\(696\) 1.83017e17 0.0610284
\(697\) 3.79008e17 0.125209
\(698\) 5.85296e18 1.91565
\(699\) −2.39456e18 −0.776471
\(700\) 6.40776e17 0.205859
\(701\) 3.20852e18 1.02126 0.510631 0.859800i \(-0.329412\pi\)
0.510631 + 0.859800i \(0.329412\pi\)
\(702\) 1.14269e18 0.360360
\(703\) −1.29938e18 −0.405999
\(704\) −3.13163e18 −0.969500
\(705\) 1.53674e18 0.471379
\(706\) −1.82697e17 −0.0555264
\(707\) −2.00206e18 −0.602908
\(708\) 3.59503e17 0.107272
\(709\) −3.96499e18 −1.17231 −0.586154 0.810200i \(-0.699359\pi\)
−0.586154 + 0.810200i \(0.699359\pi\)
\(710\) −6.85753e18 −2.00904
\(711\) 1.77732e18 0.515957
\(712\) −2.58492e18 −0.743580
\(713\) −3.54834e18 −1.01145
\(714\) 3.17210e17 0.0896002
\(715\) 2.43291e18 0.680985
\(716\) −7.15581e18 −1.98483
\(717\) −5.99922e17 −0.164900
\(718\) 6.11276e18 1.66505
\(719\) 3.22681e17 0.0871036 0.0435518 0.999051i \(-0.486133\pi\)
0.0435518 + 0.999051i \(0.486133\pi\)
\(720\) 4.53107e17 0.121210
\(721\) −6.92109e18 −1.83483
\(722\) 6.93110e17 0.182100
\(723\) −2.19437e16 −0.00571361
\(724\) 8.90263e18 2.29730
\(725\) 8.21690e16 0.0210141
\(726\) 2.23583e18 0.566696
\(727\) −3.93382e18 −0.988191 −0.494095 0.869408i \(-0.664501\pi\)
−0.494095 + 0.869408i \(0.664501\pi\)
\(728\) −3.50268e18 −0.872060
\(729\) 1.50095e17 0.0370370
\(730\) 5.54781e17 0.135682
\(731\) 6.26604e17 0.151890
\(732\) −3.25366e18 −0.781719
\(733\) −3.56933e18 −0.849985 −0.424993 0.905197i \(-0.639723\pi\)
−0.424993 + 0.905197i \(0.639723\pi\)
\(734\) 9.34264e18 2.20519
\(735\) −4.33754e17 −0.101479
\(736\) −6.35375e18 −1.47341
\(737\) −3.04698e18 −0.700374
\(738\) −3.12352e18 −0.711669
\(739\) −3.49941e18 −0.790325 −0.395163 0.918611i \(-0.629312\pi\)
−0.395163 + 0.918611i \(0.629312\pi\)
\(740\) 2.56555e18 0.574347
\(741\) −2.93857e18 −0.652105
\(742\) 3.95969e18 0.871035
\(743\) −2.67608e18 −0.583542 −0.291771 0.956488i \(-0.594244\pi\)
−0.291771 + 0.956488i \(0.594244\pi\)
\(744\) −1.55410e18 −0.335935
\(745\) 1.63872e18 0.351147
\(746\) 9.55596e18 2.02989
\(747\) 1.45712e18 0.306840
\(748\) 3.79929e17 0.0793126
\(749\) 3.47260e18 0.718658
\(750\) −4.62417e18 −0.948714
\(751\) 5.54941e18 1.12872 0.564361 0.825528i \(-0.309122\pi\)
0.564361 + 0.825528i \(0.309122\pi\)
\(752\) 1.69683e18 0.342155
\(753\) −3.93459e18 −0.786561
\(754\) −1.50066e18 −0.297419
\(755\) −3.92683e18 −0.771590
\(756\) −1.53716e18 −0.299451
\(757\) −3.98699e18 −0.770056 −0.385028 0.922905i \(-0.625808\pi\)
−0.385028 + 0.922905i \(0.625808\pi\)
\(758\) −4.87198e17 −0.0932944
\(759\) −2.13975e18 −0.406249
\(760\) 3.09474e18 0.582553
\(761\) −4.32091e18 −0.806445 −0.403222 0.915102i \(-0.632110\pi\)
−0.403222 + 0.915102i \(0.632110\pi\)
\(762\) −4.72606e18 −0.874566
\(763\) −6.82469e18 −1.25220
\(764\) 6.62915e18 1.20601
\(765\) −1.57271e17 −0.0283693
\(766\) 5.68850e18 1.01744
\(767\) −8.82294e17 −0.156474
\(768\) −9.53715e17 −0.167715
\(769\) −3.75159e18 −0.654175 −0.327088 0.944994i \(-0.606067\pi\)
−0.327088 + 0.944994i \(0.606067\pi\)
\(770\) −5.56598e18 −0.962392
\(771\) −1.76059e18 −0.301860
\(772\) 5.89025e18 1.00143
\(773\) 3.44844e18 0.581374 0.290687 0.956818i \(-0.406116\pi\)
0.290687 + 0.956818i \(0.406116\pi\)
\(774\) −5.16404e18 −0.863323
\(775\) −6.97743e17 −0.115674
\(776\) −4.87968e18 −0.802214
\(777\) 1.66812e18 0.271951
\(778\) 6.73425e18 1.08873
\(779\) 8.03252e18 1.28783
\(780\) 5.80206e18 0.922501
\(781\) −5.34034e18 −0.842049
\(782\) 1.05305e18 0.164666
\(783\) −1.97115e17 −0.0305681
\(784\) −4.78942e17 −0.0736594
\(785\) 1.98305e18 0.302468
\(786\) −6.48729e18 −0.981333
\(787\) 5.71704e18 0.857701 0.428850 0.903376i \(-0.358919\pi\)
0.428850 + 0.903376i \(0.358919\pi\)
\(788\) 1.23506e19 1.83767
\(789\) −4.82964e18 −0.712712
\(790\) 1.53478e19 2.24631
\(791\) 1.37330e19 1.99350
\(792\) −9.37169e17 −0.134929
\(793\) 7.98515e18 1.14027
\(794\) 1.14727e19 1.62493
\(795\) −1.96319e18 −0.275788
\(796\) 1.38163e19 1.92511
\(797\) −1.02867e19 −1.42166 −0.710829 0.703364i \(-0.751680\pi\)
−0.710829 + 0.703364i \(0.751680\pi\)
\(798\) 6.72281e18 0.921577
\(799\) −5.88960e17 −0.0800814
\(800\) −1.24940e18 −0.168506
\(801\) 2.78404e18 0.372447
\(802\) 8.94161e18 1.18654
\(803\) 4.32039e17 0.0568686
\(804\) −7.26648e18 −0.948768
\(805\) −9.07115e18 −1.17487
\(806\) 1.27430e19 1.63716
\(807\) −1.56835e18 −0.199878
\(808\) −2.91094e18 −0.368010
\(809\) 8.06911e18 1.01195 0.505977 0.862547i \(-0.331132\pi\)
0.505977 + 0.862547i \(0.331132\pi\)
\(810\) 1.29612e18 0.161247
\(811\) 1.58560e19 1.95685 0.978425 0.206603i \(-0.0662407\pi\)
0.978425 + 0.206603i \(0.0662407\pi\)
\(812\) 2.01870e18 0.247148
\(813\) −2.92726e18 −0.355527
\(814\) 3.39788e18 0.409401
\(815\) −4.72954e18 −0.565320
\(816\) −1.73655e17 −0.0205921
\(817\) 1.32800e19 1.56226
\(818\) 2.07241e19 2.41869
\(819\) 3.77249e18 0.436800
\(820\) −1.58598e19 −1.82183
\(821\) −1.61392e19 −1.83929 −0.919646 0.392749i \(-0.871524\pi\)
−0.919646 + 0.392749i \(0.871524\pi\)
\(822\) 5.29506e18 0.598693
\(823\) 1.13957e19 1.27833 0.639163 0.769071i \(-0.279281\pi\)
0.639163 + 0.769071i \(0.279281\pi\)
\(824\) −1.00631e19 −1.11996
\(825\) −4.20760e17 −0.0464605
\(826\) 2.01850e18 0.221135
\(827\) −3.46550e18 −0.376686 −0.188343 0.982103i \(-0.560312\pi\)
−0.188343 + 0.982103i \(0.560312\pi\)
\(828\) −5.10292e18 −0.550328
\(829\) 2.23042e17 0.0238662 0.0119331 0.999929i \(-0.496201\pi\)
0.0119331 + 0.999929i \(0.496201\pi\)
\(830\) 1.25827e19 1.33588
\(831\) 9.73800e17 0.102580
\(832\) 1.83289e19 1.91573
\(833\) 1.66238e17 0.0172400
\(834\) −2.26709e18 −0.233286
\(835\) 6.11020e18 0.623868
\(836\) 8.05204e18 0.815765
\(837\) 1.67381e18 0.168264
\(838\) 1.20285e19 1.19984
\(839\) −1.29547e19 −1.28226 −0.641128 0.767434i \(-0.721533\pi\)
−0.641128 + 0.767434i \(0.721533\pi\)
\(840\) −3.97298e18 −0.390212
\(841\) −1.00018e19 −0.974771
\(842\) −6.85345e18 −0.662797
\(843\) 7.48438e18 0.718251
\(844\) 9.69102e18 0.922876
\(845\) −4.38222e18 −0.414120
\(846\) 4.85380e18 0.455171
\(847\) 7.38139e18 0.686904
\(848\) −2.16771e18 −0.200183
\(849\) 3.72775e18 0.341623
\(850\) 2.07071e17 0.0188320
\(851\) 5.53769e18 0.499788
\(852\) −1.27357e19 −1.14069
\(853\) 2.04089e19 1.81406 0.907029 0.421069i \(-0.138345\pi\)
0.907029 + 0.421069i \(0.138345\pi\)
\(854\) −1.82683e19 −1.61147
\(855\) −3.33313e18 −0.291791
\(856\) 5.04905e18 0.438662
\(857\) −6.96086e17 −0.0600188 −0.0300094 0.999550i \(-0.509554\pi\)
−0.0300094 + 0.999550i \(0.509554\pi\)
\(858\) 7.68438e18 0.657569
\(859\) 1.63956e19 1.39242 0.696212 0.717836i \(-0.254867\pi\)
0.696212 + 0.717836i \(0.254867\pi\)
\(860\) −2.62206e19 −2.21005
\(861\) −1.03120e19 −0.862629
\(862\) −1.86131e19 −1.54533
\(863\) 1.62974e19 1.34291 0.671457 0.741043i \(-0.265669\pi\)
0.671457 + 0.741043i \(0.265669\pi\)
\(864\) 2.99717e18 0.245116
\(865\) 1.96612e19 1.59590
\(866\) −1.37501e19 −1.10775
\(867\) −7.16016e18 −0.572531
\(868\) −1.71419e19 −1.36045
\(869\) 1.19522e19 0.941495
\(870\) −1.70215e18 −0.133083
\(871\) 1.78334e19 1.38394
\(872\) −9.92289e18 −0.764331
\(873\) 5.25556e18 0.401816
\(874\) 2.23178e19 1.69367
\(875\) −1.52663e19 −1.14996
\(876\) 1.03034e18 0.0770375
\(877\) −2.11466e19 −1.56944 −0.784718 0.619853i \(-0.787192\pi\)
−0.784718 + 0.619853i \(0.787192\pi\)
\(878\) −5.91658e18 −0.435869
\(879\) −7.67375e18 −0.561151
\(880\) 3.04706e18 0.221179
\(881\) 1.78682e19 1.28747 0.643734 0.765249i \(-0.277384\pi\)
0.643734 + 0.765249i \(0.277384\pi\)
\(882\) −1.37002e18 −0.0979896
\(883\) −1.04409e19 −0.741302 −0.370651 0.928772i \(-0.620865\pi\)
−0.370651 + 0.928772i \(0.620865\pi\)
\(884\) −2.22366e18 −0.156721
\(885\) −1.00076e18 −0.0700161
\(886\) 2.14827e19 1.49200
\(887\) 2.06682e19 1.42495 0.712474 0.701699i \(-0.247575\pi\)
0.712474 + 0.701699i \(0.247575\pi\)
\(888\) 2.42540e18 0.165996
\(889\) −1.56027e19 −1.06008
\(890\) 2.40411e19 1.62151
\(891\) 1.00936e18 0.0675835
\(892\) −3.04904e19 −2.02671
\(893\) −1.24821e19 −0.823673
\(894\) 5.17591e18 0.339073
\(895\) 1.99198e19 1.29549
\(896\) −2.04250e19 −1.31874
\(897\) 1.25236e19 0.802747
\(898\) 3.02200e19 1.92309
\(899\) −2.19817e18 −0.138875
\(900\) −1.00344e18 −0.0629380
\(901\) 7.52400e17 0.0468530
\(902\) −2.10051e19 −1.29862
\(903\) −1.70486e19 −1.04645
\(904\) 1.99673e19 1.21682
\(905\) −2.47825e19 −1.49944
\(906\) −1.24029e19 −0.745059
\(907\) 2.43732e19 1.45367 0.726835 0.686812i \(-0.240991\pi\)
0.726835 + 0.686812i \(0.240991\pi\)
\(908\) 3.73556e19 2.21206
\(909\) 3.13517e18 0.184330
\(910\) 3.25767e19 1.90168
\(911\) 5.74736e18 0.333119 0.166559 0.986031i \(-0.446734\pi\)
0.166559 + 0.986031i \(0.446734\pi\)
\(912\) −3.68036e18 −0.211799
\(913\) 9.79888e18 0.559908
\(914\) −4.33036e19 −2.45682
\(915\) 9.05730e18 0.510225
\(916\) −2.65193e19 −1.48334
\(917\) −2.14172e19 −1.18949
\(918\) −4.96742e17 −0.0273939
\(919\) 1.79988e19 0.985584 0.492792 0.870147i \(-0.335976\pi\)
0.492792 + 0.870147i \(0.335976\pi\)
\(920\) −1.31892e19 −0.717128
\(921\) 1.44504e18 0.0780175
\(922\) 3.38656e19 1.81555
\(923\) 3.12561e19 1.66389
\(924\) −1.03371e19 −0.546425
\(925\) 1.08893e18 0.0571581
\(926\) 3.40063e19 1.77251
\(927\) 1.08382e19 0.560969
\(928\) −3.93610e18 −0.202304
\(929\) 1.51694e18 0.0774224 0.0387112 0.999250i \(-0.487675\pi\)
0.0387112 + 0.999250i \(0.487675\pi\)
\(930\) 1.44539e19 0.732566
\(931\) 3.52317e18 0.177321
\(932\) −3.84028e19 −1.91937
\(933\) 1.02070e19 0.506603
\(934\) −3.55324e19 −1.75134
\(935\) −1.05762e18 −0.0517671
\(936\) 5.48509e18 0.266619
\(937\) −2.76656e19 −1.33547 −0.667733 0.744401i \(-0.732735\pi\)
−0.667733 + 0.744401i \(0.732735\pi\)
\(938\) −4.07990e19 −1.95583
\(939\) 2.84947e18 0.135656
\(940\) 2.46454e19 1.16521
\(941\) −1.97743e19 −0.928474 −0.464237 0.885711i \(-0.653671\pi\)
−0.464237 + 0.885711i \(0.653671\pi\)
\(942\) 6.26347e18 0.292068
\(943\) −3.42331e19 −1.58533
\(944\) −1.10502e18 −0.0508218
\(945\) 4.27902e18 0.195451
\(946\) −3.47272e19 −1.57535
\(947\) 9.54996e18 0.430256 0.215128 0.976586i \(-0.430983\pi\)
0.215128 + 0.976586i \(0.430983\pi\)
\(948\) 2.85037e19 1.27540
\(949\) −2.52865e18 −0.112372
\(950\) 4.38856e18 0.193695
\(951\) −1.65525e19 −0.725587
\(952\) 1.52266e18 0.0662922
\(953\) −2.35086e19 −1.01654 −0.508269 0.861198i \(-0.669714\pi\)
−0.508269 + 0.861198i \(0.669714\pi\)
\(954\) −6.20075e18 −0.266305
\(955\) −1.84537e19 −0.787159
\(956\) −9.62122e18 −0.407619
\(957\) −1.32556e18 −0.0557792
\(958\) −9.84988e18 −0.411675
\(959\) 1.74812e19 0.725688
\(960\) 2.07899e19 0.857213
\(961\) −5.75166e18 −0.235554
\(962\) −1.98872e19 −0.808976
\(963\) −5.43798e18 −0.219719
\(964\) −3.51921e17 −0.0141236
\(965\) −1.63968e19 −0.653630
\(966\) −2.86513e19 −1.13447
\(967\) −3.01315e19 −1.18508 −0.592541 0.805540i \(-0.701875\pi\)
−0.592541 + 0.805540i \(0.701875\pi\)
\(968\) 1.07323e19 0.419280
\(969\) 1.27743e18 0.0495717
\(970\) 4.53835e19 1.74937
\(971\) 1.65229e19 0.632648 0.316324 0.948651i \(-0.397551\pi\)
0.316324 + 0.948651i \(0.397551\pi\)
\(972\) 2.40714e18 0.0915525
\(973\) −7.48459e18 −0.282771
\(974\) 2.32224e18 0.0871512
\(975\) 2.46263e18 0.0918058
\(976\) 1.00009e19 0.370351
\(977\) −1.30217e19 −0.479019 −0.239510 0.970894i \(-0.576987\pi\)
−0.239510 + 0.970894i \(0.576987\pi\)
\(978\) −1.49383e19 −0.545882
\(979\) 1.87222e19 0.679623
\(980\) −6.95632e18 −0.250848
\(981\) 1.06873e19 0.382840
\(982\) 2.02766e19 0.721556
\(983\) 3.54880e19 1.25454 0.627269 0.778803i \(-0.284173\pi\)
0.627269 + 0.778803i \(0.284173\pi\)
\(984\) −1.49934e19 −0.526541
\(985\) −3.43807e19 −1.19944
\(986\) 6.52356e17 0.0226092
\(987\) 1.60244e19 0.551722
\(988\) −4.71272e19 −1.61195
\(989\) −5.65966e19 −1.92316
\(990\) 8.71615e18 0.294236
\(991\) −1.14308e19 −0.383354 −0.191677 0.981458i \(-0.561393\pi\)
−0.191677 + 0.981458i \(0.561393\pi\)
\(992\) 3.34236e19 1.11360
\(993\) 2.06845e17 0.00684659
\(994\) −7.15072e19 −2.35146
\(995\) −3.84607e19 −1.25651
\(996\) 2.33685e19 0.758483
\(997\) 3.63547e19 1.17231 0.586155 0.810199i \(-0.300641\pi\)
0.586155 + 0.810199i \(0.300641\pi\)
\(998\) −2.80526e19 −0.898722
\(999\) −2.61222e18 −0.0831447
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.1.6 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.a.1.6 30 1.1 even 1 trivial