Properties

Label 177.14.a.a.1.14
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 1.14
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-28.5091 q^{2} +729.000 q^{3} -7379.23 q^{4} -13887.1 q^{5} -20783.1 q^{6} +351614. q^{7} +443921. q^{8} +531441. q^{9} +O(q^{10})\) \(q-28.5091 q^{2} +729.000 q^{3} -7379.23 q^{4} -13887.1 q^{5} -20783.1 q^{6} +351614. q^{7} +443921. q^{8} +531441. q^{9} +395908. q^{10} +8.63075e6 q^{11} -5.37946e6 q^{12} -2.28844e7 q^{13} -1.00242e7 q^{14} -1.01237e7 q^{15} +4.77949e7 q^{16} -1.05266e6 q^{17} -1.51509e7 q^{18} -3.21912e7 q^{19} +1.02476e8 q^{20} +2.56327e8 q^{21} -2.46055e8 q^{22} -5.53544e8 q^{23} +3.23619e8 q^{24} -1.02785e9 q^{25} +6.52412e8 q^{26} +3.87420e8 q^{27} -2.59464e9 q^{28} +2.88836e8 q^{29} +2.88617e8 q^{30} -8.59752e9 q^{31} -4.99919e9 q^{32} +6.29182e9 q^{33} +3.00105e7 q^{34} -4.88289e9 q^{35} -3.92163e9 q^{36} -1.31624e10 q^{37} +9.17741e8 q^{38} -1.66827e10 q^{39} -6.16477e9 q^{40} +3.93009e10 q^{41} -7.30763e9 q^{42} +7.30345e10 q^{43} -6.36883e10 q^{44} -7.38016e9 q^{45} +1.57810e10 q^{46} +7.35107e10 q^{47} +3.48425e10 q^{48} +2.67435e10 q^{49} +2.93031e10 q^{50} -7.67392e8 q^{51} +1.68869e11 q^{52} +1.27010e11 q^{53} -1.10450e10 q^{54} -1.19856e11 q^{55} +1.56089e11 q^{56} -2.34674e10 q^{57} -8.23445e9 q^{58} +4.21805e10 q^{59} +7.47050e10 q^{60} -2.72300e11 q^{61} +2.45107e11 q^{62} +1.86862e11 q^{63} -2.49014e11 q^{64} +3.17797e11 q^{65} -1.79374e11 q^{66} +1.83024e11 q^{67} +7.76785e9 q^{68} -4.03533e11 q^{69} +1.39207e11 q^{70} -3.93666e11 q^{71} +2.35918e11 q^{72} +1.61325e10 q^{73} +3.75249e11 q^{74} -7.49304e11 q^{75} +2.37546e11 q^{76} +3.03469e12 q^{77} +4.75609e11 q^{78} -1.21179e12 q^{79} -6.63732e11 q^{80} +2.82430e11 q^{81} -1.12043e12 q^{82} +2.98190e12 q^{83} -1.89149e12 q^{84} +1.46184e10 q^{85} -2.08215e12 q^{86} +2.10561e11 q^{87} +3.83137e12 q^{88} -4.57582e12 q^{89} +2.10402e11 q^{90} -8.04647e12 q^{91} +4.08473e12 q^{92} -6.26759e12 q^{93} -2.09572e12 q^{94} +4.47042e11 q^{95} -3.64441e12 q^{96} +7.94437e12 q^{97} -7.62432e11 q^{98} +4.58674e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} + O(q^{10}) \) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} - 5352519q^{10} - 13950782q^{11} + 83541942q^{12} - 17256988q^{13} + 33780109q^{14} - 100413918q^{15} + 499996762q^{16} - 317583695q^{17} - 73338858q^{18} - 863401469q^{19} - 1841280623q^{20} - 641113947q^{21} - 2723764842q^{22} - 3142075981q^{23} - 635907429q^{24} + 5435751692q^{25} - 6441414040q^{26} + 11622614670q^{27} - 7538400046q^{28} - 4604589283q^{29} - 3901986351q^{30} + 4308675373q^{31} + 6094556360q^{32} - 10170120078q^{33} + 38097713432q^{34} - 15447827315q^{35} + 60902075718q^{36} - 19633376949q^{37} - 18152222923q^{38} - 12580344252q^{39} + 14680384170q^{40} - 103644439493q^{41} + 24625699461q^{42} - 64494894924q^{43} - 199714496208q^{44} - 73201746222q^{45} - 265425792847q^{46} - 293365585139q^{47} + 364497639498q^{48} + 414396765797q^{49} - 126058522207q^{50} - 231518513655q^{51} + 156029960316q^{52} - 76747013118q^{53} - 53464027482q^{54} - 433465885754q^{55} - 502955241518q^{56} - 629419670901q^{57} - 1755031845830q^{58} + 1265416009230q^{59} - 1342293574167q^{60} - 2022612531219q^{61} - 3816005187046q^{62} - 467372067363q^{63} - 3570205594131q^{64} - 3889749040576q^{65} - 1985624569818q^{66} - 502618987776q^{67} - 8953998390517q^{68} - 2290573390149q^{69} - 6805178272420q^{70} - 1599540605456q^{71} - 463576515741q^{72} - 3826795087235q^{73} - 7573387813210q^{74} + 3962662983468q^{75} - 19498723328388q^{76} - 9088623115219q^{77} - 4695790835160q^{78} - 8595482172338q^{79} - 17452527463963q^{80} + 8472886094430q^{81} - 11181116792901q^{82} - 13548556984389q^{83} - 5495493633534q^{84} - 12851795888367q^{85} + 8539949468848q^{86} - 3356745587307q^{87} - 25134826741387q^{88} - 21826401667403q^{89} - 2844548049879q^{90} - 26577050621355q^{91} - 34908210763168q^{92} + 3141024346917q^{93} - 26426808959500q^{94} - 29105233533993q^{95} + 4442931586440q^{96} + 417815797414q^{97} + 29159956938360q^{98} - 7414017536862q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −28.5091 −0.314984 −0.157492 0.987520i \(-0.550341\pi\)
−0.157492 + 0.987520i \(0.550341\pi\)
\(3\) 729.000 0.577350
\(4\) −7379.23 −0.900785
\(5\) −13887.1 −0.397471 −0.198736 0.980053i \(-0.563684\pi\)
−0.198736 + 0.980053i \(0.563684\pi\)
\(6\) −20783.1 −0.181856
\(7\) 351614. 1.12961 0.564806 0.825224i \(-0.308951\pi\)
0.564806 + 0.825224i \(0.308951\pi\)
\(8\) 443921. 0.598716
\(9\) 531441. 0.333333
\(10\) 395908. 0.125197
\(11\) 8.63075e6 1.46891 0.734457 0.678656i \(-0.237437\pi\)
0.734457 + 0.678656i \(0.237437\pi\)
\(12\) −5.37946e6 −0.520069
\(13\) −2.28844e7 −1.31494 −0.657472 0.753479i \(-0.728374\pi\)
−0.657472 + 0.753479i \(0.728374\pi\)
\(14\) −1.00242e7 −0.355809
\(15\) −1.01237e7 −0.229480
\(16\) 4.77949e7 0.712199
\(17\) −1.05266e6 −0.0105772 −0.00528861 0.999986i \(-0.501683\pi\)
−0.00528861 + 0.999986i \(0.501683\pi\)
\(18\) −1.51509e7 −0.104995
\(19\) −3.21912e7 −0.156978 −0.0784890 0.996915i \(-0.525010\pi\)
−0.0784890 + 0.996915i \(0.525010\pi\)
\(20\) 1.02476e8 0.358036
\(21\) 2.56327e8 0.652181
\(22\) −2.46055e8 −0.462684
\(23\) −5.53544e8 −0.779688 −0.389844 0.920881i \(-0.627471\pi\)
−0.389844 + 0.920881i \(0.627471\pi\)
\(24\) 3.23619e8 0.345669
\(25\) −1.02785e9 −0.842016
\(26\) 6.52412e8 0.414186
\(27\) 3.87420e8 0.192450
\(28\) −2.59464e9 −1.01754
\(29\) 2.88836e8 0.0901705 0.0450852 0.998983i \(-0.485644\pi\)
0.0450852 + 0.998983i \(0.485644\pi\)
\(30\) 2.88617e8 0.0722825
\(31\) −8.59752e9 −1.73989 −0.869946 0.493148i \(-0.835846\pi\)
−0.869946 + 0.493148i \(0.835846\pi\)
\(32\) −4.99919e9 −0.823047
\(33\) 6.29182e9 0.848077
\(34\) 3.00105e7 0.00333165
\(35\) −4.88289e9 −0.448988
\(36\) −3.92163e9 −0.300262
\(37\) −1.31624e10 −0.843384 −0.421692 0.906739i \(-0.638564\pi\)
−0.421692 + 0.906739i \(0.638564\pi\)
\(38\) 9.17741e8 0.0494455
\(39\) −1.66827e10 −0.759184
\(40\) −6.16477e9 −0.237973
\(41\) 3.93009e10 1.29213 0.646066 0.763281i \(-0.276413\pi\)
0.646066 + 0.763281i \(0.276413\pi\)
\(42\) −7.30763e9 −0.205426
\(43\) 7.30345e10 1.76191 0.880954 0.473202i \(-0.156902\pi\)
0.880954 + 0.473202i \(0.156902\pi\)
\(44\) −6.36883e10 −1.32318
\(45\) −7.38016e9 −0.132490
\(46\) 1.57810e10 0.245589
\(47\) 7.35107e10 0.994751 0.497375 0.867535i \(-0.334297\pi\)
0.497375 + 0.867535i \(0.334297\pi\)
\(48\) 3.48425e10 0.411189
\(49\) 2.67435e10 0.276022
\(50\) 2.93031e10 0.265221
\(51\) −7.67392e8 −0.00610676
\(52\) 1.68869e11 1.18448
\(53\) 1.27010e11 0.787127 0.393564 0.919297i \(-0.371242\pi\)
0.393564 + 0.919297i \(0.371242\pi\)
\(54\) −1.10450e10 −0.0606186
\(55\) −1.19856e11 −0.583851
\(56\) 1.56089e11 0.676317
\(57\) −2.34674e10 −0.0906313
\(58\) −8.23445e9 −0.0284022
\(59\) 4.21805e10 0.130189
\(60\) 7.47050e10 0.206712
\(61\) −2.72300e11 −0.676711 −0.338356 0.941018i \(-0.609871\pi\)
−0.338356 + 0.941018i \(0.609871\pi\)
\(62\) 2.45107e11 0.548037
\(63\) 1.86862e11 0.376537
\(64\) −2.49014e11 −0.452953
\(65\) 3.17797e11 0.522653
\(66\) −1.79374e11 −0.267131
\(67\) 1.83024e11 0.247185 0.123593 0.992333i \(-0.460558\pi\)
0.123593 + 0.992333i \(0.460558\pi\)
\(68\) 7.76785e9 0.00952781
\(69\) −4.03533e11 −0.450153
\(70\) 1.39207e11 0.141424
\(71\) −3.93666e11 −0.364711 −0.182355 0.983233i \(-0.558372\pi\)
−0.182355 + 0.983233i \(0.558372\pi\)
\(72\) 2.35918e11 0.199572
\(73\) 1.61325e10 0.0124768 0.00623839 0.999981i \(-0.498014\pi\)
0.00623839 + 0.999981i \(0.498014\pi\)
\(74\) 3.75249e11 0.265652
\(75\) −7.49304e11 −0.486138
\(76\) 2.37546e11 0.141404
\(77\) 3.03469e12 1.65930
\(78\) 4.75609e11 0.239130
\(79\) −1.21179e12 −0.560855 −0.280428 0.959875i \(-0.590476\pi\)
−0.280428 + 0.959875i \(0.590476\pi\)
\(80\) −6.63732e11 −0.283079
\(81\) 2.82430e11 0.111111
\(82\) −1.12043e12 −0.407001
\(83\) 2.98190e12 1.00112 0.500560 0.865702i \(-0.333128\pi\)
0.500560 + 0.865702i \(0.333128\pi\)
\(84\) −1.89149e12 −0.587475
\(85\) 1.46184e10 0.00420414
\(86\) −2.08215e12 −0.554972
\(87\) 2.10561e11 0.0520600
\(88\) 3.83137e12 0.879462
\(89\) −4.57582e12 −0.975965 −0.487982 0.872853i \(-0.662267\pi\)
−0.487982 + 0.872853i \(0.662267\pi\)
\(90\) 2.10402e11 0.0417323
\(91\) −8.04647e12 −1.48538
\(92\) 4.08473e12 0.702332
\(93\) −6.26759e12 −1.00453
\(94\) −2.09572e12 −0.313330
\(95\) 4.47042e11 0.0623943
\(96\) −3.64441e12 −0.475187
\(97\) 7.94437e12 0.968374 0.484187 0.874965i \(-0.339115\pi\)
0.484187 + 0.874965i \(0.339115\pi\)
\(98\) −7.62432e11 −0.0869424
\(99\) 4.58674e12 0.489638
\(100\) 7.58476e12 0.758476
\(101\) −1.54993e13 −1.45285 −0.726427 0.687243i \(-0.758821\pi\)
−0.726427 + 0.687243i \(0.758821\pi\)
\(102\) 2.18776e10 0.00192353
\(103\) −8.48603e12 −0.700265 −0.350133 0.936700i \(-0.613864\pi\)
−0.350133 + 0.936700i \(0.613864\pi\)
\(104\) −1.01589e13 −0.787279
\(105\) −3.55963e12 −0.259223
\(106\) −3.62094e12 −0.247932
\(107\) −1.86668e13 −1.20248 −0.601238 0.799070i \(-0.705326\pi\)
−0.601238 + 0.799070i \(0.705326\pi\)
\(108\) −2.85887e12 −0.173356
\(109\) −1.05822e13 −0.604371 −0.302186 0.953249i \(-0.597716\pi\)
−0.302186 + 0.953249i \(0.597716\pi\)
\(110\) 3.41698e12 0.183904
\(111\) −9.59542e12 −0.486928
\(112\) 1.68054e13 0.804509
\(113\) 1.22087e13 0.551645 0.275823 0.961209i \(-0.411050\pi\)
0.275823 + 0.961209i \(0.411050\pi\)
\(114\) 6.69033e11 0.0285474
\(115\) 7.68711e12 0.309904
\(116\) −2.13139e12 −0.0812242
\(117\) −1.21617e13 −0.438315
\(118\) −1.20253e12 −0.0410074
\(119\) −3.70132e11 −0.0119482
\(120\) −4.49412e12 −0.137394
\(121\) 3.99672e13 1.15771
\(122\) 7.76301e12 0.213153
\(123\) 2.86503e13 0.746013
\(124\) 6.34431e13 1.56727
\(125\) 3.12259e13 0.732149
\(126\) −5.32727e12 −0.118603
\(127\) 1.91808e13 0.405641 0.202821 0.979216i \(-0.434989\pi\)
0.202821 + 0.979216i \(0.434989\pi\)
\(128\) 4.80525e13 0.965720
\(129\) 5.32422e13 1.01724
\(130\) −9.06010e12 −0.164627
\(131\) −6.83174e13 −1.18105 −0.590525 0.807020i \(-0.701079\pi\)
−0.590525 + 0.807020i \(0.701079\pi\)
\(132\) −4.64288e13 −0.763936
\(133\) −1.13189e13 −0.177324
\(134\) −5.21785e12 −0.0778592
\(135\) −5.38014e12 −0.0764934
\(136\) −4.67300e11 −0.00633276
\(137\) −6.79224e13 −0.877666 −0.438833 0.898569i \(-0.644608\pi\)
−0.438833 + 0.898569i \(0.644608\pi\)
\(138\) 1.15044e13 0.141791
\(139\) −4.06817e13 −0.478413 −0.239207 0.970969i \(-0.576887\pi\)
−0.239207 + 0.970969i \(0.576887\pi\)
\(140\) 3.60320e13 0.404442
\(141\) 5.35893e13 0.574320
\(142\) 1.12230e13 0.114878
\(143\) −1.97509e14 −1.93154
\(144\) 2.54002e13 0.237400
\(145\) −4.01109e12 −0.0358402
\(146\) −4.59922e11 −0.00392998
\(147\) 1.94960e13 0.159361
\(148\) 9.71287e13 0.759708
\(149\) 7.21391e13 0.540082 0.270041 0.962849i \(-0.412963\pi\)
0.270041 + 0.962849i \(0.412963\pi\)
\(150\) 2.13620e13 0.153126
\(151\) −2.69194e14 −1.84806 −0.924029 0.382322i \(-0.875125\pi\)
−0.924029 + 0.382322i \(0.875125\pi\)
\(152\) −1.42904e13 −0.0939853
\(153\) −5.59429e11 −0.00352574
\(154\) −8.65163e13 −0.522653
\(155\) 1.19394e14 0.691557
\(156\) 1.23106e14 0.683861
\(157\) 1.62695e13 0.0867015 0.0433508 0.999060i \(-0.486197\pi\)
0.0433508 + 0.999060i \(0.486197\pi\)
\(158\) 3.45470e13 0.176660
\(159\) 9.25903e13 0.454448
\(160\) 6.94242e13 0.327138
\(161\) −1.94634e14 −0.880745
\(162\) −8.05180e12 −0.0349982
\(163\) 1.38855e14 0.579886 0.289943 0.957044i \(-0.406364\pi\)
0.289943 + 0.957044i \(0.406364\pi\)
\(164\) −2.90010e14 −1.16393
\(165\) −8.73750e13 −0.337087
\(166\) −8.50112e13 −0.315336
\(167\) 5.31168e14 1.89485 0.947425 0.319977i \(-0.103675\pi\)
0.947425 + 0.319977i \(0.103675\pi\)
\(168\) 1.13789e14 0.390472
\(169\) 2.20820e14 0.729079
\(170\) −4.16758e11 −0.00132424
\(171\) −1.71077e13 −0.0523260
\(172\) −5.38939e14 −1.58710
\(173\) 6.72325e14 1.90669 0.953344 0.301886i \(-0.0976163\pi\)
0.953344 + 0.301886i \(0.0976163\pi\)
\(174\) −6.00291e12 −0.0163980
\(175\) −3.61407e14 −0.951151
\(176\) 4.12506e14 1.04616
\(177\) 3.07496e13 0.0751646
\(178\) 1.30452e14 0.307413
\(179\) 2.07313e14 0.471065 0.235533 0.971866i \(-0.424317\pi\)
0.235533 + 0.971866i \(0.424317\pi\)
\(180\) 5.44599e13 0.119345
\(181\) −4.27304e14 −0.903287 −0.451644 0.892198i \(-0.649162\pi\)
−0.451644 + 0.892198i \(0.649162\pi\)
\(182\) 2.29397e14 0.467869
\(183\) −1.98506e14 −0.390699
\(184\) −2.45730e14 −0.466812
\(185\) 1.82788e14 0.335221
\(186\) 1.78683e14 0.316409
\(187\) −9.08528e12 −0.0155370
\(188\) −5.42452e14 −0.896057
\(189\) 1.36223e14 0.217394
\(190\) −1.27447e13 −0.0196532
\(191\) −9.23322e14 −1.37606 −0.688028 0.725684i \(-0.741523\pi\)
−0.688028 + 0.725684i \(0.741523\pi\)
\(192\) −1.81531e14 −0.261513
\(193\) −3.94874e14 −0.549966 −0.274983 0.961449i \(-0.588672\pi\)
−0.274983 + 0.961449i \(0.588672\pi\)
\(194\) −2.26486e14 −0.305022
\(195\) 2.31674e14 0.301754
\(196\) −1.97346e14 −0.248636
\(197\) −1.08265e15 −1.31964 −0.659821 0.751423i \(-0.729368\pi\)
−0.659821 + 0.751423i \(0.729368\pi\)
\(198\) −1.30764e14 −0.154228
\(199\) 3.77522e14 0.430920 0.215460 0.976513i \(-0.430875\pi\)
0.215460 + 0.976513i \(0.430875\pi\)
\(200\) −4.56285e14 −0.504129
\(201\) 1.33425e14 0.142712
\(202\) 4.41870e14 0.457625
\(203\) 1.01559e14 0.101858
\(204\) 5.66276e12 0.00550088
\(205\) −5.45774e14 −0.513586
\(206\) 2.41929e14 0.220572
\(207\) −2.94176e14 −0.259896
\(208\) −1.09376e15 −0.936503
\(209\) −2.77834e14 −0.230587
\(210\) 1.01482e14 0.0816512
\(211\) −3.40644e14 −0.265745 −0.132872 0.991133i \(-0.542420\pi\)
−0.132872 + 0.991133i \(0.542420\pi\)
\(212\) −9.37237e14 −0.709033
\(213\) −2.86982e14 −0.210566
\(214\) 5.32174e14 0.378760
\(215\) −1.01424e15 −0.700308
\(216\) 1.71984e14 0.115223
\(217\) −3.02301e15 −1.96540
\(218\) 3.01689e14 0.190367
\(219\) 1.17606e13 0.00720347
\(220\) 8.84445e14 0.525924
\(221\) 2.40896e13 0.0139085
\(222\) 2.73556e14 0.153374
\(223\) −2.17805e15 −1.18601 −0.593003 0.805200i \(-0.702058\pi\)
−0.593003 + 0.805200i \(0.702058\pi\)
\(224\) −1.75779e15 −0.929724
\(225\) −5.46243e14 −0.280672
\(226\) −3.48059e14 −0.173759
\(227\) −2.22259e15 −1.07818 −0.539089 0.842249i \(-0.681232\pi\)
−0.539089 + 0.842249i \(0.681232\pi\)
\(228\) 1.73171e14 0.0816394
\(229\) −3.60209e15 −1.65053 −0.825267 0.564743i \(-0.808975\pi\)
−0.825267 + 0.564743i \(0.808975\pi\)
\(230\) −2.19152e14 −0.0976147
\(231\) 2.21229e15 0.957998
\(232\) 1.28220e14 0.0539865
\(233\) 1.70998e15 0.700130 0.350065 0.936725i \(-0.386159\pi\)
0.350065 + 0.936725i \(0.386159\pi\)
\(234\) 3.46719e14 0.138062
\(235\) −1.02085e15 −0.395385
\(236\) −3.11260e14 −0.117272
\(237\) −8.83394e14 −0.323810
\(238\) 1.05521e13 0.00376347
\(239\) 8.90085e14 0.308919 0.154460 0.987999i \(-0.450636\pi\)
0.154460 + 0.987999i \(0.450636\pi\)
\(240\) −4.83860e14 −0.163436
\(241\) −3.26021e15 −1.07185 −0.535926 0.844265i \(-0.680037\pi\)
−0.535926 + 0.844265i \(0.680037\pi\)
\(242\) −1.13943e15 −0.364659
\(243\) 2.05891e14 0.0641500
\(244\) 2.00936e15 0.609571
\(245\) −3.71389e14 −0.109711
\(246\) −8.16794e14 −0.234982
\(247\) 7.36676e14 0.206417
\(248\) −3.81662e15 −1.04170
\(249\) 2.17381e15 0.577996
\(250\) −8.90220e14 −0.230615
\(251\) 2.75607e15 0.695683 0.347842 0.937553i \(-0.386915\pi\)
0.347842 + 0.937553i \(0.386915\pi\)
\(252\) −1.37890e15 −0.339179
\(253\) −4.77750e15 −1.14529
\(254\) −5.46826e14 −0.127770
\(255\) 1.06568e13 0.00242726
\(256\) 6.69987e14 0.148767
\(257\) 3.87564e15 0.839031 0.419516 0.907748i \(-0.362200\pi\)
0.419516 + 0.907748i \(0.362200\pi\)
\(258\) −1.51788e15 −0.320413
\(259\) −4.62810e15 −0.952696
\(260\) −2.34510e15 −0.470798
\(261\) 1.53499e14 0.0300568
\(262\) 1.94767e15 0.372011
\(263\) −3.36264e15 −0.626568 −0.313284 0.949659i \(-0.601429\pi\)
−0.313284 + 0.949659i \(0.601429\pi\)
\(264\) 2.79307e15 0.507758
\(265\) −1.76380e15 −0.312861
\(266\) 3.22691e14 0.0558542
\(267\) −3.33577e15 −0.563474
\(268\) −1.35058e15 −0.222661
\(269\) −3.02785e15 −0.487241 −0.243621 0.969871i \(-0.578335\pi\)
−0.243621 + 0.969871i \(0.578335\pi\)
\(270\) 1.53383e14 0.0240942
\(271\) 1.12641e16 1.72741 0.863707 0.503994i \(-0.168137\pi\)
0.863707 + 0.503994i \(0.168137\pi\)
\(272\) −5.03120e13 −0.00753309
\(273\) −5.86588e15 −0.857582
\(274\) 1.93640e15 0.276450
\(275\) −8.87114e15 −1.23685
\(276\) 2.97777e15 0.405492
\(277\) −9.99312e15 −1.32918 −0.664588 0.747210i \(-0.731393\pi\)
−0.664588 + 0.747210i \(0.731393\pi\)
\(278\) 1.15980e15 0.150692
\(279\) −4.56907e15 −0.579964
\(280\) −2.16762e15 −0.268817
\(281\) 2.44336e15 0.296071 0.148036 0.988982i \(-0.452705\pi\)
0.148036 + 0.988982i \(0.452705\pi\)
\(282\) −1.52778e15 −0.180901
\(283\) 5.35686e15 0.619866 0.309933 0.950758i \(-0.399693\pi\)
0.309933 + 0.950758i \(0.399693\pi\)
\(284\) 2.90495e15 0.328526
\(285\) 3.25894e14 0.0360234
\(286\) 5.63081e15 0.608403
\(287\) 1.38187e16 1.45961
\(288\) −2.65678e15 −0.274349
\(289\) −9.90347e15 −0.999888
\(290\) 1.14352e14 0.0112891
\(291\) 5.79144e15 0.559091
\(292\) −1.19045e14 −0.0112389
\(293\) −4.38241e15 −0.404644 −0.202322 0.979319i \(-0.564849\pi\)
−0.202322 + 0.979319i \(0.564849\pi\)
\(294\) −5.55813e14 −0.0501962
\(295\) −5.85764e14 −0.0517464
\(296\) −5.84309e15 −0.504948
\(297\) 3.34373e15 0.282692
\(298\) −2.05662e15 −0.170117
\(299\) 1.26675e16 1.02525
\(300\) 5.52929e15 0.437906
\(301\) 2.56800e16 1.99027
\(302\) 7.67448e15 0.582108
\(303\) −1.12990e16 −0.838806
\(304\) −1.53858e15 −0.111800
\(305\) 3.78145e15 0.268973
\(306\) 1.59488e13 0.00111055
\(307\) 1.56810e16 1.06899 0.534496 0.845171i \(-0.320501\pi\)
0.534496 + 0.845171i \(0.320501\pi\)
\(308\) −2.23937e16 −1.49467
\(309\) −6.18632e15 −0.404298
\(310\) −3.40382e15 −0.217829
\(311\) −2.23004e16 −1.39756 −0.698780 0.715336i \(-0.746273\pi\)
−0.698780 + 0.715336i \(0.746273\pi\)
\(312\) −7.40581e15 −0.454536
\(313\) −1.44804e16 −0.870446 −0.435223 0.900323i \(-0.643331\pi\)
−0.435223 + 0.900323i \(0.643331\pi\)
\(314\) −4.63829e14 −0.0273096
\(315\) −2.59497e15 −0.149663
\(316\) 8.94207e15 0.505210
\(317\) −3.38376e16 −1.87290 −0.936450 0.350802i \(-0.885909\pi\)
−0.936450 + 0.350802i \(0.885909\pi\)
\(318\) −2.63966e15 −0.143144
\(319\) 2.49287e15 0.132453
\(320\) 3.45807e15 0.180036
\(321\) −1.36081e16 −0.694249
\(322\) 5.54883e15 0.277420
\(323\) 3.38865e13 0.00166039
\(324\) −2.08411e15 −0.100087
\(325\) 2.35218e16 1.10720
\(326\) −3.95863e15 −0.182655
\(327\) −7.71442e15 −0.348934
\(328\) 1.74465e16 0.773621
\(329\) 2.58474e16 1.12368
\(330\) 2.49098e15 0.106177
\(331\) −3.60933e16 −1.50850 −0.754249 0.656589i \(-0.771999\pi\)
−0.754249 + 0.656589i \(0.771999\pi\)
\(332\) −2.20041e16 −0.901793
\(333\) −6.99506e15 −0.281128
\(334\) −1.51431e16 −0.596847
\(335\) −2.54167e15 −0.0982490
\(336\) 1.22511e16 0.464483
\(337\) 3.87035e16 1.43931 0.719657 0.694330i \(-0.244299\pi\)
0.719657 + 0.694330i \(0.244299\pi\)
\(338\) −6.29537e15 −0.229648
\(339\) 8.90015e15 0.318492
\(340\) −1.07873e14 −0.00378703
\(341\) −7.42030e16 −2.55575
\(342\) 4.87725e14 0.0164818
\(343\) −2.46642e16 −0.817814
\(344\) 3.24216e16 1.05488
\(345\) 5.60390e15 0.178923
\(346\) −1.91674e16 −0.600575
\(347\) −1.73062e16 −0.532181 −0.266091 0.963948i \(-0.585732\pi\)
−0.266091 + 0.963948i \(0.585732\pi\)
\(348\) −1.55378e15 −0.0468948
\(349\) −1.01041e16 −0.299319 −0.149659 0.988738i \(-0.547818\pi\)
−0.149659 + 0.988738i \(0.547818\pi\)
\(350\) 1.03034e16 0.299597
\(351\) −8.86588e15 −0.253061
\(352\) −4.31468e16 −1.20899
\(353\) −2.85177e16 −0.784475 −0.392237 0.919864i \(-0.628299\pi\)
−0.392237 + 0.919864i \(0.628299\pi\)
\(354\) −8.76643e14 −0.0236756
\(355\) 5.46687e15 0.144962
\(356\) 3.37661e16 0.879135
\(357\) −2.69826e14 −0.00689827
\(358\) −5.91029e15 −0.148378
\(359\) −7.41117e15 −0.182714 −0.0913572 0.995818i \(-0.529121\pi\)
−0.0913572 + 0.995818i \(0.529121\pi\)
\(360\) −3.27621e15 −0.0793242
\(361\) −4.10167e16 −0.975358
\(362\) 1.21820e16 0.284521
\(363\) 2.91361e16 0.668402
\(364\) 5.93768e16 1.33801
\(365\) −2.24033e14 −0.00495916
\(366\) 5.65923e15 0.123064
\(367\) 6.15779e16 1.31551 0.657757 0.753230i \(-0.271505\pi\)
0.657757 + 0.753230i \(0.271505\pi\)
\(368\) −2.64566e16 −0.555294
\(369\) 2.08861e16 0.430711
\(370\) −5.21111e15 −0.105589
\(371\) 4.46585e16 0.889148
\(372\) 4.62500e16 0.904863
\(373\) −7.92109e16 −1.52292 −0.761461 0.648211i \(-0.775517\pi\)
−0.761461 + 0.648211i \(0.775517\pi\)
\(374\) 2.59013e14 0.00489391
\(375\) 2.27637e16 0.422706
\(376\) 3.26330e16 0.595573
\(377\) −6.60983e15 −0.118569
\(378\) −3.88358e15 −0.0684755
\(379\) 1.00585e17 1.74332 0.871662 0.490108i \(-0.163043\pi\)
0.871662 + 0.490108i \(0.163043\pi\)
\(380\) −3.29883e15 −0.0562039
\(381\) 1.39828e16 0.234197
\(382\) 2.63230e16 0.433435
\(383\) −5.05935e16 −0.819035 −0.409518 0.912302i \(-0.634303\pi\)
−0.409518 + 0.912302i \(0.634303\pi\)
\(384\) 3.50303e16 0.557559
\(385\) −4.21430e16 −0.659525
\(386\) 1.12575e16 0.173230
\(387\) 3.88135e16 0.587303
\(388\) −5.86233e16 −0.872297
\(389\) −7.82463e16 −1.14496 −0.572482 0.819918i \(-0.694019\pi\)
−0.572482 + 0.819918i \(0.694019\pi\)
\(390\) −6.60481e15 −0.0950475
\(391\) 5.82696e14 0.00824694
\(392\) 1.18720e16 0.165259
\(393\) −4.98034e16 −0.681879
\(394\) 3.08652e16 0.415666
\(395\) 1.68282e16 0.222924
\(396\) −3.38466e16 −0.441059
\(397\) 1.93045e16 0.247468 0.123734 0.992315i \(-0.460513\pi\)
0.123734 + 0.992315i \(0.460513\pi\)
\(398\) −1.07628e16 −0.135733
\(399\) −8.25147e15 −0.102378
\(400\) −4.91261e16 −0.599684
\(401\) −7.95006e16 −0.954843 −0.477421 0.878675i \(-0.658428\pi\)
−0.477421 + 0.878675i \(0.658428\pi\)
\(402\) −3.80381e15 −0.0449520
\(403\) 1.96749e17 2.28786
\(404\) 1.14373e17 1.30871
\(405\) −3.92212e15 −0.0441635
\(406\) −2.89535e15 −0.0320835
\(407\) −1.13602e17 −1.23886
\(408\) −3.40662e14 −0.00365622
\(409\) 2.84293e16 0.300307 0.150153 0.988663i \(-0.452023\pi\)
0.150153 + 0.988663i \(0.452023\pi\)
\(410\) 1.55595e16 0.161771
\(411\) −4.95154e16 −0.506721
\(412\) 6.26204e16 0.630789
\(413\) 1.48313e16 0.147063
\(414\) 8.38668e15 0.0818630
\(415\) −4.14099e16 −0.397916
\(416\) 1.14403e17 1.08226
\(417\) −2.96570e16 −0.276212
\(418\) 7.92080e15 0.0726312
\(419\) 1.64125e17 1.48178 0.740890 0.671626i \(-0.234404\pi\)
0.740890 + 0.671626i \(0.234404\pi\)
\(420\) 2.62673e16 0.233505
\(421\) −9.53757e16 −0.834842 −0.417421 0.908713i \(-0.637066\pi\)
−0.417421 + 0.908713i \(0.637066\pi\)
\(422\) 9.71144e15 0.0837053
\(423\) 3.90666e16 0.331584
\(424\) 5.63825e16 0.471266
\(425\) 1.08198e15 0.00890620
\(426\) 8.18160e15 0.0663248
\(427\) −9.57444e16 −0.764420
\(428\) 1.37747e17 1.08317
\(429\) −1.43984e17 −1.11517
\(430\) 2.89149e16 0.220586
\(431\) −1.02116e17 −0.767343 −0.383672 0.923470i \(-0.625341\pi\)
−0.383672 + 0.923470i \(0.625341\pi\)
\(432\) 1.85167e16 0.137063
\(433\) −1.80916e17 −1.31919 −0.659594 0.751622i \(-0.729272\pi\)
−0.659594 + 0.751622i \(0.729272\pi\)
\(434\) 8.61831e16 0.619069
\(435\) −2.92408e15 −0.0206923
\(436\) 7.80885e16 0.544409
\(437\) 1.78192e16 0.122394
\(438\) −3.35283e14 −0.00226898
\(439\) 1.37200e17 0.914817 0.457409 0.889257i \(-0.348778\pi\)
0.457409 + 0.889257i \(0.348778\pi\)
\(440\) −5.32066e16 −0.349561
\(441\) 1.42126e16 0.0920073
\(442\) −6.86771e14 −0.00438094
\(443\) −1.81802e16 −0.114281 −0.0571404 0.998366i \(-0.518198\pi\)
−0.0571404 + 0.998366i \(0.518198\pi\)
\(444\) 7.08068e16 0.438617
\(445\) 6.35448e16 0.387918
\(446\) 6.20943e16 0.373573
\(447\) 5.25894e16 0.311817
\(448\) −8.75567e16 −0.511661
\(449\) −3.30969e16 −0.190628 −0.0953139 0.995447i \(-0.530385\pi\)
−0.0953139 + 0.995447i \(0.530385\pi\)
\(450\) 1.55729e16 0.0884071
\(451\) 3.39196e17 1.89803
\(452\) −9.00909e16 −0.496914
\(453\) −1.96243e17 −1.06698
\(454\) 6.33639e16 0.339609
\(455\) 1.11742e17 0.590395
\(456\) −1.04177e16 −0.0542624
\(457\) 3.29643e17 1.69273 0.846366 0.532602i \(-0.178786\pi\)
0.846366 + 0.532602i \(0.178786\pi\)
\(458\) 1.02692e17 0.519891
\(459\) −4.07824e14 −0.00203559
\(460\) −5.67250e16 −0.279157
\(461\) −1.54107e17 −0.747765 −0.373882 0.927476i \(-0.621974\pi\)
−0.373882 + 0.927476i \(0.621974\pi\)
\(462\) −6.30704e16 −0.301754
\(463\) 2.39877e17 1.13165 0.565826 0.824525i \(-0.308557\pi\)
0.565826 + 0.824525i \(0.308557\pi\)
\(464\) 1.38049e16 0.0642194
\(465\) 8.70385e16 0.399271
\(466\) −4.87501e16 −0.220530
\(467\) −2.00169e17 −0.892971 −0.446485 0.894791i \(-0.647324\pi\)
−0.446485 + 0.894791i \(0.647324\pi\)
\(468\) 8.97440e16 0.394828
\(469\) 6.43539e16 0.279223
\(470\) 2.91034e16 0.124540
\(471\) 1.18605e16 0.0500572
\(472\) 1.87248e16 0.0779462
\(473\) 6.30343e17 2.58809
\(474\) 2.51847e16 0.101995
\(475\) 3.30878e16 0.132178
\(476\) 2.73129e15 0.0107627
\(477\) 6.74984e16 0.262376
\(478\) −2.53755e16 −0.0973045
\(479\) 2.23924e17 0.847071 0.423536 0.905879i \(-0.360789\pi\)
0.423536 + 0.905879i \(0.360789\pi\)
\(480\) 5.06102e16 0.188873
\(481\) 3.01214e17 1.10900
\(482\) 9.29456e16 0.337616
\(483\) −1.41888e17 −0.508498
\(484\) −2.94927e17 −1.04284
\(485\) −1.10324e17 −0.384901
\(486\) −5.86976e15 −0.0202062
\(487\) 6.07459e16 0.206338 0.103169 0.994664i \(-0.467102\pi\)
0.103169 + 0.994664i \(0.467102\pi\)
\(488\) −1.20880e17 −0.405158
\(489\) 1.01225e17 0.334797
\(490\) 1.05879e16 0.0345571
\(491\) −2.21938e17 −0.714829 −0.357414 0.933946i \(-0.616342\pi\)
−0.357414 + 0.933946i \(0.616342\pi\)
\(492\) −2.11418e17 −0.671998
\(493\) −3.04047e14 −0.000953754 0
\(494\) −2.10019e16 −0.0650181
\(495\) −6.36964e16 −0.194617
\(496\) −4.10917e17 −1.23915
\(497\) −1.38418e17 −0.411981
\(498\) −6.19732e16 −0.182059
\(499\) −6.83126e16 −0.198083 −0.0990415 0.995083i \(-0.531578\pi\)
−0.0990415 + 0.995083i \(0.531578\pi\)
\(500\) −2.30423e17 −0.659509
\(501\) 3.87222e17 1.09399
\(502\) −7.85731e16 −0.219129
\(503\) −3.67361e17 −1.01135 −0.505675 0.862724i \(-0.668756\pi\)
−0.505675 + 0.862724i \(0.668756\pi\)
\(504\) 8.29521e16 0.225439
\(505\) 2.15240e17 0.577468
\(506\) 1.36202e17 0.360749
\(507\) 1.60978e17 0.420934
\(508\) −1.41539e17 −0.365396
\(509\) −8.54196e16 −0.217717 −0.108858 0.994057i \(-0.534720\pi\)
−0.108858 + 0.994057i \(0.534720\pi\)
\(510\) −3.03816e14 −0.000764548 0
\(511\) 5.67241e15 0.0140939
\(512\) −4.12747e17 −1.01258
\(513\) −1.24715e16 −0.0302104
\(514\) −1.10491e17 −0.264281
\(515\) 1.17846e17 0.278335
\(516\) −3.92886e17 −0.916313
\(517\) 6.34452e17 1.46120
\(518\) 1.31943e17 0.300084
\(519\) 4.90125e17 1.10083
\(520\) 1.41077e17 0.312921
\(521\) 2.39318e17 0.524239 0.262120 0.965035i \(-0.415578\pi\)
0.262120 + 0.965035i \(0.415578\pi\)
\(522\) −4.37612e15 −0.00946741
\(523\) −2.06052e17 −0.440267 −0.220134 0.975470i \(-0.570649\pi\)
−0.220134 + 0.975470i \(0.570649\pi\)
\(524\) 5.04130e17 1.06387
\(525\) −2.63466e17 −0.549147
\(526\) 9.58658e16 0.197359
\(527\) 9.05030e15 0.0184032
\(528\) 3.00717e17 0.604000
\(529\) −1.97626e17 −0.392086
\(530\) 5.02843e16 0.0985460
\(531\) 2.24165e16 0.0433963
\(532\) 8.35247e16 0.159731
\(533\) −8.99376e17 −1.69908
\(534\) 9.50998e16 0.177485
\(535\) 2.59228e17 0.477950
\(536\) 8.12483e16 0.147994
\(537\) 1.51131e17 0.271970
\(538\) 8.63211e16 0.153473
\(539\) 2.30816e17 0.405452
\(540\) 3.97013e16 0.0689041
\(541\) 2.86330e17 0.491004 0.245502 0.969396i \(-0.421047\pi\)
0.245502 + 0.969396i \(0.421047\pi\)
\(542\) −3.21129e17 −0.544107
\(543\) −3.11504e17 −0.521513
\(544\) 5.26247e15 0.00870556
\(545\) 1.46956e17 0.240220
\(546\) 1.67231e17 0.270124
\(547\) −1.15937e17 −0.185057 −0.0925284 0.995710i \(-0.529495\pi\)
−0.0925284 + 0.995710i \(0.529495\pi\)
\(548\) 5.01215e17 0.790588
\(549\) −1.44711e17 −0.225570
\(550\) 2.52908e17 0.389587
\(551\) −9.29798e15 −0.0141548
\(552\) −1.79137e17 −0.269514
\(553\) −4.26082e17 −0.633549
\(554\) 2.84894e17 0.418669
\(555\) 1.33252e17 0.193540
\(556\) 3.00200e17 0.430948
\(557\) −5.43030e17 −0.770487 −0.385244 0.922815i \(-0.625883\pi\)
−0.385244 + 0.922815i \(0.625883\pi\)
\(558\) 1.30260e17 0.182679
\(559\) −1.67135e18 −2.31681
\(560\) −2.33377e17 −0.319769
\(561\) −6.62317e15 −0.00897031
\(562\) −6.96579e16 −0.0932576
\(563\) −3.96722e17 −0.525027 −0.262513 0.964928i \(-0.584551\pi\)
−0.262513 + 0.964928i \(0.584551\pi\)
\(564\) −3.95448e17 −0.517339
\(565\) −1.69543e17 −0.219263
\(566\) −1.52719e17 −0.195248
\(567\) 9.93062e16 0.125512
\(568\) −1.74757e17 −0.218358
\(569\) −5.32908e17 −0.658298 −0.329149 0.944278i \(-0.606762\pi\)
−0.329149 + 0.944278i \(0.606762\pi\)
\(570\) −9.29092e15 −0.0113468
\(571\) 9.76614e17 1.17920 0.589601 0.807695i \(-0.299285\pi\)
0.589601 + 0.807695i \(0.299285\pi\)
\(572\) 1.45747e18 1.73990
\(573\) −6.73102e17 −0.794466
\(574\) −3.93959e17 −0.459753
\(575\) 5.68961e17 0.656511
\(576\) −1.32336e17 −0.150984
\(577\) 1.00111e18 1.12938 0.564691 0.825303i \(-0.308995\pi\)
0.564691 + 0.825303i \(0.308995\pi\)
\(578\) 2.82339e17 0.314948
\(579\) −2.87863e17 −0.317523
\(580\) 2.95988e16 0.0322843
\(581\) 1.04848e18 1.13088
\(582\) −1.65109e17 −0.176104
\(583\) 1.09619e18 1.15622
\(584\) 7.16155e15 0.00747005
\(585\) 1.68890e17 0.174218
\(586\) 1.24938e17 0.127456
\(587\) 6.07115e17 0.612524 0.306262 0.951947i \(-0.400922\pi\)
0.306262 + 0.951947i \(0.400922\pi\)
\(588\) −1.43866e17 −0.143550
\(589\) 2.76764e17 0.273125
\(590\) 1.66996e16 0.0162993
\(591\) −7.89249e17 −0.761896
\(592\) −6.29098e17 −0.600658
\(593\) −1.05140e17 −0.0992918 −0.0496459 0.998767i \(-0.515809\pi\)
−0.0496459 + 0.998767i \(0.515809\pi\)
\(594\) −9.53266e16 −0.0890435
\(595\) 5.14005e15 0.00474905
\(596\) −5.32331e17 −0.486498
\(597\) 2.75213e17 0.248792
\(598\) −3.61139e17 −0.322936
\(599\) 5.11951e17 0.452850 0.226425 0.974029i \(-0.427296\pi\)
0.226425 + 0.974029i \(0.427296\pi\)
\(600\) −3.32632e17 −0.291059
\(601\) 4.35137e17 0.376653 0.188327 0.982106i \(-0.439694\pi\)
0.188327 + 0.982106i \(0.439694\pi\)
\(602\) −7.32112e17 −0.626903
\(603\) 9.72665e16 0.0823950
\(604\) 1.98645e18 1.66470
\(605\) −5.55027e17 −0.460155
\(606\) 3.22123e17 0.264210
\(607\) 6.37842e17 0.517591 0.258795 0.965932i \(-0.416674\pi\)
0.258795 + 0.965932i \(0.416674\pi\)
\(608\) 1.60930e17 0.129200
\(609\) 7.40364e16 0.0588075
\(610\) −1.07806e17 −0.0847222
\(611\) −1.68225e18 −1.30804
\(612\) 4.12816e15 0.00317594
\(613\) −1.89096e18 −1.43943 −0.719713 0.694272i \(-0.755726\pi\)
−0.719713 + 0.694272i \(0.755726\pi\)
\(614\) −4.47051e17 −0.336715
\(615\) −3.97870e17 −0.296519
\(616\) 1.34717e18 0.993451
\(617\) −3.63664e17 −0.265367 −0.132684 0.991158i \(-0.542359\pi\)
−0.132684 + 0.991158i \(0.542359\pi\)
\(618\) 1.76366e17 0.127347
\(619\) −1.56151e18 −1.11572 −0.557860 0.829935i \(-0.688377\pi\)
−0.557860 + 0.829935i \(0.688377\pi\)
\(620\) −8.81039e17 −0.622944
\(621\) −2.14454e17 −0.150051
\(622\) 6.35764e17 0.440209
\(623\) −1.60892e18 −1.10246
\(624\) −7.97349e17 −0.540690
\(625\) 8.21066e17 0.551008
\(626\) 4.12822e17 0.274176
\(627\) −2.02541e17 −0.133130
\(628\) −1.20057e17 −0.0780995
\(629\) 1.38556e16 0.00892066
\(630\) 7.39802e16 0.0471413
\(631\) −1.19333e18 −0.752607 −0.376304 0.926496i \(-0.622805\pi\)
−0.376304 + 0.926496i \(0.622805\pi\)
\(632\) −5.37939e17 −0.335793
\(633\) −2.48330e17 −0.153428
\(634\) 9.64678e17 0.589933
\(635\) −2.66365e17 −0.161231
\(636\) −6.83246e17 −0.409360
\(637\) −6.12008e17 −0.362953
\(638\) −7.10694e16 −0.0417204
\(639\) −2.09210e17 −0.121570
\(640\) −6.67309e17 −0.383846
\(641\) −1.40011e18 −0.797230 −0.398615 0.917118i \(-0.630509\pi\)
−0.398615 + 0.917118i \(0.630509\pi\)
\(642\) 3.87955e17 0.218677
\(643\) 1.60800e17 0.0897251 0.0448626 0.998993i \(-0.485715\pi\)
0.0448626 + 0.998993i \(0.485715\pi\)
\(644\) 1.43625e18 0.793362
\(645\) −7.39378e17 −0.404323
\(646\) −9.66073e14 −0.000522996 0
\(647\) 5.35884e17 0.287206 0.143603 0.989635i \(-0.454131\pi\)
0.143603 + 0.989635i \(0.454131\pi\)
\(648\) 1.25376e17 0.0665240
\(649\) 3.64050e17 0.191236
\(650\) −6.70583e17 −0.348751
\(651\) −2.20377e18 −1.13472
\(652\) −1.02464e18 −0.522353
\(653\) −1.01990e18 −0.514780 −0.257390 0.966308i \(-0.582862\pi\)
−0.257390 + 0.966308i \(0.582862\pi\)
\(654\) 2.19931e17 0.109908
\(655\) 9.48730e17 0.469433
\(656\) 1.87838e18 0.920256
\(657\) 8.57346e15 0.00415893
\(658\) −7.36885e17 −0.353941
\(659\) 2.60808e18 1.24041 0.620207 0.784438i \(-0.287049\pi\)
0.620207 + 0.784438i \(0.287049\pi\)
\(660\) 6.44760e17 0.303643
\(661\) −1.54930e18 −0.722481 −0.361240 0.932473i \(-0.617647\pi\)
−0.361240 + 0.932473i \(0.617647\pi\)
\(662\) 1.02899e18 0.475152
\(663\) 1.75613e16 0.00803006
\(664\) 1.32373e18 0.599386
\(665\) 1.57186e17 0.0704813
\(666\) 1.99423e17 0.0885507
\(667\) −1.59883e17 −0.0703049
\(668\) −3.91961e18 −1.70685
\(669\) −1.58780e18 −0.684741
\(670\) 7.24607e16 0.0309468
\(671\) −2.35015e18 −0.994030
\(672\) −1.28143e18 −0.536776
\(673\) −2.84284e18 −1.17938 −0.589691 0.807629i \(-0.700750\pi\)
−0.589691 + 0.807629i \(0.700750\pi\)
\(674\) −1.10340e18 −0.453360
\(675\) −3.98211e17 −0.162046
\(676\) −1.62948e18 −0.656744
\(677\) −7.89265e17 −0.315062 −0.157531 0.987514i \(-0.550353\pi\)
−0.157531 + 0.987514i \(0.550353\pi\)
\(678\) −2.53735e17 −0.100320
\(679\) 2.79335e18 1.09389
\(680\) 6.48943e15 0.00251709
\(681\) −1.62027e18 −0.622487
\(682\) 2.11546e18 0.805019
\(683\) −3.01912e18 −1.13801 −0.569004 0.822335i \(-0.692671\pi\)
−0.569004 + 0.822335i \(0.692671\pi\)
\(684\) 1.26242e17 0.0471345
\(685\) 9.43243e17 0.348847
\(686\) 7.03152e17 0.257598
\(687\) −2.62593e18 −0.952936
\(688\) 3.49068e18 1.25483
\(689\) −2.90655e18 −1.03503
\(690\) −1.59762e17 −0.0563578
\(691\) 1.38525e18 0.484084 0.242042 0.970266i \(-0.422183\pi\)
0.242042 + 0.970266i \(0.422183\pi\)
\(692\) −4.96124e18 −1.71752
\(693\) 1.61276e18 0.553100
\(694\) 4.93383e17 0.167628
\(695\) 5.64951e17 0.190156
\(696\) 9.34727e16 0.0311691
\(697\) −4.13706e16 −0.0136672
\(698\) 2.88060e17 0.0942805
\(699\) 1.24658e18 0.404220
\(700\) 2.66691e18 0.856783
\(701\) −3.52896e18 −1.12326 −0.561628 0.827390i \(-0.689825\pi\)
−0.561628 + 0.827390i \(0.689825\pi\)
\(702\) 2.52758e17 0.0797101
\(703\) 4.23715e17 0.132393
\(704\) −2.14917e18 −0.665349
\(705\) −7.44199e17 −0.228276
\(706\) 8.13013e17 0.247097
\(707\) −5.44976e18 −1.64116
\(708\) −2.26909e17 −0.0677072
\(709\) 1.25029e18 0.369666 0.184833 0.982770i \(-0.440826\pi\)
0.184833 + 0.982770i \(0.440826\pi\)
\(710\) −1.55855e17 −0.0456607
\(711\) −6.43994e17 −0.186952
\(712\) −2.03131e18 −0.584326
\(713\) 4.75910e18 1.35657
\(714\) 7.69248e15 0.00217284
\(715\) 2.74283e18 0.767732
\(716\) −1.52981e18 −0.424329
\(717\) 6.48872e17 0.178355
\(718\) 2.11285e17 0.0575520
\(719\) 2.28080e18 0.615673 0.307837 0.951439i \(-0.400395\pi\)
0.307837 + 0.951439i \(0.400395\pi\)
\(720\) −3.52734e17 −0.0943596
\(721\) −2.98381e18 −0.791028
\(722\) 1.16935e18 0.307222
\(723\) −2.37669e18 −0.618834
\(724\) 3.15317e18 0.813668
\(725\) −2.96881e17 −0.0759250
\(726\) −8.30642e17 −0.210536
\(727\) 3.07421e18 0.772253 0.386127 0.922446i \(-0.373813\pi\)
0.386127 + 0.922446i \(0.373813\pi\)
\(728\) −3.57200e18 −0.889319
\(729\) 1.50095e17 0.0370370
\(730\) 6.38697e15 0.00156206
\(731\) −7.68808e16 −0.0186361
\(732\) 1.46483e18 0.351936
\(733\) −2.26677e18 −0.539799 −0.269899 0.962889i \(-0.586990\pi\)
−0.269899 + 0.962889i \(0.586990\pi\)
\(734\) −1.75553e18 −0.414366
\(735\) −2.70742e17 −0.0633416
\(736\) 2.76727e18 0.641721
\(737\) 1.57964e18 0.363093
\(738\) −5.95443e17 −0.135667
\(739\) 6.19047e18 1.39809 0.699044 0.715078i \(-0.253609\pi\)
0.699044 + 0.715078i \(0.253609\pi\)
\(740\) −1.34883e18 −0.301962
\(741\) 5.37037e17 0.119175
\(742\) −1.27317e18 −0.280067
\(743\) −1.26049e18 −0.274860 −0.137430 0.990511i \(-0.543884\pi\)
−0.137430 + 0.990511i \(0.543884\pi\)
\(744\) −2.78232e18 −0.601426
\(745\) −1.00180e18 −0.214667
\(746\) 2.25823e18 0.479695
\(747\) 1.58470e18 0.333706
\(748\) 6.70424e16 0.0139955
\(749\) −6.56352e18 −1.35833
\(750\) −6.48971e17 −0.133146
\(751\) 7.96765e18 1.62058 0.810290 0.586029i \(-0.199310\pi\)
0.810290 + 0.586029i \(0.199310\pi\)
\(752\) 3.51344e18 0.708461
\(753\) 2.00918e18 0.401653
\(754\) 1.88440e17 0.0373474
\(755\) 3.73832e18 0.734550
\(756\) −1.00522e18 −0.195825
\(757\) 2.89061e17 0.0558298 0.0279149 0.999610i \(-0.491113\pi\)
0.0279149 + 0.999610i \(0.491113\pi\)
\(758\) −2.86758e18 −0.549118
\(759\) −3.48280e18 −0.661236
\(760\) 1.98451e17 0.0373565
\(761\) 4.62524e18 0.863245 0.431623 0.902054i \(-0.357941\pi\)
0.431623 + 0.902054i \(0.357941\pi\)
\(762\) −3.98636e17 −0.0737682
\(763\) −3.72085e18 −0.682704
\(764\) 6.81341e18 1.23953
\(765\) 7.76883e15 0.00140138
\(766\) 1.44237e18 0.257983
\(767\) −9.65276e17 −0.171191
\(768\) 4.88420e17 0.0858907
\(769\) −7.42290e18 −1.29435 −0.647176 0.762341i \(-0.724050\pi\)
−0.647176 + 0.762341i \(0.724050\pi\)
\(770\) 1.20146e18 0.207740
\(771\) 2.82534e18 0.484415
\(772\) 2.91387e18 0.495401
\(773\) 6.76017e17 0.113970 0.0569850 0.998375i \(-0.481851\pi\)
0.0569850 + 0.998375i \(0.481851\pi\)
\(774\) −1.10654e18 −0.184991
\(775\) 8.83698e18 1.46502
\(776\) 3.52667e18 0.579781
\(777\) −3.37389e18 −0.550039
\(778\) 2.23073e18 0.360645
\(779\) −1.26514e18 −0.202836
\(780\) −1.70958e18 −0.271815
\(781\) −3.39763e18 −0.535728
\(782\) −1.66121e16 −0.00259765
\(783\) 1.11901e17 0.0173533
\(784\) 1.27820e18 0.196583
\(785\) −2.25936e17 −0.0344614
\(786\) 1.41985e18 0.214781
\(787\) −1.48624e18 −0.222973 −0.111486 0.993766i \(-0.535561\pi\)
−0.111486 + 0.993766i \(0.535561\pi\)
\(788\) 7.98910e18 1.18871
\(789\) −2.45137e18 −0.361749
\(790\) −4.79757e17 −0.0702174
\(791\) 4.29275e18 0.623144
\(792\) 2.03615e18 0.293154
\(793\) 6.23141e18 0.889837
\(794\) −5.50352e17 −0.0779484
\(795\) −1.28581e18 −0.180630
\(796\) −2.78582e18 −0.388166
\(797\) 1.89092e17 0.0261332 0.0130666 0.999915i \(-0.495841\pi\)
0.0130666 + 0.999915i \(0.495841\pi\)
\(798\) 2.35242e17 0.0322474
\(799\) −7.73820e16 −0.0105217
\(800\) 5.13843e18 0.693019
\(801\) −2.43178e18 −0.325322
\(802\) 2.26649e18 0.300760
\(803\) 1.39235e17 0.0183273
\(804\) −9.84571e17 −0.128553
\(805\) 2.70290e18 0.350071
\(806\) −5.60913e18 −0.720639
\(807\) −2.20730e18 −0.281309
\(808\) −6.88045e18 −0.869848
\(809\) −3.14457e18 −0.394363 −0.197182 0.980367i \(-0.563179\pi\)
−0.197182 + 0.980367i \(0.563179\pi\)
\(810\) 1.11816e17 0.0139108
\(811\) −1.07894e19 −1.33156 −0.665782 0.746147i \(-0.731902\pi\)
−0.665782 + 0.746147i \(0.731902\pi\)
\(812\) −7.49426e17 −0.0917518
\(813\) 8.21153e18 0.997323
\(814\) 3.23868e18 0.390220
\(815\) −1.92829e18 −0.230488
\(816\) −3.66774e16 −0.00434923
\(817\) −2.35107e18 −0.276581
\(818\) −8.10493e17 −0.0945917
\(819\) −4.27623e18 −0.495125
\(820\) 4.02740e18 0.462631
\(821\) 6.50342e18 0.741159 0.370579 0.928801i \(-0.379159\pi\)
0.370579 + 0.928801i \(0.379159\pi\)
\(822\) 1.41164e18 0.159609
\(823\) 8.81513e18 0.988848 0.494424 0.869221i \(-0.335379\pi\)
0.494424 + 0.869221i \(0.335379\pi\)
\(824\) −3.76713e18 −0.419260
\(825\) −6.46706e18 −0.714095
\(826\) −4.22826e17 −0.0463224
\(827\) −1.30734e19 −1.42103 −0.710516 0.703681i \(-0.751538\pi\)
−0.710516 + 0.703681i \(0.751538\pi\)
\(828\) 2.17079e18 0.234111
\(829\) −9.25838e18 −0.990673 −0.495337 0.868701i \(-0.664955\pi\)
−0.495337 + 0.868701i \(0.664955\pi\)
\(830\) 1.18056e18 0.125337
\(831\) −7.28498e18 −0.767400
\(832\) 5.69852e18 0.595608
\(833\) −2.81519e16 −0.00291954
\(834\) 8.45493e17 0.0870023
\(835\) −7.37637e18 −0.753149
\(836\) 2.05020e18 0.207709
\(837\) −3.33085e18 −0.334842
\(838\) −4.67905e18 −0.466736
\(839\) 5.55006e18 0.549345 0.274672 0.961538i \(-0.411431\pi\)
0.274672 + 0.961538i \(0.411431\pi\)
\(840\) −1.58020e18 −0.155201
\(841\) −1.01772e19 −0.991869
\(842\) 2.71907e18 0.262962
\(843\) 1.78121e18 0.170937
\(844\) 2.51369e18 0.239379
\(845\) −3.06654e18 −0.289788
\(846\) −1.11375e18 −0.104443
\(847\) 1.40530e19 1.30776
\(848\) 6.07043e18 0.560592
\(849\) 3.90515e18 0.357880
\(850\) −3.08463e16 −0.00280531
\(851\) 7.28599e18 0.657577
\(852\) 2.11771e18 0.189675
\(853\) 1.09917e19 0.977001 0.488501 0.872563i \(-0.337544\pi\)
0.488501 + 0.872563i \(0.337544\pi\)
\(854\) 2.72958e18 0.240780
\(855\) 2.37576e17 0.0207981
\(856\) −8.28661e18 −0.719942
\(857\) 1.31498e19 1.13382 0.566911 0.823779i \(-0.308138\pi\)
0.566911 + 0.823779i \(0.308138\pi\)
\(858\) 4.10486e18 0.351262
\(859\) −1.16888e19 −0.992690 −0.496345 0.868125i \(-0.665325\pi\)
−0.496345 + 0.868125i \(0.665325\pi\)
\(860\) 7.48428e18 0.630827
\(861\) 1.00739e19 0.842705
\(862\) 2.91122e18 0.241701
\(863\) 1.12732e19 0.928919 0.464459 0.885594i \(-0.346249\pi\)
0.464459 + 0.885594i \(0.346249\pi\)
\(864\) −1.93679e18 −0.158396
\(865\) −9.33663e18 −0.757854
\(866\) 5.15776e18 0.415523
\(867\) −7.21963e18 −0.577286
\(868\) 2.23075e19 1.77040
\(869\) −1.04587e19 −0.823848
\(870\) 8.33629e16 0.00651775
\(871\) −4.18839e18 −0.325035
\(872\) −4.69766e18 −0.361847
\(873\) 4.22196e18 0.322791
\(874\) −5.08010e17 −0.0385521
\(875\) 1.09795e19 0.827044
\(876\) −8.67841e16 −0.00648878
\(877\) 2.49089e19 1.84866 0.924330 0.381594i \(-0.124625\pi\)
0.924330 + 0.381594i \(0.124625\pi\)
\(878\) −3.91144e18 −0.288152
\(879\) −3.19478e18 −0.233621
\(880\) −5.72850e18 −0.415818
\(881\) −1.57792e19 −1.13695 −0.568474 0.822701i \(-0.692466\pi\)
−0.568474 + 0.822701i \(0.692466\pi\)
\(882\) −4.05187e17 −0.0289808
\(883\) 2.74760e19 1.95078 0.975390 0.220485i \(-0.0707639\pi\)
0.975390 + 0.220485i \(0.0707639\pi\)
\(884\) −1.77763e17 −0.0125285
\(885\) −4.27022e17 −0.0298758
\(886\) 5.18299e17 0.0359966
\(887\) 2.05266e19 1.41518 0.707592 0.706622i \(-0.249782\pi\)
0.707592 + 0.706622i \(0.249782\pi\)
\(888\) −4.25961e18 −0.291532
\(889\) 6.74423e18 0.458217
\(890\) −1.81160e18 −0.122188
\(891\) 2.43758e18 0.163213
\(892\) 1.60724e19 1.06834
\(893\) −2.36640e18 −0.156154
\(894\) −1.49927e18 −0.0982171
\(895\) −2.87897e18 −0.187235
\(896\) 1.68959e19 1.09089
\(897\) 9.23462e18 0.591927
\(898\) 9.43562e17 0.0600446
\(899\) −2.48327e18 −0.156887
\(900\) 4.03085e18 0.252825
\(901\) −1.33699e17 −0.00832562
\(902\) −9.67016e18 −0.597849
\(903\) 1.87207e19 1.14908
\(904\) 5.41970e18 0.330279
\(905\) 5.93400e18 0.359031
\(906\) 5.59469e18 0.336080
\(907\) 1.15329e18 0.0687848 0.0343924 0.999408i \(-0.489050\pi\)
0.0343924 + 0.999408i \(0.489050\pi\)
\(908\) 1.64010e19 0.971208
\(909\) −8.23694e18 −0.484285
\(910\) −3.18566e18 −0.185965
\(911\) −1.98215e19 −1.14886 −0.574429 0.818554i \(-0.694776\pi\)
−0.574429 + 0.818554i \(0.694776\pi\)
\(912\) −1.12162e18 −0.0645476
\(913\) 2.57361e19 1.47056
\(914\) −9.39780e18 −0.533183
\(915\) 2.75668e18 0.155292
\(916\) 2.65807e19 1.48678
\(917\) −2.40214e19 −1.33413
\(918\) 1.16267e16 0.000641177 0
\(919\) 2.36827e19 1.29682 0.648411 0.761291i \(-0.275434\pi\)
0.648411 + 0.761291i \(0.275434\pi\)
\(920\) 3.41247e18 0.185544
\(921\) 1.14315e19 0.617183
\(922\) 4.39343e18 0.235534
\(923\) 9.00880e18 0.479574
\(924\) −1.63250e19 −0.862950
\(925\) 1.35290e19 0.710143
\(926\) −6.83868e18 −0.356452
\(927\) −4.50982e18 −0.233422
\(928\) −1.44395e18 −0.0742146
\(929\) −3.24255e19 −1.65495 −0.827474 0.561504i \(-0.810223\pi\)
−0.827474 + 0.561504i \(0.810223\pi\)
\(930\) −2.48139e18 −0.125764
\(931\) −8.60905e17 −0.0433294
\(932\) −1.26184e19 −0.630667
\(933\) −1.62570e19 −0.806882
\(934\) 5.70663e18 0.281271
\(935\) 1.26168e17 0.00617552
\(936\) −5.39884e18 −0.262426
\(937\) −2.25450e19 −1.08829 −0.544144 0.838992i \(-0.683145\pi\)
−0.544144 + 0.838992i \(0.683145\pi\)
\(938\) −1.83467e18 −0.0879507
\(939\) −1.05562e19 −0.502552
\(940\) 7.53308e18 0.356157
\(941\) −2.02666e19 −0.951585 −0.475793 0.879558i \(-0.657839\pi\)
−0.475793 + 0.879558i \(0.657839\pi\)
\(942\) −3.38131e17 −0.0157672
\(943\) −2.17548e19 −1.00746
\(944\) 2.01601e18 0.0927205
\(945\) −1.89173e18 −0.0864078
\(946\) −1.79705e19 −0.815206
\(947\) 2.79538e19 1.25941 0.629704 0.776835i \(-0.283176\pi\)
0.629704 + 0.776835i \(0.283176\pi\)
\(948\) 6.51877e18 0.291683
\(949\) −3.69182e17 −0.0164063
\(950\) −9.43302e17 −0.0416339
\(951\) −2.46676e19 −1.08132
\(952\) −1.64309e17 −0.00715355
\(953\) −1.55403e18 −0.0671978 −0.0335989 0.999435i \(-0.510697\pi\)
−0.0335989 + 0.999435i \(0.510697\pi\)
\(954\) −1.92431e18 −0.0826441
\(955\) 1.28222e19 0.546943
\(956\) −6.56814e18 −0.278270
\(957\) 1.81730e18 0.0764716
\(958\) −6.38387e18 −0.266814
\(959\) −2.38825e19 −0.991421
\(960\) 2.52093e18 0.103944
\(961\) 4.94998e19 2.02722
\(962\) −8.58734e18 −0.349318
\(963\) −9.92032e18 −0.400825
\(964\) 2.40579e19 0.965509
\(965\) 5.48364e18 0.218596
\(966\) 4.04510e18 0.160169
\(967\) 4.03274e19 1.58609 0.793045 0.609163i \(-0.208494\pi\)
0.793045 + 0.609163i \(0.208494\pi\)
\(968\) 1.77423e19 0.693138
\(969\) 2.47033e16 0.000958628 0
\(970\) 3.14524e18 0.121237
\(971\) −4.44653e19 −1.70254 −0.851269 0.524730i \(-0.824166\pi\)
−0.851269 + 0.524730i \(0.824166\pi\)
\(972\) −1.51932e18 −0.0577854
\(973\) −1.43043e19 −0.540421
\(974\) −1.73181e18 −0.0649930
\(975\) 1.71474e19 0.639245
\(976\) −1.30145e19 −0.481953
\(977\) 2.19233e19 0.806477 0.403238 0.915095i \(-0.367885\pi\)
0.403238 + 0.915095i \(0.367885\pi\)
\(978\) −2.88584e18 −0.105456
\(979\) −3.94928e19 −1.43361
\(980\) 2.74057e18 0.0988259
\(981\) −5.62381e18 −0.201457
\(982\) 6.32724e18 0.225159
\(983\) −4.97073e19 −1.75720 −0.878601 0.477556i \(-0.841523\pi\)
−0.878601 + 0.477556i \(0.841523\pi\)
\(984\) 1.27185e19 0.446650
\(985\) 1.50348e19 0.524520
\(986\) 8.66810e15 0.000300417 0
\(987\) 1.88427e19 0.648758
\(988\) −5.43610e18 −0.185938
\(989\) −4.04278e19 −1.37374
\(990\) 1.81592e18 0.0613012
\(991\) 4.02493e19 1.34983 0.674915 0.737895i \(-0.264180\pi\)
0.674915 + 0.737895i \(0.264180\pi\)
\(992\) 4.29806e19 1.43201
\(993\) −2.63120e19 −0.870932
\(994\) 3.94618e18 0.129767
\(995\) −5.24267e18 −0.171278
\(996\) −1.60410e19 −0.520651
\(997\) −5.73143e19 −1.84818 −0.924091 0.382173i \(-0.875176\pi\)
−0.924091 + 0.382173i \(0.875176\pi\)
\(998\) 1.94753e18 0.0623929
\(999\) −5.09940e18 −0.162309
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.1.14 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.a.1.14 30 1.1 even 1 trivial