Properties

Label 177.14.a.a.1.8
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 1.8
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-108.701 q^{2} +729.000 q^{3} +3623.83 q^{4} -15679.8 q^{5} -79242.8 q^{6} -222995. q^{7} +496563. q^{8} +531441. q^{9} +O(q^{10})\) \(q-108.701 q^{2} +729.000 q^{3} +3623.83 q^{4} -15679.8 q^{5} -79242.8 q^{6} -222995. q^{7} +496563. q^{8} +531441. q^{9} +1.70441e6 q^{10} +5.89635e6 q^{11} +2.64177e6 q^{12} +5.02542e6 q^{13} +2.42398e7 q^{14} -1.14306e7 q^{15} -8.36631e7 q^{16} +1.53014e8 q^{17} -5.77680e7 q^{18} -3.69560e8 q^{19} -5.68211e7 q^{20} -1.62564e8 q^{21} -6.40937e8 q^{22} -5.84237e8 q^{23} +3.61994e8 q^{24} -9.74846e8 q^{25} -5.46266e8 q^{26} +3.87420e8 q^{27} -8.08098e8 q^{28} +4.10315e9 q^{29} +1.24251e9 q^{30} -3.52084e9 q^{31} +5.02640e9 q^{32} +4.29844e9 q^{33} -1.66327e10 q^{34} +3.49653e9 q^{35} +1.92585e9 q^{36} +1.57485e10 q^{37} +4.01714e10 q^{38} +3.66353e9 q^{39} -7.78601e9 q^{40} -4.03243e10 q^{41} +1.76708e10 q^{42} -2.10059e10 q^{43} +2.13674e10 q^{44} -8.33290e9 q^{45} +6.35070e10 q^{46} +6.19726e10 q^{47} -6.09904e10 q^{48} -4.71620e10 q^{49} +1.05966e11 q^{50} +1.11547e11 q^{51} +1.82113e10 q^{52} +2.85355e11 q^{53} -4.21129e10 q^{54} -9.24537e10 q^{55} -1.10731e11 q^{56} -2.69409e11 q^{57} -4.46015e11 q^{58} +4.21805e10 q^{59} -4.14226e10 q^{60} -1.72604e11 q^{61} +3.82718e11 q^{62} -1.18509e11 q^{63} +1.38996e11 q^{64} -7.87977e10 q^{65} -4.67243e11 q^{66} +4.13709e10 q^{67} +5.54497e11 q^{68} -4.25909e11 q^{69} -3.80075e11 q^{70} -6.91656e11 q^{71} +2.63894e11 q^{72} +1.67509e12 q^{73} -1.71188e12 q^{74} -7.10663e11 q^{75} -1.33922e12 q^{76} -1.31486e12 q^{77} -3.98228e11 q^{78} -9.79322e11 q^{79} +1.31182e12 q^{80} +2.82430e11 q^{81} +4.38328e12 q^{82} -4.95100e12 q^{83} -5.89104e11 q^{84} -2.39923e12 q^{85} +2.28336e12 q^{86} +2.99120e12 q^{87} +2.92791e12 q^{88} +1.48553e11 q^{89} +9.05792e11 q^{90} -1.12065e12 q^{91} -2.11718e12 q^{92} -2.56669e12 q^{93} -6.73647e12 q^{94} +5.79463e12 q^{95} +3.66424e12 q^{96} +7.18251e11 q^{97} +5.12655e12 q^{98} +3.13356e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} + O(q^{10}) \) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} - 5352519q^{10} - 13950782q^{11} + 83541942q^{12} - 17256988q^{13} + 33780109q^{14} - 100413918q^{15} + 499996762q^{16} - 317583695q^{17} - 73338858q^{18} - 863401469q^{19} - 1841280623q^{20} - 641113947q^{21} - 2723764842q^{22} - 3142075981q^{23} - 635907429q^{24} + 5435751692q^{25} - 6441414040q^{26} + 11622614670q^{27} - 7538400046q^{28} - 4604589283q^{29} - 3901986351q^{30} + 4308675373q^{31} + 6094556360q^{32} - 10170120078q^{33} + 38097713432q^{34} - 15447827315q^{35} + 60902075718q^{36} - 19633376949q^{37} - 18152222923q^{38} - 12580344252q^{39} + 14680384170q^{40} - 103644439493q^{41} + 24625699461q^{42} - 64494894924q^{43} - 199714496208q^{44} - 73201746222q^{45} - 265425792847q^{46} - 293365585139q^{47} + 364497639498q^{48} + 414396765797q^{49} - 126058522207q^{50} - 231518513655q^{51} + 156029960316q^{52} - 76747013118q^{53} - 53464027482q^{54} - 433465885754q^{55} - 502955241518q^{56} - 629419670901q^{57} - 1755031845830q^{58} + 1265416009230q^{59} - 1342293574167q^{60} - 2022612531219q^{61} - 3816005187046q^{62} - 467372067363q^{63} - 3570205594131q^{64} - 3889749040576q^{65} - 1985624569818q^{66} - 502618987776q^{67} - 8953998390517q^{68} - 2290573390149q^{69} - 6805178272420q^{70} - 1599540605456q^{71} - 463576515741q^{72} - 3826795087235q^{73} - 7573387813210q^{74} + 3962662983468q^{75} - 19498723328388q^{76} - 9088623115219q^{77} - 4695790835160q^{78} - 8595482172338q^{79} - 17452527463963q^{80} + 8472886094430q^{81} - 11181116792901q^{82} - 13548556984389q^{83} - 5495493633534q^{84} - 12851795888367q^{85} + 8539949468848q^{86} - 3356745587307q^{87} - 25134826741387q^{88} - 21826401667403q^{89} - 2844548049879q^{90} - 26577050621355q^{91} - 34908210763168q^{92} + 3141024346917q^{93} - 26426808959500q^{94} - 29105233533993q^{95} + 4442931586440q^{96} + 417815797414q^{97} + 29159956938360q^{98} - 7414017536862q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −108.701 −1.20098 −0.600492 0.799631i \(-0.705029\pi\)
−0.600492 + 0.799631i \(0.705029\pi\)
\(3\) 729.000 0.577350
\(4\) 3623.83 0.442363
\(5\) −15679.8 −0.448783 −0.224391 0.974499i \(-0.572039\pi\)
−0.224391 + 0.974499i \(0.572039\pi\)
\(6\) −79242.8 −0.693388
\(7\) −222995. −0.716405 −0.358203 0.933644i \(-0.616610\pi\)
−0.358203 + 0.933644i \(0.616610\pi\)
\(8\) 496563. 0.669714
\(9\) 531441. 0.333333
\(10\) 1.70441e6 0.538981
\(11\) 5.89635e6 1.00353 0.501766 0.865004i \(-0.332684\pi\)
0.501766 + 0.865004i \(0.332684\pi\)
\(12\) 2.64177e6 0.255398
\(13\) 5.02542e6 0.288762 0.144381 0.989522i \(-0.453881\pi\)
0.144381 + 0.989522i \(0.453881\pi\)
\(14\) 2.42398e7 0.860391
\(15\) −1.14306e7 −0.259105
\(16\) −8.36631e7 −1.24668
\(17\) 1.53014e8 1.53749 0.768746 0.639554i \(-0.220881\pi\)
0.768746 + 0.639554i \(0.220881\pi\)
\(18\) −5.77680e7 −0.400328
\(19\) −3.69560e8 −1.80213 −0.901065 0.433683i \(-0.857214\pi\)
−0.901065 + 0.433683i \(0.857214\pi\)
\(20\) −5.68211e7 −0.198525
\(21\) −1.62564e8 −0.413617
\(22\) −6.40937e8 −1.20522
\(23\) −5.84237e8 −0.822921 −0.411461 0.911428i \(-0.634981\pi\)
−0.411461 + 0.911428i \(0.634981\pi\)
\(24\) 3.61994e8 0.386659
\(25\) −9.74846e8 −0.798594
\(26\) −5.46266e8 −0.346799
\(27\) 3.87420e8 0.192450
\(28\) −8.08098e8 −0.316911
\(29\) 4.10315e9 1.28095 0.640473 0.767981i \(-0.278738\pi\)
0.640473 + 0.767981i \(0.278738\pi\)
\(30\) 1.24251e9 0.311181
\(31\) −3.52084e9 −0.712517 −0.356259 0.934387i \(-0.615948\pi\)
−0.356259 + 0.934387i \(0.615948\pi\)
\(32\) 5.02640e9 0.827527
\(33\) 4.29844e9 0.579389
\(34\) −1.66327e10 −1.84650
\(35\) 3.49653e9 0.321510
\(36\) 1.92585e9 0.147454
\(37\) 1.57485e10 1.00909 0.504544 0.863386i \(-0.331661\pi\)
0.504544 + 0.863386i \(0.331661\pi\)
\(38\) 4.01714e10 2.16433
\(39\) 3.66353e9 0.166717
\(40\) −7.78601e9 −0.300556
\(41\) −4.03243e10 −1.32578 −0.662890 0.748717i \(-0.730670\pi\)
−0.662890 + 0.748717i \(0.730670\pi\)
\(42\) 1.76708e10 0.496747
\(43\) −2.10059e10 −0.506754 −0.253377 0.967368i \(-0.581541\pi\)
−0.253377 + 0.967368i \(0.581541\pi\)
\(44\) 2.13674e10 0.443925
\(45\) −8.33290e9 −0.149594
\(46\) 6.35070e10 0.988315
\(47\) 6.19726e10 0.838617 0.419309 0.907844i \(-0.362273\pi\)
0.419309 + 0.907844i \(0.362273\pi\)
\(48\) −6.09904e10 −0.719770
\(49\) −4.71620e10 −0.486764
\(50\) 1.05966e11 0.959099
\(51\) 1.11547e11 0.887672
\(52\) 1.82113e10 0.127738
\(53\) 2.85355e11 1.76845 0.884224 0.467062i \(-0.154688\pi\)
0.884224 + 0.467062i \(0.154688\pi\)
\(54\) −4.21129e10 −0.231129
\(55\) −9.24537e10 −0.450367
\(56\) −1.10731e11 −0.479786
\(57\) −2.69409e11 −1.04046
\(58\) −4.46015e11 −1.53839
\(59\) 4.21805e10 0.130189
\(60\) −4.14226e10 −0.114618
\(61\) −1.72604e11 −0.428951 −0.214476 0.976729i \(-0.568804\pi\)
−0.214476 + 0.976729i \(0.568804\pi\)
\(62\) 3.82718e11 0.855722
\(63\) −1.18509e11 −0.238802
\(64\) 1.38996e11 0.252832
\(65\) −7.87977e10 −0.129591
\(66\) −4.67243e11 −0.695837
\(67\) 4.13709e10 0.0558739 0.0279369 0.999610i \(-0.491106\pi\)
0.0279369 + 0.999610i \(0.491106\pi\)
\(68\) 5.54497e11 0.680129
\(69\) −4.25909e11 −0.475114
\(70\) −3.80075e11 −0.386129
\(71\) −6.91656e11 −0.640783 −0.320391 0.947285i \(-0.603814\pi\)
−0.320391 + 0.947285i \(0.603814\pi\)
\(72\) 2.63894e11 0.223238
\(73\) 1.67509e12 1.29551 0.647754 0.761849i \(-0.275708\pi\)
0.647754 + 0.761849i \(0.275708\pi\)
\(74\) −1.71188e12 −1.21190
\(75\) −7.10663e11 −0.461069
\(76\) −1.33922e12 −0.797195
\(77\) −1.31486e12 −0.718935
\(78\) −3.98228e11 −0.200224
\(79\) −9.79322e11 −0.453262 −0.226631 0.973981i \(-0.572771\pi\)
−0.226631 + 0.973981i \(0.572771\pi\)
\(80\) 1.31182e12 0.559487
\(81\) 2.82430e11 0.111111
\(82\) 4.38328e12 1.59224
\(83\) −4.95100e12 −1.66221 −0.831104 0.556117i \(-0.812291\pi\)
−0.831104 + 0.556117i \(0.812291\pi\)
\(84\) −5.89104e11 −0.182969
\(85\) −2.39923e12 −0.690000
\(86\) 2.28336e12 0.608603
\(87\) 2.99120e12 0.739554
\(88\) 2.92791e12 0.672078
\(89\) 1.48553e11 0.0316845 0.0158422 0.999875i \(-0.494957\pi\)
0.0158422 + 0.999875i \(0.494957\pi\)
\(90\) 9.05792e11 0.179660
\(91\) −1.12065e12 −0.206871
\(92\) −2.11718e12 −0.364030
\(93\) −2.56669e12 −0.411372
\(94\) −6.73647e12 −1.00717
\(95\) 5.79463e12 0.808765
\(96\) 3.66424e12 0.477773
\(97\) 7.18251e11 0.0875508 0.0437754 0.999041i \(-0.486061\pi\)
0.0437754 + 0.999041i \(0.486061\pi\)
\(98\) 5.12655e12 0.584595
\(99\) 3.13356e12 0.334510
\(100\) −3.53268e12 −0.353268
\(101\) −4.51100e11 −0.0422847 −0.0211424 0.999776i \(-0.506730\pi\)
−0.0211424 + 0.999776i \(0.506730\pi\)
\(102\) −1.21252e13 −1.06608
\(103\) 1.45809e13 1.20321 0.601605 0.798794i \(-0.294528\pi\)
0.601605 + 0.798794i \(0.294528\pi\)
\(104\) 2.49544e12 0.193388
\(105\) 2.54897e12 0.185624
\(106\) −3.10183e13 −2.12388
\(107\) 1.93892e13 1.24901 0.624503 0.781023i \(-0.285302\pi\)
0.624503 + 0.781023i \(0.285302\pi\)
\(108\) 1.40395e12 0.0851327
\(109\) 1.35000e13 0.771015 0.385507 0.922705i \(-0.374026\pi\)
0.385507 + 0.922705i \(0.374026\pi\)
\(110\) 1.00498e13 0.540884
\(111\) 1.14807e13 0.582598
\(112\) 1.86565e13 0.893127
\(113\) 2.23948e13 1.01190 0.505950 0.862563i \(-0.331142\pi\)
0.505950 + 0.862563i \(0.331142\pi\)
\(114\) 2.92849e13 1.24958
\(115\) 9.16074e12 0.369313
\(116\) 1.48691e13 0.566642
\(117\) 2.67071e12 0.0962541
\(118\) −4.58505e12 −0.156355
\(119\) −3.41214e13 −1.10147
\(120\) −5.67600e12 −0.173526
\(121\) 2.44235e11 0.00707461
\(122\) 1.87622e13 0.515164
\(123\) −2.93964e13 −0.765440
\(124\) −1.27589e13 −0.315191
\(125\) 3.44258e13 0.807178
\(126\) 1.28820e13 0.286797
\(127\) −2.82759e13 −0.597989 −0.298994 0.954255i \(-0.596651\pi\)
−0.298994 + 0.954255i \(0.596651\pi\)
\(128\) −5.62852e13 −1.13117
\(129\) −1.53133e13 −0.292574
\(130\) 8.56536e12 0.155637
\(131\) 1.00006e13 0.172887 0.0864437 0.996257i \(-0.472450\pi\)
0.0864437 + 0.996257i \(0.472450\pi\)
\(132\) 1.55768e13 0.256300
\(133\) 8.24101e13 1.29106
\(134\) −4.49704e12 −0.0671036
\(135\) −6.07468e12 −0.0863683
\(136\) 7.59810e13 1.02968
\(137\) 1.21278e14 1.56711 0.783553 0.621325i \(-0.213405\pi\)
0.783553 + 0.621325i \(0.213405\pi\)
\(138\) 4.62966e13 0.570604
\(139\) −2.91391e13 −0.342673 −0.171337 0.985213i \(-0.554809\pi\)
−0.171337 + 0.985213i \(0.554809\pi\)
\(140\) 1.26708e13 0.142224
\(141\) 4.51780e13 0.484176
\(142\) 7.51835e13 0.769570
\(143\) 2.96316e13 0.289782
\(144\) −4.44620e13 −0.415559
\(145\) −6.43367e13 −0.574866
\(146\) −1.82084e14 −1.55589
\(147\) −3.43811e13 −0.281033
\(148\) 5.70701e13 0.446383
\(149\) −7.22942e11 −0.00541243 −0.00270622 0.999996i \(-0.500861\pi\)
−0.00270622 + 0.999996i \(0.500861\pi\)
\(150\) 7.72495e13 0.553736
\(151\) −1.45349e14 −0.997844 −0.498922 0.866647i \(-0.666271\pi\)
−0.498922 + 0.866647i \(0.666271\pi\)
\(152\) −1.83510e14 −1.20691
\(153\) 8.13179e13 0.512497
\(154\) 1.42926e14 0.863429
\(155\) 5.52062e13 0.319765
\(156\) 1.32760e13 0.0737493
\(157\) 3.36777e14 1.79471 0.897356 0.441308i \(-0.145485\pi\)
0.897356 + 0.441308i \(0.145485\pi\)
\(158\) 1.06453e14 0.544360
\(159\) 2.08024e14 1.02101
\(160\) −7.88130e13 −0.371380
\(161\) 1.30282e14 0.589545
\(162\) −3.07003e13 −0.133443
\(163\) −1.95831e14 −0.817827 −0.408913 0.912573i \(-0.634092\pi\)
−0.408913 + 0.912573i \(0.634092\pi\)
\(164\) −1.46128e14 −0.586476
\(165\) −6.73988e13 −0.260020
\(166\) 5.38177e14 1.99629
\(167\) −4.48292e14 −1.59920 −0.799602 0.600530i \(-0.794956\pi\)
−0.799602 + 0.600530i \(0.794956\pi\)
\(168\) −8.07231e13 −0.277005
\(169\) −2.77620e14 −0.916616
\(170\) 2.60798e14 0.828679
\(171\) −1.96399e14 −0.600710
\(172\) −7.61220e13 −0.224169
\(173\) 5.90983e13 0.167601 0.0838003 0.996483i \(-0.473294\pi\)
0.0838003 + 0.996483i \(0.473294\pi\)
\(174\) −3.25145e14 −0.888193
\(175\) 2.17386e14 0.572117
\(176\) −4.93307e14 −1.25108
\(177\) 3.07496e13 0.0751646
\(178\) −1.61478e13 −0.0380525
\(179\) 2.93637e14 0.667215 0.333608 0.942712i \(-0.391734\pi\)
0.333608 + 0.942712i \(0.391734\pi\)
\(180\) −3.01970e13 −0.0661749
\(181\) −1.37598e14 −0.290871 −0.145435 0.989368i \(-0.546458\pi\)
−0.145435 + 0.989368i \(0.546458\pi\)
\(182\) 1.21815e14 0.248448
\(183\) −1.25829e14 −0.247655
\(184\) −2.90110e14 −0.551122
\(185\) −2.46934e14 −0.452861
\(186\) 2.79001e14 0.494051
\(187\) 9.02224e14 1.54292
\(188\) 2.24578e14 0.370973
\(189\) −8.63930e13 −0.137872
\(190\) −6.29880e14 −0.971314
\(191\) −6.54949e14 −0.976091 −0.488046 0.872818i \(-0.662290\pi\)
−0.488046 + 0.872818i \(0.662290\pi\)
\(192\) 1.01328e14 0.145972
\(193\) 9.63404e14 1.34179 0.670897 0.741550i \(-0.265909\pi\)
0.670897 + 0.741550i \(0.265909\pi\)
\(194\) −7.80744e13 −0.105147
\(195\) −5.74435e13 −0.0748197
\(196\) −1.70907e14 −0.215326
\(197\) 1.25137e14 0.152530 0.0762652 0.997088i \(-0.475700\pi\)
0.0762652 + 0.997088i \(0.475700\pi\)
\(198\) −3.40620e14 −0.401742
\(199\) −1.21862e15 −1.39099 −0.695494 0.718532i \(-0.744815\pi\)
−0.695494 + 0.718532i \(0.744815\pi\)
\(200\) −4.84072e14 −0.534829
\(201\) 3.01594e13 0.0322588
\(202\) 4.90348e13 0.0507833
\(203\) −9.14984e14 −0.917676
\(204\) 4.04228e14 0.392673
\(205\) 6.32277e14 0.594987
\(206\) −1.58495e15 −1.44504
\(207\) −3.10488e14 −0.274307
\(208\) −4.20442e14 −0.359994
\(209\) −2.17905e15 −1.80849
\(210\) −2.77075e14 −0.222931
\(211\) −1.39131e15 −1.08539 −0.542697 0.839929i \(-0.682597\pi\)
−0.542697 + 0.839929i \(0.682597\pi\)
\(212\) 1.03408e15 0.782295
\(213\) −5.04217e14 −0.369956
\(214\) −2.10761e15 −1.50004
\(215\) 3.29369e14 0.227422
\(216\) 1.92379e14 0.128886
\(217\) 7.85132e14 0.510451
\(218\) −1.46746e15 −0.925976
\(219\) 1.22114e15 0.747962
\(220\) −3.35037e14 −0.199226
\(221\) 7.68959e14 0.443970
\(222\) −1.24796e15 −0.699690
\(223\) 1.05743e14 0.0575796 0.0287898 0.999585i \(-0.490835\pi\)
0.0287898 + 0.999585i \(0.490835\pi\)
\(224\) −1.12086e15 −0.592844
\(225\) −5.18073e14 −0.266198
\(226\) −2.43433e15 −1.21528
\(227\) −3.35126e15 −1.62570 −0.812850 0.582473i \(-0.802085\pi\)
−0.812850 + 0.582473i \(0.802085\pi\)
\(228\) −9.76294e14 −0.460261
\(229\) 7.61807e13 0.0349071 0.0174536 0.999848i \(-0.494444\pi\)
0.0174536 + 0.999848i \(0.494444\pi\)
\(230\) −9.95778e14 −0.443539
\(231\) −9.58532e14 −0.415077
\(232\) 2.03747e15 0.857867
\(233\) 9.95149e14 0.407450 0.203725 0.979028i \(-0.434695\pi\)
0.203725 + 0.979028i \(0.434695\pi\)
\(234\) −2.90308e14 −0.115600
\(235\) −9.71720e14 −0.376357
\(236\) 1.52855e14 0.0575907
\(237\) −7.13926e14 −0.261691
\(238\) 3.70902e15 1.32284
\(239\) −2.71528e15 −0.942386 −0.471193 0.882030i \(-0.656176\pi\)
−0.471193 + 0.882030i \(0.656176\pi\)
\(240\) 9.56319e14 0.323020
\(241\) 3.45190e14 0.113487 0.0567437 0.998389i \(-0.481928\pi\)
0.0567437 + 0.998389i \(0.481928\pi\)
\(242\) −2.65485e13 −0.00849650
\(243\) 2.05891e14 0.0641500
\(244\) −6.25490e14 −0.189752
\(245\) 7.39492e14 0.218451
\(246\) 3.19541e15 0.919281
\(247\) −1.85719e15 −0.520387
\(248\) −1.74832e15 −0.477183
\(249\) −3.60928e15 −0.959676
\(250\) −3.74211e15 −0.969408
\(251\) 1.14308e15 0.288534 0.144267 0.989539i \(-0.453918\pi\)
0.144267 + 0.989539i \(0.453918\pi\)
\(252\) −4.29457e14 −0.105637
\(253\) −3.44487e15 −0.825827
\(254\) 3.07361e15 0.718175
\(255\) −1.74904e15 −0.398372
\(256\) 4.97958e15 1.10569
\(257\) −3.33503e15 −0.721995 −0.360997 0.932567i \(-0.617564\pi\)
−0.360997 + 0.932567i \(0.617564\pi\)
\(258\) 1.66457e15 0.351377
\(259\) −3.51185e15 −0.722916
\(260\) −2.85550e14 −0.0573264
\(261\) 2.18058e15 0.426982
\(262\) −1.08707e15 −0.207635
\(263\) 7.95745e14 0.148273 0.0741364 0.997248i \(-0.476380\pi\)
0.0741364 + 0.997248i \(0.476380\pi\)
\(264\) 2.13444e15 0.388025
\(265\) −4.47432e15 −0.793649
\(266\) −8.95804e15 −1.55054
\(267\) 1.08295e14 0.0182930
\(268\) 1.49921e14 0.0247165
\(269\) −8.89539e15 −1.43145 −0.715723 0.698384i \(-0.753903\pi\)
−0.715723 + 0.698384i \(0.753903\pi\)
\(270\) 6.60322e14 0.103727
\(271\) −5.35745e15 −0.821596 −0.410798 0.911726i \(-0.634750\pi\)
−0.410798 + 0.911726i \(0.634750\pi\)
\(272\) −1.28016e16 −1.91676
\(273\) −8.16950e14 −0.119437
\(274\) −1.31830e16 −1.88207
\(275\) −5.74804e15 −0.801414
\(276\) −1.54342e15 −0.210173
\(277\) −6.20275e15 −0.825022 −0.412511 0.910953i \(-0.635348\pi\)
−0.412511 + 0.910953i \(0.635348\pi\)
\(278\) 3.16744e15 0.411545
\(279\) −1.87112e15 −0.237506
\(280\) 1.73625e15 0.215320
\(281\) 1.00835e16 1.22186 0.610930 0.791685i \(-0.290796\pi\)
0.610930 + 0.791685i \(0.290796\pi\)
\(282\) −4.91088e15 −0.581488
\(283\) −8.89753e15 −1.02957 −0.514787 0.857318i \(-0.672129\pi\)
−0.514787 + 0.857318i \(0.672129\pi\)
\(284\) −2.50645e15 −0.283458
\(285\) 4.22429e15 0.466941
\(286\) −3.22098e15 −0.348023
\(287\) 8.99213e15 0.949796
\(288\) 2.67123e15 0.275842
\(289\) 1.35087e16 1.36388
\(290\) 6.99344e15 0.690405
\(291\) 5.23605e14 0.0505475
\(292\) 6.07026e15 0.573085
\(293\) −3.28434e15 −0.303255 −0.151628 0.988438i \(-0.548451\pi\)
−0.151628 + 0.988438i \(0.548451\pi\)
\(294\) 3.73725e15 0.337516
\(295\) −6.61383e14 −0.0584265
\(296\) 7.82014e15 0.675800
\(297\) 2.28437e15 0.193130
\(298\) 7.85842e13 0.00650025
\(299\) −2.93604e15 −0.237629
\(300\) −2.57532e15 −0.203959
\(301\) 4.68423e15 0.363041
\(302\) 1.57996e16 1.19839
\(303\) −3.28852e14 −0.0244131
\(304\) 3.09185e16 2.24668
\(305\) 2.70641e15 0.192506
\(306\) −8.83931e15 −0.615501
\(307\) −9.09345e15 −0.619911 −0.309955 0.950751i \(-0.600314\pi\)
−0.309955 + 0.950751i \(0.600314\pi\)
\(308\) −4.76483e15 −0.318030
\(309\) 1.06295e16 0.694674
\(310\) −6.00095e15 −0.384033
\(311\) 1.40180e16 0.878503 0.439252 0.898364i \(-0.355244\pi\)
0.439252 + 0.898364i \(0.355244\pi\)
\(312\) 1.81917e15 0.111653
\(313\) −2.17374e15 −0.130668 −0.0653340 0.997863i \(-0.520811\pi\)
−0.0653340 + 0.997863i \(0.520811\pi\)
\(314\) −3.66079e16 −2.15542
\(315\) 1.85820e15 0.107170
\(316\) −3.54890e15 −0.200506
\(317\) 1.68840e16 0.934522 0.467261 0.884120i \(-0.345241\pi\)
0.467261 + 0.884120i \(0.345241\pi\)
\(318\) −2.26123e16 −1.22622
\(319\) 2.41936e16 1.28547
\(320\) −2.17943e15 −0.113467
\(321\) 1.41347e16 0.721114
\(322\) −1.41618e16 −0.708034
\(323\) −5.65478e16 −2.77076
\(324\) 1.02348e15 0.0491514
\(325\) −4.89901e15 −0.230604
\(326\) 2.12869e16 0.982197
\(327\) 9.84153e15 0.445146
\(328\) −2.00235e16 −0.887893
\(329\) −1.38196e16 −0.600790
\(330\) 7.32629e15 0.312279
\(331\) −2.34060e16 −0.978241 −0.489121 0.872216i \(-0.662682\pi\)
−0.489121 + 0.872216i \(0.662682\pi\)
\(332\) −1.79416e16 −0.735299
\(333\) 8.36942e15 0.336363
\(334\) 4.87296e16 1.92062
\(335\) −6.48688e14 −0.0250752
\(336\) 1.36006e16 0.515647
\(337\) 1.19509e16 0.444432 0.222216 0.974997i \(-0.428671\pi\)
0.222216 + 0.974997i \(0.428671\pi\)
\(338\) 3.01775e16 1.10084
\(339\) 1.63258e16 0.584221
\(340\) −8.69441e15 −0.305230
\(341\) −2.07601e16 −0.715033
\(342\) 2.13487e16 0.721443
\(343\) 3.21227e16 1.06513
\(344\) −1.04308e16 −0.339380
\(345\) 6.67818e15 0.213223
\(346\) −6.42403e15 −0.201286
\(347\) 1.62883e16 0.500881 0.250440 0.968132i \(-0.419425\pi\)
0.250440 + 0.968132i \(0.419425\pi\)
\(348\) 1.08396e16 0.327151
\(349\) 2.82702e15 0.0837460 0.0418730 0.999123i \(-0.486668\pi\)
0.0418730 + 0.999123i \(0.486668\pi\)
\(350\) −2.36300e16 −0.687103
\(351\) 1.94695e15 0.0555723
\(352\) 2.96374e16 0.830449
\(353\) −5.21024e16 −1.43325 −0.716625 0.697458i \(-0.754314\pi\)
−0.716625 + 0.697458i \(0.754314\pi\)
\(354\) −3.34250e15 −0.0902715
\(355\) 1.08450e16 0.287572
\(356\) 5.38331e14 0.0140160
\(357\) −2.48745e16 −0.635932
\(358\) −3.19185e16 −0.801315
\(359\) 1.76819e16 0.435928 0.217964 0.975957i \(-0.430059\pi\)
0.217964 + 0.975957i \(0.430059\pi\)
\(360\) −4.13781e15 −0.100185
\(361\) 9.45214e16 2.24767
\(362\) 1.49570e16 0.349331
\(363\) 1.78047e14 0.00408453
\(364\) −4.06103e15 −0.0915119
\(365\) −2.62652e16 −0.581402
\(366\) 1.36777e16 0.297430
\(367\) −9.04870e15 −0.193311 −0.0966556 0.995318i \(-0.530815\pi\)
−0.0966556 + 0.995318i \(0.530815\pi\)
\(368\) 4.88791e16 1.02592
\(369\) −2.14300e16 −0.441927
\(370\) 2.68419e16 0.543879
\(371\) −6.36329e16 −1.26693
\(372\) −9.30127e15 −0.181976
\(373\) 7.31250e14 0.0140591 0.00702957 0.999975i \(-0.497762\pi\)
0.00702957 + 0.999975i \(0.497762\pi\)
\(374\) −9.80723e16 −1.85302
\(375\) 2.50964e16 0.466024
\(376\) 3.07733e16 0.561633
\(377\) 2.06201e16 0.369889
\(378\) 9.39098e15 0.165582
\(379\) −5.04940e16 −0.875154 −0.437577 0.899181i \(-0.644163\pi\)
−0.437577 + 0.899181i \(0.644163\pi\)
\(380\) 2.09988e16 0.357767
\(381\) −2.06132e16 −0.345249
\(382\) 7.11934e16 1.17227
\(383\) 2.01642e16 0.326430 0.163215 0.986591i \(-0.447814\pi\)
0.163215 + 0.986591i \(0.447814\pi\)
\(384\) −4.10319e16 −0.653083
\(385\) 2.06168e16 0.322645
\(386\) −1.04723e17 −1.61147
\(387\) −1.11634e16 −0.168918
\(388\) 2.60282e15 0.0387292
\(389\) −8.84541e16 −1.29433 −0.647166 0.762349i \(-0.724046\pi\)
−0.647166 + 0.762349i \(0.724046\pi\)
\(390\) 6.24415e15 0.0898572
\(391\) −8.93964e16 −1.26524
\(392\) −2.34189e16 −0.325992
\(393\) 7.29045e15 0.0998166
\(394\) −1.36025e16 −0.183187
\(395\) 1.53556e16 0.203416
\(396\) 1.13555e16 0.147975
\(397\) −1.49539e17 −1.91697 −0.958484 0.285145i \(-0.907958\pi\)
−0.958484 + 0.285145i \(0.907958\pi\)
\(398\) 1.32465e17 1.67056
\(399\) 6.00770e16 0.745391
\(400\) 8.15587e16 0.995590
\(401\) −1.50861e17 −1.81192 −0.905959 0.423365i \(-0.860849\pi\)
−0.905959 + 0.423365i \(0.860849\pi\)
\(402\) −3.27835e15 −0.0387423
\(403\) −1.76937e16 −0.205748
\(404\) −1.63471e15 −0.0187052
\(405\) −4.42844e15 −0.0498647
\(406\) 9.94594e16 1.10211
\(407\) 9.28590e16 1.01265
\(408\) 5.53901e16 0.594486
\(409\) −1.27486e17 −1.34667 −0.673336 0.739336i \(-0.735139\pi\)
−0.673336 + 0.739336i \(0.735139\pi\)
\(410\) −6.87290e16 −0.714570
\(411\) 8.84116e16 0.904769
\(412\) 5.28387e16 0.532255
\(413\) −9.40607e15 −0.0932680
\(414\) 3.37502e16 0.329438
\(415\) 7.76308e16 0.745970
\(416\) 2.52597e16 0.238958
\(417\) −2.12424e16 −0.197842
\(418\) 2.36865e17 2.17197
\(419\) −1.56729e17 −1.41501 −0.707504 0.706710i \(-0.750179\pi\)
−0.707504 + 0.706710i \(0.750179\pi\)
\(420\) 9.23704e15 0.0821131
\(421\) −1.86804e17 −1.63513 −0.817565 0.575836i \(-0.804677\pi\)
−0.817565 + 0.575836i \(0.804677\pi\)
\(422\) 1.51236e17 1.30354
\(423\) 3.29348e16 0.279539
\(424\) 1.41697e17 1.18435
\(425\) −1.49165e17 −1.22783
\(426\) 5.48088e16 0.444312
\(427\) 3.84900e16 0.307303
\(428\) 7.02631e16 0.552513
\(429\) 2.16015e16 0.167306
\(430\) −3.58026e16 −0.273130
\(431\) 2.66341e16 0.200141 0.100070 0.994980i \(-0.468093\pi\)
0.100070 + 0.994980i \(0.468093\pi\)
\(432\) −3.24128e16 −0.239923
\(433\) −3.73070e16 −0.272031 −0.136016 0.990707i \(-0.543430\pi\)
−0.136016 + 0.990707i \(0.543430\pi\)
\(434\) −8.53443e16 −0.613044
\(435\) −4.69014e16 −0.331899
\(436\) 4.89219e16 0.341068
\(437\) 2.15911e17 1.48301
\(438\) −1.32739e17 −0.898291
\(439\) 1.67544e17 1.11715 0.558574 0.829455i \(-0.311349\pi\)
0.558574 + 0.829455i \(0.311349\pi\)
\(440\) −4.59091e16 −0.301617
\(441\) −2.50638e16 −0.162255
\(442\) −8.35863e16 −0.533201
\(443\) −1.61581e17 −1.01570 −0.507851 0.861445i \(-0.669560\pi\)
−0.507851 + 0.861445i \(0.669560\pi\)
\(444\) 4.16041e16 0.257719
\(445\) −2.32928e15 −0.0142194
\(446\) −1.14943e16 −0.0691522
\(447\) −5.27025e14 −0.00312487
\(448\) −3.09954e16 −0.181130
\(449\) −6.95012e16 −0.400305 −0.200153 0.979765i \(-0.564144\pi\)
−0.200153 + 0.979765i \(0.564144\pi\)
\(450\) 5.63149e16 0.319700
\(451\) −2.37766e17 −1.33046
\(452\) 8.11551e16 0.447627
\(453\) −1.05960e17 −0.576105
\(454\) 3.64284e17 1.95244
\(455\) 1.75715e16 0.0928400
\(456\) −1.33778e17 −0.696811
\(457\) −8.78228e16 −0.450974 −0.225487 0.974246i \(-0.572397\pi\)
−0.225487 + 0.974246i \(0.572397\pi\)
\(458\) −8.28089e15 −0.0419229
\(459\) 5.92807e16 0.295891
\(460\) 3.31970e16 0.163370
\(461\) 3.70986e17 1.80012 0.900059 0.435768i \(-0.143523\pi\)
0.900059 + 0.435768i \(0.143523\pi\)
\(462\) 1.04193e17 0.498501
\(463\) −1.05637e17 −0.498358 −0.249179 0.968458i \(-0.580161\pi\)
−0.249179 + 0.968458i \(0.580161\pi\)
\(464\) −3.43283e17 −1.59693
\(465\) 4.02453e16 0.184617
\(466\) −1.08173e17 −0.489341
\(467\) 1.34010e17 0.597829 0.298914 0.954280i \(-0.403375\pi\)
0.298914 + 0.954280i \(0.403375\pi\)
\(468\) 9.67822e15 0.0425792
\(469\) −9.22552e15 −0.0400283
\(470\) 1.05627e17 0.451999
\(471\) 2.45510e17 1.03618
\(472\) 2.09453e16 0.0871893
\(473\) −1.23858e17 −0.508543
\(474\) 7.76042e16 0.314287
\(475\) 3.60264e17 1.43917
\(476\) −1.23650e17 −0.487248
\(477\) 1.51649e17 0.589483
\(478\) 2.95153e17 1.13179
\(479\) −2.99679e17 −1.13364 −0.566820 0.823842i \(-0.691826\pi\)
−0.566820 + 0.823842i \(0.691826\pi\)
\(480\) −5.74547e16 −0.214416
\(481\) 7.91430e16 0.291387
\(482\) −3.75224e16 −0.136296
\(483\) 9.49758e16 0.340374
\(484\) 8.85066e14 0.00312954
\(485\) −1.12620e16 −0.0392913
\(486\) −2.23805e16 −0.0770432
\(487\) 4.24453e17 1.44176 0.720878 0.693062i \(-0.243739\pi\)
0.720878 + 0.693062i \(0.243739\pi\)
\(488\) −8.57089e16 −0.287275
\(489\) −1.42761e17 −0.472173
\(490\) −8.03833e16 −0.262356
\(491\) 2.82075e16 0.0908519 0.0454260 0.998968i \(-0.485535\pi\)
0.0454260 + 0.998968i \(0.485535\pi\)
\(492\) −1.06528e17 −0.338602
\(493\) 6.27839e17 1.96944
\(494\) 2.01878e17 0.624977
\(495\) −4.91337e16 −0.150122
\(496\) 2.94565e17 0.888280
\(497\) 1.54236e17 0.459060
\(498\) 3.92331e17 1.15256
\(499\) −9.74998e16 −0.282716 −0.141358 0.989959i \(-0.545147\pi\)
−0.141358 + 0.989959i \(0.545147\pi\)
\(500\) 1.24753e17 0.357065
\(501\) −3.26805e17 −0.923301
\(502\) −1.24253e17 −0.346525
\(503\) −4.98003e16 −0.137101 −0.0685504 0.997648i \(-0.521837\pi\)
−0.0685504 + 0.997648i \(0.521837\pi\)
\(504\) −5.88471e16 −0.159929
\(505\) 7.07316e15 0.0189767
\(506\) 3.74459e17 0.991805
\(507\) −2.02385e17 −0.529209
\(508\) −1.02467e17 −0.264528
\(509\) −4.57244e17 −1.16542 −0.582710 0.812680i \(-0.698008\pi\)
−0.582710 + 0.812680i \(0.698008\pi\)
\(510\) 1.90122e17 0.478438
\(511\) −3.73538e17 −0.928109
\(512\) −8.01958e16 −0.196742
\(513\) −1.43175e17 −0.346820
\(514\) 3.62520e17 0.867104
\(515\) −2.28626e17 −0.539980
\(516\) −5.54929e16 −0.129424
\(517\) 3.65412e17 0.841578
\(518\) 3.81741e17 0.868211
\(519\) 4.30827e16 0.0967643
\(520\) −3.91280e16 −0.0867892
\(521\) 4.43418e17 0.971332 0.485666 0.874144i \(-0.338577\pi\)
0.485666 + 0.874144i \(0.338577\pi\)
\(522\) −2.37031e17 −0.512798
\(523\) −1.27369e17 −0.272146 −0.136073 0.990699i \(-0.543448\pi\)
−0.136073 + 0.990699i \(0.543448\pi\)
\(524\) 3.62406e16 0.0764789
\(525\) 1.58475e17 0.330312
\(526\) −8.64980e16 −0.178073
\(527\) −5.38738e17 −1.09549
\(528\) −3.59621e17 −0.722311
\(529\) −1.62703e17 −0.322800
\(530\) 4.86361e17 0.953160
\(531\) 2.24165e16 0.0433963
\(532\) 2.98641e17 0.571115
\(533\) −2.02646e17 −0.382835
\(534\) −1.17718e16 −0.0219696
\(535\) −3.04018e17 −0.560532
\(536\) 2.05432e16 0.0374195
\(537\) 2.14061e17 0.385217
\(538\) 9.66934e17 1.71914
\(539\) −2.78084e17 −0.488482
\(540\) −2.20136e16 −0.0382061
\(541\) 2.09010e17 0.358413 0.179207 0.983811i \(-0.442647\pi\)
0.179207 + 0.983811i \(0.442647\pi\)
\(542\) 5.82359e17 0.986723
\(543\) −1.00309e17 −0.167934
\(544\) 7.69109e17 1.27232
\(545\) −2.11678e17 −0.346018
\(546\) 8.88031e16 0.143442
\(547\) 9.22458e17 1.47241 0.736206 0.676758i \(-0.236616\pi\)
0.736206 + 0.676758i \(0.236616\pi\)
\(548\) 4.39491e17 0.693229
\(549\) −9.17291e16 −0.142984
\(550\) 6.24815e17 0.962485
\(551\) −1.51636e18 −2.30843
\(552\) −2.11491e17 −0.318190
\(553\) 2.18384e17 0.324719
\(554\) 6.74243e17 0.990838
\(555\) −1.80015e17 −0.261460
\(556\) −1.05595e17 −0.151586
\(557\) −1.22276e18 −1.73493 −0.867466 0.497497i \(-0.834253\pi\)
−0.867466 + 0.497497i \(0.834253\pi\)
\(558\) 2.03392e17 0.285241
\(559\) −1.05564e17 −0.146331
\(560\) −2.92531e17 −0.400820
\(561\) 6.57721e17 0.890806
\(562\) −1.09609e18 −1.46743
\(563\) −1.25872e18 −1.66580 −0.832902 0.553421i \(-0.813322\pi\)
−0.832902 + 0.553421i \(0.813322\pi\)
\(564\) 1.63718e17 0.214181
\(565\) −3.51147e17 −0.454123
\(566\) 9.67167e17 1.23650
\(567\) −6.29805e16 −0.0796006
\(568\) −3.43451e17 −0.429141
\(569\) 9.77509e17 1.20751 0.603756 0.797170i \(-0.293670\pi\)
0.603756 + 0.797170i \(0.293670\pi\)
\(570\) −4.59183e17 −0.560788
\(571\) −8.17555e17 −0.987147 −0.493574 0.869704i \(-0.664310\pi\)
−0.493574 + 0.869704i \(0.664310\pi\)
\(572\) 1.07380e17 0.128189
\(573\) −4.77458e17 −0.563547
\(574\) −9.77450e17 −1.14069
\(575\) 5.69542e17 0.657180
\(576\) 7.38680e16 0.0842773
\(577\) −8.66108e17 −0.977078 −0.488539 0.872542i \(-0.662470\pi\)
−0.488539 + 0.872542i \(0.662470\pi\)
\(578\) −1.46840e18 −1.63800
\(579\) 7.02322e17 0.774686
\(580\) −2.33145e17 −0.254299
\(581\) 1.10405e18 1.19081
\(582\) −5.69162e16 −0.0607067
\(583\) 1.68255e18 1.77469
\(584\) 8.31789e17 0.867620
\(585\) −4.18763e16 −0.0431972
\(586\) 3.57010e17 0.364205
\(587\) 1.48954e17 0.150281 0.0751407 0.997173i \(-0.476059\pi\)
0.0751407 + 0.997173i \(0.476059\pi\)
\(588\) −1.24592e17 −0.124319
\(589\) 1.30116e18 1.28405
\(590\) 7.18928e16 0.0701693
\(591\) 9.12251e16 0.0880635
\(592\) −1.31757e18 −1.25801
\(593\) 1.21099e18 1.14363 0.571813 0.820384i \(-0.306240\pi\)
0.571813 + 0.820384i \(0.306240\pi\)
\(594\) −2.48312e17 −0.231946
\(595\) 5.35017e17 0.494319
\(596\) −2.61982e15 −0.00239426
\(597\) −8.88375e17 −0.803088
\(598\) 3.19149e17 0.285388
\(599\) −1.99866e18 −1.76793 −0.883963 0.467556i \(-0.845134\pi\)
−0.883963 + 0.467556i \(0.845134\pi\)
\(600\) −3.52889e17 −0.308784
\(601\) 7.84877e17 0.679388 0.339694 0.940536i \(-0.389677\pi\)
0.339694 + 0.940536i \(0.389677\pi\)
\(602\) −5.09178e17 −0.436006
\(603\) 2.19862e16 0.0186246
\(604\) −5.26721e17 −0.441409
\(605\) −3.82956e15 −0.00317496
\(606\) 3.57464e16 0.0293197
\(607\) 1.47836e17 0.119965 0.0599823 0.998199i \(-0.480896\pi\)
0.0599823 + 0.998199i \(0.480896\pi\)
\(608\) −1.85755e18 −1.49131
\(609\) −6.67023e17 −0.529820
\(610\) −2.94188e17 −0.231197
\(611\) 3.11438e17 0.242161
\(612\) 2.94682e17 0.226710
\(613\) −7.80291e17 −0.593969 −0.296984 0.954882i \(-0.595981\pi\)
−0.296984 + 0.954882i \(0.595981\pi\)
\(614\) 9.88464e17 0.744503
\(615\) 4.60930e17 0.343516
\(616\) −6.52910e17 −0.481480
\(617\) 1.41434e18 1.03205 0.516024 0.856574i \(-0.327411\pi\)
0.516024 + 0.856574i \(0.327411\pi\)
\(618\) −1.15543e18 −0.834292
\(619\) −2.15988e17 −0.154326 −0.0771632 0.997018i \(-0.524586\pi\)
−0.0771632 + 0.997018i \(0.524586\pi\)
\(620\) 2.00058e17 0.141452
\(621\) −2.26345e17 −0.158371
\(622\) −1.52377e18 −1.05507
\(623\) −3.31266e16 −0.0226989
\(624\) −3.06502e17 −0.207842
\(625\) 6.50207e17 0.436347
\(626\) 2.36287e17 0.156930
\(627\) −1.58853e18 −1.04413
\(628\) 1.22042e18 0.793913
\(629\) 2.40975e18 1.55147
\(630\) −2.01987e17 −0.128710
\(631\) −1.79839e18 −1.13421 −0.567106 0.823645i \(-0.691937\pi\)
−0.567106 + 0.823645i \(0.691937\pi\)
\(632\) −4.86295e17 −0.303556
\(633\) −1.01426e18 −0.626652
\(634\) −1.83530e18 −1.12235
\(635\) 4.43362e17 0.268367
\(636\) 7.53844e17 0.451658
\(637\) −2.37009e17 −0.140559
\(638\) −2.62986e18 −1.54383
\(639\) −3.67574e17 −0.213594
\(640\) 8.82541e17 0.507651
\(641\) 2.38786e18 1.35966 0.679831 0.733369i \(-0.262053\pi\)
0.679831 + 0.733369i \(0.262053\pi\)
\(642\) −1.53645e18 −0.866046
\(643\) 5.98871e17 0.334166 0.167083 0.985943i \(-0.446565\pi\)
0.167083 + 0.985943i \(0.446565\pi\)
\(644\) 4.72121e17 0.260793
\(645\) 2.40110e17 0.131302
\(646\) 6.14678e18 3.32764
\(647\) −2.24528e18 −1.20335 −0.601677 0.798740i \(-0.705500\pi\)
−0.601677 + 0.798740i \(0.705500\pi\)
\(648\) 1.40244e17 0.0744126
\(649\) 2.48711e17 0.130649
\(650\) 5.32526e17 0.276952
\(651\) 5.72361e17 0.294709
\(652\) −7.09658e17 −0.361776
\(653\) −1.57701e18 −0.795972 −0.397986 0.917392i \(-0.630291\pi\)
−0.397986 + 0.917392i \(0.630291\pi\)
\(654\) −1.06978e18 −0.534613
\(655\) −1.56808e17 −0.0775889
\(656\) 3.37366e18 1.65282
\(657\) 8.90213e17 0.431836
\(658\) 1.50220e18 0.721539
\(659\) −3.46469e17 −0.164782 −0.0823908 0.996600i \(-0.526256\pi\)
−0.0823908 + 0.996600i \(0.526256\pi\)
\(660\) −2.44242e17 −0.115023
\(661\) 7.70176e17 0.359154 0.179577 0.983744i \(-0.442527\pi\)
0.179577 + 0.983744i \(0.442527\pi\)
\(662\) 2.54425e18 1.17485
\(663\) 5.60571e17 0.256326
\(664\) −2.45848e18 −1.11320
\(665\) −1.29218e18 −0.579403
\(666\) −9.09762e17 −0.403966
\(667\) −2.39721e18 −1.05412
\(668\) −1.62454e18 −0.707428
\(669\) 7.70864e16 0.0332436
\(670\) 7.05129e16 0.0301149
\(671\) −1.01774e18 −0.430466
\(672\) −8.17110e17 −0.342279
\(673\) −9.65115e17 −0.400388 −0.200194 0.979756i \(-0.564157\pi\)
−0.200194 + 0.979756i \(0.564157\pi\)
\(674\) −1.29907e18 −0.533756
\(675\) −3.77675e17 −0.153690
\(676\) −1.00605e18 −0.405477
\(677\) −3.92149e18 −1.56540 −0.782699 0.622400i \(-0.786158\pi\)
−0.782699 + 0.622400i \(0.786158\pi\)
\(678\) −1.77463e18 −0.701640
\(679\) −1.60167e17 −0.0627218
\(680\) −1.19137e18 −0.462102
\(681\) −2.44307e18 −0.938598
\(682\) 2.25664e18 0.858744
\(683\) 6.77789e16 0.0255482 0.0127741 0.999918i \(-0.495934\pi\)
0.0127741 + 0.999918i \(0.495934\pi\)
\(684\) −7.11718e17 −0.265732
\(685\) −1.90162e18 −0.703290
\(686\) −3.49176e18 −1.27920
\(687\) 5.55357e16 0.0201536
\(688\) 1.75742e18 0.631759
\(689\) 1.43403e18 0.510661
\(690\) −7.25922e17 −0.256077
\(691\) −4.59196e18 −1.60469 −0.802344 0.596862i \(-0.796414\pi\)
−0.802344 + 0.596862i \(0.796414\pi\)
\(692\) 2.14163e17 0.0741402
\(693\) −6.98770e17 −0.239645
\(694\) −1.77055e18 −0.601550
\(695\) 4.56896e17 0.153786
\(696\) 1.48532e18 0.495289
\(697\) −6.17018e18 −2.03838
\(698\) −3.07299e17 −0.100578
\(699\) 7.25464e17 0.235242
\(700\) 7.87772e17 0.253083
\(701\) −3.91029e18 −1.24463 −0.622317 0.782765i \(-0.713808\pi\)
−0.622317 + 0.782765i \(0.713808\pi\)
\(702\) −2.11635e17 −0.0667415
\(703\) −5.82003e18 −1.81851
\(704\) 8.19568e17 0.253725
\(705\) −7.08384e17 −0.217290
\(706\) 5.66357e18 1.72131
\(707\) 1.00593e17 0.0302930
\(708\) 1.11431e17 0.0332500
\(709\) 3.21057e18 0.949252 0.474626 0.880188i \(-0.342583\pi\)
0.474626 + 0.880188i \(0.342583\pi\)
\(710\) −1.17886e18 −0.345370
\(711\) −5.20452e17 −0.151087
\(712\) 7.37659e16 0.0212195
\(713\) 2.05701e18 0.586346
\(714\) 2.70387e18 0.763745
\(715\) −4.64619e17 −0.130049
\(716\) 1.06409e18 0.295151
\(717\) −1.97944e18 −0.544087
\(718\) −1.92203e18 −0.523542
\(719\) 6.18425e18 1.66936 0.834679 0.550737i \(-0.185653\pi\)
0.834679 + 0.550737i \(0.185653\pi\)
\(720\) 6.97157e17 0.186496
\(721\) −3.25147e18 −0.861986
\(722\) −1.02745e19 −2.69942
\(723\) 2.51644e17 0.0655220
\(724\) −4.98631e17 −0.128670
\(725\) −3.99994e18 −1.02296
\(726\) −1.93538e16 −0.00490545
\(727\) −3.41497e18 −0.857855 −0.428927 0.903339i \(-0.641108\pi\)
−0.428927 + 0.903339i \(0.641108\pi\)
\(728\) −5.56471e17 −0.138544
\(729\) 1.50095e17 0.0370370
\(730\) 2.85504e18 0.698254
\(731\) −3.21420e18 −0.779130
\(732\) −4.55982e17 −0.109553
\(733\) 7.38761e18 1.75925 0.879626 0.475667i \(-0.157793\pi\)
0.879626 + 0.475667i \(0.157793\pi\)
\(734\) 9.83600e17 0.232164
\(735\) 5.39090e17 0.126123
\(736\) −2.93661e18 −0.680989
\(737\) 2.43937e17 0.0560712
\(738\) 2.32945e18 0.530747
\(739\) 1.68606e18 0.380790 0.190395 0.981708i \(-0.439023\pi\)
0.190395 + 0.981708i \(0.439023\pi\)
\(740\) −8.94849e17 −0.200329
\(741\) −1.35389e18 −0.300446
\(742\) 6.91694e18 1.52156
\(743\) 4.13569e18 0.901821 0.450910 0.892569i \(-0.351099\pi\)
0.450910 + 0.892569i \(0.351099\pi\)
\(744\) −1.27452e18 −0.275502
\(745\) 1.13356e16 0.00242901
\(746\) −7.94874e16 −0.0168848
\(747\) −2.63116e18 −0.554069
\(748\) 3.26951e18 0.682531
\(749\) −4.32369e18 −0.894794
\(750\) −2.72800e18 −0.559688
\(751\) 2.78525e18 0.566507 0.283253 0.959045i \(-0.408586\pi\)
0.283253 + 0.959045i \(0.408586\pi\)
\(752\) −5.18482e18 −1.04549
\(753\) 8.33305e17 0.166585
\(754\) −2.24141e18 −0.444230
\(755\) 2.27905e18 0.447815
\(756\) −3.13074e17 −0.0609895
\(757\) −6.22247e18 −1.20182 −0.600911 0.799316i \(-0.705195\pi\)
−0.600911 + 0.799316i \(0.705195\pi\)
\(758\) 5.48873e18 1.05105
\(759\) −2.51131e18 −0.476792
\(760\) 2.87740e18 0.541641
\(761\) −6.95135e18 −1.29738 −0.648692 0.761051i \(-0.724684\pi\)
−0.648692 + 0.761051i \(0.724684\pi\)
\(762\) 2.24066e18 0.414638
\(763\) −3.01045e18 −0.552359
\(764\) −2.37343e18 −0.431786
\(765\) −1.27505e18 −0.230000
\(766\) −2.19186e18 −0.392037
\(767\) 2.11975e17 0.0375936
\(768\) 3.63012e18 0.638370
\(769\) 9.83745e18 1.71538 0.857692 0.514164i \(-0.171898\pi\)
0.857692 + 0.514164i \(0.171898\pi\)
\(770\) −2.24105e18 −0.387492
\(771\) −2.43123e18 −0.416844
\(772\) 3.49122e18 0.593560
\(773\) 3.78743e18 0.638525 0.319262 0.947666i \(-0.396565\pi\)
0.319262 + 0.947666i \(0.396565\pi\)
\(774\) 1.21347e18 0.202868
\(775\) 3.43228e18 0.569012
\(776\) 3.56657e17 0.0586339
\(777\) −2.56014e18 −0.417376
\(778\) 9.61502e18 1.55447
\(779\) 1.49022e19 2.38923
\(780\) −2.08166e17 −0.0330974
\(781\) −4.07825e18 −0.643046
\(782\) 9.71745e18 1.51953
\(783\) 1.58964e18 0.246518
\(784\) 3.94572e18 0.606837
\(785\) −5.28060e18 −0.805435
\(786\) −7.92477e17 −0.119878
\(787\) 1.63498e18 0.245288 0.122644 0.992451i \(-0.460863\pi\)
0.122644 + 0.992451i \(0.460863\pi\)
\(788\) 4.53477e17 0.0674737
\(789\) 5.80098e17 0.0856053
\(790\) −1.66916e18 −0.244300
\(791\) −4.99394e18 −0.724931
\(792\) 1.55601e18 0.224026
\(793\) −8.67409e17 −0.123865
\(794\) 1.62549e19 2.30225
\(795\) −3.26178e18 −0.458213
\(796\) −4.41608e18 −0.615321
\(797\) 7.73550e18 1.06908 0.534539 0.845144i \(-0.320485\pi\)
0.534539 + 0.845144i \(0.320485\pi\)
\(798\) −6.53041e18 −0.895203
\(799\) 9.48267e18 1.28937
\(800\) −4.89997e18 −0.660858
\(801\) 7.89471e16 0.0105615
\(802\) 1.63987e19 2.17608
\(803\) 9.87694e18 1.30008
\(804\) 1.09293e17 0.0142701
\(805\) −2.04280e18 −0.264578
\(806\) 1.92332e18 0.247100
\(807\) −6.48474e18 −0.826446
\(808\) −2.23999e17 −0.0283187
\(809\) −1.10550e18 −0.138642 −0.0693210 0.997594i \(-0.522083\pi\)
−0.0693210 + 0.997594i \(0.522083\pi\)
\(810\) 4.81375e17 0.0598868
\(811\) −7.65197e18 −0.944360 −0.472180 0.881502i \(-0.656533\pi\)
−0.472180 + 0.881502i \(0.656533\pi\)
\(812\) −3.31575e18 −0.405945
\(813\) −3.90558e18 −0.474348
\(814\) −1.00938e19 −1.21618
\(815\) 3.07059e18 0.367027
\(816\) −9.33238e18 −1.10664
\(817\) 7.76295e18 0.913236
\(818\) 1.38578e19 1.61733
\(819\) −5.95557e17 −0.0689569
\(820\) 2.29127e18 0.263200
\(821\) 4.27254e18 0.486918 0.243459 0.969911i \(-0.421718\pi\)
0.243459 + 0.969911i \(0.421718\pi\)
\(822\) −9.61040e18 −1.08661
\(823\) 5.01299e18 0.562339 0.281169 0.959658i \(-0.409278\pi\)
0.281169 + 0.959658i \(0.409278\pi\)
\(824\) 7.24032e18 0.805807
\(825\) −4.19032e18 −0.462697
\(826\) 1.02245e18 0.112013
\(827\) 8.17322e18 0.888397 0.444199 0.895928i \(-0.353488\pi\)
0.444199 + 0.895928i \(0.353488\pi\)
\(828\) −1.12516e18 −0.121343
\(829\) 1.32811e19 1.42112 0.710559 0.703637i \(-0.248442\pi\)
0.710559 + 0.703637i \(0.248442\pi\)
\(830\) −8.43852e18 −0.895898
\(831\) −4.52180e18 −0.476327
\(832\) 6.98512e17 0.0730083
\(833\) −7.21645e18 −0.748395
\(834\) 2.30906e18 0.237606
\(835\) 7.02914e18 0.717695
\(836\) −7.89653e18 −0.800010
\(837\) −1.36405e18 −0.137124
\(838\) 1.70366e19 1.69940
\(839\) 6.20921e18 0.614587 0.307293 0.951615i \(-0.400577\pi\)
0.307293 + 0.951615i \(0.400577\pi\)
\(840\) 1.26572e18 0.124315
\(841\) 6.57522e18 0.640821
\(842\) 2.03057e19 1.96376
\(843\) 7.35089e18 0.705441
\(844\) −5.04187e18 −0.480138
\(845\) 4.35304e18 0.411362
\(846\) −3.58003e18 −0.335722
\(847\) −5.44633e16 −0.00506829
\(848\) −2.38737e19 −2.20469
\(849\) −6.48630e18 −0.594425
\(850\) 1.62143e19 1.47461
\(851\) −9.20089e18 −0.830401
\(852\) −1.82720e18 −0.163655
\(853\) 8.60050e18 0.764460 0.382230 0.924067i \(-0.375156\pi\)
0.382230 + 0.924067i \(0.375156\pi\)
\(854\) −4.18389e18 −0.369066
\(855\) 3.07950e18 0.269588
\(856\) 9.62793e18 0.836476
\(857\) 1.07445e18 0.0926426 0.0463213 0.998927i \(-0.485250\pi\)
0.0463213 + 0.998927i \(0.485250\pi\)
\(858\) −2.34809e18 −0.200931
\(859\) 4.33075e18 0.367797 0.183898 0.982945i \(-0.441128\pi\)
0.183898 + 0.982945i \(0.441128\pi\)
\(860\) 1.19358e18 0.100603
\(861\) 6.55526e18 0.548365
\(862\) −2.89515e18 −0.240366
\(863\) 3.00588e17 0.0247686 0.0123843 0.999923i \(-0.496058\pi\)
0.0123843 + 0.999923i \(0.496058\pi\)
\(864\) 1.94733e18 0.159258
\(865\) −9.26651e17 −0.0752163
\(866\) 4.05530e18 0.326705
\(867\) 9.84783e18 0.787438
\(868\) 2.84519e18 0.225804
\(869\) −5.77442e18 −0.454863
\(870\) 5.09822e18 0.398605
\(871\) 2.07906e17 0.0161343
\(872\) 6.70361e18 0.516359
\(873\) 3.81708e17 0.0291836
\(874\) −2.34696e19 −1.78107
\(875\) −7.67680e18 −0.578266
\(876\) 4.42522e18 0.330871
\(877\) 5.68672e18 0.422051 0.211025 0.977481i \(-0.432320\pi\)
0.211025 + 0.977481i \(0.432320\pi\)
\(878\) −1.82122e19 −1.34168
\(879\) −2.39428e18 −0.175085
\(880\) 7.73497e18 0.561463
\(881\) −2.30035e19 −1.65749 −0.828744 0.559628i \(-0.810944\pi\)
−0.828744 + 0.559628i \(0.810944\pi\)
\(882\) 2.72446e18 0.194865
\(883\) 1.11208e19 0.789571 0.394786 0.918773i \(-0.370819\pi\)
0.394786 + 0.918773i \(0.370819\pi\)
\(884\) 2.78658e18 0.196396
\(885\) −4.82148e17 −0.0337326
\(886\) 1.75640e19 1.21984
\(887\) −1.02391e19 −0.705923 −0.352962 0.935638i \(-0.614825\pi\)
−0.352962 + 0.935638i \(0.614825\pi\)
\(888\) 5.70088e18 0.390174
\(889\) 6.30541e18 0.428402
\(890\) 2.53195e17 0.0170773
\(891\) 1.66530e18 0.111503
\(892\) 3.83194e17 0.0254711
\(893\) −2.29026e19 −1.51130
\(894\) 5.72879e16 0.00375292
\(895\) −4.60417e18 −0.299435
\(896\) 1.25513e19 0.810379
\(897\) −2.14037e18 −0.137195
\(898\) 7.55483e18 0.480760
\(899\) −1.44465e19 −0.912696
\(900\) −1.87741e18 −0.117756
\(901\) 4.36633e19 2.71898
\(902\) 2.58453e19 1.59786
\(903\) 3.41480e18 0.209602
\(904\) 1.11204e19 0.677684
\(905\) 2.15751e18 0.130538
\(906\) 1.15179e19 0.691893
\(907\) 1.48848e19 0.887761 0.443881 0.896086i \(-0.353601\pi\)
0.443881 + 0.896086i \(0.353601\pi\)
\(908\) −1.21444e19 −0.719149
\(909\) −2.39733e17 −0.0140949
\(910\) −1.91004e18 −0.111499
\(911\) 1.33460e19 0.773540 0.386770 0.922176i \(-0.373591\pi\)
0.386770 + 0.922176i \(0.373591\pi\)
\(912\) 2.25396e19 1.29712
\(913\) −2.91928e19 −1.66808
\(914\) 9.54639e18 0.541613
\(915\) 1.97297e18 0.111143
\(916\) 2.76066e17 0.0154416
\(917\) −2.23009e18 −0.123857
\(918\) −6.44385e18 −0.355360
\(919\) −2.89001e19 −1.58252 −0.791260 0.611480i \(-0.790575\pi\)
−0.791260 + 0.611480i \(0.790575\pi\)
\(920\) 4.54888e18 0.247334
\(921\) −6.62912e18 −0.357906
\(922\) −4.03264e19 −2.16191
\(923\) −3.47586e18 −0.185034
\(924\) −3.47356e18 −0.183615
\(925\) −1.53524e19 −0.805852
\(926\) 1.14828e19 0.598519
\(927\) 7.74888e18 0.401070
\(928\) 2.06241e19 1.06002
\(929\) 1.62264e19 0.828169 0.414085 0.910238i \(-0.364102\pi\)
0.414085 + 0.910238i \(0.364102\pi\)
\(930\) −4.37469e18 −0.221722
\(931\) 1.74292e19 0.877212
\(932\) 3.60626e18 0.180241
\(933\) 1.02191e19 0.507204
\(934\) −1.45670e19 −0.717983
\(935\) −1.41467e19 −0.692436
\(936\) 1.32618e18 0.0644627
\(937\) 2.81456e19 1.35864 0.679318 0.733844i \(-0.262276\pi\)
0.679318 + 0.733844i \(0.262276\pi\)
\(938\) 1.00282e18 0.0480734
\(939\) −1.58466e18 −0.0754412
\(940\) −3.52135e18 −0.166486
\(941\) −2.97283e19 −1.39585 −0.697923 0.716172i \(-0.745892\pi\)
−0.697923 + 0.716172i \(0.745892\pi\)
\(942\) −2.66871e19 −1.24443
\(943\) 2.35589e19 1.09101
\(944\) −3.52896e18 −0.162304
\(945\) 1.35463e18 0.0618747
\(946\) 1.34635e19 0.610752
\(947\) −1.34786e19 −0.607253 −0.303626 0.952791i \(-0.598197\pi\)
−0.303626 + 0.952791i \(0.598197\pi\)
\(948\) −2.58715e18 −0.115762
\(949\) 8.41804e18 0.374094
\(950\) −3.91609e19 −1.72842
\(951\) 1.23084e19 0.539546
\(952\) −1.69434e19 −0.737668
\(953\) 8.08120e18 0.349440 0.174720 0.984618i \(-0.444098\pi\)
0.174720 + 0.984618i \(0.444098\pi\)
\(954\) −1.64844e19 −0.707960
\(955\) 1.02695e19 0.438053
\(956\) −9.83973e18 −0.416876
\(957\) 1.76371e19 0.742166
\(958\) 3.25753e19 1.36148
\(959\) −2.70444e19 −1.12268
\(960\) −1.58880e18 −0.0655099
\(961\) −1.20212e19 −0.492319
\(962\) −8.60290e18 −0.349951
\(963\) 1.03042e19 0.416335
\(964\) 1.25091e18 0.0502026
\(965\) −1.51060e19 −0.602174
\(966\) −1.03239e19 −0.408784
\(967\) 1.29236e19 0.508290 0.254145 0.967166i \(-0.418206\pi\)
0.254145 + 0.967166i \(0.418206\pi\)
\(968\) 1.21278e17 0.00473797
\(969\) −4.12233e19 −1.59970
\(970\) 1.22419e18 0.0471882
\(971\) 4.54011e19 1.73837 0.869184 0.494489i \(-0.164645\pi\)
0.869184 + 0.494489i \(0.164645\pi\)
\(972\) 7.46115e17 0.0283776
\(973\) 6.49789e18 0.245493
\(974\) −4.61384e19 −1.73153
\(975\) −3.57138e18 −0.133139
\(976\) 1.44406e19 0.534764
\(977\) −1.55782e19 −0.573062 −0.286531 0.958071i \(-0.592502\pi\)
−0.286531 + 0.958071i \(0.592502\pi\)
\(978\) 1.55182e19 0.567072
\(979\) 8.75920e17 0.0317963
\(980\) 2.67980e18 0.0966346
\(981\) 7.17447e18 0.257005
\(982\) −3.06617e18 −0.109112
\(983\) −8.04089e18 −0.284254 −0.142127 0.989848i \(-0.545394\pi\)
−0.142127 + 0.989848i \(0.545394\pi\)
\(984\) −1.45972e19 −0.512625
\(985\) −1.96213e18 −0.0684530
\(986\) −6.82465e19 −2.36527
\(987\) −1.00745e19 −0.346866
\(988\) −6.73016e18 −0.230200
\(989\) 1.22724e19 0.417018
\(990\) 5.34086e18 0.180295
\(991\) −4.02795e18 −0.135085 −0.0675423 0.997716i \(-0.521516\pi\)
−0.0675423 + 0.997716i \(0.521516\pi\)
\(992\) −1.76971e19 −0.589627
\(993\) −1.70630e19 −0.564788
\(994\) −1.67656e19 −0.551324
\(995\) 1.91078e19 0.624252
\(996\) −1.30794e19 −0.424525
\(997\) −6.13845e19 −1.97943 −0.989715 0.143052i \(-0.954308\pi\)
−0.989715 + 0.143052i \(0.954308\pi\)
\(998\) 1.05983e19 0.339537
\(999\) 6.10131e18 0.194199
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.1.8 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.a.1.8 30 1.1 even 1 trivial