Properties

Label 177.12.a.a.1.10
Level $177$
Weight $12$
Character 177.1
Self dual yes
Analytic conductor $135.997$
Analytic rank $1$
Dimension $26$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(135.996742959\)
Analytic rank: \(1\)
Dimension: \(26\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-35.6107 q^{2} -243.000 q^{3} -779.875 q^{4} -1849.70 q^{5} +8653.41 q^{6} +64152.0 q^{7} +100703. q^{8} +59049.0 q^{9} +O(q^{10})\) \(q-35.6107 q^{2} -243.000 q^{3} -779.875 q^{4} -1849.70 q^{5} +8653.41 q^{6} +64152.0 q^{7} +100703. q^{8} +59049.0 q^{9} +65869.2 q^{10} -256626. q^{11} +189510. q^{12} +1.02774e6 q^{13} -2.28450e6 q^{14} +449477. q^{15} -1.98891e6 q^{16} -1.90460e6 q^{17} -2.10278e6 q^{18} -1.21243e7 q^{19} +1.44254e6 q^{20} -1.55889e7 q^{21} +9.13866e6 q^{22} -3.64620e6 q^{23} -2.44708e7 q^{24} -4.54067e7 q^{25} -3.65987e7 q^{26} -1.43489e7 q^{27} -5.00306e7 q^{28} +2.53853e7 q^{29} -1.60062e7 q^{30} +5.61268e7 q^{31} -1.35412e8 q^{32} +6.23602e7 q^{33} +6.78242e7 q^{34} -1.18662e8 q^{35} -4.60509e7 q^{36} -5.07666e7 q^{37} +4.31756e8 q^{38} -2.49742e8 q^{39} -1.86270e8 q^{40} +1.16411e9 q^{41} +5.55134e8 q^{42} -1.61126e8 q^{43} +2.00137e8 q^{44} -1.09223e8 q^{45} +1.29844e8 q^{46} -7.75113e6 q^{47} +4.83306e8 q^{48} +2.13815e9 q^{49} +1.61697e9 q^{50} +4.62818e8 q^{51} -8.01511e8 q^{52} +3.09350e9 q^{53} +5.10975e8 q^{54} +4.74682e8 q^{55} +6.46028e9 q^{56} +2.94621e9 q^{57} -9.03990e8 q^{58} +7.14924e8 q^{59} -3.50536e8 q^{60} -6.22795e9 q^{61} -1.99872e9 q^{62} +3.78811e9 q^{63} +8.89543e9 q^{64} -1.90102e9 q^{65} -2.22069e9 q^{66} -1.55950e10 q^{67} +1.48535e9 q^{68} +8.86026e8 q^{69} +4.22564e9 q^{70} -2.68594e10 q^{71} +5.94640e9 q^{72} +2.50826e10 q^{73} +1.80783e9 q^{74} +1.10338e10 q^{75} +9.45547e9 q^{76} -1.64631e10 q^{77} +8.89348e9 q^{78} -1.58824e10 q^{79} +3.67889e9 q^{80} +3.48678e9 q^{81} -4.14548e10 q^{82} +3.36086e10 q^{83} +1.21574e10 q^{84} +3.52294e9 q^{85} +5.73782e9 q^{86} -6.16863e9 q^{87} -2.58430e10 q^{88} +1.40070e10 q^{89} +3.88951e9 q^{90} +6.59318e10 q^{91} +2.84358e9 q^{92} -1.36388e10 q^{93} +2.76023e8 q^{94} +2.24264e10 q^{95} +3.29052e10 q^{96} +7.46648e10 q^{97} -7.61412e10 q^{98} -1.51535e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 26q - 78q^{2} - 6318q^{3} + 23070q^{4} + 3808q^{5} + 18954q^{6} - 98819q^{7} - 117645q^{8} + 1535274q^{9} + O(q^{10}) \) \( 26q - 78q^{2} - 6318q^{3} + 23070q^{4} + 3808q^{5} + 18954q^{6} - 98819q^{7} - 117645q^{8} + 1535274q^{9} - 859751q^{10} + 579094q^{11} - 5606010q^{12} - 2018538q^{13} + 4157413q^{14} - 925344q^{15} + 20190274q^{16} - 13084493q^{17} - 4605822q^{18} + 9917231q^{19} + 10165633q^{20} + 24013017q^{21} - 89820518q^{22} - 63513223q^{23} + 28587735q^{24} + 218986852q^{25} - 77999532q^{26} - 373071582q^{27} - 444601862q^{28} + 81530981q^{29} + 208919493q^{30} - 408861231q^{31} - 26253128q^{32} - 140719842q^{33} - 508910076q^{34} - 75731421q^{35} + 1362260430q^{36} - 802381301q^{37} + 732704675q^{38} + 490504734q^{39} - 646130800q^{40} - 1354472849q^{41} - 1010251359q^{42} + 282952194q^{43} + 1846047996q^{44} + 224858592q^{45} + 9629305849q^{46} - 1196794197q^{47} - 4906236582q^{48} + 10889725683q^{49} - 6236232091q^{50} + 3179531799q^{51} - 1968200812q^{52} - 8276044236q^{53} + 1119214746q^{54} - 6672895076q^{55} + 2579741342q^{56} - 2409887133q^{57} - 9401656060q^{58} + 18588031774q^{59} - 2470248819q^{60} - 21181559029q^{61} - 6117706514q^{62} - 5835163131q^{63} + 42975855037q^{64} + 25680681860q^{65} + 21826385874q^{66} + 26234163394q^{67} + 19707344091q^{68} + 15433713189q^{69} + 129203099090q^{70} + 52088830406q^{71} - 6946819605q^{72} + 20943384867q^{73} + 41969200146q^{74} - 53213805036q^{75} + 223987219368q^{76} + 94604773153q^{77} + 18953886276q^{78} + 68965662774q^{79} + 218947784293q^{80} + 90656394426q^{81} + 11938614923q^{82} + 17947446393q^{83} + 108038252466q^{84} - 52849386709q^{85} + 384986147852q^{86} - 19812028383q^{87} - 49061112607q^{88} + 38570593981q^{89} - 50767436799q^{90} - 226268806999q^{91} - 79559686310q^{92} + 99353279133q^{93} - 16709400108q^{94} - 252795831501q^{95} + 6379510104q^{96} - 186894587836q^{97} - 252443311612q^{98} + 34194921606q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −35.6107 −0.786894 −0.393447 0.919347i \(-0.628717\pi\)
−0.393447 + 0.919347i \(0.628717\pi\)
\(3\) −243.000 −0.577350
\(4\) −779.875 −0.380799
\(5\) −1849.70 −0.264708 −0.132354 0.991203i \(-0.542253\pi\)
−0.132354 + 0.991203i \(0.542253\pi\)
\(6\) 8653.41 0.454313
\(7\) 64152.0 1.44268 0.721342 0.692579i \(-0.243526\pi\)
0.721342 + 0.692579i \(0.243526\pi\)
\(8\) 100703. 1.08654
\(9\) 59049.0 0.333333
\(10\) 65869.2 0.208297
\(11\) −256626. −0.480443 −0.240221 0.970718i \(-0.577220\pi\)
−0.240221 + 0.970718i \(0.577220\pi\)
\(12\) 189510. 0.219854
\(13\) 1.02774e6 0.767708 0.383854 0.923394i \(-0.374597\pi\)
0.383854 + 0.923394i \(0.374597\pi\)
\(14\) −2.28450e6 −1.13524
\(15\) 449477. 0.152829
\(16\) −1.98891e6 −0.474194
\(17\) −1.90460e6 −0.325338 −0.162669 0.986681i \(-0.552010\pi\)
−0.162669 + 0.986681i \(0.552010\pi\)
\(18\) −2.10278e6 −0.262298
\(19\) −1.21243e7 −1.12334 −0.561672 0.827360i \(-0.689842\pi\)
−0.561672 + 0.827360i \(0.689842\pi\)
\(20\) 1.44254e6 0.100800
\(21\) −1.55889e7 −0.832934
\(22\) 9.13866e6 0.378057
\(23\) −3.64620e6 −0.118124 −0.0590619 0.998254i \(-0.518811\pi\)
−0.0590619 + 0.998254i \(0.518811\pi\)
\(24\) −2.44708e7 −0.627315
\(25\) −4.54067e7 −0.929930
\(26\) −3.65987e7 −0.604104
\(27\) −1.43489e7 −0.192450
\(28\) −5.00306e7 −0.549372
\(29\) 2.53853e7 0.229823 0.114911 0.993376i \(-0.463342\pi\)
0.114911 + 0.993376i \(0.463342\pi\)
\(30\) −1.60062e7 −0.120260
\(31\) 5.61268e7 0.352112 0.176056 0.984380i \(-0.443666\pi\)
0.176056 + 0.984380i \(0.443666\pi\)
\(32\) −1.35412e8 −0.713401
\(33\) 6.23602e7 0.277384
\(34\) 6.78242e7 0.256006
\(35\) −1.18662e8 −0.381889
\(36\) −4.60509e7 −0.126933
\(37\) −5.07666e7 −0.120356 −0.0601781 0.998188i \(-0.519167\pi\)
−0.0601781 + 0.998188i \(0.519167\pi\)
\(38\) 4.31756e8 0.883953
\(39\) −2.49742e8 −0.443236
\(40\) −1.86270e8 −0.287616
\(41\) 1.16411e9 1.56922 0.784608 0.619992i \(-0.212864\pi\)
0.784608 + 0.619992i \(0.212864\pi\)
\(42\) 5.55134e8 0.655430
\(43\) −1.61126e8 −0.167144 −0.0835718 0.996502i \(-0.526633\pi\)
−0.0835718 + 0.996502i \(0.526633\pi\)
\(44\) 2.00137e8 0.182952
\(45\) −1.09223e8 −0.0882359
\(46\) 1.29844e8 0.0929508
\(47\) −7.75113e6 −0.00492977 −0.00246488 0.999997i \(-0.500785\pi\)
−0.00246488 + 0.999997i \(0.500785\pi\)
\(48\) 4.83306e8 0.273776
\(49\) 2.13815e9 1.08134
\(50\) 1.61697e9 0.731756
\(51\) 4.62818e8 0.187834
\(52\) −8.01511e8 −0.292342
\(53\) 3.09350e9 1.01609 0.508046 0.861330i \(-0.330368\pi\)
0.508046 + 0.861330i \(0.330368\pi\)
\(54\) 5.10975e8 0.151438
\(55\) 4.74682e8 0.127177
\(56\) 6.46028e9 1.56754
\(57\) 2.94621e9 0.648563
\(58\) −9.03990e8 −0.180846
\(59\) 7.14924e8 0.130189
\(60\) −3.50536e8 −0.0581970
\(61\) −6.22795e9 −0.944128 −0.472064 0.881564i \(-0.656491\pi\)
−0.472064 + 0.881564i \(0.656491\pi\)
\(62\) −1.99872e9 −0.277075
\(63\) 3.78811e9 0.480894
\(64\) 8.89543e9 1.03556
\(65\) −1.90102e9 −0.203218
\(66\) −2.22069e9 −0.218271
\(67\) −1.55950e10 −1.41115 −0.705576 0.708634i \(-0.749312\pi\)
−0.705576 + 0.708634i \(0.749312\pi\)
\(68\) 1.48535e9 0.123888
\(69\) 8.86026e8 0.0681988
\(70\) 4.22564e9 0.300506
\(71\) −2.68594e10 −1.76675 −0.883376 0.468664i \(-0.844735\pi\)
−0.883376 + 0.468664i \(0.844735\pi\)
\(72\) 5.94640e9 0.362180
\(73\) 2.50826e10 1.41611 0.708056 0.706157i \(-0.249573\pi\)
0.708056 + 0.706157i \(0.249573\pi\)
\(74\) 1.80783e9 0.0947075
\(75\) 1.10338e10 0.536895
\(76\) 9.45547e9 0.427768
\(77\) −1.64631e10 −0.693127
\(78\) 8.89348e9 0.348780
\(79\) −1.58824e10 −0.580721 −0.290361 0.956917i \(-0.593775\pi\)
−0.290361 + 0.956917i \(0.593775\pi\)
\(80\) 3.67889e9 0.125523
\(81\) 3.48678e9 0.111111
\(82\) −4.14548e10 −1.23481
\(83\) 3.36086e10 0.936528 0.468264 0.883589i \(-0.344880\pi\)
0.468264 + 0.883589i \(0.344880\pi\)
\(84\) 1.21574e10 0.317180
\(85\) 3.52294e9 0.0861194
\(86\) 5.73782e9 0.131524
\(87\) −6.16863e9 −0.132688
\(88\) −2.58430e10 −0.522021
\(89\) 1.40070e10 0.265889 0.132944 0.991123i \(-0.457557\pi\)
0.132944 + 0.991123i \(0.457557\pi\)
\(90\) 3.88951e9 0.0694322
\(91\) 6.59318e10 1.10756
\(92\) 2.84358e9 0.0449814
\(93\) −1.36388e10 −0.203292
\(94\) 2.76023e8 0.00387920
\(95\) 2.24264e10 0.297358
\(96\) 3.29052e10 0.411882
\(97\) 7.46648e10 0.882818 0.441409 0.897306i \(-0.354479\pi\)
0.441409 + 0.897306i \(0.354479\pi\)
\(98\) −7.61412e10 −0.850896
\(99\) −1.51535e10 −0.160148
\(100\) 3.54116e10 0.354116
\(101\) 2.53766e10 0.240251 0.120126 0.992759i \(-0.461670\pi\)
0.120126 + 0.992759i \(0.461670\pi\)
\(102\) −1.64813e10 −0.147805
\(103\) 8.90840e10 0.757173 0.378586 0.925566i \(-0.376410\pi\)
0.378586 + 0.925566i \(0.376410\pi\)
\(104\) 1.03497e11 0.834147
\(105\) 2.88349e10 0.220484
\(106\) −1.10162e11 −0.799557
\(107\) 5.21521e10 0.359469 0.179734 0.983715i \(-0.442476\pi\)
0.179734 + 0.983715i \(0.442476\pi\)
\(108\) 1.11904e10 0.0732847
\(109\) −3.18182e10 −0.198075 −0.0990377 0.995084i \(-0.531576\pi\)
−0.0990377 + 0.995084i \(0.531576\pi\)
\(110\) −1.69038e10 −0.100075
\(111\) 1.23363e10 0.0694876
\(112\) −1.27593e11 −0.684112
\(113\) 4.14883e9 0.0211833 0.0105917 0.999944i \(-0.496629\pi\)
0.0105917 + 0.999944i \(0.496629\pi\)
\(114\) −1.04917e11 −0.510350
\(115\) 6.74438e9 0.0312683
\(116\) −1.97974e10 −0.0875163
\(117\) 6.06872e10 0.255903
\(118\) −2.54590e10 −0.102445
\(119\) −1.22184e11 −0.469360
\(120\) 4.52636e10 0.166055
\(121\) −2.19455e11 −0.769175
\(122\) 2.21782e11 0.742928
\(123\) −2.82879e11 −0.905987
\(124\) −4.37719e10 −0.134084
\(125\) 1.74306e11 0.510867
\(126\) −1.34897e11 −0.378413
\(127\) −2.47912e11 −0.665850 −0.332925 0.942953i \(-0.608036\pi\)
−0.332925 + 0.942953i \(0.608036\pi\)
\(128\) −3.94482e10 −0.101478
\(129\) 3.91537e10 0.0965004
\(130\) 6.76966e10 0.159911
\(131\) 1.83558e11 0.415700 0.207850 0.978161i \(-0.433353\pi\)
0.207850 + 0.978161i \(0.433353\pi\)
\(132\) −4.86332e10 −0.105627
\(133\) −7.77800e11 −1.62063
\(134\) 5.55349e11 1.11043
\(135\) 2.65412e10 0.0509430
\(136\) −1.91798e11 −0.353493
\(137\) −1.86742e11 −0.330582 −0.165291 0.986245i \(-0.552856\pi\)
−0.165291 + 0.986245i \(0.552856\pi\)
\(138\) −3.15521e10 −0.0536652
\(139\) 6.72902e11 1.09994 0.549972 0.835183i \(-0.314638\pi\)
0.549972 + 0.835183i \(0.314638\pi\)
\(140\) 9.25416e10 0.145423
\(141\) 1.88352e9 0.00284620
\(142\) 9.56484e11 1.39025
\(143\) −2.63746e11 −0.368840
\(144\) −1.17443e11 −0.158065
\(145\) −4.69552e10 −0.0608359
\(146\) −8.93211e11 −1.11433
\(147\) −5.19571e11 −0.624309
\(148\) 3.95916e10 0.0458314
\(149\) −1.23789e12 −1.38089 −0.690445 0.723385i \(-0.742585\pi\)
−0.690445 + 0.723385i \(0.742585\pi\)
\(150\) −3.92923e11 −0.422479
\(151\) −8.09856e11 −0.839527 −0.419763 0.907634i \(-0.637887\pi\)
−0.419763 + 0.907634i \(0.637887\pi\)
\(152\) −1.22095e12 −1.22056
\(153\) −1.12465e11 −0.108446
\(154\) 5.86263e11 0.545417
\(155\) −1.03818e11 −0.0932068
\(156\) 1.94767e11 0.168784
\(157\) −2.64498e10 −0.0221297 −0.0110648 0.999939i \(-0.503522\pi\)
−0.0110648 + 0.999939i \(0.503522\pi\)
\(158\) 5.65585e11 0.456966
\(159\) −7.51721e11 −0.586641
\(160\) 2.50473e11 0.188843
\(161\) −2.33911e11 −0.170415
\(162\) −1.24167e11 −0.0874326
\(163\) 1.81641e12 1.23647 0.618234 0.785994i \(-0.287849\pi\)
0.618234 + 0.785994i \(0.287849\pi\)
\(164\) −9.07860e11 −0.597555
\(165\) −1.15348e11 −0.0734256
\(166\) −1.19683e12 −0.736948
\(167\) 5.52860e11 0.329363 0.164681 0.986347i \(-0.447340\pi\)
0.164681 + 0.986347i \(0.447340\pi\)
\(168\) −1.56985e12 −0.905017
\(169\) −7.35905e11 −0.410625
\(170\) −1.25454e11 −0.0677668
\(171\) −7.15930e11 −0.374448
\(172\) 1.25658e11 0.0636480
\(173\) −6.45797e11 −0.316842 −0.158421 0.987372i \(-0.550640\pi\)
−0.158421 + 0.987372i \(0.550640\pi\)
\(174\) 2.19669e11 0.104412
\(175\) −2.91293e12 −1.34159
\(176\) 5.10408e11 0.227823
\(177\) −1.73727e11 −0.0751646
\(178\) −4.98800e11 −0.209226
\(179\) 6.07973e11 0.247282 0.123641 0.992327i \(-0.460543\pi\)
0.123641 + 0.992327i \(0.460543\pi\)
\(180\) 8.51803e10 0.0336001
\(181\) 1.62761e12 0.622757 0.311378 0.950286i \(-0.399209\pi\)
0.311378 + 0.950286i \(0.399209\pi\)
\(182\) −2.34788e12 −0.871531
\(183\) 1.51339e12 0.545093
\(184\) −3.67182e11 −0.128346
\(185\) 9.39029e10 0.0318592
\(186\) 4.85688e11 0.159969
\(187\) 4.88771e11 0.156306
\(188\) 6.04491e9 0.00187725
\(189\) −9.20511e11 −0.277645
\(190\) −7.98620e11 −0.233989
\(191\) −3.35256e12 −0.954318 −0.477159 0.878817i \(-0.658333\pi\)
−0.477159 + 0.878817i \(0.658333\pi\)
\(192\) −2.16159e12 −0.597884
\(193\) 6.68094e11 0.179586 0.0897930 0.995960i \(-0.471379\pi\)
0.0897930 + 0.995960i \(0.471379\pi\)
\(194\) −2.65887e12 −0.694684
\(195\) 4.61947e11 0.117328
\(196\) −1.66749e12 −0.411771
\(197\) 1.14574e11 0.0275120 0.0137560 0.999905i \(-0.495621\pi\)
0.0137560 + 0.999905i \(0.495621\pi\)
\(198\) 5.39628e11 0.126019
\(199\) −7.33403e12 −1.66591 −0.832954 0.553343i \(-0.813352\pi\)
−0.832954 + 0.553343i \(0.813352\pi\)
\(200\) −4.57258e12 −1.01041
\(201\) 3.78958e12 0.814729
\(202\) −9.03678e11 −0.189052
\(203\) 1.62852e12 0.331562
\(204\) −3.60940e11 −0.0715269
\(205\) −2.15325e12 −0.415383
\(206\) −3.17235e12 −0.595814
\(207\) −2.15304e11 −0.0393746
\(208\) −2.04409e12 −0.364042
\(209\) 3.11142e12 0.539703
\(210\) −1.02683e12 −0.173497
\(211\) −9.42510e12 −1.55143 −0.775716 0.631082i \(-0.782611\pi\)
−0.775716 + 0.631082i \(0.782611\pi\)
\(212\) −2.41255e12 −0.386927
\(213\) 6.52684e12 1.02004
\(214\) −1.85718e12 −0.282864
\(215\) 2.98035e11 0.0442442
\(216\) −1.44497e12 −0.209105
\(217\) 3.60065e12 0.507986
\(218\) 1.13307e12 0.155864
\(219\) −6.09508e12 −0.817592
\(220\) −3.70193e11 −0.0484287
\(221\) −1.95744e12 −0.249765
\(222\) −4.39304e11 −0.0546794
\(223\) −5.99688e12 −0.728197 −0.364098 0.931361i \(-0.618623\pi\)
−0.364098 + 0.931361i \(0.618623\pi\)
\(224\) −8.68698e12 −1.02921
\(225\) −2.68122e12 −0.309977
\(226\) −1.47743e11 −0.0166690
\(227\) 1.12448e13 1.23825 0.619124 0.785293i \(-0.287488\pi\)
0.619124 + 0.785293i \(0.287488\pi\)
\(228\) −2.29768e12 −0.246972
\(229\) −6.49006e12 −0.681010 −0.340505 0.940243i \(-0.610598\pi\)
−0.340505 + 0.940243i \(0.610598\pi\)
\(230\) −2.40172e11 −0.0246048
\(231\) 4.00053e12 0.400177
\(232\) 2.55637e12 0.249712
\(233\) −2.50458e12 −0.238934 −0.119467 0.992838i \(-0.538119\pi\)
−0.119467 + 0.992838i \(0.538119\pi\)
\(234\) −2.16112e12 −0.201368
\(235\) 1.43373e10 0.00130495
\(236\) −5.57552e11 −0.0495757
\(237\) 3.85943e12 0.335279
\(238\) 4.35106e12 0.369336
\(239\) 6.55750e12 0.543938 0.271969 0.962306i \(-0.412325\pi\)
0.271969 + 0.962306i \(0.412325\pi\)
\(240\) −8.93971e11 −0.0724706
\(241\) −6.37839e12 −0.505379 −0.252690 0.967547i \(-0.581315\pi\)
−0.252690 + 0.967547i \(0.581315\pi\)
\(242\) 7.81494e12 0.605259
\(243\) −8.47289e11 −0.0641500
\(244\) 4.85702e12 0.359523
\(245\) −3.95494e12 −0.286238
\(246\) 1.00735e13 0.712916
\(247\) −1.24607e13 −0.862401
\(248\) 5.65212e12 0.382584
\(249\) −8.16688e12 −0.540705
\(250\) −6.20717e12 −0.401998
\(251\) 8.28791e12 0.525097 0.262548 0.964919i \(-0.415437\pi\)
0.262548 + 0.964919i \(0.415437\pi\)
\(252\) −2.95426e12 −0.183124
\(253\) 9.35711e11 0.0567517
\(254\) 8.82832e12 0.523953
\(255\) −8.56074e11 −0.0497211
\(256\) −1.68131e13 −0.955712
\(257\) 1.57395e13 0.875707 0.437853 0.899046i \(-0.355739\pi\)
0.437853 + 0.899046i \(0.355739\pi\)
\(258\) −1.39429e12 −0.0759356
\(259\) −3.25678e12 −0.173636
\(260\) 1.48256e12 0.0773851
\(261\) 1.49898e12 0.0766077
\(262\) −6.53662e12 −0.327112
\(263\) −2.95972e13 −1.45042 −0.725211 0.688527i \(-0.758258\pi\)
−0.725211 + 0.688527i \(0.758258\pi\)
\(264\) 6.27984e12 0.301389
\(265\) −5.72205e12 −0.268967
\(266\) 2.76980e13 1.27526
\(267\) −3.40370e12 −0.153511
\(268\) 1.21622e13 0.537365
\(269\) 3.30233e12 0.142949 0.0714747 0.997442i \(-0.477229\pi\)
0.0714747 + 0.997442i \(0.477229\pi\)
\(270\) −9.45151e11 −0.0400867
\(271\) −2.81967e13 −1.17184 −0.585919 0.810370i \(-0.699266\pi\)
−0.585919 + 0.810370i \(0.699266\pi\)
\(272\) 3.78809e12 0.154273
\(273\) −1.60214e13 −0.639450
\(274\) 6.65003e12 0.260133
\(275\) 1.16526e13 0.446778
\(276\) −6.90990e11 −0.0259700
\(277\) 1.63593e13 0.602736 0.301368 0.953508i \(-0.402557\pi\)
0.301368 + 0.953508i \(0.402557\pi\)
\(278\) −2.39626e13 −0.865539
\(279\) 3.31423e12 0.117371
\(280\) −1.19496e13 −0.414938
\(281\) −3.16455e13 −1.07752 −0.538762 0.842458i \(-0.681108\pi\)
−0.538762 + 0.842458i \(0.681108\pi\)
\(282\) −6.70737e10 −0.00223966
\(283\) 2.01915e13 0.661215 0.330607 0.943768i \(-0.392746\pi\)
0.330607 + 0.943768i \(0.392746\pi\)
\(284\) 2.09470e13 0.672777
\(285\) −5.44961e12 −0.171680
\(286\) 9.39219e12 0.290238
\(287\) 7.46800e13 2.26388
\(288\) −7.99597e12 −0.237800
\(289\) −3.06444e13 −0.894155
\(290\) 1.67211e12 0.0478714
\(291\) −1.81435e13 −0.509695
\(292\) −1.95613e13 −0.539253
\(293\) 6.35243e13 1.71857 0.859287 0.511494i \(-0.170908\pi\)
0.859287 + 0.511494i \(0.170908\pi\)
\(294\) 1.85023e13 0.491265
\(295\) −1.32240e12 −0.0344620
\(296\) −5.11233e12 −0.130772
\(297\) 3.68231e12 0.0924612
\(298\) 4.40823e13 1.08661
\(299\) −3.74736e12 −0.0906846
\(300\) −8.60502e12 −0.204449
\(301\) −1.03366e13 −0.241135
\(302\) 2.88396e13 0.660618
\(303\) −6.16651e12 −0.138709
\(304\) 2.41143e13 0.532683
\(305\) 1.15198e13 0.249918
\(306\) 4.00495e12 0.0853355
\(307\) 9.58100e12 0.200516 0.100258 0.994961i \(-0.468033\pi\)
0.100258 + 0.994961i \(0.468033\pi\)
\(308\) 1.28392e13 0.263942
\(309\) −2.16474e13 −0.437154
\(310\) 3.69703e12 0.0733438
\(311\) −1.56977e13 −0.305953 −0.152976 0.988230i \(-0.548886\pi\)
−0.152976 + 0.988230i \(0.548886\pi\)
\(312\) −2.51497e13 −0.481595
\(313\) 6.24401e13 1.17482 0.587408 0.809291i \(-0.300149\pi\)
0.587408 + 0.809291i \(0.300149\pi\)
\(314\) 9.41898e11 0.0174137
\(315\) −7.00687e12 −0.127296
\(316\) 1.23863e13 0.221138
\(317\) 8.62202e13 1.51281 0.756403 0.654106i \(-0.226955\pi\)
0.756403 + 0.654106i \(0.226955\pi\)
\(318\) 2.67693e13 0.461624
\(319\) −6.51454e12 −0.110417
\(320\) −1.64539e13 −0.274122
\(321\) −1.26730e13 −0.207539
\(322\) 8.32974e12 0.134099
\(323\) 2.30920e13 0.365467
\(324\) −2.71926e12 −0.0423109
\(325\) −4.66664e13 −0.713915
\(326\) −6.46838e13 −0.972968
\(327\) 7.73183e12 0.114359
\(328\) 1.17229e14 1.70502
\(329\) −4.97250e11 −0.00711210
\(330\) 4.10762e12 0.0577781
\(331\) −1.00373e14 −1.38855 −0.694275 0.719710i \(-0.744275\pi\)
−0.694275 + 0.719710i \(0.744275\pi\)
\(332\) −2.62105e13 −0.356628
\(333\) −2.99771e12 −0.0401187
\(334\) −1.96878e13 −0.259174
\(335\) 2.88461e13 0.373543
\(336\) 3.10051e13 0.394972
\(337\) −8.43673e13 −1.05733 −0.528664 0.848831i \(-0.677307\pi\)
−0.528664 + 0.848831i \(0.677307\pi\)
\(338\) 2.62061e13 0.323118
\(339\) −1.00817e12 −0.0122302
\(340\) −2.74745e12 −0.0327941
\(341\) −1.44036e13 −0.169170
\(342\) 2.54948e13 0.294651
\(343\) 1.03174e13 0.117341
\(344\) −1.62259e13 −0.181608
\(345\) −1.63888e12 −0.0180527
\(346\) 2.29973e13 0.249321
\(347\) 1.98663e13 0.211985 0.105992 0.994367i \(-0.466198\pi\)
0.105992 + 0.994367i \(0.466198\pi\)
\(348\) 4.81076e12 0.0505275
\(349\) −1.08915e13 −0.112602 −0.0563012 0.998414i \(-0.517931\pi\)
−0.0563012 + 0.998414i \(0.517931\pi\)
\(350\) 1.03732e14 1.05569
\(351\) −1.47470e13 −0.147745
\(352\) 3.47504e13 0.342748
\(353\) −2.77510e13 −0.269474 −0.134737 0.990881i \(-0.543019\pi\)
−0.134737 + 0.990881i \(0.543019\pi\)
\(354\) 6.18653e12 0.0591465
\(355\) 4.96819e13 0.467673
\(356\) −1.09237e13 −0.101250
\(357\) 2.96907e13 0.270985
\(358\) −2.16504e13 −0.194585
\(359\) 3.68376e13 0.326041 0.163020 0.986623i \(-0.447876\pi\)
0.163020 + 0.986623i \(0.447876\pi\)
\(360\) −1.09990e13 −0.0958719
\(361\) 3.05092e13 0.261903
\(362\) −5.79604e13 −0.490043
\(363\) 5.33275e13 0.444083
\(364\) −5.14186e13 −0.421757
\(365\) −4.63954e13 −0.374855
\(366\) −5.38930e13 −0.428930
\(367\) 3.19123e13 0.250204 0.125102 0.992144i \(-0.460074\pi\)
0.125102 + 0.992144i \(0.460074\pi\)
\(368\) 7.25198e12 0.0560136
\(369\) 6.87395e13 0.523072
\(370\) −3.34395e12 −0.0250698
\(371\) 1.98454e14 1.46590
\(372\) 1.06366e13 0.0774133
\(373\) −1.72704e14 −1.23852 −0.619262 0.785185i \(-0.712568\pi\)
−0.619262 + 0.785185i \(0.712568\pi\)
\(374\) −1.74055e13 −0.122996
\(375\) −4.23564e13 −0.294949
\(376\) −7.80560e11 −0.00535640
\(377\) 2.60896e13 0.176437
\(378\) 3.27801e13 0.218477
\(379\) −2.30989e13 −0.151731 −0.0758657 0.997118i \(-0.524172\pi\)
−0.0758657 + 0.997118i \(0.524172\pi\)
\(380\) −1.74898e13 −0.113233
\(381\) 6.02426e13 0.384429
\(382\) 1.19387e14 0.750947
\(383\) −6.49064e13 −0.402434 −0.201217 0.979547i \(-0.564490\pi\)
−0.201217 + 0.979547i \(0.564490\pi\)
\(384\) 9.58591e12 0.0585884
\(385\) 3.04518e13 0.183476
\(386\) −2.37913e13 −0.141315
\(387\) −9.51434e12 −0.0557145
\(388\) −5.82292e13 −0.336176
\(389\) 2.01526e13 0.114712 0.0573560 0.998354i \(-0.481733\pi\)
0.0573560 + 0.998354i \(0.481733\pi\)
\(390\) −1.64503e13 −0.0923247
\(391\) 6.94455e12 0.0384302
\(392\) 2.15318e14 1.17492
\(393\) −4.46045e13 −0.240005
\(394\) −4.08007e12 −0.0216490
\(395\) 2.93777e13 0.153721
\(396\) 1.18179e13 0.0609839
\(397\) −2.26240e14 −1.15139 −0.575694 0.817666i \(-0.695268\pi\)
−0.575694 + 0.817666i \(0.695268\pi\)
\(398\) 2.61170e14 1.31089
\(399\) 1.89005e14 0.935672
\(400\) 9.03101e13 0.440967
\(401\) −2.19454e14 −1.05694 −0.528468 0.848953i \(-0.677233\pi\)
−0.528468 + 0.848953i \(0.677233\pi\)
\(402\) −1.34950e14 −0.641105
\(403\) 5.76839e13 0.270319
\(404\) −1.97906e13 −0.0914872
\(405\) −6.44951e12 −0.0294120
\(406\) −5.79927e13 −0.260904
\(407\) 1.30280e13 0.0578242
\(408\) 4.66070e13 0.204089
\(409\) −2.37577e14 −1.02642 −0.513212 0.858262i \(-0.671545\pi\)
−0.513212 + 0.858262i \(0.671545\pi\)
\(410\) 7.66790e13 0.326862
\(411\) 4.53784e13 0.190862
\(412\) −6.94744e13 −0.288330
\(413\) 4.58638e13 0.187821
\(414\) 7.66715e12 0.0309836
\(415\) −6.21658e13 −0.247906
\(416\) −1.39169e14 −0.547684
\(417\) −1.63515e14 −0.635053
\(418\) −1.10800e14 −0.424689
\(419\) 8.85726e13 0.335060 0.167530 0.985867i \(-0.446421\pi\)
0.167530 + 0.985867i \(0.446421\pi\)
\(420\) −2.24876e13 −0.0839599
\(421\) 6.42170e13 0.236646 0.118323 0.992975i \(-0.462248\pi\)
0.118323 + 0.992975i \(0.462248\pi\)
\(422\) 3.35635e14 1.22081
\(423\) −4.57696e11 −0.00164326
\(424\) 3.11524e14 1.10403
\(425\) 8.64817e13 0.302542
\(426\) −2.32426e14 −0.802659
\(427\) −3.99535e14 −1.36208
\(428\) −4.06722e13 −0.136885
\(429\) 6.40903e13 0.212950
\(430\) −1.06133e13 −0.0348155
\(431\) −2.80219e14 −0.907555 −0.453778 0.891115i \(-0.649924\pi\)
−0.453778 + 0.891115i \(0.649924\pi\)
\(432\) 2.85387e13 0.0912587
\(433\) −2.24303e13 −0.0708192 −0.0354096 0.999373i \(-0.511274\pi\)
−0.0354096 + 0.999373i \(0.511274\pi\)
\(434\) −1.28222e14 −0.399731
\(435\) 1.14101e13 0.0351236
\(436\) 2.48143e13 0.0754268
\(437\) 4.42077e13 0.132694
\(438\) 2.17050e14 0.643358
\(439\) 9.75244e13 0.285469 0.142734 0.989761i \(-0.454411\pi\)
0.142734 + 0.989761i \(0.454411\pi\)
\(440\) 4.78018e13 0.138183
\(441\) 1.26256e14 0.360445
\(442\) 6.97059e13 0.196538
\(443\) 4.85637e14 1.35236 0.676179 0.736737i \(-0.263635\pi\)
0.676179 + 0.736737i \(0.263635\pi\)
\(444\) −9.62076e12 −0.0264608
\(445\) −2.59088e13 −0.0703828
\(446\) 2.13553e14 0.573013
\(447\) 3.00808e14 0.797257
\(448\) 5.70660e14 1.49399
\(449\) 5.64094e14 1.45880 0.729401 0.684086i \(-0.239799\pi\)
0.729401 + 0.684086i \(0.239799\pi\)
\(450\) 9.54803e13 0.243919
\(451\) −2.98741e14 −0.753918
\(452\) −3.23557e12 −0.00806658
\(453\) 1.96795e14 0.484701
\(454\) −4.00434e14 −0.974370
\(455\) −1.21954e14 −0.293179
\(456\) 2.96692e14 0.704691
\(457\) −6.46165e13 −0.151637 −0.0758184 0.997122i \(-0.524157\pi\)
−0.0758184 + 0.997122i \(0.524157\pi\)
\(458\) 2.31116e14 0.535882
\(459\) 2.73289e13 0.0626113
\(460\) −5.25977e12 −0.0119069
\(461\) −1.14661e14 −0.256483 −0.128242 0.991743i \(-0.540933\pi\)
−0.128242 + 0.991743i \(0.540933\pi\)
\(462\) −1.42462e14 −0.314897
\(463\) −3.67887e14 −0.803562 −0.401781 0.915736i \(-0.631609\pi\)
−0.401781 + 0.915736i \(0.631609\pi\)
\(464\) −5.04892e13 −0.108981
\(465\) 2.52277e13 0.0538129
\(466\) 8.91900e13 0.188015
\(467\) −6.88247e14 −1.43384 −0.716921 0.697154i \(-0.754449\pi\)
−0.716921 + 0.697154i \(0.754449\pi\)
\(468\) −4.73284e13 −0.0974473
\(469\) −1.00045e15 −2.03585
\(470\) −5.10560e11 −0.00102685
\(471\) 6.42731e12 0.0127766
\(472\) 7.19948e13 0.141456
\(473\) 4.13493e13 0.0803029
\(474\) −1.37437e14 −0.263829
\(475\) 5.50526e14 1.04463
\(476\) 9.52882e13 0.178731
\(477\) 1.82668e14 0.338698
\(478\) −2.33517e14 −0.428022
\(479\) 4.85519e13 0.0879753 0.0439876 0.999032i \(-0.485994\pi\)
0.0439876 + 0.999032i \(0.485994\pi\)
\(480\) −6.08648e13 −0.109028
\(481\) −5.21750e13 −0.0923984
\(482\) 2.27139e14 0.397680
\(483\) 5.68404e13 0.0983893
\(484\) 1.71147e14 0.292901
\(485\) −1.38107e14 −0.233689
\(486\) 3.01726e13 0.0504792
\(487\) 9.11754e14 1.50823 0.754116 0.656741i \(-0.228066\pi\)
0.754116 + 0.656741i \(0.228066\pi\)
\(488\) −6.27172e14 −1.02583
\(489\) −4.41388e14 −0.713875
\(490\) 1.40838e14 0.225239
\(491\) 6.96377e14 1.10128 0.550638 0.834744i \(-0.314384\pi\)
0.550638 + 0.834744i \(0.314384\pi\)
\(492\) 2.20610e14 0.344999
\(493\) −4.83489e13 −0.0747702
\(494\) 4.43735e14 0.678618
\(495\) 2.80295e13 0.0423923
\(496\) −1.11631e14 −0.166969
\(497\) −1.72309e15 −2.54886
\(498\) 2.90829e14 0.425477
\(499\) −9.18652e14 −1.32922 −0.664612 0.747189i \(-0.731403\pi\)
−0.664612 + 0.747189i \(0.731403\pi\)
\(500\) −1.35937e14 −0.194537
\(501\) −1.34345e14 −0.190158
\(502\) −2.95138e14 −0.413195
\(503\) −4.53959e14 −0.628627 −0.314314 0.949319i \(-0.601774\pi\)
−0.314314 + 0.949319i \(0.601774\pi\)
\(504\) 3.81473e14 0.522512
\(505\) −4.69390e13 −0.0635963
\(506\) −3.33214e13 −0.0446575
\(507\) 1.78825e14 0.237074
\(508\) 1.93340e14 0.253555
\(509\) −6.03821e14 −0.783358 −0.391679 0.920102i \(-0.628106\pi\)
−0.391679 + 0.920102i \(0.628106\pi\)
\(510\) 3.04854e13 0.0391252
\(511\) 1.60910e15 2.04300
\(512\) 6.79516e14 0.853522
\(513\) 1.73971e14 0.216188
\(514\) −5.60495e14 −0.689088
\(515\) −1.64779e14 −0.200429
\(516\) −3.05350e13 −0.0367472
\(517\) 1.98914e12 0.00236847
\(518\) 1.15976e14 0.136633
\(519\) 1.56929e14 0.182929
\(520\) −1.91438e14 −0.220805
\(521\) −1.34344e15 −1.53325 −0.766624 0.642097i \(-0.778065\pi\)
−0.766624 + 0.642097i \(0.778065\pi\)
\(522\) −5.33797e13 −0.0602821
\(523\) −5.11309e14 −0.571379 −0.285690 0.958322i \(-0.592223\pi\)
−0.285690 + 0.958322i \(0.592223\pi\)
\(524\) −1.43152e14 −0.158298
\(525\) 7.07843e14 0.774570
\(526\) 1.05398e15 1.14133
\(527\) −1.06899e14 −0.114555
\(528\) −1.24029e14 −0.131534
\(529\) −9.39515e14 −0.986047
\(530\) 2.03767e14 0.211649
\(531\) 4.22156e13 0.0433963
\(532\) 6.06587e14 0.617134
\(533\) 1.19641e15 1.20470
\(534\) 1.21208e14 0.120797
\(535\) −9.64658e13 −0.0951541
\(536\) −1.57046e15 −1.53328
\(537\) −1.47737e14 −0.142768
\(538\) −1.17598e14 −0.112486
\(539\) −5.48707e14 −0.519520
\(540\) −2.06988e13 −0.0193990
\(541\) −1.49339e15 −1.38544 −0.692720 0.721206i \(-0.743588\pi\)
−0.692720 + 0.721206i \(0.743588\pi\)
\(542\) 1.00411e15 0.922112
\(543\) −3.95509e14 −0.359549
\(544\) 2.57907e14 0.232097
\(545\) 5.88542e13 0.0524320
\(546\) 5.70535e14 0.503179
\(547\) −5.32530e14 −0.464958 −0.232479 0.972601i \(-0.574684\pi\)
−0.232479 + 0.972601i \(0.574684\pi\)
\(548\) 1.45636e14 0.125885
\(549\) −3.67754e14 −0.314709
\(550\) −4.14956e14 −0.351567
\(551\) −3.07780e14 −0.258170
\(552\) 8.92253e13 0.0741008
\(553\) −1.01889e15 −0.837797
\(554\) −5.82568e14 −0.474289
\(555\) −2.28184e13 −0.0183939
\(556\) −5.24780e14 −0.418857
\(557\) −1.29608e15 −1.02430 −0.512151 0.858896i \(-0.671151\pi\)
−0.512151 + 0.858896i \(0.671151\pi\)
\(558\) −1.18022e14 −0.0923583
\(559\) −1.65596e14 −0.128317
\(560\) 2.36008e14 0.181090
\(561\) −1.18771e14 −0.0902435
\(562\) 1.12692e15 0.847897
\(563\) −2.22397e15 −1.65704 −0.828518 0.559962i \(-0.810816\pi\)
−0.828518 + 0.559962i \(0.810816\pi\)
\(564\) −1.46891e12 −0.00108383
\(565\) −7.67409e12 −0.00560739
\(566\) −7.19033e14 −0.520306
\(567\) 2.23684e14 0.160298
\(568\) −2.70482e15 −1.91965
\(569\) −1.05219e15 −0.739569 −0.369784 0.929118i \(-0.620568\pi\)
−0.369784 + 0.929118i \(0.620568\pi\)
\(570\) 1.94065e14 0.135094
\(571\) −1.22798e15 −0.846631 −0.423316 0.905982i \(-0.639134\pi\)
−0.423316 + 0.905982i \(0.639134\pi\)
\(572\) 2.05689e14 0.140454
\(573\) 8.14672e14 0.550976
\(574\) −2.65941e15 −1.78143
\(575\) 1.65562e14 0.109847
\(576\) 5.25267e14 0.345188
\(577\) −2.13168e15 −1.38757 −0.693786 0.720182i \(-0.744058\pi\)
−0.693786 + 0.720182i \(0.744058\pi\)
\(578\) 1.09127e15 0.703605
\(579\) −1.62347e14 −0.103684
\(580\) 3.66192e13 0.0231662
\(581\) 2.15606e15 1.35111
\(582\) 6.46105e14 0.401076
\(583\) −7.93875e14 −0.488174
\(584\) 2.52589e15 1.53866
\(585\) −1.12253e14 −0.0677394
\(586\) −2.26215e15 −1.35233
\(587\) 6.85096e14 0.405735 0.202867 0.979206i \(-0.434974\pi\)
0.202867 + 0.979206i \(0.434974\pi\)
\(588\) 4.05201e14 0.237736
\(589\) −6.80500e14 −0.395543
\(590\) 4.70915e13 0.0271179
\(591\) −2.78415e13 −0.0158841
\(592\) 1.00970e14 0.0570722
\(593\) 6.09078e14 0.341092 0.170546 0.985350i \(-0.445447\pi\)
0.170546 + 0.985350i \(0.445447\pi\)
\(594\) −1.31130e14 −0.0727571
\(595\) 2.26004e14 0.124243
\(596\) 9.65403e14 0.525840
\(597\) 1.78217e15 0.961812
\(598\) 1.33446e14 0.0713591
\(599\) −2.10851e15 −1.11719 −0.558596 0.829440i \(-0.688660\pi\)
−0.558596 + 0.829440i \(0.688660\pi\)
\(600\) 1.11114e15 0.583359
\(601\) −3.51373e15 −1.82793 −0.913963 0.405799i \(-0.866993\pi\)
−0.913963 + 0.405799i \(0.866993\pi\)
\(602\) 3.68093e14 0.189748
\(603\) −9.20869e14 −0.470384
\(604\) 6.31587e14 0.319691
\(605\) 4.05925e14 0.203606
\(606\) 2.19594e14 0.109149
\(607\) −1.15275e15 −0.567801 −0.283901 0.958854i \(-0.591629\pi\)
−0.283901 + 0.958854i \(0.591629\pi\)
\(608\) 1.64179e15 0.801396
\(609\) −3.95730e14 −0.191427
\(610\) −4.10230e14 −0.196659
\(611\) −7.96617e12 −0.00378462
\(612\) 8.77085e13 0.0412961
\(613\) −3.88504e15 −1.81286 −0.906428 0.422361i \(-0.861202\pi\)
−0.906428 + 0.422361i \(0.861202\pi\)
\(614\) −3.41186e14 −0.157785
\(615\) 5.23241e14 0.239822
\(616\) −1.65788e15 −0.753111
\(617\) −3.26822e15 −1.47144 −0.735720 0.677286i \(-0.763156\pi\)
−0.735720 + 0.677286i \(0.763156\pi\)
\(618\) 7.70880e14 0.343994
\(619\) 1.74251e15 0.770683 0.385341 0.922774i \(-0.374084\pi\)
0.385341 + 0.922774i \(0.374084\pi\)
\(620\) 8.09649e13 0.0354930
\(621\) 5.23190e13 0.0227329
\(622\) 5.59007e14 0.240752
\(623\) 8.98577e14 0.383594
\(624\) 4.96714e14 0.210180
\(625\) 1.89471e15 0.794700
\(626\) −2.22354e15 −0.924454
\(627\) −7.56076e14 −0.311598
\(628\) 2.06276e13 0.00842694
\(629\) 9.66900e13 0.0391564
\(630\) 2.49520e14 0.100169
\(631\) 1.38785e15 0.552307 0.276153 0.961114i \(-0.410940\pi\)
0.276153 + 0.961114i \(0.410940\pi\)
\(632\) −1.59940e15 −0.630978
\(633\) 2.29030e15 0.895720
\(634\) −3.07037e15 −1.19042
\(635\) 4.58562e14 0.176256
\(636\) 5.86249e14 0.223392
\(637\) 2.19747e15 0.830150
\(638\) 2.31988e14 0.0868862
\(639\) −1.58602e15 −0.588918
\(640\) 7.29673e13 0.0268620
\(641\) 2.45583e15 0.896352 0.448176 0.893945i \(-0.352074\pi\)
0.448176 + 0.893945i \(0.352074\pi\)
\(642\) 4.51294e14 0.163311
\(643\) 1.80437e15 0.647388 0.323694 0.946162i \(-0.395075\pi\)
0.323694 + 0.946162i \(0.395075\pi\)
\(644\) 1.82421e14 0.0648939
\(645\) −7.24226e13 −0.0255444
\(646\) −8.22324e14 −0.287583
\(647\) 4.67983e15 1.62277 0.811384 0.584514i \(-0.198715\pi\)
0.811384 + 0.584514i \(0.198715\pi\)
\(648\) 3.51129e14 0.120727
\(649\) −1.83468e14 −0.0625483
\(650\) 1.66183e15 0.561775
\(651\) −8.74957e14 −0.293286
\(652\) −1.41658e15 −0.470845
\(653\) −3.01278e15 −0.992989 −0.496494 0.868040i \(-0.665380\pi\)
−0.496494 + 0.868040i \(0.665380\pi\)
\(654\) −2.75336e14 −0.0899883
\(655\) −3.39527e14 −0.110039
\(656\) −2.31531e15 −0.744113
\(657\) 1.48110e15 0.472037
\(658\) 1.77075e13 0.00559646
\(659\) −2.52199e15 −0.790450 −0.395225 0.918584i \(-0.629333\pi\)
−0.395225 + 0.918584i \(0.629333\pi\)
\(660\) 8.99568e13 0.0279603
\(661\) 3.09070e15 0.952684 0.476342 0.879260i \(-0.341962\pi\)
0.476342 + 0.879260i \(0.341962\pi\)
\(662\) 3.57434e15 1.09264
\(663\) 4.75658e14 0.144202
\(664\) 3.38448e15 1.01758
\(665\) 1.43870e15 0.428993
\(666\) 1.06751e14 0.0315692
\(667\) −9.25599e13 −0.0271476
\(668\) −4.31162e14 −0.125421
\(669\) 1.45724e15 0.420425
\(670\) −1.02723e15 −0.293938
\(671\) 1.59826e15 0.453599
\(672\) 2.11094e15 0.594216
\(673\) 3.83543e15 1.07085 0.535427 0.844581i \(-0.320151\pi\)
0.535427 + 0.844581i \(0.320151\pi\)
\(674\) 3.00438e15 0.832005
\(675\) 6.51537e14 0.178965
\(676\) 5.73914e14 0.156365
\(677\) 4.12234e15 1.11405 0.557027 0.830494i \(-0.311942\pi\)
0.557027 + 0.830494i \(0.311942\pi\)
\(678\) 3.59015e13 0.00962387
\(679\) 4.78989e15 1.27363
\(680\) 3.54770e14 0.0935723
\(681\) −2.73247e15 −0.714903
\(682\) 5.12924e14 0.133119
\(683\) 6.95455e15 1.79042 0.895211 0.445643i \(-0.147025\pi\)
0.895211 + 0.445643i \(0.147025\pi\)
\(684\) 5.58336e14 0.142589
\(685\) 3.45417e14 0.0875076
\(686\) −3.67409e14 −0.0923351
\(687\) 1.57708e15 0.393181
\(688\) 3.20466e14 0.0792585
\(689\) 3.17933e15 0.780062
\(690\) 5.83618e13 0.0142056
\(691\) 2.64766e15 0.639343 0.319671 0.947528i \(-0.396427\pi\)
0.319671 + 0.947528i \(0.396427\pi\)
\(692\) 5.03641e14 0.120653
\(693\) −9.72130e14 −0.231042
\(694\) −7.07453e14 −0.166809
\(695\) −1.24467e15 −0.291164
\(696\) −6.21198e14 −0.144171
\(697\) −2.21716e15 −0.510526
\(698\) 3.87854e14 0.0886061
\(699\) 6.08613e14 0.137948
\(700\) 2.27172e15 0.510877
\(701\) 3.22140e15 0.718779 0.359389 0.933188i \(-0.382985\pi\)
0.359389 + 0.933188i \(0.382985\pi\)
\(702\) 5.25151e14 0.116260
\(703\) 6.15511e14 0.135201
\(704\) −2.28280e15 −0.497530
\(705\) −3.48395e12 −0.000753412 0
\(706\) 9.88233e14 0.212048
\(707\) 1.62796e15 0.346606
\(708\) 1.35485e14 0.0286226
\(709\) −7.37651e14 −0.154631 −0.0773155 0.997007i \(-0.524635\pi\)
−0.0773155 + 0.997007i \(0.524635\pi\)
\(710\) −1.76921e15 −0.368009
\(711\) −9.37841e14 −0.193574
\(712\) 1.41054e15 0.288899
\(713\) −2.04650e14 −0.0415928
\(714\) −1.05731e15 −0.213236
\(715\) 4.87851e14 0.0976346
\(716\) −4.74143e14 −0.0941646
\(717\) −1.59347e15 −0.314043
\(718\) −1.31181e15 −0.256559
\(719\) 1.65357e15 0.320933 0.160467 0.987041i \(-0.448700\pi\)
0.160467 + 0.987041i \(0.448700\pi\)
\(720\) 2.17235e14 0.0418409
\(721\) 5.71492e15 1.09236
\(722\) −1.08645e15 −0.206090
\(723\) 1.54995e15 0.291781
\(724\) −1.26933e15 −0.237145
\(725\) −1.15266e15 −0.213719
\(726\) −1.89903e15 −0.349446
\(727\) −1.93205e15 −0.352841 −0.176420 0.984315i \(-0.556452\pi\)
−0.176420 + 0.984315i \(0.556452\pi\)
\(728\) 6.63951e15 1.20341
\(729\) 2.05891e14 0.0370370
\(730\) 1.65217e15 0.294971
\(731\) 3.06881e14 0.0543782
\(732\) −1.18026e15 −0.207570
\(733\) −1.52030e15 −0.265373 −0.132686 0.991158i \(-0.542360\pi\)
−0.132686 + 0.991158i \(0.542360\pi\)
\(734\) −1.13642e15 −0.196884
\(735\) 9.61051e14 0.165259
\(736\) 4.93741e14 0.0842696
\(737\) 4.00209e15 0.677978
\(738\) −2.44786e15 −0.411602
\(739\) −1.10640e16 −1.84658 −0.923291 0.384100i \(-0.874512\pi\)
−0.923291 + 0.384100i \(0.874512\pi\)
\(740\) −7.32326e13 −0.0121319
\(741\) 3.02795e15 0.497907
\(742\) −7.06711e15 −1.15351
\(743\) −8.63150e15 −1.39845 −0.699226 0.714900i \(-0.746472\pi\)
−0.699226 + 0.714900i \(0.746472\pi\)
\(744\) −1.37347e15 −0.220885
\(745\) 2.28973e15 0.365532
\(746\) 6.15012e15 0.974586
\(747\) 1.98455e15 0.312176
\(748\) −3.81180e14 −0.0595212
\(749\) 3.34566e15 0.518600
\(750\) 1.50834e15 0.232094
\(751\) −1.80297e15 −0.275403 −0.137701 0.990474i \(-0.543971\pi\)
−0.137701 + 0.990474i \(0.543971\pi\)
\(752\) 1.54163e13 0.00233767
\(753\) −2.01396e15 −0.303165
\(754\) −9.29069e14 −0.138837
\(755\) 1.49799e15 0.222229
\(756\) 7.17884e14 0.105727
\(757\) 2.21410e15 0.323721 0.161860 0.986814i \(-0.448251\pi\)
0.161860 + 0.986814i \(0.448251\pi\)
\(758\) 8.22568e14 0.119396
\(759\) −2.27378e14 −0.0327656
\(760\) 2.25840e15 0.323092
\(761\) −8.34704e15 −1.18554 −0.592771 0.805371i \(-0.701966\pi\)
−0.592771 + 0.805371i \(0.701966\pi\)
\(762\) −2.14528e15 −0.302505
\(763\) −2.04120e15 −0.285760
\(764\) 2.61458e15 0.363403
\(765\) 2.08026e14 0.0287065
\(766\) 2.31136e15 0.316672
\(767\) 7.34758e14 0.0999471
\(768\) 4.08558e15 0.551781
\(769\) 1.19175e16 1.59805 0.799027 0.601296i \(-0.205349\pi\)
0.799027 + 0.601296i \(0.205349\pi\)
\(770\) −1.08441e15 −0.144376
\(771\) −3.82470e15 −0.505589
\(772\) −5.21030e14 −0.0683861
\(773\) −2.58218e15 −0.336511 −0.168256 0.985743i \(-0.553813\pi\)
−0.168256 + 0.985743i \(0.553813\pi\)
\(774\) 3.38813e14 0.0438414
\(775\) −2.54854e15 −0.327440
\(776\) 7.51894e15 0.959218
\(777\) 7.91397e14 0.100249
\(778\) −7.17649e14 −0.0902661
\(779\) −1.41141e16 −1.76277
\(780\) −3.60261e14 −0.0446783
\(781\) 6.89284e15 0.848823
\(782\) −2.47301e14 −0.0302404
\(783\) −3.64251e14 −0.0442295
\(784\) −4.25260e15 −0.512763
\(785\) 4.89243e13 0.00585789
\(786\) 1.58840e15 0.188858
\(787\) −1.06275e16 −1.25478 −0.627392 0.778703i \(-0.715878\pi\)
−0.627392 + 0.778703i \(0.715878\pi\)
\(788\) −8.93535e13 −0.0104765
\(789\) 7.19212e15 0.837401
\(790\) −1.04616e15 −0.120962
\(791\) 2.66156e14 0.0305608
\(792\) −1.52600e15 −0.174007
\(793\) −6.40073e15 −0.724815
\(794\) 8.05657e15 0.906019
\(795\) 1.39046e15 0.155288
\(796\) 5.71963e15 0.634375
\(797\) 5.37985e15 0.592583 0.296292 0.955098i \(-0.404250\pi\)
0.296292 + 0.955098i \(0.404250\pi\)
\(798\) −6.73062e15 −0.736274
\(799\) 1.47628e13 0.00160384
\(800\) 6.14864e15 0.663413
\(801\) 8.27100e14 0.0886296
\(802\) 7.81491e15 0.831696
\(803\) −6.43687e15 −0.680360
\(804\) −2.95540e15 −0.310248
\(805\) 4.32665e14 0.0451102
\(806\) −2.05417e15 −0.212713
\(807\) −8.02465e14 −0.0825319
\(808\) 2.55549e15 0.261043
\(809\) 1.16160e16 1.17853 0.589265 0.807940i \(-0.299418\pi\)
0.589265 + 0.807940i \(0.299418\pi\)
\(810\) 2.29672e14 0.0231441
\(811\) −1.16748e16 −1.16851 −0.584256 0.811569i \(-0.698614\pi\)
−0.584256 + 0.811569i \(0.698614\pi\)
\(812\) −1.27004e15 −0.126258
\(813\) 6.85181e15 0.676561
\(814\) −4.63938e14 −0.0455015
\(815\) −3.35982e15 −0.327302
\(816\) −9.20505e14 −0.0890698
\(817\) 1.95355e15 0.187760
\(818\) 8.46030e15 0.807686
\(819\) 3.89321e15 0.369187
\(820\) 1.67927e15 0.158177
\(821\) 2.93787e15 0.274881 0.137441 0.990510i \(-0.456112\pi\)
0.137441 + 0.990510i \(0.456112\pi\)
\(822\) −1.61596e15 −0.150188
\(823\) −1.24942e16 −1.15348 −0.576740 0.816928i \(-0.695675\pi\)
−0.576740 + 0.816928i \(0.695675\pi\)
\(824\) 8.97100e15 0.822700
\(825\) −2.83157e15 −0.257947
\(826\) −1.63324e15 −0.147795
\(827\) 1.35197e16 1.21531 0.607654 0.794202i \(-0.292111\pi\)
0.607654 + 0.794202i \(0.292111\pi\)
\(828\) 1.67911e14 0.0149938
\(829\) −1.02560e16 −0.909761 −0.454881 0.890552i \(-0.650318\pi\)
−0.454881 + 0.890552i \(0.650318\pi\)
\(830\) 2.21377e15 0.195076
\(831\) −3.97532e15 −0.347990
\(832\) 9.14222e15 0.795011
\(833\) −4.07233e15 −0.351800
\(834\) 5.82290e15 0.499719
\(835\) −1.02263e15 −0.0871848
\(836\) −2.42652e15 −0.205518
\(837\) −8.05358e14 −0.0677640
\(838\) −3.15414e15 −0.263656
\(839\) −1.43075e16 −1.18816 −0.594079 0.804407i \(-0.702483\pi\)
−0.594079 + 0.804407i \(0.702483\pi\)
\(840\) 2.90375e15 0.239565
\(841\) −1.15561e16 −0.947181
\(842\) −2.28681e15 −0.186215
\(843\) 7.68985e15 0.622109
\(844\) 7.35041e15 0.590783
\(845\) 1.36120e15 0.108695
\(846\) 1.62989e13 0.00129307
\(847\) −1.40785e16 −1.10968
\(848\) −6.15271e15 −0.481825
\(849\) −4.90653e15 −0.381753
\(850\) −3.07968e15 −0.238068
\(851\) 1.85105e14 0.0142169
\(852\) −5.09012e15 −0.388428
\(853\) −1.00565e16 −0.762477 −0.381239 0.924477i \(-0.624502\pi\)
−0.381239 + 0.924477i \(0.624502\pi\)
\(854\) 1.42278e16 1.07181
\(855\) 1.32426e15 0.0991193
\(856\) 5.25186e15 0.390578
\(857\) −5.67045e15 −0.419008 −0.209504 0.977808i \(-0.567185\pi\)
−0.209504 + 0.977808i \(0.567185\pi\)
\(858\) −2.28230e15 −0.167569
\(859\) −3.48425e15 −0.254183 −0.127092 0.991891i \(-0.540564\pi\)
−0.127092 + 0.991891i \(0.540564\pi\)
\(860\) −2.32430e14 −0.0168481
\(861\) −1.81472e16 −1.30705
\(862\) 9.97882e15 0.714150
\(863\) −1.46753e16 −1.04358 −0.521791 0.853074i \(-0.674736\pi\)
−0.521791 + 0.853074i \(0.674736\pi\)
\(864\) 1.94302e15 0.137294
\(865\) 1.19453e15 0.0838704
\(866\) 7.98758e14 0.0557272
\(867\) 7.44659e15 0.516241
\(868\) −2.80806e15 −0.193440
\(869\) 4.07585e15 0.279003
\(870\) −4.06323e14 −0.0276385
\(871\) −1.60276e16 −1.08335
\(872\) −3.20418e15 −0.215217
\(873\) 4.40888e15 0.294273
\(874\) −1.57427e15 −0.104416
\(875\) 1.11821e16 0.737019
\(876\) 4.75340e15 0.311338
\(877\) 4.80789e15 0.312937 0.156469 0.987683i \(-0.449989\pi\)
0.156469 + 0.987683i \(0.449989\pi\)
\(878\) −3.47292e15 −0.224634
\(879\) −1.54364e16 −0.992219
\(880\) −9.44101e14 −0.0603065
\(881\) −7.85415e15 −0.498576 −0.249288 0.968429i \(-0.580197\pi\)
−0.249288 + 0.968429i \(0.580197\pi\)
\(882\) −4.49606e15 −0.283632
\(883\) −9.07255e15 −0.568781 −0.284391 0.958708i \(-0.591791\pi\)
−0.284391 + 0.958708i \(0.591791\pi\)
\(884\) 1.52656e15 0.0951100
\(885\) 3.21342e14 0.0198966
\(886\) −1.72939e16 −1.06416
\(887\) 2.32586e16 1.42234 0.711170 0.703020i \(-0.248165\pi\)
0.711170 + 0.703020i \(0.248165\pi\)
\(888\) 1.24230e15 0.0755012
\(889\) −1.59040e16 −0.960611
\(890\) 9.22630e14 0.0553838
\(891\) −8.94801e14 −0.0533825
\(892\) 4.67682e15 0.277296
\(893\) 9.39772e13 0.00553783
\(894\) −1.07120e16 −0.627356
\(895\) −1.12457e15 −0.0654574
\(896\) −2.53068e15 −0.146401
\(897\) 9.10607e14 0.0523568
\(898\) −2.00878e16 −1.14792
\(899\) 1.42480e15 0.0809235
\(900\) 2.09102e15 0.118039
\(901\) −5.89189e15 −0.330574
\(902\) 1.06384e16 0.593253
\(903\) 2.51179e15 0.139220
\(904\) 4.17799e14 0.0230166
\(905\) −3.01059e15 −0.164848
\(906\) −7.00802e15 −0.381408
\(907\) 2.26790e16 1.22683 0.613413 0.789762i \(-0.289796\pi\)
0.613413 + 0.789762i \(0.289796\pi\)
\(908\) −8.76951e15 −0.471523
\(909\) 1.49846e15 0.0800837
\(910\) 4.34287e15 0.230701
\(911\) −9.60184e15 −0.506994 −0.253497 0.967336i \(-0.581581\pi\)
−0.253497 + 0.967336i \(0.581581\pi\)
\(912\) −5.85976e15 −0.307545
\(913\) −8.62485e15 −0.449948
\(914\) 2.30104e15 0.119322
\(915\) −2.79932e15 −0.144290
\(916\) 5.06143e15 0.259327
\(917\) 1.17756e16 0.599724
\(918\) −9.73204e14 −0.0492685
\(919\) 2.29750e16 1.15617 0.578084 0.815978i \(-0.303801\pi\)
0.578084 + 0.815978i \(0.303801\pi\)
\(920\) 6.79177e14 0.0339743
\(921\) −2.32818e15 −0.115768
\(922\) 4.08315e15 0.201825
\(923\) −2.76046e16 −1.35635
\(924\) −3.11992e15 −0.152387
\(925\) 2.30514e15 0.111923
\(926\) 1.31007e16 0.632318
\(927\) 5.26032e15 0.252391
\(928\) −3.43749e15 −0.163956
\(929\) −1.95032e16 −0.924740 −0.462370 0.886687i \(-0.653001\pi\)
−0.462370 + 0.886687i \(0.653001\pi\)
\(930\) −8.98378e14 −0.0423451
\(931\) −2.59237e16 −1.21471
\(932\) 1.95326e15 0.0909856
\(933\) 3.81454e15 0.176642
\(934\) 2.45090e16 1.12828
\(935\) −9.04079e14 −0.0413754
\(936\) 6.11137e15 0.278049
\(937\) 1.01829e16 0.460580 0.230290 0.973122i \(-0.426033\pi\)
0.230290 + 0.973122i \(0.426033\pi\)
\(938\) 3.56268e16 1.60199
\(939\) −1.51729e16 −0.678280
\(940\) −1.11813e13 −0.000496922 0
\(941\) −1.58357e16 −0.699672 −0.349836 0.936811i \(-0.613763\pi\)
−0.349836 + 0.936811i \(0.613763\pi\)
\(942\) −2.28881e14 −0.0100538
\(943\) −4.24458e15 −0.185362
\(944\) −1.42192e15 −0.0617348
\(945\) 1.70267e15 0.0734946
\(946\) −1.47248e15 −0.0631899
\(947\) −2.42419e16 −1.03429 −0.517145 0.855898i \(-0.673005\pi\)
−0.517145 + 0.855898i \(0.673005\pi\)
\(948\) −3.00987e15 −0.127674
\(949\) 2.57785e16 1.08716
\(950\) −1.96046e16 −0.822014
\(951\) −2.09515e16 −0.873419
\(952\) −1.23043e16 −0.509979
\(953\) −2.71994e16 −1.12085 −0.560427 0.828204i \(-0.689363\pi\)
−0.560427 + 0.828204i \(0.689363\pi\)
\(954\) −6.50495e15 −0.266519
\(955\) 6.20123e15 0.252615
\(956\) −5.11403e15 −0.207131
\(957\) 1.58303e15 0.0637491
\(958\) −1.72897e15 −0.0692272
\(959\) −1.19799e16 −0.476925
\(960\) 3.99829e15 0.158264
\(961\) −2.22583e16 −0.876017
\(962\) 1.85799e15 0.0727077
\(963\) 3.07953e15 0.119823
\(964\) 4.97435e15 0.192448
\(965\) −1.23577e15 −0.0475378
\(966\) −2.02413e15 −0.0774219
\(967\) −3.21332e16 −1.22211 −0.611053 0.791590i \(-0.709254\pi\)
−0.611053 + 0.791590i \(0.709254\pi\)
\(968\) −2.20997e16 −0.835740
\(969\) −5.61136e15 −0.211002
\(970\) 4.91811e15 0.183888
\(971\) −4.64451e15 −0.172677 −0.0863385 0.996266i \(-0.527517\pi\)
−0.0863385 + 0.996266i \(0.527517\pi\)
\(972\) 6.60779e14 0.0244282
\(973\) 4.31680e16 1.58687
\(974\) −3.24682e16 −1.18682
\(975\) 1.13399e16 0.412179
\(976\) 1.23869e16 0.447700
\(977\) 5.01867e14 0.0180372 0.00901858 0.999959i \(-0.497129\pi\)
0.00901858 + 0.999959i \(0.497129\pi\)
\(978\) 1.57182e16 0.561743
\(979\) −3.59457e15 −0.127744
\(980\) 3.08436e15 0.108999
\(981\) −1.87884e15 −0.0660251
\(982\) −2.47985e16 −0.866587
\(983\) 5.28237e16 1.83563 0.917813 0.397013i \(-0.129953\pi\)
0.917813 + 0.397013i \(0.129953\pi\)
\(984\) −2.84867e16 −0.984393
\(985\) −2.11928e14 −0.00728263
\(986\) 1.72174e15 0.0588362
\(987\) 1.20832e14 0.00410617
\(988\) 9.71779e15 0.328401
\(989\) 5.87498e14 0.0197436
\(990\) −9.98151e14 −0.0333582
\(991\) 4.61147e16 1.53262 0.766310 0.642471i \(-0.222091\pi\)
0.766310 + 0.642471i \(0.222091\pi\)
\(992\) −7.60027e15 −0.251197
\(993\) 2.43905e16 0.801679
\(994\) 6.13604e16 2.00569
\(995\) 1.35658e16 0.440978
\(996\) 6.36915e15 0.205899
\(997\) 3.25603e16 1.04680 0.523402 0.852086i \(-0.324663\pi\)
0.523402 + 0.852086i \(0.324663\pi\)
\(998\) 3.27139e16 1.04596
\(999\) 7.28445e14 0.0231625
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 177.12.a.a.1.10 26
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.a.1.10 26 1.1 even 1 trivial