Properties

Label 177.12.a.d.1.14
Level $177$
Weight $12$
Character 177.1
Self dual yes
Analytic conductor $135.997$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $1$

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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: \(0\)
Dimension: \(28\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-5.21206 q^{2} +243.000 q^{3} -2020.83 q^{4} -8551.43 q^{5} -1266.53 q^{6} -16524.4 q^{7} +21207.0 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q-5.21206 q^{2} +243.000 q^{3} -2020.83 q^{4} -8551.43 q^{5} -1266.53 q^{6} -16524.4 q^{7} +21207.0 q^{8} +59049.0 q^{9} +44570.6 q^{10} -89297.0 q^{11} -491063. q^{12} -114841. q^{13} +86126.0 q^{14} -2.07800e6 q^{15} +4.02814e6 q^{16} -2.27567e6 q^{17} -307767. q^{18} -1.31943e7 q^{19} +1.72810e7 q^{20} -4.01542e6 q^{21} +465421. q^{22} -2.62891e7 q^{23} +5.15331e6 q^{24} +2.42989e7 q^{25} +598558. q^{26} +1.43489e7 q^{27} +3.33930e7 q^{28} -1.02740e8 q^{29} +1.08307e7 q^{30} -2.81409e8 q^{31} -6.44269e7 q^{32} -2.16992e7 q^{33} +1.18609e7 q^{34} +1.41307e8 q^{35} -1.19328e8 q^{36} -9.42260e7 q^{37} +6.87696e7 q^{38} -2.79063e7 q^{39} -1.81350e8 q^{40} -1.20015e9 q^{41} +2.09286e7 q^{42} -6.09679e8 q^{43} +1.80454e8 q^{44} -5.04954e8 q^{45} +1.37020e8 q^{46} -2.59230e9 q^{47} +9.78837e8 q^{48} -1.70427e9 q^{49} -1.26647e8 q^{50} -5.52988e8 q^{51} +2.32074e8 q^{52} +5.94524e9 q^{53} -7.47874e7 q^{54} +7.63617e8 q^{55} -3.50433e8 q^{56} -3.20622e9 q^{57} +5.35486e8 q^{58} +7.14924e8 q^{59} +4.19929e9 q^{60} +4.54803e9 q^{61} +1.46672e9 q^{62} -9.75747e8 q^{63} -7.91383e9 q^{64} +9.82054e8 q^{65} +1.13097e8 q^{66} +9.68563e9 q^{67} +4.59875e9 q^{68} -6.38824e9 q^{69} -7.36501e8 q^{70} +1.70954e10 q^{71} +1.25225e9 q^{72} -8.07569e9 q^{73} +4.91112e8 q^{74} +5.90463e9 q^{75} +2.66635e10 q^{76} +1.47557e9 q^{77} +1.45450e8 q^{78} +3.36701e10 q^{79} -3.44463e10 q^{80} +3.48678e9 q^{81} +6.25527e9 q^{82} -2.87180e10 q^{83} +8.11450e9 q^{84} +1.94602e10 q^{85} +3.17769e9 q^{86} -2.49657e10 q^{87} -1.89372e9 q^{88} -2.72935e9 q^{89} +2.63185e9 q^{90} +1.89767e9 q^{91} +5.31258e10 q^{92} -6.83823e10 q^{93} +1.35113e10 q^{94} +1.12830e11 q^{95} -1.56557e10 q^{96} +1.22050e11 q^{97} +8.88278e9 q^{98} -5.27290e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 96q^{2} + 6804q^{3} + 29214q^{4} + 26562q^{5} + 23328q^{6} + 142333q^{7} + 332331q^{8} + 1653372q^{9} + O(q^{10}) \) \( 28q + 96q^{2} + 6804q^{3} + 29214q^{4} + 26562q^{5} + 23328q^{6} + 142333q^{7} + 332331q^{8} + 1653372q^{9} + 616281q^{10} + 1082362q^{11} + 7099002q^{12} + 503712q^{13} + 1321669q^{14} + 6454566q^{15} + 34870338q^{16} + 13513579q^{17} + 5668704q^{18} + 35971687q^{19} + 96105997q^{20} + 34586919q^{21} - 47598882q^{22} + 61380539q^{23} + 80756433q^{24} + 294744746q^{25} + 62820734q^{26} + 401769396q^{27} + 148068294q^{28} + 322339307q^{29} + 149756283q^{30} + 151247077q^{31} + 466383494q^{32} + 263013966q^{33} + 684479860q^{34} + 960297361q^{35} + 1725057486q^{36} + 863508437q^{37} + 992640509q^{38} + 122402016q^{39} + 3067680252q^{40} + 3081170377q^{41} + 321165567q^{42} + 2554238300q^{43} + 4350123570q^{44} + 1568459538q^{45} - 1987059155q^{46} + 6203398333q^{47} + 8473492134q^{48} + 10327857997q^{49} + 17577682253q^{50} + 3283799697q^{51} + 32137181618q^{52} + 14571770754q^{53} + 1377495072q^{54} + 18251419334q^{55} + 33498842836q^{56} + 8741119941q^{57} + 11860778276q^{58} + 20017880372q^{59} + 23353757271q^{60} + 2761613771q^{61} + 13785829526q^{62} + 8404621317q^{63} + 86547545293q^{64} + 32034985256q^{65} - 11566528326q^{66} + 39381333296q^{67} + 38995496621q^{68} + 14915470977q^{69} + 8551800364q^{70} + 26130020296q^{71} + 19623813219q^{72} + 41382402799q^{73} + 23815315058q^{74} + 71622973278q^{75} + 10611720128q^{76} - 8426124313q^{77} + 15265438362q^{78} + 59825111206q^{79} + 4009687655q^{80} + 97629963228q^{81} - 39592715115q^{82} + 35433122727q^{83} + 35980595442q^{84} - 8950496085q^{85} - 182032360688q^{86} + 78328451601q^{87} - 220003602335q^{88} + 102303043039q^{89} + 36390776769q^{90} - 111146323655q^{91} - 163000203526q^{92} + 36753039711q^{93} - 81314346008q^{94} + 208102168887q^{95} + 113331189042q^{96} - 171891031490q^{97} + 72304707792q^{98} + 63912393738q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.21206 −0.115171 −0.0575857 0.998341i \(-0.518340\pi\)
−0.0575857 + 0.998341i \(0.518340\pi\)
\(3\) 243.000 0.577350
\(4\) −2020.83 −0.986736
\(5\) −8551.43 −1.22378 −0.611891 0.790942i \(-0.709591\pi\)
−0.611891 + 0.790942i \(0.709591\pi\)
\(6\) −1266.53 −0.0664943
\(7\) −16524.4 −0.371608 −0.185804 0.982587i \(-0.559489\pi\)
−0.185804 + 0.982587i \(0.559489\pi\)
\(8\) 21207.0 0.228815
\(9\) 59049.0 0.333333
\(10\) 44570.6 0.140945
\(11\) −89297.0 −0.167177 −0.0835886 0.996500i \(-0.526638\pi\)
−0.0835886 + 0.996500i \(0.526638\pi\)
\(12\) −491063. −0.569692
\(13\) −114841. −0.0857843 −0.0428922 0.999080i \(-0.513657\pi\)
−0.0428922 + 0.999080i \(0.513657\pi\)
\(14\) 86126.0 0.0427987
\(15\) −2.07800e6 −0.706551
\(16\) 4.02814e6 0.960383
\(17\) −2.27567e6 −0.388723 −0.194361 0.980930i \(-0.562263\pi\)
−0.194361 + 0.980930i \(0.562263\pi\)
\(18\) −307767. −0.0383905
\(19\) −1.31943e7 −1.22248 −0.611240 0.791445i \(-0.709329\pi\)
−0.611240 + 0.791445i \(0.709329\pi\)
\(20\) 1.72810e7 1.20755
\(21\) −4.01542e6 −0.214548
\(22\) 465421. 0.0192540
\(23\) −2.62891e7 −0.851671 −0.425836 0.904801i \(-0.640020\pi\)
−0.425836 + 0.904801i \(0.640020\pi\)
\(24\) 5.15331e6 0.132107
\(25\) 2.42989e7 0.497641
\(26\) 598558. 0.00987990
\(27\) 1.43489e7 0.192450
\(28\) 3.33930e7 0.366679
\(29\) −1.02740e8 −0.930142 −0.465071 0.885273i \(-0.653971\pi\)
−0.465071 + 0.885273i \(0.653971\pi\)
\(30\) 1.08307e7 0.0813745
\(31\) −2.81409e8 −1.76542 −0.882710 0.469918i \(-0.844284\pi\)
−0.882710 + 0.469918i \(0.844284\pi\)
\(32\) −6.44269e7 −0.339424
\(33\) −2.16992e7 −0.0965198
\(34\) 1.18609e7 0.0447698
\(35\) 1.41307e8 0.454767
\(36\) −1.19328e8 −0.328912
\(37\) −9.42260e7 −0.223389 −0.111694 0.993743i \(-0.535628\pi\)
−0.111694 + 0.993743i \(0.535628\pi\)
\(38\) 6.87696e7 0.140795
\(39\) −2.79063e7 −0.0495276
\(40\) −1.81350e8 −0.280020
\(41\) −1.20015e9 −1.61780 −0.808901 0.587945i \(-0.799937\pi\)
−0.808901 + 0.587945i \(0.799937\pi\)
\(42\) 2.09286e7 0.0247098
\(43\) −6.09679e8 −0.632448 −0.316224 0.948685i \(-0.602415\pi\)
−0.316224 + 0.948685i \(0.602415\pi\)
\(44\) 1.80454e8 0.164960
\(45\) −5.04954e8 −0.407927
\(46\) 1.37020e8 0.0980882
\(47\) −2.59230e9 −1.64872 −0.824362 0.566064i \(-0.808466\pi\)
−0.824362 + 0.566064i \(0.808466\pi\)
\(48\) 9.78837e8 0.554477
\(49\) −1.70427e9 −0.861907
\(50\) −1.26647e8 −0.0573141
\(51\) −5.52988e8 −0.224429
\(52\) 2.32074e8 0.0846464
\(53\) 5.94524e9 1.95277 0.976387 0.216031i \(-0.0693112\pi\)
0.976387 + 0.216031i \(0.0693112\pi\)
\(54\) −7.47874e7 −0.0221648
\(55\) 7.63617e8 0.204588
\(56\) −3.50433e8 −0.0850296
\(57\) −3.20622e9 −0.705799
\(58\) 5.35486e8 0.107126
\(59\) 7.14924e8 0.130189
\(60\) 4.19929e9 0.697179
\(61\) 4.54803e9 0.689460 0.344730 0.938702i \(-0.387970\pi\)
0.344730 + 0.938702i \(0.387970\pi\)
\(62\) 1.46672e9 0.203326
\(63\) −9.75747e8 −0.123869
\(64\) −7.91383e9 −0.921291
\(65\) 9.82054e8 0.104981
\(66\) 1.13097e8 0.0111163
\(67\) 9.68563e9 0.876428 0.438214 0.898871i \(-0.355611\pi\)
0.438214 + 0.898871i \(0.355611\pi\)
\(68\) 4.59875e9 0.383567
\(69\) −6.38824e9 −0.491713
\(70\) −7.36501e8 −0.0523762
\(71\) 1.70954e10 1.12450 0.562248 0.826968i \(-0.309937\pi\)
0.562248 + 0.826968i \(0.309937\pi\)
\(72\) 1.25225e9 0.0762717
\(73\) −8.07569e9 −0.455936 −0.227968 0.973669i \(-0.573208\pi\)
−0.227968 + 0.973669i \(0.573208\pi\)
\(74\) 4.91112e8 0.0257280
\(75\) 5.90463e9 0.287313
\(76\) 2.66635e10 1.20626
\(77\) 1.47557e9 0.0621244
\(78\) 1.45450e8 0.00570416
\(79\) 3.36701e10 1.23111 0.615554 0.788095i \(-0.288932\pi\)
0.615554 + 0.788095i \(0.288932\pi\)
\(80\) −3.44463e10 −1.17530
\(81\) 3.48678e9 0.111111
\(82\) 6.25527e9 0.186325
\(83\) −2.87180e10 −0.800247 −0.400123 0.916461i \(-0.631033\pi\)
−0.400123 + 0.916461i \(0.631033\pi\)
\(84\) 8.11450e9 0.211702
\(85\) 1.94602e10 0.475712
\(86\) 3.17769e9 0.0728400
\(87\) −2.49657e10 −0.537018
\(88\) −1.89372e9 −0.0382527
\(89\) −2.72935e9 −0.0518102 −0.0259051 0.999664i \(-0.508247\pi\)
−0.0259051 + 0.999664i \(0.508247\pi\)
\(90\) 2.63185e9 0.0469816
\(91\) 1.89767e9 0.0318782
\(92\) 5.31258e10 0.840374
\(93\) −6.83823e10 −1.01927
\(94\) 1.35113e10 0.189886
\(95\) 1.12830e11 1.49605
\(96\) −1.56557e10 −0.195966
\(97\) 1.22050e11 1.44309 0.721545 0.692368i \(-0.243432\pi\)
0.721545 + 0.692368i \(0.243432\pi\)
\(98\) 8.88278e9 0.0992671
\(99\) −5.27290e9 −0.0557257
\(100\) −4.91041e10 −0.491041
\(101\) 9.32657e10 0.882987 0.441493 0.897265i \(-0.354449\pi\)
0.441493 + 0.897265i \(0.354449\pi\)
\(102\) 2.88221e9 0.0258478
\(103\) −1.62092e11 −1.37770 −0.688852 0.724902i \(-0.741885\pi\)
−0.688852 + 0.724902i \(0.741885\pi\)
\(104\) −2.43543e9 −0.0196288
\(105\) 3.43376e10 0.262560
\(106\) −3.09869e10 −0.224904
\(107\) 1.14640e10 0.0790180 0.0395090 0.999219i \(-0.487421\pi\)
0.0395090 + 0.999219i \(0.487421\pi\)
\(108\) −2.89968e10 −0.189897
\(109\) −1.94706e11 −1.21208 −0.606042 0.795433i \(-0.707244\pi\)
−0.606042 + 0.795433i \(0.707244\pi\)
\(110\) −3.98002e9 −0.0235627
\(111\) −2.28969e10 −0.128974
\(112\) −6.65624e10 −0.356886
\(113\) −3.50109e11 −1.78761 −0.893804 0.448458i \(-0.851973\pi\)
−0.893804 + 0.448458i \(0.851973\pi\)
\(114\) 1.67110e10 0.0812879
\(115\) 2.24809e11 1.04226
\(116\) 2.07620e11 0.917804
\(117\) −6.78124e9 −0.0285948
\(118\) −3.72623e9 −0.0149940
\(119\) 3.76040e10 0.144453
\(120\) −4.40682e10 −0.161670
\(121\) −2.77338e11 −0.972052
\(122\) −2.37046e10 −0.0794061
\(123\) −2.91637e11 −0.934038
\(124\) 5.68680e11 1.74200
\(125\) 2.09760e11 0.614777
\(126\) 5.08566e9 0.0142662
\(127\) −4.12670e11 −1.10836 −0.554182 0.832396i \(-0.686969\pi\)
−0.554182 + 0.832396i \(0.686969\pi\)
\(128\) 1.73194e11 0.445530
\(129\) −1.48152e11 −0.365144
\(130\) −5.11853e9 −0.0120908
\(131\) −1.90011e11 −0.430316 −0.215158 0.976579i \(-0.569027\pi\)
−0.215158 + 0.976579i \(0.569027\pi\)
\(132\) 4.38504e10 0.0952395
\(133\) 2.18027e11 0.454284
\(134\) −5.04821e10 −0.100940
\(135\) −1.22704e11 −0.235517
\(136\) −4.82602e10 −0.0889457
\(137\) 3.59136e11 0.635764 0.317882 0.948130i \(-0.397028\pi\)
0.317882 + 0.948130i \(0.397028\pi\)
\(138\) 3.32959e10 0.0566312
\(139\) 8.45010e11 1.38128 0.690638 0.723201i \(-0.257330\pi\)
0.690638 + 0.723201i \(0.257330\pi\)
\(140\) −2.85558e11 −0.448735
\(141\) −6.29930e11 −0.951891
\(142\) −8.91023e10 −0.129510
\(143\) 1.02549e10 0.0143412
\(144\) 2.37857e11 0.320128
\(145\) 8.78572e11 1.13829
\(146\) 4.20910e10 0.0525108
\(147\) −4.14138e11 −0.497622
\(148\) 1.90415e11 0.220426
\(149\) −6.07518e11 −0.677695 −0.338848 0.940841i \(-0.610037\pi\)
−0.338848 + 0.940841i \(0.610037\pi\)
\(150\) −3.07753e10 −0.0330903
\(151\) 5.39506e11 0.559272 0.279636 0.960106i \(-0.409786\pi\)
0.279636 + 0.960106i \(0.409786\pi\)
\(152\) −2.79812e11 −0.279722
\(153\) −1.34376e11 −0.129574
\(154\) −7.69079e9 −0.00715496
\(155\) 2.40645e12 2.16049
\(156\) 5.63940e10 0.0488706
\(157\) −4.28284e11 −0.358331 −0.179165 0.983819i \(-0.557340\pi\)
−0.179165 + 0.983819i \(0.557340\pi\)
\(158\) −1.75491e11 −0.141788
\(159\) 1.44469e12 1.12743
\(160\) 5.50942e11 0.415381
\(161\) 4.34410e11 0.316488
\(162\) −1.81733e10 −0.0127968
\(163\) 1.99661e12 1.35913 0.679567 0.733613i \(-0.262168\pi\)
0.679567 + 0.733613i \(0.262168\pi\)
\(164\) 2.42531e12 1.59634
\(165\) 1.85559e11 0.118119
\(166\) 1.49680e11 0.0921656
\(167\) 2.56504e12 1.52810 0.764052 0.645155i \(-0.223207\pi\)
0.764052 + 0.645155i \(0.223207\pi\)
\(168\) −8.51551e10 −0.0490919
\(169\) −1.77897e12 −0.992641
\(170\) −1.01428e11 −0.0547884
\(171\) −7.79110e11 −0.407493
\(172\) 1.23206e12 0.624059
\(173\) −2.30931e12 −1.13300 −0.566500 0.824062i \(-0.691703\pi\)
−0.566500 + 0.824062i \(0.691703\pi\)
\(174\) 1.30123e11 0.0618491
\(175\) −4.01524e11 −0.184928
\(176\) −3.59700e11 −0.160554
\(177\) 1.73727e11 0.0751646
\(178\) 1.42256e10 0.00596705
\(179\) 1.60705e12 0.653638 0.326819 0.945087i \(-0.394023\pi\)
0.326819 + 0.945087i \(0.394023\pi\)
\(180\) 1.02043e12 0.402516
\(181\) 3.40265e12 1.30192 0.650961 0.759111i \(-0.274366\pi\)
0.650961 + 0.759111i \(0.274366\pi\)
\(182\) −9.89078e9 −0.00367145
\(183\) 1.10517e12 0.398060
\(184\) −5.57513e11 −0.194875
\(185\) 8.05767e11 0.273379
\(186\) 3.56413e11 0.117390
\(187\) 2.03210e11 0.0649856
\(188\) 5.23862e12 1.62685
\(189\) −2.37107e11 −0.0715161
\(190\) −5.88078e11 −0.172302
\(191\) −5.66849e12 −1.61355 −0.806777 0.590856i \(-0.798790\pi\)
−0.806777 + 0.590856i \(0.798790\pi\)
\(192\) −1.92306e12 −0.531907
\(193\) 1.68647e12 0.453330 0.226665 0.973973i \(-0.427218\pi\)
0.226665 + 0.973973i \(0.427218\pi\)
\(194\) −6.36132e11 −0.166203
\(195\) 2.38639e11 0.0606110
\(196\) 3.44405e12 0.850475
\(197\) −5.21431e11 −0.125208 −0.0626041 0.998038i \(-0.519941\pi\)
−0.0626041 + 0.998038i \(0.519941\pi\)
\(198\) 2.74827e10 0.00641801
\(199\) −9.64663e11 −0.219121 −0.109560 0.993980i \(-0.534944\pi\)
−0.109560 + 0.993980i \(0.534944\pi\)
\(200\) 5.15307e11 0.113868
\(201\) 2.35361e12 0.506006
\(202\) −4.86107e11 −0.101695
\(203\) 1.69771e12 0.345649
\(204\) 1.11750e12 0.221452
\(205\) 1.02630e13 1.97984
\(206\) 8.44832e11 0.158672
\(207\) −1.55234e12 −0.283890
\(208\) −4.62594e11 −0.0823858
\(209\) 1.17821e12 0.204371
\(210\) −1.78970e11 −0.0302394
\(211\) 1.06069e13 1.74595 0.872977 0.487760i \(-0.162186\pi\)
0.872977 + 0.487760i \(0.162186\pi\)
\(212\) −1.20143e13 −1.92687
\(213\) 4.15418e12 0.649228
\(214\) −5.97512e10 −0.00910061
\(215\) 5.21363e12 0.773978
\(216\) 3.04298e11 0.0440355
\(217\) 4.65010e12 0.656045
\(218\) 1.01482e12 0.139597
\(219\) −1.96239e12 −0.263235
\(220\) −1.54314e12 −0.201875
\(221\) 2.61340e11 0.0333463
\(222\) 1.19340e11 0.0148541
\(223\) −4.74343e12 −0.575991 −0.287995 0.957632i \(-0.592989\pi\)
−0.287995 + 0.957632i \(0.592989\pi\)
\(224\) 1.06461e12 0.126133
\(225\) 1.43483e12 0.165880
\(226\) 1.82479e12 0.205881
\(227\) −1.00024e13 −1.10144 −0.550719 0.834691i \(-0.685646\pi\)
−0.550719 + 0.834691i \(0.685646\pi\)
\(228\) 6.47923e12 0.696437
\(229\) −1.55990e13 −1.63682 −0.818412 0.574632i \(-0.805145\pi\)
−0.818412 + 0.574632i \(0.805145\pi\)
\(230\) −1.17172e12 −0.120039
\(231\) 3.58565e11 0.0358675
\(232\) −2.17880e12 −0.212831
\(233\) −3.16513e12 −0.301949 −0.150975 0.988538i \(-0.548241\pi\)
−0.150975 + 0.988538i \(0.548241\pi\)
\(234\) 3.53442e10 0.00329330
\(235\) 2.21679e13 2.01768
\(236\) −1.44474e12 −0.128462
\(237\) 8.18184e12 0.710780
\(238\) −1.95994e11 −0.0166368
\(239\) −4.40436e12 −0.365337 −0.182669 0.983175i \(-0.558474\pi\)
−0.182669 + 0.983175i \(0.558474\pi\)
\(240\) −8.37046e12 −0.678559
\(241\) −1.99297e12 −0.157909 −0.0789545 0.996878i \(-0.525158\pi\)
−0.0789545 + 0.996878i \(0.525158\pi\)
\(242\) 1.44550e12 0.111953
\(243\) 8.47289e11 0.0641500
\(244\) −9.19081e12 −0.680315
\(245\) 1.45740e13 1.05479
\(246\) 1.52003e12 0.107575
\(247\) 1.51524e12 0.104870
\(248\) −5.96784e12 −0.403955
\(249\) −6.97846e12 −0.462023
\(250\) −1.09328e12 −0.0708048
\(251\) 1.99837e13 1.26611 0.633053 0.774108i \(-0.281801\pi\)
0.633053 + 0.774108i \(0.281801\pi\)
\(252\) 1.97182e12 0.122226
\(253\) 2.34753e12 0.142380
\(254\) 2.15086e12 0.127652
\(255\) 4.72884e12 0.274652
\(256\) 1.53048e13 0.869978
\(257\) 3.10791e13 1.72917 0.864583 0.502491i \(-0.167583\pi\)
0.864583 + 0.502491i \(0.167583\pi\)
\(258\) 7.72178e11 0.0420542
\(259\) 1.55702e12 0.0830131
\(260\) −1.98457e12 −0.103589
\(261\) −6.06668e12 −0.310047
\(262\) 9.90352e11 0.0495601
\(263\) 1.67030e12 0.0818535 0.0409268 0.999162i \(-0.486969\pi\)
0.0409268 + 0.999162i \(0.486969\pi\)
\(264\) −4.60175e11 −0.0220852
\(265\) −5.08403e13 −2.38977
\(266\) −1.13637e12 −0.0523205
\(267\) −6.63233e11 −0.0299126
\(268\) −1.95731e13 −0.864803
\(269\) 4.16327e13 1.80217 0.901087 0.433638i \(-0.142770\pi\)
0.901087 + 0.433638i \(0.142770\pi\)
\(270\) 6.39540e11 0.0271248
\(271\) −2.71374e13 −1.12782 −0.563908 0.825838i \(-0.690703\pi\)
−0.563908 + 0.825838i \(0.690703\pi\)
\(272\) −9.16671e12 −0.373323
\(273\) 4.61134e11 0.0184049
\(274\) −1.87184e12 −0.0732219
\(275\) −2.16982e12 −0.0831943
\(276\) 1.29096e13 0.485190
\(277\) −2.19871e13 −0.810082 −0.405041 0.914299i \(-0.632743\pi\)
−0.405041 + 0.914299i \(0.632743\pi\)
\(278\) −4.40425e12 −0.159083
\(279\) −1.66169e13 −0.588474
\(280\) 2.99670e12 0.104058
\(281\) −2.21421e13 −0.753934 −0.376967 0.926227i \(-0.623033\pi\)
−0.376967 + 0.926227i \(0.623033\pi\)
\(282\) 3.28324e12 0.109631
\(283\) 3.42500e11 0.0112159 0.00560796 0.999984i \(-0.498215\pi\)
0.00560796 + 0.999984i \(0.498215\pi\)
\(284\) −3.45470e13 −1.10958
\(285\) 2.74177e13 0.863744
\(286\) −5.34494e10 −0.00165169
\(287\) 1.98318e13 0.601189
\(288\) −3.80434e12 −0.113141
\(289\) −2.90932e13 −0.848894
\(290\) −4.57917e12 −0.131099
\(291\) 2.96581e13 0.833168
\(292\) 1.63196e13 0.449888
\(293\) 4.84850e13 1.31170 0.655851 0.754890i \(-0.272310\pi\)
0.655851 + 0.754890i \(0.272310\pi\)
\(294\) 2.15851e12 0.0573119
\(295\) −6.11363e12 −0.159323
\(296\) −1.99825e12 −0.0511147
\(297\) −1.28131e12 −0.0321733
\(298\) 3.16642e12 0.0780511
\(299\) 3.01906e12 0.0730600
\(300\) −1.19323e13 −0.283502
\(301\) 1.00746e13 0.235023
\(302\) −2.81194e12 −0.0644121
\(303\) 2.26636e13 0.509793
\(304\) −5.31485e13 −1.17405
\(305\) −3.88922e13 −0.843748
\(306\) 7.00376e11 0.0149233
\(307\) 7.50703e13 1.57111 0.785556 0.618791i \(-0.212377\pi\)
0.785556 + 0.618791i \(0.212377\pi\)
\(308\) −2.98189e12 −0.0613004
\(309\) −3.93883e13 −0.795418
\(310\) −1.25426e13 −0.248827
\(311\) −2.70953e13 −0.528094 −0.264047 0.964510i \(-0.585057\pi\)
−0.264047 + 0.964510i \(0.585057\pi\)
\(312\) −5.91810e11 −0.0113327
\(313\) 5.44038e13 1.02361 0.511806 0.859101i \(-0.328977\pi\)
0.511806 + 0.859101i \(0.328977\pi\)
\(314\) 2.23225e12 0.0412695
\(315\) 8.34404e12 0.151589
\(316\) −6.80418e13 −1.21478
\(317\) 6.63376e13 1.16395 0.581974 0.813207i \(-0.302280\pi\)
0.581974 + 0.813207i \(0.302280\pi\)
\(318\) −7.52983e12 −0.129848
\(319\) 9.17434e12 0.155498
\(320\) 6.76746e13 1.12746
\(321\) 2.78575e12 0.0456210
\(322\) −2.26417e12 −0.0364504
\(323\) 3.00259e13 0.475206
\(324\) −7.04621e12 −0.109637
\(325\) −2.79051e12 −0.0426898
\(326\) −1.04065e13 −0.156533
\(327\) −4.73135e13 −0.699797
\(328\) −2.54517e13 −0.370178
\(329\) 4.28362e13 0.612679
\(330\) −9.67145e11 −0.0136039
\(331\) 7.23224e13 1.00050 0.500252 0.865880i \(-0.333241\pi\)
0.500252 + 0.865880i \(0.333241\pi\)
\(332\) 5.80342e13 0.789632
\(333\) −5.56395e12 −0.0744629
\(334\) −1.33691e13 −0.175994
\(335\) −8.28260e13 −1.07256
\(336\) −1.61747e13 −0.206048
\(337\) −1.52367e14 −1.90954 −0.954768 0.297353i \(-0.903896\pi\)
−0.954768 + 0.297353i \(0.903896\pi\)
\(338\) 9.27212e12 0.114324
\(339\) −8.50766e13 −1.03208
\(340\) −3.93259e13 −0.469402
\(341\) 2.51289e13 0.295138
\(342\) 4.06077e12 0.0469316
\(343\) 6.08361e13 0.691900
\(344\) −1.29295e13 −0.144714
\(345\) 5.46286e13 0.601749
\(346\) 1.20363e13 0.130489
\(347\) −1.14214e14 −1.21873 −0.609363 0.792891i \(-0.708575\pi\)
−0.609363 + 0.792891i \(0.708575\pi\)
\(348\) 5.04516e13 0.529895
\(349\) −6.78528e13 −0.701500 −0.350750 0.936469i \(-0.614073\pi\)
−0.350750 + 0.936469i \(0.614073\pi\)
\(350\) 2.09277e12 0.0212984
\(351\) −1.64784e12 −0.0165092
\(352\) 5.75313e12 0.0567439
\(353\) −7.72969e13 −0.750588 −0.375294 0.926906i \(-0.622458\pi\)
−0.375294 + 0.926906i \(0.622458\pi\)
\(354\) −9.05474e11 −0.00865682
\(355\) −1.46190e14 −1.37614
\(356\) 5.51557e12 0.0511229
\(357\) 9.13777e12 0.0833998
\(358\) −8.37603e12 −0.0752804
\(359\) 1.37432e14 1.21638 0.608190 0.793792i \(-0.291896\pi\)
0.608190 + 0.793792i \(0.291896\pi\)
\(360\) −1.07086e13 −0.0933399
\(361\) 5.75994e13 0.494457
\(362\) −1.77348e13 −0.149944
\(363\) −6.73931e13 −0.561214
\(364\) −3.83488e12 −0.0314553
\(365\) 6.90587e13 0.557966
\(366\) −5.76022e12 −0.0458451
\(367\) −1.97753e14 −1.55045 −0.775227 0.631683i \(-0.782364\pi\)
−0.775227 + 0.631683i \(0.782364\pi\)
\(368\) −1.05896e14 −0.817930
\(369\) −7.08678e13 −0.539267
\(370\) −4.19971e12 −0.0314855
\(371\) −9.82412e13 −0.725667
\(372\) 1.38189e14 1.00575
\(373\) −1.38885e14 −0.995997 −0.497998 0.867178i \(-0.665931\pi\)
−0.497998 + 0.867178i \(0.665931\pi\)
\(374\) −1.05915e12 −0.00748448
\(375\) 5.09717e13 0.354942
\(376\) −5.49751e13 −0.377253
\(377\) 1.17987e13 0.0797916
\(378\) 1.23581e12 0.00823661
\(379\) −6.00439e13 −0.394415 −0.197207 0.980362i \(-0.563187\pi\)
−0.197207 + 0.980362i \(0.563187\pi\)
\(380\) −2.28011e14 −1.47620
\(381\) −1.00279e14 −0.639914
\(382\) 2.95445e13 0.185835
\(383\) 1.50750e14 0.934684 0.467342 0.884077i \(-0.345212\pi\)
0.467342 + 0.884077i \(0.345212\pi\)
\(384\) 4.20861e13 0.257227
\(385\) −1.26183e13 −0.0760267
\(386\) −8.79001e12 −0.0522106
\(387\) −3.60010e13 −0.210816
\(388\) −2.46643e14 −1.42395
\(389\) 1.37224e14 0.781098 0.390549 0.920582i \(-0.372285\pi\)
0.390549 + 0.920582i \(0.372285\pi\)
\(390\) −1.24380e12 −0.00698065
\(391\) 5.98252e13 0.331064
\(392\) −3.61425e13 −0.197217
\(393\) −4.61728e13 −0.248443
\(394\) 2.71773e12 0.0144204
\(395\) −2.87928e14 −1.50661
\(396\) 1.06556e13 0.0549865
\(397\) 1.01916e14 0.518674 0.259337 0.965787i \(-0.416496\pi\)
0.259337 + 0.965787i \(0.416496\pi\)
\(398\) 5.02789e12 0.0252365
\(399\) 5.29807e13 0.262281
\(400\) 9.78793e13 0.477926
\(401\) −3.55470e14 −1.71202 −0.856009 0.516960i \(-0.827063\pi\)
−0.856009 + 0.516960i \(0.827063\pi\)
\(402\) −1.22672e13 −0.0582775
\(403\) 3.23172e13 0.151445
\(404\) −1.88474e14 −0.871274
\(405\) −2.98170e13 −0.135976
\(406\) −8.84856e12 −0.0398088
\(407\) 8.41409e12 0.0373455
\(408\) −1.17272e13 −0.0513528
\(409\) 1.58196e14 0.683469 0.341734 0.939797i \(-0.388986\pi\)
0.341734 + 0.939797i \(0.388986\pi\)
\(410\) −5.34916e13 −0.228021
\(411\) 8.72701e13 0.367059
\(412\) 3.27560e14 1.35943
\(413\) −1.18137e13 −0.0483793
\(414\) 8.09091e12 0.0326961
\(415\) 2.45580e14 0.979327
\(416\) 7.39884e12 0.0291172
\(417\) 2.05337e14 0.797480
\(418\) −6.14091e12 −0.0235377
\(419\) −4.16354e14 −1.57502 −0.787510 0.616302i \(-0.788630\pi\)
−0.787510 + 0.616302i \(0.788630\pi\)
\(420\) −6.93906e13 −0.259077
\(421\) −4.53385e14 −1.67077 −0.835383 0.549668i \(-0.814754\pi\)
−0.835383 + 0.549668i \(0.814754\pi\)
\(422\) −5.52836e13 −0.201084
\(423\) −1.53073e14 −0.549574
\(424\) 1.26081e14 0.446824
\(425\) −5.52963e13 −0.193445
\(426\) −2.16519e13 −0.0747726
\(427\) −7.51533e13 −0.256209
\(428\) −2.31669e13 −0.0779698
\(429\) 2.49195e12 0.00827988
\(430\) −2.71738e13 −0.0891402
\(431\) 5.47784e14 1.77412 0.887062 0.461650i \(-0.152742\pi\)
0.887062 + 0.461650i \(0.152742\pi\)
\(432\) 5.77994e13 0.184826
\(433\) −3.13894e14 −0.991059 −0.495530 0.868591i \(-0.665026\pi\)
−0.495530 + 0.868591i \(0.665026\pi\)
\(434\) −2.42366e13 −0.0755576
\(435\) 2.13493e14 0.657192
\(436\) 3.93468e14 1.19601
\(437\) 3.46866e14 1.04115
\(438\) 1.02281e13 0.0303171
\(439\) 7.60946e13 0.222740 0.111370 0.993779i \(-0.464476\pi\)
0.111370 + 0.993779i \(0.464476\pi\)
\(440\) 1.61940e13 0.0468129
\(441\) −1.00636e14 −0.287302
\(442\) −1.36212e12 −0.00384054
\(443\) −1.57927e14 −0.439780 −0.219890 0.975525i \(-0.570570\pi\)
−0.219890 + 0.975525i \(0.570570\pi\)
\(444\) 4.62709e13 0.127263
\(445\) 2.33399e13 0.0634043
\(446\) 2.47230e13 0.0663377
\(447\) −1.47627e14 −0.391268
\(448\) 1.30771e14 0.342359
\(449\) 5.86221e13 0.151602 0.0758012 0.997123i \(-0.475849\pi\)
0.0758012 + 0.997123i \(0.475849\pi\)
\(450\) −7.47840e12 −0.0191047
\(451\) 1.07170e14 0.270460
\(452\) 7.07513e14 1.76390
\(453\) 1.31100e14 0.322896
\(454\) 5.21329e13 0.126854
\(455\) −1.62278e13 −0.0390119
\(456\) −6.79943e13 −0.161498
\(457\) −2.69689e13 −0.0632883 −0.0316441 0.999499i \(-0.510074\pi\)
−0.0316441 + 0.999499i \(0.510074\pi\)
\(458\) 8.13031e13 0.188515
\(459\) −3.26534e13 −0.0748098
\(460\) −4.54302e14 −1.02843
\(461\) 7.62958e14 1.70665 0.853327 0.521376i \(-0.174581\pi\)
0.853327 + 0.521376i \(0.174581\pi\)
\(462\) −1.86886e12 −0.00413092
\(463\) −1.72470e14 −0.376720 −0.188360 0.982100i \(-0.560317\pi\)
−0.188360 + 0.982100i \(0.560317\pi\)
\(464\) −4.13849e14 −0.893292
\(465\) 5.84767e14 1.24736
\(466\) 1.64969e13 0.0347759
\(467\) 4.90313e14 1.02148 0.510741 0.859735i \(-0.329371\pi\)
0.510741 + 0.859735i \(0.329371\pi\)
\(468\) 1.37038e13 0.0282155
\(469\) −1.60049e14 −0.325688
\(470\) −1.15541e14 −0.232379
\(471\) −1.04073e14 −0.206882
\(472\) 1.51614e13 0.0297892
\(473\) 5.44425e13 0.105731
\(474\) −4.26443e13 −0.0818616
\(475\) −3.20607e14 −0.608357
\(476\) −7.59914e13 −0.142537
\(477\) 3.51060e14 0.650924
\(478\) 2.29558e13 0.0420764
\(479\) 7.87631e14 1.42718 0.713588 0.700566i \(-0.247069\pi\)
0.713588 + 0.700566i \(0.247069\pi\)
\(480\) 1.33879e14 0.239820
\(481\) 1.08210e13 0.0191632
\(482\) 1.03875e13 0.0181866
\(483\) 1.05562e14 0.182724
\(484\) 5.60454e14 0.959158
\(485\) −1.04370e15 −1.76603
\(486\) −4.41612e12 −0.00738825
\(487\) −6.23331e14 −1.03112 −0.515560 0.856853i \(-0.672416\pi\)
−0.515560 + 0.856853i \(0.672416\pi\)
\(488\) 9.64502e13 0.157759
\(489\) 4.85177e14 0.784696
\(490\) −7.59605e13 −0.121481
\(491\) 3.47269e13 0.0549184 0.0274592 0.999623i \(-0.491258\pi\)
0.0274592 + 0.999623i \(0.491258\pi\)
\(492\) 5.89350e14 0.921649
\(493\) 2.33802e14 0.361568
\(494\) −7.89755e12 −0.0120780
\(495\) 4.50908e13 0.0681961
\(496\) −1.13355e15 −1.69548
\(497\) −2.82490e14 −0.417872
\(498\) 3.63722e13 0.0532118
\(499\) −1.72369e14 −0.249405 −0.124703 0.992194i \(-0.539798\pi\)
−0.124703 + 0.992194i \(0.539798\pi\)
\(500\) −4.23890e14 −0.606622
\(501\) 6.23304e14 0.882251
\(502\) −1.04156e14 −0.145819
\(503\) −1.52985e14 −0.211848 −0.105924 0.994374i \(-0.533780\pi\)
−0.105924 + 0.994374i \(0.533780\pi\)
\(504\) −2.06927e13 −0.0283432
\(505\) −7.97555e14 −1.08058
\(506\) −1.22355e13 −0.0163981
\(507\) −4.32290e14 −0.573102
\(508\) 8.33937e14 1.09366
\(509\) 3.75714e14 0.487427 0.243714 0.969847i \(-0.421634\pi\)
0.243714 + 0.969847i \(0.421634\pi\)
\(510\) −2.46470e13 −0.0316321
\(511\) 1.33446e14 0.169430
\(512\) −4.34470e14 −0.545727
\(513\) −1.89324e14 −0.235266
\(514\) −1.61986e14 −0.199150
\(515\) 1.38612e15 1.68601
\(516\) 2.99391e14 0.360301
\(517\) 2.31485e14 0.275629
\(518\) −8.11531e12 −0.00956074
\(519\) −5.61163e14 −0.654137
\(520\) 2.08264e13 0.0240213
\(521\) 1.37663e13 0.0157112 0.00785560 0.999969i \(-0.497499\pi\)
0.00785560 + 0.999969i \(0.497499\pi\)
\(522\) 3.16199e13 0.0357086
\(523\) −4.65180e14 −0.519831 −0.259915 0.965631i \(-0.583695\pi\)
−0.259915 + 0.965631i \(0.583695\pi\)
\(524\) 3.83982e14 0.424608
\(525\) −9.75703e13 −0.106768
\(526\) −8.70570e12 −0.00942719
\(527\) 6.40393e14 0.686260
\(528\) −8.74072e13 −0.0926959
\(529\) −2.61695e14 −0.274656
\(530\) 2.64983e14 0.275233
\(531\) 4.22156e13 0.0433963
\(532\) −4.40597e14 −0.448258
\(533\) 1.37827e14 0.138782
\(534\) 3.45681e12 0.00344508
\(535\) −9.80337e13 −0.0967007
\(536\) 2.05403e14 0.200540
\(537\) 3.90512e14 0.377378
\(538\) −2.16992e14 −0.207559
\(539\) 1.52186e14 0.144091
\(540\) 2.47964e14 0.232393
\(541\) −8.31910e14 −0.771776 −0.385888 0.922546i \(-0.626105\pi\)
−0.385888 + 0.922546i \(0.626105\pi\)
\(542\) 1.41442e14 0.129892
\(543\) 8.26843e14 0.751665
\(544\) 1.46614e14 0.131942
\(545\) 1.66501e15 1.48333
\(546\) −2.40346e12 −0.00211971
\(547\) −1.37546e15 −1.20093 −0.600466 0.799651i \(-0.705018\pi\)
−0.600466 + 0.799651i \(0.705018\pi\)
\(548\) −7.25755e14 −0.627331
\(549\) 2.68557e14 0.229820
\(550\) 1.13092e13 0.00958160
\(551\) 1.35558e15 1.13708
\(552\) −1.35476e14 −0.112511
\(553\) −5.56378e14 −0.457490
\(554\) 1.14598e14 0.0932983
\(555\) 1.95801e14 0.157835
\(556\) −1.70762e15 −1.36295
\(557\) 1.83778e15 1.45241 0.726206 0.687477i \(-0.241282\pi\)
0.726206 + 0.687477i \(0.241282\pi\)
\(558\) 8.66084e13 0.0677753
\(559\) 7.00161e13 0.0542541
\(560\) 5.69204e14 0.436751
\(561\) 4.93801e13 0.0375194
\(562\) 1.15406e14 0.0868316
\(563\) 1.22975e15 0.916262 0.458131 0.888885i \(-0.348519\pi\)
0.458131 + 0.888885i \(0.348519\pi\)
\(564\) 1.27298e15 0.939264
\(565\) 2.99394e15 2.18764
\(566\) −1.78513e12 −0.00129175
\(567\) −5.76169e13 −0.0412898
\(568\) 3.62542e14 0.257302
\(569\) −7.10444e14 −0.499358 −0.249679 0.968329i \(-0.580325\pi\)
−0.249679 + 0.968329i \(0.580325\pi\)
\(570\) −1.42903e14 −0.0994786
\(571\) −2.86714e15 −1.97675 −0.988373 0.152048i \(-0.951413\pi\)
−0.988373 + 0.152048i \(0.951413\pi\)
\(572\) −2.07235e13 −0.0141509
\(573\) −1.37744e15 −0.931586
\(574\) −1.03364e14 −0.0692398
\(575\) −6.38795e14 −0.423827
\(576\) −4.67304e14 −0.307097
\(577\) 1.78351e15 1.16094 0.580468 0.814283i \(-0.302869\pi\)
0.580468 + 0.814283i \(0.302869\pi\)
\(578\) 1.51636e14 0.0977684
\(579\) 4.09813e14 0.261730
\(580\) −1.77545e15 −1.12319
\(581\) 4.74546e14 0.297378
\(582\) −1.54580e14 −0.0959572
\(583\) −5.30891e14 −0.326459
\(584\) −1.71261e14 −0.104325
\(585\) 5.79893e13 0.0349938
\(586\) −2.52707e14 −0.151071
\(587\) −9.89640e14 −0.586095 −0.293047 0.956098i \(-0.594669\pi\)
−0.293047 + 0.956098i \(0.594669\pi\)
\(588\) 8.36905e14 0.491022
\(589\) 3.71299e15 2.15819
\(590\) 3.18646e13 0.0183494
\(591\) −1.26708e14 −0.0722890
\(592\) −3.79555e14 −0.214539
\(593\) 3.41739e15 1.91379 0.956894 0.290437i \(-0.0938008\pi\)
0.956894 + 0.290437i \(0.0938008\pi\)
\(594\) 6.67829e12 0.00370544
\(595\) −3.21568e14 −0.176779
\(596\) 1.22769e15 0.668706
\(597\) −2.34413e14 −0.126509
\(598\) −1.57355e13 −0.00841443
\(599\) −1.53010e15 −0.810725 −0.405362 0.914156i \(-0.632855\pi\)
−0.405362 + 0.914156i \(0.632855\pi\)
\(600\) 1.25220e14 0.0657417
\(601\) 7.71695e14 0.401454 0.200727 0.979647i \(-0.435670\pi\)
0.200727 + 0.979647i \(0.435670\pi\)
\(602\) −5.25093e13 −0.0270679
\(603\) 5.71927e14 0.292143
\(604\) −1.09025e15 −0.551853
\(605\) 2.37164e15 1.18958
\(606\) −1.18124e14 −0.0587136
\(607\) −1.94990e15 −0.960451 −0.480225 0.877145i \(-0.659445\pi\)
−0.480225 + 0.877145i \(0.659445\pi\)
\(608\) 8.50068e14 0.414939
\(609\) 4.12543e14 0.199560
\(610\) 2.02708e14 0.0971757
\(611\) 2.97702e14 0.141435
\(612\) 2.71552e14 0.127856
\(613\) −2.81617e15 −1.31409 −0.657047 0.753850i \(-0.728195\pi\)
−0.657047 + 0.753850i \(0.728195\pi\)
\(614\) −3.91271e14 −0.180947
\(615\) 2.49392e15 1.14306
\(616\) 3.12926e13 0.0142150
\(617\) 3.74732e15 1.68715 0.843573 0.537014i \(-0.180448\pi\)
0.843573 + 0.537014i \(0.180448\pi\)
\(618\) 2.05294e14 0.0916094
\(619\) 9.40230e14 0.415849 0.207924 0.978145i \(-0.433329\pi\)
0.207924 + 0.978145i \(0.433329\pi\)
\(620\) −4.86303e15 −2.13183
\(621\) −3.77219e14 −0.163904
\(622\) 1.41222e14 0.0608213
\(623\) 4.51008e13 0.0192531
\(624\) −1.12410e14 −0.0475654
\(625\) −2.98022e15 −1.24999
\(626\) −2.83556e14 −0.117891
\(627\) 2.86305e14 0.117993
\(628\) 8.65492e14 0.353578
\(629\) 2.14427e14 0.0868363
\(630\) −4.34897e13 −0.0174587
\(631\) 4.12374e15 1.64108 0.820540 0.571589i \(-0.193673\pi\)
0.820540 + 0.571589i \(0.193673\pi\)
\(632\) 7.14044e14 0.281696
\(633\) 2.57747e15 1.00803
\(634\) −3.45756e14 −0.134054
\(635\) 3.52892e15 1.35639
\(636\) −2.91948e15 −1.11248
\(637\) 1.95720e14 0.0739381
\(638\) −4.78173e13 −0.0179090
\(639\) 1.00947e15 0.374832
\(640\) −1.48105e15 −0.545232
\(641\) −7.38983e14 −0.269721 −0.134861 0.990865i \(-0.543059\pi\)
−0.134861 + 0.990865i \(0.543059\pi\)
\(642\) −1.45195e13 −0.00525424
\(643\) −5.39380e15 −1.93524 −0.967620 0.252412i \(-0.918776\pi\)
−0.967620 + 0.252412i \(0.918776\pi\)
\(644\) −8.77870e14 −0.312290
\(645\) 1.26691e15 0.446857
\(646\) −1.56497e14 −0.0547302
\(647\) −2.67699e14 −0.0928268 −0.0464134 0.998922i \(-0.514779\pi\)
−0.0464134 + 0.998922i \(0.514779\pi\)
\(648\) 7.39443e13 0.0254239
\(649\) −6.38406e13 −0.0217646
\(650\) 1.45443e13 0.00491665
\(651\) 1.12997e15 0.378768
\(652\) −4.03483e15 −1.34111
\(653\) 4.11687e14 0.135689 0.0678445 0.997696i \(-0.478388\pi\)
0.0678445 + 0.997696i \(0.478388\pi\)
\(654\) 2.46601e14 0.0805966
\(655\) 1.62487e15 0.526613
\(656\) −4.83438e15 −1.55371
\(657\) −4.76861e14 −0.151979
\(658\) −2.23265e14 −0.0705631
\(659\) −1.67225e15 −0.524121 −0.262061 0.965051i \(-0.584402\pi\)
−0.262061 + 0.965051i \(0.584402\pi\)
\(660\) −3.74984e14 −0.116552
\(661\) −7.32781e14 −0.225874 −0.112937 0.993602i \(-0.536026\pi\)
−0.112937 + 0.993602i \(0.536026\pi\)
\(662\) −3.76949e14 −0.115229
\(663\) 6.35056e13 0.0192525
\(664\) −6.09022e14 −0.183109
\(665\) −1.86445e15 −0.555944
\(666\) 2.89997e13 0.00857600
\(667\) 2.70093e15 0.792175
\(668\) −5.18351e15 −1.50783
\(669\) −1.15265e15 −0.332548
\(670\) 4.31695e14 0.123528
\(671\) −4.06125e14 −0.115262
\(672\) 2.58701e14 0.0728228
\(673\) −5.90906e15 −1.64982 −0.824908 0.565267i \(-0.808773\pi\)
−0.824908 + 0.565267i \(0.808773\pi\)
\(674\) 7.94149e14 0.219924
\(675\) 3.48663e14 0.0957711
\(676\) 3.59501e15 0.979474
\(677\) −2.93415e15 −0.792949 −0.396474 0.918046i \(-0.629766\pi\)
−0.396474 + 0.918046i \(0.629766\pi\)
\(678\) 4.43425e14 0.118866
\(679\) −2.01680e15 −0.536264
\(680\) 4.12694e14 0.108850
\(681\) −2.43057e15 −0.635915
\(682\) −1.30974e14 −0.0339915
\(683\) −2.31821e15 −0.596815 −0.298407 0.954439i \(-0.596455\pi\)
−0.298407 + 0.954439i \(0.596455\pi\)
\(684\) 1.57445e15 0.402088
\(685\) −3.07113e15 −0.778037
\(686\) −3.17082e14 −0.0796871
\(687\) −3.79056e15 −0.945021
\(688\) −2.45587e15 −0.607392
\(689\) −6.82756e14 −0.167517
\(690\) −2.84728e14 −0.0693043
\(691\) 5.28556e15 1.27633 0.638163 0.769901i \(-0.279695\pi\)
0.638163 + 0.769901i \(0.279695\pi\)
\(692\) 4.66674e15 1.11797
\(693\) 8.71312e13 0.0207081
\(694\) 5.95289e14 0.140362
\(695\) −7.22605e15 −1.69038
\(696\) −5.29449e14 −0.122878
\(697\) 2.73115e15 0.628877
\(698\) 3.53653e14 0.0807928
\(699\) −7.69127e14 −0.174331
\(700\) 8.11413e14 0.182475
\(701\) 5.74005e15 1.28076 0.640378 0.768060i \(-0.278778\pi\)
0.640378 + 0.768060i \(0.278778\pi\)
\(702\) 8.58865e12 0.00190139
\(703\) 1.24325e15 0.273088
\(704\) 7.06681e14 0.154019
\(705\) 5.38680e15 1.16491
\(706\) 4.02877e14 0.0864462
\(707\) −1.54116e15 −0.328125
\(708\) −3.51073e14 −0.0741676
\(709\) −7.44495e14 −0.156066 −0.0780328 0.996951i \(-0.524864\pi\)
−0.0780328 + 0.996951i \(0.524864\pi\)
\(710\) 7.61952e14 0.158492
\(711\) 1.98819e15 0.410369
\(712\) −5.78815e13 −0.0118550
\(713\) 7.39797e15 1.50356
\(714\) −4.76266e13 −0.00960527
\(715\) −8.76944e13 −0.0175505
\(716\) −3.24758e15 −0.644967
\(717\) −1.07026e15 −0.210928
\(718\) −7.16306e14 −0.140092
\(719\) −6.85041e15 −1.32956 −0.664779 0.747040i \(-0.731474\pi\)
−0.664779 + 0.747040i \(0.731474\pi\)
\(720\) −2.03402e15 −0.391766
\(721\) 2.67846e15 0.511966
\(722\) −3.00212e14 −0.0569473
\(723\) −4.84291e14 −0.0911688
\(724\) −6.87619e15 −1.28465
\(725\) −2.49646e15 −0.462877
\(726\) 3.51257e14 0.0646359
\(727\) −5.98546e15 −1.09310 −0.546548 0.837428i \(-0.684058\pi\)
−0.546548 + 0.837428i \(0.684058\pi\)
\(728\) 4.02440e13 0.00729421
\(729\) 2.05891e14 0.0370370
\(730\) −3.59939e14 −0.0642618
\(731\) 1.38743e15 0.245847
\(732\) −2.23337e15 −0.392780
\(733\) −6.65829e15 −1.16223 −0.581113 0.813823i \(-0.697383\pi\)
−0.581113 + 0.813823i \(0.697383\pi\)
\(734\) 1.03070e15 0.178568
\(735\) 3.54148e15 0.608981
\(736\) 1.69372e15 0.289077
\(737\) −8.64897e14 −0.146519
\(738\) 3.69368e14 0.0621082
\(739\) −8.08499e15 −1.34938 −0.674692 0.738100i \(-0.735723\pi\)
−0.674692 + 0.738100i \(0.735723\pi\)
\(740\) −1.62832e15 −0.269753
\(741\) 3.68204e14 0.0605465
\(742\) 5.12040e14 0.0835761
\(743\) −8.56884e15 −1.38830 −0.694150 0.719830i \(-0.744220\pi\)
−0.694150 + 0.719830i \(0.744220\pi\)
\(744\) −1.45019e15 −0.233224
\(745\) 5.19515e15 0.829351
\(746\) 7.23879e14 0.114710
\(747\) −1.69577e15 −0.266749
\(748\) −4.10655e14 −0.0641236
\(749\) −1.89435e14 −0.0293637
\(750\) −2.65668e14 −0.0408792
\(751\) −4.53331e15 −0.692462 −0.346231 0.938149i \(-0.612539\pi\)
−0.346231 + 0.938149i \(0.612539\pi\)
\(752\) −1.04422e16 −1.58340
\(753\) 4.85604e15 0.730987
\(754\) −6.14956e13 −0.00918971
\(755\) −4.61355e15 −0.684426
\(756\) 4.79153e14 0.0705674
\(757\) 2.66059e15 0.389001 0.194501 0.980902i \(-0.437691\pi\)
0.194501 + 0.980902i \(0.437691\pi\)
\(758\) 3.12953e14 0.0454253
\(759\) 5.70450e14 0.0822031
\(760\) 2.39279e15 0.342319
\(761\) 5.68425e15 0.807342 0.403671 0.914904i \(-0.367734\pi\)
0.403671 + 0.914904i \(0.367734\pi\)
\(762\) 5.22659e14 0.0736998
\(763\) 3.21739e15 0.450420
\(764\) 1.14551e16 1.59215
\(765\) 1.14911e15 0.158571
\(766\) −7.85720e14 −0.107649
\(767\) −8.21025e13 −0.0111682
\(768\) 3.71907e15 0.502282
\(769\) 1.54022e15 0.206532 0.103266 0.994654i \(-0.467071\pi\)
0.103266 + 0.994654i \(0.467071\pi\)
\(770\) 6.57673e13 0.00875611
\(771\) 7.55223e15 0.998334
\(772\) −3.40808e15 −0.447317
\(773\) −7.67995e14 −0.100086 −0.0500428 0.998747i \(-0.515936\pi\)
−0.0500428 + 0.998747i \(0.515936\pi\)
\(774\) 1.87639e14 0.0242800
\(775\) −6.83792e15 −0.878547
\(776\) 2.58832e15 0.330201
\(777\) 3.78357e14 0.0479276
\(778\) −7.15218e14 −0.0899602
\(779\) 1.58352e16 1.97773
\(780\) −4.82250e14 −0.0598070
\(781\) −1.52657e15 −0.187990
\(782\) −3.11813e14 −0.0381291
\(783\) −1.47420e15 −0.179006
\(784\) −6.86504e15 −0.827761
\(785\) 3.66245e15 0.438519
\(786\) 2.40656e14 0.0286136
\(787\) 5.07026e15 0.598645 0.299322 0.954152i \(-0.403239\pi\)
0.299322 + 0.954152i \(0.403239\pi\)
\(788\) 1.05373e15 0.123547
\(789\) 4.05883e14 0.0472582
\(790\) 1.50070e15 0.173518
\(791\) 5.78533e15 0.664290
\(792\) −1.11822e14 −0.0127509
\(793\) −5.22299e14 −0.0591448
\(794\) −5.31193e14 −0.0597364
\(795\) −1.23542e16 −1.37973
\(796\) 1.94942e15 0.216214
\(797\) 7.88311e15 0.868314 0.434157 0.900837i \(-0.357046\pi\)
0.434157 + 0.900837i \(0.357046\pi\)
\(798\) −2.76139e14 −0.0302073
\(799\) 5.89923e15 0.640896
\(800\) −1.56550e15 −0.168911
\(801\) −1.61166e14 −0.0172701
\(802\) 1.85273e15 0.197176
\(803\) 7.21134e14 0.0762221
\(804\) −4.75625e15 −0.499294
\(805\) −3.71483e15 −0.387312
\(806\) −1.68439e14 −0.0174422
\(807\) 1.01167e16 1.04049
\(808\) 1.97789e15 0.202041
\(809\) −9.15896e15 −0.929243 −0.464622 0.885509i \(-0.653810\pi\)
−0.464622 + 0.885509i \(0.653810\pi\)
\(810\) 1.55408e14 0.0156605
\(811\) 1.35494e16 1.35615 0.678073 0.734994i \(-0.262815\pi\)
0.678073 + 0.734994i \(0.262815\pi\)
\(812\) −3.43079e15 −0.341064
\(813\) −6.59440e15 −0.651144
\(814\) −4.38548e13 −0.00430113
\(815\) −1.70739e16 −1.66328
\(816\) −2.22751e15 −0.215538
\(817\) 8.04429e15 0.773155
\(818\) −8.24530e14 −0.0787161
\(819\) 1.12056e14 0.0106261
\(820\) −2.07399e16 −1.95358
\(821\) −1.53313e15 −0.143447 −0.0717237 0.997425i \(-0.522850\pi\)
−0.0717237 + 0.997425i \(0.522850\pi\)
\(822\) −4.54858e14 −0.0422747
\(823\) −1.19210e16 −1.10056 −0.550279 0.834981i \(-0.685479\pi\)
−0.550279 + 0.834981i \(0.685479\pi\)
\(824\) −3.43748e15 −0.315240
\(825\) −5.27266e14 −0.0480322
\(826\) 6.15736e13 0.00557191
\(827\) −4.09891e15 −0.368459 −0.184229 0.982883i \(-0.558979\pi\)
−0.184229 + 0.982883i \(0.558979\pi\)
\(828\) 3.13703e15 0.280125
\(829\) −3.92677e15 −0.348326 −0.174163 0.984717i \(-0.555722\pi\)
−0.174163 + 0.984717i \(0.555722\pi\)
\(830\) −1.27998e15 −0.112791
\(831\) −5.34286e15 −0.467701
\(832\) 9.08830e14 0.0790323
\(833\) 3.87836e15 0.335043
\(834\) −1.07023e15 −0.0918469
\(835\) −2.19347e16 −1.87006
\(836\) −2.38097e15 −0.201660
\(837\) −4.03791e15 −0.339755
\(838\) 2.17007e15 0.181397
\(839\) 6.60581e15 0.548574 0.274287 0.961648i \(-0.411558\pi\)
0.274287 + 0.961648i \(0.411558\pi\)
\(840\) 7.28198e14 0.0600777
\(841\) −1.64507e15 −0.134836
\(842\) 2.36307e15 0.192425
\(843\) −5.38052e15 −0.435284
\(844\) −2.14347e16 −1.72280
\(845\) 1.52128e16 1.21478
\(846\) 7.97826e14 0.0632953
\(847\) 4.58283e15 0.361223
\(848\) 2.39482e16 1.87541
\(849\) 8.32275e13 0.00647552
\(850\) 2.88208e14 0.0222793
\(851\) 2.47711e15 0.190254
\(852\) −8.39491e15 −0.640617
\(853\) 1.19891e16 0.909007 0.454503 0.890745i \(-0.349817\pi\)
0.454503 + 0.890745i \(0.349817\pi\)
\(854\) 3.91704e14 0.0295080
\(855\) 6.66251e15 0.498683
\(856\) 2.43118e14 0.0180805
\(857\) −9.30733e15 −0.687750 −0.343875 0.939015i \(-0.611740\pi\)
−0.343875 + 0.939015i \(0.611740\pi\)
\(858\) −1.29882e13 −0.000953606 0
\(859\) 2.79249e15 0.203718 0.101859 0.994799i \(-0.467521\pi\)
0.101859 + 0.994799i \(0.467521\pi\)
\(860\) −1.05359e16 −0.763712
\(861\) 4.81912e15 0.347096
\(862\) −2.85508e15 −0.204328
\(863\) 4.56386e15 0.324544 0.162272 0.986746i \(-0.448118\pi\)
0.162272 + 0.986746i \(0.448118\pi\)
\(864\) −9.24456e14 −0.0653221
\(865\) 1.97480e16 1.38654
\(866\) 1.63604e15 0.114142
\(867\) −7.06965e15 −0.490109
\(868\) −9.39708e15 −0.647343
\(869\) −3.00664e15 −0.205813
\(870\) −1.11274e15 −0.0756898
\(871\) −1.11231e15 −0.0751838
\(872\) −4.12913e15 −0.277343
\(873\) 7.20693e15 0.481030
\(874\) −1.80789e15 −0.119911
\(875\) −3.46615e15 −0.228456
\(876\) 3.96567e15 0.259743
\(877\) 3.01027e16 1.95933 0.979667 0.200633i \(-0.0642997\pi\)
0.979667 + 0.200633i \(0.0642997\pi\)
\(878\) −3.96610e14 −0.0256533
\(879\) 1.17818e16 0.757311
\(880\) 3.07595e15 0.196483
\(881\) 1.13358e15 0.0719592 0.0359796 0.999353i \(-0.488545\pi\)
0.0359796 + 0.999353i \(0.488545\pi\)
\(882\) 5.24519e14 0.0330890
\(883\) −1.68216e16 −1.05459 −0.527295 0.849682i \(-0.676794\pi\)
−0.527295 + 0.849682i \(0.676794\pi\)
\(884\) −5.28124e14 −0.0329040
\(885\) −1.48561e15 −0.0919851
\(886\) 8.23125e14 0.0506501
\(887\) 2.54107e16 1.55395 0.776974 0.629533i \(-0.216754\pi\)
0.776974 + 0.629533i \(0.216754\pi\)
\(888\) −4.85575e14 −0.0295111
\(889\) 6.81910e15 0.411877
\(890\) −1.21649e14 −0.00730237
\(891\) −3.11359e14 −0.0185752
\(892\) 9.58568e15 0.568350
\(893\) 3.42036e16 2.01553
\(894\) 7.69440e14 0.0450628
\(895\) −1.37426e16 −0.799910
\(896\) −2.86191e15 −0.165563
\(897\) 7.33631e14 0.0421812
\(898\) −3.05542e14 −0.0174603
\(899\) 2.89118e16 1.64209
\(900\) −2.89955e15 −0.163680
\(901\) −1.35294e16 −0.759088
\(902\) −5.58577e14 −0.0311492
\(903\) 2.44812e15 0.135691
\(904\) −7.42478e15 −0.409032
\(905\) −2.90975e16 −1.59327
\(906\) −6.83301e14 −0.0371884
\(907\) −8.67146e15 −0.469086 −0.234543 0.972106i \(-0.575359\pi\)
−0.234543 + 0.972106i \(0.575359\pi\)
\(908\) 2.02131e16 1.08683
\(909\) 5.50724e15 0.294329
\(910\) 8.45804e13 0.00449306
\(911\) 1.89333e14 0.00999713 0.00499856 0.999988i \(-0.498409\pi\)
0.00499856 + 0.999988i \(0.498409\pi\)
\(912\) −1.29151e16 −0.677837
\(913\) 2.56443e15 0.133783
\(914\) 1.40563e14 0.00728900
\(915\) −9.45080e15 −0.487138
\(916\) 3.15230e16 1.61511
\(917\) 3.13982e15 0.159909
\(918\) 1.70191e14 0.00861595
\(919\) 2.69305e16 1.35522 0.677610 0.735421i \(-0.263016\pi\)
0.677610 + 0.735421i \(0.263016\pi\)
\(920\) 4.76753e15 0.238485
\(921\) 1.82421e16 0.907081
\(922\) −3.97659e15 −0.196558
\(923\) −1.96325e15 −0.0964642
\(924\) −7.24600e14 −0.0353918
\(925\) −2.28959e15 −0.111167
\(926\) 8.98925e14 0.0433874
\(927\) −9.57135e15 −0.459235
\(928\) 6.61920e15 0.315712
\(929\) 2.50400e14 0.0118727 0.00593633 0.999982i \(-0.498110\pi\)
0.00593633 + 0.999982i \(0.498110\pi\)
\(930\) −3.04784e15 −0.143660
\(931\) 2.24867e16 1.05366
\(932\) 6.39620e15 0.297944
\(933\) −6.58415e15 −0.304895
\(934\) −2.55554e15 −0.117646
\(935\) −1.73774e15 −0.0795282
\(936\) −1.43810e14 −0.00654292
\(937\) 1.27295e16 0.575764 0.287882 0.957666i \(-0.407049\pi\)
0.287882 + 0.957666i \(0.407049\pi\)
\(938\) 8.34185e14 0.0375100
\(939\) 1.32201e16 0.590982
\(940\) −4.47977e16 −1.99091
\(941\) 4.30849e15 0.190363 0.0951815 0.995460i \(-0.469657\pi\)
0.0951815 + 0.995460i \(0.469657\pi\)
\(942\) 5.42436e14 0.0238269
\(943\) 3.15509e16 1.37784
\(944\) 2.87981e15 0.125031
\(945\) 2.02760e15 0.0875200
\(946\) −2.83758e14 −0.0121772
\(947\) −8.23320e15 −0.351272 −0.175636 0.984455i \(-0.556198\pi\)
−0.175636 + 0.984455i \(0.556198\pi\)
\(948\) −1.65342e16 −0.701352
\(949\) 9.27419e14 0.0391122
\(950\) 1.67102e15 0.0700653
\(951\) 1.61200e16 0.672006
\(952\) 7.97469e14 0.0330530
\(953\) −1.84384e15 −0.0759821 −0.0379911 0.999278i \(-0.512096\pi\)
−0.0379911 + 0.999278i \(0.512096\pi\)
\(954\) −1.82975e15 −0.0749679
\(955\) 4.84737e16 1.97464
\(956\) 8.90047e15 0.360491
\(957\) 2.22936e15 0.0897771
\(958\) −4.10518e15 −0.164370
\(959\) −5.93450e15 −0.236255
\(960\) 1.64449e16 0.650938
\(961\) 5.37824e16 2.11671
\(962\) −5.63997e13 −0.00220706
\(963\) 6.76938e14 0.0263393
\(964\) 4.02746e15 0.155814
\(965\) −1.44218e16 −0.554777
\(966\) −5.50194e14 −0.0210446
\(967\) 3.36559e16 1.28002 0.640009 0.768368i \(-0.278931\pi\)
0.640009 + 0.768368i \(0.278931\pi\)
\(968\) −5.88151e15 −0.222420
\(969\) 7.29629e15 0.274360
\(970\) 5.43984e15 0.203396
\(971\) −2.08661e15 −0.0775775 −0.0387888 0.999247i \(-0.512350\pi\)
−0.0387888 + 0.999247i \(0.512350\pi\)
\(972\) −1.71223e15 −0.0632991
\(973\) −1.39632e16 −0.513293
\(974\) 3.24884e15 0.118756
\(975\) −6.78093e14 −0.0246470
\(976\) 1.83201e16 0.662145
\(977\) −4.70144e15 −0.168970 −0.0844851 0.996425i \(-0.526925\pi\)
−0.0844851 + 0.996425i \(0.526925\pi\)
\(978\) −2.52877e15 −0.0903746
\(979\) 2.43723e14 0.00866147
\(980\) −2.94516e16 −1.04080
\(981\) −1.14972e16 −0.404028
\(982\) −1.80999e14 −0.00632503
\(983\) 2.49311e16 0.866358 0.433179 0.901308i \(-0.357392\pi\)
0.433179 + 0.901308i \(0.357392\pi\)
\(984\) −6.18476e15 −0.213722
\(985\) 4.45899e15 0.153228
\(986\) −1.21859e15 −0.0416423
\(987\) 1.04092e16 0.353731
\(988\) −3.06206e15 −0.103479
\(989\) 1.60279e16 0.538638
\(990\) −2.35016e14 −0.00785424
\(991\) 1.15949e16 0.385357 0.192678 0.981262i \(-0.438283\pi\)
0.192678 + 0.981262i \(0.438283\pi\)
\(992\) 1.81303e16 0.599226
\(993\) 1.75743e16 0.577641
\(994\) 1.47236e15 0.0481270
\(995\) 8.24925e15 0.268156
\(996\) 1.41023e16 0.455894
\(997\) 6.17929e16 1.98662 0.993311 0.115467i \(-0.0368366\pi\)
0.993311 + 0.115467i \(0.0368366\pi\)
\(998\) 8.98397e14 0.0287244
\(999\) −1.35204e15 −0.0429912
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.d.1.14 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.d.1.14 28 1.1 even 1 trivial