Properties

Label 177.10.a.a.1.2
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $1$
Dimension $21$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(91.1613430010\)
Analytic rank: \(1\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-43.5628 q^{2} +81.0000 q^{3} +1385.72 q^{4} +1597.21 q^{5} -3528.58 q^{6} -10966.0 q^{7} -38061.5 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q-43.5628 q^{2} +81.0000 q^{3} +1385.72 q^{4} +1597.21 q^{5} -3528.58 q^{6} -10966.0 q^{7} -38061.5 q^{8} +6561.00 q^{9} -69578.8 q^{10} +52965.0 q^{11} +112243. q^{12} -146184. q^{13} +477709. q^{14} +129374. q^{15} +948577. q^{16} -276332. q^{17} -285815. q^{18} +999877. q^{19} +2.21327e6 q^{20} -888246. q^{21} -2.30730e6 q^{22} +1.88611e6 q^{23} -3.08298e6 q^{24} +597945. q^{25} +6.36817e6 q^{26} +531441. q^{27} -1.51958e7 q^{28} -6.91128e6 q^{29} -5.63588e6 q^{30} -1.40963e6 q^{31} -2.18352e7 q^{32} +4.29017e6 q^{33} +1.20378e7 q^{34} -1.75150e7 q^{35} +9.09168e6 q^{36} +4.90587e6 q^{37} -4.35574e7 q^{38} -1.18409e7 q^{39} -6.07921e7 q^{40} +2.05841e7 q^{41} +3.86945e7 q^{42} -3.94179e6 q^{43} +7.33945e7 q^{44} +1.04793e7 q^{45} -8.21642e7 q^{46} +6.35577e6 q^{47} +7.68347e7 q^{48} +7.98995e7 q^{49} -2.60481e7 q^{50} -2.23829e7 q^{51} -2.02569e8 q^{52} -7.48000e7 q^{53} -2.31510e7 q^{54} +8.45961e7 q^{55} +4.17382e8 q^{56} +8.09900e7 q^{57} +3.01075e8 q^{58} +1.21174e7 q^{59} +1.79275e8 q^{60} -7.46185e7 q^{61} +6.14074e7 q^{62} -7.19479e7 q^{63} +4.65530e8 q^{64} -2.33486e8 q^{65} -1.86892e8 q^{66} +2.24949e7 q^{67} -3.82918e8 q^{68} +1.52775e8 q^{69} +7.63001e8 q^{70} -2.63688e8 q^{71} -2.49721e8 q^{72} +1.35213e8 q^{73} -2.13714e8 q^{74} +4.84335e7 q^{75} +1.38554e9 q^{76} -5.80815e8 q^{77} +5.15821e8 q^{78} +1.42336e8 q^{79} +1.51507e9 q^{80} +4.30467e7 q^{81} -8.96702e8 q^{82} -1.25542e7 q^{83} -1.23086e9 q^{84} -4.41360e8 q^{85} +1.71715e8 q^{86} -5.59814e8 q^{87} -2.01593e9 q^{88} -8.08199e8 q^{89} -4.56506e8 q^{90} +1.60305e9 q^{91} +2.61361e9 q^{92} -1.14180e8 q^{93} -2.76875e8 q^{94} +1.59701e9 q^{95} -1.76865e9 q^{96} -1.04265e8 q^{97} -3.48065e9 q^{98} +3.47504e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21q - 66q^{2} + 1701q^{3} + 5206q^{4} - 2964q^{5} - 5346q^{6} - 30775q^{7} - 24621q^{8} + 137781q^{9} + O(q^{10}) \) \( 21q - 66q^{2} + 1701q^{3} + 5206q^{4} - 2964q^{5} - 5346q^{6} - 30775q^{7} - 24621q^{8} + 137781q^{9} - 54663q^{10} - 151769q^{11} + 421686q^{12} - 153611q^{13} - 286771q^{14} - 240084q^{15} + 805530q^{16} - 723621q^{17} - 433026q^{18} - 549388q^{19} - 527311q^{20} - 2492775q^{21} + 2973158q^{22} + 169962q^{23} - 1994301q^{24} + 8035779q^{25} - 2337392q^{26} + 11160261q^{27} - 22659054q^{28} - 16845442q^{29} - 4427703q^{30} - 19307976q^{31} - 44923568q^{32} - 12293289q^{33} - 35547496q^{34} - 34882596q^{35} + 34156566q^{36} - 41561129q^{37} - 52335371q^{38} - 12442491q^{39} - 125735038q^{40} - 68169291q^{41} - 23228451q^{42} - 25719587q^{43} - 126277032q^{44} - 19446804q^{45} - 292814271q^{46} - 174095332q^{47} + 65247930q^{48} + 7479350q^{49} - 227877439q^{50} - 58613301q^{51} - 232397708q^{52} - 228390500q^{53} - 35075106q^{54} - 29426208q^{55} + 326778474q^{56} - 44500428q^{57} + 480343762q^{58} + 254464581q^{59} - 42712191q^{60} - 183928964q^{61} - 21753862q^{62} - 201914775q^{63} + 310571245q^{64} + 5308466q^{65} + 240825798q^{66} - 82724114q^{67} - 138336205q^{68} + 13766922q^{69} + 1030274876q^{70} - 404721965q^{71} - 161538381q^{72} + 154162574q^{73} + 36352054q^{74} + 650898099q^{75} + 1068940636q^{76} - 448535481q^{77} - 189328752q^{78} + 272529635q^{79} - 345587859q^{80} + 903981141q^{81} - 38412637q^{82} + 432518643q^{83} - 1835383374q^{84} - 126211490q^{85} - 3699273072q^{86} - 1364480802q^{87} + 170111045q^{88} - 1255621070q^{89} - 358643943q^{90} + 1448885849q^{91} + 1568933320q^{92} - 1563946056q^{93} - 1908445164q^{94} - 2896546490q^{95} - 3638809008q^{96} + 1007235486q^{97} - 9506868248q^{98} - 995756409q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −43.5628 −1.92522 −0.962610 0.270889i \(-0.912682\pi\)
−0.962610 + 0.270889i \(0.912682\pi\)
\(3\) 81.0000 0.577350
\(4\) 1385.72 2.70648
\(5\) 1597.21 1.14287 0.571434 0.820648i \(-0.306387\pi\)
0.571434 + 0.820648i \(0.306387\pi\)
\(6\) −3528.58 −1.11153
\(7\) −10966.0 −1.72626 −0.863132 0.504979i \(-0.831500\pi\)
−0.863132 + 0.504979i \(0.831500\pi\)
\(8\) −38061.5 −3.28534
\(9\) 6561.00 0.333333
\(10\) −69578.8 −2.20027
\(11\) 52965.0 1.09074 0.545371 0.838195i \(-0.316389\pi\)
0.545371 + 0.838195i \(0.316389\pi\)
\(12\) 112243. 1.56258
\(13\) −146184. −1.41956 −0.709780 0.704423i \(-0.751206\pi\)
−0.709780 + 0.704423i \(0.751206\pi\)
\(14\) 477709. 3.32344
\(15\) 129374. 0.659835
\(16\) 948577. 3.61853
\(17\) −276332. −0.802438 −0.401219 0.915982i \(-0.631413\pi\)
−0.401219 + 0.915982i \(0.631413\pi\)
\(18\) −285815. −0.641740
\(19\) 999877. 1.76017 0.880086 0.474814i \(-0.157485\pi\)
0.880086 + 0.474814i \(0.157485\pi\)
\(20\) 2.21327e6 3.09315
\(21\) −888246. −0.996659
\(22\) −2.30730e6 −2.09992
\(23\) 1.88611e6 1.40537 0.702686 0.711500i \(-0.251984\pi\)
0.702686 + 0.711500i \(0.251984\pi\)
\(24\) −3.08298e6 −1.89679
\(25\) 597945. 0.306148
\(26\) 6.36817e6 2.73297
\(27\) 531441. 0.192450
\(28\) −1.51958e7 −4.67209
\(29\) −6.91128e6 −1.81454 −0.907272 0.420543i \(-0.861839\pi\)
−0.907272 + 0.420543i \(0.861839\pi\)
\(30\) −5.63588e6 −1.27033
\(31\) −1.40963e6 −0.274143 −0.137072 0.990561i \(-0.543769\pi\)
−0.137072 + 0.990561i \(0.543769\pi\)
\(32\) −2.18352e7 −3.68114
\(33\) 4.29017e6 0.629740
\(34\) 1.20378e7 1.54487
\(35\) −1.75150e7 −1.97289
\(36\) 9.09168e6 0.902159
\(37\) 4.90587e6 0.430337 0.215168 0.976577i \(-0.430970\pi\)
0.215168 + 0.976577i \(0.430970\pi\)
\(38\) −4.35574e7 −3.38872
\(39\) −1.18409e7 −0.819583
\(40\) −6.07921e7 −3.75471
\(41\) 2.05841e7 1.13764 0.568820 0.822462i \(-0.307400\pi\)
0.568820 + 0.822462i \(0.307400\pi\)
\(42\) 3.86945e7 1.91879
\(43\) −3.94179e6 −0.175827 −0.0879135 0.996128i \(-0.528020\pi\)
−0.0879135 + 0.996128i \(0.528020\pi\)
\(44\) 7.33945e7 2.95207
\(45\) 1.04793e7 0.380956
\(46\) −8.21642e7 −2.70565
\(47\) 6.35577e6 0.189989 0.0949943 0.995478i \(-0.469717\pi\)
0.0949943 + 0.995478i \(0.469717\pi\)
\(48\) 7.68347e7 2.08916
\(49\) 7.98995e7 1.97999
\(50\) −2.60481e7 −0.589402
\(51\) −2.23829e7 −0.463288
\(52\) −2.02569e8 −3.84200
\(53\) −7.48000e7 −1.30215 −0.651074 0.759014i \(-0.725681\pi\)
−0.651074 + 0.759014i \(0.725681\pi\)
\(54\) −2.31510e7 −0.370509
\(55\) 8.45961e7 1.24657
\(56\) 4.17382e8 5.67137
\(57\) 8.09900e7 1.01624
\(58\) 3.01075e8 3.49340
\(59\) 1.21174e7 0.130189
\(60\) 1.79275e8 1.78583
\(61\) −7.46185e7 −0.690021 −0.345010 0.938599i \(-0.612125\pi\)
−0.345010 + 0.938599i \(0.612125\pi\)
\(62\) 6.14074e7 0.527786
\(63\) −7.19479e7 −0.575421
\(64\) 4.65530e8 3.46847
\(65\) −2.33486e8 −1.62237
\(66\) −1.86892e8 −1.21239
\(67\) 2.24949e7 0.136379 0.0681896 0.997672i \(-0.478278\pi\)
0.0681896 + 0.997672i \(0.478278\pi\)
\(68\) −3.82918e8 −2.17178
\(69\) 1.52775e8 0.811392
\(70\) 7.63001e8 3.79825
\(71\) −2.63688e8 −1.23148 −0.615741 0.787949i \(-0.711143\pi\)
−0.615741 + 0.787949i \(0.711143\pi\)
\(72\) −2.49721e8 −1.09511
\(73\) 1.35213e8 0.557271 0.278636 0.960397i \(-0.410118\pi\)
0.278636 + 0.960397i \(0.410118\pi\)
\(74\) −2.13714e8 −0.828494
\(75\) 4.84335e7 0.176755
\(76\) 1.38554e9 4.76386
\(77\) −5.80815e8 −1.88291
\(78\) 5.15821e8 1.57788
\(79\) 1.42336e8 0.411142 0.205571 0.978642i \(-0.434095\pi\)
0.205571 + 0.978642i \(0.434095\pi\)
\(80\) 1.51507e9 4.13551
\(81\) 4.30467e7 0.111111
\(82\) −8.96702e8 −2.19021
\(83\) −1.25542e7 −0.0290360 −0.0145180 0.999895i \(-0.504621\pi\)
−0.0145180 + 0.999895i \(0.504621\pi\)
\(84\) −1.23086e9 −2.69743
\(85\) −4.41360e8 −0.917080
\(86\) 1.71715e8 0.338506
\(87\) −5.59814e8 −1.04763
\(88\) −2.01593e9 −3.58346
\(89\) −8.08199e8 −1.36541 −0.682705 0.730694i \(-0.739197\pi\)
−0.682705 + 0.730694i \(0.739197\pi\)
\(90\) −4.56506e8 −0.733425
\(91\) 1.60305e9 2.45053
\(92\) 2.61361e9 3.80361
\(93\) −1.14180e8 −0.158277
\(94\) −2.76875e8 −0.365770
\(95\) 1.59701e9 2.01165
\(96\) −1.76865e9 −2.12530
\(97\) −1.04265e8 −0.119582 −0.0597909 0.998211i \(-0.519043\pi\)
−0.0597909 + 0.998211i \(0.519043\pi\)
\(98\) −3.48065e9 −3.81191
\(99\) 3.47504e8 0.363581
\(100\) 8.28582e8 0.828582
\(101\) −1.91315e9 −1.82938 −0.914689 0.404159i \(-0.867564\pi\)
−0.914689 + 0.404159i \(0.867564\pi\)
\(102\) 9.75061e8 0.891931
\(103\) −3.75074e8 −0.328359 −0.164180 0.986430i \(-0.552498\pi\)
−0.164180 + 0.986430i \(0.552498\pi\)
\(104\) 5.56397e9 4.66374
\(105\) −1.41871e9 −1.13905
\(106\) 3.25850e9 2.50692
\(107\) 3.35288e8 0.247281 0.123641 0.992327i \(-0.460543\pi\)
0.123641 + 0.992327i \(0.460543\pi\)
\(108\) 7.36426e8 0.520861
\(109\) 1.50110e9 1.01857 0.509283 0.860599i \(-0.329911\pi\)
0.509283 + 0.860599i \(0.329911\pi\)
\(110\) −3.68524e9 −2.39993
\(111\) 3.97376e8 0.248455
\(112\) −1.04021e10 −6.24654
\(113\) −5.24785e8 −0.302781 −0.151390 0.988474i \(-0.548375\pi\)
−0.151390 + 0.988474i \(0.548375\pi\)
\(114\) −3.52815e9 −1.95648
\(115\) 3.01251e9 1.60616
\(116\) −9.57707e9 −4.91102
\(117\) −9.59111e8 −0.473187
\(118\) −5.27866e8 −0.250642
\(119\) 3.03026e9 1.38522
\(120\) −4.92416e9 −2.16778
\(121\) 4.47347e8 0.189719
\(122\) 3.25059e9 1.32844
\(123\) 1.66731e9 0.656817
\(124\) −1.95334e9 −0.741961
\(125\) −2.16450e9 −0.792982
\(126\) 3.13425e9 1.10781
\(127\) −5.21327e8 −0.177825 −0.0889126 0.996039i \(-0.528339\pi\)
−0.0889126 + 0.996039i \(0.528339\pi\)
\(128\) −9.10015e9 −2.99643
\(129\) −3.19285e8 −0.101514
\(130\) 1.01713e10 3.12342
\(131\) 3.86658e9 1.14711 0.573557 0.819166i \(-0.305563\pi\)
0.573557 + 0.819166i \(0.305563\pi\)
\(132\) 5.94495e9 1.70438
\(133\) −1.09646e10 −3.03852
\(134\) −9.79942e8 −0.262560
\(135\) 8.48821e8 0.219945
\(136\) 1.05176e10 2.63628
\(137\) −1.63775e8 −0.0397197 −0.0198598 0.999803i \(-0.506322\pi\)
−0.0198598 + 0.999803i \(0.506322\pi\)
\(138\) −6.65530e9 −1.56211
\(139\) 5.02768e9 1.14235 0.571177 0.820827i \(-0.306487\pi\)
0.571177 + 0.820827i \(0.306487\pi\)
\(140\) −2.42708e10 −5.33958
\(141\) 5.14817e8 0.109690
\(142\) 1.14870e10 2.37087
\(143\) −7.74262e9 −1.54837
\(144\) 6.22361e9 1.20618
\(145\) −1.10387e10 −2.07379
\(146\) −5.89027e9 −1.07287
\(147\) 6.47186e9 1.14314
\(148\) 6.79815e9 1.16470
\(149\) 7.02775e9 1.16810 0.584048 0.811719i \(-0.301468\pi\)
0.584048 + 0.811719i \(0.301468\pi\)
\(150\) −2.10990e9 −0.340292
\(151\) −4.38989e9 −0.687159 −0.343580 0.939124i \(-0.611640\pi\)
−0.343580 + 0.939124i \(0.611640\pi\)
\(152\) −3.80568e10 −5.78277
\(153\) −1.81302e9 −0.267479
\(154\) 2.53019e10 3.62501
\(155\) −2.25147e9 −0.313309
\(156\) −1.64081e10 −2.21818
\(157\) 7.13429e9 0.937135 0.468568 0.883428i \(-0.344770\pi\)
0.468568 + 0.883428i \(0.344770\pi\)
\(158\) −6.20053e9 −0.791538
\(159\) −6.05880e9 −0.751796
\(160\) −3.48753e10 −4.20705
\(161\) −2.06831e10 −2.42604
\(162\) −1.87523e9 −0.213913
\(163\) −1.51240e10 −1.67812 −0.839061 0.544038i \(-0.816895\pi\)
−0.839061 + 0.544038i \(0.816895\pi\)
\(164\) 2.85238e10 3.07900
\(165\) 6.85229e9 0.719710
\(166\) 5.46895e8 0.0559007
\(167\) −6.77132e9 −0.673674 −0.336837 0.941563i \(-0.609357\pi\)
−0.336837 + 0.941563i \(0.609357\pi\)
\(168\) 3.38080e10 3.27437
\(169\) 1.07652e10 1.01515
\(170\) 1.92269e10 1.76558
\(171\) 6.56019e9 0.586724
\(172\) −5.46220e9 −0.475871
\(173\) −1.25124e9 −0.106202 −0.0531009 0.998589i \(-0.516910\pi\)
−0.0531009 + 0.998589i \(0.516910\pi\)
\(174\) 2.43871e10 2.01692
\(175\) −6.55707e9 −0.528492
\(176\) 5.02414e10 3.94689
\(177\) 9.81506e8 0.0751646
\(178\) 3.52074e10 2.62872
\(179\) −1.64348e10 −1.19653 −0.598266 0.801297i \(-0.704143\pi\)
−0.598266 + 0.801297i \(0.704143\pi\)
\(180\) 1.45213e10 1.03105
\(181\) −4.40038e7 −0.00304745 −0.00152372 0.999999i \(-0.500485\pi\)
−0.00152372 + 0.999999i \(0.500485\pi\)
\(182\) −6.98333e10 −4.71782
\(183\) −6.04410e9 −0.398384
\(184\) −7.17881e10 −4.61713
\(185\) 7.83570e9 0.491818
\(186\) 4.97400e9 0.304717
\(187\) −1.46359e10 −0.875253
\(188\) 8.80729e9 0.514200
\(189\) −5.82778e9 −0.332220
\(190\) −6.95702e10 −3.87286
\(191\) −1.43446e10 −0.779896 −0.389948 0.920837i \(-0.627507\pi\)
−0.389948 + 0.920837i \(0.627507\pi\)
\(192\) 3.77079e10 2.00252
\(193\) −2.20418e10 −1.14351 −0.571754 0.820425i \(-0.693737\pi\)
−0.571754 + 0.820425i \(0.693737\pi\)
\(194\) 4.54206e9 0.230221
\(195\) −1.89123e10 −0.936676
\(196\) 1.10718e11 5.35878
\(197\) −3.24597e10 −1.53549 −0.767745 0.640755i \(-0.778621\pi\)
−0.767745 + 0.640755i \(0.778621\pi\)
\(198\) −1.51382e10 −0.699973
\(199\) −1.55333e10 −0.702141 −0.351070 0.936349i \(-0.614182\pi\)
−0.351070 + 0.936349i \(0.614182\pi\)
\(200\) −2.27587e10 −1.00580
\(201\) 1.82209e9 0.0787386
\(202\) 8.33422e10 3.52196
\(203\) 7.57891e10 3.13238
\(204\) −3.10163e10 −1.25388
\(205\) 3.28771e10 1.30017
\(206\) 1.63393e10 0.632164
\(207\) 1.23748e10 0.468458
\(208\) −1.38666e11 −5.13673
\(209\) 5.29585e10 1.91989
\(210\) 6.18031e10 2.19292
\(211\) 7.41772e9 0.257632 0.128816 0.991669i \(-0.458882\pi\)
0.128816 + 0.991669i \(0.458882\pi\)
\(212\) −1.03652e11 −3.52423
\(213\) −2.13587e10 −0.710996
\(214\) −1.46061e10 −0.476071
\(215\) −6.29586e9 −0.200947
\(216\) −2.02274e10 −0.632264
\(217\) 1.54580e10 0.473243
\(218\) −6.53919e10 −1.96097
\(219\) 1.09523e10 0.321741
\(220\) 1.17226e11 3.37382
\(221\) 4.03952e10 1.13911
\(222\) −1.73108e10 −0.478331
\(223\) 2.99814e10 0.811858 0.405929 0.913905i \(-0.366948\pi\)
0.405929 + 0.913905i \(0.366948\pi\)
\(224\) 2.39445e11 6.35461
\(225\) 3.92312e9 0.102049
\(226\) 2.28611e10 0.582920
\(227\) 3.94298e10 0.985618 0.492809 0.870138i \(-0.335970\pi\)
0.492809 + 0.870138i \(0.335970\pi\)
\(228\) 1.12229e11 2.75042
\(229\) −1.03992e10 −0.249886 −0.124943 0.992164i \(-0.539875\pi\)
−0.124943 + 0.992164i \(0.539875\pi\)
\(230\) −1.31233e11 −3.09221
\(231\) −4.70460e10 −1.08710
\(232\) 2.63054e11 5.96140
\(233\) −6.95843e10 −1.54671 −0.773356 0.633972i \(-0.781423\pi\)
−0.773356 + 0.633972i \(0.781423\pi\)
\(234\) 4.17815e10 0.910989
\(235\) 1.01515e10 0.217132
\(236\) 1.67912e10 0.352353
\(237\) 1.15292e10 0.237373
\(238\) −1.32006e11 −2.66685
\(239\) −4.09211e10 −0.811254 −0.405627 0.914039i \(-0.632947\pi\)
−0.405627 + 0.914039i \(0.632947\pi\)
\(240\) 1.22721e11 2.38764
\(241\) −6.90087e10 −1.31773 −0.658866 0.752261i \(-0.728963\pi\)
−0.658866 + 0.752261i \(0.728963\pi\)
\(242\) −1.94877e10 −0.365251
\(243\) 3.48678e9 0.0641500
\(244\) −1.03400e11 −1.86752
\(245\) 1.27616e11 2.26286
\(246\) −7.26329e10 −1.26452
\(247\) −1.46166e11 −2.49867
\(248\) 5.36526e10 0.900654
\(249\) −1.01689e9 −0.0167639
\(250\) 9.42918e10 1.52666
\(251\) 8.87595e10 1.41151 0.705754 0.708457i \(-0.250609\pi\)
0.705754 + 0.708457i \(0.250609\pi\)
\(252\) −9.96994e10 −1.55736
\(253\) 9.98978e10 1.53290
\(254\) 2.27104e10 0.342353
\(255\) −3.57501e10 −0.529477
\(256\) 1.58077e11 2.30032
\(257\) 9.45600e10 1.35210 0.676049 0.736857i \(-0.263691\pi\)
0.676049 + 0.736857i \(0.263691\pi\)
\(258\) 1.39089e10 0.195436
\(259\) −5.37978e10 −0.742875
\(260\) −3.23545e11 −4.39090
\(261\) −4.53449e10 −0.604848
\(262\) −1.68439e11 −2.20845
\(263\) −1.00500e11 −1.29529 −0.647644 0.761943i \(-0.724246\pi\)
−0.647644 + 0.761943i \(0.724246\pi\)
\(264\) −1.63290e11 −2.06891
\(265\) −1.19471e11 −1.48818
\(266\) 4.77650e11 5.84982
\(267\) −6.54641e10 −0.788320
\(268\) 3.11716e10 0.369107
\(269\) −6.93801e9 −0.0807885 −0.0403942 0.999184i \(-0.512861\pi\)
−0.0403942 + 0.999184i \(0.512861\pi\)
\(270\) −3.69770e10 −0.423443
\(271\) 9.60064e10 1.08128 0.540640 0.841254i \(-0.318182\pi\)
0.540640 + 0.841254i \(0.318182\pi\)
\(272\) −2.62122e11 −2.90365
\(273\) 1.29847e11 1.41482
\(274\) 7.13450e9 0.0764691
\(275\) 3.16702e10 0.333928
\(276\) 2.11702e11 2.19601
\(277\) −1.82037e11 −1.85781 −0.928905 0.370318i \(-0.879249\pi\)
−0.928905 + 0.370318i \(0.879249\pi\)
\(278\) −2.19020e11 −2.19928
\(279\) −9.24858e9 −0.0913810
\(280\) 6.66646e11 6.48162
\(281\) −1.73949e11 −1.66435 −0.832173 0.554517i \(-0.812903\pi\)
−0.832173 + 0.554517i \(0.812903\pi\)
\(282\) −2.24269e10 −0.211178
\(283\) −1.91984e11 −1.77921 −0.889603 0.456734i \(-0.849019\pi\)
−0.889603 + 0.456734i \(0.849019\pi\)
\(284\) −3.65397e11 −3.33297
\(285\) 1.29358e11 1.16142
\(286\) 3.37290e11 2.98096
\(287\) −2.25726e11 −1.96387
\(288\) −1.43261e11 −1.22705
\(289\) −4.22284e10 −0.356094
\(290\) 4.80879e11 3.99250
\(291\) −8.44545e9 −0.0690405
\(292\) 1.87367e11 1.50824
\(293\) −5.44405e10 −0.431536 −0.215768 0.976445i \(-0.569226\pi\)
−0.215768 + 0.976445i \(0.569226\pi\)
\(294\) −2.81932e11 −2.20081
\(295\) 1.93539e10 0.148789
\(296\) −1.86725e11 −1.41380
\(297\) 2.81478e10 0.209913
\(298\) −3.06148e11 −2.24884
\(299\) −2.75718e11 −1.99501
\(300\) 6.71151e10 0.478382
\(301\) 4.32257e10 0.303524
\(302\) 1.91236e11 1.32293
\(303\) −1.54965e11 −1.05619
\(304\) 9.48460e11 6.36925
\(305\) −1.19181e11 −0.788603
\(306\) 7.89800e10 0.514957
\(307\) −6.62838e10 −0.425877 −0.212939 0.977066i \(-0.568303\pi\)
−0.212939 + 0.977066i \(0.568303\pi\)
\(308\) −8.04844e11 −5.09605
\(309\) −3.03810e10 −0.189578
\(310\) 9.80802e10 0.603190
\(311\) 8.07048e9 0.0489190 0.0244595 0.999701i \(-0.492214\pi\)
0.0244595 + 0.999701i \(0.492214\pi\)
\(312\) 4.50681e11 2.69261
\(313\) 1.54810e10 0.0911696 0.0455848 0.998960i \(-0.485485\pi\)
0.0455848 + 0.998960i \(0.485485\pi\)
\(314\) −3.10790e11 −1.80419
\(315\) −1.14916e11 −0.657631
\(316\) 1.97237e11 1.11274
\(317\) −3.29987e11 −1.83540 −0.917699 0.397276i \(-0.869956\pi\)
−0.917699 + 0.397276i \(0.869956\pi\)
\(318\) 2.63938e11 1.44737
\(319\) −3.66056e11 −1.97920
\(320\) 7.43547e11 3.96400
\(321\) 2.71583e10 0.142768
\(322\) 9.01012e11 4.67067
\(323\) −2.76298e11 −1.41243
\(324\) 5.96505e10 0.300720
\(325\) −8.74098e10 −0.434595
\(326\) 6.58845e11 3.23075
\(327\) 1.21589e11 0.588070
\(328\) −7.83462e11 −3.73754
\(329\) −6.96974e10 −0.327970
\(330\) −2.98505e11 −1.38560
\(331\) −1.41539e11 −0.648113 −0.324057 0.946038i \(-0.605047\pi\)
−0.324057 + 0.946038i \(0.605047\pi\)
\(332\) −1.73965e10 −0.0785853
\(333\) 3.21874e10 0.143446
\(334\) 2.94978e11 1.29697
\(335\) 3.59291e10 0.155863
\(336\) −8.42570e11 −3.60644
\(337\) 7.94755e10 0.335659 0.167830 0.985816i \(-0.446324\pi\)
0.167830 + 0.985816i \(0.446324\pi\)
\(338\) −4.68960e11 −1.95439
\(339\) −4.25076e10 −0.174811
\(340\) −6.11599e11 −2.48206
\(341\) −7.46610e10 −0.299019
\(342\) −2.85780e11 −1.12957
\(343\) −4.33661e11 −1.69171
\(344\) 1.50030e11 0.577652
\(345\) 2.44013e11 0.927315
\(346\) 5.45073e10 0.204462
\(347\) 2.42349e11 0.897343 0.448671 0.893697i \(-0.351897\pi\)
0.448671 + 0.893697i \(0.351897\pi\)
\(348\) −7.75743e11 −2.83538
\(349\) 1.34335e11 0.484703 0.242352 0.970188i \(-0.422081\pi\)
0.242352 + 0.970188i \(0.422081\pi\)
\(350\) 2.85644e11 1.01746
\(351\) −7.76880e10 −0.273194
\(352\) −1.15650e12 −4.01517
\(353\) 2.89766e11 0.993258 0.496629 0.867963i \(-0.334571\pi\)
0.496629 + 0.867963i \(0.334571\pi\)
\(354\) −4.27571e10 −0.144708
\(355\) −4.21164e11 −1.40742
\(356\) −1.11993e12 −3.69545
\(357\) 2.45451e11 0.799756
\(358\) 7.15943e11 2.30359
\(359\) 2.09948e11 0.667092 0.333546 0.942734i \(-0.391755\pi\)
0.333546 + 0.942734i \(0.391755\pi\)
\(360\) −3.98857e11 −1.25157
\(361\) 6.77066e11 2.09821
\(362\) 1.91693e9 0.00586701
\(363\) 3.62351e10 0.109534
\(364\) 2.22137e12 6.63231
\(365\) 2.15964e11 0.636887
\(366\) 2.63298e11 0.766976
\(367\) 2.83366e11 0.815363 0.407681 0.913124i \(-0.366337\pi\)
0.407681 + 0.913124i \(0.366337\pi\)
\(368\) 1.78912e12 5.08539
\(369\) 1.35052e11 0.379214
\(370\) −3.41345e11 −0.946859
\(371\) 8.20257e11 2.24785
\(372\) −1.58221e11 −0.428372
\(373\) −2.03235e11 −0.543636 −0.271818 0.962349i \(-0.587625\pi\)
−0.271818 + 0.962349i \(0.587625\pi\)
\(374\) 6.37582e11 1.68505
\(375\) −1.75325e11 −0.457828
\(376\) −2.41910e11 −0.624178
\(377\) 1.01032e12 2.57586
\(378\) 2.53874e11 0.639596
\(379\) 7.46197e10 0.185771 0.0928853 0.995677i \(-0.470391\pi\)
0.0928853 + 0.995677i \(0.470391\pi\)
\(380\) 2.21300e12 5.44447
\(381\) −4.22275e10 −0.102667
\(382\) 6.24889e11 1.50147
\(383\) −2.80797e11 −0.666803 −0.333401 0.942785i \(-0.608196\pi\)
−0.333401 + 0.942785i \(0.608196\pi\)
\(384\) −7.37112e11 −1.72999
\(385\) −9.27681e11 −2.15192
\(386\) 9.60203e11 2.20151
\(387\) −2.58621e10 −0.0586090
\(388\) −1.44481e11 −0.323645
\(389\) 4.02766e11 0.891824 0.445912 0.895077i \(-0.352879\pi\)
0.445912 + 0.895077i \(0.352879\pi\)
\(390\) 8.23874e11 1.80331
\(391\) −5.21193e11 −1.12772
\(392\) −3.04109e12 −6.50493
\(393\) 3.13193e11 0.662286
\(394\) 1.41404e12 2.95616
\(395\) 2.27339e11 0.469881
\(396\) 4.81541e11 0.984023
\(397\) −1.15594e11 −0.233549 −0.116775 0.993158i \(-0.537255\pi\)
−0.116775 + 0.993158i \(0.537255\pi\)
\(398\) 6.76673e11 1.35178
\(399\) −8.88136e11 −1.75429
\(400\) 5.67197e11 1.10781
\(401\) −5.68027e11 −1.09703 −0.548516 0.836140i \(-0.684807\pi\)
−0.548516 + 0.836140i \(0.684807\pi\)
\(402\) −7.93753e10 −0.151589
\(403\) 2.06065e11 0.389162
\(404\) −2.65108e12 −4.95117
\(405\) 6.87545e10 0.126985
\(406\) −3.30159e12 −6.03053
\(407\) 2.59840e11 0.469387
\(408\) 8.51926e11 1.52206
\(409\) −4.33352e11 −0.765749 −0.382874 0.923800i \(-0.625066\pi\)
−0.382874 + 0.923800i \(0.625066\pi\)
\(410\) −1.43222e12 −2.50312
\(411\) −1.32658e10 −0.0229322
\(412\) −5.19746e11 −0.888697
\(413\) −1.32879e11 −0.224740
\(414\) −5.39079e11 −0.901884
\(415\) −2.00516e10 −0.0331843
\(416\) 3.19195e12 5.22559
\(417\) 4.07242e11 0.659539
\(418\) −2.30702e12 −3.69622
\(419\) −9.10366e11 −1.44296 −0.721478 0.692438i \(-0.756537\pi\)
−0.721478 + 0.692438i \(0.756537\pi\)
\(420\) −1.96593e12 −3.08281
\(421\) 5.30818e11 0.823524 0.411762 0.911291i \(-0.364913\pi\)
0.411762 + 0.911291i \(0.364913\pi\)
\(422\) −3.23136e11 −0.495998
\(423\) 4.17002e10 0.0633296
\(424\) 2.84700e12 4.27800
\(425\) −1.65231e11 −0.245665
\(426\) 9.30445e11 1.36882
\(427\) 8.18266e11 1.19116
\(428\) 4.64614e11 0.669260
\(429\) −6.27152e11 −0.893954
\(430\) 2.74265e11 0.386868
\(431\) −1.05184e12 −1.46826 −0.734130 0.679009i \(-0.762410\pi\)
−0.734130 + 0.679009i \(0.762410\pi\)
\(432\) 5.04113e11 0.696387
\(433\) 3.32873e11 0.455074 0.227537 0.973769i \(-0.426933\pi\)
0.227537 + 0.973769i \(0.426933\pi\)
\(434\) −6.73393e11 −0.911097
\(435\) −8.94139e11 −1.19730
\(436\) 2.08009e12 2.75673
\(437\) 1.88588e12 2.47370
\(438\) −4.77112e11 −0.619422
\(439\) −1.34032e12 −1.72233 −0.861166 0.508323i \(-0.830265\pi\)
−0.861166 + 0.508323i \(0.830265\pi\)
\(440\) −3.21985e12 −4.09543
\(441\) 5.24221e11 0.659995
\(442\) −1.75973e12 −2.19303
\(443\) 2.01187e11 0.248189 0.124095 0.992270i \(-0.460397\pi\)
0.124095 + 0.992270i \(0.460397\pi\)
\(444\) 5.50650e11 0.672438
\(445\) −1.29086e12 −1.56048
\(446\) −1.30607e12 −1.56301
\(447\) 5.69248e11 0.674400
\(448\) −5.10500e12 −5.98749
\(449\) −6.42787e11 −0.746377 −0.373189 0.927756i \(-0.621736\pi\)
−0.373189 + 0.927756i \(0.621736\pi\)
\(450\) −1.70902e11 −0.196467
\(451\) 1.09024e12 1.24087
\(452\) −7.27203e11 −0.819469
\(453\) −3.55581e11 −0.396732
\(454\) −1.71767e12 −1.89753
\(455\) 2.56040e12 2.80064
\(456\) −3.08260e12 −3.33868
\(457\) 1.43216e12 1.53592 0.767959 0.640499i \(-0.221272\pi\)
0.767959 + 0.640499i \(0.221272\pi\)
\(458\) 4.53020e11 0.481086
\(459\) −1.46854e11 −0.154429
\(460\) 4.17448e12 4.34702
\(461\) 4.59275e11 0.473607 0.236804 0.971558i \(-0.423900\pi\)
0.236804 + 0.971558i \(0.423900\pi\)
\(462\) 2.04945e12 2.09290
\(463\) 1.91038e12 1.93199 0.965997 0.258553i \(-0.0832457\pi\)
0.965997 + 0.258553i \(0.0832457\pi\)
\(464\) −6.55589e12 −6.56599
\(465\) −1.82369e11 −0.180889
\(466\) 3.03128e12 2.97776
\(467\) −4.19414e11 −0.408053 −0.204027 0.978965i \(-0.565403\pi\)
−0.204027 + 0.978965i \(0.565403\pi\)
\(468\) −1.32905e12 −1.28067
\(469\) −2.46680e11 −0.235426
\(470\) −4.42227e11 −0.418027
\(471\) 5.77878e11 0.541055
\(472\) −4.61205e11 −0.427715
\(473\) −2.08777e11 −0.191782
\(474\) −5.02243e11 −0.456995
\(475\) 5.97871e11 0.538873
\(476\) 4.19908e12 3.74906
\(477\) −4.90763e11 −0.434049
\(478\) 1.78264e12 1.56184
\(479\) −2.11271e12 −1.83371 −0.916855 0.399220i \(-0.869281\pi\)
−0.916855 + 0.399220i \(0.869281\pi\)
\(480\) −2.82490e12 −2.42894
\(481\) −7.17159e11 −0.610889
\(482\) 3.00621e12 2.53692
\(483\) −1.67533e12 −1.40068
\(484\) 6.19896e11 0.513469
\(485\) −1.66532e11 −0.136666
\(486\) −1.51894e11 −0.123503
\(487\) −5.93927e11 −0.478468 −0.239234 0.970962i \(-0.576896\pi\)
−0.239234 + 0.970962i \(0.576896\pi\)
\(488\) 2.84009e12 2.26695
\(489\) −1.22505e12 −0.968864
\(490\) −5.55931e12 −4.35651
\(491\) −6.03440e11 −0.468562 −0.234281 0.972169i \(-0.575274\pi\)
−0.234281 + 0.972169i \(0.575274\pi\)
\(492\) 2.31042e12 1.77766
\(493\) 1.90981e12 1.45606
\(494\) 6.36738e12 4.81049
\(495\) 5.55035e11 0.415525
\(496\) −1.33714e12 −0.991996
\(497\) 2.89160e12 2.12586
\(498\) 4.42985e10 0.0322743
\(499\) −2.35555e12 −1.70075 −0.850375 0.526177i \(-0.823625\pi\)
−0.850375 + 0.526177i \(0.823625\pi\)
\(500\) −2.99939e12 −2.14619
\(501\) −5.48477e11 −0.388946
\(502\) −3.86661e12 −2.71746
\(503\) 1.90452e12 1.32657 0.663285 0.748367i \(-0.269162\pi\)
0.663285 + 0.748367i \(0.269162\pi\)
\(504\) 2.73844e12 1.89046
\(505\) −3.05570e12 −2.09074
\(506\) −4.35183e12 −2.95117
\(507\) 8.71978e11 0.586097
\(508\) −7.22411e11 −0.481280
\(509\) −1.32499e12 −0.874951 −0.437475 0.899230i \(-0.644127\pi\)
−0.437475 + 0.899230i \(0.644127\pi\)
\(510\) 1.55737e12 1.01936
\(511\) −1.48275e12 −0.961997
\(512\) −2.22698e12 −1.43219
\(513\) 5.31375e11 0.338745
\(514\) −4.11929e12 −2.60309
\(515\) −5.99071e11 −0.375272
\(516\) −4.42438e11 −0.274744
\(517\) 3.36633e11 0.207229
\(518\) 2.34358e12 1.43020
\(519\) −1.01350e11 −0.0613156
\(520\) 8.88680e12 5.33004
\(521\) 1.19512e12 0.710625 0.355312 0.934748i \(-0.384374\pi\)
0.355312 + 0.934748i \(0.384374\pi\)
\(522\) 1.97535e12 1.16447
\(523\) 1.76481e12 1.03143 0.515717 0.856759i \(-0.327526\pi\)
0.515717 + 0.856759i \(0.327526\pi\)
\(524\) 5.35798e12 3.10463
\(525\) −5.31122e11 −0.305125
\(526\) 4.37807e12 2.49372
\(527\) 3.89526e11 0.219983
\(528\) 4.06956e12 2.27874
\(529\) 1.75626e12 0.975073
\(530\) 5.20450e12 2.86508
\(531\) 7.95020e10 0.0433963
\(532\) −1.51939e13 −8.22368
\(533\) −3.00906e12 −1.61495
\(534\) 2.85180e12 1.51769
\(535\) 5.35524e11 0.282610
\(536\) −8.56191e11 −0.448052
\(537\) −1.33121e12 −0.690818
\(538\) 3.02239e11 0.155536
\(539\) 4.23188e12 2.15965
\(540\) 1.17622e12 0.595276
\(541\) 1.82271e12 0.914807 0.457403 0.889259i \(-0.348780\pi\)
0.457403 + 0.889259i \(0.348780\pi\)
\(542\) −4.18231e12 −2.08170
\(543\) −3.56431e9 −0.00175945
\(544\) 6.03376e12 2.95388
\(545\) 2.39756e12 1.16409
\(546\) −5.65650e12 −2.72383
\(547\) 8.23239e10 0.0393172 0.0196586 0.999807i \(-0.493742\pi\)
0.0196586 + 0.999807i \(0.493742\pi\)
\(548\) −2.26946e11 −0.107500
\(549\) −4.89572e11 −0.230007
\(550\) −1.37964e12 −0.642886
\(551\) −6.91043e12 −3.19391
\(552\) −5.81484e12 −2.66570
\(553\) −1.56085e12 −0.709739
\(554\) 7.93005e12 3.57669
\(555\) 6.34691e11 0.283952
\(556\) 6.96693e12 3.09175
\(557\) −1.73608e12 −0.764225 −0.382113 0.924116i \(-0.624803\pi\)
−0.382113 + 0.924116i \(0.624803\pi\)
\(558\) 4.02894e11 0.175929
\(559\) 5.76225e11 0.249597
\(560\) −1.66143e13 −7.13898
\(561\) −1.18551e12 −0.505327
\(562\) 7.57770e12 3.20423
\(563\) −1.36719e12 −0.573512 −0.286756 0.958004i \(-0.592577\pi\)
−0.286756 + 0.958004i \(0.592577\pi\)
\(564\) 7.13390e11 0.296873
\(565\) −8.38190e11 −0.346039
\(566\) 8.36336e12 3.42537
\(567\) −4.72050e11 −0.191807
\(568\) 1.00364e13 4.04584
\(569\) 9.42095e11 0.376782 0.188391 0.982094i \(-0.439673\pi\)
0.188391 + 0.982094i \(0.439673\pi\)
\(570\) −5.63519e12 −2.23600
\(571\) 3.43206e12 1.35112 0.675558 0.737306i \(-0.263903\pi\)
0.675558 + 0.737306i \(0.263903\pi\)
\(572\) −1.07291e13 −4.19064
\(573\) −1.16191e12 −0.450273
\(574\) 9.83323e12 3.78088
\(575\) 1.12779e12 0.430252
\(576\) 3.05434e12 1.15616
\(577\) 2.01638e12 0.757322 0.378661 0.925535i \(-0.376385\pi\)
0.378661 + 0.925535i \(0.376385\pi\)
\(578\) 1.83959e12 0.685560
\(579\) −1.78539e12 −0.660205
\(580\) −1.52966e13 −5.61265
\(581\) 1.37669e11 0.0501238
\(582\) 3.67907e11 0.132918
\(583\) −3.96179e12 −1.42031
\(584\) −5.14642e12 −1.83083
\(585\) −1.53190e12 −0.540790
\(586\) 2.37158e12 0.830803
\(587\) −5.89110e11 −0.204797 −0.102399 0.994743i \(-0.532652\pi\)
−0.102399 + 0.994743i \(0.532652\pi\)
\(588\) 8.96816e12 3.09389
\(589\) −1.40946e12 −0.482539
\(590\) −8.43111e11 −0.286451
\(591\) −2.62924e12 −0.886516
\(592\) 4.65360e12 1.55719
\(593\) −2.77303e12 −0.920893 −0.460446 0.887687i \(-0.652311\pi\)
−0.460446 + 0.887687i \(0.652311\pi\)
\(594\) −1.22620e12 −0.404130
\(595\) 4.83995e12 1.58312
\(596\) 9.73847e12 3.16142
\(597\) −1.25820e12 −0.405381
\(598\) 1.20111e13 3.84084
\(599\) −1.80709e12 −0.573533 −0.286766 0.958001i \(-0.592580\pi\)
−0.286766 + 0.958001i \(0.592580\pi\)
\(600\) −1.84345e12 −0.580699
\(601\) −1.82846e11 −0.0571678 −0.0285839 0.999591i \(-0.509100\pi\)
−0.0285839 + 0.999591i \(0.509100\pi\)
\(602\) −1.88303e12 −0.584350
\(603\) 1.47589e11 0.0454597
\(604\) −6.08314e12 −1.85978
\(605\) 7.14506e11 0.216824
\(606\) 6.75072e12 2.03340
\(607\) 3.01684e12 0.901994 0.450997 0.892526i \(-0.351069\pi\)
0.450997 + 0.892526i \(0.351069\pi\)
\(608\) −2.18325e13 −6.47943
\(609\) 6.13892e12 1.80848
\(610\) 5.19186e12 1.51823
\(611\) −9.29109e11 −0.269700
\(612\) −2.51232e12 −0.723926
\(613\) −4.80257e12 −1.37373 −0.686866 0.726784i \(-0.741014\pi\)
−0.686866 + 0.726784i \(0.741014\pi\)
\(614\) 2.88750e12 0.819908
\(615\) 2.66305e12 0.750656
\(616\) 2.21067e13 6.18600
\(617\) 1.11287e12 0.309145 0.154572 0.987981i \(-0.450600\pi\)
0.154572 + 0.987981i \(0.450600\pi\)
\(618\) 1.32348e12 0.364980
\(619\) 1.60721e12 0.440012 0.220006 0.975499i \(-0.429392\pi\)
0.220006 + 0.975499i \(0.429392\pi\)
\(620\) −3.11990e12 −0.847964
\(621\) 1.00236e12 0.270464
\(622\) −3.51572e11 −0.0941798
\(623\) 8.86271e12 2.35706
\(624\) −1.12320e13 −2.96569
\(625\) −4.62502e12 −1.21242
\(626\) −6.74396e11 −0.175522
\(627\) 4.28964e12 1.10845
\(628\) 9.88610e12 2.53633
\(629\) −1.35565e12 −0.345319
\(630\) 5.00605e12 1.26608
\(631\) −2.45294e12 −0.615964 −0.307982 0.951392i \(-0.599654\pi\)
−0.307982 + 0.951392i \(0.599654\pi\)
\(632\) −5.41750e12 −1.35074
\(633\) 6.00835e11 0.148744
\(634\) 1.43752e13 3.53355
\(635\) −8.32667e11 −0.203231
\(636\) −8.39578e12 −2.03472
\(637\) −1.16800e13 −2.81071
\(638\) 1.59464e13 3.81040
\(639\) −1.73006e12 −0.410494
\(640\) −1.45348e13 −3.42452
\(641\) −6.74129e12 −1.57718 −0.788591 0.614918i \(-0.789189\pi\)
−0.788591 + 0.614918i \(0.789189\pi\)
\(642\) −1.18309e12 −0.274860
\(643\) 6.95200e11 0.160384 0.0801919 0.996779i \(-0.474447\pi\)
0.0801919 + 0.996779i \(0.474447\pi\)
\(644\) −2.86609e13 −6.56603
\(645\) −5.09964e11 −0.116017
\(646\) 1.20363e13 2.71924
\(647\) 1.92451e11 0.0431769 0.0215884 0.999767i \(-0.493128\pi\)
0.0215884 + 0.999767i \(0.493128\pi\)
\(648\) −1.63842e12 −0.365038
\(649\) 6.41796e11 0.142003
\(650\) 3.80781e12 0.836692
\(651\) 1.25210e12 0.273227
\(652\) −2.09576e13 −4.54180
\(653\) −1.88242e12 −0.405142 −0.202571 0.979268i \(-0.564930\pi\)
−0.202571 + 0.979268i \(0.564930\pi\)
\(654\) −5.29675e12 −1.13216
\(655\) 6.17573e12 1.31100
\(656\) 1.95256e13 4.11659
\(657\) 8.87134e11 0.185757
\(658\) 3.03621e12 0.631416
\(659\) 5.08014e12 1.04928 0.524640 0.851324i \(-0.324200\pi\)
0.524640 + 0.851324i \(0.324200\pi\)
\(660\) 9.49532e12 1.94788
\(661\) −1.03648e12 −0.211181 −0.105591 0.994410i \(-0.533673\pi\)
−0.105591 + 0.994410i \(0.533673\pi\)
\(662\) 6.16584e12 1.24776
\(663\) 3.27201e12 0.657664
\(664\) 4.77831e11 0.0953932
\(665\) −1.75128e13 −3.47263
\(666\) −1.40217e12 −0.276165
\(667\) −1.30354e13 −2.55011
\(668\) −9.38313e12 −1.82328
\(669\) 2.42849e12 0.468727
\(670\) −1.56517e12 −0.300072
\(671\) −3.95217e12 −0.752635
\(672\) 1.93950e13 3.66884
\(673\) 8.29211e12 1.55811 0.779053 0.626958i \(-0.215700\pi\)
0.779053 + 0.626958i \(0.215700\pi\)
\(674\) −3.46217e12 −0.646218
\(675\) 3.17773e11 0.0589182
\(676\) 1.49174e13 2.74748
\(677\) 4.71501e12 0.862648 0.431324 0.902197i \(-0.358047\pi\)
0.431324 + 0.902197i \(0.358047\pi\)
\(678\) 1.85175e12 0.336549
\(679\) 1.14337e12 0.206430
\(680\) 1.67988e13 3.01292
\(681\) 3.19382e12 0.569047
\(682\) 3.25244e12 0.575678
\(683\) 4.44301e12 0.781240 0.390620 0.920552i \(-0.372261\pi\)
0.390620 + 0.920552i \(0.372261\pi\)
\(684\) 9.09056e12 1.58795
\(685\) −2.61583e11 −0.0453943
\(686\) 1.88915e13 3.25692
\(687\) −8.42338e11 −0.144272
\(688\) −3.73909e12 −0.636236
\(689\) 1.09345e13 1.84848
\(690\) −1.06299e13 −1.78529
\(691\) −8.76609e11 −0.146270 −0.0731349 0.997322i \(-0.523300\pi\)
−0.0731349 + 0.997322i \(0.523300\pi\)
\(692\) −1.73386e12 −0.287432
\(693\) −3.81072e12 −0.627636
\(694\) −1.05574e13 −1.72758
\(695\) 8.03024e12 1.30556
\(696\) 2.13073e13 3.44182
\(697\) −5.68806e12 −0.912886
\(698\) −5.85202e12 −0.933161
\(699\) −5.63633e12 −0.892995
\(700\) −9.08623e12 −1.43035
\(701\) −3.11983e12 −0.487978 −0.243989 0.969778i \(-0.578456\pi\)
−0.243989 + 0.969778i \(0.578456\pi\)
\(702\) 3.38430e12 0.525960
\(703\) 4.90527e12 0.757467
\(704\) 2.46568e13 3.78320
\(705\) 8.22270e11 0.125361
\(706\) −1.26230e13 −1.91224
\(707\) 2.09796e13 3.15799
\(708\) 1.36009e12 0.203431
\(709\) 1.64768e12 0.244887 0.122443 0.992475i \(-0.460927\pi\)
0.122443 + 0.992475i \(0.460927\pi\)
\(710\) 1.83471e13 2.70960
\(711\) 9.33863e11 0.137047
\(712\) 3.07612e13 4.48584
\(713\) −2.65871e12 −0.385273
\(714\) −1.06925e13 −1.53971
\(715\) −1.23666e13 −1.76959
\(716\) −2.27739e13 −3.23839
\(717\) −3.31461e12 −0.468378
\(718\) −9.14590e12 −1.28430
\(719\) 1.69332e12 0.236298 0.118149 0.992996i \(-0.462304\pi\)
0.118149 + 0.992996i \(0.462304\pi\)
\(720\) 9.94040e12 1.37850
\(721\) 4.11306e12 0.566835
\(722\) −2.94949e13 −4.03951
\(723\) −5.58970e12 −0.760793
\(724\) −6.09767e10 −0.00824785
\(725\) −4.13257e12 −0.555519
\(726\) −1.57850e12 −0.210878
\(727\) −8.00586e12 −1.06293 −0.531463 0.847082i \(-0.678358\pi\)
−0.531463 + 0.847082i \(0.678358\pi\)
\(728\) −6.10144e13 −8.05084
\(729\) 2.82430e11 0.0370370
\(730\) −9.40797e12 −1.22615
\(731\) 1.08924e12 0.141090
\(732\) −8.37540e12 −1.07822
\(733\) 1.40134e13 1.79299 0.896493 0.443058i \(-0.146106\pi\)
0.896493 + 0.443058i \(0.146106\pi\)
\(734\) −1.23442e13 −1.56975
\(735\) 1.03369e13 1.30646
\(736\) −4.11835e13 −5.17337
\(737\) 1.19145e12 0.148755
\(738\) −5.88326e12 −0.730070
\(739\) −1.20312e13 −1.48392 −0.741960 0.670444i \(-0.766104\pi\)
−0.741960 + 0.670444i \(0.766104\pi\)
\(740\) 1.08580e13 1.33109
\(741\) −1.18394e13 −1.44261
\(742\) −3.57327e13 −4.32761
\(743\) −6.82684e12 −0.821808 −0.410904 0.911679i \(-0.634787\pi\)
−0.410904 + 0.911679i \(0.634787\pi\)
\(744\) 4.34586e12 0.519993
\(745\) 1.12248e13 1.33498
\(746\) 8.85347e12 1.04662
\(747\) −8.23680e10 −0.00967867
\(748\) −2.02813e13 −2.36885
\(749\) −3.67677e12 −0.426872
\(750\) 7.63763e12 0.881420
\(751\) 1.18371e13 1.35789 0.678944 0.734190i \(-0.262438\pi\)
0.678944 + 0.734190i \(0.262438\pi\)
\(752\) 6.02894e12 0.687481
\(753\) 7.18952e12 0.814934
\(754\) −4.40122e13 −4.95909
\(755\) −7.01156e12 −0.785332
\(756\) −8.07565e12 −0.899144
\(757\) 5.81566e12 0.643676 0.321838 0.946795i \(-0.395699\pi\)
0.321838 + 0.946795i \(0.395699\pi\)
\(758\) −3.25064e12 −0.357650
\(759\) 8.09172e12 0.885020
\(760\) −6.07846e13 −6.60894
\(761\) −5.38603e12 −0.582154 −0.291077 0.956700i \(-0.594014\pi\)
−0.291077 + 0.956700i \(0.594014\pi\)
\(762\) 1.83955e12 0.197658
\(763\) −1.64610e13 −1.75831
\(764\) −1.98775e13 −2.11077
\(765\) −2.89576e12 −0.305693
\(766\) 1.22323e13 1.28374
\(767\) −1.77136e12 −0.184811
\(768\) 1.28042e13 1.32809
\(769\) 4.49355e12 0.463363 0.231681 0.972792i \(-0.425577\pi\)
0.231681 + 0.972792i \(0.425577\pi\)
\(770\) 4.04124e13 4.14291
\(771\) 7.65936e12 0.780634
\(772\) −3.05437e13 −3.09488
\(773\) 8.71587e12 0.878017 0.439008 0.898483i \(-0.355330\pi\)
0.439008 + 0.898483i \(0.355330\pi\)
\(774\) 1.12662e12 0.112835
\(775\) −8.42881e11 −0.0839283
\(776\) 3.96847e12 0.392867
\(777\) −4.35762e12 −0.428899
\(778\) −1.75456e13 −1.71696
\(779\) 2.05816e13 2.00244
\(780\) −2.62071e13 −2.53509
\(781\) −1.39662e13 −1.34323
\(782\) 2.27046e13 2.17112
\(783\) −3.67294e12 −0.349209
\(784\) 7.57909e13 7.16465
\(785\) 1.13949e13 1.07102
\(786\) −1.36436e13 −1.27505
\(787\) −1.99079e13 −1.84986 −0.924930 0.380137i \(-0.875877\pi\)
−0.924930 + 0.380137i \(0.875877\pi\)
\(788\) −4.49800e13 −4.15577
\(789\) −8.14052e12 −0.747835
\(790\) −9.90353e12 −0.904624
\(791\) 5.75479e12 0.522679
\(792\) −1.32265e13 −1.19449
\(793\) 1.09080e13 0.979526
\(794\) 5.03560e12 0.449634
\(795\) −9.67716e12 −0.859203
\(796\) −2.15247e13 −1.90033
\(797\) −2.67783e11 −0.0235082 −0.0117541 0.999931i \(-0.503742\pi\)
−0.0117541 + 0.999931i \(0.503742\pi\)
\(798\) 3.86897e13 3.37740
\(799\) −1.75630e12 −0.152454
\(800\) −1.30562e13 −1.12697
\(801\) −5.30259e12 −0.455137
\(802\) 2.47448e13 2.11203
\(803\) 7.16158e12 0.607839
\(804\) 2.52490e12 0.213104
\(805\) −3.30351e13 −2.77265
\(806\) −8.97675e12 −0.749224
\(807\) −5.61979e11 −0.0466433
\(808\) 7.28174e13 6.01013
\(809\) −5.14983e12 −0.422693 −0.211346 0.977411i \(-0.567785\pi\)
−0.211346 + 0.977411i \(0.567785\pi\)
\(810\) −2.99514e12 −0.244475
\(811\) −6.19815e12 −0.503116 −0.251558 0.967842i \(-0.580943\pi\)
−0.251558 + 0.967842i \(0.580943\pi\)
\(812\) 1.05022e14 8.47772
\(813\) 7.77652e12 0.624278
\(814\) −1.13193e13 −0.903673
\(815\) −2.41562e13 −1.91787
\(816\) −2.12319e13 −1.67642
\(817\) −3.94130e12 −0.309486
\(818\) 1.88780e13 1.47424
\(819\) 1.05176e13 0.816845
\(820\) 4.55583e13 3.51889
\(821\) 6.20987e12 0.477022 0.238511 0.971140i \(-0.423341\pi\)
0.238511 + 0.971140i \(0.423341\pi\)
\(822\) 5.77895e11 0.0441495
\(823\) −1.59932e13 −1.21517 −0.607584 0.794255i \(-0.707861\pi\)
−0.607584 + 0.794255i \(0.707861\pi\)
\(824\) 1.42759e13 1.07877
\(825\) 2.56528e12 0.192794
\(826\) 5.78858e12 0.432675
\(827\) 2.11594e12 0.157300 0.0786500 0.996902i \(-0.474939\pi\)
0.0786500 + 0.996902i \(0.474939\pi\)
\(828\) 1.71479e13 1.26787
\(829\) −1.83713e13 −1.35097 −0.675484 0.737374i \(-0.736065\pi\)
−0.675484 + 0.737374i \(0.736065\pi\)
\(830\) 8.73504e11 0.0638872
\(831\) −1.47450e13 −1.07261
\(832\) −6.80528e13 −4.92369
\(833\) −2.20788e13 −1.58881
\(834\) −1.77406e13 −1.26976
\(835\) −1.08152e13 −0.769920
\(836\) 7.33854e13 5.19615
\(837\) −7.49135e11 −0.0527588
\(838\) 3.96581e13 2.77801
\(839\) −1.08393e13 −0.755221 −0.377611 0.925964i \(-0.623254\pi\)
−0.377611 + 0.925964i \(0.623254\pi\)
\(840\) 5.39983e13 3.74217
\(841\) 3.32587e13 2.29257
\(842\) −2.31239e13 −1.58547
\(843\) −1.40899e13 −0.960910
\(844\) 1.02788e13 0.697274
\(845\) 1.71942e13 1.16018
\(846\) −1.81658e12 −0.121923
\(847\) −4.90561e12 −0.327505
\(848\) −7.09536e13 −4.71187
\(849\) −1.55507e13 −1.02723
\(850\) 7.19794e12 0.472959
\(851\) 9.25301e12 0.604784
\(852\) −2.95971e13 −1.92429
\(853\) 1.39415e13 0.901649 0.450825 0.892613i \(-0.351130\pi\)
0.450825 + 0.892613i \(0.351130\pi\)
\(854\) −3.56459e13 −2.29324
\(855\) 1.04780e13 0.670548
\(856\) −1.27616e13 −0.812403
\(857\) −4.55558e12 −0.288489 −0.144245 0.989542i \(-0.546075\pi\)
−0.144245 + 0.989542i \(0.546075\pi\)
\(858\) 2.73205e13 1.72106
\(859\) 1.96628e13 1.23218 0.616092 0.787674i \(-0.288715\pi\)
0.616092 + 0.787674i \(0.288715\pi\)
\(860\) −8.72426e12 −0.543858
\(861\) −1.82838e13 −1.13384
\(862\) 4.58212e13 2.82673
\(863\) 1.15472e13 0.708644 0.354322 0.935123i \(-0.384712\pi\)
0.354322 + 0.935123i \(0.384712\pi\)
\(864\) −1.16041e13 −0.708435
\(865\) −1.99848e12 −0.121375
\(866\) −1.45009e13 −0.876119
\(867\) −3.42050e12 −0.205591
\(868\) 2.14204e13 1.28082
\(869\) 7.53881e12 0.448450
\(870\) 3.89512e13 2.30507
\(871\) −3.28839e12 −0.193598
\(872\) −5.71340e13 −3.34634
\(873\) −6.84081e11 −0.0398606
\(874\) −8.21540e13 −4.76242
\(875\) 2.37359e13 1.36890
\(876\) 1.51767e13 0.870783
\(877\) 2.43420e13 1.38950 0.694750 0.719251i \(-0.255515\pi\)
0.694750 + 0.719251i \(0.255515\pi\)
\(878\) 5.83879e13 3.31587
\(879\) −4.40968e12 −0.249148
\(880\) 8.02459e13 4.51077
\(881\) 1.12417e13 0.628698 0.314349 0.949308i \(-0.398214\pi\)
0.314349 + 0.949308i \(0.398214\pi\)
\(882\) −2.28365e13 −1.27064
\(883\) 1.39656e13 0.773101 0.386550 0.922268i \(-0.373667\pi\)
0.386550 + 0.922268i \(0.373667\pi\)
\(884\) 5.59763e13 3.08297
\(885\) 1.56767e12 0.0859032
\(886\) −8.76425e12 −0.477819
\(887\) −2.71387e13 −1.47208 −0.736042 0.676936i \(-0.763307\pi\)
−0.736042 + 0.676936i \(0.763307\pi\)
\(888\) −1.51247e13 −0.816260
\(889\) 5.71687e12 0.306973
\(890\) 5.62335e13 3.00428
\(891\) 2.27997e12 0.121194
\(892\) 4.15457e13 2.19727
\(893\) 6.35498e12 0.334413
\(894\) −2.47980e13 −1.29837
\(895\) −2.62497e13 −1.36748
\(896\) 9.97922e13 5.17262
\(897\) −2.23332e13 −1.15182
\(898\) 2.80016e13 1.43694
\(899\) 9.74235e12 0.497445
\(900\) 5.43632e12 0.276194
\(901\) 2.06697e13 1.04489
\(902\) −4.74939e13 −2.38896
\(903\) 3.50128e12 0.175239
\(904\) 1.99741e13 0.994739
\(905\) −7.02832e10 −0.00348283
\(906\) 1.54901e13 0.763796
\(907\) −2.64168e13 −1.29613 −0.648065 0.761585i \(-0.724421\pi\)
−0.648065 + 0.761585i \(0.724421\pi\)
\(908\) 5.46385e13 2.66755
\(909\) −1.25522e13 −0.609792
\(910\) −1.11538e14 −5.39185
\(911\) 2.67036e13 1.28451 0.642255 0.766491i \(-0.277999\pi\)
0.642255 + 0.766491i \(0.277999\pi\)
\(912\) 7.68253e13 3.67729
\(913\) −6.64933e11 −0.0316708
\(914\) −6.23888e13 −2.95698
\(915\) −9.65367e12 −0.455300
\(916\) −1.44104e13 −0.676310
\(917\) −4.24009e13 −1.98022
\(918\) 6.39738e12 0.297310
\(919\) 4.08123e12 0.188743 0.0943715 0.995537i \(-0.469916\pi\)
0.0943715 + 0.995537i \(0.469916\pi\)
\(920\) −1.14660e14 −5.27677
\(921\) −5.36898e12 −0.245880
\(922\) −2.00073e13 −0.911799
\(923\) 3.85469e13 1.74816
\(924\) −6.51923e13 −2.94220
\(925\) 2.93344e12 0.131747
\(926\) −8.32216e13 −3.71952
\(927\) −2.46086e12 −0.109453
\(928\) 1.50909e14 6.67959
\(929\) −6.82957e12 −0.300831 −0.150416 0.988623i \(-0.548061\pi\)
−0.150416 + 0.988623i \(0.548061\pi\)
\(930\) 7.94450e12 0.348252
\(931\) 7.98897e13 3.48512
\(932\) −9.64240e13 −4.18614
\(933\) 6.53709e11 0.0282434
\(934\) 1.82708e13 0.785593
\(935\) −2.33766e13 −1.00030
\(936\) 3.65052e13 1.55458
\(937\) 1.15809e13 0.490812 0.245406 0.969420i \(-0.421079\pi\)
0.245406 + 0.969420i \(0.421079\pi\)
\(938\) 1.07460e13 0.453248
\(939\) 1.25396e12 0.0526368
\(940\) 1.40671e13 0.587663
\(941\) 3.00051e13 1.24750 0.623752 0.781622i \(-0.285608\pi\)
0.623752 + 0.781622i \(0.285608\pi\)
\(942\) −2.51740e13 −1.04165
\(943\) 3.88239e13 1.59881
\(944\) 1.14943e13 0.471093
\(945\) −9.30817e12 −0.379683
\(946\) 9.09491e12 0.369223
\(947\) 3.23056e13 1.30528 0.652640 0.757668i \(-0.273662\pi\)
0.652640 + 0.757668i \(0.273662\pi\)
\(948\) 1.59762e13 0.642443
\(949\) −1.97660e13 −0.791080
\(950\) −2.60449e13 −1.03745
\(951\) −2.67290e13 −1.05967
\(952\) −1.15336e14 −4.55092
\(953\) 2.22295e13 0.872994 0.436497 0.899706i \(-0.356219\pi\)
0.436497 + 0.899706i \(0.356219\pi\)
\(954\) 2.13790e13 0.835641
\(955\) −2.29112e13 −0.891319
\(956\) −5.67050e13 −2.19564
\(957\) −2.96506e13 −1.14269
\(958\) 9.20356e13 3.53030
\(959\) 1.79596e12 0.0685666
\(960\) 6.02273e13 2.28862
\(961\) −2.44526e13 −0.924846
\(962\) 3.12414e13 1.17610
\(963\) 2.19982e12 0.0824270
\(964\) −9.56264e13 −3.56641
\(965\) −3.52053e13 −1.30688
\(966\) 7.29820e13 2.69661
\(967\) −3.16973e13 −1.16574 −0.582872 0.812564i \(-0.698071\pi\)
−0.582872 + 0.812564i \(0.698071\pi\)
\(968\) −1.70267e13 −0.623291
\(969\) −2.23801e13 −0.815466
\(970\) 7.25461e12 0.263113
\(971\) 3.75422e13 1.35529 0.677647 0.735387i \(-0.263000\pi\)
0.677647 + 0.735387i \(0.263000\pi\)
\(972\) 4.83169e12 0.173620
\(973\) −5.51335e13 −1.97200
\(974\) 2.58731e13 0.921156
\(975\) −7.08019e12 −0.250914
\(976\) −7.07814e13 −2.49686
\(977\) 9.74926e11 0.0342331 0.0171166 0.999854i \(-0.494551\pi\)
0.0171166 + 0.999854i \(0.494551\pi\)
\(978\) 5.33664e13 1.86528
\(979\) −4.28063e13 −1.48931
\(980\) 1.76840e14 6.12438
\(981\) 9.84870e12 0.339522
\(982\) 2.62875e13 0.902086
\(983\) −2.80063e13 −0.956676 −0.478338 0.878176i \(-0.658761\pi\)
−0.478338 + 0.878176i \(0.658761\pi\)
\(984\) −6.34605e13 −2.15787
\(985\) −5.18449e13 −1.75486
\(986\) −8.31966e13 −2.80324
\(987\) −5.64549e12 −0.189354
\(988\) −2.02544e14 −6.76259
\(989\) −7.43465e12 −0.247102
\(990\) −2.41789e13 −0.799977
\(991\) 3.41237e13 1.12389 0.561947 0.827173i \(-0.310053\pi\)
0.561947 + 0.827173i \(0.310053\pi\)
\(992\) 3.07795e13 1.00916
\(993\) −1.14647e13 −0.374188
\(994\) −1.25966e14 −4.09275
\(995\) −2.48099e13 −0.802455
\(996\) −1.40912e12 −0.0453712
\(997\) 1.72440e13 0.552724 0.276362 0.961054i \(-0.410871\pi\)
0.276362 + 0.961054i \(0.410871\pi\)
\(998\) 1.02614e14 3.27432
\(999\) 2.60718e12 0.0828184
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 177.10.a.a.1.2 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.a.1.2 21 1.1 even 1 trivial