Properties

Label 177.12.a.c.1.4
Level $177$
Weight $12$
Character 177.1
Self dual yes
Analytic conductor $135.997$
Analytic rank $0$
Dimension $27$
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: \(27\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-70.9666 q^{2} -243.000 q^{3} +2988.26 q^{4} +3032.24 q^{5} +17244.9 q^{6} -62069.7 q^{7} -66727.2 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q-70.9666 q^{2} -243.000 q^{3} +2988.26 q^{4} +3032.24 q^{5} +17244.9 q^{6} -62069.7 q^{7} -66727.2 q^{8} +59049.0 q^{9} -215188. q^{10} +299288. q^{11} -726148. q^{12} -1.56341e6 q^{13} +4.40488e6 q^{14} -736834. q^{15} -1.38456e6 q^{16} -569100. q^{17} -4.19051e6 q^{18} -2.09189e7 q^{19} +9.06113e6 q^{20} +1.50829e7 q^{21} -2.12395e7 q^{22} +2.52186e7 q^{23} +1.62147e7 q^{24} -3.96336e7 q^{25} +1.10950e8 q^{26} -1.43489e7 q^{27} -1.85481e8 q^{28} -8.20111e7 q^{29} +5.22906e7 q^{30} -1.20933e8 q^{31} +2.34915e8 q^{32} -7.27270e7 q^{33} +4.03871e7 q^{34} -1.88210e8 q^{35} +1.76454e8 q^{36} +3.75335e8 q^{37} +1.48454e9 q^{38} +3.79908e8 q^{39} -2.02333e8 q^{40} +3.35558e8 q^{41} -1.07039e9 q^{42} +1.05595e9 q^{43} +8.94351e8 q^{44} +1.79051e8 q^{45} -1.78968e9 q^{46} -5.28373e8 q^{47} +3.36447e8 q^{48} +1.87532e9 q^{49} +2.81267e9 q^{50} +1.38291e8 q^{51} -4.67187e9 q^{52} -5.65789e9 q^{53} +1.01829e9 q^{54} +9.07513e8 q^{55} +4.14174e9 q^{56} +5.08329e9 q^{57} +5.82005e9 q^{58} -7.14924e8 q^{59} -2.20185e9 q^{60} -7.64605e9 q^{61} +8.58220e9 q^{62} -3.66516e9 q^{63} -1.38355e10 q^{64} -4.74063e9 q^{65} +5.16119e9 q^{66} -9.27226e9 q^{67} -1.70062e9 q^{68} -6.12812e9 q^{69} +1.33567e10 q^{70} -1.76284e10 q^{71} -3.94017e9 q^{72} +8.95732e8 q^{73} -2.66363e10 q^{74} +9.63098e9 q^{75} -6.25111e10 q^{76} -1.85767e10 q^{77} -2.69608e10 q^{78} +1.22188e9 q^{79} -4.19831e9 q^{80} +3.48678e9 q^{81} -2.38134e10 q^{82} -6.96998e10 q^{83} +4.50718e10 q^{84} -1.72565e9 q^{85} -7.49371e10 q^{86} +1.99287e10 q^{87} -1.99706e10 q^{88} +1.97819e10 q^{89} -1.27066e10 q^{90} +9.70403e10 q^{91} +7.53597e10 q^{92} +2.93867e10 q^{93} +3.74968e10 q^{94} -6.34310e10 q^{95} -5.70842e10 q^{96} -1.55752e11 q^{97} -1.33085e11 q^{98} +1.76727e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 46q^{2} - 6561q^{3} + 26142q^{4} - 2442q^{5} + 11178q^{6} + 170093q^{7} - 19341q^{8} + 1594323q^{9} + O(q^{10}) \) \( 27q - 46q^{2} - 6561q^{3} + 26142q^{4} - 2442q^{5} + 11178q^{6} + 170093q^{7} - 19341q^{8} + 1594323q^{9} + 140249q^{10} + 256992q^{11} - 6352506q^{12} + 2436978q^{13} + 5233061q^{14} + 593406q^{15} + 28295194q^{16} - 4565351q^{17} - 2716254q^{18} + 33607699q^{19} - 19208463q^{20} - 41332599q^{21} + 79735622q^{22} + 43966161q^{23} + 4699863q^{24} + 406675819q^{25} + 42605404q^{26} - 387420489q^{27} + 635747682q^{28} - 107217773q^{29} - 34080507q^{30} + 570926627q^{31} + 526569236q^{32} - 62449056q^{33} + 129790240q^{34} + 134356079q^{35} + 1543658958q^{36} - 107121371q^{37} + 208302581q^{38} - 592185654q^{39} - 958762162q^{40} - 1935967559q^{41} - 1271633823q^{42} + 1725943824q^{43} + 196885756q^{44} - 144197658q^{45} - 13265966407q^{46} + 1801256065q^{47} - 6875732142q^{48} + 10484289252q^{49} - 10067682271q^{50} + 1109380293q^{51} - 882697024q^{52} - 6214238922q^{53} + 660049722q^{54} + 4460552366q^{55} + 28328012310q^{56} - 8166670857q^{57} + 12220116750q^{58} - 19302956073q^{59} + 4667656509q^{60} + 13167821039q^{61} - 1162130230q^{62} + 10043821557q^{63} - 5337557395q^{64} - 16849896006q^{65} - 19375756146q^{66} - 16856763152q^{67} - 36171071977q^{68} - 10683777123q^{69} - 120177261588q^{70} - 5198545690q^{71} - 1142066709q^{72} - 25075321857q^{73} - 182979651978q^{74} - 98822224017q^{75} - 3501293988q^{76} - 42787697701q^{77} - 10353113172q^{78} + 6850314702q^{79} - 261464428159q^{80} + 94143178827q^{81} - 148881516273q^{82} + 30908370899q^{83} - 154486686726q^{84} - 49419624969q^{85} - 220725475224q^{86} + 26053918839q^{87} - 53091280787q^{88} + 28988060121q^{89} + 8281563201q^{90} + 97120614047q^{91} + 45374597708q^{92} - 138735170361q^{93} + 208966927220q^{94} - 125253904969q^{95} - 127956324348q^{96} + 367722840268q^{97} - 48265639912q^{98} + 15175120608q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −70.9666 −1.56816 −0.784078 0.620663i \(-0.786864\pi\)
−0.784078 + 0.620663i \(0.786864\pi\)
\(3\) −243.000 −0.577350
\(4\) 2988.26 1.45911
\(5\) 3032.24 0.433939 0.216969 0.976178i \(-0.430383\pi\)
0.216969 + 0.976178i \(0.430383\pi\)
\(6\) 17244.9 0.905375
\(7\) −62069.7 −1.39586 −0.697928 0.716168i \(-0.745894\pi\)
−0.697928 + 0.716168i \(0.745894\pi\)
\(8\) −66727.2 −0.719959
\(9\) 59049.0 0.333333
\(10\) −215188. −0.680484
\(11\) 299288. 0.560312 0.280156 0.959955i \(-0.409614\pi\)
0.280156 + 0.959955i \(0.409614\pi\)
\(12\) −726148. −0.842419
\(13\) −1.56341e6 −1.16784 −0.583920 0.811811i \(-0.698482\pi\)
−0.583920 + 0.811811i \(0.698482\pi\)
\(14\) 4.40488e6 2.18892
\(15\) −736834. −0.250535
\(16\) −1.38456e6 −0.330104
\(17\) −569100. −0.0972119 −0.0486060 0.998818i \(-0.515478\pi\)
−0.0486060 + 0.998818i \(0.515478\pi\)
\(18\) −4.19051e6 −0.522719
\(19\) −2.09189e7 −1.93818 −0.969088 0.246714i \(-0.920649\pi\)
−0.969088 + 0.246714i \(0.920649\pi\)
\(20\) 9.06113e6 0.633165
\(21\) 1.50829e7 0.805898
\(22\) −2.12395e7 −0.878656
\(23\) 2.52186e7 0.816992 0.408496 0.912760i \(-0.366053\pi\)
0.408496 + 0.912760i \(0.366053\pi\)
\(24\) 1.62147e7 0.415669
\(25\) −3.96336e7 −0.811697
\(26\) 1.10950e8 1.83136
\(27\) −1.43489e7 −0.192450
\(28\) −1.85481e8 −2.03671
\(29\) −8.20111e7 −0.742478 −0.371239 0.928537i \(-0.621067\pi\)
−0.371239 + 0.928537i \(0.621067\pi\)
\(30\) 5.22906e7 0.392877
\(31\) −1.20933e8 −0.758674 −0.379337 0.925259i \(-0.623848\pi\)
−0.379337 + 0.925259i \(0.623848\pi\)
\(32\) 2.34915e8 1.23761
\(33\) −7.27270e7 −0.323496
\(34\) 4.03871e7 0.152443
\(35\) −1.88210e8 −0.605716
\(36\) 1.76454e8 0.486371
\(37\) 3.75335e8 0.889836 0.444918 0.895571i \(-0.353233\pi\)
0.444918 + 0.895571i \(0.353233\pi\)
\(38\) 1.48454e9 3.03936
\(39\) 3.79908e8 0.674253
\(40\) −2.02333e8 −0.312418
\(41\) 3.35558e8 0.452331 0.226166 0.974089i \(-0.427381\pi\)
0.226166 + 0.974089i \(0.427381\pi\)
\(42\) −1.07039e9 −1.26377
\(43\) 1.05595e9 1.09538 0.547692 0.836680i \(-0.315507\pi\)
0.547692 + 0.836680i \(0.315507\pi\)
\(44\) 8.94351e8 0.817557
\(45\) 1.79051e8 0.144646
\(46\) −1.78968e9 −1.28117
\(47\) −5.28373e8 −0.336049 −0.168024 0.985783i \(-0.553739\pi\)
−0.168024 + 0.985783i \(0.553739\pi\)
\(48\) 3.36447e8 0.190586
\(49\) 1.87532e9 0.948414
\(50\) 2.81267e9 1.27287
\(51\) 1.38291e8 0.0561253
\(52\) −4.67187e9 −1.70401
\(53\) −5.65789e9 −1.85839 −0.929195 0.369589i \(-0.879499\pi\)
−0.929195 + 0.369589i \(0.879499\pi\)
\(54\) 1.01829e9 0.301792
\(55\) 9.07513e8 0.243141
\(56\) 4.14174e9 1.00496
\(57\) 5.08329e9 1.11901
\(58\) 5.82005e9 1.16432
\(59\) −7.14924e8 −0.130189
\(60\) −2.20185e9 −0.365558
\(61\) −7.64605e9 −1.15911 −0.579553 0.814934i \(-0.696773\pi\)
−0.579553 + 0.814934i \(0.696773\pi\)
\(62\) 8.58220e9 1.18972
\(63\) −3.66516e9 −0.465285
\(64\) −1.38355e10 −1.61067
\(65\) −4.74063e9 −0.506772
\(66\) 5.16119e9 0.507292
\(67\) −9.27226e9 −0.839024 −0.419512 0.907750i \(-0.637799\pi\)
−0.419512 + 0.907750i \(0.637799\pi\)
\(68\) −1.70062e9 −0.141843
\(69\) −6.12812e9 −0.471690
\(70\) 1.33567e10 0.949857
\(71\) −1.76284e10 −1.15956 −0.579778 0.814775i \(-0.696861\pi\)
−0.579778 + 0.814775i \(0.696861\pi\)
\(72\) −3.94017e9 −0.239986
\(73\) 8.95732e8 0.0505711 0.0252856 0.999680i \(-0.491950\pi\)
0.0252856 + 0.999680i \(0.491950\pi\)
\(74\) −2.66363e10 −1.39540
\(75\) 9.63098e9 0.468634
\(76\) −6.25111e10 −2.82802
\(77\) −1.85767e10 −0.782114
\(78\) −2.69608e10 −1.05733
\(79\) 1.22188e9 0.0446765 0.0223383 0.999750i \(-0.492889\pi\)
0.0223383 + 0.999750i \(0.492889\pi\)
\(80\) −4.19831e9 −0.143245
\(81\) 3.48678e9 0.111111
\(82\) −2.38134e10 −0.709326
\(83\) −6.96998e10 −1.94224 −0.971118 0.238598i \(-0.923312\pi\)
−0.971118 + 0.238598i \(0.923312\pi\)
\(84\) 4.50718e10 1.17590
\(85\) −1.72565e9 −0.0421840
\(86\) −7.49371e10 −1.71773
\(87\) 1.99287e10 0.428670
\(88\) −1.99706e10 −0.403401
\(89\) 1.97819e10 0.375511 0.187755 0.982216i \(-0.439879\pi\)
0.187755 + 0.982216i \(0.439879\pi\)
\(90\) −1.27066e10 −0.226828
\(91\) 9.70403e10 1.63014
\(92\) 7.53597e10 1.19208
\(93\) 2.93867e10 0.438021
\(94\) 3.74968e10 0.526977
\(95\) −6.34310e10 −0.841050
\(96\) −5.70842e10 −0.714537
\(97\) −1.55752e11 −1.84157 −0.920784 0.390073i \(-0.872450\pi\)
−0.920784 + 0.390073i \(0.872450\pi\)
\(98\) −1.33085e11 −1.48726
\(99\) 1.76727e10 0.186771
\(100\) −1.18436e11 −1.18436
\(101\) 1.66195e11 1.57344 0.786721 0.617309i \(-0.211777\pi\)
0.786721 + 0.617309i \(0.211777\pi\)
\(102\) −9.81407e9 −0.0880133
\(103\) −5.38134e10 −0.457389 −0.228695 0.973498i \(-0.573446\pi\)
−0.228695 + 0.973498i \(0.573446\pi\)
\(104\) 1.04322e11 0.840798
\(105\) 4.57351e10 0.349710
\(106\) 4.01521e11 2.91425
\(107\) 1.15660e11 0.797211 0.398605 0.917123i \(-0.369494\pi\)
0.398605 + 0.917123i \(0.369494\pi\)
\(108\) −4.28783e10 −0.280806
\(109\) −2.39276e11 −1.48954 −0.744771 0.667320i \(-0.767441\pi\)
−0.744771 + 0.667320i \(0.767441\pi\)
\(110\) −6.44031e10 −0.381283
\(111\) −9.12065e10 −0.513747
\(112\) 8.59391e10 0.460778
\(113\) −2.36020e11 −1.20508 −0.602542 0.798087i \(-0.705845\pi\)
−0.602542 + 0.798087i \(0.705845\pi\)
\(114\) −3.60744e11 −1.75478
\(115\) 7.64688e10 0.354524
\(116\) −2.45071e11 −1.08336
\(117\) −9.23176e10 −0.389280
\(118\) 5.07358e10 0.204156
\(119\) 3.53239e10 0.135694
\(120\) 4.91669e10 0.180375
\(121\) −1.95738e11 −0.686051
\(122\) 5.42615e11 1.81766
\(123\) −8.15406e10 −0.261154
\(124\) −3.61379e11 −1.10699
\(125\) −2.68237e11 −0.786166
\(126\) 2.60104e11 0.729640
\(127\) −9.17727e10 −0.246486 −0.123243 0.992376i \(-0.539330\pi\)
−0.123243 + 0.992376i \(0.539330\pi\)
\(128\) 5.00755e11 1.28816
\(129\) −2.56595e11 −0.632420
\(130\) 3.36426e11 0.794697
\(131\) −3.46489e11 −0.784689 −0.392344 0.919818i \(-0.628336\pi\)
−0.392344 + 0.919818i \(0.628336\pi\)
\(132\) −2.17327e11 −0.472017
\(133\) 1.29843e12 2.70542
\(134\) 6.58021e11 1.31572
\(135\) −4.35093e10 −0.0835116
\(136\) 3.79744e10 0.0699886
\(137\) 2.17262e11 0.384610 0.192305 0.981335i \(-0.438404\pi\)
0.192305 + 0.981335i \(0.438404\pi\)
\(138\) 4.34892e11 0.739684
\(139\) 2.54946e10 0.0416741 0.0208371 0.999783i \(-0.493367\pi\)
0.0208371 + 0.999783i \(0.493367\pi\)
\(140\) −5.62422e11 −0.883808
\(141\) 1.28395e11 0.194018
\(142\) 1.25103e12 1.81836
\(143\) −4.67909e11 −0.654355
\(144\) −8.17567e10 −0.110035
\(145\) −2.48677e11 −0.322190
\(146\) −6.35671e10 −0.0793034
\(147\) −4.55704e11 −0.547567
\(148\) 1.12160e12 1.29837
\(149\) 4.60011e10 0.0513149 0.0256575 0.999671i \(-0.491832\pi\)
0.0256575 + 0.999671i \(0.491832\pi\)
\(150\) −6.83478e11 −0.734890
\(151\) −2.82488e11 −0.292837 −0.146419 0.989223i \(-0.546775\pi\)
−0.146419 + 0.989223i \(0.546775\pi\)
\(152\) 1.39586e12 1.39541
\(153\) −3.36048e10 −0.0324040
\(154\) 1.31833e12 1.22648
\(155\) −3.66698e11 −0.329218
\(156\) 1.13526e12 0.983811
\(157\) −1.35295e12 −1.13196 −0.565982 0.824417i \(-0.691503\pi\)
−0.565982 + 0.824417i \(0.691503\pi\)
\(158\) −8.67127e10 −0.0700598
\(159\) 1.37487e12 1.07294
\(160\) 7.12317e11 0.537049
\(161\) −1.56531e12 −1.14040
\(162\) −2.47445e11 −0.174240
\(163\) 7.64129e11 0.520158 0.260079 0.965587i \(-0.416251\pi\)
0.260079 + 0.965587i \(0.416251\pi\)
\(164\) 1.00274e12 0.660002
\(165\) −2.20526e11 −0.140378
\(166\) 4.94636e12 3.04573
\(167\) 2.78895e12 1.66150 0.830750 0.556645i \(-0.187912\pi\)
0.830750 + 0.556645i \(0.187912\pi\)
\(168\) −1.00644e12 −0.580214
\(169\) 6.52081e11 0.363852
\(170\) 1.22463e11 0.0661511
\(171\) −1.23524e12 −0.646059
\(172\) 3.15545e12 1.59829
\(173\) −2.71827e11 −0.133364 −0.0666820 0.997774i \(-0.521241\pi\)
−0.0666820 + 0.997774i \(0.521241\pi\)
\(174\) −1.41427e12 −0.672221
\(175\) 2.46005e12 1.13301
\(176\) −4.14381e11 −0.184961
\(177\) 1.73727e11 0.0751646
\(178\) −1.40385e12 −0.588860
\(179\) −3.97647e12 −1.61736 −0.808680 0.588249i \(-0.799817\pi\)
−0.808680 + 0.588249i \(0.799817\pi\)
\(180\) 5.35050e11 0.211055
\(181\) 2.86120e12 1.09475 0.547376 0.836887i \(-0.315627\pi\)
0.547376 + 0.836887i \(0.315627\pi\)
\(182\) −6.88662e12 −2.55631
\(183\) 1.85799e12 0.669210
\(184\) −1.68276e12 −0.588201
\(185\) 1.13811e12 0.386135
\(186\) −2.08547e12 −0.686884
\(187\) −1.70325e11 −0.0544690
\(188\) −1.57892e12 −0.490333
\(189\) 8.90633e11 0.268633
\(190\) 4.50149e12 1.31890
\(191\) 2.22610e12 0.633666 0.316833 0.948481i \(-0.397381\pi\)
0.316833 + 0.948481i \(0.397381\pi\)
\(192\) 3.36203e12 0.929919
\(193\) 5.70171e12 1.53264 0.766320 0.642459i \(-0.222086\pi\)
0.766320 + 0.642459i \(0.222086\pi\)
\(194\) 1.10532e13 2.88787
\(195\) 1.15197e12 0.292585
\(196\) 5.60396e12 1.38384
\(197\) −5.58793e12 −1.34180 −0.670898 0.741550i \(-0.734091\pi\)
−0.670898 + 0.741550i \(0.734091\pi\)
\(198\) −1.25417e12 −0.292885
\(199\) −1.96680e12 −0.446754 −0.223377 0.974732i \(-0.571708\pi\)
−0.223377 + 0.974732i \(0.571708\pi\)
\(200\) 2.64464e12 0.584389
\(201\) 2.25316e12 0.484410
\(202\) −1.17943e13 −2.46740
\(203\) 5.09041e12 1.03639
\(204\) 4.13251e11 0.0818931
\(205\) 1.01749e12 0.196284
\(206\) 3.81896e12 0.717258
\(207\) 1.48913e12 0.272331
\(208\) 2.16463e12 0.385509
\(209\) −6.26077e12 −1.08598
\(210\) −3.24567e12 −0.548400
\(211\) −7.57343e12 −1.24663 −0.623317 0.781969i \(-0.714215\pi\)
−0.623317 + 0.781969i \(0.714215\pi\)
\(212\) −1.69072e13 −2.71160
\(213\) 4.28370e12 0.669469
\(214\) −8.20801e12 −1.25015
\(215\) 3.20189e12 0.475329
\(216\) 9.57462e11 0.138556
\(217\) 7.50627e12 1.05900
\(218\) 1.69806e13 2.33583
\(219\) −2.17663e11 −0.0291972
\(220\) 2.71189e12 0.354770
\(221\) 8.89735e11 0.113528
\(222\) 6.47262e12 0.805636
\(223\) 1.44883e13 1.75930 0.879652 0.475619i \(-0.157776\pi\)
0.879652 + 0.475619i \(0.157776\pi\)
\(224\) −1.45811e13 −1.72753
\(225\) −2.34033e12 −0.270566
\(226\) 1.67495e13 1.88976
\(227\) 1.25150e13 1.37813 0.689063 0.724702i \(-0.258023\pi\)
0.689063 + 0.724702i \(0.258023\pi\)
\(228\) 1.51902e13 1.63276
\(229\) −5.33646e12 −0.559962 −0.279981 0.960006i \(-0.590328\pi\)
−0.279981 + 0.960006i \(0.590328\pi\)
\(230\) −5.42673e12 −0.555949
\(231\) 4.51415e12 0.451554
\(232\) 5.47237e12 0.534554
\(233\) 5.51437e12 0.526064 0.263032 0.964787i \(-0.415278\pi\)
0.263032 + 0.964787i \(0.415278\pi\)
\(234\) 6.55147e12 0.610452
\(235\) −1.60215e12 −0.145825
\(236\) −2.13638e12 −0.189960
\(237\) −2.96917e11 −0.0257940
\(238\) −2.50682e12 −0.212789
\(239\) 3.89823e12 0.323354 0.161677 0.986844i \(-0.448310\pi\)
0.161677 + 0.986844i \(0.448310\pi\)
\(240\) 1.02019e12 0.0827025
\(241\) −1.68649e12 −0.133626 −0.0668128 0.997766i \(-0.521283\pi\)
−0.0668128 + 0.997766i \(0.521283\pi\)
\(242\) 1.38909e13 1.07583
\(243\) −8.47289e11 −0.0641500
\(244\) −2.28484e13 −1.69127
\(245\) 5.68644e12 0.411554
\(246\) 5.78666e12 0.409529
\(247\) 3.27047e13 2.26348
\(248\) 8.06951e12 0.546214
\(249\) 1.69371e13 1.12135
\(250\) 1.90359e13 1.23283
\(251\) −1.40972e13 −0.893155 −0.446578 0.894745i \(-0.647357\pi\)
−0.446578 + 0.894745i \(0.647357\pi\)
\(252\) −1.09524e13 −0.678903
\(253\) 7.54762e12 0.457770
\(254\) 6.51280e12 0.386529
\(255\) 4.19332e11 0.0243550
\(256\) −7.20175e12 −0.409372
\(257\) 1.57343e12 0.0875417 0.0437708 0.999042i \(-0.486063\pi\)
0.0437708 + 0.999042i \(0.486063\pi\)
\(258\) 1.82097e13 0.991733
\(259\) −2.32970e13 −1.24208
\(260\) −1.41662e13 −0.739436
\(261\) −4.84268e12 −0.247493
\(262\) 2.45892e13 1.23051
\(263\) −2.86686e13 −1.40491 −0.702457 0.711727i \(-0.747914\pi\)
−0.702457 + 0.711727i \(0.747914\pi\)
\(264\) 4.85287e12 0.232904
\(265\) −1.71561e13 −0.806428
\(266\) −9.21451e13 −4.24251
\(267\) −4.80700e12 −0.216801
\(268\) −2.77079e13 −1.22423
\(269\) −1.17146e12 −0.0507095 −0.0253548 0.999679i \(-0.508072\pi\)
−0.0253548 + 0.999679i \(0.508072\pi\)
\(270\) 3.08771e12 0.130959
\(271\) −4.07109e13 −1.69192 −0.845959 0.533247i \(-0.820971\pi\)
−0.845959 + 0.533247i \(0.820971\pi\)
\(272\) 7.87951e11 0.0320901
\(273\) −2.35808e13 −0.941160
\(274\) −1.54183e13 −0.603128
\(275\) −1.18619e13 −0.454803
\(276\) −1.83124e13 −0.688249
\(277\) −2.26706e12 −0.0835264 −0.0417632 0.999128i \(-0.513298\pi\)
−0.0417632 + 0.999128i \(0.513298\pi\)
\(278\) −1.80926e12 −0.0653515
\(279\) −7.14097e12 −0.252891
\(280\) 1.25587e13 0.436091
\(281\) 1.76306e13 0.600319 0.300159 0.953889i \(-0.402960\pi\)
0.300159 + 0.953889i \(0.402960\pi\)
\(282\) −9.11173e12 −0.304250
\(283\) −3.71101e13 −1.21525 −0.607626 0.794223i \(-0.707878\pi\)
−0.607626 + 0.794223i \(0.707878\pi\)
\(284\) −5.26782e13 −1.69192
\(285\) 1.54137e13 0.485581
\(286\) 3.32059e13 1.02613
\(287\) −2.08280e13 −0.631389
\(288\) 1.38715e13 0.412538
\(289\) −3.39480e13 −0.990550
\(290\) 1.76478e13 0.505244
\(291\) 3.78476e13 1.06323
\(292\) 2.67668e12 0.0737889
\(293\) 8.31149e12 0.224857 0.112429 0.993660i \(-0.464137\pi\)
0.112429 + 0.993660i \(0.464137\pi\)
\(294\) 3.23398e13 0.858671
\(295\) −2.16782e12 −0.0564940
\(296\) −2.50451e13 −0.640646
\(297\) −4.29446e12 −0.107832
\(298\) −3.26454e12 −0.0804698
\(299\) −3.94269e13 −0.954116
\(300\) 2.87799e13 0.683789
\(301\) −6.55424e13 −1.52900
\(302\) 2.00472e13 0.459215
\(303\) −4.03854e13 −0.908427
\(304\) 2.89634e13 0.639800
\(305\) −2.31847e13 −0.502981
\(306\) 2.38482e12 0.0508145
\(307\) 3.75209e13 0.785257 0.392628 0.919697i \(-0.371566\pi\)
0.392628 + 0.919697i \(0.371566\pi\)
\(308\) −5.55121e13 −1.14119
\(309\) 1.30767e13 0.264074
\(310\) 2.60233e13 0.516265
\(311\) 5.51443e13 1.07478 0.537388 0.843335i \(-0.319411\pi\)
0.537388 + 0.843335i \(0.319411\pi\)
\(312\) −2.53502e13 −0.485435
\(313\) 1.64291e13 0.309114 0.154557 0.987984i \(-0.450605\pi\)
0.154557 + 0.987984i \(0.450605\pi\)
\(314\) 9.60141e13 1.77510
\(315\) −1.11136e13 −0.201905
\(316\) 3.65130e12 0.0651881
\(317\) 3.54426e13 0.621871 0.310935 0.950431i \(-0.399358\pi\)
0.310935 + 0.950431i \(0.399358\pi\)
\(318\) −9.75696e13 −1.68254
\(319\) −2.45450e13 −0.416019
\(320\) −4.19526e13 −0.698931
\(321\) −2.81054e13 −0.460270
\(322\) 1.11085e14 1.78833
\(323\) 1.19049e13 0.188414
\(324\) 1.04194e13 0.162124
\(325\) 6.19635e13 0.947933
\(326\) −5.42277e13 −0.815688
\(327\) 5.81440e13 0.859988
\(328\) −2.23908e13 −0.325660
\(329\) 3.27960e13 0.469076
\(330\) 1.56500e13 0.220134
\(331\) −8.28933e13 −1.14674 −0.573371 0.819296i \(-0.694364\pi\)
−0.573371 + 0.819296i \(0.694364\pi\)
\(332\) −2.08281e14 −2.83394
\(333\) 2.21632e13 0.296612
\(334\) −1.97923e14 −2.60549
\(335\) −2.81157e13 −0.364085
\(336\) −2.08832e13 −0.266030
\(337\) 9.76603e13 1.22392 0.611961 0.790888i \(-0.290381\pi\)
0.611961 + 0.790888i \(0.290381\pi\)
\(338\) −4.62760e13 −0.570577
\(339\) 5.73528e13 0.695756
\(340\) −5.15669e12 −0.0615512
\(341\) −3.61938e13 −0.425094
\(342\) 8.76607e13 1.01312
\(343\) 6.33122e12 0.0720062
\(344\) −7.04604e13 −0.788631
\(345\) −1.85819e13 −0.204685
\(346\) 1.92906e13 0.209135
\(347\) 1.34099e14 1.43091 0.715456 0.698658i \(-0.246219\pi\)
0.715456 + 0.698658i \(0.246219\pi\)
\(348\) 5.95522e13 0.625478
\(349\) 1.45916e14 1.50856 0.754281 0.656552i \(-0.227986\pi\)
0.754281 + 0.656552i \(0.227986\pi\)
\(350\) −1.74581e14 −1.77674
\(351\) 2.24332e13 0.224751
\(352\) 7.03071e13 0.693449
\(353\) −6.07598e13 −0.590005 −0.295003 0.955496i \(-0.595320\pi\)
−0.295003 + 0.955496i \(0.595320\pi\)
\(354\) −1.23288e13 −0.117870
\(355\) −5.34535e13 −0.503176
\(356\) 5.91134e13 0.547913
\(357\) −8.58370e12 −0.0783429
\(358\) 2.82197e14 2.53627
\(359\) −1.72255e14 −1.52459 −0.762295 0.647230i \(-0.775927\pi\)
−0.762295 + 0.647230i \(0.775927\pi\)
\(360\) −1.19476e13 −0.104139
\(361\) 3.21109e14 2.75653
\(362\) −2.03049e14 −1.71674
\(363\) 4.75644e13 0.396092
\(364\) 2.89982e14 2.37855
\(365\) 2.71608e12 0.0219448
\(366\) −1.31855e14 −1.04943
\(367\) 1.04491e14 0.819247 0.409623 0.912255i \(-0.365660\pi\)
0.409623 + 0.912255i \(0.365660\pi\)
\(368\) −3.49166e13 −0.269692
\(369\) 1.98144e13 0.150777
\(370\) −8.07676e13 −0.605519
\(371\) 3.51184e14 2.59405
\(372\) 8.78151e13 0.639121
\(373\) −9.84499e12 −0.0706020 −0.0353010 0.999377i \(-0.511239\pi\)
−0.0353010 + 0.999377i \(0.511239\pi\)
\(374\) 1.20874e13 0.0854158
\(375\) 6.51817e13 0.453893
\(376\) 3.52568e13 0.241941
\(377\) 1.28217e14 0.867097
\(378\) −6.32052e13 −0.421258
\(379\) 2.09842e14 1.37840 0.689201 0.724570i \(-0.257962\pi\)
0.689201 + 0.724570i \(0.257962\pi\)
\(380\) −1.89549e14 −1.22719
\(381\) 2.23008e13 0.142309
\(382\) −1.57978e14 −0.993686
\(383\) 2.56401e14 1.58974 0.794870 0.606780i \(-0.207539\pi\)
0.794870 + 0.606780i \(0.207539\pi\)
\(384\) −1.21684e14 −0.743721
\(385\) −5.63291e13 −0.339390
\(386\) −4.04631e14 −2.40342
\(387\) 6.23527e13 0.365128
\(388\) −4.65426e14 −2.68705
\(389\) −1.78306e14 −1.01495 −0.507475 0.861667i \(-0.669421\pi\)
−0.507475 + 0.861667i \(0.669421\pi\)
\(390\) −8.17516e13 −0.458818
\(391\) −1.43519e13 −0.0794213
\(392\) −1.25135e14 −0.682820
\(393\) 8.41968e13 0.453040
\(394\) 3.96556e14 2.10415
\(395\) 3.70503e12 0.0193869
\(396\) 5.28105e13 0.272519
\(397\) −3.29642e14 −1.67762 −0.838811 0.544422i \(-0.816749\pi\)
−0.838811 + 0.544422i \(0.816749\pi\)
\(398\) 1.39577e14 0.700579
\(399\) −3.15518e14 −1.56197
\(400\) 5.48750e13 0.267945
\(401\) −3.50313e14 −1.68718 −0.843592 0.536985i \(-0.819563\pi\)
−0.843592 + 0.536985i \(0.819563\pi\)
\(402\) −1.59899e14 −0.759631
\(403\) 1.89067e14 0.886010
\(404\) 4.96634e14 2.29583
\(405\) 1.05728e13 0.0482154
\(406\) −3.61249e14 −1.62523
\(407\) 1.12333e14 0.498586
\(408\) −9.22779e12 −0.0404079
\(409\) −4.41416e13 −0.190709 −0.0953543 0.995443i \(-0.530398\pi\)
−0.0953543 + 0.995443i \(0.530398\pi\)
\(410\) −7.22080e13 −0.307804
\(411\) −5.27946e13 −0.222054
\(412\) −1.60809e14 −0.667382
\(413\) 4.43752e13 0.181725
\(414\) −1.05679e14 −0.427057
\(415\) −2.11347e14 −0.842812
\(416\) −3.67267e14 −1.44534
\(417\) −6.19518e12 −0.0240606
\(418\) 4.44306e14 1.70299
\(419\) −1.07012e14 −0.404813 −0.202407 0.979302i \(-0.564876\pi\)
−0.202407 + 0.979302i \(0.564876\pi\)
\(420\) 1.36668e14 0.510267
\(421\) −3.01198e14 −1.10994 −0.554971 0.831870i \(-0.687271\pi\)
−0.554971 + 0.831870i \(0.687271\pi\)
\(422\) 5.37461e14 1.95492
\(423\) −3.11999e13 −0.112016
\(424\) 3.77535e14 1.33797
\(425\) 2.25555e13 0.0789066
\(426\) −3.03999e14 −1.04983
\(427\) 4.74589e14 1.61795
\(428\) 3.45623e14 1.16322
\(429\) 1.13702e14 0.377792
\(430\) −2.27227e14 −0.745390
\(431\) 2.67511e14 0.866398 0.433199 0.901298i \(-0.357385\pi\)
0.433199 + 0.901298i \(0.357385\pi\)
\(432\) 1.98669e13 0.0635286
\(433\) −3.05057e14 −0.963158 −0.481579 0.876403i \(-0.659937\pi\)
−0.481579 + 0.876403i \(0.659937\pi\)
\(434\) −5.32695e14 −1.66068
\(435\) 6.04286e13 0.186017
\(436\) −7.15018e14 −2.17341
\(437\) −5.27544e14 −1.58347
\(438\) 1.54468e13 0.0457858
\(439\) 3.76231e14 1.10129 0.550643 0.834741i \(-0.314383\pi\)
0.550643 + 0.834741i \(0.314383\pi\)
\(440\) −6.05558e13 −0.175052
\(441\) 1.10736e14 0.316138
\(442\) −6.31415e13 −0.178030
\(443\) 3.92462e14 1.09289 0.546446 0.837494i \(-0.315980\pi\)
0.546446 + 0.837494i \(0.315980\pi\)
\(444\) −2.72549e14 −0.749615
\(445\) 5.99834e13 0.162949
\(446\) −1.02819e15 −2.75886
\(447\) −1.11783e13 −0.0296267
\(448\) 8.58767e14 2.24826
\(449\) −4.48564e14 −1.16003 −0.580015 0.814606i \(-0.696953\pi\)
−0.580015 + 0.814606i \(0.696953\pi\)
\(450\) 1.66085e14 0.424289
\(451\) 1.00429e14 0.253446
\(452\) −7.05289e14 −1.75835
\(453\) 6.86446e13 0.169070
\(454\) −8.88147e14 −2.16111
\(455\) 2.94249e14 0.707380
\(456\) −3.39193e14 −0.805639
\(457\) 3.33614e14 0.782899 0.391449 0.920200i \(-0.371974\pi\)
0.391449 + 0.920200i \(0.371974\pi\)
\(458\) 3.78711e14 0.878107
\(459\) 8.16596e12 0.0187084
\(460\) 2.28509e14 0.517291
\(461\) −3.00279e14 −0.671691 −0.335846 0.941917i \(-0.609022\pi\)
−0.335846 + 0.941917i \(0.609022\pi\)
\(462\) −3.20354e14 −0.708107
\(463\) −4.53030e14 −0.989536 −0.494768 0.869025i \(-0.664747\pi\)
−0.494768 + 0.869025i \(0.664747\pi\)
\(464\) 1.13549e14 0.245095
\(465\) 8.91075e13 0.190074
\(466\) −3.91336e14 −0.824950
\(467\) 7.82679e14 1.63057 0.815287 0.579057i \(-0.196579\pi\)
0.815287 + 0.579057i \(0.196579\pi\)
\(468\) −2.75869e14 −0.568004
\(469\) 5.75527e14 1.17116
\(470\) 1.13699e14 0.228676
\(471\) 3.28766e14 0.653540
\(472\) 4.77049e13 0.0937307
\(473\) 3.16033e14 0.613756
\(474\) 2.10712e13 0.0404490
\(475\) 8.29091e14 1.57321
\(476\) 1.05557e14 0.197993
\(477\) −3.34093e14 −0.619464
\(478\) −2.76644e14 −0.507070
\(479\) 3.60866e14 0.653884 0.326942 0.945044i \(-0.393982\pi\)
0.326942 + 0.945044i \(0.393982\pi\)
\(480\) −1.73093e14 −0.310065
\(481\) −5.86802e14 −1.03919
\(482\) 1.19684e14 0.209546
\(483\) 3.80370e14 0.658412
\(484\) −5.84917e14 −1.00103
\(485\) −4.72276e14 −0.799128
\(486\) 6.01292e13 0.100597
\(487\) 1.02107e15 1.68906 0.844532 0.535506i \(-0.179879\pi\)
0.844532 + 0.535506i \(0.179879\pi\)
\(488\) 5.10200e14 0.834509
\(489\) −1.85683e14 −0.300313
\(490\) −4.03547e14 −0.645380
\(491\) 2.63607e14 0.416878 0.208439 0.978035i \(-0.433162\pi\)
0.208439 + 0.978035i \(0.433162\pi\)
\(492\) −2.43665e14 −0.381052
\(493\) 4.66725e13 0.0721777
\(494\) −2.32094e15 −3.54949
\(495\) 5.35877e13 0.0810470
\(496\) 1.67439e14 0.250441
\(497\) 1.09419e15 1.61857
\(498\) −1.20197e15 −1.75845
\(499\) 1.49421e14 0.216201 0.108100 0.994140i \(-0.465523\pi\)
0.108100 + 0.994140i \(0.465523\pi\)
\(500\) −8.01563e14 −1.14710
\(501\) −6.77716e14 −0.959268
\(502\) 1.00043e15 1.40061
\(503\) 6.46178e14 0.894805 0.447402 0.894333i \(-0.352349\pi\)
0.447402 + 0.894333i \(0.352349\pi\)
\(504\) 2.44565e14 0.334986
\(505\) 5.03943e14 0.682778
\(506\) −5.35629e14 −0.717854
\(507\) −1.58456e14 −0.210070
\(508\) −2.74241e14 −0.359651
\(509\) 2.83806e14 0.368192 0.184096 0.982908i \(-0.441064\pi\)
0.184096 + 0.982908i \(0.441064\pi\)
\(510\) −2.97586e13 −0.0381924
\(511\) −5.55979e13 −0.0705900
\(512\) −5.14462e14 −0.646203
\(513\) 3.00163e14 0.373002
\(514\) −1.11661e14 −0.137279
\(515\) −1.63175e14 −0.198479
\(516\) −7.66774e14 −0.922771
\(517\) −1.58136e14 −0.188292
\(518\) 1.65331e15 1.94778
\(519\) 6.60539e13 0.0769977
\(520\) 3.16329e14 0.364855
\(521\) 4.28729e14 0.489301 0.244650 0.969611i \(-0.421327\pi\)
0.244650 + 0.969611i \(0.421327\pi\)
\(522\) 3.43668e14 0.388107
\(523\) −3.18577e14 −0.356005 −0.178002 0.984030i \(-0.556963\pi\)
−0.178002 + 0.984030i \(0.556963\pi\)
\(524\) −1.03540e15 −1.14495
\(525\) −5.97792e14 −0.654145
\(526\) 2.03451e15 2.20312
\(527\) 6.88229e13 0.0737522
\(528\) 1.00695e14 0.106787
\(529\) −3.16833e14 −0.332525
\(530\) 1.21751e15 1.26460
\(531\) −4.22156e13 −0.0433963
\(532\) 3.88004e15 3.94751
\(533\) −5.24614e14 −0.528251
\(534\) 3.41136e14 0.339978
\(535\) 3.50709e14 0.345941
\(536\) 6.18712e14 0.604063
\(537\) 9.66283e14 0.933783
\(538\) 8.31345e13 0.0795204
\(539\) 5.61262e14 0.531408
\(540\) −1.30017e14 −0.121853
\(541\) −1.68448e15 −1.56272 −0.781359 0.624082i \(-0.785473\pi\)
−0.781359 + 0.624082i \(0.785473\pi\)
\(542\) 2.88911e15 2.65319
\(543\) −6.95271e14 −0.632055
\(544\) −1.33690e14 −0.120311
\(545\) −7.25541e14 −0.646370
\(546\) 1.67345e15 1.47589
\(547\) 8.84142e13 0.0771955 0.0385977 0.999255i \(-0.487711\pi\)
0.0385977 + 0.999255i \(0.487711\pi\)
\(548\) 6.49235e14 0.561188
\(549\) −4.51492e14 −0.386369
\(550\) 8.41797e14 0.713202
\(551\) 1.71558e15 1.43905
\(552\) 4.08912e14 0.339598
\(553\) −7.58418e13 −0.0623620
\(554\) 1.60885e14 0.130982
\(555\) −2.76560e14 −0.222935
\(556\) 7.61845e13 0.0608072
\(557\) 3.30265e14 0.261011 0.130506 0.991448i \(-0.458340\pi\)
0.130506 + 0.991448i \(0.458340\pi\)
\(558\) 5.06770e14 0.396573
\(559\) −1.65088e15 −1.27923
\(560\) 2.60588e14 0.199949
\(561\) 4.13889e13 0.0314477
\(562\) −1.25118e15 −0.941394
\(563\) 9.30546e14 0.693333 0.346666 0.937988i \(-0.387314\pi\)
0.346666 + 0.937988i \(0.387314\pi\)
\(564\) 3.83677e14 0.283094
\(565\) −7.15669e14 −0.522933
\(566\) 2.63358e15 1.90571
\(567\) −2.16424e14 −0.155095
\(568\) 1.17629e15 0.834832
\(569\) 1.31150e15 0.921827 0.460913 0.887445i \(-0.347522\pi\)
0.460913 + 0.887445i \(0.347522\pi\)
\(570\) −1.09386e15 −0.761466
\(571\) −2.01426e15 −1.38872 −0.694362 0.719626i \(-0.744313\pi\)
−0.694362 + 0.719626i \(0.744313\pi\)
\(572\) −1.39823e15 −0.954777
\(573\) −5.40941e14 −0.365847
\(574\) 1.47809e15 0.990117
\(575\) −9.99504e14 −0.663150
\(576\) −8.16974e14 −0.536889
\(577\) 2.68955e14 0.175070 0.0875350 0.996161i \(-0.472101\pi\)
0.0875350 + 0.996161i \(0.472101\pi\)
\(578\) 2.40918e15 1.55334
\(579\) −1.38552e15 −0.884870
\(580\) −7.43113e14 −0.470112
\(581\) 4.32625e15 2.71108
\(582\) −2.68592e15 −1.66731
\(583\) −1.69334e15 −1.04128
\(584\) −5.97697e13 −0.0364091
\(585\) −2.79929e14 −0.168924
\(586\) −5.89839e14 −0.352611
\(587\) 8.38181e14 0.496396 0.248198 0.968709i \(-0.420162\pi\)
0.248198 + 0.968709i \(0.420162\pi\)
\(588\) −1.36176e15 −0.798962
\(589\) 2.52978e15 1.47044
\(590\) 1.53843e14 0.0885914
\(591\) 1.35787e15 0.774686
\(592\) −5.19673e14 −0.293739
\(593\) 4.77555e14 0.267438 0.133719 0.991019i \(-0.457308\pi\)
0.133719 + 0.991019i \(0.457308\pi\)
\(594\) 3.04763e14 0.169097
\(595\) 1.07111e14 0.0588828
\(596\) 1.37463e14 0.0748742
\(597\) 4.77932e14 0.257933
\(598\) 2.79799e15 1.49620
\(599\) 3.98555e14 0.211174 0.105587 0.994410i \(-0.466328\pi\)
0.105587 + 0.994410i \(0.466328\pi\)
\(600\) −6.42648e14 −0.337397
\(601\) 5.90443e14 0.307163 0.153581 0.988136i \(-0.450919\pi\)
0.153581 + 0.988136i \(0.450919\pi\)
\(602\) 4.65132e15 2.39771
\(603\) −5.47518e14 −0.279675
\(604\) −8.44148e14 −0.427283
\(605\) −5.93526e14 −0.297704
\(606\) 2.86602e15 1.42456
\(607\) 2.99345e15 1.47447 0.737233 0.675638i \(-0.236132\pi\)
0.737233 + 0.675638i \(0.236132\pi\)
\(608\) −4.91415e15 −2.39871
\(609\) −1.23697e15 −0.598362
\(610\) 1.64534e15 0.788753
\(611\) 8.26062e14 0.392452
\(612\) −1.00420e14 −0.0472810
\(613\) 1.79423e15 0.837231 0.418615 0.908164i \(-0.362516\pi\)
0.418615 + 0.908164i \(0.362516\pi\)
\(614\) −2.66273e15 −1.23140
\(615\) −2.47251e14 −0.113325
\(616\) 1.23957e15 0.563090
\(617\) −1.69089e15 −0.761283 −0.380642 0.924723i \(-0.624297\pi\)
−0.380642 + 0.924723i \(0.624297\pi\)
\(618\) −9.28007e14 −0.414109
\(619\) −3.88016e15 −1.71613 −0.858067 0.513537i \(-0.828335\pi\)
−0.858067 + 0.513537i \(0.828335\pi\)
\(620\) −1.09579e15 −0.480366
\(621\) −3.61859e14 −0.157230
\(622\) −3.91340e15 −1.68542
\(623\) −1.22786e15 −0.524159
\(624\) −5.26004e14 −0.222574
\(625\) 1.12188e15 0.470549
\(626\) −1.16592e15 −0.484740
\(627\) 1.52137e15 0.626993
\(628\) −4.04296e15 −1.65166
\(629\) −2.13603e14 −0.0865027
\(630\) 7.88697e14 0.316619
\(631\) 2.23385e15 0.888979 0.444490 0.895784i \(-0.353385\pi\)
0.444490 + 0.895784i \(0.353385\pi\)
\(632\) −8.15326e13 −0.0321653
\(633\) 1.84034e15 0.719745
\(634\) −2.51524e15 −0.975190
\(635\) −2.78277e14 −0.106960
\(636\) 4.10846e15 1.56554
\(637\) −2.93190e15 −1.10760
\(638\) 1.74187e15 0.652383
\(639\) −1.04094e15 −0.386518
\(640\) 1.51841e15 0.558984
\(641\) −4.12814e15 −1.50673 −0.753365 0.657603i \(-0.771570\pi\)
−0.753365 + 0.657603i \(0.771570\pi\)
\(642\) 1.99455e15 0.721775
\(643\) 4.10311e15 1.47215 0.736076 0.676899i \(-0.236676\pi\)
0.736076 + 0.676899i \(0.236676\pi\)
\(644\) −4.67756e15 −1.66398
\(645\) −7.78059e14 −0.274431
\(646\) −8.44853e14 −0.295462
\(647\) −3.20964e15 −1.11297 −0.556484 0.830858i \(-0.687850\pi\)
−0.556484 + 0.830858i \(0.687850\pi\)
\(648\) −2.32663e14 −0.0799955
\(649\) −2.13968e14 −0.0729464
\(650\) −4.39734e15 −1.48651
\(651\) −1.82402e15 −0.611414
\(652\) 2.28342e15 0.758968
\(653\) −3.00682e15 −0.991025 −0.495512 0.868601i \(-0.665020\pi\)
−0.495512 + 0.868601i \(0.665020\pi\)
\(654\) −4.12628e15 −1.34859
\(655\) −1.05064e15 −0.340507
\(656\) −4.64599e14 −0.149316
\(657\) 5.28921e13 0.0168570
\(658\) −2.32742e15 −0.735584
\(659\) 3.44573e15 1.07997 0.539984 0.841675i \(-0.318430\pi\)
0.539984 + 0.841675i \(0.318430\pi\)
\(660\) −6.58988e14 −0.204827
\(661\) 1.31737e15 0.406070 0.203035 0.979171i \(-0.434919\pi\)
0.203035 + 0.979171i \(0.434919\pi\)
\(662\) 5.88266e15 1.79827
\(663\) −2.16206e14 −0.0655455
\(664\) 4.65087e15 1.39833
\(665\) 3.93715e15 1.17399
\(666\) −1.57285e15 −0.465134
\(667\) −2.06820e15 −0.606599
\(668\) 8.33412e15 2.42432
\(669\) −3.52066e15 −1.01573
\(670\) 1.99528e15 0.570942
\(671\) −2.28837e15 −0.649461
\(672\) 3.54320e15 0.997390
\(673\) 3.38796e15 0.945922 0.472961 0.881083i \(-0.343185\pi\)
0.472961 + 0.881083i \(0.343185\pi\)
\(674\) −6.93062e15 −1.91930
\(675\) 5.68699e14 0.156211
\(676\) 1.94859e15 0.530901
\(677\) 8.15250e14 0.220320 0.110160 0.993914i \(-0.464864\pi\)
0.110160 + 0.993914i \(0.464864\pi\)
\(678\) −4.07014e15 −1.09105
\(679\) 9.66745e15 2.57056
\(680\) 1.15148e14 0.0303708
\(681\) −3.04115e15 −0.795661
\(682\) 2.56855e15 0.666613
\(683\) −4.51673e15 −1.16281 −0.581407 0.813613i \(-0.697497\pi\)
−0.581407 + 0.813613i \(0.697497\pi\)
\(684\) −3.69122e15 −0.942672
\(685\) 6.58790e14 0.166897
\(686\) −4.49305e14 −0.112917
\(687\) 1.29676e15 0.323294
\(688\) −1.46202e15 −0.361590
\(689\) 8.84558e15 2.17030
\(690\) 1.31870e15 0.320978
\(691\) 7.60364e15 1.83608 0.918041 0.396485i \(-0.129770\pi\)
0.918041 + 0.396485i \(0.129770\pi\)
\(692\) −8.12289e14 −0.194593
\(693\) −1.09694e15 −0.260705
\(694\) −9.51654e15 −2.24389
\(695\) 7.73057e13 0.0180840
\(696\) −1.32979e15 −0.308625
\(697\) −1.90966e14 −0.0439720
\(698\) −1.03552e16 −2.36566
\(699\) −1.33999e15 −0.303723
\(700\) 7.35127e15 1.65319
\(701\) 3.60745e14 0.0804917 0.0402458 0.999190i \(-0.487186\pi\)
0.0402458 + 0.999190i \(0.487186\pi\)
\(702\) −1.59201e15 −0.352445
\(703\) −7.85159e15 −1.72466
\(704\) −4.14081e15 −0.902475
\(705\) 3.89323e14 0.0841919
\(706\) 4.31192e15 0.925220
\(707\) −1.03157e16 −2.19630
\(708\) 5.19141e14 0.109674
\(709\) −6.11599e15 −1.28207 −0.641037 0.767510i \(-0.721495\pi\)
−0.641037 + 0.767510i \(0.721495\pi\)
\(710\) 3.79341e15 0.789058
\(711\) 7.21508e13 0.0148922
\(712\) −1.31999e15 −0.270353
\(713\) −3.04976e15 −0.619830
\(714\) 6.09157e14 0.122854
\(715\) −1.41881e15 −0.283950
\(716\) −1.18827e16 −2.35991
\(717\) −9.47269e14 −0.186689
\(718\) 1.22244e16 2.39079
\(719\) 6.80359e15 1.32047 0.660236 0.751058i \(-0.270456\pi\)
0.660236 + 0.751058i \(0.270456\pi\)
\(720\) −2.47906e14 −0.0477483
\(721\) 3.34019e15 0.638450
\(722\) −2.27880e16 −4.32267
\(723\) 4.09817e14 0.0771488
\(724\) 8.55000e15 1.59736
\(725\) 3.25040e15 0.602667
\(726\) −3.37549e15 −0.621133
\(727\) 3.38511e15 0.618206 0.309103 0.951029i \(-0.399971\pi\)
0.309103 + 0.951029i \(0.399971\pi\)
\(728\) −6.47522e15 −1.17363
\(729\) 2.05891e14 0.0370370
\(730\) −1.92751e14 −0.0344128
\(731\) −6.00940e14 −0.106484
\(732\) 5.55216e15 0.976453
\(733\) 3.69274e15 0.644581 0.322290 0.946641i \(-0.395547\pi\)
0.322290 + 0.946641i \(0.395547\pi\)
\(734\) −7.41536e15 −1.28471
\(735\) −1.38180e15 −0.237611
\(736\) 5.92421e15 1.01112
\(737\) −2.77508e15 −0.470115
\(738\) −1.40616e15 −0.236442
\(739\) −7.29990e15 −1.21835 −0.609176 0.793035i \(-0.708500\pi\)
−0.609176 + 0.793035i \(0.708500\pi\)
\(740\) 3.40096e15 0.563414
\(741\) −7.94724e15 −1.30682
\(742\) −2.49223e16 −4.06787
\(743\) −7.54909e15 −1.22308 −0.611542 0.791212i \(-0.709450\pi\)
−0.611542 + 0.791212i \(0.709450\pi\)
\(744\) −1.96089e15 −0.315357
\(745\) 1.39486e14 0.0222675
\(746\) 6.98666e14 0.110715
\(747\) −4.11570e15 −0.647412
\(748\) −5.08975e14 −0.0794763
\(749\) −7.17900e15 −1.11279
\(750\) −4.62572e15 −0.711775
\(751\) −6.57937e15 −1.00500 −0.502498 0.864578i \(-0.667586\pi\)
−0.502498 + 0.864578i \(0.667586\pi\)
\(752\) 7.31563e14 0.110931
\(753\) 3.42562e15 0.515663
\(754\) −9.09911e15 −1.35974
\(755\) −8.56571e14 −0.127074
\(756\) 2.66144e15 0.391965
\(757\) −5.29589e15 −0.774304 −0.387152 0.922016i \(-0.626541\pi\)
−0.387152 + 0.922016i \(0.626541\pi\)
\(758\) −1.48917e16 −2.16155
\(759\) −1.83407e15 −0.264294
\(760\) 4.23257e15 0.605522
\(761\) −1.15832e16 −1.64518 −0.822588 0.568638i \(-0.807471\pi\)
−0.822588 + 0.568638i \(0.807471\pi\)
\(762\) −1.58261e15 −0.223163
\(763\) 1.48518e16 2.07919
\(764\) 6.65215e15 0.924589
\(765\) −1.01898e14 −0.0140613
\(766\) −1.81959e16 −2.49296
\(767\) 1.11772e15 0.152040
\(768\) 1.75003e15 0.236351
\(769\) 7.21946e15 0.968076 0.484038 0.875047i \(-0.339170\pi\)
0.484038 + 0.875047i \(0.339170\pi\)
\(770\) 3.99749e15 0.532216
\(771\) −3.82343e14 −0.0505422
\(772\) 1.70382e16 2.23629
\(773\) 2.28654e15 0.297983 0.148991 0.988838i \(-0.452397\pi\)
0.148991 + 0.988838i \(0.452397\pi\)
\(774\) −4.42496e15 −0.572577
\(775\) 4.79301e15 0.615813
\(776\) 1.03929e16 1.32585
\(777\) 5.66116e15 0.717117
\(778\) 1.26538e16 1.59160
\(779\) −7.01950e15 −0.876698
\(780\) 3.44239e15 0.426914
\(781\) −5.27596e15 −0.649712
\(782\) 1.01851e15 0.124545
\(783\) 1.17677e15 0.142890
\(784\) −2.59649e15 −0.313075
\(785\) −4.10246e15 −0.491204
\(786\) −5.97516e15 −0.710438
\(787\) −8.50369e15 −1.00403 −0.502015 0.864859i \(-0.667408\pi\)
−0.502015 + 0.864859i \(0.667408\pi\)
\(788\) −1.66982e16 −1.95783
\(789\) 6.96646e15 0.811127
\(790\) −2.62934e14 −0.0304017
\(791\) 1.46497e16 1.68212
\(792\) −1.17925e15 −0.134467
\(793\) 1.19539e16 1.35365
\(794\) 2.33936e16 2.63077
\(795\) 4.16893e15 0.465591
\(796\) −5.87731e15 −0.651864
\(797\) −4.81836e15 −0.530736 −0.265368 0.964147i \(-0.585493\pi\)
−0.265368 + 0.964147i \(0.585493\pi\)
\(798\) 2.23913e16 2.44942
\(799\) 3.00697e14 0.0326680
\(800\) −9.31052e15 −1.00457
\(801\) 1.16810e15 0.125170
\(802\) 2.48605e16 2.64577
\(803\) 2.68082e14 0.0283356
\(804\) 6.73303e15 0.706809
\(805\) −4.74640e15 −0.494865
\(806\) −1.34175e16 −1.38940
\(807\) 2.84665e14 0.0292772
\(808\) −1.10897e16 −1.13281
\(809\) −6.50899e15 −0.660384 −0.330192 0.943914i \(-0.607114\pi\)
−0.330192 + 0.943914i \(0.607114\pi\)
\(810\) −7.50314e14 −0.0756093
\(811\) 1.13742e16 1.13843 0.569215 0.822189i \(-0.307247\pi\)
0.569215 + 0.822189i \(0.307247\pi\)
\(812\) 1.52115e16 1.51221
\(813\) 9.89275e15 0.976830
\(814\) −7.97192e15 −0.781860
\(815\) 2.31702e15 0.225717
\(816\) −1.91472e14 −0.0185272
\(817\) −2.20892e16 −2.12305
\(818\) 3.13258e15 0.299061
\(819\) 5.73013e15 0.543379
\(820\) 3.04053e15 0.286400
\(821\) 1.18256e16 1.10646 0.553230 0.833028i \(-0.313395\pi\)
0.553230 + 0.833028i \(0.313395\pi\)
\(822\) 3.74665e15 0.348216
\(823\) −1.42822e16 −1.31854 −0.659272 0.751904i \(-0.729136\pi\)
−0.659272 + 0.751904i \(0.729136\pi\)
\(824\) 3.59082e15 0.329302
\(825\) 2.88244e15 0.262581
\(826\) −3.14916e15 −0.284973
\(827\) −6.37640e15 −0.573186 −0.286593 0.958052i \(-0.592523\pi\)
−0.286593 + 0.958052i \(0.592523\pi\)
\(828\) 4.44992e15 0.397361
\(829\) 9.48269e15 0.841166 0.420583 0.907254i \(-0.361826\pi\)
0.420583 + 0.907254i \(0.361826\pi\)
\(830\) 1.49986e16 1.32166
\(831\) 5.50895e14 0.0482240
\(832\) 2.16306e16 1.88100
\(833\) −1.06725e15 −0.0921972
\(834\) 4.39651e14 0.0377307
\(835\) 8.45677e15 0.720990
\(836\) −1.87088e16 −1.58457
\(837\) 1.73526e15 0.146007
\(838\) 7.59427e15 0.634811
\(839\) 1.13775e16 0.944835 0.472417 0.881375i \(-0.343382\pi\)
0.472417 + 0.881375i \(0.343382\pi\)
\(840\) −3.05177e15 −0.251777
\(841\) −5.47468e15 −0.448726
\(842\) 2.13750e16 1.74056
\(843\) −4.28423e15 −0.346594
\(844\) −2.26314e16 −1.81898
\(845\) 1.97727e15 0.157890
\(846\) 2.21415e15 0.175659
\(847\) 1.21494e16 0.957628
\(848\) 7.83367e15 0.613462
\(849\) 9.01775e15 0.701627
\(850\) −1.60069e15 −0.123738
\(851\) 9.46543e15 0.726989
\(852\) 1.28008e16 0.976831
\(853\) 9.34134e15 0.708255 0.354128 0.935197i \(-0.384778\pi\)
0.354128 + 0.935197i \(0.384778\pi\)
\(854\) −3.36799e16 −2.53719
\(855\) −3.74554e15 −0.280350
\(856\) −7.71768e15 −0.573959
\(857\) 2.95045e15 0.218018 0.109009 0.994041i \(-0.465232\pi\)
0.109009 + 0.994041i \(0.465232\pi\)
\(858\) −8.06904e15 −0.592436
\(859\) −1.13917e16 −0.831047 −0.415523 0.909583i \(-0.636402\pi\)
−0.415523 + 0.909583i \(0.636402\pi\)
\(860\) 9.56808e15 0.693559
\(861\) 5.06120e15 0.364533
\(862\) −1.89844e16 −1.35865
\(863\) 7.36154e15 0.523491 0.261746 0.965137i \(-0.415702\pi\)
0.261746 + 0.965137i \(0.415702\pi\)
\(864\) −3.37077e15 −0.238179
\(865\) −8.24244e14 −0.0578718
\(866\) 2.16489e16 1.51038
\(867\) 8.24937e15 0.571894
\(868\) 2.24307e16 1.54520
\(869\) 3.65694e14 0.0250328
\(870\) −4.28841e15 −0.291703
\(871\) 1.44963e16 0.979846
\(872\) 1.59662e16 1.07241
\(873\) −9.19697e15 −0.613856
\(874\) 3.74380e16 2.48313
\(875\) 1.66494e16 1.09737
\(876\) −6.50434e14 −0.0426021
\(877\) −5.53741e14 −0.0360420 −0.0180210 0.999838i \(-0.505737\pi\)
−0.0180210 + 0.999838i \(0.505737\pi\)
\(878\) −2.66998e16 −1.72699
\(879\) −2.01969e15 −0.129821
\(880\) −1.25650e15 −0.0802618
\(881\) 3.59656e15 0.228307 0.114154 0.993463i \(-0.463584\pi\)
0.114154 + 0.993463i \(0.463584\pi\)
\(882\) −7.85856e15 −0.495754
\(883\) −1.07013e16 −0.670890 −0.335445 0.942060i \(-0.608887\pi\)
−0.335445 + 0.942060i \(0.608887\pi\)
\(884\) 2.65876e15 0.165650
\(885\) 5.26781e14 0.0326168
\(886\) −2.78517e16 −1.71382
\(887\) −1.84287e15 −0.112698 −0.0563488 0.998411i \(-0.517946\pi\)
−0.0563488 + 0.998411i \(0.517946\pi\)
\(888\) 6.08595e15 0.369877
\(889\) 5.69631e15 0.344060
\(890\) −4.25682e15 −0.255529
\(891\) 1.04355e15 0.0622568
\(892\) 4.32948e16 2.56702
\(893\) 1.10530e16 0.651322
\(894\) 7.93284e14 0.0464593
\(895\) −1.20576e16 −0.701835
\(896\) −3.10817e16 −1.79809
\(897\) 9.58074e15 0.550859
\(898\) 3.18331e16 1.81911
\(899\) 9.91784e15 0.563299
\(900\) −6.99351e15 −0.394786
\(901\) 3.21990e15 0.180658
\(902\) −7.12707e15 −0.397443
\(903\) 1.59268e16 0.882767
\(904\) 1.57489e16 0.867611
\(905\) 8.67583e15 0.475055
\(906\) −4.87147e15 −0.265128
\(907\) −1.54577e16 −0.836188 −0.418094 0.908404i \(-0.637302\pi\)
−0.418094 + 0.908404i \(0.637302\pi\)
\(908\) 3.73981e16 2.01084
\(909\) 9.81366e15 0.524481
\(910\) −2.08819e16 −1.10928
\(911\) −1.52321e16 −0.804280 −0.402140 0.915578i \(-0.631734\pi\)
−0.402140 + 0.915578i \(0.631734\pi\)
\(912\) −7.03810e15 −0.369389
\(913\) −2.08603e16 −1.08826
\(914\) −2.36755e16 −1.22771
\(915\) 5.63388e15 0.290396
\(916\) −1.59468e16 −0.817047
\(917\) 2.15065e16 1.09531
\(918\) −5.79511e14 −0.0293378
\(919\) −5.82353e15 −0.293056 −0.146528 0.989207i \(-0.546810\pi\)
−0.146528 + 0.989207i \(0.546810\pi\)
\(920\) −5.10255e15 −0.255243
\(921\) −9.11757e15 −0.453368
\(922\) 2.13098e16 1.05332
\(923\) 2.75603e16 1.35418
\(924\) 1.34894e16 0.658868
\(925\) −1.48759e16 −0.722277
\(926\) 3.21500e16 1.55175
\(927\) −3.17763e15 −0.152463
\(928\) −1.92656e16 −0.918901
\(929\) 1.07919e16 0.511696 0.255848 0.966717i \(-0.417645\pi\)
0.255848 + 0.966717i \(0.417645\pi\)
\(930\) −6.32366e15 −0.298066
\(931\) −3.92297e16 −1.83819
\(932\) 1.64784e16 0.767586
\(933\) −1.34001e16 −0.620523
\(934\) −5.55441e16 −2.55699
\(935\) −5.16466e14 −0.0236362
\(936\) 6.16009e15 0.280266
\(937\) 9.99098e13 0.00451898 0.00225949 0.999997i \(-0.499281\pi\)
0.00225949 + 0.999997i \(0.499281\pi\)
\(938\) −4.08432e16 −1.83656
\(939\) −3.99227e15 −0.178467
\(940\) −4.78765e15 −0.212775
\(941\) −1.28886e15 −0.0569458 −0.0284729 0.999595i \(-0.509064\pi\)
−0.0284729 + 0.999595i \(0.509064\pi\)
\(942\) −2.33314e16 −1.02485
\(943\) 8.46230e15 0.369551
\(944\) 9.89853e14 0.0429759
\(945\) 2.70061e15 0.116570
\(946\) −2.24278e16 −0.962465
\(947\) 2.82850e16 1.20679 0.603395 0.797443i \(-0.293814\pi\)
0.603395 + 0.797443i \(0.293814\pi\)
\(948\) −8.87265e14 −0.0376364
\(949\) −1.40039e15 −0.0590590
\(950\) −5.88378e16 −2.46704
\(951\) −8.61256e15 −0.359037
\(952\) −2.35706e15 −0.0976940
\(953\) −3.20456e16 −1.32056 −0.660280 0.751020i \(-0.729562\pi\)
−0.660280 + 0.751020i \(0.729562\pi\)
\(954\) 2.37094e16 0.971415
\(955\) 6.75005e15 0.274972
\(956\) 1.16489e16 0.471810
\(957\) 5.96442e15 0.240189
\(958\) −2.56095e16 −1.02539
\(959\) −1.34854e16 −0.536860
\(960\) 1.01945e16 0.403528
\(961\) −1.07837e16 −0.424414
\(962\) 4.16434e16 1.62961
\(963\) 6.82962e15 0.265737
\(964\) −5.03967e15 −0.194975
\(965\) 1.72890e16 0.665072
\(966\) −2.69936e16 −1.03249
\(967\) 5.13314e16 1.95226 0.976129 0.217190i \(-0.0696892\pi\)
0.976129 + 0.217190i \(0.0696892\pi\)
\(968\) 1.30611e16 0.493929
\(969\) −2.89290e15 −0.108781
\(970\) 3.35158e16 1.25316
\(971\) 2.54272e16 0.945351 0.472676 0.881237i \(-0.343288\pi\)
0.472676 + 0.881237i \(0.343288\pi\)
\(972\) −2.53192e15 −0.0936021
\(973\) −1.58244e15 −0.0581711
\(974\) −7.24618e16 −2.64871
\(975\) −1.50571e16 −0.547289
\(976\) 1.05864e16 0.382626
\(977\) 1.00877e16 0.362552 0.181276 0.983432i \(-0.441977\pi\)
0.181276 + 0.983432i \(0.441977\pi\)
\(978\) 1.31773e16 0.470938
\(979\) 5.92048e15 0.210403
\(980\) 1.69926e16 0.600503
\(981\) −1.41290e16 −0.496514
\(982\) −1.87073e16 −0.653730
\(983\) −5.10173e16 −1.77285 −0.886427 0.462868i \(-0.846820\pi\)
−0.886427 + 0.462868i \(0.846820\pi\)
\(984\) 5.44098e15 0.188020
\(985\) −1.69439e16 −0.582257
\(986\) −3.31219e15 −0.113186
\(987\) −7.96942e15 −0.270821
\(988\) 9.77302e16 3.30267
\(989\) 2.66295e16 0.894919
\(990\) −3.80294e15 −0.127094
\(991\) −4.29328e16 −1.42687 −0.713435 0.700721i \(-0.752862\pi\)
−0.713435 + 0.700721i \(0.752862\pi\)
\(992\) −2.84089e16 −0.938945
\(993\) 2.01431e16 0.662071
\(994\) −7.76509e16 −2.53817
\(995\) −5.96381e15 −0.193864
\(996\) 5.06124e16 1.63618
\(997\) 2.03181e16 0.653221 0.326610 0.945159i \(-0.394093\pi\)
0.326610 + 0.945159i \(0.394093\pi\)
\(998\) −1.06039e16 −0.339037
\(999\) −5.38565e15 −0.171249
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.c.1.4 27
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.c.1.4 27 1.1 even 1 trivial