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lfunc_lfunctions • Show schema
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{'A10': 1, 'A2': 1, 'A3': 0, 'A4': 1, 'A5': 1, 'A6': 0, 'A7': 1, 'A8': 1, 'A9': 0, 'Lhash': '720066382109127109', 'a10': [0.31622776601683794, 0], 'a2': [0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 608.6996146082207, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1]], [5, [1, -1]], [7, [1, -1]], [11, [1]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '76230.1', 'coefficient_field': '1.1.1.1', 'conductor': 76230, 'conductor_radical': 2310, 'degree': 2, 'euler_factors': [[1, -1], [1], [1, -1], [1, -1], [1], [1, -6, 13], [1, -2, 17], [1, 0, 19], [1, 0, 23], [1, -6, 29], [1, -8, 31], [1, 10, 37], [1, -2, 41], [1, 4, 43], [1, 8, 47], [1, -2, 53], [1, -8, 59], [1, -14, 61], [1, 12, 67], [1, -16, 71], [1, 2, 73], [1, -8, 79], [1, -8, 83], [1, 10, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 67, 'label': '2-76230-1.1-c1-0-67', 'leading_term': '6.57486764682', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'EllipticCurve/Q/76230/fg', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [6.574867646818544, 5.676737201634539, 3.296493670292872, 0.5005457285076167, -1.140247719176071, -0.7090947560912056, 0.9607596505040031, 1.795904802324427, 0.5898396167881664, -1.481029635859421, -2.02832061071877, -0.3364369830438143, 1.589589093970626, 1.515448325970644, -0.01863610548913114, -0.417184080731926, 1.210706779594712, 2.605758853873365, 1.648559111785963, -0.3477163323866199, -0.5680822940756401, 0.8814646969370245, 1.147612419462527, -0.6008035958569806, -1.679444508905225, -0.5466891059477441, 0.2545656110541011, -1.387444467084663, 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2.469703180649354, -0.3868144452855684, -5.689101434531528, -4.67560958361766, -0.4344765314426892, 0.2568539317473495, -0.3771509687724411, 0.3402928441292267, -0.9114210764842432, -3.370862871081448, -1.873720414986722, 1.268761724389658, 0.4089905795621452, -1.538857425113166, -0.3964138502736253, 0.01197682177856186, -2.084747413780088, -1.690978868505549, 0.5696015155049373, -0.9189277278946868, -3.281386893108852, -1.086373843766309, 1.155894586320422, -0.371147037701592, -0.0189024433672307, 2.735879581537846, 0.8811046123561694, -2.352050575798319, 0.9452008486821293, 3.513072635407096, -3.285319506065214, -8.879989210362517, -3.660725179992408, 1.87145615375147, -0.1058420782865134, -1.040113051616635, 1.562461497539902, -0.3109424432070263, -4.119061254916469, -1.859939907801317, 1.516255854574708, -0.1749595230524444, -1.401483923099641], 'positive_zeros': ['0.8036202257214043', '1.361932488100788', '2.069269226195511', '2.786589236652486', '3.496659158261299', '3.839649662895920', '4.697271204490248', '5.107386404610967', '5.676126902324592', '6.345489685802262', '6.572176443941464', '7.230192147009678', '8.061616007653127', '8.434278492704306', '8.771597812518727', '9.684059455402721', '10.12973207419958', '10.59970792590299', '11.09280755562849', '11.71960594585965', '11.95622925770598', '12.67527237540845', '13.14689114316789', '13.63667973080404', '13.97043358906687', '14.36023579061293', '14.98353315746152', '15.54749999177641', '15.84830312287004', '16.36441488875364', '16.83902383075355', '17.46935764156432', '17.91054847686783', '18.19066521947154', '18.93197040100453', '19.30253665188939', '19.73327454177911'], 'prelabel': '2-76230-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 24.671838492666506, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 720066382109127109, 'z1': {'__RealLiteral__': 0, 'data': '0.8036202257214043', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.361932488100788', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.069269226195511', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 608.6996146082207, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 76230, 'conductor_radical': 2310, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 6, 1, 0, 1, 2, 0, 0, 1, 0, 0, 0, 0, 1, 6, 0, 1, 6, 0, 8, 1, 0, 2, 1, 0, -10, 0, 0, 1, 2, 0, -4, 0, 0, 0, -8, 0, 1, 1, 0, 6, 2, 0, 0, 1, 0, 6, 8, 0, 14, 8, 0, 1, 6, 0, -12, 2, 0, 1, 16, 0, -2, -10, 0, 0, 0, 0, 8, 1, 0, 2, 8, 0, 2, -4, 0, 0, -10, 0, 6, 0, 0, -8, 0, 0, 2, 1, 0, 1], 'euler11': [1, 0, 0], 'euler13': [1, -6, 13], 'euler17': [1, -2, 17], 'euler19': [1, 0, 19], 'euler2': [1, -1, 0], 'euler23': [1, 0, 23], 'euler29': [1, -6, 29], 'euler3': [1, 0, 0], 'euler31': [1, -8, 31], 'euler37': [1, 10, 37], 'euler41': [1, -2, 41], 'euler43': [1, 4, 43], 'euler47': [1, 8, 47], 'euler5': [1, -1, 0], 'euler53': [1, -2, 53], 'euler59': [1, -8, 59], 'euler61': [1, -14, 61], 'euler67': [1, 12, 67], 'euler7': [1, -1, 0], 'euler71': [1, -16, 71], 'euler73': [1, 2, 73], 'euler79': [1, -8, 79], 'euler83': [1, -8, 83], 'euler89': [1, 10, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, -1, 0], [1, 0, 0], [1, -1, 0], [1, -1, 0], [1, 0, 0], [1, -6, 13], [1, -2, 17], [1, 0, 19], [1, 0, 23], [1, -6, 29], [1, -8, 31], [1, 10, 37], [1, -2, 41], [1, 4, 43], [1, 8, 47], [1, -2, 53], [1, -8, 59], [1, -14, 61], [1, 12, 67], [1, -16, 71], [1, 2, 73], [1, -8, 79], [1, -8, 83], [1, 10, 89], [1, -2, 97]], 'index': 67, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/76230/fg'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-76230-1.1-c1-0-67', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-76230-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 24.671838492666506, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 720066382109127109, 'z1': {'__RealLiteral__': 0, 'data': '0.8036202257214043', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '720066382109127109', 'Lhash_array': ['720066382109127109'], 'label': '2-76230-1.1-c1-0-67', 'type': 'ECQ', 'url': 'EllipticCurve/Q/76230/fg'}