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lfunc_lfunctions • Show schema
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{'Lhash': '1455752411477471590793905610407', 'a10': 1, 'a2': 1, 'a3': -1, 'a4': 1, 'a5': 1, 'a6': -1, 'a7': 0, 'a8': 1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.738009097128222, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, 1]], [5, [1, -1]], [7, [1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1470.1', 'coefficient_field': '1.1.1.1', 'conductor': 1470, 'conductor_radical': 210, 'degree': 2, 'euler_factors': [[1, -1], [1, 1], [1, -1], [1], [1, -2, 11], [1, -2, 13], [1, 4, 17], [1, 0, 19], [1, -8, 23], [1, 0, 29], [1, 2, 31], [1, -8, 37], [1, 2, 41], [1, 2, 43], [1, -10, 47], [1, 2, 53], [1, -4, 59], [1, 10, 61], [1, -2, 67], [1, 12, 71], [1, -10, 73], [1, -16, 79], [1, -16, 83], [1, -14, 89], [1, -6, 97], [1, 14, 101], [1, 20, 103], [1, -12, 107], [1, 2, 109], [1, 14, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [[[1, 1], 1]], [[[1, -1], 1]], [1], [[[1, -2, 11], 1]], [[[1, -2, 13], 1]], [[[1, 4, 17], 1]], [[[1, 0, 19], 1]], [[[1, -8, 23], 1]], [[[1, 0, 29], 1]], [[[1, 2, 31], 1]], [[[1, -8, 37], 1]], [[[1, 2, 41], 1]], [[[1, 2, 43], 1]], [[[1, -10, 47], 1]], [[[1, 2, 53], 1]], [[[1, -4, 59], 1]], [[[1, 10, 61], 1]], [[[1, -2, 67], 1]], [[[1, 12, 71], 1]], [[[1, -10, 73], 1]], [[[1, -16, 79], 1]], [[[1, -16, 83], 1]], [[[1, -14, 89], 1]], [[[1, -6, 97], 1]], [[[1, 14, 101], 1]], [[[1, 20, 103], 1]], [[[1, -12, 107], 1]], [[[1, 2, 109], 1]], [[[1, 14, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 12, 'label': '2-1470-1.1-c1-0-12', 'leading_term': '2.55106762495902552340386131835000000000000000000000000000000000000000000000000000000000000', 'load_key': 'CMFs-workshop', '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': 'ModularForm/GL2/Q/holomorphic/1470/2/a/n', 'plot_delta': {'__RealLiteral__': 0, 'data': 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3.2783762983174847, 3.1877689539416822, 2.9776164338115647, 2.6598111482335125, 2.2536962658004636, 1.7848619119861842, 1.2834818452391121, 0.7822991479098275, 0.31439624544988093, -0.08909769906671106, -0.40120171443051406, -0.601023925669959, -0.675307186311453, -0.6194635963375343], 'positive_zeros': ['1.14838616509578909491858361321240', '2.41846334213277678783501330002921', '3.61784426087409943129297947528777', '4.56361178578709645761945260895956', '5.32234060729049876880170623804234', '6.26866033555376129285213632855333', '6.71448030263619857726292129732264', '7.67452669104186096573712814721768', '8.893883320761320325127642296502445', '9.438318904212609891056159882541197'], 'prelabel': '2-1470-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.4260778007990744, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 1389457362715127255, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.14838616509578909491858361321', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.41846334213277678783501330003', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.61784426087409943129297947529', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.738009097128222, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 1470, 'conductor_radical': 210, 'degree': 2, 'dirichlet_coefficients': [1, 1, -1, 1, 1, -1, 0, 1, 1, 1, 2, -1, 2, 0, -1, 1, -4, 1, 0, 1, 0, 2, 8, -1, 1, 2, -1, 0, 0, -1, -2, 1, -2, -4, 0, 1, 8, 0, -2, 1, -2, 0, -2, 2, 1, 8, 10, -1, 0, 1, 4, 2, -2, -1, 2, 0, 0, 0, 4, -1, -10, -2, 0, 1, 2, -2, 2, -4, -8, 0, -12, 1, 10, 8, -1, 0, 0, -2, 16, 1, 1, -2, 16, 0, -4, -2, 0, 2, 14, 1, 0, 8, 2, 10, 0, -1, 6, 0, 2, 1], 'euler11': [1, -2, 11], 'euler13': [1, -2, 13], 'euler17': [1, 4, 17], 'euler19': [1, 0, 19], 'euler2': [1, -1, 0], 'euler23': [1, -8, 23], 'euler29': [1, 0, 29], 'euler3': [1, 1, 0], 'euler31': [1, 2, 31], 'euler37': [1, -8, 37], 'euler41': [1, 2, 41], 'euler43': [1, 2, 43], 'euler47': [1, -10, 47], 'euler5': [1, -1, 0], 'euler53': [1, 2, 53], 'euler59': [1, -4, 59], 'euler61': [1, 10, 61], 'euler67': [1, -2, 67], 'euler7': [1, 0, 0], 'euler71': [1, 12, 71], 'euler73': [1, -10, 73], 'euler79': [1, -16, 79], 'euler83': [1, -16, 83], 'euler89': [1, -14, 89], 'euler97': [1, -6, 97], 'euler_factors': [[1, -1, 0], [1, 1, 0], [1, -1, 0], [1, 0, 0], [1, -2, 11], [1, -2, 13], [1, 4, 17], [1, 0, 19], [1, -8, 23], [1, 0, 29], [1, 2, 31], [1, -8, 37], [1, 2, 41], [1, 2, 43], [1, -10, 47], [1, 2, 53], [1, -4, 59], [1, 10, 61], [1, -2, 67], [1, 12, 71], [1, -10, 73], [1, -16, 79], [1, -16, 83], [1, -14, 89], [1, -6, 97]], 'index': 12, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1470/n', 'ModularForm/GL2/Q/holomorphic/1470/2/a/n/1/1', 'ModularForm/GL2/Q/holomorphic/1470/2/a/n'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, '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': '2-1470-1.1-c1-0-12', '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': '2-1470-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.4260778007990744, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1389457362715127255, 'z1': {'__RealLiteral__': 0, 'data': '1.14838616509578909491858361321', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20573776
{'Lhash': '1455752411477471590793905610407', 'Lhash_array': ['1455752411477471590793905610407'], 'label': '2-1470-1.1-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1470/2/a/n'}
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id: 24553260
{'Lhash': '1455752411477471590793905610407', 'Lhash_array': ['1455752411477471590793905610407'], 'label': '2-1470-1.1-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1470/2/a/n/1/1'}
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id: 96317
{'Lhash': '1389457362715127255', 'Lhash_array': ['1389457362715127255'], 'label': '2-1470-1.1-c1-0-12', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1470/n'}