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lfunc_lfunctions • Show schema
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{'Lhash': '2566847502278525081182168315398', 'a10': -1, 'a2': -1, 'a3': 0, 'a4': 1, 'a5': 1, 'a6': 0, 'a7': 1, 'a8': -1, 'a9': -3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.148480955638592, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [5, [1, -1]], [7, [1, -1]], [11, [1, 1]]], 'bad_primes': [2, 5, 7, 11], 'central_character': '770.1', 'coefficient_field': '1.1.1.1', 'conductor': 770, 'conductor_radical': 770, 'degree': 2, 'euler_factors': [[1, 1], [1, 0, 3], [1, -1], [1, -1], [1, 1], [1, 6, 13], [1, 2, 17], [1, 4, 19], [1, 4, 23], [1, -6, 29], [1, 0, 31], [1, 2, 37], [1, 6, 41], [1, 4, 43], [1, -4, 47], [1, 2, 53], [1, -12, 59], [1, 2, 61], [1, 8, 67], [1, 8, 71], [1, 10, 73], [1, 8, 79], [1, 12, 83], [1, -10, 89], [1, 6, 97], [1, -14, 101], [1, 4, 103], [1, -4, 107], [1, -14, 109], [1, 6, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [[[1, 0, 3], 1]], [[[1, -1], 1]], [[[1, -1], 1]], [[[1, 1], 1]], [[[1, 6, 13], 1]], [[[1, 2, 17], 1]], [[[1, 4, 19], 1]], [[[1, 4, 23], 1]], [[[1, -6, 29], 1]], [[[1, 0, 31], 1]], [[[1, 2, 37], 1]], [[[1, 6, 41], 1]], [[[1, 4, 43], 1]], [[[1, -4, 47], 1]], [[[1, 2, 53], 1]], [[[1, -12, 59], 1]], [[[1, 2, 61], 1]], [[[1, 8, 67], 1]], [[[1, 8, 71], 1]], [[[1, 10, 73], 1]], [[[1, 8, 79], 1]], [[[1, 12, 83], 1]], [[[1, -10, 89], 1]], [[[1, 6, 97], 1]], [[[1, -14, 101], 1]], [[[1, 4, 103], 1]], [[[1, -4, 107], 1]], [[[1, -14, 109], 1]], [[[1, 6, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 18, 'label': '2-770-1.1-c1-0-18', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/770/2/a/d', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [-3.9903811241129694e-120, 0.2224070591418592, 0.4473745565389468, 0.6756706001282603, 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-0.6496174579654772, -2.2731220720637615, -2.9682573573833877, -2.6071055535455443, -1.422826147146408, 0.06887537466088123, 1.2466849832665168, 1.5987605719874336], 'positive_zeros': ['2.02488564421173045830172664748987', '2.84631505847919077884555890958499', '4.55174504902523336463882421352626', '5.51130120255433556946095894515617', '6.48198458599832188346302162345433', '7.41245154202477197034737063100515', '8.363523700282027049152069102286544', '8.916730340641706279929786137233334', '10.04063769026327802642478703475134'], 'prelabel': '2-770-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.4796130657097675, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 1026401358982709658, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.02488564421173045830172664749', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.84631505847919077884555890958', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.55174504902523336463882421353', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.148480955638592, 'bad_primes': [2, 5, 7, 11], 'central_character': '1.1', 'conductor': 770, 'conductor_radical': 770, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, 1, 0, 1, -1, -3, -1, -1, 0, -6, -1, 0, 1, -2, 3, -4, 1, 0, 1, -4, 0, 1, 6, 0, 1, 6, 0, 0, -1, 0, 2, 1, -3, -2, 4, 0, -1, -6, 0, -4, -1, -3, 4, 4, 0, 1, -1, 0, -6, -2, 0, -1, -1, 0, -6, 12, 0, -2, 0, -3, 1, -6, 0, -8, -2, 0, -1, -8, 3, -10, 2, 0, -4, -1, 0, -8, 1, 9, 6, -12, 0, -2, 4, 0, 1, 10, 3, -6, -4, 0, -4, -4, 0, -6, -1, 3, 1], 'euler11': [1, 1, 0], 'euler13': [1, 6, 13], 'euler17': [1, 2, 17], 'euler19': [1, 4, 19], 'euler2': [1, 1, 0], 'euler23': [1, 4, 23], 'euler29': [1, -6, 29], 'euler3': [1, 0, 3], 'euler31': [1, 0, 31], 'euler37': [1, 2, 37], 'euler41': [1, 6, 41], 'euler43': [1, 4, 43], 'euler47': [1, -4, 47], 'euler5': [1, -1, 0], 'euler53': [1, 2, 53], 'euler59': [1, -12, 59], 'euler61': [1, 2, 61], 'euler67': [1, 8, 67], 'euler7': [1, -1, 0], 'euler71': [1, 8, 71], 'euler73': [1, 10, 73], 'euler79': [1, 8, 79], 'euler83': [1, 12, 83], 'euler89': [1, -10, 89], 'euler97': [1, 6, 97], 'euler_factors': [[1, 1, 0], [1, 0, 3], [1, -1, 0], [1, -1, 0], [1, 1, 0], [1, 6, 13], [1, 2, 17], [1, 4, 19], [1, 4, 23], [1, -6, 29], [1, 0, 31], [1, 2, 37], [1, 6, 41], [1, 4, 43], [1, -4, 47], [1, 2, 53], [1, -12, 59], [1, 2, 61], [1, 8, 67], [1, 8, 71], [1, 10, 73], [1, 8, 79], [1, 12, 83], [1, -10, 89], [1, 6, 97]], 'index': 18, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/770/d', 'ModularForm/GL2/Q/holomorphic/770/2/a/d/1/1', 'ModularForm/GL2/Q/holomorphic/770/2/a/d'], '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': '2-770-1.1-c1-0-18', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-770-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.4796130657097675, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1026401358982709658, 'z1': {'__RealLiteral__': 0, 'data': '2.02488564421173045830172664749', 'prec': 103}}
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lfunc_instances • Show schema
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id: 14430757
{'Lhash': '2566847502278525081182168315398', 'Lhash_array': ['2566847502278525081182168315398'], 'label': '2-770-1.1-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/770/2/a/d'}
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id: 24550480
{'Lhash': '2566847502278525081182168315398', 'Lhash_array': ['2566847502278525081182168315398'], 'label': '2-770-1.1-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/770/2/a/d/1/1'}
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id: 22487
{'Lhash': '1026401358982709658', 'Lhash_array': ['1026401358982709658'], 'label': '2-770-1.1-c1-0-18', 'type': 'ECQ', 'url': 'EllipticCurve/Q/770/d'}