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lfunc_lfunctions • Show schema
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{'Lhash': '1983852498603655348630589792956', 'a10': [0, 0], 'a2': [-1.0, 0], 'a3': [1.618033988749895, -0.6180339887498949], 'a4': [1.0, 0], 'a5': [0, 0], 'a6': [-1.618033988749895, 0.6180339887498949], 'a7': [-2.618033988749895, 0.38196601125010515], 'a8': [-1.0, 0], 'a9': [2.23606797749979, -2.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.384292212234444, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [3, [[1.0, 0], [-1.618033988749895, 0.6180339887498949]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [2.618033988749895, -0.38196601125010515]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1050.1049', 'coefficient_field': 'CDF', 'conductor': 1050, 'conductor_radical': 210, 'conjugate': '871969735357427595348112316830', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.618033988749895, 0.6180339887498949]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.618033988749895, 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0.19743299105114617], 'positive_zeros': ['1.56498367787344561701578016593654', '2.76375530068146975103706504166037', '3.68637642880711241865340992746585', '4.70978642584108604608231674039639', '6.11830750166606748965352006976074', '7.05472481595408918973595704434012', '7.65158186309498253443356264646711', '8.707589042795951768865823187840701', '9.243340424942700415282910325047717', '10.02649089078198391010181842825077'], 'prelabel': '2-1050-105.104-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8955642303762565, 'root_angle': 0.4853284384982143, 'root_number': '0.0460757512925714907904411163351988278752803344177179744 + 0.9989379485948189247496051944076996035314528018236049805*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.24266421924910717', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.56498367787344561701578016594', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.76375530068146975103706504166', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.68637642880711241865340992747', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.384292212234444, 'bad_primes': [2, 3, 5, 7], 'central_character': '105.104', 'conductor': 1050, 'conductor_radical': 210, 'degree': 2, 'index': 35, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1050/2/d/c/1049/3'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '2-1050-105.104-c1-0-35', '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': '2-1050-105.104-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8955642303762565, 'root_angle': 0.24266421924910714, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.56498367787344561701578016594', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1983852498603655348630589792956', 'Lhash_array': ['1983852498603655348630589792956'], 'label': '2-1050-105.104-c1-0-35', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1050/2/d/c/1049/3'}