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lfunc_lfunctions • Show schema
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{'Lhash': '2091593313199389544120943295730', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.766044443118978, -0.6427876096865394], 'a4': [0.0, 0.0], 'a5': [3.3635072140483695, 1.2242165086532466], 'a6': [0.0, 0.0], 'a7': [4.080125636136762, 1.485044283620235], 'a8': [0.0, 0.0], 'a9': [0.17364817766693036, -0.984807753012208], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.090715699489701, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.766044443118978, 0.6427876096865394]]], [37, [[1.0, 0], [-3.509305993488355, 4.968377143903903]]]], 'bad_primes': [2, 3, 37], 'central_character': '888.145', 'coefficient_field': 'CDF', 'conductor': 888, 'conductor_radical': 222, 'conjugate': '2165771450367554912516490983168', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.766044443118978, 0.6427876096865394]], [[1.0, 0], [-3.3635072140483695, -1.2242165086532466], [3.83022221559489, 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-1.5760284266790359, -2.5164189589617068, -2.642939313172266], 'positive_zeros': ['1.64997619440468569556008087976620', '2.14285725948800810259605667391743', '4.05798240972212201837405581344511', '4.76801667603002046220291708659575', '5.56739449707929748598915382641786', '6.69907168652311225383193144220619', '7.73384213754903057790472508587267', '8.593446971202131491745348468635557', '9.395834692861006950477485445127072', '9.889835476417950775433645120196541'], 'prelabel': '2-888-37.34-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6628397810401023, 'root_angle': 0.008064382748561714, 'root_number': '0.9996790859114367 + 0.02533229542055546*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.00403219137428', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.64997619440468569556008087977', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.14285725948800810259605667392', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.05798240972212201837405581345', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.090715699489701, 'bad_primes': [2, 3, 37], 'central_character': '37.34', 'conductor': 888, 'conductor_radical': 222, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/888/2/bo/c/145/3'], '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': '2-888-37.34-c1-0-16', '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': '2-888-37.34-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6628397810401023, 'root_angle': 0.004032191374280857, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.64997619440468569556008087977', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2091593313199389544120943295730', 'Lhash_array': ['2091593313199389544120943295730'], 'label': '2-888-37.34-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/888/2/bo/c/145/3'}