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lfunc_lfunctions • Show schema
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{'Lhash': '771483873829637228849503921028', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, -0.8989794855663562], 'a6': [0, 0], 'a7': [0, -2.8284271247461903], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 31.389726454306206, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1152.703', 'coefficient_field': 'CDF', 'conductor': 1152, 'conductor_radical': 6, 'conjugate': '1368457062177136508999135198706', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0.8989794855663562], [-25.0, 0]], [[1.0, 0], [0, 2.8284271247461903], [-49.0, 0]], [[1.0, 0], [-4.3855052687092515, 0], [121.0, 0]], [[1.0, 0], [0, -13.797958971132712], [-169.0, 0]], [[1.0, 0], [17.595917942265423, 0], [289.0, 0]], [[1.0, 0], [-4.3855052687092515, 0], [361.0, 0]], [[1.0, 0], [0, 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'3.14547347215066988069520483739824', '4.28762488847794343008658520324176', '5.26550406282137635494512324295005', '6.15534029376808959964269055066164', '6.97978921706370354005670495175082', '7.87952322668835523352987544285903', '8.806038160377762976010464929017621', '9.327361288408794287107706511247280'], 'prelabel': '2-1152-8.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.602653519030621, 'root_angle': -0.25, 'root_number': '0.7071067811865475244008443621048490392848359376884740366 - 0.7071067811865475244008443621048490392848359376884740366*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.125', 'prec': 20}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.60859346707266048397303410690', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.18569705934990931900120175901', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.14547347215066988069520483740', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 31.389726454306206, 'bad_primes': [2, 3], 'central_character': '8.3', 'conductor': 1152, 'conductor_radical': 6, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1152/3/b/j/703/3'], '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': '2-1152-8.3-c2-0-11', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-1152-8.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.602653519030621, 'root_angle': -0.125, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.60859346707266048397303410690', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '771483873829637228849503921028', 'Lhash_array': ['771483873829637228849503921028'], 'label': '2-1152-8.3-c2-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1152/3/b/j/703/3'}