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lfunc_lfunctions • Show schema
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{'Lhash': '4169786813084868404902050171422', 'a10': [-7.0, 12.12435565298214], 'a2': [1.0, -1.7320508075688772], 'a3': [0.0, 0.0], 'a4': [-2.0, -3.4641016151377544], 'a5': [-7.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, -8.660254037844387], 'a8': [-8.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.9427868550912066, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 1.7320508075688772]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '108.55', 'coefficient_field': 'CDF', 'conductor': 108, 'conductor_radical': 6, 'conjugate': '1016409836482466707075218299255', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [7.0, 0], [25.0, 0]], [[1.0, 0], [0, 8.660254037844387], [-49.0, 0]], [[1.0, 0], [0, 8.660254037844387], [-121.0, 0]], [[1.0, 0], [-20.0, 0], [169.0, 0]], [[1.0, 0], [-8.0, 0], [289.0, 0]], [[1.0, 0], [0, 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'12.70382142159322865412156595752895', '14.11159480552858193627565991504917'], 'prelabel': '2-108-4.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.715455290904198, 'root_angle': 0.8333333333333334, 'root_number': '-0.8660254037844387 + 0.49999999999999994*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.416666666667', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.28938179994876724343884246102', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.58790222975333020474746093491', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.94959904048751100675937442017', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.9427868550912066, 'bad_primes': [2, 3], 'central_character': '4.3', 'conductor': 108, 'conductor_radical': 6, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/108/3/d/b/55/1'], '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': '2-108-4.3-c2-0-15', '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': '2-108-4.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.715455290904198, 'root_angle': 0.4166666666666667, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '3.28938179994876724343884246102', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4169786813084868404902050171422', 'Lhash_array': ['4169786813084868404902050171422'], 'label': '2-108-4.3-c2-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/108/3/d/b/55/1'}