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lfunc_lfunctions • Show schema
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{'Lhash': '1241778293871498103269043609663', 'a10': [-1.309241641185733, 0.0], 'a2': [1.309241641185733, 0.0], 'a3': [0.0, 0.0], 'a4': [-0.28588632498528826, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [4.281406965138927, 0.0], 'a8': [-2.992777563687763, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 31.98008600952281, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [89, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 5, 89], 'central_character': '4005.1', 'coefficient_field': 'CDF', 'conductor': 4005, 'conductor_radical': 1335, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.309241641185733, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-4.281406965138927, 0], [7.0, 0]], [[1.0, 0], [-3.7131377982798486, 0], [11.0, 0]], [[1.0, 0], [-1.1796476394149429, 0], [13.0, 0]], [[1.0, 0], [-7.722819669058767, 0], [17.0, 0]], [[1.0, 0], 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'3.81312536916455116433556153442933', '4.69162687385132939659527700463458', '5.34181033310566599589943505617130', '5.91016465669130389290811062187569', '6.96586473095799599033089812190276', '7.77456192782299785586631076575395', '8.360298009019187963673175581681608'], 'prelabel': '2-4005-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.655093810850781, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.979590348987273610100237029596', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.98426297850536132153276409565', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.46243032117449528132042646479', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 31.98008600952281, 'bad_primes': [3, 5, 89], 'central_character': '1.1', 'conductor': 4005, 'conductor_radical': 1335, 'degree': 2, 'index': 61, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4005/2/a/w/1/13'], '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': '2-4005-1.1-c1-0-61', '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': '2-4005-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.655093810850781, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.979590348987273610100237029596', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1241778293871498103269043609663', 'Lhash_array': ['1241778293871498103269043609663'], 'label': '2-4005-1.1-c1-0-61', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4005/2/a/w/1/13'}