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lfunc_lfunctions • Show schema
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{'Lhash': '701040340596206656078064623042', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, -2.23606797749979], 'a6': [0, 0], 'a7': [0, 11.898925852298472], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 112.80682944516293, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 2.23606797749979]]], [23, [[1.0, 0], [22.894821384034916, 2.1970784676787307]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '4140.2161', 'coefficient_field': 'CDF', 'conductor': 4140, 'conductor_radical': 690, 'conjugate': '1342819076935643142235433778360', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 2.23606797749979]], [[1.0, 0], [0, -11.898925852298472], [-49.0, 0]], [[1.0, 0], [0, 2.1585328608508587], [-121.0, 0]], [[1.0, 0], [-21.955112481329746, 0], [169.0, 0]], [[1.0, 0], [0, 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'1.30227846394927643533332727303148', '2.63046480818693384431336124447740', '3.59410318357083733963267698067471', '4.14743038095556434504021417065324', '4.92396095075860564339346948684758', '6.18950856847950701078185257470471', '6.51988452317429959129628225195875', '7.43590292704238353631499840977303', '7.88591895783334628667809078830373'], 'prelabel': '2-4140-23.22-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.621055947746576, 'root_angle': -0.46954696555772313, 'root_number': '0.0955251507686404629006613490126999076780728047629019456 - 0.9954270166971702744572863924951620902570786660132435576*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.23477348277886156', 'prec': 67}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.55302331767917001362238655203', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.30227846394927643533332727303', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.63046480818693384431336124448', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 112.80682944516293, 'bad_primes': [2, 3, 5, 23], 'central_character': '23.22', 'conductor': 4140, 'conductor_radical': 690, 'degree': 2, 'index': 33, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4140/3/d/c/2161/16'], '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': '2-4140-23.22-c2-0-33', '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': '2-4140-23.22-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.621055947746576, 'root_angle': -0.23477348277886156, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.55302331767917001362238655203', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '701040340596206656078064623042', 'Lhash_array': ['701040340596206656078064623042'], 'label': '2-4140-23.22-c2-0-33', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4140/3/d/c/2161/16'}