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lfunc_lfunctions • Show schema
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{'Lhash': '1479028574365949639498362541296', 'a10': [358.371538897227, -620.7177133566435], 'a2': [-5.311167082636945, -9.199211234614557], 'a3': [0.0, 0.0], 'a4': [-40.416991559372455, 70.00428286991557], 'a5': [33.73755083593595, 58.435152170778906], 'a6': [0.0, 0.0], 'a7': [-120.28111573289479, -48.36789429001399], 'a8': [518.7308873086524, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.104180648217781, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [120.28111573289479, 48.36789429001399]]]], 'bad_primes': [3, 7], 'central_character': '63.46', 'coefficient_field': 'CDF', 'conductor': 63, 'conductor_radical': 21, 'conjugate': '986589294453564403159934553423', 'degree': 2, 'euler_factors': [[[1.0, 0], [5.311167082636945, 9.199211234614557], [-16.0, 27.712812921102035]], [[1.0, 0], [0, 0]], [[1.0, 0], [-33.73755083593595, -58.435152170778906], [-1562.5, 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'7.05379802971351711302089765124662', '8.545271457428020632198469267392893', '9.368453490530290319742816124793873', '10.07286699652073792609285388436283', '12.39980819437300246411606326622305', '13.50728749473909027221021674899572', '14.69224272701816078196723551041256'], 'prelabel': '2-63-7.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.178707386378586, 'root_angle': 0.6418742375333728, 'root_number': '-0.43109958390255826 + 0.9023043548376796*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.320937118767', 'prec': 47}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.16674782002206560927525559365', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.82456766904081632903964068600', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.00796439260602000888974011442', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.104180648217781, 'bad_primes': [3, 7], 'central_character': '7.4', 'conductor': 63, 'conductor_radical': 21, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/63/6/e/f/46/1'], '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': '2-63-7.4-c5-0-6', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-63-7.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.178707386378586, 'root_angle': 0.3209371187666864, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.16674782002206560927525559365', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1479028574365949639498362541296', 'Lhash_array': ['1479028574365949639498362541296'], 'label': '2-63-7.4-c5-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/63/6/e/f/46/1'}