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  • lfunc_lfunctions • Show schema
    {'Lhash': '1165434251067075451528011107354', 'a10': [0, 0], 'a2': [-1.0, 0], 'a3': [0, 0], 'a4': [1.0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [2.5, 0.8660254037844386], 'a8': [-1.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.0550355892132, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-2.5, -0.8660254037844386]]]], 'bad_primes': [2, 3, 7], 'central_character': '1134.865', 'coefficient_field': 'CDF', 'conductor': 1134, 'conductor_radical': 42, 'conjugate': '1503069632855881928799914338960', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-2.5, -4.330127018922194]], [[1.0, 0], [-2.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-5.5, 9.526279441628825]], [[1.0, 0], [-2.0, -3.4641016151377544], [-6.5, 11.258330249197702]], [[1.0, 0], [-3.0, 5.196152422706632], [-8.5, -14.722431864335457]], [[1.0, 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3.466752161427568], 'positive_zeros': ['0.919365518272345084312670568733990', '2.09709791278411172227671144391248', '3.46058886128328040526502467194702', '4.51186295546731558450092998557453', '5.69775137207133593565392116213537', '6.40811020488025342340455604687088', '7.60498116260930810576729796684129', '8.218229652425791815592869543153733', '8.629019942972356023061823142025145', '10.00762452544365622256816864013081'], 'prelabel': '2-1134-63.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.00915861815445, 'root_angle': -0.07572850860950169, 'root_number': '0.88891912170059988624064212768942347417496444384190817029 - 0.4580641822660161762428872949230161411327298952261922774*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.07572850860950167', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.919365518272345084312670568734', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': 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  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 9.0550355892132, 'bad_primes': [2, 3, 7], 'central_character': '63.25', 'conductor': 1134, 'conductor_radical': 42, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1134/2/e/d/865/1'], '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': '2-1134-63.25-c1-0-12', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1134-63.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.00915861815445, 'root_angle': -0.07572850860950169, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.919365518272345084312670568734', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1165434251067075451528011107354', 'Lhash_array': ['1165434251067075451528011107354'], 'factors': ['2-1134-63.25-c1-0-12'], 'label': '2-1134-63.25-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1134/2/e/d/865/1'}