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  • lfunc_lfunctions • Show schema
    {'Lhash': '420977453714537972003086412917', 'a10': [0, 0], 'a2': [91.78235124467012, 0], 'a3': [275.3470537340104, 675.0], 'a4': [4328.0, 0], 'a5': [0, 0], 'a6': [25272.0, 61953.08709015234], 'a7': [0, 40250.0], 'a8': [21293.50548876347, 0], 'a9': [-379809.0, 371718.522540914], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 68.54953629572142, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '6.0', 'prec': 7}, 'bad_lfactors': [[3, [[1.0, 0], [-275.3470537340104, -675.0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '75.74', 'coefficient_field': 'CDF', 'conductor': 75, 'conductor_radical': 15, 'conjugate': '2765092458335228845582002031873', 'degree': 2, 'euler_factors': [[[1.0, 0], [-91.78235124467012, 0], [4096.0, 0]], [[1.0, 0], [-275.3470537340104, -675.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -40250.0], [-13841287201.0, 0]], [[1.0, 0], [0, -1161046.743245077], [-3138428376721.0, 0]], [[1.0, 0], [0, 1284050.0], [-23298085122481.0, 0]], 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'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4878515427477633', 'prec': 54}, 'spectral_label': 'c12-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.33209265521488702333430184545', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '1.93003837311573836504831850566', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.13385180473722374498553261487', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 68.54953629572142, 'bad_primes': [3, 5], 'central_character': '15.14', 'conductor': 75, 'conductor_radical': 15, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/75/13/d/b/74/4'], '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': '2-75-15.14-c12-0-16', 'motivic_weight': 12, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [12], 'order_of_vanishing': 0, 'prelabel': '2-75-15.14-c12-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.279464734855836, 'root_angle': -0.4878515427477633, 'self_dual': False, 'spectral_label': 'c12-0', 'z1': {'__RealLiteral__': 0, 'data': '0.33209265521488702333430184545', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '420977453714537972003086412917', 'Lhash_array': ['420977453714537972003086412917'], 'factors': ['2-75-15.14-c12-0-16'], 'label': '2-75-15.14-c12-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/75/13/d/b/74/4'}