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lfunc_lfunctions • Show schema
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{'Lhash': '1919984529518533798228926507951', 'a10': [0.0, 0.0], 'a2': [-1.0850432433130168, 1.8793500258274647], 'a3': [-1.4759390608579575, 2.5564014422814756], 'a4': [-1.3546376797184614, -2.346301287119591], 'a5': [0.0, 0.0], 'a6': [-3.2029154110513725, -5.547612224286333], 'a7': [0.5916198371231286, 0.0], 'a8': [1.5391888728108891, 0.0], 'a9': [-2.8567922227325386, -4.948109276440381], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.79289409601082, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [2.2642273254147884, -3.724684499235471]]]], 'bad_primes': [5, 19], 'central_character': '475.201', 'coefficient_field': 'CDF', 'conductor': 475, 'conductor_radical': 95, 'conjugate': '264094457301129265447205347611', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0850432433130168, -1.8793500258274647], [-1.0, -1.7320508075688772]], [[1.0, 0], [1.4759390608579575, -2.5564014422814756], [-1.5, 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'10.33780934533785417938834378678997', '11.35071469558657578430102098174809'], 'prelabel': '2-475-19.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': -0.06055704469474454, 'root_number': '0.9819578280463989 - 0.18910003685456792*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0302785223474', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.51460073396632903357543777364', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.05755558609525390689132929757', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.82899261827583705117741769017', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.79289409601082, 'bad_primes': [5, 19], 'central_character': '19.11', 'conductor': 475, 'conductor_radical': 95, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/475/2/e/f/201/1'], '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': '2-475-19.11-c1-0-14', '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': '2-475-19.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': -0.03027852234737227, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.51460073396632903357543777364', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1919984529518533798228926507951', 'Lhash_array': ['1919984529518533798228926507951'], 'label': '2-475-19.11-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/475/2/e/f/201/1'}