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lfunc_lfunctions • Show schema
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{'Lhash': '108684333963382050611532688420', 'a10': [-2231.157775647308, 1872.1636666439765], 'a2': [6.128355544951824, 5.142300877492315], 'a3': [-67.03260524422805, 24.397873034215547], 'a4': [11.113483370683543, 63.02769619278131], 'a5': [-63.22030094153138, 358.54014336046725], 'a6': [-536.2608419538244, -195.18298427372437], 'a7': [-158.49091506491575, -274.5143174305177], 'a8': [-256.0, 443.40500673763256], 'a9': [2222.7747601336023, -1865.129481418273], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.870630968396632, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-6.128355544951824, -5.142300877492315]]], [19, [[1.0, 0], [-29798.79384064685, -2429.737566616465]]]], 'bad_primes': [2, 19], 'central_character': '38.35', 'coefficient_field': 'CDF', 'conductor': 38, 'conductor_radical': 38, 'conjugate': '4278564091202046801764966460934', 'degree': 2, 'euler_factors': [[[1.0, 0], [-6.128355544951824, 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0.9711622527570313*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.288314664756', 'prec': 47}, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.085736822073696322175387795826', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.57078154209341050579205143055', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.48462210898595668282420511186', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.870630968396632, 'bad_primes': [2, 19], 'central_character': '19.16', 'conductor': 38, 'conductor_radical': 38, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/38/8/e/a/35/1'], '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': '2-38-19.16-c7-0-1', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-38-19.16-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.445378203970739, 'root_angle': 0.28831466475626927, 'self_dual': False, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '0.085736822073696322175387795826', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '108684333963382050611532688420', 'Lhash_array': ['108684333963382050611532688420'], 'label': '2-38-19.16-c7-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/38/8/e/a/35/1'}