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lfunc_lfunctions • Show schema
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{'Lhash': '1732354695016924180390989191567', 'a10': [0, 0], 'a2': [10.022547445857395, -10.022547445857395], 'a3': [-112.0576111270724, -84.41618202983253], 'a4': [0, 311.0970853910748], 'a5': [0, 0], 'a6': [-1969.1679137826518, 277.0375345983898], 'a7': [-2707.778371115476, -2707.778371115476], 'a8': [8249.529590878983, 8249.529590878983], 'a9': [5430.81642301236, 18918.95139746226], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 38.627687712290495, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [112.0576111270724, 84.41618202983253]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '75.32', 'coefficient_field': 'CDF', 'conductor': 75, 'conductor_radical': 15, 'conjugate': '306278708778807056990330190049', 'degree': 2, 'euler_factors': [[[1.0, 0], [-10.022547445857395, 10.022547445857395], [0, -512.0]], [[1.0, 0], [112.0576111270724, 84.41618202983253]], [[1.0, 0], [0, 0]], [[1.0, 0], 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'prelabel': '2-75-15.2-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.2151176748546355, 'root_angle': 0.8817179314279279, 'root_number': '-0.9317497182016256 + 0.36310117409778697*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.440858965713964', 'prec': 57}, 'spectral_label': 'c9-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.36658689287492063801879381930134', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '3.70472018611425232347737424190607', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '4.90161487111987670670090269582872', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 38.627687712290495, 'bad_primes': [3, 5], 'central_character': '15.2', 'conductor': 75, 'conductor_radical': 15, 'degree': 2, 'index': 38, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/75/10/e/f/32/11'], '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': '2-75-15.2-c9-0-38', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 0, 'prelabel': '2-75-15.2-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.2151176748546355, 'root_angle': 0.44085896571396394, 'self_dual': False, 'spectral_label': 'c9-0', 'z1': {'__RealLiteral__': 0, 'data': '1.36658689287492063801879381930134', 'prec': 113}}
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lfunc_instances • Show schema
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{'Lhash': '1732354695016924180390989191567', 'Lhash_array': ['1732354695016924180390989191567'], 'label': '2-75-15.2-c9-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/75/10/e/f/32/11'}