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lfunc_lfunctions • Show schema
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{'Lhash': '737883011220073112532875880554', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 1.7320508075688772], 'a4': [-1.0, 1.7320508075688772], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.5, 0.8660254037844386], 'a8': [0.0, 0.0], 'a9': [-3.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, -1.7320508075688772]]], [7, [[1.0, 0], [2.5, -0.8660254037844386]]], [13, [[1.0, 0], [-1.0, 3.4641016151377544]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.152', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '3936039873057718256974362424074', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [1.0, -1.7320508075688772]], [[1.0, 0], [0, -1.7320508075688772]], [[1.0, 0], [0, 0], [-2.5, -4.330127018922194]], [[1.0, 0], [2.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-11.0, 0]], [[1.0, 0], [-1.0, 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'positive_zeros': ['0.58208706017827288621124243377554', '2.38166414081353019223230660417882', '4.16755189048506287075935004495364', '5.60374273128433385286993151283255', '6.55919735561680489925539031099928', '7.27174023488180175545848110315456', '8.886356997181741808525570788830088', '9.311893064436845493695050786215149', '10.65370307297799945834805003724969', '11.42376862483112469163445446794453'], 'prelabel': '2-273-273.152-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': -0.8909714291600027, 'root_number': '-0.9419101579580714 - 0.33586493466183837*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.44548571458', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.58208706017827288621124243378', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.38166414081353019223230660418', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.16755189048506287075935004495', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'bad_primes': [3, 7, 13], 'central_character': '273.152', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/2/bf/a/152/1'], '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': '2-273-273.152-c1-0-5', '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': '2-273-273.152-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': -0.44548571458000136, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.58208706017827288621124243378', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '737883011220073112532875880554', 'Lhash_array': ['737883011220073112532875880554'], 'label': '2-273-273.152-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/2/bf/a/152/1'}