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lfunc_lfunctions • Show schema
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{'Lhash': '1395411738623547287585309853895', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-1.4142135623730951, 1.4142135623730951], 'a4': [0, 0], 'a5': [1.4142135623730951, 1.4142135623730951], 'a6': [0, 0], 'a7': [0, -4.0], 'a8': [0, 0], 'a9': [0, -1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.176681166979115, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]]], 'bad_primes': [2], 'central_character': '1024.769', 'coefficient_field': 'CDF', 'conductor': 1024, 'conductor_radical': 2, 'conjugate': '1204240809916511711481902776094', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.4142135623730951, -1.4142135623730951], [0, -3.0]], [[1.0, 0], [-1.4142135623730951, -1.4142135623730951], [0, 5.0]], [[1.0, 0], [0, 4.0], [-7.0, 0]], [[1.0, 0], [-1.4142135623730951, -1.4142135623730951], [0, 11.0]], [[1.0, 0], [-1.4142135623730951, 1.4142135623730951], [0, -13.0]], [[1.0, 0], [-2.0, 0], [17.0, 0]], 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'2.08258155784625936442467934634002', '3.52195504667435645060392012954031', '5.13313904663649993546507091065173', '5.71825374667437010823562266657673', '6.21706140665644193498539726895197', '7.22701457878079858275664800471620', '8.358257775398827819072167173388748', '9.115936908234249311858173439329901', '9.620850926648493260592906246202524'], 'prelabel': '2-2e10-16.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8594896689757623, 'root_angle': -0.12500000000000003, 'root_number': '0.9238795325112867561281831893967882868224166258636424862 - 0.3826834323650897717284599840303988667613445624856270415*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0625', 'prec': 24}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.10078576728659743524075207070', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.08258155784625936442467934634', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.52195504667435645060392012954', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.176681166979115, 'bad_primes': [2], 'central_character': '16.5', 'conductor': 1024, 'conductor_radical': 2, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1024/2/e/i/769/1'], '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': '2-2e10-16.5-c1-0-13', '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': '2-2e10-16.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8594896689757623, 'root_angle': -0.06250000000000001, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.10078576728659743524075207070', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1395411738623547287585309853895', 'Lhash_array': ['1395411738623547287585309853895'], 'label': '2-2e10-16.5-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1024/2/e/i/769/1'}