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lfunc_lfunctions • Show schema
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{'Lhash': '1301080873138030696654550923912', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-1.4363160277608433, -2.4877723358072905], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [3.545677699309884, 0], 'a8': [0, 0], 'a9': [-2.6260074632053754, 4.54837834732677], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.17157638404328, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [0.8637597431793923, 4.2724605447052015]]]], 'bad_primes': [2, 5, 19], 'central_character': '1900.501', 'coefficient_field': 'CDF', 'conductor': 1900, 'conductor_radical': 190, 'conjugate': '951826526750987836550821956173', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.4363160277608433, 2.4877723358072905], [-1.5, 2.598076211353316]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.545677699309884, 0], [7.0, 0]], [[1.0, 0], [1.81575245447762, 0], [11.0, 0]], [[1.0, 0], [1.6068102633324863, 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[-33.5, -58.023702053557386]], [[1.0, 0], [2.9436452847904393, 5.098543192717598], [-35.5, 61.48780366869514]], [[1.0, 0], [1.6322605194771185, 2.8271581509231383], [-36.5, 63.21985447626402]], [[1.0, 0], [2.0873884248958223, 3.615462807050736], [-39.5, 68.41600689897065]], [[1.0, 0], [-6.302682320202565, 0], [83.0, 0]], [[1.0, 0], [2.7364568488983623, -4.739682295011794], [-44.5, -77.07626093681505]], [[1.0, 0], [3.990962312507824, 6.912549496356132], [-48.5, 84.00446416709055]], [[1.0, 0], [-2.467312738456173, 4.273511021167993], [-50.5, -87.4685657822283]], [[1.0, 0], [-5.562913997194314, 0], [103.0, 0]], [[1.0, 0], [-9.122513229954825, 0], [107.0, 0]], [[1.0, 0], [7.572248121562514, 13.115518474064267], [-54.5, 94.39676901250381]], [[1.0, 0], [-4.46090526773478, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 12, 'label': '2-1900-19.7-c1-0-12', 'leading_term': '1.425424620550882499353386134604303181242582442159482368', 'load_key': 'CMFs-workshop', 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'2-1900-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8950707803637252, 'root_angle': 0.5042567001075724, 'root_number': '-0.0133724192081869521272261132120995955449479099462622192 + 0.9999105852047574521907757186854317554068294554353564703*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.25212835005378625', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.02637183534941131803959385383', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.77112325581464928045796028204', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.75750970139935277572892923622', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.17157638404328, 'bad_primes': [2, 5, 19], 'central_character': '19.7', 'conductor': 1900, 'conductor_radical': 190, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1900/2/i/g/501/1'], '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': '2-1900-19.7-c1-0-12', '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': '2-1900-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8950707803637252, 'root_angle': 0.2521283500537862, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.02637183534941131803959385383', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1301080873138030696654550923912', 'Lhash_array': ['1301080873138030696654550923912'], 'label': '2-1900-19.7-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1900/2/i/g/501/1'}