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lfunc_lfunctions • Show schema
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{'Lhash': '1190107774765680466415156581942', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 4.962608190557792], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [-6.977762729808863, 0], 'a8': [0, 0], 'a9': [-15.627480052991281, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 62.67046080286829, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [12.286520597448078, 19.443287057709252]]]], 'bad_primes': [2, 5, 23], 'central_character': '2300.1149', 'coefficient_field': 'CDF', 'conductor': 2300, 'conductor_radical': 230, 'conjugate': '167233820240875054737912111513', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -4.962608190557792], [-9.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [6.977762729808863, 0], [49.0, 0]], [[1.0, 0], [0, -10.286157764725685], [-121.0, 0]], [[1.0, 0], [0, -10.106284265927602], [-169.0, 0]], [[1.0, 0], [-27.018564506075403, 0], [289.0, 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'3.19422231421500607154791928982412', '3.48849348090769144219704744446176', '5.45820023542200193943847064549015', '5.87226310419040687343412368227905', '6.53036628372435154832455975491923', '7.52130104461099646888349843683383', '7.86975867950168143536836840786962', '8.618748282907863955103806807621071'], 'prelabel': '2-2300-115.114-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.916467697329933, 'root_angle': 0.17303060650057311, 'root_number': '0.85585653993713240474443435683536827830313876484013144368 + 0.5172132858375156676434875663740717386206495323905859930*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.08651530325028654', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.938829496512218723612580385519', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.84510149924133527338309007249', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.19422231421500607154791928982', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 62.67046080286829, 'bad_primes': [2, 5, 23], 'central_character': '115.114', 'conductor': 2300, 'conductor_radical': 230, 'degree': 2, 'index': 43, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2300/3/d/c/1149/6'], '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': '2-2300-115.114-c2-0-43', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-2300-115.114-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.916467697329933, 'root_angle': 0.08651530325028656, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.938829496512218723612580385519', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1190107774765680466415156581942', 'Lhash_array': ['1190107774765680466415156581942'], 'label': '2-2300-115.114-c2-0-43', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2300/3/d/c/1149/6'}