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lfunc_lfunctions • Show schema
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{'Lhash': '2584574078995372437628983282698', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -2.515605283305978], 'a4': [0, 0], 'a5': [-1.926547295559964, 1.1350839255185443], 'a6': [0, 0], 'a7': [0, -4.64022445420112], 'a8': [0, 0], 'a9': [-3.3282699413969503, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.692473971915598, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.926547295559964, -1.1350839255185443]]], [23, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [2, 5, 23], 'central_character': '1840.369', 'coefficient_field': 'CDF', 'conductor': 1840, 'conductor_radical': 230, 'conjugate': '241073621844316465112652324753', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 2.515605283305978], [-3.0, 0]], [[1.0, 0], [1.926547295559964, -1.1350839255185443]], [[1.0, 0], [0, 4.64022445420112], [-7.0, 0]], [[1.0, 0], [-1.6494438206181201, 0], [11.0, 0]], [[1.0, 0], [0, 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['2.03886944756705237537917863311849', '3.34266691492945401110820064807208', '3.93267034635741324815670278759057', '4.95674362587552535375056111074674', '5.43738663000797774391253721949640', '6.34918073758110925545117192255005', '7.68781141756687540576361515545392', '8.557674356238466238511845656501937', '9.007527408416018541495190192978450', '9.527112899346983569932053485263906'], 'prelabel': '2-1840-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.833076306560515, 'root_angle': -0.6694764380598383, 'root_number': '-0.5076249635253546368091004140779001058284318238160461825 - 0.8615781429480917226431497141669395038962324768212055016*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3347382190299191', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.03886944756705237537917863312', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.34266691492945401110820064807', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.93267034635741324815670278759', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.692473971915598, 'bad_primes': [2, 5, 23], 'central_character': '5.4', 'conductor': 1840, 'conductor_radical': 230, 'degree': 2, 'index': 60, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1840/2/e/h/369/4'], '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': '2-1840-5.4-c1-0-60', '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': '2-1840-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.833076306560515, 'root_angle': -0.3347382190299191, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.03886944756705237537917863312', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2584574078995372437628983282698', 'Lhash_array': ['2584574078995372437628983282698'], 'label': '2-1840-5.4-c1-0-60', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1840/2/e/h/369/4'}