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lfunc_lfunctions • Show schema
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{'Lhash': '2935301955531426197724100051777', 'a10': [700.0, -100.0], 'a2': [4.0, 4.0], 'a3': [0, 0], 'a4': [0, 32.0], 'a5': [75.0, -100.0], 'a6': [0, 0], 'a7': [-247.0, -247.0], 'a8': [-128.0, 128.0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 20.704867525786593, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-4.0, -4.0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-75.0, 100.0]]]], 'bad_primes': [2, 3, 5], 'central_character': '90.37', 'coefficient_field': 'CDF', 'conductor': 90, 'conductor_radical': 30, 'conjugate': '145485959626332778526103022446', 'degree': 2, 'euler_factors': [[[1.0, 0], [-4.0, -4.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-75.0, 100.0]], [[1.0, 0], [247.0, 247.0], [0, 117649.0]], [[1.0, 0], [1402.0, 0], [1771561.0, 0]], [[1.0, 0], [2703.0, -2703.0], [0, -4826809.0]], [[1.0, 0], [2593.0, 2593.0], [0, 24137569.0]], [[1.0, 0], [0, -1720.0], [-47045881.0, 0]], [[1.0, 0], [2137.0, 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'7.52732887570071554203270932563722', '9.284889288292758594728136392404417', '10.26051239797065738713836479426348', '11.04082163577976276153011677281766', '12.72080597963365331754577819677886', '12.90659162306233259521310846467761'], 'prelabel': '2-90-5.2-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.550260160231126, 'root_angle': 0.38931228676217505, 'root_number': '-0.7677517301185269 + 0.6407474392457676*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.38931228676217505', 'prec': 64}, 'spectral_label': 'c6-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.31554495773752701089792040816135', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '3.12002662920330230389779545959252', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '5.16219390518300436757912977726606', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 20.704867525786593, 'bad_primes': [2, 3, 5], 'central_character': '5.2', 'conductor': 90, 'conductor_radical': 30, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/90/7/g/a/37/1'], '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': '2-90-5.2-c6-0-13', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'prelabel': '2-90-5.2-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.550260160231126, 'root_angle': 0.38931228676217505, 'self_dual': False, 'spectral_label': 'c6-0', 'z1': {'__RealLiteral__': 0, 'data': '2.31554495773752701089792040816135', 'prec': 113}}
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lfunc_instances • Show schema
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{'Lhash': '2935301955531426197724100051777', 'Lhash_array': ['2935301955531426197724100051777'], 'factors': ['2-90-5.2-c6-0-13'], 'label': '2-90-5.2-c6-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/90/7/g/a/37/1'}