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lfunc_lfunctions • Show schema
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{'Lhash': '328427064066735603174855718169', 'a10': [0, -2.449489742783178], 'a2': [0, 1.0], 'a3': [0, 0], 'a4': [-1.0, 0], 'a5': [-2.449489742783178, 0], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, -1.0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.1284163748308, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -1.0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '2646.2645', 'coefficient_field': 'CDF', 'conductor': 2646, 'conductor_radical': 42, 'conjugate': '1235067298210837640986457251631', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.449489742783178, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 4.242640687119285], [-11.0, 0]], [[1.0, 0], [0, 0.7174389352143008], [-13.0, 0]], [[1.0, 0], [2.449489742783178, 0], [17.0, 0]], [[1.0, 0], [0, 4.898979485566356], [-19.0, 0]], [[1.0, 0], [0, -6.0], 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'4.00243269800576322729836035343863', '4.19422762646589139150766650825864', '5.17767759794147524341159931460594', '6.34306744170816537766240625882761', '7.16087502938463608532203302139064', '8.014582683106447552186947954705738', '8.414486176313004542930674134874343'], 'prelabel': '2-2646-21.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.596565715273828, 'root_angle': -0.7728144741714951, 'root_number': '-0.7559289460184544544290330724683601216315026237378429087 - 0.6546536707079771437982924562468583555692080823954245575*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.38640723708574753', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.25908327105876428669170023508', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.79222205244829719042190605170', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.68535881997343551267743626001', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.1284163748308, 'bad_primes': [2, 3, 7], 'central_character': '21.20', 'conductor': 2646, 'conductor_radical': 42, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2646/2/d/d/2645/5'], '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': '2-2646-21.20-c1-0-8', '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': '2-2646-21.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.596565715273828, 'root_angle': -0.38640723708574753, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.25908327105876428669170023508', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '328427064066735603174855718169', 'Lhash_array': ['328427064066735603174855718169'], 'label': '2-2646-21.20-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2646/2/d/d/2645/5'}