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lfunc_lfunctions • Show schema
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{'Lhash': '137633949266406084615749044775', 'a10': [25.56375985966911, 0.0], 'a2': [-2.0, 0.0], 'a3': [-3.0, 0.0], 'a4': [4.0, 0.0], 'a5': [-12.781879929834554, 0.0], 'a6': [6.0, 0.0], 'a7': [-7.0, 0.0], 'a8': [-8.0, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 56.99584506554546, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [2.0, 0]]], [3, [[1.0, 0], [3.0, 0]]], [7, [[1.0, 0], [7.0, 0]]], [23, [[1.0, 0], [23.0, 0]]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '966.1', 'coefficient_field': 'CDF', 'conductor': 966, 'conductor_radical': 966, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.0, 0]], [[1.0, 0], [3.0, 0]], [[1.0, 0], [12.781879929834554, 0], [125.0, 0]], [[1.0, 0], [7.0, 0]], [[1.0, 0], [4.5631906179542305, 0], [1331.0, 0]], [[1.0, 0], [70.66459739103661, 0], [2197.0, 0]], [[1.0, 0], [78.37807622801867, 0], [4913.0, 0]], [[1.0, 0], [43.16875542033848, 0], [6859.0, 0]], 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'3.20500551258018533160326695376618', '4.37435964369630439039932267253384', '5.22805145584909756714635375428901', '6.63164466820457276007241104807499', '7.03909071940489186211916395090327', '7.993863698147338260624729006285808', '8.720894512365698480086632147368689', '9.744395233796035301212770589491495'], 'prelabel': '2-966-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.549559262999758, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.10857404180743991762080103180', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.91780160769727424060674135603', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.20500551258018533160326695377', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 56.99584506554546, 'bad_primes': [2, 3, 7, 23], 'central_character': '1.1', 'conductor': 966, 'conductor_radical': 966, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/966/4/a/m/1/1'], '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': '2-966-1.1-c3-0-0', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-966-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.549559262999758, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.10857404180743991762080103180', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '137633949266406084615749044775', 'Lhash_array': ['137633949266406084615749044775'], 'label': '2-966-1.1-c3-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/966/4/a/m/1/1'}