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lfunc_lfunctions • Show schema
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{'Lhash': '501104718999130785458900941644', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0.06898645444084249, -4.999524064258885], 'a6': [0, 0], 'a7': [-2.420963376085834, 1.3977438568813816], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 44.1418028263681, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.06898645444084249, 4.999524064258885]]]], 'bad_primes': [2, 3, 5], 'central_character': '1620.1349', 'coefficient_field': 'CDF', 'conductor': 1620, 'conductor_radical': 30, 'conjugate': '1043971429413083674222769715729', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.06898645444084249, 4.999524064258885]], [[1.0, 0], [2.420963376085834, -1.3977438568813816], [24.5, -42.4352447854375]], [[1.0, 0], [15.715360457894612, -9.073267590777455], [60.5, -104.78907385791707]], [[1.0, 0], 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'primitive': True, 'rational': False, 'root_analytic_conductor': 6.643929772835358, 'root_angle': -0.21783026877657244, 'root_number': '0.7748402531631811897954165674851473950945239930166173578 - 0.6321570865520826242045268259218952136202622283037609360*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.10891513438828625', 'prec': 67}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.39530192224017506427680425247', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.29274716801329512256576936074', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.92294595704197794348286656476', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 44.1418028263681, 'bad_primes': [2, 3, 5], 'central_character': '45.14', 'conductor': 1620, 'conductor_radical': 30, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1620/3/t/d/1349/2'], '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': '2-1620-45.14-c2-0-13', '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': '2-1620-45.14-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.643929772835358, 'root_angle': -0.10891513438828622, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.39530192224017506427680425247', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '501104718999130785458900941644', 'Lhash_array': ['501104718999130785458900941644'], 'label': '2-1620-45.14-c2-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1620/3/t/d/1349/2'}