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lfunc_lfunctions • Show schema
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{'Lhash': '1599402877551862604808448308328', 'a10': [3.7987761972900023, -6.579673380289577], 'a2': [0.0, 2.1093884625501], 'a3': [-1.130824202928435, 1.958644973900628], 'a4': [-2.449519685939474, 0.0], 'a5': [-3.1192326577605445, -1.8008898146231223], 'a6': [-4.131543110177726, -2.385347526829654], 'a7': [0.0, 0.0], 'a8': [0.0, -0.9482116392098715], 'a9': [-1.057526755857461, -1.8316900715086102], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.086470608755563, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [1.17348727575741, 3.4092415012192157]]]], 'bad_primes': [7, 13], 'central_character': '637.569', 'coefficient_field': 'CDF', 'conductor': 637, 'conductor_radical': 91, 'conjugate': '236159712965859600582395231043', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -2.1093884625501], [-2.0, 0]], [[1.0, 0], [1.130824202928435, -1.958644973900628], [-1.5, -2.598076211353316]], [[1.0, 0], 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'10.08062508167888862525208303078735', '10.98921335374442295179669099630860'], 'prelabel': '2-637-91.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': -0.06109362992574662, 'root_number': '0.9816376609614242 - 0.19075508533767546*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0305468149629', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.26170640179865343641330087164', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.62558530090715252721349774550', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.62895304599972484950548247093', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.086470608755563, 'bad_primes': [7, 13], 'central_character': '91.23', 'conductor': 637, 'conductor_radical': 91, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/k/h/569/6'], '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': '2-637-91.23-c1-0-18', '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': '2-637-91.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': -0.03054681496287331, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.26170640179865343641330087164', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1599402877551862604808448308328', 'Lhash_array': ['1599402877551862604808448308328'], 'label': '2-637-91.23-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/k/h/569/6'}