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lfunc_lfunctions • Show schema
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{'Lhash': '3317106005193715239953593970596', 'a10': [-0.07294901687515773, -0.1263514035899726], 'a2': [-0.19098300562505258, -0.33079226912480375], 'a3': [0.19098300562505258, 0.33079226912480375], 'a4': [0.9270509831248422, -1.6056994039789048], 'a5': [0.38196601125010515, 0.0], 'a6': [0.07294901687515773, -0.1263514035899726], 'a7': [-0.5, 0.8660254037844386], 'a8': [-1.4721359549995794, 0.0], 'a9': [1.4270509831248424, -2.4717248077633434], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0.5, -0.8660254037844386]]], [13, [[1.0, 0], [2.5, 2.598076211353316]]]], 'bad_primes': [7, 13], 'central_character': '91.29', 'coefficient_field': 'CDF', 'conductor': 91, 'conductor_radical': 91, 'conjugate': '2569844776137479070104735997888', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.19098300562505258, 0.33079226912480375], [-1.0, 1.7320508075688772]], 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'prelabel': '2-91-13.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': 0.17074856945180006, 'root_number': '0.8595425350987749 + 0.5110642135348272*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0853742847259', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.61673524597116849145203397389', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.41789987200615332892665062700', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.42749491066853244813148334199', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'bad_primes': [7, 13], 'central_character': '13.3', 'conductor': 91, 'conductor_radical': 91, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/91/2/f/a/29/2'], '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': '2-91-13.3-c1-0-4', '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': '2-91-13.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': 0.08537428472590003, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.61673524597116849145203397389', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3317106005193715239953593970596', 'Lhash_array': ['3317106005193715239953593970596'], 'label': '2-91-13.3-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/91/2/f/a/29/2'}