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lfunc_lfunctions • Show schema
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{'Lhash': '1650431640063600461162685395586', 'a10': [0.585786437626905, -1.0146118723545765], 'a2': [0.20710678118654752, -0.3587194676071504], 'a3': [-0.5, 0.8660254037844386], 'a4': [0.914213562373095, 1.5834643389987395], 'a5': [2.8284271247461903, 0.0], 'a6': [0.20710678118654752, 0.3587194676071504], 'a7': [1.4142135623730951, 2.449489742783178], 'a8': [1.5857864376269049, 0.0], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.048415382478917, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.5, -0.8660254037844386]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '507.22', 'coefficient_field': 'CDF', 'conductor': 507, 'conductor_radical': 39, 'conjugate': '2693222329693791027894239826517', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.20710678118654752, 0.3587194676071504], [-1.0, -1.7320508075688772]], [[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 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'rational': False, 'root_analytic_conductor': 2.0120674398436345, 'root_angle': -0.32516952776306657, 'root_number': '0.5220443854178448 - 0.8529183194501714*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.162584763882', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.30196099758597099383030985737', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.20169886619449693510770836419', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.21130956263690406268950429095', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.048415382478917, 'bad_primes': [3, 13], 'central_character': '13.9', 'conductor': 507, 'conductor_radical': 39, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/507/2/e/d/22/2'], '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': '2-507-13.9-c1-0-9', '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': '2-507-13.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0120674398436345, 'root_angle': -0.16258476388153328, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.30196099758597099383030985737', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1650431640063600461162685395586', 'Lhash_array': ['1650431640063600461162685395586'], 'label': '2-507-13.9-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/507/2/e/d/22/2'}