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lfunc_lfunctions • Show schema
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{'Lhash': '3181534324314969658906576304459', 'a10': [0.40952023179894553, 0.0], 'a2': [0.48282702883820255, 0.0], 'a3': [-0.30021025981186106, 0.0], 'a4': [-1.7668780602232734, 0.0], 'a5': [0.8481717205939139, 0.0], 'a6': [-0.14494962777170572, 0.0], 'a7': [-1.7467374582351844, 0.0], 'a8': [-1.8187505418134151, 0.0], 'a9': [-2.909873799903695, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.217971201457601, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[13, [[1.0, 0], [-1.0, 0]]], [31, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [13, 31], 'central_character': '403.1', 'coefficient_field': 'CDF', 'conductor': 403, 'conductor_radical': 403, 'conjugate': '3181534324314969658906576304459', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.48282702883820255, 0], [2.0, 0]], [[1.0, 0], [0.30021025981186106, 0], [3.0, 0]], [[1.0, 0], [-0.8481717205939139, 0], [5.0, 0]], [[1.0, 0], [1.7467374582351844, 0], [7.0, 0]], [[1.0, 0], 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'3.87371325859849779412001030454589', '4.88745098211830776598720783277494', '6.03382729112380228889567579457741', '6.64317893000343521001371337419889', '8.464595160018949820176891713716999', '8.820812524337246866330274233523211', '9.859098402759306244550152832849059', '10.81802565437829790649441826833177'], 'prelabel': '2-403-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7938704528080063, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.50978804707082711516881848957', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.87371325859849779412001030455', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.88745098211830776598720783277', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.217971201457601, 'bad_primes': [13, 31], 'central_character': '1.1', 'conductor': 403, 'conductor_radical': 403, 'degree': 2, 'index': 24, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/403/2/a/b/1/4'], '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': '2-403-1.1-c1-0-24', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-403-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7938704528080063, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.50978804707082711516881848957', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3181534324314969658906576304459', 'Lhash_array': ['3181534324314969658906576304459'], 'label': '2-403-1.1-c1-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/403/2/a/b/1/4'}