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lfunc_lfunctions • Show schema
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{'Lhash': '2722741421039431371705992212511', 'a10': [13012527917842426, 0.0], 'a2': [61269.13128225437, 0.0], 'a3': [-43046721.0, 0.0], 'a4': [-4836028143.917879, 0.0], 'a5': [212383098070.97427, 0.0], 'a6': [-2637435200219.576, 0.0], 'a7': [158202902939123.94, 0.0], 'a8': [-822597073457607.6, 0.0], 'a9': [1853020188851841.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 20.694848664302253, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '16.5', 'prec': 14}, 'bad_lfactors': [[3, [[1.0, 0], [43046721.0, 0]]]], 'bad_primes': [3], 'central_character': '3.1', 'coefficient_field': 'CDF', 'conductor': 3, 'conductor_radical': 3, 'conjugate': '2722741421039431371705992212511', 'degree': 2, 'euler_factors': [[[1.0, 0], [-61269.13128225437, 0], [8589934592.0, 0]], [[1.0, 0], [43046721.0, 0]], [[1.0, 0], [-212383098070.97427, 0], [116415321826934800000000, 0]], [[1.0, 0], [-158202902939123.94, 0], [7730993719707444000000000000, 0]], [[1.0, 0], [262905875171069380, 0], 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'15.00328542007060913660329522519914', '17.43837582324422302370154741095491'], 'prelabel': '2-3-1.1-c33-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.549159116177654, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c33-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.14786426208390986970260053324', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.72396043192429427116059972957', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.43460478094096448163200830958', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 20.694848664302253, 'bad_primes': [3], 'central_character': '1.1', 'conductor': 3, 'conductor_radical': 3, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3/34/a/b/1/2'], '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': '2-3-1.1-c33-0-4', 'motivic_weight': 33, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [33], 'order_of_vanishing': 1, 'prelabel': '2-3-1.1-c33-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.549159116177654, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c33-0', 'z1': {'__RealLiteral__': 0, 'data': '2.14786426208390986970260053324', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2722741421039431371705992212511', 'Lhash_array': ['2722741421039431371705992212511'], 'label': '2-3-1.1-c33-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3/34/a/b/1/2'}