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lfunc_lfunctions • Show schema
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{'Lhash': '1352691489154148211225472016707,2285172071477896145379493599495', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -6, 'a8': 0, 'a9': -1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1864.7799021900141, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [13, [1]]], 'bad_primes': [2, 13], 'central_character': '5408.1', 'coefficient_field': '1.1.1.1', 'conductor': 29246464, 'conductor_radical': 26, 'degree': 4, 'euler_factors': [[1], [1, -2, 5, -6, 9], [1, 0, 2, 0, 25], [1, 6, 21, 42, 49], [1, -2, 5, -22, 121], [1], [1, 6, 35, 102, 289], [1, 6, 29, 114, 361], [1, -6, 37, -138, 529], [1, -6, 35, -174, 841], [1, 0, 30, 0, 961], [1, -2, 3, -74, 1369], [1, 6, 83, 246, 1681], [1, -6, 45, -258, 1849], [1, 12, 130, 564, 2209], [1, 0, 98, 0, 2809], [1, 6, 109, 354, 3481], [1, -14, 171, -854, 3721], [1, 18, 197, 1206, 4489], [1, -6, 133, -426, 5041], [1, -8, 90, -584, 5329], [1, -12, 194, -948, 6241], [1, 8, 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6.571384740913323, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 1686166359723837857, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.06708543261889983059449495965', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.80268290889182784593386835245', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.49754545051375097154283043208', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1864.7799021900141, 'bad_primes': [2, 13], 'central_character': '1.1', 'conductor': 29246464, 'conductor_radical': 26, 'degree': 4, 'dirichlet_coefficients': [1, 0, 2, 0, 0, 0, -6, 0, -1, 0, 2, 0, 0, 0, 0, 0, -6, 0, -6, 0, -12, 0, 6, 0, -2, 0, -6, 0, 6, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, -6, 0, 6, 0, 0, 0, -12, 0, 15, 0, -12, 0, 0, 0, 0, 0, -12, 0, -6, 0, 14, 0, 6, 0, 0, 0, -18, 0, 12, 0, 6, 0, 8, 0, -4, 0, -12, 0, 12, 0, -4, 0, -8, 0, 0, 0, 12, 0, -18, 0, 0, 0, 0, 0, 0, 0, -18, 0, -2, 0], 'euler11': [1, -2, 5, -22, 121], 'euler13': [1, 0, 0, 0, 0], 'euler17': [1, 6, 35, 102, 289], 'euler19': [1, 6, 29, 114, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -6, 37, -138, 529], 'euler29': [1, -6, 35, -174, 841], 'euler3': [1, -2, 5, -6, 9], 'euler31': [1, 0, 30, 0, 961], 'euler37': [1, -2, 3, -74, 1369], 'euler41': [1, 6, 83, 246, 1681], 'euler43': [1, -6, 45, -258, 1849], 'euler47': [1, 12, 130, 564, 2209], 'euler5': [1, 0, 2, 0, 25], 'euler53': [1, 0, 98, 0, 2809], 'euler59': [1, 6, 109, 354, 3481], 'euler61': [1, -14, 171, -854, 3721], 'euler67': [1, 18, 197, 1206, 4489], 'euler7': [1, 6, 21, 42, 49], 'euler71': [1, -6, 133, -426, 5041], 'euler73': [1, -8, 90, -584, 5329], 'euler79': [1, -12, 194, -948, 6241], 'euler83': [1, 8, 182, 664, 6889], 'euler89': [1, 18, 227, 1602, 7921], 'euler97': [1, 18, 275, 1746, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -2, 5, -6, 9], [1, 0, 2, 0, 25], [1, 6, 21, 42, 49], [1, -2, 5, -22, 121], [1, 0, 0, 0, 0], [1, 6, 35, 102, 289], [1, 6, 29, 114, 361], [1, -6, 37, -138, 529], [1, -6, 35, -174, 841], [1, 0, 30, 0, 961], [1, -2, 3, -74, 1369], [1, 6, 83, 246, 1681], [1, -6, 45, -258, 1849], [1, 12, 130, 564, 2209], [1, 0, 98, 0, 2809], [1, 6, 109, 354, 3481], [1, -14, 171, -854, 3721], [1, 18, 197, 1206, 4489], [1, -6, 133, -426, 5041], [1, -8, 90, -584, 5329], [1, -12, 194, -948, 6241], [1, 8, 182, 664, 6889], [1, 18, 227, 1602, 7921], [1, 18, 275, 1746, 9409]], 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5408/2/a/be'], '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': '4-5408e2-1.1-c1e2-0-13', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 2, 'prelabel': '4-5408e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.571384740913323, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1686166359723837857, 'z1': {'__RealLiteral__': 0, 'data': '1.06708543261889983059449495965', 'prec': 103}}
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{'Lhash': '1352691489154148211225472016707,2285172071477896145379493599495', 'Lhash_array': ['1352691489154148211225472016707', '2285172071477896145379493599495'], 'factors': ['2-5408-1.1-c1-0-82', '2-5408-1.1-c1-0-151'], 'label': '4-5408e2-1.1-c1e2-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5408/2/a/be'}