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lfunc_lfunctions • Show schema
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{'Lhash': '1210902145563216639395394617322,1395299980581904295158151805760', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 2, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1353.876826855227, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '4608.1', 'coefficient_field': '1.1.1.1', 'conductor': 21233664, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1], [1, -2, 2, -10, 25], [1, 0, 2, 0, 49], [1, -8, 32, -88, 121], [1, -6, 18, -78, 169], [1, -12, 70, -204, 289], [1, -8, 32, -152, 361], [1, 0, 18, 0, 529], [1, -6, 18, -174, 841], [1, 8, 78, 248, 961], [1, -2, 2, -74, 1369], [1, 0, -78, 0, 1681], [1, -8, 32, -344, 1849], [1, 16, 158, 752, 2209], [1, 14, 98, 742, 2809], [1, 0, 0, 0, 3481], [1, 6, 18, 366, 3721], [1, 16, 128, 1072, 4489], [1, 0, -142, 0, 5041], [1, 0, -46, 0, 5329], [1, -24, 302, -1896, 6241], [1, 8, 32, 664, 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'7.947885281363358547833914804976800', '8.569028267117341858163542905322944'], 'prelabel': '4-4608e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.065893606996913, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1190224553813016878, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.955233362683064482232371904822', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.10069760573670121670120322937', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.58221874533219103996538297112', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1353.876826855227, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 21233664, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 8, 0, 6, 0, 0, 0, 12, 0, 8, 0, 0, 0, 0, 0, 2, 0, 0, 0, 6, 0, -8, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 8, 0, 0, 0, -16, 0, -2, 0, 0, 0, -14, 0, 16, 0, 0, 0, 0, 0, -6, 0, 0, 0, 12, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, -8, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 16, 0, 0, 0], 'euler11': [1, -8, 32, -88, 121], 'euler13': [1, -6, 18, -78, 169], 'euler17': [1, -12, 70, -204, 289], 'euler19': [1, -8, 32, -152, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 18, 0, 529], 'euler29': [1, -6, 18, -174, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 8, 78, 248, 961], 'euler37': [1, -2, 2, -74, 1369], 'euler41': [1, 0, -78, 0, 1681], 'euler43': [1, -8, 32, -344, 1849], 'euler47': [1, 16, 158, 752, 2209], 'euler5': [1, -2, 2, -10, 25], 'euler53': [1, 14, 98, 742, 2809], 'euler59': [1, 0, 0, 0, 3481], 'euler61': [1, 6, 18, 366, 3721], 'euler67': [1, 16, 128, 1072, 4489], 'euler7': [1, 0, 2, 0, 49], 'euler71': [1, 0, -142, 0, 5041], 'euler73': [1, 0, -46, 0, 5329], 'euler79': [1, -24, 302, -1896, 6241], 'euler83': [1, 8, 32, 664, 6889], 'euler89': [1, 0, 78, 0, 7921], 'euler97': [1, -16, 258, -1552, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, -2, 2, -10, 25], [1, 0, 2, 0, 49], [1, -8, 32, -88, 121], [1, -6, 18, -78, 169], [1, -12, 70, -204, 289], [1, -8, 32, -152, 361], [1, 0, 18, 0, 529], [1, -6, 18, -174, 841], [1, 8, 78, 248, 961], [1, -2, 2, -74, 1369], [1, 0, -78, 0, 1681], [1, -8, 32, -344, 1849], [1, 16, 158, 752, 2209], [1, 14, 98, 742, 2809], [1, 0, 0, 0, 3481], [1, 6, 18, 366, 3721], [1, 16, 128, 1072, 4489], [1, 0, -142, 0, 5041], [1, 0, -46, 0, 5329], [1, -24, 302, -1896, 6241], [1, 8, 32, 664, 6889], [1, 0, 78, 0, 7921], [1, -16, 258, -1552, 9409]], 'index': 46, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4608/2/k/u'], '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': '4-4608e2-1.1-c1e2-0-46', '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': 0, 'prelabel': '4-4608e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.065893606996913, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1190224553813016878, 'z1': {'__RealLiteral__': 0, 'data': '0.955233362683064482232371904822', 'prec': 107}}
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{'Lhash': '1210902145563216639395394617322,1395299980581904295158151805760', 'Lhash_array': ['1210902145563216639395394617322', '1395299980581904295158151805760'], 'label': '4-4608e2-1.1-c1e2-0-46', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4608/2/k/u'}