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lfunc_lfunctions • Show schema
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{'Lhash': '497727563837695318942492694294,1080931693949430714854411394486', 'a10': 4, 'a2': -1, 'a3': 2, 'a4': 1, 'a5': -4, 'a6': -2, 'a7': 0, 'a8': -3, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2316.0962156552932, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -2, 1]], [7, [1]], [41, [1, -2, 1]]], 'bad_primes': [3, 7, 41], 'central_character': '6027.1', 'coefficient_field': '1.1.1.1', 'conductor': 36324729, 'conductor_radical': 861, 'degree': 4, 'euler_factors': [[1, 1, 0, 2, 4], [1, -2, 1], [1, 4, 14, 20, 25], [1], [1, -9, 38, -99, 121], [1, 2, 10, 26, 169], [1, 5, 36, 85, 289], [1, 6, 30, 114, 361], [1, 0, 46, 0, 529], [1, 1, 20, 29, 841], [1, 15, 114, 465, 961], [1, -7, 48, -259, 1369], [1, -2, 1], [1, 13, 90, 559, 1849], [1, -5, 62, -235, 2209], [1, -4, 110, -212, 2809], [1, -8, 134, -472, 3481], [1, -13, 160, -793, 3721], [1, -2, -18, -134, 4489], [1, -13, 146, -923, 5041], [1, -9, 60, -657, 5329], 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'8.169639455523469205995892284690959'], 'prelabel': '4-6027e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.937278810760435, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 845591422561145799, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.39263781656245326990218885502', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.852704754571029603161369632427', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.85380477883707391145628812344', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2316.0962156552932, 'bad_primes': [3, 7, 41], 'central_character': '1.1', 'conductor': 36324729, 'conductor_radical': 861, 'degree': 4, 'dirichlet_coefficients': [1, -1, 2, 1, -4, -2, 0, -3, 3, 4, 9, 2, -2, 0, -8, 1, -5, -3, -6, -4, 0, -9, 0, -6, 2, 2, 4, 0, -1, 8, -15, 1, 18, 5, 0, 3, 7, 6, -4, 12, 2, 0, -13, 9, -12, 0, 5, 2, 0, -2, -10, -2, 4, -4, -36, 0, -12, 1, 8, -8, 13, 15, 0, 1, 8, -18, 2, -5, 0, 0, 13, -9, 9, -7, 4, -6, 0, 4, -2, -4, 5, -2, 10, 0, 20, 13, -2, -27, -8, 12, 0, 0, -30, -5, 24, 2, 36, 0, 27, 2], 'euler11': [1, -9, 38, -99, 121], 'euler13': [1, 2, 10, 26, 169], 'euler17': [1, 5, 36, 85, 289], 'euler19': [1, 6, 30, 114, 361], 'euler2': [1, 1, 0, 2, 4], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, 1, 20, 29, 841], 'euler3': [1, -2, 1, 0, 0], 'euler31': [1, 15, 114, 465, 961], 'euler37': [1, -7, 48, -259, 1369], 'euler41': [1, -2, 1, 0, 0], 'euler43': [1, 13, 90, 559, 1849], 'euler47': [1, -5, 62, -235, 2209], 'euler5': [1, 4, 14, 20, 25], 'euler53': [1, -4, 110, -212, 2809], 'euler59': [1, -8, 134, -472, 3481], 'euler61': [1, -13, 160, -793, 3721], 'euler67': [1, -2, -18, -134, 4489], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, -13, 146, -923, 5041], 'euler73': [1, -9, 60, -657, 5329], 'euler79': [1, 2, 142, 158, 6241], 'euler83': [1, -10, 174, -830, 6889], 'euler89': [1, 8, 126, 712, 7921], 'euler97': [1, -36, 518, -3492, 9409], 'euler_factors': [[1, 1, 0, 2, 4], [1, -2, 1, 0, 0], [1, 4, 14, 20, 25], [1, 0, 0, 0, 0], [1, -9, 38, -99, 121], [1, 2, 10, 26, 169], [1, 5, 36, 85, 289], [1, 6, 30, 114, 361], [1, 0, 46, 0, 529], [1, 1, 20, 29, 841], [1, 15, 114, 465, 961], [1, -7, 48, -259, 1369], [1, -2, 1, 0, 0], [1, 13, 90, 559, 1849], [1, -5, 62, -235, 2209], [1, -4, 110, -212, 2809], [1, -8, 134, -472, 3481], [1, -13, 160, -793, 3721], [1, -2, -18, -134, 4489], [1, -13, 146, -923, 5041], [1, -9, 60, -657, 5329], [1, 2, 142, 158, 6241], [1, -10, 174, -830, 6889], [1, 8, 126, 712, 7921], [1, -36, 518, -3492, 9409]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6027/2/a/k'], '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': '4-6027e2-1.1-c1e2-0-1', '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': '4-6027e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.937278810760435, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 845591422561145799, 'z1': {'__RealLiteral__': 0, 'data': '0.39263781656245326990218885502', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '497727563837695318942492694294,1080931693949430714854411394486', 'Lhash_array': ['497727563837695318942492694294', '1080931693949430714854411394486'], 'label': '4-6027e2-1.1-c1e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6027/2/a/k'}