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lfunc_lfunctions • Show schema
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{'Lhash': '347559643983095765824601190593,2053542071575586173942414175231', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 155.16844600323714, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 2, 1]], [5, [1, 0, 1]], [13, [1, 6, 13]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1560.1', 'coefficient_field': '1.1.1.1', 'conductor': 2433600, 'conductor_radical': 390, 'degree': 4, 'euler_factors': [[1], [1, 2, 1], [1, 0, 1], [1, 0, 2, 0, 49], [1, 0, -6, 0, 121], [1, 6, 13], [1, -16, 98, -272, 289], [1, 0, -38, 0, 361], [1, 12, 82, 276, 529], [1, 16, 122, 464, 841], [1, 0, -58, 0, 961], [1, 0, -58, 0, 1369], [1, 0, 18, 0, 1681], [1, 8, 102, 344, 1849], [1, 0, -30, 0, 2209], [1, 20, 206, 1060, 2809], [1, 0, 26, 0, 3481], [1, 4, 126, 244, 3721], [1, 0, -130, 0, 4489], [1, 0, 2, 0, 5041], [1, 0, -142, 0, 5329], [1, -16, 222, -1264, 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'prelabel': '4-1560e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.5293997670028463, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1697637893785303671, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.27417621537079751493502458474', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.58719029553208689077713907126', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.61995905749254872580956168927', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 155.16844600323714, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 2433600, 'conductor_radical': 390, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, 0, 0, 0, 0, 0, 3, 0, 0, 0, -6, 0, 0, 0, 16, 0, 0, 0, 0, 0, -12, 0, -1, 0, -4, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, -8, 0, 0, 0, 0, 0, -2, 0, -32, 0, -20, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 2, 0, 0, 0, 16, 0, 5, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, -6, 0, 121], 'euler13': [1, 6, 13, 0, 0], 'euler17': [1, -16, 98, -272, 289], 'euler19': [1, 0, -38, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 12, 82, 276, 529], 'euler29': [1, 16, 122, 464, 841], 'euler3': [1, 2, 1, 0, 0], 'euler31': [1, 0, -58, 0, 961], 'euler37': [1, 0, -58, 0, 1369], 'euler41': [1, 0, 18, 0, 1681], 'euler43': [1, 8, 102, 344, 1849], 'euler47': [1, 0, -30, 0, 2209], 'euler5': [1, 0, 1, 0, 0], 'euler53': [1, 20, 206, 1060, 2809], 'euler59': [1, 0, 26, 0, 3481], 'euler61': [1, 4, 126, 244, 3721], 'euler67': [1, 0, -130, 0, 4489], 'euler7': [1, 0, 2, 0, 49], 'euler71': [1, 0, 2, 0, 5041], 'euler73': [1, 0, -142, 0, 5329], 'euler79': [1, -16, 222, -1264, 6241], 'euler83': [1, 0, -102, 0, 6889], 'euler89': [1, 0, -142, 0, 7921], 'euler97': [1, 0, -94, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 2, 1, 0, 0], [1, 0, 1, 0, 0], [1, 0, 2, 0, 49], [1, 0, -6, 0, 121], [1, 6, 13, 0, 0], [1, -16, 98, -272, 289], [1, 0, -38, 0, 361], [1, 12, 82, 276, 529], [1, 16, 122, 464, 841], [1, 0, -58, 0, 961], [1, 0, -58, 0, 1369], [1, 0, 18, 0, 1681], [1, 8, 102, 344, 1849], [1, 0, -30, 0, 2209], [1, 20, 206, 1060, 2809], [1, 0, 26, 0, 3481], [1, 4, 126, 244, 3721], [1, 0, -130, 0, 4489], [1, 0, 2, 0, 5041], [1, 0, -142, 0, 5329], [1, -16, 222, -1264, 6241], [1, 0, -102, 0, 6889], [1, 0, -142, 0, 7921], [1, 0, -94, 0, 9409]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1560/2/g/c'], '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': '4-1560e2-1.1-c1e2-0-0', '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': '4-1560e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.5293997670028463, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1697637893785303671, 'z1': {'__RealLiteral__': 0, 'data': '0.27417621537079751493502458474', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '347559643983095765824601190593,2053542071575586173942414175231', 'Lhash_array': ['347559643983095765824601190593', '2053542071575586173942414175231'], 'label': '4-1560e2-1.1-c1e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1560/2/g/c'}