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lfunc_lfunctions • Show schema
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{'Lhash': '2618200447069276018352548977713,4563599033841929871113950556426', 'a10': 1, 'a2': 1, 'a3': -1, 'a4': 0, 'a5': 1, 'a6': -1, 'a7': -1, 'a8': -1, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.3124282484450452, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1, 1]], [5, [1, -1, 1]], [7, [1, 1, 7]]], 'bad_primes': [2, 5, 7], 'central_character': '70.1', 'coefficient_field': '1.1.1.1', 'conductor': 4900, 'conductor_radical': 70, 'degree': 4, 'euler_factors': [[1, -1, 1], [1, 1, -2, 3, 9], [1, -1, 1], [1, 1, 7], [1, -6, 25, -66, 121], [1, 8, 42, 104, 169], [1, 0, -17, 0, 289], [1, 2, -15, 38, 361], [1, -3, -14, -69, 529], [1, 6, 67, 174, 841], [1, 8, 33, 248, 961], [1, -4, -21, -148, 1369], [1, -18, 163, -738, 1681], [1, 14, 135, 602, 1849], [1, 0, -47, 0, 2209], [1, -6, -17, -318, 2809], [1, -6, -23, -354, 3481], [1, 5, -36, 305, 3721], [1, 5, -42, 335, 4489], [1, 12, 178, 852, 5041], [1, -16, 183, 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'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 2214329742827592728, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.06539597472512688526896396217', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.60004486490227968671810948230', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.36637257403942965751068337280', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.3124282484450452, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 4900, 'conductor_radical': 70, 'degree': 4, 'dirichlet_coefficients': [1, 1, -1, 0, 1, -1, -1, -1, 3, 1, 6, 0, -8, -1, -1, -1, 0, 3, -2, 0, 1, 6, 3, 1, 0, -8, -8, 0, -6, -1, -8, 0, -6, 0, -1, 0, 4, -2, 8, -1, 18, 1, -14, 0, 3, 3, 0, 1, -6, 0, 0, 0, 6, -8, 6, 1, 2, -6, 6, 0, -5, -8, -3, 1, -8, -6, -5, 0, -3, -1, -12, -3, 16, 4, 0, 0, -6, 8, -2, -1, 8, 18, 6, 0, 0, -14, 6, -6, 15, 3, 8, 0, 8, 0, -2, 0, 28, -6, 18, 0], 'euler11': [1, -6, 25, -66, 121], 'euler13': [1, 8, 42, 104, 169], 'euler17': [1, 0, -17, 0, 289], 'euler19': [1, 2, -15, 38, 361], 'euler2': [1, -1, 1, 0, 0], 'euler23': [1, -3, -14, -69, 529], 'euler29': [1, 6, 67, 174, 841], 'euler3': [1, 1, -2, 3, 9], 'euler31': [1, 8, 33, 248, 961], 'euler37': [1, -4, -21, -148, 1369], 'euler41': [1, -18, 163, -738, 1681], 'euler43': [1, 14, 135, 602, 1849], 'euler47': [1, 0, -47, 0, 2209], 'euler5': [1, -1, 1, 0, 0], 'euler53': [1, -6, -17, -318, 2809], 'euler59': [1, -6, -23, -354, 3481], 'euler61': [1, 5, -36, 305, 3721], 'euler67': [1, 5, -42, 335, 4489], 'euler7': [1, 1, 7, 0, 0], 'euler71': [1, 12, 178, 852, 5041], 'euler73': [1, -16, 183, -1168, 5329], 'euler79': [1, 2, -75, 158, 6241], 'euler83': [1, -6, 175, -498, 6889], 'euler89': [1, -15, 136, -1335, 7921], 'euler97': [1, -28, 390, -2716, 9409], 'euler_factors': [[1, -1, 1, 0, 0], [1, 1, -2, 3, 9], [1, -1, 1, 0, 0], [1, 1, 7, 0, 0], [1, -6, 25, -66, 121], [1, 8, 42, 104, 169], [1, 0, -17, 0, 289], [1, 2, -15, 38, 361], [1, -3, -14, -69, 529], [1, 6, 67, 174, 841], [1, 8, 33, 248, 961], [1, -4, -21, -148, 1369], [1, -18, 163, -738, 1681], [1, 14, 135, 602, 1849], [1, 0, -47, 0, 2209], [1, -6, -17, -318, 2809], [1, -6, -23, -354, 3481], [1, 5, -36, 305, 3721], [1, 5, -42, 335, 4489], [1, 12, 178, 852, 5041], [1, -16, 183, -1168, 5329], [1, 2, -75, 158, 6241], [1, -6, 175, -498, 6889], [1, -15, 136, -1335, 7921], [1, -28, 390, -2716, 9409]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/70/2/e/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': '4-70e2-1.1-c1e2-0-2', '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': '4-70e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.7476314694747426, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2214329742827592728, 'z1': {'__RealLiteral__': 0, 'data': '2.06539597472512688526896396217', 'prec': 103}}
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{'Lhash': '2618200447069276018352548977713,4563599033841929871113950556426', 'Lhash_array': ['2618200447069276018352548977713', '4563599033841929871113950556426'], 'label': '4-70e2-1.1-c1e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/70/2/e/c'}