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lfunc_lfunctions • Show schema
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{'Lhash': '2077906100796583383213889406502', 'a10': 1, 'a2': -1, 'a3': 0, 'a4': 1, 'a5': -1, 'a6': 0, 'a7': 0, 'a8': -1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.34249703648981, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [5, [1, 1]], [13, [1, -1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1170.1', 'coefficient_field': '1.1.1.1', 'conductor': 1170, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[1, 1], [1], [1, 1], [1, 0, 7], [1, 4, 11], [1, -1], [1, -6, 17], [1, -4, 19], [1, 8, 23], [1, 6, 29], [1, 8, 31], [1, 10, 37], [1, -6, 41], [1, -4, 43], [1, 0, 47], [1, -10, 53], [1, 4, 59], [1, 2, 61], [1, 12, 67], [1, 16, 71], [1, -2, 73], [1, 16, 79], [1, -12, 83], [1, 10, 89], [1, 6, 97], [1, -2, 101], [1, 0, 103], [1, -12, 107], [1, 10, 109], [1, 10, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [1], [[[1, 1], 1]], [[[1, 0, 7], 1]], [[[1, 4, 11], 1]], [[[1, -1], 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-2.5065870695572388, -2.0940276943917207, -1.5476544831526107, -0.9023832610755325, -0.1980226563370513, 0.5231764311057289, 1.2190918425544932, 1.8502608943054268, 2.3822127734646634, 2.787457367039186], 'positive_zeros': ['1.63917888763865576740316873481351', '2.98523621593750721047361308357267', '3.89256533853822824063870308537486', '5.36101206913072414201885147070427', '5.88475078175345459986396322171542', '7.45586944398122020573570806181719', '7.54788789198252757941968322284204', '8.490403204098803911613209618504124', '9.402437326353945088461831893247644'], 'prelabel': '2-1170-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.0565498583353437, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 432767590300769702, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.63917888763865576740316873481', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.98523621593750721047361308357', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.89256533853822824063870308537', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.34249703648981, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 1170, 'conductor_radical': 390, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, -1, 0, 0, -1, 0, 1, -4, 0, 1, 0, 0, 1, 6, 0, 4, -1, 0, 4, -8, 0, 1, -1, 0, 0, -6, 0, -8, -1, 0, -6, 0, 0, -10, -4, 0, 1, 6, 0, 4, -4, 0, 8, 0, 0, -7, -1, 0, 1, 10, 0, 4, 0, 0, 6, -4, 0, -2, 8, 0, 1, -1, 0, -12, 6, 0, 0, -16, 0, 2, 10, 0, 4, 0, 0, -16, -1, 0, -6, 12, 0, -6, -4, 0, 4, -10, 0, 0, -8, 0, 0, -4, 0, -6, 7, 0, 1], 'euler11': [1, 4, 11], 'euler13': [1, -1, 0], 'euler17': [1, -6, 17], 'euler19': [1, -4, 19], 'euler2': [1, 1, 0], 'euler23': [1, 8, 23], 'euler29': [1, 6, 29], 'euler3': [1, 0, 0], 'euler31': [1, 8, 31], 'euler37': [1, 10, 37], 'euler41': [1, -6, 41], 'euler43': [1, -4, 43], 'euler47': [1, 0, 47], 'euler5': [1, 1, 0], 'euler53': [1, -10, 53], 'euler59': [1, 4, 59], 'euler61': [1, 2, 61], 'euler67': [1, 12, 67], 'euler7': [1, 0, 7], 'euler71': [1, 16, 71], 'euler73': [1, -2, 73], 'euler79': [1, 16, 79], 'euler83': [1, -12, 83], 'euler89': [1, 10, 89], 'euler97': [1, 6, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, 1, 0], [1, 0, 7], [1, 4, 11], [1, -1, 0], [1, -6, 17], [1, -4, 19], [1, 8, 23], [1, 6, 29], [1, 8, 31], [1, 10, 37], [1, -6, 41], [1, -4, 43], [1, 0, 47], [1, -10, 53], [1, 4, 59], [1, 2, 61], [1, 12, 67], [1, 16, 71], [1, -2, 73], [1, 16, 79], [1, -12, 83], [1, 10, 89], [1, 6, 97]], 'index': 13, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1170/a', 'ModularForm/GL2/Q/holomorphic/1170/2/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/1170/2/a/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-1170-1.1-c1-0-13', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-1170-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.0565498583353437, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 432767590300769702, 'z1': {'__RealLiteral__': 0, 'data': '1.63917888763865576740316873481', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20607858
{'Lhash': '2077906100796583383213889406502', 'Lhash_array': ['2077906100796583383213889406502'], 'label': '2-1170-1.1-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1170/2/a/a'}
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id: 24552056
{'Lhash': '2077906100796583383213889406502', 'Lhash_array': ['2077906100796583383213889406502'], 'label': '2-1170-1.1-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1170/2/a/a/1/1'}
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id: 99902
{'Lhash': '432767590300769702', 'Lhash_array': ['432767590300769702'], 'label': '2-1170-1.1-c1-0-13', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1170/a'}