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lfunc_lfunctions • Show schema
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{'Lhash': '1467986029688545458280232481073,1938442531124885939161750135215', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 2, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': -4, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2419.4443559584297, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, -2, 1]], [7, [1, 2, 1]], [11, [1, -2, 1]]], 'bad_primes': [2, 5, 7, 11], 'central_character': '6160.1', 'coefficient_field': '1.1.1.1', 'conductor': 37945600, 'conductor_radical': 770, 'degree': 4, 'euler_factors': [[1], [1, 0, 4, 0, 9], [1, -2, 1], [1, 2, 1], [1, -2, 1], [1, 4, 28, 52, 169], [1, 4, 20, 68, 289], [1, 0, 6, 0, 361], [1, -4, 50, -92, 529], [1, 12, 86, 348, 841], [1, -12, 96, -372, 961], [1, 0, 66, 0, 1369], [1, 0, 64, 0, 1681], [1, -4, 90, -172, 1849], [1, -8, 92, -376, 2209], [1, -8, 50, -424, 2809], [1, 12, 152, 708, 3481], [1, 16, 168, 976, 3721], [1, -4, 10, -268, 4489], [1, 8, 86, 568, 5041], [1, 12, 164, 876, 5329], [1, 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'1.52916152982208687347970503710602', '2.35087845947482301143616888193669', '2.52275961003715365304911276551368', '2.97704764759380362073760594718095', '3.13014187461231133808357420609046', '3.97639587985772572970906002800059', '4.17582616753130764743716611404508', '4.71453486660785567636391838403577', '4.96477846896915680601718248084677', '5.64250746522713364796212185125407', '5.71873819111444741285944103848994', '6.20664932831447427557819146354625', '6.20998939761085791182204724002454', '6.88411464538576420339306210799284', '7.15358351546254101976085321243716', '7.49327368956507461160020217529780', '7.68688458720070061845835381524370'], 'prelabel': '4-6160e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.013404853928564, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 1055809087799979864, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.15803678823190508109324474005', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.52916152982208687347970503711', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.35087845947482301143616888194', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2419.4443559584297, 'bad_primes': [2, 5, 7, 11], 'central_character': '1.1', 'conductor': 37945600, 'conductor_radical': 770, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 2, 0, -2, 0, -4, 0, 2, 0, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, 0, 3, 0, 0, 0, -12, 0, 12, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, -8, 0, 8, 0, 3, 0, 0, 0, 8, 0, 4, 0, 0, 0, -12, 0, -16, 0, 8, 0, -8, 0, 4, 0, 0, 0, -8, 0, -12, 0, 0, 0, -4, 0, -20, 0, 7, 0, -24, 0, -8, 0, 0, 0, -12, 0, 8, 0, 0, 0, 0, 0, 4, 0, -8, 0], 'euler11': [1, -2, 1, 0, 0], 'euler13': [1, 4, 28, 52, 169], 'euler17': [1, 4, 20, 68, 289], 'euler19': [1, 0, 6, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -4, 50, -92, 529], 'euler29': [1, 12, 86, 348, 841], 'euler3': [1, 0, 4, 0, 9], 'euler31': [1, -12, 96, -372, 961], 'euler37': [1, 0, 66, 0, 1369], 'euler41': [1, 0, 64, 0, 1681], 'euler43': [1, -4, 90, -172, 1849], 'euler47': [1, -8, 92, -376, 2209], 'euler5': [1, -2, 1, 0, 0], 'euler53': [1, -8, 50, -424, 2809], 'euler59': [1, 12, 152, 708, 3481], 'euler61': [1, 16, 168, 976, 3721], 'euler67': [1, -4, 10, -268, 4489], 'euler7': [1, 2, 1, 0, 0], 'euler71': [1, 8, 86, 568, 5041], 'euler73': [1, 12, 164, 876, 5329], 'euler79': [1, 20, 250, 1580, 6241], 'euler83': [1, 24, 278, 1992, 6889], 'euler89': [1, 12, 206, 1068, 7921], 'euler97': [1, -4, 70, -388, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 4, 0, 9], [1, -2, 1, 0, 0], [1, 2, 1, 0, 0], [1, -2, 1, 0, 0], [1, 4, 28, 52, 169], [1, 4, 20, 68, 289], [1, 0, 6, 0, 361], [1, -4, 50, -92, 529], [1, 12, 86, 348, 841], [1, -12, 96, -372, 961], [1, 0, 66, 0, 1369], [1, 0, 64, 0, 1681], [1, -4, 90, -172, 1849], [1, -8, 92, -376, 2209], [1, -8, 50, -424, 2809], [1, 12, 152, 708, 3481], [1, 16, 168, 976, 3721], [1, -4, 10, -268, 4489], [1, 8, 86, 568, 5041], [1, 12, 164, 876, 5329], [1, 20, 250, 1580, 6241], [1, 24, 278, 1992, 6889], [1, 12, 206, 1068, 7921], [1, -4, 70, -388, 9409]], 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6160/2/a/bb'], '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': '4-6160e2-1.1-c1e2-0-10', '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': 2, 'prelabel': '4-6160e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.013404853928564, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1055809087799979864, 'z1': {'__RealLiteral__': 0, 'data': '1.15803678823190508109324474005', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1467986029688545458280232481073,1938442531124885939161750135215', 'Lhash_array': ['1467986029688545458280232481073', '1938442531124885939161750135215'], 'label': '4-6160e2-1.1-c1e2-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6160/2/a/bb'}