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lfunc_lfunctions • Show schema
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{'Lhash': '2325871443430586908192945549498', 'a10': [100.36753236814714, 0.0], 'a2': [0.0, 2.8284271247461903], 'a3': [0.0, 0.0], 'a4': [-8.0, 0.0], 'a5': [0.0, -35.48528137423857], 'a6': [0.0, 0.0], 'a7': [93.36753236814714, 0.0], 'a8': [0.0, -22.627416997969522], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.581978006527596, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -2.8284271247461903]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '54.53', 'coefficient_field': 'CDF', 'conductor': 54, 'conductor_radical': 6, 'conjugate': '1606389178495252299210847948092', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -2.8284271247461903]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 35.48528137423857], [-625.0, 0]], [[1.0, 0], [-93.36753236814714, 0], [2401.0, 0]], [[1.0, 0], [0, -57.852813742385706], [-14641.0, 0]], [[1.0, 0], [-22.735064736294266, 0], [28561.0, 0]], [[1.0, 0], [0, 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'positive_zeros': ['1.83478905229235413994641605801769', '3.62626130915886602052590877592291', '5.45570448561220037766443098899482', '7.36932935266496174644784991866936', '8.566307815326426324135323642326085', '10.38691995029766219840567698987068', '11.07596304458746757732372054211450', '11.89348098963337437727930009954035', '13.71592863094937237798549765784233', '14.44916877926601649076243812924154'], 'prelabel': '2-54-3.2-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3626210035737, 'root_angle': -6.484500163930735e-64, 'root_number': '1.0 - 2.0371658077206606e-63*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.000000000000000000000000000000000000000000000000000000000000000324225008197', 'prec': 260}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.83478905229235413994641605802', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.62626130915886602052590877592', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.45570448561220037766443098899', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.581978006527596, 'bad_primes': [2, 3], 'central_character': '3.2', 'conductor': 54, 'conductor_radical': 6, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/54/5/b/b/53/3'], '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': '2-54-3.2-c4-0-3', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-54-3.2-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3626210035737, 'root_angle': -3.242250081965368e-64, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '1.83478905229235413994641605802', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2325871443430586908192945549498', 'Lhash_array': ['2325871443430586908192945549498'], 'label': '2-54-3.2-c4-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/54/5/b/b/53/3'}