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lfunc_lfunctions • Show schema
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{'Lhash': '2090655086015659363653485633784', 'a10': [-155.65999587148517, -94.41954277385521], 'a2': [-3.6411582977033365, -6.306671170023183], 'a3': [4.5654312766090435, 7.756083886766563], 'a4': [-18.51606749786772, 32.07076966268163], 'a5': [21.916064551804883, -12.028554134272392], 'a6': [32.29161266553268, -57.03380301289561], 'a7': [38.45671555702227, -22.202995078995677], 'a8': [153.16266571627767, 0.0], 'a9': [-39.313674517119836, 70.819735921295], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.651648338772996, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-4.5654312766090435, -7.756083886766563]]], [5, [[1.0, 0], [-21.916064551804883, 12.028554134272392]]]], 'bad_primes': [3, 5], 'central_character': '45.14', 'coefficient_field': 'CDF', 'conductor': 45, 'conductor_radical': 15, 'conjugate': '1732130125268980348810380212044', 'degree': 2, 'euler_factors': [[[1.0, 0], [3.6411582977033365, 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'5.45699747194281236165354475353752', '6.77378860080874726817883516765822', '7.56600167115423078721520040763333', '9.016079942362914780117430445403356', '9.715467962296888563964945228649622', '11.84252222489808121079567247242841', '13.71994481301948075912511351301790', '14.54092791222606041706531532026439', '15.01817316919299471980947262910988'], 'prelabel': '2-45-45.14-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.156768030821348, 'root_angle': 0.2229878980862167, 'root_number': '0.168908391227036 + 0.985631754446403*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.222987898086', 'prec': 47}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.64923606365922534483694633676', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.45699747194281236165354475354', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.77378860080874726817883516766', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.651648338772996, 'bad_primes': [3, 5], 'central_character': '45.14', 'conductor': 45, 'conductor_radical': 15, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/45/5/h/a/14/2'], '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': '2-45-45.14-c4-0-8', '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': '2-45-45.14-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.156768030821348, 'root_angle': 0.2229878980862167, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '1.64923606365922534483694633676', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2090655086015659363653485633784', 'Lhash_array': ['2090655086015659363653485633784'], 'factors': ['2-45-45.14-c4-0-8'], 'label': '2-45-45.14-c4-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/45/5/h/a/14/2'}