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lfunc_lfunctions • Show schema
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{'Lhash': '2840735429518832853686853285805', 'a10': [18.742825970825766, 2.562159445785959e-60], 'a2': [-1.8742825970825765, 3.2463526858891694], 'a3': [-4.057239731494822, -3.2463526858891694], 'a4': [-3.0258705074532157, -5.24096145603319], 'a5': [-2.5, -4.330127018922194], 'a6': [18.143219582112554, -7.086648756480118], 'a7': [15.67458880615416, -27.149184200009397], 'a8': [-7.303175820741278, 0.0], 'a9': [5.922388477640354, 26.342462199268937], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.655085950258329, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [4.057239731494822, 3.2463526858891694]]], [5, [[1.0, 0], [2.5, 4.330127018922194]]]], 'bad_primes': [3, 5], 'central_character': '45.16', 'coefficient_field': 'CDF', 'conductor': 45, 'conductor_radical': 15, 'conjugate': '759293459206793920825308766544', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.8742825970825765, -3.2463526858891694], [-4.0, 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'8.723883964749828005219153453434472', '9.630931514163198316417603448056750', '10.97623768218919830589676682747261', '11.67233495560359753251896719279230', '12.38509043940459619458740043904410', '14.79585893286629569408204543185083', '15.35764160361634160069584554715846'], 'prelabel': '2-45-9.7-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6294434480086533, 'root_angle': 0.3184959753708082, 'root_number': '0.5398102758078186 + 0.8417867105937743*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.159247987685', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.24094512242362626547816312287', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.56382228414181258301496955753', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.36374215188516684101746101515', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.655085950258329, 'bad_primes': [3, 5], 'central_character': '9.7', 'conductor': 45, 'conductor_radical': 15, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/45/4/e/b/16/1'], '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': '2-45-9.7-c3-0-6', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-45-9.7-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6294434480086533, 'root_angle': 0.1592479876854041, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.24094512242362626547816312287', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2840735429518832853686853285805', 'Lhash_array': ['2840735429518832853686853285805'], 'label': '2-45-9.7-c3-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/45/4/e/b/16/1'}