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lfunc_lfunctions • Show schema
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{'Lhash': '586731898811309801346374897563', 'a10': [5297.892130962235, 0], 'a2': [-25.808046857463136, 14.900282800414818], 'a3': [0, 0], 'a4': [316.0368550646753, -547.3918900362991], 'a5': [-153.96047287757645, -88.88912046043085], 'a6': [0, 0], 'a7': [-1695.4072080567464, -2936.5314238727833], 'a8': [0, 11207.2092694571], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.997667414951316, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '81.53', 'coefficient_field': 'CDF', 'conductor': 81, 'conductor_radical': 3, 'conjugate': '484200008073345899939038727904', 'degree': 2, 'euler_factors': [[[1.0, 0], [25.808046857463136, -14.900282800414818], [128.0, -221.70250336881628]], [[1.0, 0], [0, 0]], [[1.0, 0], [153.96047287757645, 88.88912046043085], [195312.5, 338291.17335329636]], [[1.0, 0], [1695.4072080567464, 2936.5314238727833], [-2882400.5, 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'2.49199800729044545302689965462149', '3.05603150160676022861650781337233', '5.67785593362325059994310975805106', '7.49067035476941408301655170841257', '8.329489159953913335754830096217372', '9.388303540837289385709951903729646', '10.33420292142943438558509603552910', '11.23350243781549141664544531821332', '12.39876019507074165775304164106677'], 'prelabel': '2-3e4-9.5-c8-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.744359617481423, 'root_angle': -0.06944444444444445, 'root_number': '0.9063077870366499 - 0.42261826174069944*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.06944444444444445', 'prec': 67}, 'spectral_label': 'c8-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.46284985681833295037441073667381', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.49199800729044545302689965462149', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.05603150160676022861650781337233', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.997667414951316, 'bad_primes': [3], 'central_character': '9.5', 'conductor': 81, 'conductor_radical': 3, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/81/9/d/g/53/1'], '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': '2-3e4-9.5-c8-0-7', 'motivic_weight': 8, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [8], 'order_of_vanishing': 0, 'prelabel': '2-3e4-9.5-c8-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.744359617481423, 'root_angle': -0.06944444444444445, 'self_dual': False, 'spectral_label': 'c8-0', 'z1': {'__RealLiteral__': 0, 'data': '0.46284985681833295037441073667381', 'prec': 113}}
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lfunc_instances • Show schema
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{'Lhash': '586731898811309801346374897563', 'Lhash_array': ['586731898811309801346374897563'], 'factors': ['2-3e4-9.5-c8-0-7'], 'label': '2-3e4-9.5-c8-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/81/9/d/g/53/1'}