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lfunc_lfunctions • Show schema
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{'Lhash': '1323741983535830071277799256912', 'a10': [-1.2935617555058703, 0], 'a2': [0.12935617555058704, 0.22405146832641573], 'a3': [0, 0], 'a4': [3.9665339596938516, -6.870238348137112], 'a5': [-2.5, 4.330127018922194], 'a6': [0, 0], 'a7': [-7.258712351101174, -12.572458589634973], 'a8': [4.1220814616794845, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.89577355232496, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [2.5, -4.330127018922194]]]], 'bad_primes': [3, 5], 'central_character': '405.271', 'coefficient_field': 'CDF', 'conductor': 405, 'conductor_radical': 15, 'conjugate': '1218215756462850499716079853949', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.12935617555058704, -0.22405146832641573], [-4.0, 6.928203230275509]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.5, -4.330127018922194]], [[1.0, 0], [7.258712351101174, 12.572458589634973], [-171.5, 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[[1.0, 0], [-27.272871630875795, -47.23799933298074], [-113490.5, 196571.31217639567]], [[1.0, 0], [-38.02788437449705, 65.8662278409835], [-150381.5, -260468.39851841913]], [[1.0, 0], [-728.3030361667726, 0], [357911.0, 0]], [[1.0, 0], [501.8151445051068, 0], [389017.0, 0]], [[1.0, 0], [198.80484576082034, 344.340093648635], [-246519.5, 426984.29905647587]], [[1.0, 0], [-684.7306670485958, -1185.9883048286965], [-285893.5, 495182.06755369285]], [[1.0, 0], [-1468.1304378107886, 0], [704969.0, 0]], [[1.0, 0], [167.51167415328206, 290.13873049440684], [-456336.5, 790398.003348155]], [[1.0, 0], [-603.0430531701662, -1044.5012072421878], [-515150.5, 892266.8395445109]], [[1.0, 0], [530.5547273234482, -918.947743920064], [-546363.5, -946329.3414011582]], [[1.0, 0], [475.57807563001234, 0], [1225043.0, 0]], [[1.0, 0], [-1320.4182809270255, 0], [1295029.0, 0]], [[1.0, 0], [-34.087513658979326, 59.04130556105028], [-721448.5, -1249585.457044355]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 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'7.963945637464063248608317251328874', '9.013024793919455504614288329740524', '9.884354676366408203953961538915101', '11.15432951299846003576869340596346'], 'prelabel': '2-405-9.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.8883303440259604, 'root_angle': 0.1111111111111111, 'root_number': '0.93969262078590838405410927732473146993620813426446463309 + 0.3420201433256687330440996146822595807630833675141606285*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.05555555555555555', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.04424829941113261563497570213', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.04438348941421696905258326635', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.39375058236226087965472242223', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 23.89577355232496, 'bad_primes': [3, 5], 'central_character': '9.4', 'conductor': 405, 'conductor_radical': 15, 'degree': 2, 'index': 24, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/405/4/e/t/271/2'], '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': '2-405-9.4-c3-0-24', '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': '2-405-9.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.8883303440259604, 'root_angle': 0.05555555555555555, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.04424829941113261563497570213', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1323741983535830071277799256912', 'Lhash_array': ['1323741983535830071277799256912'], 'label': '2-405-9.4-c3-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/405/4/e/t/271/2'}