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lfunc_lfunctions • Show schema
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{'Lhash': '1406413031390509537527739492171', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, -3.997181297977813], 'a6': [0, 0], 'a7': [0, 7.747421614388648], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 47.084589681459306, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1728.1567', 'coefficient_field': 'CDF', 'conductor': 1728, 'conductor_radical': 6, 'conjugate': '383067856789086810139638294000', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 3.997181297977813], [-25.0, 0]], [[1.0, 0], [0, -7.747421614388648], [-49.0, 0]], [[1.0, 0], [7.689695758231743, 0], [121.0, 0]], [[1.0, 0], [0, -1.4273839698449935], [-169.0, 0]], [[1.0, 0], [22.31894374800426, 0], [289.0, 0]], [[1.0, 0], [-21.946370142574118, 0], [361.0, 0]], [[1.0, 0], [0, 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'3.33411535201120495182752487766572', '4.41769376757482740190142269420427', '5.17238506218695064463017763901685', '6.45378846783430724973504876312846', '6.92651663517791171334911762346848', '7.67727900089923745901563411118615', '8.478971645240419979061707877663751', '9.479743610352975667477366710808237'], 'prelabel': '2-12e3-8.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.861821163616792, 'root_angle': 0.5833333333333334, 'root_number': '-0.2588190451025207623488988376240483283490689013199305138 + 0.9659258262890682867497431997288973676339048390084045504*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.2916666666666667', 'prec': 60}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.10946425705734464540746263077', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.57479472643802334869460541131', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.33411535201120495182752487767', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 47.084589681459306, 'bad_primes': [2, 3], 'central_character': '8.3', 'conductor': 1728, 'conductor_radical': 6, 'degree': 2, 'index': 43, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1728/3/b/i/1567/4'], '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': '2-12e3-8.3-c2-0-43', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-12e3-8.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.861821163616792, 'root_angle': 0.2916666666666667, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.10946425705734464540746263077', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1406413031390509537527739492171', 'Lhash_array': ['1406413031390509537527739492171'], 'label': '2-12e3-8.3-c2-0-43', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1728/3/b/i/1567/4'}