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lfunc_lfunctions • Show schema
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{'Lhash': '701055495873832500416343786079', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, 2.0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 53.10171900516658, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '900.649', 'coefficient_field': 'CDF', 'conductor': 900, 'conductor_radical': 30, 'conjugate': '1378620142146824686522960013944', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -2.0], [-343.0, 0]], [[1.0, 0], [-30.0, 0], [1331.0, 0]], [[1.0, 0], [0, -4.0], [-2197.0, 0]], [[1.0, 0], [0, -90.0], [-4913.0, 0]], [[1.0, 0], [-28.0, 0], [6859.0, 0]], [[1.0, 0], [0, 120.0], [-12167.0, 0]], [[1.0, 0], [210.0, 0], [24389.0, 0]], [[1.0, 0], [4.0, 0], [29791.0, 0]], [[1.0, 0], [0, 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'root_analytic_conductor': 7.287092630477987, 'root_angle': -0.35241638234956674, 'root_number': '0.4472135954999579392818347337462552470881236719223051449 - 0.8944271909999158785636694674925104941762473438446102897*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.17620819117478337', 'prec': 67}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.55303527308519681293374018256', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.85831384695908548445332944375', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.18367518960115744679590450596', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 53.10171900516658, 'bad_primes': [2, 3, 5], 'central_character': '5.4', 'conductor': 900, 'conductor_radical': 30, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/900/4/d/i/649/2'], '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': '2-30e2-5.4-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': '2-30e2-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.287092630477987, 'root_angle': -0.17620819117478337, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.55303527308519681293374018256', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '701055495873832500416343786079', 'Lhash_array': ['701055495873832500416343786079'], 'label': '2-30e2-5.4-c3-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/900/4/d/i/649/2'}