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lfunc_lfunctions • Show schema
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{'Lhash': '56202558160022585276189732748', 'a10': [0, 0], 'a2': [0, 0], 'a3': [2.707774120942769, -1.2914949902932709], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [-3.000805075852537, 1.7325156183290575], 'a8': [0, 0], 'a9': [5.6640813800947685, -6.9941534240867025], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 24.523223792426723, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-2.707774120942769, 1.2914949902932709]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '900.149', 'coefficient_field': 'CDF', 'conductor': 900, 'conductor_radical': 30, 'conjugate': '2413121998307266007375627204626', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-2.707774120942769, 1.2914949902932709]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.000805075852537, -1.7325156183290575], [24.5, -42.4352447854375]], [[1.0, 0], [12.377008929990819, -7.145869437492601], [60.5, 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'9.567550582725443871791241883887579'], 'prelabel': '2-30e2-45.14-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.9520928699315325, 'root_angle': -0.8579629332015433, 'root_number': '-0.9020837107208173722782030187970333726424862684569067047 - 0.4315610951559010499101779735260837993721101330923978754*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.42898146660077163', 'prec': 67}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.04433600090585198028911897658', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.13120608483178271133744792033', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.95879238743270528555018245862', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 24.523223792426723, 'bad_primes': [2, 3, 5], 'central_character': '45.14', 'conductor': 900, 'conductor_radical': 30, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/900/3/u/d/149/15'], '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': '2-30e2-45.14-c2-0-1', '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': '2-30e2-45.14-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.9520928699315325, 'root_angle': -0.42898146660077163, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.04433600090585198028911897658', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '56202558160022585276189732748', 'Lhash_array': ['56202558160022585276189732748'], 'label': '2-30e2-45.14-c2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/900/3/u/d/149/15'}