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lfunc_lfunctions • Show schema
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{'Lhash': '1922867898227228622417779687443', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.9510565162951535, 0.30901699437494745], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-0.5877852522924731, -0.8090169943749475], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5970080404256077, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.9510565162951535, -0.30901699437494745]]]], 'bad_primes': [2, 5], 'central_character': '3200.2113', 'coefficient_field': 'CDF', 'conductor': 3200, 'conductor_radical': 10, 'conjugate': '1135848630176182650949064184394', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0.5877852522924731, 0.8090169943749475]], [[1.0, 0], [-0.9510565162951535, -0.30901699437494745]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [-0.30901699437494745, -0.9510565162951535]], [[1.0, 0], 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[[1.0, 0], [0, 0], [0.5877852522924731, -0.8090169943749475]], [[1.0, 0], [0, 0], [-0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [-0.2787682579175257, -1.760073510670101], [-0.9510565162951535, 0.30901699437494745]], [[1.0, 0], [0, 0], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0, 0], [-0.5877852522924731, 0.8090169943749475]], [[1.0, 0], [-0.6909830056250525, 0.9510565162951535], [-0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [-1.760073510670101, -0.8968022466674206], [0.5877852522924731, 0.8090169943749475]], [[1.0, 0], [0, -1.1755705045849463], [-1.0, 0]], [[1.0, 0], [0, 0], [-0.5877852522924731, -0.8090169943749475]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [-1.5388417685876268, 1.118033988749895], [0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [1.9510565162951536, 0.30901699437494745], [0.9510565162951535, 0.30901699437494745]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-3200-200.13-c0-0-1', 'leading_term': 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'9.138983840347317819625382775696469'], 'prelabel': '2-3200-200.13-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2637278347910232, 'root_angle': 0.24000000000000002, 'root_number': '0.72896862742141152314673031905556 + 0.68454710592868867373228335762154*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.12', 'prec': 14}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.51687531081595597247784871128', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.23382739782826012951355945531', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.29300853141968039400977298610', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.5970080404256077, 'bad_primes': [2, 5], 'central_character': '200.13', 'conductor': 3200, 'conductor_radical': 10, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3200/1/bz/b/2113/1'], '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': '2-3200-200.13-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3200-200.13-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2637278347910232, 'root_angle': 0.12000000000000001, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.51687531081595597247784871128', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1922867898227228622417779687443', 'Lhash_array': ['1922867898227228622417779687443'], 'label': '2-3200-200.13-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3200/1/bz/b/2113/1'}