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lfunc_lfunctions • Show schema
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{'Lhash': '4663494867405781313070587947231', 'a10': [0.0, 0.0], 'a2': [0.30901699437494745, -0.9510565162951535], 'a3': [-0.5, 0.36327126400268045], 'a4': [-0.8090169943749475, -0.5877852522924731], 'a5': [0.0, 0.0], 'a6': [0.19098300562505258, 0.5877852522924731], 'a7': [0.0, 0.0], 'a8': [-0.8090169943749475, 0.5877852522924731], 'a9': [-0.19098300562505258, 0.5877852522924731], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.043917721111704215, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.30901699437494745, 0.9510565162951535]]], [11, [[1.0, 0], [0.8090169943749475, -0.5877852522924731]]]], 'bad_primes': [2, 11], 'central_character': '88.75', 'coefficient_field': 'CDF', 'conductor': 88, 'conductor_radical': 22, 'conjugate': '3407342318603762758786273345022', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0.5, -0.36327126400268045], [0.30901699437494745, 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[0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0, 0], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [1.618033988749895, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0.5, 0.36327126400268045], [0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0, 0], [0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [-0.19098300562505258, -0.5877852522924731], [-0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [-0.6180339887498949, 0], [1.0, 0]], [[1.0, 0], [-0.19098300562505258, 0.5877852522924731], [-0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0, 0], [0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0, 0], [-0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0.5, -0.36327126400268045], [0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.3090169943749475, 0.9510565162951535], [0.30901699437494745, -0.9510565162951535]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-88-88.75-c0-0-0', 'leading_term': '0.50206178440910868707292439028519', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/88/1/l/a/75/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0859375', 'prec': 30}, 'plot_values': [0.5020617844091086, 0.5181688823750007, 0.550420283939203, 0.598127594868604, 0.6600941397791104, 0.7350259903267189, 0.8217685055339232, 0.9193713428272019, 1.0270535766524087, 1.144130771914361, 1.2699377572070945, 1.4037606141434325, 1.5447813067058118, 1.692034488595816, 1.844375038645771, 2.000454994821323, 2.1587089879770978, 2.317347707997781, 2.474359267506467, 2.6275185428407757, 2.7744046763797323, 2.912426933041712, 3.038859031157735, 3.1508819264716523, 3.2456348287098753, 3.3202739831775934, 3.372038465300447, 3.398321924608135, 3.3967488879677097, 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'12.63529772308978450025900787089363', '13.57082369504535396098154693606630', '14.63897058595544622008336749037993'], 'prelabel': '2-88-88.75-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.20956555325650306, 'root_angle': 0.2854342601392135, 'root_number': '0.62417735821399263386961876627007 + 0.78128267963202737461068725062413*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1427171300696068', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.67884878259526706903463378333', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.50038095571044670886224694877', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.29990722230209404329316790795', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.043917721111704215, 'bad_primes': [2, 11], 'central_character': '88.75', 'conductor': 88, 'conductor_radical': 22, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/88/1/l/a/75/1'], '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': '2-88-88.75-c0-0-0', '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': '2-88-88.75-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.20956555325650306, 'root_angle': 0.14271713006960676, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.67884878259526706903463378333', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4663494867405781313070587947231', 'Lhash_array': ['4663494867405781313070587947231'], 'label': '2-88-88.75-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/88/1/l/a/75/1'}