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lfunc_lfunctions • Show schema
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{'Lhash': '742551425518619952856835018513', 'a10': [0, 0], 'a2': [0, 0], 'a3': [4.5, -7.794228634059948], 'a4': [0, 0], 'a5': [-47.9558265337491, 0], 'a6': [0, 0], 'a7': [5.030656828406709, 8.713353222243727], 'a8': [0, 0], 'a9': [-40.5, -70.14805770653953], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 50.03975178164997, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-4.5, 7.794228634059948]]], [13, [[1.0, 0], [469.8554410527071, 387.980495016394]]]], 'bad_primes': [2, 3, 13], 'central_character': '312.217', 'coefficient_field': 'CDF', 'conductor': 312, 'conductor_radical': 78, 'conjugate': '1011261065696316677487006270439', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-4.5, 7.794228634059948]], [[1.0, 0], [47.9558265337491, 0], [3125.0, 0]], [[1.0, 0], [-5.030656828406709, -8.713353222243727], [-8403.5, 14555.28896140506]], [[1.0, 0], [90.61286962950025, 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 11, 'label': '2-312-13.9-c5-0-11', 'leading_term': '1.582979365425016506540997278163614111533758856286773086', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/312/6/q/d/217/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.5829793654250166, 1.5249699663644307, 1.436889658927139, 1.319580018328465, 1.1742839275663106, 1.0026346505313353, 0.8066410245291128, 0.5886686852527803, 0.35141723058333935, 0.09789323519063624, -0.16862095258447177, -0.44460266551571737, -0.7263286076648134, -1.0099186977750643, -1.2913839027900877, -1.5666778036810178, -1.8317515291157673, -2.0826115763877717, -2.3153799164579048, -2.5263556544723773, -2.7120773926531965, -2.869385323313679, -2.995481970473271, -3.0879904038102852, 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'5.72053615347670042434958071153367', '7.29448362414430680282520231741914', '7.83668837310345823203649605857361', '9.043500260982270720999992663075099', '9.805236114250800409124262491054023', '10.84587599171577309739312446776992'], 'prelabel': '2-312-13.9-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.073878128837814, 'root_angle': -0.014123969477199887, 'root_number': '0.99606487762740691474857371040422774134490571550198411507 - 0.0886270813978373535291706487779970986038603267667409173*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.014123969477199887', 'prec': 70}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.58576978970777126152662309811', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.48839495288858035313496001491', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.64874954927995205133373053206', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 50.03975178164997, 'bad_primes': [2, 3, 13], 'central_character': '13.9', 'conductor': 312, 'conductor_radical': 78, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/312/6/q/d/217/4'], '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': '2-312-13.9-c5-0-11', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-312-13.9-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.073878128837814, 'root_angle': -0.014123969477199887, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.58576978970777126152662309811', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '742551425518619952856835018513', 'Lhash_array': ['742551425518619952856835018513'], 'factors': ['2-312-13.9-c5-0-11'], 'label': '2-312-13.9-c5-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/312/6/q/d/217/4'}