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lfunc_lfunctions • Show schema
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{'Lhash': '751575487342801293893861950096', 'a10': [-20108.665466488364, -56871.48399472366], 'a2': [30.52070402797, 30.52070402797], 'a3': [-129.27580887530127, -54.50472676416773], 'a4': [0.0, 1351.0267487258886], 'a5': [-1261.1135934260449, -602.260329488875], 'a6': [-2282.0660669649487, -5609.1113343540255], 'a7': [-2749.1635945569883, 2749.1635945569883], 'a8': [-25607.6870694128, 25607.6870694128], 'a9': [13741.469520726836, 14092.285279930129], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.725537542458099, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [129.27580887530127, 54.50472676416773]]], [5, [[1.0, 0], [1261.1135934260449, 602.260329488875]]]], 'bad_primes': [3, 5], 'central_character': '15.8', 'coefficient_field': 'CDF', 'conductor': 15, 'conductor_radical': 15, 'conjugate': '5043093595796711439079681220530', 'degree': 2, 'euler_factors': [[[1.0, 0], [-30.52070402797, -30.52070402797], [0, 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'12.05606404050965148992132102443215', '13.27400505055870406278268423499829', '14.94023815380526191066468351300981', '15.97340045639437394292169053924041'], 'prelabel': '2-15-15.8-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.77948512182708, 'root_angle': 0.9450328623421059, 'root_number': '-0.9851270708810634 + 0.1718273965853416*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.472516431171', 'prec': 47}, 'spectral_label': 'c9-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.59288851928716532929711517672', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.34299702250280626020430318322', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.62278214533908473450070609028', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.725537542458099, 'bad_primes': [3, 5], 'central_character': '15.8', 'conductor': 15, 'conductor_radical': 15, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/15/10/e/a/8/16'], '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': '2-15-15.8-c9-0-2', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 0, 'prelabel': '2-15-15.8-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.77948512182708, 'root_angle': 0.47251643117105296, 'self_dual': False, 'spectral_label': 'c9-0', 'z1': {'__RealLiteral__': 0, 'data': '0.59288851928716532929711517672', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '751575487342801293893861950096', 'Lhash_array': ['751575487342801293893861950096'], 'label': '2-15-15.8-c9-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/15/10/e/a/8/16'}