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lfunc_lfunctions • Show schema
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{'Lhash': '3180160150867017752899836500601', 'a10': [0.7659880454414725, 0.0], 'a2': [0.0, 0.22131843082877123], 'a3': [1.1109497623803994, -1.3288305480635723], 'a4': [1.9510181521754903, 0.0], 'a5': [0.0, -3.4610223946242376], 'a6': [0.2940946917347659, 0.24587365813962628], 'a7': [0.0, 4.183557582228996], 'a8': [0.0, 0.8744331376154708], 'a9': [-0.5315812509338679, -2.952527963230083], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.892454527904346, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.1109497623803994, 1.3288305480635723]]], [79, [[1.0, 0], [-0.4468383159957164, 8.876955306824414]]]], 'bad_primes': [3, 79], 'central_character': '237.236', 'coefficient_field': 'CDF', 'conductor': 237, 'conductor_radical': 237, 'conjugate': '2206131181649568813783649460663', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -0.22131843082877123], [-2.0, 0]], [[1.0, 0], [-1.1109497623803994, 1.3288305480635723]], 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5.213868056258947], 'positive_zeros': ['2.50870401536074509564518608103754', '3.32519331799289595911085718339886', '4.62184312722732578725602480181278', '6.65628107394341635281304399302819', '7.10835914922670913190742528735979', '8.131899444611225691112555284212275', '9.960946034519642216738488257110595', '10.34793365691066612007597405738407', '10.94740930750243884313146274020022', '11.93384985568938203508327103842096'], 'prelabel': '2-237-237.236-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3756651220062046, 'root_angle': 0.23765825561937948, 'root_number': '0.7339849361426218 + 0.6791657481909047*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.11882912781', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.50870401536074509564518608104', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.32519331799289595911085718340', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.62184312722732578725602480181', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.892454527904346, 'bad_primes': [3, 79], 'central_character': '237.236', 'conductor': 237, 'conductor_radical': 237, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/237/2/b/a/236/14'], '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': '2-237-237.236-c1-0-20', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-237-237.236-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3756651220062046, 'root_angle': 0.11882912780968974, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.50870401536074509564518608104', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3180160150867017752899836500601', 'Lhash_array': ['3180160150867017752899836500601'], 'label': '2-237-237.236-c1-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/237/2/b/a/236/14'}