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lfunc_lfunctions • Show schema
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{'Lhash': '180371314056972631519778278513', 'a10': [0.0, 0.0], 'a2': [0.23699501130794828, -0.41048740072572704], 'a3': [-2.4531555920413597, -4.580614330112961], 'a4': [3.887666729230291, 6.733636297921981], 'a5': [0.0, 0.0], 'a6': [-2.461670107371085, -0.07859328240963127], 'a7': [-4.103285422697085, 7.107098830068088], 'a8': [7.477350662749041, 0.0], 'a9': [-14.964055282472412, 22.473919317802793], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.275429751291645, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [2.4531555920413597, 4.580614330112961]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '225.151', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '2547365280535183479525150914662', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.23699501130794828, 0.41048740072572704], [-4.0, -6.928203230275509]], [[1.0, 0], [2.4531555920413597, 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'6.89091499400819411339739024535245', '8.781226466921025624418715983694580', '9.638037146136694028165761149311490', '10.58058651074799547449690969089768', '11.16379163763953543304322613061985'], 'prelabel': '2-15e2-9.7-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6435463152389933, 'root_angle': -0.7574594388006185, 'root_number': '-0.723481816830907 - 0.6903434367871183*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3787297194', 'prec': 44}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.14228787808288684142514123467', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.24538444031778879710323453735', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.19284624516161212130479040219', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.275429751291645, 'bad_primes': [3, 5], 'central_character': '9.7', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/4/e/g/151/9'], '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': '2-15e2-9.7-c3-0-5', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-15e2-9.7-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6435463152389933, 'root_angle': -0.37872971940030925, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.14228787808288684142514123467', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '180371314056972631519778278513', 'Lhash_array': ['180371314056972631519778278513'], 'label': '2-15e2-9.7-c3-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/4/e/g/151/9'}