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lfunc_lfunctions • Show schema
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{'Lhash': '2733554463720564466392284741573', 'a10': [0, 0], 'a2': [0, 0], 'a3': [1.5908414145993355, -2.7554181568707943], 'a4': [0, 0], 'a5': [-1.2807764064044151, 2.218369809027932], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [-3.5615528128088303, -6.168790425624741], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.7098088857877, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-0.6974999434983001, -4.302730973326112]]]], 'bad_primes': [2, 19], 'central_character': '1216.961', 'coefficient_field': 'CDF', 'conductor': 1216, 'conductor_radical': 38, 'conjugate': '370314779403146809557757724835', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.5908414145993355, 2.7554181568707943], [-1.5, -2.598076211353316]], [[1.0, 0], [1.2807764064044151, -2.218369809027932], [-2.5, -4.330127018922194]], [[1.0, 0], [0, 0], [7.0, 0]], [[1.0, 0], [4.968365771400742, 0], [11.0, 0]], 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'10.09269433845270582164810546999494'], 'prelabel': '2-1216-19.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.11605662429098, 'root_angle': -0.9522416755357498, 'root_number': '-0.98876551796134268262567158226774153779916684531718940603 - 0.1494749159245046067429886802301447801913713531964783389*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.47612083776787495', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.15639424872154195928723125206', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.29392176849403236236755819825', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.13371225680253503070498848818', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.7098088857877, 'bad_primes': [2, 19], 'central_character': '19.11', 'conductor': 1216, 'conductor_radical': 38, 'degree': 2, 'index': 35, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1216/2/i/p/961/4'], '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': '2-1216-19.11-c1-0-35', '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': '2-1216-19.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.11605662429098, 'root_angle': -0.4761208377678749, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.15639424872154195928723125206', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2733554463720564466392284741573', 'Lhash_array': ['2733554463720564466392284741573'], 'label': '2-1216-19.11-c1-0-35', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1216/2/i/p/961/4'}