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lfunc_lfunctions • Show schema
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{'Lhash': '1015372818966704515868745442538', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [1.597329120398448, 0], 'a6': [0, 0], 'a7': [0, 1.1641769178978976], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 41.394448407831774, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '5184.2591', 'coefficient_field': 'CDF', 'conductor': 5184, 'conductor_radical': 6, 'conjugate': '1137964395851605914850430919225', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.597329120398448, 0], [5.0, 0]], [[1.0, 0], [0, -1.1641769178978976], [-7.0, 0]], [[1.0, 0], [0, 1.9809173184726043], [-11.0, 0]], [[1.0, 0], [0, 0.1641769178978975], [-13.0, 0]], [[1.0, 0], [0, -3.5782464388710524], [-17.0, 0]], [[1.0, 0], [-3.1641769178978976, 0], [19.0, 0]], [[1.0, 0], [-1.2137409223242919, 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'3.63686432990809203143293497138265', '4.65798079069937062988985451195229', '5.18902417944002685955752438909022', '6.03607346403273660204416087668212', '6.83881337884632543934075966770256', '7.34710856949679658925211332328688', '8.130575485642006195231907886743414'], 'prelabel': '2-72e2-24.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.433851755195466, 'root_angle': -0.08333333333333333, 'root_number': '0.96592582628906828674974319972889736763390483900840455041 - 0.2588190451025207623488988376240483283490689013199305139*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.04166666666666667', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.800987921106885069141632984949', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.85291591291755721933988230716', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.75488713780447143108221926333', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 41.394448407831774, 'bad_primes': [2, 3], 'central_character': '24.11', 'conductor': 5184, 'conductor_radical': 6, 'degree': 2, 'index': 50, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5184/2/f/e/2591/12'], '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': '2-72e2-24.11-c1-0-50', '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': '2-72e2-24.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.433851755195466, 'root_angle': -0.041666666666666664, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.800987921106885069141632984949', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1015372818966704515868745442538', 'Lhash_array': ['1015372818966704515868745442538'], 'label': '2-72e2-24.11-c1-0-50', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5184/2/f/e/2591/12'}