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lfunc_lfunctions • Show schema
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{'Lhash': '729160792793762276600987405159', 'a10': [0, 0], 'a2': [0, 0], 'a3': [2.449489742783178, -4.58257569495584], 'a4': [0, 0], 'a5': [-17.281273744680597, 0], 'a6': [0, 0], 'a7': [0, 0.269691090396697], 'a8': [0, 0], 'a9': [-15.0, -22.44994432064365], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.656733442204406, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-2.449489742783178, 4.58257569495584]]]], 'bad_primes': [2, 3], 'central_character': '384.191', 'coefficient_field': 'CDF', 'conductor': 384, 'conductor_radical': 6, 'conjugate': '1316870038152940488753075651626', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-2.449489742783178, 4.58257569495584]], [[1.0, 0], [17.281273744680597, 0], [125.0, 0]], [[1.0, 0], [0, -0.269691090396697], [-343.0, 0]], [[1.0, 0], [0, -41.16515138991168], [-1331.0, 0]], [[1.0, 0], [0, -64.66060555964673], [-2197.0, 0]], [[1.0, 0], 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0.14300963169491807, 0.25233722777955064], 'positive_zeros': ['0.57520644305495793112511196889726', '3.13130538175012750713476397561647', '3.55989685177603178916149582489341', '4.79484162651440739982909314959663', '5.84642339151171680112903754472454', '7.54738059446851909058873940698544', '8.133028867931426739151730572066102', '8.817345332214858537716387811299124', '10.12358075381004856130152448774292', '10.82679203300196649222654940874532'], 'prelabel': '2-384-24.11-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.759908974151124, 'root_angle': -0.09374719054413498, 'root_number': '0.95694289779565689759729145538609155029266996796312115772 - 0.2902762311289902309306247887194248836260033012964544911*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.04687359527206749', 'prec': 67}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.57520644305495793112511196890', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.13130538175012750713476397562', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.55989685177603178916149582489', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 22.656733442204406, 'bad_primes': [2, 3], 'central_character': '24.11', 'conductor': 384, 'conductor_radical': 6, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/384/4/f/g/191/5'], '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': '2-384-24.11-c3-0-13', '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': '2-384-24.11-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.759908974151124, 'root_angle': -0.04687359527206749, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.57520644305495793112511196890', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '729160792793762276600987405159', 'Lhash_array': ['729160792793762276600987405159'], 'label': '2-384-24.11-c3-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/384/4/f/g/191/5'}