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lfunc_lfunctions • Show schema
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{'Lhash': '2339613606201324371650157784429', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-0.18966689810087872, -0.32851270402471094], 'a4': [0, 0], 'a5': [-0.5, -0.8660254037844386], 'a6': [0, 0], 'a7': [-1.8930675031969755, 0], 'a8': [0, 0], 'a9': [1.4280529355295817, -2.473460240235118], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.137261107234623, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.5, 0.8660254037844386]]], [19, [[1.0, 0], [2.105962326440448, 3.8164017974544473]]]], 'bad_primes': [2, 5, 19], 'central_character': '1520.881', 'coefficient_field': 'CDF', 'conductor': 1520, 'conductor_radical': 190, 'conjugate': '100734690728594952704340636153', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.18966689810087872, 0.32851270402471094], [-1.5, 2.598076211353316]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [1.8930675031969755, 0], [7.0, 0]], [[1.0, 0], 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'0.2051606135090847817384223672278026686210409172154838070', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1520/2/q/o/881/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.2051606135090848, 0.35918726614524576, 0.5155079957713744, 0.6740186267373304, 0.8344792141241122, 0.9964522289263202, 1.159251852511752, 1.3219068731434325, 1.4831386057964342, 1.6413543079723705, 1.7946558292092525, 1.9408627304220174, 2.0775488073778954, 2.20209078869203, 2.311727886261104, 2.4036307996823694, 2.474978678883941, 2.5230424128381896, 2.5452724346790134, 2.539389024152775, 2.5034728637162775, 2.436053385157116, 2.3361922510029993, 2.2035591703506494, 2.0384971715279714, 1.8420744611235373, 1.6161201041391282, 1.3632409734406816, 1.0868177442825175, 0.7909781529378652, 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'9.295004206791034694842500681008132', '9.982061422963699771565645924511494'], 'prelabel': '2-1520-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.483857216826577, 'root_angle': -0.9260841585847874, 'root_number': '-0.97315939008949021559544023536428012507338880917246667453 - 0.2301321391736743335144825528559993069678703125068360217*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4630420792923937', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.84562970725537258309089945938', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.06911508356420823020047129651', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.85100646275465312001260682401', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.137261107234623, 'bad_primes': [2, 5, 19], 'central_character': '19.7', 'conductor': 1520, 'conductor_radical': 190, 'degree': 2, 'index': 36, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1520/2/q/o/881/2'], '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': '2-1520-19.7-c1-0-36', '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': '2-1520-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.483857216826577, 'root_angle': -0.4630420792923937, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.84562970725537258309089945938', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2339613606201324371650157784429', 'Lhash_array': ['2339613606201324371650157784429'], 'label': '2-1520-19.7-c1-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1520/2/q/o/881/2'}