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lfunc_lfunctions • Show schema
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{'Lhash': '2479503340733640667617806757067', 'a10': [-0.14231483827328514, -0.9898214418809327], 'a2': [0.41541501300188644, -0.9096319953545183], 'a3': [0.9594929736144974, 0.28173255684142967], 'a4': [-0.6548607339452851, -0.7557495743542583], 'a5': [0.8412535328311812, -0.5406408174555976], 'a6': [0.6548607339452851, -0.7557495743542583], 'a7': [0.09031976297094056, -0.6281877497732604], 'a8': [-0.9594929736144974, 0.28173255684142967], 'a9': [0.8412535328311812, 0.5406408174555976], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.50967773946835, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.41541501300188644, 0.9096319953545183]]], [3, [[1.0, 0], [-0.9594929736144974, -0.28173255684142967]]], [5, [[1.0, 0], [-0.8412535328311812, 0.5406408174555976]]], [23, [[1.0, 0], [-4.65689685821179, 1.1459981029553041]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '690.121', 'coefficient_field': 'CDF', 'conductor': 690, 'conductor_radical': 690, 'conjugate': '1229133642588873947002352292670', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.41541501300188644, 0.9096319953545183]], [[1.0, 0], [-0.9594929736144974, -0.28173255684142967]], [[1.0, 0], [-0.8412535328311812, 0.5406408174555976]], [[1.0, 0], [-0.09031976297094056, 0.6281877497732604], [-6.7164508153014815, -1.9721278978900079]], [[1.0, 0], [1.9287030107521124, 4.223270496265729], [-7.2034680733981356, 8.313245317896842]], [[1.0, 0], [0.5803057634077017, 4.036115238841198], [-12.473408656988466, 3.662523238938586]], [[1.0, 0], [0.8214142327166453, -0.947962558396427], [-2.4193522506458476, -16.826964511975856]], [[1.0, 0], [-0.992446778222601, -1.1453446379236614], [-2.7039819271924177, 18.80660739573772]], [[1.0, 0], [-4.65689685821179, 1.1459981029553041]], [[1.0, 0], [-3.0845488556349046, 3.5597591424923722], [-4.127130309925269, -28.70482181454705]], [[1.0, 0], [-4.341897720197419, 1.2748962002786581], [26.078859517766617, 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[-75.7999449155453, 22.256871990472945]], [[1.0, 0], [-0.774422625682694, -0.49769120136250483], [34.479446079156574, 75.49945561442503]], [[1.0, 0], [-2.7226544553488607, -0.799443479207105], [74.87156442197512, 48.11703275354819]], [[1.0, 0], [-5.732751048776256, 3.6842153908693236], [40.295256261182985, -88.23430354938829]], [[1.0, 0], [11.73585349860778, 7.542175077319653], [41.956916313190526, 91.87283153080635]], [[1.0, 0], [0.4221046847952405, 0.9242803333086113], [-67.45065559636436, 77.84220615848861]], [[1.0, 0], [-3.9970128589503284, 1.1736288680031395], [90.01412801293638, -57.84856746774894]], [[1.0, 0], [12.288848297787892, -14.18208695214458], [-15.51231737178808, -107.89053716502167]], [[1.0, 0], [2.447257984656952, -5.358747503236412], [-73.99926293581721, -85.39970190203118]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 13, 'label': '2-690-23.6-c1-0-13', '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/690/2/m/c/121/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.033502512816231, 2.229990579500915, 2.42658243203274, 2.619702504669159, 2.800555244242798, 2.9559083334074074, 3.069473120886111, 3.1236355078859233, 3.101379219190877, 2.9883027820560106, 2.7746337973344866, 2.457107547245079, 2.040530723998511, 1.5388181359654316, 0.9752852064150204, 0.38200976226681294, -0.20185452324368944, -0.7328263335765203, -1.1667882263526197, -1.4633579050499468, -1.5905354129657219, -1.5291088954894645, -1.2762372371828052, -0.8476324276423028, -0.27785118622513, 0.38162257157334534, 1.0665748164899886, 1.7063075938418097, 2.2313861971959805, 2.582050092252676, 2.716239012323467, 2.6160976457672738, 2.2918913373828054, 1.7825051660898976, 1.1520979904447084, 0.48300185750206726, -0.1344702315431985, 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'root_analytic_conductor': 2.3472702740563025, 'root_angle': 0.5515814489045733, 'root_number': '-0.1613396148007654 + 0.9868989455339086*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.275790724452', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.95598324986966265086174153376', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.05408234905318957663372524754', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.47088992388582246139393995163', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.50967773946835, 'bad_primes': [2, 3, 5, 23], 'central_character': '23.6', 'conductor': 690, 'conductor_radical': 690, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/690/2/m/c/121/2'], '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': '2-690-23.6-c1-0-13', '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': '2-690-23.6-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3472702740563025, 'root_angle': 0.27579072445228664, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.95598324986966265086174153376', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2479503340733640667617806757067', 'Lhash_array': ['2479503340733640667617806757067'], 'label': '2-690-23.6-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/690/2/m/c/121/2'}