-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '499717227592210136853080113682', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.5, 0.8660254037844386], 'a4': [0.0, 0.0], 'a5': [0.0, 3.4641016151377544], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [1.5, -2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.282356664340774, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.5, -0.8660254037844386]]], [19, [[1.0, 0], [-4.0, -1.7320508075688772]]]], 'bad_primes': [2, 3, 19], 'central_character': '912.113', 'coefficient_field': 'CDF', 'conductor': 912, 'conductor_radical': 114, 'conjugate': '2535997237782707094964947048282', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.5, -0.8660254037844386]], [[1.0, 0], [0, -3.4641016151377544], [-5.0, 0]], [[1.0, 0], [1.0, 0], [7.0, 0]], [[1.0, 0], [0, -3.4641016151377544], [-11.0, 0]], [[1.0, 0], [0, -1.7320508075688772], [-13.0, 0]], [[1.0, 0], [0, -1.7320508075688772], [-17.0, 0]], [[1.0, 0], [-4.0, -1.7320508075688772]], [[1.0, 0], [0, -5.196152422706632], [-23.0, 0]], [[1.0, 0], [9.0, 0], [29.0, 0]], [[1.0, 0], [0, 10.392304845413264], [-31.0, 0]], [[1.0, 0], [0, 6.928203230275509], [-37.0, 0]], [[1.0, 0], [0, 0], [41.0, 0]], [[1.0, 0], [2.0, 0], [43.0, 0]], [[1.0, 0], [0, 3.4641016151377544], [-47.0, 0]], [[1.0, 0], [-9.0, 0], [53.0, 0]], [[1.0, 0], [3.0, 0], [59.0, 0]], [[1.0, 0], [8.0, 0], [61.0, 0]], [[1.0, 0], [0, -8.660254037844387], [-67.0, 0]], [[1.0, 0], [12.0, 0], [71.0, 0]], [[1.0, 0], [-11.0, 0], [73.0, 0]], [[1.0, 0], [0, -6.928203230275509], [-79.0, 0]], [[1.0, 0], [0, 10.392304845413264], [-83.0, 0]], [[1.0, 0], [6.0, 0], [89.0, 0]], [[1.0, 0], [0, -13.856406460551018], [-97.0, 0]], [[1.0, 0], [0, 10.392304845413264], [-101.0, 0]], [[1.0, 0], [0, -3.4641016151377544], [-103.0, 0]], [[1.0, 0], [-3.0, 0], [107.0, 0]], [[1.0, 0], [0, -15.588457268119896], [-109.0, 0]], [[1.0, 0], [-12.0, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-912-57.56-c1-0-4', '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/912/2/f/a/113/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.7108945336826237, 0.47234116311220703, 0.2458665381418398, 0.03165707988418601, -0.16673464154392195, -0.3415332215240613, -0.48080372442541003, -0.5693518513365856, -0.5903130797423869, -0.527272193249328, -0.3667410000013853, -0.10078393071690102, 0.2704738073854887, 0.7367728191993909, 1.276425825797757, 1.856134486571382, 2.4321800764025996, 2.9531269456868237, 3.3640019212176306, 3.6117012669897126, 3.6511546977370504, 3.451575960453057, 3.0019881558524366, 2.315164128981892, 1.4291948137360275, 0.4061039022239738, -0.6727414762840396, -1.71424688079511, -2.6235842470094473, -3.3154662658459904, -3.725258925291802, -3.8183200333665637, -3.5960145220783475, -3.097178895376464, -2.394372443208532, -1.5850016909807336, -0.7782349411624625, -0.07940346204022464, 0.4258280213281173, 0.684975134433362, 0.6875325432411162, 0.4672410983181744, 0.09697406500703773, -0.3233862069376045, -0.6844304395403177, -0.8873055436562173, -0.8629327847129892, -0.5867639617978776, -0.08601179955248535, 0.5625435403445443, 1.244431586136, 1.8274726153766034, 2.1865841657255087, 2.2289274226658407, 1.9144819125950683, 1.267653201808912, 0.3769619060629338, -0.617974232551841, -1.550447702180415, -2.2575787714068962, -2.612349670889065, -2.5503099611726507, -2.0851468885586226, -1.3092193577065743, -0.37802530663396644, 0.5191244730704337, 1.196892267460721, 1.5126867335544232, 1.3982697635122496, 0.8770774618578556, 0.06278593777507568, -0.8615482452061076, -1.6802545538927893, -2.1905299763918675, -2.2471404392404017, -1.7965210080894227, -0.8923042201621517, 0.3119517686157765, 1.5921680648077245, 2.6996205256783194, 3.4136718309000043, 3.589808704069023, 3.1920658963896096, 2.3021044773304333, 1.102326785167476, -0.16366429306839317, -1.2445907437734103, -1.9368454173326035, -2.1287914488635584, -1.823518564298588, -1.1345449826464729, -0.2554257143551497, 0.5893633333554427, 1.200155366765855, 1.45050847746267, 1.3160488799695451, 0.8763381310074031, 0.2892609350849532, -0.25534657109006176, -0.5904458561319386, -0.6199976573782185, -0.34707285890122175, 0.1265702651220963, 0.6302773444903653, 0.9763251656725737, 1.0199236007908357, 0.7105082499375623, 0.11893371278264404, -0.5689814085899197, -1.0932869578766864, -1.186302739190256, -0.6481075112045767, 0.5889629907930393, 2.4251955516836294, 4.599338255637142, 6.736653079541697, 8.429227524259014, 9.329513492736366, 9.233689557262432, 8.133171991431313, 6.220207749073176, 3.8451161545285926, 1.4353685711574833, -0.6031145661013805, -1.9771745521903175, -2.5667354143641457, -2.4391144495438506, -1.8146977125537775, -0.9946442606708402, -0.27163146333799604, 0.1509124569787584, 0.20846006775030482, -0.019373765995884414, -0.34809191440617493, -0.5589313058204233, -0.47834043107744045, -0.041203286500259485, 0.682307190204002, 1.5051378301139928, 2.1817767585006833, 2.488666057090825, 2.301158976443042, 1.6419419613295496, 0.6841083668437863, -0.2941025663329815, -0.9906478057091606, -1.1729254973739782, -0.7539949293345719, 0.17297868953770199, 1.3546809314411623, 2.4480737196858717, 3.1213990516827947, 3.155549372693604, 2.514362145488925, 1.3609753653539967, 0.013427120800690634, -1.1485863813902224, -1.7982644484735644, -1.7625590970904899, -1.077609654998056, 0.019622168959375356, 1.162381458376763, 1.9669866609677682, 2.153062673719325, 1.633565011527414, 0.5457218350332014, -0.7879327625123356, -1.957384242084978, -2.591950273251811, -2.476521670573238, -1.6204128741001136, -0.2565411970652064, 1.229457768355229, 2.4182488518822143, 2.9864579113347163, 2.8058137875271, 1.9801898218173741, 0.8088399998351998, -0.3120672126140315, -1.0175264207756725, -1.0897241413653007, -0.5244456787455669, 0.47322787112786757, 1.5615416971744656, 2.377951306812913, 2.658972884918273, 2.32374120380789, 1.4937195337327098, 0.4431070189003445, -0.5015529125059583, -1.0765170373302555, -1.169725092253164, -0.8518787458910365, -0.3389291723670628, 0.09996437213400973, 0.25477727766666775, 0.06487426575267836, -0.34813854439732755, -0.7200798619532272, -0.745036142756206, -0.20265166846571622, 0.9346293113004376, 2.456296789505599, 3.9524573373785103, 4.929551110569261, 4.968263008371722, 3.871751491334486, 1.752641498835274, -0.9744919320497153, -3.6978666141341554, -5.780515203036262, -6.746087489005919, -6.418869619982057, -4.972393571568165, -2.8705802677769148, -0.7206884311326444, 0.91360531415689, 1.6779053822546945, 1.5184612607167045, 0.6720510972001763, -0.4378512044005801, -1.3592187944040288, -1.7671946178471531, -1.5636113661984745, -0.8884429191672916, -0.044100780672364795, 0.6348674623959537, 0.9151442567755308, 0.7500721430533853, 0.28580503602546464, -0.21188085816484625, -0.4791432559863855, -0.37406268781707835, 0.0544242603480031, 0.5782692774773637, 0.8804898289349073, 0.6898255805400942, -0.09328804507849628, -1.3314771263859815, -2.6763395779545474, -3.6815022316433215, -3.9644601364770122, -3.3578042155103236, -1.9913270581813334, -0.2697818830389768, 1.2512843991002143, 2.0509648327982717, 1.8246353541528901, 0.5958276816048018, -1.2840428204406245, -3.250507597238279, -4.716065411778099, -5.267989683327146, -4.802966444125476, -3.5502767235474586, -1.9760357668962902, -0.6048755363214767], 'positive_zeros': ['0.39420738451292526617359265396551', '1.41257393692893365059355368388899', '3.17224876554612289124470968073932', '4.64152189035303064600392259548858', '5.27897725139969926680995703297234', '6.01787168329570719286958867728737', '7.04780362551873855628173892356968', '8.050569957155588787338996736995507', '8.758646213835674476160718874746168', '9.594327308765145281382590752132280'], 'prelabel': '2-912-57.56-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.698584196266771, 'root_angle': 0.9634068024798363, 'root_number': '-0.9933992677987828 + 0.11470786693528083*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.48170340124', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.39420738451292526617359265397', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.41257393692893365059355368389', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.17224876554612289124470968074', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 7.282356664340774, 'bad_primes': [2, 3, 19], 'central_character': '57.56', 'conductor': 912, 'conductor_radical': 114, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/912/2/f/a/113/2'], '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': '2-912-57.56-c1-0-4', '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': '2-912-57.56-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.698584196266771, 'root_angle': 0.48170340123991817, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.39420738451292526617359265397', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '499717227592210136853080113682', 'Lhash_array': ['499717227592210136853080113682'], 'label': '2-912-57.56-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/912/2/f/a/113/2'}