-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1934275874536234919860198468382', 'a10': [-0.07193881157066817, 1.412382670309219], 'a2': [1.412382670309219, 0.07193881157066817], 'a3': [0.0, -1.1628912656895867], 'a4': [1.9896496147796, 0.20321026157010408], 'a5': [0.0, 1.0], 'a6': [0.08365701563961898, -1.6424474711139259], 'a7': [0.4942963852605565, 0.0], 'a8': [2.795527931185802, 0.4301436805999006], 'a9': [1.647683904182871, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.068630553617312, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.412382670309219, -0.07193881157066817]]], [5, [[1.0, 0], [0, -1.0]]], [19, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 5, 19], 'central_character': '760.381', 'coefficient_field': 'CDF', 'conductor': 760, 'conductor_radical': 190, 'conjugate': '2073161838807204865515504199829', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.412382670309219, -0.07193881157066817]], [[1.0, 0], [0, 1.1628912656895867], [-3.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [-0.4942963852605565, 0], [7.0, 0]], [[1.0, 0], [0, -3.064885580737477], [-11.0, 0]], [[1.0, 0], [0, 1.3161246157782927], [-13.0, 0]], [[1.0, 0], [-0.9650880682340628, 0], [17.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [7.419495472013918, 0], [23.0, 0]], [[1.0, 0], [0, 6.537737231805433], [-29.0, 0]], [[1.0, 0], [-8.536939622906553, 0], [31.0, 0]], [[1.0, 0], [0, 0.8356778679773702], [-37.0, 0]], [[1.0, 0], [-3.673236884372893, 0], [41.0, 0]], [[1.0, 0], [0, -7.66670006623479], [-43.0, 0]], [[1.0, 0], [10.030790020171526, 0], [47.0, 0]], [[1.0, 0], [0, 11.750153934184707], [-53.0, 0]], [[1.0, 0], [0, -1.1180520150525919], [-59.0, 0]], [[1.0, 0], [0, 3.529157008051777], [-61.0, 0]], [[1.0, 0], [0, -13.204615974466853], [-67.0, 0]], [[1.0, 0], [7.0392226816508545, 0], [71.0, 0]], [[1.0, 0], [6.560622379741049, 0], [73.0, 0]], [[1.0, 0], [10.307019243426048, 0], [79.0, 0]], [[1.0, 0], [0, 16.31691374235407], [-83.0, 0]], [[1.0, 0], [0.45415747685769914, 0], [89.0, 0]], [[1.0, 0], [-16.802361121344152, 0], [97.0, 0]], [[1.0, 0], [0, -17.360710599538866], [-101.0, 0]], [[1.0, 0], [9.259082263670297, 0], [103.0, 0]], [[1.0, 0], [0, -16.902718911816436], [-107.0, 0]], [[1.0, 0], [0, -6.606622101592991], [-109.0, 0]], [[1.0, 0], [14.006254266892999, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 46, 'label': '2-760-8.5-c1-0-46', '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/760/2/f/b/381/44', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [3.12047397323382, 3.1247348472816943, 3.1193091990800057, 3.0946710212785544, 3.037066218526471, 2.9308056502883075, 2.7607249101186713, 2.514495615562923, 2.1846351912476494, 1.770132993614127, 1.2776060938962819, 0.7218688215794435, 0.12578601963486247, -0.48069999825062687, -1.0624206095112487, -1.5816707645422645, -2.001584857176018, -2.289925631218194, -2.422904408915153, -2.3885734078320193, -2.1893034131216558, -1.8428973423277142, -1.3819998115326535, -0.8516422141813293, -0.3049978364163721, 0.20231394460151858, 0.6187773762654913, 0.9035775579487056, 1.032319875945392, 1.0009526114636087, 0.8271251386313124, 0.5485098283011594, 0.21803008183957365, -0.10358053606811653, -0.35698297103819926, -0.49390030490460324, -0.4857165978183691, -0.3294735078163157, -0.04999240672463015, 0.3026344497263317, 0.6602249982477589, 0.9475874877292415, 1.0959455576043267, 1.0565532539272586, 0.8120581756626055, 0.38329318558184033, -0.17025995949857833, -0.7571350382390812, -1.2672513304714526, -1.5902740549095409, -1.636122960555786, -1.3540593401295675, -0.7466420250415117, 0.12461102012606128, 1.1438099554497543, 2.155766836788386, 2.9898421048449015, 3.4890156201742046, 3.5392863953271574, 3.093959693778134, 2.1878283564528442, 0.9377115518322892, -0.4719068100659297, -1.8166656498417666, -2.869378940647827, -3.440087489054255, -3.411796044861301, -2.764887600493288, -1.5849189525305083, -0.05138687679390514, 1.5913817649077386, 3.0764952339967793, 4.162355084724365, 4.67706252261633, 4.550599651702973, 3.8280903531367048, 2.661003253560636, 1.2775326286676385, -0.06229887505665147, -1.1179497154866433, -1.7156394340126409, -1.7817498706438344, -1.3552267024287177, -0.5762179289271353, 0.3467227363553888, 1.183818005932616, 1.7353049421457858, 1.8753523174528333, 1.57878294175622, 0.9245166981929828, 0.07492545158641363, -0.7641318089866145, -1.393247501463039, -1.6675671423804672, -1.5315426437023794, -1.0318960194771813, -0.30552949817036124, 0.4548017035037957, 1.0487236631995063, 1.3184883551936515, 1.188657336029989, 0.6851221719697357, -0.07156272006239185, -0.8970888822298656, -1.5908521095508577, -1.9878617688512699, -2.001633036326606, -1.6467089744505743, -1.034609582121811, -0.34392404942253146, 0.22783159193096963, 0.5179211900886241, 0.44321515566563985, 0.023779521173895646, -0.6216192859533632, -1.3073930349906933, -1.8321096486273374, -2.034760858271751, -1.8406526266770478, -1.2837220962182962, -0.4983622872356517, 0.3176936114393308, 0.9595197312170923, 1.274409977348825, 1.2072204752565805, 0.817686694642098, 0.2633628344541965, -0.24831901100026746, -0.5260077092366859, -0.4594160262175002, -0.06340904102232364, 0.5138513557230584, 1.0241449315287972, 1.1873902084465395, 0.7775533289208173, -0.2975595889567986, -1.9466155817135706, -3.8924320804083203, -5.722132347359944, -6.980450321731828, -7.284072590907743, -6.427496558335126, -4.451248754580022, -1.6517729705856414, 1.473079382002985, 4.332018444431015, 6.376034376749895, 7.227802537811463, 6.771328264715708, 5.178090646944087, 2.8623184242888535, 0.3767062654071379, -1.7242671156511287, -3.0176665531758653, -3.307464153726947, -2.657959105041059, -1.358444420309858, 0.16881251655264695, 1.4899786717114423, 2.2758863760593173, 2.38121601606585, 1.8665162198495309, 0.9601996661747811, -0.02476803918846866, -0.7920896149639663, -1.1497988495378058, -1.0584933265251841, -0.6276236342563764, -0.06415813240615384, 0.4070807917200115, 0.6236956547234258, 0.5396282702358124, 0.23526532113888513, -0.11855948205810207, -0.32920883124811534, -0.2589377932429842, 0.11774490555832975, 0.6969040020063124, 1.2752993029176187, 1.618506967993557, 1.5442228957403443, 0.991955561218047, 0.05410761187003071, -1.044035113583022, -2.0106767728689707, -2.57936312318128, -2.5959007114088823, -2.0705203072712393, -1.1763149761944638, -0.19275041242959615, 0.5881148232008935, 0.9615765866902858, 0.8819895528242856, 0.4802664022868673, 0.018970053513664015, -0.20184848764164914, 0.04283940410069728, 0.8109696874938785, 1.9553954053355618, 3.1566033483104934, 4.01917121713456, 4.20260140583569, 3.543687516281748, 2.1280360490766896, 0.2832814779136974, -1.5084928690667871, -2.7545841588760607, -3.107161289095601, -2.4798331250682066, -1.085362880899782, 0.6210091505502123, 2.0776897589044614, 2.790761264557807, 2.4906688479587737, 1.22048521546964, -0.6741721254027064, -2.651946013122731, -4.145960846553879, -4.742895812569029, -4.312803467631073, -3.047226695736096, -1.3930844568749083, 0.09585667793543427, 0.9407998110239978, 0.8928663419612994, 0.010095143598474703, -1.3683550180996094, -2.741066033050155, -3.6153341382711437, -3.672080204232949, -2.8691556334401818, -1.449065025230098, 0.14984377511578154, 1.4466010600751633, 2.0814492101984126, 1.933659237249861, 1.1535738797007546, 0.09965553743081637, -0.7953091554073205, -1.1802565959547155, -0.9085984990744408, -0.0849535721218177, 0.9790410444690557, 1.882015615156769, 2.2796039267078454, 2.007277009059171, 1.1356478839110093, -0.059997805408714584, -1.2026140224659245, -1.9492999570829115, -2.109635044959682, -1.7036816975225624, -0.9404567205150719, -0.12796653334787106, 0.4485742461186472, 0.6325980678947827, 0.445756947258626], 'positive_zeros': ['1.52587461733381853736912208547368', '3.07311747155891620286824690397171', '4.08287496556439766173043169522043', '4.76884412786879417583099327798832', '5.71336648075314117085799983943348', '6.60874501699885659394789846866981', '7.70853337600671601011762988699357', '8.628931016547224906613185441904890', '9.743724234465492138172637547995345', '10.45332955445195345800543307983728'], 'prelabel': '2-760-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4634590627037647, 'root_angle': 0.024298368937856078, 'root_number': '0.9883683785689404 + 0.15207875671836504*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0242983689379', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.52587461733381853736912208547', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.07311747155891620286824690397', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.08287496556439766173043169522', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 6.068630553617312, 'bad_primes': [2, 5, 19], 'central_character': '8.5', 'conductor': 760, 'conductor_radical': 190, 'degree': 2, 'index': 46, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/760/2/f/b/381/44'], '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': '2-760-8.5-c1-0-46', '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': '2-760-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4634590627037647, 'root_angle': 0.024298368937856078, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.52587461733381853736912208547', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1934275874536234919860198468382', 'Lhash_array': ['1934275874536234919860198468382'], 'factors': ['2-760-8.5-c1-0-46'], 'label': '2-760-8.5-c1-0-46', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/760/2/f/b/381/44'}