Formats: - HTML - YAML - JSON - 2026-10-12T03:51:50.393061
  • lfunc_lfunctions • Show schema
    {'Lhash': '1843060463638431141060212675953', 'a10': -5, 'a2': -1, 'a3': 3, 'a4': -7, 'a5': 5, 'a6': -3, 'a7': 24, 'a8': 15, 'a9': 9, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 107.08846666041927, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 7}, 'bad_lfactors': [[3, [1, -3]], [5, [1, -5]], [11, [1]]], 'bad_primes': [3, 5, 11], 'central_character': '1815.1', 'coefficient_field': '1.1.1.1', 'conductor': 1815, 'conductor_radical': 165, 'degree': 2, 'euler_factors': [[1, 1, 8], [1, -3], [1, -5], [1, -24, 343], [1], [1, 22, 2197], [1, -14, 4913], [1, -20, 6859], [1, 168, 12167], [1, 230, 24389], [1, 288, 29791], [1, 34, 50653], [1, 122, 68921], [1, -188, 79507], [1, -256, 103823], [1, 338, 148877], [1, -100, 205379], [1, 742, 226981], [1, 84, 300763], [1, 328, 357911], [1, -38, 389017], [1, -240, 493039], [1, 1212, 571787], [1, -330, 704969], [1, -866, 912673], [1, -1218, 1030301], [1, 88, 1092727], [1, 36, 1225043], [1, -970, 1295029], [1, -1042, 1442897]], 'euler_factors_factorization': [[[[1, 1, 8], 1]], [[[1, -3], 1]], [[[1, -5], 1]], [[[1, -24, 343], 1]], [1], [[[1, 22, 2197], 1]], [[[1, -14, 4913], 1]], [[[1, -20, 6859], 1]], [[[1, 168, 12167], 1]], [[[1, 230, 24389], 1]], [[[1, 288, 29791], 1]], [[[1, 34, 50653], 1]], [[[1, 122, 68921], 1]], [[[1, -188, 79507], 1]], [[[1, -256, 103823], 1]], [[[1, 338, 148877], 1]], [[[1, -100, 205379], 1]], [[[1, 742, 226981], 1]], [[[1, 84, 300763], 1]], [[[1, 328, 357911], 1]], [[[1, -38, 389017], 1]], [[[1, -240, 493039], 1]], [[[1, 1212, 571787], 1]], [[[1, -330, 704969], 1]], [[[1, -866, 912673], 1]], [[[1, -1218, 1030301], 1]], [[[1, 88, 1092727], 1]], [[[1, 36, 1225043], 1]], [[[1, -970, 1295029], 1]], [[[1, -1042, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 191, 'label': '2-1815-1.1-c3-0-191', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/1815/4/a/e', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 24}, 'plot_values': [-1.1965934650496668e-60, 0.23982537689436084, 0.47665629350552874, 0.7075292412096561, 0.9295427864295793, 1.1398890125789276, 1.3358853787105778, 1.5150070227383037, 1.6749194483794736, 1.813511431793371, 1.9289278709222615, 2.0196021829200865, 2.0842877382008433, 2.1220877090678334, 2.1324826120083706, 2.1153547406937867, 2.071008626217415, 2.0001866262698638, 1.9040787392395648, 1.7843257652976598, 1.643014996169293, 1.482667709360204, 1.3062178709602863, 1.1169816126205336, 0.9186172406858941, 0.7150757555041799, 0.5105421023291715, 0.3093676367125654, 0.11599456062835876, -0.0651266362410954, -0.22962542034680455, -0.3733035694460669, -0.49222982107470964, -0.5828347807070201, -0.6420038777818021, -0.6671660252940897, -0.6563755596351925, -0.6083850186239075, -0.522706362822344, -0.3996583624068347, -0.24039806147021284, -0.046934494109132786, 0.17787683970269197, 0.43035982961798336, 0.706064571265895, 0.9998352590592011, 1.3058987160212485, 1.617972538071767, 1.9293912340293153, 2.233248149955452, 2.5225503951836297, 2.790383455975318, 3.030081709957841, 3.23540065867286, 3.4006863940546923, 3.521037623186484, 3.592455507710059, 3.6119766403826348, 3.577784688639996, 3.489296586878171, 3.3472196544195594, 3.1535766490926185, 2.911696526573436, 2.626169547893068, 2.3027663419749103, 1.9483215626100336, 1.570583851984629, 1.178034904678443, 0.7796814835594267, 0.3848252374266558, 0.0028160744996356883, -0.3572043783537365, -0.6865620856536387, -0.9773051121844013, -1.2224455490816053, -1.4161810975123141, -1.5540888179881835, -1.633284071690056, -1.6525384461999721, -1.6123514602918516, -1.5149720609156558, -1.3643673318027425, -1.1661373908607133, -0.9273771191856371, -0.6564870884805132, -0.36293778158578566, -0.056992875240727076, 0.2506010836475446, 0.5489498851098492, 0.827361857252415, 1.0757022819070077, 1.2847406746700198, 1.4464793628621888, 1.5544519569997728, 1.6039808640007964, 1.5923839326771168, 1.5191216394951892, 1.3858778866287946, 1.19656945287214, 0.9572813561378071, 0.6761277876780086, 0.363040786852733, 0.029491357883009692, -0.3118498014530514, -0.6475024745220133, -0.963606446607937, -1.246377067196934, -1.4825722027008175, -1.6599550467626978, -1.7677368880732205, -1.7969841161560596, -1.7409744883697742, -1.595488980896249, -1.3590273764985277, -1.0329380554421408, -0.6214551865164522, -0.13163957778960936, 0.4267772588622552, 1.041642862250406, 1.6987210179650085, 2.382106737468026, 3.074706335405962, 3.758767270017342, 4.416440247961858, 5.030354514511078, 5.584186330293151, 6.063200431533097, 6.45474481121683, 6.748680445353857, 6.9377295942415325, 7.01772897728307, 6.987777367815833, 6.850270872620955, 6.610823218523251, 6.278072617573969, 5.863381062494937, 5.380436049059682, 4.844768566044292, 4.27320457760069, 3.6832700025088907, 3.0925712450338008, 2.518174554225414, 1.9760078144082092, 1.480307765794103, 1.0431341241127248, 0.6739696533772468, 0.3794220253390231, 0.16303938707999976, 0.02524710039545551, -0.03659171459402549, -0.027994211554154512, 0.04293820538058834, 0.16591783491255804, 0.3289541163150125, 0.5189024130928988, 0.7220551069807458, 0.9247500042351277, 1.1139701304150451, 1.2779091606454143, 1.4064780136445636, 1.4917304956343493, 1.5281892330101123, 1.5130573532524705, 1.446306293828362, 1.33063553574709, 1.1713057422087891, 0.9758524862884864, 0.7536932209376469, 0.5156451302394071, 0.27337576900100313, 0.03881174122920107, -0.17646708364095848, -0.36181928971060134, -0.5080913063082781, -0.6080977828030946, -0.6570090941630855, -0.6526261235227013, -0.5955274691590035, -0.48908001778135846, -0.3393101628230609, -0.1546395428628772, 0.05450427054264537, 0.27618550225237637, 0.4975441322458194, 0.705439267650064, 0.8871216513284363, 1.030902929231361, 1.1267886910049758, 1.167043250807164, 1.14665664288063, 1.0636882905036142, 0.9194671167455507, 0.7186342832622461, 0.4690219928279711, 0.18136954889314916, -0.13111422551509597, -0.453325420599722, -0.7689524447724854, -1.0612463833601147, -1.3138394254536112, -1.5115731461611095, -1.6412968463483408, -1.692596432932446, -1.6584165080996918, -1.5355423732931661, -1.3249144009146983, -1.0317544547437205, -0.6654924428854003, -0.23949029343504136, 0.22942976709387855, 0.7216362292350282, 1.2154932089503985, 1.688285822150722, 2.117225955896971, 2.480493462752816, 2.7582649202259417, 2.933681422949886, 2.9937085000041015, 2.9298451533787366, 2.7386450650386633, 2.422020980932496, 1.9873128137015452, 1.447110690236078, 0.8188355179095427, 0.12409112264200689, -0.6121869277670182, -1.3627506034903476, -2.0991829570295315, -2.793115385829088, -3.4174636438006862, -3.9476257550355593, -4.36258579367164, -4.645871006289421, -4.786315848735014, -4.7785949399747905, -4.623497333656786, -4.3279264014600365, -3.9046224560611607, -3.371618403578637, -2.7514515658955965, -2.0701667162268507, -1.3561557262037685, -0.6388874955405647, 0.05241241349582788, 0.6900701060861559, 1.249197436848404, 1.708792811627805, 2.0526558012025258, 2.2700714591546656, 2.3562313047200814, 2.31237074007409, 2.145616595771941, 1.8685528476346893, 1.4985266013410823, 1.0567294803743845, 0.5671009037096941, 0.055108804061007696], 'positive_zeros': ['1.45391834572287050326864920532196', '2.09321481864337913153636490983308', '3.55507148039555621237041862496779', '4.37656358417063700981146737998457', '5.18409271346909968904575429061236', '5.90313607328616586839250961594796', '7.53014566471801599835571048915390', '7.64238058691923613510999831675005', '8.641569477463814017183032857648812'], 'prelabel': '2-1815-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.348355746707748, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c3-0', 'trace_hash': 1370562288652184237, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.45391834572287050326864920532', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.09321481864337913153636490983', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.55507148039555621237041862497', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 107.08846666041927, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 1815, 'conductor_radical': 165, 'degree': 2, 'dirichlet_coefficients': [1, -1, 3, -7, 5, -3, 24, 15, 9, -5, 0, -21, -22, -24, 15, 41, 14, -9, 20, -35, 72, 0, -168, 45, 25, 22, 27, -168, -230, -15, -288, -161, 0, -14, 120, -63, -34, -20, -66, 75, -122, -72, 188, 0, 45, 168, 256, 123, 233, -25, 42, 154, -338, -27, 0, 360, 60, 230, 100, -105, -742, 288, 216, -167, -110, 0, -84, -98, -504, -120, -328, 135, 38, 34, 75, -140, 0, 66, 240, 205, 81, 122, -1212, -504, 70, -188, -690, 0, 330, -45, -528, 1176, -864, -256, 100, -483, 866, -233, 0, -175], 'euler11': [1, 0, 0], 'euler13': [1, 22, 2197], 'euler17': [1, -14, 4913], 'euler19': [1, -20, 6859], 'euler2': [1, 1, 8], 'euler23': [1, 168, 12167], 'euler29': [1, 230, 24389], 'euler3': [1, -3, 0], 'euler31': [1, 288, 29791], 'euler37': [1, 34, 50653], 'euler41': [1, 122, 68921], 'euler43': [1, -188, 79507], 'euler47': [1, -256, 103823], 'euler5': [1, -5, 0], 'euler53': [1, 338, 148877], 'euler59': [1, -100, 205379], 'euler61': [1, 742, 226981], 'euler67': [1, 84, 300763], 'euler7': [1, -24, 343], 'euler71': [1, 328, 357911], 'euler73': [1, -38, 389017], 'euler79': [1, -240, 493039], 'euler83': [1, 1212, 571787], 'euler89': [1, -330, 704969], 'euler97': [1, -866, 912673], 'euler_factors': [[1, 1, 8], [1, -3, 0], [1, -5, 0], [1, -24, 343], [1, 0, 0], [1, 22, 2197], [1, -14, 4913], [1, -20, 6859], [1, 168, 12167], [1, 230, 24389], [1, 288, 29791], [1, 34, 50653], [1, 122, 68921], [1, -188, 79507], [1, -256, 103823], [1, 338, 148877], [1, -100, 205379], [1, 742, 226981], [1, 84, 300763], [1, 328, 357911], [1, -38, 389017], [1, -240, 493039], [1, 1212, 571787], [1, -330, 704969], [1, -866, 912673]], 'index': 191, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1815/4/a/e/1/1', 'ModularForm/GL2/Q/holomorphic/1815/4/a/e'], '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': '2-1815-1.1-c3-0-191', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-1815-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.348355746707748, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 1370562288652184237, 'z1': {'__RealLiteral__': 0, 'data': '1.45391834572287050326864920532', 'prec': 100}}
  • lfunc_instances • Show schema
    • id: 21027191
      {'Lhash': '1843060463638431141060212675953', 'Lhash_array': ['1843060463638431141060212675953'], 'factors': ['2-1815-1.1-c3-0-191'], 'label': '2-1815-1.1-c3-0-191', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1815/4/a/e'}
    • id: 24592298
      {'Lhash': '1843060463638431141060212675953', 'Lhash_array': ['1843060463638431141060212675953'], 'factors': ['2-1815-1.1-c3-0-191'], 'label': '2-1815-1.1-c3-0-191', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1815/4/a/e/1/1'}