-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '247481408804557396365796256366', 'a10': [1.872587383741392, 1.0811388300841898], 'a2': [-3.525901212589449, 0.9447623825052591], 'a3': [-1.0811388300841898, 1.872587383741392], 'a4': [8.075301786404976, -4.662277660168379], 'a5': [-0.41886116991581035, -0.41886116991581035], 'a6': [2.042838593858575, -7.6239774239427645], 'a7': [-1.9382004025483057, -0.5193392326324955], 'a8': [-13.743416490252569, 13.743416490252569], 'a9': [2.1622776601683795, 3.745174767482784], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.604916467689018, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[13, [[1.0, 0], [0, 0]]]], 'bad_primes': [13], 'central_character': '169.150', 'coefficient_field': 'CDF', 'conductor': 169, 'conductor_radical': 13, 'conjugate': '2505934270252313117966900543409', 'degree': 2, 'euler_factors': [[[1.0, 0], [3.525901212589449, -0.9447623825052591], [3.4641016151377544, -2.0]], [[1.0, 0], [1.0811388300841898, -1.872587383741392], [-4.5, -7.794228634059948]], [[1.0, 0], [0.41886116991581035, 0.41886116991581035], [0, 25.0]], [[1.0, 0], [1.9382004025483057, 0.5193392326324955], [42.4352447854375, 24.5]], [[1.0, 0], [-2.6809733186677205, -10.00552863900448], [-104.78907385791707, 60.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [13.833600513801667, -7.986832980505138], [144.5, -250.28134169370276]], [[1.0, 0], [-1.1574739574416408, 4.31975161761002], [-312.63517076618234, -180.5]], [[1.0, 0], [23.804295630697386, 13.743416490252569], [264.5, 458.12743860196804]], [[1.0, 0], [12.905694150420949, -22.35331797547354], [-420.5, -728.3273645827129]], [[1.0, 0], [19.486832980505138, 19.486832980505138], [0, 961.0]], [[1.0, 0], [-1.5483787706429977, -5.778628241400704], [-1185.5887777808964, 684.5]], [[1.0, 0], [-15.247954847885529, 4.08567718771715], [1455.7887037616413, -840.5]], [[1.0, 0], [9.97069511689572, -5.756583509747431], [924.5, -1601.280971597427]], [[1.0, 0], [35.36619309193636, -35.36619309193636], [0, -2209.0]], [[1.0, 0], [4.188611699158104, 0], [2809.0, 0]], [[1.0, 0], [41.35216699355814, 11.080279751200832], [3014.634430573631, 1740.5]], [[1.0, 0], [-33.83772233983162, -58.6086543049968], [-1860.5, 3222.4805274818964]], [[1.0, 0], [110.76181421406359, -29.678538670864388], [3887.5880375883453, -2244.5]], [[1.0, 0], [18.46422294532448, -68.90941815423001], [-4365.634060477355, -2520.5]], [[1.0, 0], [-31.622776601683793, 31.622776601683793], [0, -5329.0]], [[1.0, 0], [-50.785054261852174, 0], [6241.0, 0]], [[1.0, 0], [18.622776601683793, 18.622776601683793], [0, 6889.0]], [[1.0, 0], [33.348431635963266, 124.45804121815219], [-6859.787223376538, 3960.5]], [[1.0, 0], [31.974208731238694, -119.3293715167952], [-8148.433024207783, -4704.5]], [[1.0, 0], [-7.725810793811895, -4.460498941515414], [5100.5, 8834.325144005059]], [[1.0, 0], [0, -59.43416490252569], [-10609.0, 0]], [[1.0, 0], [-71.78505426185217, 124.33536120561673], [-5724.5, -9915.124847928038]], [[1.0, 0], [-84.77402395547233, -84.77402395547233], [0, 11881.0]], [[1.0, 0], [-54.27188724235731, -94.00166612641203], [-6384.5, 11058.278380923497]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-13e2-13.7-c2-0-1', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/169/3/f/d/150/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.17904706946676888, 0.06293882448509848, -0.04776974906882544, -0.15175749097994612, -0.24717723677597467, -0.3314830421189008, -0.40136149303400426, -0.45277650185004314, -0.4811298293321402, -0.4815343830316586, -0.44919297746352393, -0.3798703235766001, -0.270439622920898, -0.11947707974171506, 0.0721316102270194, 0.3006182069020482, 0.558846122453594, 0.8359715709924469, 1.117313303296018, 1.384489206798397, 1.615868387913999, 1.7873707977178872, 1.8736230401032514, 1.8494494833448414, 1.6916437791981909, 1.3809298171965696, 0.9039862060510442, 0.25537835464979874, -0.5607788224637643, -1.5296126850598346, -2.6249161054160335, -3.809352450992076, -5.035546644256479, -6.248102646413375, -7.386509121484498, -8.388807491390345, -9.19580772858823, -9.755556160307881, -10.027696069554427, -9.987325428273435, -9.627954643792208, -8.963206012417066, -8.026977177621, -6.871910277925182, -5.566158751581807, -4.188612365559842, -2.8229115074526367, -1.5507352305173907, -0.4449645992609456, 0.43661399865247247, 1.056405019713487, 1.4003170078046814, 1.4788613262846955, 1.3258178382795256, 0.9945049700135499, 0.5519637191939302, 0.07162176245203078, -0.3747881693717047, -0.725152252089592, -0.9338110856700443, -0.976462479191963, -0.8524857643660064, -0.5843356217441883, -0.21401107306283776, 0.20301581952410494, 0.6056763437788629, 0.9359788542554499, 1.1473208847476408, 1.2112808182096877, 1.12189248590078, 0.8967188544578114, 0.5744699753837444, 0.20940141342033614, -0.13678537395924936, -0.40441224626861794, -0.5452726014316746, -0.5306008059258692, -0.35625695172407273, -0.04418453289379721, 0.3602674544474421, 0.794933329807629, 1.1904661080538292, 1.4816102358456975, 1.6183470911875484, 1.5750547191935713, 1.3560264789312444, 0.9961839085377707, 0.5565395977760359, 0.11481589146061086, -0.2475254631352533, -0.4598804615446675, -0.4763294682326896, -0.2862288665235595, 0.08055343847382364, 0.555148774533053, 1.0383058343695115, 1.4152982154757836, 1.575160148659173, 1.431377668434335, 0.9406561176036086, 0.11640328082507233, -0.9658485864653197, -2.1727605926980376, -3.3274544921058853, -4.232315724833323, -4.697401410049311, -4.570373801501233, -3.7633189924784123, -2.2719738363868807, -0.18379401029389666, 2.3271492930642164, 5.018475747831718, 7.6089346769484045, 9.815025663768099, 11.389519394925768, 12.156066048725936, 12.034475168844844, 11.052550635616559, 9.342386137508441, 7.121457006336146, 4.6612861352410295, 2.248500103523652, 0.14436693204279086, -1.4508190696476213, -2.4229364481610243, -2.7549997762725993, -2.522477454871718, -1.8742108563980853, -1.0026140671007642, -0.10860528070626943, 0.6324914689132614, 1.0981784736645577, 1.2346658654681488, 1.0591337172929378, 0.6487074216528679, 0.11896971451882873, -0.4032663249045969, -0.807254953596534, -1.0202116273023032, -1.0196154910008772, -0.8338475676873652, -0.5315979811768194, -0.20285305270242343, 0.06397683406218445, 0.2034775228799672, 0.1883031603975968, 0.034501082513145966, -0.20404730305263355, -0.45067083058420854, -0.6267930389175348, -0.6735682501083479, -0.5688891297790257, -0.3353474793910642, -0.03676730917299981, 0.2363873948318495, 0.3896934145581738, 0.3503495121223871, 0.08943363556732724, -0.3650065391946604, -0.9280781746524662, -1.4725556623880498, -1.8555954868681537, -1.9523747177727284, -1.6892790626174785, -1.068722436974354, -0.17892282661190614, 0.8151664052994079, 1.6996003202473544, 2.2534450015058725, 2.2970356970510997, 1.736410910385937, 0.5938458059091857, -0.983367274426484, -2.739639647275132, -4.351853194421306, -5.48748327708175, -5.869260064698476, -5.333490082446744, -3.8697257276904597, -1.6326785071994006, 1.0774372737424005, 3.8636077727992806, 6.3011772633734715, 8.014370999866122, 8.745187768226408, 8.400842506482087, 7.070037614190669, 5.004563478440038, 2.5697927476662517, 0.17404293967289877, -1.8088478742314378, -3.108023948300127, -3.6014517175515164, -3.3302487406764616, -2.4794211038151905, -1.330092166658088, -0.19429041396426786, 0.6531477403697233, 1.0307733756330772, 0.8830830790046696, 0.2833168632489995, -0.5927555598886335, -1.514769455626183, -2.255418669134513, -2.6440110756825628, -2.603567796247534, -2.1634422205232653, -1.4455644109296883, -0.6288409525231519, 0.0985983371648657, 0.5869540942746565, 0.7602109296004009, 0.6309957481752979, 0.2918112923245198, -0.11426267342304709, -0.4350906267757497, -0.5519262665063279, -0.4114720845447705, -0.03919382797642154, 0.4693466314971146, 0.9764340081325835, 1.3415245775968525, 1.4610117428475404, 1.2974071542934618, 0.8898358773817975, 0.3429088303439426, -0.20294111735944956, -0.6113318908157745, -0.7886883483422418, -0.7106825934545864, -0.4284548030187685, -0.05234722914101121, 0.28264345666258134, 0.459973703111292, 0.4205362641837305, 0.18538292948888682, -0.145867682073158, -0.42233738820284084, -0.48881213664120193, -0.23990059853916146, 0.3341764990239029, 1.124821331478792, 1.914818896439124, 2.4218790811992346, 2.3679160051765686, 1.558109949043098, -0.05048318504297245, -2.310248404032678, -4.887760698804621, -7.3155011816009266, -9.082422046515795, -9.744808504857152, -9.032420085719531, -6.924271532037645, -3.674110721911708, 0.22344260410990346, 4.121496619322192], 'positive_zeros': ['0.19522840817493442878729903362066', '1.70586153202770492188417130457939', '3.41689430262510694381191948601924', '6.05873395134088100670143431364513', '7.01897234179318709943787291856857', '7.939748114391092505784258053918140', '9.073343775646452045144121430326749', '9.764810074301590795687534423353457', '11.03564115531802258545807548414182', '11.60125754952310532568389535238228'], 'prelabel': '2-13e2-13.7-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.145906910303664, 'root_angle': 0.42281223614903307, 'root_number': '-0.8846819310751071 + 0.4661951102588052*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.422812236149', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.19522840817493442878729903362', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.70586153202770492188417130458', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.41689430262510694381191948602', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.604916467689018, 'bad_primes': [13], 'central_character': '13.7', 'conductor': 169, 'conductor_radical': 13, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/169/3/f/d/150/1'], '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': '2-13e2-13.7-c2-0-1', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-13e2-13.7-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.145906910303664, 'root_angle': 0.42281223614903307, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.19522840817493442878729903362', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '247481408804557396365796256366', 'Lhash_array': ['247481408804557396365796256366'], 'factors': ['2-13e2-13.7-c2-0-1'], 'label': '2-13e2-13.7-c2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/169/3/f/d/150/1'}