-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '4231143406478330438289014209490', 'a10': [-28.170062622667935, 29.365270079769534], 'a2': [1.958030661443257, -2.041106545197502], 'a3': [0.0, -3.0], 'a4': [-0.3322318576961633, -7.993098397538451], 'a5': [-14.386936413908805, 0.0], 'a6': [-6.123319635592505, -5.8740919843297705], 'a7': [-4.16267566377655, 18.046388317838073], 'a8': [-16.965285619700737, -14.972611123046487], 'a9': [-9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.912320880964428, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.958030661443257, 2.041106545197502]]], [3, [[1.0, 0], [0, 3.0]]], [7, [[1.0, 0], [4.16267566377655, -18.046388317838073]]]], 'bad_primes': [2, 3, 7], 'central_character': '168.139', 'coefficient_field': 'CDF', 'conductor': 168, 'conductor_radical': 42, 'conjugate': '203845435413760997295105100442', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.958030661443257, 2.041106545197502]], [[1.0, 0], [0, 3.0]], [[1.0, 0], [14.386936413908805, 0], [125.0, 0]], [[1.0, 0], [4.16267566377655, -18.046388317838073]], [[1.0, 0], [-20.672342303285344, 0], [1331.0, 0]], [[1.0, 0], [55.348619710164726, 0], [2197.0, 0]], [[1.0, 0], [0, -35.08162546827442], [-4913.0, 0]], [[1.0, 0], [0, 45.44607381102583], [-6859.0, 0]], [[1.0, 0], [0, 14.359169944062366], [-12167.0, 0]], [[1.0, 0], [0, 223.5308141516203], [-24389.0, 0]], [[1.0, 0], [186.24610519478563, 0], [29791.0, 0]], [[1.0, 0], [0, 57.016141646138486], [-50653.0, 0]], [[1.0, 0], [0, 29.18190967159481], [-68921.0, 0]], [[1.0, 0], [461.06799481361776, 0], [79507.0, 0]], [[1.0, 0], [-101.00139905603649, 0], [103823.0, 0]], [[1.0, 0], [0, -342.0105858892592], [-148877.0, 0]], [[1.0, 0], [0, 621.4425140528358], [-205379.0, 0]], [[1.0, 0], [-877.1738202257939, 0], [226981.0, 0]], [[1.0, 0], [633.331497773826, 0], [300763.0, 0]], [[1.0, 0], [0, 28.65209411429857], [-357911.0, 0]], [[1.0, 0], [0, 575.3898226954487], [-389017.0, 0]], [[1.0, 0], [0, 596.7801418939767], [-493039.0, 0]], [[1.0, 0], [0, 1022.5999843669696], [-571787.0, 0]], [[1.0, 0], [0, -968.0503918563262], [-704969.0, 0]], [[1.0, 0], [0, -1578.1132048955378], [-912673.0, 0]], [[1.0, 0], [-806.1233032137701, 0], [1030301.0, 0]], [[1.0, 0], [110.52884392367736, 0], [1092727.0, 0]], [[1.0, 0], [-1954.9809623359145, 0], [1225043.0, 0]], [[1.0, 0], [0, 1951.3287305588972], [-1295029.0, 0]], [[1.0, 0], [42.89599784650642, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 47, 'label': '2-168-56.27-c3-0-47', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/168/4/p/a/139/33', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.45701447618969476, 0.8373497160590926, 1.2361611495286777, 1.6498422817471536, 2.074043917388677, 2.5033921719247085, 2.9312700105835754, 3.34969392076045, 3.7493113525008006, 4.119537239873628, 4.448839521831986, 4.725174166774751, 4.936559742714027, 5.071770139575187, 5.1211119685995445, 5.077241093980669, 4.935961683900854, 4.6969423575459, 4.364278852133243, 3.9468325265661304, 3.458280146083683, 2.9168235550428574, 2.344528266886186, 1.766287172927534, 1.2084381483390363, 0.6971000995580479, 0.2563279328705491, -0.09378062180021282, -0.33886842305454695, -0.47182112136029253, -0.4938180701137265, -0.41478057858389633, -0.2531031951798815, -0.03460820452539526, 0.20926756277782815, 0.4439663558217937, 0.6348160472877633, 0.7503082679745384, 0.7653486863441057, 0.6641464726593458, 0.44240852438623246, 0.10853945131604367, -0.31637818322030886, -0.7999404846092143, -1.3010974403498314, -1.7739783762403316, -2.172550459959812, -2.4556634807863773, -2.591942029388982, -2.5639476220873965, -2.3710597888462814, -2.030621531985789, -1.577057467804433, -1.0588900211034813, -0.5338293025700499, -0.06236782430720118, 0.2994601479772611, 0.5073256634926733, 0.5349487492727606, 0.3786567369819406, 0.05942043731034047, -0.3781126323608508, -0.869723849706095, -1.338606602962609, -1.7045639841870313, -1.8944058721665589, -1.8522802091732993, -1.5485699314891395, -0.9860590613544611, -0.2023261209167079, 0.7322573997735893, 1.72100403275157, 2.6513436353380846, 3.4081150865795897, 3.8881438867323275, 4.014238970038232, 3.746685353779083, 3.0905179373177836, 2.097327523670671, 0.8610263441848122, -0.4921944432136204, -1.8186558585297903, -2.974941742621596, -3.836301475550548, -4.313181177670506, -4.3634982745648685, -3.998769883217876, -3.283006520979337, -2.324287238941623, -1.2600003693363844, -0.23770659006808575, 0.6056963991854508, 1.163480470692281, 1.3743381909265742, 1.2310071367367093, 0.780841288462964, 0.11810713390482029, -0.6309356392990629, -1.3279504847919128, -1.8443766161017734, -2.0817809042441087, -1.987442130366926, -1.5626100516401085, -0.8620326668460969, 0.015239171356610877, 0.9423095793591296, 1.7854567631340852, 2.4262011316251293, 2.7806827656999418, 2.813023360087263, 2.540352073104218, 2.028609366616706, 1.3798654830860742, 0.7134149856612462, 0.14405673658035, -0.23848117243954187, -0.385179185276592, -0.29550996258257645, -0.015893605897320116, 0.3708945714191879, 0.7633377827378628, 1.0623872663035443, 1.1920695497887543, 1.1153220204165804, 0.8417416964462514, 0.42547685206998276, -0.04655126616860283, -0.47391146847058074, -0.7655857973832189, -0.8617947602553067, -0.74996307522772, -0.4710400785334057, -0.11419820572471444, 0.19974631200281892, 0.34345817416278035, 0.21204843198732867, -0.24995329673489003, -1.0294581859461005, -2.0381572777764214, -3.1207718430566582, -4.077790306569566, -4.699310435549562, -4.804140234406531, -4.27686378818781, -3.095500262468295, -1.343769604279327, 0.7953689625436972, 3.0647823249074038, 5.173096635292373, 6.842707190743916, 7.857212782515669, 8.099379774601413, 7.57223492182781, 6.398887857224827, 4.800651878154332, 3.057206017917096, 1.4560932618052735, 0.24104751896028345, -0.4309943033716211, -0.5159292160487222, -0.08657609036112217, 0.6858668060989547, 1.5691720294973743, 2.3186466877350846, 2.7270640551111467, 2.6658724444687736, 2.1094263567504816, 1.1375382133087588, -0.08381277841344602, -1.339208054820974, -2.409917975475234, -3.1194902938245574, -3.3690950347493005, -3.1552573537461948, -2.5665398672804267, -1.760399885124872, -0.9258132711426685, -0.24035031777837168, 0.1684882490339807, 0.2489745928668977, 0.032288252001872526, -0.38015168332548543, -0.8457387614378631, -1.2188511986114907, -1.388744994640506, -1.3078659045219287, -1.003605328859939, -0.5705544124478595, -0.14509818072674854, 0.1314056834363092, 0.15167485585999302, -0.1261508918640239, -0.6630980320867322, -1.3443446657471203, -2.004087311215783, -2.4647805072312767, -2.581461038467944, -2.2802705078511374, -1.5813359486318739, -0.5996852766135017, 0.4769244194830443, 1.4287309215758517, 2.05397850616323, 2.2163504002004824, 1.8781977295058636, 1.1110648262788811, 0.08034127030408109, -0.9928390593340425, -1.8836121542607747, -2.4167654033256416, -2.508241792889308, -2.1841109253229005, -1.5716974493041467, -0.8644226417236955, -0.2686332886731317, 0.05442830538625228, 0.03661471293038416, -0.2721229796082344, -0.7093616917939897, -1.0366472004402607, -0.9991027633375767, -0.3943037980519077, 0.8665333166629092, 2.720953284220474, 4.952110936106275, 7.222968051175719, 9.141734490577203, 10.344580786757207, 10.576891459561637, 9.753953147712263, 7.986206778209632, 5.5621353788534975, 2.8916681023828263, 0.422311357442293, -1.4532094900625976, -2.4768445368333296, -2.5745182259674717, -1.8638809311641764, -0.6193825079980415, 0.796388064406731, 2.0182920874858934, 2.7606379875913936, 2.8763926363708197, 2.3804264745421384, 1.4327681089965123, 0.28781461769897626, -0.776297644525702, -1.5294844046528802, -1.8443896167739438, -1.7207593677518764, -1.2747059630035025, -0.6974725952460756, -0.1962612949028351, 0.06591932421192606, 0.014718213034492349, -0.31862604258384164, -0.8117434069653608], 'positive_zeros': ['3.33778361775441125565942550866388', '4.14313694710982616960524311206549', '5.15924637606295904478203992478438', '6.89370559628449480138302834861338', '7.51873640853693207463882497712695', '8.653416042908866717127991945328710', '9.954960405784669011243274247781111', '11.28197787282277086793647502587813', '12.02008405787398228894776130869885', '12.99793889844094483712380785659327'], 'prelabel': '2-168-56.27-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.148383852227112, 'root_angle': -0.34883671282152134, 'root_number': '-0.5818563785133137 - 0.8132915558293787*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.348836712822', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.33778361775441125565942550866', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.14313694710982616960524311207', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.15924637606295904478203992478', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 9.912320880964428, 'bad_primes': [2, 3, 7], 'central_character': '56.27', 'conductor': 168, 'conductor_radical': 42, 'degree': 2, 'index': 47, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/168/4/p/a/139/33'], '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': '2-168-56.27-c3-0-47', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-168-56.27-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.148383852227112, 'root_angle': -0.34883671282152134, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '3.33778361775441125565942550866', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '4231143406478330438289014209490', 'Lhash_array': ['4231143406478330438289014209490'], 'factors': ['2-168-56.27-c3-0-47'], 'label': '2-168-56.27-c3-0-47', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/168/4/p/a/139/33'}