-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2752322051478702689840846685334', 'a10': [9.621865435700597, 0.0], 'a2': [2.820928193259294, 0.0], 'a3': [3.0, 0.0], 'a4': [-0.04236412847485685, 0.0], 'a5': [3.4108863382954517, 0.0], 'a6': [8.462784579777882, 0.0], 'a7': [-13.344175407088635, 0.0], 'a8': [-22.68693171047193, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.913968372910507, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-3.0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '507.1', 'coefficient_field': 'CDF', 'conductor': 507, 'conductor_radical': 39, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.820928193259294, 0], [8.0, 0]], [[1.0, 0], [-3.0, 0]], [[1.0, 0], [-3.4108863382954517, 0], [125.0, 0]], [[1.0, 0], [13.344175407088635, 0], [343.0, 0]], [[1.0, 0], [35.452932029319015, 0], [1331.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-69.6525821428103, 0], [4913.0, 0]], [[1.0, 0], [12.401351149753209, 0], [6859.0, 0]], [[1.0, 0], [126.25126311858818, 0], [12167.0, 0]], [[1.0, 0], [179.05976494367422, 0], [24389.0, 0]], [[1.0, 0], [255.9348478238386, 0], [29791.0, 0]], [[1.0, 0], [207.23500570857186, 0], [50653.0, 0]], [[1.0, 0], [-117.7011365351709, 0], [68921.0, 0]], [[1.0, 0], [-553.2239047228163, 0], [79507.0, 0]], [[1.0, 0], [62.918470303989054, 0], [103823.0, 0]], [[1.0, 0], [147.03092493426294, 0], [148877.0, 0]], [[1.0, 0], [274.08682172414257, 0], [205379.0, 0]], [[1.0, 0], [-603.0389567826383, 0], [226981.0, 0]], [[1.0, 0], [-741.0185886851108, 0], [300763.0, 0]], [[1.0, 0], [572.5743238874708, 0], [357911.0, 0]], [[1.0, 0], [26.71547058502454, 0], [389017.0, 0]], [[1.0, 0], [207.79812177767636, 0], [493039.0, 0]], [[1.0, 0], [-1031.3744984524342, 0], [571787.0, 0]], [[1.0, 0], [1229.6567910635513, 0], [704969.0, 0]], [[1.0, 0], [1795.1153559282627, 0], [912673.0, 0]], [[1.0, 0], [769.6973094464811, 0], [1030301.0, 0]], [[1.0, 0], [-1543.6614103732554, 0], [1092727.0, 0]], [[1.0, 0], [-2027.63974256415, 0], [1225043.0, 0]], [[1.0, 0], [1644.9723851956899, 0], [1295029.0, 0]], [[1.0, 0], [654.5138313228232, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 73, 'label': '2-507-1.1-c3-0-73', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/507/4/a/o/1/7', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [-2.050860318183398e-59, 0.3176672557444554, 0.6333704477603993, 0.9451431337132666, 1.2510147564255885, 1.5490101687864377, 1.8371509922656137, 2.113459314117259, 2.375964142294371, 2.622710935253901, 2.8517744094999187, 3.0612747043872015, 3.249396854945536, 3.4144133927793394, 3.5547097657932283, 3.668812142740553, 3.7554170513239664, 3.8134221915230726, 3.8419576715251487, 3.840416834466571, 3.808485782380707, 3.7461706613700296, 3.65382175098836, 3.5321534028444463, 3.382258899975104, 3.2056193607123045, 3.0041058893020383, 2.779974280644445, 2.535851717850396, 2.2747150578185558, 1.9998604799613335, 1.7148644739915715, 1.423536360948518, 1.129862773192676, 0.8379447589378197, 0.5519284192778976, 0.2759302242197372, 0.013958382036436174, -0.23016815397206428, -0.452901272952276, -0.6510439685095472, -0.8218272443383878, -0.9629815680894912, -1.0728007662783463, -1.1501962987139984, -1.1947399576359554, -1.2066932065107356, -1.1870216065352788, -1.137393073687664, -1.0601590619821888, -0.9583181736418639, -0.8354621462957812, -0.6957046510865609, -0.5435938418629657, -0.3840101108620509, -0.2220510154718735, -0.06290582778465256, 0.08827739293195, 0.22652891174782944, 0.34719499926538566, 0.44607233406614016, 0.5195351446407387, 0.5646510880110645, 0.5792819623167281, 0.5621655772870982, 0.5129754615301403, 0.4323555666342404, 0.32192772856266627, 0.1842703556391726, 0.022867614075801096, -0.1579707432540717, -0.3532178348600027, -0.5572643788268075, -0.7640767349339165, -0.967374403654523, -1.160822295344026, -1.338232356772683, -1.4937685505045273, -1.6221487540111434, -1.718836904712687, -1.7802186844349037, -1.8037542262773842, -1.7881017460424264, -1.7332066490889209, -1.6403515336156473, -1.5121635864886662, -1.3525771230510066, -1.166750425152315, -0.960937541833727, -0.74231728823716, -0.5187832587935414, -0.298700205412773, -0.09063356327844681, 0.0969398208598703, 0.2559306448374171, 0.3789358846698073, 0.45952691242106625, 0.4925164616978906, 0.47419412783803044, 0.40252069323203993, 0.27727255047861055, 0.10012884242702175, -0.1253043805291685, -0.3935367125268212, -0.6973041721644094, -1.0277473541194497, -1.3746536337948252, -1.7267576424309146, -2.0720918560723853, -2.3983769505203725, -2.6934396570495167, -2.9456442959157094, -3.144323043172905, -3.2801893651853575, -3.345718982884612, -3.3354832342296517, -3.2464207977770982, -3.0780354098945373, -2.8325094172338194, -2.514725696211459, -2.132193562400343, -1.6948776853005596, -1.214932601612566, -0.706349053611677, -0.18452193075570045, 0.33424707895706085, 0.8332960553079971, 1.2961800850526237, 1.7072587689120071, 2.052272442340891, 2.318885194115658, 2.4971732396237236, 2.58003852992765, 2.56352963644387, 2.4470548933835454, 2.233476421134452, 1.9290778768129933, 1.5434034380052724, 1.088970453056598, 0.5808631989477476, 0.03622007750129897, -0.5263688493053704, -1.0875330306450857, -1.6278369971541709, -2.12851353164444, -2.572186145955609, -2.9435521664507895, -3.2299984753476303, -3.42212385761891, -3.514144925626246, -3.504166649783877, -3.3943034806967907, -3.1906427309774386, -2.903048080999375, -2.5448075405917505, -2.132136676447515, -1.6835541315448348, -1.2191521486136978, -0.7597897084707221, -0.32623977472188936, 0.061675196373483405, 0.3859240177610189, 0.6310484964670554, 0.7848524618017223, 0.8389675531364579, 0.7892697141692163, 0.636126051146221, 0.3844584302014389, 0.043617650630119874, -0.37293006704372816, -0.8480945286992758, -1.3618134273026228, -1.8918399037799634, -2.414634817166898, -2.9063276650076806, -3.343706488755197, -3.7051951479797043, -3.971776175885838, -4.127819084636872, -4.161777438926693, -4.06672314495925, -3.8406930155310857, -3.48683050425362, -3.013314225338301, -2.4330741137798855, -1.7633054260745789, -1.0247998116675412, -0.241120983308016, 0.5623403115287803, 1.3593916140723983, 2.124100025365188, 2.831843104104356, 3.460303188321421, 3.990361174491962, 4.406850069916499, 4.69913479146049, 4.861492453160315, 4.893276422516902, 4.798857319631435, 4.587344425671362, 4.272101171607656, 3.870078005099749, 3.400994513287832, 2.886409786083543, 2.3487252776981213, 1.8101675874469387, 1.2917994579530916, 0.8126058138623827, 0.38869788708076486, 0.03267256091526021, -0.2468437097074172, -0.44544630906681926, -0.5629894100879635, -0.6034094947359091, -0.5743472811671014, -0.4865901234809372, -0.35336607626863675, -0.1895283581691405, -0.010674501101520878, 0.1677522725603916, 0.331331135444131, 0.46745467878104197, 0.5660006167805314, 0.6198484613570369, 0.6252139571403038, 0.5817840848937184, 0.4926464540340452, 0.3640183268502702, 0.20479173189810987, 0.025921516833223336, -0.16030781883941955, -0.3410935966828851, -0.503957083439645, -0.6375665024306327, -0.7324918466160008, -0.7818458795428458, -0.7817718268672345, -0.7317467232675147, -0.6346797516457818, -0.49679664213453056, -0.32731364848823497, -0.1379170957280065, 0.057923714487691604, 0.2457720326583066, 0.41112099122024576, 0.5403202008612549, 0.6214760982527106, 0.6452707106825939, 0.605646911906932, 0.50031476556313, 0.3310428923616625, 0.1037104912669674, -0.17189091737064485, -0.48250250363443564, -0.8120717035229394, -1.1426221243087131, -1.4552749556390088], 'positive_zeros': ['2.17119926498924165780560523215041', '3.30514636936669444734156886819990', '4.05070595507757101734618876710936', '5.41798253331965019922314861986948', '5.94548107302142102338945664911288', '7.28633008684206433612564951591199', '8.206932620225255561177694262571056', '9.365078152800384422775789599042868', '9.850379171780329086862876859683679'], 'prelabel': '2-507-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.469366359361064, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.17119926498924165780560523215', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.30514636936669444734156886820', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.05070595507757101734618876711', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 29.913968372910507, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 507, 'conductor_radical': 39, 'degree': 2, 'index': 73, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/507/4/a/o/1/7'], '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': '2-507-1.1-c3-0-73', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-507-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.469366359361064, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.17119926498924165780560523215', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2752322051478702689840846685334', 'Lhash_array': ['2752322051478702689840846685334'], 'label': '2-507-1.1-c3-0-73', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/507/4/a/o/1/7'}