-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1927080637667888048664717042176', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 4.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [3.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.0220851458723894, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]]], 'bad_primes': [2], 'central_character': '128.65', 'coefficient_field': 'CDF', 'conductor': 128, 'conductor_radical': 2, 'conjugate': '3263983786115997841916595230851', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-3.0, 0]], [[1.0, 0], [0, -4.0], [-5.0, 0]], [[1.0, 0], [0, 0], [7.0, 0]], [[1.0, 0], [0, 0], [-11.0, 0]], [[1.0, 0], [0, 4.0], [-13.0, 0]], [[1.0, 0], [2.0, 0], [17.0, 0]], [[1.0, 0], [0, 0], [-19.0, 0]], [[1.0, 0], [0, 0], [23.0, 0]], [[1.0, 0], [0, 4.0], [-29.0, 0]], [[1.0, 0], [0, 0], [31.0, 0]], [[1.0, 0], [0, 12.0], [-37.0, 0]], [[1.0, 0], [-10.0, 0], [41.0, 0]], [[1.0, 0], [0, 0], [-43.0, 0]], [[1.0, 0], [0, 0], [47.0, 0]], [[1.0, 0], [0, -4.0], [-53.0, 0]], [[1.0, 0], [0, 0], [-59.0, 0]], [[1.0, 0], [0, -12.0], [-61.0, 0]], [[1.0, 0], [0, 0], [-67.0, 0]], [[1.0, 0], [0, 0], [71.0, 0]], [[1.0, 0], [-6.0, 0], [73.0, 0]], [[1.0, 0], [0, 0], [79.0, 0]], [[1.0, 0], [0, 0], [-83.0, 0]], [[1.0, 0], [10.0, 0], [89.0, 0]], [[1.0, 0], [18.0, 0], [97.0, 0]], [[1.0, 0], [0, -20.0], [-101.0, 0]], [[1.0, 0], [0, 0], [103.0, 0]], [[1.0, 0], [0, 0], [-107.0, 0]], [[1.0, 0], [0, 20.0], [-109.0, 0]], [[1.0, 0], [14.0, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-2e7-8.5-c1-0-1', '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/128/2/b/b/65/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.1024393989965828, 1.0629448407031084, 1.0311919293818377, 1.0029597895918658, 0.9731026026616466, 0.9359726195152133, 0.8857895695524722, 0.8169400070357623, 0.7242299587618624, 0.6031243212545596, 0.44999704705550425, 0.2624003861204581, 0.039346807146272055, -0.2184139049128424, -0.5081474798367991, -0.8249475959666894, -1.16163942274176, -1.5088048668178928, -1.8549562869648994, -2.1868785115625236, -2.4901489135101547, -2.749832272362767, -2.95133170712295, -3.0813599817570205, -3.128978215898027, -3.086633036518165, -2.9511102651027374, -2.7243152132582305, -2.413788323107917, -2.0328716936978526, -1.600457906307735, -1.140277683066157, -0.6797165518173913, -0.24819108980891733, 0.12484031413768788, 0.4121126361401591, 0.5908753932377312, 0.6451084921510375, 0.5674237449198201, 0.3604431321798493, 0.03746559624413362, -0.3777234302181805, -0.8519824700905029, -1.344886871205944, -1.8116550270198337, -2.2067441759868807, -2.4878437978700054, -2.6199233084947386, -2.5789463738094973, -2.354855181639383, -1.9534600759825969, -1.3969448292943858, -0.7228125834881478, 0.018755790705763956, 0.7689931682833072, 1.465781039436236, 2.049568966522615, 2.4694032350466117, 2.688426082293515, 2.688210321167771, 2.4713710790848364, 2.0620454079005492, 1.504041368733096, 0.8567117520240772, 0.18887734428477332, -0.4286208179236535, -0.9309543159304959, -1.2670112970925538, -1.405830974786857, -1.3409160297693146, -1.0917717124395616, -0.7023198441848663, -0.23620332364034924, 0.23060957526064021, 0.6191409933468404, 0.8575618608838877, 0.8909367618758258, 0.689272755699299, 0.25273097979572984, -0.3868369182782193, -1.1684290485996902, -2.008391640555343, -2.81021825355079, -3.476508540240361, -3.921587052386854, -4.083109246492092, -3.9310306813203906, -3.4725947090118034, -2.7524794673764115, -1.8478807247630782, -0.8590111747075712, 0.10382870407423092, 0.9349085051782221, 1.5474281767833127, 1.8855075147795062, 1.9319882195122566, 1.710771543145197, 1.2831726395602567, 0.7386469783788885, 0.18110795412451533, -0.2872249502313953, -0.5820505205281604, -0.6507763722996156, -0.4816443006022619, -0.10659589938012644, 0.4027982093293635, 0.9459539727119229, 1.4089865165823587, 1.683197495868997, 1.683472414981106, 1.36361734474979, 0.7260346862640246, -0.17605267699401955, -1.2444812987224714, -2.3494882433527104, -3.348624452638537, -4.108364300855933, -4.524983474772049, -4.54127356123193, -4.156231497328637, -3.425934676487717, -2.455228035068418, -1.3813813236447465, -0.35226553575782676, 0.49739812522804244, 1.0677348998041591, 1.3096222020319932, 1.2319710666836061, 0.8989785566390754, 0.4176690240926935, -0.08223505221586987, -0.4726557125506676, -0.6514142305263565, -0.5619973391810031, -0.20512677547955274, 0.36018784404287674, 1.0265754225355492, 1.6576672612887398, 2.1135678813907153, 2.2778671459522593, 2.0811959486643423, 1.5168089719424778, 0.6450169684321919, -0.41473079771929566, -1.5030432712224877, -2.4478471519754046, -3.0948808272942303, -3.335839639376926, -3.1288655859292596, -2.507364545328055, -1.5752262223511537, -0.489042502929255, 0.5696012035280611, 1.426728664791701, 1.9473936038926074, 2.0599454284040335, 1.7684298954010709, 1.1506254001988854, 0.34196747068162303, -0.4916197344292384, -1.1867326307603114, -1.6148438602957955, -1.7075351722370655, -1.4694604851582962, -0.9762812488361636, -0.357819217205321, 0.23030358971781, 0.6408370712306968, 0.7678634087875933, 0.5716091293985048, 0.08969356104964725, -0.5679187963437884, -1.2396708922872677, -1.7449857735937788, -1.9221957607748321, -1.6640598360141134, -0.9433797912638338, 0.17692362826689964, 1.5518328996898376, 2.979213531344002, 4.237053436949204, 5.125601067951655, 5.5058591940922, 5.326477898490363, 4.633366359195799, 3.559866065046408, 2.299377133958064, 1.0660510541019383, 0.05175208772490724, -0.6116359871561491, -0.8765465284621293, -0.7855136540025592, -0.457194181147906, -0.055732508175110204, 0.24972794934239653, 0.326326229019623, 0.11021243515339149, -0.3768300696209115, -1.0309064458626438, -1.6892209092806112, -2.1680358653389544, -2.30697064526066, -2.009584055483757, -1.2707767672412802, -0.1843020138275195, 1.0719827179125785, 2.2704989729192775, 3.1808195922345845, 3.6188704512983283, 3.4875197490892282, 2.7992939732491147, 1.6757797413927724, 0.3234079173405579, -1.0093730987086185, -2.0842551364391464, -2.7230445692062593, -2.8442955440459046, -2.4783600682533264, -1.7574610243169868, -0.8830868509526977, -0.07823669507596029, 0.464413381569355, 0.626353984043579, 0.38884578460991354, -0.16571414043720226, -0.8769395040895084, -1.5485376805329614, -1.9991538662397195, -2.109582962936511, -1.8546875031952397, -1.3119207048959702, -0.6439384939218455, -0.059083254157255106, 0.2409755510799451, 0.1138041074220771, -0.4840155957317016, -1.4800620116589562, -2.69702481549632, -3.8895967848715745, -4.799117743091674, -5.213277410627485, -5.016669557462118, -4.219897513074688, -2.959865317997513, -1.4707042800671475, -0.03185113427742143, 1.0946131352556827, 1.7225309558154092, 1.7821694365501306, 1.3329690827450589, 0.5455596511467429, -0.34243672475461323, -1.0858490230254785, -1.491905898259426, -1.4658172767717255, -1.030707363798782, -0.31707057739178746], 'positive_zeros': ['1.52019857626457482641329780176444', '4.20531702035781344901108809042135', '5.01237511108207605464128768469831', '6.62189904477336838247127256570702', '8.036557796973512610753317860724868', '9.061941896594789261995051039124611', '9.803680106827546855846298258803804', '11.36090455256956921638940592955055', '12.41930941597087059874329181038232', '13.02824755955478473580174590461450'], 'prelabel': '2-2e7-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0109822678328189, 'root_angle': -0.25, 'root_number': '0.7071067811865476 - 0.7071067811865475*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.125', 'prec': 20}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.52019857626457482641329780176', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.20531702035781344901108809042', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.01237511108207605464128768470', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.0220851458723894, 'bad_primes': [2], 'central_character': '8.5', 'conductor': 128, 'conductor_radical': 2, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/128/2/b/b/65/2'], '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': '2-2e7-8.5-c1-0-1', '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': '2-2e7-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0109822678328189, 'root_angle': -0.125, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.52019857626457482641329780176', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1927080637667888048664717042176', 'Lhash_array': ['1927080637667888048664717042176'], 'label': '2-2e7-8.5-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/128/2/b/b/65/2'}