-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 1, 'A5': -2, 'A6': 0, 'A7': -1, 'A8': 0, 'A9': 0, 'Lhash': '686417491481491251,853737024938082094', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [-0.894427190999916, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 63.77285407260262, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, -1]], [3, [1]], [7, [1, 1]]], 'bad_primes': [2, 3, 7], 'central_character': '1000188.1', 'coefficient_field': '1.1.1.1', 'conductor': 1000188, 'conductor_radical': 42, 'degree': 4, 'euler_factors': [[1, 0, -1], [1], [1, 2, 11, 10, 25], [1, 1], [1, 0, -3, 0, 121], [1, 0, 26, 0, 169], [1, 4, 38, 68, 289], [1, 0, 37, 0, 361], [1, 0, 45, 0, 529], [1, 0, 42, 0, 841], [1, 0, -19, 0, 961], [1, -10, 99, -370, 1369], [1, -18, 163, -738, 1681], [1, 20, 186, 860, 1849], [1, 12, 130, 564, 2209], [1, 0, -38, 0, 2809], [1, -28, 314, -1652, 3481], [1, 0, 122, 0, 3721], [1, 16, 198, 1072, 4489], [1, 0, -27, 0, 5041], [1, 0, 142, 0, 5329], [1, -12, 194, -948, 6241], [1, -8, 182, -664, 6889], [1, -18, 259, -1602, 7921], [1, 0, -62, 0, 9409], [1, -28, 398, -2828, 10201], [1, 0, 205, 0, 10609], [1, 0, 70, 0, 11449], [1, -14, 267, -1526, 11881], [1, 0, 222, 0, 12769]], 'gamma_factors': [[], [0, 0]], 'index': 20, 'label': '4-1000188-1.1-c1e2-0-20', 'load_key': 'Costa', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 1, 'origin': 'EllipticCurve/2.2.21.1/2268.1/j', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.048828125', 'prec': 37}, 'plot_values': [-3.323475372102167e-75, 0.18693322535591278, 0.37243792668636105, 0.5549706128710079, 0.732765010479197, 0.9037383950887502, 1.065418738030524, 1.2148988221149368, 1.3488227473287346, 1.4634092677963422, 1.5545151477637942, 1.6177401794942023, 1.6485736677337177, 1.6425800731555151, 1.5956191666409008, 1.5040935530760315, 1.365213884676707, 1.1772696373686349, 0.9398911337855257, 0.6542867470587056, 0.3234381044513377, -0.04776418061613204, -0.4524610138704399, -0.8818564906424861, -1.3253526065026904, -1.7707946025636163, -2.2048291030856415, -2.613370775988889, -2.982166095438412, -3.297435273220845, -3.5465660030849113, -3.7188258492094497, -3.80605446728964, -3.8032929407524407, -3.7093058750898877, -3.526952967031375, -3.2633708685978404, -2.9299334399759642, -2.5419688571278356, -2.1182251970674524, -1.6800915002213221, -1.2505980937205596, -0.8532371218704481, -0.5106605714111943, -0.2433273020770562, -0.06818139049680591, 0.0025497460015734582, -0.03765152957926014, -0.18889184248035024, -0.44452811727376895, -0.7912431560855465, -1.2095625589123387, -1.6748109544519891, -2.1584737132030107, -2.629898012453583, -3.058236786973209, -3.4145133167851047, -3.673665473402401, -3.8164191588307226, -3.830841888754531, -3.7134407238443092, -3.4696938815072835, -3.113941413316643, -2.668605342625418, -2.162760699918463, -1.6301322478395799, -1.106643074630278, -0.6276861386625178, -0.2253238923644124, 0.07435953091092098, 0.2535273105647623, 0.304271265761885, 0.22953329892489355, 0.043148915900167985, -0.2310368892703289, -0.5609535844037579, -0.9088806079764731, -1.23462973786903, -1.4990844786674444, -1.667799545288503, -1.7143401609140412, -1.6230451536851684, -1.3909313593764645, -1.0285186228506473, -0.559440997379053, -0.01881420885337731, 0.549556495215281, 1.0969304968766758, 1.57404825323286, 1.93583018956903, 2.145929188623041, 2.1806967709654366, 2.032153547998622, 1.7096263173250987, 1.2398229326200674, 0.6652535316129067, 0.041061148340328396, -0.5695180064888968, -1.100699634385584, -1.4902198770176986, -1.6853694050898897, -1.6484102592337089, -1.360824156561921, -0.8259289652941211, -0.06953873933941586, 0.8614792200078141, 1.9026953811806642, 2.9773967726793007, 4.003204712254932, 4.8994312493293, 5.594477300914287, 6.03254590790712, 6.178987927234636, 6.023713536879242, 5.5822821492401635, 4.894509493979578, 4.020681717125203, 3.0357166002562153, 2.0218345905573085, 1.0604722122094878, 0.22426722581737596, -0.43004460942997497, -0.8670613900402857, -1.075880773816533, -1.0706394062571405, -0.8883464505101969, -0.5842281525206985, -0.22508014414434124, 0.11864497254420568, 0.38113306729764146, 0.5089477670986517, 0.46732309299496305, 0.2442713584430759, -0.14799031787170594, -0.6744866860319303, -1.2816617904135972, -1.903819756431874, -2.4710847668449603, -2.9179418945941404, -3.1913345849040002, -3.257330424600454, -3.105523487963473, -2.750603305130583, -2.2308582350693977, -1.6037552718518842, -0.9391037595996173, -0.31062140663570553, 0.21306307392774065, 0.5768452920303692, 0.7459419948211276, 0.710159733604026, 0.48505083825234324, 0.10976002475973858, -0.3582116736390815, -0.8506935971834844, -1.2980163888438014, -1.638483174621163, -1.8268882487036278, -1.840924441090018, -1.6845699801786316, -1.3879233272108287, -1.0034145881810836, -0.5988065584198967, -0.24784369760633937, -0.01975266885897855, 0.031006181700261818, -0.12667751155086254, -0.49488399642584335, -1.0447769412662855, -1.7189194135343864, -2.4376466434243773, -3.1087944387519055, -3.639600481005392, -3.949255759758121, -3.9804363744768896, -3.7082189806273242, -3.145074624667332, -2.341114249301095, -1.3793668194110928, -0.36653016579009695, 0.5797422605493892, 1.3454542993980068, 1.8349081537075573, 1.983437540712544, 1.7664916603508463, 1.2037649266588097, 0.35769331063538373, -0.6736256812384167, -1.768283066646678, -2.7957117680838977, -3.6331980744746133, -4.181579970980784, -4.3780255690925145, -4.204138479556512, -3.6882383439465762, -2.9014368984100196, -1.9479700614708038, -0.9510396303697106, -0.03605291529470379, 0.6864668295350232, 1.1359509172326323, 1.272738897222558, 1.1033650764325236, 0.6794005341949025, 0.08996664299764578, -0.5510744368633338, -1.1214875468534062, -1.5083068729643743, -1.6242681305131306, -1.420696335509143, -0.895000161500745, -0.09167862954437551, 0.9033353041581877, 1.9742177388567832, 2.9910594990566595, 3.827692215198996, 4.378995729024824, 4.575218913567607, 4.391277848661682, 3.849726951378537, 3.017023949867056, 1.993692228872264, 0.8998777202278276, -0.14153231065811672, -1.021716573919226, -1.6601756596041117, -2.0143690653538866, -2.0833902333633385, -1.9052650340129924, -1.5484491187111293, -1.0989972816790412, -0.6455425629947341, -0.26454850801940305, -0.008231208608518809, 0.10290358396979972, 0.08172970561189617, -0.029840711626563182, -0.17042274427831572, -0.2722797235149958, -0.27571521296445406, -0.14220667325273242, 0.13607529484835115, 0.532148044123506, 0.9864030070558644, 1.414948149336422, 1.7229027555397074, 1.8205580805521302, 1.6397584232155669, 1.1477230510185827, 0.3558542456171811, -0.6781799844422435, -1.8557488528923975, -3.049413199519722, -4.120251976128866, -4.937775888201433, -5.399333648642015, -5.4458983192069175], 'positive_zeros': ['1.01936668222152272292011651269610', '2.24049119020186278469176393362781', '2.26551691900571842895890768282944', '3.35511404251805033708538922756745', '3.57313298834818934312909000629574', '4.15202289907072344630083460584259', '4.69069334189536458166730202416436', '5.08207234913297047777508467305630', '5.87450213364309522501266401701993', '6.23227538486956081778076113567900', '6.47784583599995832693494924500246', '7.15629851020103523042213387688414', '7.43396451799616319962951174764258', '8.015044568391676191880321656496316'], 'prelabel': '4-1000188-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.825914146012304, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1540154516419573345, 'z1': {'__RealLiteral__': 0, 'data': '1.01936668222152272292011651269610', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.24049119020186278469176393362781', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.26551691900571842895890768282944', 'prec': 113}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 63.77285407260262, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 1000188, 'conductor_radical': 42, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 1, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -4, 0, 0, -2, 0, 0, 0, 0, -7, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0, 10, 0, 0, 0, 18, 0, -20, 0, 0, 0, -12, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 1, 0, 0, -16, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, -2, 0, 0, 8, 0, 8, 0, 0, 0, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7], 'euler11': [1, 0, -3, 0, 121], 'euler13': [1, 0, 26, 0, 169], 'euler17': [1, 4, 38, 68, 289], 'euler19': [1, 0, 37, 0, 361], 'euler2': [1, 0, -1, 0, 0], 'euler23': [1, 0, 45, 0, 529], 'euler29': [1, 0, 42, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, -19, 0, 961], 'euler37': [1, -10, 99, -370, 1369], 'euler41': [1, -18, 163, -738, 1681], 'euler43': [1, 20, 186, 860, 1849], 'euler47': [1, 12, 130, 564, 2209], 'euler5': [1, 2, 11, 10, 25], 'euler53': [1, 0, -38, 0, 2809], 'euler59': [1, -28, 314, -1652, 3481], 'euler61': [1, 0, 122, 0, 3721], 'euler67': [1, 16, 198, 1072, 4489], 'euler7': [1, 1, 0, 0, 0], 'euler71': [1, 0, -27, 0, 5041], 'euler73': [1, 0, 142, 0, 5329], 'euler79': [1, -12, 194, -948, 6241], 'euler83': [1, -8, 182, -664, 6889], 'euler89': [1, -18, 259, -1602, 7921], 'euler97': [1, 0, -62, 0, 9409], 'euler_factors': [[1, 0, -1, 0, 0], [1, 0, 0, 0, 0], [1, 2, 11, 10, 25], [1, 1, 0, 0, 0], [1, 0, -3, 0, 121], [1, 0, 26, 0, 169], [1, 4, 38, 68, 289], [1, 0, 37, 0, 361], [1, 0, 45, 0, 529], [1, 0, 42, 0, 841], [1, 0, -19, 0, 961], [1, -10, 99, -370, 1369], [1, -18, 163, -738, 1681], [1, 20, 186, 860, 1849], [1, 12, 130, 564, 2209], [1, 0, -38, 0, 2809], [1, -28, 314, -1652, 3481], [1, 0, 122, 0, 3721], [1, 16, 198, 1072, 4489], [1, 0, -27, 0, 5041], [1, 0, 142, 0, 5329], [1, -12, 194, -948, 6241], [1, -8, 182, -664, 6889], [1, -18, 259, -1602, 7921], [1, 0, -62, 0, 9409]], 'index': 20, 'instance_types': ['HMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.21.1/holomorphic/2.2.21.1-2268.1-j', 'EllipticCurve/2.2.21.1/2268.1/j'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-1000188-1.1-c1e2-0-20', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 1, 'prelabel': '4-1000188-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.825914146012304, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1540154516419573345, 'z1': {'__RealLiteral__': 0, 'data': '1.01936668222152272292011651269610', 'prec': 113}}
-
lfunc_instances • Show schema
Hide schema
-
id: 9546424
{'Lhash': '686417491481491251,853737024938082094', 'Lhash_array': ['686417491481491251', '853737024938082094'], 'label': '4-1000188-1.1-c1e2-0-20', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.21.1/2268.1/j'}
-
id: 9546874
{'Lhash': '686417491481491251,853737024938082094', 'Lhash_array': ['686417491481491251', '853737024938082094'], 'label': '4-1000188-1.1-c1e2-0-20', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.21.1/holomorphic/2.2.21.1-2268.1-j'}