-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '1142972884310461384,1690899098723847747', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 28.793387376695364, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 0, -1]], [7, [1, 0, -1]]], 'bad_primes': [2, 3, 7], 'central_character': '451584.1', 'coefficient_field': '1.1.1.1', 'conductor': 451584, 'conductor_radical': 42, 'degree': 4, 'euler_factors': [[1], [1, 0, -1], [1, 0, 10, 0, 25], [1, 0, -1], [1, 0, 18, 0, 121], [1, 4, 30, 52, 169], [1, -8, 50, -136, 289], [1, 0, 22, 0, 361], [1, 0, 10, 0, 529], [1, 4, 62, 116, 841], [1, 0, 62, 0, 961], [1, 12, 110, 444, 1369], [1, -16, 146, -656, 1681], [1, 0, 22, 0, 1849], [1, 0, 78, 0, 2209], [1, 12, 142, 636, 2809], [1, 0, 118, 0, 3481], [1, 28, 318, 1708, 3721], [1, 0, 118, 0, 4489], [1, 0, 138, 0, 5041], [1, 4, 150, 292, 5329], [1, 0, 142, 0, 6241], [1, 0, 22, 0, 6889], [1, 0, 178, 0, 7921], [1, -12, 230, -1164, 9409], [1, -24, 346, -2424, 10201], [1, 0, 142, 0, 10609], [1, 0, 178, 0, 11449], [1, 36, 542, 3924, 11881], [1, -36, 550, -4068, 12769]], 'gamma_factors': [[], [0, 0]], 'index': 68, 'label': '4-672e2-1.1-c1e2-0-68', '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/2.0.4.1/28224.1/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.048828125', 'prec': 37}, 'plot_values': [-1.3932395564693589e-74, 0.1828223487764388, 0.36560764215542535, 0.548228145635188, 0.7303783155286694, 0.9114947552674041, 1.0906867636833977, 1.2666809127580907, 1.43778296517191, 1.601860228471225, 1.7563471133063457, 1.8982761891719417, 2.024336387414118, 2.1309591701029618, 2.2144324572560232, 2.2710408898176855, 2.2972296237101095, 2.289787340932858, 2.2460425855148722, 2.1640659618407794, 2.0428692637913985, 1.8825913418925544, 1.6846595773955921, 1.451915334204469, 1.1886918135387783, 0.9008334395563834, 0.5956473304765522, 0.28177959943497666, -0.03098781935058488, -0.3320204618555875, -0.610191120026564, -0.8543077930855788, -1.053596548788718, -1.198221162344038, -1.2798168848909357, -1.2920118755587566, -1.2309070551265389, -1.0954837334797956, -0.8879086147430368, -0.6137079131500545, -0.28178644627742566, 0.09572627910687498, 0.5038129333827155, 0.9250884655371264, 1.3404928561754008, 1.7301344242967263, 2.0742501048128834, 2.354238422429268, 2.5537118003634927, 2.6595081630004773, 2.6625982576345892, 2.558825341307342, 2.3494182742101017, 2.0412278061259514, 1.6466488229369602, 1.183208105511861, 0.6728169884265628, 0.14071012870153676, -0.38588592199908056, -0.8792890279284287, -1.313018219061365, -1.6634714177580603, -1.9115152602799945, -2.0438755382790883, -2.054221862369275, -1.9438532481078377, -1.7219122233413742, -1.4050829181765132, -1.0167619731088515, -0.5857279711219477, -0.14437298767316156, 0.2734040312906616, 0.6345109178322824, 0.9090278633807086, 1.072455844869781, 1.1076766613699376, 1.0064641625354438, 0.7704101964354024, 0.41116500448458076, -0.05006169928992641, -0.5837388546711325, -1.1539338314293375, -1.7207996692170278, -2.243464450146433, -2.6831163903027204, -3.0060513032869, -3.1864395119963635, -3.20857904243903, -3.068431504880931, -2.77428527261537, -2.346454539262377, -1.8159981369981628, -1.2225228995709196, -0.6112162378443079, -0.029324480525459492, 0.4776493289253718, 0.8697179865900988, 1.1158314147896684, 1.1966411923677622, 1.1063466842765355, 0.8534303446340467, 0.4601795632260379, -0.03900417793520845, -0.6003997292432091, -1.1746515212321038, -1.7110437031557482, -2.1619955555088772, -2.487375708217907, -2.658233546443281, -2.659584509200993, -2.4919600931694585, -2.1715380635380392, -1.7287952193021423, -1.205763033796011, -0.6521028817966552, -0.12033912420834672, 0.3393174635972557, 0.6840670637979815, 0.8830389374069822, 0.9207674711199285, 0.7992475859522543, 0.5383160887169289, 0.17426102751075395, -0.24326719796177046, -0.6557977827700159, -1.0016353906463125, -1.2219906876257407, -1.2670535731232688, -1.1014013293321154, -0.7081790042972315, -0.09159329008804033, 0.7225842885793174, 1.6886177698287055, 2.7444139207748472, 3.8168322836181816, 4.8282114463083134, 5.7034864719145615, 6.377194551677387, 6.799659040660601, 6.941709365218667, 6.797431307172735, 6.384636639458414, 5.7429740919577945, 4.929851329026977, 4.014573672005039, 3.0713036287457705, 2.171582996717236, 1.377219330197228, 0.734311838023296, 0.26907857230509236, -0.0140429658960051, -0.1317970255584294, -0.11906669153999333, -0.023720701612623768, 0.10006731051620925, 0.19925593539825565, 0.22925363586418512, 0.16023509645491, -0.018329037603801997, -0.2955232018684316, -0.6395463109215196, -1.0009937229331074, -1.318551035691133, -1.5264902899042612, -1.5631228362829253, -1.3792192371134309, -0.9453753365317177, -0.2573926334533438, 0.6610561029546242, 1.7589086379865333, 2.9614172738166, 4.176771044514744, 5.304976934091395, 6.248052625611695, 6.920398475988812, 7.258160542803415, 7.2264802858529045, 6.8237442074675885, 6.082275956311832, 5.065317818828758, 3.8605813089823875, 2.571056113407589, 1.3041026458615586, 0.1600731695802376, -0.7782197877823808, -1.4539536373294042, -1.8416666969617075, -1.948914108273503, -1.8140185891600722, -1.5002016169406185, -1.0868275908280332, -0.658855147150283, -0.2958189417465998, -0.06173040450873223, 0.002824113823970731, -0.11461608135859842, -0.3974838130675437, -0.8031881856454576, -1.2696235441992254, -1.724317507946973, -2.0949950821173915, -2.3201344654489446, -2.3580743159706765, -2.193407834175454, -1.8397468145409206, -1.3384162311964394, -0.753186079074589, -0.16169049226717755, 0.35534844544509125, 0.7256480699257708, 0.8960610966303757, 0.8409308574893047, 0.5668770602179453, 0.11323856660951956, -0.45202750238690226, -1.0405752942597468, -1.5550372122525442, -1.9020800737157244, -2.0054294636294605, -1.8170951392187298, -1.3252230518328343, -0.5574112393715897, 0.4210928372389099, 1.5142217183728122, 2.606173745797897, 3.575394326544871, 4.309671969491702, 4.720380656755695, 4.753975265006879, 4.399180211062731, 3.688862953901391, 2.696282133887841, 1.526151826421514, 0.3016661094648209, -0.8508159168487999, -1.8173946744204963, -2.5104797576990765, -2.879012802508166, -2.9137029101046235, -2.6465985657476687, -2.1451042840558, -1.5013248263685632, -0.8182749726349634, -0.19493394252341556, 0.2877148143110029, 0.5776620028091916, 0.6583055176148105, 0.5494369992133777, 0.30267921538492887, -0.00790868809438629, -0.29861971471906695, -0.49032742970480714, -0.5219695544800078, -0.36119436847433356, -0.010484383303303507, 0.4922622550671119, 1.0788819180597067], 'positive_zeros': ['1.36229546664790534828076487478725', '1.99001705800767037924689990797520', '2.79609515636067281736780650551146', '3.43433897571752185423069296584161', '3.85252585768054816532884619372365', '4.59244879976712680478557977306621', '4.97691463353523376663815741347303', '5.62712164599905299138472285079075', '5.97779432028631552865085959087887', '6.35375124938765540482595553493490', '7.32082126936645491942637559694185', '7.48026155837481865360444931206248', '7.71090868218694782736415188361568', '8.169181262276573842859231210132853'], 'prelabel': '4-672e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.3164513843010055, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 528028973820615180, 'z1': {'__RealLiteral__': 0, 'data': '1.36229546664790534828076487478725', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.99001705800767037924689990797520', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.79609515636067281736780650551146', 'prec': 113}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 28.793387376695364, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 451584, 'conductor_radical': 42, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -4, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0], 'euler11': [1, 0, 18, 0, 121], 'euler13': [1, 4, 30, 52, 169], 'euler17': [1, -8, 50, -136, 289], 'euler19': [1, 0, 22, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 10, 0, 529], 'euler29': [1, 4, 62, 116, 841], 'euler3': [1, 0, -1, 0, 0], 'euler31': [1, 0, 62, 0, 961], 'euler37': [1, 12, 110, 444, 1369], 'euler41': [1, -16, 146, -656, 1681], 'euler43': [1, 0, 22, 0, 1849], 'euler47': [1, 0, 78, 0, 2209], 'euler5': [1, 0, 10, 0, 25], 'euler53': [1, 12, 142, 636, 2809], 'euler59': [1, 0, 118, 0, 3481], 'euler61': [1, 28, 318, 1708, 3721], 'euler67': [1, 0, 118, 0, 4489], 'euler7': [1, 0, -1, 0, 0], 'euler71': [1, 0, 138, 0, 5041], 'euler73': [1, 4, 150, 292, 5329], 'euler79': [1, 0, 142, 0, 6241], 'euler83': [1, 0, 22, 0, 6889], 'euler89': [1, 0, 178, 0, 7921], 'euler97': [1, -12, 230, -1164, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, -1, 0, 0], [1, 0, 10, 0, 25], [1, 0, -1, 0, 0], [1, 0, 18, 0, 121], [1, 4, 30, 52, 169], [1, -8, 50, -136, 289], [1, 0, 22, 0, 361], [1, 0, 10, 0, 529], [1, 4, 62, 116, 841], [1, 0, 62, 0, 961], [1, 12, 110, 444, 1369], [1, -16, 146, -656, 1681], [1, 0, 22, 0, 1849], [1, 0, 78, 0, 2209], [1, 12, 142, 636, 2809], [1, 0, 118, 0, 3481], [1, 28, 318, 1708, 3721], [1, 0, 118, 0, 4489], [1, 0, 138, 0, 5041], [1, 4, 150, 292, 5329], [1, 0, 142, 0, 6241], [1, 0, 22, 0, 6889], [1, 0, 178, 0, 7921], [1, -12, 230, -1164, 9409]], 'index': 68, 'instance_types': ['BMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/28224.1/c', 'EllipticCurve/2.0.4.1/28224.1/c'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, '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': '4-672e2-1.1-c1e2-0-68', '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': '4-672e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.3164513843010055, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 528028973820615180, 'z1': {'__RealLiteral__': 0, 'data': '1.36229546664790534828076487478725', 'prec': 113}}
-
lfunc_instances • Show schema
Hide schema
-
id: 9664072
{'Lhash': '1142972884310461384,1690899098723847747', 'Lhash_array': ['1142972884310461384', '1690899098723847747'], 'label': '4-672e2-1.1-c1e2-0-68', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/28224.1/c'}
-
id: 9663254
{'Lhash': '1142972884310461384,1690899098723847747', 'Lhash_array': ['1142972884310461384', '1690899098723847747'], 'label': '4-672e2-1.1-c1e2-0-68', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/28224.1/c'}