-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1099867090257073615544773894353', 'a10': [-1.8556564719691302, 3.2140912908445456], 'a2': [0.8660254037844386, 0.5], 'a3': [0, 0], 'a4': [0.5, 0.8660254037844386], 'a5': [0, 3.7113129439382604], 'a6': [0, 0], 'a7': [-0.8660254037844386, 0.5], 'a8': [0, 1.0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.079495851085733, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, -0.5]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.8660254037844386, -0.5]]], [13, [[1.0, 0], [-2.877573771964661, 2.172456947076529]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '1638.1135', 'coefficient_field': 'CDF', 'conductor': 1638, 'conductor_radical': 546, 'conjugate': '2275343142047997366522904329934', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -3.7113129439382604], [-5.0, 0]], [[1.0, 0], [0.8660254037844386, -0.5]], [[1.0, 0], [-5.001179436364914, -2.887432293850904], [5.5, 9.526279441628825]], [[1.0, 0], [-2.877573771964661, 2.172456947076529]], [[1.0, 0], [-0.10609849993404483, -0.1837679924926088], [-8.5, 14.722431864335457]], [[1.0, 0], [-1.8508146327681017, 1.0685683264487618], [9.5, -16.454482671904334]], [[1.0, 0], [1.2396994501488425, -2.147222433772996], [-11.5, -19.91858428704209]], [[1.0, 0], [0.049282986347981804, -0.08536063630342784], [-14.5, -25.11473670974872]], [[1.0, 0], [0, -2.3107629725640533], [-31.0, 0]], [[1.0, 0], [-6.8185908802372195, -3.936715280198886], [18.5, 32.04293994002423]], [[1.0, 0], [6.5135432179925195, 3.760595930286242], [20.5, 35.50704155516198]], [[1.0, 0], [-2.2898664924266536, -3.9661651074324977], [-21.5, 37.239092362730865]], [[1.0, 0], [0, 9.15569751530353], [-47.0, 0]], [[1.0, 0], [12.094797518292879, 0], [53.0, 0]], [[1.0, 0], [-0.20084345328711117, 0.11595702182028766], [29.5, -51.09549882328188]], [[1.0, 0], [4.016054640936371, 6.956010684074579], [-30.5, 52.827549630850754]], [[1.0, 0], [11.232346188003962, 6.484998095275154], [33.5, 58.023702053557386]], [[1.0, 0], [6.37720974904713, -3.681883765291066], [35.5, -61.48780366869514]], [[1.0, 0], [0, -5.6041433150949524], [-73.0, 0]], [[1.0, 0], [9.197490475578329, 0], [79.0, 0]], [[1.0, 0], [0, 3.171858207806871], [-83.0, 0]], [[1.0, 0], [-10.233525624368875, -5.908328773988304], [44.5, 77.07626093681505]], [[1.0, 0], [-12.195247718190384, 7.040929552931388], [48.5, -84.00446416709055]], [[1.0, 0], [-3.076216969028727, 5.328164085463291], [-50.5, -87.4685657822283]], [[1.0, 0], [-19.34906100629237, 0], [103.0, 0]], [[1.0, 0], [-5.82506008645227, 10.08930002687689], [-53.5, -92.66471820493493]], [[1.0, 0], [0, 5.733071627427009], [-109.0, 0]], [[1.0, 0], [-8.259711874356412, -14.30624062226527], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 15, 'label': '2-1638-13.4-c1-0-15', 'leading_term': '2.563456621064589875451401779078372570697733116066962785', '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/1638/2/bj/g/1135/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.56345662106459, 2.3986903147959877, 2.232516420051223, 2.0646553050391834, 1.894767900317085, 1.722548690988038, 1.5478149391864369, 1.3705870131147533, 1.1911558195747411, 1.0101345965772697, 0.8284935125802951, 0.6475765053054114, 0.4691005254788295, 0.2951378458893615, 0.12808241015028754, -0.029398602120747967, -0.1744266629144512, -0.3039857523297123, -0.41500651966240143, -0.5044588663719755, -0.5694508148912426, -0.60733125190087, -0.6157938563475526, -0.592979263372583, -0.5375722986647368, -0.44889096614776086, -0.3269638060724, -0.17259227836887883, 0.012605018269239035, 0.2261691978079156, 0.46480149918082525, 0.7243892019897186, 1.0000583145922857, 1.2862535168196858, 1.5768449580141193, 1.865260559012952, 2.1446414738148225, 2.4080173673239917, 2.6484971978891827, 2.8594702979482864, 3.0348117646360366, 3.1690855457997773, 3.2577381742213243, 3.2972758984480826, 3.2854180108757003, 3.221219503079456, 3.105156795816497, 2.939171196670218, 2.726665920107716, 2.472453938366807, 2.182655580037485, 1.8645466072146195, 1.5263594212639398, 1.1770420015999157, 0.82598109410448, 0.48269795397386184, 0.15652652847714976, -0.1437147429529887, -0.4100454061465093, -0.6356271442331348, -0.8150369859727908, -0.9444974545227633, -1.0220525768444644, -1.0476802372207152, -1.0233334188336765, -0.9529053809088253, -0.8421166878290278, -0.6983251412122791, -0.5302629474875103, -0.3477087481198663, -0.16110530329504788, 0.01886349577490468, 0.1817201518603849, 0.3176475935489478, 0.41793047035038183, 0.47536403574059044, 0.48461136108321845, 0.44249092594875106, 0.34817881294970315, 0.20331275245836136, 0.011989027290089768, -0.21935236814513243, -0.4821540806737037, -0.766073933018365, -1.0594131777823066, -1.3496250777363712, -1.6238839336886717, -1.8696908773534917, -2.0754898438158307, -2.2312653260045927, -2.3290929408893146, -2.363614602126796, -2.332412236175137, -2.236257473728417, -2.07921950384394, -1.8686191356924813, -1.6148238507452548, -1.3308859687448635, -1.032033670738089, -0.7350321662798331, -0.457439387713234, -0.21678687143363526, -0.029721593324028316, 0.08885184921304796, 0.12658742876327506, 0.07443100649088584, -0.07276841743907844, -0.3158046467472953, -0.6508465615076382, -1.0693781507260625, -1.5583586118360366, -2.100604668070656, -2.675386524435326, -3.2592180882774033, -3.8268117597982525, -4.352158792223596, -4.8096884462172556, -5.175453380495734, -5.42828531232211, -5.550864225445709, -5.530646453281298, -5.36060183812687, -5.039717734208485, -4.573237609131187, -3.972613992919491, -3.255168991778953, -2.4434698906776, -1.564441809737209, -0.6482532126571995, 0.2729774492273925, 1.1665952353622417, 2.0008758628558785, 2.746475404178525, 3.3777903564495975, 3.874158523184622, 4.220837459938645, 4.40970702714773, 4.439655462940459, 4.316623751850907, 4.053300182927146, 3.668475002532809, 3.1860830347694833, 2.6339790979541418, 2.0425060438059326, 1.4429274176881555, 0.8658053410577954, 0.3394086815386629, -0.11176345736428799, -0.46826254715399673, -0.7167045055591368, -0.8504586288942305, -0.8699703027920598, -0.7826955608593529, -0.6026465371678744, -0.3495683266289327, -0.04778853532505706, 0.27520031440098075, 0.590349472181674, 0.8687657670536066, 1.0834313707965137, 1.210834414455502, 1.232416893425258, 1.1357552296130236, 0.9154027904991144, 0.573341897578623, 0.11901442655331139, -0.4310761733022181, -1.054174069036004, -1.7224501235490588, -2.404487605499857, -3.0669926645583505, -3.6766335923289937, -4.201904181285622, -4.614903805747229, -4.892930446395248, -5.01979265794222, -4.986761959444517, -4.79310747615166, -4.44617873756986, -3.961028947311472, -3.359598226527665, -2.6695026580897943, -1.9224988097450288, -1.152713300720676, -0.3947416251520733, 0.3182711136024861, 0.9564532735969914, 1.4948246348692196, 1.9146124580687984, 2.2041870539756037, 2.359561497531149, 2.3844269581205486, 2.2897239237857185, 2.0927785710003257, 1.8160608357887873, 1.4856446178339406, 1.1294694323867787, 0.7755154496741876, 0.4500093489079716, 0.17577633544812826, -0.029155916394748595, -0.15261217560863752, -0.18891668759801022, -0.13909259965642135, -0.010603835485593483, 0.18333991065750682, 0.4248649816423672, 0.692826070365281, 0.9644115124983942, 1.2168492847181773, 1.429094240019117, 1.5833780521102543, 1.6665124506774067, 1.6708530862170743, 1.5948547126393877, 1.4431767928453456, 1.226330216907315, 0.9598884224956771, 0.6633175626831976, 0.358508262985273, 0.06811393362766463, -0.18618411464822834, -0.3853575634226666, -0.5145328423993107, -0.5641996460508644, -0.5310315396328295, -0.41825058142885635, -0.23549990184708824, 0.0017765646169861677, 0.2734119529834675, 0.5559824319492616, 0.8245617364288846, 1.0546412528836533, 1.2240774974422959, 1.3149233138968899, 1.315003862094602, 1.2191133735378996, 1.0297328971129143, 0.7572013317501116, 0.4193098342113989, 0.04033062644345476, -0.35046755452859873, -0.7207265751375653, -1.037204767108191, -1.2681326949170482, -1.3855550032402428, -1.3674908869055715, -1.199753999389274, -0.8772925022389431, -0.4049403221842596, 0.20249039162512403, 0.9208007112960819, 1.7176575633932394, 2.554437481973046, 3.3885479173407824, 4.176076120289019, 4.8745890655626445], 'positive_zeros': ['0.867642148442995386340932855182406', '1.63691278720637472048026839068106', '3.31106223181897185569106254608792', '4.15380511798108468171866969361797', '4.69078700147954747819462794068540', '5.98831891808345238221922356505436', '6.18662494714937627388306525089945', '7.54114135018657498134688094215823', '8.597655397426621352890477173609926', '9.090818814422220670430474699483335'], 'prelabel': '2-1638-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6165585645867444, 'root_angle': -0.709922978488332, 'root_number': '-0.61271584173370998765197559258186118934222643191922164283 - 0.79030329449430441697537269554758924315726550668817232165*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.354961489244166', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.867642148442995386340932855182', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.63691278720637472048026839068', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.31106223181897185569106254609', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 13.079495851085733, 'bad_primes': [2, 3, 7, 13], 'central_character': '13.4', 'conductor': 1638, 'conductor_radical': 546, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1638/2/bj/g/1135/6'], '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': '2-1638-13.4-c1-0-15', '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': '2-1638-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6165585645867444, 'root_angle': -0.354961489244166, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.867642148442995386340932855182', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1099867090257073615544773894353', 'Lhash_array': ['1099867090257073615544773894353'], 'label': '2-1638-13.4-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1638/2/bj/g/1135/6'}