-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '5020808969315194855222038570971', 'a10': [0.0, 2.23606797749979], 'a2': [-1.0, 0.0], 'a3': [0.0, -4.47213595499958], 'a4': [-3.0, 0.0], 'a5': [0.0, -2.23606797749979], 'a6': [0.0, 4.47213595499958], 'a7': [7.0, 0.0], 'a8': [7.0, 0.0], 'a9': [-11.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9536809252610392, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 2.23606797749979]]], [7, [[1.0, 0], [-7.0, 0]]]], 'bad_primes': [5, 7], 'central_character': '35.6', 'coefficient_field': 'CDF', 'conductor': 35, 'conductor_radical': 35, 'conjugate': '1740655347830028051477131474807', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0], [4.0, 0]], [[1.0, 0], [0, 4.47213595499958], [-9.0, 0]], [[1.0, 0], [0, 2.23606797749979]], [[1.0, 0], [-7.0, 0]], [[1.0, 0], [-2.0, 0], [121.0, 0]], [[1.0, 0], [0, -13.416407864998739], [-169.0, 0]], [[1.0, 0], [0, 26.832815729997478], [-289.0, 0]], [[1.0, 0], [0, -13.416407864998739], [-361.0, 0]], [[1.0, 0], [-26.0, 0], [529.0, 0]], [[1.0, 0], [22.0, 0], [841.0, 0]], [[1.0, 0], [0, -53.665631459994955], [-961.0, 0]], [[1.0, 0], [-14.0, 0], [1369.0, 0]], [[1.0, 0], [0, -26.832815729997478], [-1681.0, 0]], [[1.0, 0], [34.0, 0], [1849.0, 0]], [[1.0, 0], [0, -26.832815729997478], [-2209.0, 0]], [[1.0, 0], [34.0, 0], [2809.0, 0]], [[1.0, 0], [0, -40.24922359499622], [-3481.0, 0]], [[1.0, 0], [0, 93.91485505499116], [-3721.0, 0]], [[1.0, 0], [-14.0, 0], [4489.0, 0]], [[1.0, 0], [-62.0, 0], [5041.0, 0]], [[1.0, 0], [0, -53.665631459994955], [-5329.0, 0]], [[1.0, 0], [-38.0, 0], [6241.0, 0]], [[1.0, 0], [0, 40.24922359499622], [-6889.0, 0]], [[1.0, 0], [0, -26.832815729997478], [-7921.0, 0]], [[1.0, 0], [0, -26.832815729997478], [-9409.0, 0]], [[1.0, 0], [0, 67.08203932499369], [-10201.0, 0]], [[1.0, 0], [0, 160.99689437998487], [-10609.0, 0]], [[1.0, 0], [106.0, 0], [11449.0, 0]], [[1.0, 0], [142.0, 0], [11881.0, 0]], [[1.0, 0], [34.0, 0], [12769.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-35-7.6-c2-0-3', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/35/3/d/a/6/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.7545094721189903, 0.8103760833556383, 0.8710794126923374, 0.9375353869508751, 1.01035018081273, 1.0898044822212563, 1.1758440552778415, 1.2680734736306887, 1.3657506876041083, 1.4677815828806682, 1.572715301727138, 1.678742421289212, 1.783698949119703, 1.8850795070999526, 1.980063108320659, 2.065554669209659, 2.138244898219859, 2.1946904921055266, 2.2314156626264774, 2.2450349161384913, 2.2323957265245715, 2.1907383013525448, 2.1178680823903253, 2.0123350048573987, 1.8736119454927638, 1.7022633169821346, 1.5000935304031797, 1.2702641734523288, 1.017368369087743, 0.747451010345012, 0.467964520450169, 0.1876515442682292, -0.08365141938739752, -0.33529199136819465, -0.5561598200873782, -0.7351178906939797, -0.8614953999246923, -0.9256248878398998, -0.9194010068389319, -0.836833542583445, -0.674563494045932, -0.4323085896818879, -0.11320395770570724, 0.2759948843500631, 0.7248757620482514, 1.2195230894700162, 1.742874762400068, 2.275286006902312, 2.7952909259585583, 3.28053881437585, 3.708868343289808, 4.0594694081380664, 4.314070840753604, 4.458083386832733, 4.481622369283297, 4.380334175615279, 4.155955765647135, 3.816547111279277, 3.376352770962976, 2.8552701354954797, 2.2779272552973597, 1.6724011134668533, 1.068635886888208, 0.4966479850219316, -0.015371839006694789, -0.4429315425386759, -0.7669488999430303, -0.9751639761522068, -1.063127529153363, -1.0346622266169416, -0.9017263079932993, -0.6836508750371547, -0.4057697922441324, -0.09751183645340661, 0.20992576274371935, 0.48615925952703026, 0.7042585398270912, 0.8432278792527568, 0.8901062988055385, 0.8414819588075022, 0.7042497827882558, 0.49549427947496266, 0.24144728128718285, -0.024451693397715295, -0.26428267282396456, -0.43897125717644536, -0.5119562145595771, -0.4528908823991168, -0.24104422004375878, 0.13193030526544006, 0.6601565039943464, 1.3228626538799735, 2.08501809657846, 2.8993119883632374, 3.709384165580792, 4.454094676922344, 5.0725064070629236, 5.509166163062222, 5.719214097704462, 5.672837392523019, 5.3586161831766965, 4.7853879613261245, 3.982376642855242, 2.997485071376042, 1.8938218200708952, 0.7447086712249298, -0.37242353430422626, -1.3827132942590301, -2.2205009826311097, -2.8352711472129646, -3.1963004515813687, -3.2955115968820143, -3.148194963912984, -2.7914642585726783, -2.2805407669699584, -1.6831897769357422, -1.0728376507830368, -0.5210554352370248, -0.09018511474080958, 0.17310568397597428, 0.24263064698665432, 0.11530079444246284, -0.18877805003280365, -0.6287834722856036, -1.1480000928016567, -1.6804861193923026, -2.15885537123241, -2.5222978335377526, -2.7239086697666175, -2.7364494111655846, -2.555824180395072, -2.201804039776231, -1.7158479687679626, -1.1562144677501647, -0.5908928354318694, -0.08916650317801258, 0.2871845459269941, 0.49195715660251466, 0.5008423122149459, 0.3151382361329184, -0.03769189828552873, -0.506790973096196, -1.02376634410815, -1.510993908677161, -1.8913913457715084, -2.098460721181113, -2.085322196127535, -1.831543373927236, -1.3468091109971292, -0.6708499738432663, 0.13048901706136504, 0.9726609255867953, 1.7624659490493841, 2.4095189930603964, 2.837690873146573, 2.9950337214115454, 2.860852374495411, 2.448918101691704, 1.8063014236843375, 1.0078680439533911, 0.14706279066640654, -0.6758773397540725, -1.3667612286003679, -1.849628740634163, -2.0766217718954585, -2.0341527670923165, -1.7444554366888345, -1.2622178371149033, -0.6666750167687702, -0.05018448594723529, 0.4951691846910185, 0.8910726999547325, 1.0846501948418326, 1.056568362719434, 0.8243121612021947, 0.4400208834559473, -0.01695682778605664, -0.4518576255385286, -0.7690509609328875, -0.8872850188985493, -0.7534010444120552, -0.3524285469188955, 0.28757425646444673, 1.0968635242675313, 1.971597065883918, 2.7868181664935356, 3.41317131586613, 3.7350824807117964, 3.667844042964677, 3.1711157564857118, 2.2567896728174754, 0.989916471996016, -0.517647702186253, -2.1201765300734534, -3.6559299522979614, -4.96752659210999, -5.922018365845352, -6.4278494142793585, -6.446291915750329, -5.9957237932506295, -5.148139090957082, -4.018410977194235, -2.74789078097568, -1.4847614066969452, -0.36403892124507775, 0.5098458553710347, 1.0753646282975764, 1.3193873835261283, 1.2752058214907138, 1.0136062090859603, 0.6286036490696677, 0.22028244209466052, -0.12237456542655802, -0.3358163528233181, -0.39106402416649205, -0.29620561872327605, -0.09193386861141624, 0.15897908237961875, 0.38631076781513884, 0.5284203227786559, 0.5466969653919341, 0.43566893035498516, 0.22673540219543145, -0.015419926058054744, -0.20338041066691767, -0.2428850955883875, -0.05139346245471324, 0.4239380108076961, 1.1921853108871947, 2.21128420995471, 3.389110889091358, 4.593384084259642, 5.669244845038331, 6.461988782684164, 6.8414182100700165, 6.723835421799436, 6.087911587527066, 4.981526774681673, 3.518062377822366, 1.862320332827328, 0.20796643971536224, -1.2501439556539, -2.3444571826986342, -2.959480192933688, -3.048765604322428, -2.641278812902148, -1.8360045399094878, -0.7855775703030515, 0.3284479693905659, 1.3246594257189703, 2.050391462961791, 2.405142877881979, 2.3549305985934406, 1.935240326503287, 1.242182989603685, 0.41349810335079307, -0.39719537000723965], 'positive_zeros': ['3.96071990847575989867755262541552', '5.28862869321859185071245216462348', '7.995953454681235411202412604988168', '9.164014712372264624353312867507203', '10.36326966463145767838290231595403', '11.08651718063902348434576701937295', '13.20739135960693087104765265339072', '14.78419501369660308067686865692122', '15.18054868318445563270778672280823', '16.90062779357632364130977895505012'], 'prelabel': '2-35-7.6-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9765658837277899, 'root_angle': 0.5, 'root_number': '6.123233995736766e-17 + 1.0*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.96071990847575989867755262542', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.28862869321859185071245216462', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.995953454681235411202412604988', 'prec': 107}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.9536809252610392, 'bad_primes': [5, 7], 'central_character': '7.6', 'conductor': 35, 'conductor_radical': 35, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/35/3/d/a/6/1'], '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': '2-35-7.6-c2-0-3', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-35-7.6-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9765658837277899, 'root_angle': 0.25, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '3.96071990847575989867755262542', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '5020808969315194855222038570971', 'Lhash_array': ['5020808969315194855222038570971'], 'label': '2-35-7.6-c2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/35/3/d/a/6/1'}