-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1310291420628852915637313493147', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.359720671983229, 1.0729211034281485], 'a4': [0.0, 0.0], 'a5': [1.16481483589514, 3.200302459467639], 'a6': [0.0, 0.0], 'a7': [4.3283380584573825, -0.7632027813333296], 'a8': [0.0, 0.0], 'a9': [0.6976806116370483, -2.9177460074766195], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.4495373673193144, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.359720671983229, -1.0729211034281485]]]], 'bad_primes': [2, 3], 'central_character': '432.383', 'coefficient_field': 'CDF', 'conductor': 432, 'conductor_radical': 6, 'conjugate': '2327737182218088466391208663999', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.359720671983229, -1.0729211034281485]], [[1.0, 0], [-1.16481483589514, -3.200302459467639], [-3.83022221559489, 3.2139380484326967]], [[1.0, 0], [-4.3283380584573825, 0.7632027813333296], [6.5778483455013586, -2.3941410032796813]], [[1.0, 0], [3.889695273961006, 1.4157333000877275], [8.426488874308758, 7.070663706551932]], [[1.0, 0], [-4.639664101970739, -3.8931404367501132], [2.2574263096700946, 12.802500789158705]], [[1.0, 0], [-0.9458658934748113, -0.5460959282149682], [8.5, 14.722431864335457]], [[1.0, 0], [2.4510691590164595, -1.4151254387605425], [9.5, -16.454482671904334]], [[1.0, 0], [0.3270669066227439, -1.8548886013281705], [-21.612930278075893, -7.866463296490381]], [[1.0, 0], [3.457280573466806, 4.120226544035236], [-5.03579715234098, 28.559424837354033]], [[1.0, 0], [-1.5204137613468693, -0.26808996796589407], [29.13047124436316, 10.602624443095731]], [[1.0, 0], [2.4892596463181933, -4.311524180654044], [-18.5, -32.04293994002423]], [[1.0, 0], [3.2969771056908077, -3.92918431040788], [-7.119575284344144, -40.37711787350053]], [[1.0, 0], [-1.4311243611121156, 3.9319818665869604], [-32.93991105411605, -27.639867216521193]], [[1.0, 0], [-1.5165391635330985, -8.600720986883509], [-44.16555317693769, 16.07494673630643]], [[1.0, 0], [0, 12.17407587495914], [-53.0, 0]], [[1.0, 0], [-3.0939154822200985, 1.1260931428634797], [45.196622144019706, -37.92446897150582]], [[1.0, 0], [0.4636302823278321, 2.62937799119006], [-57.32124986794041, 20.863228742865793]], [[1.0, 0], [-2.3281930817632746, 2.774632469444368], [-11.634427903684333, -65.98211945181794]], [[1.0, 0], [0.8421602396307378, -1.4586643231548186], [-35.5, -61.48780366869514]], [[1.0, 0], [5.582045447608263, 9.668386325416067], [-36.5, 63.21985447626402]], [[1.0, 0], [6.261685224289635, 7.462385861741254], [-13.718206035687498, 77.79981248796443]], [[1.0, 0], [0.24013378417020242, -0.20149616973042142], [14.412798746355218, -81.73904350001327]], [[1.0, 0], [-6.605732250755887, 3.813821293168504], [44.5, -77.07626093681505]], [[1.0, 0], [-0.9038867742289625, -0.32898788096623743], [74.30631098254086, 62.35039813959431]], [[1.0, 0], [-13.89082331546614, 2.4493269347708932], [94.90895469937675, -34.544034475892545]], [[1.0, 0], [-2.889210828131332, -7.938041510334624], [-78.90257764125474, 66.20712379771355]], [[1.0, 0], [-5.484939344458038, 0], [107.0, 0]], [[1.0, 0], [-7.870817659795617, 0], [109.0, 0]], [[1.0, 0], [3.887797521203213, 10.681635900917481], [-86.56302207244451, 72.63499989457894]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-432-108.59-c1-0-3', '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/432/2/be/b/383/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.3225293404530192, 1.2036143906768109, 1.081455322863057, 0.950947230289489, 0.806903199441262, 0.6454034646207715, 0.46491382346570637, 0.2671045541793291, 0.05736614287184218, -0.15497465953705228, -0.35675451616029946, -0.5314221486396281, -0.6598696271759412, -0.7216609202818236, -0.6966365276070444, -0.5668255364472564, -0.318543409365468, 0.05549776690688129, 0.5542822849977467, 1.167028223556586, 1.8724115727935529, 2.6386906796369693, 3.424883207691645, 4.183054740273921, 4.86165903161166, 5.4097351427058005, 5.781631062772785, 5.941804863661622, 5.869172139375322, 5.560440295782346, 5.031909804320116, 4.31933636764416, 3.475633183695517, 2.5664354555695597, 1.6638255289050259, 0.8387930467536205, 0.1532412004382675, -0.34749218722570485, -0.6405857313944172, -0.7292365829626862, -0.6430262826954758, -0.4348240608286538, -0.17435290316869034, 0.060969613793716175, 0.19685087765167333, 0.17319248641911422, -0.04617413692091796, -0.46662081695607344, -1.0599715810959998, -1.7666045687023637, -2.5024669588530246, -3.1703084172265954, -3.6737192433621635, -3.931995689662949, -3.8935553776772576, -3.54566719531462, -2.918670652052669, -2.0836081568113585, -1.1431878745333375, -0.21709056818510566, 0.5763456338900863, 1.139265231805441, 1.4111120558794763, 1.380134998121183, 1.0872844090762472, 0.6213446072885693, 0.10558357914725362, -0.32230180074909026, -0.5338701117546063, -0.43332772680005577, 0.023500169357124366, 0.8182301602106811, 1.869416048408826, 3.0431571630684178, 4.1735339993586695, 5.089730811290283, 5.645311817041454, 5.744479049472169, 5.360425957700935, 4.542117203791734, 3.407798514554025, 2.1259392309663427, 0.8866975198598288, -0.13108913629427332, -0.7913468898359043, -1.0246869681589927, -0.8401039424610417, -0.321979692401086, 0.3872684286480179, 1.1157065334837157, 1.6960677850017938, 1.9988189943666541, 1.9573945876780168, 1.5803396945655783, 0.9477091437142076, 0.19232243127402596, -0.5302871285159128, -1.0768622400958583, -1.3487415170882193, -1.3142721534477264, -1.0160549384789497, -0.5609812087851963, -0.09482876858704008, 0.23324220225330478, 0.3084239102111141, 0.08149529958533265, -0.4140915211530008, -1.064037715090486, -1.6945830203012402, -2.1096155389799462, -2.1358349857225494, -1.666018080178206, -0.6903158867045821, 0.6923038382426453, 2.286252842976211, 3.833762306629734, 5.065055678208275, 5.753870610667261, 5.766267127140383, 5.091661330790409, 3.8485934960018944, 2.263158531391043, 0.6241141624464468, -0.7759499534458076, -1.7006252450934691, -2.0175967400452466, -1.7237065346139013, -0.9415063705569463, 0.11185613695225947, 1.1761562864428101, 2.007961760068105, 2.4348158985785706, 2.391062635658722, 1.9270857705306694, 1.1902279675658682, 0.3826292282657682, -0.29304618950258915, -0.6860005121298968, -0.734311131576476, -0.4770135710131287, -0.03818993702252498, 0.4126288349828533, 0.7130555161972651, 0.7590480938055623, 0.5403745367848064, 0.14987032728456623, -0.23717650666285256, -0.40915321746336086, -0.17825375861305656, 0.5612293779169707, 1.7925487497700916, 3.366120416979066, 5.023703082929161, 6.452726995445775, 7.358160908381299, 7.534118915622664, 6.916735772947369, 5.604029156824382, 3.8365821299212386, 1.942895721769217, 0.26257503791917003, -0.9333838704328941, -1.5047734570881273, -1.4706158798921005, -0.9963000057705904, -0.3426924137029343, 0.20931614552184016, 0.4386131605264784, 0.24638594991614554, -0.31583594073187105, -1.06062009938086, -1.7180096939092242, -2.0135242605537917, -1.7494456456331993, -0.8667987667497098, 0.5295892386629408, 2.1906288882389755, 3.7825541265925944, 4.970848785842059, 5.50587024590581, 5.286813588660553, 4.386464551232828, 3.0299672136287867, 1.533599021016507, 0.2207021292824602, -0.661729734577261, -1.002630663814735, -0.8463911925203842, -0.3677654839473236, 0.18942996203876733, 0.5908816863361926, 0.6837121409387132, 0.4400392912667499, -0.040870549461151824, -0.5721545518301379, -0.9479262570721488, -1.0188980707092217, -0.7504044674040942, -0.24309688682511096, 0.292197558866849, 0.5996937710563714, 0.46515614306105746, -0.20282464231401917, -1.3231684013071152, -2.642357678003921, -3.7880789062212403, -4.364233667211891, -4.061942724342358, -2.755024759940214, -0.5514195266789181, 2.216422804705114, 5.062201125263182, 7.459981526834684, 8.97160351552099, 9.352564091036102, 8.6073251147186, 6.979138290547189, 4.878056760369016, 2.7683495202004433, 1.0478422081939789, -0.046611234741767385, -0.48177225875826224, -0.4090399805951524, -0.09281502876990377, 0.18917124761432097, 0.24111533728266724, 0.00993294027920736, -0.4066716907408674, -0.8056699111469121, -0.9609932907901042, -0.7139336140824679, -0.04037167031093489, 0.9287416005687146, 1.941663302828943, 2.704505305239602, 2.9786314327997316, 2.6642089423656534, 1.8410538578152937, 0.7513577452422778, -0.2721721537667336, -0.9109106025992664, -0.9641820928134818, -0.4180346473106934, 0.5450125883917257, 1.6005249358143248, 2.3853039834742567, 2.616943422399822, 2.191154993502499, 1.2242397625773747, 0.024934281525872716, -0.9976407529162753, -1.4622487488751241, -1.139806679965157, -0.03362033110240744, 1.611303595141965, 3.374619599069284, 4.783297906724807], 'positive_zeros': ['1.03363767618060245263022119865503', '2.10883778508925389218447896739524', '4.53339203075232413372264827664890', '5.33883414367633301461301269350283', '5.73116194035680112590758637016448', '7.40654413467655757394075608465600', '8.277265774517082126392120522489419', '8.745321167099796961938544891519868', '10.35644923614826823924842181849978', '10.93414443316968364132223619279161'], 'prelabel': '2-432-108.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.857293021394124, 'root_angle': -0.4897864463763689, 'root_number': '0.03208131940599664 - 0.9994852619949783*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.244893223188', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.03363767618060245263022119866', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.10883778508925389218447896740', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.53339203075232413372264827665', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.4495373673193144, 'bad_primes': [2, 3], 'central_character': '108.59', 'conductor': 432, 'conductor_radical': 6, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/432/2/be/b/383/2'], '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': '2-432-108.59-c1-0-3', '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': '2-432-108.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.857293021394124, 'root_angle': -0.24489322318818446, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.03363767618060245263022119866', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1310291420628852915637313493147', 'Lhash_array': ['1310291420628852915637313493147'], 'label': '2-432-108.59-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/432/2/be/b/383/2'}