-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2660685407442620083335290999053', 'a10': [-13.506471253163022, 0], 'a2': [0, -2.2080166496247546], 'a3': [0, 0], 'a4': [-0.8753375250201264, 0], 'a5': [0, -6.117015130052757], 'a6': [0, 0], 'a7': [0.5794875059712513, 0], 'a8': [0, -6.899306769213254], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17.411488892622973, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [71, [[1.0, 0], [0, -8.426149773176359]]]], 'bad_primes': [3, 71], 'central_character': '639.143', 'coefficient_field': 'CDF', 'conductor': 639, 'conductor_radical': 213, 'conjugate': '587356400617561725062578655121', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.2080166496247546], [-4.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 6.117015130052757], [-25.0, 0]], [[1.0, 0], [-0.5794875059712513, 0], [49.0, 0]], [[1.0, 0], [0, -7.563634647057164], [-121.0, 0]], [[1.0, 0], [1.137990520899088, 0], [169.0, 0]], [[1.0, 0], [0, 16.310667765482798], [-289.0, 0]], [[1.0, 0], [34.73832864888414, 0], [361.0, 0]], [[1.0, 0], [0, 21.2239530552903], [-529.0, 0]], [[1.0, 0], [0, -5.662660462284446], [-841.0, 0]], [[1.0, 0], [-23.873805883394883, 0], [961.0, 0]], [[1.0, 0], [-11.266743177992248, 0], [1369.0, 0]], [[1.0, 0], [0, 2.279456040385539], [-1681.0, 0]], [[1.0, 0], [-21.872816058528223, 0], [1849.0, 0]], [[1.0, 0], [0, 18.992954324252306], [-2209.0, 0]], [[1.0, 0], [0, 0.9029741004674104], [-2809.0, 0]], [[1.0, 0], [0, -59.886526858859014], [-3481.0, 0]], [[1.0, 0], [82.40751183954288, 0], [3721.0, 0]], [[1.0, 0], [-9.450289504914332, 0], [4489.0, 0]], [[1.0, 0], [0, -8.426149773176359]], [[1.0, 0], [85.6385014571482, 0], [5329.0, 0]], [[1.0, 0], [14.049432194522392, 0], [6241.0, 0]], [[1.0, 0], [0, 33.82622582876729], [-6889.0, 0]], [[1.0, 0], [0, -81.59185518525618], [-7921.0, 0]], [[1.0, 0], [-43.48165857408328, 0], [9409.0, 0]], [[1.0, 0], [0, 117.08280425391366], [-10201.0, 0]], [[1.0, 0], [-109.68634636655746, 0], [10609.0, 0]], [[1.0, 0], [0, -33.02435492409909], [-11449.0, 0]], [[1.0, 0], [-191.09340388191958, 0], [11881.0, 0]], [[1.0, 0], [0, 88.55848059954349], [-12769.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 45, 'label': '2-639-3.2-c2-0-45', 'leading_term': '1.346105665793241074963777196803274274669135144879861136', '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/639/3/c/a/143/12', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.346105665793241, 1.5491414639924408, 1.7543756441532763, 1.9607510027913946, 2.167097302486193, 2.3721064487430223, 2.57431193983556, 2.7720739836354844, 2.9635714598897476, 3.1468016587632084, 3.3195884622613603, 3.4795993667479284, 3.624371480481089, 3.7513463742142648, 3.8579134165295885, 3.9414609877607805, 3.9994347354590434, 4.0294018091255, 4.029119792418056, 3.9966088390633354, 3.9302253180479934, 3.828735089971869, 3.6913843769244425, 3.5179660612339405, 3.3088791628974232, 3.065179210475602, 2.788617244309762, 2.481665281676923, 2.1475262370327286, 1.7901265309292609, 1.4140899402965579, 1.0246916395834846, 0.6277918528171106, 0.22974907383798193, -0.16268659457439413, -0.5424987958521832, -0.9025471201078913, -1.2357236322599507, -1.535120556639396, -1.7942053321189722, -2.006998700382713, -2.168251026793504, -2.2736117026919267, -2.3197862625384835, -2.304675789135343, -2.2274932916292007, -2.088852035868365, -1.8908212911933573, -1.6369456317940816, -1.3322247873565256, -0.9830520625161049, -0.5971105158359605, -0.18322737751206464, 0.24881144523619936, 0.6884835172338308, 1.12478402015972, 1.5465058923980468, 1.9425387329707522, 2.3021781730093056, 2.615436568326379, 2.873345279308923, 3.068238520122373, 3.1940088101819923, 3.246324468674278, 3.222800367124533, 3.1231142916420027, 2.949062747171246, 2.704551827698686, 2.395520831192416, 2.0297985546326647, 1.6168945890931308, 1.1677303635762664, 0.694317067857521, 0.2093898234123212, -0.2739905285013114, -0.7428549840128743, -1.1847489895436878, -1.5881450590474353, -1.942830130250828, -2.2402527673769876, -2.4738162942081097, -2.639105513868502, -2.734036807499418, -2.7589240444464087, -2.71645579824091, -2.6115827392912245, -2.451317640980175, -2.2444540496944327, -2.0012131800847257, -1.732831849571669, -1.4511071085283447, -1.1679155121970102, -0.894726591486351, -0.6421309100230853, -0.41940307132388827, -0.23411912433688578, -0.09184600776844948, 0.004081986064523909, 0.052688177317482855, 0.05537242400157772, 0.01582110870605937, -0.06018983359999892, -0.16509189566329588, -0.2899091965472375, -0.4247156355364229, -0.5591438549451253, -0.6829227821983841, -0.7864184199866796, -0.8611515771778115, -0.900266479368996, -0.8989257091895327, -0.8546096862802981, -0.7673028273219126, -0.639553488616771, -0.47640059121758305, -0.28516621436261197, -0.07512012877119438, 0.14297109010096815, 0.3573914094401826, 0.5560945484791308, 0.7273658052995572, 0.8604938821586282, 0.9464182162371518, 0.9783171122315371, 0.9521035140484905, 0.8667985480170436, 0.7247579334492339, 0.5317328127726861, 0.2967542427382408, 0.031839174534019715, -0.24847516412024373, -0.5277524306881947, -0.7884090893395906, -1.0125644582746323, -1.1829497239816615, -1.2838319617676568, -1.3019064505610871, -1.2271101053405928, -1.0533108008411574, -0.7788317336870129, -0.4067766487937755, 0.0548695043751018, 0.5933794827860834, 1.19166555949565, 1.8288952247340238, 2.4813193752098464, 3.1232797817830855, 3.7283520525521228, 4.270571576380464, 4.725683577637582, 5.072354870367521, 5.293284472497406, 5.376153078551613, 5.314357475494482, 5.107485129526435, 4.761496009248794, 4.288592720705832, 3.7067755526945882, 3.0390952987504045, 2.312632896894692, 1.5572501429042735, 0.8041691386978531, 0.08444895046570493, -0.572564502258352, -1.1407355473212712, -1.5985034374909772, -1.9300398063332154, -2.126132863563434, -2.1847448626492176, -2.111205203682867, -1.9180198720217465, -1.6242978428710575, -1.2548155699573327, -0.8387606231231975, -0.4082138386817697, 0.0035550539952138036, 0.36389140225759076, 0.6425647053243686, 0.8134856847080584, 0.8562368511050763, 0.7573299135404319, 0.5111161651997723, 0.1202931386172494, -0.4040284853418175, -1.0427105632584028, -1.7694142031451296, -2.551831607994571, -3.3532642633411043, -4.134468557786949, -4.855673754857464, -5.478666017703545, -5.968826666366155, -6.297013454654326, -6.441180483839293, -6.387645162350075, -6.13192876498474, -5.679119710658267, -5.043734458046218, -4.249078496141007, -3.32613773123969, -2.3120570479188607, -1.2482864020193676, -0.17849408215766627, 0.8536394265472241, 1.8066261044658742, 2.6432521506814917, 3.3324218252540376, 3.850661510881262, 4.183201259264259, 4.324575158259304, 4.278709485034659, 4.058497187730787, 3.684887014594555, 3.1855438020407463, 2.593161332894626, 1.9435292552466084, 1.273469560822332, 0.6187651689666567, 0.012202777910375542, -0.5181556857096258, -0.9503735165638519, -1.2696330132895624, -1.4687697903554888, -1.5483238071662098, -1.5161137079641633, -1.3863709644223947, -1.1784977992043393, -0.915536177263247, -0.6224527708974719, -0.32435557892697003, -0.04476108956311372, 0.19597371171203645, 0.38195229665262864, 0.5026891731414567, 0.5536511236705763, 0.5363584259718516, 0.4580457001962751, 0.33091235043088757, 0.17102084141099758, -0.0030746589447504897, -0.17186811597500895, -0.31649714244219873, -0.4202775718807048, -0.47006480647896975, -0.45734190474997766, -0.3789537551423118, -0.2374319044718458, -0.040883962504181054, 0.19754703694277456, 0.46061657097610204, 0.7282400599893539, 0.9789913569940334, 1.1917294363065831, 1.3472336348245635, 1.4297255237612772, 1.428162022861336, 1.3371993863016267], 'positive_zeros': ['2.09891069902352190004258715997368', '3.27674105462611446086768142814416', '4.58945012132787460500747083257974', '6.05903125712338415938231635933729', '6.26559623311871414074082226676234', '7.27162217863441747532043449473755', '8.069707835749350989360428584594987', '8.805617874240358403774972230914999', '10.13265924436106518438303034908153', '10.93693258795747249214094287732202'], 'prelabel': '2-639-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.172707621272185, 'root_angle': -0.8040867239846964, 'root_number': '-0.81649658092772603273242802490196379732198249355222337615 - 0.57735026918962576450914878050195745564760175127012687602*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4020433619923482', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.09891069902352190004258715997', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.27674105462611446086768142814', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.58945012132787460500747083258', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 17.411488892622973, 'bad_primes': [3, 71], 'central_character': '3.2', 'conductor': 639, 'conductor_radical': 213, 'degree': 2, 'index': 45, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/639/3/c/a/143/12'], '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': '2-639-3.2-c2-0-45', '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': '2-639-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.172707621272185, 'root_angle': -0.4020433619923482, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.09891069902352190004258715997', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2660685407442620083335290999053', 'Lhash_array': ['2660685407442620083335290999053'], 'label': '2-639-3.2-c2-0-45', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/639/3/c/a/143/12'}