-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1868162018838310073338741502254', 'a10': [0.0, 0.0], 'a2': [1.2709319135386046, 0.0], 'a3': [1.0, 0.0], 'a4': [-0.3847320711491008, 0.0], 'a5': [0.0, 0.0], 'a6': [1.2709319135386046, 0.0], 'a7': [0.48329109547250304, 0.0], 'a8': [-3.0308320944624065, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 72.46423983431198, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '9075.1', 'coefficient_field': 'CDF', 'conductor': 9075, 'conductor_radical': 165, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.2709319135386046, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.48329109547250304, 0], [7.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.1441244931034724, 0], [13.0, 0]], [[1.0, 0], [2.510128794231344, 0], [17.0, 0]], [[1.0, 0], [3.7201478808400585, 0], [19.0, 0]], [[1.0, 0], [-8.53217679578766, 0], [23.0, 0]], [[1.0, 0], [9.982925351892574, 0], [29.0, 0]], [[1.0, 0], [5.789844494706208, 0], [31.0, 0]], [[1.0, 0], [-3.2076452316160333, 0], [37.0, 0]], [[1.0, 0], [7.865645264188067, 0], [41.0, 0]], [[1.0, 0], [5.970162961866583, 0], [43.0, 0]], [[1.0, 0], [6.130968140064904, 0], [47.0, 0]], [[1.0, 0], [-1.5821992630901744, 0], [53.0, 0]], [[1.0, 0], [0.3779324668840678, 0], [59.0, 0]], [[1.0, 0], [-3.0085153552075568, 0], [61.0, 0]], [[1.0, 0], [5.980823634804797, 0], [67.0, 0]], [[1.0, 0], [-8.344184382005754, 0], [71.0, 0]], [[1.0, 0], [0.15141556984422505, 0], [73.0, 0]], [[1.0, 0], [-7.485412829493423, 0], [79.0, 0]], [[1.0, 0], [-4.057227846216437, 0], [83.0, 0]], [[1.0, 0], [17.031678814467117, 0], [89.0, 0]], [[1.0, 0], [3.6097746729017417, 0], [97.0, 0]], [[1.0, 0], [-7.595726343518748, 0], [101.0, 0]], [[1.0, 0], [-3.80758067134797, 0], [103.0, 0]], [[1.0, 0], [-0.47746507335280325, 0], [107.0, 0]], [[1.0, 0], [6.9208259531194525, 0], [109.0, 0]], [[1.0, 0], [-10.86409931433976, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 308, 'label': '2-9075-1.1-c1-0-308', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/9075/2/a/dy/1/10', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-2.543900581360033e-60, 0.3333126306693155, 0.6650011596599551, 0.9933783637598593, 1.3166355043693012, 1.6327930415105647, 1.9396641853024177, 2.2348341399320897, 2.5156568940432353, 2.779270381362218, 3.022629858720286, 3.242558483440656, 3.435813349679047, 3.5991646716782393, 3.7294853722603594, 3.8238480293741643, 3.8796259318607116, 3.8945948798626953, 3.867032322493864, 3.7958104482220762, 3.6804799297497692, 3.5213411766318377, 3.3195001692147303, 3.0769062409515615, 2.796369546010333, 2.481556396468563, 2.136961176406314, 1.7678541334563573, 1.3802050026164039, 0.9805831193076076, 0.5760354120682811, 0.17394440994288785, -0.2181308670845729, -0.5926275689838952, -0.9421610267676463, -1.2597113648907199, -1.538809531230266, -1.7737172622773023, -1.959595359115549, -2.0926546807190927, -2.170284476599174, -2.1911530866686677, -2.155276631755066, -2.0640520959672455, -1.9202521474463232, -1.7279801350985462, -1.4925849070464865, -1.2205363867785828, -0.9192641749285317, -0.5969627735827652, -0.2623683084018358, 0.07548719723619242, 0.4075369108022772, 0.7249477194428049, 1.0193876750103024, 1.283283500690932, 1.510059272585668, 1.694347673931104, 1.832165827245125, 1.9210486355333283, 1.960133790280762, 1.9501941011670219, 1.8936145279646128, 1.7943131953087843, 1.6576076825113588, 1.490029931965101, 1.2990951340482326, 1.093031844117504, 0.8804822887782747, 0.6701832482584489, 0.47063899030807543, 0.2897984195287694, 0.13474884834210155, 0.011438561504760424, -0.07556037748728496, -0.12323883596341205, -0.13027825759275877, -0.09711273509155702, -0.02592141577075307, 0.0794501803639132, 0.21363851491417174, 0.36997575609079164, 0.5407617521761982, 0.7175844971495985, 0.8916770028649382, 1.0542965786349283, 1.1971111199438975, 1.312576204641866, 1.3942866470370865, 1.4372867021119353, 1.438324349803191, 1.39603699925266, 1.3110584812062749, 1.1860402599566089, 1.0255832838143857, 0.8360806708204706, 0.6254753411468766, 0.40294059324978865, 0.17849530494951374, -0.037431248012422334, -0.23446718711980538, -0.4027785757448011, -0.5335415565441611, -0.6193845262932809, -0.6547793436165381, -0.6363620799378242, -0.5631662748964641, -0.4367549727654076, -0.2612418819968645, -0.043196662696303394, 0.20856558053906418, 0.48330525439667466, 0.7687791029571278, 1.0517453705649151, 1.3185333278715161, 1.5556534875003827, 1.750422076139251, 1.8915716758558947, 1.969819520186043, 1.9783657993866817, 1.9132965061962115, 1.7738687901157888, 1.562661375490528, 1.2855781691320085, 0.9516995165971638, 0.5729823974573593, 0.1638178797170339, -0.25953893873430056, -0.6796448160219154, -1.0786227060079645, -1.4389625564299529, -1.7443332717633024, -1.9803687774378573, -2.1353910215277927, -2.2010343854622354, -2.172739333490052, -2.0500881158876934, -1.8369617763528054, -1.541505346940401, -1.1758966248813698, -0.7559229414572151, -0.3003794427097311, 0.169688825355305, 0.6318707280381675, 1.0633616189758088, 1.441982261176623, 1.7471982242322883, 1.961092514419665, 2.0692450226313763, 2.061475437669596, 1.9324114925570748, 1.6818516047699148, 1.3148998510505214, 0.841861405431577, 0.27789761086523146, -0.35754876030137656, -1.0415363174439445, -1.74858376169027, -2.451763170880261, -3.123879149539901, -3.73867992422538, -4.272043746400756, -4.7030839393673896, -5.015118665713889, -5.19645693474124, -5.2409603161402245, -5.148349946882853, -4.9242402647817665, -4.579893927446435, -4.131705958189344, -3.6004386346999064, -3.010241323567051, -2.387500707405622, -1.7595760508076794, -1.1534807942248233, -0.5945754557748574, -0.10533730493047624, 0.29573054836795887, 0.5949940610938014, 0.7843396263569974, 0.8615460241347037, 0.8303547875882791, 0.700231933278581, 0.4858297690618203, 0.20617310991858345, -0.11639111206629994, -0.45742894257789224, -0.7917768384487942, -1.0949516541014186, -1.3445394741309924, -1.5214894397054306, -1.611242433841577, -1.604631956432395, -1.4985054199042724, -1.2960279282561669, -1.0066466976957356, -0.6457118334406872, -0.23376729687267206, 0.20445636686777768, 0.6412995655848593, 1.0476193078218292, 1.3943496547345078, 1.6540961918295078, 1.8026804055675665, 1.820550923410465, 1.6939840814306422, 1.4160060119106326, 0.9869819546697335, 0.41483513869699795, -0.28512347735468535, -1.0907530481800123, -1.9740061763922998, -2.9021759431046963, -3.839407037282807, -4.748396474629169, -5.592198223447771, -6.336039281670808, -6.949052810171344, -7.405837001746548, -7.6877563624391305, -7.783914642673875, -7.69174516640064, -7.417183928709081, -6.974412545520234, -6.385180793175123, -5.6777408535007785, -4.885446262161069, -4.045086791571499, -3.195045061866268, -2.3733707311770984, -1.6158730749383319, -0.9543323028659855, -0.4149240576520104, -0.016940468616341773, 0.2281245364444529, 0.31707739880071434, 0.2550884786151256, 0.055314571766918244, -0.26189812649546085, -0.6701863487867521, -1.1386527154428818, -1.6335778081970735, -2.120267471286462, -2.5649342888084785, -2.9365106444942817, -3.2082949519497506, -3.359342326775126, -3.375525618545015, -3.2502115055587244, -2.9845182126861265, -2.5871450957024935, -2.0737884876258654, -1.4661814356595777, -0.7908159326797454, -0.077423754089823, 0.6426949616084766, 1.3383984525292025], 'positive_zeros': ['1.47371998128030219370969057321952', '2.38012605046993913819898222165639', '3.42704174991659492421519494812039', '3.66921238182464638194816182878038', '4.63226247551807518749196370453811', '5.11782782460578241711876085014158', '5.92447081646321119274640749614219', '6.63935671821335519928071640348900', '7.23980611290080458811607553393311'], 'prelabel': '2-9075-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.512593014723068, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.47371998128030219370969057322', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.38012605046993913819898222166', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.42704174991659492421519494812', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 72.46423983431198, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 9075, 'conductor_radical': 165, 'degree': 2, 'index': 308, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9075/2/a/dy/1/10'], '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': '2-9075-1.1-c1-0-308', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-9075-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.512593014723068, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.47371998128030219370969057322', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1868162018838310073338741502254', 'Lhash_array': ['1868162018838310073338741502254'], 'label': '2-9075-1.1-c1-0-308', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9075/2/a/dy/1/10'}