-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1979510815154860070082924516276', 'a10': [0.0, 0.0], 'a2': [-0.2225209339563144, 0.9749279121818236], 'a3': [0.7774790660436856, -0.9749279121818236], 'a4': [-0.9009688679024191, -0.4338837391175581], 'a5': [0.0, 0.0], 'a6': [0.7774790660436856, 0.9749279121818236], 'a7': [0.6234898018587335, -0.7818314824680298], 'a8': [0.6234898018587335, -0.7818314824680298], 'a9': [-0.12348980185873352, -0.5410441730642654], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.2225209339563144, -0.9749279121818236]]], [7, [[1.0, 0], [-0.6234898018587335, 0.7818314824680298]]], [17, [[1.0, 0], [0.9009688679024191, -0.4338837391175581]]]], 'bad_primes': [2, 7, 17], 'central_character': '3332.407', 'coefficient_field': 'CDF', 'conductor': 3332, 'conductor_radical': 238, 'conjugate': '1149594719867968723772133004547', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.2225209339563144, -0.9749279121818236]], [[1.0, 0], [-0.7774790660436856, 0.9749279121818236], [-0.2225209339563144, -0.9749279121818236]], [[1.0, 0], [0, 0], [0.2225209339563144, 0.9749279121818236]], [[1.0, 0], [-0.6234898018587335, 0.7818314824680298]], [[1.0, 0], [-0.09903113209758087, 0.4338837391175581], [-0.9009688679024191, -0.4338837391175581]], [[1.0, 0], [-0.09903113209758087, 0.4338837391175581], [-0.9009688679024191, -0.4338837391175581]], [[1.0, 0], [0.9009688679024191, -0.4338837391175581]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-0.40096886790241915, -0.1930964297137938], [0.6234898018587335, 0.7818314824680298]], [[1.0, 0], [0, 0], [-0.6234898018587335, 0.7818314824680298]], [[1.0, 0], [-1.246979603717467, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-0.6234898018587335, 0.7818314824680298]], [[1.0, 0], [0, 0], [0.2225209339563144, 0.9749279121818236]], [[1.0, 0], [0, 0], [0.2225209339563144, -0.9749279121818236]], [[1.0, 0], [0, 0], [0.9009688679024191, 0.4338837391175581]], [[1.0, 0], [1.1234898018587336, 0.5410441730642654], [0.6234898018587335, 0.7818314824680298]], [[1.0, 0], [0, 0], [0.2225209339563144, -0.9749279121818236]], [[1.0, 0], [0, 0], [-0.6234898018587335, 0.7818314824680298]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.1234898018587336, 0.5410441730642654], [0.6234898018587335, 0.7818314824680298]], [[1.0, 0], [0, 0], [0.9009688679024191, -0.4338837391175581]], [[1.0, 0], [0.4450418679126288, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0.9009688679024191, -0.4338837391175581]], [[1.0, 0], [0.2774790660436856, 1.215715221585588], [-0.9009688679024191, 0.4338837391175581]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0.2774790660436856, -0.3479477433504717], [-0.2225209339563144, -0.9749279121818236]], [[1.0, 0], [0, 0], [0.2225209339563144, 0.9749279121818236]], [[1.0, 0], [-0.40096886790241915, -1.7567593946498534], [-0.9009688679024191, 0.4338837391175581]], [[1.0, 0], [0, 0], [0.9009688679024191, 0.4338837391175581]], [[1.0, 0], [0, 0], [0.9009688679024191, -0.4338837391175581]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-3332-3332.407-c0-0-2', 'leading_term': '1.4150688233633067332920238354144', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3332/1/be/b/407/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.4150688233633066, 1.4711891334820708, 1.5392206574139102, 1.6186371427433468, 1.7075752566321603, 1.803123862443949, 1.901656940693105, 1.9991376395781804, 2.091362160768416, 2.1741435752169243, 2.243450200196923, 2.2955153134648905, 2.3269313017802244, 2.3347362722074108, 2.316496707193777, 2.2703864671657206, 2.19526026500045, 2.090718416926291, 1.9571589905493934, 1.7958132596351948, 1.6087605295218763, 1.3989188475043162, 1.1700088121281516, 0.9264886069919475, 0.6734594733256677, 0.4165420634509081, 0.16172544098244312, -0.08480813635700687, -0.31687815503776934, -0.5285147190352394, -0.7141744169263351, -0.8689552859837966, -0.9888022830847529, -1.0706942981059888, -1.1128037387599286, -1.11462011241924, -1.0770298508477458, -1.0023458702344321, -0.8942820136382134, -0.7578695465336353, -0.599315207456006, -0.42580287263631833, -0.24524357481377995, -0.06598130505878994, 0.10353540619388327, 0.25510382144300037, 0.38112501393369086, 0.47495394159408044, 0.5312251786688003, 0.5461378625646675, 0.5176841586752506, 0.44580711075771473, 0.33247612019562656, 0.181671433577797, -0.0007271794218245358, -0.20714804306563525, -0.4286272848520769, -0.6551916002485115, -0.8763102893993072, -1.081398372660231, -1.2603487718380892, -1.4040685569585811, -1.504992324102654, -1.5575450711555583, -1.5585276080648096, -1.5073996479854013, -1.4064392768260678, -1.2607624163389934, -1.0781920267024512, -0.8689739085904548, -0.6453437616200065, -0.420958275549488, -0.21021106725783137, -0.02746179822893077, 0.11378662345733816, 0.20172265512959625, 0.22702899529572465, 0.18360878373786427, 0.06919107927270637, -0.11422514134579782, -0.36012353850387885, -0.6574466574176603, -0.9908130837677235, -1.3409812076700758, -1.685552699129432, -1.9998957220224123, -2.2582550294803205, -2.4350040968784232, -2.5059840631473924, -2.4498661292995227, -2.2494687866397602, -1.892959279340161, -1.3748703580599728, -0.6968687850212, 0.13177885966853803, 1.0940850183944626, 2.1655911528862544, 3.314997700019515, 4.505163643166405, 5.694445728420318, 6.838328283576183, 7.891277145415903, 8.80873639829092, 9.549175412071865, 10.076086827051743, 10.35983425031195, 10.379251837655193, 10.12290669319036, 9.589948883918845, 8.790492300454815, 7.745491777411619, 6.486106750811859, 5.052568010712842, 3.4925904075707295, 1.859399235153047, 0.20946000951122495, -1.3999808304968975, -2.9134242933621595, -4.279589978151436, -5.453704138891588, -6.399486172257692, -7.090729071660171, -7.512389501522336, -7.66112833581337, -7.545271457688719, -7.184191756282366, -6.607144833374326, -5.851621125101545, -4.961304165660002, -3.9837469296380026, -2.967894195318544, -1.961587623102846, -1.0091911074494557, -0.14946677038235753, 0.5861829579541429, 1.175013576870612, 1.6037110071550515, 1.868603862232777, 1.9753147636444646, 1.9378837862587697, 1.7774289075975667, 1.520436078339836, 1.1967934405602354, 0.8376988583554549, 0.4735763036535469, 0.13213429309442987, -0.16331140069882183, -0.3951474700429013, -0.5523276153607036, -0.630745068722405, -0.6331000778705728, -0.5682839446163898, -0.45033427287442257, -0.2970453227266435, -0.12834075318546595, 0.03546808902317333, 0.17540797155424862, 0.27542533728457796, 0.3237064872962802, 0.3136388902301501, 0.24434288054457387, 0.12073503006189959, -0.04688049567128152, -0.24366076122227465, -0.4514477950672662, -0.650273091262906, -0.8200266129174709, -0.9421603840192501, -1.0012927227769328, -0.9865851999749657, -0.8927802139846075, -0.7208116428478092, -0.4779326734279251, -0.17734136515834512, 0.162676880179195, 0.520032882625776, 0.8704519505150768, 1.1893075480165265, 1.4535316665811564, 1.643454057198344, 1.7444245237304197, 1.7480858219383801, 1.6531886078146547, 1.4658727616751284, 1.1993789828179222, 0.8731979326733192, 0.5117081621618582, 0.14239521925165008, -0.20622055452893737, -0.5067938398664942, -0.7353330708622404, -0.8731770497087058, -0.9086092775599006, -0.837973432336533, -0.6661882925035849, -0.4066041680398899, -0.08019242263139366, 0.2858887158957789, 0.6602590964370842, 1.0096753743227604, 1.3016119070981207, 1.5068698356689874, 1.602012407665222, 1.5714320696698885, 1.4088776253245052, 1.1183065025344632, 0.7139754449264673, 0.21973932228504786, -0.33241190621688593, -0.9044883196420295, -1.455163050674356, -1.9427741955013547, -2.3284452429535807, -2.5790884845703284, -2.670058545596447, -2.5872439699531835, -2.328422564223913, -1.903758461343284, -1.3353819071273594, -0.6560619610298108, 0.09294760927218666, 0.8647434255003301, 1.6100870314561695, 2.2809559530606056, 2.8340650051365444, 3.2340884270686288, 3.4563312453452446, 3.4886361099842196, 3.3323672074201562, 3.0023817413423877, 2.525976754890217, 1.9408788154555816, 1.2924200365948137, 0.6301099681520362, 0.0038635940107089864, -0.5398233118870572, -0.961451777151053, -1.2315657270953229, -1.3330203386812551, -1.262284938352646, -1.029667297724757, -0.6584310978544066, -0.18286695569310604, 0.3545373481540408, 0.9066068928201746, 1.4253910408951236, 1.8661607645211769, 2.1911647802921257, 2.372832281027038, 2.3961507072699, 2.26001060544832, 1.9773914136149107, 1.5743556518395974, 1.0879170222007297, 0.5629423774068494, 0.048330560163187763, -0.4072243138454082], 'positive_zeros': ['1.56155869353784588912339738545310', '2.54178433631714906095271459887197', '3.16384483852969260352581428575915', '4.28736852378233598901268534655215', '4.59501675266173305164309397264758', '5.49912617461983661980282345265943', '6.74578121952291483845094408159163', '7.80405078711136000542316992611103', '8.520954206152058642092261634863402', '9.068828447965179267013278841147222'], 'prelabel': '2-3332-3332.407-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': 0.20408163265306123, 'root_number': '0.80141362186795665978698328953346 + 0.59811053049121596205926635490525*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.10204081632653061', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.56155869353784588912339738545', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.54178433631714906095271459887', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.16384483852969260352581428576', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'bad_primes': [2, 7, 17], 'central_character': '3332.407', 'conductor': 3332, 'conductor_radical': 238, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3332/1/be/b/407/1'], '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': '2-3332-3332.407-c0-0-2', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3332-3332.407-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': 0.10204081632653061, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.56155869353784588912339738545', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1979510815154860070082924516276', 'Lhash_array': ['1979510815154860070082924516276'], 'label': '2-3332-3332.407-c0-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3332/1/be/b/407/1'}