-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2035377056139939677089358016610', 'a10': [1.3246817089013687, -2.2944160236743363], 'a2': [0.2740870157172977, 1.554424709230784], 'a3': [0.0, 0.0], 'a4': [-0.46172724291057643, 0.16805497276925024], 'a5': [-1.2858113932622866, -1.0789238658499292], 'a6': [0.0, 0.0], 'a7': [-2.6116706850211377, -0.9505703910533168], 'a8': [1.1906219716593345, 2.062217747521799], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.82', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '927226220164822925116527554465', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.2740870157172977, -1.554424709230784], [-1.8793852415718169, 0.6840402866513374]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.2858113932622866, 1.0789238658499292], [0.8682408883346517, 4.924038765061041]], [[1.0, 0], [2.6116706850211377, 0.9505703910533168], [5.362311101832846, 4.499513267805775]], [[1.0, 0], [-3.1800206368335493, 2.66835414350317], [1.9101299543362338, -10.832885283134289]], [[1.0, 0], [-1.1940126863598977, 6.77158244054579], [-12.216004070216808, -4.446261863233693]], [[1.0, 0], [-0.48827562245501116, 0.8457181861893983], [-8.5, -14.722431864335457]], [[1.0, 0], [1.342644497436104, 2.3255284860621135], [-9.5, 16.454482671904334]], [[1.0, 0], [-1.5158837048685272, 0.5517365471813166], [17.619022191736494, -14.784115022790404]], [[1.0, 0], [-1.4287557974551384, -8.102876778780729], [-27.251086002791343, 9.918584156444393]], [[1.0, 0], [0.9811041644106213, -0.35709271256008057], [23.747377736688318, -19.92641590028272]], [[1.0, 0], [-0.6541723177697278, 1.1330596912822615], [-18.5, -32.04293994002423]], [[1.0, 0], [-0.8418758848131289, 4.774515399915271], [-38.527397452222246, -14.022825876352417]], [[1.0, 0], [-7.538052375170068, 6.325176967800223], [7.466871639678005, -42.34673337952495]], [[1.0, 0], [-11.74399696898135, -4.274465328021712], [36.00408882659197, 30.211017655267348]], [[1.0, 0], [7.3427960798548115, 0], [53.0, 0]], [[1.0, 0], [6.934139262079426, 5.818433697342743], [10.24524248234889, 58.10365742772028]], [[1.0, 0], [-1.2082021239132406, -0.43974961008162544], [46.728711030257664, 39.2100441908789]], [[1.0, 0], [0.8068214222975882, -4.575711663954415], [-62.95940559265586, -22.915349602819806]], [[1.0, 0], [-2.811867242232503, 4.8702969276852786], [-35.5, -61.48780366869514]], [[1.0, 0], [-2.2807215449285905, -3.950325593733303], [-36.5, 63.21985447626402]], [[1.0, 0], [-0.8086450142647256, -4.586053767924041], [-74.23571704208676, 27.01959132272783]], [[1.0, 0], [1.0009761425293702, 5.676817798997883], [-77.9944875252304, 28.387671896030504]], [[1.0, 0], [-2.272209372379202, -3.9355820783949684], [-44.5, 77.07626093681505]], [[1.0, 0], [-6.569169052272548, 5.512187328903097], [16.843873233692243, -95.52635204218419]], [[1.0, 0], [7.3349615672262525, 2.6697076799569297], [77.37048875501678, 64.92154857834048]], [[1.0, 0], [1.659365037894476, 1.392372591285728], [17.885762299693827, 101.43519856025743]], [[1.0, 0], [12.584949885350023, 0], [107.0, 0]], [[1.0, 0], [12.213999771064275, 0], [109.0, 0]], [[1.0, 0], [0.345358145548415, 0.28978989255374443], [19.62224407636313, 111.28327609037952]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 23, 'label': '2-3e6-27.13-c1-0-23', '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/729/2/e/k/82/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.4372266726035516, 1.5478976497419112, 1.636078610445752, 1.69973611322415, 1.7331483031886648, 1.7283988328411815, 1.677173277214184, 1.57256350247909, 1.410694327855939, 1.1920533855673905, 0.92242228534276, 0.6133029664032836, 0.2817358710642425, -0.05056719480629475, -0.35879783114930736, -0.6172753996284936, -0.802165857616315, -0.894439376359953, -0.8827231687675483, -0.7656483048960697, -0.5532783670982904, -0.267256220530952, 0.06058121444292292, 0.3911949939481851, 0.682795174222448, 0.8963584318440825, 1.0015878168093264, 0.9825103920898021, 0.8418204376946881, 0.6031117664146598, 0.31032051102772823, 0.024017215246787994, -0.18538208012983784, -0.246922274720486, -0.09988351253168214, 0.2954227500590638, 0.9485072986860973, 1.8328655828536329, 2.884822033974804, 4.007873699153747, 5.082577912325896, 5.981137544530961, 6.584962569645535, 6.802780914979449, 6.586480510680605, 5.941899256389918, 4.932291431058259, 3.6731607954925924, 2.3184506497584074, 1.0395319273450225, -0.00020699316770021278, -0.6713437102955745, -0.9006948021414346, -0.6858433601641373, -0.09887235100560117, 0.7221237791181507, 1.593153573736918, 2.3133806716470966, 2.6986428242193754, 2.613854263036058, 1.9985305803138347, 0.8805453593708651, -0.624934600668513, -2.331857667270022, -4.01276963211492, -5.436565866069261, -6.407941323936653, -6.8013592708357455, -6.58310509411696, -5.817022609629549, -4.652515052108849, -3.296783744533962, -1.9764092045978552, -0.8956011052885715, -0.19925654186014935, 0.05185939724073063, -0.11114441875881817, -0.5761216653251768, -1.1769502743449543, -1.7310269154635654, -2.0791388239023316, -2.1191054093645945, -1.8259164687754739, -1.2540727698612533, -0.5218323570722978, 0.2188029614799934, 0.8192134410572528, 1.169555293708185, 1.2239464645980072, 1.0093753649757806, 0.6161927900256908, 0.17258991329048662, -0.190476080241034, -0.3748986981724015, -0.3422295843176461, -0.12436591021271194, 0.1851882159528055, 0.4577627978558727, 0.567139102790934, 0.42850126673029476, 0.02799967235954722, -0.5658747401802272, -1.2135226732302913, -1.7366551759242619, -1.9646408312230652, -1.7832325923821053, -1.1726233975044, -0.22365417558843792, 0.8740167084665633, 1.87098419588766, 2.516329248799032, 2.6212725480294186, 2.11207196998891, 1.0576411855340848, -0.3370489076167776, -1.7724221874579615, -2.922230487648468, -3.512208523288331, -3.3899711727032478, -2.5678224858909995, -1.2261478581119334, 0.3253862972807645, 1.72081632284001, 2.627798715018697, 2.8320313781165902, 2.2942003265909165, 1.1637087583339891, -0.2559153985878252, -1.5826143459770046, -2.45408808061031, -2.6238824837300228, -2.0301313471287235, -0.8181824389502276, 0.6901214052869462, 2.0739382886144706, 2.9186951708235798, 2.9224097484447005, 1.975548513457653, 0.1933922972234155, -2.1079353649662456, -4.485924034768183, -6.477485225269946, -7.708740535404341, -7.980496569913693, -7.30781701897642, -5.904614899121984, -4.119064475139482, -2.3387424808921935, -0.8921004891568745, 0.026981152478854395, 0.3921783805650525, 0.32857391874828396, 0.05501465172017487, -0.1956455453037309, -0.2532969115142902, -0.061080805590479306, 0.31473376374624207, 0.7168266308670883, 0.9589388023017269, 0.8967802714901424, 0.4839769869714856, -0.2056263063560259, -0.9969230853628753, -1.6678174678929725, -2.0211475314137175, -1.9505183923610765, -1.477921845382675, -0.7499374929944594, 0.007240067322602721, 0.5600295778194845, 0.7436207323325231, 0.5168103447374006, -0.023319624785815105, -0.6728302174221781, -1.189109187445637, -1.3737590720839927, -1.1423721175665391, -0.5567482509767265, 0.1931167570639569, 0.8533496878021294, 1.196823928635775, 1.1099533811587872, 0.6450373211424542, 0.01738584172137344, -0.45608987274642043, -0.4604776072744897, 0.2031325680968211, 1.530874884938561, 3.2879453385721957, 5.053427727743247, 6.329683815357553, 6.686398704196709, 5.8962658546458675, 4.01926192917595, 1.4061854561299243, -1.3841175011735458, -3.732779919233304, -5.1319804182021524, -5.3281247415546265, -4.393170229013124, -2.7010643726044448, -0.8149918178722309, 0.6812581384679938, 1.3567559762091868, 1.0586598400504765, -0.04923763149480243, -1.5462065056154397, -2.8933429899677194, -3.607387437389247, -3.414647377172103, -2.336623387668204, -0.680931490602555, 1.0585005301160615, 2.359035304475382, 2.8336637706251366, 2.3495489116531614, 1.0638256081252642, -0.6329000041961879, -2.244817480598518, -3.3275794269674233, -3.621896697670147, -3.121682335077793, -2.057329683975408, -0.8035713294868522, 0.2537524582483813, 0.8451696570601187, 0.896320776510291, 0.5335579772357953, 0.018464127962825577, -0.36169443000374896, -0.40592107811900857, -0.07284324424716825, 0.5101051116458729, 1.1028678295303491, 1.4511981771759348, 1.388881477120966, 0.9045043612648046, 0.14747303575872528, -0.6286142110505555, -1.1630887009337871, -1.2880769299208272, -0.9921822453655957, -0.42287620673228965, 0.1738010979748565, 0.553011920052982, 0.5711055122932147, 0.24552849499908402, -0.2508316185203513, -0.6609998134426338, -0.7546814776085771, -0.4349741355521426, 0.20329079250375362, 0.891274577907801, 1.2791226282714678, 1.0734482326672865, 0.16860755819356102, -1.280561738665298], 'positive_zeros': ['1.60562938697263097818521600661060', '2.72743771537326474042167179692799', '3.88671489359827757663981382465552', '4.29054841486621335523643122531573', '6.24997036199589835030902002406241', '6.76654655199948731335929363381979', '7.70106403637083899927317665675874', '9.322106914989496476700348676822313', '9.448853068026077320347973608974659', '10.58663808475116933059323227954974'], 'prelabel': '2-3e6-27.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.03703703703703704, 'root_number': '0.993238357741943 + 0.11609291412523025*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0185185185185', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.60562938697263097818521600661', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.72743771537326474042167179693', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.88671489359827757663981382466', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '27.13', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/e/k/82/2'], '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': '2-3e6-27.13-c1-0-23', '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': '2-3e6-27.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.01851851851851852, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.60562938697263097818521600661', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2035377056139939677089358016610', 'Lhash_array': ['2035377056139939677089358016610'], 'label': '2-3e6-27.13-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/e/k/82/2'}