-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '448195395061501240534909804981', 'a10': [-1.5938484880959447, 0.0], 'a2': [-1.0, 0.0], 'a3': [-3.2157813243953868, 0.0], 'a4': [1.0, 0.0], 'a5': [1.5938484880959447, 0.0], 'a6': [3.2157813243953868, 0.0], 'a7': [1.0, 0.0], 'a8': [-1.0, 0.0], 'a9': [7.341249526330149, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 40.35639318155513, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 7, 19], 'central_character': '5054.1', 'coefficient_field': 'CDF', 'conductor': 5054, 'conductor_radical': 266, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [3.2157813243953868, 0], [3.0, 0]], [[1.0, 0], [-1.5938484880959447, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.215781324395387, 0], [11.0, 0]], [[1.0, 0], [4.719316690030706, 0], [13.0, 0]], [[1.0, 0], [7.5570308507255355, 0], [17.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [6.528946502522038, 0], [23.0, 0]], [[1.0, 0], [0.11839747066412286, 0], [29.0, 0]], [[1.0, 0], [6.313165178126651, 0], [31.0, 0]], [[1.0, 0], [-5.187696976191889, 0], [37.0, 0]], [[1.0, 0], [7.215781324395387, 0], [41.0, 0]], [[1.0, 0], [0.31316517812665096, 0], [43.0, 0]], [[1.0, 0], [-0.11839747066412286, 0], [47.0, 0]], [[1.0, 0], [-2.313165178126651, 0], [53.0, 0]], [[1.0, 0], [1.252598961765796, 0], [59.0, 0]], [[1.0, 0], [-7.844784891965468, 0], [61.0, 0]], [[1.0, 0], [12.772812175120922, 0], [67.0, 0]], [[1.0, 0], [-4.971915651796502, 0], [71.0, 0]], [[1.0, 0], [-13.585115198929033, 0], [73.0, 0]], [[1.0, 0], [-6.250936403869524, 0], [79.0, 0]], [[1.0, 0], [9.991266710833088, 0], [83.0, 0]], [[1.0, 0], [-14.431562648790774, 0], [89.0, 0]], [[1.0, 0], [7.64734397318616, 0], [97.0, 0]], [[1.0, 0], [5.125468201934762, 0], [101.0, 0]], [[1.0, 0], [4.874531798065238, 0], [103.0, 0]], [[1.0, 0], [2.0561686964069956, 0], [107.0, 0]], [[1.0, 0], [-12.98152276824567, 0], [109.0, 0]], [[1.0, 0], [-8.125468201934762, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 11, 'label': '2-5054-1.1-c1-0-11', 'leading_term': '0.30197867845574902758087372802941', '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/5054/2/a/w/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.30197867845574905, 0.2956647564965204, 0.2767369579337856, 0.24524246084731732, 0.20127705565446588, 0.1450094354686925, 0.076712451763424, -0.00320109580981343, -0.09414086955879154, -0.19530244063409113, -0.30563453891187475, -0.4238126673535896, -0.5482213437902356, -0.6769468752104466, -0.8077821770207163, -0.9382447368503437, -1.0656083956068148, -1.186949178869237, -1.2992049585712224, -1.3992482580780818, -1.4839710353604532, -1.550379794490287, -1.5956988942661965, -1.6174794570128297, -1.6137108460353264, -1.5829312945781597, -1.5243339514704428, -1.4378643782976785, -1.3243054086018247, -1.1853452782589406, -1.0236250721079259, -0.8427618157651753, -0.6473439795283475, -0.4428967542833806, -0.23581520248712118, -0.03326426946271568, 0.1569543561719472, 0.3265674431185687, 0.46702522091458304, 0.569722728224794, 0.6262428564573095, 0.6286153004792041, 0.5695845880642645, 0.44287946486489044, 0.24347520765922867, -0.032160032185931615, -0.385843953252581, -0.8174928938321779, -1.3249772602374952, -1.904027408814782, -2.5481967046842158, -3.2488870672342163, -3.995440604860666, -4.7752989790889915, -5.574229973662469, -6.376618441918241, -7.165816440577596, -7.9245450128534, -8.635337846901713, -9.281014997867683, -9.845173112782911, -10.312677222313297, -10.670138238292681, -10.906359885383361, -11.012738947701536, -10.983603456725506, -10.816474793903906, -10.512241615660326, -10.07523599144507, -9.513205114496172, -8.837175314267876, -8.06120876214105, -7.202057093001108, -6.278720025391072, -5.311920803806147, -4.323513756208914, -3.3358423083584006, -2.3710682832268186, -1.4504951130175507, -0.5939085988738233, 0.18104100794755457, 0.8593926053154555, 1.4293422217179605, 1.8826066782592983, 2.2146676557040417, 2.424885042837652, 2.516473179717708, 2.4963387612361245, 2.3747845363898534, 2.1650883122501443, 1.8829719246699166, 1.5459795458216732, 1.1727887468219484, 0.7824809265812309, 0.3937998893055879, 0.024428374275782382, -0.3096878705574989, -0.594940357126045, -0.8205570741572381, -0.9789791428007748, -1.0660983154373505, -1.0813444809861388, -1.0276187133276742, -0.9110741205701323, -0.7407535295955793, -0.5280995673175257, -0.28635867261758924, -0.02990570108189934, 0.22648019249100712, 0.4683550097629619, 0.6823301073861726, 0.8567389192504172, 0.9822179749857134, 1.0521735467314446, 1.0631102593874435, 1.0148042491288856, 0.9103106869705871, 0.755803378415239, 0.5602523437259262, 0.3349533864733071, 0.09293127251331086, -0.15175512004253744, -0.3847718142562352, -0.592295082124377, -0.761783117812933, -0.8826937928453815, -0.9471100300212428, -0.950238099472349, -0.8907497640166931, -0.770946454930602, -0.5967322267630809, -0.3773917272674865, -0.12517937264507484, 0.14526415292985725, 0.41764255810943385, 0.6748478826225116, 0.8998769519147256, 1.0767745973960732, 1.191555105561043, 1.2330529892993927, 1.1936563153997932, 1.0698804416157826, 0.8627469535065567, 0.5779415590890381, 0.2257352970342118, -0.1793348569412555, -0.6190176140878663, -1.0721106316441822, -1.515403287004492, -1.9247566422770281, -2.27626995926696, -2.547477187917333, -2.718513670972248, -2.773193129110014, -2.6999379083808344, -2.492511419477207, -2.150510448411245, -1.679586188282527, -1.0913759109280636, -0.40314152924508034, 0.3628738245990272, 1.180345431635038, 2.0199834106594925, 2.850814617791587, 3.6415692211816055, 4.362104640766984, 4.984796416136085, 5.48582606128077, 5.846300133101415, 6.053142433879252, 6.0997121456127825, 5.986114235175817, 5.7191839968913465, 5.312144314121762, 4.783951243379514, 4.15835993826245, 3.4627578365606126, 2.72682459814749, 1.981087783249987, 1.255449136072311, 0.5777582143332679, -0.027492176043198157, -0.540280647765219, -0.9459240554298625, -1.2356519407691735, -1.406860026481296, -1.4630318290223363, -1.413335810786476, -1.2719235169762197, -1.056970814043989, -0.7895186994842012, -0.49218134137492886, -0.18779635592237082, 0.10190461860448471, 0.3575284593547442, 0.5630855532813906, 0.7068266947827108, 0.7818050387237346, 0.7861327920835036, 0.7229207255251267, 0.5999077679283922, 0.4288067669659505, 0.2244098173334978, 0.0035113098865806503, -0.21628188541727641, -0.4177766483160096, -0.585377450012682, -0.7061515603827945, -0.7707067198193855, -0.7738241191766752, -0.7148049958809695, -0.5975074192078317, -0.43006979228803244, -0.2243380064334271, 0.0049672422967708945, 0.24128898250227218, 0.46741011248846154, 0.6666889036910788, 0.8242705105935465, 0.9281913949403074, 0.9702992757865324, 0.9469221086867154, 0.859235083304949, 0.7132938068600234, 0.5197235505642813, 0.29307732605271625, 0.05089816759927762, -0.18745815652728332, -0.40216609900399347, -0.5743517732670896, -0.687497811315114, -0.7287347444456861, -0.6899265340363008, -0.5684686428776945, -0.36773352646901974, -0.0971197371423686, 0.2283142675961598, 0.5886235459049463, 0.9601218914106675, 1.3168374349404794, 1.632194332143802, 1.8808180545399489, 2.040349640059951, 2.093149109540369, 2.027770685521736, 1.8401025583501087, 1.534081342163846, 1.1219151809952979, 0.6237783959111589, 0.06697293281984139, -0.5154142700615043, -1.0862956298227555, -1.6067161140190966, -2.0382166807556947, -2.345290176958612, -2.4977806988335782, -2.4730751473391894], 'positive_zeros': ['0.35356382506410487270675695500607', '1.78593354612866230391885798252349', '2.27989591391008451978474511790818', '4.05008639603235380534897777812209', '4.82773305671488249301872950540156', '5.43946086385307213053936249598358', '6.11294053701414816795562520540236', '6.72687525184989099773346751447889', '7.34147391909188753795629215989140', '8.101479493803469141412662546557613'], 'prelabel': '2-5054-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.352668193881617, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.35356382506410487270675695501', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.78593354612866230391885798252', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.27989591391008451978474511791', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 40.35639318155513, 'bad_primes': [2, 7, 19], 'central_character': '1.1', 'conductor': 5054, 'conductor_radical': 266, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5054/2/a/w/1/1'], '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': '2-5054-1.1-c1-0-11', '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': '2-5054-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.352668193881617, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.35356382506410487270675695501', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '448195395061501240534909804981', 'Lhash_array': ['448195395061501240534909804981'], 'label': '2-5054-1.1-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5054/2/a/w/1/1'}