-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1754696576556392494235499714070', 'a10': [0, 0], 'a2': [0, 1.4142135623730951], 'a3': [-1.7320508075688772, 0], 'a4': [-2.0, 0], 'a5': [0, 0], 'a6': [0, -2.449489742783178], 'a7': [3.166928677997479, -6.242640687119285], 'a8': [0, -2.8284271247461903], 'a9': [3.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 28.61042775783118, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -1.4142135623730951]]], [3, [[1.0, 0], [1.7320508075688772, 0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-3.166928677997479, 6.242640687119285]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1050.349', 'coefficient_field': 'CDF', 'conductor': 1050, 'conductor_radical': 210, 'conjugate': '337830273279949540995219047742', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.4142135623730951]], [[1.0, 0], [1.7320508075688772, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.166928677997479, 6.242640687119285]], [[1.0, 0], [1.7573593128807148, 0], [121.0, 0]], [[1.0, 0], [-18.755385946117375, 0], [169.0, 0]], [[1.0, 0], [23.480285555477206, 0], [289.0, 0]], [[1.0, 0], [0, 23.06001955740318], [-361.0, 0]], [[1.0, 0], [0, -18.727922061357855], [-529.0, 0]], [[1.0, 0], [30.0, 0], [841.0, 0]], [[1.0, 0], [0, 8.60926722257161], [-961.0, 0]], [[1.0, 0], [0, -70.91168824543142], [-1369.0, 0]], [[1.0, 0], [0, 41.39513950544653], [-1681.0, 0]], [[1.0, 0], [0, -10.426406871192851], [-1849.0, 0]], [[1.0, 0], [38.699463640795855, 0], [2209.0, 0]], [[1.0, 0], [0, 37.02943725152286], [-2809.0, 0]], [[1.0, 0], [0, 97.48721746759213], [-3481.0, 0]], [[1.0, 0], [0, 16.726162201408222], [-3721.0, 0]], [[1.0, 0], [0, 60.97056274847714], [-4489.0, 0]], [[1.0, 0], [110.61017305526642, 0], [5041.0, 0]], [[1.0, 0], [56.75853008208712, 0], [5329.0, 0]], [[1.0, 0], [-69.82337649086284, 0], [6241.0, 0]], [[1.0, 0], [-6.435830986540512, 0], [6889.0, 0]], [[1.0, 0], [0, 42.09145901027264], [-7921.0, 0]], [[1.0, 0], [51.71533810519882, 0], [9409.0, 0]], [[1.0, 0], [0, 6.6099108627470375], [-10201.0, 0]], [[1.0, 0], [-175.87088923665382, 0], [10609.0, 0]], [[1.0, 0], [0, -46.242640687119284], [-11449.0, 0]], [[1.0, 0], [-35.94112549695428, 0], [11881.0, 0]], [[1.0, 0], [0, 73.02943725152286], [-12769.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 41, 'label': '2-1050-35.34-c2-0-41', 'leading_term': '0.757851950866779068094919412716561955267497696270111610', '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/1050/3/h/a/349/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.757851950866779, 0.9113197356781138, 1.0522620807933134, 1.1792565525699106, 1.290945685984025, 1.386034640106696, 1.4632980925948558, 1.521596553951353, 1.5599017058783682, 1.5773298279313797, 1.5731818968580997, 1.5469885396227694, 1.4985577030145283, 1.4280226730249777, 1.3358879352426054, 1.223070310970759, 1.0909328299871057, 0.9413089077897063, 0.7765145816204633, 0.5993468248595363, 0.41306630275189177, 0.2213633520818952, 0.028306459708229245, -0.16172692649438292, -0.34413680534411956, -0.5142031408455415, -0.667202698175202, -0.7985377126231457, -0.9038732338491983, -0.9792793594402599, -1.0213740164839327, -1.0274614967922417, -0.9956616290999959, -0.9250243067598704, -0.815624105630224, -0.668629942775615, -0.4863451549689182, -0.27221402214777163, -0.030791621862531447, 0.23232503596245335, 0.510605401012296, 0.7967327163360042, 1.0827882099210082, 1.3604685044412699, 1.621331050842498, 1.8570609012263033, 2.0597507778361965, 2.2221852358775727, 2.3381188245595093, 2.4025375842461387, 2.4118930308405706, 2.364298013001546, 2.259674510678094, 2.099844584971897, 1.888557280725549, 1.6314462953067943, 1.3359156096368243, 1.0109529597462181, 0.6668739188324215, 0.31500235372444485, -0.03270400503274118, -0.3640713137912245, -0.6671565782077346, -0.9307075913824411, -1.144618025513822, -1.3003589203603942, -1.3913676189818798, -1.4133758135742307, -1.3646598135164032, -1.2461984300552207, -1.0617269449456772, -0.8176794118629835, -0.5230159087115321, -0.18893615911809086, 0.1715140160695336, 0.54393188501803, 0.9131262264455458, 1.2637441522464192, 1.5809317368205318, 1.8510009879703255, 2.0620739036413043, 2.204673800868793, 2.2722348821771456, 2.261503167594789, 2.172805451453008, 2.0101677594888367, 1.7812707334096975, 1.4972362424189918, 1.1722470413987953, 0.823009142006446, 0.46807437848515493, 0.12704805669616656, -0.1802868079618701, -0.4348916952043154, -0.6194002793781899, -0.7190084560346328, -0.722283270703717, -0.6218491490370261, -0.4149137533497878, -0.10360173503097639, 0.3049275739443465, 0.7985931757744075, 1.3607403093236687, 1.9707162693922629, 2.6046558542986986, 3.2364472297636087, 3.8388390351055413, 4.384641104466824, 4.847964728133289, 5.205444355129049, 5.437381351398985, 5.528752064486084, 5.4700270490185705, 5.257755768301551, 4.894881142250114, 4.390760549302233, 3.760883765240794, 3.0262931802216935, 2.2127267416856755, 1.349518645795066, 0.4683060598811285, -0.39839864256898627, -1.2187021800402935, -1.9628180386548513, -2.6044728304093057, -3.122158968629393, -3.500167498834239, -3.729344794806265, -3.807529955428667, -3.7396455105543316, -3.5374316894789617, -3.218833118913877, -2.807065409641866, -2.329406641335663, -1.8157742670045947, -1.2971605179704644, -0.8040082200223189, -0.3646134407173846, -0.003641212744304931, 0.25916438950473103, 0.41000414129560486, 0.44172364437718253, 0.3541488148616174, 0.15403621887307306, -0.14536097783890664, -0.5250889348193799, -0.9616076167829646, -1.428161868862391, -1.8963317904405415, -2.337674044293679, -2.7253596801762714, -3.0357134604859453, -3.249564690781425, -3.3533299859187915, -3.339763717702611, -3.208331257389733, -2.965182444864406, -2.62272667865007, -2.198835189314632, -1.7157189505581092, -1.1985508609942515, -0.6739169964870133, -0.16819281174246412, 0.2940546189953563, 0.6915383149587672, 1.00750446115269, 1.2306876224088326, 1.35590746761983, 1.3842690618575013, 1.3229541827747717, 1.1846176265990378, 0.9864283824277854, 0.7488191678311884, 0.49402754415085326, 0.24452629784660915, 0.02144893359502535, -0.15688268044133327, -0.2762274516644902, -0.3274028038597528, -0.3069018855461777, -0.21710515856975124, -0.0660687917123289, 0.13309854318239397, 0.36323000205374906, 0.6043989699263832, 0.8354320566246553, 1.0355305979615663, 1.1858850490121895, 1.2711650453617809, 1.2807745102542032, 1.2097757374608928, 1.0594080586857635, 0.8371541686662662, 0.5563386482260051, 0.23527658316659664, -0.10397687907914303, -0.43719500329324557, -0.7397597176578453, -0.988529064573298, -1.163657344188257, -1.2502328595371262, -1.2396072500208308, -1.1303087820486137, -0.928458623610842, -0.6476424161317373, -0.30822720322891384, 0.06384657131096799, 0.4387294935449723, 0.78468040032674, 1.0703038977243768, 1.266855361904624, 1.3504505410464915, 1.3040181090626686, 1.1188463237405903, 0.7955987678042131, 0.34470765226916805, -0.2139057443432529, -0.8517879284446341, -1.53354398166841, -2.218972717776272, -2.865615319046908, -3.431553240362465, -3.8782684486075683, -4.173368882450579, -4.29298546902728, -4.22366427354204, -3.96360755838438, -3.523158912527286, -2.924477551667334, -2.2004020705784306, -1.3925605699946908, -0.5488381913218324, 0.27963924265644513, 1.0418091226073969, 1.69004240297837, 2.183349626275504, 2.4901982137996765, 2.5907389916849604, 2.478277073969915, 2.159871835438261, 1.6560095059969366, 0.9993558978203342, 0.23266146482586936, -0.594048329892671, -1.4268119369215488, -2.21137438217737, -2.896883359719761, -3.4393811480698226, -3.8048457327429794, -3.971563317654425, -3.9316592300193083, -3.6916720781716905, -3.2721229150181284, -2.7061023672738167, -2.0369690929905553, -1.3153173844809907, -0.5954254549723674], 'positive_zeros': ['1.38421152977048622487233128098012', '2.38255923385605402318527166480756', '3.74402905928937343598455154313974', '4.59567554010414089615932834470961', '5.71229561913815764276020377046093', '6.20477182964265407471520936866620', '7.53349174093131993534307493977290', '8.625724438192866710922166612432401', '8.971990389889952019940985124188891', '10.14691324225751912352947685926495'], 'prelabel': '2-1050-35.34-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.348871634076778, 'root_angle': 0.5018549993066368, 'root_number': '-0.0058276192082026679744352154773308018401154929182127597 + 0.9999830192830097189025767485072874060657650419732993748*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.2509274996533184', 'prec': 60}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.38421152977048622487233128098', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.38255923385605402318527166481', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.74402905928937343598455154314', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 28.61042775783118, 'bad_primes': [2, 3, 5, 7], 'central_character': '35.34', 'conductor': 1050, 'conductor_radical': 210, 'degree': 2, 'index': 41, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1050/3/h/a/349/6'], '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': '2-1050-35.34-c2-0-41', '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': '2-1050-35.34-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.348871634076778, 'root_angle': 0.2509274996533184, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.38421152977048622487233128098', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1754696576556392494235499714070', 'Lhash_array': ['1754696576556392494235499714070'], 'label': '2-1050-35.34-c2-0-41', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1050/3/h/a/349/6'}