-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2180276902107514828749933972810', 'a10': [-0.3584407085710257, 0.6208375187460057], 'a2': [-0.11878234922776941, -0.6736481776669303], 'a3': [0.0, 0.0], 'a4': [1.4396926207859084, -0.5240052604587699], 'a5': [-0.8028226358791068, -0.6736481776669303], 'a6': [0.0, 0.0], 'a7': [0.11334079845283873, 0.04125267696479814], 'a8': [-1.2080455471101075, -2.092396265452048], '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': '1175436444440452276661730326694', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.11878234922776941, 0.6736481776669303], [-1.8793852415718169, 0.6840402866513374]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.8028226358791068, 0.6736481776669303], [0.8682408883346517, 4.924038765061041]], [[1.0, 0], [-0.11334079845283873, -0.04125267696479814], [5.362311101832846, 4.499513267805775]], [[1.0, 0], [-4.162468806146731, 3.4927260400246554], [1.9101299543362338, -10.832885283134289]], [[1.0, 0], [0.7942629360951136, -4.5044889494724005], [-12.216004070216808, -4.446261863233693]], [[1.0, 0], [-2.389165321613056, 4.138155724715451], [-8.5, -14.722431864335457]], [[1.0, 0], [-0.29426293609511356, -0.5096783561011304], [-9.5, 16.454482671904334]], [[1.0, 0], [7.325802954923615, -2.666374217691586], [17.619022191736494, -14.784115022790404]], [[1.0, 0], [0.8803523081420781, 4.992726040024656], [-27.251086002791343, 9.918584156444393]], [[1.0, 0], [-8.230551990167498, 2.9956759360014225], [23.747377736688318, -19.92641590028272]], [[1.0, 0], [-1.0923962654520476, 1.8920858337614448], [-18.5, -32.04293994002423]], [[1.0, 0], [1.3125009919802373, -7.4435630140477285], [-38.527397452222246, -14.022825876352417]], [[1.0, 0], [1.0, -0.83909963117728], [7.466871639678005, -42.34673337952495]], [[1.0, 0], [-2.2703829723852866, -0.8263518223330697], [36.00408882659197, 30.211017655267348]], [[1.0, 0], [-3.046279835657235, 0], [53.0, 0]], [[1.0, 0], [-0.03362949038190401, -0.028218492976135545], [10.24524248234889, 58.10365742772028]], [[1.0, 0], [-9.596266658713867, -3.4927554238530334], [46.728711030257664, 39.2100441908789]], [[1.0, 0], [0.32294825561954565, -1.8315305707723821], [-62.95940559265586, -22.915349602819806]], [[1.0, 0], [3.2551907253974948, -5.638155724715451], [-35.5, -61.48780366869514]], [[1.0, 0], [6.117211191714659, 10.595320584678749], [-36.5, 63.21985447626402]], [[1.0, 0], [-0.12195893190172223, -0.6916634732342316], [-74.23571704208676, 27.01959132272783]], [[1.0, 0], [1.1767442334785592, 6.67364817766693], [-77.9944875252304, 28.387671896030504]], [[1.0, 0], [-3.4278246198395816, -5.937166400997627], [-44.5, 77.07626093681505]], [[1.0, 0], [6.915344521071593, -5.802663037094998], [16.843873233692243, -95.52635204218419]], [[1.0, 0], [-12.208589043019858, -4.4435630140477285], [77.37048875501678, 64.92154857834048]], [[1.0, 0], [-6.949492800549534, -5.831316845810277], [17.885762299693827, 101.43519856025743]], [[1.0, 0], [11.386463821116486, 0], [107.0, 0]], [[1.0, 0], [-2.898985601099069, 0], [109.0, 0]], [[1.0, 0], [-8.870892963692766, -7.4435630140477285], [19.62224407636313, 111.28327609037952]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 25, 'label': '2-3e6-27.13-c1-0-25', '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/q/82/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.6597694463146753, 1.8213999781694572, 1.9766949659545154, 2.1212164452324695, 2.2459405936307943, 2.3380610874492893, 2.382382610149559, 2.363067769045114, 2.2655724566752102, 2.0786514949194563, 1.7963134656854067, 1.4195682908127085, 0.9577708113224485, 0.4293403573538109, -0.13835596361576954, -0.7101226948858502, -1.2451394363084745, -1.700209543338233, -2.0338712809337594, -2.211036598792522, -2.2076839746998362, -2.0150300879153105, -1.642563730171863, -1.1193633507629075, -0.4932476649281635, 0.1724743537312332, 0.8045974713970792, 1.3275680224387227, 1.6722616258248653, 1.784984058499926, 1.6355093498202424, 1.2229389418038645, 0.5783137549637974, -0.23675763885639603, -1.135700914740319, -2.0164586247712686, -2.773884246317422, -3.313530871017318, -3.5649421411152535, -3.492433999392327, -3.1015463157846326, -2.4398505172043956, -1.5915760496108984, -0.6664646014886806, 0.215766447126695, 0.9431364891898812, 1.4285418641289207, 1.6234682202655193, 1.525801401056283, 1.1801147883255017, 0.6700238406311306, 0.10358474070005065, -0.40596702094197656, -0.7608438712436587, -0.8969450860898346, -0.7961684027073676, -0.4901639397627724, -0.05438664441651989, 0.4068732856453525, 0.7819744922539512, 0.9759472313059743, 0.9322968603806076, 0.6479514283653175, 0.17779390671141462, -0.3728876464158849, -0.8673128120309938, -1.164341087476059, -1.1487219150386605, -0.758318648084306, -0.002333296998136484, 1.033994124163892, 2.2002187184659405, 3.3059244386922035, 4.156092309239488, 4.589882944658385, 4.514922207709641, 3.929604875096709, 2.928001317769349, 1.6853334758008447, 0.4260303854188706, -0.6197639803981468, -1.2625424442418454, -1.3928830663270884, -1.0052481867827143, -0.200399048921746, 0.8348595191747832, 1.866922102588523, 2.6655429412067018, 3.0540681962076497, 2.948458518629399, 2.3759480687947754, 1.4685200368939781, 0.4320228134738277, -0.5025498794708358, -1.1346756382558112, -1.3438517788726336, -1.12107132341779, -0.574082373653151, 0.09574387991508863, 0.6403719428334358, 0.825407285844306, 0.489646772100541, -0.41057246257992414, -1.7835188075713984, -3.4159753075506916, -5.016650958399318, -6.279595916435018, -6.952978682438104, -6.896883662994303, -6.11607144977401, -4.759468322726137, -3.086161144036091, -1.405912118700593, -0.008594686911063576, 0.9001843900649716, 1.2414851294905054, 1.0731896415732318, 0.5658716533666439, -0.04882804385770141, -0.5433984432200519, -0.7557945554718939, -0.6305851903729945, -0.22908609617061387, 0.2938649809814292, 0.7396340740213057, 0.9277589160806904, 0.7523831445923954, 0.21680869046693932, -0.5641022578299213, -1.3948232988402305, -2.054861289666698, -2.363336463449084, -2.2335249030228783, -1.7008659047792527, -0.9152590514168638, -0.09873585858468842, 0.5201000753365965, 0.7761282722433278, 0.6214215655988885, 0.1457372112592592, -0.44395992394405925, -0.8808719518977924, -0.9174218542768943, -0.40360581071525015, 0.6586248065119094, 2.1022925426181316, 3.6296748188841965, 4.886397226715471, 5.555838508784882, 5.447593625812884, 4.554399112050857, 3.060097217804214, 1.2947875815504073, -0.3515092957520733, -1.532991549169213, -2.04053465371624, -1.8556830088610263, -1.1500538446292121, -0.22974428766581942, 0.5594389908033643, 0.9381929331100377, 0.7797262558976341, 0.1493981258461799, -0.7146954045094894, -1.4752483788466846, -1.801911318397247, -1.4782203778183616, -0.47646393950260413, 1.0233047693528097, 2.677392844664522, 4.073898339389655, 4.8516818652625435, 4.807327317326305, 3.9574727343595875, 2.536875845256466, 0.9318231495554328, -0.431814408759382, -1.21250439054497, -1.2515776096448676, -0.6164426821116251, 0.4246442043642599, 1.4883997781646119, 2.1963683252546593, 2.29171356581199, 1.7168501629464692, 0.6281301303603948, -0.656389851114182, -1.7590048139230852, -2.3615166994244015, -2.3035857653659435, -1.629338081518903, -0.5681709734776722, 0.5429530199886516, 1.3695594869942045, 1.68567313676445, 1.4411850206359875, 0.7691922638951213, -0.0678094203933552, -0.7734540301670305, -1.1214080977126024, -1.031739289136687, -0.593563998393444, -0.026547845630255997, 0.4047442904811239, 0.49294596348695857, 0.1696077212282821, -0.46353027144419867, -1.1662653223449337, -1.644871828954426, -1.6610481296537272, -1.126093413886755, -0.14546957403288968, 1.0046399911300716, 1.9635907870291955, 2.407570079324888, 2.164510627764789, 1.2816920955397653, 0.020026445855620134, -1.226308561064294, -2.0601129342227966, -2.218051866651377, -1.6668859270176188, -0.6240080185170497, 0.5078464137986982, 1.2725399538264968, 1.3162712669678098, 0.514612717619752, -0.9734839685816346, -2.7453710164866614, -4.277310680563882, -5.0907289552903086, -4.90717166298421, -3.7398886074240036, -1.8907670412402906, 0.146812852601846, 1.846578037179204, 2.8156750506008947, 2.9122574570063238, 2.274806066869638, 1.2544247255689662, 0.27535741929989993, -0.3257635932471861, -0.4239303287461817, -0.1481336500347694, 0.17353233591023498, 0.14651886575463263, -0.5278079328821544, -1.919672421020672, -3.818094689926553, -5.779727572692797, -7.2650112253169485, -7.815639463363058, -7.211638595426124, -5.552500484111903, -3.2328386038351082, -0.8198248703111946, 1.1258679133392362], 'positive_zeros': ['1.71993521062899748954086536967136', '3.09258351734180223961451967149596', '4.09059409237896830166057466752294', '5.46792663807120536977249553499447', '6.39853653814362893390645565890938', '7.13950886958184406815143406961485', '7.915950702661919477052707389531826', '8.625318137016238253904861917678494', '9.921567360978443820498486200008571', '10.52558525683564270878820393589655'], 'prelabel': '2-3e6-27.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.5370370370370371, 'root_number': '-0.1160929141252304 + 0.993238357741943*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.268518518519', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.71993521062899748954086536967', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.09258351734180223961451967150', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.09059409237896830166057466752', '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': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/e/q/82/1'], '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': '2-3e6-27.13-c1-0-25', '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': 0.26851851851851855, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.71993521062899748954086536967', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2180276902107514828749933972810', 'Lhash_array': ['2180276902107514828749933972810'], 'label': '2-3e6-27.13-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/e/q/82/1'}