-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1572957262168357809332611478747', 'a10': [24.475077880397496, -3.6233571209080884], 'a2': [-0.41421356237309503, -2.7979326519318133], 'a3': [0, 0], 'a4': [-7.656854249492381, 2.317883302073355], 'a5': [0, 8.747557902617437], 'a6': [0, 0], 'a7': [-13.800757035633916, 12.35067225876393], 'a8': [9.65685424949238, 20.463263816020675], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.868481321446641, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.41421356237309503, 2.7979326519318133]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [13.800757035633916, -12.35067225876393]]]], 'bad_primes': [2, 3, 7], 'central_character': '252.55', 'coefficient_field': 'CDF', 'conductor': 252, 'conductor_radical': 42, 'conjugate': '621031905020575833216902592138', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.41421356237309503, 2.7979326519318133]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -8.747557902617437], [-125.0, 0]], [[1.0, 0], [13.800757035633916, -12.35067225876393]], [[1.0, 0], [0, 0.3976859026395207], [-1331.0, 0]], [[1.0, 0], [0, 75.72633380195441], [-2197.0, 0]], [[1.0, 0], [0, 84.47389170457186], [-4913.0, 0]], [[1.0, 0], [-20.05362941737459, 0], [6859.0, 0]], [[1.0, 0], [0, 122.38189699348452], [-12167.0, 0]], [[1.0, 0], [-175.82337649086284, 0], [24389.0, 0]], [[1.0, 0], [128.09185013716296, 0], [29791.0, 0]], [[1.0, 0], [-253.1959594928933, 0], [50653.0, 0]], [[1.0, 0], [0, 81.47220438296932], [-68921.0, 0]], [[1.0, 0], [0, -69.13881315956112], [-79507.0, 0]], [[1.0, 0], [-147.92329057551538, 0], [103823.0, 0]], [[1.0, 0], [283.9209229614209, 0], [148877.0, 0]], [[1.0, 0], [632.9113660319216, 0], [205379.0, 0]], [[1.0, 0], [0, 3.259191383792647], [-226981.0, 0]], [[1.0, 0], [0, 551.5080548859878], [-300763.0, 0]], [[1.0, 0], [0, -486.2778686390581], [-357911.0, 0]], [[1.0, 0], [0, 165.94609608754118], [-389017.0, 0]], [[1.0, 0], [0, 279.0096001678454], [-493039.0, 0]], [[1.0, 0], [-622.1831331006177, 0], [571787.0, 0]], [[1.0, 0], [0, 696.8029448877925], [-704969.0, 0]], [[1.0, 0], [0, 1623.0140663164802], [-912673.0, 0]], [[1.0, 0], [0, 774.5009497625889], [-1030301.0, 0]], [[1.0, 0], [28.85840474143986, 0], [1092727.0, 0]], [[1.0, 0], [0, 51.91356189847729], [-1225043.0, 0]], [[1.0, 0], [-132.19682604467053, 0], [1295029.0, 0]], [[1.0, 0], [318.04877323527904, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 33, 'label': '2-252-28.27-c3-0-33', 'leading_term': '1.020160294072626005205940910055337904745500097468178237', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/252/4/b/d/55/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.07421875', 'prec': 34}, 'plot_values': [1.020160294072626, 1.133667941382328, 1.231852511347788, 1.3131648385173271, 1.3760544137153154, 1.4189732470354488, 1.4403865331054573, 1.4387905339199625, 1.412737792493898, 1.3608694814079856, 1.281954383239664, 1.1749337026124238, 1.0389706283877957, 0.8735033044473698, 0.6782996329881055, 0.45351212957813075, 0.19973087901936815, -0.08196748940457134, -0.389976973466787, -0.7221277149257035, -1.0756620336483826, -1.447223057922651, -1.8328578650386436, -2.22803680440416, -2.627690353847337, -3.0262644579531948, -3.417794817883252, -3.7960000511706147, -4.1543930272168526, -4.486409023256445, -4.785548653856719, -5.045532825679318, -5.260466282572279, -5.425005661054288, -5.534527401698939, -5.585290387488828, -5.574587835260565, -5.500882778706161, -5.363921475893231, -5.164819271412468, -4.9061138577858205, -4.591781520313797, -4.22721281348669, -3.819145195608357, -3.3755514217030673, -2.9054839332748617, -2.4188770472350427, -1.9263103860689965, -1.4387386495242918, -0.967194440492585, -0.5224723554113622, -0.1148038613941149, 0.24646646183996965, 0.5531920036037217, 0.7987108635161512, 0.9780966657249199, 1.088362400527514, 1.128607270380903, 1.1000980194369065, 1.0062781846074154, 0.8527010767748231, 0.6468850160065737, 0.3980923162512702, 0.1170366356780381, -0.18447354458493, -0.49394451278069784, -0.7986464014947967, -1.0860857601777536, -1.3444837697271235, -1.5632410212597094, -1.7333693084368287, -1.8478712343886714, -1.9020496526753026, -1.89373105174125, -1.8233899182258226, -1.694164798286809, -1.5117610979132, -1.284240463817159, -1.0217016720337297, -0.7358631001594064, -0.43956183062776494, -0.14618897755562518, 0.1309152970550592, 0.3790806400857078, 0.5869109294300289, 0.7448453452427133, 0.8456479336776204, 0.8847996795320856, 0.8607706673414123, 0.7751547680387291, 0.6326552721988632, 0.4409167641734421, 0.2102059958972938, -0.04704777322248519, -0.3168349360286012, -0.5842451343044895, -0.8342131375893204, -1.0522950650626384, -1.2254358606974656, -1.3426876729869264, -1.3958395963370511, -1.3799221738815308, -1.2935551020089584, -1.1391135599716806, -0.9226972429179231, -0.6538961251051938, -0.3453577497502092, -0.01217188739815796, 0.3289008672391646, 0.6603201896724579, 0.9647321626321215, 1.2259595945001511, 1.4299619703622206, 1.5657096673852617, 1.6259193155496396, 1.6076025407412353, 1.5123886528356605, 1.346592822167265, 1.1210144391475183, 0.850465037173651, 0.5530406176117951, 0.24916859967052052, -0.03952596321046567, -0.29147768893006565, -0.4864945862162403, -0.6070545702380117, -0.6395085873400858, -0.5751158857375501, -0.41084310480267505, -0.14986926859910424, 0.1982469348303439, 0.6177636730289053, 1.0873224704716902, 1.580869660840863, 2.068896421128671, 2.5199408107851187, 2.9022774122630532, 3.185705892858521, 3.34334009558767, 3.3532949076496523, 3.200169652877561, 2.876234284027386, 2.382238029901083, 1.7277788365720663, 0.9311950401046003, 0.018967020508412768, -0.9753553352278987, -2.012655308659271, -3.0501114383485652, -4.043324847863551, -4.948598962982896, -5.725246176379799, -6.337790503791906, -6.757937431319978, -6.966192118902712, -6.953024559692928, -6.7195043801274945, -6.2773574364072084, -5.648429572475706, -4.863577912219853, -3.9610447442971393, -2.9844012505435216, -1.9801759437467248, -0.9953038571250993, -0.07454575776753239, 0.7419691065473523, 1.420928473322529, 1.9376171414882912, 2.2771813942936943, 2.4352982411065462, 2.4182062732230003, 2.242094615860942, 1.931887007035774, 1.5194968199368826, 1.0416632949570452, 0.5375070111585373, 0.04596174394379703, -0.3967511025547294, -0.7594411181565284, -1.017908942565931, -1.1564191424062387, -1.1685891867579945, -1.057636550441161, -0.8359690575512047, -0.524148110773354, -0.14929739398670416, 0.25693200471285516, 0.6606980560954133, 1.0284423843137092, 1.3293293034366602, 1.5374774776339928, 1.6338264004064822, 1.607505217032526, 1.4566064054498657, 1.1883091066345153, 0.8183435096053555, 0.3698353340692117, -0.12838533330037097, -0.6438871384086887, -1.1429980591623552, -1.5932494532021217, -1.9657225977044523, -2.2371232566440074, -2.391429397000824, -2.420988567626536, -2.3269824530590295, -2.119223753984173, -1.81530130262025, -1.4391393686159721, -1.0190826050626312, -0.5856554572253257, -0.16917109770312763, 0.2026221481828288, 0.5066705817242698, 0.7263511362165637, 0.8526735888333872, 0.8848504261421274, 0.8301857097769242, 0.7032888143957938, 0.5246738061925367, 0.31885611713054385, 0.11210088798913308, -0.06999170106921805, -0.20486236569869518, -0.2751279066328929, -0.27028992378935535, -0.18786321468841216, -0.03381528419026167, 0.17773633043142084, 0.42556119956061295, 0.6830179853407965, 0.9202939179278204, 1.1070057087046534, 1.2149504248157315, 1.2207760015573526, 1.1083408210245227, 0.8705506978355062, 0.510498690212538, 0.04178587935891139, -0.5120342485611392, -1.1188738923773451, -1.7403051606619375, -2.334376509136388, -2.8588404448425235, -3.2745401320763614, -3.548680635963346, -3.6577105896210167, -3.5895627660835228, -3.3450462272100836, -2.93824545058282, -2.395858522163746, -1.7554912527953612, -1.063010205782514, -0.3691380645703929, 0.2744572717402028, 0.8192789775257321, 1.2239956831418426], 'positive_zeros': ['1.24084448970809512818125974726791', '3.80765250014432627294164915545761', '4.70502370528893507951738886304537', '6.05010910718309676323554715708125', '6.88915496543217349459998875721135', '7.944062025704278679215674814918606', '9.044074389801328591620605665531136', '9.608304938169377126183280429580761', '10.76318480695355258497993865975998', '12.17823230410806252477840970595466'], 'prelabel': '2-252-28.27-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8559669761872497, 'root_angle': 0.6740647689335005, 'root_number': '-0.5199911581848529607742101042220525028798003960506122060 + 0.8541716428268824388205776082201582437616345230677967219*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3370323844667503', 'prec': 60}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.24084448970809512818125974727', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.80765250014432627294164915546', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.70502370528893507951738886305', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 14.868481321446641, 'bad_primes': [2, 3, 7], 'central_character': '28.27', 'conductor': 252, 'conductor_radical': 42, 'degree': 2, 'index': 33, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/252/4/b/d/55/2'], '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': '2-252-28.27-c3-0-33', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-252-28.27-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8559669761872497, 'root_angle': 0.33703238446675027, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.24084448970809512818125974727', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1572957262168357809332611478747', 'Lhash_array': ['1572957262168357809332611478747'], 'label': '2-252-28.27-c3-0-33', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/252/4/b/d/55/2'}