-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '775261889865657787527442392995', 'a10': [1.881680151048764, 1.2080065435042564], 'a2': [-0.35836794954530027, -0.9335804264972017], 'a3': [-0.5892237834060818, -0.9073250599132978], 'a4': [-0.7431448254773942, 0.6691306063588582], 'a5': [-1.8021051215275505, 1.323788929914498], 'a6': [-0.635901997322894, 0.8752440123067399], 'a7': [-2.6442298965588074, -0.0897120624252952], 'a8': [0.8910065241883679, 0.4539904997395468], 'a9': [0.7441558318121084, -1.6714013637652765], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.148480955638592, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.35836794954530027, 0.9335804264972017]]], [5, [[1.0, 0], [1.8021051215275505, -1.323788929914498]]], [7, [[1.0, 0], [2.6442298965588074, 0.0897120624252952]]], [11, [[1.0, 0], [-3.168260795092272, -0.9808789600563794]]]], 'bad_primes': [2, 5, 7, 11], 'central_character': '770.157', 'coefficient_field': 'CDF', 'conductor': 770, 'conductor_radical': 770, 'conjugate': '1222157103945459228283103788463', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.35836794954530027, 0.9335804264972017]], [[1.0, 0], [0.5892237834060818, 0.9073250599132978], [-1.2202099292274007, 2.7406363729278027]], [[1.0, 0], [1.8021051215275505, -1.323788929914498]], [[1.0, 0], [2.6442298965588074, 0.0897120624252952]], [[1.0, 0], [-3.168260795092272, -0.9808789600563794]], [[1.0, 0], [3.583106487277973, 0.567508315610737], [12.363734711836996, 4.017220926874317]], [[1.0, 0], [1.212352748934285, -3.1582868888001756], [-12.633462033115702, -11.37522030810059]], [[1.0, 0], [2.2001030168529203, -2.4434619444303163], [-1.986040802085416, -18.895916011997194]], [[1.0, 0], [-8.067949916971996, -2.16180066482739], [19.91858428704209, 11.5]], [[1.0, 0], [-2.7235479593695677, -0.8849343756341119], [23.461492836873475, 17.04577231648172]], [[1.0, 0], [-8.70218475710541, 0.9146364740361905], [30.322575622747976, -6.445262415350539]], [[1.0, 0], [-8.759663006841956, -5.688591670494503], [15.049255793804608, 33.80118193277623]], [[1.0, 0], [-4.043750362761693, 1.3138941395102341], [33.16969676937284, -24.099195343991397]], [[1.0, 0], [-0.10181140901833524, 0.10181140901833524], [0, -43.0]], [[1.0, 0], [0.020520662702965847, 0.39155756995805757], [-46.74252908230885, 4.912837773579713]], [[1.0, 0], [4.116757607634482, 3.3336845791964795], [11.019319613341246, 51.8418228388917]], [[1.0, 0], [7.547930055359567, 8.382825580537737], [-6.167179332791555, 58.67679182672813]], [[1.0, 0], [-13.468751143160372, -1.4156227888855764], [59.66700364476215, 12.682613139883319]], [[1.0, 0], [12.20368046938918, -3.269966326460295], [58.023702053557386, -33.5]], [[1.0, 0], [1.5652480974459728, 1.1372193096739784], [21.940206600621266, 67.52501265695591]], [[1.0, 0], [0.45084718912912614, -8.602676841050908], [-72.60009836188395, -7.630577818538703]], [[1.0, 0], [6.721591698940894, -15.096942134990563], [-52.861317902349796, -58.70844121271414]], [[1.0, 0], [-0.4252516305153322, -2.6849331262842107], [-78.93769085249775, 25.648410533120636]], [[1.0, 0], [-1.6406531683363696, -2.8416946451574465], [-44.5, 77.07626093681505]], [[1.0, 0], [-0.4982415155859052, 3.145773123704498], [-92.2524820806299, -29.974648454369902]], [[1.0, 0], [-4.065508378475587, 0.42730214908587694], [98.79290767411437, -20.999080772593693]], [[1.0, 0], [-12.436854066818817, -8.07658746648148], [41.89387423680742, 94.09518213718789]], [[1.0, 0], [-1.8673716584659137, 0.09786480171628821], [106.41384280440525, -11.18454556963892]], [[1.0, 0], [-7.237534544534123, -4.178592517555991], [54.5, 94.39676901250381]], [[1.0, 0], [-12.373313811126781, -6.304518281349997], [66.41973350904946, 91.41892036436906]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 9, 'label': '2-770-385.157-c1-0-9', '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/770/2/bv/a/157/9', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.7709466621035416, 0.7045271161096242, 0.599244597413659, 0.44744313500750227, 0.23984598846650887, -0.03260867774332772, -0.3767773419993758, -0.7953941232834391, -1.2853822535812334, -1.8365263761174477, -2.430650191412238, -3.0414585237335707, -3.635195136338224, -4.172225646777039, -4.609576788015971, -4.904354332650482, -5.01783327478345, -4.9198812298126, -4.593259050663708, -4.03726274100169, -3.2701482720145485, -2.3298319327730836, -1.2724915276023592, -0.16890524607878818, 0.901360441365894, 1.8574940050938056, 2.6259911588466607, 3.1492455932117736, 3.393060173148138, 3.3519549525970387, 3.051309051966054, 2.5457025135714355, 1.9132964314389962, 1.2466518167651794, 0.6409630452493672, 0.18117914836355806, -0.07018651992034856, -0.08267778874126151, 0.13671843081515683, 0.5435791002790741, 1.061845534389456, 1.5949132044349315, 2.0405915560707295, 2.3077470641987996, 2.331974383180466, 2.0875874267837933, 1.593639220068464, 0.9125412735721912, 0.1410496131906126, -0.6052699821401493, -1.2117247292701663, -1.5850214048757802, -1.6709371616633673, -1.4657013493720814, -1.0185934814465998, -0.42475296574374094, 0.19100196541964926, 0.6967617678412361, 0.9785179987179211, 0.9628258472489252, 0.6325576612997731, 0.03225523229356854, -0.7385387103029172, -1.5432521503295484, -2.2344859770307703, -2.683491044096668, -2.8069855917787874, -2.5855809278274053, -2.069514397960022, -1.3698352291708, -0.6361995513658798, -0.025394278587280026, 0.3330255409320794, 0.36658456155153446, 0.07836726203756723, -0.4506158155856321, -1.0766137205155017, -1.6234567651511314, -1.922029208018348, -1.8504536728450902, -1.3658479073630725, -0.5198541794496367, 0.5466413905337985, 1.6296966384601566, 2.5046993190892453, 2.9762080915769693, 2.9242344263247144, 2.3360925710283205, 1.3156260230923897, 0.06637828406558852, -1.1488718967611502, -2.064155251541577, -2.469807812305428, -2.2618368647824836, -1.4692448324740643, -0.2519707368457999, 1.1313447661807539, 2.3795028197686507, 3.2166194045859426, 3.4562690803383815, 3.046711002193345, 2.085931463276867, 0.8020257547584781, -0.497430786384706, -1.4958346853326825, -1.9415604703970397, -1.7079674523684196, -0.8248141495806683, 0.5268992565257397, 2.0559036350820112, 3.427949674056782, 4.34335359163439, 4.606064984248083, 4.167491372655456, 3.134519277316987, 1.7401018798148018, 0.28418598108804105, -0.9397987661383502, -1.714129323989347, -1.9442418688212608, -1.6729398574359615, -1.058779540226789, -0.3256239776856244, 0.3020270766082777, 0.6597556121207026, 0.6833025521464355, 0.4174676248216867, -0.007589695142133191, -0.42456930504889745, -0.6865367370937677, -0.7157865167727568, -0.5287540761012752, -0.228933390299461, 0.030394248267799236, 0.10227310476257599, -0.09666321394812098, -0.5465766715006146, -1.1165918475033938, -1.593616399839799, -1.7414472598971957, -1.373915814439806, -0.42038907160058475, 1.037162141842877, 2.7690283572366545, 4.4462463056430135, 5.7213845235162255, 6.319981156788938, 6.116588516663718, 5.172547524970863, 3.7227819415930283, 2.1133611315929026, 0.7061980725752284, -0.22235420258177505, -0.5593848755613056, -0.38603734809297624, 0.049673870206600905, 0.4114548660330816, 0.38268322735864707, -0.22797702934625041, -1.4154726788495664, -2.964759950101868, -4.501242369842697, -5.5927645730029525, -5.874736763148488, -5.1620188154633455, -3.513905735907829, -1.2314429839896925, 1.214227481229003, 3.303427382765776, 4.605218075897352, 4.89099857466493, 4.191528780173565, 2.7809194615295656, 1.0926745709238679, -0.40696819327117356, -1.3505441884612037, -1.5667309262221498, -1.1153625671557164, -0.2512666099208243, 0.6698790252931369, 1.3126943184348232, 1.4713339249747805, 1.1322991320367393, 0.47166283481741417, -0.21106407206533487, -0.5996444548010749, -0.47255929605505387, 0.21797907111530843, 1.3257219327847125, 2.5555096958507573, 3.5587428971663, 4.047266875665242, 3.8874851950601776, 3.143019608137771, 2.0514171586133156, 0.9425906563904887, 0.12644186164668883, -0.21224330397381505, -0.07572499734675862, 0.34941693801960144, 0.7592512370918322, 0.8412884505395485, 0.3880898008603277, -0.62340778948835, -2.0146535703140906, -3.457152751478588, -4.5762890923635275, -5.072469823076257, -4.818503509397982, -3.899993716185882, -2.5849722933230592, -1.2333719752615946, -0.17778926132569478, 0.3830364542380699, 0.44113897359382215, 0.16736290082400224, -0.16415849371318075, -0.2868902807640966, -0.0470374108822098, 0.5362904747616436, 1.2788444522722635, 1.9048287118750504, 2.159340501448361, 1.9171369229559354, 1.2450358130709978, 0.3910715104658195, -0.2998920568187639, -0.5164085934143153, -0.10976909215717061, 0.8271505573036059, 1.9656235747817805, 2.8365695726173916, 2.988397474652677, 2.1551252800225975, 0.37531341162126414, -1.9842367974404451, -4.315564592970533, -5.9453311987116955, -6.3453883027832925, -5.309571698284655, -3.0364746053025864, -0.08717894130529662, 2.772366308188057, 4.796115921285559, 5.478583659170253, 4.700685327128206, 2.754401857291656, 0.23988854961130104, -2.1292844828177695, -3.7473498005609134, -4.2913630491228885, -3.794917477728516, -2.6014166346868333, -1.219384958960124, -0.13490369580782913, 0.351427615601166, 0.20748792161768814], 'positive_zeros': ['0.61157379622277516063531361923996', '2.89423424359532708741762929001794', '4.45142303175115608391098608525578', '4.68751506891189212142512459268720', '6.02272549945604031015198568255841', '6.96005320310388604105061898244797', '7.63067959206218330261679038889585', '8.881404151061563577360047201802065', '9.271817738048828797666818558501092', '10.18778656266788447777026235463985'], 'prelabel': '2-770-385.157-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4796130657097675, 'root_angle': 0.0790423264142241, 'root_number': '0.9693269897378389 + 0.24577466705455925*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0395211632071', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.61157379622277516063531361924', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.89423424359532708741762929002', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.45142303175115608391098608526', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 6.148480955638592, 'bad_primes': [2, 5, 7, 11], 'central_character': '385.157', 'conductor': 770, 'conductor_radical': 770, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/770/2/bv/a/157/9'], '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': '2-770-385.157-c1-0-9', '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': '2-770-385.157-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4796130657097675, 'root_angle': 0.03952116320711205, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.61157379622277516063531361924', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '775261889865657787527442392995', 'Lhash_array': ['775261889865657787527442392995'], 'label': '2-770-385.157-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/770/2/bv/a/157/9'}