-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '772881855642653732668040354424', 'a10': [0, 0], 'a2': [0, 0.536546909413681], 'a3': [0, -1.0], 'a4': [1.7121174139986273, 0], 'a5': [0, 0], 'a6': [0.536546909413681, 0], 'a7': [0, 2.5731796224518124], 'a8': [0, 1.991725125861669], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.97195037899008, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 1.0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '1875.1249', 'coefficient_field': 'CDF', 'conductor': 1875, 'conductor_radical': 15, 'conjugate': '1900031058053883483087248716186', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -0.536546909413681], [-2.0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -2.5731796224518124], [-7.0, 0]], [[1.0, 0], [5.1436884284657545, 0], [11.0, 0]], [[1.0, 0], [0, -1.4749232162847457], [-13.0, 0]], [[1.0, 0], [0, -0.6878593892163742], [-17.0, 0]], [[1.0, 0], [-8.092652348466608, 0], [19.0, 0]], [[1.0, 0], [0, 0.3727499645599928], [-23.0, 0]], [[1.0, 0], [0.03567227832395454, 0], [29.0, 0]], [[1.0, 0], [4.489021726677728, 0], [31.0, 0]], [[1.0, 0], [0, -1.9093523925062474], [-37.0, 0]], [[1.0, 0], [5.169246578365193, 0], [41.0, 0]], [[1.0, 0], [0, -11.450583934114325], [-43.0, 0]], [[1.0, 0], [0, -8.521135809066307], [-47.0, 0]], [[1.0, 0], [0, -9.123174219457084], [-53.0, 0]], [[1.0, 0], [-0.1761898535536761, 0], [59.0, 0]], [[1.0, 0], [6.411522883540633, 0], [61.0, 0]], [[1.0, 0], [0, -0.0834377243116968], [-67.0, 0]], [[1.0, 0], [-12.157829673545148, 0], [71.0, 0]], [[1.0, 0], [0, -12.051806903065241], [-73.0, 0]], [[1.0, 0], [4.9568673767365725, 0], [79.0, 0]], [[1.0, 0], [0, 9.3632236247039], [-83.0, 0]], [[1.0, 0], [-0.012318982494175458, 0], [89.0, 0]], [[1.0, 0], [0, 7.620412160289999], [-97.0, 0]], [[1.0, 0], [-8.275180094204398, 0], [101.0, 0]], [[1.0, 0], [0, 10.38601852669547], [-103.0, 0]], [[1.0, 0], [0, 12.273743055273373], [-107.0, 0]], [[1.0, 0], [-4.229017601480484, 0], [109.0, 0]], [[1.0, 0], [0, -18.368655719024492], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 22, 'label': '2-1875-5.4-c1-0-22', 'leading_term': '1.757020532702276400310621851501635959379289151226231051', '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/1875/2/b/h/1249/10', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.7570205327022763, 1.6270220643316462, 1.4891969650782377, 1.3433175399962085, 1.1890879113850992, 1.0262292983348218, 0.854566602716563, 0.6741109363558906, 0.4851335279390749, 0.2882274750645935, 0.08435485870334941, -0.12512232694834052, -0.3384282253624217, -0.5533763846019906, -0.7673900680893698, -0.9775391280383361, -1.180592695065534, -1.373086672340466, -1.5514047298558133, -1.711871162075951, -1.8508536019591477, -1.9648731881176977, -2.0507193788708733, -2.1055662208452066, -2.1270865365387808, -2.113560221307529, -2.0639726609415776, -1.9780992194606133, -1.8565718226017238, -1.700923890844269, -1.5136102664249231, -1.2979993350939325, -1.0583352618670536, -0.7996691298334403, -0.5277587736201222, -0.2489382081919561, 0.03004126419099909, 0.30219497088316943, 0.5605093090774352, 0.7981610685102244, 1.008744969958987, 1.1865018939340335, 1.326539632677151, 1.4250376213422635, 1.4794270307904531, 1.4885378654323687, 1.4527053243156978, 1.3738286582238128, 1.2553770811372593, 1.1023389463724713, 0.9211123351511669, 0.7193373714014948, 0.5056728994641353, 0.2895225562067251, 0.08071764049618334, -0.11083357144443165, -0.27551840221807034, -0.40440090022586456, -0.48959693259975534, -0.5246279363796149, -0.5047378896132783, -0.4271585762149881, -0.29130939918815785, -0.0989198442005549, 0.14593482254809284, 0.4368909847466387, 0.7654500658739977, 1.1212268227691653, 1.4922873919753608, 1.8655678026933329, 2.2273596766879358, 2.5638461723868873, 2.8616680845860465, 3.1084975588935637, 3.2935952778327913, 3.4083263513233586, 3.446610589290165, 3.4052843959352135, 3.284354202211012, 3.0871250912906234, 2.8201929638901175, 2.4932940767267624, 2.119011860919416, 1.7123473394579891, 1.290165933973963, 0.8705396807379397, 0.47200955704227, 0.11279745256966843, -0.18999897042395492, -0.42119293775141964, -0.5682403569555469, -0.6218812296930805, -0.5766577603455998, -0.43128051439967924, -0.18881982178438403, 0.14329317467370747, 0.5534631379119479, 1.0263231139352131, 1.5433120101631381, 2.083416682181343, 2.6240496752829348, 3.142026035316418, 3.6145964271903925, 4.02048945371491, 4.340913853249572, 4.560471379608103, 4.667933730709074, 4.656841872799356, 4.525893359238776, 4.279092497870115, 3.9256490943042683, 3.479623504147265, 2.959328298651268, 2.3865093639948496, 1.7853410682049256, 1.1812806037732813, 0.5998351530232059, 0.06530160821372238, -0.4004582023618036, -0.7791437546673312, -1.056983696542945, -1.2254919103580446, -1.2819677431445873, -1.229708389968753, -1.0779154935567377, -0.8412934876186433, -0.5393532854276857, -0.1954507592242033, 0.16439578859359574, 0.5128521254974141, 0.8227113623998412, 1.068359954222654, 1.227189320813254, 1.2808769950269325, 1.2164663613262598, 1.0271831901312922, 0.7129399159631344, 0.2804943534660772, -0.2567524901568287, -0.8793155990019021, -1.5625187237434184, -2.27767867839377, -2.9935223229800254, -3.677763521237733, -4.2987572326663495, -4.827142180079558, -5.2373826591592, -5.509124191120819, -5.628286744701252, -5.587832764394176, -5.388164562173762, -5.03712584435257, -4.549604145646892, -3.9467534883020314, -3.254878371846727, -2.504039938409486, -1.7264616498681264, -0.9548240218273825, -0.2205450827983414, 0.44785525113858804, 1.026212966058558, 1.495915891253861, 1.8447688221501815, 2.067478211640227, 2.1657293796693224, 2.1478536359540774, 2.0281075683808285, 1.8256104947358724, 1.563007220465966, 1.26494043435046, 0.9564291715594141, 0.6612559408976242, 0.40046486876253706, 0.19106647174734018, 0.045031759816741644, -0.03135997975669354, -0.03777806948737363, 0.020313990118126974, 0.13221326030900912, 0.2828947918089676, 0.4542296485633815, 0.6264207433656458, 0.779558218878502, 0.8951869536155568, 0.9577766724539294, 0.9559903701419709, 0.8836591087985498, 0.7403900425896559, 0.5317586251683379, 0.2690638570237331, -0.03134467093928783, -0.3491292634015779, -0.6613495535743614, -0.9440803435683655, -1.1741530303525913, -1.3309005693354299, -1.3977826952428916, -1.3637732994099627, -1.2244053098242813, -0.9823894236876124, -0.6477503556884594, -0.23745617810939823, 0.2254492294224953, 0.7131659316060758, 1.194832677784228, 1.6384913349219454, 2.013194124846018, 2.291113335118067, 2.4495090244176505, 2.4724159232070324, 2.3519261107477076, 2.088968330102782, 1.6935165480018122, 1.184197587078335, 0.5873079334813096, -0.06470954272059119, -0.735240015529328, -1.385800269101116, -1.978523862040468, -2.4786643142481037, -2.8569475425390083, -3.0916110369961363, -3.169984845916306, -3.0894973800916943, -2.8580256701118927, -2.493552681639704, -2.023140783599509, -1.4812773311853715, -0.9076923282310333, -0.34478615591022677, 0.16516537158510677, 0.5828430570640064, 0.8745620679429177, 1.0146112556572136, 0.9870900764951409, 0.7871110118867763, 0.42127695944141097, -0.09260838839338724, -0.7265869218563259, -1.4442866615303935, -2.2032451478400685, -2.9576626818512253, -3.661400898055553, -4.27102314181397, -4.748668173855191, -5.064558391400315, -5.198967563608012, -5.143509530100171, -4.901655974883249, -4.488445059716358, -3.9293996208247215, -3.258729747978596, -2.5169458193575145, -1.748050695713925, -0.9965105919026968, -0.30422076732307446, 0.292316762545752], 'positive_zeros': ['0.60969628027115919443968825257124', '2.10302258569434093205369963044714', '3.18794621301568533676371771586095', '3.71653884986924876357979866903128', '5.11808470565630478282608610966523', '5.54290994423802529083328168022698', '6.86313736957999975190972906587296', '7.47327163144598043087873613796505', '8.059231639996512188732327888216577', '9.276410952393817326859317262963024'], 'prelabel': '2-1875-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8693604612377586, 'root_angle': -0.5, 'root_number': '0.e-55 - 1.0000000000000000000000000000000000000000000000000000000*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25', 'prec': 17}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.60969628027115919443968825257', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.10302258569434093205369963045', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.18794621301568533676371771586', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 14.97195037899008, 'bad_primes': [3, 5], 'central_character': '5.4', 'conductor': 1875, 'conductor_radical': 15, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1875/2/b/h/1249/10'], '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': '2-1875-5.4-c1-0-22', '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': '2-1875-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8693604612377586, 'root_angle': -0.25, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.60969628027115919443968825257', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '772881855642653732668040354424', 'Lhash_array': ['772881855642653732668040354424'], 'label': '2-1875-5.4-c1-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1875/2/b/h/1249/10'}