-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1215746183155573921056383959872', 'a10': [0, 0], 'a2': [0, 1.0], 'a3': [0, 1.0], 'a4': [-1.0, 0], 'a5': [0, 0], 'a6': [-1.0, 0], 'a7': [0, 2.5615528128088303], 'a8': [0, -1.0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 37.1304369398954, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -1.0]]], [3, [[1.0, 0], [0, -1.0]]], [5, [[1.0, 0], [0, 0]]], [31, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '4650.3349', 'coefficient_field': 'CDF', 'conductor': 4650, 'conductor_radical': 930, 'conjugate': '878988691925137762283799390423', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -2.5615528128088303], [-7.0, 0]], [[1.0, 0], [-2.5615528128088303, 0], [11.0, 0]], [[1.0, 0], [0, 2.0], [-13.0, 0]], [[1.0, 0], [0, 3.1231056256176606], [-17.0, 0]], [[1.0, 0], [-7.68465843842649, 0], [19.0, 0]], [[1.0, 0], [0, 1.4384471871911697], [-23.0, 0]], [[1.0, 0], [7.123105625617661, 0], [29.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 3.1231056256176606], [-37.0, 0]], [[1.0, 0], [-7.123105625617661, 0], [41.0, 0]], [[1.0, 0], [0, 12.807764064044152], [-43.0, 0]], [[1.0, 0], [0, -5.123105625617661], [-47.0, 0]], [[1.0, 0], [0, 7.43844718719117], [-53.0, 0]], [[1.0, 0], [-13.12310562561766, 0], [59.0, 0]], [[1.0, 0], [-6.0, 0], [61.0, 0]], [[1.0, 0], [0, 15.36931687685298], [-67.0, 0]], [[1.0, 0], [7.68465843842649, 0], [71.0, 0]], [[1.0, 0], [0, -10.807764064044152], [-73.0, 0]], [[1.0, 0], [-4.31534156157351, 0], [79.0, 0]], [[1.0, 0], [0, 14.246211251235321], [-83.0, 0]], [[1.0, 0], [-13.68465843842649, 0], [89.0, 0]], [[1.0, 0], [0, 6.0], [-97.0, 0]], [[1.0, 0], [0.5615528128088303, 0], [101.0, 0]], [[1.0, 0], [0, -1.7537887487646788], [-103.0, 0]], [[1.0, 0], [0, 2.5615528128088303], [-107.0, 0]], [[1.0, 0], [5.369316876852982, 0], [109.0, 0]], [[1.0, 0], [0, -1.6846584384264909], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 59, 'label': '2-4650-5.4-c1-0-59', 'leading_term': '1.911338867567835497185545288680942881250115700518877529', '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/4650/2/d/bd/3349/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.9113388675678356, 1.903264377191941, 1.8798285599342548, 1.8416969927919997, 1.789463450583173, 1.723688920571478, 1.644948293816083, 1.553881023713152, 1.4512419890892747, 1.3379490116328248, 1.2151238890508436, 1.0841243410458996, 0.9465648567265789, 0.8043250274690418, 0.6595445161179808, 0.514604336943565, 0.3720945990043628, 0.23476930387143782, 0.10548919482364133, -0.012845964765808397, -0.11737394776391642, -0.20535338300482317, -0.27425145999897255, -0.3218333698540205, -0.3462506111377773, -0.34612512741162005, -0.3206261546858473, -0.2695366544591422, -0.1933063020291523, -0.09308819862413031, 0.02924321541898763, 0.17109514960739136, 0.3291819302602527, 0.49957389425889914, 0.6777699440605177, 0.8587932143865508, 1.0373084690082635, 1.2077589920352407, 1.3645198913244445, 1.502063923835035, 1.6151352171991566, 1.6989256319864714, 1.7492480176063445, 1.7627002915910932, 1.7368141433690207, 1.6701822505623536, 1.5625582127829236, 1.4149239615944078, 1.229520193860955, 1.0098363878788923, 0.76055817658347, 0.48747123916643387, 0.19732239181652428, -0.1023598382239965, -0.40348123889258125, -0.6976290233968394, -0.9763430042079029, -1.2314024694809798, -1.4551192849370682, -1.6406269146249755, -1.7821545631200009, -1.8752755328007689, -1.9171191938708925, -1.9065366983371794, -1.8442117326145078, -1.732709179779337, -1.576456516721619, -1.3816550506693162, -1.1561206339453833, -0.9090562002692478, -0.6507612425543201, -0.3922860935208067, -0.14504146334969875, 0.07962398149563271, 0.2708632584127466, 0.4187717091428979, 0.514811509760521, 0.5522026452956326, 0.5262633576624978, 0.43468420036459243, 0.27772166470632487, 0.058299845108278806, -0.21798827975222798, -0.5429847528138146, -0.9061765248909989, -1.2950078622403867, -1.695287485804559, -2.091678421602904, -2.4682545940854, -2.809104711662045, -3.0989611480029184, -3.3238294680258207, -3.4715931119176004, -3.532567629333838, -3.4999798053803644, -3.370349052748268, -3.143751526482252, -2.823951467679472, -2.4183891717035157, -1.9380205336361205, -1.3970091390561157, -0.8122781016156545, -0.20293503868048446, 0.410410549776728, 1.0064129470217036, 1.563809936252886, 2.0622642093889234, 2.483192015840513, 2.8105439235456564, 3.03150339563145, 3.137071248734733, 3.1225079099388924, 2.987610615744777, 2.736809118393891, 2.379070840002424, 1.9276144474849086, 1.399439172996393, 0.8146855090629104, 0.1958507856630295, -0.43310978605818345, -1.0477600938623166, -1.6241971581843004, -2.1400585088959336, -2.5754783584713383, -2.9139491962151127, -3.143048618571631, -3.2549963373038127, -3.2470131934482382, -3.1214623838325086, -2.8857626318653273, -2.55207329212179, -2.1367619068229553, -1.6596750411345287, -1.1432428171527074, -0.6114559656992924, -0.08876098509332549, 0.40107623354320937, 0.8360854691017799, 1.1971330574120862, 1.4688382543187362, 1.640319723261, 1.7057340943649897, 1.6645778465506484, 1.5217346702956651, 1.2872624813788291, 0.9759268110529004, 0.6064997887683975, 0.20085573931154768, -0.2170950660989256, -0.6225842903253851, -0.9912184726554654, -1.3002067995753774, -1.5295227442789556, -1.6629409290606747, -1.688895869379183, -1.601117350585144, -1.3990077171530892, -1.0877388351761665, -0.6780603251420663, -0.18582517268488713, 0.3687467217909208, 0.9620328439806001, 1.5681538815360607, 2.1602447777154934, 2.711787546128531, 3.1979383402519166, 3.5967806821357735, 3.890439700937602, 4.065998623989488, 4.116168327018595, 4.039673037767279, 3.8413296962423242, 3.5318142773472907, 3.127124760737585, 2.647766524304492, 2.1177008762537386, 1.5631104063132362, 1.0110451002940042, 0.48802012795530203, 0.01863945404278254, -0.3756812961210181, -0.6778239824868301, -0.8758488526420024, -0.9635987981419982, -0.9409931866390409, -0.8139941232863761, -0.5942457450073365, -0.2984050540254316, 0.05280013763933026, 0.43573531275848726, 0.825181965845403, 1.195746308796694, 1.5232761224588756, 1.7862070028693144, 1.9667627571129143, 2.0519424797272015, 2.034238496352774, 1.9120442796536294, 1.6897288104479808, 1.3773727091188344, 0.9901807340010135, 0.5476038304096619, 0.07222073606648072, -0.41155678714064986, -0.8788805653206185, -1.3058837314032399, -1.6710372662086577, -1.9563663307969417, -2.1484552729002226, -2.2391823471647627, -2.226140915149524, -2.1127222917969113, -1.9078554144661504, -1.625418952316079, -1.2833611298447223, -0.9025802214580365, -0.5056332994351097, -0.11535147073916574, 0.24655416818132314, 0.5608107088869544, 0.8117448544701142, 0.9882159466436757, 1.0842626671686912, 1.0994228751077688, 1.0387060805874906, 0.9122195367936685, 0.734470542003519, 0.5233879430115206, 0.2991237365755724, 0.08270992924965864, -0.10534449880287615, -0.24642723834252345, -0.32507876335227864, -0.3300495069578626, -0.25508867086188786, -0.09941176207834226, 0.1321859618324693, 0.4295805348436663, 0.7779218452730318, 1.1585519297589542, 1.5501823942444155, 1.930256916961138, 2.2764118938901556, 2.5679408401807167, 2.787166728354901, 2.9206312153873335, 2.9600204786727256, 2.9027635468722273, 2.752259616479407, 2.5177146235809587, 2.213592797319936, 1.8587144234652442, 1.4750549246978022, 1.086321022876903, 0.7163957698877071, 0.387754474269208, 0.11995722219069396], 'positive_zeros': ['0.959054634563096058020569026454376', '1.51204612730515605206824358823646', '2.67415892373530616426787958422484', '3.68828068135981655495204589273228', '4.12487037964941697116975643156033', '5.19643992305739386259010314903536', '6.00799539325854842257781910292064', '6.86435719330280045372485413155687', '7.48924980060939509274298621947457', '8.091775877390436927965937711105907'], 'prelabel': '2-4650-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.093474947835217, 'root_angle': -0.35241638234956674, 'root_number': '0.4472135954999579392818347337462552470881236719223051449 - 0.8944271909999158785636694674925104941762473438446102897*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.17620819117478337', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.959054634563096058020569026454', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.51204612730515605206824358824', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.67415892373530616426787958422', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 37.1304369398954, 'bad_primes': [2, 3, 5, 31], 'central_character': '5.4', 'conductor': 4650, 'conductor_radical': 930, 'degree': 2, 'index': 59, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4650/2/d/bd/3349/4'], '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': '2-4650-5.4-c1-0-59', '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': '2-4650-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.093474947835217, 'root_angle': -0.17620819117478337, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.959054634563096058020569026454', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1215746183155573921056383959872', 'Lhash_array': ['1215746183155573921056383959872'], 'label': '2-4650-5.4-c1-0-59', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4650/2/d/bd/3349/4'}