-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '814130948636873288135286421360,2244857345480746094898648210389', 'a10': -16, 'a2': 4, 'a3': 0, 'a4': 8, 'a5': -4, 'a6': 0, 'a7': 0, 'a8': 8, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 108.58635057308634, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1, 4, 5]], [29, [1, -4, 29]]], 'bad_primes': [3, 5, 29], 'central_character': '1305.1', 'coefficient_field': '1.1.1.1', 'conductor': 1703025, 'conductor_radical': 435, 'degree': 4, 'euler_factors': [[1, -4, 8, -8, 4], [1], [1, 4, 5], [1, 0, 2, 0, 49], [1, 0, -21, 0, 121], [1, 0, -22, 0, 169], [1, -12, 70, -204, 289], [1, 0, -22, 0, 361], [1, 0, 35, 0, 529], [1, -4, 29], [1, 0, -58, 0, 961], [1, 2, 75, 74, 1369], [1, 0, -1, 0, 1681], [1, 2, 87, 86, 1849], [1, 16, 158, 752, 2209], [1, 0, -25, 0, 2809], [1, 16, 182, 944, 3481], [1, 0, -86, 0, 3721], [1, 0, 10, 0, 4489], [1, 4, 146, 284, 5041], [1, -30, 371, -2190, 5329], [1, 0, -142, 0, 6241], [1, 0, -117, 0, 6889], [1, 0, -174, 0, 7921], [1, -22, 315, -2134, 9409], [1, 0, -193, 0, 10201], [1, 0, -170, 0, 10609], [1, 0, -198, 0, 11449], [1, 2, 219, 218, 11881], [1, -16, 290, -1808, 12769]], 'euler_factors_factorization': [[[[1, -2, 2], 2]], [1], [[[1, 4, 5], 1]], [[[1, 0, 2, 0, 49], 1]], [[[1, 0, -21, 0, 121], 1]], [[[1, 0, -22, 0, 169], 1]], [[[1, -6, 17], 2]], [[[1, 0, -22, 0, 361], 1]], [[[1, 0, 35, 0, 529], 1]], [[[1, -4, 29], 1]], [[[1, 0, -58, 0, 961], 1]], [[[1, 1, 37], 2]], [[[1, 0, -1, 0, 1681], 1]], [[[1, 1, 43], 2]], [[[1, 8, 47], 2]], [[[1, 0, -25, 0, 2809], 1]], [[[1, 8, 59], 2]], [[[1, 0, -86, 0, 3721], 1]], [[[1, 0, 10, 0, 4489], 1]], [[[1, 2, 71], 2]], [[[1, -15, 73], 2]], [[[1, 0, -142, 0, 6241], 1]], [[[1, 0, -117, 0, 6889], 1]], [[[1, 0, -174, 0, 7921], 1]], [[[1, -11, 97], 2]], [[[1, 0, -193, 0, 10201], 1]], [[[1, 0, -170, 0, 10609], 1]], [[[1, 0, -198, 0, 11449], 1]], [[[1, 1, 109], 2]], [[[1, -8, 113], 2]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 4, 'label': '4-1305e2-1.1-c1e2-0-4', 'leading_term': '6.01957349742774192995617083973271452793842426296696830793818101223211269164042941075795250', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1305/2/f/d', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.029296875', 'prec': 37}, 'plot_values': [6.019573497427741, 6.007087476438074, 5.975144558768638, 5.919739098949977, 5.840812352912229, 5.738965160354949, 5.613575930152745, 5.463767685769121, 5.288878009288583, 5.088279048895935, 4.861248842952228, 4.607084779147784, 4.325162231937433, 4.01495213086576, 3.6760579639663336, 3.3082378073402254, 2.9114718911888136, 2.4859603262807983, 2.0322025598531304, 1.5509774063251465, 1.04343264950895, 0.5110456360784266, -0.04428438516076992, -0.6202937100689132, -1.2142658259214218, -1.8231053767683159, -2.443260979275751, -3.0708132095309995, -3.701415411132084, -4.33039236404009, -4.952705207660323, -5.563056504262895, -6.155884225702053, -6.725467992627579, -7.26595547142402, -7.771463726214671, -8.236139380033974, -8.654248373790928, -9.020268948457952, -9.328962783380124, -9.57549737991248, -9.755491668094962, -9.86516188257831, -9.901335379473995, -9.861611789784774, -9.744340039988478, -9.548784660907623, -9.2750628697621, -8.924304615600121, -8.498549010073214, -8.000886191255658, -7.435315271158478, -6.806856535919379, -6.12137622884077, -5.385659042873957, -4.607208237710887, -3.79427079701639, -2.955624301368025, -2.1005503945851247, -1.2386221942577589, -0.37962561495029484, 0.4666374041117172, 1.2904759497226657, 2.082475431877542, 2.8336650798806113, 3.5356370289991843, 4.1807426498102735, 4.762152987241605, 5.274069506708537, 5.711717066738751, 6.071553088847798, 6.351188984724071, 6.549581654467692, 6.666884811909936, 6.704608193778437, 6.665406072472171, 6.553192555622754, 6.37288019995216, 6.130444058824099, 5.832628135090415, 5.486955990995661, 5.101426251164597, 4.684473090752203, 4.244673664524477, 3.7906670238762463, 3.3308959032178755, 2.873496964254942, 2.426096722918295, 1.9956889284616814, 1.5884997080743406, 1.2098689514726297, 0.8641933753068892, 0.5548278016987253, 0.2841074091739847, 0.05328181695812368, -0.1373899335549399, -0.2886642346630048, -0.4021588103558031, -0.48033404391823076, -0.5262991115554696, -0.5437534917274032, -0.5367763136160463, -0.5097375002211366, -0.46709431992708134, -0.41328610720350123, -0.35256021314982017, -0.2888668067602621, -0.22573198769482125, -0.16616935338314695, -0.11261147528835196, -0.06685259795851618, -0.030041802260119398, -0.0026666171624831654, 0.015396977125268692, 0.02485650983587175, 0.026908384408800844, 0.023168971273844857, 0.01555306844874496, 0.0061745223690625245, -0.002781615219708973, -0.009173016883572787, -0.011013853755224262, -0.006584073520737164, 0.005487926702902686, 0.026140271969474774, 0.05583707451113118, 0.09452454089359051, 0.14163584051273562, 0.19609967333303455, 0.2563854560094477, 0.32056799932283153, 0.3864003327374257, 0.45142947387829657, 0.5130786562741276, 0.5688008739556516, 0.6161497685553575, 0.6529510853414053, 0.677342574849776, 0.687939884810326, 0.6838305270108976, 0.6647108182008135, 0.6308266369685888, 0.58306200313625, 0.5228288400675191, 0.4520951792160584, 0.37323590383206706, 0.2889982920035319, 0.20233405426854467, 0.11631041077165871, 0.03394908813295866, -0.041899454125332164, -0.10868317727623915, -0.16428687609366038, -0.2071019932490488, -0.23615106933052782, -0.25108446586877664, -0.2522667921172944, -0.2406957770616458, -0.21803396453669283, -0.18645747377702832, -0.14862739853872275, -0.10748804963139653, -0.06618561882945728, -0.02784450570871436, 0.004546428328618507, 0.028346532694171193, 0.041379282129709406, 0.04210254442526787, 0.029691539788983402, 0.004142776604286673, -0.03370947191669551, -0.08216701339322224, -0.1387428346392774, -0.2002086910256885, -0.2627724971888404, -0.32217986307122765, -0.3739862971011681, -0.4136798993555918, -0.43702193793134364, -0.4401504783318446, -0.4199466929013979, -0.3740793308578458, -0.3013440404401744, -0.20161700311847094, -0.07611313721886963, 0.07276685613068526, 0.24130511502265073, 0.42472080247126204, 0.6171935867454453, 0.8121909725533172, 1.002650155470298, 1.181330317401181, 1.3411289755465858, 1.4753978009560738, 1.5783442351620083, 1.645246298299484, 1.6728719945886956, 1.659537382803887, 1.605469347849225, 1.5126715365924897, 1.385162916559016, 1.2286454010771428, 1.0505713325424078, 0.8596401068466584, 0.6656797258919755, 0.4790315436537845, 0.3102692949261255, 0.1695549782152394, 0.0662565050896008, 0.008368328977116708, 0.002118670918300736, 0.05154241727783037, 0.15818410525035057, 0.32088733032184913, 0.5356957707122318, 0.7958856193354554, 1.0921425573170667, 1.4128173880635098, 1.7444145170085104, 2.0720041243850598, 2.3800035898578433, 2.6526412426540658, 2.8749554314816166, 3.0331834633248165, 3.11585426999246, 3.1139775032938157, 3.022075159799382, 2.8380720358400513, 2.564106957571393, 2.206074385885581, 1.7740805746298332, 1.2816499122719651, 0.7457436019313811, 0.18571249366673157, -0.3771315480163958, -0.9206748379502739, -1.422806704825512, -1.862510417160856, -2.2208984992235377, -2.4820468913617986, -2.6340616539844373, -2.669494988546616, -2.5862243194428016, -2.38734958673758, -2.081686129759508, -1.683128735921955, -1.2106202487072788, -0.6870651055793908, -0.13872805874226815, 0.40612931138711833, 0.918356014004568, 1.3693125475680292, 1.732314211648004, 1.9838034207472734, 2.104876052860468, 2.0819813786849832, 1.9082381379018052, 1.5834893476057372, 1.1151282026023253, 0.517445791837149, -0.18824361362186348, -0.974891126648202, -1.8103820751298974, -2.6592587948449142, -3.4841314104190704, -4.247528445618572, -4.913849051952502, -5.450979952232974, -5.832466641830595, -6.0385441747275745, -6.058135769528977, -5.889021653344749, -5.539275886301315, -5.026432724385699, -4.378052643664788, -3.6299181740370683, -2.8255697475148853, -2.013742408373575, -1.2469086158865519, -0.5783195460585889, -0.059801574040138285, 0.26114053611409954, 0.3438434093596261, 0.15685051879110679, -0.31980112713224496, -1.093138455387853, -2.1557745340897267, -3.4856208412371648, -5.045714244436849, -6.7850992118166165, -8.64027469827436, -10.53702556509353, -12.393547971380558, -14.12279877079592, -15.637066918477547, -16.85026754259653, -17.68345199004606, -18.066432712962996, -17.943517213582965, -17.273926815290295, -16.036942148921213, -14.23076783292121, -11.87631383849744, -9.014431736179867, -5.707728500597052, -2.0364128290189543, 1.902178013562116, 5.9985872758032315, 10.13396791414762, 14.185189906872141, 18.029437890417444, 21.548556579264556, 24.63482995744348, 27.193748004222492, 29.15009440775051, 30.448508169937732, 31.05897076182892, 30.97484700984217, 30.216987132523705, 28.829312339187666, 26.88101333624655, 24.460131797985962, 21.673698963630642, 18.640085555718446, 15.487317289421465, 12.34516329508121, 9.3422177622777, 6.598731842389481, 4.223296491497037, 2.307285536934775, 0.9220671260511608, 0.11563813311011595, -0.08878837412733118, 0.3062353523415062, 1.2729636052870847, 2.7596348319152826, 4.6932815385561355, 6.982470290513471, 9.52219824453577, 12.197341232034164, 14.889105223558033, 17.47823205642325, 19.852189040612753, 21.907264148658445, 23.55553926140265, 24.72525047778754, 25.366624114784393, 25.450235767936583, 24.970984331174545, 23.944586596255117, 22.4092837060397, 20.420979388697393, 18.052653181185256, 15.388919766762367, 12.523491610799898, 9.554054808242007, 6.578412298892787, 3.6905187110134388, 0.9760934864279267, -1.4895524992170432, -3.6456401926076007, -5.445993430760182, -6.862246660941719, -7.881872887593176, -8.510075789985702, -8.766178497503704, -8.684105674212558, -8.307791716926708, -7.6904536173244775, -6.889796757462673, -5.966505665658677, -4.979993792328768, -3.986655647908839, -3.036738427221443, -2.1728897831136362, -1.4284653497145086, -0.8267833044864099, -0.38088125700845277, -0.0936870459210488, 0.04103616444577441, 0.03762377851827836, -0.08316727999037349, -0.2958929419257532, -0.5722927120974305, -0.8833274782369476, -1.2007440755859302, -1.4990080767592613, -1.7562024606805466, -1.9555002956873195, -2.0852399726137874, -2.1397134706023264, -2.1184747195802034, -2.0263911207331926, -1.8724185651736855, -1.6690336002543844, -1.4308115820535015, -1.1734842451840164, -0.9126694004628919, -0.662856329104924, -0.43656190098349446, -0.24352545364757247, -0.09043257914327617, 0.019486999520480927, 0.08618251520299644, 0.11271625956451947, 0.10458548057542029, 0.0692567579655425, 0.01532452967460526, -0.04818246158617484, -0.11255174264544705, -0.1700880937529542, -0.21457100802263393, -0.24175806920898602, -0.24944912556109952, -0.23765858527647254, -0.20830770224796893, -0.16503727237235735, -0.11265657448432893, -0.056675498100496366, -0.002703033557746639, 0.04414243271199142, 0.07968614344693659, 0.10121975355734038, 0.10765818510432015, 0.09983390803855514, 0.08030174356329817, 0.05331877566514182, 0.024346122217695897, -0.0002693711333445618, -0.01395977765116256, -0.010437714489655562, 0.01565459304339886, 0.06824204229672688, 0.14935577027746463, 0.25882486623886947, 0.39411521111725856, 0.5503704816085256, 0.7205674141658835, 0.8959714277533176, 1.0665239746212132, 1.221666340830399, 1.350797054350022, 1.4443135819697204, 1.493946619553227, 1.4938026326579301, 1.4404074854584237, 1.3335225558997152, 1.1758067659113853, 0.9732296252979408, 0.7343678369407954, 0.4703377245313658, 0.19385055183503638, -0.08129152995034336, -0.3411791766565543, -0.5725805311038044, -0.7637364903187446, -0.9051987584013942, -0.9902459615607321, -1.0155365143381605, -0.9810453315543723, -0.890345341296689, -0.7500854560269652, -0.5698168496829364, -0.361151823356967, -0.1371754894859716, 0.08849044129240138, 0.30253718533209023, 0.4927501740934416, 0.6488964932196306, 0.7631418764063687, 0.8307450569981794, 0.8499982924082777, 0.822554275854094, 0.7529058904265781, 0.6482764336694673, 0.5177780563889803, 0.37191992230453863, 0.22167026736997955, 0.07774450090249546, -0.050180897671754744, -0.15417827050124275, -0.22850052305305546, -0.27007173387948097, -0.27846408282141055, -0.2560204881251334, -0.20740598710240885, -0.1393264203972225, -0.05980392447926583, 0.02242039190258018, 0.09866087069077704, 0.16101435710741008, 0.2029488122437829, 0.21993097843751924, 0.20965371237578712, 0.1723619779476053, 0.11065643006258274, 0.029404759362591536, -0.0648072151307879, -0.16416339039965588, -0.2603373647882555, -0.34524313740625506, -0.41167469625067665, -0.45408121328783846, -0.4689308642362579, -0.45529751394036744, -0.41470917543386354, -0.3513049444087506, -0.2714391589007372, -0.18334272119692271, -0.0959983067431065, -0.019147693939688286, 0.03764574774772029], 'positive_zeros': ['0.64223607711012492924852643118990', '1.77088019764797899931344369182366', '2.76150253355720034799778383644174', '3.28478753548417363019912845807554', '3.47663691456538662284798495538584', '3.59254007917073859749384693798239', '4.37797694144427953366951522618729', '4.80012059859727431091523076309316', '4.95488288955330625006751518499554', '5.40613569696574780957360186736349', '6.13340633299569553057515089107443', '6.14885502234064744496038314249021', '6.83579944325227858511132406863298', '7.27300529849285495151592315097678', '7.60973984109287156553467338298093', '8.207370617276444456773597116116840', '8.302843257897433570293909223489788', '8.950893201578666372078248978392285', '9.705241165562487214321846287697235', '9.738429152327209098155837035283331'], 'prelabel': '4-1305e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.2280764340047923, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1341404329179308077, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.64223607711012492924852643119', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.77088019764797899931344369182', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.76150253355720034799778383644', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 108.58635057308634, 'bad_primes': [3, 5, 29], 'central_character': '1.1', 'conductor': 1703025, 'conductor_radical': 435, 'degree': 4, 'dirichlet_coefficients': [1, 4, 0, 8, -4, 0, 0, 8, 0, -16, 0, 0, 0, 0, 0, -4, 12, 0, 0, -32, 0, 0, 0, 0, 11, 0, 0, 0, 4, 0, 0, -32, 0, 48, 0, 0, -2, 0, 0, -32, 0, 0, -2, 0, 0, 0, -16, 0, -2, 44, 0, 0, 0, 0, 0, 0, 0, 16, -16, 0, 0, 0, 0, -64, 0, 0, 0, 96, 0, 0, -4, 0, 30, -8, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, -48, -8, 0, 0, 0, 0, 0, 0, 0, -64, 0, 0, 22, -8, 0, 88], 'euler11': [1, 0, -21, 0, 121], 'euler13': [1, 0, -22, 0, 169], 'euler17': [1, -12, 70, -204, 289], 'euler19': [1, 0, -22, 0, 361], 'euler2': [1, -4, 8, -8, 4], 'euler23': [1, 0, 35, 0, 529], 'euler29': [1, -4, 29, 0, 0], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, -58, 0, 961], 'euler37': [1, 2, 75, 74, 1369], 'euler41': [1, 0, -1, 0, 1681], 'euler43': [1, 2, 87, 86, 1849], 'euler47': [1, 16, 158, 752, 2209], 'euler5': [1, 4, 5, 0, 0], 'euler53': [1, 0, -25, 0, 2809], 'euler59': [1, 16, 182, 944, 3481], 'euler61': [1, 0, -86, 0, 3721], 'euler67': [1, 0, 10, 0, 4489], 'euler7': [1, 0, 2, 0, 49], 'euler71': [1, 4, 146, 284, 5041], 'euler73': [1, -30, 371, -2190, 5329], 'euler79': [1, 0, -142, 0, 6241], 'euler83': [1, 0, -117, 0, 6889], 'euler89': [1, 0, -174, 0, 7921], 'euler97': [1, -22, 315, -2134, 9409], 'euler_factors': [[1, -4, 8, -8, 4], [1, 0, 0, 0, 0], [1, 4, 5, 0, 0], [1, 0, 2, 0, 49], [1, 0, -21, 0, 121], [1, 0, -22, 0, 169], [1, -12, 70, -204, 289], [1, 0, -22, 0, 361], [1, 0, 35, 0, 529], [1, -4, 29, 0, 0], [1, 0, -58, 0, 961], [1, 2, 75, 74, 1369], [1, 0, -1, 0, 1681], [1, 2, 87, 86, 1849], [1, 16, 158, 752, 2209], [1, 0, -25, 0, 2809], [1, 16, 182, 944, 3481], [1, 0, -86, 0, 3721], [1, 0, 10, 0, 4489], [1, 4, 146, 284, 5041], [1, -30, 371, -2190, 5329], [1, 0, -142, 0, 6241], [1, 0, -117, 0, 6889], [1, 0, -174, 0, 7921], [1, -22, 315, -2134, 9409]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1305/2/f/d'], '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': '4-1305e2-1.1-c1e2-0-4', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-1305e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.2280764340047923, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1341404329179308077, 'z1': {'__RealLiteral__': 0, 'data': '0.64223607711012492924852643119', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '814130948636873288135286421360,2244857345480746094898648210389', 'Lhash_array': ['814130948636873288135286421360', '2244857345480746094898648210389'], 'factors': ['2-1305-145.144-c1-0-22', '2-1305-145.144-c1-0-60'], 'label': '4-1305e2-1.1-c1e2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1305/2/f/d'}