-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1134930599399688216167594654068,1387487440894979596739416670482', 'a10': 4, 'a2': 2, 'a3': 0, 'a4': 3, 'a5': 2, 'a6': 0, 'a7': 2, 'a8': 4, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3062.109263009888, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2, 1]], [3, [1]], [5, [1, -2, 1]], [7, [1, -2, 1]], [11, [1, 2, 1]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '6930.1', 'coefficient_field': '1.1.1.1', 'conductor': 48024900, 'conductor_radical': 2310, 'degree': 4, 'euler_factors': [[1, -2, 1], [1], [1, -2, 1], [1, -2, 1], [1, 2, 1], [1, -6, 22, -78, 169], [1, -2, 22, -34, 289], [1, -4, 42, -76, 361], [1, -2, 34, -46, 529], [1, -12, 94, -348, 841], [1, 8, 78, 248, 961], [1, 6, 70, 222, 1369], [1, -8, 46, -328, 1681], [1, 0, 34, 0, 1849], [1, -8, 58, -376, 2209], [1, -8, 70, -424, 2809], [1, 0, 118, 0, 3481], [1, 12, 106, 732, 3721], [1, 2, 18, 134, 4489], [1, 4, -62, 284, 5041], [1, 20, 246, 1460, 5329], [1, -12, 142, -948, 6241], [1, 4, 118, 332, 6889], [1, -10, 190, -890, 7921], [1, -24, 286, -2328, 9409], [1, -12, 238, -1212, 10201], [1, -16, 270, -1648, 10609], [1, 0, 214, 0, 11449], [1, -10, 126, -1090, 11881], [1, -10, 238, -1130, 12769]], 'euler_factors_factorization': [[[[1, -1], 2]], [1], [[[1, -1], 2]], [[[1, -1], 2]], [[[1, 1], 2]], [[[1, -6, 22, -78, 169], 1]], [[[1, -2, 22, -34, 289], 1]], [[[1, -2, 19], 2]], [[[1, -2, 34, -46, 529], 1]], [[[1, -6, 29], 2]], [[[1, 4, 31], 2]], [[[1, 6, 70, 222, 1369], 1]], [[[1, -8, 46, -328, 1681], 1]], [[[1, 0, 34, 0, 1849], 1]], [[[1, -8, 58, -376, 2209], 1]], [[[1, -8, 70, -424, 2809], 1]], [[[1, 0, 59], 2]], [[[1, 12, 106, 732, 3721], 1]], [[[1, 2, 18, 134, 4489], 1]], [[[1, 4, -62, 284, 5041], 1]], [[[1, 10, 73], 2]], [[[1, -12, 142, -948, 6241], 1]], [[[1, 4, 118, 332, 6889], 1]], [[[1, -10, 190, -890, 7921], 1]], [[[1, -24, 286, -2328, 9409], 1]], [[[1, -6, 101], 2]], [[[1, -8, 103], 2]], [[[1, 0, 107], 2]], [[[1, -10, 126, -1090, 11881], 1]], [[[1, -10, 238, -1130, 12769], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 10, 'label': '4-6930e2-1.1-c1e2-0-10', 'leading_term': '17.0475167139040999027796038604709499331928067700954901174826640000000000000000000000000000', '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/6930/2/a/cc', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0234375', 'prec': 30}, 'plot_values': [17.0475167139041, 17.01943251323249, 16.965287831996395, 16.864659726564447, 16.71924641214278, 16.534841050760622, 16.311430279715676, 16.048084645870237, 15.745563964394718, 15.405058270001927, 15.027508658222256, 14.61396822703161, 14.165810856130326, 13.684637732735496, 13.1722758136763, 12.630775311938983, 12.062481114577148, 11.469975162401232, 10.856141846402394, 10.224093362699227, 9.577242951444664, 8.919205188079935, 8.25386658813606, 7.5852667950048716, 6.917662575458501, 6.255394030934233, 5.602937330645806, 4.964762026511919, 4.345369609609072, 3.749148601934336, 3.180397623604919, 2.6431854009403355, 2.1413589578366987, 1.6784156341938763, 1.2574989464053243, 0.881289195329575, 0.5519913338789708, 0.2712497226591163, 0.04013380984915591, -0.1409189139048251, -0.27211263760441523, -0.35431996242381514, -0.38907987865532345, -0.3785943438190022, -0.3257077110405314, -0.2338757743504735, -0.10712092173948157, 0.050021254726193114, 0.2325750387372212, 0.435193035338705, 0.6522590919155654, 0.8779625508517399, 1.1064298725681863, 1.3317942004197487, 1.5483516428848016, 1.7506152124966117, 1.9334889475845223, 2.092295772875354, 2.2229602924576133, 2.322001587184903, 2.3867138782209643, 2.415117688256581, 2.4061269027831726, 2.35945494313488, 2.2757572078868233, 2.15649270387135, 2.004032496735085, 1.821481304729793, 1.6127453671471543, 1.3823224466735595, 1.1353262492251353, 0.8772566972501764, 0.6139823934956564, 0.35150552503644894, 0.09590844434254034, -0.14687119657386347, -0.37111934980884065, -0.5715448649942027, -0.7433699074830094, -0.8824901926448203, -0.9855605878790328, -1.0501061937138088, -1.0745860156165679, -1.0584494922578125, -1.0021621368315854, -0.9072077084340622, -0.7760625675002414, -0.6121496456408736, -0.4197527620681696, -0.2039342441257073, 0.029613769712509178, 0.27467142382173876, 0.5246993372743457, 0.7729405134667319, 1.0126779937125003, 1.2373154195099973, 1.4406683304223087, 1.6170032424190814, 1.7613424431288118, 1.869444814839149, 1.9381017126965134, 1.96504824300243, 1.9492280091718008, 1.8906306661415613, 1.7905061204825774, 1.6511322003742959, 1.4759641275616224, 1.2693441868981217, 1.0365794646105346, 0.7836125209486756, 0.5170287517693882, 0.24371235460461824, -0.029206741588945075, -0.29468462123657824, -0.5458591805797303, -0.776342947270447, -0.9803379935602119, -1.1528667568100317, -1.2898792446715788, -1.388405295484803, -1.4466273036050912, -1.4639461838140408, -1.4409963299107797, -1.3796277136524966, -1.2828464459660596, -1.1547257460556566, -1.0002646065662972, -0.8252495180669731, -0.6360342811583162, -0.4393811420774843, -0.24217542654463273, -0.05127814656619869, 0.1268015600427078, 0.2860108580108241, 0.4210933202070265, 0.5276235509799768, 0.6023272100800842, 0.6430273120690434, 0.6489128572482282, 0.6203893445975892, 0.5592703620960071, 0.4685372901134059, 0.35243767731438785, 0.21617132080841955, 0.06589144317623119, -0.09165535403201727, -0.24921572514850673, -0.3994013435853985, -0.5348411928686881, -0.6485282284156569, -0.7340048038806632, -0.7856500511316207, -0.7988595227523567, -0.7702466570508106, -0.6977763764334488, -0.5808656270615704, -0.4204348232669853, -0.2189066963594851, 0.01985120367284299, 0.2906151499296688, 0.5869850492127459, 0.9015327892360776, 1.2261019245389857, 1.5519777509200623, 1.8702883706792504, 2.1721533384747933, 2.4491535697475837, 2.6934162193773354, 2.8981109576553004, 3.0574357117642257, 3.1670925720340435, 3.224151413504326, 3.2274609259763247, 3.1773833772461124, 3.0761048778688944, 2.927252446947804, 2.736081572769901, 2.509003748039207, 2.2536467831770053, 1.978334559200113, 1.6920339174555656, 1.4038364008585278, 1.1228221709276682, 0.8575945757752995, 0.6161038876125381, 0.40527923724872567, 0.23086104199356605, 0.09716186323300317, 0.006955118966844185, -0.038621525625699094, -0.040082181985036956, 0.000446428233630005, 0.0793283930776745, 0.19156701689739086, 0.3310330443123734, 0.4906796098552133, 0.6628806540836337, 0.8396597510089797, 1.013106124255129, 1.175562613780728, 1.3200736394911732, 1.4404839125091204, 1.5318667826792447, 1.5904992723067277, 1.6142216249464096, 1.602273815983232, 1.5555476182716632, 1.4762919378420591, 1.3682358120360554, 1.2361912268247088, 1.0860465063327662, 0.9243122197407255, 0.7580060019335536, 0.5941968826852383, 0.43982108419700255, 0.30128082985575527, 0.18424287646173765, 0.09333924416335744, 0.03200389508093753, 0.0023060761880773334, 0.004874768808038311, 0.03887306376402961, 0.10204548631547879, 0.1908176605529314, 0.30048060861453735, 0.42537798795291754, 0.5592174358243401, 0.6952917259439912, 0.8268843107671657, 0.9474637886692562, 1.0511330932173533, 1.132740185357818, 1.1883112059241256, 1.2150340354194047, 1.2116171373801088, 1.1781244860054378, 1.1162139564135831, 1.0288285141230618, 0.9202891024676715, 0.7958733697273913, 0.6617646027029345, 0.5245708952924297, 0.3911591415178407, 0.26818032250310286, 0.16184086057195662, 0.07750092425990167, 0.01945000693503288, -0.009365913924420516, -0.007495075680503361, 0.024910027745454946, 0.08607468973823362, 0.17265947676888946, 0.27991161942494097, 0.40186323595059237, 0.5316577856013258, 0.6618341306131283, 0.7847996731812096, 0.8931260487776763, 0.980109490493841, 1.0399975089930515, 1.068555058387001, 1.063149907343664, 1.0232351502359684, 0.9502433916468231, 0.8479046482167275, 0.7219325712034077, 0.580121538289959, 0.43184633470318745, 0.2879199350481184, 0.15996444828509732, 0.0600557986375501, 5.1291035186313635e-05, -0.008908553555584321, 0.04298241848665259, 0.16366050120715483, 0.3587223257788349, 0.6309769208059839, 0.9801927988901019, 1.4028611700372207, 1.8921897914556693, 2.4381776811202953, 3.0278371595587004, 3.64563774022353, 4.2738885267904205, 4.893553119080093, 5.484683611447431, 6.027548403609574, 6.502984782934665, 6.893727872669897, 7.1845470245875696, 7.363626721607934, 7.422374896691086, 7.35669308638334, 7.166390095831088, 6.856192891181221, 6.434760247793036, 5.9153268123045715, 5.314378623277399, 4.651884603868403, 3.949757451466344, 3.231699535008045, 2.5216171446888134, 1.8431787914472286, 1.2183690431519998, 0.6669135593650294, 0.20514571538962126, -0.154516715358231, -0.4042629066444661, -0.5411779050355728, -0.567431657628444, -0.49018709851394227, -0.3213097092057957, -0.0768139263219885, 0.22380062087417824, 0.5585608100664261, 0.9038823836690308, 1.2359475699508646, 1.5315504831148692, 1.769671911654479, 1.9320878733562101, 2.004923293407722, 1.978838555916343, 1.8503322266816402, 1.62138982271895, 1.3003366887725307, 0.900926255479685, 0.4426146603639747, -0.05083341659053782, -0.5516772344248807, -1.029908067940738, -1.4541054058384533, -1.793227613052641, -2.017803255527118, -2.101550834347946, -2.022638028159342, -1.7649016344973483, -1.318871306020948, -0.6824301928568637, 0.1386850826175311, 1.130839038512269, 2.272742691203399, 3.5359590502317126, 4.886006377121872, 6.283234536236768, 7.684764716236548, 9.045467375582003, 10.320580639523147, 11.466475787955927, 12.443681970276444, 13.21713562333043, 13.759267586071932, 14.049499694110114, 14.077036154447331, 13.839484729665285, 13.345041851942897, 12.610259048985188, 11.661414174583303, 10.531591601655704, 9.26117325622245, 7.89452717668196, 6.479707284277702, 5.065125523279224, 3.6986906233077317, 2.4248577784183167, 1.2835378306666942, 0.3078694696231864, -0.4767283793042443, -1.0538273271508762, -1.416448842148792, -1.567297837364834, -1.5184820662236715, -1.2908003952738532, -0.9126141935082192, -0.4184415914013809, 0.15295908291608593, 0.7603198178790617, 1.3623456320367766, 1.9193463192603675, 2.3959389499402373, 2.7621777266004512, 2.9960674307842714, 3.0838810514855943, 3.0220890502446394, 2.816703805619802, 2.4843198303293197, 2.0505034455705937, 1.5497919737224117, 1.0233236317024175, 0.5178332028130397, 0.08285792214732178, -0.2310404686325502, -0.3750801098480927, -0.30442061838407036, 0.019435280843238426, 0.6265838721946989, 1.5370538440214123, 2.7593545452826493, 4.289729518723729, 6.111740978044467, 8.19644154505764, 10.503276011045534, 12.980977049318932, 15.569864518405662, 18.203109804543303, 20.81029499064563, 23.318591912095048, 25.657246622652405, 27.75820350669472, 29.5610392792175, 31.012634742293322, 32.07202176263495, 32.70885425828626, 32.90766131247345, 32.66506894727807, 31.99306635192533, 30.91514524228935, 29.468362379774028, 27.698754792216178, 25.66218739498871, 23.419534993626073, 21.036500985061657, 18.579106411928493, 16.11281874771849, 13.698845142874763, 11.392992508371915, 9.243134373577867, 7.288222204339371, 5.557106484962778, 4.068038032595538, 2.8288086800860364, 1.8369392197022072, 1.0809026090742837, 0.5410224598929144, 0.1913882929440505, 0.001320821819842031, -0.0624891057870688, -0.03422102769189022, 0.05297867690151103, 0.1687130065826034, 0.28663467480478144, 0.3857923767015759, 0.4511126350761828, 0.4741317506564774, 0.45262566381234287, 0.3906183749961406, 0.2973006585577711, 0.1863643256070009, 0.0744834080106912, -0.019828215549027372, -0.07783299797710011, -0.08188480320903768, -0.016812463050222173, 0.12893878891857366, 0.3624049754226932, 0.6854517265291964, 1.0944692439475119, 1.5804304110839114, 2.129145773341711, 2.7221097561643215, 3.337138001044453, 3.9499228750371738, 4.534778528589096, 5.066687164996607, 5.521844133315605, 5.879883246375123, 6.123951534518743, 6.24277430677313, 6.23008802718986, 6.086248841043336, 5.816990313306625, 5.4343828192221, 4.955030134844915, 4.400328649549215, 3.79434078182928, 3.163451777334139, 2.534231591894818, 1.9327112006305727, 1.3825519071899457, 0.9042363131772918, 0.5138033754463106, 0.22225640784641734, 0.03500674690893883, -0.04825825617619869, -0.033425415729620704, 0.06850303431094024, 0.2421191513925159, 0.4686498446870827, 0.7269688281194241, 0.9950739643049148, 1.2510886009653737, 1.4749283750034505, 1.6489914307078344, 1.7597213247690542, 1.7977623943549061, 1.7591461875090149, 1.644811196089729, 1.4612213897679496, 1.219294780122343, 0.934392044328064, 0.6248205805974929, 0.3112617294688078, 0.015136103800072406, -0.24230956773701137, -0.4415520451955642, -0.5657837408021984, -0.6019401971413573, -0.5415729012532273, -0.38153058451196514, -0.12333744451736976, 0.22636253472312812, 0.6513294564793659, 1.1313844439709306], 'positive_zeros': ['0.895302380005463563714144706960041', '1.09453459860719871893868975334964', '1.74345612692942493406017137352178', '2.10647872262808169559194285954606', '2.62247176332169232122297000866883', '3.07685517067846681006432250319995', '3.38487334257725442424994041631735', '3.70129670201707167518996699307193', '4.40873610093171376815225683631080', '4.47638867629421961909613697970724', '5.13838584779232935879511658229748', '5.14689016651181565802307930929338', '5.77839112101603002545706262208454', '5.82033943104007380940734703320950', '6.35159663180195628750397799417864', '6.38211178893026106986610275858444', '7.16093841394744168814278542692751', '7.31885201401973075353684691486583', '7.66168859234389668970808913447451', '7.918248148303613953466409665413433'], 'prelabel': '4-6930e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.438839197129304, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1511786040097897028, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.895302380005463563714144706960', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.09453459860719871893868975335', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.74345612692942493406017137352', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3062.109263009888, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 48024900, 'conductor_radical': 2310, 'degree': 4, 'dirichlet_coefficients': [1, 2, 0, 3, 2, 0, 2, 4, 0, 4, -2, 0, 6, 4, 0, 5, 2, 0, 4, 6, 0, -4, 2, 0, 3, 12, 0, 6, 12, 0, -8, 6, 0, 4, 4, 0, -6, 8, 0, 8, 8, 0, 0, -6, 0, 4, 8, 0, 3, 6, 0, 18, 8, 0, -4, 8, 0, 24, 0, 0, -12, -16, 0, 7, 12, 0, -2, 6, 0, 8, -4, 0, -20, -12, 0, 12, -4, 0, 12, 10, 0, 16, -4, 0, 4, 0, 0, -8, 10, 0, 12, 6, 0, 16, 8, 0, 24, 6, 0, 9], 'euler11': [1, 2, 1, 0, 0], 'euler13': [1, -6, 22, -78, 169], 'euler17': [1, -2, 22, -34, 289], 'euler19': [1, -4, 42, -76, 361], 'euler2': [1, -2, 1, 0, 0], 'euler23': [1, -2, 34, -46, 529], 'euler29': [1, -12, 94, -348, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 8, 78, 248, 961], 'euler37': [1, 6, 70, 222, 1369], 'euler41': [1, -8, 46, -328, 1681], 'euler43': [1, 0, 34, 0, 1849], 'euler47': [1, -8, 58, -376, 2209], 'euler5': [1, -2, 1, 0, 0], 'euler53': [1, -8, 70, -424, 2809], 'euler59': [1, 0, 118, 0, 3481], 'euler61': [1, 12, 106, 732, 3721], 'euler67': [1, 2, 18, 134, 4489], 'euler7': [1, -2, 1, 0, 0], 'euler71': [1, 4, -62, 284, 5041], 'euler73': [1, 20, 246, 1460, 5329], 'euler79': [1, -12, 142, -948, 6241], 'euler83': [1, 4, 118, 332, 6889], 'euler89': [1, -10, 190, -890, 7921], 'euler97': [1, -24, 286, -2328, 9409], 'euler_factors': [[1, -2, 1, 0, 0], [1, 0, 0, 0, 0], [1, -2, 1, 0, 0], [1, -2, 1, 0, 0], [1, 2, 1, 0, 0], [1, -6, 22, -78, 169], [1, -2, 22, -34, 289], [1, -4, 42, -76, 361], [1, -2, 34, -46, 529], [1, -12, 94, -348, 841], [1, 8, 78, 248, 961], [1, 6, 70, 222, 1369], [1, -8, 46, -328, 1681], [1, 0, 34, 0, 1849], [1, -8, 58, -376, 2209], [1, -8, 70, -424, 2809], [1, 0, 118, 0, 3481], [1, 12, 106, 732, 3721], [1, 2, 18, 134, 4489], [1, 4, -62, 284, 5041], [1, 20, 246, 1460, 5329], [1, -12, 142, -948, 6241], [1, 4, 118, 332, 6889], [1, -10, 190, -890, 7921], [1, -24, 286, -2328, 9409]], 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6930/2/a/cc'], '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': '4-6930e2-1.1-c1e2-0-10', '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': '4-6930e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.438839197129304, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1511786040097897028, 'z1': {'__RealLiteral__': 0, 'data': '0.895302380005463563714144706960', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1134930599399688216167594654068,1387487440894979596739416670482', 'Lhash_array': ['1134930599399688216167594654068', '1387487440894979596739416670482'], 'label': '4-6930e2-1.1-c1e2-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6930/2/a/cc'}