-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2573152337522969077287777664826', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, -173.9482681718907], 'a6': [0, 0], 'a7': [-484.0, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 132.5111521650342, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '576.449', 'coefficient_field': 'CDF', 'conductor': 576, 'conductor_radical': 6, 'conjugate': '61147513499246637460708249801', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 173.9482681718907], [-15625.0, 0]], [[1.0, 0], [484.0, 0], [117649.0, 0]], [[1.0, 0], [0, 1340.674457129694], [-1771561.0, 0]], [[1.0, 0], [3368.0, 0], [4826809.0, 0]], [[1.0, 0], [0, -12.727922061357855], [-24137569.0, 0]], [[1.0, 0], [5744.0, 0], [47045881.0, 0]], [[1.0, 0], [0, 3377.141986946951], [-148035889.0, 0]], [[1.0, 0], [0, 29354.830914178336], [-594823321.0, 0]], [[1.0, 0], [39796.0, 0], [887503681.0, 0]], [[1.0, 0], [52526.0, 0], [2565726409.0, 0]], [[1.0, 0], [0, 37042.49583923848], [-4750104241.0, 0]], [[1.0, 0], [3800.0, 0], [6321363049.0, 0]], [[1.0, 0], [0, -76791.79643685906], [-10779215329.0, 0]], [[1.0, 0], [0, 238737.6341048893], [-22164361129.0, 0]], [[1.0, 0], [0, -249840.62478308045], [-42180533641.0, 0]], [[1.0, 0], [13250.0, 0], [51520374361.0, 0]], [[1.0, 0], [168968.0, 0], [90458382169.0, 0]], [[1.0, 0], [0, 531467.1135940587], [-128100283921.0, 0]], [[1.0, 0], [-236144.0, 0], [151334226289.0, 0]], [[1.0, 0], [35116.0, 0], [243087455521.0, 0]], [[1.0, 0], [0, -10979.95409826471], [-326940373369.0, 0]], [[1.0, 0], [0, 129328.41606545718], [-496981290961.0, 0]], [[1.0, 0], [321424.0, 0], [832972004929.0, 0]], [[1.0, 0], [0, 668780.1794326743], [-1061520150601.0, 0]], [[1.0, 0], [-1993412.0, 0], [1194052296529.0, 0]], [[1.0, 0], [0, -260667.8438166089], [-1500730351849.0, 0]], [[1.0, 0], [194456.0, 0], [1677100110841.0, 0]], [[1.0, 0], [0, 821897.0818308092], [-2081951752609.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 47, 'label': '2-24e2-3.2-c6-0-47', 'leading_term': '0.132030203534294489869574668086760159771560520227518442', 'load_key': 'CMFs-workshop', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/576/7/e/b/449/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.13203020353429448, 0.3375461055612451, 0.578366416539503, 0.8498145922885573, 1.1464548650572244, 1.462205253645848, 1.790464543477963, 2.1242510178270044, 2.4563504903931945, 2.7794709790437593, 3.086401174762519, 3.370169703585951, 3.6242020582044954, 3.8424719962661325, 4.019644170894028, 4.151204782259967, 4.233577123715091, 4.264219047803897, 4.241699601274303, 4.165752377306768, 4.0373035091547536, 3.8584726815723887, 3.6325460616696588, 3.363920643318182, 3.0580201501827653, 2.7211833401795893, 2.3605262840694015, 1.983780935665145, 1.599113051018138, 1.2149232271847539, 0.8396354945401674, 0.4814784860640932, 0.14826469849712876, -0.15282626952469808, -0.41545438988360217, -0.6343096098882667, -0.8052799232039509, -0.9255913399870753, -0.9939144827686618, -1.010433221346421, -0.9768716331251768, -0.8964766212025879, -0.7739547202072211, -0.6153629417066007, -0.42795492261293167, -0.21998510123371073, -0.00047511130594845793, 0.2210519943550182, 0.43486275320923756, 0.6313214194844384, 0.8012061112017914, 0.9360231453719217, 1.0283092802298626, 1.0719114563888685, 1.0622338492845258, 0.9964426281888091, 0.8736197651731745, 0.694858540264481, 0.4632950224341154, 0.18407173183404657, -0.13576814480835275, -0.48745527065922806, -0.8607342475973998, -1.2441636557789, -1.6254680327911162, -1.99193155742119, -2.330821237818815, -2.6298257859756764, -2.87749517095817, -3.063665151623925, -3.1798509499032317, -3.2195946740949766, -3.178752152999699, -3.055706488122817, -2.8514978405425584, -2.569861684902676, -2.2171709053114292, -1.8022805748581756, -1.3362779311912418, -0.8321437992031597, -0.3043353720103127, 0.23169630815664025, 0.7600377769392089, 1.2648745623438162, 1.7310617892633475, 2.1446820588375517, 2.4935684114221512, 2.7677707987593902, 2.959946016758516, 3.065653463492009, 3.0835423270570352, 3.015419775847608, 2.8661942842754478, 2.643693212488658, 2.358358974881158, 2.0228333653055324, 1.6514446318996814, 1.259616484589503, 0.8632221552154346, 0.4779097139507405, 0.11842690480177895, -0.20202533626388722, -0.472381862757767, -0.6842176092992389, -0.8321428951443719, -0.9140695169975387, -0.9313325333050458, -0.8886586268506758, -0.7939785397966159, -0.658088029188289, -0.49416878716845986, -0.3171874893703622, -0.14319725694269334, 0.011428963687324302, 0.1307995607067275, 0.20030378860516393, 0.20737246806932486, 0.14216331277019031, -0.00186326555049563, -0.2275079476838544, -0.5335603415561456, -0.9147083427362852, -1.3616384788117921, -1.8613279595011487, -2.397520099550913, -2.951365832186131, -3.502205622725812, -4.028458650873748, -4.508580050993013, -4.922042625280923, -5.250297046987667, -5.477664333927254, -5.592116380480383, -5.585904564524408, -5.4560027580759405, -5.204339221580964, -4.837801505410266, -4.368009184529615, -3.8108605111736265, -3.18587033768079, -2.515327370150399, -1.8233084050540498, -1.1345951553447908, -0.47354513637796514, 0.1370285060943816, 0.676912630120422, 1.1294316983216943, 1.4822187361837496, 1.7277785387163278, 1.8638118145286848, 1.893280607406882, 1.8242082825806043, 1.6692209655635062, 1.4448508788344163, 1.170634819665271, 0.8680523636041713, 0.5593576215900531, 0.26636497648695284, 0.009252754696279309, -0.19455101920675655, -0.3313398795150085, -0.3919028745435552, -0.37205657682999727, -0.27290280865681965, -0.10079407666579925, 0.1329956582995319, 0.41288114233747325, 0.7198274771306363, 1.03241937683162, 1.3280818221919959, 1.5843864096930855, 1.7803716414917887, 1.8978032126602744, 1.9223022441599256, 1.8442753787664425, 1.6595904686169543, 1.3699547797420288, 0.9829685594225057, 0.5118446225743468, -0.02519665027039739, -0.6058288910407089, -1.2047724465751066, -1.7951375194708041, -2.34988495739711, -2.8433236969339966, -3.252560129008565, -3.558815700897464, -3.7485349576326783, -3.814216727132789, -3.7549157680472294, -3.576380174262615, -3.2908101970725787, -2.9162457725654347, -2.4756116930266607, -1.9954697701098338, -1.5045452790824883, -1.0321093380388544, -0.6063087385289444, -0.25253942394435713, 0.008041079982956726, 0.15977350898168502, 0.19345210654838535, 0.1069150787945989, -0.09476937709760283, -0.3995378138663629, -0.7889787019100991, -1.239359054778156, -1.7229744589632225, -2.2097463340624137, -2.668974366598433, -3.0711414597466358, -3.3896639667863075, -3.6024818211967187, -3.6933914493521054, -3.6530386669958297, -3.479508352731749, -3.1784714541190917, -2.7628764275097404, -2.2521999535494017, -1.6712990116286477, -1.0489314404561596, -0.41603336292432286, 0.1961420789563541, 0.7579104427649546, 1.2429491297750077, 1.6298854282750472, 1.903578567378072, 2.0560130527662013, 2.086744200916505, 2.0028645121834625, 1.818489632670851, 1.5537932722048806, 1.2336496242901545, 0.885967681682954, 0.5398226435118316, 0.2235039436321462, -0.03739373837446764, -0.22171136126198535, -0.3141825463300108, -0.3065080139911716, -0.1979724166546122, 0.0044424806117343155, 0.28646189585112153, 0.6274192046381536, 1.0016009656815326, 1.3799525126182057, 1.7320357679161016, 2.0281126102497717, 2.2412168621515915, 2.3490765789377064, 2.335756060336729, 2.192903520956847, 1.920514704416094, 1.5271534304865861, 1.0296051964445188, 0.4519772535376652, -0.17570439906835356], 'positive_zeros': ['2.02985928224993188831161217902636', '2.87513367723826408985859619114923', '3.72432729673021651103889937211172', '5.03548391886707498778162653087289', '6.27210631400804706917432337394760', '7.05743335762494203404048075633728', '7.37436806806884325193501357667465', '8.985396480364529280009836643966487', '9.877492568020404259030051185343477', '10.27876645180557098915012920920810'], 'prelabel': '2-24e2-3.2-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.511348842122464, 'root_angle': -0.3040867239846964, 'root_number': '0.5773502691896257645091487805019574556476017512701268761 - 0.8164965809277260327324280249019637973219824935522233762*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1520433619923482', 'prec': 64}, 'spectral_label': 'c6-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.02985928224993188831161217903', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.87513367723826408985859619115', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.72432729673021651103889937211', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 132.5111521650342, 'bad_primes': [2, 3], 'central_character': '3.2', 'conductor': 576, 'conductor_radical': 6, 'degree': 2, 'index': 47, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/576/7/e/b/449/1'], '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': '2-24e2-3.2-c6-0-47', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'prelabel': '2-24e2-3.2-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.511348842122464, 'root_angle': -0.1520433619923482, 'self_dual': False, 'spectral_label': 'c6-0', 'z1': {'__RealLiteral__': 0, 'data': '2.02985928224993188831161217903', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2573152337522969077287777664826', 'Lhash_array': ['2573152337522969077287777664826'], 'label': '2-24e2-3.2-c6-0-47', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/576/7/e/b/449/1'}