-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '712949645781177442794902313724,2940272121576651807420246833342', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -8, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.00684658325947, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, 8, 25]]], 'bad_primes': [2, 5], 'central_character': '160.1', 'coefficient_field': '1.1.1.1', 'conductor': 25600, 'conductor_radical': 10, 'degree': 4, 'euler_factors': [[1], [1, 0, 0, 0, 81], [1, 8, 25], [1, 0, 0, 0, 2401], [1, 0, 242, 0, 14641], [1, 34, 578, 5746, 28561], [1, -14, 98, -4046, 83521], [1, 0, -722, 0, 130321], [1, 0, 0, 0, 279841], [1, 0, -82, 0, 707281], [1, 0, 1922, 0, 923521], [1, 94, 4418, 128686, 1874161], [1, -160, 9762, -268960, 2825761], [1, 0, 0, 0, 3418801], [1, 0, 0, 0, 4879681], [1, -34, 578, -95506, 7890481], [1, 0, -6962, 0, 12117361], [1, -240, 21842, -893040, 13845841], [1, 0, 0, 0, 20151121], [1, 0, 10082, 0, 25411681], [1, 206, 21218, 1097774, 28398241], [1, 0, -12482, 0, 38950081], [1, 0, 0, 0, 47458321], [1, 0, 9758, 0, 62742241], [1, 14, 98, 131726, 88529281], [1, -396, 59606, -4039596, 104060401], [1, 0, 0, 0, 112550881], [1, 0, 0, 0, 131079601], [1, 0, 9362, 0, 141158161], [1, 194, 18818, 2477186, 163047361]], 'euler_factors_factorization': [[1], [[[1, 0, 0, 0, 81], 1]], [[[1, 8, 25], 1]], [[[1, 0, 0, 0, 2401], 1]], [[[1, 0, 121], 2]], [[[1, 10, 169], 1], [[1, 24, 169], 1]], [[[1, -30, 289], 1], [[1, 16, 289], 1]], [[[1, -19], 2], [[1, 19], 2]], [[[1, 0, 0, 0, 279841], 1]], [[[1, -42, 841], 1], [[1, 42, 841], 1]], [[[1, 0, 961], 2]], [[[1, 24, 1369], 1], [[1, 70, 1369], 1]], [[[1, -80, 1681], 2]], [[[1, 0, 0, 0, 3418801], 1]], [[[1, 0, 0, 0, 4879681], 1]], [[[1, -90, 2809], 1], [[1, 56, 2809], 1]], [[[1, -59], 2], [[1, 59], 2]], [[[1, -120, 3721], 2]], [[[1, 0, 0, 0, 20151121], 1]], [[[1, 0, 5041], 2]], [[[1, 96, 5329], 1], [[1, 110, 5329], 1]], [[[1, -79], 2], [[1, 79], 2]], [[[1, 0, 0, 0, 47458321], 1]], [[[1, -78, 7921], 1], [[1, 78, 7921], 1]], [[[1, -130, 9409], 1], [[1, 144, 9409], 1]], [[[1, -198, 10201], 2]], [[[1, 0, 0, 0, 112550881], 1]], [[[1, 0, 0, 0, 131079601], 1]], [[[1, -120, 11881], 1], [[1, 120, 11881], 1]], [[[1, -30, 12769], 1], [[1, 224, 12769], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 0, 'label': '4-160e2-1.1-c2e2-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2, 2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/160/3/p/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.8232023196504504, 0.812665021462884, 0.7837596179038883, 0.7343943103435089, 0.6643997201184878, 0.5739202314086589, 0.46253531485693616, 0.3297867024662366, 0.17550453774699665, -0.0002523866350830574, -0.19711468349565783, -0.4143410670690524, -0.6506177912473468, -0.9040821070396533, -1.1721242983828772, -1.4514581428541597, -1.7379369585407172, -2.0266928764602468, -2.3120157318528154, -2.587559566903938, -2.8463272436764346, -3.08093499062353, -3.283740020913534, -3.4471366313932736, -3.5638459606984836, -3.627198428635995, -3.631576703521383, -3.5726214915810455, -3.4477833030145564, -3.2563777903772646, -3.0001655524535487, -2.683185688647062, -2.3122550384417804, -1.896529791917354, -1.4478069042506585, -0.9798057015461339, -0.5081738519835959, -0.04954079955285634, 0.3788173625788386, 0.7600329587252265, 1.0782886871608324, 1.3198019921599273, 1.4736462280969613, 1.5324539904633694, 1.493206769087986, 1.3574629425995572, 1.1318606757974685, 0.8277504859252338, 0.46117527086000143, 0.05191621514627364, -0.37719107947321284, -0.8016270760233678, -1.1965149950946716, -1.5380828792090973, -1.8054168542375686, -1.9815921705472155, -2.0554635045671708, -2.0220475207912605, -1.8838724299212668, -1.6503282914863637, -1.3381460031386416, -0.9696834110621775, -0.5723054380596799, -0.1758907045314702, 0.18879284210375577, 0.4927845578495123, 0.7111060809515233, 0.8249228650004187, 0.8235383845590714, 0.7053342907277373, 0.47877526975264395, 0.1617365976653572, -0.21909308368432018, -0.6304023140610039, -1.0346121045055248, -1.3929479212282334, -1.6691047152510388, -1.8321502822929836, -1.8604949720718802, -1.7434690324260163, -1.4843026749158492, -1.0995174950240356, -0.6197644946033883, -0.08683565751733502, 0.4481893440926998, 0.9296577340893102, 1.3015178321434213, 1.512372143587535, 1.5206635403925348, 1.2983661520888015, 0.8352783938904227, 0.13995547058518776, -0.7587603412269609, -1.8140565749256419, -2.9635002647052726, -4.133854327389447, -5.2471469702875355, -6.226110393027153, -7.002443603322233, -7.520460778949194, -7.745104567429406, -7.661757114669829, -7.281520007827348, -6.636386845187817, -5.7802541696384875, -4.780383493905925, -3.714249322957451, -2.6597700953739176, -1.6898017909416192, -0.8643161557918105, -0.2253769455120991, 0.20610289079677394, 0.4322279070566678, 0.475839616415579, 0.37793953075959136, 0.19114492388009707, -0.026533604003005883, -0.21944581091089715, -0.34150424918808636, -0.36154765295435276, -0.26812230259752234, -0.06990861646333481, 0.2044505896188051, 0.5111198159103255, 0.7965093533574868, 1.0049695593431143, 1.0871924001148028, 1.0069896900404198, 0.7485992375512838, 0.31895582995039157, -0.2500698119765702, -0.9053925295710398, -1.5774188285155364, -2.188177108742771, -2.6615797173805773, -2.9318264990093166, -2.9549252638517047, -2.7125749568032673, -2.219622599571715, -1.5204146762667428, -0.6884561273011799, 0.1842237515180508, 0.9952894305106736, 1.645511170362936, 2.0508963363943127, 2.152821379018982, 1.9277422451767439, 1.3891185273179285, 0.5890648727375576, -0.38903343950959024, -1.4388919517378167, -2.444345626205865, -3.2947325866132933, -3.8965842740208823, -4.189264327883122, -4.148447116769147, -3.7948306717144713, -3.18621784208504, -2.4155011071413037, -1.5937974382258238, -0.839537288021503, -0.25980615152961534, 0.06264549202664749, 0.08153377321362362, -0.20626749424448107, -0.7602110380017675, -1.501114758885079, -2.3212217235372634, -3.1002899388268412, -3.7193783670181273, -4.081245492630159, -4.118776253812929, -3.8103150824754453, -3.176435469812888, -2.2832765593921405, -1.2278469130322123, -0.12878996284159586, 0.8929154119852034, 1.7295417354016083, 2.3006323249440985, 2.5653895401374416, 2.524082707488899, 2.219861658813988, 1.727103228411616, 1.1418190975654512, 0.5638348093811708, 0.08205758883002018, -0.23914808611216304, -0.3702508877291743, -0.31823442516939965, -0.1255364422255097, 0.14063542290404846, 0.4003878327174076, 0.5769313733100013, 0.6119572926292101, 0.4760102766406441, 0.17664791383574052, -0.24371307105205917, -0.7133740957102594, -1.1449248336340219, -1.4524040595579792, -1.5672161262396491, -1.4566823713343124, -1.1307652941896569, -0.6497773785334101, -0.11541508852794972, 0.3387157949756801, 0.5684576485051394, 0.44133762366364737, -0.14143268367738998, -1.2235064140473595, -2.7838940064906414, -4.731310036495311, -6.913065589816474, -9.132423101877745, -11.169948611436299, -12.81822095933889, -13.9006005039685, -14.307435439623623, -13.997020518209789, -13.016397423577164, -11.478861139178884, -9.561565790055711, -7.4678563228526516, -5.407725365272595, -3.5629129140492903, -2.0661514577606046, -0.9860493320143696, -0.32064614512883094, -0.007762343192583584, 0.06212502132568447, 0.019211157059265953, -0.009117196364028484, 0.07680488174932229, 0.3313074072177558, 0.7556009049911855, 1.2989319189600546, 1.8707794176679362, 2.3610168789512525, 2.6610205002469174, 2.6898792454721057, 2.40748186893416, 1.8292612229061196, 1.0205776002426676, 0.08998526746842224, -0.831713348915691, -1.6150920413107495, -2.1530442188687178, -2.3851655482160687, -2.302192397823592, -1.9548373455037467, -1.436063082659258, -0.8697112259314055, -0.3804001446000571, -0.07265246115224377, -0.007198578434387838, -0.18923143275281573, -0.5655987773204396, -1.0350750549203902, -1.4659198268584421, -1.7252024959191201, -1.701079128209208, -1.3334719626398301, -0.6213815183321921, 0.36533558453902915, 1.5026756811928814, 2.6275852201070684, 3.569609363790885, 4.181921299862167, 4.366358758054151, 4.097531618621631, 3.42263269326638, 2.460102939244232, 1.3727644219112265, 0.3407817653111545, -0.4738424883801273, -0.9609299479870218, -1.080766091492917, -0.8792859566277886, -0.4751516443009707, -0.04395405186377577, 0.21891928055392704, 0.13467465488842867, -0.4224171602840549, -1.4951805110677294, -3.0323870156375228, -4.890449573241626, -6.853712534861324, -8.67222763764628, -10.095765731979121, -10.92765939162194, -11.043254773655178, -10.428803802317539, -9.164857714050155, -7.429937217934148, -5.453963139191747, -3.4912594113930187, -1.7707293232725425, -0.46352829341248813, 0.3406814833930534, 0.6444611362118066, 0.5294097116753304, 0.13667858952109888, -0.3680727971774508, -0.8291491174061879, -1.1285995097027197, -1.209513375688022, -1.075528034760522, -0.7869827388759101, -0.43470265738441016, -0.11583095713756936, 0.09517849409833712, 0.16752078069521187, 0.12167700109754931, 0.02689179717359222, -0.0181535637694111, 0.0892900931523323, 0.42714106435658517, 1.0223495951758244, 1.8380551167856072, 2.7724003629109917, 3.6735616923677306, 4.370729902929829, 4.703987738146695, 4.568039559687523, 3.9289161996600668, 2.8480461416977896, 1.4663347599195435, -0.011294613451084417, -1.3571754602852366, -2.366198134686868, -2.8914681161820384, -2.8862997903795224, -2.402872575578775, -1.599978285990284, -0.6985225458207814, 0.04836111408640542, 0.41691766378008044, 0.25185432235882604, -0.4945261601661624, -1.7528799289632269, -3.3426948014473057, -5.010758898430645, -6.469252739119673, -7.464029047556018, -7.8062201037067265, -7.428549425282151, -6.376375215220949, -4.818481705197101, -2.995765770734856, -1.1870821874665936, 0.3516430592539527, 1.4328592477896387, 1.9660267496812516, 1.9750008860310266, 1.5767082797071594, 0.9569803709097865, 0.31961705135450524, -0.15700541655371322, -0.3588375284282365, -0.2604327654630251, 0.07734252536035958, 0.5235629358056791, 0.914439506239522, 1.096219252415959, 0.9623765955402414, 0.48577719352971527, -0.27700756260325504, -1.1931128036389202, -2.084403736330326, -2.7698508970303632, -3.1021212101469047, -3.0106279694530627, -2.508026535132407, -1.6994880169145092, -0.7492724886444514, 0.14851903793002155, 0.8179457908970513, 1.139936961310701, 1.0760100758196336, 0.679230759098898, 0.0754145394245337, -0.565828090961065, -1.073441303491009, -1.319613202003889, -1.2457212627234775, -0.8835299700227073, -0.3392085072271081, 0.22757466792711878, 0.6492323809789551, 0.7931122512742265, 0.5966148460596039, 0.08977476398387663, -0.6120707786816703, -1.3322098361511892, -1.8761723171125233, -2.086658594743721, -1.8824361038223458, -1.2979080579504902, -0.4768894182785256, 0.340305870542036, 0.8708839191504937, 0.8478774491086403, 0.0817287598411495, -1.4853539443313772, -3.760024541103076, -6.499467806367737, -9.3494142409477, -11.912211944778822, -13.806794889589936, -14.761035001523416, -14.635502399367116, -13.478851722299083, -11.483756764711957, -8.974855701976162, -6.320143028349558, -3.8755878539558144, -1.9122937694175368, -0.5738511188143383, 0.13295292141420245, 0.32910391861463467, 0.21263156563040603, 0.008475335746157298, -0.09273388043034576, 0.021908227750945784, 0.367294014275455, 0.8637193329195194, 1.3673099356842715, 1.716166350242913, 1.7749163638331906, 1.4801170720268038, 0.8529282733713552, 0.0019462412877000515, -0.9076896870062962, -1.6955158379120734, -2.2075410629151624, -2.362403277192597, -2.159478943659987, -1.6884512526609374, -1.0909823879474596, -0.5299856530878891, -0.13714653099075588, 0.020482950079720303, -0.03970572496847445, -0.2213973651422601, -0.3780464146626475, -0.3601274736634032, -0.060581188511565624, 0.5383507503862045, 1.3526459764146475, 2.198468237318325, 2.831526263622275, 3.004071449890806, 2.5230825232066394, 1.31502920128439, -0.5529944662457733, -2.8620057202447384, -5.281950449745192, -7.433154565184921, -8.95517568035264, -9.597618775049698, -9.251200621652828, -7.998197604710682, -6.067497639544806, -3.8102109257322585, -1.6056675654906138, 0.20622930515623492, 1.39676538081668, 1.8909627375318006, 1.7638581285428983, 1.2159013424262333, 0.506050614944936, -0.11725233381531032, -0.479876635896678, -0.5303403259279389, -0.3408172292742333, -0.08991082212009908, -0.001576402324132339, -0.2815376533482699, -1.0521554530596937, -2.3088917328109853, -3.9098013859910528, -5.60327802744759, -7.075030556617494, -8.03409656265917, -8.26187546570164, -7.690116431083869, -6.392163997561583, -4.5943314848443055, -2.6036577370690006, -0.75510522076472, 0.6688936300746815, 1.4965812723054015, 1.690981360319918, 1.3554112099208535, 0.6879975520540692, -0.06839676133274575, -0.6919645469168693, -1.036405099056426, -1.0536831456211941, -0.8008847249514337, -0.4031507261497585, -0.012223311565371842, 0.2475329751462315, 0.31965948238560615, 0.22927374521633842, 0.07732367070612955, 3.4620258748270474e-05, 0.12390486805795771, 0.5196656334317259, 1.1516889196322484, 1.8748858075662151], 'positive_zeros': ['0.56241810294793935787052276502465', '2.31946572742306242166285091624574', '3.07014799261480417326737520363058', '3.96665623126252917653167449733181', '4.46503362035632265470202646384030', '5.19750001638651342043084405508238', '5.69816290538786908188894351379417', '6.90384934763302524516276848972839', '7.24230357182732721034206893490678', '7.57980161974997963906567376393766', '8.099069955660332990069149443384505', '8.799190185937891743962117613845872', '9.288574210560027430377715916439680', '10.10708646442063944472817739810055', '10.21296172549479647578563963136125', '11.00748677334921265502286097673447', '11.63807752129268011768333407435225', '11.90549422290975687265989816486694', '12.27793305373324612995885856158446', '12.82671548808803046709025181605951'], 'prelabel': '4-160e2-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.0879856871551468, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c2e2-0', 'trace_hash': 1437706449950834013, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.56241810294793935787052276502', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.31946572742306242166285091625', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.07014799261480417326737520363', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 19.00684658325947, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 25600, 'conductor_radical': 10, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -34, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 39, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -94, 0, 0, 0, 160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 34, 0, 0, 0, 0, 0, 0, 0, 240, 0, 0, 0, 272, 0, 0, 0, 0, 0, 0, 0, -206, 0, 0, 0, 0, 0, 0, 0, -81, 0, 0, 0, -112, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0], 'euler11': [1, 0, 242, 0, 14641], 'euler13': [1, 34, 578, 5746, 28561], 'euler17': [1, -14, 98, -4046, 83521], 'euler19': [1, 0, -722, 0, 130321], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 0, 0, 279841], 'euler29': [1, 0, -82, 0, 707281], 'euler3': [1, 0, 0, 0, 81], 'euler31': [1, 0, 1922, 0, 923521], 'euler37': [1, 94, 4418, 128686, 1874161], 'euler41': [1, -160, 9762, -268960, 2825761], 'euler43': [1, 0, 0, 0, 3418801], 'euler47': [1, 0, 0, 0, 4879681], 'euler5': [1, 8, 25, 0, 0], 'euler53': [1, -34, 578, -95506, 7890481], 'euler59': [1, 0, -6962, 0, 12117361], 'euler61': [1, -240, 21842, -893040, 13845841], 'euler67': [1, 0, 0, 0, 20151121], 'euler7': [1, 0, 0, 0, 2401], 'euler71': [1, 0, 10082, 0, 25411681], 'euler73': [1, 206, 21218, 1097774, 28398241], 'euler79': [1, 0, -12482, 0, 38950081], 'euler83': [1, 0, 0, 0, 47458321], 'euler89': [1, 0, 9758, 0, 62742241], 'euler97': [1, 14, 98, 131726, 88529281], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 81], [1, 8, 25, 0, 0], [1, 0, 0, 0, 2401], [1, 0, 242, 0, 14641], [1, 34, 578, 5746, 28561], [1, -14, 98, -4046, 83521], [1, 0, -722, 0, 130321], [1, 0, 0, 0, 279841], [1, 0, -82, 0, 707281], [1, 0, 1922, 0, 923521], [1, 94, 4418, 128686, 1874161], [1, -160, 9762, -268960, 2825761], [1, 0, 0, 0, 3418801], [1, 0, 0, 0, 4879681], [1, -34, 578, -95506, 7890481], [1, 0, -6962, 0, 12117361], [1, -240, 21842, -893040, 13845841], [1, 0, 0, 0, 20151121], [1, 0, 10082, 0, 25411681], [1, 206, 21218, 1097774, 28398241], [1, 0, -12482, 0, 38950081], [1, 0, 0, 0, 47458321], [1, 0, 9758, 0, 62742241], [1, 14, 98, 131726, 88529281]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/160/3/p/a'], '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': '4-160e2-1.1-c2e2-0-0', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2, 2], 'order_of_vanishing': 0, 'prelabel': '4-160e2-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.0879856871551468, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c2e2-0', 'trace_hash': 1437706449950834013, 'z1': {'__RealLiteral__': 0, 'data': '0.56241810294793935787052276502', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '712949645781177442794902313724,2940272121576651807420246833342', 'Lhash_array': ['712949645781177442794902313724', '2940272121576651807420246833342'], 'label': '4-160e2-1.1-c2e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/160/3/p/a'}