-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2210930610733681280792476383373', 'a10': -2, 'a2': 1, 'a3': 0, 'a4': 1, 'a5': -2, 'a6': 0, 'a7': -1, 'a8': 1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.116186243894532, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1]], [7, [1, 1]], [19, [1, 1]]], 'bad_primes': [2, 3, 7, 19], 'central_character': '2394.1', 'coefficient_field': '1.1.1.1', 'conductor': 2394, 'conductor_radical': 798, 'degree': 2, 'euler_factors': [[1, -1], [1], [1, 2, 5], [1, 1], [1, 0, 11], [1, -2, 13], [1, 2, 17], [1, 1], [1, 8, 23], [1, 2, 29], [1, -4, 31], [1, -2, 37], [1, 6, 41], [1, 12, 43], [1, -8, 47], [1, 10, 53], [1, -4, 59], [1, 10, 61], [1, -4, 67], [1, 8, 71], [1, -10, 73], [1, 4, 79], [1, 0, 83], [1, 6, 89], [1, 6, 97], [1, 10, 101], [1, 4, 103], [1, 12, 107], [1, 6, 109], [1, 6, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [1], [[[1, 2, 5], 1]], [[[1, 1], 1]], [[[1, 0, 11], 1]], [[[1, -2, 13], 1]], [[[1, 2, 17], 1]], [[[1, 1], 1]], [[[1, 8, 23], 1]], [[[1, 2, 29], 1]], [[[1, -4, 31], 1]], [[[1, -2, 37], 1]], [[[1, 6, 41], 1]], [[[1, 12, 43], 1]], [[[1, -8, 47], 1]], [[[1, 10, 53], 1]], [[[1, -4, 59], 1]], [[[1, 10, 61], 1]], [[[1, -4, 67], 1]], [[[1, 8, 71], 1]], [[[1, -10, 73], 1]], [[[1, 4, 79], 1]], [[[1, 0, 83], 1]], [[[1, 6, 89], 1]], [[[1, 6, 97], 1]], [[[1, 10, 101], 1]], [[[1, 4, 103], 1]], [[[1, 12, 107], 1]], [[[1, 6, 109], 1]], [[[1, 6, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 40, 'label': '2-2394-1.1-c1-0-40', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/2394/2/a/h', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.678512519282468e-60, 0.20700166000317255, 0.4138630237616674, 0.6203893078685687, 0.8262796970594167, 1.0310814462093587, 1.2341518961704476, 1.434630102997271, 1.6314191620744563, 1.8231797141401278, 2.008334603643727, 2.1850842502282624, 2.351431996030798, 2.5052184914332845, 2.6441640562596107, 2.7659178759949845, 2.8681128400551748, 2.9484247840241, 3.0046348495592863, 3.0346936202085177, 3.0367856297545464, 3.0093927766874065, 2.9513551210713307, 2.861927496603029, 2.7408303493993866, 2.5882932238389498, 2.4050893614395212, 2.1925599667581466, 1.9526268285303636, 1.6877921668418225, 1.4011248082919787, 1.0962320691702052, 0.7772170479587261, 0.4486213874012363, 0.115353955456555, -0.21739369552834564, -0.5442438119294346, -0.8597391665477392, -1.1584579301171007, -1.4351342116528705, -1.6847814614817624, -1.9028156564653829, -2.085174982681471, -2.2284326086955653, -2.3298991128993376, -2.387711199394981, -2.4009035141187507, -2.369460658829324, -2.2943468943649545, -2.1775115216939134, -2.0218685214684897, -1.8312497079711834, -1.6103313957542447, -1.3645353677257555, -1.0999057496882805, -0.8229642136395393, -0.5405467239022733, -0.25962577870516745, 0.012877242644488703, 0.27028446741903117, 0.5063530762785465, 0.7154601732104595, 0.8927750566274432, 1.0344130719420541, 1.1375655247508822, 1.2006006310954769, 1.2231311723260894, 1.206045394986363, 1.151498731813614, 1.062865092400378, 0.9446477487865649, 0.8023511839973309, 0.6423166373204292, 0.4715254224580603, 0.29737536511593227, 0.1274368562766042, -0.030804001059905908, -0.170206904633101, -0.2842347601931438, -0.36719798378905566, -0.4144767721096592, -0.42271280717388127, -0.3899625782844594, -0.3158055349363935, -0.20140160792091719, -0.04949421868942127, 0.13564330591397905, 0.34831804074952233, 0.5815825687440679, 0.8274508917522895, 1.0771591328409402, 1.3214631308565998, 1.5509633517761556, 1.756446148181707, 1.92922935470867, 2.061499569921423, 2.1466282874175358, 2.1794543294858926, 2.1565208166288645, 2.0762561684616823, 1.9390903494494351, 1.7474997009560662, 1.505976175084041, 1.2209195248967213, 0.9004539145157908, 0.5541733845919108, 0.1928235294301999, -0.1720705061340398, -0.5286171357410988, -0.8649979018965679, -1.1699172890930027, -1.4330455672807327, -1.6454371048463559, -1.7999069286951805, -1.8913493499208833, -1.9169842044567464, -1.876518637798757, -1.7722153216463896, -1.608861431450785, -1.3936365165256495, -1.1358814174092267, -0.8467744720827495, -0.5389252374910812, -0.22589966667689132, 0.07830604012147682, 0.3598230035049169, 0.6054767815624845, 0.803341036617802, 0.9432545412665512, 1.0172790610440343, 1.0200773655327815, 0.9491932656116988, 0.8052190758757326, 0.5918401424382175, 0.31575090546256745, -0.013557800372245502, -0.38413507364674926, -0.782019365730888, -1.1917853133191083, -1.5971676537054578, -1.9817379499072685, -2.329606814904964, -2.626122355376418, -2.858534779314943, -3.0165976054892867, -3.093077699930302, -3.0841494138931242, -2.9896523209012047, -2.813197304539425, -2.562111839992054, -2.2472220032740826, -1.8824757599109492, -1.4844191323992293, -1.0715436140756038, -0.6635293783767403, -0.2804141344598842, 0.05827836074740891, 0.33441332950255914, 0.5320854731549154, 0.6383872560681136, 0.6440693361158913, 0.5440611920462795, 0.3378252090866306, 0.02952403344100191, -0.3720113576313137, -0.8535170092283574, -1.3977300658651441, -1.9840079925891139, -2.589110837593111, -3.1881166611900458, -3.7554336052423074, -4.265866879621196, -4.695695472965796, -5.023711857949902, -5.232178477952032, -5.307657403299965, -5.2416741671630165, -5.031183275082987, -4.678810979425666, -4.192860291011691, -3.58707346719956, -2.8801579198216434, -2.095092147030249, -1.258238419738418, -0.39829806820878105, 0.45484712460451504, 1.2713580937121383, 2.0226732207195206, 2.682700297307132, 3.2289125506940595, 3.643299169653936, 3.9131267197936594, 4.031475889976995, 3.997527827751691, 3.8165854695801156, 3.499827248810662, 3.063802818611422, 2.5296923827977777, 1.922362312611129, 1.2692594016013279, 0.5991938919091416, -0.05893310525535412, -0.677399268586195, -1.2308691345661777, -1.6974845605949949, -2.0597869330370333, -2.3054283109430145, -2.42763866100637, -2.4254279639113685, -2.3035147039106345, -2.071985476831842, -1.745703518412458, -1.3434962156289583, -0.8871625010269653, -0.40034988996836257, 0.09264265822161728, 0.5680762358989886, 1.0039373716564262, 1.3809992345062028, 1.6837259367598012, 1.9009752631919803, 2.026465511584183, 2.05898428159439, 2.0023303818603475, 1.8649938579345102, 1.6595927611126036, 1.4020979688288946, 1.1108884601430837, 0.8056883506248492, 0.5064432143793308, 0.23219641802997637, 2.6169850882407488e-05, -0.1758992762973343, -0.285097178521589, -0.3213346739520297, -0.2829514416821993, -0.1729232945109807, 0.0013365102841520315, 0.22842704277197778, 0.49363547963062515, 0.779801232452838, 1.0683201774100555, 1.3402327426976115, 1.5773346719010795, 1.7632477023231508, 1.8843892973734735, 1.9307858804993636, 1.8966824742799924, 1.7809128136478718, 1.5870072818738414, 1.3230306915915047, 1.0011571931905139, 0.6370045884598069, 0.2487642111360358, -0.1438254880252781, -0.5206041451394777, -0.8621497692808414], 'positive_zeros': ['1.74411672296421629506581859943858', '2.94285784851423154213390802202005', '3.84907283320357724315521311958797', '4.33084839581572636702073752348539', '5.40960412801561297413267643753040', '6.28352954329121793129107491158166', '6.85350902861062329638401661290531', '7.912508640806354969373892342739876', '8.281501563887625996464501642974443'], 'prelabel': '2-2394-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.372206107206582, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 412399085643671991, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.74411672296421629506581859944', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.94285784851423154213390802202', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.84907283320357724315521311959', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 19.116186243894532, 'bad_primes': [2, 3, 7, 19], 'central_character': '1.1', 'conductor': 2394, 'conductor_radical': 798, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, 1, -2, 0, -1, 1, 0, -2, 0, 0, 2, -1, 0, 1, -2, 0, -1, -2, 0, 0, -8, 0, -1, 2, 0, -1, -2, 0, 4, 1, 0, -2, 2, 0, 2, -1, 0, -2, -6, 0, -12, 0, 0, -8, 8, 0, 1, -1, 0, 2, -10, 0, 0, -1, 0, -2, 4, 0, -10, 4, 0, 1, -4, 0, 4, -2, 0, 2, -8, 0, 10, 2, 0, -1, 0, 0, -4, -2, 0, -6, 0, 0, 4, -12, 0, 0, -6, 0, -2, -8, 0, 8, 2, 0, -6, 1, 0, -1], 'euler11': [1, 0, 11], 'euler13': [1, -2, 13], 'euler17': [1, 2, 17], 'euler19': [1, 1, 0], 'euler2': [1, -1, 0], 'euler23': [1, 8, 23], 'euler29': [1, 2, 29], 'euler3': [1, 0, 0], 'euler31': [1, -4, 31], 'euler37': [1, -2, 37], 'euler41': [1, 6, 41], 'euler43': [1, 12, 43], 'euler47': [1, -8, 47], 'euler5': [1, 2, 5], 'euler53': [1, 10, 53], 'euler59': [1, -4, 59], 'euler61': [1, 10, 61], 'euler67': [1, -4, 67], 'euler7': [1, 1, 0], 'euler71': [1, 8, 71], 'euler73': [1, -10, 73], 'euler79': [1, 4, 79], 'euler83': [1, 0, 83], 'euler89': [1, 6, 89], 'euler97': [1, 6, 97], 'euler_factors': [[1, -1, 0], [1, 0, 0], [1, 2, 5], [1, 1, 0], [1, 0, 11], [1, -2, 13], [1, 2, 17], [1, 1, 0], [1, 8, 23], [1, 2, 29], [1, -4, 31], [1, -2, 37], [1, 6, 41], [1, 12, 43], [1, -8, 47], [1, 10, 53], [1, -4, 59], [1, 10, 61], [1, -4, 67], [1, 8, 71], [1, -10, 73], [1, 4, 79], [1, 0, 83], [1, 6, 89], [1, 6, 97]], 'index': 40, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/2394/h', 'ModularForm/GL2/Q/holomorphic/2394/2/a/h/1/1', 'ModularForm/GL2/Q/holomorphic/2394/2/a/h'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-2394-1.1-c1-0-40', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-2394-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.372206107206582, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 412399085643671991, 'z1': {'__RealLiteral__': 0, 'data': '1.74411672296421629506581859944', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 20620191
{'Lhash': '2210930610733681280792476383373', 'Lhash_array': ['2210930610733681280792476383373'], 'label': '2-2394-1.1-c1-0-40', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2394/2/a/h'}
-
id: 24557005
{'Lhash': '2210930610733681280792476383373', 'Lhash_array': ['2210930610733681280792476383373'], 'label': '2-2394-1.1-c1-0-40', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2394/2/a/h/1/1'}
-
id: 99197
{'Lhash': '412399085643671991', 'Lhash_array': ['412399085643671991'], 'label': '2-2394-1.1-c1-0-40', 'type': 'ECQ', 'url': 'EllipticCurve/Q/2394/h'}