-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2016492088685378981231668207609', 'a10': [-3.0, 0.0], 'a2': [1.0, 0.0], 'a3': [0.0, 0.0], 'a4': [1.0, 0.0], 'a5': [-3.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [1.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 24.290492294873506, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 13], 'central_character': '3042.1', 'coefficient_field': 'CDF', 'conductor': 3042, 'conductor_radical': 78, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.0, 0], [5.0, 0]], [[1.0, 0], [0, 0], [7.0, 0]], [[1.0, 0], [0, 0], [11.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-5.196152422706632, 0], [17.0, 0]], [[1.0, 0], [6.928203230275509, 0], [19.0, 0]], [[1.0, 0], [0, 0], [23.0, 0]], [[1.0, 0], [5.196152422706632, 0], [29.0, 0]], [[1.0, 0], [-6.928203230275509, 0], [31.0, 0]], [[1.0, 0], [-1.7320508075688772, 0], [37.0, 0]], [[1.0, 0], [9.0, 0], [41.0, 0]], [[1.0, 0], [-4.0, 0], [43.0, 0]], [[1.0, 0], [12.0, 0], [47.0, 0]], [[1.0, 0], [5.196152422706632, 0], [53.0, 0]], [[1.0, 0], [12.0, 0], [59.0, 0]], [[1.0, 0], [5.0, 0], [61.0, 0]], [[1.0, 0], [-13.856406460551018, 0], [67.0, 0]], [[1.0, 0], [12.0, 0], [71.0, 0]], [[1.0, 0], [8.660254037844387, 0], [73.0, 0]], [[1.0, 0], [-4.0, 0], [79.0, 0]], [[1.0, 0], [12.0, 0], [83.0, 0]], [[1.0, 0], [-6.0, 0], [89.0, 0]], [[1.0, 0], [-13.856406460551018, 0], [97.0, 0]], [[1.0, 0], [-5.196152422706632, 0], [101.0, 0]], [[1.0, 0], [-4.0, 0], [103.0, 0]], [[1.0, 0], [0, 0], [107.0, 0]], [[1.0, 0], [6.928203230275509, 0], [109.0, 0]], [[1.0, 0], [15.588457268119896, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 52, 'label': '2-3042-1.1-c1-0-52', '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/3042/2/a/u/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-1.5654772808369435e-60, 0.19790365260963516, 0.39545373358965835, 0.5922568698722094, 0.7878420939244462, 0.9816269291431372, 1.1728889660890214, 1.3607441992377367, 1.5441330075219926, 1.7218142726565384, 1.8923677703689878, 2.0542046630412485, 2.205585677438475, 2.344646367138876, 2.4694287276031455, 2.5779183404049753, 2.668086159227072, 2.7379340026583088, 2.785542779303968, 2.8091224341915417, 2.8070625699325067, 2.7779826621353907, 2.7207807585783397, 2.63467952926728, 2.5192685239702786, 2.3745414994995784, 2.2009277050273437, 1.999316063648092, 1.7710712650700458, 1.5180408896602884, 1.2425528190125739, 0.9474023526095512, 0.6358286427635125, 0.3114802784765243, -0.021629910300225395, -0.35918049782014716, -0.6966069558336274, -1.0291761166426352, -1.3520684515276251, -1.6604667429140816, -1.9496494782451648, -2.2150870682132062, -2.452538799959877, -2.658148284952531, -2.8285350587758122, -2.960879942494169, -3.0530017878898255, -3.103423305757529, -3.1114238199592714, -3.0770770007526926, -3.00127190771996, -2.8857160121162315, -2.7329192652148655, -2.5461587257559684, -2.3294237464053205, -2.08734223484012, -1.8250890366867627, -1.5482780206693665, -1.2628399655933984, -0.9748888381817582, -0.6905794941385984, -0.41596021631263386, -0.15682380849452834, 0.081438822377582, 0.2939785507002004, 0.47661733773468196, 0.6259630296370382, 0.7395059575411017, 0.8156940079869418, 0.8539833072057514, 0.8548622464291039, 0.8198472555618029, 0.7514494935807471, 0.6531124467659686, 0.5291212881385251, 0.3844857285453251, 0.22479895508415734, 0.05607607826850878, -0.11542373252770975, -0.2833865826295619, -0.44163926953636246, -0.5843450009886368, -0.7061933961097253, -0.802578697575847, -0.869760258470365, -0.9049996982839532, -0.9066696471256246, -0.8743297078211518, -0.8087661478261382, -0.7119928659443052, -0.5872123357862569, -0.4387364762785768, -0.2718687021752627, -0.09274972357937908, 0.09182905038706596, 0.2746394368871699, 0.44825157353330713, 0.6052830887826061, 0.7386545228973361, 0.8418426740120873, 0.9091233046501106, 0.9357946850644537, 0.9183737819018888, 0.8547575251482878, 0.7443424942320866, 0.5880975363389097, 0.38858523708157217, 0.14992976673401442, -0.12226962334226983, -0.4210783346860257, -0.7384163894237661, -1.06529378972275, -1.392084680339587, -1.708832143136599, -2.005574097053039, -2.272679706087293, -2.501184960999471, -2.6831157373962617, -2.811786671507964, -2.8820646498318303, -2.89058657990532, -2.8359223816349943, -2.718675781411205, -2.5415174594264207, -2.309147335122768, -2.0281852052449723, -1.7069914921990892, -1.35542242845351, -0.9845265022128382, -0.6061913260076415, -0.2327521709478123, 0.1234248511596615, 0.4503706547853558, 0.7369369557442845, 0.9732005069134514, 1.150832602729583, 1.2634194886409802, 1.3067207014173476, 1.2788542851533053, 1.1804002221277212, 1.0144162134833115, 0.7863630499819576, 0.5039401206452608, 0.17683499798355845, -0.1836056137283006, -0.5647731054783666, -0.9532490290289202, -1.3352962094051606, -1.6973711871461659, -2.0266389682165165, -2.311470446380275, -2.5419029880598587, -2.710045552589978, -2.810411351733609, -2.8401633921204077, -2.79926122449455, -2.6905007483883256, -2.5194428694178495, -2.2942310373546584, -2.0253020490479816, -1.724998813506696, -1.4070978754373846, -1.0862682095249099, -0.7774809716457638, -0.49539238230836374, -0.2537236018738871, -0.06466224475404371, 0.06168998803444679, 0.1178002242837163, 0.09909665778358853, 0.0042518950686412935, -0.16465697352740583, -0.40212145299421886, -0.699312713643441, -1.0443301227323931, -1.4225812084920084, -1.8172816149862463, -2.2100585020958974, -2.581636263630457, -2.912579577804696, -3.1840658441479985, -3.3786571438697113, -3.481041092862689, -3.478710400010513, -3.362552612574837, -3.1273243896791496, -2.7719886090047603, -2.2998975478464976, -1.718811111223016, -1.0407453930093133, -0.2816535077556208, 0.5390526425040995, 1.3991244737819752, 2.2742214470227595, 3.1387518360726383, 3.9667785911237328, 4.732956151115932, 5.413462178769947, 5.986887738449668, 6.435050457987367, 6.743697698478378, 6.903070626929377, 6.908305211833793, 6.759652352100829, 6.462506367467834, 6.027238646151094, 5.4688410569691985, 4.806391466269151, 4.062361029756905, 3.261789542026512, 2.4313607333504867, 1.5984137531503866, 0.7899299709632587, 0.031535516226964336, -0.65344040818855, -1.2448134721345032, -1.7262641403572214, -2.085900446242396, -2.316640923937486, -2.416402446498788, -2.3880858580193665, -2.2393607825981654, -1.9822594775392581, -1.632597703107597, -1.2092479493848944, -0.7332966633150384, -0.22712207024391753, 0.2865674447882607, 0.7856928011499736, 1.249720134061638, 1.660493782562188, 2.002950762613395, 2.2656865074531813, 2.441348392975809, 2.5268413676846917, 2.5233385270926285, 2.436098327601142, 2.274098922142482, 2.0495084158279937, 1.7770172991372497, 1.4730655695488513, 1.1550018035311511, 0.8402144603735705, 0.545276837211334, 0.2851462874286698, 0.07245558999215217, -0.08307016653511062, -0.17504393999803722, -0.2006745164009062, -0.16084029960579027, -0.05997665667874116, 0.09421652621149787, 0.29123161163484185, 0.5183507503168763, 0.7613536748778588, 1.0052997334459222, 1.2353443980149565], 'positive_zeros': ['1.59073177445135688052121487724376', '2.93657157978365226984459472846104', '3.62470125974034823452427526504595', '4.38298962523770002752781485058763', '5.04208262510933275150718684135076', '6.12402114764985458034363130796607', '6.72656485044841777917526710777940', '7.80217389174266032176109521013951', '7.970240796448642570782047959670992'], 'prelabel': '2-3042-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.928538555684992, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.59073177445135688052121487724', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.93657157978365226984459472846', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.62470125974034823452427526505', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 24.290492294873506, 'bad_primes': [2, 3, 13], 'central_character': '1.1', 'conductor': 3042, 'conductor_radical': 78, 'degree': 2, 'index': 52, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3042/2/a/u/1/2'], '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': '2-3042-1.1-c1-0-52', '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': '2-3042-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.928538555684992, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.59073177445135688052121487724', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2016492088685378981231668207609', 'Lhash_array': ['2016492088685378981231668207609'], 'label': '2-3042-1.1-c1-0-52', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3042/2/a/u/1/2'}