-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2276643760315575513194553271676', 'a10': [2.7580162627198717, 0.0], 'a2': [2.7580162627198717, 0.0], 'a3': [1.4919184254326407, 0.0], 'a4': [5.606653705427288, 0.0], 'a5': [1.0, 0.0], 'a6': [4.114735279994647, 0.0], 'a7': [-2.848637442707416, 0.0], 'a8': [9.947209573567344, 0.0], 'a9': [-0.7741794118545903, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.412997564841117, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 19], 'central_character': '1805.1', 'coefficient_field': 'CDF', 'conductor': 1805, 'conductor_radical': 95, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.7580162627198717, 0], [2.0, 0]], [[1.0, 0], [-1.4919184254326407, 0], [3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [2.848637442707416, 0], [7.0, 0]], [[1.0, 0], [0.8648005918421348, 0], [11.0, 0]], [[1.0, 0], [-0.6432809827252246, 0], [13.0, 0]], [[1.0, 0], [-3.7418531135851527, 0], [17.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.4174603945798149, 0], [23.0, 0]], [[1.0, 0], [9.705225836287216, 0], [29.0, 0]], [[1.0, 0], [-4.933492920019558, 0], [31.0, 0]], [[1.0, 0], [-6.364669968147159, 0], [37.0, 0]], [[1.0, 0], [4.013716653547786, 0], [41.0, 0]], [[1.0, 0], [2.058294881718107, 0], [43.0, 0]], [[1.0, 0], [3.9539570481827764, 0], [47.0, 0]], [[1.0, 0], [10.987486822709165, 0], [53.0, 0]], [[1.0, 0], [-2.4595921271632033, 0], [59.0, 0]], [[1.0, 0], [-6.334790165464654, 0], [61.0, 0]], [[1.0, 0], [2.532195674574462, 0], [67.0, 0]], [[1.0, 0], [1.782130362726974, 0], [71.0, 0]], [[1.0, 0], [7.130898429129366, 0], [73.0, 0]], [[1.0, 0], [-1.8245233427003136, 0], [79.0, 0]], [[1.0, 0], [7.439127998999985, 0], [83.0, 0]], [[1.0, 0], [-4.445875473615417, 0], [89.0, 0]], [[1.0, 0], [10.854141897992868, 0], [97.0, 0]], [[1.0, 0], [5.295977639969736, 0], [101.0, 0]], [[1.0, 0], [0.3851340963103775, 0], [103.0, 0]], [[1.0, 0], [6.4333622963245825, 0], [107.0, 0]], [[1.0, 0], [-6.568822951872399, 0], [109.0, 0]], [[1.0, 0], [-0.294512916322833, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 91, 'label': '2-1805-1.1-c1-0-91', 'leading_term': '7.61655674810523301028577646368', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1805/2/a/o/1/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [7.616556748105233, 7.6148408747121685, 7.609338811762821, 7.599006786992087, 7.582168703803055, 7.556605903521758, 7.5196727654340965, 7.468430075489805, 7.3997880203455715, 7.310651435041157, 7.198061202670584, 7.059327124766154, 6.892148885213341, 6.694722766726637, 6.465832502810021, 6.2049230922083245, 5.912156641273039, 5.588449418858171, 5.23548938776573, 4.855733578994295, 4.452384842961862, 4.029347769645203, 3.591163925572754, 3.1429270057038594, 2.690179028833167, 2.238789295721276, 1.7948184541516803, 1.3643706456703093, 0.953437313995499, 0.5677368033360186, 0.21255433487364872, -0.10741270820011195, -0.3881990593138855, -0.626700253239071, -0.820780714798941, -0.9693566015620889, -1.072449303367753, -1.1312062511810157, -1.1478866216923123, -1.1258106208982503, -1.0692722595596722, -0.9834168576473293, -0.8740858880663029, -0.7476331405086555, -0.6107174983291853, -0.47007881672842056, -0.33230441120612747, -0.2035944558086555, -0.08953510104294046, 0.005111690628503619, 0.07659275961111718, 0.12231452058171198, 0.1409525115595782, 0.1325136207529508, 0.09834650525462699, 0.04109761827976534, -0.03538760971093661, -0.12621661338877815, -0.22565039976383228, -0.3273466658133266, -0.4246367212418557, -0.5108257105854148, -0.5795040804442465, -0.6248571340657082, -0.6419589356565142, -0.6270368308339095, -0.5776934747125773, -0.4930745160034558, -0.37397195598030325, -0.22285563686777154, -0.04382823666145793, 0.15749755033573262, 0.3741974181909154, 0.5983035659260796, 0.8211330818498495, 1.0336638294357834, 1.226942170268778, 1.3925045508600604, 1.5227934087610047, 1.611547140581903, 1.654144106954301, 1.6478818726733577, 1.5921750934133172, 1.4886586132768915, 1.3411863295024757, 1.1557210628149355, 0.9401158507887454, 0.7037925264217201, 0.45732889601927346, 0.21197101389237644, -0.02090831292590462, -0.2303798374167033, -0.4065292908523015, -0.5410006994286382, -0.6274823124954589, -0.6621072794359711, -0.6437441544871335, -0.5741567063866282, -0.4580182197664423, -0.3027722773199384, -0.11833961480014879, 0.08332130619730933, 0.28878425613784453, 0.4838322375012541, 0.654211099825904, 0.7864236163657887, 0.8685237278361733, 0.8908684150608648, 0.8467845456940476, 0.733110180562421, 0.5505742398146911, 0.3039850146922042, 0.0022065417708831796, -0.3420880101186836, -0.712885503546048, -1.0915122074792107, -1.4574991274630416, -1.7895977403916132, -2.0669005513224503, -2.2700127286383545, -2.382215325437194, -2.3905577014445174, -2.2868170335884823, -2.068266403347382, -1.738199862590563, -1.3061729143774656, -0.7879296291288683, -0.20500260893336553, 0.41601147571318364, 1.044480829526699, 1.6470349633124244, 2.189075674578544, 2.636435709001364, 2.957107163506516, 3.1229542168051294, 3.111321468453162, 2.9064504083288085, 2.50062247052932, 1.8949576458456865, 1.099812376876649, 0.13473883393951389, -0.9720111625026531, -2.184431366282261, -3.4601257174377467, -4.752039662010347, -6.010484474489244, -7.18536295638393, -8.228491155591142, -9.095902115449684, -9.75001477469062, -10.161554362944408, -10.311120010302094, -10.1903105144089, -9.802339651030383, -9.162097129193176, -8.295639065984659, -7.239121264959051, -6.037218065141104, -4.741097471229899, -3.406048103161977, -2.088873765990725, -0.8451859049477325, 0.27326806684393457, 1.2211021871979186, 1.9614838547400681, 2.467903386832018, 2.725425431563482, 2.731353081808772, 2.4952663879305796, 2.0384303635723753, 1.3926016875614606, 0.5982962074756407, -0.2973908377060371, -1.2432949783517593, -2.18688750446801, -3.07702854862978, -3.8666185469517393, -4.515003854072179, -4.990006016186747, -5.2694654520794915, -5.342217881909249, -5.208454211955073, -4.879449862181363, -4.376685649247192, -3.730417175192497, -2.9777811433100165, -2.160553234597464, -1.3226915414976073, -0.5078108868870286, 0.24326404422845727, 0.8947251320618232, 1.4176599961735539, 1.7914795244355273, 2.004817998862406, 2.055863122603528, 1.952108672736749, 1.709558056550382, 1.3514404954175712, 0.9065307908011242, 0.40718679913438954, -0.11276559752983004, -0.6201630583730601, -1.084515638306472, -1.4797731278893014, -1.7857405144948164, -1.9890613604526644, -2.083718061082106, -2.0710310723127754, -1.9591730397127736, -1.7622460285543313, -1.4989985686774765, -1.1912820688597752, -0.8623617966114645, -0.5352050343394104, -0.23086775873702367, 0.03290859822890232, 0.24279630705231925, 0.3906064430881252, 0.47359868952732687, 0.4943659324572977, 0.4603153944247425, 0.3827977166215229, 0.2759609045592769, 0.15542553135470472, 0.03688961959581859, -0.06522468212311937, -0.13897541104223546, -0.1758619878412526, -0.17146952863517062, -0.12574849897081228, -0.04291161460233082, 0.06903903588660981, 0.19911161938880856, 0.3343812321851111, 0.461212730315386, 0.5665448565178659, 0.6391252253544095, 0.6705890817138945, 0.656286881127921, 0.5957858077283155, 0.4929968609053417, 0.3559100804614922, 0.19595342661988982, 0.027023158992971617, -0.13573736893279248, -0.27731020542949797, -0.38421065391785647, -0.44580813297505334, -0.45544127362672243, -0.41122206882702345, -0.31644667605841353, -0.179560897790517, -0.013664198820117943, 0.16442537116465814, 0.3354848406978987, 0.4794834051343813, 0.5773395732110277], 'positive_zeros': ['1.79595525762831313268118671784471', '2.86754082881879396300246703029737', '3.25572831647002704529776690324828', '4.11481977160444074387543562783061', '5.26796861619405731763144706432794', '5.89412080158017210107251601799114', '6.56289709165895704729721456629358', '7.46101228642419869243027143209970', '8.210641440477554150810095754989055', '9.477105475227032730908261940951794'], 'prelabel': '2-1805-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7964453854679796, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.79595525762831313268118671784', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.86754082881879396300246703030', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.25572831647002704529776690325', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 14.412997564841117, 'bad_primes': [5, 19], 'central_character': '1.1', 'conductor': 1805, 'conductor_radical': 95, 'degree': 2, 'index': 91, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1805/2/a/o/1/4'], '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': '2-1805-1.1-c1-0-91', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1805-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7964453854679796, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.79595525762831313268118671784', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2276643760315575513194553271676', 'Lhash_array': ['2276643760315575513194553271676'], 'factors': ['2-1805-1.1-c1-0-91'], 'label': '2-1805-1.1-c1-0-91', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1805/2/a/o/1/4'}