-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': -4, 'A4': -4, 'A5': -6, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 6, 'Lhash': '1179168559984707758,1510806314696843907', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-2.309401076758503, 0], 'a4': [-2.0, 0], 'a5': [-2.6832815729997477, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [2.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 63.88845252452729, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [1, 0, -1]], [11, [1, 0, 11]], [13, [1, 0, -1]]], 'bad_primes': [7, 11, 13], 'central_character': '1002001.1', 'coefficient_field': '1.1.1.1', 'conductor': 1002001, 'conductor_radical': 1001, 'degree': 4, 'euler_factors': [[1, 0, 4, 0, 4], [1, 4, 10, 12, 9], [1, 6, 19, 30, 25], [1, 0, -1], [1, 0, 11], [1, 0, -1], [1, 0, -2, 0, 289], [1, 0, -11, 0, 361], [1, -6, 55, -138, 529], [1, 0, -23, 0, 841], [1, -10, 87, -310, 961], [1, -4, 78, -148, 1369], [1, 0, 46, 0, 1681], [1, 0, 85, 0, 1849], [1, -6, 103, -282, 2209], [1, 18, 187, 954, 2809], [1, 0, 118, 0, 3481], [1, 0, 22, 0, 3721], [1, -28, 330, -1876, 4489], [1, 12, 178, 852, 5041], [1, 0, 25, 0, 5329], [1, 0, 157, 0, 6241], [1, 0, 157, 0, 6889], [1, -30, 403, -2670, 7921], [1, 2, 195, 194, 9409], [1, 0, 202, 0, 10201], [1, 8, 222, 824, 10609], [1, 0, 70, 0, 11449], [1, 0, -38, 0, 11881], [1, -18, 307, -2034, 12769]], 'gamma_factors': [[], [0, 0]], 'index': 2, 'label': '4-1001e2-1.1-c1e2-0-2', 'load_key': 'Costa', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 1, 'origin': 'EllipticCurve/2.0.11.1/8281.1/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.048828125', 'prec': 37}, 'plot_values': [5.797034737303797e-75, 0.030174599860755446, 0.05925880684142756, 0.08616059888992691, 0.1097903689302604, 0.12907607216159245, 0.1429944136647274, 0.15062226171163132, 0.15121145009481554, 0.14428883188614045, 0.12978186642871523, 0.1081681732206274, 0.08064540123765725, 0.04931549399006492, 0.017375060023257585, -0.01069880451867638, -0.028980111584078167, -0.029957771642036914, -0.0044477660414966366, 0.05842939193681364, 0.17118916669098974, 0.34782597022779504, 0.6035455219948497, 0.9543772719505862, 1.4166626326193852, 2.0064211058230583, 2.7386038367526364, 3.6262524136595355, 4.679589477491965, 5.90507643033208, 7.304481664010399, 8.874009636602763, 10.603546141139063, 12.47607758785161, 14.467341471981893, 16.545760953741784, 18.672708336640166, 20.803130117438972, 22.886550380985426, 24.868450103279947, 26.691998186187398, 28.30008684897959, 29.637600674453882, 30.653826677069993, 31.304893866855796, 31.55611657288748, 31.38410779740711, 30.778528386118555, 29.743345739621756, 28.297492583420723, 26.47484180343948, 24.323446739458415, 21.90403614667976, 19.287797192348744, 16.553525714108964, 13.784267492519366, 11.063614234156258, 8.471850095155457, 6.08216594230361, 3.9571667277501112, 2.145890700374421, 0.6815370333409548, -0.4199387131108426, -1.1602523793381243, -1.558194333765952, -1.6480276421913111, -1.4769704975022504, -1.1019183485026398, -0.5856187870226729, 0.007443696345914532, 0.6151696863019341, 1.1816846094777853, 1.6606240321258385, 2.0176307928645723, 2.2318885347928217, 2.296590151712151, 2.2183237236445894, 2.0154459275773817, 1.7155962655002561, 1.3525773369232337, 0.96288004988552, 0.5821627006737152, 0.24199576619619867, -0.03284108550780784, -0.22627537599162542, -0.3319120017805267, -0.3529886829692929, -0.30134711146041404, -0.19554769642768477, -0.05834203921936171, 0.08621672841156085, 0.21570718940274128, 0.31199192728310743, 0.3632924601080828, 0.3654509368865486, 0.32223029873810055, 0.24461086797978168, 0.14915544735814493, 0.0556247937440191, -0.01588155568545005, -0.047918810909429135, -0.028455632075067117, 0.046958587723169756, 0.1739197474361926, 0.3389974808995036, 0.5207528888144398, 0.6918932022249814, 0.8223699642380803, 0.8831007345419475, 0.8498978578846071, 0.7071346447408381, 0.450678368480553, 0.0896742790675605, -0.35312740080292104, -0.8426579253715409, -1.334405763443867, -1.7786671465464703, -2.1257785822473503, -2.331793824362621, -2.3639761112372892, -2.2054521552678166, -1.8584248306738897, -1.345465923262224, -0.7085990945865185, -0.006118588461725116, 0.6926532724030341, 1.314215746360672, 1.7886777110096312, 2.057664280919641, 2.081456571690775, 1.8445119243661054, 1.3586452463578345, 0.6633765482509557, -0.17675558063810487, -1.077780294015179, -1.9443088456168363, -2.6792041062178718, -3.193904918151379, -3.418281795553529, -3.3089014741750042, -2.8547091421251105, -2.0793897866374946, -1.0400199579907339, 0.17796848735133378, 1.4690663735051812, 2.7183713077074443, 3.8135363114469487, 4.656658834613041, 5.174753756006739, 5.32758181536007, 5.11188352226282, 4.561469757317933, 3.7430996094709634, 2.7485776392977783, 1.6839659070726354, 0.6571723618579112, -0.23460198822284606, -0.9160314721398639, -1.3420694516338978, -1.5025286762678673, -1.4222423670086104, -1.1567595180717412, -0.7840966535153017, -0.39358409760331964, -0.07323973140333606, 0.10267753798945661, 0.08427266291708131, -0.14667659657074072, -0.5737562846412696, -1.1477932077687276, -1.7934302833018383, -2.4196211689827125, -2.932711958354286, -3.2503850245684096, -3.314565598902593, -3.1014662352695272, -2.6272667088527593, -1.948462762478901, -1.1566022997011793, -0.3678756723033172, 0.2912603746462019, 0.7006645557405895, 0.7631716496848744, 0.4191094496901309, -0.343352336969915, -1.4835706814968597, -2.910367042996392, -4.490551553548705, -6.063186397797775, -7.45796153170411, -8.515467416513472, -9.106836140475949, -9.150233480370728, -8.622027100634508, -7.5610927243482084, -6.065572716898751, -4.2823611275060705, -2.3905300229698145, -0.58070806567468, 0.9670349454177776, 2.1040306876630765, 2.729964359727337, 2.8038138306148355, 2.347431684142864, 1.4413839274976787, 0.21366844716870428, -1.1771396810920638, -2.5620559629794735, -3.782502586107366, -4.709066428081516, -5.255818131349174, -5.388457054909042, -5.1254204708296225, -4.532072671302862, -3.709032228893559, -2.7764706748732495, -1.8567153567196817, -1.0576458063817742, -0.45916958772580446, -0.10453608859248581, 0.002521755831834216, -0.10528072610647309, -0.36699374024981063, -0.7052758837900672, -1.0398658046478966, -1.3005191801055698, -1.4374231543259663, -1.4275804678706345, -1.2763585491467917, -1.0142091318081616, -0.6893500794660304, -0.35783682493369356, -0.07283538551252738, 0.1250168220934956, 0.21452004961362323, 0.19696623322708567, 0.09491388227170007, -0.05297644718681254, -0.20001080393834464, -0.3008917524056098, -0.32073522887993827, -0.24198587825439094, -0.06793214737957752, 0.17785043419840854, 0.45604378168230963, 0.7192850559001829, 0.9215729824273533, 1.027581546775262, 1.0200487127143594, 0.9037171987711219, 0.7049093626957306, 0.4666193865789103, 0.23986476143124283, 0.07280103424854938, -0.00037502475217676283, 0.03146426072459003, 0.15122601356937757], 'positive_zeros': ['0.71239963936312711175952583959483', '0.883826827840201941525555392848830', '3.00675363687601775920051816087812', '3.36854503826664578071054317861704', '4.04609643315305459582542236808309', '4.36526056113723032255916840173782', '4.82094210358198316082444203410440', '4.95454046107923865998450494115930', '5.47928828118502604201716906159494', '6.05510665689561164799845565622900', '6.48432181419363077598714474935585', '6.97556725662558611504386870793484', '7.60332298682950357021318080506777', '8.023034081311283559976527256532836'], 'prelabel': '4-1001e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.827193881277011, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 384131865467857714, 'z1': {'__RealLiteral__': 0, 'data': '0.71239963936312711175952583959483', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '0.883826827840201941525555392848830', 'prec': 117}, 'z3': {'__RealLiteral__': 0, 'data': '3.00675363687601775920051816087812', 'prec': 113}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 63.88845252452729, 'bad_primes': [7, 11, 13], 'central_character': '1.1', 'conductor': 1002001, 'conductor_radical': 1001, 'degree': 4, 'dirichlet_coefficients': [1, 0, -4, -4, -6, 0, 0, 0, 6, 0, 0, 16, 0, 0, 24, 12, 0, 0, 0, 24, 0, 0, 6, 0, 17, 0, 4, 0, 0, 0, 10, 0, 0, 0, 0, -24, 4, 0, 0, 0, 0, 0, 0, 0, -36, 0, 6, -48, 1, 0, 0, 0, -18, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, -32, 0, 0, 28, 0, -24, 0, -12, 0, 0, 0, -68, 0, 0, 0, 0, -72, -37, 0, 0, 0, 0, 0, 0, 0, 30, 0, 0, -24, -40, 0, 0, 0, -2, 0, 0, -68], 'euler11': [1, 0, 11, 0, 0], 'euler13': [1, 0, -1, 0, 0], 'euler17': [1, 0, -2, 0, 289], 'euler19': [1, 0, -11, 0, 361], 'euler2': [1, 0, 4, 0, 4], 'euler23': [1, -6, 55, -138, 529], 'euler29': [1, 0, -23, 0, 841], 'euler3': [1, 4, 10, 12, 9], 'euler31': [1, -10, 87, -310, 961], 'euler37': [1, -4, 78, -148, 1369], 'euler41': [1, 0, 46, 0, 1681], 'euler43': [1, 0, 85, 0, 1849], 'euler47': [1, -6, 103, -282, 2209], 'euler5': [1, 6, 19, 30, 25], 'euler53': [1, 18, 187, 954, 2809], 'euler59': [1, 0, 118, 0, 3481], 'euler61': [1, 0, 22, 0, 3721], 'euler67': [1, -28, 330, -1876, 4489], 'euler7': [1, 0, -1, 0, 0], 'euler71': [1, 12, 178, 852, 5041], 'euler73': [1, 0, 25, 0, 5329], 'euler79': [1, 0, 157, 0, 6241], 'euler83': [1, 0, 157, 0, 6889], 'euler89': [1, -30, 403, -2670, 7921], 'euler97': [1, 2, 195, 194, 9409], 'euler_factors': [[1, 0, 4, 0, 4], [1, 4, 10, 12, 9], [1, 6, 19, 30, 25], [1, 0, -1, 0, 0], [1, 0, 11, 0, 0], [1, 0, -1, 0, 0], [1, 0, -2, 0, 289], [1, 0, -11, 0, 361], [1, -6, 55, -138, 529], [1, 0, -23, 0, 841], [1, -10, 87, -310, 961], [1, -4, 78, -148, 1369], [1, 0, 46, 0, 1681], [1, 0, 85, 0, 1849], [1, -6, 103, -282, 2209], [1, 18, 187, 954, 2809], [1, 0, 118, 0, 3481], [1, 0, 22, 0, 3721], [1, -28, 330, -1876, 4489], [1, 12, 178, 852, 5041], [1, 0, 25, 0, 5329], [1, 0, 157, 0, 6241], [1, 0, 157, 0, 6889], [1, -30, 403, -2670, 7921], [1, 2, 195, 194, 9409]], 'index': 2, 'instance_types': ['BMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/8281.1/a', 'EllipticCurve/2.0.11.1/8281.1/a'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, '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': '4-1001e2-1.1-c1e2-0-2', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 1, 'prelabel': '4-1001e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.827193881277011, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 384131865467857714, 'z1': {'__RealLiteral__': 0, 'data': '0.71239963936312711175952583959483', 'prec': 113}}
-
lfunc_instances • Show schema
Hide schema
-
id: 9947872
{'Lhash': '1179168559984707758,1510806314696843907', 'Lhash_array': ['1179168559984707758', '1510806314696843907'], 'label': '4-1001e2-1.1-c1e2-0-2', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.11.1/8281.1/a'}
-
id: 9947657
{'Lhash': '1179168559984707758,1510806314696843907', 'Lhash_array': ['1179168559984707758', '1510806314696843907'], 'label': '4-1001e2-1.1-c1e2-0-2', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/8281.1/a'}