-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1524451188256107013574379760725', 'a10': [-1.3427719663353965, -0.4438056403694898], 'a2': [0.635665185148849, 1.2633011408170578], 'a3': [0.7071067811865476, 0.7071067811865476], 'a4': [-1.1918595447793592, 1.6060731071524543], 'a5': [-0.7071067811865476, 0.7071067811865476], 'a6': [-0.4438056403694898, 1.3427719663353965], 'a7': [0.0, 1.4142135623730951], 'a8': [-2.786577606704886, -0.48475276359281166], 'a9': [0.0, 1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.9164096485107303, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.635665185148849, -1.2633011408170578]]], [3, [[1.0, 0], [-0.7071067811865476, -0.7071067811865476]]], [5, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]]], 'bad_primes': [2, 3, 5], 'central_character': '240.61', 'coefficient_field': 'CDF', 'conductor': 240, 'conductor_radical': 30, 'conjugate': '3746400399312973739155712524313', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.635665185148849, -1.2633011408170578]], [[1.0, 0], [-0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0, -1.4142135623730951], [-7.0, 0]], [[1.0, 0], [-1.1123887192610205, 1.1123887192610205], [0, -11.0]], [[1.0, 0], [0.2713303702976979, 0.2713303702976979], [0, 13.0]], [[1.0, 0], [-0.7447280886635824, 0], [17.0, 0]], [[1.0, 0], [-5.212146214304909, -5.212146214304909], [0, 19.0]], [[1.0, 0], [0, 4.767438179117437], [-23.0, 0]], [[1.0, 0], [1.2121462143049084, 1.2121462143049084], [0, 29.0]], [[1.0, 0], [-7.754806954900304, 0], [31.0, 0]], [[1.0, 0], [5.324534933565929, -5.324534933565929], [0, -37.0]], [[1.0, 0], [0, 7.338970947419026], [-41.0, 0]], [[1.0, 0], [-6.785301427714681, 6.785301427714681], [0, -43.0]], [[1.0, 0], [0.7353212611948762, 0], [47.0, 0]], [[1.0, 0], [9.552739606832118, -9.552739606832118], [0, -53.0]], [[1.0, 0], [-1.6229325419338556, 1.6229325419338556], [0, -59.0]], [[1.0, 0], [5.701602391632073, 5.701602391632073], [0, 61.0]], [[1.0, 0], [-5.595865303863627, -5.595865303863627], [0, 67.0]], [[1.0, 0], [0, 8.603649686224148], [-71.0, 0]], [[1.0, 0], [0, 4.2857663841507945], [-73.0, 0]], [[1.0, 0], [1.0126312242171325, 0], [79.0, 0]], [[1.0, 0], [-1.682116697926645, -1.682116697926645], [0, 83.0]], [[1.0, 0], [0, 10.399029980175552], [-89.0, 0]], [[1.0, 0], [16.966953169205212, 0], [97.0, 0]], [[1.0, 0], [5.353224616744342, -5.353224616744342], [0, -101.0]], [[1.0, 0], [0, 10.580681721666084], [-103.0, 0]], [[1.0, 0], [10.742175730683172, -10.742175730683172], [0, -107.0]], [[1.0, 0], [1.4768249531100324, 1.4768249531100324], [0, 109.0]], [[1.0, 0], [-0.4722649674979362, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-240-16.13-c1-0-5', '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/240/2/s/b/61/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.5297406522556767, 1.3890591695970376, 1.259440380770312, 1.1334281343927863, 1.0036282080833514, 0.8635848603618451, 0.7084369022723451, 0.5353543958715714, 0.343803875061181, 0.1356851582149683, -0.08464415260288395, -0.3104657071703454, -0.5329419611179684, -0.7415264937293596, -0.9245583879369927, -1.0700395385951647, -1.1665723019977507, -1.2044107772669814, -1.1765547238167433, -1.0797934593389247, -0.9155910752000851, -0.6906969985337194, -0.4173700586477377, -0.113121795997459, 0.20008334517812762, 0.49718773469652144, 0.7519202169134335, 0.9390921553055784, 1.0371420246135643, 1.0307032662996003, 0.9129277301622317, 0.6872777072186257, 0.3685100520189749, -0.017379490569492638, -0.4344040570593122, -0.8390667172137308, -1.1839813980940255, -1.4223947509314885, -1.5132297580660847, -1.4261551946721152, -1.1461104193499871, -0.6766984775311221, -0.04191335649066385, 0.7142066377702201, 1.530213082988751, 2.3321352777217856, 3.040311030623375, 3.577575614715571, 3.8779886416065117, 3.895117770507922, 3.608842865637654, 3.029715270808835, 2.2001106329423785, 1.1917391436176168, 0.09949494405430612, -0.967908962867055, -1.8996204517658257, -2.5953635943006903, -2.9776655888320436, -3.0020086059323923, -2.6634664835210136, -1.9987422738897171, -1.083058028543034, -0.022003645538388045, 1.0608556475322295, 2.0391798680781377, 2.799951661441666, 3.258319661043914, 3.369090087713966, 3.133129560772264, 2.597579914796886, 1.8496252997133307, 1.0044803239599056, 0.18915005876815946, -0.4757903004552965, -0.8937564202763133, -1.0064104173241903, -0.8023688819524597, -0.31889569193716516, 0.36384523829878795, 1.1352440884195587, 1.8715816489106842, 2.455581682038744, 2.7950720871165866, 2.8377028738888326, 2.5792350704881803, 2.0639209322254413, 1.3767912321695515, 0.6290402109148358, -0.06108254958099652, -0.588622500204586, -0.8799635550099335, -0.9053379581640788, -0.6834892388674598, -0.2775394765028943, 0.21730167845888404, 0.6920237962213118, 1.0447587036670745, 1.200447630859238, 1.1254313556675106, 0.83402570190121, 0.38560966498494936, -0.12743443377557773, -0.5987658848274381, -0.9304750075554468, -1.0543541330587654, -0.9476186341124497, -0.6395720690397633, -0.2073938089616739, 0.23862523340057928, 0.5778701754007277, 0.7058697415242233, 0.5590677044341644, 0.13253108536286767, -0.5136563256980751, -1.261501098222626, -1.9552398957479111, -2.4313068009021954, -2.5526592843621425, -2.2406987373296663, -1.4980248085318835, -0.41664935709689244, 0.8311279188758974, 2.0186642905317984, 2.9037961869837012, 3.273752892697682, 2.9877295672889015, 2.008642608680663, 0.41724687702031854, -1.5950916741976593, -3.7546589386154197, -5.7502353608515255, -7.286620079194027, -8.136930578706409, -8.183667628282365, -7.440430335209667, -6.049747358015209, -4.2570831283091914, -2.365773267931821, -0.6814799559795914, 0.5430764892846982, 1.1523448509779033, 1.112557124309984, 0.5121327695016439, -0.4617738771297253, -1.5653384073128294, -2.549705082232368, -3.2112862610437762, -3.4302697157936275, -3.189588895098245, -2.570982531733411, -1.7298450390473052, -0.8552202949951305, -0.12447454320156122, 0.3368226970482702, 0.4807065515519737, 0.3427294760331087, 0.0271926763820261, -0.32413492218481693, -0.5717017606536873, -0.616176045627043, -0.4251521245473736, -0.041780987965550236, 0.4269256786973437, 0.8392325769157357, 1.0578903638268449, 0.9893439638119781, 0.6126512117841648, -0.009789134007620643, -0.7431452065724192, -1.4106828389387467, -1.8367953955749332, -1.891948441714476, -1.5280761368171647, -0.7949784479107471, 0.16723914366182388, 1.1587226963479302, 1.9665715286472156, 2.4164699941997636, 2.416369698125255, 1.9809011594686345, 1.2297003490537335, 0.3592503846392365, -0.4054062895624382, -0.8673521956555702, -0.9085752987642389, -0.5215582733511357, 0.18713659509260946, 1.023178118234807, 1.7548794317793615, 2.175425060282628, 2.1610419803275493, 1.7096240491146657, 0.9487266600470061, 0.10931568457660197, -0.5296167317227479, -0.7126655793546469, -0.2781449192211792, 0.7914325650288864, 2.352515766444726, 4.123361387364338, 5.742800762726616, 6.851918324169924, 7.179339681262111, 6.6091939650909435, 5.214413883827307, 3.2461178632765724, 1.080460370878671, -0.865093773096463, -2.226303225710349, -2.7747162660401963, -2.4681516354535065, -1.4567268921513912, -0.04301624836056237, 1.3936816441440611, 2.4900448052241524, 2.985304666037027, 2.780303546423706, 1.954794380790358, 0.7395206820481127, -0.5487846125373552, -1.5919432105908302, -2.1521369900074374, -2.1298346951215272, -1.5833906251113832, -0.7062914200774272, 0.2306283355235812, 0.9554736569806855, 1.2689508749096243, 1.0954864459772864, 0.49852111973983765, -0.3431242174538144, -1.1900475417254819, -1.8119437224625885, -2.052064186111385, -1.8682914189078415, -1.3397366981935452, -0.6379276650907965, 0.02804831327031508, 0.47562025471041997, 0.6027474262543487, 0.4158427544339172, 0.02357971118762026, -0.40105896731759405, -0.6784555713589948, -0.6816598672903906, -0.3786451892175157, 0.1560119606552696, 0.7641683541682198, 1.25516113624922, 1.4691564982933416, 1.3327458757675172, 0.8885236173166562, 0.2879457196835196, -0.2520225046245892, -0.5164375728116303, -0.3637650526329234], 'positive_zeros': ['1.20257994433295965988366961678677', '2.92005587483305609350615346356961', '4.11966878623242114374011044104216', '5.25740023395859639896031838072239', '6.76133441868883457879465868737789', '7.87751520378398968998170624036120', '9.157036239478735546931611750121926', '9.811781125732730687015677134132945', '11.11292034295606834696471631938307', '11.82111427378720817371869976523561'], 'prelabel': '2-240-16.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.384344483324411, 'root_angle': -0.7185673124238825, 'root_number': '-0.633949525856277 - 0.7733744233336151*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.359283656212', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.20257994433295965988366961679', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.92005587483305609350615346357', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.11966878623242114374011044104', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.9164096485107303, 'bad_primes': [2, 3, 5], 'central_character': '16.13', 'conductor': 240, 'conductor_radical': 30, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/240/2/s/b/61/3'], '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': '2-240-16.13-c1-0-5', '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': '2-240-16.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.384344483324411, 'root_angle': -0.35928365621194125, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.20257994433295965988366961679', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1524451188256107013574379760725', 'Lhash_array': ['1524451188256107013574379760725'], 'label': '2-240-16.13-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/240/2/s/b/61/3'}