-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1171197837689511103116183585783', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [-13.486832980505138, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 98.09289516970689, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '3600.1601', 'coefficient_field': 'CDF', 'conductor': 3600, 'conductor_radical': 30, 'conjugate': '258998530599557158670948661420', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [13.486832980505138, 0], [49.0, 0]], [[1.0, 0], [0, 17.659048552118023], [-121.0, 0]], [[1.0, 0], [-7.486832980505138, 0], [169.0, 0]], [[1.0, 0], [0, -16.97056274847714], [-289.0, 0]], [[1.0, 0], [-10.973665961010276, 0], [361.0, 0]], [[1.0, 0], [0, -21.90168923923731], [-529.0, 0]], [[1.0, 0], [0, -47.35753336195302], [-841.0, 0]], [[1.0, 0], [-16.973665961010276, 0], [961.0, 0]], [[1.0, 0], [-5.539501058484586, 0], [1369.0, 0]], [[1.0, 0], [0, 66.39355352135281], [-1681.0, 0]], [[1.0, 0], [-38.973665961010276, 0], [1849.0, 0]], [[1.0, 0], [0, 32.56415388967252], [-2209.0, 0]], [[1.0, 0], [0, -11.2392245888021], [-2809.0, 0]], [[1.0, 0], [0, 31.875668086031634], [-3481.0, 0]], [[1.0, 0], [-46.92099788303083, 0], [3721.0, 0]], [[1.0, 0], [76.0, 0], [4489.0, 0]], [[1.0, 0], [0, 77.7445039754289], [-5041.0, 0]], [[1.0, 0], [94.92099788303082, 0], [5329.0, 0]], [[1.0, 0], [-6.920997883030828, 0], [6241.0, 0]], [[1.0, 0], [0, -62.15091283423352], [-6889.0, 0]], [[1.0, 0], [0, -62.26263869950751], [-7921.0, 0]], [[1.0, 0], [-124.97366596101027, 0], [9409.0, 0]], [[1.0, 0], [0, -112.26238941075007], [-10201.0, 0]], [[1.0, 0], [170.30249470757707, 0], [10609.0, 0]], [[1.0, 0], [0, 93.33809511662427], [-11449.0, 0]], [[1.0, 0], [68.86832980505137, 0], [11881.0, 0]], [[1.0, 0], [0, 110.30865786510141], [-12769.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 50, 'label': '2-60e2-3.2-c2-0-50', 'leading_term': '0.751259335691114131443188773078363596557829079354964716', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3600/3/l/n/1601/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.7512593356911141, 0.9145407363481671, 1.0629725904600722, 1.1940374466193369, 1.3053710933651017, 1.394780751591681, 1.4602671675675305, 1.5000508288548995, 1.512602169597111, 1.4966752719507366, 1.4513442248616135, 1.3760409862028256, 1.2705933234290614, 1.1352611925487395, 0.9707697637596858, 0.778337220242032, 0.5596954476264011, 0.31710179668369465, 0.05334024005929278, -0.22828954704167717, -0.5239963764295092, -0.8295358638333716, -1.1402633388714452, -1.451201376964811, -1.7571215099417172, -2.0526391765445733, -2.3323204685123633, -2.590798727147232, -2.8228985652063, -3.023764446308737, -3.1889905659014848, -3.3147484611235765, -3.3979085478536253, -3.436151656654946, -3.4280666280576186, -3.373230141760412, -3.2722652007060296, -3.126875072502887, -2.9398500058896033, -2.7150446826855914, -2.45732512480853, -2.1724846353229625, -1.867129291088263, -1.5485344968184809, -1.2244751266446998, -0.9030327866807754, -0.5923846953591292, -0.3005795608676663, -0.03530660028263252, 0.19633554233747488, 0.38806279412697103, 0.5346151691677193, 0.631944425676063, 0.6773727635128758, 0.6697159964982748, 0.6093654293063633, 0.49832371330313724, 0.340191229265137, 0.14010101729194818, -0.09539809425607572, -0.35850876662713543, -0.640399643815871, -0.9314620786776198, -1.2216023911675802, -1.5005613787507024, -1.7582514258555557, -1.9851004550649332, -2.1723911845200057, -2.3125837520186256, -2.39960977358264, -2.4291263465464583, -2.398719392983222, -2.308047060524856, -2.1589156290708487, -1.9552824708692318, -1.7031830185621102, -1.4105813361165298, -1.0871466727636654, -0.7439612110596201, -0.3931669904532891, -0.047562587208405546, 0.2798375492758633, 0.5762662691218884, 0.8296731137471823, 1.0291827416884034, 1.1655249307983169, 1.2314190899736452, 1.2218972841067153, 1.134551515811692, 0.9696933786197784, 0.7304171331433761, 0.4225606682094999, 0.05456257727524734, -0.3627824296545449, -0.8166634987921648, -1.2926787429414077, -1.7753315333227364, -2.2485807286060377, -2.6964248825980084, -3.1034984672214128, -3.4556569641684587, -3.7405273993528834, -3.9480015668951607, -4.070650823443588, -4.104043898252958, -4.04695258765, -3.9014343725175107, -3.672785765643618, -3.3693653816514386, -3.0022911196859803, -2.585021234437739, -2.1328342122618658, -1.6622270353179174, -1.1902553886814105, -0.7338424460444161, -0.3090848933418918, 0.06941430879737158, 0.389157340998731, 0.6402797388948441, 0.8159709782676633, 0.9127671219731708, 0.9307003535605112, 0.8732961785954125, 0.747415611956504, 0.5629465123300478, 0.3323550745457334, 0.07011503610530466, -0.20796191095016933, -0.4854659777261295, -0.7461670059902086, -0.97479516442901, -1.1577887420795008, -1.2839738196876462, -1.3451428943071568, -1.336503412664196, -1.2569725019630047, -1.1093007675747835, -0.9000155846488862, -0.6391825193896592, -0.339992008475458, -0.01818680950244742, 0.3086463883163354, 0.6218908238559465, 0.902782898535251, 1.1333245260142828, 1.2971819794151256, 1.3805282295333994, 1.3727874218009672, 1.267243814287825, 1.0614830722874282, 0.7576410696229677, 0.36244397703477466, -0.11296695795967983, -0.6534223590409153, -1.2403095689712114, -1.8523317498493326, -2.4664086877932094, -3.058679232867188, -3.605559567451543, -4.084807869336666, -4.47654465063488, -4.76417923066247, -4.9351964409676965, -4.981763641043284, -4.9011262006303635, -4.6957694237118135, -4.373335998121314, -3.9462999242422145, -3.431409925713188, -2.848926969913984, -2.221691128456234, -1.5740620276821002, -0.9307840834186056, -0.3158321847456926, 0.24870479210806065, 0.7436464414008264, 1.1535971390318849, 1.4676309152188762, 1.6797488702633236, 1.7890844034917897, 1.7998442811596047, 1.7209871548677145, 1.5656548627416724, 1.35038498336986, 1.094144964094227, 0.8172380598572447, 0.54013873388217, 0.2823196448982856, 0.061133582344027174, -0.10918841766451708, -0.21836698810163388, -0.2606851251933055, -0.23534363176602904, -0.14653864213484988, -0.0032533798356850024, 0.18122819780106117, 0.3900628552942602, 0.6038072442829935, 0.8015447936509469, 0.9621202511430995, 1.0654148208102379, 1.093591408070297, 1.0322398596293176, 0.8713563234792943, 0.606098797788887, 0.23727222223502023, -0.22848946546420618, -0.778860753689123, -1.3962805657301167, -2.058708341401988, -2.7406447608510454, -3.4143664106603, -4.051310952439641, -4.623539900197194, -5.105200533240297, -5.4739071494432, -5.71196495175393, -5.8073672666091465, -5.754508179818155, -5.5545674761964206, -5.215542213187544, -4.751918411470277, -4.183996158493764, -3.536900788545033, -2.8393306248076655, -2.1221070122470036, -1.4166041306008237, -0.7531436323393195, -0.15944200676010933, 0.34080350570278745, 0.7291115906588547, 0.993128798374401, 1.1272049102032509, 1.1325985309195865, 1.0173004442262807, 0.7954839488619145, 0.4866127738855597, 0.1142570114355619, -0.29531536888337656, -0.7146904803688964, -1.11691420728828, -1.4770582205418008, -1.7736546989819142, -1.9899153093400976, -2.1146622160733246, -2.142915497560253, -2.076101410444186, -1.9218683235746816, -1.6935205359185999, -1.409103217785001, -1.0901929914405821, -0.7604668988881034, -0.44413655708997773, -0.16434327360930523, 0.05838682045167972, 0.20753124383276567, 0.27171543328741976], 'positive_zeros': ['0.923912186432639386413852387468375', '2.44475434725568436289809054309278', '2.97632856003991694980726257195065', '4.06965983306130057801523154073064', '4.67883655695569554359389073052693', '5.88074199798297924241705593696979', '6.41139811423753346276701977880561', '7.11219501990289888416038314478257', '7.70735195610107693022623751963685', '8.812886665025206908851589870041724'], 'prelabel': '2-60e2-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.904185739863065, 'root_angle': 0.6959132760153036, 'root_number': '-0.577350269189625764509148780501957455647601751270126876 + 0.816496580927726032732428024901963797321982493552223376*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3479566380076518', 'prec': 60}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.923912186432639386413852387468', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.44475434725568436289809054309', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.97632856003991694980726257195', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 98.09289516970689, 'bad_primes': [2, 3, 5], 'central_character': '3.2', 'conductor': 3600, 'conductor_radical': 30, 'degree': 2, 'index': 50, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3600/3/l/n/1601/1'], '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': '2-60e2-3.2-c2-0-50', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-60e2-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.904185739863065, 'root_angle': 0.3479566380076518, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.923912186432639386413852387468', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1171197837689511103116183585783', 'Lhash_array': ['1171197837689511103116183585783'], 'label': '2-60e2-3.2-c2-0-50', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3600/3/l/n/1601/1'}