-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2581029876750867186909268733811', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 214.3891620725999], 'a4': [0.0, 0.0], 'a5': [-3264.6633704148926, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, -5808.1451353665225], 'a8': [0.0, 0.0], 'a9': [13086.287185808495, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.165716042779591, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '5.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]]], 'bad_primes': [2], 'central_character': '16.15', 'coefficient_field': 'CDF', 'conductor': 16, 'conductor_radical': 2, 'conjugate': '235128413216643483424922644353', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -214.3891620725999], [-59049.0, 0]], [[1.0, 0], [3264.6633704148926, 0], [9765625.0, 0]], [[1.0, 0], [0, 5808.1451353665225], [-282475249.0, 0]], [[1.0, 0], [0, 271362.6444798834], [-25937424601.0, 0]], [[1.0, 0], [557957.7725586275, 0], [137858491849.0, 0]], [[1.0, 0], [795475.5640709575, 0], [2015993900449.0, 0]], [[1.0, 0], [0, 4017945.5905149346], [-6131066257801.0, 0]], [[1.0, 0], [0, -7934540.768264955], [-41426511213649.0, 0]], [[1.0, 0], [-7814404.643592904, 0], [420707233300201.0, 0]], [[1.0, 0], [0, -11557373.041709505], [-819628286980801.0, 0]], [[1.0, 0], [107594851.5376816, 0], [4808584372417849.0, 0]], [[1.0, 0], [58235424.511713296, 0], [13422659310152400, 0]], [[1.0, 0], [0, 75819259.01986955], [-21611482313284250, 0]], [[1.0, 0], [0, 119492525.63401257], [-52599132235830050, 0]], [[1.0, 0], [468891091.7551425, 0], [174887470365513060, 0]], [[1.0, 0], [0, -813125866.9712114], [-511116753300641400, 0]], [[1.0, 0], [439743818.3213983, 0], [713342911662882600, 0]], [[1.0, 0], [0, 1141362568.7531006], [-1822837804551761400, 0]], [[1.0, 0], [0, 9192197.472731728], [-3255243551009881000, 0]], [[1.0, 0], [889952198.6621768, 0], [4297625829703557600, 0]], [[1.0, 0], [0, 5961939646.447093], [-9468276082626847000, 0]], [[1.0, 0], [0, -200196393.33960354], [-15516041187205853000, 0]], [[1.0, 0], [-7641003291.735335, 0], [31181719929966182000, 0]], [[1.0, 0], [6435574873.192794, 0], [73742412689492830000, 0]], [[1.0, 0], [-11363228282.999552, 0], [110462212541120450000, 0]], [[1.0, 0], [0, -5644228313.100314], [-134391637934412190000, 0]], [[1.0, 0], [0, -7550129763.948346], [-196715135728956540000, 0]], [[1.0, 0], [-18358268185.826134, 0], [236736367459211740000, 0]], [[1.0, 0], [20624517701.657097, 0], [339456738992222300000, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-2e4-4.3-c10-0-3', 'load_key': 'CMFs-workshop', 'motivic_weight': 10, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [10], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/16/11/c/b/15/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [0.40941521047409885, 0.7546855472045112, 1.0448019148797998, 1.2684520002639945, 1.4167127838934626, 1.483405375953164, 1.4653991421070256, 1.3628529206320354, 1.1793776326340422, 0.9221017376073388, 0.6016193272527084, 0.23180070524751206, -0.1705524638462916, -0.5862205758040471, -0.9942536942967156, -1.372828700750403, -1.70025861525296, -1.9561220947075306, -2.122465490967926, -2.185014439303561, -2.134318236492955, -1.9667399472457185, -1.685200013131172, -1.299582808253988, -0.8267254842468867, -0.2899274644575924, 0.282052747246856, 0.8565099289430785, 1.3987665652656516, 1.8745147830265514, 2.2523838947038355, 2.5065491579950687, 2.6191649955607956, 2.5823889407452767, 2.3997656419801427, 2.0867667620067754, 1.6703340078359292, 1.187347777449281, 0.6820390659325816, 0.2024703787227794, -0.20367728511259703, -0.4936716752240874, -0.6342300795614116, -0.6054863904818371, -0.40395577088092477, -0.04407921569309786, 0.4419643313912795, 1.0063352299417825, 1.5894624753382576, 2.1255727245622165, 2.5493539988755347, 2.8031055317018585, 2.843597765217164, 2.647818758191749, 2.2168319452120184, 1.5771216312382434, 0.7790503439434698, -0.10762414968288292, -1.0008581969754224, -1.8153792075288981, -2.472697426241229, -2.9108654366795683, -3.092704745984663, -3.0113123282955763, -2.6919262426682837, -2.189649733438776, -1.5830641642058316, -0.9643378649733962, -0.4269812018815129, -0.05282446878685529, 0.09997074397951823, 0.006068700809580188, -0.3222308334033726, -0.8355117985404086, -1.4533417273199918, -2.0753744783182095, -2.596068632040594, -2.9209750188633796, -2.982156190221335, -2.7502656541530923, -2.2411727525054843, -1.5157463753535123, -0.6724198638999657, 0.1666924560803814, 0.8742493594034886, 1.3379525469322313, 1.4793976760537368, 1.2683037304767466, 0.7294961067866845, -0.05891353151487355, -0.9762986156971676, -1.8778591052419906, -2.6177635819370253, -3.073332388101813, -3.166116132344445, -2.8760545389556778, -2.245938042864657, -1.3749975782025001, -0.4023596069957799, 0.5170106294769731, 1.2397486711454546, 1.659966510325123, 1.7286874570385165, 1.4629635432114843, 0.9425954659933748, 0.29466944954691665, -0.3314995545084138, -0.7944349304522285, -0.9897969768724315, -0.8730237282374538, -0.47048630795372687, 0.12357930158901116, 0.7643472860708246, 1.284969446886265, 1.5310662864104319, 1.3942935707321478, 0.8379947788639773, -0.0907475626041935, -1.2657927968469065, -2.5031444966532073, -3.594997926578385, -4.350095879115852, -4.632243213855958, -4.388876179666998, -3.663363037585222, -2.5879306506653346, -1.358139712386356, -0.19382878306272394, 0.7054649227085377, 1.2011462680520724, 1.243380701590105, 0.8797791990587474, 0.24271602206657455, -0.482226468630764, -1.0998599363761838, -1.4512846565674742, -1.4515301523139061, -1.1100138191693865, -0.5286435713324668, 0.12250773448848938, 0.6467222850551037, 0.8698539876593153, 0.6855806831112632, 0.08557481946180112, -0.8332866994461842, -1.8872850563693382, -2.84629502561382, -3.4872874978015567, -3.648359529271097, -3.2701412612004446, -2.4140156066529297, -1.251870132463139, -0.028889855772960892, 0.9924243610240946, 1.5939276736565322, 1.6542784496575444, 1.1790619057947624, 0.3006386039513965, -0.7529259744249079, -1.712793326689462, -2.3349319958131276, -2.460142847284475, -2.05337465360152, -1.2121252594900536, -0.1414253560754711, 0.8985532201789105, 1.6590331998110246, 1.966168565913557, 1.7649336032730123, 1.1316182780891162, 0.251324898265521, -0.6338355997295013, -1.2921448188973357, -1.5670653101911836, -1.42152620264099, -0.9490296454973365, -0.3477418460442074, 0.13610681462747287, 0.2804603367048359, -0.044572983450396404, -0.8323347686980314, -1.93225150803998, -3.0830232012423564, -3.9786870673933765, -4.3504231812865815, -4.041978071016524, -3.057607438931352, -1.5683960787305298, 0.12605756703259638, 1.6713019948556593, 2.74770483259649, 3.151923933484099, 2.8477778530447946, 1.9722874538673931, 0.795025095514187, -0.3579667612568253, -1.1942899285437034, -1.5337839249365717, -1.3532022371099313, -0.7842837400391381, -0.06608858986597191, 0.534032783826171, 0.807019479847329, 0.6699071322547095, 0.19388659788159252, -0.4165866842730269, -0.888022690507532, -0.9664124079279459, -0.5030158809141009, 0.4894914749534948, 1.8290726673695998, 3.2088437404990984, 4.2822741993866495, 4.764392142447352, 4.518596183849257, 3.602125203137568, 2.25506734367836, 0.8346080016803672, -0.2870150463956109, -0.8308367861243156, -0.6931457308558147, 0.024140200309594406, 1.0446504548040847, 2.0015355053938495, 2.5491232616892607, 2.4682795194057263, 1.7330489122300143, 0.5178477864921035, -0.8571682421716772, -2.025598280806875, -2.687961909813162, -2.702842726935, -2.1271311300414033, -1.1926241121447003, -0.226657240128232, 0.4573846731298154, 0.6638412516857398, 0.37858560110659006, -0.22852551061997162, -0.8638448030701068, -1.2131794752587728, -1.0537470644072786, -0.3369089230856796, 0.7872336513379535, 2.013370187551094, 2.9798709727719377, 3.3911953264616663, 3.1230763564733577, 2.2742720679003483, 1.1454871297368479, 0.14986651603016035, -0.3175461954492297, -0.009533906536394406, 1.0870999837403574, 2.738225352356961, 4.527890358881366, 5.982687538334609], 'positive_zeros': ['2.03607356497616562148237030664308', '4.48437215658643818055072984821765', '6.93794030710311867454845399939260', '7.927923402745418275615064704655105', '9.998594944504876633032118969232012', '12.16660310188118915971574994011789', '12.48532577753635673357753047248301', '14.55352604477001767903157294021937', '15.63264426413728961230109419768844', '17.30056017659169056970151707366936'], 'prelabel': '2-2e4-4.3-c10-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1883720050802715, 'root_angle': 0.6666666666666667, 'root_number': '-0.5000000000000002 + 0.8660254037844385*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.333333333333', 'prec': 47}, 'spectral_label': 'c10-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.03607356497616562148237030664', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.48437215658643818055072984822', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.93794030710311867454845399939', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 10.165716042779591, 'bad_primes': [2], 'central_character': '4.3', 'conductor': 16, 'conductor_radical': 2, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/16/11/c/b/15/3'], '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': '2-2e4-4.3-c10-0-3', 'motivic_weight': 10, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [10], 'order_of_vanishing': 0, 'prelabel': '2-2e4-4.3-c10-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1883720050802715, 'root_angle': 0.33333333333333337, 'self_dual': False, 'spectral_label': 'c10-0', 'z1': {'__RealLiteral__': 0, 'data': '2.03607356497616562148237030664', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2581029876750867186909268733811', 'Lhash_array': ['2581029876750867186909268733811'], 'label': '2-2e4-4.3-c10-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/16/11/c/b/15/3'}