-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1915279558106364358325991980572,2333359344201314584606956183405', 'a10': 0, 'a2': -3, 'a3': 2, 'a4': 4, 'a5': 0, 'a6': -6, 'a7': 0, 'a8': -3, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 166.71483765276056, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -2, 1]], [7, [1]], [11, [1, 2, 1]]], 'bad_primes': [3, 7, 11], 'central_character': '1617.1', 'coefficient_field': '1.1.1.1', 'conductor': 2614689, 'conductor_radical': 231, 'degree': 4, 'euler_factors': [[1, 3, 5, 6, 4], [1, -2, 1], [1, 0, 5, 0, 25], [1], [1, 2, 1], [1, -2, 7, -26, 169], [1, 12, 70, 204, 289], [1, -4, 37, -76, 361], [1, -4, 30, -92, 529], [1, 16, 117, 464, 841], [1, 8, 58, 248, 961], [1, 10, 79, 370, 1369], [1, 12, 118, 492, 1681], [1, -8, 82, -344, 1849], [1, 14, 123, 658, 2209], [1, 8, 42, 424, 2809], [1, -6, 47, -354, 3481], [1, 4, 46, 244, 3721], [1, 12, 125, 804, 4489], [1, 0, 122, 0, 5041], [1, -2, 147, -146, 5329], [1, -4, 142, -316, 6241], [1, 16, 210, 1328, 6889], [1, 0, -2, 0, 7921], [1, 4, 118, 388, 9409], [1, 16, 246, 1616, 10201], [1, 12, None, 1236, 10609], [1, None, None, None, 11449], [1, -12, 254, -1308, 11881], [1, -4, 210, -452, 12769]], 'euler_factors_factorization': [[[[1, 3, 5, 6, 4], 1]], [[[1, -1], 2]], [[[1, 0, 5, 0, 25], 1]], [1], [[[1, 1], 2]], [[[1, -2, 7, -26, 169], 1]], [[[1, 6, 17], 2]], [[[1, -4, 37, -76, 361], 1]], [[[1, -4, 30, -92, 529], 1]], [[[1, 16, 117, 464, 841], 1]], [[[1, 8, 58, 248, 961], 1]], [[[1, 10, 79, 370, 1369], 1]], [[[1, 6, 41], 2]], [[[1, -8, 82, -344, 1849], 1]], [[[1, 14, 123, 658, 2209], 1]], [[[1, 8, 42, 424, 2809], 1]], [[[1, -6, 47, -354, 3481], 1]], [[[1, 4, 46, 244, 3721], 1]], [[[1, 12, 125, 804, 4489], 1]], [[[1, 0, 122, 0, 5041], 1]], [[[1, -1, 73], 2]], [[[1, -4, 142, -316, 6241], 1]], [[[1, 16, 210, 1328, 6889], 1]], [[[1, 0, -2, 0, 7921], 1]], [[[1, 4, 118, 388, 9409], 1]], [[[1, 16, 246, 1616, 10201], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 9, 'label': '4-1617e2-1.1-c1e2-0-9', 'load_key': 'CMFs-workshop', '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': 2, 'origin': 'ModularForm/GL2/Q/holomorphic/1617/2/a/l', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.029296875', 'prec': 37}, 'plot_values': [1.9398059665759966e-120, 0.003513540139362128, 0.01404757621977121, 0.03158181880450358, 0.056080108663703616, 0.08748767108005566, 0.12572623875630337, 0.1706894929288358, 0.22223603049971546, 0.28018382837264855, 0.34430111158709187, 0.41430211493800606, 0.48983507344524585, 0.5704820101637443, 0.655744054966617, 0.745046096961643, 0.8377225607090322, 0.9330249097547264, 1.030112862962208, 1.128062405202813, 1.2258656392338947, 1.3224396144068542, 1.4166345043492503, 1.5072458351142992, 1.5930291497403777, 1.6727167771604396, 1.7450390138257963, 1.8087432298146064, 1.8626229011910196, 1.9055359831147218, 1.9364407175005376, 1.9544125034930795, 1.958681765196888, 1.9486496383280136, 1.9239234220565862, 1.8843274793480462, 1.8299368409023617, 1.7610739225850434, 1.6783440724413061, 1.5826098598393186, 1.4750272665803585, 1.3569985681305783, 1.2301980887193333, 1.096514695967736, 0.9580524976946058, 0.8170737217330645, 0.6759688178784014, 0.5372006404927209, 0.4032522893204034, 0.2765650716666069, 0.1594793530270199, 0.05416237799712908, -0.03744826250484637, -0.11371947119409842, -0.17337489172659587, -0.21555765181915096, -0.23987761930416554, -0.24644991128028526, -0.23592951600474507, -0.20952206079335392, -0.1689925582993241, -0.11665017231571943, -0.05531886184453399, 0.011700826441260912, 0.08070643440028434, 0.14765020696743256, 0.20826166848857589, 0.25811415648274166, 0.29279399036902415, 0.30796439803341313, 0.2995749554730872, 0.26390789764539646, 0.1978164349201779, 0.09873656699457295, -0.03506041840860758, -0.2045082102784461, -0.4094962600227877, -0.6489759118599118, -0.9207356537560629, -1.2215794309753158, -1.547147546959585, -1.892169046372148, -2.2503393191479515, -2.6146489183083923, -2.9773151416349584, -3.330183803726457, -3.664708819794391, -3.97240104196651, -4.244861382528807, -4.474221595377348, -4.653241941336842, -4.775684506312891, -4.8364628599957245, -4.831915426766964, -4.759955405744901, -4.620244155069385, -4.414274450469418, -4.145444955115196, -3.8190382196511377, -3.4421750145341745, -3.0236868893822146, -2.5739261160146363, -2.1045442070688742, -1.628169038862234, -1.1580883289318304, -0.7078443699526742, -0.29083049501240477, 0.08014369193458426, 0.3932931232957652, 0.6382859087366531, 0.8066469129664008, 0.892133113010438, 0.8910482017251071, 0.8024810191666524, 0.6285172515317011, 0.37425336128877257, 0.047887280727383, -0.33951784406452046, -0.7741166057371905, -1.239730614468487, -1.7181399531387194, -2.1897100891277415, -2.63384115297897, -3.029768887607439, -3.357061418759748, -3.5965530343048546, -3.730820394337589, -3.7450896706988592, -3.6277067546065487, -3.3708040854396755, -2.9707567248264337, -2.428488651597575, -1.749792899342913, -0.9452974227280598, -0.030477808621009746, 0.9746679040705357, 2.0459652663440653, 3.1557084496956302, 4.273284596430237, 5.36613197213016, 6.400607063748158, 7.343037259195341, 8.16092709067028, 8.823763260010509, 9.304576603269254, 9.580354069104642, 9.633604228385277, 9.452615631856094, 9.032399939594622, 8.375115222226846, 7.490003622449014, 6.3939019426140185, 5.110385498379718, 3.6698109778517924, 2.108270969053666, 0.4666850260490835, -1.2100850549219717, -2.874997219236625, -4.479701466698659, -5.976546784189368, -7.319777125208966, -8.467179001566587, -9.38159510078875, -10.032030033397481, -10.395089881472389, -10.455616241131429, -10.207628499764775, -9.654502324494162, -8.809225335913103, -7.694032325171667, -6.3399593444858935, -4.785935942927856, -3.077636160625798, -1.2661939642518842, 0.5935880811336598, 2.4447031217481516, 4.230136621548165, 5.894359684499909, 7.3856036510524135, 8.657156075948123, 9.669495071269514, 10.391029456417867, 10.799988173855693, 10.884320351076166, 10.643139340281527, 10.08583161393996, 9.232665441440057, 8.113441100564803, 6.7669817978394375, 5.239582316881922, 3.5835022522695836, 1.8552373489210847, 0.11348848080731153, -1.5827704359586972, -3.1763639238376262, -4.613848722478478, -5.847360602779326, -6.8361796651115405, -7.54817892089835, -7.9607483735675615, -8.06161040797243, -7.849057367653961, -7.331909277325231, -6.529134028376671, -5.468907806464825, -4.187696464433101, -2.7285720365207373, -1.1399238642097649, 0.5267731979003737, 2.2182972053644128, 3.8822629318374915, 5.468164543085275, 6.930015162114569, 8.226898377080998, 9.325264598869225, 10.198934544479185, 10.830740022412568, 11.211910368966738, 11.343002055704444, 11.232565185371316, 10.897487687374234, 10.360994611348275, 9.652506207734387, 8.805276259001204, 7.855804471815181, 6.841540171936712, 5.799969942912555, 4.766704940354823, 3.7745167710078658, 2.8519613089869416, 2.0226584942562855, 1.3045365431034655, 0.7095254108731941, 0.24346602810700427, -0.09374197246870399, -0.30763605953752116, -0.4085988540793007, -0.41097509196066084, -0.33209076855151304, -0.19126095699854503, -0.008581172314593726, 0.1959612485603459, 0.40368276426421806, 0.5978320647308784, 0.764563411245912, 0.8931711530172595, 0.976731462297615, 1.011869304210378, 0.9990301905290365, 0.9418299894959574, 0.846953564293994, 0.7232516218795507, 0.5813251761122957, 0.43256206308445144, 0.28855349900071503, 0.16023293445358955, 0.05731199806942768, -0.01234799437840219, -0.0431222496582508, -0.03193037980106089, 0.021655596745498894, 0.11543739572680696, 0.2447998263020164, 0.40301109548833114, 0.5817036642592782, 0.7713576030109842, 0.9619209477867745, 1.1433682589012417, 1.3063096186455796, 1.4424721869758435, 1.545212057994095, 1.6097345412766122, 1.6334840669015658, 1.6159952918619354, 1.559120956715491, 1.4665611814721897, 1.3438625407145985, 1.197788123668371, 1.0360749463565744, 0.8668019476343193, 0.6980064651313783, 0.5371472114340702, 0.3907385369406942, 0.26397832799089255, 0.16052384778589943, 0.082345747612312, 0.029699951893805882, 0.0012235834293124368, -0.005890840903784391, 0.004389437783647685, 0.02727207043859173, 0.0575242642811485, 0.08986677793835604, 0.11936847067472794, 0.1417771679050523, 0.1538258969109976, 0.15342456337922716, 0.1397727014484736, 0.1133983830028203, 0.07602658439730768, 0.030470742478437195, -0.019690701467558587, -0.07036148521432456, -0.11731552431929955, -0.15653315169641346, -0.1845337011625508, -0.19868994150501074, -0.19743220868502384, -0.18041981668651175, -0.1485769043669649, -0.10405233075705458, -0.05007909419479955, 0.009277217661092527, 0.06939060111852938, 0.12548451274426373, 0.1729431607104077, 0.2077762210927508, 0.2268709531464081, 0.22837065253597486, 0.21179196784215024, 0.1781924834820193, 0.13009740233743344, 0.07140699042681084, 0.007107224211559297, -0.05705186565355914, -0.11501492649541833, -0.1608948943273956, -0.18947546128030218, -0.19672423522445148, -0.18018708216470736, -0.13938855978259376, -0.0760079560044207, 0.005996769963101279, 0.10047180311356901, 0.1993340626531463, 0.2928808987540685, 0.37047028023140754, 0.4209479835852622, 0.4336685122837644, 0.398868067527098, 0.30886635164045595, 0.1581989886935192, -0.05521930142182401, -0.33035738957488536, -0.6621552256617981, -1.0422773041925615, -1.4585914853765103, -1.896404558627221, -2.3383933760440065, -2.7661538108234707, -3.1605754483963597, -3.503404978497586, -3.77794392464674, -3.970324022448909, -4.070255253678657, -4.07181135398643, -3.9738943906108113, -3.7804058770313054, -3.500217390813559, -3.1466487404358885, -2.7369222626827385, -2.291013617570694, -1.8306676338950396, -1.3779316481720174, -0.9538589991881382, -0.5771646046240623, -0.26289586092122713, -0.02152253958582921, 0.14193885495668915, 0.2283016458430053, 0.24419942547186474, 0.2018679125297705, 0.11817597193265454, 0.013718308595698793, -0.0888091838388634, -0.1661583016565088, -0.19638216303323688, -0.1606419099787201, -0.0449163618998031, 0.15851001586794283, 0.4498783332079732, 0.8212435930629223, 1.256291078489237, 1.7305839191478605, 2.212677122282268, 2.665266267376349, 3.047607021117223, 3.3172672126144516, 3.4335685109753915, 3.359382822860455, 3.065096987373152, 2.5297777746029406, 1.7449597155727203, 0.7146246134134395, -0.5419652764638766, -1.9918228024811955, -3.586890172422578, -5.267301285905514, -6.9616380035303305, -8.591709987082721, -10.07428296366972, -11.326571888659837, -12.269215676405254, -12.831290481663094, -12.95396462523482, -12.59407463506848, -11.72732520680607, -10.350052753950171, -8.480702884024627, -6.159655510993814, -3.4483690839813583, -0.4271260377523308, 2.807999732148601, 6.149183499069566, 9.48169689659667, 12.68855638404476, 15.656850157665666, 18.281467282445156, 20.471994303735816, 22.154752843023704, 23.278391196746988, 23.81442143252702, 23.75974618524193, 23.135799361918487, 21.98767513135678, 20.38134173152789, 18.400540044089137, 16.141631469363826, 13.709692378458596, 11.211809550507153, 8.753084989236532, 6.430223055591634, 4.327874422798609, 2.5141848873788417, 1.0382158088535576, -0.07175307264343089, -0.8089648649726268, -1.1870494020854252, -1.2386251780254884, -1.0126048663466793, -0.5687826842419499, 0.027202057962337052, 0.6958028823984321, 1.3623686841634988], 'positive_zeros': ['1.51088916595908606697405159221265', '1.84069596447255548673900203893021', '2.16099573002650604749150685811147', '3.12806557848555480053285195220797', '3.40230264114730994288873085529487', '3.92670638612145572212418942777973', '4.54919738362808015152712971307614', '5.08833377946787577344317188998844', '5.62692514355561985503532827542360', '6.08458139083664908339960167012250', '6.84612894136881739739190128480953', '7.03252398659051344961708471275944', '7.52275297217827678920123400386638', '7.60782286100225971478383860506659', '8.410384676094100896686091956837033', '8.458543213076420806943974649736112', '8.807030341900377071986106821698243', '9.136129125392656469050322013340510'], 'prelabel': '4-1617e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.5933007119974034, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 1119686625915146720, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.51088916595908606697405159221', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.84069596447255548673900203893', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.16099573002650604749150685811', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 166.71483765276056, 'bad_primes': [3, 7, 11], 'central_character': '1.1', 'conductor': 2614689, 'conductor_radical': 231, 'degree': 4, 'dirichlet_coefficients': [1, -3, 2, 4, 0, -6, 0, -3, 3, 0, -2, 8, 2, 0, 0, 3, -12, -9, 4, 0, 0, 6, 4, -6, -5, -6, 4, 0, -16, 0, -8, -6, -4, 36, 0, 12, -10, -12, 4, 0, -12, 0, 8, -8, 0, -12, -14, 6, 0, 15, -24, 8, -8, -12, 0, 0, 8, 48, 6, 0, -4, 24, 0, 5, 0, 12, -12, -48, 8, 0, 0, -9, 2, 30, -10, 16, 0, -12, 4, 0, 5, 36, -16, 0, 0, -24, -32, 6, 0, 0, 0, 16, -16, 42, 0, -12, -4, 0, -6, -20], 'euler11': [1, 2, 1, 0, 0], 'euler13': [1, -2, 7, -26, 169], 'euler17': [1, 12, 70, 204, 289], 'euler19': [1, -4, 37, -76, 361], 'euler2': [1, 3, 5, 6, 4], 'euler23': [1, -4, 30, -92, 529], 'euler29': [1, 16, 117, 464, 841], 'euler3': [1, -2, 1, 0, 0], 'euler31': [1, 8, 58, 248, 961], 'euler37': [1, 10, 79, 370, 1369], 'euler41': [1, 12, 118, 492, 1681], 'euler43': [1, -8, 82, -344, 1849], 'euler47': [1, 14, 123, 658, 2209], 'euler5': [1, 0, 5, 0, 25], 'euler53': [1, 8, 42, 424, 2809], 'euler59': [1, -6, 47, -354, 3481], 'euler61': [1, 4, 46, 244, 3721], 'euler67': [1, 12, 125, 804, 4489], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 0, 122, 0, 5041], 'euler73': [1, -2, 147, -146, 5329], 'euler79': [1, -4, 142, -316, 6241], 'euler83': [1, 16, 210, 1328, 6889], 'euler89': [1, 0, -2, 0, 7921], 'euler97': [1, 4, 118, 388, 9409], 'euler_factors': [[1, 3, 5, 6, 4], [1, -2, 1, 0, 0], [1, 0, 5, 0, 25], [1, 0, 0, 0, 0], [1, 2, 1, 0, 0], [1, -2, 7, -26, 169], [1, 12, 70, 204, 289], [1, -4, 37, -76, 361], [1, -4, 30, -92, 529], [1, 16, 117, 464, 841], [1, 8, 58, 248, 961], [1, 10, 79, 370, 1369], [1, 12, 118, 492, 1681], [1, -8, 82, -344, 1849], [1, 14, 123, 658, 2209], [1, 8, 42, 424, 2809], [1, -6, 47, -354, 3481], [1, 4, 46, 244, 3721], [1, 12, 125, 804, 4489], [1, 0, 122, 0, 5041], [1, -2, 147, -146, 5329], [1, -4, 142, -316, 6241], [1, 16, 210, 1328, 6889], [1, 0, -2, 0, 7921], [1, 4, 118, 388, 9409]], 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1617/2/a/l'], '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': '4-1617e2-1.1-c1e2-0-9', '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': 2, 'prelabel': '4-1617e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.5933007119974034, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1119686625915146720, 'z1': {'__RealLiteral__': 0, 'data': '1.51088916595908606697405159221', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1915279558106364358325991980572,2333359344201314584606956183405', 'Lhash_array': ['1915279558106364358325991980572', '2333359344201314584606956183405'], 'label': '4-1617e2-1.1-c1e2-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1617/2/a/l'}