-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2830255398609326229077724799715', 'a10': [-1.7303555939300552, -1.4519407406722526], 'a2': [-0.6862416378687336, -0.7273736415730487], 'a3': [0.22450532960315558, -1.7174391858170055], 'a4': [-0.05814482891047583, 0.9983081582712682], 'a5': [2.2435454807649324, -0.26223285760593096], 'a6': [-1.4032848998650964, 1.0152790206690012], 'a7': [3.76234787669041, 1.8895221218380196], 'a8': [0.766044443118978, -0.6427876096865394], 'a9': [-2.899194713959557, -0.771148500970444], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.293576512744743, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.6862416378687336, 0.7273736415730487]]], [3, [[1.0, 0], [-0.22450532960315558, 1.7174391858170055]]]], 'bad_primes': [2, 3], 'central_character': '162.103', 'coefficient_field': 'CDF', 'conductor': 162, 'conductor_radical': 6, 'conjugate': '2040547909988933288518633494024', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.6862416378687336, 0.7273736415730487]], [[1.0, 0], [-0.22450532960315558, 1.7174391858170055]], [[1.0, 0], [-2.2435454807649324, 0.26223285760593096], [4.865224352899119, -1.1530793537122008]], [[1.0, 0], [-3.76234787669041, -1.8895221218380196], [4.180110141919503, 5.614862349285307]], [[1.0, 0], [1.4225298715616168, 3.297794920574339], [-7.548658016556069, 8.001110057303535]], [[1.0, 0], [4.268362287424527, 1.0116204455936748], [11.61722432420436, 5.834389342606008]], [[1.0, 0], [0.2413474453347829, -1.3687493789383331], [-15.974774553360442, -5.814342436536369]], [[1.0, 0], [-0.8830441356766403, -5.007992152582965], [-17.854159794932258, 6.498382723187706]], [[1.0, 0], [0.26189536849033257, -0.1315287975987775], [13.734647609164082, -18.44883343336601]], [[1.0, 0], [-2.137412701460011, 7.13945561956502], [-24.229146530975157, -15.935760364053374]], [[1.0, 0], [-6.75905437243712, -4.445499994358657], [12.278472747213861, 28.464699313288495]], [[1.0, 0], [2.900341350916788, -1.0556379209451372], [28.343644395402187, -23.783141558401955]], [[1.0, 0], [5.070945775199469, -5.374888510381888], [-2.383937985329509, -40.930634489122]], [[1.0, 0], [-1.6606669904999283, 2.2306628875997085], [-12.33253900657688, -41.19354902956602]], [[1.0, 0], [0.8344128782830286, -0.548801983429303], [18.61574900384037, -43.15615702337288]], [[1.0, 0], [5.962573321500795, -10.327479936694095], [-26.5, -45.89934640057525]], [[1.0, 0], [3.665922261311071, -8.49856305604363], [-40.48825663425528, -42.91504485280987]], [[1.0, 0], [0.8630132669089087, 14.81736555417534], [-60.58753982225852, 7.081667761639044]], [[1.0, 0], [1.6006312522384425, 5.346480715137148], [-55.97768336466674, 36.817101530744004]], [[1.0, 0], [-4.889851389737927, -4.103072497640805], [12.329020614352055, 69.92135046386677]], [[1.0, 0], [-4.664396127594306, 3.913893070329115], [12.676316969685915, -71.89096596989118]], [[1.0, 0], [-8.31654777764669, -8.815025653544263], [-4.593441483927591, 78.86634450343018]], [[1.0, 0], [-2.1267067322895774, -2.25417744284308], [-4.826020799569494, 82.85957713651526]], [[1.0, 0], [0.706078146781056, -0.5924699125463214], [15.4546878123568, -87.64789001808651]], [[1.0, 0], [-1.8541020194305633, -0.21671344531087144], [94.38535244624292, 22.369739462016696]], [[1.0, 0], [0.41702849758846866, 7.160102784293689], [-100.31707413193624, 11.725384326648253]], [[1.0, 0], [-2.163518305911048, 5.015599195797982], [-70.68288870047957, -74.91948508202401]], [[1.0, 0], [6.913741509523453, 11.974951564892566], [-53.5, 92.66471820493493]], [[1.0, 0], [8.520706385498194, -14.758296376059436], [-54.5, -94.39676901250381]], [[1.0, 0], [5.253090175819343, 7.056124658013032], [-32.408765296353195, 108.25281489165025]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-162-81.22-c1-0-6', '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/162/2/g/b/103/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.113232221032331, 1.1750338000226734, 1.2481427848813083, 1.3319117834756657, 1.4238564242899077, 1.5198277678381216, 1.61424912399233, 1.700360335241846, 1.770460419216195, 1.8161698383735991, 1.8287417297571995, 1.7994449195531046, 1.7200286681826091, 1.5832645796668747, 1.3835469425482254, 1.1175197016782246, 0.7846868096294465, 0.3879535598628904, -0.06595942739877862, -0.5662895750279123, -1.0982495122332954, -1.6433348704924247, -2.1799535503250613, -2.6843850820797384, -3.1320511529890207, -3.499047120407104, -3.763851760370812, -3.9091016436711223, -3.923290871436512, -3.8022400764698654, -3.5501740185632196, -3.1802575266877335, -2.71446661727227, -2.1827154797700996, -1.6212189760748037, -1.0701406756455907, -0.5706526420825628, -0.16160796675641753, 0.12390790158348569, 0.2618342616865313, 0.23986747448589524, 0.05934727345719583, -0.2639762328878598, -0.7004845610532844, -1.2086166465428683, -1.7381157655296238, -2.234387592038741, -2.643617882068158, -2.9181797502790703, -3.021781738262327, -2.93378306218394, -2.652141039866086, -2.194560609429831, -1.597582073211676, -0.9135574509597473, -0.20570714784450822, 0.45830987579514565, 1.0136677115059602, 1.40569031512422, 1.5963501651676861, 1.569120777075465, 1.3314981275840665, 0.9147485870074463, 0.3707606475750377, -0.23376051544065465, -0.8251572254107878, -1.3318353902550795, -1.6933146740036809, -1.8681189160118088, -1.8393942099206706, -1.6173828677744084, -1.2382617249388677, -0.7593308950712033, -0.25105419847651345, 0.21306590601653466, 0.5674205724215576, 0.7644699923353495, 0.7826064089704026, 0.6303881629061318, 0.3462812867030555, -0.0063379457875941785, -0.34846486385661213, -0.5978916464373405, -0.6830691918105591, -0.5563498993614014, -0.20449474043794671, 0.3454122202659053, 1.0259325701357305, 1.7356071089871983, 2.351190064442915, 2.744374159108801, 2.800798721227408, 2.438618627626871, 1.6237827474481001, 0.3794750456157802, -1.212107425653362, -3.0164125093764733, -4.861158914742432, -6.557217527284951, -7.922984210711615, -8.808801637780205, -9.117811943492582, -8.820005785157901, -7.9571455001089415, -6.637560866872304, -5.021351888202931, -3.29804430417447, -1.6599819691664464, -0.27549049800672937, 0.734035208743476, 1.309524875190573, 1.4596789150994605, 1.2556349232411945, 0.8157956340316116, 0.28340970766959916, -0.19926349008808494, -0.5157717734563588, -0.5949958312286906, -0.4220193263186176, -0.03850169592388399, 0.4674137632349492, 0.9797275054000628, 1.3782450287251662, 1.5628177750381318, 1.4735705277981368, 1.1032426572007554, 0.49923667954044887, -0.24507965613329347, -1.0081928812777772, -1.6639527825031681, -2.1061615213040645, -2.269335321887575, -2.141397591821438, -1.7655924967882928, -1.2310260633875594, -0.6535443060084205, -0.15068822029854198, 0.1841966204476185, 0.3032708985291782, 0.21626158435830872, -0.009653975311861795, -0.2626423324810185, -0.4095578797029259, -0.3254006009203333, 0.07704101187900053, 0.8236232222114259, 1.8666676878490378, 3.0873840282029437, 4.313245682778235, 5.347597366399002, 6.006116000216679, 6.153076659878326, 5.7300819482357355, 4.77111996778175, 3.400338707500692, 1.8122965822869335, 0.23800567142026718, -1.0969058334961952, -2.013770520433867, -2.413860975337023, -2.2959593386104853, -1.7546936806415991, -0.9596935894571698, -0.11959513730064589, 0.5618312570736833, 0.9283580273635872, 0.9037844531577713, 0.5072171520910572, -0.15232839026866973, -0.9011115803827149, -1.5404549841520547, -1.8926799113411767, -1.843205898228405, -1.3694369612389363, -0.5497254879278151, 0.45008968449169984, 1.410208499264347, 2.103618883414831, 2.346138260434107, 2.0388273054310697, 1.1932465958550154, -0.06644735456591179, -1.525633962265537, -2.92136705639196, -3.995822281881302, -4.54970447340574, -4.484069797553182, -3.8213709232691166, -2.7009610996341076, -1.349842355333102, -0.034889321982192745, 0.9931014731842209, 1.551342382594143, 1.5616446654083909, 1.0637701196697165, 0.2028644244857996, -0.8058728793588598, -1.727009454628279, -2.3577035907916253, -2.57147962775252, -2.343138385074336, -1.749498769328183, -0.9464014290256231, -0.12800427687032173, 0.5214731227479642, 0.8717374424972606, 0.8755327467057351, 0.5760596976270022, 0.09134342812525555, -0.4200311664380518, -0.802731619919331, -0.9465728972090744, -0.8155566325490402, -0.45644544582860835, 0.015416528096014586, 0.44934748045332645, 0.7028382765596831, 0.6836321232036708, 0.378790538238685, -0.1376607772913315, -0.7214146551896403, -1.1953482967170377, -1.3984749047289604, -1.2335675863092461, -0.7003702766324591, 0.09551246985308069, 0.9620124051359814, 1.6649678022804932, 1.9873734698577745, 1.7889206213990803, 1.0502956764232907, -0.11026784990891329, -1.4542908075692105, -2.672019234947351, -3.452730093367638, -3.5601079051841076, -2.8943207946657776, -1.5248332849065243, 0.31550529402665245, 2.275438633208505, 3.960140749471035, 5.01909910291449, 5.2265230754298635, 4.534987736423765, 3.0890167525749996, 1.1946924543385589, -0.7481004791852659, -2.3351266697541746, -3.247937175356595, -3.3234426579225422, -2.586643009013401, -1.2392123321544921, 0.3925991940475168, 1.9374306847802574, 3.0658570737436692, 3.5637663866427336, 3.374702326023576], 'positive_zeros': ['2.23267783575360868593342997521971', '4.68822441305766771718200806987095', '5.15234379411811509904703396456155', '6.91228500039942436959242725254520', '7.952183288933059962937843141307314', '9.189930189610492671919700857999573', '9.997807513571883671086422882352482', '10.67625613763018563661901398817587', '11.78204588971976333806584346338695', '13.52951646849528027988487835532187'], 'prelabel': '2-162-81.22-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1373550513119213, 'root_angle': 0.4371056236203907, 'root_number': '0.19630533544590334 + 0.9805428166456941*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.21855281181', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.23267783575360868593342997522', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.68822441305766771718200806987', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.15234379411811509904703396456', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.293576512744743, 'bad_primes': [2, 3], 'central_character': '81.22', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/2/g/b/103/2'], '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': '2-162-81.22-c1-0-6', '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': '2-162-81.22-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1373550513119213, 'root_angle': 0.21855281181019534, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.23267783575360868593342997522', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2830255398609326229077724799715', 'Lhash_array': ['2830255398609326229077724799715'], 'label': '2-162-81.22-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/2/g/b/103/2'}