-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '295417665735407865336826955212', 'a10': [-769.6631576431014, 0], 'a2': [4.898979485566356, 2.8284271247461903], 'a3': [0, 0], 'a4': [16.0, 27.712812921102035], 'a5': [-117.83012562780556, 68.02925474986097], 'a6': [0, 0], 'a7': [93.52652298297919, -161.99268966177826], 'a8': [0, 181.01933598375618], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 37.26876154641587, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-4.898979485566356, -2.8284271247461903]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '162.107', 'coefficient_field': 'CDF', 'conductor': 162, 'conductor_radical': 6, 'conjugate': '2385294884874250492295525190751', 'degree': 2, 'euler_factors': [[[1.0, 0], [-4.898979485566356, -2.8284271247461903]], [[1.0, 0], [0, 0]], [[1.0, 0], [117.83012562780556, -68.02925474986097], [7812.5, -13531.646934131853]], [[1.0, 0], [-93.52652298297919, 161.99268966177826], [-58824.5, -101887.02272983543]], [[1.0, 0], [-1594.466311410357, -920.5655541065594], [885780.5, 1534216.830353764]], [[1.0, 0], [-290.7637419345152, -503.61757402942567], [-2413404.5, 4180139.2132153627]], [[1.0, 0], [0, -1756.70315791857], [-24137569.0, 0]], [[1.0, 0], [7719.533685172819, 0], [47045881.0, 0]], [[1.0, 0], [12733.942521697425, -7351.94514274723], [74017944.5, -128202840.54581334]], [[1.0, 0], [27624.70606704627, 15949.131484093454], [297411660.5, 515132106.74942577]], [[1.0, 0], [17013.39968826075, 29468.07266954412], [-443751840.5, 768600733.6982006]], [[1.0, 0], [77087.63839288341, 0], [2565726409.0, 0]], [[1.0, 0], [-9833.909988848007, 5677.610579247947], [2375052120.5, -4113710943.3301992]], [[1.0, 0], [-25148.861546697015, 43559.10595139445], [-3160681524.5, -5474460986.978255]], [[1.0, 0], [22409.660028612485, 12938.223249967414], [5389607664.5, 9335074307.776636]], [[1.0, 0], [0, -195102.1360126177], [-22164361129.0, 0]], [[1.0, 0], [-331853.2914853079, 191595.58717050587], [21090266820.5, -36529413678.29012]], [[1.0, 0], [223217.85934893027, -386624.67354911077], [-25760187180.5, -44617953009.110466]], [[1.0, 0], [232361.63763561982, 402462.1621148021], [-45229191084.5, 78339256943.59529]], [[1.0, 0], [0, -248915.93901431662], [-128100283921.0, 0]], [[1.0, 0], [545586.6872382975, 0], [151334226289.0, 0]], [[1.0, 0], [55131.44711128264, -95490.46749153794], [-121543727760.5, -210519911822.5058]], [[1.0, 0], [-41039.30617693458, -23694.05446860865], [163470186684.5, 283138668860.32336]], [[1.0, 0], [0, -37879.46912308519], [-496981290961.0, 0]], [[1.0, 0], [-448580.3753082097, 776964.0013121347], [-416486002464.5, -721374916909.7706]], [[1.0, 0], [-1479840.0098537656, -854386.02804665], [530760075300.5, 919303417049.5492]], [[1.0, 0], [-278687.8778723781, -482701.56392850913], [-597026148264.5, 1034079622241.2635]], [[1.0, 0], [0, -1535178.1338946037], [-1500730351849.0, 0]], [[1.0, 0], [2284912.740965942, 0], [1677100110841.0, 0]], [[1.0, 0], [1476585.8192422015, -852507.2202210691], [1040975876304.5, -1803023107212.929]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-162-9.2-c6-0-3', 'leading_term': '1.033269075421485029881327403107774866175463240734318474', 'load_key': 'CMFs-workshop', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/162/7/d/g/107/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [1.033269075421485, 0.716325451238598, 0.4019591116161893, 0.0945365039286686, -0.20169593127925184, -0.48266458223888686, -0.7445202208332203, -0.9836879203642992, -1.196914922242121, -1.3813159872323988, -1.5344157130920775, -1.6541872466178882, -1.7390867680298483, -1.788083083063594, -1.800681627044966, -1.7769421693672107, -1.7174895097601817, -1.62351648274703, -1.4967786364501385, -1.339580028537489, -1.154749686956465, -0.9456084166988707, -0.7159257957512015, -0.4698673921632716, -0.211932447302217, 0.05311749576161191, 0.32033828986558915, 0.5846902182750481, 0.841131113251004, 1.0847140460724427, 1.3106878285498527, 1.5145983399002754, 1.6923884970323202, 1.8404945299865991, 1.9559361164069966, 2.0363978778166527, 2.080299753561984, 2.0868538517363464, 2.056105534777873, 1.9889567334163991, 1.8871697966804641, 1.7533505757726073, 1.590909901140969, 1.4040031376142215, 1.1974480818188515, 0.9766220863091543, 0.7473399403673315, 0.5157146904051347, 0.2880042235006723, 0.07044704454827, -0.13090877138240511, -0.31037899696238147, -0.4628142133831472, -0.5837632341821586, -0.6696237986430432, -0.7177753816149056, -0.7266891722241223, -0.6960106516086813, -0.6266107509069264, -0.5206022908640165, -0.3813192829587533, -0.21325769189281937, -0.021977397269381967, 0.18603368110390373, 0.4035310495806421, 0.6227171597776986, 0.8354721767252453, 1.0336060029582887, 1.2091244981966494, 1.3545019353427756, 1.4629510466533742, 1.528681578559814, 1.5471381230839487, 1.5152081536492639, 1.4313916794285229, 1.2959247505211822, 1.1108501896985292, 0.8800303761480359, 0.6090986307696494, 0.30534770675521794, -0.02244398276169058, -0.36424553298802975, -0.7090609778066311, -1.0452636317029507, -1.360967912283512, -1.6444273543435117, -1.8844459747098794, -2.0707889793616556, -2.194578088679881, -2.248656548165571, -2.2279092295375778, -2.1295241309456863, -1.9531830543793036, -1.701171250196069, -1.378398327136932, -0.9923256627738305, -0.5527988243072256, -0.07178701421204858, 0.43696483519520496, 0.9583621159986602, 1.4764521419132475, 1.9749655984652261, 2.437889531413868, 2.8500515232009076, 3.1976933738533115, 3.469012062130504, 3.654646077829992, 3.748086418214188, 3.745993626591438, 3.648405178299082, 3.458821210431644, 3.184160932166183, 2.8345868946262356, 2.4231994661648564, 1.9656091511135951, 1.4793995922960825, 0.9834989877739404, 0.49748201048517454, 0.04082793776930414, -0.36783660986016703, -0.7114803099348382, -0.9753647334666649, -1.1476673188846258, -1.220002280416159, -1.1878153811043566, -1.0506330219330646, -0.8121516162537358, -0.4801595313544931, -0.06629074081730982, 0.4143835386814679, 0.9439118592453126, 1.502148095155533, 2.0675393566821754, 2.617984971491933, 3.1317313554434865, 3.588265153951634, 3.9691661999660988, 4.258882697806928, 4.445393621357995, 4.520727549000598, 4.481312905111781, 4.328141621652542, 4.06673628698633, 3.706919568098, 3.262393688369707, 2.7501466005775783, 2.189709790440094, 1.602299968865967, 1.0098828829053772, 0.43420177089675177, -0.10418464825180943, -0.5868094969772246, -0.998107123566763, -1.3260853438059268, -1.5628273739030158, -1.704798080327791, -1.7529383758238493, -1.7125417852361322, -1.5929179054868847, -1.4068581659398924, -1.1699294182018893, -0.8996299198115403, -0.6144497356139597, -0.3328830416020117, -0.07244294688771645, 0.15126997049692528, 0.3253962834757393, 0.44049903021130976, 0.4910603554991925, 0.47576531820445017, 0.397555588543174, 0.2634477868605634, 0.08412377390502095, -0.12668736751698229, -0.35300428967787634, -0.5775237241310879, -0.7826365161709062, -0.9514740399058194, -1.0689269756267001, -1.1225788505830585, -1.1035003505831935, -1.0068570878971923, -0.8322929724107436, -0.5840631265421387, -0.27090381557706555, 0.09435857545788864, 0.49544268753102366, 0.9134604103137755, 1.3279343235065686, 1.7179298504016376, 2.063239797126091, 2.3455544814479277, 2.549549884076496, 2.66382933065097, 2.681661066249669, 2.6014644297794263, 2.427010677130595, 2.1673201558906143, 1.8362546626324252, 1.451821467234533, 1.0352226586051305, 0.6096991408590025, 0.19923183258089866, -0.17282744805513234, -0.4851169687170915, -0.719537968080636, -0.8623625947982838, -0.9051077831508302, -0.8451179602220112, -0.6858151912271396, -0.43659396129878286, -0.11235824790390853, 0.2672802993582437, 0.6791036206325678, 1.0976296342172522, 1.4966215164653105, 1.8506776971807526, 2.1368092610851845, 2.3359096863153415, 2.4340257267254777, 2.4233476875618574, 2.302851949014459, 2.078547631822119, 1.7633017573250784, 1.3762418785830635, 0.9417605290001811, 0.4881704429613991, 0.046081843798355775, -0.35340824411065636, -0.6806109500491879, -0.9091131937375008, -1.0175050582301066, -0.9908593660607573, -0.8218679677752492, -0.5115573696412334, -0.06952958147352271, 0.4862988221406051, 1.1304570118628876, 1.831147168610121, 2.5518775191854557, 3.253414205711674, 3.8959439582462885, 4.441324502667846, 4.855291714700649, 5.1094923725283605, 5.18321914797115, 5.064739906084947, 4.752135671789172, 4.253589543475232, 3.587100784444541, 2.77963241509808, 1.8657348001591474, 0.8857198660561406, -0.11651133202700689, -1.0958627584438634, -2.008519458862, -2.8143592615501842], 'positive_zeros': ['0.23304344721031213084842847811865', '1.74380972623232787267677881507012', '3.46917549839837624646708447334055', '4.36703639959571861023820529301917', '5.62030442685593088673105250455268', '6.83042265828379852335026468494052', '8.303499294084954796240758472273467', '9.010247021687123412912706362051425', '10.53275692559766929017124840589473', '11.55259392632215622121593750348790'], 'prelabel': '2-162-9.2-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.104814620151529, 'root_angle': 0.9722222222222222, 'root_number': '-0.99619469809174553229501040247388804618356267264585097453 + 0.0871557427476581735580642708374735513777011561497026726*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.48611111111111116', 'prec': 64}, 'spectral_label': 'c6-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.23304344721031213084842847812', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.74380972623232787267677881507', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.46917549839837624646708447334', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 37.26876154641587, 'bad_primes': [2, 3], 'central_character': '9.2', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/7/d/g/107/6'], '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': '2-162-9.2-c6-0-3', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'prelabel': '2-162-9.2-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.104814620151529, 'root_angle': 0.4861111111111111, 'self_dual': False, 'spectral_label': 'c6-0', 'z1': {'__RealLiteral__': 0, 'data': '0.23304344721031213084842847812', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '295417665735407865336826955212', 'Lhash_array': ['295417665735407865336826955212'], 'label': '2-162-9.2-c6-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/7/d/g/107/6'}