-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1914471563767011900107754038225', 'a10': [-1.4118539999795807, 2.4454028608339824], 'a2': [-2.3313589819648324, -1.346010735815048], 'a3': [0.5, -0.8660254037844386], 'a4': [2.6234898018587334, 4.544017629958133], 'a5': [0.0, -1.0489173395223053], 'a6': [-2.3313589819648324, 1.346010735815048], 'a7': [-0.48060784042442345, 0.2774790660436856], 'a8': [0.0, -8.740938811152402], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.048415382478917, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.5, 0.8660254037844386]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '507.316', 'coefficient_field': 'CDF', 'conductor': 507, 'conductor_radical': 39, 'conjugate': '817537191389145629916412731636', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.3313589819648324, 1.346010735815048], [1.0, 1.7320508075688772]], [[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 1.0489173395223053], [-5.0, 0]], [[1.0, 0], [0.48060784042442345, -0.2774790660436856], [3.5, -6.06217782649107]], [[1.0, 0], [-2.521739536093649, -1.4559269999897904], [5.5, 9.526279441628825]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.425427537663572, 4.200963725309983], [-8.5, 14.722431864335457]], [[1.0, 0], [0.6521347927484986, -0.37651019814126646], [9.5, -16.454482671904334]], [[1.0, 0], [-2.8813545376533622, 4.9906524538347545], [-11.5, -19.91858428704209]], [[1.0, 0], [-0.9559269999897904, 1.6557141323092104], [-14.5, -25.11473670974872]], [[1.0, 0], [0, 9.515729471589257], [-31.0, 0]], [[1.0, 0], [-4.982261811670692, -2.8765101981412666], [18.5, 32.04293994002423]], [[1.0, 0], [4.253790343662526, 2.4559269999897904], [20.5, 35.50704155516198]], [[1.0, 0], [5.548917339522306, 9.611006759052556], [-21.5, 37.239092362730865]], [[1.0, 0], [0, 0.7530203962825329], [-47.0, 0]], [[1.0, 0], [7.582105207455354, 0], [53.0, 0]], [[1.0, 0], [3.5488289325614844, -2.0489173395223053], [29.5, -51.09549882328188]], [[1.0, 0], [-1.7116358018791529, -2.96464017290859], [-30.5, 52.827549630850754]], [[1.0, 0], [-1.6217411157614086, -0.9363126697407332], [33.5, 58.023702053557386]], [[1.0, 0], [9.09642590208033, -5.251823943229563], [35.5, -61.48780366869514]], [[1.0, 0], [0, 10.476500811091142], [-73.0, 0]], [[1.0, 0], [-1.3351256037378865, 0], [79.0, 0]], [[1.0, 0], [0, -2.6431041321077906], [-83.0, 0]], [[1.0, 0], [-8.596964459851165, -4.9634597451087155], [44.5, 77.07626093681505]], [[1.0, 0], [-14.78623326247783, 8.536835754392174], [48.5, -84.00446416709055]], [[1.0, 0], [-3.6615220093038774, 6.341942153145999], [-50.5, -87.4685657822283]], [[1.0, 0], [-4.219832528349484, 0], [103.0, 0]], [[1.0, 0], [3.1968658111421915, -5.537134009878167], [-53.5, -92.66471820493493]], [[1.0, 0], [0, 3.4601073581504793], [-109.0, 0]], [[1.0, 0], [4.678447933946105, 8.103309522160297], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 14, 'label': '2-507-13.4-c1-0-14', '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/507/2/j/i/316/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.6230833858447609, 0.7308125010629748, 0.835638633288802, 0.9348468012879867, 1.022836883629325, 1.0911308726633095, 1.128793670158644, 1.1231907130204701, 1.0610284140761093, 0.9296436754092399, 0.718504264654747, 0.42085335147013586, 0.03538942606004481, -0.4321713598267835, -0.9678397652808342, -1.5486145370272018, -2.1424668299652136, -2.7092239369684554, -3.2024667216377773, -3.5724637538406188, -3.7700490233354365, -3.7512189189328606, -3.4820919105234185, -2.943758421310243, -2.136467719946237, -1.0825715195984142, 0.17231504697208808, 1.5603572396792131, 2.99497919004392, 4.376751456067972, 5.601366616929912, 6.569079697078595, 7.194721532579131, 7.417200474686706, 7.207329758594739, 6.572882839722463, 5.559999011038454, 4.2504276893115, 2.7545799332666348, 1.2008964050280302, -0.27742814997731213, -1.556881101393921, -2.5374666671941353, -3.1541208492817474, -3.3840877982837725, -3.2490907169945475, -2.8117910825881443, -2.166817881358435, -1.4274529756785324, -0.7097547074938009, -0.11636953184128411, 0.27757303584952037, 0.43431267431705634, 0.3574763738663677, 0.08956012678636317, -0.2967858763312361, -0.7122901727700093, -1.0671781640610702, -1.2871338858476458, -1.3263136422771347, -1.1750659492355155, -0.8609043091901756, -0.4424798698819367, 0.002395878009672014, 0.3924634038301479, 0.6594532554485728, 0.7619947145306547, 0.6941247958618096, 0.48650748952485695, 0.19988976507692452, -0.08808531130098499, -0.3001329460971351, -0.37706936759543, -0.29215540104289855, -0.05865819065777525, 0.27147753221076354, 0.6181258452495914, 0.8908823430835102, 1.0107924597739284, 0.9311426931266873, 0.6523259601435974, 0.22666252923551886, -0.24906159263342148, -0.6530023535256358, -0.8665060949184756, -0.8057228508642083, -0.4497011782793486, 0.14195280078392594, 0.8272794325444415, 1.3986138589920665, 1.6165388094763238, 1.256125286462508, 0.15723522110051952, -1.7311249409639702, -4.3222523051821025, -7.386600711309845, -10.57359283056963, -13.458796529854675, -15.60961890394271, -16.658412160765046, -16.36958615220078, -14.687601166258368, -11.755682204107996, -7.900296508709037, -3.582909750401556, 0.6730028197557566, 4.366616123777717, 7.100400464287069, 8.641580734907839, 8.95286850826936, 8.186989181853813, 6.646788863691917, 4.7196369505522675, 2.799945164540863, 1.2157791268094877, 0.17425767396496253, -0.26400561572336373, -0.17777166515166876, 0.2510121654929264, 0.7925336656076419, 1.2297782075385977, 1.4101642420398002, 1.2765940322539728, 0.8718381157469676, 0.3169523719142166, -0.22916692335115438, -0.6175334113810271, -0.7511627287429514, -0.6104980397760588, -0.25593719274147403, 0.1924421503693421, 0.5916597605238784, 0.8183843707595266, 0.8050654701794431, 0.5593504133258289, 0.16125218761440288, -0.26113602297464733, -0.5704245982645157, -0.6619950497279778, -0.4970110271499499, -0.1164264644467541, 0.36863683079693205, 0.8079679898506639, 1.0562529364194118, 1.0173241090384832, 0.6754884221778377, 0.10405514619361232, -0.5524585663569871, -1.1182827757303144, -1.4375257548269675, -1.4215827249817656, -1.0782281044873516, -0.5124662230096809, 0.10287057617933652, 0.5797657411940431, 0.7763571935831138, 0.648696769586302, 0.2761004620677018, -0.15018215351008035, -0.37513063403200664, -0.15411425344159338, 0.6664970173150374, 2.0855564508096482, 3.920786299272853, 5.831581390974135, 7.389767279570026, 8.183453789405824, 7.9285584106472395, 6.558285070645916, 4.264462644151161, 1.4756930988449033, -1.2268493446872588, -3.2384648134702108, -4.074396970830807, -3.4918373572679626, -1.5584126991105804, 1.3523854933879416, 4.640204916838709, 7.613508964692797, 9.649160965356202, 10.336414225595977, 9.569325138794852, 7.56462213991465, 4.801211543024134, 1.897694868127431, -0.5399176470613493, -2.060952011471303, -2.467320258881132, -1.842257125027933, -0.5063577982186435, 1.083803121817569, 2.4644773511266984, 3.2849954561941677, 3.3876790196511823, 2.8285102027821334, 1.837293436612811, 0.7332100728459695, -0.17659083441648382, -0.6846289914026361, -0.732344765642256, -0.40949196348492894, 0.09191169013176137, 0.5509835290069584, 0.7933071013790343, 0.743839817502048, 0.44182439111261307, 0.01553172309944542, -0.3718300888698381, -0.5845337378065895, -0.5626609936972453, -0.3397442685683781, -0.024542788616184488, 0.24521558645035632, 0.3592287728468572, 0.27965233273780443, 0.057436334945911306, -0.18683118821803, -0.3111334116585243, -0.21160541583070833, 0.1293043859105275, 0.6257677481355091, 1.1116946324339794, 1.3985240800393508, 1.3486256880754632, 0.9377250636953534, 0.2813996886249413, -0.38843509255745495, -0.7941961807434583, -0.7101489027027038, -0.05460747632507748, 1.056956431390271, 2.3216107631053, 3.325910029767605, 3.671870823954072, 3.115106712918188, 1.670250507152971, -0.3550036047704428, -2.4163930414908807, -3.871808651956468, -4.166869352861808, -3.0140679728374504, -0.5098351967919459, 2.8512059250437787, 6.276963203647307, 8.871742028497673, 9.872289037886446, 8.860028921165416, 5.887806436448526, 1.4824138701498462, -3.4806429733463187, -7.996732491329176, -11.185091717576242, -12.504626953429227, -11.87319284486707, -9.659813230828103, -6.55678097946833, -3.3732278690563273], 'positive_zeros': ['1.51025177081313103338233497783536', '3.23375014122491870645571997168574', '4.97552456095678876855048488894964', '6.28042500133211928780701606466484', '6.78150583435903008830309337168967', '7.87430452050113637516013673426120', '8.709691072770402764267228584485942', '9.274240850936022821180951505849149', '10.18431178632801406804241177938338', '10.84796608143393060307737152855978'], 'prelabel': '2-507-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0120674398436345, 'root_angle': 0.8331973976153866, 'root_number': '-0.8658117974935148 + 0.5003697945730227*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.416598698808', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.51025177081313103338233497784', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.23375014122491870645571997169', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.97552456095678876855048488895', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.048415382478917, 'bad_primes': [3, 13], 'central_character': '13.4', 'conductor': 507, 'conductor_radical': 39, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/507/2/j/i/316/1'], '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': '2-507-13.4-c1-0-14', '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': '2-507-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0120674398436345, 'root_angle': 0.4165986988076933, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.51025177081313103338233497784', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1914471563767011900107754038225', 'Lhash_array': ['1914471563767011900107754038225'], 'label': '2-507-13.4-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/507/2/j/i/316/1'}