-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '247902044346204929061622570668', 'a10': [-1.7071067811865475, 2.956795678960466], 'a2': [-0.5, -0.8660254037844386], 'a3': [0.20710678118654752, -0.3587194676071504], 'a4': [-0.5, 0.8660254037844386], 'a5': [-1.7071067811865475, -2.956795678960466], 'a6': [-0.41421356237309503, 0], 'a7': [0, 0], 'a8': [1.0, 0], 'a9': [1.4142135623730951, 2.449489742783178], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.607873337894029, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, 0.8660254037844386]]], [7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0.5, -0.8660254037844386]]]], 'bad_primes': [2, 7, 11], 'central_character': '1078.67', 'coefficient_field': 'CDF', 'conductor': 1078, 'conductor_radical': 154, 'conjugate': '1780407596061610685237240390581', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [-0.20710678118654752, 0.3587194676071504], [-1.5, -2.598076211353316]], [[1.0, 0], [1.7071067811865475, 2.956795678960466], [-2.5, 4.330127018922194]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [1.82842712474619, 0], [13.0, 0]], [[1.0, 0], [3.8284271247461903, -6.631030293135233], [-8.5, -14.722431864335457]], [[1.0, 0], [1.7071067811865475, 2.956795678960466], [-9.5, 16.454482671904334]], [[1.0, 0], [1.1213203435596426, 1.9421838066058899], [-11.5, 19.91858428704209]], [[1.0, 0], [8.65685424949238, 0], [29.0, 0]], [[1.0, 0], [2.0, -3.4641016151377544], [-15.5, -26.846787517317598]], [[1.0, 0], [-3.2928932188134525, -5.70345835888392], [-18.5, 32.04293994002423]], [[1.0, 0], [-2.585786437626905, 0], [41.0, 0]], [[1.0, 0], [-5.656854249492381, 0], [43.0, 0]], [[1.0, 0], [-3.242640687119285, -5.616418420780657], [-23.5, 40.703193977868615]], [[1.0, 0], [-5.949747468305833, 10.30526490731], [-26.5, -45.89934640057525]], [[1.0, 0], [4.207106781186548, -7.28692269788266], [-29.5, -51.09549882328188]], [[1.0, 0], [-3.085786437626905, -5.34473889127677], [-30.5, 52.827549630850754]], [[1.0, 0], [5.621320343559643, -9.736412440665838], [-33.5, -58.023702053557386]], [[1.0, 0], [-3.071067811865475, 0], [71.0, 0]], [[1.0, 0], [3.2928932188134525, -5.70345835888392], [-36.5, -63.21985447626402]], [[1.0, 0], [-2.3786796564403576, -4.119994019885181], [-39.5, 68.41600689897065]], [[1.0, 0], [16.14213562373095, 0], [83.0, 0]], [[1.0, 0], [2.242640687119285, 3.8843676132117797], [-44.5, 77.07626093681505]], [[1.0, 0], [1.82842712474619, 0], [97.0, 0]], [[1.0, 0], [-5.914213562373095, 10.243718376843127], [-50.5, -87.4685657822283]], [[1.0, 0], [-5.292893218813452, -9.167559974021675], [-51.5, 89.20061658979718]], [[1.0, 0], [5.535533905932738, 9.5878259720957], [-53.5, 92.66471820493493]], [[1.0, 0], [-0.24264068711928516, 0.4202659980740251], [-54.5, -94.39676901250381]], [[1.0, 0], [13.82842712474619, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-1078-7.4-c1-0-1', 'leading_term': '0.388077184263279603858702480200073899201961043593050412', '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/1078/2/e/m/67/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.3880771842632796, 0.28146288006507963, 0.16680592024814123, 0.04360724269390874, -0.08865220073304748, -0.23045485604173202, -0.382188815196939, -0.5440917001890425, -0.7161985208006273, -0.8982953049793759, -1.0898797917726741, -1.2901300663404558, -1.497881730473009, -1.711614031231917, -1.9294452845537597, -2.1491378918920785, -2.3681132202200317, -2.583476570370409, -2.7920523763616485, -2.990429648447573, -3.175017491854085, -3.3421103038624285, -3.487961980497559, -3.6088681599271233, -3.701255204172831, -3.76177428672785, -3.787398624998457, -3.7755215875959967, -3.724053132101318, -3.631511803590518, -3.4971093619934197, -3.320825020307769, -3.1034662773821875, -2.8467134279836963, -2.553145036244874, -2.2262419704012153, -1.870368017587885, -1.4907256241442453, -1.0932859320423478, -0.684692994112847, -0.27214283380671295, 0.13676115071468062, 0.534174077160882, 0.9121935421571391, 1.2630576031275758, 1.5793519553407047, 1.8542208041068664, 2.081575381483108, 2.256293662281296, 2.3744046231515483, 2.4332503842577435, 2.4316197932994075, 2.3698474673968413, 2.249873002950514, 2.0752559917683033, 1.8511436291699321, 1.584189042708407, 1.2824199756104437, 0.9550590852626025, 0.6122988143743427, 0.26503550450477326, -0.07543091288217225, -0.39772375810797467, -0.6907337094114303, -0.9439697659164199, -1.1479058186780935, -1.294311089827324, -1.376552600613496, -1.3898581518769044, -1.3315290608701456, -1.2010930961603514, -1.000389670240154, -0.7335813524553061, -0.40708810040455756, -0.029443206933431897, 0.3889272619079939, 0.8359969017673468, 1.2984958044236676, 1.7623216168914786, 2.2129921979040494, 2.6361251515487045, 3.017927886888138, 3.345680773281002, 3.608195506372908, 3.796231020518634, 3.902850205963078, 3.9237023121356973, 3.8572182113921114, 3.7047086003035807, 3.4703586391375314, 3.161116358752714, 2.7864762587252354, 2.3581637234937225, 1.8897300242197308, 1.396071576370903, 0.8928906115294754, 0.39611733048684855, -0.07868421587575943, -0.5169029458072317, -0.9054363154728118, -1.233191311733421, -1.4915091862263408, -1.6744948789271912, -1.7792356229019557, -1.8058975585184747, -1.7576941542831828, -1.6407256362395866, -1.463694243544576, -1.2375057099417774, -0.9747726657522806, -0.6892404112948992, -0.39515949299020536, -0.10663250631807034, 0.16303561915251907, 0.40195405568783643, 0.6002002570226921, 0.7502850966346721, 0.8475056906349702, 0.8901673426653914, 0.8796617793412403, 0.8203953588357722, 0.719567948120172, 0.5868103566337365, 0.4336952448158727, 0.27314294839358705, 0.1187493381612314, -0.01593263699272999, -0.11812296140855158, -0.1765198575515987, -0.18194437220225154, -0.1278902756843823, -0.010949106240618121, 0.16891438041496093, 0.40825425648006775, 0.7002129058854956, 1.0347691797276013, 1.3991574076361477, 1.7784405103054663, 2.1562120887811616, 2.5153950138712364, 2.8390981168323908, 3.1114884447026916, 3.3186344658212183, 3.4492757722411422, 3.495477295247536, 3.4531307796256456, 3.3222730833417793, 3.107199497667616, 2.816360328755492, 2.4620399664076063, 2.059829043167444, 1.627911469882423, 1.186198524268343, 0.7553511887015798, 0.3557390563643488, 0.006388907026151646, -0.2760218395810754, -0.47807235693892314, -0.590355602308, -0.6080412764683171, -0.531209482603099, -0.36493130401438406, -0.11908544367688176, 0.19208602028134952, 0.5506655327339882, 0.9359607037679318, 1.3255743655496912, 1.6965902737922938, 2.0268128586648877, 2.295994735158307, 2.4869844785200286, 2.586729636394779, 2.587076069046137, 2.485314262887581, 2.2844358329291525, 1.9930784172497187, 1.6251538170096491, 1.1991716764603795, 0.7372882830814786, 0.26412622962759597, -0.19457522056803062, -0.613408039720214, -0.968763037389305, -1.240235202415363, -1.411885940191698, -1.473287038781147, -1.4202812649567702, -1.2554085160553912, -0.9879637658814996, -0.6336727657465966, -0.2139925538699089, 0.2449348634807486, 0.7136269666875059, 1.1608364528650157, 1.5552764663250418, 1.8674028330447097, 2.0711550027496237, 2.145556991941407, 2.0760847743385704, 1.8557171419355127, 1.4856026056518825, 0.9752946670841874, 0.3425307571373384, -0.38744492323557084, -1.1829888831817517, -2.007545665403402, -2.821442108137581, -3.5838968242164757, -4.255139131285642, -4.798523308715797, -5.182521990205743, -5.382486981689441, -5.382076702516746, -5.17426628792045, -4.761878310029398, -4.157597906140469, -3.3834644268005776, -2.469860938125395, -1.4540513544454416, -0.3783409744839373, 0.7120418043230166, 1.7712281562776917, 2.755031172927476, 3.623179981130644, 4.341341899073623, 4.882820271326366, 5.229833622303934, 5.374305398483289, 5.318121491787917, 5.072843331862209, 4.658895803375045, 4.1042797105003235, 3.442886136998384, 2.7125131510437925, 1.9527024507605228, 1.2025236603165457, 0.49843640941922357, -0.12764512915003365, -0.649973613179669, -1.0501840452758207, -1.3180371327361686, -1.451653726483166, -1.457235323600546, -1.3482976067193617, -1.144474203871153, -0.8699743657851293, -0.5517993762921533, -0.2178368703104522, 0.10504110823482021, 0.3927519705679568, 0.625533604627193, 0.7891348425757224, 0.8755911040855332, 0.8835392558649325, 0.8180570570439896, 0.6900448427323888, 0.5151981892208093], 'positive_zeros': ['0.19556023110908663204122553118672', '2.38261911480719988017602144868175', '3.56103390192155205347672395576640', '4.34023566181138521046815865278228', '5.67361227770173730523194917778801', '6.58503505583875957714547337521288', '7.37519485085291131560772692777846', '7.68003058040779525782300595885977', '9.083209414753065558805633933324176', '9.515916960006289856075114318843564'], 'prelabel': '2-1078-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': -0.3736792394412256, 'root_number': '0.3865135727591552881869185769990697126707082293252108640 - 0.9222837188593069656715137745867251124838836430784361633*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1868396197206128', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.19556023110908663204122553119', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.38261911480719988017602144868', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.56103390192155205347672395577', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 8.607873337894029, 'bad_primes': [2, 7, 11], 'central_character': '7.4', 'conductor': 1078, 'conductor_radical': 154, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1078/2/e/m/67/2'], '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': '2-1078-7.4-c1-0-1', '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': '2-1078-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': -0.1868396197206128, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.19556023110908663204122553119', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '247902044346204929061622570668', 'Lhash_array': ['247902044346204929061622570668'], 'label': '2-1078-7.4-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1078/2/e/m/67/2'}