-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1192881143283681038851565061210', 'a10': [-0.39242298733137293, 0.6796965521158959], 'a2': [-0.2460783215731632, 0.9183767987523176], 'a3': [-0.8660254037844386, -0.5], 'a4': [0.9491894034305876, 0.54801475758259], 'a5': [0.7973538360117167, 0.21365031644119736], 'a6': [0.6722984771791544, -0.6722984771791544], 'a7': [-2.229654436675707, 1.4243037221787829], 'a8': [-2.0814559283472662, 2.0814559283472662], 'a9': [0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.8660254037844386, 0.5]]], [7, [[1.0, 0], [2.229654436675707, -1.4243037221787829]]], [13, [[1.0, 0], [-3.5732569074951046, -0.4814925472305059]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.73', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '2690004054719446278341282316852', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.2460783215731632, -0.9183767987523176], [-1.7320508075688772, -1.0]], [[1.0, 0], [0.8660254037844386, 0.5]], [[1.0, 0], [-0.7973538360117167, -0.21365031644119736], [4.330127018922194, 2.5]], [[1.0, 0], [2.229654436675707, -1.4243037221787829]], [[1.0, 0], [-0.43033207998541756, -1.6060211866323724], [-9.526279441628825, 5.5]], [[1.0, 0], [-3.5732569074951046, -0.4814925472305059]], [[1.0, 0], [1.3169049493914349, -2.280946281084886], [-8.5, -14.722431864335457]], [[1.0, 0], [-6.01702242451744, -1.6122562994894039], [16.454482671904334, 9.5]], [[1.0, 0], [6.64217761727483, -3.83486303533893], [11.5, -19.91858428704209]], [[1.0, 0], [1.6267867965364915, 0], [29.0, 0]], [[1.0, 0], [0.07123120949477035, 0.2658384929190656], [-26.846787517317598, 15.5]], [[1.0, 0], [-11.459899172332824, -3.0706707285686714], [32.04293994002423, 18.5]], [[1.0, 0], [-6.989367353912607, 6.989367353912607], [0, -41.0]], [[1.0, 0], [0, 2.911416916215694], [-43.0, 0]], [[1.0, 0], [-2.054564102219043, 7.667737616888605], [-40.703193977868615, -23.5]], [[1.0, 0], [-3.4127083530696782, 5.910984258931389], [-26.5, -45.89934640057525]], [[1.0, 0], [7.055123745942618, -1.8904147102269617], [51.09549882328188, -29.5]], [[1.0, 0], [-5.640728696605384, 3.2566762314107653], [30.5, -52.827549630850754]], [[1.0, 0], [7.264386394768848, -1.9464864679859477], [58.023702053557386, -33.5]], [[1.0, 0], [-11.001319328619914, -11.001319328619914], [0, 71.0]], [[1.0, 0], [2.812070381079629, -0.753491987669766], [63.21985447626402, -36.5]], [[1.0, 0], [7.636779965127534, 13.227290905824969], [-39.5, 68.41600689897065]], [[1.0, 0], [-10.928950192513, 10.928950192513], [0, -83.0]], [[1.0, 0], [-0.6891146979965754, 2.5718110651657025], [-77.07626093681505, -44.5]], [[1.0, 0], [4.735036838539871, -4.735036838539871], [0, -97.0]], [[1.0, 0], [0.9794961775892195, -1.696537145404036], [-50.5, -87.4685657822283]], [[1.0, 0], [1.6263031860902328, 2.816839746819426], [-51.5, 89.20061658979718]], [[1.0, 0], [-4.813400126863602, -8.337053576886237], [-53.5, 92.66471820493493]], [[1.0, 0], [-0.5262470114875744, 0.1410074617473873], [94.39676901250381, -54.5]], [[1.0, 0], [0.025594073157643362, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-273-91.73-c1-0-2', '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/273/2/bz/b/73/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.0619230283130494, 0.9519400992641158, 0.8418924385842594, 0.7261840161915197, 0.5990509093811792, 0.45545295177762857, 0.2917965274019615, 0.10647064610572404, -0.09977913619540235, -0.32361632605514384, -0.5590180355893549, -0.7973390418619347, -1.027566691392858, -1.236796556906062, -1.4109466089081104, -1.5357070337921812, -1.5976961072099738, -1.5857623569315396, -1.4923427023602573, -1.3147589120203003, -1.0563145066625408, -0.7270451237718857, -0.343980897205224, 0.06919782658613008, 0.4831890673760938, 0.8648013679959394, 1.1793365071377202, 1.3934892973809998, 1.4785504715084392, 1.4136278069089512, 1.1885499663999455, 0.8060970806300148, 0.28321999787737767, -0.3490288497399978, -1.0470257687275446, -1.7575981371634701, -2.422401241129134, -2.9833342897091004, -3.3885140048780906, -3.5981925199449902, -3.5899315955068576, -3.362345737438626, -2.93681387078277, -2.356734067500185, -1.684148024124406, -0.9938690130839812, -0.36557554635455797, 0.12535810105991865, 0.4172782148760824, 0.47075849331083214, 0.2750384073388156, -0.14861420865434838, -0.7473199724955283, -1.4410567546900894, -2.1309402997299562, -2.710545060825874, -3.079016573519119, -3.1543775257080706, -2.8852714110601307, -2.259462007582017, -1.3077255716790592, -0.10231200950439273, 1.2501477065421283, 2.6206372884080698, 3.8732666998540752, 4.882325409262906, 5.548566993783369, 5.812399725353502, 5.661990350548106, 5.134942400634764, 4.313106830693182, 3.311097365666038, 2.2600627828918207, 1.2890547715016636, 0.5067842703903385, -0.013412544594493243, -0.24300471020464903, -0.20053734209849075, 0.05368198843260015, 0.4296571879527194, 0.8245536252130374, 1.141473647802248, 1.3069010174993663, 1.2837072085321026, 1.0773201396953827, 0.7338238548276845, 0.33019865845827434, -0.04162356768313137, -0.29399352430010384, -0.36243709540474645, -0.2204894824999689, 0.11262895244296664, 0.5733514674466337, 1.0643055890632427, 1.4724436229180986, 1.6915615266722863, 1.6449467659848829, 1.3036095169700592, 0.696142480129573, -0.09233653368296775, -0.9327021377114842, -1.6741011662384853, -2.1722457515669547, -2.3185279980409246, -2.0642564976260656, -1.4349035372884147, -0.5308912438676917, 0.48612378608701645, 1.4197189000821187, 2.0735657611164315, 2.2884176175263824, 1.9741859444395762, 1.1306485427991, -0.14777645716288013, -1.6848584441919137, -3.2512773097843732, -4.60433875383914, -5.5314155152371285, -5.888835510939581, -5.628544355412537, -4.8070440553713905, -3.5744749181386313, -2.145623116910521, -0.7583181006639256, 0.37263724299653095, 1.096777214309199, 1.356091381893216, 1.194083624087789, 0.7437637641306295, 0.19693779310264195, -0.23886021617204423, -0.3867321366971803, -0.14017118302000386, 0.5124273168935563, 1.4839739548403506, 2.6066692650102192, 3.6680821797997827, 4.45761389697301, 4.81322861784481, 4.65811477710037, 4.019015214280383, 3.0219220147172186, 1.86582597116499, 0.7801387793766315, -0.02484923993026836, -0.4034286108808287, -0.3056030607643565, 0.2131932935239724, 1.00605368248671, 1.869076372241778, 2.588454250776136, 2.9892990027735555, 2.974865392074472, 2.547047049355091, 1.8034059375340386, 0.9115630477714419, 0.06720335694851169, -0.554076456402241, -0.8393118564103086, -0.7646583671904392, -0.3992777512884102, 0.11435169931066412, 0.5987813445580573, 0.8889213348427222, 0.8762790425378678, 0.538643782081472, -0.05270634052344918, -0.7505571350301631, -1.36998825192064, -1.7377200295693533, -1.739857015290908, -1.3553508618384122, -0.6658433057356163, 0.16156988793915367, 0.9151263133958297, 1.3928884941796493, 1.457107878592322, 1.0741053476925695, 0.32851948114902213, -0.5929758951606733, -1.4455970937466889, -1.9877763616780333, -2.044657107567059, -1.5573022753561196, -0.6041705079364753, 0.6119498613666344, 1.8096802044305376, 2.6970505148790407, 3.0451610067583297, 2.748788608265683, 1.8578682336986956, 0.5706853358357344, -0.8108569231416491, -1.9537665863184288, -2.5766809005769358, -2.521994156491082, -1.7987104630864086, -0.5843152234949598, 0.8158468428788482, 2.0423477515108184, 2.77055996944457, 2.792355303254495, 2.0697491593273685, 0.7464635351327896, -0.8860298995781328, -2.4597867209211017, -3.6211206589607974, -4.117786294145877, -3.8604086704390475, -2.9425409114862577, -1.6144244243993797, -0.2175354003295119, 0.9028442470229795, 1.4841951229656924, 1.4100881791764142, 0.7342824806333249, -0.33979823780757007, -1.5176649946484473, -2.4938591980839693, -3.031553170200694, -3.020324427074453, -2.497273026168985, -1.627137279578868, -0.6485694991278461, 0.19698504224882452, 0.7329138779684002, 0.8922849127033357, 0.7277855366461162, 0.3852036905256968, 0.04979545544305373, -0.11712257495377101, -0.03129815661912915, 0.2882929040608782, 0.7284300134081545, 1.122889464054556, 1.3127464439567404, 1.206169546561742, 0.8177553818796625, 0.27332437818858374, -0.22339765561196187, -0.45374425755267245, -0.2583289690332799, 0.4005284686419309, 1.4089649565292208, 2.5163356649233473, 3.3936540699154745, 3.721449347559965, 3.2830395315016805, 2.0361689537988323, 0.14080721454855274, -2.0674521635611907, -4.153696403544546, -5.6904956003410305, -6.366537977263645, -6.066975906851565, -4.902581019608539, -3.1788407335660214], 'positive_zeros': ['0.941017298511840111158518989970440', '2.85433769346762917397727308357140', '4.05821303447567151722844320668997', '5.83844881795091596502813290708761', '6.33745951428476263466737372843259', '7.63480180466602330828739790254148', '9.370597954211438255477590102892118', '9.729098660168505667541163275175298', '10.85936350412849387996061441897053', '11.33898380320768233400784549052105'], 'prelabel': '2-273-91.73-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': -0.5850742144712517, 'root_number': '-0.26409793093305195 - 0.9644958698080988*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.292537107236', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.941017298511840111158518989970', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.85433769346762917397727308357', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.05821303447567151722844320669', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'bad_primes': [3, 7, 13], 'central_character': '91.73', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/2/bz/b/73/3'], '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': '2-273-91.73-c1-0-2', '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': '2-273-91.73-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': -0.29253710723562587, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.941017298511840111158518989970', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1192881143283681038851565061210', 'Lhash_array': ['1192881143283681038851565061210'], 'label': '2-273-91.73-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/2/bz/b/73/3'}