-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1774540421405584927864989966000', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.8000978467980638, 1.3858101216807064], 'a4': [0.0, 0.0], 'a5': [0.0, -1.0], 'a6': [0.0, 0.0], 'a7': [3.751835525465145, -2.1661232505825025], 'a8': [0.0, 0.0], 'a9': [0.21968687109820387, 0.38050882249792384], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.076110452553291, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 1.0]]], [13, [[1.0, 0], [3.112559630066801, -1.8198825646943315]]]], 'bad_primes': [2, 5, 13], 'central_character': '260.121', 'coefficient_field': 'CDF', 'conductor': 260, 'conductor_radical': 130, 'conjugate': '2047479007973714150748232199548', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.8000978467980638, -1.3858101216807064], [-1.5, -2.598076211353316]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [-3.751835525465145, 2.1661232505825025], [3.5, -6.06217782649107]], [[1.0, 0], [-1.5, -0.8660254037844386], [5.5, 9.526279441628825]], [[1.0, 0], [3.112559630066801, -1.8198825646943315]], [[1.0, 0], [-3.751835525465145, -6.498369751747507], [-8.5, 14.722431864335457]], [[1.0, 0], [-4.652129065859336, 2.6859079684787703], [9.5, -16.454482671904334]], [[1.0, 0], [0.58041097569986, -1.0053012991827825], [-11.5, -19.91858428704209]], [[1.0, 0], [-1.0123639364706734, 1.7534657737176376], [-14.5, -25.11473670974872]], [[1.0, 0], [0, 7.864884389522265], [-31.0, 0]], [[1.0, 0], [8.255506576395435, 4.7663189441786304], [18.5, 32.04293994002423]], [[1.0, 0], [-6.696152422706632, -3.866025403784439], [20.5, 35.50704155516198]], [[1.0, 0], [-2.0927749121705332, -3.6247924766848585], [-21.5, 37.239092362730865]], [[1.0, 0], [0, 3.4641016151377544], [-47.0, 0]], [[1.0, 0], [12.647107231249244, 0], [53.0, 0]], [[1.0, 0], [-5.496739503495015, 3.1735440320080968], [29.5, -51.09549882328188]], [[1.0, 0], [1.8515419850709534, 3.206964790489827], [-30.5, 52.827549630850754]], [[1.0, 0], [4.555683102758513, 2.630224865720257], [33.5, 58.023702053557386]], [[1.0, 0], [10.837678890200403, -6.257136824647928], [35.5, -61.48780366869514]], [[1.0, 0], [0, -5.238982355004152], [-73.0, 0]], [[1.0, 0], [8.167185585279661, 0], [79.0, 0]], [[1.0, 0], [0, -0.4567595132771745], [-83.0, 0]], [[1.0, 0], [11.496739503495014, 6.637645647145852], [44.5, 77.07626093681505]], [[1.0, 0], [2.433714298875922, -1.4051056055866549], [48.5, -84.00446416709055]], [[1.0, 0], [3.3198825646943315, -5.750205277212652], [-50.5, -87.4685657822283]], [[1.0, 0], [-7.3760549014431644, 0], [103.0, 0]], [[1.0, 0], [-3.95668083371216, 6.853172233323446], [-53.5, -92.66471820493493]], [[1.0, 0], [0, -9.183005616111489], [-109.0, 0]], [[1.0, 0], [-2.887929603923518, -5.002040802677797], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-260-13.4-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/260/2/x/a/121/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.2692823857657434, 1.238897336739045, 1.2081295614436565, 1.1726272558419215, 1.1265113701665626, 1.0632059932849212, 0.9762472485407551, 0.8600100609862081, 0.7103515986999694, 0.5251877059303672, 0.3050060570018551, 0.053296587560904087, -0.22314100449957008, -0.5140656415231839, -0.8058952577315444, -1.0820888794256214, -1.3238444376336982, -1.511122316423244, -1.6239735407199554, -1.6441154862366092, -1.5566600936285817, -1.3518636909572737, -1.0267382109336638, -0.586345614189989, -0.04459518683162492, 0.5756193656946977, 1.2430674786548426, 1.9196786052211723, 2.5628749829660977, 3.1286361575781263, 3.5750961975718996, 3.8663859090464947, 3.9763617996481613, 3.8918227188884416, 3.6148140592604223, 3.1636649153622862, 2.572497673982998, 1.8890882520956285, 1.1711282857170333, 0.4811315104809071, -0.11958611245198227, -0.5772636614592335, -0.8516941582586358, -0.9211359957758616, -0.785462281311662, -0.46702038999837653, -0.008905908222968972, 0.5293480971708298, 1.0783357398173932, 1.5669439832329757, 1.9311968159418114, 2.122681798019043, 2.115420383352221, 1.9101529756293683, 1.535272746146439, 1.0440382473841079, 0.5081813753596415, 0.00854360841662651, -0.37615232832264467, -0.5809299820324952, -0.5649428302269635, -0.3190183649565457, 0.1309457903963331, 0.7255348842887926, 1.378449078814484, 1.98759618888313, 2.4493091397160285, 2.673778606251704, 2.5994636063485896, 2.2042335868146483, 1.511333517212846, 0.5889245845254021, -0.45714093084936985, -1.4966257768332, -2.3926185018902477, -3.021178145950378, -3.2899884109064654, -3.1530827903709384, -2.619161510103734, -1.7519113618053483, -0.66194241286588, 0.5087086662617475, 1.6073057891246685, 2.493214535222954, 3.059146525482008, 3.24733199448088, 3.0578248847059553, 2.5473776940213626, 1.8188828986924253, 1.003007469621977, 0.23506176195059342, -0.3689199171286943, -0.7326455067911576, -0.8328262408601308, -0.7026728541069138, -0.42477812260748427, -0.1144755880889774, 0.10341919182623756, 0.12023103657695389, -0.13344352340476273, -0.6716538299757482, -1.4474371506532457, -2.3590762825659337, -3.2675064031072285, -4.021894502692552, -4.488685283936642, -4.578522213460235, -4.2656282812434165, -3.5954865350127396, -2.678800569264151, -1.6723577049192109, -0.7500591994395831, -0.06949232389962426, 0.2594526446374016, 0.1975476488465224, -0.21417505062285663, -0.8606511595303525, -1.5741979678621216, -2.1673662262202065, -2.4710072231608677, -2.3700230720522373, -1.8294478524722813, -0.9052034251825933, 0.2631997873285761, 1.477145956892026, 2.516156510596465, 3.1807051489358913, 3.3320540200409905, 2.9209319595910177, 1.9989668253748363, 0.7102104118617195, -0.735827204218781, -2.1043350506505862, -3.18040209083097, -3.8099379578058556, -3.927788373115001, -3.5671701734683703, -2.8485208549419685, -1.950307727072188, -1.0683003276704568, -0.372385120302119, 0.029414509854350637, 0.11163478944481452, -0.06784868649861824, -0.3870283792263909, -0.6943695840301317, -0.8505397986362622, -0.7671665025610341, -0.43304137215796795, 0.07901148553580989, 0.6268909442357512, 1.0327054227060142, 1.1274401450157048, 0.796246595097374, 0.013215090006522705, -1.1434328134317135, -2.5004592157490197, -3.822114011319115, -4.859457298814523, -5.405622233386852, -5.3442631444074635, -4.679528188653057, -3.539811390660874, -2.1534414539807325, -0.8010115530907312, 0.24530049088252395, 0.7817113929114241, 0.7182027201043304, 0.09848238553890713, -0.9105001593247305, -2.057421082466941, -3.065006390324956, -3.6944102790654414, -3.800354797558663, -3.3638912867104627, -2.4949134831540496, -1.4038091228281107, -0.34913404452109087, 0.4259148945024992, 0.752649238714629, 0.5771130450199543, -0.028502964872365144, -0.8859665732369547, -1.7574254662088367, -2.4062869347294527, -2.657011288876379, -2.438537742101748, -1.8002590024730023, -0.8965603552303402, 0.05586334716890133, 0.8365279976476884, 1.2798853284141882, 1.3184638092760732, 0.9986841391022924, 0.46486228888681863, -0.08449902831041252, -0.45638084052023753, -0.522499567198526, -0.2614688423622136, 0.22855603760370116, 0.7514238806340021, 1.0641290254214317, 0.9446399108132689, 0.25842893640014375, -0.994644400303446, -2.66684250596328, -4.487713974933791, -6.122982147599356, -7.2530183156082755, -7.651049828048721, -7.240684085643572, -6.117201849419099, -4.526226304133177, -2.804458450445677, -1.297252109165901, -0.27414885161622005, 0.13568257818050605, -0.028813864557744654, -0.5769496122938079, -1.2223530256114787, -1.6636750237686666, -1.6682249501969646, -1.1359933838602407, -0.12681671015101592, 1.156525387759955, 2.4244297828903965, 3.3801877400489095, 3.8011947746047983, 3.59917879364391, 2.8428690931144525, 1.7370776665331669, 0.5644258224149391, -0.3935325263209617, -0.933262300339066, -0.9823877098476452, -0.6140592837182637, -0.018842651054286164, 0.5572037478242341, 0.8896924301014445, 0.8452245810067301, 0.4220270207274444, -0.25047706353684007, -0.9533080232813888, -1.4484571836104692, -1.5569868742078865, -1.2206225179284158, -0.5271817986633458, 0.3093459046000012, 1.0097199868498377, 1.3143786732909246, 1.0674491163338569, 0.27418218195422117, -0.8869172892459906, -2.103238143419447, -3.0094812301840212, -3.289503163691375, -2.769901894630096], 'positive_zeros': ['1.39986556318128548056087364612455', '3.00947218793149423274226479324727', '4.97294123988410212046570306359367', '5.75218331614347540317694535221683', '7.12735531189307262137125887124101', '7.71823335052398096655621167211475', '8.946230427809921154683229676980334', '10.07069151761804094447778347420542', '11.29377016224982480029539199269209', '12.05507265919353402136166020535114'], 'prelabel': '2-260-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4408714212424685, 'root_angle': -0.1724952379707715, 'root_number': '0.8567252351098564 - 0.51577308142822*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0862476189854', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.39986556318128548056087364612', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.00947218793149423274226479325', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.97294123988410212046570306359', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2.076110452553291, 'bad_primes': [2, 5, 13], 'central_character': '13.4', 'conductor': 260, 'conductor_radical': 130, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/260/2/x/a/121/2'], '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': '2-260-13.4-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': '2-260-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4408714212424685, 'root_angle': -0.08624761898538574, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.39986556318128548056087364612', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1774540421405584927864989966000', 'Lhash_array': ['1774540421405584927864989966000'], 'label': '2-260-13.4-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/260/2/x/a/121/2'}