-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1187765408899405780041094039173', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.9417973987334713, 0.0], 'a4': [0.0, 0.0], 'a5': [-3.6823347470319145, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.514837265284755, 0.0], 'a8': [0.0, 0.0], 'a9': [0.7705771377280761, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.668013710043065, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [167, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 167], 'central_character': '1336.1', 'coefficient_field': 'CDF', 'conductor': 1336, 'conductor_radical': 334, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.9417973987334713, 0], [3.0, 0]], [[1.0, 0], [3.6823347470319145, 0], [5.0, 0]], [[1.0, 0], [2.514837265284755, 0], [7.0, 0]], [[1.0, 0], [-2.5313077084386424, 0], [11.0, 0]], [[1.0, 0], [-1.4024129503445524, 0], [13.0, 0]], [[1.0, 0], [-6.242422157879026, 0], [17.0, 0]], [[1.0, 0], [-6.032195148326723, 0], [19.0, 0]], [[1.0, 0], [0.9900622050401932, 0], [23.0, 0]], [[1.0, 0], [-2.8156696170840654, 0], [29.0, 0]], [[1.0, 0], [-8.198628608510916, 0], [31.0, 0]], [[1.0, 0], [5.906780509663546, 0], [37.0, 0]], [[1.0, 0], [-11.903135684282026, 0], [41.0, 0]], [[1.0, 0], [7.715905147605975, 0], [43.0, 0]], [[1.0, 0], [11.401300564635017, 0], [47.0, 0]], [[1.0, 0], [-13.35286254542177, 0], [53.0, 0]], [[1.0, 0], [-12.756980421687782, 0], [59.0, 0]], [[1.0, 0], [-10.017130431025011, 0], [61.0, 0]], [[1.0, 0], [-5.225423133206952, 0], [67.0, 0]], [[1.0, 0], [-13.556269032070574, 0], [71.0, 0]], [[1.0, 0], [15.168873159117938, 0], [73.0, 0]], [[1.0, 0], [-8.025092165892797, 0], [79.0, 0]], [[1.0, 0], [8.790464005399606, 0], [83.0, 0]], [[1.0, 0], [8.44998974220646, 0], [89.0, 0]], [[1.0, 0], [-3.290097933812673, 0], [97.0, 0]], [[1.0, 0], [2.483105856996414, 0], [101.0, 0]], [[1.0, 0], [-8.249511044613985, 0], [103.0, 0]], [[1.0, 0], [1.8128922142773831, 0], [107.0, 0]], [[1.0, 0], [11.56060187549128, 0], [109.0, 0]], [[1.0, 0], [6.229789215494663, 0], [113.0, 0]], [[1.0, 0], [-5.8211704104504305, 0], [127.0, 0]], [[1.0, 0], [-11.572210186476237, 0], [131.0, 0]], [[1.0, 0], [-8.120288746049937, 0], [137.0, 0]], [[1.0, 0], [19.055033499249156, 0], [139.0, 0]], [[1.0, 0], [12.186976963150089, 0], [149.0, 0]], [[1.0, 0], [-3.399298426785574, 0], [151.0, 0]], [[1.0, 0], [2.741337038019495, 0], [157.0, 0]], [[1.0, 0], [-0.6542536011934869, 0], [163.0, 0]], [[1.0, 0], [-1.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 9, 'label': '2-1336-1.1-c1-0-9', 'leading_term': '1.73620550891380199428103939995', '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/1336/2/a/e/1/9', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.736205508913802, 1.731072477992729, 1.715536354788003, 1.6891952835507946, 1.6514095823801445, 1.6013445009377854, 1.538025752727315, 1.4604042888430093, 1.3674266635982202, 1.2581075713678547, 1.1316015737568812, 0.9872715504614813, 0.8247518903670551, 0.6440048305574836, 0.44536863134452576, 0.2295964575106119, -0.002115050610178093, -0.2481084523793159, -0.5062602843319588, -0.7739886885992845, -1.0482744879629458, -1.3256960933399735, -1.6024783587318963, -1.8745551689361446, -2.1376451633702005, -2.3873395759032436, -2.6192007195146316, -2.828869182324577, -3.0121773464252746, -3.1652664126759302, -3.28470373362326, -3.3675969434190525, -3.411701147782345, -3.415515316970248, -3.378364026356728, -3.300460825429244, -3.1829497957338906, -3.027922285804011, -2.8384063853678745, -2.6183274153204588, -2.372438551113006, -2.1062216461813517, -1.8257593535210919, -1.5375807265439185, -1.248483578904482, -0.965337956980896, -0.6948760851705491, -0.44347503876793987, -0.21693913782486912, -0.020289596038324285, 0.14243073665514702, 0.26832966257322827, 0.3558073365410334, 0.4046603216292248, 0.41614181810342743, 0.3929730598647175, 0.33930233046116043, 0.26060975531197883, 0.16355793071411387, 0.05579049403873016, -0.054317146805435416, -0.1579486017368182, -0.24617047049345578, -0.31027933393930773, -0.34216003859104466, -0.3346423377504609, -0.2818421681980579, -0.1794735459720809, -0.025117305668599217, 0.18156628652006446, 0.43869263814210985, 0.7420853132154482, 1.0852931038694085, 1.4596960062036806, 1.8547011600788503, 2.25802630846859, 2.6560647085993034, 3.034321827537676, 3.3779107310461387, 3.672089980982757, 3.9028252439262396, 4.057353821875275, 4.124730066863888, 4.096329232840615, 3.966287817524081, 3.731859886160726, 3.3936712410620675, 2.9558565570680013, 2.426068653471065, 1.8153537868934706, 1.137892059609921, 0.41060754466828137, -0.3473416908490837, -1.115178069503983, -1.8712028973955552, -2.593553721764821, -3.260992231875191, -3.853691880756149, -4.353993233138081, -4.747095212319085, -5.021651980180597, -5.170248133372703, -5.189729163993518, -5.081369579900279, -4.85086751197067, -4.508161802011668, -4.067075168513621, -3.5447947569329896, -2.961208845605329, -2.3381253426418076, -1.6984036310128188, -1.065035986260785, -0.4602179382968842, 0.09555162837966347, 0.5843002723165032, 0.9913036560728252, 1.3056652185397148, 1.520725905195399, 1.634283390708817, 1.6486087967078094, 1.5702582776835492, 1.4096865869986541, 1.1806793753097935, 0.8996300355212525, 0.5846949232208549, 0.2548673167752022, -0.07098483637432511, -0.37506980346332114, -0.6415637974128413, -0.8573979912283076, -1.0128998467573342, -1.102254593020901, -1.1237614158983544, -1.0798691725480276, -0.976987729793392, -0.8250827838840585, -0.6370736436271474, -0.4280643305559126, -0.21444786844569416, -0.012931252115940659, 0.1604661623347191, 0.2913855695454591, 0.36801805428326395, 0.3818588860327364, 0.32828160515314686, 0.20689569408178557, 0.021662821807080953, -0.2192404654348531, -0.5038118187181557, -0.816847929564057, -1.1407754235276044, -1.4566456298127597, -1.7452405955545238, -1.9882299030905235, -2.1693132057848423, -2.27528228354071, -2.2969390075962077, -2.2298118673371397, -2.074623413081382, -1.8374736690733628, -1.5297196465951828, -1.1675477587693734, -0.7712533101689432, -0.36425833999057095, 0.028085045281986347, 0.3798450486979211, 0.6659428441687596, 0.8635892169748883, 0.9536442516298559, 0.9218210447859555, 0.7596608962813766, 0.4652182402867261, 0.04340823068152126, -0.49401233752949675, -1.1288401366771255, -1.8371847601434919, -2.590559871194669, -3.357253730393967, -4.1039095924779785, -4.797232809883439, -5.405732254676949, -5.901399529295834, -6.261230755701861, -6.468502578622623, -6.513726134534245, -6.395219549308101, -6.119260166603019, -5.69980105912944, -5.1577611287403355, -4.519922834474237, -3.8174948404452773, -3.08441723942577, -2.355503212096077, -1.664521972944706, -1.042332865484986, -0.5151790766189479, -0.10324159308644532, 0.1804599392298115, 0.3307521534786709, 0.3505350982180437, 0.25053466569367094, 0.04859153303241161, -0.23147428020564387, -0.5613581968759985, -0.9100377910230751, -1.245706615679157, -1.5377591008770357, -1.758706166944577, -1.8859042111854183, -1.9029903926997562, -1.8009341422049652, -1.578637613161676, -1.243045039567414, -0.8087510426683118, -0.2971289943641417, 0.26496933529001987, 0.8468643544653437, 1.4159483099824433, 1.9397163600973788, 2.387802107683376, 2.7338893051262976, 2.9573782444820367, 3.0446999641327683, 2.9901930048823084, 2.796484738847005, 2.474350589692321, 2.042057792341726, 1.524233570460337, 0.950328579996735, 0.3527731300682057, -0.23505574780956628, -0.7809252777628755, -1.2557603025692041, -1.6354476908049498, -1.9023134703025433, -2.0461753364256263, -2.0649007950157108, -1.964433694904416, -1.7582871690959485, -1.4665367050941351, -1.1143808070094576, -0.7303661948789, -0.34439766342628386, 0.014332056549449107, 0.31935095965650534, 0.548716965405203, 0.6865026631751878, 0.723852333615101, 0.6595370485226023, 0.4999681582203476, 0.25866710054681785, -0.044772362368482546, -0.38615730574903756, -0.7385006143831078, -1.074029684882428, -1.3662550293583358, -1.591949191098198], 'positive_zeros': ['0.936981695654590475031906063505108', '2.87776047521485678437424041950747', '3.48658528809858754299586765306277', '3.99236380584660112494209816084685', '5.36396717595794799157273539542145', '6.61054942499210962070124017625595', '7.36981842949359397039920861446521', '8.148539315885339744179523757958863', '8.560522381793952243659357320343613', '9.605019673728936951204347517237132'], 'prelabel': '2-1336-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.266192540258927, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.936981695654590475031906063505', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.87776047521485678437424041951', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.48658528809858754299586765306', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 10.668013710043065, 'bad_primes': [2, 167], 'central_character': '1.1', 'conductor': 1336, 'conductor_radical': 334, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1336/2/a/e/1/9'], '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': '2-1336-1.1-c1-0-9', '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': '2-1336-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.266192540258927, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.936981695654590475031906063505', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1187765408899405780041094039173', 'Lhash_array': ['1187765408899405780041094039173'], 'label': '2-1336-1.1-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1336/2/a/e/1/9'}