-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1931463900195431729609715633993', 'a10': [-2.0, -1.1836878462028269e-60], 'a2': [-0.30901699437494745, 0.9510565162951535], 'a3': [0.8090169943749475, -0.5877852522924731], 'a4': [-0.8090169943749475, -0.5877852522924731], 'a5': [0.6180339887498949, 1.902113032590307], 'a6': [0.30901699437494745, 0.9510565162951535], 'a7': [-3.23606797749979, -2.3511410091698925], 'a8': [0.8090169943749475, -0.5877852522924731], 'a9': [0.30901699437494745, -0.9510565162951535], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.797139186744959, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.30901699437494745, -0.9510565162951535]]], [3, [[1.0, 0], [-0.8090169943749475, 0.5877852522924731]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 11], 'central_character': '726.493', 'coefficient_field': 'CDF', 'conductor': 726, 'conductor_radical': 66, 'conjugate': '950399065061084757055706237408', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [-0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [-0.6180339887498949, -1.902113032590307], [-4.045084971874737, 2.9389262614623655]], [[1.0, 0], [3.23606797749979, 2.3511410091698925], [2.163118960624632, 6.657395614066075]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.8541019662496845, 5.706339097770922], [-10.517220926874316, -7.641208279802151]], [[1.0, 0], [0.6180339887498949, 1.902113032590307], [-13.753288904374106, 9.992349288972044]], [[1.0, 0], [-3.23606797749979, 2.3511410091698925], [5.871322893124001, -18.07007380960792]], [[1.0, 0], [-4.0, 0], [23.0, 0]], [[1.0, 0], [-4.854101966249685, -3.526711513754839], [8.961492836873475, 27.580638972559452]], [[1.0, 0], [0, 0], [-25.079526825623372, -18.221342821066667]], [[1.0, 0], [4.854101966249685, 3.526711513754839], [11.433628791873055, 35.189091102920685]], [[1.0, 0], [4.854101966249685, -3.526711513754839], [12.669696769372845, -38.9933171681013]], [[1.0, 0], [4.0, 0], [43.0, 0]], [[1.0, 0], [-9.70820393249937, 7.053423027509678], [14.52379873562253, -44.69965626587222]], [[1.0, 0], [-0.6180339887498949, 1.902113032590307], [-42.877900701872214, -31.152618371501077]], [[1.0, 0], [9.70820393249937, 7.053423027509678], [18.232002668121897, 56.11233446141406]], [[1.0, 0], [-4.326237921249264, -13.31479122813215], [-49.350036656871794, 35.854900389840864]], [[1.0, 0], [-4.0, 0], [67.0, 0]], [[1.0, 0], [3.708203932499369, 11.412678195541844], [-57.440206600621266, 41.73275291276559]], [[1.0, 0], [4.854101966249685, 3.526711513754839], [22.558240589371163, 69.42712568954622]], [[1.0, 0], [-1.2360679774997898, 3.804226065180614], [-63.912342555620846, -46.43503493110538]], [[1.0, 0], [1.2360679774997898, 3.804226065180614], [-67.14841053312064, 48.78617594027527]], [[1.0, 0], [-10.0, 0], [89.0, 0]], [[1.0, 0], [4.326237921249264, -13.31479122813215], [-78.4746484543699, -57.01516947236989]], [[1.0, 0], [4.326237921249264, -13.31479122813215], [-81.71071643186968, -59.366310481539784]], [[1.0, 0], [0, 0], [31.828750420619585, 97.95882117840081]], [[1.0, 0], [-3.23606797749979, 2.3511410091698925], [33.06481839811937, -101.76304724358143]], [[1.0, 0], [-6.0, 0], [109.0, 0]], [[1.0, 0], [1.618033988749895, -1.1755705045849463], [34.91892036436906, -107.46938634135235]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 11, 'label': '2-726-11.9-c1-0-11', '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/726/2/e/o/493/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.323067787082629, 1.4287354885657932, 1.5139807510231758, 1.5759243346433784, 1.6081724426779882, 1.602137649641309, 1.548719336912215, 1.4400703367343037, 1.2712676299346894, 1.0417603458447555, 0.756478365205653, 0.42647421646406775, 0.06896674646106182, -0.29332566585690356, -0.6336249968784767, -0.9232903170431483, -1.1346538885916522, -1.2442674256848807, -1.2362230015654831, -1.1051305031840848, -0.8582933493069724, -0.5166425499139428, -0.11407654095231795, 0.3049877070935186, 0.6898273599387527, 0.9891057182458387, 1.157491989028357, 1.162423151675275, 0.990064712117789, 0.6494861020177743, 0.17417055812969193, -0.3797613273099714, -0.9388342914928272, -1.4207247212317473, -1.7451681941430812, -1.8459507947660525, -1.6823054025283768, -1.247887878186217, -0.5756352500367843, 0.262770306929769, 1.16341791495004, 2.0023694458214036, 2.6522988878643003, 3.001452687882138, 2.9721857088522383, 2.5360801734945495, 1.7228805169692503, 0.621195560115976, -0.6299342505977201, -1.8580825324770878, -2.8810897698049227, -3.5340292735441987, -3.6953491103339284, -3.307850452338414, -2.390700859271367, -1.0399327380665262, 0.5833194483012274, 2.2755158807610423, 3.821029170447312, 5.025248120935808, 5.744892994549347, 5.910208017228385, 5.534939909149764, 4.7120866984269885, 3.59596184282106, 2.3736957326234727, 1.2313840957466644, 0.32124838557224217, -0.2638856302702963, -0.5038099459656807, -0.4492601009936146, -0.2057495914761122, 0.0936612258705302, 0.3208344678970433, 0.3831964306959081, 0.24573295448312127, -0.06073067481040466, -0.44709627801490437, -0.7880066273814603, -0.9535490782277276, -0.8434742183181551, -0.41587828231254126, 0.2967562497177164, 1.188622419812172, 2.099393949040593, 2.8472512747021126, 3.2690592172734543, 3.2585695424057075, 2.7935245237532347, 1.944714502070912, 0.8639928628736656, -0.24687554159989042, -1.1799867034298512, -1.7678201115506795, -1.9215438193744983, -1.6516517385339091, -1.065383781681433, -0.3408291732782116, 0.31665475063766396, 0.7254715320896404, 0.7737578238149515, 0.448554696980888, -0.15980968669348586, -0.8801533129100126, -1.5049494177893867, -1.846279671628558, -1.7891379628853536, -1.3279792184726307, -0.5760351528259684, 0.25655255535090005, 0.9118320667193098, 1.149127275909931, 0.81009383577195, -0.13313613481025283, -1.560130934136443, -3.2209363406018134, -4.788609164389145, -5.933829929643186, -6.403693079258082, -6.0849100352489955, -5.034848192093093, -3.471457996603429, -1.7233994336420808, -0.15197944805550836, 0.935859582279204, 1.3614196023770706, 1.1157873925284325, 0.3578502774619815, -0.6311946358970005, -1.5253273023146494, -2.042970230721329, -2.0243170645914565, -1.475809001452694, -0.5693517206773682, 0.40408648311357037, 1.114467056003965, 1.2848918405517789, 0.7709941682586721, -0.39438414652036613, -2.0039040996685, -3.7256478739780343, -5.187084752495685, -6.0704436882462876, -6.1935739186347964, -5.5543042134037695, -4.326423409739412, -2.808898125895697, -1.3430076473680745, -0.22097230749878008, 0.388201320286331, 0.4751893008230561, 0.1798180621076761, -0.2619790212424404, -0.5968316995580292, -0.6340417034126207, -0.30292202174688015, 0.32955853715816275, 1.0853544206554517, 1.7369371314724698, 2.0838397452692443, 2.01950075965648, 1.56691855865961, 0.8716215295723482, 0.15420088924445333, -0.3621816555599325, -0.5255411872153702, -0.30553930728894674, 0.1966040516172797, 0.7829259653240985, 1.227578970211991, 1.3572689880089461, 1.1160847788523696, 0.591687303463845, -0.008144066021805356, -0.42334079493463167, -0.43315026787730637, 0.058364295576677876, 0.9726681180022502, 2.0626638728607674, 2.9767442327328597, 3.364520566879024, 2.9929180303016283, 1.8357476946336344, 0.10586888212069029, -1.7846634733164157, -3.3291883464249747, -4.067705235633251, -3.7237438348294365, -2.295003346960644, -0.06820176397577002, 2.449449119488683, 4.664586327244477, 6.0597653406467105, 6.3358101684404575, 5.492054039327583, 3.820315921501597, 1.8144365877539557, 0.022913101006637102, -1.1104561580956498, -1.3695362248755947, -0.8157028841854687, 0.24898321947147484, 1.3914718215728203, 2.1936756016982435, 2.387141622627876, 1.9333760685664456, 1.0251464482155568, 0.01035173837022513, -0.7344512991488071, -0.9374585000725374, -0.5268001881989994, 0.3443268755587413, 1.3504630035371301, 2.1060559422625706, 2.2983925563759136, 1.7958435945784517, 0.6946293649143899, -0.7115086307432936, -2.027915840280681, -2.888504266727564, -3.073718749208093, -2.5770236118651444, -1.5981934472589399, -0.467381186450037, 0.4719508069908568, 0.9791062172243655, 0.9900970803110984, 0.6239941279426002, 0.12101296757317838, -0.26333060591256824, -0.3674835586996925, -0.19462678342964312, 0.08289580638809724, 0.1887562076454432, -0.14556378665245498, -1.0636641089004055, -2.5065430735307443, -4.206022283878906, -5.755783296796451, -6.738135542490595, -6.863363606699382, -6.072323958144429, -4.564545881535668, -2.7396868960953, -1.0708360719521508, 0.04717734146018345, 0.42173357231805086, 0.11520254382018415, -0.5917000896624326, -1.312101614104112, -1.6993797524339769, -1.573873622269317, -0.98315070081191, -0.1736996108443105, 0.5148532605009687, 0.7923165245154512, 0.5418504610207444], 'positive_zeros': ['1.52365636070987427475540665166264', '2.78390143034955716429162935229314', '3.79050882073325751712452197253779', '4.83757683351575665102165089222031', '5.93790377519816496494005664002633', '6.95652619955459433972446286041107', '8.434331800088014902295768890693160', '8.959988472564092582342182719378593', '9.478773466264669439795240497141631', '10.20289555200772000805147224541678'], 'prelabel': '2-726-11.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.407724898476767, 'root_angle': 0.15573357186974024, 'root_number': '0.8826849005956153 + 0.4699652819735822*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0778667859349', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.52365636070987427475540665166', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.78390143034955716429162935229', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.79050882073325751712452197254', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 5.797139186744959, 'bad_primes': [2, 3, 11], 'central_character': '11.9', 'conductor': 726, 'conductor_radical': 66, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/726/2/e/o/493/1'], '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': '2-726-11.9-c1-0-11', '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': '2-726-11.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.407724898476767, 'root_angle': 0.07786678593487012, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.52365636070987427475540665166', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1931463900195431729609715633993', 'Lhash_array': ['1931463900195431729609715633993'], 'label': '2-726-11.9-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/726/2/e/o/493/1'}