-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1660808519401701982665169657600', 'a10': [0, 0], 'a2': [-1.224744871391589, 0.7071067811865476], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0.5, -2.598076211353316], 'a8': [0, -2.8284271247461903], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.576438318351666, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-0.5, 2.598076211353316]]]], 'bad_primes': [3, 5, 7], 'central_character': '1575.1151', 'coefficient_field': 'CDF', 'conductor': 1575, 'conductor_radical': 105, 'conjugate': '349713637292719617180082022208', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.224744871391589, -0.7071067811865476], [1.0, -1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.5, 2.598076211353316]], [[1.0, 0], [1.224744871391589, 0.7071067811865476], [5.5, 9.526279441628825]], [[1.0, 0], [0, -5.196152422706632], [-13.0, 0]], [[1.0, 0], [-2.449489742783178, 4.242640687119285], [-8.5, -14.722431864335457]], [[1.0, 0], [-1.5, 0.8660254037844386], [9.5, -16.454482671904334]], [[1.0, 0], [4.898979485566356, -2.8284271247461903], [11.5, -19.91858428704209]], [[1.0, 0], [0, 2.8284271247461903], [-29.0, 0]], [[1.0, 0], [-1.5, -0.8660254037844386], [15.5, 26.846787517317598]], [[1.0, 0], [0.5, 0.8660254037844386], [-18.5, 32.04293994002423]], [[1.0, 0], [7.3484692283495345, 0], [41.0, 0]], [[1.0, 0], [-1.0, 0], [43.0, 0]], [[1.0, 0], [6.123724356957945, 10.606601717798213], [-23.5, 40.703193977868615]], [[1.0, 0], [2.449489742783178, 1.4142135623730951], [26.5, 45.89934640057525]], [[1.0, 0], [2.449489742783178, -4.242640687119285], [-29.5, -51.09549882328188]], [[1.0, 0], [3.0, -1.7320508075688772], [30.5, -52.827549630850754]], [[1.0, 0], [-5.5, 9.526279441628825], [-33.5, -58.023702053557386]], [[1.0, 0], [0, 7.0710678118654755], [-71.0, 0]], [[1.0, 0], [1.5, 0.8660254037844386], [36.5, 63.21985447626402]], [[1.0, 0], [2.5, 4.330127018922194], [-39.5, 68.41600689897065]], [[1.0, 0], [7.3484692283495345, 0], [83.0, 0]], [[1.0, 0], [-2.449489742783178, -4.242640687119285], [-44.5, 77.07626093681505]], [[1.0, 0], [0, -10.392304845413264], [-97.0, 0]], [[1.0, 0], [-8.573214099741124, 14.849242404917497], [-50.5, -87.4685657822283]], [[1.0, 0], [-7.5, 4.330127018922194], [51.5, -89.20061658979718]], [[1.0, 0], [-2.449489742783178, 1.4142135623730951], [53.5, -92.66471820493493]], [[1.0, 0], [-0.5, 0.8660254037844386], [-54.5, -94.39676901250381]], [[1.0, 0], [0, 1.4142135623730951], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 38, 'label': '2-1575-21.17-c1-0-38', 'leading_term': '0.490856927917295790852929736052502237773546306706217665', '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/1575/2/bk/c/1151/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.4908569279172958, 0.5792824402413593, 0.6617641405509254, 0.7379812362648354, 0.8074763724556445, 0.8696411473683646, 0.9237165187780153, 0.9688076302480434, 1.003911727341104, 1.0279572408753583, 1.0398517828142657, 1.0385366781589105, 1.023045670713817, 0.9925655224804995, 0.9464963240225673, 0.8845094172982405, 0.8066008945589704, 0.7131386834672049, 0.6049012750911029, 0.4831062171330756, 0.34942659879757365, 0.20599391270353842, 0.055385905841061796, -0.09940166625246699, -0.25500008709909183, -0.40772977608611016, -0.5536791542547067, -0.6887994125195278, -0.8090136863994553, -0.9103384885383679, -0.9890145970667258, -1.0416439699610611, -1.0653286807136593, -1.0578073775542667, -1.017584385829059, -0.9440463283455462, -0.8375610564225254, -0.6995537861070724, -0.532555635491604, -0.3402202699117481, -0.12730508424579692, 0.1003857205195805, 0.33609769087312286, 0.5722625443237083, 0.8006732854433835, 1.0126953293022498, 1.1995093993972903, 1.3523804360865594, 1.4629452989090153, 1.5235107365620881, 1.5273519966503422, 1.46900161619489, 1.3445174306770422, 1.1517187133111406, 0.8903796455278057, 0.562370048867538, 0.17173448623057888, -0.2752975425076279, -0.7703755573607034, -1.3031690629519799, -1.8615856886389657, -2.432063772370423, -2.9999336468750415, -3.549838880331565, -4.0662058433763875, -4.533747347554492, -4.937983853852251, -5.265764004281803, -5.505765093145301, -5.648953658429663, -5.688986705534145, -5.622535215133431, -5.44951354260006, -5.173201061703715, -4.800245877979753, -4.340544539081711, -3.8069962683718486, -3.215135181068204, -2.5826490210024677, -1.9287979730868603, -1.2737518436773398, -0.6378681380872152, -0.04093708950555623, 0.49857768735962904, 0.9642726971393752, 1.3424816506382877, 1.6228665033049978, 1.7988950568018294, 1.868181265040837, 1.8326691130617467, 1.698646715161926, 1.4765839058058203, 1.1807938213081215, 0.8289264994063092, 0.4413100352877898, 0.04016198789789794, -0.35129981025090945, -0.7098124478834318, -1.0130504184045723, -1.2405941136850156, -1.3748422356236991, -1.4018270799709733, -1.3118945863253848, -1.100215823198199, -0.767103041202311, -0.3181113475236689, 0.2360838821259235, 0.8800339132064311, 1.5940777907144854, 2.355097601861862, 3.1374383687691325, 3.913954778322208, 4.6571401846260185, 5.340288452353826, 5.938636545391554, 6.430435505758154, 6.797899702473656, 7.027988927737821, 7.112984923316418, 7.050832957152534, 6.84522975093141, 6.505450899475247, 6.045923363383738, 5.485561049418474, 4.846893291844204, 4.155026598281622, 3.4364887570741036, 2.7180108281522135, 2.025306269871556, 1.3819072338883318, 0.8081157800392935, 0.32012247299125113, -0.07066326737116178, -0.35803721390452076, -0.5411573835180845, -0.6244264561772681, -0.617106282428742, -0.5326853939951341, -0.3880336925540936, -0.20239008060741595, 0.003761949611215304, 0.20986939006181896, 0.396471005284886, 0.5462808425670265, 0.6451339906922577, 0.6827420363887596, 0.6532161353170151, 0.5553285886787892, 0.3924986025540251, 0.17250369005762645, -0.09306593485853358, -0.3895775466101162, -0.700304882460826, -1.0074992492693036, -1.2935184553369776, -1.541945318297262, -1.7386275735355807, -1.8725751680459424, -1.936659000875759, -1.928066753387344, -1.8484859095030683, -1.704000577867072, -1.5047063297203414, -1.2640649033966775, -0.9980372155345351, -0.7240476143775647, -0.4598437684128477, -0.222324224163721, -0.026408926844983128, 0.11597342877847912, 0.1967134838281168, 0.2121075719681466, 0.16315962653924973, 0.05557341965028556, -0.10057055892703948, -0.2914389155990499, -0.5003352767868314, -0.7088035551282843, -0.8978765490414777, -1.0493906295398008, -1.147280871298341, -1.1787699789096466, -1.1353689649774485, -1.0136176207017904, -0.815507891147748, -0.5485524984021511, -0.2254834233124177, 0.13641119464458107, 0.516279056874472, 0.8909691919418391, 1.236495705620936, 1.5296090676514997, 1.749374161696096, 1.8786505695704985, 1.9053735468140776, 1.823543899265603, 1.6338510734591645, 1.3438753823169427, 0.9678411684795641, 0.5259213066273948, 0.04312297938740989, -0.4521867758064901, -0.9300315639166812, -1.3607469558631156, -1.7169525766522198, -1.9754474195817315, -2.1189014730935027, -2.1372257005498794, -2.0285193830959796, -1.799517972731859, -1.4654945591973978, -1.0496020566744593, -0.5816791679976623, -0.09657879313251463, 0.36788952713230705, 0.7732835416518642, 1.0829779135984057, 1.2645862732895052, 1.292199432590778, 1.1482905637992922, 0.8251551215824318, 0.3257793474702613, -0.33593510079458005, -1.1356234966932166, -2.0395778795275397, -3.006481759491624, -3.989666223325141, -4.939758127607148, -5.8075627128345975, -6.5470041562780965, -7.117939777364699, -7.48866759712782, -7.637962752898562, -7.556505118335837, -7.247596863185786, -6.727112423948933, -6.022671723729949, -5.1720773848211445, -4.221104857606011, -3.220777624646726, -2.2242949712432836, -1.2838047517105282, -0.44722627727933323, 0.2446721565049285, 0.7607506891392141, 1.08136673599218, 1.1995098129778827, 1.1211238258180412, 0.8645910475274385, 0.4594071235969256, -0.0558697368931356, -0.6362633462746369, -1.2334452851138735, -1.799019775033886, -2.287809509107242, -2.6609226857744077, -2.8883947347152965], 'positive_zeros': ['1.31014691201399497390169003223648', '2.37687159569534293598171328942949', '3.30459046626302054501277281538322', '4.80890258032329613704687775350375', '5.57229399138998772021144677361960', '6.18722293082823443726536666062327', '7.72254936078861763013555739276662', '8.202072855054626173012037032921712', '8.769460424719282397230800744894630', '9.853041989291713805400777150602411'], 'prelabel': '2-1575-21.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.546327440938254, 'root_angle': 0.49092634370530913, 'root_number': '0.0285018715975856927934977682693885153963269628464678507 + 0.9995937391337716546912588645724170048286198880226152905*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.2454631718526546', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.31014691201399497390169003224', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.37687159569534293598171328943', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.30459046626302054501277281538', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 12.576438318351666, 'bad_primes': [3, 5, 7], 'central_character': '21.17', 'conductor': 1575, 'conductor_radical': 105, 'degree': 2, 'index': 38, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1575/2/bk/c/1151/1'], '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': '2-1575-21.17-c1-0-38', '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': '2-1575-21.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.546327440938254, 'root_angle': 0.24546317185265457, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.31014691201399497390169003224', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1660808519401701982665169657600', 'Lhash_array': ['1660808519401701982665169657600'], 'label': '2-1575-21.17-c1-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1575/2/bk/c/1151/1'}