-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '989988457604225829432687902865', 'a10': [10.0, 0], 'a2': [-1.0, -1.7320508075688772], 'a3': [0, 0], 'a4': [-2.0, 3.4641016151377544], 'a5': [-2.5, 4.330127018922194], 'a6': [0, 0], 'a7': [-7.0, -12.12435565298214], 'a8': [8.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 47.79154710464992, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 1.7320508075688772]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [2.5, -4.330127018922194]]]], 'bad_primes': [2, 3, 5], 'central_character': '810.271', 'coefficient_field': 'CDF', 'conductor': 810, 'conductor_radical': 30, 'conjugate': '550406033640688074679757721538', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.5, -4.330127018922194]], [[1.0, 0], [7.0, 12.12435565298214], [-171.5, 297.04671349806245]], [[1.0, 0], [-3.0, -5.196152422706632], [-665.5, 1152.6798124370878]], [[1.0, 0], [34.0, -58.88972745734183], [-1098.5, -1902.6578121144116]], [[1.0, 0], [78.0, 0], [4913.0, 0]], [[1.0, 0], [-44.0, 0], [6859.0, 0]], [[1.0, 0], [-60.0, 103.92304845413264], [-6083.5, -10536.931087845265]], [[1.0, 0], [-63.0, -109.11920087683927], [-12194.5, 21121.493572898675]], [[1.0, 0], [-122.0, 211.31019852340302], [-14895.5, -25799.76280414221]], [[1.0, 0], [304.0, 0], [50653.0, 0]], [[1.0, 0], [240.0, -415.69219381653056], [-34460.5, -59687.336854227295]], [[1.0, 0], [52.0, 90.06664199358161], [-39753.5, 68855.08177868936]], [[1.0, 0], [-300.0, -519.6152422706632], [-51911.5, 89913.35549711177]], [[1.0, 0], [-258.0, 0], [148877.0, 0]], [[1.0, 0], [-267.0, 462.45756562089025], [-102689.5, -177863.43140384424]], [[1.0, 0], [181.0, 313.5011961699668], [-113490.5, 196571.31217639567]], [[1.0, 0], [-134.0, 232.09480821422954], [-150381.5, -260468.39851841913]], [[1.0, 0], [-972.0, 0], [357911.0, 0]], [[1.0, 0], [-470.0, 0], [389017.0, 0]], [[1.0, 0], [622.0, 1077.3356023078418], [-246519.5, 426984.29905647587]], [[1.0, 0], [-198.0, -342.9460598986377], [-285893.5, 495182.06755369285]], [[1.0, 0], [-972.0, 0], [704969.0, 0]], [[1.0, 0], [-23.0, -39.83716857408418], [-456336.5, 790398.003348155]], [[1.0, 0], [753.0, 1304.2342580993645], [-515150.5, 892266.8395445109]], [[1.0, 0], [-737.0, 1276.5214451782626], [-546363.5, -946329.3414011582]], [[1.0, 0], [924.0, 0], [1225043.0, 0]], [[1.0, 0], [-698.0, 0], [1295029.0, 0]], [[1.0, 0], [111.0, -192.25763964014538], [-721448.5, -1249585.457044355]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 24, 'label': '2-810-9.4-c3-0-24', 'leading_term': '1.011085024035116437081825093279245180826502066439357091', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/810/4/e/a/271/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.0110850240351164, 1.0789345962233896, 1.1252452206026697, 1.1488723020497535, 1.1489017103675514, 1.1246652064454359, 1.0757570760855082, 1.0020517098674433, 0.9037216871403564, 0.7812557521884983, 0.6354759180547458, 0.46755280496267876, 0.2790182214257967, 0.07177393166018398, -0.1519044735285187, -0.38936967104836473, -0.6376116773825614, -0.893274811477267, -1.152683321190851, -1.4118762644851819, -1.66665201742613, -1.9126225279189755, -2.145277151750205, -2.360055601847992, -2.5524292196978213, -2.7179894475844826, -2.852542050763223, -2.952205319610335, -3.0135101837427585, -3.033499903932006, -3.0098267844240922, -2.9408431788928096, -2.8256839580368234, -2.6643375751852947, -2.4577029162597364, -2.2076292583490584, -1.9169368911267608, -1.5894162789788753, -1.2298040577699236, -0.8437346642936308, -0.4376669809950075, -0.01878603251449603, 0.40511952032000814, 0.8258025967094692, 1.234723365934926, 1.6232323562985211, 1.9827672595487, 2.305059014893198, 2.5823421664591693, 2.8075640058777545, 2.974586661959425, 3.078376104204548, 3.115172004799541, 3.0826325690860603, 2.979948806342623, 2.807923274177049, 2.5690090873744165, 2.2673059251170167, 1.908510881279064, 1.499823255984198, 1.0498037508951532, 0.5681899675934463, 0.06567157431508303, -0.44637004658570667, -0.9561514804057254, -1.4517988446389054, -1.9216727058429166, -2.354696955372665, -2.7406816525456454, -3.0706295483069335, -3.3370160384998555, -3.5340326823651123, -3.657785166292873, -3.7064376899214713, -3.68029718289339, -3.5818324939151593, -3.4156256839891075, -3.188254745199644, -2.9081093866869163, -2.585143902825975, -2.230573480923342, -1.8565225289378335, -1.4756356192310822, -1.1006633663970793, -0.7440369064335115, -0.41744555142886736, -0.13143260233002405, 0.10497582770990745, 0.2845948165168966, 0.4023445491872919, 0.45544302164547984, 0.44351868721894677, 0.36863691155444056, 0.23523715228644507, 0.049981067947243406, -0.17848483361886913, -0.43984500357182105, -0.7224988679697746, -1.013999841222358, -1.301533582056543, -1.5724177282278125, -1.814603977796036, -2.017162738977262, -2.1707307033807632, -2.267902634836272, -2.3035504013712393, -2.2750547705999717, -2.182438664312455, -2.028394319516573, -1.8182009944006785, -1.559534327647907, -1.262173028285991, -0.9376130488481003, -0.5986035809923566, -0.2586229181727233, 0.06868472418697227, 0.3700881113521458, 0.6333390100012906, 0.847708472047003, 1.0044653596847786, 1.0972750080874147, 1.1224988788653383, 1.0793799570538416, 0.9701033449907465, 0.7997268239948138, 0.5759818698068923, 0.3089514740316944, 0.010636878433766319, -0.3055692960969478, -0.6254813096189137, -0.9347638831401425, -1.21959226762224, -1.4672984665978677, -1.6669731435496111, -1.8099940361143778, -1.8904544025120071, -1.9054690619020476, -1.8553408137121137, -1.743576223180532, -1.5767466784539974, -1.3641979512693718, -1.1176188899295265, -0.8504869852267253, -0.5774150229231503, -0.31342853390772085, -0.07320797373262271, 0.12966774339740342, 0.28343874967715676, 0.37880599920052, 0.40946322425393805, 0.37248943417828684, 0.26857838353428726, 0.10208886975676923, -0.11909179988516137, -0.3838696928871823, -0.6784406433558743, -0.9869411769626831, -1.2922255668214158, -1.576733340153262, -1.8234058345528688, -2.0166065815936594, -2.1429986338620757, -2.1923326086935027, -2.1581022452870195, -2.0380295901709737, -1.8343493482510962, -1.553871157624663, -1.2078091577210857, -0.8113797279930699, -0.3831801205644269, 0.05562770004905592, 0.4822929666313151, 0.8735674335475361, 1.2068604543858796, 1.4614012328047457, 1.6193494883096655, 1.6667965441422024, 1.5946026104916233, 1.3990227058963096, 1.082082981761621, 0.6516807916473502, 0.121395149908387, -0.48999138251139035, -1.1592435774068903, -1.8596669856607737, -2.562300502145235, -3.237253214949506, -3.8551218327646573, -4.388419163071088, -4.812941735875069, -5.109005955763307, -5.262487154490178, -5.265604447792906, -5.117406021842381, -4.8239238553874495, -4.397983235485318, -3.8586699357451675, -3.2304757000055444, -2.5421597766213857, -1.8253797552081716, -1.113158006014279, -0.43825985880640805, 0.16843431661016317, 0.6794791620276239, 1.072255157508768, 1.330125846330742, 1.443298153304132, 1.4093371464949331, 1.2333041151561954, 0.9275063394273575, 0.510867394049304, 0.007947167648815333, -0.552340117089944, -1.1382447928859063, -1.7168589128188696, -2.2558635715023145, -2.7252534294255466, -3.098945651084045, -3.3561857040170846, -3.482672569843446, -3.4713404091913542, -3.3227518653723984, -3.045079034167734, -2.6536705480812826, -2.1702259933785095, -1.621620726954484, -1.0384438481217348, -0.45332847041522323, 0.10083443783629184, 0.5927002587455223, 0.99419294697985, 1.2820492294868369, 1.4390982055040362, 1.4552042256805893, 1.327819606578651, 1.062115607712649, 0.6706839355786517, 0.1728254850398486, -0.406533328086594, -1.0382348306045859, -1.6905151365019975, -2.33076669510414, -2.9273369730085776, -3.4512596992472053, -3.877818972633332, -4.18785628966595, -4.368745667003656, -4.414981644389915, -4.328347922865311, -4.1176593657241405, -3.798095577243188, -3.3901687412311183, -2.9183903584779514, -2.4097196173924984, -1.891889235873918, -1.391711889658289, -0.9334713077289771], 'positive_zeros': ['0.78096319082402285598252826912308', '2.40494693836797730481215758587939', '3.64036039217303153172313992456954', '5.06998141274431255076505812897439', '5.52153334075868838309731534712305', '6.72567292619690724621766534315102', '7.44341749514887886407294045500221', '8.515850179315590759417505213659166', '8.934941243252355244726807936089112', '9.953484201120309725964394893902026'], 'prelabel': '2-810-9.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.913143069881451, 'root_angle': 0.4444444444444444, 'root_number': '0.1736481776669303488517166267693147960003756771840693873 + 0.9848077530122080593667430245895230136706432517198424188*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.2222222222222222', 'prec': 60}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.78096319082402285598252826912', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.40494693836797730481215758588', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.64036039217303153172313992457', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 47.79154710464992, 'bad_primes': [2, 3, 5], 'central_character': '9.4', 'conductor': 810, 'conductor_radical': 30, 'degree': 2, 'index': 24, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/810/4/e/a/271/1'], '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': '2-810-9.4-c3-0-24', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-810-9.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.913143069881451, 'root_angle': 0.2222222222222222, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.78096319082402285598252826912', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '989988457604225829432687902865', 'Lhash_array': ['989988457604225829432687902865'], 'label': '2-810-9.4-c3-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/810/4/e/a/271/1'}