-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1261975847950959368405438636310', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0.8660254037844386, 0.5], 'a6': [0, 0], 'a7': [3.67227812599095, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 27.308837491277906, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.8660254037844386, -0.5]]], [19, [[1.0, 0], [-4.349707159534212, 0.28292689214144184]]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '3420.521', 'coefficient_field': 'CDF', 'conductor': 3420, 'conductor_radical': 570, 'conjugate': '1437030568900627060259872040380', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [-3.67227812599095, 0], [7.0, 0]], [[1.0, 0], [0, 2.0], [-11.0, 0]], [[1.0, 0], [-0.34949272553734795, 0.20177971916880383], [6.5, -11.258330249197702]], [[1.0, 0], [-6.309168926967771, -3.6426003783476646], [8.5, 14.722431864335457]], [[1.0, 0], [-4.349707159534212, 0.28292689214144184]], [[1.0, 0], [6.229654608699809, -3.5966927652912277], [11.5, -19.91858428704209]], [[1.0, 0], [-3.9498746037710912, -6.841383497257518], [-14.5, 25.11473670974872]], [[1.0, 0], [0, 8.623959567176017], [-31.0, 0]], [[1.0, 0], [0, -1.011879180362929], [-37.0, 0]], [[1.0, 0], [-4.144680802576122, 7.1787977312171956], [-20.5, -35.50704155516198]], [[1.0, 0], [4.25035262536857, -7.36182669722213], [-21.5, -37.239092362730865]], [[1.0, 0], [6.287577951027725, -3.6301348225766126], [23.5, -40.703193977868615]], [[1.0, 0], [1.4791518821166945, 2.5619662119372455], [-26.5, 45.89934640057525]], [[1.0, 0], [-1.0472478127112843, 1.8138864197313203], [-29.5, -51.09549882328188]], [[1.0, 0], [1.08885826904953, 1.8859578442352887], [-30.5, 52.827549630850754]], [[1.0, 0], [-10.228233661909215, 5.9052734580376764], [33.5, -58.023702053557386]], [[1.0, 0], [6.835807566668292, -11.839966016233257], [-35.5, -61.48780366869514]], [[1.0, 0], [-3.2101786126091727, 5.5601924584100555], [-36.5, -63.21985447626402]], [[1.0, 0], [-10.024575347504816, -5.787691275393592], [39.5, 68.41600689897065]], [[1.0, 0], [0, 8.70472444959026], [-83.0, 0]], [[1.0, 0], [-0.7021121349823193, -1.2160938904000347], [-44.5, 77.07626093681505]], [[1.0, 0], [5.048114336063071, 2.9145301708260227], [48.5, 84.00446416709055]], [[1.0, 0], [8.332440231813958, -4.810736610844257], [50.5, -87.4685657822283]], [[1.0, 0], [0, 9.632755554850231], [-103.0, 0]], [[1.0, 0], [4.2456805129807424, 0], [107.0, 0]], [[1.0, 0], [10.427774262319806, 6.0204782773989916], [54.5, 94.39676901250381]], [[1.0, 0], [-10.441366741354123, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 16, 'label': '2-3420-57.8-c1-0-16', 'leading_term': '2.6500112512640963798806601207534446720884906284498000304', '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/3420/2/dg/c/521/15', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.6500112512640963, 2.621453864387313, 2.5811554698487265, 2.528986556091469, 2.464715438224525, 2.3880460056515393, 2.2986644805290157, 2.1962923313963625, 2.0807423007189554, 1.9519745454396265, 1.8101501038813488, 1.655679227912673, 1.4892624975455035, 1.3119230209179202, 1.125028387997623, 0.9303013796687836, 0.7298187359230137, 0.5259975660626668, 0.3215692516604503, 0.11954096068483978, -0.07685483270096746, -0.2642221387642145, -0.4390735658828359, -0.5979114554987172, -0.7373164177344951, -0.8540413331150197, -0.9451085881148711, -1.0079080434693954, -1.0402930077120962, -1.0406713176147466, -1.0080885248567701, -0.9423001658471687, -0.8438301588602377, -0.714012536867847, -0.5550139901604041, -0.36983506129193183, -0.16228830371317185, 0.06304772151051508, 0.3008990893948043, 0.5453915565385209, 0.7901690005724757, 1.0285334456210597, 1.2536040592789381, 1.4584917202715828, 1.6364850182080508, 1.7812428867210548, 1.8869885176266479, 1.948698783977937, 1.9622831390146676, 1.9247458774005828, 1.8343257614756712, 1.6906073395105652, 1.4945988195350313, 1.2487721083396428, 0.9570615700731311, 0.6248191838413883, 0.25872505829316667, -0.13334634076933177, -0.5425024171760606, -0.9590477848029649, -1.3727338923818315, -1.7730366890435216, -2.149454801943924, -2.49181959626389, -2.7906076221740403, -3.0372453692000776, -3.22439598462256, -3.3462176985199528, -3.3985841520675653, -3.3792576533468544, -3.2880075780857445, -3.126667668993269, -2.8991278298035845, -2.6112581080024566, -2.2707648498087547, -1.8869814174601351, -1.4705982983667243, -1.0333398181703983, -0.5875969020303717, -0.1460273178287587, 0.27886350712436575, 0.6751467585594187, 1.0318844949771946, 1.3395185632413285, 1.5902191800349823, 1.7781791166099727, 1.8998409303918549, 1.954046741086978, 1.9421025966850685, 1.8677524392571587, 1.737059964074776, 1.558200152819862, 1.341165822933639, 1.0973980313976313, 0.8393524591503014, 0.5800168401159197, 0.33239695214293313, 0.10899053519199628, -0.07873035669681822, -0.2208077058665366, -0.3092361948959617, -0.33833311717989206, -0.3050226184439889, -0.20902027799346282, -0.05290764700294825, 0.1579094691102796, 0.41536061810651803, 0.7089850195050587, 1.026312563251291, 1.3533387685295872, 1.6750766626598648, 1.9761647865962406, 2.2415075286224155, 2.4569218883550303, 2.6097637032276046, 2.689506413589416, 2.688246639564406, 2.601113183127036, 2.4265594921551816, 2.1665240191758293, 1.8264481185730046, 1.415146952483902, 0.9445350828446144, 0.42921475462644904, -0.11405895232384093, -0.6670161870801509, -1.2105886565652388, -1.725675185677801, -2.193924556273755, -2.5985020878650675, -2.9248062857631143, -3.1611032450588383, -3.299049346806953, -3.3340770331030396, -3.2656239502682127, -3.0971922912563965, -2.8362324817706517, -2.4938531269468847, -2.084367022817861, -1.6246906785590942, -1.1336218310381294, -0.6310255185901207, -0.1369641060745349, 0.32919004245604316, 0.749618960664285, 1.108860516671873, 1.3945089907333024, 1.597780853607972, 1.7139174533125725, 1.742403431591052, 1.6869879704619681, 1.5555050483981083, 1.3594983506888259, 1.1136658843757805, 0.8351482400327184, 0.5426923778530549, 0.25572938544237395, -0.006590493903315642, -0.22635940972932306, -0.3878232090936406, -0.47819728072068424, -0.4883455741782721, -0.4132873943048145, -0.25250440414519143, -0.010029627460281982, 0.30568930422859514, 0.6821493598502798, 1.1033593532241512, 1.55059017725398, 2.0032733898087165, 2.440005463661013, 2.839608946363427, 3.1821980441702085, 3.4501949888853667, 3.6292450844472843, 3.7089825431411896, 3.6836059542063677, 3.552231191856023, 3.3190003551845297, 2.992937425143757, 2.587554129870979, 2.1202223841279793, 1.611341947518566, 1.083342980754969, 0.5595723703213397, 0.06311952238771033, -0.3843586088739275, -0.76375246538407, -1.059496133521262, -1.2603914603219462, -1.3602147281408519, -1.358071231779071, -1.2584757707154235, -1.0711511235849653, -0.8105512954647054, -0.4951309524773707, -0.14639620284844085, 0.21221600092621173, 0.5565727563898739, 0.8631303888285556, 1.110202272373388, 1.2791415889881244, 1.3553748864207982, 1.3292293705607776, 1.196507132670939, 0.9587724706906939, 0.6233334624617642, 0.20291520898764198, -0.2849611753130503, -0.818863593150285, -1.3745530244474116, -1.926249095469893, -2.4479900643539314, -2.9150140937680282, -3.305086574642209, -3.5997002722522926, -3.785081147068681, -3.85294259006446, -3.80094402094164, -3.6328256487693578, -3.358208848101377, -2.992070103301395, -2.553914797759683, -2.066694242017552, -1.5555242634815936, -1.0462755437446933, -0.5641139680336528, -0.1320730266132011, 0.23026050364221995, 0.5078717961291858, 0.6911881366726085, 0.7766417195800447, 0.766889662809456, 0.6706749657402233, 0.5023324741774603, 0.28096431479221234, 0.02932854548578668, -0.22749818680972972, -0.463609399964215, -0.6538246731946051, -0.7752234539074353, -0.8085676634001527, -0.7395292664812342, -0.5596491747364213, -0.266968468014199, 0.13370883995465094, 0.6309414064049376, 1.2071621498241314, 1.839550982420313, 2.501222536292114, 3.162663847594135, 3.793341636695666, 4.363388008216416, 4.845267792837599, 5.2153307657499814, 5.4551576811832705, 5.552620199044808], 'positive_zeros': ['0.995523409781647763520181316352795', '1.86503073287295623449434724833751', '2.87756572872208216863075156046646', '4.02887535014128069877180487197491', '4.95388859014949327328178036596561', '5.29523806398668772653210656193776', '6.28634602302931689886504850584737', '7.22545862998780897769917067946615', '7.971287176855845407758332751035507', '8.329930039739693722246787634029928'], 'prelabel': '2-3420-57.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.225785825239866, 'root_angle': -0.08108205500054826, 'root_number': '0.96773217596221647013115960345512773303492640260629114599 - 0.25198102231603414770768459984155489197565921494679195135*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.04054102750027414', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.995523409781647763520181316353', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.86503073287295623449434724834', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.87756572872208216863075156047', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 27.308837491277906, 'bad_primes': [2, 3, 5, 19], 'central_character': '57.8', 'conductor': 3420, 'conductor_radical': 570, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3420/2/dg/c/521/15'], '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': '2-3420-57.8-c1-0-16', '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': '2-3420-57.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.225785825239866, 'root_angle': -0.04054102750027413, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.995523409781647763520181316353', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1261975847950959368405438636310', 'Lhash_array': ['1261975847950959368405438636310'], 'label': '2-3420-57.8-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3420/2/dg/c/521/15'}