-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1104326987224241488880848335918', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -14, 'a6': 0, 'a7': -7, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.868481321446641, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1, 7]]], 'bad_primes': [2, 3, 7], 'central_character': '252.1', 'coefficient_field': '1.1.1.1', 'conductor': 252, 'conductor_radical': 42, 'degree': 2, 'euler_factors': [[1], [1], [1, 14, 125], [1, 7], [1, 4, 1331], [1, -54, 2197], [1, -14, 4913], [1, -92, 6859], [1, -152, 12167], [1, -106, 24389], [1, 144, 29791], [1, -158, 50653], [1, -390, 68921], [1, 508, 79507], [1, -528, 103823], [1, 606, 148877], [1, -364, 205379], [1, -678, 226981], [1, -844, 300763], [1, -8, 357911], [1, 422, 389017], [1, -384, 493039], [1, -548, 571787], [1, 1194, 704969], [1, 1502, 912673], [1, 398, 1030301], [1, -1160, 1092727], [1, 324, 1225043], [1, 938, 1295029], [1, -622, 1442897]], 'euler_factors_factorization': [[1], [1], [[[1, 14, 125], 1]], [[[1, 7], 1]], [[[1, 4, 1331], 1]], [[[1, -54, 2197], 1]], [[[1, -14, 4913], 1]], [[[1, -92, 6859], 1]], [[[1, -152, 12167], 1]], [[[1, -106, 24389], 1]], [[[1, 144, 29791], 1]], [[[1, -158, 50653], 1]], [[[1, -390, 68921], 1]], [[[1, 508, 79507], 1]], [[[1, -528, 103823], 1]], [[[1, 606, 148877], 1]], [[[1, -364, 205379], 1]], [[[1, -678, 226981], 1]], [[[1, -844, 300763], 1]], [[[1, -8, 357911], 1]], [[[1, 422, 389017], 1]], [[[1, -384, 493039], 1]], [[[1, -548, 571787], 1]], [[[1, 1194, 704969], 1]], [[[1, 1502, 912673], 1]], [[[1, 398, 1030301], 1]], [[[1, -1160, 1092727], 1]], [[[1, 324, 1225043], 1]], [[[1, 938, 1295029], 1]], [[[1, -622, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-252-1.1-c3-0-0', 'leading_term': '1.372920706791819544511026817580200000000000000000000000000000000000000000000000000000000000', '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/252/4/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [1.3729207067918194, 1.3634792217811729, 1.3351835926693465, 1.2881226250102917, 1.2224519844310207, 1.138405324695885, 1.036309167420456, 0.9166008641314415, 0.7798488209602972, 0.6267740426494336, 0.4582719582135587, 0.275433426781211, 0.0795637891659544, -0.12780117166734, -0.3448834703663609, -0.5696564110082494, -0.7998442962675221, -1.0329292037166338, -1.2661655347257077, -1.4966028686557236, -1.7211174545399068, -1.9364524455982044, -2.13926673100108, -2.3261919476684443, -2.493896967195615, -2.639158855227787, -2.758939000104689, -2.8504628130065055, -2.9113011229312313, -2.9394511373168637, -2.933414624294567, -2.8922708069672916, -2.815741355109564, -2.7042448259703114, -2.5589379529487264, -2.3817413166195442, -2.175347162501286, -1.9432074569594195, -1.6895006964136141, -1.4190765017198574, -1.1373776315344906, -0.8503397239493401, -0.5642698090034289, -0.28570540622795365, -0.021256807987653503, 0.2225640752291286, 0.439524195943662, 0.6238544003284421, 0.7704336671938796, 0.8749667812276652, 0.9341493932490205, 0.9458143322128261, 0.909053151663929, 0.8243072324209147, 0.6934233316323198, 0.5196692661785238, 0.3077064370623983, 0.06351712296420295, -0.2057141320052545, -0.4917641760635015, -0.7855774648301468, -1.0775106785171373, -1.3576099398810262, -1.6159132707478872, -1.842769516205878, -2.0291637755540006, -2.1670384714155193, -2.2495986208135847, -2.27158969340856, -2.22953668983516, -2.121933770274447, -1.9493749167645833, -1.714617710904558, -1.4225743209806105, -1.0802261691022845, -0.6964614206461367, -0.28183731853719823, 0.1517276283127354, 0.5913236138945102, 1.0234708235815377, 1.4345786111794623, 1.8114269205256621, 2.141652592078285, 2.414222081168294, 2.6198716884846918, 2.7514967272037176, 2.8044721591088555, 2.776889126504931, 2.669694455976309, 2.4867235471403815, 2.2346209828492167, 1.9226475725488235, 1.5623772046745061, 1.1672916506174666, 0.7522861290382007, 0.33310279392053616, -0.07428685759333079, -0.4543265505922173, -0.7925204538805783, -1.076051579960956, -1.2943458847600045, -1.4395558092773446, -1.5069394583303688, -1.4951152499773062, -1.406176588435187, -1.245656752220303, -1.022340534345231, -0.7479259639478868, -0.4365463843885935, -0.10416994385344726, 0.2321001563744857, 0.5547958348662025, 0.8468915396724834, 1.0926127205907499, 1.278207783029117, 1.392646260211113, 1.4282080484111586, 1.3809324288960974, 1.2509011429768317, 1.042336798144171, 0.7635060862274053, 0.42642633845487654, 0.04638341768722669, -0.35872159600612824, -0.7691705053826517, -1.1643364558549156, -1.5236617270286164, -1.8276590197297644, -2.0588877063091506, -2.2028561524344052, -2.2488033096236912, -2.190317312232748, -2.02575565633412, -1.758440430780606, -1.3966126342870238, -0.9531413642928533, -0.44499603825132383, 0.10749781647538527, 0.681586940282845, 1.2531601841288804, 1.7979085645073876, 2.2925181376866886, 2.7158349853993973, 3.0499413932673756, 3.281085318732328, 3.400411439432377, 3.4044512233032598, 3.295341175647538, 3.080752147911883, 2.773527658128923, 2.3910447946896567, 1.9543266140267475, 1.4869491440600506, 1.013798345834846, 0.5597419220631603, 0.14828707429593735, -0.19970225406247225, -0.467156710974453, -0.6417551791618904, -0.7166240156932615, -0.6907381857291894, -0.5689964272562601, -0.3619604323627019, -0.08526692834865876, 0.2412595654887048, 0.5947477318283786, 0.9506129862670881, 1.284009821171117, 1.5713206798117083, 1.791595088394818, 1.927853721220925, 1.9681780484998699, 1.906517011999157, 1.7431572926481023, 1.484822405084869, 1.144387068950426, 0.7402158733255784, 0.2951578582137581, -0.16475006896541436, -0.6117993005198774, -1.0182588639783328, -1.3580615094308468, -1.6084257036441285, -1.7513142524452885, -1.7746379032129211, -1.6731256724047072, -1.448802134734114, -1.1110345029882365, -0.6761377401271549, -0.1665526859210045, 0.39036136883926975, 0.9638537126673626, 1.5215418934949674, 2.031300991924958, 2.4631693624920863, 2.791154463209497, 2.9948263255177205, 3.0605972636789196, 2.9826040607350786, 2.763132140833663, 2.4125488043046674, 1.9487428121831738, 1.3960985983678182, 0.7840631992513599, 0.14539068677697256, -0.48582931278969277, -1.076237048248791, -1.5952322186859864, -2.0168382765681443, -2.321280799673748, -2.4961760168719547, -2.5372493799367586, -2.448533535504584, -2.2420283531335805, -1.936840695184373, -1.5578560949640572, -1.1340261465099526, -0.6963820425988793, -0.2759044499033105, 0.09860867944983197, 0.40253262841788046, 0.6171285164041803, 0.7308585174085824, 0.7402093840962668, 0.6499619567999348, 0.47288113468267823, 0.22883999071590705, -0.05656929854034488, -0.3538489298247755, -0.6317138828333696, -0.8593727223640155, -1.0088145580132986, -1.0569427402850609, -0.9874036312637183, -0.7919771826919451, -0.4714240302906954, -0.03571962754642399, 0.49635273209844605, 1.0982340815534373, 1.7371874050861122, 2.376360516630203, 2.977179738907756, 3.501914435671734, 3.9162376687578893, 4.191605435896164, 4.307286527207171, 4.2518965837720755, 4.0243221602084605, 3.633961410446594, 3.100254703589849, 2.4515278326933587, 1.7232190459078893, 0.9556054357914461, 0.19118103336610537, -0.5281344931359336, -1.1637634179154508, -1.6830200493907241], 'positive_zeros': ['0.871160386801707880068417972706360', '3.09962663529711795514319748122426', '4.02492502434093766009312278551549', '5.38967628174797762816757374267775', '6.73689945832073349827511786315826', '7.68576081818539569826698250944747', '8.586336500963135596512388445969151', '9.619435359985852412357928789070060', '10.92664613291796964048540556197914', '11.48016647561398649217381205682506'], 'prelabel': '2-252-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.8559669761872497, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 1004609851600754933, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.871160386801707880068417972706', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.09962663529711795514319748122', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.02492502434093766009312278552', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 14.868481321446641, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 252, 'conductor_radical': 42, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -14, 0, -7, 0, 0, 0, -4, 0, 54, 0, 0, 0, 14, 0, 92, 0, 0, 0, 152, 0, 71, 0, 0, 0, 106, 0, -144, 0, 0, 0, 98, 0, 158, 0, 0, 0, 390, 0, -508, 0, 0, 0, 528, 0, 49, 0, 0, 0, -606, 0, 56, 0, 0, 0, 364, 0, 678, 0, 0, 0, -756, 0, 844, 0, 0, 0, 8, 0, -422, 0, 0, 0, 28, 0, 384, 0, 0, 0, 548, 0, -196, 0, 0, 0, -1194, 0, -378, 0, 0, 0, -1288, 0, -1502, 0, 0, 0], 'euler11': [1, 4, 1331], 'euler13': [1, -54, 2197], 'euler17': [1, -14, 4913], 'euler19': [1, -92, 6859], 'euler2': [1, 0, 0], 'euler23': [1, -152, 12167], 'euler29': [1, -106, 24389], 'euler3': [1, 0, 0], 'euler31': [1, 144, 29791], 'euler37': [1, -158, 50653], 'euler41': [1, -390, 68921], 'euler43': [1, 508, 79507], 'euler47': [1, -528, 103823], 'euler5': [1, 14, 125], 'euler53': [1, 606, 148877], 'euler59': [1, -364, 205379], 'euler61': [1, -678, 226981], 'euler67': [1, -844, 300763], 'euler7': [1, 7, 0], 'euler71': [1, -8, 357911], 'euler73': [1, 422, 389017], 'euler79': [1, -384, 493039], 'euler83': [1, -548, 571787], 'euler89': [1, 1194, 704969], 'euler97': [1, 1502, 912673], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 14, 125], [1, 7, 0], [1, 4, 1331], [1, -54, 2197], [1, -14, 4913], [1, -92, 6859], [1, -152, 12167], [1, -106, 24389], [1, 144, 29791], [1, -158, 50653], [1, -390, 68921], [1, 508, 79507], [1, -528, 103823], [1, 606, 148877], [1, -364, 205379], [1, -678, 226981], [1, -844, 300763], [1, -8, 357911], [1, 422, 389017], [1, -384, 493039], [1, -548, 571787], [1, 1194, 704969], [1, 1502, 912673]], 'index': 0, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/252/4/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/252/4/a/a'], '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': '2-252-1.1-c3-0-0', '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': '2-252-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.8559669761872497, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 1004609851600754933, 'z1': {'__RealLiteral__': 0, 'data': '0.871160386801707880068417972706', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
-
id: 20642146
{'Lhash': '1104326987224241488880848335918', 'Lhash_array': ['1104326987224241488880848335918'], 'label': '2-252-1.1-c3-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/252/4/a/a'}
-
id: 24554850
{'Lhash': '1104326987224241488880848335918', 'Lhash_array': ['1104326987224241488880848335918'], 'label': '2-252-1.1-c3-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/252/4/a/a/1/1'}