-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '4015432577771316272841444425789', 'a10': [0.9493322096668463, 1.6442916204046079], 'a2': [1.5795407573249762, -0.5749058194765863], 'a3': [0.0, 0.0], 'a4': [0.6323434165447581, -0.5305991276000876], 'a5': [0.19614327467493967, 1.112383787704268], 'a6': [0.0, 0.0], 'a7': [-2.994408478871007, -2.5126070502147817], 'a8': [-0.9871444918729285, 1.7097844143356749], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6467882563723715, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '81.19', 'coefficient_field': 'CDF', 'conductor': 81, 'conductor_radical': 3, 'conjugate': '3878789108390980081659139543795', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.5795407573249762, 0.5749058194765863], [1.532088886237956, -1.2855752193730787]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.19614327467493967, -1.112383787704268], [-4.698463103929542, 1.7101007166283437]], [[1.0, 0], [2.994408478871007, 2.5126070502147817], [1.2155372436685123, 6.893654271085456]], [[1.0, 0], [-0.3248012583258514, 1.8420394713323562], [-10.336618828644992, -3.762221576582356]], [[1.0, 0], [-0.6884168846593182, -0.25056325478226127], [9.958577760546714, 8.35623892592501]], [[1.0, 0], [-0.9448217388973584, -1.6364792558658006], [-8.5, 14.722431864335457]], [[1.0, 0], [1.37142809153723, -2.3753831334697035], [-9.5, -16.454482671904334]], [[1.0, 0], [-4.464276787029554, 3.745973005469792], [3.993908086339398, -22.650578319280786]], [[1.0, 0], [4.999103910008468, -1.8195250212468705], [22.215288850450364, -18.64084068090964]], [[1.0, 0], [-1.0269597681265061, 0.8617215626688562], [5.3830935076748405, -30.52904034337845]], [[1.0, 0], [1.6980564735402561, 2.9411200862929605], [-18.5, 32.04293994002423]], [[1.0, 0], [-1.688000281292766, -0.6143818578235435], [31.4078221678781, 26.354291997148113]], [[1.0, 0], [-0.8734768852357164, 4.953733579093623], [-40.406782693794064, -14.706866163003756]], [[1.0, 0], [1.3089227849304028, 1.098316626074639], [8.161464350345726, 46.28596439157378]], [[1.0, 0], [2.844942653440345, 0], [53.0, 0]], [[1.0, 0], [-1.9552863656539377, -11.088980017679562], [-55.44186462636859, 20.179188456214455]], [[1.0, 0], [-4.007097206625411, -3.3623537881708914], [10.592538837682751, 60.07327293374469]], [[1.0, 0], [-1.7751056601951045, -0.6460856229884739], [51.32497768897153, 43.066769848998135]], [[1.0, 0], [6.091933862434504, 10.551538966085873], [-35.5, 61.48780366869514]], [[1.0, 0], [4.9438395737176855, -8.562981326148691], [-36.5, -63.21985447626402]], [[1.0, 0], [11.607905521648265, -4.224932092054263], [60.51751100639927, -50.780221165236604]], [[1.0, 0], [10.978583091004399, -3.995877459543839], [63.581688778875176, -53.35137160398276]], [[1.0, 0], [2.864366148514562, -4.961227700707601], [-44.5, -77.07626093681505]], [[1.0, 0], [0.05962702616927358, -0.3381616694716707], [-91.15018421623311, -33.17595390258987]], [[1.0, 0], [-13.33089970629261, -11.18595302681144], [17.538465944359967, 99.46558305423301]], [[1.0, 0], [2.745899068964697, 15.572767468324683], [-96.78833994094856, 35.228074762543876]], [[1.0, 0], [-16.52982155410854, 0], [107.0, 0]], [[1.0, 0], [4.718439893591352, 0], [109.0, 0]], [[1.0, 0], [3.463380697038023, 19.641807981526654], [-106.18526614880764, 38.64827619580057]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-3e4-27.7-c1-0-1', '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/81/2/e/a/19/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.4057882650104234, 1.4274589202000734, 1.4702705196352086, 1.5328867623959934, 1.6129300535087763, 1.7072243365833413, 1.8120032981779894, 1.923047471040582, 2.03575910434611, 2.1452054755987744, 2.2461629144925443, 2.3331859526354486, 2.4007164152937004, 2.4432390431114728, 2.45548377999922, 2.43266967002996, 2.3707808185157115, 2.266860784728187, 2.1193080435208267, 1.9281519385053645, 1.6952861378168207, 1.4246353487853605, 1.1222313156724977, 0.7961762418487924, 0.45647598395957395, 0.11473176702038358, -0.2163123023045898, -0.5233582673956405, -0.793260513167122, -1.01381738624688, -1.174604488558291, -1.2677952888270954, -1.288906714231145, -1.2374032100082666, -1.117093459168567, -0.936260361796128, -0.7074774327054814, -0.4470834440021746, -0.1743112889843319, 0.0899045827488223, 0.3243870971192995, 0.5093561822165971, 0.6281357631179983, 0.6687931559762365, 0.6255632506953672, 0.4999088367136993, 0.3010808935623212, 0.04606950680096705, -0.2411231351910495, -0.5309033282680761, -0.7901540932657386, -0.9848395905208013, -1.0829705982131355, -1.0577007830744731, -0.8902834377863398, -0.5725994546158724, -0.10897426605124762, 0.48296299523435865, 1.1725606910871744, 1.9176588668500965, 2.667319360169596, 3.365634110888592, 3.956353523362597, 4.38796904574725, 4.618801906647857, 4.621604720245897, 4.387183353013332, 3.9265980193959424, 3.2716050451997436, 2.4731485325723384, 1.5978930947097885, 0.7229887192705604, -0.0705432421054297, -0.7052397504049764, -1.1147490752150717, -1.2507490926996045, -1.0884836665116395, -0.630262683657525, 0.0935572633061336, 1.02635725428546, 2.0897695365153024, 3.1905867956734455, 4.22945361924422, 5.110497108938428, 5.750905269815439, 6.08941767271664, 6.09276528209322, 5.75928441838141, 5.119218574934099, 4.2315827872869285, 3.17785907935616, 2.0531720113705862, 0.9559129204687125, -0.0230029603856369, -0.8099832668206154, -1.3565205131161804, -1.6439072791763145, -1.6842994750571914, -1.5179700069691358, -1.2070788276083155, -0.8267431181740273, -0.4545610935143689, -0.1599710180055422, 0.005123733656412734, 0.013176918642805936, -0.13569156445432565, -0.41438994928799816, -0.773487273703842, -1.1491552650726662, -1.4732969763138843, -1.6843918304798682, -1.737441416215072, -1.6114881530353355, -1.3134975840120362, -0.8779079067747964, -0.36178973722176605, 0.163765431650047, 0.6247989939582154, 0.9565030957385534, 1.1142145100467982, 1.0815707057559412, 0.8743766689775649, 0.5393408757209622, 0.14761449792919962, -0.21610300140849822, -0.46737388993021894, -0.5366729041496836, -0.38254483918306204, -0.0010330872046892335, 0.5703959050717201, 1.2554348638819437, 1.948047397968883, 2.527088502386709, 2.874468741087346, 2.8942084879041574, 2.52942144524741, 1.7744126803092655, 0.6796789889119309, -0.6514112959023961, -2.0742419991441454, -3.4215529848115507, -4.526533705163541, -5.2470821135499595, -5.48755529093544, -5.214553922815938, -4.464057023123217, -3.3384584652147438, -1.9935757253527657, -0.6172719555183329, 0.597295882127292, 1.4798472051557188, 1.9082659120638137, 1.8270375137737307, 1.2558444035100653, 0.286815178570832, -0.9293073101222434, -2.2060453972142207, -3.349601405074268, -4.188359936826267, -4.598805123421103, -4.523720319466477, -3.9797682435262205, -3.053277095574593, -1.884999750246171, -0.6464424280257101, 0.4882378325001722, 1.3700378169778749, 1.8979635641865702, 2.033165903367245, 1.8021227503333361, 1.2885636909174147, 0.6158135240607471, -0.07708911365726388, -0.6610689498447099, -1.039790470708666, -1.16542909068114, -1.0446812315095082, -0.7341169769288938, -0.32600496580790234, 0.0724494474127704, 0.36226144767361446, 0.4735840442405517, 0.38020677012058096, 0.10473710450439157, -0.28657018661785005, -0.6982810479762803, -1.0265880464548371, -1.1821585259187144, -1.1102416715276584, -0.8037302041214368, -0.3062457974648311, 0.295669599909714, 0.8899133981561046, 1.3623360246952294, 1.6215937592862928, 1.6200585302560477, 1.3661181306311085, 0.9248152156134278, 0.40609573400498544, -0.05748193649985504, -0.33940831919670406, -0.34852171934309445, -0.05275909453004927, 0.5080213768356663, 1.223567553925296, 1.9297650403028113, 2.437779651193656, 2.570696090760971, 2.200715381539328, 1.279462764122714, -0.14507458304060186, -1.9291408048483476, -3.8522303101606594, -5.6518299177863165, -7.067961723145391, -7.889422640953027, -7.9929516886179215, -7.367598792737521, -6.1191732448136, -4.453350254296467, -2.6401082129440496, -0.9658531519198117, 0.31788571899770457, 1.0394692686015468, 1.13721351309, 0.6686420269646021, -0.20294056833269702, -1.2419958513406524, -2.1878925941184133, -2.8064072704705554, -2.935466960263222, -2.5161580224291074, -1.6029752545828715, -0.3514613322895039, 1.0140606788002888, 2.245960215409088, 3.1226566118175456, 3.491843844536184, 3.298937363937119, 2.5952494269153346, 1.5246662705822431, 0.292080278732658, -0.8794260835519973, -1.7934326969547743, -2.3176359244196583, -2.4062722863376873, -2.1033000694366133, -1.526405728269094, -0.8360908646505245, -0.19726911468533875, 0.25773771336934315, 0.45648158849007825, 0.39807474089039, 0.14716698742708717, -0.1877009659578125, -0.4856199511277749, -0.6466888709297047], 'positive_zeros': ['3.16761777815462144155723855215722', '4.83137412678742614477004440869227', '5.89569942669989025626940443100221', '7.02501178964556677212114939915395', '8.987985031120237624713940020776187', '9.735870766597500111039117182288744', '11.62179024204801028589029035421326', '12.86813358238099881722972175672836', '13.01936866281577302566801372628261', '14.46020590864643005662271034150573'], 'prelabel': '2-3e4-27.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8042314693994332, 'root_angle': 0.05308146342085302, 'root_number': '0.944895633826028 + 0.32737171712979224*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0530814634209', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.16761777815462144155723855216', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.83137412678742614477004440869', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.89569942669989025626940443100', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.6467882563723715, 'bad_primes': [3], 'central_character': '27.7', 'conductor': 81, 'conductor_radical': 3, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/81/2/e/a/19/2'], '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': '2-3e4-27.7-c1-0-1', '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': '2-3e4-27.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8042314693994332, 'root_angle': 0.05308146342085302, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.16761777815462144155723855216', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '4015432577771316272841444425789', 'Lhash_array': ['4015432577771316272841444425789'], 'factors': ['2-3e4-27.7-c1-0-1'], 'label': '2-3e4-27.7-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/81/2/e/a/19/2'}