-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1174521506551130627587111607484', 'a10': [10.816201132610322, -1.712312693348587e-60], 'a2': [0.6180339887498949, -1.902113032590307], 'a3': [-6.128908383917136, 4.452912591164408], 'a4': [-3.23606797749979, -2.3511410091698925], 'a5': [1.6711949822770717, 5.143409284364034], 'a6': [4.682069377444313, 14.40992784287275], 'a7': [-17.919580452626917, -13.01933728284701], 'a8': [-6.47213595499958, 4.702282018339785], 'a9': [9.391628585775669, -28.904460685706287], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.278462221389235, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.6180339887498949, 1.902113032590307]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 11], 'central_character': '242.9', 'coefficient_field': 'CDF', 'conductor': 242, 'conductor_radical': 22, 'conjugate': '680283620842152698711091016546', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.6180339887498949, 1.902113032590307]], [[1.0, 0], [6.128908383917136, -4.452912591164408], [8.34345884812358, -25.678525939969145]], [[1.0, 0], [-1.6711949822770717, -5.143409284364034], [-101.12712429686843, 73.47315653655915]], [[1.0, 0], [17.919580452626917, 13.01933728284701], [105.99282907060697, 326.21238508923767]], [[1.0, 0], [0, 0]], [[1.0, 0], [23.740827118001093, -73.06675277999578], [-1777.4103366417594, -1291.3641992865635]], [[1.0, 0], [18.321103210183868, 56.38655773287157], [-3974.7004933641165, 2887.7889445129204]], [[1.0, 0], [-77.06902580623687, 55.993924840173726], [2119.5475644177645, -6523.296645268459]], [[1.0, 0], [-142.48390326982002, 0], [12167.0, 0]], [[1.0, 0], [16.51875455930939, 12.001577697020725], [7536.615475810593, 23195.3173759225]], [[1.0, 0], [-65.91460200978719, 202.8642854649809], [-24101.42527942406, -17510.710451045066]], [[1.0, 0], [-117.77471336791726, -85.56833798543337], [15652.637816074212, 48173.865719898415]], [[1.0, 0], [-67.01295349585062, 48.687760641981], [21297.76026931575, -65547.76615957828]], [[1.0, 0], [-151.37286315005133, 0], [79507.0, 0]], [[1.0, 0], [73.10627261785038, -53.114816120822105], [32083.071406990166, -98741.54069131173]], [[1.0, 0], [72.57227913515716, -223.35450874956035], [-120444.02307155904, -87507.70500554652]], [[1.0, 0], [244.72559818598089, 177.80355477366672], [63465.60128773233, 195327.03626018236]], [[1.0, 0], [-46.12988569649818, -141.97318977988863], [-183631.48640021993, 133416.08435059784]], [[1.0, 0], [-826.2363997853488, 0], [300763.0, 0]], [[1.0, 0], [277.79554150170554, 854.966764780484], [-289556.0814737318, 210374.80743325135]], [[1.0, 0], [111.6389963808786, 81.11047865454488], [120212.86410075892, 369977.1527995918]], [[1.0, 0], [-94.08288431875448, 289.55734419779446], [-398876.9298896297, -289801.05300502863]], [[1.0, 0], [-236.17971443412225, -726.8864189286506], [-462585.4001626681, 336087.96605255635]], [[1.0, 0], [313.0996894617915, 0], [704969.0, 0]], [[1.0, 0], [180.00409213234585, -553.9956309798984], [-738367.9673071664, -536455.7295655283]], [[1.0, 0], [-43.742706709538474, 134.62620831143207], [-833531.0183215027, -605595.7332221874]], [[1.0, 0], [680.6907504696351, 494.55077863607494], [337671.2132123532, 1039245.1338816542]], [[1.0, 0], [52.12653059605392, -37.872141315405806], [378559.1058400687, -1165085.1278917638]], [[1.0, 0], [1559.0406139506042, 0], [1295029.0, 0]], [[1.0, 0], [-1811.5035496752116, 1316.134368471713], [445879.6941326285, -1372276.5941927282]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 12, 'label': '2-242-11.9-c3-0-12', '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/242/4/c/q/9/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.8901455550592535, 0.9656912529796571, 0.9834776698833511, 0.9406989782628534, 0.8352222806282568, 0.6658838921063871, 0.4329041667273253, 0.1383816188727963, -0.21318632496911957, -0.6144181398281995, -1.05466598144959, -1.5198043129519956, -1.9922525402156535, -2.4512843650471465, -2.8736599726765086, -3.2345943914655853, -3.5090469566087097, -3.6732841229030373, -3.7066331239454855, -3.5933102204756104, -3.3241782348762685, -2.898267803144476, -2.323889290587865, -1.6191710290860486, -0.8118867183973382, 0.06151890354351274, 0.9577331769749641, 1.8291569256869997, 2.62712861797896, 3.3055715306610787, 3.8247704971539895, 4.154931932145493, 4.279158228398472, 4.195482777445087, 3.9176688568274445, 3.4745740279049055, 2.908015838181613, 2.2692334626607726, 1.614207540395375, 0.9982574059151098, 0.4704601853135991, 0.06850986039812022, -0.18535967490780594, -0.286834741584775, -0.24996112573547627, -0.10537480443647128, 0.10359985519618665, 0.32662712595039534, 0.5131918036651673, 0.6197586856060947, 0.6163166392067612, 0.49136611518832657, 0.2545414569734168, -0.06368158972968666, -0.415380004113654, -0.7414402902802212, -0.9800048685374873, -1.0760549294913206, -0.9908122804544305, -0.7095455547913205, -0.24646844507097854, 0.35427482355224177, 1.0220534112132809, 1.667525979647395, 2.193992487458405, 2.510956130633616, 2.5480694257197523, 2.2674119921137375, 1.6721130202613155, 0.8097067674367876, -0.23073413513114502, -1.3277812705510448, -2.3422919015522234, -3.1357533921011997, -3.589873490999909, -3.6245834827359884, -3.2116572114099164, -2.3816245790235397, -1.2225321141266958, 0.1297338607047074, 1.508559624525264, 2.7389393793778782, 3.6618872874462647, 4.157294521068643, 4.161670852093426, 3.6778613756781224, 2.7749869845042974, 1.578358639726285, 0.25072773751684224, -1.0323082544756867, -2.108879934239258, -2.855099896672899, -3.202976886238238, -3.1489513675186047, -2.7515551217698317, -2.1185524954529384, -1.3857732940922862, -0.6913649127954766, -0.15008597387392428, 0.16765308176819974, 0.24807372752880932, 0.13523660001566432, -0.07920363595996317, -0.27590956073836265, -0.3337556293635801, -0.15676387640817077, 0.3032169453033481, 1.0327319161886546, 1.9549035270357595, 2.9404049650752917, 3.8295654641621675, 4.461694786491171, 4.7061411420866905, 4.4890456885517676, 3.810378526275146, 2.747559836194194, 1.4444863711584013, 0.08762526125066065, -1.1265545578410403, -2.026702839670778, -2.497478580174482, -2.5001039203243502, -2.078404818152649, -1.3489929967781298, -0.4774214936478264, 0.35497647681822597, 0.9868867314823301, 1.3081512352499018, 1.2798382572970501, 0.9391056185826285, 0.387906261878619, -0.2319609317543193, -0.7719738930052427, -1.110861915088545, -1.1818437076014463, -0.9869532361589624, -0.5951059812118695, -0.12421355424506828, 0.28865988549718097, 0.522225246939287, 0.5027167631628734, 0.22467608715927104, -0.24470007771644267, -0.7794304869236766, -1.2243446063304666, -1.434015905184933, -1.3120602437757498, -0.8412164925825524, -0.09623874111052096, 0.7647925082315636, 1.5303143287308387, 1.980847246371618, 1.9408045174769544, 1.3249735641322626, 0.16854968526873848, -1.3673665418808572, -3.017842181150554, -4.460761619505525, -5.3793845894338, -5.528130384833007, -4.787542133186503, -3.196097149188292, -0.9510592766977947, 1.6229954426635407, 4.132388933200959, 6.187762371377975, 7.477641691702182, 7.8267902852945035, 7.227093491212768, 5.83457842588213, 3.9335070604589406, 1.8756436745519367, 0.008155435906608124, -1.3940816595343974, -2.1772733678689504, -2.32866602392664, -1.9645405072653435, -1.2905250199246951, -0.5447905339029543, 0.061653239390376, 0.393171995924087, 0.41516058987451554, 0.19202553483130358, -0.14051733923275736, -0.42039559628493073, -0.5087734247759397, -0.33082078724058667, 0.10314026561970846, 0.7014321635637527, 1.3182324607906901, 1.7962624521006632, 2.0127637664382787, 1.9156323262450088, 1.539242920138098, 0.9950939547916868, 0.439454073543199, 0.026795859802885232, -0.1378737989839641, -0.033892316193073396, 0.2637788190824199, 0.6014395697562358, 0.7884785418600149, 0.6536696414740227, 0.10078301614266962, -0.8523578254463468, -2.0636051722392055, -3.2900423869733326, -4.2414499706863635, -4.651400887886644, -4.348220580454743, -3.3070606006747685, -1.6683134465820495, 0.2843087875097969, 2.1824871360410882, 3.6555433010075395, 4.416364324556944, 4.329518002338027, 3.444013007326299, 1.9817955016720732, 0.28425619816380193, -1.2701464663865523, -2.3564391940302114, -2.7788687930398948, -2.5125649040985563, -1.7007467357306183, -0.6087959643913772, 0.45204695524723865, 1.2105307666286236, 1.5074671820228847, 1.334555128675226, 0.8296713398824318, 0.23041505862270448, -0.20065393814089433, -0.2576508932249175, 0.14362143812232656, 0.9362562402732058, 1.917457632918488, 2.8047837598617913, 3.317993076913465, 3.263418802287378, 2.5965578038933126, 1.4442051419959192, 0.0785291035589363, -1.1510629832871702, -1.9103335043359648, -1.9716969125116364, -1.2792732123360269, 0.03111447048429226, 1.6633918806259953, 3.2363066439214845, 4.382069916498763, 4.8417679895752945, 4.531447332897769, 3.5608049151709262, 2.199561036888155, 0.8011645718809322, -0.29464870859397796], 'positive_zeros': ['0.926534098859471454309355588595717', '3.11637567383177645001055206971160', '5.15229574365334668651345438848131', '5.69097153505213744173120381917150', '6.60162842629267688038479152002321', '7.55405069155389282499670104724377', '8.723388979616989474783411525521658', '9.863360858596557204756842062143958', '11.02358271026014203007456372694297', '12.29784454989459956095710556509773'], 'prelabel': '2-242-11.9-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7786852503733668, 'root_angle': 0.306998265656443, 'root_number': '0.5698578268317503 + 0.8217433037138756*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.153499132828', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.926534098859471454309355588596', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.11637567383177645001055206971', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.15229574365334668651345438848', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 14.278462221389235, 'bad_primes': [2, 11], 'central_character': '11.9', 'conductor': 242, 'conductor_radical': 22, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/242/4/c/q/9/1'], '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': '2-242-11.9-c3-0-12', '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': '2-242-11.9-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7786852503733668, 'root_angle': 0.1534991328282215, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.926534098859471454309355588596', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1174521506551130627587111607484', 'Lhash_array': ['1174521506551130627587111607484'], 'label': '2-242-11.9-c3-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/242/4/c/q/9/1'}