-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1210200901326504292873393198616', 'a10': [-3.5962666587138683, 0.0], 'a2': [1.532088886237956, 0.0], 'a3': [-2.879385241571817, 0.0], 'a4': [0.3472963553338607, 0.0], 'a5': [-2.3472963553338606, 0.0], 'a6': [-4.411474127809773, 0.0], 'a7': [0.0, 0.0], 'a8': [-2.5320888862379562, 0.0], 'a9': [5.2908593693815895, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 47.34330335841716, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [7, 11], 'central_character': '5929.1', 'coefficient_field': 'CDF', 'conductor': 5929, 'conductor_radical': 77, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.532088886237956, 0], [2.0, 0]], [[1.0, 0], [2.879385241571817, 0], [3.0, 0]], [[1.0, 0], [2.3472963553338606, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.18479253090409536, 0], [13.0, 0]], [[1.0, 0], [3.9212743075733987, 0], [17.0, 0]], [[1.0, 0], [-0.7733184030943225, 0], [19.0, 0]], [[1.0, 0], [-8.355037141857501, 0], [23.0, 0]], [[1.0, 0], [-8.170244610953407, 0], [29.0, 0]], [[1.0, 0], [2.6527036446661394, 0], [31.0, 0]], [[1.0, 0], [6.822948255619545, 0], [37.0, 0]], [[1.0, 0], [-0.4260220477604618, 0], [41.0, 0]], [[1.0, 0], [1.1847925309040954, 0], [43.0, 0]], [[1.0, 0], [-7.680044790717033, 0], [47.0, 0]], [[1.0, 0], [-6.554377592712286, 0], [53.0, 0]], [[1.0, 0], [0.20439289043134742, 0], [59.0, 0]], [[1.0, 0], [-14.581718738763179, 0], [61.0, 0]], [[1.0, 0], [-3.7587704831436337, 0], [67.0, 0]], [[1.0, 0], [9.965851720522059, 0], [71.0, 0]], [[1.0, 0], [-0.12061475842818323, 0], [73.0, 0]], [[1.0, 0], [0.32769599580660863, 0], [79.0, 0]], [[1.0, 0], [-3.3550371418575016, 0], [83.0, 0]], [[1.0, 0], [-4.652703644666139, 0], [89.0, 0]], [[1.0, 0], [13.120614758428184, 0], [97.0, 0]], [[1.0, 0], [5.901673948046147, 0], [101.0, 0]], [[1.0, 0], [0.9212743075733989, 0], [103.0, 0]], [[1.0, 0], [-10.34729635533386, 0], [107.0, 0]], [[1.0, 0], [0.475651900285685, 0], [109.0, 0]], [[1.0, 0], [3.1429034649025134, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 170, 'label': '2-77e2-1.1-c1-0-170', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/5929/2/a/u/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-4.4241749241044054e-61, 0.1333240733127807, 0.2650298896624615, 0.39346356247991293, 0.5169028201626068, 0.6335298024810999, 0.7414117178215526, 0.8384911729540061, 0.9225874146147002, 0.9914091283777827, 1.0425788704525698, 1.0736686941868907, 1.0822460925111639, 1.0659290147841325, 1.0224484267863092, 0.9497166562858174, 0.8458995927946593, 0.7094906794428687, 0.5393845409178033, 0.33494803121427935, 0.096086458792922, -0.17669724258658823, -0.4822525772654113, -0.8187428672724197, -1.1836198812184926, -1.5736134421020624, -1.9847374831453697, -2.412313702989654, -2.8510135983755247, -3.29491922811953, -3.7376025935227504, -4.172223016471649, -4.591641368835636, -4.988549468772961, -5.355612426369516, -5.685621209092575, -5.9716522241024315, -6.207230297070397, -6.386491083037617, -6.504338690325117, -6.556594148316635, -6.540130316630847, -6.452988926523198, -6.29447567169446, -6.065229627573647, -5.767263773896185, -5.403974018822798, -4.980114863116193, -4.5017406845753065, -3.9761125461580016, -3.4115714120699163, -2.8173796670838764, -2.203533845155378, -1.5805524516856517, -0.9592436762008372, -0.3504586054730147, 0.23516377085835713, 0.7874529489345022, 1.2969575460649263, 1.7551829091302553, 2.15480851958816, 2.489878348141566, 2.7559578749325344, 2.9502522804515223, 3.0716813131594503, 3.120907528880393, 3.1003159432656284, 3.013944603803555, 2.867367127489314, 2.6675298149539928, 2.422547488736713, 2.1414636579283055, 1.8339819293143942, 1.5101767143361118, 1.1801921739042045, 0.8539389578902788, 0.5407985997122101, 0.24934539543390058, -0.01290478091921047, -0.23970999839939616, -0.42627445683828646, -0.5693710365639062, -0.6674095389655075, -0.7204477979298617, -0.7301448498875349, -0.6996574446605075, -0.6334832844187158, -0.5372564141488961, -0.4175020737852379, -0.28135998171635745, -0.13628637963801782, 0.01025383362202337, 0.15109296812835274, 0.27965236520071013, 0.3902084720633893, 0.4781222784203742, 0.5400224959124749, 0.5739345545243548, 0.5793495504671347, 0.5572296362128817, 0.5099489085402448, 0.44117152593046033, 0.35567146520133763, 0.2591008972739956, 0.15771651193836783, 0.058075144746378135, -0.03328834140541056, -0.11018687486206655, -0.16709612785956718, -0.1994441307067433, -0.20386180136327395, -0.178381995243204, -0.12257662002288533, -0.03762382656153067, 0.073699808345996, 0.20710395965795358, 0.35694451493409574, 0.5164537579180183, 0.6780323300791596, 0.8335913942558973, 0.9749306965503389, 1.0941360360756711, 1.1839781272593577, 1.238294072069853, 1.2523327159949984, 1.2230460741105662, 1.1493107774209397, 1.0320660616677064, 0.8743581195550884, 0.681284545040255, 0.4598369644574042, 0.21864459580912507, -0.032373794099694306, -0.28243746622868243, -0.5203944969309665, -0.7352557536070436, -0.9167490823167262, -1.0558686941204045, -1.1453937502421825, -1.1803503030193223, -1.1583920954113642, -1.0800782500473562, -0.9490295288452029, -0.7719495018818581, -0.5585024642030062, -0.3210460706553065, -0.07422317239964532, 0.16557604328286257, 0.38086408098454555, 0.5537948670186307, 0.6669625591137777, 0.7042277070677847, 0.6515352102441139, 0.4976871588071216, 0.23503387905403275, -0.13995161132863335, -0.6262470074459815, -1.2180281734116127, -1.9046103757659072, -2.6705953920799463, -3.4962280987281344, -4.357957125126221, -5.229185004102991, -6.081184352972325, -6.884148394968791, -7.608336969459859, -8.225273442498713, -8.7089439271628, -9.0369481995734, -9.191551815236194, -9.160591264550913, -8.938188531968521, -8.525238016662486, -7.929637212543136, -7.166242519962993, -6.2565426788096605, -5.228054116627898, -4.1134544939284, -2.9494823755815913, -1.7756417348124027, -0.6327594005878648, 0.4385488671271418, 1.3994426345488704, 2.214387505834093, 2.8525882834717375, 3.289263228817816, 3.506703468506257, 3.495069549223108, 3.252887367632489, 2.78721778881483, 2.113487715792442, 1.2549846113870242, 0.2420308798370226, -0.8891315536540506, -2.0977033064986657, -3.3398819720577686, -4.570545770747609, -5.744997060673909, -6.820693136724766, -7.758891716066608, -8.526141703078153, -9.09555614326031, -9.447813462267291, -9.571844754312535, -9.465178524047438, -9.133929288944676, -8.59243213518382, -7.8625409689919135, -6.972623091222056, -5.9562961482662855, -4.850964842486944, -3.696223479635191, -2.53219607007785, -1.397888009156858, -0.32962222197391755, 0.6403718827153978, 1.4851560330950377, 2.1840172199794985, 2.723101115783984, 3.095722119655966, 3.3023428848466705, 3.350231926943201, 3.252823101436994, 3.0288146300524694, 2.701057264690509, 2.2952905216939103, 1.8387922421515783, 1.3590097335833673, 0.882240291052632, 0.4324250247030424, 0.03011285436783591, -0.30835834654307925, -0.5714286375089184, -0.7526099054206511, -0.8505004470642293, -0.8685287469929627, -0.8144491266207426, -0.6996247012312962, -0.5381437626113366, -0.3458237462866336, -0.13916192694886856, 0.06570633727399613, 0.25398269212072616, 0.4130600514348245, 0.5332098189053208, 0.608066295743617, 0.6348848661723959, 0.6145641274698723, 0.5514361449962077, 0.4528426668215886, 0.3285276478454415, 0.18988709301844942, 0.04912542046216987, -0.08162720603512831, -0.19118012650256558, -0.2700749392842728, -0.3112553533140944], 'positive_zeros': ['0.954680178519710563075561897996356', '2.60589970755245546968989790957762', '3.65379481563052012702485099070263', '4.26231114425030977646293325885338', '4.95096334864514581471005721872804', '5.31392015531216517195243986525905', '6.18148798512721077916137345437563', '6.85795993428164263643926945729094', '7.24970918825858773898352241654914'], 'prelabel': '2-77e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.8806470159729285, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.954680178519710563075561897996', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.60589970755245546968989790958', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.65379481563052012702485099070', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 47.34330335841716, 'bad_primes': [7, 11], 'central_character': '1.1', 'conductor': 5929, 'conductor_radical': 77, 'degree': 2, 'index': 170, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5929/2/a/u/1/3'], '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': '2-77e2-1.1-c1-0-170', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-77e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.8806470159729285, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.954680178519710563075561897996', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1210200901326504292873393198616', 'Lhash_array': ['1210200901326504292873393198616'], 'factors': ['2-77e2-1.1-c1-0-170'], 'label': '2-77e2-1.1-c1-0-170', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5929/2/a/u/1/3'}