-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1446212391216188703364351538856', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-2.5615528128088303, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-4.56155281280883, 0.0], 'a8': [0.0, 0.0], 'a9': [3.5615528128088303, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17.567088444681694, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 11], 'central_character': '2200.1', 'coefficient_field': 'CDF', 'conductor': 2200, 'conductor_radical': 110, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [2.5615528128088303, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.56155281280883, 0], [7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.1231056256176606, 0], [13.0, 0]], [[1.0, 0], [-7.68465843842649, 0], [17.0, 0]], [[1.0, 0], [-1.4384471871911697, 0], [19.0, 0]], [[1.0, 0], [1.1231056256176606, 0], [23.0, 0]], [[1.0, 0], [-8.56155281280883, 0], [29.0, 0]], [[1.0, 0], [1.4384471871911697, 0], [31.0, 0]], [[1.0, 0], [7.43844718719117, 0], [37.0, 0]], [[1.0, 0], [12.246211251235321, 0], [41.0, 0]], [[1.0, 0], [-3.1231056256176606, 0], [43.0, 0]], [[1.0, 0], [-11.36931687685298, 0], [47.0, 0]], [[1.0, 0], [9.68465843842649, 0], [53.0, 0]], [[1.0, 0], [-1.1231056256176606, 0], [59.0, 0]], [[1.0, 0], [12.56155281280883, 0], [61.0, 0]], [[1.0, 0], [0, 0], [67.0, 0]], [[1.0, 0], [-3.684658438426491, 0], [71.0, 0]], [[1.0, 0], [1.1231056256176606, 0], [73.0, 0]], [[1.0, 0], [11.36931687685298, 0], [79.0, 0]], [[1.0, 0], [-6.0, 0], [83.0, 0]], [[1.0, 0], [-9.68465843842649, 0], [89.0, 0]], [[1.0, 0], [-4.876894374382339, 0], [97.0, 0]], [[1.0, 0], [2.0, 0], [101.0, 0]], [[1.0, 0], [0, 0], [103.0, 0]], [[1.0, 0], [7.123105625617661, 0], [107.0, 0]], [[1.0, 0], [4.246211251235321, 0], [109.0, 0]], [[1.0, 0], [0.8768943743823394, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 19, 'label': '2-2200-1.1-c1-0-19', '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/2200/2/a/l/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-7.790923424041e-61, 0.09043950597781343, 0.1802158726448141, 0.2686328206553801, 0.35492984044794396, 0.4382550476649943, 0.5176435959513442, 0.5920028871859611, 0.660105409291121, 0.7205896297466932, 0.771969013215866, 0.8126489332090996, 0.8409510145908429, 0.8551442689028608, 0.8534822545730204, 0.8342453940153676, 0.795787495991758, 0.7365854545850838, 0.655291020180308, 0.5507834614458833, 0.4222218622454499, 0.2690957278763217, 0.09127251671936122, -0.11095932728716773, -0.3368532824541787, -0.5851750247722697, -0.8541814489128252, -1.1416097234039333, -1.4446775362531272, -1.7600955103554654, -2.0840925464378692, -2.412454586643712, -2.7405769874487453, -3.0635303514228593, -3.3761393000886426, -3.673073283044678, -3.948948121340934, -4.198436586800237, -4.416385935574728, -4.597939956425601, -4.73866277509913, -4.834661388792798, -4.882703701653518, -4.880328705203845, -4.825945406852474, -4.718917163675573, -4.559628233640569, -4.349529615888717, -4.0911616160734114, -3.7881510392405033, -3.4451814750166787, -3.067935788049548, -2.6630106472822486, -2.237803703921973, -1.800374839949304, -1.3592837341006547, -0.9234068056838276, -0.5017373721208945, -0.10317356680490565, 0.2637008170990125, 0.5908368896288206, 0.8709366059786198, 1.0976578610071854, 1.2658024900196372, 1.3714811005565681, 1.4122490284160816, 1.3872082775631338, 1.297071061827756, 1.144181503409146, 0.9324931393838107, 0.6675011162290237, 0.35612928122705584, 0.006573770492139805, -0.3718938962102115, -0.7691598194230115, -1.1745311177826139, -1.577022825725225, -1.9656603762789198, -2.329788944482763, -2.659380367069942, -2.9453280757075424, -3.179720508037836, -3.35608380730165, -3.4695852912038005, -3.5171901563833234, -3.4977651671956425, -3.412124625688715, -3.2630156916896853, -3.0550420655999226, -2.794527100729302, -2.489319508583703, -2.1485468862961064, -1.7823242547142257, -1.4014265730922284, -1.016935719510215, -0.6398736286510256, -0.28083410277611875, 0.05037378852610673, 0.34505786139321976, 0.5959381958057663, 0.7973944147532589, 0.9456549986621163, 1.0389206453059476, 1.0774159248027821, 1.0633660112367276, 1.0008980116364932, 0.8958692623998011, 0.7556278171100781, 0.5887130975924195, 0.4045072108951518, 0.21284964129739947, 0.02362980926793887, -0.15362673807495408, -0.31016204802552216, -0.4383628754599867, -0.5320952628989831, -0.5869819144455121, -0.6006095756381125, -0.5726560973635497, -0.5049298315481573, -0.401317378070316, -0.26763935424190044, -0.111417651787322, 0.05843856855426912, 0.23201727377305142, 0.3988441745765017, 0.5483625559654631, 0.6704330890349366, 0.7558328815061982, 0.796732325383807, 0.7871284712963732, 0.7232147267794217, 0.6036686296874345, 0.42984224010166033, 0.20584323932283036, -0.06150099757795778, -0.36279943053453173, -0.6863715983319777, -1.0186331257303944, -1.344580582413578, -1.6483591424803996, -1.913892381786347, -2.125550161503878, -2.2688280503835476, -2.331010274188065, -2.301787848463488, -2.1738044051912406, -1.9431042709600665, -1.609460549038962, -1.17656520396778, -0.6520683000336788, -0.04745941496287196, 0.622209389680847, 1.3387530657012945, 2.0814230143115613, 2.8275977030434047, 3.5535700784278705, 4.2354026255274135, 4.849817257034461, 5.375084833564409, 5.79187816459056, 6.084052899665847, 6.23932281182876, 6.249799552315954, 6.1123719039956805, 5.828905702516518, 5.4062526933239266, 4.8560643645514165, 4.194414917577321, 3.4412456614796834, 2.619650887870926, 1.755032348068897, 0.874155487007027, 0.00414529731410162, -0.8285371956433831, -1.599095395059175, -2.285332540814757, -2.868482342109122, -3.3338991786120586, -3.671577921896125, -3.8764805519752707, -3.9486549863444496, -3.8931405473062624, -3.7196638711172922, -3.4421383877639253, -3.0779893449229934, -2.647334299500853, -2.1720556741893615, -1.6748070460619155, -1.1779980396368892, -0.7028038611465595, -0.2682445501068924, 0.10962404608688861, 0.41837063319084067, 0.6496700709956983, 0.7995844433613122, 0.8686312533819461, 0.8616364906053406, 0.7873805956449702, 0.6580553196135738, 0.48855865453816133, 0.295662940041124, 0.09709752865436094, -0.08940831054101753, -0.24707448801182674, -0.36096368996608347, -0.41877459694682545, -0.4114947265159106, -0.3338798218807237, -0.18473534682839857, 0.03301440979340112, 0.3124733559535183, 0.6431294372582719, 1.0114012219158257, 1.4013472168428516, 1.7955013126485406, 2.1757909738792964, 2.5244901909196855, 2.8251570583625476, 3.0635062862616067, 3.228169998105224, 3.311305699870316, 3.3090180637625766, 3.2215707828936857, 3.0533757401313073, 2.812758535947356, 2.5115114236649374, 2.1642562717611304, 1.7876506888765527, 1.399479329515087, 1.0176791448186973, 0.6593515553965811, 0.33981593185736386, 0.07175724818202968, -0.13548364723326117, -0.27643583237331004, -0.349808386537315, -0.3585643623129179, -0.3097510225615073, -0.2140921127648874, -0.08536128193632857, 0.06043168031090195, 0.2059990589166732, 0.33382621172077676, 0.42725740583042815, 0.47155533364335817, 0.45487324378130795, 0.3690820917341754, 0.2104018470213185, -0.02020420599526208, -0.31690113089430055, -0.669134822584927, -1.062064901931655, -1.4772619890483045, -1.8936381905880493, -2.2885658364229053, -2.6391278214907645], 'positive_zeros': ['1.14086041607664668277828186316088', '2.95911103601770103329387322428891', '3.65716234947209555278738095568476', '4.91771582944466859018289888002308', '5.64324103213377772433090446760377', '6.22890009525466020544546426678438', '6.84440514355326304137414267431251', '7.67172082986766673362073512417145', '8.785402291776056964809231708807527'], 'prelabel': '2-2200-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.191311065130062, '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': '1.14086041607664668277828186316', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.95911103601770103329387322429', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.65716234947209555278738095568', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 17.567088444681694, 'bad_primes': [2, 5, 11], 'central_character': '1.1', 'conductor': 2200, 'conductor_radical': 110, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2200/2/a/l/1/1'], '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': '2-2200-1.1-c1-0-19', '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': '2-2200-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.191311065130062, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.14086041607664668277828186316', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1446212391216188703364351538856', 'Lhash_array': ['1446212391216188703364351538856'], 'factors': ['2-2200-1.1-c1-0-19'], 'label': '2-2200-1.1-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2200/2/a/l/1/1'}