-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1439996580395968491222551193091', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [3.5615528128088303, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.756354293532622, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [11, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 7, 11], 'central_character': '1848.1', 'coefficient_field': 'CDF', 'conductor': 1848, 'conductor_radical': 462, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-3.5615528128088303, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-0.4384471871911697, 0], [13.0, 0]], [[1.0, 0], [-2.0, 0], [17.0, 0]], [[1.0, 0], [-1.5615528128088303, 0], [19.0, 0]], [[1.0, 0], [0, 0], [23.0, 0]], [[1.0, 0], [-0.4384471871911697, 0], [29.0, 0]], [[1.0, 0], [-3.1231056256176606, 0], [31.0, 0]], [[1.0, 0], [-9.807764064044152, 0], [37.0, 0]], [[1.0, 0], [1.1231056256176606, 0], [41.0, 0]], [[1.0, 0], [10.246211251235321, 0], [43.0, 0]], [[1.0, 0], [8.68465843842649, 0], [47.0, 0]], [[1.0, 0], [-2.8768943743823394, 0], [53.0, 0]], [[1.0, 0], [4.68465843842649, 0], [59.0, 0]], [[1.0, 0], [8.246211251235321, 0], [61.0, 0]], [[1.0, 0], [1.5615528128088303, 0], [67.0, 0]], [[1.0, 0], [-6.246211251235321, 0], [71.0, 0]], [[1.0, 0], [-7.56155281280883, 0], [73.0, 0]], [[1.0, 0], [6.246211251235321, 0], [79.0, 0]], [[1.0, 0], [-7.123105625617661, 0], [83.0, 0]], [[1.0, 0], [4.246211251235321, 0], [89.0, 0]], [[1.0, 0], [-13.12310562561766, 0], [97.0, 0]], [[1.0, 0], [-14.0, 0], [101.0, 0]], [[1.0, 0], [4.876894374382339, 0], [103.0, 0]], [[1.0, 0], [-15.807764064044152, 0], [107.0, 0]], [[1.0, 0], [8.246211251235321, 0], [109.0, 0]], [[1.0, 0], [-2.0, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 12, 'label': '2-1848-1.1-c1-0-12', 'leading_term': '2.1842102216431733362012138441227', '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/1848/2/a/r/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.1842102216431734, 2.1794311188060287, 2.164970538283296, 2.1404696574985147, 2.105366192098197, 2.058945047823651, 2.0004037488122606, 1.9289281246876402, 1.8437735386418717, 1.7443471691608161, 1.6302873616943399, 1.501536683041018, 1.3584059160140731, 1.2016267529711302, 1.0323913616790836, 0.8523773196992408, 0.6637566779684893, 0.46918816052074025, 0.27179177185978337, 0.07510539420619264, -0.11697666906659698, -0.300282803315214, -0.4704599338151788, -0.6230846381000789, -0.7537874317482147, -0.8583875152776671, -0.9330346542170421, -0.9743542865996736, -0.9795914422202119, -0.9467486463187702, -0.8747126961735702, -0.7633650692730148, -0.6136707694959102, -0.4277406612492071, -0.20886279274803085, 0.03850112684297998, 0.30875705958078054, 0.5952596754534998, 0.8904337471958751, 1.1859351729660088, 1.472849411287666, 1.7419235746383557, 1.983826893238576, 2.1894327901652035, 2.350114467296156, 2.4580447540025148, 2.5064900802030046, 2.490087860790891, 2.4050963700977412, 2.249606382762066, 2.023704487410761, 1.7295790523350507, 1.371561330459905, 0.9560961079131759, 0.49163858034889263, -0.011523281470139472, -0.5415188238907833, -1.0852123012892259, -1.6285800979461917, -2.15713692320703, -2.6563977765582525, -3.1123603023235327, -3.5119904634327175, -3.8436933655889116, -4.097750644381757, -4.266706152121405, -4.3456827837659056, -4.332615165610625, -4.228385565129576, -4.036853698506329, -3.7647750117104857, -3.4216063561254595, -3.0192026062031943, -2.57141248632145, -2.093586482418176, -1.6020139985542265, -1.1133106682512703, -0.643779745733781, -0.2087736052923975, 0.1779175782529558, 0.5046230140190928, 0.7622687303219765, 0.9447522101131067, 1.0491949081942797, 1.0760581190409677, 1.0291133356879416, 0.9152645734911442, 0.7442268606909278, 0.528071919700164, 0.28065865700314513, 0.016972117186010754, -0.24760028079464647, -0.49802241216227794, -0.7203576301942539, -0.9024751110279806, -1.0346787750035251, -1.1102257479540516, -1.1257056074320009, -1.0812575406398608, -0.9806098016508464, -0.8309341931615379, -0.6425173404675731, -0.42825984615507046, -0.2030235515106182, 0.017144389857908792, 0.21587456299781113, 0.37738359609068534, 0.48738195720549377, 0.53393379525708, 0.5082220774017658, 0.40517542987023053, 0.22391863989811964, -0.03198346463853972, -0.3545093870163884, -0.7314010921686565, -1.1466183388313063, -1.5810122483181968, -2.0131910373305897, -2.420539691322768, -2.7803457944936305, -3.070976338115108, -3.273045584211505, -3.3705123274476425, -3.351646387358998, -3.2098089223584307, -2.94399905663627, -2.559130044647296, -2.0660112912598443, -1.4810273761734545, -0.8255210559069249, -0.12490320847956699, 0.5924720236008496, 1.296614910275252, 1.9573272961471129, 2.545677640927585, 3.0354477007044145, 3.4044740027031013, 3.6358108433762686, 3.718649241162103, 3.6489378037291167, 3.4296663010937833, 3.0707901417793275, 2.5887930295395143, 2.005904808220091, 1.3490107865432825, 0.648306567636826, -0.0642324614113336, -0.7564862312533708, -1.3978416370811482, -1.9607702161063496, -2.422243970726524, -2.764909158769998, -2.977950337331485, -3.057593563985299, -3.007217560402924, -2.837063742144478, -2.5635590678789573, -2.2082883240883504, -1.7966733868185731, -1.3564349073780493, -0.9159256184117788, -0.50243313526955, -0.14055310235520452, 0.14926949811513487, 0.35194204260316747, 0.45859465484597883, 0.4670642588138002, 0.38196024013789354, 0.21430498486616234, -0.019231269794416722, -0.29745643227269974, -0.5960755075033425, -0.8893153930400336, -1.151654314449679, -1.3595467054619292, -1.4930330880349363, -1.5371302148949275, -1.4829091864934838, -1.3281877968541063, -1.0777869462774894, -0.7433281843762466, -0.3425786491121441, 0.10162098527510842, 0.5627823308152956, 1.0124616069392476, 1.4221123237099642, 1.7649798454868972, 2.017914468505614, 2.1629826989620007, 2.188767380426755, 2.0912656443390167, 1.8743183034339224, 1.5495337944778433, 1.1357022699210952, 0.6577288634817402, 0.1451473279661846, -0.3696959871924192, -0.8536744621375071, -1.2750001351455678, -1.6052914649721823, -1.8214530786583463, -1.907240689670667, -1.8544030360088137, -1.6633189133283461, -1.3430795615279478, -0.9110027653983246, -0.3916027022816924, 0.1849236940260775, 0.7845997814461351, 1.371840048851603, 1.911747307849312, 2.3723842079637483, 2.7268665802561673, 2.9551359987495722, 3.0452887052311053, 2.994366505717621, 2.80855062812051, 2.5027395288989296, 2.099533583998069, 1.627690638553441, 1.1201536672107282, 0.6117826614321729, 0.13694505235542195, -0.27286920396341513, -0.5912413201775464, -0.7986707829377933, -0.8839427456101489, -0.8449145198470659, -0.6886595385330179, -0.43095170360252266, -0.09511950329967897, 0.2896555626060601, 0.6904810933251654, 1.073188157199653, 1.404886512643291, 1.6564579539030297, 1.8048065783262885, 1.8346992634771133, 1.7400563092529677, 1.5245893623992564, 1.2017289345740783, 0.7938339625145582, 0.3307274368329611, -0.15234853045239682, -0.6172213062072085, -1.0255486441102757, -1.3416577760741506, -1.5352593546196263, -1.5838381702930926, -1.4745421712575022, -1.2054241032810025, -0.785933933105565, -0.23661214240623432, 0.4120096304341994, 1.1212372697422979, 1.8466556403997219, 2.541020623141843], 'positive_zeros': ['1.13595700592632520635733462761737', '2.04204062564621713530009498999412', '3.22135372980770518582582174201547', '4.60091343536064424272029901452791', '5.27716616218414770588336266536622', '6.08903391970779655645997043621028', '6.55597401311922205622931187792734', '7.62741994722189564411576355491568', '8.549375854566871081684669441821226', '9.518589989847936184268152410446441'], 'prelabel': '2-1848-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.841400043412899, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.13595700592632520635733462762', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.04204062564621713530009498999', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.22135372980770518582582174202', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 14.756354293532622, 'bad_primes': [2, 3, 7, 11], 'central_character': '1.1', 'conductor': 1848, 'conductor_radical': 462, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1848/2/a/r/1/2'], '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': '2-1848-1.1-c1-0-12', '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': '2-1848-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.841400043412899, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.13595700592632520635733462762', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1439996580395968491222551193091', 'Lhash_array': ['1439996580395968491222551193091'], 'factors': ['2-1848-1.1-c1-0-12'], 'label': '2-1848-1.1-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1848/2/a/r/1/2'}