-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1191842324369654064299110760025', 'a10': [0, 0], 'a2': [0, 1.0], 'a3': [0, -1.0], 'a4': [-1.0, 0], 'a5': [0, 0], 'a6': [1.0, 0], 'a7': [0, 0], 'a8': [0, -1.0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 20.36185251542651, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -1.0]]], [3, [[1.0, 0], [0, 1.0]]], [5, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 3, 5, 17], 'central_character': '2550.2449', 'coefficient_field': 'CDF', 'conductor': 2550, 'conductor_radical': 510, 'conjugate': '665038623865054670337543677758', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-7.0, 0]], [[1.0, 0], [4.0, 0], [11.0, 0]], [[1.0, 0], [0, -2.0], [-13.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [4.0, 0], [19.0, 0]], [[1.0, 0], [0, 0], [-23.0, 0]], [[1.0, 0], [-10.0, 0], [29.0, 0]], [[1.0, 0], [-8.0, 0], [31.0, 0]], [[1.0, 0], [0, 2.0], [-37.0, 0]], [[1.0, 0], [-10.0, 0], [41.0, 0]], [[1.0, 0], [0, 12.0], [-43.0, 0]], [[1.0, 0], [0, 0], [-47.0, 0]], [[1.0, 0], [0, 6.0], [-53.0, 0]], [[1.0, 0], [12.0, 0], [59.0, 0]], [[1.0, 0], [10.0, 0], [61.0, 0]], [[1.0, 0], [0, 12.0], [-67.0, 0]], [[1.0, 0], [0, 0], [71.0, 0]], [[1.0, 0], [0, 10.0], [-73.0, 0]], [[1.0, 0], [-8.0, 0], [79.0, 0]], [[1.0, 0], [0, 4.0], [-83.0, 0]], [[1.0, 0], [-6.0, 0], [89.0, 0]], [[1.0, 0], [0, 14.0], [-97.0, 0]], [[1.0, 0], [10.0, 0], [101.0, 0]], [[1.0, 0], [0, -8.0], [-103.0, 0]], [[1.0, 0], [0, 4.0], [-107.0, 0]], [[1.0, 0], [-10.0, 0], [109.0, 0]], [[1.0, 0], [0, 2.0], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 25, 'label': '2-2550-5.4-c1-0-25', 'leading_term': '1.256666194774451391833658919705963763914598830977566861', '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/2550/2/d/m/2449/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.2566661947744513, 1.319001415640713, 1.3656711709276401, 1.3962568566498847, 1.4101292756421016, 1.4064778382111185, 1.3843622585779294, 1.3427826203417719, 1.2807628018457524, 1.1974419198886548, 1.0921685534123462, 0.96459289274603, 0.8147524785881116, 0.6431477412295038, 0.4508040663656886, 0.23931758385455154, 0.01088231403779883, -0.23170325821196416, -0.4850516466296216, -0.7452248073532118, -1.0077959112045485, -1.2679341159784316, -1.5205112581587859, -1.7602285708372734, -1.981760685680718, -2.1799133231496777, -2.3497902539043394, -2.4869643661650978, -2.587647041088088, -2.648849562915205, -2.6685300121598714, -2.6457190430880018, -2.580618159120944, -2.474664590568876, -2.330557656714937, -2.152242555001202, -1.9448488469875038, -1.7145824731243076, -1.4685718816506026, -1.2146707433827613, -0.961221674265491, -0.7167873220024966, -0.48985700551837913, -0.2885387363756456, -0.12024780970990834, 0.00859585668282021, 0.09284890929465196, 0.12889150591574025, 0.11482776902352124, 0.05062858052976846, -0.061792782880680165, -0.2185794624508085, -0.4140088625110495, -0.6406509999840462, -0.8896054194513944, -1.1508111598234756, -1.41342067162833, -1.6662251509708748, -1.8981156495147842, -2.098561710008604, -2.2580873243955226, -2.3687228580097424, -2.4244113429118874, -2.421348294808062, -2.3582359877924834, -2.236435918468919, -2.0600069442423647, -1.8356211764590404, -1.5723549842778577, -1.2813582105973929, -0.9754106692191126, -0.6683809057174652, -0.3746077689099893, -0.10823025743460124, 0.11750490989824075, 0.2909257604453661, 0.40257395139673957, 0.4457666439700596, 0.41704979892092986, 0.31651486091233655, 0.14795594462844214, -0.08114876817056213, -0.3598399066563044, -0.6740638572607436, -1.0072343780495119, -1.3409502245209575, -1.655841280244316, -1.9325077199099068, -2.1525101123134056, -2.299363516643972, -2.3594858908044225, -2.3230507794576227, -2.1846964369496806, -1.944048296806398, -1.6060189221515362, -1.180859020960388, -0.683944415765116, -0.1352965290176424, 0.44115260754546665, 1.018526252859097, 1.5681622362653047, 2.0609164331221224, 2.4685515874983985, 2.765145567825904, 2.92844917750038, 2.9411231404836657, 2.7917870336740878, 2.4758197467109517, 1.995861321337489, 1.3619793642852758, 0.5914790618512523, -0.29164659011884553, -1.257611261113098, -2.2720409979340963, -3.2974403926088836, -4.294853167181979, -5.225638843319287, -6.053278619841754, -6.745119392310716, -7.273965405345047, -7.619432470843381, -7.76898988615229, -7.71862974603825, -7.473121601463078, -7.045831484111183, -6.458107105027094, -5.738254329437289, -4.920152538173929, -4.041576921027016, -3.1423128973562426, -2.2621606629732254, -1.4389354757419353, -0.7065711462651899, -0.09343004273159922, 0.3790871580813683, 0.6975542980716259, 0.857097728977575, 0.8615059460592979, 0.7228635511598911, 0.4607292672437587, 0.1009040133078071, -0.32614098278947495, -0.7870858739804745, -1.2477284057696145, -1.6749803078544598, -2.038777171578339, -2.313789733465594, -2.4808358991237536, -2.5279104667569805, -2.45077235983899, -2.2530559235529504, -1.9459018789421698, -1.5471330864188535, -1.0800285033694492, -0.5717738347498188, -0.051687740947670306, 0.45066327311387355, 0.907340999926706, 1.2937828981364452, 1.5903090808078033, 1.7832927928973126, 1.8659200880927749, 1.8384912695602096, 1.7082468240753406, 1.488732102530466, 1.1987458056736797, 0.8609453575843731, 0.5002055765097857, 0.14184405127787245, -0.1901639318110501, -0.47485693441289994, -0.6957287691776144, -0.8418386162201631, -0.9085113373861484, -0.8975777987811988, -0.8171371543413541, -0.6808568202683501, -0.5068589451452971, -0.31627222063841853, -0.13155271708127186, 0.025304776204530255, 0.13453405774712146, 0.18021249448333138, 0.15160199699215804, 0.0441125348679377, -0.14018924472398958, -0.3925716406271958, -0.6981391352463966, -1.0368152825672887, -1.3847432608575798, -1.7160080363020154, -2.0045583865185446, -2.226189717421718, -2.360441123376217, -2.3922632586006842, -2.3133273229457783, -2.1228690584614496, -1.8279936061293531, -1.443405236976406, -0.990567691447464, -0.4963431503339463, 0.008802382952798622, 0.49290528077461065, 0.9247740270966452, 1.2762587338910263, 1.5243527102676118, 1.6529667174308929, 1.6542369267985477, 1.529258798089938, 1.2881790666059207, 0.9496240267339207, 0.5394910542528246, 0.0891782645859341, -0.3666292346505937, -0.7924622296227452, -1.1546799694478684, -1.4240005455935112, -1.5777588123184674, -1.6017174380250143, -1.491285963494049, -1.2520435992969206, -0.8995111476480409, -0.4581723773056824, 0.04019858070543709, 0.5587939085271484, 1.0584565824378056, 1.5006006801456186, 1.8501534166028268, 2.0782982856329104, 2.1648086234828767, 2.0997869590121603, 1.8846660908308228, 1.5323802112608755, 1.0666748950381817, 0.5205889952570222, -0.06579534153565203, -0.6481810316584709, -1.1812623318454214, -1.6220758061511733, -1.9332469397056096, -2.085886099535021, -2.061909040197356, -1.8555961761850386, -1.4742587963006926, -0.9379454774894912, -0.2781934285065133, 0.46409797655235246, 1.2415261604107912, 2.003573214698278, 2.7002752766958364, 3.285900292060622, 3.722355771917787, 3.9820641248031787, 4.050079539910036, 3.9252747996515365, 3.6204949449973522, 3.161652371084296], 'positive_zeros': ['0.940197814882960083574972967080911', '2.63209985225203183245732193591519', '2.90052049639930777569910855694166', '4.30393605622137117591546751804374', '4.72689083643345171935497120211142', '5.69750401876247945288874825376600', '6.48525353000009579257296300100626', '7.80323405699484606229033304584778', '8.217657119251712969813260519889594', '9.087910543834248305861046634847370'], 'prelabel': '2-2550-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.512410942658759, 'root_angle': 0.14758361765043326, 'root_number': '0.8944271909999158785636694674925104941762473438446102897 + 0.4472135954999579392818347337462552470881236719223051449*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.07379180882521663', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.940197814882960083574972967081', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.63209985225203183245732193592', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.90052049639930777569910855694', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 20.36185251542651, 'bad_primes': [2, 3, 5, 17], 'central_character': '5.4', 'conductor': 2550, 'conductor_radical': 510, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2550/2/d/m/2449/2'], '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': '2-2550-5.4-c1-0-25', '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': '2-2550-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.512410942658759, 'root_angle': 0.07379180882521663, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.940197814882960083574972967081', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1191842324369654064299110760025', 'Lhash_array': ['1191842324369654064299110760025'], 'label': '2-2550-5.4-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2550/2/d/m/2449/2'}