-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2492376058386338189821738431593', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -2.0], 'a4': [0, 0], 'a5': [0, -4.0], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.04108607387354, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 7], 'central_character': '3136.1569', 'coefficient_field': 'CDF', 'conductor': 3136, 'conductor_radical': 14, 'conjugate': '559636139867793248301312777105', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 2.0], [-3.0, 0]], [[1.0, 0], [0, 4.0], [-5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 2.0], [-11.0, 0]], [[1.0, 0], [0, 4.0], [-13.0, 0]], [[1.0, 0], [2.0, 0], [17.0, 0]], [[1.0, 0], [0, -6.0], [-19.0, 0]], [[1.0, 0], [0, 0], [23.0, 0]], [[1.0, 0], [0, 8.0], [-29.0, 0]], [[1.0, 0], [-8.0, 0], [31.0, 0]], [[1.0, 0], [0, -8.0], [-37.0, 0]], [[1.0, 0], [10.0, 0], [41.0, 0]], [[1.0, 0], [0, 2.0], [-43.0, 0]], [[1.0, 0], [8.0, 0], [47.0, 0]], [[1.0, 0], [0, 0], [-53.0, 0]], [[1.0, 0], [0, 10.0], [-59.0, 0]], [[1.0, 0], [0, -4.0], [-61.0, 0]], [[1.0, 0], [0, 2.0], [-67.0, 0]], [[1.0, 0], [-8.0, 0], [71.0, 0]], [[1.0, 0], [-6.0, 0], [73.0, 0]], [[1.0, 0], [-8.0, 0], [79.0, 0]], [[1.0, 0], [0, -6.0], [-83.0, 0]], [[1.0, 0], [10.0, 0], [89.0, 0]], [[1.0, 0], [2.0, 0], [97.0, 0]], [[1.0, 0], [0, 4.0], [-101.0, 0]], [[1.0, 0], [-16.0, 0], [103.0, 0]], [[1.0, 0], [0, -6.0], [-107.0, 0]], [[1.0, 0], [0, 8.0], [-109.0, 0]], [[1.0, 0], [-2.0, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 79, 'label': '2-56e2-8.5-c1-0-79', 'leading_term': '1.3672657878444389685484819399438850134295338675566289645', '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/3136/2/b/a/1569/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.367265787844439, 1.5941051583133463, 1.8299789422504218, 2.0742121058527827, 2.325840057240331, 2.5835183487141324, 2.8454499249682423, 3.109335039296052, 3.372347142324724, 3.631136342779279, 3.8818606088582097, 4.120243772128047, 4.341658577532101, 4.541232411240576, 4.7139728420854405, 4.854909658537028, 4.959249626775218, 5.0225397218874965, 5.040834104640144, 5.010859659958636, 4.930174520468814, 4.7973137139789825, 4.611915941888269, 4.374825556056414, 4.088164087197056, 3.755366211306401, 3.3811758336476267, 2.9715990214265746, 2.53381181213573, 2.076022436429591, 1.607289180493511, 1.1372969184284936, 0.6760972038808007, 0.23381864611927347, -0.1796439737976598, -0.5549518527169742, -0.8836443269816746, -1.1584488928121657, -1.373566467792342, -1.5249193066300855, -1.6103495544289494, -1.6297575528591712, -1.5851707076713863, -1.4807359524436365, -1.322631548250581, -1.1188970595794634, -0.8791837347389484, -0.614431062505421, -0.33647882528146045, -0.05762735890341917, 0.2098382095425312, 0.4541414103573565, 0.6645053219961626, 0.8316195458075923, 0.9480616998890956, 1.0086526445213286, 1.010726447742826, 0.954298901893981, 0.8421221471730248, 0.6796175316639541, 0.47468407435814663, 0.23738558846347452, -0.020474581348534162, -0.2858764287055211, -0.54518352169671, -0.7847955624443298, -0.9918243665378244, -1.1547616943541121, -1.2641061085668674, -1.312916333783273, -1.2972605377337958, -1.2165345417569116, -1.0736271191367903, -0.8749170839193011, -0.6300945569605055, -0.35180729077531164, -0.055141847152256215, 0.24304168850405572, 0.5248943708284353, 0.7724479073340215, 0.9685284524872618, 1.0976698787641759, 1.1469796123123, 1.1069103707582675, 0.9718938643616946, 0.7407977072081232, 0.41717428570961046, 0.009279865658821069, -0.4701466226583148, -1.0043434206256412, -1.5732099451548403, -2.154187933904207, -2.7233010113624543, -3.2563038268153077, -3.7298839886265354, -4.122854840989893, -4.41727511983921, -4.599432947566687, -4.660636564678718, -4.597762538499768, -4.413523623374911, -4.1164324706140505, -3.7204533239977837, -3.244350869792256, -2.7107626183397486, -2.1450376029894467, -1.5738988174043336, -1.0239987576662994, -0.5204458889197433, -0.085384182524878, 0.2632923533863346, 0.5130131736476863, 0.6573253239540237, 0.69635462350638, 0.6368977716037102, 0.49212942160379186, 0.2809300897072986, 0.026863014655405467, -0.2431505433225023, -0.5003888815015665, -0.7160358349161182, -0.8629393544614247, -0.9173208583906598, -0.8603333672126653, -0.6793723373346822, -0.3690549391041409, 0.0681992325960575, 0.6220312349306287, 1.274469691571213, 2.0007144717902383, 2.7703425744462065, 3.5488754777575835, 4.299623988984862, 4.985707870969787, 5.572134523418121, 6.027814726377294, 6.3273944914981355, 6.452790552413019, 6.3943326331186086, 6.1514375771420875, 5.732767490347376, 5.1558546754747105, 4.446208474503277, 3.6359511822550328, 2.7620599115718765, 1.864316732211868, 0.9830888522950312, 0.15707268645580547, -0.5788605732409583, -1.195585212799989, -1.6712879229947022, -1.992583614702205, -2.155110321811599, -2.1635662664733846, -2.0311878528988516, -1.7787035499098358, -1.4328329212793425, -1.0244301442178312, -0.5863951327112124, -0.15149114956111964, 0.24978564583665594, 0.5911424980983916, 0.8521029446420364, 1.0191889709560076, 1.0865946531651247, 1.0563087196136698, 0.9376819715242938, 0.7464746579290141, 0.5034559514161896, 0.2326599601697246, -0.040572137535087496, -0.2916181546809366, -0.4985177402508361, -0.6436858221671375, -0.7152664645483925, -0.7080227630924838, -0.6236923148481083, -0.47077748473375874, -0.263782343354722, -0.02195067717338873, 0.2324012845878222, 0.47583081528441973, 0.6858426124861849, 0.8429268108504663, 0.9323961658536158, 0.945868994171599, 0.8822679681205621, 0.7482389322031723, 0.5579362638113606, 0.33216897783665195, 0.09695133306233403, -0.11845054759023735, -0.28384223814327514, -0.37062747247877537, -0.35434836868570535, -0.21704203601200392, 0.05077738268126217, 0.44868109905037024, 0.9655677537761153, 1.579674461978719, 2.259391867365585, 2.9648595195692193, 3.6502589374523544, 4.26666693368159, 4.7652853639542325, 5.100829136803493, 5.234834990499124, 5.138651089102144, 4.79588258029307, 4.204100272526945, 3.375666628243022, 2.337592261877149, 1.1304030333831656, -0.1939320959084727, -1.5748941181142346, -2.946948443433404, -4.243491754262184, -5.400948268053867, -6.362736855692253, -7.082834792561261, -7.52868821046292, -7.683262134565685, -7.546081479511128, -7.133184463356369, -6.475986555344426, -5.619130703251154, -4.61747242551408, -3.532410914371833, -2.427824789826385, -1.3658998592236347, -0.4031438427450228, 0.41313122857572304, 1.0476134354441873, 1.4788903230894341, 1.7003193549285838, 1.7198230182563297, 1.5586429390562826, 1.249165383396496, 0.8319997127846918, 0.3525463194023695, -0.14267302879094027, -0.6096345442019859, -1.0101012872235515, -1.314331132764167, -1.5030029331785097, -1.5682252771732739, -1.5135681028860732, -1.353137718189958, -1.1097939945664466, -0.812678243725429, -0.49427582166821, -0.18727422520361967, 0.07850773702965118, 0.27885250032458886, 0.39730179060336723, 0.42655495972822066, 0.3689893016438529], 'positive_zeros': ['1.96613803356982411648777077715724', '2.88342213822445727805302303954706', '3.62826074722234604933079682280374', '4.46388080741141509418774897392508', '5.09887299327169344857220318140233', '6.39972437515509583460445999501927', '6.86135303238179194493046585278824', '7.37465255585159860174696195791416', '8.625126234669142390965667685909197', '9.337740345186374845700511101938054'], 'prelabel': '2-56e2-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.004106920707584, 'root_angle': -0.75, 'root_number': '-0.70710678118654752440084436210484903928483593768847403659 - 0.70710678118654752440084436210484903928483593768847403659*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.375', 'prec': 20}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.96613803356982411648777077716', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.88342213822445727805302303955', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.62826074722234604933079682280', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 25.04108607387354, 'bad_primes': [2, 7], 'central_character': '8.5', 'conductor': 3136, 'conductor_radical': 14, 'degree': 2, 'index': 79, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3136/2/b/a/1569/1'], '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': '2-56e2-8.5-c1-0-79', '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': '2-56e2-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.004106920707584, 'root_angle': -0.375, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.96613803356982411648777077716', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2492376058386338189821738431593', 'Lhash_array': ['2492376058386338189821738431593'], 'label': '2-56e2-8.5-c1-0-79', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3136/2/b/a/1569/1'}