-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '965986415387047977421342127406', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [1.618033988749895, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 46.28129301153413, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [23, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '5796.1', 'coefficient_field': 'CDF', 'conductor': 5796, 'conductor_radical': 966, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.618033988749895, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-3.0, 0], [11.0, 0]], [[1.0, 0], [-0.6180339887498949, 0], [13.0, 0]], [[1.0, 0], [6.708203932499369, 0], [17.0, 0]], [[1.0, 0], [4.23606797749979, 0], [19.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.7639320225002102, 0], [29.0, 0]], [[1.0, 0], [3.0, 0], [31.0, 0]], [[1.0, 0], [-9.47213595499958, 0], [37.0, 0]], [[1.0, 0], [-11.94427190999916, 0], [41.0, 0]], [[1.0, 0], [9.090169943749475, 0], [43.0, 0]], [[1.0, 0], [-9.23606797749979, 0], [47.0, 0]], [[1.0, 0], [-9.326237921249264, 0], [53.0, 0]], [[1.0, 0], [-9.618033988749895, 0], [59.0, 0]], [[1.0, 0], [-5.854101966249685, 0], [61.0, 0]], [[1.0, 0], [-6.562305898749053, 0], [67.0, 0]], [[1.0, 0], [-4.618033988749895, 0], [71.0, 0]], [[1.0, 0], [-1.7639320225002102, 0], [73.0, 0]], [[1.0, 0], [6.708203932499369, 0], [79.0, 0]], [[1.0, 0], [-7.47213595499958, 0], [83.0, 0]], [[1.0, 0], [-16.798373876248842, 0], [89.0, 0]], [[1.0, 0], [12.416407864998739, 0], [97.0, 0]], [[1.0, 0], [5.326237921249264, 0], [101.0, 0]], [[1.0, 0], [-19.41640786499874, 0], [103.0, 0]], [[1.0, 0], [10.618033988749895, 0], [107.0, 0]], [[1.0, 0], [2.090169943749474, 0], [109.0, 0]], [[1.0, 0], [3.326237921249264, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 15, 'label': '2-5796-1.1-c1-0-15', 'leading_term': '2.10676714305564414239923018628', '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/5796/2/a/l/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.1067671430556443, 2.09727191924569, 2.068741727899215, 2.0210521641092707, 1.9540257237735639, 1.86747425917068, 1.761254070445168, 1.6353298296297982, 1.4898431063092272, 1.32518116411531, 1.1420418711446063, 0.9414909414743996, 0.7250082246164208, 0.4945203229065209, 0.2524174004264693, 0.0015526273461227054, -0.2547767276727837, -0.5128669854599889, -0.7686643980322125, -1.0178394600773801, -1.2558779442233143, -1.4781868493275727, -1.6802128911293177, -1.8575706222129924, -2.006176760273514, -2.122386850229916, -2.2031300087697114, -2.2460372219058007, -2.249558508751014, -2.2130642474823636, -2.136926098517674, -2.0225732668841836, -1.8725203267268749, -1.6903634856416234, -1.4807429878136646, -1.2492703282364757, -1.0024200535690357, -0.7473871291952081, -0.4919121207749439, -0.24407773012743356, -0.012081493039356189, 0.19600935933062438, 0.3725138047698622, 0.5103957363747372, 0.6035168386769375, 0.6468746006453511, 0.6368163367025506, 0.5712203231146532, 0.449635742109584, 0.27337406385178903, 0.04554577715704413, -0.22896202074990218, -0.5435697860686315, -0.8901519470566793, -1.2592438193554423, -1.6403049106105376, -2.0220321647375576, -2.3927144521306256, -2.7406175621225968, -3.054387192830359, -3.323456050709008, -3.5384402478861623, -3.6915097864058852, -3.7767180943965704, -3.7902763588350523, -3.7307597887073047, -3.5992349215551935, -3.399299610243481, -3.137030324070286, -2.8208347734017907, -2.4612115022149132, -2.0704218523729963, -1.6620834376755786, -1.2506978173449281, -0.8511282687480632, -0.47804627426578683, -0.14536741621216415, 0.13430130509060842, 0.35018024724647573, 0.49377996252225903, 0.5592874565371966, 0.5438575566288941, 0.44779428226509926, 0.27461109685896984, 0.03096355431372274, -0.27354703653178697, -0.6266949217347225, -1.0140667426308456, -1.41959921294227, -1.82619811494686, -2.2164149324792226, -2.573154147693792, -2.8803819964539112, -3.123806449479415, -3.2914984603043598, -3.374426138776459, -3.3668764524599775, -3.26674324803403, -3.0756656794435173, -2.799007330372642, -2.4456731758032064, -2.027768749674361, -1.5601131520191762, -1.0596245027551365, -0.5446027935755413, -0.03394048299972244, 0.4537046665107881, 0.9007373380604307, 1.2914148146470439, 1.612562115697109, 1.8541772487708927, 2.0098960021537104, 2.0772915881284346, 2.0579916931176574, 1.9576037952288985, 1.7854486042342526, 1.5541107480566436, 1.2788249287134983, 0.9767242465887339, 0.6659848063043576, 0.36490666858884224, 0.09097535711341795, -0.14004979789228003, -0.3149743669503047, -0.4238909428958868, -0.46074577126111527, -0.42371780443155055, -0.31538672566089737, -0.14267655071180543, 0.08342755916724619, 0.34838018055390907, 0.6347737954136636, 0.9232032339839107, 1.1932560759003006, 1.424581191124522, 1.5979823490912377, 1.6964811585792081, 1.7062937373631284, 1.6176685255669963, 1.4255384774756126, 1.1299492715821147, 0.7362358032838877, 0.2549315760493486, -0.2985909141322567, -0.9047367767999974, -1.5405366250715318, -2.180687432805857, -2.7987370486271415, -3.368354427262726, -3.8646218463644257, -4.265282813105473, -4.551880250199783, -4.7107239268410765, -4.733633820386574, -4.618416828394119, -4.369047494369963, -3.995538510760102, -3.513502947168176, -2.943426568727312, -2.3096843722158167, -1.6393497020850378, -0.9608562029675051, -0.30258171585440174, 0.308571520988965, 0.8485247155163602, 1.297225589413964, 1.6396407304586467, 1.8664819252051592, 1.9746250411656054, 1.967196432094593, 1.8533199081259057, 1.6475360634266865, 1.3689241458484578, 1.0399736406508053, 0.6852673350120702, 0.3300489573492617, -0.0012441615467720948, -0.2864000747090509, -0.506721355857757, -0.6481094250540573, -0.701880047467735, -0.6652607964270681, -0.5415391528552526, -0.3398498861076247, -0.07461130118958707, 0.23535936083617523, 0.5680018353404654, 0.8993738898736486, 1.205138356255771, 1.4620884470862676, 1.6496201986128123, 1.7510627735488784, 1.7547845936478594, 1.6550055209004135, 1.452261930402598, 1.1534916047169217, 0.7717277900444043, 0.3254151868170213, -0.16261628889040042, -0.6664628382541369, -1.1586678579425007, -1.6118634448059426, -2.0004342088659146, -2.3021022797316215, -2.4993354895375868, -2.5804898352666017, -2.5406120233834653, -2.3818473887787066, -2.113421657867316, -1.751190543842638, -1.3167775013116054, -0.8363455276014354, -0.3390720945678516, 0.1445843426210083, 0.5847235475740848, 0.9538375079717536, 1.2285268279078871, 1.3909924844427037, 1.4302080116133502, 1.342695325360874, 1.1328505995033868, 0.8127934949019175, 0.4017420244788958, -0.07505536136487836, -0.5877710809298882, -1.1037491852046342, -1.5894519446356896, -2.012485078181301, -2.3435780019442283, -2.558396652747369, -2.63907528596185, -2.5753697191686977, -2.365356891868019, -2.015633018801256, -1.5409933734498473, -0.9636089518861114, -0.3117469151940233, 0.3818892251965945, 1.0820991139969105, 1.7532856764637816, 2.361585632344551, 2.8768971798585583, 3.274677099059654, 3.537393209015279, 3.6555392372348052, 3.628146453283362, 3.4627581944022876, 3.174867667299251, 2.7868539556940837, 2.3264837568791332, 1.8250748679285977, 1.315439937018311, 0.8297439484936125, 0.39741525683577406, 0.043247211140460234, -0.21418440119018164, -0.36368303654056905], 'positive_zeros': ['0.76202891807342699441491496494158', '2.03402978391882401862834238524346', '2.54808807299819027260777583289839', '3.88443672459926241105274017623304', '4.27125519440573059816496619224826', '5.33546866402550345257446633865974', '6.16326257762804670589160905582779', '6.53321223720773139165057428001447', '7.23504956966065202411745843266712', '8.251085227317418494539049818839598'], 'prelabel': '2-5796-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.803035573296242, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.76202891807342699441491496494', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.03402978391882401862834238524', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.54808807299819027260777583290', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 46.28129301153413, 'bad_primes': [2, 3, 7, 23], 'central_character': '1.1', 'conductor': 5796, 'conductor_radical': 966, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5796/2/a/l/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': '2-5796-1.1-c1-0-15', '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': '2-5796-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.803035573296242, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.76202891807342699441491496494', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '965986415387047977421342127406', 'Lhash_array': ['965986415387047977421342127406'], 'label': '2-5796-1.1-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5796/2/a/l/1/2'}