-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2086122935978304150275109622040', 'a10': [-0.22355110648605617, 0.0], 'a2': [-2.4016211964122847, 0.0], 'a3': [0.0, 0.0], 'a4': [3.767784371056773, 0.0], 'a5': [0.09308341666038465, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.5798613497330564, 0.0], 'a8': [-4.245548416216305, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.1', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '2086122935978304150275109622040', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.4016211964122847, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.09308341666038465, 0], [5.0, 0]], [[1.0, 0], [0.5798613497330564, 0], [7.0, 0]], [[1.0, 0], [3.0930834166603844, 0], [11.0, 0]], [[1.0, 0], [-4.201733098817233, 0], [13.0, 0]], [[1.0, 0], [1.9909861120868604, 0], [17.0, 0]], [[1.0, 0], [3.845422855570232, 0], [19.0, 0]], [[1.0, 0], [4.452815547071087, 0], [23.0, 0]], [[1.0, 0], [-6.399509051538438, 0], [29.0, 0]], [[1.0, 0], [-1.6574998342465155, 0], [31.0, 0]], [[1.0, 0], [-4.03009405312479, 0], [37.0, 0]], [[1.0, 0], [1.096155938368118, 0], [41.0, 0]], [[1.0, 0], [6.90112199906533, 0], [43.0, 0]], [[1.0, 0], [-3.593194137006135, 0], [47.0, 0]], [[1.0, 0], [-5.400335707214843, 0], [53.0, 0]], [[1.0, 0], [10.284656357254235, 0], [59.0, 0]], [[1.0, 0], [13.19632040012922, 0], [61.0, 0]], [[1.0, 0], [8.837293592045386, 0], [67.0, 0]], [[1.0, 0], [-1.1449467474089925, 0], [71.0, 0]], [[1.0, 0], [-0.19547211797798977, 0], [73.0, 0]], [[1.0, 0], [7.2079940796564745, 0], [79.0, 0]], [[1.0, 0], [14.900446427560594, 0], [83.0, 0]], [[1.0, 0], [1.553125819134319, 0], [89.0, 0]], [[1.0, 0], [-5.295534225612428, 0], [97.0, 0]], [[1.0, 0], [7.268982299315665, 0], [101.0, 0]], [[1.0, 0], [-6.401373031983491, 0], [103.0, 0]], [[1.0, 0], [5.543653097700145, 0], [107.0, 0]], [[1.0, 0], [6.231369994043947, 0], [109.0, 0]], [[1.0, 0], [11.84397969078619, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 16, 'label': '2-3e6-1.1-c1-0-16', '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/729/2/a/a/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [-1.2925270282023437e-120, 0.1426105497602392, 0.285172029563309, 0.42630045455862725, 0.5622675452172262, 0.6865202880941311, 0.7897824361204671, 0.8606956325496922, 0.8869259009050753, 0.8566542915077643, 0.7603542449730485, 0.5927218254506323, 0.3545749358757831, 0.054487708677935766, -0.2901086744653613, -0.6526341297713146, -0.9981202016641897, -1.2851897771345258, -1.469301315897865, -1.507143429827455, -1.3618826098711991, -1.0087820895427355, -0.4405506008359378, 0.32832398644667987, 1.2590212428819993, 2.2882949566914124, 3.3313199268060614, 4.287649477161066, 5.050060860599091, 5.51563061257646, 5.597963198785671, 5.239160568047325, 4.419933404215973, 3.1662712046979222, 1.5513391560475551, -0.3082457619024865, -2.2619276035218836, -4.139883445611466, -5.771415883394862, -7.004933079065299, -7.726928635828701, -7.877261254680711, -7.458324251108029, -6.5363881194969835, -5.234428272876783, -3.7169826779961457, -2.1688380145896624, -0.7704117442278124, 0.32661561370229975, 1.0197090645421267, 1.2686689836080016, 1.0993672055326609, 0.5972596196340147, -0.10841472625901713, -0.8672285646827305, -1.5331919694272311, -1.9890170185396867, -2.1647712790317497, -2.0475986680162466, -1.6807705863466236, -1.1523012112911972, -0.5753553861080436, -0.0643040270350872, 0.28880229100495514, 0.432585428794794, 0.36574760569166914, 0.13556492826096253, -0.1742302296515739, -0.4635885787297722, -0.6399086769276598, -0.6401208573967555, -0.44601721794209226, -0.08913806753263989, 0.35619151820159606, 0.7903691691519558, 1.1127196829945116, 1.2467802410476763, 1.160515632129941, 0.8762187343030013, 0.4670784073077349, 0.040502118966444886, -0.2884224435370871, -0.42724005206699167, -0.33272540875975587, -0.026620028132548105, 0.4044872237299679, 0.8265544171409505, 1.0899296841612949, 1.0688963728327163, 0.6995752430675337, 0.006325798924828396, -0.8913212223451322, -1.7951210372972706, -2.466477143611675, -2.6796659015028252, -2.278520076306602, -1.223182513682791, 0.38537146052885485, 2.3111777431558105, 4.221128340122297, 5.748997278094202, 6.573139352942444, 6.4911052388430575, 5.473816191368994, 3.6854019902185695, 1.4617847028491504, -0.749843344469328, -2.4793771079728852, -3.3317148438986623, -3.072851904495766, -1.6845140874218114, 0.6259004584149364, 3.463551178528475, 6.325136716904524, 8.701722430662386, 10.182755947522066, 10.53808040907779, 9.759694484515116, 8.054331692223744, 5.78944069113949, 3.406055478686768, 1.3196629321653637, -0.16739582284046137, -0.9218261203944065, -0.9917343803019547, -0.5747185922784925, 0.04794302763611008, 0.5924681366910806, 0.8473981453712875, 0.7229546810739116, 0.2633821208086639, -0.3788107846501295, -0.9973538023345229, -1.3985423870026736, -1.4598367394649587, -1.1641393951747372, -0.6007831356703973, 0.06570111472976059, 0.648457603161438, 0.9960426882356478, 1.0371674240759128, 0.7989191259751116, 0.393354109311916, -0.022704969579102934, -0.30142038653693215, -0.3537237642240657, -0.17886874787821, 0.13606062807203434, 0.4467967416937462, 0.602872920072466, 0.5021516501280422, 0.13041553875582682, -0.4281286186075491, -1.0144080411737908, -1.4458466376954646, -1.5795578015738359, -1.3664527431549396, -0.8770678841347253, -0.28811780492234357, 0.1688194683473355, 0.2822687536267037, -0.0637977197094235, -0.8395960970108891, -1.8634339080721858, -2.8462996711997386, -3.477535880522212, -3.527725006117274, -2.93710931148308, -1.859503495936251, -0.6429576153101474, 0.2534292433005167, 0.3873171782911501, -0.5291395257710099, -2.5223381655941983, -5.315813110134572, -8.372228505513236, -11.01324541637858, -12.588498961876219, -12.648850336863621, -11.075352885804449, -8.125696944728764, -4.381827252302312, -0.6099273207764724, 2.4308870805408342, 4.1795095026820555, 4.4110417396681365, 3.284257880522278, 1.2858451978221763, -0.9118259063747458, -2.638270115112792, -3.4043569214403115, -3.023641550753571, -1.6435079318696495, 0.3188590926566993, 2.3127604147507577, 3.8193208181008877, 4.495971929432585, 4.258784382852108, 3.28220804443447, 1.9220456675992736, 0.5907806218609598, -0.37253738044765616, -0.7965663143119167, -0.7089292242046935, -0.2994857882807363, 0.16663849566553413, 0.4528523646154005, 0.43467243404639466, 0.13519203991618198, -0.2970281922598752, -0.656163485634081, -0.7658349457723536, -0.551052740048279, -0.06863283208080719, 0.514538800501757, 0.9862690184728939, 1.1716120818203928, 1.0014147636946726, 0.5404344627728519, -0.03603921126119635, -0.5085002546216706, -0.6973445871352938, -0.53243039315164, -0.08075041203747003, 0.47946842365610065, 0.929350143987602, 1.097971529900033, 0.9342401884798367, 0.5324267146736912, 0.098641108539567, -0.13170156453436252, 0.004749799758110918, 0.5188557839987871, 1.2440148908207755, 1.8820890524870229, 2.1091511392136946, 1.7055960532617287, 0.6623169563676587, -0.7809307919957492, -2.187503822414088, -3.057066530353771, -2.9998624814400685, -1.8929379006402114, 0.03990066055410152, 2.2606697843866983, 4.061979133494553, 4.784332753489427, 4.038046455364245, 1.8552623369913301, -1.2838119662477612, -4.5674662455576085, -7.082167641779639, -8.086713385855065, -7.2446021593739784, -4.738877311684555, -1.2296830552935238, 2.3351736568032866], 'positive_zeros': ['1.64566082767815986874265981994184', '2.82521821242815915221485454620431', '4.35498958548368895676105017199082', '5.95809874712577181210718782331582', '6.60701432257266788520877779124696', '7.76859638391169032683917969800169', '8.306305418352720175676067053459371', '9.026208247321778619573227470579970', '10.01295853930506894902884859787439'], 'prelabel': '2-3e6-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 1.0, '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': '1.64566082767815986874265981994', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.82521821242815915221485454620', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.35498958548368895676105017199', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '1.1', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/a/a/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': '2-3e6-1.1-c1-0-16', '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': '2-3e6-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.64566082767815986874265981994', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2086122935978304150275109622040', 'Lhash_array': ['2086122935978304150275109622040'], 'label': '2-3e6-1.1-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/a/a/1/1'}