-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2709129413090723750244998052385', 'a10': [3.0, 1.7320508075688772], 'a2': [-0.5, 0.8660254037844386], 'a3': [-1.5, -0.8660254037844386], 'a4': [-0.5, -0.8660254037844386], 'a5': [0.0, -3.4641016151377544], 'a6': [1.5, -0.8660254037844386], 'a7': [0.5, -2.598076211353316], 'a8': [1.0, 0.0], 'a9': [1.5, 2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.359831950361911, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, -0.8660254037844386]]], [3, [[1.0, 0], [1.5, 0.8660254037844386]]], [7, [[1.0, 0], [-0.5, 2.598076211353316]]], [13, [[1.0, 0], [3.5, -0.8660254037844386]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '546.251', 'coefficient_field': 'CDF', 'conductor': 546, 'conductor_radical': 546, 'conjugate': '564868658760625027416037950204', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [1.5, 0.8660254037844386]], [[1.0, 0], [0, 3.4641016151377544], [-5.0, 0]], [[1.0, 0], [-0.5, 2.598076211353316]], [[1.0, 0], [-1.5, 2.598076211353316], [-5.5, -9.526279441628825]], [[1.0, 0], [3.5, -0.8660254037844386]], [[1.0, 0], [1.5, 2.598076211353316], [-8.5, 14.722431864335457]], [[1.0, 0], [-3.5, -6.06217782649107], [-9.5, 16.454482671904334]], [[1.0, 0], [6.0, 3.4641016151377544], [11.5, 19.91858428704209]], [[1.0, 0], [-1.5, -0.8660254037844386], [14.5, 25.11473670974872]], [[1.0, 0], [-4.0, 0], [31.0, 0]], [[1.0, 0], [6.0, 3.4641016151377544], [18.5, 32.04293994002423]], [[1.0, 0], [4.5, 2.598076211353316], [20.5, 35.50704155516198]], [[1.0, 0], [-4.0, -6.928203230275509], [-21.5, 37.239092362730865]], [[1.0, 0], [0, -8.660254037844387], [-47.0, 0]], [[1.0, 0], [0, 8.660254037844387], [-53.0, 0]], [[1.0, 0], [-9.0, 5.196152422706632], [29.5, -51.09549882328188]], [[1.0, 0], [4.5, -2.598076211353316], [30.5, -52.827549630850754]], [[1.0, 0], [0, 0], [33.5, 58.023702053557386]], [[1.0, 0], [3.0, 5.196152422706632], [-35.5, 61.48780366869514]], [[1.0, 0], [-4.0, 0], [73.0, 0]], [[1.0, 0], [11.0, 0], [79.0, 0]], [[1.0, 0], [0, -13.856406460551018], [-83.0, 0]], [[1.0, 0], [7.5, 4.330127018922194], [44.5, 77.07626093681505]], [[1.0, 0], [1.0, 1.7320508075688772], [-48.5, 84.00446416709055]], [[1.0, 0], [0, 0], [-50.5, -87.4685657822283]], [[1.0, 0], [0, 3.4641016151377544], [-103.0, 0]], [[1.0, 0], [-4.5, -2.598076211353316], [53.5, 92.66471820493493]], [[1.0, 0], [0, -3.4641016151377544], [-109.0, 0]], [[1.0, 0], [-12.0, 6.928203230275509], [56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 27, 'label': '2-546-273.251-c1-0-27', '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/546/2/q/a/251/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.5950255752393094, 0.769399541247416, 0.9507008917591756, 1.1388495170444444, 1.3308951822245343, 1.5206584103737595, 1.6988753277800108, 1.8537508979232518, 1.9718380002279579, 2.039186856030155, 2.0427164457201874, 1.9717408579985432, 1.8195479739867637, 1.584887994524632, 1.273196348689901, 0.8973586718901364, 0.47783190572459167, 0.04196984272940602, -0.37753475615857907, -0.745088224551213, -1.0253991971994638, -1.187210632989262, -1.2072086621823126, -1.0736639621219448, -0.78931066905829, -0.37297480864649085, 0.14046022055122404, 0.7020165360317014, 1.2525671966797636, 1.728561310644019, 2.0690522828733284, 2.223299570706322, 2.1580230081033855, 1.863298528905865, 1.3561257383200458, 0.6808869613766557, -0.09375050210564577, -0.8814900537940286, -1.588109062233583, -2.12319266509854, -2.412458420261723, -2.408971647952631, -2.1015167471164604, -1.5186176434253589, -0.7271898275104326, 0.1744868588837608, 1.0689473935150329, 1.8354951732386477, 2.3678272556641327, 2.590761892489628, 2.4733980006066267, 2.036358714297357, 1.351509779012314, 0.5336186562886192, -0.2753149180181086, -0.9270674411569261, -1.2905130777934355, -1.2736169371471822, -0.840411438389424, -0.019845882722581858, 1.0954421882180942, 2.3608027641817158, 3.60030504488067, 4.633496536228897, 5.303950440269255, 5.504828543175069, 5.196974935352055, 4.416168393813408, 3.2679457651359933, 1.910574383272894, 0.5289143161038983, -0.6963387320328905, -1.618558583416553, -2.14878895794953, -2.2686501622701525, -2.030114409337975, -1.5422050490194936, -0.9472349320548233, -0.39131106779150265, 0.004954213815624573, 0.16955948800424867, 0.09130741442076681, -0.18142412112382267, -0.5549828905502252, -0.9146090278462045, -1.153021257766628, -1.1968736392431647, -1.0248658441002654, -0.6730496637859158, -0.22573228549496321, 0.2062652399965381, 0.515126222732005, 0.6263404858349163, 0.5222130836039119, 0.25218994398162, -0.07359594529033156, -0.3073101607256399, -0.2986320119352875, 0.06541981022825746, 0.8254082791933528, 1.9281354251627694, 3.2254869840219604, 4.495649838990189, 5.4837817359485435, 5.9544143036869315, 5.744535575580137, 4.805315929774232, 3.222203107677788, 1.2073844265652296, -0.9354466902537352, -2.867770420750401, -4.282892984515149, -4.968252730123818, -4.849392542761769, -4.005206863159394, -2.6502436444506206, -1.0872515449352533, 0.35989028300451753, 1.417908089669945, 1.924133215656736, 1.8607496540836463, 1.3550575644493696, 0.6454213025507368, 0.020741588624056104, -0.2522449049690036, 0.003595851084394286, 0.8299968692781274, 2.1204250804166698, 3.643494414194867, 5.097106244561239, 6.1801281738112355, 6.663984083848893, 6.4464675728714695, 5.574494258475163, 4.23031955903334, 2.6850100205376712, 1.2312951694316667, 0.11316510390032102, -0.5296889765245485, -0.6885105393217374, -0.4768599358741502, -0.08986928477868404, 0.25686618145046086, 0.39152524437193625, 0.23541610198447246, -0.1763653197983184, -0.7087133688100022, -1.1706942632952297, -1.3773358600858252, -1.2109617292086385, -0.6637952739103387, 0.1514155481423785, 1.0270421662532707, 1.716335117248011, 2.004168711791869, 1.7727421210200278, 1.0429201641495391, -0.02181137857558808, -1.1515606302197765, -2.0378258076245133, -2.4150068732597307, -2.1333125481184285, -1.2025307956094302, 0.20617753951936701, 1.8017620553921592, 3.2471809275633183, 4.245561845342629, 4.614806606734707, 4.329954971024752, 3.521776387724212, 2.432658146314602, 1.3432561121337965, 0.49189548912506753, 0.010749607615946424, -0.10233988153368878, 0.03152035368803853, 0.22563925496639675, 0.3015176681002984, 0.15873669820431777, -0.18258487253968528, -0.5820607695700172, -0.8239147017439444, -0.6937682637087328, -0.06344014910474582, 1.0442922326491804, 2.434465606223981, 3.7734592537668465, 4.671921943844934, 4.795779935996144, 3.973638321190119, 2.2676055318187807, -0.016740585077471098, -2.388986394477132, -4.28907084128332, -5.22974649464479, -4.927614325737279, -3.3855644298606573, -0.9018923968506185, 1.9986034906562913, 4.694286832495814, 6.622393548643943, 7.418333692304188, 7.000548907451702, 5.578319439305528, 3.5819044550960215, 1.5364885339625236, -0.08294367652189492, -0.9741043133968326, -1.0733577877214655, -0.5489182591064726, 0.2727912242742348, 1.0219204947780103, 1.40401921241831, 1.2861613462627683, 0.725377641241011, -0.06634730769857407, -0.8057722382466412, -1.240899553979164, -1.2373553400848039, -0.8202645310397453, -0.15900938448145427, 0.49808778859839353, 0.9151849395528683, 0.953920497366741, 0.6221323142967554, 0.06935346461405777, -0.4691173321068786, -0.7596518240152678, -0.6580810208344549, -0.1662869057436827, 0.5632558140967692, 1.2776387161888185, 1.7115780161460672, 1.6826760251538087, 1.1598609241666202, 0.27964456902020185, -0.6972461627043558, -1.4752068581745723, -1.8284795399563283, -1.6840593907609582, -1.1519668386959911, -0.489683055217877, -0.010596620350092062, 0.033133949315695514, -0.44780290751262125, -1.3315190824841963, -2.3107076008395806, -2.988336424532003, -3.0141210514354477, -2.216596237211158, -0.6844172038593679, 1.2347130906665664, 3.022730448254233, 4.143314306068487, 4.210624565433353, 3.120089070801658, 1.0968571756263952], 'positive_zeros': ['2.13712628117161676740446058654293', '3.21746659207947276617197482878381', '4.48526993614419494642454052670497', '5.60125147789500580165917733626860', '6.70584308427017024290162313095664', '7.37750264933425711881560841238782', '8.801074340813380316353018812771506', '9.872861492526706940933631951139281', '10.17552540039730066391807440924323', '11.18768309659210800717838757322892'], 'prelabel': '2-546-273.251-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': 0.8125598105544052, 'root_number': '-0.8315739894918478 + 0.555413989741537*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.406279905277', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.13712628117161676740446058654', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.21746659207947276617197482878', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.48526993614419494642454052670', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.359831950361911, 'bad_primes': [2, 3, 7, 13], 'central_character': '273.251', 'conductor': 546, 'conductor_radical': 546, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/546/2/q/a/251/1'], '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': '2-546-273.251-c1-0-27', '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': '2-546-273.251-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': 0.4062799052772026, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.13712628117161676740446058654', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2709129413090723750244998052385', 'Lhash_array': ['2709129413090723750244998052385'], 'label': '2-546-273.251-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/2/q/a/251/1'}