-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '5738166768343612167695706831274', 'a10': [0.0, 34.291340506137374], 'a2': [0.0, -5.5059972410069635], 'a3': [0.0, -4.250640180911373], 'a4': [-14.316005617976296, 0.0], 'a5': [-6.227998127341235, 0.0], 'a6': [-23.40401310861136, 0.0], 'a7': [8.367988764047407, 0.0], 'a8': [0.0, -9.272068421293737], 'a9': [62.93205805242173, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.9640292985930428, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[19, [[1.0, 0], [215.00410674154963, -289.9900585955807]]]], 'bad_primes': [19], 'central_character': '19.18', 'coefficient_field': 'CDF', 'conductor': 19, 'conductor_radical': 19, 'conjugate': '2006144056128170249563773803644', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 5.5059972410069635], [-16.0, 0]], [[1.0, 0], [0, 4.250640180911373], [-81.0, 0]], [[1.0, 0], [6.227998127341235, 0], [625.0, 0]], [[1.0, 0], [-8.367988764047407, 0], [2401.0, 0]], [[1.0, 0], [-128.12403183519902, 0], [14641.0, 0]], [[1.0, 0], [0, -101.81701440009473], [-28561.0, 0]], [[1.0, 0], [27.528044943810375, 0], [83521.0, 0]], [[1.0, 0], [215.00410674154963, -289.9900585955807]], [[1.0, 0], [-463.23621161044053, 0], [279841.0, 0]], [[1.0, 0], [0, -1132.4955055867144], [-707281.0, 0]], [[1.0, 0], [0, -1094.4154821926484], [-923521.0, 0]], [[1.0, 0], [0, 1858.7373149895825], [-1874161.0, 0]], [[1.0, 0], [0, 2520.601860145804], [-2825761.0, 0]], [[1.0, 0], [-2245.9726573032267, 0], [3418801.0, 0]], [[1.0, 0], [1531.379840824005, 0], [4879681.0, 0]], [[1.0, 0], [0, 855.4331057680041], [-7890481.0, 0]], [[1.0, 0], [0, -2664.443285067887], [-12117361.0, 0]], [[1.0, 0], [691.0123202246489, 0], [13845841.0, 0]], [[1.0, 0], [0, -2998.413486468598], [-20151121.0, 0]], [[1.0, 0], [0, -1183.3449058041579], [-25411681.0, 0]], [[1.0, 0], [5253.024640449298, 0], [28398241.0, 0]], [[1.0, 0], [0, -3439.4430921592057], [-38950081.0, 0]], [[1.0, 0], [-7199.735509363403, 0], [47458321.0, 0]], [[1.0, 0], [0, 10651.204980485225], [-62742241.0, 0]], [[1.0, 0], [0, -3226.293421580661], [-88529281.0, 0]], [[1.0, 0], [13626.244531834212, 0], [104060401.0, 0]], [[1.0, 0], [0, -19402.702664863697], [-112550881.0, 0]], [[1.0, 0], [0, 20844.58328992462], [-131079601.0, 0]], [[1.0, 0], [0, -4563.12590890411], [-141158161.0, 0]], [[1.0, 0], [0, -368.75841176111805], [-163047361.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-19-19.18-c4-0-4', 'load_key': 'CMFs-workshop', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/19/5/b/b/18/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [1.2603742465107186, 1.3946185396440718, 1.5327118577011818, 1.675422418452878, 1.822950616319048, 1.9748180801574806, 2.1297755983542785, 2.2857333822512396, 2.4397185162922836, 2.5878661211368916, 2.7254523142921308, 2.8469780187142617, 2.946312613464841, 3.016905009420523, 3.052066754834827, 3.045327149103981, 2.9908541330229417, 2.883927162156721, 2.7214397801287973, 2.5024008226564987, 2.2283949417947664, 1.90395646663703, 1.5368066592919243, 1.137904360202594, 0.7212649211926004, 0.30351301561774824, -0.09684822280138687, -0.4604464677788617, -0.7682948163646075, -1.003227730704613, -1.151422809286857, -1.2038843144511762, -1.1577426330831184, -1.017213019261832, -0.7940608455716446, -0.5074420871478732, -0.18302833010843803, 0.14861532589834192, 0.4543564991265734, 0.7013983973847958, 0.8605454986288091, 0.9095401699763702, 0.8361198537758106, 0.6404166054597864, 0.33633305805992986, -0.04841248856315423, -0.4737728210386715, -0.8904419720792046, -1.2443791457729803, -1.4824614415582629, -1.5587538675083195, -1.4407333247098386, -1.1147120900106562, -0.5896980344623464, 0.10098197062735213, 0.9007787036429097, 1.733939116579719, 2.512300461718721, 3.14433686579271, 3.5455774913810205, 3.6492295460257718, 3.4156755720358447, 2.839512549830298, 1.9529822520351519, 0.8250057830976025, -0.4444492489450919, -1.7343293630114385, -2.9158156789339036, -3.867481693769419, -4.490376281435596, -4.720972244401415, -4.540063458181428, -3.9761349785886133, -3.1024322633003716, -2.0278337362107686, -0.8825634650624427, 0.19937595162065078, 1.0985600096578636, 1.7265409075541305, 2.0377087365351514, 2.0346367260760325, 1.7658995953701697, 1.3165526472474738, 0.7927002421610543, 0.30265247419845154, -0.062133651090241784, -0.24296009036192337, -0.22369581263501126, -0.03252840883749981, 0.2648908239188684, 0.5798593512733734, 0.8200427028437529, 0.9102395468869062, 0.8103566710686293, 0.5267605326276787, 0.11425384834904863, -0.3323648166381609, -0.6961528451331029, -0.8622778172796121, -0.7441135550728685, -0.3058690182439609, 0.42328408448399596, 1.347290989344722, 2.3150084489389737, 3.1445309776409167, 3.656194950982735, 3.708308769968941, 3.2286126530321453, 2.2347820403092027, 0.838997830824809, -0.7655309413104766, -2.334698350389999, -3.6154226310100417, -4.3917875611115225, -4.526514148621703, -3.9893072629970754, -2.865834042220308, -1.344724185815847, 0.31564845092358623, 1.8346255436378753, 2.961830111903249, 3.524337791954368, 3.458761311840434, 2.8214630243465226, 1.774573285124029, 0.5505953260736528, -0.5969829496414679, -1.446522756906622, -1.853105187496782, -1.775703226131586, -1.2808226123954052, -0.5220803788941364, 0.29930181693911, 0.9836812587036512, 1.3801676072897056, 1.4205716682987166, 1.132094418368397, 0.6259026787584574, 0.06469956510973522, -0.3823188702819453, -0.5854668027006517, -0.4895187576449527, -0.12831798217434418, 0.38504137252234344, 0.8901253380382332, 1.224836874399219, 1.272555816461292, 0.9976233424528494, 0.4587517348151206, -0.2044053384010662, -0.8090567725829133, -1.1820573611871152, -1.2135451474767596, -0.8961887114111814, -0.3378110368887502, 0.2582741898231682, 0.6423216398158345, 0.5853804933638915, -0.05237206790124723, -1.2708307566066264, -2.9119662502254573, -4.682182702976578, -6.212319819510612, -7.142405804312034, -7.210898320882239, -6.325733887731644, -4.597958593675279, -2.327415798292316, 0.05814672294850703, 2.097140973493597, 3.3989621382826085, 3.7337175800784697, 3.084241127317862, 1.647026703466569, -0.2183194349552468, -2.0782237293911634, -3.5299718165393053, -4.295292266208489, -4.278961008810282, -3.5782776308689996, -2.4426611174272526, -1.1961204929921652, -0.1451981605446984, 0.5016182590452256, 0.6810280162852198, 0.47685317128834737, 0.07853220715306987, -0.28930493383099487, -0.4433993755296023, -0.3005105969905105, 0.09980125495762039, 0.6145815892234743, 1.051822976894738, 1.2411935737968312, 1.0971852959207855, 0.6529950012390416, 0.05285833143621664, -0.49577049202299295, -0.7951716862282576, -0.7312866871471032, -0.3229719012103658, 0.27209414586128555, 0.7999876637569516, 0.9907542061098269, 0.6520917389178597, -0.2538299329342087, -1.5773391532572425, -3.006536103472375, -4.147473877175035, -4.637909794066846, -4.26109056989331, -3.023811537969534, -1.1720013356385128, 0.8649396691146581, 2.588119236262036, 3.569782210561867, 3.5791879153121684, 2.6550744280772447, 1.1009126756528689, -0.5980544599048768, -1.9131352007558637, -2.42553603883601, -1.9489431099179908, -0.5841491060426469, 1.3111859021007486, 3.22873554233812, 4.6594387174046075, 5.241476763193132, 4.861384137771787, 3.678237835127279, 2.0651453669161213, 0.4881994650391922, -0.6376461381737862, -1.069906447116744, -0.7996878685030501, -0.035652619826142665, 0.8805125251328361, 1.5962460327825425, 1.8655759622205152, 1.6226757968226215, 0.9886465245594851, 0.21251316869419937, -0.4295845669774211, -0.7389406579538409, -0.6642294499589761, -0.3120697722605834, 0.10410499867480379, 0.35597028988040175, 0.2966907793913554, -0.07644304097583451, -0.618709678700883, -1.096904142039251, -1.2890149656569903, -1.0860739935841177, -0.554738438777679, 0.06786381607199556, 0.4508260683199335], 'positive_zeros': ['4.52661543118466984280265281181936', '6.42450242004923506748029341892904', '7.889404077562547067488969293782438', '9.468481148024772974935029083732897', '11.36544530996201354536132130057647', '13.32520667665192961893481826871116', '14.90481355015220468058284164611048', '15.49039243739655895365458016368170', '16.74372118655657124795938320184420', '17.65953641644730041384599825594789'], 'prelabel': '2-19-19.18-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4014382963916188, 'root_angle': 0.7030774224759361, 'root_number': '-0.5955792430513841 + 0.8032965612065948*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.351538711238', 'prec': 47}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '4.52661543118466984280265281182', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '6.42450242004923506748029341893', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.889404077562547067488969293782', 'prec': 107}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.9640292985930428, 'bad_primes': [19], 'central_character': '19.18', 'conductor': 19, 'conductor_radical': 19, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/19/5/b/b/18/1'], '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': '2-19-19.18-c4-0-4', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-19-19.18-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4014382963916188, 'root_angle': 0.35153871123796804, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '4.52661543118466984280265281182', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '5738166768343612167695706831274', 'Lhash_array': ['5738166768343612167695706831274'], 'label': '2-19-19.18-c4-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/19/5/b/b/18/1'}