-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '900528903734934404139679611282', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 1.7320508075688772], 'a6': [0, 0], 'a7': [4.3546128987939285, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 41.394448407831774, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '5184.2593', 'coefficient_field': 'CDF', 'conductor': 5184, 'conductor_radical': 6, 'conjugate': '1873926174091877056187537202984', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -1.7320508075688772], [-5.0, 0]], [[1.0, 0], [-4.3546128987939285, 0], [7.0, 0]], [[1.0, 0], [0, -5.8350214287827775], [-11.0, 0]], [[1.0, 0], [0, -4.019889871542109], [-13.0, 0]], [[1.0, 0], [1.7073893592230958, 0], [17.0, 0]], [[1.0, 0], [0, -2.0], [-19.0, 0]], [[1.0, 0], [-6.64245196276716, 0], [23.0, 0]], [[1.0, 0], [0, -4.689335926045748], [-29.0, 0]], [[1.0, 0], [-4.861429395454812, 0], [31.0, 0]], [[1.0, 0], [0, 5.7519406791109855], [-37.0, 0]], [[1.0, 0], [-1.2926106407769042, 0], [41.0, 0]], [[1.0, 0], [0, 3.5424107880058733], [-43.0, 0]], [[1.0, 0], [10.613370074565797, 0], [47.0, 0]], [[1.0, 0], [0, -0.5068164966608836], [-53.0, 0]], [[1.0, 0], [0, -1.8723679304403182], [-59.0, 0]], [[1.0, 0], [0, -1.2252343109079937], [-61.0, 0]], [[1.0, 0], [0, -1.579757289663414], [-67.0, 0]], [[1.0, 0], [9.88548834875238, 0], [71.0, 0]], [[1.0, 0], [7.962653498342459, 0], [73.0, 0]], [[1.0, 0], [-2.0667738348206974, 0], [79.0, 0]], [[1.0, 0], [0, 1.5424107880058733], [-83.0, 0]], [[1.0, 0], [3.9626534983424593, 0], [89.0, 0]], [[1.0, 0], [-6.122168077669287, 0], [97.0, 0]], [[1.0, 0], [0, 11.55285311796544], [-101.0, 0]], [[1.0, 0], [-0.22106522915253377, 0], [103.0, 0]], [[1.0, 0], [0, -0.3299571424344451], [-107.0, 0]], [[1.0, 0], [0, 17.925268091836596], [-109.0, 0]], [[1.0, 0], [-18.084821576011745, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 40, 'label': '2-72e2-8.5-c1-0-40', 'leading_term': '2.4602975570694613198461292046648049727156942534880966948', '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/5184/2/d/r/2593/12', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.4602975570694614, 2.3021941451426366, 2.13691231620696, 1.965252912660415, 1.7880283622961424, 1.6061220766848598, 1.4205463927880853, 1.232494769192659, 1.0433844834234556, 0.8548868127115394, 0.6689425157834328, 0.48776127975244793, 0.31380459144038614, 0.14975220201876452, -0.0015470325319367957, -0.13713862876362165, -0.25403851595425114, -0.3493194952941267, -0.4202056327148562, -0.46417179952377435, -0.4790453154714016, -0.4631064359269775, -0.4151842684033016, -0.3347446163441182, -0.2219662434330393, -0.0778021427116479, 0.09597740738688293, 0.29676290529329763, 0.5211072803444404, 0.7647530618599961, 1.022686323286833, 1.2892178962085872, 1.5580914981216007, 1.8226175029192329, 2.0758301304392877, 2.3106648718529135, 2.520152035098403, 2.6976214252703885, 2.8369124061871744, 2.93258295824143, 2.9801108891865695, 2.9760801003729678, 2.918344787754396, 2.806164684830907, 2.6403049457564403, 2.42309502419201, 2.1584419201837064, 1.8517944258394399, 1.510056472513686, 1.1414493286506722, 0.7553241695525745, 0.36192838055452886, -0.02786920130743736, -0.4028871248582623, -0.7519656209914323, -1.0643163099231132, -1.3298761255612175, -1.5396534607198493, -1.6860541327475234, -1.7631748052953768, -1.7670520059101777, -1.6958558615058763, -1.5500191266234085, -1.3322939752750673, -1.0477313188543436, -0.7035800336483388, -0.3091063477436754, 0.12466335104165534, 0.5852699790442494, 1.0592102264046044, 1.5323740183347343, 1.9905165396213844, 2.419748430201314, 2.8070263510983455, 3.140625354419226, 3.410574434297307, 3.6090373274009657, 3.730622082244241, 3.772605104780354, 3.735058259752404, 3.6208710769547103, 3.435664062532719, 3.187593404339996, 2.8870518215580168, 2.5462747604440765, 2.178865389303932, 1.7992557045749271, 1.4221243416099414, 1.061794219748875, 0.7316347973682515, 0.4434943568558445, 0.20718730890014928, 0.030059971490553627, -0.08334433907429457, -0.13150370118407473, -0.11600679161052409, -0.04150549072425212, 0.0844707270989333, 0.2518341509033284, 0.4483813600099282, 0.660342477912809, 0.8730153708300726, 1.0714584573004542, 1.2412122728207153, 1.3690176428890035, 1.4434974135098406, 1.4557692668758524, 1.3999592430845706, 1.273589158292027, 1.077816046624193, 0.8175078795028798, 0.5011468903236527, 0.14055955841817372, -0.24951965523668473, -0.652035744714059, -1.048329143823367, -1.4189508944742888, -1.744542052818613, -2.0067382714630297, -2.1890580945874967, -2.2777329908230244, -2.262438616381789, -2.136890245512942, -1.8992706278220277, -1.5524655379945436, -1.1040906892622333, -0.5663031250154144, 0.04459974301942847, 0.7087800879332223, 1.4036354110657128, 2.1047178840782292, 2.7867574238755957, 3.4247426948683497, 3.995010372867965, 4.476291476328368, 4.850664516753995, 5.104368663849698, 5.228435959934341, 5.219109625358114, 5.078025328190873, 4.812143500036887, 4.433432834564461, 3.9583174163133084, 3.4069118743044444, 2.8020799185581855, 2.168361011625598, 1.53081723028326, 0.9138571574113259, 0.3400956030579085, -0.1706930815413241, -0.6024743784811177, -0.9436588608647082, -1.187576011939535, -1.332690896928121, -1.3825511550576686, -1.3454658549173264, -1.233932002037903, -1.063838146374318, -0.853486864201758, -0.6224881916341838, -0.39058376520395, -0.1764660054603698, 0.0033421544176229856, 0.13548388004162712, 0.21058416029411095, 0.22383656150194386, 0.17532489684700253, 0.07005789410315143, -0.08228936360561653, -0.2679170991790215, -0.469699364266299, -0.6681982026936264, -0.8428392509624499, -0.973184356650845, -1.040229982122498, -1.0276572091320029, -0.9229603235282493, -0.7183862666707819, -0.4116264867623597, -0.006215476908711611, 0.4883940937825071, 1.0570920834637598, 1.6797010845680291, 2.3318709943472475, 2.986235015272635, 3.6137684096856866, 4.185278585051861, 4.672946125281538, 5.051831804497018, 5.301264779224938, 5.406032145939322, 5.357299689777996, 5.15320748156719, 4.799101296190506, 4.307380700797768, 3.6969660028029376, 2.992407852748714, 2.2226839225073705, 1.4197455122167013, 0.6168920695338536, -0.15293750811481283, -0.8588619848889407, -1.4736479649681886, -1.9751027653682263, -2.347189906459421, -2.580802249352303, -2.674146918593161, -2.632718202576179, -2.4688583693342783, -2.2009303946038106, -1.8521495508002341, -1.4491412684132985, -1.0203093977701987, -0.5941109135186085, -0.19733943056919465, 0.14647982490676542, 0.4184868291233196, 0.6055903763427503, 0.7012105605985374, 0.7056135472092137, 0.6258164958487998, 0.47506657002563, 0.2719241083914169, 0.03900464328658063, -0.19854399963300745, -0.41473616828789783, -0.5845094947920314, -0.6854424992155687, -0.6993200661504584, -0.6134464655903121, -0.4216202270647204, -0.12470534146205016, 0.2692422168235785, 0.7453062502061027, 1.2824853633648383, 1.8548681752735867, 2.43313990518655, 2.9863297641779796, 3.4836922339176044, 3.8966054804396353, 4.200367549521726, 4.37577589302462, 4.410387982447464, 4.299379610869859, 4.045941868900288, 3.6611862357861997, 3.163558002228664, 2.577789409583783, 1.9334534682762743, 1.26320549406184, 0.6008202562361006, -0.020853142976658464, -0.5718899497485893, -1.0271148701615966, -1.3676362375762372, -1.5819892809149974, -1.6668126030013353], 'positive_zeros': ['0.71039204617802575300516597231194', '1.29330298167760678930966722712924', '2.63694722120329487913008470626509', '3.38813143978794715050301499449388', '4.68287054223049590838576045008572', '4.89396139557123109836429172462831', '5.70613236849721507873308631916891', '6.44567564900858303459361268958919', '7.54861544594576713872668173853259', '8.225491032814015451492805728046661'], 'prelabel': '2-72e2-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.433851755195466, 'root_angle': -0.5833333333333334, 'root_number': '-0.25881904510252076234889883762404832834906890131993051381 - 0.96592582628906828674974319972889736763390483900840455040*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2916666666666667', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.71039204617802575300516597231', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.29330298167760678930966722713', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.63694722120329487913008470627', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 41.394448407831774, 'bad_primes': [2, 3], 'central_character': '8.5', 'conductor': 5184, 'conductor_radical': 6, 'degree': 2, 'index': 40, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5184/2/d/r/2593/12'], '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': '2-72e2-8.5-c1-0-40', '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': '2-72e2-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.433851755195466, 'root_angle': -0.2916666666666667, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.71039204617802575300516597231', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '900528903734934404139679611282', 'Lhash_array': ['900528903734934404139679611282'], 'label': '2-72e2-8.5-c1-0-40', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5184/2/d/r/2593/12'}