-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1383210719247900228876399390910', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-2.4728339089952556, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [3.114907541476756, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.065546335746074, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [13, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 5, 7, 13], 'central_character': '3640.1', 'coefficient_field': 'CDF', 'conductor': 3640, 'conductor_radical': 910, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [2.4728339089952556, 0], [3.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-3.5877414504720115, 0], [11.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [7.7026489919487675, 0], [17.0, 0]], [[1.0, 0], [1.4728339089952556, 0], [19.0, 0]], [[1.0, 0], [2.871888715435012, 0], [23.0, 0]], [[1.0, 0], [-8.290390442420778, 0], [29.0, 0]], [[1.0, 0], [-6.472833908995256, 0], [31.0, 0]], [[1.0, 0], [7.756981173958256, 0], [37.0, 0]], [[1.0, 0], [4.3447226244302675, 0], [41.0, 0]], [[1.0, 0], [-0.9456678179905111, 0], [43.0, 0]], [[1.0, 0], [-8.156035980398013, 0], [47.0, 0]], [[1.0, 0], [-5.175482900944023, 0], [53.0, 0]], [[1.0, 0], [1.4533869884492452, 0], [59.0, 0]], [[1.0, 0], [9.587741450472011, 0], [61.0, 0]], [[1.0, 0], [-6.1149075414767555, 0], [67.0, 0]], [[1.0, 0], [-12.121150718934533, 0], [71.0, 0]], [[1.0, 0], [-13.331518881342035, 0], [73.0, 0]], [[1.0, 0], [-9.060575359467267, 0], [79.0, 0]], [[1.0, 0], [14.459630165907024, 0], [83.0, 0]], [[1.0, 0], [1.6009451935602437, 0], [89.0, 0]], [[1.0, 0], [9.249262003499522, 0], [97.0, 0]], [[1.0, 0], [-13.331518881342035, 0], [101.0, 0]], [[1.0, 0], [1.0954606209307454, 0], [103.0, 0]], [[1.0, 0], [9.661520553027511, 0], [107.0, 0]], [[1.0, 0], [13.027924695833024, 0], [109.0, 0]], [[1.0, 0], [4.4945154273705015, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 34, 'label': '2-3640-1.1-c1-0-34', '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/3640/2/a/o/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-6.539027772440028e-61, 0.10566809550307744, 0.21029143708551332, 0.31278881704535055, 0.412009083989244, 0.5067033510332293, 0.5955052112007222, 0.6769207078841202, 0.749329181390517, 0.8109954864469421, 0.8600935008845321, 0.8947403524494287, 0.9130403884671692, 0.913137596210964, 0.8932749358073246, 0.8518588553178039, 0.7875271042880482, 0.6992178372643999, 0.5862378977981715, 0.44832809669632523, 0.28572325019480477, 0.09920473146056014, -0.10985667919588844, -0.3394697752758851, -0.5870057209917997, -0.84919643752536, -1.1221500708464718, -1.4013846813542412, -1.6818808750743766, -1.9581536123366543, -2.2243428912759224, -2.4743224217984676, -2.7018247954284553, -2.900581034938418, -3.0644717943447093, -3.187686895887156, -3.2648893582560987, -3.2913796121705823, -3.2632552375853883, -3.1775613121390816, -3.0324263515828997, -2.827178865405134, -2.56243975631326, -2.2401861675726487, -1.863782928958737, -1.4379784658738082, -0.9688629063496635, -0.4637871301144421, 0.06875737079457102, 0.6192967387069096, 1.1775687599665443, 1.732749018129943, 2.273704327271708, 2.7892674142561082, 3.2685257733965156, 3.7011167387326256, 4.077520150475482, 4.389339570764991, 4.629562861249231, 4.792793094700976, 4.875441249103805, 4.875872928908351, 4.7945024664850795, 4.633829157133527, 4.398412041154155, 4.094781522490465, 3.7312881504600504, 3.3178910247470794, 2.8658904420804197, 2.3876115084257017, 1.896047412882565, 1.4044728188036768, 0.9260392972801141, 0.47336583796241494, 0.05813816182535801, -0.30926921773626664, -0.620134517471309, -0.8676809157264521, -1.0473079216004648, -1.1567520998091254, -1.1961695989999561, -1.1681355366721524, -1.0775581918663837, -0.9315090483776899, -0.7389729046171146, -0.5105254006845301, -0.2579482835311392, 0.006204587458480427, 0.26907521867744916, 0.5179864113304409, 0.7409254597699492, 0.92700796944979, 1.0669034041082437, 1.153204977714527, 1.1807282482801, 1.1467252056864607, 1.0510037011022042, 0.8959456388867533, 0.6864213142325722, 0.4296014801563625, 0.13467299808000113, -0.1875319108372749, -0.5249789222305469, -0.864930072264018, -1.1944773471648877, -1.5010893080961245, -1.773147539019017, -2.000449551910793, -2.174655641253367, -2.2896590474742045, -2.3418616216218533, -2.330340890893305, -2.2568988739251665, -2.1259880146663583, -1.944514990286398, -1.7215286733453272, -1.4678039473655657, -1.1953381390691133, -0.9167812971740655, -0.6448251917132597, -0.3915785330159492, -0.16795735847344664, 0.016880301360606278, 0.15602754220232615, 0.2452240665306087, 0.2831323778171815, 0.2714779554564181, 0.21504254133917367, 0.1215062435373414, 0.0011411658793262507, -0.13363360851356423, -0.268818946766079, -0.38950141840575436, -0.48058928952862356, -0.5275858467001121, -0.5173642124562352, -0.43890648414708977, -0.2839704146625469, -0.04764900120156026, 0.27120778183950595, 0.6697343999221245, 1.1409727531509677, 1.673987191938935, 2.254173235713341, 2.86375253135159, 3.4824374827037943, 4.088240355388286, 4.658393942652579, 5.170344470461397, 5.602772675803979, 5.936596195898553, 6.155905757222214, 6.248789254316399, 6.208001655336671, 6.031444651025857, 5.722427855110344, 5.2896928453604115, 4.747191995851037, 4.1136254115356525, 3.411750805838908, 2.6674923054743886, 1.9088843708792813, 1.1648957617610853, 0.464185287968394, -0.16615441953047386, -0.7018069867667602, -1.122338957524633, -1.4121494243284372, -1.5612153526491779, -1.5655940932169237, -1.4276554129336527, -1.1560277885566639, -0.7652571219951357, -0.2751898099468191, 0.2898944419724413, 0.9023622055714978, 1.5324696315643962, 2.1497121594429798, 2.724217391913953, 3.228114987017036, 3.6368177548806906, 3.930151758832109, 4.09327998743599, 4.117373795880193, 3.9999983697848775, 3.745192366308871, 3.363236954253598, 2.8701249515399825, 2.2867558547487334, 1.6378964869558825, 0.9509590197351635, 0.25465760304306867, -0.42238876368880873, -1.0530365371031316, -1.6129112277005782, -2.0815487549323013, -2.4433268365666483, -2.6881395863418245, -2.811781927850308, -2.8160257107316964, -2.7083857355003427, -2.5015903860017397, -2.2127873426015903, -1.86252904099278, -1.4735943623638839, -1.0697118219803663, -0.674254755358659, -0.30898036450432553, 0.007118127574617292, 0.25878344586262875, 0.4352376036180712, 0.530656881002133, 0.5443540226959355, 0.4806599949666351, 0.3485149074295873, 0.1607944920775559, -0.0665861261286137, -0.3157366348133213, -0.5679591046079209, -0.8049481588790992, -1.0099509457295905, -1.1688163704502608, -1.2708695044910474, -1.309557416189262, -1.2828263051069044, -1.193205998418697, -1.0475956546146357, -0.8567628765426409, -0.6345862709995741, -0.39708772653371843, -0.16131431229261775, 0.05586013625475507, 0.23893765706542444, 0.37492549549295523, 0.4543179060666498, 0.47186413647710923, 0.42706849065698993, 0.32438413348741624, 0.17308075954311827, -0.013213668450319122, -0.21727639149111866, -0.4193181159313298, -0.5982179804144552, -0.7328926436790149, -0.8037165335011431, -0.7939047790301924, -0.6907701426248074, -0.48677051560191964, -0.1802740595846388, 0.22401564874556606, 0.7150128883323226, 1.27559779924553, 1.8833517387716041, 2.5116486965752465, 3.1310488136139423, 3.7109200363896204, 4.22119785669543], 'positive_zeros': ['1.09116086009730539222697759361831', '2.43105821699929996494480473551238', '3.76539612772925655093572598667654', '4.41678277950667169391252262665770', '5.09976910111768756783504393043574', '6.19012579089818219402307887556750', '6.55122751257959955769606582166524', '7.01631279828185222672799976139254', '8.314053787790308873324009933418054'], 'prelabel': '2-3640-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.3912471966833495, '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': '1.09116086009730539222697759362', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.43105821699929996494480473551', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.76539612772925655093572598668', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 29.065546335746074, 'bad_primes': [2, 5, 7, 13], 'central_character': '1.1', 'conductor': 3640, 'conductor_radical': 910, 'degree': 2, 'index': 34, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3640/2/a/o/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': '2-3640-1.1-c1-0-34', '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': '2-3640-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.3912471966833495, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.09116086009730539222697759362', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1383210719247900228876399390910', 'Lhash_array': ['1383210719247900228876399390910'], 'label': '2-3640-1.1-c1-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3640/2/a/o/1/1'}