-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2648697014359514513309501235885', 'a10': [2.9297780294291567, -1.9502067332007704], 'a2': [0.6277096033912964, -1.2672729200177606], 'a3': [0.0, 0.0], 'a4': [-1.2119613076206825, -1.5909587640257572], 'a5': [2.1552469931495737, 1.244332431665038], 'a6': [0.0, 0.0], 'a7': [2.6445308016341063, -0.08035445979204626], 'a8': [-2.7769387102469443, 0.5372256504784905], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.0122301309362665, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.6277096033912964, 1.2672729200177606]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-2.6445308016341063, 0.08035445979204626]]]], 'bad_primes': [2, 3, 7], 'central_character': '252.107', 'coefficient_field': 'CDF', 'conductor': 252, 'conductor_radical': 42, 'conjugate': '2076226902251021659056917999620', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.6277096033912964, 1.2672729200177606]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.1552469931495737, -1.244332431665038], [2.5, 4.330127018922194]], [[1.0, 0], [-2.6445308016341063, 0.08035445979204626]], [[1.0, 0], [2.3039346782091754, 3.9905319199781433], [-5.5, 9.526279441628825]], [[1.0, 0], [-5.222209035424072, 0], [13.0, 0]], [[1.0, 0], [4.859276587725819, -2.8055046459903474], [8.5, -14.722431864335457]], [[1.0, 0], [2.7656976811489913, 1.596776300708494], [9.5, 16.454482671904334]], [[1.0, 0], [0.35936566520269375, -0.6224395906268525], [-11.5, -19.91858428704209]], [[1.0, 0], [0, -4.536557991023714], [-29.0, 0]], [[1.0, 0], [-1.0194405177970267, 0.5885742573729248], [15.5, -26.846787517317598]], [[1.0, 0], [1.3564782019482422, -2.3494891651340315], [-18.5, -32.04293994002423]], [[1.0, 0], [0, 3.8366997405173486], [-41.0, 0]], [[1.0, 0], [0, -11.177327507893386], [-43.0, 0]], [[1.0, 0], [2.7090523210831523, -4.692216260478416], [-23.5, -40.703193977868615]], [[1.0, 0], [-1.7911369975376978, 1.034113427683888], [26.5, -45.89934640057525]], [[1.0, 0], [-2.0582073798415568, -3.5649197543987916], [-29.5, 51.09549882328188]], [[1.0, 0], [-0.5051254851975953, 0.8749030045601158], [-30.5, -52.827549630850754]], [[1.0, 0], [10.950537093043739, -6.322295538439785], [33.5, -58.023702053557386]], [[1.0, 0], [7.310120770317382, 0], [71.0, 0]], [[1.0, 0], [4.818935436410925, 8.346641014257823], [-36.5, 63.21985447626402]], [[1.0, 0], [7.65523639095317, 4.419752791027031], [39.5, 68.41600689897065]], [[1.0, 0], [-13.765737431901792, 0], [83.0, 0]], [[1.0, 0], [7.38368827778841, 4.2629744147934225], [44.5, 77.07626093681505]], [[1.0, 0], [10.723207374291675, 0], [97.0, 0]], [[1.0, 0], [3.3226794419811876, -1.9183498702586743], [50.5, -87.4685657822283]], [[1.0, 0], [-14.443051419747668, -8.338699625110923], [51.5, 89.20061658979718]], [[1.0, 0], [-2.8684426655895114, 4.968288435399336], [-53.5, -92.66471820493493]], [[1.0, 0], [-1.4135245694083376, -2.4482963719621607], [-54.5, 94.39676901250381]], [[1.0, 0], [0, 5.596512230620331], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 11, 'label': '2-252-84.23-c1-0-11', '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/252/2/be/a/107/10', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.7386039192437486, 1.8186756368616974, 1.9119614235150333, 2.0162321890683854, 2.126329090725485, 2.2345831664785347, 2.331361466276003, 2.4056447747346508, 2.445617700366841, 2.439295723964717, 2.3752199951742683, 2.2432335361612887, 2.035326504370702, 1.7465118283720722, 1.3756698712280777, 0.926283772778579, 0.40697721723130026, -0.16823504379789742, -0.7800652472671777, -1.404501671757466, -2.0138215652503866, -2.5780617100591114, -3.0668940379161636, -3.451803807125453, -3.7084192936436255, -3.818800500576529, -3.7734661781111236, -3.572929245297538, -3.2285251427613266, -2.762358369485953, -2.206259396269298, -1.5997339808699333, -0.9869928560515896, -0.413261805238269, 0.07932227107237423, 0.45583846681105306, 0.6922901239911426, 0.7784465726855214, 0.7194182088958401, 0.5356672176368295, 0.26130854098512785, -0.05925467421152893, -0.3761092991484232, -0.6395713253572795, -0.8062661384502436, -0.8448239993696538, -0.7404412380481216, -0.49763053662815887, -0.14065506131622668, 0.28860035465990636, 0.7352475560823637, 1.1380849211875153, 1.4376174507215402, 1.5844123326155648, 1.546655876069746, 1.3157856054244612, 0.9092418703027879, 0.3697096810432077, -0.23932738335142428, -0.8413768562882392, -1.3572029305995619, -1.7162545780082519, -1.8676509358248248, -1.7890408126653812, -1.4918236696288223, -1.021637555182761, -0.4536456546108148, 0.11708915745243914, 0.5890685047393824, 0.8698987514640265, 0.8916675977377322, 0.6237487152913255, 0.08082196379516676, -0.6755401498321211, -1.5424951183291518, -2.3884650146308704, -3.0711700673830054, -3.458765995292698, -3.451011831874072, -2.9971570046018754, -2.107513330957669, -0.8564650448765095, 0.6241217538058709, 2.1606670728596082, 3.5609071091337294, 4.6409938982403665, 5.252637019191008, 5.306035848481218, 4.7848143118503685, 3.7502849960356888, 2.333985509520642, 0.7193006592384729, -0.8851964553727891, -2.276597929173375, -3.287804122893594, -3.8120393383793516, -3.817655303870634, -3.350703020255998, -2.5248039621765863, -1.5000397782166999, -0.4545172913872063, 0.44640654139831354, 1.0777990014115204, 1.3748111038753856, 1.3408483110385399, 1.0428889731147262, 0.594987441719801, 0.1332397664206618, -0.21286339827477882, -0.34705409483276617, -0.22560692145905387, 0.13448446512540924, 0.6601075585312552, 1.2384612730016689, 1.7419343695692613, 2.0562601532922415, 2.106016688506723, 1.8720007832740446, 1.3966213721457095, 0.7759298211398633, 0.13973615277589083, -0.37613856392157424, -0.6596159880864266, -0.6476650661043768, -0.3414863036274799, 0.1920485223297979, 0.8334150869665061, 1.4354579814780728, 1.8552179377648286, 1.9856782921860217, 1.7803251778253029, 1.264778856488512, 0.5324622571969527, -0.27522139324353184, -1.0001811319943315, -1.5035894974698953, -1.698318138629086, -1.5701294022590737, -1.1821397907187854, -0.6606936789123641, -0.16502947472034926, 0.152954350432788, 0.1898378586780233, -0.07703707259105264, -0.5744550385804464, -1.1402563700881152, -1.55240156049838, -1.5751776660222276, -1.0132977190499393, 0.23776351551627536, 2.1567641513528586, 4.585884533921804, 7.24813514872904, 9.79101240578965, 11.848577531125942, 13.10974307160393, 13.378674220374105, 12.614372785496299, 10.940566343154861, 8.623167377903169, 6.0194869442975625, 3.5095534913763076, 1.423892724432341, -0.016985707519476777, -0.7386408503229946, -0.8169087163475147, -0.44995272594814345, 0.0949821708002902, 0.5476195758086855, 0.6982440215851365, 0.4443306946971707, -0.19016425019229086, -1.0666854883716446, -1.9715461796993337, -2.672867355901322, -2.9808063189359566, -2.7962688718613893, -2.1362804388140164, -1.1300504690338895, 0.012934250735845846, 1.0545128669601134, 1.7860261702594193, 2.078396843847513, 1.9116025516079327, 1.3763480339891254, 0.6478761971054998, -0.06101196121992528, -0.5553662505955081, -0.7074819535959149, -0.48752127189239464, 0.03237259235291606, 0.7011418288755987, 1.3324924810842655, 1.7571201078267926, 1.8691517179429118, 1.654078439856969, 1.1905389418780556, 0.6255399215285913, 0.13012086832103653, -0.1519530490919039, -0.14773205480092158, 0.1219383296833796, 0.5471939098923086, 0.9610894119487643, 1.1902386989050744, 1.10997281224058, 0.6879293682083308, 0.0025915351481817675, -0.7701462846571192, -1.4004759742006903, -1.6676050584743427, -1.4253336246625123, -0.6517571942558995, 0.5320496222081218, 1.8817181024596699, 3.084728491807694, 3.838105383808307, 3.9288096726923185, 3.2951322065532334, 2.0514143882450933, 0.46746871034460036, -1.0941019562948588, -2.267990918745324, -2.7809633602020463, -2.5263810562836846, -1.5979409738857795, -0.2721812984118311, 1.057444418078505, 1.9791883367444763, 2.1694600641122705, 1.4794939936714333, -0.02084335252488542, -2.054392666750884, -4.201196744145808, -6.0001617511069, -7.06194671352572, -7.163981297311294, -6.303074520526146, -4.692211476323288, -2.7028834011518503, -0.7686840450837074, 0.7239745647446099, 1.529079551537415, 1.593986810286035, 1.0592543143458932, 0.20712435315930294, -0.6255881101824663, -1.1450513530731132, -1.1810332890222848, -0.7286670044536612, 0.05900501122497333, 0.9238248656684692, 1.583911195920657, 1.8191246761053808, 1.5355530055305728, 0.790740106749388, -0.22661201794232524], 'positive_zeros': ['2.08945352440383792346221913314013', '4.22795278924439776774188312135256', '5.10236763332923915576683500105565', '6.04258275085697579499351386961734', '7.20160746503712628329335294157943', '8.348287257231553354993041279213586', '9.014935790711252634045998372986930', '10.19877124282119769573068249736713', '11.42996776263410620728719261765092', '12.55932950945964272028804860045004'], 'prelabel': '2-252-84.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4185309763753016, 'root_angle': 0.40035906368564445, 'root_number': '0.3079439759680916 + 0.9514044921404162*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.200179531843', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.08945352440383792346221913314', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.22795278924439776774188312135', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.10236763332923915576683500106', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2.0122301309362665, 'bad_primes': [2, 3, 7], 'central_character': '84.23', 'conductor': 252, 'conductor_radical': 42, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/252/2/be/a/107/10'], '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': '2-252-84.23-c1-0-11', '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': '2-252-84.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4185309763753016, 'root_angle': 0.20017953184282222, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.08945352440383792346221913314', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2648697014359514513309501235885', 'Lhash_array': ['2648697014359514513309501235885'], 'label': '2-252-84.23-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/252/2/be/a/107/10'}