-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1918054417663469792744825098043', 'a10': [-4.269064167331899, 0.0534610124732631], 'a2': [-1.1326634314723638, -0.8468019550079287], 'a3': [0.09861441930256495, -0.12851681336310422], 'a4': [0.5658528979894999, 1.9182832162735732], 'a5': [2.395070989533398, -1.83780260839445], 'a6': [-0.22052523536716345, 0.062059411768363326], 'a7': [0.13436865305734982, 2.6423370460778757], 'a8': [0.9834850926539908, -2.6519345905446783], 'a9': [0.7696653676849374, 2.872430257026368], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.7886490052766815, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.1326634314723638, 0.8468019550079287]]], [7, [[1.0, 0], [-0.13436865305734982, -2.6423370460778757]]]], 'bad_primes': [2, 7], 'central_character': '224.37', 'coefficient_field': 'CDF', 'conductor': 224, 'conductor_radical': 14, 'conjugate': '2033063052117076916551401685787', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.1326634314723638, 0.8468019550079287]], [[1.0, 0], [-0.09861441930256495, 0.12851681336310422], [-0.7764571353075623, -2.897777478867205]], [[1.0, 0], [-2.395070989533398, 1.83780260839445], [1.294095225512604, -4.8296291314453415]], [[1.0, 0], [-0.13436865305734982, -2.6423370460778757]], [[1.0, 0], [0.2309801152780524, -0.03040910906938021], [10.62518408917975, -2.8470094961277286]], [[1.0, 0], [-0.45131086200850434, 0.1869390798902149], [9.192388155425117, -9.192388155425117]], [[1.0, 0], [-5.152843914297011, 2.9749958210115044], [8.5, -14.722431864335457]], [[1.0, 0], [-0.45623299855311034, 3.4654336751207153], [-18.352590699492296, -4.917561856947894]], [[1.0, 0], [-0.7925130584142557, -2.9576989996638035], [-19.91858428704209, 11.5]], [[1.0, 0], [3.0133139570525613, 7.274783422804432], [-20.506096654409877, 20.506096654409877]], [[1.0, 0], [1.654064789529131, 2.8649242544751763], [-15.5, 26.846787517317598]], [[1.0, 0], [-3.4895910577112823, 2.6776573955919125], [9.576304668793268, -35.73925557269553]], [[1.0, 0], [7.623591683540917, -7.623591683540917], [0, -41.0]], [[1.0, 0], [3.493965724537208, -8.435179438644466], [-30.405591591021544, -30.405591591021544]], [[1.0, 0], [3.1115098778029706, 1.7964310655357247], [23.5, 40.703193977868615]], [[1.0, 0], [-0.6173706701364723, 0.08127839066067089], [51.19406879332062, -13.7174093904336]], [[1.0, 0], [-1.443618096519843, -10.96536809384505], [-56.98962375105503, 15.270323661048725]], [[1.0, 0], [1.3623623873744675, 0.17935841091697594], [58.92147540363317, 15.787961751253766]], [[1.0, 0], [1.1355398270589447, -1.4798643144949315], [-17.34087602186889, -64.71703036136758]], [[1.0, 0], [6.136453470371007, 6.136453470371007], [0, 71.0]], [[1.0, 0], [-5.348146202161681, -1.4330314558727983], [63.21985447626402, 36.5]], [[1.0, 0], [12.75965428512586, 7.366789836283977], [39.5, 68.41600689897065]], [[1.0, 0], [-5.175197417493903, 2.1436369582841914], [58.68986283848344, -58.68986283848344]], [[1.0, 0], [-11.013077787792652, 2.950945299420176], [77.07626093681505, -44.5]], [[1.0, 0], [12.805942129438415, 0], [97.0, 0]], [[1.0, 0], [0.6436921654807386, 4.889327413279278], [-97.55850845519589, 26.140723555354597]], [[1.0, 0], [4.43413159510872, -1.1881219800427074], [89.20061658979718, -51.5]], [[1.0, 0], [12.316419900994878, 16.051070917542898], [-27.69363782596972, 103.3540634129303]], [[1.0, 0], [0.09971023728920203, 0.07651035604979081], [28.211275916174763, 105.28591506550845]], [[1.0, 0], [0, -9.270964397401627], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 15, 'label': '2-224-224.37-c1-0-15', '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/224/2/bd/a/37/7', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.0462410897822527, 1.0587256338071664, 1.0720257906391728, 1.0828722811563947, 1.0861580357198977, 1.0754150812593855, 1.0433564518383254, 0.982426497572964, 0.8853535712564954, 0.745721547889152, 0.5585728160130985, 0.3210378041954561, 0.03296514519773079, -0.3024922269447984, -0.6783939822599588, -1.0836996936212069, -1.5031956798371042, -1.917724750227453, -2.3047682112853383, -2.6394071185798493, -2.89565955313474, -3.0481541558892298, -3.074059779619422, -2.955150427075367, -2.679847973250918, -2.2450573511965706, -1.6575947733165681, -0.9350134658046454, -0.10565641472560584, 0.7921869729406688, 1.7120747014174371, 2.6021247626491877, 3.4085176831927138, 4.079561482618867, 4.570001902099803, 4.845192171396907, 4.88470027020127, 4.684936871718538, 4.260439646454586, 3.6435501737429536, 2.882363357588963, 2.0370048369454468, 1.1744826058360538, 0.3625437263163128, -0.3368778284667634, -0.8739334818673108, -1.216132910866274, -1.3519513435225217, -1.292246208862212, -1.0691785908585085, -0.7326153808539368, -0.34429829129503553, 0.029631757021262382, 0.32691305854050534, 0.49723742704519897, 0.509067876930475, 0.3542392664189517, 0.04961190906537223, -0.36460203575580474, -0.8297884999202855, -1.2766483738217187, -1.6347493929017802, -1.8426591687112164, -1.8572401903745084, -1.6607172253053373, -1.2643646465452503, -0.7080880867554692, -0.05574298082577409, 0.6133328823352799, 1.215486987690519, 1.675048095340404, 1.9359019559380375, 1.970491553994201, 1.784674041460285, 1.417426132516484, 0.9351539172105657, 0.42122468594153895, -0.037835289029403335, -0.3673807790518278, -0.5184732731757747, -0.4780643843819178, -0.2735410676319236, 0.02956202935784493, 0.33681146003895884, 0.54004027299763, 0.536294689941273, 0.24761211678382286, -0.36169812660765593, -1.2734420395498485, -2.412056326968054, -3.6505269782101673, -4.8254925067664916, -5.759744237876118, -6.288955684135573, -6.2885331320978874, -5.696173897755457, -4.526144527160392, -2.8724246073500033, -0.8995530065022417, 1.177995865097865, 3.1251158223579365, 4.719672751247473, 5.785110031137678, 6.216707259125996, 5.997016407729421, 5.197685031971886, 3.9671133193423302, 2.5058060613312514, 1.0334468266823778, -0.24676020851901528, -1.1803642578256737, -1.6849545730713107, -1.7603960899110398, -1.4842640553155264, -0.9934083285223798, -0.45513444544667847, -0.033435477579440036, 0.14333891445292535, 0.007238323661700788, -0.4368161355996248, -1.1131922172347868, -1.8918406028840298, -2.6154378134509573, -3.1319239603232107, -3.3258752112609415, -3.1423521125604315, -2.5983588964133597, -1.7795560821095076, -0.8228932662222412, 0.11124549568577037, 0.8715774150572083, 1.3463089555378496, 1.4849570729563417, 1.306969897606918, 0.8953204420933494, 0.3764930156346511, -0.10872882079248096, -0.4371920880153333, -0.5308661351023957, -0.37364799772582064, -0.013564264247825664, 0.45027512304498796, 0.8931121549445414, 1.1965596565878354, 1.2797002626318834, 1.1217464411708882, 0.7704768602151325, 0.3338173289855995, -0.04416566288780049, -0.217818029843855, -0.07719575604528604, 0.42075310145718525, 1.235007962221643, 2.2423025574061017, 3.2587552597881877, 4.077475283808949, 4.514337286251324, 4.451743813399816, 3.8700669873504783, 2.8587262613416664, 1.6031168920395882, 0.34896861299919885, -0.6490020926344242, -1.1833086599348546, -1.1422639260647889, -0.5395035394035089, 0.483147116236512, 1.6813635533924105, 2.758071454800285, 3.4271099249340984, 3.4771044826842914, 2.8212754476727286, 1.5215725556711501, -0.21906843189542902, -2.095556537175937, -3.762747968398606, -4.907567000541246, -5.315342436789888, -4.915559419231501, -3.796635483349137, -2.186198802950575, -0.4011296243411795, 1.2214722212817342, 2.396834658068992, 2.9521893934371484, 2.860168645800824, 2.2386336561107396, 1.3174835721708467, 0.38069812854572355, -0.30239934055828477, -0.5402909854638127, -0.2620080039883404, 0.47024242100497526, 1.4808616538375081, 2.527445094185297, 3.362112023896336, 3.7921278095906565, 3.724854224390375, 3.1862922567865706, 2.3093625066912247, 1.2958361101600238, 0.3624896448356455, -0.3141013646294244, -0.6396778837694228, -0.6206284111563307, -0.35439449881530805, 0.004591651421319109, 0.29336917505608123, 0.3894029751241158, 0.24610914463874442, -0.09513247441971213, -0.5198943432928327, -0.8782741425376652, -1.0342679489888504, -0.9124632529999772, -0.5279867135220345, 0.009922617156995736, 0.5230267668920615, 0.8119787971950732, 0.7142407480180171, 0.15580334676638796, -0.8185327555552457, -2.04621189664158, -3.28084353875678, -4.251349703856201, -4.731273611505071, -4.599645365349037, -3.8763033693694338, -2.7209042904154996, -1.3944544861822423, -0.19252282431776224, 0.6324961231332954, 0.9389796618800208, 0.7344349428616322, 0.17289569650821388, -0.489422880972333, -0.9693789586544308, -1.043144722480352, -0.6195596937477127, 0.220781140704731, 1.233570428168455, 2.066405010959877, 2.3493435750736986, 1.7976071940946985, 0.29925507499081083, -2.0365070380423678, -4.885231639080587, -7.768384748963408, -10.156271146601528, -11.587913213666006, -11.778035579466222, -10.68406051606587, -8.515953849155913, -5.686318855812874, -2.713468225873108, -0.10221119880825912, 1.7674557150150967], 'positive_zeros': ['1.51307814418116543587059029588531', '3.51509706419430527667912349983529', '5.43666329284451298505164338744054', '6.48937086994238964695688135106582', '7.14153408154893086026786922334462', '8.385318089357887924396758117096600', '9.613492565155751424003429417216064', '10.23853311765012942548325741728622', '10.80904178410599106917543190131427', '12.30407382820529777881867689847980'], 'prelabel': '2-224-224.37-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3374038302908666, 'root_angle': 0.1728911330543742, 'root_number': '0.8560830844721202 + 0.5168382266054831*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0864455665272', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.51307814418116543587059029589', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.51509706419430527667912349984', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.43666329284451298505164338744', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.7886490052766815, 'bad_primes': [2, 7], 'central_character': '224.37', 'conductor': 224, 'conductor_radical': 14, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/224/2/bd/a/37/7'], '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': '2-224-224.37-c1-0-15', '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': '2-224-224.37-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3374038302908666, 'root_angle': 0.0864455665271871, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.51307814418116543587059029589', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1918054417663469792744825098043', 'Lhash_array': ['1918054417663469792744825098043'], 'label': '2-224-224.37-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/224/2/bd/a/37/7'}