-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '630174209855410508410705472711', 'a10': [5.183725224669975, 8.465226243419601e-61], 'a2': [-1.912835294271044, -2.632791915873822], 'a3': [0.0, 0.0], 'a4': [-2.036586431781769, 6.267968533129242], 'a5': [-0.9362714204418372, 1.2886670557500095], 'a6': [0.0, 0.0], 'a7': [-3.362036860626276, 10.347285497325862], 'a8': [8.017781205476037, -2.6051350337451797], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.6975546171669396, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [5.256072393445553, -9.66300693339602]]]], 'bad_primes': [3, 11], 'central_character': '99.80', 'coefficient_field': 'CDF', 'conductor': 99, 'conductor_radical': 33, 'conjugate': '2670464264642172862554557856574', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.912835294271044, 2.632791915873822], [-1.2360679774997898, 3.804226065180614]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.9362714204418372, -1.2886670557500095], [-7.725424859373685, -23.77641290737884]], [[1.0, 0], [3.362036860626276, -10.347285497325862], [-39.64183272437242, -28.801477362331184]], [[1.0, 0], [5.256072393445553, -9.66300693339602]], [[1.0, 0], [-7.473844428645306, 5.430065825106742], [52.223872049366115, -160.72855125388097]], [[1.0, 0], [2.8310566762210616, -3.896615224979882], [-89.30591137435981, -274.8553332092994]], [[1.0, 0], [7.7528144915530195, 23.86070952742646], [-292.055134969356, 212.1904760775828]], [[1.0, 0], [0, -36.689162983540015], [-529.0, 0]], [[1.0, 0], [23.25477735425859, 7.55593519390957], [680.3832922693308, 494.3273971779699]], [[1.0, 0], [47.07032877833784, -34.19859566465706], [296.9653315943245, -913.9653121596426]], [[1.0, 0], [-3.954740545304997, 12.171439870084674], [-1107.544265299303, -804.6780103883957]], [[1.0, 0], [11.808941528501535, -3.836957694272871], [1359.9575675442866, -988.0670091036474]], [[1.0, 0], [-19.698372006676426, 0], [1849.0, 0]], [[1.0, 0], [-61.76756286373093, 20.0694977627304], [1787.1185405742588, -1298.4176223140732]], [[1.0, 0], [-29.098827196899595, -40.05109966072748], [-868.0287371992273, 2671.517754273086]], [[1.0, 0], [-22.912520914750782, -7.444729335550938], [2816.188157419192, 2046.080463230099]], [[1.0, 0], [35.79100257528736, 26.00368549089566], [1149.8522360691793, 3538.8812971342663]], [[1.0, 0], [-33.08982156486446, 0], [4489.0, 0]], [[1.0, 0], [-44.04803016455987, 60.62691235086909], [-1557.7546686441099, -4794.275898643869]], [[1.0, 0], [-12.785946647664096, 39.351097504716904], [-4311.251563024095, -3132.3076094665894]], [[1.0, 0], [51.75307517501496, -37.60081006970685], [1928.575061894047, -5935.543718198053]], [[1.0, 0], [24.79616807528207, -34.128997435782736], [-2128.8180742490126, -6551.828340757313]], [[1.0, 0], [0, 111.11112487679033], [-7921.0, 0]], [[1.0, 0], [-87.45729481242088, 63.5414440655264], [2907.5409000738805, -8948.4907618211]], [[1.0, 0], [-68.42851244372318, -94.1837673722773], [-3152.2823596188387, 9701.727522726862]], [[1.0, 0], [33.76926463727778, -103.93110983666426], [-8582.861293323816, -6235.813741570847]], [[1.0, 0], [41.061231920769345, -13.341603002645293], [9262.435568598774, -6729.553353496525]], [[1.0, 0], [-75.30633610626418, 0], [11881.0, 0]], [[1.0, 0], [3.349642171005454, -1.088364716692025], [10330.338001173704, -7505.429886522589]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-99-33.14-c2-0-1', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/99/3/l/a/80/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.4855683585501663, 0.3864321432010665, 0.273585334281129, 0.14450814228108438, -0.0036505999169648257, -0.17384953414263118, -0.36890805662102316, -0.591246713889084, -0.8426220631392521, -1.1238621499227759, -1.4346094766721655, -1.7730806573105897, -2.135855123146486, -2.51770843475534, -2.9115082515446873, -3.3081922683422884, -3.6968470480738715, -4.064904386688905, -4.398467483260939, -4.6827727269486505, -4.9027844804861465, -5.043910145911497, -5.092811552023294, -5.038277019473166, -4.87210724252263, -4.589958429524642, -4.192079104137983, -3.68387371750485, -3.0762277744435074, -2.385536313333702, -1.6333907173524895, -0.8458979157691037, -0.05263043468535782, 0.7147657612522692, 1.424247979994534, 2.0452498543843474, 2.550634923770106, 2.918593282249679, 3.134331053702094, 3.191401095672918, 3.0925352353276403, 2.8498643263262817, 2.4844520401281454, 2.025119689369344, 1.5065991752368673, 0.9671146548485717, 0.4455549742945607, -0.021548067905648317, -0.40298236808802196, -0.6754881697725645, -0.8257970417112919, -0.8518478531007954, -0.7630115224204036, -0.5792408552994095, -0.329163451339314, -0.047245456733079165, 0.22973914849625457, 0.466607060858932, 0.6336400702788125, 0.7100152162745922, 0.6863863422806112, 0.5662755210432737, 0.36604035996647005, 0.11332766087532517, -0.15590776097869438, -0.4015655004397826, -0.5843285177187737, -0.6708172280457371, -0.638353925282992, -0.4787170250439044, -0.20033422010888727, 0.17149231803743345, 0.5965273616490809, 1.0236564335385465, 1.3967273018284603, 1.6615987450314424, 1.7736090029936018, 1.7045488741266646, 1.448200842337657, 1.0235991923286119, 0.47537628245374675, -0.12912870870268658, -0.705940563789009, -1.163230728230388, -1.411957199416088, -1.3771945348839563, -1.0087967706548457, -0.2900037920155829, 0.7572545877502007, 2.071286558670269, 3.554266523449024, 5.080473585981278, 6.508460897772784, 7.695931127119583, 8.51566751237923, 8.870628878519236, 8.706305845594418, 8.018671602011613, 6.856528985208129, 5.317708327777897, 3.5393311445290556, 1.683126899404973, -0.0825303018897856, -1.6017088527811396, -2.748752099911577, -3.4425662563917188, -3.655475925428492, -3.415432816476811, -2.8012253315760423, -1.9312735740704714, -0.9474759412127971, 0.003728092237544115, 0.7905057793583306, 1.3123659396550413, 1.5121832811031133, 1.381879558161481, 0.9610428978376828, 0.3287989054130635, -0.40975559529426575, -1.1404361367548894, -1.7575590008259867, -2.179529319082076, -2.3600534085850406, -2.2933075341337528, -2.012374637296981, -1.5813580718384317, -1.0826196711663114, -0.6013957636157385, -0.21047980521441842, 0.04235691137833023, 0.14201133362765822, 0.10743037685220873, -0.013491711837493632, -0.15455035066742098, -0.24542815277328622, -0.22678826777755112, -0.06337553097704607, 0.24746186190359132, 0.6736282223050984, 1.153159510749627, 1.6054529844710148, 1.9469263385860371, 2.1082422428949767, 2.0497866780642866, 1.7722462860345425, 1.3198936783900728, 0.7754504315571681, 0.24694694577264595, -0.1514375727953987, -0.32128574564704976, -0.20058429402393982, 0.22096075740332796, 0.8952725362578987, 1.7198550305251132, 2.5524337659472898, 3.2343768481979787, 3.619214966330034, 3.6013706336352085, 3.139822175980678, 2.2719888649376023, 1.114584554617221, -0.14966628434155851, -1.2980773944050736, -2.103064823788311, -2.3706411010965684, -1.9758232098349626, -0.8886273395768389, 0.814345856352641, 2.9554466028895274, 5.278474011253955, 7.485019641108143, 9.279021035801215, 10.412282951775866, 10.723350497988081, 10.163084400502566, 8.802457720943027, 6.821103610031906, 4.478467876136766, 2.072459641606569, -0.10731153351269244, -1.823687189789496, -2.925984338119522, -3.36825040186759, -3.2090055208597867, -2.5931163636448025, -1.7196857596364385, -0.802322765747087, -0.02940763140121088, 0.4682493027600199, 0.6365866332926926, 0.5012594216670262, 0.1546092105697458, -0.26999327394478106, -0.6306439820805669, -0.8092514108824517, -0.7369954311837494, -0.4077992183401542, 0.12261499122850945, 0.7513795197502569, 1.3532019186920554, 1.8093998354482692, 2.034661436533093, 1.9955587725843809, 1.716772551004153, 1.27380817008114, 0.7740705907617221, 0.33083044194530314, 0.036252238281326496, -0.06011437967549856, 0.03777102502769009, 0.2748449083781225, 0.5601919892747915, 0.7915950602257823, 0.8834985151609128, 0.7914972521346878, 0.52706634646625, 0.1583744321016444, -0.20376597149504105, -0.43217490926761065, -0.41604262051407803, -0.09244466463530952, 0.5312449254039457, 1.3702596204027253, 2.2736504817471266, 3.0526494763584804, 3.520905141701739, 3.5381419268145406, 3.0473754731124605, 2.096574240463662, 0.838547867475751, -0.49266829815114294, -1.625498708493751, -2.3064347785903028, -2.3562327011962045, -1.714513793371959, -0.46236051370557274, 1.1833391650503116, 2.90430907565544, 4.338444745939584, 5.149698711399112, 5.096378846229923, 4.083709140509436, 2.189275912194302, -0.3447321636473005, -3.1518495760466254, -5.806816946510253, -7.90346662199319, -9.12950973425053, -9.32321359468109, -8.5006247777802, -6.848080514412775, -4.681963676217381, -2.3844396509692114, -0.3287952239922258, 1.1900785505249356, 2.005961204075442, 2.102703963830684], 'positive_zeros': ['0.49711979763347499265543301967305', '4.00838268619567529810782452450407', '5.86875105490812122378900494080120', '6.89572232460815120021325459309702', '7.927496287310622857196943797463991', '8.820446971603992290861127625416982', '10.09844487046605956645082274417122', '10.91354465938557519435143801612903', '12.74383188902313306867126229425142', '13.87447591748378948053891638000738'], 'prelabel': '2-99-33.14-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6424233976557139, 'root_angle': -0.23794463880253472, 'root_number': '0.733373594208621 - 0.6798258389598978*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.118972319401', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.49711979763347499265543301967', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.00838268619567529810782452450', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.86875105490812122378900494080', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2.6975546171669396, 'bad_primes': [3, 11], 'central_character': '33.14', 'conductor': 99, 'conductor_radical': 33, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/99/3/l/a/80/1'], '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': '2-99-33.14-c2-0-1', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-99-33.14-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6424233976557139, 'root_angle': -0.11897231940126736, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.49711979763347499265543301967', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '630174209855410508410705472711', 'Lhash_array': ['630174209855410508410705472711'], 'label': '2-99-33.14-c2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/99/3/l/a/80/1'}