Formats: - HTML - YAML - JSON - 2026-09-07T12:21:12.062341
  • lfunc_lfunctions • Show schema
    {'Lhash': '2365447303431162928595133580359', 'a10': [100.0, 0.0], 'a2': [4.0, 0.0], 'a3': [-9.472707310399723, 0.0], 'a4': [16.0, 0.0], 'a5': [25.0, 0.0], 'a6': [-37.890829241598894, 0.0], 'a7': [37.17921293374775, 0.0], 'a8': [64.0, 0.0], 'a9': [-153.26781621149965, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 36.888278556985554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [-4.0, 0]]], [5, [[1.0, 0], [-25.0, 0]]], [23, [[1.0, 0], [529.0, 0]]]], 'bad_primes': [2, 5, 23], 'central_character': '230.1', 'coefficient_field': 'CDF', 'conductor': 230, 'conductor_radical': 230, 'degree': 2, 'euler_factors': [[[1.0, 0], [-4.0, 0]], [[1.0, 0], [9.472707310399723, 0], [243.0, 0]], [[1.0, 0], [-25.0, 0]], [[1.0, 0], [-37.17921293374775, 0], [16807.0, 0]], [[1.0, 0], [642.7409095004001, 0], [161051.0, 0]], [[1.0, 0], [-803.9417231076625, 0], [371293.0, 0]], [[1.0, 0], [-285.84936830928666, 0], [1419857.0, 0]], [[1.0, 0], [2353.8279523858955, 0], [2476099.0, 0]], [[1.0, 0], [529.0, 0]], [[1.0, 0], [4925.023650580992, 0], [20511149.0, 0]], [[1.0, 0], [4420.849689552638, 0], [28629151.0, 0]], [[1.0, 0], [-10232.7830764767, 0], [69343957.0, 0]], [[1.0, 0], [6340.421368712882, 0], [115856201.0, 0]], [[1.0, 0], [19250.14326855536, 0], [147008443.0, 0]], [[1.0, 0], [13293.851620562542, 0], [229345007.0, 0]], [[1.0, 0], [-21717.04988189532, 0], [418195493.0, 0]], [[1.0, 0], [2645.858245738133, 0], [714924299.0, 0]], [[1.0, 0], [52328.396190575215, 0], [844596301.0, 0]], [[1.0, 0], [70672.30451476984, 0], [1350125107.0, 0]], [[1.0, 0], [-3524.5892742535393, 0], [1804229351.0, 0]], [[1.0, 0], [87528.57355115913, 0], [2073071593.0, 0]], [[1.0, 0], [-75802.8297951152, 0], [3077056399.0, 0]], [[1.0, 0], [-10147.63559026575, 0], [3939040643.0, 0]], [[1.0, 0], [3051.8922788928157, 0], [5584059449.0, 0]], [[1.0, 0], [-105530.52640136317, 0], [8587340257.0, 0]], [[1.0, 0], [-103881.93713596804, 0], [10510100501.0, 0]], [[1.0, 0], [-117607.24243693832, 0], [11592740743.0, 0]], [[1.0, 0], [-227003.75573606908, 0], [14025517307.0, 0]], [[1.0, 0], [25463.633205452417, 0], [15386239549.0, 0]], [[1.0, 0], [206746.37618066496, 0], [18424351793.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 30, 'label': '2-230-1.1-c5-0-30', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/230/6/a/d/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 10}, 'plot_values': [-2.127007175050195e-60, 0.28346336669410666, 0.563894599782035, 0.8382881248989241, 1.1036915202869204, 1.3572321683324038, 1.596143969496847, 1.8177940939413861, 2.019709709083316, 2.1996045773618125, 2.3554053691259442, 2.485277482506256, 2.587650107288637, 2.6612402152098, 2.705075106862275, 2.7185130976999634, 2.701261884630461, 2.653394102464286, 2.5753595580470736, 2.467993621046066, 2.3325212556960633, 2.1705561986625757, 1.9840948255629873, 1.775504303247055, 1.5475046969151043, 1.3031447903394686, 1.0457714831682074, 0.7789927503452432, 0.5066342833773979, 0.23269007929718605, -0.03873260201864235, -0.3034733312271662, -0.5573829105474999, -0.796391179543176, -1.0165771695479195, -1.2142404086674696, -1.3859720533510786, -1.5287244173826795, -1.6398773894597545, -1.7173001807218826, -1.7594068276749173, -1.7652038973930255, -1.7343289034285012, -1.6670780444282065, -1.5644220239702524, -1.4280088994141418, -1.2601531382159443, -1.0638103295327943, -0.8425373030433276, -0.6004377404313286, -0.3420937213143468, -0.07248401672572455, 0.2031096793411037, 0.47920701619267786, 0.7502418270892459, 1.010681286992451, 1.2551488328282128, 1.4785480420973682, 1.6761844743608911, 1.8438823568455565, 1.9780929486823977, 2.0759914550444143, 2.1355594877043518, 2.1556502850586097, 2.1360342127175613, 2.077422462877855, 1.981467351529733, 1.8507381688376638, 1.6886721585798075, 1.4995008733645159, 1.2881528569138538, 1.0601343242219474, 0.8213902242427632, 0.5781487560136787, 0.33675304514862403, 0.10348425077643499, -0.1156191587088989, -0.314940869785936, -0.4894596172298401, -0.6349101258343155, -0.7479268095429347, -0.8261651949015453, -0.868396463546595, -0.8745711032153868, -0.8458484098522642, -0.7845894804138472, -0.6943123569254536, -0.5796091018209331, -0.44602577233533885, -0.299907483240657, -0.14821196472620993, 0.0017038043272482458, 0.14231821915181125, 0.2661942971574302, 0.3662361232591636, 0.435944468358631, 0.46966319319266137, 0.4628079438870868, 0.4120688156044567, 0.31557911642769765, 0.17304310563769223, -0.014183400434997995, -0.24306438513790438, -0.5089102760620966, -0.8054615086268093, -1.1250288044956749, -1.4586880395417283, -1.7965256309849973, -2.127928470289532, -2.4419106356987297, -2.727467504078591, -2.9739465116344252, -3.171422747592707, -3.311066857056169, -3.385492421986455, -3.3890701136350034, -3.3181964828612065, -3.1715062785211043, -2.950018644182597, -2.6572094089948366, -2.299003912486483, -1.8836873228361501, -1.421732147259728, -0.9255455032747816, -0.40914162325449976, 0.1122521015966053, 0.62264457381889, 1.1057725971924734, 1.5456192992210056, 1.9269424992591078, 2.2357951686619906, 2.4600197495929015, 2.589698363363189, 2.61754186443639, 2.5392022754028525, 2.3534953392243207, 2.0625226908232848, 1.6716863997278268, 1.1895922662095209, 0.6278421435513916, 0.00071957217766706, -0.6752229995017759, -1.3816633193938663, -2.099079186693691, -2.8073704680295966, -3.4865122732482323, -4.1172165934331835, -4.681578813501361, -5.163685488283352, -5.5501606436955315, -5.830629628467189, -5.998082156434894, -6.049119568965968, -5.984075402393095, -5.807002926814948, -5.525528264769684, -5.150572815581327, -4.69595380487081, -4.177876644553642, -3.6143372250632297, -3.024456078137264, -2.427769374326586, -1.843503810724901, -1.2898634917704095, -0.7833568398025581, -0.338190367086364, 0.03424618123408456, 0.32578217435055723, 0.5317390980907898, 0.6510624565825412, 0.6863064774565762, 0.6434715400811619, 0.5317003705962251, 0.3628450229289364, 0.15092223318915188, -0.08852035174743335, -0.33910053778993815, -0.5843310465921834, -0.8083508513299882, -0.9966267515004207, -1.1365945180467114, -1.218211263635839, -1.2343943003487696, -1.1813265048154753, -1.0586139306144013, -0.8692878534087762, -0.6196503311606354, -0.318969408082677, 0.02096302913379454, 0.38639133680955395, 0.7622491219782379, 1.1328755961014256, 1.482762429484536, 1.7972964563310478, 2.0634633531313655, 2.2704788058034557, 2.4103166615314575, 2.4781080222939806, 2.4723909992073954, 2.395197664975008, 2.2519723150702036, 2.0513231329037507, 1.8046173784382338, 1.5254379010226793, 1.2289257403734153, 0.931039474837041, 0.6477664965658199, 0.3943242912423576, 0.18439090033512678, 0.029402954443650178, -0.06204301520744296, -0.08465476362087865, -0.03674889889510112, 0.07962182685960616, 0.25872767665377194, 0.49140760676202616, 0.7654922412403721, 1.0663858989148405, 1.377781132644779, 1.6824720991267843, 1.9632274735354862, 2.2036798723152042, 2.3891870798405725, 2.507620921961453, 2.5500424149614505, 2.5112267532321506, 2.390008583221067, 2.1894265414831224, 1.9166558163963432, 1.5827280582501315, 1.2020487913146718, 0.7917330279999248, 0.3707895038871881, -0.04080767346817692, -0.4231146002550577, -0.7572306310001853, -1.0262772439744885, -1.216291745152417, -1.3169881779188441, -1.3223436781598874, -1.2309766751441267, -1.0462934181802774, -0.7763908289493731, -0.43371607426070247, -0.03449589867209825, 0.4020390027523661, 0.8545981031176434, 1.3008976596651134, 1.7187965072798679, 2.0874430196238714, 2.3883734806849173, 2.6065034650068086, 2.730958283202507, 2.75569594665193, 2.6798861180924525, 2.5080206731422847, 2.249745206350434], 'positive_zeros': ['1.86600890103730857219163369138954', '3.20401977045866140019417786566343', '4.71641648741731201090524816589808', '5.68677348827185313872501447031850', '6.30822307679827517691332951853085', '7.79899926446203058446203783920916', '8.750068715637185044374882517223526', '10.36865201787981306942771777662418', '10.91495551574699757688170150044094'], 'prelabel': '2-230-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.073572141416084, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.86600890103730857219163369139', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '3.20401977045866140019417786566', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '4.71641648741731201090524816590', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 36.888278556985554, 'bad_primes': [2, 5, 23], 'central_character': '1.1', 'conductor': 230, 'conductor_radical': 230, 'degree': 2, 'index': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/230/6/a/d/1/2'], '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': '2-230-1.1-c5-0-30', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-230-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.073572141416084, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.86600890103730857219163369139', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '2365447303431162928595133580359', 'Lhash_array': ['2365447303431162928595133580359'], 'factors': ['2-230-1.1-c5-0-30'], 'label': '2-230-1.1-c5-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/230/6/a/d/1/2'}