-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1989229905558270400833398985260', 'a10': [0.10435607626104, 0.18075002616265368], 'a2': [0.0, 0.45685025174785665], 'a3': [-1.39564392373896, -2.4173261851906624], 'a4': [1.79128784747792, 0.0], 'a5': [0.39564392373896, -0.22842512587392833], 'a6': [1.10435607626104, -0.6376002779105103], 'a7': [0.0, 0.0], 'a8': [0.0, 1.7320508075688772], 'a9': [-2.39564392373896, 4.14937699275954], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.086470608755563, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-3.5, 0.8660254037844386]]]], 'bad_primes': [7, 13], 'central_character': '637.459', 'coefficient_field': 'CDF', 'conductor': 637, 'conductor_radical': 91, 'conjugate': '1343732877530133714462143786263', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -0.45685025174785665], [-2.0, 0]], [[1.0, 0], [1.39564392373896, 2.4173261851906624], [-1.5, 2.598076211353316]], [[1.0, 0], [-0.39564392373896, 0.22842512587392833], [2.5, -4.330127018922194]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.39564392373896, 1.9604759334428057], [5.5, -9.526279441628825]], [[1.0, 0], [-3.5, 0.8660254037844386]], [[1.0, 0], [-3.0, 0], [17.0, 0]], [[1.0, 0], [1.18693177121688, 0.6852753776217849], [9.5, 16.454482671904334]], [[1.0, 0], [1.58257569495584, 0], [23.0, 0]], [[1.0, 0], [-3.39564392373896, 5.881427800328417], [-14.5, -25.11473670974872]], [[1.0, 0], [7.5, 4.330127018922194], [15.5, 26.846787517317598]], [[1.0, 0], [0, 6.928203230275509], [-37.0, 0]], [[1.0, 0], [-6.79128784747792, -3.9209518668856114], [20.5, 35.50704155516198]], [[1.0, 0], [4.68693177121688, 8.118003959356425], [-21.5, 37.239092362730865]], [[1.0, 0], [8.29128784747792, -4.78697727067005], [23.5, -40.703193977868615]], [[1.0, 0], [3.08257569495584, -5.339177721840456], [-26.5, -45.89934640057525]], [[1.0, 0], [0, -12.31505605182724], [-59.0, 0]], [[1.0, 0], [-7.37386354243376, 12.771906303575097], [-30.5, -52.827549630850754]], [[1.0, 0], [-3.87386354243376, 2.2365761590280084], [33.5, -58.023702053557386]], [[1.0, 0], [-3.79128784747792, 2.1889010593167337], [35.5, -61.48780366869514]], [[1.0, 0], [-3.0, -1.7320508075688772], [36.5, 63.21985447626402]], [[1.0, 0], [-3.0, -5.196152422706632], [-39.5, 68.41600689897065]], [[1.0, 0], [0, 7.023553429698058], [-83.0, 0]], [[1.0, 0], [0, -16.140657719290303], [-89.0, 0]], [[1.0, 0], [6.31306822878312, -3.6448516413004084], [48.5, -84.00446416709055]], [[1.0, 0], [2.60435607626104, 4.510877045084847], [-50.5, 87.4685657822283]], [[1.0, 0], [2.29128784747792, 3.968626966596886], [-51.5, 89.20061658979718]], [[1.0, 0], [5.20871215252208, 0], [107.0, 0]], [[1.0, 0], [-6.87386354243376, -3.968626966596886], [54.5, 94.39676901250381]], [[1.0, 0], [5.29128784747792, 9.164779389303519], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 23, 'label': '2-637-91.4-c1-0-23', '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/637/2/k/d/459/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.561687679045855, 1.6695189310937795, 1.7685594475163822, 1.8539734729402644, 1.9170492161221613, 1.946116783992213, 1.9279020113768477, 1.849102819739981, 1.698052223682471, 1.4663771536953545, 1.150560329000278, 0.7532833173464495, 0.28439763662283996, -0.23864466918972557, -0.7910588544422481, -1.3418103831498354, -1.855558198328142, -2.2954066214399402, -2.62630063395388, -2.8187824947065288, -2.8527241119104843, -2.7205774938303375, -2.429662367690208, -2.0030494579233995, -1.4787070811833716, -0.9067555109876284, -0.34490490623619996, 0.14758578124447375, 0.5168334665339107, 0.7213291601922853, 0.7380693537260868, 0.5668686831447365, 0.23203156736794156, -0.21916558100097056, -0.7213313357140345, -1.1988251552802456, -1.5758045252663593, -1.7871883775206072, -1.7889746455761864, -1.566261997429194, -1.1374920561427542, -0.5538572568565955, 0.1065241359801309, 0.7492596324824565, 1.2779177439468892, 1.6098732189229346, 1.691303142297006, 1.508749137057537, 1.0949619089537537, 0.5274717842251678, -0.08059350335310395, -0.5966432270831215, -0.8896318465295758, -0.8528133468888135, -0.4245062537645481, 0.3968762273092095, 1.546624199604071, 2.8981861180318904, 4.2784023760901135, 5.491757214291372, 6.350161297750232, 6.703536064882649, 6.465987787896509, 5.632787625630227, 4.284707372567619, 2.5783188897139, 0.7233135455869262, -1.0497008843191962, -2.5255765469023963, -3.5388398990414207, -3.999575643226496, -3.906165425739304, -3.3424065083204373, -2.4594492519302156, -1.4459247059507856, -0.49199311205063273, 0.24567669449072135, 0.6710985118077378, 0.7629687094876368, 0.5728078759135397, 0.20790137650659476, -0.19704290074780945, -0.5131169716291765, -0.6477829248465853, -0.5657879765638927, -0.2955570055651932, 0.08048478130552884, 0.44941676509694767, 0.6995157566641915, 0.7523096090213287, 0.5867661816405637, 0.24897289550599092, -0.15604829193204267, -0.489442568534238, -0.6152588563640301, -0.4402284331098823, 0.053420654660738164, 0.7911622439650997, 1.611175838178177, 2.292027255858191, 2.598398618151366, 2.3354617762321155, 1.3996443104326806, -0.18655136063425282, -2.265141404964015, -4.56279799980082, -6.738000607721723, -8.446207781672436, -9.40935975434754, -9.474320153454524, -8.646722820572016, -7.091832622021172, -5.101366039967203, -3.0330676817932702, -1.2363207941294296, 0.019440552558657884, 0.5972009823739753, 0.5137949286829181, -0.07425822667636513, -0.9164995693104254, -1.7341728902488482, -2.289263671752926, -2.439743162942025, -2.16750473829369, -1.5726488112229458, -0.8366186716920296, -0.1649133647305946, 0.27448692446300643, 0.39974921729813717, 0.23722553089331205, -0.08934936258084487, -0.39949451613388054, -0.5148463397676083, -0.31910678916970603, 0.1988903618657234, 0.9326854507639566, 1.681605973810107, 2.2051921794581357, 2.2944578347543345, 1.8401448314175126, 0.8778521189678096, -0.40464722521475405, -1.702712287719374, -2.6658375263436436, -2.987041928564309, -2.4872782201704062, -1.171657160155345, 0.759122215163038, 2.9472927115141494, 4.958336484372583, 6.383411626034497, 6.9376961748758745, 6.528938441234177, 5.278017604765613, 3.4859442751805694, 1.5560578332379693, -0.10775887454726472, -1.1996294728487518, -1.5809036534487801, -1.3023346780577678, -0.5748050392774643, 0.3013708435961973, 1.0271092030336317, 1.3886115090217472, 1.3109117769599565, 0.8666676950438335, 0.23968183254006137, -0.3436725947121685, -0.6924485732286421, -0.713460349536142, -0.4382949431814495, -0.0069291640925158845, 0.3859658363276771, 0.563695629520722, 0.43443210257413095, 0.029140835297598762, -0.5034019643158585, -0.9443657063706057, -1.08076511823423, -0.7846946707545923, -0.0687155213561351, 0.903257115091946, 1.8565252303201123, 2.4878749775613525, 2.56532309596231, 2.0137506715535114, 0.9572871721356416, -0.29868275189322857, -1.3448074824558494, -1.784357427033928, -1.3554883590956253, -0.02178167252700873, 1.9985833014248855, 4.277301916486439, 6.2843768175367165, 7.530937983456186, 7.705335243430633, 6.762069909701673, 4.936218680597901, 2.6778002395388785, 0.5245204281955184, -1.0498694640965047, -1.766678779569248, -1.6139164789178366, -0.837529274089706, 0.14415885140978715, 0.8757281455942825, 1.0075232996102965, 0.4020533298909705, -0.8282224425625483, -2.361977850577518, -3.77429971249396, -4.671499574256432, -4.812119673378024, -4.176152791557887, -2.9620270367818833, -1.514780157956741, -0.21116743344514857, 0.6591384643596768, 0.9769462010606706, 0.815247894211118, 0.3945781864119356, -0.009774730657866503, -0.17430867957780044, -0.0091812069444284, 0.41349571650183126, 0.8941861086590649, 1.189629730585452, 1.1140364165234649, 0.619438883233163, -0.1759076556637035, -1.0234596441748338, -1.6333340969878631, -1.7847498915266757, -1.4171560352498906, -0.6665885397204058, 0.16965850115679199, 0.7314403073135265, 0.7250782856071546, 0.038375157590107054, -1.2012859155580022, -2.650396344876726, -3.851350382786143, -4.382176373898559, -4.004762516104175, -2.7604022572552913, -0.9772073367396071, 0.817478344567257, 2.054553192764753, 2.300974628145957, 1.4000980400183847, -0.4721592548316153, -2.8549105843668827, -5.139120076814011, -6.749579623068684, -7.313138570629649, -6.759314274848055], 'positive_zeros': ['1.56922570399140501144258352673767', '3.33473671278930713498370274384296', '4.06722926122427706905716311438648', '5.23009486497388365542472260836830', '6.23294361841214697552853423746099', '6.82152337185676039283662164617902', '8.299408809323139093153817896978242', '9.452764038797859625091863957228687', '10.06306393533723756994617105062772', '10.72434972235414617573360021568274'], 'prelabel': '2-637-91.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.3783617119513411, 'root_number': '0.37290506072652435 + 0.9278695035857937*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.189180855976', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.56922570399140501144258352674', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.33473671278930713498370274384', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.06722926122427706905716311439', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 5.086470608755563, 'bad_primes': [7, 13], 'central_character': '91.4', 'conductor': 637, 'conductor_radical': 91, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/k/d/459/2'], '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': '2-637-91.4-c1-0-23', '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': '2-637-91.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.18918085597567055, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.56922570399140501144258352674', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1989229905558270400833398985260', 'Lhash_array': ['1989229905558270400833398985260'], 'label': '2-637-91.4-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/k/d/459/2'}