-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2002459796623470195651460884397', 'a10': [3.6081077531127574, 0.0], 'a2': [1.8921396725731083, 0.0], 'a3': [0.11125089363239621, 0.0], 'a4': [1.5801925405250694, 0.0], 'a5': [1.9068929241392183, 0.0], 'a6': [0.21050222945106786, 0.0], 'a7': [-0.9772247776509074, 0.0], 'a8': [-0.7943343489146437, 0.0], 'a9': [-2.9876232386659933, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 73.86960690988651, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [-1.0, 0]]], [29, [[1.0, 0], [0, 0]]]], 'bad_primes': [11, 29], 'central_character': '9251.1', 'coefficient_field': 'CDF', 'conductor': 9251, 'conductor_radical': 319, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.8921396725731083, 0], [2.0, 0]], [[1.0, 0], [-0.11125089363239621, 0], [3.0, 0]], [[1.0, 0], [-1.9068929241392183, 0], [5.0, 0]], [[1.0, 0], [0.9772247776509074, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-3.2214964816121934, 0], [13.0, 0]], [[1.0, 0], [0.04062503975118415, 0], [17.0, 0]], [[1.0, 0], [5.586752305449246, 0], [19.0, 0]], [[1.0, 0], [-1.3573365325497135, 0], [23.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.26627738987140803, 0], [31.0, 0]], [[1.0, 0], [1.3952197831625948, 0], [37.0, 0]], [[1.0, 0], [-2.4630004306336244, 0], [41.0, 0]], [[1.0, 0], [-4.361736251153004, 0], [43.0, 0]], [[1.0, 0], [-3.0677626292830165, 0], [47.0, 0]], [[1.0, 0], [-0.521285890917411, 0], [53.0, 0]], [[1.0, 0], [8.363495360389152, 0], [59.0, 0]], [[1.0, 0], [-4.941477874952373, 0], [61.0, 0]], [[1.0, 0], [12.300805299825369, 0], [67.0, 0]], [[1.0, 0], [6.286022123302795, 0], [71.0, 0]], [[1.0, 0], [8.731916423817847, 0], [73.0, 0]], [[1.0, 0], [17.091429938535025, 0], [79.0, 0]], [[1.0, 0], [-9.008079196929378, 0], [83.0, 0]], [[1.0, 0], [8.834591105573338, 0], [89.0, 0]], [[1.0, 0], [-2.6555722485977924, 0], [97.0, 0]], [[1.0, 0], [11.627891820199993, 0], [101.0, 0]], [[1.0, 0], [1.1424769041774945, 0], [103.0, 0]], [[1.0, 0], [7.076141492552454, 0], [107.0, 0]], [[1.0, 0], [17.26046353120302, 0], [109.0, 0]], [[1.0, 0], [-3.061010491291407, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 614, 'label': '2-9251-1.1-c1-0-614', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/9251/2/a/ba/1/33', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-2.0868978968921055e-60, 0.4030849012469557, 0.8045699301068312, 1.202779968221482, 1.5958946937605707, 1.9818888121472058, 2.3584866476204254, 2.723134292176355, 3.0729913935567694, 3.404943520293202, 3.7156349619376376, 4.001520871211643, 4.258936866106968, 4.484183591578367, 4.6736232810361855, 4.823785035768513, 4.931475331467356, 4.993890143763675, 5.008725043426552, 4.974279637621179, 4.889552823312931, 4.7543254739997405, 4.56922740552704, 4.33578576564031, 4.056452369165314, 3.734607958134615, 3.37454190256481, 2.9814064679866097, 2.5611454512752414, 2.1203977137973458, 1.6663769034927116, 1.2067294348887996, 0.749373564961907, 0.3023231378207113, -0.12649975427474136, -0.5294583590099892, -0.8993957933804, -1.2298248713069881, -1.5151074109160785, -1.7506172043796075, -1.9328810242252092, -2.059692427175864, -2.130193699907586, -2.144922063580311, -2.1058172012087004, -2.0161882721413926, -1.8806398022709239, -1.7049571517542759, -1.4959536230007051, -1.2612826350138608, -1.009219707332168, -0.7484202178485808, -0.4876599741591967, -0.23556652057041377, -0.00034974957259315497, 0.21045923919871934, 0.3902520163272165, 0.5335606668673207, 0.6362414065007933, 0.6956166725002028, 0.7105695967703032, 0.6815862493802779, 0.6107427568282987, 0.5016362962633104, 0.3592609815035167, 0.18983171737498925, 0.000561128454538958, -0.20060341329630368, -0.40527391007359925, -0.6049367968348804, -0.791277601437432, -0.9565031436230469, -1.0936489257146729, -1.1968595569747593, -1.2616307292418298, -1.2850024175037935, -1.2656945892565128, -1.2041787246327655, -1.1026808100955054, -0.9651140893906998, -0.7969426391742159, -0.6049796746812035, -0.3971272671654702, -0.1820667511208608, 0.031088600662621715, 0.23316516109191607, 0.4153099248369169, 0.5693651957626185, 0.6882211287680757, 0.7661307625193909, 0.798973347186204, 0.7844535883046324, 0.7222268399610228, 0.613943204760525, 0.46320682548292663, 0.2754502523923115, 0.05772749165876195, -0.1815669766807319, -0.4330424443190294, -0.6867056066420367, -0.932387115634722, -1.1601826586983799, -1.3608890095921475, -1.5264151914350745, -1.6501494837832325, -1.7272645026183742, -1.7549449484741861, -1.7325257769052163, -1.661532380003057, -1.545618724200385, -1.3904040838445297, -1.2032138340797496, -0.9927344977590388, -0.7685976517894815, -0.5409111665245145, -0.3197593720348431, -0.11469593879565791, 0.06574561426076056, 0.21449891086179892, 0.32634558334631397, 0.3982088363140424, 0.42934210620827906, 0.42139979117037146, 0.3783824209102963, 0.30645462200306, 0.21364054226459422, 0.1094077336434328, 0.0041565471287728925, -0.0913624435040849, -0.16667589339774683, -0.21222948687166043, -0.2200114944844392, -0.1841249578264457, -0.10127645649367811, 0.028847866164826094, 0.20334404320944294, 0.4160090819199211, 0.6574291630928821, 0.9152417116152702, 1.1745673550681874, 1.418599146094294, 1.6293280126937884, 1.7883756429150954, 1.8778993172836924, 1.8815279498404902, 1.78528510815576, 1.5784533024163394, 1.2543345234285137, 0.8108649287054897, 0.25104667685675536, -0.41683296419467636, -1.179216223928759, -2.017533855118901, -2.9087080452321734, -3.825886998963393, -4.73938740701952, -5.6178101256377655, -6.42928473923255, -7.142790784464968, -7.729497730737186, -8.164062700704848, -8.425824622680869, -8.499836152661464, -8.377680264346258, -8.0580267133832, -7.546894327859773, -6.857597820087654, -6.010372000204617, -5.031681254892575, -3.9532372282063406, -2.8107620718029196, -1.6425476923622047, -0.4878724329494351, 0.6146550188953248, 1.6287494886145952, 2.522024202823809, 3.267411917601356, 3.8443631174388133, 4.239761235963526, 4.448507111855846, 4.47373977266962, 4.326677465274471, 4.026080838478454, 3.597358466182306, 3.0713525761002125, 2.482859025341068, 1.868949399229506, 1.267173860827154, 0.7137304413084425, 0.2416894041926912, -0.12064009265164491, -0.35111959024135914, -0.4348956684444558, -0.36516120112369355, -0.14352248727170044, 0.22004966860953823, 0.7076863513894759, 1.2944849577728428, 1.9497320149174628, 2.638426311032756, 3.323028504135064, 3.9653511779696564, 4.528495349253996, 4.978736169208352, 5.287262239022089, 5.4316795538227165, 5.39720232587144, 5.177468290854173, 4.774934823277677, 4.200833342299013, 3.474682000823106, 2.6233793553205054, 1.6799234230810842, 0.6818200968122299, -0.3307387471778171, -1.3168348345436454, -2.2368206581032557, -3.054251819494555, -3.7376552302272383, -4.2620421923229275, -4.610088559366432, -4.772921530105277, -4.75047324467208, -4.551384149391324, -4.192462854244808, -3.6977326499722465, -3.097116709917027, -2.424833083433937, -1.7175858457368742, -1.012649359974726, -0.34594793986389505, 0.24976702856872085, 0.7465462370984769, 1.1225926462220817, 1.3632631674840832, 1.4616717467526645, 1.4188659133405508, 1.2435724759575222, 0.9515318018960396, 0.5644626780068704, 0.10871985300025161, -0.38627713008995623, -0.8897532124792331, -1.3713278104267093, -1.8027068831698945, -2.159222824594521, -2.421137655054469, -2.574639488444332, -2.6124806611358506, -2.534227150070027, -2.3461117287667452, -2.0605063721337826, -1.6950513706728862, -1.2714981660887765, -0.8143389311770621, -0.349307457007796, 0.09815768228089412], 'positive_zeros': ['1.57966224783307389769829445024239', '2.53132313107242513295743726630326', '3.09388378474759386419775619518810', '3.93055793226906627881615674524777', '4.51163372774824573762817108192612', '5.46641320902968966428662808941456', '5.95503567743707208014316186297917', '6.27215690553564329276071191634808', '7.00285560980507782326564633965796'], 'prelabel': '2-9251-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.594742981025465, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.57966224783307389769829445024', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.53132313107242513295743726630', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.09388378474759386419775619519', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 73.86960690988651, 'bad_primes': [11, 29], 'central_character': '1.1', 'conductor': 9251, 'conductor_radical': 319, 'degree': 2, 'index': 614, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9251/2/a/ba/1/33'], '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': '2-9251-1.1-c1-0-614', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-9251-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.594742981025465, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.57966224783307389769829445024', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2002459796623470195651460884397', 'Lhash_array': ['2002459796623470195651460884397'], 'label': '2-9251-1.1-c1-0-614', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9251/2/a/ba/1/33'}