-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2290532977480021349191974283218', 'a10': [-1.0579139216796287, 0.0], 'a2': [-1.4400800750277762, 0.0], 'a3': [1.0, 0.0], 'a4': [0.07383062249200557, 0.0], 'a5': [0.7346215950243071, 0.0], 'a6': [-1.4400800750277762, 0.0], 'a7': [3.7361752570944553, 0.0], 'a8': [2.7738381416779174, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.978065444458213, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [23, [[1.0, 0], [-1.0, 0]]], [29, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 23, 29], 'central_character': '2001.1', 'coefficient_field': 'CDF', 'conductor': 2001, 'conductor_radical': 2001, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.4400800750277762, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-0.7346215950243071, 0], [5.0, 0]], [[1.0, 0], [-3.7361752570944553, 0], [7.0, 0]], [[1.0, 0], [2.702130209138678, 0], [11.0, 0]], [[1.0, 0], [2.8719318078512797, 0], [13.0, 0]], [[1.0, 0], [2.7511962800975596, 0], [17.0, 0]], [[1.0, 0], [5.544627474610768, 0], [19.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [10.260551694609058, 0], [31.0, 0]], [[1.0, 0], [11.495056602973193, 0], [37.0, 0]], [[1.0, 0], [1.8102773069448126, 0], [41.0, 0]], [[1.0, 0], [-0.18116301651669428, 0], [43.0, 0]], [[1.0, 0], [6.024526857984727, 0], [47.0, 0]], [[1.0, 0], [0.6620808202990796, 0], [53.0, 0]], [[1.0, 0], [0.17437172729850212, 0], [59.0, 0]], [[1.0, 0], [5.378425574121309, 0], [61.0, 0]], [[1.0, 0], [-15.995912247922066, 0], [67.0, 0]], [[1.0, 0], [-12.004679124614986, 0], [71.0, 0]], [[1.0, 0], [-0.9908422461765002, 0], [73.0, 0]], [[1.0, 0], [2.9632327932258105, 0], [79.0, 0]], [[1.0, 0], [-1.0899526222125229, 0], [83.0, 0]], [[1.0, 0], [-5.213374940282599, 0], [89.0, 0]], [[1.0, 0], [3.971223441881686, 0], [97.0, 0]], [[1.0, 0], [-18.485495674556567, 0], [101.0, 0]], [[1.0, 0], [2.249484162795913, 0], [103.0, 0]], [[1.0, 0], [12.923067894309693, 0], [107.0, 0]], [[1.0, 0], [-16.27252500787464, 0], [109.0, 0]], [[1.0, 0], [11.322650846106887, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 91, 'label': '2-2001-1.1-c1-0-91', '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/2001/2/a/i/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.4427185810197608e-60, 0.11846153965198214, 0.23674097433112518, 0.354624594284755, 0.4718373521937654, 0.58801672607316, 0.7026916290026194, 0.8152674617417154, 0.9250180156163361, 1.0310845561144149, 1.1324820858921902, 1.2281125173727394, 1.3167842830432812, 1.397237768090442, 1.46817585116051, 1.5282987692138639, 1.576342467835364, 1.6111195487781707, 1.6315618760174035, 1.636763848214814, 1.626025290529728, 1.5988928657737647, 1.5551988590770867, 1.495096157306247, 1.4190882303639, 1.3280529317975414, 1.2232589757762753, 1.1063740204821686, 0.9794633972338495, 0.8449786719083806, 0.705735410805429, 0.5648797459387896, 0.4258435923106281, 0.29228865800595605, 0.16803970145711694, 0.057007822083491644, -0.03689508747903217, -0.10984925652330438, -0.1582255144208381, -0.17868721456763506, -0.16829320600486153, -0.12459921712913034, -0.0457548331386737, 0.06940686862789763, 0.22129000400142915, 0.4094698263544134, 0.6326427393407099, 0.8885949653133466, 1.1741921405294395, 1.4853916993832654, 1.8172794129825123, 2.164130870197698, 2.5194980428862506, 2.876320375472785, 3.227059099550777, 3.563852716386351, 3.8786908360872405, 4.163602835352544, 4.4108571207725245, 4.6131661865297415, 4.763892158485025, 4.857247144078328, 4.888482480065861, 4.854060905577335, 4.7518058000971655, 4.581021923831832, 4.342582585231836, 4.038978834996486, 3.674327139235961, 3.254333001675757, 2.7862091645168756, 2.278548292292741, 1.741151399590354, 1.18481468366794, 0.6210788246325085, 0.061946173913764765, -0.4804274802504855, -0.9940587502755421, -1.4674713199045148, -1.8900299520662076, -2.252263871865016, -2.5461693873226445, -2.7654817483342096, -2.9059067085757535, -2.9653030488056404, -2.9438084351349145, -2.843902402998143, -2.6704019459206316, -2.430387105917946, -2.1330560574487363, -1.7895113882794087, -1.412481540091264, -1.0159836055247098, -0.6149358099580889, -0.22472995855720235, 0.13922417282131652, 0.4619691501847394, 0.7294705564667879, 0.929073137136823, 1.0499274491503896, 1.0833724701229763, 1.0232605550257328, 0.8662125537942984, 0.6117927962162429, 0.2625959635510152, -0.17575946435650538, -0.694733551671256, -1.2830622741943205, -1.9270459370873976, -2.6109214878304567, -3.3173085340761173, -4.027716098525264, -4.723094731874531, -5.384416659585271, -5.993265244648209, -6.532414275461134, -6.986377483717524, -7.341909286998351, -7.588439034713575, -7.718422988276696, -7.727600834995119, -7.615146643159744, -7.383707713245637, -7.039328647026468, -6.591262006737646, -6.051671022851597, -5.435233778256478, -4.758661995228632, -4.0401508320518635, -3.298778822922667, -2.5538791501068294, -1.8244047264426582, -1.1283100220745093, -0.4819721557806426, 0.10032751391866211, 0.6068421871135088, 1.028702596313556, 1.3601515110515505, 1.5986612410893086, 1.7449301069173548, 1.8027585612202852, 1.778810386818939, 1.6822689725724873, 1.5244028885325056, 1.318058665488235, 1.0771016705058014, 0.8158281234439433, 0.5483725162176478, 0.2881349107514803, 0.04725177839741554, -0.16386777816953507, -0.33692134739182134, -0.4659926115796963, -0.5477196729835053, -0.5813459742372481, -0.5686526298861722, -0.5137762274513965, -0.4229212639487155, -0.30398112785492676, -0.16608569961736536, -0.01909702993918686, 0.12692300076590607, 0.2622477619428451, 0.37799818284068143, 0.4666077319854751, 0.5222176054610742, 0.5409828378115036, 0.5212741689980765, 0.4637653895138285, 0.37140132770337897, 0.24924739208361635, 0.10422737057478121, -0.05523825637021764, -0.21967618035622266, -0.3790647032813065, -0.5233738271130757, -0.6431139132700875, -0.7298649574070809, -0.7767590113106494, -0.7788901345288431, -0.7336294152410424, -0.6408269387985054, -0.5028879186780919, -0.32471630012473235, -0.11352571985926081, 0.12147555679252592, 0.36951252651641725, 0.6187648930247418, 0.8569575249607881, 1.0719912117637875, 1.2525821623626006, 1.3888773640041556, 1.4730132133184854, 1.4995867813199881, 1.466012629615067, 1.3727431264102128, 1.2233365102859546, 1.0243642397955899, 0.7851571123935353, 0.5173978584174982, 0.23457601052142293, -0.04867159465548925, -0.3173047045715988, -0.5566726273003458, -0.7533172792030371, -0.8957454167463851, -0.975129296074138, -0.9858971937977298, -0.9261794291673378, -0.7980816064770554, -0.6077645038774075, -0.365319037820999, -0.08443462252049172, 0.21813044527415212, 0.5232577166574944, 0.8103279436799721, 1.0581940274128068, 1.2462235577220309, 1.3553619248309985, 1.3691642383237128, 1.2747440266103127, 1.0635890008801374, 0.7321990180436543, 0.2825086047541152, -0.2779342770343928, -0.9360505330770125, -1.673578414402774, -2.467680447628038, -3.291788263833148, -4.116652572251463, -4.911554582399327, -5.645626071605493, -6.289218527559856, -6.815257767699347, -7.200519422908884, -7.426762802438182, -7.481665906269493, -7.359512539440165, -7.061593276876495, -6.596294954656695, -5.978867832801349, -5.230874902121443, -4.379343250049654, -3.4556521909983506, -2.4942062538380285, -1.5309524043578098, -0.6018094562652816, 0.25891699383571287, 1.0200589170931131, 1.65497613175467, 2.1427446539706354, 2.469084219835666, 2.6269781039867253, 2.616952901398277, 2.447002304539683, 2.132156300051177, 1.6937147626682343], 'positive_zeros': ['1.80691191805346908965086357817029', '2.15497642808473395639846435874712', '3.81429446373271666524148456147794', '4.80422054537689023147445070983274', '5.31282909916464794060561828894392', '6.79547412556635043790966842538103', '7.57710162090899735183185396188717', '8.131549011821224595789246283597314', '8.717118578015768752766380862944017'], 'prelabel': '2-2001-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.9972572402158724, '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': '1.80691191805346908965086357817', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.15497642808473395639846435875', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.81429446373271666524148456148', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 15.978065444458213, 'bad_primes': [3, 23, 29], 'central_character': '1.1', 'conductor': 2001, 'conductor_radical': 2001, 'degree': 2, 'index': 91, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2001/2/a/i/1/3'], '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': '2-2001-1.1-c1-0-91', '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': '2-2001-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.9972572402158724, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.80691191805346908965086357817', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2290532977480021349191974283218', 'Lhash_array': ['2290532977480021349191974283218'], 'label': '2-2001-1.1-c1-0-91', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2001/2/a/i/1/3'}