-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1233176726016789870724943905072', 'a10': [0, 0], 'a2': [0, 0], 'a3': [1.7148333702053975, 0.24361139634671836], 'a4': [0, 0], 'a5': [-1.3401128136417388, 2.3211434811015743], 'a6': [0, 0], 'a7': [2.48655584085678, 4.3068410522210945], 'a8': [0, 0], 'a9': [2.8813069751400042, 0.8355059036353718], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.198766312851504, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.7148333702053975, -0.24361139634671836]]]], 'bad_primes': [2, 3], 'central_character': '1152.769', 'coefficient_field': 'CDF', 'conductor': 1152, 'conductor_radical': 6, 'conjugate': '2287082808560222144540421587382', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.7148333702053975, -0.24361139634671836]], [[1.0, 0], [1.3401128136417388, -2.3211434811015743], [-2.5, -4.330127018922194]], [[1.0, 0], [-2.48655584085678, -4.3068410522210945], [-3.5, 6.06217782649107]], [[1.0, 0], [1.269471690846883, 2.1987894673171717], [-5.5, 9.526279441628825]], [[1.0, 0], [-2.2148333702053975, 3.836203927494757], [-6.5, -11.258330249197702]], [[1.0, 0], [2.434168300019794, 0], [17.0, 0]], [[1.0, 0], [-4.183609413147111, 0], [19.0, 0]], [[1.0, 0], [0.5706411227948558, -0.988379417568841], [-11.5, -19.91858428704209]], [[1.0, 0], [-3.0043356387718463, -5.203661969342735], [-14.5, 25.11473670974872]], [[1.0, 0], [2.6530294457913866, -4.595181794086982], [-15.5, -26.846787517317598]], [[1.0, 0], [-0.2415557676546851, 0], [37.0, 0]], [[1.0, 0], [3.2110515522965057, -5.561704434300459], [-20.5, -35.50704155516198]], [[1.0, 0], [5.572725981762202, 9.652244537071288], [-21.5, 37.239092362730865]], [[1.0, 0], [2.377279199573809, 4.11756835743851], [-23.5, 40.703193977868615]], [[1.0, 0], [9.383453739655698, 0], [53.0, 0]], [[1.0, 0], [-5.40905697749505, 9.368761506056371], [-29.5, -51.09549882328188]], [[1.0, 0], [-4.160441007221215, -7.206095206400179], [-30.5, 52.827549630850754]], [[1.0, 0], [1.13269100486617, -1.961878369704453], [-33.5, -58.023702053557386]], [[1.0, 0], [4.526386270952377, 0], [71.0, 0]], [[1.0, 0], [3.3472784174142642, 0], [73.0, 0]], [[1.0, 0], [3.141590108795363, 5.4413936849894045], [-39.5, 68.41600689897065]], [[1.0, 0], [0.7382477337885968, 1.2786825834944326], [-41.5, 71.88010851410841]], [[1.0, 0], [-14.882335965910334, 0], [89.0, 0]], [[1.0, 0], [-5.898840815397767, -10.217091998029957], [-48.5, 84.00446416709055]], [[1.0, 0], [5.812106721609934, 10.066864140840986], [-50.5, 87.4685657822283]], [[1.0, 0], [-9.549619481384655, 16.540426134707772], [-51.5, -89.20061658979718]], [[1.0, 0], [-4.996937923791215, 0], [107.0, 0]], [[1.0, 0], [2.1569014325398856, 0], [109.0, 0]], [[1.0, 0], [-10.245142015570593, 17.74510650172688], [-56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 19, 'label': '2-1152-9.4-c1-0-19', 'leading_term': '2.307977460618145868810233265088537162012572967869871787', '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/1152/2/i/h/769/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.307977460618146, 2.2039591702883414, 2.0970859917351863, 1.9868741160446142, 1.8727223681556489, 1.7539806910089673, 1.6300209984657974, 1.5003064835367117, 1.364456048651596, 1.2223012899416403, 1.073934254112713, 0.9197448732377527, 0.7604475068483973, 0.597096372834212, 0.4310898567033547, 0.26416379860404365, 0.09837391759547541, -0.06393241568468458, -0.22015477367525063, -0.3674882370261181, -0.5029813738658225, -0.6236028710661361, -0.726315809873483, -0.8081583037006207, -0.8663289254430606, -0.8982750601876566, -0.9017820421829629, -0.8750606881931127, -0.8168306382835122, -0.7263967743089013, -0.6037159192347846, -0.44945103849933143, -0.2650102772329373, -0.052568380867947705, 0.18493163514659955, 0.44379827842002195, 0.719634024996309, 1.00740099256949, 1.3015097242060398, 1.595930210416581, 1.8843234816108838, 2.160191290794341, 2.4170406055018456, 2.6485588684064165, 2.8487952991563765, 3.0123429274597986, 3.134515600021263, 3.2115139202271914, 3.2405739845345782, 3.2200928935620854, 3.1497253530277214, 3.0304462468011693, 2.864574860128757, 2.6557574453324464, 2.4089060354531076, 2.130092794486221, 1.82640070804496, 1.5057330191038962, 1.1765854462885998, 0.8477868276021234, 0.5282153472899938, 0.22649886288555543, -0.04929101064720125, -0.2919405428098723, -0.49538021280295014, -0.6549445288282044, -0.7675944184655559, -0.8320919658976885, -0.8491184068392842, -0.8213278500033317, -0.7533311433380457, -0.6516065944894432, -0.5243368209108961, -0.3811737626721734, -0.23293674349908725, -0.0912513053777699, 0.0318607453172624, 0.12442717393381357, 0.17499202080477103, 0.1730865151317142, 0.10968646470418726, -0.0223620497243113, -0.22796658409993778, -0.5094787606626532, -0.8664664074309618, -1.295580166352238, -1.7905242518196667, -2.342137408637006, -2.938586049743232, -3.5656671941950546, -4.207214341143677, -4.845594986958705, -5.462284309372719, -6.038495793828336, -6.555846444195734, -6.997031867079265, -7.346485085444523, -7.590992530017249, -7.720241343281261, -7.727273933835658, -7.608828613193534, -7.365549058057089, -7.002050145016803, -6.526833231893441, -5.952050000321961, -5.29312028424604, -4.568215621606802, -3.7976263018841325, -3.003035160144482, -2.206726021345371, -1.4307582850182468, -0.6961414565198452, -0.02204432287230127, 0.5749271558700392, 1.081351342919083, 1.4874835902324586, 1.7875969221122527, 1.9801538572275261, 2.067799715151321, 2.0571756289241554, 1.9585576624190701, 1.7853365345409626, 1.553360094694833, 1.2801674960538045, 0.9841496218014321, 0.6836744263470349, 0.39621821202893215, 0.137544302204324, -0.07903098767373495, -0.2432487239606239, -0.34836313295879445, -0.3914189195518926, -0.3733346986339393, -0.2987865259721406, -0.1758954642340082, -0.01573311753872475, 0.16833139161005337, 0.36141094569572707, 0.5479672402934846, 0.7127203392576283, 0.8415532837140938, 0.9223633017010442, 0.9458129136606422, 0.9059384709510906, 0.8005802543212098, 0.6316069226505205, 0.40491744624053827, 0.13021518822821573, -0.17943906287371336, -0.5082761842104431, -0.8386395505532402, -1.15193706654274, -1.429675586173514, -1.6545230246733234, -1.8113403699264157, -1.8881257425935096, -1.8768157363416216, -1.773895425297809, -1.5807774186954846, -1.303921773734352, -0.9546819013045077, -0.5488761478401846, -0.10609975297046481, 0.3511934414408469, 0.7987966363376875, 1.2119885980069045, 1.5668416350943881, 1.8415298723343716, 2.0175665571438324, 2.0809008871227506, 2.022810478727705, 1.8405349171250873, 1.5376084300112711, 1.1238650135111126, 0.6151065368463412, 0.03244256397671628, -0.5986711300132536, -1.2496511189066004, -1.890202461892459, -2.4898605358393087, -3.0195779652452237, -3.4532715877193483, -3.769244547742755, -3.951403499845029, -3.9902003732712354, -3.8832417880093044, -3.635526352282229, -3.259289832062423, -2.7734595083297147, -2.2027407548302937, -1.576379752322109, -0.9266650957143037, -0.28724672643001037, 0.30863783304898845, 0.8299333035650865, 1.2494346009155142, 1.5452592455150276, 1.7020402457185626, 1.7117701255052442, 1.5742456397298612, 1.2970847936418002, 0.8953118314766654, 0.3905305130052465, -0.19027017593897586, -0.8162121460597233, -1.4542423896734673, -2.0709680925918725, -2.6345077116424336, -3.116251322725092, -3.492428099033093, -3.7453894449757117, -3.864532539084476, -3.8468099330715035, -3.6967952195371665, -3.4263011907051832, -3.0535737886059824, -2.6021108612843378, -2.0991777016250346, -1.574110109848469, -1.0565090774404713, -0.5744382441384216, -0.15273551252033676, 0.18845648459032258, 0.4348496504190079, 0.578787136203081, 0.6195890515986919, 0.5634458383544761, 0.42286668092457913, 0.2157188304867965, -0.036079803388934545, -0.3081297056769138, -0.5752778841248607, -0.8133914690992782, -1.0010593942409092, -1.1211085728569896, -1.1618322437102298, -1.117846245932811, -0.9905128159383733, -0.787899606028863, -0.5242722267741181, -0.21914974056984798, 0.10401785968220646, 0.41946504331724777, 0.7009130335292095, 0.9234389438221066, 1.06528541906748, 1.1094865006926962, 1.0451958480953325, 0.8686216654666585, 0.5834976264099486, 0.2010492104827365, -0.26055175713709405, -0.7772171174445129, -1.3203964568432751, -1.8588650030023062, -2.360730859016103, -2.7955301454423873], 'positive_zeros': ['0.972804908383088517223607528806985', '1.94708046151848859554131640247246', '3.62184788843428865791370583493957', '4.43673910946034153847196959252503', '4.73806358879758609061965837319753', '6.56452863828157092801488720005193', '7.47706456909388674580892688454448', '7.915407429491164271206592118729445', '8.638567720524405498048792835192205', '9.505837074521635118416341371127312'], 'prelabel': '2-1152-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.032946803498456, 'root_angle': -0.4657176788754282, 'root_number': '0.10749299535183595185529852143669626442470221734856575595 - 0.99420584184075793150672802887606436454380107752270088773*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2328588394377141', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.972804908383088517223607528807', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.94708046151848859554131640247', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.62184788843428865791370583494', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 9.198766312851504, 'bad_primes': [2, 3], 'central_character': '9.4', 'conductor': 1152, 'conductor_radical': 6, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1152/2/i/h/769/5'], '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': '2-1152-9.4-c1-0-19', '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': '2-1152-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.032946803498456, 'root_angle': -0.2328588394377141, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.972804908383088517223607528807', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1233176726016789870724943905072', 'Lhash_array': ['1233176726016789870724943905072'], 'label': '2-1152-9.4-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1152/2/i/h/769/5'}