-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2554928352943652557125643262258', 'a10': 1, 'a2': 1, 'a3': -1, 'a4': 1, 'a5': 1, 'a6': -1, 'a7': -1, 'a8': 1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.21958860555852106, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [5, [1, -1]], [11, [1, -1]]], 'bad_primes': [2, 5, 11], 'central_character': '440.109', 'coefficient_field': '1.1.1.1', 'conductor': 440, 'conductor_radical': 110, 'degree': 2, 'euler_factors': [[1, -1], [1, 1, 1], [1, -1], [1, 1, 1], [1, -1], [1, 0, -1], [1, 1, 1], [1, 1, 1], [1, 0, -1], [1, 1, 1], [1, 1, 1], [1, 1, 1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 1, 1], [1, 0, -1], [1, 1, 1], [1, -2, 1], [1, 1, 1], [1, -2, 1], [1, 0, -1], [1, 0, -1], [1, 1, 1], [1, 0, -1], [1, -2, 1], [1, 0, -1], [1, 0, -1], [1, -2, 1], [1, 0, -1]], 'euler_factors_factorization': [[[[1, -1], 1]], [[[1, 1, 1], 1]], [[[1, -1], 1]], [[[1, 1, 1], 1]], [[[1, -1], 1]], [[[1, -1], 1], [[1, 1], 1]], [[[1, 1, 1], 1]], [[[1, 1, 1], 1]], [[[1, -1], 1], [[1, 1], 1]], [[[1, 1, 1], 1]], [[[1, 1, 1], 1]], [[[1, 1, 1], 1]], [[[1, -1], 1], [[1, 1], 1]], [[[1, -1], 1], [[1, 1], 1]], [[[1, -1], 1], [[1, 1], 1]], [[[1, 1, 1], 1]], [[[1, -1], 1], [[1, 1], 1]], [[[1, 1, 1], 1]], [[[1, -1], 2]], [[[1, 1, 1], 1]], [[[1, -1], 2]], [[[1, -1], 1], [[1, 1], 1]], [[[1, -1], 1], [[1, 1], 1]], [[[1, 1, 1], 1]], [[[1, -1], 1], [[1, 1], 1]], [[[1, -1], 2]], [[[1, -1], 1], [[1, 1], 1]], [[[1, -1], 1], [[1, 1], 1]], [[[1, -1], 2]], [[[1, -1], 1], [[1, 1], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-440-440.109-c0-0-3', 'leading_term': '1.203590666580723529875970597158000000000000000000000000000000000000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/440/1/o/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [1.2035906665807234, 1.2145517476643877, 1.2466304748633765, 1.2975976825316624, 1.3642497710758628, 1.4429080091760722, 1.5297992339769297, 1.6212687087729334, 1.7138587927037212, 1.8043105385148748, 1.889534907558393, 1.966581987303438, 2.032622042919334, 2.084943372231195, 2.1209673137338565, 2.1382786220280168, 2.1346685510988896, 2.108187680171993, 2.057205432865964, 1.9804732242919083, 1.8771881669296522, 1.747054265377567, 1.5903380436164896, 1.4079155949726114, 1.2013081445497893, 0.9727033848235986, 0.7249601022883289, 0.4615939671650474, 0.1867428149230917, -0.09488969193916216, -0.3781124761473428, -0.6573472426562589, -0.9267493583570097, -1.1803474532473537, -1.4121989041985643, -1.6165574988682483, -1.7880487637880624, -1.9218477155208373, -2.0138531961855017, -2.060852522887533, -2.0606699502659724, -2.012292447438025, -1.91596654946462, -1.773260574989958, -1.5870873116814306, -1.3616833536941253, -1.1025426121758808, -0.8163030792166214, -0.5105876628698603, -0.19380176864848833, 0.12510778728642213, 0.43692606390541316, 0.7324672366153739, 1.002885974188347, 1.2399918397786838, 1.436554680236034, 1.5865884846036906, 1.6856012104804294, 1.7307986383933014, 1.721231440689722, 1.6578763394554703, 1.5436444476763433, 1.3833125815878653, 1.1833764146018133, 0.9518277030315581, 0.69786131673088, 0.43152130086585944, 0.16329851284316432, -0.09630465020604795, -0.3372244617709469, -0.5502812591584167, -0.7275992918416312, -0.8629802443477963, -0.9522105925487311, -0.9932849131973409, -0.9865302294848316, -0.9346203689052438, -0.842474009880271, -0.7170354258920382, -0.5669426799437993, -0.4020939194453004, -0.23312818557989146, -0.07084248001767035, 0.0744285771417693, 0.1934405987315925, 0.2786426079362256, 0.32472256562290563, 0.3290631164958021, 0.29207797837732385, 0.21740365276257856, 0.11192698504780377, -0.014363644094243257, -0.14870734055457463, -0.2760746423014987, -0.3798316328476127, -0.4425401439190058, -0.44686128987376517, -0.37652204371657405, -0.21729865281604127, 0.04203317784797694, 0.40883289662883365, 0.8858649470693271, 1.4707504295691398, 2.155640632952087, 2.9271434358951147, 3.7665223442757187, 4.6501749799343965, 5.5503837591529415, 6.43631698348378, 7.2752443657913926, 8.033917913222725, 8.680057855515932, 9.18387465340346, 9.519552658896687, 9.666619196809519, 9.611124988831449, 9.346568038745803, 8.874503211204688, 8.204793413068254, 7.355474954486505, 6.352228558521492, 5.227467671291848, 4.019076148321174, 2.768846940834559, 1.5206909577936263, 0.31869977533812727, -0.794843630525115, -1.7814061901434106, -2.607997640406465, -3.248719555484134, -3.68598544281438, -3.9113422661312955, -3.9258435187660483, -3.7399470920995093, -3.372936457840375, -2.851889728718965, -2.210246503464352, -1.4860455496482279, -0.7199259201679505, 0.047001210850815496, 0.7752938684283157, 1.4292153236963185, 1.9785509759449733, 2.400103466404474, 2.678780952135562, 2.8082163410094267, 2.790882245539632, 2.6376959097376305, 2.3671386538131496, 2.003943623304544, 1.577431994454115, 1.1195995806046533, 0.6630715534791514, 0.23905163144132358, -0.12460708637970797, -0.40508964324574864, -0.5859599861166233, -0.6580716011252479, -0.6199920071908616, -0.47791635252632103, -0.2450785567263082, 0.05929857252472408, 0.4114422277678758, 0.7847593514981639, 1.151739268718497, 1.4858991145907738, 1.7636385331323123, 1.9658757379797622, 2.0793514616132462, 2.0975097337451176, 2.020893412831165, 1.857026050602764, 1.6197877344762965, 1.3283285438174184, 1.005596639502266, 0.6765863742559596, 0.36643305572277557, 0.09849346430943755, -0.10744613997141489, -0.23670037730769414, -0.280836800757423, -0.2383592569049153, -0.11486555033498413, 0.07733940389715666, 0.3201534509895048, 0.5910490943520613, 0.8648106445747056, 1.1155105203806666, 1.3185780624478889, 1.4528042002723947, 1.5021268135640875, 1.4570548258743645, 1.3156132652113042, 1.0837251895596887, 0.7749872188410601, 0.4098405511991974, 0.014185479515415413, -0.3824688952384005, -0.7491902050922898, -1.0559850647302487, -1.2761617835708217, -1.388512545590824, -1.379142983267445, -1.2427993606025778, -0.9835779061172919, -0.6149449118420016, -0.15904693837971826, 0.3546558606591606, 0.8913476927029297, 1.4132733195421672, 1.8824409545546654, 2.263413983127387, 2.5259817962205497, 2.647504025144953, 2.614742415335933, 2.4250293691717073, 2.086669529309615, 1.6185273295625422, 1.0488150619525205, 0.41315803470657664, -0.24792899915702596, -0.891971396063344, -1.47765192232414, -1.9678782774894308, -2.3325621743617937, -2.5508888762241524, -2.612891474320706, -2.520195060035608, -2.285858688831912, -1.9333129869709798, -1.4944630546708244, -1.0070943111235289, -0.5117775933473002, -0.048514237267844325, 0.34661188911601976, 0.6445029456060356, 0.8255800813518006, 0.8815618954798475, 0.8163253776556482, 0.6457567952592735, 0.39657980390871395, 0.10423101606994324, -0.19006723407022555, -0.4428176508403169, -0.6120692924855856, -0.661243400138486, -0.5626484842450347, -0.30038545410051926, 0.12761572987536982, 0.7086236695172163, 1.4153128944053204, 2.207174604363153, 3.033058099413235, 3.834677095947508, 4.550832816036802, 5.122041144371256, 5.495209935864666], 'positive_zeros': ['2.01548309327795849820138984267300', '3.48796811994734313649172580571798', '4.75471478260800469118493250091754', '5.79859937462210122165599987861167', '6.39079666766011395590792057464127', '6.95124049271711626634931610215915', '8.808518338963401595855599801284385', '9.769061055061837628316273718683250', '10.80237501820045346716064373015779', '11.30760242304718401420675634499037'], 'prelabel': '2-440-440.109-c0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.4686028228238932, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c0-0', 'trace_hash': 2101339153026504295, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.01548309327795849820138984267', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.48796811994734313649172580572', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.75471478260800469118493250092', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.21958860555852106, 'bad_primes': [2, 5, 11], 'central_character': '440.109', 'conductor': 440, 'conductor_radical': 110, 'degree': 2, 'dirichlet_coefficients': [1, 1, -1, 1, 1, -1, -1, 1, 0, 1, 1, -1, 0, -1, -1, 1, -1, 0, -1, 1, 1, 1, 0, -1, 1, 0, 1, -1, -1, -1, -1, 1, -1, -1, -1, 0, -1, -1, 0, 1, 0, 1, 0, 1, 0, 0, 0, -1, 0, 1, 1, 0, -1, 1, 1, -1, 1, -1, 0, -1, -1, -1, 0, 1, 0, -1, 2, -1, 0, -1, -1, 0, 2, -1, -1, -1, -1, 0, 0, 1, -1, 0, 0, 1, -1, 0, 1, 1, -1, 0, 0, 0, 1, 0, -1, -1, 0, 0, 0, 1], 'euler11': [1, -1, 0], 'euler13': [1, 0, -1], 'euler17': [1, 1, 1], 'euler19': [1, 1, 1], 'euler2': [1, -1, 0], 'euler23': [1, 0, -1], 'euler29': [1, 1, 1], 'euler3': [1, 1, 1], 'euler31': [1, 1, 1], 'euler37': [1, 1, 1], 'euler41': [1, 0, -1], 'euler43': [1, 0, -1], 'euler47': [1, 0, -1], 'euler5': [1, -1, 0], 'euler53': [1, 1, 1], 'euler59': [1, 0, -1], 'euler61': [1, 1, 1], 'euler67': [1, -2, 1], 'euler7': [1, 1, 1], 'euler71': [1, 1, 1], 'euler73': [1, -2, 1], 'euler79': [1, 0, -1], 'euler83': [1, 0, -1], 'euler89': [1, 1, 1], 'euler97': [1, 0, -1], 'euler_factors': [[1, -1, 0], [1, 1, 1], [1, -1, 0], [1, 1, 1], [1, -1, 0], [1, 0, -1], [1, 1, 1], [1, 1, 1], [1, 0, -1], [1, 1, 1], [1, 1, 1], [1, 1, 1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 1, 1], [1, 0, -1], [1, 1, 1], [1, -2, 1], [1, 1, 1], [1, -2, 1], [1, 0, -1], [1, 0, -1], [1, 1, 1], [1, 0, -1]], 'index': 3, 'instance_types': ['CMF', 'CMF', 'Artin', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/440/1/o/c/109/1', 'ModularForm/GL2/Q/holomorphic/440/1/o/c', 'ArtinRepresentation/2.440.3t2.a.a', 'ArtinRepresentation/2.440.3t2.a'], 'is_instance_Artin': True, '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': '2-440-440.109-c0-0-3', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-440-440.109-c0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.4686028228238932, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0-0', 'trace_hash': 2101339153026504295, 'z1': {'__RealLiteral__': 0, 'data': '2.01548309327795849820138984267', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 24603205
{'Lhash': '2554928352943652557125643262258', 'Lhash_array': ['2554928352943652557125643262258'], 'factors': ['2-440-440.109-c0-0-3'], 'label': '2-440-440.109-c0-0-3', 'type': 'Artin', 'url': 'ArtinRepresentation/2.440.3t2.a'}
-
id: 24596771
{'Lhash': '2554928352943652557125643262258', 'Lhash_array': ['2554928352943652557125643262258'], 'factors': ['2-440-440.109-c0-0-3'], 'label': '2-440-440.109-c0-0-3', 'type': 'Artin', 'url': 'ArtinRepresentation/2.440.3t2.a.a'}
-
id: 19803632
{'Lhash': '2554928352943652557125643262258', 'Lhash_array': ['2554928352943652557125643262258'], 'factors': ['2-440-440.109-c0-0-3'], 'label': '2-440-440.109-c0-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/440/1/o/c'}
-
id: 24545921
{'Lhash': '2554928352943652557125643262258', 'Lhash_array': ['2554928352943652557125643262258'], 'factors': ['2-440-440.109-c0-0-3'], 'label': '2-440-440.109-c0-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/440/1/o/c/109/1'}