-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1493182373022578710975923796869', 'a10': [-2.4661037436596525, 0.0], 'a2': [-1.246979603717467, 0.0], 'a3': [0.0, 0.0], 'a4': [0.5549581320873712, 0.0], 'a5': [1.977661652450257, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.5549581320873712, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.9358731840034165, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [431, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 431], 'central_character': '3879.3016', 'coefficient_field': 'CDF', 'conductor': 3879, 'conductor_radical': 1293, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.246979603717467, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.977661652450257, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-0.1494601871728485, 0], [1.0, 0]], [[1.0, 0], [1.9111456115722814, 0], [1.0, 0]], [[1.0, 0], [-1.4661037436596527, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-0.4450418679126288, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0.1494601871728485, 0], [1.0, 0]], [[1.0, 0], [0.7306820487327901, 0], [1.0, 0]], [[1.0, 0], [1.8019377358048383, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.4661037436596527, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.246979603717467, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.4661037436596527, 0], [1.0, 0]], [[1.0, 0], [1.6524775486319898, 0], [1.0, 0]], [[1.0, 0], [1.977661652450257, 0], [1.0, 0]], [[1.0, 0], [1.0, 0], [1.0, 0]], [[1.0, 0], [-1.9111456115722814, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.9111456115722814, 0], [1.0, 0]], [[1.0, 0], [-1.8019377358048383, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0.7306820487327901, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.0, 0], [1.0, 0]], [[1.0, 0], [-1.4661037436596527, 0], [1.0, 0]], [[1.0, 0], [-1.6524775486319898, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0.7306820487327901, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.6524775486319898, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-0.7306820487327901, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.246979603717467, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.8019377358048383, 0], [1.0, 0]], [[1.0, 0], [-1.8019377358048383, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.246979603717467, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0], [1.0, 0]], [[1.0, 0], [-0.7306820487327901, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-3879-431.430-c0-0-5', 'leading_term': '1.0426557322608810379897095700896', '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/3879/1/d/c/3016/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.042655732260881, 1.0451260947014087, 1.0522161151217968, 1.0630020432689358, 1.0760646908171116, 1.0896369111001205, 1.101760164995782, 1.1104266749016547, 1.1136956369633044, 1.1097820484560807, 1.0971223801565604, 1.0744230470859073, 1.0406969945298579, 0.9952921485223778, 0.9379138417066163, 0.8686419898155878, 0.7879428486719937, 0.6966745891750445, 0.5960856155746674, 0.48780445147006396, 0.3738200746971267, 0.2564517579832514, 0.1383077396549761, 0.022232387729265637, -0.08875808465997731, -0.19155085869503724, -0.2830217473445891, -0.3601289984897092, -0.42001375877911684, -0.46010484029596044, -0.47822501602301676, -0.4726957086698047, -0.4424366483823687, -0.38705687522999616, -0.3069333678398646, -0.20327360375296047, -0.07815851083576152, 0.06543744025495668, 0.22365182178377904, 0.3917677626511161, 0.5642769385029288, 0.7349727651605615, 0.8970735982856932, 1.0433747385235086, 1.1664269859766923, 1.2587384132066772, 1.3129949682159776, 1.322294516938412, 1.28038802907182, 1.1819208421879512, 1.0226663461284777, 0.7997440489496481, 0.5118138487066642, 0.15923846755684995, -0.25579357632282534, -0.7291913690468621, -1.2549372752354897, -1.8251194980244798, -2.4300245894578896, -3.058291206344209, -3.6971244612871317, -4.332568153849654, -4.9498300479435615, -5.533653260809354, -6.068724823376604, -6.540110640551557, -6.933704501534413, -7.236677539300723, -7.437913682615143, -7.528416241027794, -7.5016708578403675, -7.353950686926489, -7.08455080752452, -6.695940578062559, -6.193824816484568, -5.587107330318729, -4.887753334464991, -4.11055059911094, -3.272772658464053, -2.3937509637928596, -1.4943663526712283, -0.596473496290923, 0.2777250558706675, 1.1063361187447482, 1.8684433700525904, 2.5447628380342784, 3.1182636402834745, 3.5747315817959495, 3.903254411194117, 4.096609563785408, 4.1515380495438405, 4.068891700506662, 3.8536451701995436, 3.514768742402036, 3.0649629968000944, 2.520261513208203, 1.899512878302096, 1.2237580866613276, 0.5155238001830461, -0.20194434484050297, -0.905481288710621, -1.5728059252938271, -2.1832984154682813, -2.718721843743549, -3.16386010298286, -3.5070465327823817, -3.7405615711971025, -3.8608823898551754, -3.868773006371016, -3.7692095023648515, -3.5711414841677005, -3.2870975460069762, -2.9326489577778716, -2.525751824550498, -2.085993285384183, -1.633771689048683, -1.1894438913266923, -0.7724746939450267, -0.40062387297560537, -0.08920516878331294, 0.14955096121325154, 0.30700301672447167, 0.3784500166636703, 0.36331276031675475, 0.2651357730690125, 0.09140862122926786, -0.14678682665929166, -0.435288876780758, -0.757506678190917, -1.095181146328732, -1.4292229676850576, -1.7405906854902473, -2.0111696563310395, -2.2246122073006385, -2.3671006681750346, -2.4279980758084343, -2.400356137122247, -2.281256300438628, -2.071967256212256, -1.7779105379554598, -1.408434743781796, -0.976407837866021, -0.49764559553286775, 0.009797890873841282, 0.5264450145817946, 1.032276902392485, 1.5076417702801044, 1.934146527249555, 2.295489303481786, 2.5781931752909957, 2.7722059193531643, 2.8713369549426337, 2.8735104366550823, 2.7808223731224695, 2.599399238908182, 2.339065344509684, 2.012835741794874, 1.6362601838029787, 1.226651174213197, 0.802235033613289, 0.38126885466288685, -0.018832010592059904, -0.3823118083110196, -0.6957962741375036, -0.9488822297886558, -1.1345654738464055, -1.2494860643223042, -1.2939797573605072, -1.2719346889929184, -1.1904628192494005, -1.0594056391429534, -0.8907026249920521, -0.6976584099640224, -0.49415020149919325, -0.2938202753883561, -0.10929921106552604, 0.04849618089767389, 0.1709504881576613, 0.2521896178140166, 0.2893481839712347, 0.2826494807569022, 0.235294067401563, 0.15316425466902892, 0.04436275934063122, -0.0813861521730453, -0.21343617752672195, -0.34097581008795136, -0.45379512908496283, -0.5430139208072338, -0.6017241214479738, -0.6255040458999227, -0.6127689988826628, -0.5649322976363855, -0.4863619674880857, -0.3841307822582955, -0.2675702036580538, -0.14765137259950564, -0.0362278604821524, 0.054815321315580444, 0.1144545694316343, 0.13340604468139156, 0.10493200384700614, 0.02551985152160577, -0.10461562671212674, -0.2812474559905673, -0.49609796858117816, -0.7370615655370327, -0.9886883430287408, -1.2329122418770389, -1.4499917842465875, -1.6196171513699862, -1.722125226001712, -1.7397550718410755, -1.657870801363272, -1.4660773551949204, -1.1591576184636119, -0.7377665251324027, -0.2088290894504288, 0.41439585335204754, 1.1126067504892028, 1.8611062704502648, 2.630784675890884, 3.389400158731947, 4.103098091150088, 4.738095195143355, 5.262442319425774, 5.647771672499008, 5.870931600593689, 5.9154146504496214, 5.772492749087592, 5.441986581697671, 4.932614063418904, 4.261884307778561, 3.4555275803918013, 2.54647709492631, 1.5734437501336942, 0.5791485784261728, -0.3917016168853155, -1.2945934807682618, -2.087428033565764, -2.732665027929167, -3.1992738429610097, -3.4643820106039462, -3.5145267675612426, -3.3464349714810084, -2.9672813066248263, -2.3944026327992396, -1.6544760786482384, -0.7821983823092796, 0.1814676722276861, 1.1913887450500622, 2.20058697317459, 3.162670748166504, 4.034236960230411, 4.777111444254841, 5.360302004161602, 5.761553349980251], 'positive_zeros': ['1.17791319844264995944488994242661', '1.85649036724588609712676777828909', '2.71178508903859154680448900015733', '4.14770101540649931468450194611429', '5.01302087650233792161109723965074', '6.06010587904895189451466372441787', '6.36865132478836235443473812951449', '7.26075315580192662716665750044853', '8.173298186009065670378446396134956', '8.920755159919623405935925309041068'], 'prelabel': '2-3879-431.430-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3913565984331322, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.17791319844264995944488994243', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.85649036724588609712676777829', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.71178508903859154680448900016', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.9358731840034165, 'bad_primes': [3, 431], 'central_character': '431.430', 'conductor': 3879, 'conductor_radical': 1293, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3879/1/d/c/3016/2'], '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': '2-3879-431.430-c0-0-5', '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': '2-3879-431.430-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3913565984331322, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.17791319844264995944488994243', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1493182373022578710975923796869', 'Lhash_array': ['1493182373022578710975923796869'], 'label': '2-3879-431.430-c0-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3879/1/d/c/3016/2'}