-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -3, 'A8': 0, 'A9': -2, 'Lhash': '3494228461892713838574995272311', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-1.1338934190276817, 0], 'a8': [0.0, 0], 'a9': [-0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.11425947371704509, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1, 3, 3, -7]]], 'bad_primes': [2, 7], 'central_character': '1792.1', 'coefficient_field': '1.1.1.1', 'conductor': 1792, 'conductor_radical': 14, 'degree': 4, 'euler_factors': [[1], [1, 0, 2, 0, 9], [1, 0, -2, 0, 25], [1, 3, 3, -7], [1, 0, -2, 0, 121], [1, 0, -2, 0, 169], [1, 0, -2, 0, 289], [1, 0, 10, 0, 361], [1, 0, 46, 0, 529], [1, 0, 22, 0, 841], [1, -4, 30, -124, 961], [1, 0, 22, 0, 1369], [1, 12, 118, 492, 1681], [1, 0, -50, 0, 1849], [1, -12, 94, -564, 2209], [1, 0, 22, 0, 2809], [1, 0, -62, 0, 3481], [1, 0, -50, 0, 3721], [1, 0, -74, 0, 4489], [1, 12, 142, 852, 5041], [1, -16, 174, -1168, 5329], [1, -4, 126, -316, 6241], [1, 0, -38, 0, 6889], [1, 0, 142, 0, 7921], [1, 8, 174, 776, 9409], [1, 0, 94, 0, 10201], [1, -16, 270, -1648, 10609], [1, 0, 22, 0, 11449], [1, 0, -74, 0, 11881], [1, 12, 262, 1356, 12769]], 'gamma_factors': [[], [0, 0]], 'index': 0, 'label': '4-1792-1.1-c1e2-0-0', 'leading_term': '0.571547619576', 'load_key': 'Costa', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'origin': 'EllipticCurve/2.2.8.1/28.1/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.5715476195764474, 0.573968583809711, 0.5812348646557488, 0.5933560079777347, 0.6103458644398702, 0.632219511212948, 0.6589889649866363, 0.690657713265005, 0.7272141046952931, 0.7686236572339136, 0.8148203659328569, 0.8656971204849344, 0.9210953766127579, 0.9807942648596235, 1.044499364953216, 1.1118314229133528, 1.1823153403091404, 1.2553698189536866, 1.330298097820422, 1.4062802695845806, 1.482367709008046, 1.5574801810667245, 1.630406219603148, 1.699807373470543, 1.764226902606007, 1.822103467271462, 1.8717902861251352, 1.9115801396080023, 1.9397364618615116, 1.954530595562243, 1.9542850794949775, 1.9374225998025558, 1.9025199659145848, 1.8483661765129256, 1.7740233271366168, 1.6788887891034041, 1.5627567716069417, 1.425877079623212, 1.269008616050294, 1.0934649652498585, 0.9011492557200722, 0.6945754510432307, 0.476873278812535, 0.25177419345392427, 0.023576094269340025, -0.20291500599848844, -0.42246754030550526, -0.6295315760804235, -0.8183701198017004, -0.9832129871910169, -1.118430559826005, -1.2187235644582302, -1.279323817346064, -1.2961997265598555, -1.2662593011628467, -1.1875425426191706, -1.0593944577972283, -0.8826096002280537, -0.6595390774899503, -0.39415140927193626, -0.09203952106989739, 0.23963246660656215, 0.5922471446820844, 0.9559186108419245, 1.3197436520300796, 1.6721158006794472, 2.0010955308930023, 2.2948265662347014, 2.5419850589898956, 2.732245445829878, 2.8567442707319524, 2.9085213776529155, 2.8829167883311095, 2.7779014495562384, 2.59432098184681, 2.3360336665477237, 2.0099271956151354, 1.6258031397550228, 1.1961235593068178, 0.7356205100159052, 0.26077613412686984, -0.2108117368838445, -0.6611563750420658, -1.0726725596222357, -1.4289960158350377, -1.7157928415838732, -1.9215171162352005, -2.038074171119341, -2.0613485808714382, -1.9915599465462543, -1.8334159933799308, -1.5960412592473316, -1.2926704109828608, -0.940107548307084, -0.5579661507730687, -0.16771788360978693, 0.2084084923283123, 0.5486252048363703, 0.8328182015970984, 1.0437457257979863, 1.1681311323146288, 1.197579686307858, 1.1292548505303925, 0.9662597616683493, 0.7176839427217748, 0.3982932234386025, 0.027861482319209895, -0.36983493683056934, -0.768316766769754, -1.1399306182041573, -1.4575236942248044, -1.6961665558508192, -1.8348169807289656, -1.8578153031652855, -1.7561060740903331, -1.528092657372399, -1.1800502138595332, -0.7260476297869947, -0.18735903060943448, 0.40862115986533615, 1.0299112116472633, 1.6418415112735865, 2.20920924231916, 2.6985536193145996, 3.080401548540242, 3.3313279232056927, 3.4356798967214304, 3.3868307358954706, 3.187855749385804, 2.851558998265925, 2.3998229150432557, 1.8623007850827547, 1.2745209558582882, 0.6755180058088075, 0.10514625328585493, -0.3987385139853585, -0.8030252594192735, -1.0818147461493182, -1.2184127425186082, -1.2066828170169357, -1.0516345717991964, -0.7691773273380712, -0.3850315151145892, 0.06714417888565537, 0.5482876477112781, 1.0169505015707587, 1.4325722885924184, 1.7587572140841277, 1.9662888443589797, 2.035629595824997, 1.958684505602703, 1.7396612020713575, 1.394926728336591, 0.9518419301126141, 0.44663927319148067, -0.07850680014438997, -0.578993750070724, -1.011607654186848, -1.33832491871175, -1.5297706359228311, -1.5680227986415647, -1.448496991294534, -1.1807167328141561, -0.7878652732260824, -0.3051182159009049, 0.22313579701936415, 0.746976405628507, 1.2152368793268806, 1.5800307089551093, 1.801122017711467, 1.8497423530425998, 1.7114925520884268, 1.3880388879914625, 0.8974125747054937, 0.27284293679622296, -0.43981322652483074, -1.1858522105598106, -1.906401903112574, -2.543592926878304, -3.045758515588062, -3.3721821750238514, -3.4969399893805826, -3.411456183972565, -3.1255010640389584, -2.6665005599034446, -2.077183900209429, -1.4117557899272997, -0.7309264133085873, -0.0962517727944711, 0.43568439209054677, 0.8186867937676523, 1.0214278108003625, 1.0305335619265563, 0.8519472610900858, 0.5104034757423382, 0.047031542510863666, -0.4847054846778119, -1.024357348577028, -1.5106005312108348, -1.8875115051417515, -2.110360892319856, -2.150324727917846, -1.997607022901451, -1.6626210628601013, -1.1750711385842476, -0.580992615354103, 0.06197565184897096, 0.6906194064732736, 1.2428614668773248, 1.6644549570477007, 1.9149388842690378, 1.9721995147509228, 1.8351152496271403, 1.5239571306140365, 1.0784525308323878, 0.5536717023064412, 0.01413867905364334, -0.47322721304722776, -0.8465889482589564, -1.0562726327219434, -1.0706583015585367, -0.8801983963737395, -0.49907144833732275, 0.035771573400845635, 0.6681267794419787, 1.3282939357718868, 1.9404827581575816, 2.431081816331226, 2.7368862200161534, 2.812362254672553, 2.6351127927740565, 2.2088899158614104, 1.5637627389372188, 0.7533613136439069, -0.15055267686186108, -1.0656283210990758, -1.907768083330505, -2.6002922407757545, -3.0823901124620883, -3.3158846022672708, -3.2895122842906432, -3.0201935177147754, -2.5511064540598745, -1.946747112763719, -1.2855122828039114, -0.6506406363482713, -0.12055338963696086, 0.24027755021903902, 0.3888518586325371, 0.30864723908837816, 0.011491473097403221, -0.46395113175561026, -1.0569257072260325, -1.6920188418347977, -2.2883964674542923, -2.7697350647890016, -3.0736334490849386], 'positive_zeros': ['2.75646022749770999248825075408328', '3.76784593849749485024605323535216', '5.03435508364857530236755864837918', '5.96486295797288004275263855106448', '6.62947344847081355188711857037940', '7.39515097778537885145910103710751', '8.387252653197497723949103538111113', '8.928595102227002440896862141069444', '9.678099476978539892491368486263534', '10.28638500753365554891315811068809', '10.89959748266339602534578702655642', '11.76031412251701343638631858204363', '12.19325986489256484230240936608163', '12.86901379746632539235112958179495', '13.50168732309307683260627329345283'], 'prelabel': '4-1792-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.581397359246617, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 361698798966946105, 'z1': {'__RealLiteral__': 0, 'data': '2.75646022749770999248825075408328', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '3.76784593849749485024605323535216', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '5.03435508364857530236755864837918', 'prec': 113}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.11425947371704509, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 1792, 'conductor_radical': 14, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -3, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 12, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, -12, 0, 16, 0, 0, 0, 0, 0, 4, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0], 'euler11': [1, 0, -2, 0, 121], 'euler13': [1, 0, -2, 0, 169], 'euler17': [1, 0, -2, 0, 289], 'euler19': [1, 0, 10, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, 0, 22, 0, 841], 'euler3': [1, 0, 2, 0, 9], 'euler31': [1, -4, 30, -124, 961], 'euler37': [1, 0, 22, 0, 1369], 'euler41': [1, 12, 118, 492, 1681], 'euler43': [1, 0, -50, 0, 1849], 'euler47': [1, -12, 94, -564, 2209], 'euler5': [1, 0, -2, 0, 25], 'euler53': [1, 0, 22, 0, 2809], 'euler59': [1, 0, -62, 0, 3481], 'euler61': [1, 0, -50, 0, 3721], 'euler67': [1, 0, -74, 0, 4489], 'euler7': [1, 3, 3, -7, 0], 'euler71': [1, 12, 142, 852, 5041], 'euler73': [1, -16, 174, -1168, 5329], 'euler79': [1, -4, 126, -316, 6241], 'euler83': [1, 0, -38, 0, 6889], 'euler89': [1, 0, 142, 0, 7921], 'euler97': [1, 8, 174, 776, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 2, 0, 9], [1, 0, -2, 0, 25], [1, 3, 3, -7, 0], [1, 0, -2, 0, 121], [1, 0, -2, 0, 169], [1, 0, -2, 0, 289], [1, 0, 10, 0, 361], [1, 0, 46, 0, 529], [1, 0, 22, 0, 841], [1, -4, 30, -124, 961], [1, 0, 22, 0, 1369], [1, 12, 118, 492, 1681], [1, 0, -50, 0, 1849], [1, -12, 94, -564, 2209], [1, 0, 22, 0, 2809], [1, 0, -62, 0, 3481], [1, 0, -50, 0, 3721], [1, 0, -74, 0, 4489], [1, 12, 142, 852, 5041], [1, -16, 174, -1168, 5329], [1, -4, 126, -316, 6241], [1, 0, -38, 0, 6889], [1, 0, 142, 0, 7921], [1, 8, 174, 776, 9409]], 'index': 0, 'instance_types': ['G2Q', 'HMF', 'ECNF', 'HMF', 'ECNF'], 'instance_urls': ['Genus2Curve/Q/1792/a', 'ModularForm/GL2/TotallyReal/2.2.8.1/holomorphic/2.2.8.1-28.1-a', 'EllipticCurve/2.2.8.1/28.1/a', 'ModularForm/GL2/TotallyReal/2.2.8.1/holomorphic/2.2.8.1-28.2-a', 'EllipticCurve/2.2.8.1/28.2/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': True, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-1792-1.1-c1e2-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-1792-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.581397359246617, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 361698798966946105, 'z1': {'__RealLiteral__': 0, 'data': '2.75646022749770999248825075408328', 'prec': 113}}
-
lfunc_instances • Show schema
Hide schema
-
id: 9557650
{'Lhash': '3494228461892713838574995272311', 'Lhash_array': ['3494228461892713838574995272311'], 'label': '4-1792-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.8.1/28.2/a'}
-
id: 9557470
{'Lhash': '3494228461892713838574995272311', 'Lhash_array': ['3494228461892713838574995272311'], 'label': '4-1792-1.1-c1e2-0-0', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.8.1/holomorphic/2.2.8.1-28.2-a'}
-
id: 9557047
{'Lhash': '3494228461892713838574995272311', 'Lhash_array': ['3494228461892713838574995272311'], 'label': '4-1792-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.8.1/28.1/a'}
-
id: 9556873
{'Lhash': '3494228461892713838574995272311', 'Lhash_array': ['3494228461892713838574995272311'], 'label': '4-1792-1.1-c1e2-0-0', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.8.1/holomorphic/2.2.8.1-28.1-a'}
-
id: 1222049
{'Lhash': '361698798966946105', 'Lhash_array': ['361698798966946105'], 'label': '4-1792-1.1-c1e2-0-0', 'type': 'G2Q', 'url': 'Genus2Curve/Q/1792/a'}