-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 2, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '1616888476782506793,1854787975424203039', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.894427190999916, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 359.95406846810107, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [11, [1, 5, 11]]], 'bad_primes': [2, 3, 11], 'central_character': '5645376.1', 'coefficient_field': '1.1.1.1', 'conductor': 5645376, 'conductor_radical': 66, 'degree': 4, 'euler_factors': [[1], [1], [1, -2, 11, -10, 25], [1, 0, 5, 0, 49], [1, 5, 11], [1, 0, 10, 0, 169], [1, 0, -30, 0, 289], [1, 0, 34, 0, 361], [1, 4, 50, 92, 529], [1, 0, 22, 0, 841], [1, 14, 111, 434, 961], [1, 12, 110, 444, 1369], [1, 0, 46, 0, 1681], [1, 0, 82, 0, 1849], [1, 12, 130, 564, 2209], [1, 10, 131, 530, 2809], [1, -8, 134, -472, 3481], [1, 0, 58, 0, 3721], [1, 20, 234, 1340, 4489], [1, -16, 206, -1136, 5041], [1, 0, 145, 0, 5329], [1, 0, -98, 0, 6241], [1, 0, 45, 0, 6889], [1, 12, 214, 1068, 7921], [1, 2, 195, 194, 9409], [1, 0, 121, 0, 10201], [1, -8, 222, -824, 10609], [1, 0, 133, 0, 11449], [1, 0, 118, 0, 11881], [1, -12, 262, -1356, 12769]], 'gamma_factors': [[], [0, 0]], 'index': 0, 'label': '4-2376e2-1.1-c1e2-0-0', 'leading_term': '0.316829861513', '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/2.0.11.1/46656.4/j', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.04296875', 'prec': 34}, 'plot_values': [0.3168298615127931, 0.29709729855771055, 0.2379666086525479, 0.1396551091712244, 0.002578341628612326, -0.17257357054793268, -0.3847362199254341, -0.6323547773299689, -0.9132598814366174, -1.2245452511281, -1.5624575510828649, -1.9223094053382284, -2.2984262804338487, -2.6841371944646597, -3.0718178145309496, -3.4529924712761506, -3.8184989657477577, -4.158716828562655, -4.463856014101085, -4.724299017077683, -4.930985272572007, -5.075822669832327, -5.152107332456908, -5.1549297697529814, -5.081543366711425, -4.9316702185848165, -4.707719759899094, -4.414897658116537, -4.061186130705676, -3.65718219380283, -3.215787239816865, -2.7517495262196654, -2.281070270305126, -1.8202936006729455, -1.3857100331261498, -0.9925117638535366, -0.6539452207996199, -0.38051131249707015, -0.1792660539890859, -0.053273241321868746, -0.0012562691756339668, -0.017487937059625137, -0.09194531775888326, -0.21074189180316427, -0.3568318860870308, -0.5109630559362788, -0.6528351998436002, -0.7624038330284351, -0.8212530809286627, -0.8139503706798926, -0.7292891443910962, -0.5613255894495606, -0.31012191856587906, 0.01787777107682944, 0.40989289409036705, 0.847300951928899, 1.3065789244322201, 1.760656338987924, 2.180611878875363, 2.537614681195884, 2.804985630202921, 2.9602354174495753, 2.9869270132067465, 2.876212019335293, 2.6279039643802617, 2.2509768975882274, 1.7634136291164595, 1.191372679563676, 0.5676935880585486, -0.07018690096958216, -0.682784179788367, -1.231412065086032, -1.6811226805176782, -2.0035156730149826, -2.1791882260254987, -2.1996112991503916, -2.0682499338401485, -1.8007949795555487, -1.42443732150719, -0.9761893072622808, -0.5003360828529855, -0.04517568302118198, 0.3407255984743238, 0.6124831203435792, 0.7327369894107144, 0.6750679400680449, 0.4266839100199036, -0.00987976823860504, -0.6162342039624444, -1.3588831585798562, -2.1912374381319504, -3.056785713379493, -3.8932065963857876, -4.637116884737544, -5.229083159669677, -5.618485586001172, -5.767818747446272, -5.65604674637781, -5.280697470850223, -4.65847944930384, -3.824326560790463, -2.828910982515413, -1.7348013318737303, -0.6115684738829841, 0.4697561696198159, 1.4423962253651044, 2.2492189377771155, 2.847313928831689, 3.211343080626886, 3.3353472982912487, 3.232833279720066, 2.935121226832015, 2.4880980815018443, 1.9476745997253753, 1.3743729944269447, 0.8275615111712826, 0.3598930545895045, 0.012491304912558645, -0.18864058797780717, -0.23463134901752536, -0.13397205716187138, 0.08905484163007857, 0.3975824232020103, 0.7466636953064227, 1.0885941764190812, 1.3784799552342033, 1.5794441457981958, 1.666894614486, 1.631368889702838, 1.4796201470561074, 1.2337967226381095, 0.9287774381364023, 0.6079337832284454, 0.317774642170365, 0.1020685180639296, -0.003884936385149535, 0.021841416905108126, 0.18432635059681934, 0.47021195915946273, 0.8482620668448866, 1.2720892471433927, 1.6848237667093136, 2.0252656576880987, 2.2348724810034177, 2.2648133168423707, 2.082280607084526, 1.675303368219441, 1.0554456238710883, 0.25799009471936296, -0.6605225424778187, -1.62723300299733, -2.5599276673803675, -3.3753272011870075, -3.9978228978713743, -4.367701799815494, -4.4479259705021565, -4.228663310265373, -3.7289956443865804, -2.9955314754571685, -2.0979934247830414, -1.1221956974126153, -0.1611349332325775, 0.6948484359027645, 1.3677512658076512, 1.8003363938465677, 1.9623331109372086, 1.8536690909942577, 1.5043211748493883, 0.9707563074981094, 0.3293302082671263, -0.33262659583883386, -0.9270218349020449, -1.3753301984979145, -1.6178214741711088, -1.6205836968892722, -1.3794832711520495, -0.9205585423769581, -0.296765599339074, 0.4185645006803201, 1.140792604949335, 1.7844781295532945, 2.274048003723962, 2.5533104457575893, 2.592617857809948, 2.3927551413963646, 1.9850216906485485, 1.4274411854194031, 0.7975166739108082, 0.18238930116147595, -0.33239875820043085, -0.674138218676071, -0.7927580889819305, -0.6679298780491777, -0.3125143613137315, 0.2281615684289873, 0.881192819325978, 1.5546162618457298, 2.148560285144706, 2.5676686832373714, 2.7332570011004087, 2.593665234617947, 2.131472138589183, 1.3666112985297205, 0.35493270092636603, -0.8176765809164823, -2.0449349544056163, -3.2124091426296766, -4.210851532108865, -4.9489726174649435, -5.364047237360562, -5.429018530668368, -5.155204022166878, -4.590268552771561, -3.811736837049653, -2.916894818496393, -2.0103973263099064, -1.1911967628770963, -0.5404926121575784, -0.112261284266985, 0.07242284548677033, 0.026576103280714875, -0.20608827496738494, -0.5586081297148672, -0.9511968807625605, -1.3031642613868157, -1.5446537042177089, -1.6265499378143555, -1.5271731726465538, -1.2548339975509883, -0.8459133214945589, -0.3587725076335061, 0.13559987869962153, 0.5648223998843135, 0.8665727077942381, 0.9985500419866504, 0.9454445494603751, 0.7218344620135886, 0.3705203901728091, -0.04352481758742952, -0.44275783196742713, -0.7488414238067188, -0.8948670788885289, -0.8361903208333871, -0.5582090943860871, -0.07982963458623706, 0.5480260312854295, 1.248796075579868, 1.9307347402248738, 2.500014528103304, 2.8746052025259843, 2.9968874689671385, 2.8430826657731707, 2.4279896129231715, 1.804164094414092, 1.0554676465131358, 0.2857387883947695, -0.39591837926567675], 'positive_zeros': ['0.17258259200106663880130073876845', '1.72279183927496192016704996647182', '1.73582051333148490489274132763446', '2.27521607666270957351120023905262', '2.96008069711960973958577277809961', '3.48503979598989868638885321848677', '3.73747142820058336171656741047526', '4.44970129802461299250291539437260', '5.02930381294477970138380086091767', '5.18432945826177342955590271236167', '5.79729187121046804129336776899210', '5.83114431882706306108946061614523', '6.37188903195207275650146805703755', '6.92555186812727586069118504522313', '7.28290021897970859593133073894672'], 'prelabel': '4-2376e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.355738229078537, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1165833442993015881, 'z1': {'__RealLiteral__': 0, 'data': '0.17258259200106663880130073876845', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.72279183927496192016704996647182', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '1.73582051333148490489274132763446', 'prec': 113}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 359.95406846810107, 'bad_primes': [2, 3, 11], 'central_character': '1.1', 'conductor': 5645376, 'conductor_radical': 66, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 2, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -7, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, -5, 0, 0, 0, -10, 0, -10, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0], 'euler11': [1, 5, 11, 0, 0], 'euler13': [1, 0, 10, 0, 169], 'euler17': [1, 0, -30, 0, 289], 'euler19': [1, 0, 34, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 4, 50, 92, 529], 'euler29': [1, 0, 22, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 14, 111, 434, 961], 'euler37': [1, 12, 110, 444, 1369], 'euler41': [1, 0, 46, 0, 1681], 'euler43': [1, 0, 82, 0, 1849], 'euler47': [1, 12, 130, 564, 2209], 'euler5': [1, -2, 11, -10, 25], 'euler53': [1, 10, 131, 530, 2809], 'euler59': [1, -8, 134, -472, 3481], 'euler61': [1, 0, 58, 0, 3721], 'euler67': [1, 20, 234, 1340, 4489], 'euler7': [1, 0, 5, 0, 49], 'euler71': [1, -16, 206, -1136, 5041], 'euler73': [1, 0, 145, 0, 5329], 'euler79': [1, 0, -98, 0, 6241], 'euler83': [1, 0, 45, 0, 6889], 'euler89': [1, 12, 214, 1068, 7921], 'euler97': [1, 2, 195, 194, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, -2, 11, -10, 25], [1, 0, 5, 0, 49], [1, 5, 11, 0, 0], [1, 0, 10, 0, 169], [1, 0, -30, 0, 289], [1, 0, 34, 0, 361], [1, 4, 50, 92, 529], [1, 0, 22, 0, 841], [1, 14, 111, 434, 961], [1, 12, 110, 444, 1369], [1, 0, 46, 0, 1681], [1, 0, 82, 0, 1849], [1, 12, 130, 564, 2209], [1, 10, 131, 530, 2809], [1, -8, 134, -472, 3481], [1, 0, 58, 0, 3721], [1, 20, 234, 1340, 4489], [1, -16, 206, -1136, 5041], [1, 0, 145, 0, 5329], [1, 0, -98, 0, 6241], [1, 0, 45, 0, 6889], [1, 12, 214, 1068, 7921], [1, 2, 195, 194, 9409]], 'index': 0, 'instance_types': ['ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.11.1/46656.4/j', 'ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/46656.4/j'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, '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': '4-2376e2-1.1-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': '4-2376e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.355738229078537, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1165833442993015881, 'z1': {'__RealLiteral__': 0, 'data': '0.17258259200106663880130073876845', 'prec': 113}}
-
lfunc_instances • Show schema
Hide schema
-
id: 9938734
{'Lhash': '1616888476782506793,1854787975424203039', 'Lhash_array': ['1616888476782506793', '1854787975424203039'], 'label': '4-2376e2-1.1-c1e2-0-0', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/46656.4/j'}
-
id: 9938875
{'Lhash': '1616888476782506793,1854787975424203039', 'Lhash_array': ['1616888476782506793', '1854787975424203039'], 'label': '4-2376e2-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.11.1/46656.4/j'}