-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': 0, 'A4': -2, 'A5': 0, 'A6': 0, 'A7': -2, 'A8': 0, 'A9': 0, 'Lhash': '1983314035537852959', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [-1.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 3020.141830449879, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]], [41, [1]]], 'bad_primes': [3, 5, 41], 'central_character': '378225.1', 'coefficient_field': '1.1.1.1', 'conductor': 378225, 'conductor_radical': 615, 'degree': 2, 'euler_factors': [[1, 0, 2], [1], [1], [1, 2, 7], [1, 0, 11], [1, 2, 13], [1, 7, 17], [1, 6, 19], [1, 0, 23], [1, 7, 29], [1, 0, 31], [1, -3, 37], [1], [1, 5, 43], [1, 0, 47], [1, 7, 53], [1, -14, 59], [1, -1, 61], [1, 2, 67], [1, -7, 71], [1, -3, 73], [1, 10, 79], [1, 14, 83], [1, 7, 89], [1, -12, 97]], 'gamma_factors': [[], [0]], 'index': 16, 'label': '2-615e2-1.1-c1-0-16', 'leading_term': '2.49780253009', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'EllipticCurve/Q/378225/bd', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.3630620846388532, -0.5522044460884404, -2.631981938570137, -3.871396550885957, -2.246521265554455, 1.296283359103911, 3.05449248982736, 1.141848208348063, -1.431984336688535, -0.6462073754516005, 2.408065533901827, 2.869136507362879, -0.2661710968361364, -2.443794310792547, -1.078843197797765, 0.4400015877116182, -0.6260648687007225, -1.390044189450949, 0.4248546533158062, 1.263210734151658, -1.300122268569611, -2.750310452503838, 0.1648876292527669, 2.49401844269867, 0.2679994590670763, -1.631866846012143, 0.4943290805982042, 1.121702867760009, -3.063686181719104, -5.173765286047896, -1.242431087498808, 1.668852426844885, -0.662924167795352, -2.26035876667353, -0.3169603591425965, 0.1764981452392545, -1.098120196013808, 0.3327082351221698, 2.183452363139596, 0.62646275089213, 0.3992479594291482, 4.019294770632825, 4.072685094911847, -0.7263409654602522, -1.148829959054028, 2.445281868273859, -0.05335105550486186, -6.277441229727085, -5.607598737335007, -0.6609402657086728, 0.3082387192936841, -0.3124891374165962, 0.2296721361136982, -1.826689243714711, -3.931017778165779, -0.8676840048827177, 1.572020274947146, -1.091770661914405, -1.632586178518586, 0.9548564246374128, -1.017716022693556, -3.819108127224929, -0.3749707620618767, 1.331354877714387, -3.801097582964322, -5.279349394368692, -0.6404082900853526, 0.6976054902556718, -0.007533215556296589, 2.495220667158193, 2.443227617520664, -1.144015032585677, -0.6503687954727211, 1.067751278429355, -1.407268122502764, -1.804822716434001, 1.051945678749068, 0.2654958204430098, -0.4090558470710777, 2.284520800666623, -0.7458164921339155, -7.120401731851684, -4.03554728534488, 1.94778032615356, -0.7523977521627441, -3.463063614486961, -0.1189020304361923, 0.9608887257119064, -0.08793954209838398, 1.104078129083528, 0.0667714503835799, -1.39870862000623, 1.789644790440888, 2.442291704818364, -1.064547782423003, -0.03715838313518763, 0.9083706387075554, -3.353925766552161, -1.447084035352932, 5.993181219746364, 4.705273431771517, -0.2585008622602794, 0.7606019917600073, 0.01352812406860956, -3.431379661368527, -1.784464285284825, 0.05238121766611781, -0.4425247465751333, 2.505813321338673, 3.318971459018354, -1.01547717020928, -0.7761607208469739, 1.701636097055662, -0.2244626734613793, 1.045535025395327, 4.176465986056326, 0.4213892410260313, -1.134407907710833, 3.38103083258904, 1.819768902039022], 'positive_zeros': ['0.4012425844559446', '1.409043392901820', '2.092310644711255', '2.555811890168406', '3.231520406607339', '3.881172905158931', '4.153785583188022', '4.703287493852727', '5.146672188946981', '5.739390622617197', '6.270297290339822', '6.706103685889185', '7.088059176283905', '7.815984370260016', '8.200065770026286', '8.792068765290938', '9.034074733815548', '9.468406541593388', '10.09488787878044', '10.19118311495740', '10.95916062971060', '11.32620152899394', '11.74787003172042', '12.55635611751393', '12.82436823582937', '13.11737981540045', '13.32308161121569', '14.05074782374666', '14.41820314291767', '14.89120471259278', '15.18532397004645', '15.77011569654536', '16.08541330488387', '16.79254400991023', '17.13749671553231', '17.25185288649471', '17.91096405186019', '18.30891044313208', '18.63738929188742', '19.14638555002347', '19.52936874282518', '19.79483777856229'], 'prelabel': '2-615e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.955817075627934, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1983314035537852959, 'z1': {'__RealLiteral__': 0, 'data': '0.4012425844559446', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.409043392901820', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.092310644711255', 'prec': 57}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3020.141830449879, 'bad_primes': [3, 5, 41], 'central_character': '1.1', 'conductor': 378225, 'conductor_radical': 615, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 4, -7, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 4, -7, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, -3, 0, 0, 4, -7, 0, 0, 0, 0, 0, 14, 0, 1, 0, 0, -8, 0, 0, -2, 14, 0, 0, 7, 0, 3, 0, 0, 12, 0, 0, -10, 0, 0, 0, -14, 0, 0, 0, 0, 0, -7, 0, 4, 0, 0, 0, 0, 0, 12, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 2, 13], 'euler17': [1, 7, 17], 'euler19': [1, 6, 19], 'euler2': [1, 0, 2], 'euler23': [1, 0, 23], 'euler29': [1, 7, 29], 'euler3': [1, 0, 0], 'euler31': [1, 0, 31], 'euler37': [1, -3, 37], 'euler41': [1, 0, 0], 'euler43': [1, 5, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, 7, 53], 'euler59': [1, -14, 59], 'euler61': [1, -1, 61], 'euler67': [1, 2, 67], 'euler7': [1, 2, 7], 'euler71': [1, -7, 71], 'euler73': [1, -3, 73], 'euler79': [1, 10, 79], 'euler83': [1, 14, 83], 'euler89': [1, 7, 89], 'euler97': [1, -12, 97], 'euler_factors': [[1, 0, 2], [1, 0, 0], [1, 0, 0], [1, 2, 7], [1, 0, 11], [1, 2, 13], [1, 7, 17], [1, 6, 19], [1, 0, 23], [1, 7, 29], [1, 0, 31], [1, -3, 37], [1, 0, 0], [1, 5, 43], [1, 0, 47], [1, 7, 53], [1, -14, 59], [1, -1, 61], [1, 2, 67], [1, -7, 71], [1, -3, 73], [1, 10, 79], [1, 14, 83], [1, 7, 89], [1, -12, 97]], 'index': 16, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/378225/bd'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-615e2-1.1-c1-0-16', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-615e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.955817075627934, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1983314035537852959, 'z1': {'__RealLiteral__': 0, 'data': '0.4012425844559446', 'prec': 60}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1983314035537852959', 'Lhash_array': ['1983314035537852959'], 'factors': ['2-615e2-1.1-c1-0-16'], 'label': '2-615e2-1.1-c1-0-16', 'type': 'ECQ', 'url': 'EllipticCurve/Q/378225/bd'}