-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1778381282185764823369080654483', 'a10': [-1.7915787619285775, 1.7856845128927619], 'a2': [-0.3682757009993502, 1.3654204510162564], 'a3': [-1.2660963944586847, -1.1819475114990168], 'a4': [-1.7287460161068744, -1.0057023475137215], 'a5': [1.549002538705787, 0.8943170326971999], 'a6': [2.0801278414305515, -1.2934713616100957], 'a7': [2.635730879701317, 0.2300494072779199], 'a8': [2.0098617038618865, -1.9900894279778973], 'a9': [0.206000160122563, 2.99291896549664], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.341486753957511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.3682757009993502, -1.3654204510162564]]], [3, [[1.0, 0], [1.2660963944586847, 1.1819475114990168]]], [7, [[1.0, 0], [-2.635730879701317, -0.2300494072779199]]]], 'bad_primes': [2, 3, 7], 'central_character': '168.5', 'coefficient_field': 'CDF', 'conductor': 168, 'conductor_radical': 42, 'conjugate': '2068210972986185472815328591222', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.3682757009993502, -1.3654204510162564]], [[1.0, 0], [1.2660963944586847, 1.1819475114990168]], [[1.0, 0], [-1.549002538705787, -0.8943170326971999], [2.5, 4.330127018922194]], [[1.0, 0], [-2.635730879701317, -0.2300494072779199]], [[1.0, 0], [-0.50134649744451, -0.8683576057705915], [-5.5, 9.526279441628825]], [[1.0, 0], [-2.4730161636137193, 0], [13.0, 0]], [[1.0, 0], [-3.329626876362197, -5.767082920106181], [-8.5, 14.722431864335457]], [[1.0, 0], [-1.8594072482235695, 3.2205878258850573], [-9.5, -16.454482671904334]], [[1.0, 0], [6.852436906154952, 3.956256292373488], [11.5, 19.91858428704209]], [[1.0, 0], [-0.7484030466911374, 0], [29.0, 0]], [[1.0, 0], [-2.8725431189808517, 1.658463543002402], [15.5, -26.846787517317598]], [[1.0, 0], [3.2242944667580846, 1.8615472783294011], [18.5, 32.04293994002423]], [[1.0, 0], [2.010439485497974, 0], [41.0, 0]], [[1.0, 0], [0, -9.196505862147088], [-43.0, 0]], [[1.0, 0], [1.1984028961795452, -2.0756947041206626], [-23.5, -40.703193977868615]], [[1.0, 0], [6.338839963443413, 10.979192877732036], [-26.5, 45.89934640057525]], [[1.0, 0], [7.349223321469181, -4.243076062984907], [29.5, -51.09549882328188]], [[1.0, 0], [2.02441885780793, -3.5063963175238895], [-30.5, -52.827549630850754]], [[1.0, 0], [6.89842602036172, -3.982808119840558], [33.5, -58.023702053557386]], [[1.0, 0], [0, 5.468433386112341], [-71.0, 0]], [[1.0, 0], [5.685458974416592, -3.282501269345993], [36.5, -63.21985447626402]], [[1.0, 0], [-2.5398816176764227, 4.399204007025795], [-39.5, -68.41600689897065]], [[1.0, 0], [0, -5.654567120458184], [-83.0, 0]], [[1.0, 0], [-7.394953441062705, 12.808435079526905], [-44.5, -77.07626093681505]], [[1.0, 0], [0, -1.755768322666538], [-97.0, 0]], [[1.0, 0], [-12.680342460439226, 7.320999132951228], [50.5, -87.4685657822283]], [[1.0, 0], [8.540556715728057, 4.93089271885486], [51.5, 89.20061658979718]], [[1.0, 0], [3.481104227043754, -6.0294493876825666], [-53.5, -92.66471820493493]], [[1.0, 0], [-2.3637323280032105, 1.3647014958648744], [54.5, -94.39676901250381]], [[1.0, 0], [0, -0.5311536003025426], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-168-168.5-c1-0-6', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/168/2/ba/c/5/10', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.9312205286375975, 0.9056231608324189, 0.881551557908396, 0.855731134580577, 0.8237734089684751, 0.7807000136822332, 0.7214309557891919, 0.6412080291619776, 0.5359653793183415, 0.40267089747950446, 0.23965325357911424, 0.04691318819163073, -0.17359754448429343, -0.41775724824391636, -0.6791492951982285, -0.9490665821710311, -1.2166779884592016, -1.4693819560048762, -1.6933605019669502, -1.8743311253221513, -1.9984749062161424, -2.0534978154682935, -2.0297605429505743, -1.921392150832046, -1.7272870073867288, -1.451875315767774, -1.1055575193629579, -0.7047038712951307, -0.27114363252155044, 0.16889626310448475, 0.5863969918615946, 0.9516376773290629, 1.236650797884947, 1.4178683668171994, 1.4787359892348784, 1.4120387595420274, 1.2216710881735255, 0.9235969798053619, 0.5457909679063633, 0.12702293930836034, -0.2855508189063421, -0.6399097090420527, -0.8835961334186285, -0.9687168433916362, -0.857082469648885, -0.524977979746716, 0.03296830892671873, 0.8013189212875709, 1.7431758661226238, 2.8016069736535774, 3.9032174053404574, 4.963707116310108, 5.895020318633539, 6.613477109931132, 7.0481084073335385, 7.148318869339827, 6.889998394571017, 6.279301623257743, 5.353515434404789, 4.178722469833061, 2.8443172099617713, 1.454802374961417, 0.1196428325697576, -1.0577645337367667, -1.9907753430070803, -2.6185772634934477, -2.912532528357728, -2.8789314917703215, -2.5577130110921797, -2.017197867771367, -1.3453945097011024, -0.6389039232530546, 0.009194896617754484, 0.5209123056303611, 0.8428229776583754, 0.9521410604385611, 0.8585216660946736, 0.6012933028459889, 0.2424732606836517, -0.14345729248680344, -0.4815342668318056, -0.7082565263599336, -0.7816575199819797, -0.6878965254807737, -0.4432572593412586, -0.09113374206683568, 0.3056246737307496, 0.6758663361321412, 0.9530217473395651, 1.0875864952467418, 1.0570369473880492, 0.8713399560941183, 0.572872832116951, 0.23046417169174518, -0.07173544791639795, -0.24890380153838443, -0.23135173379089938, 0.021241262107466585, 0.5097939619242638, 1.1920731379760103, 1.986353351761858, 2.782397701792778, 3.4583831986975087, 3.9012552846849995, 4.027214057456193, 3.798771973363075, 3.235162015455312, 2.413799720465113, 1.4618912588835191, 0.5389219113287617, -0.18761560983491898, -0.5695714381901886, -0.5041185027902856, 0.046129142716556965, 1.0426153972529615, 2.372282835714249, 3.861362378759332, 5.299826703658205, 6.472913504467795, 7.1947468986685195, 7.338509494153498, 6.857985495769271, 5.796585742710274, 4.281990021317441, 2.506969619858345, 0.6993644950462923, -0.9138504903084231, -2.142338047182053, -2.8618570264551075, -3.032280274775108, -2.7010225485361, -1.9913209619150791, -1.0775518836873232, -0.1521512486673027, 0.6097266358122363, 1.0812389822739787, 1.2048013079467879, 0.9990918117898195, 0.5509317928309625, -0.006201473745891808, -0.5226445185372015, -0.8658200697137367, -0.9495423375682621, -0.7533425780178211, -0.3277808311911717, 0.21546541086435625, 0.7268300202821171, 1.0507238996005817, 1.0594978783752342, 0.6824227204745741, -0.07647589889116346, -1.135672626438362, -2.3493518129738895, -3.5341164294656813, -4.503878899357502, -5.105822848138986, -5.250003405613852, -4.926402879352646, -4.205842917256876, -3.2245451678013044, -2.1556140405967414, -1.1735343046661755, -0.41930586837382966, 0.026281484799674067, 0.1555043044432021, 0.030029656533715234, -0.2382561315506106, -0.5173629978258029, -0.6891752184253658, -0.6792625283944309, -0.47538586293437707, -0.13013241367798853, 0.2531786537981263, 0.5481671269813551, 0.6400995572818621, 0.45914989476779605, 0.003741270304213389, -0.6524564265954714, -1.3726144565070086, -1.9861363599359316, -2.3292392848764174, -2.2875104909738027, -1.830148465526389, -1.0269104818263577, -0.042308345454107714, 0.89338520947019, 1.5313294076520183, 1.659928052716581, 1.1570444069806818, 0.026430891956333573, -1.590982035945551, -3.4351672903330077, -5.172322340382574, -6.459099373157185, -7.0127917058027425, -6.6725977450751195, -5.438400116247523, -3.4778831062232776, -1.099386793651992, 1.3047471661637091, 3.3330757273466896, 4.652764235005679, 5.063820460038023, 4.536300686853556, 3.212695862187543, 1.3752359422423048, -0.6145316599738, -2.390552693838238, -3.6551505482991145, -4.234376413805207, -4.1044409944864135, -3.3845958748518257, -2.2995305781044184, -1.1211904284584242, -0.1043033791708545, 0.5691747468544534, 0.8241974990897675, 0.6984814026320973, 0.3203495336997505, -0.1342902502214016, -0.49378122803055874, -0.6375686493333388, -0.5260688332301877, -0.20640333671069896, 0.20655455142464896, 0.5677481330664478, 0.7471324532216392, 0.6695931891453781, 0.338275026980368, -0.16532294849540521, -0.704617827755471, -1.128115472966698, -1.3151341559827323, -1.2139159732150884, -0.8607832172784967, -0.3740334034007183, 0.07678312415490138, 0.3185544860481516, 0.22648884222412877, -0.2343699627769596, -0.9903615662732294, -1.8698274168900595, -2.6419935362771576, -3.0751356897049273, -2.9992876075843915, -2.3567400293128453, -1.226015152199313, 0.18858287366359955, 1.600909033642214, 2.7105067229018385, 3.277114193796757, 3.182979959263743, 2.466256850724377, 1.315714794347793, 0.02682235614696434, -1.0706154114890776, -1.6952962272486771], 'positive_zeros': ['1.40289546809316607456639871687187', '3.57672627795837465257541343925656', '4.91258667785655471552357243651172', '5.74377701130514924892732715222512', '7.76182442089430710756422499884641', '8.998059161906758038909580213466361', '9.827981081630063117698598092244911', '10.65415931518280662764307726057742', '11.71665966016874313801215584247200', '12.11776652572312104226203195178811'], 'prelabel': '2-168-168.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': -0.2746390486279316, 'root_number': '0.6503099021979993 - 0.7596690273423212*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.137319524314', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.40289546809316607456639871687', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.57672627795837465257541343926', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.91258667785655471552357243651', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.341486753957511, 'bad_primes': [2, 3, 7], 'central_character': '168.5', 'conductor': 168, 'conductor_radical': 42, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/168/2/ba/c/5/10'], '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': '2-168-168.5-c1-0-6', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-168-168.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': -0.1373195243139658, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.40289546809316607456639871687', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1778381282185764823369080654483', 'Lhash_array': ['1778381282185764823369080654483'], 'label': '2-168-168.5-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/168/2/ba/c/5/10'}