-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '230402293285620983923030716392', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-1.5811388300841898, -0.7071067811865476], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, 4.242640687119285], 'a8': [0, 0], 'a9': [2.0, 2.23606797749979], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.58204824255365, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.5811388300841898, 0.7071067811865476]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '1200.1151', 'coefficient_field': 'CDF', 'conductor': 1200, 'conductor_radical': 30, 'conjugate': '2189569894693371737945466066713', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.5811388300841898, 0.7071067811865476]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -4.242640687119285], [-7.0, 0]], [[1.0, 0], [0, 0], [11.0, 0]], [[1.0, 0], [0, 0], [13.0, 0]], [[1.0, 0], [0, 0], [-17.0, 0]], [[1.0, 0], [0, 0], [-19.0, 0]], [[1.0, 0], [9.486832980505138, 0], [23.0, 0]], [[1.0, 0], [0, 8.94427190999916], [-29.0, 0]], [[1.0, 0], [0, 0], [-31.0, 0]], [[1.0, 0], [0, 0], [37.0, 0]], [[1.0, 0], [0, -4.47213595499958], [-41.0, 0]], [[1.0, 0], [0, -12.727922061357855], [-43.0, 0]], [[1.0, 0], [9.486832980505138, 0], [47.0, 0]], [[1.0, 0], [0, 0], [-53.0, 0]], [[1.0, 0], [0, 0], [59.0, 0]], [[1.0, 0], [8.0, 0], [61.0, 0]], [[1.0, 0], [0, 4.242640687119285], [-67.0, 0]], [[1.0, 0], [0, 0], [71.0, 0]], [[1.0, 0], [0, 0], [73.0, 0]], [[1.0, 0], [0, 0], [-79.0, 0]], [[1.0, 0], [9.486832980505138, 0], [83.0, 0]], [[1.0, 0], [0, -17.88854381999832], [-89.0, 0]], [[1.0, 0], [0, 0], [97.0, 0]], [[1.0, 0], [0, -8.94427190999916], [-101.0, 0]], [[1.0, 0], [0, 12.727922061357855], [-103.0, 0]], [[1.0, 0], [-9.486832980505138, 0], [107.0, 0]], [[1.0, 0], [16.0, 0], [109.0, 0]], [[1.0, 0], [0, 0], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-1200-12.11-c1-0-1', 'leading_term': '0.3782701749729078894584705419414451428171525506077949746', '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/1200/2/h/l/1151/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.3782701749729079, 0.256953741485255, 0.13502029072466568, 0.012517757647064953, -0.11041510307779928, -0.23349361060188242, -0.35623942497184985, -0.4779425100747861, -0.5976343040072389, -0.7140728571399626, -0.8257400932121294, -0.930850921615366, -1.0273736648479361, -1.1130611213339179, -1.185491508778787, -1.2421184801676568, -1.2803293388388275, -1.2975104804497324, -1.2911189505976917, -1.2587588298031596, -1.1982609517678635, -1.1077642396925726, -0.9857967245151471, -0.8313541044546117, -0.6439735332145664, -0.4238001996850122, -0.17164419864788227, 0.11097479832748942, 0.42179747029239634, 0.7578115891181356, 1.1152575171727974, 1.4896540307171273, 1.8758455768746722, 2.2680715241616074, 2.6600573435406734, 3.0451269729939816, 3.4163348916228995, 3.76661568064706, 4.088948102736884, 4.376530014584853, 4.622959768795915, 4.822419189016504, 4.969852745303186, 5.061137242113696, 5.093236183324698, 5.0643330177515935, 4.97393771006851, 4.8229615349053, 4.613755658189899, 4.350109943564035, 4.0372094885753, 3.68154763236347, 3.2907955522329044, 2.873630041325501, 2.439522586889647, 1.9984943957335528, 1.560843483335338, 1.1368512962682675, 0.7364775143112174, 0.36905262117466264, 0.04297848811419476, -0.23455246309292302, -0.4578089985816441, -0.6227336341619352, -0.7271067879848191, -0.7706545371004598, -0.7550936149347447, -0.6841092514492099, -0.5632637087566196, -0.3998358323055519, -0.20259453773245947, 0.018488208855451035, 0.2525767871381249, 0.48835316592697386, 0.7144273451195301, 0.9197626123003213, 1.0940999720499223, 1.2283654057305387, 1.3150435388497888, 1.3485018718644093, 1.32525098288991, 1.2441280239205699, 1.1063933635168972, 0.9157333070747884, 0.6781653514647096, 0.4018462794015871, 0.09678742428655734, -0.22551452402030422, -0.5525189206564439, -0.8711389753850093, -1.168277129593961, -1.4313767824281713, -1.6489675731234448, -1.8111807652148222, -1.9102116061694672, -1.9407068890308854, -1.9000583126348358, -1.7885855693262394, -1.6095972828133074, -1.3693228282319552, -1.076713505673615, -0.7431172873084149, -0.38183717101660886, -0.0075887885913523525, 0.3641219318195331, 0.7176758193764426, 1.0380435299475959, 1.3114836243824368, 1.5262036672852186, 1.6729528080078253, 1.7455162318166637, 1.7410852486530242, 1.6604815268248343, 1.5082199175579152, 1.2924012270648964, 1.0244338920256253, 0.7185914722271249, 0.3914208281370598, 0.06102342238945413, -0.2537610053302438, -0.5342334489392249, -0.7627381385532382, -0.9235467923632388, -1.0036822226534259, -0.9936402538563335, -0.8879722845419116, -0.6856961371313598, -0.39050990697112964, -0.01079207001649857, 0.44061922505147005, 0.9468643999991503, 1.487704385657828, 2.0403421638079347, 2.580390392399817, 3.0829434873561, 3.523706197595275, 3.8801265209600815, 4.132479050808691, 4.26484568717278, 4.265944138049906, 4.129760688134193, 3.855952103087925, 3.449991919009431, 2.9230482766529726, 2.2915933414260463, 1.5767575775750338, 0.8034550538931002, -0.0006821209620247873, -0.8065118429161908, -1.5846760573725955, -2.3069189189117223, -2.9473648089587092, -3.4836928224137007, -3.898148480309547, -4.178340716772643, -4.317782320999349, -4.316144524670208, -4.179210708105705, -3.9185295385079555, -3.550783458260676, -3.0969034821242967, -2.5809749192851044, -2.028990143179485, -1.4675132197076406, -0.9223265408779608, -0.4171312346793589, 0.02762913269730477, 0.39575813449543085, 0.676055576204247, 0.8627851122132018, 0.9558346286564866, 0.960560525000841, 0.8873246571758622, 0.7507500950962046, 0.5687380073930169, 0.36130197284743687, 0.14928699023883232, -0.046952271856501124, -0.20883636721069174, -0.32073286463170314, -0.3709446376194171, -0.3524542948020435, -0.26337814863413267, -0.10709984753985784, 0.10792742593278758, 0.3687015284616679, 0.6584864465673818, 0.9578753950097213, 1.2460396117494632, 1.5020881878616799, 1.7064561875056967, 1.8422350769374243, 1.8963613957237921, 1.8605866682973413, 1.7321634594487718, 1.514198612472259, 1.215644190962969, 0.850918366729993, 0.43917118467273225, 0.0032324272713855034, -0.43170067746306084, -0.8395607109811271, -1.1950038562030803, -1.4750037023244618, -1.6603461986131278, -1.7369305988465433, -1.6967909096884135, -1.5387675450740408, -1.2687787929872925, -0.8996652068865081, -0.45060577572501265, 0.053868835473448395, 0.585215170354876, 1.1124942069104315, 1.6041741807955485, 2.030012602133141, 2.362903677388297, 2.5805768516292713, 2.667038774447991, 2.6136644230331623, 2.419862712052416, 2.093266602817015, 1.6494260690869567, 1.111012594999675, 0.5065743188504808, -0.13109040960308319, -0.7668482575082336, -1.3653223604482951, -1.8930342999065755, -2.32046536900854, -2.6239084511536683, -2.786992507401936, -2.8017799408649937, -2.669361978453486, -2.3999072399628156, -2.0121520510809465, -1.5323557489807969, -0.9927780504431052, -0.429766339043671, 0.11843353217741086, 0.6140103602259488, 1.0219212046732475, 1.3120801254019439, 1.461263936879251, 1.4546130083158983, 1.2866292584099512, 0.961604164647753, 0.4934449524497882, -0.09509506333989974, -0.7737381508317089, -1.5064765473917063, -2.2537295194458538, -2.9747290970741815, -3.629984950805341, -4.183672881098718, -4.605795431483928, -4.873977059435602], 'positive_zeros': ['0.18175536164629201967457014113085', '1.55974140955655215379962410734995', '3.52403684896991389277666314903611', '4.15542377000874807303169106812958', '5.05688802381976880694073409834669', '6.03634019887939705435999547990500', '6.92509261156463247815173193532072', '7.50150924273585404240967450969520', '8.613231900772013984016295079342889', '9.722626701631854934566639801313653'], 'prelabel': '2-1200-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.095488368990207, 'root_angle': -0.866139763599385, 'root_number': '-0.9128709291752768557616163046680035565879078249966387571 - 0.4082482904638630163662140124509818986609912467761116881*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4330698817996925', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.18175536164629201967457014113', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.55974140955655215379962410735', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.52403684896991389277666314904', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 9.58204824255365, 'bad_primes': [2, 3, 5], 'central_character': '12.11', 'conductor': 1200, 'conductor_radical': 30, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1200/2/h/l/1151/1'], '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': '2-1200-12.11-c1-0-1', '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': '2-1200-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.095488368990207, 'root_angle': -0.4330698817996925, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.18175536164629201967457014113', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '230402293285620983923030716392', 'Lhash_array': ['230402293285620983923030716392'], 'label': '2-1200-12.11-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1200/2/h/l/1151/1'}