Formats: - HTML - YAML - JSON - 2026-07-18T15:25:26.894498
  • lfunc_lfunctions • Show schema
    {'Lhash': '2521585112687989656415791372261', 'a10': [0, 0], 'a2': [0, -442.56726064353995], 'a3': [0, -6561.0], 'a4': [-64793.780193527, 0], 'a5': [0, 0], 'a6': [-2903683.7970822654, 0], 'a7': [0, -24799334.518289838], 'a8': [0, -29332570.180081166], 'a9': [-43046721.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 137.41656550841986, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '8.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 6561.0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '75.49', 'coefficient_field': 'CDF', 'conductor': 75, 'conductor_radical': 15, 'conjugate': '140522854907471444342743100031', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 442.56726064353995], [-131072.0, 0]], [[1.0, 0], [0, 6561.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 24799334.518289838], [-232630513987207.0, 0]], [[1.0, 0], [7666842.668239197, 0], [505447028499293760, 0]], [[1.0, 0], [0, 3400859763.5513706], [-8650415919381338000, 0]], [[1.0, 0], [0, -53530641617.471085], [-827240261886336800000, 0]], [[1.0, 0], [-129759793667.2896, 0], [5480386857784803000000, 0]], [[1.0, 0], [0, -211421780701.8586], [-141050039560662970000000, 0]], [[1.0, 0], [4139749497626.768, 0], [7257147736730074000000000, 0]], [[1.0, 0], [5313774168322.508, 0], [22550116774162744000000000, 0]], [[1.0, 0], [0, 18563350834151.133], [-456487940826035130000000000, 0]], [[1.0, 0], [55740400024915.95, 0], [2614120267500775300000000000, 0]], [[1.0, 0], [0, 73164780418441.16], [-5874403106360420000000000000, 0]], [[1.0, 0], [0, -122506770900677.83], [-26647936506962194000000000000, 0]], [[1.0, 0], [0, -274251316735184.75], [-205442259656281400000000000000, 0]], [[1.0, 0], [631976904958257.8, 0], [1271991467017507700000000000000, 0]], [[1.0, 0], [1143609843953429.5, 0], [2241853325254885400000000000000, 0]], [[1.0, 0], [0, 608292132442216.2], [-11047694236668359000000000000000, 0]], [[1.0, 0], [-1255184542645171.0, 0], [29606831241262270000000000000000, 0]], [[1.0, 0], [0, -7713759375680208.0], [-47477585226700100000000000000000, 0]], [[1.0, 0], [-26307606376242252, 0], [181827912146592060000000000000000, 0]], [[1.0, 0], [0, -14546619677326072], [-421044084813170700000000000000000, 0]], [[1.0, 0], [26144975096135996, 0], [1379209096840925500000000000000000, 0]], [[1.0, 0], [0, -9649715316695418.0], [-5958260438588052000000000000000000, 0]], [[1.0, 0], [25686314985857210, 0], [11843044313729356000000000000000000, 0]], [[1.0, 0], [0, 26301518501067690], [-16528476322717512000000000000000000, 0]], [[1.0, 0], [0, 203576024370053220], [-31588152109649857000000000000000000, 0]], [[1.0, 0], [79645265641406130, 0], [43276334103547420000000000000000000, 0]], [[1.0, 0], [0, 340819400921533300], [-79860778452816620000000000000000000, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 51, 'label': '2-75-5.4-c17-0-51', 'leading_term': '0.555985377067350777747770465084415631350529002087006294', 'load_key': 'CMFs-workshop', 'motivic_weight': 17, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [17], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/75/18/b/d/49/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [0.5559853770673507, 0.9695289005572147, 1.4223352266022995, 1.9060027765896645, 2.410864009320742, 2.9262202681872247, 3.4406115581672143, 3.942114072761982, 4.418657410957977, 4.858352763801311, 5.249822929391966, 5.582524847798563, 5.847055440479292, 6.035431892108971, 6.141338118958219, 6.160330012842534, 6.089993112156077, 5.93004760442594, 5.682396975426809, 5.351118150721158, 4.942392585305775, 4.464379401920489, 3.9270333130331387, 3.341871639751806, 2.7216962180429602, 2.0802773159251284, 1.4320078354023698, 0.7915370049492407, 0.17339345305695775, -0.4083920321432626, -0.9406536234782642, -1.4114371868303774, -1.810316814345064, -2.1286720914264663, -2.359918041145796, -2.4996809437335736, -2.5459146937974237, -2.4989539949928, -2.3615024565931395, -2.1385554997553773, -1.8372598510404152, -1.4667132429334007, -1.0377097014722587, -0.5624374267161202, -0.054137712654286546, 0.473265436297922, 1.005554394518949, 1.5286144743150494, 2.0288264075996665, 2.4934432325139864, 2.9109404433061568, 3.2713289783193678, 3.5664216620697693, 3.7900450568619006, 3.938190281218728, 4.009098171763854, 4.003276149547239, 3.9234462423363907, 3.7744258476749253, 3.5629449313660477, 3.2974053755603445, 2.987590054268226, 2.6443308598141986, 2.2791462750032103, 1.9038601336098737, 1.530213896581174, 1.1694850642797185, 0.8321242295132546, 0.5274227483177829, 0.2632220752910309, 0.04567450105907836, -0.12093662229390187, -0.23431102747412594, -0.2941760888809326, -0.3022601731440798, -0.2621955984867896, -0.17935445717799461, -0.060622917678736815, 0.08587817433811862, 0.25111661370985144, 0.42550463933052307, 0.5992745170166732, 0.7628603512552259, 0.9072722000790341, 1.0244486840153562, 1.1075748953151863, 1.151353516429429, 1.1522186181201626, 1.1084835815663896, 1.0204169130635938, 0.8902423177234816, 0.7220621811605255, 0.5217064774724257, 0.29651197390472267, 0.055039331144704065, -0.1932618015389426, -0.43842742439488563, -0.6703795314320463, -0.8793368729992004, -1.0562201432718916, -1.1930354901716007, -1.283220752911489, -1.3219399540602201, -1.3063132825588226, -1.2355720520408897, -1.1111308334254997, -0.9365720502039098, -0.7175416798938191, -0.46155820281586807, -0.17774044722890153, 0.12353663912207459, 0.4310461433635395, 0.7331583964682058, 1.018318155384296, 1.2755310832202653, 1.4948399574463818, 1.667770897058441, 1.7877305456972332, 1.8503365777291498, 1.853666075890164, 1.798409198795899, 1.6879190212656654, 1.5281523698327633, 1.3275007467044535, 1.0965148762731984, 0.8475308452040817, 0.5942100605158105, 0.3510091416376948, 0.13259922247395556, -0.04674318582593092, -0.17374976260702374, -0.2367534280353645, -0.22623597619734703, -0.1353064567447524, 0.039911456526170876, 0.30000184426573173, 0.6421035121901867, 1.0598917793718807, 1.5437001269438986, 2.080781198500991, 2.655700940304119, 3.2508540448203336, 3.8470835497858267, 4.424382676168813, 4.962652976319743, 5.442489797811022, 5.84596410516406, 6.157368955913081, 6.3638994670087365, 6.456236948401827, 6.42901098459995, 6.2811175195815006, 6.015876301057174, 5.641017174384571, 5.168491451151029, 4.614111646877591, 3.9970299987935247, 3.3390730401568605, 2.663955826242288, 1.9964048978902171, 1.3612234779004009, 0.7823355093097404, 0.28184679816451, -0.12083838947633513, -0.40980844754335205, -0.5733095406601939, -0.604255567536135, -0.5005597507198316, -0.26527163751931554, 0.09348886980965011, 0.5628005008822141, 1.1254041787344424, 1.7603444366068814, 2.4437642679014138, 3.1498222055574145, 3.85169487947425, 4.522624252431891, 5.136966390683989, 5.671198117887766, 6.104839283878603, 6.421251623010463, 6.608280166238796, 6.658709711822614, 6.570516682679631, 6.34690547213541, 5.996127722898222, 5.531092482638807, 4.968784405303034, 4.329515697206371, 3.6360449430357504, 2.9126019351990506, 2.1838618781589636, 1.4739146316349871, 0.8052748652298586, 0.19797709047062784, -0.3312044179052768, -0.7693766357222873, -1.1079630230882376, -1.3429350092249381, -1.4748313863088722, -1.5085673241688644, -1.4530447186348472, -1.3205850500523284, -1.1262143903278272, -0.8868372349586254, -0.6203410932428665, -0.34467697083397586, -0.07696184783950293, 0.16735207457140694, 0.37520016879281765, 0.5364847009006221, 0.64448265839507, 0.6960630242541432, 0.6917044071358294, 0.6353144209549225, 0.5338626666769146, 0.39684906224712174, 0.23563807140719606, 0.06269662548767521, -0.1092211852194715, -0.26789655536735013, -0.40242888328840953, -0.5039344551506758, -0.5661205836442287, -0.5857015362743468, -0.5626311584256036, -0.5001371584118887, -0.4045530553622512, -0.28495521318964984, -0.152623579513594, -0.020355101218902737, 0.09833228516793001, 0.19006020873566848, 0.2424654739396922, 0.2450392971723488, 0.18987964746771346, 0.07230993038767952, -0.10867626806233874, -0.3501757596408385, -0.645362145206073, -0.9837061821627336, -1.3514251725742217, -1.7321432144938926, -2.1077316036547513, -2.4592874779909124, -2.7681996221491847, -3.017243758601694, -3.1916460848254773, -3.280053556521723, -3.275352574940772, -3.175284236742776, -2.9828138858084263, -2.7062249291573424, -2.3589211466811997, -1.958937310076291, -1.5281740100784733, -1.0913883018660038], 'positive_zeros': ['1.98917991458687458124530985468425', '3.10105376187411707214717213892282', '4.93910996920203595078030840740874', '5.44454859742561201110356998228433', '6.62503005704474734433785193376705', '7.70587037138289900334487433650035', '9.050104068032412107916511838200519', '9.408494732447589939939024996256193', '11.43776670420843438141086250917294', '11.86652506551090012840280662780966'], 'prelabel': '2-75-5.4-c17-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.722481201026508, 'root_angle': -0.07379180882521663, 'root_number': '0.89442719099991587856366946749251049417624734384461028971 - 0.4472135954999579392818347337462552470881236719223051449*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.07379180882521663', 'prec': 67}, 'spectral_label': 'c17-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.98917991458687458124530985468', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.10105376187411707214717213892', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.93910996920203595078030840741', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 137.41656550841986, 'bad_primes': [3, 5], 'central_character': '5.4', 'conductor': 75, 'conductor_radical': 15, 'degree': 2, 'index': 51, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/75/18/b/d/49/2'], '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': '2-75-5.4-c17-0-51', 'motivic_weight': 17, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [17], 'order_of_vanishing': 0, 'prelabel': '2-75-5.4-c17-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.722481201026508, 'root_angle': -0.07379180882521663, 'self_dual': False, 'spectral_label': 'c17-0', 'z1': {'__RealLiteral__': 0, 'data': '1.98917991458687458124530985468', 'prec': 103}}
  • lfunc_instances • Show schema
    {'Lhash': '2521585112687989656415791372261', 'Lhash_array': ['2521585112687989656415791372261'], 'factors': ['2-75-5.4-c17-0-51'], 'label': '2-75-5.4-c17-0-51', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/75/18/b/d/49/2'}