-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '870663305711567429177523819355', 'a10': [-2.8984098195957135, 0.0], 'a2': [-0.8711600703198188, 0.0], 'a3': [-3.0645797274814375, 0.0], 'a4': [-1.2410801318803684, 0.0], 'a5': [3.327069178608765, 0.0], 'a6': [2.66973949089342, 0.0], 'a7': [-2.0645797274814375, 0.0], 'a8': [2.8234995956010693, 0.0], 'a9': [6.391648906090203, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.84418973575603, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [1.0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [11, 13], 'central_character': '1859.1', 'coefficient_field': 'CDF', 'conductor': 1859, 'conductor_radical': 143, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8711600703198188, 0], [2.0, 0]], [[1.0, 0], [3.0645797274814375, 0], [3.0, 0]], [[1.0, 0], [-3.327069178608765, 0], [5.0, 0]], [[1.0, 0], [2.0645797274814375, 0], [7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.156089678956076, 0], [17.0, 0]], [[1.0, 0], [-4.635920368468386, 0], [19.0, 0]], [[1.0, 0], [-6.389168888571665, 0], [23.0, 0]], [[1.0, 0], [-3.755728537621817, 0], [29.0, 0]], [[1.0, 0], [7.809229442369502, 0], [31.0, 0]], [[1.0, 0], [-0.7274303199430241, 0], [37.0, 0]], [[1.0, 0], [0.9084900485253619, 0], [41.0, 0]], [[1.0, 0], [11.627208133224329, 0], [43.0, 0]], [[1.0, 0], [-0.3530008087978616, 0], [47.0, 0]], [[1.0, 0], [2.5948292668987762, 0], [53.0, 0]], [[1.0, 0], [-7.064429284211326, 0], [59.0, 0]], [[1.0, 0], [-1.0386110840510718, 0], [61.0, 0]], [[1.0, 0], [11.37052686766807, 0], [67.0, 0]], [[1.0, 0], [-8.012409803178075, 0], [71.0, 0]], [[1.0, 0], [-2.0905113576705343, 0], [73.0, 0]], [[1.0, 0], [1.6265690826589414, 0], [79.0, 0]], [[1.0, 0], [-8.35696802741578, 0], [83.0, 0]], [[1.0, 0], [-11.573707228476644, 0], [89.0, 0]], [[1.0, 0], [1.809229442369502, 0], [97.0, 0]], [[1.0, 0], [-5.416136125806134, 0], [101.0, 0]], [[1.0, 0], [14.31587692584617, 0], [103.0, 0]], [[1.0, 0], [-13.894507176118621, 0], [107.0, 0]], [[1.0, 0], [-14.74701630237776, 0], [109.0, 0]], [[1.0, 0], [-8.308737759830779, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 24, 'label': '2-1859-1.1-c1-0-24', 'leading_term': '0.63806112836252251711363784423772', '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/1859/2/a/n/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.6380611283625225, 0.6334870041348963, 0.6197288964724091, 0.5966874738168545, 0.5642228006587262, 0.5221906570743267, 0.47048947343829434, 0.4091145845974758, 0.3382162694213206, 0.25815809219242547, 0.16957230857261468, 0.0734094442203457, -0.02902047744824259, -0.13601723503179866, -0.24547210223887078, -0.3548635170884276, -0.4612680343158222, -0.561387575410372, -0.6515936591655002, -0.7279889093423115, -0.7864856867344134, -0.8229011800692927, -0.8330677205686005, -0.8129564718328094, -0.7588120086922007, -0.6672946588967973, -0.5356268665259188, -0.36173927463003486, -0.1444117469051144, 0.11659581585118214, 0.42042823044293154, 0.7650407763582705, 1.1471312132693963, 1.5621030086552654, 2.0040641516895055, 2.4658651484232887, 2.939178798997533, 3.4146231658687487, 3.8819277782626775, 4.330141617388584, 4.74787983368557, 5.123604514182628, 5.445933204551125, 5.703967361383822, 5.8876315333574345, 5.988012913293268, 5.997690032290214, 5.911038842095456, 5.7245043040945, 5.436825912478785, 5.049206350561623, 4.565413721246401, 3.9918094948881566, 3.337296449759867, 2.6131833910391435, 1.8329662525459993, 1.012028221482727, 0.16726467377593462, -0.683358153291733, -1.5212988223077275, -2.3279760295376684, -3.0853266188111426, -3.776367477108097, -4.385741343727584, -4.900226122724559, -5.309187640122686, -5.604956969909296, -5.783115468950269, -5.842673477358759, -5.786132186677948, -5.61942234571727, -5.351718120586548, -4.995129378420175, -4.564280725771617, -4.0757905877011975, -3.547668238700794, -2.9986507696583478, -2.4475052857198527, -1.9123239902363658, -1.4098410647732535, -0.9548002913066496, -0.5594011172547116, -0.23284833012925446, 0.01897326042170905, 0.19368262527746852, 0.2924341325132226, 0.3197928640640049, 0.283456520268419, 0.19383393723655692, 0.0634971815580973, -0.09346941124457649, -0.26219435526785295, -0.4277850323365205, -0.5760984318970764, -0.6944791578189684, -0.7724277474128992, -0.8021646776223086, -0.7790595557431836, -0.7019007787457445, -0.572988177884817, -0.3980395418602217, -0.18591105805946584, 0.05185880365170219, 0.3016630849524821, 0.5485701892703168, 0.7771625117336728, 0.9724284442680298, 1.1206621297903914, 1.2103233227002386, 1.2328100968723923, 1.1831000060810493, 1.060220597253707, 0.8675177257995322, 0.612699619076702, 0.30764565681277656, -0.032019135495722856, -0.3875704499282794, -0.738026289303064, -1.0611468633159051, -1.3345460961927, -1.5368604074231347, -1.6489153897786613, -1.6548289517808523, -1.5429906390263808, -1.3068612588838708, -0.9455444890548917, -0.4640925588309252, 0.12647910852116503, 0.8094788229584173, 1.5631220240962032, 2.3613901814494, 3.175128993064843, 3.9733359178058416, 4.72457560172671, 5.398453273503706, 5.967071250086467, 6.406392694227638, 6.697439874928906, 6.8272613491599845, 6.789613426789762, 6.585315496075631, 6.222255568263926, 5.71504087296493, 5.084307503979605, 4.355721911700122, 3.558724386816994, 2.7250795572052877, 1.887310416082978, 1.0770997765653474, 0.3237457873182792, -0.3472440146860746, -0.9153426753382709, -1.3659119868458889, -1.6907786031269005, -1.888446604266606, -1.9639358445750736, -1.9282571584970845, -1.7975568597366594, -1.591982662716483, -1.3343399636492035, -1.0486202698048368, -0.7584916056354339, -0.48584337439951464, -0.2494751538478963, -0.0640103381955031, 0.060898162245614174, 0.12102102559507927, 0.1176366807212601, 0.05724220448794864, -0.04908935876477915, -0.18666248730146082, -0.33836005404882924, -0.4860112878924426, -0.6118346225523892, -0.6998571495632868, -0.737212652807218, -0.7152269229581397, -0.6302119313072986, -0.4839087747962386, -0.28354200431437754, -0.04147361889918832, 0.22552797957487433, 0.4973621833296585, 0.7519472435710806, 0.9667614022652431, 1.1204721194982135, 1.1945427551662413, 1.174704645693774, 1.0521886385421055, 0.8246236013236644, 0.4965295030389096, 0.07935820210958107, -0.4089355010503509, -0.9447785576855466, -1.5002747488089725, -2.0448355962882565, -2.547047587192295, -2.97665725814269, -3.3065442457544396, -3.5145494549744782, -3.5850314764171776, -3.510039150349535, -3.2900109806839835, -2.9339416296446363, -2.458990157904341, -1.8895418123663816, -1.2557725504443196, -0.5918005813277569, 0.06646046222363192, 0.6836087451522272, 1.2270692758122714, 1.6692596391565155, 1.9894553393337662, 2.1752202519385024, 2.223293950705789, 2.1398621010506558, 1.9401765742962067, 1.6475358248919212, 1.291680469294016, 0.9067008700699988, 0.5285899086485941, 0.19260236368650693, -0.06939977734252624, -0.2314306853939023, -0.2755138916850125, -0.19330553327392705, 0.012921545407491977, 0.33002165407004314, 0.7344892729642408, 1.1937306076860186, 1.6680305261276709, 2.113102043121897, 2.4830621930571346, 2.7336443031396125, 2.8254349210284855, 2.7269157643284423, 2.41709793833751, 1.8875572086462442, 1.1437141992568818, 0.20524993711455647, -0.8943977359896081, -2.1094512847975757, -3.3840574723553556, -4.655273656852, -5.856601100942913, -6.921850048437935, -7.789095071230433, -8.40446867268352, -8.725547337262357, -8.724106986920052, -8.38806284212074, -7.722459613018083, -6.749438460809467, -5.507173257488577, -4.047835882441908, -2.434714043248912, -0.7386610017423797], 'positive_zeros': ['0.68683224348634562025056212640217', '1.67423679797966075355041775245642', '3.35135748919387977943987320870748', '4.85815230909321599322927298661733', '5.23944071140075318062808776182344', '5.96414979662492194214692189229811', '6.73292373574841754762268399486325', '7.42965367510506120961938367289139', '8.757724872761822255297324273205964', '9.635708492622176783179870554240712'], 'prelabel': '2-1859-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8528158190803814, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.68683224348634562025056212640', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.67423679797966075355041775246', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.35135748919387977943987320871', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 14.84418973575603, 'bad_primes': [11, 13], 'central_character': '1.1', 'conductor': 1859, 'conductor_radical': 143, 'degree': 2, 'index': 24, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1859/2/a/n/1/3'], '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': '2-1859-1.1-c1-0-24', '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': '2-1859-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8528158190803814, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.68683224348634562025056212640', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '870663305711567429177523819355', 'Lhash_array': ['870663305711567429177523819355'], 'label': '2-1859-1.1-c1-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1859/2/a/n/1/3'}