-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1379121467868689604201981699998', 'a10': -1988037109375, 'a2': 8143, 'a3': -531441, 'a4': 49531233, 'a5': -244140625, 'a6': -4327524063, 'a7': 0, 'a8': 266715960431, 'a9': 282429536481, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 54.74507283870649, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '12.0', 'prec': 14}, 'bad_lfactors': [[3, [1, 531441]], [5, [1, 244140625]]], 'bad_primes': [3, 5], 'central_character': '15.14', 'coefficient_field': '1.1.1.1', 'conductor': 15, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[1, -8143, 16777216], [1, 531441], [1, 244140625], [1, 0, -191581231380566414401], [1, 0, -9849732675807611094711841], [1, 0, -542800770374370512771595361], [1, 432524144062082, 339448671314611904643504117121], [1, -1904424373265762, 4898762930960846817716295277921], [1, -37214344554868798, 480250763996501976790165756943041], [1, 0, -125184900814733057351483732809459681], [1, -1458725602323329282, 620412660965527688188300451573157121], [1, 0, -43335257111193343900365036083324748961], [1, 0, -509111094534718962173411120845918138561], [1, 0, -1596772093453535767288998989560362112801], [1, -51418335280297668478, 13500460747057082764996435506735298654081], [1, 347328853598147231522, 241335311011519234780052665404754645838881], [1, 0, -3165543453070218706859776348972393302368161], [1, 5299065689612439877918, 7045568477354647704120453346932251277539041], [1, 0, -66956888672235945457062019127709902451882721], [1, 0, -269277687648484922418719360310447236922646081], [1, 0, -524503804723748275248688345080154231098133441], [1, 20553733200969854686078, 3491806676006468166913468087133050334443236481], [1, -25938127244873567233438, 11425473754371035063280217037137346730160045921], [1, 0, -61004259453331056987939675478443460082004997441], [1, 0, -481417221911723703707680699904910046003049191681], [1, 0, -1269734648531914468903714880493455422104626762401], [1, 0, -2032794106460402682668537709613472275016051561281], [1, 4494973339928688884681762, 5072366953385878222451914929597073120434548877601], [1, -1969661120239347098145122, 7911083174681817456101384654963105793419507652961], [1, 3167494327371611373436802, 18788090506095351190346404972544930679782531948161]], 'euler_factors_factorization': [[[[1, -8143, 16777216], 1]], [[[1, 531441], 1]], [[[1, 244140625], 1]], [[[1, -13841287201], 1], [[1, 13841287201], 1]], [[[1, -3138428376721], 1], [[1, 3138428376721], 1]], [[[1, -23298085122481], 1], [[1, 23298085122481], 1]], [[[1, 432524144062082, 339448671314611904643504117121], 1]], [[[1, -1904424373265762, 4898762930960846817716295277921], 1]], [[[1, -37214344554868798, 480250763996501976790165756943041], 1]], [[[1, -353814783205469041], 1], [[1, 353814783205469041], 1]], [[[1, -1458725602323329282, 620412660965527688188300451573157121], 1]], [[[1, -6582952005840035281], 1], [[1, 6582952005840035281], 1]], [[[1, -22563490300366186081], 1], [[1, 22563490300366186081], 1]], [[[1, -39959630797262576401], 1], [[1, 39959630797262576401], 1]], [[[1, -51418335280297668478, 13500460747057082764996435506735298654081], 1]], [[[1, 347328853598147231522, 241335311011519234780052665404754645838881], 1]], [[[1, -1779197418239532716881], 1], [[1, 1779197418239532716881], 1]], [[[1, 5299065689612439877918, 7045568477354647704120453346932251277539041], 1]], [[[1, -8182718904632857144561], 1], [[1, 8182718904632857144561], 1]], [[[1, -16409682740640811134241], 1], [[1, 16409682740640811134241], 1]], [[[1, -22902048046490258711521], 1], [[1, 22902048046490258711521], 1]], [[[1, 20553733200969854686078, 3491806676006468166913468087133050334443236481], 1]], [[[1, -25938127244873567233438, 11425473754371035063280217037137346730160045921], 1]], [[[1, -246990403565262140303521], 1], [[1, 246990403565262140303521], 1]], [[[1, -693842360995438000295041], 1], [[1, 693842360995438000295041], 1]], [[[1, -1126825030131969720661201], 1], [[1, 1126825030131969720661201], 1]], [[[1, -1425760886846178945447841], 1], [[1, 1425760886846178945447841], 1]], [[[1, 4494973339928688884681762, 5072366953385878222451914929597073120434548877601], 1]], [[[1, -1969661120239347098145122, 7911083174681817456101384654963105793419507652961], 1]], [[[1, 3167494327371611373436802, 18788090506095351190346404972544930679782531948161], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 31, 'label': '2-15-15.14-c24-0-31', 'leading_term': '5.52776714175798968913795225812706689655875235897575063400000000000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 24, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [24], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/15/25/d/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.08203125', 'prec': 34}, 'plot_values': [5.52776714175799, 5.484914361660643, 5.357252171808629, 5.147447966807486, 4.859877733125173, 4.500523341934562, 4.076832312674913, 3.5975434953403433, 3.072482956687832, 2.512335086704061, 1.9283945485560392, 1.332305162662898, 0.73579213164239, 0.1503941695704241, -0.4127979079884564, -0.943389747578322, -1.431913120369588, -1.8700311120028292, -2.2507138918624587, -2.568380862977456, -2.819005849834032, -3.000182923281941, -3.111151465950865, -3.152780122967752, -3.1275103349628197, -3.0392611865770047, -2.893298297328487, -2.696070407005142, -2.455018140476302, -2.1783601548509806, -1.874862455862632, -1.553597104093522, -1.2236968027297177, -0.8941119585992734, -0.5733767332782684, -0.2693903515566227, 0.010780484380976754, 0.26107280548371975, 0.4765676661744264, 0.653595822171337, 0.7898060622617368, 0.8841945007061964, 0.9370942311911613, 0.9501258622516454, 0.9261105674464513, 0.8689483605227163, 0.7834653160549357, 0.6752343705751683, 0.5503751311165175, 0.4153387633404852, 0.27668450957866464, 0.14085468200029017, 0.013955076315814592, -0.0984523492440938, -0.19153798714609402, -0.2613682421908419, -0.305038982402929, -0.320774274277685, -0.3079868999986126, -0.2672982788242921, -0.2005166312019012, -0.11057349860678913, -0.0014200284243838397, 0.12211428638113564, 0.25449649680288977, 0.38969366612110107, 0.5213988600854818, 0.643272756577779, 0.7491933174393235, 0.8335055252696806, 0.8912629820791084, 0.9184532071834026, 0.9121987641511045, 0.8709268890643742, 0.7945010753991014, 0.6843090775167814, 0.5433030008900337, 0.3759885217941676, 0.18836178527616945, -0.012205874387592219, -0.21713360799009446, -0.4168437049470028, -0.6010162339585852, -0.7588792082751648, -0.8795264975058071, -0.9522545924669686, -0.9669084548318183, -0.9142260837786333, -0.7861711345103758, -0.5762429469914435, -0.27975369671815403, 0.10593693797329644, 0.5812381967292147, 1.1442030532066683, 1.7904671703884683, 2.5132559515683677, 3.3034616800617282, 4.149790657913164, 5.038978113369781, 5.956066514186463, 6.884740866266316, 7.8077126617755965, 8.707142432326764, 9.565089421108247, 10.36397576626696, 11.0870518310795, 11.718848958748579, 12.245605993447313, 12.655656403943693, 12.939763767496002, 13.091394701423056, 13.106920035655213, 12.985737056242968, 12.730307959647131, 12.34611217242331, 11.841512833709357, 11.227540425398676, 10.517599179914267, 9.727104409999301, 8.873061202805179, 7.973596920656372, 7.047461579963293, 6.113511375239239, 5.190191327564999, 4.295033231854152, 3.444184737472019, 2.65198452267337, 1.9305971339331665, 1.289719193873829, 0.736366391024589, 0.27474802209681354, -0.09376705208337323, -0.37059225582878486, -0.5597753174189519, -0.667765923299325, -0.7031074200325363, -0.6760636604224948, -0.5981944109794207, -0.48189460543181517, -0.33991406782760764, -0.1848750810074925, -0.0288053042061804, 0.11729696825521738, 0.24384935891414347, 0.3430096654896229, 0.4089260108982126, 0.4379038289003825, 0.4284837610145341, 0.38142793279330994, 0.2996156059393821, 0.18785273413602807, 0.05260334878397002, -0.09834616804762551, -0.25627612911379916, -0.4119598831411507, -0.5561098062879537, -0.6798243577212045, -0.7750174046710564, -0.8348115691889466, -0.8538786443965999, -0.8287121355571784, -0.7578196346174655, -0.6418259420536314, -0.4834814882693718, -0.2875745391502295, -0.060749741752053485, 0.188760388216594, 0.45148058354678916, 0.7171006002732501, 0.974928722334025, 1.2143717381366637, 1.42542056531539, 1.5991199846304618, 1.7280011317162753, 1.8064565026855532, 1.831039234810696, 1.8006712666044153, 1.7167485654818042, 1.583135804463329, 1.4060475109431467, 1.1938176153133673, 0.9565642932025709, 0.705761811344306, 0.4537355424707859, 0.21310020667234442, -0.0038354594621173447, -0.18567216765381914, -0.32250503340095077, -0.4064632905303126, -0.4321791013378099, -0.39716201448598326, -0.30205892766812303, -0.15078369887295873, 0.04949433410266829, 0.2885079151710476, 0.5531943429000756, 0.8281353710855547, 1.0961208510276124, 1.338816610803462, 1.5375118948245083, 1.6739174056992094, 1.7309818131123382, 1.693692693274585, 1.549827359837382, 1.290620008547786, 0.9113140273892113, 0.41157216193704654, -0.2042776504677852, -0.9271767366382491, -1.7434592971742175, -2.6351663509785874, -3.580543240736602, -4.554706033303843, -5.530454662282783, -6.479203913405638, -7.3719976582275875, -8.18056737217814, -8.87839315267699, -9.44172434325204, -9.850517560951397, -10.089252430472007, -10.1475895833901, -10.020841339933066, -9.710232734732896, -9.22293889127267, -8.571893851190305, -7.775375441674241, -6.856380209043799, -5.841811443955585, -4.761511469366923, -3.6471762820087155, -2.53119600471584, -1.4454681570062615, -0.42023229815137, 0.5170259588766409, 1.3425562287061437, 2.0371692795340515, 2.586873471717253, 2.9832956601297234, 3.2238698124200953, 3.3117867056892636, 3.255708531793779, 3.0692625910703937, 2.7703380089910725, 2.380218114410085, 1.9225883590167991, 1.4224650861336279, 0.9050938050366609, 0.3948667218437723, -0.0856919476943285, -0.5168278615820711, -0.8823062374787444, -1.1699774432907237, -1.3721356073577813, -1.4856574642031244, -1.5119193547444234, -1.4565010833030867], 'positive_zeros': ['1.08793500955262502783059938237954', '2.94980983629975211166127980005872', '4.27519131185009954580365468711669', '5.08693055766113894876843730158168', '6.47556373397802188895733843287962', '7.44411685358830076027684109270201', '10.72314002369396620659421421190689', '11.58197295983240027769016140129909', '12.41604745351859331430990182718743', '13.55571330915529829283217657340284'], 'prelabel': '2-15-15.14-c24-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.398991339277705, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c24-0', 'trace_hash': 64931870025853221, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.08793500955262502783059938238', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.94980983629975211166127980006', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.27519131185009954580365468712', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 54.74507283870649, 'bad_primes': [3, 5], 'central_character': '15.14', 'conductor': 15, 'conductor_radical': 15, 'degree': 2, 'dirichlet_coefficients': [1, 8143, -531441, 49531233, -244140625, -4327524063, 0, 266715960431, 282429536481, -1988037109375, 0, -26322927996753, 0, 0, 129746337890625, 1340871871002305, -432524144062082, 2299823715564783, 1904424373265762, -12092586181640625, 0, 0, 37214344554868798, -141743796727411071, 59604644775390625, 0, -150094635296999121, 0, 0, 1056524429443359375, 1458725602323329282, 6443968366773429519, 0, -3522044105097533726, 0, 13989083177522411073, 0, 15507727671503099966, 0, -65116201277099609375, 0, 0, 0, 0, -68952523554931640625, 303036407710296622114, 51418335280297668478, -712594287997335971505, 191581231380566414401, 485360622406005859375, 229861063644496920162, 0, -347328853598147231522, -1222220615223463842303, 0, 0, -1012089193352729823042, 0, 0, 6426496092957275390625, -5299065689612439877918, 11878402579718870343326, 0, 29977137402506229090337, 0, 0, 0, -21423454157664550007106, -19777228484584028877918, 0, 0, 75328465076612066983311, 0, 0, -31676352024078369140625, 94328487363105428544546, 0, 0, -20553733200969854686078, -327361296631422119140625, 79766443076872509863361, 0, 25938127244873567233438, 0, 105596714858906738281250, 0, 0, 0, 0, -561480399307808349609375, 0, 1843272371089487718167934, -775226592824312436955362, 418699504187463914416354, -464947356754336425781250, -3424588992806438157006879, 0, 1560045967131952312467343, 0, 2952291548252105712890625], 'euler11': [1, 0, -9849732675807611094711841], 'euler13': [1, 0, -542800770374370512771595361], 'euler17': [1, 432524144062082, 339448671314611904643504117121], 'euler19': [1, -1904424373265762, 4898762930960846817716295277921], 'euler2': [1, -8143, 16777216], 'euler23': [1, -37214344554868798, 480250763996501976790165756943041], 'euler29': [1, 0, -125184900814733057351483732809459681], 'euler3': [1, 531441, 0], 'euler31': [1, -1458725602323329282, 620412660965527688188300451573157121], 'euler37': [1, 0, -43335257111193343900365036083324748961], 'euler41': [1, 0, -509111094534718962173411120845918138561], 'euler43': [1, 0, -1596772093453535767288998989560362112801], 'euler47': [1, -51418335280297668478, 13500460747057082764996435506735298654081], 'euler5': [1, 244140625, 0], 'euler53': [1, 347328853598147231522, 241335311011519234780052665404754645838881], 'euler59': [1, 0, -3165543453070218706859776348972393302368161], 'euler61': [1, 5299065689612439877918, 7045568477354647704120453346932251277539041], 'euler67': [1, 0, -66956888672235945457062019127709902451882721], 'euler7': [1, 0, -191581231380566414401], 'euler71': [1, 0, -269277687648484922418719360310447236922646081], 'euler73': [1, 0, -524503804723748275248688345080154231098133441], 'euler79': [1, 20553733200969854686078, 3491806676006468166913468087133050334443236481], 'euler83': [1, -25938127244873567233438, 11425473754371035063280217037137346730160045921], 'euler89': [1, 0, -61004259453331056987939675478443460082004997441], 'euler97': [1, 0, -481417221911723703707680699904910046003049191681], 'euler_factors': [[1, -8143, 16777216], [1, 531441, 0], [1, 244140625, 0], [1, 0, -191581231380566414401], [1, 0, -9849732675807611094711841], [1, 0, -542800770374370512771595361], [1, 432524144062082, 339448671314611904643504117121], [1, -1904424373265762, 4898762930960846817716295277921], [1, -37214344554868798, 480250763996501976790165756943041], [1, 0, -125184900814733057351483732809459681], [1, -1458725602323329282, 620412660965527688188300451573157121], [1, 0, -43335257111193343900365036083324748961], [1, 0, -509111094534718962173411120845918138561], [1, 0, -1596772093453535767288998989560362112801], [1, -51418335280297668478, 13500460747057082764996435506735298654081], [1, 347328853598147231522, 241335311011519234780052665404754645838881], [1, 0, -3165543453070218706859776348972393302368161], [1, 5299065689612439877918, 7045568477354647704120453346932251277539041], [1, 0, -66956888672235945457062019127709902451882721], [1, 0, -269277687648484922418719360310447236922646081], [1, 0, -524503804723748275248688345080154231098133441], [1, 20553733200969854686078, 3491806676006468166913468087133050334443236481], [1, -25938127244873567233438, 11425473754371035063280217037137346730160045921], [1, 0, -61004259453331056987939675478443460082004997441], [1, 0, -481417221911723703707680699904910046003049191681]], 'index': 31, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/15/25/d/b', 'ModularForm/GL2/Q/holomorphic/15/25/d/b/14/1'], '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': '2-15-15.14-c24-0-31', 'motivic_weight': 24, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [24], 'order_of_vanishing': 0, 'prelabel': '2-15-15.14-c24-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.398991339277705, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c24-0', 'trace_hash': 64931870025853221, 'z1': {'__RealLiteral__': 0, 'data': '1.08793500955262502783059938238', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 24576993
{'Lhash': '1379121467868689604201981699998', 'Lhash_array': ['1379121467868689604201981699998'], 'label': '2-15-15.14-c24-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/15/25/d/b/14/1'}
-
id: 24500340
{'Lhash': '1379121467868689604201981699998', 'Lhash_array': ['1379121467868689604201981699998'], 'label': '2-15-15.14-c24-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/15/25/d/b'}