-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2504320754373908652705823887444', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, -1.9318516525781366], 'a6': [0.0, 0.0], 'a7': [0.0, 1.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3654418745638945, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [2, 3, 19], 'central_character': '2736.2735', 'coefficient_field': 'CDF', 'conductor': 2736, 'conductor_radical': 114, 'conjugate': '426203456635601777585173051803', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.9318516525781366], [-1.0, 0]], [[1.0, 0], [0, -1.0], [-1.0, 0]], [[1.0, 0], [1.9318516525781366, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0.5176380902050415], [-1.0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [1.4142135623730951, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 1.7320508075688772], [-1.0, 0]], [[1.0, 0], [-0.5176380902050415, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.7320508075688772, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [-1.4142135623730951, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, -1.4142135623730951], [-1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 10, 'label': '2-2736-228.227-c0-0-10', 'leading_term': '0.57898433809950358515067335535138', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2736/1/b/b/2735/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.5789843380995036, 0.6823304839282195, 0.7949552304547881, 0.9191886395569091, 1.056401843705283, 1.2069628703887858, 1.3702938257743627, 1.544979118618662, 1.7288856702552984, 1.919274839737389, 2.112900853300907, 2.3060987983326493, 2.4948681515374105, 2.6749577009526324, 2.841956323714732, 2.99139233795158, 3.1188424658380036, 3.2200499595769068, 3.2910501738271343, 3.328300804299576, 3.328813138983201, 3.290279980314346, 3.2111953971444573, 3.0909611645312576, 2.9299746600995866, 2.729693120668258, 2.492669531603809, 2.2225560280226015, 1.9240715281219756, 1.60293138217813, 1.265738083653629, 0.9198335183863693, 0.573114780416262, 0.2338172051547422, -0.08973009987327389, -0.3893693786486494, -0.6573917239732824, -0.8868174456008184, -1.0716688679101878, -1.2072245294235082, -1.290243581126392, -1.3191494626784992, -1.294162705394188, -1.2173739792562128, -1.0927502574274888, -0.9260691816372458, -0.7247793173251831, -0.4977869068525345, -0.25517285882421253, -0.007846928942991672, 0.2328507848095646, 0.455587939907846, 0.6495019256046142, 0.8046678779438091, 0.9125534008092343, 0.9664399188526394, 0.9617906906300865, 0.8965465170490607, 0.7713321134651407, 0.5895589532302291, 0.35741407101269596, 0.0837287251974066, -0.2202741940954438, -0.5413497550928349, -0.8647077907814843, -1.1745817097285847, -1.454869029360022, -1.6898189061114972, -1.8647383741510852, -1.966686551663366, -1.9851249212151572, -1.9124920774051333, -1.7446731376927305, -1.4813373374875463, -1.1261221090934244, -0.6866480294247543, -0.1743561919049412, 0.39583247681203565, 1.0060280234951795, 1.6360360024316611, 2.2641512434814453, 2.868049055617823, 3.425735965556205, 3.9165175647361927, 4.3219383997188965, 4.626648323371881, 4.819151462069157, 4.892397972205426, 4.844184964080782, 4.6773411490214025, 4.399679587274381, 4.02371394616316, 3.566145399801443, 3.047139129516184, 2.4894206991082832, 1.917232759096813, 1.3552009878497524, 0.827164378677924, 0.35502850170598665, -0.04229909490282223, -0.349834780895213, -0.5572551986418344, -0.659401900908677, -0.6565233384003745, -0.5542365681746282, -0.3632057642829438, -0.09854996429979343, 0.22099235338237228, 0.5741001545575855, 0.9380542615523848, 1.2900057764501855, 1.6082587063911185, 1.8734944589967832, 2.069867404078757, 2.185906335860243, 2.215166239889709, 2.1565878557572913, 2.0145384929868286, 1.7985255706756826, 1.5225934254431448, 1.204432979248719, 0.8642517499018286, 0.5234673187924496, 0.20329973106590155, -0.07665346111244827, -0.29977233025841626, -0.4536143669192845, -0.5308803090011109, -0.5300792535140345, -0.45584260719068553, -0.31885634270065294, -0.135403448810475, 0.07346788721605244, 0.2831113540234947, 0.46672398700559564, 0.5969823471881397, 0.6477791746847954, 0.5959570622194533, 0.4229325444453922, 0.11610731585858226, -0.3300269200318372, -0.913167603298226, -1.6229209585223086, -2.4409933324705193, -3.341857475601751, -4.293868035205633, -5.260772314292698, -6.203536694587541, -7.0823877108994555, -7.858951067424697, -8.498363055088328, -8.971227610430589, -9.255298933604816, -9.33678394057231, -9.21118014739523, -8.883591688273004, -8.368497462643006, -7.688978984088147, -6.875449258876102, -5.963955781023177, -4.994158393693237, -4.007104447721891, -3.0429378467090102, -2.13868412159667, -1.3262500856516883, -0.6307639368030816, -0.0693605584718955, 0.3495115386098824, 0.6262189424332724, 0.769502079753933, 0.7954962115962452, 0.7262831375831319, 0.5880741065008374, 0.4091500505232373, 0.21770258933200262, 0.039726948321562365, -0.10288470392980661, -0.19391397710636127, -0.22393813568197468, -0.19092108342993847, -0.1002285022010483, 0.03593696250350055, 0.19964278107084046, 0.36879838571899687, 0.5190793199692543, 0.6260636956778021, 0.6674229772025675, 0.6250021646844973, 0.4866292745022971, 0.2475105283060489, -0.08890506198307495, -0.5106717054384646, -0.9977404761627768, -1.5229909801158563, -2.0538443795572268, -2.554357037580757, -2.9876562148465076, -3.31855054982659, -3.516130780209768, -3.5561718423604516, -3.4231567415778303, -3.1117650717070235, -2.6277034622326343, -1.9877993302436912, -1.2193301408115276, -0.35861439933791667, 0.5510560352491357, 1.46201390682103, 2.3251757489859104, 3.0931639562843523, 3.723377779150488, 4.180798781594839, 4.440331256075736, 4.488507716443687, 4.324432007097183, 3.9598849145211554, 3.4185757967996824, 2.734584472802036, 1.9500960154513018, 1.1125828417606927, 0.27162966929077953, -0.5243756870709534, -1.2314513043920945, -1.8129012338482295, -2.2416605592037024, -2.5019373342905107, -2.590034126394074, -2.5142918778971812, -2.294163552984077, -1.9584897393974179, -1.5431081383890588, -1.0879791138869284, -0.6340462590774073, -0.22007132198651919, 0.12031492572903708, 0.36112055692115747, 0.48586748945834496, 0.4886907603236394, 0.37457937091164173, 0.15874301046051775, -0.13484232878075542, -0.4755917874635, -0.8289978370030093, -1.1596280587584982, -1.4341913149143024, -1.624422254399299, -1.7095471485002507, -1.6781262273619995, -1.529116663861388, -1.2720624244675907, -0.9263875736121668, -0.5198427361542864, -0.08622444106746667, 0.33745170674257063, 0.7140957304168726, 1.009748135400376, 1.1965783447714229], 'positive_zeros': ['1.97556073725916873941508651806560', '2.87296423400372615319595313312816', '3.59084606235859465546508087826259', '4.47160297415081273664609038225796', '5.79389342278027564452531630299249', '6.22992941158733707669985663770447', '7.24849135833409535718776060619967', '7.71415707032317004086231541543419', '8.161680858577362267074985390650353', '9.735021410767016169660010183776362'], 'prelabel': '2-2736-228.227-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1685212341091173, 'root_angle': 0.8625799426819702, 'root_number': '-0.90824829046386301636621401245108 + 0.41843164659173464214626997185355*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4312899713409851', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.97556073725916873941508651807', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.87296423400372615319595313313', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.59084606235859465546508087826', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.3654418745638945, 'bad_primes': [2, 3, 19], 'central_character': '228.227', 'conductor': 2736, 'conductor_radical': 114, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2736/1/b/b/2735/2'], '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': '2-2736-228.227-c0-0-10', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-2736-228.227-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1685212341091173, 'root_angle': 0.4312899713409851, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.97556073725916873941508651807', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2504320754373908652705823887444', 'Lhash_array': ['2504320754373908652705823887444'], 'label': '2-2736-228.227-c0-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2736/1/b/b/2735/2'}