-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2583585573112863572174213182175', 'a10': [-3.1555626481273578, -0.2059717789976505], 'a2': [-1.279846935642088, 0.6016575615144855], 'a3': [1.5525532970915947, -1.5525532970915947], 'a4': [1.2760163573448864, -1.5400591728204105], 'a5': [1.9573563535699523, 1.0810902391286954], 'a6': [-1.0529251488542946, 2.9211360105531012], 'a7': [3.0295256892642777, -3.0295256892642777], 'a8': [-0.7065173782698887, 2.738764903054412], 'a9': [0.0, -1.820843480619963], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.076110452553291, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.279846935642088, -0.6016575615144855]]], [5, [[1.0, 0], [-1.9573563535699523, -1.0810902391286954]]], [13, [[1.0, 0], [0.9336593422829315, -3.482568051390784]]]], 'bad_primes': [2, 5, 13], 'central_character': '260.103', 'coefficient_field': 'CDF', 'conductor': 260, 'conductor_radical': 130, 'conjugate': '2023888102990399705703670859145', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.279846935642088, -0.6016575615144855]], [[1.0, 0], [-1.5525532970915947, 1.5525532970915947], [0, -3.0]], [[1.0, 0], [-1.9573563535699523, -1.0810902391286954]], [[1.0, 0], [-3.0295256892642777, 3.0295256892642777], [0, -7.0]], [[1.0, 0], [4.004180515500765, 0], [11.0, 0]], [[1.0, 0], [0.9336593422829315, -3.482568051390784]], [[1.0, 0], [0.753954734483801, -0.753954734483801], [0, -17.0]], [[1.0, 0], [0, 4.019289953586823], [-19.0, 0]], [[1.0, 0], [3.757998465281778, -3.757998465281778], [0, -23.0]], [[1.0, 0], [0, 6.60247267260383], [-29.0, 0]], [[1.0, 0], [-2.3563569182836908, 0], [31.0, 0]], [[1.0, 0], [0.45448683939485063, 0.45448683939485063], [0, 37.0]], [[1.0, 0], [0, -5.012580864359753], [-41.0, 0]], [[1.0, 0], [4.326858777145555, -4.326858777145555], [0, -43.0]], [[1.0, 0], [-3.8721078074722928, 3.8721078074722928], [0, -47.0]], [[1.0, 0], [-1.3470916092736824, -1.3470916092736824], [0, 53.0]], [[1.0, 0], [0, -0.8380041122630446], [-59.0, 0]], [[1.0, 0], [13.358552008651685, 0], [61.0, 0]], [[1.0, 0], [3.6964932183704784, -3.6964932183704784], [0, -67.0]], [[1.0, 0], [14.683932444636541, 0], [71.0, 0]], [[1.0, 0], [-5.33956007915042, 5.33956007915042], [0, -73.0]], [[1.0, 0], [3.439735337511942, 0], [79.0, 0]], [[1.0, 0], [-4.47418279656524, -4.47418279656524], [0, 83.0]], [[1.0, 0], [-6.306980348297531, 0], [89.0, 0]], [[1.0, 0], [-9.646164888495225, -9.646164888495225], [0, 97.0]], [[1.0, 0], [-10.340909345870923, 0], [101.0, 0]], [[1.0, 0], [3.3339993038489077, -3.3339993038489077], [0, -103.0]], [[1.0, 0], [7.789162177824631, 7.789162177824631], [0, 107.0]], [[1.0, 0], [-3.1676043621689556, 0], [109.0, 0]], [[1.0, 0], [-9.758445455964287, -9.758445455964287], [0, 113.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 23, 'label': '2-260-260.103-c1-0-23', '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/260/2/p/d/103/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.3141880478706511, 1.3516684446647504, 1.394546009865349, 1.4403812423885767, 1.484682595067603, 1.521456504971906, 1.5438421932460547, 1.5447500907576492, 1.5174830885787254, 1.4563491843648486, 1.3572725434262138, 1.218391879544349, 1.0406131222770065, 0.828064734442801, 0.5883920290962233, 0.33282290481441285, 0.0759424337463072, -0.16487180279516958, -0.3703778480424925, -0.5207526803987386, -0.597183118346739, -0.5836736667259689, -0.46893793301227266, -0.2482029242622934, 0.07527082148134433, 0.4891602188199764, 0.9717374229934868, 1.49237454088759, 2.0129946710755235, 2.490484922868972, 2.879985652188127, 3.1388597558128684, 3.2310379954397987, 3.1313444043884573, 2.829343831673104, 2.3322343904141927, 1.6663407080959676, 0.8768541988696887, 0.025612403903326628, -0.8130983035943595, -1.5585102210104675, -2.130676655633514, -2.4584655519683354, -2.4874425455180584, -2.186760049567456, -1.5541849571340232, -0.6185217831211961, 0.5610815831316588, 1.8991385568130403, 3.2909536621267406, 4.6222979926792345, 5.78069106289672, 6.667075851984993, 7.20653140211455, 7.356688881433401, 7.112715627141532, 6.5080967766545, 5.6109402831229085, 4.51610059087055, 3.333984916672428, 2.177392887770632, 1.1480687140336352, 0.3247552568975111, -0.24560105327667903, -0.5522336385547031, -0.6198615388862607, -0.5029766332675338, -0.2759239145800966, -0.02025089659485745, 0.18873165952425838, 0.294054704585898, 0.2658902037528557, 0.105553664283717, -0.15603111050061808, -0.4652343071500952, -0.756889054393142, -0.9678366581856979, -1.0504527095230267, -0.9836454942903302, -0.7791432995964256, -0.48162346680018636, -0.16228108474358427, 0.09337638459492827, 0.2015946806887212, 0.09752723126036666, -0.2497030761718726, -0.8270702048888929, -1.575155517425346, -2.3942142522535157, -3.158404228774164, -3.736231706359823, -4.013956049175426, -3.9178823704702306, -3.431350069166511, -2.6028716337440425, -1.5432291973524526, -0.41119782304897023, 0.610374583372195, 1.3445104179638392, 1.6510938204449999, 1.4534083984691435, 0.755175065625969, -0.3555363873817583, -1.7169678890143678, -3.1177720130202466, -4.330897520222352, -5.151632482564052, -5.433144112680791, -5.113015939415938, -4.225670600569614, -2.897978276831208, -1.3283753912398775, 0.24709637215472624, 1.5958664219047591, 2.529556754737403, 2.9367564664656154, 2.801597214220956, 2.204471184121919, 1.3046134039829878, 0.3077937308632125, -0.574667253660921, -1.1675423972161605, -1.3657496445711477, -1.1539805296771073, -0.6079109684273495, 0.12329367372917066, 0.849632764199147, 1.3813675787603126, 1.570018222260494, 1.3406485568555646, 0.7085729166669364, -0.22315134188711622, -1.2850229610161912, -2.276731740455277, -3.009536681047497, -3.3462545134486716, -3.2301522651896017, -2.696378244169352, -1.863344450173054, -0.9058821969273041, -0.016062617473838095, 0.6396130117407215, 0.9570495488653519, 0.91707461026503, 0.5884598715956537, 0.11066956488978813, -0.3397997793922875, -0.5918039453854524, -0.5208768021518001, -0.07985851725219252, 0.6884148011364543, 1.6594693092832822, 2.654784173677769, 3.482234449094876, 3.979895057330763, 4.052832375939589, 3.69411213622334, 2.9850006376811034, 2.07436097677459, 1.1423417118817292, 0.3573661035669209, -0.16284291947452859, -0.37640872185110863, -0.3222676998788406, -0.10374917055516024, 0.14485693698612692, 0.2997657060728835, 0.285815098667921, 0.10036612208210262, -0.18446550692572172, -0.443123802110338, -0.5369695723686482, -0.3636115768008773, 0.0981051083338762, 0.7607146563518847, 1.4280570221842848, 1.8258614679997138, 1.6586150442026102, 0.6811503456247187, -1.2314224774786036, -4.032872674774527, -7.488332374448904, -11.197427777819488, -14.656230538839658, -17.346939346445822, -18.83707612015678, -18.866821128075305, -17.40485151873684, -14.659461548477553, -11.041454674654702, -7.08608376947703, -3.3506266745848476, -0.3097665621257162, 1.7285924038756126, 2.6692704733370958, 2.628705034426312, 1.8889714878768118, 0.8194448271021868, -0.2142308071801927, -0.9319462339874001, -1.192936194202148, -1.010509757292209, -0.5268303147737929, 0.04302833418693965, 0.4811240992875234, 0.6313200789709157, 0.44148494989716563, -0.02705405247517874, -0.6236997009550524, -1.1579614398919877, -1.4588003743556006, -1.4263591712980357, -1.061127891132176, -0.4624335394121939, 0.20278851520882432, 0.751274886798335, 1.0392498589166654, 1.0059577091643976, 0.6917336448639374, 0.22499203995656847, -0.21819005527340965, -0.4698858677456862, -0.4246335382566317, -0.07542986767816338, 0.48029567448812527, 1.0676413152845388, 1.4871049586040193, 1.5781754248499598, 1.274539662107304, 0.6334668319007272, -0.1711136607685124, -0.8919295778004377, -1.2772746277807294, -1.146509111068221, -0.450185872378227, 0.7038074784838483, 2.0677305080538617, 3.3125404804258616, 4.112953737833855, 4.236151650956351, 3.609210281907885, 2.3453723273016593, 0.7202248993068389, -0.8972472842950954, -2.1408034680057613, -2.744105670294859, -2.611709623376399, -1.843447979236472, -0.7045482266142038, 0.45086833605837284, 1.2817824900416004, 1.5589321140271606, 1.2317185629852627, 0.44359621512119174, -0.5092849210389394, -1.2650633988661864, -1.5042066469981141], 'positive_zeros': ['2.03808965392176013663625205666154', '2.97400272712245451568766907795269', '4.75373170673852127244828492348114', '5.81822630676286412818251083799782', '7.81390945796863846274443032907839', '8.510477064169096786927919422144159', '9.055083650863794571591616572327370', '10.19781293643616045592718488159369', '10.54534228937755372560072934102182', '12.04749267379940251657829326551134'], 'prelabel': '2-260-260.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4408714212424685, 'root_angle': 0.14045303670304746, 'root_number': '0.9042201429721503 + 0.4270666611237925*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0702265183515', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.03808965392176013663625205666', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.97400272712245451568766907795', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.75373170673852127244828492348', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2.076110452553291, 'bad_primes': [2, 5, 13], 'central_character': '260.103', 'conductor': 260, 'conductor_radical': 130, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/260/2/p/d/103/5'], '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': '2-260-260.103-c1-0-23', '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': '2-260-260.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4408714212424685, 'root_angle': 0.07022651835152373, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.03808965392176013663625205666', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2583585573112863572174213182175', 'Lhash_array': ['2583585573112863572174213182175'], 'label': '2-260-260.103-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/260/2/p/d/103/5'}