-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2042428801290498179054653390461', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [3.1622776601683795, 0.0], 'a6': [0.0, 0.0], 'a7': [5.162277660168379, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.611613287362019, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 23], 'central_character': '828.1', 'coefficient_field': 'CDF', 'conductor': 828, 'conductor_radical': 138, 'conjugate': '2042428801290498179054653390461', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.1622776601683795, 0], [5.0, 0]], [[1.0, 0], [-5.162277660168379, 0], [7.0, 0]], [[1.0, 0], [0, 0], [11.0, 0]], [[1.0, 0], [-4.0, 0], [13.0, 0]], [[1.0, 0], [7.162277660168379, 0], [17.0, 0]], [[1.0, 0], [1.1622776601683793, 0], [19.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [8.324555320336758, 0], [29.0, 0]], [[1.0, 0], [6.324555320336759, 0], [31.0, 0]], [[1.0, 0], [8.324555320336758, 0], [37.0, 0]], [[1.0, 0], [-2.0, 0], [41.0, 0]], [[1.0, 0], [-1.1622776601683793, 0], [43.0, 0]], [[1.0, 0], [0.32455532033675866, 0], [47.0, 0]], [[1.0, 0], [5.486832980505138, 0], [53.0, 0]], [[1.0, 0], [-8.324555320336758, 0], [59.0, 0]], [[1.0, 0], [-0.32455532033675866, 0], [61.0, 0]], [[1.0, 0], [-1.1622776601683793, 0], [67.0, 0]], [[1.0, 0], [0, 0], [71.0, 0]], [[1.0, 0], [14.649110640673518, 0], [73.0, 0]], [[1.0, 0], [-13.16227766016838, 0], [79.0, 0]], [[1.0, 0], [-4.0, 0], [83.0, 0]], [[1.0, 0], [-9.486832980505138, 0], [89.0, 0]], [[1.0, 0], [3.6754446796632414, 0], [97.0, 0]], [[1.0, 0], [6.0, 0], [101.0, 0]], [[1.0, 0], [7.486832980505138, 0], [103.0, 0]], [[1.0, 0], [-16.0, 0], [107.0, 0]], [[1.0, 0], [-14.0, 0], [109.0, 0]], [[1.0, 0], [11.16227766016838, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-828-1.1-c1-0-3', '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/828/2/a/f/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.366683913324901, 2.361527185598242, 2.3436400463969567, 2.306354971903627, 2.240318775371033, 2.135604991916596, 1.9839292145491412, 1.78065965061292, 1.5264488973795745, 1.2283743156232076, 0.9004794947844453, 0.5636020447440084, 0.24438665872315948, -0.02656827491865073, -0.21739685599116407, -0.29833827714809014, -0.24552423700140735, -0.04479088468275606, 0.30496555872624287, 0.7894114330722092, 1.3778719317247028, 2.02429113326105, 2.6702608192936634, 3.2500702569449853, 3.6974339420603473, 3.9532546785938862, 3.973521775952598, 3.736277516011976, 3.2465528926296416, 2.538305448537008, 1.6726953906336968, 0.7324911142236961, -0.18704737058851362, -0.9898740440762851, -1.591999325751165, -1.9336602724790053, -1.9888990449271646, -1.7708209021621113, -1.3313049913799375, -0.7547111074687683, -0.14606598194780218, 0.3848184395203439, 0.741011885676329, 0.8551078747417677, 0.701938723540411, 0.3048720288579475, -0.26590448284731727, -0.9034259650345564, -1.481175436522, -1.8749490723763436, -1.985759135277341, -1.7596808228746528, -1.2007797950601193, -0.37423733289893774, 0.6015954246441836, 1.573486315667493, 2.3792020159486795, 2.8765703768975484, 2.970388779755973, 2.631891529858265, 1.906590066843868, 0.9083176114044733, -0.2000902316333444, -1.2363508029202053, -2.033152077105422, -2.4707648245974134, -2.501179395771217, -2.1584824819549198, -1.5527677231086747, -0.8481802674410546, -0.22907045905266737, 0.1390479584594033, 0.1456083672973337, -0.23970258922718546, -0.9583268529217535, -1.8733957718899807, -2.7978360279843026, -3.5344115494042465, -3.9191736919907867, -3.85865556439545, -3.3521553007993528, -2.4934978599788202, -1.4511557564381834, -0.4305811280938441, 0.37308309266576273, 0.8211387876132188, 0.8653538040554117, 0.5613147957516413, 0.05712309518861924, -0.44081433847275836, -0.7175543728316863, -0.6035220814850625, -0.01962611230458244, 0.9977578177534809, 2.298851809210616, 3.650184496771878, 4.7857947330509205, 5.468267381071013, 5.545084701860018, 4.986416416006437, 3.8945964029436895, 2.482252420200931, 1.0237732838327835, -0.2084071560278005, -1.0071304558104373, -1.2776105122127177, -1.0562867271137295, -0.4964357341613695, 0.17593756518741668, 0.7245786669387714, 0.9674302639774337, 0.8258122624687945, 0.3448529138049793, -0.32081968275985845, -0.9527771809349617, -1.3338142695014907, -1.3145298334037545, -0.8626953670711445, -0.08078311217489943, 0.8146265890618436, 1.5474324478829937, 1.8568047312615497, 1.5721882648861887, 0.6676354117612392, -0.7205223826657422, -2.319133277646637, -3.781611281951836, -4.773411546527473, -5.057170107902751, -4.554530872687161, -3.3675132416303577, -1.7530409292299693, -0.0570586332363002, 1.3740637125313604, 2.280643447750739, 2.551369514038654, 2.242692274834376, 1.5510652024168547, 0.7467500013621361, 0.08908711902627572, -0.25138626476593967, -0.24055804849872148, 0.016315128168736898, 0.3172711467876672, 0.43880733225499413, 0.220091949660811, -0.37065446411489, -1.2097330442090706, -2.041895417905335, -2.549691411774247, -2.448932751722753, -1.5820100244657656, 0.01981714690964527, 2.1258311675133124, 4.3528225180480895, 6.258339207565511, 7.454676790607483, 7.711094886117917, 7.01441360558264, 5.56989168743283, 3.7417473319868013, 1.9506323848217495, 0.5583099534916381, -0.22635983232614557, -0.3925888139177039, -0.11154811301027742, 0.3344308592114901, 0.6537112911607648, 0.64500053464159, 0.2624609773967776, -0.3747236492137139, -1.0311055902813158, -1.4455023980228217, -1.4325868113838593, -0.9605686578647112, -0.17725660751175074, 0.6265609571387237, 1.1066856881582994, 0.9801258369618933, 0.12738186015466868, -1.3523638101369229, -3.1537189836331048, -4.844334728832066, -5.98821522823294, -6.275300113368011, -5.616395637176767, -4.172655550967667, -2.3091997670235287, -0.48664437169433367, 0.8755700212245968, 1.5208178224315916, 1.4233440287420542, 0.7815574002231307, -0.06014153754310397, -0.7341811729173111, -0.9757783541272482, -0.7096845269845131, -0.06880083255023449, 0.6609488748362116, 1.1497496650121324, 1.1485522486049546, 0.5851606868398161, -0.4027162669289713, -1.5101591724431707, -2.3696608337983807, -2.681727057387847, -2.325570291788281, -1.4099944216771385, -0.2447053949655856, 0.7601799938155015, 1.2332091315057987, 0.9716540276475435, 0.01693887938636433, -1.3521707828520824, -2.708144117852679, -3.616045057004211, -3.779756462224701, -3.1426216431512803, -1.9071457466585717, -0.4661215856448224, 0.7316394040766824, 1.334690652516581, 1.2080585008136993, 0.4763146275936372, -0.5246377628424951, -1.3701399692264602, -1.700329255814371, -1.3500355085223874, -0.4085663576192544, 0.8121951951916166, 1.8901250874843265, 2.445329879420729, 2.2777469834885724, 1.4399597432542515, 0.21858194628691957, -0.9692678023552352, -1.7268197489749555, -1.8206933152787588, -1.2635316834360557, -0.3056020165102603, 0.661749905474007, 1.2550823542576999, 1.2446368132104337, 0.6418367600411181, -0.30538946742900364, -1.209113257826299, -1.694649444329521, -1.5532092436504739, -0.835470924196137, 0.15162993931586713, 0.9471572026649483, 1.1026154864254316, 0.35272693839653246, -1.2725712393631978, -3.437916715797456, -5.600675528046901, -7.184541479678876], 'positive_zeros': ['1.61119223303548843822803153001004', '2.14444362300537962490348661757883', '3.97367952161048494125997948308849', '5.03167345791127829130952304270376', '5.69509868360448891261747734117128', '6.67419979706049240262632824264411', '7.72743195267520578806323410302326', '8.814210656265356122233352271983858', '9.062606422950711948310847894300471', '10.43613806945451780802420112718461'], 'prelabel': '2-828-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5713057553239405, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.61119223303548843822803153001', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.14444362300537962490348661758', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.97367952161048494125997948309', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 6.611613287362019, 'bad_primes': [2, 3, 23], 'central_character': '1.1', 'conductor': 828, 'conductor_radical': 138, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/828/2/a/f/1/2'], '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': '2-828-1.1-c1-0-3', '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': '2-828-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5713057553239405, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.61119223303548843822803153001', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2042428801290498179054653390461', 'Lhash_array': ['2042428801290498179054653390461'], 'factors': ['2-828-1.1-c1-0-3'], 'label': '2-828-1.1-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/828/2/a/f/1/2'}