-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1657185640358837509542143366890', 'a10': 0, 'a2': 0, 'a3': -3, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 3, 'a8': 0, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.544648747873758, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]], [37, [1, -1]]], 'bad_primes': [2, 5, 37], 'central_character': '3700.1', 'coefficient_field': '1.1.1.1', 'conductor': 3700, 'conductor_radical': 370, 'degree': 2, 'euler_factors': [[1], [1, 3, 3], [1], [1, -3, 7], [1, -5, 11], [1, 2, 13], [1, 4, 17], [1, 4, 19], [1, 6, 23], [1, -6, 29], [1, 4, 31], [1, -1], [1, 9, 41], [1, 10, 43], [1, -11, 47], [1, -11, 53], [1, 8, 59], [1, 8, 61], [1, -8, 67], [1, -3, 71], [1, 7, 73], [1, -8, 79], [1, -9, 83], [1, 16, 89], [1, 12, 97], [1, 9, 101], [1, -6, 103], [1, 4, 107], [1, -12, 109], [1, 14, 113]], 'euler_factors_factorization': [[1], [[[1, 3, 3], 1]], [1], [[[1, -3, 7], 1]], [[[1, -5, 11], 1]], [[[1, 2, 13], 1]], [[[1, 4, 17], 1]], [[[1, 4, 19], 1]], [[[1, 6, 23], 1]], [[[1, -6, 29], 1]], [[[1, 4, 31], 1]], [[[1, -1], 1]], [[[1, 9, 41], 1]], [[[1, 10, 43], 1]], [[[1, -11, 47], 1]], [[[1, -11, 53], 1]], [[[1, 8, 59], 1]], [[[1, 8, 61], 1]], [[[1, -8, 67], 1]], [[[1, -3, 71], 1]], [[[1, 7, 73], 1]], [[[1, -8, 79], 1]], [[[1, -9, 83], 1]], [[[1, 16, 89], 1]], [[[1, 12, 97], 1]], [[[1, 9, 101], 1]], [[[1, -6, 103], 1]], [[[1, 4, 107], 1]], [[[1, -12, 109], 1]], [[[1, 14, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 38, 'label': '2-3700-1.1-c1-0-38', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/3700/2/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-7.833463567542004e-61, 0.12492754188801554, 0.24901025157113096, 0.37136638841835656, 0.49104342052362626, 0.6069899543441579, 0.7180358221197017, 0.8228820900318718, 0.9201021006907257, 1.0081540164198337, 1.0854047378992042, 1.1501645670393574, 1.200731573330671, 1.2354443031038422, 1.2527412257731987, 1.2512251222215378, 1.2297304722316476, 1.1873917794085542, 1.123710678300616, 1.0386195997186582, 0.9325397310743376, 0.8064310061684375, 0.6618319018308085, 0.5008869157722298, 0.3263597585953723, 0.1416305189740765, -0.049324642004408364, -0.24197234281128152, -0.4312800176590364, -0.6117932739118491, -0.777732152600667, -0.9231052767630351, -1.0418402483879972, -1.1279280219289352, -1.1755783607856884, -1.1793828946603229, -1.134481763082656, -1.0367293767691808, -0.8828544763438985, -0.6706094383858683, -0.39890369049409835, -0.06791616553419173, 0.32081803821301935, 0.7643512132221805, 1.258300651042914, 1.7968633821580755, 2.3728702120294694, 2.9778801632719687, 3.6023152640386087, 4.235634368622102, 4.8665433944012255, 5.483238050597337, 6.073673863321914, 6.625857114635077, 7.128149257856364, 7.569576493031697, 7.9401355281170645, 8.231086151099941, 8.435221127316614, 8.547104137695152, 8.563267000816795, 8.48235827678253, 8.305236524238712, 8.035002951521024, 7.676969934279217, 7.238563818755746, 6.729162534732167, 6.1598707381279265, 5.5432374158620155, 4.8929230352037445, 4.2233253243473285, 3.5491745488602673, 2.8851106223300858, 2.2452554884460385, 1.6427948757248823, 1.0895837083014974, 0.5957891258548922, 0.16958421022977563, -0.18309585717380736, -0.45872534680533145, -0.656279685959413, -0.7772424405022775, -0.825525661145634, -0.8073048305374104, -0.73077286464973, -0.6058207844664013, -0.4436556545521228, -0.25636905771528773, -0.0564716201801973, 0.14358918816823757, 0.3319096694917896, 0.49759023106004896, 0.6311570856619926, 0.724928070852872, 0.7733071767717845, 0.7729948995030784, 0.7231046742521178, 0.6251792817539413, 0.483105128089395, 0.3029265167281441, 0.09256629069210909, -0.13853665823811956, -0.37985871938932086, -0.6202741390088847, -0.8485686086366621, -1.0539617904284153, -1.2266157693452804, -1.3581064694869762, -1.4418361346388215, -1.4733670410644073, -1.4506596280950328, -1.3742020986628003, -1.2470231147994022, -1.074584311774003, -0.8645547673209365, -0.6264750548156891, -0.37132383370174815, -0.11100483706799151, 0.14222363572637597, 0.37635124418110366, 0.5802223700790009, 0.7441182509929746, 0.8602858363880821, 0.9233862878504959, 0.9308389397018599, 0.8830406711375645, 0.7834458688944232, 0.6384982758581045, 0.45741277147607246, 0.25181221976844853, 0.035231627753604854, -0.17749135477396605, -0.3709144281497162, -0.5297467968898344, -0.6396292398838825, -0.6879014244177267, -0.6643190227700698, -0.561684179125055, -0.3763556407043113, -0.10860934503293761, 0.23717370496085516, 0.6525080757167988, 1.1250004478547897, 1.6387404116459148, 2.174874542823357, 2.712343664256881, 3.2287547070578517, 3.7013511561712895, 4.108040095931051, 4.428429699452482, 4.644828896031461, 4.743161075988492, 4.713746123064706, 4.551909761129425, 4.258386013342607, 3.8394872384134136, 3.3070263712247114, 2.677987209777388, 1.9739503470157367, 1.2202940914543834, 0.4452008844105158, -0.3214902554841343, -1.049536368636426, -1.7095931350057643, -2.274508497395372, -2.7205473936514273, -3.028489487762653, -3.1845464562463603, -3.1810527399125137, -3.01689341913569, -2.6976445931621438, -2.2354148113386145, -1.6483901013441256, -0.9600992944681149, -0.19842996425760243, 0.6055623136225173, 1.4189981461889603, 2.208610618451124, 2.94220714219599, 3.5900882703353743, 4.126356209476488, 4.530050427474661, 4.786055581598129, 4.88573764235477, 4.827277062469888, 4.615682515594532, 4.262484381663061, 3.785122998723534, 3.206061924525505, 2.5516702639630844, 1.8509297903430886, 1.1340314898125614, 0.43093179562078054, -0.23005917644938337, -0.8235867713958295, -1.3283930709203517, -1.7282338621984807, -2.01252666126457, -2.1766993456384895, -2.222224794572257, -2.156343590940908, -1.9914934129881987, -1.7444793372434089, -1.4354330294435005, -1.0866199527900027, -0.7211616418071839, -0.36174431696571274, -0.029385391910705074, 0.2576742887517778, 0.4848921644653138, 0.6421102388968678, 0.7239702773140136, 0.7300380600398839, 0.6646337757975237, 0.5363827760529825, 0.35751725288469477, 0.14297399422858498, -0.09065465297703391, -0.32625084254657954, -0.5473117796267615, -0.7390296607725092, -0.8892436021153234, -0.9892039480320697, -1.0341008202399313, -1.0233232638428493, -0.9604320375524225, -0.8528470007744489, -0.7112681023311477, -0.5488660792303962, -0.3802940720193499, -0.22058350075747254, -0.0839959286709007, 0.017093312488373317, 0.0732045803947783, 0.07858664653337898, 0.031812694326482226, -0.06390660261819575, -0.20072210650736655, -0.3664672881389425, -0.5452909506522886, -0.7185710029686749, -0.866059859144723, -0.9671957958121886, -1.0025020010705483, -0.9549869647754158, -0.81145690786778, -0.5636534448290113, -0.20913761129316555, 0.24814557142153293, 0.7976703414342154, 1.4225286218845097, 2.1000277133002765, 2.802667102614978, 3.499450500147681, 4.157467432350933, 4.743660265614725, 5.226678623933751], 'positive_zeros': ['1.30728896437273467280345954384239', '2.09146483456977231198455242249591', '3.93322311807360794055015553666069', '4.48295490912051991181364428828808', '5.09888884088066200767920008704416', '5.96334860425801266051119721220395', '6.60981396730997064078221589990867', '7.07577695780277543069908710611090', '8.154290748669424388477852300388563'], 'prelabel': '2-3700-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.435498941943946, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 1686559431193864007, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.30728896437273467280345954384', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.09146483456977231198455242250', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.93322311807360794055015553666', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 29.544648747873758, 'bad_primes': [2, 5, 37], 'central_character': '1.1', 'conductor': 3700, 'conductor_radical': 370, 'degree': 2, 'dirichlet_coefficients': [1, 0, -3, 0, 0, 0, 3, 0, 6, 0, 5, 0, -2, 0, 0, 0, -4, 0, -4, 0, -9, 0, -6, 0, 0, 0, -9, 0, 6, 0, -4, 0, -15, 0, 0, 0, 1, 0, 6, 0, -9, 0, -10, 0, 0, 0, 11, 0, 2, 0, 12, 0, 11, 0, 0, 0, 12, 0, -8, 0, -8, 0, 18, 0, 0, 0, 8, 0, 18, 0, 3, 0, -7, 0, 0, 0, 15, 0, 8, 0, 9, 0, 9, 0, 0, 0, -18, 0, -16, 0, -6, 0, 12, 0, 0, 0, -12, 0, 30, 0], 'euler11': [1, -5, 11], 'euler13': [1, 2, 13], 'euler17': [1, 4, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 6, 23], 'euler29': [1, -6, 29], 'euler3': [1, 3, 3], 'euler31': [1, 4, 31], 'euler37': [1, -1, 0], 'euler41': [1, 9, 41], 'euler43': [1, 10, 43], 'euler47': [1, -11, 47], 'euler5': [1, 0, 0], 'euler53': [1, -11, 53], 'euler59': [1, 8, 59], 'euler61': [1, 8, 61], 'euler67': [1, -8, 67], 'euler7': [1, -3, 7], 'euler71': [1, -3, 71], 'euler73': [1, 7, 73], 'euler79': [1, -8, 79], 'euler83': [1, -9, 83], 'euler89': [1, 16, 89], 'euler97': [1, 12, 97], 'euler_factors': [[1, 0, 0], [1, 3, 3], [1, 0, 0], [1, -3, 7], [1, -5, 11], [1, 2, 13], [1, 4, 17], [1, 4, 19], [1, 6, 23], [1, -6, 29], [1, 4, 31], [1, -1, 0], [1, 9, 41], [1, 10, 43], [1, -11, 47], [1, -11, 53], [1, 8, 59], [1, 8, 61], [1, -8, 67], [1, -3, 71], [1, 7, 73], [1, -8, 79], [1, -9, 83], [1, 16, 89], [1, 12, 97]], 'index': 38, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/3700/a', 'ModularForm/GL2/Q/holomorphic/3700/2/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/3700/2/a/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-3700-1.1-c1-0-38', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-3700-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.435498941943946, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1686559431193864007, 'z1': {'__RealLiteral__': 0, 'data': '1.30728896437273467280345954384', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 20037505
{'Lhash': '1657185640358837509542143366890', 'Lhash_array': ['1657185640358837509542143366890'], 'label': '2-3700-1.1-c1-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3700/2/a/a'}
-
id: 24562693
{'Lhash': '1657185640358837509542143366890', 'Lhash_array': ['1657185640358837509542143366890'], 'label': '2-3700-1.1-c1-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3700/2/a/a/1/1'}
-
id: 22640
{'Lhash': '1686559431193864007', 'Lhash_array': ['1686559431193864007'], 'label': '2-3700-1.1-c1-0-38', 'type': 'ECQ', 'url': 'EllipticCurve/Q/3700/a'}