-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1491447605783311069064260896689', 'a10': [-0.25881904510252074, -0.9659258262890683], 'a2': [-0.7071067811865476, 0.7071067811865476], 'a3': [0.9659258262890683, 0.25881904510252074], 'a4': [0.0, -1.0], 'a5': [-0.5, 0.8660254037844386], 'a6': [-0.8660254037844386, 0.5], 'a7': [0.0, 0.0], 'a8': [0.7071067811865476, 0.7071067811865476], 'a9': [0.8660254037844386, 0.5], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8683731219814242, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]], [3, [[1.0, 0], [-0.9659258262890683, -0.25881904510252074]]], [5, [[1.0, 0], [0.5, -0.8660254037844386]]], [29, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5, 29], 'central_character': '1740.347', 'coefficient_field': 'CDF', 'conductor': 1740, 'conductor_radical': 870, 'conjugate': '1801356967548518063365192378260', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [-0.9659258262890683, -0.25881904510252074]], [[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0, 0.5176380902050415], [-1.0, 0]], [[1.0, 0], [-1.3660254037844386, 1.3660254037844386], [0, -1.0]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0, -1.4142135623730951], [-1.0, 0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-0.5176380902050415, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [1.224744871391589, -1.224744871391589], [0, -1.0]], [[1.0, 0], [0.7071067811865476, -0.7071067811865476], [0, -1.0]], [[1.0, 0], [1.3660254037844386, 1.3660254037844386], [0, 1.0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0, 1.9318516525781366], [-1.0, 0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0, -1.0], [-1.0, 0]], [[1.0, 0], [0, 0], [0, -1.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-1740-1740.347-c0-0-4', 'leading_term': '1.100118759366440029485784358472', '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/1740/1/v/c/347/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.10011875936644, 1.0766057744621373, 1.0619081595443778, 1.0538256761683717, 1.0496318333187988, 1.046381387436554, 1.0411723078367332, 1.0313324832335498, 1.014533898400009, 0.9888530978503639, 0.9527987633001124, 0.9053223400372532, 0.8458213787872135, 0.7741401506934371, 0.6905687008814686, 0.595839559458943, 0.49112038188801393, 0.3780004711649872, 0.2584691907245239, 0.13488455679016217, 0.00993071441150364, -0.1134364969839166, -0.2320561246541881, -0.3426404722021083, -0.44186428666814936, -0.5264631768038518, -0.5933390776398643, -0.6396700144903668, -0.6630209160121113, -0.661451803638177, -0.633619366530803, -0.5788677391191839, -0.49730425220811497, -0.38985604518949146, -0.25830371822427695, -0.10528867596451837, 0.06570853155068487, 0.2504207371562077, 0.443878433644977, 0.6405255576016912, 0.834365312790512, 1.0191332767703607, 1.1884937274779195, 1.3362538535652577, 1.4565893290241716, 1.5442736967263908, 1.5949031742440505, 1.6051079230739884, 1.5727405579854496, 1.497032757181176, 1.3787112959568064, 1.220065682934954, 1.024960829795484, 0.798789816913861, 0.5483637948362107, 0.2817383334021255, 0.007978027433710061, -0.26313619496797475, -0.5214499373434762, -0.7568186393675115, -0.9595191629136895, -1.1206753811001027, -1.232681790647827, -1.2896079937466522, -1.2875663419809313, -1.2250251760148616, -1.1030509807048967, -0.9254644275618441, -0.6988976845528907, -0.43274349252037203, -0.13899025849676017, 0.16805831473441032, 0.4721759017266734, 0.7557105275937713, 1.000172992766265, 1.1868992596472532, 1.2977650915997538, 1.3159276488188092, 1.226565993691913, 1.0175907168954028, 0.6802923083540849, 0.20989856594442666, -0.39398668857779534, -1.1270880360511608, -1.9803259559582373, -2.9398616782283473, -3.987327099015496, -5.10024018931266, -6.252598626501398, -7.415636578984338, -8.558722014663209, -9.650364935878253, -10.659300910100875, -11.555609486991692, -12.311823847888213, -12.90398654689189, -13.312606627185165, -13.523475804634892, -13.528305786685452, -13.325155028468378, -12.91862111762189, -12.319784234318412, -11.545897384913502, -10.619829923575683, -9.569281776933199, -8.425796267672743, -7.223608988015407, -5.998378320207198, -4.78584950395782, -3.620508247509407, -2.534281500367974, -1.5553419931676467, -0.7070694686837595, -0.007215273181696053, 0.5326916243626645, 0.9076697147305656, 1.1193257914928398, 1.1756093193355748, 1.0902915517048373, 0.8821937737243731, 0.5742012252692663, 0.19210982909604543, -0.236638761799579, -0.6842725503385243, -1.1239910414654848, -1.531190058063487, -1.884549769216752, -2.166933024006978, -2.3660507520439946, -2.47486321834546, -2.491699707631462, -2.4200940542039677, -2.2683485464074127, -2.0488533036247247, -1.7772014438063795, -1.4711514813058082, -1.149496768209945, -0.8309069060118301, -0.532807568559193, -0.27036294769630215, -0.055619125427069115, 0.10314263196532869, 0.20180589259005208, 0.24055011841021323, 0.22370644461217523, 0.1593483581974839, 0.058643542380390455, -0.06499213236654236, -0.19688504985521696, -0.32217592337828577, -0.4269050125351442, -0.499040398952148, -0.5293819301459666, -0.5122803411498303, -0.44612184052059456, -0.33354252447395644, -0.18135356694918495, -0.0001762566390485387, 0.1961954736094064, 0.39166949906134035, 0.5689153572082548, 0.7105447470955242, 0.8003385175975986, 0.8244410553167172, 0.7724429455355204, 0.6382777725407377, 0.42086877060786543, 0.1244752451740975, -0.24129352316853356, -0.6618088290657901, -1.1180877971321765, -1.5877619074262115, -2.0462970585121383, -2.468395852562733, -2.829499121435193, -3.107294949420205, -3.2831402888698866, -3.343303072806448, -3.2799414958661828, -3.091751470729729, -2.784232411157616, -2.3695443524826962, -1.8659546317036078, -1.2968983560017424, -0.6897020373252761, -0.07404241564465212, 0.5197688969498957, 1.0625710587962764, 1.5280991280076186, 1.8945779431704752, 2.146061237576314, 2.2734265592018597, 2.274956792461389, 2.156464273765447, 1.9309421405269374, 1.6177578624906144, 1.2414339261639786, 0.8300883941280159, 0.41363165351976494, 0.021833438679121547, -0.31761515991885136, -0.5809173868371155, -0.7497426941587414, -0.8124472872037413, -0.7648573267585665, -0.6105564862853424, -0.3606517928502263, -0.03302636733859555, 0.3488774564354894, 0.7576684651932752, 1.163905937918235, 1.538161866322707, 1.8531061720129938, 2.0854706525330036, 2.2177527535607067, 2.239535291123505, 2.148322152413327, 1.9498213739354207, 1.6576438682242565, 1.2924260507727716, 0.8804250336541081, 0.451673125037354, 0.03781141318709497, -0.3302521982985161, -0.6246989701847133, -0.8230024154441412, -0.9098176739034296, -0.878413785751322, -0.731533357955222, -0.48160080007833295, -0.15024348539260401, 0.2328629476797107, 0.6317665493739153, 1.0065250155469168, 1.3158636599626985, 1.5200334352650184, 1.5836781269927436, 1.478513610946561, 1.1856292717970556, 0.6972421824681763, 0.0177673640086961, -0.835889568175229, -1.83486052948369, -2.9396522424915847, -4.102225709858912, -5.268698851153593, -6.382508126738502, -7.387830042037622, -8.233041354739164, -8.873989404236603, -9.276852072843868, -9.420390235376923, -9.29743285124155, -8.915483793745231, -8.296396927342021, -7.475128012239992, -6.497634515564512], 'positive_zeros': ['1.17654470838793353186971995529218', '2.08749309471942615241661129991878', '3.28295562416785701597970150049861', '4.12822176593897267908685090858615', '4.76796261795818881804319049977441', '6.62177527530703877729981099985796', '7.11665935546558348038615293503992', '8.221336948596840343416919075696512', '8.583414417162089165668108904243801', '9.199272734735406085247546194140625'], 'prelabel': '2-1740-1740.347-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9318653990686768, 'root_angle': -0.21310409558739168, 'root_number': '0.22975292054736118352393736938184 - 0.97324898946773016378805774830813*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.21310409558739168', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.17654470838793353186971995529', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.08749309471942615241661129992', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.28295562416785701597970150050', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.8683731219814242, 'bad_primes': [2, 3, 5, 29], 'central_character': '1740.347', 'conductor': 1740, 'conductor_radical': 870, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1740/1/v/c/347/2'], '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': '2-1740-1740.347-c0-0-4', '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': '2-1740-1740.347-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9318653990686768, 'root_angle': -0.21310409558739168, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.17654470838793353186971995529', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1491447605783311069064260896689', 'Lhash_array': ['1491447605783311069064260896689'], 'factors': ['2-1740-1740.347-c0-0-4'], 'label': '2-1740-1740.347-c0-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1740/1/v/c/347/2'}