-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2450136949098847204047158078582', 'a10': [7.859300623245923, 0.0], 'a2': [-2.599637929274334, 0.0], 'a3': [2.0948422546893815, 0.0], 'a4': [4.758117363321746, 0.0], 'a5': [-3.0232289407470594, 0.0], 'a6': [-5.44583138113708, 0.0], 'a7': [-0.5613896169960825, 0.0], 'a8': [-7.170106511081331, 0.0], 'a9': [1.3883640720320918, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.367816990564039, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[547, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [547], 'central_character': '547.1', 'coefficient_field': 'CDF', 'conductor': 547, 'conductor_radical': 547, 'conjugate': '2450136949098847204047158078582', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.599637929274334, 0], [2.0, 0]], [[1.0, 0], [-2.0948422546893815, 0], [3.0, 0]], [[1.0, 0], [3.0232289407470594, 0], [5.0, 0]], [[1.0, 0], [0.5613896169960825, 0], [7.0, 0]], [[1.0, 0], [-4.2311110349177925, 0], [11.0, 0]], [[1.0, 0], [4.879635953687952, 0], [13.0, 0]], [[1.0, 0], [6.399646734782715, 0], [17.0, 0]], [[1.0, 0], [-6.296278610122305, 0], [19.0, 0]], [[1.0, 0], [9.213571677511844, 0], [23.0, 0]], [[1.0, 0], [-1.147495231095097, 0], [29.0, 0]], [[1.0, 0], [7.521674758131629, 0], [31.0, 0]], [[1.0, 0], [-8.743465644528492, 0], [37.0, 0]], [[1.0, 0], [-2.8188961253704803, 0], [41.0, 0]], [[1.0, 0], [1.5702337591074544, 0], [43.0, 0]], [[1.0, 0], [4.0812633338071524, 0], [47.0, 0]], [[1.0, 0], [4.004341882578047, 0], [53.0, 0]], [[1.0, 0], [12.287197701662038, 0], [59.0, 0]], [[1.0, 0], [0.47360250315272623, 0], [61.0, 0]], [[1.0, 0], [-1.8068374916791181, 0], [67.0, 0]], [[1.0, 0], [1.7687109200107383, 0], [71.0, 0]], [[1.0, 0], [-0.6116816514109197, 0], [73.0, 0]], [[1.0, 0], [2.496418055202281, 0], [79.0, 0]], [[1.0, 0], [-8.293364752168088, 0], [83.0, 0]], [[1.0, 0], [14.85214254314848, 0], [89.0, 0]], [[1.0, 0], [7.365876228676039, 0], [97.0, 0]], [[1.0, 0], [-5.055694557352149, 0], [101.0, 0]], [[1.0, 0], [-1.9028892329671967, 0], [103.0, 0]], [[1.0, 0], [-11.830652919560245, 0], [107.0, 0]], [[1.0, 0], [-4.766030712140193, 0], [109.0, 0]], [[1.0, 0], [-12.60491953059749, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 27, 'label': '2-547-1.1-c1-0-27', '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/547/2/a/b/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [-2.2022269275009153e-120, 0.14972539502743165, 0.30138832170515595, 0.45570751911176133, 0.6112271940422951, 0.7637821160496292, 0.9064151646613662, 1.0297061614836764, 1.1224575016986222, 1.1726922838673017, 1.1689220798556985, 1.101622577462106, 0.9648194934454499, 0.7576438355284395, 0.4856752855769353, 0.16186505167538093, -0.19317632544140334, -0.5517181274649806, -0.8804122078748153, -1.1428075087909548, -1.3028070714912598, -1.3288612593954439, -1.1985489219797314, -0.903070068804955, -0.45108053307925916, 0.12873789653374226, 0.7869417549199355, 1.4548735590456656, 2.0487361017901016, 2.476157949229265, 2.6448880436830087, 2.472919719196824, 1.8990417393461647, 0.892595435839808, -0.5388715920484846, -2.345288976709259, -4.434062030808765, -6.674935231745722, -8.90970730661991, -10.966147014424724, -12.674829767105653, -13.887087937129692, -14.491932693513217, -14.429735730594055, -13.700696912191711, -12.36666755392626, -10.545699521401911, -8.399651937183808, -6.116178176850622, -3.8872853567120558, -1.8872603084074933, -0.2529731515734889, 0.9306624686545623, 1.6379701187437843, 1.9014716439902872, 1.8027264203661928, 1.4565247718203531, 0.9909938059562915, 0.5268636240790119, 0.15929836973627137, -0.0547341567216471, -0.10154896706124103, -0.00763489312611365, 0.1707961405842574, 0.36336824507855714, 0.5029916124529842, 0.5416062973203443, 0.46094947401851544, 0.2760763300494512, 0.030866866062812314, -0.21353103667104045, -0.3947869254693342, -0.46635850390531314, -0.4113410654543283, -0.24969472097721235, -0.03667050756565334, 0.14784085248024276, 0.21721192276417609, 0.09956278737193887, -0.24199517082297942, -0.7953169216445529, -1.4953524017014213, -2.2324191430953086, -2.871954615547113, -3.2823484828648333, -3.3652367312218994, -3.081494279404786, -2.46645452318226, -1.629685435560244, -0.7376982396819086, 0.01831585306982608, 0.4640119421955764, 0.48429293488190844, 0.057147777764092106, -0.7295451329318532, -1.6837680394668897, -2.538730030527159, -3.0018168468584547, -2.8144396360511332, -1.8109618671229948, 0.03591687398014224, 2.5940461912273096, 5.5813310711269715, 8.606145906561153, 11.232410319602385, 13.057489403755735, 13.787720740621456, 13.296109472033496, 11.649793795976134, 9.100755319052515, 6.040761904735726, 2.929089288356983, 0.2074950994106606, -1.7801603403528239, -2.8470807894674146, -2.989412366032098, -2.373975826509482, -1.2913547380744397, -0.08544824049763247, 0.9243098601789689, 1.5104913438783762, 1.580095692960186, 1.1831286006084563, 0.48676717314772633, -0.27725178506570775, -0.8781146469915196, -1.1475776960961939, -1.0224235235996924, -0.5575373268003323, 0.09291429409894934, 0.7204866516989188, 1.1212374780827499, 1.1524545380840383, 0.7722269593682484, 0.05144633396594018, -0.8447551821977272, -1.7009319165087222, -2.3086410527864274, -2.5216285426905607, -2.294019923565168, -1.6913407741747386, -0.8716484170872663, -0.04224314190875154, 0.5959147194567177, 0.9006815867720375, 0.8237387023177306, 0.4188411257178601, -0.17830052126860876, -0.7920091113333159, -1.257814985176929, -1.467669975262422, -1.3960806378791586, -1.0999897922950224, -0.6933737363851288, -0.3054127843270558, -0.03630663404609142, 0.07434503274814433, 0.05560014353171529, -0.013682686897234553, -0.044864428601811876, 0.012770480948947218, 0.13389030122389736, 0.2041801632470949, 0.041216152412269086, -0.5527575346926671, -1.7190924444862765, -3.4730902516414055, -5.659846075839994, -7.954270079102548, -9.912945088986746, -11.07083451257241, -11.061628601796734, -9.730959249722778, -7.210056863946083, -3.92485645706345, -0.5307338183852268, 2.2177080593198153, 3.634171272115846, 3.265842445824534, 1.0144018812208415, -2.8200374979103233, -7.586831204199383, -12.416464453999156, -16.40631123116869, -18.816371399614255, -19.227617845172084, -17.62465833785821, -14.38356208161944, -10.169867055107543, -5.7744838978870705, -1.930325053845534, 0.8440134840739146, 2.33609484490621, 2.648217066776967, 2.126922148732056, 1.2384836964987194, 0.42835583605533545, 0.004236319001822192, 0.07278328103687737, 0.5423963324759774, 1.1843456981097897, 1.7279754674043557, 1.9574954800467532, 1.780077692353577, 1.2463803300556557, 0.5212175719171954, -0.18162456911126373, -0.675653734574845, -0.8622306895231544, -0.7556658266475978, -0.46647193918878893, -0.15137292941558245, 0.04991926502571986, 0.06716150217945711, -0.07803741585608213, -0.2876219183782448, -0.433686729300053, -0.4177907857902371, -0.21939369619824364, 0.08656722731498179, 0.3517185302677958, 0.4097262378103658, 0.14571080492143346, -0.4466074013632764, -1.243568767153367, -2.0179835839210245, -2.5084121325989135, -2.5101619264724104, -1.9570161098275292, -0.9632707637967057, 0.19287608963334082, 1.1444841185297856, 1.5490099279837004, 1.2040302405507668, 0.1264960688211343, -1.43402751596237, -3.057434213039873, -4.275031475525125, -4.714891779259061, -4.224094749705085, -2.9263857953649466, -1.1929833953330748, 0.4680682361136546, 1.5713437420748808, 1.8119246425178177, 1.1696229366137443, -0.07706125949311368, -1.4354942020116568, -2.357920648254884, -2.4252271626849042, -1.4955464819738804, 0.2329736075657712, 2.2695777157019994, 3.9774942270989384, 4.7757541859521515, 4.3326334438760785, 2.6876542875175975], 'positive_zeros': ['1.93281725158156473046768149933273', '3.09905397639925749868674914954264', '4.20694160453719964937338947381622', '6.39797918579590970291747243450782', '7.45687439028094087940947598551463', '7.75638552375296588600312977708839', '8.640102991994114300422135320979517', '9.396780810399117537433914868590709', '9.796166812587156100633519476369027'], 'prelabel': '2-547-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.089932293296613, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.93281725158156473046768149933', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.09905397639925749868674914954', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.20694160453719964937338947382', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.367816990564039, 'bad_primes': [547], 'central_character': '1.1', 'conductor': 547, 'conductor_radical': 547, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/547/2/a/b/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': '2-547-1.1-c1-0-27', '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': '2-547-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.089932293296613, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.93281725158156473046768149933', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2450136949098847204047158078582', 'Lhash_array': ['2450136949098847204047158078582'], 'label': '2-547-1.1-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/547/2/a/b/1/2'}