-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1210855911163422160688388272545', 'a10': [0.0, 0.0], 'a2': [-0.7700712752213337, 0.0], 'a3': [1.0, 0.0], 'a4': [-1.406990231078989, 0.0], 'a5': [0.0, 0.0], 'a6': [-0.7700712752213337, 0.0], 'a7': [3.988079649296098, 0.0], 'a8': [2.6236253119136235, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.97195037899008, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '1875.1', 'coefficient_field': 'CDF', 'conductor': 1875, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7700712752213337, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.988079649296098, 0], [7.0, 0]], [[1.0, 0], [6.3501371526709915, 0], [11.0, 0]], [[1.0, 0], [-5.354333985007143, 0], [13.0, 0]], [[1.0, 0], [3.4574606155497514, 0], [17.0, 0]], [[1.0, 0], [-2.3202628142572617, 0], [19.0, 0]], [[1.0, 0], [-0.955220568069247, 0], [23.0, 0]], [[1.0, 0], [-7.266304333219616, 0], [29.0, 0]], [[1.0, 0], [-6.40484219622629, 0], [31.0, 0]], [[1.0, 0], [2.833478967161207, 0], [37.0, 0]], [[1.0, 0], [5.351637259213766, 0], [41.0, 0]], [[1.0, 0], [-3.9359330354725155, 0], [43.0, 0]], [[1.0, 0], [-2.4834770662249817, 0], [47.0, 0]], [[1.0, 0], [-3.9507862808559002, 0], [53.0, 0]], [[1.0, 0], [-0.09412316981650684, 0], [59.0, 0]], [[1.0, 0], [6.611741134747689, 0], [61.0, 0]], [[1.0, 0], [10.281062342282837, 0], [67.0, 0]], [[1.0, 0], [5.815873021856066, 0], [71.0, 0]], [[1.0, 0], [-3.7989664836182393, 0], [73.0, 0]], [[1.0, 0], [5.444796338832478, 0], [79.0, 0]], [[1.0, 0], [-9.246960355933759, 0], [83.0, 0]], [[1.0, 0], [-10.12780856929136, 0], [89.0, 0]], [[1.0, 0], [-7.899357963955761, 0], [97.0, 0]], [[1.0, 0], [-8.729735270391714, 0], [101.0, 0]], [[1.0, 0], [3.8238952000655835, 0], [103.0, 0]], [[1.0, 0], [-14.166177656738661, 0], [107.0, 0]], [[1.0, 0], [-14.055673299855183, 0], [109.0, 0]], [[1.0, 0], [-9.265571797967775, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 22, 'label': '2-1875-1.1-c1-0-22', 'leading_term': '1.578388290933131777132970914228', '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/1875/2/a/o/1/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.5783882909331317, 1.5745041119542833, 1.5627954006963753, 1.5430979064400863, 1.5151518585572725, 1.478622057505619, 1.4331243472460315, 1.3782570356405026, 1.313635684712492, 1.2389296732134683, 1.1538990125922874, 1.0584300393760784, 0.9525687781737332, 0.8365509429232044, 0.710827702212684, 0.5760864697508674, 0.4332660933823898, 0.2835659106805966, 0.12844822398477618, -0.030366168748209747, -0.19090966109771626, -0.3509869150482097, -0.5082013808856685, -0.6599891768183547, -0.8036600901832107, -0.9364452907581157, -1.0555511620427287, -1.1582184628172285, -1.2417858342588834, -1.3037564735889096, -1.3418666103968446, -1.3541542535547686, -1.3390265322258257, -1.2953238410296963, -1.2223789237593197, -1.1200689983839336, -0.988859043844856, -0.8298344407203829, -0.6447212862900815, -0.43589289145795335, -0.20636121231108526, 0.040247729120089434, 0.299735025921258, 0.5673868589958705, 0.8380490110646281, 1.1062172022137589, 1.3661420401023903, 1.6119468861267936, 1.8377564566998146, 2.037833521614751, 2.206720645022752, 2.3393835547159743, 2.43135243757722, 2.4788572576419297, 2.478953091088777, 2.4296314804082018, 2.329913936155089, 2.1799239641352033, 1.9809343701506306, 1.7353870912315519, 1.4468834152202732, 1.1201431690614807, 0.76093226542603, 0.37595887857654303, -0.027260548805981628, -0.4405633114876222, -0.8553273537846583, -1.2626790660746086, -1.6537170944576218, -2.019746540077339, -2.3525172998029884, -2.6444598307189624, -2.888911332086301, -3.080325250782277, -3.214457145069971, -3.288520296124183, -3.3013050393779757, -3.253256593354227, -3.1465071793479042, -2.9848594304331617, -2.7737194544540777, -2.5199794074312027, -2.2318510092980555, -1.9186530458421422, -1.5905574978848434, -1.2583004672957983, -0.9328654748032721, -0.6251479331950213, -0.34561060086547407, -0.10394054916787561, 0.09128140606276826, 0.2328877832584709, 0.3153972850433623, 0.3352433368214994, 0.2909492542579084, 0.18324235185331314, 0.01510099597829698, -0.2082694266739547, -0.47953346489511794, -0.7893949767995928, -1.1268359869991604, -1.4794196619451063, -1.8336496902939814, -2.1753761752924925, -2.4902362180758746, -2.764115772954225, -2.9836181584881207, -3.1365238704503398, -3.2122261096941482, -3.202126738264696, -3.0999782214325533, -2.902158492960072, -2.60786756715693, -2.2192370656921, -1.7413465624101085, -1.1821436911005587, -0.5522682101195441, 0.13521643682286344, 0.8651772012027278, 1.6208411104909075, 2.3842875958865095, 3.136987983770219, 3.860374626237327, 4.536420684422471, 5.1482107690810235, 5.680482536365089, 6.12011995813534, 6.456580333645246, 6.682239153190178, 6.792639606637434, 6.786636766340756, 6.666430156247341, 6.437482417673539, 6.10832595150837, 5.690263599603516, 5.196973462676314, 4.64403167713004, 4.048370235345685, 3.4276895938696037, 2.7998477523676573, 2.1822486098157694, 1.5912526500946305, 1.0416323478198093, 0.5460931239222471, 0.11487826327235226, -0.24452698608337978, -0.5275807662439689, -0.7327524194487441, -0.861470475048223, -0.917953407492253, -0.9089305906713853, -0.8432654596674838, -0.7314970334141225, -0.5853194672818142, -0.4170220318690794, -0.2389137219059238, -0.06275749222962104, 0.10076115704619673, 0.2425078749935599, 0.3552944513250727, 0.43417746347474595, 0.47664710318854875, 0.4826975275597673, 0.45477535505919403, 0.3976084310359376, 0.31792247754585945, 0.22405847215108257, 0.125508328246197, 0.03239045104160178, -0.045110178448442784, -0.09731074407480508, -0.11558071517777095, -0.09284636516501438, -0.024024434961297043, 0.09363736860154419, 0.2603313013811248, 0.47358520991005437, 0.7282904113865822, 1.0168631789727645, 1.3295347865295004, 1.6547587642655874, 1.9797181103580659, 2.2909099825030927, 2.5747811221594263, 2.8183841698510124, 3.010023289721237, 3.1398572536856806, 3.200429391472382, 3.1870965729794385, 3.098333561915909, 2.9358945028406316, 2.7048197513526, 2.4132834477428444, 2.0722848426853275, 1.6951940549624016, 1.2971703080054489, 0.8944773904499612, 0.5037267738896695, 0.14108319528961563, -0.1785296766176784, -0.4421848026593908, -0.639630649405677, -0.763858102406636, -0.811524559050968, -0.7832103863099166, -0.6834903472888546, -0.5208110748725985, -0.3071748200412182, -0.05763910209020197, 0.21034891094550673, 0.47775591307850657, 0.7248690177305024, 0.9322645282247691, 1.0817939085902906, 1.1575398252773894, 1.1466952364719538, 1.0403208903340233, 0.8339412028777083, 0.5279451564185217, 0.12776732143511846, -0.3561660056529823, -0.9087296824697234, -1.510624397624439, -2.139114628925734, -2.76895068327705, -3.373436081311119, -3.925593651926497, -4.399377868209026, -4.770877520577326, -5.019452009412998, -5.128746448270517, -5.0875353685980595, -4.890351942869705, -4.537869001740896, -4.037009301884246, -3.4007749947834514, -2.6477994669534297, -1.8016380340738616, -0.8898267225378309, 0.05725007669783392, 1.0076325373758832, 1.9291409124356647, 2.7907508987652165, 3.5639243783004333, 4.223832458020953, 4.750412245746171, 5.129206256389763, 5.351943418655169, 5.416832881403726, 5.32855562152239, 5.0979535608650535, 4.7414307814368355, 4.280095737148537, 3.738686365881471, 3.144331030807946, 2.5252066790921277, 1.9091610359041224], 'positive_zeros': ['0.955196890172590259597388944449473', '2.07394473359768718010818376466187', '3.24661801500335696125460887379775', '4.54493202434009524628866520920815', '4.87885539136114565002967159812168', '5.93169724519740317179316018846329', '7.32763295541994004436168192651313', '7.940743068118509057651718148692043', '8.550900567513695091894034688601792', '8.797484528100568429970181427242709'], 'prelabel': '2-1875-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8693604612377586, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.955196890172590259597388944449', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.07394473359768718010818376466', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.24661801500335696125460887380', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 14.97195037899008, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 1875, 'conductor_radical': 15, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1875/2/a/o/1/4'], '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': '2-1875-1.1-c1-0-22', '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': '2-1875-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8693604612377586, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.955196890172590259597388944449', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1210855911163422160688388272545', 'Lhash_array': ['1210855911163422160688388272545'], 'label': '2-1875-1.1-c1-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1875/2/a/o/1/4'}