-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2459241620020596543703693530545', 'a10': [2.0, -0.3360827212213939], 'a2': [0.0, 0.9069676505260347], 'a3': [0.0, 3.217890514265296], 'a4': [1.1774096808992847, 0.0], 'a5': [-0.3705564592369621, -2.205150314721825], 'a6': [-2.9185225993732087, 0.0], 'a7': [0.0, -2.5963653283915815], 'a8': [0.0, 2.881807793043902], 'a9': [-7.354819361798569, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.758578819202164, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0.3705564592369621, 2.205150314721825]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [5, 19], 'central_character': '95.39', 'coefficient_field': 'CDF', 'conductor': 95, 'conductor_radical': 95, 'conjugate': '4546962526567598540271758353941', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -0.9069676505260347], [-2.0, 0]], [[1.0, 0], [0, -3.217890514265296], [-3.0, 0]], [[1.0, 0], [0.3705564592369621, 2.205150314721825]], [[1.0, 0], [0, 2.5963653283915815], [-7.0, 0]], [[1.0, 0], [-0.7411129184739242, 0], [11.0, 0]], [[1.0, 0], [0, 3.7887754435699366], [-13.0, 0]], [[1.0, 0], [0, -3.1672502576962223], [-17.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, -0.5708849293046409], [-23.0, 0]], [[1.0, 0], [6.0, 0], [29.0, 0]], [[1.0, 0], [-5.837045198746417, 0], [31.0, 0]], [[1.0, 0], [0, -1.4039552132132262], [-37.0, 0]], [[1.0, 0], [3.837045198746418, 0], [41.0, 0]], [[1.0, 0], [0, 2.5963653283915815], [-43.0, 0]], [[1.0, 0], [0, 5.082466071886438], [-47.0, 0]], [[1.0, 0], [0, 0.16090484146579767], [-53.0, 0]], [[1.0, 0], [8.354819361798569, 0], [59.0, 0]], [[1.0, 0], [8.578158117220342, 0], [61.0, 0]], [[1.0, 0], [0, -14.84640219957905], [-67.0, 0]], [[1.0, 0], [-3.6451806382014307, 0], [71.0, 0]], [[1.0, 0], [0, 10.846081657974242], [-73.0, 0]], [[1.0, 0], [1.8370451987464176, 0], [79.0, 0]], [[1.0, 0], [0, 4.198755531408779], [-83.0, 0]], [[1.0, 0], [-16.901503284142127, 0], [89.0, 0]], [[1.0, 0], [0, -3.7887754435699366], [-97.0, 0]], [[1.0, 0], [-8.354819361798569, 0], [101.0, 0]], [[1.0, 0], [0, -2.076120655656014], [-103.0, 0]], [[1.0, 0], [0, -5.703991257760153], [-107.0, 0]], [[1.0, 0], [1.645180638201431, 0], [109.0, 0]], [[1.0, 0], [0, 3.8900559567080837], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-95-5.4-c1-0-2', '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/95/2/b/b/39/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.0849150665840674, 1.0311742485997848, 0.9903468824176137, 0.9583054942740459, 0.9306160944225813, 0.9028822765492164, 0.87101118374135, 0.8314000381878143, 0.7810722422869892, 0.717795641417198, 0.6402042862490114, 0.5479307546307614, 0.44174448669656985, 0.32368378764401945, 0.19716450752157821, 0.06704607333891419, -0.06036498879205513, -0.1773928220601728, -0.27516735380552393, -0.34390836007633674, -0.37332386271807716, -0.35312033342651894, -0.27361283119154983, -0.12641285617168488, 0.09483898902627363, 0.39373864660272756, 0.770434414958563, 1.22105098488933, 1.7372823650822933, 2.3062124033091616, 2.9104143524901973, 3.528367981473302, 4.135214151429197, 4.703843176458877, 5.206285861967077, 5.615346661107479, 5.906389234250166, 6.059158566242769, 6.059503621424026, 5.900853171639417, 5.585297434954088, 5.124141350098467, 4.537822532939892, 3.8551278160570988, 3.1116949370699456, 2.3478471169710193, 1.6058732811792713, 0.9269297369832254, 0.3477937650700405, -0.1022607586025128, -0.4041769078162002, -0.5511355747487133, -0.5496370848126308, -0.4194606119530564, -0.19240752002705774, 0.09015675349193923, 0.38082863343163786, 0.6305081414773973, 0.7931991848770448, 0.8308317422294281, 0.7176270644004652, 0.4435306215140131, 0.016291570115462048, -0.5381285103342496, -1.1769871135461574, -1.8440223037696717, -2.474338984126395, -3.000524707173437, -3.3594366368996305, -3.498985942432723, -3.3841959720366788, -3.00183767499976, -2.3630536150793433, -1.5035650271544307, -0.48129967335711077, 0.6284419080083407, 1.7398780280302562, 2.7650328541321305, 3.622558176126885, 4.24612040793566, 4.591383514141477, 4.640735720089909, 4.405135702096582, 3.9227716030661393, 3.254599697373176, 2.477215057738622, 1.673855523144243, 0.9246051963408805, 0.29700481550520574, -0.16173253668246743, -0.4298687337093666, -0.5129311540759952, -0.44185019583426666, -0.2676314324210143, -0.05323155731322301, 0.1362806516840262, 0.2439161237321705, 0.22984525911448456, 0.0780019134597444, -0.2008498488184747, -0.5701756008972196, -0.9728627592850388, -1.3399342443979643, -1.6016116224107788, -1.6991367581806869, -1.5955553916867478, -1.2837182026045837, -0.7900737070451, -0.17338214172231262, 0.4817979587871756, 1.0762068619191478, 1.5101751292805121, 1.6991373417279576, 1.5880754130602146, 1.162606974445408, 0.4547913512188168, -0.4576003326585051, -1.4586962248149955, -2.408343299125526, -3.1604841438701556, -3.5836531944628653, -3.5806924069319503, -3.104738476226537, -2.1689310567447624, -0.8480973924414936, 0.7282191928470556, 2.39075737732342, 3.951708605017856, 5.229211734972927, 6.071722308134376, 6.378711726881353, 6.114596859131714, 5.3137376046136255, 4.075639286713103, 2.5509654246991262, 0.9203767072098556, -0.6306630501211962, -1.937322120572473, -2.8772258081537125, -3.3853756360016134, -3.459961863741545, -3.1583325976356846, -2.5839807488460886, -1.8668769201111601, -1.1405620878496012, -0.5199274252558437, -0.08345220372150829, 0.13713934052151258, 0.15817397978392495, 0.03627900226852243, -0.1467738203954863, -0.30363162869263394, -0.3615100170613535, -0.27897994225336337, -0.056050040333509556, 0.26455121734171255, 0.6053189996406994, 0.8697742784821153, 0.9631771654852082, 0.8141410666755279, 0.39281146682034895, -0.27822755113095304, -1.1228963943550254, -2.0211819616401696, -2.8280558899835255, -3.3986107935476926, -3.6149230367168723, -3.4096009464705155, -2.78137031679882, -1.7993487483212782, -0.5946555387452701, 0.6596590330378589, 1.777135865017855, 2.589931698562399, 2.978553131452281, 2.8937332330961687, 2.3661772049695653, 1.5020533889454375, 0.46472881073333333, -0.5541448938296542, -1.3690023136943197, -1.8338513392501563, -1.868578235410389, -1.4730307814902543, -0.726102350662236, 0.23010869174121348, 1.218094399800366, 2.0593479524368465, 2.6086885778948288, 2.7817414806579523, 2.5701018680453585, 2.0411207776085556, 1.3223208167356635, 0.5735766349947202, -0.04725635638315088, -0.41814565864322517, -0.4789982529250894, -0.24444396123880444, 0.19967779868036295, 0.7157210452076013, 1.145741544702019, 1.348643566798101, 1.2350919022488271, 0.7925193681267505, 0.09438242616430433, -0.7090690575185273, -1.4174454819292632, -1.819523076078138, -1.7375849325921995, -1.06782166884976, 0.19172740488229856, 1.9319771132157784, 3.9450255521819995, 5.95622944156197, 7.67048742992663, 8.824083502529717, 9.23212790623583, 8.822320394482372, 7.648345650491246, 5.880190170153959, 3.773239638501576, 1.6222356442697983, -0.2908388324195331, -1.7447444240004268, -2.613610701940703, -2.881841954473061, -2.6371048225774687, -2.0437632134809687, -1.3031150412344559, -0.6093451710657145, -0.1106967257218866, 0.11613029075989831, 0.07356612562317451, -0.16782971621159243, -0.49528771833367474, -0.7876885895016661, -0.9487697262757595, -0.9315206412609196, -0.7479909582037371, -0.46249062754470815, -0.17039517081953853, 0.0315429565981087, 0.07523882906604122, -0.05667517112461164, -0.3232371565985528, -0.6348134527175925, -0.8783891429376376, -0.9526071689135722, -0.8037123475082135, -0.4526779033542157, -0.005312771081057341, 0.3591824269588371, 0.4207067686934467, -0.03395933895119989, -1.1580530980275154, -2.9984851686803142, -5.467707841274627], 'positive_zeros': ['1.93999957052663533849038393354388', '2.95155312134369826333245775074531', '6.09282140385043929191562418674690', '6.83650645212953768084237113682269', '7.75408327969934629343156968148592', '9.304872903419843423133457051055344', '11.07485810908296983207483240049158', '11.78191174422480223340105178181182', '12.29063795155086185514024688352718', '13.53304662281376563406825596224367'], 'prelabel': '2-95-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8709643042066443, 'root_angle': -0.5529941137908199, 'root_number': '-0.16571788647109556 - 0.9861732008646114*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.276497056895', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.93999957052663533849038393354', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.95155312134369826333245775075', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.09282140385043929191562418675', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.758578819202164, 'bad_primes': [5, 19], 'central_character': '5.4', 'conductor': 95, 'conductor_radical': 95, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/95/2/b/b/39/4'], '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': '2-95-5.4-c1-0-2', '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': '2-95-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8709643042066443, 'root_angle': -0.27649705689540993, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.93999957052663533849038393354', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2459241620020596543703693530545', 'Lhash_array': ['2459241620020596543703693530545'], 'label': '2-95-5.4-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/95/2/b/b/39/4'}