-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '463107114577349828610935204599', 'a10': [-2.2353268563252855, 0.05756600898895398], 'a2': [0.8090169943749475, 0.5877852522924731], 'a3': [-0.2082967897872547, 0.6410716007746882], 'a4': [0.30901699437494745, 0.9510565162951535], 'a5': [-1.7745809636328393, 1.3604640397717036], 'a6': [-0.5453280754105247, 0.39620403850106073], 'a7': [-1.138903431510942, -2.388074323318393], 'a8': [-0.30901699437494745, 0.9510565162951535], 'a9': [2.059465738440697, 1.4962894439471313], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.148480955638592, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8090169943749475, -0.5877852522924731]]], [5, [[1.0, 0], [1.7745809636328393, -1.3604640397717036]]], [7, [[1.0, 0], [1.138903431510942, 2.388074323318393]]], [11, [[1.0, 0], [2.0038938558447046, -2.642803324976689]]]], 'bad_primes': [2, 5, 7, 11], 'central_character': '770.139', 'coefficient_field': 'CDF', 'conductor': 770, 'conductor_radical': 770, 'conjugate': '2933695087963560333578736615570', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0.2082967897872547, -0.6410716007746882], [-2.4270509831248424, -1.7633557568774194]], [[1.0, 0], [1.7745809636328393, -1.3604640397717036]], [[1.0, 0], [1.138903431510942, 2.388074323318393]], [[1.0, 0], [2.0038938558447046, -2.642803324976689]], [[1.0, 0], [1.4011938860204787, -1.928577931793333], [-4.017220926874317, -12.363734711836996]], [[1.0, 0], [3.289437016812755, 4.527521638469708], [-5.253288904374106, 16.167960777017612]], [[1.0, 0], [1.5173388076638785, -4.669888668664247], [-15.371322893124, -11.16791979355699]], [[1.0, 0], [0, 3.091435038431421], [-23.0, 0]], [[1.0, 0], [5.398736442266264, -1.754155804862676], [23.461492836873475, -17.04577231648172]], [[1.0, 0], [4.985163757381519, -6.861489266248068], [-9.57952682562337, -29.48275200514976]], [[1.0, 0], [0.465541040493769, -0.15126345346118655], [29.933628791873055, -21.748054334821507]], [[1.0, 0], [-2.8154779357445725, 8.665150092121237], [-33.16969676937284, -24.099195343991397]], [[1.0, 0], [-5.1374263881098745, 0], [43.0, 0]], [[1.0, 0], [1.6631657323300324, -5.118697793986165], [-38.02379873562253, -27.625906857746237]], [[1.0, 0], [3.441701417282806, -4.737095606408069], [-16.377900701872214, -50.405995363643136]], [[1.0, 0], [-11.8449667342734, 3.8486629931889937], [47.7320026681219, -34.67932988525592]], [[1.0, 0], [-1.977447874814665, 1.4366999779666751], [18.850036656871794, -58.014447494004365]], [[1.0, 0], [0, -13.400845740717767], [-67.0, 0]], [[1.0, 0], [-10.941418573557284, 7.949405910397119], [21.940206600621266, -67.52501265695591]], [[1.0, 0], [0.782562726727374, -0.25427004345145326], [59.05824058937116, -42.90832341735054]], [[1.0, 0], [9.46039452388397, -13.021115983198392], [-24.412342555620846, -75.13346478731714]], [[1.0, 0], [2.442838783820517, 3.362279136676349], [-25.648410533120636, 78.93769085249775]], [[1.0, 0], [0, 10.687542559114418], [-89.0, 0]], [[1.0, 0], [-5.14075226290118, -3.734975144937503], [29.974648454369902, 92.2524820806299]], [[1.0, 0], [-11.843338110063195, -8.604688810507547], [31.210716431869688, 96.05670814581052]], [[1.0, 0], [-5.883237964907846, -18.10674462988132], [-83.32875042061958, 60.54188098612473]], [[1.0, 0], [2.9535997501302114, -9.090245326380694], [-86.56481839811937, -62.893021995294625]], [[1.0, 0], [0, -5.783764449923293], [-109.0, 0]], [[1.0, 0], [-10.005531385164135, -3.2509942183163414], [91.41892036436906, 66.41973350904946]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-770-385.139-c1-0-3', '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/770/2/w/b/139/11', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.9105164282091276, 0.5950462900449162, 0.2852550370403743, -0.023974459350401565, -0.3343315498007506, -0.6428365653757373, -0.9414696945969827, -1.2175847453772473, -1.4549672729100542, -1.6354089812257406, -1.7406836222766144, -1.754794029815073, -1.6663177385934087, -1.4706263482619941, -1.171710312348192, -0.783322665505129, -0.32917469889629036, 0.1580191239781049, 0.6387398945336495, 1.0700507583300647, 1.4099420195237042, 1.622229403184348, 1.6814475762816912, 1.577081224929058, 1.3164552898956283, 0.9256834985624319, 0.44825706026254225, -0.05886566209004544, -0.5314592297571984, -0.9059371681275721, -1.1280356962281743, -1.1610938528618653, -0.9926442820140058, -0.6381150257777187, -0.14073588927286249, 0.43277300240592953, 1.0005300711434941, 1.4769616087251767, 1.7859121581184128, 1.8734436813323538, 1.7181909905218837, 1.3373031933223845, 0.7865243482630516, 0.15380712306114597, -0.4530970577476514, -0.9235305940193143, -1.1628118104939218, -1.1099974041818619, -0.7512908425316633, -0.12631020783635266, 0.6745650901816619, 1.5221079908957929, 2.2681009481864196, 2.7702368606684353, 2.917962554641001, 2.6546132771810425, 1.991461284363879, 1.0104331426656883, -0.14589394800938124, -1.2961162802561101, -2.250428700569763, -2.8445359763440625, -2.9708772517160593, -2.601052729279862, -1.7946098499201038, -0.6916680914128455, 0.5101435290653011, 1.5908458752051364, 2.3491617672992597, 2.641716327147042, 2.412568931499946, 1.7067738159201797, 0.6645600727029625, -0.5035169014896901, -1.556204452786852, -2.2684955832948397, -2.4765988793204667, -2.1116925433563107, -1.2152182990036806, 0.06790583648274798, 1.5172326454928526, 2.880457479137446, 3.9238855754116044, 4.479106459062374, 4.475904386036616, 3.9542756066324833, 3.052927445500781, 1.976832419472989, 0.9511329076771793, 0.1718315258322331, -0.2355192292486971, -0.2397464259789725, 0.09469916817337312, 0.6290854096189222, 1.1887742158172383, 1.608904410789036, 1.7758306877631846, 1.6538070875931765, 1.29012587683265, 0.7974588843725664, 0.3181324078142145, -0.020036550233887142, -0.14422207815630517, -0.061924371752595124, 0.13655151841437596, 0.30019803094499975, 0.25900250871591685, -0.12541313479670962, -0.9139064984961143, -2.0618421633576243, -3.418034964799775, -4.752768710076792, -5.809235789161529, -6.366030251380212, -6.29460422680233, -5.596045286110335, -4.40625923491981, -2.9665947150904715, -1.5661272747734771, -0.4697876633871621, 0.1489738188792321, 0.2526666548379144, -0.05153341518925692, -0.5425564324346888, -0.9487177128896483, -1.0272617972085305, -0.6386929795266061, 0.20513354015378113, 1.333891186801939, 2.456685828123509, 3.236728166626516, 3.383918245709934, 2.740617508433294, 1.3365942342654964, -0.603488828236361, -2.704385419372353, -4.52673054925033, -5.674152298712327, -5.893160214194596, -5.13903566824154, -3.5894428007327295, -1.6012266984662011, 0.378821053150263, 1.9258098938624713, 2.74142513478758, 2.7234625718813175, 1.9818854005632671, 0.7978976531730383, -0.46158974228479827, -1.4493189672835591, -1.9327559560082992, -1.8520860735202977, -1.325427101209334, -0.6011754432673133, 0.02701118746033072, 0.3161629987767321, 0.15146018697814184, -0.41832518145452424, -1.1979176589505316, -1.9094304734536025, -2.2828313799554625, -2.1444581944628776, -1.47559005793966, -0.42235180755512625, 0.7465623777275796, 1.7214120931166386, 2.2467168597982226, 2.200273563225833, 1.6306926786674405, 0.7412114021418994, -0.17544353094153387, -0.830666519231939, -1.0322392497809447, -0.7455586203795951, -0.10383543979697778, 0.6364245459255863, 1.180618069845507, 1.294468308486148, 0.8835751218357233, 0.027782225777887352, -1.041431359261385, -2.013706147957266, -2.5992214843894192, -2.6221719203804943, -2.077277178560033, -1.1302822293202401, -0.06198174077772813, 0.825629682190861, 1.3093560453256166, 1.3166405604566167, 0.9440592407913372, 0.4153065005241202, -0.007467672254928111, -0.12823781000586726, 0.09987909962800269, 0.544548612883315, 0.9311061037422966, 0.9373238940176403, 0.315867222189807, -0.9974751013505726, -2.8295279666810904, -4.793151053999739, -6.386951921280385, -7.143801611299528, -6.782378404863123, -5.3120528220933565, -3.053888993011451, -0.5659561269222602, 1.508381542157661, 2.6248932150342488, 2.4991717718485367, 1.1929052208107611, -0.9026116698210623, -3.18205693736976, -5.0056689077202305, -5.887227216739204, -5.632039575493542, -4.382626080519503, -2.5595790350755605, -0.7188177365515348, 0.6269798463502407, 1.1643837061107414, 0.8630717314717649, -0.03693106718730516, -1.1262863880682712, -1.977956273033757, -2.2957744942640446, -2.00911336420305, -1.2830150916906466, -0.44358748769966894, 0.15168260065076433, 0.250258604228716, -0.20212694464190667, -1.0442364308314842, -1.9630002396990396, -2.613294309194196, -2.7487366862998996, -2.314800562458772, -1.4698264500331468, -0.5264045783707015, 0.1648282731558331, 0.3455932104640667, -0.054012774530873865, -0.8895860945784373, -1.8560566320786935, -2.600588835349089, -2.8522195592447774, -2.5194666638256455, -1.7193263006812882, -0.7272022901363001, 0.1324418440292607, 0.6120624111317697, 0.6343967898814725, 0.31638364311393735, -0.08620367790401463, -0.2919127093511276, -0.11945745766947799], 'positive_zeros': ['0.36532709761977901779137356399125', '2.08478998360268392202553268047327', '3.36036165873605899425756877418440', '4.28157674169938719478250908600312', '5.40530491727097767345376422436208', '6.14615361517417011030024889708786', '7.23461247208766849268017446455743', '8.196733801626132731653260586763242', '9.071130330315300720793110344170118', '9.868950282078510034448616725628913'], 'prelabel': '2-770-385.139-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4796130657097675, 'root_angle': 0.97879311668673, 'root_number': '-0.997781482819624 + 0.06657411315423163*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.489396558343', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.36532709761977901779137356399', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.08478998360268392202553268047', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.36036165873605899425756877418', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 6.148480955638592, 'bad_primes': [2, 5, 7, 11], 'central_character': '385.139', 'conductor': 770, 'conductor_radical': 770, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/770/2/w/b/139/11'], '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': '2-770-385.139-c1-0-3', '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': '2-770-385.139-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4796130657097675, 'root_angle': 0.489396558343365, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.36532709761977901779137356399', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '463107114577349828610935204599', 'Lhash_array': ['463107114577349828610935204599'], 'label': '2-770-385.139-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/770/2/w/b/139/11'}