-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3937819120489686228551536077598', 'a10': [0.8660254037844386, -1.5], 'a2': [0.8660254037844386, 0.5], 'a3': [0.5, -0.8660254037844386], 'a4': [0.5, 0.8660254037844386], 'a5': [0.0, -1.7320508075688772], 'a6': [0.8660254037844386, -0.5], 'a7': [-4.098076211353316, 2.366025403784439], 'a8': [0.0, 1.0], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6228331357659873, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, -0.5]]], [3, [[1.0, 0], [-0.5, 0.8660254037844386]]], [13, [[1.0, 0], [3.598076211353316, -0.2320508075688773]]]], 'bad_primes': [2, 3, 13], 'central_character': '78.43', 'coefficient_field': 'CDF', 'conductor': 78, 'conductor_radical': 78, 'conjugate': '3528698468538308496468745417622', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 1.7320508075688772], [-5.0, 0]], [[1.0, 0], [4.098076211353316, -2.366025403784439], [3.5, -6.06217782649107]], [[1.0, 0], [-4.098076211353316, -2.366025403784439], [5.5, 9.526279441628825]], [[1.0, 0], [3.598076211353316, -0.2320508075688773]], [[1.0, 0], [2.598076211353316, 4.5], [-8.5, 14.722431864335457]], [[1.0, 0], [-1.098076211353316, 0.6339745962155614], [9.5, -16.454482671904334]], [[1.0, 0], [-1.098076211353316, 1.901923788646684], [-11.5, -19.91858428704209]], [[1.0, 0], [-1.5, 2.598076211353316], [-14.5, -25.11473670974872]], [[1.0, 0], [0, -2.5358983848622456], [-31.0, 0]], [[1.0, 0], [-2.598076211353316, -1.5], [18.5, 32.04293994002423]], [[1.0, 0], [-0.40192378864668404, -0.2320508075688773], [20.5, 35.50704155516198]], [[1.0, 0], [-3.098076211353316, -5.366025403784438], [-21.5, 37.239092362730865]], [[1.0, 0], [0, -1.2679491924311228], [-47.0, 0]], [[1.0, 0], [-3.0, 0], [53.0, 0]], [[1.0, 0], [12.0, -6.928203230275509], [29.5, -51.09549882328188]], [[1.0, 0], [2.401923788646684, 4.160254037844386], [-30.5, 52.827549630850754]], [[1.0, 0], [9.294228634059948, 5.366025403784438], [33.5, 58.023702053557386]], [[1.0, 0], [-7.098076211353316, 4.098076211353316], [35.5, -61.48780366869514]], [[1.0, 0], [0, -12.12435565298214], [-73.0, 0]], [[1.0, 0], [12.392304845413264, 0], [79.0, 0]], [[1.0, 0], [0, 11.660254037844387], [-83.0, 0]], [[1.0, 0], [-2.196152422706632, -1.2679491924311228], [44.5, 77.07626093681505]], [[1.0, 0], [-5.196152422706632, 3.0], [48.5, -84.00446416709055]], [[1.0, 0], [0.6961524227066319, -1.2057713659400522], [-50.5, -87.4685657822283]], [[1.0, 0], [-4.196152422706632, 0], [103.0, 0]], [[1.0, 0], [4.098076211353316, -7.098076211353316], [-53.5, -92.66471820493493]], [[1.0, 0], [0, -16.392304845413264], [-109.0, 0]], [[1.0, 0], [5.598076211353316, 9.696152422706632], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-78-13.4-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/78/2/i/b/43/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.2421743197581099, 1.251683228068031, 1.2789583068872066, 1.3223582647108005, 1.379348309856212, 1.4467445101615461, 1.520920442942722, 1.5979474866019658, 1.6736801214153396, 1.743815325234622, 1.8039548272891845, 1.8496907357542363, 1.8767257526917047, 1.8810314454049446, 1.8590420872096776, 1.807876888986075, 1.7255795126782751, 1.6113603331022248, 1.4658239814844383, 1.2911624243360265, 1.0912924698708126, 0.8719164601358492, 0.6404863012492973, 0.4060541530446804, 0.17899819174503567, -0.029381113315113522, -0.20738996430669165, -0.34358096979457853, -0.42747808779048807, -0.450350015446878, -0.40598488253056847, -0.2914105889437463, -0.10749956752669843, 0.1406048007168322, 0.4432995486831183, 0.786621830403537, 1.15267292356841, 1.5203823490549297, 1.8666030881728286, 2.167500704452779, 2.4001696077638712, 2.5443811458198033, 2.584343408797713, 2.5103344407245016, 2.320061677911074, 2.0196031571314843, 1.623801897471739, 1.156014391512395, 0.6471566430001735, 0.13404459480736364, -0.34291333738029145, -0.742550259293078, -1.0261191731093815, -1.160581859893947, -1.1217378900499015, -0.8969076060417072, -0.4868920618424098, 0.09303080037662115, 0.8132512207130905, 1.631204240001582, 2.493962861244958, 3.3419177435900025, 4.113299175755098, 4.749195238610641, 5.198642352202598, 5.423321341159954, 5.401391793156048, 5.130044213715633, 4.626443102103268, 3.9268692998732977, 3.0840364238732003, 2.1627390253900383, 1.2341711438544238, 0.3694133703539601, -0.36729488828310136, -0.9248200871036895, -1.2702661324033655, -1.392384460853648, -1.3028263217672122, -1.0350119448759545, -0.6406415184906856, -0.1841365829929016, 0.2644520300318379, 0.6373323271531881, 0.8767899999413485, 0.9420383059714742, 0.814269174249536, 0.4992484556686421, 0.027059711487724403, -0.5510750273463809, -1.1686184090788139, -1.7515702458653013, -2.227457512323962, -2.5343895805331513, -2.629051624796718, -2.492594637552369, -2.133603684642328, -1.5876660694829852, -0.9134803518718378, -0.1858950569893729, 0.513315344553818, 1.105797592376741, 1.5267546141313937, 1.7335077494937885, 1.7112838162484172, 1.4753547254215582, 1.0691233401888538, 0.5582938719681072, 0.021816471679343797, -0.45922342417974965, -0.813261961114503, -0.9888109111999099, -0.9623492874698159, -0.7423115293932001, -0.36844553350081083, 0.09354033223765106, 0.5614318686764649, 0.9488204423747709, 1.1785423466923637, 1.1952653891032503, 0.9752725552594356, 0.531817086049997, -0.0849903991621643, -0.7940274539536021, -1.4941460873242376, -2.07889425409904, -2.4529225024114374, -2.547657859745776, -2.3338074312606416, -1.8286052040992105, -1.0964038993474985, -0.2421522385965391, 0.601643973569162, 1.2928574084832916, 1.7001268473361186, 1.722760725113569, 1.3071548815918204, 0.4571142837999184, -0.7637220000120608, -2.238032138676561, -3.8089464568142506, -5.300341608134093, -6.540472952617414, -7.385527801519798, -7.739595418417486, -7.568004810144531, -6.901925475118426, -5.8334259468200775, -4.5016444603733685, -3.0721167453970857, -1.7124023790270606, -0.5677683026722846, 0.259286478139273, 0.7224659309807403, 0.8359861873550204, 0.6691433033967248, 0.33211403324342303, -0.044588979217786, -0.3335281641635991, -0.43265576108816894, -0.2827545600654526, 0.12294089823147718, 0.738540858840833, 1.474675607446316, 2.215364732657288, 2.839531074641228, 3.243273186751256, 3.3588595908128274, 3.1669832534240157, 2.700025095548416, 2.03571310911393, 1.2823377364512198, 0.5582709444172637, -0.030361888086746676, -0.4096077219032679, -0.5513523726770917, -0.47800299552231906, -0.25713915595444126, 0.012995036429566625, 0.22448138596754175, 0.28318468398186897, 0.13005668935833925, -0.24405993193252798, -0.7933476260070145, -1.4230755373751105, -2.006093004707595, -2.4069581507945172, -2.509283474756147, -2.241053424777779, -1.592828375205979, -0.6249040300541037, 0.5385386028282372, 1.7278281669772484, 2.755837844810648, 3.4507758592491102, 3.6877306790148427, 3.4129659725210106, 2.6561122512114634, 1.5275303538811789, 0.2008501715309238, -1.1164906847527192, -2.2195127045027725, -2.942123743255064, -3.1868614030998157, -2.942204839729553, -2.2839597248305568, -1.3602039195046978, -0.36244003411474796, 0.5116786960008255, 1.0969459634940428, 1.293033490378062, 1.084339495982506, 0.5431961526603614, -0.18441635192312714, -0.9080633689219059, -1.4313787911686444, -1.5923982459260952, -1.2977028824012808, -0.5434803219548167, 0.5808885963017821, 1.9076868961060942, 3.2214626995836206, 4.299494073456729, 4.954195718387847, 5.069075694409039, 4.621070230888996, 3.684769419868685, 2.417666952212256, 1.0293928563933696, -0.25886414667561075, -1.256543722671307, -1.8389925913493606, -1.9687575902310124, -1.6987277154076097, -1.1567440157777336, -0.515163779130903, 0.04799928555630946, 0.38800297906733366, 0.42406070177961275, 0.1552920341132466, -0.3413313395119363, -0.9303882415940891, -1.4503152804177377, -1.7513535265128939, -1.7306386898036927, -1.3565811306574513, -0.6770695024284424, 0.1903510501050592, 1.0841238820600871, 1.8343642071774244, 2.300492824447012, 2.402243367964119, 2.1369255511035057, 1.578929143120165, 0.8615146763881808, 0.14504182392455067, -0.4210082500152906], 'positive_zeros': ['3.10639155598610243462545224339227', '4.05794074943596429287036818958006', '6.15874339313983288500300342784900', '7.10699435434673673449135277964463', '9.184375554998852900409044871601545', '10.17494998809962064716079754731523', '11.00628850508995611589443769635333', '12.40716194884352239996051409916519', '13.50523769679742012855965949555534', '14.35055208016376764816169793016097'], 'prelabel': '2-78-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7891977798790284, 'root_angle': -0.024582277929465535, 'root_number': '0.997019438134932 - 0.07715076137734848*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0122911389647', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.10639155598610243462545224339', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.05794074943596429287036818958', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.15874339313983288500300342785', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.6228331357659873, 'bad_primes': [2, 3, 13], 'central_character': '13.4', 'conductor': 78, 'conductor_radical': 78, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/78/2/i/b/43/2'], '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': '2-78-13.4-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': '2-78-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7891977798790284, 'root_angle': -0.012291138964732768, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.10639155598610243462545224339', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3937819120489686228551536077598', 'Lhash_array': ['3937819120489686228551536077598'], 'label': '2-78-13.4-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/78/2/i/b/43/2'}