-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1650818385479867111555187889610', 'a10': [0.0, 0.0], 'a2': [2.6214026021120853, 2.6214026021120853], 'a3': [0.0, 0.0], 'a4': [0.0, 5.743503204720022], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [10.86517254176112, -10.86517254176112], 'a8': [5.915186570804515, -5.915186570804515], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.275429751291645, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '225.143', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '1958822364372547400324999525560', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.6214026021120853, -2.6214026021120853], [0, 8.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-10.86517254176112, 10.86517254176112], [0, -343.0]], [[1.0, 0], [0, -37.89047576669579], [-1331.0, 0]], [[1.0, 0], [-48.10851121584332, -48.10851121584332], [0, 2197.0]], [[1.0, 0], [-60.34582633809685, -60.34582633809685], [0, 4913.0]], [[1.0, 0], [0, 109.67771259873112], [-6859.0, 0]], [[1.0, 0], [39.76599415425228, -39.76599415425228], [0, -12167.0]], [[1.0, 0], [-90.35527923292511, 0], [24389.0, 0]], [[1.0, 0], [233.67771259873112, 0], [29791.0, 0]], [[1.0, 0], [-19.004233430088025, 19.004233430088025], [0, -50653.0]], [[1.0, 0], [0, 260.7833414217593], [-68921.0, 0]], [[1.0, 0], [176.21636430913534, 176.21636430913534], [0, 79507.0]], [[1.0, 0], [-145.7883422081632, -145.7883422081632], [0, 103823.0]], [[1.0, 0], [-183.28531227852702, 183.28531227852702], [0, -148877.0]], [[1.0, 0], [-279.5635583844245, 0], [205379.0, 0]], [[1.0, 0], [390.26702242627255, 0], [226981.0, 0]], [[1.0, 0], [150.44448609120323, -150.44448609120323], [0, -300763.0]], [[1.0, 0], [0, -470.04209319146406], [-357911.0, 0]], [[1.0, 0], [480.7651281860939, 480.7651281860939], [0, 389017.0]], [[1.0, 0], [0, 1322.4405373558955], [-493039.0, 0]], [[1.0, 0], [456.19170488873925, -456.19170488873925], [0, -571787.0]], [[1.0, 0], [1364.8488937702264, 0], [704969.0, 0]], [[1.0, 0], [-785.3082980213663, 785.3082980213663], [0, -912673.0]], [[1.0, 0], [0, -111.55460140806454], [-1030301.0, 0]], [[1.0, 0], [13.882034740153685, 13.882034740153685], [0, 1092727.0]], [[1.0, 0], [776.1653886466997, 776.1653886466997], [0, 1225043.0]], [[1.0, 0], [0, 410.5788685997115], [-1295029.0, 0]], [[1.0, 0], [521.3279301217333, -521.3279301217333], [0, -1442897.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 10, 'label': '2-15e2-15.8-c3-0-10', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/225/4/f/c/143/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [3.291801837500927, 3.1303112078531687, 2.920730521461522, 2.667205855549039, 2.374198077275298, 2.046810528547113, 1.6911207586123793, 1.3144618880429246, 0.9256025866060631, 0.5347822664038139, 0.15356920502395718, -0.20547666270689252, -0.5293380711655213, -0.8052552248345348, -1.0215847770069308, -1.168746945624689, -1.240186480819019, -1.2332584479461763, -1.1499407680234586, -0.9972743855069891, -0.7874407026058838, -0.537405747632495, -0.2680916452918868, -0.003077263931811536, 0.23312108343577292, 0.4170852873737966, 0.5286926753747851, 0.5532766424637355, 0.4835233412903769, 0.32086833755568916, 0.07617362351498722, -0.2304901831285724, -0.5710594633180167, -0.9116978498619637, -1.2159150449034202, -1.448359398784339, -1.57894832598527, -1.5869120381505284, -1.4642746520946999, -1.2182948991769331, -0.8724445766412905, -0.46561861320860215, -0.04944084147295412, 0.31625898641398525, 0.5694894732603781, 0.653129895001292, 0.5222275649384416, 0.150713101968703, -0.46334687791942986, -1.2947659509637828, -2.2911429083826493, -3.375986833210513, -4.455027303433259, -5.4252700233991735, -6.185963906209084, -6.6503157764748035, -6.756575231381503, -6.477056837309987, -5.823794836196524, -4.849839325008373, -3.6456791328837723, -2.3308665778404194, -1.0415528125809994, 0.08476412927731673, 0.9255097318753792, 1.3882898607768885, 1.4230976125830288, 1.0297104257839405, 0.2590593531589715, -0.7918978594183801, -1.9914027796502318, -3.1889604209096545, -4.234244889847276, -4.9963597025451145, -5.380809997642503, -5.341766652560079, -4.887793100937165, -4.0800960232800145, -3.0234312876413796, -1.850890790702621, -0.7047448797241842, 0.2838375330894336, 1.0131401650485514, 1.4245161346093418, 1.5091649982738218, 1.307025062978025, 0.8979959517905372, 0.3869639595439385, -0.11485389243424346, -0.509087512861199, -0.7266349162771387, -0.7384949601211132, -0.5591329230932234, -0.24180977433590736, 0.13324978820570382, 0.47565304974336703, 0.7034470676026146, 0.7599912017303042, 0.6258056745418763, 0.3229982500724178, -0.08874846141890266, -0.5240194881283133, -0.8891592518981469, -1.1020252892856734, -1.1100279352016575, -0.9026565543806767, -0.5156398903288664, -0.02545864423259476, 0.4651568671064728, 0.8482171234518441, 1.0339350829911889, 0.9718826822293842, 0.6652362751517162, 0.17463085116869198, -0.3899431653685799, -0.8884024802294797, -1.177832408298106, -1.1427085531969943, -0.7220621889719764, 0.0722434152009706, 1.1505713519923177, 2.3559600042331468, 3.4890449534692727, 4.343544942838585, 4.746000652825927, 4.592167988921367, 3.8726282752683074, 2.681844372373436, 1.2078189542244595, -0.29681819610447563, -1.5577521651256698, -2.3284015262763407, -2.436599915527832, -1.8194207423731763, -0.5389414603652457, 1.2248192582605733, 3.203227808468624, 5.085677063477005, 6.575042062461882, 7.441480945460393, 7.56418347839711, 6.952831379872113, 5.744407009283682, 4.175822313085061, 2.5376674529851906, 1.1182015603310322, 0.14871434903811567, -0.23887253516033227, -0.03380181632910252, 0.6564326450598492, 1.6326909347972747, 2.648552903579408, 3.462863134964958, 3.889277703195293, 3.8324473094115916, 3.3035194132959416, 2.4122589953416083, 1.3382522034584563, 0.28821795921849586, -0.5506131520304177, -1.050445211769727, -1.1673591887128012, -0.9452081291042495, -0.4988305615461166, 0.018676326855450634, 0.45619029451585014, 0.7022417566869329, 0.710896790804883, 0.5096851021646821, 0.18799713376072053, -0.13066057911023238, -0.32505100894528705, -0.3115133676105251, -0.06872812577446807, 0.3548182996344734, 0.852925063123989, 1.2904008655780685, 1.5409642249053845, 1.5241747404865997, 1.2311628382174242, 0.731552062885932, 0.15872100735686284, -0.3237309411227164, -0.5662296244967047, -0.4767709128772159, -0.05187951612371699, 0.6142515499152617, 1.3464335922430604, 1.928364257721908, 2.1568154452592854, 1.896876182395664, 1.123845090780379, -0.060115082491700764, -1.4407016606612293, -2.736039228498579, -3.6618120408793144, -4.001855675999817, -3.666780335057787, -2.7251622120037253, -1.397815483651239, -0.014338766951224236, 1.0595394952607842, 1.5076282561953473, 1.141766869318703, -0.04621460443679821, -1.8727773276280995, -3.9956562317148228, -5.98531672085834, -7.419145363014413, -7.976689211866799, -7.513458900534863, -6.095489840495545, -3.98598282874221, -1.5867499728089658, 0.6519134822821525, 2.331638091780378, 3.1928720272852353, 3.1677931107368464, 2.387158541344795, 1.1403557754264202, -0.20061664760519346, -1.273815654956012, -1.8135131320245634, -1.7088437897458042, -1.0213715945913564, 0.04123821312985949, 1.1869936197132953, 2.119517235706259, 2.6147458668470023, 2.5745643485683867, 2.0443307564621507, 1.1913243996730065, 0.2517460912619787, -0.5378587114492053, -1.0052043011092093, -1.0851569210494596, -0.8298715927276752, -0.38475596031344755, 0.06136260660224507, 0.3363126538111643, 0.3368004746866627, 0.057452921410307625, -0.4114162564335249, -0.915879735713763, -1.2898559499952096, -1.4096794804053445, -1.2346275898069794, -0.8205985543748218, -0.3024471234362675, 0.14972647605571157, 0.38673082016912663, 0.3310306944767805, 0.0054527975359736644, -0.4703300465866243, -0.9158474668077489, -1.1483694154882476, -1.0462276793429257], 'positive_zeros': ['1.30226608592513718068294178292380', '2.87651144190281946613445622995179', '3.78309046010550123818256756626082', '5.26552677814666436265864695408637', '5.91058942008442019936408549242625', '7.86454903655888390680623538137602', '8.533493000592066893122451307525111', '10.08610435316090518829572533230578', '10.96976876622391924353888372490479', '11.70590102939686350540432575794874'], 'prelabel': '2-15e2-15.8-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6435463152389933, 'root_angle': -0.372121467190087, 'root_number': '0.39102247747950386 - 0.9203811287210266*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.186060733595', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.30226608592513718068294178292', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.87651144190281946613445622995', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.78309046010550123818256756626', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 13.275429751291645, 'bad_primes': [3, 5], 'central_character': '15.8', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/4/f/c/143/5'], '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': '2-15e2-15.8-c3-0-10', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-15e2-15.8-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6435463152389933, 'root_angle': -0.1860607335950435, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.30226608592513718068294178292', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1650818385479867111555187889610', 'Lhash_array': ['1650818385479867111555187889610'], 'label': '2-15e2-15.8-c3-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/4/f/c/143/5'}