-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1274765495629265965908333460203', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [2.1904735317346415, 3.7940114495992368], 'a6': [0, 0], 'a7': [-0.5, 0.8660254037844386], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 24.1467615712352, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.5, -0.8660254037844386]]]], 'bad_primes': [2, 3, 7], 'central_character': '3024.2017', 'coefficient_field': 'CDF', 'conductor': 3024, 'conductor_radical': 42, 'conjugate': '1558169121218799173937553519686', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.1904735317346415, -3.7940114495992368], [-2.5, 4.330127018922194]], [[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [-2.6904735317346415, 4.660036853383676], [-5.5, -9.526279441628825]], [[1.0, 0], [-1.2717388533774938, -2.2027163080092063], [-6.5, 11.258330249197702]], [[1.0, 0], [-2.580577137752676, 0], [17.0, 0]], [[1.0, 0], [-6.724794695940878, 0], [19.0, 0]], [[1.0, 0], [-0.40018496285830363, -0.693140688095646], [-11.5, 19.91858428704209]], [[1.0, 0], [-1.8715538905191902, 3.2416264274824376], [-14.5, -25.11473670974872]], [[1.0, 0], [-1.696851807491941, -2.9390335434911252], [-15.5, 26.846787517317598]], [[1.0, 0], [-4.380947063469283, 0], [37.0, 0]], [[1.0, 0], [3.196851807491941, 5.537109754844441], [-20.5, 35.50704155516198]], [[1.0, 0], [0.3816352473594595, -0.6610116383857], [-21.5, -37.239092362730865]], [[1.0, 0], [-4.134136201347933, 7.160533946144418], [-23.5, -40.703193977868615]], [[1.0, 0], [-4.948767649707361, 0], [53.0, 0]], [[1.0, 0], [2.787510302084886, 4.828109469832692], [-29.5, 51.09549882328188]], [[1.0, 0], [-4.143292743896684, 7.176393543060521], [-30.5, -52.827549630850754]], [[1.0, 0], [0.946440936404743, 1.6392837882160798], [-33.5, 58.023702053557386]], [[1.0, 0], [-1.3438476324715949, 0], [71.0, 0]], [[1.0, 0], [8.650595833945502, 0], [73.0, 0]], [[1.0, 0], [6.640514477105232, -11.501708462742938], [-39.5, -68.41600689897065]], [[1.0, 0], [1.8623973479704392, -3.2257668305663345], [-41.5, -71.88010851410841]], [[1.0, 0], [-6.998623632219648, 0], [89.0, 0]], [[1.0, 0], [1.4807621006109797, -2.5647551921806344], [-48.5, -84.00446416709055]], [[1.0, 0], [8.564939247329503, -14.834909940115438], [-50.5, -87.4685657822283]], [[1.0, 0], [6.017861531608668, 10.423241925660474], [-51.5, 89.20061658979718]], [[1.0, 0], [6.925801138004624, 0], [107.0, 0]], [[1.0, 0], [4.419422862247324, 0], [109.0, 0]], [[1.0, 0], [-6.418046494466972, -11.11638261375612], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 19, 'label': '2-3024-9.7-c1-0-19', 'leading_term': '2.582246371938490950903408746996343482688131458805111026', '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/3024/2/r/m/2017/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.582246371938491, 2.5065907216416896, 2.4223569299239074, 2.329748862196786, 2.2288939159784467, 2.1198885436880204, 2.002848206255829, 1.8779587529447939, 1.745526320647936, 1.6060231262480773, 1.4601269237672536, 1.3087523493897684, 1.1530728293660264, 0.9945321436164344, 0.834845105262153, 0.6759871319611481, 0.5201727572341626, 0.36982337190764647, 0.22752471076543138, 0.09597481850650798, -0.022076550653027244, -0.12389592099018817, -0.20684006468906085, -0.2684343204658951, -0.306453411921015, -0.3190027166269534, -0.3045977654616579, -0.26223961885913444, -0.19148368295244825, -0.0924995037581365, 0.03388087991695066, 0.18612832748873606, 0.3619978386653138, 0.5585274771394915, 0.7720564493407277, 0.9982633774449138, 1.2322253010319086, 1.4684973760579019, 1.701212625882161, 1.9242004525395013, 2.1311219554438594, 2.3156194495733144, 2.4714769478896144, 2.5927877962565873, 2.674125146689381, 2.710710549111627, 2.6985756542600075, 2.6347118700315058, 2.5172028163540836, 2.3453345915343813, 2.119679203210034, 1.842147031322754, 1.5160048748310655, 1.1458569778464305, 0.7375874177656321, 0.29826334475393973, -0.16400024038324534, -0.6402122286838269, -1.120710452764445, -1.5953955836090585, -2.0539882364306012, -2.4863025844373046, -2.882528875121283, -3.233516540229284, -3.5310491253228036, -3.7681020692018405, -3.939074461236147, -4.039986310545822, -4.068633579485198, -4.024694258380149, -3.9097800706922845, -3.7274299677510765, -3.4830433585459053, -3.1837529708788757, -2.838239294236381, -2.456490643279998, -2.0495149297123887, -1.629011162358539, -1.207010433404764, -0.7954976184860697, -0.406026151227991, -0.04933896936240721, 0.2649909781559362, 0.5288874589731525, 0.7360523960581259, 0.8821906667930455, 0.9651685586219915, 0.9850982576496677, 0.9443432015797661, 0.8474418817829096, 0.7009506390505685, 0.5132090588567408, 0.2940346205206051, 0.05435617111102783, -0.19420154086955052, -0.43976774103654354, -0.6706935621644573, -0.8760204304481719, -1.0459306910604125, -1.1721623445106166, -1.2483705723232046, -1.270420257543696, -1.2365959214918807, -1.1477183423257051, -1.00716050410304, -0.8207593316325584, -0.5966237583040841, -0.3448438951143461, -0.07711025081429464, 0.19374407869257934, 0.4542617517193078, 0.690920521553137, 0.890711712262591, 1.0417144555020412, 1.133641723049687, 1.158334577382329, 1.1101824500907287, 0.9864496247554164, 0.7874913837027661, 0.5168473716817796, 0.18120448970912734, -0.2097731195749234, -0.643743904539809, -1.1061098815545607, -1.580544683824089, -2.049609634298099, -2.495434473209499, -2.9004359127800616, -3.2480447772848673, -3.523411256788374, -3.714057851200099, -3.8104509485167353, -3.806464650932869, -3.6997143602096627, -3.4917426273007552, -3.188045675260344, -2.7979355862968167, -2.33424013255802, -1.812849327485113, -1.252124667152096, -0.6721934046351578, -0.09415575410344035, 0.4607626185064221, 0.9720773271068122, 1.4208940991183086, 1.7907025828678829, 2.0680796585434775, 2.243270076636294, 2.3106170713379606, 2.268821768821436, 2.1210174833423983, 1.8746530608568086, 1.5411879377211688, 1.135610147730792, 0.6757967374826805, 0.18174354597102207, -0.32530229870359556, -0.8237688407474945, -1.2927031119318664, -1.71268930310406, -2.066698896130767, -2.34083297348415, -2.5249214669601514, -2.6129504074180785, -2.6032960294963243, -2.4987535255423055, -2.306357923600743, -2.0370045310694014, -1.7048861591481288, -1.3267734417491153, -0.9211725257989818, -0.5074008223612143, -0.10462602094339006, 0.2690840801890919, 0.5976533484680362, 0.8677854640787691, 1.0696078597057324, 1.197137644859106, 1.2485443012184403, 1.2261939567983338, 1.1364710173513202, 0.9893843161286855, 0.7979761669991206, 0.5775631945355308, 0.3448470154064735, 0.11694025842214772, -0.08964138409140769, -0.2599676996980689, -0.3816097568639043, -0.44543243909689473, -0.4462186921250625, -0.3830884342017133, -0.2596851561464838, -0.0841149428949823, 0.13136459192336256, 0.3708947954165447, 0.6157823225779757, 0.8454458216652112, 1.0384970837346488, 1.1739026062289541, 1.2321660022096967, 1.1964691768152793, 1.0537108910481556, 0.795385275656744, 0.4182499096922924, -0.07525706329286763, -0.6768791016587496, -1.3726970729294417, -2.143578042585149, -2.965901083616969, -3.8125293644359375, -4.653984304751649, -5.459766175751883, -6.199756809612787, -6.84563459067012, -7.372229981688344, -7.758751664613497, -7.989818919562444, -8.056244901814035, -7.955527585063016, -7.692019727244422, -7.276765544680304, -6.727009004899989, -6.065395857808221, -5.318907792703182, -4.517581543315242, -3.6930775569847114, -2.877171319843735, -2.1002450798011534, -1.3898582267285675, -0.7694708898112501, -0.2573875415136738, 0.1340240712024915, 0.39879793183690837, 0.5374948935895555, 0.5569825294293109, 0.4698830909147868, 0.293721197581802, 0.04981948288912445, -0.23799553902204756, -0.5448044646274538, -0.846043290189399, -1.118907235615185, -1.3436307455597052, -1.504571237908354, -1.5910352733870778, -1.5978005104050372, -1.5253042833186992, -1.3794889259292058, -1.1713139630855833, -0.9159648628005237, -0.631806038958276, -0.3391411550216227, -0.058855574612010415, 0.18897669782549495, 0.38643653686345697, 0.5189709318760577], 'positive_zeros': ['1.00561266282661451801774813099543', '1.51082273483431850333379143013759', '2.82596076244788986177645948345002', '4.12078682392186730616660447834674', '4.73383258220406374972579069592218', '5.49878311007369358150457725760841', '6.11809112037735926748129888789235', '7.16857463480351103806418860235599', '7.889332430323087578459293682608906', '8.748105372237664210307822028420019'], 'prelabel': '2-3024-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.9139354463846185, 'root_angle': -0.34766301326025034, 'root_number': '0.46051985081247791561945229261605732405680865068799589547 - 0.8876494054567113175007021805765967440198663930455259466*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.17383150663012517', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.00561266282661451801774813100', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.51082273483431850333379143014', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.82596076244788986177645948345', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 24.1467615712352, 'bad_primes': [2, 3, 7], 'central_character': '9.7', 'conductor': 3024, 'conductor_radical': 42, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3024/2/r/m/2017/4'], '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': '2-3024-9.7-c1-0-19', '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': '2-3024-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.9139354463846185, 'root_angle': -0.17383150663012517, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.00561266282661451801774813100', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1274765495629265965908333460203', 'Lhash_array': ['1274765495629265965908333460203'], 'label': '2-3024-9.7-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3024/2/r/m/2017/4'}