-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3712046716112977425358701083322', 'a10': [-3.435861348370356, -1.9836954743798556], 'a2': [0.25881904510252074, -0.9659258262890683], 'a3': [-1.2221504900036393, -1.2273337686969523], 'a4': [-0.8660254037844386, -0.5], 'a5': [1.0268363369063724, -3.832205380392495], 'a6': [-1.5018292074553998, 0.8628493678701318], 'a7': [1.1359679654746837, 1.1359679654746837], 'a8': [-0.7071067811865476, 0.7071067811865476], 'a9': [-0.012696359567728412, 2.9999731336219875], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.868499407297962, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.25881904510252074, 0.9659258262890683]]], [3, [[1.0, 0], [1.2221504900036393, 1.2273337686969523]]], [13, [[1.0, 0], [-3.509561738236535, -0.8264238655231043]]]], 'bad_primes': [2, 3, 13], 'central_character': '234.227', 'coefficient_field': 'CDF', 'conductor': 234, 'conductor_radical': 78, 'conjugate': '1148633564851471742735369575494', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.25881904510252074, 0.9659258262890683]], [[1.0, 0], [1.2221504900036393, 1.2273337686969523]], [[1.0, 0], [-1.0268363369063724, 3.832205380392495], [-4.330127018922194, -2.5]], [[1.0, 0], [-1.1359679654746837, -1.1359679654746837], [0, 7.0]], [[1.0, 0], [4.794423744863131, 1.284661970608675], [9.526279441628825, 5.5]], [[1.0, 0], [-3.509561738236535, -0.8264238655231043]], [[1.0, 0], [0.584080352316197, 1.0116568459143833], [-8.5, 14.722431864335457]], [[1.0, 0], [4.166464896186503, 1.116400904225795], [16.454482671904334, 9.5]], [[1.0, 0], [-3.2699989001251657, 0], [23.0, 0]], [[1.0, 0], [-6.500123089681242, 3.752847815593167], [14.5, -25.11473670974872]], [[1.0, 0], [-7.254676349003271, -1.9438846690645921], [26.846787517317598, 15.5]], [[1.0, 0], [4.287753581983616, -1.1489001096361637], [32.04293994002423, -18.5]], [[1.0, 0], [-3.9612403629497535, -3.9612403629497535], [0, 41.0]], [[1.0, 0], [0, -0.8896210613820201], [-43.0, 0]], [[1.0, 0], [-0.6531873783276292, -2.4377284827814263], [-40.703193977868615, 23.5]], [[1.0, 0], [0, 6.601807713256441], [-53.0, 0]], [[1.0, 0], [2.1276073949345045, 7.940338896454833], [-51.09549882328188, 29.5]], [[1.0, 0], [-14.11854338617038, 0], [61.0, 0]], [[1.0, 0], [-2.33691507231039, 2.33691507231039], [0, -67.0]], [[1.0, 0], [0.9427010003149081, -3.5182080295212415], [-61.48780366869514, -35.5]], [[1.0, 0], [3.3334337338956086, 3.3334337338956086], [0, 73.0]], [[1.0, 0], [1.1690183477044405, -2.0247991732043107], [-39.5, -68.41600689897065]], [[1.0, 0], [10.553207654869741, -2.8277234686802895], [71.88010851410841, -41.5]], [[1.0, 0], [-1.7829730469859344, -6.654145999877398], [-77.07626093681505, 44.5]], [[1.0, 0], [4.523853633068573, -4.523853633068573], [0, -97.0]], [[1.0, 0], [-8.148061732369401, -14.112856903671487], [-50.5, 87.4685657822283]], [[1.0, 0], [2.002313435039165, -1.156036200721866], [51.5, -89.20061658979718]], [[1.0, 0], [-8.908516710357258, -5.143334520805042], [53.5, 92.66471820493493]], [[1.0, 0], [-5.932265598865105, 5.932265598865105], [0, -109.0]], [[1.0, 0], [3.056892519744651, 1.7648977191583275], [56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 13, 'label': '2-234-117.110-c1-0-13', '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/234/2/z/a/227/10', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.0241889538513742, 1.1817920713454315, 1.3590302080911392, 1.559132662333564, 1.7831206058983942, 2.029576396432671, 2.2945948230440925, 2.5718383641708438, 2.8526603432530164, 3.1263029897890138, 3.38020119513186, 3.600426401876877, 3.7722950304587703, 3.8811481171370095, 3.9132872057507493, 3.8570283310517404, 3.703813008822388, 3.449294464616075, 3.0943011203303312, 2.6455700252052368, 2.1161427984932484, 1.525327664255509, 0.8981544415960856, 0.2642849122597508, -0.34361258120513855, -0.8919611176895208, -1.348724849683422, -1.6860341571591546, -1.882764077705699, -1.926813898460653, -1.8168284464438647, -1.563121656938029, -1.1876128518160176, -0.7226650244721431, -0.20881778633339718, 0.3084728710649504, 0.782852011080052, 1.1714905710263763, 1.4394793801846937, 1.5637059777611078, 1.5357316632742184, 1.3632491003439895, 1.0698231327923944, 0.692791908052591, 0.2794166082736209, -0.11840639580602089, -0.45034492973094786, -0.6740466694310867, -0.7609775366380984, -0.7008841101304677, -0.5041814233953626, -0.20177215083028113, 0.15790310886469588, 0.5144319350460999, 0.8030902791215634, 0.9637375175936506, 0.9498342568032492, 0.7363472819034067, 0.32534387287145766, -0.25171094990110776, -0.9355677040592711, -1.6448321382909097, -2.2851847925682094, -2.761182539629117, -2.989186545380699, -2.909674335605843, -2.4971373047040952, -1.7659695538586861, -0.7712130300910001, 0.39630865777891244, 1.620142646990571, 2.7725128180134018, 3.730947680560368, 4.394925521245443, 4.700078031379129, 4.627708482456991, 4.207960006622453, 3.515850292476815, 2.660453550359607, 1.7686017774099139, 0.9654207583210181, 0.35464769574486577, 0.0018712341670220941, -0.07647180889973716, 0.08370056659903354, 0.3995799181852377, 0.7550749297499196, 1.0206518449987794, 1.0763511646391277, 0.8342278814125312, 0.2563639077539374, -0.6348456952275473, -1.7562820735565805, -2.974135054144027, -4.12318117738428, -5.032459040163793, -5.553253232067794, -5.5847087468193575, -5.092598355324505, -4.117761446171531, -2.772386858010692, -1.2243603873258648, 0.32800948905433847, 1.6868122134171315, 2.68572938645069, 3.2162249765193374, 3.2441140977557663, 2.8135151702494543, 2.0374052726425296, 1.0764140913008227, 0.10966174413181166, -0.6970474082794761, -1.2198254327756952, -1.3968093116266498, -1.2360757161498774, -0.8099872308323071, -0.23722692909402812, 0.34379704804292965, 0.8047655687090043, 1.054399973431524, 1.0570217418506698, 0.8388836622740046, 0.4809500259920652, 0.09963986461909524, -0.1803777215865775, -0.2554827998086381, -0.06808916750376942, 0.37828702345618165, 1.0174341774122322, 1.7330121665707237, 2.3828510782187236, 2.82987493760555, 2.9729031535156922, 2.770382564334047, 2.251446023037807, 1.5113452075786558, 0.691730339278536, -0.0502850042374145, -0.5776067006311764, -0.8051805675192215, -0.7209555067229102, -0.390361432302095, 0.05760721611922784, 0.46046816896857834, 0.6623925864065332, 0.5556274887664586, 0.11357649038069345, -0.5927819933999147, -1.40019138406017, -2.0805746984040474, -2.3861209934858674, -2.1032169982535804, -1.103910982243459, 0.6165545272485926, 2.9252207380915283, 5.564469373411372, 8.191490556014735, 10.437252912599709, 11.973593088625783, 12.574876150192686, 12.161384760626655, 10.81511391902356, 8.764286498447111, 6.339471674931056, 3.910248830297953, 1.8155550325049623, 0.30221536863714304, -0.5156647909111681, -0.6683969311462844, -0.3118672739414255, 0.31671125850846227, 0.9577615829966257, 1.3892579683320916, 1.4739660457754153, 1.183682602998316, 0.5958406333876627, -0.13543808351683698, -0.8256335045577724, -1.311199157367627, -1.4927654082160275, -1.3592449444705261, -0.9869682883807274, -0.5145107015769245, -0.10023768341648885, 0.12582823969103668, 0.10262312650146416, -0.1402181891104542, -0.4860054231725349, -0.7598700467819255, -0.7759560505535164, -0.3908830020633628, 0.45065354687363574, 1.6907192945555898, 3.1610845045927722, 4.614874869673774, 5.780085425203976, 6.422217731120745, 6.400535042781053, 5.7036008219518, 4.454673527877991, 2.884994164639759, 1.281141721471067, -0.08066077120700858, -0.9969139975109279, -1.380212363380018, -1.2727450612883253, -0.8267682437712666, -0.25752596042916787, 0.21861494491158623, 0.44408163298284414, 0.36180374076030813, 0.02732839693686168, -0.4119988995162583, -0.7650336739869804, -0.8585725377948137, -0.5952577972981127, 0.00928683192808297, 0.8216445148370995, 1.6209032712273477, 2.1570075300999556, 2.221881830516759, 1.7137695483108957, 0.6762282258437079, -0.7005859810684218, -2.1188439501699796, -3.243713742830364, -3.788222592763163, -3.5901126230400173, -2.659723387063366, -1.1849158473108472, 0.5099210627297269, 2.0415367455065465, 3.0628147794719562, 3.3505685583715668, 2.8628827995618464, 1.7503151076464738, 0.317240778255069, -1.057146821652075, -2.0177392628207262, -2.326263618585767, -1.9231496249294062, -0.9418075036753605, 0.3287421303594087, 1.5230550469975954, 2.299077077079337, 2.4316998428141265, 1.8747566312248534, 0.7746450399692125, -0.5681249939426122, -1.7790040840398111, -2.50934042499757, -2.52909877396163, -1.787407034677922, -0.42495772459502473, 1.2643902855115747, 2.911543011397164, 4.167740687765892], 'positive_zeros': ['2.92828853269556760051384227960453', '4.29992620083932690138460538483685', '5.58628938669139488601429362043606', '6.44628196813613205479982037323014', '7.32411883871353106782419090097763', '8.583885237002034899044042260597239', '10.25109982947113481202887633704881', '10.45309831808155778528269567740863', '11.29036485697885812888988789850258', '12.72278892416242944694038509669327'], 'prelabel': '2-234-117.110-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3669306519710362, 'root_angle': 0.4464038327908724, 'root_number': '-0.9438319811725888 + 0.3304257727778296*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.446403832791', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.92828853269556760051384227960', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.29992620083932690138460538484', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.58628938669139488601429362044', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.868499407297962, 'bad_primes': [2, 3, 13], 'central_character': '117.110', 'conductor': 234, 'conductor_radical': 78, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/234/2/z/a/227/10'], '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': '2-234-117.110-c1-0-13', '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': '2-234-117.110-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3669306519710362, 'root_angle': 0.4464038327908724, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.92828853269556760051384227960', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3712046716112977425358701083322', 'Lhash_array': ['3712046716112977425358701083322'], 'factors': ['2-234-117.110-c1-0-13'], 'label': '2-234-117.110-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/234/2/z/a/227/10'}