-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2414252001879463370174031495829', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.0, -1.7320508075688772], 'a4': [1.0, -1.7320508075688772], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [4.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.79289409601082, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [3.5, -2.598076211353316]]]], 'bad_primes': [5, 19], 'central_character': '475.26', 'coefficient_field': 'CDF', 'conductor': 475, 'conductor_radical': 95, 'conjugate': '1573105490487381678961414396416', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-1.0, 1.7320508075688772]], [[1.0, 0], [1.0, 1.7320508075688772], [-1.5, 2.598076211353316]], [[1.0, 0], [0, 0]], [[1.0, 0], [-4.0, 0], [7.0, 0]], [[1.0, 0], [-3.0, 0], [11.0, 0]], [[1.0, 0], [-1.0, 1.7320508075688772], [-6.5, -11.258330249197702]], [[1.0, 0], [-3.0, -5.196152422706632], [-8.5, 14.722431864335457]], [[1.0, 0], [3.5, -2.598076211353316]], [[1.0, 0], [0, 0], [-11.5, -19.91858428704209]], [[1.0, 0], [-1.5, 2.598076211353316], [-14.5, -25.11473670974872]], [[1.0, 0], [7.0, 0], [31.0, 0]], [[1.0, 0], [8.0, 0], [37.0, 0]], [[1.0, 0], [-3.0, -5.196152422706632], [-20.5, 35.50704155516198]], [[1.0, 0], [2.0, 3.4641016151377544], [-21.5, 37.239092362730865]], [[1.0, 0], [-3.0, 5.196152422706632], [-23.5, -40.703193977868615]], [[1.0, 0], [3.0, -5.196152422706632], [-26.5, -45.89934640057525]], [[1.0, 0], [-7.5, -12.99038105676658], [-29.5, 51.09549882328188]], [[1.0, 0], [2.5, -4.330127018922194], [-30.5, -52.827549630850754]], [[1.0, 0], [-1.0, 1.7320508075688772], [-33.5, -58.023702053557386]], [[1.0, 0], [-1.5, -2.598076211353316], [-35.5, 61.48780366869514]], [[1.0, 0], [-4.0, -6.928203230275509], [-36.5, 63.21985447626402]], [[1.0, 0], [2.5, 4.330127018922194], [-39.5, 68.41600689897065]], [[1.0, 0], [12.0, 0], [83.0, 0]], [[1.0, 0], [-7.5, 12.99038105676658], [-44.5, -77.07626093681505]], [[1.0, 0], [-4.0, -6.928203230275509], [-48.5, 84.00446416709055]], [[1.0, 0], [7.5, -12.99038105676658], [-50.5, -87.4685657822283]], [[1.0, 0], [-16.0, 0], [103.0, 0]], [[1.0, 0], [0, 0], [107.0, 0]], [[1.0, 0], [5.5, 9.526279441628825], [-54.5, 94.39676901250381]], [[1.0, 0], [6.0, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 21, 'label': '2-475-19.7-c1-0-21', '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/475/2/e/b/26/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.5799343955493261, 1.7123633319650062, 1.849622531890148, 1.9888742939212225, 2.1235192959675344, 2.2436158300506506, 2.3366754291986367, 2.388685068142973, 2.385276172823911, 2.3130071570598867, 2.1607303471986685, 1.920988018908748, 1.5913445471269816, 1.1755269062774505, 0.6842233482436166, 0.135385969062781, -0.446099288228925, -1.02947028266913, -1.579905063170395, -2.0610453010086203, -2.4380806235167936, -2.6811518176405684, -2.7687462203586133, -2.6906990727580347, -2.4503935135696366, -2.0657799185887034, -1.5689183424598094, -1.0038850543747126, -0.42306672494649467, 0.11792348362587067, 0.5662594844913278, 0.8782091684129782, 1.0249681466812215, 0.9972098605060561, 0.8076044081643186, 0.49073615901971807, 0.10013487650352167, -0.2974989270103723, -0.6303885636796799, -0.831220601067509, -0.8469418573533783, -0.6474498971354146, -0.23181755475495008, 0.3690980659834109, 1.094401664341135, 1.8594283697561589, 2.5660376383088748, 3.115771424849921, 3.4241589940354697, 3.4341033584912077, 3.1262268921689307, 2.5243287495283937, 1.6947065878990442, 0.7389565309039003, -0.21912646243504894, -1.0509235034063464, -1.6421904711564765, -1.9111341556178139, -1.8223735868854973, -1.3942480436935536, -0.6978550466296994, 0.15252572598728742, 1.0165341284819476, 1.7499136621492053, 2.2283039564224687, 2.3686705792402556, 2.144569904723899, 1.5923029554471995, 0.8064528294269556, -0.07489418450192212, -0.8930789782764245, -1.496203734140281, -1.7661353008854161, -1.6402779463537496, -1.1239563133243118, -0.2908128737106875, 0.7292383499935071, 1.7726266248282116, 2.6713458258693294, 3.2834030764276396, 3.518686150972138, 3.3551396838314487, 2.8418882866774497, 2.088445242165345, 1.2419289521360297, 0.45671895515514366, -0.1373148362462097, -0.4613793795313514, -0.5033681389455107, -0.3188949801106938, -0.017141362632767432, 0.2658145152828605, 0.40065955867500314, 0.2981785143195526, -0.0653392290759754, -0.6368299489956581, -1.2926968361848115, -1.862191233174091, -2.1636892552105547, -2.046471188546807, -1.4289331339842093, -0.32441285071353526, 1.151950455774664, 2.798067726354136, 4.359546862166382, 5.577731926599559, 6.241438163758225, 6.2313891667798815, 5.547455351259527, 4.312145354485749, 2.7487616420540824, 1.1381464996362494, -0.2372141306163354, -1.1499233524679073, -1.4729642683867539, -1.2035634365159409, -0.46026333770464567, 0.5462040045609649, 1.561706646273786, 2.346088309248516, 2.726016478379246, 2.6312006892434643, 2.1057649714135995, 1.2924489364206615, 0.39382400169410725, -0.37972912277766174, -0.8623118141255158, -0.972053391171725, -0.7281056395606125, -0.2410009680076078, 0.32087513792011846, 0.7797180367650095, 0.9986619658151004, 0.9203987366548528, 0.5833051219837381, 0.11017507323089977, -0.32801097207295027, -0.5639176142440679, -0.4872624498831307, -0.08471779077271785, 0.5457946235041351, 1.2121141455581081, 1.6735904528257795, 1.7050041466601842, 1.1625089541216833, 0.033892422994779035, -1.5414595935480437, -3.2903737492659437, -4.859470031168068, -5.893073621902027, -6.117127650865028, -5.408352104134668, -3.8307557290328877, -1.6292073220257552, 0.8197124483427036, 3.088585582675827, 4.792547670339823, 5.672542129048851, 5.64812680594653, 4.827145407475333, 3.4705554071531157, 1.9221751541685241, 0.5220277635069981, -0.47408832556932107, -0.9482749953537356, -0.9345388309195506, -0.5912543986088233, -0.14165911891311594, 0.19939479468663573, 0.29077688072798624, 0.10362605182041665, -0.27756001023235155, -0.6906670012695638, -0.956794991035936, -0.9467659226669005, -0.6319871867688597, -0.10286999386012456, 0.4522723203267755, 0.8027831352389506, 0.7496559010669371, 0.19550025730558826, -0.81180451885824, -2.0770791266959763, -3.3008206758124428, -4.1570882378327525, -4.385150944279598, -3.8685446486103414, -2.677608846946866, -1.0612150568118972, 0.6123340402204108, 1.9504165224134544, 2.6413589534926625, 2.540163868513133, 1.7097281232990174, 0.4047515539957782, -0.9982237047200946, -2.105564146024967, -2.6165948159365437, -2.4074634287490055, -1.5645260151042157, -0.35739021041810975, 0.8407292274356095, 1.6622300848920675, 1.8520337295394143, 1.3409166321706725, 0.2639051340330279, -1.0812987517416477, -2.3230218263467837, -3.1245903485216746, -3.280800036569574, -2.773174170583835, -1.7681068028379063, -0.5596340849241876, 0.5243855898974, 1.2227738806129735, 1.4165875164441717, 1.1563545008775038, 0.6332843341427821, 0.10486823916292355, -0.19991715519730827, -0.16390679954945225, 0.17467342282700277, 0.6335901345798393, 0.9500165216190771, 0.875518287094088, 0.27103496212857286, -0.8306398079785421, -2.2175541220354464, -3.551539527063553, -4.466657216582958, -4.682835719826911, -4.0982829305509, -2.8298885863862053, -1.1866944862665538, 0.4172975171323676, 1.5849571710298067, 2.05464315955157, 1.7779028051321306, 0.9309314472208228, -0.14466459551576638, -1.053514667954064, -1.475012828345955, -1.267209939670258, -0.5119930959331784, 0.5138151118969405, 1.432746384454119, 1.8960580327212566, 1.7058480986185205, 0.8892590705586872, -0.30080334904206063, -1.4602657566733332, -2.1608961107859974, -2.0892391166051283, -1.1524448859611434, 0.48387443572503086, 2.438916049936096, 4.2280237218278485], 'positive_zeros': ['1.90450901963427336876409659813664', '3.59627781104575035677850307992510', '4.53081813332288507663557053441890', '5.30231486765980986190015992088134', '6.72053709103147934181714728346799', '7.60332834659405498782401041704819', '8.614350793160160309967491943005593', '9.412174090981647598879264232347757', '10.71593279964040892144337013763944', '11.25680112181617328687651782648604'], 'prelabel': '2-475-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': 0.5311600905421131, 'root_number': '-0.09773603764763142 + 0.995212372785297*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.265580045271', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.90450901963427336876409659814', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.59627781104575035677850307993', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.53081813332288507663557053442', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.79289409601082, 'bad_primes': [5, 19], 'central_character': '19.7', 'conductor': 475, 'conductor_radical': 95, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/475/2/e/b/26/1'], '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': '2-475-19.7-c1-0-21', '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': '2-475-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': 0.26558004527105655, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.90450901963427336876409659814', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2414252001879463370174031495829', 'Lhash_array': ['2414252001879463370174031495829'], 'label': '2-475-19.7-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/475/2/e/b/26/1'}