Lfunction data - 16-33e16-1.1-c0e8-0-2

Formats: - HTML - YAML - JSON - 2025-03-09T06:13:33.869749

• lfunc_lfunctions •

  Column	Type
  A10	numeric
  A2	numeric
  A3	numeric
  A4	numeric
  A5	numeric
  A6	numeric
  A7	numeric
  A8	numeric
  A9	numeric
  Lhash	text
  a10	jsonb
  a2	jsonb
  a3	jsonb
  a4	jsonb
  a5	jsonb
  a6	jsonb
  a7	jsonb
  a8	jsonb
  a9	jsonb
  accuracy	smallint
  algebraic	boolean
  analytic_conductor	double precision
  analytic_normalization	numeric
  bad_lfactors	jsonb
  bad_primes	bigint[]
  central_character	text
  coeff_info	jsonb
  coefficient_field	text
  conductor	numeric
  conductor_radical	integer
  conjugate	text
  credit	text
  degree	smallint
  dirichlet_coefficients	jsonb
  euler_factors	jsonb
  euler_factors_factorization	jsonb
  gamma_factors	jsonb
  group	text
  index	smallint
  instance_types	text[]
  instance_urls	text[]
  label	text
  leading_term	text
  load_key	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  origin	text
  plot_delta	numeric
  plot_values	jsonb
  positive_zeros	jsonb
  precision	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  root_number	text
  self_dual	boolean
  sign_arg	numeric
  spectral_label	text
  st_group	text
  symmetry_type	text
  trace_hash	bigint
  types	jsonb
  values	jsonb
  z1	numeric
  z2	numeric
  z3	numeric

  
  {'Lhash': '933654826846150012406189601463,965932912568040427297424001405,1111235573662217878011171400454,1830831901993540725769786595528,1977611873716092534985853924307,2042726419682162137428690232434,2469997970795989873363380253517,2719557685971893498947715958439', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -2, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.007611671428410052, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [1]], [11, [1]]], 'bad_primes': [3, 11], 'central_character': '1089.1', 'coefficient_field': '1.1.1.1', 'conductor': 1977985201462558877934081, 'conductor_radical': 33, 'degree': 16, 'euler_factors': [[1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], [1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1], [1], [1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1], [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], [1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1], [1, 0, 8, 0, 28, 0, 56, 0, 70, 0, 56, 0, 28, 0, 8, 0, 1], [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], [1, 0, 0, 0, 4, 0, 0, 0, 6, 0, 0, 0, 4, 0, 0, 0, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1], [1, 0, 8, 0, 28, 0, 56, 0, 70, 0, 56, 0, 28, 0, 8, 0, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1], [1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1], [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], [1, 0, 8, 0, 28, 0, 56, 0, 70, 0, 56, 0, 28, 0, 8, 0, 1], [1, -4, 10, -20, 35, -52, 68, -80, 85, -80, 68, -52, 35, -20, 10, -4, 1], [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], [1, -4, 10, -20, 35, -52, 68, -80, 85, -80, 68, -52, 35, -20, 10, -4, 1], [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], [1, 0, 0, 0, 4, 0, 0, 0, 6, 0, 0, 0, 4, 0, 0, 0, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1]], 'euler_factors_factorization': [[[[1, -1, 1, -1, 1], 2], [[1, 1, 1, 1, 1], 2]], [1], [[[1, 0, -1, 0, 1, 0, -1, 0, 1], 2]], [[[1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1], 1]], [1], [[[1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1], 1]], [[[1, -1, 1, -1, 1], 2], [[1, 1, 1, 1, 1], 2]], [[[1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1], 1]], [[[1, 0, 1], 8]], [[[1, -1, 1, -1, 1], 2], [[1, 1, 1, 1, 1], 2]], [[[1, 0, -1, 0, 1, 0, -1, 0, 1], 2]], [[[1, 0, -1, 0, 1, 0, -1, 0, 1], 2]], [[[1, -1, 1, -1, 1], 2], [[1, 1, 1, 1, 1], 2]], [[[1, 0, 0, 0, 1], 4]], [[[1, 0, -1, 0, 1, 0, -1, 0, 1], 2]], [[[1, 0, -1, 0, 1, 0, -1, 0, 1], 2]], [[[1, 0, -1, 0, 1, 0, -1, 0, 1], 2]], [[[1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1], 1]], [[[1, 0, 1], 8]], [[[1, 0, -1, 0, 1, 0, -1, 0, 1], 2]], [[[1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1], 1]], [[[1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1], 1]], [[[1, -1, 1, -1, 1], 2], [[1, 1, 1, 1, 1], 2]], [[[1, 0, 1], 8]], [[[1, -1, 1, -1, 1], 4]], [[[1, -1, 1, -1, 1], 2], [[1, 1, 1, 1, 1], 2]], [[[1, -1, 1, -1, 1], 4]], [[[1, -1, 1, -1, 1], 2], [[1, 1, 1, 1, 1], 2]], [[[1, 0, 0, 0, 1], 4]], [[[1, 0, -1, 0, 1, 0, -1, 0, 1], 2]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 2, 'label': '16-33e16-1.1-c0e8-0-2', 'leading_term': '0.45261770038599498120814413501541848358255591740409692376821218184213753112353708397654904', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0, 0, 0, 0, 0, 0, 0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1089/1/k/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0078125', 'prec': 30}, 'plot_values': [0.452617700385995, 0.4540561931401353, 0.45545170001383, 0.456906097231671, 0.45852210449698133, 0.46040353970288433, 0.4626557764774794, 0.4653864089213973, 0.46870533326468544, 0.4726899515289743, 0.47732990912638906, 0.4825968453448641, 0.4884625763963471, 0.49489863783528587, 0.5018758410791371, 0.509363842518118, 0.5173324445535471, 0.5257607694020867, 0.534645083458672, 0.5439853699900841, 0.5537812036774571, 0.5640316353745339, 0.5747350708530918, 0.5858890634694683, 0.5974883720939561, 0.6095225011923154, 0.6219706870877852, 0.6348075662032487, 0.6480049444324386, 0.6615315470726519, 0.6753527733173692, 0.6894307540151807, 0.7037250784100295, 0.7181919549972516, 0.7327842273624284, 0.7474508631049901, 0.7621366823881669, 0.7767822434959667, 0.7913237783061637, 0.8056936295983534, 0.8198203038505364, 0.8336278719656811, 0.847035496996154, 0.859958141241016, 0.8723069460829784, 0.8839894869373324, 0.8949104715342254, 0.9049733307544809, 0.9140796556964917, 0.9221295743238355, 0.9290230413324295, 0.9346599729168663, 0.9389407982295023, 0.9417673377275976, 0.9430449163029718, 0.9426834183142784, 0.9405971477338274, 0.9367061452334755, 0.9309382479966536, 0.9232294074238344, 0.9135245773713775, 0.9017794011719351, 0.8879628920842918, 0.8720571839226133, 0.854058189878983, 0.8339770747918539, 0.8118423997017125, 0.7876999265381069, 0.7616131261369041, 0.7336651583762493, 0.7039593374414238, 0.6726181453659741, 0.6397833186519812, 0.6056161296037984, 0.5702980427368913, 0.5340289671145267, 0.4970264144618646, 0.4595253993394425, 0.4217755600041252, 0.3840388934776938, 0.3465875843814921, 0.30970174511954557, 0.27366716422896276, 0.2387711630703288, 0.20529945237750094, 0.17353197389382347, 0.1437378555676504, 0.11617092799162075, 0.09106503588795097, 0.06862923474038764, 0.04904284841803637, 0.03244982597595649, 0.018953515001777412, 0.00861085127451715, 0.0014270821772729592, -0.002649225831944222, -0.0037309698298071685, -0.001997047142917, 0.002303303751705097, 0.008846778096743538, 0.01723289602428723, 0.026981679539251395, 0.03753211332229573, 0.04824141425350296, 0.058385185364413617, 0.06715845511741328, 0.07367767302737536, 0.07698455909133478, 0.07605098711220107, 0.06978490840853281, 0.05703749396970024, 0.036611504300286285, 0.007270886751889716, -0.03224836406885689, -0.08322500237285257, -0.14693832003837054, -0.2246542210908302, -0.3176098521214844, -0.42699737599538573, -0.5539470494310973, -0.699509749322968, -0.8646381160467878, -1.050164814413583, -1.256786274103194, -1.4850457741471108, -1.7353162328287075, -2.0077837586344693, -2.30243220388777, -2.6190287483720582, -2.957106463475275, -3.3159538411816674, -3.6946101703605416, -4.09185941622178, -4.506226736222303, -4.935977728370311, -5.3791205852631085, -5.833408693237647, -6.29634238055849, -6.7651947457515496, -7.237026770615494, -7.708705060330232, -8.176924430572159, -8.638233690914028, -9.089064108069369, -9.525752630161003, -9.944580324748975, -10.341833625948269, -10.713834491308065, -11.056977376041157, -11.3677712539199, -11.642882248753732, -11.87917345045536, -12.073738716745224, -12.223961053170262, -12.32758046985787, -12.38271241643809, -12.387875005865382, -12.342019712413236, -12.244557698431185, -12.095375825930159, -11.894854811762125, -11.64389707191976, -11.343961170967566, -10.997032101168283, -10.605602600028492, -10.172656945875598, -9.701646571199488, -9.196456978884658, -8.661376233038679, -8.101062114234574, -7.5205169543157, -6.925000755733387, -6.319959463583058, -5.71095814360502, -5.103609402716425, -4.503501124021773, -3.916123148873937, -3.3467970737427737, -2.800613733358487, -2.282334278303251, -1.7963110534235918, -1.3464190894861294, -0.9359927467904042, -0.5677690395232391, -0.2438377286138703, 0.034398634049184536, 0.2662551573214894, 0.45179790885403087, 0.5918569959416466, 0.6880253730658029, 0.7426458182006961, 0.7587859467552514, 0.7402011887792284, 0.6912863773619531, 0.6170176873571012, 0.5228806500779787, 0.4147864170544616, 0.2989790117656502, 0.18193462985466285, 0.07025444686353263, -0.029447561759171754, -0.1106599854398429, -0.1670916836175048, -0.19279148959369113, -0.1822641570984793, -0.13058136194062622, -0.033486120978661875, 0.11251121317431056, 0.31004723234899995, 0.5608309086361077, 0.865580318429621, 1.2239795891488736, 1.6346524105723896, 2.0951521656471184, 2.6019701929164145, 3.1505626636897026, 3.735396110846223, 4.350011855788677, 4.987111198393671, 5.638658367631121, 6.295997488030936, 6.949981856746598, 7.591116322463287, 8.209709746421225, 8.796035123021499, 9.34049977736803, 9.833832381658606, 10.267244659075883, 10.632586885731428, 10.922502180628472, 11.130571976867904, 11.251448751589153, 11.280973349840322, 11.216284069936558, 11.055929716969613, 10.799898161812603, 10.449632208133838, 10.008034053728487, 9.47944439950755, 8.869595796412717, 8.185540491494853, 7.435563883246223, 6.6290900207402546, 5.776497492566595, 4.888942697992093, 3.9781781689661866, 3.0563574867104473, 2.1358301251343845, 1.2289298457919788, 0.347763469547262, -0.49600209315316884, -1.2913688780778894, -2.028208826958196, -2.697445693155382, -3.291218940486815, -3.80302624017688, -4.227842454749196, -4.562217910097049, -4.804352607986355, -4.954116814317888, -5.013040481073547, -4.984272793953029, -4.872509422900526, -4.68388864361649, -4.425860702571109, -4.107031090314474, -3.736983940415012, -3.326052119335234, -2.8850840497144232, -2.4252048771497257, -1.9575710074186146, -1.4931234675888867, -1.0423447094328402, -0.6150219029980942, -0.22002307379192187, 0.13491467358093992, 0.44336234828043725, 0.7003449983027464, 0.9024549237205467, 1.0479300405949785, 1.1366937829080372, 1.1703574924666722, 1.1521914553350243, 1.0870320596418488, 0.9811529523791209, 0.8421023989827369, 0.6785069026532138, 0.49984464749075086, 0.31619149986512346, 0.13795045645944845, -0.024431358116076572, -0.16077445737940518, -0.2614694326976462, -0.31776938970494495, -0.3220694507270905, -0.2681657356170248, -0.1514867621319354, 0.0307063564710035, 0.2791515679562255, 0.5924678263909116, 0.9670881017042939, 1.3972428387007552, 1.874998302291516, 2.3903464826724137, 2.9313466691693946, 3.484315535691853, 4.034061915988465, 4.5641806064523704, 5.057379662500209, 5.495844033848675, 5.861621608383277, 6.137017401899296, 6.305000001761462, 6.349609256650801, 6.256359267036498, 6.012614465782128, 5.607940055280516, 5.0344259817855646, 4.28694619073358, 3.3633713686326083, 2.264728392369781, 0.995299375894972, -0.43734955301600265, -2.022418792311527, -3.7459810324257803, -5.591157175414672, -7.538360543278133, -9.565595329963486, -11.648808728743306, -13.762302545632117, -15.879225525814284, -17.97204143943384, -20.013026596272418, -21.97476678687141, -23.83065640960762, -25.555388630747583, -27.125423664095912, -28.519456455254545, -29.71892113416451, -30.70828753482977, -31.475312789705207, -32.01123163902471, -32.31089836541616, -32.37285777020775, -32.19934294355972, -31.79624087904303, -31.1730774938806, -30.342698866779983, -29.320905850539667, -28.12609669974885, -26.778872978451698, -25.301607764215454, -23.717985964309086, -22.052560589685427, -20.33036901673489, -18.57631856110546, -16.81465833284313, -15.068536072218663, -13.359593003047852, -11.70760410189206, -10.130170905262048, -8.642490168954076, -7.25720226735209, -5.984189559414114, -4.8305078360018046, -3.8004073955971562, -2.8954187115017467, -2.114498441961807, -1.4542301570932117, -0.9090757132629655, -0.47166352048379295, -0.13309257752572878, 0.11672345849094377, 0.2886974406427278, 0.3942097156041326, 0.44475884795371967, 0.4516315303032047, 0.4256009293562066, 0.3766613115031869, 0.31380001390903683, 0.24481785001520442, 0.17620180312560116, 0.11305126046924086, 0.059057943766753496, 0.016538047050892103, -0.013486335393476072, -0.031161691109205872, -0.037638910997958276, -0.03487670290281835, -0.025421565405076212, -0.012173251478894148, 0.0018550823552708037, 0.013772482994854823, 0.021032265455689897, 0.02163258220265113, 0.014287578579658792, -0.0014383002155052386, -0.025038106920570433, -0.055016359164692, -0.08889299721169248, -0.12325604610673746, -0.15386061100671114, -0.17577478507610492, -0.18356571978405903, -0.1715204462775408, -0.13389452050250122, -0.0651802599787242, 0.039616565670359066, 0.18470409736363588, 0.373240587399755, 0.6070924638005536, 0.8866227164347139, 1.2105172799509676, 1.5756584327492176, 1.97706313217594, 2.4078804027892167, 2.85943656460743, 3.321352834851935, 3.781739394005926, 4.2274220733489685, 4.644226551434886, 5.01732554619445, 5.331656528230578, 5.572307530161535, 5.724931530954756, 5.776186849374358, 5.714189826774239, 5.528885093084698, 5.212405697775965, 4.759443410886144, 4.167523326492212, 3.4371664828528146, 2.572021228789985, 1.5789236620062443, 0.4678677478390526, -0.7481398750390815, -2.0532682103094255, -3.429109254573401, -4.855069187353924, -6.308790459649111, -7.766614254871562, -9.20410314131745, -10.59665132723597, -11.920014913285366, -13.150860431675929, -14.267323005010335, -15.249508830042165, -16.079952862709845, -16.744021719404003, -17.230287597112703, -17.530905954032956, -17.641707545154624, -17.562308116312806, -17.296051846974912, -16.849885767696367, -16.234165494966533, -15.462381481926135, -14.55084596608418, -13.518368333471669, -12.385725978582764, -11.175116027248773, -9.909552179472685, -8.612314844272516, -7.3064119373514655, -6.014061224248233, -4.756218488293328, -3.5521691139166602, -2.4191211292146817, -1.371818660307696, -0.4222907296942245, 0.4203012992281588, 1.149734477279287, 1.7627142432187441, 2.258791737968496, 2.6402125287365052, 2.9116938068850318, 3.0801500325186675, 3.154352379933506, 3.1445543044393323, 3.062097007547989, 2.9190076760392354, 2.7276094663191652, 2.5001602275744648, 2.248477021994089, 1.9836112169066595, 1.7155786315613732, 1.453144604188244, 1.2036679912360877, 0.9730059479855823, 0.765481901583361, 0.5839130167089175, 0.4296736362415404, 0.30281921395276895, 0.20225460743402363, 0.12593382979565468, 0.07108127672413969, 0.03442404819172362, 0.012425090947462943, 0.0015067475144774488, -0.0017450279633822636, -0.0004018181473997033, 0.0029519889173852806, 0.006324156232810029, 0.008376385183962064, 0.008441500377676213, 0.006496565254982339, 0.0030943914966872787, -0.0007424788592229728, -0.003659081486693165, -0.004129188486651088, -0.0006317961454459809, 0.008166341764179632, 0.023231836989869494, 0.04499904999977311, 0.07322672097254367, 0.10688536388565047, 0.14408224264180214, 0.18202947128149466, 0.2170590992510417, 0.24468747010688705, 0.25972797847708445, 0.2564490902343607, 0.2287722041776018, 0.17050429625286193, 0.07559793376151082, -0.06157115538271863, -0.2459194702201244, -0.4813766777268449, -0.7706228582990912, -1.1148569867926437, -1.5136204564313265, -1.9646460196583708, -2.4637623698488773, -3.004863343889792, -3.579950074881831, -4.179239660139284, -4.7913319547515645, -5.403460402572774, -6.001843605725237, -6.571996071237149, -7.099095850945905, -7.568401333801012, -7.965700560770292, -8.277727461709816, -8.492574355437172, -8.600107209769096, -8.59238145383628, -8.463867213602256, -8.211658079033668, -7.835651444173407, -7.338628586385432, -6.726233550275182, -6.0068909354220645, -5.191650685055866, -4.293945781751561, -3.329223871447519, -2.3145651836216246, -1.2682612537372226, -0.20933773474437567, 0.8429286134967763, 1.8694953515382817, 2.8520543419950726, 3.773573278025392, 4.61867687602106, 5.374003356820763, 6.0285134572154035, 6.573707708569231, 7.003776150032189, 7.315671031616819, 7.509137018104084, 7.586731734353882, 7.553557346471584, 7.41701620994654, 7.186489542606683, 6.872986116908485, 6.4887679492546715, 6.046956717426684, 5.561158243339442, 5.045124249559489, 4.512288801623171, 3.97538722159754, 3.446127533699861, 2.934935172053957, 2.4507553850314903, 2.0009155905584373, 1.5910558080049406, 1.2251240690529228, 0.9053858550177071, 0.6325018299236187, 0.4056739974529326, 0.22283329617830355, 0.08085483509317179, -0.02420924889498281, -0.09688971145886875, -0.14206322343018501, -0.1647267507105073, -0.1697880830690937, -0.16188078368913755, -0.1452125403900181, -0.12345050919940985, -0.09964528422041506, -0.07619360202436797, -0.05483769944140839, -0.036695977322754265, -0.02232382575499748, -0.01179793161978503, -0.004816883792558729, -0.0008109221459879852, 0.0009463101710538411, 0.0012308128447053356, 0.0007721796818703812, 0.0001734757684516355, -0.00014861562197924518, -7.433825285359339e-07, 0.0005741497894772084, 0.0013074697407304367, 0.001737408571112636, 0.001260068596452739, -0.0008050097630128107, -0.005140202207771624, -0.012351732059086327, -0.02289402582753329, -0.037002223292322056, -0.05463810563513068, -0.07545417214850693, -0.09877948342300029, -0.12363042670075793, -0.1487442578291817, -0.17263557773663404, -0.19367369696227038, -0.21017686448160702, -0.22051858177334502, -0.2232401823896638, -0.21716229340320625, -0.20149206071760462, -0.1759061904498394, -0.14061380404715793, -0.09639324687812456, -0.044597281547334416, 0.01287615013582005, 0.07364928835608875, 0.1349631801409407, 0.19380738527844024, 0.2470803311851147, 0.29176451452725366, 0.32511010972753907, 0.3448184156308291, 0.3492147988462112, 0.33739667433709014, 0.30934931153103784, 0.26601950390268075, 0.20933123467942047, 0.14214374848243297, 0.0681478635681585, -0.008301546271393238, -0.08241611980563467, -0.14926078267320356, -0.20408968871690703, -0.2427241571883445, -0.26194373629601014, -0.25988072440275334, -0.23640173007900103, -0.1934557928977157, -0.135366869484962, -0.0690547780138956, -0.0041671374887110755, 0.04689997757083301, 0.06910790605475087, 0.04499974811121085, -0.04494901273986096, -0.22185623896466589, -0.5078427582301778, -0.925336716228405, -1.496282361956752, -2.241263123794103, -3.178629749924619, -4.323622366706625, -5.687534151890881, -7.276919324330296, -9.092890604639981, -11.130541263981403, -13.378525555089897, -15.818858423181226, -18.426897586673924, -21.17158971275436, -24.01591620536617, -26.917469048514064, -29.82926652630007, -32.700756731670495, -35.47905003201028, -38.11046468945274, -40.54185051299515, -42.72214981961681, -44.60373373663668, -46.143742566248264, -47.30537636626586, -48.059050801949965, -48.383498896024854, -48.26691280741999, -47.70726263850663, -46.71240069011413, -45.29981160138698, -43.496232133266815, -41.337007254617426, -38.8651916565803, -36.13052577559965, -33.18840427247032, -30.098076788274398, -26.920746120800356, -23.717843299935947, -20.549360529719685, -17.472246723529036, -14.538915890695748, -11.795954463425318, -9.283077963626296, -7.032003236357539, -5.065750874643169, -3.398347373096207, -2.034823770587833, -0.9715020941705743, -0.19655349358706767, 0.3091997386834228, 0.5712853942695839, 0.620380557833025, 0.49095342792127006, 0.21983635186074507, -0.15521341636609154, -0.5969124659767715, -1.069759402388688, -1.5412112893449668, -1.9827160831637696, -2.3705113704838077, -2.6861705207806916, -2.916899957448222, -3.0555847357924226, -3.100591667425806, -3.055351195403616, -2.927757817222516, -2.7294134667102927, -2.474678663651189, -2.1796734423859365, -1.8612667892740953, -1.5360912874756651, -1.2196289140360475, -0.9254114896645783, -0.6643658357081539, -0.4443361219499016, -0.26978599541470005, -0.1417252864627695, -0.05784775681235832, -0.012863625246390344, 0.0009938300357265923, -0.006683446232088431, -0.02523931036936454, -0.04378185017010253, -0.052034494635023736, -0.04116092722870935, -0.004517901501047597, 0.061706130271744666, 0.15800416944998877, 0.28124663863413346, 0.4245805757429599, 0.5775455121556979, 0.7264014989326705, 0.8546606130520717, 0.9438030355770946, 0.9741495234827627, 0.9258536086531178, 0.7799568267834619, 0.5194634080506789, 0.13036430517294975, -0.39741472096202984, -1.0691895670620113, -1.8848688580906392, -2.838525549474856, -3.9182166078752605, -5.106048873395505, -6.378552041427063, -7.70743646535793, -9.060366384081506, -10.401965281493435, -11.695037692355571, -12.901958271049475, -13.986046090853348, -14.912958949231447, -15.652142914418105, -16.178364117621054, -16.47251295167171, -16.522344365269614, -16.323113912221245, -15.877869708080164, -15.197379026588084, -14.299813121321293, -13.21021981835607, -11.95981249413304, -10.584513020958275, -9.123552724155028, -7.618047713625109, -6.109418032831247, -4.637850833822122, -3.240841134590857, -1.95185610977316, -0.7991213534789235, 0.19540593114579677, 1.0166788512703986, 1.6568944609017655, 2.1155008144935814, 2.3988890498443087, 2.519795320071735, 2.4964739666541003, 2.3517070967377265, 2.111426946381401, 1.8032888363462212, 1.4552180748907741, 1.0939994809294227, 0.7439720884629841, 0.42588612042112156, 0.15598732636405227, -0.054641106112608785, -0.20052745208110848, -0.2818750424197808, -0.3042802777788518, -0.27814108814497773, -0.21778750586842052, -0.14037746400559434, -0.06461347299653994, -0.009342759333665728, 0.007905968262751304, -0.027643343946126227, -0.12669469180562382, -0.294745590362456, -0.53120138400205, -0.8287917652936836, -1.1733265379759883, -1.5438138532864905, -1.9129805431889506, -2.248158440279642, -2.5125102529774153, -2.6665505096671303, -2.669901111361708, -2.4832087585930376, -2.0701403971707713, -1.3993569444292449, -0.4463772673266559, 0.8047538924839629, 2.3600780527869993, 4.214687240798814, 6.352099501156119, 8.744090011445602, 11.351066872040292, 14.123034786830589, 17.00082875646038, 19.917796060213508, 22.801865074137815, 25.577903527579764, 28.170279048666142, 30.50555413433119, 32.51533693676616, 34.13904463107148, 35.325966492445296, 36.037150574261894, 36.24696817816258, 35.944211174238674, 35.132675841174404, 33.8312484089288, 32.07343425697269, 29.906433557120955, 27.38920484132364, 24.590326645842698, 21.58561057525609, 18.45546016669792, 15.282060803378828, 12.146470522574122, 9.125896195227853, 6.291147057091647, 3.7041802029961803, 1.4161735098220851, -0.5339147580355124, -2.1202953071467663, -3.3308570873050822, -4.167021536580159, -4.642993246048239, -4.784651981214855, -4.627954014575884, -4.216990537666818, -3.60180460432672, -2.8360682585092443, -1.974700139024944, -1.071443685849437, -0.17667215786826143, 0.664571505528144, 1.4141661542824717, 2.0421080969115057, 2.5272865165508906, 2.857842289411021, 3.03106054122934, 3.052787503748263, 2.936493496350595, 2.7020288954216936, 2.3740471474950233, 1.9803029400968353, 1.5498982527664744, 1.1115435691721878, 0.6918764760060323, 0.31399773460335834, -0.0037281568573355054, -0.24856802734098327, -0.4139465954125124, -0.4995991255358636, -0.5113672604365638, -0.46064136277418394, -0.3634765565009524, -0.23945568670299935, -0.11036219923479841, 0.0012672253561407491, 0.07361679981267136, 0.08700503649815847, 0.025178905675545746, -0.12359592023979621, -0.36571076959270804, -0.7016934807921156, -1.1260282450053396, -1.6273603210434617, -2.1890134016891736, -2.789796888147113, -3.4050915644268565, -4.0081449706041266, -4.571494637522523, -5.0684515283781995, -5.474601445396757, -5.769295438373127, -5.936758428524721, -5.9670131958320365, -5.856496488678112, -5.608346915780196, -5.232348961172689, -4.744526294116159, -4.166428147894714, -3.524142435761559, -2.8468854632812928, -2.1654658892095444, -1.5106637819114745, -0.9116197560269391, -0.39429278700171266, 0.019934240804163453, 0.315428294927097, 0.4832070849650549, 0.5214998590512299, 0.435893108259737, 0.23907328107710457, -0.0498119406194336, -0.4061472116925858, -0.8011536072286406, -1.2034498405656808, -1.5808138952585962, -1.9020196554078006, -2.138660949843563, -2.266859479736882, -2.268777382528229, -2.133855672414697, -1.8597111715756856, -1.452650982644304, -0.9277600277655439, -0.30843954743501517, 0.3744577372275262, 1.083877638893195, 1.7781612571903593, 2.41291908719493, 2.9430994728643562, 3.3251911277785173, 3.5195150868417664, 3.492255587822228, 3.2172679440292127, 2.677596112121342, 1.8666076176413056, 0.7886877773423172, -0.5405459381225403, -2.0945000176363573, -3.836300408603469, -5.720206320989114, -7.693349312162464, -9.69776378389519, -11.672661734467093, -13.556854579040394, -15.291262824121969, -16.821324448437288, -18.099176597106858, -19.085629189508296, -19.751715606237603, -20.07979372406214, -20.064162687102115, -19.711197376851, -19.0390174773304, -18.076489390710318, -16.86182426876699, -15.440832316723906, -13.864891038336303, -12.188718351299748, -10.468055174301771, -8.75739292549416, -7.107747591050766, -5.564603985236684, -4.1661809363001625, -2.942249686681729, -1.913322910108991, -1.0902662622249384, -0.47436643595156774, -0.057836330159911915, 0.1752746217179123, 0.24780676600731777, 0.18791159509953131, 0.02722616856354512, -0.20097185528900977, -0.46359180243723025, -0.7294703466689525, -0.9709404489705157, -1.1651429224674947, -1.2950387296829164, -1.3500862678412149, -1.3264258701293048, -1.2267079281685356, -1.0595834308625371, -0.8388776760623236, -0.5824754438437246, -0.311008722133112, -0.04641402648909966, 0.1895837794378091, 0.37691615911120635, 0.49846285066601415, 0.5411561946692578, 0.496835455877687, 0.3627935806954513, 0.14200130151408172, -0.15700451097306634, -0.5206022587776618, -0.9308987607409465, -1.3667520220644669, -1.8049717806240855, -2.221662363879262, -2.5936077946465126, -2.89962772905011, -3.1218785643012303, -3.247101178479893, -3.26737330530801, -3.1806063018769333, -2.9907633440452144, -2.7077476955674746, -2.34697061965859, -1.9286204635626785, -1.4767066898877654, -1.0179317686548655, -0.5801468102184634, -0.19084351242300737, 0.12430491572588735, 0.3428161956279981, 0.44661833642375975, 0.42305557370935515, 0.2656280881846626, -0.025556577163727445, -0.4436477713856205, -0.9753047207181201, -1.6012811870468207, -2.2973008836609985, -3.03517985720161, -3.7841398009857716, -4.5122572321213745, -5.188008457800301, -5.7817637319837685, -6.2671624509439905, -6.622326548608059, -6.830851306349502, -6.882526497095913, -6.773756840563697, -6.507689688251451, -6.0940662065653175, -5.548600262636499, -4.8921308017961636, -4.149578871471683, -3.3487359653081477, -2.518945806123196, -1.6897456238403392, -0.8895306985550602, -0.14427956167821857, 0.5235654873685808, 1.095977022912415, 1.5599752472076114, 1.9079954569371806, 2.137980803568488, 2.2532057287037595, 2.261871473247977, 2.1764620675961925, 2.012849596463067, 1.7893059161483795, 1.5254506025616636, 1.2411828971283052, 0.9556526603948858, 0.6863230532309322, 0.44816591160254887, 0.2530158983736951, 0.1091432293498216, 0.021048028167188895, -0.010531385751238726, 0.011593148607213881, 0.08145411121277214, 0.19047734056796445, 0.32815326831752845, 0.4827935795952419, 0.642301697390429, 0.7949182611029353, 0.9299077886026454, 1.0381502640516085, 1.1126110357671881, 1.1486705957384127, 1.1442877384366763, 1.1000078627140921, 1.0187800760921104, 0.9056569271995146, 0.767391201978901, 0.6119517352324596, 0.44799175307393035, 0.2842942887970687, 0.12923016837916548, -0.009743147283213186, -0.12647758556136965, -0.21642735722985318, -0.27683337317270124, -0.3067917903710155, -0.3072087370697099, -0.28064324977342686, -0.23105925706171943, -0.163498962888737, -0.08368686985752609, 0.002369067942543171, 0.08876521929948343, 0.17006057688702098, 0.24158507949078556, 0.2996777800868969, 0.3418512629567011, 0.3668853875309499, 0.3747896559190746, 0.3666904865352081, 0.3446574134822397, 0.3114786114871107, 0.27039843989946155, 0.22484328520610947, 0.17815897707417877, 0.1333755898857879, 0.09298813717590165, 0.0588110985373004, 0.03190332436460435, 0.012559352004113547, 0.0003655686718997716, -0.005686045148360998, -0.0070388952519022975, -0.0053827142373327926, -0.0024499669853303703, 0.00018493224622437093, 0.0012835436266675803, 8.279142451658401e-05, -0.003616355535604934, -0.009418683197381577, -0.016366059674381667, -0.02302869367717291, -0.027650102181327515, -0.028333252680211547, -0.023252130281558904, -0.010869983291846736, 0.009854431059699294, 0.039291535282930716, 0.07701419212592829, 0.12173691163826389, 0.1713281090565748, 0.2228971793830437, 0.2729572174397305, 0.31765367028796665, 0.35304503269966964, 0.3754170681110646, 0.38161236517465735, 0.36935737021514264, 0.3375225811630054, 0.28631809997823743, 0.21740496489408148, 0.13390243524200046, 0.040281836368996016, -0.057854954824305874, -0.15410477253408914, -0.24169083189333082, -0.3139764107504631, -0.3650072559682067, -0.3900538943446261, -0.3861173148649043, -0.3523580017839316, -0.29041000866401034, -0.2045494839520776, -0.10169147175424403, 0.00883320245306353, 0.11569722876486395, 0.2061880717616103, 0.2669940220803402, 0.2851320933379936, 0.24897265349073217, 0.14930840884925706, -0.019582497688336187, -0.25897001223312066, -0.5648636170485088, -0.9274211199569956, -1.3306344639407683, -1.7523409478273813, -2.164592813239115, -2.534345692404459, -2.824487935125352, -2.995251140622196, -3.005890808855869, -2.8165987869609728, -2.390573797270544, -1.6961619223612265, -0.7088565884996083, 0.5872252178278039, 2.1976554973642686, 4.116418443087966, 6.325085628994946, 8.792457764795804, 11.47472550541031, 14.316209524822824, 17.251459246983824, 20.207519172807142, 23.10595363562212, 25.865295495047544, 28.403795285407313, 30.6423656874955, 32.5075400572599, 33.934743723135554, 34.87228462253939, 35.28268132181207, 35.14447117757796, 34.452686402385794, 33.21903453580236, 31.4716347252936, 29.254185265547722, 26.625486811394246, 23.65729198642434, 20.430784994199165, 17.03379498167796, 13.557033942987287, 10.090717444251641, 6.721428761813638, 3.529376093169155, 0.5861969998663225, -2.0479660126719947, -4.326350891341904, -6.216811232632671, -7.70229441267093, -8.78055120559448, -9.46325483428329, -9.774547604537847, -9.749308169033391, -9.43107707797139, -8.869681167958221, -8.118829836194758, -7.233346364019198, -6.266674413844079, -5.268719788811703, -4.284059145252656, -3.350487310584087, -2.4980407543988834, -1.7485126465632217, -1.1154178054741228, -0.6043063909296729, -0.213539469688637, 0.06460719252127493, 0.2426390325206757, 0.3364150183849604, 0.3636807308471866, 0.34266643283357334, 0.2908297018243071, 0.2237857359093993, 0.1545003019502014, 0.09277591881920835, 0.04503570307856084, 0.014395339649266932, 0.000990476909408723, 0.002512493684918029, 0.014895734617411364, 0.033091719541788134, 0.05185943136818776, 0.06650398660704375, 0.07350290361016741, 0.07097205538224849, 0.058937543304776845, 0.039396711199940274, 0.016166680028502373, -0.00547270623827673, -0.01929864010228699, -0.018781970855485688, 0.0022147572229008795, 0.048737406511761144, 0.12409924274602536, 0.2293545092831108, 0.36293289487408986, 0.5204906472104761, 0.6949913491382672, 0.8770116911517237, 1.0552652481825298, 1.2173140955186905, 1.3504235609988502, 1.4425006757292007, 1.4830475398284029, 1.4640797262885763, 1.3808877128314812, 1.2326155849322542, 1.0226054020290196, 0.7584648076638425, 0.45183713772809964, 0.11785983380794715, -0.22569410263710019, -0.5594507465826264, -0.8636394485196267, -1.1193928811068552, -1.3100582554964166, -1.4224325965177358, -1.4478350856177917, -1.3829509032996625, -1.2303629209166878, -0.9985793238444809, -0.7017219645469258, -0.3588464087122181, 0.0071033887478157125, 0.37065861954946866, 0.7054385459363937, 0.9859619199401354, 1.1895752814881695, 1.298153694908825, 1.299602238549543, 1.189069795570153, 0.9697701025658682, 0.6533380823820667, 0.25968794284760865, -0.1836363311119532, -0.6427910752545556, -1.0794528682292734, -1.4529418825020273, -1.722600255680809, -1.8503072255262503, -1.80298997801658, -1.5549781690742301, -1.0901176123621168, -0.4034894497656273, 0.49769761874839474, 1.593829274072387, 2.8532748637456056, 4.233481508788976, 5.68274466441224, 7.142602091849004, 8.550765384023343, 9.844578130545594, 10.964436575123417, 11.857127087669395, 12.478948301851572, 12.798413075190686, 12.798418171883318, 12.477638465399258, 11.851100157582731, 10.950050203130523, 9.820245474902011, 8.519546002983327, 7.1148314452148975, 5.67830112378036, 4.283339658108794, 3.00003941557042, 1.8907934775162065, 1.0061277404493165, 0.38086351354944353, 0.031189783751846237, -0.04729557959852686, 0.11952012952007908, 0.4845202508802735, 0.9808089543042408, 1.524324658069843, 2.0175626272994442, 2.3542225427981696, 2.4245164680053355, 2.1208987368950414, 1.3439356256285295, 0.007990653322495772, -1.953531059742102, -4.583638357669308, -7.898203447376702, -11.883774350277864, -16.496660637532113, -21.663493232909353, -27.283198332088222, -33.23017011083885, -39.35866467070459, -45.50836113623589, -51.51120446078097, -57.19787222762757, -62.404547064642905, -66.97993123049781, -70.79103035752145, -73.72828749885699, -75.7098134326552, -76.6847363973703, -76.63584958620007, -75.57891916204042, -73.56158009958386, -70.6607005257058, -66.97813254427452, -62.63599632003542, -57.77129952771941, -52.53030592705851, -47.062929441016436, -41.51621214763546, -36.02893046304487, -30.726409634939625, -25.71657732417057, -21.087156126212186, -16.90394113577123, -13.21017170660122, -10.02690892710166, -7.3544991918113665, -5.174842302209316, -3.4543306768863102, -2.1473417624591744, -1.1999491156075757, -0.5536349480592121, -0.14878522074000744, 0.07219183609715582, 0.16212378130084776, 0.16705362807787946, 0.12492476363551969, 0.06495858581711601, 0.007685749634389057, -0.0344469441383918, -0.056002242154080506, -0.05714260546221672, -0.042018553477617404, -0.017103169113896595, 0.010372198821701102, 0.03376190737926075, 0.04803896078384811, 0.050457622184922155, 0.04082168982218135, 0.021366421177509632, -0.003714004363943153, -0.02900232562735531, -0.0487600295319068, -0.05788720068089165, -0.052827804499105215, -0.03231345800715728, 0.002148343886128837, 0.04612446280560892, 0.09248296037080023, 0.13198838968873025, 0.15423694318473807, 0.14886809596355408, 0.10696025113059197, 0.022495033143604747, -0.10623008955114242, -0.27536801174211173, -0.4747132242457832, -0.6873419425808522, -0.8897865123434274, -1.05280654176052, -1.1427691279853807, -1.123623244067135, -0.9593764497637558, -0.6169382852672595, -0.06918463212953523, 0.7019959903495114, 1.7028615685900481, 2.9253868331110557, 4.345438556577385, 5.921728077662704, 7.595773128265718, 9.292994336539818, 10.9248149320229, 12.391787321238974, 13.587678716935295, 14.404352939995418, 14.737260064678987, 14.491231412865282, 13.586306657125922, 11.963304215847307, 9.588513034222034, 6.457531903358061, 2.597964020063795, -1.9292797899053864, -7.030262066954914, -12.57994002983807, -18.425853264258105, -24.393975853987193, -30.294775026387324, -35.93038126682671, -41.102624107318036, -45.62157095718176, -49.31391111391525, -52.030667657735115, -53.654616786712815, -54.10733367057402, -53.3518874796855, -51.39460554417032, -48.285486526280195, -44.11679853320181, -39.01933519451217, -33.1571542070655, -26.721086768702822, -19.920968087124685, -12.975762861571997, -6.104305496555272, 0.4835858135616954, 6.59559459765078, 12.064394443610217, 16.753789456094363, 20.56357386587194, 23.433323603065357, 25.34284143129017, 26.310873127141104, 26.392362496079134, 25.67388315247728, 24.267837239851033, 22.3057404816676, 19.93114056456022, 17.29259640305249, 14.535318285959868, 11.794115350334247, 9.187438438680417, 6.812603831987988, 4.742502134106291, 3.023816023534807, 1.6768183344050174, 0.6966561712992911, 0.0556469285207889, -0.29301186287898634, -0.41059310854103803, -0.3676285597043261, -0.23847728492867978, -0.09599878048790668, -0.006632090345435334, -0.026194434069448366, -0.19664632982568483, -0.5438736445707762, -1.0766164812920924, -1.786563700680613, -2.649554391330418, -3.627766493322096, -4.6728004856408045, -5.729610149392636, -6.740355651654765, -7.648300228476604, -8.401567197062247, -8.956480126881537, -9.28029023234968, -9.353142659784146, -9.16930492885915, -8.737687118725372, -8.080615236034829, -7.232055454687543, -6.235330712357514, -5.140342446160499, -4.000482252044067, -2.869431201089465, -1.7980629424005217, -0.8315601184773479, -0.0068369919848422726, 0.6492154335328119, 1.120753587113567, 1.4032900895425466, 1.5033006213202966, 1.4371848594775034, 1.2296936834191141, 0.9118923265010132, 0.5187085376347701, 0.08643986200783228, -0.3496451878518994, -0.7574802655880871, -1.1100217426525747, -1.3866213208205664, -1.5739206110008743, -1.6662622851980173, -1.6653705960442022, -1.579544212723183, -1.4224650088050632, -1.2117109550078171, -0.9670983182567379, -0.7089857592543455, -0.45667546498550693, -0.2270256087096367, -0.033237363289645556, 0.1159023618726793, 0.2163332253290368, 0.26861254778294513, 0.2774173799206853, 0.25071904312317556, 0.19871622076233114, 0.13263892505964625, 0.06351195460171434, 0.0009998660458218386, -0.04754633431557281, -0.0777506795721366, -0.0885162092643076, -0.08193584190052, -0.06280765088106158, -0.03778621501087069, -0.014236917186570794, 0.001126525435017988, 0.0037063931673927534, -0.007540462579903043, -0.028819990509850443, -0.05049694567719793, -0.05648184803040731, -0.024095762600329442, 0.07554522200352867, 0.2765948093161908, 0.6170038468160208, 1.1366062772462608, 1.8748407248167098, 2.8681631727220807, 4.147383888816983, 5.735214515678854, 7.643903712647071, 9.873216744009902, 12.409019113169597, 15.222758687591304, 18.271256482030832, 21.49727131992488, 24.83110197486054, 28.193562891728863, 31.498363383846222, 34.655132239198096, 37.57345654700476, 40.1667091261273, 42.35522451457441, 44.06965367606629, 45.25438494840287, 45.871297205596825, 45.90023304744779, 45.33960653514894, 44.20700641894854, 42.53775891835911, 40.38314603104721, 37.808181997231664, 34.88918970642079, 31.7114067311934, 28.364167286890368, 24.93727374100418, 21.51748957575067, 18.18511671774226, 15.011369999661072, 12.056313344093223, 9.367498390185057, 6.979250400727041, 4.912006642796248, 3.1727994509835353, 1.7563180336567086, 0.6465260223574033, -0.18136467617901753, -0.7587205820145929, -1.121253730223739, -1.306880715610281, -1.3536631167074198, -1.2979541666216639, -1.172886104084131, -1.0072668775214302, -0.8248868878771431, -0.6442220024564654, -0.4785021560811849, -0.3360873202618955, -0.2210488710108846, -0.13394289562214015, -0.07268728423805676, -0.03345020774863654, -0.01148043958201316, -0.001825395262228137, 0.00010120167863348706, -0.0018772611421281505, -0.0049225037635378804, -0.007239358729614231, -0.007994145860147869, -0.007129198849122251, -0.0051148348425451825, -0.002681111170510966, -0.0005685898770942147, 0.0006695266597365897, 0.0007904197549229778, -0.0001016685691008644, -0.001603564197662652, -0.003133050511033387, -0.004097437583449718, -0.00408028245306405, -0.0030116628354133644, -0.001286753461459365, 0.00019820497010392644, 0.00011556328324370947, -0.0031055514253878168, -0.01097220497683466, -0.02451519414165021, -0.0437986054838004, -0.0673931856475272, -0.09186354179524098, -0.11131758192246356, -0.11707523057910513, -0.09750986108987081, -0.03810763671457376, 0.07822136558938647, 0.27056657686182783, 0.5591930490410575, 0.9645104313509691, 1.505854374223366, 2.200133623350657, 3.0604227677355618, 4.094583624985262, 5.3040354958355795, 6.682857252658348, 8.217152752892213, 9.88502891213937, 11.656653729079013, 13.494763665043857, 15.355649246638384, 17.19055671464047, 18.947742410633165, 20.57466248870204, 22.02018285061207, 23.23752287687102, 24.185907395450183, 24.832277197614417, 25.152882732339517, 25.134642922532162, 24.77636975065277, 24.088536218191194, 23.092967990653623, 21.82250468217626, 20.318719123234526, 18.629789513388054, 16.808354956061432, 14.909482635494276, 12.988189059115944, 11.096768889213314, 9.282763524735968, 7.587321568026057, 6.0433485027697, 4.674551608149221, 3.495162024037892, 2.510183071071229, 1.715888605656827, 1.1008888232412068, 0.6475811146671313, 0.33381788802637974, 0.13466034865193502, 0.024203704947156193, -0.022712257522554968, -0.029038799908010334, -0.014353053477134082, 0.0059547333183450355, 0.021098691007415786, 0.02492047941689028, 0.015540304754389304, -0.005311961225261522, -0.033205983162778466, -0.06206852993077789, -0.08529171633313198, -0.09679487121713698, -0.09195218427571498, -0.06831186555704558, -0.026028675522247795, 0.03200979434852397, 0.10036845059067503, 0.17153910568614672, 0.23665797203639688, 0.28640199216315165, 0.3119879962606938, 0.3061965779458263, 0.2642938970190611, 0.18477515393658192, 0.06985334002203798, -0.07434984524335451, -0.23794147721562323, -0.40772881586370896, -0.5680002303806139, -0.7015747541326364, -0.7910815189928635, -0.8203228909942444, -0.7756170208307596, -0.6470401597389089, -0.42946710858478643, -0.12332284595408212, 0.2650236447108566, 0.7232729138393519, 1.2336570594887233, 1.7738090731131788, 2.3179756038001895, 2.8385149906726967, 3.307589165614664, 3.6989413995359444, 3.989648062664835, 4.161770657088763, 4.203648879224073, 4.110761286870001, 3.8862056784414074, 3.540708708180875, 3.092150879099472, 2.5646267637347644, 1.9870811285081906, 1.391537500941205, 0.811127188544976, 0.27809660168002776, -0.1781388887602509, -0.5327759405051427, -0.7671260272648969, -0.8697453893787054, -0.8371846911255642, -0.6742212188624936, -0.3933238382120037, -0.013746654128359088, 0.4397554824959411, 0.9385352925605664, 1.4518808834726002, 1.948924941674409, 2.4005338315783895, 2.7812741572765844, 3.070878806105147, 3.255310027819469, 3.3274106563068466, 3.2870939710791816, 3.141071083939254, 2.9021385964949613, 2.5881302385590867, 2.220544422971894, 1.8228602993931329, 1.4188639541119923, 1.0310518374072528, 0.679198502301784, 0.37918093568967814, 0.14213006667766248, -0.026062657330119986, -0.12485282806101045, -0.15864922164248185, -0.13609832446081246, -0.06910911571734217, 0.0283106577699189, 0.1413085735172973, 0.25543647438482464, 0.3578114201884031, 0.4381218980986463, 0.48931164524562354, 0.5079314676598361, 0.49416613772851853, 0.45154382076360194, 0.3863643691301855, 0.30690419471988273, 0.22247928715091425, 0.14244465738889164, 0.07518879281769128, 0.027285300443853383, 0.0028579976241981005, 0.003206886874385658, 0.026727811564455656, 0.06913286672754568, 0.1239545269886255, 0.18330322394018173, 0.23878403922270872, 0.2824831015945356, 0.30793462270916777, 0.3109735494407662, 0.2903829077211505, 0.2482679319458415, 0.1901151401705821, 0.1245078202141211, 0.06243809789776151, 0.016345150526170124, -0.0010603154855684412, 0.02190002906466092, 0.0945526882691285, 0.22265510230346963, 0.4073940343841811, 0.6447081836993638, 0.9250632539582997, 1.2337042194679755, 1.551402522065863, 1.855660350826693, 2.1223159414839583, 2.327453364362863, 2.449506258065978, 2.4714288548498686, 2.3825706945484435, 2.180232724115748, 1.870723899987975, 1.4697793998574744, 1.0022826132492675, 0.5012351703939406, 0.005970921608842641, -0.4404064216323968, -0.794137867444785, -1.0142207459175774, -1.0659504021207873, -0.9243590254236003, -0.5773092260858742, -0.02799944459377235, 0.7032834911619115, 1.5783138158253127, 2.5416488331492957, 3.5224771114918614, 4.437511452854169, 5.1949047821018, 5.69901772674072, 5.855802480326811, 5.578512000908824, 4.79336840353572, 3.444861944519788, 1.5006592503821534, -1.0445364332400673, -4.166411440105738, -7.809939754962345, -11.889910422277309, -16.29341281211593, -20.887008990724972, -25.52523525064225, -30.0570401120062, -34.33321551232722, -38.21364492613916, -41.57388082533705], 'positive_zeros': ['0.73652379186982093346515039048107', '0.76198671179119282246770457431811', '0.876610300552967539927896933029918', '1.44427171151413130515009200183023', '1.56006069287549804082634985708220', '1.61142701254934689006492194805930', '1.94848483513618685276119927008954', '2.14535273795654806424150270437631', '2.26437847382682777689274174187541', '2.31917304404941302629406842304208', '2.51332928671590422618556932016293', '2.90227370705713524909050056627380', '3.00389255426501251501802060626201', '3.05361966177090638218079065431122', '3.09317449994281244609463585815727', '3.17705554271808749388478793726948', '3.39370624573737144402028576321539', '3.66785063532021729064990312176887', '3.89275023384104356986805901375828', '3.90734582682606064973369848354000', '3.95937128375413067679711817757946', '3.98516837862355863464745061496649', '4.09836508095924963361008301762029', '4.36092048291769080420979355835900', '4.62295279559899667408415720096596', '4.74484380664329132083583427078799', '4.77646640401081482785739911087980', '4.78907726706602976450175361737498', '4.82585345691841437999834019677423', '4.99048785404188417271629906793795', '5.10852393856463258337694558068108', '5.19585701014324314453978684123355', '5.22346012892849327190364256641569', '5.62759272033274842212929847937264', '5.66884884602400640713793558030784', '5.86529299030125554315179142402766', '5.87022071246022123282800388835741', '5.91473680511968734111925871521594', '6.01776256090067706358635154855462', '6.27179176729091800798712160692132', '6.38835720984360471504549436386193', '6.45530849275597084072011207610849', '6.46425185041849582752605857256575', '6.58894840832320962476003324715056', '6.84927620247096804116122476174329', '6.94690017419879446322267815242697', '7.07020946031931932317995637474048', '7.14052110300060959759244997026409', '7.16579577214964534334286757147190', '7.37456768357368292289237611418322', '7.42066626237970297436982704259527', '7.52703240013495333953531927629574', '7.62198942973925509796427741920994', '7.86867275712211780736987152490456', '7.899477059972208865377789057461544', '8.009256356972757416304581333066087', '8.066446769714938404558133247545902', '8.223221898001873622749823420390021', '8.265057042609235963932222246621112', '8.454730587934013441016343683431818', '8.597248280288605353954266199815604', '8.607123413207573461843242586894213', '8.765036093098545803853242524840939', '8.843536126443338871361876580556347', '8.992513199378266023443944369790511', '9.030564040896637976408327841117948', '9.047133809835957975543022214988531', '9.113872714005021449851708913364640', '9.245410120655651657865548641000380', '9.335315909755807050048303636413393', '9.389863853636531788431732428665487', '9.504501649496733303221856958297829', '9.743845595838672347232538664351963', '9.911954113452877835483747869359660', '10.00287834441950506099861226646639', '10.00296344056715117179984648396966', '10.08378027266777955122824549368790', '10.10883800679017843194707261203535', '10.26049455229931172736442924704669', '10.35922380486440221924224025000482'], 'prelabel': '16-33e16-1.1-c0e8-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.7372121802828133, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c0e8-0', 'trace_hash': 770304249620728845, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.73652379186982093346515039048', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.76198671179119282246770457432', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.876610300552967539927896933030', 'prec': 107}}
• lfunc_search •

  Column	Type
  algebraic	boolean
  analytic_conductor	double precision
  bad_primes	bigint[]
  central_character	text
  conductor	numeric
  conductor_radical	bigint
  degree	smallint
  dirichlet_coefficients	numeric[]
  euler11	numeric[]
  euler13	numeric[]
  euler17	numeric[]
  euler19	numeric[]
  euler2	numeric[]
  euler23	numeric[]
  euler29	numeric[]
  euler3	numeric[]
  euler31	numeric[]
  euler37	numeric[]
  euler41	numeric[]
  euler43	numeric[]
  euler47	numeric[]
  euler5	numeric[]
  euler53	numeric[]
  euler59	numeric[]
  euler61	numeric[]
  euler67	numeric[]
  euler7	numeric[]
  euler71	numeric[]
  euler73	numeric[]
  euler79	numeric[]
  euler83	numeric[]
  euler89	numeric[]
  euler97	numeric[]
  euler_factors	numeric[]
  index	smallint
  instance_types	text[]
  instance_urls	text[]
  is_instance_Artin	boolean
  is_instance_BMF	boolean
  is_instance_CMF	boolean
  is_instance_DIR	boolean
  is_instance_ECNF	boolean
  is_instance_ECQ	boolean
  is_instance_G2Q	boolean
  is_instance_HMF	boolean
  is_instance_MaassGL3	boolean
  is_instance_MaassGL4	boolean
  is_instance_MaassGSp4	boolean
  is_instance_NF	boolean
  label	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  self_dual	boolean
  spectral_label	text
  trace_hash	bigint
  z1	numeric

  
  {'algebraic': True, 'analytic_conductor': 0.007611671428410052, 'bad_primes': [3, 11], 'central_character': '1.1', 'conductor': 1977985201462558877934081, 'conductor_radical': 33, 'degree': 16, 'dirichlet_coefficients': [1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -4], 'euler11': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler13': [1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1], 'euler17': [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], 'euler19': [1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1], 'euler2': [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], 'euler23': [1, 0, 8, 0, 28, 0, 56, 0, 70, 0, 56, 0, 28, 0, 8, 0, 1], 'euler29': [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], 'euler37': [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], 'euler41': [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], 'euler43': [1, 0, 0, 0, 4, 0, 0, 0, 6, 0, 0, 0, 4, 0, 0, 0, 1], 'euler47': [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], 'euler5': [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], 'euler53': [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], 'euler59': [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], 'euler61': [1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1], 'euler67': [1, 0, 8, 0, 28, 0, 56, 0, 70, 0, 56, 0, 28, 0, 8, 0, 1], 'euler7': [1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1], 'euler71': [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], 'euler73': [1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1], 'euler79': [1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1], 'euler83': [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], 'euler89': [1, 0, 8, 0, 28, 0, 56, 0, 70, 0, 56, 0, 28, 0, 8, 0, 1], 'euler97': [1, -4, 10, -20, 35, -52, 68, -80, 85, -80, 68, -52, 35, -20, 10, -4, 1], 'euler_factors': [[1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1], [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], [1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1], [1, 0, 8, 0, 28, 0, 56, 0, 70, 0, 56, 0, 28, 0, 8, 0, 1], [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], [1, 0, 0, 0, 4, 0, 0, 0, 6, 0, 0, 0, 4, 0, 0, 0, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1], [1, 0, 8, 0, 28, 0, 56, 0, 70, 0, 56, 0, 28, 0, 8, 0, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1], [1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1], [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], [1, 0, 8, 0, 28, 0, 56, 0, 70, 0, 56, 0, 28, 0, 8, 0, 1], [1, -4, 10, -20, 35, -52, 68, -80, 85, -80, 68, -52, 35, -20, 10, -4, 1]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1089/1/k/a'], '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': '16-33e16-1.1-c0e8-0-2', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0, 0, 0, 0, 0, 0, 0], 'order_of_vanishing': 0, 'prelabel': '16-33e16-1.1-c0e8-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.7372121802828133, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e8-0', 'trace_hash': 770304249620728845, 'z1': {'__RealLiteral__': 0, 'data': '0.73652379186982093346515039048', 'prec': 103}}
• lfunc_instances •

  Column	Type
  Lhash	text
  Lhash_array	text[]
  label	text
  type	text
  url	text

  
  {'Lhash': '933654826846150012406189601463,965932912568040427297424001405,1111235573662217878011171400454,1830831901993540725769786595528,1977611873716092534985853924307,2042726419682162137428690232434,2469997970795989873363380253517,2719557685971893498947715958439', 'Lhash_array': ['933654826846150012406189601463', '965932912568040427297424001405', '1111235573662217878011171400454', '1830831901993540725769786595528', '1977611873716092534985853924307', '2042726419682162137428690232434', '2469997970795989873363380253517', '2719557685971893498947715958439'], 'label': '16-33e16-1.1-c0e8-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1089/1/k/a'}