Lfunction data - 20-603e10-1.1-c0e10-0-0

Formats: - HTML - YAML - JSON - 2025-01-05T06:56:39.230957

• 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': '885992549523689132305177609084,1371181061457691477655683990401,1637550147128010331815357602058,2004085253263447885128030522998,2013898790787347276721997661178,2219361772463423996196966258511,2221467548847800616968422754267,2368599942232536565227856787475,2946899023586562547009497194760,3266883027332427181970194446667', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -1, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.091782163647771e-06, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [1]], [67, [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1]]], 'bad_primes': [3, 67], 'central_character': '603.1', 'coefficient_field': '1.1.1.1', 'conductor': 6355842422464168617446357049, 'conductor_radical': 201, 'degree': 20, 'euler_factors': [[1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], [1, -2, 3, -4, 5, -6, 7, -8, 9, -10, 11, -10, 9, -8, 7, -6, 5, -4, 3, -2, 1], [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], [1, 0, 10, 0, 45, 0, 120, 0, 210, 0, 252, 0, 210, 0, 120, 0, 45, 0, 10, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, -2, 3, -4, 5, -6, 7, -8, 9, -10, 11, -10, 9, -8, 7, -6, 5, -4, 3, -2, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], [1, 9, 36, 84, 126, 126, 84, 36, 9, 1, 0, 1, 9, 36, 84, 126, 126, 84, 36, 9, 1], [1, 11, 56, 176, 386, 638, 848, 968, 1013, 1023, 1024, 1023, 1013, 968, 848, 638, 386, 176, 56, 11, 1], [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, -2, 3, -4, 5, -6, 7, -8, 9, -10, 11, -10, 9, -8, 7, -6, 5, -4, 3, -2, 1], [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]], 'euler_factors_factorization': [[[[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 1], [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 1]], [1], [[[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 1], [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 1]], [[[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 1], [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 1]], [[[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 1], [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 1]], [[[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 1], [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 1]], [[[1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], 1]], [[[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 2]], [[[1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], 1]], [[[1, 0, 1], 10]], [[[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 1], [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 1]], [[[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 2]], [[[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 1], [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 1]], [[[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 1], [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 1]], [[[1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], 1]], [[[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 1], [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 1]], [[[1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], 1]], [[[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 1], [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 1]], [[[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 1]], [[[1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], 1]], [[[1, 1], 10], [[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 1]], [[[1, 1], 10], [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 1]], [[[1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], 1]], [[[1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], 1]], [[[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 1], [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 1]], [[[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 1], [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 1]], [[[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 2]], [[[1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], 1]], [[[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 1], [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 1]], [[[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 1], [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 1]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 0, 'label': '20-603e10-1.1-c0e10-0-0', 'leading_term': '0.21506221030225007604420673734973549906081367737462542255854031709308100119428842042153542', '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}, {'__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, 0, 0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/603/1/x/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.00703125', 'prec': 34}, 'plot_values': [0.21506221030225003, 0.21602680070548755, 0.21700035136796794, 0.21803118698715396, 0.21916842074366105, 0.22046212593745393, 0.2219636086195383, 0.2237257852711381, 0.22580367125524767, 0.22825497804012412, 0.23113080155678808, 0.23445221511072856, 0.23821970500202916, 0.24243054383483775, 0.24708282096357928, 0.25217521530542925, 0.2577067685374992, 0.2636766564438094, 0.27008397867142103, 0.2769311979807596, 0.28422855284115855, 0.29198888222283026, 0.30023004032861683, 0.3089719803117761, 0.3182357381600139, 0.32804344393799184, 0.3384183306510099, 0.3493847075147773, 0.36096597084104387, 0.37318312171672197, 0.38605723548475934, 0.3996089742555642, 0.413856436343704, 0.42881662918242, 0.44450585699181605, 0.46093949442958154, 0.478131767033461, 0.4960963173600177, 0.5148462286646551, 0.5343929259915772, 0.5547458265273502, 0.5759120458262368, 0.59789614455169, 0.6206996963794403, 0.6443208748309128, 0.6687540561496371, 0.693989643565687, 0.7200136477116966, 0.7468070340814144, 0.7743452342844819, 0.8025976465922117, 0.8315269857563883, 0.8610883221032262, 0.891228899499813, 0.9218878380227047, 0.9529969475359081, 0.984479941411773, 1.0162511109553674, 1.048214816033544, 1.0802650078307534, 1.112284775355299, 1.144145906528151, 1.1757084554922963, 1.2068207038615104, 1.2373207571023952, 1.2670355689065813, 1.2957799258311202, 1.3233563858557003, 1.3495553079283444, 1.3741549759061569, 1.3969218261170555, 1.4176107702290393, 1.4359661190296795, 1.4517247273405347, 1.46461517993139, 1.4743577268628647, 1.480665302598019, 1.4832446996352087, 1.481797901205581, 1.4760235776228696, 1.4656187497991844, 1.4502814881184074, 1.4297156434981024, 1.4036306255784698, 1.3717428508314933, 1.333778171838554, 1.2894744499831994, 1.2385842628730963, 1.1808777356970217, 1.1161454848134686, 1.0442029550733944, 0.9648960114784091, 0.8781010355409244, 0.7837273532740143, 0.681720320215319, 0.5720643778475999, 0.4547860519990886, 0.3299568623773158, 0.19769612066396736, 0.058175174166339945, -0.08837856200366646, -0.2416826689546426, -0.40139840044878183, -0.5671292293681989, -0.738419735252313, -0.9147548767212969, -1.0955596851402225, -1.280199388532939, -1.4679786245649455, -1.6581423529019699, -1.8498802234206528, -2.0423292741186883, -2.234577088866846, -2.4256653785598967, -2.6145941975290206, -2.800326798486909, -2.98179508156365, -3.1579053824318004, -3.327546051017002, -3.4895957648903786, -3.642931408353035, -3.786436494872857, -3.9190102797526984, -4.039576575518545, -4.147093045302801, -4.240560939831122, -4.319036858842151, -4.381643539455053, -4.427578639912128, -4.456124356954172, -4.466656845015082, -4.4586555075180785, -4.4317122624334555, -4.385538922444651, -4.319974729303812, -4.234997474081239, -4.130728254740429, -4.007433174220804, -3.8655265593668147, -3.705573018974488, -3.5282882121474417, -3.334538489959672, -3.125339468300284, -2.9018524567797663, -2.6653850185303325, -2.4173806336450765, -2.159406968392228, -1.8931457878035487, -1.6203814141838166, -1.3429877670556813, -1.0629140579314575, -0.7821693062214798, -0.5028067456129379, -0.22691002461581622, 0.043430789304954365, 0.30614111740664185, 0.5591819002807792, 0.8005698694663264, 1.0283978508480263, 1.2408548790385519, 1.4362458947360126, 1.6130103557813964, 1.7697402207566357, 1.9052002057958726, 2.0183439791076436, 2.1083279435049604, 2.1745231204892135, 2.216524941209872, 2.2341607676477397, 2.227494988858037, 2.196832228756687, 2.1427196864576525, 2.065944606614409, 1.9675267053943724, 1.8487086401839032, 1.7109440275645835, 1.5558827480960786, 1.385353656406996, 1.2013448641051012, 1.0059837288103513, 0.80151509967903, 0.5902718015332983, 0.3746463429311275, 0.15706108239575733, -0.06006163103369567, -0.2743294304748109, -0.48340980611167156, -0.6850594390675264, -0.8771507960223438, -1.0576991094192396, -1.2248914185939839, -1.3771106395205952, -1.5129576424627322, -1.6312685910377407, -1.7311291231991541, -1.8118852140417352, -1.8731502570031084, -1.9148081068462277, -1.9370133109823549, -1.9401869672270917, -1.9250074534044486, -1.8923975923424505, -1.843508918538125, -1.7796990040645106, -1.702506467345969, -1.6136236432304296, -1.5148681545107132, -1.4081510273883657, -1.2954417349402594, -1.1787332814374585, -1.0600070126462375, -0.9411980606773893, -0.8241621011703334, -0.7106416331649815, -0.6022357134165409, -0.5003741499682136, -0.4062926453532102, -0.32101170955161623, -0.24532120950137323, -0.17976980177604684, -0.12465951438281654, -0.08004569954822342, -0.045742367580335744, -0.021332783650814622, -0.00618569508253796, 0.0005241024190199028, -0.0002100140286181289, -0.007256765127986665, -0.019380809206966974, -0.0352794297959093, -0.053621259055368235, -0.07308618444212457, -0.09240554425745563, -0.11040108729925363, -0.12602267663620198, -0.13838298869100585, -0.14678800140394918, -0.15076237656851613, -0.1500687733818841, -0.14472021216246814, -0.13498471144540197, -0.12138164669982422, -0.10466946792343522, -0.08582349682426782, -0.0660043031371555, -0.046516785932912925, -0.028760168457747516, -0.014169410243143828, -0.004148761510244315, 1.5955456985655685e-06, -0.002835325731774881, -0.013509610520378551, -0.03251769945366579, -0.05991488401604488, -0.09522890894750122, -0.13737657620977084, -0.18458545845426017, -0.23432287360311646, -0.2832342751262916, -0.3270929477500037, -0.36076322226841445, -0.3781802367918816, -0.372347781127467, -0.3353546347070271, -0.25841096639762573, -0.13190597281227792, 0.05451272391441988, 0.31183769415668006, 0.6515783109614005, 1.085615601023624, 1.6260370875234065, 2.2849522701482017, 3.07428931831528, 4.005581581148122, 5.0897421002973795, 6.3368293400385225, 7.755808269722409, 9.354310695169511, 11.138399144670656, 13.11233834894068, 15.278378613812304, 17.63655704359021, 20.184525132712437, 22.917395643572416, 25.827618988920978, 28.904894154853427, 32.13612546780268, 35.505412687122764, 38.99407389782826, 42.58071747087049, 46.24135873091646, 49.94959222655308, 53.67683740465963, 57.39257004655752, 61.06460983314964, 64.65949079924125, 68.14282305456581, 71.47966709969704, 74.63495506168083, 77.57393221081298, 80.26261232964438, 82.66826503391488, 84.75996003241599, 86.50897206132342, 87.8892728875853, 88.87790715803378, 89.45533676635945, 89.60578692976661, 89.31754978598019, 88.58323942074796, 87.39999309780936, 85.76964580831694, 83.69892429828172, 81.1994465741126, 78.2875478077593, 74.98411026069728, 71.31436671222443, 67.30763994727997, 62.997021148173026, 58.41899111731877, 53.61298925726265, 48.62097810961434, 43.487025949527805, 38.25658394888777, 32.97586178196493, 27.69123898303738, 22.44867289547839, 17.293112350562474, 12.267926197421957, 7.4143556371139185, 2.77100069925326, -1.626665125602257, -5.746742325616788, -9.561302041191182, -13.046690986862075, -16.18376203892268, -18.958034813924833, -21.359784244395595, -23.38405651929595, -25.03063616319691, -26.303952983717892, -27.212851238543514, -27.77032788108773, -27.993189918774817, -27.901668437632186, -27.518993992326532, -26.87093719570611, -25.985323668914155, -24.891564054462567, -23.6201532373576, -22.20210180230491, -20.668426278949667, -19.049659014941152, -17.375383539685735, -15.673815050544418, -13.97142522125717, -12.292616039397267, -10.659464161025529, -9.091491403287762, -7.6054737541526265, -6.215340112037803, -4.932124633125735, -3.7639613478117155, -2.7161766552261875, -1.7914211885698166, -0.9898398929386322, -0.30928110202905923, 0.25446913287038236, 0.7074213144560545, 1.0570928754782882, 1.3122075949355405, 1.482398087183519, 1.5779208236574842, 1.6093387163079644, 1.5872402730439161, 1.521993438374986, 1.4235190632212722, 1.3010930986649438, 1.163186257768299, 1.0173397094819159, 0.870077376590677, 0.7268565281784506, 0.592054371270429, 0.46897433531883564, 0.35989334949270846, 0.26613375745129203, 0.18815874704290717, 0.12568656934285002, 0.07781690867174024, 0.04316429395037308, 0.019993536181209352, 0.006352446078333155, 0.00019716126900020333, -0.0004937225533964601, 0.002381210079718393, 0.00712948366096238, 0.012328486668009715, 0.016868521566896607, 0.019974898598110503, 0.02120961533487838, 0.020453911863141085, 0.017873700668010507, 0.013870472933484094, 0.009020379452557327, 0.004005155907532161, -0.0004612362970573672, -0.003706414939619374, -0.005170048901850317, -0.004467431334098349, -0.0014429322514970312, 0.0037894255768889723, 0.010820487423868813, 0.018937504962498197, 0.027133493734199425, 0.034134182067943664, 0.03844184606128469, 0.03839452083988718, 0.03223837803886531, 0.018210440759893844, -0.005371714551883947, -0.040017125354016164, -0.0869686329681066, -0.1471122506502355, -0.2209003381136069, -0.30828766325762236, -0.4086836279511347, -0.5209243078830361, -0.6432666433354424, -0.773407144372816, -0.9085255285719108, -1.0453509525226072, -1.1802499088984117, -1.3093317050641764, -1.4285820432137193, -1.5340074258825411, -1.6217869017662143, -1.6884275368596076, -1.7309205413259896, -1.7468876295104812, -1.7347090639415823, -1.6936340478460776, -1.6238651323727373, -1.5266118886062496, -1.4041156188113728, -1.2596338653871817, -1.0973849863269682, -0.9224553483912094, -0.7406640485099707, -0.558389759044613, -0.38236766093606517, -0.2194591646070894, -0.07640066459096284, 0.04046117661690049, 0.1254394633314492, 0.17377356664099497, 0.1818822302600909, 0.14759386648454959, 0.07034388280910485, -0.048669412391105664, -0.20637792605000604, -0.3977926411905745, -0.6160135807027005, -0.8523048758767784, -1.0962368957181083, -1.3358973302949269, -1.5581628016949334, -1.7490280248484658, -1.8939877817635418, -1.97846201338977, -1.9882534467051545, -1.9100256002446343, -1.7317878784167446, -1.4433741368964195, -1.0368979420420674, -0.5071605880384343, 0.14799045976319855, 0.9273673744923637, 1.826226343019648, 2.836141214183741, 3.9449750483752837, 5.136955773397097, 6.392866821202197, 7.690369287324043, 9.004391295510509, 10.307617144041705, 11.571070141269841, 12.764771983079713, 13.858464110292797, 14.822374121433613, 15.628008346116564, 16.248962363180723, 16.66173216698395, 16.846444636868956, 16.787498944194645, 16.474147798737764, 15.900986942281012, 15.068328395792262, 13.982443287501038, 12.655663079542531, 11.106327513891351, 9.358557287611365, 7.441883399329443, 5.390743408850667, 3.2438134386229667, 1.0432344590622828, -1.1662631613555718, -3.3383229767665514, -5.425992470485985, -7.382846245311629, -9.164116282290951, -10.727693153051222, -12.035139168721779, -13.052650509308966, -13.751897215931415, -14.110749192338751, -14.11387006748256, -13.753161148268754, -13.028099145958716, -11.945812206104096, -10.52089277939444, -8.775117406796717, -6.736995507505767, -4.441133735598251, -1.9274848752972942, 0.7595246503686864, 3.571975161402857, 6.459548640811191, 9.37070897826439, 12.253847757930089, 15.058409940578082, 17.73598316671678, 20.24135642238347, 22.53356194134084, 24.576613285714753, 26.34017567132533, 27.800263841025423, 28.939603530676223, 29.747742694778285, 30.221079252460292, 30.36272740739143, 30.18222830202993, 29.695153996094845, 28.9226415871074, 27.89059647431094, 26.629033156158897, 25.171103719589752, 23.552102972707967, 21.808554205632156, 19.977307138127248, 18.094670510048037, 16.195600595303148, 14.31298263119726, 12.477037518241563, 10.714759264238468, 9.049369672677226, 7.499987678230209, 6.081468778810767, 4.804368957346596, 3.6750268527285455, 2.6957548809533054, 1.8651273147169287, 1.1783563386313332, 0.6277301612784532, 0.20306784444681025, -0.10775132873498967, -0.3182376254384223, -0.44274780177364437, -0.49596565087333966, -0.492420784062171, -0.44605808470113234, -0.36986901645606046, -0.27559137651280646, -0.17347450131673406, -0.07211897737623331, 0.02160482387298232, 0.10256528881104765, 0.1673122214177563, 0.21396193397338847, 0.24203456661246936, 0.25225533074740003, 0.2463308456760487, 0.22670832375151975, 0.19633241474536728, 0.15840715125526736, 0.11617628208653415, 0.07272979746907726, 0.030842497179807044, -0.007151063993357003, -0.03944254009993327, -0.06479770803969602, -0.08256717756677386, -0.09266108098583295, -0.09549382836349862, -0.09190292327641371, -0.08304969520328254, -0.07030937182563993, -0.055157584534229934, -0.03906058090960691, -0.02337456356375326, -0.009259324207823882, 0.002388373393492202, 0.010979102526221807, 0.016251526570882475, 0.01826898775628745, 0.017393025731368392, 0.014236836007207819, 0.009602488077268979, 0.004406683920157461, -0.00039992807473537124, -0.003914315802560043, -0.005357880283520013, -0.004143349645679916, 7.261311789019391e-05, 0.0073546121484030485, 0.0174746054012356, 0.029919862457213293, 0.04392251331867845, 0.05850910888467057, 0.07256728914234561, 0.08492547527198444, 0.09444055203953534, 0.10008776798259393, 0.10104679137672014, 0.09677822496635731, 0.08708416551122156, 0.07214727212179008, 0.052544685885954893, 0.029234094737863522, 0.0035106056072100136, -0.023065102336881693, -0.048765077269401, -0.07181483708471911, -0.09053089356920094, -0.10346773222685947, -0.10956557160256389, -0.10828977586270705, -0.09975241816406173, -0.08480641442149663, -0.06510327972846142, -0.04310665645731848, -0.02205535170230768, -0.005871610432399859, 0.0009870564668109838, -0.0062693027167928655, -0.03250883795867092, -0.08237881464041148, -0.15997125831185263, -0.2684655078288421, -0.4097621966049483, -0.5841250723680343, -0.7898487511686392, -1.022972651022956, -1.2770603537933327, -1.543047538830418, -1.809182455683351, -2.06107219525583, -2.281842980051504, -2.452420208828316, -2.551929704604764, -2.5582113012253647, -2.4484283185758504, -2.199784094422701, -1.7903156023593458, -1.1997075601800529, -0.41014451097099286, 0.5928330252169346, 1.819502863992823, 3.2751978307472656, 4.9596963838302495, 6.866761422729379, 8.983709483872284, 11.291214052688877, 13.763382435035417, 16.367939689552212, 19.066615330473415, 21.815747698486327, 24.56709206697835, 27.26900561790784, 29.86769044503409, 32.30828308168172, 34.53620020435701, 36.4986396417582, 38.14631434024612, 39.43466454818567, 40.32509527635063, 40.78618937118824, 40.79503324305774, 40.33799451318031, 39.41104127612657, 38.020061893305034, 36.18093380040221, 33.91945394369888, 31.27125029845246, 28.28063545964912, 24.999486715924235, 21.486169593985423, 17.803942582576873, 14.019242234279053, 10.200042293804467, 6.414179727647613, 2.7276932277487083, -0.796684982008459, -4.10079982106368, -7.132806104320841, -9.84852472343616, -12.21242422195925, -14.19825643672166, -15.789420198886404, -16.9790460269437, -17.769805873458292, -18.173460503555173, -18.210135152463334, -17.90738749320427, -17.299389485545422, -16.42557978588939, -15.329217637739793, -14.055947223184695, -12.652364966136702, -11.164635348220395, -9.637197500766964, -8.111600162902748, -6.625510507321148, -5.211919216445395, -3.8984509499416493, -2.7069421343665936, -1.6532604261277237, -0.7473410253619032, 0.006575376775841016, 0.6095248186927316, 1.06724973557076, 1.3895121716685612, 1.5893291677701051, 1.682134172992397, 1.6849200265146949, 1.615403773636085, 1.491244962007013, 1.329345491540657, 1.1452538931346026, 0.9526909688338664, 0.763210798795894, 0.5859937138425333, 0.42776284905029643, 0.2928375084995355, 0.18329958559583562, 0.0992552641150073, 0.039169368984357356, 0.00024794425806665176, -0.02115599552298241, -0.02913847309875525, -0.027864917226489507, -0.021234242540641362, -0.012605066404446972, -0.004596622460455974, 0.0010282518581063188, 0.003395668856823777, 0.0024717729850338753, -0.0010598127543315862, -0.005982055308290157, -0.010774644941558512, -0.013871818550522195, -0.013927742530631936, -0.010069240992765238, -0.002116408009295802, 0.009246505977027666, 0.022364385148646703, 0.03457940799196735, 0.04228041807992047, 0.041034848927552096, 0.025798790400181976, -0.008803586344902454, -0.06814456884205285, -0.15721883607509132, -0.2802517749808941, -0.44031265025104804, -0.6389562198853853, -0.875920036041457, -1.1488943997488223, -1.4533807823352738, -1.7826568409834005, -2.127856803363138, -2.478171399793981, -2.8211659919956307, -3.1432094746591623, -3.4299996930546137, -3.667186001894829, -3.8410081583088447, -3.938951829323264, -3.950405850460518, -3.8672795594536398, -3.6845491450130323, -3.400703793840953, -3.0180609999521515, -2.5429247562242896, -1.985610337920461, -1.3602483770821574, -0.6844335460386793, 0.021277859051193743, 0.7340177468864191, 1.42938208498508, 2.082305116911166, 2.6679990038239345, 3.1629402092950984, 3.5458851772523996, 3.798715254721401, 3.907206122276628, 3.861683817788135, 3.657521135565846, 3.2954501648057617, 2.7816737514042167, 2.127766580926077, 1.3503699873870998, 0.4706637988206698, -0.4864009902985057, -1.492992354563063, -2.5193843460077883, -3.5350229347710767, -4.509630411924687, -5.414304720731387, -6.222570072576341, -6.911373204785007, -7.461973447793239, -7.860562802840461, -8.098743764272548, -8.173709834124562, -8.088232549346818, -7.850445338942203, -7.473420921310887, -6.974562332526399, -6.374882053375772, -5.698108633815224, -4.9695989058549275, -4.215291317881026, -3.4606687906736435, -2.7297497337140397, -2.0441963856321372, -1.422557682777332, -0.8796702178710467, -0.42624292546317355, -0.06860662267288577, 0.1913276931573594, 0.355887321340317, 0.4312760744635527, 0.427054659490013, 0.35547055844552294, 0.23070472438046422, 0.06807014212302788, -0.1167922449426775, -0.30870996432970954, -0.4937201683168183, -0.6596983663219997, -0.7968569210273685, -0.8980963032728764, -0.9592008856286666, -0.9788493641999274, -0.9584662515943311, -0.9019348408377277, -0.8151837778242705, -0.7056693705392765, -0.5817942524590224, -0.4522985659055037, -0.32566042617319896, -0.2095418294932911, -0.11031055994171415, -0.03266304674484319, 0.020618711235936078, 0.04877510418312164, 0.05302972432513994, 0.03640751800252574, 0.0034257406583904663, -0.04032101812338102, -0.08865381246992794, -0.13534777062510084, -0.17468159016171714, -0.20195550983750513, -0.2139410198472538, -0.20922926510480475, -0.18844977755887032, -0.15433892689471612, -0.11164618143759432, -0.06687595253689967, -0.027872943737317867, -0.003269198924713507, -0.0018186594373507873, -0.03165482791445575, -0.09952162480253354, -0.2100226873677052, -0.3649375328883626, -0.5626526910396017, -0.79775223054949, -1.0608057985229882, -1.3383868695416041, -1.613345362160791, -1.8653255526454833, -2.071525894811904, -2.2076763239322736, -2.249197402001108, -2.1724928294750137, -1.9563167234185583, -1.5831493406437198, -1.0405209030491622, -0.322198492289249, 0.5708721628230897, 1.6298948966058402, 2.8378891420235832, 4.169716811638112, 5.592500785013102, 7.066442649102552, 8.54602701250569, 9.98159486951665, 11.321230060131297, 12.512842570465624, 13.506429091695827, 14.256468967033054, 14.724105286477114, 14.87917228372419, 14.701969670592025, 14.184665788466257, 13.332281136979404, 12.163091692838961, 10.708401492155495, 9.011773194127233, 7.127712547762997, 5.119861848679199, 3.0584460022591196, 1.0173838210304154, -0.9288647140819236, -2.708637316224539, -4.256453892362444, -5.516249149568302, -6.444322185508632, -7.011870796965651, -7.206971809488497, -7.035903571987286, -6.523772153992997, -5.7142761681334715, -4.668605690903125, -3.4634823321993533, -2.1884363326968423, -0.9424012892833412, 0.1702662766761444, 1.0441983658460128, 1.5776903589429156, 1.6774568705003137, 1.2632767291858185, 0.27231083280084417, -1.337199730473544, -3.5829209781636937, -6.456238840878999, -9.921037477648294, -13.913527464205469, -18.34316858275162, -23.09470264964955, -28.03133984227516, -32.99918962597266, -37.83210921238681, -42.35714576282199, -46.40051428488172, -49.79380515704274, -52.3801916072298, -54.020402766929315, -54.5982320422112, -54.025605608937745, -52.24725113621053, -49.24279012399782, -45.02807417563474, -39.65551999299343, -33.21318192661748, -25.82258220792389, -17.635364791038615, -8.82888257922118, 0.3989516795153115, 9.835563796808023, 19.26098836221368, 28.454807958111026, 37.20293632872066, 45.30415041351919, 52.57614852630876, 58.860929625597535, 64.02931526949966, 67.98455849994865, 70.6649697193781, 72.04493612293898, 72.13433738249688, 70.9772582476432, 68.64962309359709, 65.25580901682721, 60.92444883551993, 55.80359744034954, 50.05560794744171, 43.85158715374656, 37.36544314876904, 30.76809416136951, 24.22143127822052, 17.874494308728785, 11.859953023560822, 6.291111595600664, 1.2597510298191494, -3.1651803118029345, -6.938093010035066, -10.03637634054374, -12.459190254791398, -14.22583816177433, -15.373977025859997, -15.955783938414188, -16.03449301783548, -15.681106214792955, -14.971205623005908, -13.981813895846326, -12.788450187783015, -11.462612891783888, -10.069692806288637, -8.667441133825534, -7.304993521554985, -6.021831757978502, -4.8475678703178, -3.802279427984434, -2.897165747411188, -2.1355076100387578, -1.5138612336302744, -1.0233827769558939, -0.6512040967894583, -0.38179229161780354, -0.19821815693998307, -0.08325908104750808, -0.02037196133739995, 0.005531768556765162, 0.0075334326845314945, -0.0036253143755763384, -0.019670414828464083, -0.03474397704696715, -0.04520583053944263, -0.04932458237789298, -0.04689761317223477, -0.03884015208180529, -0.02677135395440018, -0.012631540154266334, 0.0016442474705267434, 0.014379901600790033, 0.024330293329014076, 0.030770521126321147, 0.0335080564518822, 0.03282923789049255, 0.029395787104983313, 0.02410897672369158, 0.017961053254412437, 0.011892342122643947, 0.006669920550661307, 0.0028001569488536604, 0.00048293782052882985, -0.0003895156444494214, -0.0001912702728955721, 0.0005147162239902188, 0.0010796002114870644, 0.0008841227113600399, -0.0005478343964620563, -0.003451858915683731, -0.007754531917315049, -0.013043834944035895, -0.018584584225466088, -0.02338068816825757, -0.026280705680752824, -0.026117327907874383, -0.02186918259713172, -0.012827960593488563, 0.0012470419832821197, 0.020005797519009577, 0.04243382390058678, 0.06684313929785822, 0.09093983206302224, 0.11197328347600559, 0.1269618273842564, 0.13298782331726977, 0.12754591396632264, 0.10892029843516474, 0.07656269114486804, 0.031438112103245604, -0.023696778810458098, -0.08412082977742538, -0.14311572637223868, -0.19209113273723621, -0.2208875251897866, -0.2182657347777666, -0.17257920641756458, -0.07260844807658896, 0.09146980321806321, 0.3270200199734316, 0.6378326853416257, 1.023056744978528, 1.4762470145500242, 1.9845690434027483, 2.5282432352755304, 3.0802974864431696, 3.60669197851055, 4.066823301079107, 4.4144514242170265, 4.599072169937652, 4.567683148861513, 4.2668821112318325, 3.645254657151292, 2.6559632398209305, 1.259434406201524, -0.5739863097042635, -2.861592034090366, -5.606121532396183, -8.794038890710656, -12.39437410377117, -16.35814187176253, -20.61845589936417, -25.091383703363718, -29.677559151538386, -34.264538012143035, -38.72995712698324, -42.94568444637432, -46.782308098655236, -50.11338708089748, -52.81989698244124, -54.79477301873215, -55.94722396763314, -56.20663543265811, -55.525890931703785, -53.88395674683023, -51.287987966765535, -47.775182627193225, -43.41111932662036, -38.28778734800122, -32.521008060639865, -26.246941166429508, -19.617796239476686, -12.796903746002616, -5.953327861426448, 0.7435369213967788, 7.12936069203575, 13.051357946373333, 18.37369046958782, 22.981878291627563, 26.786356138116368, 29.725058900175014, 31.764944057623758, 32.90240238153084, 33.162486987157735, 32.597166369373376, 31.282857580994957, 29.316996938909575, 26.813284190514747, 23.896620904074645, 20.697884183181998, 17.348668153159934, 13.976212512845558, 10.698713000849086, 7.621217853282031, 4.832265861424379, 2.401362247096454, 0.37735178397259744, -1.2123008925159804, -2.3611490549824032, -3.082471933470031, -3.407178450445305, -3.381056172562553, -3.061479602775838, -2.513766853830221, -1.807419700668153, -1.012415445935644, -0.19571708881212954, 0.5819095156764188, 1.2685283483333287, 1.8230312793604966, 2.21645550536064, 2.432577266997898, 2.4677819137309984, 2.3302759585315322, 2.0387179750251807, 1.62037875700056, 1.108959235323313, 0.5421487041765313, -0.040880088013762854, -0.6019017319579705, -1.1058712188024606, -1.5228358626083682, -1.8294402000260614, -2.0099636203770643, -2.0568571032357106, -1.9707770372967037, -1.7601411897622399, -1.4402342478616685, -1.0319476915827839, -0.5602659453829826, -0.052596128688538794, 0.46296010606869387, 0.9592853253014333, 1.4117787001967455, 1.799657975205838, 2.106967878113467, 2.3232587532610736, 2.4438805303565245, 2.469874472568651, 2.407537263789735, 2.2676947725025074, 2.064737265614328, 1.8154878141399209, 1.5379831144555867, 1.2502483784080052, 0.9691448509979951, 0.7093578487174625, 0.4825951111217885, 0.2970432828025469, 0.15709829800530134, 0.06337500682508787, 0.012984067770496899, 4.701301644387897e-05, 0.016405451971293172, 0.05246973511622572, 0.0981451328185586, 0.14375666703705345, 0.1809070749923778, 0.2032119699473519, 0.20686258235549518, 0.19097794954031275, 0.15772290060857347, 0.11218396735974369, 0.06201085970093624, 0.016850452969080897, -0.012377462534529494, -0.014316157584546884, 0.021938374906873417, 0.10595346866639499, 0.24514014763747652, 0.44405342545327664, 0.7038614212024499, 1.0220619909703457, 1.3924672371380091, 1.8053519233926483, 2.247851852290975, 2.7045930715756206, 3.1584539257632827, 3.5914489329467028, 3.9856859657250543, 4.3243406123842485, 4.592737802568309, 4.779231098241085, 4.875689493326874, 4.877920142155513, 4.785895667361232, 4.603774986307947, 4.339597632985623, 4.004802034603313, 3.613591295519172, 3.182295578884487, 2.7284080558206765, 2.2694907924171703, 1.8222653673497438, 1.4017905107454653, 1.0207703510579347, 0.6890245560170578, 0.4131266596975307, 0.19627466106975514, 0.03838941281774304, -0.06367573575547793, -0.11571736857804053, -0.1255873207160832, -0.10251030321735947, -0.0563634916912012, 0.003032370581644137, 0.06656538390231746, 0.1263853892353882, 0.17631360915089417, 0.21211199319852703, 0.23158530402061112, 0.2345083812761216, 0.22239763430954504, 0.19815323158169718, 0.16560730883632332, 0.12902033185432493, 0.09256964571643275, 0.059870154258629835, 0.03357610750049724, 0.015094834917381646, 0.004439418809707828, 0.00023472904707987056, -0.00012210040213675262, -0.00015858882134829426, -0.0039051966698242005, -0.015389383266247376, -0.038087495839949914, -0.07438291337507716, -0.12508097236019383, -0.18902794654249191, -0.26287514329940254, -0.34101959193577164, -0.41574045841242213, -0.47753603049377447, -0.5156515477639827, -0.5187739704166665, -0.4758508161421043, -0.37697628530620964, -0.2142865641874902, 0.017201525328485123, 0.31887524572821124, 0.6879958252706198, 1.1174062456303044, 1.595516349992909, 2.106589273380571, 2.631335881780646, 3.1478109975914905, 3.632539207315695, 4.061826946978553, 4.413190231848831, 4.666808613655201, 4.806911111312759, 4.823005181760126, 4.710841635382604, 4.473026328238767, 4.119250981387683, 3.6660917713255654, 3.1363100991956743, 2.557720446080211, 1.9616606952753028, 1.3811284559202879, 0.8486790460244567, 0.39419676676849746, 0.042680412290141294, -0.18781871435709419, -0.28797804131378496, -0.2585748091491148, -0.11130955167040314, 0.13097746257273676, 0.43475765356695195, 0.7569541413488957, 1.046741992015981, 1.2479541979700628, 1.302000398712726, 1.1511705951028406, 0.7421694915900465, 0.029690840587903458, -1.020187245119066, -2.426947944421349, -4.19325803477582, -6.303215771538943, -8.721313418527961, -11.392360305208834, -14.242372654550724, -17.18043875158886, -20.101558003676022, -22.8904256419056, -25.425769153094294, -27.58563585450373, -29.252342692930828, -30.317397566490293, -30.68645549346054, -30.283879378230402, -29.056688516740017, -26.97770158305577, -24.047646429066155, -20.29595105376528, -15.780703886032406, -10.586828850180288, -4.8234016267084305, 1.3798502496619178, 7.876881166609567, 14.510319449846127, 21.11691375335066, 27.53321082809571, 33.601760363766466, 39.17842434434254, 44.1361154077034, 48.3683049170298, 51.79210599979825, 54.35038968151724, 56.01287836930757, 56.77620542270438, 56.66297348121915, 55.72014967806347, 54.01730929934353, 51.64372829585646, 48.70239345901679, 45.30509093229654, 41.56797714180012, 37.60729648883172, 33.53541130109047, 29.457286491498934, 25.467684148873243, 21.64889898365856, 18.06896413420259, 14.781121097819641, 11.822697954153426, 9.215467530810189, 6.966843108158843, 5.071528040728143, 3.5134953002460887, 2.2681822036420543, 1.3047253523426734, 0.5881561184912911, 0.08153979301919849, -0.2521118064032574, -0.44838405627987016, -0.540163545100789, -0.5566675393449454, -0.5228386965249916, -0.4590807133455471, -0.3812867688403128, -0.30110824533480607, -0.226412055800419, -0.1618611884798315, -0.10955912952946428, -0.06970297218230408, -0.041196466212430866, -0.022192796883934853, -0.010542443619958246, -0.004132705675891842, -0.0011165903148847925, -3.857209447485256e-05, 0.0001276712329962933, 9.52948627382027e-06, -8.865139565187348e-05, -8.634563590778644e-05, -2.4332399240708527e-05, 2.4849308724295347e-05, 2.217859694590925e-05, -2.575786768784809e-06, 5.4128563548714185e-05, 0.0003487008230901671, 0.0010515550141838661, 0.0023003219603379616, 0.004155644108123052, 0.006569268899663422, 0.00937196567631908, 0.012284635747139314, 0.014952372320592756, 0.016997507529808557, 0.01808392690546106, 0.017982373075084466, 0.016625132601397773, 0.014138677036876714, 0.010844704018329527, 0.007223334543329753, 0.0038361248094808463, 0.0012135878302232616, -0.0002836710236064473, -0.0006159177251122724, -0.0002087074030295257, -6.943954385539962e-05, -0.0018541059651247327, -0.00786416708139684, -0.020958912633061422, -0.04437506859206415, -0.08145320402418206, -0.13528078011679187, -0.20827212230039907, -0.3017158602405379, -0.4153293951583863, -0.5468667259166512, -0.6918372678428641, -0.8433945419892858, -0.9923930179104945, -1.1276654561513553, -1.2365417933634797, -1.3056064776191727, -1.3216721392616873, -1.2729257593593875, -1.1501809717007718, -0.9481535868086283, -0.6666133937994485, -0.3112865302583553, 0.10554352087219904, 0.5648740363064341, 1.041347531100553, 1.5042219387279983, 1.9189932080530288, 2.2496796974269113, 2.4618302599132025, 2.5260690288916856, 2.4217820675244024, 2.141058996755097, 1.692602079871854, 1.1053126289651856, 0.43132527970522083, -0.2517837066870306, -0.839877692090099, -1.202499874855776, -1.1848495134064243, -0.6113594958329938, 0.7091747958209177, 2.976879954743514, 6.39268409314184, 11.149026322530952, 17.41967711702951, 25.3490500532004, 35.04120431816852, 46.54981914668395, 59.86963022364436, 74.92924856240202, 91.58606711083657, 109.62385833823917, 128.75381238525543, 148.61780823997157, 168.79496657934303, 188.8128003992974, 208.1606482893268, 226.30459265146786, 242.70474100442453, 256.8338381985783, 268.19650159831855, 276.34876975457314, 280.9176842171213, 281.6169082840964, 278.2640641663737, 270.78933402801215, 259.23960154417665, 243.78026046424156, 224.6926709738083, 202.36725455806757, 177.29241310958162, 150.03987558643797, 121.24755767310837, 91.59993593539961, 61.80120432227013, 32.54992718930391, 4.515540001139513, -21.683860875935345, -45.50155644932595, -66.47928413331921, -84.26070106598866, -98.60090165231175, -109.37253999139163, -116.56654486834664, -120.28717575866878, -120.74277435898937, -118.23277857135737, -113.13167182302631, -105.87065639432534, -96.91791692668684, -86.75876046767459, -75.8764282173466, -64.73241280914527, -53.74893466844535, -43.29478787702056, -33.674617246326875, -25.12180319991567, -17.795073772883736, -11.778780272969831, -7.086675833118763, -3.6685809521842065, -1.4193936980186586, -0.19033481309444975, 0.19855544272940676, -0.054603848553593744, -0.7463304339024475, -1.6796923338766254, -2.6747737189677605, -3.5772310599269908, -4.264619562307171, -4.650319766076986, -4.685002581939705, -4.355743863215325, -3.682999291855914, -2.7157939883593483, -1.525544809235693, -0.1989804593027352, 1.1694253977312088, 2.4849131604700085, 3.6592128385316856, 4.616429353670178, 5.297687600983253, 5.664303385545832, 5.699435109754146, 5.408188192148213, 4.816259801582741, 3.967361174823305, 2.9194034383609524, 1.7399314093227838, 0.5012949368557439, -0.7242201990127812, -1.8690148214108753, -2.8742790623009986, -3.69312782525248, -4.292864144324703, -4.656324871311505, -4.7820346549026045, -4.683247169593104, -4.386134011292189, -3.927252084347755, -3.3504957376624134, -2.703756235503536, -2.0355030039137176, -1.3915890141472533, -0.8124668224587409, -0.33085143570068254, 0.029889251887235242, 0.2565732565128964, 0.34630232761550545, 0.3058618733681252, 0.15050963290395175, -0.09772554630144932, -0.41210459653026116, -0.7634239721141952, -1.122274552385431, -1.461123461989343, -1.7560903906084968, -1.9883233073337498, -2.1449064718416873, -2.2192710338579205, -2.211115697258049, -2.1259006103264784, -1.9739989939627185, -1.769420235069878, -1.5284082242522996, -1.2680187402743293, -1.004766354939314, -0.7534393388440708, -0.5261612232440261, -0.3317532065008949, -0.17543049960975107, -0.0588209319539041, 0.0197409919885161, 0.06463754867893046, 0.08220265734688616, 0.07985762405595444, 0.06523200836428435, 0.045349485686117706, 0.025948294677911002, 0.010990367488700635, 0.00239398655500397, 3.1544242231490495e-06, 0.0017871557405417244, 0.004239167291377057, 0.0029219792302275834, -0.006898106332010262, -0.029595175931238685, -0.06857186835069635, -0.12575253247715573, -0.20123231197251165, -0.29311820697899177, -0.397582686317808, -0.5091407176566989, -0.6210865447312721, -0.7260643836077755, -0.8167233101660772, -0.8863918162704314, -0.9297122510548457, -0.9431673734208768, -0.9254399504853897, -0.8775775778467082, -0.8029479614186547, -0.7069863635797563, -0.5966828479673457, -0.47993267977392295, -0.3647966187083188, -0.25873077805296807, -0.16785000537619965, -0.09630314058726772, -0.04582877016000383, -0.015537410024531751, -0.0019513140098203776, 0.0006900103023268664, -0.00012909778840838396, 0.004024491933990711, 0.02160917831739974, 0.060117290469222574, 0.12510802403007965, 0.21935939609562208, 0.34222929077107356, 0.4893033153069677, 0.6523881445707719, 0.819885967131411, 0.9775459929475319, 1.1095586775694728, 1.1999252075209348, 1.2340090491676345, 1.200153120116199, 1.0912298492667305, 0.9059859491094657, 0.6500483641237905, 0.33647432177608483, -0.014259059903543293, -0.3749063044073072, -0.7126685973288979, -0.9909724923117157, -1.171742728486807, -1.2180378082759777, -1.0968864029973922, -0.7821344088043839, -0.25709576160262415, 0.48321107466328045, 1.4305117088983488, 2.5625312157473408, 3.843096633607802, 5.223189536355057, 6.642958952930443, 8.034636281916187, 9.326229054306262, 10.445809493038471, 11.326243505256702, 11.910115508949394, 12.154120988288803, 12.03279358382184, 11.541468901569301, 10.698202310163081, 9.544419902445636, 8.144179752456663, 6.581999354069587, 4.959334098053385, 3.3897065995945077, 1.9926746728004234, 0.887266670001325, 0.18514579633459008, -0.016159033433991245, 0.3604211955253054, 1.3659978391350889, 3.0214062931128085, 5.31442818869456, 8.198879040088714, 11.595496708832215, 15.394786827653567, 19.46202478700904, 23.643117121088984, 27.771666792870285, 31.676951891694866, 35.192334295457734, 38.1642185242662, 40.46028536697776, 41.975834980285306, 42.639158121381044, 42.41555128980406, 41.30991357793867, 39.36537517833602, 36.66059831435901, 33.30562433544981, 29.436820572735623, 25.209501372065002, 20.789135915079175, 16.342885884441475, 12.031268605876164, 8.000433952794397, 4.375321520405208, 1.2537374918152857, -1.297382298208723, -3.2436392990569423, -4.583454022813296, -5.346370957845492, -5.589454883322261, -5.392297728448282, -4.850982305939755, -4.07143343489276, -3.162560561194746, -2.229300157107212, -1.366419477622059, -0.6533361293611462, -0.1501902825906323, 0.1046122808876229, 0.09530824080940424, -0.1718404538576207, -0.670570432134062, -1.3578402848129651, -2.178004071001966, -3.0676832911377625, -3.9608777930609005, -4.793938450581362, -5.510071344978455, -6.063084333028235, -6.420153348189891, -6.56346426026968, -6.490671124674798, -6.214243817670183, -5.759856327264245, -5.163585648323646, -4.468535679477165, -3.7211582911476304, -2.9675274707364183, -2.249856409333303, -1.603517424992237, -1.0547764310697987, -0.6193924740862325, -0.30216076769741385, -0.0973850042195452, 0.00980263921525466, 0.0413303119758379, 0.023533343386760528, -0.015783945526371496, -0.0503072678537477, -0.0579296768836498, -0.022986955390608958, 0.062188009644970066, 0.1965328928571182, 0.37041331051882903, 0.5666824886362373, 0.7625720607462723, 0.9322598972758198, 1.0499053016341229, 1.0928973993500113, 1.0450348898868544, 0.899354473779572, 0.6603563730791298, 0.34539921241225763, -0.01490699428642714, -0.3774111372215153, -0.6882503163010306, -0.8857299554724416, -0.9041036978439906, -0.6779795957501468, -0.14705237902383328, 0.7390522145431889, 2.0162085357415354, 3.701834291994584, 5.7918832803051945, 8.259015185080646, 11.052122896273465, 14.097351425028354, 17.300947826863414, 20.553224579495417, 23.733328199469312, 26.71513172378223, 29.373728605258787, 31.59220767147789, 33.2683949625747, 34.3206910597409, 34.693054974817386, 34.35906502895274, 33.32373655400891, 31.623636890714995, 29.325639725828903, 26.52405464709602, 23.33626440121048, 19.89710827789362, 16.352278206704046, 12.85098137163297, 9.538417841073239, 6.5486255226206085, 3.9981408194115713, 1.9806367129519125, 0.5628001739710348, -0.2183528141652361, -0.3566069137354849, 0.1239116615178822, 1.170856096795423, 2.707606898936595, 4.638094511189151, 6.852230799277411, 9.231834895793945, 11.656690177117115, 14.010411598152897, 16.185826894609477, 18.089614453014537, 19.646367687134305, 20.802391874231933, 21.52596700735714, 21.806890642461543, 21.655270658554553, 21.09937694316869, 20.182740526665576, 18.960716211720527, 17.496738392935764, 15.858735574905225, 14.115809202601943, 12.334230251859257, 10.574068739406476, 8.886907666636104, 7.314376676389797, 5.88741081812895, 4.626192102447256, 3.5406952070188, 2.6317839302674706, 1.892607668752262, 1.3101086561324295, 0.8668178496724992, 0.5425984806573508, 0.3163031381167934, 0.16720340993634375, 0.07612037378892833, 0.026228725296126718, 0.00353590790084399, -0.0029438998240629245, -0.0012709758189857882, 0.0031403834012934785, 0.0071004380669239305, 0.009145460962528235, 0.009022137949878243, 0.00720700775509989, 0.0044999389129113864, 0.001715774076156452, -0.0005169483624353504, -0.0018542483185710582, -0.0022466546344081, -0.0018836247355171205, -0.001098828189808463, -0.00026252738986489425, 0.0003152042934650486, 0.0004527919968705238, 0.00012705821506942192, -0.0005371204675921525, -0.0013116213103171472, -0.0019325098655580538, -0.002174510615060249, -0.0019158440337822135, -0.0011784436329776897, -0.00013261373156748878, 0.0009385292874351896, 0.0017120145054570395, 0.0019248074345855082, 0.001483636602268744, 0.0005637315383925961, -0.0003265491640987382, -0.0003367143173439049, 0.0016625621135376717, 0.0069348194485845775, 0.016653743469672827, 0.031615320399947244, 0.05191265071846535, 0.07661008448080624, 0.10346245864752945, 0.12872904979883004, 0.1471310227613791, 0.15199454401642176, 0.13560893449288935, 0.08981169112254771, 0.006786738500368708, -0.11996954994754011, -0.294567290711793, -0.517613762410254, -0.785182530600702, -1.087980793709377, -1.4108402675588083, -1.7326524410141986, -2.0268676845922564, -2.2626502099496943, -2.406584919640849, -2.4250234142249294, -2.287010492008944, -1.9676658400050298, -1.4518556885050782, -0.7379417005031186, 0.15864469615951357, 1.2022995560939118, 2.3350780161364413, 3.47569357798091, 4.519393893161167, 5.33925103460623, 5.788983099630812, 5.707304292249652, 4.923752565034823, 3.2658532314533213, 0.5676251872186181, -3.321083862223351, -8.525844137429862, -15.139222708622404, -23.21302741938976, -32.75152204183218, -43.70620900227981, -55.972562061925956, -69.38901755851349, -83.73877158028046, -98.75477454531028, -114.12669226299094, -129.51072324964633, -144.54326191869697, -158.85231090616028, -172.0702250113211, -183.84725330790576, -193.86481528818769, -201.8499037445072, -207.58685040661624, -210.92384744964139, -211.77859731946089, -210.14236312931502, -206.08309639191333, -199.73877793559706, -191.31010305682645, -181.05200671134176, -169.26540091081264, -156.28415921993027, -142.45952191071865, -128.14657899249266, -113.69129639215703, -99.41911887740507, -85.625657346154, -72.56570287378001, -60.44656444101426, -49.42522151936282, -39.60623626281948, -31.042340967824067, -23.73807441356399, -17.655247998257636, -12.719802625297259, -8.8296485748421, -5.862927695923183, -3.6859109793691363, -2.160881937584627, -1.1531325246887874, -0.5369271331181883, -0.20014566012687027, -0.047442474295372135, -0.0019292527874072392, -0.005479445281747754, -0.017827453024722377, -0.014695846359815995, 0.014789051591536295, 0.07112392066154855, 0.14761186466248394, 0.23343804927154346, 0.3164167908185226, 0.3852436458690086, 0.43114685876660047, 0.4488947274866816, 0.4371766716554966, 0.39842675652431997, 0.3381744348846016, 0.26407840482325623, 0.1847954180770264, 0.10883109658736863, 0.043506851445311336, -0.005848822419587964, -0.03640999872664919, -0.048027362510203335, -0.0430681739647634, -0.025957251399236582, -0.002486911533928145, 0.021012257028039816, 0.038539011338087535, 0.045227181855804426, 0.03799903704351776, 0.015994520695881812, -0.019270167266222087, -0.06403359226622841, -0.11269198045752861, -0.1584272925015202, -0.19399934028423443, -0.21261299970836234, -0.20876786951218076, -0.178998750642845, -0.12242457836706144, -0.04104159008622749, 0.06028458057379472, 0.17413298436743746, 0.29111947521908144, 0.40072049860483366, 0.49225780923377377, 0.5559545014291596, 0.5839625354404918, 0.5712615329973366, 0.5163322193690063, 0.42152143120117846, 0.29306889311126527, 0.14078115660607146, -0.022634914451700874, -0.18252951926281613, -0.32348036708777267, -0.43058711718083187, -0.49078323057217854, -0.4940722568141172, -0.4345048379856669, -0.31082101036704207, -0.12674733408093652, 0.1091094563547142, 0.38378870784330615, 0.6809153575305918, 0.9818728733241954, 1.2671967988124155, 1.5181424608124017, 1.7181825770853754, 1.8542860591263863, 1.9179457922788852, 1.9058499646304865, 1.8201378129913122, 1.6682280081995735, 1.4622271517326022, 1.217869867192596, 0.9532535634091852, 0.6872645495135217, 0.4379779860032215, 0.22119092046637986, 0.04916878108386255, -0.07028838005639589, -0.13437985209677916, -0.14539282440546303, -0.11033818803004002, -0.04016007164593994, 0.051435133820184616, 0.14940846303068953, 0.23892704460753536, 0.306872111948133, 0.3431777014877156, 0.34187525367011506, 0.30174407539261383, 0.22650292877739492, 0.12451430380426391, 0.007996521430510835, -0.10817069404495641, -0.207934575899071, -0.2757159557681655, -0.29806016540428154, -0.26513445009624476, -0.1719243596960356, -0.01900525555242984, 0.18720087812716102, 0.4347297729075121, 0.7069691870868983, 0.9840327626041084, 1.2445002824487552, 1.4673751993332194, 1.6340789537461458, 1.7302908151240401, 1.7474605518593307, 1.6838237241120675, 1.544750721214237, 1.342418000005254, 1.094757272852075, 0.8237707900021246, 0.5533504623844618, 0.3067905188184447, 0.10422928281257125, -0.03972005099477538, -0.11788879592602719, -0.13177233952098985, -0.09185412353581346, -0.016907990228872658, 0.06777143503401116, 0.1331491855241426, 0.15008349491949102, 0.09356074035524117, -0.05280494624839114, -0.2924211603005448, -0.6119322292055204, -0.978414356019265, -1.3379514428429504, -1.6159222078970312, -1.719191785592754, -1.5403062973335726, -0.963632316954566, 0.12680932347316842, 1.8383024956739342, 4.259614004415216, 7.450979018787143, 11.434612736727908, 16.18652929122448, 21.630557034588257, 27.63483658639912, 34.01152644111567, 40.52099433951598, 46.878880138755214, 52.76596691841686, 57.84157198319226, 61.759539494782494, 64.1860934496821, 64.81885646050077, 63.406226092331835, 59.76446690948287, 53.79382765025091, 45.48826246432401, 34.941140196737784, 22.34714161898671, 7.9990793547211965, -7.720437522735965, -24.352283235070356, -41.378635260428545, -58.24527419882948, -74.38840382345097, -89.26067419888162, -102.35580459398669, -113.23187192435572, -121.53176256628348, -126.99970399666879, -129.49298902733526, -128.98825164537794, -125.58356662885816, -119.49764833679032, -111.05278680144772, -100.65591975597036, -88.77756722679784, -75.92816761489158, -62.633094029828506, -49.40767583691994, -36.7335253007812, -25.038280119099515, -14.678712482372454, -5.924057062148472, 1.0524047762690796, 6.1754534901473415, 9.464735807452625, 11.026746877965527, 11.04268400089459, 9.753063910285642, 7.440091495119009, 4.4091085715826095, 0.96981507285203, -2.5821979107084605, -5.980877468137424, -9.002117344680228, -11.47269423977645, -13.27536306826882, -14.350101636950301, -14.691816683542346, -14.34490233258122, -13.39496731648732, -11.958801755204602, -10.17335005897324, -8.183636879895117, -6.131766903681514, -4.147402637033841, -2.340101787037184, -0.7939353073778082, 0.4356117557525986, 1.3224243986686914, 1.8682020486005597, 2.099004422763144, 2.060377477866912, 1.811359925724003, 1.4180710354972559, 0.9474685874884718, 0.46174191439506707, 0.013750379481491305, -0.3562500711839028, -0.6224485933165526, -0.7738562944010385, -0.8133202374535481, -0.7553881743809318, -0.6233075517584001, -0.4454830093297362, -0.2517610343948939, -0.06996412047617448, 0.07704245084352895, 0.17354642940005924, 0.21227680817158986, 0.19471999961568046, 0.13049215478039053, 0.035878449300499014, -0.0682820968961427, -0.15913063378041256, -0.21443993466046854, -0.21510800201844316, -0.14727746079284593, -0.0038867364172631763, 0.214481330849702, 0.49951842138618147, 0.8358718206873345, 1.202533408499214, 1.574832699123384, 1.9266937050154682, 2.2329688527768488, 2.47166889405651, 2.6258744492454396, 2.6851601070523907, 2.646409955831898, 2.5139611600585994, 2.299096044180636, 2.018945937745614, 1.6947439197895853, 1.349810154872962, 1.0074363579380703, 0.688846639707318, 0.41142627657454917, 0.1873825835016665, 0.02295984192062263, -0.08172691060352737, -0.13225147736331166, -0.1388147610970414, -0.11466949709417167, -0.07426228747752002, -0.0312809060747479, 0.003202448370290075, 0.022310645637241222, 0.024508884044694566, 0.014207636475692195, 0.0017338376339139548, 0.0026311237392360894, 0.03633768890581166, 0.12431225404664742, 0.2877448754918077, 0.5450465989146247, 0.909350978406012, 1.3862903216142424, 1.9731343597747208, 2.659693221294798, 3.428742890198886, 4.257389903474928, 5.119020978492342, 5.985311385965964, 6.828231475025892, 7.621879470815152], 'positive_zeros': ['0.69892488463632954080049801154402', '1.08167113336342232021338488684845', '1.29179929140820329567421659300690', '1.58094450702948420210521010288595', '1.58868602312400784293260916095054', '1.75076773683840588523257063324308', '1.75242890150317825559568806169934', '1.86849589453599506482216752853172', '2.32469343134141155024194326992784', '2.57711630219261795855528040253227', '2.75672644026665761760217654210186', '2.76516195765349480175014134749330', '2.84685167386361119024353477069449', '2.87802444583166537838806422201274', '2.94473655255086045954646538006785', '3.17548301210851036533894362356241', '3.21771539877576185127359244040711', '3.33836695661678577911828177384576', '3.54706420153946336799167714219889', '3.68242528829453880750944554045912', '3.96290099593183505446946579414828', '4.03424171486995322608799756395449', '4.12594544828655133336517240552000', '4.21715688595092454354017600331695', '4.27435616543027688599293677642467', '4.30303614741715968221742696625653', '4.41655718856941009212755252853312', '4.51167900772820538936218123804989', '4.51694185368309456361417825426547', '4.67181356009759640494547325871262', '4.92728211334998262407824971900257', '5.11165067738625088016993416568962', '5.24537175711563151612792788016298', '5.29290647433709432763528592694366', '5.31388113850336895736423075191545', '5.35927112105940427775239026534007', '5.40561262747461187878143608390877', '5.59666395868016421165784858846193', '5.70586004560543452217094277226953', '5.89380902730138805147289864985681', '5.94406303034001711086965690269275', '6.07186956747623885500942892831419', '6.10372996718466171452642731237206', '6.19665482023662209398362709505646', '6.20030342167373170552057812577946', '6.33082224720112659433220290839045', '6.50049254850791842361383825201445', '6.60118075920448996265039787227454', '6.63891013325751643506536516144761', '6.82001308470713655911223875151427', '7.00502159396321278931585453721339', '7.20463472799048699962209792798808', '7.21928966074401204854877349668084', '7.28354033152345626580383033123309', '7.37139635633646761731864896599519', '7.38496207794092084230508181009170', '7.40895467587262347789703142793731', '7.48071415296837526920889921304990', '7.56272487992331995564961089885100', '7.61832162504029627729656605240297', '7.73938148756038747843641448497688', '7.944518889506522074496276916402176', '8.101504817196048801056103086591696', '8.172030248698898933025317667774321', '8.254191448050776962099371046780140', '8.339777551692575766201336303197617', '8.492352283569794649590153694681897', '8.493639106956915661775305809502285', '8.581531096933220064041983889545719', '8.596005007117868165049421264053526', '8.826463914515575876748608442561485', '8.866067464769811840017111462029171', '8.980041649467024683216504472391706', '8.987846285820546744220578433762580', '8.991723383906002214315223545133587', '9.105011546612357433350426301277880', '9.275274886223014655142332256852289', '9.305864898151225342315397977276719', '9.365861102899285223212664116522762', '9.532841644839207859605731192261682', '9.781916091412628672682392649143657', '9.907634839635450973141096397321376', '9.921588278842032983135559572342678', '9.944957592369350687529872552665439', '9.961924746620929448984832494677019', '9.965536072002555115953592771242805', '10.09497725063524907866220463412142', '10.11529833137180412414193035459919', '10.11621821218917870352779865544690', '10.27798518780679424793239651909166', '10.36845159506557929983113229272212', '10.40303804568085267783619366206748', '10.66054979992176061294593933878731', '10.84422192717041471731034715964196', '10.85545211085577777546965700502151', '10.94164887489757042394218859720970', '11.03487554408533755547804289615216', '11.15086272146456864712577242481714', '11.39728731208748837274958687875967', '11.39746230090687073563468215905164'], 'prelabel': '20-603e10-1.1-c0e10-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.5485765239396415, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c0e10-0', 'trace_hash': 1099356525989144377, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.69892488463632954080049801154', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.08167113336342232021338488685', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.29179929140820329567421659301', 'prec': 103}}
• 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': 6.091782163647771e-06, 'bad_primes': [3, 67], 'central_character': '1.1', 'conductor': 6355842422464168617446357049, 'conductor_radical': 201, 'degree': 20, 'dirichlet_coefficients': [1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -9, 0, 0, -2, 0, 0, -11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'euler11': [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], 'euler13': [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], 'euler17': [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], 'euler19': [1, -2, 3, -4, 5, -6, 7, -8, 9, -10, 11, -10, 9, -8, 7, -6, 5, -4, 3, -2, 1], 'euler2': [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], 'euler23': [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], 'euler29': [1, 0, 10, 0, 45, 0, 120, 0, 210, 0, 252, 0, 210, 0, 120, 0, 45, 0, 10, 0, 1], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], 'euler37': [1, -2, 3, -4, 5, -6, 7, -8, 9, -10, 11, -10, 9, -8, 7, -6, 5, -4, 3, -2, 1], 'euler41': [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], 'euler43': [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], 'euler47': [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], 'euler5': [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], 'euler53': [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], 'euler59': [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], 'euler61': [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], 'euler67': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler7': [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], 'euler71': [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], 'euler73': [1, 9, 36, 84, 126, 126, 84, 36, 9, 1, 0, 1, 9, 36, 84, 126, 126, 84, 36, 9, 1], 'euler79': [1, 11, 56, 176, 386, 638, 848, 968, 1013, 1023, 1024, 1023, 1013, 968, 848, 638, 386, 176, 56, 11, 1], 'euler83': [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], 'euler89': [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], 'euler97': [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], 'euler_factors': [[1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], [1, -2, 3, -4, 5, -6, 7, -8, 9, -10, 11, -10, 9, -8, 7, -6, 5, -4, 3, -2, 1], [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], [1, 0, 10, 0, 45, 0, 120, 0, 210, 0, 252, 0, 210, 0, 120, 0, 45, 0, 10, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, -2, 3, -4, 5, -6, 7, -8, 9, -10, 11, -10, 9, -8, 7, -6, 5, -4, 3, -2, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], [1, 9, 36, 84, 126, 126, 84, 36, 9, 1, 0, 1, 9, 36, 84, 126, 126, 84, 36, 9, 1], [1, 11, 56, 176, 386, 638, 848, 968, 1013, 1023, 1024, 1023, 1013, 968, 848, 638, 386, 176, 56, 11, 1], [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/603/1/x/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': '20-603e10-1.1-c0e10-0-0', '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}, {'__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, 0, 0], 'order_of_vanishing': 0, 'prelabel': '20-603e10-1.1-c0e10-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.5485765239396415, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e10-0', 'trace_hash': 1099356525989144377, 'z1': {'__RealLiteral__': 0, 'data': '0.69892488463632954080049801154', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '885992549523689132305177609084,1371181061457691477655683990401,1637550147128010331815357602058,2004085253263447885128030522998,2013898790787347276721997661178,2219361772463423996196966258511,2221467548847800616968422754267,2368599942232536565227856787475,2946899023586562547009497194760,3266883027332427181970194446667', 'Lhash_array': ['885992549523689132305177609084', '1371181061457691477655683990401', '1637550147128010331815357602058', '2004085253263447885128030522998', '2013898790787347276721997661178', '2219361772463423996196966258511', '2221467548847800616968422754267', '2368599942232536565227856787475', '2946899023586562547009497194760', '3266883027332427181970194446667'], 'label': '20-603e10-1.1-c0e10-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/603/1/x/a'}