Lfunction data - 2-4001-1.1-c1-0-119

Formats: - HTML - YAML - JSON - 2024-12-26T19:51:10.864108

• 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': '1059154537273907908886793444813', 'a10': [7.5298989771859475, 0.0], 'a2': [-1.8222507681052746, 0.0], 'a3': [2.6860568675584067, 0.0], 'a4': [1.3205978618602632, 0.0], 'a5': [-4.1321969012065916, 0.0], 'a6': [-4.894669190082754, 0.0], 'a7': [5.175653604973875, 0.0], 'a8': [1.2380410680775011, 0.0], 'a9': [4.2149014957576805, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 31.948145848714297, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [], 'bad_primes': [4001], 'central_character': '4001.1', 'coefficient_field': 'CDF', 'conductor': 4001, 'conductor_radical': 4001, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.8222507681052746, 0], [2.0, 0]], [[1.0, 0], [-2.6860568675584067, 0], [3.0, 0]], [[1.0, 0], [4.1321969012065916, 0], [5.0, 0]], [[1.0, 0], [-5.175653604973875, 0], [7.0, 0]], [[1.0, 0], [3.0057792646962302, 0], [11.0, 0]], [[1.0, 0], [-0.4873037555144178, 0], [13.0, 0]], [[1.0, 0], [-1.2745561018156124, 0], [17.0, 0]], [[1.0, 0], [-5.379398905030023, 0], [19.0, 0]], [[1.0, 0], [0.08847479180424335, 0], [23.0, 0]], [[1.0, 0], [-2.3262194515992927, 0], [29.0, 0]], [[1.0, 0], [-7.572110548605826, 0], [31.0, 0]], [[1.0, 0], [4.843455907116237, 0], [37.0, 0]], [[1.0, 0], [1.449115929643512, 0], [41.0, 0]], [[1.0, 0], [10.7400260566324, 0], [43.0, 0]], [[1.0, 0], [-1.0241247186989526, 0], [47.0, 0]], [[1.0, 0], [-2.552997671056547, 0], [53.0, 0]], [[1.0, 0], [0.41568689937414577, 0], [59.0, 0]], [[1.0, 0], [4.779107496245184, 0], [61.0, 0]], [[1.0, 0], [3.5593477329069496, 0], [67.0, 0]], [[1.0, 0], [5.501772564426999, 0], [71.0, 0]], [[1.0, 0], [-4.20005791034133, 0], [73.0, 0]], [[1.0, 0], [-16.62517848386499, 0], [79.0, 0]], [[1.0, 0], [-11.060373001872337, 0], [83.0, 0]], [[1.0, 0], [-7.342811619469918, 0], [89.0, 0]], [[1.0, 0], [16.741214042887414, 0], [97.0, 0]], [[1.0, 0], [7.016323952896866, 0], [101.0, 0]], [[1.0, 0], [0.9481464796974735, 0], [103.0, 0]], [[1.0, 0], [-1.5175881910841051, 0], [107.0, 0]], [[1.0, 0], [-14.332778495984936, 0], [109.0, 0]], [[1.0, 0], [-13.479611925346244, 0], [113.0, 0]], [[1.0, 0], [-3.8822631642731196, 0], [127.0, 0]], [[1.0, 0], [-11.622532871730373, 0], [131.0, 0]], [[1.0, 0], [13.76343799684486, 0], [137.0, 0]], [[1.0, 0], [-18.73509511504866, 0], [139.0, 0]], [[1.0, 0], [-17.098705538937857, 0], [149.0, 0]], [[1.0, 0], [-0.1020873217587426, 0], [151.0, 0]], [[1.0, 0], [-6.494647524785015, 0], [157.0, 0]], [[1.0, 0], [-6.359267198316139, 0], [163.0, 0]], [[1.0, 0], [6.027805324359678, 0], [167.0, 0]], [[1.0, 0], [21.162851145530862, 0], [173.0, 0]], [[1.0, 0], [-15.551486490824384, 0], [179.0, 0]], [[1.0, 0], [6.44124812983572, 0], [181.0, 0]], [[1.0, 0], [-5.656048731294474, 0], [191.0, 0]], [[1.0, 0], [8.10005985580299, 0], [193.0, 0]], [[1.0, 0], [10.583766201181618, 0], [197.0, 0]], [[1.0, 0], [21.155077058307633, 0], [199.0, 0]], [[1.0, 0], [0.5923616295925963, 0], [211.0, 0]], [[1.0, 0], [-12.434932623318439, 0], [223.0, 0]], [[1.0, 0], [-15.863774714680394, 0], [227.0, 0]], [[1.0, 0], [-9.32801503189796, 0], [229.0, 0]], [[1.0, 0], [-21.020202977916327, 0], [233.0, 0]], [[1.0, 0], [8.075364115432478, 0], [239.0, 0]], [[1.0, 0], [-16.075605409686922, 0], [241.0, 0]], [[1.0, 0], [-3.307271770395519, 0], [251.0, 0]], [[1.0, 0], [2.7339726917349676, 0], [257.0, 0]], [[1.0, 0], [-23.827985160569426, 0], [263.0, 0]], [[1.0, 0], [-12.168229079090905, 0], [269.0, 0]], [[1.0, 0], [20.338431321821993, 0], [271.0, 0]], [[1.0, 0], [-9.702527225878445, 0], [277.0, 0]], [[1.0, 0], [-26.263671676233248, 0], [281.0, 0]], [[1.0, 0], [-8.582080912624141, 0], [283.0, 0]], [[1.0, 0], [0.13331835193266894, 0], [293.0, 0]], [[1.0, 0], [26.582343121340564, 0], [307.0, 0]], [[1.0, 0], [-19.425496703706624, 0], [311.0, 0]], [[1.0, 0], [5.800863150551898, 0], [313.0, 0]], [[1.0, 0], [-31.44236896694211, 0], [317.0, 0]], [[1.0, 0], [-11.417733044070898, 0], [331.0, 0]], [[1.0, 0], [-26.187102437770633, 0], [337.0, 0]], [[1.0, 0], [28.580527279708793, 0], [347.0, 0]], [[1.0, 0], [-24.130068266568813, 0], [349.0, 0]], [[1.0, 0], [33.33886020454577, 0], [353.0, 0]], [[1.0, 0], [-21.55356641039363, 0], [359.0, 0]], [[1.0, 0], [-17.480740972435925, 0], [367.0, 0]], [[1.0, 0], [-4.907800015265053, 0], [373.0, 0]], [[1.0, 0], [22.657439076728583, 0], [379.0, 0]], [[1.0, 0], [5.15568898818938, 0], [383.0, 0]], [[1.0, 0], [27.033869364855722, 0], [389.0, 0]], [[1.0, 0], [-20.348026700113913, 0], [397.0, 0]], [[1.0, 0], [37.36935395323804, 0], [401.0, 0]], [[1.0, 0], [-30.480134828693842, 0], [409.0, 0]], [[1.0, 0], [-21.63027247138194, 0], [419.0, 0]], [[1.0, 0], [22.12900874236869, 0], [421.0, 0]], [[1.0, 0], [-30.467605323059754, 0], [431.0, 0]], [[1.0, 0], [-20.375319289527557, 0], [433.0, 0]], [[1.0, 0], [-27.803705004917912, 0], [439.0, 0]], [[1.0, 0], [13.037904726533675, 0], [443.0, 0]], [[1.0, 0], [-2.1215910295547156, 0], [449.0, 0]], [[1.0, 0], [-31.217379237367258, 0], [457.0, 0]], [[1.0, 0], [-15.816251124531819, 0], [461.0, 0]], [[1.0, 0], [2.894697311767413, 0], [463.0, 0]], [[1.0, 0], [-8.961526430875566, 0], [467.0, 0]], [[1.0, 0], [35.262264813588644, 0], [479.0, 0]], [[1.0, 0], [9.78816338448128, 0], [487.0, 0]], [[1.0, 0], [-10.20683697309852, 0], [491.0, 0]], [[1.0, 0], [7.898856958492355, 0], [499.0, 0]], [[1.0, 0], [-42.06624555717111, 0], [503.0, 0]], [[1.0, 0], [20.133320522488425, 0], [509.0, 0]], [[1.0, 0], [16.01051941080706, 0], [521.0, 0]], [[1.0, 0], [-1.3551462999074817, 0], [523.0, 0]], [[1.0, 0], [-33.10803009963694, 0], [541.0, 0]], [[1.0, 0], [26.353074031626377, 0], [547.0, 0]], [[1.0, 0], [-24.185755475401834, 0], [557.0, 0]], [[1.0, 0], [19.543415327706487, 0], [563.0, 0]], [[1.0, 0], [10.00909443286815, 0], [569.0, 0]], [[1.0, 0], [8.285336062404541, 0], [571.0, 0]], [[1.0, 0], [-9.429527589260903, 0], [577.0, 0]], [[1.0, 0], [21.825730301156813, 0], [587.0, 0]], [[1.0, 0], [-39.59616084326592, 0], [593.0, 0]], [[1.0, 0], [-29.400420563573224, 0], [599.0, 0]], [[1.0, 0], [24.857956150811603, 0], [601.0, 0]], [[1.0, 0], [-24.25232813910015, 0], [607.0, 0]], [[1.0, 0], [17.99988953753437, 0], [613.0, 0]], [[1.0, 0], [30.069597618148023, 0], [617.0, 0]], [[1.0, 0], [43.503594699759674, 0], [619.0, 0]], [[1.0, 0], [32.68877752552569, 0], [631.0, 0]], [[1.0, 0], [-28.351458744089157, 0], [641.0, 0]], [[1.0, 0], [5.7884298942169226, 0], [643.0, 0]], [[1.0, 0], [-25.47870755960126, 0], [647.0, 0]], [[1.0, 0], [-23.058659552538288, 0], [653.0, 0]], [[1.0, 0], [24.61131447170126, 0], [659.0, 0]], [[1.0, 0], [19.86084646921007, 0], [661.0, 0]], [[1.0, 0], [26.932735198910326, 0], [673.0, 0]], [[1.0, 0], [18.92889356657889, 0], [677.0, 0]], [[1.0, 0], [38.85895074533356, 0], [683.0, 0]], [[1.0, 0], [43.62664176847107, 0], [691.0, 0]], [[1.0, 0], [46.156846101419674, 0], [701.0, 0]], [[1.0, 0], [8.255974933642667, 0], [709.0, 0]], [[1.0, 0], [-8.867490581390994, 0], [719.0, 0]], [[1.0, 0], [31.012661710604416, 0], [727.0, 0]], [[1.0, 0], [6.913229605564305, 0], [733.0, 0]], [[1.0, 0], [-32.232047693411495, 0], [739.0, 0]], [[1.0, 0], [46.51432255617376, 0], [743.0, 0]], [[1.0, 0], [-41.36712549749878, 0], [751.0, 0]], [[1.0, 0], [3.996125757485105, 0], [757.0, 0]], [[1.0, 0], [-18.363200679104782, 0], [761.0, 0]], [[1.0, 0], [18.265833430202377, 0], [769.0, 0]], [[1.0, 0], [13.055895124132084, 0], [773.0, 0]], [[1.0, 0], [42.34105761072043, 0], [787.0, 0]], [[1.0, 0], [-54.003010085360586, 0], [797.0, 0]], [[1.0, 0], [-18.99007151710142, 0], [809.0, 0]], [[1.0, 0], [1.9900768322676818, 0], [811.0, 0]], [[1.0, 0], [13.631968215806294, 0], [821.0, 0]], [[1.0, 0], [21.417222154758264, 0], [823.0, 0]], [[1.0, 0], [9.715691589317908, 0], [827.0, 0]], [[1.0, 0], [32.085116617066, 0], [829.0, 0]], [[1.0, 0], [-2.5223263896643013, 0], [839.0, 0]], [[1.0, 0], [28.378294154112044, 0], [853.0, 0]], [[1.0, 0], [-20.001301945255914, 0], [857.0, 0]], [[1.0, 0], [55.84590709164796, 0], [859.0, 0]], [[1.0, 0], [10.765370748022331, 0], [863.0, 0]], [[1.0, 0], [13.82070921552333, 0], [877.0, 0]], [[1.0, 0], [5.2664548119462715, 0], [881.0, 0]], [[1.0, 0], [5.439370285661112, 0], [883.0, 0]], [[1.0, 0], [-25.59933611401778, 0], [887.0, 0]], [[1.0, 0], [22.59120788823116, 0], [907.0, 0]], [[1.0, 0], [-40.52382107578468, 0], [911.0, 0]], [[1.0, 0], [-56.529427333412606, 0], [919.0, 0]], [[1.0, 0], [24.70821932753459, 0], [929.0, 0]], [[1.0, 0], [-40.69153938982032, 0], [937.0, 0]], [[1.0, 0], [-25.75009695485646, 0], [941.0, 0]], [[1.0, 0], [-53.06533879067967, 0], [947.0, 0]], [[1.0, 0], [-17.797832794170407, 0], [953.0, 0]], [[1.0, 0], [33.37582899457678, 0], [967.0, 0]], [[1.0, 0], [18.54270026883167, 0], [971.0, 0]], [[1.0, 0], [-32.60892325562932, 0], [977.0, 0]], [[1.0, 0], [59.83241046639277, 0], [983.0, 0]], [[1.0, 0], [28.06614873665378, 0], [991.0, 0]], [[1.0, 0], [40.715967887723174, 0], [997.0, 0]], [[1.0, 0], [-26.748412922197073, 0], [1009.0, 0]], [[1.0, 0], [49.557099710600156, 0], [1013.0, 0]], [[1.0, 0], [44.651637493624065, 0], [1019.0, 0]], [[1.0, 0], [-9.01203459495576, 0], [1021.0, 0]], [[1.0, 0], [12.558910253193563, 0], [1031.0, 0]], [[1.0, 0], [26.809623070928975, 0], [1033.0, 0]], [[1.0, 0], [29.221930182261943, 0], [1039.0, 0]], [[1.0, 0], [11.325858792261185, 0], [1049.0, 0]], [[1.0, 0], [-53.366840734683876, 0], [1051.0, 0]], [[1.0, 0], [-51.72926212914435, 0], [1061.0, 0]], [[1.0, 0], [6.812977304071393, 0], [1063.0, 0]], [[1.0, 0], [8.848039364978534, 0], [1069.0, 0]], [[1.0, 0], [7.467693021569776, 0], [1087.0, 0]], [[1.0, 0], [28.531486371510702, 0], [1091.0, 0]], [[1.0, 0], [-62.54191942507169, 0], [1093.0, 0]], [[1.0, 0], [30.006718371230775, 0], [1097.0, 0]], [[1.0, 0], [39.89312577040887, 0], [1103.0, 0]], [[1.0, 0], [52.36516759429463, 0], [1109.0, 0]], [[1.0, 0], [34.2455287648589, 0], [1117.0, 0]], [[1.0, 0], [64.82258887773952, 0], [1123.0, 0]], [[1.0, 0], [-21.07207547728843, 0], [1129.0, 0]], [[1.0, 0], [11.43438585282547, 0], [1151.0, 0]], [[1.0, 0], [45.319287887800186, 0], [1153.0, 0]], [[1.0, 0], [55.1373936053621, 0], [1163.0, 0]], [[1.0, 0], [-40.69878616517256, 0], [1171.0, 0]], [[1.0, 0], [-11.475511106273391, 0], [1181.0, 0]], [[1.0, 0], [-7.78165886233936, 0], [1187.0, 0]], [[1.0, 0], [-49.66003041744621, 0], [1193.0, 0]], [[1.0, 0], [-14.793466720016411, 0], [1201.0, 0]], [[1.0, 0], [0.24646469739884694, 0], [1213.0, 0]], [[1.0, 0], [68.00439775734596, 0], [1217.0, 0]], [[1.0, 0], [-49.43904024511275, 0], [1223.0, 0]], [[1.0, 0], [13.994680424798666, 0], [1229.0, 0]], [[1.0, 0], [-16.842945398607238, 0], [1231.0, 0]], [[1.0, 0], [5.493723171512897, 0], [1237.0, 0]], [[1.0, 0], [-20.090144619839133, 0], [1249.0, 0]], [[1.0, 0], [42.035450727052854, 0], [1259.0, 0]], [[1.0, 0], [-65.17224062328137, 0], [1277.0, 0]], [[1.0, 0], [-28.25752825866222, 0], [1279.0, 0]], [[1.0, 0], [42.37184395365697, 0], [1283.0, 0]], [[1.0, 0], [2.5783536533198843, 0], [1289.0, 0]], [[1.0, 0], [-4.116049541893059, 0], [1291.0, 0]], [[1.0, 0], [-44.526350848504656, 0], [1297.0, 0]], [[1.0, 0], [-53.61589010325216, 0], [1301.0, 0]], [[1.0, 0], [-17.096847673261784, 0], [1303.0, 0]], [[1.0, 0], [63.39898668214411, 0], [1307.0, 0]], [[1.0, 0], [1.0681196672810251, 0], [1319.0, 0]], [[1.0, 0], [14.900442838560123, 0], [1321.0, 0]], [[1.0, 0], [-2.779864969979231, 0], [1327.0, 0]], [[1.0, 0], [-12.159574724332192, 0], [1361.0, 0]], [[1.0, 0], [10.074745652370297, 0], [1367.0, 0]], [[1.0, 0], [29.716967627290124, 0], [1373.0, 0]], [[1.0, 0], [-48.68273853510618, 0], [1381.0, 0]], [[1.0, 0], [-22.565771596328563, 0], [1399.0, 0]], [[1.0, 0], [-22.52706161330577, 0], [1409.0, 0]], [[1.0, 0], [17.89643562073709, 0], [1423.0, 0]], [[1.0, 0], [72.69488766775724, 0], [1427.0, 0]], [[1.0, 0], [-45.277566921791326, 0], [1429.0, 0]], [[1.0, 0], [14.41517540153901, 0], [1433.0, 0]], [[1.0, 0], [51.97450171921122, 0], [1439.0, 0]], [[1.0, 0], [67.71822074983248, 0], [1447.0, 0]], [[1.0, 0], [-17.828986240079008, 0], [1451.0, 0]], [[1.0, 0], [60.66620830307266, 0], [1453.0, 0]], [[1.0, 0], [23.947170321743677, 0], [1459.0, 0]], [[1.0, 0], [27.694333609748394, 0], [1471.0, 0]], [[1.0, 0], [-7.193346775861697, 0], [1481.0, 0]], [[1.0, 0], [26.24192211545607, 0], [1483.0, 0]], [[1.0, 0], [55.285271630810264, 0], [1487.0, 0]], [[1.0, 0], [60.32657298037705, 0], [1489.0, 0]], [[1.0, 0], [-2.9324307165990504, 0], [1493.0, 0]], [[1.0, 0], [38.794357936337875, 0], [1499.0, 0]], [[1.0, 0], [2.480440376694463, 0], [1511.0, 0]], [[1.0, 0], [53.77914357397728, 0], [1523.0, 0]], [[1.0, 0], [-25.48129194871779, 0], [1531.0, 0]], [[1.0, 0], [-29.256359234565362, 0], [1543.0, 0]], [[1.0, 0], [-30.21959370098851, 0], [1549.0, 0]], [[1.0, 0], [-9.175396846555456, 0], [1553.0, 0]], [[1.0, 0], [-47.500094738452916, 0], [1559.0, 0]], [[1.0, 0], [46.10854448722499, 0], [1567.0, 0]], [[1.0, 0], [41.01243195362836, 0], [1571.0, 0]], [[1.0, 0], [29.634810370026692, 0], [1579.0, 0]], [[1.0, 0], [-48.85252531668629, 0], [1583.0, 0]], [[1.0, 0], [37.15525040358008, 0], [1597.0, 0]], [[1.0, 0], [56.38740101627004, 0], [1601.0, 0]], [[1.0, 0], [40.44396792848479, 0], [1607.0, 0]], [[1.0, 0], [41.106127026020445, 0], [1609.0, 0]], [[1.0, 0], [-8.772356686441697, 0], [1613.0, 0]], [[1.0, 0], [-28.089168052686105, 0], [1619.0, 0]], [[1.0, 0], [27.335486380983106, 0], [1621.0, 0]], [[1.0, 0], [18.294218509996938, 0], [1627.0, 0]], [[1.0, 0], [55.952736265767676, 0], [1637.0, 0]], [[1.0, 0], [-29.464227856701573, 0], [1657.0, 0]], [[1.0, 0], [-43.58562938302404, 0], [1663.0, 0]], [[1.0, 0], [-56.63212651884594, 0], [1667.0, 0]], [[1.0, 0], [12.700498014658367, 0], [1669.0, 0]], [[1.0, 0], [65.24626032528815, 0], [1693.0, 0]], [[1.0, 0], [33.160920744411776, 0], [1697.0, 0]], [[1.0, 0], [70.37005293159636, 0], [1699.0, 0]], [[1.0, 0], [40.65993297159732, 0], [1709.0, 0]], [[1.0, 0], [14.460383571333153, 0], [1721.0, 0]], [[1.0, 0], [-10.572450285320597, 0], [1723.0, 0]], [[1.0, 0], [23.981274502457318, 0], [1733.0, 0]], [[1.0, 0], [-50.68796291088095, 0], [1741.0, 0]], [[1.0, 0], [2.0764982847516733, 0], [1747.0, 0]], [[1.0, 0], [-19.653524720971586, 0], [1753.0, 0]], [[1.0, 0], [-13.756529497221003, 0], [1759.0, 0]], [[1.0, 0], [-54.754407942803375, 0], [1777.0, 0]], [[1.0, 0], [-30.007497647237756, 0], [1783.0, 0]], [[1.0, 0], [-14.627354755289142, 0], [1787.0, 0]], [[1.0, 0], [-9.151508301054381, 0], [1789.0, 0]], [[1.0, 0], [8.817732767905694, 0], [1801.0, 0]], [[1.0, 0], [43.7291840019834, 0], [1811.0, 0]], [[1.0, 0], [19.224691926641633, 0], [1823.0, 0]], [[1.0, 0], [-57.26575620482117, 0], [1831.0, 0]], [[1.0, 0], [-31.731344298191065, 0], [1847.0, 0]], [[1.0, 0], [-75.38325190582519, 0], [1861.0, 0]], [[1.0, 0], [-26.198100369395018, 0], [1867.0, 0]], [[1.0, 0], [-13.524265207261452, 0], [1871.0, 0]], [[1.0, 0], [-65.62776787066964, 0], [1873.0, 0]], [[1.0, 0], [-43.69617799683353, 0], [1877.0, 0]], [[1.0, 0], [-5.779109143161859, 0], [1879.0, 0]], [[1.0, 0], [-36.1709986436565, 0], [1889.0, 0]], [[1.0, 0], [-63.39624697067406, 0], [1901.0, 0]], [[1.0, 0], [1.0656770535550977, 0], [1907.0, 0]], [[1.0, 0], [72.45900207165774, 0], [1913.0, 0]], [[1.0, 0], [20.961898972262752, 0], [1931.0, 0]], [[1.0, 0], [21.59294753853271, 0], [1933.0, 0]], [[1.0, 0], [-0.3166186710739553, 0], [1949.0, 0]], [[1.0, 0], [-41.15145340355558, 0], [1951.0, 0]], [[1.0, 0], [-24.112160934775616, 0], [1973.0, 0]], [[1.0, 0], [1.9343129062768385, 0], [1979.0, 0]], [[1.0, 0], [-3.3636617583901627, 0], [1987.0, 0]], [[1.0, 0], [-41.74733380177239, 0], [1993.0, 0]], [[1.0, 0], [-34.213133489814275, 0], [1997.0, 0]], [[1.0, 0], [-84.51377443092447, 0], [1999.0, 0]], [[1.0, 0], [-37.9668535214633, 0], [2003.0, 0]], [[1.0, 0], [29.181054486085706, 0], [2011.0, 0]], [[1.0, 0], [-47.68215095852079, 0], [2017.0, 0]], [[1.0, 0], [-37.51133653347254, 0], [2027.0, 0]], [[1.0, 0], [-72.23978405603913, 0], [2029.0, 0]], [[1.0, 0], [27.019644168271352, 0], [2039.0, 0]], [[1.0, 0], [-27.03203468899749, 0], [2053.0, 0]], [[1.0, 0], [-35.05774264255009, 0], [2063.0, 0]], [[1.0, 0], [71.21838885894681, 0], [2069.0, 0]], [[1.0, 0], [85.83796816151785, 0], [2081.0, 0]], [[1.0, 0], [-34.406264677438585, 0], [2083.0, 0]], [[1.0, 0], [-34.393144575198065, 0], [2087.0, 0]], [[1.0, 0], [-26.856800806892732, 0], [2089.0, 0]], [[1.0, 0], [-85.87572219774889, 0], [2099.0, 0]], [[1.0, 0], [77.73177405122273, 0], [2111.0, 0]], [[1.0, 0], [67.04736561274218, 0], [2113.0, 0]], [[1.0, 0], [73.74010011383328, 0], [2129.0, 0]], [[1.0, 0], [9.617611563456586, 0], [2131.0, 0]], [[1.0, 0], [21.78347770742554, 0], [2137.0, 0]], [[1.0, 0], [35.14303716068747, 0], [2141.0, 0]], [[1.0, 0], [-61.67660415343452, 0], [2143.0, 0]], [[1.0, 0], [11.608545282399856, 0], [2153.0, 0]], [[1.0, 0], [-22.977285927730307, 0], [2161.0, 0]], [[1.0, 0], [-63.69942936690621, 0], [2179.0, 0]], [[1.0, 0], [-15.357682353342595, 0], [2203.0, 0]], [[1.0, 0], [61.001882573673186, 0], [2207.0, 0]], [[1.0, 0], [45.83636521622963, 0], [2213.0, 0]], [[1.0, 0], [70.13251789293425, 0], [2221.0, 0]], [[1.0, 0], [-53.933570349587725, 0], [2237.0, 0]], [[1.0, 0], [34.11320584935037, 0], [2239.0, 0]], [[1.0, 0], [-61.44805185750628, 0], [2243.0, 0]], [[1.0, 0], [-0.4645501266477637, 0], [2251.0, 0]], [[1.0, 0], [-4.332466779248088, 0], [2267.0, 0]], [[1.0, 0], [37.29074700007681, 0], [2269.0, 0]], [[1.0, 0], [-11.263144238432004, 0], [2273.0, 0]], [[1.0, 0], [-41.578188151221, 0], [2281.0, 0]], [[1.0, 0], [-46.37383929820871, 0], [2287.0, 0]], [[1.0, 0], [-38.40211638118783, 0], [2293.0, 0]], [[1.0, 0], [25.45828699628403, 0], [2297.0, 0]], [[1.0, 0], [51.372586936180355, 0], [2309.0, 0]], [[1.0, 0], [14.48944545131997, 0], [2311.0, 0]], [[1.0, 0], [-34.60027234087955, 0], [2333.0, 0]], [[1.0, 0], [24.065002747083348, 0], [2339.0, 0]], [[1.0, 0], [-21.64895127574274, 0], [2341.0, 0]], [[1.0, 0], [5.555094965925588, 0], [2347.0, 0]], [[1.0, 0], [-38.56450121543306, 0], [2351.0, 0]], [[1.0, 0], [-11.863423430346577, 0], [2357.0, 0]], [[1.0, 0], [38.6839878717057, 0], [2371.0, 0]], [[1.0, 0], [-4.970517046606598, 0], [2377.0, 0]], [[1.0, 0], [52.085576520150966, 0], [2381.0, 0]], [[1.0, 0], [-70.36707519960494, 0], [2383.0, 0]], [[1.0, 0], [82.48957629561009, 0], [2389.0, 0]], [[1.0, 0], [-64.44658151110127, 0], [2393.0, 0]], [[1.0, 0], [7.730290265516197, 0], [2399.0, 0]], [[1.0, 0], [-79.44292456669754, 0], [2411.0, 0]], [[1.0, 0], [-22.678622379166477, 0], [2417.0, 0]], [[1.0, 0], [-49.02925984259291, 0], [2423.0, 0]], [[1.0, 0], [60.42256772932737, 0], [2437.0, 0]], [[1.0, 0], [-24.607106921765162, 0], [2441.0, 0]], [[1.0, 0], [33.72087051834193, 0], [2447.0, 0]], [[1.0, 0], [-38.59520849375352, 0], [2459.0, 0]], [[1.0, 0], [49.076814478589355, 0], [2467.0, 0]], [[1.0, 0], [-34.343711322177406, 0], [2473.0, 0]], [[1.0, 0], [-82.29839573485073, 0], [2477.0, 0]], [[1.0, 0], [32.61822105274292, 0], [2503.0, 0]], [[1.0, 0], [68.96446466917662, 0], [2521.0, 0]], [[1.0, 0], [18.860893790002994, 0], [2531.0, 0]], [[1.0, 0], [-31.376879005796855, 0], [2539.0, 0]], [[1.0, 0], [77.75186397383894, 0], [2543.0, 0]], [[1.0, 0], [-56.77927900576744, 0], [2549.0, 0]], [[1.0, 0], [23.882447323766126, 0], [2551.0, 0]], [[1.0, 0], [19.5667074096898, 0], [2557.0, 0]], [[1.0, 0], [-10.60670634946444, 0], [2579.0, 0]], [[1.0, 0], [-29.589705157988675, 0], [2591.0, 0]], [[1.0, 0], [79.90198571175466, 0], [2593.0, 0]], [[1.0, 0], [86.32936849157448, 0], [2609.0, 0]], [[1.0, 0], [-0.08029543995712767, 0], [2617.0, 0]], [[1.0, 0], [-48.98277409791626, 0], [2621.0, 0]], [[1.0, 0], [56.97729515693195, 0], [2633.0, 0]], [[1.0, 0], [-60.84463393063196, 0], [2647.0, 0]], [[1.0, 0], [18.155778224617073, 0], [2657.0, 0]], [[1.0, 0], [85.87524774926766, 0], [2659.0, 0]], [[1.0, 0], [-22.400674285080072, 0], [2663.0, 0]], [[1.0, 0], [55.33455464441452, 0], [2671.0, 0]], [[1.0, 0], [-76.83353148132029, 0], [2677.0, 0]], [[1.0, 0], [62.022753730829265, 0], [2683.0, 0]], [[1.0, 0], [-28.1926410606616, 0], [2687.0, 0]], [[1.0, 0], [-96.7312958414553, 0], [2689.0, 0]], [[1.0, 0], [36.39098437904857, 0], [2693.0, 0]], [[1.0, 0], [-48.6474428769681, 0], [2699.0, 0]], [[1.0, 0], [15.806432745098293, 0], [2707.0, 0]], [[1.0, 0], [56.69504611641116, 0], [2711.0, 0]], [[1.0, 0], [17.34407238352932, 0], [2713.0, 0]], [[1.0, 0], [-62.72007045955774, 0], [2719.0, 0]], [[1.0, 0], [-28.790227041763952, 0], [2729.0, 0]], [[1.0, 0], [-26.826940133931036, 0], [2731.0, 0]], [[1.0, 0], [-48.28697046503471, 0], [2741.0, 0]], [[1.0, 0], [-0.3661319270459726, 0], [2749.0, 0]], [[1.0, 0], [-31.94727236290866, 0], [2753.0, 0]], [[1.0, 0], [30.021447263594922, 0], [2767.0, 0]], [[1.0, 0], [55.288315382256215, 0], [2777.0, 0]], [[1.0, 0], [6.745198187972243, 0], [2789.0, 0]], [[1.0, 0], [-67.40780170786502, 0], [2791.0, 0]], [[1.0, 0], [59.46744007735033, 0], [2797.0, 0]], [[1.0, 0], [77.32089539662358, 0], [2801.0, 0]], [[1.0, 0], [-41.800436827495496, 0], [2803.0, 0]], [[1.0, 0], [27.918389671892722, 0], [2819.0, 0]], [[1.0, 0], [-84.32280247969615, 0], [2833.0, 0]], [[1.0, 0], [-41.881431927076164, 0], [2837.0, 0]], [[1.0, 0], [-57.47903992134632, 0], [2843.0, 0]], [[1.0, 0], [-10.778174800408925, 0], [2851.0, 0]], [[1.0, 0], [-24.871882233767973, 0], [2857.0, 0]], [[1.0, 0], [-24.111547070249998, 0], [2861.0, 0]], [[1.0, 0], [-1.8498893709609485, 0], [2879.0, 0]], [[1.0, 0], [29.86927315628227, 0], [2887.0, 0]], [[1.0, 0], [47.05822407152481, 0], [2897.0, 0]], [[1.0, 0], [-16.767153572700515, 0], [2903.0, 0]], [[1.0, 0], [-29.138521734441795, 0], [2909.0, 0]], [[1.0, 0], [55.50022345881571, 0], [2917.0, 0]], [[1.0, 0], [11.217589645748829, 0], [2927.0, 0]], [[1.0, 0], [-78.06508885275498, 0], [2939.0, 0]], [[1.0, 0], [93.94036367959538, 0], [2953.0, 0]], [[1.0, 0], [0.41129279043279643, 0], [2957.0, 0]], [[1.0, 0], [85.34182731493007, 0], [2963.0, 0]], [[1.0, 0], [1.155526164428536, 0], [2969.0, 0]], [[1.0, 0], [89.29752774832495, 0], [2971.0, 0]], [[1.0, 0], [60.32989784906938, 0], [2999.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 119, 'label': '2-4001-1.1-c1-0-119', 'leading_term': '1.496325075033650156273812547143', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/4001/2/a/b/1/40', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.49632507503365, 1.49061887055295, 1.4734693241413512, 1.4447895346528214, 1.4044539045090703, 1.3523255673107695, 1.288292086528809, 1.2123070612177502, 1.1244350060475226, 1.0248968049477185, 0.9141131358411221, 0.7927434817796277, 0.6617186345928707, 0.5222649225601825, 0.3759187276534225, 0.2245301871249621, 0.07025529525112408, -0.0844640630030224, -0.23693229772275878, -0.3842443465955402, -0.5233414466843685, -0.6510775907810913, -0.7642954571713467, -0.8599102416889438, -0.9349994666916767, -0.9868965046964765, -1.0132852483399652, -1.012293097647387, -0.982579235210187, -0.9234150342940578, -0.8347534074790771, -0.7172839656565164, -0.5724710280071851, -0.4025718087204302, -0.21063250770863992, -0.00046054827336139566, 0.22342817208721774, 0.4558874321551307, 0.6912438537616041, 0.9234238411059492, 1.1461021557412485, 1.352869091450721, 1.537412340192403, 1.6937088267244114, 1.8162210700150192, 1.9000920383751383, 1.9413320350764722, 1.9369909116503707, 1.8853088822605955, 1.785839423840946, 1.6395382053209004, 1.448812699257724, 1.2175280854894848, 0.9509662442615644, 0.6557360309295114, 0.3396345911975201, 0.011461170928693636, -0.31921335459282113, -0.642316220049798, -0.947575028046606, -1.2248441545261592, -1.4644454959482647, -1.6575125719124513, -1.7963261333425495, -1.8746289355900323, -1.8879072635362684, -1.8336271750020987, -1.7114142775990182, -1.5231671738940429, -1.273096483631277, -0.9676835442013078, -0.6155554472663131, -0.22727591815991868, 0.1849454032781502, 0.6076195690983855, 1.0264119658542485, 1.426631136516473, 1.7937581762655905, 2.113999727306169, 2.37484572223566, 2.5656117464555828, 2.6779452934502452, 2.706275336813656, 2.648185578556992, 2.504693464712799, 2.2804195659519246, 1.9836351503039154, 1.6261796428372977, 1.223244058798685, 0.7930212703489671, 0.35622895760469125, -0.0644838806589053, -0.44523111673244453, -0.7616641379267228, -0.9898027448016818, -1.1068948846399058, -1.092275478633627, -0.9281933092103989, -0.6005747712222905, -0.09969431537513126, 0.579276363049544, 1.4358649478525374, 2.464061026132554, 3.65225918365672, 4.98339115291212, 6.435248750484291, 7.980992287180769, 9.589832042954827, 11.227863551718178, 12.859031121969183, 14.446188500090246, 15.952221113303887, 17.34119112301986, 18.57946474580425, 19.63678107337493, 20.48722299860255, 21.110053819467826, 21.490387567752517, 21.619666947968774, 21.495929766422563, 21.123852616911407, 20.514569059514788, 19.68526824018036, 18.65858849019415, 17.46182855140146, 16.126006343034618, 14.6848012957059, 13.173420948052387, 11.62743550998363, 10.081625291126803, 8.568885199539217, 7.119227943017822, 5.7589232071861645, 4.509804117249619, 3.3887649662612986, 2.4074658302988476, 1.572250660921948, 0.8842761545019174, 0.339839570800796, -0.06911486856196969, -0.3543389281287567, -0.5305067948173243, -0.614363721100574, -0.6238383119860776, -0.5771606189465367, -0.49202690180440084, -0.3848486516826036, -0.27011839517502884, -0.15991817403261668, -0.06358874831942077, 0.012431098749498642, 0.06459482670325666, 0.0920766124140115, 0.09645508614919139, 0.08127680456938273, 0.051529973507416636, 0.01306326129682113, -0.02801307444603766, -0.06590622206378598, -0.09566429161587128, -0.11361232756603908, -0.11767458688562771, -0.10756395435714951, -0.08482763089770917, -0.05274715715553262, -0.01609992117253969, 0.019201973808317778, 0.046571745215074026, 0.059276609546743804, 0.051000053139455076, 0.016399901787689578, -0.048376103032809724, -0.14525369346163652, -0.2739068208972936, -0.4315699961261444, -0.6130065524251898, -0.8106419179646018, -1.0148609222989051, -1.2144578556538868, -1.3972180542888628, -1.550600802001798, -1.6624858799253333, -1.7219406550030116, -1.7199615599507636, -1.6501434435484075, -1.5092326715151299, -1.2975249877923933, -1.0190767951741244, -0.6817083196618148, -0.29678858280299275, 0.12119539541325215, 0.5552699019513723, 0.9867786469277244, 1.3963207041727281, 1.7647738526156307, 2.0743479310402653, 2.309608827140756, 2.458413045947577, 2.5126956049153204, 2.4690602485387334, 2.3291304275278955, 2.09963171410126, 1.792190716348384, 1.4228513532537905, 1.0113256909342436, 0.5800124902518504, 0.15283123567833504, -0.24606819196901653, -0.5936506703675087, -0.8693206030633387, -1.056149539517325, -1.1419327230165952, -1.1200078490268344, -0.9897806347545582, -0.7569167205623105, -0.4331772096438271, -0.035894876495645864, 0.4128913347518066, 0.8876056032290922, 1.3605515731590399, 1.8035027900813292, 2.189381699739373, 2.493933583781629, 2.697298812365462, 2.785389242265192, 2.750982519392029, 2.594461180537611, 2.3241412049581966, 1.9561561710780708, 1.5138873122831527, 1.0269552369938346, 0.5298144635353599, 0.060015763183650345, -0.34377780622516435, -0.6439186415133447, -0.8059322364624749, -0.8005856266033902, -0.6057488991245652, -0.20794008353417312, 0.39654179312188875, 1.2009704726619137, 2.1880830502298654, 3.330528925748043, 4.591868299857755, 5.928080778957468, 7.289515536575242, 8.623188548194753, 9.875311220757785, 10.993919585107239, 11.931465098371376, 12.647227617718114, 13.109418432624407, 13.296856107638375, 13.200119578245037, 12.822110337246764, 12.17798717575405, 11.29447105814484], 'positive_zeros': ['0.835525607042836882384023763814636', '1.77745110315459571451055771229872', '2.84550774838359319946702894730030', '3.68450858139528394682990171382610', '4.61306452712965762009848664808285', '5.03572154527174686783160112096638', '7.04876103806521891481222542999237', '7.60772037153071719913547346466078', '7.938019106887271706660682463154077', '8.401280728236478298669228120001323'], 'prelabel': '2-4001-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.652269088491303, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.835525607042836882384023763815', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.77745110315459571451055771230', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.84550774838359319946702894730', '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': 31.948145848714297, 'bad_primes': [4001], 'central_character': '1.1', 'conductor': 4001, 'conductor_radical': 4001, 'degree': 2, 'index': 119, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4001/2/a/b/1/40'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-4001-1.1-c1-0-119', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-4001-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.652269088491303, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.835525607042836882384023763815', 'prec': 107}}
• lfunc_instances •

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

  
  {'Lhash': '1059154537273907908886793444813', 'Lhash_array': ['1059154537273907908886793444813'], 'label': '2-4001-1.1-c1-0-119', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4001/2/a/b/1/40'}