Lfunction data - 20-833e10-1.1-c1e10-0-0

Formats: - HTML - YAML - JSON - 2024-06-09T14:23:10.119219

• 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': '57416065760192866217927463116,337725817505049105287664304849,1160339402579849259261757200627,1222092695802432184618653037739,1299273475441589075808490037853,1571591737935833039327250248618,1737745527011037037952386517208,1960834937706734492129048131513,2004524204932378380083350885698,2360470585571928218554593116705', 'a10': 0, 'a2': -2, 'a3': -2, 'a4': 2, 'a5': 0, 'a6': 4, 'a7': 0, 'a8': 0, 'a9': 4, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 169520054.84422916, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [1]], [17, [1, -5, 15, -30, 45, -51, 45, -30, 15, -5, 1]]], 'bad_primes': [7, 17], 'central_character': '833.1', 'coefficient_field': '1.1.1.1', 'conductor': 160860722158988106150421688449, 'conductor_radical': 119, 'degree': 20, 'euler_factors': [[1, 2, 2, 0, -6, -11, -2, 8, 10, -10, -39, -20, 40, 64, -32, -352, -384, 0, 512, 1024, 1024], [1, 2, 0, -16, -30, -16, 140, 312, 256, -732, -1875, -2196, 2304, 8424, 11340, -3888, -21870, -34992, 0, 39366, 59049], [1, 0, -2, -36, -32, 38, 612, 1090, 650, -5508, -16701, -27540, 16250, 136250, 382500, 118750, -500000, -2812500, -781250, 0, 9765625], [1], [1, -2, -7, 74, -229, 108, 4338, -15228, 24133, 137098, -741573, 1508078, 2920093, -20268468, 63512658, 17393508, -405687469, 1442050654, -1500512167, -4715895382, 25937424601], [1, 4, 54, 196, 1781, 6560, 43400, 143360, 795058, 2416904, 11781956, 31419752, 134364802, 314961920, 1239547400, 2435682080, 8596546829, 12298709332, 44049458934, 42417997492, 137858491849], [1, -5, 15, -30, 45, -51, 45, -30, 15, -5, 1], [1, -6, -47, 302, 1515, -8444, -39422, 141676, 945381, -1144098, -18964573, -21737862, 341282541, 971755684, -5137514462, -20908179956, 71274509715, 269949265178, -798227462927, -1936126186674, 6131066257801], [1, -10, -7, 482, -1321, -7820, 46686, -103132, 288013, 2301282, -27273737, 52929486, 152358877, -1254807044, 13064656926, -50332202260, -195555409369, 1641125865454, -548176896967, -18011526614630, 41426511213649], [1, 16, 210, 2096, 19477, 153632, 1157912, 7803360, 50234674, 295160448, 1666734956, 8559652992, 42247360834, 190316147040, 818969157272, 3151168843168, 11585373823117, 36155740743664, 105051746721810, 232114335613904, 420707233300201], [1, 0, -122, 188, 8420, -17312, -379004, 727986, 13152610, -11124172, -411431899, -344849332, 12639658210, 21687430926, -350018153084, -495627862112, 7472780994020, 5172371452868, -104052706567802, 0, 819628286980801], [1, 8, -17, -856, -5185, -1408, 290514, 2278208, 5950285, -64405144, -651604271, -2382990328, 8145940165, 115398069824, 544470008754, -97636291456, -13303291430665, -81261686825848, -59712150716657, 1039693918360616, 4808584372417849], [1, 36, 892, 16256, 242012, 3036396, 32968580, 314284024, 2658442092, 20063182828, 135701884710, 822590495948, 4468841156652, 21660769218104, 93161327589380, 351785305291596, 1149582227572892, 3165925476209536, 7122553304375932, 11785749638182596, 13422659310152401], [1, -16, 432, -5264, 81712, -803704, 9135440, -74562768, 675178832, -4626050512, 34617153926, -198920172016, 1248405660368, -5928261995376, 31232251407440, -118151273672872, 516531217459888, -1430853168867248, 5049302519923632, -8041481790989488, 21611482313284249], [1, 10, -87, -258, 11711, 140, -576698, 1685420, 18948893, -50459410, -574319601, -2371592270, 41858104637, 174985360660, -2814102273338, 32108300980, 126235390717919, -130708765079454, -2071581939573207, 11191304731027670, 52599132235830049], [1, 4, -216, -616, 27592, 53174, -2557048, -2536764, 188155648, 54851304, -11074176673, 2907119112, 528529215232, -377665814028, -20176338660088, 22237127144782, 611559052271368, -723622062139592, -13448093128853976, 13199054367208532, 174887470365513049], [1, -8, -151, 776, 15335, -28464, -1227498, 392592, 79109629, 6761320, -4754678001, 398917880, 275380618549, 80630152368, -14874036392778, -20349605246736, 646838483384735, 1931193552219544, -22171396078252471, -69303966549239512, 511116753300641401], [1, -22, 36, 960, 20726, -229206, -1431408, 7610292, 185235172, -317522464, -11655910785, -19368870304, 689260075012, 1727391688452, -19819047574128, -193586539767006, 1067811279006086, 3017033122580160, 6901463267902116, -257271214042351102, 713342911662882601], [1, 16, -128, -1824, 30720, 222452, -3589184, -12433392, 354427968, 359391712, -26398984099, 24079244704, 1591027148352, -3739504278096, -72326081075264, 300338030302364, 2778881500231680, -11054737968109152, -51976662727250048, 435304550340719152, 1822837804551761449], [1, 4, 242, -132, 28173, -141168, 2787192, -17345232, 295866018, -1177252232, 25576143532, -83584908472, 1491460596738, -6208049330352, 70827233989752, -254699449021968, 3608969298906333, -1200555860907612, 156272354561474162, 183394002873796124, 3255243551009881201], [1, -10, -88, -464, 17954, 65190, -10816, -15626056, -38472344, 111514864, 12217591683, 8140585072, -205019121176, -6078801426952, -307155374656, 135143537147670, 2717054698792706, -5125992912861008, -70968488086679128, -588715867082679130, 4297625829703557649], [1, 18, -111, -2458, 27415, 330796, -3242722, -22364388, 344455757, 659142630, -30517436849, 52072267770, 2149748379437, -11026515495132, -126304284560482, 1017877948563604, 6664242593108215, -47203208287978822, -168399077899628271, 2157328727687129742, 9468276082626847201], [1, -24, 846, -14488, 298133, -4034352, 61691240, -691943408, 8549925202, -81060578912, 837825364564, -6728028049696, 58900434716578, -395644245430096, 2927762670808040, -15891476496168336, 97471714333620077, -393147106737715976, 1905439228389628686, -4486566126420969672, 15516041187205853449], [1, -20, 55, 236, 9347, -9048, 115358, -18729272, 70022805, 321343508, 2223302725, 28599572212, 554650638405, -13203556152568, 7237819437278, -50524569894552, 4645284126612467, 10438595035344844, 216512384313614455, -7007128074149704180, 31181719929966183601], [1, 24, 636, 9684, 159284, 1852028, 25266068, 267862044, 3394918948, 33564207104, 378471303158, 3255728089088, 31942792381732, 244470455283612, 2236786833737108, 15903994601491196, 132679112833110836, 782450586886046292, 4984607766023747196, 18245545407709565208, 73742412689492826049], [1, 8, -281, -3096, 40599, 561024, -2739270, -61962240, -30545571, 2652185384, 20762279313, 267870723784, -311595369771, -63839757834240, -285049534647270, 5896418623473024, 43096656594249999, -331933105012330296, -3042827342814905081, 8749482181474887208, 110462212541120451001], [1, 36, 373, 1116, 44295, 830752, 1590870, 13096496, 1311229389, 10004898148, 8525963851, 1030504509244, 13910832587901, 14310894784592, 179053820056470, 9630692557728736, 52890546474752055, 137253923381415492, 4725052403575808053, 46971834617852804988, 134391637934412192049], [1, -16, -127, 2976, 4431, -154568, -1136834, -2287768, 292905469, 425262488, -40733713281, 45503086216, 3353474714581, -2802614174024, -149015747123234, -2167896159108376, 6649736189042919, 477880567399980768, -2182096448386538527, -29415347398722472112, 196715135728956532249], [1, 34, 331, -670, -13009, 207676, 2401530, 40936964, 827359261, 2547168774, -46925594715, 277641396366, 9829855379941, 53014555551956, 338995558386330, 3195352684578124, -21817395341930569, -122478621094718230, 6595382343994535851, 73844371501038519226, 236736367459211723401], [1, 16, 1074, 15248, 527293, 6550528, 155358456, 1667811584, 30343555874, 277699893856, 4098381327020, 31380088005728, 387456864955106, 2406480331118848, 25330786259834616, 120689232301896704, 1097798585488457437, 3587252836587369616, 28551690631815080754, 48064671007748292368, 339456738992222314849]], 'euler_factors_factorization': [[[[1, 2, 2, 0, -6, -11, -2, 8, 10, -10, -39, -20, 40, 64, -32, -352, -384, 0, 512, 1024, 1024], 1]], [[[1, 2, 0, -16, -30, -16, 140, 312, 256, -732, -1875, -2196, 2304, 8424, 11340, -3888, -21870, -34992, 0, 39366, 59049], 1]], [[[1, 0, -2, -36, -32, 38, 612, 1090, 650, -5508, -16701, -27540, 16250, 136250, 382500, 118750, -500000, -2812500, -781250, 0, 9765625], 1]], [1], [[[1, -2, -7, 74, -229, 108, 4338, -15228, 24133, 137098, -741573, 1508078, 2920093, -20268468, 63512658, 17393508, -405687469, 1442050654, -1500512167, -4715895382, 25937424601], 1]], [[[1, 2, 25, 48, 482, 1116, 6266, 8112, 54925, 57122, 371293], 2]], [[[1, -1, 1], 5]], [[[1, -6, -47, 302, 1515, -8444, -39422, 141676, 945381, -1144098, -18964573, -21737862, 341282541, 971755684, -5137514462, -20908179956, 71274509715, 269949265178, -798227462927, -1936126186674, 6131066257801], 1]], [[[1, -10, -7, 482, -1321, -7820, 46686, -103132, 288013, 2301282, -27273737, 52929486, 152358877, -1254807044, 13064656926, -50332202260, -195555409369, 1641125865454, -548176896967, -18011526614630, 41426511213649], 1]], [[[1, 8, 73, 464, 3362, 16048, 97498, 390224, 1780397, 5658248, 20511149], 2]], [[[1, 0, -122, 188, 8420, -17312, -379004, 727986, 13152610, -11124172, -411431899, -344849332, 12639658210, 21687430926, -350018153084, -495627862112, 7472780994020, 5172371452868, -104052706567802, 0, 819628286980801], 1]], [[[1, 8, -17, -856, -5185, -1408, 290514, 2278208, 5950285, -64405144, -651604271, -2382990328, 8145940165, 115398069824, 544470008754, -97636291456, -13303291430665, -81261686825848, -59712150716657, 1039693918360616, 4808584372417849], 1]], [[[1, 18, 284, 3016, 26390, 186634, 1081990, 5069896, 19573564, 50863698, 115856201], 2]], [[[1, -8, 184, -1160, 14648, -71228, 629864, -2144840, 14629288, -27350408, 147008443], 2]], [[[1, 10, -87, -258, 11711, 140, -576698, 1685420, 18948893, -50459410, -574319601, -2371592270, 41858104637, 174985360660, -2814102273338, 32108300980, 126235390717919, -130708765079454, -2071581939573207, 11191304731027670, 52599132235830049], 1]], [[[1, 4, -216, -616, 27592, 53174, -2557048, -2536764, 188155648, 54851304, -11074176673, 2907119112, 528529215232, -377665814028, -20176338660088, 22237127144782, 611559052271368, -723622062139592, -13448093128853976, 13199054367208532, 174887470365513049], 1]], [[[1, -8, -151, 776, 15335, -28464, -1227498, 392592, 79109629, 6761320, -4754678001, 398917880, 275380618549, 80630152368, -14874036392778, -20349605246736, 646838483384735, 1931193552219544, -22171396078252471, -69303966549239512, 511116753300641401], 1]], [[[1, -22, 36, 960, 20726, -229206, -1431408, 7610292, 185235172, -317522464, -11655910785, -19368870304, 689260075012, 1727391688452, -19819047574128, -193586539767006, 1067811279006086, 3017033122580160, 6901463267902116, -257271214042351102, 713342911662882601], 1]], [[[1, 16, -128, -1824, 30720, 222452, -3589184, -12433392, 354427968, 359391712, -26398984099, 24079244704, 1591027148352, -3739504278096, -72326081075264, 300338030302364, 2778881500231680, -11054737968109152, -51976662727250048, 435304550340719152, 1822837804551761449], 1]], [[[1, 2, 119, -304, 7614, -49636, 540594, -1532464, 42591409, 50823362, 1804229351], 2]], [[[1, -10, -88, -464, 17954, 65190, -10816, -15626056, 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0.8438342532116617, -0.6700545183395413, -0.091571666339911, 0.7586599120615439, 0.8644543192020363, 0.039480132833899166, -1.3111579928106434, -2.56290166264972, -3.2220013327406183, -3.123822158969783, -2.4375949504600514, -1.5207788833451785, -0.7205897489134029, -0.2254490969335981, -0.028079718646249398, 0.00238669146489419, -0.0020964954812034194, -0.001215220758380319, -0.051736515242891225, -0.22863541135565146, -0.514490919164076, -0.7200535941017998, -0.48090893122799716, 0.656589260863528, 3.0782468097706346], 'positive_zeros': ['0.04529328960981488577251694266862', '0.26641869411353927192761001453295', '0.915346391482747927679348436059522', '0.964061150274693267439179648029756', '1.02494604996650200951131583561046', '1.23976728102592441070394986795722', '1.37083950948169089901850399821704', '1.54682602394832086575259599223346', '1.58129077884038498623860087882090', '1.67159705497359184285802303202678', '1.86208296288184310282254609845361', '2.12407676530089895449020053449234', '2.33060190955236257756060936564337', '2.52572408928614389652683360278066', '2.56943159171694245143573290403064', '2.71520711042459873059246037554190', '2.78590686399840408898511631155775', '2.83897262040444831133543342953008', '2.91928572722945563006361825655368', '3.22498440221638579024495872031852', '3.48829124190202128634937440661368', '3.55725142384839940136331053143370', '3.57319769113942052999650135666068', '3.60143441767355678167968091353079', '3.61290622328630246613613785999212', '3.81123446600973333037722504231351', '3.81768620136772962044745892210538', '3.90021720177390114321583993259335', '4.28282402760590020307564183158598', '4.30714149663282446426192465261473', '4.51940624897924182262345049799463', '4.53419903774071333807475274799768', '4.67057392207122160075970360690321', '4.86301854098668541300823673307273', '4.95397770571340950574743685313324', '4.99125133865244291627991333464901', '5.04245805559037478076533500911264', '5.09727870663869878811339829187252', '5.24471893606328689630443990970812', '5.24944665626708585009032808824697', '5.30965232689635569812669846499741', '5.33917323996728500603168557020491', '5.52099389976806770336711659747247', '5.77203650661717287875699781480307', '5.82395120580444469246315401249210', '5.92697445705870738133672019131731', '6.00612853200263661916687636892131', '6.07679952145000877089615147016541', '6.13379518596884960050419123726541', '6.33544612066298510613331079894336', '6.42164628962710208054268347274810', '6.42174394061020245323570582594075', '6.58974475354744607004422390412572', '6.81606338093340182677155351633331', '6.83631527331865668447161192486488', '6.89794406403635685165770677349003', '6.93519583734665641457565855969083', '6.94780116127612252916545763871450', '6.96882231667368144501370133386841', '7.30941972549207660233565251960780', '7.31914874651011340826096860526649', '7.35100897213625893914833037845008', '7.45084364473620661324710527658528', '7.47779440050577234805477468207736', '7.49749054650680336324406468033686', '7.61074310729333007591605190747947', '7.76220076739023406126039240314876', '7.85236585088063360301387046570184', '8.083132692384254154345845791843659', '8.125015147496585645110505919717249', '8.207016309035453304600585578205477', '8.246048451135570543843280504308968', '8.339645327036709758482081720413863', '8.383642509805993378533020867669934', '8.500206191506741561677532308585041', '8.577172900485973636075791129406702', '8.594663826903997037460655960360217', '8.651559230251406096832797374542252', '8.963885050762380403681065349130943', '9.008284382789595595800809376890595', '9.086336215857805121805623115006583', '9.130478028772722077000182195123971', '9.139011586320747084944834702824758', '9.144843036107861715106390277329786', '9.385996942354058137329415817012618', '9.437748182692612385733451709810995', '9.520307576111420314808613161590457', '9.594157645412992998336776797142772', '9.697961437916567306267148284309939', '9.854468433126218861280456563392672', '9.881782893508387669333411560015756', '10.03223095518118202044717955102340', '10.06516051957098511765276588033984', '10.07756395732913052320446181302419', '10.09879785940334589082486168795116', '10.13595085029483238774346801463185', '10.14415192111793868742228294179129', '10.39577354840722062154727678515714', '10.42150979560346894770284641897227', '10.59285633374738429280457130180399'], 'prelabel': '20-833e10-1.1-c1e10-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.5790576744952136, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e10-0', 'trace_hash': 790583685119481115, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.04529328960981488577251694267', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.26641869411353927192761001453', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.915346391482747927679348436060', 'prec': 107}}
• lfunc_search •

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

  
  {'algebraic': True, 'analytic_conductor': 169520054.84422916, 'bad_primes': [7, 17], 'central_character': '1.1', 'conductor': 160860722158988106150421688449, 'conductor_radical': 119, 'degree': 20, 'dirichlet_coefficients': [1, -2, -2, 2, 0, 4, 0, 0, 4, 0, 2, -4, -4, 0, 0, 2, 5, -8, 6, 0, 0, -4, 10, 0, 2, 8, 8, 0, -16, 0, 0, -5, -4, -10, 0, 8, -8, -12, 8, 0, -36, 0, 16, 4, 0, -20, -10, -4, 0, -4, -10, -8, -4, -16, 0, 0, -12, 32, 8, 0, 22, 0, 0, -2, 0, 8, -16, 10, -20, 0, -4, 0, 10, 16, -4, 12, 0, -16, -18, 0, -18, 72, 24, 0, 0, -32, 32, 0, 20, 0, 0, 20, 0, 20, 0, 10, -24, 0, 8, 4], 'euler11': [1, -2, -7, 74, -229, 108, 4338, -15228, 24133, 137098, -741573, 1508078, 2920093, -20268468, 63512658, 17393508, -405687469, 1442050654, -1500512167, -4715895382, 25937424601], 'euler13': [1, 4, 54, 196, 1781, 6560, 43400, 143360, 795058, 2416904, 11781956, 31419752, 134364802, 314961920, 1239547400, 2435682080, 8596546829, 12298709332, 44049458934, 42417997492, 137858491849], 'euler17': [1, -5, 15, -30, 45, -51, 45, -30, 15, -5, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler19': [1, -6, -47, 302, 1515, -8444, -39422, 141676, 945381, -1144098, -18964573, -21737862, 341282541, 971755684, -5137514462, -20908179956, 71274509715, 269949265178, -798227462927, -1936126186674, 6131066257801], 'euler2': [1, 2, 2, 0, -6, -11, -2, 8, 10, -10, -39, -20, 40, 64, -32, -352, -384, 0, 512, 1024, 1024], 'euler23': [1, -10, -7, 482, -1321, -7820, 46686, -103132, 288013, 2301282, -27273737, 52929486, 152358877, -1254807044, 13064656926, -50332202260, -195555409369, 1641125865454, -548176896967, -18011526614630, 41426511213649], 'euler29': [1, 16, 210, 2096, 19477, 153632, 1157912, 7803360, 50234674, 295160448, 1666734956, 8559652992, 42247360834, 190316147040, 818969157272, 3151168843168, 11585373823117, 36155740743664, 105051746721810, 232114335613904, 420707233300201], 'euler3': [1, 2, 0, -16, -30, -16, 140, 312, 256, -732, -1875, -2196, 2304, 8424, 11340, -3888, -21870, -34992, 0, 39366, 59049], 'euler31': [1, 0, -122, 188, 8420, -17312, -379004, 727986, 13152610, -11124172, -411431899, -344849332, 12639658210, 21687430926, -350018153084, -495627862112, 7472780994020, 5172371452868, -104052706567802, 0, 819628286980801], 'euler37': [1, 8, -17, -856, -5185, -1408, 290514, 2278208, 5950285, -64405144, -651604271, -2382990328, 8145940165, 115398069824, 544470008754, -97636291456, -13303291430665, -81261686825848, -59712150716657, 1039693918360616, 4808584372417849], 'euler41': [1, 36, 892, 16256, 242012, 3036396, 32968580, 314284024, 2658442092, 20063182828, 135701884710, 822590495948, 4468841156652, 21660769218104, 93161327589380, 351785305291596, 1149582227572892, 3165925476209536, 7122553304375932, 11785749638182596, 13422659310152401], 'euler43': [1, -16, 432, -5264, 81712, -803704, 9135440, -74562768, 675178832, -4626050512, 34617153926, -198920172016, 1248405660368, -5928261995376, 31232251407440, -118151273672872, 516531217459888, -1430853168867248, 5049302519923632, -8041481790989488, 21611482313284249], 'euler47': [1, 10, -87, -258, 11711, 140, -576698, 1685420, 18948893, -50459410, -574319601, -2371592270, 41858104637, 174985360660, -2814102273338, 32108300980, 126235390717919, -130708765079454, -2071581939573207, 11191304731027670, 52599132235830049], 'euler5': [1, 0, -2, -36, -32, 38, 612, 1090, 650, -5508, -16701, -27540, 16250, 136250, 382500, 118750, -500000, -2812500, -781250, 0, 9765625], 'euler53': [1, 4, -216, -616, 27592, 53174, -2557048, -2536764, 188155648, 54851304, -11074176673, 2907119112, 528529215232, -377665814028, -20176338660088, 22237127144782, 611559052271368, -723622062139592, -13448093128853976, 13199054367208532, 174887470365513049], 'euler59': [1, -8, -151, 776, 15335, -28464, -1227498, 392592, 79109629, 6761320, -4754678001, 398917880, 275380618549, 80630152368, -14874036392778, -20349605246736, 646838483384735, 1931193552219544, -22171396078252471, -69303966549239512, 511116753300641401], 'euler61': [1, -22, 36, 960, 20726, -229206, -1431408, 7610292, 185235172, -317522464, -11655910785, -19368870304, 689260075012, 1727391688452, -19819047574128, -193586539767006, 1067811279006086, 3017033122580160, 6901463267902116, -257271214042351102, 713342911662882601], 'euler67': [1, 16, -128, -1824, 30720, 222452, -3589184, -12433392, 354427968, 359391712, -26398984099, 24079244704, 1591027148352, -3739504278096, -72326081075264, 300338030302364, 2778881500231680, -11054737968109152, -51976662727250048, 435304550340719152, 1822837804551761449], 'euler7': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler71': [1, 4, 242, -132, 28173, -141168, 2787192, -17345232, 295866018, -1177252232, 25576143532, -83584908472, 1491460596738, -6208049330352, 70827233989752, -254699449021968, 3608969298906333, -1200555860907612, 156272354561474162, 183394002873796124, 3255243551009881201], 'euler73': [1, -10, -88, -464, 17954, 65190, -10816, -15626056, -38472344, 111514864, 12217591683, 8140585072, -205019121176, -6078801426952, -307155374656, 135143537147670, 2717054698792706, -5125992912861008, -70968488086679128, -588715867082679130, 4297625829703557649], 'euler79': [1, 18, -111, -2458, 27415, 330796, -3242722, -22364388, 344455757, 659142630, -30517436849, 52072267770, 2149748379437, -11026515495132, -126304284560482, 1017877948563604, 6664242593108215, -47203208287978822, -168399077899628271, 2157328727687129742, 9468276082626847201], 'euler83': [1, -24, 846, -14488, 298133, -4034352, 61691240, -691943408, 8549925202, -81060578912, 837825364564, -6728028049696, 58900434716578, -395644245430096, 2927762670808040, -15891476496168336, 97471714333620077, -393147106737715976, 1905439228389628686, -4486566126420969672, 15516041187205853449], 'euler89': [1, -20, 55, 236, 9347, -9048, 115358, -18729272, 70022805, 321343508, 2223302725, 28599572212, 554650638405, -13203556152568, 7237819437278, -50524569894552, 4645284126612467, 10438595035344844, 216512384313614455, -7007128074149704180, 31181719929966183601], 'euler97': [1, 24, 636, 9684, 159284, 1852028, 25266068, 267862044, 3394918948, 33564207104, 378471303158, 3255728089088, 31942792381732, 244470455283612, 2236786833737108, 15903994601491196, 132679112833110836, 782450586886046292, 4984607766023747196, 18245545407709565208, 73742412689492826049], 'euler_factors': [[1, 2, 2, 0, -6, -11, -2, 8, 10, -10, -39, -20, 40, 64, -32, -352, -384, 0, 512, 1024, 1024], [1, 2, 0, -16, -30, -16, 140, 312, 256, -732, -1875, -2196, 2304, 8424, 11340, -3888, -21870, -34992, 0, 39366, 59049], [1, 0, -2, -36, -32, 38, 612, 1090, 650, -5508, -16701, -27540, 16250, 136250, 382500, 118750, -500000, -2812500, -781250, 0, 9765625], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -2, -7, 74, -229, 108, 4338, -15228, 24133, 137098, -741573, 1508078, 2920093, -20268468, 63512658, 17393508, -405687469, 1442050654, -1500512167, -4715895382, 25937424601], [1, 4, 54, 196, 1781, 6560, 43400, 143360, 795058, 2416904, 11781956, 31419752, 134364802, 314961920, 1239547400, 2435682080, 8596546829, 12298709332, 44049458934, 42417997492, 137858491849], [1, -5, 15, -30, 45, -51, 45, -30, 15, -5, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -6, -47, 302, 1515, -8444, -39422, 141676, 945381, -1144098, -18964573, -21737862, 341282541, 971755684, -5137514462, -20908179956, 71274509715, 269949265178, -798227462927, -1936126186674, 6131066257801], [1, -10, -7, 482, -1321, -7820, 46686, -103132, 288013, 2301282, -27273737, 52929486, 152358877, -1254807044, 13064656926, -50332202260, -195555409369, 1641125865454, -548176896967, -18011526614630, 41426511213649], [1, 16, 210, 2096, 19477, 153632, 1157912, 7803360, 50234674, 295160448, 1666734956, 8559652992, 42247360834, 190316147040, 818969157272, 3151168843168, 11585373823117, 36155740743664, 105051746721810, 232114335613904, 420707233300201], [1, 0, -122, 188, 8420, -17312, -379004, 727986, 13152610, -11124172, -411431899, -344849332, 12639658210, 21687430926, -350018153084, -495627862112, 7472780994020, 5172371452868, -104052706567802, 0, 819628286980801], [1, 8, -17, -856, -5185, -1408, 290514, 2278208, 5950285, -64405144, -651604271, -2382990328, 8145940165, 115398069824, 544470008754, -97636291456, -13303291430665, -81261686825848, -59712150716657, 1039693918360616, 4808584372417849], [1, 36, 892, 16256, 242012, 3036396, 32968580, 314284024, 2658442092, 20063182828, 135701884710, 822590495948, 4468841156652, 21660769218104, 93161327589380, 351785305291596, 1149582227572892, 3165925476209536, 7122553304375932, 11785749638182596, 13422659310152401], [1, -16, 432, -5264, 81712, -803704, 9135440, -74562768, 675178832, -4626050512, 34617153926, -198920172016, 1248405660368, -5928261995376, 31232251407440, -118151273672872, 516531217459888, -1430853168867248, 5049302519923632, -8041481790989488, 21611482313284249], [1, 10, -87, -258, 11711, 140, -576698, 1685420, 18948893, -50459410, -574319601, -2371592270, 41858104637, 174985360660, -2814102273338, 32108300980, 126235390717919, -130708765079454, -2071581939573207, 11191304731027670, 52599132235830049], [1, 4, -216, -616, 27592, 53174, -2557048, -2536764, 188155648, 54851304, -11074176673, 2907119112, 528529215232, -377665814028, -20176338660088, 22237127144782, 611559052271368, -723622062139592, -13448093128853976, 13199054367208532, 174887470365513049], [1, -8, -151, 776, 15335, -28464, -1227498, 392592, 79109629, 6761320, -4754678001, 398917880, 275380618549, 80630152368, -14874036392778, -20349605246736, 646838483384735, 1931193552219544, -22171396078252471, -69303966549239512, 511116753300641401], [1, -22, 36, 960, 20726, -229206, -1431408, 7610292, 185235172, -317522464, -11655910785, -19368870304, 689260075012, 1727391688452, -19819047574128, -193586539767006, 1067811279006086, 3017033122580160, 6901463267902116, -257271214042351102, 713342911662882601], [1, 16, -128, -1824, 30720, 222452, -3589184, -12433392, 354427968, 359391712, -26398984099, 24079244704, 1591027148352, -3739504278096, -72326081075264, 300338030302364, 2778881500231680, -11054737968109152, -51976662727250048, 435304550340719152, 1822837804551761449], [1, 4, 242, -132, 28173, -141168, 2787192, -17345232, 295866018, -1177252232, 25576143532, -83584908472, 1491460596738, -6208049330352, 70827233989752, -254699449021968, 3608969298906333, -1200555860907612, 156272354561474162, 183394002873796124, 3255243551009881201], [1, -10, -88, -464, 17954, 65190, -10816, -15626056, -38472344, 111514864, 12217591683, 8140585072, -205019121176, -6078801426952, -307155374656, 135143537147670, 2717054698792706, -5125992912861008, -70968488086679128, -588715867082679130, 4297625829703557649], [1, 18, -111, -2458, 27415, 330796, -3242722, -22364388, 344455757, 659142630, -30517436849, 52072267770, 2149748379437, -11026515495132, -126304284560482, 1017877948563604, 6664242593108215, -47203208287978822, -168399077899628271, 2157328727687129742, 9468276082626847201], [1, -24, 846, -14488, 298133, -4034352, 61691240, -691943408, 8549925202, -81060578912, 837825364564, -6728028049696, 58900434716578, -395644245430096, 2927762670808040, -15891476496168336, 97471714333620077, -393147106737715976, 1905439228389628686, -4486566126420969672, 15516041187205853449], [1, -20, 55, 236, 9347, -9048, 115358, -18729272, 70022805, 321343508, 2223302725, 28599572212, 554650638405, -13203556152568, 7237819437278, -50524569894552, 4645284126612467, 10438595035344844, 216512384313614455, -7007128074149704180, 31181719929966183601], [1, 24, 636, 9684, 159284, 1852028, 25266068, 267862044, 3394918948, 33564207104, 378471303158, 3255728089088, 31942792381732, 244470455283612, 2236786833737108, 15903994601491196, 132679112833110836, 782450586886046292, 4984607766023747196, 18245545407709565208, 73742412689492826049]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/833/2/e/h'], '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': '20-833e10-1.1-c1e10-0-0', 'motivic_weight': 1, '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': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '20-833e10-1.1-c1e10-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.5790576744952136, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e10-0', 'trace_hash': 790583685119481115, 'z1': {'__RealLiteral__': 0, 'data': '0.04529328960981488577251694267', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '57416065760192866217927463116,337725817505049105287664304849,1160339402579849259261757200627,1222092695802432184618653037739,1299273475441589075808490037853,1571591737935833039327250248618,1737745527011037037952386517208,1960834937706734492129048131513,2004524204932378380083350885698,2360470585571928218554593116705', 'Lhash_array': ['57416065760192866217927463116', '337725817505049105287664304849', '1160339402579849259261757200627', '1222092695802432184618653037739', '1299273475441589075808490037853', '1571591737935833039327250248618', '1737745527011037037952386517208', '1960834937706734492129048131513', '2004524204932378380083350885698', '2360470585571928218554593116705'], 'label': '20-833e10-1.1-c1e10-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/833/2/e/h'}