Lfunction data - 32-3751e16-1.1-c0e16-0-0

Formats: - HTML - YAML - JSON - 2025-09-26T17:31:21.145100

• 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
  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': '203445811651157265027214744809,322439372031265278085090523299,869603373819729933215545395852,980523822843874155639963853024,1013371344847119768144593500520,1160338055074334165482291145180,1222850520375245493219765697966,1298586417441187766099951469756,1396506179483238814898611852317,1442980528971204137904346328445,1650927045274714380430027224988,1722669332786575009491651997790,1832098181158298398407667851429,1882272315045725796209578556865,2023618584199980973742907176815,2071767685877679325144006456885', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -4, 'a5': 2, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22744.00887459064, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[11, [1]], [31, [1, -2, 1, 2, -4, 4, -1, -4, 7, -4, -1, 4, -4, 2, 1, -2, 1]]], 'bad_primes': [11, 31], 'central_character': '3751.1', 'coefficient_field': '1.1.1.1', 'conductor': 1535864939197747909132527046561772589421209551017312560001, 'conductor_radical': 341, 'degree': 32, 'euler_factors': [[1, 0, 4, 0, 10, 0, 20, 0, 35, 0, 52, 0, 68, 0, 80, 0, 85, 0, 80, 0, 68, 0, 52, 0, 35, 0, 20, 0, 10, 0, 4, 0, 1], [1, 0, 2, 0, 1, 0, -2, 0, -4, 0, -4, 0, -1, 0, 4, 0, 7, 0, 4, 0, -1, 0, -4, 0, -4, 0, -2, 0, 1, 0, 2, 0, 1], [1, -2, 3, -6, 9, -10, 14, -18, 18, -22, 27, -26, 30, -36, 34, -36, 41, -36, 34, -36, 30, -26, 27, -22, 18, -18, 14, -10, 9, -6, 3, -2, 1], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], [1], [1, 0, -2, 0, 1, 0, 2, 0, -4, 0, 4, 0, -1, 0, -4, 0, 7, 0, -4, 0, -1, 0, 4, 0, -4, 0, 2, 0, 1, 0, -2, 0, 1], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], [1, 0, -2, 0, 1, 0, 2, 0, -4, 0, 4, 0, -1, 0, -4, 0, 7, 0, -4, 0, -1, 0, 4, 0, -4, 0, 2, 0, 1, 0, -2, 0, 1], [1, -16, 136, -800, 3620, -13328, 41328, -110448, 258570, -536640, 996216, -1665456, 2520336, -3465840, 4343160, -4969152, 5196627, -4969152, 4343160, -3465840, 2520336, -1665456, 996216, -536640, 258570, -110448, 41328, -13328, 3620, -800, 136, -16, 1], [1, 0, 0, 0, -2, 0, 0, 0, 3, 0, 0, 0, -4, 0, 0, 0, 5, 0, 0, 0, -4, 0, 0, 0, 3, 0, 0, 0, -2, 0, 0, 0, 1], [1, -2, 1, 2, -4, 4, -1, -4, 7, -4, -1, 4, -4, 2, 1, -2, 1], [1, 2, 3, 6, 9, 10, 14, 18, 18, 22, 27, 26, 30, 36, 34, 36, 41, 36, 34, 36, 30, 26, 27, 22, 18, 18, 14, 10, 9, 6, 3, 2, 1], [1, 0, -2, 0, 1, 0, 2, 0, -4, 0, 4, 0, -1, 0, -4, 0, 7, 0, -4, 0, -1, 0, 4, 0, -4, 0, 2, 0, 1, 0, -2, 0, 1], [1, 0, 8, 0, 36, 0, 112, 0, 266, 0, 504, 0, 784, 0, 1016, 0, 1107, 0, 1016, 0, 784, 0, 504, 0, 266, 0, 112, 0, 36, 0, 8, 0, 1], [1, -4, 6, 0, -15, 28, -22, -12, 60, -80, 36, 56, -129, 120, -20, -108, 167, -108, -20, 120, -129, 56, 36, -80, 60, -12, -22, 28, -15, 0, 6, -4, 1], [1, -2, 3, -6, 9, -10, 14, -18, 18, -22, 27, -26, 30, -36, 34, -36, 41, -36, 34, -36, 30, -26, 27, -22, 18, -18, 14, -10, 9, -6, 3, -2, 1], [1, 2, 3, 6, 9, 10, 14, 18, 18, 22, 27, 26, 30, 36, 34, 36, 41, 36, 34, 36, 30, 26, 27, 22, 18, 18, 14, 10, 9, 6, 3, 2, 1], [1, 0, 0, 0, -2, 0, 0, 0, 3, 0, 0, 0, -4, 0, 0, 0, 5, 0, 0, 0, -4, 0, 0, 0, 3, 0, 0, 0, -2, 0, 0, 0, 1], [1, 8, 28, 64, 134, 280, 504, 792, 1233, 1848, 2472, 3144, 3990, 4704, 5124, 5544, 5796, 5544, 5124, 4704, 3990, 3144, 2472, 1848, 1233, 792, 504, 280, 134, 64, 28, 8, 1], [1, 2, 3, 6, 9, 10, 14, 18, 18, 22, 27, 26, 30, 36, 34, 36, 41, 36, 34, 36, 30, 26, 27, 22, 18, 18, 14, 10, 9, 6, 3, 2, 1], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], [1, 16, 136, 800, 3620, 13328, 41328, 110448, 258570, 536640, 996216, 1665456, 2520336, 3465840, 4343160, 4969152, 5196627, 4969152, 4343160, 3465840, 2520336, 1665456, 996216, 536640, 258570, 110448, 41328, 13328, 3620, 800, 136, 16, 1], [1, 4, 6, 0, -15, -28, -22, 12, 60, 80, 36, -56, -129, -120, -20, 108, 167, 108, -20, -120, -129, -56, 36, 80, 60, 12, -22, -28, -15, 0, 6, 4, 1], [1, 0, 4, 0, 10, 0, 20, 0, 35, 0, 52, 0, 68, 0, 80, 0, 85, 0, 80, 0, 68, 0, 52, 0, 35, 0, 20, 0, 10, 0, 4, 0, 1], [1, 0, 2, 0, 1, 0, -2, 0, -4, 0, -4, 0, -1, 0, 4, 0, 7, 0, 4, 0, -1, 0, -4, 0, -4, 0, -2, 0, 1, 0, 2, 0, 1], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], [1, 0, -16, 0, 120, 0, -560, 0, 1820, 0, -4368, 0, 8008, 0, -11440, 0, 12870, 0, -11440, 0, 8008, 0, -4368, 0, 1820, 0, -560, 0, 120, 0, -16, 0, 1], [1, -2, 3, -6, 9, -10, 14, -18, 18, -22, 27, -26, 30, -36, 34, -36, 41, -36, 34, -36, 30, -26, 27, -22, 18, -18, 14, -10, 9, -6, 3, -2, 1]], 'euler_factors_factorization': [[[[1, -1, 1, -1, 1], 4], [[1, 1, 1, 1, 1], 4]], [[[1, 0, 1, 0, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1], 2]], [[[1, -1, 1, -1, 1], 4], [[1, 1, 0, -1, -1, -1, 0, 1, 1], 2]], [[[1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], 1]], [1], [[[1, -1, 0, 1, -1, 1, 0, -1, 1], 2], [[1, 1, 0, -1, -1, -1, 0, 1, 1], 2]], [[[1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], 1]], [[[1, -1, 0, 1, -1, 1, 0, -1, 1], 2], [[1, 1, 0, -1, -1, -1, 0, 1, 1], 2]], [[[1, -1, 1], 16]], [[[1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1], 2]], [[[1, -1, 0, 1, -1, 1, 0, -1, 1], 2]], [[[1, 1, 1, 1, 1], 4], [[1, -1, 0, 1, -1, 1, 0, -1, 1], 2]], [[[1, -1, 0, 1, -1, 1, 0, -1, 1], 2], [[1, 1, 0, -1, -1, -1, 0, 1, 1], 2]], [[[1, -1, 1], 8], [[1, 1, 1], 8]], [[[1, -1, 0, 1, -1, 1, 0, -1, 1], 4]], [[[1, -1, 1, -1, 1], 4], [[1, 1, 0, -1, -1, -1, 0, 1, 1], 2]], [[[1, 1, 1, 1, 1], 4], [[1, -1, 0, 1, -1, 1, 0, -1, 1], 2]], [[[1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1], 2]], [[[1, 1], 16], [[1, -1, 1], 8]], [[[1, 1, 1, 1, 1], 4], [[1, -1, 0, 1, -1, 1, 0, -1, 1], 2]], [[[1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], 1]], [[[1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], 1]], [[[1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], 1]], [[[1, 1, 1], 16]], [[[1, 1, 0, -1, -1, -1, 0, 1, 1], 4]], [[[1, -1, 1, -1, 1], 4], [[1, 1, 1, 1, 1], 4]], [[[1, 0, 1, 0, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1], 2]], [[[1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], 1]], [[[1, -1], 16], [[1, 1], 16]], [[[1, -1, 1, -1, 1], 4], [[1, 1, 0, -1, -1, -1, 0, 1, 1], 2]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 0, 'label': '32-3751e16-1.1-c0e16-0-0', 'leading_term': '0.31627829776002317596051266286484885174804258170043679334975202747167040672995647328017570', '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}, {'__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, 0, 0, 0, 0, 0, 0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3751/1/cf/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.003662109375', 'prec': 47}, 'plot_values': [0.3162782977600232, 0.3161947950957564, 0.3157543456331477, 0.31495827946560967, 0.313808175858625, 0.3123057914147114, 0.3104529887327972, 0.3082516658388352, 0.3057036866348651, 0.3028108125876122, 0.29957463585563293, 0.29599651403649585, 0.29207750670315263, 0.28781831389204476, 0.28321921493452623, 0.27827899390786337, 0.27299358130887497, 0.26735905201804594, 0.2613725272315406, 0.2550317850828289, 0.24833521809696482, 0.24128193509583948, 0.23387186808184446, 0.22610588420768332, 0.21798590291165817, 0.20951501826586727, 0.20069762654922216, 0.19153955901775133, 0.18204821748614788, 0.17223245247011965, 0.16210232156250148, 0.1516695099450108, 0.14094752001817637, 0.1299517811191367, 0.11869971266489257, 0.10721109169096311, 0.09550828473280615, 0.08361643402805759, 0.07156365211894579, 0.05938122495312409, 0.04710382355416703, 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'2.83692620174961221981532127493339', '2.84498572795137907166653263386077', '2.97987170689198882129569860268790', '3.01392111168825161347935902751150', '3.01771066451511865137229255957468', '3.06722562582153649767959227202037', '3.10665300171432287119803422474410', '3.23557732129194828553527642726450', '3.24693167426525039883735487428470', '3.26895135639921304944306867492234', '3.31298837983655971569208197724247', '3.33931974350888314631898890328407', '3.42645107130359719626506519891334', '3.43606687208882018583256788831001', '3.52010167569235446292198469643750', '3.67795116982169214624866039148202', '3.82223418900114967783464383249757', '3.92269675928228318596580791335806', '3.94918234805706706717147661555508', '4.02399952471508788172220349392782', '4.04660362292131266546701116423847', '4.10007571303515805093173103306201', '4.11332462605003937737110950022040', '4.22643023807281448800962060928510', '4.24434340699504819649892571456834', '4.26169667228388230211319133556326', '4.33654842950690752164160797918054', '4.37926584922047040152608058509420', '4.41645375464386684686686680266655', '4.44130811773602967253220850528356', '4.50133160695597564392062872750273', '4.50246753714074250992628085853791', '4.58732187666231938072335795628480', '4.58883334920725045595403971487814', '4.64689722502734905492761030880594', '4.71494131890319529485022198751088', '4.83635861729297656367350499421489', '4.92994108778783084296705512849775', '4.95146142677846979626576513572524', '4.99895554782757800951642721420965', '5.04655276742574819375556217574610', '5.05663983403060143591243666932434', '5.11347145001364198072536410039893', '5.14843657159137273783557272609866', '5.17338544134380586977574255888712', '5.21314612920380691871044845093359', '5.22746244442144458040691498680570', '5.33480330880544458181086844424044', '5.41351087434102243408272089854627', '5.43940558136548851785595632331812', '5.50362132718553972658428496017451', '5.53262241789197067754269760869818', '5.56170960012485855331430484410678', '5.57238696291690584392374898979942', '5.57912785028734850793166199243725', '5.59881075913832806835944684954529', '5.63357641986482482061445563370752', '5.69904242415939563520168516089301', '5.76077423361990856674347599433147', '5.99876678609172901711307480726796', '6.03021590204484500904977114606322', '6.05450742959217305427673859952801', '6.06321824462568372957204169419831', '6.06388537044801337449120777442280', '6.08056376121104954496567771303424', '6.15769396959068691770844794549121', '6.24360781502376393263676098203003', '6.26633122487541610693071951062313', '6.36975328324863848519654262407571', '6.45905681186632293256437994305574', '6.48701109810626010851424035106246', '6.50695577900179557753672601584085', '6.59724539304977529550596098354642', '6.59822052223500549529934599644909', '6.68001109560326979756447635076186', '6.72128863297476242158785636529960', '6.79603089233589362716082126639455', '6.87656087569953255015675579540653', '6.90549365460199844265747849821071', '6.92756573947338908418091109742863', '6.93593575410358549245836991796926', '6.95040387674782041910742067504889', '6.99713090364313297146900261566418', '7.07321673013176443777147796641024', '7.07421037826423225559913431040124', '7.18672355134788368214616798769189', '7.22878832964689279194910673241980', '7.28474145321552220074089593534854', '7.31856707733738669437305759350812', '7.32218887631644951463751674947077', '7.33125402477652670403756186371923', '7.39255031110046611309439044305010', '7.44050661656579692800804834282137', '7.50395213658678624072654474135081', '7.51167839555284875452480001351907', '7.51957264503002954166632656090258', '7.62700221622692475068991866490198', '7.65695554860540344828633718091280', '7.67580025788631478217483227207381', '7.82970110805615334293515117009155', '7.83799879879361965504562763724017', '7.88036478893348093821198073826142', '7.956561040263279543853093094475152', '7.996304019358085506118528298367573', '8.108353466603443279994438963732485', '8.234901520834538175145182611219345', '8.271734174380279428611614401436376', '8.279396004746243735114887423458814', '8.303842388299104445499806529439482', '8.374528255931719247532185322850311', '8.446939847131711181608006528543450', '8.493307475710990899332080281566857', '8.583795450796871371964282304446360', '8.608675048323029392951913272021289', '8.623617837336449719195708022379891', '8.642079486896520084429983732878284', '8.650928659604730848163354125814860', '8.664654706783085948397361014280551', '8.668594722228407100049797817591189', '8.675618119260131107795066482149619', '8.684070805062481918073287864513397', '8.703579488299729960683378655296812', '8.715471409552253658523290269962939', '8.889938583837061693533292843757739', '9.041471763044843788212206856936595', '9.052994589817796752417108009996613', '9.057550288140418279298356074373039'], 'prelabel': '32-3751e16-1.1-c0e16-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.3682079017409559, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c0e16-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.16049044714255539052317022285', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.25435981489947852331373513280', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.68599610465467807361203350766', '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': 22744.00887459064, 'bad_primes': [11, 31], 'central_character': '1.1', 'conductor': 1535864939197747909132527046561772589421209551017312560001, 'conductor_radical': 341, 'degree': 32, 'dirichlet_coefficients': [1, 0, 0, -4, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, -8, 0, 0, 16, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 8, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -4, 0, 0, -8, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 12, 3, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, -64, 0, 0, 0, 0, -4, 0, 0, -4], 'euler11': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler13': [1, 0, -2, 0, 1, 0, 2, 0, -4, 0, 4, 0, -1, 0, -4, 0, 7, 0, -4, 0, -1, 0, 4, 0, -4, 0, 2, 0, 1, 0, -2, 0, 1], 'euler17': [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], 'euler19': [1, 0, -2, 0, 1, 0, 2, 0, -4, 0, 4, 0, -1, 0, -4, 0, 7, 0, -4, 0, -1, 0, 4, 0, -4, 0, 2, 0, 1, 0, -2, 0, 1], 'euler2': [1, 0, 4, 0, 10, 0, 20, 0, 35, 0, 52, 0, 68, 0, 80, 0, 85, 0, 80, 0, 68, 0, 52, 0, 35, 0, 20, 0, 10, 0, 4, 0, 1], 'euler23': [1, -16, 136, -800, 3620, -13328, 41328, -110448, 258570, -536640, 996216, -1665456, 2520336, -3465840, 4343160, -4969152, 5196627, -4969152, 4343160, -3465840, 2520336, -1665456, 996216, -536640, 258570, -110448, 41328, -13328, 3620, -800, 136, -16, 1], 'euler29': [1, 0, 0, 0, -2, 0, 0, 0, 3, 0, 0, 0, -4, 0, 0, 0, 5, 0, 0, 0, -4, 0, 0, 0, 3, 0, 0, 0, -2, 0, 0, 0, 1], 'euler3': [1, 0, 2, 0, 1, 0, -2, 0, -4, 0, -4, 0, -1, 0, 4, 0, 7, 0, 4, 0, -1, 0, -4, 0, -4, 0, -2, 0, 1, 0, 2, 0, 1], 'euler31': [1, -2, 1, 2, -4, 4, -1, -4, 7, -4, -1, 4, -4, 2, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler37': [1, 2, 3, 6, 9, 10, 14, 18, 18, 22, 27, 26, 30, 36, 34, 36, 41, 36, 34, 36, 30, 26, 27, 22, 18, 18, 14, 10, 9, 6, 3, 2, 1], 'euler41': [1, 0, -2, 0, 1, 0, 2, 0, -4, 0, 4, 0, -1, 0, -4, 0, 7, 0, -4, 0, -1, 0, 4, 0, -4, 0, 2, 0, 1, 0, -2, 0, 1], 'euler43': [1, 0, 8, 0, 36, 0, 112, 0, 266, 0, 504, 0, 784, 0, 1016, 0, 1107, 0, 1016, 0, 784, 0, 504, 0, 266, 0, 112, 0, 36, 0, 8, 0, 1], 'euler47': [1, -4, 6, 0, -15, 28, -22, -12, 60, -80, 36, 56, -129, 120, -20, -108, 167, -108, -20, 120, -129, 56, 36, -80, 60, -12, -22, 28, -15, 0, 6, -4, 1], 'euler5': [1, -2, 3, -6, 9, -10, 14, -18, 18, -22, 27, -26, 30, -36, 34, -36, 41, -36, 34, -36, 30, -26, 27, -22, 18, -18, 14, -10, 9, -6, 3, -2, 1], 'euler53': [1, -2, 3, -6, 9, -10, 14, -18, 18, -22, 27, -26, 30, -36, 34, -36, 41, -36, 34, -36, 30, -26, 27, -22, 18, -18, 14, -10, 9, -6, 3, -2, 1], 'euler59': [1, 2, 3, 6, 9, 10, 14, 18, 18, 22, 27, 26, 30, 36, 34, 36, 41, 36, 34, 36, 30, 26, 27, 22, 18, 18, 14, 10, 9, 6, 3, 2, 1], 'euler61': [1, 0, 0, 0, -2, 0, 0, 0, 3, 0, 0, 0, -4, 0, 0, 0, 5, 0, 0, 0, -4, 0, 0, 0, 3, 0, 0, 0, -2, 0, 0, 0, 1], 'euler67': [1, 8, 28, 64, 134, 280, 504, 792, 1233, 1848, 2472, 3144, 3990, 4704, 5124, 5544, 5796, 5544, 5124, 4704, 3990, 3144, 2472, 1848, 1233, 792, 504, 280, 134, 64, 28, 8, 1], 'euler7': [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], 'euler71': [1, 2, 3, 6, 9, 10, 14, 18, 18, 22, 27, 26, 30, 36, 34, 36, 41, 36, 34, 36, 30, 26, 27, 22, 18, 18, 14, 10, 9, 6, 3, 2, 1], 'euler73': [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], 'euler79': [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], 'euler83': [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], 'euler89': [1, 16, 136, 800, 3620, 13328, 41328, 110448, 258570, 536640, 996216, 1665456, 2520336, 3465840, 4343160, 4969152, 5196627, 4969152, 4343160, 3465840, 2520336, 1665456, 996216, 536640, 258570, 110448, 41328, 13328, 3620, 800, 136, 16, 1], 'euler97': [1, 4, 6, 0, -15, -28, -22, 12, 60, 80, 36, -56, -129, -120, -20, 108, 167, 108, -20, -120, -129, -56, 36, 80, 60, 12, -22, -28, -15, 0, 6, 4, 1], 'euler_factors': [[1, 0, 4, 0, 10, 0, 20, 0, 35, 0, 52, 0, 68, 0, 80, 0, 85, 0, 80, 0, 68, 0, 52, 0, 35, 0, 20, 0, 10, 0, 4, 0, 1], [1, 0, 2, 0, 1, 0, -2, 0, -4, 0, -4, 0, -1, 0, 4, 0, 7, 0, 4, 0, -1, 0, -4, 0, -4, 0, -2, 0, 1, 0, 2, 0, 1], [1, -2, 3, -6, 9, -10, 14, -18, 18, -22, 27, -26, 30, -36, 34, -36, 41, -36, 34, -36, 30, -26, 27, -22, 18, -18, 14, -10, 9, -6, 3, -2, 1], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -2, 0, 1, 0, 2, 0, -4, 0, 4, 0, -1, 0, -4, 0, 7, 0, -4, 0, -1, 0, 4, 0, -4, 0, 2, 0, 1, 0, -2, 0, 1], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], [1, 0, -2, 0, 1, 0, 2, 0, -4, 0, 4, 0, -1, 0, -4, 0, 7, 0, -4, 0, -1, 0, 4, 0, -4, 0, 2, 0, 1, 0, -2, 0, 1], [1, -16, 136, -800, 3620, -13328, 41328, -110448, 258570, -536640, 996216, -1665456, 2520336, -3465840, 4343160, -4969152, 5196627, -4969152, 4343160, -3465840, 2520336, -1665456, 996216, -536640, 258570, -110448, 41328, -13328, 3620, -800, 136, -16, 1], [1, 0, 0, 0, -2, 0, 0, 0, 3, 0, 0, 0, -4, 0, 0, 0, 5, 0, 0, 0, -4, 0, 0, 0, 3, 0, 0, 0, -2, 0, 0, 0, 1], [1, -2, 1, 2, -4, 4, -1, -4, 7, -4, -1, 4, -4, 2, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, 3, 6, 9, 10, 14, 18, 18, 22, 27, 26, 30, 36, 34, 36, 41, 36, 34, 36, 30, 26, 27, 22, 18, 18, 14, 10, 9, 6, 3, 2, 1], [1, 0, -2, 0, 1, 0, 2, 0, -4, 0, 4, 0, -1, 0, -4, 0, 7, 0, -4, 0, -1, 0, 4, 0, -4, 0, 2, 0, 1, 0, -2, 0, 1], [1, 0, 8, 0, 36, 0, 112, 0, 266, 0, 504, 0, 784, 0, 1016, 0, 1107, 0, 1016, 0, 784, 0, 504, 0, 266, 0, 112, 0, 36, 0, 8, 0, 1], [1, -4, 6, 0, -15, 28, -22, -12, 60, -80, 36, 56, -129, 120, -20, -108, 167, -108, -20, 120, -129, 56, 36, -80, 60, -12, -22, 28, -15, 0, 6, -4, 1], [1, -2, 3, -6, 9, -10, 14, -18, 18, -22, 27, -26, 30, -36, 34, -36, 41, -36, 34, -36, 30, -26, 27, -22, 18, -18, 14, -10, 9, -6, 3, -2, 1], [1, 2, 3, 6, 9, 10, 14, 18, 18, 22, 27, 26, 30, 36, 34, 36, 41, 36, 34, 36, 30, 26, 27, 22, 18, 18, 14, 10, 9, 6, 3, 2, 1], [1, 0, 0, 0, -2, 0, 0, 0, 3, 0, 0, 0, -4, 0, 0, 0, 5, 0, 0, 0, -4, 0, 0, 0, 3, 0, 0, 0, -2, 0, 0, 0, 1], [1, 8, 28, 64, 134, 280, 504, 792, 1233, 1848, 2472, 3144, 3990, 4704, 5124, 5544, 5796, 5544, 5124, 4704, 3990, 3144, 2472, 1848, 1233, 792, 504, 280, 134, 64, 28, 8, 1], [1, 2, 3, 6, 9, 10, 14, 18, 18, 22, 27, 26, 30, 36, 34, 36, 41, 36, 34, 36, 30, 26, 27, 22, 18, 18, 14, 10, 9, 6, 3, 2, 1], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], [1, 16, 136, 800, 3620, 13328, 41328, 110448, 258570, 536640, 996216, 1665456, 2520336, 3465840, 4343160, 4969152, 5196627, 4969152, 4343160, 3465840, 2520336, 1665456, 996216, 536640, 258570, 110448, 41328, 13328, 3620, 800, 136, 16, 1], [1, 4, 6, 0, -15, -28, -22, 12, 60, 80, 36, -56, -129, -120, -20, 108, 167, 108, -20, -120, -129, -56, 36, 80, 60, 12, -22, -28, -15, 0, 6, 4, 1]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3751/1/cf/b'], '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': '32-3751e16-1.1-c0e16-0-0', '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}, {'__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, 0, 0, 0, 0, 0, 0], 'order_of_vanishing': 0, 'prelabel': '32-3751e16-1.1-c0e16-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.3682079017409559, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e16-0', 'z1': {'__RealLiteral__': 0, 'data': '0.16049044714255539052317022285', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '203445811651157265027214744809,322439372031265278085090523299,869603373819729933215545395852,980523822843874155639963853024,1013371344847119768144593500520,1160338055074334165482291145180,1222850520375245493219765697966,1298586417441187766099951469756,1396506179483238814898611852317,1442980528971204137904346328445,1650927045274714380430027224988,1722669332786575009491651997790,1832098181158298398407667851429,1882272315045725796209578556865,2023618584199980973742907176815,2071767685877679325144006456885', 'Lhash_array': ['203445811651157265027214744809', '322439372031265278085090523299', '869603373819729933215545395852', '980523822843874155639963853024', '1013371344847119768144593500520', '1160338055074334165482291145180', '1222850520375245493219765697966', '1298586417441187766099951469756', '1396506179483238814898611852317', '1442980528971204137904346328445', '1650927045274714380430027224988', '1722669332786575009491651997790', '1832098181158298398407667851429', '1882272315045725796209578556865', '2023618584199980973742907176815', '2071767685877679325144006456885'], 'factors': ['2-3751-341.211-c0-0-0', '2-3751-341.304-c0-0-0', '2-3751-341.160-c0-0-0', '2-3751-341.160-c0-0-1', '2-3751-341.149-c0-0-0', '2-3751-341.222-c0-0-1', '2-3751-341.304-c0-0-2', '2-3751-341.315-c0-0-1', '2-3751-341.118-c0-0-0', '2-3751-341.211-c0-0-1', '2-3751-341.129-c0-0-0', '2-3751-341.315-c0-0-2', '2-3751-341.149-c0-0-2', '2-3751-341.129-c0-0-1', '2-3751-341.118-c0-0-1', '2-3751-341.222-c0-0-2'], 'label': '32-3751e16-1.1-c0e16-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3751/1/cf/b'}