Lfunction data - 8-390e4-1.1-c1e4-0-16

Formats: - HTML - YAML - JSON - 2023-05-29T15:33:28.669026

• 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': '1492477714583259116767256471213,1737722547790401036206754315007,1897280542666040442963295006620,2494356253703910726851242380518', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': 1, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 94.05174466820122, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, -1, 0, 1]], [3, [1, -2, 3, -2, 1]], [5, [1, 0, 2, 0, 1]], [13, [1, -4, 30, -52, 169]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '390.1', 'coefficient_field': '1.1.1.1', 'conductor': 23134410000, 'conductor_radical': 390, 'degree': 8, 'euler_factors': [[1, 0, -1, 0, 1], [1, -2, 3, -2, 1], [1, 0, 2, 0, 1], [1, 0, 10, 0, 51, 0, 490, 0, 2401], [1, -12, 73, -300, 1032, -3300, 8833, -15972, 14641], [1, -4, 30, -52, 169], [1, -8, 14, -128, 1123, -2176, 4046, -39304, 83521], [1, -12, 82, -408, 1707, -7752, 29602, -82308, 130321], [1, 4, -31, 4, 1312, 92, -16399, 48668, 279841], [1, 4, -43, 4, 2176, 116, -36163, 97556, 707281], [1, 0, -118, 0, 5403, 0, -113398, 0, 923521], [1, -18, 193, -1530, 9852, -56610, 264217, -911754, 1874161], [1, 0, 78, 0, 4403, 0, 131118, 0, 2825761], [1, 10, 37, -230, -2180, -9890, 68413, 795070, 3418801], [1, 0, -66, 0, 3155, 0, -145794, 0, 4879681], [1, 24, 332, 3528, 29718, 186984, 932588, 3573048, 7890481], [1, -12, 153, -1260, 10376, -74340, 532593, -2464548, 12117361], [1, 0, -14, 0, -3525, 0, -52094, 0, 13845841], [1, 12, 130, 984, 5451, 65928, 583570, 3609156, 20151121], [1, 36, 678, 8856, 86147, 628776, 3417798, 12884796, 25411681], [1, 0, -284, 0, 30822, 0, -1513436, 0, 28398241], [1, 28, 514, 6664, 68731, 526456, 3207874, 13805092, 38950081], [1, 0, -228, 0, 26006, 0, -1570692, 0, 47458321], [1, -12, 222, -2088, 26627, -185832, 1758462, -8459628, 62742241], [1, 12, 238, 2280, 31347, 221160, 2239342, 10952076, 88529281], [1, -8, -106, 256, 12235, 25856, -1081306, -8242408, 104060401], [1, -8, 52, -968, 24838, -99704, 551668, -8741816, 112550881], [1, 12, 86, -1872, -23493, -200304, 984614, 14700516, 131079601], [1, 0, -44, 0, 21174, 0, -522764, 0, 141158161], [1, 12, -91, 108, 26184, 12204, -1161979, 17314764, 163047361]], 'euler_factors_factorization': [[[[1, 0, -1, 0, 1], 1]], [[[1, -1, 1], 2]], [[[1, 0, 1], 2]], [[[1, 0, 10, 0, 51, 0, 490, 0, 2401], 1]], [[[1, -12, 73, -300, 1032, -3300, 8833, -15972, 14641], 1]], [[[1, -2, 13], 2]], [[[1, -4, -1, -68, 289], 2]], [[[1, -12, 82, -408, 1707, -7752, 29602, -82308, 130321], 1]], [[[1, 4, -31, 4, 1312, 92, -16399, 48668, 279841], 1]], [[[1, 4, -43, 4, 2176, 116, -36163, 97556, 707281], 1]], [[[1, -11, 31], 2], [[1, 11, 31], 2]], [[[1, -18, 193, -1530, 9852, -56610, 264217, -911754, 1874161], 1]], [[[1, 0, 78, 0, 4403, 0, 131118, 0, 2825761], 1]], [[[1, 10, 37, -230, -2180, -9890, 68413, 795070, 3418801], 1]], [[[1, 0, -66, 0, 3155, 0, -145794, 0, 4879681], 1]], [[[1, 12, 94, 636, 2809], 2]], [[[1, -12, 153, -1260, 10376, -74340, 532593, -2464548, 12117361], 1]], [[[1, 0, -14, 0, -3525, 0, -52094, 0, 13845841], 1]], [[[1, 12, 130, 984, 5451, 65928, 583570, 3609156, 20151121], 1]], [[[1, 36, 678, 8856, 86147, 628776, 3417798, 12884796, 25411681], 1]], [[[1, 0, -142, 0, 5329], 2]], [[[1, 14, 159, 1106, 6241], 2]], [[[1, 0, -228, 0, 26006, 0, -1570692, 0, 47458321], 1]], [[[1, -12, 222, -2088, 26627, -185832, 1758462, -8459628, 62742241], 1]], [[[1, 12, 238, 2280, 31347, 221160, 2239342, 10952076, 88529281], 1]], [[[1, -8, -106, 256, 12235, 25856, -1081306, -8242408, 104060401], 1]], [[[1, -4, 18, -412, 10609], 2]], [[[1, 12, 86, -1872, -23493, -200304, 984614, 14700516, 131079601], 1]], [[[1, 0, -44, 0, 21174, 0, -522764, 0, 141158161], 1]], [[[1, 12, -91, 108, 26184, 12204, -1161979, 17314764, 163047361], 1]]], 'gamma_factors': [[], [0, 0, 0, 0]], 'group': 'GL2', 'index': 16, 'label': '8-390e4-1.1-c1e4-0-16', 'load_key': 'CMFs-workshop', '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}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/390/2/bb/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.03125', 'prec': 24}, 'plot_values': [6.514727461351934, 6.511328394037315, 6.506236668536168, 6.49815734130091, 6.485790847862208, 6.467865125392733, 6.4432370737404945, 6.4108102191957705, 6.369514197054952, 6.318166677795121, 6.255042191581023, 6.178351653151543, 6.086421424342813, 5.977684920867811, 5.850603415321814, 5.703838814688366, 5.536341989355118, 5.347394283834529, 5.136637239482348, 4.904143801400291, 4.650470291416931, 4.376730436817231, 4.084718847126398, 3.77680130858372, 3.4558762080052445, 3.125411942442667, 2.7895423733016678, 2.452790984170478, 2.1199260351332367, 1.795912247826441, 1.4859009413426294, 1.1948418506190688, 0.9272681047330021, 0.6871797420210146, 0.4779423061615061, 0.3019370822218522, 0.1604001725701691, 0.053352786176255634, -0.02045505327482364, -0.06365258196784093, -0.08019026526650842, -0.0752064550682286, -0.05486068931564067, -0.026079762423147548, 0.0037890961676704704, 0.027363226073825433, 0.037648945971750246, 0.028527664106848236, -0.004779046906749086, -0.0652752433599335, -0.1537693750307127, -0.26856175459598186, -0.4052594301386061, -0.556703541947079, -0.7130143318421389, -0.8618772325488414, -0.9889823580324208, -1.0786080244080871, -1.1143818353119774, -1.080170394158407, -0.9610264690282924, -0.7441897129030879, -0.42014065614473844, 0.016534513011353953, 0.5663915981008927, 1.2245439676230456, 1.9803769111849745, 2.817544725934748, 3.7142033704337365, 4.643669772194861, 5.575800781068929, 6.477968353890614, 7.316278682501765, 8.05738435593043, 8.671226070977267, 9.13183145924959, 9.418367794020162, 9.516836437432781, 9.422556853072212, 9.13911433466347, 8.677818917027183, 8.057864516910353, 7.306970043591113, 6.4580531146219355, 5.546997344709857, 4.6113002131306, 3.689055255760688, 2.8151874827067482, 2.0193337724238387, 1.3247622916994077, 0.7476935913670657, 0.29580685241123533, -0.03169135345653573, -0.2431772615447545, -0.3533840504706051, -0.3819341949909768, -0.35122143747613704, -0.2841833979725986, -0.20220984271107575, -0.12314627453623277, -0.05973567820812918, -0.018663978327969167, -0.0002450648232330585, 0.001230533478312304, -0.0035634127722125562, -0.0006215734552436761, 0.025344480480450658, 0.0886412795428423, 0.20034257261428348, 0.36630381517962723, 0.5857762390696586, 0.8506263289411523, 1.1452808641718006, 1.4476416665179612, 1.7312967788436489, 1.9676616088977257, 2.128565113840947, 2.1894783614906648, 2.133375025851216, 1.9522861396953481, 1.6485529145068738, 1.2358468747601268, 0.7394847058265661, 0.19346456680447738, -0.36251915464094403, -0.8862939109462388, -1.337270006256584, -1.6813614698944885, -1.8945096793784135, -1.9653575795809897, -1.8974000967337499, -1.7086459181506366, -1.4294141478744726, -1.0989584265884256, -0.7610202458052182, -0.457185239544124, -0.22039094939282414, -0.06907813424963838, -0.002232500207214004, 0.004109945978287887, -0.002319743850043449, 0.04813099303212507, 0.2424327415631322, 0.6775555803538316, 1.4510107710583784, 2.6500819695390776, 4.341055433811155, 6.558766840590419, 9.297562735771114, 12.505777771798702, 16.087189052557893, 19.901781011088502, 23.770253869125202, 27.48588266005367, 30.837854520260233, 33.620550843655145, 35.64572439321905, 36.76174509899316, 36.88162140055669, 35.978692929366176, 34.08558449158178, 31.29874674040238, 27.7860823768256, 23.758126673978158, 19.448146048274623, 15.099320198187383, 10.953606753428897, 7.220405785432424, 4.060133739456918, 1.5769867363140062, -0.1845164026859604, -1.2441148890958953, -1.678372691247049, -1.6075236891266311, -1.18017467174312, -0.5558267055243484, 0.11364172832849619, 0.7001876036385478, 1.112047453140501, 1.3013833458372666, 1.266155741375977, 1.0463505465689102, 0.7150814560306673, 0.36555094519929376, 0.09623946046026383, -0.004263504006757266, 0.12928797272700857, 0.5292125816214611, 1.1894194692663393, 2.06508214685417, 3.0796480142672595, 4.134116123125305, 5.118309795747673, 5.925264243270112, 6.469400527481901, 6.694107306476281, 6.576730656852229, 6.132544596305521, 5.416829757434782, 4.511786198028857, 3.514170122943314, 2.5242011790535703, 1.6344228492202397, 0.9144420517476328, 0.40305593916366883, 0.10587906986609288, -0.003005667297743079, 0.024741116199465056, 0.12251241332819603, 0.22159787984035736, 0.2643005112449073, 0.21554972811698994, 0.07087006286510972, -0.14047874133175434, -0.35774453521621136, -0.4964868557644877, -0.46077950432785375, -0.15829078743940986, 0.4844708344451353, 1.5083769486286387, 2.9106452872890567, 4.639566181977085, 6.5998536762203415, 8.658785282964852, 10.656483452858614, 12.42390899879921, 13.811579420886156, 14.699809314120355, 15.008450507664966, 14.709523109580065, 13.841773689787042, 12.493810638066526, 10.789847733685663, 8.878944405285425, 6.924319126558445, 5.0748222936988405, 3.4484653759906863, 2.124457007692506, 1.1398102700393775, 0.4866020028837939, 0.11977908385402528, -0.030067382586833395, -0.04243426756472116, 0.007202167992567992, 0.059858606881055716, 0.08118551836219215, 0.06410662220299569, 0.025896738702387092, 0.0003410075943423785, 0.02634206217782866, 0.13546664500704844, 0.3409054355736027, 0.6291498999853066, 0.9566716932197517, 1.2550196835776668, 1.4387580083826519, 1.4167282630055524, 1.1078578361327134, 0.4615446329788898, -0.5339860385575268, -1.8464609019543665, -3.396848304341482, -5.062260578561379, -6.694207646503914, -8.136436174109658, -9.243130915379203, -9.900137940261589, -10.041334452057141, -9.656029469752543, -8.790756706932706, -7.54678593542302, -6.06295165764745, -4.495420511961383, -2.9976451531944157, -1.7014866505554003, -0.69873073136606, -0.03123500672290076, 0.3107838930043295, 0.3829833858478398, 0.2740522187755131, 0.0886111058576481, -0.0715511597815118, -0.12489744290785565, -0.022642289252661433, 0.24462754315680368, 0.6472208235078221, 1.1255875363161028, 1.6027481887278507, 1.9981648631167193, 2.2433983828296564, 2.2986910464594645, 2.1564901146922195, 1.8406356139771625, 1.402725448710295, 0.9143068638044127, 0.4492789851756573, 0.07031301026823754, -0.1808920548052343, -0.2904114924388396, -0.27358130031335304, -0.16886130086888906, -0.027572092984039023, 0.09837661073048448, 0.16965316015616777, 0.16933138335363768, 0.10735838811998895, 0.018808490332523152, -0.04401791605769972, -0.024250288264601474, 0.12453124696550646, 0.4246451904909778, 0.8651660545687324, 1.3984782759133376, 1.9451762981444802, 2.410493692464787, 2.701459386064118, 2.745661199085367, 2.5119585252704115, 2.0298644090683973, 1.3869296507749471, 0.7194742692328344, 0.19689210083639622, -0.004867234756913373, 0.25903647405907804, 1.0727251411249692, 2.436926661333681, 4.253472794035137, 6.331173873728989, 8.408993855040388, 10.191266386958905, 11.394060543947356, 11.796836719318291, 11.286184666356348, 9.887256338978773, 7.7789235252494855, 5.280372094760038, 2.8162809969751237, 0.8636933326621257, -0.11434303798533946, 0.26291612140319104, 2.2320088673573917, 5.838925859129158, 10.926761201355786, 17.144717754297616, 23.97547140110963, 30.794038400678012, 36.97440311110651, 41.945750924338, 45.24369646425381, 46.57333742509974, 45.88531744499665, 43.32944796747708, 39.211633164366376, 33.96323085225009, 28.112030158204757, 22.17411694175508, 16.589982234554274, 11.693165240024747, 7.6956470464771956, 4.667936074511338, 2.557601334876926, 1.2252629987370542, 0.48474965095906014, 0.1405794618555679, 0.020977600251795084, -0.0008069729717701348, 0.001016838699176087, -0.00044931898659146503, 0.0008688429093268407, 0.025422149348952303, 0.0905299398321581, 0.19847286443531828, 0.33202202250784996, 0.4582555859947385, 0.5405711318894377, 0.5507862474913816, 0.47925742799831406, 0.3411976621054112, 0.1757912084739416, 0.03255592918456543, -0.04611825093535686, -0.04387423475804047, 0.011972849173663338, 0.041391389877048906, -0.08461016825653025, -0.5280398784738272, -1.4545948028561015, -2.9965527035671324, -5.216433561685587, -8.07730630910036, -11.425762920439718, -14.99530925250124, -18.430404136000426, -21.33094379755792, -23.31397242167859, -24.068721862632064, -23.409680583366896, -21.318799221380033, -17.958774952521715, -13.651515342463721, -8.843571039004859, -4.047258705670109, 0.25358893073437816, 3.6620696020504493, 5.912194103747803, 6.910595626083147, 6.770095458779091, 5.753405297394408, 4.2158360966844475, 2.5520121555775614, 1.1364946519499177, 0.24278620378310628, 0.005298913889258236, 0.41106701472753454, 1.3112219283668547, 2.459205111525957, 3.5693792590237234, 4.378448215270555, 4.699920764602887, 4.461462281734905, 3.717730433329553, 2.6378047903716575, 1.4689765078413026, 0.4836799188167584, -0.07597360210950985, -0.048692925077583105, 0.6124325242759648, 1.8315800614114692, 3.4215874135341924, 5.116909175628137, 6.6328874530842405, 7.713934160091947, 8.172838728350541, 7.9252849085776145, 7.015923601685924, 5.591773407152537, 3.8681033888937884, 2.0926728379302815, 0.505454198515798, -0.7110186517764173, -1.4568555863879775, -1.721489913946638, -1.5767915369870789, -1.153643103373104, -0.6086874571334314, -0.09081521028798278, 0.2869466586226468, 0.46469067253854085, 0.43942544396891825, 0.2565116998829719, -0.009145205892219298, -0.27581429205307745, -0.475081797971654, -0.5669512839634483, -0.5464629919691496, -0.43805390257525956, -0.2846766285960156, -0.1337693687006527, -0.02190156077341173, 0.03395976714912546, 0.03765856754548591, 0.009618868975577267, -0.02233453510067324, -0.036464666000967726, -0.026283266071650203, -0.003861134163370301, 0.0034508361737217003, -0.036326983374466125, -0.14493001421839113, -0.31950316670063983, -0.522598875393355, -0.6812501610584614, -0.6970582007775706, -0.4662051630616237, 0.09516853738422357, 1.0251958035198938, 2.2947696530345767, 3.798694221379715, 5.37136338374549, 6.807462762841699, 7.891656130021493, 8.442161424065644, 8.367073857704959, 7.672931853392203, 6.462953137109208, 4.928338696987775, 3.3239043895527085, 1.8973107630254986, 0.8339565182644714, 0.21679755555024732, -0.0010825309606411512, -0.001717082059719711, -0.07107445574777797, -0.5452284536064925, -1.7410750473176337, -3.8837736167639765, -7.047923870341377, -11.124417714131457, -15.823698028627573, -20.708472893722117, -25.253003363978355, -28.927902315013824, -31.30522231014018, -32.110436850683065, -31.258188314009423, -28.872763015525656, -25.28169569702098, -20.93006320355018, -16.304818879432734, -11.86724872034047, -7.988760751475798, -4.896850659856198, -2.666367442478607, -1.237430763657767, -0.45179086207769037, -0.10696177107732545, -0.007252506101071833, -0.0012204865904317755, -0.001505936734414809, 0.016897383614697965, 0.036940635839750546, 0.028519472676799495, -0.02210502397582667, -0.09334876873056454, -0.1260399247763112, -0.03825598783953189, 0.2469180018358824, 0.7687357974291179, 1.499807538558388, 2.332134799068051, 3.092882015001829, 3.5717650243509804, 3.560594309237316, 2.908829908102155, 1.5901449975069293, -0.29003894374693834, -2.503507158613044, -4.7209465048487775, -6.559012201526778, -7.675562592897521, -7.839565728892055, -6.9785799877035855, -5.208822773565979, -2.82287625601943, -0.23248608049702646, 2.11013367087768, 3.7986874806413757, 4.559428216007468, 4.308332275086439, 3.1665657000696106, 1.4293539586200625, -0.4967440122163257, -2.1802794716972977, -3.2621588125335172, -3.540960091620778, -3.0039288336118677, -1.826707037737985, -0.33568912608718027, 1.0775089600566998, 2.05137216299124, 2.331011234716128, 1.8294542036102057, 0.661855660082444, -0.8989528211492926, -2.491278543513211, -3.745399176209156, -4.377584396206741, -4.266980112987062, -3.4815563502520224, -2.2636620556276204, -0.9799216806558775, -0.023861207937846463, 0.2857642324067124, -0.2112223748883951, -1.4648253843055152, -3.209970609234223, -5.013036007111983, -6.361452856799541, -6.779636832357226, -5.931828918437092, -3.704344237924805, -0.2492055347435292, 4.042241485461247, 8.611383222923447, 12.822082051300345, 16.078092863811463, 17.970650425929957, 18.321192187002595, 17.186938966293948, 14.849457211801585, 11.777886548317163, 8.48966429998193, 5.445958579782905, 2.983664984981463, 1.2741358366672506, 0.30495306610136375, -0.07945451428994361, -0.10898492141482595, -0.012227614359418219, 0.0506400665278646, 0.029723851540064038, -0.007938630822867786, 0.09328320522940087, 0.5238177374133794, 1.4433363601275044, 2.920369172392891, 4.902608530443357, 7.2118996292030815, 9.563721343428444, 11.620290949450547, 13.084958721603716, 13.74571751642091, 13.504876813607956, 12.404903680353819, 10.643041009447828, 8.497161526549599, 6.262658702523637, 4.2055453558939835, 2.524998790666068, 1.3131724662498327, 0.5580152002378137, 0.17098286842911464, 0.025603220144869994, -0.0020785160532196464, 0.0002949927180528723, -0.0013153034005386967, 0.010363388199686133, 0.08494319751936272, 0.2758291311643023, 0.6110107325902587, 1.0754780653337361, 1.6073568116275752, 2.107148309102364, 2.4620622229894797, 2.5858620751263115, 2.4387889826045397, 2.0374782465149766, 1.45734849879307, 0.822875474783324, 0.2680533651533308, -0.09664920228600798, -0.20805735728473995, -0.06542411369637909, 0.2699722544386629, 0.694281258256707, 1.089788418592947, 1.3560331680338158, 1.434660272601311, 1.3206721232768754, 1.0590203234209636, 0.7276764047098546, 0.41014906231728443, 0.17049000270011808, 0.03626037261740573, -0.005983564187599887, -8.06234160082345e-05, 0.00016387469821013014, -0.04554869780391045, -0.145668398880571, -0.2719601848036172, -0.36929484920316014, -0.37867076870955335, -0.2699468747441515, -0.06627878277084093, 0.14620165432863258, 0.2275025601626681, 0.017109789651733986, -0.6122219346088691, -1.6993125296614913, -3.1494515351308445, -4.71459794846902, -6.0126764204436505, -6.583818459737832, -5.9782053603775696, -3.8621251510676573, -0.10762955992019817, 5.140842660793709, 11.449811168133222, 18.17214912025477, 24.52719169541776, 29.703482504270422, 33.009820838762266, 34.077870661101166, 32.85589880258131, 29.58562834031159, 24.784490200124022, 19.205963839530664, 13.614109969571674, 8.643863152817774, 4.728115019425997, 2.0591910452569184, 0.5622923980832129, -0.03681999427306604, -0.108255134740164, -0.013844775813475386, -0.01998333676863763, -0.2448451017371559, -0.6540869085754489, -1.1010484161710836, -1.394184358382566, -1.3727174237538822, -0.9697856036411371, -0.23665322222258378, 0.6701981832662848, 1.5278230793338343, 2.1111448349411344, 2.2767109464028263, 1.9939199587969347, 1.3474175927281244, 0.5188638111143156, -0.257608288861022, -0.7803738012493115, -0.9382910032849796, -0.7378275271151048, -0.30010371782447737, 0.18210703681603627, 0.5158055583201062, 0.581489640713036, 0.3894928470360137, 0.09934718176468127, -0.008584517202254243, 0.3955304576500413, 1.5948675177244556, 3.7306200139590735, 6.728578152179945, 10.275516169325366, 13.882395565006378, 16.968216850538248, 18.966369640157183, 19.46092638845044, 18.33857212624094, 15.779289273968695, 12.20885358374875, 8.22883024881107, 4.506969745818504, 1.5843504523354381, -0.23865400583304516, -0.9477770584444006, -0.8031252403202364, -0.25676242674218347, 0.18909386927646252, 0.13194876732393968, -0.6070289886804413, -1.9180273690316034, -3.4182540347160257, -4.545728329282131, -4.707873031791418, -3.4430863133307765, -0.5658347786944478, 3.746663297964392, 8.988114049477362, 14.407349577586729, 19.134109886991897, 22.366084727805777, 23.615321124617765, 22.75214955084856, 19.998530754811174, 15.89859219385556, 11.241851199867899, 6.817872988388128, 3.2473582554314966, 0.8845529096013416, -0.2287641044380375, -0.3505933247888533, 0.06757499910890306, 0.5237217293090615, 0.6058489439490268, 0.0987340482099152, -0.9685598375443942, -2.344559738761487, -3.644019809712397, -4.4636920255262424, -4.4971656930696335, -3.6286023292609766, -1.9724211815289312, 0.16419897788869672, 2.3522731509409347, 4.142319624752182, 5.193813583205981, 5.343064964338776, 4.622809029922414, 3.2501024056479872, 1.5789150424129417, -0.013256693125829338, -1.2158031881550702, -1.8449223959698444, -1.8746039536417969, -1.4245408232237426, -0.7082720354064518, 0.0339017392450223, 0.6009161654405283, 0.8790068315583861, 0.8578712172334637, 0.6167837112995443, 0.2868131863794041, 0.00252896587697828, -0.13906950170674218, -0.10419302607651632, 0.07603647825451733, 0.3264176036826294, 0.5563975126570003, 0.6911725436575765, 0.6990500072844702, 0.5933345346204235, 0.4198319604661202, 0.23781155176910918, 0.09803138626904076, 0.022366552137349668, 0.0004597512901465494, -0.00010147056056824344, -0.015404157850270654, -0.06520427120236819, -0.14012111642499142, -0.20213683453770304, -0.19916003865223825, -0.08834140973493719, 0.13964122026890546, 0.4457798591967489, 0.7499440331496176, 0.9524245617327655, 0.9669390429376458, 0.7623201284910843, 0.3993474824231208, 0.025026685030920637, -0.15327484131697572, 0.08587405275091711, 0.9045787413157462, 2.3383528249928576, 4.262369200116996, 6.389812708673213, 8.309647034678617, 9.579273855783825, 9.829443310550259, 8.861311821656294, 6.720454611879839, 3.7064042276486915, 0.32377374995199854, -2.8163100514211723, -5.130677579870554, -6.1923710172461055, -5.826208071567389, -4.1544181223633725, -1.56275430798961, 1.3971187037876445, 4.1229612158594175, 6.095473285524647, 7.019610489156697, 6.850226114927434, 5.766831458495259, 4.120298362223823, 2.346186635334265, 0.822855851874511, -0.2119167860245218, -0.6920925601920724, -0.7130994406938074, -0.4741909020068766, -0.19137967838894943, -0.017581927539994168, 0.008317832885341013, -0.030070188139345214, 0.03576915129522025, 0.3891300174309053, 1.1517987872608533, 2.326552313044505, 3.771328071341604, 5.221284895505924, 6.374684811105448, 6.966536607444283, 6.833008711666302, 5.968786298209189, 4.560112042504348, 2.904959912111468, 1.3278918043913646, 0.10466034184797067, -0.6047295167000699, -0.8040260243753486, -0.6371036915721219, -0.32136512220239755, -0.06191031155947519, 0.03340200293524041, 0.0061256284245274515, 0.046890702322924714, 0.4409857110072053, 1.474479370965018, 3.3247717853421377, 5.970037774350257, 9.167979142684139, 12.48041164243299, 15.34407910283204, 17.201571600934624, 17.691140767569337, 16.701510268651287, 14.385427785097267, 11.148587346918228, 7.591389915942561, 4.310878705455169, 1.7620141960193163, 0.17870145250444328, -0.4579372569689484, -0.39300225598808286, 0.008682270970576727, 0.3922743900742554, 0.527514964387723, 0.37773511643632646, 0.10009317731422798, -0.022581981218628616, 0.3051879849663627, 1.2725225195907868, 2.8685057541595977, 4.849043879582427, 6.806119627614775, 8.268709600485506, 8.821689253106427, 8.241333423757956, 6.618209386040147, 4.3046524253685625, 1.8162950614530333, -0.28992064057329825, -1.5672311928292897, -1.8398750487756796, -1.2501699974980836, -0.21320368457010172, 0.7046688394529594, 0.973642241496459, 0.28825143627771943, -1.3013432550615611, -3.3511795211093984, -5.103122313958028, -5.6637778771316905, -4.245773183970786, -0.39977631930623236, 5.832129639489432, 13.850495402950918, 22.56799853671593, 30.682095334188237, 36.912693878006024, 40.22180788041386, 40.047545996701444, 36.52843071945672, 30.350361855769393, 22.55497200307813, 14.354308294664273, 6.927532399678307, 1.1269128095231276, -2.640416220031508, -4.406102791149755, -4.557179530531574, -3.687170936158925, -2.4158928035202187, -1.2387208054257384, -0.43709010259882464, -0.06512017585748689, -0.0007380018632362883, -0.036564994492007605, 0.020368017618325976, 0.2766506399681677, 0.7226459470758481, 1.246514057634472, 1.693290019782874, 1.9252389075926852, 1.8665996232746414, 1.530052397268364, 1.0168844705302391, 0.46783447730967054, 0.014022510284562433, -0.25999711839762574, -0.33737471902978383, -0.26574066915061184, -0.12832589565563832, -0.0068228299070036465, 0.04977863896181698, 0.03806887700693102, -0.007834491580041748, -0.04112776570797303, -0.03331437863124524, 0.0051204027067242724, 0.023679661941331615, -0.04700161354177081, -0.25559647962747445, -0.5924817363350566, -0.9666651276109942, -1.2081168778545501, -1.1130888599548907, -0.5078593163324464, 0.689284434650045, 2.415120474769284, 4.432792016491117, 6.380455161133361, 7.853943703843834, 8.506099038051747, 8.152519170442227, 6.838298713073393, 4.841837438027535, 2.618482455458731, 0.6915786320081754, -0.4859598582630265, -0.6527108704550324, 0.1835113289465096, 1.746841590610685, 3.5720331388618476, 5.119829961978467, 5.921907980386048, 5.735917193160473, 4.58774285412402, 2.749409938427124, 0.6714122521874514, -1.1388493478745543, -2.280497824017664, -2.5593534647671405, -2.0278091605915374, -0.9688983803634403, 0.20687522956959958, 1.0982015923837196, 1.435126077155163, 1.1535034608199057, 0.40103422727742793, -0.511997551523541, -1.2037797247970468, -1.3392172587048516, -0.7656019767204415, 0.40196054455341473, 1.8157949024223587, 3.150720265250765, 4.246463478708301], 'positive_zeros': ['1.17735732094833667893933524256953', '1.37082138207289870932682328219629', '1.49669044634574517470979148697739', '1.96770013224055879699421583161170', '2.87138954784061684477933101437409', '3.18842569997507225046348647153022', '3.22727748026356694840297128845669', '3.28280422320829006610625162403102', '3.85457115966113509359783228066670', '4.31498322252172755025692376795267', '4.35518390664800572302136329604958', '4.38025457321253419724202458380005', '5.30852660327261309616696853991453', '5.49456691732621386830599719431425', '5.77407397996638689192526797987646', '5.78617412331234509461318941351760', '6.43490527312637545586264229065925', '6.45520172121432949839163273473985', '6.63623566718143719176609460135036', '6.79082252273857290333450803592989', '7.52100024155861497188637053801411', '7.58993471480117470236079886203148', '7.75338668018561427806800200379404', '7.75357349541346647192320341784094', '8.078373952676704552512322283424655', '8.626997887928937813892154417958591', '8.765550053429603303729873530968910', '8.847346073073651922932644429918729', '9.257212128458081610940022676657378', '9.412425011472397068456333371022332', '9.569670128619518044723870423904432', '9.632955798680517045224361016152412', '10.05719180685212250643458355281110', '10.06633265487803078178147423636800', '10.55542212491616481116556327535900', '10.58482941794237321934998320690745', '11.40015385130113339053797071740714', '11.42391371656786079508589163952753', '11.46402647924584353568484137662868', '11.49662851803774000723928917145668'], 'prelabel': '8-390e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e4-0', 'trace_hash': 357496205875656832, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.17735732094833667893933524257', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.37082138207289870932682328220', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.49669044634574517470979148698', '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': 94.05174466820122, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 23134410000, 'conductor_radical': 390, 'degree': 8, 'dirichlet_coefficients': [1, 0, 2, 1, 0, 0, 0, 0, 1, 0, 12, 2, 4, 0, 0, 0, 8, 0, 12, 0, 0, 0, -4, 0, -2, 0, -2, 0, -4, 0, 0, 0, 24, 0, 0, 1, 18, 0, 8, 0, 0, 0, -10, 12, 0, 0, 0, 0, -10, 0, 16, 4, -24, 0, 0, 0, 24, 0, 12, 0, 0, 0, 0, -1, 0, 0, -12, 8, -8, 0, -36, 0, 0, 0, -4, 12, 0, 0, -28, 0, -4, 0, 0, 0, 0, 0, -8, 0, 12, 0, 0, -4, 0, 0, 0, 0, -12, 0, 12, -2], 'euler11': [1, -12, 73, -300, 1032, -3300, 8833, -15972, 14641], 'euler13': [1, -4, 30, -52, 169, 0, 0, 0, 0], 'euler17': [1, -8, 14, -128, 1123, -2176, 4046, -39304, 83521], 'euler19': [1, -12, 82, -408, 1707, -7752, 29602, -82308, 130321], 'euler2': [1, 0, -1, 0, 1, 0, 0, 0, 0], 'euler23': [1, 4, -31, 4, 1312, 92, -16399, 48668, 279841], 'euler29': [1, 4, -43, 4, 2176, 116, -36163, 97556, 707281], 'euler3': [1, -2, 3, -2, 1, 0, 0, 0, 0], 'euler31': [1, 0, -118, 0, 5403, 0, -113398, 0, 923521], 'euler37': [1, -18, 193, -1530, 9852, -56610, 264217, -911754, 1874161], 'euler41': [1, 0, 78, 0, 4403, 0, 131118, 0, 2825761], 'euler43': [1, 10, 37, -230, -2180, -9890, 68413, 795070, 3418801], 'euler47': [1, 0, -66, 0, 3155, 0, -145794, 0, 4879681], 'euler5': [1, 0, 2, 0, 1, 0, 0, 0, 0], 'euler53': [1, 24, 332, 3528, 29718, 186984, 932588, 3573048, 7890481], 'euler59': [1, -12, 153, -1260, 10376, -74340, 532593, -2464548, 12117361], 'euler61': [1, 0, -14, 0, -3525, 0, -52094, 0, 13845841], 'euler67': [1, 12, 130, 984, 5451, 65928, 583570, 3609156, 20151121], 'euler7': [1, 0, 10, 0, 51, 0, 490, 0, 2401], 'euler71': [1, 36, 678, 8856, 86147, 628776, 3417798, 12884796, 25411681], 'euler73': [1, 0, -284, 0, 30822, 0, -1513436, 0, 28398241], 'euler79': [1, 28, 514, 6664, 68731, 526456, 3207874, 13805092, 38950081], 'euler83': [1, 0, -228, 0, 26006, 0, -1570692, 0, 47458321], 'euler89': [1, -12, 222, -2088, 26627, -185832, 1758462, -8459628, 62742241], 'euler97': [1, 12, 238, 2280, 31347, 221160, 2239342, 10952076, 88529281], 'euler_factors': [[1, 0, -1, 0, 1, 0, 0, 0, 0], [1, -2, 3, -2, 1, 0, 0, 0, 0], [1, 0, 2, 0, 1, 0, 0, 0, 0], [1, 0, 10, 0, 51, 0, 490, 0, 2401], [1, -12, 73, -300, 1032, -3300, 8833, -15972, 14641], [1, -4, 30, -52, 169, 0, 0, 0, 0], [1, -8, 14, -128, 1123, -2176, 4046, -39304, 83521], [1, -12, 82, -408, 1707, -7752, 29602, -82308, 130321], [1, 4, -31, 4, 1312, 92, -16399, 48668, 279841], [1, 4, -43, 4, 2176, 116, -36163, 97556, 707281], [1, 0, -118, 0, 5403, 0, -113398, 0, 923521], [1, -18, 193, -1530, 9852, -56610, 264217, -911754, 1874161], [1, 0, 78, 0, 4403, 0, 131118, 0, 2825761], [1, 10, 37, -230, -2180, -9890, 68413, 795070, 3418801], [1, 0, -66, 0, 3155, 0, -145794, 0, 4879681], [1, 24, 332, 3528, 29718, 186984, 932588, 3573048, 7890481], [1, -12, 153, -1260, 10376, -74340, 532593, -2464548, 12117361], [1, 0, -14, 0, -3525, 0, -52094, 0, 13845841], [1, 12, 130, 984, 5451, 65928, 583570, 3609156, 20151121], [1, 36, 678, 8856, 86147, 628776, 3417798, 12884796, 25411681], [1, 0, -284, 0, 30822, 0, -1513436, 0, 28398241], [1, 28, 514, 6664, 68731, 526456, 3207874, 13805092, 38950081], [1, 0, -228, 0, 26006, 0, -1570692, 0, 47458321], [1, -12, 222, -2088, 26627, -185832, 1758462, -8459628, 62742241], [1, 12, 238, 2280, 31347, 221160, 2239342, 10952076, 88529281]], 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/390/2/bb/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': '8-390e4-1.1-c1e4-0-16', '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}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-390e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 357496205875656832, 'z1': {'__RealLiteral__': 0, 'data': '1.17735732094833667893933524257', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '1492477714583259116767256471213,1737722547790401036206754315007,1897280542666040442963295006620,2494356253703910726851242380518', 'Lhash_array': ['1492477714583259116767256471213', '1737722547790401036206754315007', '1897280542666040442963295006620', '2494356253703910726851242380518'], 'label': '8-390e4-1.1-c1e4-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/390/2/bb/b'}