Lfunction data - 12-378e6-1.1-c1e6-0-1

Formats: - HTML - YAML - JSON - 2023-12-06T17:48:34.410747

• 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': '607423875388522700011757474377,822048902412772951461853550540,1537612015767349038413718166512,2187245875906569998609419164350,2287940936520619113945081166790,2443196485447762240270043619030', 'a10': -6, 'a2': -3, 'a3': 0, 'a4': 3, 'a5': 2, 'a6': 0, 'a7': -4, 'a8': 2, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 756.1595493200377, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 3, 6, 7, 6, 3, 1]], [3, [1]], [7, [1, 4, 14, 55, 98, 196, 343]]], 'bad_primes': [2, 3, 7], 'central_character': '378.1', 'coefficient_field': '1.1.1.1', 'conductor': 2917096519063104, 'conductor_radical': 42, 'degree': 12, 'euler_factors': [[1, 3, 6, 7, 6, 3, 1], [1], [1, -2, 19, -44, 197, -374, 1279, -1870, 4925, -5500, 11875, -6250, 15625], [1, 4, 14, 55, 98, 196, 343], [1, 2, 55, 104, 1373, 2186, 19567, 24046, 166133, 138424, 805255, 322102, 1771561], [1, -8, 24, -42, -32, 1408, -7901, 18304, -5408, -92274, 685464, -2970344, 4826809], [1, -4, -23, 68, 410, -220, -8111, -3740, 118490, 334084, -1920983, -5679428, 24137569], [1, 3, -12, -67, -153, 54, 6315, 1026, -55233, -459553, -1563852, 7428297, 47045881], [1, 14, 211, 1784, 14837, 86138, 483607, 1981174, 7848773, 21705928, 59046451, 90108802, 148035889], [1, -5, 4, -251, 197, 3418, 20293, 99122, 165677, -6121639, 2829124, -102555745, 594823321], [1, -20, 186, -1398, 10342, -62234, 331987, -1929254, 9938662, -41647818, 171774906, -572583020, 887503681], [1, -3, -105, 104, 8109, -4221, -342138, -156177, 11101221, 5267912, -196786905, -208031871, 2565726409], [1, 0, -90, -18, 4410, 810, -194177, 33210, 7413210, -1240578, -254318490, 0, 4750104241], [1, 6, -24, -418, -1314, 3474, 88971, 149382, -2429586, -33233926, -82051224, 882050658, 6321363049], [1, -9, -6, 531, -2433, -3438, 104623, -161586, -5374497, 55130013, -29278086, -2064105063, 10779215329], [1, 15, 0, 33, 13635, 60360, -225155, 3199080, 38300715, 4912941, 0, 6272932395, 22164361129], [1, -14, -20, 154, 11666, -35126, -499301, -2072434, 40609346, 31628366, -242347220, -10008940186, 42180533641], [1, -8, -114, 342, 13762, -13214, -937217, -806054, 51208402, 77627502, -1578425874, -6756770408, 51520374361], [1, -1, -88, -243, 2035, 14290, 72259, 957430, 9135115, -73085409, -1773298648, -1350125107, 90458382169], [1, 14, 79, -988, -6031, 67514, 1600591, 4793494, -30402271, -353616068, 2007522799, 25259210914, 128100283921], [1, -19, 134, -27, -5759, 41986, -314903, 3064978, -30689711, -10503459, 3805364294, -39388360267, 151334226289], [1, -5, -138, 123, 11347, 21118, -1048937, 1668322, 70816627, 60643797, -5375111178, -15385281995, 243087455521], [1, 2, -182, 2, 18788, -13564, -1721225, -1125812, 129430532, 1143574, -8637414422, 7878081286, 326940373369], [1, -9, -144, 1197, 16101, -73314, -1141967, -6524946, 127536021, 843847893, -9034882704, -50256535041, 496981290961], [1, -28, 281, -2724, 45178, -388196, 2169217, -37655012, 425079802, -2486121252, 24876727961, -240445527196, 832972004929], [1, 58, 1795, 38656, 642593, 8628154, 95374567, 871443554, 6555091193, 39827315456, 186788419795, 609585829058, 1061520150601], [1, 0, 540, -22, 128520, -5940, 17202975, -611820, 1363468680, -24039994, 60777475740, 0, 1194052296529], [1, 27, 288, 1665, 9027, 19386, -481061, 2074302, 103350123, 2039696595, 37750925088, 378688967289, 1500730351849], [1, 5, -298, -507, 63817, 50038, -7953107, 5454142, 758209777, -656579703, -42065131978, 76931197745, 1677100110841], [1, -35, 544, -6473, 82973, -971966, 10198537, -109832158, 1059482237, -9339872281, 88697764384, -644852312755, 2081951752609]], 'euler_factors_factorization': [[[[1, 1, 1], 3]], [1], [[[1, -1, 9, -13, 45, -25, 125], 2]], [[[1, 4, 14, 55, 98, 196, 343], 1]], [[[1, 1, 27, 25, 297, 121, 1331], 2]], [[[1, -8, 24, -42, -32, 1408, -7901, 18304, -5408, -92274, 685464, -2970344, 4826809], 1]], [[[1, -4, -23, 68, 410, -220, -8111, -3740, 118490, 334084, -1920983, -5679428, 24137569], 1]], [[[1, 3, -12, -67, -153, 54, 6315, 1026, -55233, -459553, -1563852, 7428297, 47045881], 1]], [[[1, 7, 81, 325, 1863, 3703, 12167], 2]], [[[1, -5, 4, -251, 197, 3418, 20293, 99122, 165677, -6121639, 2829124, -102555745, 594823321], 1]], [[[1, -20, 186, -1398, 10342, -62234, 331987, -1929254, 9938662, -41647818, 171774906, -572583020, 887503681], 1]], [[[1, -11, 37], 3], [[1, 10, 37], 3]], [[[1, 0, -90, -18, 4410, 810, -194177, 33210, 7413210, -1240578, -254318490, 0, 4750104241], 1]], [[[1, -12, -6, 547, -258, -22188, 79507], 1], [[1, 18, 198, 1519, 8514, 33282, 79507], 1]], [[[1, -9, -6, 531, -2433, -3438, 104623, -161586, -5374497, 55130013, -29278086, -2064105063, 10779215329], 1]], [[[1, 15, 0, 33, 13635, 60360, -225155, 3199080, 38300715, 4912941, 0, 6272932395, 22164361129], 1]], [[[1, -14, -20, 154, 11666, -35126, -499301, -2072434, 40609346, 31628366, -242347220, -10008940186, 42180533641], 1]], [[[1, -8, -114, 342, 13762, -13214, -937217, -806054, 51208402, 77627502, -1578425874, -6756770408, 51520374361], 1]], [[[1, -1, -88, -243, 2035, 14290, 72259, 957430, 9135115, -73085409, -1773298648, -1350125107, 90458382169], 1]], [[[1, 7, 15, -599, 1065, 35287, 357911], 2]], [[[1, -19, 134, -27, -5759, 41986, -314903, 3064978, -30689711, -10503459, 3805364294, -39388360267, 151334226289], 1]], [[[1, -5, -138, 123, 11347, 21118, -1048937, 1668322, 70816627, 60643797, -5375111178, -15385281995, 243087455521], 1]], [[[1, 2, -182, 2, 18788, -13564, -1721225, -1125812, 129430532, 1143574, -8637414422, 7878081286, 326940373369], 1]], [[[1, -9, -144, 1197, 16101, -73314, -1141967, -6524946, 127536021, 843847893, -9034882704, -50256535041, 496981290961], 1]], [[[1, -28, 281, -2724, 45178, -388196, 2169217, -37655012, 425079802, -2486121252, 24876727961, -240445527196, 832972004929], 1]], [[[1, 29, 477, 5495, 48177, 295829, 1030301], 2]], [[[1, 0, 270, -11, 27810, 0, 1092727], 2]], [[[1, 27, 288, 1665, 9027, 19386, -481061, 2074302, 103350123, 2039696595, 37750925088, 378688967289, 1500730351849], 1]], [[[1, 5, -298, -507, 63817, 50038, -7953107, 5454142, 758209777, -656579703, -42065131978, 76931197745, 1677100110841], 1]], [[[1, -35, 544, -6473, 82973, -971966, 10198537, -109832158, 1059482237, -9339872281, 88697764384, -644852312755, 2081951752609], 1]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 1, 'label': '12-378e6-1.1-c1e6-0-1', '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}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/378/2/h/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0208333333333', 'prec': 50}, 'plot_values': [0.5460866819576049, 0.5439653485840961, 0.5395652432139241, 0.5327588157139134, 0.5234310002325291, 0.5114830694687232, 0.49683689039790313, 0.4794590936022772, 0.4594223423056874, 0.4368464365433369, 0.41188044682680236, 0.3847048294673108, 0.3555335412654685, 0.3246084524719941, 0.2921822426119184, 0.25855055015617195, 0.22406304850985664, 0.1891253056702219, 0.15419986614027334, 0.11980797429247234, 0.08653304247678564, 0.05501234822210541, 0.025929889100683237, 8.939828217793642e-06, -0.02199741024691654, -0.039317386096447006, -0.05117512331412272, -0.05681301321644646, -0.05551317677382952, -0.0466201424660329, -0.02956539510818276, -0.0038954713975543134, 0.030690658589050148, 0.0743126200281288, 0.1268824514596867, 0.18807918271176807, 0.25732613232697243, 0.333767233022068, 0.4162367047415964, 0.5032635329907255, 0.5930793496860427, 0.6836313749103546, 0.7726053123508023, 0.8574556582890858, 0.935444762206286, 1.0037182653060905, 1.0593817831491912, 1.099583360662912, 1.12160419900035, 1.1229603718441756, 1.101526412680318, 1.0556388437911413, 0.9841922829476024, 0.8867295883616069, 0.763519528916109, 0.6156312922464625, 0.44501816172971304, 0.25449331959749244, 0.04769306102122573, -0.17097989668696034, -0.39644619645256235, -0.6230607823118443, -0.8447440899601029, -1.0552291698741594, -1.2482964705513786, -1.4180098878537533, -1.5589602574278294, -1.6665105712295325, -1.7370555575748698, -1.7682486202448922, -1.75916497164452, -1.7104117080902903, -1.6241771136885461, -1.5042294581921394, -1.3558801869884272, -1.1857524438839744, -1.0014905654162698, -0.8114142829030073, -0.6241122935479699, -0.448002485600968, -0.2908705145698614, -0.15930340715599134, -0.05819531184261347, 0.009676596639028695, 0.04399671320245443, 0.047151409254209874, 0.024351389853273387, -0.01640085421661952, -0.0645333787854605, -0.10729951174651645, -0.13033620467767787, -0.11837602972687884, -0.056110819064378946, 0.0708601990095373, 0.27504551402474725, 0.56608416199072, 0.949832607561785, 1.427566404336214, 1.9953632564147974, 2.643785557609267, 3.3578255994373727, 4.11715117791656, 4.896674931005681, 5.667510527564911, 6.398449385877025, 7.057386776260221, 7.612932320007346, 8.03616311671531, 8.302388673645499, 8.393013953030925, 8.297617124665475, 8.014583077142593, 7.551562663014941, 6.925621454696866, 6.162868103800756, 5.297738679646834, 4.371978214072712, 3.4317604663265064, 2.5249804585396, 1.6985406236289609, 0.9955463647612095, 0.4526153759952272, 0.09729827622550791, -0.05447506058505983, 0.00015683013479691086, 0.250413731604053, 0.6721456300761316, 1.2289312250908557, 1.8739437965924672, 2.553063055974568, 3.2086580344372346, 3.7837589912742264, 4.226413613083345, 4.493983098179844, 4.557236409788408, 4.403696681935363, 4.039848468352847, 3.492116655556571, 2.8064877242756556, 2.0467760258949963, 1.291542400051894, 0.629217806939132, 0.15233101589743892, -0.04888673216050073, 0.10679759408158458, 0.6850261342161471, 1.7297689827193847, 3.2584293056313696, 5.258556401849274, 7.686360125557707, 10.467212456523574, 13.498385968868755, 16.654541151863793, 19.794348820646984, 22.768387530271657, 25.42799685968791, 27.634441107321628, 29.268414346501704, 30.24017548108347, 30.494423146390318, 30.013700498202585, 28.81993577795494, 26.973433235105947, 24.569940859558432, 21.736155239848333, 18.61900045785898, 15.37521767884849, 12.161062108349318, 9.122129913106251, 6.384135891036367, 4.045009020366672, 2.1684702841784436, 0.7813280326343314, -0.1261552900751147, -0.5971070510866886, -0.7024451022154019, -0.5331599799854794, -0.1904140995508513, 0.22447656118247097, 0.619494988676337, 0.9201356230523381, 1.0757758327834002, 1.063787176299015, 0.8899513432867248, 0.5857834637129357, 0.2032670533960064, -0.19254088812946754, -0.532365320813052, -0.7525274155338564, -0.8042632162316031, -0.661002665452983, -0.3231381659697664, 0.18024672031047836, 0.792832295779263, 1.4357483354012202, 2.0167426550710483, 2.441306537874373, 2.6247973684384953, 2.504547762153973, 2.050749458237949, 1.2751238855388074, 0.23565645260035453, -0.9636852809762809, -2.1782007176037776, -3.232504358708082, -3.934847629948738, -4.095026393284455, -3.5439461410556343, -2.1528218766111933, 0.14968101422167623, 3.3641149726088715, 7.412303145751903, 12.136625377086874, 17.307010169416895, 22.634594256034745, 27.791558924466138, 32.435837537960076, 36.239889032689945, 38.92309528628702, 40.276008883447396, 40.18037054215755, 38.62313644240987, 35.702137932148105, 31.623620488568964, 26.691504502849007, 21.279177690014194, 15.79775601566585, 10.661402534982528, 6.251103075454417, 2.880065369847071, 0.7631926988643596, -0.006386071626406051, 0.531559231204956, 2.204990652448551, 4.721885204992335, 7.6937824839551014, 10.670047790092632, 13.17807695920102, 14.765796296061492, 15.043394416379167, 13.72075901711084, 10.637619947508455, 5.782208675531876, -0.7061193848364378, -8.545543995893016, -17.331803141457385, -26.568432245448722, -35.70721428622685, -44.20120618692734, -51.54576031284407, -57.315183294372524, -61.19384970369878, -62.997900696748616, -62.68986413731764, -60.388350465194016, -56.3404224821751, -50.89158739548231, -44.453272215502395, -37.46695963570451, -30.369962250991236, -23.564872845872216, -17.382142536049415, -12.059458347558417, -7.733560039273769, -4.441863620181183, -2.1329985487717993, -0.6841050437197754, 0.07712541790098329, 0.34671564300785107, 0.3194870358315387, 0.16773381234506585, 0.02537974264728264, -0.021214241100651465, 0.06476158784568536, 0.2753822027402011, 0.5681360410056561, 0.8795730539555583, 1.1404843068273107, 1.2906616571773197, 1.2902013552070652, 1.1265824720912465, 0.8169710606088215, 0.4056439551345455, -0.042907213445516845, -0.4543851012173582, -0.7566368041442849, -0.890735962426165, -0.8200279703869688, -0.5359873164108018, -0.060122281417158384, 0.5587546627858374, 1.2517643388385227, 1.9394882745515838, 2.542675004045272, 2.99278175541259, 3.2413341676572087, 3.267346552705367, 3.0784730291345683, 2.708398418183694, 2.211081689630475, 1.6524367565984908, 1.1008306028319128, 0.6175025355604675, 0.24711638297261793, 0.012310026580438203, -0.08781406474591867, -0.07544421606969416, 0.011527351283638219, 0.12759134400305508, 0.22899118771416982, 0.2826655751861381, 0.2731222400573203, 0.20605901362316895, 0.1080394237506067, 0.022037393562681792, -0.0007370188010025121, 0.08874565245463134, 0.32628152602649885, 0.724549193162273, 1.2662695477871924, 1.9023502779794517, 2.5553214465417375, 3.128049817249075, 3.5171377653786733, 3.6295456318436248, 3.400745583003084, 2.812061904625164, 1.9013119397547735, 0.7677050399778971, -0.43048855224529314, -1.4864542383997947, -2.163447962112054, -2.220924525493271, -1.4431262966021656, 0.33289465498365695, 3.1921169071176876, 7.122277390949772, 12.003808643864364, 17.614513770751852, 23.644312391510674, 29.71815428272825, 35.4265536069678, 40.36089414376006, 44.15396645362007, 46.52770232431903, 47.311974577320086, 46.456225303303086, 44.033044358606006, 40.23046798436594, 35.337091262342646, 29.722047587457407, 23.786163817920556, 17.921520541631878, 12.477887084752828, 7.7352644825103, 3.8853518712139765, 1.0221766851540077, -0.8599023126775972, -1.8537154677492085, -2.118355587784143, -1.8537219165113623, -1.273610202163411, -0.580008322890078, 0.0583008654833409, 0.5200073397097769, 0.7378511644966848, 0.697719745382042, 0.43132697196016273, 0.0037625112465793343, -0.5024373146336498, -1.0026420373619067, -1.4232613531937328, -1.711355700242793, -1.8401023241465133, -1.8100579828096233, -1.6446141554358331, -1.382808166657726, -1.0710028637323257, -0.7546641030084859, -0.4715169528074035, -0.24684836657201928, -0.09137818658956255, -0.0023839314175498516, 0.03294909773346887, 0.0329346441064582, 0.01653555465345094, -0.000835844228338904, -0.010093234315352759, -0.009321851698378559, -0.002780330537215721, 0.001532509799475559, -0.004899609553308854, -0.027890529124189163, -0.06816953739842044, -0.12037954326993708, -0.1736740144964248, -0.21382342830117335, -0.22647912843147877, -0.2010005481093042, -0.13358593111858869, -0.029242440761540884, 0.0978541763668855, 0.22585251134605605, 0.3285047840848178, 0.3799600191538668, 0.35977764215550384, 0.25723444839980986, 0.07426428137426432, -0.17358586766268796, -0.45852454872073906, -0.7444930977992981, -0.9930391063988313, -1.169619409846345, -1.2494884285654642, -1.2221930473044056, -1.0940029429878844, -0.8877891686158124, -0.6386537883387401, -0.38742807258951084, -0.17295620218811994, -0.024216696188665537, 0.04638534797173528, 0.04737252545619695, 0.00917450772253266, -0.01895128649254223, 0.02439632283245244, 0.20329321043926488, 0.5735453506474876, 1.1723481559733826, 2.0100013054339887, 3.064760030065535, 4.281815133855496, 5.576782631854763, 6.844444598186918, 7.973890662564462, 8.860375489041308, 9.416925381122631, 9.58471463915347, 9.340286789212321, 8.699986453382456, 7.721542168299177, 6.4921919924049725, 5.116730056504762, 3.705560077350258, 2.3628466546447786, 1.1763807204632046, 0.20957862838367197, -0.5045816975736457, -0.963201050682817, -1.1890933429642039, -1.2239206207575921, -1.1201388393602831, -0.9329596448585029, -0.7124285110405701, -0.4979450941392047, -0.31558047057410876, -0.17796922749814473, -0.0863079957371124, -0.033714409898481255, -0.00914000397151365, -0.0010321659716270493, -9.03230282638715e-06, -0.0002197387758298304, 0.0006042790435545441, 0.002128300232729687, 0.002935802848656243, 0.0020174653120126696, -0.00023802302470621138, -0.0018271840730287102, 0.00026812181790239736, 0.00887361525596396, 0.02524652127624123, 0.047995654781737764, 0.0726849914686632, 0.09236119494603309, 0.09906714413812603, 0.08618604239498563, 0.050705478502838304, -0.005007030766777971, -0.07239556505882619, -0.1372693502207987, -0.18186436467633105, -0.18836747671263215, -0.14307886591317653, -0.04020253352381419, 0.11541849010981724, 0.3072956624119808, 0.5085066537153574, 0.6855648006620138, 0.8041096836964359, 0.8351335018145573, 0.7607984850323608, 0.5787505976617326, 0.30416140047755935, -0.031174409650356717, -0.38416118238257324, -0.7076808413434554, -0.9586878987050468, -1.105810846528951, -1.1350968854502523, -1.052875920783346, -0.8839422582929262, -0.6658654295068355, -0.44072898375831754, -0.24593489830282372, -0.1061039648186985, -0.028104534593986454, -0.001047895121575142, -0.0017367067446896216, -0.004882625836498258, 0.0035448483171609513, 0.012454789147844156, -0.025004734031247523, -0.195468240389343, -0.6211297552225893, -1.4464254311557372, -2.8161997310531093, -4.846934060257746, -7.5944256067981755, -11.02964335508095, -15.02356215945076, -19.344357291114058, -23.669716785854845, -27.61565809866128, -30.78464743075256, -32.81887282482336, -33.45047296183099, -32.543777339078716, -30.122697884682093, -26.38033269841761, -21.66902426856555, -16.45252744615343, -11.244349315550519, -6.539663087139911, -2.748365223779238, -0.13920366739857756, 1.196337676292054, 1.3533516494991311, 0.5925530816771899, -0.7063745995731011, -2.1099649085358045, -3.2058551616557, -3.676683791594544, -3.35036494873271, -2.2253964976951544, -0.4678080204571018, 1.6210560732168762, 3.662322404886958, 5.278077284518879, 6.16788791223955, 6.16901346425005, 5.293845664040408, 3.7378808941443027, 1.8564148467380945, 0.10879851644392709, -1.0262273927101992, -1.1355303919224629, 0.053261414683502074, 2.6171227784781586, 6.4117222611623115, 11.080537876925353, 16.10879559116032, 20.901343139650347, 24.872135115255904, 27.53248715929923, 28.566445713570868, 27.883914989990313, 25.62356054351885, 22.120439270591245, 17.8459799827152, 13.329208968103227, 9.07262806092487, 5.474813562277121, 2.7747328458546208, 1.0330793097134672, 0.14717457615485377, -0.10592584299242429, -0.007237342104970969, 0.17424062494564546, 0.24364420638793813, 0.11780612194513222, -0.16631216964234774, -0.47279203350811533, -0.6134653543262597, -0.4130858287319443, 0.22644348324511887, 1.2792226825757222, 2.575660670419154, 3.815981865693788, 4.61648710588567, 4.58428933180178, 3.410308093812155, 0.9543107023262369, -2.69390995845014, -7.190738003344475, -11.961385647818043, -16.271143391679658, -19.3322715428059, -20.43205119037255, -19.061934342474192, -15.025767000780176, -8.506204564298725, -0.0639855434846459, 9.428063361994234, 18.894139008640156, 27.199764879932832, 33.312452060349266, 36.46340106760643, 36.29319758558927, 32.88680565372236, 26.75158612798335, 18.743135297556982, 9.942794946333604, 1.5041143505926542, -5.521457565206156, -10.347556087700475, -12.550108427860225, -12.103559604767762, -9.357637200301252, -4.964398561664671, 0.23285366349533795, 5.357862064667562, 9.642954046129987, 12.53648541160842, 13.766243317720551, 13.35296513013642, 11.576887006921142, 8.902231208270024, 5.876136950212964, 3.0250928527524685, 0.7668683644267277, -0.6489199198517529, -1.1632276339393806, -0.8892865951034452, -0.06648917485077295, 1.0024987694946847, 2.0185256672153824, 2.74464982785789, 3.04688996061105, 2.9029386894114992, 2.387727106536888, 1.642486766356514, 0.834814364941936, 0.11849505865287441, -0.3997117730008326, -0.6758512985174435, -0.7261428150137654, -0.6112035928495375, -0.41267561851154705, -0.20887788969849513, -0.05515169089360164, 0.02664328742344387, 0.045530816506293245, 0.02937434074124115, 0.008426114590305898, 0.00010969841476031758, 0.00021656933798238568, -0.015966056244317014, -0.0823859272537723, -0.22421664455842932, -0.43872089904722994, -0.6816885196600772, -0.866294735646355, -0.8767029916460307, -0.5951115625057868, 0.06253770002653358, 1.110308988331025, 2.4651121187173644, 3.939418129162529, 5.261293327692806, 6.118181303154373, 6.21945689991775, 5.367412842073047, 3.523134891446005, 0.8493104857461509, -2.292414983192855, -5.383523896337357, -7.828794279306075, -9.065633195310308, -8.688210227540948, -6.5667671507761245, -2.9095339008458625, 1.7319397276082704, 6.519121759270875, 10.443975030956853, 12.494970206073186, 11.851822043383038, 8.061332911147888, 1.1567892574166874, -8.296656441685872, -19.244004480397365, -30.276493760449863, -39.866693847105545, -46.618692842918605, -49.50262562514484, -48.042776020397405, -42.42376156341034, -33.501843442975556, -22.70871559925114, -11.783730552764334, -2.4767074294905678, 3.744980868866385, 5.948397811590873, 3.905528238263995, -1.845642088652357, -10.090182345869552, -19.15446472453209, -27.20505473756919, -32.578766202724154, -34.091665161278605, -31.279283650110155, -24.49605104775181, -14.869301356444984, -4.1184181811934035, 5.734533452558395, 12.715870586753573, 15.248887534164071, 12.43641275745925, 4.231403058718061, -8.527799124535429, -24.223655523951493, -40.70664160356371, -55.67891458758542, -67.03014621809604, -73.13544475084355, -73.08510705305909, -66.80595178621718, -55.06824010149629, -39.364709749548005, -21.608041214274802, -3.8303488081398522, 12.097281286627263, 24.70105103080432, 33.076420144797545, 36.98850382336488, 36.803637010629664, 33.34340794790421, 27.700566161755606, 21.04222837900709, 14.433738036352336, 8.70173613705542, 4.339492269200453, 1.501413770595179, 0.05765272566121807, -0.31535624169370813, -0.029982937555838793, 0.5124672796325682, 0.998295866287325, 1.2411305789636748, 1.1858215897363948, 0.8836442638257904, 0.44998316368294095, 0.016291372285466604, -0.31183777739138224, -0.47874572312533786, -0.483987928415875, -0.37159628600238537, -0.20902856094627714, -0.06281712747977025, 0.02173556697250844, 0.030591924784951822, -0.02012730911583056, -0.09443539987834812, -0.15191815452976515, -0.16320079132011472, -0.11985512060082296, -0.03608323891967562, 0.05763221262897729, 0.12663953353403679, 0.1461877408176375, 0.11291865074708424, 0.0486467338464929, -0.0043873569806626095, 0.004403267296306833, 0.11749179046202993, 0.3528188022156129, 0.692810746456392, 1.0831376542307973, 1.4416399731581604, 1.675770346375063, 1.7048632998880633, 1.4826585573918043, 1.0146603505442402, 0.3600543420648325, -0.3785715793834485, -1.0758183239767518, -1.6106150563855728, -1.8942981454878969, -1.893818966441797, -1.639698935022703, -1.2174985957876636, -0.745111005838349, -0.3402609672580019, -0.08529588636142227, 0.0026659199588267204, -0.012337855901878294, 0.0106211828544156, 0.26499129400986826, 0.9557791602478788, 2.2495531702109046, 4.228262627437687, 6.855838164811969, 9.964181281803329, 13.263172506041245, 16.37471032938974, 18.891256459480168, 20.458364584607263, 20.826609500252793, 19.890067483622065, 17.706623474659324, 14.493163365095175, 10.599291950857559, 6.460417878161317, 2.514558602403397, -0.8630776359025397, -3.4069425015204287, -4.987832091228321, -5.617816751015034, -5.435776353670704, -4.666887290971782, -3.572442316703694, -2.4022827185196816, -1.3569707084663558, -0.5649521023333347, -0.07621115485709413, 0.12950311485762508, 0.12125171071545526, -0.009608941008223277, -0.17443575997494598, -0.30613485833680437, -0.369109012418311, -0.35851264207360123, -0.2923517620336694, -0.1999403298784925, -0.11026664413185856, -0.04333199603119206, -0.006256587037963034, 0.0054747429610584085, 0.0031141576983570356, -0.0014729318034158716, -0.0009151748241604394, 0.005252205133397794, 0.011611190970248125, 0.010507632184965364, -0.0034278438431965246, -0.029684781939323085, -0.06072079745797345, -0.08410828113356535, -0.08795670891576014, -0.06735272875308772, -0.029575367135177395, 0.0036980271092852267, -0.0015133169982917269, -0.08474961705917677, -0.28024025826887095, -0.6052852186257609, -1.0512261425671205, -1.5793196828598794, -2.1231797816014133, -2.598509819617532, -2.919991466377988, -3.0184862872575224, -2.8561397666195383, -2.4364351316565775, -1.8064941265594443, -1.05090244529558, -0.2767722030415738, 0.40874281871345364, 0.9185975806510538, 1.2012502204256341, 1.2488294572420913, 1.0969071076994008, 0.8156965701091475, 0.4907971849176146, 0.20327488675427272, 0.01296418048594965, -0.05223271747225201, 0.0007844999879676936, 0.13543766660273115, 0.2982787770317618, 0.43501245227367846, 0.5049785028682188, 0.49074018283336834, 0.4007897652097449, 0.2650784112983362, 0.1244945794860466, 0.017878418105388625, -0.02955061441806461, -0.013224343663362222, 0.0502169815347977, 0.12925337253167773, 0.18830394823751764, 0.19965632078320622, 0.15314005850635046, 0.06064347615856025, -0.046151648581673005, -0.12498864219253535, -0.13643660475544422, -0.057124444702825336, 0.11057476432767978, 0.33529107327008817, 0.5615168940239419, 0.7229441213998985, 0.7595944227281394, 0.6343118313342858, 0.34492802439254866, -0.07123613539389338, -0.5422390914495959, -0.9762843426457264, -1.2829896908049119, -1.3940441027747261, -1.279402834779022, -0.9554182518653774, -0.4826203427302152, 0.048125356147200656, 0.5369640836048678, 0.8967831886294728, 1.0714024307217485, 1.0464613707730843, 0.8513334405968498, 0.5511886265286818, 0.22604289721293325, -0.049947434144283424, -0.2251469623390457, -0.2802669482967255, -0.22954137899395397, -0.11340098564242518, 0.016394536402866765, 0.11359200107896344, 0.15063507103601131, 0.12486214830453046, 0.05657124623678052, -0.020004939683513655, -0.07069080625364467, -0.07448799783260893, -0.03124429186308588, 0.038761394477844775, 0.10342095843143025, 0.13274369235307903, 0.11338463548061181, 0.05834289183973236, 0.007190363780240256, 0.014706090440692422, 0.1294582017523455, 0.36962846884018835, 0.7043759500865107, 1.046732755403854, 1.263722015137921, 1.2057385467211743, 0.754701291697078, -0.1145077769657932, -1.294230390767689, -2.52609403219221, -3.412547904770703, -3.4633550289721744, -2.1758595073765075, 0.8548986322312374, 5.830801766106668, 12.67332590511853, 20.98725865652174, 30.077121798240118, 39.02378714156718, 46.83009120458945, 52.575862564672946, 55.56161422151219, 55.42261529466869, 52.19109365043671, 46.30552040946562, 38.56590961374552, 29.95404472547115, 21.458226725893745, 13.920144441480288, 7.917987708347091, 3.706051799969897, 1.2145725872493962, 0.10430773043957284, -0.11779121151518375, 0.03348024429679829, 0.13793443405562647, -0.05234016857616107, -0.5879363263247803, -1.3505582822573916, -2.1219682032826648, -2.671115902547818, -2.8346189451637565, -2.5698352811905187, -1.9668767495741053, -1.2113133732684347, -0.5181534453209087, -0.05675969273231117, 0.11160833718874902, 0.06377845062926848, 0.00041861022891888887, 0.18987222791148187, 0.8851226683303353, 2.2357631513678515, 4.218613439168875, 6.610660420224423, 9.028228201153913, 11.006874869952304, 12.106505735517738, 12.020936020399965, 10.664663889388315, 8.218290457964423, 5.115747018254141, 1.9367350931961238, -0.7300210784041029, -2.426186728646094, -2.938214638608238, -2.35922055559284, -1.0801085502563872, 0.29912067597342584, 1.1144003509729503, 0.804876293897412, -0.9350004080071231, -4.056139088717081, -8.146368935556813, -12.509604914572106, -16.304979812055553, -18.723075876682373, -19.163734160473968, -17.3862857099899, -13.598576178231642, -8.387128775161607, -2.587769180351414, 2.8802244382622555, 7.191769493230581, 9.773808687246795, 10.424393064327957, 9.327185112513174, 6.969211497109247, 4.004944241998952, 1.100260114778304, -1.2065104628435228, -2.5998298307501138, -3.033349138934507, -2.693693748157129, -1.9091610354649022, -1.036450873078833, -0.356943583484589, -0.01016385416085347, 0.016002412561909252, -0.15338769686725712, -0.3505237152641066, -0.4407735248964609, -0.37728136949023944, -0.2127786918614821, -0.05692798240429909, 0.0033763579958886784, -0.006435947532636974, 0.11849662951321542, 0.7763307075986869, 2.4989073547757017, 5.821089228121174, 11.10467261813427, 18.356287938725696, 27.0866866051655, 36.266453306937734, 44.44131698741218, 49.934017036154216, 51.125164486300214, 46.77434070497928, 36.31660771573483, 20.090433248668674, -0.5602719299103597, -23.5015366322797, -46.132571459079564, -65.78179379935617, -80.12828705734844, -87.57922984925155, -87.55038740680615, -80.54138806666924, -67.99573694142079, -52.00817226366696, -34.939998706349414, -19.00857918529613, -5.911859270482276, 3.379573916168625, 8.66727411242164, 10.42538607811041, 9.589468545359747, 7.292714785545694, 4.602612474146606, 2.2939551825476605, 0.7580896449978544, 0.026300234084343337, -0.1235751008498597, -0.016775296542811628, 0.0673380419028296, -0.0004527294823167494, -0.16825421980737465, -0.24578343024578858, 5.222741281148537e-05, 0.7313651120432753, 1.9488883042052458, 3.455546889470866, 4.885926900890174, 5.794796899298963, 5.781466079726939, 4.617645663500775, 2.33729991415074, -0.7566675382641862, -4.15129741817543, -7.235942235650744, -9.443455847582026, -10.39082960422669, -9.98934806050096, -8.448704821732552, -6.207641379558146, -3.8141643517730826, -1.782609122964739, -0.4640694733430842, 0.03868111755031444, -0.11493686446981437, -0.5727078872999608, -0.9130227359980226, -0.7862986346212557, -0.035772904764979484, 1.2382589259774963, 2.6956242572869007, 3.8459554999823204, 4.1869494200764015, 3.355356698207485, 1.2502312841224388, -1.913495242904568, -5.643957090195325, -9.279991340550854, -12.143299745061352, -13.699162071039037, -13.691553551748552, -12.219862137194403, -9.683796763344827, -6.664615375832523, -3.77343454696436, -1.5000900704372802, -0.10144077208435595, 0.4434590212303952, 0.3903095930955146, 0.10927407751772868, -0.06459780262775136, 0.035504470435853475, 0.33219579791378867, 0.5141449484576193, 0.13666692472260972, -1.2176917237233398, -3.7663502731253518, -7.394303422905977, -11.608522983885532, -15.613711057776472, -18.49905564629942, -19.483930539853212, -18.16326992906579, -14.685088476739198, -9.803810549763984, -4.77106842773975, -1.0558265869728407, 0.017985501112525656, -2.359622583171174, -8.196936715170134, -16.582274771585595, -25.817572952906538, -33.76036744945205, -38.30701796263622, -37.93259685308779, -32.171892794232114, -21.935808608515554, -9.551871377810535, 1.589498587304444, 7.608247396851573, 4.853384640375985, -9.34315602898212, -36.01829679562151, -74.2214360615766, -121.05477178778403, -172.02791845526042, -221.67777887011036, -264.35882881539334, -295.1459902474674, -310.81095816295846, -310.1200009017531, -293.8424492202375, -264.5106501899675, -225.9380609921208, -182.62515291368513, -139.13528437502262, -99.286871035681, -65.7149101395554, -39.729268704906815, -21.40233072353595, -9.834632397960481, -3.523257115017442, -0.7599030380896195, 0.024247861494654865, 0.0303066093083788, -0.003036919622975518, 0.22652132601279565, 0.6996415749312065, 1.2299741936143676, 1.606695717890692, 1.6938710191888202, 1.4738087928706312, 1.0378544186205494, 0.53890755214381, 0.12762548208378832, -0.09712847677572113, -0.11235008886656453, 0.03304281656245526, 0.24516579917139858, 0.42495414297354117, 0.5032920873329781, 0.4600794242407142, 0.32447301101932857, 0.15865794198911667, 0.03205796526913301, -0.005197316570231877, 0.0601800389882674, 0.20251709148614763, 0.36844139161118006, 0.496512570899571, 0.5387756971782465, 0.477874482813261, 0.3308643551674077, 0.14118673027093742, -0.03720235921724347, -0.15812911992512602, -0.19786746411716089, -0.16173003879385087, -0.08086640778442847, -5.7988732560531436e-05, 0.038473916852667114, 0.009733306494584721, -0.08579847763594567, -0.22383447779672527, -0.36554960323499835, -0.47058764706966916, -0.509993625269765, -0.4750139882067017, -0.37940212432137416, -0.2542111409800883, -0.1346563681637538, -0.0480347697797726, -0.005776368670093594, -0.001473934600424472, -0.015273054538595763, -0.02307565565777567, -0.007106502150352413, 0.036744203328659734, 0.09752510517501778, 0.15410999014827642, 0.18458465397410734, 0.1767490996277366, 0.13428665510903554, 0.07571470962555354, 0.025861729100495574, 0.00214931686038458, 0.00022718268917429368, -0.015362242746444833, -0.1102171178105265, -0.3668984825866946, -0.8615966663189603, -1.6359391298838268, -2.672284691509314, -3.88369028964057, -5.119528705620827, -6.187787926315617, -6.8913975512355625, -7.071120000693085, -6.64753245848646, -5.651609204362617, -4.215573212401607, -2.5463603384866342, -0.8855981078077177, 0.5377954352517872, 1.5532102781815165, 2.0845814130385145, 2.15692940404933, 1.8766573904471844, 1.3962378324780065, 0.8726883497780158, 0.43065836614746605, 0.13805183872246068, -0.0011120551111503292, -0.030719167072439386, -0.013460054750533097, 0.00040628858196529023, -0.0038389170088310785, 0.0020789362703869238, 0.07878724628032974, 0.2940717014493795, 0.6914012474606617, 1.2626344389515518, 1.9356540376756912, 2.586447245321669, 3.066326621769799, 3.2391154504697037, 3.0196789560555826, 2.402724564429012, 1.4741268145007855, 0.39774629081585705, -0.6286712582924463, -1.4216769921522912, -1.8551401053529961, -1.8889439240717725, -1.5768495965136167, -1.05112062385884, -0.4796307287908836, -0.01708988207835461, 0.2361370271976778, 0.2577135207183558, 0.10321542419523436, -0.11830105831672375, -0.28444892142309114, -0.30250614586923935, -0.14196297283970696, 0.15317616481264837, 0.4767573570247722, 0.6963709462918762, 0.6994914074506884, 0.4336129451939632, -0.07036188439252558, -0.6990144284690212, -1.2836988324740592, -1.6519479464135989, -1.6833374979472364, -1.351571445432376, -0.7430287507436635, -0.04572114860108372, 0.4900981584735641, 0.6138411799058227, 0.14424439739466607, -0.9788877960532812, -2.671178075703992, -4.713685220832132, -6.795686845652995, -8.584432065889139, -9.796119682039864, -10.25229268096238, -9.911617490680083, -8.870886504768672, -7.3377763580542155, -5.581110859356127, -3.863413717344759, -2.3898262889880812, -1.2785618990207022, -0.5548041473498057, -0.16611302281023085, -0.01309891398652314, 0.013109009123383322, 0.0006850884675458387, 0.0008081110689775066, 0.026416602152019585, 0.06327064474054904, 0.08780565139103863, 0.08375153819083068, 0.051332992394567255, 0.007183411312848149, -0.02354894296917392, -0.01896180802468705, 0.028952344069600768, 0.10990429977580506, 0.19875354777625984, 0.2649887636162248, 0.28455365205049155, 0.2496737850545146, 0.17277236572414748, 0.08134662550393788, 0.007309663220867461, -0.025242795217777492, -0.009440145201275377, 0.04143052683858997, 0.09906966489173111, 0.13214599353405485, 0.11985317047307695, 0.06176198296032129, -0.02006479130489256, -0.08843103863523177, -0.10622462656313524, -0.05244755699763213, 0.06671896873090288, 0.21627183682655607, 0.34203281649938544, 0.3901090431712471, 0.3313149399890751, 0.17627749549033603, -0.024007933576431353, -0.1930851764137559, -0.25633129914644975, -0.1725768793865212, 0.04064409267315933, 0.3027794832311893, 0.49546223698758446, 0.512807086152958, 0.32472702715733776, 0.03466717336149429, -0.08959295648094105, 0.3689721618278992, 1.9091358229435642, 4.997843540721624, 9.930551692106667, 16.70295025985895, 24.955622414677276, 33.974153826930326, 42.760571864336804, 50.177381657788324, 55.1402052338836, 56.8498743300216, 55.0433497567817, 49.98948330661265, 42.41484701557004, 33.369150745330565, 24.03373991149276, 15.519130304951933, 8.676775955402183, 3.91426879213165, 1.1772210104267802, 0.043602410383986635, -0.11627488071973638, 0.04395313805609439, 0.011207214823531602, -0.47903458983709196, -1.4175187352125171, -2.577362787140845, -3.6257219765211897, -4.253810553233365, -4.286397702403018, -3.73179502958168, -2.767797451712447, -1.6744977723120302, -0.7382054075965933, -0.15848550992359178, 0.010186783668595456, -0.14052505744912616, -0.42132725536977206, -0.6232706546381163, -0.5988852677240354, -0.31955388028853104, 0.1140760422716543, 0.5182445551535092, 0.7012806009594905, 0.5415129831080033, 0.04184707667058489, -0.6580819058532857, -1.3214756689682612, -1.701954300247334, -1.6359358429516517, -1.1077589785476933, -0.2645728282624744, 0.6278966744761673, 1.280274549654171, 1.4899835430454753, 1.2231384062127724, 0.6350765257855598, 0.014764405334739732, -0.3362205144331865, -0.25425475685110266, 0.16858216275419946, 0.5597822269533165, 0.3633399207433447, -0.9434223827571705, -3.554379612980927, -7.052633964683499, -10.250902996903498, -11.220131843595508, -7.545071879578876, 3.205694977384559, 22.84857233704188, 51.90690351049332, 89.22225912473587, 131.8548684205188, 175.328383027292, 214.22779863756884, 243.10686428042052, 257.6357444263978, 255.42306384130617, 236.47893013389867, 203.26512217395387, 160.2916710206836, 113.34386622920785, 68.42712375800419, 30.548124880088597, 2.900383032973148, -13.501746911937119, -19.727699174236083, -18.43136981215747, -13.063683334036352, -6.902170336608579, -2.282673796329379, -0.17775955604757665, -0.17376827236909162, -0.8190962821336313, -0.23176473176876367, 3.215340035149361, 10.331942130768626, 20.811355305009084, 33.25669372272095, 45.52645624090746, 55.33886252191586, 60.83957171836676, 61.03290479203177, 55.99282354992607, 46.80562461494006, 35.27554399865442, 23.459004856647013, 13.140549788669576, 5.477176711124423, 0.8469063634857074, -1.0937267911699735, -1.1819730175424041, -0.4184108437647934, 0.36752868084861035, 0.7140662871833424, 0.5666727575576943, 0.17632722645951976, -0.09582653145331473, 0.00029731605822011276, 0.4469406080575931, 0.9333106566486271, 0.9570062613371653, 0.011165662937258581, -2.207908117522235, -5.649934799957021, -9.873238021436531, -14.12928330617528, -17.545401650380214, -19.35547674757655, -19.11457794882231, -16.848114509616266, -13.080787307493207, -8.690413019707515, -4.644446119892426, -1.7093421345065754, -0.229423793771668, -0.07053662004300236, -0.7738273591089491, -1.7620526376962227, -2.5115888706469107], 'positive_zeros': ['0.47917294819184509109412475082285', '0.64848224129327926610869568509691', '1.21296200663693563952143453750789', '1.72543276160858166446234379667270', '1.80486715827586510244283793886831', '1.92734219114311631730865400328776', '2.55147765920002646137517570120449', '2.58332120179096718550293936343158', '2.97002455780179579234501584556438', '2.99197892063502348043752662188143', '3.60050624706311344299279063643890', '3.69721634376078247122664610305563', '3.86472451637733685311821579133696', '3.99317401508695538031094859079155', '4.19174952634560981867959741388269', '4.35302998245710172781996760259042', '4.81146958152562143543122396891847', '4.81664585564264533858711100716719', '5.06043877812093635130566172817786', '5.55940084735348107065927736711525', '5.65171965761350440612036963253527', '5.67587743052420171466070092199550', '5.89381929066827786350808604127127', '6.02304779982039994760018645355362', '6.33494758858488591759251296798933', '6.39360013178579474315822769516902', '6.55167411460536584485989717777463', '6.56306645923745034013988641707634', '6.84660254686393453745340411891573', '6.95522896531781704814822976054930', '7.42667138031756938272507302554882', '7.56037032028413341592125498857769', '7.66682594770704328895198652805942', '7.959176723345529284096229554915988', '8.040453910574620024323675229421731', '8.113658215841622770996367541887084', '8.135812797060768007880511251695305', '8.338357570662908724774989279573904', '8.485915307753444226217294737255768', '8.755022131637625542872844524263706', '8.817130951228127687827628812753005', '8.847915687339621451727062839948483', '9.297056691059508565107549911203046', '9.597382888290522271631012122467989', '9.603360608405160181028994887320879', '9.634404470272099906715239586507678', '9.727104775925431944125837671448690', '9.769661439535378098621529712380967', '9.956711435928012677571310782685840', '10.08938640986445483370144474858769', '10.28982942262321705074592652744380', '10.56567793432145524084938723652771', '10.57594986926823079797590206614487', '10.61904579019137042977631485426778', '10.65854808284521445423340039809971', '11.14733736667289451866259235612823', '11.21847873660925762458660780043696', '11.35899864675022016392162119691622', '11.54317444974217256483310657107505', '11.98647974666041346932303693559672'], 'prelabel': '12-378e6-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.737338538225754, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e6-0', 'trace_hash': 1722918404973143710, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.47917294819184509109412475082', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.64848224129327926610869568510', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.21296200663693563952143453751', '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': 756.1595493200377, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 2917096519063104, 'conductor_radical': 42, 'degree': 12, 'dirichlet_coefficients': [1, -3, 0, 3, 2, 0, -4, 2, 0, -6, -2, 0, 8, 12, 0, -9, 4, 0, -3, 6, 0, 6, -14, 0, -15, -24, 0, -12, 5, 0, 20, 9, 0, -12, -8, 0, 3, 9, 0, 4, 0, 0, -6, -6, 0, 42, 9, 0, 2, 45, 0, 24, -15, 0, -4, -8, 0, -15, 14, 0, 8, -60, 0, 3, 16, 0, 1, 12, 0, 24, -14, 0, 19, -9, 0, -9, 8, 0, 5, -18, 0, 0, -2, 0, 8, 18, 0, -4, 9, 0, -32, -42, 0, -27, -6, 0, 28, -6, 0, -45], 'euler11': [1, 2, 55, 104, 1373, 2186, 19567, 24046, 166133, 138424, 805255, 322102, 1771561], 'euler13': [1, -8, 24, -42, -32, 1408, -7901, 18304, -5408, -92274, 685464, -2970344, 4826809], 'euler17': [1, -4, -23, 68, 410, -220, -8111, -3740, 118490, 334084, -1920983, -5679428, 24137569], 'euler19': [1, 3, -12, -67, -153, 54, 6315, 1026, -55233, -459553, -1563852, 7428297, 47045881], 'euler2': [1, 3, 6, 7, 6, 3, 1, 0, 0, 0, 0, 0, 0], 'euler23': [1, 14, 211, 1784, 14837, 86138, 483607, 1981174, 7848773, 21705928, 59046451, 90108802, 148035889], 'euler29': [1, -5, 4, -251, 197, 3418, 20293, 99122, 165677, -6121639, 2829124, -102555745, 594823321], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, -20, 186, -1398, 10342, -62234, 331987, -1929254, 9938662, -41647818, 171774906, -572583020, 887503681], 'euler37': [1, -3, -105, 104, 8109, -4221, -342138, -156177, 11101221, 5267912, -196786905, -208031871, 2565726409], 'euler41': [1, 0, -90, -18, 4410, 810, -194177, 33210, 7413210, -1240578, -254318490, 0, 4750104241], 'euler43': [1, 6, -24, -418, -1314, 3474, 88971, 149382, -2429586, -33233926, -82051224, 882050658, 6321363049], 'euler47': [1, -9, -6, 531, -2433, -3438, 104623, -161586, -5374497, 55130013, -29278086, -2064105063, 10779215329], 'euler5': [1, -2, 19, -44, 197, -374, 1279, -1870, 4925, -5500, 11875, -6250, 15625], 'euler53': [1, 15, 0, 33, 13635, 60360, -225155, 3199080, 38300715, 4912941, 0, 6272932395, 22164361129], 'euler59': [1, -14, -20, 154, 11666, -35126, -499301, -2072434, 40609346, 31628366, -242347220, -10008940186, 42180533641], 'euler61': [1, -8, -114, 342, 13762, -13214, -937217, -806054, 51208402, 77627502, -1578425874, -6756770408, 51520374361], 'euler67': [1, -1, -88, -243, 2035, 14290, 72259, 957430, 9135115, -73085409, -1773298648, -1350125107, 90458382169], 'euler7': [1, 4, 14, 55, 98, 196, 343, 0, 0, 0, 0, 0, 0], 'euler71': [1, 14, 79, -988, -6031, 67514, 1600591, 4793494, -30402271, -353616068, 2007522799, 25259210914, 128100283921], 'euler73': [1, -19, 134, -27, -5759, 41986, -314903, 3064978, -30689711, -10503459, 3805364294, -39388360267, 151334226289], 'euler79': [1, -5, -138, 123, 11347, 21118, -1048937, 1668322, 70816627, 60643797, -5375111178, -15385281995, 243087455521], 'euler83': [1, 2, -182, 2, 18788, -13564, -1721225, -1125812, 129430532, 1143574, -8637414422, 7878081286, 326940373369], 'euler89': [1, -9, -144, 1197, 16101, -73314, -1141967, -6524946, 127536021, 843847893, -9034882704, -50256535041, 496981290961], 'euler97': [1, -28, 281, -2724, 45178, -388196, 2169217, -37655012, 425079802, -2486121252, 24876727961, -240445527196, 832972004929], 'euler_factors': [[1, 3, 6, 7, 6, 3, 1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -2, 19, -44, 197, -374, 1279, -1870, 4925, -5500, 11875, -6250, 15625], [1, 4, 14, 55, 98, 196, 343, 0, 0, 0, 0, 0, 0], [1, 2, 55, 104, 1373, 2186, 19567, 24046, 166133, 138424, 805255, 322102, 1771561], [1, -8, 24, -42, -32, 1408, -7901, 18304, -5408, -92274, 685464, -2970344, 4826809], [1, -4, -23, 68, 410, -220, -8111, -3740, 118490, 334084, -1920983, -5679428, 24137569], [1, 3, -12, -67, -153, 54, 6315, 1026, -55233, -459553, -1563852, 7428297, 47045881], [1, 14, 211, 1784, 14837, 86138, 483607, 1981174, 7848773, 21705928, 59046451, 90108802, 148035889], [1, -5, 4, -251, 197, 3418, 20293, 99122, 165677, -6121639, 2829124, -102555745, 594823321], [1, -20, 186, -1398, 10342, -62234, 331987, -1929254, 9938662, -41647818, 171774906, -572583020, 887503681], [1, -3, -105, 104, 8109, -4221, -342138, -156177, 11101221, 5267912, -196786905, -208031871, 2565726409], [1, 0, -90, -18, 4410, 810, -194177, 33210, 7413210, -1240578, -254318490, 0, 4750104241], [1, 6, -24, -418, -1314, 3474, 88971, 149382, -2429586, -33233926, -82051224, 882050658, 6321363049], [1, -9, -6, 531, -2433, -3438, 104623, -161586, -5374497, 55130013, -29278086, -2064105063, 10779215329], [1, 15, 0, 33, 13635, 60360, -225155, 3199080, 38300715, 4912941, 0, 6272932395, 22164361129], [1, -14, -20, 154, 11666, -35126, -499301, -2072434, 40609346, 31628366, -242347220, -10008940186, 42180533641], [1, -8, -114, 342, 13762, -13214, -937217, -806054, 51208402, 77627502, -1578425874, -6756770408, 51520374361], [1, -1, -88, -243, 2035, 14290, 72259, 957430, 9135115, -73085409, -1773298648, -1350125107, 90458382169], [1, 14, 79, -988, -6031, 67514, 1600591, 4793494, -30402271, -353616068, 2007522799, 25259210914, 128100283921], [1, -19, 134, -27, -5759, 41986, -314903, 3064978, -30689711, -10503459, 3805364294, -39388360267, 151334226289], [1, -5, -138, 123, 11347, 21118, -1048937, 1668322, 70816627, 60643797, -5375111178, -15385281995, 243087455521], [1, 2, -182, 2, 18788, -13564, -1721225, -1125812, 129430532, 1143574, -8637414422, 7878081286, 326940373369], [1, -9, -144, 1197, 16101, -73314, -1141967, -6524946, 127536021, 843847893, -9034882704, -50256535041, 496981290961], [1, -28, 281, -2724, 45178, -388196, 2169217, -37655012, 425079802, -2486121252, 24876727961, -240445527196, 832972004929]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/378/2/h/c'], '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': '12-378e6-1.1-c1e6-0-1', '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}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '12-378e6-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.737338538225754, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e6-0', 'trace_hash': 1722918404973143710, 'z1': {'__RealLiteral__': 0, 'data': '0.47917294819184509109412475082', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '607423875388522700011757474377,822048902412772951461853550540,1537612015767349038413718166512,2187245875906569998609419164350,2287940936520619113945081166790,2443196485447762240270043619030', 'Lhash_array': ['607423875388522700011757474377', '822048902412772951461853550540', '1537612015767349038413718166512', '2187245875906569998609419164350', '2287940936520619113945081166790', '2443196485447762240270043619030'], 'label': '12-378e6-1.1-c1e6-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/378/2/h/c'}