-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1422407378788977158360850463185,2566844240081537650544675677865,2583339580657784878879448641176,3547118864709879692175481896906', 'a10': 0, 'a2': 0, 'a3': 5, 'a4': 0, 'a5': -5, 'a6': 0, 'a7': 6, 'a8': 0, 'a9': 13, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.504717062986346, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, 5, 15, 25, 25]]], 'bad_primes': [2, 5], 'central_character': '200.1', 'coefficient_field': '1.1.1.1', 'conductor': 1600000000, 'conductor_radical': 10, 'degree': 8, 'euler_factors': [[1], [1, -5, 12, -25, 49, -75, 108, -135, 81], [1, 5, 15, 25, 25], [1, -6, 39, -132, 449, -924, 1911, -2058, 2401], [1, -6, 5, 6, 49, 66, 605, -7986, 14641], [1, 7, 11, -79, -536, -1027, 1859, 15379, 28561], [1, 8, 7, -110, -579, -1870, 2023, 39304, 83521], [1, 9, 27, -83, -960, -1577, 9747, 61731, 130321], [1, -9, 38, -255, 1741, -5865, 20102, -109503, 279841], [1, 3, 5, -87, -116, -2523, 4205, 73167, 707281], [1, -13, 108, -821, 5525, -25451, 103788, -387283, 923521], [1, -1, 14, 103, 739, 3811, 19166, -50653, 1874161], [1, -16, 95, -534, 4109, -21894, 159695, -1102736, 2825761], [1, -22, 351, -3476, 27329, -149468, 648999, -1749154, 3418801], [1, -4, -1, -318, 3479, -14946, -2209, -415292, 4879681], [1, 19, 188, 1765, 15251, 93545, 528092, 2828663, 7890481], [1, 6, -43, -402, 475, -23718, -149683, 1232274, 12117361], [1, 23, 318, 3511, 31355, 214171, 1183278, 5220563, 13845841], [1, 22, 117, -970, -16399, -64990, 525213, 6616786, 20151121], [1, -10, -11, 790, -6489, 56090, -55451, -3579110, 25411681], [1, 11, 48, -275, -6529, -20075, 255792, 4279187, 28398241], [1, -15, 111, -1495, 19536, -118105, 692751, -7395585, 38950081], [1, 1, 58, 335, 7041, 27805, 399562, 571787, 47458321], [1, 4, -73, -648, 3905, -57672, -578233, 2819876, 62742241], [1, -36, 749, -11172, 124789, -1083684, 7047341, -32856228, 88529281], [1, 36, 730, 10944, 127059, 1105344, 7446730, 37090836, 104060401], [1, 1, -27, 905, 9716, 93215, -286443, 1092727, 112550881], [1, -40, 938, -15040, 180859, -1609280, 10739162, -49001720, 131079601], [1, -26, 167, 692, -15395, 75428, 1984127, -33670754, 141158161], [1, 22, 191, 2436, 36869, 275268, 2438879, 31743734, 163047361]], 'euler_factors_factorization': [[1], [[[1, -5, 12, -25, 49, -75, 108, -135, 81], 1]], [[[1, 5, 15, 25, 25], 1]], [[[1, -3, 15, -21, 49], 2]], [[[1, -6, 5, 6, 49, 66, 605, -7986, 14641], 1]], [[[1, 7, 11, -79, -536, -1027, 1859, 15379, 28561], 1]], [[[1, 8, 7, -110, -579, -1870, 2023, 39304, 83521], 1]], [[[1, 9, 27, -83, -960, -1577, 9747, 61731, 130321], 1]], [[[1, -9, 38, -255, 1741, -5865, 20102, -109503, 279841], 1]], [[[1, 3, 5, -87, -116, -2523, 4205, 73167, 707281], 1]], [[[1, -13, 108, -821, 5525, -25451, 103788, -387283, 923521], 1]], [[[1, -1, 14, 103, 739, 3811, 19166, -50653, 1874161], 1]], [[[1, -16, 95, -534, 4109, -21894, 159695, -1102736, 2825761], 1]], [[[1, -11, 115, -473, 1849], 2]], [[[1, -4, -1, -318, 3479, -14946, -2209, -415292, 4879681], 1]], [[[1, 19, 188, 1765, 15251, 93545, 528092, 2828663, 7890481], 1]], [[[1, 6, -43, -402, 475, -23718, -149683, 1232274, 12117361], 1]], [[[1, 23, 318, 3511, 31355, 214171, 1183278, 5220563, 13845841], 1]], [[[1, 22, 117, -970, -16399, -64990, 525213, 6616786, 20151121], 1]], [[[1, -10, -11, 790, -6489, 56090, -55451, -3579110, 25411681], 1]], [[[1, 11, 48, -275, -6529, -20075, 255792, 4279187, 28398241], 1]], [[[1, -15, 111, -1495, 19536, -118105, 692751, -7395585, 38950081], 1]], [[[1, 1, 58, 335, 7041, 27805, 399562, 571787, 47458321], 1]], [[[1, 4, -73, -648, 3905, -57672, -578233, 2819876, 62742241], 1]], [[[1, -36, 749, -11172, 124789, -1083684, 7047341, -32856228, 88529281], 1]], [[[1, 18, 203, 1818, 10201], 2]], [[[1, 1, -27, 905, 9716, 93215, -286443, 1092727, 112550881], 1]], [[[1, -20, 269, -2140, 11449], 2]], [[[1, -26, 167, 692, -15395, 75428, 1984127, -33670754, 141158161], 1]], [[[1, 22, 191, 2436, 36869, 275268, 2438879, 31743734, 163047361], 1]]], 'gamma_factors': [[], [0, 0, 0, 0]], 'group': 'GL2', 'index': 4, 'label': '8-200e4-1.1-c1e4-0-4', '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/200/2/m/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.03125', 'prec': 24}, 'plot_values': [3.64014711430818, 3.6479440232896683, 3.6542291894878156, 3.6613424394010288, 3.6716036932735356, 3.6867267766980114, 3.7060123402499245, 3.7281164479233206, 3.7516325416466594, 3.775189046551761, 3.7977825001660874, 3.818456039474058, 3.836186395562011, 3.8498157597861926, 3.857857613665666, 3.8586936582328986, 3.850643472158532, 3.8319801969482006, 3.800972092418361, 3.755890012825978, 3.6950234762413654, 3.6167167385084564, 3.5194381942161246, 3.4017984444691023, 3.2625803369198034, 3.1008094330806952, 2.9158918563458873, 2.7075809293762343, 2.4759908154081502, 2.2216755794578247, 1.9457851824834864, 1.6499771705635433, 1.336395693150156, 1.0077257609014014, 0.6673173916839831, 0.31902031943121806, -0.03289656971451535, -0.38375290685435126, -0.7284205118588423, -1.061559346985929, -1.3777596665690799, -1.6716262386846164, -1.937855315254933, -2.1714895192702706, -2.3680811763540524, -2.523821219273802, -2.635694367699651, -2.701651396214551, -2.7207089193546303, -2.693041502464269, -2.6201160634036658, -2.504667947252996, -2.350644593555447, -2.163167574881627, -1.9485312629154385, -1.7139328404580316, -1.4672289529293847, -1.2167352495336128, -0.9710471492670999, -0.7386108282493594, -0.5273847957242894, -0.3445672247609838, -0.19634062807418734, -0.08750883288700056, -0.021266783281260408, 0.0009476863563617805, -0.020434390536246606, -0.08306066709834876, -0.18273048346857715, -0.31354743093745696, -0.4681354899731071, -0.6379650367898203, -0.8137405158596428, -0.9858363023874617, -1.144796054479052, -1.2818017496245877, -1.3891177187349666, -1.4605309040999688, -1.4918064653884502, -1.4808667513707807, -1.4279018448181726, -1.3354394427161547, -1.2083629024268316, -1.053513859745541, -0.8792792066472448, -0.6951587162620588, -0.5112655179325553, -0.33754734197432834, -0.1831221803963005, -0.05567958480373987, 0.0391026087562467, 0.09808121172493692, 0.12095323569094689, 0.11040942887642209, 0.07214360842238077, 0.014569261774130786, -0.051640822422113306, -0.11415868820902977, -0.1597875324969118, -0.17539243291711853, -0.1488179165335243, -0.06981117998755697, 0.06902040880797719, 0.27153373848458173, 0.5375745761661295, 0.8626709017984815, 1.2379446220191006, 1.6505165196512006, 2.084102759136198, 2.519829184819992, 2.9373952816741706, 3.316307735123737, 3.637086896950851, 3.8825595756061078, 4.039369670426844, 4.09870140290452, 4.0567923012153955, 3.915378734027336, 3.682109839646727, 3.36967094794032, 2.9948306939747993, 2.577477651399094, 2.139577576423118, 1.7032731003175314, 1.2893124758645325, 0.9157417200376484, 0.5967698447897518, 0.34175044834852697, 0.15473224251767206, 0.034441324736389174, -0.025344199910939967, -0.034875515053076483, -0.007242163755311145, 0.043007650694887836, 0.10142823995114218, 0.15517124138158658, 0.19416630808204294, 0.21203069762569232, 0.20668592023755236, 0.18014694890542296, 0.13787044180440403, 0.08778706847605837, 0.03902078302851486, 0.00011344121255558332, -0.02251725931930689, -0.02579522767667049, -0.010788660916500152, 0.017150840948188435, 0.049198165762567844, 0.07476372820440665, 0.08412877317415532, 0.0718981287157533, 0.04096731837392052, 0.006743735308668412, 0.0012060341072431197, 0.0761414805036751, 0.3053186578861467, 0.78513967907961, 1.6328350572169235, 2.9826311073500262, 4.979882779627147, 7.772813549980702, 11.501294674751756, 16.285438123689197, 22.213512371338584, 29.329707794957294, 37.623187503006235, 47.019320660516186, 57.37329488275461, 68.46857306606304, 80.02449255595012, 91.7006925267018, 103.10616096895947, 113.81766684700187, 123.41323165421703, 131.484094463749, 137.65176849083852, 141.5958407323951, 143.09598418757017, 142.02897629400178, 138.37211771258075, 132.2165071091183, 123.78851725120266, 113.41581643568068, 101.50481500929236, 88.52799613366028, 75.01468195858995, 61.50001211907435, 48.49184625266074, 36.44903952790059, 25.763320516506187, 16.727130045358038, 9.520342966822037, 4.207652921923541, 0.7411536495942627, -1.032237972436454, -1.3529030568332228, -0.5258360812473007, 1.1046838808934214, 3.1836643641758515, 5.3723007881756235, 7.371824032760469, 8.94398607618782, 9.924223611281535, 10.227681943643805, 9.849163587301, 8.85701163606601, 7.3786803922867685, 5.583524856407261, 3.6634952843706725, 1.8119525671029417, 0.2045681947367927, -1.0161393896018887, -1.753054174857813, -1.9625311269778825, -1.653779475933703, -0.8846867770856711, 0.24591356300319317, 1.611062315278567, 3.07038096414391, 4.483294293460704, 5.7223163774620565, 6.68755120976662, 7.312058935097219, 7.563994720080168, 7.447516104067279, 7.002570957993236, 6.294184977234875, 5.402645668247273, 4.415064531556024, 3.4175548768711983, 2.4845108751900606, 1.6724352099315327, 1.0170250389973126, 0.5324905649186086, 0.2129148493531413, 0.03628144513303156, -0.03023253543949701, -0.024418354898768296, 0.01685062108109509, 0.062291603139028595, 0.08947003634976904, 0.08651640961260748, 0.05180489934076955, -0.00784388163994299, -0.07992259391277508, -0.14967421680355691, -0.20353852760074334, -0.23181807377598304, -0.2304523962662089, -0.2017604475019125, -0.1535545629285271, -0.09733952098025989, -0.045956578049305565, -0.01093637419038768, 2.1311859370885214e-05, -0.015270007735795425, -0.0527725825944568, -0.10271346595792602, -0.15116477221302077, -0.1823632704901654, -0.18154644348617419, -0.13805935699461716, -0.04747475454677935, 0.08714087413582171, 0.2549214019730279, 0.43823827105476015, 0.6152089453250832, 0.7626773581976823, 0.8595933116791857, 0.8907735856490729, 0.8492023940819784, 0.7371926132306591, 0.5665192645373964, 0.35732947289348777, 0.13491524700539567, -0.07388654750772204, -0.24449148846608929, -0.3584642508414822, -0.40604362354301987, -0.3872425114192086, -0.31174288470009587, -0.1974645797713038, -0.0667527273010764, 0.05754759777485714, 0.15581606737054415, 0.2150211242911208, 0.2309759304049538, 0.2084611575429114, 0.15963935663558196, 0.10099649500485997, 0.04881932353864843, 0.014564918750416997, 0.0010317652496086998, 0.000115267765102024, -0.007019542269339567, -0.046802188886009746, -0.14726763604385046, -0.3299139305020139, -0.6003899839881279, -0.9391601104753514, -1.293979432779172, -1.5777467711491824, -1.6697182318040915, -1.4213527936836126, -0.6689222569619617, 0.7440305415812466, 2.947803714477067, 6.026591137715018, 9.997418778179417, 14.790469508468792, 20.24476607700065, 26.109869208049275, 32.05689193227908, 37.70578245939564, 42.65337917119065, 46.50515041763193, 48.91614748745439, 49.644710210327446, 48.56585946397252, 45.68280625843013, 41.1402429818121, 35.234656917692845, 28.367787870166513, 21.007518023875008, 13.65305740674469, 6.795274081908027, 0.8561535909539589, -3.8477611751388903, -7.128173905989639, -8.941166574053469, -9.383789957354562, -8.671726672587091, -7.108343938678949, -5.048406472761758, -2.8488623812071556, -0.8262389400513336, 0.7764915988741169, 1.8131158476609697, 2.244487849054225, 2.1324626396899586, 1.6211627392429597, 0.9080323861350686, 0.2085385853290902, -0.278618186377264, -0.40247206903088817, -0.08258859910998302, 0.6819504775691698, 1.8143230950124098, 3.17310532085009, 4.579452353640264, 5.844797715094956, 6.7971364094317375, 7.307671199995118, 7.317317002230424, 6.836634480517809, 5.938893759177391, 4.749637556443792, 3.431159909392467, 2.1480687418708846, 1.041400714592226, 0.21069842161638647, -0.29800538486441575, -0.4981425946677773, -0.4539891803589531, -0.26339238223953004, -0.035620060478020056, 0.1336991472838014, 0.18511521299794267, 0.11102765163343138, -0.0377916993685724, -0.15683400621935756, -0.10346291244084, 0.27890364827261327, 1.1330392470975075, 2.5592290855806845, 4.589649603406903, 7.172127086274664, 10.173439210878476, 13.386213661830704, 16.544983570534267, 19.35766010462119, 21.558372910645577, 22.930375726469613, 23.327083565149547, 22.69667875764418, 21.10836889608216, 18.724791607784475, 15.775477605063813, 12.533409541970048, 9.289754769527228, 6.304354862881492, 3.775384163196367, 1.823250571566471, 0.48404809092012385, -0.28709261488328336, -0.5974161640370158, -0.5906360150987091, -0.4182873334995763, -0.21053853117942026, -0.05522590535128767, 0.012787129408261015, 0.010939725937126462, -0.003192299786821115, 0.046658767314458234, 0.22917619141927922, 0.5798131319944138, 1.080827232851836, 1.65013393832403, 2.142614066424563, 2.3688822955747995, 2.1204226303346005, 1.2007853045680443, -0.5376901564235671, -3.155657969141545, -6.609772240326988, -10.745140092437662, -15.299965592509269, -19.93167477400257, -24.25505636931327, -27.882370176727513, -30.470312642268826, -31.778286010220373, -31.68793986306103, -30.211787978406605, -27.496841486160697, -23.82134812109102, -19.543456721859965, -15.054452414495334, -10.737323877430367, -6.927645011795883, -3.8710138293844945, -1.7023667600613819, -0.4414213471848379, -0.002305362070020812, -0.2176113861856257, -0.8693077196459319, -1.723156430749108, -2.565599233190011, -3.2289534384586327, -3.6055139963979195, -3.654123517378068, -3.3995236077835616, -2.9124451524115225, -2.2888020637384145, -1.630704890215576, -1.0292777093985221, -0.5478693244283507, -0.2158715807833508, -0.030035913299487425, 0.038953021549862285, 0.03596875815846441, 0.009202103150442682, -0.0007987401590130543, 0.03109129315851155, 0.11141258486524955, 0.22935899077614322, 0.3616696577377095, 0.48048093061352304, 0.5607404480872227, 0.5859815802435788, 0.5520201782481035, 0.46796981983260166, 0.35251611558933416, 0.22880001375238013, 0.11892550208825725, 0.03882656464453846, -0.0051858085422084275, -0.01693826524000971, -0.008426933777128996, 0.004190776440681755, 0.005664963608189538, -0.013872027026817, -0.055899148665869564, -0.11296157681279873, -0.17077467094356835, -0.2120279720777261, -0.22131882550822604, -0.19053853911996524, -0.12143971880462309, -0.025802414972675033, 0.07661153922591879, 0.16247609703754246, 0.211544361882781, 0.21228792109121772, 0.16558053417276009, 0.08548196159401299, -0.003930893376414362, -0.07499483947754226, -0.10503669603585783, -0.08549907502856283, -0.027794911663002245, 0.03476327385358493, 0.050126932084100385, -0.04255679981820198, -0.29871460542400685, -0.7533493977287804, -1.4066251324381742, -2.213152627906201, -3.082793968791667, -3.88968510000759, -4.489668505099534, -4.747682535345052, -4.566172262100209, -3.908876511285922, -2.81825293728627, -1.4217279631365627, 0.08531041538335467, 1.4693492406296174, 2.499781723471059, 3.001017975550499, 2.8993109550613148, 2.25588655752701, 1.2835750498206318, 0.33984206529120126, -0.11581682851180497, 0.41573706733455285, 2.3957958957007843, 6.162080771017118, 11.853925358330716, 19.357685413089005, 28.285221664894166, 38.01035310877237, 47.72122104008138, 56.497247166035294, 63.42806654770719, 67.7884298900368, 69.09649404415956, 67.16114541848249, 62.13578759234757, 54.566237229426726, 45.24983727049465, 35.11607242142094, 25.12892078438992, 16.188177458999842, 8.966338851947247, 3.833471753959497, 0.8405811146898363, -0.25989213866857735, 0.041291916714142216, 1.1131286381259886, 2.301531849416702, 3.0437293359618254, 2.9575994068683897, 1.8931773760515893, -0.0575332281253859, -2.5929369946275047, -5.277622770230503, -7.6342160361691835, -9.238875960900863, -9.806242217172075, -9.238103807649289, -7.6369970063714305, -5.284760489048292, -2.5812515661902564, 0.03755539382062465, 2.177309023422187, 3.5564194207332944, 4.063741553883472, 3.76042246996327, 2.851892077502195, 1.6398678749016913, 0.45585369972783074, -0.42036837462492205, -0.8184571677860555, -0.7088662156065155, -0.20501446407176233, 0.4725758606682601, 1.0584704254166997, 1.316914393539378, 1.1170297956931192, 0.4886045238792704, -0.35452209322295924, -1.0287000426121546, -1.0351189136972307, 0.15620124472773145, 3.0057758253309514, 7.802348512966085, 14.588190771209518, 23.11853796424137, 32.853330214716, 43.00312725417687, 52.662397877725255, 60.90370506531249, 66.87639645274436, 69.93270881691602, 69.78540610680867, 66.48535303181434, 60.38801356331146, 52.12380288708604, 42.55589184919098, 32.606743241000366, 23.13453527147572, 14.847975618180996, 8.241974494778917, 3.545381487588128, 0.7288624433806823, -0.4522965625975974, -0.3928010457713903, 0.44560475097402785, 1.6097674481322113, 2.7179215089978825, 3.506681562876902, 3.843516279477068, 3.715809664148757, 3.2062985607128285, 2.457948470986163, 1.6284002034173193, 0.856685322970582, 0.24147740262384298, -0.17036521770603588, -0.3805203688410986, -0.4261123447581596, -0.3634397337891852, -0.2515909851285084, -0.13805250876006103, -0.05186843094126658, -0.003046818899821256, 0.013426560037382634, 0.010425238857970467, 0.0015655219692070116, -0.0038497964718091707, -0.0029326679958829407, 0.0018713777311434277, 0.005861235848897479, 0.005549811276123608, 0.0010738601366288754, -0.003695648243892154, -0.003334464998865145, 0.005402936567717091, 0.019648418706192772, 0.028191247621025525, 0.012001600254014257, -0.05192093523743651, -0.18331529895072798, -0.3907426718778146, -0.6645844185083576, -0.9728616169043194, -1.2630518275138076, -1.4691558883052944, -1.5225145711147845, -1.366328670334511, -0.9729124160820118, -0.3514732562438439, 0.44934957968290185, 1.3446554837118097, 2.2250931462841277, 2.9771301938313304, 3.5020951893375067, 3.7340534900420117, 3.655940593827119, 3.2993099006201057, 2.7358804861138073, 2.064111828502358, 1.3914735078389173, 0.8095076232028222, 0.3772334798574486, 0.11336786739766218, -0.0026743155288295847, -0.02090997482454628, -0.0036945679128731757, -0.006577548919501514, -0.06219556660205649, -0.17187054752139647, -0.3063626056461056, -0.41628594037865746, -0.45184884951974896, -0.38196467149431584, -0.20954199318317276, 0.01969189117899574, 0.22043963415532458, 0.28688880333538214, 0.11759532462154493, -0.3567328129639483, -1.1452944753318857, -2.184130212429945, -3.3392124678809467, -4.4261852535784, -5.248294938326808, -5.637136586893128, -5.4914075018663135, -4.809896792265595, -3.709871206566353, -2.400746452190894, -1.1451262056395815, -0.20885462853329442, 0.20085079663814098, -0.00608907787495507, -0.7747715473252355, -1.9043810024731331, -3.077493590137253, -3.928300457015672, -4.124360791391416, -3.4481847102442527, -1.8671659991593976, 0.43405507432931706, 3.065851347861762, 5.48893776502199, 7.113668313790679, 7.416836044335593, 6.053860125699772, 2.9514826895661814, -1.6429366655688549, -7.183726553939425, -12.896575115509096, -17.896350351906417, -21.35711262832813, -22.650767200133103, -21.455742431167334, -17.83035177223722, -12.227291038746344, -5.40244570997608, 1.705666427773936, 8.13066426998932, 13.073573939303413, 16.009585006322567, 16.745150726965306, 15.447336868618722, 12.634049232913137, 8.995913039562119, 5.2460688234276684, 2.00442198093964, -0.29808510640103575, -1.5154034679244783, -1.7718107853102496, -1.3831186828027358, -0.746612227984538, -0.21726443284911232, 0.01110831212044781, -0.020417639607101936, -0.024436801374620152, 0.4803267846059152, 2.05871387214024, 5.212039764055706, 10.241602281761953, 17.135127598693316, 25.494448288215896, 34.54489849841897, 43.28347061142686, 50.60013219452351, 55.42208903820682, 56.907975488242805, 54.69056948755597, 48.87383820854291, 39.99868568154437, 28.99596588386608, 17.096796663781582, 5.577325894642038, -4.430333871363918, -12.076346983947184, -16.90293042036029, -18.87912626092504, -18.34968934715198, -15.939118537442907, -12.429233801690108, -8.5956092448842, -5.0830138353693695, -2.325517064083214, -0.5118709083389804, 0.3976182426225559, 0.6116115885205609, 0.4273830097398634, 0.14556806709296477, -0.00028108733189884176, 0.11597770371951682, 0.5028602204274156, 1.0738727477845404, 1.689014111694608, 2.198835272956413, 2.48625507837222, 2.501588220442376, 2.2623213784200904, 1.837849868172566, 1.3277148505868142, 0.8359769142776358, 0.43985830652168845, 0.17551086031021454, 0.038415229621697425, -0.005835843140491232, -0.004112318950315263, 0.003487711667546735, -0.002803225425969266, -0.018516377465889616, -0.02112823007959593, 0.015867915706003308, 0.10566549395398633, 0.23640888698056509, 0.3669724850161376, 0.4311815762747766, 0.3531050635566552, 0.0758441597806781, -0.4204005204845466, -1.1073310324375472, -1.9050829044595865, -2.690798177733193, -3.3271463525337057, -3.6926808585161908, -3.7115346949861876, -3.379359392127503, -2.7621860324668064, -1.98146143300737, -1.1891051712051204, -0.5326743326832555, -0.11060501925160605, 0.05347906331219945, 0.018354080997768113, -0.08524758805295911, -0.08659899534400704, 0.17951564699018285, 0.8264874676964222, 1.880258490182454, 3.2614227727868896, 4.791243541601317, 6.223734615987332, 7.305071267780666, 7.825562954852239, 7.665300276115234, 6.829525538270732, 5.464150872535607, 3.818591041090439, 2.195069448967191, 0.8900003380152669, 0.13157528209058747, 0.028181961597642444, 0.5472943543665871, 1.5233181907299291, 2.697603417210157, 3.777174406949693, 4.496172369232992, 4.673804405735157, 4.26009502520052, 3.3354530977715453, 2.0869551534542206, 0.7668354551960129, -0.36599195002700396, -1.1068476038757515, -1.3455590648738531, -1.0863186466672436, -0.44317127815009505, 0.39618984419938286, 1.216163810450437, 1.8221975603731864, 2.0884576129315686, 1.977917752631801, 1.54052944455291, 0.8960358166942093, 0.20275528633829987, -0.3891672626649975, -0.7721081874748885, -0.9010176403481914, -0.7983921225409897, -0.5405872281543799, -0.23144929257144004, 0.027898909716636146, 0.16657902323672077, 0.15938725821894073, 0.0282759674072093, -0.16861246501171126, -0.35851517526679977, -0.47742938455517075, -0.48777822088546974, -0.3881042586583774, -0.2119029672895171, -0.013099208352447567, 0.15159869239300208, 0.23998434297763407, 0.23796678002008106, 0.1609940517250505, 0.04637569935006417, -0.05988996608543291, -0.11945050662932834, -0.11517188767428391, -0.05533770316170113, 0.03069226518365936, 0.10437314112833293, 0.13470334115665303, 0.11159498512480105, 0.05187454341406942, -0.004302658566262669, -0.007786192834829876, 0.0799860210340524, 0.2686598665648301, 0.5296113719677219, 0.7989161881594956, 0.992992450900737, 1.0359437059699048, 0.8936598410765312, 0.5901539371323604, 0.20890580082560384, -0.12293517801462757, -0.2720242395510129, -0.15345198554559722, 0.22683047575253085, 0.7511381201157903, 1.204919404027123, 1.3392375873448195, 0.9684621185473212, 0.0882315845765097, -1.0078603610479921, -1.667618057991228, -0.8921115943617116, 2.5670522385272445, 10.010594018424715, 22.518668345663965, 40.653246940221024, 64.1952363714246, 92.02210752092883, 122.06365824901457, 151.39777857807923, 176.5844724095333, 194.34783822694504, 201.9145931141444, 197.37277275666466, 180.1324878299096, 151.43659814246536, 113.92952378411513, 71.25204823820698, 27.68647562259069, -12.274725071590625, -44.84741784486129, -67.47171339057604, -79.04536839723418, -79.98600931338326, -72.11918434221644, -58.2497515338921, -41.60340374675845, -25.24622602814012, -11.60144278924985, -2.121116214962062, 2.8444200248954905, 3.957805906769959, 2.5687289486942766, 0.3199073929141634, -1.2634650926937865, -1.1309282136458128, 1.087046822073192, 5.042801136716166, 9.791804640046987, 14.084798265910049, 16.680853478852736, 16.623884781248126, 13.472476172974522, 7.447063641081721, -0.6641435979412832, -9.679962961283243, -18.252863546244402, -25.150048690805182, -29.484403818011728, -30.839060802789927, -29.31088825313673, -25.478454285555824, -20.206928359875974, -14.449051184098888, -9.070467096363204, -4.709761164062386, -1.6863018500498133, -0.003244124651645959, 0.5857457864528101, 0.4698301851361319, 0.06136877287965629, -0.3026149914587796, -0.42355757063419397, -0.25541829554723433, 0.12486079148955745, 0.5680962909727956, 0.9146227170059394, 1.0583803188954346, 0.9696771371860087, 0.6923118878954829, 0.3249663944669914, -0.009990679454851159, -0.21211749783687195, -0.23114639046055796, -0.07616638709119221, 0.19369837250011984, 0.4907394427986608, 0.7262281191049806, 0.8370290270148156, 0.8048927422983863, 0.6538628671730645, 0.4378118347545361, 0.2225468394507886, 0.0650811034320488, -0.00482994567210937, 0.009956793308399724, 0.07894063741097455, 0.15665689149703219, 0.1996604565113773, 0.18115287823494863, 0.09911369147418314, -0.024783286209816558, -0.15401116900572326, -0.24968746730987051, -0.28366543215034323, -0.24883523713188052, -0.1592117955595317, -0.04402906868200433, 0.06200306113446946, 0.13058548217400445, 0.1487218822815654, 0.12103077641025167, 0.06644962797087421, 0.010306969144082863, -0.02661979611561328, -0.0356552684820186, -0.02266011015207791, -0.004701779331078018, -0.0017223390236333089, -0.026839228645604923, -0.07900581434042571, -0.14172781096803028, -0.18898309234343608, -0.19618255680521804, -0.15317560906836236, -0.07470087311142364, -0.0016967507902092523, 0.005330737203046042, -0.11893994964903049, -0.4180767460799167, -0.8851818853670076, -1.447394826174147, -1.9827749321841417, -2.4012121829013973, -2.6627233097719647], 'positive_zeros': ['1.12208157242451914798598511814732', '2.02488307079206194451136367776757', '2.03789560009096921956091206354444', '2.79818339854156340071020354115944', '2.97578655875082507004543226993416', '3.17370587119169730974811346610204', '4.04559620663862811180051570608069', '4.13023400979335061773916604682164', '4.46887371405670977437919867622125', '4.57583726517368218232392400119096', '4.79085624826043896341536773143250', '4.81081477263425944096717602594028', '6.07248932314260346534353139733824', '6.16775937932023986386626557285598', '6.59829440124508259258889095090947', '6.77508143638941654374302885483980', '7.38688724523140684504483379588318', '7.45746876674645464331543824589132', '7.62136861894541484636262768885204', '7.963095905909545202809939208295638', '7.969011993015351599427181722138443', '8.230891427521361793792822089440638', '8.613459789247073535035353261223260', '8.859993352833541823017662914575797', '9.168205984833807359921736757613882', '9.178165556473027426063589102187293', '9.192739938592850615959794040885535', '9.548089632907229589582055311376680', '10.22383703559096009277236116306163', '10.51486471394432982832110319264133', '10.72996876180955721722164304554277', '10.81694224337134835432520764625948', '11.29194642353876405929920555029521', '11.44289945410288717086188345183399', '11.55500109148100400191305351101399', '11.63736653099691810447406156224931', '12.32948248778445937128870309130619', '12.52099533652145591866653048902014', '12.57958193139949027027315000714873', '12.60122340024677383136741084253335'], 'prelabel': '8-200e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.2637278347910235, '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': 39085210196943694, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.12208157242451914798598511815', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.02488307079206194451136367777', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.03789560009096921956091206354', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 6.504717062986346, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 1600000000, 'conductor_radical': 10, 'degree': 8, 'dirichlet_coefficients': [1, 0, 5, 0, -5, 0, 6, 0, 13, 0, 6, 0, -7, 0, -25, 0, -8, 0, -9, 0, 30, 0, 9, 0, 10, 0, 30, 0, -3, 0, 13, 0, 30, 0, -30, 0, 1, 0, -35, 0, 16, 0, 22, 0, -65, 0, 4, 0, -3, 0, -40, 0, -19, 0, -30, 0, -45, 0, -6, 0, -23, 0, 78, 0, 35, 0, -22, 0, 45, 0, 10, 0, -11, 0, 50, 0, 36, 0, 15, 0, 70, 0, -1, 0, 40, 0, -15, 0, -4, 0, -42, 0, 65, 0, 45, 0, 36, 0, 78, 0], 'euler11': [1, -6, 5, 6, 49, 66, 605, -7986, 14641], 'euler13': [1, 7, 11, -79, -536, -1027, 1859, 15379, 28561], 'euler17': [1, 8, 7, -110, -579, -1870, 2023, 39304, 83521], 'euler19': [1, 9, 27, -83, -960, -1577, 9747, 61731, 130321], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, -9, 38, -255, 1741, -5865, 20102, -109503, 279841], 'euler29': [1, 3, 5, -87, -116, -2523, 4205, 73167, 707281], 'euler3': [1, -5, 12, -25, 49, -75, 108, -135, 81], 'euler31': [1, -13, 108, -821, 5525, -25451, 103788, -387283, 923521], 'euler37': [1, -1, 14, 103, 739, 3811, 19166, -50653, 1874161], 'euler41': [1, -16, 95, -534, 4109, -21894, 159695, -1102736, 2825761], 'euler43': [1, -22, 351, -3476, 27329, -149468, 648999, -1749154, 3418801], 'euler47': [1, -4, -1, -318, 3479, -14946, -2209, -415292, 4879681], 'euler5': [1, 5, 15, 25, 25, 0, 0, 0, 0], 'euler53': [1, 19, 188, 1765, 15251, 93545, 528092, 2828663, 7890481], 'euler59': [1, 6, -43, -402, 475, -23718, -149683, 1232274, 12117361], 'euler61': [1, 23, 318, 3511, 31355, 214171, 1183278, 5220563, 13845841], 'euler67': [1, 22, 117, -970, -16399, -64990, 525213, 6616786, 20151121], 'euler7': [1, -6, 39, -132, 449, -924, 1911, -2058, 2401], 'euler71': [1, -10, -11, 790, -6489, 56090, -55451, -3579110, 25411681], 'euler73': [1, 11, 48, -275, -6529, -20075, 255792, 4279187, 28398241], 'euler79': [1, -15, 111, -1495, 19536, -118105, 692751, -7395585, 38950081], 'euler83': [1, 1, 58, 335, 7041, 27805, 399562, 571787, 47458321], 'euler89': [1, 4, -73, -648, 3905, -57672, -578233, 2819876, 62742241], 'euler97': [1, -36, 749, -11172, 124789, -1083684, 7047341, -32856228, 88529281], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -5, 12, -25, 49, -75, 108, -135, 81], [1, 5, 15, 25, 25, 0, 0, 0, 0], [1, -6, 39, -132, 449, -924, 1911, -2058, 2401], [1, -6, 5, 6, 49, 66, 605, -7986, 14641], [1, 7, 11, -79, -536, -1027, 1859, 15379, 28561], [1, 8, 7, -110, -579, -1870, 2023, 39304, 83521], [1, 9, 27, -83, -960, -1577, 9747, 61731, 130321], [1, -9, 38, -255, 1741, -5865, 20102, -109503, 279841], [1, 3, 5, -87, -116, -2523, 4205, 73167, 707281], [1, -13, 108, -821, 5525, -25451, 103788, -387283, 923521], [1, -1, 14, 103, 739, 3811, 19166, -50653, 1874161], [1, -16, 95, -534, 4109, -21894, 159695, -1102736, 2825761], [1, -22, 351, -3476, 27329, -149468, 648999, -1749154, 3418801], [1, -4, -1, -318, 3479, -14946, -2209, -415292, 4879681], [1, 19, 188, 1765, 15251, 93545, 528092, 2828663, 7890481], [1, 6, -43, -402, 475, -23718, -149683, 1232274, 12117361], [1, 23, 318, 3511, 31355, 214171, 1183278, 5220563, 13845841], [1, 22, 117, -970, -16399, -64990, 525213, 6616786, 20151121], [1, -10, -11, 790, -6489, 56090, -55451, -3579110, 25411681], [1, 11, 48, -275, -6529, -20075, 255792, 4279187, 28398241], [1, -15, 111, -1495, 19536, -118105, 692751, -7395585, 38950081], [1, 1, 58, 335, 7041, 27805, 399562, 571787, 47458321], [1, 4, -73, -648, 3905, -57672, -578233, 2819876, 62742241], [1, -36, 749, -11172, 124789, -1083684, 7047341, -32856228, 88529281]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/200/2/m/a'], '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': '8-200e4-1.1-c1e4-0-4', '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': '8-200e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.2637278347910235, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 39085210196943694, 'z1': {'__RealLiteral__': 0, 'data': '1.12208157242451914798598511815', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1422407378788977158360850463185,2566844240081537650544675677865,2583339580657784878879448641176,3547118864709879692175481896906', 'Lhash_array': ['1422407378788977158360850463185', '2566844240081537650544675677865', '2583339580657784878879448641176', '3547118864709879692175481896906'], 'label': '8-200e4-1.1-c1e4-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/200/2/m/a'}