Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [354,6,Mod(353,354)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(354, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("354.353");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 354 = 2 \cdot 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 354.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(56.7758722138\) |
Analytic rank: | \(0\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 353.16 | ||
Character | \(\chi\) | \(=\) | 354.353 |
Dual form | 354.6.c.a.353.15 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/354\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.00000 | −0.707107 | ||||||||
\(3\) | −9.75722 | + | 12.1572i | −0.625926 | + | 0.779883i | ||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | − | 43.2791i | − | 0.774200i | −0.922038 | − | 0.387100i | \(-0.873477\pi\) | ||
0.922038 | − | 0.387100i | \(-0.126523\pi\) | |||||||
\(6\) | 39.0289 | − | 48.6287i | 0.442596 | − | 0.551460i | ||||
\(7\) | −5.13563 | −0.0396140 | −0.0198070 | − | 0.999804i | \(-0.506305\pi\) | ||||
−0.0198070 | + | 0.999804i | \(0.506305\pi\) | |||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | −52.5934 | − | 237.240i | −0.216434 | − | 0.976297i | ||||
\(10\) | 173.116i | 0.547442i | ||||||||
\(11\) | 262.706 | 0.654618 | 0.327309 | − | 0.944917i | \(-0.393858\pi\) | ||||
0.327309 | + | 0.944917i | \(0.393858\pi\) | |||||||
\(12\) | −156.115 | + | 194.515i | −0.312963 | + | 0.389941i | ||||
\(13\) | 296.127i | 0.485981i | 0.970029 | + | 0.242990i | \(0.0781283\pi\) | ||||
−0.970029 | + | 0.242990i | \(0.921872\pi\) | |||||||
\(14\) | 20.5425 | 0.0280113 | ||||||||
\(15\) | 526.151 | + | 422.283i | 0.603785 | + | 0.484591i | ||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 1334.77i | 1.12017i | 0.828434 | + | 0.560087i | \(0.189232\pi\) | ||||
−0.828434 | + | 0.560087i | \(0.810768\pi\) | |||||||
\(18\) | 210.374 | + | 948.961i | 0.153042 | + | 0.690346i | ||||
\(19\) | −1340.55 | −0.851922 | −0.425961 | − | 0.904742i | \(-0.640064\pi\) | ||||
−0.425961 | + | 0.904742i | \(0.640064\pi\) | |||||||
\(20\) | − | 692.465i | − | 0.387100i | ||||||
\(21\) | 50.1095 | − | 62.4347i | 0.0247954 | − | 0.0308943i | ||||
\(22\) | −1050.82 | −0.462885 | ||||||||
\(23\) | −1858.55 | −0.732581 | −0.366290 | − | 0.930501i | \(-0.619372\pi\) | ||||
−0.366290 | + | 0.930501i | \(0.619372\pi\) | |||||||
\(24\) | 624.462 | − | 778.059i | 0.221298 | − | 0.275730i | ||||
\(25\) | 1251.92 | 0.400615 | ||||||||
\(26\) | − | 1184.51i | − | 0.343640i | ||||||
\(27\) | 3397.33 | + | 1675.42i | 0.896869 | + | 0.442297i | ||||
\(28\) | −82.1701 | −0.0198070 | ||||||||
\(29\) | 1127.52i | 0.248960i | 0.992222 | + | 0.124480i | \(0.0397263\pi\) | ||||
−0.992222 | + | 0.124480i | \(0.960274\pi\) | |||||||
\(30\) | −2104.60 | − | 1689.13i | −0.426940 | − | 0.342658i | ||||
\(31\) | − | 6100.77i | − | 1.14020i | −0.821576 | − | 0.570099i | \(-0.806905\pi\) | ||
0.821576 | − | 0.570099i | \(-0.193095\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | −2563.28 | + | 3193.76i | −0.409742 | + | 0.510525i | ||||
\(34\) | − | 5339.10i | − | 0.792083i | ||||||
\(35\) | 222.265i | 0.0306691i | ||||||||
\(36\) | −841.494 | − | 3795.84i | −0.108217 | − | 0.488149i | ||||
\(37\) | − | 6962.90i | − | 0.836153i | −0.908412 | − | 0.418077i | \(-0.862704\pi\) | ||
0.908412 | − | 0.418077i | \(-0.137296\pi\) | |||||||
\(38\) | 5362.21 | 0.602399 | ||||||||
\(39\) | −3600.06 | − | 2889.37i | −0.379008 | − | 0.304188i | ||||
\(40\) | 2769.86i | 0.273721i | ||||||||
\(41\) | − | 1648.54i | − | 0.153158i | −0.997064 | − | 0.0765791i | \(-0.975600\pi\) | ||
0.997064 | − | 0.0765791i | \(-0.0243998\pi\) | |||||||
\(42\) | −200.438 | + | 249.739i | −0.0175330 | + | 0.0218455i | ||||
\(43\) | 1565.02i | 0.129077i | 0.997915 | + | 0.0645383i | \(0.0205575\pi\) | ||||
−0.997915 | + | 0.0645383i | \(0.979443\pi\) | |||||||
\(44\) | 4203.29 | 0.327309 | ||||||||
\(45\) | −10267.5 | + | 2276.19i | −0.755849 | + | 0.167563i | ||||
\(46\) | 7434.22 | 0.518013 | ||||||||
\(47\) | −13521.2 | −0.892837 | −0.446418 | − | 0.894824i | \(-0.647301\pi\) | ||||
−0.446418 | + | 0.894824i | \(0.647301\pi\) | |||||||
\(48\) | −2497.85 | + | 3112.23i | −0.156481 | + | 0.194971i | ||||
\(49\) | −16780.6 | −0.998431 | ||||||||
\(50\) | −5007.69 | −0.283278 | ||||||||
\(51\) | −16227.1 | − | 13023.7i | −0.873605 | − | 0.701146i | ||||
\(52\) | 4738.02i | 0.242990i | ||||||||
\(53\) | 12816.2i | 0.626714i | 0.949635 | + | 0.313357i | \(0.101454\pi\) | ||||
−0.949635 | + | 0.313357i | \(0.898546\pi\) | |||||||
\(54\) | −13589.3 | − | 6701.67i | −0.634182 | − | 0.312751i | ||||
\(55\) | − | 11369.7i | − | 0.506805i | ||||||
\(56\) | 328.680 | 0.0140057 | ||||||||
\(57\) | 13080.1 | − | 16297.3i | 0.533240 | − | 0.664399i | ||||
\(58\) | − | 4510.09i | − | 0.176042i | ||||||
\(59\) | 14183.6 | + | 22666.1i | 0.530464 | + | 0.847707i | ||||
\(60\) | 8418.41 | + | 6756.53i | 0.301892 | + | 0.242296i | ||||
\(61\) | − | 50754.6i | − | 1.74643i | −0.487336 | − | 0.873215i | \(-0.662031\pi\) | ||
0.487336 | − | 0.873215i | \(-0.337969\pi\) | |||||||
\(62\) | 24403.1i | 0.806242i | ||||||||
\(63\) | 270.100 | + | 1218.38i | 0.00857381 | + | 0.0386750i | ||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 12816.1 | 0.376246 | ||||||||
\(66\) | 10253.1 | − | 12775.0i | 0.289732 | − | 0.360996i | ||||
\(67\) | 1305.77i | 0.0355368i | 0.999842 | + | 0.0177684i | \(0.00565615\pi\) | ||||
−0.999842 | + | 0.0177684i | \(0.994344\pi\) | |||||||
\(68\) | 21356.4i | 0.560087i | ||||||||
\(69\) | 18134.3 | − | 22594.8i | 0.458541 | − | 0.571327i | ||||
\(70\) | − | 889.061i | − | 0.0216864i | ||||||
\(71\) | 17624.9i | 0.414936i | 0.978242 | + | 0.207468i | \(0.0665222\pi\) | ||||
−0.978242 | + | 0.207468i | \(0.933478\pi\) | |||||||
\(72\) | 3365.98 | + | 15183.4i | 0.0765209 | + | 0.345173i | ||||
\(73\) | 16392.2i | 0.360023i | 0.983664 | + | 0.180012i | \(0.0576135\pi\) | ||||
−0.983664 | + | 0.180012i | \(0.942386\pi\) | |||||||
\(74\) | 27851.6i | 0.591250i | ||||||||
\(75\) | −12215.3 | + | 15219.8i | −0.250755 | + | 0.312433i | ||||
\(76\) | −21448.8 | −0.425961 | ||||||||
\(77\) | −1349.16 | −0.0259320 | ||||||||
\(78\) | 14400.2 | + | 11557.5i | 0.267999 | + | 0.215093i | ||||
\(79\) | 66615.5 | 1.20090 | 0.600451 | − | 0.799662i | \(-0.294988\pi\) | ||||
0.600451 | + | 0.799662i | \(0.294988\pi\) | |||||||
\(80\) | − | 11079.4i | − | 0.193550i | ||||||
\(81\) | −53516.9 | + | 24954.5i | −0.906313 | + | 0.422607i | ||||
\(82\) | 6594.17i | 0.108299i | ||||||||
\(83\) | 52720.6 | 0.840011 | 0.420005 | − | 0.907522i | \(-0.362028\pi\) | ||||
0.420005 | + | 0.907522i | \(0.362028\pi\) | |||||||
\(84\) | 801.751 | − | 998.955i | 0.0123977 | − | 0.0154471i | ||||
\(85\) | 57767.8 | 0.867239 | ||||||||
\(86\) | − | 6260.06i | − | 0.0912709i | ||||||
\(87\) | −13707.5 | − | 11001.5i | −0.194160 | − | 0.155831i | ||||
\(88\) | −16813.2 | −0.231442 | ||||||||
\(89\) | 89751.0 | 1.20106 | 0.600529 | − | 0.799603i | \(-0.294957\pi\) | ||||
0.600529 | + | 0.799603i | \(0.294957\pi\) | |||||||
\(90\) | 41070.1 | − | 9104.77i | 0.534466 | − | 0.118485i | ||||
\(91\) | − | 1520.80i | − | 0.0192516i | ||||||
\(92\) | −29736.9 | −0.366290 | ||||||||
\(93\) | 74168.1 | + | 59526.5i | 0.889221 | + | 0.713680i | ||||
\(94\) | 54085.0 | 0.631331 | ||||||||
\(95\) | 58017.8i | 0.659557i | ||||||||
\(96\) | 9991.39 | − | 12448.9i | 0.110649 | − | 0.137865i | ||||
\(97\) | − | 24987.9i | − | 0.269650i | −0.990869 | − | 0.134825i | \(-0.956953\pi\) | ||
0.990869 | − | 0.134825i | \(-0.0430473\pi\) | |||||||
\(98\) | 67122.5 | 0.705997 | ||||||||
\(99\) | −13816.6 | − | 62324.4i | −0.141681 | − | 0.639102i | ||||
\(100\) | 20030.8 | 0.200308 | ||||||||
\(101\) | 118534. | 1.15622 | 0.578110 | − | 0.815959i | \(-0.303790\pi\) | ||||
0.578110 | + | 0.815959i | \(0.303790\pi\) | |||||||
\(102\) | 64908.3 | + | 52094.8i | 0.617732 | + | 0.495785i | ||||
\(103\) | − | 21499.7i | − | 0.199682i | −0.995003 | − | 0.0998409i | \(-0.968167\pi\) | ||
0.995003 | − | 0.0998409i | \(-0.0318334\pi\) | |||||||
\(104\) | − | 18952.1i | − | 0.171820i | ||||||
\(105\) | −2702.12 | − | 2168.69i | −0.0239183 | − | 0.0191966i | ||||
\(106\) | − | 51264.8i | − | 0.443154i | ||||||
\(107\) | 172067.i | 1.45291i | 0.687216 | + | 0.726453i | \(0.258833\pi\) | ||||
−0.687216 | + | 0.726453i | \(0.741167\pi\) | |||||||
\(108\) | 54357.4 | + | 26806.7i | 0.448434 | + | 0.221148i | ||||
\(109\) | − | 220183.i | − | 1.77508i | −0.460733 | − | 0.887539i | \(-0.652413\pi\) | ||
0.460733 | − | 0.887539i | \(-0.347587\pi\) | |||||||
\(110\) | 45478.7i | 0.358365i | ||||||||
\(111\) | 84649.2 | + | 67938.6i | 0.652102 | + | 0.523370i | ||||
\(112\) | −1314.72 | −0.00990350 | ||||||||
\(113\) | 171524. | 1.26366 | 0.631829 | − | 0.775108i | \(-0.282305\pi\) | ||||
0.631829 | + | 0.775108i | \(0.282305\pi\) | |||||||
\(114\) | −52320.2 | + | 65189.2i | −0.377057 | + | 0.469801i | ||||
\(115\) | 80436.5i | 0.567164i | ||||||||
\(116\) | 18040.4i | 0.124480i | ||||||||
\(117\) | 70253.1 | − | 15574.3i | 0.474462 | − | 0.105183i | ||||
\(118\) | −56734.4 | − | 90664.2i | −0.375095 | − | 0.599420i | ||||
\(119\) | − | 6854.91i | − | 0.0443746i | ||||||
\(120\) | −33673.7 | − | 27026.1i | −0.213470 | − | 0.171329i | ||||
\(121\) | −92036.7 | −0.571475 | ||||||||
\(122\) | 203018.i | 1.23491i | ||||||||
\(123\) | 20041.6 | + | 16085.2i | 0.119445 | + | 0.0958657i | ||||
\(124\) | − | 97612.3i | − | 0.570099i | ||||||
\(125\) | − | 189429.i | − | 1.08436i | ||||||
\(126\) | −1080.40 | − | 4873.51i | −0.00606260 | − | 0.0273474i | ||||
\(127\) | 265527. | 1.46083 | 0.730416 | − | 0.683003i | \(-0.239326\pi\) | ||||
0.730416 | + | 0.683003i | \(0.239326\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | −19026.2 | − | 15270.2i | −0.100665 | − | 0.0807924i | ||||
\(130\) | −51264.3 | −0.266046 | ||||||||
\(131\) | 23529.0 | 0.119791 | 0.0598956 | − | 0.998205i | \(-0.480923\pi\) | ||||
0.0598956 | + | 0.998205i | \(0.480923\pi\) | |||||||
\(132\) | −41012.4 | + | 51100.1i | −0.204871 | + | 0.255263i | ||||
\(133\) | 6884.58 | 0.0337480 | ||||||||
\(134\) | − | 5223.06i | − | 0.0251283i | ||||||
\(135\) | 72510.5 | − | 147033.i | 0.342426 | − | 0.694355i | ||||
\(136\) | − | 85425.6i | − | 0.396042i | ||||||
\(137\) | − | 232717.i | − | 1.05932i | −0.848210 | − | 0.529660i | \(-0.822319\pi\) | ||
0.848210 | − | 0.529660i | \(-0.177681\pi\) | |||||||
\(138\) | −72537.3 | + | 90379.0i | −0.324238 | + | 0.403989i | ||||
\(139\) | 315311. | 1.38421 | 0.692105 | − | 0.721797i | \(-0.256683\pi\) | ||||
0.692105 | + | 0.721797i | \(0.256683\pi\) | |||||||
\(140\) | 3556.25i | 0.0153346i | ||||||||
\(141\) | 131930. | − | 164380.i | 0.558850 | − | 0.696308i | ||||
\(142\) | − | 70499.6i | − | 0.293404i | ||||||
\(143\) | 77794.2i | 0.318132i | ||||||||
\(144\) | −13463.9 | − | 60733.5i | −0.0541084 | − | 0.244074i | ||||
\(145\) | 48798.1 | 0.192745 | ||||||||
\(146\) | − | 65568.9i | − | 0.254575i | ||||||
\(147\) | 163732. | − | 204005.i | 0.624944 | − | 0.778659i | ||||
\(148\) | − | 111406.i | − | 0.418077i | ||||||
\(149\) | −388721. | −1.43441 | −0.717204 | − | 0.696863i | \(-0.754579\pi\) | ||||
−0.717204 | + | 0.696863i | \(0.754579\pi\) | |||||||
\(150\) | 48861.1 | − | 60879.3i | 0.177311 | − | 0.220923i | ||||
\(151\) | 1572.47i | 0.00561230i | 0.999996 | + | 0.00280615i | \(0.000893227\pi\) | ||||
−0.999996 | + | 0.00280615i | \(0.999107\pi\) | |||||||
\(152\) | 85795.3 | 0.301200 | ||||||||
\(153\) | 316662. | − | 70200.3i | 1.09362 | − | 0.242444i | ||||
\(154\) | 5396.64 | 0.0183367 | ||||||||
\(155\) | −264036. | −0.882741 | ||||||||
\(156\) | −57601.0 | − | 46229.9i | −0.189504 | − | 0.152094i | ||||
\(157\) | 99590.7i | 0.322455i | 0.986917 | + | 0.161228i | \(0.0515454\pi\) | ||||
−0.986917 | + | 0.161228i | \(0.948455\pi\) | |||||||
\(158\) | −266462. | −0.849166 | ||||||||
\(159\) | −155809. | − | 125050.i | −0.488764 | − | 0.392277i | ||||
\(160\) | 44317.8i | 0.136860i | ||||||||
\(161\) | 9544.85 | 0.0290205 | ||||||||
\(162\) | 214067. | − | 99818.2i | 0.640860 | − | 0.298829i | ||||
\(163\) | 580713. | 1.71196 | 0.855978 | − | 0.517012i | \(-0.172956\pi\) | ||||
0.855978 | + | 0.517012i | \(0.172956\pi\) | |||||||
\(164\) | − | 26376.7i | − | 0.0765791i | ||||||
\(165\) | 138223. | + | 110936.i | 0.395248 | + | 0.317222i | ||||
\(166\) | −210882. | −0.593977 | ||||||||
\(167\) | 101767.i | 0.282367i | 0.989983 | + | 0.141184i | \(0.0450908\pi\) | ||||
−0.989983 | + | 0.141184i | \(0.954909\pi\) | |||||||
\(168\) | −3207.01 | + | 3995.82i | −0.00876651 | + | 0.0109228i | ||||
\(169\) | 283602. | 0.763823 | ||||||||
\(170\) | −231071. | −0.613230 | ||||||||
\(171\) | 70504.2 | + | 318033.i | 0.184385 | + | 0.831729i | ||||
\(172\) | 25040.2i | 0.0645383i | ||||||||
\(173\) | 64078.2 | 0.162778 | 0.0813888 | − | 0.996682i | \(-0.474064\pi\) | ||||
0.0813888 | + | 0.996682i | \(0.474064\pi\) | |||||||
\(174\) | 54829.9 | + | 44005.9i | 0.137292 | + | 0.110189i | ||||
\(175\) | −6429.41 | −0.0158700 | ||||||||
\(176\) | 67252.7 | 0.163655 | ||||||||
\(177\) | −413947. | − | 48725.3i | −0.993143 | − | 0.116902i | ||||
\(178\) | −359004. | −0.849276 | ||||||||
\(179\) | 412538. | 0.962347 | 0.481173 | − | 0.876625i | \(-0.340211\pi\) | ||||
0.481173 | + | 0.876625i | \(0.340211\pi\) | |||||||
\(180\) | −164281. | + | 36419.1i | −0.377924 | + | 0.0837815i | ||||
\(181\) | 37016.7 | 0.0839850 | 0.0419925 | − | 0.999118i | \(-0.486629\pi\) | ||||
0.0419925 | + | 0.999118i | \(0.486629\pi\) | |||||||
\(182\) | 6083.19i | 0.0136130i | ||||||||
\(183\) | 617032. | + | 495224.i | 1.36201 | + | 1.09314i | ||||
\(184\) | 118947. | 0.259006 | ||||||||
\(185\) | −301348. | −0.647350 | ||||||||
\(186\) | −296672. | − | 238106.i | −0.628774 | − | 0.504648i | ||||
\(187\) | 350653.i | 0.733286i | ||||||||
\(188\) | −216340. | −0.446418 | ||||||||
\(189\) | −17447.5 | − | 8604.33i | −0.0355286 | − | 0.0175211i | ||||
\(190\) | − | 232071.i | − | 0.466377i | ||||||
\(191\) | −155943. | −0.309301 | −0.154651 | − | 0.987969i | \(-0.549425\pi\) | ||||
−0.154651 | + | 0.987969i | \(0.549425\pi\) | |||||||
\(192\) | −39965.6 | + | 49795.8i | −0.0782407 | + | 0.0974853i | ||||
\(193\) | −520302. | −1.00545 | −0.502727 | − | 0.864445i | \(-0.667670\pi\) | ||||
−0.502727 | + | 0.864445i | \(0.667670\pi\) | |||||||
\(194\) | 99951.7i | 0.190671i | ||||||||
\(195\) | −125049. | + | 155807.i | −0.235502 | + | 0.293428i | ||||
\(196\) | −268490. | −0.499215 | ||||||||
\(197\) | 264785.i | 0.486103i | 0.970013 | + | 0.243052i | \(0.0781484\pi\) | ||||
−0.970013 | + | 0.243052i | \(0.921852\pi\) | |||||||
\(198\) | 55266.4 | + | 249298.i | 0.100184 | + | 0.451913i | ||||
\(199\) | 79805.9 | 0.142857 | 0.0714286 | − | 0.997446i | \(-0.477244\pi\) | ||||
0.0714286 | + | 0.997446i | \(0.477244\pi\) | |||||||
\(200\) | −80123.0 | −0.141639 | ||||||||
\(201\) | −15874.4 | − | 12740.6i | −0.0277145 | − | 0.0222434i | ||||
\(202\) | −474137. | −0.817571 | ||||||||
\(203\) | − | 5790.54i | − | 0.00986231i | ||||||
\(204\) | −259633. | − | 208379.i | −0.436802 | − | 0.350573i | ||||
\(205\) | −71347.4 | −0.118575 | ||||||||
\(206\) | 85998.6i | 0.141196i | ||||||||
\(207\) | 97747.7 | + | 440924.i | 0.158555 | + | 0.715217i | ||||
\(208\) | 75808.4i | 0.121495i | ||||||||
\(209\) | −352171. | −0.557683 | ||||||||
\(210\) | 10808.5 | + | 8674.76i | 0.0169128 | + | 0.0135741i | ||||
\(211\) | 115465.i | 0.178543i | 0.996007 | + | 0.0892717i | \(0.0284540\pi\) | ||||
−0.996007 | + | 0.0892717i | \(0.971546\pi\) | |||||||
\(212\) | 205059.i | 0.313357i | ||||||||
\(213\) | −214269. | − | 171970.i | −0.323601 | − | 0.259719i | ||||
\(214\) | − | 688267.i | − | 1.02736i | ||||||
\(215\) | 67732.4 | 0.0999310 | ||||||||
\(216\) | −217429. | − | 107227.i | −0.317091 | − | 0.156376i | ||||
\(217\) | 31331.3i | 0.0451678i | ||||||||
\(218\) | 880732.i | 1.25517i | ||||||||
\(219\) | −199283. | − | 159942.i | −0.280776 | − | 0.225348i | ||||
\(220\) | − | 181915.i | − | 0.253402i | ||||||
\(221\) | −395262. | −0.544383 | ||||||||
\(222\) | −338597. | − | 271754.i | −0.461105 | − | 0.370078i | ||||
\(223\) | 949938. | 1.27918 | 0.639592 | − | 0.768715i | \(-0.279103\pi\) | ||||
0.639592 | + | 0.768715i | \(0.279103\pi\) | |||||||
\(224\) | 5258.89 | 0.00700283 | ||||||||
\(225\) | −65842.8 | − | 297006.i | −0.0867066 | − | 0.391119i | ||||
\(226\) | −686097. | −0.893541 | ||||||||
\(227\) | −372043. | −0.479213 | −0.239607 | − | 0.970870i | \(-0.577018\pi\) | ||||
−0.239607 | + | 0.970870i | \(0.577018\pi\) | |||||||
\(228\) | 209281. | − | 260757.i | 0.266620 | − | 0.332199i | ||||
\(229\) | − | 354826.i | − | 0.447122i | −0.974690 | − | 0.223561i | \(-0.928232\pi\) | ||
0.974690 | − | 0.223561i | \(-0.0717683\pi\) | |||||||
\(230\) | − | 321746.i | − | 0.401045i | ||||||
\(231\) | 13164.0 | − | 16402.0i | 0.0162315 | − | 0.0202239i | ||||
\(232\) | − | 72161.4i | − | 0.0880208i | ||||||
\(233\) | 1.25262e6 | 1.51158 | 0.755790 | − | 0.654814i | \(-0.227253\pi\) | ||||
0.755790 | + | 0.654814i | \(0.227253\pi\) | |||||||
\(234\) | −281013. | + | 62297.2i | −0.335495 | + | 0.0743753i | ||||
\(235\) | 585187.i | 0.691234i | ||||||||
\(236\) | 226937. | + | 362657.i | 0.265232 | + | 0.423854i | ||||
\(237\) | −649982. | + | 809855.i | −0.751675 | + | 0.936562i | ||||
\(238\) | 27419.6i | 0.0313776i | ||||||||
\(239\) | − | 168819.i | − | 0.191174i | −0.995421 | − | 0.0955868i | \(-0.969527\pi\) | ||
0.995421 | − | 0.0955868i | \(-0.0304727\pi\) | |||||||
\(240\) | 134695. | + | 108105.i | 0.150946 | + | 0.121148i | ||||
\(241\) | 340564. | 0.377708 | 0.188854 | − | 0.982005i | \(-0.439523\pi\) | ||||
0.188854 | + | 0.982005i | \(0.439523\pi\) | |||||||
\(242\) | 368147. | 0.404094 | ||||||||
\(243\) | 218799. | − | 894100.i | 0.237700 | − | 0.971338i | ||||
\(244\) | − | 812074.i | − | 0.873215i | ||||||
\(245\) | 726250.i | 0.772985i | ||||||||
\(246\) | −80166.4 | − | 64340.7i | −0.0844607 | − | 0.0677873i | ||||
\(247\) | − | 396973.i | − | 0.414017i | ||||||
\(248\) | 390449.i | 0.403121i | ||||||||
\(249\) | −514406. | + | 640933.i | −0.525785 | + | 0.655110i | ||||
\(250\) | 757716.i | 0.766755i | ||||||||
\(251\) | − | 44476.4i | − | 0.0445600i | −0.999752 | − | 0.0222800i | \(-0.992907\pi\) | ||
0.999752 | − | 0.0222800i | \(-0.00709253\pi\) | |||||||
\(252\) | 4321.60 | + | 19494.1i | 0.00428690 | + | 0.0193375i | ||||
\(253\) | −488253. | −0.479561 | ||||||||
\(254\) | −1.06211e6 | −1.03296 | ||||||||
\(255\) | −563653. | + | 702293.i | −0.542827 | + | 0.676344i | ||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | − | 485768.i | − | 0.458771i | −0.973336 | − | 0.229386i | \(-0.926328\pi\) | ||
0.973336 | − | 0.229386i | \(-0.0736717\pi\) | |||||||
\(258\) | 76104.6 | + | 61080.8i | 0.0711806 | + | 0.0571288i | ||||
\(259\) | 35758.9i | 0.0331234i | ||||||||
\(260\) | 205057. | 0.188123 | ||||||||
\(261\) | 267494. | − | 59300.2i | 0.243059 | − | 0.0538834i | ||||
\(262\) | −94115.9 | −0.0847051 | ||||||||
\(263\) | − | 1.65840e6i | − | 1.47843i | −0.673471 | − | 0.739214i | \(-0.735197\pi\) | ||
0.673471 | − | 0.739214i | \(-0.264803\pi\) | |||||||
\(264\) | 164050. | − | 204401.i | 0.144866 | − | 0.180498i | ||||
\(265\) | 554673. | 0.485202 | ||||||||
\(266\) | −27538.3 | −0.0238635 | ||||||||
\(267\) | −875720. | + | 1.09112e6i | −0.751773 | + | 0.936684i | ||||
\(268\) | 20892.3i | 0.0177684i | ||||||||
\(269\) | 548436. | 0.462110 | 0.231055 | − | 0.972941i | \(-0.425782\pi\) | ||||
0.231055 | + | 0.972941i | \(0.425782\pi\) | |||||||
\(270\) | −290042. | + | 588134.i | −0.242132 | + | 0.490983i | ||||
\(271\) | −653560. | −0.540583 | −0.270292 | − | 0.962779i | \(-0.587120\pi\) | ||||
−0.270292 | + | 0.962779i | \(0.587120\pi\) | |||||||
\(272\) | 341702.i | 0.280044i | ||||||||
\(273\) | 18488.6 | + | 14838.7i | 0.0150140 | + | 0.0120501i | ||||
\(274\) | 930869.i | 0.749053i | ||||||||
\(275\) | 328887. | 0.262250 | ||||||||
\(276\) | 290149. | − | 361516.i | 0.229271 | − | 0.285664i | ||||
\(277\) | −1.01496e6 | −0.794784 | −0.397392 | − | 0.917649i | \(-0.630085\pi\) | ||||
−0.397392 | + | 0.917649i | \(0.630085\pi\) | |||||||
\(278\) | −1.26124e6 | −0.978785 | ||||||||
\(279\) | −1.44735e6 | + | 320860.i | −1.11317 | + | 0.246777i | ||||
\(280\) | − | 14225.0i | − | 0.0108432i | ||||||
\(281\) | − | 1.98324e6i | − | 1.49834i | −0.662378 | − | 0.749170i | \(-0.730453\pi\) | ||
0.662378 | − | 0.749170i | \(-0.269547\pi\) | |||||||
\(282\) | −527719. | + | 657520.i | −0.395166 | + | 0.492364i | ||||
\(283\) | − | 2.06818e6i | − | 1.53505i | −0.641021 | − | 0.767523i | \(-0.721489\pi\) | ||
0.641021 | − | 0.767523i | \(-0.278511\pi\) | |||||||
\(284\) | 281998.i | 0.207468i | ||||||||
\(285\) | −705332. | − | 566093.i | −0.514377 | − | 0.412834i | ||||
\(286\) | − | 311177.i | − | 0.224953i | ||||||
\(287\) | 8466.30i | 0.00606721i | ||||||||
\(288\) | 53855.6 | + | 242934.i | 0.0382604 | + | 0.172587i | ||||
\(289\) | −361767. | −0.254791 | ||||||||
\(290\) | −195192. | −0.136291 | ||||||||
\(291\) | 303782. | + | 243813.i | 0.210295 | + | 0.168781i | ||||
\(292\) | 262275.i | 0.180012i | ||||||||
\(293\) | − | 438652.i | − | 0.298505i | −0.988799 | − | 0.149252i | \(-0.952313\pi\) | ||
0.988799 | − | 0.149252i | \(-0.0476866\pi\) | |||||||
\(294\) | −654929. | + | 816019.i | −0.441902 | + | 0.550595i | ||||
\(295\) | 980966. | − | 613853.i | 0.656295 | − | 0.410685i | ||||
\(296\) | 445626.i | 0.295625i | ||||||||
\(297\) | 892499. | + | 440142.i | 0.587106 | + | 0.289535i | ||||
\(298\) | 1.55489e6 | 1.01428 | ||||||||
\(299\) | − | 550367.i | − | 0.356020i | ||||||
\(300\) | −195444. | + | 243517.i | −0.125378 | + | 0.156216i | ||||
\(301\) | − | 8037.34i | − | 0.00511324i | ||||||
\(302\) | − | 6289.90i | − | 0.00396850i | ||||||
\(303\) | −1.15657e6 | + | 1.44104e6i | −0.723708 | + | 0.901716i | ||||
\(304\) | −343181. | −0.212980 | ||||||||
\(305\) | −2.19661e6 | −1.35208 | ||||||||
\(306\) | −1.26665e6 | + | 280801.i | −0.773309 | + | 0.171434i | ||||
\(307\) | 815525. | 0.493846 | 0.246923 | − | 0.969035i | \(-0.420581\pi\) | ||||
0.246923 | + | 0.969035i | \(0.420581\pi\) | |||||||
\(308\) | −21586.6 | −0.0129660 | ||||||||
\(309\) | 261375. | + | 209777.i | 0.155728 | + | 0.124986i | ||||
\(310\) | 1.05614e6 | 0.624192 | ||||||||
\(311\) | 1.29979e6i | 0.762028i | 0.924569 | + | 0.381014i | \(0.124425\pi\) | ||||
−0.924569 | + | 0.381014i | \(0.875575\pi\) | |||||||
\(312\) | 230404. | + | 184920.i | 0.134000 | + | 0.107547i | ||||
\(313\) | 1.44214e6i | 0.832045i | 0.909354 | + | 0.416023i | \(0.136576\pi\) | ||||
−0.909354 | + | 0.416023i | \(0.863424\pi\) | |||||||
\(314\) | − | 398363.i | − | 0.228010i | ||||||
\(315\) | 52730.3 | − | 11689.7i | 0.0299422 | − | 0.00663784i | ||||
\(316\) | 1.06585e6 | 0.600451 | ||||||||
\(317\) | − | 167603.i | − | 0.0936769i | −0.998902 | − | 0.0468384i | \(-0.985085\pi\) | ||
0.998902 | − | 0.0468384i | \(-0.0149146\pi\) | |||||||
\(318\) | 623235. | + | 500202.i | 0.345608 | + | 0.277381i | ||||
\(319\) | 296207.i | 0.162974i | ||||||||
\(320\) | − | 177271.i | − | 0.0967749i | ||||||
\(321\) | −2.09184e6 | − | 1.67889e6i | −1.13310 | − | 0.909412i | ||||
\(322\) | −38179.4 | −0.0205206 | ||||||||
\(323\) | − | 1.78933e6i | − | 0.954301i | ||||||
\(324\) | −856270. | + | 399273.i | −0.453156 | + | 0.211304i | ||||
\(325\) | 370727.i | 0.194691i | ||||||||
\(326\) | −2.32285e6 | −1.21054 | ||||||||
\(327\) | 2.67680e6 | + | 2.14837e6i | 1.38435 | + | 1.11107i | ||||
\(328\) | 105507.i | 0.0541496i | ||||||||
\(329\) | 69440.1 | 0.0353688 | ||||||||
\(330\) | −552892. | − | 443745.i | −0.279483 | − | 0.224310i | ||||
\(331\) | 73742.6 | 0.0369955 | 0.0184977 | − | 0.999829i | \(-0.494112\pi\) | ||||
0.0184977 | + | 0.999829i | \(0.494112\pi\) | |||||||
\(332\) | 843529. | 0.420005 | ||||||||
\(333\) | −1.65188e6 | + | 366203.i | −0.816334 | + | 0.180972i | ||||
\(334\) | − | 407067.i | − | 0.199664i | ||||||
\(335\) | 56512.3 | 0.0275126 | ||||||||
\(336\) | 12828.0 | − | 15983.3i | 0.00619886 | − | 0.00772357i | ||||
\(337\) | − | 3.49548e6i | − | 1.67661i | −0.545202 | − | 0.838305i | \(-0.683547\pi\) | ||
0.545202 | − | 0.838305i | \(-0.316453\pi\) | |||||||
\(338\) | −1.13441e6 | −0.540104 | ||||||||
\(339\) | −1.67360e6 | + | 2.08525e6i | −0.790956 | + | 0.985504i | ||||
\(340\) | 924285. | 0.433619 | ||||||||
\(341\) | − | 1.60271e6i | − | 0.746394i | ||||||
\(342\) | −282017. | − | 1.27213e6i | −0.130380 | − | 0.588121i | ||||
\(343\) | 172494. | 0.0791658 | ||||||||
\(344\) | − | 100161.i | − | 0.0456355i | ||||||
\(345\) | −977880. | − | 784836.i | −0.442321 | − | 0.355002i | ||||
\(346\) | −256313. | −0.115101 | ||||||||
\(347\) | 81574.5 | 0.0363689 | 0.0181845 | − | 0.999835i | \(-0.494211\pi\) | ||||
0.0181845 | + | 0.999835i | \(0.494211\pi\) | |||||||
\(348\) | −219320. | − | 176024.i | −0.0970799 | − | 0.0779153i | ||||
\(349\) | − | 3.25809e6i | − | 1.43186i | −0.698173 | − | 0.715929i | \(-0.746003\pi\) | ||
0.698173 | − | 0.715929i | \(-0.253997\pi\) | |||||||
\(350\) | 25717.6 | 0.0112218 | ||||||||
\(351\) | −496136. | + | 1.00604e6i | −0.214948 | + | 0.435861i | ||||
\(352\) | −269011. | −0.115721 | ||||||||
\(353\) | 1.76544e6 | 0.754077 | 0.377039 | − | 0.926198i | \(-0.376942\pi\) | ||||
0.377039 | + | 0.926198i | \(0.376942\pi\) | |||||||
\(354\) | 1.65579e6 | + | 194901.i | 0.702258 | + | 0.0826621i | ||||
\(355\) | 762789. | 0.321243 | ||||||||
\(356\) | 1.43602e6 | 0.600529 | ||||||||
\(357\) | 83336.3 | + | 66884.9i | 0.0346070 | + | 0.0277752i | ||||
\(358\) | −1.65015e6 | −0.680482 | ||||||||
\(359\) | − | 2.73460e6i | − | 1.11985i | −0.828545 | − | 0.559923i | \(-0.810831\pi\) | ||
0.828545 | − | 0.559923i | \(-0.189169\pi\) | |||||||
\(360\) | 657122. | − | 145676.i | 0.267233 | − | 0.0592424i | ||||
\(361\) | −679020. | −0.274230 | ||||||||
\(362\) | −148067. | −0.0593864 | ||||||||
\(363\) | 898022. | − | 1.11891e6i | 0.357701 | − | 0.445684i | ||||
\(364\) | − | 24332.7i | − | 0.00962582i | ||||||
\(365\) | 709440. | 0.278730 | ||||||||
\(366\) | −2.46813e6 | − | 1.98090e6i | −0.963086 | − | 0.772963i | ||||
\(367\) | 1.54107e6i | 0.597252i | 0.954370 | + | 0.298626i | \(0.0965284\pi\) | ||||
−0.954370 | + | 0.298626i | \(0.903472\pi\) | |||||||
\(368\) | −475790. | −0.183145 | ||||||||
\(369\) | −391100. | + | 86702.4i | −0.149528 | + | 0.0331486i | ||||
\(370\) | 1.20539e6 | 0.457745 | ||||||||
\(371\) | − | 65819.3i | − | 0.0248267i | ||||||
\(372\) | 1.18669e6 | + | 952425.i | 0.444610 | + | 0.356840i | ||||
\(373\) | 1.35221e6 | 0.503236 | 0.251618 | − | 0.967827i | \(-0.419037\pi\) | ||||
0.251618 | + | 0.967827i | \(0.419037\pi\) | |||||||
\(374\) | − | 1.40261e6i | − | 0.518512i | ||||||
\(375\) | 2.30292e6 | + | 1.84830e6i | 0.845670 | + | 0.678726i | ||||
\(376\) | 865360. | 0.315665 | ||||||||
\(377\) | −333889. | −0.120990 | ||||||||
\(378\) | 69789.8 | + | 34417.3i | 0.0251225 | + | 0.0123893i | ||||
\(379\) | 856323. | 0.306224 | 0.153112 | − | 0.988209i | \(-0.451070\pi\) | ||||
0.153112 | + | 0.988209i | \(0.451070\pi\) | |||||||
\(380\) | 928285.i | 0.329779i | ||||||||
\(381\) | −2.59081e6 | + | 3.22806e6i | −0.914372 | + | 1.13928i | ||||
\(382\) | 623771. | 0.218709 | ||||||||
\(383\) | 3.33532e6i | 1.16183i | 0.813966 | + | 0.580913i | \(0.197304\pi\) | ||||
−0.813966 | + | 0.580913i | \(0.802696\pi\) | |||||||
\(384\) | 159862. | − | 199183.i | 0.0553245 | − | 0.0689325i | ||||
\(385\) | 58390.4i | 0.0200766i | ||||||||
\(386\) | 2.08121e6 | 0.710963 | ||||||||
\(387\) | 371285. | − | 82309.5i | 0.126017 | − | 0.0279365i | ||||
\(388\) | − | 399807.i | − | 0.134825i | ||||||
\(389\) | 2.94144e6i | 0.985565i | 0.870152 | + | 0.492783i | \(0.164020\pi\) | ||||
−0.870152 | + | 0.492783i | \(0.835980\pi\) | |||||||
\(390\) | 500197. | − | 623229.i | 0.166525 | − | 0.207485i | ||||
\(391\) | − | 2.48075e6i | − | 0.820619i | ||||||
\(392\) | 1.07396e6 | 0.352999 | ||||||||
\(393\) | −229577. | + | 286046.i | −0.0749804 | + | 0.0934230i | ||||
\(394\) | − | 1.05914e6i | − | 0.343727i | ||||||
\(395\) | − | 2.88306e6i | − | 0.929737i | ||||||
\(396\) | −221065. | − | 997190.i | −0.0708407 | − | 0.319551i | ||||
\(397\) | 1.44954e6i | 0.461589i | 0.973003 | + | 0.230794i | \(0.0741324\pi\) | ||||
−0.973003 | + | 0.230794i | \(0.925868\pi\) | |||||||
\(398\) | −319224. | −0.101015 | ||||||||
\(399\) | −67174.3 | + | 83697.0i | −0.0211238 | + | 0.0263195i | ||||
\(400\) | 320492. | 0.100154 | ||||||||
\(401\) | −9021.61 | −0.00280171 | −0.00140085 | − | 0.999999i | \(-0.500446\pi\) | ||||
−0.00140085 | + | 0.999999i | \(0.500446\pi\) | |||||||
\(402\) | 63497.6 | + | 50962.6i | 0.0195971 | + | 0.0157285i | ||||
\(403\) | 1.80660e6 | 0.554114 | ||||||||
\(404\) | 1.89655e6 | 0.578110 | ||||||||
\(405\) | 1.08001e6 | + | 2.31616e6i | 0.327182 | + | 0.701667i | ||||
\(406\) | 23162.2i | 0.00697371i | ||||||||
\(407\) | − | 1.82919e6i | − | 0.547361i | ||||||
\(408\) | 1.03853e6 | + | 833516.i | 0.308866 | + | 0.247893i | ||||
\(409\) | 1.87499e6i | 0.554232i | 0.960836 | + | 0.277116i | \(0.0893786\pi\) | ||||
−0.960836 | + | 0.277116i | \(0.910621\pi\) | |||||||
\(410\) | 285389. | 0.0838452 | ||||||||
\(411\) | 2.82918e6 | + | 2.27067e6i | 0.826146 | + | 0.663056i | ||||
\(412\) | − | 343994.i | − | 0.0998409i | ||||||
\(413\) | −72841.7 | − | 116404.i | −0.0210138 | − | 0.0335811i | ||||
\(414\) | −390991. | − | 1.76370e6i | −0.112115 | − | 0.505735i | ||||
\(415\) | − | 2.28170e6i | − | 0.650336i | ||||||
\(416\) | − | 303234.i | − | 0.0859100i | ||||||
\(417\) | −3.07656e6 | + | 3.83329e6i | −0.866413 | + | 1.07952i | ||||
\(418\) | 1.40868e6 | 0.394342 | ||||||||
\(419\) | 6.23979e6 | 1.73634 | 0.868171 | − | 0.496265i | \(-0.165296\pi\) | ||||
0.868171 | + | 0.496265i | \(0.165296\pi\) | |||||||
\(420\) | −43233.9 | − | 34699.1i | −0.0119592 | − | 0.00959830i | ||||
\(421\) | − | 3.47111e6i | − | 0.954472i | −0.878775 | − | 0.477236i | \(-0.841639\pi\) | ||
0.878775 | − | 0.477236i | \(-0.158361\pi\) | |||||||
\(422\) | − | 461860.i | − | 0.126249i | ||||||
\(423\) | 711128. | + | 3.20778e6i | 0.193240 | + | 0.871674i | ||||
\(424\) | − | 820237.i | − | 0.221577i | ||||||
\(425\) | 1.67103e6i | 0.448759i | ||||||||
\(426\) | 857075. | + | 687880.i | 0.228821 | + | 0.183649i | ||||
\(427\) | 260657.i | 0.0691830i | ||||||||
\(428\) | 2.75307e6i | 0.726453i | ||||||||
\(429\) | −945757. | − | 759055.i | −0.248105 | − | 0.199127i | ||||
\(430\) | −270930. | −0.0706619 | ||||||||
\(431\) | −1.55792e6 | −0.403973 | −0.201986 | − | 0.979388i | \(-0.564740\pi\) | ||||
−0.201986 | + | 0.979388i | \(0.564740\pi\) | |||||||
\(432\) | 869718. | + | 428907.i | 0.224217 | + | 0.110574i | ||||
\(433\) | 4.97595e6 | 1.27543 | 0.637714 | − | 0.770273i | \(-0.279880\pi\) | ||||
0.637714 | + | 0.770273i | \(0.279880\pi\) | |||||||
\(434\) | − | 125325.i | − | 0.0319385i | ||||||
\(435\) | −476134. | + | 593247.i | −0.120644 | + | 0.150318i | ||||
\(436\) | − | 3.52293e6i | − | 0.887539i | ||||||
\(437\) | 2.49149e6 | 0.624102 | ||||||||
\(438\) | 797132. | + | 639770.i | 0.198539 | + | 0.159345i | ||||
\(439\) | 2.37372e6 | 0.587852 | 0.293926 | − | 0.955828i | \(-0.405038\pi\) | ||||
0.293926 | + | 0.955828i | \(0.405038\pi\) | |||||||
\(440\) | 727658.i | 0.179183i | ||||||||
\(441\) | 882550. | + | 3.98104e6i | 0.216094 | + | 0.974765i | ||||
\(442\) | 1.58105e6 | 0.384937 | ||||||||
\(443\) | −512210. | −0.124005 | −0.0620024 | − | 0.998076i | \(-0.519749\pi\) | ||||
−0.0620024 | + | 0.998076i | \(0.519749\pi\) | |||||||
\(444\) | 1.35439e6 | + | 1.08702e6i | 0.326051 | + | 0.261685i | ||||
\(445\) | − | 3.88434e6i | − | 0.929859i | ||||||
\(446\) | −3.79975e6 | −0.904520 | ||||||||
\(447\) | 3.79284e6 | − | 4.72575e6i | 0.897833 | − | 1.11867i | ||||
\(448\) | −21035.5 | −0.00495175 | ||||||||
\(449\) | 2.22031e6i | 0.519753i | 0.965642 | + | 0.259876i | \(0.0836819\pi\) | ||||
−0.965642 | + | 0.259876i | \(0.916318\pi\) | |||||||
\(450\) | 263371. | + | 1.18803e6i | 0.0613108 | + | 0.276563i | ||||
\(451\) | − | 433082.i | − | 0.100260i | ||||||
\(452\) | 2.74439e6 | 0.631829 | ||||||||
\(453\) | −19116.8 | − | 15343.0i | −0.00437694 | − | 0.00351289i | ||||
\(454\) | 1.48817e6 | 0.338855 | ||||||||
\(455\) | −65818.7 | −0.0149046 | ||||||||
\(456\) | −837124. | + | 1.04303e6i | −0.188529 | + | 0.234900i | ||||
\(457\) | − | 784209.i | − | 0.175647i | −0.996136 | − | 0.0878237i | \(-0.972009\pi\) | ||
0.996136 | − | 0.0878237i | \(-0.0279912\pi\) | |||||||
\(458\) | 1.41930e6i | 0.316163i | ||||||||
\(459\) | −2.23631e6 | + | 4.53468e6i | −0.495450 | + | 1.00465i | ||||
\(460\) | 1.28698e6i | 0.283582i | ||||||||
\(461\) | − | 4.67620e6i | − | 1.02480i | −0.858746 | − | 0.512402i | \(-0.828756\pi\) | ||
0.858746 | − | 0.512402i | \(-0.171244\pi\) | |||||||
\(462\) | −52656.2 | + | 65607.8i | −0.0114774 | + | 0.0143005i | ||||
\(463\) | − | 2.00844e6i | − | 0.435417i | −0.976014 | − | 0.217709i | \(-0.930142\pi\) | ||
0.976014 | − | 0.217709i | \(-0.0698583\pi\) | |||||||
\(464\) | 288646.i | 0.0622401i | ||||||||
\(465\) | 2.57625e6 | − | 3.20993e6i | 0.552530 | − | 0.688434i | ||||
\(466\) | −5.01050e6 | −1.06885 | ||||||||
\(467\) | 8.02525e6 | 1.70281 | 0.851406 | − | 0.524508i | \(-0.175751\pi\) | ||||
0.851406 | + | 0.524508i | \(0.175751\pi\) | |||||||
\(468\) | 1.12405e6 | − | 249189.i | 0.237231 | − | 0.0525913i | ||||
\(469\) | − | 6705.93i | − | 0.00140775i | ||||||
\(470\) | − | 2.34075e6i | − | 0.488776i | ||||||
\(471\) | −1.21074e6 | − | 971728.i | −0.251477 | − | 0.201833i | ||||
\(472\) | −907750. | − | 1.45063e6i | −0.187547 | − | 0.299710i | ||||
\(473\) | 411139.i | 0.0844959i | ||||||||
\(474\) | 2.59993e6 | − | 3.23942e6i | 0.531515 | − | 0.662250i | ||||
\(475\) | −1.67827e6 | −0.341293 | ||||||||
\(476\) | − | 109679.i | − | 0.0221873i | ||||||
\(477\) | 3.04052e6 | − | 674048.i | 0.611859 | − | 0.135642i | ||||
\(478\) | 675278.i | 0.135180i | ||||||||
\(479\) | 2.59531e6i | 0.516834i | 0.966033 | + | 0.258417i | \(0.0832008\pi\) | ||||
−0.966033 | + | 0.258417i | \(0.916799\pi\) | |||||||
\(480\) | −538778. | − | 432418.i | −0.106735 | − | 0.0856645i | ||||
\(481\) | 2.06190e6 | 0.406354 | ||||||||
\(482\) | −1.36226e6 | −0.267080 | ||||||||
\(483\) | −93131.2 | + | 116038.i | −0.0181647 | + | 0.0226326i | ||||
\(484\) | −1.47259e6 | −0.285738 | ||||||||
\(485\) | −1.08145e6 | −0.208763 | ||||||||
\(486\) | −875197. | + | 3.57640e6i | −0.168080 | + | 0.686840i | ||||
\(487\) | 751189. | 0.143525 | 0.0717624 | − | 0.997422i | \(-0.477138\pi\) | ||||
0.0717624 | + | 0.997422i | \(0.477138\pi\) | |||||||
\(488\) | 3.24830e6i | 0.617456i | ||||||||
\(489\) | −5.66615e6 | + | 7.05983e6i | −1.07156 | + | 1.33512i | ||||
\(490\) | − | 2.90500e6i | − | 0.546583i | ||||||
\(491\) | − | 1.04218e6i | − | 0.195093i | −0.995231 | − | 0.0975463i | \(-0.968901\pi\) | ||
0.995231 | − | 0.0975463i | \(-0.0310994\pi\) | |||||||
\(492\) | 320666. | + | 257363.i | 0.0597227 | + | 0.0479328i | ||||
\(493\) | −1.50499e6 | −0.278879 | ||||||||
\(494\) | 1.58789e6i | 0.292754i | ||||||||
\(495\) | −2.69734e6 | + | 597969.i | −0.494792 | + | 0.109690i | ||||
\(496\) | − | 1.56180e6i | − | 0.285050i | ||||||
\(497\) | − | 90515.0i | − | 0.0164373i | ||||||
\(498\) | 2.05762e6 | − | 2.56373e6i | 0.371786 | − | 0.463233i | ||||
\(499\) | −4.89287e6 | −0.879655 | −0.439827 | − | 0.898082i | \(-0.644960\pi\) | ||||
−0.439827 | + | 0.898082i | \(0.644960\pi\) | |||||||
\(500\) | − | 3.03087e6i | − | 0.542178i | ||||||
\(501\) | −1.23719e6 | − | 992959.i | −0.220213 | − | 0.176741i | ||||
\(502\) | 177905.i | 0.0315087i | ||||||||
\(503\) | −4.85721e6 | −0.855987 | −0.427994 | − | 0.903782i | \(-0.640779\pi\) | ||||
−0.427994 | + | 0.903782i | \(0.640779\pi\) | |||||||
\(504\) | −17286.4 | − | 77976.2i | −0.00303130 | − | 0.0136737i | ||||
\(505\) | − | 5.13005e6i | − | 0.895145i | ||||||
\(506\) | 1.95301e6 | 0.339101 | ||||||||
\(507\) | −2.76717e6 | + | 3.44780e6i | −0.478096 | + | 0.595692i | ||||
\(508\) | 4.24844e6 | 0.730416 | ||||||||
\(509\) | 6.13492e6 | 1.04958 | 0.524788 | − | 0.851233i | \(-0.324144\pi\) | ||||
0.524788 | + | 0.851233i | \(0.324144\pi\) | |||||||
\(510\) | 2.25461e6 | − | 2.80917e6i | 0.383837 | − | 0.478248i | ||||
\(511\) | − | 84184.4i | − | 0.0142620i | ||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | −4.55430e6 | − | 2.24598e6i | −0.764062 | − | 0.376802i | ||||
\(514\) | 1.94307e6i | 0.324400i | ||||||||
\(515\) | −930485. | −0.154594 | ||||||||
\(516\) | −304418. | − | 244323.i | −0.0503323 | − | 0.0403962i | ||||
\(517\) | −3.55211e6 | −0.584467 | ||||||||
\(518\) | − | 143036.i | − | 0.0234218i | ||||||
\(519\) | −625225. | + | 779009.i | −0.101887 | + | 0.126947i | ||||
\(520\) | −820229. | −0.133023 | ||||||||
\(521\) | 8.88459e6i | 1.43398i | 0.697083 | + | 0.716990i | \(0.254481\pi\) | ||||
−0.697083 | + | 0.716990i | \(0.745519\pi\) | |||||||
\(522\) | −1.06997e6 | + | 237201.i | −0.171869 | + | 0.0381013i | ||||
\(523\) | −9.38714e6 | −1.50065 | −0.750325 | − | 0.661069i | \(-0.770103\pi\) | ||||
−0.750325 | + | 0.661069i | \(0.770103\pi\) | |||||||
\(524\) | 376463. | 0.0598956 | ||||||||
\(525\) | 62733.1 | − | 78163.4i | 0.00993342 | − | 0.0123767i | ||||
\(526\) | 6.63360e6i | 1.04541i | ||||||||
\(527\) | 8.14315e6 | 1.27722 | ||||||||
\(528\) | −656199. | + | 817602.i | −0.102436 | + | 0.127631i | ||||
\(529\) | −2.98212e6 | −0.463325 | ||||||||
\(530\) | −2.21869e6 | −0.343090 | ||||||||
\(531\) | 4.63134e6 | − | 4.55700e6i | 0.712804 | − | 0.701363i | ||||
\(532\) | 110153. | 0.0168740 | ||||||||
\(533\) | 488177. | 0.0744319 | ||||||||
\(534\) | 3.50288e6 | − | 4.36447e6i | 0.531584 | − | 0.662336i | ||||
\(535\) | 7.44689e6 | 1.12484 | ||||||||
\(536\) | − | 83569.0i | − | 0.0125642i | ||||||
\(537\) | −4.02523e6 | + | 5.01530e6i | −0.602358 | + | 0.750517i | ||||
\(538\) | −2.19374e6 | −0.326761 | ||||||||
\(539\) | −4.40837e6 | −0.653591 | ||||||||
\(540\) | 1.16017e6 | − | 2.35254e6i | 0.171213 | − | 0.347178i | ||||
\(541\) | 3.12504e6i | 0.459052i | 0.973303 | + | 0.229526i | \(0.0737176\pi\) | ||||
−0.973303 | + | 0.229526i | \(0.926282\pi\) | |||||||
\(542\) | 2.61424e6 | 0.382250 | ||||||||
\(543\) | −361180. | + | 450019.i | −0.0525684 | + | 0.0654984i | ||||
\(544\) | − | 1.36681e6i | − | 0.198021i | ||||||
\(545\) | −9.52931e6 | −1.37426 | ||||||||
\(546\) | −73954.3 | − | 59355.0i | −0.0106165 | − | 0.00852070i | ||||
\(547\) | −1.07410e6 | −0.153489 | −0.0767444 | − | 0.997051i | \(-0.524453\pi\) | ||||
−0.0767444 | + | 0.997051i | \(0.524453\pi\) | |||||||
\(548\) | − | 3.72348e6i | − | 0.529660i | ||||||
\(549\) | −1.20410e7 | + | 2.66936e6i | −1.70503 | + | 0.377986i | ||||
\(550\) | −1.31555e6 | −0.185439 | ||||||||
\(551\) | − | 1.51150e6i | − | 0.212095i | ||||||
\(552\) | −1.16060e6 | + | 1.44606e6i | −0.162119 | + | 0.201995i | ||||
\(553\) | −342112. | −0.0475725 | ||||||||
\(554\) | 4.05983e6 | 0.561997 | ||||||||
\(555\) | 2.94032e6 | − | 3.66354e6i | 0.405193 | − | 0.504857i | ||||
\(556\) | 5.04498e6 | 0.692105 | ||||||||
\(557\) | − | 5.89668e6i | − | 0.805321i | −0.915349 | − | 0.402661i | \(-0.868085\pi\) | ||
0.915349 | − | 0.402661i | \(-0.131915\pi\) | |||||||
\(558\) | 5.78939e6 | − | 1.28344e6i | 0.787132 | − | 0.174498i | ||||
\(559\) | −463443. | −0.0627287 | ||||||||
\(560\) | 56899.9i | 0.00766728i | ||||||||
\(561\) | −4.26295e6 | − | 3.42140e6i | −0.571877 | − | 0.458983i | ||||
\(562\) | 7.93298e6i | 1.05949i | ||||||||
\(563\) | 8.58589e6 | 1.14160 | 0.570800 | − | 0.821089i | \(-0.306633\pi\) | ||||
0.570800 | + | 0.821089i | \(0.306633\pi\) | |||||||
\(564\) | 2.11088e6 | − | 2.63008e6i | 0.279425 | − | 0.348154i | ||||
\(565\) | − | 7.42341e6i | − | 0.978323i | ||||||
\(566\) | 8.27271e6i | 1.08544i | ||||||||
\(567\) | 274843. | − | 128157.i | 0.0359027 | − | 0.0167412i | ||||
\(568\) | − | 1.12799e6i | − | 0.146702i | ||||||
\(569\) | −1.86963e6 | −0.242089 | −0.121045 | − | 0.992647i | \(-0.538624\pi\) | ||||
−0.121045 | + | 0.992647i | \(0.538624\pi\) | |||||||
\(570\) | 2.82133e6 | + | 2.26437e6i | 0.363720 | + | 0.291918i | ||||
\(571\) | − | 1.46089e6i | − | 0.187511i | −0.995595 | − | 0.0937555i | \(-0.970113\pi\) | ||
0.995595 | − | 0.0937555i | \(-0.0298872\pi\) | |||||||
\(572\) | 1.24471e6i | 0.159066i | ||||||||
\(573\) | 1.52157e6 | − | 1.89582e6i | 0.193600 | − | 0.241219i | ||||
\(574\) | − | 33865.2i | − | 0.00429017i | ||||||
\(575\) | −2.32677e6 | −0.293483 | ||||||||
\(576\) | −215423. | − | 971736.i | −0.0270542 | − | 0.122037i | ||||
\(577\) | 4.34585e6 | 0.543419 | 0.271709 | − | 0.962379i | \(-0.412411\pi\) | ||||
0.271709 | + | 0.962379i | \(0.412411\pi\) | |||||||
\(578\) | 1.44707e6 | 0.180165 | ||||||||
\(579\) | 5.07670e6 | − | 6.32539e6i | 0.629339 | − | 0.784135i | ||||
\(580\) | 780770. | 0.0963725 | ||||||||
\(581\) | −270753. | −0.0332762 | ||||||||
\(582\) | −1.21513e6 | − | 975250.i | −0.148701 | − | 0.119346i | ||||
\(583\) | 3.36689e6i | 0.410258i | ||||||||
\(584\) | − | 1.04910e6i | − | 0.127287i | ||||||
\(585\) | −674041. | − | 3.04049e6i | −0.0814323 | − | 0.367328i | ||||
\(586\) | 1.75461e6i | 0.211075i | ||||||||
\(587\) | −1.24558e7 | −1.49203 | −0.746013 | − | 0.665931i | \(-0.768034\pi\) | ||||
−0.746013 | + | 0.665931i | \(0.768034\pi\) | |||||||
\(588\) | 2.61972e6 | − | 3.26408e6i | 0.312472 | − | 0.389329i | ||||
\(589\) | 8.17840e6i | 0.971359i | ||||||||
\(590\) | −3.92386e6 | + | 2.45541e6i | −0.464070 | + | 0.290398i | ||||
\(591\) | −3.21904e6 | − | 2.58357e6i | −0.379103 | − | 0.304264i | ||||
\(592\) | − | 1.78250e6i | − | 0.209038i | ||||||
\(593\) | 5.16014e6i | 0.602594i | 0.953530 | + | 0.301297i | \(0.0974196\pi\) | ||||
−0.953530 | + | 0.301297i | \(0.902580\pi\) | |||||||
\(594\) | −3.57000e6 | − | 1.76057e6i | −0.415147 | − | 0.204732i | ||||
\(595\) | −296674. | −0.0343548 | ||||||||
\(596\) | −6.21954e6 | −0.717204 | ||||||||
\(597\) | −778684. | + | 970214.i | −0.0894181 | + | 0.111412i | ||||
\(598\) | 2.20147e6i | 0.251744i | ||||||||
\(599\) | − | 1.08002e6i | − | 0.122989i | −0.998107 | − | 0.0614943i | \(-0.980413\pi\) | ||
0.998107 | − | 0.0614943i | \(-0.0195866\pi\) | |||||||
\(600\) | 781778. | − | 974069.i | 0.0886554 | − | 0.110462i | ||||
\(601\) | 5.28734e6i | 0.597105i | 0.954393 | + | 0.298553i | \(0.0965039\pi\) | ||||
−0.954393 | + | 0.298553i | \(0.903496\pi\) | |||||||
\(602\) | 32149.4i | 0.00361561i | ||||||||
\(603\) | 309780. | − | 68674.7i | 0.0346945 | − | 0.00769136i | ||||
\(604\) | 25159.6i | 0.00280615i | ||||||||
\(605\) | 3.98326e6i | 0.442436i | ||||||||
\(606\) | 4.62626e6 | − | 5.76417e6i | 0.511739 | − | 0.637610i | ||||
\(607\) | −5.30029e6 | −0.583886 | −0.291943 | − | 0.956436i | \(-0.594302\pi\) | ||||
−0.291943 | + | 0.956436i | \(0.594302\pi\) | |||||||
\(608\) | 1.37273e6 | 0.150600 | ||||||||
\(609\) | 70396.5 | + | 56499.5i | 0.00769145 | + | 0.00617308i | ||||
\(610\) | 8.78645e6 | 0.956068 | ||||||||
\(611\) | − | 4.00400e6i | − | 0.433901i | ||||||
\(612\) | 5.06660e6 | − | 1.12321e6i | 0.546812 | − | 0.121222i | ||||
\(613\) | − | 5.94190e6i | − | 0.638667i | −0.947642 | − | 0.319333i | \(-0.896541\pi\) | ||
0.947642 | − | 0.319333i | \(-0.103459\pi\) | |||||||
\(614\) | −3.26210e6 | −0.349202 | ||||||||
\(615\) | 696152. | − | 867382.i | 0.0742192 | − | 0.0924746i | ||||
\(616\) | 86346.2 | 0.00916836 | ||||||||
\(617\) | 3.58168e6i | 0.378768i | 0.981903 | + | 0.189384i | \(0.0606491\pi\) | ||||
−0.981903 | + | 0.189384i | \(0.939351\pi\) | |||||||
\(618\) | −1.04550e6 | − | 839107.i | −0.110117 | − | 0.0883784i | ||||
\(619\) | 3.86115e6 | 0.405032 | 0.202516 | − | 0.979279i | \(-0.435088\pi\) | ||||
0.202516 | + | 0.979279i | \(0.435088\pi\) | |||||||
\(620\) | −4.22457e6 | −0.441371 | ||||||||
\(621\) | −6.31413e6 | − | 3.11386e6i | −0.657029 | − | 0.324018i | ||||
\(622\) | − | 5.19914e6i | − | 0.538835i | ||||||
\(623\) | −460928. | −0.0475787 | ||||||||
\(624\) | −921615. | − | 739679.i | −0.0947520 | − | 0.0760470i | ||||
\(625\) | −4.28606e6 | −0.438892 | ||||||||
\(626\) | − | 5.76856e6i | − | 0.588345i | ||||||
\(627\) | 3.43621e6 | − | 4.28140e6i | 0.349068 | − | 0.434927i | ||||
\(628\) | 1.59345e6i | 0.161228i | ||||||||
\(629\) | 9.29391e6 | 0.936638 | ||||||||
\(630\) | −210921. | + | 46758.8i | −0.0211723 | + | 0.00469366i | ||||
\(631\) | −9.39799e6 | −0.939640 | −0.469820 | − | 0.882762i | \(-0.655681\pi\) | ||||
−0.469820 | + | 0.882762i | \(0.655681\pi\) | |||||||
\(632\) | −4.26339e6 | −0.424583 | ||||||||
\(633\) | −1.40373e6 | − | 1.12662e6i | −0.139243 | − | 0.111755i | ||||
\(634\) | 670410.i | 0.0662396i | ||||||||
\(635\) | − | 1.14918e7i | − | 1.13098i | ||||||
\(636\) | −2.49294e6 | − | 2.00081e6i | −0.244382 | − | 0.196138i | ||||
\(637\) | − | 4.96919e6i | − | 0.485218i | ||||||
\(638\) | − | 1.18483e6i | − | 0.115240i | ||||||
\(639\) | 4.18134e6 | − | 926953.i | 0.405101 | − | 0.0898061i | ||||
\(640\) | 709084.i | 0.0684302i | ||||||||
\(641\) | − | 1.45277e7i | − | 1.39653i | −0.715837 | − | 0.698267i | \(-0.753955\pi\) | ||
0.715837 | − | 0.698267i | \(-0.246045\pi\) | |||||||
\(642\) | 8.36738e6 | + | 6.71557e6i | 0.801220 | + | 0.643051i | ||||
\(643\) | 8.06246e6 | 0.769024 | 0.384512 | − | 0.923120i | \(-0.374370\pi\) | ||||
0.384512 | + | 0.923120i | \(0.374370\pi\) | |||||||
\(644\) | 152718. | 0.0145102 | ||||||||
\(645\) | −660880. | + | 823434.i | −0.0625494 | + | 0.0779345i | ||||
\(646\) | 7.15734e6i | 0.674793i | ||||||||
\(647\) | 1.30624e7i | 1.22677i | 0.789784 | + | 0.613385i | \(0.210192\pi\) | ||||
−0.789784 | + | 0.613385i | \(0.789808\pi\) | |||||||
\(648\) | 3.42508e6 | − | 1.59709e6i | 0.320430 | − | 0.149414i | ||||
\(649\) | 3.72611e6 | + | 5.95450e6i | 0.347252 | + | 0.554924i | ||||
\(650\) | − | 1.48291e6i | − | 0.137667i | ||||||
\(651\) | −380900. | − | 305706.i | −0.0352256 | − | 0.0282717i | ||||
\(652\) | 9.29141e6 | 0.855978 | ||||||||
\(653\) | 8.12008e6i | 0.745208i | 0.927990 | + | 0.372604i | \(0.121535\pi\) | ||||
−0.927990 | + | 0.372604i | \(0.878465\pi\) | |||||||
\(654\) | −1.07072e7 | − | 8.59349e6i | −0.978885 | − | 0.785643i | ||||
\(655\) | − | 1.01831e6i | − | 0.0927422i | ||||||
\(656\) | − | 422027.i | − | 0.0382896i | ||||||
\(657\) | 3.88889e6 | − | 862122.i | 0.351490 | − | 0.0779212i | ||||
\(658\) | −277761. | −0.0250095 | ||||||||
\(659\) | −1.16495e7 | −1.04495 | −0.522475 | − | 0.852655i | \(-0.674991\pi\) | ||||
−0.522475 | + | 0.852655i | \(0.674991\pi\) | |||||||
\(660\) | 2.21157e6 | + | 1.77498e6i | 0.197624 | + | 0.158611i | ||||
\(661\) | −4.25595e6 | −0.378873 | −0.189436 | − | 0.981893i | \(-0.560666\pi\) | ||||
−0.189436 | + | 0.981893i | \(0.560666\pi\) | |||||||
\(662\) | −294971. | −0.0261598 | ||||||||
\(663\) | 3.85666e6 | − | 4.80527e6i | 0.340743 | − | 0.424555i | ||||
\(664\) | −3.37412e6 | −0.296989 | ||||||||
\(665\) | − | 297958.i | − | 0.0261277i | ||||||
\(666\) | 6.60752e6 | − | 1.46481e6i | 0.577236 | − | 0.127966i | ||||
\(667\) | − | 2.09556e6i | − | 0.182384i | ||||||
\(668\) | 1.62827e6i | 0.141184i | ||||||||
\(669\) | −9.26875e6 | + | 1.15485e7i | −0.800674 | + | 0.997613i | ||||
\(670\) | −226049. | −0.0194543 | ||||||||
\(671\) | − | 1.33335e7i | − | 1.14324i | ||||||
\(672\) | −51312.1 | + | 63933.1i | −0.00438325 | + | 0.00546139i | ||||
\(673\) | 1.68599e7i | 1.43488i | 0.696619 | + | 0.717441i | \(0.254687\pi\) | ||||
−0.696619 | + | 0.717441i | \(0.745313\pi\) | |||||||
\(674\) | 1.39819e7i | 1.18554i | ||||||||
\(675\) | 4.25320e6 | + | 2.09749e6i | 0.359299 | + | 0.177191i | ||||
\(676\) | 4.53763e6 | 0.381911 | ||||||||
\(677\) | − | 18963.6i | − | 0.00159019i | −1.00000 | 0.000795094i | \(-0.999747\pi\) | |||
1.00000 | 0.000795094i | \(-0.000253086\pi\) | ||||||||
\(678\) | 6.69440e6 | − | 8.34099e6i | 0.559290 | − | 0.696857i | ||||
\(679\) | 128329.i | 0.0106819i | ||||||||
\(680\) | −3.69714e6 | −0.306615 | ||||||||
\(681\) | 3.63011e6 | − | 4.52299e6i | 0.299952 | − | 0.373730i | ||||
\(682\) | 6.41083e6i | 0.527781i | ||||||||
\(683\) | 7.53196e6 | 0.617812 | 0.308906 | − | 0.951093i | \(-0.400037\pi\) | ||||
0.308906 | + | 0.951093i | \(0.400037\pi\) | |||||||
\(684\) | 1.12807e6 | + | 5.08853e6i | 0.0921923 | + | 0.415864i | ||||
\(685\) | −1.00718e7 | −0.820125 | ||||||||
\(686\) | −689975. | −0.0559787 | ||||||||
\(687\) | 4.31368e6 | + | 3.46211e6i | 0.348703 | + | 0.279865i | ||||
\(688\) | 400644.i | 0.0322692i | ||||||||
\(689\) | −3.79522e6 | −0.304571 | ||||||||
\(690\) | 3.91152e6 | + | 3.13935e6i | 0.312768 | + | 0.251025i | ||||
\(691\) | 2.00757e7i | 1.59947i | 0.600353 | + | 0.799735i | \(0.295027\pi\) | ||||
−0.600353 | + | 0.799735i | \(0.704973\pi\) | |||||||
\(692\) | 1.02525e6 | 0.0813888 | ||||||||
\(693\) | 70956.9 | + | 320075.i | 0.00561257 | + | 0.0253174i | ||||
\(694\) | −326298. | −0.0257167 | ||||||||
\(695\) | − | 1.36464e7i | − | 1.07166i | ||||||
\(696\) | 877278. | + | 704095.i | 0.0686459 | + | 0.0550945i | ||||
\(697\) | 2.20043e6 | 0.171564 | ||||||||
\(698\) | 1.30324e7i | 1.01248i | ||||||||
\(699\) | −1.22221e7 | + | 1.52284e7i | −0.946137 | + | 1.17885i | ||||
\(700\) | −102871. | −0.00793498 | ||||||||
\(701\) | 2.02660e6 | 0.155766 | 0.0778832 | − | 0.996962i | \(-0.475184\pi\) | ||||
0.0778832 | + | 0.996962i | \(0.475184\pi\) | |||||||
\(702\) | 1.98454e6 | − | 4.02416e6i | 0.151991 | − | 0.308200i | ||||
\(703\) | 9.33413e6i | 0.712337i | ||||||||
\(704\) | 1.07604e6 | 0.0818273 | ||||||||
\(705\) | −7.11422e6 | − | 5.70980e6i | −0.539081 | − | 0.432661i | ||||
\(706\) | −7.06175e6 | −0.533213 | ||||||||
\(707\) | −608748. | −0.0458025 | ||||||||
\(708\) | −6.62316e6 | − | 779605.i | −0.496572 | − | 0.0584510i | ||||
\(709\) | −1.86937e7 | −1.39662 | −0.698311 | − | 0.715794i | \(-0.746065\pi\) | ||||
−0.698311 | + | 0.715794i | \(0.746065\pi\) | |||||||
\(710\) | −3.05116e6 | −0.227153 | ||||||||
\(711\) | −3.50353e6 | − | 1.58039e7i | −0.259916 | − | 1.17244i | ||||
\(712\) | −5.74406e6 | −0.424638 | ||||||||
\(713\) | 1.13386e7i | 0.835288i | ||||||||
\(714\) | −333345. | − | 267539.i | −0.0244708 | − | 0.0196400i | ||||
\(715\) | 3.36686e6 | 0.246297 | ||||||||
\(716\) | 6.60061e6 | 0.481173 | ||||||||
\(717\) | 2.05237e6 | + | 1.64721e6i | 0.149093 | + | 0.119660i | ||||
\(718\) | 1.09384e7i | 0.791850i | ||||||||
\(719\) | 2.52490e7 | 1.82147 | 0.910736 | − | 0.412990i | \(-0.135516\pi\) | ||||
0.910736 | + | 0.412990i | \(0.135516\pi\) | |||||||
\(720\) | −2.62849e6 | + | 582706.i | −0.188962 | + | 0.0418907i | ||||
\(721\) | 110414.i | 0.00791019i | ||||||||
\(722\) | 2.71608e6 | 0.193910 | ||||||||
\(723\) | −3.32296e6 | + | 4.14029e6i | −0.236417 | + | 0.294568i | ||||
\(724\) | 592268. | 0.0419925 | ||||||||
\(725\) | 1.41157e6i | 0.0997373i | ||||||||
\(726\) | −3.59209e6 | + | 4.47562e6i | −0.252933 | + | 0.315146i | ||||
\(727\) | −3.88302e6 | −0.272479 | −0.136240 | − | 0.990676i | \(-0.543502\pi\) | ||||
−0.136240 | + | 0.990676i | \(0.543502\pi\) | |||||||
\(728\) | 97331.0i | 0.00680648i | ||||||||
\(729\) | 8.73486e6 | + | 1.13839e7i | 0.608747 | + | 0.793364i | ||||
\(730\) | −2.83776e6 | −0.197092 | ||||||||
\(731\) | −2.08894e6 | −0.144588 | ||||||||
\(732\) | 9.87252e6 | + | 7.92358e6i | 0.681005 | + | 0.546568i | ||||
\(733\) | −1.94836e7 | −1.33939 | −0.669697 | − | 0.742635i | \(-0.733576\pi\) | ||||
−0.669697 | + | 0.742635i | \(0.733576\pi\) | |||||||
\(734\) | − | 6.16429e6i | − | 0.422321i | ||||||
\(735\) | −8.82914e6 | − | 7.08618e6i | −0.602837 | − | 0.483831i | ||||
\(736\) | 1.90316e6 | 0.129503 | ||||||||
\(737\) | 343032.i | 0.0232630i | ||||||||
\(738\) | 1.56440e6 | − | 346810.i | 0.105732 | − | 0.0234396i | ||||
\(739\) | 1.83794e7i | 1.23800i | 0.785392 | + | 0.618998i | \(0.212461\pi\) | ||||
−0.785392 | + | 0.618998i | \(0.787539\pi\) | |||||||
\(740\) | −4.82157e6 | −0.323675 | ||||||||
\(741\) | 4.82607e6 | + | 3.87335e6i | 0.322885 | + | 0.259144i | ||||
\(742\) | 263277.i | 0.0175551i | ||||||||
\(743\) | − | 1.41912e7i | − | 0.943077i | −0.881845 | − | 0.471539i | \(-0.843699\pi\) | ||
0.881845 | − | 0.471539i | \(-0.156301\pi\) | |||||||
\(744\) | −4.74676e6 | − | 3.80970e6i | −0.314387 | − | 0.252324i | ||||
\(745\) | 1.68235e7i | 1.11052i | ||||||||
\(746\) | −5.40884e6 | −0.355842 | ||||||||
\(747\) | −2.77275e6 | − | 1.25074e7i | −0.181807 | − | 0.820100i | ||||
\(748\) | 5.61045e6i | 0.366643i | ||||||||
\(749\) | − | 883672.i | − | 0.0575554i | ||||||
\(750\) | −9.21169e6 | − | 7.39320e6i | −0.597979 | − | 0.479932i | ||||
\(751\) | 3.45413e6i | 0.223480i | 0.993737 | + | 0.111740i | \(0.0356424\pi\) | ||||
−0.993737 | + | 0.111740i | \(0.964358\pi\) | |||||||
\(752\) | −3.46144e6 | −0.223209 | ||||||||
\(753\) | 540707. | + | 433966.i | 0.0347516 | + | 0.0278912i | ||||
\(754\) | 1.33556e6 | 0.0855528 | ||||||||
\(755\) | 68055.2 | 0.00434504 | ||||||||
\(756\) | −279159. | − | 137669.i | −0.0177643 | − | 0.00876057i | ||||
\(757\) | 1.30006e7 | 0.824564 | 0.412282 | − | 0.911056i | \(-0.364732\pi\) | ||||
0.412282 | + | 0.911056i | \(0.364732\pi\) | |||||||
\(758\) | −3.42529e6 | −0.216533 | ||||||||
\(759\) | 4.76399e6 | − | 5.93577e6i | 0.300169 | − | 0.374001i | ||||
\(760\) | − | 3.71314e6i | − | 0.233189i | ||||||
\(761\) | − | 7.83517e6i | − | 0.490441i | −0.969467 | − | 0.245221i | \(-0.921140\pi\) | ||
0.969467 | − | 0.245221i | \(-0.0788604\pi\) | |||||||
\(762\) | 1.03632e7 | − | 1.29122e7i | 0.646559 | − | 0.805591i | ||||
\(763\) | 1.13078e6i | 0.0703179i | ||||||||
\(764\) | −2.49508e6 | −0.154651 | ||||||||
\(765\) | −3.03821e6 | − | 1.37049e7i | −0.187700 | − | 0.846683i | ||||
\(766\) | − | 1.33413e7i | − | 0.821535i | ||||||
\(767\) | −6.71202e6 | + | 4.20014e6i | −0.411969 | + | 0.257795i | ||||
\(768\) | −639449. | + | 796732.i | −0.0391204 | + | 0.0487427i | ||||
\(769\) | − | 1.56964e7i | − | 0.957161i | −0.878044 | − | 0.478581i | \(-0.841151\pi\) | ||
0.878044 | − | 0.478581i | \(-0.158849\pi\) | |||||||
\(770\) | − | 233562.i | − | 0.0141963i | ||||||
\(771\) | 5.90556e6 | + | 4.73975e6i | 0.357788 | + | 0.287157i | ||||
\(772\) | −8.32483e6 | −0.502727 | ||||||||
\(773\) | −2.41197e7 | −1.45186 | −0.725929 | − | 0.687770i | \(-0.758590\pi\) | ||||
−0.725929 | + | 0.687770i | \(0.758590\pi\) | |||||||
\(774\) | −1.48514e6 | + | 329238.i | −0.0891076 | + | 0.0197541i | ||||
\(775\) | − | 7.63769e6i | − | 0.456781i | ||||||
\(776\) | 1.59923e6i | 0.0953357i | ||||||||
\(777\) | −434727. | − | 348907.i | −0.0258323 | − | 0.0207328i | ||||
\(778\) | − | 1.17657e7i | − | 0.696900i | ||||||
\(779\) | 2.20996e6i | 0.130479i | ||||||||
\(780\) | −2.00079e6 | + | 2.49292e6i | −0.117751 | + | 0.146714i | ||||
\(781\) | 4.63016e6i | 0.271624i | ||||||||
\(782\) | 9.92301e6i | 0.580265i | ||||||||
\(783\) | −1.88907e6 | + | 3.83057e6i | −0.110114 | + | 0.223285i | ||||
\(784\) | −4.29584e6 | −0.249608 | ||||||||
\(785\) | 4.31019e6 | 0.249645 | ||||||||
\(786\) | 918309. | − | 1.14418e6i | 0.0530191 | − | 0.0660600i | ||||
\(787\) | −1.37090e7 | −0.788985 | −0.394492 | − | 0.918899i | \(-0.629080\pi\) | ||||
−0.394492 | + | 0.918899i | \(0.629080\pi\) | |||||||
\(788\) | 4.23657e6i | 0.243052i | ||||||||
\(789\) | 2.01615e7 | + | 1.61814e7i | 1.15300 | + | 0.925386i | ||||
\(790\) | 1.15322e7i | 0.657424i | ||||||||
\(791\) | −880885. | −0.0500585 | ||||||||
\(792\) | 884262. | + | 3.98876e6i | 0.0500920 | + | 0.225957i | ||||
\(793\) | 1.50298e7 | 0.848731 | ||||||||
\(794\) | − | 5.79817e6i | − | 0.326392i | ||||||
\(795\) | −5.41207e6 | + | 6.74325e6i | −0.303700 | + | 0.378401i | ||||
\(796\) | 1.27689e6 | 0.0714286 | ||||||||
\(797\) | −1.32372e7 | −0.738157 | −0.369079 | − | 0.929398i | \(-0.620327\pi\) | ||||
−0.369079 | + | 0.929398i | \(0.620327\pi\) | |||||||
\(798\) | 268697. | − | 334788.i | 0.0149368 | − | 0.0186107i | ||||
\(799\) | − | 1.80478e7i | − | 1.00013i | ||||||
\(800\) | −1.28197e6 | −0.0708194 | ||||||||
\(801\) | −4.72031e6 | − | 2.12925e7i | −0.259950 | − | 1.17259i | ||||
\(802\) | 36086.4 | 0.00198111 | ||||||||
\(803\) | 4.30633e6i | 0.235678i | ||||||||
\(804\) | −253991. | − | 203850.i | −0.0138573 | − | 0.0111217i | ||||
\(805\) | − | 413092.i | − | 0.0224676i | ||||||
\(806\) | −7.22640e6 | −0.391818 | ||||||||
\(807\) | −5.35121e6 | + | 6.66743e6i | −0.289247 | + | 0.360392i | ||||
\(808\) | −7.58620e6 | −0.408786 | ||||||||
\(809\) | −2.44918e7 | −1.31568 | −0.657840 | − | 0.753158i | \(-0.728530\pi\) | ||||
−0.657840 | + | 0.753158i | \(0.728530\pi\) | |||||||
\(810\) | −4.32004e6 | − | 9.26464e6i | −0.231353 | − | 0.496153i | ||||
\(811\) | 1.54861e7i | 0.826779i | 0.910554 | + | 0.413389i | \(0.135655\pi\) | ||||
−0.910554 | + | 0.413389i | \(0.864345\pi\) | |||||||
\(812\) | − | 92648.6i | − | 0.00493116i | ||||||
\(813\) | 6.37693e6 | − | 7.94544e6i | 0.338365 | − | 0.421591i | ||||
\(814\) | 7.31678e6i | 0.387043i | ||||||||
\(815\) | − | 2.51327e7i | − | 1.32540i | ||||||
\(816\) | −4.15413e6 | − | 3.33406e6i | −0.218401 | − | 0.175287i | ||||
\(817\) | − | 2.09798e6i | − | 0.109963i | ||||||
\(818\) | − | 7.49998e6i | − | 0.391901i | ||||||
\(819\) | −360794. | + | 79983.9i | −0.0187953 | + | 0.00416670i | ||||
\(820\) | −1.14156e6 | −0.0592875 | ||||||||
\(821\) | −2.89142e7 | −1.49711 | −0.748554 | − | 0.663073i | \(-0.769252\pi\) | ||||
−0.748554 | + | 0.663073i | \(0.769252\pi\) | |||||||
\(822\) | −1.13167e7 | − | 9.08269e6i | −0.584173 | − | 0.468851i | ||||
\(823\) | 1.88475e7i | 0.969961i | 0.874525 | + | 0.484980i | \(0.161173\pi\) | ||||
−0.874525 | + | 0.484980i | \(0.838827\pi\) | |||||||
\(824\) | 1.37598e6i | 0.0705982i | ||||||||
\(825\) | −3.20902e6 | + | 3.99834e6i | −0.164149 | + | 0.204524i | ||||
\(826\) | 291367. | + | 465618.i | 0.0148590 | + | 0.0237454i | ||||
\(827\) | 1.33149e7i | 0.676979i | 0.940970 | + | 0.338490i | \(0.109916\pi\) | ||||
−0.940970 | + | 0.338490i | \(0.890084\pi\) | |||||||
\(828\) | 1.56396e6 | + | 7.05478e6i | 0.0792776 | + | 0.357608i | ||||
\(829\) | −3.82902e7 | −1.93509 | −0.967545 | − | 0.252700i | \(-0.918681\pi\) | ||||
−0.967545 | + | 0.252700i | \(0.918681\pi\) | |||||||
\(830\) | 9.12679e6i | 0.459857i | ||||||||
\(831\) | 9.90317e6 | − | 1.23390e7i | 0.497476 | − | 0.619838i | ||||
\(832\) | 1.21293e6i | 0.0607476i | ||||||||
\(833\) | − | 2.23984e7i | − | 1.11842i | ||||||
\(834\) | 1.23062e7 | − | 1.53332e7i | 0.612647 | − | 0.763337i | ||||
\(835\) | 4.40437e6 | 0.218609 | ||||||||
\(836\) | −5.63473e6 | −0.278842 | ||||||||
\(837\) | 1.02213e7 | − | 2.07264e7i | 0.504306 | − | 1.02261i | ||||
\(838\) | −2.49592e7 | −1.22778 | ||||||||
\(839\) | −3.15083e7 | −1.54532 | −0.772662 | − | 0.634818i | \(-0.781075\pi\) | ||||
−0.772662 | + | 0.634818i | \(0.781075\pi\) | |||||||
\(840\) | 172935. | + | 138796.i | 0.00845641 | + | 0.00678703i | ||||
\(841\) | 1.92398e7 | 0.938019 | ||||||||
\(842\) | 1.38844e7i | 0.674914i | ||||||||
\(843\) | 2.41106e7 | + | 1.93509e7i | 1.16853 | + | 0.937850i | ||||
\(844\) | 1.84744e6i | 0.0892717i | ||||||||
\(845\) | − | 1.22740e7i | − | 0.591351i | ||||||
\(846\) | −2.84451e6 | − | 1.28311e7i | −0.136641 | − | 0.616367i | ||||
\(847\) | 472666. | 0.0226384 | ||||||||
\(848\) | 3.28095e6i | 0.156679i | ||||||||
\(849\) | 2.51432e7 | + | 2.01797e7i | 1.19716 | + | 0.960825i | ||||
\(850\) | − | 6.68414e6i | − | 0.317320i | ||||||
\(851\) | 1.29409e7i | 0.612550i | ||||||||
\(852\) | −3.42830e6 | − | 2.75152e6i | −0.161801 | − | 0.129859i | ||||
\(853\) | −4.06416e6 | −0.191248 | −0.0956242 | − | 0.995418i | \(-0.530485\pi\) | ||||
−0.0956242 | + | 0.995418i | \(0.530485\pi\) | |||||||
\(854\) | − | 1.04263e6i | − | 0.0489198i | ||||||
\(855\) | 1.37642e7 | − | 3.05136e6i | 0.643924 | − | 0.142750i | ||||
\(856\) | − | 1.10123e7i | − | 0.513680i | ||||||
\(857\) | 8.69830e6 | 0.404559 | 0.202280 | − | 0.979328i | \(-0.435165\pi\) | ||||
0.202280 | + | 0.979328i | \(0.435165\pi\) | |||||||
\(858\) | 3.78303e6 | + | 3.03622e6i | 0.175437 | + | 0.140804i | ||||
\(859\) | 1.70914e7i | 0.790303i | 0.918616 | + | 0.395151i | \(0.129308\pi\) | ||||
−0.918616 | + | 0.395151i | \(0.870692\pi\) | |||||||
\(860\) | 1.08372e6 | 0.0499655 | ||||||||
\(861\) | −102926. | − | 82607.6i | −0.00473171 | − | 0.00379762i | ||||
\(862\) | 6.23168e6 | 0.285652 | ||||||||
\(863\) | 1.68836e7 | 0.771682 | 0.385841 | − | 0.922565i | \(-0.373911\pi\) | ||||
0.385841 | + | 0.922565i | \(0.373911\pi\) | |||||||
\(864\) | −3.47887e6 | − | 1.71563e6i | −0.158545 | − | 0.0781878i | ||||
\(865\) | − | 2.77324e6i | − | 0.126022i | ||||||
\(866\) | −1.99038e7 | −0.901864 | ||||||||
\(867\) | 3.52984e6 | − | 4.39806e6i | 0.159480 | − | 0.198707i | ||||
\(868\) | 501301.i | 0.0225839i | ||||||||
\(869\) | 1.75003e7 | 0.786132 | ||||||||
\(870\) | 1.90454e6 | − | 2.37299e6i | 0.0853082 | − | 0.106291i | ||||
\(871\) | −386672. | −0.0172702 | ||||||||
\(872\) | 1.40917e7i | 0.627585i | ||||||||
\(873\) | −5.92814e6 | + | 1.31420e6i | −0.263259 | + | 0.0583614i | ||||
\(874\) | −9.96595e6 | −0.441306 | ||||||||
\(875\) | 972838.i | 0.0429557i | ||||||||
\(876\) | −3.18853e6 | − | 2.55908e6i | −0.140388 | − | 0.112674i | ||||
\(877\) | 920002. | 0.0403915 | 0.0201957 | − | 0.999796i | \(-0.493571\pi\) | ||||
0.0201957 | + | 0.999796i | \(0.493571\pi\) | |||||||
\(878\) | −9.49487e6 | −0.415674 | ||||||||
\(879\) | 5.33276e6 | + | 4.28002e6i | 0.232798 | + | 0.186842i | ||||
\(880\) | − | 2.91063e6i | − | 0.126701i | ||||||
\(881\) | 6.50122e6 | 0.282199 | 0.141099 | − | 0.989995i | \(-0.454936\pi\) | ||||
0.141099 | + | 0.989995i | \(0.454936\pi\) | |||||||
\(882\) | −3.53020e6 | − | 1.59242e7i | −0.152802 | − | 0.689263i | ||||
\(883\) | 3.31385e7 | 1.43031 | 0.715156 | − | 0.698965i | \(-0.246356\pi\) | ||||
0.715156 | + | 0.698965i | \(0.246356\pi\) | |||||||
\(884\) | −6.32420e6 | −0.272192 | ||||||||
\(885\) | −2.10879e6 | + | 1.79153e7i | −0.0905054 | + | 0.768891i | ||||
\(886\) | 2.04884e6 | 0.0876846 | ||||||||
\(887\) | 4.39283e7 | 1.87472 | 0.937358 | − | 0.348369i | \(-0.113264\pi\) | ||||
0.937358 | + | 0.348369i | \(0.113264\pi\) | |||||||
\(888\) | −5.41755e6 | − | 4.34807e6i | −0.230553 | − | 0.185039i | ||||
\(889\) | −1.36365e6 | −0.0578694 | ||||||||
\(890\) | 1.55374e7i | 0.657509i | ||||||||
\(891\) | −1.40592e7 | + | 6.55570e6i | −0.593289 | + | 0.276646i | ||||
\(892\) | 1.51990e7 | 0.639592 | ||||||||
\(893\) | 1.81259e7 | 0.760627 | ||||||||
\(894\) | −1.51714e7 | + | 1.89030e7i | −0.634864 | + | 0.791019i | ||||
\(895\) | − | 1.78543e7i | − | 0.745048i | ||||||
\(896\) | 84142.2 | 0.00350142 | ||||||||
\(897\) | 6.69091e6 | + | 5.37005e6i | 0.277654 | + | 0.222842i | ||||
\(898\) | − | 8.88122e6i | − | 0.367521i | ||||||
\(899\) | 6.87875e6 | 0.283864 | ||||||||
\(900\) | −1.05349e6 | − | 4.75210e6i | −0.0433533 | − | 0.195560i | ||||
\(901\) | −1.71067e7 | −0.702029 | ||||||||
\(902\) | 1.73233e6i | 0.0708946i | ||||||||
\(903\) | 97711.3 | + | 78422.1i | 0.00398773 | + | 0.00320051i | ||||
\(904\) | −1.09775e7 | −0.446770 | ||||||||
\(905\) | − | 1.60205e6i | − | 0.0650211i | ||||||
\(906\) | 76467.3 | + | 61371.9i | 0.00309496 | + | 0.00248399i | ||||
\(907\) | −1.96151e6 | −0.0791723 | −0.0395862 | − | 0.999216i | \(-0.512604\pi\) | ||||
−0.0395862 | + | 0.999216i | \(0.512604\pi\) | |||||||
\(908\) | −5.95269e6 | −0.239607 | ||||||||
\(909\) | −6.23412e6 | − | 2.81211e7i | −0.250245 | − | 1.12881i | ||||
\(910\) | 263275. | 0.0105391 | ||||||||
\(911\) | − | 3.45674e7i | − | 1.37997i | −0.723821 | − | 0.689987i | \(-0.757616\pi\) | ||
0.723821 | − | 0.689987i | \(-0.242384\pi\) | |||||||
\(912\) | 3.34849e6 | − | 4.17211e6i | 0.133310 | − | 0.166100i | ||||
\(913\) | 1.38500e7 | 0.549886 | ||||||||
\(914\) | 3.13684e6i | 0.124201i | ||||||||
\(915\) | 2.14328e7 | − | 2.67046e7i | 0.846305 | − | 1.05447i | ||||
\(916\) | − | 5.67721e6i | − | 0.223561i | ||||||
\(917\) | −120836. | −0.00474540 | ||||||||
\(918\) | 8.94522e6 | − | 1.81387e7i | 0.350336 | − | 0.710395i | ||||
\(919\) | − | 2.45944e7i | − | 0.960612i | −0.877101 | − | 0.480306i | \(-0.840526\pi\) | ||
0.877101 | − | 0.480306i | \(-0.159474\pi\) | |||||||
\(920\) | − | 5.14794e6i | − | 0.200523i | ||||||
\(921\) | −7.95725e6 | + | 9.91447e6i | −0.309111 | + | 0.385142i | ||||
\(922\) | 1.87048e7i | 0.724646i | ||||||||
\(923\) | −5.21920e6 | −0.201651 | ||||||||
\(924\) | 210625. | − | 262431.i | 0.00811577 | − | 0.0101120i | ||||
\(925\) | − | 8.71701e6i | − | 0.334976i | ||||||
\(926\) | 8.03375e6i | 0.307887i | ||||||||
\(927\) | −5.10058e6 | + | 1.13074e6i | −0.194949 | + | 0.0432179i | ||||
\(928\) | − | 1.15458e6i | − | 0.0440104i | ||||||
\(929\) | 2.25317e7 | 0.856552 | 0.428276 | − | 0.903648i | \(-0.359121\pi\) | ||||
0.428276 | + | 0.903648i | \(0.359121\pi\) | |||||||
\(930\) | −1.03050e7 | + | 1.28397e7i | −0.390698 | + | 0.486797i | ||||
\(931\) | 2.24953e7 | 0.850585 | ||||||||
\(932\) | 2.00420e7 | 0.755790 | ||||||||
\(933\) | −1.58017e7 | − | 1.26823e7i | −0.594292 | − | 0.476973i | ||||
\(934\) | −3.21010e7 | −1.20407 | ||||||||
\(935\) | 1.51759e7 | 0.567710 | ||||||||
\(936\) | −4.49620e6 | + | 996755.i | −0.167747 | + | 0.0371877i | ||||
\(937\) | 1.16192e7i | 0.432344i | 0.976355 | + | 0.216172i | \(0.0693571\pi\) | ||||
−0.976355 | + | 0.216172i | \(0.930643\pi\) | |||||||
\(938\) | 26823.7i | 0.000995433i | ||||||||
\(939\) | −1.75323e7 | − | 1.40713e7i | −0.648897 | − | 0.520798i | ||||
\(940\) | 9.36299e6i | 0.345617i | ||||||||
\(941\) | −2.31486e6 | −0.0852218 | −0.0426109 | − | 0.999092i | \(-0.513568\pi\) | ||||
−0.0426109 | + | 0.999092i | \(0.513568\pi\) | |||||||
\(942\) | 4.84296e6 | + | 3.88691e6i | 0.177821 | + | 0.142718i | ||||
\(943\) | 3.06390e6i | 0.112201i | ||||||||
\(944\) | 3.63100e6 | + | 5.80251e6i | 0.132616 | + | 0.211927i | ||||
\(945\) | −372387. | + | 755110.i | −0.0135649 | + | 0.0275062i | ||||
\(946\) | − | 1.64455e6i | − | 0.0597476i | ||||||
\(947\) | 5.80247e6i | 0.210251i | 0.994459 | + | 0.105125i | \(0.0335244\pi\) | ||||
−0.994459 | + | 0.105125i | \(0.966476\pi\) | |||||||
\(948\) | −1.03997e7 | + | 1.29577e7i | −0.375838 | + | 0.468281i | ||||
\(949\) | −4.85417e6 | −0.174964 | ||||||||
\(950\) | 6.71307e6 | 0.241330 | ||||||||
\(951\) | 2.03757e6 | + | 1.63533e6i | 0.0730570 | + | 0.0586348i | ||||
\(952\) | 438714.i | 0.0156888i | ||||||||
\(953\) | 8.74975e6i | 0.312078i | 0.987751 | + | 0.156039i | \(0.0498726\pi\) | ||||
−0.987751 | + | 0.156039i | \(0.950127\pi\) | |||||||
\(954\) | −1.21621e7 | + | 2.69619e6i | −0.432650 | + | 0.0959135i | ||||
\(955\) | 6.74906e6i | 0.239461i | ||||||||
\(956\) | − | 2.70111e6i | − | 0.0955868i | ||||||
\(957\) | −3.60103e6 | − | 2.89015e6i | −0.127101 | − | 0.102010i | ||||
\(958\) | − | 1.03813e7i | − | 0.365457i | ||||||
\(959\) | 1.19515e6i | 0.0419639i | ||||||||
\(960\) | 2.15511e6 | + | 1.72967e6i | 0.0754731 | + | 0.0605739i | ||||
\(961\) | −8.59024e6 | −0.300052 | ||||||||
\(962\) | −8.24760e6 | −0.287336 | ||||||||
\(963\) | 4.08212e7 | − | 9.04958e6i | 1.41847 | − | 0.314458i | ||||
\(964\) | 5.44903e6 | 0.188854 | ||||||||
\(965\) | 2.25182e7i | 0.778421i | ||||||||
\(966\) | 372525. | − | 464153.i | 0.0128444 | − | 0.0160036i | ||||
\(967\) | 94538.9i | 0.00325121i | 0.999999 | + | 0.00162560i | \(0.000517446\pi\) | ||||
−0.999999 | + | 0.00162560i | \(0.999483\pi\) | |||||||
\(968\) | 5.89035e6 | 0.202047 | ||||||||
\(969\) | 2.17532e7 | + | 1.74589e7i | 0.744243 | + | 0.597322i | ||||
\(970\) | 4.32582e6 | 0.147618 | ||||||||
\(971\) | 6.08747e6i | 0.207200i | 0.994619 | + | 0.103600i | \(0.0330361\pi\) | ||||
−0.994619 | + | 0.103600i | \(0.966964\pi\) | |||||||
\(972\) | 3.50079e6 | − | 1.43056e7i | 0.118850 | − | 0.485669i | ||||
\(973\) | −1.61932e6 | −0.0548341 | ||||||||
\(974\) | −3.00476e6 | −0.101487 | ||||||||
\(975\) | −4.50699e6 | − | 3.61727e6i | −0.151836 | − | 0.121862i | ||||
\(976\) | − | 1.29932e7i | − | 0.436607i | ||||||
\(977\) | 5.01560e7 | 1.68107 | 0.840537 | − | 0.541754i | \(-0.182240\pi\) | ||||
0.840537 | + | 0.541754i | \(0.182240\pi\) | |||||||
\(978\) | 2.26646e7 | − | 2.82393e7i | 0.757706 | − | 0.944076i | ||||
\(979\) | 2.35781e7 | 0.786234 | ||||||||
\(980\) | 1.16200e7i | 0.386492i | ||||||||
\(981\) | −5.22363e7 | + | 1.15802e7i | −1.73300 | + | 0.384187i | ||||
\(982\) | 4.16874e6i | 0.137951i | ||||||||
\(983\) | 4.76773e7 | 1.57372 | 0.786861 | − | 0.617131i | \(-0.211705\pi\) | ||||
0.786861 | + | 0.617131i | \(0.211705\pi\) | |||||||
\(984\) | −1.28266e6 | − | 1.02945e6i | −0.0422303 | − | 0.0338936i | ||||
\(985\) | 1.14597e7 | 0.376341 | ||||||||
\(986\) | 6.01995e6 | 0.197197 | ||||||||
\(987\) | −677542. | + | 844195.i | −0.0221383 | + | 0.0275835i | ||||
\(988\) | − | 6.35157e6i | − | 0.207009i | ||||||
\(989\) | − | 2.90867e6i | − | 0.0945591i | ||||||
\(990\) | 1.07894e7 | − | 2.39188e6i | 0.349871 | − | 0.0775623i | ||||
\(991\) | 2.87525e7i | 0.930019i | 0.885306 | + | 0.465010i | \(0.153949\pi\) | ||||
−0.885306 | + | 0.465010i | \(0.846051\pi\) | |||||||
\(992\) | 6.24719e6i | 0.201560i | ||||||||
\(993\) | −719523. | + | 896501.i | −0.0231564 | + | 0.0288521i | ||||
\(994\) | 362060.i | 0.0116229i | ||||||||
\(995\) | − | 3.45393e6i | − | 0.110600i | ||||||
\(996\) | −8.23050e6 | + | 1.02549e7i | −0.262892 | + | 0.327555i | ||||
\(997\) | 171824. | 0.00547452 | 0.00273726 | − | 0.999996i | \(-0.499129\pi\) | ||||
0.00273726 | + | 0.999996i | \(0.499129\pi\) | |||||||
\(998\) | 1.95715e7 | 0.622010 | ||||||||
\(999\) | 1.16658e7 | − | 2.36553e7i | 0.369828 | − | 0.749920i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 354.6.c.a.353.16 | yes | 50 | |
3.2 | odd | 2 | 354.6.c.b.353.15 | yes | 50 | ||
59.58 | odd | 2 | 354.6.c.b.353.16 | yes | 50 | ||
177.176 | even | 2 | inner | 354.6.c.a.353.15 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
354.6.c.a.353.15 | ✓ | 50 | 177.176 | even | 2 | inner | |
354.6.c.a.353.16 | yes | 50 | 1.1 | even | 1 | trivial | |
354.6.c.b.353.15 | yes | 50 | 3.2 | odd | 2 | ||
354.6.c.b.353.16 | yes | 50 | 59.58 | odd | 2 |