Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [152,6,Mod(75,152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(152, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("152.75");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 152 = 2^{3} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 152.b (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: | \(24.3783406116\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 75.14 | ||
Character | \(\chi\) | \(=\) | 152.75 |
Dual form | 152.6.b.b.75.13 |
$q$-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 \(\left(\mathbb{Z}/152\mathbb{Z}\right)^\times\).
\(n\) | \(39\) | \(77\) | \(97\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.05036 | + | 2.54831i | −0.892785 | + | 0.450483i | ||||
\(3\) | − | 27.1983i | − | 1.74477i | −0.488818 | − | 0.872386i | \(-0.662572\pi\) | ||
0.488818 | − | 0.872386i | \(-0.337428\pi\) | |||||||
\(4\) | 19.0122 | − | 25.7398i | 0.594131 | − | 0.804368i | ||||
\(5\) | − | 36.9812i | − | 0.661540i | −0.943711 | − | 0.330770i | \(-0.892692\pi\) | ||
0.943711 | − | 0.330770i | \(-0.107308\pi\) | |||||||
\(6\) | 69.3098 | + | 137.361i | 0.785989 | + | 1.55771i | ||||
\(7\) | − | 150.607i | − | 1.16172i | −0.814004 | − | 0.580859i | \(-0.802717\pi\) | ||
0.814004 | − | 0.580859i | \(-0.197283\pi\) | |||||||
\(8\) | −30.4253 | + | 178.444i | −0.168077 | + | 0.985774i | ||||
\(9\) | −496.748 | −2.04423 | ||||||||
\(10\) | 94.2398 | + | 186.768i | 0.298012 | + | 0.590613i | ||||
\(11\) | −603.531 | −1.50390 | −0.751948 | − | 0.659223i | \(-0.770885\pi\) | ||||
−0.751948 | + | 0.659223i | \(0.770885\pi\) | |||||||
\(12\) | −700.078 | − | 517.099i | −1.40344 | − | 1.03662i | ||||
\(13\) | 566.677 | 0.929987 | 0.464993 | − | 0.885314i | \(-0.346057\pi\) | ||||
0.464993 | + | 0.885314i | \(0.346057\pi\) | |||||||
\(14\) | 383.795 | + | 760.620i | 0.523334 | + | 1.03716i | ||||
\(15\) | −1005.83 | −1.15424 | ||||||||
\(16\) | −301.073 | − | 978.739i | −0.294017 | − | 0.955800i | ||||
\(17\) | −1989.92 | −1.66999 | −0.834995 | − | 0.550258i | \(-0.814529\pi\) | ||||
−0.834995 | + | 0.550258i | \(0.814529\pi\) | |||||||
\(18\) | 2508.75 | − | 1265.87i | 1.82506 | − | 0.920889i | ||||
\(19\) | 1308.75 | − | 873.651i | 0.831713 | − | 0.555206i | ||||
\(20\) | −951.889 | − | 703.094i | −0.532122 | − | 0.393041i | ||||
\(21\) | −4096.26 | −2.02693 | ||||||||
\(22\) | 3048.04 | − | 1537.99i | 1.34266 | − | 0.677479i | ||||
\(23\) | − | 1465.34i | − | 0.577591i | −0.957391 | − | 0.288795i | \(-0.906745\pi\) | ||
0.957391 | − | 0.288795i | \(-0.0932547\pi\) | |||||||
\(24\) | 4853.38 | + | 827.515i | 1.71995 | + | 0.293257i | ||||
\(25\) | 1757.39 | 0.562365 | ||||||||
\(26\) | −2861.92 | + | 1444.07i | −0.830279 | + | 0.418943i | ||||
\(27\) | 6901.50i | 1.82194i | ||||||||
\(28\) | −3876.60 | − | 2863.37i | −0.934449 | − | 0.690213i | ||||
\(29\) | 4744.43 | 1.04759 | 0.523793 | − | 0.851846i | \(-0.324517\pi\) | ||||
0.523793 | + | 0.851846i | \(0.324517\pi\) | |||||||
\(30\) | 5079.78 | − | 2563.16i | 1.03049 | − | 0.519964i | ||||
\(31\) | 1904.96 | 0.356026 | 0.178013 | − | 0.984028i | \(-0.443033\pi\) | ||||
0.178013 | + | 0.984028i | \(0.443033\pi\) | |||||||
\(32\) | 4014.66 | + | 4175.75i | 0.693065 | + | 0.720875i | ||||
\(33\) | 16415.0i | 2.62395i | ||||||||
\(34\) | 10049.8 | − | 5070.95i | 1.49094 | − | 0.752301i | ||||
\(35\) | −5569.64 | −0.768523 | ||||||||
\(36\) | −9444.26 | + | 12786.2i | −1.21454 | + | 1.64431i | ||||
\(37\) | −9126.91 | −1.09602 | −0.548011 | − | 0.836471i | \(-0.684615\pi\) | ||||
−0.548011 | + | 0.836471i | \(0.684615\pi\) | |||||||
\(38\) | −4383.33 | + | 7747.36i | −0.492431 | + | 0.870352i | ||||
\(39\) | − | 15412.6i | − | 1.62261i | ||||||
\(40\) | 6599.08 | + | 1125.16i | 0.652129 | + | 0.111190i | ||||
\(41\) | − | 2640.62i | − | 0.245327i | −0.992448 | − | 0.122664i | \(-0.960856\pi\) | ||
0.992448 | − | 0.122664i | \(-0.0391436\pi\) | |||||||
\(42\) | 20687.6 | − | 10438.6i | 1.80962 | − | 0.913098i | ||||
\(43\) | 10081.0 | 0.831443 | 0.415721 | − | 0.909492i | \(-0.363529\pi\) | ||||
0.415721 | + | 0.909492i | \(0.363529\pi\) | |||||||
\(44\) | −11474.4 | + | 15534.7i | −0.893511 | + | 1.20969i | ||||
\(45\) | 18370.3i | 1.35234i | ||||||||
\(46\) | 3734.16 | + | 7400.51i | 0.260195 | + | 0.515664i | ||||
\(47\) | − | 20444.0i | − | 1.34996i | −0.737836 | − | 0.674980i | \(-0.764152\pi\) | ||
0.737836 | − | 0.674980i | \(-0.235848\pi\) | |||||||
\(48\) | −26620.0 | + | 8188.68i | −1.66765 | + | 0.512992i | ||||
\(49\) | −5875.55 | −0.349589 | ||||||||
\(50\) | −8875.44 | + | 4478.38i | −0.502071 | + | 0.253335i | ||||
\(51\) | 54122.5i | 2.91375i | ||||||||
\(52\) | 10773.8 | − | 14586.1i | 0.552534 | − | 0.748052i | ||||
\(53\) | −30065.0 | −1.47018 | −0.735092 | − | 0.677967i | \(-0.762861\pi\) | ||||
−0.735092 | + | 0.677967i | \(0.762861\pi\) | |||||||
\(54\) | −17587.2 | − | 34855.0i | −0.820752 | − | 1.62660i | ||||
\(55\) | 22319.3i | 0.994887i | ||||||||
\(56\) | 26875.0 | + | 4582.26i | 1.14519 | + | 0.195259i | ||||
\(57\) | −23761.8 | − | 35595.8i | −0.968707 | − | 1.45115i | ||||
\(58\) | −23961.1 | + | 12090.3i | −0.935269 | + | 0.471919i | ||||
\(59\) | − | 15138.2i | − | 0.566167i | −0.959095 | − | 0.283084i | \(-0.908643\pi\) | ||
0.959095 | − | 0.283084i | \(-0.0913574\pi\) | |||||||
\(60\) | −19123.0 | + | 25889.8i | −0.685768 | + | 0.928431i | ||||
\(61\) | 38264.3i | 1.31665i | 0.752735 | + | 0.658323i | \(0.228734\pi\) | ||||
−0.752735 | + | 0.658323i | \(0.771266\pi\) | |||||||
\(62\) | −9620.72 | + | 4854.43i | −0.317855 | + | 0.160383i | ||||
\(63\) | 74813.8i | 2.37482i | ||||||||
\(64\) | −30916.6 | − | 10858.4i | −0.943500 | − | 0.331373i | ||||
\(65\) | − | 20956.4i | − | 0.615224i | ||||||
\(66\) | −41830.6 | − | 82901.6i | −1.18205 | − | 2.34263i | ||||
\(67\) | 45900.3i | 1.24919i | 0.780949 | + | 0.624595i | \(0.214736\pi\) | ||||
−0.780949 | + | 0.624595i | \(0.785264\pi\) | |||||||
\(68\) | −37832.8 | + | 51220.2i | −0.992192 | + | 1.34329i | ||||
\(69\) | −39854.9 | −1.00776 | ||||||||
\(70\) | 28128.7 | − | 14193.2i | 0.686126 | − | 0.346206i | ||||
\(71\) | 59869.1 | 1.40947 | 0.704737 | − | 0.709468i | \(-0.251065\pi\) | ||||
0.704737 | + | 0.709468i | \(0.251065\pi\) | |||||||
\(72\) | 15113.7 | − | 88641.7i | 0.343589 | − | 2.01515i | ||||
\(73\) | 21567.5 | 0.473688 | 0.236844 | − | 0.971548i | \(-0.423887\pi\) | ||||
0.236844 | + | 0.971548i | \(0.423887\pi\) | |||||||
\(74\) | 46094.1 | − | 23258.2i | 0.978513 | − | 0.493739i | ||||
\(75\) | − | 47798.0i | − | 0.981198i | ||||||
\(76\) | 2394.66 | − | 50297.0i | 0.0475565 | − | 0.998869i | ||||
\(77\) | 90896.1i | 1.74710i | ||||||||
\(78\) | 39276.2 | + | 77839.3i | 0.730960 | + | 1.44865i | ||||
\(79\) | 72787.8 | 1.31217 | 0.656087 | − | 0.754686i | \(-0.272211\pi\) | ||||
0.656087 | + | 0.754686i | \(0.272211\pi\) | |||||||
\(80\) | −36195.0 | + | 11134.1i | −0.632300 | + | 0.194504i | ||||
\(81\) | 66999.5 | 1.13464 | ||||||||
\(82\) | 6729.12 | + | 13336.1i | 0.110516 | + | 0.219025i | ||||
\(83\) | 14628.7 | 0.233083 | 0.116541 | − | 0.993186i | \(-0.462819\pi\) | ||||
0.116541 | + | 0.993186i | \(0.462819\pi\) | |||||||
\(84\) | −77878.9 | + | 105437.i | −1.20426 | + | 1.63040i | ||||
\(85\) | 73589.7i | 1.10476i | ||||||||
\(86\) | −50912.6 | + | 25689.5i | −0.742300 | + | 0.374550i | ||||
\(87\) | − | 129041.i | − | 1.82780i | ||||||
\(88\) | 18362.6 | − | 107696.i | 0.252771 | − | 1.48250i | ||||
\(89\) | 18633.0i | 0.249349i | 0.992198 | + | 0.124675i | \(0.0397887\pi\) | ||||
−0.992198 | + | 0.124675i | \(0.960211\pi\) | |||||||
\(90\) | −46813.4 | − | 92776.7i | −0.609205 | − | 1.20735i | ||||
\(91\) | − | 85345.6i | − | 1.08038i | ||||||
\(92\) | −37717.7 | − | 27859.4i | −0.464596 | − | 0.343164i | ||||
\(93\) | − | 51811.7i | − | 0.621184i | ||||||
\(94\) | 52097.7 | + | 103249.i | 0.608134 | + | 1.20523i | ||||
\(95\) | −32308.7 | − | 48399.3i | −0.367291 | − | 0.550212i | ||||
\(96\) | 113573. | − | 109192.i | 1.25776 | − | 1.20924i | ||||
\(97\) | − | 20961.5i | − | 0.226200i | −0.993584 | − | 0.113100i | \(-0.963922\pi\) | ||
0.993584 | − | 0.113100i | \(-0.0360780\pi\) | |||||||
\(98\) | 29673.6 | − | 14972.7i | 0.312108 | − | 0.157484i | ||||
\(99\) | 299802. | 3.07431 | ||||||||
\(100\) | 33411.8 | − | 45234.8i | 0.334118 | − | 0.452348i | ||||
\(101\) | − | 83763.7i | − | 0.817057i | −0.912745 | − | 0.408529i | \(-0.866042\pi\) | ||
0.912745 | − | 0.408529i | \(-0.133958\pi\) | |||||||
\(102\) | −137921. | − | 273338.i | −1.31259 | − | 2.60135i | ||||
\(103\) | −171162. | −1.58970 | −0.794848 | − | 0.606809i | \(-0.792449\pi\) | ||||
−0.794848 | + | 0.606809i | \(0.792449\pi\) | |||||||
\(104\) | −17241.3 | + | 101120.i | −0.156310 | + | 0.916757i | ||||
\(105\) | 151485.i | 1.34090i | ||||||||
\(106\) | 151839. | − | 76615.1i | 1.31256 | − | 0.662292i | ||||
\(107\) | 106661.i | 0.900628i | 0.892870 | + | 0.450314i | \(0.148688\pi\) | ||||
−0.892870 | + | 0.450314i | \(0.851312\pi\) | |||||||
\(108\) | 177643. | + | 131213.i | 1.46551 | + | 1.08247i | ||||
\(109\) | 74162.6 | 0.597886 | 0.298943 | − | 0.954271i | \(-0.403366\pi\) | ||||
0.298943 | + | 0.954271i | \(0.403366\pi\) | |||||||
\(110\) | −56876.6 | − | 112720.i | −0.448179 | − | 0.888221i | ||||
\(111\) | 248236.i | 1.91231i | ||||||||
\(112\) | −147405. | + | 45343.8i | −1.11037 | + | 0.341565i | ||||
\(113\) | 57356.7i | 0.422560i | 0.977426 | + | 0.211280i | \(0.0677632\pi\) | ||||
−0.977426 | + | 0.211280i | \(0.932237\pi\) | |||||||
\(114\) | 210715. | + | 119219.i | 1.51857 | + | 0.859179i | ||||
\(115\) | −54190.2 | −0.382099 | ||||||||
\(116\) | 90202.1 | − | 122121.i | 0.622403 | − | 0.842645i | ||||
\(117\) | −281495. | −1.90111 | ||||||||
\(118\) | 38576.9 | + | 76453.4i | 0.255048 | + | 0.505466i | ||||
\(119\) | 299697.i | 1.94006i | ||||||||
\(120\) | 30602.5 | − | 179484.i | 0.194001 | − | 1.13782i | ||||
\(121\) | 203198. | 1.26170 | ||||||||
\(122\) | −97509.5 | − | 193248.i | −0.593126 | − | 1.17548i | ||||
\(123\) | −71820.3 | −0.428040 | ||||||||
\(124\) | 36217.4 | − | 49033.2i | 0.211526 | − | 0.286376i | ||||
\(125\) | − | 180557.i | − | 1.03357i | ||||||
\(126\) | −190649. | − | 377836.i | −1.06981 | − | 2.12020i | ||||
\(127\) | 263384. | 1.44904 | 0.724518 | − | 0.689256i | \(-0.242062\pi\) | ||||
0.724518 | + | 0.689256i | \(0.242062\pi\) | |||||||
\(128\) | 183811. | − | 23946.4i | 0.991620 | − | 0.129186i | ||||
\(129\) | − | 274186.i | − | 1.45068i | ||||||
\(130\) | 53403.5 | + | 105837.i | 0.277148 | + | 0.549263i | ||||
\(131\) | 30274.3 | 0.154133 | 0.0770665 | − | 0.997026i | \(-0.475445\pi\) | ||||
0.0770665 | + | 0.997026i | \(0.475445\pi\) | |||||||
\(132\) | 422519. | + | 312085.i | 2.11063 | + | 1.55897i | ||||
\(133\) | −131578. | − | 197108.i | −0.644993 | − | 0.966216i | ||||
\(134\) | −116968. | − | 231813.i | −0.562738 | − | 1.11526i | ||||
\(135\) | 255226. | 1.20529 | ||||||||
\(136\) | 60543.9 | − | 355090.i | 0.280687 | − | 1.64623i | ||||
\(137\) | −249038. | −1.13361 | −0.566807 | − | 0.823851i | \(-0.691821\pi\) | ||||
−0.566807 | + | 0.823851i | \(0.691821\pi\) | |||||||
\(138\) | 201281. | − | 101563.i | 0.899717 | − | 0.453980i | ||||
\(139\) | −423617. | −1.85967 | −0.929837 | − | 0.367972i | \(-0.880052\pi\) | ||||
−0.929837 | + | 0.367972i | \(0.880052\pi\) | |||||||
\(140\) | −105891. | + | 143361.i | −0.456603 | + | 0.618176i | ||||
\(141\) | −556042. | −2.35537 | ||||||||
\(142\) | −302360. | + | 152565.i | −1.25836 | + | 0.634944i | ||||
\(143\) | −342007. | −1.39860 | ||||||||
\(144\) | 149557. | + | 486186.i | 0.601038 | + | 1.95387i | ||||
\(145\) | − | 175455.i | − | 0.693020i | ||||||
\(146\) | −108924. | + | 54960.7i | −0.422902 | + | 0.213388i | ||||
\(147\) | 159805.i | 0.609953i | ||||||||
\(148\) | −173523. | + | 234925.i | −0.651181 | + | 0.881606i | ||||
\(149\) | 14258.2i | 0.0526136i | 0.999654 | + | 0.0263068i | \(0.00837469\pi\) | ||||
−0.999654 | + | 0.0263068i | \(0.991625\pi\) | |||||||
\(150\) | 121804. | + | 241397.i | 0.442013 | + | 0.875999i | ||||
\(151\) | −257437. | −0.918814 | −0.459407 | − | 0.888226i | \(-0.651938\pi\) | ||||
−0.459407 | + | 0.888226i | \(0.651938\pi\) | |||||||
\(152\) | 116079. | + | 260120.i | 0.407515 | + | 0.913198i | ||||
\(153\) | 988489. | 3.41384 | ||||||||
\(154\) | −231632. | − | 459058.i | −0.787039 | − | 1.55979i | ||||
\(155\) | − | 70447.7i | − | 0.235525i | ||||||
\(156\) | −396718. | − | 293028.i | −1.30518 | − | 0.964046i | ||||
\(157\) | − | 588545.i | − | 1.90560i | −0.303605 | − | 0.952798i | \(-0.598190\pi\) | ||
0.303605 | − | 0.952798i | \(-0.401810\pi\) | |||||||
\(158\) | −367605. | + | 185486.i | −1.17149 | + | 0.591111i | ||||
\(159\) | 817717.i | 2.56514i | ||||||||
\(160\) | 154424. | − | 148467.i | 0.476888 | − | 0.458491i | ||||
\(161\) | −220692. | −0.670998 | ||||||||
\(162\) | −338371. | + | 170736.i | −1.01299 | + | 0.511136i | ||||
\(163\) | −410287. | −1.20953 | −0.604767 | − | 0.796402i | \(-0.706734\pi\) | ||||
−0.604767 | + | 0.796402i | \(0.706734\pi\) | |||||||
\(164\) | −67968.9 | − | 50203.9i | −0.197333 | − | 0.145757i | ||||
\(165\) | 607047. | 1.73585 | ||||||||
\(166\) | −73880.1 | + | 37278.5i | −0.208093 | + | 0.105000i | ||||
\(167\) | −130499. | −0.362089 | −0.181045 | − | 0.983475i | \(-0.557948\pi\) | ||||
−0.181045 | + | 0.983475i | \(0.557948\pi\) | |||||||
\(168\) | 124630. | − | 730954.i | 0.340682 | − | 1.99810i | ||||
\(169\) | −50170.7 | −0.135124 | ||||||||
\(170\) | −187530. | − | 371654.i | −0.497677 | − | 0.986318i | ||||
\(171\) | −650120. | + | 433984.i | −1.70021 | + | 1.13497i | ||||
\(172\) | 191662. | − | 259483.i | 0.493986 | − | 0.668786i | ||||
\(173\) | 60471.8 | 0.153616 | 0.0768082 | − | 0.997046i | \(-0.475527\pi\) | ||||
0.0768082 | + | 0.997046i | \(0.475527\pi\) | |||||||
\(174\) | 328836. | + | 651701.i | 0.823391 | + | 1.63183i | ||||
\(175\) | − | 264676.i | − | 0.653309i | ||||||
\(176\) | 181707. | + | 590699.i | 0.442171 | + | 1.43742i | ||||
\(177\) | −411734. | −0.987832 | ||||||||
\(178\) | −47482.8 | − | 94103.4i | −0.112328 | − | 0.222616i | ||||
\(179\) | 202401.i | 0.472150i | 0.971735 | + | 0.236075i | \(0.0758611\pi\) | ||||
−0.971735 | + | 0.236075i | \(0.924139\pi\) | |||||||
\(180\) | 472848. | + | 349260.i | 1.08778 | + | 0.803467i | ||||
\(181\) | −260264. | −0.590498 | −0.295249 | − | 0.955420i | \(-0.595403\pi\) | ||||
−0.295249 | + | 0.955420i | \(0.595403\pi\) | |||||||
\(182\) | 217487. | + | 431026.i | 0.486694 | + | 0.964550i | ||||
\(183\) | 1.04072e6 | 2.29725 | ||||||||
\(184\) | 261482. | + | 44583.5i | 0.569374 | + | 0.0970799i | ||||
\(185\) | 337524.i | 0.725063i | ||||||||
\(186\) | 132032. | + | 261667.i | 0.279832 | + | 0.554584i | ||||
\(187\) | 1.20098e6 | 2.51149 | ||||||||
\(188\) | −526224. | − | 388685.i | −1.08587 | − | 0.802053i | ||||
\(189\) | 1.03942e6 | 2.11658 | ||||||||
\(190\) | 286507. | + | 162101.i | 0.575773 | + | 0.325763i | ||||
\(191\) | − | 33320.5i | − | 0.0660888i | −0.999454 | − | 0.0330444i | \(-0.989480\pi\) | ||
0.999454 | − | 0.0330444i | \(-0.0105203\pi\) | |||||||
\(192\) | −295330. | + | 840879.i | −0.578169 | + | 1.64619i | ||||
\(193\) | − | 689608.i | − | 1.33263i | −0.745671 | − | 0.666314i | \(-0.767871\pi\) | ||
0.745671 | − | 0.666314i | \(-0.232129\pi\) | |||||||
\(194\) | 53416.4 | + | 105863.i | 0.101899 | + | 0.201948i | ||||
\(195\) | −569978. | −1.07342 | ||||||||
\(196\) | −111707. | + | 151235.i | −0.207702 | + | 0.281199i | ||||
\(197\) | 636722.i | 1.16892i | 0.811423 | + | 0.584460i | \(0.198694\pi\) | ||||
−0.811423 | + | 0.584460i | \(0.801306\pi\) | |||||||
\(198\) | −1.51411e6 | + | 763991.i | −2.74469 | + | 1.38492i | ||||
\(199\) | − | 379147.i | − | 0.678695i | −0.940661 | − | 0.339348i | \(-0.889794\pi\) | ||
0.940661 | − | 0.339348i | \(-0.110206\pi\) | |||||||
\(200\) | −53469.0 | + | 313596.i | −0.0945208 | + | 0.554364i | ||||
\(201\) | 1.24841e6 | 2.17955 | ||||||||
\(202\) | 213456. | + | 423037.i | 0.368070 | + | 0.729457i | ||||
\(203\) | − | 714546.i | − | 1.21700i | ||||||
\(204\) | 1.39310e6 | + | 1.02899e6i | 2.34373 | + | 1.73115i | ||||
\(205\) | −97653.3 | −0.162294 | ||||||||
\(206\) | 864428. | − | 436174.i | 1.41926 | − | 0.716130i | ||||
\(207\) | 727906.i | 1.18073i | ||||||||
\(208\) | −170611. | − | 554629.i | −0.273432 | − | 0.888882i | ||||
\(209\) | −789872. | + | 527275.i | −1.25081 | + | 0.834971i | ||||
\(210\) | −386031. | − | 765052.i | −0.604051 | − | 1.19713i | ||||
\(211\) | 1.10273e6i | 1.70515i | 0.522608 | + | 0.852573i | \(0.324959\pi\) | ||||
−0.522608 | + | 0.852573i | \(0.675041\pi\) | |||||||
\(212\) | −571602. | + | 773867.i | −0.873482 | + | 1.18257i | ||||
\(213\) | − | 1.62834e6i | − | 2.45921i | ||||||
\(214\) | −271805. | − | 538675.i | −0.405717 | − | 0.804067i | ||||
\(215\) | − | 372808.i | − | 0.550033i | ||||||
\(216\) | −1.23153e6 | − | 209980.i | −1.79602 | − | 0.306227i | ||||
\(217\) | − | 286901.i | − | 0.413602i | ||||||
\(218\) | −374547. | + | 188989.i | −0.533784 | + | 0.269337i | ||||
\(219\) | − | 586599.i | − | 0.826478i | ||||||
\(220\) | 574494. | + | 424339.i | 0.800256 | + | 0.591093i | ||||
\(221\) | −1.12764e6 | −1.55307 | ||||||||
\(222\) | −632584. | − | 1.25368e6i | −0.861462 | − | 1.70728i | ||||
\(223\) | 12624.3 | 0.0169998 | 0.00849991 | − | 0.999964i | \(-0.497294\pi\) | ||||
0.00849991 | + | 0.999964i | \(0.497294\pi\) | |||||||
\(224\) | 628899. | − | 604637.i | 0.837453 | − | 0.805147i | ||||
\(225\) | −872979. | −1.14960 | ||||||||
\(226\) | −146163. | − | 289672.i | −0.190356 | − | 0.377255i | ||||
\(227\) | − | 581264.i | − | 0.748701i | −0.927287 | − | 0.374351i | \(-0.877866\pi\) | ||
0.927287 | − | 0.374351i | \(-0.122134\pi\) | |||||||
\(228\) | −1.36799e6 | − | 65130.6i | −1.74280 | − | 0.0829752i | ||||
\(229\) | 1.01092e6i | 1.27388i | 0.770915 | + | 0.636938i | \(0.219799\pi\) | ||||
−0.770915 | + | 0.636938i | \(0.780201\pi\) | |||||||
\(230\) | 273680. | − | 138094.i | 0.341133 | − | 0.172129i | ||||
\(231\) | 2.47222e6 | 3.04830 | ||||||||
\(232\) | −144351. | + | 846616.i | −0.176075 | + | 1.03268i | ||||
\(233\) | −722717. | −0.872124 | −0.436062 | − | 0.899917i | \(-0.643627\pi\) | ||||
−0.436062 | + | 0.899917i | \(0.643627\pi\) | |||||||
\(234\) | 1.42165e6 | − | 717338.i | 1.69728 | − | 0.856415i | ||||
\(235\) | −756044. | −0.893053 | ||||||||
\(236\) | −389654. | − | 287811.i | −0.455407 | − | 0.336377i | ||||
\(237\) | − | 1.97971e6i | − | 2.28944i | ||||||
\(238\) | −763721. | − | 1.51357e6i | −0.873962 | − | 1.73205i | ||||
\(239\) | − | 586425.i | − | 0.664076i | −0.943266 | − | 0.332038i | \(-0.892264\pi\) | ||
0.943266 | − | 0.332038i | \(-0.107736\pi\) | |||||||
\(240\) | 302827. | + | 984442.i | 0.339365 | + | 1.10322i | ||||
\(241\) | − | 636052.i | − | 0.705424i | −0.935732 | − | 0.352712i | \(-0.885260\pi\) | ||
0.935732 | − | 0.352712i | \(-0.114740\pi\) | |||||||
\(242\) | −1.02622e6 | + | 517813.i | −1.12643 | + | 0.568374i | ||||
\(243\) | − | 145207.i | − | 0.157751i | ||||||
\(244\) | 984915. | + | 727488.i | 1.05907 | + | 0.782261i | ||||
\(245\) | 217285.i | 0.231267i | ||||||||
\(246\) | 362718. | − | 183021.i | 0.382148 | − | 0.192825i | ||||
\(247\) | 741639. | − | 495077.i | 0.773482 | − | 0.516334i | ||||
\(248\) | −57958.9 | + | 339929.i | −0.0598399 | + | 0.350961i | ||||
\(249\) | − | 397875.i | − | 0.406676i | ||||||
\(250\) | 460115. | + | 911876.i | 0.465604 | + | 0.922753i | ||||
\(251\) | 395054. | 0.395797 | 0.197898 | − | 0.980223i | \(-0.436588\pi\) | ||||
0.197898 | + | 0.980223i | \(0.436588\pi\) | |||||||
\(252\) | 1.92569e6 | + | 1.42237e6i | 1.91023 | + | 1.41095i | ||||
\(253\) | 884380.i | 0.868636i | ||||||||
\(254\) | −1.33018e6 | + | 671184.i | −1.29368 | + | 0.652766i | ||||
\(255\) | 2.00152e6 | 1.92756 | ||||||||
\(256\) | −867286. | + | 589345.i | −0.827108 | + | 0.562043i | ||||
\(257\) | − | 1.32766e6i | − | 1.25388i | −0.779069 | − | 0.626939i | \(-0.784308\pi\) | ||
0.779069 | − | 0.626939i | \(-0.215692\pi\) | |||||||
\(258\) | 698712. | + | 1.38474e6i | 0.653505 | + | 1.29514i | ||||
\(259\) | 1.37458e6i | 1.27327i | ||||||||
\(260\) | −539413. | − | 398427.i | −0.494866 | − | 0.365523i | ||||
\(261\) | −2.35679e6 | −2.14150 | ||||||||
\(262\) | −152896. | + | 77148.4i | −0.137608 | + | 0.0694342i | ||||
\(263\) | 689459.i | 0.614638i | 0.951607 | + | 0.307319i | \(0.0994318\pi\) | ||||
−0.951607 | + | 0.307319i | \(0.900568\pi\) | |||||||
\(264\) | −2.92916e6 | − | 499431.i | −2.58663 | − | 0.441027i | ||||
\(265\) | 1.11184e6i | 0.972586i | ||||||||
\(266\) | 1.16681e6 | + | 660161.i | 1.01110 | + | 0.572066i | ||||
\(267\) | 506787. | 0.435058 | ||||||||
\(268\) | 1.18146e6 | + | 872665.i | 1.00481 | + | 0.742182i | ||||
\(269\) | −977952. | −0.824018 | −0.412009 | − | 0.911180i | \(-0.635173\pi\) | ||||
−0.412009 | + | 0.911180i | \(0.635173\pi\) | |||||||
\(270\) | −1.28898e6 | + | 650396.i | −1.07606 | + | 0.542961i | ||||
\(271\) | − | 1.49359e6i | − | 1.23540i | −0.786413 | − | 0.617701i | \(-0.788064\pi\) | ||
0.786413 | − | 0.617701i | \(-0.211936\pi\) | |||||||
\(272\) | 599112. | + | 1.94761e6i | 0.491005 | + | 1.59618i | ||||
\(273\) | −2.32126e6 | −1.88502 | ||||||||
\(274\) | 1.25773e6 | − | 634628.i | 1.01207 | − | 0.510673i | ||||
\(275\) | −1.06064e6 | −0.845737 | ||||||||
\(276\) | −757729. | + | 1.02586e6i | −0.598744 | + | 0.810613i | ||||
\(277\) | − | 1.32182e6i | − | 1.03507i | −0.855661 | − | 0.517537i | \(-0.826849\pi\) | ||
0.855661 | − | 0.517537i | \(-0.173151\pi\) | |||||||
\(278\) | 2.13942e6 | − | 1.07951e6i | 1.66029 | − | 0.837751i | ||||
\(279\) | −946284. | −0.727798 | ||||||||
\(280\) | 169458. | − | 993870.i | 0.129171 | − | 0.757590i | ||||
\(281\) | 2.25632e6i | 1.70465i | 0.523016 | + | 0.852323i | \(0.324807\pi\) | ||||
−0.523016 | + | 0.852323i | \(0.675193\pi\) | |||||||
\(282\) | 2.80821e6 | − | 1.41697e6i | 2.10284 | − | 1.06105i | ||||
\(283\) | 849766. | 0.630715 | 0.315358 | − | 0.948973i | \(-0.397876\pi\) | ||||
0.315358 | + | 0.948973i | \(0.397876\pi\) | |||||||
\(284\) | 1.13824e6 | − | 1.54102e6i | 0.837412 | − | 1.13374i | ||||
\(285\) | −1.31638e6 | + | 878741.i | −0.959994 | + | 0.640839i | ||||
\(286\) | 1.72726e6 | − | 871540.i | 1.24865 | − | 0.630046i | ||||
\(287\) | −397696. | −0.285001 | ||||||||
\(288\) | −1.99427e6 | − | 2.07430e6i | −1.41678 | − | 1.47363i | ||||
\(289\) | 2.53993e6 | 1.78886 | ||||||||
\(290\) | 447114. | + | 886110.i | 0.312193 | + | 0.618718i | ||||
\(291\) | −570116. | −0.394667 | ||||||||
\(292\) | 410045. | − | 555143.i | 0.281433 | − | 0.381020i | ||||
\(293\) | −1.23388e6 | −0.839659 | −0.419830 | − | 0.907603i | \(-0.637910\pi\) | ||||
−0.419830 | + | 0.907603i | \(0.637910\pi\) | |||||||
\(294\) | −407233. | − | 807072.i | −0.274773 | − | 0.544557i | ||||
\(295\) | −559830. | −0.374542 | ||||||||
\(296\) | 277689. | − | 1.62864e6i | 0.184217 | − | 1.08043i | ||||
\(297\) | − | 4.16527e6i | − | 2.74001i | ||||||
\(298\) | −36334.3 | − | 72008.9i | −0.0237015 | − | 0.0469727i | ||||
\(299\) | − | 830376.i | − | 0.537152i | ||||||
\(300\) | −1.23031e6 | − | 908745.i | −0.789244 | − | 0.582960i | ||||
\(301\) | − | 1.51827e6i | − | 0.965902i | ||||||
\(302\) | 1.30015e6 | − | 656029.i | 0.820304 | − | 0.413910i | ||||
\(303\) | −2.27823e6 | −1.42558 | ||||||||
\(304\) | −1.24911e6 | − | 1.01789e6i | −0.775203 | − | 0.631712i | ||||
\(305\) | 1.41506e6 | 0.871015 | ||||||||
\(306\) | −4.99222e6 | + | 2.51898e6i | −3.04783 | + | 1.53788i | ||||
\(307\) | 19289.4i | 0.0116808i | 0.999983 | + | 0.00584041i | \(0.00185907\pi\) | ||||
−0.999983 | + | 0.00584041i | \(0.998141\pi\) | |||||||
\(308\) | 2.33965e6 | + | 1.72813e6i | 1.40531 | + | 1.03801i | ||||
\(309\) | 4.65531e6i | 2.77366i | ||||||||
\(310\) | 179523. | + | 355786.i | 0.106100 | + | 0.210274i | ||||
\(311\) | − | 696484.i | − | 0.408329i | −0.978937 | − | 0.204165i | \(-0.934552\pi\) | ||
0.978937 | − | 0.204165i | \(-0.0654478\pi\) | |||||||
\(312\) | 2.75029e6 | + | 468933.i | 1.59953 | + | 0.272725i | ||||
\(313\) | −1.56308e6 | −0.901819 | −0.450909 | − | 0.892570i | \(-0.648900\pi\) | ||||
−0.450909 | + | 0.892570i | \(0.648900\pi\) | |||||||
\(314\) | 1.49980e6 | + | 2.97236e6i | 0.858438 | + | 1.70129i | ||||
\(315\) | 2.76671e6 | 1.57104 | ||||||||
\(316\) | 1.38386e6 | − | 1.87354e6i | 0.779603 | − | 1.05547i | ||||
\(317\) | 1.55098e6 | 0.866880 | 0.433440 | − | 0.901183i | \(-0.357300\pi\) | ||||
0.433440 | + | 0.901183i | \(0.357300\pi\) | |||||||
\(318\) | −2.08380e6 | − | 4.12976e6i | −1.15555 | − | 2.29011i | ||||
\(319\) | −2.86341e6 | −1.57546 | ||||||||
\(320\) | −401557. | + | 1.14333e6i | −0.219216 | + | 0.624163i | ||||
\(321\) | 2.90099e6 | 1.57139 | ||||||||
\(322\) | 1.11457e6 | − | 562391.i | 0.599057 | − | 0.302273i | ||||
\(323\) | −2.60431e6 | + | 1.73850e6i | −1.38895 | + | 0.927188i | ||||
\(324\) | 1.27381e6 | − | 1.72455e6i | 0.674126 | − | 0.912670i | ||||
\(325\) | 995871. | 0.522992 | ||||||||
\(326\) | 2.07209e6 | − | 1.04554e6i | 1.07985 | − | 0.544874i | ||||
\(327\) | − | 2.01710e6i | − | 1.04317i | ||||||
\(328\) | 471203. | + | 80341.5i | 0.241837 | + | 0.0412340i | ||||
\(329\) | −3.07901e6 | −1.56827 | ||||||||
\(330\) | −3.06580e6 | + | 1.54695e6i | −1.54974 | + | 0.781971i | ||||
\(331\) | 515679.i | 0.258708i | 0.991598 | + | 0.129354i | \(0.0412903\pi\) | ||||
−0.991598 | + | 0.129354i | \(0.958710\pi\) | |||||||
\(332\) | 278123. | − | 376539.i | 0.138482 | − | 0.187484i | ||||
\(333\) | 4.53377e6 | 2.24052 | ||||||||
\(334\) | 659066. | − | 332552.i | 0.323268 | − | 0.163115i | ||||
\(335\) | 1.69745e6 | 0.826389 | ||||||||
\(336\) | 1.23328e6 | + | 4.00917e6i | 0.595953 | + | 1.93734i | ||||
\(337\) | 180334.i | 0.0864972i | 0.999064 | + | 0.0432486i | \(0.0137708\pi\) | ||||
−0.999064 | + | 0.0432486i | \(0.986229\pi\) | |||||||
\(338\) | 253380. | − | 127851.i | 0.120637 | − | 0.0608712i | ||||
\(339\) | 1.56001e6 | 0.737271 | ||||||||
\(340\) | 1.89418e6 | + | 1.39910e6i | 0.888638 | + | 0.656375i | ||||
\(341\) | −1.14970e6 | −0.535425 | ||||||||
\(342\) | 2.17741e6 | − | 3.84848e6i | 1.00664 | − | 1.77920i | ||||
\(343\) | − | 1.64636e6i | − | 0.755594i | ||||||
\(344\) | −306717. | + | 1.79889e6i | −0.139747 | + | 0.819614i | ||||
\(345\) | 1.47388e6i | 0.666676i | ||||||||
\(346\) | −305404. | + | 154101.i | −0.137146 | + | 0.0692015i | ||||
\(347\) | 2.02177e6 | 0.901379 | 0.450690 | − | 0.892681i | \(-0.351178\pi\) | ||||
0.450690 | + | 0.892681i | \(0.351178\pi\) | |||||||
\(348\) | −3.32148e6 | − | 2.45334e6i | −1.47022 | − | 1.08595i | ||||
\(349\) | 3.23137e6i | 1.42011i | 0.704144 | + | 0.710057i | \(0.251331\pi\) | ||||
−0.704144 | + | 0.710057i | \(0.748669\pi\) | |||||||
\(350\) | 674477. | + | 1.33671e6i | 0.294304 | + | 0.583265i | ||||
\(351\) | 3.91092e6i | 1.69438i | ||||||||
\(352\) | −2.42297e6 | − | 2.52019e6i | −1.04230 | − | 1.08412i | ||||
\(353\) | 368290. | 0.157309 | 0.0786545 | − | 0.996902i | \(-0.474938\pi\) | ||||
0.0786545 | + | 0.996902i | \(0.474938\pi\) | |||||||
\(354\) | 2.07940e6 | − | 1.04923e6i | 0.881922 | − | 0.445001i | ||||
\(355\) | − | 2.21403e6i | − | 0.932424i | ||||||
\(356\) | 479610. | + | 354255.i | 0.200569 | + | 0.148146i | ||||
\(357\) | 8.15124e6 | 3.38496 | ||||||||
\(358\) | −515781. | − | 1.02220e6i | −0.212695 | − | 0.421529i | ||||
\(359\) | 61762.2i | 0.0252922i | 0.999920 | + | 0.0126461i | \(0.00402549\pi\) | ||||
−0.999920 | + | 0.0126461i | \(0.995975\pi\) | |||||||
\(360\) | −3.27808e6 | − | 558922.i | −1.33310 | − | 0.227298i | ||||
\(361\) | 949567. | − | 2.28679e6i | 0.383493 | − | 0.923544i | ||||
\(362\) | 1.31443e6 | − | 663236.i | 0.527188 | − | 0.266009i | ||||
\(363\) | − | 5.52665e6i | − | 2.20138i | ||||||
\(364\) | −2.19678e6 | − | 1.62261e6i | −0.869026 | − | 0.641889i | ||||
\(365\) | − | 797592.i | − | 0.313364i | ||||||
\(366\) | −5.25603e6 | + | 2.65209e6i | −2.05095 | + | 1.03487i | ||||
\(367\) | 529501.i | 0.205211i | 0.994722 | + | 0.102606i | \(0.0327180\pi\) | ||||
−0.994722 | + | 0.102606i | \(0.967282\pi\) | |||||||
\(368\) | −1.43419e6 | + | 441176.i | −0.552061 | + | 0.169821i | ||||
\(369\) | 1.31172e6i | 0.501505i | ||||||||
\(370\) | −860118. | − | 1.70462e6i | −0.326628 | − | 0.647325i | ||||
\(371\) | 4.52801e6i | 1.70794i | ||||||||
\(372\) | −1.33362e6 | − | 985053.i | −0.499661 | − | 0.369064i | ||||
\(373\) | −4.19693e6 | −1.56192 | −0.780961 | − | 0.624580i | \(-0.785270\pi\) | ||||
−0.780961 | + | 0.624580i | \(0.785270\pi\) | |||||||
\(374\) | −6.06537e6 | + | 3.06047e6i | −2.24222 | + | 1.13138i | ||||
\(375\) | −4.91084e6 | −1.80334 | ||||||||
\(376\) | 3.64811e6 | + | 622014.i | 1.33076 | + | 0.226898i | ||||
\(377\) | 2.68856e6 | 0.974241 | ||||||||
\(378\) | −5.24942e6 | + | 2.64876e6i | −1.88965 | + | 0.953483i | ||||
\(379\) | − | 870364.i | − | 0.311245i | −0.987817 | − | 0.155623i | \(-0.950262\pi\) | ||
0.987817 | − | 0.155623i | \(-0.0497384\pi\) | |||||||
\(380\) | −1.86005e6 | − | 88557.4i | −0.660792 | − | 0.0314605i | ||||
\(381\) | − | 7.16358e6i | − | 2.52824i | ||||||
\(382\) | 84911.0 | + | 168280.i | 0.0297718 | + | 0.0590031i | ||||
\(383\) | 3.88095e6 | 1.35189 | 0.675945 | − | 0.736952i | \(-0.263736\pi\) | ||||
0.675945 | + | 0.736952i | \(0.263736\pi\) | |||||||
\(384\) | −651300. | − | 4.99933e6i | −0.225400 | − | 1.73015i | ||||
\(385\) | 3.36145e6 | 1.15578 | ||||||||
\(386\) | 1.75734e6 | + | 3.48276e6i | 0.600325 | + | 1.18975i | ||||
\(387\) | −5.00771e6 | −1.69966 | ||||||||
\(388\) | −539543. | − | 398523.i | −0.181948 | − | 0.134392i | ||||
\(389\) | − | 55797.8i | − | 0.0186958i | −0.999956 | − | 0.00934788i | \(-0.997024\pi\) | ||
0.999956 | − | 0.00934788i | \(-0.00297557\pi\) | |||||||
\(390\) | 2.87859e6 | − | 1.45248e6i | 0.958338 | − | 0.483559i | ||||
\(391\) | 2.91592e6i | 0.964570i | ||||||||
\(392\) | 178765. | − | 1.04846e6i | 0.0587580 | − | 0.344616i | ||||
\(393\) | − | 823409.i | − | 0.268927i | ||||||
\(394\) | −1.62257e6 | − | 3.21568e6i | −0.526578 | − | 1.04359i | ||||
\(395\) | − | 2.69178e6i | − | 0.868055i | ||||||
\(396\) | 5.69990e6 | − | 7.71685e6i | 1.82654 | − | 2.47287i | ||||
\(397\) | 2.63936e6i | 0.840470i | 0.907415 | + | 0.420235i | \(0.138052\pi\) | ||||
−0.907415 | + | 0.420235i | \(0.861948\pi\) | |||||||
\(398\) | 966185. | + | 1.91483e6i | 0.305740 | + | 0.605929i | ||||
\(399\) | −5.36099e6 | + | 3.57870e6i | −1.68583 | + | 1.12536i | ||||
\(400\) | −529103. | − | 1.72003e6i | −0.165345 | − | 0.537508i | ||||
\(401\) | 4.73912e6i | 1.47176i | 0.677112 | + | 0.735880i | \(0.263231\pi\) | ||||
−0.677112 | + | 0.735880i | \(0.736769\pi\) | |||||||
\(402\) | −6.30491e6 | + | 3.18134e6i | −1.94587 | + | 0.981849i | ||||
\(403\) | 1.07950e6 | 0.331099 | ||||||||
\(404\) | −2.15606e6 | − | 1.59253e6i | −0.657215 | − | 0.485439i | ||||
\(405\) | − | 2.47772e6i | − | 0.750611i | ||||||
\(406\) | 1.82089e6 | + | 3.60871e6i | 0.548237 | + | 1.08652i | ||||
\(407\) | 5.50837e6 | 1.64830 | ||||||||
\(408\) | −9.65784e6 | − | 1.64669e6i | −2.87230 | − | 0.489735i | ||||
\(409\) | − | 1.03043e6i | − | 0.304585i | −0.988335 | − | 0.152293i | \(-0.951334\pi\) | ||
0.988335 | − | 0.152293i | \(-0.0486656\pi\) | |||||||
\(410\) | 493184. | − | 248851.i | 0.144894 | − | 0.0731106i | ||||
\(411\) | 6.77342e6i | 1.97790i | ||||||||
\(412\) | −3.25416e6 | + | 4.40567e6i | −0.944487 | + | 1.27870i | ||||
\(413\) | −2.27992e6 | −0.657727 | ||||||||
\(414\) | −1.85493e6 | − | 3.67619e6i | −0.531897 | − | 1.05414i | ||||
\(415\) | − | 540987.i | − | 0.154194i | ||||||
\(416\) | 2.27502e6 | + | 2.36630e6i | 0.644542 | + | 0.670404i | ||||
\(417\) | 1.15217e7i | 3.24471i | ||||||||
\(418\) | 2.64547e6 | − | 4.67577e6i | 0.740564 | − | 1.30892i | ||||
\(419\) | 792428. | 0.220508 | 0.110254 | − | 0.993903i | \(-0.464834\pi\) | ||||
0.110254 | + | 0.993903i | \(0.464834\pi\) | |||||||
\(420\) | 3.89919e6 | + | 2.88006e6i | 1.07858 | + | 0.796669i | ||||
\(421\) | −408226. | −0.112252 | −0.0561262 | − | 0.998424i | \(-0.517875\pi\) | ||||
−0.0561262 | + | 0.998424i | \(0.517875\pi\) | |||||||
\(422\) | −2.81009e6 | − | 5.56916e6i | −0.768139 | − | 1.52233i | ||||
\(423\) | 1.01555e7i | 2.75963i | ||||||||
\(424\) | 914736. | − | 5.36492e6i | 0.247105 | − | 1.44927i | ||||
\(425\) | −3.49707e6 | −0.939143 | ||||||||
\(426\) | 4.14952e6 | + | 8.22369e6i | 1.10783 | + | 2.19555i | ||||
\(427\) | 5.76288e6 | 1.52957 | ||||||||
\(428\) | 2.74543e6 | + | 2.02786e6i | 0.724437 | + | 0.535091i | ||||
\(429\) | 9.30200e6i | 2.44024i | ||||||||
\(430\) | 950031. | + | 1.88281e6i | 0.247780 | + | 0.491061i | ||||
\(431\) | 1.00984e6 | 0.261854 | 0.130927 | − | 0.991392i | \(-0.458205\pi\) | ||||
0.130927 | + | 0.991392i | \(0.458205\pi\) | |||||||
\(432\) | 6.75477e6 | − | 2.07786e6i | 1.74141 | − | 0.535681i | ||||
\(433\) | − | 1.59950e6i | − | 0.409982i | −0.978764 | − | 0.204991i | \(-0.934283\pi\) | ||
0.978764 | − | 0.204991i | \(-0.0657165\pi\) | |||||||
\(434\) | 731113. | + | 1.44895e6i | 0.186320 | + | 0.369257i | ||||
\(435\) | −4.77208e6 | −1.20916 | ||||||||
\(436\) | 1.40999e6 | − | 1.90893e6i | 0.355223 | − | 0.480921i | ||||
\(437\) | −1.28020e6 | − | 1.91777e6i | −0.320682 | − | 0.480390i | ||||
\(438\) | 1.49484e6 | + | 2.96253e6i | 0.372314 | + | 0.737867i | ||||
\(439\) | −6.61321e6 | −1.63776 | −0.818882 | − | 0.573962i | \(-0.805406\pi\) | ||||
−0.818882 | + | 0.573962i | \(0.805406\pi\) | |||||||
\(440\) | −3.98275e6 | − | 679070.i | −0.980734 | − | 0.167218i | ||||
\(441\) | 2.91866e6 | 0.714640 | ||||||||
\(442\) | 5.69499e6 | − | 2.87359e6i | 1.38656 | − | 0.699630i | ||||
\(443\) | 2.90633e6 | 0.703617 | 0.351808 | − | 0.936072i | \(-0.385567\pi\) | ||||
0.351808 | + | 0.936072i | \(0.385567\pi\) | |||||||
\(444\) | 6.38955e6 | + | 4.71952e6i | 1.53820 | + | 1.13616i | ||||
\(445\) | 689072. | 0.164955 | ||||||||
\(446\) | −63757.1 | + | 32170.6i | −0.0151772 | + | 0.00765812i | ||||
\(447\) | 387798. | 0.0917988 | ||||||||
\(448\) | −1.63536e6 | + | 4.65627e6i | −0.384962 | + | 1.09608i | ||||
\(449\) | 1.22462e6i | 0.286671i | 0.989674 | + | 0.143336i | \(0.0457828\pi\) | ||||
−0.989674 | + | 0.143336i | \(0.954217\pi\) | |||||||
\(450\) | 4.40885e6 | − | 2.22462e6i | 1.02635 | − | 0.517876i | ||||
\(451\) | 1.59369e6i | 0.368947i | ||||||||
\(452\) | 1.47635e6 | + | 1.09048e6i | 0.339894 | + | 0.251056i | ||||
\(453\) | 7.00184e6i | 1.60312i | ||||||||
\(454\) | 1.48124e6 | + | 2.93559e6i | 0.337277 | + | 0.668429i | ||||
\(455\) | −3.15618e6 | −0.714717 | ||||||||
\(456\) | 7.07483e6 | − | 3.15714e6i | 1.59332 | − | 0.711021i | ||||
\(457\) | −3.30328e6 | −0.739869 | −0.369935 | − | 0.929058i | \(-0.620620\pi\) | ||||
−0.369935 | + | 0.929058i | \(0.620620\pi\) | |||||||
\(458\) | −2.57614e6 | − | 5.10549e6i | −0.573859 | − | 1.13730i | ||||
\(459\) | − | 1.37334e7i | − | 3.04262i | ||||||
\(460\) | −1.03027e6 | + | 1.39484e6i | −0.227017 | + | 0.307349i | ||||
\(461\) | − | 7.00106e6i | − | 1.53430i | −0.641465 | − | 0.767152i | \(-0.721673\pi\) | ||
0.641465 | − | 0.767152i | \(-0.278327\pi\) | |||||||
\(462\) | −1.24856e7 | + | 6.29999e6i | −2.72147 | + | 1.37320i | ||||
\(463\) | − | 3.15394e6i | − | 0.683755i | −0.939745 | − | 0.341878i | \(-0.888937\pi\) | ||
0.939745 | − | 0.341878i | \(-0.111063\pi\) | |||||||
\(464\) | −1.42842e6 | − | 4.64357e6i | −0.308008 | − | 1.00128i | ||||
\(465\) | −1.91606e6 | −0.410938 | ||||||||
\(466\) | 3.64998e6 | − | 1.84171e6i | 0.778620 | − | 0.392877i | ||||
\(467\) | 2.07779e6 | 0.440869 | 0.220435 | − | 0.975402i | \(-0.429252\pi\) | ||||
0.220435 | + | 0.975402i | \(0.429252\pi\) | |||||||
\(468\) | −5.35184e6 | + | 7.24563e6i | −1.12951 | + | 1.52919i | ||||
\(469\) | 6.91291e6 | 1.45121 | ||||||||
\(470\) | 3.81829e6 | − | 1.92664e6i | 0.797305 | − | 0.402305i | ||||
\(471\) | −1.60074e7 | −3.32483 | ||||||||
\(472\) | 2.70132e6 | + | 460584.i | 0.558113 | + | 0.0951599i | ||||
\(473\) | −6.08419e6 | −1.25040 | ||||||||
\(474\) | 5.04491e6 | + | 9.99822e6i | 1.03135 | + | 2.04398i | ||||
\(475\) | 2.29999e6 | − | 1.53534e6i | 0.467726 | − | 0.312228i | ||||
\(476\) | 7.71413e6 | + | 5.69789e6i | 1.56052 | + | 1.15265i | ||||
\(477\) | 1.49347e7 | 3.00539 | ||||||||
\(478\) | 1.49440e6 | + | 2.96166e6i | 0.299155 | + | 0.592877i | ||||
\(479\) | − | 8.24274e6i | − | 1.64147i | −0.571310 | − | 0.820734i | \(-0.693565\pi\) | ||
0.571310 | − | 0.820734i | \(-0.306435\pi\) | |||||||
\(480\) | −4.03805e6 | − | 4.20008e6i | −0.799961 | − | 0.832060i | ||||
\(481\) | −5.17201e6 | −1.01929 | ||||||||
\(482\) | 1.62086e6 | + | 3.21229e6i | 0.317781 | + | 0.629792i | ||||
\(483\) | 6.00243e6i | 1.17074i | ||||||||
\(484\) | 3.86324e6 | − | 5.23028e6i | 0.749616 | − | 1.01487i | ||||
\(485\) | −775180. | −0.149640 | ||||||||
\(486\) | 370032. | + | 733345.i | 0.0710639 | + | 0.140837i | ||||
\(487\) | −2.01001e6 | −0.384039 | −0.192020 | − | 0.981391i | \(-0.561504\pi\) | ||||
−0.192020 | + | 0.981391i | \(0.561504\pi\) | |||||||
\(488\) | −6.82804e6 | − | 1.16420e6i | −1.29792 | − | 0.221299i | ||||
\(489\) | 1.11591e7i | 2.11036i | ||||||||
\(490\) | −553710. | − | 1.09737e6i | −0.104182 | − | 0.206472i | ||||
\(491\) | −6.35888e6 | −1.19036 | −0.595178 | − | 0.803594i | \(-0.702918\pi\) | ||||
−0.595178 | + | 0.803594i | \(0.702918\pi\) | |||||||
\(492\) | −1.36546e6 | + | 1.84864e6i | −0.254312 | + | 0.344302i | ||||
\(493\) | −9.44105e6 | −1.74946 | ||||||||
\(494\) | −2.48393e6 | + | 4.39025e6i | −0.457954 | + | 0.809416i | ||||
\(495\) | − | 1.10871e7i | − | 2.03378i | ||||||
\(496\) | −573532. | − | 1.86446e6i | −0.104678 | − | 0.340290i | ||||
\(497\) | − | 9.01673e6i | − | 1.63741i | ||||||
\(498\) | 1.01391e6 | + | 2.00941e6i | 0.183201 | + | 0.363074i | ||||
\(499\) | −1.82256e6 | −0.327665 | −0.163833 | − | 0.986488i | \(-0.552386\pi\) | ||||
−0.163833 | + | 0.986488i | \(0.552386\pi\) | |||||||
\(500\) | −4.64749e6 | − | 3.43278e6i | −0.831369 | − | 0.614074i | ||||
\(501\) | 3.54935e6i | 0.631763i | ||||||||
\(502\) | −1.99516e6 | + | 1.00672e6i | −0.353361 | + | 0.178299i | ||||
\(503\) | − | 5.97846e6i | − | 1.05358i | −0.849994 | − | 0.526792i | \(-0.823395\pi\) | ||
0.849994 | − | 0.526792i | \(-0.176605\pi\) | |||||||
\(504\) | −1.33501e7 | − | 2.27623e6i | −2.34103 | − | 0.399153i | ||||
\(505\) | −3.09769e6 | −0.540516 | ||||||||
\(506\) | −2.25368e6 | − | 4.46644e6i | −0.391305 | − | 0.775505i | ||||
\(507\) | 1.36456e6i | 0.235761i | ||||||||
\(508\) | 5.00750e6 | − | 6.77944e6i | 0.860917 | − | 1.16556i | ||||
\(509\) | 4.68133e6 | 0.800894 | 0.400447 | − | 0.916320i | \(-0.368855\pi\) | ||||
0.400447 | + | 0.916320i | \(0.368855\pi\) | |||||||
\(510\) | −1.01084e7 | + | 5.10049e6i | −1.72090 | + | 0.868333i | ||||
\(511\) | − | 3.24822e6i | − | 0.550292i | ||||||
\(512\) | 2.87827e6 | − | 5.18652e6i | 0.485239 | − | 0.874381i | ||||
\(513\) | 6.02950e6 | + | 9.03236e6i | 1.01155 | + | 1.51533i | ||||
\(514\) | 3.38330e6 | + | 6.70517e6i | 0.564850 | + | 1.11944i | ||||
\(515\) | 6.32977e6i | 1.05165i | ||||||||
\(516\) | −7.05749e6 | − | 5.21288e6i | −1.16688 | − | 0.861893i | ||||
\(517\) | 1.23386e7i | 2.03020i | ||||||||
\(518\) | −3.50286e6 | − | 6.94211e6i | −0.573586 | − | 1.13676i | ||||
\(519\) | − | 1.64473e6i | − | 0.268026i | ||||||
\(520\) | 3.73954e6 | + | 637604.i | 0.606471 | + | 0.103405i | ||||
\(521\) | 2.59329e6i | 0.418559i | 0.977856 | + | 0.209280i | \(0.0671119\pi\) | ||||
−0.977856 | + | 0.209280i | \(0.932888\pi\) | |||||||
\(522\) | 1.19026e7 | − | 6.00583e6i | 1.91190 | − | 0.964710i | ||||
\(523\) | − | 1.21768e7i | − | 1.94661i | −0.229511 | − | 0.973306i | \(-0.573713\pi\) | ||
0.229511 | − | 0.973306i | \(-0.426287\pi\) | |||||||
\(524\) | 575580. | − | 779253.i | 0.0915751 | − | 0.123980i | ||||
\(525\) | −7.19873e6 | −1.13988 | ||||||||
\(526\) | −1.75696e6 | − | 3.48201e6i | −0.276884 | − | 0.548739i | ||||
\(527\) | −3.79072e6 | −0.594559 | ||||||||
\(528\) | 1.60660e7 | − | 4.94212e6i | 2.50798 | − | 0.771487i | ||||
\(529\) | 4.28911e6 | 0.666389 | ||||||||
\(530\) | −2.83332e6 | − | 5.61519e6i | −0.438133 | − | 0.868310i | ||||
\(531\) | 7.51987e6i | 1.15737i | ||||||||
\(532\) | −7.57510e6 | − | 360653.i | −1.16040 | − | 0.0552472i | ||||
\(533\) | − | 1.49638e6i | − | 0.228151i | ||||||
\(534\) | −2.55945e6 | + | 1.29145e6i | −0.388413 | + | 0.195986i | ||||
\(535\) | 3.94445e6 | 0.595802 | ||||||||
\(536\) | −8.19063e6 | − | 1.39653e6i | −1.23142 | − | 0.209960i | ||||
\(537\) | 5.50496e6 | 0.823794 | ||||||||
\(538\) | 4.93900e6 | − | 2.49213e6i | 0.735671 | − | 0.371206i | ||||
\(539\) | 3.54607e6 | 0.525746 | ||||||||
\(540\) | 4.85240e6 | − | 6.56946e6i | 0.716098 | − | 0.969495i | ||||
\(541\) | 2.89110e6i | 0.424688i | 0.977195 | + | 0.212344i | \(0.0681097\pi\) | ||||
−0.977195 | + | 0.212344i | \(0.931890\pi\) | |||||||
\(542\) | 3.80614e6 | + | 7.54316e6i | 0.556527 | + | 1.10295i | ||||
\(543\) | 7.07875e6i | 1.03028i | ||||||||
\(544\) | −7.98886e6 | − | 8.30942e6i | −1.15741 | − | 1.20385i | ||||
\(545\) | − | 2.74262e6i | − | 0.395526i | ||||||
\(546\) | 1.17232e7 | − | 5.91529e6i | 1.68292 | − | 0.849169i | ||||
\(547\) | − | 5.14595e6i | − | 0.735355i | −0.929953 | − | 0.367678i | \(-0.880153\pi\) | ||
0.929953 | − | 0.367678i | \(-0.119847\pi\) | |||||||
\(548\) | −4.73477e6 | + | 6.41020e6i | −0.673515 | + | 0.911843i | ||||
\(549\) | − | 1.90077e7i | − | 2.69153i | ||||||
\(550\) | 5.35660e6 | − | 2.70284e6i | 0.755062 | − | 0.380990i | ||||
\(551\) | 6.20929e6 | − | 4.14498e6i | 0.871290 | − | 0.581625i | ||||
\(552\) | 1.21259e6 | − | 7.11187e6i | 0.169382 | − | 0.993427i | ||||
\(553\) | − | 1.09624e7i | − | 1.52438i | ||||||
\(554\) | 3.36840e6 | + | 6.67564e6i | 0.466283 | + | 0.924100i | ||||
\(555\) | 9.18009e6 | 1.26507 | ||||||||
\(556\) | −8.05389e6 | + | 1.09038e7i | −1.10489 | + | 1.49586i | ||||
\(557\) | 1.15665e7i | 1.57967i | 0.613323 | + | 0.789833i | \(0.289833\pi\) | ||||
−0.613323 | + | 0.789833i | \(0.710167\pi\) | |||||||
\(558\) | 4.77907e6 | − | 2.41143e6i | 0.649767 | − | 0.327860i | ||||
\(559\) | 5.71266e6 | 0.773231 | ||||||||
\(560\) | 1.67687e6 | + | 5.45123e6i | 0.225959 | + | 0.734555i | ||||
\(561\) | − | 3.26646e7i | − | 4.38197i | ||||||
\(562\) | −5.74980e6 | − | 1.13952e7i | −0.767913 | − | 1.52188i | ||||
\(563\) | 1.26700e7i | 1.68463i | 0.538986 | + | 0.842315i | \(0.318807\pi\) | ||||
−0.538986 | + | 0.842315i | \(0.681193\pi\) | |||||||
\(564\) | −1.05716e7 | + | 1.43124e7i | −1.39940 | + | 1.89459i | ||||
\(565\) | 2.12112e6 | 0.279540 | ||||||||
\(566\) | −4.29162e6 | + | 2.16547e6i | −0.563093 | + | 0.284126i | ||||
\(567\) | − | 1.00906e7i | − | 1.31813i | ||||||
\(568\) | −1.82153e6 | + | 1.06833e7i | −0.236901 | + | 1.38942i | ||||
\(569\) | − | 6.08549e6i | − | 0.787980i | −0.919115 | − | 0.393990i | \(-0.871094\pi\) | ||
0.919115 | − | 0.393990i | \(-0.128906\pi\) | |||||||
\(570\) | 4.40887e6 | − | 7.79250e6i | 0.568381 | − | 1.00459i | ||||
\(571\) | 9.25086e6 | 1.18739 | 0.593693 | − | 0.804692i | \(-0.297669\pi\) | ||||
0.593693 | + | 0.804692i | \(0.297669\pi\) | |||||||
\(572\) | −6.50229e6 | + | 8.80318e6i | −0.830953 | + | 1.12499i | ||||
\(573\) | −906260. | −0.115310 | ||||||||
\(574\) | 2.00851e6 | − | 1.01345e6i | 0.254445 | − | 0.128388i | ||||
\(575\) | − | 2.57518e6i | − | 0.324817i | ||||||
\(576\) | 1.53577e7 | + | 5.39389e6i | 1.92873 | + | 0.677401i | ||||
\(577\) | −3.88697e6 | −0.486040 | −0.243020 | − | 0.970021i | \(-0.578138\pi\) | ||||
−0.243020 | + | 0.970021i | \(0.578138\pi\) | |||||||
\(578\) | −1.28276e7 | + | 6.47254e6i | −1.59707 | + | 0.805852i | ||||
\(579\) | −1.87562e7 | −2.32513 | ||||||||
\(580\) | −4.51617e6 | − | 3.33578e6i | −0.557443 | − | 0.411745i | ||||
\(581\) | − | 2.20319e6i | − | 0.270776i | ||||||
\(582\) | 2.87929e6 | − | 1.45283e6i | 0.352353 | − | 0.177791i | ||||
\(583\) | 1.81452e7 | 2.21100 | ||||||||
\(584\) | −656196. | + | 3.84859e6i | −0.0796163 | + | 0.466949i | ||||
\(585\) | 1.04100e7i | 1.25766i | ||||||||
\(586\) | 6.23152e6 | − | 3.14431e6i | 0.749635 | − | 0.378252i | ||||
\(587\) | 2.42989e6 | 0.291066 | 0.145533 | − | 0.989353i | \(-0.453510\pi\) | ||||
0.145533 | + | 0.989353i | \(0.453510\pi\) | |||||||
\(588\) | 4.11334e6 | + | 3.03824e6i | 0.490627 | + | 0.362392i | ||||
\(589\) | 2.49312e6 | − | 1.66427e6i | 0.296111 | − | 0.197668i | ||||
\(590\) | 2.82734e6 | − | 1.42662e6i | 0.334386 | − | 0.168725i | ||||
\(591\) | 1.73178e7 | 2.03950 | ||||||||
\(592\) | 2.74787e6 | + | 8.93287e6i | 0.322249 | + | 1.04758i | ||||
\(593\) | −1.21632e7 | −1.42040 | −0.710199 | − | 0.704001i | \(-0.751395\pi\) | ||||
−0.710199 | + | 0.704001i | \(0.751395\pi\) | |||||||
\(594\) | 1.06144e7 | + | 2.10361e7i | 1.23433 | + | 2.44624i | ||||
\(595\) | 1.10831e7 | 1.28343 | ||||||||
\(596\) | 367002. | + | 271079.i | 0.0423207 | + | 0.0312594i | ||||
\(597\) | −1.03121e7 | −1.18417 | ||||||||
\(598\) | 2.11606e6 | + | 4.19370e6i | 0.241977 | + | 0.479561i | ||||
\(599\) | 7.66883e6 | 0.873297 | 0.436649 | − | 0.899632i | \(-0.356165\pi\) | ||||
0.436649 | + | 0.899632i | \(0.356165\pi\) | |||||||
\(600\) | 8.52927e6 | + | 1.45427e6i | 0.967239 | + | 0.164917i | ||||
\(601\) | 925541.i | 0.104522i | 0.998633 | + | 0.0522612i | \(0.0166429\pi\) | ||||
−0.998633 | + | 0.0522612i | \(0.983357\pi\) | |||||||
\(602\) | 3.86903e6 | + | 7.66781e6i | 0.435122 | + | 0.862343i | ||||
\(603\) | − | 2.28008e7i | − | 2.55363i | ||||||
\(604\) | −4.89443e6 | + | 6.62636e6i | −0.545896 | + | 0.739065i | ||||
\(605\) | − | 7.51452e6i | − | 0.834666i | ||||||
\(606\) | 1.15059e7 | − | 5.80565e6i | 1.27274 | − | 0.642198i | ||||
\(607\) | −3.05032e6 | −0.336027 | −0.168013 | − | 0.985785i | \(-0.553735\pi\) | ||||
−0.168013 | + | 0.985785i | \(0.553735\pi\) | |||||||
\(608\) | 8.90235e6 | + | 1.95761e6i | 0.976665 | + | 0.214767i | ||||
\(609\) | −1.94344e7 | −2.12339 | ||||||||
\(610\) | −7.14656e6 | + | 3.60602e6i | −0.777629 | + | 0.392377i | ||||
\(611\) | − | 1.15851e7i | − | 1.25545i | ||||||
\(612\) | 1.87933e7 | − | 2.54435e7i | 2.02827 | − | 2.74598i | ||||
\(613\) | 9.58896e6i | 1.03067i | 0.856988 | + | 0.515336i | \(0.172333\pi\) | ||||
−0.856988 | + | 0.515336i | \(0.827667\pi\) | |||||||
\(614\) | −49155.5 | − | 97418.4i | −0.00526200 | − | 0.0104285i | ||||
\(615\) | 2.65600e6i | 0.283166i | ||||||||
\(616\) | −1.62199e7 | − | 2.76554e6i | −1.72225 | − | 0.293648i | ||||
\(617\) | 1.60113e7 | 1.69323 | 0.846613 | − | 0.532209i | \(-0.178638\pi\) | ||||
0.846613 | + | 0.532209i | \(0.178638\pi\) | |||||||
\(618\) | −1.18632e7 | − | 2.35110e7i | −1.24948 | − | 2.47628i | ||||
\(619\) | −1.43260e7 | −1.50279 | −0.751394 | − | 0.659854i | \(-0.770618\pi\) | ||||
−0.751394 | + | 0.659854i | \(0.770618\pi\) | |||||||
\(620\) | −1.81331e6 | − | 1.33937e6i | −0.189449 | − | 0.139933i | ||||
\(621\) | 1.01131e7 | 1.05234 | ||||||||
\(622\) | 1.77486e6 | + | 3.51749e6i | 0.183945 | + | 0.364550i | ||||
\(623\) | 2.80627e6 | 0.289674 | ||||||||
\(624\) | −1.50850e7 | + | 4.64033e6i | −1.55090 | + | 0.477076i | ||||
\(625\) | −1.18537e6 | −0.121382 | ||||||||
\(626\) | 7.89409e6 | − | 3.98321e6i | 0.805131 | − | 0.406254i | ||||
\(627\) | 1.43410e7 | + | 2.14832e7i | 1.45683 | + | 2.18238i | ||||
\(628\) | −1.51490e7 | − | 1.11895e7i | −1.53280 | − | 1.13217i | ||||
\(629\) | 1.81618e7 | 1.83035 | ||||||||
\(630\) | −1.39728e7 | + | 7.05043e6i | −1.40260 | + | 0.707725i | ||||
\(631\) | 1.53824e6i | 0.153798i | 0.997039 | + | 0.0768990i | \(0.0245019\pi\) | ||||
−0.997039 | + | 0.0768990i | \(0.975498\pi\) | |||||||
\(632\) | −2.21459e6 | + | 1.29886e7i | −0.220547 | + | 1.29351i | ||||
\(633\) | 2.99923e7 | 2.97509 | ||||||||
\(634\) | −7.83301e6 | + | 3.95239e6i | −0.773937 | + | 0.390514i | ||||
\(635\) | − | 9.74025e6i | − | 0.958596i | ||||||
\(636\) | 2.10479e7 | + | 1.55466e7i | 2.06331 | + | 1.52403i | ||||
\(637\) | −3.32953e6 | −0.325113 | ||||||||
\(638\) | 1.44612e7 | − | 7.29687e6i | 1.40655 | − | 0.709717i | ||||
\(639\) | −2.97398e7 | −2.88129 | ||||||||
\(640\) | −885566. | − | 6.79754e6i | −0.0854616 | − | 0.655997i | ||||
\(641\) | − | 4.45367e6i | − | 0.428128i | −0.976820 | − | 0.214064i | \(-0.931330\pi\) | ||
0.976820 | − | 0.214064i | \(-0.0686701\pi\) | |||||||
\(642\) | −1.46510e7 | + | 7.39264e6i | −1.40291 | + | 0.707884i | ||||
\(643\) | −9.68595e6 | −0.923878 | −0.461939 | − | 0.886912i | \(-0.652846\pi\) | ||||
−0.461939 | + | 0.886912i | \(0.652846\pi\) | |||||||
\(644\) | −4.19583e6 | + | 5.68055e6i | −0.398660 | + | 0.539729i | ||||
\(645\) | −1.01397e7 | −0.959682 | ||||||||
\(646\) | 8.72248e6 | − | 1.54166e7i | 0.822354 | − | 1.45348i | ||||
\(647\) | − | 1.23914e7i | − | 1.16375i | −0.813277 | − | 0.581877i | \(-0.802319\pi\) | ||
0.813277 | − | 0.581877i | \(-0.197681\pi\) | |||||||
\(648\) | −2.03848e6 | + | 1.19557e7i | −0.190708 | + | 1.11850i | ||||
\(649\) | 9.13637e6i | 0.851456i | ||||||||
\(650\) | −5.02950e6 | + | 2.53779e6i | −0.466919 | + | 0.235599i | ||||
\(651\) | −7.80321e6 | −0.721640 | ||||||||
\(652\) | −7.80045e6 | + | 1.05607e7i | −0.718622 | + | 0.972911i | ||||
\(653\) | 1.22140e7i | 1.12093i | 0.828180 | + | 0.560463i | \(0.189377\pi\) | ||||
−0.828180 | + | 0.560463i | \(0.810623\pi\) | |||||||
\(654\) | 5.14019e6 | + | 1.01870e7i | 0.469932 | + | 0.931331i | ||||
\(655\) | − | 1.11958e6i | − | 0.101965i | ||||||
\(656\) | −2.58448e6 | + | 795019.i | −0.234484 | + | 0.0721304i | ||||
\(657\) | −1.07136e7 | −0.968327 | ||||||||
\(658\) | 1.55501e7 | − | 7.84630e6i | 1.40013 | − | 0.706480i | ||||
\(659\) | − | 1.71867e7i | − | 1.54162i | −0.637064 | − | 0.770811i | \(-0.719851\pi\) | ||
0.637064 | − | 0.770811i | \(-0.280149\pi\) | |||||||
\(660\) | 1.15413e7 | − | 1.56253e7i | 1.03132 | − | 1.39626i | ||||
\(661\) | −1.24496e7 | −1.10828 | −0.554141 | − | 0.832423i | \(-0.686953\pi\) | ||||
−0.554141 | + | 0.832423i | \(0.686953\pi\) | |||||||
\(662\) | −1.31411e6 | − | 2.60436e6i | −0.116543 | − | 0.230970i | ||||
\(663\) | 3.06699e7i | 2.70975i | ||||||||
\(664\) | −445081. | + | 2.61040e6i | −0.0391759 | + | 0.229767i | ||||
\(665\) | −7.28928e6 | + | 4.86592e6i | −0.639191 | + | 0.426689i | ||||
\(666\) | −2.28972e7 | + | 1.15535e7i | −2.00030 | + | 1.00932i | ||||
\(667\) | − | 6.95223e6i | − | 0.605076i | ||||||
\(668\) | −2.48107e6 | + | 3.35901e6i | −0.215128 | + | 0.291253i | ||||
\(669\) | − | 343359.i | − | 0.0296608i | ||||||
\(670\) | −8.57272e6 | + | 4.32563e6i | −0.737788 | + | 0.372274i | ||||
\(671\) | − | 2.30937e7i | − | 1.98010i | ||||||
\(672\) | −1.64451e7 | − | 1.71050e7i | −1.40480 | − | 1.46117i | ||||
\(673\) | − | 3.43928e6i | − | 0.292705i | −0.989232 | − | 0.146353i | \(-0.953247\pi\) | ||
0.989232 | − | 0.146353i | \(-0.0467534\pi\) | |||||||
\(674\) | −459547. | − | 910749.i | −0.0389655 | − | 0.0772234i | ||||
\(675\) | 1.21286e7i | 1.02459i | ||||||||
\(676\) | −953856. | + | 1.29138e6i | −0.0802816 | + | 0.108690i | ||||
\(677\) | 9.71121e6 | 0.814332 | 0.407166 | − | 0.913354i | \(-0.366517\pi\) | ||||
0.407166 | + | 0.913354i | \(0.366517\pi\) | |||||||
\(678\) | −7.87859e6 | + | 3.97539e6i | −0.658224 | + | 0.332128i | ||||
\(679\) | −3.15695e6 | −0.262780 | ||||||||
\(680\) | −1.31317e7 | − | 2.23899e6i | −1.08905 | − | 0.185686i | ||||
\(681\) | −1.58094e7 | −1.30631 | ||||||||
\(682\) | 5.80640e6 | − | 2.92980e6i | 0.478020 | − | 0.241200i | ||||
\(683\) | 5.58761e6i | 0.458325i | 0.973388 | + | 0.229163i | \(0.0735988\pi\) | ||||
−0.973388 | + | 0.229163i | \(0.926401\pi\) | |||||||
\(684\) | −1.18954e6 | + | 2.49849e7i | −0.0972163 | + | 2.04192i | ||||
\(685\) | 9.20975e6i | 0.749931i | ||||||||
\(686\) | 4.19543e6 | + | 8.31468e6i | 0.340382 | + | 0.674583i | ||||
\(687\) | 2.74952e7 | 2.22262 | ||||||||
\(688\) | −3.03512e6 | − | 9.86667e6i | −0.244458 | − | 0.794693i | ||||
\(689\) | −1.70371e7 | −1.36725 | ||||||||
\(690\) | −3.75591e6 | − | 7.44363e6i | −0.300326 | − | 0.595199i | ||||
\(691\) | 1.96566e7 | 1.56608 | 0.783039 | − | 0.621973i | \(-0.213669\pi\) | ||||
0.783039 | + | 0.621973i | \(0.213669\pi\) | |||||||
\(692\) | 1.14970e6 | − | 1.55653e6i | 0.0912683 | − | 0.123564i | ||||
\(693\) | − | 4.51524e7i | − | 3.57148i | ||||||
\(694\) | −1.02106e7 | + | 5.15210e6i | −0.804738 | + | 0.406056i | ||||
\(695\) | 1.56659e7i | 1.23025i | ||||||||
\(696\) | 2.30265e7 | + | 3.92609e6i | 1.80179 | + | 0.307211i | ||||
\(697\) | 5.25462e6i | 0.409694i | ||||||||
\(698\) | −8.23454e6 | − | 1.63196e7i | −0.639736 | − | 1.26786i | ||||
\(699\) | 1.96567e7i | 1.52166i | ||||||||
\(700\) | −6.81269e6 | − | 5.03206e6i | −0.525501 | − | 0.388151i | ||||
\(701\) | 7.29308e6i | 0.560552i | 0.959919 | + | 0.280276i | \(0.0904260\pi\) | ||||
−0.959919 | + | 0.280276i | \(0.909574\pi\) | |||||||
\(702\) | −9.96625e6 | − | 1.97515e7i | −0.763289 | − | 1.51272i | ||||
\(703\) | −1.19449e7 | + | 7.97373e6i | −0.911576 | + | 0.608518i | ||||
\(704\) | 1.86591e7 | + | 6.55339e6i | 1.41893 | + | 0.498350i | ||||
\(705\) | 2.05631e7i | 1.55817i | ||||||||
\(706\) | −1.86000e6 | + | 938519.i | −0.140443 | + | 0.0708649i | ||||
\(707\) | −1.26154e7 | −0.949190 | ||||||||
\(708\) | −7.82796e6 | + | 1.05979e7i | −0.586902 | + | 0.794581i | ||||
\(709\) | 8.20141e6i | 0.612735i | 0.951913 | + | 0.306368i | \(0.0991136\pi\) | ||||
−0.951913 | + | 0.306368i | \(0.900886\pi\) | |||||||
\(710\) | 5.64205e6 | + | 1.11817e7i | 0.420041 | + | 0.832454i | ||||
\(711\) | −3.61572e7 | −2.68238 | ||||||||
\(712\) | −3.32495e6 | − | 566915.i | −0.245802 | − | 0.0419100i | ||||
\(713\) | − | 2.79142e6i | − | 0.205637i | ||||||
\(714\) | −4.11667e7 | + | 2.07719e7i | −3.02204 | + | 1.52486i | ||||
\(715\) | 1.26478e7i | 0.925232i | ||||||||
\(716\) | 5.20976e6 | + | 3.84809e6i | 0.379783 | + | 0.280519i | ||||
\(717\) | −1.59498e7 | −1.15866 | ||||||||
\(718\) | −157389. | − | 311921.i | −0.0113937 | − | 0.0225805i | ||||
\(719\) | 8.13778e6i | 0.587062i | 0.955950 | + | 0.293531i | \(0.0948303\pi\) | ||||
−0.955950 | + | 0.293531i | \(0.905170\pi\) | |||||||
\(720\) | 1.79798e7 | − | 5.53082e6i | 1.29257 | − | 0.397611i | ||||
\(721\) | 2.57782e7i | 1.84678i | ||||||||
\(722\) | 1.03180e6 | + | 1.39689e7i | 0.0736634 | + | 0.997283i | ||||
\(723\) | −1.72995e7 | −1.23080 | ||||||||
\(724\) | −4.94820e6 | + | 6.69915e6i | −0.350833 | + | 0.474978i | ||||
\(725\) | 8.33782e6 | 0.589125 | ||||||||
\(726\) | 1.40836e7 | + | 2.79115e7i | 0.991683 | + | 1.96536i | ||||
\(727\) | − | 3.38258e6i | − | 0.237363i | −0.992932 | − | 0.118681i | \(-0.962133\pi\) | ||
0.992932 | − | 0.118681i | \(-0.0378667\pi\) | |||||||
\(728\) | 1.52294e7 | + | 2.59666e6i | 1.06501 | + | 0.181588i | ||||
\(729\) | 1.23315e7 | 0.859403 | ||||||||
\(730\) | 2.03252e6 | + | 4.02812e6i | 0.141165 | + | 0.279767i | ||||
\(731\) | −2.00604e7 | −1.38850 | ||||||||
\(732\) | 1.97864e7 | − | 2.67880e7i | 1.36487 | − | 1.84783i | ||||
\(733\) | − | 2.60792e7i | − | 1.79281i | −0.443233 | − | 0.896407i | \(-0.646168\pi\) | ||
0.443233 | − | 0.896407i | \(-0.353832\pi\) | |||||||
\(734\) | −1.34933e6 | − | 2.67417e6i | −0.0924442 | − | 0.183210i | ||||
\(735\) | 5.90978e6 | 0.403509 | ||||||||
\(736\) | 6.11892e6 | − | 5.88286e6i | 0.416371 | − | 0.400308i | ||||
\(737\) | − | 2.77022e7i | − | 1.87865i | ||||||
\(738\) | −3.34268e6 | − | 6.62465e6i | −0.225919 | − | 0.447736i | ||||
\(739\) | 9.29414e6 | 0.626035 | 0.313017 | − | 0.949747i | \(-0.398660\pi\) | ||||
0.313017 | + | 0.949747i | \(0.398660\pi\) | |||||||
\(740\) | 8.68780e6 | + | 6.41708e6i | 0.583218 | + | 0.430782i | ||||
\(741\) | −1.34653e7 | − | 2.01713e7i | −0.900885 | − | 1.34955i | ||||
\(742\) | −1.15388e7 | − | 2.28681e7i | −0.769397 | − | 1.52482i | ||||
\(743\) | 7.55420e6 | 0.502015 | 0.251007 | − | 0.967985i | \(-0.419238\pi\) | ||||
0.251007 | + | 0.967985i | \(0.419238\pi\) | |||||||
\(744\) | 9.24548e6 | + | 1.57638e6i | 0.612347 | + | 0.104407i | ||||
\(745\) | 527285. | 0.0348060 | ||||||||
\(746\) | 2.11960e7 | − | 1.06951e7i | 1.39446 | − | 0.703618i | ||||
\(747\) | −7.26676e6 | −0.476474 | ||||||||
\(748\) | 2.28332e7 | − | 3.09129e7i | 1.49215 | − | 2.02016i | ||||
\(749\) | 1.60639e7 | 1.04628 | ||||||||
\(750\) | 2.48015e7 | − | 1.25144e7i | 1.60999 | − | 0.812373i | ||||
\(751\) | 4.11726e6 | 0.266384 | 0.133192 | − | 0.991090i | \(-0.457477\pi\) | ||||
0.133192 | + | 0.991090i | \(0.457477\pi\) | |||||||
\(752\) | −2.00093e7 | + | 6.15514e6i | −1.29029 | + | 0.396911i | ||||
\(753\) | − | 1.07448e7i | − | 0.690575i | ||||||
\(754\) | −1.35782e7 | + | 6.85129e6i | −0.869788 | + | 0.438878i | ||||
\(755\) | 9.52032e6i | 0.607833i | ||||||||
\(756\) | 1.97616e7 | − | 2.67544e7i | 1.25753 | − | 1.70251i | ||||
\(757\) | 2.99636e6i | 0.190044i | 0.995475 | + | 0.0950219i | \(0.0302921\pi\) | ||||
−0.995475 | + | 0.0950219i | \(0.969708\pi\) | |||||||
\(758\) | 2.21796e6 | + | 4.39565e6i | 0.140211 | + | 0.277875i | ||||
\(759\) | 2.40536e7 | 1.51557 | ||||||||
\(760\) | 9.61956e6 | − | 4.29273e6i | 0.604117 | − | 0.269588i | ||||
\(761\) | 1.82731e7 | 1.14380 | 0.571900 | − | 0.820323i | \(-0.306206\pi\) | ||||
0.571900 | + | 0.820323i | \(0.306206\pi\) | |||||||
\(762\) | 1.82551e7 | + | 3.61787e7i | 1.13893 | + | 2.25717i | ||||
\(763\) | − | 1.11694e7i | − | 0.694575i | ||||||
\(764\) | −857662. | − | 633495.i | −0.0531597 | − | 0.0392654i | ||||
\(765\) | − | 3.65555e7i | − | 2.25839i | ||||||
\(766\) | −1.96002e7 | + | 9.88988e6i | −1.20695 | + | 0.609003i | ||||
\(767\) | − | 8.57847e6i | − | 0.526528i | ||||||
\(768\) | 1.60292e7 | + | 2.35887e7i | 0.980637 | + | 1.44311i | ||||
\(769\) | 2.24831e7 | 1.37101 | 0.685505 | − | 0.728068i | \(-0.259581\pi\) | ||||
0.685505 | + | 0.728068i | \(0.259581\pi\) | |||||||
\(770\) | −1.69765e7 | + | 8.56603e6i | −1.03186 | + | 0.520658i | ||||
\(771\) | −3.61102e7 | −2.18773 | ||||||||
\(772\) | −1.77504e7 | − | 1.31110e7i | −1.07192 | − | 0.791755i | ||||
\(773\) | 2.42067e6 | 0.145709 | 0.0728545 | − | 0.997343i | \(-0.476789\pi\) | ||||
0.0728545 | + | 0.997343i | \(0.476789\pi\) | |||||||
\(774\) | 2.52907e7 | − | 1.27612e7i | 1.51743 | − | 0.765667i | ||||
\(775\) | 3.34775e6 | 0.200216 | ||||||||
\(776\) | 3.74045e6 | + | 637758.i | 0.222982 | + | 0.0380191i | ||||
\(777\) | 3.73862e7 | 2.22156 | ||||||||
\(778\) | 142190. | + | 281799.i | 0.00842211 | + | 0.0166913i | ||||
\(779\) | −2.30698e6 | − | 3.45591e6i | −0.136207 | − | 0.204042i | ||||
\(780\) | −1.08365e7 | + | 1.46711e7i | −0.637755 | + | 0.863429i | ||||
\(781\) | −3.61329e7 | −2.11970 | ||||||||
\(782\) | −7.43068e6 | − | 1.47264e7i | −0.434522 | − | 0.861154i | ||||
\(783\) | 3.27437e7i | 1.90864i | ||||||||
\(784\) | 1.76897e6 | + | 5.75063e6i | 0.102785 | + | 0.334137i | ||||
\(785\) | −2.17651e7 | −1.26063 | ||||||||
\(786\) | 2.09830e6 | + | 4.15851e6i | 0.121147 | + | 0.240094i | ||||
\(787\) | 1.59992e7i | 0.920794i | 0.887713 | + | 0.460397i | \(0.152293\pi\) | ||||
−0.887713 | + | 0.460397i | \(0.847707\pi\) | |||||||
\(788\) | 1.63891e7 | + | 1.21055e7i | 0.940242 | + | 0.694491i | ||||
\(789\) | 1.87521e7 | 1.07240 | ||||||||
\(790\) | 6.85951e6 | + | 1.35945e7i | 0.391044 | + | 0.774987i | ||||
\(791\) | 8.63834e6 | 0.490896 | ||||||||
\(792\) | −9.12156e6 | + | 5.34980e7i | −0.516721 | + | 3.03057i | ||||
\(793\) | 2.16835e7i | 1.22446i | ||||||||
\(794\) | −6.72591e6 | − | 1.33297e7i | −0.378617 | − | 0.750359i | ||||
\(795\) | 3.02402e7 | 1.69694 | ||||||||
\(796\) | −9.75916e6 | − | 7.20841e6i | −0.545921 | − | 0.403234i | ||||
\(797\) | −2.14331e7 | −1.19519 | −0.597597 | − | 0.801797i | \(-0.703878\pi\) | ||||
−0.597597 | + | 0.801797i | \(0.703878\pi\) | |||||||
\(798\) | 1.79553e7 | − | 3.17352e7i | 0.998124 | − | 1.76414i | ||||
\(799\) | 4.06819e7i | 2.25442i | ||||||||
\(800\) | 7.05533e6 | + | 7.33842e6i | 0.389755 | + | 0.405394i | ||||
\(801\) | − | 9.25591e6i | − | 0.509727i | ||||||
\(802\) | −1.20768e7 | − | 2.39342e7i | −0.663002 | − | 1.31397i | ||||
\(803\) | −1.30166e7 | −0.712377 | ||||||||
\(804\) | 2.37350e7 | − | 3.21338e7i | 1.29494 | − | 1.75316i | ||||
\(805\) | 8.16144e6i | 0.443892i | ||||||||
\(806\) | −5.45184e6 | + | 2.75089e6i | −0.295601 | + | 0.149154i | ||||
\(807\) | 2.65986e7i | 1.43772i | ||||||||
\(808\) | 1.49471e7 | + | 2.54853e6i | 0.805434 | + | 0.137329i | ||||
\(809\) | −2.78269e6 | −0.149484 | −0.0747418 | − | 0.997203i | \(-0.523813\pi\) | ||||
−0.0747418 | + | 0.997203i | \(0.523813\pi\) | |||||||
\(810\) | 6.31401e6 | + | 1.25134e7i | 0.338137 | + | 0.670135i | ||||
\(811\) | 1.93966e7i | 1.03555i | 0.855516 | + | 0.517777i | \(0.173240\pi\) | ||||
−0.855516 | + | 0.517777i | \(0.826760\pi\) | |||||||
\(812\) | −1.83923e7 | − | 1.35851e7i | −0.978916 | − | 0.723057i | ||||
\(813\) | −4.06231e7 | −2.15549 | ||||||||
\(814\) | −2.78192e7 | + | 1.40371e7i | −1.47158 | + | 0.742532i | ||||
\(815\) | 1.51729e7i | 0.800156i | ||||||||
\(816\) | 5.29718e7 | − | 1.62948e7i | 2.78496 | − | 0.856692i | ||||
\(817\) | 1.31935e7 | − | 8.80727e6i | 0.691522 | − | 0.461622i | ||||
\(818\) | 2.62585e6 | + | 5.20402e6i | 0.137210 | + | 0.271929i | ||||
\(819\) | 4.23952e7i | 2.20855i | ||||||||
\(820\) | −1.85660e6 | + | 2.51357e6i | −0.0964238 | + | 0.130544i | ||||
\(821\) | 9.94941e6i | 0.515157i | 0.966257 | + | 0.257579i | \(0.0829246\pi\) | ||||
−0.966257 | + | 0.257579i | \(0.917075\pi\) | |||||||
\(822\) | −1.72608e7 | − | 3.42082e7i | −0.891008 | − | 1.76584i | ||||
\(823\) | − | 3.58026e7i | − | 1.84253i | −0.388936 | − | 0.921265i | \(-0.627157\pi\) | ||
0.388936 | − | 0.921265i | \(-0.372843\pi\) | |||||||
\(824\) | 5.20764e6 | − | 3.05428e7i | 0.267192 | − | 1.56708i | ||||
\(825\) | 2.88476e7i | 1.47562i | ||||||||
\(826\) | 1.15144e7 | − | 5.80996e6i | 0.587209 | − | 0.296294i | ||||
\(827\) | − | 1.95579e7i | − | 0.994394i | −0.867638 | − | 0.497197i | \(-0.834363\pi\) | ||
0.867638 | − | 0.497197i | \(-0.165637\pi\) | |||||||
\(828\) | 1.87362e7 | + | 1.38391e7i | 0.949740 | + | 0.701507i | ||||
\(829\) | 2.71049e7 | 1.36982 | 0.684908 | − | 0.728630i | \(-0.259843\pi\) | ||||
0.684908 | + | 0.728630i | \(0.259843\pi\) | |||||||
\(830\) | 1.37860e6 | + | 2.73218e6i | 0.0694615 | + | 0.137662i | ||||
\(831\) | −3.59512e7 | −1.80597 | ||||||||
\(832\) | −1.75197e7 | − | 6.15321e6i | −0.877443 | − | 0.308172i | ||||
\(833\) | 1.16919e7 | 0.583810 | ||||||||
\(834\) | −2.93608e7 | − | 5.81885e7i | −1.46168 | − | 2.89683i | ||||
\(835\) | 4.82601e6i | 0.239537i | ||||||||
\(836\) | −1.44525e6 | + | 3.03558e7i | −0.0715200 | + | 1.50219i | ||||
\(837\) | 1.31471e7i | 0.648658i | ||||||||
\(838\) | −4.00204e6 | + | 2.01936e6i | −0.196867 | + | 0.0993351i | ||||
\(839\) | 1.30660e7 | 0.640820 | 0.320410 | − | 0.947279i | \(-0.396179\pi\) | ||||
0.320410 | + | 0.947279i | \(0.396179\pi\) | |||||||
\(840\) | −2.70316e7 | − | 4.60896e6i | −1.32182 | − | 0.225375i | ||||
\(841\) | 1.99851e6 | 0.0974353 | ||||||||
\(842\) | 2.06169e6 | − | 1.04029e6i | 0.100217 | − | 0.0505677i | ||||
\(843\) | 6.13679e7 | 2.97422 | ||||||||
\(844\) | 2.83839e7 | + | 2.09652e7i | 1.37157 | + | 1.01308i | ||||
\(845\) | 1.85538e6i | 0.0893902i | ||||||||
\(846\) | −2.58794e7 | − | 5.12889e7i | −1.24316 | − | 2.46376i | ||||
\(847\) | − | 3.06031e7i | − | 1.46574i | ||||||
\(848\) | 9.05177e6 | + | 2.94258e7i | 0.432259 | + | 1.40520i | ||||
\(849\) | − | 2.31122e7i | − | 1.10045i | ||||||
\(850\) | 1.76614e7 | − | 8.91162e6i | 0.838453 | − | 0.423067i | ||||
\(851\) | 1.33741e7i | 0.633052i | ||||||||
\(852\) | −4.19131e7 | − | 3.09583e7i | −1.97811 | − | 1.46109i | ||||
\(853\) | 8.29122e6i | 0.390163i | 0.980787 | + | 0.195081i | \(0.0624971\pi\) | ||||
−0.980787 | + | 0.195081i | \(0.937503\pi\) | |||||||
\(854\) | −2.91046e7 | + | 1.46856e7i | −1.36558 | + | 0.689046i | ||||
\(855\) | 1.60493e7 | + | 2.40422e7i | 0.750827 | + | 1.12476i | ||||
\(856\) | −1.90330e7 | − | 3.24518e6i | −0.887815 | − | 0.151375i | ||||
\(857\) | − | 3.08173e7i | − | 1.43332i | −0.697424 | − | 0.716659i | \(-0.745671\pi\) | ||
0.697424 | − | 0.716659i | \(-0.254329\pi\) | |||||||
\(858\) | −2.37044e7 | − | 4.69784e7i | −1.09929 | − | 2.17861i | ||||
\(859\) | 2.55864e7 | 1.18311 | 0.591557 | − | 0.806263i | \(-0.298513\pi\) | ||||
0.591557 | + | 0.806263i | \(0.298513\pi\) | |||||||
\(860\) | −9.59599e6 | − | 7.08789e6i | −0.442429 | − | 0.326791i | ||||
\(861\) | 1.08167e7i | 0.497262i | ||||||||
\(862\) | −5.10004e6 | + | 2.57339e6i | −0.233779 | + | 0.117961i | ||||
\(863\) | 1.18111e7 | 0.539836 | 0.269918 | − | 0.962883i | \(-0.413003\pi\) | ||||
0.269918 | + | 0.962883i | \(0.413003\pi\) | |||||||
\(864\) | −2.88190e7 | + | 2.77072e7i | −1.31339 | + | 1.26272i | ||||
\(865\) | − | 2.23632e6i | − | 0.101623i | ||||||
\(866\) | 4.07603e6 | + | 8.07805e6i | 0.184690 | + | 0.366026i | ||||
\(867\) | − | 6.90818e7i | − | 3.12116i | ||||||
\(868\) | −7.38476e6 | − | 5.45461e6i | −0.332688 | − | 0.245734i | ||||
\(869\) | −4.39297e7 | −1.97337 | ||||||||
\(870\) | 2.41007e7 | − | 1.21608e7i | 1.07952 | − | 0.544706i | ||||
\(871\) | 2.60106e7i | 1.16173i | ||||||||
\(872\) | −2.25641e6 | + | 1.32339e7i | −0.100491 | + | 0.589380i | ||||
\(873\) | 1.04126e7i | 0.462404i | ||||||||
\(874\) | 1.13526e7 | + | 6.42309e6i | 0.502707 | + | 0.284423i | ||||
\(875\) | −2.71932e7 | −1.20071 | ||||||||
\(876\) | −1.50989e7 | − | 1.11525e7i | −0.664792 | − | 0.491036i | ||||
\(877\) | 2.57059e7 | 1.12858 | 0.564292 | − | 0.825575i | \(-0.309149\pi\) | ||||
0.564292 | + | 0.825575i | \(0.309149\pi\) | |||||||
\(878\) | 3.33991e7 | − | 1.68525e7i | 1.46217 | − | 0.737784i | ||||
\(879\) | 3.35594e7i | 1.46501i | ||||||||
\(880\) | 2.18448e7 | − | 6.71975e6i | 0.950913 | − | 0.292514i | ||||
\(881\) | 8.50822e6 | 0.369317 | 0.184658 | − | 0.982803i | \(-0.440882\pi\) | ||||
0.184658 | + | 0.982803i | \(0.440882\pi\) | |||||||
\(882\) | −1.47403e7 | + | 7.43767e6i | −0.638020 | + | 0.321933i | ||||
\(883\) | 1.68717e7 | 0.728212 | 0.364106 | − | 0.931358i | \(-0.381375\pi\) | ||||
0.364106 | + | 0.931358i | \(0.381375\pi\) | |||||||
\(884\) | −2.14389e7 | + | 2.90253e7i | −0.922726 | + | 1.24924i | ||||
\(885\) | 1.52264e7i | 0.653491i | ||||||||
\(886\) | −1.46780e7 | + | 7.40625e6i | −0.628178 | + | 0.316967i | ||||
\(887\) | −2.00106e6 | −0.0853986 | −0.0426993 | − | 0.999088i | \(-0.513596\pi\) | ||||
−0.0426993 | + | 0.999088i | \(0.513596\pi\) | |||||||
\(888\) | −4.42963e7 | − | 7.55266e6i | −1.88510 | − | 0.321416i | ||||
\(889\) | − | 3.96675e7i | − | 1.68337i | ||||||
\(890\) | −3.48006e6 | + | 1.75597e6i | −0.147269 | + | 0.0743092i | ||||
\(891\) | −4.04362e7 | −1.70638 | ||||||||
\(892\) | 240015. | − | 324946.i | 0.0101001 | − | 0.0136741i | ||||
\(893\) | −1.78609e7 | − | 2.67561e7i | −0.749506 | − | 1.12278i | ||||
\(894\) | −1.95852e6 | + | 988232.i | −0.0819566 | + | 0.0413538i | ||||
\(895\) | 7.48504e6 | 0.312346 | ||||||||
\(896\) | −3.60650e6 | − | 2.76832e7i | −0.150077 | − | 1.15198i | ||||
\(897\) | −2.25848e7 | −0.937207 | ||||||||
\(898\) | −3.12070e6 | − | 6.18474e6i | −0.129140 | − | 0.255936i | ||||
\(899\) | 9.03795e6 | 0.372967 | ||||||||
\(900\) | −1.65972e7 | + | 2.24703e7i | −0.683014 | + | 0.924703i | ||||
\(901\) | 5.98270e7 | 2.45519 | ||||||||
\(902\) | −4.06123e6 | − | 8.04872e6i | −0.166204 | − | 0.329390i | ||||
\(903\) | −4.12944e7 | −1.68528 | ||||||||
\(904\) | −1.02350e7 | − | 1.74509e6i | −0.416549 | − | 0.0710228i | ||||
\(905\) | 9.62490e6i | 0.390638i | ||||||||
\(906\) | −1.78429e7 | − | 3.53618e7i | −0.722178 | − | 1.43124i | ||||
\(907\) | − | 1.33783e7i | − | 0.539985i | −0.962862 | − | 0.269993i | \(-0.912979\pi\) | ||
0.962862 | − | 0.269993i | \(-0.0870213\pi\) | |||||||
\(908\) | −1.49616e7 | − | 1.10511e7i | −0.602231 | − | 0.444826i | ||||
\(909\) | 4.16094e7i | 1.67025i | ||||||||
\(910\) | 1.59399e7 | − | 8.04295e6i | 0.638088 | − | 0.321967i | ||||
\(911\) | −1.78700e6 | −0.0713393 | −0.0356696 | − | 0.999364i | \(-0.511356\pi\) | ||||
−0.0356696 | + | 0.999364i | \(0.511356\pi\) | |||||||
\(912\) | −2.76850e7 | + | 3.39736e7i | −1.10219 | + | 1.35255i | ||||
\(913\) | −8.82886e6 | −0.350532 | ||||||||
\(914\) | 1.66827e7 | − | 8.41780e6i | 0.660544 | − | 0.333298i | ||||
\(915\) | − | 3.84873e7i | − | 1.51972i | ||||||
\(916\) | 2.60208e7 | + | 1.92198e7i | 1.02467 | + | 0.756849i | ||||
\(917\) | − | 4.55953e6i | − | 0.179059i | ||||||
\(918\) | 3.49971e7 | + | 6.93588e7i | 1.37065 | + | 2.71641i | ||||
\(919\) | − | 3.22979e7i | − | 1.26149i | −0.775989 | − | 0.630747i | \(-0.782749\pi\) | ||
0.775989 | − | 0.630747i | \(-0.217251\pi\) | |||||||
\(920\) | 1.64875e6 | − | 9.66993e6i | 0.0642223 | − | 0.376664i | ||||
\(921\) | 524639. | 0.0203804 | ||||||||
\(922\) | 1.78409e7 | + | 3.53578e7i | 0.691177 | + | 1.36980i | ||||
\(923\) | 3.39264e7 | 1.31079 | ||||||||
\(924\) | 4.70023e7 | − | 6.36344e7i | 1.81109 | − | 2.45195i | ||||
\(925\) | −1.60395e7 | −0.616364 | ||||||||
\(926\) | 8.03722e6 | + | 1.59285e7i | 0.308020 | + | 0.610446i | ||||
\(927\) | 8.50242e7 | 3.24970 | ||||||||
\(928\) | 1.90473e7 | + | 1.98116e7i | 0.726045 | + | 0.755178i | ||||
\(929\) | 2.14880e7 | 0.816875 | 0.408438 | − | 0.912786i | \(-0.366074\pi\) | ||||
0.408438 | + | 0.912786i | \(0.366074\pi\) | |||||||
\(930\) | 9.67678e6 | − | 4.88272e6i | 0.366879 | − | 0.185120i | ||||
\(931\) | −7.68964e6 | + | 5.13318e6i | −0.290758 | + | 0.194094i | ||||
\(932\) | −1.37404e7 | + | 1.86026e7i | −0.518156 | + | 0.701509i | ||||
\(933\) | −1.89432e7 | −0.712441 | ||||||||
\(934\) | −1.04936e7 | + | 5.29486e6i | −0.393601 | + | 0.198604i | ||||
\(935\) | − | 4.44137e7i | − | 1.66145i | ||||||
\(936\) | 8.56456e6 | − | 5.02312e7i | 0.319533 | − | 1.87406i | ||||
\(937\) | −3.69853e7 | −1.37619 | −0.688097 | − | 0.725619i | \(-0.741554\pi\) | ||||
−0.688097 | + | 0.725619i | \(0.741554\pi\) | |||||||
\(938\) | −3.49127e7 | + | 1.76163e7i | −1.29562 | + | 0.653743i | ||||
\(939\) | 4.25130e7i | 1.57347i | ||||||||
\(940\) | −1.43741e7 | + | 1.94604e7i | −0.530591 | + | 0.718344i | ||||
\(941\) | −1.46476e7 | −0.539252 | −0.269626 | − | 0.962965i | \(-0.586900\pi\) | ||||
−0.269626 | + | 0.962965i | \(0.586900\pi\) | |||||||
\(942\) | 8.08432e7 | − | 4.07920e7i | 2.96836 | − | 1.49778i | ||||
\(943\) | −3.86941e6 | −0.141699 | ||||||||
\(944\) | −1.48164e7 | + | 4.55771e6i | −0.541143 | + | 0.166463i | ||||
\(945\) | − | 3.84389e7i | − | 1.40020i | ||||||
\(946\) | 3.07273e7 | − | 1.55044e7i | 1.11634 | − | 0.563285i | ||||
\(947\) | 1.57533e7 | 0.570816 | 0.285408 | − | 0.958406i | \(-0.407871\pi\) | ||||
0.285408 | + | 0.958406i | \(0.407871\pi\) | |||||||
\(948\) | −5.09572e7 | − | 3.76385e7i | −1.84156 | − | 1.36023i | ||||
\(949\) | 1.22218e7 | 0.440524 | ||||||||
\(950\) | −7.70321e6 | + | 1.36151e7i | −0.276926 | + | 0.489455i | ||||
\(951\) | − | 4.21841e7i | − | 1.51251i | ||||||
\(952\) | −5.34791e7 | − | 9.11835e6i | −1.91246 | − | 0.326080i | ||||
\(953\) | − | 5.45212e7i | − | 1.94461i | −0.233709 | − | 0.972307i | \(-0.575086\pi\) | ||
0.233709 | − | 0.972307i | \(-0.424914\pi\) | |||||||
\(954\) | −7.54256e7 | + | 3.80584e7i | −2.68317 | + | 1.35388i | ||||
\(955\) | −1.23223e6 | −0.0437204 | ||||||||
\(956\) | −1.50945e7 | − | 1.11492e7i | −0.534162 | − | 0.394548i | ||||
\(957\) | 7.78799e7i | 2.74882i | ||||||||
\(958\) | 2.10051e7 | + | 4.16287e7i | 0.739453 | + | 1.46548i | ||||
\(959\) | 3.75070e7i | 1.31694i | ||||||||
\(960\) | 3.10967e7 | + | 1.09217e7i | 1.08902 | + | 0.382482i | ||||
\(961\) | −2.50003e7 | −0.873246 | ||||||||
\(962\) | 2.61205e7 | − | 1.31799e7i | 0.910004 | − | 0.459171i | ||||
\(963\) | − | 5.29835e7i | − | 1.84109i | ||||||
\(964\) | −1.63718e7 | − | 1.20927e7i | −0.567421 | − | 0.419114i | ||||
\(965\) | −2.55025e7 | −0.881587 | ||||||||
\(966\) | −1.52961e7 | − | 3.03144e7i | −0.527397 | − | 1.04522i | ||||
\(967\) | 5.94249e6i | 0.204363i | 0.994766 | + | 0.102181i | \(0.0325822\pi\) | ||||
−0.994766 | + | 0.102181i | \(0.967418\pi\) | |||||||
\(968\) | −6.18236e6 | + | 3.62595e7i | −0.212063 | + | 1.24375i | ||||
\(969\) | 4.72842e7 | + | 7.08329e7i | 1.61773 | + | 2.42340i | ||||
\(970\) | 3.91494e6 | − | 1.97540e6i | 0.133597 | − | 0.0674103i | ||||
\(971\) | − | 758200.i | − | 0.0258069i | −0.999917 | − | 0.0129034i | \(-0.995893\pi\) | ||
0.999917 | − | 0.0129034i | \(-0.00410741\pi\) | |||||||
\(972\) | −3.73759e6 | − | 2.76070e6i | −0.126890 | − | 0.0937245i | ||||
\(973\) | 6.37998e7i | 2.16042i | ||||||||
\(974\) | 1.01513e7 | − | 5.12214e6i | 0.342865 | − | 0.173003i | ||||
\(975\) | − | 2.70860e7i | − | 0.912501i | ||||||
\(976\) | 3.74508e7 | − | 1.15204e7i | 1.25845 | − | 0.387116i | ||||
\(977\) | 1.14601e7i | 0.384107i | 0.981384 | + | 0.192054i | \(0.0615148\pi\) | ||||
−0.981384 | + | 0.192054i | \(0.938485\pi\) | |||||||
\(978\) | −2.84369e7 | − | 5.63574e7i | −0.950681 | − | 1.88410i | ||||
\(979\) | − | 1.12456e7i | − | 0.374995i | ||||||
\(980\) | 5.59287e6 | + | 4.13106e6i | 0.186024 | + | 0.137403i | ||||
\(981\) | −3.68401e7 | −1.22222 | ||||||||
\(982\) | 3.21146e7 | − | 1.62044e7i | 1.06273 | − | 0.536234i | ||||
\(983\) | 4.07508e7 | 1.34509 | 0.672546 | − | 0.740055i | \(-0.265201\pi\) | ||||
0.672546 | + | 0.740055i | \(0.265201\pi\) | |||||||
\(984\) | 2.18515e6 | − | 1.28159e7i | 0.0719439 | − | 0.421951i | ||||
\(985\) | 2.35468e7 | 0.773287 | ||||||||
\(986\) | 4.76807e7 | − | 2.40588e7i | 1.56189 | − | 0.788100i | ||||
\(987\) | 8.37440e7i | 2.73628i | ||||||||
\(988\) | 1.35700e6 | − | 2.85021e7i | 0.0442269 | − | 0.928935i | ||||
\(989\) | − | 1.47721e7i | − | 0.480234i | ||||||
\(990\) | 2.82533e7 | + | 5.59936e7i | 0.916181 | + | 1.81573i | ||||
\(991\) | −5.70617e7 | −1.84570 | −0.922849 | − | 0.385161i | \(-0.874146\pi\) | ||||
−0.922849 | + | 0.385161i | \(0.874146\pi\) | |||||||
\(992\) | 7.64777e6 | + | 7.95464e6i | 0.246749 | + | 0.256650i | ||||
\(993\) | 1.40256e7 | 0.451386 | ||||||||
\(994\) | 2.29775e7 | + | 4.55377e7i | 0.737626 | + | 1.46186i | ||||
\(995\) | −1.40213e7 | −0.448984 | ||||||||
\(996\) | −1.02412e7 | − | 7.56448e6i | −0.327117 | − | 0.241619i | ||||
\(997\) | − | 3.72819e7i | − | 1.18785i | −0.804522 | − | 0.593923i | \(-0.797578\pi\) | ||
0.804522 | − | 0.593923i | \(-0.202422\pi\) | |||||||
\(998\) | 9.20458e6 | − | 4.64446e6i | 0.292535 | − | 0.147608i | ||||
\(999\) | − | 6.29894e7i | − | 1.99689i |
(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 | 152.6.b.b.75.14 | yes | 96 | |
4.3 | odd | 2 | 608.6.b.b.303.93 | 96 | |||
8.3 | odd | 2 | inner | 152.6.b.b.75.84 | yes | 96 | |
8.5 | even | 2 | 608.6.b.b.303.94 | 96 | |||
19.18 | odd | 2 | inner | 152.6.b.b.75.83 | yes | 96 | |
76.75 | even | 2 | 608.6.b.b.303.3 | 96 | |||
152.37 | odd | 2 | 608.6.b.b.303.4 | 96 | |||
152.75 | even | 2 | inner | 152.6.b.b.75.13 | ✓ | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.6.b.b.75.13 | ✓ | 96 | 152.75 | even | 2 | inner | |
152.6.b.b.75.14 | yes | 96 | 1.1 | even | 1 | trivial | |
152.6.b.b.75.83 | yes | 96 | 19.18 | odd | 2 | inner | |
152.6.b.b.75.84 | yes | 96 | 8.3 | odd | 2 | inner | |
608.6.b.b.303.3 | 96 | 76.75 | even | 2 | |||
608.6.b.b.303.4 | 96 | 152.37 | odd | 2 | |||
608.6.b.b.303.93 | 96 | 4.3 | odd | 2 | |||
608.6.b.b.303.94 | 96 | 8.5 | even | 2 |