Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [48,5,Mod(5,48)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(48, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("48.5");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.i (of order \(4\), degree \(2\), 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: | \(4.96175822802\) |
Analytic rank: | \(0\) |
Dimension: | \(60\) |
Relative dimension: | \(30\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 5.18 | ||
Character | \(\chi\) | \(=\) | 48.5 |
Dual form | 48.5.i.a.29.18 |
$q$-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 \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(31\) | \(37\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.13167 | − | 3.83658i | 0.282917 | − | 0.959144i | ||||
\(3\) | 0.466380 | + | 8.98791i | 0.0518200 | + | 0.998656i | ||||
\(4\) | −13.4387 | − | 8.68346i | −0.839916 | − | 0.542716i | ||||
\(5\) | −23.5639 | + | 23.5639i | −0.942556 | + | 0.942556i | −0.998437 | − | 0.0558818i | \(-0.982203\pi\) |
0.0558818 | + | 0.998437i | \(0.482203\pi\) | |||||||
\(6\) | 35.0106 | + | 8.38202i | 0.972517 | + | 0.232834i | ||||
\(7\) | 30.4899i | 0.622242i | 0.950370 | + | 0.311121i | \(0.100704\pi\) | ||||
−0.950370 | + | 0.311121i | \(0.899296\pi\) | |||||||
\(8\) | −48.5229 | + | 41.7317i | −0.758170 | + | 0.652057i | ||||
\(9\) | −80.5650 | + | 8.38356i | −0.994629 | + | 0.103501i | ||||
\(10\) | 63.7382 | + | 117.071i | 0.637382 | + | 1.17071i | ||||
\(11\) | −22.5385 | + | 22.5385i | −0.186269 | + | 0.186269i | −0.794081 | − | 0.607812i | \(-0.792047\pi\) |
0.607812 | + | 0.794081i | \(0.292047\pi\) | |||||||
\(12\) | 71.7786 | − | 124.835i | 0.498463 | − | 0.866911i | ||||
\(13\) | 86.0911 | − | 86.0911i | 0.509415 | − | 0.509415i | −0.404932 | − | 0.914347i | \(-0.632705\pi\) |
0.914347 | + | 0.404932i | \(0.132705\pi\) | |||||||
\(14\) | 116.977 | + | 34.5044i | 0.596820 | + | 0.176043i | ||||
\(15\) | −222.780 | − | 200.800i | −0.990132 | − | 0.892446i | ||||
\(16\) | 105.195 | + | 233.388i | 0.410918 | + | 0.911672i | ||||
\(17\) | 406.437i | 1.40635i | 0.711014 | + | 0.703177i | \(0.248236\pi\) | ||||
−0.711014 | + | 0.703177i | \(0.751764\pi\) | |||||||
\(18\) | −59.0086 | + | 318.581i | −0.182125 | + | 0.983275i | ||||
\(19\) | 340.364 | − | 340.364i | 0.942836 | − | 0.942836i | −0.0556164 | − | 0.998452i | \(-0.517712\pi\) |
0.998452 | + | 0.0556164i | \(0.0177124\pi\) | |||||||
\(20\) | 521.283 | − | 112.051i | 1.30321 | − | 0.280127i | ||||
\(21\) | −274.040 | + | 14.2199i | −0.621406 | + | 0.0322446i | ||||
\(22\) | 60.9647 | + | 111.977i | 0.125960 | + | 0.231357i | ||||
\(23\) | −549.957 | −1.03962 | −0.519808 | − | 0.854283i | \(-0.673997\pi\) | ||||
−0.519808 | + | 0.854283i | \(0.673997\pi\) | |||||||
\(24\) | −397.710 | − | 416.656i | −0.690469 | − | 0.723362i | ||||
\(25\) | − | 485.514i | − | 0.776822i | ||||||
\(26\) | −232.869 | − | 427.722i | −0.344480 | − | 0.632724i | ||||
\(27\) | −112.925 | − | 720.201i | −0.154903 | − | 0.987930i | ||||
\(28\) | 264.758 | − | 409.743i | 0.337701 | − | 0.522631i | ||||
\(29\) | 190.284 | + | 190.284i | 0.226259 | + | 0.226259i | 0.811128 | − | 0.584869i | \(-0.198854\pi\) |
−0.584869 | + | 0.811128i | \(0.698854\pi\) | |||||||
\(30\) | −1022.50 | + | 627.473i | −1.13611 | + | 0.697192i | ||||
\(31\) | −1712.72 | −1.78223 | −0.891113 | − | 0.453781i | \(-0.850075\pi\) | ||||
−0.891113 | + | 0.453781i | \(0.850075\pi\) | |||||||
\(32\) | 1014.46 | − | 139.471i | 0.990681 | − | 0.136202i | ||||
\(33\) | −213.086 | − | 192.063i | −0.195671 | − | 0.176366i | ||||
\(34\) | 1559.33 | + | 459.951i | 1.34890 | + | 0.397882i | ||||
\(35\) | −718.460 | − | 718.460i | −0.586498 | − | 0.586498i | ||||
\(36\) | 1155.48 | + | 586.919i | 0.891577 | + | 0.452870i | ||||
\(37\) | 1227.54 | + | 1227.54i | 0.896669 | + | 0.896669i | 0.995140 | − | 0.0984713i | \(-0.0313953\pi\) |
−0.0984713 | + | 0.995140i | \(0.531395\pi\) | |||||||
\(38\) | −920.653 | − | 1691.01i | −0.637572 | − | 1.17106i | ||||
\(39\) | 813.930 | + | 733.627i | 0.535128 | + | 0.482332i | ||||
\(40\) | 160.027 | − | 2126.75i | 0.100017 | − | 1.32922i | ||||
\(41\) | 1560.26 | 0.928175 | 0.464087 | − | 0.885789i | \(-0.346382\pi\) | ||||
0.464087 | + | 0.885789i | \(0.346382\pi\) | |||||||
\(42\) | −255.567 | + | 1067.47i | −0.144879 | + | 0.605141i | ||||
\(43\) | 1290.04 | + | 1290.04i | 0.697695 | + | 0.697695i | 0.963913 | − | 0.266218i | \(-0.0857741\pi\) |
−0.266218 | + | 0.963913i | \(0.585774\pi\) | |||||||
\(44\) | 498.600 | − | 107.175i | 0.257541 | − | 0.0553591i | ||||
\(45\) | 1700.88 | − | 2095.97i | 0.839938 | − | 1.03505i | ||||
\(46\) | −622.368 | + | 2109.95i | −0.294125 | + | 0.997142i | ||||
\(47\) | 1736.02i | 0.785884i | 0.919563 | + | 0.392942i | \(0.128543\pi\) | ||||
−0.919563 | + | 0.392942i | \(0.871457\pi\) | |||||||
\(48\) | −2048.61 | + | 1054.33i | −0.889154 | + | 0.457609i | ||||
\(49\) | 1471.37 | 0.612815 | ||||||||
\(50\) | −1862.71 | − | 549.440i | −0.745085 | − | 0.219776i | ||||
\(51\) | −3653.01 | + | 189.554i | −1.40447 | + | 0.0728773i | ||||
\(52\) | −1904.52 | + | 409.380i | −0.704333 | + | 0.151398i | ||||
\(53\) | −3108.96 | + | 3108.96i | −1.10678 | + | 1.10678i | −0.113213 | + | 0.993571i | \(0.536114\pi\) |
−0.993571 | + | 0.113213i | \(0.963886\pi\) | |||||||
\(54\) | −2890.90 | − | 381.784i | −0.991392 | − | 0.130927i | ||||
\(55\) | − | 1062.19i | − | 0.351138i | ||||||
\(56\) | −1272.39 | − | 1479.46i | −0.405737 | − | 0.471765i | ||||
\(57\) | 3217.90 | + | 2900.42i | 0.990427 | + | 0.892711i | ||||
\(58\) | 945.376 | − | 514.700i | 0.281027 | − | 0.153003i | ||||
\(59\) | 2976.70 | − | 2976.70i | 0.855129 | − | 0.855129i | −0.135630 | − | 0.990760i | \(-0.543306\pi\) |
0.990760 | + | 0.135630i | \(0.0433060\pi\) | |||||||
\(60\) | 1250.22 | + | 4632.99i | 0.347283 | + | 1.28694i | ||||
\(61\) | 170.193 | − | 170.193i | 0.0457385 | − | 0.0457385i | −0.683868 | − | 0.729606i | \(-0.739703\pi\) |
0.729606 | + | 0.683868i | \(0.239703\pi\) | |||||||
\(62\) | −1938.23 | + | 6570.98i | −0.504222 | + | 1.70941i | ||||
\(63\) | −255.614 | − | 2456.41i | −0.0644025 | − | 0.618900i | ||||
\(64\) | 612.937 | − | 4049.88i | 0.149643 | − | 0.988740i | ||||
\(65\) | 4057.28i | 0.960303i | ||||||||
\(66\) | −978.006 | + | 600.169i | −0.224519 | + | 0.137780i | ||||
\(67\) | 2622.93 | − | 2622.93i | 0.584301 | − | 0.584301i | −0.351781 | − | 0.936082i | \(-0.614424\pi\) |
0.936082 | + | 0.351781i | \(0.114424\pi\) | |||||||
\(68\) | 3529.28 | − | 5461.96i | 0.763252 | − | 1.18122i | ||||
\(69\) | −256.489 | − | 4942.96i | −0.0538729 | − | 1.03822i | ||||
\(70\) | −3569.48 | + | 1943.37i | −0.728466 | + | 0.396606i | ||||
\(71\) | 115.787 | 0.0229690 | 0.0114845 | − | 0.999934i | \(-0.496344\pi\) | ||||
0.0114845 | + | 0.999934i | \(0.496344\pi\) | |||||||
\(72\) | 3559.38 | − | 3768.90i | 0.686610 | − | 0.727026i | ||||
\(73\) | 9618.19i | 1.80488i | 0.430819 | + | 0.902438i | \(0.358225\pi\) | ||||
−0.430819 | + | 0.902438i | \(0.641775\pi\) | |||||||
\(74\) | 6098.72 | − | 3320.38i | 1.11372 | − | 0.606352i | ||||
\(75\) | 4363.75 | − | 226.434i | 0.775778 | − | 0.0402549i | ||||
\(76\) | −7529.57 | + | 1618.50i | −1.30360 | + | 0.280211i | ||||
\(77\) | −687.197 | − | 687.197i | −0.115904 | − | 0.115904i | ||||
\(78\) | 3735.72 | − | 2292.48i | 0.614023 | − | 0.376805i | ||||
\(79\) | −5150.26 | −0.825230 | −0.412615 | − | 0.910906i | \(-0.635384\pi\) | ||||
−0.412615 | + | 0.910906i | \(0.635384\pi\) | |||||||
\(80\) | −7978.34 | − | 3020.73i | −1.24661 | − | 0.471989i | ||||
\(81\) | 6420.43 | − | 1350.84i | 0.978575 | − | 0.205890i | ||||
\(82\) | 1765.70 | − | 5986.06i | 0.262596 | − | 0.890254i | ||||
\(83\) | 653.536 | + | 653.536i | 0.0948667 | + | 0.0948667i | 0.752947 | − | 0.658081i | \(-0.228631\pi\) |
−0.658081 | + | 0.752947i | \(0.728631\pi\) | |||||||
\(84\) | 3806.21 | + | 2188.52i | 0.539429 | + | 0.310164i | ||||
\(85\) | −9577.23 | − | 9577.23i | −1.32557 | − | 1.32557i | ||||
\(86\) | 6409.22 | − | 3489.44i | 0.866580 | − | 0.471800i | ||||
\(87\) | −1621.51 | + | 1799.00i | −0.214230 | + | 0.237680i | ||||
\(88\) | 153.064 | − | 2034.21i | 0.0197655 | − | 0.262681i | ||||
\(89\) | −2000.77 | −0.252590 | −0.126295 | − | 0.991993i | \(-0.540309\pi\) | ||||
−0.126295 | + | 0.991993i | \(0.540309\pi\) | |||||||
\(90\) | −6116.54 | − | 8897.48i | −0.755128 | − | 1.09845i | ||||
\(91\) | 2624.90 | + | 2624.90i | 0.316979 | + | 0.316979i | ||||
\(92\) | 7390.68 | + | 4775.53i | 0.873190 | + | 0.564217i | ||||
\(93\) | −798.778 | − | 15393.8i | −0.0923550 | − | 1.77983i | ||||
\(94\) | 6660.36 | + | 1964.59i | 0.753776 | + | 0.222340i | ||||
\(95\) | 16040.6i | 1.77735i | ||||||||
\(96\) | 1726.68 | + | 9052.80i | 0.187356 | + | 0.982292i | ||||
\(97\) | −13229.4 | −1.40603 | −0.703017 | − | 0.711173i | \(-0.748164\pi\) | ||||
−0.703017 | + | 0.711173i | \(0.748164\pi\) | |||||||
\(98\) | 1665.10 | − | 5645.02i | 0.173376 | − | 0.587778i | ||||
\(99\) | 1626.86 | − | 2004.77i | 0.165990 | − | 0.204548i | ||||
\(100\) | −4215.94 | + | 6524.65i | −0.421594 | + | 0.652465i | ||||
\(101\) | −295.112 | + | 295.112i | −0.0289297 | + | 0.0289297i | −0.721424 | − | 0.692494i | \(-0.756512\pi\) |
0.692494 | + | 0.721424i | \(0.256512\pi\) | |||||||
\(102\) | −3406.76 | + | 14229.6i | −0.327447 | + | 1.36770i | ||||
\(103\) | − | 12718.5i | − | 1.19884i | −0.800434 | − | 0.599422i | \(-0.795397\pi\) | ||
0.800434 | − | 0.599422i | \(-0.204603\pi\) | |||||||
\(104\) | −584.662 | + | 7770.11i | −0.0540553 | + | 0.718390i | ||||
\(105\) | 6122.37 | − | 6792.52i | 0.555317 | − | 0.616102i | ||||
\(106\) | 8409.44 | + | 15446.1i | 0.748438 | + | 1.37469i | ||||
\(107\) | −5195.48 | + | 5195.48i | −0.453794 | + | 0.453794i | −0.896612 | − | 0.442818i | \(-0.853979\pi\) |
0.442818 | + | 0.896612i | \(0.353979\pi\) | |||||||
\(108\) | −4736.28 | + | 10659.1i | −0.406060 | + | 0.913847i | ||||
\(109\) | −5099.86 | + | 5099.86i | −0.429245 | + | 0.429245i | −0.888371 | − | 0.459126i | \(-0.848163\pi\) |
0.459126 | + | 0.888371i | \(0.348163\pi\) | |||||||
\(110\) | −4075.18 | − | 1202.05i | −0.336792 | − | 0.0993428i | ||||
\(111\) | −10460.5 | + | 11605.5i | −0.848999 | + | 0.941929i | ||||
\(112\) | −7115.97 | + | 3207.38i | −0.567281 | + | 0.255690i | ||||
\(113\) | − | 19322.8i | − | 1.51326i | −0.653844 | − | 0.756630i | \(-0.726845\pi\) | ||
0.653844 | − | 0.756630i | \(-0.273155\pi\) | |||||||
\(114\) | 14769.3 | − | 9063.40i | 1.13645 | − | 0.697399i | ||||
\(115\) | 12959.1 | − | 12959.1i | 0.979896 | − | 0.979896i | ||||
\(116\) | −904.837 | − | 4209.48i | −0.0672441 | − | 0.312833i | ||||
\(117\) | −6214.18 | + | 7657.67i | −0.453954 | + | 0.559403i | ||||
\(118\) | −8051.72 | − | 14789.0i | −0.578262 | − | 1.06212i | ||||
\(119\) | −12392.2 | −0.875093 | ||||||||
\(120\) | 19189.6 | + | 446.438i | 1.33261 | + | 0.0310026i | ||||
\(121\) | 13625.0i | 0.930608i | ||||||||
\(122\) | −460.357 | − | 845.561i | −0.0309297 | − | 0.0568101i | ||||
\(123\) | 727.675 | + | 14023.5i | 0.0480980 | + | 0.926928i | ||||
\(124\) | 23016.7 | + | 14872.3i | 1.49692 | + | 0.967244i | ||||
\(125\) | −3286.84 | − | 3286.84i | −0.210358 | − | 0.210358i | ||||
\(126\) | −9713.50 | − | 1799.16i | −0.611835 | − | 0.113326i | ||||
\(127\) | 19880.3 | 1.23258 | 0.616292 | − | 0.787518i | \(-0.288634\pi\) | ||||
0.616292 | + | 0.787518i | \(0.288634\pi\) | |||||||
\(128\) | −14844.0 | − | 6934.70i | −0.906008 | − | 0.423260i | ||||
\(129\) | −10993.1 | + | 12196.4i | −0.660603 | + | 0.732912i | ||||
\(130\) | 15566.1 | + | 4591.49i | 0.921069 | + | 0.271686i | ||||
\(131\) | −5720.55 | − | 5720.55i | −0.333346 | − | 0.333346i | 0.520510 | − | 0.853856i | \(-0.325742\pi\) |
−0.853856 | + | 0.520510i | \(0.825742\pi\) | |||||||
\(132\) | 1195.82 | + | 4431.39i | 0.0686305 | + | 0.254327i | ||||
\(133\) | 10377.6 | + | 10377.6i | 0.586672 | + | 0.586672i | ||||
\(134\) | −7094.78 | − | 13031.3i | −0.395121 | − | 0.725738i | ||||
\(135\) | 19631.7 | + | 14309.8i | 1.07718 | + | 0.785174i | ||||
\(136\) | −16961.3 | − | 19721.5i | −0.917024 | − | 1.06626i | ||||
\(137\) | 14602.9 | 0.778033 | 0.389016 | − | 0.921231i | \(-0.372815\pi\) | ||||
0.389016 | + | 0.921231i | \(0.372815\pi\) | |||||||
\(138\) | −19254.3 | − | 4609.75i | −1.01104 | − | 0.242058i | ||||
\(139\) | −2965.29 | − | 2965.29i | −0.153475 | − | 0.153475i | 0.626193 | − | 0.779668i | \(-0.284612\pi\) |
−0.779668 | + | 0.626193i | \(0.784612\pi\) | |||||||
\(140\) | 3416.42 | + | 15893.9i | 0.174307 | + | 0.810911i | ||||
\(141\) | −15603.2 | + | 809.643i | −0.784828 | + | 0.0407245i | ||||
\(142\) | 131.032 | − | 444.226i | 0.00649833 | − | 0.0220306i | ||||
\(143\) | 3880.73i | 0.189776i | ||||||||
\(144\) | −10431.7 | − | 17921.0i | −0.503070 | − | 0.864246i | ||||
\(145\) | −8967.65 | −0.426523 | ||||||||
\(146\) | 36900.9 | + | 10884.6i | 1.73114 | + | 0.510630i | ||||
\(147\) | 686.217 | + | 13224.5i | 0.0317561 | + | 0.611992i | ||||
\(148\) | −5837.19 | − | 27155.8i | −0.266490 | − | 1.23976i | ||||
\(149\) | 3328.31 | − | 3328.31i | 0.149917 | − | 0.149917i | −0.628164 | − | 0.778081i | \(-0.716193\pi\) |
0.778081 | + | 0.628164i | \(0.216193\pi\) | |||||||
\(150\) | 4069.59 | − | 16998.1i | 0.180871 | − | 0.755472i | ||||
\(151\) | 7469.91i | 0.327613i | 0.986492 | + | 0.163807i | \(0.0523773\pi\) | ||||
−0.986492 | + | 0.163807i | \(0.947623\pi\) | |||||||
\(152\) | −2311.48 | + | 30719.4i | −0.100047 | + | 1.32961i | ||||
\(153\) | −3407.38 | − | 32744.6i | −0.145559 | − | 1.39880i | ||||
\(154\) | −3414.16 | + | 1858.81i | −0.143960 | + | 0.0783777i | ||||
\(155\) | 40358.3 | − | 40358.3i | 1.67985 | − | 1.67985i | ||||
\(156\) | −4567.70 | − | 16926.7i | −0.187693 | − | 0.695541i | ||||
\(157\) | 5405.91 | − | 5405.91i | 0.219316 | − | 0.219316i | −0.588894 | − | 0.808210i | \(-0.700437\pi\) |
0.808210 | + | 0.588894i | \(0.200437\pi\) | |||||||
\(158\) | −5828.38 | + | 19759.4i | −0.233471 | + | 0.791515i | ||||
\(159\) | −29393.0 | − | 26493.1i | −1.16265 | − | 1.04794i | ||||
\(160\) | −20618.1 | + | 27191.0i | −0.805394 | + | 1.06215i | ||||
\(161\) | − | 16768.1i | − | 0.646893i | ||||||
\(162\) | 2083.18 | − | 26161.2i | 0.0793775 | − | 0.996845i | ||||
\(163\) | 5872.53 | − | 5872.53i | 0.221029 | − | 0.221029i | −0.587902 | − | 0.808932i | \(-0.700046\pi\) |
0.808932 | + | 0.587902i | \(0.200046\pi\) | |||||||
\(164\) | −20967.8 | − | 13548.5i | −0.779589 | − | 0.503736i | ||||
\(165\) | 9546.88 | − | 495.385i | 0.350666 | − | 0.0181959i | ||||
\(166\) | 3246.93 | − | 1767.76i | 0.117830 | − | 0.0641515i | ||||
\(167\) | 7043.60 | 0.252558 | 0.126279 | − | 0.991995i | \(-0.459696\pi\) | ||||
0.126279 | + | 0.991995i | \(0.459696\pi\) | |||||||
\(168\) | 12703.8 | − | 12126.1i | 0.450106 | − | 0.429639i | ||||
\(169\) | 13737.7i | 0.480994i | ||||||||
\(170\) | −47582.0 | + | 25905.5i | −1.64644 | + | 0.896385i | ||||
\(171\) | −24567.9 | + | 30274.9i | −0.840188 | + | 1.03536i | ||||
\(172\) | −6134.38 | − | 28538.4i | −0.207355 | − | 0.964655i | ||||
\(173\) | 28466.0 | + | 28466.0i | 0.951119 | + | 0.951119i | 0.998860 | − | 0.0477406i | \(-0.0152021\pi\) |
−0.0477406 | + | 0.998860i | \(0.515202\pi\) | |||||||
\(174\) | 5066.99 | + | 8256.91i | 0.167360 | + | 0.272721i | ||||
\(175\) | 14803.2 | 0.483371 | ||||||||
\(176\) | −7631.17 | − | 2889.29i | −0.246357 | − | 0.0932750i | ||||
\(177\) | 28142.6 | + | 25366.1i | 0.898293 | + | 0.809667i | ||||
\(178\) | −2264.20 | + | 7676.10i | −0.0714620 | + | 0.242270i | ||||
\(179\) | 18685.4 | + | 18685.4i | 0.583170 | + | 0.583170i | 0.935773 | − | 0.352603i | \(-0.114703\pi\) |
−0.352603 | + | 0.935773i | \(0.614703\pi\) | |||||||
\(180\) | −41057.8 | + | 13397.6i | −1.26722 | + | 0.413506i | ||||
\(181\) | 6712.06 | + | 6712.06i | 0.204880 | + | 0.204880i | 0.802087 | − | 0.597207i | \(-0.203723\pi\) |
−0.597207 | + | 0.802087i | \(0.703723\pi\) | |||||||
\(182\) | 13041.2 | − | 7100.13i | 0.393708 | − | 0.214350i | ||||
\(183\) | 1609.05 | + | 1450.31i | 0.0480472 | + | 0.0433069i | ||||
\(184\) | 26685.5 | − | 22950.6i | 0.788205 | − | 0.677889i | ||||
\(185\) | −57851.2 | −1.69032 | ||||||||
\(186\) | −59963.3 | − | 14356.1i | −1.73325 | − | 0.414963i | ||||
\(187\) | −9160.49 | − | 9160.49i | −0.261960 | − | 0.261960i | ||||
\(188\) | 15074.6 | − | 23329.7i | 0.426512 | − | 0.660076i | ||||
\(189\) | 21958.8 | − | 3443.05i | 0.614731 | − | 0.0963874i | ||||
\(190\) | 61541.0 | + | 18152.6i | 1.70474 | + | 0.502842i | ||||
\(191\) | − | 50217.2i | − | 1.37653i | −0.725459 | − | 0.688265i | \(-0.758373\pi\) | ||
0.725459 | − | 0.688265i | \(-0.241627\pi\) | |||||||
\(192\) | 36685.8 | + | 3620.24i | 0.995166 | + | 0.0982053i | ||||
\(193\) | 35887.9 | 0.963460 | 0.481730 | − | 0.876320i | \(-0.340009\pi\) | ||||
0.481730 | + | 0.876320i | \(0.340009\pi\) | |||||||
\(194\) | −14971.2 | + | 50755.5i | −0.397791 | + | 1.34859i | ||||
\(195\) | −36466.5 | + | 1892.23i | −0.959013 | + | 0.0497629i | ||||
\(196\) | −19773.2 | − | 12776.6i | −0.514713 | − | 0.332585i | ||||
\(197\) | 21477.1 | − | 21477.1i | 0.553404 | − | 0.553404i | −0.374017 | − | 0.927422i | \(-0.622020\pi\) |
0.927422 | + | 0.374017i | \(0.122020\pi\) | |||||||
\(198\) | −5850.39 | − | 8510.32i | −0.149229 | − | 0.217078i | ||||
\(199\) | − | 1420.82i | − | 0.0358784i | −0.999839 | − | 0.0179392i | \(-0.994289\pi\) | ||
0.999839 | − | 0.0179392i | \(-0.00571053\pi\) | |||||||
\(200\) | 20261.3 | + | 23558.5i | 0.506532 | + | 0.588963i | ||||
\(201\) | 24797.9 | + | 22351.4i | 0.613795 | + | 0.553238i | ||||
\(202\) | 798.252 | + | 1466.19i | 0.0195631 | + | 0.0359325i | ||||
\(203\) | −5801.73 | + | 5801.73i | −0.140788 | + | 0.140788i | ||||
\(204\) | 50737.6 | + | 29173.5i | 1.21918 | + | 0.701015i | ||||
\(205\) | −36765.8 | + | 36765.8i | −0.874856 | + | 0.874856i | ||||
\(206\) | −48795.6 | − | 14393.1i | −1.14986 | − | 0.339173i | ||||
\(207\) | 44307.3 | − | 4610.60i | 1.03403 | − | 0.107601i | ||||
\(208\) | 29149.0 | + | 11036.3i | 0.673747 | + | 0.255092i | ||||
\(209\) | 15342.6i | 0.351242i | ||||||||
\(210\) | −19131.6 | − | 31175.8i | −0.433822 | − | 0.706935i | ||||
\(211\) | −40580.8 | + | 40580.8i | −0.911499 | + | 0.911499i | −0.996390 | − | 0.0848916i | \(-0.972946\pi\) |
0.0848916 | + | 0.996390i | \(0.472946\pi\) | |||||||
\(212\) | 68776.7 | − | 14783.7i | 1.53027 | − | 0.328936i | ||||
\(213\) | 54.0007 | + | 1040.68i | 0.00119026 | + | 0.0229382i | ||||
\(214\) | 14053.3 | + | 25812.4i | 0.306868 | + | 0.563639i | ||||
\(215\) | −60796.6 | −1.31523 | ||||||||
\(216\) | 35534.6 | + | 30233.7i | 0.761630 | + | 0.648013i | ||||
\(217\) | − | 52220.6i | − | 1.10898i | ||||||
\(218\) | 13794.7 | + | 25337.4i | 0.290267 | + | 0.533149i | ||||
\(219\) | −86447.4 | + | 4485.73i | −1.80245 | + | 0.0935287i | ||||
\(220\) | −9223.50 | + | 14274.4i | −0.190568 | + | 0.294926i | ||||
\(221\) | 34990.6 | + | 34990.6i | 0.716418 | + | 0.716418i | ||||
\(222\) | 32687.6 | + | 53266.1i | 0.663250 | + | 1.08080i | ||||
\(223\) | −4901.55 | −0.0985652 | −0.0492826 | − | 0.998785i | \(-0.515694\pi\) | ||||
−0.0492826 | + | 0.998785i | \(0.515694\pi\) | |||||||
\(224\) | 4252.45 | + | 30930.7i | 0.0847507 | + | 0.616443i | ||||
\(225\) | 4070.33 | + | 39115.4i | 0.0804016 | + | 0.772650i | ||||
\(226\) | −74133.4 | − | 21867.0i | −1.45143 | − | 0.428127i | ||||
\(227\) | −21233.3 | − | 21233.3i | −0.412065 | − | 0.412065i | 0.470393 | − | 0.882457i | \(-0.344112\pi\) |
−0.882457 | + | 0.470393i | \(0.844112\pi\) | |||||||
\(228\) | −18058.5 | − | 66920.2i | −0.347386 | − | 1.28732i | ||||
\(229\) | −9411.25 | − | 9411.25i | −0.179464 | − | 0.179464i | 0.611658 | − | 0.791122i | \(-0.290503\pi\) |
−0.791122 | + | 0.611658i | \(0.790503\pi\) | |||||||
\(230\) | −35053.3 | − | 64384.1i | −0.662633 | − | 1.21709i | ||||
\(231\) | 5855.97 | − | 6496.96i | 0.109742 | − | 0.121755i | ||||
\(232\) | −17174.0 | − | 1292.26i | −0.319076 | − | 0.0240089i | ||||
\(233\) | −45273.3 | −0.833932 | −0.416966 | − | 0.908922i | \(-0.636907\pi\) | ||||
−0.416966 | + | 0.908922i | \(0.636907\pi\) | |||||||
\(234\) | 22346.9 | + | 32507.1i | 0.408117 | + | 0.593672i | ||||
\(235\) | −40907.3 | − | 40907.3i | −0.740739 | − | 0.740739i | ||||
\(236\) | −65851.0 | + | 14154.8i | −1.18233 | + | 0.254144i | ||||
\(237\) | −2401.98 | − | 46290.1i | −0.0427634 | − | 0.824121i | ||||
\(238\) | −14023.8 | + | 47543.6i | −0.247579 | + | 0.839341i | ||||
\(239\) | 23326.3i | 0.408367i | 0.978933 | + | 0.204183i | \(0.0654539\pi\) | ||||
−0.978933 | + | 0.204183i | \(0.934546\pi\) | |||||||
\(240\) | 23429.1 | − | 73117.4i | 0.406755 | − | 1.26940i | ||||
\(241\) | 12230.5 | 0.210576 | 0.105288 | − | 0.994442i | \(-0.466424\pi\) | ||||
0.105288 | + | 0.994442i | \(0.466424\pi\) | |||||||
\(242\) | 52273.5 | + | 15419.0i | 0.892587 | + | 0.263285i | ||||
\(243\) | 15135.6 | + | 57076.2i | 0.256323 | + | 0.966591i | ||||
\(244\) | −3765.03 | + | 809.301i | −0.0632396 | + | 0.0135935i | ||||
\(245\) | −34671.2 | + | 34671.2i | −0.577612 | + | 0.577612i | ||||
\(246\) | 54625.7 | + | 13078.1i | 0.902665 | + | 0.216111i | ||||
\(247\) | − | 58604.5i | − | 0.960589i | ||||||
\(248\) | 83106.1 | − | 71474.6i | 1.35123 | − | 1.16211i | ||||
\(249\) | −5569.13 | + | 6178.72i | −0.0898232 | + | 0.0996552i | ||||
\(250\) | −16329.8 | + | 8890.60i | −0.261277 | + | 0.142250i | ||||
\(251\) | 26174.3 | − | 26174.3i | 0.415459 | − | 0.415459i | −0.468176 | − | 0.883635i | \(-0.655089\pi\) |
0.883635 | + | 0.468176i | \(0.155089\pi\) | |||||||
\(252\) | −17895.1 | + | 35230.5i | −0.281795 | + | 0.554777i | ||||
\(253\) | 12395.2 | − | 12395.2i | 0.193648 | − | 0.193648i | ||||
\(254\) | 22497.9 | − | 76272.5i | 0.348719 | − | 1.18223i | ||||
\(255\) | 81612.6 | − | 90545.9i | 1.25510 | − | 1.39248i | ||||
\(256\) | −43404.0 | + | 49102.5i | −0.662293 | + | 0.749245i | ||||
\(257\) | − | 87009.7i | − | 1.31735i | −0.752428 | − | 0.658675i | \(-0.771117\pi\) | ||
0.752428 | − | 0.658675i | \(-0.228883\pi\) | |||||||
\(258\) | 34351.9 | + | 55978.1i | 0.516073 | + | 0.840967i | ||||
\(259\) | −37427.5 | + | 37427.5i | −0.557945 | + | 0.557945i | ||||
\(260\) | 35231.2 | − | 54524.4i | 0.521172 | − | 0.806574i | ||||
\(261\) | −16925.5 | − | 13735.0i | −0.248462 | − | 0.201626i | ||||
\(262\) | −28421.1 | + | 15473.6i | −0.414036 | + | 0.225418i | ||||
\(263\) | 35446.8 | 0.512467 | 0.256234 | − | 0.966615i | \(-0.417518\pi\) | ||||
0.256234 | + | 0.966615i | \(0.417518\pi\) | |||||||
\(264\) | 18354.6 | + | 427.012i | 0.263353 | + | 0.00612677i | ||||
\(265\) | − | 146518.i | − | 2.08641i | ||||||
\(266\) | 51558.7 | − | 28070.6i | 0.728683 | − | 0.396724i | ||||
\(267\) | −933.117 | − | 17982.7i | −0.0130892 | − | 0.252251i | ||||
\(268\) | −58024.7 | + | 12472.5i | −0.807874 | + | 0.173654i | ||||
\(269\) | 58612.5 | + | 58612.5i | 0.810001 | + | 0.810001i | 0.984634 | − | 0.174633i | \(-0.0558738\pi\) |
−0.174633 | + | 0.984634i | \(0.555874\pi\) | |||||||
\(270\) | 77117.1 | − | 59124.5i | 1.05785 | − | 0.811036i | ||||
\(271\) | −24672.9 | −0.335956 | −0.167978 | − | 0.985791i | \(-0.553724\pi\) | ||||
−0.167978 | + | 0.985791i | \(0.553724\pi\) | |||||||
\(272\) | −94857.5 | + | 42755.1i | −1.28213 | + | 0.577896i | ||||
\(273\) | −22368.2 | + | 24816.6i | −0.300127 | + | 0.332979i | ||||
\(274\) | 16525.6 | − | 56025.1i | 0.220119 | − | 0.746246i | ||||
\(275\) | 10942.8 | + | 10942.8i | 0.144698 | + | 0.144698i | ||||
\(276\) | −39475.2 | + | 68654.0i | −0.518210 | + | 0.901255i | ||||
\(277\) | 73714.1 | + | 73714.1i | 0.960708 | + | 0.960708i | 0.999257 | − | 0.0385489i | \(-0.0122735\pi\) |
−0.0385489 | + | 0.999257i | \(0.512274\pi\) | |||||||
\(278\) | −14732.3 | + | 8020.83i | −0.190625 | + | 0.103784i | ||||
\(279\) | 137985. | − | 14358.7i | 1.77266 | − | 0.184462i | ||||
\(280\) | 64844.2 | + | 4879.21i | 0.827095 | + | 0.0622348i | ||||
\(281\) | −23746.4 | −0.300736 | −0.150368 | − | 0.988630i | \(-0.548046\pi\) | ||||
−0.150368 | + | 0.988630i | \(0.548046\pi\) | |||||||
\(282\) | −14551.3 | + | 60779.0i | −0.182980 | + | 0.764285i | ||||
\(283\) | 34554.7 | + | 34554.7i | 0.431454 | + | 0.431454i | 0.889123 | − | 0.457669i | \(-0.151315\pi\) |
−0.457669 | + | 0.889123i | \(0.651315\pi\) | |||||||
\(284\) | −1556.02 | − | 1005.43i | −0.0192921 | − | 0.0124657i | ||||
\(285\) | −144171. | + | 7481.01i | −1.77496 | + | 0.0921023i | ||||
\(286\) | 14888.7 | + | 4391.70i | 0.182023 | + | 0.0536909i | ||||
\(287\) | 47572.2i | 0.577549i | ||||||||
\(288\) | −80560.5 | + | 19741.2i | −0.971263 | + | 0.238007i | ||||
\(289\) | −81669.7 | −0.977834 | ||||||||
\(290\) | −10148.4 | + | 34405.1i | −0.120671 | + | 0.409097i | ||||
\(291\) | −6169.91 | − | 118904.i | −0.0728606 | − | 1.40414i | ||||
\(292\) | 83519.2 | − | 129256.i | 0.979536 | − | 1.51594i | ||||
\(293\) | 16514.0 | − | 16514.0i | 0.192362 | − | 0.192362i | −0.604354 | − | 0.796716i | \(-0.706569\pi\) |
0.796716 | + | 0.604354i | \(0.206569\pi\) | |||||||
\(294\) | 51513.5 | + | 12333.0i | 0.595973 | + | 0.142684i | ||||
\(295\) | 140285.i | 1.61201i | ||||||||
\(296\) | −110791. | − | 8336.47i | −1.26451 | − | 0.0951478i | ||||
\(297\) | 18777.4 | + | 13687.1i | 0.212874 | + | 0.155167i | ||||
\(298\) | −9002.78 | − | 16535.9i | −0.101378 | − | 0.186206i | ||||
\(299\) | −47346.4 | + | 47346.4i | −0.529596 | + | 0.529596i | ||||
\(300\) | −60609.2 | − | 34849.5i | −0.673436 | − | 0.387217i | ||||
\(301\) | −39333.1 | + | 39333.1i | −0.434135 | + | 0.434135i | ||||
\(302\) | 28658.9 | + | 8453.46i | 0.314229 | + | 0.0926874i | ||||
\(303\) | −2790.08 | − | 2514.81i | −0.0303900 | − | 0.0273917i | ||||
\(304\) | 115241. | + | 43632.3i | 1.24699 | + | 0.472129i | ||||
\(305\) | 8020.82i | 0.0862222i | ||||||||
\(306\) | −129483. | − | 23983.3i | −1.38283 | − | 0.256133i | ||||
\(307\) | 78874.9 | − | 78874.9i | 0.836877 | − | 0.836877i | −0.151569 | − | 0.988447i | \(-0.548433\pi\) |
0.988447 | + | 0.151569i | \(0.0484327\pi\) | |||||||
\(308\) | 3267.76 | + | 15202.3i | 0.0344467 | + | 0.160253i | ||||
\(309\) | 114313. | − | 5931.66i | 1.19723 | − | 0.0621240i | ||||
\(310\) | −109166. | − | 200510.i | −1.13596 | − | 2.08647i | ||||
\(311\) | −176831. | −1.82826 | −0.914128 | − | 0.405426i | \(-0.867123\pi\) | ||||
−0.914128 | + | 0.405426i | \(0.867123\pi\) | |||||||
\(312\) | −70109.7 | − | 1631.07i | −0.720226 | − | 0.0167557i | ||||
\(313\) | 136159.i | 1.38982i | 0.719096 | + | 0.694911i | \(0.244556\pi\) | ||||
−0.719096 | + | 0.694911i | \(0.755444\pi\) | |||||||
\(314\) | −14622.5 | − | 26857.9i | −0.148307 | − | 0.272403i | ||||
\(315\) | 63905.9 | + | 51859.4i | 0.644051 | + | 0.522645i | ||||
\(316\) | 69212.6 | + | 44722.1i | 0.693124 | + | 0.447866i | ||||
\(317\) | 94662.7 | + | 94662.7i | 0.942021 | + | 0.942021i | 0.998409 | − | 0.0563883i | \(-0.0179585\pi\) |
−0.0563883 | + | 0.998409i | \(0.517958\pi\) | |||||||
\(318\) | −134906. | + | 82787.0i | −1.33406 | + | 0.818669i | ||||
\(319\) | −8577.44 | −0.0842900 | ||||||||
\(320\) | 80987.7 | + | 109874.i | 0.790896 | + | 1.07299i | ||||
\(321\) | −49119.6 | − | 44273.5i | −0.476699 | − | 0.429668i | ||||
\(322\) | −64332.1 | − | 18975.9i | −0.620464 | − | 0.183017i | ||||
\(323\) | 138336. | + | 138336.i | 1.32596 | + | 1.32596i | ||||
\(324\) | −98012.0 | − | 37598.1i | −0.933661 | − | 0.358159i | ||||
\(325\) | −41798.4 | − | 41798.4i | −0.395725 | − | 0.395725i | ||||
\(326\) | −15884.7 | − | 29176.2i | −0.149466 | − | 0.274532i | ||||
\(327\) | −48215.6 | − | 43458.6i | −0.450912 | − | 0.406425i | ||||
\(328\) | −75708.4 | + | 65112.3i | −0.703714 | + | 0.605223i | ||||
\(329\) | −52930.9 | −0.489010 | ||||||||
\(330\) | 8903.31 | − | 37188.0i | 0.0817568 | − | 0.341487i | ||||
\(331\) | 77714.0 | + | 77714.0i | 0.709322 | + | 0.709322i | 0.966393 | − | 0.257071i | \(-0.0827573\pi\) |
−0.257071 | + | 0.966393i | \(0.582757\pi\) | |||||||
\(332\) | −3107.69 | − | 14457.6i | −0.0281943 | − | 0.131166i | ||||
\(333\) | −109188. | − | 88605.5i | −0.984659 | − | 0.799047i | ||||
\(334\) | 7971.01 | − | 27023.3i | 0.0714530 | − | 0.242240i | ||||
\(335\) | 123613.i | 1.10147i | ||||||||
\(336\) | −32146.4 | − | 62461.8i | −0.284743 | − | 0.553269i | ||||
\(337\) | 108178. | 0.952531 | 0.476265 | − | 0.879302i | \(-0.341990\pi\) | ||||
0.476265 | + | 0.879302i | \(0.341990\pi\) | |||||||
\(338\) | 52705.6 | + | 15546.5i | 0.461342 | + | 0.136081i | ||||
\(339\) | 173672. | − | 9011.77i | 1.51123 | − | 0.0784171i | ||||
\(340\) | 45541.6 | + | 211869.i | 0.393958 | + | 1.83277i | ||||
\(341\) | 38602.2 | − | 38602.2i | 0.331974 | − | 0.331974i | ||||
\(342\) | 88349.1 | + | 128518.i | 0.755353 | + | 1.09878i | ||||
\(343\) | 118068.i | 1.00356i | ||||||||
\(344\) | −116432. | − | 8760.91i | −0.983908 | − | 0.0740342i | ||||
\(345\) | 122519. | + | 110432.i | 1.02936 | + | 0.927801i | ||||
\(346\) | 141426. | − | 76998.1i | 1.18135 | − | 0.643173i | ||||
\(347\) | 50390.2 | − | 50390.2i | 0.418492 | − | 0.418492i | −0.466192 | − | 0.884684i | \(-0.654374\pi\) |
0.884684 | + | 0.466192i | \(0.154374\pi\) | |||||||
\(348\) | 37412.4 | − | 10095.8i | 0.308928 | − | 0.0833647i | ||||
\(349\) | 106626. | − | 106626.i | 0.875408 | − | 0.875408i | −0.117647 | − | 0.993055i | \(-0.537535\pi\) |
0.993055 | + | 0.117647i | \(0.0375352\pi\) | |||||||
\(350\) | 16752.4 | − | 56793.8i | 0.136754 | − | 0.463623i | ||||
\(351\) | −71724.6 | − | 52281.0i | −0.582176 | − | 0.424356i | ||||
\(352\) | −19720.9 | + | 26007.9i | −0.159163 | + | 0.209903i | ||||
\(353\) | − | 101446.i | − | 0.814111i | −0.913404 | − | 0.407055i | \(-0.866556\pi\) | ||
0.913404 | − | 0.407055i | \(-0.133444\pi\) | |||||||
\(354\) | 129167. | − | 79265.4i | 1.03073 | − | 0.632524i | ||||
\(355\) | −2728.39 | + | 2728.39i | −0.0216496 | + | 0.0216496i | ||||
\(356\) | 26887.6 | + | 17373.6i | 0.212155 | + | 0.137085i | ||||
\(357\) | −5779.47 | − | 111380.i | −0.0453473 | − | 0.873917i | ||||
\(358\) | 92833.4 | − | 50542.2i | 0.724333 | − | 0.394356i | ||||
\(359\) | 131908. | 1.02348 | 0.511742 | − | 0.859139i | \(-0.329001\pi\) | ||||
0.511742 | + | 0.859139i | \(0.329001\pi\) | |||||||
\(360\) | 4937.12 | + | 172683.i | 0.0380951 | + | 1.33243i | ||||
\(361\) | − | 101374.i | − | 0.777879i | ||||||
\(362\) | 33347.2 | − | 18155.5i | 0.254473 | − | 0.138545i | ||||
\(363\) | −122461. | + | 6354.44i | −0.929357 | + | 0.0482241i | ||||
\(364\) | −12481.9 | − | 58068.4i | −0.0942061 | − | 0.438266i | ||||
\(365\) | −226642. | − | 226642.i | −1.70120 | − | 1.70120i | ||||
\(366\) | 7385.12 | − | 4532.00i | 0.0551310 | − | 0.0338320i | ||||
\(367\) | 25251.8 | 0.187482 | 0.0937411 | − | 0.995597i | \(-0.470117\pi\) | ||||
0.0937411 | + | 0.995597i | \(0.470117\pi\) | |||||||
\(368\) | −57852.7 | − | 128353.i | −0.427197 | − | 0.947789i | ||||
\(369\) | −125702. | + | 13080.5i | −0.923190 | + | 0.0960667i | ||||
\(370\) | −65468.3 | + | 221951.i | −0.478220 | + | 1.62126i | ||||
\(371\) | −94791.6 | − | 94791.6i | −0.688687 | − | 0.688687i | ||||
\(372\) | −122937. | + | 213808.i | −0.888374 | + | 1.54503i | ||||
\(373\) | −107875. | − | 107875.i | −0.775362 | − | 0.775362i | 0.203676 | − | 0.979038i | \(-0.434711\pi\) |
−0.979038 | + | 0.203676i | \(0.934711\pi\) | |||||||
\(374\) | −45511.5 | + | 24778.3i | −0.325371 | + | 0.177145i | ||||
\(375\) | 28008.9 | − | 31074.7i | 0.199174 | − | 0.220976i | ||||
\(376\) | −72446.9 | − | 84236.5i | −0.512441 | − | 0.595833i | ||||
\(377\) | 32763.5 | 0.230519 | ||||||||
\(378\) | 11640.5 | − | 88143.1i | 0.0814685 | − | 0.616886i | ||||
\(379\) | −20049.2 | − | 20049.2i | −0.139578 | − | 0.139578i | 0.633865 | − | 0.773444i | \(-0.281467\pi\) |
−0.773444 | + | 0.633865i | \(0.781467\pi\) | |||||||
\(380\) | 139288. | − | 215564.i | 0.964597 | − | 1.49283i | ||||
\(381\) | 9271.79 | + | 178683.i | 0.0638725 | + | 1.23093i | ||||
\(382\) | −192662. | − | 56829.2i | −1.32029 | − | 0.389444i | ||||
\(383\) | 164611.i | 1.12218i | 0.827755 | + | 0.561090i | \(0.189618\pi\) | ||||
−0.827755 | + | 0.561090i | \(0.810382\pi\) | |||||||
\(384\) | 55405.5 | − | 136651.i | 0.375742 | − | 0.926724i | ||||
\(385\) | 32386.1 | 0.218493 | ||||||||
\(386\) | 40613.2 | − | 137687.i | 0.272579 | − | 0.924098i | ||||
\(387\) | −114747. | − | 93116.7i | −0.766160 | − | 0.621736i | ||||
\(388\) | 177785. | + | 114877.i | 1.18095 | + | 0.763077i | ||||
\(389\) | −121664. | + | 121664.i | −0.804012 | + | 0.804012i | −0.983720 | − | 0.179708i | \(-0.942485\pi\) |
0.179708 | + | 0.983720i | \(0.442485\pi\) | |||||||
\(390\) | −34008.2 | + | 142048.i | −0.223591 | + | 0.933911i | ||||
\(391\) | − | 223523.i | − | 1.46207i | ||||||
\(392\) | −71395.0 | + | 61402.6i | −0.464618 | + | 0.399590i | ||||
\(393\) | 48747.8 | − | 54083.7i | 0.315624 | − | 0.350172i | ||||
\(394\) | −58093.5 | − | 106703.i | −0.374227 | − | 0.687362i | ||||
\(395\) | 121360. | − | 121360.i | 0.777825 | − | 0.777825i | ||||
\(396\) | −39271.2 | + | 12814.6i | −0.250429 | + | 0.0817175i | ||||
\(397\) | 185011. | − | 185011.i | 1.17386 | − | 1.17386i | 0.192576 | − | 0.981282i | \(-0.438316\pi\) |
0.981282 | − | 0.192576i | \(-0.0616843\pi\) | |||||||
\(398\) | −5451.09 | − | 1607.90i | −0.0344126 | − | 0.0101506i | ||||
\(399\) | −88433.4 | + | 98113.2i | −0.555483 | + | 0.616285i | ||||
\(400\) | 113313. | − | 51073.6i | 0.708207 | − | 0.319210i | ||||
\(401\) | 116396.i | 0.723849i | 0.932207 | + | 0.361925i | \(0.117880\pi\) | ||||
−0.932207 | + | 0.361925i | \(0.882120\pi\) | |||||||
\(402\) | 113816. | − | 69844.8i | 0.704288 | − | 0.432197i | ||||
\(403\) | −147450. | + | 147450.i | −0.907892 | + | 0.907892i | ||||
\(404\) | 6528.51 | − | 1403.32i | 0.0399992 | − | 0.00859791i | ||||
\(405\) | −119459. | + | 183121.i | −0.728299 | + | 1.11642i | ||||
\(406\) | 15693.1 | + | 28824.4i | 0.0952046 | + | 0.174867i | ||||
\(407\) | −55333.9 | −0.334043 | ||||||||
\(408\) | 169344. | − | 161644.i | 1.01730 | − | 0.971045i | ||||
\(409\) | 281444.i | 1.68246i | 0.540674 | + | 0.841232i | \(0.318169\pi\) | ||||
−0.540674 | + | 0.841232i | \(0.681831\pi\) | |||||||
\(410\) | 99448.3 | + | 182662.i | 0.591602 | + | 1.08663i | ||||
\(411\) | 6810.49 | + | 131249.i | 0.0403176 | + | 0.776987i | ||||
\(412\) | −110441. | + | 170920.i | −0.650632 | + | 1.00693i | ||||
\(413\) | 90759.3 | + | 90759.3i | 0.532097 | + | 0.532097i | ||||
\(414\) | 32452.2 | − | 175206.i | 0.189340 | − | 1.02223i | ||||
\(415\) | −30799.7 | −0.178834 | ||||||||
\(416\) | 75328.5 | − | 99342.9i | 0.435284 | − | 0.574051i | ||||
\(417\) | 25268.8 | − | 28034.7i | 0.145315 | − | 0.161222i | ||||
\(418\) | 58863.1 | + | 17362.7i | 0.336892 | + | 0.0993723i | ||||
\(419\) | −153518. | − | 153518.i | −0.874442 | − | 0.874442i | 0.118511 | − | 0.992953i | \(-0.462188\pi\) |
−0.992953 | + | 0.118511i | \(0.962188\pi\) | |||||||
\(420\) | −141259. | + | 38119.0i | −0.800789 | + | 0.216094i | ||||
\(421\) | −110511. | − | 110511.i | −0.623508 | − | 0.623508i | 0.322918 | − | 0.946427i | \(-0.395336\pi\) |
−0.946427 | + | 0.322918i | \(0.895336\pi\) | |||||||
\(422\) | 109767. | + | 201616.i | 0.616380 | + | 1.13214i | ||||
\(423\) | −14554.0 | − | 139862.i | −0.0813395 | − | 0.781663i | ||||
\(424\) | 21113.6 | − | 280597.i | 0.117444 | − | 1.56082i | ||||
\(425\) | 197331. | 1.09249 | ||||||||
\(426\) | 4053.77 | + | 970.529i | 0.0223378 | + | 0.00534797i | ||||
\(427\) | 5189.16 | + | 5189.16i | 0.0284604 | + | 0.0284604i | ||||
\(428\) | 114935. | − | 24705.5i | 0.627430 | − | 0.134867i | ||||
\(429\) | −34879.7 | + | 1809.90i | −0.189521 | + | 0.00983420i | ||||
\(430\) | −68801.5 | + | 233251.i | −0.372101 | + | 1.26150i | ||||
\(431\) | − | 122350.i | − | 0.658640i | −0.944218 | − | 0.329320i | \(-0.893181\pi\) | ||
0.944218 | − | 0.329320i | \(-0.106819\pi\) | |||||||
\(432\) | 156207. | − | 102117.i | 0.837016 | − | 0.547179i | ||||
\(433\) | −113160. | −0.603557 | −0.301779 | − | 0.953378i | \(-0.597580\pi\) | ||||
−0.301779 | + | 0.953378i | \(0.597580\pi\) | |||||||
\(434\) | −200348. | − | 59096.3i | −1.06367 | − | 0.313748i | ||||
\(435\) | −4182.33 | − | 80600.4i | −0.0221024 | − | 0.425950i | ||||
\(436\) | 112820. | − | 24250.8i | 0.593488 | − | 0.127572i | ||||
\(437\) | −187185. | + | 187185.i | −0.980187 | + | 0.980187i | ||||
\(438\) | −80619.9 | + | 336738.i | −0.420237 | + | 1.75527i | ||||
\(439\) | − | 17070.6i | − | 0.0885766i | −0.999019 | − | 0.0442883i | \(-0.985898\pi\) | ||
0.999019 | − | 0.0442883i | \(-0.0141020\pi\) | |||||||
\(440\) | 44327.0 | + | 51540.6i | 0.228962 | + | 0.266222i | ||||
\(441\) | −118541. | + | 12335.3i | −0.609524 | + | 0.0634268i | ||||
\(442\) | 173842. | − | 94646.3i | 0.889835 | − | 0.484461i | ||||
\(443\) | 154820. | − | 154820.i | 0.788897 | − | 0.788897i | −0.192416 | − | 0.981313i | \(-0.561632\pi\) |
0.981313 | + | 0.192416i | \(0.0616323\pi\) | |||||||
\(444\) | 241351. | − | 65129.0i | 1.22429 | − | 0.330376i | ||||
\(445\) | 47145.9 | − | 47145.9i | 0.238080 | − | 0.238080i | ||||
\(446\) | −5546.93 | + | 18805.2i | −0.0278858 | + | 0.0945383i | ||||
\(447\) | 31466.8 | + | 28362.3i | 0.157484 | + | 0.141947i | ||||
\(448\) | 123480. | + | 18688.4i | 0.615236 | + | 0.0931141i | ||||
\(449\) | 54358.7i | 0.269635i | 0.990870 | + | 0.134817i | \(0.0430448\pi\) | ||||
−0.990870 | + | 0.134817i | \(0.956955\pi\) | |||||||
\(450\) | 154676. | + | 28649.5i | 0.763830 | + | 0.141479i | ||||
\(451\) | −35166.0 | + | 35166.0i | −0.172890 | + | 0.172890i | ||||
\(452\) | −167789. | + | 259673.i | −0.821270 | + | 1.27101i | ||||
\(453\) | −67138.9 | + | 3483.82i | −0.327173 | + | 0.0169769i | ||||
\(454\) | −105492. | + | 57434.1i | −0.511810 | + | 0.278649i | ||||
\(455\) | −123706. | −0.597541 | ||||||||
\(456\) | −277181. | − | 6448.48i | −1.33301 | − | 0.0310118i | ||||
\(457\) | 40139.2i | 0.192193i | 0.995372 | + | 0.0960963i | \(0.0306357\pi\) | ||||
−0.995372 | + | 0.0960963i | \(0.969364\pi\) | |||||||
\(458\) | −46757.4 | + | 25456.6i | −0.222905 | + | 0.121358i | ||||
\(459\) | 292716. | − | 45896.7i | 1.38938 | − | 0.217849i | ||||
\(460\) | −286683. | + | 61623.2i | −1.35484 | + | 0.291225i | ||||
\(461\) | −54027.7 | − | 54027.7i | −0.254223 | − | 0.254223i | 0.568476 | − | 0.822700i | \(-0.307533\pi\) |
−0.822700 | + | 0.568476i | \(0.807533\pi\) | |||||||
\(462\) | −18299.1 | − | 29819.3i | −0.0857324 | − | 0.139705i | ||||
\(463\) | −236693. | −1.10414 | −0.552069 | − | 0.833798i | \(-0.686161\pi\) | ||||
−0.552069 | + | 0.833798i | \(0.686161\pi\) | |||||||
\(464\) | −24393.1 | + | 64426.9i | −0.113300 | + | 0.299248i | ||||
\(465\) | 381559. | + | 343915.i | 1.76464 | + | 1.59054i | ||||
\(466\) | −51234.3 | + | 173695.i | −0.235933 | + | 0.799861i | ||||
\(467\) | −112758. | − | 112758.i | −0.517026 | − | 0.517026i | 0.399644 | − | 0.916670i | \(-0.369134\pi\) |
−0.916670 | + | 0.399644i | \(0.869134\pi\) | |||||||
\(468\) | 150005. | − | 48948.3i | 0.684881 | − | 0.223484i | ||||
\(469\) | 79972.7 | + | 79972.7i | 0.363577 | + | 0.363577i | ||||
\(470\) | −203238. | + | 110651.i | −0.920043 | + | 0.500908i | ||||
\(471\) | 51109.0 | + | 46066.6i | 0.230386 | + | 0.207656i | ||||
\(472\) | −20215.4 | + | 268661.i | −0.0907400 | + | 1.20593i | ||||
\(473\) | −58151.1 | −0.259918 | ||||||||
\(474\) | −180314. | − | 43169.6i | −0.802550 | − | 0.192142i | ||||
\(475\) | −165251. | − | 165251.i | −0.732416 | − | 0.732416i | ||||
\(476\) | 166534. | + | 107607.i | 0.735005 | + | 0.474927i | ||||
\(477\) | 224409. | − | 276537.i | 0.986287 | − | 1.21539i | ||||
\(478\) | 89493.2 | + | 26397.6i | 0.391683 | + | 0.115534i | ||||
\(479\) | 61599.1i | 0.268475i | 0.990949 | + | 0.134237i | \(0.0428585\pi\) | ||||
−0.990949 | + | 0.134237i | \(0.957142\pi\) | |||||||
\(480\) | −254006. | − | 172632.i | −1.10246 | − | 0.749271i | ||||
\(481\) | 211360. | 0.913552 | ||||||||
\(482\) | 13840.8 | − | 46923.1i | 0.0595755 | − | 0.201973i | ||||
\(483\) | 150710. | − | 7820.31i | 0.646024 | − | 0.0335220i | ||||
\(484\) | 118312. | − | 183102.i | 0.505056 | − | 0.781632i | ||||
\(485\) | 311735. | − | 311735.i | 1.32526 | − | 1.32526i | ||||
\(486\) | 236106. | + | 6522.40i | 0.999619 | + | 0.0276144i | ||||
\(487\) | 314355.i | 1.32545i | 0.748864 | + | 0.662724i | \(0.230600\pi\) | ||||
−0.748864 | + | 0.662724i | \(0.769400\pi\) | |||||||
\(488\) | −1155.82 | + | 15360.7i | −0.00485343 | + | 0.0645017i | ||||
\(489\) | 55520.6 | + | 50042.9i | 0.232186 | + | 0.209279i | ||||
\(490\) | 93782.4 | + | 172255.i | 0.390597 | + | 0.717430i | ||||
\(491\) | −154216. | + | 154216.i | −0.639684 | + | 0.639684i | −0.950478 | − | 0.310793i | \(-0.899405\pi\) |
0.310793 | + | 0.950478i | \(0.399405\pi\) | |||||||
\(492\) | 111993. | − | 194776.i | 0.462660 | − | 0.804645i | ||||
\(493\) | −77338.3 | + | 77338.3i | −0.318200 | + | 0.318200i | ||||
\(494\) | −224841. | − | 66320.9i | −0.921343 | − | 0.271767i | ||||
\(495\) | 8904.94 | + | 85575.4i | 0.0363430 | + | 0.349252i | ||||
\(496\) | −180170. | − | 399728.i | −0.732349 | − | 1.62481i | ||||
\(497\) | 3530.33i | 0.0142923i | ||||||||
\(498\) | 17402.7 | + | 28358.7i | 0.0701712 | + | 0.114348i | ||||
\(499\) | 24132.3 | − | 24132.3i | 0.0969167 | − | 0.0969167i | −0.656986 | − | 0.753903i | \(-0.728169\pi\) |
0.753903 | + | 0.656986i | \(0.228169\pi\) | |||||||
\(500\) | 15629.6 | + | 72711.8i | 0.0625182 | + | 0.290847i | ||||
\(501\) | 3284.99 | + | 63307.2i | 0.0130876 | + | 0.252219i | ||||
\(502\) | −70799.1 | − | 130040.i | −0.280945 | − | 0.516025i | ||||
\(503\) | 142974. | 0.565096 | 0.282548 | − | 0.959253i | \(-0.408820\pi\) | ||||
0.282548 | + | 0.959253i | \(0.408820\pi\) | |||||||
\(504\) | 114913. | + | 108525.i | 0.452386 | + | 0.427237i | ||||
\(505\) | − | 13908.0i | − | 0.0545358i | ||||||
\(506\) | −33528.0 | − | 61582.5i | −0.130950 | − | 0.240523i | ||||
\(507\) | −123473. | + | 6406.97i | −0.480347 | + | 0.0249251i | ||||
\(508\) | −267165. | − | 172630.i | −1.03527 | − | 0.668943i | ||||
\(509\) | 65627.8 | + | 65627.8i | 0.253310 | + | 0.253310i | 0.822326 | − | 0.569016i | \(-0.192676\pi\) |
−0.569016 | + | 0.822326i | \(0.692676\pi\) | |||||||
\(510\) | −255028. | − | 415581.i | −0.980499 | − | 1.59777i | ||||
\(511\) | −293257. | −1.12307 | ||||||||
\(512\) | 139267. | + | 222091.i | 0.531260 | + | 0.847209i | ||||
\(513\) | −283566. | − | 206695.i | −1.07750 | − | 0.785407i | ||||
\(514\) | −333819. | − | 98466.0i | −1.26353 | − | 0.372701i | ||||
\(515\) | 299698. | + | 299698.i | 1.12998 | + | 1.12998i | ||||
\(516\) | 253639. | − | 68445.0i | 0.952614 | − | 0.257065i | ||||
\(517\) | −39127.3 | − | 39127.3i | −0.146386 | − | 0.146386i | ||||
\(518\) | 101238. | + | 185949.i | 0.377298 | + | 0.693002i | ||||
\(519\) | −242574. | + | 269126.i | −0.900554 | + | 0.999128i | ||||
\(520\) | −169317. | − | 196871.i | −0.626173 | − | 0.728073i | ||||
\(521\) | 414184. | 1.52587 | 0.762935 | − | 0.646475i | \(-0.223758\pi\) | ||||
0.762935 | + | 0.646475i | \(0.223758\pi\) | |||||||
\(522\) | −71849.2 | + | 49392.5i | −0.263682 | + | 0.181267i | ||||
\(523\) | 274563. | + | 274563.i | 1.00378 | + | 1.00378i | 0.999993 | + | 0.00378778i | \(0.00120569\pi\) |
0.00378778 | + | 0.999993i | \(0.498794\pi\) | |||||||
\(524\) | 27202.3 | + | 126551.i | 0.0990703 | + | 0.460895i | ||||
\(525\) | 6903.94 | + | 133050.i | 0.0250483 | + | 0.482722i | ||||
\(526\) | 40114.0 | − | 135995.i | 0.144986 | − | 0.491530i | ||||
\(527\) | − | 696112.i | − | 2.50644i | ||||||
\(528\) | 22409.6 | − | 69935.8i | 0.0803834 | − | 0.250860i | ||||
\(529\) | 22611.6 | 0.0808014 | ||||||||
\(530\) | −562128. | − | 165810.i | −2.00117 | − | 0.590281i | ||||
\(531\) | −214863. | + | 264774.i | −0.762030 | + | 0.939043i | ||||
\(532\) | −49347.7 | − | 229575.i | −0.174359 | − | 0.811152i | ||||
\(533\) | 134325. | − | 134325.i | 0.472826 | − | 0.472826i | ||||
\(534\) | −70048.0 | − | 16770.5i | −0.245648 | − | 0.0588116i | ||||
\(535\) | − | 244852.i | − | 0.855451i | ||||||
\(536\) | −17812.8 | + | 236731.i | −0.0620017 | + | 0.823997i | ||||
\(537\) | −159228. | + | 176657.i | −0.552167 | + | 0.612607i | ||||
\(538\) | 291201. | − | 158542.i | 1.00607 | − | 0.547745i | ||||
\(539\) | −33162.5 | + | 33162.5i | −0.114148 | + | 0.114148i | ||||
\(540\) | −139565. | − | 362775.i | −0.478617 | − | 1.24409i | ||||
\(541\) | −94841.5 | + | 94841.5i | −0.324044 | + | 0.324044i | −0.850316 | − | 0.526272i | \(-0.823589\pi\) |
0.526272 | + | 0.850316i | \(0.323589\pi\) | |||||||
\(542\) | −27921.5 | + | 94659.6i | −0.0950475 | + | 0.322230i | ||||
\(543\) | −57197.0 | + | 63457.8i | −0.193988 | + | 0.215221i | ||||
\(544\) | 56686.1 | + | 412313.i | 0.191549 | + | 1.39325i | ||||
\(545\) | − | 240345.i | − | 0.809175i | ||||||
\(546\) | 69897.5 | + | 113901.i | 0.234464 | + | 0.382071i | ||||
\(547\) | 365888. | − | 365888.i | 1.22285 | − | 1.22285i | 0.256238 | − | 0.966614i | \(-0.417517\pi\) |
0.966614 | − | 0.256238i | \(-0.0824832\pi\) | |||||||
\(548\) | −196243. | − | 126804.i | −0.653482 | − | 0.422251i | ||||
\(549\) | −12284.8 | + | 15138.4i | −0.0407589 | + | 0.0502269i | ||||
\(550\) | 54366.4 | − | 29599.2i | 0.179724 | − | 0.0978487i | ||||
\(551\) | 129531. | 0.426650 | ||||||||
\(552\) | 218724. | + | 229143.i | 0.717823 | + | 0.752018i | ||||
\(553\) | − | 157031.i | − | 0.513493i | ||||||
\(554\) | 366230. | − | 199390.i | 1.19326 | − | 0.649657i | ||||
\(555\) | −26980.6 | − | 519961.i | −0.0875924 | − | 1.68805i | ||||
\(556\) | 14100.5 | + | 65598.4i | 0.0456127 | + | 0.212199i | ||||
\(557\) | −61177.0 | − | 61177.0i | −0.197187 | − | 0.197187i | 0.601606 | − | 0.798793i | \(-0.294528\pi\) |
−0.798793 | + | 0.601606i | \(0.794528\pi\) | |||||||
\(558\) | 101065. | − | 545640.i | 0.324589 | − | 1.75242i | ||||
\(559\) | 222121. | 0.710832 | ||||||||
\(560\) | 92101.6 | − | 243258.i | 0.293691 | − | 0.775696i | ||||
\(561\) | 78061.3 | − | 86605.9i | 0.248033 | − | 0.275183i | ||||
\(562\) | −26873.1 | + | 91105.1i | −0.0850834 | + | 0.288450i | ||||
\(563\) | −335144. | − | 335144.i | −1.05734 | − | 1.05734i | −0.998253 | − | 0.0590876i | \(-0.981181\pi\) |
−0.0590876 | − | 0.998253i | \(-0.518819\pi\) | |||||||
\(564\) | 216716. | + | 124609.i | 0.681291 | + | 0.391734i | ||||
\(565\) | 455320. | + | 455320.i | 1.42633 | + | 1.42633i | ||||
\(566\) | 171676. | − | 93467.4i | 0.535892 | − | 0.291761i | ||||
\(567\) | 41187.0 | + | 195758.i | 0.128113 | + | 0.608911i | ||||
\(568\) | −5618.31 | + | 4831.98i | −0.0174144 | + | 0.0149771i | ||||
\(569\) | −217758. | −0.672589 | −0.336294 | − | 0.941757i | \(-0.609174\pi\) | ||||
−0.336294 | + | 0.941757i | \(0.609174\pi\) | |||||||
\(570\) | −134453. | + | 561590.i | −0.413827 | + | 1.72850i | ||||
\(571\) | 158164. | + | 158164.i | 0.485103 | + | 0.485103i | 0.906757 | − | 0.421654i | \(-0.138550\pi\) |
−0.421654 | + | 0.906757i | \(0.638550\pi\) | |||||||
\(572\) | 33698.2 | − | 52151.9i | 0.102995 | − | 0.159396i | ||||
\(573\) | 451348. | − | 23420.3i | 1.37468 | − | 0.0713318i | ||||
\(574\) | 182514. | + | 53835.9i | 0.553953 | + | 0.163398i | ||||
\(575\) | 267012.i | 0.807597i | ||||||||
\(576\) | −15428.9 | + | 331417.i | −0.0465038 | + | 0.998918i | ||||
\(577\) | −636708. | −1.91244 | −0.956222 | − | 0.292644i | \(-0.905465\pi\) | ||||
−0.956222 | + | 0.292644i | \(0.905465\pi\) | |||||||
\(578\) | −92422.9 | + | 313332.i | −0.276646 | + | 0.937884i | ||||
\(579\) | 16737.4 | + | 322557.i | 0.0499265 | + | 0.962166i | ||||
\(580\) | 120513. | + | 77870.3i | 0.358244 | + | 0.231481i | ||||
\(581\) | −19926.2 | + | 19926.2i | −0.0590300 | + | 0.0590300i | ||||
\(582\) | −463168. | − | 110889.i | −1.36739 | − | 0.327372i | ||||
\(583\) | − | 140143.i | − | 0.412319i | ||||||
\(584\) | −401383. | − | 466702.i | −1.17688 | − | 1.36840i | ||||
\(585\) | −34014.4 | − | 326875.i | −0.0993921 | − | 0.955146i | ||||
\(586\) | −44669.0 | − | 82045.8i | −0.130080 | − | 0.238925i | ||||
\(587\) | −157284. | + | 157284.i | −0.456465 | + | 0.456465i | −0.897493 | − | 0.441028i | \(-0.854614\pi\) |
0.441028 | + | 0.897493i | \(0.354614\pi\) | |||||||
\(588\) | 105613. | − | 183679.i | 0.305465 | − | 0.531256i | ||||
\(589\) | −582948. | + | 582948.i | −1.68035 | + | 1.68035i | ||||
\(590\) | 538216. | + | 158757.i | 1.54615 | + | 0.456066i | ||||
\(591\) | 203050. | + | 183017.i | 0.581338 | + | 0.523983i | ||||
\(592\) | −157362. | + | 415624.i | −0.449011 | + | 1.18593i | ||||
\(593\) | 360966.i | 1.02650i | 0.858240 | + | 0.513248i | \(0.171558\pi\) | ||||
−0.858240 | + | 0.513248i | \(0.828442\pi\) | |||||||
\(594\) | 73761.5 | − | 56551.8i | 0.209053 | − | 0.160278i | ||||
\(595\) | 292008. | − | 292008.i | 0.824824 | − | 0.824824i | ||||
\(596\) | −73629.3 | + | 15826.8i | −0.207280 | + | 0.0445553i | ||||
\(597\) | 12770.2 | − | 662.642i | 0.0358302 | − | 0.00185922i | ||||
\(598\) | 128068. | + | 235228.i | 0.358127 | + | 0.657790i | ||||
\(599\) | 397239. | 1.10713 | 0.553565 | − | 0.832806i | \(-0.313267\pi\) | ||||
0.553565 | + | 0.832806i | \(0.313267\pi\) | |||||||
\(600\) | −202292. | + | 193094.i | −0.561923 | + | 0.536372i | ||||
\(601\) | − | 484580.i | − | 1.34158i | −0.741647 | − | 0.670790i | \(-0.765955\pi\) | ||
0.741647 | − | 0.670790i | \(-0.234045\pi\) | |||||||
\(602\) | 106392. | + | 195416.i | 0.293574 | + | 0.539222i | ||||
\(603\) | −189327. | + | 233306.i | −0.520688 | + | 0.641639i | ||||
\(604\) | 64864.7 | − | 100386.i | 0.177801 | − | 0.275168i | ||||
\(605\) | −321059. | − | 321059.i | −0.877150 | − | 0.877150i | ||||
\(606\) | −12805.7 | + | 7858.42i | −0.0348705 | + | 0.0213988i | ||||
\(607\) | 608447. | 1.65137 | 0.825687 | − | 0.564128i | \(-0.190788\pi\) | ||||
0.825687 | + | 0.564128i | \(0.190788\pi\) | |||||||
\(608\) | 297814. | − | 392755.i | 0.805633 | − | 1.06247i | ||||
\(609\) | −54851.2 | − | 49439.6i | −0.147894 | − | 0.133303i | ||||
\(610\) | 30772.5 | + | 9076.90i | 0.0826996 | + | 0.0243937i | ||||
\(611\) | 149456. | + | 149456.i | 0.400341 | + | 0.400341i | ||||
\(612\) | −238545. | + | 469631.i | −0.636895 | + | 1.25387i | ||||
\(613\) | −27255.3 | − | 27255.3i | −0.0725321 | − | 0.0725321i | 0.669910 | − | 0.742442i | \(-0.266333\pi\) |
−0.742442 | + | 0.669910i | \(0.766333\pi\) | |||||||
\(614\) | −213349. | − | 391870.i | −0.565920 | − | 1.03945i | ||||
\(615\) | −347595. | − | 313301.i | −0.919016 | − | 0.828346i | ||||
\(616\) | 62022.6 | + | 4666.90i | 0.163451 | + | 0.0122989i | ||||
\(617\) | −346131. | −0.909223 | −0.454611 | − | 0.890690i | \(-0.650222\pi\) | ||||
−0.454611 | + | 0.890690i | \(0.650222\pi\) | |||||||
\(618\) | 106607. | − | 445283.i | 0.279131 | − | 1.16589i | ||||
\(619\) | −432060. | − | 432060.i | −1.12762 | − | 1.12762i | −0.990563 | − | 0.137056i | \(-0.956236\pi\) |
−0.137056 | − | 0.990563i | \(-0.543764\pi\) | |||||||
\(620\) | −892812. | + | 191912.i | −2.32261 | + | 0.499250i | ||||
\(621\) | 62103.6 | + | 396079.i | 0.161040 | + | 1.02707i | ||||
\(622\) | −200114. | + | 678425.i | −0.517245 | + | 1.75356i | ||||
\(623\) | − | 61003.1i | − | 0.157172i | ||||||
\(624\) | −85598.6 | + | 267135.i | −0.219835 | + | 0.686060i | ||||
\(625\) | 458347. | 1.17337 | ||||||||
\(626\) | 522386. | + | 154087.i | 1.33304 | + | 0.393204i | ||||
\(627\) | −137898. | + | 7155.48i | −0.350770 | + | 0.0182014i | ||||
\(628\) | −119590. | + | 25706.2i | −0.303233 | + | 0.0651805i | ||||
\(629\) | −498917. | + | 498917.i | −1.26103 | + | 1.26103i | ||||
\(630\) | 271283. | − | 186492.i | 0.683505 | − | 0.469873i | ||||
\(631\) | 7438.98i | 0.0186834i | 0.999956 | + | 0.00934168i | \(0.00297359\pi\) | ||||
−0.999956 | + | 0.00934168i | \(0.997026\pi\) | |||||||
\(632\) | 249905. | − | 214929.i | 0.625664 | − | 0.538097i | ||||
\(633\) | −383663. | − | 345811.i | −0.957508 | − | 0.863040i | ||||
\(634\) | 470308. | − | 256054.i | 1.17005 | − | 0.637020i | ||||
\(635\) | −468458. | + | 468458.i | −1.16178 | + | 1.16178i | ||||
\(636\) | 164951. | + | 611264.i | 0.407793 | + | 1.51117i | ||||
\(637\) | 126672. | − | 126672.i | 0.312177 | − | 0.312177i | ||||
\(638\) | −9706.81 | + | 32908.0i | −0.0238471 | + | 0.0808463i | ||||
\(639\) | −9328.37 | + | 970.707i | −0.0228457 | + | 0.00237731i | ||||
\(640\) | 513192. | − | 186375.i | 1.25291 | − | 0.455017i | ||||
\(641\) | − | 51319.1i | − | 0.124900i | −0.998048 | − | 0.0624501i | \(-0.980109\pi\) | ||
0.998048 | − | 0.0624501i | \(-0.0198914\pi\) | |||||||
\(642\) | −225446. | + | 138348.i | −0.546980 | + | 0.335663i | ||||
\(643\) | −507202. | + | 507202.i | −1.22676 | + | 1.22676i | −0.261576 | + | 0.965183i | \(0.584242\pi\) |
−0.965183 | + | 0.261576i | \(0.915758\pi\) | |||||||
\(644\) | −145605. | + | 225341.i | −0.351079 | + | 0.543336i | ||||
\(645\) | −28354.3 | − | 546434.i | −0.0681553 | − | 1.31347i | ||||
\(646\) | 687288. | − | 374187.i | 1.64693 | − | 0.896652i | ||||
\(647\) | 100093. | 0.239107 | 0.119554 | − | 0.992828i | \(-0.461854\pi\) | ||||
0.119554 | + | 0.992828i | \(0.461854\pi\) | |||||||
\(648\) | −255165. | + | 333482.i | −0.607674 | + | 0.794186i | ||||
\(649\) | 134181.i | 0.318568i | ||||||||
\(650\) | −207665. | + | 113061.i | −0.491514 | + | 0.267600i | ||||
\(651\) | 469354. | − | 24354.6i | 1.10749 | − | 0.0574671i | ||||
\(652\) | −129913. | + | 27925.0i | −0.305602 | + | 0.0656899i | ||||
\(653\) | −168524. | − | 168524.i | −0.395217 | − | 0.395217i | 0.481325 | − | 0.876542i | \(-0.340156\pi\) |
−0.876542 | + | 0.481325i | \(0.840156\pi\) | |||||||
\(654\) | −221296. | + | 135802.i | −0.517391 | + | 0.317505i | ||||
\(655\) | 269597. | 0.628394 | ||||||||
\(656\) | 164132. | + | 364147.i | 0.381404 | + | 0.846191i | ||||
\(657\) | −80634.6 | − | 774889.i | −0.186806 | − | 1.79518i | ||||
\(658\) | −59900.2 | + | 203074.i | −0.138349 | + | 0.469031i | ||||
\(659\) | 568986. | + | 568986.i | 1.31018 | + | 1.31018i | 0.921280 | + | 0.388899i | \(0.127145\pi\) |
0.388899 | + | 0.921280i | \(0.372855\pi\) | |||||||
\(660\) | −132599. | − | 76242.6i | −0.304405 | − | 0.175029i | ||||
\(661\) | −131299. | − | 131299.i | −0.300511 | − | 0.300511i | 0.540703 | − | 0.841214i | \(-0.318158\pi\) |
−0.841214 | + | 0.540703i | \(0.818158\pi\) | |||||||
\(662\) | 386102. | − | 210209.i | 0.881021 | − | 0.479663i | ||||
\(663\) | −298173. | + | 330811.i | −0.678330 | + | 0.752580i | ||||
\(664\) | −58984.6 | − | 4438.30i | −0.133784 | − | 0.0100665i | ||||
\(665\) | −489075. | −1.10594 | ||||||||
\(666\) | −463506. | + | 318636.i | −1.04498 | + | 0.718366i | ||||
\(667\) | −104648. | − | 104648.i | −0.235222 | − | 0.235222i | ||||
\(668\) | −94656.5 | − | 61162.8i | −0.212128 | − | 0.137068i | ||||
\(669\) | −2285.98 | − | 44054.7i | −0.00510765 | − | 0.0984328i | ||||
\(670\) | 474250. | + | 139889.i | 1.05647 | + | 0.311625i | ||||
\(671\) | 7671.81i | 0.0170393i | ||||||||
\(672\) | −276019. | + | 52646.1i | −0.611223 | + | 0.116581i | ||||
\(673\) | −526792. | −1.16308 | −0.581539 | − | 0.813518i | \(-0.697549\pi\) | ||||
−0.581539 | + | 0.813518i | \(0.697549\pi\) | |||||||
\(674\) | 122421. | − | 415033.i | 0.269487 | − | 0.913615i | ||||
\(675\) | −349667. | + | 54826.4i | −0.767446 | + | 0.120332i | ||||
\(676\) | 119290. | − | 184616.i | 0.261043 | − | 0.403994i | ||||
\(677\) | 632296. | − | 632296.i | 1.37957 | − | 1.37957i | 0.534225 | − | 0.845342i | \(-0.320604\pi\) |
0.845342 | − | 0.534225i | \(-0.179396\pi\) | |||||||
\(678\) | 161964. | − | 676503.i | 0.352338 | − | 1.47167i | ||||
\(679\) | − | 403362.i | − | 0.874893i | ||||||
\(680\) | 864388. | + | 65040.9i | 1.86935 | + | 0.140659i | ||||
\(681\) | 180940. | − | 200746.i | 0.390158 | − | 0.432864i | ||||
\(682\) | −104416. | − | 191785.i | −0.224490 | − | 0.412331i | ||||
\(683\) | −303020. | + | 303020.i | −0.649575 | + | 0.649575i | −0.952890 | − | 0.303315i | \(-0.901907\pi\) |
0.303315 | + | 0.952890i | \(0.401907\pi\) | |||||||
\(684\) | 593051. | − | 193519.i | 1.26759 | − | 0.413629i | ||||
\(685\) | −344101. | + | 344101.i | −0.733339 | + | 0.733339i | ||||
\(686\) | 452977. | + | 133614.i | 0.962560 | + | 0.283924i | ||||
\(687\) | 80198.3 | − | 88976.7i | 0.169923 | − | 0.188522i | ||||
\(688\) | −165374. | + | 436785.i | −0.349374 | + | 0.922764i | ||||
\(689\) | 535307.i | 1.12762i | ||||||||
\(690\) | 562330. | − | 345083.i | 1.18112 | − | 0.724812i | ||||
\(691\) | 219958. | − | 219958.i | 0.460664 | − | 0.460664i | −0.438209 | − | 0.898873i | \(-0.644387\pi\) |
0.898873 | + | 0.438209i | \(0.144387\pi\) | |||||||
\(692\) | −135362. | − | 629729.i | −0.282672 | − | 1.31505i | ||||
\(693\) | 61125.2 | + | 49602.9i | 0.127278 | + | 0.103286i | ||||
\(694\) | −136301. | − | 250351.i | −0.282996 | − | 0.519793i | ||||
\(695\) | 139747. | 0.289317 | ||||||||
\(696\) | 3605.09 | − | 154961.i | 0.00744213 | − | 0.319892i | ||||
\(697\) | 634147.i | 1.30534i | ||||||||
\(698\) | −288413. | − | 529742.i | −0.591975 | − | 1.08731i | ||||
\(699\) | −21114.6 | − | 406912.i | −0.0432143 | − | 0.832811i | ||||
\(700\) | −198936. | − | 128543.i | −0.405991 | − | 0.262334i | ||||
\(701\) | 342309. | + | 342309.i | 0.696598 | + | 0.696598i | 0.963675 | − | 0.267077i | \(-0.0860578\pi\) |
−0.267077 | + | 0.963675i | \(0.586058\pi\) | |||||||
\(702\) | −281749. | + | 216012.i | −0.571726 | + | 0.438333i | ||||
\(703\) | 835620. | 1.69082 | ||||||||
\(704\) | 77463.7 | + | 105093.i | 0.156298 | + | 0.212045i | ||||
\(705\) | 348593. | − | 386750.i | 0.701359 | − | 0.778129i | ||||
\(706\) | −389204. | − | 114803.i | −0.780850 | − | 0.230326i | ||||
\(707\) | −8997.93 | − | 8997.93i | −0.0180013 | − | 0.0180013i | ||||
\(708\) | −157934. | − | 585261.i | −0.315071 | − | 1.16757i | ||||
\(709\) | −133031. | − | 133031.i | −0.264644 | − | 0.264644i | 0.562294 | − | 0.826937i | \(-0.309919\pi\) |
−0.826937 | + | 0.562294i | \(0.809919\pi\) | |||||||
\(710\) | 7380.05 | + | 13555.3i | 0.0146401 | + | 0.0268901i | ||||
\(711\) | 414931. | − | 43177.5i | 0.820798 | − | 0.0854119i | ||||
\(712\) | 97082.9 | − | 83495.3i | 0.191506 | − | 0.164703i | ||||
\(713\) | 941922. | 1.85283 | ||||||||
\(714\) | −433858. | − | 103872.i | −0.851042 | − | 0.203751i | ||||
\(715\) | −91445.2 | − | 91445.2i | −0.178875 | − | 0.178875i | ||||
\(716\) | −88852.5 | − | 413360.i | −0.173318 | − | 0.806310i | ||||
\(717\) | −209655. | + | 10878.9i | −0.407818 | + | 0.0211616i | ||||
\(718\) | 149275. | − | 506073.i | 0.289561 | − | 0.981668i | ||||
\(719\) | − | 216815.i | − | 0.419404i | −0.977765 | − | 0.209702i | \(-0.932751\pi\) | ||
0.977765 | − | 0.209702i | \(-0.0672493\pi\) | |||||||
\(720\) | 668099. | + | 176478.i | 1.28877 | + | 0.340428i | ||||
\(721\) | 387786. | 0.745971 | ||||||||
\(722\) | −388929. | − | 114722.i | −0.746098 | − | 0.220075i | ||||
\(723\) | 5704.04 | + | 109926.i | 0.0109120 | + | 0.210293i | ||||
\(724\) | −31917.2 | − | 148485.i | −0.0608902 | − | 0.283273i | ||||
\(725\) | 92385.4 | − | 92385.4i | 0.175763 | − | 0.175763i | ||||
\(726\) | −114205. | + | 477020.i | −0.216677 | + | 0.905031i | ||||
\(727\) | − | 426356.i | − | 0.806684i | −0.915049 | − | 0.403342i | \(-0.867849\pi\) | ||
0.915049 | − | 0.403342i | \(-0.132151\pi\) | |||||||
\(728\) | −236909. | − | 17826.3i | −0.447013 | − | 0.0336355i | ||||
\(729\) | −505937. | + | 162657.i | −0.952010 | + | 0.306067i | ||||
\(730\) | −1.12601e6 | + | 613046.i | −2.11299 | + | 1.15040i | ||||
\(731\) | −524318. | + | 524318.i | −0.981206 | + | 0.981206i | ||||
\(732\) | −9029.86 | − | 33462.3i | −0.0168523 | − | 0.0624502i | ||||
\(733\) | 259277. | − | 259277.i | 0.482564 | − | 0.482564i | −0.423385 | − | 0.905950i | \(-0.639158\pi\) |
0.905950 | + | 0.423385i | \(0.139158\pi\) | |||||||
\(734\) | 28576.6 | − | 96880.5i | 0.0530419 | − | 0.179823i | ||||
\(735\) | −327791. | − | 295451.i | −0.606768 | − | 0.546904i | ||||
\(736\) | −557908. | + | 76703.1i | −1.02993 | + | 0.141598i | ||||
\(737\) | 118234.i | 0.217674i | ||||||||
\(738\) | −92068.9 | + | 497070.i | −0.169044 | + | 0.912651i | ||||
\(739\) | −180349. | + | 180349.i | −0.330236 | + | 0.330236i | −0.852676 | − | 0.522440i | \(-0.825022\pi\) |
0.522440 | + | 0.852676i | \(0.325022\pi\) | |||||||
\(740\) | 777442. | + | 502349.i | 1.41973 | + | 0.917364i | ||||
\(741\) | 526732. | − | 27332.0i | 0.959298 | − | 0.0497777i | ||||
\(742\) | −470948. | + | 256403.i | −0.855392 | + | 0.465709i | ||||
\(743\) | −694270. | −1.25762 | −0.628812 | − | 0.777557i | \(-0.716458\pi\) | ||||
−0.628812 | + | 0.777557i | \(0.716458\pi\) | |||||||
\(744\) | 681167. | + | 713615.i | 1.23057 | + | 1.28919i | ||||
\(745\) | 156856.i | 0.282611i | ||||||||
\(746\) | −535951. | + | 291793.i | −0.963048 | + | 0.524321i | ||||
\(747\) | −58131.1 | − | 47173.2i | −0.104176 | − | 0.0845384i | ||||
\(748\) | 43559.9 | + | 202649.i | 0.0778545 | + | 0.362195i | ||||
\(749\) | −158410. | − | 158410.i | −0.282369 | − | 0.282369i | ||||
\(750\) | −87523.8 | − | 142624.i | −0.155598 | − | 0.253555i | ||||
\(751\) | −267385. | −0.474085 | −0.237043 | − | 0.971499i | \(-0.576178\pi\) | ||||
−0.237043 | + | 0.971499i | \(0.576178\pi\) | |||||||
\(752\) | −405166. | + | 182620.i | −0.716468 | + | 0.322934i | ||||
\(753\) | 247459. | + | 223045.i | 0.436429 | + | 0.393371i | ||||
\(754\) | 37077.3 | − | 125700.i | 0.0652178 | − | 0.221101i | ||||
\(755\) | −176020. | − | 176020.i | −0.308794 | − | 0.308794i | ||||
\(756\) | −324995. | − | 144409.i | −0.568634 | − | 0.252667i | ||||
\(757\) | −297097. | − | 297097.i | −0.518450 | − | 0.518450i | 0.398652 | − | 0.917102i | \(-0.369478\pi\) |
−0.917102 | + | 0.398652i | \(0.869478\pi\) | |||||||
\(758\) | −99609.3 | + | 54231.2i | −0.173365 | + | 0.0943868i | ||||
\(759\) | 117188. | + | 105626.i | 0.203423 | + | 0.183353i | ||||
\(760\) | −669400. | − | 778335.i | −1.15893 | − | 1.34753i | ||||
\(761\) | −186767. | −0.322500 | −0.161250 | − | 0.986914i | \(-0.551553\pi\) | ||||
−0.161250 | + | 0.986914i | \(0.551553\pi\) | |||||||
\(762\) | 696023. | + | 166637.i | 1.19871 | + | 0.286987i | ||||
\(763\) | −155494. | − | 155494.i | −0.267094 | − | 0.267094i | ||||
\(764\) | −436059. | + | 674852.i | −0.747065 | + | 1.15617i | ||||
\(765\) | 851880. | + | 691298.i | 1.45565 | + | 1.18125i | ||||
\(766\) | 631545. | + | 186285.i | 1.07633 | + | 0.317484i | ||||
\(767\) | − | 512535.i | − | 0.871230i | ||||||
\(768\) | −461572. | − | 367211.i | −0.782558 | − | 0.622577i | ||||
\(769\) | −150698. | −0.254832 | −0.127416 | − | 0.991849i | \(-0.540668\pi\) | ||||
−0.127416 | + | 0.991849i | \(0.540668\pi\) | |||||||
\(770\) | 36650.3 | − | 124252.i | 0.0618153 | − | 0.209566i | ||||
\(771\) | 782035. | − | 40579.5i | 1.31558 | − | 0.0682651i | ||||
\(772\) | −482286. | − | 311632.i | −0.809226 | − | 0.522886i | ||||
\(773\) | 71720.9 | − | 71720.9i | 0.120029 | − | 0.120029i | −0.644541 | − | 0.764570i | \(-0.722951\pi\) |
0.764570 | + | 0.644541i | \(0.222951\pi\) | |||||||
\(774\) | −487105. | + | 334858.i | −0.813094 | + | 0.558958i | ||||
\(775\) | 831549.i | 1.38447i | ||||||||
\(776\) | 641927. | − | 552084.i | 1.06601 | − | 0.916814i | ||||
\(777\) | −353850. | − | 318940.i | −0.586108 | − | 0.528283i | ||||
\(778\) | 329090. | + | 604456.i | 0.543695 | + | 0.998632i | ||||
\(779\) | 531056. | − | 531056.i | 0.875116 | − | 0.875116i | ||||
\(780\) | 506491. | + | 291226.i | 0.832497 | + | 0.478675i | ||||
\(781\) | −2609.67 | + | 2609.67i | −0.00427842 | + | 0.00427842i | ||||
\(782\) | −857562. | − | 252953.i | −1.40234 | − | 0.413644i | ||||
\(783\) | 115555. | − | 158530.i | 0.188480 | − | 0.258576i | ||||
\(784\) | 154781. | + | 343400.i | 0.251817 | + | 0.558686i | ||||
\(785\) | 254768.i | 0.413434i | ||||||||
\(786\) | −152330. | − | 248230.i | −0.246570 | − | 0.401799i | ||||
\(787\) | −318079. | + | 318079.i | −0.513553 | + | 0.513553i | −0.915613 | − | 0.402060i | \(-0.868294\pi\) |
0.402060 | + | 0.915613i | \(0.368294\pi\) | |||||||
\(788\) | −475118. | + | 102128.i | −0.765155 | + | 0.164472i | ||||
\(789\) | 16531.7 | + | 318593.i | 0.0265560 | + | 0.511779i | ||||
\(790\) | −328268. | − | 602947.i | −0.525987 | − | 0.966106i | ||||
\(791\) | 589150. | 0.941613 | ||||||||
\(792\) | 4722.29 | + | 165169.i | 0.00752840 | + | 0.263316i | ||||
\(793\) | − | 29304.2i | − | 0.0465997i | ||||||
\(794\) | −500437. | − | 919178.i | −0.793795 | − | 1.45800i | ||||
\(795\) | 1.31689e6 | − | 68333.1i | 2.08361 | − | 0.108118i | ||||
\(796\) | −12337.6 | + | 19093.9i | −0.0194718 | + | 0.0301348i | ||||
\(797\) | −148578. | − | 148578.i | −0.233905 | − | 0.233905i | 0.580416 | − | 0.814320i | \(-0.302890\pi\) |
−0.814320 | + | 0.580416i | \(0.802890\pi\) | |||||||
\(798\) | 276342. | + | 450313.i | 0.433951 | + | 0.707145i | ||||
\(799\) | −705581. | −1.10523 | ||||||||
\(800\) | −67715.1 | − | 492533.i | −0.105805 | − | 0.769583i | ||||
\(801\) | 161192. | − | 16773.5i | 0.251234 | − | 0.0261433i | ||||
\(802\) | 446561. | + | 131721.i | 0.694276 | + | 0.204789i | ||||
\(803\) | −216780. | − | 216780.i | −0.336192 | − | 0.336192i | ||||
\(804\) | −139164. | − | 515704.i | −0.215285 | − | 0.797790i | ||||
\(805\) | 395122. | + | 395122.i | 0.609732 | + | 0.609732i | ||||
\(806\) | 398839. | + | 732567.i | 0.613942 | + | 1.12766i | ||||
\(807\) | −499468. | + | 554139.i | −0.766939 | + | 0.850887i | ||||
\(808\) | 2004.17 | − | 26635.2i | 0.00306981 | − | 0.0407975i | ||||
\(809\) | 651511. | 0.995462 | 0.497731 | − | 0.867332i | \(-0.334167\pi\) | ||||
0.497731 | + | 0.867332i | \(0.334167\pi\) | |||||||
\(810\) | 567372. | + | 665547.i | 0.864764 | + | 1.01440i | ||||
\(811\) | 427993. | + | 427993.i | 0.650721 | + | 0.650721i | 0.953167 | − | 0.302445i | \(-0.0978030\pi\) |
−0.302445 | + | 0.953167i | \(0.597803\pi\) | |||||||
\(812\) | 128346. | − | 27588.3i | 0.194658 | − | 0.0418421i | ||||
\(813\) | −11506.9 | − | 221758.i | −0.0174092 | − | 0.335504i | ||||
\(814\) | −62619.6 | + | 212293.i | −0.0945064 | + | 0.320395i | ||||
\(815\) | 276759.i | 0.416665i | ||||||||
\(816\) | −428518. | − | 832630.i | −0.643560 | − | 1.25047i | ||||
\(817\) | 878164. | 1.31562 | ||||||||
\(818\) | 1.07978e6 | + | 318501.i | 1.61373 | + | 0.475998i | ||||
\(819\) | −233481. | − | 189469.i | −0.348084 | − | 0.282469i | ||||
\(820\) | 813338. | − | 174829.i | 1.20960 | − | 0.260007i | ||||
\(821\) | −813397. | + | 813397.i | −1.20675 | + | 1.20675i | −0.234672 | + | 0.972075i | \(0.575402\pi\) |
−0.972075 | + | 0.234672i | \(0.924598\pi\) | |||||||
\(822\) | 511256. | + | 122402.i | 0.756650 | + | 0.181152i | ||||
\(823\) | 801720.i | 1.18365i | 0.806067 | + | 0.591824i | \(0.201592\pi\) | ||||
−0.806067 | + | 0.591824i | \(0.798408\pi\) | |||||||
\(824\) | 530765. | + | 617139.i | 0.781714 | + | 0.908927i | ||||
\(825\) | −93249.2 | + | 103456.i | −0.137005 | + | 0.152002i | ||||
\(826\) | 450914. | − | 245496.i | 0.660897 | − | 0.359819i | ||||
\(827\) | 89642.7 | − | 89642.7i | 0.131070 | − | 0.131070i | −0.638528 | − | 0.769598i | \(-0.720456\pi\) |
0.769598 | + | 0.638528i | \(0.220456\pi\) | |||||||
\(828\) | −635466. | − | 322780.i | −0.926897 | − | 0.470811i | ||||
\(829\) | 216189. | − | 216189.i | 0.314576 | − | 0.314576i | −0.532104 | − | 0.846679i | \(-0.678598\pi\) |
0.846679 | + | 0.532104i | \(0.178598\pi\) | |||||||
\(830\) | −34855.0 | + | 118166.i | −0.0505952 | + | 0.171528i | ||||
\(831\) | −628157. | + | 696915.i | −0.909633 | + | 1.00920i | ||||
\(832\) | −295890. | − | 401427.i | −0.427448 | − | 0.579909i | ||||
\(833\) | 598018.i | 0.861835i | ||||||||
\(834\) | −78961.3 | − | 128671.i | −0.113523 | − | 0.184991i | ||||
\(835\) | −165975. | + | 165975.i | −0.238050 | + | 0.238050i | ||||
\(836\) | 133227. | − | 206184.i | 0.190625 | − | 0.295014i | ||||
\(837\) | 193408. | + | 1.23350e6i | 0.276073 | + | 1.76071i | ||||
\(838\) | −762715. | + | 415252.i | −1.08611 | + | 0.591322i | ||||
\(839\) | 522748. | 0.742623 | 0.371311 | − | 0.928508i | \(-0.378908\pi\) | ||||
0.371311 | + | 0.928508i | \(0.378908\pi\) | |||||||
\(840\) | −13611.8 | + | 585090.i | −0.0192911 | + | 0.829209i | ||||
\(841\) | − | 634865.i | − | 0.897614i | ||||||
\(842\) | −549047. | + | 298923.i | −0.774436 | + | 0.421634i | ||||
\(843\) | −11074.9 | − | 213431.i | −0.0155841 | − | 0.300332i | ||||
\(844\) | 897734. | − | 192970.i | 1.26027 | − | 0.270897i | ||||
\(845\) | −323713. | − | 323713.i | −0.453363 | − | 0.453363i | ||||
\(846\) | −553062. | − | 102440.i | −0.772740 | − | 0.143129i | ||||
\(847\) | −415425. | −0.579063 | ||||||||
\(848\) | −1.05264e6 | − | 398547.i | −1.46382 | − | 0.554227i | ||||
\(849\) | −294459. | + | 326690.i | −0.408516 | + | 0.453232i | ||||
\(850\) | 223313. | − | 757074.i | 0.309083 | − | 1.04785i | ||||
\(851\) | −675094. | − | 675094.i | −0.932191 | − | 0.932191i | ||||
\(852\) | 8311.03 | − | 14454.3i | 0.0114492 | − | 0.0199121i | ||||
\(853\) | 661424. | + | 661424.i | 0.909038 | + | 0.909038i | 0.996195 | − | 0.0871568i | \(-0.0277781\pi\) |
−0.0871568 | + | 0.996195i | \(0.527778\pi\) | |||||||
\(854\) | 25781.0 | − | 14036.2i | 0.0353496 | − | 0.0192457i | ||||
\(855\) | −134477. | − | 1.29231e6i | −0.183957 | − | 1.76780i | ||||
\(856\) | 35283.6 | − | 468916.i | 0.0481532 | − | 0.639952i | ||||
\(857\) | 144053. | 0.196137 | 0.0980685 | − | 0.995180i | \(-0.468734\pi\) | ||||
0.0980685 | + | 0.995180i | \(0.468734\pi\) | |||||||
\(858\) | −32528.4 | + | 135867.i | −0.0441863 | + | 0.184561i | ||||
\(859\) | −545660. | − | 545660.i | −0.739496 | − | 0.739496i | 0.232984 | − | 0.972481i | \(-0.425151\pi\) |
−0.972481 | + | 0.232984i | \(0.925151\pi\) | |||||||
\(860\) | 817025. | + | 527925.i | 1.10468 | + | 0.713798i | ||||
\(861\) | −427574. | + | 22186.7i | −0.576773 | + | 0.0299286i | ||||
\(862\) | −469404. | − | 138459.i | −0.631731 | − | 0.186340i | ||||
\(863\) | − | 484415.i | − | 0.650423i | −0.945641 | − | 0.325212i | \(-0.894564\pi\) | ||
0.945641 | − | 0.325212i | \(-0.105436\pi\) | |||||||
\(864\) | −215004. | − | 714863.i | −0.288018 | − | 0.957625i | ||||
\(865\) | −1.34154e6 | −1.79297 | ||||||||
\(866\) | −128060. | + | 434149.i | −0.170757 | + | 0.578899i | ||||
\(867\) | −38089.1 | − | 734039.i | −0.0506713 | − | 0.976520i | ||||
\(868\) | −453455. | + | 701775.i | −0.601860 | + | 0.931447i | ||||
\(869\) | 116079. | − | 116079.i | 0.153715 | − | 0.153715i | ||||
\(870\) | −313963. | − | 75167.1i | −0.414801 | − | 0.0993091i | ||||
\(871\) | − | 451621.i | − | 0.595303i | ||||||
\(872\) | 34634.2 | − | 460286.i | 0.0455483 | − | 0.605333i | ||||
\(873\) | 1.06582e6 | − | 110909.i | 1.39848 | − | 0.145525i | ||||
\(874\) | 506320. | + | 929983.i | 0.662830 | + | 1.21745i | ||||
\(875\) | 100215. | − | 100215.i | 0.130893 | − | 0.130893i | ||||
\(876\) | 1.20069e6 | + | 690380.i | 1.56467 | + | 0.899664i | ||||
\(877\) | 663775. | − | 663775.i | 0.863022 | − | 0.863022i | −0.128666 | − | 0.991688i | \(-0.541070\pi\) |
0.991688 | + | 0.128666i | \(0.0410695\pi\) | |||||||
\(878\) | −65492.6 | − | 19318.2i | −0.0849578 | − | 0.0250598i | ||||
\(879\) | 156129. | + | 140725.i | 0.202071 | + | 0.182135i | ||||
\(880\) | 247903. | − | 111737.i | 0.320122 | − | 0.144289i | ||||
\(881\) | − | 15986.6i | − | 0.0205970i | −0.999947 | − | 0.0102985i | \(-0.996722\pi\) | ||
0.999947 | − | 0.0102985i | \(-0.00327817\pi\) | |||||||
\(882\) | −86823.4 | + | 468750.i | −0.111609 | + | 0.602566i | ||||
\(883\) | 320959. | − | 320959.i | 0.411650 | − | 0.411650i | −0.470663 | − | 0.882313i | \(-0.655985\pi\) |
0.882313 | + | 0.470663i | \(0.155985\pi\) | |||||||
\(884\) | −166387. | − | 774065.i | −0.212919 | − | 0.990542i | ||||
\(885\) | −1.26087e6 | + | 65426.3i | −1.60985 | + | 0.0835345i | ||||
\(886\) | −418775. | − | 769185.i | −0.533474 | − | 0.979859i | ||||
\(887\) | −37948.9 | −0.0482339 | −0.0241169 | − | 0.999709i | \(-0.507677\pi\) | ||||
−0.0241169 | + | 0.999709i | \(0.507677\pi\) | |||||||
\(888\) | 23256.8 | − | 999667.i | 0.0294933 | − | 1.26774i | ||||
\(889\) | 606149.i | 0.766965i | ||||||||
\(890\) | −127525. | − | 234232.i | −0.160996 | − | 0.295710i | ||||
\(891\) | −114261. | + | 175153.i | −0.143927 | + | 0.220629i | ||||
\(892\) | 65870.3 | + | 42562.4i | 0.0827865 | + | 0.0534930i | ||||
\(893\) | 590877. | + | 590877.i | 0.740959 | + | 0.740959i | ||||
\(894\) | 144424. | − | 88628.2i | 0.180703 | − | 0.110891i | ||||
\(895\) | −880599. | −1.09934 | ||||||||
\(896\) | 211438. | − | 452593.i | 0.263370 | − | 0.563756i | ||||
\(897\) | −447626. | − | 403463.i | −0.556328 | − | 0.501440i | ||||
\(898\) | 208551. | + | 61516.0i | 0.258619 | + | 0.0762843i | ||||
\(899\) | −325903. | − | 325903.i | −0.403245 | − | 0.403245i | ||||
\(900\) | 284957. | − | 561003.i | 0.351799 | − | 0.692597i | ||||
\(901\) | −1.26359e6 | − | 1.26359e6i | −1.55653 | − | 1.55653i | ||||
\(902\) | 95120.9 | + | 174713.i | 0.116913 | + | 0.214740i | ||||
\(903\) | −371866. | − | 335178.i | −0.456049 | − | 0.411055i | ||||
\(904\) | 806373. | + | 937598.i | 0.986731 | + | 1.14731i | ||||
\(905\) | −316325. | −0.386221 | ||||||||
\(906\) | −62613.0 | + | 261526.i | −0.0762795 | + | 0.318609i | ||||
\(907\) | −16740.0 | − | 16740.0i | −0.0203489 | − | 0.0203489i | 0.696859 | − | 0.717208i | \(-0.254580\pi\) |
−0.717208 | + | 0.696859i | \(0.754580\pi\) | |||||||
\(908\) | 100968. | + | 469725.i | 0.122466 | + | 0.569734i | ||||
\(909\) | 21301.6 | − | 26249.8i | 0.0257801 | − | 0.0317686i | ||||
\(910\) | −139994. | + | 474607.i | −0.169054 | + | 0.573128i | ||||
\(911\) | 94930.1i | 0.114384i | 0.998363 | + | 0.0571922i | \(0.0182148\pi\) | ||||
−0.998363 | + | 0.0571922i | \(0.981785\pi\) | |||||||
\(912\) | −338417. | + | 1.05613e6i | −0.406876 | + | 1.26978i | ||||
\(913\) | −29459.5 | −0.0353414 | ||||||||
\(914\) | 153997. | + | 45424.3i | 0.184340 | + | 0.0543745i | ||||
\(915\) | −72090.4 | + | 3740.75i | −0.0861064 | + | 0.00446803i | ||||
\(916\) | 44752.3 | + | 208197.i | 0.0533365 | + | 0.248132i | ||||
\(917\) | 174419. | − | 174419.i | 0.207422 | − | 0.207422i | ||||
\(918\) | 155171. | − | 1.17497e6i | 0.184130 | − | 1.39425i | ||||
\(919\) | − | 651943.i | − | 0.771931i | −0.922513 | − | 0.385965i | \(-0.873868\pi\) | ||
0.922513 | − | 0.385965i | \(-0.126132\pi\) | |||||||
\(920\) | −88008.1 | + | 1.16962e6i | −0.103979 | + | 1.38188i | ||||
\(921\) | 745706. | + | 672134.i | 0.879120 | + | 0.792386i | ||||
\(922\) | −268423. | + | 146140.i | −0.315761 | + | 0.171913i | ||||
\(923\) | 9968.22 | − | 9968.22i | 0.0117008 | − | 0.0117008i | ||||
\(924\) | −135112. | + | 36460.3i | −0.158253 | + | 0.0427048i | ||||
\(925\) | 595987. | − | 595987.i | 0.696552 | − | 0.696552i | ||||
\(926\) | −267858. | + | 908091.i | −0.312379 | + | 1.05903i | ||||
\(927\) | 106626. | + | 1.02467e6i | 0.124081 | + | 1.19240i | ||||
\(928\) | 219574. | + | 166496.i | 0.254967 | + | 0.193333i | ||||
\(929\) | − | 1.22508e6i | − | 1.41950i | −0.704456 | − | 0.709748i | \(-0.748809\pi\) | ||
0.704456 | − | 0.709748i | \(-0.251191\pi\) | |||||||
\(930\) | 1.75125e6 | − | 1.07469e6i | 2.02481 | − | 1.24255i | ||||
\(931\) | 500800. | − | 500800.i | 0.577784 | − | 0.577784i | ||||
\(932\) | 608413. | + | 393129.i | 0.700433 | + | 0.452588i | ||||
\(933\) | −82470.3 | − | 1.58934e6i | −0.0947402 | − | 1.82580i | ||||
\(934\) | −560208. | + | 305000.i | −0.642178 | + | 0.349627i | ||||
\(935\) | 431713. | 0.493824 | ||||||||
\(936\) | −18037.9 | − | 630900.i | −0.0205889 | − | 0.720127i | ||||
\(937\) | − | 1.14806e6i | − | 1.30763i | −0.756655 | − | 0.653814i | \(-0.773168\pi\) | ||
0.756655 | − | 0.653814i | \(-0.226832\pi\) | |||||||
\(938\) | 397324. | − | 216319.i | 0.451585 | − | 0.245861i | ||||
\(939\) | −1.22379e6 | + | 63502.0i | −1.38795 | + | 0.0720205i | ||||
\(940\) | 194522. | + | 904956.i | 0.220147 | + | 1.02417i | ||||
\(941\) | −834218. | − | 834218.i | −0.942107 | − | 0.942107i | 0.0563062 | − | 0.998414i | \(-0.482068\pi\) |
−0.998414 | + | 0.0563062i | \(0.982068\pi\) | |||||||
\(942\) | 234576. | − | 143952.i | 0.264352 | − | 0.162224i | ||||
\(943\) | −858077. | −0.964945 | ||||||||
\(944\) | 1.00786e6 | + | 381593.i | 1.13099 | + | 0.428210i | ||||
\(945\) | −436303. | + | 598567.i | −0.488568 | + | 0.670269i | ||||
\(946\) | −65807.7 | + | 223101.i | −0.0735351 | + | 0.249299i | ||||
\(947\) | 863775. | + | 863775.i | 0.963165 | + | 0.963165i | 0.999345 | − | 0.0361806i | \(-0.0115191\pi\) |
−0.0361806 | + | 0.999345i | \(0.511519\pi\) | |||||||
\(948\) | −369679. | + | 642934.i | −0.411346 | + | 0.715401i | ||||
\(949\) | 828040. | + | 828040.i | 0.919430 | + | 0.919430i | ||||
\(950\) | −821009. | + | 446990.i | −0.909705 | + | 0.495280i | ||||
\(951\) | −806671. | + | 894968.i | −0.891939 | + | 0.989570i | ||||
\(952\) | 601305. | − | 517147.i | 0.663469 | − | 0.570611i | ||||
\(953\) | 742853. | 0.817932 | 0.408966 | − | 0.912550i | \(-0.365889\pi\) | ||||
0.408966 | + | 0.912550i | \(0.365889\pi\) | |||||||
\(954\) | −807000. | − | 1.17391e6i | −0.886700 | − | 1.28985i | ||||
\(955\) | 1.18331e6 | + | 1.18331e6i | 1.29746 | + | 1.29746i | ||||
\(956\) | 202553. | − | 313474.i | 0.221627 | − | 0.342994i | ||||
\(957\) | −4000.34 | − | 77093.2i | −0.00436791 | − | 0.0841768i | ||||
\(958\) | 236330. | + | 69709.7i | 0.257506 | + | 0.0759560i | ||||
\(959\) | 445240.i | 0.484125i | ||||||||
\(960\) | −949767. | + | 779153.i | −1.03056 | + | 0.845436i | ||||
\(961\) | 2.00989e6 | 2.17633 | ||||||||
\(962\) | 239190. | − | 810900.i | 0.258459 | − | 0.876228i | ||||
\(963\) | 375017. | − | 462131.i | 0.404388 | − | 0.498324i | ||||
\(964\) | −164361. | − | 106203.i | −0.176866 | − | 0.114283i | ||||
\(965\) | −845659. | + | 845659.i | −0.908115 | + | 0.908115i | ||||
\(966\) | 140551. | − | 587061.i | 0.150619 | − | 0.629114i | ||||
\(967\) | 896572.i | 0.958810i | 0.877594 | + | 0.479405i | \(0.159147\pi\) | ||||
−0.877594 | + | 0.479405i | \(0.840853\pi\) | |||||||
\(968\) | −568595. | − | 661125.i | −0.606809 | − | 0.705559i | ||||
\(969\) | −1.17884e6 | + | 1.30787e6i | −1.25547 | + | 1.39289i | ||||
\(970\) | −843216. | − | 1.54878e6i | −0.896181 | − | 1.64606i | ||||
\(971\) | 232381. | − | 232381.i | 0.246468 | − | 0.246468i | −0.573051 | − | 0.819520i | \(-0.694240\pi\) |
0.819520 | + | 0.573051i | \(0.194240\pi\) | |||||||
\(972\) | 292217. | − | 898458.i | 0.309295 | − | 0.950966i | ||||
\(973\) | 90411.1 | − | 90411.1i | 0.0954984 | − | 0.0954984i | ||||
\(974\) | 1.20605e6 | + | 355746.i | 1.27130 | + | 0.374992i | ||||
\(975\) | 356186. | − | 395174.i | 0.374686 | − | 0.415699i | ||||
\(976\) | 57624.5 | + | 21817.6i | 0.0604933 | + | 0.0229038i | ||||
\(977\) | − | 2282.94i | − | 0.00239169i | −0.999999 | − | 0.00119584i | \(-0.999619\pi\) | ||
0.999999 | − | 0.00119584i | \(-0.000380649\pi\) | |||||||
\(978\) | 254824. | − | 156377.i | 0.266418 | − | 0.163492i | ||||
\(979\) | 45094.4 | − | 45094.4i | 0.0470497 | − | 0.0470497i | ||||
\(980\) | 767000. | − | 164868.i | 0.798625 | − | 0.171666i | ||||
\(981\) | 368115. | − | 453625.i | 0.382513 | − | 0.471367i | ||||
\(982\) | 417140. | + | 766181.i | 0.432572 | + | 0.794527i | ||||
\(983\) | −1.44762e6 | −1.49812 | −0.749062 | − | 0.662500i | \(-0.769496\pi\) | ||||
−0.749062 | + | 0.662500i | \(0.769496\pi\) | |||||||
\(984\) | −620532. | − | 650093.i | −0.640876 | − | 0.671406i | ||||
\(985\) | 1.01217e6i | 1.04323i | ||||||||
\(986\) | 209193. | + | 384236.i | 0.215176 | + | 0.395224i | ||||
\(987\) | −24685.9 | − | 475738.i | −0.0253405 | − | 0.488353i | ||||
\(988\) | −508890. | + | 787566.i | −0.521327 | + | 0.806814i | ||||
\(989\) | −709465. | − | 709465.i | −0.725335 | − | 0.725335i | ||||
\(990\) | 338394. | + | 62678.4i | 0.345265 | + | 0.0639511i | ||||
\(991\) | 590798. | 0.601577 | 0.300789 | − | 0.953691i | \(-0.402750\pi\) | ||||
0.300789 | + | 0.953691i | \(0.402750\pi\) | |||||||
\(992\) | −1.73748e6 | + | 238875.i | −1.76562 | + | 0.242743i | ||||
\(993\) | −662242. | + | 734731.i | −0.671612 | + | 0.745126i | ||||
\(994\) | 13544.4 | + | 3995.16i | 0.0137084 | + | 0.00404353i | ||||
\(995\) | 33480.1 | + | 33480.1i | 0.0338174 | + | 0.0338174i | ||||
\(996\) | 128494. | − | 34674.4i | 0.129528 | − | 0.0349535i | ||||
\(997\) | −1.08683e6 | − | 1.08683e6i | −1.09338 | − | 1.09338i | −0.995165 | − | 0.0982134i | \(-0.968687\pi\) |
−0.0982134 | − | 0.995165i | \(-0.531313\pi\) | |||||||
\(998\) | −65275.8 | − | 119895.i | −0.0655377 | − | 0.120376i | ||||
\(999\) | 745455. | − | 1.02269e6i | 0.746949 | − | 1.02474i |
(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 | 48.5.i.a.5.18 | yes | 60 | |
3.2 | odd | 2 | inner | 48.5.i.a.5.13 | ✓ | 60 | |
4.3 | odd | 2 | 192.5.i.a.113.16 | 60 | |||
12.11 | even | 2 | 192.5.i.a.113.30 | 60 | |||
16.3 | odd | 4 | 192.5.i.a.17.30 | 60 | |||
16.13 | even | 4 | inner | 48.5.i.a.29.13 | yes | 60 | |
48.29 | odd | 4 | inner | 48.5.i.a.29.18 | yes | 60 | |
48.35 | even | 4 | 192.5.i.a.17.16 | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.5.i.a.5.13 | ✓ | 60 | 3.2 | odd | 2 | inner | |
48.5.i.a.5.18 | yes | 60 | 1.1 | even | 1 | trivial | |
48.5.i.a.29.13 | yes | 60 | 16.13 | even | 4 | inner | |
48.5.i.a.29.18 | yes | 60 | 48.29 | odd | 4 | inner | |
192.5.i.a.17.16 | 60 | 48.35 | even | 4 | |||
192.5.i.a.17.30 | 60 | 16.3 | odd | 4 | |||
192.5.i.a.113.16 | 60 | 4.3 | odd | 2 | |||
192.5.i.a.113.30 | 60 | 12.11 | even | 2 |