Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [275,2,Mod(26,275)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(275, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("275.26");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 275 = 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 275.h (of order \(5\), degree \(4\), 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: | \(2.19588605559\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.13140625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 55) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 26.2 | ||
Root | \(0.418926 - 1.28932i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 275.26 |
Dual form | 275.2.h.a.201.2 |
$q$-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 \(\left(\mathbb{Z}/275\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) |
\(\chi(n)\) | \(e\left(\frac{1}{5}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.09676 | + | 0.796845i | 0.775529 | + | 0.563455i | 0.903634 | − | 0.428306i | \(-0.140889\pi\) |
−0.128105 | + | 0.991761i | \(0.540889\pi\) | |||||||
\(3\) | −0.177837 | + | 0.547326i | −0.102674 | + | 0.315999i | −0.989178 | − | 0.146723i | \(-0.953127\pi\) |
0.886503 | + | 0.462722i | \(0.153127\pi\) | |||||||
\(4\) | −0.0501062 | − | 0.154211i | −0.0250531 | − | 0.0771056i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.631180 | + | 0.458579i | −0.257678 | + | 0.187214i | ||||
\(7\) | 1.12773 | + | 3.47080i | 0.426242 | + | 1.31184i | 0.901800 | + | 0.432154i | \(0.142246\pi\) |
−0.475558 | + | 0.879685i | \(0.657754\pi\) | |||||||
\(8\) | 0.905781 | − | 2.78771i | 0.320242 | − | 0.985603i | ||||
\(9\) | 2.15911 | + | 1.56869i | 0.719704 | + | 0.522895i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.490303 | + | 3.28018i | 0.147832 | + | 0.989012i | ||||
\(12\) | 0.0933146 | 0.0269376 | ||||||||
\(13\) | −2.29029 | − | 1.66399i | −0.635212 | − | 0.461509i | 0.222990 | − | 0.974821i | \(-0.428418\pi\) |
−0.858202 | + | 0.513312i | \(0.828418\pi\) | |||||||
\(14\) | −1.52884 | + | 4.70527i | −0.408599 | + | 1.25754i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.95244 | − | 2.14507i | 0.738109 | − | 0.536268i | ||||
\(17\) | 2.98685 | − | 2.17008i | 0.724419 | − | 0.526321i | −0.163374 | − | 0.986564i | \(-0.552238\pi\) |
0.887793 | + | 0.460243i | \(0.152238\pi\) | |||||||
\(18\) | 1.11803 | + | 3.44095i | 0.263523 | + | 0.811041i | ||||
\(19\) | −0.0293950 | + | 0.0904686i | −0.00674368 | + | 0.0207549i | −0.954372 | − | 0.298621i | \(-0.903473\pi\) |
0.947628 | + | 0.319376i | \(0.103473\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.10021 | −0.458304 | ||||||||
\(22\) | −2.07605 | + | 3.98828i | −0.442616 | + | 0.850304i | ||||
\(23\) | −1.16215 | −0.242324 | −0.121162 | − | 0.992633i | \(-0.538662\pi\) | ||||
−0.121162 | + | 0.992633i | \(0.538662\pi\) | |||||||
\(24\) | 1.36470 | + | 0.991515i | 0.278569 | + | 0.202392i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.18596 | − | 3.65001i | −0.232586 | − | 0.715827i | ||||
\(27\) | −2.63930 | + | 1.91757i | −0.507934 | + | 0.369036i | ||||
\(28\) | 0.478730 | − | 0.347817i | 0.0904714 | − | 0.0657313i | ||||
\(29\) | −2.08707 | − | 6.42333i | −0.387559 | − | 1.19278i | −0.934607 | − | 0.355682i | \(-0.884249\pi\) |
0.547049 | − | 0.837101i | \(-0.315751\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.48382 | − | 3.98423i | −0.984923 | − | 0.715588i | −0.0261194 | − | 0.999659i | \(-0.508315\pi\) |
−0.958803 | + | 0.284071i | \(0.908315\pi\) | |||||||
\(32\) | −0.914918 | −0.161736 | ||||||||
\(33\) | −1.88253 | − | 0.314983i | −0.327706 | − | 0.0548314i | ||||
\(34\) | 5.00509 | 0.858366 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.133724 | − | 0.411560i | 0.0222873 | − | 0.0685933i | ||||
\(37\) | −3.04066 | − | 9.35820i | −0.499882 | − | 1.53848i | −0.809208 | − | 0.587523i | \(-0.800103\pi\) |
0.309326 | − | 0.950956i | \(-0.399897\pi\) | |||||||
\(38\) | −0.104329 | + | 0.0757994i | −0.0169244 | + | 0.0122963i | ||||
\(39\) | 1.31805 | − | 0.957617i | 0.211056 | − | 0.153341i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.57047 | + | 7.91110i | −0.401440 | + | 1.23551i | 0.522391 | + | 0.852706i | \(0.325040\pi\) |
−0.923831 | + | 0.382800i | \(0.874960\pi\) | |||||||
\(42\) | −2.30344 | − | 1.67354i | −0.355428 | − | 0.258234i | ||||
\(43\) | 2.96862 | 0.452710 | 0.226355 | − | 0.974045i | \(-0.427319\pi\) | ||||
0.226355 | + | 0.974045i | \(0.427319\pi\) | |||||||
\(44\) | 0.481274 | − | 0.239968i | 0.0725547 | − | 0.0361765i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.27460 | − | 0.926052i | −0.187930 | − | 0.136539i | ||||
\(47\) | 0.687534 | − | 2.11601i | 0.100287 | − | 0.308652i | −0.888308 | − | 0.459248i | \(-0.848119\pi\) |
0.988595 | + | 0.150595i | \(0.0481191\pi\) | |||||||
\(48\) | 0.649001 | + | 1.99742i | 0.0936753 | + | 0.288303i | ||||
\(49\) | −5.11155 | + | 3.71376i | −0.730221 | + | 0.530537i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.656567 | + | 2.02070i | 0.0919377 | + | 0.282955i | ||||
\(52\) | −0.141849 | + | 0.436565i | −0.0196708 | + | 0.0605407i | ||||
\(53\) | 2.42214 | + | 1.75979i | 0.332706 | + | 0.241725i | 0.741578 | − | 0.670867i | \(-0.234078\pi\) |
−0.408872 | + | 0.912592i | \(0.634078\pi\) | |||||||
\(54\) | −4.42270 | −0.601853 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 10.6970 | 1.42945 | ||||||||
\(57\) | −0.0442883 | − | 0.0321774i | −0.00586613 | − | 0.00426200i | ||||
\(58\) | 2.82938 | − | 8.70794i | 0.371516 | − | 1.14341i | ||||
\(59\) | −2.62930 | − | 8.09216i | −0.342306 | − | 1.05351i | −0.963010 | − | 0.269465i | \(-0.913153\pi\) |
0.620704 | − | 0.784045i | \(-0.286847\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.86076 | − | 4.98464i | 0.878431 | − | 0.638217i | −0.0544052 | − | 0.998519i | \(-0.517326\pi\) |
0.932836 | + | 0.360302i | \(0.117326\pi\) | |||||||
\(62\) | −2.83964 | − | 8.73951i | −0.360634 | − | 1.10992i | ||||
\(63\) | −3.00970 | + | 9.26289i | −0.379186 | + | 1.16702i | ||||
\(64\) | −6.90832 | − | 5.01919i | −0.863541 | − | 0.627399i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.81369 | − | 1.84554i | −0.223250 | − | 0.227171i | ||||
\(67\) | 13.4153 | 1.63894 | 0.819469 | − | 0.573123i | \(-0.194268\pi\) | ||||
0.819469 | + | 0.573123i | \(0.194268\pi\) | |||||||
\(68\) | −0.484310 | − | 0.351872i | −0.0587312 | − | 0.0426707i | ||||
\(69\) | 0.206673 | − | 0.636074i | 0.0248805 | − | 0.0765743i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.71734 | + | 4.88043i | −0.797202 | + | 0.579201i | −0.910092 | − | 0.414406i | \(-0.863989\pi\) |
0.112890 | + | 0.993607i | \(0.463989\pi\) | |||||||
\(72\) | 6.32872 | − | 4.59808i | 0.745846 | − | 0.541889i | ||||
\(73\) | 0.407912 | + | 1.25542i | 0.0477425 | + | 0.146936i | 0.972086 | − | 0.234625i | \(-0.0753864\pi\) |
−0.924343 | + | 0.381562i | \(0.875386\pi\) | |||||||
\(74\) | 4.12215 | − | 12.6867i | 0.479190 | − | 1.47480i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.0154241 | 0.00176927 | ||||||||
\(77\) | −10.8319 | + | 5.40091i | −1.23441 | + | 0.615491i | ||||
\(78\) | 2.20866 | 0.250081 | ||||||||
\(79\) | 11.2179 | + | 8.15028i | 1.26211 | + | 0.916978i | 0.998859 | − | 0.0477484i | \(-0.0152046\pi\) |
0.263253 | + | 0.964727i | \(0.415205\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.89395 | + | 5.82899i | 0.210439 | + | 0.647665i | ||||
\(82\) | −9.12312 | + | 6.62834i | −1.00748 | + | 0.731977i | ||||
\(83\) | −8.61155 | + | 6.25666i | −0.945240 | + | 0.686757i | −0.949676 | − | 0.313233i | \(-0.898588\pi\) |
0.00443607 | + | 0.999990i | \(0.498588\pi\) | |||||||
\(84\) | 0.105234 | + | 0.323876i | 0.0114819 | + | 0.0353378i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.25587 | + | 2.36553i | 0.351090 | + | 0.255082i | ||||
\(87\) | 3.88682 | 0.416710 | ||||||||
\(88\) | 9.58829 | + | 1.60431i | 1.02212 | + | 0.171020i | ||||
\(89\) | −12.1612 | −1.28908 | −0.644540 | − | 0.764570i | \(-0.722951\pi\) | ||||
−0.644540 | + | 0.764570i | \(0.722951\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.19256 | − | 9.82567i | 0.334671 | − | 1.03001i | ||||
\(92\) | 0.0582308 | + | 0.179216i | 0.00607098 | + | 0.0186846i | ||||
\(93\) | 3.15590 | − | 2.29290i | 0.327252 | − | 0.237762i | ||||
\(94\) | 2.44020 | − | 1.77291i | 0.251687 | − | 0.182861i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.162706 | − | 0.500759i | 0.0166062 | − | 0.0511085i | ||||
\(97\) | −3.50412 | − | 2.54589i | −0.355789 | − | 0.258496i | 0.395504 | − | 0.918464i | \(-0.370570\pi\) |
−0.751294 | + | 0.659968i | \(0.770570\pi\) | |||||||
\(98\) | −8.56545 | −0.865241 | ||||||||
\(99\) | −4.08696 | + | 7.85141i | −0.410755 | + | 0.789096i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.01388 | − | 5.82242i | −0.797411 | − | 0.579353i | 0.112743 | − | 0.993624i | \(-0.464036\pi\) |
−0.910153 | + | 0.414271i | \(0.864036\pi\) | |||||||
\(102\) | −0.890091 | + | 2.73942i | −0.0881321 | + | 0.271243i | ||||
\(103\) | −1.25643 | − | 3.86690i | −0.123800 | − | 0.381017i | 0.869880 | − | 0.493263i | \(-0.164196\pi\) |
−0.993681 | + | 0.112245i | \(0.964196\pi\) | |||||||
\(104\) | −6.71323 | + | 4.87744i | −0.658286 | + | 0.478273i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.25424 | + | 3.86014i | 0.121822 | + | 0.374930i | ||||
\(107\) | −0.599053 | + | 1.84369i | −0.0579126 | + | 0.178237i | −0.975828 | − | 0.218539i | \(-0.929871\pi\) |
0.917916 | + | 0.396776i | \(0.129871\pi\) | |||||||
\(108\) | 0.427956 | + | 0.310928i | 0.0411801 | + | 0.0299191i | ||||
\(109\) | 6.12664 | 0.586825 | 0.293413 | − | 0.955986i | \(-0.405209\pi\) | ||||
0.293413 | + | 0.955986i | \(0.405209\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.66273 | 0.537483 | ||||||||
\(112\) | 10.7747 | + | 7.82825i | 1.01811 | + | 0.739700i | ||||
\(113\) | −1.78775 | + | 5.50212i | −0.168177 | + | 0.517596i | −0.999256 | − | 0.0385582i | \(-0.987724\pi\) |
0.831079 | + | 0.556154i | \(0.187724\pi\) | |||||||
\(114\) | −0.0229335 | − | 0.0705819i | −0.00214791 | − | 0.00661060i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.885974 | + | 0.643698i | −0.0822606 | + | 0.0597659i | ||||
\(117\) | −2.33471 | − | 7.18549i | −0.215844 | − | 0.664299i | ||||
\(118\) | 3.56448 | − | 10.9703i | 0.328137 | − | 1.00990i | ||||
\(119\) | 10.9003 | + | 7.91951i | 0.999226 | + | 0.725980i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.5192 | + | 3.21657i | −0.956291 | + | 0.292415i | ||||
\(122\) | 11.4966 | 1.04085 | ||||||||
\(123\) | −3.87283 | − | 2.81377i | −0.349201 | − | 0.253710i | ||||
\(124\) | −0.339639 | + | 1.04530i | −0.0305005 | + | 0.0938708i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −10.6820 | + | 7.76094i | −0.951630 | + | 0.691400i | ||||
\(127\) | 1.97224 | − | 1.43292i | 0.175008 | − | 0.127151i | −0.496833 | − | 0.867846i | \(-0.665504\pi\) |
0.671841 | + | 0.740695i | \(0.265504\pi\) | |||||||
\(128\) | −3.01183 | − | 9.26945i | −0.266211 | − | 0.819312i | ||||
\(129\) | −0.527931 | + | 1.62480i | −0.0464817 | + | 0.143056i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.04156 | 0.615224 | 0.307612 | − | 0.951512i | \(-0.400470\pi\) | ||||
0.307612 | + | 0.951512i | \(0.400470\pi\) | |||||||
\(132\) | 0.0457524 | + | 0.306089i | 0.00398224 | + | 0.0266416i | ||||
\(133\) | −0.347148 | −0.0301016 | ||||||||
\(134\) | 14.7134 | + | 10.6899i | 1.27104 | + | 0.923468i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.34410 | − | 10.2921i | −0.286754 | − | 0.882539i | ||||
\(137\) | −7.74461 | + | 5.62678i | −0.661666 | + | 0.480729i | −0.867225 | − | 0.497916i | \(-0.834099\pi\) |
0.205559 | + | 0.978645i | \(0.434099\pi\) | |||||||
\(138\) | 0.733524 | − | 0.532936i | 0.0624417 | − | 0.0453666i | ||||
\(139\) | 0.159299 | + | 0.490271i | 0.0135116 | + | 0.0415843i | 0.957585 | − | 0.288151i | \(-0.0930405\pi\) |
−0.944073 | + | 0.329735i | \(0.893041\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.03588 | + | 0.752611i | 0.0872369 | + | 0.0633813i | ||||
\(142\) | −11.2563 | −0.944607 | ||||||||
\(143\) | 4.33527 | − | 8.32843i | 0.362533 | − | 0.696459i | ||||
\(144\) | 9.73958 | 0.811632 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.552996 | + | 1.70195i | −0.0457663 | + | 0.140854i | ||||
\(147\) | −1.12361 | − | 3.45813i | −0.0926742 | − | 0.285222i | ||||
\(148\) | −1.29078 | + | 0.937809i | −0.106102 | + | 0.0770874i | ||||
\(149\) | 6.60144 | − | 4.79623i | 0.540811 | − | 0.392922i | −0.283575 | − | 0.958950i | \(-0.591521\pi\) |
0.824386 | + | 0.566028i | \(0.191521\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.599563 | − | 1.84526i | 0.0487917 | − | 0.150165i | −0.923692 | − | 0.383135i | \(-0.874844\pi\) |
0.972484 | + | 0.232970i | \(0.0748443\pi\) | |||||||
\(152\) | 0.225574 | + | 0.163889i | 0.0182965 | + | 0.0132932i | ||||
\(153\) | 9.85312 | 0.796577 | ||||||||
\(154\) | −16.1838 | − | 2.70785i | −1.30412 | − | 0.218205i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.213718 | − | 0.155275i | −0.0171111 | − | 0.0124319i | ||||
\(157\) | −6.57418 | + | 20.2332i | −0.524676 | + | 1.61479i | 0.240279 | + | 0.970704i | \(0.422761\pi\) |
−0.764955 | + | 0.644084i | \(0.777239\pi\) | |||||||
\(158\) | 5.80887 | + | 17.8779i | 0.462129 | + | 1.42229i | ||||
\(159\) | −1.39392 | + | 1.01274i | −0.110545 | + | 0.0803159i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.31059 | − | 4.03358i | −0.103289 | − | 0.317891i | ||||
\(162\) | −2.56758 | + | 7.90221i | −0.201728 | + | 0.620856i | ||||
\(163\) | −12.9289 | − | 9.39337i | −1.01267 | − | 0.735746i | −0.0479001 | − | 0.998852i | \(-0.515253\pi\) |
−0.964767 | + | 0.263107i | \(0.915253\pi\) | |||||||
\(164\) | 1.34878 | 0.105322 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.4304 | −1.12002 | ||||||||
\(167\) | 14.3269 | + | 10.4091i | 1.10865 | + | 0.805481i | 0.982450 | − | 0.186524i | \(-0.0597223\pi\) |
0.126199 | + | 0.992005i | \(0.459722\pi\) | |||||||
\(168\) | −1.90233 | + | 5.85477i | −0.146768 | + | 0.451706i | ||||
\(169\) | −1.54066 | − | 4.74168i | −0.118513 | − | 0.364744i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.205384 | + | 0.149220i | −0.0157061 | + | 0.0114112i | ||||
\(172\) | −0.148746 | − | 0.457794i | −0.0113418 | − | 0.0349065i | ||||
\(173\) | −4.90888 | + | 15.1080i | −0.373216 | + | 1.14864i | 0.571459 | + | 0.820631i | \(0.306378\pi\) |
−0.944675 | + | 0.328009i | \(0.893622\pi\) | |||||||
\(174\) | 4.26292 | + | 3.09719i | 0.323171 | + | 0.234798i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 8.48382 | + | 8.63280i | 0.639492 | + | 0.650722i | ||||
\(177\) | 4.89664 | 0.368054 | ||||||||
\(178\) | −13.3379 | − | 9.69057i | −0.999719 | − | 0.726339i | ||||
\(179\) | −5.21653 | + | 16.0548i | −0.389902 | + | 1.19999i | 0.542960 | + | 0.839759i | \(0.317304\pi\) |
−0.932862 | + | 0.360235i | \(0.882696\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.4871 | − | 14.1582i | 1.44846 | − | 1.05237i | 0.462277 | − | 0.886735i | \(-0.347032\pi\) |
0.986187 | − | 0.165636i | \(-0.0529676\pi\) | |||||||
\(182\) | 11.3310 | − | 8.23247i | 0.839911 | − | 0.610231i | ||||
\(183\) | 1.50812 | + | 4.64153i | 0.111484 | + | 0.343112i | ||||
\(184\) | −1.05265 | + | 3.23972i | −0.0776024 | + | 0.238836i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 5.28836 | 0.387761 | ||||||||
\(187\) | 8.58271 | + | 8.73343i | 0.627630 | + | 0.638652i | ||||
\(188\) | −0.360762 | −0.0263113 | ||||||||
\(189\) | −9.63191 | − | 6.99800i | −0.700619 | − | 0.509029i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.66337 | + | 5.11934i | 0.120358 | + | 0.370422i | 0.993027 | − | 0.117890i | \(-0.0376129\pi\) |
−0.872669 | + | 0.488312i | \(0.837613\pi\) | |||||||
\(192\) | 3.97569 | − | 2.88851i | 0.286921 | − | 0.208460i | ||||
\(193\) | 14.7921 | − | 10.7471i | 1.06476 | − | 0.773593i | 0.0897961 | − | 0.995960i | \(-0.471378\pi\) |
0.974963 | + | 0.222367i | \(0.0713785\pi\) | |||||||
\(194\) | −1.81451 | − | 5.58448i | −0.130274 | − | 0.400942i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.828823 | + | 0.602175i | 0.0592017 | + | 0.0430125i | ||||
\(197\) | −2.64566 | −0.188496 | −0.0942478 | − | 0.995549i | \(-0.530045\pi\) | ||||
−0.0942478 | + | 0.995549i | \(0.530045\pi\) | |||||||
\(198\) | −10.7388 | + | 5.35447i | −0.763172 | + | 0.380525i | ||||
\(199\) | 6.52800 | 0.462757 | 0.231379 | − | 0.972864i | \(-0.425676\pi\) | ||||
0.231379 | + | 0.972864i | \(0.425676\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.38574 | + | 7.34254i | −0.168277 | + | 0.517903i | ||||
\(202\) | −4.14976 | − | 12.7716i | −0.291976 | − | 0.898610i | ||||
\(203\) | 19.9404 | − | 14.4876i | 1.39954 | − | 1.01683i | ||||
\(204\) | 0.278717 | − | 0.202500i | 0.0195141 | − | 0.0141778i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.70331 | − | 5.24226i | 0.118676 | − | 0.365246i | ||||
\(207\) | −2.50920 | − | 1.82304i | −0.174402 | − | 0.126710i | ||||
\(208\) | −10.3313 | −0.716349 | ||||||||
\(209\) | −0.311166 | − | 0.0520641i | −0.0215238 | − | 0.00360135i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.2057 | + | 16.1334i | 1.52871 | + | 1.11067i | 0.956953 | + | 0.290243i | \(0.0937362\pi\) |
0.571752 | + | 0.820426i | \(0.306264\pi\) | |||||||
\(212\) | 0.150014 | − | 0.461697i | 0.0103030 | − | 0.0317095i | ||||
\(213\) | −1.47660 | − | 4.54450i | −0.101175 | − | 0.311384i | ||||
\(214\) | −2.12616 | + | 1.54474i | −0.145341 | + | 0.105597i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.95498 | + | 9.09450i | 0.201061 | + | 0.618802i | ||||
\(217\) | 7.64418 | − | 23.5264i | 0.518921 | − | 1.59707i | ||||
\(218\) | 6.71947 | + | 4.88198i | 0.455100 | + | 0.330650i | ||||
\(219\) | −0.759669 | −0.0513337 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.4518 | −0.703061 | ||||||||
\(222\) | 6.21068 | + | 4.51232i | 0.416834 | + | 0.302847i | ||||
\(223\) | 1.57040 | − | 4.83321i | 0.105162 | − | 0.323656i | −0.884606 | − | 0.466338i | \(-0.845573\pi\) |
0.989768 | + | 0.142683i | \(0.0455729\pi\) | |||||||
\(224\) | −1.03178 | − | 3.17550i | −0.0689388 | − | 0.212172i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.34507 | + | 4.60997i | −0.422068 | + | 0.306650i | ||||
\(227\) | −1.15566 | − | 3.55676i | −0.0767040 | − | 0.236071i | 0.905351 | − | 0.424663i | \(-0.139607\pi\) |
−0.982055 | + | 0.188593i | \(0.939607\pi\) | |||||||
\(228\) | −0.00274299 | + | 0.00844204i | −0.000181659 | + | 0.000559088i | ||||
\(229\) | −21.7821 | − | 15.8256i | −1.43940 | − | 1.04578i | −0.988168 | − | 0.153378i | \(-0.950985\pi\) |
−0.451232 | − | 0.892407i | \(-0.649015\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.02974 | − | 6.88908i | −0.0677520 | − | 0.453268i | ||||
\(232\) | −19.7968 | −1.29972 | ||||||||
\(233\) | 14.8185 | + | 10.7663i | 0.970794 | + | 0.705323i | 0.955632 | − | 0.294562i | \(-0.0951737\pi\) |
0.0151615 | + | 0.999885i | \(0.495174\pi\) | |||||||
\(234\) | 3.16510 | − | 9.74119i | 0.206909 | − | 0.636801i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.11616 | + | 0.810936i | −0.0726557 | + | 0.0527874i | ||||
\(237\) | −6.45582 | + | 4.69043i | −0.419351 | + | 0.304676i | ||||
\(238\) | 5.64439 | + | 17.3717i | 0.365872 | + | 1.12604i | ||||
\(239\) | −3.38555 | + | 10.4196i | −0.218993 | + | 0.673991i | 0.779853 | + | 0.625963i | \(0.215294\pi\) |
−0.998846 | + | 0.0480283i | \(0.984706\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.99444 | −0.643798 | −0.321899 | − | 0.946774i | \(-0.604321\pi\) | ||||
−0.321899 | + | 0.946774i | \(0.604321\pi\) | |||||||
\(242\) | −14.1002 | − | 4.85437i | −0.906394 | − | 0.312050i | ||||
\(243\) | −13.3143 | −0.854110 | ||||||||
\(244\) | −1.11245 | − | 0.808245i | −0.0712175 | − | 0.0517426i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.00543 | − | 6.17209i | −0.127862 | − | 0.393518i | ||||
\(247\) | 0.217862 | − | 0.158286i | 0.0138622 | − | 0.0100715i | ||||
\(248\) | −16.0740 | + | 11.6784i | −1.02070 | + | 0.741581i | ||||
\(249\) | −1.89298 | − | 5.82599i | −0.119963 | − | 0.369207i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.81303 | − | 5.67650i | −0.493154 | − | 0.358297i | 0.313242 | − | 0.949673i | \(-0.398585\pi\) |
−0.806396 | + | 0.591376i | \(0.798585\pi\) | |||||||
\(252\) | 1.57925 | 0.0994832 | ||||||||
\(253\) | −0.569804 | − | 3.81206i | −0.0358233 | − | 0.239662i | ||||
\(254\) | 3.30490 | 0.207368 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.19443 | + | 3.67608i | −0.0746520 | + | 0.229755i | ||||
\(257\) | −3.22230 | − | 9.91721i | −0.201001 | − | 0.618618i | −0.999854 | − | 0.0170916i | \(-0.994559\pi\) |
0.798853 | − | 0.601527i | \(-0.205441\pi\) | |||||||
\(258\) | −1.87373 | + | 1.36135i | −0.116654 | + | 0.0847538i | ||||
\(259\) | 29.0514 | − | 21.1071i | 1.80517 | − | 1.31153i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.56998 | − | 17.1426i | 0.344773 | − | 1.06110i | ||||
\(262\) | 7.72292 | + | 5.61103i | 0.477124 | + | 0.346651i | ||||
\(263\) | 10.9619 | 0.675937 | 0.337968 | − | 0.941157i | \(-0.390260\pi\) | ||||
0.337968 | + | 0.941157i | \(0.390260\pi\) | |||||||
\(264\) | −2.58323 | + | 4.96262i | −0.158987 | + | 0.305428i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.380739 | − | 0.276623i | −0.0233446 | − | 0.0169609i | ||||
\(267\) | 2.16271 | − | 6.65613i | 0.132355 | − | 0.407348i | ||||
\(268\) | −0.672190 | − | 2.06879i | −0.0410605 | − | 0.126371i | ||||
\(269\) | 0.0722816 | − | 0.0525156i | 0.00440708 | − | 0.00320193i | −0.585580 | − | 0.810615i | \(-0.699133\pi\) |
0.589987 | + | 0.807413i | \(0.299133\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.14069 | − | 12.7437i | −0.251529 | − | 0.774126i | −0.994494 | − | 0.104796i | \(-0.966581\pi\) |
0.742965 | − | 0.669330i | \(-0.233419\pi\) | |||||||
\(272\) | 4.16353 | − | 12.8140i | 0.252451 | − | 0.776965i | ||||
\(273\) | 4.81010 | + | 3.49474i | 0.291120 | + | 0.211511i | ||||
\(274\) | −12.9777 | −0.784010 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.108445 | −0.00652764 | ||||||||
\(277\) | −3.16057 | − | 2.29629i | −0.189901 | − | 0.137971i | 0.488773 | − | 0.872411i | \(-0.337445\pi\) |
−0.678673 | + | 0.734440i | \(0.737445\pi\) | |||||||
\(278\) | −0.215957 | + | 0.664648i | −0.0129523 | + | 0.0398630i | ||||
\(279\) | −5.59017 | − | 17.2048i | −0.334675 | − | 1.03002i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.24381 | − | 0.903680i | 0.0741994 | − | 0.0539090i | −0.550067 | − | 0.835120i | \(-0.685398\pi\) |
0.624267 | + | 0.781211i | \(0.285398\pi\) | |||||||
\(282\) | 0.536401 | + | 1.65087i | 0.0319422 | + | 0.0983081i | ||||
\(283\) | 1.67231 | − | 5.14683i | 0.0994083 | − | 0.305947i | −0.888969 | − | 0.457967i | \(-0.848578\pi\) |
0.988377 | + | 0.152020i | \(0.0485778\pi\) | |||||||
\(284\) | 1.08920 | + | 0.791349i | 0.0646320 | + | 0.0469579i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 11.3912 | − | 5.67979i | 0.673578 | − | 0.335853i | ||||
\(287\) | −30.3566 | −1.79190 | ||||||||
\(288\) | −1.97541 | − | 1.43522i | −0.116402 | − | 0.0845711i | ||||
\(289\) | −1.04122 | + | 3.20456i | −0.0612484 | + | 0.188503i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.01659 | − | 1.46514i | 0.118215 | − | 0.0858881i | ||||
\(292\) | 0.173162 | − | 0.125809i | 0.0101335 | − | 0.00736243i | ||||
\(293\) | −3.52789 | − | 10.8577i | −0.206102 | − | 0.634315i | −0.999666 | − | 0.0258295i | \(-0.991777\pi\) |
0.793565 | − | 0.608486i | \(-0.208223\pi\) | |||||||
\(294\) | 1.52326 | − | 4.68810i | 0.0888381 | − | 0.273415i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −28.8421 | −1.67641 | ||||||||
\(297\) | −7.58403 | − | 7.71721i | −0.440070 | − | 0.447798i | ||||
\(298\) | 11.0621 | 0.640808 | ||||||||
\(299\) | 2.66165 | + | 1.93381i | 0.153927 | + | 0.111835i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.34780 | + | 10.3035i | 0.192964 | + | 0.593883i | ||||
\(302\) | 2.12797 | − | 1.54606i | 0.122451 | − | 0.0889657i | ||||
\(303\) | 4.61193 | − | 3.35077i | 0.264949 | − | 0.192496i | ||||
\(304\) | 0.107275 | + | 0.330157i | 0.00615262 | + | 0.0189358i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 10.8065 | + | 7.85141i | 0.617769 | + | 0.448835i | ||||
\(307\) | 4.25008 | 0.242565 | 0.121282 | − | 0.992618i | \(-0.461299\pi\) | ||||
0.121282 | + | 0.992618i | \(0.461299\pi\) | |||||||
\(308\) | 1.37563 | + | 1.39978i | 0.0783836 | + | 0.0797601i | ||||
\(309\) | 2.33990 | 0.133112 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.13570 | + | 15.8061i | −0.291219 | + | 0.896279i | 0.693247 | + | 0.720700i | \(0.256180\pi\) |
−0.984465 | + | 0.175579i | \(0.943820\pi\) | |||||||
\(312\) | −1.47569 | − | 4.54172i | −0.0835447 | − | 0.257124i | ||||
\(313\) | −21.5012 | + | 15.6215i | −1.21532 | + | 0.882982i | −0.995703 | − | 0.0926041i | \(-0.970481\pi\) |
−0.219617 | + | 0.975586i | \(0.570481\pi\) | |||||||
\(314\) | −23.3331 | + | 16.9525i | −1.31676 | + | 0.956683i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.694778 | − | 2.13831i | 0.0390843 | − | 0.120289i | ||||
\(317\) | 4.68982 | + | 3.40736i | 0.263407 | + | 0.191376i | 0.711648 | − | 0.702537i | \(-0.247949\pi\) |
−0.448241 | + | 0.893913i | \(0.647949\pi\) | |||||||
\(318\) | −2.33581 | −0.130985 | ||||||||
\(319\) | 20.0464 | − | 9.99534i | 1.12238 | − | 0.559632i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.902569 | − | 0.655755i | −0.0503765 | − | 0.0366007i | ||||
\(322\) | 1.77673 | − | 5.46822i | 0.0990134 | − | 0.304732i | ||||
\(323\) | 0.108525 | + | 0.334006i | 0.00603850 | + | 0.0185846i | ||||
\(324\) | 0.803996 | − | 0.584137i | 0.0446664 | − | 0.0324521i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6.69484 | − | 20.6046i | −0.370793 | − | 1.14118i | ||||
\(327\) | −1.08954 | + | 3.35327i | −0.0602519 | + | 0.185436i | ||||
\(328\) | 19.7255 | + | 14.3314i | 1.08916 | + | 0.791321i | ||||
\(329\) | 8.11961 | 0.447648 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.9230 | −0.710311 | −0.355155 | − | 0.934807i | \(-0.615572\pi\) | ||||
−0.355155 | + | 0.934807i | \(0.615572\pi\) | |||||||
\(332\) | 1.39634 | + | 1.01450i | 0.0766340 | + | 0.0556779i | ||||
\(333\) | 8.11495 | − | 24.9752i | 0.444696 | − | 1.36863i | ||||
\(334\) | 7.41878 | + | 22.8327i | 0.405938 | + | 1.24935i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −6.20075 | + | 4.50511i | −0.338278 | + | 0.245774i | ||||
\(337\) | −4.13631 | − | 12.7303i | −0.225319 | − | 0.693461i | −0.998259 | − | 0.0589818i | \(-0.981215\pi\) |
0.772940 | − | 0.634479i | \(-0.218785\pi\) | |||||||
\(338\) | 2.08864 | − | 6.42817i | 0.113607 | − | 0.349646i | ||||
\(339\) | −2.69353 | − | 1.95696i | −0.146292 | − | 0.106288i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.3803 | − | 19.9414i | 0.562123 | − | 1.07989i | ||||
\(342\) | −0.344163 | −0.0186102 | ||||||||
\(343\) | 2.01291 | + | 1.46246i | 0.108687 | + | 0.0789656i | ||||
\(344\) | 2.68892 | − | 8.27564i | 0.144977 | − | 0.446193i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −17.4226 | + | 12.6583i | −0.936646 | + | 0.680513i | ||||
\(347\) | −6.83538 | + | 4.96619i | −0.366942 | + | 0.266599i | −0.755942 | − | 0.654639i | \(-0.772821\pi\) |
0.389000 | + | 0.921238i | \(0.372821\pi\) | |||||||
\(348\) | −0.194754 | − | 0.599391i | −0.0104399 | − | 0.0321307i | ||||
\(349\) | −3.21341 | + | 9.88987i | −0.172010 | + | 0.529393i | −0.999484 | − | 0.0321111i | \(-0.989777\pi\) |
0.827474 | + | 0.561504i | \(0.189777\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.23559 | 0.492959 | ||||||||
\(352\) | −0.448587 | − | 3.00110i | −0.0239098 | − | 0.159959i | ||||
\(353\) | −19.1073 | −1.01698 | −0.508489 | − | 0.861069i | \(-0.669796\pi\) | ||||
−0.508489 | + | 0.861069i | \(0.669796\pi\) | |||||||
\(354\) | 5.37046 | + | 3.90187i | 0.285437 | + | 0.207382i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.609350 | + | 1.87539i | 0.0322955 | + | 0.0993953i | ||||
\(357\) | −6.27303 | + | 4.55762i | −0.332004 | + | 0.241215i | ||||
\(358\) | −18.5145 | + | 13.4516i | −0.978522 | + | 0.710938i | ||||
\(359\) | −1.36405 | − | 4.19813i | −0.0719920 | − | 0.221569i | 0.908586 | − | 0.417698i | \(-0.137163\pi\) |
−0.980578 | + | 0.196129i | \(0.937163\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.3640 | + | 11.1626i | 0.808632 | + | 0.587505i | ||||
\(362\) | 32.6546 | 1.71629 | ||||||||
\(363\) | 0.110193 | − | 6.32946i | 0.00578362 | − | 0.332211i | ||||
\(364\) | −1.67520 | −0.0878041 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.04453 | + | 6.29240i | −0.106869 | + | 0.328909i | ||||
\(367\) | 9.07327 | + | 27.9247i | 0.473621 | + | 1.45766i | 0.847809 | + | 0.530302i | \(0.177922\pi\) |
−0.374188 | + | 0.927353i | \(0.622078\pi\) | |||||||
\(368\) | −3.43117 | + | 2.49289i | −0.178862 | + | 0.129951i | ||||
\(369\) | −17.9600 | + | 13.0487i | −0.934958 | + | 0.679287i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.37634 | + | 10.3913i | −0.175291 | + | 0.539490i | ||||
\(372\) | −0.511720 | − | 0.371787i | −0.0265315 | − | 0.0192762i | ||||
\(373\) | 4.96478 | 0.257067 | 0.128533 | − | 0.991705i | \(-0.458973\pi\) | ||||
0.128533 | + | 0.991705i | \(0.458973\pi\) | |||||||
\(374\) | 2.45401 | + | 16.4176i | 0.126894 | + | 0.848934i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.27606 | − | 3.83329i | −0.272092 | − | 0.197687i | ||||
\(377\) | −5.90839 | + | 18.1842i | −0.304298 | + | 0.936532i | ||||
\(378\) | −4.98761 | − | 15.3503i | −0.256535 | − | 0.789534i | ||||
\(379\) | −6.40996 | + | 4.65711i | −0.329258 | + | 0.239220i | −0.740116 | − | 0.672480i | \(-0.765229\pi\) |
0.410858 | + | 0.911699i | \(0.365229\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.433536 | + | 1.33429i | 0.0222107 | + | 0.0683576i | ||||
\(382\) | −2.25499 | + | 6.94016i | −0.115375 | + | 0.355089i | ||||
\(383\) | −19.8335 | − | 14.4099i | −1.01344 | − | 0.736309i | −0.0485140 | − | 0.998823i | \(-0.515449\pi\) |
−0.964928 | + | 0.262514i | \(0.915449\pi\) | |||||||
\(384\) | 5.60903 | 0.286235 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 24.7872 | 1.26164 | ||||||||
\(387\) | 6.40958 | + | 4.65683i | 0.325817 | + | 0.236720i | ||||
\(388\) | −0.217026 | + | 0.667939i | −0.0110179 | + | 0.0339095i | ||||
\(389\) | 1.68752 | + | 5.19366i | 0.0855608 | + | 0.263329i | 0.984679 | − | 0.174377i | \(-0.0557911\pi\) |
−0.899118 | + | 0.437706i | \(0.855791\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.47116 | + | 2.52195i | −0.175544 | + | 0.127540i | ||||
\(392\) | 5.72292 | + | 17.6133i | 0.289051 | + | 0.889608i | ||||
\(393\) | −1.25225 | + | 3.85403i | −0.0631677 | + | 0.194410i | ||||
\(394\) | −2.90166 | − | 2.10818i | −0.146184 | − | 0.106209i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.41556 | + | 0.236850i | 0.0711344 | + | 0.0119022i | ||||
\(397\) | 6.43455 | 0.322941 | 0.161470 | − | 0.986878i | \(-0.448376\pi\) | ||||
0.161470 | + | 0.986878i | \(0.448376\pi\) | |||||||
\(398\) | 7.15967 | + | 5.20180i | 0.358882 | + | 0.260743i | ||||
\(399\) | 0.0617358 | − | 0.190003i | 0.00309066 | − | 0.00951206i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.8947 | − | 8.64197i | 0.593991 | − | 0.431560i | −0.249750 | − | 0.968310i | \(-0.580348\pi\) |
0.843741 | + | 0.536751i | \(0.180348\pi\) | |||||||
\(402\) | −8.46746 | + | 6.15197i | −0.422319 | + | 0.306832i | ||||
\(403\) | 5.92981 | + | 18.2501i | 0.295385 | + | 0.909101i | ||||
\(404\) | −0.496337 | + | 1.52757i | −0.0246937 | + | 0.0759994i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 33.4143 | 1.65832 | ||||||||
\(407\) | 29.2058 | − | 14.5623i | 1.44768 | − | 0.721826i | ||||
\(408\) | 6.22784 | 0.308324 | ||||||||
\(409\) | −3.55625 | − | 2.58376i | −0.175845 | − | 0.127759i | 0.496381 | − | 0.868105i | \(-0.334662\pi\) |
−0.672226 | + | 0.740346i | \(0.734662\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.70241 | − | 5.23948i | −0.0839737 | − | 0.258444i | ||||
\(412\) | −0.533365 | + | 0.387512i | −0.0262770 | + | 0.0190914i | ||||
\(413\) | 25.1211 | − | 18.2516i | 1.23613 | − | 0.898101i | ||||
\(414\) | −1.29932 | − | 3.99890i | −0.0638581 | − | 0.196535i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.09543 | + | 1.52242i | 0.102737 | + | 0.0746427i | ||||
\(417\) | −0.296668 | −0.0145279 | ||||||||
\(418\) | −0.299789 | − | 0.305053i | −0.0146631 | − | 0.0149206i | ||||
\(419\) | 17.8526 | 0.872159 | 0.436079 | − | 0.899908i | \(-0.356367\pi\) | ||||
0.436079 | + | 0.899908i | \(0.356367\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.49210 | + | 4.59221i | −0.0727205 | + | 0.223811i | −0.980810 | − | 0.194965i | \(-0.937541\pi\) |
0.908090 | + | 0.418776i | \(0.137541\pi\) | |||||||
\(422\) | 11.4986 | + | 35.3891i | 0.559743 | + | 1.72271i | ||||
\(423\) | 4.80382 | − | 3.49018i | 0.233570 | − | 0.169698i | ||||
\(424\) | 7.09969 | − | 5.15823i | 0.344792 | − | 0.250506i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.00179 | − | 6.16086i | 0.0969868 | − | 0.298495i | ||||
\(427\) | 25.0378 | + | 18.1910i | 1.21166 | + | 0.880324i | ||||
\(428\) | 0.314335 | 0.0151939 | ||||||||
\(429\) | 3.78740 | + | 3.85391i | 0.182857 | + | 0.186069i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.1234 | + | 14.6205i | 0.969312 | + | 0.704247i | 0.955295 | − | 0.295655i | \(-0.0955380\pi\) |
0.0140175 | + | 0.999902i | \(0.495538\pi\) | |||||||
\(432\) | −3.67906 | + | 11.3230i | −0.177009 | + | 0.544778i | ||||
\(433\) | 6.56669 | + | 20.2102i | 0.315575 | + | 0.971240i | 0.975517 | + | 0.219923i | \(0.0705807\pi\) |
−0.659942 | + | 0.751316i | \(0.729419\pi\) | |||||||
\(434\) | 27.1307 | − | 19.7116i | 1.30232 | − | 0.946188i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.306983 | − | 0.944796i | −0.0147018 | − | 0.0452475i | ||||
\(437\) | 0.0341614 | − | 0.105138i | 0.00163416 | − | 0.00502943i | ||||
\(438\) | −0.833177 | − | 0.605339i | −0.0398107 | − | 0.0289242i | ||||
\(439\) | −15.9119 | −0.759434 | −0.379717 | − | 0.925103i | \(-0.623979\pi\) | ||||
−0.379717 | + | 0.925103i | \(0.623979\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −16.8621 | −0.802958 | ||||||||
\(442\) | −11.4631 | − | 8.32843i | −0.545244 | − | 0.396143i | ||||
\(443\) | −8.12332 | + | 25.0010i | −0.385951 | + | 1.18783i | 0.549838 | + | 0.835272i | \(0.314690\pi\) |
−0.935788 | + | 0.352562i | \(0.885310\pi\) | |||||||
\(444\) | −0.283738 | − | 0.873257i | −0.0134656 | − | 0.0414429i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5.57368 | − | 4.04952i | 0.263922 | − | 0.191750i | ||||
\(447\) | 1.45112 | + | 4.46609i | 0.0686356 | + | 0.211239i | ||||
\(448\) | 9.62987 | − | 29.6377i | 0.454969 | − | 1.40025i | ||||
\(449\) | 6.62554 | + | 4.81373i | 0.312678 | + | 0.227174i | 0.733045 | − | 0.680180i | \(-0.238098\pi\) |
−0.420366 | + | 0.907354i | \(0.638098\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −27.2102 | − | 4.55278i | −1.28128 | − | 0.214382i | ||||
\(452\) | 0.938065 | 0.0441229 | ||||||||
\(453\) | 0.903337 | + | 0.656313i | 0.0424425 | + | 0.0308363i | ||||
\(454\) | 1.56670 | − | 4.82181i | 0.0735289 | − | 0.226299i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.129817 | + | 0.0943172i | −0.00607922 | + | 0.00441681i | ||||
\(457\) | 9.64056 | − | 7.00428i | 0.450966 | − | 0.327646i | −0.339011 | − | 0.940782i | \(-0.610092\pi\) |
0.789977 | + | 0.613136i | \(0.210092\pi\) | |||||||
\(458\) | −11.2792 | − | 34.7139i | −0.527043 | − | 1.62207i | ||||
\(459\) | −3.72195 | + | 11.4550i | −0.173726 | + | 0.534673i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.96172 | 0.324240 | 0.162120 | − | 0.986771i | \(-0.448167\pi\) | ||||
0.162120 | + | 0.986771i | \(0.448167\pi\) | |||||||
\(462\) | 4.36015 | − | 8.37624i | 0.202853 | − | 0.389698i | ||||
\(463\) | −12.4762 | −0.579817 | −0.289909 | − | 0.957054i | \(-0.593625\pi\) | ||||
−0.289909 | + | 0.957054i | \(0.593625\pi\) | |||||||
\(464\) | −19.9404 | − | 14.4876i | −0.925712 | − | 0.672569i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.67335 | + | 23.6161i | 0.355461 | + | 1.09400i | ||||
\(467\) | −4.97235 | + | 3.61263i | −0.230093 | + | 0.167172i | −0.696858 | − | 0.717209i | \(-0.745419\pi\) |
0.466765 | + | 0.884381i | \(0.345419\pi\) | |||||||
\(468\) | −0.991100 | + | 0.720076i | −0.0458136 | + | 0.0332855i | ||||
\(469\) | 15.1288 | + | 46.5618i | 0.698585 | + | 2.15002i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.90505 | − | 7.19644i | −0.456401 | − | 0.331594i | ||||
\(472\) | −24.9401 | −1.14796 | ||||||||
\(473\) | 1.45552 | + | 9.73762i | 0.0669250 | + | 0.447736i | ||||
\(474\) | −10.8181 | −0.496890 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.675105 | − | 2.07776i | 0.0309434 | − | 0.0952340i | ||||
\(477\) | 2.46911 | + | 7.59915i | 0.113053 | + | 0.347941i | ||||
\(478\) | −12.0160 | + | 8.73013i | −0.549599 | + | 0.399307i | ||||
\(479\) | −17.9555 | + | 13.0454i | −0.820406 | + | 0.596060i | −0.916829 | − | 0.399281i | \(-0.869260\pi\) |
0.0964228 | + | 0.995340i | \(0.469260\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.60798 | + | 26.4926i | −0.392490 | + | 1.20796i | ||||
\(482\) | −10.9615 | − | 7.96402i | −0.499284 | − | 0.362751i | ||||
\(483\) | 2.44076 | 0.111058 | ||||||||
\(484\) | 1.02311 | + | 1.46101i | 0.0465049 | + | 0.0664095i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −14.6026 | − | 10.6094i | −0.662387 | − | 0.481252i | ||||
\(487\) | 10.5778 | − | 32.5553i | 0.479328 | − | 1.47522i | −0.360702 | − | 0.932681i | \(-0.617463\pi\) |
0.840030 | − | 0.542539i | \(-0.182537\pi\) | |||||||
\(488\) | −7.68135 | − | 23.6408i | −0.347719 | − | 1.07017i | ||||
\(489\) | 7.44047 | − | 5.40582i | 0.336470 | − | 0.244460i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.25197 | − | 16.1639i | −0.237018 | − | 0.729467i | −0.996847 | − | 0.0793441i | \(-0.974717\pi\) |
0.759829 | − | 0.650123i | \(-0.225283\pi\) | |||||||
\(492\) | −0.239863 | + | 0.738221i | −0.0108138 | + | 0.0332816i | ||||
\(493\) | −20.1729 | − | 14.6565i | −0.908541 | − | 0.660094i | ||||
\(494\) | 0.365073 | 0.0164254 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −24.7371 | −1.11073 | ||||||||
\(497\) | −24.5144 | − | 17.8107i | −1.09962 | − | 0.798920i | ||||
\(498\) | 2.56626 | − | 7.89815i | 0.114997 | − | 0.353925i | ||||
\(499\) | 1.61599 | + | 4.97352i | 0.0723418 | + | 0.222645i | 0.980690 | − | 0.195570i | \(-0.0626558\pi\) |
−0.908348 | + | 0.418215i | \(0.862656\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.24504 | + | 5.99037i | −0.368361 | + | 0.267630i | ||||
\(502\) | −4.04575 | − | 12.4515i | −0.180571 | − | 0.555740i | ||||
\(503\) | −12.9617 | + | 39.8919i | −0.577931 | + | 1.77869i | 0.0480416 | + | 0.998845i | \(0.484702\pi\) |
−0.625973 | + | 0.779845i | \(0.715298\pi\) | |||||||
\(504\) | 23.0961 | + | 16.7803i | 1.02878 | + | 0.747454i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.41268 | − | 4.63497i | 0.107257 | − | 0.206050i | ||||
\(507\) | 2.86923 | 0.127427 | ||||||||
\(508\) | −0.319794 | − | 0.232344i | −0.0141886 | − | 0.0103086i | ||||
\(509\) | 6.29399 | − | 19.3709i | 0.278976 | − | 0.858601i | −0.709163 | − | 0.705044i | \(-0.750927\pi\) |
0.988140 | − | 0.153557i | \(-0.0490728\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.89731 | + | 2.83156i | −0.172407 | + | 0.125261i | ||||
\(512\) | −20.0094 | + | 14.5377i | −0.884300 | + | 0.642481i | ||||
\(513\) | −0.0958972 | − | 0.295141i | −0.00423396 | − | 0.0130308i | ||||
\(514\) | 4.36838 | − | 13.4445i | 0.192681 | − | 0.593012i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.277016 | 0.0121949 | ||||||||
\(517\) | 7.27801 | + | 1.21775i | 0.320086 | + | 0.0535566i | ||||
\(518\) | 48.6816 | 2.13895 | ||||||||
\(519\) | −7.39602 | − | 5.37352i | −0.324649 | − | 0.235872i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.47391 | + | 13.7693i | 0.196005 | + | 0.603243i | 0.999963 | + | 0.00855656i | \(0.00272367\pi\) |
−0.803958 | + | 0.594686i | \(0.797276\pi\) | |||||||
\(522\) | 19.7690 | − | 14.3630i | 0.865265 | − | 0.628652i | ||||
\(523\) | 9.02873 | − | 6.55975i | 0.394799 | − | 0.286838i | −0.372620 | − | 0.927984i | \(-0.621541\pi\) |
0.767419 | + | 0.641146i | \(0.221541\pi\) | |||||||
\(524\) | −0.352826 | − | 1.08589i | −0.0154133 | − | 0.0474372i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.0226 | + | 8.73490i | 0.524209 | + | 0.380860i | ||||
\(527\) | −25.0254 | −1.09013 | ||||||||
\(528\) | −6.23370 | + | 3.10818i | −0.271287 | + | 0.135266i | ||||
\(529\) | −21.6494 | −0.941279 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.01710 | − | 21.5964i | 0.304516 | − | 0.937205i | ||||
\(532\) | 0.0173943 | + | 0.0535341i | 0.000754138 | + | 0.00232100i | ||||
\(533\) | 19.0511 | − | 13.8415i | 0.825197 | − | 0.599540i | ||||
\(534\) | 7.67588 | − | 5.57685i | 0.332168 | − | 0.241334i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 12.1513 | − | 37.3979i | 0.524857 | − | 1.61534i | ||||
\(537\) | −7.85954 | − | 5.71029i | −0.339164 | − | 0.246417i | ||||
\(538\) | 0.121123 | 0.00522197 | ||||||||
\(539\) | −14.6880 | − | 14.9459i | −0.632658 | − | 0.643768i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.64094 | − | 6.27801i | −0.371503 | − | 0.269913i | 0.386331 | − | 0.922360i | \(-0.373742\pi\) |
−0.757834 | + | 0.652447i | \(0.773742\pi\) | |||||||
\(542\) | 5.61343 | − | 17.2763i | 0.241117 | − | 0.742083i | ||||
\(543\) | 4.28363 | + | 13.1837i | 0.183828 | + | 0.565765i | ||||
\(544\) | −2.73273 | + | 1.98544i | −0.117165 | + | 0.0851251i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.49077 | + | 7.66581i | 0.106595 | + | 0.328066i | ||||
\(547\) | −0.540038 | + | 1.66207i | −0.0230904 | + | 0.0710648i | −0.961938 | − | 0.273269i | \(-0.911895\pi\) |
0.938847 | + | 0.344334i | \(0.111895\pi\) | |||||||
\(548\) | 1.25577 | + | 0.912367i | 0.0536437 | + | 0.0389744i | ||||
\(549\) | 22.6325 | 0.965930 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.642459 | 0.0273697 | ||||||||
\(552\) | −1.58599 | − | 1.15229i | −0.0675041 | − | 0.0490446i | ||||
\(553\) | −15.6372 | + | 48.1264i | −0.664962 | + | 2.04654i | ||||
\(554\) | −1.63661 | − | 5.03698i | −0.0695331 | − | 0.214001i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.0676235 | − | 0.0491313i | 0.00286787 | − | 0.00208363i | ||||
\(557\) | 6.02100 | + | 18.5307i | 0.255118 | + | 0.785173i | 0.993806 | + | 0.111126i | \(0.0354456\pi\) |
−0.738688 | + | 0.674047i | \(0.764554\pi\) | |||||||
\(558\) | 7.57845 | − | 23.3241i | 0.320821 | − | 0.987387i | ||||
\(559\) | −6.79900 | − | 4.93976i | −0.287567 | − | 0.208930i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.30636 | + | 3.14442i | −0.266255 | + | 0.132757i | ||||
\(562\) | 2.08426 | 0.0879191 | ||||||||
\(563\) | −11.8838 | − | 8.63407i | −0.500842 | − | 0.363883i | 0.308497 | − | 0.951225i | \(-0.400174\pi\) |
−0.809338 | + | 0.587343i | \(0.800174\pi\) | |||||||
\(564\) | 0.0641570 | − | 0.197455i | 0.00270150 | − | 0.00831435i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 5.93535 | − | 4.31228i | 0.249481 | − | 0.181259i | ||||
\(567\) | −18.0954 | + | 13.1471i | −0.759934 | + | 0.552124i | ||||
\(568\) | 7.52078 | + | 23.1466i | 0.315565 | + | 0.971209i | ||||
\(569\) | 6.15980 | − | 18.9579i | 0.258232 | − | 0.794758i | −0.734943 | − | 0.678129i | \(-0.762791\pi\) |
0.993176 | − | 0.116629i | \(-0.0372088\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.24422 | 0.219464 | 0.109732 | − | 0.993961i | \(-0.465001\pi\) | ||||
0.109732 | + | 0.993961i | \(0.465001\pi\) | |||||||
\(572\) | −1.50156 | − | 0.251240i | −0.0627834 | − | 0.0105049i | ||||
\(573\) | −3.09776 | −0.129411 | ||||||||
\(574\) | −33.2940 | − | 24.1895i | −1.38967 | − | 1.00965i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −7.04230 | − | 21.6740i | −0.293429 | − | 0.903083i | ||||
\(577\) | 30.4194 | − | 22.1010i | 1.26637 | − | 0.920075i | 0.267323 | − | 0.963607i | \(-0.413861\pi\) |
0.999052 | + | 0.0435320i | \(0.0138610\pi\) | |||||||
\(578\) | −3.69551 | + | 2.68495i | −0.153713 | + | 0.111679i | ||||
\(579\) | 3.25158 | + | 10.0073i | 0.135131 | + | 0.415891i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −31.4271 | − | 22.8331i | −1.30382 | − | 0.947278i | ||||
\(582\) | 3.37922 | 0.140073 | ||||||||
\(583\) | −4.58484 | + | 8.80789i | −0.189885 | + | 0.364785i | ||||
\(584\) | 3.86923 | 0.160110 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.78267 | − | 14.7195i | 0.197570 | − | 0.608059i | ||||
\(587\) | −7.90191 | − | 24.3196i | −0.326147 | − | 1.00378i | −0.970920 | − | 0.239403i | \(-0.923048\pi\) |
0.644774 | − | 0.764373i | \(-0.276952\pi\) | |||||||
\(588\) | −0.476982 | + | 0.346548i | −0.0196704 | + | 0.0142914i | ||||
\(589\) | 0.521644 | − | 0.378997i | 0.0214940 | − | 0.0156163i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.470497 | − | 1.44804i | 0.0193536 | − | 0.0595644i | ||||
\(592\) | −29.0514 | − | 21.1071i | −1.19400 | − | 0.867495i | ||||
\(593\) | −40.2260 | −1.65188 | −0.825942 | − | 0.563754i | \(-0.809356\pi\) | ||||
−0.825942 | + | 0.563754i | \(0.809356\pi\) | |||||||
\(594\) | −2.16846 | − | 14.5073i | −0.0889731 | − | 0.595240i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.07040 | − | 0.777695i | −0.0438455 | − | 0.0318556i | ||||
\(597\) | −1.16092 | + | 3.57295i | −0.0475133 | + | 0.146231i | ||||
\(598\) | 1.37826 | + | 4.24185i | 0.0563613 | + | 0.173462i | ||||
\(599\) | −3.98843 | + | 2.89776i | −0.162963 | + | 0.118399i | −0.666278 | − | 0.745704i | \(-0.732114\pi\) |
0.503315 | + | 0.864103i | \(0.332114\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.2425 | + | 43.8338i | 0.580963 | + | 1.78802i | 0.614912 | + | 0.788596i | \(0.289191\pi\) |
−0.0339497 | + | 0.999424i | \(0.510809\pi\) | |||||||
\(602\) | −4.53853 | + | 13.9682i | −0.184977 | + | 0.569300i | ||||
\(603\) | 28.9651 | + | 21.0444i | 1.17955 | + | 0.856993i | ||||
\(604\) | −0.314602 | −0.0128010 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 7.72824 | 0.313938 | ||||||||
\(607\) | −36.5162 | − | 26.5306i | −1.48215 | − | 1.07684i | −0.976857 | − | 0.213891i | \(-0.931386\pi\) |
−0.505288 | − | 0.862951i | \(-0.668614\pi\) | |||||||
\(608\) | 0.0268941 | − | 0.0827714i | 0.00109070 | − | 0.00335682i | ||||
\(609\) | 4.38328 | + | 13.4904i | 0.177620 | + | 0.546657i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.09568 | + | 3.70223i | −0.206149 | + | 0.149776i | ||||
\(612\) | −0.493703 | − | 1.51946i | −0.0199567 | − | 0.0614206i | ||||
\(613\) | −1.46294 | + | 4.50247i | −0.0590877 | + | 0.181853i | −0.976244 | − | 0.216675i | \(-0.930479\pi\) |
0.917156 | + | 0.398528i | \(0.130479\pi\) | |||||||
\(614\) | 4.66133 | + | 3.38666i | 0.188116 | + | 0.136674i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.24479 | + | 35.0883i | 0.211319 | + | 1.41375i | ||||
\(617\) | −17.8468 | −0.718486 | −0.359243 | − | 0.933244i | \(-0.616965\pi\) | ||||
−0.359243 | + | 0.933244i | \(0.616965\pi\) | |||||||
\(618\) | 2.56632 | + | 1.86454i | 0.103232 | + | 0.0750027i | ||||
\(619\) | 0.110304 | − | 0.339482i | 0.00443351 | − | 0.0136449i | −0.948815 | − | 0.315832i | \(-0.897717\pi\) |
0.953249 | + | 0.302187i | \(0.0977166\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.06726 | − | 2.22850i | 0.123085 | − | 0.0894264i | ||||
\(622\) | −18.2276 | + | 13.2431i | −0.730861 | + | 0.531002i | ||||
\(623\) | −13.7145 | − | 42.2089i | −0.549461 | − | 1.69107i | ||||
\(624\) | 1.83729 | − | 5.65461i | 0.0735506 | − | 0.226365i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −36.0297 | −1.44004 | ||||||||
\(627\) | 0.0838329 | − | 0.161051i | 0.00334796 | − | 0.00643174i | ||||
\(628\) | 3.44960 | 0.137654 | ||||||||
\(629\) | −29.3900 | − | 21.3531i | −1.17186 | − | 0.851404i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.88614 | − | 30.4264i | −0.393561 | − | 1.21126i | −0.930077 | − | 0.367366i | \(-0.880260\pi\) |
0.536516 | − | 0.843890i | \(-0.319740\pi\) | |||||||
\(632\) | 32.8815 | − | 23.8898i | 1.30796 | − | 0.950287i | ||||
\(633\) | −12.7792 | + | 9.28466i | −0.507929 | + | 0.369032i | ||||
\(634\) | 2.42849 | + | 7.47413i | 0.0964477 | + | 0.296836i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.226021 | + | 0.164214i | 0.00896231 | + | 0.00651150i | ||||
\(637\) | 17.8866 | 0.708693 | ||||||||
\(638\) | 29.9509 | + | 5.01136i | 1.18577 | + | 0.198402i | ||||
\(639\) | −22.1594 | −0.876610 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.312987 | − | 0.963274i | 0.0123622 | − | 0.0380470i | −0.944685 | − | 0.327979i | \(-0.893633\pi\) |
0.957047 | + | 0.289932i | \(0.0936326\pi\) | |||||||
\(642\) | −0.467370 | − | 1.43842i | −0.0184456 | − | 0.0567697i | ||||
\(643\) | −12.1130 | + | 8.80057i | −0.477688 | + | 0.347061i | −0.800430 | − | 0.599426i | \(-0.795395\pi\) |
0.322742 | + | 0.946487i | \(0.395395\pi\) | |||||||
\(644\) | −0.556354 | + | 0.404215i | −0.0219234 | + | 0.0159283i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.147125 | + | 0.452803i | −0.00578855 | + | 0.0178153i | ||||
\(647\) | 14.4712 | + | 10.5139i | 0.568920 | + | 0.413345i | 0.834713 | − | 0.550686i | \(-0.185634\pi\) |
−0.265793 | + | 0.964030i | \(0.585634\pi\) | |||||||
\(648\) | 17.9650 | 0.705732 | ||||||||
\(649\) | 25.2546 | − | 12.5922i | 0.991331 | − | 0.494287i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.5172 | + | 8.36772i | 0.451394 | + | 0.327957i | ||||
\(652\) | −0.800746 | + | 2.46444i | −0.0313596 | + | 0.0965150i | ||||
\(653\) | −14.1419 | − | 43.5244i | −0.553416 | − | 1.70324i | −0.700089 | − | 0.714055i | \(-0.746856\pi\) |
0.146673 | − | 0.989185i | \(-0.453144\pi\) | |||||||
\(654\) | −3.86701 | + | 2.80955i | −0.151212 | + | 0.109862i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 9.38072 | + | 28.8709i | 0.366255 | + | 1.12722i | ||||
\(657\) | −1.08864 | + | 3.35049i | −0.0424719 | + | 0.130715i | ||||
\(658\) | 8.90529 | + | 6.47007i | 0.347164 | + | 0.252230i | ||||
\(659\) | −9.54036 | −0.371640 | −0.185820 | − | 0.982584i | \(-0.559494\pi\) | ||||
−0.185820 | + | 0.982584i | \(0.559494\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.7769 | 0.613651 | 0.306825 | − | 0.951766i | \(-0.400733\pi\) | ||||
0.306825 | + | 0.951766i | \(0.400733\pi\) | |||||||
\(662\) | −14.1734 | − | 10.2976i | −0.550866 | − | 0.400228i | ||||
\(663\) | 1.85871 | − | 5.72052i | 0.0721863 | − | 0.222167i | ||||
\(664\) | 9.64154 | + | 29.6736i | 0.374164 | + | 1.15156i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 28.8016 | − | 20.9256i | 1.11604 | − | 0.810850i | ||||
\(667\) | 2.42548 | + | 7.46486i | 0.0939149 | + | 0.289040i | ||||
\(668\) | 0.887333 | − | 2.73093i | 0.0343319 | − | 0.105663i | ||||
\(669\) | 2.36607 | + | 1.71905i | 0.0914774 | + | 0.0664622i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.7144 | + | 20.0606i | 0.761065 | + | 0.774430i | ||||
\(672\) | 1.92152 | 0.0741243 | ||||||||
\(673\) | 38.2690 | + | 27.8041i | 1.47516 | + | 1.07177i | 0.979076 | + | 0.203494i | \(0.0652299\pi\) |
0.496086 | + | 0.868273i | \(0.334770\pi\) | |||||||
\(674\) | 5.60749 | − | 17.2581i | 0.215992 | − | 0.664756i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.654023 | + | 0.475175i | −0.0251547 | + | 0.0182760i | ||||
\(677\) | 22.2828 | − | 16.1894i | 0.856399 | − | 0.622210i | −0.0705039 | − | 0.997512i | \(-0.522461\pi\) |
0.926903 | + | 0.375301i | \(0.122461\pi\) | |||||||
\(678\) | −1.39477 | − | 4.29265i | −0.0535657 | − | 0.164858i | ||||
\(679\) | 4.88457 | − | 15.0332i | 0.187453 | − | 0.576920i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.15223 | 0.0824736 | ||||||||
\(682\) | 27.2749 | − | 13.5995i | 1.04441 | − | 0.520753i | ||||
\(683\) | 27.1617 | 1.03931 | 0.519656 | − | 0.854375i | \(-0.326060\pi\) | ||||
0.519656 | + | 0.854375i | \(0.326060\pi\) | |||||||
\(684\) | 0.0333024 | + | 0.0241956i | 0.00127335 | + | 0.000925143i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.04233 | + | 3.20795i | 0.0397962 | + | 0.122480i | ||||
\(687\) | 12.5354 | − | 9.10752i | 0.478256 | − | 0.347474i | ||||
\(688\) | 8.76467 | − | 6.36790i | 0.334150 | − | 0.242774i | ||||
\(689\) | −2.61913 | − | 8.06084i | −0.0997808 | − | 0.307094i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.08931 | + | 4.42414i | 0.231648 | + | 0.168302i | 0.697554 | − | 0.716532i | \(-0.254272\pi\) |
−0.465906 | + | 0.884834i | \(0.654272\pi\) | |||||||
\(692\) | 2.57579 | 0.0979167 | ||||||||
\(693\) | −31.8597 | − | 5.33073i | −1.21025 | − | 0.202498i | ||||
\(694\) | −11.4541 | −0.434791 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.52060 | − | 10.8353i | 0.133448 | − | 0.410711i | ||||
\(697\) | 9.49007 | + | 29.2074i | 0.359462 | + | 1.10631i | ||||
\(698\) | −11.4051 | + | 8.28625i | −0.431688 | + | 0.313639i | ||||
\(699\) | −8.52796 | + | 6.19593i | −0.322557 | + | 0.234351i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.83315 | + | 30.2633i | −0.371393 | + | 1.14303i | 0.574487 | + | 0.818513i | \(0.305201\pi\) |
−0.945880 | + | 0.324516i | \(0.894799\pi\) | |||||||
\(702\) | 10.1293 | + | 7.35934i | 0.382304 | + | 0.277760i | ||||
\(703\) | 0.936004 | 0.0353021 | ||||||||
\(704\) | 13.0767 | − | 25.1215i | 0.492847 | − | 0.946802i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −20.9562 | − | 15.2255i | −0.788696 | − | 0.573021i | ||||
\(707\) | 11.1710 | − | 34.3807i | 0.420127 | − | 1.29302i | ||||
\(708\) | −0.245352 | − | 0.755117i | −0.00922091 | − | 0.0283790i | ||||
\(709\) | 11.6807 | − | 8.48651i | 0.438677 | − | 0.318718i | −0.346432 | − | 0.938075i | \(-0.612607\pi\) |
0.785109 | + | 0.619357i | \(0.212607\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.4355 | + | 35.1947i | 0.428863 | + | 1.31991i | ||||
\(712\) | −11.0153 | + | 33.9017i | −0.412817 | + | 1.27052i | ||||
\(713\) | 6.37300 | + | 4.63026i | 0.238671 | + | 0.173405i | ||||
\(714\) | −10.5117 | −0.393392 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.73721 | 0.102294 | ||||||||
\(717\) | −5.10087 | − | 3.70600i | −0.190496 | − | 0.138403i | ||||
\(718\) | 1.84921 | − | 5.69129i | 0.0690120 | − | 0.212397i | ||||
\(719\) | 1.67179 | + | 5.14526i | 0.0623474 | + | 0.191886i | 0.977378 | − | 0.211498i | \(-0.0678341\pi\) |
−0.915031 | + | 0.403383i | \(0.867834\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.0043 | − | 8.72166i | 0.447065 | − | 0.324811i | ||||
\(722\) | 7.95581 | + | 24.4855i | 0.296085 | + | 0.911255i | ||||
\(723\) | 1.77738 | − | 5.47022i | 0.0661016 | − | 0.203440i | ||||
\(724\) | −3.15978 | − | 2.29571i | −0.117432 | − | 0.0853195i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 5.16446 | − | 6.85412i | 0.191671 | − | 0.254380i | ||||
\(727\) | 16.7753 | 0.622161 | 0.311080 | − | 0.950384i | \(-0.399309\pi\) | ||||
0.311080 | + | 0.950384i | \(0.399309\pi\) | |||||||
\(728\) | −24.4993 | − | 17.7998i | −0.908006 | − | 0.659705i | ||||
\(729\) | −3.31409 | + | 10.1997i | −0.122744 | + | 0.377767i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.86684 | − | 6.44213i | 0.327952 | − | 0.238271i | ||||
\(732\) | 0.640209 | − | 0.465139i | 0.0236628 | − | 0.0171920i | ||||
\(733\) | 4.35252 | + | 13.3957i | 0.160764 | + | 0.494781i | 0.998699 | − | 0.0509889i | \(-0.0162373\pi\) |
−0.837935 | + | 0.545770i | \(0.816237\pi\) | |||||||
\(734\) | −12.3004 | + | 37.8567i | −0.454016 | + | 1.39732i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.06327 | 0.0391926 | ||||||||
\(737\) | 6.57756 | + | 44.0046i | 0.242287 | + | 1.62093i | ||||
\(738\) | −30.0956 | −1.10783 | ||||||||
\(739\) | 29.4043 | + | 21.3635i | 1.08165 | + | 0.785868i | 0.977971 | − | 0.208743i | \(-0.0669371\pi\) |
0.103683 | + | 0.994610i | \(0.466937\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.0478902 | + | 0.147391i | 0.00175929 | + | 0.00541454i | ||||
\(742\) | −11.9833 | + | 8.70640i | −0.439922 | + | 0.319622i | ||||
\(743\) | −1.58338 | + | 1.15039i | −0.0580884 | + | 0.0422037i | −0.616451 | − | 0.787394i | \(-0.711430\pi\) |
0.558362 | + | 0.829597i | \(0.311430\pi\) | |||||||
\(744\) | −3.53336 | − | 10.8746i | −0.129539 | − | 0.398681i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5.44519 | + | 3.95617i | 0.199363 | + | 0.144846i | ||||
\(747\) | −28.4080 | −1.03939 | ||||||||
\(748\) | 0.916745 | − | 1.76115i | 0.0335195 | − | 0.0643940i | ||||
\(749\) | −7.07466 | −0.258503 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.78189 | − | 17.7948i | 0.210984 | − | 0.649342i | −0.788430 | − | 0.615124i | \(-0.789106\pi\) |
0.999414 | − | 0.0342181i | \(-0.0108941\pi\) | |||||||
\(752\) | −2.50910 | − | 7.72220i | −0.0914973 | − | 0.281600i | ||||
\(753\) | 4.49634 | − | 3.26678i | 0.163856 | − | 0.119048i | ||||
\(754\) | −20.9701 | + | 15.2356i | −0.763685 | + | 0.554850i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.596550 | + | 1.83599i | −0.0216963 | + | 0.0667744i | ||||
\(757\) | −11.7688 | − | 8.55054i | −0.427744 | − | 0.310775i | 0.353002 | − | 0.935623i | \(-0.385161\pi\) |
−0.780746 | + | 0.624848i | \(0.785161\pi\) | |||||||
\(758\) | −10.7412 | −0.390138 | ||||||||
\(759\) | 2.18777 | + | 0.366056i | 0.0794111 | + | 0.0132870i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.6309 | − | 7.72383i | −0.385371 | − | 0.279989i | 0.378185 | − | 0.925730i | \(-0.376548\pi\) |
−0.763556 | + | 0.645741i | \(0.776548\pi\) | |||||||
\(762\) | −0.587734 | + | 1.80886i | −0.0212914 | + | 0.0655281i | ||||
\(763\) | 6.90920 | + | 21.2643i | 0.250130 | + | 0.769820i | ||||
\(764\) | 0.706114 | − | 0.513022i | 0.0255463 | − | 0.0185605i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.2702 | − | 31.6084i | −0.371077 | − | 1.14206i | ||||
\(767\) | −7.44344 | + | 22.9085i | −0.268767 | + | 0.827180i | ||||
\(768\) | −1.79960 | − | 1.30749i | −0.0649376 | − | 0.0471799i | ||||
\(769\) | 38.9767 | 1.40554 | 0.702768 | − | 0.711419i | \(-0.251947\pi\) | ||||
0.702768 | + | 0.711419i | \(0.251947\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.00099 | 0.216121 | ||||||||
\(772\) | −2.39850 | − | 1.74261i | −0.0863239 | − | 0.0627179i | ||||
\(773\) | 11.9756 | − | 36.8571i | 0.430733 | − | 1.32566i | −0.466664 | − | 0.884435i | \(-0.654544\pi\) |
0.897397 | − | 0.441225i | \(-0.145456\pi\) | |||||||
\(774\) | 3.31902 | + | 10.2149i | 0.119300 | + | 0.367167i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −10.2712 | + | 7.46243i | −0.368713 | + | 0.267886i | ||||
\(777\) | 6.38604 | + | 19.6542i | 0.229098 | + | 0.705091i | ||||
\(778\) | −2.28773 | + | 7.04091i | −0.0820192 | + | 0.252429i | ||||
\(779\) | −0.640147 | − | 0.465094i | −0.0229356 | − | 0.0166637i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.3023 | − | 19.6412i | −0.690689 | − | 0.702818i | ||||
\(782\) | −5.81665 | −0.208003 | ||||||||
\(783\) | 17.8256 | + | 12.9510i | 0.637034 | + | 0.462832i | ||||
\(784\) | −7.12525 | + | 21.9293i | −0.254473 | + | 0.783188i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4.44449 | + | 3.22911i | −0.158530 | + | 0.115179i | ||||
\(787\) | −17.3002 | + | 12.5693i | −0.616685 | + | 0.448048i | −0.851762 | − | 0.523929i | \(-0.824466\pi\) |
0.235077 | + | 0.971977i | \(0.424466\pi\) | |||||||
\(788\) | 0.132564 | + | 0.407990i | 0.00472240 | + | 0.0145341i | ||||
\(789\) | −1.94943 | + | 5.99971i | −0.0694014 | + | 0.213595i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −21.1128 | −0.750686 | ||||||||
\(792\) | 18.1855 | + | 18.5049i | 0.646195 | + | 0.657543i | ||||
\(793\) | −24.0075 | −0.852533 | ||||||||
\(794\) | 7.05718 | + | 5.12734i | 0.250450 | + | 0.181963i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.327093 | − | 1.00669i | −0.0115935 | − | 0.0356812i | ||||
\(797\) | −1.79970 | + | 1.30756i | −0.0637488 | + | 0.0463162i | −0.619203 | − | 0.785231i | \(-0.712544\pi\) |
0.555454 | + | 0.831547i | \(0.312544\pi\) | |||||||
\(798\) | 0.219113 | − | 0.159195i | 0.00775651 | − | 0.00563543i | ||||
\(799\) | −2.53834 | − | 7.81222i | −0.0898002 | − | 0.276377i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −26.2573 | − | 19.0770i | −0.927756 | − | 0.674054i | ||||
\(802\) | 19.9319 | 0.703821 | ||||||||
\(803\) | −3.91802 | + | 1.95356i | −0.138264 | + | 0.0689398i | ||||
\(804\) | 1.25184 | 0.0441491 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.03889 | + | 24.7412i | −0.283158 | + | 0.871470i | ||||
\(807\) | 0.0158888 | + | 0.0489008i | 0.000559314 | + | 0.00172139i | ||||
\(808\) | −23.4900 | + | 17.0665i | −0.826376 | + | 0.600397i | ||||
\(809\) | −17.1254 | + | 12.4424i | −0.602098 | + | 0.437450i | −0.846623 | − | 0.532193i | \(-0.821368\pi\) |
0.244525 | + | 0.969643i | \(0.421368\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.3462 | + | 34.9201i | −0.398420 | + | 1.22621i | 0.527845 | + | 0.849341i | \(0.323000\pi\) |
−0.926266 | + | 0.376871i | \(0.877000\pi\) | |||||||
\(812\) | −3.23329 | − | 2.34912i | −0.113466 | − | 0.0824380i | ||||
\(813\) | 7.71135 | 0.270449 | ||||||||
\(814\) | 43.6357 | + | 7.30109i | 1.52943 | + | 0.255903i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 6.27303 | + | 4.55762i | 0.219600 | + | 0.159549i | ||||
\(817\) | −0.0872627 | + | 0.268567i | −0.00305294 | + | 0.00939597i | ||||
\(818\) | −1.84150 | − | 5.66756i | −0.0643866 | − | 0.198161i | ||||
\(819\) | 22.3065 | − | 16.2066i | 0.779451 | − | 0.566305i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.2585 | − | 37.7278i | −0.427825 | − | 1.31671i | −0.900264 | − | 0.435345i | \(-0.856626\pi\) |
0.472439 | − | 0.881363i | \(-0.343374\pi\) | |||||||
\(822\) | 2.30791 | − | 7.10303i | 0.0804977 | − | 0.247747i | ||||
\(823\) | −37.1568 | − | 26.9960i | −1.29520 | − | 0.941021i | −0.295308 | − | 0.955402i | \(-0.595422\pi\) |
−0.999897 | + | 0.0143810i | \(0.995422\pi\) | |||||||
\(824\) | −11.9178 | −0.415178 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 42.0956 | 1.46469 | ||||||||
\(827\) | −32.1139 | − | 23.3321i | −1.11671 | − | 0.811337i | −0.133002 | − | 0.991116i | \(-0.542462\pi\) |
−0.983707 | + | 0.179779i | \(0.942462\pi\) | |||||||
\(828\) | −0.155407 | + | 0.478293i | −0.00540076 | + | 0.0166218i | ||||
\(829\) | 2.36578 | + | 7.28113i | 0.0821671 | + | 0.252884i | 0.983697 | − | 0.179832i | \(-0.0575553\pi\) |
−0.901530 | + | 0.432716i | \(0.857555\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.81889 | − | 1.32150i | 0.0630966 | − | 0.0458423i | ||||
\(832\) | 7.47017 | + | 22.9908i | 0.258982 | + | 0.797063i | ||||
\(833\) | −7.20831 | + | 22.1849i | −0.249753 | + | 0.768661i | ||||
\(834\) | −0.325374 | − | 0.236398i | −0.0112668 | − | 0.00818580i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.00756251 | + | 0.0505940i | 0.000261555 | + | 0.00174983i | ||||
\(837\) | 22.1135 | 0.764354 | ||||||||
\(838\) | 19.5801 | + | 14.2258i | 0.676384 | + | 0.491422i | ||||
\(839\) | 8.52536 | − | 26.2383i | 0.294328 | − | 0.905848i | −0.689118 | − | 0.724649i | \(-0.742002\pi\) |
0.983446 | − | 0.181200i | \(-0.0579980\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.4418 | + | 9.76607i | −0.463512 | + | 0.336761i | ||||
\(842\) | −5.29576 | + | 3.84760i | −0.182504 | + | 0.132597i | ||||
\(843\) | 0.273412 | + | 0.841477i | 0.00941683 | + | 0.0289820i | ||||
\(844\) | 1.37531 | − | 4.23276i | 0.0473400 | − | 0.145697i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 8.04979 | 0.276757 | ||||||||
\(847\) | −23.0269 | − | 32.8826i | −0.791213 | − | 1.12986i | ||||
\(848\) | 10.9261 | 0.375203 | ||||||||
\(849\) | 2.51960 | + | 1.83059i | 0.0864724 | + | 0.0628258i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.53370 | + | 10.8756i | 0.121134 | + | 0.372811i | ||||
\(852\) | −0.626826 | + | 0.455416i | −0.0214747 | + | 0.0156023i | ||||
\(853\) | 34.0998 | − | 24.7749i | 1.16755 | − | 0.848277i | 0.176840 | − | 0.984240i | \(-0.443413\pi\) |
0.990714 | + | 0.135962i | \(0.0434126\pi\) | |||||||
\(854\) | 12.9651 | + | 39.9024i | 0.443656 | + | 1.36543i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.59707 | + | 3.33997i | 0.157125 | + | 0.114158i | ||||
\(857\) | 45.0850 | 1.54008 | 0.770038 | − | 0.637998i | \(-0.220237\pi\) | ||||
0.770038 | + | 0.637998i | \(0.220237\pi\) | |||||||
\(858\) | 1.08291 | + | 7.24480i | 0.0369700 | + | 0.247333i | ||||
\(859\) | −11.8257 | −0.403488 | −0.201744 | − | 0.979438i | \(-0.564661\pi\) | ||||
−0.201744 | + | 0.979438i | \(0.564661\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.39854 | − | 16.6150i | 0.183982 | − | 0.566237i | ||||
\(862\) | 10.4204 | + | 32.0705i | 0.354919 | + | 1.09233i | ||||
\(863\) | 22.5484 | − | 16.3823i | 0.767555 | − | 0.557662i | −0.133663 | − | 0.991027i | \(-0.542674\pi\) |
0.901218 | + | 0.433365i | \(0.142674\pi\) | |||||||
\(864\) | 2.41475 | − | 1.75442i | 0.0821514 | − | 0.0596865i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −8.90229 | + | 27.3984i | −0.302512 | + | 0.931037i | ||||
\(867\) | −1.56877 | − | 1.13978i | −0.0532782 | − | 0.0387089i | ||||
\(868\) | −4.01105 | −0.136144 | ||||||||
\(869\) | −21.2342 | + | 40.7929i | −0.720323 | + | 1.38380i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30.7249 | − | 22.3230i | −1.04107 | − | 0.756384i | ||||
\(872\) | 5.54939 | − | 17.0793i | 0.187926 | − | 0.578377i | ||||
\(873\) | −3.57207 | − | 10.9937i | −0.120896 | − | 0.372081i | ||||
\(874\) | 0.121246 | − | 0.0880900i | 0.00410119 | − | 0.00297969i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.0380642 | + | 0.117149i | 0.00128607 | + | 0.00395811i | ||||
\(877\) | 3.53736 | − | 10.8869i | 0.119448 | − | 0.367624i | −0.873401 | − | 0.487003i | \(-0.838090\pi\) |
0.992849 | + | 0.119379i | \(0.0380902\pi\) | |||||||
\(878\) | −17.4516 | − | 12.6793i | −0.588963 | − | 0.427907i | ||||
\(879\) | 6.57011 | 0.221604 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47.0037 | 1.58360 | 0.791798 | − | 0.610783i | \(-0.209145\pi\) | ||||
0.791798 | + | 0.610783i | \(0.209145\pi\) | |||||||
\(882\) | −18.4938 | − | 13.4365i | −0.622717 | − | 0.452431i | ||||
\(883\) | 14.4974 | − | 44.6185i | 0.487877 | − | 1.50153i | −0.339894 | − | 0.940464i | \(-0.610391\pi\) |
0.827770 | − | 0.561067i | \(-0.189609\pi\) | |||||||
\(884\) | 0.523698 | + | 1.61178i | 0.0176139 | + | 0.0542099i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −28.8313 | + | 20.9472i | −0.968607 | + | 0.703734i | ||||
\(887\) | 8.60386 | + | 26.4800i | 0.288889 | + | 0.889110i | 0.985206 | + | 0.171375i | \(0.0548210\pi\) |
−0.696316 | + | 0.717735i | \(0.745179\pi\) | |||||||
\(888\) | 5.12920 | − | 15.7860i | 0.172125 | − | 0.529745i | ||||
\(889\) | 7.19754 | + | 5.22932i | 0.241398 | + | 0.175386i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −18.1915 | + | 9.07048i | −0.609439 | + | 0.303872i | ||||
\(892\) | −0.824022 | −0.0275903 | ||||||||
\(893\) | 0.171223 | + | 0.124401i | 0.00572975 | + | 0.00416290i | ||||
\(894\) | −1.96725 | + | 6.05456i | −0.0657946 | + | 0.202495i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 28.7759 | − | 20.9069i | 0.961335 | − | 0.698451i | ||||
\(897\) | −1.53176 | + | 1.11289i | −0.0511441 | + | 0.0371584i | ||||
\(898\) | 3.43085 | + | 10.5591i | 0.114489 | + | 0.352360i | ||||
\(899\) | −14.1469 | + | 43.5397i | −0.471826 | + | 1.45213i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.0534 | 0.368244 | ||||||||
\(902\) | −26.2153 | − | 26.6756i | −0.872872 | − | 0.888201i | ||||
\(903\) | −6.23473 | −0.207479 | ||||||||
\(904\) | 13.7190 | + | 9.96742i | 0.456287 | + | 0.331512i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.467767 | + | 1.43964i | 0.0155405 | + | 0.0478288i | ||||
\(907\) | −23.1567 | + | 16.8243i | −0.768907 | + | 0.558643i | −0.901629 | − | 0.432510i | \(-0.857628\pi\) |
0.132723 | + | 0.991153i | \(0.457628\pi\) | |||||||
\(908\) | −0.490586 | + | 0.356432i | −0.0162807 | + | 0.0118286i | ||||
\(909\) | −8.16930 | − | 25.1425i | −0.270959 | − | 0.833925i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.14883 | − | 3.01430i | −0.137457 | − | 0.0998682i | 0.516932 | − | 0.856026i | \(-0.327074\pi\) |
−0.654389 | + | 0.756158i | \(0.727074\pi\) | |||||||
\(912\) | −0.199781 | −0.00661542 | ||||||||
\(913\) | −24.7452 | − | 25.1798i | −0.818948 | − | 0.833330i | ||||
\(914\) | 16.1547 | 0.534351 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.34907 | + | 4.15200i | −0.0445744 | + | 0.137186i | ||||
\(917\) | 7.94098 | + | 24.4398i | 0.262234 | + | 0.807074i | ||||
\(918\) | −13.2100 | + | 9.59759i | −0.435993 | + | 0.316768i | ||||
\(919\) | −28.5429 | + | 20.7376i | −0.941544 | + | 0.684072i | −0.948792 | − | 0.315902i | \(-0.897693\pi\) |
0.00724799 | + | 0.999974i | \(0.497693\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.755822 | + | 2.32618i | −0.0249052 | + | 0.0766503i | ||||
\(922\) | 7.63536 | + | 5.54742i | 0.251457 | + | 0.182694i | ||||
\(923\) | 23.5057 | 0.773699 | ||||||||
\(924\) | −1.01078 | + | 0.503984i | −0.0332521 | + | 0.0165798i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −13.6834 | − | 9.94159i | −0.449665 | − | 0.326701i | ||||
\(927\) | 3.35318 | − | 10.3200i | 0.110133 | − | 0.338954i | ||||
\(928\) | 1.90950 | + | 5.87682i | 0.0626823 | + | 0.192916i | ||||
\(929\) | 47.8474 | − | 34.7632i | 1.56982 | − | 1.14054i | 0.642498 | − | 0.766287i | \(-0.277898\pi\) |
0.927325 | − | 0.374256i | \(-0.122102\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.185724 | − | 0.571601i | −0.00608687 | − | 0.0187335i | ||||
\(932\) | 0.917781 | − | 2.82464i | 0.0300629 | − | 0.0925242i | ||||
\(933\) | −7.73775 | − | 5.62181i | −0.253323 | − | 0.184050i | ||||
\(934\) | −8.33220 | −0.272638 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −22.1458 | −0.723857 | ||||||||
\(937\) | 11.6843 | + | 8.48911i | 0.381708 | + | 0.277327i | 0.762049 | − | 0.647519i | \(-0.224193\pi\) |
−0.380341 | + | 0.924846i | \(0.624193\pi\) | |||||||
\(938\) | −20.5098 | + | 63.1226i | −0.669668 | + | 2.06103i | ||||
\(939\) | −4.72637 | − | 14.5463i | −0.154239 | − | 0.474700i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.0955 | − | 10.9675i | 0.492100 | − | 0.357532i | −0.313891 | − | 0.949459i | \(-0.601633\pi\) |
0.805991 | + | 0.591927i | \(0.201633\pi\) | |||||||
\(942\) | −5.12905 | − | 15.7856i | −0.167113 | − | 0.514322i | ||||
\(943\) | 2.98727 | − | 9.19386i | 0.0972788 | − | 0.299393i | ||||
\(944\) | −25.1211 | − | 18.2516i | −0.817623 | − | 0.594038i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.16301 | + | 11.8397i | −0.200377 | + | 0.384942i | ||||
\(947\) | 0.991391 | 0.0322159 | 0.0161079 | − | 0.999870i | \(-0.494872\pi\) | ||||
0.0161079 | + | 0.999870i | \(0.494872\pi\) | |||||||
\(948\) | 1.04679 | + | 0.760540i | 0.0339983 | + | 0.0247012i | ||||
\(949\) | 1.15478 | − | 3.55405i | 0.0374858 | − | 0.115369i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.69896 | + | 1.96091i | −0.0875198 | + | 0.0635869i | ||||
\(952\) | 31.9505 | − | 23.2134i | 1.03552 | − | 0.752351i | ||||
\(953\) | 2.55373 | + | 7.85957i | 0.0827234 | + | 0.254597i | 0.983860 | − | 0.178938i | \(-0.0572662\pi\) |
−0.901137 | + | 0.433535i | \(0.857266\pi\) | |||||||
\(954\) | −3.34731 | + | 10.3020i | −0.108373 | + | 0.333539i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.77646 | 0.0574549 | ||||||||
\(957\) | 1.90572 | + | 12.7495i | 0.0616031 | + | 0.412132i | ||||
\(958\) | −30.0881 | −0.972101 | ||||||||
\(959\) | −28.2633 | − | 20.5345i | −0.912669 | − | 0.663093i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.61867 | + | 14.2148i | 0.148989 | + | 0.458542i | ||||
\(962\) | −30.5515 | + | 22.1969i | −0.985019 | + | 0.715658i | ||||
\(963\) | −4.18560 | + | 3.04102i | −0.134879 | + | 0.0979954i | ||||
\(964\) | 0.500784 | + | 1.54125i | 0.0161292 | + | 0.0496404i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.67693 | + | 1.94491i | 0.0861289 | + | 0.0625763i | ||||
\(967\) | −7.36029 | −0.236691 | −0.118345 | − | 0.992972i | \(-0.537759\pi\) | ||||
−0.118345 | + | 0.992972i | \(0.537759\pi\) | |||||||
\(968\) | −0.561246 | + | 32.2380i | −0.0180391 | + | 1.03617i | ||||
\(969\) | −0.202110 | −0.00649271 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.53808 | + | 4.73372i | −0.0493593 | + | 0.151912i | −0.972698 | − | 0.232074i | \(-0.925449\pi\) |
0.923339 | + | 0.383986i | \(0.125449\pi\) | |||||||
\(972\) | 0.667127 | + | 2.05321i | 0.0213981 | + | 0.0658566i | ||||
\(973\) | −1.52199 | + | 1.10579i | −0.0487927 | + | 0.0354500i | ||||
\(974\) | 37.5429 | − | 27.2765i | 1.20295 | − | 0.873996i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.56357 | − | 29.4337i | 0.306123 | − | 0.942148i | ||||
\(977\) | 8.36266 | + | 6.07583i | 0.267545 | + | 0.194383i | 0.713467 | − | 0.700689i | \(-0.247124\pi\) |
−0.445922 | + | 0.895072i | \(0.647124\pi\) | |||||||
\(978\) | 12.4680 | 0.398684 | ||||||||
\(979\) | −5.96266 | − | 39.8908i | −0.190567 | − | 1.27492i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.2281 | + | 9.61077i | 0.422340 | + | 0.306848i | ||||
\(982\) | 7.11996 | − | 21.9130i | 0.227207 | − | 0.699272i | ||||
\(983\) | 8.98045 | + | 27.6390i | 0.286432 | + | 0.881547i | 0.985966 | + | 0.166947i | \(0.0533910\pi\) |
−0.699534 | + | 0.714599i | \(0.746609\pi\) | |||||||
\(984\) | −11.3519 | + | 8.24764i | −0.361886 | + | 0.262925i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −10.4460 | − | 32.1493i | −0.332667 | − | 1.02384i | ||||
\(987\) | −1.44397 | + | 4.44408i | −0.0459620 | + | 0.141456i | ||||
\(988\) | −0.0353258 | − | 0.0256657i | −0.00112386 | − | 0.000816534i | ||||
\(989\) | −3.44997 | −0.109703 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.70381 | 0.244719 | 0.122360 | − | 0.992486i | \(-0.460954\pi\) | ||||
0.122360 | + | 0.992486i | \(0.460954\pi\) | |||||||
\(992\) | 5.01724 | + | 3.64524i | 0.159298 | + | 0.115737i | ||||
\(993\) | 2.29818 | − | 7.07308i | 0.0729307 | − | 0.224458i | ||||
\(994\) | −12.6941 | − | 39.0683i | −0.402631 | − | 1.23917i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.803583 | + | 0.583837i | −0.0254625 | + | 0.0184996i | ||||
\(997\) | 0.885080 | + | 2.72400i | 0.0280308 | + | 0.0862698i | 0.964093 | − | 0.265564i | \(-0.0855582\pi\) |
−0.936062 | + | 0.351834i | \(0.885558\pi\) | |||||||
\(998\) | −2.19076 | + | 6.74247i | −0.0693473 | + | 0.213429i | ||||
\(999\) | 25.9702 | + | 18.8685i | 0.821661 | + | 0.596972i |
(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 | 275.2.h.a.26.2 | 8 | ||
5.2 | odd | 4 | 275.2.z.a.224.1 | 16 | |||
5.3 | odd | 4 | 275.2.z.a.224.4 | 16 | |||
5.4 | even | 2 | 55.2.g.b.26.1 | ✓ | 8 | ||
11.3 | even | 5 | inner | 275.2.h.a.201.2 | 8 | ||
11.5 | even | 5 | 3025.2.a.bd.1.1 | 4 | |||
11.6 | odd | 10 | 3025.2.a.w.1.4 | 4 | |||
15.14 | odd | 2 | 495.2.n.e.136.2 | 8 | |||
20.19 | odd | 2 | 880.2.bo.h.81.1 | 8 | |||
55.3 | odd | 20 | 275.2.z.a.124.1 | 16 | |||
55.4 | even | 10 | 605.2.g.m.251.2 | 8 | |||
55.9 | even | 10 | 605.2.g.m.511.2 | 8 | |||
55.14 | even | 10 | 55.2.g.b.36.1 | yes | 8 | ||
55.19 | odd | 10 | 605.2.g.k.366.2 | 8 | |||
55.24 | odd | 10 | 605.2.g.e.511.1 | 8 | |||
55.29 | odd | 10 | 605.2.g.e.251.1 | 8 | |||
55.39 | odd | 10 | 605.2.a.k.1.1 | 4 | |||
55.47 | odd | 20 | 275.2.z.a.124.4 | 16 | |||
55.49 | even | 10 | 605.2.a.j.1.4 | 4 | |||
55.54 | odd | 2 | 605.2.g.k.81.2 | 8 | |||
165.14 | odd | 10 | 495.2.n.e.91.2 | 8 | |||
165.104 | odd | 10 | 5445.2.a.bp.1.1 | 4 | |||
165.149 | even | 10 | 5445.2.a.bi.1.4 | 4 | |||
220.39 | even | 10 | 9680.2.a.cm.1.2 | 4 | |||
220.159 | odd | 10 | 9680.2.a.cn.1.2 | 4 | |||
220.179 | odd | 10 | 880.2.bo.h.641.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
55.2.g.b.26.1 | ✓ | 8 | 5.4 | even | 2 | ||
55.2.g.b.36.1 | yes | 8 | 55.14 | even | 10 | ||
275.2.h.a.26.2 | 8 | 1.1 | even | 1 | trivial | ||
275.2.h.a.201.2 | 8 | 11.3 | even | 5 | inner | ||
275.2.z.a.124.1 | 16 | 55.3 | odd | 20 | |||
275.2.z.a.124.4 | 16 | 55.47 | odd | 20 | |||
275.2.z.a.224.1 | 16 | 5.2 | odd | 4 | |||
275.2.z.a.224.4 | 16 | 5.3 | odd | 4 | |||
495.2.n.e.91.2 | 8 | 165.14 | odd | 10 | |||
495.2.n.e.136.2 | 8 | 15.14 | odd | 2 | |||
605.2.a.j.1.4 | 4 | 55.49 | even | 10 | |||
605.2.a.k.1.1 | 4 | 55.39 | odd | 10 | |||
605.2.g.e.251.1 | 8 | 55.29 | odd | 10 | |||
605.2.g.e.511.1 | 8 | 55.24 | odd | 10 | |||
605.2.g.k.81.2 | 8 | 55.54 | odd | 2 | |||
605.2.g.k.366.2 | 8 | 55.19 | odd | 10 | |||
605.2.g.m.251.2 | 8 | 55.4 | even | 10 | |||
605.2.g.m.511.2 | 8 | 55.9 | even | 10 | |||
880.2.bo.h.81.1 | 8 | 20.19 | odd | 2 | |||
880.2.bo.h.641.1 | 8 | 220.179 | odd | 10 | |||
3025.2.a.w.1.4 | 4 | 11.6 | odd | 10 | |||
3025.2.a.bd.1.1 | 4 | 11.5 | even | 5 | |||
5445.2.a.bi.1.4 | 4 | 165.149 | even | 10 | |||
5445.2.a.bp.1.1 | 4 | 165.104 | odd | 10 | |||
9680.2.a.cm.1.2 | 4 | 220.39 | even | 10 | |||
9680.2.a.cn.1.2 | 4 | 220.159 | odd | 10 |