Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(161,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.161");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.o (of order \(6\), 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: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 491.17 | ||
Character | \(\chi\) | \(=\) | 930.491 |
Dual form | 930.2.o.e.161.7 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0.500302 | + | 1.65822i | 0.288850 | + | 0.957375i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0.866025 | − | 0.500000i | 0.387298 | − | 0.223607i | ||||
\(6\) | −1.65822 | + | 0.500302i | −0.676966 | + | 0.204247i | ||||
\(7\) | −1.28701 | + | 2.22916i | −0.486443 | + | 0.842543i | −0.999879 | − | 0.0155847i | \(-0.995039\pi\) |
0.513436 | + | 0.858128i | \(0.328372\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −2.49940 | + | 1.65922i | −0.833132 | + | 0.553074i | ||||
\(10\) | 0.500000 | + | 0.866025i | 0.158114 | + | 0.273861i | ||||
\(11\) | 2.56707 | + | 4.44629i | 0.774000 | + | 1.34061i | 0.935355 | + | 0.353711i | \(0.115080\pi\) |
−0.161355 | + | 0.986897i | \(0.551586\pi\) | |||||||
\(12\) | −0.500302 | − | 1.65822i | −0.144425 | − | 0.478687i | ||||
\(13\) | 4.59412 | − | 2.65242i | 1.27418 | − | 0.735648i | 0.298408 | − | 0.954438i | \(-0.403544\pi\) |
0.975772 | + | 0.218790i | \(0.0702109\pi\) | |||||||
\(14\) | −2.22916 | − | 1.28701i | −0.595768 | − | 0.343967i | ||||
\(15\) | 1.26238 | + | 1.18591i | 0.325946 | + | 0.306201i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.59376 | + | 4.49252i | −0.629079 | + | 1.08960i | 0.358658 | + | 0.933469i | \(0.383234\pi\) |
−0.987737 | + | 0.156127i | \(0.950099\pi\) | |||||||
\(18\) | −1.65922 | − | 2.49940i | −0.391083 | − | 0.589113i | ||||
\(19\) | −0.264764 | + | 0.458584i | −0.0607410 | + | 0.105206i | −0.894797 | − | 0.446474i | \(-0.852680\pi\) |
0.834056 | + | 0.551680i | \(0.186013\pi\) | |||||||
\(20\) | −0.866025 | + | 0.500000i | −0.193649 | + | 0.111803i | ||||
\(21\) | −4.34033 | − | 1.01889i | −0.947138 | − | 0.222339i | ||||
\(22\) | −4.44629 | + | 2.56707i | −0.947953 | + | 0.547301i | ||||
\(23\) | 3.03318 | 0.632462 | 0.316231 | − | 0.948682i | \(-0.397583\pi\) | ||||
0.316231 | + | 0.948682i | \(0.397583\pi\) | |||||||
\(24\) | 1.65822 | − | 0.500302i | 0.338483 | − | 0.102124i | ||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | 2.65242 | + | 4.59412i | 0.520182 | + | 0.900982i | ||||
\(27\) | −4.00181 | − | 3.31444i | −0.770149 | − | 0.637864i | ||||
\(28\) | 1.28701 | − | 2.22916i | 0.243221 | − | 0.421272i | ||||
\(29\) | −8.44680 | −1.56853 | −0.784265 | − | 0.620426i | \(-0.786960\pi\) | ||||
−0.784265 | + | 0.620426i | \(0.786960\pi\) | |||||||
\(30\) | −1.18591 | + | 1.26238i | −0.216517 | + | 0.230479i | ||||
\(31\) | 0.790363 | − | 5.51138i | 0.141953 | − | 0.989873i | ||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | −6.08863 | + | 6.48126i | −1.05989 | + | 1.12824i | ||||
\(34\) | −4.49252 | − | 2.59376i | −0.770461 | − | 0.444826i | ||||
\(35\) | 2.57401i | 0.435087i | ||||||||
\(36\) | 2.49940 | − | 1.65922i | 0.416566 | − | 0.276537i | ||||
\(37\) | 0.580888 | + | 0.335376i | 0.0954974 | + | 0.0551355i | 0.546988 | − | 0.837140i | \(-0.315774\pi\) |
−0.451491 | + | 0.892276i | \(0.649108\pi\) | |||||||
\(38\) | −0.458584 | − | 0.264764i | −0.0743922 | − | 0.0429504i | ||||
\(39\) | 6.69674 | + | 6.29106i | 1.07234 | + | 1.00738i | ||||
\(40\) | −0.500000 | − | 0.866025i | −0.0790569 | − | 0.136931i | ||||
\(41\) | −9.85425 | + | 5.68936i | −1.53898 | + | 0.888528i | −0.540077 | + | 0.841616i | \(0.681605\pi\) |
−0.998899 | + | 0.0469123i | \(0.985062\pi\) | |||||||
\(42\) | 1.01889 | − | 4.34033i | 0.157218 | − | 0.669728i | ||||
\(43\) | −6.69156 | − | 3.86337i | −1.02045 | − | 0.589159i | −0.106218 | − | 0.994343i | \(-0.533874\pi\) |
−0.914235 | + | 0.405184i | \(0.867207\pi\) | |||||||
\(44\) | −2.56707 | − | 4.44629i | −0.387000 | − | 0.670304i | ||||
\(45\) | −1.33493 | + | 2.68663i | −0.198999 | + | 0.400499i | ||||
\(46\) | 3.03318i | 0.447218i | ||||||||
\(47\) | − | 6.75256i | − | 0.984961i | −0.870323 | − | 0.492481i | \(-0.836090\pi\) | ||
0.870323 | − | 0.492481i | \(-0.163910\pi\) | |||||||
\(48\) | 0.500302 | + | 1.65822i | 0.0722124 | + | 0.239344i | ||||
\(49\) | 0.187231 | + | 0.324294i | 0.0267473 | + | 0.0463278i | ||||
\(50\) | 0.866025 | + | 0.500000i | 0.122474 | + | 0.0707107i | ||||
\(51\) | −8.74726 | − | 2.05341i | −1.22486 | − | 0.287535i | ||||
\(52\) | −4.59412 | + | 2.65242i | −0.637090 | + | 0.367824i | ||||
\(53\) | 0.822328 | + | 1.42431i | 0.112955 | + | 0.195644i | 0.916961 | − | 0.398978i | \(-0.130635\pi\) |
−0.804005 | + | 0.594622i | \(0.797302\pi\) | |||||||
\(54\) | 3.31444 | − | 4.00181i | 0.451038 | − | 0.544578i | ||||
\(55\) | 4.44629 | + | 2.56707i | 0.599538 | + | 0.346143i | ||||
\(56\) | 2.22916 | + | 1.28701i | 0.297884 | + | 0.171983i | ||||
\(57\) | −0.892896 | − | 0.209606i | −0.118267 | − | 0.0277630i | ||||
\(58\) | − | 8.44680i | − | 1.10912i | ||||||
\(59\) | 10.4486 | + | 6.03251i | 1.36029 | + | 0.785366i | 0.989663 | − | 0.143414i | \(-0.0458079\pi\) |
0.370632 | + | 0.928780i | \(0.379141\pi\) | |||||||
\(60\) | −1.26238 | − | 1.18591i | −0.162973 | − | 0.153100i | ||||
\(61\) | 7.06279i | 0.904297i | 0.891943 | + | 0.452149i | \(0.149342\pi\) | ||||
−0.891943 | + | 0.452149i | \(0.850658\pi\) | |||||||
\(62\) | 5.51138 | + | 0.790363i | 0.699946 | + | 0.100376i | ||||
\(63\) | −0.481936 | − | 7.70698i | −0.0607182 | − | 0.970988i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 2.65242 | − | 4.59412i | 0.328992 | − | 0.569831i | ||||
\(66\) | −6.48126 | − | 6.08863i | −0.797787 | − | 0.749458i | ||||
\(67\) | 3.98360 | + | 6.89980i | 0.486675 | + | 0.842945i | 0.999883 | − | 0.0153191i | \(-0.00487642\pi\) |
−0.513208 | + | 0.858264i | \(0.671543\pi\) | |||||||
\(68\) | 2.59376 | − | 4.49252i | 0.314539 | − | 0.544798i | ||||
\(69\) | 1.51751 | + | 5.02968i | 0.182686 | + | 0.605503i | ||||
\(70\) | −2.57401 | −0.307653 | ||||||||
\(71\) | 8.45327 | − | 4.88050i | 1.00322 | − | 0.579208i | 0.0940192 | − | 0.995570i | \(-0.470028\pi\) |
0.909199 | + | 0.416362i | \(0.136695\pi\) | |||||||
\(72\) | 1.65922 | + | 2.49940i | 0.195541 | + | 0.294557i | ||||
\(73\) | −3.21521 | + | 1.85630i | −0.376312 | + | 0.217264i | −0.676212 | − | 0.736707i | \(-0.736380\pi\) |
0.299901 | + | 0.953970i | \(0.403047\pi\) | |||||||
\(74\) | −0.335376 | + | 0.580888i | −0.0389867 | + | 0.0675269i | ||||
\(75\) | 1.68621 | + | 0.395836i | 0.194707 | + | 0.0457072i | ||||
\(76\) | 0.264764 | − | 0.458584i | 0.0303705 | − | 0.0526032i | ||||
\(77\) | −13.2153 | −1.50603 | ||||||||
\(78\) | −6.29106 | + | 6.69674i | −0.712322 | + | 0.758257i | ||||
\(79\) | 8.75345 | + | 5.05381i | 0.984841 | + | 0.568598i | 0.903728 | − | 0.428107i | \(-0.140819\pi\) |
0.0811125 | + | 0.996705i | \(0.474153\pi\) | |||||||
\(80\) | 0.866025 | − | 0.500000i | 0.0968246 | − | 0.0559017i | ||||
\(81\) | 3.49396 | − | 8.29411i | 0.388218 | − | 0.921568i | ||||
\(82\) | −5.68936 | − | 9.85425i | −0.628284 | − | 1.08822i | ||||
\(83\) | −3.97145 | − | 6.87875i | −0.435923 | − | 0.755041i | 0.561447 | − | 0.827513i | \(-0.310245\pi\) |
−0.997371 | + | 0.0724712i | \(0.976911\pi\) | |||||||
\(84\) | 4.34033 | + | 1.01889i | 0.473569 | + | 0.111170i | ||||
\(85\) | 5.18752i | 0.562665i | ||||||||
\(86\) | 3.86337 | − | 6.69156i | 0.416598 | − | 0.721569i | ||||
\(87\) | −4.22595 | − | 14.0067i | −0.453069 | − | 1.50167i | ||||
\(88\) | 4.44629 | − | 2.56707i | 0.473976 | − | 0.273650i | ||||
\(89\) | 14.8905 | 1.57839 | 0.789195 | − | 0.614143i | \(-0.210498\pi\) | ||||
0.789195 | + | 0.614143i | \(0.210498\pi\) | |||||||
\(90\) | −2.68663 | − | 1.33493i | −0.283195 | − | 0.140714i | ||||
\(91\) | 13.6547i | 1.43140i | ||||||||
\(92\) | −3.03318 | −0.316231 | ||||||||
\(93\) | 9.53451 | − | 1.44676i | 0.988683 | − | 0.150022i | ||||
\(94\) | 6.75256 | 0.696473 | ||||||||
\(95\) | 0.529528i | 0.0543284i | ||||||||
\(96\) | −1.65822 | + | 0.500302i | −0.169242 | + | 0.0510619i | ||||
\(97\) | −6.46323 | −0.656242 | −0.328121 | − | 0.944636i | \(-0.606415\pi\) | ||||
−0.328121 | + | 0.944636i | \(0.606415\pi\) | |||||||
\(98\) | −0.324294 | + | 0.187231i | −0.0327587 | + | 0.0189132i | ||||
\(99\) | −13.7935 | − | 6.85371i | −1.38630 | − | 0.688823i | ||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | − | 8.88476i | − | 0.884067i | −0.896999 | − | 0.442034i | \(-0.854257\pi\) | ||
0.896999 | − | 0.442034i | \(-0.145743\pi\) | |||||||
\(102\) | 2.05341 | − | 8.74726i | 0.203318 | − | 0.866107i | ||||
\(103\) | −5.26044 | − | 9.11135i | −0.518327 | − | 0.897768i | −0.999773 | − | 0.0212926i | \(-0.993222\pi\) |
0.481447 | − | 0.876475i | \(-0.340111\pi\) | |||||||
\(104\) | −2.65242 | − | 4.59412i | −0.260091 | − | 0.450491i | ||||
\(105\) | −4.26828 | + | 1.28778i | −0.416542 | + | 0.125675i | ||||
\(106\) | −1.42431 | + | 0.822328i | −0.138342 | + | 0.0798715i | ||||
\(107\) | −11.2096 | − | 6.47185i | −1.08367 | − | 0.625657i | −0.151786 | − | 0.988413i | \(-0.548503\pi\) |
−0.931884 | + | 0.362756i | \(0.881836\pi\) | |||||||
\(108\) | 4.00181 | + | 3.31444i | 0.385075 | + | 0.318932i | ||||
\(109\) | −1.35138 | −0.129439 | −0.0647193 | − | 0.997904i | \(-0.520615\pi\) | ||||
−0.0647193 | + | 0.997904i | \(0.520615\pi\) | |||||||
\(110\) | −2.56707 | + | 4.44629i | −0.244760 | + | 0.423937i | ||||
\(111\) | −0.265508 | + | 1.13103i | −0.0252009 | + | 0.107353i | ||||
\(112\) | −1.28701 | + | 2.22916i | −0.121611 | + | 0.210636i | ||||
\(113\) | 4.08230 | − | 2.35692i | 0.384030 | − | 0.221720i | −0.295540 | − | 0.955330i | \(-0.595500\pi\) |
0.679570 | + | 0.733610i | \(0.262166\pi\) | |||||||
\(114\) | 0.209606 | − | 0.892896i | 0.0196314 | − | 0.0836274i | ||||
\(115\) | 2.62681 | − | 1.51659i | 0.244951 | − | 0.141423i | ||||
\(116\) | 8.44680 | 0.784265 | ||||||||
\(117\) | −7.08158 | + | 14.2521i | −0.654692 | + | 1.31761i | ||||
\(118\) | −6.03251 | + | 10.4486i | −0.555338 | + | 0.961873i | ||||
\(119\) | −6.67636 | − | 11.5638i | −0.612021 | − | 1.06005i | ||||
\(120\) | 1.18591 | − | 1.26238i | 0.108258 | − | 0.115239i | ||||
\(121\) | −7.67968 | + | 13.3016i | −0.698152 | + | 1.20924i | ||||
\(122\) | −7.06279 | −0.639435 | ||||||||
\(123\) | −14.3643 | − | 13.4941i | −1.29519 | − | 1.21673i | ||||
\(124\) | −0.790363 | + | 5.51138i | −0.0709767 | + | 0.494937i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 7.70698 | − | 0.481936i | 0.686593 | − | 0.0429343i | ||||
\(127\) | 13.5026 | + | 7.79574i | 1.19816 | + | 0.691760i | 0.960146 | − | 0.279500i | \(-0.0901688\pi\) |
0.238018 | + | 0.971261i | \(0.423502\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 3.05853 | − | 13.0289i | 0.269288 | − | 1.14713i | ||||
\(130\) | 4.59412 | + | 2.65242i | 0.402931 | + | 0.232632i | ||||
\(131\) | 16.4069 | + | 9.47252i | 1.43348 | + | 0.827618i | 0.997384 | − | 0.0722837i | \(-0.0230287\pi\) |
0.436093 | + | 0.899902i | \(0.356362\pi\) | |||||||
\(132\) | 6.08863 | − | 6.48126i | 0.529947 | − | 0.564121i | ||||
\(133\) | −0.681505 | − | 1.18040i | −0.0590940 | − | 0.102354i | ||||
\(134\) | −6.89980 | + | 3.98360i | −0.596052 | + | 0.344131i | ||||
\(135\) | −5.12289 | − | 0.869482i | −0.440908 | − | 0.0748331i | ||||
\(136\) | 4.49252 | + | 2.59376i | 0.385231 | + | 0.222413i | ||||
\(137\) | −2.98906 | − | 5.17720i | −0.255373 | − | 0.442318i | 0.709624 | − | 0.704580i | \(-0.248865\pi\) |
−0.964997 | + | 0.262262i | \(0.915531\pi\) | |||||||
\(138\) | −5.02968 | + | 1.51751i | −0.428155 | + | 0.129179i | ||||
\(139\) | 20.6001i | 1.74728i | 0.486573 | + | 0.873640i | \(0.338247\pi\) | ||||
−0.486573 | + | 0.873640i | \(0.661753\pi\) | |||||||
\(140\) | − | 2.57401i | − | 0.217544i | ||||||
\(141\) | 11.1972 | − | 3.37832i | 0.942977 | − | 0.284506i | ||||
\(142\) | 4.88050 | + | 8.45327i | 0.409562 | + | 0.709382i | ||||
\(143\) | 23.5869 | + | 13.6179i | 1.97243 | + | 1.13878i | ||||
\(144\) | −2.49940 | + | 1.65922i | −0.208283 | + | 0.138269i | ||||
\(145\) | −7.31514 | + | 4.22340i | −0.607489 | + | 0.350734i | ||||
\(146\) | −1.85630 | − | 3.21521i | −0.153629 | − | 0.266093i | ||||
\(147\) | −0.444079 | + | 0.472716i | −0.0366271 | + | 0.0389890i | ||||
\(148\) | −0.580888 | − | 0.335376i | −0.0477487 | − | 0.0275677i | ||||
\(149\) | 20.8920 | + | 12.0620i | 1.71154 | + | 0.988160i | 0.932486 | + | 0.361206i | \(0.117635\pi\) |
0.779057 | + | 0.626953i | \(0.215698\pi\) | |||||||
\(150\) | −0.395836 | + | 1.68621i | −0.0323199 | + | 0.137679i | ||||
\(151\) | − | 16.5788i | − | 1.34916i | −0.738201 | − | 0.674581i | \(-0.764324\pi\) | ||
0.738201 | − | 0.674581i | \(-0.235676\pi\) | |||||||
\(152\) | 0.458584 | + | 0.264764i | 0.0371961 | + | 0.0214752i | ||||
\(153\) | −0.971266 | − | 15.5322i | −0.0785222 | − | 1.25570i | ||||
\(154\) | − | 13.2153i | − | 1.06492i | ||||||
\(155\) | −2.07122 | − | 5.16818i | −0.166364 | − | 0.415118i | ||||
\(156\) | −6.69674 | − | 6.29106i | −0.536169 | − | 0.503688i | ||||
\(157\) | 14.6508 | 1.16926 | 0.584631 | − | 0.811300i | \(-0.301239\pi\) | ||||
0.584631 | + | 0.811300i | \(0.301239\pi\) | |||||||
\(158\) | −5.05381 | + | 8.75345i | −0.402059 | + | 0.696387i | ||||
\(159\) | −1.95041 | + | 2.07619i | −0.154678 | + | 0.164652i | ||||
\(160\) | 0.500000 | + | 0.866025i | 0.0395285 | + | 0.0684653i | ||||
\(161\) | −3.90372 | + | 6.76144i | −0.307656 | + | 0.532876i | ||||
\(162\) | 8.29411 | + | 3.49396i | 0.651647 | + | 0.274511i | ||||
\(163\) | 22.4774 | 1.76056 | 0.880281 | − | 0.474452i | \(-0.157354\pi\) | ||||
0.880281 | + | 0.474452i | \(0.157354\pi\) | |||||||
\(164\) | 9.85425 | − | 5.68936i | 0.769488 | − | 0.444264i | ||||
\(165\) | −2.03228 | + | 8.65725i | −0.158213 | + | 0.673966i | ||||
\(166\) | 6.87875 | − | 3.97145i | 0.533895 | − | 0.308244i | ||||
\(167\) | −8.21327 | + | 14.2258i | −0.635562 | + | 1.10083i | 0.350833 | + | 0.936438i | \(0.385898\pi\) |
−0.986396 | + | 0.164388i | \(0.947435\pi\) | |||||||
\(168\) | −1.01889 | + | 4.34033i | −0.0786089 | + | 0.334864i | ||||
\(169\) | 7.57064 | − | 13.1127i | 0.582357 | − | 1.00867i | ||||
\(170\) | −5.18752 | −0.397864 | ||||||||
\(171\) | −0.0991442 | − | 1.58549i | −0.00758174 | − | 0.121245i | ||||
\(172\) | 6.69156 | + | 3.86337i | 0.510226 | + | 0.294579i | ||||
\(173\) | −2.51861 | + | 1.45412i | −0.191486 | + | 0.110554i | −0.592678 | − | 0.805439i | \(-0.701929\pi\) |
0.401192 | + | 0.915994i | \(0.368596\pi\) | |||||||
\(174\) | 14.0067 | − | 4.22595i | 1.06184 | − | 0.320368i | ||||
\(175\) | 1.28701 | + | 2.22916i | 0.0972885 | + | 0.168509i | ||||
\(176\) | 2.56707 | + | 4.44629i | 0.193500 | + | 0.335152i | ||||
\(177\) | −4.77578 | + | 20.3442i | −0.358969 | + | 1.52916i | ||||
\(178\) | 14.8905i | 1.11609i | ||||||||
\(179\) | −2.85826 | + | 4.95065i | −0.213637 | + | 0.370029i | −0.952850 | − | 0.303442i | \(-0.901864\pi\) |
0.739213 | + | 0.673471i | \(0.235197\pi\) | |||||||
\(180\) | 1.33493 | − | 2.68663i | 0.0994997 | − | 0.200249i | ||||
\(181\) | −13.2525 | + | 7.65134i | −0.985051 | + | 0.568719i | −0.903791 | − | 0.427974i | \(-0.859228\pi\) |
−0.0812595 | + | 0.996693i | \(0.525894\pi\) | |||||||
\(182\) | −13.6547 | −1.01215 | ||||||||
\(183\) | −11.7117 | + | 3.53353i | −0.865751 | + | 0.261206i | ||||
\(184\) | − | 3.03318i | − | 0.223609i | ||||||
\(185\) | 0.670752 | 0.0493146 | ||||||||
\(186\) | 1.44676 | + | 9.53451i | 0.106081 | + | 0.699104i | ||||
\(187\) | −26.6334 | −1.94763 | ||||||||
\(188\) | 6.75256i | 0.492481i | ||||||||
\(189\) | 12.5388 | − | 4.65498i | 0.912061 | − | 0.338600i | ||||
\(190\) | −0.529528 | −0.0384160 | ||||||||
\(191\) | 4.31841 | − | 2.49324i | 0.312470 | − | 0.180404i | −0.335562 | − | 0.942018i | \(-0.608926\pi\) |
0.648031 | + | 0.761614i | \(0.275593\pi\) | |||||||
\(192\) | −0.500302 | − | 1.65822i | −0.0361062 | − | 0.119672i | ||||
\(193\) | 8.08463 | − | 14.0030i | 0.581945 | − | 1.00796i | −0.413304 | − | 0.910593i | \(-0.635625\pi\) |
0.995249 | − | 0.0973645i | \(-0.0310413\pi\) | |||||||
\(194\) | − | 6.46323i | − | 0.464033i | ||||||
\(195\) | 8.94508 | + | 2.09985i | 0.640571 | + | 0.150373i | ||||
\(196\) | −0.187231 | − | 0.324294i | −0.0133737 | − | 0.0231639i | ||||
\(197\) | −4.30925 | − | 7.46384i | −0.307021 | − | 0.531777i | 0.670688 | − | 0.741740i | \(-0.265999\pi\) |
−0.977709 | + | 0.209963i | \(0.932666\pi\) | |||||||
\(198\) | 6.85371 | − | 13.7935i | 0.487072 | − | 0.980262i | ||||
\(199\) | 4.91862 | − | 2.83976i | 0.348671 | − | 0.201306i | −0.315429 | − | 0.948949i | \(-0.602148\pi\) |
0.664100 | + | 0.747644i | \(0.268815\pi\) | |||||||
\(200\) | −0.866025 | − | 0.500000i | −0.0612372 | − | 0.0353553i | ||||
\(201\) | −9.44840 | + | 10.0577i | −0.666438 | + | 0.709414i | ||||
\(202\) | 8.88476 | 0.625130 | ||||||||
\(203\) | 10.8711 | − | 18.8293i | 0.763000 | − | 1.32155i | ||||
\(204\) | 8.74726 | + | 2.05341i | 0.612430 | + | 0.143767i | ||||
\(205\) | −5.68936 | + | 9.85425i | −0.397362 | + | 0.688251i | ||||
\(206\) | 9.11135 | − | 5.26044i | 0.634818 | − | 0.366512i | ||||
\(207\) | −7.58112 | + | 5.03272i | −0.526924 | + | 0.349798i | ||||
\(208\) | 4.59412 | − | 2.65242i | 0.318545 | − | 0.183912i | ||||
\(209\) | −2.71867 | −0.188054 | ||||||||
\(210\) | −1.28778 | − | 4.26828i | −0.0888655 | − | 0.294539i | ||||
\(211\) | 0.695561 | − | 1.20475i | 0.0478844 | − | 0.0829382i | −0.841090 | − | 0.540896i | \(-0.818085\pi\) |
0.888974 | + | 0.457957i | \(0.151419\pi\) | |||||||
\(212\) | −0.822328 | − | 1.42431i | −0.0564777 | − | 0.0978222i | ||||
\(213\) | 12.3221 | + | 11.5757i | 0.844298 | + | 0.793151i | ||||
\(214\) | 6.47185 | − | 11.2096i | 0.442407 | − | 0.766271i | ||||
\(215\) | −7.72674 | −0.526960 | ||||||||
\(216\) | −3.31444 | + | 4.00181i | −0.225519 | + | 0.272289i | ||||
\(217\) | 11.2685 | + | 8.85503i | 0.764959 | + | 0.601118i | ||||
\(218\) | − | 1.35138i | − | 0.0915269i | ||||||
\(219\) | −4.68674 | − | 4.40282i | −0.316700 | − | 0.297515i | ||||
\(220\) | −4.44629 | − | 2.56707i | −0.299769 | − | 0.173072i | ||||
\(221\) | 27.5189i | 1.85112i | ||||||||
\(222\) | −1.13103 | − | 0.265508i | −0.0759098 | − | 0.0178197i | ||||
\(223\) | 11.5712 | + | 6.68062i | 0.774863 | + | 0.447368i | 0.834607 | − | 0.550846i | \(-0.185695\pi\) |
−0.0597434 | + | 0.998214i | \(0.519028\pi\) | |||||||
\(224\) | −2.22916 | − | 1.28701i | −0.148942 | − | 0.0859917i | ||||
\(225\) | 0.187231 | + | 2.99415i | 0.0124821 | + | 0.199610i | ||||
\(226\) | 2.35692 | + | 4.08230i | 0.156780 | + | 0.271550i | ||||
\(227\) | 13.4583 | − | 7.77017i | 0.893261 | − | 0.515724i | 0.0182532 | − | 0.999833i | \(-0.494190\pi\) |
0.875008 | + | 0.484109i | \(0.160856\pi\) | |||||||
\(228\) | 0.892896 | + | 0.209606i | 0.0591335 | + | 0.0138815i | ||||
\(229\) | 12.6066 | + | 7.27845i | 0.833071 | + | 0.480974i | 0.854903 | − | 0.518788i | \(-0.173617\pi\) |
−0.0218323 | + | 0.999762i | \(0.506950\pi\) | |||||||
\(230\) | 1.51659 | + | 2.62681i | 0.100001 | + | 0.173207i | ||||
\(231\) | −6.61166 | − | 21.9139i | −0.435015 | − | 1.44183i | ||||
\(232\) | 8.44680i | 0.554559i | ||||||||
\(233\) | − | 2.89624i | − | 0.189739i | −0.995490 | − | 0.0948694i | \(-0.969757\pi\) | ||
0.995490 | − | 0.0948694i | \(-0.0302434\pi\) | |||||||
\(234\) | −14.2521 | − | 7.08158i | −0.931690 | − | 0.462937i | ||||
\(235\) | −3.37628 | − | 5.84788i | −0.220244 | − | 0.381474i | ||||
\(236\) | −10.4486 | − | 6.03251i | −0.680147 | − | 0.392683i | ||||
\(237\) | −4.00096 | + | 17.0436i | −0.259890 | + | 1.10710i | ||||
\(238\) | 11.5638 | − | 6.67636i | 0.749570 | − | 0.432764i | ||||
\(239\) | −2.74446 | − | 4.75354i | −0.177524 | − | 0.307481i | 0.763508 | − | 0.645799i | \(-0.223476\pi\) |
−0.941032 | + | 0.338318i | \(0.890142\pi\) | |||||||
\(240\) | 1.26238 | + | 1.18591i | 0.0814866 | + | 0.0765502i | ||||
\(241\) | −4.61436 | − | 2.66410i | −0.297237 | − | 0.171610i | 0.343964 | − | 0.938983i | \(-0.388230\pi\) |
−0.641201 | + | 0.767373i | \(0.721564\pi\) | |||||||
\(242\) | −13.3016 | − | 7.67968i | −0.855059 | − | 0.493668i | ||||
\(243\) | 15.5015 | + | 1.64420i | 0.994422 | + | 0.105475i | ||||
\(244\) | − | 7.06279i | − | 0.452149i | ||||||
\(245\) | 0.324294 | + | 0.187231i | 0.0207184 | + | 0.0119618i | ||||
\(246\) | 13.4941 | − | 14.3643i | 0.860355 | − | 0.915835i | ||||
\(247\) | 2.80906i | 0.178736i | ||||||||
\(248\) | −5.51138 | − | 0.790363i | −0.349973 | − | 0.0501881i | ||||
\(249\) | 9.41957 | − | 10.0270i | 0.596941 | − | 0.635435i | ||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 0.392937 | − | 0.680586i | 0.0248019 | − | 0.0429582i | −0.853358 | − | 0.521325i | \(-0.825438\pi\) |
0.878160 | + | 0.478367i | \(0.158771\pi\) | |||||||
\(252\) | 0.481936 | + | 7.70698i | 0.0303591 | + | 0.485494i | ||||
\(253\) | 7.78638 | + | 13.4864i | 0.489526 | + | 0.847883i | ||||
\(254\) | −7.79574 | + | 13.5026i | −0.489148 | + | 0.847230i | ||||
\(255\) | −8.60205 | + | 2.59533i | −0.538681 | + | 0.162526i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −10.4435 | + | 6.02954i | −0.651446 | + | 0.376113i | −0.789010 | − | 0.614380i | \(-0.789406\pi\) |
0.137564 | + | 0.990493i | \(0.456073\pi\) | |||||||
\(258\) | 13.0289 | + | 3.05853i | 0.811146 | + | 0.190416i | ||||
\(259\) | −1.49521 | + | 0.863261i | −0.0929080 | + | 0.0536405i | ||||
\(260\) | −2.65242 | + | 4.59412i | −0.164496 | + | 0.284915i | ||||
\(261\) | 21.1119 | − | 14.0151i | 1.30679 | − | 0.867514i | ||||
\(262\) | −9.47252 | + | 16.4069i | −0.585214 | + | 1.01362i | ||||
\(263\) | −2.04756 | −0.126258 | −0.0631291 | − | 0.998005i | \(-0.520108\pi\) | ||||
−0.0631291 | + | 0.998005i | \(0.520108\pi\) | |||||||
\(264\) | 6.48126 | + | 6.08863i | 0.398894 | + | 0.374729i | ||||
\(265\) | 1.42431 | + | 0.822328i | 0.0874949 | + | 0.0505152i | ||||
\(266\) | 1.18040 | − | 0.681505i | 0.0723751 | − | 0.0417858i | ||||
\(267\) | 7.44975 | + | 24.6917i | 0.455917 | + | 1.51111i | ||||
\(268\) | −3.98360 | − | 6.89980i | −0.243337 | − | 0.421473i | ||||
\(269\) | −13.5077 | − | 23.3961i | −0.823581 | − | 1.42648i | −0.902999 | − | 0.429642i | \(-0.858640\pi\) |
0.0794184 | − | 0.996841i | \(-0.474694\pi\) | |||||||
\(270\) | 0.869482 | − | 5.12289i | 0.0529150 | − | 0.311769i | ||||
\(271\) | 3.17938i | 0.193134i | 0.995327 | + | 0.0965668i | \(0.0307861\pi\) | ||||
−0.995327 | + | 0.0965668i | \(0.969214\pi\) | |||||||
\(272\) | −2.59376 | + | 4.49252i | −0.157270 | + | 0.272399i | ||||
\(273\) | −22.6425 | + | 6.83148i | −1.37039 | + | 0.413460i | ||||
\(274\) | 5.17720 | − | 2.98906i | 0.312766 | − | 0.180576i | ||||
\(275\) | 5.13414 | 0.309600 | ||||||||
\(276\) | −1.51751 | − | 5.02968i | −0.0913431 | − | 0.302751i | ||||
\(277\) | 16.5427i | 0.993955i | 0.867763 | + | 0.496978i | \(0.165557\pi\) | ||||
−0.867763 | + | 0.496978i | \(0.834443\pi\) | |||||||
\(278\) | −20.6001 | −1.23551 | ||||||||
\(279\) | 7.16918 | + | 15.0865i | 0.429208 | + | 0.903206i | ||||
\(280\) | 2.57401 | 0.153827 | ||||||||
\(281\) | − | 1.55339i | − | 0.0926672i | −0.998926 | − | 0.0463336i | \(-0.985246\pi\) | ||
0.998926 | − | 0.0463336i | \(-0.0147537\pi\) | |||||||
\(282\) | 3.37832 | + | 11.1972i | 0.201176 | + | 0.666785i | ||||
\(283\) | −3.03122 | −0.180187 | −0.0900936 | − | 0.995933i | \(-0.528717\pi\) | ||||
−0.0900936 | + | 0.995933i | \(0.528717\pi\) | |||||||
\(284\) | −8.45327 | + | 4.88050i | −0.501609 | + | 0.289604i | ||||
\(285\) | −0.878074 | + | 0.264924i | −0.0520126 | + | 0.0156927i | ||||
\(286\) | −13.6179 | + | 23.5869i | −0.805242 | + | 1.39472i | ||||
\(287\) | − | 29.2889i | − | 1.72887i | ||||||
\(288\) | −1.65922 | − | 2.49940i | −0.0977707 | − | 0.147278i | ||||
\(289\) | −4.95516 | − | 8.58260i | −0.291480 | − | 0.504859i | ||||
\(290\) | −4.22340 | − | 7.31514i | −0.248006 | − | 0.429560i | ||||
\(291\) | −3.23357 | − | 10.7175i | −0.189555 | − | 0.628269i | ||||
\(292\) | 3.21521 | − | 1.85630i | 0.188156 | − | 0.108632i | ||||
\(293\) | −6.74006 | − | 3.89138i | −0.393759 | − | 0.227337i | 0.290029 | − | 0.957018i | \(-0.406335\pi\) |
−0.683787 | + | 0.729681i | \(0.739668\pi\) | |||||||
\(294\) | −0.472716 | − | 0.444079i | −0.0275694 | − | 0.0258992i | ||||
\(295\) | 12.0650 | 0.702453 | ||||||||
\(296\) | 0.335376 | − | 0.580888i | 0.0194933 | − | 0.0337634i | ||||
\(297\) | 4.46404 | − | 26.3016i | 0.259030 | − | 1.52617i | ||||
\(298\) | −12.0620 | + | 20.8920i | −0.698734 | + | 1.21024i | ||||
\(299\) | 13.9348 | − | 8.04526i | 0.805870 | − | 0.465270i | ||||
\(300\) | −1.68621 | − | 0.395836i | −0.0973535 | − | 0.0228536i | ||||
\(301\) | 17.2241 | − | 9.94437i | 0.992783 | − | 0.573184i | ||||
\(302\) | 16.5788 | 0.954002 | ||||||||
\(303\) | 14.7329 | − | 4.44507i | 0.846383 | − | 0.255362i | ||||
\(304\) | −0.264764 | + | 0.458584i | −0.0151852 | + | 0.0263016i | ||||
\(305\) | 3.53139 | + | 6.11655i | 0.202207 | + | 0.350233i | ||||
\(306\) | 15.5322 | − | 0.971266i | 0.887917 | − | 0.0555236i | ||||
\(307\) | −5.71957 | + | 9.90659i | −0.326433 | + | 0.565399i | −0.981801 | − | 0.189911i | \(-0.939180\pi\) |
0.655368 | + | 0.755310i | \(0.272513\pi\) | |||||||
\(308\) | 13.2153 | 0.753013 | ||||||||
\(309\) | 12.4768 | − | 13.2814i | 0.709782 | − | 0.755552i | ||||
\(310\) | 5.16818 | − | 2.07122i | 0.293533 | − | 0.117637i | ||||
\(311\) | 7.22744i | 0.409831i | 0.978780 | + | 0.204915i | \(0.0656919\pi\) | ||||
−0.978780 | + | 0.204915i | \(0.934308\pi\) | |||||||
\(312\) | 6.29106 | − | 6.69674i | 0.356161 | − | 0.379129i | ||||
\(313\) | 11.2641 | + | 6.50334i | 0.636686 | + | 0.367591i | 0.783337 | − | 0.621598i | \(-0.213516\pi\) |
−0.146651 | + | 0.989188i | \(0.546849\pi\) | |||||||
\(314\) | 14.6508i | 0.826793i | ||||||||
\(315\) | −4.27086 | − | 6.43347i | −0.240636 | − | 0.362485i | ||||
\(316\) | −8.75345 | − | 5.05381i | −0.492420 | − | 0.284299i | ||||
\(317\) | −19.7129 | − | 11.3812i | −1.10718 | − | 0.639233i | −0.169086 | − | 0.985601i | \(-0.554082\pi\) |
−0.938099 | + | 0.346368i | \(0.887415\pi\) | |||||||
\(318\) | −2.07619 | − | 1.95041i | −0.116427 | − | 0.109374i | ||||
\(319\) | −21.6835 | − | 37.5569i | −1.21404 | − | 2.10278i | ||||
\(320\) | −0.866025 | + | 0.500000i | −0.0484123 | + | 0.0279508i | ||||
\(321\) | 5.12359 | − | 21.8258i | 0.285971 | − | 1.21820i | ||||
\(322\) | −6.76144 | − | 3.90372i | −0.376801 | − | 0.217546i | ||||
\(323\) | −1.37347 | − | 2.37891i | −0.0764217 | − | 0.132366i | ||||
\(324\) | −3.49396 | + | 8.29411i | −0.194109 | + | 0.460784i | ||||
\(325\) | − | 5.30484i | − | 0.294259i | ||||||
\(326\) | 22.4774i | 1.24491i | ||||||||
\(327\) | −0.676098 | − | 2.24089i | −0.0373883 | − | 0.123921i | ||||
\(328\) | 5.68936 | + | 9.85425i | 0.314142 | + | 0.544110i | ||||
\(329\) | 15.0525 | + | 8.69058i | 0.829873 | + | 0.479127i | ||||
\(330\) | −8.65725 | − | 2.03228i | −0.476566 | − | 0.111873i | ||||
\(331\) | 4.25023 | − | 2.45387i | 0.233614 | − | 0.134877i | −0.378624 | − | 0.925550i | \(-0.623603\pi\) |
0.612238 | + | 0.790673i | \(0.290269\pi\) | |||||||
\(332\) | 3.97145 | + | 6.87875i | 0.217962 | + | 0.377521i | ||||
\(333\) | −2.00833 | + | 0.125586i | −0.110056 | + | 0.00688206i | ||||
\(334\) | −14.2258 | − | 8.21327i | −0.778402 | − | 0.449410i | ||||
\(335\) | 6.89980 | + | 3.98360i | 0.376977 | + | 0.217647i | ||||
\(336\) | −4.34033 | − | 1.01889i | −0.236785 | − | 0.0555849i | ||||
\(337\) | − | 27.0752i | − | 1.47488i | −0.675414 | − | 0.737439i | \(-0.736035\pi\) | ||
0.675414 | − | 0.737439i | \(-0.263965\pi\) | |||||||
\(338\) | 13.1127 | + | 7.57064i | 0.713239 | + | 0.411789i | ||||
\(339\) | 5.95067 | + | 5.59018i | 0.323196 | + | 0.303617i | ||||
\(340\) | − | 5.18752i | − | 0.281333i | ||||||
\(341\) | 26.5341 | − | 10.6339i | 1.43690 | − | 0.575858i | ||||
\(342\) | 1.58549 | − | 0.0991442i | 0.0857333 | − | 0.00536110i | ||||
\(343\) | −18.9820 | −1.02493 | ||||||||
\(344\) | −3.86337 | + | 6.69156i | −0.208299 | + | 0.360785i | ||||
\(345\) | 3.82904 | + | 3.59708i | 0.206149 | + | 0.193660i | ||||
\(346\) | −1.45412 | − | 2.51861i | −0.0781738 | − | 0.135401i | ||||
\(347\) | 10.2487 | − | 17.7512i | 0.550178 | − | 0.952936i | −0.448084 | − | 0.893992i | \(-0.647893\pi\) |
0.998261 | − | 0.0589439i | \(-0.0187733\pi\) | |||||||
\(348\) | 4.22595 | + | 14.0067i | 0.226535 | + | 0.750836i | ||||
\(349\) | −20.0539 | −1.07346 | −0.536732 | − | 0.843753i | \(-0.680341\pi\) | ||||
−0.536732 | + | 0.843753i | \(0.680341\pi\) | |||||||
\(350\) | −2.22916 | + | 1.28701i | −0.119154 | + | 0.0687934i | ||||
\(351\) | −27.1761 | − | 4.61246i | −1.45055 | − | 0.246195i | ||||
\(352\) | −4.44629 | + | 2.56707i | −0.236988 | + | 0.136825i | ||||
\(353\) | −4.20458 | + | 7.28255i | −0.223787 | + | 0.387611i | −0.955955 | − | 0.293513i | \(-0.905175\pi\) |
0.732168 | + | 0.681125i | \(0.238509\pi\) | |||||||
\(354\) | −20.3442 | − | 4.77578i | −1.08128 | − | 0.253830i | ||||
\(355\) | 4.88050 | − | 8.45327i | 0.259030 | − | 0.448653i | ||||
\(356\) | −14.8905 | −0.789195 | ||||||||
\(357\) | 15.8351 | − | 16.8563i | 0.838085 | − | 0.892129i | ||||
\(358\) | −4.95065 | − | 2.85826i | −0.261650 | − | 0.151064i | ||||
\(359\) | 22.0093 | − | 12.7070i | 1.16160 | − | 0.670652i | 0.209916 | − | 0.977719i | \(-0.432681\pi\) |
0.951688 | + | 0.307067i | \(0.0993476\pi\) | |||||||
\(360\) | 2.68663 | + | 1.33493i | 0.141598 | + | 0.0703569i | ||||
\(361\) | 9.35980 | + | 16.2116i | 0.492621 | + | 0.853245i | ||||
\(362\) | −7.65134 | − | 13.2525i | −0.402145 | − | 0.696536i | ||||
\(363\) | −25.8991 | − | 6.07979i | −1.35935 | − | 0.319106i | ||||
\(364\) | − | 13.6547i | − | 0.715701i | ||||||
\(365\) | −1.85630 | + | 3.21521i | −0.0971633 | + | 0.168292i | ||||
\(366\) | −3.53353 | − | 11.7117i | −0.184700 | − | 0.612178i | ||||
\(367\) | 14.9832 | − | 8.65053i | 0.782114 | − | 0.451554i | −0.0550648 | − | 0.998483i | \(-0.517537\pi\) |
0.837179 | + | 0.546929i | \(0.184203\pi\) | |||||||
\(368\) | 3.03318 | 0.158115 | ||||||||
\(369\) | 15.1898 | − | 30.5704i | 0.790748 | − | 1.59143i | ||||
\(370\) | 0.670752i | 0.0348707i | ||||||||
\(371\) | −4.23336 | −0.219785 | ||||||||
\(372\) | −9.53451 | + | 1.44676i | −0.494341 | + | 0.0750109i | ||||
\(373\) | −14.4940 | −0.750471 | −0.375236 | − | 0.926929i | \(-0.622438\pi\) | ||||
−0.375236 | + | 0.926929i | \(0.622438\pi\) | |||||||
\(374\) | − | 26.6334i | − | 1.37718i | ||||||
\(375\) | 1.65822 | − | 0.500302i | 0.0856302 | − | 0.0258355i | ||||
\(376\) | −6.75256 | −0.348236 | ||||||||
\(377\) | −38.8056 | + | 22.4044i | −1.99859 | + | 1.15389i | ||||
\(378\) | 4.65498 | + | 12.5388i | 0.239426 | + | 0.644925i | ||||
\(379\) | −9.90778 | + | 17.1608i | −0.508929 | + | 0.881490i | 0.491018 | + | 0.871149i | \(0.336625\pi\) |
−0.999947 | + | 0.0103407i | \(0.996708\pi\) | |||||||
\(380\) | − | 0.529528i | − | 0.0271642i | ||||||
\(381\) | −6.17168 | + | 26.2906i | −0.316185 | + | 1.34691i | ||||
\(382\) | 2.49324 | + | 4.31841i | 0.127565 | + | 0.220949i | ||||
\(383\) | −1.97590 | − | 3.42236i | −0.100964 | − | 0.174874i | 0.811118 | − | 0.584882i | \(-0.198859\pi\) |
−0.912082 | + | 0.410008i | \(0.865526\pi\) | |||||||
\(384\) | 1.65822 | − | 0.500302i | 0.0846208 | − | 0.0255309i | ||||
\(385\) | −11.4448 | + | 6.60766i | −0.583282 | + | 0.336758i | ||||
\(386\) | 14.0030 | + | 8.08463i | 0.712734 | + | 0.411497i | ||||
\(387\) | 23.1350 | − | 1.44669i | 1.17602 | − | 0.0735393i | ||||
\(388\) | 6.46323 | 0.328121 | ||||||||
\(389\) | −9.71945 | + | 16.8346i | −0.492796 | + | 0.853547i | −0.999966 | − | 0.00829898i | \(-0.997358\pi\) |
0.507170 | + | 0.861846i | \(0.330692\pi\) | |||||||
\(390\) | −2.09985 | + | 8.94508i | −0.106330 | + | 0.452952i | ||||
\(391\) | −7.86734 | + | 13.6266i | −0.397868 | + | 0.689128i | ||||
\(392\) | 0.324294 | − | 0.187231i | 0.0163793 | − | 0.00945661i | ||||
\(393\) | −7.49914 | + | 31.9454i | −0.378281 | + | 1.61143i | ||||
\(394\) | 7.46384 | − | 4.30925i | 0.376023 | − | 0.217097i | ||||
\(395\) | 10.1076 | 0.508569 | ||||||||
\(396\) | 13.7935 | + | 6.85371i | 0.693150 | + | 0.344412i | ||||
\(397\) | 11.9703 | − | 20.7332i | 0.600772 | − | 1.04057i | −0.391932 | − | 0.919994i | \(-0.628193\pi\) |
0.992704 | − | 0.120574i | \(-0.0384735\pi\) | |||||||
\(398\) | 2.83976 | + | 4.91862i | 0.142344 | + | 0.246548i | ||||
\(399\) | 1.61641 | − | 1.72064i | 0.0809216 | − | 0.0861399i | ||||
\(400\) | 0.500000 | − | 0.866025i | 0.0250000 | − | 0.0433013i | ||||
\(401\) | 20.4973 | 1.02359 | 0.511793 | − | 0.859109i | \(-0.328981\pi\) | ||||
0.511793 | + | 0.859109i | \(0.328981\pi\) | |||||||
\(402\) | −10.0577 | − | 9.44840i | −0.501632 | − | 0.471243i | ||||
\(403\) | −10.9875 | − | 27.4163i | −0.547324 | − | 1.36571i | ||||
\(404\) | 8.88476i | 0.442034i | ||||||||
\(405\) | −1.12120 | − | 8.92989i | −0.0557128 | − | 0.443730i | ||||
\(406\) | 18.8293 | + | 10.8711i | 0.934480 | + | 0.539522i | ||||
\(407\) | 3.44373i | 0.170699i | ||||||||
\(408\) | −2.05341 | + | 8.74726i | −0.101659 | + | 0.433054i | ||||
\(409\) | 7.58719 | + | 4.38047i | 0.375163 | + | 0.216600i | 0.675712 | − | 0.737166i | \(-0.263837\pi\) |
−0.300549 | + | 0.953766i | \(0.597170\pi\) | |||||||
\(410\) | −9.85425 | − | 5.68936i | −0.486667 | − | 0.280977i | ||||
\(411\) | 7.08951 | − | 7.54669i | 0.349700 | − | 0.372251i | ||||
\(412\) | 5.26044 | + | 9.11135i | 0.259163 | + | 0.448884i | ||||
\(413\) | −26.8949 | + | 15.5278i | −1.32341 | + | 0.764071i | ||||
\(414\) | −5.03272 | − | 7.58112i | −0.247345 | − | 0.372592i | ||||
\(415\) | −6.87875 | − | 3.97145i | −0.337665 | − | 0.194951i | ||||
\(416\) | 2.65242 | + | 4.59412i | 0.130045 | + | 0.225245i | ||||
\(417\) | −34.1596 | + | 10.3063i | −1.67280 | + | 0.504701i | ||||
\(418\) | − | 2.71867i | − | 0.132974i | ||||||
\(419\) | 17.8444i | 0.871754i | 0.900006 | + | 0.435877i | \(0.143562\pi\) | ||||
−0.900006 | + | 0.435877i | \(0.856438\pi\) | |||||||
\(420\) | 4.26828 | − | 1.28778i | 0.208271 | − | 0.0628374i | ||||
\(421\) | −8.25775 | − | 14.3028i | −0.402458 | − | 0.697078i | 0.591564 | − | 0.806258i | \(-0.298511\pi\) |
−0.994022 | + | 0.109180i | \(0.965177\pi\) | |||||||
\(422\) | 1.20475 | + | 0.695561i | 0.0586462 | + | 0.0338594i | ||||
\(423\) | 11.2040 | + | 16.8773i | 0.544757 | + | 0.820603i | ||||
\(424\) | 1.42431 | − | 0.822328i | 0.0691708 | − | 0.0399358i | ||||
\(425\) | 2.59376 | + | 4.49252i | 0.125816 | + | 0.217919i | ||||
\(426\) | −11.5757 | + | 12.3221i | −0.560843 | + | 0.597009i | ||||
\(427\) | −15.7441 | − | 9.08985i | −0.761909 | − | 0.439889i | ||||
\(428\) | 11.2096 | + | 6.47185i | 0.541835 | + | 0.312829i | ||||
\(429\) | −10.7809 | + | 45.9253i | −0.520507 | + | 2.21729i | ||||
\(430\) | − | 7.72674i | − | 0.372617i | ||||||
\(431\) | −10.7198 | − | 6.18908i | −0.516354 | − | 0.298117i | 0.219087 | − | 0.975705i | \(-0.429692\pi\) |
−0.735442 | + | 0.677588i | \(0.763025\pi\) | |||||||
\(432\) | −4.00181 | − | 3.31444i | −0.192537 | − | 0.159466i | ||||
\(433\) | − | 1.18613i | − | 0.0570017i | −0.999594 | − | 0.0285008i | \(-0.990927\pi\) | ||
0.999594 | − | 0.0285008i | \(-0.00907333\pi\) | |||||||
\(434\) | −8.85503 | + | 11.2685i | −0.425055 | + | 0.540908i | ||||
\(435\) | −10.6631 | − | 10.0171i | −0.511257 | − | 0.480285i | ||||
\(436\) | 1.35138 | 0.0647193 | ||||||||
\(437\) | −0.803076 | + | 1.39097i | −0.0384163 | + | 0.0665391i | ||||
\(438\) | 4.40282 | − | 4.68674i | 0.210375 | − | 0.223941i | ||||
\(439\) | 8.22962 | + | 14.2541i | 0.392778 | + | 0.680312i | 0.992815 | − | 0.119660i | \(-0.0381806\pi\) |
−0.600036 | + | 0.799973i | \(0.704847\pi\) | |||||||
\(440\) | 2.56707 | − | 4.44629i | 0.122380 | − | 0.211969i | ||||
\(441\) | −1.00604 | − | 0.499881i | −0.0479068 | − | 0.0238039i | ||||
\(442\) | −27.5189 | −1.30894 | ||||||||
\(443\) | −20.9565 | + | 12.0992i | −0.995671 | + | 0.574851i | −0.906965 | − | 0.421207i | \(-0.861607\pi\) |
−0.0887065 | + | 0.996058i | \(0.528273\pi\) | |||||||
\(444\) | 0.265508 | − | 1.13103i | 0.0126004 | − | 0.0536763i | ||||
\(445\) | 12.8955 | − | 7.44525i | 0.611308 | − | 0.352939i | ||||
\(446\) | −6.68062 | + | 11.5712i | −0.316337 | + | 0.547911i | ||||
\(447\) | −9.54918 | + | 40.6783i | −0.451661 | + | 1.92402i | ||||
\(448\) | 1.28701 | − | 2.22916i | 0.0608053 | − | 0.105318i | ||||
\(449\) | 32.2944 | 1.52406 | 0.762032 | − | 0.647539i | \(-0.224202\pi\) | ||||
0.762032 | + | 0.647539i | \(0.224202\pi\) | |||||||
\(450\) | −2.99415 | + | 0.187231i | −0.141146 | + | 0.00882617i | ||||
\(451\) | −50.5931 | − | 29.2099i | −2.38233 | − | 1.37544i | ||||
\(452\) | −4.08230 | + | 2.35692i | −0.192015 | + | 0.110860i | ||||
\(453\) | 27.4913 | − | 8.29440i | 1.29165 | − | 0.389705i | ||||
\(454\) | 7.77017 | + | 13.4583i | 0.364672 | + | 0.631631i | ||||
\(455\) | 6.82736 | + | 11.8253i | 0.320071 | + | 0.554380i | ||||
\(456\) | −0.209606 | + | 0.892896i | −0.00981571 | + | 0.0418137i | ||||
\(457\) | 19.0886i | 0.892929i | 0.894801 | + | 0.446464i | \(0.147317\pi\) | ||||
−0.894801 | + | 0.446464i | \(0.852683\pi\) | |||||||
\(458\) | −7.27845 | + | 12.6066i | −0.340100 | + | 0.589070i | ||||
\(459\) | 25.2699 | − | 9.38137i | 1.17950 | − | 0.437885i | ||||
\(460\) | −2.62681 | + | 1.51659i | −0.122476 | + | 0.0707114i | ||||
\(461\) | 12.8115 | 0.596691 | 0.298345 | − | 0.954458i | \(-0.403565\pi\) | ||||
0.298345 | + | 0.954458i | \(0.403565\pi\) | |||||||
\(462\) | 21.9139 | − | 6.61166i | 1.01953 | − | 0.307602i | ||||
\(463\) | − | 20.6891i | − | 0.961503i | −0.876857 | − | 0.480751i | \(-0.840364\pi\) | ||
0.876857 | − | 0.480751i | \(-0.159636\pi\) | |||||||
\(464\) | −8.44680 | −0.392133 | ||||||||
\(465\) | 7.53375 | − | 6.02018i | 0.349369 | − | 0.279179i | ||||
\(466\) | 2.89624 | 0.134166 | ||||||||
\(467\) | − | 23.8528i | − | 1.10378i | −0.833918 | − | 0.551889i | \(-0.813907\pi\) | ||
0.833918 | − | 0.551889i | \(-0.186093\pi\) | |||||||
\(468\) | 7.08158 | − | 14.2521i | 0.327346 | − | 0.658804i | ||||
\(469\) | −20.5077 | −0.946957 | ||||||||
\(470\) | 5.84788 | − | 3.37628i | 0.269743 | − | 0.155736i | ||||
\(471\) | 7.32983 | + | 24.2943i | 0.337741 | + | 1.11942i | ||||
\(472\) | 6.03251 | − | 10.4486i | 0.277669 | − | 0.480937i | ||||
\(473\) | − | 39.6702i | − | 1.82404i | ||||||
\(474\) | −17.0436 | − | 4.00096i | −0.782838 | − | 0.183770i | ||||
\(475\) | 0.264764 | + | 0.458584i | 0.0121482 | + | 0.0210413i | ||||
\(476\) | 6.67636 | + | 11.5638i | 0.306011 | + | 0.530026i | ||||
\(477\) | −4.41858 | − | 2.19550i | −0.202313 | − | 0.100525i | ||||
\(478\) | 4.75354 | − | 2.74446i | 0.217422 | − | 0.125529i | ||||
\(479\) | −2.62035 | − | 1.51286i | −0.119727 | − | 0.0691243i | 0.438941 | − | 0.898516i | \(-0.355354\pi\) |
−0.558667 | + | 0.829392i | \(0.688687\pi\) | |||||||
\(480\) | −1.18591 | + | 1.26238i | −0.0541292 | + | 0.0576197i | ||||
\(481\) | 3.55823 | 0.162241 | ||||||||
\(482\) | 2.66410 | − | 4.61436i | 0.121347 | − | 0.210178i | ||||
\(483\) | −13.1650 | − | 3.09047i | −0.599029 | − | 0.140621i | ||||
\(484\) | 7.67968 | − | 13.3016i | 0.349076 | − | 0.604618i | ||||
\(485\) | −5.59732 | + | 3.23162i | −0.254161 | + | 0.146740i | ||||
\(486\) | −1.64420 | + | 15.5015i | −0.0745822 | + | 0.703162i | ||||
\(487\) | −33.0749 | + | 19.0958i | −1.49877 | + | 0.865314i | −0.999999 | − | 0.00142186i | \(-0.999547\pi\) |
−0.498768 | + | 0.866735i | \(0.666214\pi\) | |||||||
\(488\) | 7.06279 | 0.319717 | ||||||||
\(489\) | 11.2455 | + | 37.2724i | 0.508538 | + | 1.68552i | ||||
\(490\) | −0.187231 | + | 0.324294i | −0.00845825 | + | 0.0146501i | ||||
\(491\) | −12.7244 | − | 22.0394i | −0.574245 | − | 0.994622i | −0.996123 | − | 0.0879695i | \(-0.971962\pi\) |
0.421878 | − | 0.906653i | \(-0.361371\pi\) | |||||||
\(492\) | 14.3643 | + | 13.4941i | 0.647593 | + | 0.608363i | ||||
\(493\) | 21.9089 | − | 37.9474i | 0.986729 | − | 1.70907i | ||||
\(494\) | −2.80906 | −0.126385 | ||||||||
\(495\) | −15.3724 | + | 0.961271i | −0.690937 | + | 0.0432059i | ||||
\(496\) | 0.790363 | − | 5.51138i | 0.0354884 | − | 0.247468i | ||||
\(497\) | 25.1249i | 1.12701i | ||||||||
\(498\) | 10.0270 | + | 9.41957i | 0.449321 | + | 0.422101i | ||||
\(499\) | −7.16472 | − | 4.13656i | −0.320737 | − | 0.185178i | 0.330984 | − | 0.943636i | \(-0.392619\pi\) |
−0.651721 | + | 0.758459i | \(0.725953\pi\) | |||||||
\(500\) | 1.00000i | 0.0447214i | ||||||||
\(501\) | −27.6987 | − | 6.50223i | −1.23748 | − | 0.290498i | ||||
\(502\) | 0.680586 | + | 0.392937i | 0.0303760 | + | 0.0175376i | ||||
\(503\) | 12.4153 | + | 7.16797i | 0.553570 | + | 0.319604i | 0.750561 | − | 0.660802i | \(-0.229784\pi\) |
−0.196991 | + | 0.980405i | \(0.563117\pi\) | |||||||
\(504\) | −7.70698 | + | 0.481936i | −0.343296 | + | 0.0214671i | ||||
\(505\) | −4.44238 | − | 7.69443i | −0.197683 | − | 0.342398i | ||||
\(506\) | −13.4864 | + | 7.78638i | −0.599544 | + | 0.346147i | ||||
\(507\) | 25.5314 | + | 5.99347i | 1.13389 | + | 0.266179i | ||||
\(508\) | −13.5026 | − | 7.79574i | −0.599082 | − | 0.345880i | ||||
\(509\) | −17.7292 | − | 30.7078i | −0.785832 | − | 1.36110i | −0.928501 | − | 0.371331i | \(-0.878902\pi\) |
0.142668 | − | 0.989771i | \(-0.454432\pi\) | |||||||
\(510\) | −2.59533 | − | 8.60205i | −0.114923 | − | 0.380905i | ||||
\(511\) | − | 9.55629i | − | 0.422745i | ||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 2.57948 | − | 0.957625i | 0.113887 | − | 0.0422802i | ||||
\(514\) | −6.02954 | − | 10.4435i | −0.265952 | − | 0.460642i | ||||
\(515\) | −9.11135 | − | 5.26044i | −0.401494 | − | 0.231803i | ||||
\(516\) | −3.05853 | + | 13.0289i | −0.134644 | + | 0.573567i | ||||
\(517\) | 30.0238 | − | 17.3343i | 1.32045 | − | 0.762360i | ||||
\(518\) | −0.863261 | − | 1.49521i | −0.0379295 | − | 0.0656959i | ||||
\(519\) | −3.67131 | − | 3.44891i | −0.161153 | − | 0.151390i | ||||
\(520\) | −4.59412 | − | 2.65242i | −0.201466 | − | 0.116316i | ||||
\(521\) | −13.5448 | − | 7.82011i | −0.593410 | − | 0.342605i | 0.173035 | − | 0.984916i | \(-0.444643\pi\) |
−0.766445 | + | 0.642310i | \(0.777976\pi\) | |||||||
\(522\) | 14.0151 | + | 21.1119i | 0.613425 | + | 0.924042i | ||||
\(523\) | − | 26.2117i | − | 1.14616i | −0.819500 | − | 0.573078i | \(-0.805749\pi\) | ||
0.819500 | − | 0.573078i | \(-0.194251\pi\) | |||||||
\(524\) | −16.4069 | − | 9.47252i | −0.716738 | − | 0.413809i | ||||
\(525\) | −3.05255 | + | 3.24939i | −0.133224 | + | 0.141815i | ||||
\(526\) | − | 2.04756i | − | 0.0892780i | ||||||
\(527\) | 22.7100 | + | 17.8459i | 0.989263 | + | 0.777380i | ||||
\(528\) | −6.08863 | + | 6.48126i | −0.264973 | + | 0.282060i | ||||
\(529\) | −13.7998 | −0.599992 | ||||||||
\(530\) | −0.822328 | + | 1.42431i | −0.0357196 | + | 0.0618682i | ||||
\(531\) | −36.1245 | + | 2.25895i | −1.56767 | + | 0.0980302i | ||||
\(532\) | 0.681505 | + | 1.18040i | 0.0295470 | + | 0.0511769i | ||||
\(533\) | −30.1811 | + | 52.2752i | −1.30729 | + | 2.26429i | ||||
\(534\) | −24.6917 | + | 7.44975i | −1.06852 | + | 0.322382i | ||||
\(535\) | −12.9437 | −0.559605 | ||||||||
\(536\) | 6.89980 | − | 3.98360i | 0.298026 | − | 0.172065i | ||||
\(537\) | −9.63928 | − | 2.26281i | −0.415965 | − | 0.0976474i | ||||
\(538\) | 23.3961 | − | 13.5077i | 1.00868 | − | 0.582360i | ||||
\(539\) | −0.961271 | + | 1.66497i | −0.0414049 | + | 0.0717154i | ||||
\(540\) | 5.12289 | + | 0.869482i | 0.220454 | + | 0.0374166i | ||||
\(541\) | −2.17123 | + | 3.76069i | −0.0933487 | + | 0.161685i | −0.908918 | − | 0.416974i | \(-0.863090\pi\) |
0.815570 | + | 0.578659i | \(0.196424\pi\) | |||||||
\(542\) | −3.17938 | −0.136566 | ||||||||
\(543\) | −19.3179 | − | 18.1476i | −0.829009 | − | 0.778788i | ||||
\(544\) | −4.49252 | − | 2.59376i | −0.192615 | − | 0.111206i | ||||
\(545\) | −1.17033 | + | 0.675690i | −0.0501314 | + | 0.0289434i | ||||
\(546\) | −6.83148 | − | 22.6425i | −0.292360 | − | 0.969011i | ||||
\(547\) | −3.95664 | − | 6.85310i | −0.169174 | − | 0.293017i | 0.768956 | − | 0.639302i | \(-0.220777\pi\) |
−0.938130 | + | 0.346285i | \(0.887443\pi\) | |||||||
\(548\) | 2.98906 | + | 5.17720i | 0.127686 | + | 0.221159i | ||||
\(549\) | −11.7187 | − | 17.6527i | −0.500144 | − | 0.753399i | ||||
\(550\) | 5.13414i | 0.218920i | ||||||||
\(551\) | 2.23641 | − | 3.87357i | 0.0952741 | − | 0.165020i | ||||
\(552\) | 5.02968 | − | 1.51751i | 0.214078 | − | 0.0645894i | ||||
\(553\) | −22.5315 | + | 13.0086i | −0.958137 | + | 0.553180i | ||||
\(554\) | −16.5427 | −0.702833 | ||||||||
\(555\) | 0.335578 | + | 1.11225i | 0.0142445 | + | 0.0472126i | ||||
\(556\) | − | 20.6001i | − | 0.873640i | ||||||
\(557\) | 23.6372 | 1.00154 | 0.500770 | − | 0.865580i | \(-0.333050\pi\) | ||||
0.500770 | + | 0.865580i | \(0.333050\pi\) | |||||||
\(558\) | −15.0865 | + | 7.16918i | −0.638663 | + | 0.303496i | ||||
\(559\) | −40.9891 | −1.73365 | ||||||||
\(560\) | 2.57401i | 0.108772i | ||||||||
\(561\) | −13.3248 | − | 44.1641i | −0.562572 | − | 1.86461i | ||||
\(562\) | 1.55339 | 0.0655256 | ||||||||
\(563\) | 9.05588 | − | 5.22841i | 0.381660 | − | 0.220351i | −0.296880 | − | 0.954915i | \(-0.595946\pi\) |
0.678540 | + | 0.734563i | \(0.262613\pi\) | |||||||
\(564\) | −11.1972 | + | 3.37832i | −0.471488 | + | 0.142253i | ||||
\(565\) | 2.35692 | − | 4.08230i | 0.0991562 | − | 0.171744i | ||||
\(566\) | − | 3.03122i | − | 0.127412i | ||||||
\(567\) | 13.9922 | + | 18.4632i | 0.587615 | + | 0.775380i | ||||
\(568\) | −4.88050 | − | 8.45327i | −0.204781 | − | 0.354691i | ||||
\(569\) | −5.12252 | − | 8.87246i | −0.214747 | − | 0.371953i | 0.738447 | − | 0.674311i | \(-0.235559\pi\) |
−0.953194 | + | 0.302358i | \(0.902226\pi\) | |||||||
\(570\) | −0.264924 | − | 0.878074i | −0.0110964 | − | 0.0367785i | ||||
\(571\) | 27.0944 | − | 15.6430i | 1.13387 | − | 0.654638i | 0.188962 | − | 0.981984i | \(-0.439488\pi\) |
0.944904 | + | 0.327346i | \(0.106154\pi\) | |||||||
\(572\) | −23.5869 | − | 13.6179i | −0.986216 | − | 0.569392i | ||||
\(573\) | 6.29485 | + | 5.91352i | 0.262971 | + | 0.247041i | ||||
\(574\) | 29.2889 | 1.22250 | ||||||||
\(575\) | 1.51659 | − | 2.62681i | 0.0632462 | − | 0.109546i | ||||
\(576\) | 2.49940 | − | 1.65922i | 0.104141 | − | 0.0691343i | ||||
\(577\) | −12.2866 | + | 21.2810i | −0.511498 | + | 0.885941i | 0.488413 | + | 0.872613i | \(0.337576\pi\) |
−0.999911 | + | 0.0133282i | \(0.995757\pi\) | |||||||
\(578\) | 8.58260 | − | 4.95516i | 0.356989 | − | 0.206108i | ||||
\(579\) | 27.2648 | + | 6.40038i | 1.13309 | + | 0.265991i | ||||
\(580\) | 7.31514 | − | 4.22340i | 0.303745 | − | 0.175367i | ||||
\(581\) | 20.4451 | 0.848207 | ||||||||
\(582\) | 10.7175 | − | 3.23357i | 0.444253 | − | 0.134036i | ||||
\(583\) | −4.22194 | + | 7.31262i | −0.174855 | + | 0.302858i | ||||
\(584\) | 1.85630 | + | 3.21521i | 0.0768143 | + | 0.133046i | ||||
\(585\) | 0.993232 | + | 15.8835i | 0.0410651 | + | 0.656701i | ||||
\(586\) | 3.89138 | − | 6.74006i | 0.160751 | − | 0.278429i | ||||
\(587\) | 28.3116 | 1.16855 | 0.584273 | − | 0.811557i | \(-0.301380\pi\) | ||||
0.584273 | + | 0.811557i | \(0.301380\pi\) | |||||||
\(588\) | 0.444079 | − | 0.472716i | 0.0183135 | − | 0.0194945i | ||||
\(589\) | 2.31817 | + | 1.82166i | 0.0955187 | + | 0.0750603i | ||||
\(590\) | 12.0650i | 0.496709i | ||||||||
\(591\) | 10.2208 | − | 10.8799i | 0.420426 | − | 0.447538i | ||||
\(592\) | 0.580888 | + | 0.335376i | 0.0238744 | + | 0.0137839i | ||||
\(593\) | − | 26.2219i | − | 1.07680i | −0.842689 | − | 0.538401i | \(-0.819028\pi\) | ||
0.842689 | − | 0.538401i | \(-0.180972\pi\) | |||||||
\(594\) | 26.3016 | + | 4.46404i | 1.07917 | + | 0.183162i | ||||
\(595\) | −11.5638 | − | 6.67636i | −0.474070 | − | 0.273704i | ||||
\(596\) | −20.8920 | − | 12.0620i | −0.855771 | − | 0.494080i | ||||
\(597\) | 7.16975 | + | 6.73541i | 0.293438 | + | 0.275662i | ||||
\(598\) | 8.04526 | + | 13.9348i | 0.328995 | + | 0.569836i | ||||
\(599\) | −29.8917 | + | 17.2580i | −1.22134 | + | 0.705141i | −0.965204 | − | 0.261500i | \(-0.915783\pi\) |
−0.256136 | + | 0.966641i | \(0.582450\pi\) | |||||||
\(600\) | 0.395836 | − | 1.68621i | 0.0161600 | − | 0.0688393i | ||||
\(601\) | −23.6671 | − | 13.6642i | −0.965403 | − | 0.557375i | −0.0675710 | − | 0.997714i | \(-0.521525\pi\) |
−0.897832 | + | 0.440339i | \(0.854858\pi\) | |||||||
\(602\) | 9.94437 | + | 17.2241i | 0.405302 | + | 0.702004i | ||||
\(603\) | −21.4049 | − | 10.6357i | −0.871675 | − | 0.433117i | ||||
\(604\) | 16.5788i | 0.674581i | ||||||||
\(605\) | 15.3594i | 0.624447i | ||||||||
\(606\) | 4.44507 | + | 14.7329i | 0.180568 | + | 0.598483i | ||||
\(607\) | 11.0332 | + | 19.1100i | 0.447822 | + | 0.775651i | 0.998244 | − | 0.0592358i | \(-0.0188664\pi\) |
−0.550422 | + | 0.834887i | \(0.685533\pi\) | |||||||
\(608\) | −0.458584 | − | 0.264764i | −0.0185980 | − | 0.0107376i | ||||
\(609\) | 36.6619 | + | 8.60633i | 1.48561 | + | 0.348746i | ||||
\(610\) | −6.11655 | + | 3.53139i | −0.247652 | + | 0.142982i | ||||
\(611\) | −17.9106 | − | 31.0221i | −0.724585 | − | 1.25502i | ||||
\(612\) | 0.971266 | + | 15.5322i | 0.0392611 | + | 0.627852i | ||||
\(613\) | 24.3755 | + | 14.0732i | 0.984517 | + | 0.568411i | 0.903631 | − | 0.428312i | \(-0.140892\pi\) |
0.0808859 | + | 0.996723i | \(0.474225\pi\) | |||||||
\(614\) | −9.90659 | − | 5.71957i | −0.399797 | − | 0.230823i | ||||
\(615\) | −19.1869 | − | 4.50411i | −0.773692 | − | 0.181623i | ||||
\(616\) | 13.2153i | 0.532461i | ||||||||
\(617\) | −24.9200 | − | 14.3875i | −1.00324 | − | 0.579221i | −0.0940345 | − | 0.995569i | \(-0.529976\pi\) |
−0.909205 | + | 0.416348i | \(0.863310\pi\) | |||||||
\(618\) | 13.2814 | + | 12.4768i | 0.534256 | + | 0.501891i | ||||
\(619\) | 14.4354i | 0.580208i | 0.956995 | + | 0.290104i | \(0.0936899\pi\) | ||||
−0.956995 | + | 0.290104i | \(0.906310\pi\) | |||||||
\(620\) | 2.07122 | + | 5.16818i | 0.0831820 | + | 0.207559i | ||||
\(621\) | −12.1382 | − | 10.0533i | −0.487090 | − | 0.403425i | ||||
\(622\) | −7.22744 | −0.289794 | ||||||||
\(623\) | −19.1642 | + | 33.1933i | −0.767796 | + | 1.32986i | ||||
\(624\) | 6.69674 | + | 6.29106i | 0.268084 | + | 0.251844i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −6.50334 | + | 11.2641i | −0.259926 | + | 0.450205i | ||||
\(627\) | −1.36015 | − | 4.50815i | −0.0543193 | − | 0.180038i | ||||
\(628\) | −14.6508 | −0.584631 | ||||||||
\(629\) | −3.01337 | + | 1.73977i | −0.120151 | + | 0.0693691i | ||||
\(630\) | 6.43347 | − | 4.27086i | 0.256316 | − | 0.170155i | ||||
\(631\) | 18.2779 | − | 10.5528i | 0.727633 | − | 0.420099i | −0.0899227 | − | 0.995949i | \(-0.528662\pi\) |
0.817556 | + | 0.575850i | \(0.195329\pi\) | |||||||
\(632\) | 5.05381 | − | 8.75345i | 0.201030 | − | 0.348194i | ||||
\(633\) | 2.34573 | + | 0.550657i | 0.0932343 | + | 0.0218866i | ||||
\(634\) | 11.3812 | − | 19.7129i | 0.452006 | − | 0.782898i | ||||
\(635\) | 15.5915 | 0.618729 | ||||||||
\(636\) | 1.95041 | − | 2.07619i | 0.0773390 | − | 0.0823262i | ||||
\(637\) | 1.72033 | + | 0.993232i | 0.0681619 | + | 0.0393533i | ||||
\(638\) | 37.5569 | − | 21.6835i | 1.48689 | − | 0.858458i | ||||
\(639\) | −13.0302 | + | 26.2241i | −0.515468 | + | 1.03741i | ||||
\(640\) | −0.500000 | − | 0.866025i | −0.0197642 | − | 0.0342327i | ||||
\(641\) | 13.7198 | + | 23.7633i | 0.541898 | + | 0.938594i | 0.998795 | + | 0.0490748i | \(0.0156273\pi\) |
−0.456898 | + | 0.889519i | \(0.651039\pi\) | |||||||
\(642\) | 21.8258 | + | 5.12359i | 0.861397 | + | 0.202212i | ||||
\(643\) | − | 34.0135i | − | 1.34136i | −0.741747 | − | 0.670680i | \(-0.766002\pi\) | ||
0.741747 | − | 0.670680i | \(-0.233998\pi\) | |||||||
\(644\) | 3.90372 | − | 6.76144i | 0.153828 | − | 0.266438i | ||||
\(645\) | −3.86571 | − | 12.8127i | −0.152212 | − | 0.504498i | ||||
\(646\) | 2.37891 | − | 1.37347i | 0.0935971 | − | 0.0540383i | ||||
\(647\) | 12.8461 | 0.505031 | 0.252516 | − | 0.967593i | \(-0.418742\pi\) | ||||
0.252516 | + | 0.967593i | \(0.418742\pi\) | |||||||
\(648\) | −8.29411 | − | 3.49396i | −0.325823 | − | 0.137256i | ||||
\(649\) | 61.9435i | 2.43149i | ||||||||
\(650\) | 5.30484 | 0.208073 | ||||||||
\(651\) | −9.04592 | + | 23.1159i | −0.354537 | + | 0.905985i | ||||
\(652\) | −22.4774 | −0.880281 | ||||||||
\(653\) | − | 0.0217666i | − | 0.000851794i | −1.00000 | 0.000425897i | \(-0.999864\pi\) | |||
1.00000 | 0.000425897i | \(-0.000135567\pi\) | ||||||||
\(654\) | 2.24089 | − | 0.676098i | 0.0876256 | − | 0.0264375i | ||||
\(655\) | 18.9450 | 0.740244 | ||||||||
\(656\) | −9.85425 | + | 5.68936i | −0.384744 | + | 0.222132i | ||||
\(657\) | 4.95606 | − | 9.97438i | 0.193354 | − | 0.389138i | ||||
\(658\) | −8.69058 | + | 15.0525i | −0.338794 | + | 0.586808i | ||||
\(659\) | − | 42.3998i | − | 1.65166i | −0.563917 | − | 0.825832i | \(-0.690706\pi\) | ||
0.563917 | − | 0.825832i | \(-0.309294\pi\) | |||||||
\(660\) | 2.03228 | − | 8.65725i | 0.0791063 | − | 0.336983i | ||||
\(661\) | 3.57820 | + | 6.19762i | 0.139176 | + | 0.241059i | 0.927185 | − | 0.374604i | \(-0.122221\pi\) |
−0.788009 | + | 0.615664i | \(0.788888\pi\) | |||||||
\(662\) | 2.45387 | + | 4.25023i | 0.0953724 | + | 0.165190i | ||||
\(663\) | −45.6325 | + | 13.7678i | −1.77222 | + | 0.534696i | ||||
\(664\) | −6.87875 | + | 3.97145i | −0.266947 | + | 0.154122i | ||||
\(665\) | −1.18040 | − | 0.681505i | −0.0457740 | − | 0.0264276i | ||||
\(666\) | −0.125586 | − | 2.00833i | −0.00486635 | − | 0.0778213i | ||||
\(667\) | −25.6207 | −0.992036 | ||||||||
\(668\) | 8.21327 | − | 14.2258i | 0.317781 | − | 0.550413i | ||||
\(669\) | −5.28887 | + | 22.5299i | −0.204479 | + | 0.871056i | ||||
\(670\) | −3.98360 | + | 6.89980i | −0.153900 | + | 0.266563i | ||||
\(671\) | −31.4032 | + | 18.1307i | −1.21231 | + | 0.699926i | ||||
\(672\) | 1.01889 | − | 4.34033i | 0.0393044 | − | 0.167432i | ||||
\(673\) | −15.4883 | + | 8.94220i | −0.597032 | + | 0.344696i | −0.767873 | − | 0.640602i | \(-0.778685\pi\) |
0.170841 | + | 0.985299i | \(0.445351\pi\) | |||||||
\(674\) | 27.0752 | 1.04290 | ||||||||
\(675\) | −4.87129 | + | 1.80845i | −0.187496 | + | 0.0696073i | ||||
\(676\) | −7.57064 | + | 13.1127i | −0.291179 | + | 0.504336i | ||||
\(677\) | −16.7056 | − | 28.9349i | −0.642048 | − | 1.11206i | −0.984975 | − | 0.172698i | \(-0.944752\pi\) |
0.342927 | − | 0.939362i | \(-0.388582\pi\) | |||||||
\(678\) | −5.59018 | + | 5.95067i | −0.214690 | + | 0.228534i | ||||
\(679\) | 8.31822 | − | 14.4076i | 0.319224 | − | 0.552912i | ||||
\(680\) | 5.18752 | 0.198932 | ||||||||
\(681\) | 19.6179 | + | 18.4295i | 0.751759 | + | 0.706218i | ||||
\(682\) | 10.6339 | + | 26.5341i | 0.407193 | + | 1.01604i | ||||
\(683\) | − | 19.4433i | − | 0.743979i | −0.928237 | − | 0.371990i | \(-0.878676\pi\) | ||
0.928237 | − | 0.371990i | \(-0.121324\pi\) | |||||||
\(684\) | 0.0991442 | + | 1.58549i | 0.00379087 | + | 0.0606226i | ||||
\(685\) | −5.17720 | − | 2.98906i | −0.197811 | − | 0.114206i | ||||
\(686\) | − | 18.9820i | − | 0.724734i | ||||||
\(687\) | −5.76215 | + | 24.5460i | −0.219840 | + | 0.936489i | ||||
\(688\) | −6.69156 | − | 3.86337i | −0.255113 | − | 0.147290i | ||||
\(689\) | 7.55575 | + | 4.36231i | 0.287851 | + | 0.166191i | ||||
\(690\) | −3.59708 | + | 3.82904i | −0.136939 | + | 0.145769i | ||||
\(691\) | −10.6087 | − | 18.3747i | −0.403572 | − | 0.699007i | 0.590582 | − | 0.806978i | \(-0.298898\pi\) |
−0.994154 | + | 0.107970i | \(0.965565\pi\) | |||||||
\(692\) | 2.51861 | − | 1.45412i | 0.0957430 | − | 0.0552772i | ||||
\(693\) | 33.0303 | − | 21.9272i | 1.25472 | − | 0.832945i | ||||
\(694\) | 17.7512 | + | 10.2487i | 0.673827 | + | 0.389034i | ||||
\(695\) | 10.3001 | + | 17.8402i | 0.390704 | + | 0.676718i | ||||
\(696\) | −14.0067 | + | 4.22595i | −0.530921 | + | 0.160184i | ||||
\(697\) | − | 59.0273i | − | 2.23582i | ||||||
\(698\) | − | 20.0539i | − | 0.759053i | ||||||
\(699\) | 4.80260 | − | 1.44899i | 0.181651 | − | 0.0548060i | ||||
\(700\) | −1.28701 | − | 2.22916i | −0.0486443 | − | 0.0842543i | ||||
\(701\) | 28.4019 | + | 16.3979i | 1.07273 | + | 0.619338i | 0.928925 | − | 0.370268i | \(-0.120734\pi\) |
0.143801 | + | 0.989607i | \(0.454068\pi\) | |||||||
\(702\) | 4.61246 | − | 27.1761i | 0.174086 | − | 1.02570i | ||||
\(703\) | −0.307596 | + | 0.177591i | −0.0116012 | + | 0.00669796i | ||||
\(704\) | −2.56707 | − | 4.44629i | −0.0967500 | − | 0.167576i | ||||
\(705\) | 8.00793 | − | 8.52432i | 0.301596 | − | 0.321045i | ||||
\(706\) | −7.28255 | − | 4.20458i | −0.274082 | − | 0.158242i | ||||
\(707\) | 19.8056 | + | 11.4347i | 0.744865 | + | 0.430048i | ||||
\(708\) | 4.77578 | − | 20.3442i | 0.179485 | − | 0.764582i | ||||
\(709\) | 49.3472i | 1.85327i | 0.375960 | + | 0.926636i | \(0.377313\pi\) | ||||
−0.375960 | + | 0.926636i | \(0.622687\pi\) | |||||||
\(710\) | 8.45327 | + | 4.88050i | 0.317245 | + | 0.183162i | ||||
\(711\) | −30.2637 | + | 1.89246i | −1.13498 | + | 0.0709729i | ||||
\(712\) | − | 14.8905i | − | 0.558045i | ||||||
\(713\) | 2.39732 | − | 16.7170i | 0.0897802 | − | 0.626057i | ||||
\(714\) | 16.8563 | + | 15.8351i | 0.630831 | + | 0.592615i | ||||
\(715\) | 27.2358 | 1.01856 | ||||||||
\(716\) | 2.85826 | − | 4.95065i | 0.106818 | − | 0.185015i | ||||
\(717\) | 6.50937 | − | 6.92913i | 0.243097 | − | 0.258773i | ||||
\(718\) | 12.7070 | + | 22.0093i | 0.474223 | + | 0.821378i | ||||
\(719\) | 3.77117 | − | 6.53187i | 0.140641 | − | 0.243598i | −0.787097 | − | 0.616829i | \(-0.788417\pi\) |
0.927738 | + | 0.373232i | \(0.121750\pi\) | |||||||
\(720\) | −1.33493 | + | 2.68663i | −0.0497499 | + | 0.100125i | ||||
\(721\) | 27.0809 | 1.00854 | ||||||||
\(722\) | −16.2116 | + | 9.35980i | −0.603335 | + | 0.348336i | ||||
\(723\) | 2.10910 | − | 8.98449i | 0.0784382 | − | 0.334137i | ||||
\(724\) | 13.2525 | − | 7.65134i | 0.492525 | − | 0.284360i | ||||
\(725\) | −4.22340 | + | 7.31514i | −0.156853 | + | 0.271677i | ||||
\(726\) | 6.07979 | − | 25.8991i | 0.225642 | − | 0.961207i | ||||
\(727\) | 20.0826 | − | 34.7841i | 0.744822 | − | 1.29007i | −0.205456 | − | 0.978666i | \(-0.565868\pi\) |
0.950278 | − | 0.311403i | \(-0.100799\pi\) | |||||||
\(728\) | 13.6547 | 0.506077 | ||||||||
\(729\) | 5.02899 | + | 26.5275i | 0.186259 | + | 0.982501i | ||||
\(730\) | −3.21521 | − | 1.85630i | −0.119000 | − | 0.0687048i | ||||
\(731\) | 34.7126 | − | 20.0413i | 1.28389 | − | 0.741255i | ||||
\(732\) | 11.7117 | − | 3.53353i | 0.432875 | − | 0.130603i | ||||
\(733\) | 7.73727 | + | 13.4013i | 0.285783 | + | 0.494990i | 0.972799 | − | 0.231652i | \(-0.0744132\pi\) |
−0.687016 | + | 0.726642i | \(0.741080\pi\) | |||||||
\(734\) | 8.65053 | + | 14.9832i | 0.319297 | + | 0.553038i | ||||
\(735\) | −0.148226 | + | 0.631424i | −0.00546740 | + | 0.0232904i | ||||
\(736\) | 3.03318i | 0.111805i | ||||||||
\(737\) | −20.4524 | + | 35.4245i | −0.753372 | + | 1.30488i | ||||
\(738\) | 30.5704 | + | 15.1898i | 1.12531 | + | 0.559143i | ||||
\(739\) | 20.8170 | − | 12.0187i | 0.765767 | − | 0.442116i | −0.0655955 | − | 0.997846i | \(-0.520895\pi\) |
0.831362 | + | 0.555731i | \(0.187561\pi\) | |||||||
\(740\) | −0.670752 | −0.0246573 | ||||||||
\(741\) | −4.65804 | + | 1.40538i | −0.171117 | + | 0.0516278i | ||||
\(742\) | − | 4.23336i | − | 0.155412i | ||||||
\(743\) | 16.5869 | 0.608516 | 0.304258 | − | 0.952590i | \(-0.401591\pi\) | ||||
0.304258 | + | 0.952590i | \(0.401591\pi\) | |||||||
\(744\) | −1.44676 | − | 9.53451i | −0.0530407 | − | 0.349552i | ||||
\(745\) | 24.1241 | 0.883837 | ||||||||
\(746\) | − | 14.4940i | − | 0.530663i | ||||||
\(747\) | 21.3396 | + | 10.6032i | 0.780776 | + | 0.387951i | ||||
\(748\) | 26.6334 | 0.973814 | ||||||||
\(749\) | 28.8536 | − | 16.6586i | 1.05429 | − | 0.608693i | ||||
\(750\) | 0.500302 | + | 1.65822i | 0.0182684 | + | 0.0605497i | ||||
\(751\) | −15.3278 | + | 26.5485i | −0.559318 | + | 0.968768i | 0.438235 | + | 0.898860i | \(0.355604\pi\) |
−0.997553 | + | 0.0699074i | \(0.977730\pi\) | |||||||
\(752\) | − | 6.75256i | − | 0.246240i | ||||||
\(753\) | 1.32515 | + | 0.311077i | 0.0482911 | + | 0.0113363i | ||||
\(754\) | −22.4044 | − | 38.8056i | −0.815921 | − | 1.41322i | ||||
\(755\) | −8.28939 | − | 14.3576i | −0.301682 | − | 0.522528i | ||||
\(756\) | −12.5388 | + | 4.65498i | −0.456031 | + | 0.169300i | ||||
\(757\) | 15.7629 | − | 9.10072i | 0.572913 | − | 0.330771i | −0.185399 | − | 0.982663i | \(-0.559358\pi\) |
0.758312 | + | 0.651892i | \(0.226024\pi\) | |||||||
\(758\) | −17.1608 | − | 9.90778i | −0.623308 | − | 0.359867i | ||||
\(759\) | −18.4679 | + | 19.6588i | −0.670343 | + | 0.713570i | ||||
\(760\) | 0.529528 | 0.0192080 | ||||||||
\(761\) | −18.2034 | + | 31.5292i | −0.659873 | + | 1.14293i | 0.320775 | + | 0.947155i | \(0.396057\pi\) |
−0.980648 | + | 0.195778i | \(0.937277\pi\) | |||||||
\(762\) | −26.2906 | − | 6.17168i | −0.952406 | − | 0.223576i | ||||
\(763\) | 1.73923 | − | 3.01244i | 0.0629645 | − | 0.109058i | ||||
\(764\) | −4.31841 | + | 2.49324i | −0.156235 | + | 0.0902022i | ||||
\(765\) | −8.60725 | − | 12.9657i | −0.311196 | − | 0.468774i | ||||
\(766\) | 3.42236 | − | 1.97590i | 0.123655 | − | 0.0713922i | ||||
\(767\) | 64.0030 | 2.31101 | ||||||||
\(768\) | 0.500302 | + | 1.65822i | 0.0180531 | + | 0.0598359i | ||||
\(769\) | 15.0861 | − | 26.1298i | 0.544017 | − | 0.942265i | −0.454651 | − | 0.890670i | \(-0.650236\pi\) |
0.998668 | − | 0.0515956i | \(-0.0164307\pi\) | |||||||
\(770\) | −6.60766 | − | 11.4448i | −0.238124 | − | 0.412442i | ||||
\(771\) | −15.2232 | − | 14.3010i | −0.548251 | − | 0.515038i | ||||
\(772\) | −8.08463 | + | 14.0030i | −0.290972 | + | 0.503979i | ||||
\(773\) | −14.9673 | −0.538336 | −0.269168 | − | 0.963093i | \(-0.586749\pi\) | ||||
−0.269168 | + | 0.963093i | \(0.586749\pi\) | |||||||
\(774\) | 1.44669 | + | 23.1350i | 0.0520002 | + | 0.831572i | ||||
\(775\) | −4.37781 | − | 3.44017i | −0.157256 | − | 0.123574i | ||||
\(776\) | 6.46323i | 0.232016i | ||||||||
\(777\) | −2.17954 | − | 2.04750i | −0.0781904 | − | 0.0734537i | ||||
\(778\) | −16.8346 | − | 9.71945i | −0.603549 | − | 0.348459i | ||||
\(779\) | − | 6.02534i | − | 0.215880i | ||||||
\(780\) | −8.94508 | − | 2.09985i | −0.320285 | − | 0.0751866i | ||||
\(781\) | 43.4002 | + | 25.0571i | 1.55298 | + | 0.896615i | ||||
\(782\) | −13.6266 | − | 7.86734i | −0.487287 | − | 0.281335i | ||||
\(783\) | 33.8025 | + | 27.9964i | 1.20800 | + | 1.00051i | ||||
\(784\) | 0.187231 | + | 0.324294i | 0.00668684 | + | 0.0115819i | ||||
\(785\) | 12.6880 | − | 7.32540i | 0.452853 | − | 0.261455i | ||||
\(786\) | −31.9454 | − | 7.49914i | −1.13945 | − | 0.267485i | ||||
\(787\) | −0.227315 | − | 0.131240i | −0.00810290 | − | 0.00467821i | 0.495943 | − | 0.868355i | \(-0.334822\pi\) |
−0.504046 | + | 0.863677i | \(0.668156\pi\) | |||||||
\(788\) | 4.30925 | + | 7.46384i | 0.153511 | + | 0.265888i | ||||
\(789\) | −1.02440 | − | 3.39531i | −0.0364696 | − | 0.120876i | ||||
\(790\) | 10.1076i | 0.359613i | ||||||||
\(791\) | 12.1335i | 0.431416i | ||||||||
\(792\) | −6.85371 | + | 13.7935i | −0.243536 | + | 0.490131i | ||||
\(793\) | 18.7335 | + | 32.4473i | 0.665245 | + | 1.15224i | ||||
\(794\) | 20.7332 | + | 11.9703i | 0.735793 | + | 0.424810i | ||||
\(795\) | −0.651014 | + | 2.77324i | −0.0230891 | + | 0.0983566i | ||||
\(796\) | −4.91862 | + | 2.83976i | −0.174336 | + | 0.100653i | ||||
\(797\) | −4.06441 | − | 7.03976i | −0.143969 | − | 0.249361i | 0.785019 | − | 0.619472i | \(-0.212653\pi\) |
−0.928988 | + | 0.370111i | \(0.879320\pi\) | |||||||
\(798\) | 1.72064 | + | 1.61641i | 0.0609101 | + | 0.0572202i | ||||
\(799\) | 30.3360 | + | 17.5145i | 1.07321 | + | 0.619618i | ||||
\(800\) | 0.866025 | + | 0.500000i | 0.0306186 | + | 0.0176777i | ||||
\(801\) | −37.2172 | + | 24.7067i | −1.31501 | + | 0.872967i | ||||
\(802\) | 20.4973i | 0.723785i | ||||||||
\(803\) | −16.5073 | − | 9.53051i | −0.582531 | − | 0.336324i | ||||
\(804\) | 9.44840 | − | 10.0577i | 0.333219 | − | 0.354707i | ||||
\(805\) | 7.80744i | 0.275176i | ||||||||
\(806\) | 27.4163 | − | 10.9875i | 0.965699 | − | 0.387017i | ||||
\(807\) | 32.0379 | − | 34.1039i | 1.12779 | − | 1.20051i | ||||
\(808\) | −8.88476 | −0.312565 | ||||||||
\(809\) | −1.67849 | + | 2.90724i | −0.0590127 | + | 0.102213i | −0.894022 | − | 0.448022i | \(-0.852129\pi\) |
0.835010 | + | 0.550235i | \(0.185462\pi\) | |||||||
\(810\) | 8.92989 | − | 1.12120i | 0.313764 | − | 0.0393949i | ||||
\(811\) | −17.9731 | − | 31.1303i | −0.631120 | − | 1.09313i | −0.987323 | − | 0.158724i | \(-0.949262\pi\) |
0.356203 | − | 0.934409i | \(-0.384071\pi\) | |||||||
\(812\) | −10.8711 | + | 18.8293i | −0.381500 | + | 0.660777i | ||||
\(813\) | −5.27211 | + | 1.59065i | −0.184901 | + | 0.0557865i | ||||
\(814\) | −3.44373 | −0.120703 | ||||||||
\(815\) | 19.4660 | − | 11.2387i | 0.681863 | − | 0.393674i | ||||
\(816\) | −8.74726 | − | 2.05341i | −0.306215 | − | 0.0718837i | ||||
\(817\) | 3.54336 | − | 2.04576i | 0.123967 | − | 0.0715722i | ||||
\(818\) | −4.38047 | + | 7.58719i | −0.153160 | + | 0.265280i | ||||
\(819\) | −22.6562 | − | 34.1285i | −0.791672 | − | 1.19255i | ||||
\(820\) | 5.68936 | − | 9.85425i | 0.198681 | − | 0.344125i | ||||
\(821\) | 21.8066 | 0.761056 | 0.380528 | − | 0.924769i | \(-0.375742\pi\) | ||||
0.380528 | + | 0.924769i | \(0.375742\pi\) | |||||||
\(822\) | 7.54669 | + | 7.08951i | 0.263221 | + | 0.247275i | ||||
\(823\) | 18.4662 | + | 10.6615i | 0.643692 | + | 0.371636i | 0.786035 | − | 0.618181i | \(-0.212130\pi\) |
−0.142343 | + | 0.989817i | \(0.545464\pi\) | |||||||
\(824\) | −9.11135 | + | 5.26044i | −0.317409 | + | 0.183256i | ||||
\(825\) | 2.56862 | + | 8.51353i | 0.0894278 | + | 0.296403i | ||||
\(826\) | −15.5278 | − | 26.8949i | −0.540280 | − | 0.935792i | ||||
\(827\) | 12.4338 | + | 21.5359i | 0.432364 | + | 0.748877i | 0.997076 | − | 0.0764112i | \(-0.0243462\pi\) |
−0.564712 | + | 0.825288i | \(0.691013\pi\) | |||||||
\(828\) | 7.58112 | − | 5.03272i | 0.263462 | − | 0.174899i | ||||
\(829\) | − | 1.77571i | − | 0.0616728i | −0.999524 | − | 0.0308364i | \(-0.990183\pi\) | ||
0.999524 | − | 0.0308364i | \(-0.00981709\pi\) | |||||||
\(830\) | 3.97145 | − | 6.87875i | 0.137851 | − | 0.238765i | ||||
\(831\) | −27.4315 | + | 8.27635i | −0.951588 | + | 0.287104i | ||||
\(832\) | −4.59412 | + | 2.65242i | −0.159273 | + | 0.0919560i | ||||
\(833\) | −1.94253 | −0.0673047 | ||||||||
\(834\) | −10.3063 | − | 34.1596i | −0.356877 | − | 1.18285i | ||||
\(835\) | 16.4265i | 0.568464i | ||||||||
\(836\) | 2.71867 | 0.0940270 | ||||||||
\(837\) | −21.4300 | + | 19.4359i | −0.740730 | + | 0.671803i | ||||
\(838\) | −17.8444 | −0.616423 | ||||||||
\(839\) | 2.30549i | 0.0795945i | 0.999208 | + | 0.0397973i | \(0.0126712\pi\) | ||||
−0.999208 | + | 0.0397973i | \(0.987329\pi\) | |||||||
\(840\) | 1.28778 | + | 4.26828i | 0.0444327 | + | 0.147270i | ||||
\(841\) | 42.3483 | 1.46029 | ||||||||
\(842\) | 14.3028 | − | 8.25775i | 0.492909 | − | 0.284581i | ||||
\(843\) | 2.57586 | − | 0.777162i | 0.0887172 | − | 0.0267669i | ||||
\(844\) | −0.695561 | + | 1.20475i | −0.0239422 | + | 0.0414691i | ||||
\(845\) | − | 15.1413i | − | 0.520876i | ||||||
\(846\) | −16.8773 | + | 11.2040i | −0.580254 | + | 0.385201i | ||||
\(847\) | −19.7676 | − | 34.2385i | −0.679222 | − | 1.17645i | ||||
\(848\) | 0.822328 | + | 1.42431i | 0.0282388 | + | 0.0489111i | ||||
\(849\) | −1.51652 | − | 5.02643i | −0.0520470 | − | 0.172507i | ||||
\(850\) | −4.49252 | + | 2.59376i | −0.154092 | + | 0.0889652i | ||||
\(851\) | 1.76194 | + | 1.01726i | 0.0603985 | + | 0.0348711i | ||||
\(852\) | −12.3221 | − | 11.5757i | −0.422149 | − | 0.396576i | ||||
\(853\) | −28.9723 | −0.991991 | −0.495996 | − | 0.868325i | \(-0.665197\pi\) | ||||
−0.495996 | + | 0.868325i | \(0.665197\pi\) | |||||||
\(854\) | 9.08985 | − | 15.7441i | 0.311048 | − | 0.538751i | ||||
\(855\) | −0.878604 | − | 1.32350i | −0.0300476 | − | 0.0452627i | ||||
\(856\) | −6.47185 | + | 11.2096i | −0.221203 | + | 0.383135i | ||||
\(857\) | 3.20393 | − | 1.84979i | 0.109444 | − | 0.0631877i | −0.444279 | − | 0.895889i | \(-0.646540\pi\) |
0.553723 | + | 0.832701i | \(0.313207\pi\) | |||||||
\(858\) | −45.9253 | − | 10.7809i | −1.56786 | − | 0.368054i | ||||
\(859\) | −37.3943 | + | 21.5896i | −1.27588 | + | 0.736629i | −0.976088 | − | 0.217376i | \(-0.930250\pi\) |
−0.299791 | + | 0.954005i | \(0.596917\pi\) | |||||||
\(860\) | 7.72674 | 0.263480 | ||||||||
\(861\) | 48.5675 | − | 14.6533i | 1.65518 | − | 0.499384i | ||||
\(862\) | 6.18908 | − | 10.7198i | 0.210801 | − | 0.365118i | ||||
\(863\) | −7.65540 | − | 13.2595i | −0.260593 | − | 0.451360i | 0.705807 | − | 0.708405i | \(-0.250585\pi\) |
−0.966400 | + | 0.257044i | \(0.917251\pi\) | |||||||
\(864\) | 3.31444 | − | 4.00181i | 0.112759 | − | 0.136144i | ||||
\(865\) | −1.45412 | + | 2.51861i | −0.0494415 | + | 0.0856351i | ||||
\(866\) | 1.18613 | 0.0403063 | ||||||||
\(867\) | 11.7528 | − | 12.5107i | 0.399145 | − | 0.424884i | ||||
\(868\) | −11.2685 | − | 8.85503i | −0.382479 | − | 0.300559i | ||||
\(869\) | 51.8939i | 1.76038i | ||||||||
\(870\) | 10.0171 | − | 10.6631i | 0.339613 | − | 0.361513i | ||||
\(871\) | 36.6023 | + | 21.1324i | 1.24022 | + | 0.716043i | ||||
\(872\) | 1.35138i | 0.0457635i | ||||||||
\(873\) | 16.1542 | − | 10.7239i | 0.546736 | − | 0.362950i | ||||
\(874\) | −1.39097 | − | 0.803076i | −0.0470502 | − | 0.0271645i | ||||
\(875\) | 2.22916 | + | 1.28701i | 0.0753594 | + | 0.0435087i | ||||
\(876\) | 4.68674 | + | 4.40282i | 0.158350 | + | 0.148757i | ||||
\(877\) | −19.7173 | − | 34.1513i | −0.665805 | − | 1.15321i | −0.979066 | − | 0.203541i | \(-0.934755\pi\) |
0.313262 | − | 0.949667i | \(-0.398578\pi\) | |||||||
\(878\) | −14.2541 | + | 8.22962i | −0.481053 | + | 0.277736i | ||||
\(879\) | 3.08070 | − | 13.1234i | 0.103909 | − | 0.442641i | ||||
\(880\) | 4.44629 | + | 2.56707i | 0.149884 | + | 0.0865358i | ||||
\(881\) | 9.28944 | + | 16.0898i | 0.312969 | + | 0.542079i | 0.979004 | − | 0.203842i | \(-0.0653430\pi\) |
−0.666035 | + | 0.745921i | \(0.732010\pi\) | |||||||
\(882\) | 0.499881 | − | 1.00604i | 0.0168319 | − | 0.0338752i | ||||
\(883\) | 17.4530i | 0.587339i | 0.955907 | + | 0.293669i | \(0.0948765\pi\) | ||||
−0.955907 | + | 0.293669i | \(0.905123\pi\) | |||||||
\(884\) | − | 27.5189i | − | 0.925562i | ||||||
\(885\) | 6.03616 | + | 20.0065i | 0.202903 | + | 0.672511i | ||||
\(886\) | −12.0992 | − | 20.9565i | −0.406481 | − | 0.704046i | ||||
\(887\) | −43.3396 | − | 25.0221i | −1.45520 | − | 0.840161i | −0.456433 | − | 0.889758i | \(-0.650873\pi\) |
−0.998769 | + | 0.0495968i | \(0.984206\pi\) | |||||||
\(888\) | 1.13103 | + | 0.265508i | 0.0379549 | + | 0.00890986i | ||||
\(889\) | −34.7559 | + | 20.0663i | −1.16568 | + | 0.673003i | ||||
\(890\) | 7.44525 | + | 12.8955i | 0.249565 | + | 0.432260i | ||||
\(891\) | 45.8473 | − | 5.75638i | 1.53594 | − | 0.192846i | ||||
\(892\) | −11.5712 | − | 6.68062i | −0.387432 | − | 0.223684i | ||||
\(893\) | 3.09662 | + | 1.78783i | 0.103624 | + | 0.0598275i | ||||
\(894\) | −40.6783 | − | 9.54918i | −1.36049 | − | 0.319372i | ||||
\(895\) | 5.71652i | 0.191082i | ||||||||
\(896\) | 2.22916 | + | 1.28701i | 0.0744710 | + | 0.0429959i | ||||
\(897\) | 20.3124 | + | 19.0819i | 0.678212 | + | 0.637127i | ||||
\(898\) | 32.2944i | 1.07768i | ||||||||
\(899\) | −6.67604 | + | 46.5535i | −0.222658 | + | 1.55265i | ||||
\(900\) | −0.187231 | − | 2.99415i | −0.00624105 | − | 0.0998051i | ||||
\(901\) | −8.53168 | −0.284231 | ||||||||
\(902\) | 29.2099 | − | 50.5931i | 0.972584 | − | 1.68457i | ||||
\(903\) | 25.1072 | + | 23.5863i | 0.835516 | + | 0.784902i | ||||
\(904\) | −2.35692 | − | 4.08230i | −0.0783899 | − | 0.135775i | ||||
\(905\) | −7.65134 | + | 13.2525i | −0.254339 | + | 0.440528i | ||||
\(906\) | 8.29440 | + | 27.4913i | 0.275563 | + | 0.913337i | ||||
\(907\) | 10.6428 | 0.353387 | 0.176693 | − | 0.984266i | \(-0.443460\pi\) | ||||
0.176693 | + | 0.984266i | \(0.443460\pi\) | |||||||
\(908\) | −13.4583 | + | 7.77017i | −0.446630 | + | 0.257862i | ||||
\(909\) | 14.7418 | + | 22.2065i | 0.488955 | + | 0.736544i | ||||
\(910\) | −11.8253 | + | 6.82736i | −0.392006 | + | 0.226325i | ||||
\(911\) | 0.881044 | − | 1.52601i | 0.0291903 | − | 0.0505591i | −0.851061 | − | 0.525066i | \(-0.824040\pi\) |
0.880252 | + | 0.474507i | \(0.157374\pi\) | |||||||
\(912\) | −0.892896 | − | 0.209606i | −0.0295667 | − | 0.00694076i | ||||
\(913\) | 20.3900 | − | 35.3165i | 0.674809 | − | 1.16880i | ||||
\(914\) | −19.0886 | −0.631396 | ||||||||
\(915\) | −8.37583 | + | 8.91595i | −0.276897 | + | 0.294752i | ||||
\(916\) | −12.6066 | − | 7.27845i | −0.416535 | − | 0.240487i | ||||
\(917\) | −42.2315 | + | 24.3824i | −1.39461 | + | 0.805177i | ||||
\(918\) | 9.38137 | + | 25.2699i | 0.309631 | + | 0.834032i | ||||
\(919\) | 3.39521 | + | 5.88068i | 0.111998 | + | 0.193986i | 0.916576 | − | 0.399861i | \(-0.130942\pi\) |
−0.804578 | + | 0.593847i | \(0.797608\pi\) | |||||||
\(920\) | −1.51659 | − | 2.62681i | −0.0500005 | − | 0.0866034i | ||||
\(921\) | −19.2888 | − | 4.52803i | −0.635588 | − | 0.149204i | ||||
\(922\) | 12.8115i | 0.421924i | ||||||||
\(923\) | 25.8902 | − | 44.8432i | 0.852187 | − | 1.47603i | ||||
\(924\) | 6.61166 | + | 21.9139i | 0.217507 | + | 0.720916i | ||||
\(925\) | 0.580888 | − | 0.335376i | 0.0190995 | − | 0.0110271i | ||||
\(926\) | 20.6891 | 0.679885 | ||||||||
\(927\) | 28.2657 | + | 14.0446i | 0.928367 | + | 0.461286i | ||||
\(928\) | − | 8.44680i | − | 0.277280i | ||||||
\(929\) | −59.0112 | −1.93610 | −0.968048 | − | 0.250766i | \(-0.919318\pi\) | ||||
−0.968048 | + | 0.250766i | \(0.919318\pi\) | |||||||
\(930\) | 6.02018 | + | 7.53375i | 0.197410 | + | 0.247041i | ||||
\(931\) | −0.198288 | −0.00649864 | ||||||||
\(932\) | 2.89624i | 0.0948694i | ||||||||
\(933\) | −11.9847 | + | 3.61590i | −0.392361 | + | 0.118379i | ||||
\(934\) | 23.8528 | 0.780489 | ||||||||
\(935\) | −23.0652 | + | 13.3167i | −0.754313 | + | 0.435503i | ||||
\(936\) | 14.2521 | + | 7.08158i | 0.465845 | + | 0.231469i | ||||
\(937\) | 1.34945 | − | 2.33732i | 0.0440847 | − | 0.0763569i | −0.843141 | − | 0.537692i | \(-0.819296\pi\) |
0.887226 | + | 0.461335i | \(0.152630\pi\) | |||||||
\(938\) | − | 20.5077i | − | 0.669600i | ||||||
\(939\) | −5.14852 | + | 21.9320i | −0.168016 | + | 0.715725i | ||||
\(940\) | 3.37628 | + | 5.84788i | 0.110122 | + | 0.190737i | ||||
\(941\) | 4.89303 | + | 8.47498i | 0.159508 | + | 0.276276i | 0.934691 | − | 0.355460i | \(-0.115676\pi\) |
−0.775183 | + | 0.631737i | \(0.782342\pi\) | |||||||
\(942\) | −24.2943 | + | 7.32983i | −0.791550 | + | 0.238819i | ||||
\(943\) | −29.8897 | + | 17.2568i | −0.973343 | + | 0.561960i | ||||
\(944\) | 10.4486 | + | 6.03251i | 0.340074 | + | 0.196342i | ||||
\(945\) | 8.53140 | − | 10.3007i | 0.277527 | − | 0.335082i | ||||
\(946\) | 39.6702 | 1.28979 | ||||||||
\(947\) | 16.6868 | − | 28.9023i | 0.542247 | − | 0.939199i | −0.456528 | − | 0.889709i | \(-0.650907\pi\) |
0.998775 | − | 0.0494896i | \(-0.0157595\pi\) | |||||||
\(948\) | 4.00096 | − | 17.0436i | 0.129945 | − | 0.553550i | ||||
\(949\) | −9.84738 | + | 17.0562i | −0.319659 | + | 0.553666i | ||||
\(950\) | −0.458584 | + | 0.264764i | −0.0148784 | + | 0.00859007i | ||||
\(951\) | 9.01021 | − | 38.3823i | 0.292176 | − | 1.24463i | ||||
\(952\) | −11.5638 | + | 6.67636i | −0.374785 | + | 0.216382i | ||||
\(953\) | −12.6811 | −0.410781 | −0.205391 | − | 0.978680i | \(-0.565847\pi\) | ||||
−0.205391 | + | 0.978680i | \(0.565847\pi\) | |||||||
\(954\) | 2.19550 | − | 4.41858i | 0.0710819 | − | 0.143057i | ||||
\(955\) | 2.49324 | − | 4.31841i | 0.0806793 | − | 0.139741i | ||||
\(956\) | 2.74446 | + | 4.75354i | 0.0887622 | + | 0.153741i | ||||
\(957\) | 51.4294 | − | 54.7458i | 1.66248 | − | 1.76968i | ||||
\(958\) | 1.51286 | − | 2.62035i | 0.0488783 | − | 0.0846596i | ||||
\(959\) | 15.3877 | 0.496896 | ||||||||
\(960\) | −1.26238 | − | 1.18591i | −0.0407433 | − | 0.0382751i | ||||
\(961\) | −29.7507 | − | 8.71199i | −0.959698 | − | 0.281032i | ||||
\(962\) | 3.55823i | 0.114722i | ||||||||
\(963\) | 38.7554 | − | 2.42347i | 1.24888 | − | 0.0780951i | ||||
\(964\) | 4.61436 | + | 2.66410i | 0.148619 | + | 0.0858050i | ||||
\(965\) | − | 16.1693i | − | 0.520507i | ||||||
\(966\) | 3.09047 | − | 13.1650i | 0.0994342 | − | 0.423577i | ||||
\(967\) | 33.0932 | + | 19.1063i | 1.06420 | + | 0.614419i | 0.926592 | − | 0.376068i | \(-0.122724\pi\) |
0.137612 | + | 0.990486i | \(0.456057\pi\) | |||||||
\(968\) | 13.3016 | + | 7.67968i | 0.427529 | + | 0.246834i | ||||
\(969\) | 3.25762 | − | 3.46769i | 0.104650 | − | 0.111398i | ||||
\(970\) | −3.23162 | − | 5.59732i | −0.103761 | − | 0.179719i | ||||
\(971\) | −6.71435 | + | 3.87653i | −0.215474 | + | 0.124404i | −0.603853 | − | 0.797096i | \(-0.706368\pi\) |
0.388379 | + | 0.921500i | \(0.373035\pi\) | |||||||
\(972\) | −15.5015 | − | 1.64420i | −0.497211 | − | 0.0527376i | ||||
\(973\) | −45.9210 | − | 26.5125i | −1.47216 | − | 0.849951i | ||||
\(974\) | −19.0958 | − | 33.0749i | −0.611869 | − | 1.05979i | ||||
\(975\) | 8.79659 | − | 2.65402i | 0.281716 | − | 0.0849967i | ||||
\(976\) | 7.06279i | 0.226074i | ||||||||
\(977\) | − | 45.6238i | − | 1.45963i | −0.683643 | − | 0.729817i | \(-0.739605\pi\) | ||
0.683643 | − | 0.729817i | \(-0.260395\pi\) | |||||||
\(978\) | −37.2724 | + | 11.2455i | −1.19184 | + | 0.359590i | ||||
\(979\) | 38.2249 | + | 66.2075i | 1.22167 | + | 2.11600i | ||||
\(980\) | −0.324294 | − | 0.187231i | −0.0103592 | − | 0.00598089i | ||||
\(981\) | 3.37763 | − | 2.24224i | 0.107839 | − | 0.0715892i | ||||
\(982\) | 22.0394 | − | 12.7244i | 0.703304 | − | 0.406053i | ||||
\(983\) | −1.48950 | − | 2.57989i | −0.0475077 | − | 0.0822858i | 0.841294 | − | 0.540578i | \(-0.181795\pi\) |
−0.888801 | + | 0.458293i | \(0.848461\pi\) | |||||||
\(984\) | −13.4941 | + | 14.3643i | −0.430177 | + | 0.457918i | ||||
\(985\) | −7.46384 | − | 4.30925i | −0.237818 | − | 0.137304i | ||||
\(986\) | 37.9474 | + | 21.9089i | 1.20849 | + | 0.697723i | ||||
\(987\) | −6.88009 | + | 29.3083i | −0.218996 | + | 0.932894i | ||||
\(988\) | − | 2.80906i | − | 0.0893680i | ||||||
\(989\) | −20.2967 | − | 11.7183i | −0.645398 | − | 0.372620i | ||||
\(990\) | −0.961271 | − | 15.3724i | −0.0305512 | − | 0.488566i | ||||
\(991\) | − | 3.63959i | − | 0.115615i | −0.998328 | − | 0.0578077i | \(-0.981589\pi\) | ||
0.998328 | − | 0.0578077i | \(-0.0184110\pi\) | |||||||
\(992\) | 5.51138 | + | 0.790363i | 0.174987 | + | 0.0250941i | ||||
\(993\) | 6.19546 | + | 5.82014i | 0.196607 | + | 0.184697i | ||||
\(994\) | −25.1249 | −0.796914 | ||||||||
\(995\) | 2.83976 | − | 4.91862i | 0.0900266 | − | 0.155931i | ||||
\(996\) | −9.41957 | + | 10.0270i | −0.298471 | + | 0.317718i | ||||
\(997\) | −23.0520 | − | 39.9272i | −0.730064 | − | 1.26451i | −0.956855 | − | 0.290564i | \(-0.906157\pi\) |
0.226792 | − | 0.973943i | \(-0.427176\pi\) | |||||||
\(998\) | 4.13656 | − | 7.16472i | 0.130940 | − | 0.226795i | ||||
\(999\) | −1.21302 | − | 3.26743i | −0.0383783 | − | 0.103377i |
(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 | 930.2.o.e.491.17 | yes | 40 | |
3.2 | odd | 2 | inner | 930.2.o.e.491.10 | yes | 40 | |
31.6 | odd | 6 | inner | 930.2.o.e.161.20 | yes | 40 | |
93.68 | even | 6 | inner | 930.2.o.e.161.7 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.o.e.161.7 | ✓ | 40 | 93.68 | even | 6 | inner | |
930.2.o.e.161.20 | yes | 40 | 31.6 | odd | 6 | inner | |
930.2.o.e.491.10 | yes | 40 | 3.2 | odd | 2 | inner | |
930.2.o.e.491.17 | yes | 40 | 1.1 | even | 1 | trivial |