Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [52,2,Mod(31,52)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(52, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("52.31");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 52 = 2^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 52.f (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.415222090511\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.18939904.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 47.1 | ||
Root | \(0.500000 - 1.44392i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 52.47 |
Dual form | 52.2.f.b.31.1 |
$q$-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 \(\left(\mathbb{Z}/52\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(41\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.37456 | − | 0.332548i | −0.971960 | − | 0.235147i | ||||
\(3\) | 1.47363i | 0.850798i | 0.905006 | + | 0.425399i | \(0.139866\pi\) | ||||
−0.905006 | + | 0.425399i | \(0.860134\pi\) | |||||||
\(4\) | 1.77882 | + | 0.914214i | 0.889412 | + | 0.457107i | ||||
\(5\) | 0.707107 | + | 0.707107i | 0.316228 | + | 0.316228i | 0.847316 | − | 0.531089i | \(-0.178217\pi\) |
−0.531089 | + | 0.847316i | \(0.678217\pi\) | |||||||
\(6\) | 0.490051 | − | 2.02559i | 0.200063 | − | 0.826942i | ||||
\(7\) | 1.04201 | + | 1.04201i | 0.393843 | + | 0.393843i | 0.876055 | − | 0.482212i | \(-0.160166\pi\) |
−0.482212 | + | 0.876055i | \(0.660166\pi\) | |||||||
\(8\) | −2.14108 | − | 1.84818i | −0.756985 | − | 0.653432i | ||||
\(9\) | 0.828427 | 0.276142 | ||||||||
\(10\) | −0.736813 | − | 1.20711i | −0.233001 | − | 0.381721i | ||||
\(11\) | −3.55765 | − | 3.55765i | −1.07267 | − | 1.07267i | −0.997144 | − | 0.0755273i | \(-0.975936\pi\) |
−0.0755273 | − | 0.997144i | \(-0.524064\pi\) | |||||||
\(12\) | −1.34721 | + | 2.62132i | −0.388906 | + | 0.756710i | ||||
\(13\) | −3.53553 | − | 0.707107i | −0.980581 | − | 0.196116i | ||||
\(14\) | −1.08579 | − | 1.77882i | −0.290189 | − | 0.475411i | ||||
\(15\) | −1.04201 | + | 1.04201i | −0.269046 | + | 0.269046i | ||||
\(16\) | 2.32843 | + | 3.25245i | 0.582107 | + | 0.813112i | ||||
\(17\) | 0.171573i | 0.0416125i | 0.999784 | + | 0.0208063i | \(0.00662332\pi\) | ||||
−0.999784 | + | 0.0208063i | \(0.993377\pi\) | |||||||
\(18\) | −1.13872 | − | 0.275492i | −0.268399 | − | 0.0649340i | ||||
\(19\) | 5.03127 | − | 5.03127i | 1.15425 | − | 1.15425i | 0.168562 | − | 0.985691i | \(-0.446088\pi\) |
0.985691 | − | 0.168562i | \(-0.0539124\pi\) | |||||||
\(20\) | 0.611372 | + | 1.90426i | 0.136707 | + | 0.425807i | ||||
\(21\) | −1.53553 | + | 1.53553i | −0.335081 | + | 0.335081i | ||||
\(22\) | 3.70711 | + | 6.07328i | 0.790358 | + | 1.29483i | ||||
\(23\) | 2.08402 | 0.434549 | 0.217274 | − | 0.976111i | \(-0.430283\pi\) | ||||
0.217274 | + | 0.976111i | \(0.430283\pi\) | |||||||
\(24\) | 2.72353 | − | 3.15515i | 0.555939 | − | 0.644042i | ||||
\(25\) | − | 4.00000i | − | 0.800000i | ||||||
\(26\) | 4.62465 | + | 2.14769i | 0.906969 | + | 0.421198i | ||||
\(27\) | 5.64167i | 1.08574i | ||||||||
\(28\) | 0.900933 | + | 2.80617i | 0.170260 | + | 0.530317i | ||||
\(29\) | −3.41421 | −0.634004 | −0.317002 | − | 0.948425i | \(-0.602676\pi\) | ||||
−0.317002 | + | 0.948425i | \(0.602676\pi\) | |||||||
\(30\) | 1.77882 | − | 1.08579i | 0.324767 | − | 0.198237i | ||||
\(31\) | −2.08402 | + | 2.08402i | −0.374301 | + | 0.374301i | −0.869041 | − | 0.494740i | \(-0.835263\pi\) |
0.494740 | + | 0.869041i | \(0.335263\pi\) | |||||||
\(32\) | −2.11896 | − | 5.24500i | −0.374584 | − | 0.927193i | ||||
\(33\) | 5.24264 | − | 5.24264i | 0.912627 | − | 0.912627i | ||||
\(34\) | 0.0570562 | − | 0.235837i | 0.00978506 | − | 0.0404457i | ||||
\(35\) | 1.47363i | 0.249088i | ||||||||
\(36\) | 1.47363 | + | 0.757359i | 0.245604 | + | 0.126227i | ||||
\(37\) | −6.12132 | + | 6.12132i | −1.00634 | + | 1.00634i | −0.00635908 | + | 0.999980i | \(0.502024\pi\) |
−0.999980 | + | 0.00635908i | \(0.997976\pi\) | |||||||
\(38\) | −8.58892 | + | 5.24264i | −1.39331 | + | 0.850469i | ||||
\(39\) | 1.04201 | − | 5.21005i | 0.166855 | − | 0.834276i | ||||
\(40\) | −0.207107 | − | 2.82083i | −0.0327465 | − | 0.446013i | ||||
\(41\) | 4.24264 | + | 4.24264i | 0.662589 | + | 0.662589i | 0.955990 | − | 0.293400i | \(-0.0947869\pi\) |
−0.293400 | + | 0.955990i | \(0.594787\pi\) | |||||||
\(42\) | 2.62132 | − | 1.60004i | 0.404479 | − | 0.246892i | ||||
\(43\) | −5.64167 | −0.860346 | −0.430173 | − | 0.902746i | \(-0.641548\pi\) | ||||
−0.430173 | + | 0.902746i | \(0.641548\pi\) | |||||||
\(44\) | −3.07598 | − | 9.58088i | −0.463721 | − | 1.44437i | ||||
\(45\) | 0.585786 | + | 0.585786i | 0.0873239 | + | 0.0873239i | ||||
\(46\) | −2.86461 | − | 0.693037i | −0.422364 | − | 0.102183i | ||||
\(47\) | −1.04201 | − | 1.04201i | −0.151993 | − | 0.151993i | 0.627015 | − | 0.779007i | \(-0.284277\pi\) |
−0.779007 | + | 0.627015i | \(0.784277\pi\) | |||||||
\(48\) | −4.79289 | + | 3.43123i | −0.691795 | + | 0.495255i | ||||
\(49\) | − | 4.82843i | − | 0.689775i | ||||||
\(50\) | −1.33019 | + | 5.49824i | −0.188118 | + | 0.777568i | ||||
\(51\) | −0.252834 | −0.0354039 | ||||||||
\(52\) | −5.64264 | − | 4.49005i | −0.782494 | − | 0.622658i | ||||
\(53\) | 8.24264 | 1.13221 | 0.566107 | − | 0.824332i | \(-0.308449\pi\) | ||||
0.566107 | + | 0.824332i | \(0.308449\pi\) | |||||||
\(54\) | 1.87613 | − | 7.75481i | 0.255308 | − | 1.05530i | ||||
\(55\) | − | 5.03127i | − | 0.678417i | ||||||
\(56\) | −0.305198 | − | 4.15685i | −0.0407838 | − | 0.555483i | ||||
\(57\) | 7.41421 | + | 7.41421i | 0.982037 | + | 0.982037i | ||||
\(58\) | 4.69304 | + | 1.13539i | 0.616226 | + | 0.149084i | ||||
\(59\) | 7.11529 | + | 7.11529i | 0.926332 | + | 0.926332i | 0.997467 | − | 0.0711343i | \(-0.0226619\pi\) |
−0.0711343 | + | 0.997467i | \(0.522662\pi\) | |||||||
\(60\) | −2.80617 | + | 0.900933i | −0.362275 | + | 0.116310i | ||||
\(61\) | −4.82843 | −0.618217 | −0.309108 | − | 0.951027i | \(-0.600031\pi\) | ||||
−0.309108 | + | 0.951027i | \(0.600031\pi\) | |||||||
\(62\) | 3.55765 | − | 2.17157i | 0.451822 | − | 0.275790i | ||||
\(63\) | 0.863230 | + | 0.863230i | 0.108757 | + | 0.108757i | ||||
\(64\) | 1.16843 | + | 7.91421i | 0.146053 | + | 0.989277i | ||||
\(65\) | −2.00000 | − | 3.00000i | −0.248069 | − | 0.372104i | ||||
\(66\) | −8.94975 | + | 5.46289i | −1.10164 | + | 0.672435i | ||||
\(67\) | −1.47363 | + | 1.47363i | −0.180032 | + | 0.180032i | −0.791370 | − | 0.611338i | \(-0.790632\pi\) |
0.611338 | + | 0.791370i | \(0.290632\pi\) | |||||||
\(68\) | −0.156854 | + | 0.305198i | −0.0190214 | + | 0.0370107i | ||||
\(69\) | 3.07107i | 0.369713i | ||||||||
\(70\) | 0.490051 | − | 2.02559i | 0.0585723 | − | 0.242104i | ||||
\(71\) | −9.02054 | + | 9.02054i | −1.07054 | + | 1.07054i | −0.0732252 | + | 0.997315i | \(0.523329\pi\) |
−0.997315 | + | 0.0732252i | \(0.976671\pi\) | |||||||
\(72\) | −1.77373 | − | 1.53109i | −0.209036 | − | 0.180440i | ||||
\(73\) | 1.65685 | − | 1.65685i | 0.193920 | − | 0.193920i | −0.603467 | − | 0.797388i | \(-0.706215\pi\) |
0.797388 | + | 0.603467i | \(0.206215\pi\) | |||||||
\(74\) | 10.4497 | − | 6.37848i | 1.21476 | − | 0.741483i | ||||
\(75\) | 5.89450 | 0.680639 | ||||||||
\(76\) | 13.5494 | − | 4.35009i | 1.55422 | − | 0.498989i | ||||
\(77\) | − | 7.41421i | − | 0.844928i | ||||||
\(78\) | −3.16490 | + | 6.81501i | −0.358354 | + | 0.771648i | ||||
\(79\) | − | 0.863230i | − | 0.0971210i | −0.998820 | − | 0.0485605i | \(-0.984537\pi\) | ||
0.998820 | − | 0.0485605i | \(-0.0154634\pi\) | |||||||
\(80\) | −0.653382 | + | 3.94628i | −0.0730504 | + | 0.441207i | ||||
\(81\) | −5.82843 | −0.647603 | ||||||||
\(82\) | −4.42088 | − | 7.24264i | −0.488204 | − | 0.799816i | ||||
\(83\) | −0.610396 | + | 0.610396i | −0.0669996 | + | 0.0669996i | −0.739813 | − | 0.672813i | \(-0.765086\pi\) |
0.672813 | + | 0.739813i | \(0.265086\pi\) | |||||||
\(84\) | −4.13525 | + | 1.32764i | −0.451193 | + | 0.144857i | ||||
\(85\) | −0.121320 | + | 0.121320i | −0.0131590 | + | 0.0131590i | ||||
\(86\) | 7.75481 | + | 1.87613i | 0.836222 | + | 0.202308i | ||||
\(87\) | − | 5.03127i | − | 0.539409i | ||||||
\(88\) | 1.04201 | + | 14.1924i | 0.111079 | + | 1.51291i | ||||
\(89\) | −2.24264 | + | 2.24264i | −0.237719 | + | 0.237719i | −0.815905 | − | 0.578186i | \(-0.803761\pi\) |
0.578186 | + | 0.815905i | \(0.303761\pi\) | |||||||
\(90\) | −0.610396 | − | 1.00000i | −0.0643414 | − | 0.105409i | ||||
\(91\) | −2.94725 | − | 4.42088i | −0.308956 | − | 0.463434i | ||||
\(92\) | 3.70711 | + | 1.90524i | 0.386493 | + | 0.198635i | ||||
\(93\) | −3.07107 | − | 3.07107i | −0.318455 | − | 0.318455i | ||||
\(94\) | 1.08579 | + | 1.77882i | 0.111990 | + | 0.183472i | ||||
\(95\) | 7.11529 | 0.730014 | ||||||||
\(96\) | 7.72916 | − | 3.12256i | 0.788854 | − | 0.318695i | ||||
\(97\) | −2.41421 | − | 2.41421i | −0.245126 | − | 0.245126i | 0.573841 | − | 0.818967i | \(-0.305453\pi\) |
−0.818967 | + | 0.573841i | \(0.805453\pi\) | |||||||
\(98\) | −1.60568 | + | 6.63696i | −0.162199 | + | 0.670434i | ||||
\(99\) | −2.94725 | − | 2.94725i | −0.296210 | − | 0.296210i | ||||
\(100\) | 3.65685 | − | 7.11529i | 0.365685 | − | 0.711529i | ||||
\(101\) | 5.17157i | 0.514591i | 0.966333 | + | 0.257295i | \(0.0828313\pi\) | ||||
−0.966333 | + | 0.257295i | \(0.917169\pi\) | |||||||
\(102\) | 0.347535 | + | 0.0840795i | 0.0344111 | + | 0.00832511i | ||||
\(103\) | 15.0938 | 1.48724 | 0.743619 | − | 0.668603i | \(-0.233108\pi\) | ||||
0.743619 | + | 0.668603i | \(0.233108\pi\) | |||||||
\(104\) | 6.26299 | + | 8.04829i | 0.614137 | + | 0.789200i | ||||
\(105\) | −2.17157 | −0.211924 | ||||||||
\(106\) | −11.3300 | − | 2.74107i | −1.10047 | − | 0.266237i | ||||
\(107\) | − | 11.2833i | − | 1.09080i | −0.838175 | − | 0.545401i | \(-0.816377\pi\) | ||
0.838175 | − | 0.545401i | \(-0.183623\pi\) | |||||||
\(108\) | −5.15769 | + | 10.0355i | −0.496299 | + | 0.965670i | ||||
\(109\) | −3.29289 | − | 3.29289i | −0.315402 | − | 0.315402i | 0.531596 | − | 0.846998i | \(-0.321592\pi\) |
−0.846998 | + | 0.531596i | \(0.821592\pi\) | |||||||
\(110\) | −1.67314 | + | 6.91578i | −0.159528 | + | 0.659394i | ||||
\(111\) | −9.02054 | − | 9.02054i | −0.856191 | − | 0.856191i | ||||
\(112\) | −0.962841 | + | 5.81533i | −0.0909799 | + | 0.549497i | ||||
\(113\) | −7.31371 | −0.688016 | −0.344008 | − | 0.938967i | \(-0.611785\pi\) | ||||
−0.344008 | + | 0.938967i | \(0.611785\pi\) | |||||||
\(114\) | −7.72569 | − | 12.6569i | −0.723577 | − | 1.18542i | ||||
\(115\) | 1.47363 | + | 1.47363i | 0.137416 | + | 0.137416i | ||||
\(116\) | −6.07328 | − | 3.12132i | −0.563890 | − | 0.289807i | ||||
\(117\) | −2.92893 | − | 0.585786i | −0.270780 | − | 0.0541560i | ||||
\(118\) | −7.41421 | − | 12.1466i | −0.682534 | − | 1.11818i | ||||
\(119\) | −0.178781 | + | 0.178781i | −0.0163888 | + | 0.0163888i | ||||
\(120\) | 4.15685 | − | 0.305198i | 0.379467 | − | 0.0278606i | ||||
\(121\) | 14.3137i | 1.30125i | ||||||||
\(122\) | 6.63696 | + | 1.60568i | 0.600882 | + | 0.145372i | ||||
\(123\) | −6.25206 | + | 6.25206i | −0.563730 | + | 0.563730i | ||||
\(124\) | −5.61235 | + | 1.80187i | −0.504004 | + | 0.161812i | ||||
\(125\) | 6.36396 | − | 6.36396i | 0.569210 | − | 0.569210i | ||||
\(126\) | −0.899495 | − | 1.47363i | −0.0801334 | − | 0.131281i | ||||
\(127\) | −13.8730 | −1.23103 | −0.615516 | − | 0.788124i | \(-0.711052\pi\) | ||||
−0.615516 | + | 0.788124i | \(0.711052\pi\) | |||||||
\(128\) | 1.02578 | − | 11.2671i | 0.0906673 | − | 0.995881i | ||||
\(129\) | − | 8.31371i | − | 0.731981i | ||||||
\(130\) | 1.75147 | + | 4.78877i | 0.153614 | + | 0.420003i | ||||
\(131\) | − | 2.69442i | − | 0.235412i | −0.993048 | − | 0.117706i | \(-0.962446\pi\) | ||
0.993048 | − | 0.117706i | \(-0.0375541\pi\) | |||||||
\(132\) | 14.1186 | − | 4.53284i | 1.22887 | − | 0.394533i | ||||
\(133\) | 10.4853 | 0.909189 | ||||||||
\(134\) | 2.51564 | − | 1.53553i | 0.217318 | − | 0.132650i | ||||
\(135\) | −3.98926 | + | 3.98926i | −0.343341 | + | 0.343341i | ||||
\(136\) | 0.317098 | − | 0.367351i | 0.0271910 | − | 0.0315001i | ||||
\(137\) | −2.65685 | + | 2.65685i | −0.226990 | + | 0.226990i | −0.811434 | − | 0.584444i | \(-0.801313\pi\) |
0.584444 | + | 0.811434i | \(0.301313\pi\) | |||||||
\(138\) | 1.02128 | − | 4.22136i | 0.0869369 | − | 0.359346i | ||||
\(139\) | 3.20009i | 0.271428i | 0.990748 | + | 0.135714i | \(0.0433328\pi\) | ||||
−0.990748 | + | 0.135714i | \(0.956667\pi\) | |||||||
\(140\) | −1.34721 | + | 2.62132i | −0.113860 | + | 0.221542i | ||||
\(141\) | 1.53553 | − | 1.53553i | 0.129315 | − | 0.129315i | ||||
\(142\) | 15.3990 | − | 9.39949i | 1.29226 | − | 0.788788i | ||||
\(143\) | 10.0625 | + | 15.0938i | 0.841472 | + | 1.26221i | ||||
\(144\) | 1.92893 | + | 2.69442i | 0.160744 | + | 0.224535i | ||||
\(145\) | −2.41421 | − | 2.41421i | −0.200490 | − | 0.200490i | ||||
\(146\) | −2.82843 | + | 1.72646i | −0.234082 | + | 0.142883i | ||||
\(147\) | 7.11529 | 0.586860 | ||||||||
\(148\) | −16.4849 | + | 5.29256i | −1.35505 | + | 0.435045i | ||||
\(149\) | 10.4853 | + | 10.4853i | 0.858988 | + | 0.858988i | 0.991219 | − | 0.132231i | \(-0.0422141\pi\) |
−0.132231 | + | 0.991219i | \(0.542214\pi\) | |||||||
\(150\) | −8.10234 | − | 1.96021i | −0.661553 | − | 0.160050i | ||||
\(151\) | 11.1046 | + | 11.1046i | 0.903676 | + | 0.903676i | 0.995752 | − | 0.0920760i | \(-0.0293503\pi\) |
−0.0920760 | + | 0.995752i | \(0.529350\pi\) | |||||||
\(152\) | −20.0711 | + | 1.47363i | −1.62798 | + | 0.119527i | ||||
\(153\) | 0.142136i | 0.0114910i | ||||||||
\(154\) | −2.46558 | + | 10.1913i | −0.198682 | + | 0.821236i | ||||
\(155\) | −2.94725 | −0.236729 | ||||||||
\(156\) | 6.61666 | − | 8.31515i | 0.529756 | − | 0.665745i | ||||
\(157\) | 12.0000 | 0.957704 | 0.478852 | − | 0.877896i | \(-0.341053\pi\) | ||||
0.478852 | + | 0.877896i | \(0.341053\pi\) | |||||||
\(158\) | −0.287065 | + | 1.18656i | −0.0228377 | + | 0.0943977i | ||||
\(159\) | 12.1466i | 0.963285i | ||||||||
\(160\) | 2.21044 | − | 5.20711i | 0.174751 | − | 0.411658i | ||||
\(161\) | 2.17157 | + | 2.17157i | 0.171144 | + | 0.171144i | ||||
\(162\) | 8.01152 | + | 1.93823i | 0.629444 | + | 0.152282i | ||||
\(163\) | −2.69442 | − | 2.69442i | −0.211043 | − | 0.211043i | 0.593667 | − | 0.804710i | \(-0.297679\pi\) |
−0.804710 | + | 0.593667i | \(0.797679\pi\) | |||||||
\(164\) | 3.66823 | + | 11.4256i | 0.286441 | + | 0.892189i | ||||
\(165\) | 7.41421 | 0.577196 | ||||||||
\(166\) | 1.04201 | − | 0.636039i | 0.0808757 | − | 0.0493662i | ||||
\(167\) | −0.863230 | − | 0.863230i | −0.0667987 | − | 0.0667987i | 0.672918 | − | 0.739717i | \(-0.265041\pi\) |
−0.739717 | + | 0.672918i | \(0.765041\pi\) | |||||||
\(168\) | 6.12565 | − | 0.449747i | 0.472604 | − | 0.0346988i | ||||
\(169\) | 12.0000 | + | 5.00000i | 0.923077 | + | 0.384615i | ||||
\(170\) | 0.207107 | − | 0.126417i | 0.0158844 | − | 0.00969575i | ||||
\(171\) | 4.16804 | − | 4.16804i | 0.318738 | − | 0.318738i | ||||
\(172\) | −10.0355 | − | 5.15769i | −0.765202 | − | 0.393270i | ||||
\(173\) | − | 24.3848i | − | 1.85394i | −0.375135 | − | 0.926970i | \(-0.622404\pi\) | ||
0.375135 | − | 0.926970i | \(-0.377596\pi\) | |||||||
\(174\) | −1.67314 | + | 6.91578i | −0.126840 | + | 0.524284i | ||||
\(175\) | 4.16804 | − | 4.16804i | 0.315074 | − | 0.315074i | ||||
\(176\) | 3.28735 | − | 19.8548i | 0.247793 | − | 1.49661i | ||||
\(177\) | −10.4853 | + | 10.4853i | −0.788122 | + | 0.788122i | ||||
\(178\) | 3.82843 | − | 2.33686i | 0.286953 | − | 0.175155i | ||||
\(179\) | −12.7570 | −0.953500 | −0.476750 | − | 0.879039i | \(-0.658185\pi\) | ||||
−0.476750 | + | 0.879039i | \(0.658185\pi\) | |||||||
\(180\) | 0.506477 | + | 1.57754i | 0.0377506 | + | 0.117583i | ||||
\(181\) | 8.58579i | 0.638176i | 0.947725 | + | 0.319088i | \(0.103377\pi\) | ||||
−0.947725 | + | 0.319088i | \(0.896623\pi\) | |||||||
\(182\) | 2.58102 | + | 7.05686i | 0.191318 | + | 0.523089i | ||||
\(183\) | − | 7.11529i | − | 0.525978i | ||||||
\(184\) | −4.46205 | − | 3.85166i | −0.328947 | − | 0.283948i | ||||
\(185\) | −8.65685 | −0.636465 | ||||||||
\(186\) | 3.20009 | + | 5.24264i | 0.234642 | + | 0.384409i | ||||
\(187\) | 0.610396 | − | 0.610396i | 0.0446366 | − | 0.0446366i | ||||
\(188\) | −0.900933 | − | 2.80617i | −0.0657073 | − | 0.204661i | ||||
\(189\) | −5.87868 | + | 5.87868i | −0.427611 | + | 0.427611i | ||||
\(190\) | −9.78039 | − | 2.36618i | −0.709544 | − | 0.171661i | ||||
\(191\) | − | 16.8203i | − | 1.21707i | −0.793526 | − | 0.608536i | \(-0.791757\pi\) | ||
0.793526 | − | 0.608536i | \(-0.208243\pi\) | |||||||
\(192\) | −11.6626 | + | 1.72183i | −0.841675 | + | 0.124262i | ||||
\(193\) | 8.07107 | − | 8.07107i | 0.580968 | − | 0.580968i | −0.354201 | − | 0.935169i | \(-0.615247\pi\) |
0.935169 | + | 0.354201i | \(0.115247\pi\) | |||||||
\(194\) | 2.51564 | + | 4.12132i | 0.180612 | + | 0.295894i | ||||
\(195\) | 4.42088 | − | 2.94725i | 0.316586 | − | 0.211057i | ||||
\(196\) | 4.41421 | − | 8.58892i | 0.315301 | − | 0.613494i | ||||
\(197\) | 2.60660 | + | 2.60660i | 0.185713 | + | 0.185713i | 0.793840 | − | 0.608127i | \(-0.208079\pi\) |
−0.608127 | + | 0.793840i | \(0.708079\pi\) | |||||||
\(198\) | 3.07107 | + | 5.03127i | 0.218251 | + | 0.357557i | ||||
\(199\) | −20.4827 | −1.45198 | −0.725988 | − | 0.687707i | \(-0.758617\pi\) | ||||
−0.725988 | + | 0.687707i | \(0.758617\pi\) | |||||||
\(200\) | −7.39274 | + | 8.56431i | −0.522746 | + | 0.605588i | ||||
\(201\) | −2.17157 | − | 2.17157i | −0.153171 | − | 0.153171i | ||||
\(202\) | 1.71980 | − | 7.10863i | 0.121004 | − | 0.500162i | ||||
\(203\) | −3.55765 | − | 3.55765i | −0.249698 | − | 0.249698i | ||||
\(204\) | −0.449747 | − | 0.231144i | −0.0314886 | − | 0.0161833i | ||||
\(205\) | 6.00000i | 0.419058i | ||||||||
\(206\) | −20.7473 | − | 5.01942i | −1.44554 | − | 0.349720i | ||||
\(207\) | 1.72646 | 0.119997 | ||||||||
\(208\) | −5.93240 | − | 13.1456i | −0.411338 | − | 0.911483i | ||||
\(209\) | −35.7990 | −2.47627 | ||||||||
\(210\) | 2.98495 | + | 0.722152i | 0.205981 | + | 0.0498332i | ||||
\(211\) | 19.8723i | 1.36806i | 0.729453 | + | 0.684031i | \(0.239775\pi\) | ||||
−0.729453 | + | 0.684031i | \(0.760225\pi\) | |||||||
\(212\) | 14.6622 | + | 7.53553i | 1.00700 | + | 0.517543i | ||||
\(213\) | −13.2929 | − | 13.2929i | −0.910814 | − | 0.910814i | ||||
\(214\) | −3.75225 | + | 15.5096i | −0.256499 | + | 1.06022i | ||||
\(215\) | −3.98926 | − | 3.98926i | −0.272065 | − | 0.272065i | ||||
\(216\) | 10.4268 | − | 12.0793i | 0.709457 | − | 0.821889i | ||||
\(217\) | −4.34315 | −0.294832 | ||||||||
\(218\) | 3.43123 | + | 5.62132i | 0.232392 | + | 0.380724i | ||||
\(219\) | 2.44158 | + | 2.44158i | 0.164987 | + | 0.164987i | ||||
\(220\) | 4.59966 | − | 8.94975i | 0.310109 | − | 0.603392i | ||||
\(221\) | 0.121320 | − | 0.606602i | 0.00816089 | − | 0.0408044i | ||||
\(222\) | 9.39949 | + | 15.3990i | 0.630853 | + | 1.03351i | ||||
\(223\) | 9.37810 | − | 9.37810i | 0.628004 | − | 0.628004i | −0.319562 | − | 0.947565i | \(-0.603536\pi\) |
0.947565 | + | 0.319562i | \(0.103536\pi\) | |||||||
\(224\) | 3.25736 | − | 7.67333i | 0.217641 | − | 0.512696i | ||||
\(225\) | − | 3.31371i | − | 0.220914i | ||||||
\(226\) | 10.0531 | + | 2.43216i | 0.668724 | + | 0.161785i | ||||
\(227\) | 10.9258 | − | 10.9258i | 0.725169 | − | 0.725169i | −0.244484 | − | 0.969653i | \(-0.578619\pi\) |
0.969653 | + | 0.244484i | \(0.0786186\pi\) | |||||||
\(228\) | 6.41040 | + | 19.9668i | 0.424539 | + | 1.32233i | ||||
\(229\) | 13.2929 | − | 13.2929i | 0.878419 | − | 0.878419i | −0.114952 | − | 0.993371i | \(-0.536671\pi\) |
0.993371 | + | 0.114952i | \(0.0366714\pi\) | |||||||
\(230\) | −1.53553 | − | 2.51564i | −0.101250 | − | 0.165876i | ||||
\(231\) | 10.9258 | 0.718863 | ||||||||
\(232\) | 7.31010 | + | 6.31010i | 0.479931 | + | 0.414278i | ||||
\(233\) | 21.9706i | 1.43934i | 0.694317 | + | 0.719670i | \(0.255707\pi\) | ||||
−0.694317 | + | 0.719670i | \(0.744293\pi\) | |||||||
\(234\) | 3.83119 | + | 1.77921i | 0.250453 | + | 0.116310i | ||||
\(235\) | − | 1.47363i | − | 0.0961287i | ||||||
\(236\) | 6.15196 | + | 19.1618i | 0.400458 | + | 1.24732i | ||||
\(237\) | 1.27208 | 0.0826303 | ||||||||
\(238\) | 0.305198 | − | 0.186292i | 0.0197830 | − | 0.0120755i | ||||
\(239\) | 10.2413 | − | 10.2413i | 0.662456 | − | 0.662456i | −0.293502 | − | 0.955958i | \(-0.594821\pi\) |
0.955958 | + | 0.293502i | \(0.0948208\pi\) | |||||||
\(240\) | −5.81533 | − | 0.962841i | −0.375378 | − | 0.0621511i | ||||
\(241\) | −1.07107 | + | 1.07107i | −0.0689935 | + | 0.0689935i | −0.740762 | − | 0.671768i | \(-0.765535\pi\) |
0.671768 | + | 0.740762i | \(0.265535\pi\) | |||||||
\(242\) | 4.76000 | − | 19.6750i | 0.305984 | − | 1.26476i | ||||
\(243\) | 8.33609i | 0.534760i | ||||||||
\(244\) | −8.58892 | − | 4.41421i | −0.549849 | − | 0.282591i | ||||
\(245\) | 3.41421 | − | 3.41421i | 0.218126 | − | 0.218126i | ||||
\(246\) | 10.6729 | − | 6.51472i | 0.680482 | − | 0.415363i | ||||
\(247\) | −21.3459 | + | 14.2306i | −1.35821 | + | 0.905471i | ||||
\(248\) | 8.31371 | − | 0.610396i | 0.527921 | − | 0.0387602i | ||||
\(249\) | −0.899495 | − | 0.899495i | −0.0570032 | − | 0.0570032i | ||||
\(250\) | −10.8640 | + | 6.63132i | −0.687097 | + | 0.419401i | ||||
\(251\) | 15.4514 | 0.975283 | 0.487641 | − | 0.873044i | \(-0.337857\pi\) | ||||
0.487641 | + | 0.873044i | \(0.337857\pi\) | |||||||
\(252\) | 0.746357 | + | 2.32471i | 0.0470161 | + | 0.146443i | ||||
\(253\) | −7.41421 | − | 7.41421i | −0.466128 | − | 0.466128i | ||||
\(254\) | 19.0693 | + | 4.61345i | 1.19651 | + | 0.289473i | ||||
\(255\) | −0.178781 | − | 0.178781i | −0.0111957 | − | 0.0111957i | ||||
\(256\) | −5.15685 | + | 15.1462i | −0.322303 | + | 0.946636i | ||||
\(257\) | − | 10.6569i | − | 0.664756i | −0.943146 | − | 0.332378i | \(-0.892149\pi\) | ||
0.943146 | − | 0.332378i | \(-0.107851\pi\) | |||||||
\(258\) | −2.76471 | + | 11.4277i | −0.172123 | + | 0.711456i | ||||
\(259\) | −12.7570 | −0.792679 | ||||||||
\(260\) | −0.815007 | − | 7.16490i | −0.0505446 | − | 0.444348i | ||||
\(261\) | −2.82843 | −0.175075 | ||||||||
\(262\) | −0.896023 | + | 3.70363i | −0.0553565 | + | 0.228811i | ||||
\(263\) | − | 13.0098i | − | 0.802218i | −0.916030 | − | 0.401109i | \(-0.868625\pi\) | ||
0.916030 | − | 0.401109i | \(-0.131375\pi\) | |||||||
\(264\) | −20.9143 | + | 1.53553i | −1.28718 | + | 0.0945056i | ||||
\(265\) | 5.82843 | + | 5.82843i | 0.358037 | + | 0.358037i | ||||
\(266\) | −14.4126 | − | 3.48686i | −0.883695 | − | 0.213793i | ||||
\(267\) | −3.30481 | − | 3.30481i | −0.202251 | − | 0.202251i | ||||
\(268\) | −3.96853 | + | 1.27411i | −0.242416 | + | 0.0778288i | ||||
\(269\) | 20.1421 | 1.22809 | 0.614044 | − | 0.789272i | \(-0.289542\pi\) | ||||
0.614044 | + | 0.789272i | \(0.289542\pi\) | |||||||
\(270\) | 6.81010 | − | 4.15685i | 0.414449 | − | 0.252978i | ||||
\(271\) | 4.85249 | + | 4.85249i | 0.294768 | + | 0.294768i | 0.838960 | − | 0.544192i | \(-0.183164\pi\) |
−0.544192 | + | 0.838960i | \(0.683164\pi\) | |||||||
\(272\) | −0.558032 | + | 0.399495i | −0.0338357 | + | 0.0242229i | ||||
\(273\) | 6.51472 | − | 4.34315i | 0.394289 | − | 0.262859i | ||||
\(274\) | 4.53553 | − | 2.76847i | 0.274002 | − | 0.167249i | ||||
\(275\) | −14.2306 | + | 14.2306i | −0.858137 | + | 0.858137i | ||||
\(276\) | −2.80761 | + | 5.46289i | −0.168998 | + | 0.328827i | ||||
\(277\) | 6.00000i | 0.360505i | 0.983620 | + | 0.180253i | \(0.0576915\pi\) | ||||
−0.983620 | + | 0.180253i | \(0.942309\pi\) | |||||||
\(278\) | 1.06418 | − | 4.39871i | 0.0638254 | − | 0.263817i | ||||
\(279\) | −1.72646 | + | 1.72646i | −0.103360 | + | 0.103360i | ||||
\(280\) | 2.72353 | − | 3.15515i | 0.162762 | − | 0.188556i | ||||
\(281\) | −16.2426 | + | 16.2426i | −0.968955 | + | 0.968955i | −0.999532 | − | 0.0305777i | \(-0.990265\pi\) |
0.0305777 | + | 0.999532i | \(0.490265\pi\) | |||||||
\(282\) | −2.62132 | + | 1.60004i | −0.156097 | + | 0.0952812i | ||||
\(283\) | 24.2931 | 1.44408 | 0.722038 | − | 0.691853i | \(-0.243205\pi\) | ||||
0.722038 | + | 0.691853i | \(0.243205\pi\) | |||||||
\(284\) | −24.2926 | + | 7.79925i | −1.44150 | + | 0.462800i | ||||
\(285\) | 10.4853i | 0.621094i | ||||||||
\(286\) | −8.81214 | − | 24.0936i | −0.521073 | − | 1.42469i | ||||
\(287\) | 8.84175i | 0.521912i | ||||||||
\(288\) | −1.75541 | − | 4.34510i | −0.103438 | − | 0.256037i | ||||
\(289\) | 16.9706 | 0.998268 | ||||||||
\(290\) | 2.51564 | + | 4.12132i | 0.147723 | + | 0.242012i | ||||
\(291\) | 3.55765 | − | 3.55765i | 0.208553 | − | 0.208553i | ||||
\(292\) | 4.46197 | − | 1.43253i | 0.261117 | − | 0.0838326i | ||||
\(293\) | −0.807612 | + | 0.807612i | −0.0471812 | + | 0.0471812i | −0.730304 | − | 0.683123i | \(-0.760621\pi\) |
0.683123 | + | 0.730304i | \(0.260621\pi\) | |||||||
\(294\) | −9.78039 | − | 2.36618i | −0.570404 | − | 0.137998i | ||||
\(295\) | 10.0625i | 0.585864i | ||||||||
\(296\) | 24.4196 | − | 1.79289i | 1.41936 | − | 0.104210i | ||||
\(297\) | 20.0711 | − | 20.0711i | 1.16464 | − | 1.16464i | ||||
\(298\) | −10.9258 | − | 17.8995i | −0.632913 | − | 1.03689i | ||||
\(299\) | −7.36813 | − | 1.47363i | −0.426110 | − | 0.0852220i | ||||
\(300\) | 10.4853 | + | 5.38883i | 0.605368 | + | 0.311125i | ||||
\(301\) | −5.87868 | − | 5.87868i | −0.338841 | − | 0.338841i | ||||
\(302\) | −11.5711 | − | 18.9567i | −0.665840 | − | 1.09083i | ||||
\(303\) | −7.62096 | −0.437813 | ||||||||
\(304\) | 28.0789 | + | 4.64901i | 1.61044 | + | 0.266639i | ||||
\(305\) | −3.41421 | − | 3.41421i | −0.195497 | − | 0.195497i | ||||
\(306\) | 0.0472669 | − | 0.195374i | 0.00270207 | − | 0.0111688i | ||||
\(307\) | −1.72646 | − | 1.72646i | −0.0985343 | − | 0.0985343i | 0.656121 | − | 0.754656i | \(-0.272196\pi\) |
−0.754656 | + | 0.656121i | \(0.772196\pi\) | |||||||
\(308\) | 6.77817 | − | 13.1886i | 0.386222 | − | 0.751489i | ||||
\(309\) | 22.2426i | 1.26534i | ||||||||
\(310\) | 4.05117 | + | 0.980103i | 0.230091 | + | 0.0556661i | ||||
\(311\) | −29.6820 | −1.68311 | −0.841555 | − | 0.540171i | \(-0.818359\pi\) | ||||
−0.841555 | + | 0.540171i | \(0.818359\pi\) | |||||||
\(312\) | −11.8602 | + | 9.22930i | −0.671450 | + | 0.522506i | ||||
\(313\) | 3.48528 | 0.197000 | 0.0984999 | − | 0.995137i | \(-0.468596\pi\) | ||||
0.0984999 | + | 0.995137i | \(0.468596\pi\) | |||||||
\(314\) | −16.4947 | − | 3.99058i | −0.930850 | − | 0.225201i | ||||
\(315\) | 1.22079i | 0.0687838i | ||||||||
\(316\) | 0.789177 | − | 1.53553i | 0.0443946 | − | 0.0863805i | ||||
\(317\) | −15.6569 | − | 15.6569i | −0.879377 | − | 0.879377i | 0.114093 | − | 0.993470i | \(-0.463604\pi\) |
−0.993470 | + | 0.114093i | \(0.963604\pi\) | |||||||
\(318\) | 4.03932 | − | 16.6962i | 0.226514 | − | 0.936275i | ||||
\(319\) | 12.1466 | + | 12.1466i | 0.680077 | + | 0.680077i | ||||
\(320\) | −4.76999 | + | 6.42240i | −0.266651 | + | 0.359023i | ||||
\(321\) | 16.6274 | 0.928052 | ||||||||
\(322\) | −2.26280 | − | 3.70711i | −0.126101 | − | 0.206589i | ||||
\(323\) | 0.863230 | + | 0.863230i | 0.0480314 | + | 0.0480314i | ||||
\(324\) | −10.3677 | − | 5.32843i | −0.575986 | − | 0.296024i | ||||
\(325\) | −2.82843 | + | 14.1421i | −0.156893 | + | 0.784465i | ||||
\(326\) | 2.80761 | + | 4.59966i | 0.155499 | + | 0.254751i | ||||
\(327\) | 4.85249 | − | 4.85249i | 0.268343 | − | 0.268343i | ||||
\(328\) | −1.24264 | − | 16.9250i | −0.0686134 | − | 0.934527i | ||||
\(329\) | − | 2.17157i | − | 0.119723i | ||||||
\(330\) | −10.1913 | − | 2.46558i | −0.561011 | − | 0.135726i | ||||
\(331\) | 4.77844 | − | 4.77844i | 0.262647 | − | 0.262647i | −0.563482 | − | 0.826129i | \(-0.690538\pi\) |
0.826129 | + | 0.563482i | \(0.190538\pi\) | |||||||
\(332\) | −1.64382 | + | 0.527754i | −0.0902163 | + | 0.0289643i | ||||
\(333\) | −5.07107 | + | 5.07107i | −0.277893 | + | 0.277893i | ||||
\(334\) | 0.899495 | + | 1.47363i | 0.0492182 | + | 0.0806332i | ||||
\(335\) | −2.08402 | −0.113862 | ||||||||
\(336\) | −8.56963 | − | 1.41887i | −0.467511 | − | 0.0774056i | ||||
\(337\) | 13.8284i | 0.753282i | 0.926359 | + | 0.376641i | \(0.122921\pi\) | ||||
−0.926359 | + | 0.376641i | \(0.877079\pi\) | |||||||
\(338\) | −14.8320 | − | 10.8634i | −0.806753 | − | 0.590889i | ||||
\(339\) | − | 10.7777i | − | 0.585363i | ||||||
\(340\) | −0.326720 | + | 0.104895i | −0.0177189 | + | 0.00568872i | ||||
\(341\) | 14.8284 | 0.803004 | ||||||||
\(342\) | −7.11529 | + | 4.34315i | −0.384751 | + | 0.234850i | ||||
\(343\) | 12.3253 | − | 12.3253i | 0.665506 | − | 0.665506i | ||||
\(344\) | 12.0793 | + | 10.4268i | 0.651270 | + | 0.562178i | ||||
\(345\) | −2.17157 | + | 2.17157i | −0.116914 | + | 0.116914i | ||||
\(346\) | −8.10911 | + | 33.5183i | −0.435948 | + | 1.80196i | ||||
\(347\) | 21.5987i | 1.15948i | 0.814802 | + | 0.579740i | \(0.196846\pi\) | ||||
−0.814802 | + | 0.579740i | \(0.803154\pi\) | |||||||
\(348\) | 4.59966 | − | 8.94975i | 0.246568 | − | 0.479757i | ||||
\(349\) | −7.53553 | + | 7.53553i | −0.403368 | + | 0.403368i | −0.879418 | − | 0.476050i | \(-0.842068\pi\) |
0.476050 | + | 0.879418i | \(0.342068\pi\) | |||||||
\(350\) | −7.11529 | + | 4.34315i | −0.380328 | + | 0.232151i | ||||
\(351\) | 3.98926 | − | 19.9463i | 0.212931 | − | 1.06466i | ||||
\(352\) | −11.1213 | + | 26.1984i | −0.592768 | + | 1.39638i | ||||
\(353\) | −1.58579 | − | 1.58579i | −0.0844029 | − | 0.0844029i | 0.663645 | − | 0.748048i | \(-0.269009\pi\) |
−0.748048 | + | 0.663645i | \(0.769009\pi\) | |||||||
\(354\) | 17.8995 | − | 10.9258i | 0.951347 | − | 0.580698i | ||||
\(355\) | −12.7570 | −0.677069 | ||||||||
\(356\) | −6.03951 | + | 1.93901i | −0.320094 | + | 0.102767i | ||||
\(357\) | −0.263456 | − | 0.263456i | −0.0139436 | − | 0.0139436i | ||||
\(358\) | 17.5352 | + | 4.24230i | 0.926764 | + | 0.224213i | ||||
\(359\) | −2.08402 | − | 2.08402i | −0.109990 | − | 0.109990i | 0.649970 | − | 0.759960i | \(-0.274782\pi\) |
−0.759960 | + | 0.649970i | \(0.774782\pi\) | |||||||
\(360\) | −0.171573 | − | 2.33686i | −0.00904268 | − | 0.123163i | ||||
\(361\) | − | 31.6274i | − | 1.66460i | ||||||
\(362\) | 2.85519 | − | 11.8017i | 0.150065 | − | 0.620282i | ||||
\(363\) | −21.0930 | −1.10710 | ||||||||
\(364\) | −1.20101 | − | 10.5584i | −0.0629503 | − | 0.553409i | ||||
\(365\) | 2.34315 | 0.122646 | ||||||||
\(366\) | −2.36618 | + | 9.78039i | −0.123682 | + | 0.511229i | ||||
\(367\) | − | 3.81048i | − | 0.198906i | −0.995042 | − | 0.0994528i | \(-0.968291\pi\) | ||
0.995042 | − | 0.0994528i | \(-0.0317092\pi\) | |||||||
\(368\) | 4.85249 | + | 6.77817i | 0.252954 | + | 0.353337i | ||||
\(369\) | 3.51472 | + | 3.51472i | 0.182969 | + | 0.182969i | ||||
\(370\) | 11.8994 | + | 2.87882i | 0.618618 | + | 0.149663i | ||||
\(371\) | 8.58892 | + | 8.58892i | 0.445915 | + | 0.445915i | ||||
\(372\) | −2.65528 | − | 8.27050i | −0.137670 | − | 0.428805i | ||||
\(373\) | −14.6274 | −0.757379 | −0.378689 | − | 0.925524i | \(-0.623625\pi\) | ||||
−0.378689 | + | 0.925524i | \(0.623625\pi\) | |||||||
\(374\) | −1.04201 | + | 0.636039i | −0.0538811 | + | 0.0328888i | ||||
\(375\) | 9.37810 | + | 9.37810i | 0.484283 | + | 0.484283i | ||||
\(376\) | 0.305198 | + | 4.15685i | 0.0157394 | + | 0.214373i | ||||
\(377\) | 12.0711 | + | 2.41421i | 0.621692 | + | 0.124338i | ||||
\(378\) | 10.0355 | − | 6.12565i | 0.516172 | − | 0.315069i | ||||
\(379\) | 7.36813 | − | 7.36813i | 0.378475 | − | 0.378475i | −0.492077 | − | 0.870552i | \(-0.663762\pi\) |
0.870552 | + | 0.492077i | \(0.163762\pi\) | |||||||
\(380\) | 12.6569 | + | 6.50490i | 0.649283 | + | 0.333694i | ||||
\(381\) | − | 20.4437i | − | 1.04736i | ||||||
\(382\) | −5.59355 | + | 23.1205i | −0.286191 | + | 1.18295i | ||||
\(383\) | −0.178781 | + | 0.178781i | −0.00913527 | + | 0.00913527i | −0.711660 | − | 0.702524i | \(-0.752056\pi\) |
0.702524 | + | 0.711660i | \(0.252056\pi\) | |||||||
\(384\) | 16.6035 | + | 1.51162i | 0.847294 | + | 0.0771396i | ||||
\(385\) | 5.24264 | − | 5.24264i | 0.267190 | − | 0.267190i | ||||
\(386\) | −13.7782 | + | 8.41014i | −0.701291 | + | 0.428065i | ||||
\(387\) | −4.67371 | −0.237578 | ||||||||
\(388\) | −2.08735 | − | 6.50157i | −0.105969 | − | 0.330067i | ||||
\(389\) | 6.14214i | 0.311419i | 0.987803 | + | 0.155709i | \(0.0497663\pi\) | ||||
−0.987803 | + | 0.155709i | \(0.950234\pi\) | |||||||
\(390\) | −7.05686 | + | 2.58102i | −0.357338 | + | 0.130695i | ||||
\(391\) | 0.357562i | 0.0180827i | ||||||||
\(392\) | −8.92382 | + | 10.3380i | −0.450721 | + | 0.522150i | ||||
\(393\) | 3.97056 | 0.200288 | ||||||||
\(394\) | −2.71611 | − | 4.44975i | −0.136835 | − | 0.224175i | ||||
\(395\) | 0.610396 | − | 0.610396i | 0.0307123 | − | 0.0307123i | ||||
\(396\) | −2.54822 | − | 7.93706i | −0.128053 | − | 0.398852i | ||||
\(397\) | −18.4853 | + | 18.4853i | −0.927750 | + | 0.927750i | −0.997560 | − | 0.0698106i | \(-0.977761\pi\) |
0.0698106 | + | 0.997560i | \(0.477761\pi\) | |||||||
\(398\) | 28.1546 | + | 6.81147i | 1.41126 | + | 0.341428i | ||||
\(399\) | 15.4514i | 0.773537i | ||||||||
\(400\) | 13.0098 | − | 9.31371i | 0.650490 | − | 0.465685i | ||||
\(401\) | 2.51472 | − | 2.51472i | 0.125579 | − | 0.125579i | −0.641524 | − | 0.767103i | \(-0.721698\pi\) |
0.767103 | + | 0.641524i | \(0.221698\pi\) | |||||||
\(402\) | 2.26280 | + | 3.70711i | 0.112858 | + | 0.184894i | ||||
\(403\) | 8.84175 | − | 5.89450i | 0.440439 | − | 0.293626i | ||||
\(404\) | −4.72792 | + | 9.19932i | −0.235223 | + | 0.457683i | ||||
\(405\) | −4.12132 | − | 4.12132i | −0.204790 | − | 0.204790i | ||||
\(406\) | 3.70711 | + | 6.07328i | 0.183981 | + | 0.301412i | ||||
\(407\) | 43.5550 | 2.15894 | ||||||||
\(408\) | 0.541338 | + | 0.467284i | 0.0268002 | + | 0.0231340i | ||||
\(409\) | −23.1421 | − | 23.1421i | −1.14430 | − | 1.14430i | −0.987654 | − | 0.156651i | \(-0.949930\pi\) |
−0.156651 | − | 0.987654i | \(-0.550070\pi\) | |||||||
\(410\) | 1.99529 | − | 8.24735i | 0.0985403 | − | 0.407308i | ||||
\(411\) | −3.91521 | − | 3.91521i | −0.193123 | − | 0.193123i | ||||
\(412\) | 26.8492 | + | 13.7990i | 1.32277 | + | 0.679827i | ||||
\(413\) | 14.8284i | 0.729659i | ||||||||
\(414\) | −2.37312 | − | 0.574131i | −0.116633 | − | 0.0282170i | ||||
\(415\) | −0.863230 | −0.0423743 | ||||||||
\(416\) | 3.78290 | + | 20.0422i | 0.185472 | + | 0.982650i | ||||
\(417\) | −4.71573 | −0.230930 | ||||||||
\(418\) | 49.2078 | + | 11.9049i | 2.40683 | + | 0.582287i | ||||
\(419\) | − | 5.64167i | − | 0.275614i | −0.990459 | − | 0.137807i | \(-0.955995\pi\) | ||
0.990459 | − | 0.137807i | \(-0.0440053\pi\) | |||||||
\(420\) | −3.86285 | − | 1.98528i | −0.188488 | − | 0.0968718i | ||||
\(421\) | −24.0208 | − | 24.0208i | −1.17070 | − | 1.17070i | −0.982042 | − | 0.188661i | \(-0.939585\pi\) |
−0.188661 | − | 0.982042i | \(-0.560415\pi\) | |||||||
\(422\) | 6.60848 | − | 27.3156i | 0.321696 | − | 1.32970i | ||||
\(423\) | −0.863230 | − | 0.863230i | −0.0419717 | − | 0.0419717i | ||||
\(424\) | −17.6481 | − | 15.2339i | −0.857069 | − | 0.739825i | ||||
\(425\) | 0.686292 | 0.0332900 | ||||||||
\(426\) | 13.8513 | + | 22.6924i | 0.671100 | + | 1.09945i | ||||
\(427\) | −5.03127 | − | 5.03127i | −0.243480 | − | 0.243480i | ||||
\(428\) | 10.3154 | − | 20.0711i | 0.498613 | − | 0.970172i | ||||
\(429\) | −22.2426 | + | 14.8284i | −1.07388 | + | 0.715923i | ||||
\(430\) | 4.15685 | + | 6.81010i | 0.200461 | + | 0.328412i | ||||
\(431\) | −15.7783 | + | 15.7783i | −0.760012 | + | 0.760012i | −0.976324 | − | 0.216312i | \(-0.930597\pi\) |
0.216312 | + | 0.976324i | \(0.430597\pi\) | |||||||
\(432\) | −18.3492 | + | 13.1362i | −0.882828 | + | 0.632016i | ||||
\(433\) | 32.3137i | 1.55290i | 0.630180 | + | 0.776449i | \(0.282981\pi\) | ||||
−0.630180 | + | 0.776449i | \(0.717019\pi\) | |||||||
\(434\) | 5.96991 | + | 1.44430i | 0.286565 | + | 0.0693288i | ||||
\(435\) | 3.55765 | − | 3.55765i | 0.170576 | − | 0.170576i | ||||
\(436\) | −2.84707 | − | 8.86788i | −0.136350 | − | 0.424695i | ||||
\(437\) | 10.4853 | − | 10.4853i | 0.501579 | − | 0.501579i | ||||
\(438\) | −2.54416 | − | 4.16804i | −0.121564 | − | 0.199157i | ||||
\(439\) | −12.5041 | −0.596790 | −0.298395 | − | 0.954443i | \(-0.596451\pi\) | ||||
−0.298395 | + | 0.954443i | \(0.596451\pi\) | |||||||
\(440\) | −9.29872 | + | 10.7723i | −0.443299 | + | 0.513551i | ||||
\(441\) | − | 4.00000i | − | 0.190476i | ||||||
\(442\) | −0.368486 | + | 0.793465i | −0.0175271 | + | 0.0377413i | ||||
\(443\) | − | 6.14734i | − | 0.292069i | −0.989280 | − | 0.146034i | \(-0.953349\pi\) | ||
0.989280 | − | 0.146034i | \(-0.0466510\pi\) | |||||||
\(444\) | −7.79925 | − | 24.2926i | −0.370136 | − | 1.15288i | ||||
\(445\) | −3.17157 | −0.150347 | ||||||||
\(446\) | −16.0094 | + | 9.77208i | −0.758068 | + | 0.462721i | ||||
\(447\) | −15.4514 | + | 15.4514i | −0.730825 | + | 0.730825i | ||||
\(448\) | −7.02918 | + | 9.46421i | −0.332098 | + | 0.447142i | ||||
\(449\) | 25.7279 | − | 25.7279i | 1.21418 | − | 1.21418i | 0.244535 | − | 0.969640i | \(-0.421365\pi\) |
0.969640 | − | 0.244535i | \(-0.0786354\pi\) | |||||||
\(450\) | −1.10197 | + | 4.55489i | −0.0519472 | + | 0.214719i | ||||
\(451\) | − | 30.1876i | − | 1.42148i | ||||||
\(452\) | −13.0098 | − | 6.68629i | −0.611929 | − | 0.314497i | ||||
\(453\) | −16.3640 | + | 16.3640i | −0.768846 | + | 0.768846i | ||||
\(454\) | −18.6515 | + | 11.3848i | −0.875357 | + | 0.534314i | ||||
\(455\) | 1.04201 | − | 5.21005i | 0.0488502 | − | 0.244251i | ||||
\(456\) | −2.17157 | − | 29.5772i | −0.101693 | − | 1.38508i | ||||
\(457\) | 0.585786 | + | 0.585786i | 0.0274019 | + | 0.0274019i | 0.720675 | − | 0.693273i | \(-0.243832\pi\) |
−0.693273 | + | 0.720675i | \(0.743832\pi\) | |||||||
\(458\) | −22.6924 | + | 13.8513i | −1.06035 | + | 0.647231i | ||||
\(459\) | −0.967957 | −0.0451804 | ||||||||
\(460\) | 1.27411 | + | 3.96853i | 0.0594058 | + | 0.185034i | ||||
\(461\) | 6.46447 | + | 6.46447i | 0.301080 | + | 0.301080i | 0.841436 | − | 0.540356i | \(-0.181710\pi\) |
−0.540356 | + | 0.841436i | \(0.681710\pi\) | |||||||
\(462\) | −15.0181 | − | 3.63335i | −0.698706 | − | 0.169039i | ||||
\(463\) | −20.9883 | − | 20.9883i | −0.975410 | − | 0.975410i | 0.0242948 | − | 0.999705i | \(-0.492266\pi\) |
−0.999705 | + | 0.0242948i | \(0.992266\pi\) | |||||||
\(464\) | −7.94975 | − | 11.1046i | −0.369058 | − | 0.515516i | ||||
\(465\) | − | 4.34315i | − | 0.201409i | ||||||
\(466\) | 7.30627 | − | 30.1998i | 0.338456 | − | 1.39898i | ||||
\(467\) | 21.3459 | 0.987770 | 0.493885 | − | 0.869527i | \(-0.335576\pi\) | ||||
0.493885 | + | 0.869527i | \(0.335576\pi\) | |||||||
\(468\) | −4.67452 | − | 3.71968i | −0.216080 | − | 0.171942i | ||||
\(469\) | −3.07107 | −0.141809 | ||||||||
\(470\) | −0.490051 | + | 2.02559i | −0.0226044 | + | 0.0934333i | ||||
\(471\) | 17.6835i | 0.814813i | ||||||||
\(472\) | −2.08402 | − | 28.3848i | −0.0959249 | − | 1.30652i | ||||
\(473\) | 20.0711 | + | 20.0711i | 0.922869 | + | 0.922869i | ||||
\(474\) | −1.74855 | − | 0.423027i | −0.0803134 | − | 0.0194303i | ||||
\(475\) | −20.1251 | − | 20.1251i | −0.923403 | − | 0.923403i | ||||
\(476\) | −0.481463 | + | 0.154576i | −0.0220678 | + | 0.00708496i | ||||
\(477\) | 6.82843 | 0.312652 | ||||||||
\(478\) | −17.4830 | + | 10.6716i | −0.799656 | + | 0.488106i | ||||
\(479\) | −1.90524 | − | 1.90524i | −0.0870527 | − | 0.0870527i | 0.662240 | − | 0.749292i | \(-0.269606\pi\) |
−0.749292 | + | 0.662240i | \(0.769606\pi\) | |||||||
\(480\) | 7.67333 | + | 3.25736i | 0.350238 | + | 0.148677i | ||||
\(481\) | 25.9706 | − | 17.3137i | 1.18416 | − | 0.789437i | ||||
\(482\) | 1.82843 | − | 1.11606i | 0.0832826 | − | 0.0508353i | ||||
\(483\) | −3.20009 | + | 3.20009i | −0.145609 | + | 0.145609i | ||||
\(484\) | −13.0858 | + | 25.4616i | −0.594808 | + | 1.15734i | ||||
\(485\) | − | 3.41421i | − | 0.155031i | ||||||
\(486\) | 2.77215 | − | 11.4584i | 0.125747 | − | 0.519765i | ||||
\(487\) | 9.19932 | − | 9.19932i | 0.416861 | − | 0.416861i | −0.467259 | − | 0.884120i | \(-0.654759\pi\) |
0.884120 | + | 0.467259i | \(0.154759\pi\) | |||||||
\(488\) | 10.3380 | + | 8.92382i | 0.467981 | + | 0.403963i | ||||
\(489\) | 3.97056 | − | 3.97056i | 0.179555 | − | 0.179555i | ||||
\(490\) | −5.82843 | + | 3.55765i | −0.263301 | + | 0.160718i | ||||
\(491\) | 1.47363 | 0.0665038 | 0.0332519 | − | 0.999447i | \(-0.489414\pi\) | ||||
0.0332519 | + | 0.999447i | \(0.489414\pi\) | |||||||
\(492\) | −16.8370 | + | 5.40560i | −0.759073 | + | 0.243703i | ||||
\(493\) | − | 0.585786i | − | 0.0263825i | ||||||
\(494\) | 34.0735 | − | 12.4623i | 1.53304 | − | 0.560703i | ||||
\(495\) | − | 4.16804i | − | 0.187340i | ||||||
\(496\) | −11.6307 | − | 1.92568i | −0.522232 | − | 0.0864657i | ||||
\(497\) | −18.7990 | −0.843250 | ||||||||
\(498\) | 0.937283 | + | 1.53553i | 0.0420007 | + | 0.0688089i | ||||
\(499\) | 2.08402 | − | 2.08402i | 0.0932936 | − | 0.0932936i | −0.658920 | − | 0.752213i | \(-0.728986\pi\) |
0.752213 | + | 0.658920i | \(0.228986\pi\) | |||||||
\(500\) | 17.1384 | − | 5.50234i | 0.766452 | − | 0.246072i | ||||
\(501\) | 1.27208 | − | 1.27208i | 0.0568323 | − | 0.0568323i | ||||
\(502\) | −21.2388 | − | 5.13833i | −0.947935 | − | 0.229335i | ||||
\(503\) | 28.9668i | 1.29157i | 0.763520 | + | 0.645784i | \(0.223469\pi\) | ||||
−0.763520 | + | 0.645784i | \(0.776531\pi\) | |||||||
\(504\) | −0.252834 | − | 3.44365i | −0.0112621 | − | 0.153392i | ||||
\(505\) | −3.65685 | + | 3.65685i | −0.162728 | + | 0.162728i | ||||
\(506\) | 7.72569 | + | 12.6569i | 0.343449 | + | 0.562666i | ||||
\(507\) | −7.36813 | + | 17.6835i | −0.327230 | + | 0.785352i | ||||
\(508\) | −24.6777 | − | 12.6829i | −1.09489 | − | 0.562713i | ||||
\(509\) | 19.6569 | + | 19.6569i | 0.871275 | + | 0.871275i | 0.992611 | − | 0.121337i | \(-0.0387181\pi\) |
−0.121337 | + | 0.992611i | \(0.538718\pi\) | |||||||
\(510\) | 0.186292 | + | 0.305198i | 0.00824913 | + | 0.0135144i | ||||
\(511\) | 3.45292 | 0.152748 | ||||||||
\(512\) | 12.1252 | − | 19.1044i | 0.535865 | − | 0.844304i | ||||
\(513\) | 28.3848 | + | 28.3848i | 1.25322 | + | 1.25322i | ||||
\(514\) | −3.54392 | + | 14.6485i | −0.156315 | + | 0.646116i | ||||
\(515\) | 10.6729 | + | 10.6729i | 0.470306 | + | 0.470306i | ||||
\(516\) | 7.60051 | − | 14.7886i | 0.334594 | − | 0.651033i | ||||
\(517\) | 7.41421i | 0.326077i | ||||||||
\(518\) | 17.5352 | + | 4.24230i | 0.770452 | + | 0.186396i | ||||
\(519\) | 35.9340 | 1.57733 | ||||||||
\(520\) | −1.26240 | + | 10.1196i | −0.0553598 | + | 0.443774i | ||||
\(521\) | 11.0000 | 0.481919 | 0.240959 | − | 0.970535i | \(-0.422538\pi\) | ||||
0.240959 | + | 0.970535i | \(0.422538\pi\) | |||||||
\(522\) | 3.88784 | + | 0.940588i | 0.170166 | + | 0.0411684i | ||||
\(523\) | 25.5139i | 1.11565i | 0.829960 | + | 0.557823i | \(0.188363\pi\) | ||||
−0.829960 | + | 0.557823i | \(0.811637\pi\) | |||||||
\(524\) | 2.46327 | − | 4.79289i | 0.107609 | − | 0.209379i | ||||
\(525\) | 6.14214 | + | 6.14214i | 0.268065 | + | 0.268065i | ||||
\(526\) | −4.32638 | + | 17.8827i | −0.188639 | + | 0.779724i | ||||
\(527\) | −0.357562 | − | 0.357562i | −0.0155756 | − | 0.0155756i | ||||
\(528\) | 29.2585 | + | 4.84432i | 1.27331 | + | 0.210822i | ||||
\(529\) | −18.6569 | −0.811168 | ||||||||
\(530\) | −6.07328 | − | 9.94975i | −0.263807 | − | 0.432189i | ||||
\(531\) | 5.89450 | + | 5.89450i | 0.255800 | + | 0.255800i | ||||
\(532\) | 18.6515 | + | 9.58579i | 0.808644 | + | 0.415597i | ||||
\(533\) | −12.0000 | − | 18.0000i | −0.519778 | − | 0.779667i | ||||
\(534\) | 3.44365 | + | 5.64167i | 0.149021 | + | 0.244139i | ||||
\(535\) | 7.97852 | − | 7.97852i | 0.344942 | − | 0.344942i | ||||
\(536\) | 5.87868 | − | 0.431615i | 0.253920 | − | 0.0186429i | ||||
\(537\) | − | 18.7990i | − | 0.811236i | ||||||
\(538\) | −27.6865 | − | 6.69823i | −1.19365 | − | 0.288781i | ||||
\(539\) | −17.1778 | + | 17.1778i | −0.739902 | + | 0.739902i | ||||
\(540\) | −10.7432 | + | 3.44916i | −0.462315 | + | 0.148428i | ||||
\(541\) | 11.8787 | − | 11.8787i | 0.510704 | − | 0.510704i | −0.404038 | − | 0.914742i | \(-0.632394\pi\) |
0.914742 | + | 0.404038i | \(0.132394\pi\) | |||||||
\(542\) | −5.05635 | − | 8.28372i | −0.217189 | − | 0.355816i | ||||
\(543\) | −12.6522 | −0.542959 | ||||||||
\(544\) | 0.899899 | − | 0.363557i | 0.0385829 | − | 0.0155874i | ||||
\(545\) | − | 4.65685i | − | 0.199478i | ||||||
\(546\) | −10.3992 | + | 3.80345i | −0.445043 | + | 0.162773i | ||||
\(547\) | 34.1028i | 1.45813i | 0.684443 | + | 0.729066i | \(0.260045\pi\) | ||||
−0.684443 | + | 0.729066i | \(0.739955\pi\) | |||||||
\(548\) | −7.15501 | + | 2.29714i | −0.305647 | + | 0.0981291i | ||||
\(549\) | −4.00000 | −0.170716 | ||||||||
\(550\) | 24.2931 | − | 14.8284i | 1.03586 | − | 0.632286i | ||||
\(551\) | −17.1778 | + | 17.1778i | −0.731801 | + | 0.731801i | ||||
\(552\) | 5.67590 | − | 6.57539i | 0.241582 | − | 0.279867i | ||||
\(553\) | 0.899495 | − | 0.899495i | 0.0382504 | − | 0.0382504i | ||||
\(554\) | 1.99529 | − | 8.24735i | 0.0847717 | − | 0.350396i | ||||
\(555\) | − | 12.7570i | − | 0.541503i | ||||||
\(556\) | −2.92556 | + | 5.69239i | −0.124071 | + | 0.241411i | ||||
\(557\) | 4.36396 | − | 4.36396i | 0.184907 | − | 0.184907i | −0.608583 | − | 0.793490i | \(-0.708262\pi\) |
0.793490 | + | 0.608583i | \(0.208262\pi\) | |||||||
\(558\) | 2.94725 | − | 1.79899i | 0.124767 | − | 0.0761573i | ||||
\(559\) | 19.9463 | + | 3.98926i | 0.843639 | + | 0.168728i | ||||
\(560\) | −4.79289 | + | 3.43123i | −0.202537 | + | 0.144996i | ||||
\(561\) | 0.899495 | + | 0.899495i | 0.0379767 | + | 0.0379767i | ||||
\(562\) | 27.7279 | − | 16.9250i | 1.16963 | − | 0.713938i | ||||
\(563\) | −23.3252 | −0.983039 | −0.491520 | − | 0.870867i | \(-0.663558\pi\) | ||||
−0.491520 | + | 0.870867i | \(0.663558\pi\) | |||||||
\(564\) | 4.13525 | − | 1.32764i | 0.174125 | − | 0.0559036i | ||||
\(565\) | −5.17157 | − | 5.17157i | −0.217570 | − | 0.217570i | ||||
\(566\) | −33.3923 | − | 8.07863i | −1.40358 | − | 0.339570i | ||||
\(567\) | −6.07328 | − | 6.07328i | −0.255054 | − | 0.255054i | ||||
\(568\) | 35.9853 | − | 2.64205i | 1.50991 | − | 0.110858i | ||||
\(569\) | − | 12.5147i | − | 0.524644i | −0.964980 | − | 0.262322i | \(-0.915512\pi\) | ||
0.964980 | − | 0.262322i | \(-0.0844883\pi\) | |||||||
\(570\) | 3.48686 | − | 14.4126i | 0.146048 | − | 0.603679i | ||||
\(571\) | 14.4834 | 0.606112 | 0.303056 | − | 0.952973i | \(-0.401993\pi\) | ||||
0.303056 | + | 0.952973i | \(0.401993\pi\) | |||||||
\(572\) | 4.10052 | + | 36.0486i | 0.171451 | + | 1.50727i | ||||
\(573\) | 24.7868 | 1.03548 | ||||||||
\(574\) | 2.94031 | − | 12.1535i | 0.122726 | − | 0.507278i | ||||
\(575\) | − | 8.33609i | − | 0.347639i | ||||||
\(576\) | 0.967957 | + | 6.55635i | 0.0403316 | + | 0.273181i | ||||
\(577\) | 16.4853 | + | 16.4853i | 0.686291 | + | 0.686291i | 0.961410 | − | 0.275119i | \(-0.0887172\pi\) |
−0.275119 | + | 0.961410i | \(0.588717\pi\) | |||||||
\(578\) | −23.3270 | − | 5.64353i | −0.970277 | − | 0.234740i | ||||
\(579\) | 11.8937 | + | 11.8937i | 0.494287 | + | 0.494287i | ||||
\(580\) | −2.08735 | − | 6.50157i | −0.0866726 | − | 0.269963i | ||||
\(581\) | −1.27208 | −0.0527747 | ||||||||
\(582\) | −6.07328 | + | 3.70711i | −0.251746 | + | 0.153665i | ||||
\(583\) | −29.3244 | − | 29.3244i | −1.21449 | − | 1.21449i | ||||
\(584\) | −6.60963 | + | 0.485281i | −0.273508 | + | 0.0200811i | ||||
\(585\) | −1.65685 | − | 2.48528i | −0.0685025 | − | 0.102754i | ||||
\(586\) | 1.37868 | − | 0.841540i | 0.0569527 | − | 0.0347637i | ||||
\(587\) | 13.2626 | − | 13.2626i | 0.547407 | − | 0.547407i | −0.378283 | − | 0.925690i | \(-0.623485\pi\) |
0.925690 | + | 0.378283i | \(0.123485\pi\) | |||||||
\(588\) | 12.6569 | + | 6.50490i | 0.521960 | + | 0.268258i | ||||
\(589\) | 20.9706i | 0.864077i | ||||||||
\(590\) | 3.34628 | − | 13.8316i | 0.137764 | − | 0.569436i | ||||
\(591\) | −3.84116 | + | 3.84116i | −0.158004 | + | 0.158004i | ||||
\(592\) | −34.1623 | − | 5.65624i | −1.40406 | − | 0.232470i | ||||
\(593\) | −32.5563 | + | 32.5563i | −1.33693 | + | 1.33693i | −0.437910 | + | 0.899019i | \(0.644281\pi\) |
−0.899019 | + | 0.437910i | \(0.855719\pi\) | |||||||
\(594\) | −34.2635 | + | 20.9143i | −1.40585 | + | 0.858123i | ||||
\(595\) | −0.252834 | −0.0103652 | ||||||||
\(596\) | 9.06568 | + | 28.2373i | 0.371345 | + | 1.15664i | ||||
\(597\) | − | 30.1838i | − | 1.23534i | ||||||
\(598\) | 9.63787 | + | 4.47584i | 0.394122 | + | 0.183031i | ||||
\(599\) | − | 42.6918i | − | 1.74434i | −0.489204 | − | 0.872169i | \(-0.662713\pi\) | ||
0.489204 | − | 0.872169i | \(-0.337287\pi\) | |||||||
\(600\) | −12.6206 | − | 10.8941i | −0.515233 | − | 0.444751i | ||||
\(601\) | −17.9706 | −0.733035 | −0.366517 | − | 0.930411i | \(-0.619450\pi\) | ||||
−0.366517 | + | 0.930411i | \(0.619450\pi\) | |||||||
\(602\) | 6.12565 | + | 10.0355i | 0.249663 | + | 0.409018i | ||||
\(603\) | −1.22079 | + | 1.22079i | −0.0497145 | + | 0.0497145i | ||||
\(604\) | 9.60111 | + | 29.9050i | 0.390664 | + | 1.21682i | ||||
\(605\) | −10.1213 | + | 10.1213i | −0.411490 | + | 0.411490i | ||||
\(606\) | 10.4755 | + | 2.53434i | 0.425537 | + | 0.102950i | ||||
\(607\) | − | 36.7973i | − | 1.49355i | −0.665074 | − | 0.746777i | \(-0.731600\pi\) | ||
0.665074 | − | 0.746777i | \(-0.268400\pi\) | |||||||
\(608\) | −37.0501 | − | 15.7279i | −1.50258 | − | 0.637851i | ||||
\(609\) | 5.24264 | − | 5.24264i | 0.212443 | − | 0.212443i | ||||
\(610\) | 3.55765 | + | 5.82843i | 0.144045 | + | 0.235986i | ||||
\(611\) | 2.94725 | + | 4.42088i | 0.119233 | + | 0.178850i | ||||
\(612\) | −0.129942 | + | 0.252834i | −0.00525261 | + | 0.0102202i | ||||
\(613\) | −22.8701 | − | 22.8701i | −0.923713 | − | 0.923713i | 0.0735766 | − | 0.997290i | \(-0.476559\pi\) |
−0.997290 | + | 0.0735766i | \(0.976559\pi\) | |||||||
\(614\) | 1.79899 | + | 2.94725i | 0.0726013 | + | 0.118941i | ||||
\(615\) | −8.84175 | −0.356534 | ||||||||
\(616\) | −13.7028 | + | 15.8744i | −0.552103 | + | 0.639598i | ||||
\(617\) | −7.51472 | − | 7.51472i | −0.302531 | − | 0.302531i | 0.539472 | − | 0.842003i | \(-0.318624\pi\) |
−0.842003 | + | 0.539472i | \(0.818624\pi\) | |||||||
\(618\) | 7.39675 | − | 30.5738i | 0.297541 | − | 1.22986i | ||||
\(619\) | 34.7132 | + | 34.7132i | 1.39524 | + | 1.39524i | 0.813052 | + | 0.582191i | \(0.197804\pi\) |
0.582191 | + | 0.813052i | \(0.302196\pi\) | |||||||
\(620\) | −5.24264 | − | 2.69442i | −0.210550 | − | 0.108210i | ||||
\(621\) | 11.7574i | 0.471807i | ||||||||
\(622\) | 40.7996 | + | 9.87068i | 1.63592 | + | 0.395778i | ||||
\(623\) | −4.67371 | −0.187248 | ||||||||
\(624\) | 19.3717 | − | 8.74214i | 0.775488 | − | 0.349966i | ||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | −4.79072 | − | 1.15902i | −0.191476 | − | 0.0463239i | ||||
\(627\) | − | 52.7543i | − | 2.10680i | ||||||
\(628\) | 21.3459 | + | 10.9706i | 0.851793 | + | 0.437773i | ||||
\(629\) | −1.05025 | − | 1.05025i | −0.0418763 | − | 0.0418763i | ||||
\(630\) | 0.405972 | − | 1.67805i | 0.0161743 | − | 0.0668551i | ||||
\(631\) | −1.04201 | − | 1.04201i | −0.0414818 | − | 0.0414818i | 0.686062 | − | 0.727543i | \(-0.259338\pi\) |
−0.727543 | + | 0.686062i | \(0.759338\pi\) | |||||||
\(632\) | −1.59541 | + | 1.84824i | −0.0634619 | + | 0.0735191i | ||||
\(633\) | −29.2843 | −1.16395 | ||||||||
\(634\) | 16.3146 | + | 26.7279i | 0.647936 | + | 1.06150i | ||||
\(635\) | −9.80971 | − | 9.80971i | −0.389287 | − | 0.389287i | ||||
\(636\) | −11.1046 | + | 21.6066i | −0.440324 | + | 0.856757i | ||||
\(637\) | −3.41421 | + | 17.0711i | −0.135276 | + | 0.676380i | ||||
\(638\) | −12.6569 | − | 20.7355i | −0.501090 | − | 0.820926i | ||||
\(639\) | −7.47286 | + | 7.47286i | −0.295622 | + | 0.295622i | ||||
\(640\) | 8.69239 | − | 7.24171i | 0.343597 | − | 0.286254i | ||||
\(641\) | 9.85786i | 0.389362i | 0.980867 | + | 0.194681i | \(0.0623672\pi\) | ||||
−0.980867 | + | 0.194681i | \(0.937633\pi\) | |||||||
\(642\) | −22.8554 | − | 5.52941i | −0.902029 | − | 0.218229i | ||||
\(643\) | −17.4307 | + | 17.4307i | −0.687399 | + | 0.687399i | −0.961656 | − | 0.274258i | \(-0.911568\pi\) |
0.274258 | + | 0.961656i | \(0.411568\pi\) | |||||||
\(644\) | 1.87756 | + | 5.84813i | 0.0739864 | + | 0.230448i | ||||
\(645\) | 5.87868 | − | 5.87868i | 0.231473 | − | 0.231473i | ||||
\(646\) | −0.899495 | − | 1.47363i | −0.0353902 | − | 0.0579790i | ||||
\(647\) | 17.6835 | 0.695210 | 0.347605 | − | 0.937641i | \(-0.386995\pi\) | ||||
0.347605 | + | 0.937641i | \(0.386995\pi\) | |||||||
\(648\) | 12.4791 | + | 10.7720i | 0.490226 | + | 0.423164i | ||||
\(649\) | − | 50.6274i | − | 1.98730i | ||||||
\(650\) | 8.59078 | − | 18.4986i | 0.336958 | − | 0.725575i | ||||
\(651\) | − | 6.40017i | − | 0.250842i | ||||||
\(652\) | −2.32962 | − | 7.25617i | −0.0912350 | − | 0.284173i | ||||
\(653\) | −9.17157 | −0.358911 | −0.179456 | − | 0.983766i | \(-0.557434\pi\) | ||||
−0.179456 | + | 0.983766i | \(0.557434\pi\) | |||||||
\(654\) | −8.28372 | + | 5.05635i | −0.323919 | + | 0.197719i | ||||
\(655\) | 1.90524 | − | 1.90524i | 0.0744439 | − | 0.0744439i | ||||
\(656\) | −3.92029 | + | 23.6777i | −0.153062 | + | 0.924457i | ||||
\(657\) | 1.37258 | − | 1.37258i | 0.0535496 | − | 0.0535496i | ||||
\(658\) | −0.722152 | + | 2.98495i | −0.0281524 | + | 0.116366i | ||||
\(659\) | − | 34.8613i | − | 1.35801i | −0.734136 | − | 0.679003i | \(-0.762412\pi\) | ||
0.734136 | − | 0.679003i | \(-0.237588\pi\) | |||||||
\(660\) | 13.1886 | + | 6.77817i | 0.513365 | + | 0.263840i | ||||
\(661\) | −16.9289 | + | 16.9289i | −0.658459 | + | 0.658459i | −0.955015 | − | 0.296556i | \(-0.904162\pi\) |
0.296556 | + | 0.955015i | \(0.404162\pi\) | |||||||
\(662\) | −8.15731 | + | 4.97918i | −0.317043 | + | 0.193522i | ||||
\(663\) | 0.893904 | + | 0.178781i | 0.0347164 | + | 0.00694327i | ||||
\(664\) | 2.43503 | − | 0.178781i | 0.0944974 | − | 0.00693804i | ||||
\(665\) | 7.41421 | + | 7.41421i | 0.287511 | + | 0.287511i | ||||
\(666\) | 8.65685 | − | 5.28411i | 0.335446 | − | 0.204755i | ||||
\(667\) | −7.11529 | −0.275505 | ||||||||
\(668\) | −0.746357 | − | 2.32471i | −0.0288774 | − | 0.0899457i | ||||
\(669\) | 13.8198 | + | 13.8198i | 0.534305 | + | 0.534305i | ||||
\(670\) | 2.86461 | + | 0.693037i | 0.110670 | + | 0.0267744i | ||||
\(671\) | 17.1778 | + | 17.1778i | 0.663143 | + | 0.663143i | ||||
\(672\) | 11.3076 | + | 4.80013i | 0.436201 | + | 0.185169i | ||||
\(673\) | − | 3.20101i | − | 0.123390i | −0.998095 | − | 0.0616949i | \(-0.980349\pi\) | ||
0.998095 | − | 0.0616949i | \(-0.0196506\pi\) | |||||||
\(674\) | 4.59862 | − | 19.0080i | 0.177132 | − | 0.732160i | ||||
\(675\) | 22.5667 | 0.868592 | ||||||||
\(676\) | 16.7748 | + | 19.8647i | 0.645185 | + | 0.764026i | ||||
\(677\) | 11.2132 | 0.430958 | 0.215479 | − | 0.976508i | \(-0.430869\pi\) | ||||
0.215479 | + | 0.976508i | \(0.430869\pi\) | |||||||
\(678\) | −3.58409 | + | 14.8145i | −0.137646 | + | 0.568949i | ||||
\(679\) | − | 5.03127i | − | 0.193083i | ||||||
\(680\) | 0.483979 | − | 0.0355339i | 0.0185597 | − | 0.00136266i | ||||
\(681\) | 16.1005 | + | 16.1005i | 0.616973 | + | 0.616973i | ||||
\(682\) | −20.3825 | − | 4.93116i | −0.780488 | − | 0.188824i | ||||
\(683\) | −4.06332 | − | 4.06332i | −0.155478 | − | 0.155478i | 0.625081 | − | 0.780560i | \(-0.285066\pi\) |
−0.780560 | + | 0.625081i | \(0.785066\pi\) | |||||||
\(684\) | 11.2247 | − | 3.60373i | 0.429187 | − | 0.137792i | ||||
\(685\) | −3.75736 | −0.143561 | ||||||||
\(686\) | −21.0407 | + | 12.8431i | −0.803337 | + | 0.490354i | ||||
\(687\) | 19.5887 | + | 19.5887i | 0.747357 | + | 0.747357i | ||||
\(688\) | −13.1362 | − | 18.3492i | −0.500813 | − | 0.699558i | ||||
\(689\) | −29.1421 | − | 5.82843i | −1.11023 | − | 0.222045i | ||||
\(690\) | 3.70711 | − | 2.26280i | 0.141127 | − | 0.0861434i | ||||
\(691\) | 7.11529 | − | 7.11529i | 0.270679 | − | 0.270679i | −0.558695 | − | 0.829373i | \(-0.688698\pi\) |
0.829373 | + | 0.558695i | \(0.188698\pi\) | |||||||
\(692\) | 22.2929 | − | 43.3762i | 0.847449 | − | 1.64892i | ||||
\(693\) | − | 6.14214i | − | 0.233320i | ||||||
\(694\) | 7.18261 | − | 29.6887i | 0.272648 | − | 1.12697i | ||||
\(695\) | −2.26280 | + | 2.26280i | −0.0858330 | + | 0.0858330i | ||||
\(696\) | −9.29872 | + | 10.7723i | −0.352467 | + | 0.408325i | ||||
\(697\) | −0.727922 | + | 0.727922i | −0.0275720 | + | 0.0275720i | ||||
\(698\) | 12.8640 | − | 7.85211i | 0.486908 | − | 0.297207i | ||||
\(699\) | −32.3764 | −1.22459 | ||||||||
\(700\) | 11.2247 | − | 3.60373i | 0.424254 | − | 0.136208i | ||||
\(701\) | − | 39.3553i | − | 1.48643i | −0.669052 | − | 0.743215i | \(-0.733300\pi\) | ||
0.669052 | − | 0.743215i | \(-0.266700\pi\) | |||||||
\(702\) | −12.1166 | + | 26.0908i | −0.457311 | + | 0.984732i | ||||
\(703\) | 61.5961i | 2.32314i | ||||||||
\(704\) | 23.9991 | − | 32.3128i | 0.904501 | − | 1.21784i | ||||
\(705\) | 2.17157 | 0.0817862 | ||||||||
\(706\) | 1.65241 | + | 2.70711i | 0.0621891 | + | 0.101883i | ||||
\(707\) | −5.38883 | + | 5.38883i | −0.202668 | + | 0.202668i | ||||
\(708\) | −28.2373 | + | 9.06568i | −1.06122 | + | 0.340709i | ||||
\(709\) | 30.9706 | − | 30.9706i | 1.16312 | − | 1.16312i | 0.179336 | − | 0.983788i | \(-0.442605\pi\) |
0.983788 | − | 0.179336i | \(-0.0573949\pi\) | |||||||
\(710\) | 17.5352 | + | 4.24230i | 0.658084 | + | 0.159211i | ||||
\(711\) | − | 0.715123i | − | 0.0268192i | ||||||
\(712\) | 8.94648 | − | 0.656854i | 0.335284 | − | 0.0246167i | ||||
\(713\) | −4.34315 | + | 4.34315i | −0.162652 | + | 0.162652i | ||||
\(714\) | 0.274524 | + | 0.449747i | 0.0102738 | + | 0.0168314i | ||||
\(715\) | −3.55765 | + | 17.7882i | −0.133048 | + | 0.665242i | ||||
\(716\) | −22.6924 | − | 11.6626i | −0.848054 | − | 0.435851i | ||||
\(717\) | 15.0919 | + | 15.0919i | 0.563617 | + | 0.563617i | ||||
\(718\) | 2.17157 | + | 3.55765i | 0.0810424 | + | 0.132770i | ||||
\(719\) | −38.1662 | −1.42336 | −0.711679 | − | 0.702505i | \(-0.752065\pi\) | ||||
−0.711679 | + | 0.702505i | \(0.752065\pi\) | |||||||
\(720\) | −0.541280 | + | 3.26920i | −0.0201723 | + | 0.121836i | ||||
\(721\) | 15.7279 | + | 15.7279i | 0.585738 | + | 0.585738i | ||||
\(722\) | −10.5176 | + | 43.4737i | −0.391426 | + | 1.61793i | ||||
\(723\) | −1.57835 | − | 1.57835i | −0.0586996 | − | 0.0586996i | ||||
\(724\) | −7.84924 | + | 15.2726i | −0.291715 | + | 0.567602i | ||||
\(725\) | 13.6569i | 0.507203i | ||||||||
\(726\) | 28.9936 | + | 7.01445i | 1.07605 | + | 0.260331i | ||||
\(727\) | −18.5467 | −0.687860 | −0.343930 | − | 0.938995i | \(-0.611758\pi\) | ||||
−0.343930 | + | 0.938995i | \(0.611758\pi\) | |||||||
\(728\) | −1.86030 | + | 14.9125i | −0.0689474 | + | 0.552694i | ||||
\(729\) | −29.7696 | −1.10258 | ||||||||
\(730\) | −3.22079 | − | 0.779208i | −0.119207 | − | 0.0288398i | ||||
\(731\) | − | 0.967957i | − | 0.0358012i | ||||||
\(732\) | 6.50490 | − | 12.6569i | 0.240428 | − | 0.467811i | ||||
\(733\) | 14.8492 | + | 14.8492i | 0.548469 | + | 0.548469i | 0.925998 | − | 0.377529i | \(-0.123226\pi\) |
−0.377529 | + | 0.925998i | \(0.623226\pi\) | |||||||
\(734\) | −1.26717 | + | 5.23773i | −0.0467720 | + | 0.193328i | ||||
\(735\) | 5.03127 | + | 5.03127i | 0.185581 | + | 0.185581i | ||||
\(736\) | −4.41597 | − | 10.9307i | −0.162775 | − | 0.402910i | ||||
\(737\) | 10.4853 | 0.386230 | ||||||||
\(738\) | −3.66237 | − | 6.00000i | −0.134814 | − | 0.220863i | ||||
\(739\) | 15.5995 | + | 15.5995i | 0.573836 | + | 0.573836i | 0.933198 | − | 0.359362i | \(-0.117006\pi\) |
−0.359362 | + | 0.933198i | \(0.617006\pi\) | |||||||
\(740\) | −15.3990 | − | 7.91421i | −0.566079 | − | 0.290932i | ||||
\(741\) | −20.9706 | − | 31.4558i | −0.770373 | − | 1.15556i | ||||
\(742\) | −8.94975 | − | 14.6622i | −0.328556 | − | 0.538266i | ||||
\(743\) | −6.93651 | + | 6.93651i | −0.254476 | + | 0.254476i | −0.822803 | − | 0.568327i | \(-0.807591\pi\) |
0.568327 | + | 0.822803i | \(0.307591\pi\) | |||||||
\(744\) | 0.899495 | + | 12.2513i | 0.0329771 | + | 0.449154i | ||||
\(745\) | 14.8284i | 0.543272i | ||||||||
\(746\) | 20.1062 | + | 4.86432i | 0.736142 | + | 0.178095i | ||||
\(747\) | −0.505668 | + | 0.505668i | −0.0185014 | + | 0.0185014i | ||||
\(748\) | 1.64382 | − | 0.527754i | 0.0601040 | − | 0.0192966i | ||||
\(749\) | 11.7574 | − | 11.7574i | 0.429605 | − | 0.429605i | ||||
\(750\) | −9.77208 | − | 16.0094i | −0.356826 | − | 0.584581i | ||||
\(751\) | 45.6390 | 1.66539 | 0.832696 | − | 0.553731i | \(-0.186796\pi\) | ||||
0.832696 | + | 0.553731i | \(0.186796\pi\) | |||||||
\(752\) | 0.962841 | − | 5.81533i | 0.0351112 | − | 0.212063i | ||||
\(753\) | 22.7696i | 0.829769i | ||||||||
\(754\) | −15.7896 | − | 7.33269i | −0.575022 | − | 0.267041i | ||||
\(755\) | 15.7042i | 0.571535i | ||||||||
\(756\) | −15.8315 | + | 5.08277i | −0.575786 | + | 0.184858i | ||||
\(757\) | 19.2721 | 0.700456 | 0.350228 | − | 0.936665i | \(-0.386104\pi\) | ||||
0.350228 | + | 0.936665i | \(0.386104\pi\) | |||||||
\(758\) | −12.5782 | + | 7.67767i | −0.456860 | + | 0.278866i | ||||
\(759\) | 10.9258 | − | 10.9258i | 0.396581 | − | 0.396581i | ||||
\(760\) | −15.2344 | − | 13.1504i | −0.552610 | − | 0.477014i | ||||
\(761\) | −11.6569 | + | 11.6569i | −0.422561 | + | 0.422561i | −0.886084 | − | 0.463524i | \(-0.846585\pi\) |
0.463524 | + | 0.886084i | \(0.346585\pi\) | |||||||
\(762\) | −6.79850 | + | 28.1010i | −0.246284 | + | 1.01799i | ||||
\(763\) | − | 6.86246i | − | 0.248438i | ||||||
\(764\) | 15.3773 | − | 29.9203i | 0.556332 | − | 1.08248i | ||||
\(765\) | −0.100505 | + | 0.100505i | −0.00363377 | + | 0.00363377i | ||||
\(766\) | 0.305198 | − | 0.186292i | 0.0110272 | − | 0.00673099i | ||||
\(767\) | −20.1251 | − | 30.1876i | −0.726675 | − | 1.09001i | ||||
\(768\) | −22.3198 | − | 7.59927i | −0.805397 | − | 0.274215i | ||||
\(769\) | 9.65685 | + | 9.65685i | 0.348235 | + | 0.348235i | 0.859452 | − | 0.511217i | \(-0.170805\pi\) |
−0.511217 | + | 0.859452i | \(0.670805\pi\) | |||||||
\(770\) | −8.94975 | + | 5.46289i | −0.322527 | + | 0.196869i | ||||
\(771\) | 15.7042 | 0.565573 | ||||||||
\(772\) | 21.7357 | − | 6.97833i | 0.782284 | − | 0.251155i | ||||
\(773\) | 27.8787 | + | 27.8787i | 1.00273 | + | 1.00273i | 0.999996 | + | 0.00273014i | \(0.000869031\pi\) |
0.00273014 | + | 0.999996i | \(0.499131\pi\) | |||||||
\(774\) | 6.42429 | + | 1.55423i | 0.230916 | + | 0.0558658i | ||||
\(775\) | 8.33609 | + | 8.33609i | 0.299441 | + | 0.299441i | ||||
\(776\) | 0.707107 | + | 9.63093i | 0.0253837 | + | 0.345730i | ||||
\(777\) | − | 18.7990i | − | 0.674410i | ||||||
\(778\) | 2.04255 | − | 8.44273i | 0.0732291 | − | 0.302686i | ||||
\(779\) | 42.6918 | 1.52959 | ||||||||
\(780\) | 10.5584 | − | 1.20101i | 0.378051 | − | 0.0430032i | ||||
\(781\) | 64.1838 | 2.29668 | ||||||||
\(782\) | 0.118906 | − | 0.491489i | 0.00425208 | − | 0.0175756i | ||||
\(783\) | − | 19.2619i | − | 0.688363i | ||||||
\(784\) | 15.7042 | − | 11.2426i | 0.560865 | − | 0.401523i | ||||
\(785\) | 8.48528 | + | 8.48528i | 0.302853 | + | 0.302853i | ||||
\(786\) | −5.45777 | − | 1.32040i | −0.194672 | − | 0.0470972i | ||||
\(787\) | −13.8730 | − | 13.8730i | −0.494520 | − | 0.494520i | 0.415207 | − | 0.909727i | \(-0.363709\pi\) |
−0.909727 | + | 0.415207i | \(0.863709\pi\) | |||||||
\(788\) | 2.25369 | + | 7.01968i | 0.0802845 | + | 0.250066i | ||||
\(789\) | 19.1716 | 0.682526 | ||||||||
\(790\) | −1.04201 | + | 0.636039i | −0.0370731 | + | 0.0226293i | ||||
\(791\) | −7.62096 | − | 7.62096i | −0.270970 | − | 0.270970i | ||||
\(792\) | 0.863230 | + | 11.7574i | 0.0306735 | + | 0.417780i | ||||
\(793\) | 17.0711 | + | 3.41421i | 0.606211 | + | 0.121242i | ||||
\(794\) | 31.5563 | − | 19.2619i | 1.11989 | − | 0.683578i | ||||
\(795\) | −8.58892 | + | 8.58892i | −0.304618 | + | 0.304618i | ||||
\(796\) | −36.4350 | − | 18.7255i | −1.29141 | − | 0.663708i | ||||
\(797\) | − | 36.8284i | − | 1.30453i | −0.757991 | − | 0.652265i | \(-0.773819\pi\) | ||
0.757991 | − | 0.652265i | \(-0.226181\pi\) | |||||||
\(798\) | 5.13833 | − | 21.2388i | 0.181895 | − | 0.751846i | ||||
\(799\) | 0.178781 | − | 0.178781i | 0.00632481 | − | 0.00632481i | ||||
\(800\) | −20.9800 | + | 8.47586i | −0.741755 | + | 0.299667i | ||||
\(801\) | −1.85786 | + | 1.85786i | −0.0656444 | + | 0.0656444i | ||||
\(802\) | −4.29289 | + | 2.62036i | −0.151587 | + | 0.0925283i | ||||
\(803\) | −11.7890 | −0.416025 | ||||||||
\(804\) | −1.87756 | − | 5.84813i | −0.0662166 | − | 0.206248i | ||||
\(805\) | 3.07107i | 0.108241i | ||||||||
\(806\) | −14.1137 | + | 5.16203i | −0.497134 | + | 0.181825i | ||||
\(807\) | 29.6820i | 1.04485i | ||||||||
\(808\) | 9.55802 | − | 11.0727i | 0.336250 | − | 0.389538i | ||||
\(809\) | −35.1421 | −1.23553 | −0.617766 | − | 0.786362i | \(-0.711962\pi\) | ||||
−0.617766 | + | 0.786362i | \(0.711962\pi\) | |||||||
\(810\) | 4.29446 | + | 7.03553i | 0.150892 | + | 0.247203i | ||||
\(811\) | −20.1251 | + | 20.1251i | −0.706688 | + | 0.706688i | −0.965837 | − | 0.259150i | \(-0.916558\pi\) |
0.259150 | + | 0.965837i | \(0.416558\pi\) | |||||||
\(812\) | −3.07598 | − | 9.58088i | −0.107946 | − | 0.336223i | ||||
\(813\) | −7.15076 | + | 7.15076i | −0.250788 | + | 0.250788i | ||||
\(814\) | −59.8689 | − | 14.4841i | −2.09840 | − | 0.507668i | ||||
\(815\) | − | 3.81048i | − | 0.133475i | ||||||
\(816\) | −0.588706 | − | 0.822330i | −0.0206088 | − | 0.0287873i | ||||
\(817\) | −28.3848 | + | 28.3848i | −0.993058 | + | 0.993058i | ||||
\(818\) | 24.1144 | + | 39.5061i | 0.843139 | + | 1.38130i | ||||
\(819\) | −2.44158 | − | 3.66237i | −0.0853158 | − | 0.127974i | ||||
\(820\) | −5.48528 | + | 10.6729i | −0.191554 | + | 0.372715i | ||||
\(821\) | −17.7782 | − | 17.7782i | −0.620463 | − | 0.620463i | 0.325187 | − | 0.945650i | \(-0.394573\pi\) |
−0.945650 | + | 0.325187i | \(0.894573\pi\) | |||||||
\(822\) | 4.07969 | + | 6.68368i | 0.142296 | + | 0.233120i | ||||
\(823\) | −4.88317 | −0.170216 | −0.0851082 | − | 0.996372i | \(-0.527124\pi\) | ||||
−0.0851082 | + | 0.996372i | \(0.527124\pi\) | |||||||
\(824\) | −32.3170 | − | 27.8962i | −1.12582 | − | 0.971809i | ||||
\(825\) | −20.9706 | − | 20.9706i | −0.730101 | − | 0.730101i | ||||
\(826\) | 4.93116 | − | 20.3825i | 0.171577 | − | 0.709199i | ||||
\(827\) | −28.8187 | − | 28.8187i | −1.00213 | − | 1.00213i | −0.999998 | − | 0.00212804i | \(-0.999323\pi\) |
−0.00212804 | − | 0.999998i | \(-0.500677\pi\) | |||||||
\(828\) | 3.07107 | + | 1.57835i | 0.106727 | + | 0.0548516i | ||||
\(829\) | 14.3848i | 0.499604i | 0.968297 | + | 0.249802i | \(0.0803655\pi\) | ||||
−0.968297 | + | 0.249802i | \(0.919634\pi\) | |||||||
\(830\) | 1.18656 | + | 0.287065i | 0.0411861 | + | 0.00996419i | ||||
\(831\) | −8.84175 | −0.306717 | ||||||||
\(832\) | 1.46518 | − | 28.8072i | 0.0507959 | − | 0.998709i | ||||
\(833\) | 0.828427 | 0.0287033 | ||||||||
\(834\) | 6.48205 | + | 1.56821i | 0.224455 | + | 0.0543025i | ||||
\(835\) | − | 1.22079i | − | 0.0422472i | ||||||
\(836\) | −63.6801 | − | 32.7279i | −2.20242 | − | 1.13192i | ||||
\(837\) | −11.7574 | − | 11.7574i | −0.406394 | − | 0.406394i | ||||
\(838\) | −1.87613 | + | 7.75481i | −0.0648097 | + | 0.267885i | ||||
\(839\) | 16.8203 | + | 16.8203i | 0.580701 | + | 0.580701i | 0.935096 | − | 0.354395i | \(-0.115313\pi\) |
−0.354395 | + | 0.935096i | \(0.615313\pi\) | |||||||
\(840\) | 4.64951 | + | 4.01347i | 0.160423 | + | 0.138478i | ||||
\(841\) | −17.3431 | −0.598040 | ||||||||
\(842\) | 25.0299 | + | 41.0061i | 0.862589 | + | 1.41316i | ||||
\(843\) | −23.9356 | − | 23.9356i | −0.824385 | − | 0.824385i | ||||
\(844\) | −18.1675 | + | 35.3492i | −0.625351 | + | 1.21677i | ||||
\(845\) | 4.94975 | + | 12.0208i | 0.170276 | + | 0.413529i | ||||
\(846\) | 0.899495 | + | 1.47363i | 0.0309253 | + | 0.0506643i | ||||
\(847\) | −14.9150 | + | 14.9150i | −0.512487 | + | 0.512487i | ||||
\(848\) | 19.1924 | + | 26.8088i | 0.659069 | + | 0.920617i | ||||
\(849\) | 35.7990i | 1.22862i | ||||||||
\(850\) | −0.943348 | − | 0.228225i | −0.0323566 | − | 0.00782805i | ||||
\(851\) | −12.7570 | + | 12.7570i | −0.437303 | + | 0.437303i | ||||
\(852\) | −11.4932 | − | 35.7983i | −0.393749 | − | 1.22643i | ||||
\(853\) | 15.5772 | − | 15.5772i | 0.533352 | − | 0.533352i | −0.388216 | − | 0.921568i | \(-0.626909\pi\) |
0.921568 | + | 0.388216i | \(0.126909\pi\) | |||||||
\(854\) | 5.24264 | + | 8.58892i | 0.179399 | + | 0.293907i | ||||
\(855\) | 5.89450 | 0.201588 | ||||||||
\(856\) | −20.8537 | + | 24.1585i | −0.712764 | + | 0.825721i | ||||
\(857\) | 1.85786i | 0.0634634i | 0.999496 | + | 0.0317317i | \(0.0101022\pi\) | ||||
−0.999496 | + | 0.0317317i | \(0.989898\pi\) | |||||||
\(858\) | 35.5050 | − | 12.9858i | 1.21212 | − | 0.443328i | ||||
\(859\) | − | 48.0806i | − | 1.64049i | −0.572013 | − | 0.820244i | \(-0.693837\pi\) | ||
0.572013 | − | 0.820244i | \(-0.306163\pi\) | |||||||
\(860\) | −3.44916 | − | 10.7432i | −0.117615 | − | 0.366341i | ||||
\(861\) | −13.0294 | −0.444042 | ||||||||
\(862\) | 26.9352 | − | 16.4411i | 0.917416 | − | 0.559987i | ||||
\(863\) | 27.9248 | − | 27.9248i | 0.950572 | − | 0.950572i | −0.0482622 | − | 0.998835i | \(-0.515368\pi\) |
0.998835 | + | 0.0482622i | \(0.0153683\pi\) | |||||||
\(864\) | 29.5905 | − | 11.9545i | 1.00669 | − | 0.406700i | ||||
\(865\) | 17.2426 | − | 17.2426i | 0.586267 | − | 0.586267i | ||||
\(866\) | 10.7459 | − | 44.4171i | 0.365159 | − | 1.50935i | ||||
\(867\) | 25.0083i | 0.849325i | ||||||||
\(868\) | −7.72569 | − | 3.97056i | −0.262227 | − | 0.134770i | ||||
\(869\) | −3.07107 | + | 3.07107i | −0.104179 | + | 0.104179i | ||||
\(870\) | −6.07328 | + | 3.70711i | −0.205904 | + | 0.125683i | ||||
\(871\) | 6.25206 | − | 4.16804i | 0.211843 | − | 0.141229i | ||||
\(872\) | 0.964466 | + | 13.1362i | 0.0326609 | + | 0.444848i | ||||
\(873\) | −2.00000 | − | 2.00000i | −0.0676897 | − | 0.0676897i | ||||
\(874\) | −17.8995 | + | 10.9258i | −0.605459 | + | 0.369570i | ||||
\(875\) | 13.2626 | 0.448359 | ||||||||
\(876\) | 2.11102 | + | 6.57527i | 0.0713247 | + | 0.222158i | ||||
\(877\) | −18.2635 | − | 18.2635i | −0.616713 | − | 0.616713i | 0.327974 | − | 0.944687i | \(-0.393634\pi\) |
−0.944687 | + | 0.327974i | \(0.893634\pi\) | |||||||
\(878\) | 17.1877 | + | 4.15822i | 0.580055 | + | 0.140333i | ||||
\(879\) | −1.19012 | − | 1.19012i | −0.0401417 | − | 0.0401417i | ||||
\(880\) | 16.3640 | − | 11.7150i | 0.551629 | − | 0.394911i | ||||
\(881\) | 10.3137i | 0.347478i | 0.984792 | + | 0.173739i | \(0.0555849\pi\) | ||||
−0.984792 | + | 0.173739i | \(0.944415\pi\) | |||||||
\(882\) | −1.33019 | + | 5.49824i | −0.0447899 | + | 0.185135i | ||||
\(883\) | −15.1985 | −0.511472 | −0.255736 | − | 0.966747i | \(-0.582318\pi\) | ||||
−0.255736 | + | 0.966747i | \(0.582318\pi\) | |||||||
\(884\) | 0.770371 | − | 0.968125i | 0.0259104 | − | 0.0325616i | ||||
\(885\) | −14.8284 | −0.498452 | ||||||||
\(886\) | −2.04428 | + | 8.44988i | −0.0686791 | + | 0.283879i | ||||
\(887\) | 42.1861i | 1.41647i | 0.705976 | + | 0.708235i | \(0.250508\pi\) | ||||
−0.705976 | + | 0.708235i | \(0.749492\pi\) | |||||||
\(888\) | 2.64205 | + | 35.9853i | 0.0886615 | + | 1.20759i | ||||
\(889\) | −14.4558 | − | 14.4558i | −0.484833 | − | 0.484833i | ||||
\(890\) | 4.35951 | + | 1.05470i | 0.146131 | + | 0.0353536i | ||||
\(891\) | 20.7355 | + | 20.7355i | 0.694665 | + | 0.694665i | ||||
\(892\) | 25.2556 | − | 8.10840i | 0.845619 | − | 0.271489i | ||||
\(893\) | −10.4853 | −0.350877 | ||||||||
\(894\) | 26.3772 | − | 16.1005i | 0.882184 | − | 0.538481i | ||||
\(895\) | −9.02054 | − | 9.02054i | −0.301523 | − | 0.301523i | ||||
\(896\) | 12.8093 | − | 10.6716i | 0.427930 | − | 0.356512i | ||||
\(897\) | 2.17157 | − | 10.8579i | 0.0725067 | − | 0.362534i | ||||
\(898\) | −43.9203 | + | 26.8088i | −1.46564 | + | 0.894620i | ||||
\(899\) | 7.11529 | − | 7.11529i | 0.237308 | − | 0.237308i | ||||
\(900\) | 3.02944 | − | 5.89450i | 0.100981 | − | 0.196483i | ||||
\(901\) | 1.41421i | 0.0471143i | ||||||||
\(902\) | −10.0388 | + | 41.4947i | −0.334257 | + | 1.38162i | ||||
\(903\) | 8.66297 | − | 8.66297i | 0.288286 | − | 0.288286i | ||||
\(904\) | 15.6592 | + | 13.5171i | 0.520818 | + | 0.449571i | ||||
\(905\) | −6.07107 | + | 6.07107i | −0.201809 | + | 0.201809i | ||||
\(906\) | 27.9350 | − | 17.0514i | 0.928079 | − | 0.566496i | ||||
\(907\) | −0.252834 | −0.00839522 | −0.00419761 | − | 0.999991i | \(-0.501336\pi\) | ||||
−0.00419761 | + | 0.999991i | \(0.501336\pi\) | |||||||
\(908\) | 29.4235 | − | 9.44654i | 0.976454 | − | 0.313494i | ||||
\(909\) | 4.28427i | 0.142100i | ||||||||
\(910\) | −3.16490 | + | 6.81501i | −0.104915 | + | 0.225915i | ||||
\(911\) | − | 15.0938i | − | 0.500081i | −0.968235 | − | 0.250040i | \(-0.919556\pi\) | ||
0.968235 | − | 0.250040i | \(-0.0804439\pi\) | |||||||
\(912\) | −6.85090 | + | 41.3778i | −0.226856 | + | 1.37016i | ||||
\(913\) | 4.34315 | 0.143737 | ||||||||
\(914\) | −0.610396 | − | 1.00000i | −0.0201901 | − | 0.0330771i | ||||
\(915\) | 5.03127 | − | 5.03127i | 0.166329 | − | 0.166329i | ||||
\(916\) | 35.7983 | − | 11.4932i | 1.18281 | − | 0.379745i | ||||
\(917\) | 2.80761 | − | 2.80761i | 0.0927155 | − | 0.0927155i | ||||
\(918\) | 1.33051 | + | 0.321892i | 0.0439135 | + | 0.0106240i | ||||
\(919\) | 21.8516i | 0.720816i | 0.932795 | + | 0.360408i | \(0.117363\pi\) | ||||
−0.932795 | + | 0.360408i | \(0.882637\pi\) | |||||||
\(920\) | −0.431615 | − | 5.87868i | −0.0142299 | − | 0.193814i | ||||
\(921\) | 2.54416 | − | 2.54416i | 0.0838328 | − | 0.0838328i | ||||
\(922\) | −6.73604 | − | 11.0355i | −0.221840 | − | 0.363436i | ||||
\(923\) | 38.2709 | − | 25.5139i | 1.25970 | − | 0.839801i | ||||
\(924\) | 19.4350 | + | 9.98849i | 0.639366 | + | 0.328597i | ||||
\(925\) | 24.4853 | + | 24.4853i | 0.805071 | + | 0.805071i | ||||
\(926\) | 21.8701 | + | 35.8293i | 0.718695 | + | 1.17742i | ||||
\(927\) | 12.5041 | 0.410689 | ||||||||
\(928\) | 7.23460 | + | 17.9075i | 0.237487 | + | 0.587844i | ||||
\(929\) | −24.6274 | − | 24.6274i | −0.807999 | − | 0.807999i | 0.176331 | − | 0.984331i | \(-0.443577\pi\) |
−0.984331 | + | 0.176331i | \(0.943577\pi\) | |||||||
\(930\) | −1.44430 | + | 5.96991i | −0.0473606 | + | 0.195761i | ||||
\(931\) | −24.2931 | − | 24.2931i | −0.796175 | − | 0.796175i | ||||
\(932\) | −20.0858 | + | 39.0818i | −0.657932 | + | 1.28017i | ||||
\(933\) | − | 43.7401i | − | 1.43199i | ||||||
\(934\) | −29.3412 | − | 7.09853i | −0.960072 | − | 0.232271i | ||||
\(935\) | 0.863230 | 0.0282306 | ||||||||
\(936\) | 5.18843 | + | 6.66742i | 0.169589 | + | 0.217931i | ||||
\(937\) | 24.9706 | 0.815753 | 0.407876 | − | 0.913037i | \(-0.366269\pi\) | ||||
0.407876 | + | 0.913037i | \(0.366269\pi\) | |||||||
\(938\) | 4.22136 | + | 1.02128i | 0.137832 | + | 0.0333459i | ||||
\(939\) | 5.13600i | 0.167607i | ||||||||
\(940\) | 1.34721 | − | 2.62132i | 0.0439411 | − | 0.0854980i | ||||
\(941\) | 1.73654 | + | 1.73654i | 0.0566097 | + | 0.0566097i | 0.734845 | − | 0.678235i | \(-0.237255\pi\) |
−0.678235 | + | 0.734845i | \(0.737255\pi\) | |||||||
\(942\) | 5.88062 | − | 24.3070i | 0.191601 | − | 0.791966i | ||||
\(943\) | 8.84175 | + | 8.84175i | 0.287927 | + | 0.287927i | ||||
\(944\) | −6.57469 | + | 39.7096i | −0.213988 | + | 1.29244i | ||||
\(945\) | −8.31371 | −0.270445 | ||||||||
\(946\) | −20.9143 | − | 34.2635i | −0.679982 | − | 1.11400i | ||||
\(947\) | 30.7980 | + | 30.7980i | 1.00080 | + | 1.00080i | 1.00000 | 0.000801955i | \(0.000255270\pi\) | |
0.000801955 | 1.00000i | \(0.499745\pi\) | ||||||||
\(948\) | 2.26280 | + | 1.16295i | 0.0734924 | + | 0.0377709i | ||||
\(949\) | −7.02944 | + | 4.68629i | −0.228185 | + | 0.152123i | ||||
\(950\) | 20.9706 | + | 34.3557i | 0.680375 | + | 1.11465i | ||||
\(951\) | 23.0723 | − | 23.0723i | 0.748172 | − | 0.748172i | ||||
\(952\) | 0.713203 | − | 0.0523637i | 0.0231151 | − | 0.00169712i | ||||
\(953\) | − | 22.8579i | − | 0.740439i | −0.928944 | − | 0.370219i | \(-0.879282\pi\) | ||
0.928944 | − | 0.370219i | \(-0.120718\pi\) | |||||||
\(954\) | −9.38607 | − | 2.27078i | −0.303885 | − | 0.0735192i | ||||
\(955\) | 11.8937 | − | 11.8937i | 0.384872 | − | 0.384872i | ||||
\(956\) | 27.5803 | − | 8.85475i | 0.892010 | − | 0.286383i | ||||
\(957\) | −17.8995 | + | 17.8995i | −0.578608 | + | 0.578608i | ||||
\(958\) | 1.98528 | + | 3.25245i | 0.0641415 | + | 0.105082i | ||||
\(959\) | −5.53694 | −0.178797 | ||||||||
\(960\) | −9.46421 | − | 7.02918i | −0.305456 | − | 0.226866i | ||||
\(961\) | 22.3137i | 0.719797i | ||||||||
\(962\) | −41.4557 | + | 15.1623i | −1.33659 | + | 0.488851i | ||||
\(963\) | − | 9.34742i | − | 0.301216i | ||||||
\(964\) | −2.88443 | + | 0.926056i | −0.0929011 | + | 0.0298263i | ||||
\(965\) | 11.4142 | 0.367437 | ||||||||
\(966\) | 5.46289 | − | 3.33452i | 0.175766 | − | 0.107287i | ||||
\(967\) | −31.2296 | + | 31.2296i | −1.00428 | + | 1.00428i | −0.00428700 | + | 0.999991i | \(0.501365\pi\) |
−0.999991 | + | 0.00428700i | \(0.998635\pi\) | |||||||
\(968\) | 26.4544 | − | 30.6468i | 0.850276 | − | 0.985024i | ||||
\(969\) | −1.27208 | + | 1.27208i | −0.0408650 | + | 0.0408650i | ||||
\(970\) | −1.13539 | + | 4.69304i | −0.0364552 | + | 0.150684i | ||||
\(971\) | 32.8821i | 1.05524i | 0.849482 | + | 0.527618i | \(0.176915\pi\) | ||||
−0.849482 | + | 0.527618i | \(0.823085\pi\) | |||||||
\(972\) | −7.62096 | + | 14.8284i | −0.244443 | + | 0.475622i | ||||
\(973\) | −3.33452 | + | 3.33452i | −0.106900 | + | 0.106900i | ||||
\(974\) | −15.7042 | + | 9.58579i | −0.503196 | + | 0.307148i | ||||
\(975\) | −20.8402 | − | 4.16804i | −0.667421 | − | 0.133484i | ||||
\(976\) | −11.2426 | − | 15.7042i | −0.359868 | − | 0.502680i | ||||
\(977\) | −9.62742 | − | 9.62742i | −0.308008 | − | 0.308008i | 0.536128 | − | 0.844137i | \(-0.319886\pi\) |
−0.844137 | + | 0.536128i | \(0.819886\pi\) | |||||||
\(978\) | −6.77817 | + | 4.13737i | −0.216742 | + | 0.132298i | ||||
\(979\) | 15.9570 | 0.509990 | ||||||||
\(980\) | 9.19460 | − | 2.95196i | 0.293711 | − | 0.0942970i | ||||
\(981\) | −2.72792 | − | 2.72792i | −0.0870958 | − | 0.0870958i | ||||
\(982\) | −2.02559 | − | 0.490051i | −0.0646390 | − | 0.0156382i | ||||
\(983\) | −10.5989 | − | 10.5989i | −0.338052 | − | 0.338052i | 0.517582 | − | 0.855634i | \(-0.326832\pi\) |
−0.855634 | + | 0.517582i | \(0.826832\pi\) | |||||||
\(984\) | 24.9411 | − | 1.83119i | 0.795094 | − | 0.0583761i | ||||
\(985\) | 3.68629i | 0.117455i | ||||||||
\(986\) | −0.194802 | + | 0.805198i | −0.00620376 | + | 0.0256427i | ||||
\(987\) | 3.20009 | 0.101860 | ||||||||
\(988\) | −50.9804 | + | 5.79901i | −1.62190 | + | 0.184491i | ||||
\(989\) | −11.7574 | −0.373862 | ||||||||
\(990\) | −1.38607 | + | 5.72922i | −0.0440523 | + | 0.182087i | ||||
\(991\) | − | 5.38883i | − | 0.171182i | −0.996330 | − | 0.0855910i | \(-0.972722\pi\) | ||
0.996330 | − | 0.0855910i | \(-0.0272778\pi\) | |||||||
\(992\) | 15.3467 | + | 6.51472i | 0.487257 | + | 0.206843i | ||||
\(993\) | 7.04163 | + | 7.04163i | 0.223459 | + | 0.223459i | ||||
\(994\) | 25.8403 | + | 6.25157i | 0.819605 | + | 0.198288i | ||||
\(995\) | −14.4834 | − | 14.4834i | −0.459155 | − | 0.459155i | ||||
\(996\) | −0.777712 | − | 2.42237i | −0.0246428 | − | 0.0767558i | ||||
\(997\) | −2.92893 | −0.0927602 | −0.0463801 | − | 0.998924i | \(-0.514769\pi\) | ||||
−0.0463801 | + | 0.998924i | \(0.514769\pi\) | |||||||
\(998\) | −3.55765 | + | 2.17157i | −0.112615 | + | 0.0687399i | ||||
\(999\) | −34.5345 | − | 34.5345i | −1.09262 | − | 1.09262i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))