Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [17,2,Mod(2,17)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(17, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("17.2");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 17.d (of order \(8\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.135745683436\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 9.1 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 17.9 |
Dual form | 17.2.d.a.2.1 |
$q$-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 \(\left(\mathbb{Z}/17\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{8}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.292893 | + | 0.292893i | −0.207107 | + | 0.207107i | −0.803037 | − | 0.595930i | \(-0.796784\pi\) |
0.595930 | + | 0.803037i | \(0.296784\pi\) | |||||||
\(3\) | −2.41421 | − | 1.00000i | −1.39385 | − | 0.577350i | −0.445700 | − | 0.895182i | \(-0.647045\pi\) |
−0.948147 | + | 0.317832i | \(0.897045\pi\) | |||||||
\(4\) | 1.82843i | 0.914214i | ||||||||
\(5\) | 0.707107 | − | 1.70711i | 0.316228 | − | 0.763441i | −0.683220 | − | 0.730213i | \(-0.739421\pi\) |
0.999448 | − | 0.0332288i | \(-0.0105790\pi\) | |||||||
\(6\) | 1.00000 | − | 0.414214i | 0.408248 | − | 0.169102i | ||||
\(7\) | 0.414214 | + | 1.00000i | 0.156558 | + | 0.377964i | 0.982624 | − | 0.185610i | \(-0.0594260\pi\) |
−0.826066 | + | 0.563574i | \(0.809426\pi\) | |||||||
\(8\) | −1.12132 | − | 1.12132i | −0.396447 | − | 0.396447i | ||||
\(9\) | 2.70711 | + | 2.70711i | 0.902369 | + | 0.902369i | ||||
\(10\) | 0.292893 | + | 0.707107i | 0.0926210 | + | 0.223607i | ||||
\(11\) | −1.00000 | + | 0.414214i | −0.301511 | + | 0.124890i | −0.528310 | − | 0.849052i | \(-0.677174\pi\) |
0.226799 | + | 0.973942i | \(0.427174\pi\) | |||||||
\(12\) | 1.82843 | − | 4.41421i | 0.527821 | − | 1.27427i | ||||
\(13\) | − | 1.41421i | − | 0.392232i | −0.980581 | − | 0.196116i | \(-0.937167\pi\) | ||
0.980581 | − | 0.196116i | \(-0.0628330\pi\) | |||||||
\(14\) | −0.414214 | − | 0.171573i | −0.110703 | − | 0.0458548i | ||||
\(15\) | −3.41421 | + | 3.41421i | −0.881546 | + | 0.881546i | ||||
\(16\) | −3.00000 | −0.750000 | ||||||||
\(17\) | −2.82843 | + | 3.00000i | −0.685994 | + | 0.727607i | ||||
\(18\) | −1.58579 | −0.373773 | ||||||||
\(19\) | 3.41421 | − | 3.41421i | 0.783274 | − | 0.783274i | −0.197108 | − | 0.980382i | \(-0.563155\pi\) |
0.980382 | + | 0.197108i | \(0.0631548\pi\) | |||||||
\(20\) | 3.12132 | + | 1.29289i | 0.697948 | + | 0.289100i | ||||
\(21\) | − | 2.82843i | − | 0.617213i | ||||||
\(22\) | 0.171573 | − | 0.414214i | 0.0365795 | − | 0.0883106i | ||||
\(23\) | 3.82843 | − | 1.58579i | 0.798282 | − | 0.330659i | 0.0540140 | − | 0.998540i | \(-0.482798\pi\) |
0.744268 | + | 0.667881i | \(0.232798\pi\) | |||||||
\(24\) | 1.58579 | + | 3.82843i | 0.323697 | + | 0.781474i | ||||
\(25\) | 1.12132 | + | 1.12132i | 0.224264 | + | 0.224264i | ||||
\(26\) | 0.414214 | + | 0.414214i | 0.0812340 | + | 0.0812340i | ||||
\(27\) | −0.828427 | − | 2.00000i | −0.159431 | − | 0.384900i | ||||
\(28\) | −1.82843 | + | 0.757359i | −0.345540 | + | 0.143127i | ||||
\(29\) | −1.70711 | + | 4.12132i | −0.317002 | + | 0.765310i | 0.682408 | + | 0.730971i | \(0.260933\pi\) |
−0.999410 | + | 0.0343389i | \(0.989067\pi\) | |||||||
\(30\) | − | 2.00000i | − | 0.365148i | ||||||
\(31\) | −3.00000 | − | 1.24264i | −0.538816 | − | 0.223185i | 0.0966436 | − | 0.995319i | \(-0.469189\pi\) |
−0.635460 | + | 0.772134i | \(0.719189\pi\) | |||||||
\(32\) | 3.12132 | − | 3.12132i | 0.551777 | − | 0.551777i | ||||
\(33\) | 2.82843 | 0.492366 | ||||||||
\(34\) | −0.0502525 | − | 1.70711i | −0.00861824 | − | 0.292766i | ||||
\(35\) | 2.00000 | 0.338062 | ||||||||
\(36\) | −4.94975 | + | 4.94975i | −0.824958 | + | 0.824958i | ||||
\(37\) | −3.53553 | − | 1.46447i | −0.581238 | − | 0.240757i | 0.0726379 | − | 0.997358i | \(-0.476858\pi\) |
−0.653876 | + | 0.756602i | \(0.726858\pi\) | |||||||
\(38\) | 2.00000i | 0.324443i | ||||||||
\(39\) | −1.41421 | + | 3.41421i | −0.226455 | + | 0.546712i | ||||
\(40\) | −2.70711 | + | 1.12132i | −0.428031 | + | 0.177296i | ||||
\(41\) | −3.12132 | − | 7.53553i | −0.487468 | − | 1.17685i | −0.955990 | − | 0.293400i | \(-0.905213\pi\) |
0.468521 | − | 0.883452i | \(-0.344787\pi\) | |||||||
\(42\) | 0.828427 | + | 0.828427i | 0.127829 | + | 0.127829i | ||||
\(43\) | −3.41421 | − | 3.41421i | −0.520663 | − | 0.520663i | 0.397109 | − | 0.917772i | \(-0.370014\pi\) |
−0.917772 | + | 0.397109i | \(0.870014\pi\) | |||||||
\(44\) | −0.757359 | − | 1.82843i | −0.114176 | − | 0.275646i | ||||
\(45\) | 6.53553 | − | 2.70711i | 0.974260 | − | 0.403552i | ||||
\(46\) | −0.656854 | + | 1.58579i | −0.0968479 | + | 0.233811i | ||||
\(47\) | 10.8284i | 1.57949i | 0.613436 | + | 0.789744i | \(0.289787\pi\) | ||||
−0.613436 | + | 0.789744i | \(0.710213\pi\) | |||||||
\(48\) | 7.24264 | + | 3.00000i | 1.04539 | + | 0.433013i | ||||
\(49\) | 4.12132 | − | 4.12132i | 0.588760 | − | 0.588760i | ||||
\(50\) | −0.656854 | −0.0928932 | ||||||||
\(51\) | 9.82843 | − | 4.41421i | 1.37626 | − | 0.618114i | ||||
\(52\) | 2.58579 | 0.358584 | ||||||||
\(53\) | −1.00000 | + | 1.00000i | −0.137361 | + | 0.137361i | −0.772444 | − | 0.635083i | \(-0.780966\pi\) |
0.635083 | + | 0.772444i | \(0.280966\pi\) | |||||||
\(54\) | 0.828427 | + | 0.343146i | 0.112735 | + | 0.0466962i | ||||
\(55\) | 2.00000i | 0.269680i | ||||||||
\(56\) | 0.656854 | − | 1.58579i | 0.0877758 | − | 0.211910i | ||||
\(57\) | −11.6569 | + | 4.82843i | −1.54399 | + | 0.639541i | ||||
\(58\) | −0.707107 | − | 1.70711i | −0.0928477 | − | 0.224154i | ||||
\(59\) | −4.24264 | − | 4.24264i | −0.552345 | − | 0.552345i | 0.374772 | − | 0.927117i | \(-0.377721\pi\) |
−0.927117 | + | 0.374772i | \(0.877721\pi\) | |||||||
\(60\) | −6.24264 | − | 6.24264i | −0.805921 | − | 0.805921i | ||||
\(61\) | 3.53553 | + | 8.53553i | 0.452679 | + | 1.09286i | 0.971300 | + | 0.237859i | \(0.0764456\pi\) |
−0.518621 | + | 0.855004i | \(0.673554\pi\) | |||||||
\(62\) | 1.24264 | − | 0.514719i | 0.157816 | − | 0.0653693i | ||||
\(63\) | −1.58579 | + | 3.82843i | −0.199790 | + | 0.482336i | ||||
\(64\) | − | 4.17157i | − | 0.521447i | ||||||
\(65\) | −2.41421 | − | 1.00000i | −0.299446 | − | 0.124035i | ||||
\(66\) | −0.828427 | + | 0.828427i | −0.101972 | + | 0.101972i | ||||
\(67\) | 6.82843 | 0.834225 | 0.417113 | − | 0.908855i | \(-0.363042\pi\) | ||||
0.417113 | + | 0.908855i | \(0.363042\pi\) | |||||||
\(68\) | −5.48528 | − | 5.17157i | −0.665188 | − | 0.627145i | ||||
\(69\) | −10.8284 | −1.30359 | ||||||||
\(70\) | −0.585786 | + | 0.585786i | −0.0700149 | + | 0.0700149i | ||||
\(71\) | 12.0711 | + | 5.00000i | 1.43257 | + | 0.593391i | 0.957985 | − | 0.286818i | \(-0.0925974\pi\) |
0.474587 | + | 0.880209i | \(0.342597\pi\) | |||||||
\(72\) | − | 6.07107i | − | 0.715482i | ||||||
\(73\) | −2.05025 | + | 4.94975i | −0.239964 | + | 0.579324i | −0.997279 | − | 0.0737261i | \(-0.976511\pi\) |
0.757315 | + | 0.653050i | \(0.226511\pi\) | |||||||
\(74\) | 1.46447 | − | 0.606602i | 0.170241 | − | 0.0705160i | ||||
\(75\) | −1.58579 | − | 3.82843i | −0.183111 | − | 0.442069i | ||||
\(76\) | 6.24264 | + | 6.24264i | 0.716080 | + | 0.716080i | ||||
\(77\) | −0.828427 | − | 0.828427i | −0.0944080 | − | 0.0944080i | ||||
\(78\) | −0.585786 | − | 1.41421i | −0.0663273 | − | 0.160128i | ||||
\(79\) | −3.82843 | + | 1.58579i | −0.430732 | + | 0.178415i | −0.587506 | − | 0.809219i | \(-0.699890\pi\) |
0.156775 | + | 0.987634i | \(0.449890\pi\) | |||||||
\(80\) | −2.12132 | + | 5.12132i | −0.237171 | + | 0.572581i | ||||
\(81\) | − | 5.82843i | − | 0.647603i | ||||||
\(82\) | 3.12132 | + | 1.29289i | 0.344692 | + | 0.142776i | ||||
\(83\) | −0.242641 | + | 0.242641i | −0.0266333 | + | 0.0266333i | −0.720298 | − | 0.693665i | \(-0.755995\pi\) |
0.693665 | + | 0.720298i | \(0.255995\pi\) | |||||||
\(84\) | 5.17157 | 0.564265 | ||||||||
\(85\) | 3.12132 | + | 6.94975i | 0.338555 | + | 0.753806i | ||||
\(86\) | 2.00000 | 0.215666 | ||||||||
\(87\) | 8.24264 | − | 8.24264i | 0.883704 | − | 0.883704i | ||||
\(88\) | 1.58579 | + | 0.656854i | 0.169045 | + | 0.0700209i | ||||
\(89\) | − | 9.41421i | − | 0.997905i | −0.866629 | − | 0.498952i | \(-0.833718\pi\) | ||
0.866629 | − | 0.498952i | \(-0.166282\pi\) | |||||||
\(90\) | −1.12132 | + | 2.70711i | −0.118198 | + | 0.285354i | ||||
\(91\) | 1.41421 | − | 0.585786i | 0.148250 | − | 0.0614071i | ||||
\(92\) | 2.89949 | + | 7.00000i | 0.302293 | + | 0.729800i | ||||
\(93\) | 6.00000 | + | 6.00000i | 0.622171 | + | 0.622171i | ||||
\(94\) | −3.17157 | − | 3.17157i | −0.327123 | − | 0.327123i | ||||
\(95\) | −3.41421 | − | 8.24264i | −0.350291 | − | 0.845677i | ||||
\(96\) | −10.6569 | + | 4.41421i | −1.08766 | + | 0.450524i | ||||
\(97\) | 2.46447 | − | 5.94975i | 0.250229 | − | 0.604105i | −0.747994 | − | 0.663706i | \(-0.768983\pi\) |
0.998222 | + | 0.0596005i | \(0.0189827\pi\) | |||||||
\(98\) | 2.41421i | 0.243872i | ||||||||
\(99\) | −3.82843 | − | 1.58579i | −0.384771 | − | 0.159378i | ||||
\(100\) | −2.05025 | + | 2.05025i | −0.205025 | + | 0.205025i | ||||
\(101\) | −13.4142 | −1.33476 | −0.667382 | − | 0.744715i | \(-0.732585\pi\) | ||||
−0.667382 | + | 0.744715i | \(0.732585\pi\) | |||||||
\(102\) | −1.58579 | + | 4.17157i | −0.157016 | + | 0.413047i | ||||
\(103\) | −4.48528 | −0.441948 | −0.220974 | − | 0.975280i | \(-0.570924\pi\) | ||||
−0.220974 | + | 0.975280i | \(0.570924\pi\) | |||||||
\(104\) | −1.58579 | + | 1.58579i | −0.155499 | + | 0.155499i | ||||
\(105\) | −4.82843 | − | 2.00000i | −0.471206 | − | 0.195180i | ||||
\(106\) | − | 0.585786i | − | 0.0568966i | ||||||
\(107\) | −2.41421 | + | 5.82843i | −0.233391 | + | 0.563455i | −0.996572 | − | 0.0827292i | \(-0.973636\pi\) |
0.763181 | + | 0.646184i | \(0.223636\pi\) | |||||||
\(108\) | 3.65685 | − | 1.51472i | 0.351881 | − | 0.145754i | ||||
\(109\) | 1.63604 | + | 3.94975i | 0.156704 | + | 0.378317i | 0.982660 | − | 0.185418i | \(-0.0593639\pi\) |
−0.825956 | + | 0.563735i | \(0.809364\pi\) | |||||||
\(110\) | −0.585786 | − | 0.585786i | −0.0558525 | − | 0.0558525i | ||||
\(111\) | 7.07107 | + | 7.07107i | 0.671156 | + | 0.671156i | ||||
\(112\) | −1.24264 | − | 3.00000i | −0.117419 | − | 0.283473i | ||||
\(113\) | 14.9497 | − | 6.19239i | 1.40635 | − | 0.582531i | 0.454961 | − | 0.890511i | \(-0.349653\pi\) |
0.951393 | + | 0.307980i | \(0.0996531\pi\) | |||||||
\(114\) | 2.00000 | − | 4.82843i | 0.187317 | − | 0.452224i | ||||
\(115\) | − | 7.65685i | − | 0.714005i | ||||||
\(116\) | −7.53553 | − | 3.12132i | −0.699657 | − | 0.289807i | ||||
\(117\) | 3.82843 | − | 3.82843i | 0.353938 | − | 0.353938i | ||||
\(118\) | 2.48528 | 0.228789 | ||||||||
\(119\) | −4.17157 | − | 1.58579i | −0.382407 | − | 0.145369i | ||||
\(120\) | 7.65685 | 0.698972 | ||||||||
\(121\) | −6.94975 | + | 6.94975i | −0.631795 | + | 0.631795i | ||||
\(122\) | −3.53553 | − | 1.46447i | −0.320092 | − | 0.132587i | ||||
\(123\) | 21.3137i | 1.92179i | ||||||||
\(124\) | 2.27208 | − | 5.48528i | 0.204039 | − | 0.492593i | ||||
\(125\) | 11.2426 | − | 4.65685i | 1.00557 | − | 0.416522i | ||||
\(126\) | −0.656854 | − | 1.58579i | −0.0585172 | − | 0.141273i | ||||
\(127\) | −12.2426 | − | 12.2426i | −1.08636 | − | 1.08636i | −0.995900 | − | 0.0904585i | \(-0.971167\pi\) |
−0.0904585 | − | 0.995900i | \(-0.528833\pi\) | |||||||
\(128\) | 7.46447 | + | 7.46447i | 0.659772 | + | 0.659772i | ||||
\(129\) | 4.82843 | + | 11.6569i | 0.425119 | + | 1.02633i | ||||
\(130\) | 1.00000 | − | 0.414214i | 0.0877058 | − | 0.0363289i | ||||
\(131\) | 0.0710678 | − | 0.171573i | 0.00620922 | − | 0.0149904i | −0.920745 | − | 0.390166i | \(-0.872418\pi\) |
0.926954 | + | 0.375176i | \(0.122418\pi\) | |||||||
\(132\) | 5.17157i | 0.450128i | ||||||||
\(133\) | 4.82843 | + | 2.00000i | 0.418678 | + | 0.173422i | ||||
\(134\) | −2.00000 | + | 2.00000i | −0.172774 | + | 0.172774i | ||||
\(135\) | −4.00000 | −0.344265 | ||||||||
\(136\) | 6.53553 | − | 0.192388i | 0.560417 | − | 0.0164971i | ||||
\(137\) | 8.72792 | 0.745677 | 0.372838 | − | 0.927896i | \(-0.378385\pi\) | ||||
0.372838 | + | 0.927896i | \(0.378385\pi\) | |||||||
\(138\) | 3.17157 | − | 3.17157i | 0.269982 | − | 0.269982i | ||||
\(139\) | −13.8284 | − | 5.72792i | −1.17291 | − | 0.485836i | −0.290758 | − | 0.956797i | \(-0.593907\pi\) |
−0.882154 | + | 0.470961i | \(0.843907\pi\) | |||||||
\(140\) | 3.65685i | 0.309061i | ||||||||
\(141\) | 10.8284 | − | 26.1421i | 0.911918 | − | 2.20156i | ||||
\(142\) | −5.00000 | + | 2.07107i | −0.419591 | + | 0.173800i | ||||
\(143\) | 0.585786 | + | 1.41421i | 0.0489859 | + | 0.118262i | ||||
\(144\) | −8.12132 | − | 8.12132i | −0.676777 | − | 0.676777i | ||||
\(145\) | 5.82843 | + | 5.82843i | 0.484025 | + | 0.484025i | ||||
\(146\) | −0.849242 | − | 2.05025i | −0.0702838 | − | 0.169680i | ||||
\(147\) | −14.0711 | + | 5.82843i | −1.16056 | + | 0.480721i | ||||
\(148\) | 2.67767 | − | 6.46447i | 0.220103 | − | 0.531376i | ||||
\(149\) | 16.9706i | 1.39028i | 0.718873 | + | 0.695141i | \(0.244658\pi\) | ||||
−0.718873 | + | 0.695141i | \(0.755342\pi\) | |||||||
\(150\) | 1.58579 | + | 0.656854i | 0.129479 | + | 0.0536319i | ||||
\(151\) | −9.07107 | + | 9.07107i | −0.738193 | + | 0.738193i | −0.972228 | − | 0.234035i | \(-0.924807\pi\) |
0.234035 | + | 0.972228i | \(0.424807\pi\) | |||||||
\(152\) | −7.65685 | −0.621053 | ||||||||
\(153\) | −15.7782 | + | 0.464466i | −1.27559 | + | 0.0375499i | ||||
\(154\) | 0.485281 | 0.0391051 | ||||||||
\(155\) | −4.24264 | + | 4.24264i | −0.340777 | + | 0.340777i | ||||
\(156\) | −6.24264 | − | 2.58579i | −0.499811 | − | 0.207029i | ||||
\(157\) | − | 1.65685i | − | 0.132231i | −0.997812 | − | 0.0661157i | \(-0.978939\pi\) | ||
0.997812 | − | 0.0661157i | \(-0.0210606\pi\) | |||||||
\(158\) | 0.656854 | − | 1.58579i | 0.0522565 | − | 0.126158i | ||||
\(159\) | 3.41421 | − | 1.41421i | 0.270765 | − | 0.112154i | ||||
\(160\) | −3.12132 | − | 7.53553i | −0.246762 | − | 0.595736i | ||||
\(161\) | 3.17157 | + | 3.17157i | 0.249955 | + | 0.249955i | ||||
\(162\) | 1.70711 | + | 1.70711i | 0.134123 | + | 0.134123i | ||||
\(163\) | −2.17157 | − | 5.24264i | −0.170091 | − | 0.410635i | 0.815731 | − | 0.578431i | \(-0.196335\pi\) |
−0.985822 | + | 0.167796i | \(0.946335\pi\) | |||||||
\(164\) | 13.7782 | − | 5.70711i | 1.07589 | − | 0.445650i | ||||
\(165\) | 2.00000 | − | 4.82843i | 0.155700 | − | 0.375893i | ||||
\(166\) | − | 0.142136i | − | 0.0110319i | ||||||
\(167\) | 9.24264 | + | 3.82843i | 0.715217 | + | 0.296253i | 0.710461 | − | 0.703736i | \(-0.248486\pi\) |
0.00475555 | + | 0.999989i | \(0.498486\pi\) | |||||||
\(168\) | −3.17157 | + | 3.17157i | −0.244692 | + | 0.244692i | ||||
\(169\) | 11.0000 | 0.846154 | ||||||||
\(170\) | −2.94975 | − | 1.12132i | −0.226235 | − | 0.0860013i | ||||
\(171\) | 18.4853 | 1.41360 | ||||||||
\(172\) | 6.24264 | − | 6.24264i | 0.475997 | − | 0.475997i | ||||
\(173\) | −3.12132 | − | 1.29289i | −0.237310 | − | 0.0982969i | 0.260859 | − | 0.965377i | \(-0.415994\pi\) |
−0.498169 | + | 0.867080i | \(0.665994\pi\) | |||||||
\(174\) | 4.82843i | 0.366042i | ||||||||
\(175\) | −0.656854 | + | 1.58579i | −0.0496535 | + | 0.119874i | ||||
\(176\) | 3.00000 | − | 1.24264i | 0.226134 | − | 0.0936676i | ||||
\(177\) | 6.00000 | + | 14.4853i | 0.450988 | + | 1.08878i | ||||
\(178\) | 2.75736 | + | 2.75736i | 0.206673 | + | 0.206673i | ||||
\(179\) | 4.24264 | + | 4.24264i | 0.317110 | + | 0.317110i | 0.847656 | − | 0.530546i | \(-0.178013\pi\) |
−0.530546 | + | 0.847656i | \(0.678013\pi\) | |||||||
\(180\) | 4.94975 | + | 11.9497i | 0.368932 | + | 0.890682i | ||||
\(181\) | −11.5355 | + | 4.77817i | −0.857429 | + | 0.355159i | −0.767702 | − | 0.640807i | \(-0.778600\pi\) |
−0.0897278 | + | 0.995966i | \(0.528600\pi\) | |||||||
\(182\) | −0.242641 | + | 0.585786i | −0.0179857 | + | 0.0434214i | ||||
\(183\) | − | 24.1421i | − | 1.78464i | ||||||
\(184\) | −6.07107 | − | 2.51472i | −0.447565 | − | 0.185388i | ||||
\(185\) | −5.00000 | + | 5.00000i | −0.367607 | + | 0.367607i | ||||
\(186\) | −3.51472 | −0.257712 | ||||||||
\(187\) | 1.58579 | − | 4.17157i | 0.115964 | − | 0.305056i | ||||
\(188\) | −19.7990 | −1.44399 | ||||||||
\(189\) | 1.65685 | − | 1.65685i | 0.120518 | − | 0.120518i | ||||
\(190\) | 3.41421 | + | 1.41421i | 0.247693 | + | 0.102598i | ||||
\(191\) | − | 20.0000i | − | 1.44715i | −0.690246 | − | 0.723575i | \(-0.742498\pi\) | ||
0.690246 | − | 0.723575i | \(-0.257502\pi\) | |||||||
\(192\) | −4.17157 | + | 10.0711i | −0.301057 | + | 0.726817i | ||||
\(193\) | 5.12132 | − | 2.12132i | 0.368641 | − | 0.152696i | −0.190670 | − | 0.981654i | \(-0.561066\pi\) |
0.559310 | + | 0.828958i | \(0.311066\pi\) | |||||||
\(194\) | 1.02082 | + | 2.46447i | 0.0732903 | + | 0.176938i | ||||
\(195\) | 4.82843 | + | 4.82843i | 0.345771 | + | 0.345771i | ||||
\(196\) | 7.53553 | + | 7.53553i | 0.538252 | + | 0.538252i | ||||
\(197\) | −5.70711 | − | 13.7782i | −0.406615 | − | 0.981654i | −0.986022 | − | 0.166616i | \(-0.946716\pi\) |
0.579407 | − | 0.815038i | \(-0.303284\pi\) | |||||||
\(198\) | 1.58579 | − | 0.656854i | 0.112697 | − | 0.0466806i | ||||
\(199\) | −0.656854 | + | 1.58579i | −0.0465632 | + | 0.112413i | −0.945450 | − | 0.325768i | \(-0.894377\pi\) |
0.898887 | + | 0.438181i | \(0.144377\pi\) | |||||||
\(200\) | − | 2.51472i | − | 0.177817i | ||||||
\(201\) | −16.4853 | − | 6.82843i | −1.16278 | − | 0.481640i | ||||
\(202\) | 3.92893 | − | 3.92893i | 0.276439 | − | 0.276439i | ||||
\(203\) | −4.82843 | −0.338889 | ||||||||
\(204\) | 8.07107 | + | 17.9706i | 0.565088 | + | 1.25819i | ||||
\(205\) | −15.0711 | −1.05261 | ||||||||
\(206\) | 1.31371 | − | 1.31371i | 0.0915304 | − | 0.0915304i | ||||
\(207\) | 14.6569 | + | 6.07107i | 1.01872 | + | 0.421968i | ||||
\(208\) | 4.24264i | 0.294174i | ||||||||
\(209\) | −2.00000 | + | 4.82843i | −0.138343 | + | 0.333989i | ||||
\(210\) | 2.00000 | − | 0.828427i | 0.138013 | − | 0.0571669i | ||||
\(211\) | 5.72792 | + | 13.8284i | 0.394326 | + | 0.951988i | 0.988986 | + | 0.148010i | \(0.0472869\pi\) |
−0.594659 | + | 0.803978i | \(0.702713\pi\) | |||||||
\(212\) | −1.82843 | − | 1.82843i | −0.125577 | − | 0.125577i | ||||
\(213\) | −24.1421 | − | 24.1421i | −1.65419 | − | 1.65419i | ||||
\(214\) | −1.00000 | − | 2.41421i | −0.0683586 | − | 0.165032i | ||||
\(215\) | −8.24264 | + | 3.41421i | −0.562143 | + | 0.232847i | ||||
\(216\) | −1.31371 | + | 3.17157i | −0.0893865 | + | 0.215798i | ||||
\(217\) | − | 3.51472i | − | 0.238595i | ||||||
\(218\) | −1.63604 | − | 0.677670i | −0.110807 | − | 0.0458976i | ||||
\(219\) | 9.89949 | − | 9.89949i | 0.668946 | − | 0.668946i | ||||
\(220\) | −3.65685 | −0.246545 | ||||||||
\(221\) | 4.24264 | + | 4.00000i | 0.285391 | + | 0.269069i | ||||
\(222\) | −4.14214 | −0.278002 | ||||||||
\(223\) | 0.585786 | − | 0.585786i | 0.0392272 | − | 0.0392272i | −0.687221 | − | 0.726448i | \(-0.741170\pi\) |
0.726448 | + | 0.687221i | \(0.241170\pi\) | |||||||
\(224\) | 4.41421 | + | 1.82843i | 0.294937 | + | 0.122167i | ||||
\(225\) | 6.07107i | 0.404738i | ||||||||
\(226\) | −2.56497 | + | 6.19239i | −0.170619 | + | 0.411912i | ||||
\(227\) | −4.65685 | + | 1.92893i | −0.309086 | + | 0.128028i | −0.531835 | − | 0.846848i | \(-0.678497\pi\) |
0.222748 | + | 0.974876i | \(0.428497\pi\) | |||||||
\(228\) | −8.82843 | − | 21.3137i | −0.584677 | − | 1.41153i | ||||
\(229\) | 16.1421 | + | 16.1421i | 1.06670 | + | 1.06670i | 0.997610 | + | 0.0690921i | \(0.0220102\pi\) |
0.0690921 | + | 0.997610i | \(0.477990\pi\) | |||||||
\(230\) | 2.24264 | + | 2.24264i | 0.147875 | + | 0.147875i | ||||
\(231\) | 1.17157 | + | 2.82843i | 0.0770838 | + | 0.186097i | ||||
\(232\) | 6.53553 | − | 2.70711i | 0.429079 | − | 0.177730i | ||||
\(233\) | 3.87868 | − | 9.36396i | 0.254101 | − | 0.613453i | −0.744427 | − | 0.667704i | \(-0.767277\pi\) |
0.998527 | + | 0.0542508i | \(0.0172771\pi\) | |||||||
\(234\) | 2.24264i | 0.146606i | ||||||||
\(235\) | 18.4853 | + | 7.65685i | 1.20585 | + | 0.499478i | ||||
\(236\) | 7.75736 | − | 7.75736i | 0.504961 | − | 0.504961i | ||||
\(237\) | 10.8284 | 0.703382 | ||||||||
\(238\) | 1.68629 | − | 0.757359i | 0.109306 | − | 0.0490923i | ||||
\(239\) | 9.17157 | 0.593260 | 0.296630 | − | 0.954993i | \(-0.404137\pi\) | ||||
0.296630 | + | 0.954993i | \(0.404137\pi\) | |||||||
\(240\) | 10.2426 | − | 10.2426i | 0.661160 | − | 0.661160i | ||||
\(241\) | 11.3640 | + | 4.70711i | 0.732017 | + | 0.303211i | 0.717381 | − | 0.696681i | \(-0.245341\pi\) |
0.0146365 | + | 0.999893i | \(0.495341\pi\) | |||||||
\(242\) | − | 4.07107i | − | 0.261698i | ||||||
\(243\) | −8.31371 | + | 20.0711i | −0.533325 | + | 1.28756i | ||||
\(244\) | −15.6066 | + | 6.46447i | −0.999110 | + | 0.413845i | ||||
\(245\) | −4.12132 | − | 9.94975i | −0.263301 | − | 0.635666i | ||||
\(246\) | −6.24264 | − | 6.24264i | −0.398016 | − | 0.398016i | ||||
\(247\) | −4.82843 | − | 4.82843i | −0.307225 | − | 0.307225i | ||||
\(248\) | 1.97056 | + | 4.75736i | 0.125131 | + | 0.302093i | ||||
\(249\) | 0.828427 | − | 0.343146i | 0.0524994 | − | 0.0217460i | ||||
\(250\) | −1.92893 | + | 4.65685i | −0.121996 | + | 0.294525i | ||||
\(251\) | 3.51472i | 0.221847i | 0.993829 | + | 0.110924i | \(0.0353809\pi\) | ||||
−0.993829 | + | 0.110924i | \(0.964619\pi\) | |||||||
\(252\) | −7.00000 | − | 2.89949i | −0.440959 | − | 0.182651i | ||||
\(253\) | −3.17157 | + | 3.17157i | −0.199395 | + | 0.199395i | ||||
\(254\) | 7.17157 | 0.449985 | ||||||||
\(255\) | −0.585786 | − | 19.8995i | −0.0366834 | − | 1.24615i | ||||
\(256\) | 3.97056 | 0.248160 | ||||||||
\(257\) | −15.6569 | + | 15.6569i | −0.976648 | + | 0.976648i | −0.999733 | − | 0.0230858i | \(-0.992651\pi\) |
0.0230858 | + | 0.999733i | \(0.492651\pi\) | |||||||
\(258\) | −4.82843 | − | 2.00000i | −0.300605 | − | 0.124515i | ||||
\(259\) | − | 4.14214i | − | 0.257380i | ||||||
\(260\) | 1.82843 | − | 4.41421i | 0.113394 | − | 0.273758i | ||||
\(261\) | −15.7782 | + | 6.53553i | −0.976644 | + | 0.404539i | ||||
\(262\) | 0.0294373 | + | 0.0710678i | 0.00181864 | + | 0.00439058i | ||||
\(263\) | −4.58579 | − | 4.58579i | −0.282772 | − | 0.282772i | 0.551442 | − | 0.834213i | \(-0.314078\pi\) |
−0.834213 | + | 0.551442i | \(0.814078\pi\) | |||||||
\(264\) | −3.17157 | − | 3.17157i | −0.195197 | − | 0.195197i | ||||
\(265\) | 1.00000 | + | 2.41421i | 0.0614295 | + | 0.148304i | ||||
\(266\) | −2.00000 | + | 0.828427i | −0.122628 | + | 0.0507941i | ||||
\(267\) | −9.41421 | + | 22.7279i | −0.576141 | + | 1.39093i | ||||
\(268\) | 12.4853i | 0.762660i | ||||||||
\(269\) | 5.87868 | + | 2.43503i | 0.358429 | + | 0.148466i | 0.554629 | − | 0.832098i | \(-0.312860\pi\) |
−0.196200 | + | 0.980564i | \(0.562860\pi\) | |||||||
\(270\) | 1.17157 | − | 1.17157i | 0.0712997 | − | 0.0712997i | ||||
\(271\) | −6.14214 | −0.373108 | −0.186554 | − | 0.982445i | \(-0.559732\pi\) | ||||
−0.186554 | + | 0.982445i | \(0.559732\pi\) | |||||||
\(272\) | 8.48528 | − | 9.00000i | 0.514496 | − | 0.545705i | ||||
\(273\) | −4.00000 | −0.242091 | ||||||||
\(274\) | −2.55635 | + | 2.55635i | −0.154435 | + | 0.154435i | ||||
\(275\) | −1.58579 | − | 0.656854i | −0.0956265 | − | 0.0396098i | ||||
\(276\) | − | 19.7990i | − | 1.19176i | ||||||
\(277\) | 8.43503 | − | 20.3640i | 0.506812 | − | 1.22355i | −0.438897 | − | 0.898537i | \(-0.644631\pi\) |
0.945709 | − | 0.325015i | \(-0.105369\pi\) | |||||||
\(278\) | 5.72792 | − | 2.37258i | 0.343538 | − | 0.142298i | ||||
\(279\) | −4.75736 | − | 11.4853i | −0.284816 | − | 0.687606i | ||||
\(280\) | −2.24264 | − | 2.24264i | −0.134023 | − | 0.134023i | ||||
\(281\) | −12.6569 | − | 12.6569i | −0.755045 | − | 0.755045i | 0.220371 | − | 0.975416i | \(-0.429273\pi\) |
−0.975416 | + | 0.220371i | \(0.929273\pi\) | |||||||
\(282\) | 4.48528 | + | 10.8284i | 0.267095 | + | 0.644823i | ||||
\(283\) | 21.1421 | − | 8.75736i | 1.25677 | − | 0.520571i | 0.347853 | − | 0.937549i | \(-0.386911\pi\) |
0.908917 | + | 0.416978i | \(0.136911\pi\) | |||||||
\(284\) | −9.14214 | + | 22.0711i | −0.542486 | + | 1.30968i | ||||
\(285\) | 23.3137i | 1.38098i | ||||||||
\(286\) | −0.585786 | − | 0.242641i | −0.0346383 | − | 0.0143476i | ||||
\(287\) | 6.24264 | − | 6.24264i | 0.368491 | − | 0.368491i | ||||
\(288\) | 16.8995 | 0.995812 | ||||||||
\(289\) | −1.00000 | − | 16.9706i | −0.0588235 | − | 0.998268i | ||||
\(290\) | −3.41421 | −0.200490 | ||||||||
\(291\) | −11.8995 | + | 11.8995i | −0.697561 | + | 0.697561i | ||||
\(292\) | −9.05025 | − | 3.74874i | −0.529626 | − | 0.219378i | ||||
\(293\) | 23.6569i | 1.38205i | 0.722832 | + | 0.691024i | \(0.242840\pi\) | ||||
−0.722832 | + | 0.691024i | \(0.757160\pi\) | |||||||
\(294\) | 2.41421 | − | 5.82843i | 0.140800 | − | 0.339921i | ||||
\(295\) | −10.2426 | + | 4.24264i | −0.596350 | + | 0.247016i | ||||
\(296\) | 2.32233 | + | 5.60660i | 0.134983 | + | 0.325877i | ||||
\(297\) | 1.65685 | + | 1.65685i | 0.0961404 | + | 0.0961404i | ||||
\(298\) | −4.97056 | − | 4.97056i | −0.287937 | − | 0.287937i | ||||
\(299\) | −2.24264 | − | 5.41421i | −0.129695 | − | 0.313112i | ||||
\(300\) | 7.00000 | − | 2.89949i | 0.404145 | − | 0.167402i | ||||
\(301\) | 2.00000 | − | 4.82843i | 0.115278 | − | 0.278306i | ||||
\(302\) | − | 5.31371i | − | 0.305770i | ||||||
\(303\) | 32.3848 | + | 13.4142i | 1.86046 | + | 0.770626i | ||||
\(304\) | −10.2426 | + | 10.2426i | −0.587456 | + | 0.587456i | ||||
\(305\) | 17.0711 | 0.977486 | ||||||||
\(306\) | 4.48528 | − | 4.75736i | 0.256406 | − | 0.271960i | ||||
\(307\) | 2.14214 | 0.122258 | 0.0611291 | − | 0.998130i | \(-0.480530\pi\) | ||||
0.0611291 | + | 0.998130i | \(0.480530\pi\) | |||||||
\(308\) | 1.51472 | − | 1.51472i | 0.0863091 | − | 0.0863091i | ||||
\(309\) | 10.8284 | + | 4.48528i | 0.616008 | + | 0.255159i | ||||
\(310\) | − | 2.48528i | − | 0.141154i | ||||||
\(311\) | −1.72792 | + | 4.17157i | −0.0979815 | + | 0.236548i | −0.965268 | − | 0.261261i | \(-0.915862\pi\) |
0.867287 | + | 0.497809i | \(0.165862\pi\) | |||||||
\(312\) | 5.41421 | − | 2.24264i | 0.306519 | − | 0.126965i | ||||
\(313\) | −4.87868 | − | 11.7782i | −0.275759 | − | 0.665742i | 0.723950 | − | 0.689852i | \(-0.242325\pi\) |
−0.999709 | + | 0.0241106i | \(0.992325\pi\) | |||||||
\(314\) | 0.485281 | + | 0.485281i | 0.0273860 | + | 0.0273860i | ||||
\(315\) | 5.41421 | + | 5.41421i | 0.305056 | + | 0.305056i | ||||
\(316\) | −2.89949 | − | 7.00000i | −0.163109 | − | 0.393781i | ||||
\(317\) | −5.36396 | + | 2.22183i | −0.301270 | + | 0.124790i | −0.528198 | − | 0.849122i | \(-0.677132\pi\) |
0.226927 | + | 0.973912i | \(0.427132\pi\) | |||||||
\(318\) | −0.585786 | + | 1.41421i | −0.0328493 | + | 0.0793052i | ||||
\(319\) | − | 4.82843i | − | 0.270340i | ||||||
\(320\) | −7.12132 | − | 2.94975i | −0.398094 | − | 0.164896i | ||||
\(321\) | 11.6569 | − | 11.6569i | 0.650622 | − | 0.650622i | ||||
\(322\) | −1.85786 | −0.103535 | ||||||||
\(323\) | 0.585786 | + | 19.8995i | 0.0325940 | + | 1.10724i | ||||
\(324\) | 10.6569 | 0.592047 | ||||||||
\(325\) | 1.58579 | − | 1.58579i | 0.0879636 | − | 0.0879636i | ||||
\(326\) | 2.17157 | + | 0.899495i | 0.120272 | + | 0.0498184i | ||||
\(327\) | − | 11.1716i | − | 0.617789i | ||||||
\(328\) | −4.94975 | + | 11.9497i | −0.273304 | + | 0.659814i | ||||
\(329\) | −10.8284 | + | 4.48528i | −0.596991 | + | 0.247282i | ||||
\(330\) | 0.828427 | + | 2.00000i | 0.0456034 | + | 0.110096i | ||||
\(331\) | −12.5858 | − | 12.5858i | −0.691777 | − | 0.691777i | 0.270845 | − | 0.962623i | \(-0.412697\pi\) |
−0.962623 | + | 0.270845i | \(0.912697\pi\) | |||||||
\(332\) | −0.443651 | − | 0.443651i | −0.0243485 | − | 0.0243485i | ||||
\(333\) | −5.60660 | − | 13.5355i | −0.307240 | − | 0.741743i | ||||
\(334\) | −3.82843 | + | 1.58579i | −0.209482 | + | 0.0867704i | ||||
\(335\) | 4.82843 | − | 11.6569i | 0.263805 | − | 0.636882i | ||||
\(336\) | 8.48528i | 0.462910i | ||||||||
\(337\) | −31.8492 | − | 13.1924i | −1.73494 | − | 0.718635i | −0.999141 | − | 0.0414336i | \(-0.986808\pi\) |
−0.735798 | − | 0.677202i | \(-0.763192\pi\) | |||||||
\(338\) | −3.22183 | + | 3.22183i | −0.175244 | + | 0.175244i | ||||
\(339\) | −42.2843 | −2.29657 | ||||||||
\(340\) | −12.7071 | + | 5.70711i | −0.689140 | + | 0.309511i | ||||
\(341\) | 3.51472 | 0.190333 | ||||||||
\(342\) | −5.41421 | + | 5.41421i | −0.292767 | + | 0.292767i | ||||
\(343\) | 12.8284 | + | 5.31371i | 0.692670 | + | 0.286913i | ||||
\(344\) | 7.65685i | 0.412830i | ||||||||
\(345\) | −7.65685 | + | 18.4853i | −0.412231 | + | 0.995214i | ||||
\(346\) | 1.29289 | − | 0.535534i | 0.0695064 | − | 0.0287905i | ||||
\(347\) | −1.48528 | − | 3.58579i | −0.0797341 | − | 0.192495i | 0.878985 | − | 0.476849i | \(-0.158221\pi\) |
−0.958719 | + | 0.284354i | \(0.908221\pi\) | |||||||
\(348\) | 15.0711 | + | 15.0711i | 0.807894 | + | 0.807894i | ||||
\(349\) | 3.00000 | + | 3.00000i | 0.160586 | + | 0.160586i | 0.782826 | − | 0.622240i | \(-0.213777\pi\) |
−0.622240 | + | 0.782826i | \(0.713777\pi\) | |||||||
\(350\) | −0.272078 | − | 0.656854i | −0.0145432 | − | 0.0351103i | ||||
\(351\) | −2.82843 | + | 1.17157i | −0.150970 | + | 0.0625339i | ||||
\(352\) | −1.82843 | + | 4.41421i | −0.0974555 | + | 0.235278i | ||||
\(353\) | − | 14.0000i | − | 0.745145i | −0.928003 | − | 0.372572i | \(-0.878476\pi\) | ||
0.928003 | − | 0.372572i | \(-0.121524\pi\) | |||||||
\(354\) | −6.00000 | − | 2.48528i | −0.318896 | − | 0.132091i | ||||
\(355\) | 17.0711 | − | 17.0711i | 0.906038 | − | 0.906038i | ||||
\(356\) | 17.2132 | 0.912298 | ||||||||
\(357\) | 8.48528 | + | 8.00000i | 0.449089 | + | 0.423405i | ||||
\(358\) | −2.48528 | −0.131351 | ||||||||
\(359\) | 16.3848 | − | 16.3848i | 0.864755 | − | 0.864755i | −0.127131 | − | 0.991886i | \(-0.540577\pi\) |
0.991886 | + | 0.127131i | \(0.0405767\pi\) | |||||||
\(360\) | −10.3640 | − | 4.29289i | −0.546229 | − | 0.226255i | ||||
\(361\) | − | 4.31371i | − | 0.227037i | ||||||
\(362\) | 1.97918 | − | 4.77817i | 0.104024 | − | 0.251135i | ||||
\(363\) | 23.7279 | − | 9.82843i | 1.24539 | − | 0.515859i | ||||
\(364\) | 1.07107 | + | 2.58579i | 0.0561392 | + | 0.135532i | ||||
\(365\) | 7.00000 | + | 7.00000i | 0.366397 | + | 0.366397i | ||||
\(366\) | 7.07107 | + | 7.07107i | 0.369611 | + | 0.369611i | ||||
\(367\) | 10.0711 | + | 24.3137i | 0.525705 | + | 1.26917i | 0.934313 | + | 0.356455i | \(0.116015\pi\) |
−0.408607 | + | 0.912710i | \(0.633985\pi\) | |||||||
\(368\) | −11.4853 | + | 4.75736i | −0.598712 | + | 0.247994i | ||||
\(369\) | 11.9497 | − | 28.8492i | 0.622079 | − | 1.50183i | ||||
\(370\) | − | 2.92893i | − | 0.152268i | ||||||
\(371\) | −1.41421 | − | 0.585786i | −0.0734223 | − | 0.0304125i | ||||
\(372\) | −10.9706 | + | 10.9706i | −0.568797 | + | 0.568797i | ||||
\(373\) | −19.5563 | −1.01259 | −0.506295 | − | 0.862361i | \(-0.668985\pi\) | ||||
−0.506295 | + | 0.862361i | \(0.668985\pi\) | |||||||
\(374\) | 0.757359 | + | 1.68629i | 0.0391621 | + | 0.0871961i | ||||
\(375\) | −31.7990 | −1.64209 | ||||||||
\(376\) | 12.1421 | − | 12.1421i | 0.626183 | − | 0.626183i | ||||
\(377\) | 5.82843 | + | 2.41421i | 0.300179 | + | 0.124338i | ||||
\(378\) | 0.970563i | 0.0499204i | ||||||||
\(379\) | 0.414214 | − | 1.00000i | 0.0212767 | − | 0.0513665i | −0.912884 | − | 0.408219i | \(-0.866150\pi\) |
0.934161 | + | 0.356852i | \(0.116150\pi\) | |||||||
\(380\) | 15.0711 | − | 6.24264i | 0.773129 | − | 0.320241i | ||||
\(381\) | 17.3137 | + | 41.7990i | 0.887008 | + | 2.14143i | ||||
\(382\) | 5.85786 | + | 5.85786i | 0.299714 | + | 0.299714i | ||||
\(383\) | 3.89949 | + | 3.89949i | 0.199255 | + | 0.199255i | 0.799681 | − | 0.600426i | \(-0.205002\pi\) |
−0.600426 | + | 0.799681i | \(0.705002\pi\) | |||||||
\(384\) | −10.5563 | − | 25.4853i | −0.538701 | − | 1.30054i | ||||
\(385\) | −2.00000 | + | 0.828427i | −0.101929 | + | 0.0422206i | ||||
\(386\) | −0.878680 | + | 2.12132i | −0.0447236 | + | 0.107972i | ||||
\(387\) | − | 18.4853i | − | 0.939660i | ||||||
\(388\) | 10.8787 | + | 4.50610i | 0.552281 | + | 0.228762i | ||||
\(389\) | −11.4142 | + | 11.4142i | −0.578724 | + | 0.578724i | −0.934551 | − | 0.355828i | \(-0.884199\pi\) |
0.355828 | + | 0.934551i | \(0.384199\pi\) | |||||||
\(390\) | −2.82843 | −0.143223 | ||||||||
\(391\) | −6.07107 | + | 15.9706i | −0.307027 | + | 0.807666i | ||||
\(392\) | −9.24264 | −0.466824 | ||||||||
\(393\) | −0.343146 | + | 0.343146i | −0.0173094 | + | 0.0173094i | ||||
\(394\) | 5.70711 | + | 2.36396i | 0.287520 | + | 0.119095i | ||||
\(395\) | 7.65685i | 0.385258i | ||||||||
\(396\) | 2.89949 | − | 7.00000i | 0.145705 | − | 0.351763i | ||||
\(397\) | 25.1924 | − | 10.4350i | 1.26437 | − | 0.523719i | 0.353122 | − | 0.935577i | \(-0.385120\pi\) |
0.911248 | + | 0.411858i | \(0.135120\pi\) | |||||||
\(398\) | −0.272078 | − | 0.656854i | −0.0136380 | − | 0.0329251i | ||||
\(399\) | −9.65685 | − | 9.65685i | −0.483447 | − | 0.483447i | ||||
\(400\) | −3.36396 | − | 3.36396i | −0.168198 | − | 0.168198i | ||||
\(401\) | 6.53553 | + | 15.7782i | 0.326369 | + | 0.787924i | 0.998856 | + | 0.0478157i | \(0.0152260\pi\) |
−0.672487 | + | 0.740109i | \(0.734774\pi\) | |||||||
\(402\) | 6.82843 | − | 2.82843i | 0.340571 | − | 0.141069i | ||||
\(403\) | −1.75736 | + | 4.24264i | −0.0875403 | + | 0.211341i | ||||
\(404\) | − | 24.5269i | − | 1.22026i | ||||||
\(405\) | −9.94975 | − | 4.12132i | −0.494407 | − | 0.204790i | ||||
\(406\) | 1.41421 | − | 1.41421i | 0.0701862 | − | 0.0701862i | ||||
\(407\) | 4.14214 | 0.205318 | ||||||||
\(408\) | −15.9706 | − | 6.07107i | −0.790661 | − | 0.300563i | ||||
\(409\) | 19.3137 | 0.955001 | 0.477501 | − | 0.878631i | \(-0.341543\pi\) | ||||
0.477501 | + | 0.878631i | \(0.341543\pi\) | |||||||
\(410\) | 4.41421 | − | 4.41421i | 0.218002 | − | 0.218002i | ||||
\(411\) | −21.0711 | − | 8.72792i | −1.03936 | − | 0.430517i | ||||
\(412\) | − | 8.20101i | − | 0.404035i | ||||||
\(413\) | 2.48528 | − | 6.00000i | 0.122293 | − | 0.295241i | ||||
\(414\) | −6.07107 | + | 2.51472i | −0.298377 | + | 0.123592i | ||||
\(415\) | 0.242641 | + | 0.585786i | 0.0119108 | + | 0.0287551i | ||||
\(416\) | −4.41421 | − | 4.41421i | −0.216425 | − | 0.216425i | ||||
\(417\) | 27.6569 | + | 27.6569i | 1.35436 | + | 1.35436i | ||||
\(418\) | −0.828427 | − | 2.00000i | −0.0405197 | − | 0.0978232i | ||||
\(419\) | −24.8995 | + | 10.3137i | −1.21642 | + | 0.503858i | −0.896270 | − | 0.443509i | \(-0.853733\pi\) |
−0.320150 | + | 0.947367i | \(0.603733\pi\) | |||||||
\(420\) | 3.65685 | − | 8.82843i | 0.178436 | − | 0.430783i | ||||
\(421\) | 17.4142i | 0.848717i | 0.905494 | + | 0.424358i | \(0.139500\pi\) | ||||
−0.905494 | + | 0.424358i | \(0.860500\pi\) | |||||||
\(422\) | −5.72792 | − | 2.37258i | −0.278831 | − | 0.115496i | ||||
\(423\) | −29.3137 | + | 29.3137i | −1.42528 | + | 1.42528i | ||||
\(424\) | 2.24264 | 0.108912 | ||||||||
\(425\) | −6.53553 | + | 0.192388i | −0.317020 | + | 0.00933220i | ||||
\(426\) | 14.1421 | 0.685189 | ||||||||
\(427\) | −7.07107 | + | 7.07107i | −0.342193 | + | 0.342193i | ||||
\(428\) | −10.6569 | − | 4.41421i | −0.515118 | − | 0.213369i | ||||
\(429\) | − | 4.00000i | − | 0.193122i | ||||||
\(430\) | 1.41421 | − | 3.41421i | 0.0681994 | − | 0.164648i | ||||
\(431\) | −36.7990 | + | 15.2426i | −1.77254 | + | 0.734212i | −0.778200 | + | 0.628017i | \(0.783867\pi\) |
−0.994345 | + | 0.106195i | \(0.966133\pi\) | |||||||
\(432\) | 2.48528 | + | 6.00000i | 0.119573 | + | 0.288675i | ||||
\(433\) | −10.7279 | − | 10.7279i | −0.515551 | − | 0.515551i | 0.400671 | − | 0.916222i | \(-0.368777\pi\) |
−0.916222 | + | 0.400671i | \(0.868777\pi\) | |||||||
\(434\) | 1.02944 | + | 1.02944i | 0.0494146 | + | 0.0494146i | ||||
\(435\) | −8.24264 | − | 19.8995i | −0.395204 | − | 0.954108i | ||||
\(436\) | −7.22183 | + | 2.99138i | −0.345863 | + | 0.143261i | ||||
\(437\) | 7.65685 | − | 18.4853i | 0.366277 | − | 0.884271i | ||||
\(438\) | 5.79899i | 0.277086i | ||||||||
\(439\) | 10.0711 | + | 4.17157i | 0.480666 | + | 0.199098i | 0.609841 | − | 0.792523i | \(-0.291233\pi\) |
−0.129176 | + | 0.991622i | \(0.541233\pi\) | |||||||
\(440\) | 2.24264 | − | 2.24264i | 0.106914 | − | 0.106914i | ||||
\(441\) | 22.3137 | 1.06256 | ||||||||
\(442\) | −2.41421 | + | 0.0710678i | −0.114832 | + | 0.00338035i | ||||
\(443\) | 15.7990 | 0.750633 | 0.375316 | − | 0.926897i | \(-0.377534\pi\) | ||||
0.375316 | + | 0.926897i | \(0.377534\pi\) | |||||||
\(444\) | −12.9289 | + | 12.9289i | −0.613580 | + | 0.613580i | ||||
\(445\) | −16.0711 | − | 6.65685i | −0.761842 | − | 0.315565i | ||||
\(446\) | 0.343146i | 0.0162484i | ||||||||
\(447\) | 16.9706 | − | 40.9706i | 0.802680 | − | 1.93784i | ||||
\(448\) | 4.17157 | − | 1.72792i | 0.197088 | − | 0.0816366i | ||||
\(449\) | −7.19239 | − | 17.3640i | −0.339430 | − | 0.819456i | −0.997771 | − | 0.0667361i | \(-0.978741\pi\) |
0.658341 | − | 0.752720i | \(-0.271259\pi\) | |||||||
\(450\) | −1.77817 | − | 1.77817i | −0.0838240 | − | 0.0838240i | ||||
\(451\) | 6.24264 | + | 6.24264i | 0.293954 | + | 0.293954i | ||||
\(452\) | 11.3223 | + | 27.3345i | 0.532558 | + | 1.28571i | ||||
\(453\) | 30.9706 | − | 12.8284i | 1.45512 | − | 0.602732i | ||||
\(454\) | 0.798990 | − | 1.92893i | 0.0374985 | − | 0.0905293i | ||||
\(455\) | − | 2.82843i | − | 0.132599i | ||||||
\(456\) | 18.4853 | + | 7.65685i | 0.865653 | + | 0.358565i | ||||
\(457\) | −13.3137 | + | 13.3137i | −0.622789 | + | 0.622789i | −0.946244 | − | 0.323455i | \(-0.895156\pi\) |
0.323455 | + | 0.946244i | \(0.395156\pi\) | |||||||
\(458\) | −9.45584 | −0.441843 | ||||||||
\(459\) | 8.34315 | + | 3.17157i | 0.389425 | + | 0.148036i | ||||
\(460\) | 14.0000 | 0.652753 | ||||||||
\(461\) | 17.0000 | − | 17.0000i | 0.791769 | − | 0.791769i | −0.190013 | − | 0.981782i | \(-0.560853\pi\) |
0.981782 | + | 0.190013i | \(0.0608529\pi\) | |||||||
\(462\) | −1.17157 | − | 0.485281i | −0.0545065 | − | 0.0225773i | ||||
\(463\) | 30.6274i | 1.42338i | 0.702495 | + | 0.711688i | \(0.252069\pi\) | ||||
−0.702495 | + | 0.711688i | \(0.747931\pi\) | |||||||
\(464\) | 5.12132 | − | 12.3640i | 0.237751 | − | 0.573982i | ||||
\(465\) | 14.4853 | − | 6.00000i | 0.671739 | − | 0.278243i | ||||
\(466\) | 1.60660 | + | 3.87868i | 0.0744244 | + | 0.179676i | ||||
\(467\) | 8.92893 | + | 8.92893i | 0.413182 | + | 0.413182i | 0.882845 | − | 0.469664i | \(-0.155625\pi\) |
−0.469664 | + | 0.882845i | \(0.655625\pi\) | |||||||
\(468\) | 7.00000 | + | 7.00000i | 0.323575 | + | 0.323575i | ||||
\(469\) | 2.82843 | + | 6.82843i | 0.130605 | + | 0.315307i | ||||
\(470\) | −7.65685 | + | 3.17157i | −0.353184 | + | 0.146294i | ||||
\(471\) | −1.65685 | + | 4.00000i | −0.0763438 | + | 0.184310i | ||||
\(472\) | 9.51472i | 0.437950i | ||||||||
\(473\) | 4.82843 | + | 2.00000i | 0.222011 | + | 0.0919601i | ||||
\(474\) | −3.17157 | + | 3.17157i | −0.145675 | + | 0.145675i | ||||
\(475\) | 7.65685 | 0.351321 | ||||||||
\(476\) | 2.89949 | − | 7.62742i | 0.132898 | − | 0.349602i | ||||
\(477\) | −5.41421 | −0.247900 | ||||||||
\(478\) | −2.68629 | + | 2.68629i | −0.122868 | + | 0.122868i | ||||
\(479\) | −31.9706 | − | 13.2426i | −1.46077 | − | 0.605072i | −0.496039 | − | 0.868300i | \(-0.665213\pi\) |
−0.964733 | + | 0.263229i | \(0.915213\pi\) | |||||||
\(480\) | 21.3137i | 0.972833i | ||||||||
\(481\) | −2.07107 | + | 5.00000i | −0.0944326 | + | 0.227980i | ||||
\(482\) | −4.70711 | + | 1.94975i | −0.214403 | + | 0.0888086i | ||||
\(483\) | −4.48528 | − | 10.8284i | −0.204087 | − | 0.492710i | ||||
\(484\) | −12.7071 | − | 12.7071i | −0.577596 | − | 0.577596i | ||||
\(485\) | −8.41421 | − | 8.41421i | −0.382070 | − | 0.382070i | ||||
\(486\) | −3.44365 | − | 8.31371i | −0.156207 | − | 0.377117i | ||||
\(487\) | −4.07107 | + | 1.68629i | −0.184478 | + | 0.0764132i | −0.473010 | − | 0.881057i | \(-0.656833\pi\) |
0.288533 | + | 0.957470i | \(0.406833\pi\) | |||||||
\(488\) | 5.60660 | − | 13.5355i | 0.253799 | − | 0.612725i | ||||
\(489\) | 14.8284i | 0.670565i | ||||||||
\(490\) | 4.12132 | + | 1.70711i | 0.186182 | + | 0.0771192i | ||||
\(491\) | 17.7574 | − | 17.7574i | 0.801378 | − | 0.801378i | −0.181933 | − | 0.983311i | \(-0.558235\pi\) |
0.983311 | + | 0.181933i | \(0.0582353\pi\) | |||||||
\(492\) | −38.9706 | −1.75693 | ||||||||
\(493\) | −7.53553 | − | 16.7782i | −0.339383 | − | 0.755651i | ||||
\(494\) | 2.82843 | 0.127257 | ||||||||
\(495\) | −5.41421 | + | 5.41421i | −0.243351 | + | 0.243351i | ||||
\(496\) | 9.00000 | + | 3.72792i | 0.404112 | + | 0.167389i | ||||
\(497\) | 14.1421i | 0.634361i | ||||||||
\(498\) | −0.142136 | + | 0.343146i | −0.00636925 | + | 0.0153767i | ||||
\(499\) | 34.2132 | − | 14.1716i | 1.53159 | − | 0.634407i | 0.551720 | − | 0.834029i | \(-0.313972\pi\) |
0.979873 | + | 0.199622i | \(0.0639715\pi\) | |||||||
\(500\) | 8.51472 | + | 20.5563i | 0.380790 | + | 0.919308i | ||||
\(501\) | −18.4853 | − | 18.4853i | −0.825861 | − | 0.825861i | ||||
\(502\) | −1.02944 | − | 1.02944i | −0.0459460 | − | 0.0459460i | ||||
\(503\) | 5.72792 | + | 13.8284i | 0.255395 | + | 0.616579i | 0.998623 | − | 0.0524595i | \(-0.0167061\pi\) |
−0.743228 | + | 0.669039i | \(0.766706\pi\) | |||||||
\(504\) | 6.07107 | − | 2.51472i | 0.270427 | − | 0.112014i | ||||
\(505\) | −9.48528 | + | 22.8995i | −0.422089 | + | 1.01901i | ||||
\(506\) | − | 1.85786i | − | 0.0825921i | ||||||
\(507\) | −26.5563 | − | 11.0000i | −1.17941 | − | 0.488527i | ||||
\(508\) | 22.3848 | − | 22.3848i | 0.993164 | − | 0.993164i | ||||
\(509\) | −3.02944 | −0.134277 | −0.0671387 | − | 0.997744i | \(-0.521387\pi\) | ||||
−0.0671387 | + | 0.997744i | \(0.521387\pi\) | |||||||
\(510\) | 6.00000 | + | 5.65685i | 0.265684 | + | 0.250490i | ||||
\(511\) | −5.79899 | −0.256532 | ||||||||
\(512\) | −16.0919 | + | 16.0919i | −0.711167 | + | 0.711167i | ||||
\(513\) | −9.65685 | − | 4.00000i | −0.426361 | − | 0.176604i | ||||
\(514\) | − | 9.17157i | − | 0.404541i | ||||||
\(515\) | −3.17157 | + | 7.65685i | −0.139756 | + | 0.337401i | ||||
\(516\) | −21.3137 | + | 8.82843i | −0.938284 | + | 0.388650i | ||||
\(517\) | −4.48528 | − | 10.8284i | −0.197262 | − | 0.476234i | ||||
\(518\) | 1.21320 | + | 1.21320i | 0.0533051 | + | 0.0533051i | ||||
\(519\) | 6.24264 | + | 6.24264i | 0.274022 | + | 0.274022i | ||||
\(520\) | 1.58579 | + | 3.82843i | 0.0695413 | + | 0.167888i | ||||
\(521\) | 2.87868 | − | 1.19239i | 0.126117 | − | 0.0522395i | −0.318732 | − | 0.947845i | \(-0.603257\pi\) |
0.444850 | + | 0.895605i | \(0.353257\pi\) | |||||||
\(522\) | 2.70711 | − | 6.53553i | 0.118487 | − | 0.286053i | ||||
\(523\) | 6.82843i | 0.298586i | 0.988793 | + | 0.149293i | \(0.0476998\pi\) | ||||
−0.988793 | + | 0.149293i | \(0.952300\pi\) | |||||||
\(524\) | 0.313708 | + | 0.129942i | 0.0137044 | + | 0.00567656i | ||||
\(525\) | 3.17157 | − | 3.17157i | 0.138419 | − | 0.138419i | ||||
\(526\) | 2.68629 | 0.117128 | ||||||||
\(527\) | 12.2132 | − | 5.48528i | 0.532015 | − | 0.238943i | ||||
\(528\) | −8.48528 | −0.369274 | ||||||||
\(529\) | −4.12132 | + | 4.12132i | −0.179188 | + | 0.179188i | ||||
\(530\) | −1.00000 | − | 0.414214i | −0.0434372 | − | 0.0179923i | ||||
\(531\) | − | 22.9706i | − | 0.996838i | ||||||
\(532\) | −3.65685 | + | 8.82843i | −0.158545 | + | 0.382761i | ||||
\(533\) | −10.6569 | + | 4.41421i | −0.461600 | + | 0.191201i | ||||
\(534\) | −3.89949 | − | 9.41421i | −0.168748 | − | 0.407393i | ||||
\(535\) | 8.24264 | + | 8.24264i | 0.356360 | + | 0.356360i | ||||
\(536\) | −7.65685 | − | 7.65685i | −0.330726 | − | 0.330726i | ||||
\(537\) | −6.00000 | − | 14.4853i | −0.258919 | − | 0.625086i | ||||
\(538\) | −2.43503 | + | 1.00862i | −0.104982 | + | 0.0434848i | ||||
\(539\) | −2.41421 | + | 5.82843i | −0.103988 | + | 0.251048i | ||||
\(540\) | − | 7.31371i | − | 0.314732i | ||||||
\(541\) | −16.9497 | − | 7.02082i | −0.728727 | − | 0.301848i | −0.0126980 | − | 0.999919i | \(-0.504042\pi\) |
−0.716029 | + | 0.698071i | \(0.754042\pi\) | |||||||
\(542\) | 1.79899 | − | 1.79899i | 0.0772732 | − | 0.0772732i | ||||
\(543\) | 32.6274 | 1.40018 | ||||||||
\(544\) | 0.535534 | + | 18.1924i | 0.0229608 | + | 0.779992i | ||||
\(545\) | 7.89949 | 0.338377 | ||||||||
\(546\) | 1.17157 | − | 1.17157i | 0.0501387 | − | 0.0501387i | ||||
\(547\) | 22.8995 | + | 9.48528i | 0.979112 | + | 0.405561i | 0.814096 | − | 0.580730i | \(-0.197233\pi\) |
0.165015 | + | 0.986291i | \(0.447233\pi\) | |||||||
\(548\) | 15.9584i | 0.681708i | ||||||||
\(549\) | −13.5355 | + | 32.6777i | −0.577683 | + | 1.39465i | ||||
\(550\) | 0.656854 | − | 0.272078i | 0.0280084 | − | 0.0116014i | ||||
\(551\) | 8.24264 | + | 19.8995i | 0.351148 | + | 0.847747i | ||||
\(552\) | 12.1421 | + | 12.1421i | 0.516804 | + | 0.516804i | ||||
\(553\) | −3.17157 | − | 3.17157i | −0.134869 | − | 0.134869i | ||||
\(554\) | 3.49390 | + | 8.43503i | 0.148442 | + | 0.358370i | ||||
\(555\) | 17.0711 | − | 7.07107i | 0.724626 | − | 0.300150i | ||||
\(556\) | 10.4731 | − | 25.2843i | 0.444158 | − | 1.07229i | ||||
\(557\) | − | 28.2426i | − | 1.19668i | −0.801243 | − | 0.598340i | \(-0.795827\pi\) | ||
0.801243 | − | 0.598340i | \(-0.204173\pi\) | |||||||
\(558\) | 4.75736 | + | 1.97056i | 0.201395 | + | 0.0834206i | ||||
\(559\) | −4.82843 | + | 4.82843i | −0.204221 | + | 0.204221i | ||||
\(560\) | −6.00000 | −0.253546 | ||||||||
\(561\) | −8.00000 | + | 8.48528i | −0.337760 | + | 0.358249i | ||||
\(562\) | 7.41421 | 0.312750 | ||||||||
\(563\) | 27.4142 | − | 27.4142i | 1.15537 | − | 1.15537i | 0.169912 | − | 0.985459i | \(-0.445652\pi\) |
0.985459 | − | 0.169912i | \(-0.0543484\pi\) | |||||||
\(564\) | 47.7990 | + | 19.7990i | 2.01270 | + | 0.833688i | ||||
\(565\) | − | 29.8995i | − | 1.25788i | ||||||
\(566\) | −3.62742 | + | 8.75736i | −0.152472 | + | 0.368099i | ||||
\(567\) | 5.82843 | − | 2.41421i | 0.244771 | − | 0.101387i | ||||
\(568\) | −7.92893 | − | 19.1421i | −0.332691 | − | 0.803186i | ||||
\(569\) | 25.4853 | + | 25.4853i | 1.06840 | + | 1.06840i | 0.997482 | + | 0.0709163i | \(0.0225923\pi\) |
0.0709163 | + | 0.997482i | \(0.477408\pi\) | |||||||
\(570\) | −6.82843 | − | 6.82843i | −0.286011 | − | 0.286011i | ||||
\(571\) | −18.0711 | − | 43.6274i | −0.756251 | − | 1.82575i | −0.520295 | − | 0.853987i | \(-0.674178\pi\) |
−0.235956 | − | 0.971764i | \(-0.575822\pi\) | |||||||
\(572\) | −2.58579 | + | 1.07107i | −0.108117 | + | 0.0447836i | ||||
\(573\) | −20.0000 | + | 48.2843i | −0.835512 | + | 2.01710i | ||||
\(574\) | 3.65685i | 0.152634i | ||||||||
\(575\) | 6.07107 | + | 2.51472i | 0.253181 | + | 0.104871i | ||||
\(576\) | 11.2929 | − | 11.2929i | 0.470537 | − | 0.470537i | ||||
\(577\) | −12.9289 | −0.538238 | −0.269119 | − | 0.963107i | \(-0.586733\pi\) | ||||
−0.269119 | + | 0.963107i | \(0.586733\pi\) | |||||||
\(578\) | 5.26346 | + | 4.67767i | 0.218931 | + | 0.194565i | ||||
\(579\) | −14.4853 | −0.601988 | ||||||||
\(580\) | −10.6569 | + | 10.6569i | −0.442502 | + | 0.442502i | ||||
\(581\) | −0.343146 | − | 0.142136i | −0.0142361 | − | 0.00589678i | ||||
\(582\) | − | 6.97056i | − | 0.288939i | ||||||
\(583\) | 0.585786 | − | 1.41421i | 0.0242608 | − | 0.0585707i | ||||
\(584\) | 7.84924 | − | 3.25126i | 0.324804 | − | 0.134538i | ||||
\(585\) | −3.82843 | − | 9.24264i | −0.158286 | − | 0.382136i | ||||
\(586\) | −6.92893 | − | 6.92893i | −0.286232 | − | 0.286232i | ||||
\(587\) | −16.0416 | − | 16.0416i | −0.662109 | − | 0.662109i | 0.293768 | − | 0.955877i | \(-0.405091\pi\) |
−0.955877 | + | 0.293768i | \(0.905091\pi\) | |||||||
\(588\) | −10.6569 | − | 25.7279i | −0.439481 | − | 1.06100i | ||||
\(589\) | −14.4853 | + | 6.00000i | −0.596856 | + | 0.247226i | ||||
\(590\) | 1.75736 | − | 4.24264i | 0.0723493 | − | 0.174667i | ||||
\(591\) | 38.9706i | 1.60303i | ||||||||
\(592\) | 10.6066 | + | 4.39340i | 0.435929 | + | 0.180568i | ||||
\(593\) | −19.1421 | + | 19.1421i | −0.786073 | + | 0.786073i | −0.980848 | − | 0.194775i | \(-0.937602\pi\) |
0.194775 | + | 0.980848i | \(0.437602\pi\) | |||||||
\(594\) | −0.970563 | −0.0398227 | ||||||||
\(595\) | −5.65685 | + | 6.00000i | −0.231908 | + | 0.245976i | ||||
\(596\) | −31.0294 | −1.27102 | ||||||||
\(597\) | 3.17157 | − | 3.17157i | 0.129804 | − | 0.129804i | ||||
\(598\) | 2.24264 | + | 0.928932i | 0.0917084 | + | 0.0379869i | ||||
\(599\) | − | 34.6274i | − | 1.41484i | −0.706794 | − | 0.707419i | \(-0.749859\pi\) | ||
0.706794 | − | 0.707419i | \(-0.250141\pi\) | |||||||
\(600\) | −2.51472 | + | 6.07107i | −0.102663 | + | 0.247850i | ||||
\(601\) | −18.7782 | + | 7.77817i | −0.765978 | + | 0.317278i | −0.731242 | − | 0.682118i | \(-0.761059\pi\) |
−0.0347358 | + | 0.999397i | \(0.511059\pi\) | |||||||
\(602\) | 0.828427 | + | 2.00000i | 0.0337642 | + | 0.0815139i | ||||
\(603\) | 18.4853 | + | 18.4853i | 0.752779 | + | 0.752779i | ||||
\(604\) | −16.5858 | − | 16.5858i | −0.674866 | − | 0.674866i | ||||
\(605\) | 6.94975 | + | 16.7782i | 0.282547 | + | 0.682130i | ||||
\(606\) | −13.4142 | + | 5.55635i | −0.544915 | + | 0.225711i | ||||
\(607\) | −13.1421 | + | 31.7279i | −0.533423 | + | 1.28780i | 0.395820 | + | 0.918328i | \(0.370460\pi\) |
−0.929243 | + | 0.369469i | \(0.879540\pi\) | |||||||
\(608\) | − | 21.3137i | − | 0.864385i | ||||||
\(609\) | 11.6569 | + | 4.82843i | 0.472360 | + | 0.195658i | ||||
\(610\) | −5.00000 | + | 5.00000i | −0.202444 | + | 0.202444i | ||||
\(611\) | 15.3137 | 0.619526 | ||||||||
\(612\) | −0.849242 | − | 28.8492i | −0.0343286 | − | 1.16616i | ||||
\(613\) | −17.3137 | −0.699294 | −0.349647 | − | 0.936881i | \(-0.613698\pi\) | ||||
−0.349647 | + | 0.936881i | \(0.613698\pi\) | |||||||
\(614\) | −0.627417 | + | 0.627417i | −0.0253205 | + | 0.0253205i | ||||
\(615\) | 36.3848 | + | 15.0711i | 1.46718 | + | 0.607724i | ||||
\(616\) | 1.85786i | 0.0748555i | ||||||||
\(617\) | −1.29289 | + | 3.12132i | −0.0520499 | + | 0.125660i | −0.947766 | − | 0.318968i | \(-0.896664\pi\) |
0.895716 | + | 0.444627i | \(0.146664\pi\) | |||||||
\(618\) | −4.48528 | + | 1.85786i | −0.180424 | + | 0.0747343i | ||||
\(619\) | 3.68629 | + | 8.89949i | 0.148165 | + | 0.357701i | 0.980485 | − | 0.196594i | \(-0.0629880\pi\) |
−0.832320 | + | 0.554295i | \(0.812988\pi\) | |||||||
\(620\) | −7.75736 | − | 7.75736i | −0.311543 | − | 0.311543i | ||||
\(621\) | −6.34315 | − | 6.34315i | −0.254542 | − | 0.254542i | ||||
\(622\) | −0.715729 | − | 1.72792i | −0.0286981 | − | 0.0692834i | ||||
\(623\) | 9.41421 | − | 3.89949i | 0.377173 | − | 0.156230i | ||||
\(624\) | 4.24264 | − | 10.2426i | 0.169842 | − | 0.410034i | ||||
\(625\) | − | 14.5563i | − | 0.582254i | ||||||
\(626\) | 4.87868 | + | 2.02082i | 0.194991 | + | 0.0807680i | ||||
\(627\) | 9.65685 | − | 9.65685i | 0.385658 | − | 0.385658i | ||||
\(628\) | 3.02944 | 0.120888 | ||||||||
\(629\) | 14.3934 | − | 6.46447i | 0.573902 | − | 0.257755i | ||||
\(630\) | −3.17157 | −0.126358 | ||||||||
\(631\) | 4.72792 | − | 4.72792i | 0.188216 | − | 0.188216i | −0.606709 | − | 0.794924i | \(-0.707511\pi\) |
0.794924 | + | 0.606709i | \(0.207511\pi\) | |||||||
\(632\) | 6.07107 | + | 2.51472i | 0.241494 | + | 0.100030i | ||||
\(633\) | − | 39.1127i | − | 1.55459i | ||||||
\(634\) | 0.920310 | − | 2.22183i | 0.0365502 | − | 0.0882400i | ||||
\(635\) | −29.5563 | + | 12.2426i | −1.17291 | + | 0.485834i | ||||
\(636\) | 2.58579 | + | 6.24264i | 0.102533 | + | 0.247537i | ||||
\(637\) | −5.82843 | − | 5.82843i | −0.230931 | − | 0.230931i | ||||
\(638\) | 1.41421 | + | 1.41421i | 0.0559893 | + | 0.0559893i | ||||
\(639\) | 19.1421 | + | 46.2132i | 0.757251 | + | 1.82817i | ||||
\(640\) | 18.0208 | − | 7.46447i | 0.712335 | − | 0.295059i | ||||
\(641\) | −5.73654 | + | 13.8492i | −0.226580 | + | 0.547012i | −0.995757 | − | 0.0920237i | \(-0.970666\pi\) |
0.769177 | + | 0.639036i | \(0.220666\pi\) | |||||||
\(642\) | 6.82843i | 0.269497i | ||||||||
\(643\) | −37.0416 | − | 15.3431i | −1.46078 | − | 0.605075i | −0.496044 | − | 0.868297i | \(-0.665215\pi\) |
−0.964735 | + | 0.263223i | \(0.915215\pi\) | |||||||
\(644\) | −5.79899 | + | 5.79899i | −0.228512 | + | 0.228512i | ||||
\(645\) | 23.3137 | 0.917976 | ||||||||
\(646\) | −6.00000 | − | 5.65685i | −0.236067 | − | 0.222566i | ||||
\(647\) | 2.82843 | 0.111197 | 0.0555985 | − | 0.998453i | \(-0.482293\pi\) | ||||
0.0555985 | + | 0.998453i | \(0.482293\pi\) | |||||||
\(648\) | −6.53553 | + | 6.53553i | −0.256740 | + | 0.256740i | ||||
\(649\) | 6.00000 | + | 2.48528i | 0.235521 | + | 0.0975558i | ||||
\(650\) | 0.928932i | 0.0364357i | ||||||||
\(651\) | −3.51472 | + | 8.48528i | −0.137753 | + | 0.332564i | ||||
\(652\) | 9.58579 | − | 3.97056i | 0.375408 | − | 0.155499i | ||||
\(653\) | −6.77817 | − | 16.3640i | −0.265250 | − | 0.640371i | 0.733997 | − | 0.679152i | \(-0.237652\pi\) |
−0.999248 | + | 0.0387812i | \(0.987652\pi\) | |||||||
\(654\) | 3.27208 | + | 3.27208i | 0.127948 | + | 0.127948i | ||||
\(655\) | −0.242641 | − | 0.242641i | −0.00948076 | − | 0.00948076i | ||||
\(656\) | 9.36396 | + | 22.6066i | 0.365601 | + | 0.882640i | ||||
\(657\) | −18.9497 | + | 7.84924i | −0.739300 | + | 0.306228i | ||||
\(658\) | 1.85786 | − | 4.48528i | 0.0724271 | − | 0.174854i | ||||
\(659\) | 8.48528i | 0.330540i | 0.986248 | + | 0.165270i | \(0.0528495\pi\) | ||||
−0.986248 | + | 0.165270i | \(0.947151\pi\) | |||||||
\(660\) | 8.82843 | + | 3.65685i | 0.343646 | + | 0.142343i | ||||
\(661\) | 29.1421 | − | 29.1421i | 1.13350 | − | 1.13350i | 0.143906 | − | 0.989591i | \(-0.454034\pi\) |
0.989591 | − | 0.143906i | \(-0.0459664\pi\) | |||||||
\(662\) | 7.37258 | 0.286544 | ||||||||
\(663\) | −6.24264 | − | 13.8995i | −0.242444 | − | 0.539812i | ||||
\(664\) | 0.544156 | 0.0211173 | ||||||||
\(665\) | 6.82843 | − | 6.82843i | 0.264795 | − | 0.264795i | ||||
\(666\) | 5.60660 | + | 2.32233i | 0.217251 | + | 0.0899885i | ||||
\(667\) | 18.4853i | 0.715753i | ||||||||
\(668\) | −7.00000 | + | 16.8995i | −0.270838 | + | 0.653861i | ||||
\(669\) | −2.00000 | + | 0.828427i | −0.0773245 | + | 0.0320288i | ||||
\(670\) | 2.00000 | + | 4.82843i | 0.0772667 | + | 0.186538i | ||||
\(671\) | −7.07107 | − | 7.07107i | −0.272976 | − | 0.272976i | ||||
\(672\) | −8.82843 | − | 8.82843i | −0.340564 | − | 0.340564i | ||||
\(673\) | −0.121320 | − | 0.292893i | −0.00467656 | − | 0.0112902i | 0.921524 | − | 0.388321i | \(-0.126945\pi\) |
−0.926201 | + | 0.377031i | \(0.876945\pi\) | |||||||
\(674\) | 13.1924 | − | 5.46447i | 0.508152 | − | 0.210483i | ||||
\(675\) | 1.31371 | − | 3.17157i | 0.0505647 | − | 0.122074i | ||||
\(676\) | 20.1127i | 0.773565i | ||||||||
\(677\) | 40.5772 | + | 16.8076i | 1.55951 | + | 0.645969i | 0.985004 | − | 0.172533i | \(-0.0551952\pi\) |
0.574503 | + | 0.818502i | \(0.305195\pi\) | |||||||
\(678\) | 12.3848 | − | 12.3848i | 0.475634 | − | 0.475634i | ||||
\(679\) | 6.97056 | 0.267506 | ||||||||
\(680\) | 4.29289 | − | 11.2929i | 0.164625 | − | 0.433063i | ||||
\(681\) | 13.1716 | 0.504736 | ||||||||
\(682\) | −1.02944 | + | 1.02944i | −0.0394192 | + | 0.0394192i | ||||
\(683\) | −28.8995 | − | 11.9706i | −1.10581 | − | 0.458041i | −0.246316 | − | 0.969190i | \(-0.579220\pi\) |
−0.859492 | + | 0.511149i | \(0.829220\pi\) | |||||||
\(684\) | 33.7990i | 1.29234i | ||||||||
\(685\) | 6.17157 | − | 14.8995i | 0.235804 | − | 0.569280i | ||||
\(686\) | −5.31371 | + | 2.20101i | −0.202878 | + | 0.0840350i | ||||
\(687\) | −22.8284 | − | 55.1127i | −0.870959 | − | 2.10268i | ||||
\(688\) | 10.2426 | + | 10.2426i | 0.390497 | + | 0.390497i | ||||
\(689\) | 1.41421 | + | 1.41421i | 0.0538772 | + | 0.0538772i | ||||
\(690\) | −3.17157 | − | 7.65685i | −0.120740 | − | 0.291491i | ||||
\(691\) | 37.6274 | − | 15.5858i | 1.43141 | − | 0.592911i | 0.473714 | − | 0.880679i | \(-0.342913\pi\) |
0.957700 | + | 0.287767i | \(0.0929130\pi\) | |||||||
\(692\) | 2.36396 | − | 5.70711i | 0.0898643 | − | 0.216952i | ||||
\(693\) | − | 4.48528i | − | 0.170382i | ||||||
\(694\) | 1.48528 | + | 0.615224i | 0.0563805 | + | 0.0233536i | ||||
\(695\) | −19.5563 | + | 19.5563i | −0.741815 | + | 0.741815i | ||||
\(696\) | −18.4853 | −0.700683 | ||||||||
\(697\) | 31.4350 | + | 11.9497i | 1.19069 | + | 0.452629i | ||||
\(698\) | −1.75736 | −0.0665170 | ||||||||
\(699\) | −18.7279 | + | 18.7279i | −0.708355 | + | 0.708355i | ||||
\(700\) | −2.89949 | − | 1.20101i | −0.109591 | − | 0.0453939i | ||||
\(701\) | 21.6985i | 0.819540i | 0.912189 | + | 0.409770i | \(0.134391\pi\) | ||||
−0.912189 | + | 0.409770i | \(0.865609\pi\) | |||||||
\(702\) | 0.485281 | − | 1.17157i | 0.0183158 | − | 0.0442182i | ||||
\(703\) | −17.0711 | + | 7.07107i | −0.643848 | + | 0.266690i | ||||
\(704\) | 1.72792 | + | 4.17157i | 0.0651235 | + | 0.157222i | ||||
\(705\) | −36.9706 | − | 36.9706i | −1.39239 | − | 1.39239i | ||||
\(706\) | 4.10051 | + | 4.10051i | 0.154325 | + | 0.154325i | ||||
\(707\) | −5.55635 | − | 13.4142i | −0.208968 | − | 0.504493i | ||||
\(708\) | −26.4853 | + | 10.9706i | −0.995378 | + | 0.412299i | ||||
\(709\) | −4.43503 | + | 10.7071i | −0.166561 | + | 0.402114i | −0.985017 | − | 0.172455i | \(-0.944830\pi\) |
0.818456 | + | 0.574569i | \(0.194830\pi\) | |||||||
\(710\) | 10.0000i | 0.375293i | ||||||||
\(711\) | −14.6569 | − | 6.07107i | −0.549675 | − | 0.227683i | ||||
\(712\) | −10.5563 | + | 10.5563i | −0.395616 | + | 0.395616i | ||||
\(713\) | −13.4558 | −0.503925 | ||||||||
\(714\) | −4.82843 | + | 0.142136i | −0.180699 | + | 0.00531929i | ||||
\(715\) | 2.82843 | 0.105777 | ||||||||
\(716\) | −7.75736 | + | 7.75736i | −0.289906 | + | 0.289906i | ||||
\(717\) | −22.1421 | − | 9.17157i | −0.826913 | − | 0.342519i | ||||
\(718\) | 9.59798i | 0.358193i | ||||||||
\(719\) | 5.38478 | − | 13.0000i | 0.200818 | − | 0.484818i | −0.791102 | − | 0.611685i | \(-0.790492\pi\) |
0.991920 | + | 0.126867i | \(0.0404920\pi\) | |||||||
\(720\) | −19.6066 | + | 8.12132i | −0.730695 | + | 0.302664i | ||||
\(721\) | −1.85786 | − | 4.48528i | −0.0691905 | − | 0.167041i | ||||
\(722\) | 1.26346 | + | 1.26346i | 0.0470210 | + | 0.0470210i | ||||
\(723\) | −22.7279 | − | 22.7279i | −0.845261 | − | 0.845261i | ||||
\(724\) | −8.73654 | − | 21.0919i | −0.324691 | − | 0.783874i | ||||
\(725\) | −6.53553 | + | 2.70711i | −0.242724 | + | 0.100539i | ||||
\(726\) | −4.07107 | + | 9.82843i | −0.151091 | + | 0.364767i | ||||
\(727\) | 19.1127i | 0.708851i | 0.935084 | + | 0.354425i | \(0.115324\pi\) | ||||
−0.935084 | + | 0.354425i | \(0.884676\pi\) | |||||||
\(728\) | −2.24264 | − | 0.928932i | −0.0831178 | − | 0.0344285i | ||||
\(729\) | 27.7782 | − | 27.7782i | 1.02882 | − | 1.02882i | ||||
\(730\) | −4.10051 | −0.151767 | ||||||||
\(731\) | 19.8995 | − | 0.585786i | 0.736009 | − | 0.0216661i | ||||
\(732\) | 44.1421 | 1.63154 | ||||||||
\(733\) | −8.51472 | + | 8.51472i | −0.314498 | + | 0.314498i | −0.846649 | − | 0.532151i | \(-0.821384\pi\) |
0.532151 | + | 0.846649i | \(0.321384\pi\) | |||||||
\(734\) | −10.0711 | − | 4.17157i | −0.371730 | − | 0.153976i | ||||
\(735\) | 28.1421i | 1.03804i | ||||||||
\(736\) | 7.00000 | − | 16.8995i | 0.258023 | − | 0.622924i | ||||
\(737\) | −6.82843 | + | 2.82843i | −0.251528 | + | 0.104186i | ||||
\(738\) | 4.94975 | + | 11.9497i | 0.182203 | + | 0.439876i | ||||
\(739\) | 24.2426 | + | 24.2426i | 0.891780 | + | 0.891780i | 0.994691 | − | 0.102911i | \(-0.0328156\pi\) |
−0.102911 | + | 0.994691i | \(0.532816\pi\) | |||||||
\(740\) | −9.14214 | − | 9.14214i | −0.336072 | − | 0.336072i | ||||
\(741\) | 6.82843 | + | 16.4853i | 0.250849 | + | 0.605602i | ||||
\(742\) | 0.585786 | − | 0.242641i | 0.0215049 | − | 0.00890762i | ||||
\(743\) | 18.8579 | − | 45.5269i | 0.691828 | − | 1.67022i | −0.0492371 | − | 0.998787i | \(-0.515679\pi\) |
0.741065 | − | 0.671433i | \(-0.234321\pi\) | |||||||
\(744\) | − | 13.4558i | − | 0.493315i | ||||||
\(745\) | 28.9706 | + | 12.0000i | 1.06140 | + | 0.439646i | ||||
\(746\) | 5.72792 | − | 5.72792i | 0.209714 | − | 0.209714i | ||||
\(747\) | −1.31371 | −0.0480661 | ||||||||
\(748\) | 7.62742 | + | 2.89949i | 0.278886 | + | 0.106016i | ||||
\(749\) | −6.82843 | −0.249505 | ||||||||
\(750\) | 9.31371 | − | 9.31371i | 0.340089 | − | 0.340089i | ||||
\(751\) | −24.2132 | − | 10.0294i | −0.883552 | − | 0.365979i | −0.105679 | − | 0.994400i | \(-0.533702\pi\) |
−0.777873 | + | 0.628421i | \(0.783702\pi\) | |||||||
\(752\) | − | 32.4853i | − | 1.18462i | ||||||
\(753\) | 3.51472 | − | 8.48528i | 0.128083 | − | 0.309221i | ||||
\(754\) | −2.41421 | + | 1.00000i | −0.0879205 | + | 0.0364179i | ||||
\(755\) | 9.07107 | + | 21.8995i | 0.330130 | + | 0.797004i | ||||
\(756\) | 3.02944 | + | 3.02944i | 0.110180 | + | 0.110180i | ||||
\(757\) | 37.7990 | + | 37.7990i | 1.37383 | + | 1.37383i | 0.854692 | + | 0.519136i | \(0.173746\pi\) |
0.519136 | + | 0.854692i | \(0.326254\pi\) | |||||||
\(758\) | 0.171573 | + | 0.414214i | 0.00623181 | + | 0.0150449i | ||||
\(759\) | 10.8284 | − | 4.48528i | 0.393047 | − | 0.162805i | ||||
\(760\) | −5.41421 | + | 13.0711i | −0.196394 | + | 0.474137i | ||||
\(761\) | − | 21.6985i | − | 0.786569i | −0.919417 | − | 0.393285i | \(-0.871339\pi\) | ||
0.919417 | − | 0.393285i | \(-0.128661\pi\) | |||||||
\(762\) | −17.3137 | − | 7.17157i | −0.627209 | − | 0.259799i | ||||
\(763\) | −3.27208 | + | 3.27208i | −0.118457 | + | 0.118457i | ||||
\(764\) | 36.5685 | 1.32300 | ||||||||
\(765\) | −10.3640 | + | 27.2635i | −0.374710 | + | 0.985712i | ||||
\(766\) | −2.28427 | −0.0825341 | ||||||||
\(767\) | −6.00000 | + | 6.00000i | −0.216647 | + | 0.216647i | ||||
\(768\) | −9.58579 | − | 3.97056i | −0.345897 | − | 0.143275i | ||||
\(769\) | 12.7279i | 0.458981i | 0.973311 | + | 0.229490i | \(0.0737059\pi\) | ||||
−0.973311 | + | 0.229490i | \(0.926294\pi\) | |||||||
\(770\) | 0.343146 | − | 0.828427i | 0.0123661 | − | 0.0298544i | ||||
\(771\) | 53.4558 | − | 22.1421i | 1.92517 | − | 0.797430i | ||||
\(772\) | 3.87868 | + | 9.36396i | 0.139597 | + | 0.337016i | ||||
\(773\) | −3.41421 | − | 3.41421i | −0.122801 | − | 0.122801i | 0.643036 | − | 0.765836i | \(-0.277675\pi\) |
−0.765836 | + | 0.643036i | \(0.777675\pi\) | |||||||
\(774\) | 5.41421 | + | 5.41421i | 0.194610 | + | 0.194610i | ||||
\(775\) | −1.97056 | − | 4.75736i | −0.0707847 | − | 0.170889i | ||||
\(776\) | −9.43503 | + | 3.90812i | −0.338698 | + | 0.140293i | ||||
\(777\) | −4.14214 | + | 10.0000i | −0.148598 | + | 0.358748i | ||||
\(778\) | − | 6.68629i | − | 0.239715i | ||||||
\(779\) | −36.3848 | − | 15.0711i | −1.30362 | − | 0.539977i | ||||
\(780\) | −8.82843 | + | 8.82843i | −0.316108 | + | 0.316108i | ||||
\(781\) | −14.1421 | −0.506045 | ||||||||
\(782\) | −2.89949 | − | 6.45584i | −0.103686 | − | 0.230861i | ||||
\(783\) | 9.65685 | 0.345108 | ||||||||
\(784\) | −12.3640 | + | 12.3640i | −0.441570 | + | 0.441570i | ||||
\(785\) | −2.82843 | − | 1.17157i | −0.100951 | − | 0.0418152i | ||||
\(786\) | − | 0.201010i | − | 0.00716979i | ||||||
\(787\) | −19.0000 | + | 45.8701i | −0.677277 | + | 1.63509i | 0.0916786 | + | 0.995789i | \(0.470777\pi\) |
−0.768955 | + | 0.639302i | \(0.779223\pi\) | |||||||
\(788\) | 25.1924 | − | 10.4350i | 0.897442 | − | 0.371733i | ||||
\(789\) | 6.48528 | + | 15.6569i | 0.230882 | + | 0.557399i | ||||
\(790\) | −2.24264 | − | 2.24264i | −0.0797896 | − | 0.0797896i | ||||
\(791\) | 12.3848 | + | 12.3848i | 0.440352 | + | 0.440352i | ||||
\(792\) | 2.51472 | + | 6.07107i | 0.0893566 | + | 0.215726i | ||||
\(793\) | 12.0711 | − | 5.00000i | 0.428656 | − | 0.177555i | ||||
\(794\) | −4.32233 | + | 10.4350i | −0.153394 | + | 0.370325i | ||||
\(795\) | − | 6.82843i | − | 0.242179i | ||||||
\(796\) | −2.89949 | − | 1.20101i | −0.102770 | − | 0.0425687i | ||||
\(797\) | −12.1716 | + | 12.1716i | −0.431139 | + | 0.431139i | −0.889016 | − | 0.457877i | \(-0.848610\pi\) |
0.457877 | + | 0.889016i | \(0.348610\pi\) | |||||||
\(798\) | 5.65685 | 0.200250 | ||||||||
\(799\) | −32.4853 | − | 30.6274i | −1.14925 | − | 1.08352i | ||||
\(800\) | 7.00000 | 0.247487 | ||||||||
\(801\) | 25.4853 | − | 25.4853i | 0.900478 | − | 0.900478i | ||||
\(802\) | −6.53553 | − | 2.70711i | −0.230778 | − | 0.0955913i | ||||
\(803\) | − | 5.79899i | − | 0.204642i | ||||||
\(804\) | 12.4853 | − | 30.1421i | 0.440322 | − | 1.06303i | ||||
\(805\) | 7.65685 | − | 3.17157i | 0.269869 | − | 0.111783i | ||||
\(806\) | −0.727922 | − | 1.75736i | −0.0256400 | − | 0.0619003i | ||||
\(807\) | −11.7574 | − | 11.7574i | −0.413879 | − | 0.413879i | ||||
\(808\) | 15.0416 | + | 15.0416i | 0.529163 | + | 0.529163i | ||||
\(809\) | −11.3934 | − | 27.5061i | −0.400571 | − | 0.967063i | −0.987528 | − | 0.157445i | \(-0.949674\pi\) |
0.586957 | − | 0.809618i | \(-0.300326\pi\) | |||||||
\(810\) | 4.12132 | − | 1.70711i | 0.144808 | − | 0.0599816i | ||||
\(811\) | 16.9411 | − | 40.8995i | 0.594883 | − | 1.43618i | −0.283853 | − | 0.958868i | \(-0.591613\pi\) |
0.878736 | − | 0.477308i | \(-0.158387\pi\) | |||||||
\(812\) | − | 8.82843i | − | 0.309817i | ||||||
\(813\) | 14.8284 | + | 6.14214i | 0.520056 | + | 0.215414i | ||||
\(814\) | −1.21320 | + | 1.21320i | −0.0425228 | + | 0.0425228i | ||||
\(815\) | −10.4853 | −0.367283 | ||||||||
\(816\) | −29.4853 | + | 13.2426i | −1.03219 | + | 0.463585i | ||||
\(817\) | −23.3137 | −0.815643 | ||||||||
\(818\) | −5.65685 | + | 5.65685i | −0.197787 | + | 0.197787i | ||||
\(819\) | 5.41421 | + | 2.24264i | 0.189188 | + | 0.0783642i | ||||
\(820\) | − | 27.5563i | − | 0.962309i | ||||||
\(821\) | −5.50610 | + | 13.2929i | −0.192164 | + | 0.463925i | −0.990368 | − | 0.138463i | \(-0.955784\pi\) |
0.798204 | + | 0.602388i | \(0.205784\pi\) | |||||||
\(822\) | 8.72792 | − | 3.61522i | 0.304421 | − | 0.126095i | ||||
\(823\) | 9.00000 | + | 21.7279i | 0.313720 | + | 0.757388i | 0.999561 | + | 0.0296358i | \(0.00943477\pi\) |
−0.685840 | + | 0.727752i | \(0.740565\pi\) | |||||||
\(824\) | 5.02944 | + | 5.02944i | 0.175209 | + | 0.175209i | ||||
\(825\) | 3.17157 | + | 3.17157i | 0.110420 | + | 0.110420i | ||||
\(826\) | 1.02944 | + | 2.48528i | 0.0358187 | + | 0.0864740i | ||||
\(827\) | −32.0711 | + | 13.2843i | −1.11522 | + | 0.461939i | −0.862732 | − | 0.505661i | \(-0.831249\pi\) |
−0.252488 | + | 0.967600i | \(0.581249\pi\) | |||||||
\(828\) | −11.1005 | + | 26.7990i | −0.385769 | + | 0.931329i | ||||
\(829\) | − | 13.9411i | − | 0.484195i | −0.970252 | − | 0.242098i | \(-0.922165\pi\) | ||
0.970252 | − | 0.242098i | \(-0.0778354\pi\) | |||||||
\(830\) | −0.242641 | − | 0.100505i | −0.00842218 | − | 0.00348858i | ||||
\(831\) | −40.7279 | + | 40.7279i | −1.41284 | + | 1.41284i | ||||
\(832\) | −5.89949 | −0.204528 | ||||||||
\(833\) | 0.707107 | + | 24.0208i | 0.0244998 | + | 0.832272i | ||||
\(834\) | −16.2010 | −0.560995 | ||||||||
\(835\) | 13.0711 | − | 13.0711i | 0.452343 | − | 0.452343i | ||||
\(836\) | −8.82843 | − | 3.65685i | −0.305338 | − | 0.126475i | ||||
\(837\) | 7.02944i | 0.242973i | ||||||||
\(838\) | 4.27208 | − | 10.3137i | 0.147576 | − | 0.356281i | ||||
\(839\) | −3.58579 | + | 1.48528i | −0.123795 | + | 0.0512776i | −0.443721 | − | 0.896165i | \(-0.646342\pi\) |
0.319926 | + | 0.947443i | \(0.396342\pi\) | |||||||
\(840\) | 3.17157 | + | 7.65685i | 0.109430 | + | 0.264187i | ||||
\(841\) | 6.43503 | + | 6.43503i | 0.221898 | + | 0.221898i | ||||
\(842\) | −5.10051 | − | 5.10051i | −0.175775 | − | 0.175775i | ||||
\(843\) | 17.8995 | + | 43.2132i | 0.616491 | + | 1.48834i | ||||
\(844\) | −25.2843 | + | 10.4731i | −0.870321 | + | 0.360499i | ||||
\(845\) | 7.77817 | − | 18.7782i | 0.267577 | − | 0.645989i | ||||
\(846\) | − | 17.1716i | − | 0.590371i | ||||||
\(847\) | −9.82843 | − | 4.07107i | −0.337709 | − | 0.139884i | ||||
\(848\) | 3.00000 | − | 3.00000i | 0.103020 | − | 0.103020i | ||||
\(849\) | −59.7990 | −2.05230 | ||||||||
\(850\) | 1.85786 | − | 1.97056i | 0.0637242 | − | 0.0675897i | ||||
\(851\) | −15.8579 | −0.543601 | ||||||||
\(852\) | 44.1421 | − | 44.1421i | 1.51228 | − | 1.51228i | ||||
\(853\) | 39.3345 | + | 16.2929i | 1.34679 | + | 0.557858i | 0.935397 | − | 0.353601i | \(-0.115043\pi\) |
0.411392 | + | 0.911459i | \(0.365043\pi\) | |||||||
\(854\) | − | 4.14214i | − | 0.141741i | ||||||
\(855\) | 13.0711 | − | 31.5563i | 0.447021 | − | 1.07920i | ||||
\(856\) | 9.24264 | − | 3.82843i | 0.315907 | − | 0.130853i | ||||
\(857\) | −1.46447 | − | 3.53553i | −0.0500252 | − | 0.120772i | 0.896891 | − | 0.442251i | \(-0.145820\pi\) |
−0.946917 | + | 0.321479i | \(0.895820\pi\) | |||||||
\(858\) | 1.17157 | + | 1.17157i | 0.0399968 | + | 0.0399968i | ||||
\(859\) | −0.727922 | − | 0.727922i | −0.0248364 | − | 0.0248364i | 0.694580 | − | 0.719416i | \(-0.255590\pi\) |
−0.719416 | + | 0.694580i | \(0.755590\pi\) | |||||||
\(860\) | −6.24264 | − | 15.0711i | −0.212872 | − | 0.513919i | ||||
\(861\) | −21.3137 | + | 8.82843i | −0.726369 | + | 0.300872i | ||||
\(862\) | 6.31371 | − | 15.2426i | 0.215046 | − | 0.519166i | ||||
\(863\) | 34.6274i | 1.17873i | 0.807867 | + | 0.589365i | \(0.200622\pi\) | ||||
−0.807867 | + | 0.589365i | \(0.799378\pi\) | |||||||
\(864\) | −8.82843 | − | 3.65685i | −0.300349 | − | 0.124409i | ||||
\(865\) | −4.41421 | + | 4.41421i | −0.150088 | + | 0.150088i | ||||
\(866\) | 6.28427 | 0.213548 | ||||||||
\(867\) | −14.5563 | + | 41.9706i | −0.494360 | + | 1.42540i | ||||
\(868\) | 6.42641 | 0.218126 | ||||||||
\(869\) | 3.17157 | − | 3.17157i | 0.107588 | − | 0.107588i | ||||
\(870\) | 8.24264 | + | 3.41421i | 0.279452 | + | 0.115753i | ||||
\(871\) | − | 9.65685i | − | 0.327210i | ||||||
\(872\) | 2.59441 | − | 6.26346i | 0.0878578 | − | 0.212107i | ||||
\(873\) | 22.7782 | − | 9.43503i | 0.770924 | − | 0.319327i | ||||
\(874\) | 3.17157 | + | 7.65685i | 0.107280 | + | 0.258997i | ||||
\(875\) | 9.31371 | + | 9.31371i | 0.314861 | + | 0.314861i | ||||
\(876\) | 18.1005 | + | 18.1005i | 0.611559 | + | 0.611559i | ||||
\(877\) | −14.4056 | − | 34.7782i | −0.486442 | − | 1.17438i | −0.956498 | − | 0.291739i | \(-0.905766\pi\) |
0.470056 | − | 0.882637i | \(-0.344234\pi\) | |||||||
\(878\) | −4.17157 | + | 1.72792i | −0.140784 | + | 0.0583145i | ||||
\(879\) | 23.6569 | − | 57.1127i | 0.797926 | − | 1.92636i | ||||
\(880\) | − | 6.00000i | − | 0.202260i | ||||||
\(881\) | 17.1213 | + | 7.09188i | 0.576832 | + | 0.238932i | 0.651974 | − | 0.758241i | \(-0.273941\pi\) |
−0.0751422 | + | 0.997173i | \(0.523941\pi\) | |||||||
\(882\) | −6.53553 | + | 6.53553i | −0.220063 | + | 0.220063i | ||||
\(883\) | 8.00000 | 0.269221 | 0.134611 | − | 0.990899i | \(-0.457022\pi\) | ||||
0.134611 | + | 0.990899i | \(0.457022\pi\) | |||||||
\(884\) | −7.31371 | + | 7.75736i | −0.245987 | + | 0.260908i | ||||
\(885\) | 28.9706 | 0.973835 | ||||||||
\(886\) | −4.62742 | + | 4.62742i | −0.155461 | + | 0.155461i | ||||
\(887\) | 45.1421 | + | 18.6985i | 1.51572 | + | 0.627834i | 0.976729 | − | 0.214475i | \(-0.0688041\pi\) |
0.538995 | + | 0.842309i | \(0.318804\pi\) | |||||||
\(888\) | − | 15.8579i | − | 0.532155i | ||||||
\(889\) | 7.17157 | − | 17.3137i | 0.240527 | − | 0.580683i | ||||
\(890\) | 6.65685 | − | 2.75736i | 0.223138 | − | 0.0924269i | ||||
\(891\) | 2.41421 | + | 5.82843i | 0.0808792 | + | 0.195260i | ||||
\(892\) | 1.07107 | + | 1.07107i | 0.0358620 | + | 0.0358620i | ||||
\(893\) | 36.9706 | + | 36.9706i | 1.23717 | + | 1.23717i | ||||
\(894\) | 7.02944 | + | 16.9706i | 0.235100 | + | 0.567581i | ||||
\(895\) | 10.2426 | − | 4.24264i | 0.342374 | − | 0.141816i | ||||
\(896\) | −4.37258 | + | 10.5563i | −0.146078 | + | 0.352663i | ||||
\(897\) | 15.3137i | 0.511310i | ||||||||
\(898\) | 7.19239 | + | 2.97918i | 0.240013 | + | 0.0994167i | ||||
\(899\) | 10.2426 | − | 10.2426i | 0.341611 | − | 0.341611i | ||||
\(900\) | −11.1005 | −0.370017 | ||||||||
\(901\) | −0.171573 | − | 5.82843i | −0.00571592 | − | 0.194173i | ||||
\(902\) | −3.65685 | −0.121760 | ||||||||
\(903\) | −9.65685 | + | 9.65685i | −0.321360 | + | 0.321360i | ||||
\(904\) | −23.7071 | − | 9.81981i | −0.788487 | − | 0.326602i | ||||
\(905\) | 23.0711i | 0.766908i | ||||||||
\(906\) | −5.31371 | + | 12.8284i | −0.176536 | + | 0.426196i | ||||
\(907\) | −23.1421 | + | 9.58579i | −0.768422 | + | 0.318291i | −0.732233 | − | 0.681054i | \(-0.761522\pi\) |
−0.0361889 | + | 0.999345i | \(0.511522\pi\) | |||||||
\(908\) | −3.52691 | − | 8.51472i | −0.117045 | − | 0.282571i | ||||
\(909\) | −36.3137 | − | 36.3137i | −1.20445 | − | 1.20445i | ||||
\(910\) | 0.828427 | + | 0.828427i | 0.0274621 | + | 0.0274621i | ||||
\(911\) | −3.24264 | − | 7.82843i | −0.107433 | − | 0.259367i | 0.861016 | − | 0.508578i | \(-0.169829\pi\) |
−0.968449 | + | 0.249211i | \(0.919829\pi\) | |||||||
\(912\) | 34.9706 | − | 14.4853i | 1.15799 | − | 0.479656i | ||||
\(913\) | 0.142136 | − | 0.343146i | 0.00470400 | − | 0.0113565i | ||||
\(914\) | − | 7.79899i | − | 0.257968i | ||||||
\(915\) | −41.2132 | − | 17.0711i | −1.36247 | − | 0.564352i | ||||
\(916\) | −29.5147 | + | 29.5147i | −0.975194 | + | 0.975194i | ||||
\(917\) | 0.201010 | 0.00663794 | ||||||||
\(918\) | −3.37258 | + | 1.51472i | −0.111312 | + | 0.0499932i | ||||
\(919\) | −3.31371 | −0.109309 | −0.0546546 | − | 0.998505i | \(-0.517406\pi\) | ||||
−0.0546546 | + | 0.998505i | \(0.517406\pi\) | |||||||
\(920\) | −8.58579 | + | 8.58579i | −0.283065 | + | 0.283065i | ||||
\(921\) | −5.17157 | − | 2.14214i | −0.170409 | − | 0.0705858i | ||||
\(922\) | 9.95837i | 0.327961i | ||||||||
\(923\) | 7.07107 | − | 17.0711i | 0.232747 | − | 0.561901i | ||||
\(924\) | −5.17157 | + | 2.14214i | −0.170132 | + | 0.0704711i | ||||
\(925\) | −2.32233 | − | 5.60660i | −0.0763578 | − | 0.184344i | ||||
\(926\) | −8.97056 | − | 8.97056i | −0.294791 | − | 0.294791i | ||||
\(927\) | −12.1421 | − | 12.1421i | −0.398800 | − | 0.398800i | ||||
\(928\) | 7.53553 | + | 18.1924i | 0.247366 | + | 0.597194i | ||||
\(929\) | 19.3640 | − | 8.02082i | 0.635311 | − | 0.263154i | −0.0416968 | − | 0.999130i | \(-0.513276\pi\) |
0.677008 | + | 0.735976i | \(0.263276\pi\) | |||||||
\(930\) | −2.48528 | + | 6.00000i | −0.0814956 | + | 0.196748i | ||||
\(931\) | − | 28.1421i | − | 0.922321i | ||||||
\(932\) | 17.1213 | + | 7.09188i | 0.560827 | + | 0.232302i | ||||
\(933\) | 8.34315 | − | 8.34315i | 0.273142 | − | 0.273142i | ||||
\(934\) | −5.23045 | −0.171145 | ||||||||
\(935\) | −6.00000 | − | 5.65685i | −0.196221 | − | 0.184999i | ||||
\(936\) | −8.58579 | −0.280635 | ||||||||
\(937\) | 2.51472 | − | 2.51472i | 0.0821523 | − | 0.0821523i | −0.664837 | − | 0.746989i | \(-0.731499\pi\) |
0.746989 | + | 0.664837i | \(0.231499\pi\) | |||||||
\(938\) | −2.82843 | − | 1.17157i | −0.0923514 | − | 0.0382532i | ||||
\(939\) | 33.3137i | 1.08715i | ||||||||
\(940\) | −14.0000 | + | 33.7990i | −0.456630 | + | 1.10240i | ||||
\(941\) | 17.2635 | − | 7.15076i | 0.562773 | − | 0.233108i | −0.0831158 | − | 0.996540i | \(-0.526487\pi\) |
0.645888 | + | 0.763432i | \(0.276487\pi\) | |||||||
\(942\) | −0.686292 | − | 1.65685i | −0.0223606 | − | 0.0539832i | ||||
\(943\) | −23.8995 | − | 23.8995i | −0.778275 | − | 0.778275i | ||||
\(944\) | 12.7279 | + | 12.7279i | 0.414259 | + | 0.414259i | ||||
\(945\) | −1.65685 | − | 4.00000i | −0.0538975 | − | 0.130120i | ||||
\(946\) | −2.00000 | + | 0.828427i | −0.0650256 | + | 0.0269345i | ||||
\(947\) | 5.68629 | − | 13.7279i | 0.184780 | − | 0.446098i | −0.804161 | − | 0.594412i | \(-0.797385\pi\) |
0.988940 | + | 0.148315i | \(0.0473848\pi\) | |||||||
\(948\) | 19.7990i | 0.643041i | ||||||||
\(949\) | 7.00000 | + | 2.89949i | 0.227230 | + | 0.0941216i | ||||
\(950\) | −2.24264 | + | 2.24264i | −0.0727609 | + | 0.0727609i | ||||
\(951\) | 15.1716 | 0.491972 | ||||||||
\(952\) | 2.89949 | + | 6.45584i | 0.0939732 | + | 0.209235i | ||||
\(953\) | −9.69848 | −0.314165 | −0.157082 | − | 0.987586i | \(-0.550209\pi\) | ||||
−0.157082 | + | 0.987586i | \(0.550209\pi\) | |||||||
\(954\) | 1.58579 | − | 1.58579i | 0.0513417 | − | 0.0513417i | ||||
\(955\) | −34.1421 | − | 14.1421i | −1.10481 | − | 0.457629i | ||||
\(956\) | 16.7696i | 0.542366i | ||||||||
\(957\) | −4.82843 | + | 11.6569i | −0.156081 | + | 0.376813i | ||||
\(958\) | 13.2426 | − | 5.48528i | 0.427850 | − | 0.177221i | ||||
\(959\) | 3.61522 | + | 8.72792i | 0.116742 | + | 0.281839i | ||||
\(960\) | 14.2426 | + | 14.2426i | 0.459679 | + | 0.459679i | ||||
\(961\) | −14.4645 | − | 14.4645i | −0.466596 | − | 0.466596i | ||||
\(962\) | −0.857864 | − | 2.07107i | −0.0276587 | − | 0.0667739i | ||||
\(963\) | −22.3137 | + | 9.24264i | −0.719049 | + | 0.297840i | ||||
\(964\) | −8.60660 | + | 20.7782i | −0.277200 | + | 0.669220i | ||||
\(965\) | − | 10.2426i | − | 0.329722i | ||||||
\(966\) | 4.48528 | + | 1.85786i | 0.144312 | + | 0.0597758i | ||||
\(967\) | 22.8701 | − | 22.8701i | 0.735451 | − | 0.735451i | −0.236243 | − | 0.971694i | \(-0.575916\pi\) |
0.971694 | + | 0.236243i | \(0.0759160\pi\) | |||||||
\(968\) | 15.5858 | 0.500946 | ||||||||
\(969\) | 18.4853 | − | 48.6274i | 0.593833 | − | 1.56214i | ||||
\(970\) | 4.92893 | 0.158258 | ||||||||
\(971\) | −39.4142 | + | 39.4142i | −1.26486 | + | 1.26486i | −0.316155 | + | 0.948708i | \(0.602392\pi\) |
−0.948708 | + | 0.316155i | \(0.897608\pi\) | |||||||
\(972\) | −36.6985 | − | 15.2010i | −1.17710 | − | 0.487573i | ||||
\(973\) | − | 16.2010i | − | 0.519381i | ||||||
\(974\) | 0.698485 | − | 1.68629i | 0.0223809 | − | 0.0540323i | ||||
\(975\) | −5.41421 | + | 2.24264i | −0.173394 | + | 0.0718220i | ||||
\(976\) | −10.6066 | − | 25.6066i | −0.339509 | − | 0.819647i | ||||
\(977\) | 1.14214 | + | 1.14214i | 0.0365402 | + | 0.0365402i | 0.725141 | − | 0.688601i | \(-0.241775\pi\) |
−0.688601 | + | 0.725141i | \(0.741775\pi\) | |||||||
\(978\) | −4.34315 | − | 4.34315i | −0.138878 | − | 0.138878i | ||||
\(979\) | 3.89949 | + | 9.41421i | 0.124628 | + | 0.300880i | ||||
\(980\) | 18.1924 | − | 7.53553i | 0.581135 | − | 0.240714i | ||||
\(981\) | −6.26346 | + | 15.1213i | −0.199977 | + | 0.482787i | ||||
\(982\) | 10.4020i | 0.331942i | ||||||||
\(983\) | −21.7279 | − | 9.00000i | −0.693013 | − | 0.287055i | 0.00824183 | − | 0.999966i | \(-0.497377\pi\) |
−0.701255 | + | 0.712911i | \(0.747377\pi\) | |||||||
\(984\) | 23.8995 | − | 23.8995i | 0.761888 | − | 0.761888i | ||||
\(985\) | −27.5563 | −0.878018 | ||||||||
\(986\) | 7.12132 | + | 2.70711i | 0.226789 | + | 0.0862118i | ||||
\(987\) | 30.6274 | 0.974881 | ||||||||
\(988\) | 8.82843 | − | 8.82843i | 0.280870 | − | 0.280870i | ||||
\(989\) | −18.4853 | − | 7.65685i | −0.587798 | − | 0.243474i | ||||
\(990\) | − | 3.17157i | − | 0.100799i | ||||||
\(991\) | 12.2721 | − | 29.6274i | 0.389835 | − | 0.941146i | −0.600139 | − | 0.799896i | \(-0.704888\pi\) |
0.989974 | − | 0.141250i | \(-0.0451121\pi\) | |||||||
\(992\) | −13.2426 | + | 5.48528i | −0.420454 | + | 0.174158i | ||||
\(993\) | 17.7990 | + | 42.9706i | 0.564834 | + | 1.36363i | ||||
\(994\) | −4.14214 | − | 4.14214i | −0.131381 | − | 0.131381i | ||||
\(995\) | 2.24264 | + | 2.24264i | 0.0710965 | + | 0.0710965i | ||||
\(996\) | 0.627417 | + | 1.51472i | 0.0198805 | + | 0.0479957i | ||||
\(997\) | −7.12132 | + | 2.94975i | −0.225534 | + | 0.0934194i | −0.492589 | − | 0.870262i | \(-0.663950\pi\) |
0.267055 | + | 0.963681i | \(0.413950\pi\) | |||||||
\(998\) | −5.87006 | + | 14.1716i | −0.185813 | + | 0.448593i | ||||
\(999\) | 8.28427i | 0.262103i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))