Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(148,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.f (of order \(5\), degree \(4\), not 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: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 7 x^{10} - 15 x^{9} + 59 x^{8} + 118 x^{7} + 266 x^{6} + 324 x^{5} + 1036 x^{4} + \cdots + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 372.3 | ||
Root | \(-1.42513 - 1.03542i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.372 |
Dual form | 847.2.f.t.148.3 |
$q$-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 \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.853368 | − | 2.62640i | 0.603422 | − | 1.85714i | 0.0961306 | − | 0.995369i | \(-0.469353\pi\) |
0.507292 | − | 0.861774i | \(-0.330647\pi\) | |||||||
\(3\) | −1.42513 | + | 1.03542i | −0.822799 | + | 0.597798i | −0.917513 | − | 0.397706i | \(-0.869806\pi\) |
0.0947139 | + | 0.995505i | \(0.469806\pi\) | |||||||
\(4\) | −4.55169 | − | 3.30700i | −2.27584 | − | 1.65350i | ||||
\(5\) | −0.811540 | − | 2.49766i | −0.362932 | − | 1.11699i | −0.951266 | − | 0.308371i | \(-0.900216\pi\) |
0.588334 | − | 0.808618i | \(-0.299784\pi\) | |||||||
\(6\) | 1.50326 | + | 4.62655i | 0.613702 | + | 1.88878i | ||||
\(7\) | −0.809017 | − | 0.587785i | −0.305780 | − | 0.222162i | ||||
\(8\) | −8.10146 | + | 5.88605i | −2.86430 | + | 2.08103i | ||||
\(9\) | 0.0318546 | − | 0.0980384i | 0.0106182 | − | 0.0326795i | ||||
\(10\) | −7.25240 | −2.29341 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 9.91087 | 2.86102 | ||||||||
\(13\) | −0.737857 | + | 2.27089i | −0.204645 | + | 0.629832i | 0.795083 | + | 0.606501i | \(0.207427\pi\) |
−0.999728 | + | 0.0233311i | \(0.992573\pi\) | |||||||
\(14\) | −2.23415 | + | 1.62320i | −0.597101 | + | 0.433819i | ||||
\(15\) | 3.74267 | + | 2.71921i | 0.966354 | + | 0.702097i | ||||
\(16\) | 5.06841 | + | 15.5990i | 1.26710 | + | 3.89974i | ||||
\(17\) | −0.737857 | − | 2.27089i | −0.178957 | − | 0.550772i | 0.820835 | − | 0.571165i | \(-0.193508\pi\) |
−0.999792 | + | 0.0203930i | \(0.993508\pi\) | |||||||
\(18\) | −0.230304 | − | 0.167326i | −0.0542832 | − | 0.0394391i | ||||
\(19\) | 1.39902 | − | 1.01645i | 0.320957 | − | 0.233189i | −0.415627 | − | 0.909535i | \(-0.636438\pi\) |
0.736584 | + | 0.676346i | \(0.236438\pi\) | |||||||
\(20\) | −4.56588 | + | 14.0523i | −1.02096 | + | 3.14220i | ||||
\(21\) | 1.76156 | 0.384403 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.626198 | −0.130571 | −0.0652857 | − | 0.997867i | \(-0.520796\pi\) | ||||
−0.0652857 | + | 0.997867i | \(0.520796\pi\) | |||||||
\(24\) | 5.45111 | − | 16.7768i | 1.11270 | − | 3.42455i | ||||
\(25\) | −1.53464 | + | 1.11498i | −0.306928 | + | 0.222996i | ||||
\(26\) | 5.33460 | + | 3.87581i | 1.04620 | + | 0.760109i | ||||
\(27\) | −1.57694 | − | 4.85332i | −0.303482 | − | 0.934022i | ||||
\(28\) | 1.73859 | + | 5.35083i | 0.328563 | + | 1.01121i | ||||
\(29\) | −1.39902 | − | 1.01645i | −0.259791 | − | 0.188749i | 0.450264 | − | 0.892896i | \(-0.351330\pi\) |
−0.710055 | + | 0.704146i | \(0.751330\pi\) | |||||||
\(30\) | 10.3356 | − | 7.50926i | 1.88701 | − | 1.37100i | ||||
\(31\) | −0.691717 | + | 2.12889i | −0.124236 | + | 0.382359i | −0.993761 | − | 0.111530i | \(-0.964425\pi\) |
0.869525 | + | 0.493889i | \(0.164425\pi\) | |||||||
\(32\) | 25.2663 | 4.46650 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.59392 | −1.13085 | ||||||||
\(35\) | −0.811540 | + | 2.49766i | −0.137175 | + | 0.422182i | ||||
\(36\) | −0.469205 | + | 0.340897i | −0.0782008 | + | 0.0568162i | ||||
\(37\) | 5.57972 | + | 4.05391i | 0.917301 | + | 0.666458i | 0.942851 | − | 0.333216i | \(-0.108134\pi\) |
−0.0255499 | + | 0.999674i | \(0.508134\pi\) | |||||||
\(38\) | −1.47571 | − | 4.54178i | −0.239392 | − | 0.736774i | ||||
\(39\) | −1.29978 | − | 4.00030i | −0.208131 | − | 0.640561i | ||||
\(40\) | 21.2760 | + | 15.4579i | 3.36404 | + | 2.44412i | ||||
\(41\) | −8.40387 | + | 6.10577i | −1.31246 | + | 0.953561i | −0.312471 | + | 0.949927i | \(0.601157\pi\) |
−0.999993 | + | 0.00363356i | \(0.998843\pi\) | |||||||
\(42\) | 1.50326 | − | 4.62655i | 0.231958 | − | 0.713892i | ||||
\(43\) | 7.25240 | 1.10598 | 0.552990 | − | 0.833188i | \(-0.313487\pi\) | ||||
0.552990 | + | 0.833188i | \(0.313487\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.270718 | −0.0403563 | ||||||||
\(46\) | −0.534377 | + | 1.64464i | −0.0787897 | + | 0.242490i | ||||
\(47\) | −5.16780 | + | 3.75463i | −0.753801 | + | 0.547669i | −0.897003 | − | 0.442025i | \(-0.854260\pi\) |
0.143201 | + | 0.989694i | \(0.454260\pi\) | |||||||
\(48\) | −23.3746 | − | 16.9826i | −3.37383 | − | 2.45123i | ||||
\(49\) | 0.309017 | + | 0.951057i | 0.0441453 | + | 0.135865i | ||||
\(50\) | 1.61877 | + | 4.98206i | 0.228928 | + | 0.704569i | ||||
\(51\) | 3.40286 | + | 2.47232i | 0.476496 | + | 0.346194i | ||||
\(52\) | 10.8683 | − | 7.89630i | 1.50716 | − | 1.09502i | ||||
\(53\) | −2.85915 | + | 8.79955i | −0.392734 | + | 1.20871i | 0.537978 | + | 0.842959i | \(0.319188\pi\) |
−0.930712 | + | 0.365753i | \(0.880812\pi\) | |||||||
\(54\) | −14.0925 | −1.91774 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 10.0140 | 1.33817 | ||||||||
\(57\) | −0.941336 | + | 2.89714i | −0.124683 | + | 0.383735i | ||||
\(58\) | −3.86347 | + | 2.80697i | −0.507298 | + | 0.368574i | ||||
\(59\) | 1.42513 | + | 1.03542i | 0.185536 | + | 0.134800i | 0.676676 | − | 0.736281i | \(-0.263420\pi\) |
−0.491140 | + | 0.871081i | \(0.663420\pi\) | |||||||
\(60\) | −8.04307 | − | 24.7540i | −1.03836 | − | 3.19573i | ||||
\(61\) | −3.20999 | − | 9.87934i | −0.410997 | − | 1.26492i | −0.915782 | − | 0.401675i | \(-0.868428\pi\) |
0.504785 | − | 0.863245i | \(-0.331572\pi\) | |||||||
\(62\) | 5.00101 | + | 3.63345i | 0.635129 | + | 0.461448i | ||||
\(63\) | −0.0833965 | + | 0.0605911i | −0.0105070 | + | 0.00763376i | ||||
\(64\) | 11.4247 | − | 35.1616i | 1.42809 | − | 4.39519i | ||||
\(65\) | 6.27072 | 0.777787 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.42003 | −0.784332 | −0.392166 | − | 0.919895i | \(-0.628274\pi\) | ||||
−0.392166 | + | 0.919895i | \(0.628274\pi\) | |||||||
\(68\) | −4.15133 | + | 12.7765i | −0.503423 | + | 1.54938i | ||||
\(69\) | 0.892413 | − | 0.648376i | 0.107434 | − | 0.0780553i | ||||
\(70\) | 5.86731 | + | 4.26285i | 0.701278 | + | 0.509508i | ||||
\(71\) | 2.49833 | + | 7.68907i | 0.296497 | + | 0.912524i | 0.982714 | + | 0.185128i | \(0.0592699\pi\) |
−0.686217 | + | 0.727396i | \(0.740730\pi\) | |||||||
\(72\) | 0.318991 | + | 0.981752i | 0.0375934 | + | 0.115701i | ||||
\(73\) | −8.40387 | − | 6.10577i | −0.983599 | − | 0.714626i | −0.0250887 | − | 0.999685i | \(-0.507987\pi\) |
−0.958510 | + | 0.285059i | \(0.907987\pi\) | |||||||
\(74\) | 15.4087 | − | 11.1951i | 1.79123 | − | 1.30140i | ||||
\(75\) | 1.03259 | − | 3.17798i | 0.119233 | − | 0.366962i | ||||
\(76\) | −9.72928 | −1.11603 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −11.6156 | −1.31520 | ||||||||
\(79\) | 4.71325 | − | 14.5059i | 0.530282 | − | 1.63204i | −0.223346 | − | 0.974739i | \(-0.571698\pi\) |
0.753628 | − | 0.657301i | \(-0.228302\pi\) | |||||||
\(80\) | 34.8477 | − | 25.3183i | 3.89609 | − | 2.83068i | ||||
\(81\) | 7.52275 | + | 5.46559i | 0.835861 | + | 0.607288i | ||||
\(82\) | 8.86458 | + | 27.2824i | 0.978929 | + | 3.01283i | ||||
\(83\) | 3.94785 | + | 12.1502i | 0.433333 | + | 1.33366i | 0.894785 | + | 0.446496i | \(0.147328\pi\) |
−0.461453 | + | 0.887165i | \(0.652672\pi\) | |||||||
\(84\) | −8.01806 | − | 5.82546i | −0.874842 | − | 0.635610i | ||||
\(85\) | −5.07312 | + | 3.68584i | −0.550257 | + | 0.399785i | ||||
\(86\) | 6.18896 | − | 19.0477i | 0.667373 | − | 2.05396i | ||||
\(87\) | 3.04623 | 0.326590 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.1493 | −1.49982 | −0.749912 | − | 0.661538i | \(-0.769904\pi\) | ||||
−0.749912 | + | 0.661538i | \(0.769904\pi\) | |||||||
\(90\) | −0.231022 | + | 0.711014i | −0.0243519 | + | 0.0749474i | ||||
\(91\) | 1.93173 | − | 1.40349i | 0.202501 | − | 0.147125i | ||||
\(92\) | 2.85026 | + | 2.07083i | 0.297160 | + | 0.215899i | ||||
\(93\) | −1.21850 | − | 3.75015i | −0.126352 | − | 0.388873i | ||||
\(94\) | 5.45111 | + | 16.7768i | 0.562239 | + | 1.73039i | ||||
\(95\) | −3.67410 | − | 2.66939i | −0.376955 | − | 0.273874i | ||||
\(96\) | −36.0078 | + | 26.1612i | −3.67503 | + | 2.67007i | ||||
\(97\) | −2.58199 | + | 7.94653i | −0.262161 | + | 0.806848i | 0.730173 | + | 0.683262i | \(0.239439\pi\) |
−0.992334 | + | 0.123586i | \(0.960561\pi\) | |||||||
\(98\) | 2.76156 | 0.278959 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 10.6724 | 1.06724 | ||||||||
\(101\) | −4.27875 | + | 13.1686i | −0.425751 | + | 1.31033i | 0.476522 | + | 0.879163i | \(0.341897\pi\) |
−0.902273 | + | 0.431165i | \(0.858103\pi\) | |||||||
\(102\) | 9.39720 | − | 6.82746i | 0.930461 | − | 0.676019i | ||||
\(103\) | 2.36977 | + | 1.72174i | 0.233500 | + | 0.169648i | 0.698383 | − | 0.715725i | \(-0.253903\pi\) |
−0.464883 | + | 0.885372i | \(0.653903\pi\) | |||||||
\(104\) | −7.38887 | − | 22.7406i | −0.724538 | − | 2.22990i | ||||
\(105\) | −1.42957 | − | 4.39978i | −0.139512 | − | 0.429374i | ||||
\(106\) | 20.6712 | + | 15.0185i | 2.00777 | + | 1.45873i | ||||
\(107\) | −2.79804 | + | 2.03289i | −0.270496 | + | 0.196527i | −0.714762 | − | 0.699368i | \(-0.753465\pi\) |
0.444265 | + | 0.895895i | \(0.353465\pi\) | |||||||
\(108\) | −8.87217 | + | 27.3057i | −0.853725 | + | 2.62750i | ||||
\(109\) | −16.2341 | −1.55494 | −0.777471 | − | 0.628919i | \(-0.783498\pi\) | ||||
−0.777471 | + | 0.628919i | \(0.783498\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.1493 | −1.15316 | ||||||||
\(112\) | 5.06841 | − | 15.5990i | 0.478919 | − | 1.47396i | ||||
\(113\) | −5.74652 | + | 4.17509i | −0.540587 | + | 0.392759i | −0.824303 | − | 0.566149i | \(-0.808433\pi\) |
0.283716 | + | 0.958908i | \(0.408433\pi\) | |||||||
\(114\) | 6.80572 | + | 4.94465i | 0.637414 | + | 0.463109i | ||||
\(115\) | 0.508185 | + | 1.56403i | 0.0473885 | + | 0.145847i | ||||
\(116\) | 3.00651 | + | 9.25310i | 0.279148 | + | 0.859128i | ||||
\(117\) | 0.199130 | + | 0.144677i | 0.0184096 | + | 0.0133754i | ||||
\(118\) | 3.93558 | − | 2.85936i | 0.362299 | − | 0.263226i | ||||
\(119\) | −0.737857 | + | 2.27089i | −0.0676392 | + | 0.208172i | ||||
\(120\) | −46.3265 | −4.22901 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −28.6864 | −2.59714 | ||||||||
\(123\) | 5.65459 | − | 17.4030i | 0.509857 | − | 1.56918i | ||||
\(124\) | 10.1887 | − | 7.40252i | 0.914972 | − | 0.664766i | ||||
\(125\) | −6.59293 | − | 4.79005i | −0.589690 | − | 0.428435i | ||||
\(126\) | 0.0879683 | + | 0.270739i | 0.00783684 | + | 0.0241193i | ||||
\(127\) | −1.40338 | − | 4.31916i | −0.124530 | − | 0.383264i | 0.869285 | − | 0.494311i | \(-0.164580\pi\) |
−0.993815 | + | 0.111047i | \(0.964580\pi\) | |||||||
\(128\) | −41.7169 | − | 30.3091i | −3.68729 | − | 2.67897i | ||||
\(129\) | −10.3356 | + | 7.50926i | −0.909999 | + | 0.661153i | ||||
\(130\) | 5.35123 | − | 16.4694i | 0.469334 | − | 1.44446i | ||||
\(131\) | −6.27072 | −0.547875 | −0.273938 | − | 0.961747i | \(-0.588326\pi\) | ||||
−0.273938 | + | 0.961747i | \(0.588326\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.72928 | −0.149948 | ||||||||
\(134\) | −5.47865 | + | 16.8615i | −0.473283 | + | 1.45662i | ||||
\(135\) | −10.8422 | + | 7.87733i | −0.933149 | + | 0.677972i | ||||
\(136\) | 19.3443 | + | 14.0545i | 1.65876 | + | 1.20516i | ||||
\(137\) | 2.90529 | + | 8.94156i | 0.248215 | + | 0.763929i | 0.995091 | + | 0.0989648i | \(0.0315531\pi\) |
−0.746875 | + | 0.664964i | \(0.768447\pi\) | |||||||
\(138\) | −0.941336 | − | 2.89714i | −0.0801319 | − | 0.246621i | ||||
\(139\) | −12.8001 | − | 9.29978i | −1.08569 | − | 0.788797i | −0.107021 | − | 0.994257i | \(-0.534131\pi\) |
−0.978666 | + | 0.205459i | \(0.934131\pi\) | |||||||
\(140\) | 11.9536 | − | 8.68483i | 1.01027 | − | 0.734002i | ||||
\(141\) | 3.47718 | − | 10.7017i | 0.292832 | − | 0.901243i | ||||
\(142\) | 22.3265 | 1.87360 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.69075 | 0.140896 | ||||||||
\(145\) | −1.40338 | + | 4.31916i | −0.116544 | + | 0.358687i | ||||
\(146\) | −23.2078 | + | 16.8614i | −1.92069 | + | 1.39546i | ||||
\(147\) | −1.42513 | − | 1.03542i | −0.117543 | − | 0.0853998i | ||||
\(148\) | −11.9909 | − | 36.9042i | −0.985647 | − | 3.03351i | ||||
\(149\) | 1.06875 | + | 3.28929i | 0.0875558 | + | 0.269469i | 0.985242 | − | 0.171166i | \(-0.0547534\pi\) |
−0.897686 | + | 0.440635i | \(0.854753\pi\) | |||||||
\(150\) | −7.46546 | − | 5.42397i | −0.609552 | − | 0.442866i | ||||
\(151\) | 8.33176 | − | 6.05338i | 0.678029 | − | 0.492617i | −0.194674 | − | 0.980868i | \(-0.562365\pi\) |
0.872703 | + | 0.488251i | \(0.162365\pi\) | |||||||
\(152\) | −5.35123 | + | 16.4694i | −0.434042 | + | 1.33584i | ||||
\(153\) | −0.246139 | −0.0198991 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.87859 | 0.472180 | ||||||||
\(156\) | −7.31280 | + | 22.5065i | −0.585493 | + | 1.80196i | ||||
\(157\) | −9.17195 | + | 6.66381i | −0.732002 | + | 0.531830i | −0.890196 | − | 0.455578i | \(-0.849433\pi\) |
0.158194 | + | 0.987408i | \(0.449433\pi\) | |||||||
\(158\) | −34.0761 | − | 24.7577i | −2.71095 | − | 1.96962i | ||||
\(159\) | −5.03655 | − | 15.5009i | −0.399425 | − | 1.22930i | ||||
\(160\) | −20.5046 | − | 63.1068i | −1.62103 | − | 4.98903i | ||||
\(161\) | 0.506605 | + | 0.368070i | 0.0399261 | + | 0.0290080i | ||||
\(162\) | 20.7745 | − | 15.0936i | 1.63220 | − | 1.18586i | ||||
\(163\) | −3.00651 | + | 9.25310i | −0.235488 | + | 0.724758i | 0.761568 | + | 0.648085i | \(0.224430\pi\) |
−0.997056 | + | 0.0766734i | \(0.975570\pi\) | |||||||
\(164\) | 58.4436 | 4.56368 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 35.2803 | 2.73828 | ||||||||
\(167\) | 6.95436 | − | 21.4033i | 0.538145 | − | 1.65624i | −0.198609 | − | 0.980079i | \(-0.563643\pi\) |
0.736754 | − | 0.676161i | \(-0.236357\pi\) | |||||||
\(168\) | −14.2712 | + | 10.3686i | −1.10105 | + | 0.799956i | ||||
\(169\) | 5.90471 | + | 4.29002i | 0.454209 | + | 0.330002i | ||||
\(170\) | 5.35123 | + | 16.4694i | 0.410421 | + | 1.26314i | ||||
\(171\) | −0.0550856 | − | 0.169536i | −0.00421250 | − | 0.0129647i | ||||
\(172\) | −33.0107 | − | 23.9836i | −2.51704 | − | 1.82874i | ||||
\(173\) | −5.60583 | + | 4.07288i | −0.426204 | + | 0.309655i | −0.780129 | − | 0.625619i | \(-0.784847\pi\) |
0.353925 | + | 0.935274i | \(0.384847\pi\) | |||||||
\(174\) | 2.59955 | − | 8.00061i | 0.197072 | − | 0.606524i | ||||
\(175\) | 1.89692 | 0.143393 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.10308 | −0.233242 | ||||||||
\(178\) | −12.0746 | + | 37.1617i | −0.905027 | + | 2.78539i | ||||
\(179\) | −11.2802 | + | 8.19558i | −0.843125 | + | 0.612566i | −0.923242 | − | 0.384219i | \(-0.874471\pi\) |
0.0801170 | + | 0.996785i | \(0.474471\pi\) | |||||||
\(180\) | 1.23223 | + | 0.895264i | 0.0918447 | + | 0.0667291i | ||||
\(181\) | 0.978853 | + | 3.01260i | 0.0727576 | + | 0.223925i | 0.980822 | − | 0.194906i | \(-0.0624401\pi\) |
−0.908064 | + | 0.418831i | \(0.862440\pi\) | |||||||
\(182\) | −2.03763 | − | 6.27119i | −0.151039 | − | 0.464852i | ||||
\(183\) | 14.8039 | + | 10.7557i | 1.09434 | + | 0.795081i | ||||
\(184\) | 5.07312 | − | 3.68584i | 0.373995 | − | 0.271723i | ||||
\(185\) | 5.59712 | − | 17.2262i | 0.411509 | − | 1.26649i | ||||
\(186\) | −10.8892 | −0.798436 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 35.9388 | 2.62110 | ||||||||
\(189\) | −1.57694 | + | 4.85332i | −0.114705 | + | 0.353027i | ||||
\(190\) | −10.1462 | + | 7.37167i | −0.736085 | + | 0.534797i | ||||
\(191\) | −14.8499 | − | 10.7891i | −1.07450 | − | 0.780670i | −0.0977849 | − | 0.995208i | \(-0.531176\pi\) |
−0.976716 | + | 0.214537i | \(0.931176\pi\) | |||||||
\(192\) | 20.1252 | + | 61.9391i | 1.45241 | + | 4.47007i | ||||
\(193\) | −0.941336 | − | 2.89714i | −0.0677589 | − | 0.208540i | 0.911444 | − | 0.411424i | \(-0.134969\pi\) |
−0.979203 | + | 0.202884i | \(0.934969\pi\) | |||||||
\(194\) | 18.6674 | + | 13.5626i | 1.34024 | + | 0.973741i | ||||
\(195\) | −8.93659 | + | 6.49281i | −0.639962 | + | 0.464960i | ||||
\(196\) | 1.73859 | − | 5.35083i | 0.124185 | − | 0.382202i | ||||
\(197\) | 4.95377 | 0.352942 | 0.176471 | − | 0.984306i | \(-0.443532\pi\) | ||||
0.176471 | + | 0.984306i | \(0.443532\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.7047 | 1.11328 | 0.556638 | − | 0.830755i | \(-0.312091\pi\) | ||||
0.556638 | + | 0.830755i | \(0.312091\pi\) | |||||||
\(200\) | 5.86997 | − | 18.0659i | 0.415070 | − | 1.27745i | ||||
\(201\) | 9.14938 | − | 6.64741i | 0.645347 | − | 0.468872i | ||||
\(202\) | 30.9347 | + | 22.4754i | 2.17656 | + | 1.58136i | ||||
\(203\) | 0.534377 | + | 1.64464i | 0.0375059 | + | 0.115431i | ||||
\(204\) | −7.31280 | − | 22.5065i | −0.511999 | − | 1.57577i | ||||
\(205\) | 22.0702 | + | 16.0350i | 1.54145 | + | 1.11993i | ||||
\(206\) | 6.54424 | − | 4.75467i | 0.455959 | − | 0.331274i | ||||
\(207\) | −0.0199473 | + | 0.0613915i | −0.00138643 | + | 0.00426700i | ||||
\(208\) | −39.1633 | −2.71548 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −12.7755 | −0.881594 | ||||||||
\(211\) | 5.42356 | − | 16.6920i | 0.373374 | − | 1.14913i | −0.571196 | − | 0.820814i | \(-0.693520\pi\) |
0.944569 | − | 0.328312i | \(-0.106480\pi\) | |||||||
\(212\) | 42.1140 | − | 30.5976i | 2.89240 | − | 2.10145i | ||||
\(213\) | −11.5218 | − | 8.37110i | −0.789463 | − | 0.573578i | ||||
\(214\) | 2.95143 | + | 9.08356i | 0.201755 | + | 0.620939i | ||||
\(215\) | −5.88561 | − | 18.1140i | −0.401395 | − | 1.23537i | ||||
\(216\) | 41.3424 | + | 30.0370i | 2.81300 | + | 2.04376i | ||||
\(217\) | 1.81094 | − | 1.31572i | 0.122935 | − | 0.0893171i | ||||
\(218\) | −13.8536 | + | 42.6371i | −0.938287 | + | 2.88775i | ||||
\(219\) | 18.2986 | 1.23651 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.70138 | 0.383516 | ||||||||
\(222\) | −10.3678 | + | 31.9089i | −0.695844 | + | 2.14159i | ||||
\(223\) | 18.0364 | − | 13.1042i | 1.20781 | − | 0.877524i | 0.212779 | − | 0.977100i | \(-0.431749\pi\) |
0.995030 | + | 0.0995759i | \(0.0317486\pi\) | |||||||
\(224\) | −20.4409 | − | 14.8512i | −1.36577 | − | 0.992287i | ||||
\(225\) | 0.0604255 | + | 0.185971i | 0.00402837 | + | 0.0123980i | ||||
\(226\) | 6.06155 | + | 18.6555i | 0.403208 | + | 1.24095i | ||||
\(227\) | −11.5453 | − | 8.38812i | −0.766285 | − | 0.556739i | 0.134546 | − | 0.990907i | \(-0.457042\pi\) |
−0.900832 | + | 0.434168i | \(0.857042\pi\) | |||||||
\(228\) | 13.8655 | − | 10.0739i | 0.918264 | − | 0.667158i | ||||
\(229\) | −1.19855 | + | 3.68876i | −0.0792025 | + | 0.243760i | −0.982816 | − | 0.184589i | \(-0.940905\pi\) |
0.903613 | + | 0.428349i | \(0.140905\pi\) | |||||||
\(230\) | 4.54144 | 0.299453 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 17.3169 | 1.13691 | ||||||||
\(233\) | 2.06518 | − | 6.35596i | 0.135294 | − | 0.416393i | −0.860341 | − | 0.509718i | \(-0.829750\pi\) |
0.995636 | + | 0.0933253i | \(0.0297497\pi\) | |||||||
\(234\) | 0.549910 | − | 0.399533i | 0.0359487 | − | 0.0261183i | ||||
\(235\) | 13.5717 | + | 9.86040i | 0.885318 | + | 0.643221i | ||||
\(236\) | −3.06263 | − | 9.42580i | −0.199360 | − | 0.613567i | ||||
\(237\) | 8.30266 | + | 25.5530i | 0.539316 | + | 1.65984i | ||||
\(238\) | 5.33460 | + | 3.87581i | 0.345790 | + | 0.251231i | ||||
\(239\) | 3.67410 | − | 2.66939i | 0.237658 | − | 0.172668i | −0.462581 | − | 0.886577i | \(-0.653077\pi\) |
0.700239 | + | 0.713908i | \(0.253077\pi\) | |||||||
\(240\) | −23.4475 | + | 72.1638i | −1.51353 | + | 4.65816i | ||||
\(241\) | −3.70470 | −0.238641 | −0.119320 | − | 0.992856i | \(-0.538072\pi\) | ||||
−0.119320 | + | 0.992856i | \(0.538072\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.07081 | −0.0686924 | ||||||||
\(244\) | −18.0601 | + | 55.5831i | −1.15618 | + | 3.55835i | ||||
\(245\) | 2.12464 | − | 1.54364i | 0.135738 | − | 0.0986196i | ||||
\(246\) | −40.8818 | − | 29.7024i | −2.60653 | − | 1.89375i | ||||
\(247\) | 1.27596 | + | 3.92701i | 0.0811876 | + | 0.249870i | ||||
\(248\) | −6.92682 | − | 21.3186i | −0.439854 | − | 1.35373i | ||||
\(249\) | −18.2068 | − | 13.2280i | −1.15381 | − | 0.838289i | ||||
\(250\) | −18.2068 | + | 13.2280i | −1.15150 | + | 0.836611i | ||||
\(251\) | 2.62948 | − | 8.09269i | 0.165971 | − | 0.510806i | −0.833136 | − | 0.553069i | \(-0.813457\pi\) |
0.999107 | + | 0.0422626i | \(0.0134566\pi\) | |||||||
\(252\) | 0.579969 | 0.0365346 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −12.5414 | −0.786920 | ||||||||
\(255\) | 3.41347 | − | 10.5056i | 0.213760 | − | 0.657885i | ||||
\(256\) | −55.3833 | + | 40.2383i | −3.46146 | + | 2.51490i | ||||
\(257\) | 2.38965 | + | 1.73618i | 0.149062 | + | 0.108300i | 0.659817 | − | 0.751426i | \(-0.270634\pi\) |
−0.510754 | + | 0.859727i | \(0.670634\pi\) | |||||||
\(258\) | 10.9022 | + | 33.5536i | 0.678742 | + | 2.08895i | ||||
\(259\) | −2.13126 | − | 6.55936i | −0.132430 | − | 0.407579i | ||||
\(260\) | −28.5424 | − | 20.7372i | −1.77012 | − | 1.28607i | ||||
\(261\) | −0.144216 | + | 0.104779i | −0.00892675 | + | 0.00648566i | ||||
\(262\) | −5.35123 | + | 16.4694i | −0.330600 | + | 1.01748i | ||||
\(263\) | −16.0000 | −0.986602 | −0.493301 | − | 0.869859i | \(-0.664210\pi\) | ||||
−0.493301 | + | 0.869859i | \(0.664210\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 24.2986 | 1.49265 | ||||||||
\(266\) | −1.47571 | + | 4.54178i | −0.0904818 | + | 0.278474i | ||||
\(267\) | 20.1646 | − | 14.6504i | 1.23405 | − | 0.896593i | ||||
\(268\) | 29.2220 | + | 21.2310i | 1.78502 | + | 1.29689i | ||||
\(269\) | −2.09375 | − | 6.44389i | −0.127658 | − | 0.392891i | 0.866718 | − | 0.498799i | \(-0.166225\pi\) |
−0.994376 | + | 0.105907i | \(0.966225\pi\) | |||||||
\(270\) | 11.4366 | + | 35.1982i | 0.696009 | + | 2.14209i | ||||
\(271\) | −2.79804 | − | 2.03289i | −0.169969 | − | 0.123489i | 0.499549 | − | 0.866286i | \(-0.333499\pi\) |
−0.669518 | + | 0.742796i | \(0.733499\pi\) | |||||||
\(272\) | 31.6837 | − | 23.0196i | 1.92111 | − | 1.39577i | ||||
\(273\) | −1.29978 | + | 4.00030i | −0.0786661 | + | 0.242109i | ||||
\(274\) | 25.9634 | 1.56850 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.20617 | −0.373567 | ||||||||
\(277\) | −3.54089 | + | 10.8977i | −0.212752 | + | 0.654782i | 0.786554 | + | 0.617521i | \(0.211863\pi\) |
−0.999306 | + | 0.0372604i | \(0.988137\pi\) | |||||||
\(278\) | −35.3481 | + | 25.6819i | −2.12004 | + | 1.54030i | ||||
\(279\) | 0.186678 | + | 0.135630i | 0.0111761 | + | 0.00811994i | ||||
\(280\) | −8.12672 | − | 25.0115i | −0.485665 | − | 1.49472i | ||||
\(281\) | −6.89928 | − | 21.2338i | −0.411576 | − | 1.26670i | −0.915277 | − | 0.402824i | \(-0.868029\pi\) |
0.503701 | − | 0.863878i | \(-0.331971\pi\) | |||||||
\(282\) | −25.1395 | − | 18.2649i | −1.49704 | − | 1.08766i | ||||
\(283\) | 10.0020 | − | 7.26689i | 0.594558 | − | 0.431972i | −0.249385 | − | 0.968404i | \(-0.580228\pi\) |
0.843943 | + | 0.536433i | \(0.180228\pi\) | |||||||
\(284\) | 14.0561 | − | 43.2602i | 0.834076 | − | 2.56702i | ||||
\(285\) | 8.00000 | 0.473879 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.3878 | 0.613170 | ||||||||
\(288\) | 0.804850 | − | 2.47707i | 0.0474262 | − | 0.145963i | ||||
\(289\) | 9.14078 | − | 6.64117i | 0.537693 | − | 0.390657i | ||||
\(290\) | 10.1462 | + | 7.37167i | 0.595807 | + | 0.432879i | ||||
\(291\) | −4.54831 | − | 13.9983i | −0.266627 | − | 0.820593i | ||||
\(292\) | 18.0601 | + | 55.5831i | 1.05688 | + | 3.25276i | ||||
\(293\) | −1.74236 | − | 1.26590i | −0.101790 | − | 0.0739548i | 0.535726 | − | 0.844392i | \(-0.320038\pi\) |
−0.637516 | + | 0.770437i | \(0.720038\pi\) | |||||||
\(294\) | −3.93558 | + | 2.85936i | −0.229528 | + | 0.166762i | ||||
\(295\) | 1.42957 | − | 4.39978i | 0.0832330 | − | 0.256165i | ||||
\(296\) | −69.0654 | −4.01434 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 9.55102 | 0.553276 | ||||||||
\(299\) | 0.462045 | − | 1.42203i | 0.0267207 | − | 0.0822379i | ||||
\(300\) | −15.2096 | + | 11.0504i | −0.878126 | + | 0.637996i | ||||
\(301\) | −5.86731 | − | 4.26285i | −0.338186 | − | 0.245707i | ||||
\(302\) | −8.78852 | − | 27.0483i | −0.505722 | − | 1.55645i | ||||
\(303\) | −7.53726 | − | 23.1973i | −0.433004 | − | 1.33265i | ||||
\(304\) | 22.9463 | + | 16.6715i | 1.31606 | + | 0.956174i | ||||
\(305\) | −22.0702 | + | 16.0350i | −1.26374 | + | 0.918159i | ||||
\(306\) | −0.210047 | + | 0.646458i | −0.0120076 | + | 0.0369555i | ||||
\(307\) | −31.8217 | −1.81616 | −0.908081 | − | 0.418794i | \(-0.862453\pi\) | ||||
−0.908081 | + | 0.418794i | \(0.862453\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.15994 | −0.293539 | ||||||||
\(310\) | 5.01660 | − | 15.4395i | 0.284924 | − | 0.876906i | ||||
\(311\) | 8.84190 | − | 6.42402i | 0.501378 | − | 0.364273i | −0.308165 | − | 0.951333i | \(-0.599715\pi\) |
0.809543 | + | 0.587060i | \(0.199715\pi\) | |||||||
\(312\) | 34.0761 | + | 24.7577i | 1.92918 | + | 1.40163i | ||||
\(313\) | 2.28725 | + | 7.03944i | 0.129283 | + | 0.397893i | 0.994657 | − | 0.103234i | \(-0.0329190\pi\) |
−0.865374 | + | 0.501127i | \(0.832919\pi\) | |||||||
\(314\) | 9.67477 | + | 29.7759i | 0.545979 | + | 1.68035i | ||||
\(315\) | 0.219016 | + | 0.159124i | 0.0123401 | + | 0.00896563i | ||||
\(316\) | −69.4242 | + | 50.4396i | −3.90542 | + | 2.83745i | ||||
\(317\) | −2.74930 | + | 8.46147i | −0.154416 | + | 0.475244i | −0.998101 | − | 0.0615946i | \(-0.980381\pi\) |
0.843685 | + | 0.536838i | \(0.180381\pi\) | |||||||
\(318\) | −45.0096 | −2.52401 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −97.0933 | −5.42768 | ||||||||
\(321\) | 1.88267 | − | 5.79427i | 0.105081 | − | 0.323405i | ||||
\(322\) | 1.39902 | − | 1.01645i | 0.0779642 | − | 0.0566443i | ||||
\(323\) | −3.34051 | − | 2.42703i | −0.185871 | − | 0.135043i | ||||
\(324\) | −16.1665 | − | 49.7554i | −0.898139 | − | 2.76419i | ||||
\(325\) | −1.39965 | − | 4.30769i | −0.0776388 | − | 0.238948i | ||||
\(326\) | 21.7366 | + | 15.7926i | 1.20388 | + | 0.874671i | ||||
\(327\) | 23.1357 | − | 16.8090i | 1.27940 | − | 0.929542i | ||||
\(328\) | 32.1447 | − | 98.9313i | 1.77490 | − | 5.46257i | ||||
\(329\) | 6.38776 | 0.352168 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.56165 | 0.470591 | 0.235295 | − | 0.971924i | \(-0.424394\pi\) | ||||
0.235295 | + | 0.971924i | \(0.424394\pi\) | |||||||
\(332\) | 22.2114 | − | 68.3596i | 1.21901 | − | 3.75172i | ||||
\(333\) | 0.575178 | − | 0.417892i | 0.0315196 | − | 0.0229003i | ||||
\(334\) | −50.2790 | − | 36.5298i | −2.75114 | − | 1.99882i | ||||
\(335\) | 5.21011 | + | 16.0351i | 0.284659 | + | 0.876090i | ||||
\(336\) | 8.92829 | + | 27.4784i | 0.487078 | + | 1.49907i | ||||
\(337\) | 7.87115 | + | 5.71873i | 0.428769 | + | 0.311519i | 0.781157 | − | 0.624335i | \(-0.214630\pi\) |
−0.352387 | + | 0.935854i | \(0.614630\pi\) | |||||||
\(338\) | 16.3062 | − | 11.8471i | 0.886940 | − | 0.644400i | ||||
\(339\) | 3.86657 | − | 11.9001i | 0.210003 | − | 0.646324i | ||||
\(340\) | 35.2803 | 1.91334 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −0.492277 | −0.0266193 | ||||||||
\(343\) | 0.309017 | − | 0.951057i | 0.0166853 | − | 0.0513522i | ||||
\(344\) | −58.7550 | + | 42.6880i | −3.16786 | + | 2.30158i | ||||
\(345\) | −2.34365 | − | 1.70276i | −0.126178 | − | 0.0916738i | ||||
\(346\) | 5.91315 | + | 18.1988i | 0.317893 | + | 0.978374i | ||||
\(347\) | 4.58583 | + | 14.1137i | 0.246180 | + | 0.757665i | 0.995440 | + | 0.0953889i | \(0.0304095\pi\) |
−0.749260 | + | 0.662276i | \(0.769591\pi\) | |||||||
\(348\) | −13.8655 | − | 10.0739i | −0.743268 | − | 0.540016i | ||||
\(349\) | −13.1434 | + | 9.54924i | −0.703550 | + | 0.511159i | −0.881087 | − | 0.472955i | \(-0.843187\pi\) |
0.177536 | + | 0.984114i | \(0.443187\pi\) | |||||||
\(350\) | 1.61877 | − | 4.98206i | 0.0865268 | − | 0.266302i | ||||
\(351\) | 12.1849 | 0.650383 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 30.8603 | 1.64253 | 0.821263 | − | 0.570549i | \(-0.193270\pi\) | ||||
0.821263 | + | 0.570549i | \(0.193270\pi\) | |||||||
\(354\) | −2.64807 | + | 8.14993i | −0.140743 | + | 0.433164i | ||||
\(355\) | 17.1772 | − | 12.4800i | 0.911671 | − | 0.662368i | ||||
\(356\) | 64.4033 | + | 46.7917i | 3.41337 | + | 2.47996i | ||||
\(357\) | −1.29978 | − | 4.00030i | −0.0687915 | − | 0.211718i | ||||
\(358\) | 11.8986 | + | 36.6202i | 0.628862 | + | 1.93544i | ||||
\(359\) | 9.54141 | + | 6.93224i | 0.503576 | + | 0.365870i | 0.810381 | − | 0.585903i | \(-0.199260\pi\) |
−0.306805 | + | 0.951772i | \(0.599260\pi\) | |||||||
\(360\) | 2.19321 | − | 1.59346i | 0.115592 | − | 0.0839828i | ||||
\(361\) | −4.94723 | + | 15.2260i | −0.260381 | + | 0.801369i | ||||
\(362\) | 8.74760 | 0.459764 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −13.4340 | −0.704132 | ||||||||
\(365\) | −8.43008 | + | 25.9451i | −0.441250 | + | 1.35803i | ||||
\(366\) | 40.8818 | − | 29.7024i | 2.13693 | − | 1.55257i | ||||
\(367\) | 2.87637 | + | 2.08981i | 0.150145 | + | 0.109087i | 0.660322 | − | 0.750983i | \(-0.270420\pi\) |
−0.510176 | + | 0.860070i | \(0.670420\pi\) | |||||||
\(368\) | −3.17383 | − | 9.76803i | −0.165447 | − | 0.509194i | ||||
\(369\) | 0.330898 | + | 1.01840i | 0.0172259 | + | 0.0530157i | ||||
\(370\) | −40.4664 | − | 29.4005i | −2.10375 | − | 1.52846i | ||||
\(371\) | 7.48535 | − | 5.43842i | 0.388620 | − | 0.282349i | ||||
\(372\) | −6.85552 | + | 21.0991i | −0.355442 | + | 1.09394i | ||||
\(373\) | 22.5048 | 1.16525 | 0.582627 | − | 0.812740i | \(-0.302025\pi\) | ||||
0.582627 | + | 0.812740i | \(0.302025\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 14.3555 | 0.741314 | ||||||||
\(376\) | 19.7668 | − | 60.8359i | 1.01939 | − | 3.13737i | ||||
\(377\) | 3.34051 | − | 2.42703i | 0.172045 | − | 0.124998i | ||||
\(378\) | 11.4010 | + | 8.28334i | 0.586406 | + | 0.426049i | ||||
\(379\) | 7.24015 | + | 22.2829i | 0.371901 | + | 1.14460i | 0.945545 | + | 0.325490i | \(0.105529\pi\) |
−0.573644 | + | 0.819105i | \(0.694471\pi\) | |||||||
\(380\) | 7.89570 | + | 24.3005i | 0.405041 | + | 1.24659i | ||||
\(381\) | 6.47214 | + | 4.70228i | 0.331578 | + | 0.240905i | ||||
\(382\) | −41.0088 | + | 29.7947i | −2.09819 | + | 1.52443i | ||||
\(383\) | −1.05878 | + | 3.25859i | −0.0541012 | + | 0.166506i | −0.974456 | − | 0.224578i | \(-0.927900\pi\) |
0.920355 | + | 0.391084i | \(0.127900\pi\) | |||||||
\(384\) | 90.8347 | 4.63539 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.41233 | −0.428177 | ||||||||
\(387\) | 0.231022 | − | 0.711014i | 0.0117435 | − | 0.0361428i | ||||
\(388\) | 38.0316 | − | 27.6315i | 1.93076 | − | 1.40278i | ||||
\(389\) | −6.51813 | − | 4.73570i | −0.330482 | − | 0.240110i | 0.410153 | − | 0.912017i | \(-0.365475\pi\) |
−0.740635 | + | 0.671907i | \(0.765475\pi\) | |||||||
\(390\) | 9.42650 | + | 29.0118i | 0.477329 | + | 1.46907i | ||||
\(391\) | 0.462045 | + | 1.42203i | 0.0233666 | + | 0.0719150i | ||||
\(392\) | −8.10146 | − | 5.88605i | −0.409185 | − | 0.297291i | ||||
\(393\) | 8.93659 | − | 6.49281i | 0.450791 | − | 0.327519i | ||||
\(394\) | 4.22739 | − | 13.0106i | 0.212973 | − | 0.655463i | ||||
\(395\) | −40.0558 | −2.01543 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.3632 | −1.32313 | −0.661565 | − | 0.749888i | \(-0.730107\pi\) | ||||
−0.661565 | + | 0.749888i | \(0.730107\pi\) | |||||||
\(398\) | 13.4019 | − | 41.2468i | 0.671776 | − | 2.06751i | ||||
\(399\) | 2.46445 | − | 1.79053i | 0.123377 | − | 0.0896385i | ||||
\(400\) | −25.1707 | − | 18.2876i | −1.25853 | − | 0.914378i | ||||
\(401\) | −6.98293 | − | 21.4913i | −0.348711 | − | 1.07322i | −0.959567 | − | 0.281481i | \(-0.909175\pi\) |
0.610856 | − | 0.791742i | \(-0.290825\pi\) | |||||||
\(402\) | −9.65095 | − | 29.7026i | −0.481346 | − | 1.48143i | ||||
\(403\) | −4.32408 | − | 3.14163i | −0.215398 | − | 0.156496i | ||||
\(404\) | 63.0241 | − | 45.7897i | 3.13557 | − | 2.27812i | ||||
\(405\) | 7.54620 | − | 23.2248i | 0.374974 | − | 1.15405i | ||||
\(406\) | 4.77551 | 0.237005 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −42.1204 | −2.08527 | ||||||||
\(409\) | 2.87537 | − | 8.84947i | 0.142178 | − | 0.437578i | −0.854460 | − | 0.519518i | \(-0.826112\pi\) |
0.996637 | + | 0.0819399i | \(0.0261115\pi\) | |||||||
\(410\) | 60.9482 | − | 44.2815i | 3.01002 | − | 2.18691i | ||||
\(411\) | −13.3987 | − | 9.73469i | −0.660907 | − | 0.480177i | ||||
\(412\) | −5.09267 | − | 15.6736i | −0.250898 | − | 0.772184i | ||||
\(413\) | −0.544351 | − | 1.67534i | −0.0267858 | − | 0.0824381i | ||||
\(414\) | 0.144216 | + | 0.104779i | 0.00708783 | + | 0.00514961i | ||||
\(415\) | 27.1433 | − | 19.7208i | 1.33241 | − | 0.968056i | ||||
\(416\) | −18.6430 | + | 57.3771i | −0.914046 | + | 2.81314i | ||||
\(417\) | 27.8709 | 1.36484 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.8463 | −0.676437 | −0.338218 | − | 0.941068i | \(-0.609824\pi\) | ||||
−0.338218 | + | 0.941068i | \(0.609824\pi\) | |||||||
\(420\) | −8.04307 | + | 24.7540i | −0.392461 | + | 1.20787i | ||||
\(421\) | 28.9282 | − | 21.0175i | 1.40987 | − | 1.02433i | 0.416532 | − | 0.909121i | \(-0.363245\pi\) |
0.993341 | − | 0.115212i | \(-0.0367546\pi\) | |||||||
\(422\) | −39.2116 | − | 28.4889i | −1.90879 | − | 1.38682i | ||||
\(423\) | 0.203479 | + | 0.626245i | 0.00989351 | + | 0.0304491i | ||||
\(424\) | −28.6314 | − | 88.1183i | −1.39046 | − | 4.27940i | ||||
\(425\) | 3.66434 | + | 2.66230i | 0.177747 | + | 0.129140i | ||||
\(426\) | −31.8182 | + | 23.1173i | −1.54160 | + | 1.12004i | ||||
\(427\) | −3.20999 | + | 9.87934i | −0.155342 | + | 0.478095i | ||||
\(428\) | 19.4586 | 0.940565 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −52.5972 | −2.53646 | ||||||||
\(431\) | −9.67477 | + | 29.7759i | −0.466017 | + | 1.43425i | 0.391681 | + | 0.920101i | \(0.371894\pi\) |
−0.857699 | + | 0.514153i | \(0.828106\pi\) | |||||||
\(432\) | 67.7141 | − | 49.1972i | 3.25790 | − | 2.36700i | ||||
\(433\) | −17.4811 | − | 12.7008i | −0.840090 | − | 0.610361i | 0.0823059 | − | 0.996607i | \(-0.473772\pi\) |
−0.922396 | + | 0.386246i | \(0.873772\pi\) | |||||||
\(434\) | −1.91022 | − | 5.87904i | −0.0916933 | − | 0.282203i | ||||
\(435\) | −2.47214 | − | 7.60845i | −0.118530 | − | 0.364797i | ||||
\(436\) | 73.8925 | + | 53.6860i | 3.53881 | + | 2.57109i | ||||
\(437\) | −0.876063 | + | 0.636497i | −0.0419078 | + | 0.0304478i | ||||
\(438\) | 15.6155 | − | 48.0595i | 0.746136 | − | 2.29637i | ||||
\(439\) | 15.5877 | 0.743959 | 0.371979 | − | 0.928241i | \(-0.378679\pi\) | ||||
0.371979 | + | 0.928241i | \(0.378679\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.103084 | 0.00490875 | ||||||||
\(442\) | 4.86537 | − | 14.9741i | 0.231422 | − | 0.712244i | ||||
\(443\) | −19.0072 | + | 13.8095i | −0.903058 | + | 0.656110i | −0.939250 | − | 0.343235i | \(-0.888477\pi\) |
0.0361914 | + | 0.999345i | \(0.488477\pi\) | |||||||
\(444\) | 55.2999 | + | 40.1777i | 2.62442 | + | 1.90675i | ||||
\(445\) | 11.4827 | + | 35.3402i | 0.544334 | + | 1.67529i | ||||
\(446\) | −19.0252 | − | 58.5536i | −0.900870 | − | 2.77259i | ||||
\(447\) | −4.92890 | − | 3.58106i | −0.233129 | − | 0.169378i | ||||
\(448\) | −29.9102 | + | 21.7310i | −1.41312 | + | 1.02670i | ||||
\(449\) | 7.04040 | − | 21.6681i | 0.332257 | − | 1.02258i | −0.635801 | − | 0.771853i | \(-0.719330\pi\) |
0.968058 | − | 0.250728i | \(-0.0806701\pi\) | |||||||
\(450\) | 0.539998 | 0.0254558 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 39.9634 | 1.87972 | ||||||||
\(453\) | −5.60607 | + | 17.2537i | −0.263396 | + | 0.810650i | ||||
\(454\) | −31.8829 | + | 23.1643i | −1.49634 | + | 1.08715i | ||||
\(455\) | −5.07312 | − | 3.68584i | −0.237831 | − | 0.172795i | ||||
\(456\) | −9.42650 | − | 29.0118i | −0.441436 | − | 1.35860i | ||||
\(457\) | −4.48223 | − | 13.7949i | −0.209670 | − | 0.645297i | −0.999489 | − | 0.0319578i | \(-0.989826\pi\) |
0.789819 | − | 0.613339i | \(-0.210174\pi\) | |||||||
\(458\) | 8.66535 | + | 6.29574i | 0.404905 | + | 0.294181i | ||||
\(459\) | −9.85780 | + | 7.16211i | −0.460123 | + | 0.334299i | ||||
\(460\) | 2.85915 | − | 8.79955i | 0.133308 | − | 0.410281i | ||||
\(461\) | −31.1633 | −1.45142 | −0.725709 | − | 0.688002i | \(-0.758488\pi\) | ||||
−0.725709 | + | 0.688002i | \(0.758488\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.87859 | −0.273201 | −0.136601 | − | 0.990626i | \(-0.543618\pi\) | ||||
−0.136601 | + | 0.990626i | \(0.543618\pi\) | |||||||
\(464\) | 8.76470 | − | 26.9750i | 0.406891 | − | 1.25228i | ||||
\(465\) | −8.37776 | + | 6.08680i | −0.388509 | + | 0.282269i | ||||
\(466\) | −14.9309 | − | 10.8479i | −0.691662 | − | 0.502522i | ||||
\(467\) | −7.33140 | − | 22.5637i | −0.339257 | − | 1.04413i | −0.964587 | − | 0.263765i | \(-0.915036\pi\) |
0.625330 | − | 0.780360i | \(-0.284964\pi\) | |||||||
\(468\) | −0.427934 | − | 1.31705i | −0.0197813 | − | 0.0608805i | ||||
\(469\) | 5.19391 | + | 3.77360i | 0.239833 | + | 0.174249i | ||||
\(470\) | 37.4790 | − | 27.2301i | 1.72878 | − | 1.25603i | ||||
\(471\) | 6.17139 | − | 18.9936i | 0.284363 | − | 0.875179i | ||||
\(472\) | −17.6402 | −0.811954 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 74.1974 | 3.40800 | ||||||||
\(475\) | −1.01367 | + | 3.11975i | −0.0465103 | + | 0.143144i | ||||
\(476\) | 10.8683 | − | 7.89630i | 0.498149 | − | 0.361926i | ||||
\(477\) | 0.771617 | + | 0.560613i | 0.0353299 | + | 0.0256687i | ||||
\(478\) | −3.87552 | − | 11.9276i | −0.177262 | − | 0.545556i | ||||
\(479\) | 2.59955 | + | 8.00061i | 0.118777 | + | 0.365557i | 0.992716 | − | 0.120478i | \(-0.0384427\pi\) |
−0.873939 | + | 0.486035i | \(0.838443\pi\) | |||||||
\(480\) | 94.5637 | + | 68.7045i | 4.31622 | + | 3.13592i | ||||
\(481\) | −13.3230 | + | 9.67973i | −0.607477 | + | 0.441358i | ||||
\(482\) | −3.16147 | + | 9.73002i | −0.144001 | + | 0.443190i | ||||
\(483\) | −1.10308 | −0.0501920 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21.9431 | 0.996387 | ||||||||
\(486\) | −0.913794 | + | 2.81237i | −0.0414505 | + | 0.127572i | ||||
\(487\) | −20.0602 | + | 14.5746i | −0.909013 | + | 0.660436i | −0.940765 | − | 0.339059i | \(-0.889891\pi\) |
0.0317523 | + | 0.999496i | \(0.489891\pi\) | |||||||
\(488\) | 84.1560 | + | 61.1429i | 3.80956 | + | 2.76781i | ||||
\(489\) | −5.29615 | − | 16.2999i | −0.239500 | − | 0.737105i | ||||
\(490\) | −2.24111 | − | 6.89744i | −0.101243 | − | 0.311595i | ||||
\(491\) | −9.87500 | − | 7.17461i | −0.445652 | − | 0.323785i | 0.342224 | − | 0.939618i | \(-0.388820\pi\) |
−0.787877 | + | 0.615833i | \(0.788820\pi\) | |||||||
\(492\) | −83.2897 | + | 60.5135i | −3.75499 | + | 2.72816i | ||||
\(493\) | −1.27596 | + | 3.92701i | −0.0574665 | + | 0.176864i | ||||
\(494\) | 11.4028 | 0.513034 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −36.7143 | −1.64852 | ||||||||
\(497\) | 2.49833 | − | 7.68907i | 0.112065 | − | 0.344902i | ||||
\(498\) | −50.2790 | + | 36.5298i | −2.25306 | + | 1.63694i | ||||
\(499\) | −18.0625 | − | 13.1232i | −0.808590 | − | 0.587475i | 0.104831 | − | 0.994490i | \(-0.466570\pi\) |
−0.913422 | + | 0.407015i | \(0.866570\pi\) | |||||||
\(500\) | 14.1683 | + | 43.6056i | 0.633627 | + | 1.95010i | ||||
\(501\) | 12.2505 | + | 37.7032i | 0.547312 | + | 1.68445i | ||||
\(502\) | −19.0107 | − | 13.8121i | −0.848490 | − | 0.616464i | ||||
\(503\) | 3.67410 | − | 2.66939i | 0.163820 | − | 0.119022i | −0.502855 | − | 0.864371i | \(-0.667717\pi\) |
0.666675 | + | 0.745349i | \(0.267717\pi\) | |||||||
\(504\) | 0.318991 | − | 0.981752i | 0.0142090 | − | 0.0437307i | ||||
\(505\) | 36.3632 | 1.61814 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.8569 | −0.570997 | ||||||||
\(508\) | −7.89570 | + | 24.3005i | −0.350315 | + | 1.07816i | ||||
\(509\) | −3.33429 | + | 2.42250i | −0.147790 | + | 0.107375i | −0.659223 | − | 0.751947i | \(-0.729115\pi\) |
0.511433 | + | 0.859323i | \(0.329115\pi\) | |||||||
\(510\) | −24.6789 | − | 17.9303i | −1.09280 | − | 0.793966i | ||||
\(511\) | 3.20999 | + | 9.87934i | 0.142002 | + | 0.437036i | ||||
\(512\) | 26.5506 | + | 81.7142i | 1.17338 | + | 3.61129i | ||||
\(513\) | −7.13931 | − | 5.18701i | −0.315208 | − | 0.229012i | ||||
\(514\) | 6.59916 | − | 4.79457i | 0.291076 | − | 0.211479i | ||||
\(515\) | 2.37716 | − | 7.31613i | 0.104750 | − | 0.322387i | ||||
\(516\) | 71.8776 | 3.16423 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −19.0462 | −0.836843 | ||||||||
\(519\) | 3.77191 | − | 11.6088i | 0.165569 | − | 0.509568i | ||||
\(520\) | −50.8020 | + | 36.9098i | −2.22781 | + | 1.61860i | ||||
\(521\) | −31.7847 | − | 23.0929i | −1.39251 | − | 1.01172i | −0.995585 | − | 0.0938682i | \(-0.970077\pi\) |
−0.396927 | − | 0.917850i | \(-0.629923\pi\) | |||||||
\(522\) | 0.152122 | + | 0.468184i | 0.00665820 | + | 0.0204918i | ||||
\(523\) | −0.661796 | − | 2.03680i | −0.0289383 | − | 0.0890630i | 0.935544 | − | 0.353210i | \(-0.114910\pi\) |
−0.964483 | + | 0.264147i | \(0.914910\pi\) | |||||||
\(524\) | 28.5424 | + | 20.7372i | 1.24688 | + | 0.905911i | ||||
\(525\) | −2.70335 | + | 1.96410i | −0.117984 | + | 0.0857204i | ||||
\(526\) | −13.6539 | + | 42.0224i | −0.595338 | + | 1.83226i | ||||
\(527\) | 5.34485 | 0.232825 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.6079 | −0.982951 | ||||||||
\(530\) | 20.7357 | − | 63.8178i | 0.900700 | − | 2.77207i | ||||
\(531\) | 0.146908 | − | 0.106735i | 0.00637525 | − | 0.00463189i | ||||
\(532\) | 7.87115 | + | 5.71873i | 0.341258 | + | 0.247938i | ||||
\(533\) | −7.66468 | − | 23.5895i | −0.331994 | − | 1.02177i | ||||
\(534\) | −21.2700 | − | 65.4625i | −0.920445 | − | 2.83284i | ||||
\(535\) | 7.34820 | + | 5.33878i | 0.317690 | + | 0.230816i | ||||
\(536\) | 52.0116 | − | 37.7886i | 2.24656 | − | 1.63222i | ||||
\(537\) | 7.58997 | − | 23.3595i | 0.327531 | − | 1.00804i | ||||
\(538\) | −18.7110 | −0.806687 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 75.4007 | 3.24473 | ||||||||
\(541\) | −13.3020 | + | 40.9394i | −0.571898 | + | 1.76012i | 0.0746074 | + | 0.997213i | \(0.476230\pi\) |
−0.646506 | + | 0.762909i | \(0.723770\pi\) | |||||||
\(542\) | −7.72694 | + | 5.61395i | −0.331900 | + | 0.241140i | ||||
\(543\) | −4.51429 | − | 3.27982i | −0.193727 | − | 0.140751i | ||||
\(544\) | −18.6430 | − | 57.3771i | −0.799310 | − | 2.46002i | ||||
\(545\) | 13.1746 | + | 40.5472i | 0.564338 | + | 1.73685i | ||||
\(546\) | 9.39720 | + | 6.82746i | 0.402163 | + | 0.292188i | ||||
\(547\) | 23.4692 | − | 17.0514i | 1.00347 | − | 0.729065i | 0.0406426 | − | 0.999174i | \(-0.487060\pi\) |
0.962830 | + | 0.270108i | \(0.0870595\pi\) | |||||||
\(548\) | 16.3457 | − | 50.3070i | 0.698255 | − | 2.14901i | ||||
\(549\) | −1.07081 | −0.0457010 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.99042 | −0.127396 | ||||||||
\(552\) | −3.41347 | + | 10.5056i | −0.145287 | + | 0.447148i | ||||
\(553\) | −12.3394 | + | 8.96513i | −0.524727 | + | 0.381236i | ||||
\(554\) | 25.6001 | + | 18.5996i | 1.08764 | + | 0.790220i | ||||
\(555\) | 9.85965 | + | 30.3449i | 0.418519 | + | 1.28807i | ||||
\(556\) | 27.5075 | + | 84.6595i | 1.16658 | + | 3.59036i | ||||
\(557\) | 1.20965 | + | 0.878861i | 0.0512545 | + | 0.0372385i | 0.613118 | − | 0.789992i | \(-0.289915\pi\) |
−0.561863 | + | 0.827230i | \(0.689915\pi\) | |||||||
\(558\) | 0.515523 | − | 0.374549i | 0.0218238 | − | 0.0158559i | ||||
\(559\) | −5.35123 | + | 16.4694i | −0.226333 | + | 0.696581i | ||||
\(560\) | −43.0741 | −1.82021 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −61.6560 | −2.60080 | ||||||||
\(563\) | 1.93776 | − | 5.96381i | 0.0816668 | − | 0.251345i | −0.901883 | − | 0.431980i | \(-0.857815\pi\) |
0.983550 | + | 0.180635i | \(0.0578153\pi\) | |||||||
\(564\) | −51.2174 | + | 37.2116i | −2.15664 | + | 1.56689i | ||||
\(565\) | 15.0915 | + | 10.9646i | 0.634904 | + | 0.461285i | ||||
\(566\) | −10.5503 | − | 32.4706i | −0.443464 | − | 1.36484i | ||||
\(567\) | −2.87343 | − | 8.84352i | −0.120673 | − | 0.371393i | ||||
\(568\) | −65.4984 | − | 47.5873i | −2.74825 | − | 1.99672i | ||||
\(569\) | −6.32792 | + | 4.59750i | −0.265280 | + | 0.192737i | −0.712472 | − | 0.701701i | \(-0.752424\pi\) |
0.447191 | + | 0.894438i | \(0.352424\pi\) | |||||||
\(570\) | 6.82694 | − | 21.0112i | 0.285949 | − | 0.880061i | ||||
\(571\) | −15.1753 | −0.635068 | −0.317534 | − | 0.948247i | \(-0.602855\pi\) | ||||
−0.317534 | + | 0.948247i | \(0.602855\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 32.3342 | 1.35078 | ||||||||
\(574\) | 8.86458 | − | 27.2824i | 0.370000 | − | 1.13874i | ||||
\(575\) | 0.960987 | − | 0.698198i | 0.0400759 | − | 0.0291169i | ||||
\(576\) | −3.08326 | − | 2.24012i | −0.128469 | − | 0.0933382i | ||||
\(577\) | 7.30656 | + | 22.4873i | 0.304176 | + | 0.936158i | 0.979983 | + | 0.199079i | \(0.0637951\pi\) |
−0.675807 | + | 0.737078i | \(0.736205\pi\) | |||||||
\(578\) | −9.64189 | − | 29.6747i | −0.401050 | − | 1.23430i | ||||
\(579\) | 4.34127 | + | 3.15412i | 0.180417 | + | 0.131081i | ||||
\(580\) | 20.6712 | − | 15.0185i | 0.858325 | − | 0.623610i | ||||
\(581\) | 3.94785 | − | 12.1502i | 0.163784 | − | 0.504077i | ||||
\(582\) | −40.6464 | −1.68485 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 104.022 | 4.30448 | ||||||||
\(585\) | 0.199751 | − | 0.614771i | 0.00825870 | − | 0.0254177i | ||||
\(586\) | −4.81164 | + | 3.49586i | −0.198767 | + | 0.144413i | ||||
\(587\) | 8.21450 | + | 5.96818i | 0.339049 | + | 0.246333i | 0.744260 | − | 0.667890i | \(-0.232802\pi\) |
−0.405212 | + | 0.914223i | \(0.632802\pi\) | |||||||
\(588\) | 3.06263 | + | 9.42580i | 0.126301 | + | 0.388713i | ||||
\(589\) | 1.19617 | + | 3.68144i | 0.0492875 | + | 0.151691i | ||||
\(590\) | −10.3356 | − | 7.50926i | −0.425510 | − | 0.309151i | ||||
\(591\) | −7.05977 | + | 5.12922i | −0.290400 | + | 0.210988i | ||||
\(592\) | −34.9564 | + | 107.585i | −1.43670 | + | 4.42170i | ||||
\(593\) | 33.7972 | 1.38788 | 0.693942 | − | 0.720031i | \(-0.255873\pi\) | ||||
0.693942 | + | 0.720031i | \(0.255873\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.27072 | 0.257074 | ||||||||
\(596\) | 6.01303 | − | 18.5062i | 0.246303 | − | 0.758043i | ||||
\(597\) | −22.3812 | + | 16.2609i | −0.916003 | + | 0.665515i | ||||
\(598\) | −3.34051 | − | 2.42703i | −0.136604 | − | 0.0992484i | ||||
\(599\) | −5.66321 | − | 17.4296i | −0.231392 | − | 0.712153i | −0.997580 | − | 0.0695352i | \(-0.977848\pi\) |
0.766187 | − | 0.642618i | \(-0.222152\pi\) | |||||||
\(600\) | 10.3403 | + | 31.8241i | 0.422141 | + | 1.29922i | ||||
\(601\) | −39.2213 | − | 28.4960i | −1.59987 | − | 1.16237i | −0.887759 | − | 0.460308i | \(-0.847739\pi\) |
−0.712111 | − | 0.702066i | \(-0.752261\pi\) | |||||||
\(602\) | −16.2029 | + | 11.7721i | −0.660382 | + | 0.479795i | ||||
\(603\) | −0.204508 | + | 0.629410i | −0.00832819 | + | 0.0256315i | ||||
\(604\) | −57.9421 | −2.35763 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −67.3574 | −2.73621 | ||||||||
\(607\) | −6.36490 | + | 19.5891i | −0.258343 | + | 0.795099i | 0.734809 | + | 0.678274i | \(0.237272\pi\) |
−0.993153 | + | 0.116825i | \(0.962728\pi\) | |||||||
\(608\) | 35.3481 | − | 25.6819i | 1.43355 | − | 1.04154i | ||||
\(609\) | −2.46445 | − | 1.79053i | −0.0998646 | − | 0.0725559i | ||||
\(610\) | 23.2801 | + | 71.6489i | 0.942585 | + | 2.90098i | ||||
\(611\) | −4.71325 | − | 14.5059i | −0.190678 | − | 0.586846i | ||||
\(612\) | 1.12035 | + | 0.813980i | 0.0452873 | + | 0.0329032i | ||||
\(613\) | −15.2194 | + | 11.0575i | −0.614704 | + | 0.446609i | −0.851068 | − | 0.525056i | \(-0.824044\pi\) |
0.236364 | + | 0.971665i | \(0.424044\pi\) | |||||||
\(614\) | −27.1557 | + | 83.5765i | −1.09591 | + | 3.37287i | ||||
\(615\) | −48.0558 | −1.93780 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.2062 | −0.571919 | −0.285959 | − | 0.958242i | \(-0.592312\pi\) | ||||
−0.285959 | + | 0.958242i | \(0.592312\pi\) | |||||||
\(618\) | −4.40333 | + | 13.5520i | −0.177128 | + | 0.545143i | ||||
\(619\) | 12.9633 | − | 9.41840i | 0.521040 | − | 0.378557i | −0.295956 | − | 0.955202i | \(-0.595638\pi\) |
0.816995 | + | 0.576644i | \(0.195638\pi\) | |||||||
\(620\) | −26.7575 | − | 19.4405i | −1.07461 | − | 0.780749i | ||||
\(621\) | 0.987477 | + | 3.03914i | 0.0396261 | + | 0.121956i | ||||
\(622\) | −9.32662 | − | 28.7044i | −0.373964 | − | 1.15094i | ||||
\(623\) | 11.4470 | + | 8.31676i | 0.458616 | + | 0.333204i | ||||
\(624\) | 55.8127 | − | 40.5503i | 2.23430 | − | 1.62331i | ||||
\(625\) | −9.54439 | + | 29.3746i | −0.381776 | + | 1.17498i | ||||
\(626\) | 20.4402 | 0.816956 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 63.7851 | 2.54530 | ||||||||
\(629\) | 5.08894 | − | 15.6621i | 0.202909 | − | 0.624490i | ||||
\(630\) | 0.604824 | − | 0.439431i | 0.0240968 | − | 0.0175073i | ||||
\(631\) | −12.2935 | − | 8.93171i | −0.489395 | − | 0.355566i | 0.315557 | − | 0.948907i | \(-0.397809\pi\) |
−0.804951 | + | 0.593341i | \(0.797809\pi\) | |||||||
\(632\) | 47.1983 | + | 145.261i | 1.87745 | + | 5.77818i | ||||
\(633\) | 9.55392 | + | 29.4039i | 0.379734 | + | 1.16870i | ||||
\(634\) | 19.8770 | + | 14.4415i | 0.789417 | + | 0.573545i | ||||
\(635\) | −9.64891 | + | 7.01035i | −0.382905 | + | 0.278197i | ||||
\(636\) | −28.3366 | + | 87.2112i | −1.12362 | + | 3.45815i | ||||
\(637\) | −2.38776 | −0.0946063 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.833407 | 0.0329691 | ||||||||
\(640\) | −41.8470 | + | 128.792i | −1.65415 | + | 5.09095i | ||||
\(641\) | 8.27331 | − | 6.01091i | 0.326776 | − | 0.237417i | −0.412285 | − | 0.911055i | \(-0.635269\pi\) |
0.739061 | + | 0.673638i | \(0.235269\pi\) | |||||||
\(642\) | −13.6114 | − | 9.88929i | −0.537201 | − | 0.390299i | ||||
\(643\) | 6.35493 | + | 19.5585i | 0.250614 | + | 0.771310i | 0.994662 | + | 0.103184i | \(0.0329032\pi\) |
−0.744048 | + | 0.668126i | \(0.767097\pi\) | |||||||
\(644\) | −1.08870 | − | 3.35068i | −0.0429009 | − | 0.132035i | ||||
\(645\) | 27.1433 | + | 19.7208i | 1.06877 | + | 0.776506i | ||||
\(646\) | −9.22502 | + | 6.70237i | −0.362954 | + | 0.263701i | ||||
\(647\) | −7.86578 | + | 24.2084i | −0.309236 | + | 0.951730i | 0.668827 | + | 0.743418i | \(0.266797\pi\) |
−0.978063 | + | 0.208311i | \(0.933203\pi\) | |||||||
\(648\) | −93.1160 | −3.65794 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −12.5081 | −0.490609 | ||||||||
\(651\) | −1.21850 | + | 3.75015i | −0.0477567 | + | 0.146980i | ||||
\(652\) | 44.2847 | − | 32.1747i | 1.73432 | − | 1.26006i | ||||
\(653\) | 36.6091 | + | 26.5981i | 1.43263 | + | 1.04086i | 0.989520 | + | 0.144394i | \(0.0461231\pi\) |
0.443105 | + | 0.896470i | \(0.353877\pi\) | |||||||
\(654\) | −24.4040 | − | 75.1077i | −0.954271 | − | 2.93694i | ||||
\(655\) | 5.08894 | + | 15.6621i | 0.198841 | + | 0.611970i | ||||
\(656\) | −137.838 | − | 100.145i | −5.38166 | − | 3.91001i | ||||
\(657\) | −0.866302 | + | 0.629405i | −0.0337977 | + | 0.0245554i | ||||
\(658\) | 5.45111 | − | 16.7768i | 0.212506 | − | 0.654027i | ||||
\(659\) | −50.3544 | −1.96153 | −0.980765 | − | 0.195191i | \(-0.937467\pi\) | ||||
−0.980765 | + | 0.195191i | \(0.937467\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.2234 | −0.903287 | −0.451644 | − | 0.892198i | \(-0.649162\pi\) | ||||
−0.451644 | + | 0.892198i | \(0.649162\pi\) | |||||||
\(662\) | 7.30624 | − | 22.4863i | 0.283965 | − | 0.873954i | ||||
\(663\) | −8.12520 | + | 5.90330i | −0.315557 | + | 0.229265i | ||||
\(664\) | −103.500 | − | 75.1973i | −4.01659 | − | 2.91822i | ||||
\(665\) | 1.40338 | + | 4.31916i | 0.0544208 | + | 0.167490i | ||||
\(666\) | −0.606710 | − | 1.86726i | −0.0235095 | − | 0.0723549i | ||||
\(667\) | 0.876063 | + | 0.636497i | 0.0339213 | + | 0.0246453i | ||||
\(668\) | −102.435 | + | 74.4233i | −3.96332 | + | 2.87952i | ||||
\(669\) | −12.1359 | + | 37.3505i | −0.469201 | + | 1.44405i | ||||
\(670\) | 46.5606 | 1.79879 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 44.5081 | 1.71694 | ||||||||
\(673\) | −0.996422 | + | 3.06667i | −0.0384092 | + | 0.118212i | −0.968423 | − | 0.249314i | \(-0.919795\pi\) |
0.930013 | + | 0.367525i | \(0.119795\pi\) | |||||||
\(674\) | 21.7366 | − | 15.7926i | 0.837264 | − | 0.608308i | ||||
\(675\) | 7.83138 | + | 5.68983i | 0.301430 | + | 0.219002i | ||||
\(676\) | −12.6893 | − | 39.0537i | −0.488051 | − | 1.50207i | ||||
\(677\) | 13.1709 | + | 40.5358i | 0.506198 | + | 1.55792i | 0.798748 | + | 0.601666i | \(0.205496\pi\) |
−0.292550 | + | 0.956250i | \(0.594504\pi\) | |||||||
\(678\) | −27.9547 | − | 20.3103i | −1.07360 | − | 0.780012i | ||||
\(679\) | 6.75973 | − | 4.91123i | 0.259414 | − | 0.188476i | ||||
\(680\) | 19.4046 | − | 59.7213i | 0.744133 | − | 2.29021i | ||||
\(681\) | 25.1387 | 0.963317 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.5877 | 0.596445 | 0.298223 | − | 0.954496i | \(-0.403606\pi\) | ||||
0.298223 | + | 0.954496i | \(0.403606\pi\) | |||||||
\(684\) | −0.309923 | + | 0.953844i | −0.0118502 | + | 0.0364711i | ||||
\(685\) | 19.9752 | − | 14.5129i | 0.763215 | − | 0.554508i | ||||
\(686\) | −2.23415 | − | 1.62320i | −0.0853001 | − | 0.0619742i | ||||
\(687\) | −2.11132 | − | 6.49797i | −0.0805518 | − | 0.247913i | ||||
\(688\) | 36.7581 | + | 113.130i | 1.40139 | + | 4.31303i | ||||
\(689\) | −17.8732 | − | 12.9856i | −0.680914 | − | 0.494713i | ||||
\(690\) | −6.47214 | + | 4.70228i | −0.246390 | + | 0.179013i | ||||
\(691\) | 12.9574 | − | 39.8788i | 0.492923 | − | 1.51706i | −0.327245 | − | 0.944940i | \(-0.606120\pi\) |
0.820168 | − | 0.572122i | \(-0.193880\pi\) | |||||||
\(692\) | 38.9850 | 1.48199 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 40.9817 | 1.55564 | ||||||||
\(695\) | −12.8400 | + | 39.5174i | −0.487048 | + | 1.49898i | ||||
\(696\) | −24.6789 | + | 17.9303i | −0.935451 | + | 0.679645i | ||||
\(697\) | 20.0664 | + | 14.5791i | 0.760069 | + | 0.552222i | ||||
\(698\) | 13.8639 | + | 42.6688i | 0.524758 | + | 1.61504i | ||||
\(699\) | 3.63793 | + | 11.1964i | 0.137599 | + | 0.423486i | ||||
\(700\) | −8.63417 | − | 6.27310i | −0.326341 | − | 0.237101i | ||||
\(701\) | 12.4665 | − | 9.05742i | 0.470852 | − | 0.342094i | −0.326921 | − | 0.945052i | \(-0.606011\pi\) |
0.797773 | + | 0.602958i | \(0.206011\pi\) | |||||||
\(702\) | 10.3982 | − | 32.0024i | 0.392455 | − | 1.20785i | ||||
\(703\) | 11.9267 | 0.449824 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −29.5510 | −1.11296 | ||||||||
\(706\) | 26.3352 | − | 81.0513i | 0.991137 | − | 3.05041i | ||||
\(707\) | 11.2019 | − | 8.13866i | 0.421291 | − | 0.306086i | ||||
\(708\) | 14.1243 | + | 10.2619i | 0.530823 | + | 0.385665i | ||||
\(709\) | 0.883873 | + | 2.72028i | 0.0331945 | + | 0.102162i | 0.966281 | − | 0.257490i | \(-0.0828954\pi\) |
−0.933086 | + | 0.359652i | \(0.882895\pi\) | |||||||
\(710\) | −18.1189 | − | 55.7641i | −0.679989 | − | 2.09279i | ||||
\(711\) | −1.27200 | − | 0.924159i | −0.0477036 | − | 0.0346587i | ||||
\(712\) | 114.630 | − | 83.2836i | 4.29594 | − | 3.12119i | ||||
\(713\) | 0.433152 | − | 1.33310i | 0.0162217 | − | 0.0499251i | ||||
\(714\) | −11.6156 | −0.434702 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 78.4469 | 2.93170 | ||||||||
\(717\) | −2.47214 | + | 7.60845i | −0.0923236 | + | 0.284143i | ||||
\(718\) | 26.3492 | − | 19.1438i | 0.983342 | − | 0.714440i | ||||
\(719\) | 27.8889 | + | 20.2624i | 1.04008 | + | 0.755661i | 0.970301 | − | 0.241901i | \(-0.0777710\pi\) |
0.0697778 | + | 0.997563i | \(0.477771\pi\) | |||||||
\(720\) | −1.37211 | − | 4.22292i | −0.0511355 | − | 0.157379i | ||||
\(721\) | −0.905170 | − | 2.78583i | −0.0337103 | − | 0.103750i | ||||
\(722\) | 35.7678 | + | 25.9868i | 1.33114 | + | 0.967129i | ||||
\(723\) | 5.27968 | − | 3.83591i | 0.196353 | − | 0.142659i | ||||
\(724\) | 5.50722 | − | 16.9495i | 0.204674 | − | 0.629923i | ||||
\(725\) | 3.28030 | 0.121827 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −40.3309 | −1.49579 | −0.747895 | − | 0.663817i | \(-0.768935\pi\) | ||||
−0.747895 | + | 0.663817i | \(0.768935\pi\) | |||||||
\(728\) | −7.38887 | + | 22.7406i | −0.273850 | + | 0.842822i | ||||
\(729\) | −21.0422 | + | 15.2881i | −0.779341 | + | 0.566224i | ||||
\(730\) | 60.9482 | + | 44.2815i | 2.25579 | + | 1.63893i | ||||
\(731\) | −5.35123 | − | 16.4694i | −0.197922 | − | 0.609143i | ||||
\(732\) | −31.8138 | − | 97.9129i | −1.17587 | − | 3.61896i | ||||
\(733\) | 23.2701 | + | 16.9067i | 0.859501 | + | 0.624464i | 0.927749 | − | 0.373204i | \(-0.121741\pi\) |
−0.0682479 | + | 0.997668i | \(0.521741\pi\) | |||||||
\(734\) | 7.94326 | − | 5.77112i | 0.293191 | − | 0.213016i | ||||
\(735\) | −1.42957 | + | 4.39978i | −0.0527306 | + | 0.162288i | ||||
\(736\) | −15.8217 | −0.583197 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 2.95710 | 0.108852 | ||||||||
\(739\) | 10.8471 | − | 33.3840i | 0.399018 | − | 1.22805i | −0.526770 | − | 0.850008i | \(-0.676597\pi\) |
0.925788 | − | 0.378043i | \(-0.123403\pi\) | |||||||
\(740\) | −82.4432 | + | 59.8985i | −3.03067 | + | 2.20191i | ||||
\(741\) | −5.88451 | − | 4.27534i | −0.216173 | − | 0.157059i | ||||
\(742\) | −7.89570 | − | 24.3005i | −0.289860 | − | 0.892098i | ||||
\(743\) | −10.0332 | − | 30.8790i | −0.368083 | − | 1.13284i | −0.948028 | − | 0.318187i | \(-0.896926\pi\) |
0.579945 | − | 0.814655i | \(-0.303074\pi\) | |||||||
\(744\) | 31.9452 | + | 23.2096i | 1.17117 | + | 0.850904i | ||||
\(745\) | 7.34820 | − | 5.33878i | 0.269217 | − | 0.195598i | ||||
\(746\) | 19.2049 | − | 59.1065i | 0.703140 | − | 2.16404i | ||||
\(747\) | 1.31695 | 0.0481846 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.45856 | 0.126373 | ||||||||
\(750\) | 12.2505 | − | 37.7032i | 0.447325 | − | 1.37673i | ||||
\(751\) | 22.9626 | − | 16.6833i | 0.837919 | − | 0.608784i | −0.0838698 | − | 0.996477i | \(-0.526728\pi\) |
0.921788 | + | 0.387693i | \(0.126728\pi\) | |||||||
\(752\) | −84.7608 | − | 61.5823i | −3.09091 | − | 2.24568i | ||||
\(753\) | 4.63197 | + | 14.2557i | 0.168798 | + | 0.519508i | ||||
\(754\) | −3.52364 | − | 10.8447i | −0.128324 | − | 0.394939i | ||||
\(755\) | −21.8809 | − | 15.8974i | −0.796326 | − | 0.578565i | ||||
\(756\) | 23.2277 | − | 16.8759i | 0.844782 | − | 0.613770i | ||||
\(757\) | −5.26757 | + | 16.2119i | −0.191453 | + | 0.589233i | 0.808546 | + | 0.588432i | \(0.200255\pi\) |
−1.00000 | 0.000800126i | \(0.999745\pi\) | ||||||||
\(758\) | 64.7022 | 2.35009 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 45.4777 | 1.64965 | ||||||||
\(761\) | 8.63356 | − | 26.5714i | 0.312966 | − | 0.963211i | −0.663617 | − | 0.748072i | \(-0.730980\pi\) |
0.976584 | − | 0.215139i | \(-0.0690203\pi\) | |||||||
\(762\) | 17.8732 | − | 12.9856i | 0.647477 | − | 0.470419i | ||||
\(763\) | 13.1336 | + | 9.54215i | 0.475470 | + | 0.345449i | ||||
\(764\) | 31.9127 | + | 98.2171i | 1.15456 | + | 3.55337i | ||||
\(765\) | 0.199751 | + | 0.614771i | 0.00722202 | + | 0.0222271i | ||||
\(766\) | 7.65483 | + | 5.56156i | 0.276580 | + | 0.200947i | ||||
\(767\) | −3.40286 | + | 2.47232i | −0.122870 | + | 0.0892704i | ||||
\(768\) | 37.2649 | − | 114.690i | 1.34468 | − | 4.13851i | ||||
\(769\) | 6.69512 | 0.241432 | 0.120716 | − | 0.992687i | \(-0.461481\pi\) | ||||
0.120716 | + | 0.992687i | \(0.461481\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.20324 | −0.187390 | ||||||||
\(772\) | −5.29615 | + | 16.2999i | −0.190612 | + | 0.586645i | ||||
\(773\) | −22.5831 | + | 16.4076i | −0.812256 | + | 0.590139i | −0.914484 | − | 0.404622i | \(-0.867403\pi\) |
0.102228 | + | 0.994761i | \(0.467403\pi\) | |||||||
\(774\) | −1.67026 | − | 1.21351i | −0.0600361 | − | 0.0436188i | ||||
\(775\) | −1.31213 | − | 4.03832i | −0.0471331 | − | 0.145061i | ||||
\(776\) | −25.8559 | − | 79.5762i | −0.928172 | − | 2.85662i | ||||
\(777\) | 9.82900 | + | 7.14119i | 0.352613 | + | 0.256189i | ||||
\(778\) | −18.0002 | + | 13.0779i | −0.645338 | + | 0.468866i | ||||
\(779\) | −5.55098 | + | 17.0842i | −0.198885 | + | 0.612104i | ||||
\(780\) | 62.1483 | 2.22527 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 4.12910 | 0.147656 | ||||||||
\(783\) | −2.72697 | + | 8.39276i | −0.0974541 | + | 0.299933i | ||||
\(784\) | −13.2693 | + | 9.64068i | −0.473902 | + | 0.344310i | ||||
\(785\) | 24.0874 | + | 17.5005i | 0.859715 | + | 0.624619i | ||||
\(786\) | −9.42650 | − | 29.0118i | −0.336232 | − | 1.03482i | ||||
\(787\) | 6.75461 | + | 20.7886i | 0.240776 | + | 0.741032i | 0.996303 | + | 0.0859141i | \(0.0273811\pi\) |
−0.755527 | + | 0.655118i | \(0.772619\pi\) | |||||||
\(788\) | −22.5480 | − | 16.3821i | −0.803240 | − | 0.583588i | ||||
\(789\) | 22.8021 | − | 16.5667i | 0.811775 | − | 0.589789i | ||||
\(790\) | −34.1824 | + | 105.202i | −1.21615 | + | 3.74294i | ||||
\(791\) | 7.10308 | 0.252557 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.8034 | 0.880795 | ||||||||
\(794\) | −22.4975 | + | 69.2402i | −0.798406 | + | 2.45724i | ||||
\(795\) | −34.6287 | + | 25.1592i | −1.22815 | + | 0.892305i | ||||
\(796\) | −71.4829 | − | 51.9354i | −2.53365 | − | 1.84080i | ||||
\(797\) | −10.7001 | − | 32.9315i | −0.379016 | − | 1.16649i | −0.940729 | − | 0.339160i | \(-0.889857\pi\) |
0.561712 | − | 0.827333i | \(-0.310143\pi\) | |||||||
\(798\) | −2.59955 | − | 8.00061i | −0.0920232 | − | 0.283218i | ||||
\(799\) | 12.3394 | + | 8.96513i | 0.436538 | + | 0.317164i | ||||
\(800\) | −38.7747 | + | 28.1715i | −1.37089 | + | 0.996012i | ||||
\(801\) | −0.450721 | + | 1.38718i | −0.0159254 | + | 0.0490135i | ||||
\(802\) | −62.4036 | −2.20355 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −63.6281 | −2.24399 | ||||||||
\(805\) | 0.508185 | − | 1.56403i | 0.0179112 | − | 0.0551249i | ||||
\(806\) | −11.9412 | + | 8.67578i | −0.420610 | + | 0.305591i | ||||
\(807\) | 9.65598 | + | 7.01548i | 0.339907 | + | 0.246957i | ||||
\(808\) | −42.8472 | − | 131.870i | −1.50736 | − | 4.63917i | ||||
\(809\) | 10.8299 | + | 33.3309i | 0.380758 | + | 1.17185i | 0.939511 | + | 0.342519i | \(0.111280\pi\) |
−0.558753 | + | 0.829334i | \(0.688720\pi\) | |||||||
\(810\) | −54.5579 | − | 39.6387i | −1.91697 | − | 1.39276i | ||||
\(811\) | 14.6769 | − | 10.6634i | 0.515375 | − | 0.374442i | −0.299484 | − | 0.954101i | \(-0.596814\pi\) |
0.814859 | + | 0.579660i | \(0.196814\pi\) | |||||||
\(812\) | 3.00651 | − | 9.25310i | 0.105508 | − | 0.324720i | ||||
\(813\) | 6.09246 | 0.213672 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 25.5510 | 0.895013 | ||||||||
\(816\) | −21.3186 | + | 65.6118i | −0.746299 | + | 2.29687i | ||||
\(817\) | 10.1462 | − | 7.37167i | 0.354972 | − | 0.257902i | ||||
\(818\) | −20.7885 | − | 15.1037i | −0.726852 | − | 0.528089i | ||||
\(819\) | −0.0760610 | − | 0.234092i | −0.00265779 | − | 0.00817983i | ||||
\(820\) | −47.4293 | − | 145.972i | −1.65630 | − | 5.09757i | ||||
\(821\) | 2.79804 | + | 2.03289i | 0.0976522 | + | 0.0709484i | 0.635540 | − | 0.772068i | \(-0.280778\pi\) |
−0.537888 | + | 0.843016i | \(0.680778\pi\) | |||||||
\(822\) | −37.0011 | + | 26.8829i | −1.29056 | + | 0.937649i | ||||
\(823\) | −10.3616 | + | 31.8897i | −0.361182 | + | 1.11160i | 0.591155 | + | 0.806558i | \(0.298672\pi\) |
−0.952337 | + | 0.305047i | \(0.901328\pi\) | |||||||
\(824\) | −29.3328 | −1.02186 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.86464 | −0.169263 | ||||||||
\(827\) | −8.12672 | + | 25.0115i | −0.282594 | + | 0.869734i | 0.704516 | + | 0.709688i | \(0.251164\pi\) |
−0.987110 | + | 0.160046i | \(0.948836\pi\) | |||||||
\(828\) | 0.293815 | − | 0.213469i | 0.0102108 | − | 0.00741857i | ||||
\(829\) | 23.4630 | + | 17.0469i | 0.814904 | + | 0.592063i | 0.915248 | − | 0.402890i | \(-0.131994\pi\) |
−0.100344 | + | 0.994953i | \(0.531994\pi\) | |||||||
\(830\) | −28.6314 | − | 88.1183i | −0.993809 | − | 3.05863i | ||||
\(831\) | −6.23748 | − | 19.1970i | −0.216376 | − | 0.665936i | ||||
\(832\) | 71.4183 | + | 51.8884i | 2.47598 | + | 1.79891i | ||||
\(833\) | 1.93173 | − | 1.40349i | 0.0669306 | − | 0.0486280i | ||||
\(834\) | 23.7841 | − | 73.2000i | 0.823577 | − | 2.53471i | ||||
\(835\) | −59.1020 | −2.04531 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 11.4230 | 0.394835 | ||||||||
\(838\) | −11.8160 | + | 36.3659i | −0.408177 | + | 1.25624i | ||||
\(839\) | −23.5998 | + | 17.1463i | −0.814756 | + | 0.591955i | −0.915206 | − | 0.402987i | \(-0.867972\pi\) |
0.100450 | + | 0.994942i | \(0.467972\pi\) | |||||||
\(840\) | 37.4790 | + | 27.2301i | 1.29315 | + | 0.939526i | ||||
\(841\) | −8.03740 | − | 24.7366i | −0.277152 | − | 0.852986i | ||||
\(842\) | −30.5140 | − | 93.9126i | −1.05158 | − | 3.23644i | ||||
\(843\) | 31.8182 | + | 23.1173i | 1.09588 | + | 0.796201i | ||||
\(844\) | −79.8868 | + | 58.0412i | −2.74982 | + | 1.99786i | ||||
\(845\) | 5.92312 | − | 18.2295i | 0.203762 | − | 0.627114i | ||||
\(846\) | 1.81841 | 0.0625183 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −151.755 | −5.21129 | ||||||||
\(849\) | −6.72991 | + | 20.7125i | −0.230970 | + | 0.710852i | ||||
\(850\) | 10.1193 | − | 7.35209i | 0.347088 | − | 0.252175i | ||||
\(851\) | −3.49401 | − | 2.53855i | −0.119773 | − | 0.0870203i | ||||
\(852\) | 24.7606 | + | 76.2053i | 0.848285 | + | 2.61075i | ||||
\(853\) | 3.28233 | + | 10.1020i | 0.112385 | + | 0.345885i | 0.991393 | − | 0.130923i | \(-0.0417940\pi\) |
−0.879008 | + | 0.476807i | \(0.841794\pi\) | |||||||
\(854\) | 23.2078 | + | 16.8614i | 0.794154 | + | 0.576986i | ||||
\(855\) | −0.378740 | + | 0.275171i | −0.0129526 | + | 0.00941063i | ||||
\(856\) | 10.7025 | − | 32.9388i | 0.365803 | − | 1.12582i | ||||
\(857\) | 37.8463 | 1.29281 | 0.646403 | − | 0.762996i | \(-0.276273\pi\) | ||||
0.646403 | + | 0.762996i | \(0.276273\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.0785 | −0.650950 | −0.325475 | − | 0.945551i | \(-0.605524\pi\) | ||||
−0.325475 | + | 0.945551i | \(0.605524\pi\) | |||||||
\(860\) | −33.1136 | + | 101.913i | −1.12916 | + | 3.47521i | ||||
\(861\) | −14.8039 | + | 10.7557i | −0.504516 | + | 0.366552i | ||||
\(862\) | 69.9471 | + | 50.8196i | 2.38241 | + | 1.73092i | ||||
\(863\) | 3.45337 | + | 10.6284i | 0.117554 | + | 0.361794i | 0.992471 | − | 0.122479i | \(-0.0390843\pi\) |
−0.874917 | + | 0.484273i | \(0.839084\pi\) | |||||||
\(864\) | −39.8435 | − | 122.626i | −1.35550 | − | 4.17181i | ||||
\(865\) | 14.7220 | + | 10.6962i | 0.500564 | + | 0.363681i | ||||
\(866\) | −48.2752 | + | 35.0740i | −1.64046 | + | 1.19186i | ||||
\(867\) | −6.15042 | + | 18.9290i | −0.208879 | + | 0.642864i | ||||
\(868\) | −12.5939 | −0.427466 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −22.0925 | −0.749004 | ||||||||
\(871\) | 4.73706 | − | 14.5792i | 0.160509 | − | 0.493997i | ||||
\(872\) | 131.520 | − | 95.5546i | 4.45382 | − | 3.23589i | ||||
\(873\) | 0.696818 | + | 0.506268i | 0.0235837 | + | 0.0171346i | ||||
\(874\) | 0.924089 | + | 2.84405i | 0.0312578 | + | 0.0962016i | ||||
\(875\) | 2.51828 | + | 7.75046i | 0.0851333 | + | 0.262013i | ||||
\(876\) | −83.2897 | − | 60.5135i | −2.81410 | − | 2.04456i | ||||
\(877\) | 4.73953 | − | 3.44347i | 0.160043 | − | 0.116278i | −0.504882 | − | 0.863189i | \(-0.668464\pi\) |
0.664924 | + | 0.746911i | \(0.268464\pi\) | |||||||
\(878\) | 13.3020 | − | 40.9394i | 0.448921 | − | 1.38164i | ||||
\(879\) | 3.79383 | 0.127963 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.9065 | −0.872812 | −0.436406 | − | 0.899750i | \(-0.643749\pi\) | ||||
−0.436406 | + | 0.899750i | \(0.643749\pi\) | |||||||
\(882\) | 0.0879683 | − | 0.270739i | 0.00296205 | − | 0.00911625i | ||||
\(883\) | −10.8586 | + | 7.88921i | −0.365420 | + | 0.265493i | −0.755309 | − | 0.655369i | \(-0.772513\pi\) |
0.389889 | + | 0.920862i | \(0.372513\pi\) | |||||||
\(884\) | −25.9509 | − | 18.8544i | −0.872823 | − | 0.634143i | ||||
\(885\) | 2.51828 | + | 7.75046i | 0.0846509 | + | 0.260529i | ||||
\(886\) | 20.0492 | + | 61.7050i | 0.673565 | + | 2.07302i | ||||
\(887\) | 40.1328 | + | 29.1582i | 1.34753 | + | 0.979035i | 0.999131 | + | 0.0416879i | \(0.0132735\pi\) |
0.348396 | + | 0.937347i | \(0.386726\pi\) | |||||||
\(888\) | 98.4271 | − | 71.5115i | 3.30300 | − | 2.39977i | ||||
\(889\) | −1.40338 | + | 4.31916i | −0.0470679 | + | 0.144860i | ||||
\(890\) | 102.616 | 3.43971 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −125.432 | −4.19977 | ||||||||
\(893\) | −3.41347 | + | 10.5056i | −0.114227 | + | 0.351556i | ||||
\(894\) | −13.6114 | + | 9.88929i | −0.455235 | + | 0.330747i | ||||
\(895\) | 29.6241 | + | 21.5232i | 0.990226 | + | 0.719441i | ||||
\(896\) | 15.9345 | + | 49.0412i | 0.532333 | + | 1.63835i | ||||
\(897\) | 0.813918 | + | 2.50498i | 0.0271759 | + | 0.0836389i | ||||
\(898\) | −50.9010 | − | 36.9818i | −1.69859 | − | 1.23410i | ||||
\(899\) | 3.13162 | − | 2.27526i | 0.104445 | − | 0.0758841i | ||||
\(900\) | 0.339966 | − | 1.04631i | 0.0113322 | − | 0.0348769i | ||||
\(901\) | 22.0925 | 0.736006 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.7755 | 0.425142 | ||||||||
\(904\) | 21.9804 | − | 67.6486i | 0.731056 | − | 2.24996i | ||||
\(905\) | 6.73008 | − | 4.88969i | 0.223715 | − | 0.162539i | ||||
\(906\) | 40.5310 | + | 29.4475i | 1.34655 | + | 0.978328i | ||||
\(907\) | −14.7950 | − | 45.5343i | −0.491259 | − | 1.51194i | −0.822706 | − | 0.568466i | \(-0.807537\pi\) |
0.331447 | − | 0.943474i | \(-0.392463\pi\) | |||||||
\(908\) | 24.8109 | + | 76.3602i | 0.823380 | + | 2.53410i | ||||
\(909\) | 1.15473 | + | 0.838963i | 0.0383001 | + | 0.0278267i | ||||
\(910\) | −14.0097 | + | 10.1786i | −0.464417 | + | 0.337419i | ||||
\(911\) | 7.04934 | − | 21.6956i | 0.233555 | − | 0.718809i | −0.763755 | − | 0.645507i | \(-0.776646\pi\) |
0.997310 | − | 0.0733022i | \(-0.0233538\pi\) | |||||||
\(912\) | −49.9634 | −1.65445 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −40.0558 | −1.32493 | ||||||||
\(915\) | 14.8501 | − | 45.7038i | 0.490928 | − | 1.51092i | ||||
\(916\) | 17.6542 | − | 12.8265i | 0.583310 | − | 0.423799i | ||||
\(917\) | 5.07312 | + | 3.68584i | 0.167529 | + | 0.121717i | ||||
\(918\) | 10.3982 | + | 32.0024i | 0.343192 | + | 1.05624i | ||||
\(919\) | −12.3607 | − | 38.0423i | −0.407741 | − | 1.25490i | −0.918585 | − | 0.395225i | \(-0.870667\pi\) |
0.510843 | − | 0.859674i | \(-0.329333\pi\) | |||||||
\(920\) | −13.3230 | − | 9.67973i | −0.439247 | − | 0.319131i | ||||
\(921\) | 45.3501 | − | 32.9488i | 1.49434 | − | 1.08570i | ||||
\(922\) | −26.5937 | + | 81.8471i | −0.875818 | + | 2.69549i | ||||
\(923\) | −19.3044 | −0.635413 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.0829 | −0.430162 | ||||||||
\(926\) | −5.01660 | + | 15.4395i | −0.164856 | + | 0.507374i | ||||
\(927\) | 0.244284 | − | 0.177483i | 0.00802335 | − | 0.00582930i | ||||
\(928\) | −35.3481 | − | 25.6819i | −1.16036 | − | 0.843049i | ||||
\(929\) | −4.95560 | − | 15.2518i | −0.162588 | − | 0.500394i | 0.836263 | − | 0.548329i | \(-0.184736\pi\) |
−0.998850 | + | 0.0479353i | \(0.984736\pi\) | |||||||
\(930\) | 8.83704 | + | 27.1976i | 0.289778 | + | 0.891844i | ||||
\(931\) | 1.39902 | + | 1.01645i | 0.0458510 | + | 0.0333127i | ||||
\(932\) | −30.4192 | + | 22.1008i | −0.996414 | + | 0.723937i | ||||
\(933\) | −5.94932 | + | 18.3101i | −0.194772 | + | 0.599446i | ||||
\(934\) | −65.5177 | −2.14380 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.46482 | −0.0805652 | ||||||||
\(937\) | −7.81964 | + | 24.0664i | −0.255456 | + | 0.786214i | 0.738283 | + | 0.674491i | \(0.235637\pi\) |
−0.993739 | + | 0.111723i | \(0.964363\pi\) | |||||||
\(938\) | 14.3433 | − | 10.4210i | 0.468325 | − | 0.340258i | ||||
\(939\) | −10.5484 | − | 7.66386i | −0.344234 | − | 0.250101i | ||||
\(940\) | −29.1657 | − | 89.7629i | −0.951282 | − | 2.92774i | ||||
\(941\) | 6.34392 | + | 19.5246i | 0.206806 | + | 0.636484i | 0.999634 | + | 0.0270385i | \(0.00860768\pi\) |
−0.792828 | + | 0.609445i | \(0.791392\pi\) | |||||||
\(942\) | −44.6183 | − | 32.4171i | −1.45374 | − | 1.05620i | ||||
\(943\) | 5.26249 | − | 3.82342i | 0.171370 | − | 0.124508i | ||||
\(944\) | −8.92829 | + | 27.4784i | −0.290591 | + | 0.894347i | ||||
\(945\) | 13.4017 | 0.435958 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.6907 | −0.542376 | −0.271188 | − | 0.962526i | \(-0.587417\pi\) | ||||
−0.271188 | + | 0.962526i | \(0.587417\pi\) | |||||||
\(948\) | 46.7124 | − | 143.766i | 1.51715 | − | 4.66930i | ||||
\(949\) | 20.0664 | − | 14.5791i | 0.651382 | − | 0.473257i | ||||
\(950\) | 7.32868 | + | 5.32460i | 0.237774 | + | 0.172753i | ||||
\(951\) | −4.84305 | − | 14.9054i | −0.157047 | − | 0.483340i | ||||
\(952\) | −7.38887 | − | 22.7406i | −0.239474 | − | 0.737027i | ||||
\(953\) | −45.6837 | − | 33.1911i | −1.47984 | − | 1.07517i | −0.977608 | − | 0.210434i | \(-0.932512\pi\) |
−0.502232 | − | 0.864733i | \(-0.667488\pi\) | |||||||
\(954\) | 2.13086 | − | 1.54816i | 0.0689893 | − | 0.0501237i | ||||
\(955\) | −14.8962 | + | 45.8458i | −0.482030 | + | 1.48354i | ||||
\(956\) | −25.5510 | −0.826379 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 23.2311 | 0.750564 | ||||||||
\(959\) | 2.90529 | − | 8.94156i | 0.0938166 | − | 0.288738i | ||||
\(960\) | 138.371 | − | 100.532i | 4.46589 | − | 3.24466i | ||||
\(961\) | 21.0258 | + | 15.2762i | 0.678253 | + | 0.492780i | ||||
\(962\) | 14.0534 | + | 43.2519i | 0.453100 | + | 1.39450i | ||||
\(963\) | 0.110171 | + | 0.339072i | 0.00355022 | + | 0.0109264i | ||||
\(964\) | 16.8627 | + | 12.2514i | 0.543110 | + | 0.394592i | ||||
\(965\) | −6.47214 | + | 4.70228i | −0.208345 | + | 0.151372i | ||||
\(966\) | −0.941336 | + | 2.89714i | −0.0302870 | + | 0.0932138i | ||||
\(967\) | 47.3082 | 1.52133 | 0.760665 | − | 0.649145i | \(-0.224873\pi\) | ||||
0.760665 | + | 0.649145i | \(0.224873\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.27365 | 0.233663 | ||||||||
\(970\) | 18.7256 | − | 57.6314i | 0.601242 | − | 1.85043i | ||||
\(971\) | 20.4160 | − | 14.8331i | 0.655179 | − | 0.476016i | −0.209852 | − | 0.977733i | \(-0.567298\pi\) |
0.865032 | + | 0.501717i | \(0.167298\pi\) | |||||||
\(972\) | 4.87399 | + | 3.54116i | 0.156333 | + | 0.113583i | ||||
\(973\) | 4.88919 | + | 15.0474i | 0.156740 | + | 0.482396i | ||||
\(974\) | 21.1599 | + | 65.1234i | 0.678006 | + | 2.08669i | ||||
\(975\) | 6.45494 | + | 4.68979i | 0.206724 | + | 0.150193i | ||||
\(976\) | 137.838 | − | 100.145i | 4.41208 | − | 3.20556i | ||||
\(977\) | 2.19497 | − | 6.75543i | 0.0702234 | − | 0.216125i | −0.909786 | − | 0.415078i | \(-0.863754\pi\) |
0.980009 | + | 0.198953i | \(0.0637541\pi\) | |||||||
\(978\) | −47.3295 | −1.51343 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −14.7755 | −0.471986 | ||||||||
\(981\) | −0.517130 | + | 1.59156i | −0.0165107 | + | 0.0508147i | ||||
\(982\) | −27.2704 | + | 19.8131i | −0.870232 | + | 0.632261i | ||||
\(983\) | 11.4794 | + | 8.34025i | 0.366135 | + | 0.266013i | 0.755606 | − | 0.655026i | \(-0.227342\pi\) |
−0.389471 | + | 0.921039i | \(0.627342\pi\) | |||||||
\(984\) | 56.6248 | + | 174.273i | 1.80513 | + | 5.55562i | ||||
\(985\) | −4.02018 | − | 12.3729i | −0.128094 | − | 0.394232i | ||||
\(986\) | 9.22502 | + | 6.70237i | 0.293784 | + | 0.213447i | ||||
\(987\) | −9.10338 | + | 6.61399i | −0.289764 | + | 0.210526i | ||||
\(988\) | 7.17882 | − | 22.0941i | 0.228389 | − | 0.702908i | ||||
\(989\) | −4.54144 | −0.144409 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.23407 | 0.134500 | 0.0672499 | − | 0.997736i | \(-0.478578\pi\) | ||||
0.0672499 | + | 0.997736i | \(0.478578\pi\) | |||||||
\(992\) | −17.4772 | + | 53.7892i | −0.554900 | + | 1.70781i | ||||
\(993\) | −12.2015 | + | 8.86488i | −0.387202 | + | 0.281318i | ||||
\(994\) | −18.0625 | − | 13.1232i | −0.572909 | − | 0.416243i | ||||
\(995\) | −12.7450 | − | 39.2251i | −0.404043 | − | 1.24352i | ||||
\(996\) | 39.1266 | + | 120.419i | 1.23977 | + | 3.81563i | ||||
\(997\) | 22.4136 | + | 16.2844i | 0.709845 | + | 0.515733i | 0.883124 | − | 0.469140i | \(-0.155436\pi\) |
−0.173279 | + | 0.984873i | \(0.555436\pi\) | |||||||
\(998\) | −49.8807 | + | 36.2405i | −1.57895 | + | 1.14717i | ||||
\(999\) | 10.8760 | − | 33.4729i | 0.344102 | − | 1.05904i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 847.2.f.t.372.3 | 12 | ||
11.2 | odd | 10 | 847.2.f.u.729.3 | 12 | |||
11.3 | even | 5 | inner | 847.2.f.t.323.1 | 12 | ||
11.4 | even | 5 | 847.2.a.j.1.3 | yes | 3 | ||
11.5 | even | 5 | inner | 847.2.f.t.148.3 | 12 | ||
11.6 | odd | 10 | 847.2.f.u.148.1 | 12 | |||
11.7 | odd | 10 | 847.2.a.i.1.1 | ✓ | 3 | ||
11.8 | odd | 10 | 847.2.f.u.323.3 | 12 | |||
11.9 | even | 5 | inner | 847.2.f.t.729.1 | 12 | ||
11.10 | odd | 2 | 847.2.f.u.372.1 | 12 | |||
33.26 | odd | 10 | 7623.2.a.bz.1.1 | 3 | |||
33.29 | even | 10 | 7623.2.a.ce.1.3 | 3 | |||
77.48 | odd | 10 | 5929.2.a.y.1.3 | 3 | |||
77.62 | even | 10 | 5929.2.a.t.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
847.2.a.i.1.1 | ✓ | 3 | 11.7 | odd | 10 | ||
847.2.a.j.1.3 | yes | 3 | 11.4 | even | 5 | ||
847.2.f.t.148.3 | 12 | 11.5 | even | 5 | inner | ||
847.2.f.t.323.1 | 12 | 11.3 | even | 5 | inner | ||
847.2.f.t.372.3 | 12 | 1.1 | even | 1 | trivial | ||
847.2.f.t.729.1 | 12 | 11.9 | even | 5 | inner | ||
847.2.f.u.148.1 | 12 | 11.6 | odd | 10 | |||
847.2.f.u.323.3 | 12 | 11.8 | odd | 10 | |||
847.2.f.u.372.1 | 12 | 11.10 | odd | 2 | |||
847.2.f.u.729.3 | 12 | 11.2 | odd | 10 | |||
5929.2.a.t.1.1 | 3 | 77.62 | even | 10 | |||
5929.2.a.y.1.3 | 3 | 77.48 | odd | 10 | |||
7623.2.a.bz.1.1 | 3 | 33.26 | odd | 10 | |||
7623.2.a.ce.1.3 | 3 | 33.29 | even | 10 |