Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(19,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([10, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.x (of order \(12\), 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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 570.1 | ||
Character | \(\chi\) | \(=\) | 637.570 |
Dual form | 637.2.x.b.19.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.28713 | + | 0.612835i | −1.61725 | + | 0.433340i | −0.950191 | − | 0.311669i | \(-0.899112\pi\) |
−0.667055 | + | 0.745009i | \(0.732445\pi\) | |||||||
\(3\) | − | 1.20226i | − | 0.694122i | −0.937842 | − | 0.347061i | \(-0.887180\pi\) | ||
0.937842 | − | 0.347061i | \(-0.112820\pi\) | |||||||
\(4\) | 3.12335 | − | 1.80327i | 1.56167 | − | 0.901633i | ||||
\(5\) | −3.08075 | − | 0.825486i | −1.37776 | − | 0.369168i | −0.507450 | − | 0.861681i | \(-0.669412\pi\) |
−0.870305 | + | 0.492513i | \(0.836078\pi\) | |||||||
\(6\) | 0.736784 | + | 2.74971i | 0.300791 | + | 1.12257i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.68981 | + | 2.68981i | −0.950991 | + | 0.950991i | ||||
\(9\) | 1.55458 | 0.518194 | ||||||||
\(10\) | 7.55197 | 2.38814 | ||||||||
\(11\) | −3.00989 | + | 3.00989i | −0.907517 | + | 0.907517i | −0.996071 | − | 0.0885547i | \(-0.971775\pi\) |
0.0885547 | + | 0.996071i | \(0.471775\pi\) | |||||||
\(12\) | −2.16799 | − | 3.75506i | −0.625844 | − | 1.08399i | ||||
\(13\) | 3.48609 | + | 0.920440i | 0.966866 | + | 0.255284i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.992444 | + | 3.70385i | −0.256248 | + | 0.956331i | ||||
\(16\) | 0.897005 | − | 1.55366i | 0.224251 | − | 0.388414i | ||||
\(17\) | 0.721872 | + | 1.25032i | 0.175080 | + | 0.303247i | 0.940189 | − | 0.340654i | \(-0.110648\pi\) |
−0.765109 | + | 0.643901i | \(0.777315\pi\) | |||||||
\(18\) | −3.55553 | + | 0.952702i | −0.838047 | + | 0.224554i | ||||
\(19\) | 1.77447 | − | 1.77447i | 0.407092 | − | 0.407092i | −0.473631 | − | 0.880723i | \(-0.657057\pi\) |
0.880723 | + | 0.473631i | \(0.157057\pi\) | |||||||
\(20\) | −11.1108 | + | 2.97714i | −2.48446 | + | 0.665709i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.03945 | − | 8.72858i | 1.07441 | − | 1.86094i | ||||
\(23\) | 4.52952 | + | 2.61512i | 0.944470 | + | 0.545290i | 0.891359 | − | 0.453299i | \(-0.149753\pi\) |
0.0531111 | + | 0.998589i | \(0.483086\pi\) | |||||||
\(24\) | 3.23384 | + | 3.23384i | 0.660104 | + | 0.660104i | ||||
\(25\) | 4.47949 | + | 2.58624i | 0.895898 | + | 0.517247i | ||||
\(26\) | −8.53721 | + | 0.0312285i | −1.67428 | + | 0.00612442i | ||||
\(27\) | − | 5.47577i | − | 1.05381i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.34350 | + | 2.32701i | 0.249482 | + | 0.432116i | 0.963382 | − | 0.268132i | \(-0.0864063\pi\) |
−0.713900 | + | 0.700248i | \(0.753073\pi\) | |||||||
\(30\) | − | 9.07940i | − | 1.65766i | ||||||
\(31\) | −1.37793 | − | 5.14250i | −0.247483 | − | 0.923620i | −0.972119 | − | 0.234488i | \(-0.924659\pi\) |
0.724636 | − | 0.689132i | \(-0.242008\pi\) | |||||||
\(32\) | 0.869646 | − | 3.24556i | 0.153733 | − | 0.573740i | ||||
\(33\) | 3.61866 | + | 3.61866i | 0.629928 | + | 0.629928i | ||||
\(34\) | −2.41725 | − | 2.41725i | −0.414555 | − | 0.414555i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.85550 | − | 2.80333i | 0.809250 | − | 0.467221i | ||||
\(37\) | 0.160626 | + | 0.599466i | 0.0264068 | + | 0.0985516i | 0.977872 | − | 0.209206i | \(-0.0670880\pi\) |
−0.951465 | + | 0.307758i | \(0.900421\pi\) | |||||||
\(38\) | −2.97099 | + | 5.14591i | −0.481958 | + | 0.834776i | ||||
\(39\) | 1.10660 | − | 4.19116i | 0.177198 | − | 0.671123i | ||||
\(40\) | 10.5070 | − | 6.06624i | 1.66131 | − | 0.959157i | ||||
\(41\) | −5.04879 | − | 1.35282i | −0.788488 | − | 0.211275i | −0.157965 | − | 0.987445i | \(-0.550493\pi\) |
−0.630524 | + | 0.776170i | \(0.717160\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.46143 | − | 3.15316i | −0.832860 | − | 0.480852i | 0.0219711 | − | 0.999759i | \(-0.493006\pi\) |
−0.854831 | + | 0.518907i | \(0.826339\pi\) | |||||||
\(44\) | −3.97331 | + | 14.8286i | −0.598998 | + | 2.23549i | ||||
\(45\) | −4.78929 | − | 1.28329i | −0.713944 | − | 0.191301i | ||||
\(46\) | −11.9622 | − | 3.20527i | −1.76374 | − | 0.472591i | ||||
\(47\) | 1.71303 | − | 6.39313i | 0.249872 | − | 0.932533i | −0.721000 | − | 0.692935i | \(-0.756317\pi\) |
0.970872 | − | 0.239599i | \(-0.0770159\pi\) | |||||||
\(48\) | −1.86789 | − | 1.07843i | −0.269607 | − | 0.155658i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −11.8301 | − | 3.16987i | −1.67303 | − | 0.448287i | ||||
\(51\) | 1.50320 | − | 0.867874i | 0.210490 | − | 0.121527i | ||||
\(52\) | 12.5481 | − | 3.41149i | 1.74010 | − | 0.473088i | ||||
\(53\) | 3.79264 | − | 6.56904i | 0.520959 | − | 0.902328i | −0.478744 | − | 0.877955i | \(-0.658908\pi\) |
0.999703 | − | 0.0243730i | \(-0.00775895\pi\) | |||||||
\(54\) | 3.35574 | + | 12.5238i | 0.456659 | + | 1.70427i | ||||
\(55\) | 11.7574 | − | 6.78811i | 1.58536 | − | 0.915309i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.13337 | − | 2.13337i | −0.282571 | − | 0.282571i | ||||
\(58\) | −4.49884 | − | 4.49884i | −0.590727 | − | 0.590727i | ||||
\(59\) | 0.525675 | − | 1.96185i | 0.0684370 | − | 0.255410i | −0.923228 | − | 0.384252i | \(-0.874459\pi\) |
0.991665 | + | 0.128842i | \(0.0411259\pi\) | |||||||
\(60\) | 3.57928 | + | 13.3581i | 0.462083 | + | 1.72452i | ||||
\(61\) | − | 5.24062i | − | 0.670993i | −0.942041 | − | 0.335496i | \(-0.891096\pi\) | ||
0.942041 | − | 0.335496i | \(-0.108904\pi\) | |||||||
\(62\) | 6.30300 | + | 10.9171i | 0.800482 | + | 1.38648i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 11.5440i | 1.44300i | ||||||||
\(65\) | −9.97996 | − | 5.71336i | −1.23786 | − | 0.708655i | ||||
\(66\) | −10.4940 | − | 6.05870i | −1.29172 | − | 0.745775i | ||||
\(67\) | 6.19777 | + | 6.19777i | 0.757178 | + | 0.757178i | 0.975808 | − | 0.218630i | \(-0.0701586\pi\) |
−0.218630 | + | 0.975808i | \(0.570159\pi\) | |||||||
\(68\) | 4.50931 | + | 2.60345i | 0.546835 | + | 0.315715i | ||||
\(69\) | 3.14404 | − | 5.44564i | 0.378498 | − | 0.655578i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.31929 | − | 2.22915i | 0.987318 | − | 0.264551i | 0.271194 | − | 0.962525i | \(-0.412581\pi\) |
0.716124 | + | 0.697974i | \(0.245915\pi\) | |||||||
\(72\) | −4.18153 | + | 4.18153i | −0.492798 | + | 0.492798i | ||||
\(73\) | 15.2724 | − | 4.09222i | 1.78749 | − | 0.478958i | 0.795578 | − | 0.605852i | \(-0.207167\pi\) |
0.991916 | + | 0.126894i | \(0.0405008\pi\) | |||||||
\(74\) | −0.734747 | − | 1.27262i | −0.0854126 | − | 0.147939i | ||||
\(75\) | 3.10932 | − | 5.38549i | 0.359033 | − | 0.621863i | ||||
\(76\) | 2.34245 | − | 8.74214i | 0.268697 | − | 1.00279i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.0375447 | + | 10.2639i | 0.00425110 | + | 1.16216i | ||||
\(79\) | −1.00643 | − | 1.74319i | −0.113233 | − | 0.196125i | 0.803839 | − | 0.594847i | \(-0.202787\pi\) |
−0.917072 | + | 0.398722i | \(0.869454\pi\) | |||||||
\(80\) | −4.04597 | + | 4.04597i | −0.452353 | + | 0.452353i | ||||
\(81\) | −1.91953 | −0.213281 | ||||||||
\(82\) | 12.3763 | 1.36673 | ||||||||
\(83\) | 5.11623 | − | 5.11623i | 0.561579 | − | 0.561579i | −0.368177 | − | 0.929756i | \(-0.620018\pi\) |
0.929756 | + | 0.368177i | \(0.120018\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.19179 | − | 4.44782i | −0.129268 | − | 0.482434i | ||||
\(86\) | 14.4234 | + | 3.86473i | 1.55531 | + | 0.416744i | ||||
\(87\) | 2.79766 | − | 1.61523i | 0.299941 | − | 0.173171i | ||||
\(88\) | − | 16.1921i | − | 1.72608i | ||||||
\(89\) | 6.76189 | − | 1.81184i | 0.716759 | − | 0.192055i | 0.118034 | − | 0.993010i | \(-0.462341\pi\) |
0.598725 | + | 0.800955i | \(0.295674\pi\) | |||||||
\(90\) | 11.7402 | 1.23752 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 18.8630 | 1.96661 | ||||||||
\(93\) | −6.18260 | + | 1.65662i | −0.641105 | + | 0.171784i | ||||
\(94\) | 15.6717i | 1.61641i | ||||||||
\(95\) | −6.93151 | + | 4.00191i | −0.711158 | + | 0.410587i | ||||
\(96\) | −3.90200 | − | 1.04554i | −0.398246 | − | 0.106710i | ||||
\(97\) | 1.62618 | + | 6.06897i | 0.165113 | + | 0.616211i | 0.998026 | + | 0.0628062i | \(0.0200050\pi\) |
−0.832913 | + | 0.553405i | \(0.813328\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.67912 | + | 4.67912i | −0.470270 | + | 0.470270i | ||||
\(100\) | 18.6547 | 1.86547 | ||||||||
\(101\) | −13.3392 | −1.32730 | −0.663649 | − | 0.748044i | \(-0.730993\pi\) | ||||
−0.663649 | + | 0.748044i | \(0.730993\pi\) | |||||||
\(102\) | −2.90616 | + | 2.90616i | −0.287752 | + | 0.287752i | ||||
\(103\) | 3.08727 | + | 5.34730i | 0.304197 | + | 0.526885i | 0.977082 | − | 0.212862i | \(-0.0682785\pi\) |
−0.672885 | + | 0.739747i | \(0.734945\pi\) | |||||||
\(104\) | −11.8527 | + | 6.90110i | −1.16225 | + | 0.676708i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.64852 | + | 17.3485i | −0.451504 | + | 1.68504i | ||||
\(107\) | 4.27353 | − | 7.40196i | 0.413137 | − | 0.715575i | −0.582094 | − | 0.813122i | \(-0.697766\pi\) |
0.995231 | + | 0.0975469i | \(0.0310996\pi\) | |||||||
\(108\) | −9.87427 | − | 17.1027i | −0.950152 | − | 1.64571i | ||||
\(109\) | −4.50957 | + | 1.20834i | −0.431939 | + | 0.115738i | −0.468236 | − | 0.883603i | \(-0.655110\pi\) |
0.0362973 | + | 0.999341i | \(0.488444\pi\) | |||||||
\(110\) | −22.7306 | + | 22.7306i | −2.16728 | + | 2.16728i | ||||
\(111\) | 0.720711 | − | 0.193114i | 0.0684069 | − | 0.0183296i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.80118 | − | 16.9761i | 0.922018 | − | 1.59698i | 0.125729 | − | 0.992065i | \(-0.459873\pi\) |
0.796289 | − | 0.604917i | \(-0.206794\pi\) | |||||||
\(114\) | 6.18669 | + | 3.57189i | 0.579437 | + | 0.334538i | ||||
\(115\) | −11.7956 | − | 11.7956i | −1.09994 | − | 1.09994i | ||||
\(116\) | 8.39245 | + | 4.84538i | 0.779219 | + | 0.449883i | ||||
\(117\) | 5.41941 | + | 1.43090i | 0.501024 | + | 0.132287i | ||||
\(118\) | 4.80915i | 0.442718i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −7.29317 | − | 12.6321i | −0.665773 | − | 1.15315i | ||||
\(121\) | − | 7.11890i | − | 0.647173i | ||||||
\(122\) | 3.21164 | + | 11.9860i | 0.290768 | + | 1.08516i | ||||
\(123\) | −1.62643 | + | 6.06993i | −0.146651 | + | 0.547308i | ||||
\(124\) | −13.5770 | − | 13.5770i | −1.21925 | − | 1.21925i | ||||
\(125\) | −0.388969 | − | 0.388969i | −0.0347904 | − | 0.0347904i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.02476 | − | 0.591646i | 0.0909329 | − | 0.0525001i | −0.453844 | − | 0.891081i | \(-0.649948\pi\) |
0.544777 | + | 0.838581i | \(0.316614\pi\) | |||||||
\(128\) | −5.33527 | − | 19.9115i | −0.471576 | − | 1.75994i | ||||
\(129\) | −3.79090 | + | 6.56603i | −0.333770 | + | 0.578107i | ||||
\(130\) | 26.3268 | + | 6.95114i | 2.30901 | + | 0.609655i | ||||
\(131\) | −8.37536 | + | 4.83552i | −0.731758 | + | 0.422481i | −0.819065 | − | 0.573701i | \(-0.805507\pi\) |
0.0873067 | + | 0.996181i | \(0.472174\pi\) | |||||||
\(132\) | 17.8277 | + | 4.77693i | 1.55171 | + | 0.415778i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −17.9733 | − | 10.3769i | −1.55266 | − | 0.896428i | ||||
\(135\) | −4.52017 | + | 16.8695i | −0.389034 | + | 1.45190i | ||||
\(136\) | −5.30482 | − | 1.42142i | −0.454884 | − | 0.121886i | ||||
\(137\) | −6.37069 | − | 1.70702i | −0.544285 | − | 0.145841i | −0.0238082 | − | 0.999717i | \(-0.507579\pi\) |
−0.520477 | + | 0.853876i | \(0.674246\pi\) | |||||||
\(138\) | −3.85355 | + | 14.3817i | −0.328036 | + | 1.22425i | ||||
\(139\) | −19.6752 | − | 11.3595i | −1.66883 | − | 0.963500i | −0.968269 | − | 0.249909i | \(-0.919599\pi\) |
−0.700562 | − | 0.713591i | \(-0.747067\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.68617 | − | 2.05950i | −0.647292 | − | 0.173441i | ||||
\(142\) | −17.6612 | + | 10.1967i | −1.48210 | + | 0.855688i | ||||
\(143\) | −13.2632 | + | 7.72232i | −1.10912 | + | 0.645773i | ||||
\(144\) | 1.39447 | − | 2.41529i | 0.116206 | − | 0.201274i | ||||
\(145\) | −2.21808 | − | 8.27800i | −0.184202 | − | 0.687450i | ||||
\(146\) | −32.4220 | + | 18.7189i | −2.68327 | + | 1.54918i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.58269 | + | 1.58269i | 0.130096 | + | 0.130096i | ||||
\(149\) | 10.7410 | + | 10.7410i | 0.879936 | + | 0.879936i | 0.993528 | − | 0.113591i | \(-0.0362354\pi\) |
−0.113591 | + | 0.993528i | \(0.536235\pi\) | |||||||
\(150\) | −3.81099 | + | 14.2228i | −0.311166 | + | 1.16129i | ||||
\(151\) | −1.86148 | − | 6.94712i | −0.151485 | − | 0.565349i | −0.999381 | − | 0.0351862i | \(-0.988798\pi\) |
0.847896 | − | 0.530163i | \(-0.177869\pi\) | |||||||
\(152\) | 9.54598i | 0.774281i | ||||||||
\(153\) | 1.12221 | + | 1.94372i | 0.0907252 | + | 0.157141i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.9802i | 1.36389i | ||||||||
\(156\) | −4.10148 | − | 15.0860i | −0.328381 | − | 1.20784i | ||||
\(157\) | 16.4569 | + | 9.50142i | 1.31341 | + | 0.758296i | 0.982659 | − | 0.185423i | \(-0.0593656\pi\) |
0.330748 | + | 0.943719i | \(0.392699\pi\) | |||||||
\(158\) | 3.37014 | + | 3.37014i | 0.268114 | + | 0.268114i | ||||
\(159\) | −7.89767 | − | 4.55972i | −0.626326 | − | 0.361609i | ||||
\(160\) | −5.35833 | + | 9.28090i | −0.423613 | + | 0.733720i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 4.39021 | − | 1.17635i | 0.344928 | − | 0.0924231i | ||||
\(163\) | −0.717062 | + | 0.717062i | −0.0561646 | + | 0.0561646i | −0.734631 | − | 0.678467i | \(-0.762645\pi\) |
0.678467 | + | 0.734631i | \(0.262645\pi\) | |||||||
\(164\) | −18.2086 | + | 4.87899i | −1.42185 | + | 0.380985i | ||||
\(165\) | −8.16105 | − | 14.1353i | −0.635337 | − | 1.10044i | ||||
\(166\) | −8.56608 | + | 14.8369i | −0.664857 | + | 1.15157i | ||||
\(167\) | 0.522634 | − | 1.95050i | 0.0404426 | − | 0.150934i | −0.942752 | − | 0.333495i | \(-0.891772\pi\) |
0.983195 | + | 0.182561i | \(0.0584387\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.3056 | + | 6.41746i | 0.869660 | + | 0.493651i | ||||
\(170\) | 5.45155 | + | 9.44237i | 0.418115 | + | 0.724197i | ||||
\(171\) | 2.75856 | − | 2.75856i | 0.210952 | − | 0.210952i | ||||
\(172\) | −22.7439 | −1.73421 | ||||||||
\(173\) | 2.45048 | 0.186307 | 0.0931533 | − | 0.995652i | \(-0.470305\pi\) | ||||
0.0931533 | + | 0.995652i | \(0.470305\pi\) | |||||||
\(174\) | −5.40875 | + | 5.40875i | −0.410037 | + | 0.410037i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.97645 | + | 7.37623i | 0.148981 | + | 0.556004i | ||||
\(177\) | −2.35864 | − | 0.631995i | −0.177286 | − | 0.0475037i | ||||
\(178\) | −14.3550 | + | 8.28784i | −1.07595 | + | 0.621200i | ||||
\(179\) | − | 7.50965i | − | 0.561298i | −0.959811 | − | 0.280649i | \(-0.909450\pi\) | ||
0.959811 | − | 0.280649i | \(-0.0905496\pi\) | |||||||
\(180\) | −17.2727 | + | 4.62821i | −1.28743 | + | 0.344966i | ||||
\(181\) | −4.93320 | −0.366682 | −0.183341 | − | 0.983049i | \(-0.558691\pi\) | ||||
−0.183341 | + | 0.983049i | \(0.558691\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.30057 | −0.465751 | ||||||||
\(184\) | −19.2177 | + | 5.14937i | −1.41675 | + | 0.379617i | ||||
\(185\) | − | 1.97940i | − | 0.145528i | ||||||
\(186\) | 13.1252 | − | 7.57782i | 0.962384 | − | 0.555633i | ||||
\(187\) | −5.93608 | − | 1.59057i | −0.434089 | − | 0.116314i | ||||
\(188\) | −6.17811 | − | 23.0570i | −0.450585 | − | 1.68161i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 13.4008 | − | 13.4008i | 0.972193 | − | 0.972193i | ||||
\(191\) | −6.08863 | −0.440558 | −0.220279 | − | 0.975437i | \(-0.570697\pi\) | ||||
−0.220279 | + | 0.975437i | \(0.570697\pi\) | |||||||
\(192\) | 13.8788 | 1.00162 | ||||||||
\(193\) | 10.2443 | − | 10.2443i | 0.737402 | − | 0.737402i | −0.234672 | − | 0.972074i | \(-0.575402\pi\) |
0.972074 | + | 0.234672i | \(0.0754018\pi\) | |||||||
\(194\) | −7.43855 | − | 12.8840i | −0.534057 | − | 0.925014i | ||||
\(195\) | −6.86892 | + | 11.9985i | −0.491894 | + | 0.859228i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.33340 | + | 16.1725i | −0.308742 | + | 1.15224i | 0.620934 | + | 0.783863i | \(0.286754\pi\) |
−0.929676 | + | 0.368379i | \(0.879913\pi\) | |||||||
\(198\) | 7.83424 | − | 13.5693i | 0.556755 | − | 0.964328i | ||||
\(199\) | 9.90747 | + | 17.1602i | 0.702322 | + | 1.21646i | 0.967649 | + | 0.252298i | \(0.0811865\pi\) |
−0.265328 | + | 0.964158i | \(0.585480\pi\) | |||||||
\(200\) | −19.0055 | + | 5.09250i | −1.34389 | + | 0.360094i | ||||
\(201\) | 7.45130 | − | 7.45130i | 0.525574 | − | 0.525574i | ||||
\(202\) | 30.5084 | − | 8.17471i | 2.14657 | − | 0.575171i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 3.13002 | − | 5.42135i | 0.219145 | − | 0.379570i | ||||
\(205\) | 14.4373 | + | 8.33541i | 1.00835 | + | 0.582170i | ||||
\(206\) | −10.3380 | − | 10.3380i | −0.720282 | − | 0.720282i | ||||
\(207\) | 7.04151 | + | 4.06542i | 0.489419 | + | 0.282566i | ||||
\(208\) | 4.55708 | − | 4.59054i | 0.315977 | − | 0.318297i | ||||
\(209\) | 10.6819i | 0.738885i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.56393 | − | 16.5652i | −0.658408 | − | 1.14040i | −0.981028 | − | 0.193868i | \(-0.937897\pi\) |
0.322619 | − | 0.946529i | \(-0.395437\pi\) | |||||||
\(212\) | − | 27.3566i | − | 1.87886i | ||||||
\(213\) | −2.68000 | − | 10.0019i | −0.183631 | − | 0.685320i | ||||
\(214\) | −5.23793 | + | 19.5482i | −0.358058 | + | 1.33629i | ||||
\(215\) | 14.2224 | + | 14.2224i | 0.969961 | + | 0.969961i | ||||
\(216\) | 14.7288 | + | 14.7288i | 1.00217 | + | 1.00217i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 9.57347 | − | 5.52725i | 0.648397 | − | 0.374352i | ||||
\(219\) | −4.91989 | − | 18.3613i | −0.332455 | − | 1.24074i | ||||
\(220\) | 24.4816 | − | 42.4033i | 1.65055 | − | 2.85883i | ||||
\(221\) | 1.36566 | + | 5.02316i | 0.0918645 | + | 0.337894i | ||||
\(222\) | −1.53001 | + | 0.883353i | −0.102688 | + | 0.0592868i | ||||
\(223\) | −0.670621 | − | 0.179692i | −0.0449081 | − | 0.0120331i | 0.236295 | − | 0.971681i | \(-0.424067\pi\) |
−0.281203 | + | 0.959648i | \(0.590733\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.96374 | + | 4.02052i | 0.464249 | + | 0.268034i | ||||
\(226\) | −12.0130 | + | 44.8332i | −0.799094 | + | 2.98226i | ||||
\(227\) | 5.03400 | + | 1.34886i | 0.334118 | + | 0.0895267i | 0.421978 | − | 0.906606i | \(-0.361336\pi\) |
−0.0878596 | + | 0.996133i | \(0.528003\pi\) | |||||||
\(228\) | −10.5103 | − | 2.81622i | −0.696060 | − | 0.186509i | ||||
\(229\) | 0.274163 | − | 1.02319i | 0.0181172 | − | 0.0676142i | −0.956275 | − | 0.292468i | \(-0.905524\pi\) |
0.974393 | + | 0.224853i | \(0.0721903\pi\) | |||||||
\(230\) | 34.2068 | + | 19.7493i | 2.25553 | + | 1.30223i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.87299 | − | 2.64546i | −0.648193 | − | 0.173683i | ||||
\(233\) | 1.14405 | − | 0.660517i | 0.0749492 | − | 0.0432719i | −0.462057 | − | 0.886850i | \(-0.652888\pi\) |
0.537006 | + | 0.843578i | \(0.319555\pi\) | |||||||
\(234\) | −13.2718 | + | 0.0485473i | −0.867604 | + | 0.00317364i | ||||
\(235\) | −10.5549 | + | 18.2816i | −0.688524 | + | 1.19256i | ||||
\(236\) | −1.89586 | − | 7.07546i | −0.123410 | − | 0.460573i | ||||
\(237\) | −2.09577 | + | 1.20999i | −0.136135 | + | 0.0785973i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.2273 | + | 15.2273i | 0.984972 | + | 0.984972i | 0.999889 | − | 0.0149168i | \(-0.00474835\pi\) |
−0.0149168 | + | 0.999889i | \(0.504748\pi\) | |||||||
\(240\) | 4.86429 | + | 4.86429i | 0.313989 | + | 0.313989i | ||||
\(241\) | −0.908152 | + | 3.38927i | −0.0584992 | + | 0.218322i | −0.988987 | − | 0.148000i | \(-0.952716\pi\) |
0.930488 | + | 0.366322i | \(0.119383\pi\) | |||||||
\(242\) | 4.36271 | + | 16.2819i | 0.280446 | + | 1.04664i | ||||
\(243\) | − | 14.1195i | − | 0.905769i | ||||||
\(244\) | −9.45024 | − | 16.3683i | −0.604989 | − | 1.04787i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | − | 14.8795i | − | 0.948680i | ||||||
\(247\) | 7.81925 | − | 4.55266i | 0.497527 | − | 0.289679i | ||||
\(248\) | 17.5387 | + | 10.1260i | 1.11371 | + | 0.643000i | ||||
\(249\) | −6.15101 | − | 6.15101i | −0.389805 | − | 0.389805i | ||||
\(250\) | 1.12800 | + | 0.651249i | 0.0713407 | + | 0.0411886i | ||||
\(251\) | 8.75834 | − | 15.1699i | 0.552822 | − | 0.957515i | −0.445248 | − | 0.895407i | \(-0.646884\pi\) |
0.998069 | − | 0.0621079i | \(-0.0197823\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −21.5046 | + | 5.76214i | −1.35198 | + | 0.362262i | ||||
\(254\) | −1.98118 | + | 1.98118i | −0.124310 | + | 0.124310i | ||||
\(255\) | −5.34741 | + | 1.43283i | −0.334868 | + | 0.0897276i | ||||
\(256\) | 12.8609 | + | 22.2758i | 0.803807 | + | 1.39224i | ||||
\(257\) | 3.42559 | − | 5.93330i | 0.213683 | − | 0.370109i | −0.739182 | − | 0.673506i | \(-0.764788\pi\) |
0.952864 | + | 0.303397i | \(0.0981208\pi\) | |||||||
\(258\) | 4.64639 | − | 17.3406i | 0.289272 | − | 1.07958i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −41.4736 | + | 0.151708i | −2.57208 | + | 0.00940850i | ||||
\(261\) | 2.08858 | + | 3.61753i | 0.129280 | + | 0.223920i | ||||
\(262\) | 16.1922 | − | 16.1922i | 1.00036 | − | 1.00036i | ||||
\(263\) | 17.4170 | 1.07398 | 0.536989 | − | 0.843589i | \(-0.319562\pi\) | ||||
0.536989 | + | 0.843589i | \(0.319562\pi\) | |||||||
\(264\) | −19.4670 | −1.19811 | ||||||||
\(265\) | −17.1068 | + | 17.1068i | −1.05086 | + | 1.05086i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.17830 | − | 8.12952i | −0.133310 | − | 0.497518i | ||||
\(268\) | 30.5340 | + | 8.18157i | 1.86516 | + | 0.499769i | ||||
\(269\) | 0.145276 | − | 0.0838752i | 0.00885764 | − | 0.00511396i | −0.495565 | − | 0.868571i | \(-0.665039\pi\) |
0.504422 | + | 0.863457i | \(0.331706\pi\) | |||||||
\(270\) | − | 41.3529i | − | 2.51666i | ||||||
\(271\) | 2.40913 | − | 0.645525i | 0.146344 | − | 0.0392128i | −0.184903 | − | 0.982757i | \(-0.559197\pi\) |
0.331248 | + | 0.943544i | \(0.392530\pi\) | |||||||
\(272\) | 2.59009 | 0.157047 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 15.6167 | 0.943441 | ||||||||
\(275\) | −21.2671 | + | 5.69850i | −1.28245 | + | 0.343632i | ||||
\(276\) | − | 22.6782i | − | 1.36506i | ||||||
\(277\) | 7.38731 | − | 4.26506i | 0.443860 | − | 0.256263i | −0.261373 | − | 0.965238i | \(-0.584175\pi\) |
0.705234 | + | 0.708975i | \(0.250842\pi\) | |||||||
\(278\) | 51.9613 | + | 13.9230i | 3.11643 | + | 0.835046i | ||||
\(279\) | −2.14210 | − | 7.99444i | −0.128244 | − | 0.478614i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.7936 | − | 15.7936i | 0.942166 | − | 0.942166i | −0.0562508 | − | 0.998417i | \(-0.517915\pi\) |
0.998417 | + | 0.0562508i | \(0.0179146\pi\) | |||||||
\(282\) | 18.8414 | 1.12199 | ||||||||
\(283\) | −9.58097 | −0.569530 | −0.284765 | − | 0.958597i | \(-0.591915\pi\) | ||||
−0.284765 | + | 0.958597i | \(0.591915\pi\) | |||||||
\(284\) | 21.9643 | − | 21.9643i | 1.30334 | − | 1.30334i | ||||
\(285\) | 4.81132 | + | 8.33345i | 0.284998 | + | 0.493631i | ||||
\(286\) | 25.6021 | − | 25.7901i | 1.51388 | − | 1.52500i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.35194 | − | 5.04550i | 0.0796636 | − | 0.297309i | ||||
\(289\) | 7.45780 | − | 12.9173i | 0.438694 | − | 0.759841i | ||||
\(290\) | 10.1461 | + | 17.5735i | 0.595799 | + | 1.03195i | ||||
\(291\) | 7.29645 | − | 1.95508i | 0.427726 | − | 0.114609i | ||||
\(292\) | 40.3215 | − | 40.3215i | 2.35964 | − | 2.35964i | ||||
\(293\) | −14.5286 | + | 3.89292i | −0.848769 | + | 0.227427i | −0.656885 | − | 0.753991i | \(-0.728126\pi\) |
−0.191884 | + | 0.981418i | \(0.561460\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.23895 | + | 5.61003i | −0.188579 | + | 0.326628i | ||||
\(296\) | −2.04450 | − | 1.18039i | −0.118834 | − | 0.0686090i | ||||
\(297\) | 16.4815 | + | 16.4815i | 0.956352 | + | 0.956352i | ||||
\(298\) | −31.1485 | − | 17.9836i | −1.80438 | − | 1.04176i | ||||
\(299\) | 13.3832 | + | 13.2857i | 0.773972 | + | 0.768330i | ||||
\(300\) | − | 22.4277i | − | 1.29486i | ||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 8.51488 | + | 14.7482i | 0.489976 | + | 0.848663i | ||||
\(303\) | 16.0371i | 0.921307i | ||||||||
\(304\) | −1.16521 | − | 4.34863i | −0.0668295 | − | 0.249411i | ||||
\(305\) | −4.32606 | + | 16.1451i | −0.247709 | + | 0.924464i | ||||
\(306\) | −3.75782 | − | 3.75782i | −0.214820 | − | 0.214820i | ||||
\(307\) | 15.7439 | + | 15.7439i | 0.898552 | + | 0.898552i | 0.995308 | − | 0.0967560i | \(-0.0308467\pi\) |
−0.0967560 | + | 0.995308i | \(0.530847\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.42882 | − | 3.71168i | 0.365723 | − | 0.211150i | ||||
\(310\) | −10.4061 | − | 38.8360i | −0.591025 | − | 2.20574i | ||||
\(311\) | 1.94686 | − | 3.37206i | 0.110396 | − | 0.191212i | −0.805534 | − | 0.592550i | \(-0.798121\pi\) |
0.915930 | + | 0.401338i | \(0.131455\pi\) | |||||||
\(312\) | 8.29688 | + | 14.2500i | 0.469718 | + | 0.806747i | ||||
\(313\) | −8.63858 | + | 4.98749i | −0.488282 | + | 0.281910i | −0.723861 | − | 0.689946i | \(-0.757634\pi\) |
0.235580 | + | 0.971855i | \(0.424301\pi\) | |||||||
\(314\) | −43.4620 | − | 11.6456i | −2.45270 | − | 0.657199i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.28689 | − | 3.62974i | −0.353665 | − | 0.204189i | ||||
\(317\) | 4.01848 | − | 14.9972i | 0.225701 | − | 0.842326i | −0.756422 | − | 0.654084i | \(-0.773054\pi\) |
0.982123 | − | 0.188242i | \(-0.0602790\pi\) | |||||||
\(318\) | 20.8574 | + | 5.58871i | 1.16962 | + | 0.313399i | ||||
\(319\) | −11.0479 | − | 2.96026i | −0.618561 | − | 0.165743i | ||||
\(320\) | 9.52940 | − | 35.5642i | 0.532710 | − | 1.98810i | ||||
\(321\) | −8.89905 | − | 5.13787i | −0.496697 | − | 0.286768i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.49959 | + | 0.937714i | 0.194723 | + | 0.0521758i | ||||
\(324\) | −5.99535 | + | 3.46142i | −0.333075 | + | 0.192301i | ||||
\(325\) | 13.2354 | + | 13.1389i | 0.734169 | + | 0.728817i | ||||
\(326\) | 1.20057 | − | 2.07946i | 0.0664936 | − | 0.115170i | ||||
\(327\) | 1.45273 | + | 5.42166i | 0.0803361 | + | 0.299818i | ||||
\(328\) | 17.2191 | − | 9.94146i | 0.950766 | − | 0.548925i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 27.3280 | + | 27.3280i | 1.50436 | + | 1.50436i | ||||
\(331\) | −10.3551 | − | 10.3551i | −0.569166 | − | 0.569166i | 0.362729 | − | 0.931895i | \(-0.381845\pi\) |
−0.931895 | + | 0.362729i | \(0.881845\pi\) | |||||||
\(332\) | 6.75384 | − | 25.2057i | 0.370665 | − | 1.38334i | ||||
\(333\) | 0.249707 | + | 0.931919i | 0.0136839 | + | 0.0510688i | ||||
\(334\) | 4.78133i | 0.261622i | ||||||||
\(335\) | −13.9776 | − | 24.2100i | −0.763680 | − | 1.32273i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.8235i | 0.644066i | 0.946728 | + | 0.322033i | \(0.104366\pi\) | ||||
−0.946728 | + | 0.322033i | \(0.895634\pi\) | |||||||
\(338\) | −29.7902 | − | 7.74912i | −1.62037 | − | 0.421497i | ||||
\(339\) | −20.4097 | − | 11.7835i | −1.10850 | − | 0.639993i | ||||
\(340\) | −11.7430 | − | 11.7430i | −0.636852 | − | 0.636852i | ||||
\(341\) | 19.6258 | + | 11.3309i | 1.06280 | + | 0.613605i | ||||
\(342\) | −4.61865 | + | 7.99973i | −0.249748 | + | 0.432576i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 23.1716 | − | 6.20881i | 1.24933 | − | 0.334756i | ||||
\(345\) | −14.1813 | + | 14.1813i | −0.763496 | + | 0.763496i | ||||
\(346\) | −5.60457 | + | 1.50174i | −0.301303 | + | 0.0807340i | ||||
\(347\) | 5.00685 | + | 8.67212i | 0.268782 | + | 0.465544i | 0.968548 | − | 0.248829i | \(-0.0800456\pi\) |
−0.699766 | + | 0.714372i | \(0.746712\pi\) | |||||||
\(348\) | 5.82539 | − | 10.0899i | 0.312274 | − | 0.540874i | ||||
\(349\) | −4.39634 | + | 16.4073i | −0.235330 | + | 0.878265i | 0.742669 | + | 0.669658i | \(0.233559\pi\) |
−0.978000 | + | 0.208607i | \(0.933107\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.04012 | − | 19.0890i | 0.269022 | − | 1.01890i | ||||
\(352\) | 7.15125 | + | 12.3863i | 0.381163 | + | 0.660194i | ||||
\(353\) | −25.5124 | + | 25.5124i | −1.35789 | + | 1.35789i | −0.481366 | + | 0.876520i | \(0.659859\pi\) |
−0.876520 | + | 0.481366i | \(0.840141\pi\) | |||||||
\(354\) | 5.78182 | 0.307300 | ||||||||
\(355\) | −27.4698 | −1.45795 | ||||||||
\(356\) | 17.8525 | − | 17.8525i | 0.946181 | − | 0.946181i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.60217 | + | 17.1755i | 0.243232 | + | 0.907756i | ||||
\(359\) | 3.34645 | + | 0.896679i | 0.176619 | + | 0.0473249i | 0.346045 | − | 0.938218i | \(-0.387525\pi\) |
−0.169426 | + | 0.985543i | \(0.554191\pi\) | |||||||
\(360\) | 16.3341 | − | 9.43047i | 0.860880 | − | 0.497030i | ||||
\(361\) | 12.7025i | 0.668553i | ||||||||
\(362\) | 11.2829 | − | 3.02324i | 0.593014 | − | 0.158898i | ||||
\(363\) | −8.55873 | −0.449217 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −50.4284 | −2.63954 | ||||||||
\(366\) | 14.4102 | − | 3.86121i | 0.753234 | − | 0.201828i | ||||
\(367\) | − | 12.6820i | − | 0.661994i | −0.943632 | − | 0.330997i | \(-0.892615\pi\) | ||
0.943632 | − | 0.330997i | \(-0.107385\pi\) | |||||||
\(368\) | 8.12600 | − | 4.69155i | 0.423597 | − | 0.244564i | ||||
\(369\) | −7.84876 | − | 2.10307i | −0.408590 | − | 0.109481i | ||||
\(370\) | 1.21305 | + | 4.52715i | 0.0630633 | + | 0.235355i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −16.3231 | + | 16.3231i | −0.846312 | + | 0.846312i | ||||
\(373\) | 30.0385 | 1.55533 | 0.777667 | − | 0.628677i | \(-0.216403\pi\) | ||||
0.777667 | + | 0.628677i | \(0.216403\pi\) | |||||||
\(374\) | 14.5513 | 0.752432 | ||||||||
\(375\) | −0.467640 | + | 0.467640i | −0.0241488 | + | 0.0241488i | ||||
\(376\) | 12.5886 | + | 21.8040i | 0.649206 | + | 1.12446i | ||||
\(377\) | 2.54169 | + | 9.34878i | 0.130904 | + | 0.481487i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.10882 | − | 11.6023i | 0.159689 | − | 0.595969i | −0.838969 | − | 0.544180i | \(-0.816841\pi\) |
0.998658 | − | 0.0517891i | \(-0.0164924\pi\) | |||||||
\(380\) | −14.4330 | + | 24.9987i | −0.740398 | + | 1.28241i | ||||
\(381\) | −0.711310 | − | 1.23202i | −0.0364415 | − | 0.0631185i | ||||
\(382\) | 13.9255 | − | 3.73133i | 0.712490 | − | 0.190911i | ||||
\(383\) | 4.04719 | − | 4.04719i | 0.206802 | − | 0.206802i | −0.596105 | − | 0.802907i | \(-0.703286\pi\) |
0.802907 | + | 0.596105i | \(0.203286\pi\) | |||||||
\(384\) | −23.9387 | + | 6.41436i | −1.22162 | + | 0.327331i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −17.1520 | + | 29.7082i | −0.873015 | + | 1.51211i | ||||
\(387\) | −8.49024 | − | 4.90184i | −0.431583 | − | 0.249175i | ||||
\(388\) | 16.0231 | + | 16.0231i | 0.813449 | + | 0.813449i | ||||
\(389\) | 14.2446 | + | 8.22413i | 0.722231 | + | 0.416980i | 0.815573 | − | 0.578654i | \(-0.196422\pi\) |
−0.0933424 | + | 0.995634i | \(0.529755\pi\) | |||||||
\(390\) | 8.35704 | − | 31.6516i | 0.423175 | − | 1.60274i | ||||
\(391\) | 7.55112i | 0.381877i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.81352 | + | 10.0693i | 0.293253 | + | 0.507930i | ||||
\(394\) | − | 39.6442i | − | 1.99725i | ||||||
\(395\) | 1.66159 | + | 6.20115i | 0.0836038 | + | 0.312014i | ||||
\(396\) | −6.17683 | + | 23.0522i | −0.310397 | + | 1.15842i | ||||
\(397\) | −7.98783 | − | 7.98783i | −0.400898 | − | 0.400898i | 0.477652 | − | 0.878549i | \(-0.341488\pi\) |
−0.878549 | + | 0.477652i | \(0.841488\pi\) | |||||||
\(398\) | −33.1761 | − | 33.1761i | −1.66297 | − | 1.66297i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.03625 | − | 4.63973i | 0.401812 | − | 0.231987i | ||||
\(401\) | 6.26544 | + | 23.3830i | 0.312881 | + | 1.16769i | 0.925946 | + | 0.377656i | \(0.123270\pi\) |
−0.613064 | + | 0.790033i | \(0.710063\pi\) | |||||||
\(402\) | −12.4757 | + | 21.6085i | −0.622231 | + | 1.07774i | ||||
\(403\) | −0.0702158 | − | 19.1955i | −0.00349770 | − | 0.956195i | ||||
\(404\) | −41.6629 | + | 24.0541i | −2.07281 | + | 1.19674i | ||||
\(405\) | 5.91359 | + | 1.58454i | 0.293849 | + | 0.0787366i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.28780 | − | 1.32086i | −0.113402 | − | 0.0654726i | ||||
\(408\) | −1.70891 | + | 6.37774i | −0.0846037 | + | 0.315745i | ||||
\(409\) | −0.348508 | − | 0.0933824i | −0.0172326 | − | 0.00461746i | 0.250192 | − | 0.968196i | \(-0.419506\pi\) |
−0.267425 | + | 0.963579i | \(0.586173\pi\) | |||||||
\(410\) | −38.1283 | − | 10.2165i | −1.88302 | − | 0.504555i | ||||
\(411\) | −2.05228 | + | 7.65920i | −0.101231 | + | 0.377800i | ||||
\(412\) | 19.2852 | + | 11.1343i | 0.950114 | + | 0.548549i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −18.5963 | − | 4.98286i | −0.913957 | − | 0.244894i | ||||
\(415\) | −19.9852 | + | 11.5385i | −0.981036 | + | 0.566401i | ||||
\(416\) | 6.01901 | − | 10.5139i | 0.295106 | − | 0.515484i | ||||
\(417\) | −13.6570 | + | 23.6547i | −0.668787 | + | 1.15837i | ||||
\(418\) | −6.54626 | − | 24.4310i | −0.320188 | − | 1.19496i | ||||
\(419\) | 15.9181 | − | 9.19033i | 0.777651 | − | 0.448977i | −0.0579460 | − | 0.998320i | \(-0.518455\pi\) |
0.835597 | + | 0.549343i | \(0.185122\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.7439 | + | 20.7439i | 1.01099 | + | 1.01099i | 0.999939 | + | 0.0110561i | \(0.00351933\pi\) |
0.0110561 | + | 0.999939i | \(0.496481\pi\) | |||||||
\(422\) | 32.0257 | + | 32.0257i | 1.55899 | + | 1.55899i | ||||
\(423\) | 2.66305 | − | 9.93864i | 0.129482 | − | 0.483233i | ||||
\(424\) | 7.46800 | + | 27.8710i | 0.362678 | + | 1.35353i | ||||
\(425\) | 7.46772i | 0.362238i | ||||||||
\(426\) | 12.2590 | + | 21.2333i | 0.593952 | + | 1.02876i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 30.8252i | − | 1.48999i | ||||||
\(429\) | 9.28420 | + | 15.9457i | 0.448245 | + | 0.769866i | ||||
\(430\) | −41.2445 | − | 23.8125i | −1.98899 | − | 1.14834i | ||||
\(431\) | −6.82413 | − | 6.82413i | −0.328707 | − | 0.328707i | 0.523388 | − | 0.852095i | \(-0.324668\pi\) |
−0.852095 | + | 0.523388i | \(0.824668\pi\) | |||||||
\(432\) | −8.50747 | − | 4.91179i | −0.409316 | − | 0.236319i | ||||
\(433\) | −13.6960 | + | 23.7221i | −0.658186 | + | 1.14001i | 0.322899 | + | 0.946433i | \(0.395343\pi\) |
−0.981085 | + | 0.193578i | \(0.937991\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.95227 | + | 2.66670i | −0.477175 | + | 0.127859i | ||||
\(436\) | −11.9060 | + | 11.9060i | −0.570195 | + | 0.570195i | ||||
\(437\) | 12.6780 | − | 3.39705i | 0.606469 | − | 0.162503i | ||||
\(438\) | 22.5048 | + | 38.9795i | 1.07532 | + | 1.86251i | ||||
\(439\) | −17.2958 | + | 29.9571i | −0.825481 | + | 1.42978i | 0.0760695 | + | 0.997103i | \(0.475763\pi\) |
−0.901551 | + | 0.432673i | \(0.857570\pi\) | |||||||
\(440\) | −13.3663 | + | 49.8838i | −0.637214 | + | 2.37812i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.20181 | − | 10.6517i | −0.294990 | − | 0.506649i | ||||
\(443\) | −3.98607 | − | 6.90408i | −0.189384 | − | 0.328023i | 0.755661 | − | 0.654963i | \(-0.227316\pi\) |
−0.945045 | + | 0.326940i | \(0.893982\pi\) | |||||||
\(444\) | 1.90280 | − | 1.90280i | 0.0903027 | − | 0.0903027i | ||||
\(445\) | −22.3274 | −1.05842 | ||||||||
\(446\) | 1.64392 | 0.0778418 | ||||||||
\(447\) | 12.9134 | − | 12.9134i | 0.610784 | − | 0.610784i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.25579 | − | 19.6149i | −0.248036 | − | 0.925683i | −0.971833 | − | 0.235670i | \(-0.924271\pi\) |
0.723797 | − | 0.690013i | \(-0.242395\pi\) | |||||||
\(450\) | −18.3909 | − | 4.92782i | −0.866955 | − | 0.232300i | ||||
\(451\) | 19.2682 | − | 11.1245i | 0.907302 | − | 0.523831i | ||||
\(452\) | − | 70.6966i | − | 3.32529i | ||||||
\(453\) | −8.35221 | + | 2.23797i | −0.392421 | + | 0.105149i | ||||
\(454\) | −12.3400 | −0.579146 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 11.4767 | 0.537446 | ||||||||
\(457\) | −1.35752 | + | 0.363747i | −0.0635022 | + | 0.0170154i | −0.290430 | − | 0.956896i | \(-0.593798\pi\) |
0.226928 | + | 0.973912i | \(0.427132\pi\) | |||||||
\(458\) | 2.50818i | 0.117200i | ||||||||
\(459\) | 6.84646 | − | 3.95280i | 0.319565 | − | 0.184501i | ||||
\(460\) | −58.1123 | − | 15.5711i | −2.70950 | − | 0.726009i | ||||
\(461\) | 4.89285 | + | 18.2604i | 0.227883 | + | 0.850469i | 0.981229 | + | 0.192846i | \(0.0617717\pi\) |
−0.753347 | + | 0.657624i | \(0.771562\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.4573 | − | 22.4573i | 1.04368 | − | 1.04368i | 0.0446754 | − | 0.999002i | \(-0.485775\pi\) |
0.999002 | − | 0.0446754i | \(-0.0142253\pi\) | |||||||
\(464\) | 4.82051 | 0.223787 | ||||||||
\(465\) | 20.4146 | 0.946703 | ||||||||
\(466\) | −2.21180 | + | 2.21180i | −0.102460 | + | 0.102460i | ||||
\(467\) | −14.1945 | − | 24.5855i | −0.656841 | − | 1.13768i | −0.981429 | − | 0.191826i | \(-0.938559\pi\) |
0.324588 | − | 0.945855i | \(-0.394774\pi\) | |||||||
\(468\) | 19.5070 | − | 5.30343i | 0.901711 | − | 0.245151i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 12.9368 | − | 48.2807i | 0.596729 | − | 2.22702i | ||||
\(471\) | 11.4231 | − | 19.7854i | 0.526350 | − | 0.911665i | ||||
\(472\) | 3.86302 | + | 6.69096i | 0.177810 | + | 0.307976i | ||||
\(473\) | 25.9290 | − | 6.94764i | 1.19221 | − | 0.319453i | ||||
\(474\) | 4.05176 | − | 4.05176i | 0.186104 | − | 0.186104i | ||||
\(475\) | 12.5379 | − | 3.35953i | 0.575280 | − | 0.154146i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.89597 | − | 10.2121i | 0.269958 | − | 0.467581i | ||||
\(478\) | −44.1586 | − | 25.4950i | −2.01977 | − | 1.16611i | ||||
\(479\) | −2.47311 | − | 2.47311i | −0.112999 | − | 0.112999i | 0.648346 | − | 0.761346i | \(-0.275461\pi\) |
−0.761346 | + | 0.648346i | \(0.775461\pi\) | |||||||
\(480\) | 11.1580 | + | 6.44208i | 0.509291 | + | 0.294039i | ||||
\(481\) | 0.00818512 | + | 2.23764i | 0.000373209 | + | 0.102027i | ||||
\(482\) | − | 8.30825i | − | 0.378430i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −12.8373 | − | 22.2348i | −0.583512 | − | 1.01067i | ||||
\(485\) | − | 20.0394i | − | 0.909942i | ||||||
\(486\) | 8.65295 | + | 32.2933i | 0.392506 | + | 1.46485i | ||||
\(487\) | 6.29214 | − | 23.4826i | 0.285124 | − | 1.06410i | −0.663625 | − | 0.748066i | \(-0.730983\pi\) |
0.948749 | − | 0.316032i | \(-0.102351\pi\) | |||||||
\(488\) | 14.0963 | + | 14.0963i | 0.638108 | + | 0.638108i | ||||
\(489\) | 0.862092 | + | 0.862092i | 0.0389851 | + | 0.0389851i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.24444 | + | 3.02788i | −0.236678 | + | 0.136646i | −0.613649 | − | 0.789579i | \(-0.710299\pi\) |
0.376971 | + | 0.926225i | \(0.376966\pi\) | |||||||
\(492\) | 5.86579 | + | 21.8914i | 0.264450 | + | 0.986941i | ||||
\(493\) | −1.93967 | + | 3.35961i | −0.0873584 | + | 0.151309i | ||||
\(494\) | −15.0936 | + | 15.2044i | −0.679094 | + | 0.684080i | ||||
\(495\) | 18.2778 | − | 10.5527i | 0.821525 | − | 0.474308i | ||||
\(496\) | −9.22569 | − | 2.47202i | −0.414246 | − | 0.110997i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 17.8377 | + | 10.2986i | 0.799328 | + | 0.461492i | ||||
\(499\) | 4.73497 | − | 17.6712i | 0.211967 | − | 0.791070i | −0.775246 | − | 0.631660i | \(-0.782374\pi\) |
0.987212 | − | 0.159410i | \(-0.0509593\pi\) | |||||||
\(500\) | −1.91630 | − | 0.513471i | −0.0856995 | − | 0.0229631i | ||||
\(501\) | −2.34499 | − | 0.628339i | −0.104767 | − | 0.0280721i | ||||
\(502\) | −10.7348 | + | 40.0629i | −0.479119 | + | 1.78810i | ||||
\(503\) | 7.01237 | + | 4.04859i | 0.312666 | + | 0.180518i | 0.648119 | − | 0.761539i | \(-0.275556\pi\) |
−0.335453 | + | 0.942057i | \(0.608889\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 41.0947 | + | 11.0113i | 1.82869 | + | 0.489996i | ||||
\(506\) | 45.6526 | − | 26.3575i | 2.02950 | − | 1.17173i | ||||
\(507\) | 7.71543 | − | 13.5922i | 0.342654 | − | 0.603651i | ||||
\(508\) | 2.13379 | − | 3.69583i | 0.0946717 | − | 0.163976i | ||||
\(509\) | −4.18077 | − | 15.6029i | −0.185309 | − | 0.691584i | −0.994564 | − | 0.104126i | \(-0.966795\pi\) |
0.809255 | − | 0.587458i | \(-0.199871\pi\) | |||||||
\(510\) | 11.3521 | − | 6.55416i | 0.502681 | − | 0.290223i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −13.9135 | − | 13.9135i | −0.614896 | − | 0.614896i | ||||
\(513\) | −9.71660 | − | 9.71660i | −0.428998 | − | 0.428998i | ||||
\(514\) | −4.19864 | + | 15.6696i | −0.185194 | + | 0.691154i | ||||
\(515\) | −5.09699 | − | 19.0222i | −0.224600 | − | 0.838219i | ||||
\(516\) | 27.3440i | 1.20375i | ||||||||
\(517\) | 14.0866 | + | 24.3987i | 0.619527 | + | 1.07305i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 2.94610i | − | 0.129320i | ||||||
\(520\) | 42.2121 | − | 11.4763i | 1.85112 | − | 0.503271i | ||||
\(521\) | 28.0133 | + | 16.1735i | 1.22729 | + | 0.708574i | 0.966461 | − | 0.256812i | \(-0.0826721\pi\) |
0.260825 | + | 0.965386i | \(0.416005\pi\) | |||||||
\(522\) | −6.99382 | − | 6.99382i | −0.306111 | − | 0.306111i | ||||
\(523\) | −18.4602 | − | 10.6580i | −0.807210 | − | 0.466043i | 0.0387760 | − | 0.999248i | \(-0.487654\pi\) |
−0.845986 | + | 0.533205i | \(0.820987\pi\) | |||||||
\(524\) | −17.4394 | + | 30.2060i | −0.761845 | + | 1.31956i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −39.8349 | + | 10.6737i | −1.73688 | + | 0.465397i | ||||
\(527\) | 5.43507 | − | 5.43507i | 0.236755 | − | 0.236755i | ||||
\(528\) | 8.86811 | − | 2.37620i | 0.385935 | − | 0.103411i | ||||
\(529\) | 2.17769 | + | 3.77187i | 0.0946821 | + | 0.163994i | ||||
\(530\) | 28.6419 | − | 49.6092i | 1.24413 | − | 2.15489i | ||||
\(531\) | 0.817205 | − | 3.04985i | 0.0354637 | − | 0.132352i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.3553 | − | 9.36315i | −0.708428 | − | 0.405563i | ||||
\(534\) | 9.96410 | + | 17.2583i | 0.431189 | + | 0.746841i | ||||
\(535\) | −19.2759 | + | 19.2759i | −0.833370 | + | 0.833370i | ||||
\(536\) | −33.3417 | −1.44014 | ||||||||
\(537\) | −9.02852 | −0.389609 | ||||||||
\(538\) | −0.280864 | + | 0.280864i | −0.0121089 | + | 0.0121089i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 16.3021 | + | 60.8404i | 0.701532 | + | 2.61815i | ||||
\(541\) | −17.8879 | − | 4.79305i | −0.769061 | − | 0.206069i | −0.147104 | − | 0.989121i | \(-0.546995\pi\) |
−0.621957 | + | 0.783052i | \(0.713662\pi\) | |||||||
\(542\) | −5.11440 | + | 2.95280i | −0.219682 | + | 0.126834i | ||||
\(543\) | 5.93096i | 0.254522i | ||||||||
\(544\) | 4.68576 | − | 1.25555i | 0.200900 | − | 0.0538311i | ||||
\(545\) | 14.8904 | 0.637833 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −35.0943 | −1.50053 | −0.750263 | − | 0.661140i | \(-0.770073\pi\) | ||||
−0.750263 | + | 0.661140i | \(0.770073\pi\) | |||||||
\(548\) | −22.9761 | + | 6.15643i | −0.981490 | + | 0.262990i | ||||
\(549\) | − | 8.14698i | − | 0.347705i | ||||||
\(550\) | 45.1483 | − | 26.0664i | 1.92513 | − | 1.11148i | ||||
\(551\) | 6.51323 | + | 1.74521i | 0.277473 | + | 0.0743486i | ||||
\(552\) | 6.19086 | + | 23.1046i | 0.263500 | + | 0.983397i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −14.2820 | + | 14.2820i | −0.606782 | + | 0.606782i | ||||
\(555\) | −2.37975 | −0.101015 | ||||||||
\(556\) | −81.9368 | −3.47490 | ||||||||
\(557\) | −6.70621 | + | 6.70621i | −0.284151 | + | 0.284151i | −0.834762 | − | 0.550611i | \(-0.814395\pi\) |
0.550611 | + | 0.834762i | \(0.314395\pi\) | |||||||
\(558\) | 9.79854 | + | 16.9716i | 0.414805 | + | 0.718464i | ||||
\(559\) | −16.1367 | − | 16.0191i | −0.682510 | − | 0.677535i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.91227 | + | 7.13668i | −0.0807360 | + | 0.301311i | ||||
\(562\) | −26.4431 | + | 45.8008i | −1.11544 | + | 1.93199i | ||||
\(563\) | −15.8351 | − | 27.4272i | −0.667369 | − | 1.15592i | −0.978637 | − | 0.205595i | \(-0.934087\pi\) |
0.311268 | − | 0.950322i | \(-0.399246\pi\) | |||||||
\(564\) | −27.7204 | + | 7.42767i | −1.16724 | + | 0.312761i | ||||
\(565\) | −44.2086 | + | 44.2086i | −1.85987 | + | 1.85987i | ||||
\(566\) | 21.9129 | − | 5.87155i | 0.921069 | − | 0.246800i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −16.3813 | + | 28.3733i | −0.687345 | + | 1.19052i | ||||
\(569\) | 6.05848 | + | 3.49787i | 0.253985 | + | 0.146638i | 0.621587 | − | 0.783345i | \(-0.286488\pi\) |
−0.367603 | + | 0.929983i | \(0.619821\pi\) | |||||||
\(570\) | −16.1111 | − | 16.1111i | −0.674821 | − | 0.674821i | ||||
\(571\) | −13.2500 | − | 7.64990i | −0.554496 | − | 0.320139i | 0.196437 | − | 0.980516i | \(-0.437063\pi\) |
−0.750933 | + | 0.660378i | \(0.770396\pi\) | |||||||
\(572\) | −27.5001 | + | 48.0365i | −1.14984 | + | 2.00851i | ||||
\(573\) | 7.32009i | 0.305801i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.5266 | + | 23.4288i | 0.564099 | + | 0.977049i | ||||
\(576\) | 17.9461i | 0.747754i | ||||||||
\(577\) | −10.8175 | − | 40.3714i | −0.450338 | − | 1.68068i | −0.701444 | − | 0.712725i | \(-0.747461\pi\) |
0.251106 | − | 0.967960i | \(-0.419206\pi\) | |||||||
\(578\) | −9.14080 | + | 34.1139i | −0.380207 | + | 1.41895i | ||||
\(579\) | −12.3163 | − | 12.3163i | −0.511847 | − | 0.511847i | ||||
\(580\) | −21.8553 | − | 21.8553i | −0.907491 | − | 0.907491i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −15.4898 | + | 8.94304i | −0.642073 | + | 0.370701i | ||||
\(583\) | 8.35668 | + | 31.1876i | 0.346098 | + | 1.29166i | ||||
\(584\) | −30.0724 | + | 52.0870i | −1.24441 | + | 2.15538i | ||||
\(585\) | −15.5147 | − | 8.88189i | −0.641453 | − | 0.367221i | ||||
\(586\) | 30.8431 | − | 17.8073i | 1.27412 | − | 0.735611i | ||||
\(587\) | 0.941084 | + | 0.252163i | 0.0388427 | + | 0.0104079i | 0.278188 | − | 0.960527i | \(-0.410266\pi\) |
−0.239345 | + | 0.970934i | \(0.576933\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.5703 | − | 6.68012i | −0.476746 | − | 0.275250i | ||||
\(590\) | 3.96988 | − | 14.8158i | 0.163437 | − | 0.609957i | ||||
\(591\) | 19.4435 | + | 5.20986i | 0.799797 | + | 0.214305i | ||||
\(592\) | 1.07545 | + | 0.288165i | 0.0442006 | + | 0.0118435i | ||||
\(593\) | −10.2197 | + | 38.1404i | −0.419673 | + | 1.56624i | 0.355616 | + | 0.934632i | \(0.384271\pi\) |
−0.775288 | + | 0.631608i | \(0.782395\pi\) | |||||||
\(594\) | −47.7957 | − | 27.5949i | −1.96108 | − | 1.13223i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 52.9167 | + | 14.1790i | 2.16755 | + | 0.580794i | ||||
\(597\) | 20.6310 | − | 11.9113i | 0.844370 | − | 0.487497i | ||||
\(598\) | −38.7511 | − | 22.1844i | −1.58465 | − | 0.907186i | ||||
\(599\) | −8.27438 | + | 14.3316i | −0.338082 | + | 0.585575i | −0.984072 | − | 0.177771i | \(-0.943111\pi\) |
0.645990 | + | 0.763346i | \(0.276445\pi\) | |||||||
\(600\) | 6.12248 | + | 22.8494i | 0.249949 | + | 0.932824i | ||||
\(601\) | −9.99562 | + | 5.77097i | −0.407730 | + | 0.235403i | −0.689814 | − | 0.723987i | \(-0.742308\pi\) |
0.282084 | + | 0.959390i | \(0.408974\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.63495 | + | 9.63495i | 0.392365 | + | 0.392365i | ||||
\(604\) | −18.3415 | − | 18.3415i | −0.746307 | − | 0.746307i | ||||
\(605\) | −5.87655 | + | 21.9316i | −0.238916 | + | 0.891645i | ||||
\(606\) | −9.82809 | − | 36.6789i | −0.399239 | − | 1.48998i | ||||
\(607\) | 21.3778i | 0.867696i | 0.900986 | + | 0.433848i | \(0.142845\pi\) | ||||
−0.900986 | + | 0.433848i | \(0.857155\pi\) | |||||||
\(608\) | −4.21600 | − | 7.30232i | −0.170981 | − | 0.296148i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 39.5770i | − | 1.60243i | ||||||
\(611\) | 11.8563 | − | 20.7102i | 0.479653 | − | 0.837847i | ||||
\(612\) | 7.01010 | + | 4.04728i | 0.283366 | + | 0.163602i | ||||
\(613\) | 22.0693 | + | 22.0693i | 0.891372 | + | 0.891372i | 0.994652 | − | 0.103281i | \(-0.0329340\pi\) |
−0.103281 | + | 0.994652i | \(0.532934\pi\) | |||||||
\(614\) | −45.6568 | − | 26.3600i | −1.84256 | − | 1.06380i | ||||
\(615\) | 10.0213 | − | 17.3574i | 0.404097 | − | 0.699917i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.9421 | − | 7.21911i | 1.08465 | − | 0.290630i | 0.328149 | − | 0.944626i | \(-0.393575\pi\) |
0.756498 | + | 0.653996i | \(0.226909\pi\) | |||||||
\(618\) | −12.4289 | + | 12.4289i | −0.499964 | + | 0.499964i | ||||
\(619\) | −46.5004 | + | 12.4597i | −1.86901 | + | 0.500799i | −0.869025 | + | 0.494768i | \(0.835253\pi\) |
−0.999982 | + | 0.00603119i | \(0.998080\pi\) | |||||||
\(620\) | 30.6199 | + | 53.0352i | 1.22972 | + | 2.12994i | ||||
\(621\) | 14.3198 | − | 24.8026i | 0.574633 | − | 0.995294i | ||||
\(622\) | −2.38621 | + | 8.90546i | −0.0956783 | + | 0.357076i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −5.51901 | − | 5.47878i | −0.220937 | − | 0.219327i | ||||
\(625\) | −12.0539 | − | 20.8781i | −0.482158 | − | 0.835122i | ||||
\(626\) | 16.7011 | − | 16.7011i | 0.667509 | − | 0.667509i | ||||
\(627\) | 12.8424 | 0.512877 | ||||||||
\(628\) | 68.5343 | 2.73482 | ||||||||
\(629\) | −0.633571 | + | 0.633571i | −0.0252621 | + | 0.0252621i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.94853 | − | 11.0041i | −0.117379 | − | 0.438064i | 0.882075 | − | 0.471109i | \(-0.156146\pi\) |
−0.999454 | + | 0.0330448i | \(0.989480\pi\) | |||||||
\(632\) | 7.39598 | + | 1.98175i | 0.294196 | + | 0.0788296i | ||||
\(633\) | −19.9156 | + | 11.4983i | −0.791575 | + | 0.457016i | ||||
\(634\) | 36.7632i | 1.46005i | ||||||||
\(635\) | −3.64543 | + | 0.976791i | −0.144665 | + | 0.0387628i | ||||
\(636\) | −32.8896 | −1.30416 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 27.0820 | 1.07219 | ||||||||
\(639\) | 12.9330 | − | 3.46539i | 0.511622 | − | 0.137089i | ||||
\(640\) | 65.7466i | 2.59886i | ||||||||
\(641\) | 16.9100 | − | 9.76301i | 0.667906 | − | 0.385616i | −0.127377 | − | 0.991854i | \(-0.540656\pi\) |
0.795283 | + | 0.606239i | \(0.207322\pi\) | |||||||
\(642\) | 23.5020 | + | 6.29733i | 0.927548 | + | 0.248536i | ||||
\(643\) | −9.35047 | − | 34.8964i | −0.368747 | − | 1.37618i | −0.862270 | − | 0.506449i | \(-0.830958\pi\) |
0.493524 | − | 0.869732i | \(-0.335709\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 17.0990 | − | 17.0990i | 0.673272 | − | 0.673272i | ||||
\(646\) | −8.57869 | −0.337524 | ||||||||
\(647\) | −5.79390 | −0.227782 | −0.113891 | − | 0.993493i | \(-0.536331\pi\) | ||||
−0.113891 | + | 0.993493i | \(0.536331\pi\) | |||||||
\(648\) | 5.16316 | − | 5.16316i | 0.202828 | − | 0.202828i | ||||
\(649\) | 4.32272 | + | 7.48717i | 0.169682 | + | 0.293897i | ||||
\(650\) | −38.3231 | − | 21.9393i | −1.50316 | − | 0.860532i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.946581 | + | 3.53269i | −0.0370710 | + | 0.138351i | ||||
\(653\) | −18.1035 | + | 31.3562i | −0.708445 | + | 1.22706i | 0.256989 | + | 0.966414i | \(0.417270\pi\) |
−0.965434 | + | 0.260648i | \(0.916064\pi\) | |||||||
\(654\) | −6.64516 | − | 11.5098i | −0.259846 | − | 0.450067i | ||||
\(655\) | 29.7941 | − | 7.98330i | 1.16415 | − | 0.311933i | ||||
\(656\) | −6.63060 | + | 6.63060i | −0.258882 | + | 0.258882i | ||||
\(657\) | 23.7421 | − | 6.36168i | 0.926269 | − | 0.248193i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.3685 | + | 17.9588i | −0.403901 | + | 0.699576i | −0.994193 | − | 0.107613i | \(-0.965679\pi\) |
0.590292 | + | 0.807190i | \(0.299013\pi\) | |||||||
\(660\) | −50.9796 | − | 29.4331i | −1.98438 | − | 1.14568i | ||||
\(661\) | 23.9986 | + | 23.9986i | 0.933438 | + | 0.933438i | 0.997919 | − | 0.0644808i | \(-0.0205391\pi\) |
−0.0644808 | + | 0.997919i | \(0.520539\pi\) | |||||||
\(662\) | 30.0293 | + | 17.3374i | 1.16712 | + | 0.673838i | ||||
\(663\) | 6.03912 | − | 1.64188i | 0.234540 | − | 0.0637652i | ||||
\(664\) | 27.5234i | 1.06811i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.14222 | − | 1.97839i | −0.0442603 | − | 0.0766611i | ||||
\(667\) | 14.0537i | 0.544160i | ||||||||
\(668\) | −1.88490 | − | 7.03452i | −0.0729288 | − | 0.272174i | ||||
\(669\) | −0.216036 | + | 0.806257i | −0.00835243 | + | 0.0311717i | ||||
\(670\) | 46.8054 | + | 46.8054i | 1.80825 | + | 1.80825i | ||||
\(671\) | 15.7737 | + | 15.7737i | 0.608937 | + | 0.608937i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −35.7571 | + | 20.6444i | −1.37834 | + | 0.795783i | −0.991959 | − | 0.126558i | \(-0.959607\pi\) |
−0.386377 | + | 0.922341i | \(0.626274\pi\) | |||||||
\(674\) | −7.24584 | − | 27.0419i | −0.279099 | − | 1.04161i | ||||
\(675\) | 14.1616 | − | 24.5287i | 0.545082 | − | 0.944109i | ||||
\(676\) | 46.8837 | − | 0.342999i | 1.80322 | − | 0.0131923i | ||||
\(677\) | 39.1750 | − | 22.6177i | 1.50562 | − | 0.869268i | 0.505638 | − | 0.862746i | \(-0.331257\pi\) |
0.999979 | − | 0.00652270i | \(-0.00207626\pi\) | |||||||
\(678\) | 53.9009 | + | 14.4427i | 2.07005 | + | 0.554669i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 15.1695 | + | 8.75810i | 0.581723 | + | 0.335858i | ||||
\(681\) | 1.62167 | − | 6.05215i | 0.0621425 | − | 0.231919i | ||||
\(682\) | −51.8307 | − | 13.8880i | −1.98470 | − | 0.531799i | ||||
\(683\) | −42.0091 | − | 11.2563i | −1.60743 | − | 0.430710i | −0.660156 | − | 0.751129i | \(-0.729510\pi\) |
−0.947276 | + | 0.320419i | \(0.896176\pi\) | |||||||
\(684\) | 3.64153 | − | 13.5904i | 0.139237 | − | 0.519641i | ||||
\(685\) | 18.2174 | + | 10.5178i | 0.696051 | + | 0.401866i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.23013 | − | 0.329613i | −0.0469325 | − | 0.0125755i | ||||
\(688\) | −9.79785 | + | 5.65679i | −0.373539 | + | 0.215663i | ||||
\(689\) | 19.2679 | − | 19.4094i | 0.734048 | − | 0.739438i | ||||
\(690\) | 23.7437 | − | 41.1253i | 0.903907 | − | 1.56561i | ||||
\(691\) | 5.57267 | + | 20.7975i | 0.211994 | + | 0.791174i | 0.987203 | + | 0.159468i | \(0.0509780\pi\) |
−0.775209 | + | 0.631705i | \(0.782355\pi\) | |||||||
\(692\) | 7.65370 | − | 4.41887i | 0.290950 | − | 0.167980i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −16.7659 | − | 16.7659i | −0.636425 | − | 0.636425i | ||||
\(695\) | 51.2375 | + | 51.2375i | 1.94355 | + | 1.94355i | ||||
\(696\) | −3.18052 | + | 11.8699i | −0.120557 | + | 0.449926i | ||||
\(697\) | −1.95312 | − | 7.28916i | −0.0739798 | − | 0.276096i | ||||
\(698\) | − | 40.2200i | − | 1.52235i | ||||||
\(699\) | −0.794111 | − | 1.37544i | −0.0300360 | − | 0.0520239i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.77295i | 0.331350i | 0.986180 | + | 0.165675i | \(0.0529803\pi\) | ||||
−0.986180 | + | 0.165675i | \(0.947020\pi\) | |||||||
\(702\) | 0.171000 | + | 46.7478i | 0.00645399 | + | 1.76438i | ||||
\(703\) | 1.34876 | + | 0.778708i | 0.0508695 | + | 0.0293695i | ||||
\(704\) | −34.7462 | − | 34.7462i | −1.30955 | − | 1.30955i | ||||
\(705\) | 21.9791 | + | 12.6896i | 0.827781 | + | 0.477920i | ||||
\(706\) | 42.7152 | − | 73.9850i | 1.60761 | − | 2.78446i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −8.50651 | + | 2.27931i | −0.319694 | + | 0.0856618i | ||||
\(709\) | −29.9934 | + | 29.9934i | −1.12643 | + | 1.12643i | −0.135672 | + | 0.990754i | \(0.543319\pi\) |
−0.990754 | + | 0.135672i | \(0.956681\pi\) | |||||||
\(710\) | 62.8270 | − | 16.8345i | 2.35786 | − | 0.631786i | ||||
\(711\) | −1.56458 | − | 2.70994i | −0.0586765 | − | 0.101631i | ||||
\(712\) | −13.3147 | + | 23.0617i | −0.498989 | + | 0.864274i | ||||
\(713\) | 7.20689 | − | 26.8965i | 0.269900 | − | 1.00728i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 47.2352 | − | 12.8420i | 1.76650 | − | 0.480264i | ||||
\(716\) | −13.5419 | − | 23.4553i | −0.506084 | − | 0.876564i | ||||
\(717\) | 18.3071 | − | 18.3071i | 0.683691 | − | 0.683691i | ||||
\(718\) | −8.20329 | −0.306144 | ||||||||
\(719\) | −5.60019 | −0.208852 | −0.104426 | − | 0.994533i | \(-0.533301\pi\) | ||||
−0.104426 | + | 0.994533i | \(0.533301\pi\) | |||||||
\(720\) | −6.28980 | + | 6.28980i | −0.234407 | + | 0.234407i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −7.78453 | − | 29.0523i | −0.289710 | − | 1.08121i | ||||
\(723\) | 4.07477 | + | 1.09183i | 0.151542 | + | 0.0406056i | ||||
\(724\) | −15.4081 | + | 8.89587i | −0.572637 | + | 0.330612i | ||||
\(725\) | 13.8985i | 0.516176i | ||||||||
\(726\) | 19.5749 | − | 5.24509i | 0.726494 | − | 0.194664i | ||||
\(727\) | 32.0200 | 1.18756 | 0.593778 | − | 0.804629i | \(-0.297636\pi\) | ||||
0.593778 | + | 0.804629i | \(0.297636\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.7339 | −0.841996 | ||||||||
\(730\) | 115.336 | − | 30.9043i | 4.26879 | − | 1.14382i | ||||
\(731\) | − | 9.10469i | − | 0.336749i | ||||||
\(732\) | −19.6789 | + | 11.3616i | −0.727352 | + | 0.419937i | ||||
\(733\) | −0.884660 | − | 0.237044i | −0.0326757 | − | 0.00875542i | 0.242444 | − | 0.970165i | \(-0.422051\pi\) |
−0.275120 | + | 0.961410i | \(0.588718\pi\) | |||||||
\(734\) | 7.77195 | + | 29.0053i | 0.286868 | + | 1.07061i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 12.4266 | − | 12.4266i | 0.458051 | − | 0.458051i | ||||
\(737\) | −37.3092 | −1.37430 | ||||||||
\(738\) | 19.2400 | 0.708233 | ||||||||
\(739\) | 6.20218 | − | 6.20218i | 0.228151 | − | 0.228151i | −0.583769 | − | 0.811920i | \(-0.698423\pi\) |
0.811920 | + | 0.583769i | \(0.198423\pi\) | |||||||
\(740\) | −3.56939 | − | 6.18236i | −0.131213 | − | 0.227268i | ||||
\(741\) | −5.47347 | − | 9.40074i | −0.201073 | − | 0.345345i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.56609 | + | 35.7011i | −0.350946 | + | 1.30975i | 0.534564 | + | 0.845128i | \(0.320476\pi\) |
−0.885510 | + | 0.464620i | \(0.846191\pi\) | |||||||
\(744\) | 12.1740 | − | 21.0860i | 0.446321 | − | 0.773050i | ||||
\(745\) | −24.2238 | − | 41.9569i | −0.887492 | − | 1.53718i | ||||
\(746\) | −68.7019 | + | 18.4086i | −2.51536 | + | 0.673988i | ||||
\(747\) | 7.95360 | − | 7.95360i | 0.291007 | − | 0.291007i | ||||
\(748\) | −21.4087 | + | 5.73643i | −0.782778 | + | 0.209745i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0.782967 | − | 1.35614i | 0.0285899 | − | 0.0495192i | ||||
\(751\) | 10.7508 | + | 6.20698i | 0.392303 | + | 0.226496i | 0.683157 | − | 0.730271i | \(-0.260606\pi\) |
−0.290855 | + | 0.956767i | \(0.593940\pi\) | |||||||
\(752\) | −8.39613 | − | 8.39613i | −0.306175 | − | 0.306175i | ||||
\(753\) | −18.2381 | − | 10.5298i | −0.664633 | − | 0.383726i | ||||
\(754\) | −11.5424 | − | 19.8242i | −0.420350 | − | 0.721957i | ||||
\(755\) | 22.9390i | 0.834835i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.7793 | + | 20.4023i | 0.428124 | + | 0.741533i | 0.996707 | − | 0.0810934i | \(-0.0258412\pi\) |
−0.568582 | + | 0.822626i | \(0.692508\pi\) | |||||||
\(758\) | 28.4411i | 1.03303i | ||||||||
\(759\) | 6.92756 | + | 25.8540i | 0.251454 | + | 0.938441i | ||||
\(760\) | 7.88007 | − | 29.4088i | 0.285840 | − | 1.06677i | ||||
\(761\) | −9.57799 | − | 9.57799i | −0.347202 | − | 0.347202i | 0.511864 | − | 0.859066i | \(-0.328955\pi\) |
−0.859066 | + | 0.511864i | \(0.828955\pi\) | |||||||
\(762\) | 2.38189 | + | 2.38189i | 0.0862866 | + | 0.0862866i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −19.0169 | + | 10.9794i | −0.688008 | + | 0.397222i | ||||
\(765\) | −1.85273 | − | 6.91450i | −0.0669857 | − | 0.249994i | ||||
\(766\) | −6.77619 | + | 11.7367i | −0.244834 | + | 0.424064i | ||||
\(767\) | 3.63831 | − | 6.35531i | 0.131372 | − | 0.229477i | ||||
\(768\) | 26.7812 | − | 15.4621i | 0.966382 | − | 0.557941i | ||||
\(769\) | 29.8604 | + | 8.00107i | 1.07679 | + | 0.288526i | 0.753282 | − | 0.657698i | \(-0.228470\pi\) |
0.323512 | + | 0.946224i | \(0.395136\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.13334 | − | 4.11844i | −0.256901 | − | 0.148322i | ||||
\(772\) | 13.5233 | − | 50.4698i | 0.486716 | − | 1.81645i | ||||
\(773\) | −19.2999 | − | 5.17138i | −0.694167 | − | 0.186002i | −0.105551 | − | 0.994414i | \(-0.533661\pi\) |
−0.588617 | + | 0.808412i | \(0.700327\pi\) | |||||||
\(774\) | 22.4223 | + | 6.00804i | 0.805953 | + | 0.215954i | ||||
\(775\) | 7.12729 | − | 26.5994i | 0.256020 | − | 0.955480i | ||||
\(776\) | −20.6985 | − | 11.9503i | −0.743032 | − | 0.428990i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −37.6193 | − | 10.0801i | −1.34872 | − | 0.361388i | ||||
\(779\) | −11.3595 | + | 6.55839i | −0.406995 | + | 0.234979i | ||||
\(780\) | 0.182391 | + | 49.8619i | 0.00653065 | + | 1.78534i | ||||
\(781\) | −18.3307 | + | 31.7497i | −0.655923 | + | 1.13609i | ||||
\(782\) | −4.62759 | − | 17.2704i | −0.165482 | − | 0.617588i | ||||
\(783\) | 12.7422 | − | 7.35671i | 0.455369 | − | 0.262907i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −42.8565 | − | 42.8565i | −1.52961 | − | 1.52961i | ||||
\(786\) | −19.4671 | − | 19.4671i | −0.694369 | − | 0.694369i | ||||
\(787\) | 12.8359 | − | 47.9041i | 0.457549 | − | 1.70760i | −0.222934 | − | 0.974834i | \(-0.571563\pi\) |
0.680483 | − | 0.732764i | \(-0.261770\pi\) | |||||||
\(788\) | 15.6286 | + | 58.3266i | 0.556744 | + | 2.07780i | ||||
\(789\) | − | 20.9397i | − | 0.745472i | ||||||
\(790\) | −7.60056 | − | 13.1646i | −0.270416 | − | 0.468374i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − | 25.1719i | − | 0.894445i | ||||||
\(793\) | 4.82368 | − | 18.2693i | 0.171294 | − | 0.648760i | ||||
\(794\) | 23.1644 | + | 13.3740i | 0.822075 | + | 0.474625i | ||||
\(795\) | 20.5668 | + | 20.5668i | 0.729429 | + | 0.729429i | ||||
\(796\) | 61.8889 | + | 35.7316i | 2.19360 | + | 1.26647i | ||||
\(797\) | −3.67854 | + | 6.37141i | −0.130300 | + | 0.225687i | −0.923792 | − | 0.382894i | \(-0.874928\pi\) |
0.793492 | + | 0.608581i | \(0.208261\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.23003 | − | 2.47318i | 0.326535 | − | 0.0874948i | ||||
\(800\) | 12.2894 | − | 12.2894i | 0.434495 | − | 0.434495i | ||||
\(801\) | 10.5119 | − | 2.81666i | 0.371420 | − | 0.0995217i | ||||
\(802\) | −28.6598 | − | 49.6402i | −1.01201 | − | 1.75286i | ||||
\(803\) | −33.6510 | + | 58.2853i | −1.18752 | + | 2.05684i | ||||
\(804\) | 9.83634 | − | 36.7097i | 0.346901 | − | 1.29465i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 11.9243 | + | 43.8596i | 0.420014 | + | 1.54489i | ||||
\(807\) | −0.100839 | − | 0.174659i | −0.00354972 | − | 0.00614829i | ||||
\(808\) | 35.8798 | − | 35.8798i | 1.26225 | − | 1.26225i | ||||
\(809\) | 40.7796 | 1.43373 | 0.716867 | − | 0.697210i | \(-0.245575\pi\) | ||||
0.716867 | + | 0.697210i | \(0.245575\pi\) | |||||||
\(810\) | −14.4962 | −0.509345 | ||||||||
\(811\) | −2.15658 | + | 2.15658i | −0.0757278 | + | 0.0757278i | −0.743956 | − | 0.668228i | \(-0.767053\pi\) |
0.668228 | + | 0.743956i | \(0.267053\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.776086 | − | 2.89639i | −0.0272185 | − | 0.101581i | ||||
\(814\) | 6.04195 | + | 1.61894i | 0.211770 | + | 0.0567437i | ||||
\(815\) | 2.80102 | − | 1.61717i | 0.0981153 | − | 0.0566469i | ||||
\(816\) | − | 3.11395i | − | 0.109010i | ||||||
\(817\) | −15.2863 | + | 4.09596i | −0.534801 | + | 0.143299i | ||||
\(818\) | 0.854311 | 0.0298703 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 60.1238 | 2.09961 | ||||||||
\(821\) | −36.0893 | + | 9.67009i | −1.25952 | + | 0.337488i | −0.826009 | − | 0.563658i | \(-0.809394\pi\) |
−0.433516 | + | 0.901146i | \(0.642727\pi\) | |||||||
\(822\) | − | 18.7753i | − | 0.654863i | ||||||
\(823\) | −31.8883 | + | 18.4107i | −1.11156 | + | 0.641757i | −0.939232 | − | 0.343283i | \(-0.888461\pi\) |
−0.172324 | + | 0.985040i | \(0.555128\pi\) | |||||||
\(824\) | −22.6874 | − | 6.07906i | −0.790352 | − | 0.211774i | ||||
\(825\) | 6.85105 | + | 25.5685i | 0.238523 | + | 0.890179i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.2525 | + | 16.2525i | −0.565154 | + | 0.565154i | −0.930767 | − | 0.365613i | \(-0.880859\pi\) |
0.365613 | + | 0.930767i | \(0.380859\pi\) | |||||||
\(828\) | 29.3241 | 1.01908 | ||||||||
\(829\) | 13.7217 | 0.476575 | 0.238287 | − | 0.971195i | \(-0.423414\pi\) | ||||
0.238287 | + | 0.971195i | \(0.423414\pi\) | |||||||
\(830\) | 38.6376 | − | 38.6376i | 1.34113 | − | 1.34113i | ||||
\(831\) | −5.12770 | − | 8.88143i | −0.177878 | − | 0.308093i | ||||
\(832\) | −10.6256 | + | 40.2434i | −0.368375 | + | 1.39519i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 16.7390 | − | 62.4708i | 0.579624 | − | 2.16319i | ||||
\(835\) | −3.22021 | + | 5.57757i | −0.111440 | + | 0.193020i | ||||
\(836\) | 19.2624 | + | 33.3634i | 0.666203 | + | 1.15390i | ||||
\(837\) | −28.1591 | + | 7.54522i | −0.973322 | + | 0.260801i | ||||
\(838\) | −30.7747 | + | 30.7747i | −1.06309 | + | 1.06309i | ||||
\(839\) | −4.02716 | + | 1.07907i | −0.139033 | + | 0.0372537i | −0.327664 | − | 0.944794i | \(-0.606262\pi\) |
0.188631 | + | 0.982048i | \(0.439595\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.8900 | − | 18.8620i | 0.375517 | − | 0.650415i | ||||
\(842\) | −60.1565 | − | 34.7314i | −2.07313 | − | 1.19692i | ||||
\(843\) | −18.9879 | − | 18.9879i | −0.653978 | − | 0.653978i | ||||
\(844\) | −59.7430 | − | 34.4926i | −2.05644 | − | 1.18729i | ||||
\(845\) | −29.5322 | − | 29.1032i | −1.01594 | − | 1.00118i | ||||
\(846\) | 24.3630i | 0.837617i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.80403 | − | 11.7849i | −0.233651 | − | 0.404696i | ||||
\(849\) | 11.5188i | 0.395323i | ||||||||
\(850\) | −4.57648 | − | 17.0796i | −0.156972 | − | 0.585827i | ||||
\(851\) | −0.840114 | + | 3.13535i | −0.0287987 | + | 0.107478i | ||||
\(852\) | −26.4067 | − | 26.4067i | −0.904678 | − | 0.904678i | ||||
\(853\) | −3.44436 | − | 3.44436i | −0.117933 | − | 0.117933i | 0.645678 | − | 0.763610i | \(-0.276575\pi\) |
−0.763610 | + | 0.645678i | \(0.776575\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10.7756 | + | 6.22130i | −0.368518 | + | 0.212764i | ||||
\(856\) | 8.41490 | + | 31.4048i | 0.287615 | + | 1.07340i | ||||
\(857\) | −24.3123 | + | 42.1101i | −0.830491 | + | 1.43845i | 0.0671586 | + | 0.997742i | \(0.478607\pi\) |
−0.897650 | + | 0.440710i | \(0.854727\pi\) | |||||||
\(858\) | −31.0063 | − | 30.7802i | −1.05854 | − | 1.05082i | ||||
\(859\) | −21.7355 | + | 12.5490i | −0.741606 | + | 0.428167i | −0.822653 | − | 0.568544i | \(-0.807507\pi\) |
0.0810468 | + | 0.996710i | \(0.474174\pi\) | |||||||
\(860\) | 70.0684 | + | 18.7748i | 2.38931 | + | 0.640214i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 19.7898 | + | 11.4256i | 0.674042 | + | 0.389158i | ||||
\(863\) | 13.4540 | − | 50.2112i | 0.457981 | − | 1.70921i | −0.221192 | − | 0.975230i | \(-0.570995\pi\) |
0.679173 | − | 0.733978i | \(-0.262338\pi\) | |||||||
\(864\) | −17.7720 | − | 4.76198i | −0.604614 | − | 0.162006i | ||||
\(865\) | −7.54933 | − | 2.02284i | −0.256685 | − | 0.0687785i | ||||
\(866\) | 16.7867 | − | 62.6489i | 0.570436 | − | 2.12890i | ||||
\(867\) | −15.5299 | − | 8.96618i | −0.527423 | − | 0.304508i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.27609 | + | 2.21757i | 0.280747 | + | 0.0752259i | ||||
\(870\) | 21.1279 | − | 12.1982i | 0.716302 | − | 0.413557i | ||||
\(871\) | 15.9013 | + | 27.3106i | 0.538795 | + | 0.925386i | ||||
\(872\) | 8.87970 | − | 15.3801i | 0.300705 | − | 0.520836i | ||||
\(873\) | 2.52802 | + | 9.43472i | 0.0855607 | + | 0.319317i | ||||
\(874\) | −26.9143 | + | 15.5390i | −0.910390 | + | 0.525614i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −48.4768 | − | 48.4768i | −1.63788 | − | 1.63788i | ||||
\(877\) | −23.6690 | − | 23.6690i | −0.799246 | − | 0.799246i | 0.183731 | − | 0.982977i | \(-0.441183\pi\) |
−0.982977 | + | 0.183731i | \(0.941183\pi\) | |||||||
\(878\) | 21.1989 | − | 79.1153i | 0.715428 | − | 2.67001i | ||||
\(879\) | 4.68029 | + | 17.4671i | 0.157862 | + | 0.589150i | ||||
\(880\) | − | 24.3559i | − | 0.821037i | ||||||
\(881\) | −26.0483 | − | 45.1170i | −0.877590 | − | 1.52003i | −0.853978 | − | 0.520309i | \(-0.825817\pi\) |
−0.0236116 | − | 0.999721i | \(-0.507517\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.4598i | 0.755831i | 0.925840 | + | 0.377916i | \(0.123359\pi\) | ||||
−0.925840 | + | 0.377916i | \(0.876641\pi\) | |||||||
\(884\) | 13.3235 | + | 13.2264i | 0.448119 | + | 0.444852i | ||||
\(885\) | 6.74468 | + | 3.89404i | 0.226720 | + | 0.130897i | ||||
\(886\) | 13.3477 | + | 13.3477i | 0.448426 | + | 0.448426i | ||||
\(887\) | −10.3759 | − | 5.99053i | −0.348389 | − | 0.201142i | 0.315587 | − | 0.948897i | \(-0.397799\pi\) |
−0.663975 | + | 0.747754i | \(0.731132\pi\) | |||||||
\(888\) | −1.41914 | + | 2.45801i | −0.0476231 | + | 0.0824856i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 51.0656 | − | 13.6830i | 1.71172 | − | 0.458655i | ||||
\(891\) | 5.77757 | − | 5.77757i | 0.193556 | − | 0.193556i | ||||
\(892\) | −2.41861 | + | 0.648066i | −0.0809812 | + | 0.0216989i | ||||
\(893\) | −8.30469 | − | 14.3842i | −0.277906 | − | 0.481347i | ||||
\(894\) | −21.6209 | + | 37.4485i | −0.723110 | + | 1.25246i | ||||
\(895\) | −6.19911 | + | 23.1354i | −0.207213 | + | 0.773330i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.9728 | − | 16.0901i | 0.533315 | − | 0.537231i | ||||
\(898\) | 24.0414 | + | 41.6409i | 0.802271 | + | 1.38957i | ||||
\(899\) | 10.1154 | − | 10.1154i | 0.337368 | − | 0.337368i | ||||
\(900\) | 29.0002 | 0.966675 | ||||||||
\(901\) | 10.9512 | 0.364837 | ||||||||
\(902\) | −37.2513 | + | 37.2513i | −1.24033 | + | 1.24033i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 19.2993 | + | 72.0259i | 0.641885 | + | 2.39555i | ||||
\(905\) | 15.1980 | + | 4.07228i | 0.505198 | + | 0.135367i | ||||
\(906\) | 17.7311 | − | 10.2371i | 0.589076 | − | 0.340103i | ||||
\(907\) | − | 0.531924i | − | 0.0176622i | −0.999961 | − | 0.00883112i | \(-0.997189\pi\) | ||
0.999961 | − | 0.00883112i | \(-0.00281107\pi\) | |||||||
\(908\) | 18.1553 | − | 4.86469i | 0.602504 | − | 0.161440i | ||||
\(909\) | −20.7368 | −0.687798 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.16430 | 0.0717065 | 0.0358532 | − | 0.999357i | \(-0.488585\pi\) | ||||
0.0358532 | + | 0.999357i | \(0.488585\pi\) | |||||||
\(912\) | −5.22816 | + | 1.40088i | −0.173122 | + | 0.0463878i | ||||
\(913\) | 30.7986i | 1.01928i | ||||||||
\(914\) | 2.88191 | − | 1.66387i | 0.0953252 | − | 0.0550360i | ||||
\(915\) | 19.4105 | + | 5.20103i | 0.641691 | + | 0.171941i | ||||
\(916\) | −0.988776 | − | 3.69016i | −0.0326701 | − | 0.121926i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −13.2363 | + | 13.2363i | −0.436864 | + | 0.436864i | ||||
\(919\) | −25.8041 | −0.851197 | −0.425599 | − | 0.904912i | \(-0.639936\pi\) | ||||
−0.425599 | + | 0.904912i | \(0.639936\pi\) | |||||||
\(920\) | 63.4558 | 2.09207 | ||||||||
\(921\) | 18.9282 | − | 18.9282i | 0.623705 | − | 0.623705i | ||||
\(922\) | −22.3812 | − | 38.7653i | −0.737084 | − | 1.27667i | ||||
\(923\) | 31.0535 | − | 0.113592i | 1.02214 | − | 0.00373892i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.830835 | + | 3.10072i | −0.0273177 | + | 0.101951i | ||||
\(926\) | −37.6001 | + | 65.1252i | −1.23562 | + | 2.14015i | ||||
\(927\) | 4.79941 | + | 8.31282i | 0.157633 | + | 0.273029i | ||||
\(928\) | 8.72084 | − | 2.33674i | 0.286276 | − | 0.0767073i | ||||
\(929\) | 14.6922 | − | 14.6922i | 0.482034 | − | 0.482034i | −0.423747 | − | 0.905781i | \(-0.639285\pi\) |
0.905781 | + | 0.423747i | \(0.139285\pi\) | |||||||
\(930\) | −46.6908 | + | 12.5108i | −1.53105 | + | 0.410244i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 2.38218 | − | 4.12605i | 0.0780308 | − | 0.135153i | ||||
\(933\) | −4.05408 | − | 2.34063i | −0.132725 | − | 0.0766286i | ||||
\(934\) | 47.5314 | + | 47.5314i | 1.55528 | + | 1.55528i | ||||
\(935\) | 16.9746 | + | 9.80029i | 0.555129 | + | 0.320504i | ||||
\(936\) | −18.4260 | + | 10.7283i | −0.602273 | + | 0.350666i | ||||
\(937\) | − | 37.2049i | − | 1.21543i | −0.794154 | − | 0.607716i | \(-0.792086\pi\) | ||
0.794154 | − | 0.607716i | \(-0.207914\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.99623 | + | 10.3858i | 0.195680 | + | 0.338927i | ||||
\(940\) | 76.1329i | 2.48318i | ||||||||
\(941\) | 11.5462 | + | 43.0912i | 0.376397 | + | 1.40473i | 0.851293 | + | 0.524690i | \(0.175819\pi\) |
−0.474897 | + | 0.880042i | \(0.657515\pi\) | |||||||
\(942\) | −14.0010 | + | 52.2524i | −0.456177 | + | 1.70247i | ||||
\(943\) | −19.3308 | − | 19.3308i | −0.629497 | − | 0.629497i | ||||
\(944\) | −2.57650 | − | 2.57650i | −0.0838580 | − | 0.0838580i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −55.0452 | + | 31.7803i | −1.78967 | + | 1.03327i | ||||
\(947\) | 2.03021 | + | 7.57686i | 0.0659731 | + | 0.246215i | 0.991035 | − | 0.133601i | \(-0.0426540\pi\) |
−0.925062 | + | 0.379816i | \(0.875987\pi\) | |||||||
\(948\) | −4.36387 | + | 7.55844i | −0.141732 | + | 0.245487i | ||||
\(949\) | 57.0074 | − | 0.208529i | 1.85054 | − | 0.00676914i | ||||
\(950\) | −26.6170 | + | 15.3674i | −0.863571 | + | 0.498583i | ||||
\(951\) | −18.0304 | − | 4.83124i | −0.584677 | − | 0.156664i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28.7075 | + | 16.5743i | 0.929926 | + | 0.536893i | 0.886788 | − | 0.462176i | \(-0.152931\pi\) |
0.0431379 | + | 0.999069i | \(0.486265\pi\) | |||||||
\(954\) | −7.22651 | + | 26.9697i | −0.233967 | + | 0.873176i | ||||
\(955\) | 18.7576 | + | 5.02608i | 0.606981 | + | 0.162640i | ||||
\(956\) | 75.0190 | + | 20.1013i | 2.42629 | + | 0.650122i | ||||
\(957\) | −3.55899 | + | 13.2823i | −0.115046 | + | 0.429357i | ||||
\(958\) | 7.17194 | + | 4.14072i | 0.231715 | + | 0.133781i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −42.7573 | − | 11.4568i | −1.37998 | − | 0.369766i | ||||
\(961\) | 2.30019 | − | 1.32801i | 0.0741995 | − | 0.0428391i | ||||
\(962\) | −1.39002 | − | 5.11275i | −0.0448161 | − | 0.164842i | ||||
\(963\) | 6.64355 | − | 11.5070i | 0.214085 | − | 0.370807i | ||||
\(964\) | 3.27528 | + | 12.2235i | 0.105490 | + | 0.393693i | ||||
\(965\) | −40.0168 | + | 23.1037i | −1.28818 | + | 0.743734i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.9068 | − | 21.9068i | −0.704477 | − | 0.704477i | 0.260892 | − | 0.965368i | \(-0.415984\pi\) |
−0.965368 | + | 0.260892i | \(0.915984\pi\) | |||||||
\(968\) | 19.1485 | + | 19.1485i | 0.615456 | + | 0.615456i | ||||
\(969\) | 1.12737 | − | 4.20741i | 0.0362164 | − | 0.135161i | ||||
\(970\) | 12.2808 | + | 45.8327i | 0.394314 | + | 1.47160i | ||||
\(971\) | − | 20.7070i | − | 0.664518i | −0.943188 | − | 0.332259i | \(-0.892189\pi\) | ||
0.943188 | − | 0.332259i | \(-0.107811\pi\) | |||||||
\(972\) | −25.4613 | − | 44.1003i | −0.816672 | − | 1.41452i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 57.5638i | 1.84446i | ||||||||
\(975\) | 15.7964 | − | 15.9123i | 0.505888 | − | 0.509603i | ||||
\(976\) | −8.14213 | − | 4.70086i | −0.260623 | − | 0.150471i | ||||
\(977\) | −12.6510 | − | 12.6510i | −0.404740 | − | 0.404740i | 0.475159 | − | 0.879900i | \(-0.342390\pi\) |
−0.879900 | + | 0.475159i | \(0.842390\pi\) | |||||||
\(978\) | −2.50004 | − | 1.44340i | −0.0799423 | − | 0.0461547i | ||||
\(979\) | −14.8991 | + | 25.8060i | −0.476177 | + | 0.824763i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.01050 | + | 1.87846i | −0.223828 | + | 0.0599746i | ||||
\(982\) | 10.1391 | − | 10.1391i | 0.323553 | − | 0.323553i | ||||
\(983\) | −43.2530 | + | 11.5896i | −1.37955 | + | 0.369651i | −0.870959 | − | 0.491355i | \(-0.836502\pi\) |
−0.508596 | + | 0.861006i | \(0.669835\pi\) | |||||||
\(984\) | −11.9522 | − | 20.7018i | −0.381021 | − | 0.659948i | ||||
\(985\) | 26.7003 | − | 46.2463i | 0.850742 | − | 1.47353i | ||||
\(986\) | 2.37740 | − | 8.87257i | 0.0757117 | − | 0.282560i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 16.2126 | − | 28.3198i | 0.515791 | − | 0.900971i | ||||
\(989\) | −16.4918 | − | 28.5646i | −0.524407 | − | 0.908300i | ||||
\(990\) | −35.3366 | + | 35.3366i | −1.12307 | + | 1.12307i | ||||
\(991\) | −25.1560 | −0.799105 | −0.399553 | − | 0.916710i | \(-0.630835\pi\) | ||||
−0.399553 | + | 0.916710i | \(0.630835\pi\) | |||||||
\(992\) | −17.8886 | −0.567964 | ||||||||
\(993\) | −12.4494 | + | 12.4494i | −0.395071 | + | 0.395071i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16.3569 | − | 61.0449i | −0.518550 | − | 1.93525i | ||||
\(996\) | −30.3037 | − | 8.11985i | −0.960209 | − | 0.257287i | ||||
\(997\) | 10.3336 | − | 5.96610i | 0.327268 | − | 0.188948i | −0.327359 | − | 0.944900i | \(-0.606159\pi\) |
0.654628 | + | 0.755952i | \(0.272825\pi\) | |||||||
\(998\) | 43.3180i | 1.37121i | ||||||||
\(999\) | 3.28254 | − | 0.879553i | 0.103855 | − | 0.0278278i |
(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 | 637.2.x.b.570.1 | 32 | ||
7.2 | even | 3 | 637.2.bb.b.362.8 | 32 | |||
7.3 | odd | 6 | 91.2.bc.a.76.8 | yes | 32 | ||
7.4 | even | 3 | 91.2.bc.a.76.7 | yes | 32 | ||
7.5 | odd | 6 | 637.2.bb.b.362.7 | 32 | |||
7.6 | odd | 2 | inner | 637.2.x.b.570.2 | 32 | ||
13.6 | odd | 12 | 637.2.bb.b.227.7 | 32 | |||
21.11 | odd | 6 | 819.2.fm.g.622.1 | 32 | |||
21.17 | even | 6 | 819.2.fm.g.622.2 | 32 | |||
91.6 | even | 12 | 637.2.bb.b.227.8 | 32 | |||
91.19 | even | 12 | inner | 637.2.x.b.19.2 | 32 | ||
91.32 | odd | 12 | 91.2.bc.a.6.8 | yes | 32 | ||
91.45 | even | 12 | 91.2.bc.a.6.7 | ✓ | 32 | ||
91.58 | odd | 12 | inner | 637.2.x.b.19.1 | 32 | ||
273.32 | even | 12 | 819.2.fm.g.370.2 | 32 | |||
273.227 | odd | 12 | 819.2.fm.g.370.1 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.bc.a.6.7 | ✓ | 32 | 91.45 | even | 12 | ||
91.2.bc.a.6.8 | yes | 32 | 91.32 | odd | 12 | ||
91.2.bc.a.76.7 | yes | 32 | 7.4 | even | 3 | ||
91.2.bc.a.76.8 | yes | 32 | 7.3 | odd | 6 | ||
637.2.x.b.19.1 | 32 | 91.58 | odd | 12 | inner | ||
637.2.x.b.19.2 | 32 | 91.19 | even | 12 | inner | ||
637.2.x.b.570.1 | 32 | 1.1 | even | 1 | trivial | ||
637.2.x.b.570.2 | 32 | 7.6 | odd | 2 | inner | ||
637.2.bb.b.227.7 | 32 | 13.6 | odd | 12 | |||
637.2.bb.b.227.8 | 32 | 91.6 | even | 12 | |||
637.2.bb.b.362.7 | 32 | 7.5 | odd | 6 | |||
637.2.bb.b.362.8 | 32 | 7.2 | even | 3 | |||
819.2.fm.g.370.1 | 32 | 273.227 | odd | 12 | |||
819.2.fm.g.370.2 | 32 | 273.32 | even | 12 | |||
819.2.fm.g.622.1 | 32 | 21.11 | odd | 6 | |||
819.2.fm.g.622.2 | 32 | 21.17 | even | 6 |