Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,2,Mod(47,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.i (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.50967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 323.13 | ||
Character | \(\chi\) | \(=\) | 690.323 |
Dual form | 690.2.i.f.47.13 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | 1.28054 | − | 1.16628i | 0.739320 | − | 0.673355i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 1.31868 | − | 1.80585i | 0.589733 | − | 0.807599i | ||||
\(6\) | 1.73017 | + | 0.0807905i | 0.706337 | + | 0.0329826i | ||||
\(7\) | 1.43599 | − | 1.43599i | 0.542752 | − | 0.542752i | −0.381583 | − | 0.924335i | \(-0.624621\pi\) |
0.924335 | + | 0.381583i | \(0.124621\pi\) | |||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | 0.279562 | − | 2.98695i | 0.0931873 | − | 0.995649i | ||||
\(10\) | 2.20937 | − | 0.344476i | 0.698666 | − | 0.108933i | ||||
\(11\) | 3.03746i | 0.915827i | 0.888997 | + | 0.457914i | \(0.151403\pi\) | ||||
−0.888997 | + | 0.457914i | \(0.848597\pi\) | |||||||
\(12\) | 1.16628 | + | 1.28054i | 0.336677 | + | 0.369660i | ||||
\(13\) | −1.30218 | − | 1.30218i | −0.361159 | − | 0.361159i | 0.503081 | − | 0.864239i | \(-0.332200\pi\) |
−0.864239 | + | 0.503081i | \(0.832200\pi\) | |||||||
\(14\) | 2.03079 | 0.542752 | ||||||||
\(15\) | −0.417505 | − | 3.85041i | −0.107799 | − | 0.994173i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −0.0287275 | − | 0.0287275i | −0.00696745 | − | 0.00696745i | 0.703614 | − | 0.710582i | \(-0.251568\pi\) |
−0.710582 | + | 0.703614i | \(0.751568\pi\) | |||||||
\(18\) | 2.30977 | − | 1.91441i | 0.544418 | − | 0.451231i | ||||
\(19\) | 2.41296i | 0.553572i | 0.960932 | + | 0.276786i | \(0.0892693\pi\) | ||||
−0.960932 | + | 0.276786i | \(0.910731\pi\) | |||||||
\(20\) | 1.80585 | + | 1.31868i | 0.403799 | + | 0.294866i | ||||
\(21\) | 0.164069 | − | 3.51361i | 0.0358028 | − | 0.766732i | ||||
\(22\) | −2.14781 | + | 2.14781i | −0.457914 | + | 0.457914i | ||||
\(23\) | 0.707107 | − | 0.707107i | 0.147442 | − | 0.147442i | ||||
\(24\) | −0.0807905 | + | 1.73017i | −0.0164913 | + | 0.353169i | ||||
\(25\) | −1.52216 | − | 4.76267i | −0.304431 | − | 0.952534i | ||||
\(26\) | − | 1.84156i | − | 0.361159i | ||||||
\(27\) | −3.12564 | − | 4.15095i | −0.601529 | − | 0.798851i | ||||
\(28\) | 1.43599 | + | 1.43599i | 0.271376 | + | 0.271376i | ||||
\(29\) | −8.32611 | −1.54612 | −0.773060 | − | 0.634333i | \(-0.781275\pi\) | ||||
−0.773060 | + | 0.634333i | \(0.781275\pi\) | |||||||
\(30\) | 2.42743 | − | 3.01787i | 0.443187 | − | 0.550986i | ||||
\(31\) | 10.8038 | 1.94043 | 0.970214 | − | 0.242250i | \(-0.0778854\pi\) | ||||
0.970214 | + | 0.242250i | \(0.0778854\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | 3.54254 | + | 3.88958i | 0.616676 | + | 0.677089i | ||||
\(34\) | − | 0.0406269i | − | 0.00696745i | ||||||
\(35\) | −0.699560 | − | 4.48678i | −0.118247 | − | 0.758405i | ||||
\(36\) | 2.98695 | + | 0.279562i | 0.497824 | + | 0.0465937i | ||||
\(37\) | −0.399778 | + | 0.399778i | −0.0657230 | + | 0.0657230i | −0.739204 | − | 0.673481i | \(-0.764798\pi\) |
0.673481 | + | 0.739204i | \(0.264798\pi\) | |||||||
\(38\) | −1.70622 | + | 1.70622i | −0.276786 | + | 0.276786i | ||||
\(39\) | −3.18620 | − | 0.148780i | −0.510200 | − | 0.0238239i | ||||
\(40\) | 0.344476 | + | 2.20937i | 0.0544665 | + | 0.349333i | ||||
\(41\) | 9.45696i | 1.47693i | 0.674293 | + | 0.738464i | \(0.264449\pi\) | ||||
−0.674293 | + | 0.738464i | \(0.735551\pi\) | |||||||
\(42\) | 2.60051 | − | 2.36848i | 0.401267 | − | 0.365465i | ||||
\(43\) | −0.108956 | − | 0.108956i | −0.0166156 | − | 0.0166156i | 0.698750 | − | 0.715366i | \(-0.253740\pi\) |
−0.715366 | + | 0.698750i | \(0.753740\pi\) | |||||||
\(44\) | −3.03746 | −0.457914 | ||||||||
\(45\) | −5.02531 | − | 4.44368i | −0.749129 | − | 0.662424i | ||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | −0.341054 | − | 0.341054i | −0.0497478 | − | 0.0497478i | 0.681795 | − | 0.731543i | \(-0.261199\pi\) |
−0.731543 | + | 0.681795i | \(0.761199\pi\) | |||||||
\(48\) | −1.28054 | + | 1.16628i | −0.184830 | + | 0.168339i | ||||
\(49\) | 2.87588i | 0.410840i | ||||||||
\(50\) | 2.29139 | − | 4.44404i | 0.324052 | − | 0.628483i | ||||
\(51\) | −0.0702912 | − | 0.00328227i | −0.00984274 | − | 0.000459609i | ||||
\(52\) | 1.30218 | − | 1.30218i | 0.180579 | − | 0.180579i | ||||
\(53\) | −0.120552 | + | 0.120552i | −0.0165590 | + | 0.0165590i | −0.715338 | − | 0.698779i | \(-0.753727\pi\) |
0.698779 | + | 0.715338i | \(0.253727\pi\) | |||||||
\(54\) | 0.725006 | − | 5.14532i | 0.0986608 | − | 0.700190i | ||||
\(55\) | 5.48518 | + | 4.00544i | 0.739621 | + | 0.540093i | ||||
\(56\) | 2.03079i | 0.271376i | ||||||||
\(57\) | 2.81420 | + | 3.08990i | 0.372750 | + | 0.409267i | ||||
\(58\) | −5.88745 | − | 5.88745i | −0.773060 | − | 0.773060i | ||||
\(59\) | −2.10585 | −0.274159 | −0.137079 | − | 0.990560i | \(-0.543772\pi\) | ||||
−0.137079 | + | 0.990560i | \(0.543772\pi\) | |||||||
\(60\) | 3.85041 | − | 0.417505i | 0.497086 | − | 0.0538996i | ||||
\(61\) | 10.7626 | 1.37801 | 0.689003 | − | 0.724758i | \(-0.258049\pi\) | ||||
0.689003 | + | 0.724758i | \(0.258049\pi\) | |||||||
\(62\) | 7.63947 | + | 7.63947i | 0.970214 | + | 0.970214i | ||||
\(63\) | −3.88777 | − | 4.69066i | −0.489813 | − | 0.590968i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −4.06869 | + | 0.634373i | −0.504659 | + | 0.0786843i | ||||
\(66\) | −0.245398 | + | 5.25530i | −0.0302064 | + | 0.646883i | ||||
\(67\) | −6.68856 | + | 6.68856i | −0.817137 | + | 0.817137i | −0.985692 | − | 0.168555i | \(-0.946090\pi\) |
0.168555 | + | 0.985692i | \(0.446090\pi\) | |||||||
\(68\) | 0.0287275 | − | 0.0287275i | 0.00348373 | − | 0.00348373i | ||||
\(69\) | 0.0807905 | − | 1.73017i | 0.00972604 | − | 0.208287i | ||||
\(70\) | 2.67797 | − | 3.66730i | 0.320079 | − | 0.438326i | ||||
\(71\) | 5.69670i | 0.676074i | 0.941133 | + | 0.338037i | \(0.109763\pi\) | ||||
−0.941133 | + | 0.338037i | \(0.890237\pi\) | |||||||
\(72\) | 1.91441 | + | 2.30977i | 0.225615 | + | 0.272209i | ||||
\(73\) | 6.43032 | + | 6.43032i | 0.752612 | + | 0.752612i | 0.974966 | − | 0.222354i | \(-0.0713742\pi\) |
−0.222354 | + | 0.974966i | \(0.571374\pi\) | |||||||
\(74\) | −0.565371 | −0.0657230 | ||||||||
\(75\) | −7.50381 | − | 4.32352i | −0.866465 | − | 0.499237i | ||||
\(76\) | −2.41296 | −0.276786 | ||||||||
\(77\) | 4.36175 | + | 4.36175i | 0.497067 | + | 0.497067i | ||||
\(78\) | −2.14778 | − | 2.35818i | −0.243188 | − | 0.267012i | ||||
\(79\) | − | 5.14788i | − | 0.579182i | −0.957150 | − | 0.289591i | \(-0.906481\pi\) | ||
0.957150 | − | 0.289591i | \(-0.0935193\pi\) | |||||||
\(80\) | −1.31868 | + | 1.80585i | −0.147433 | + | 0.201900i | ||||
\(81\) | −8.84369 | − | 1.67007i | −0.982632 | − | 0.185564i | ||||
\(82\) | −6.68708 | + | 6.68708i | −0.738464 | + | 0.738464i | ||||
\(83\) | 3.07224 | − | 3.07224i | 0.337223 | − | 0.337223i | −0.518098 | − | 0.855321i | \(-0.673360\pi\) |
0.855321 | + | 0.518098i | \(0.173360\pi\) | |||||||
\(84\) | 3.51361 | + | 0.164069i | 0.383366 | + | 0.0179014i | ||||
\(85\) | −0.0897600 | + | 0.0139950i | −0.00973584 | + | 0.00151797i | ||||
\(86\) | − | 0.154087i | − | 0.0166156i | ||||||
\(87\) | −10.6619 | + | 9.71061i | −1.14308 | + | 1.04109i | ||||
\(88\) | −2.14781 | − | 2.14781i | −0.228957 | − | 0.228957i | ||||
\(89\) | −12.0540 | −1.27773 | −0.638863 | − | 0.769320i | \(-0.720595\pi\) | ||||
−0.638863 | + | 0.769320i | \(0.720595\pi\) | |||||||
\(90\) | −0.411275 | − | 6.69558i | −0.0433522 | − | 0.705777i | ||||
\(91\) | −3.73982 | −0.392040 | ||||||||
\(92\) | 0.707107 | + | 0.707107i | 0.0737210 | + | 0.0737210i | ||||
\(93\) | 13.8347 | − | 12.6004i | 1.43460 | − | 1.30660i | ||||
\(94\) | − | 0.482323i | − | 0.0497478i | ||||||
\(95\) | 4.35744 | + | 3.18193i | 0.447064 | + | 0.326459i | ||||
\(96\) | −1.73017 | − | 0.0807905i | −0.176584 | − | 0.00824565i | ||||
\(97\) | 7.38166 | − | 7.38166i | 0.749494 | − | 0.749494i | −0.224890 | − | 0.974384i | \(-0.572202\pi\) |
0.974384 | + | 0.224890i | \(0.0722023\pi\) | |||||||
\(98\) | −2.03356 | + | 2.03356i | −0.205420 | + | 0.205420i | ||||
\(99\) | 9.07272 | + | 0.849157i | 0.911842 | + | 0.0853435i | ||||
\(100\) | 4.76267 | − | 1.52216i | 0.476267 | − | 0.152216i | ||||
\(101\) | 15.7509i | 1.56727i | 0.621222 | + | 0.783635i | \(0.286637\pi\) | ||||
−0.621222 | + | 0.783635i | \(0.713363\pi\) | |||||||
\(102\) | −0.0473825 | − | 0.0520243i | −0.00469157 | − | 0.00515117i | ||||
\(103\) | −9.94078 | − | 9.94078i | −0.979494 | − | 0.979494i | 0.0202999 | − | 0.999794i | \(-0.493538\pi\) |
−0.999794 | + | 0.0202999i | \(0.993538\pi\) | |||||||
\(104\) | 1.84156 | 0.180579 | ||||||||
\(105\) | −6.12868 | − | 4.92961i | −0.598098 | − | 0.481081i | ||||
\(106\) | −0.170486 | −0.0165590 | ||||||||
\(107\) | −8.28163 | − | 8.28163i | −0.800616 | − | 0.800616i | 0.182576 | − | 0.983192i | \(-0.441556\pi\) |
−0.983192 | + | 0.182576i | \(0.941556\pi\) | |||||||
\(108\) | 4.15095 | − | 3.12564i | 0.399425 | − | 0.300765i | ||||
\(109\) | 5.16166i | 0.494398i | 0.968965 | + | 0.247199i | \(0.0795101\pi\) | ||||
−0.968965 | + | 0.247199i | \(0.920490\pi\) | |||||||
\(110\) | 1.04633 | + | 6.71088i | 0.0997638 | + | 0.639857i | ||||
\(111\) | −0.0456766 | + | 0.978185i | −0.00433543 | + | 0.0928452i | ||||
\(112\) | −1.43599 | + | 1.43599i | −0.135688 | + | 0.135688i | ||||
\(113\) | −10.2943 | + | 10.2943i | −0.968407 | + | 0.968407i | −0.999516 | − | 0.0311086i | \(-0.990096\pi\) |
0.0311086 | + | 0.999516i | \(0.490096\pi\) | |||||||
\(114\) | −0.194945 | + | 4.17483i | −0.0182582 | + | 0.391008i | ||||
\(115\) | −0.344476 | − | 2.20937i | −0.0321226 | − | 0.206025i | ||||
\(116\) | − | 8.32611i | − | 0.773060i | ||||||
\(117\) | −4.25357 | + | 3.52549i | −0.393243 | + | 0.325932i | ||||
\(118\) | −1.48906 | − | 1.48906i | −0.137079 | − | 0.137079i | ||||
\(119\) | −0.0825048 | −0.00756320 | ||||||||
\(120\) | 3.01787 | + | 2.42743i | 0.275493 | + | 0.221593i | ||||
\(121\) | 1.77386 | 0.161260 | ||||||||
\(122\) | 7.61029 | + | 7.61029i | 0.689003 | + | 0.689003i | ||||
\(123\) | 11.0295 | + | 12.1100i | 0.994496 | + | 1.09192i | ||||
\(124\) | 10.8038i | 0.970214i | ||||||||
\(125\) | −10.6079 | − | 3.53167i | −0.948798 | − | 0.315882i | ||||
\(126\) | 0.567733 | − | 6.06587i | 0.0505776 | − | 0.540390i | ||||
\(127\) | −6.32534 | + | 6.32534i | −0.561283 | + | 0.561283i | −0.929672 | − | 0.368389i | \(-0.879910\pi\) |
0.368389 | + | 0.929672i | \(0.379910\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | −0.266596 | − | 0.0124488i | −0.0234725 | − | 0.00109605i | ||||
\(130\) | −3.32557 | − | 2.42843i | −0.291671 | − | 0.212987i | ||||
\(131\) | − | 8.57676i | − | 0.749355i | −0.927155 | − | 0.374677i | \(-0.877753\pi\) | ||
0.927155 | − | 0.374677i | \(-0.122247\pi\) | |||||||
\(132\) | −3.88958 | + | 3.54254i | −0.338545 | + | 0.308338i | ||||
\(133\) | 3.46499 | + | 3.46499i | 0.300452 | + | 0.300452i | ||||
\(134\) | −9.45905 | −0.817137 | ||||||||
\(135\) | −11.6177 | + | 0.170634i | −0.999892 | + | 0.0146859i | ||||
\(136\) | 0.0406269 | 0.00348373 | ||||||||
\(137\) | 11.6408 | + | 11.6408i | 0.994543 | + | 0.994543i | 0.999985 | − | 0.00544239i | \(-0.00173237\pi\) |
−0.00544239 | + | 0.999985i | \(0.501732\pi\) | |||||||
\(138\) | 1.28054 | − | 1.16628i | 0.109007 | − | 0.0992807i | ||||
\(139\) | 0.224301i | 0.0190250i | 0.999955 | + | 0.00951249i | \(0.00302797\pi\) | ||||
−0.999955 | + | 0.00951249i | \(0.996972\pi\) | |||||||
\(140\) | 4.48678 | − | 0.699560i | 0.379202 | − | 0.0591236i | ||||
\(141\) | −0.834498 | − | 0.0389671i | −0.0702774 | − | 0.00328162i | ||||
\(142\) | −4.02818 | + | 4.02818i | −0.338037 | + | 0.338037i | ||||
\(143\) | 3.95530 | − | 3.95530i | 0.330759 | − | 0.330759i | ||||
\(144\) | −0.279562 | + | 2.98695i | −0.0232968 | + | 0.248912i | ||||
\(145\) | −10.9795 | + | 15.0357i | −0.911797 | + | 1.24864i | ||||
\(146\) | 9.09384i | 0.752612i | ||||||||
\(147\) | 3.35409 | + | 3.68268i | 0.276641 | + | 0.303742i | ||||
\(148\) | −0.399778 | − | 0.399778i | −0.0328615 | − | 0.0328615i | ||||
\(149\) | −5.49620 | −0.450266 | −0.225133 | − | 0.974328i | \(-0.572282\pi\) | ||||
−0.225133 | + | 0.974328i | \(0.572282\pi\) | |||||||
\(150\) | −2.24880 | − | 8.36319i | −0.183614 | − | 0.682851i | ||||
\(151\) | −9.44824 | −0.768887 | −0.384443 | − | 0.923149i | \(-0.625607\pi\) | ||||
−0.384443 | + | 0.923149i | \(0.625607\pi\) | |||||||
\(152\) | −1.70622 | − | 1.70622i | −0.138393 | − | 0.138393i | ||||
\(153\) | −0.0938387 | + | 0.0777765i | −0.00758641 | + | 0.00628785i | ||||
\(154\) | 6.16844i | 0.497067i | ||||||||
\(155\) | 14.2468 | − | 19.5101i | 1.14433 | − | 1.56709i | ||||
\(156\) | 0.148780 | − | 3.18620i | 0.0119120 | − | 0.255100i | ||||
\(157\) | 15.6517 | − | 15.6517i | 1.24914 | − | 1.24914i | 0.293039 | − | 0.956100i | \(-0.405333\pi\) |
0.956100 | − | 0.293039i | \(-0.0946667\pi\) | |||||||
\(158\) | 3.64010 | − | 3.64010i | 0.289591 | − | 0.289591i | ||||
\(159\) | −0.0137736 | + | 0.294969i | −0.00109232 | + | 0.0233925i | ||||
\(160\) | −2.20937 | + | 0.344476i | −0.174666 | + | 0.0272333i | ||||
\(161\) | − | 2.03079i | − | 0.160049i | ||||||
\(162\) | −5.07251 | − | 7.43435i | −0.398534 | − | 0.584098i | ||||
\(163\) | 2.69934 | + | 2.69934i | 0.211429 | + | 0.211429i | 0.804874 | − | 0.593446i | \(-0.202233\pi\) |
−0.593446 | + | 0.804874i | \(0.702233\pi\) | |||||||
\(164\) | −9.45696 | −0.738464 | ||||||||
\(165\) | 11.6955 | − | 1.26815i | 0.910491 | − | 0.0987255i | ||||
\(166\) | 4.34481 | 0.337223 | ||||||||
\(167\) | 4.99243 | + | 4.99243i | 0.386326 | + | 0.386326i | 0.873375 | − | 0.487049i | \(-0.161927\pi\) |
−0.487049 | + | 0.873375i | \(0.661927\pi\) | |||||||
\(168\) | 2.36848 | + | 2.60051i | 0.182732 | + | 0.200634i | ||||
\(169\) | − | 9.60867i | − | 0.739129i | ||||||
\(170\) | −0.0733659 | − | 0.0535739i | −0.00562690 | − | 0.00410893i | ||||
\(171\) | 7.20739 | + | 0.674573i | 0.551163 | + | 0.0515859i | ||||
\(172\) | 0.108956 | − | 0.108956i | 0.00830781 | − | 0.00830781i | ||||
\(173\) | −5.07836 | + | 5.07836i | −0.386101 | + | 0.386101i | −0.873294 | − | 0.487193i | \(-0.838021\pi\) |
0.487193 | + | 0.873294i | \(0.338021\pi\) | |||||||
\(174\) | −14.4055 | − | 0.672671i | −1.09208 | − | 0.0509950i | ||||
\(175\) | −9.02493 | − | 4.65334i | −0.682221 | − | 0.351760i | ||||
\(176\) | − | 3.03746i | − | 0.228957i | ||||||
\(177\) | −2.69663 | + | 2.45602i | −0.202691 | + | 0.184606i | ||||
\(178\) | −8.52350 | − | 8.52350i | −0.638863 | − | 0.638863i | ||||
\(179\) | −9.09915 | −0.680103 | −0.340051 | − | 0.940407i | \(-0.610444\pi\) | ||||
−0.340051 | + | 0.940407i | \(0.610444\pi\) | |||||||
\(180\) | 4.44368 | − | 5.02531i | 0.331212 | − | 0.374564i | ||||
\(181\) | −25.4910 | −1.89473 | −0.947367 | − | 0.320150i | \(-0.896267\pi\) | ||||
−0.947367 | + | 0.320150i | \(0.896267\pi\) | |||||||
\(182\) | −2.64445 | − | 2.64445i | −0.196020 | − | 0.196020i | ||||
\(183\) | 13.7819 | − | 12.5522i | 1.01879 | − | 0.927887i | ||||
\(184\) | 1.00000i | 0.0737210i | ||||||||
\(185\) | 0.194757 | + | 1.24912i | 0.0143188 | + | 0.0918368i | ||||
\(186\) | 18.6924 | + | 0.872848i | 1.37060 | + | 0.0640004i | ||||
\(187\) | 0.0872586 | − | 0.0872586i | 0.00638098 | − | 0.00638098i | ||||
\(188\) | 0.341054 | − | 0.341054i | 0.0248739 | − | 0.0248739i | ||||
\(189\) | −10.4491 | − | 1.47234i | −0.760059 | − | 0.107097i | ||||
\(190\) | 0.831209 | + | 5.33114i | 0.0603023 | + | 0.386762i | ||||
\(191\) | − | 16.0457i | − | 1.16103i | −0.814250 | − | 0.580514i | \(-0.802851\pi\) | ||
0.814250 | − | 0.580514i | \(-0.197149\pi\) | |||||||
\(192\) | −1.16628 | − | 1.28054i | −0.0841693 | − | 0.0924150i | ||||
\(193\) | −5.17234 | − | 5.17234i | −0.372313 | − | 0.372313i | 0.496006 | − | 0.868319i | \(-0.334799\pi\) |
−0.868319 | + | 0.496006i | \(0.834799\pi\) | |||||||
\(194\) | 10.4392 | 0.749494 | ||||||||
\(195\) | −4.47026 | + | 5.55758i | −0.320122 | + | 0.397987i | ||||
\(196\) | −2.87588 | −0.205420 | ||||||||
\(197\) | 14.5337 | + | 14.5337i | 1.03548 | + | 1.03548i | 0.999347 | + | 0.0361361i | \(0.0115050\pi\) |
0.0361361 | + | 0.999347i | \(0.488495\pi\) | |||||||
\(198\) | 5.81493 | + | 7.01582i | 0.413249 | + | 0.498593i | ||||
\(199\) | − | 12.8549i | − | 0.911262i | −0.890169 | − | 0.455631i | \(-0.849414\pi\) | ||
0.890169 | − | 0.455631i | \(-0.150586\pi\) | |||||||
\(200\) | 4.44404 | + | 2.29139i | 0.314241 | + | 0.162026i | ||||
\(201\) | −0.764202 | + | 16.3657i | −0.0539026 | + | 1.15435i | ||||
\(202\) | −11.1375 | + | 11.1375i | −0.783635 | + | 0.783635i | ||||
\(203\) | −11.9562 | + | 11.9562i | −0.839160 | + | 0.839160i | ||||
\(204\) | 0.00328227 | − | 0.0702912i | 0.000229805 | − | 0.00492137i | ||||
\(205\) | 17.0778 | + | 12.4707i | 1.19277 | + | 0.870993i | ||||
\(206\) | − | 14.0584i | − | 0.979494i | ||||||
\(207\) | −1.91441 | − | 2.30977i | −0.133061 | − | 0.160540i | ||||
\(208\) | 1.30218 | + | 1.30218i | 0.0902897 | + | 0.0902897i | ||||
\(209\) | −7.32927 | −0.506976 | ||||||||
\(210\) | −0.847866 | − | 7.81939i | −0.0585083 | − | 0.539589i | ||||
\(211\) | −24.8100 | −1.70799 | −0.853996 | − | 0.520280i | \(-0.825828\pi\) | ||||
−0.853996 | + | 0.520280i | \(0.825828\pi\) | |||||||
\(212\) | −0.120552 | − | 0.120552i | −0.00827952 | − | 0.00827952i | ||||
\(213\) | 6.64397 | + | 7.29485i | 0.455238 | + | 0.499835i | ||||
\(214\) | − | 11.7120i | − | 0.800616i | ||||||
\(215\) | −0.340436 | + | 0.0530793i | −0.0232175 | + | 0.00361998i | ||||
\(216\) | 5.14532 | + | 0.725006i | 0.350095 | + | 0.0493304i | ||||
\(217\) | 15.5142 | − | 15.5142i | 1.05317 | − | 1.05317i | ||||
\(218\) | −3.64985 | + | 3.64985i | −0.247199 | + | 0.247199i | ||||
\(219\) | 15.7338 | + | 0.734696i | 1.06320 | + | 0.0496462i | ||||
\(220\) | −4.00544 | + | 5.48518i | −0.270047 | + | 0.369810i | ||||
\(221\) | 0.0748167i | 0.00503271i | ||||||||
\(222\) | −0.723980 | + | 0.659383i | −0.0485903 | + | 0.0442549i | ||||
\(223\) | 6.63422 | + | 6.63422i | 0.444260 | + | 0.444260i | 0.893441 | − | 0.449181i | \(-0.148284\pi\) |
−0.449181 | + | 0.893441i | \(0.648284\pi\) | |||||||
\(224\) | −2.03079 | −0.135688 | ||||||||
\(225\) | −14.6514 | + | 3.21513i | −0.976759 | + | 0.214342i | ||||
\(226\) | −14.5584 | −0.968407 | ||||||||
\(227\) | −4.95555 | − | 4.95555i | −0.328911 | − | 0.328911i | 0.523261 | − | 0.852172i | \(-0.324715\pi\) |
−0.852172 | + | 0.523261i | \(0.824715\pi\) | |||||||
\(228\) | −3.08990 | + | 2.81420i | −0.204633 | + | 0.186375i | ||||
\(229\) | 11.2747i | 0.745053i | 0.928021 | + | 0.372527i | \(0.121509\pi\) | ||||
−0.928021 | + | 0.372527i | \(0.878491\pi\) | |||||||
\(230\) | 1.31868 | − | 1.80585i | 0.0869513 | − | 0.119074i | ||||
\(231\) | 10.6724 | + | 0.498352i | 0.702194 | + | 0.0327891i | ||||
\(232\) | 5.88745 | − | 5.88745i | 0.386530 | − | 0.386530i | ||||
\(233\) | 12.5504 | − | 12.5504i | 0.822206 | − | 0.822206i | −0.164218 | − | 0.986424i | \(-0.552510\pi\) |
0.986424 | + | 0.164218i | \(0.0525099\pi\) | |||||||
\(234\) | −5.50063 | − | 0.514829i | −0.359587 | − | 0.0336554i | ||||
\(235\) | −1.06563 | + | 0.166149i | −0.0695141 | + | 0.0108384i | ||||
\(236\) | − | 2.10585i | − | 0.137079i | ||||||
\(237\) | −6.00390 | − | 6.59207i | −0.389995 | − | 0.428201i | ||||
\(238\) | −0.0583397 | − | 0.0583397i | −0.00378160 | − | 0.00378160i | ||||
\(239\) | 1.23240 | 0.0797173 | 0.0398586 | − | 0.999205i | \(-0.487309\pi\) | ||||
0.0398586 | + | 0.999205i | \(0.487309\pi\) | |||||||
\(240\) | 0.417505 | + | 3.85041i | 0.0269498 | + | 0.248543i | ||||
\(241\) | −10.0383 | −0.646625 | −0.323312 | − | 0.946292i | \(-0.604796\pi\) | ||||
−0.323312 | + | 0.946292i | \(0.604796\pi\) | |||||||
\(242\) | 1.25431 | + | 1.25431i | 0.0806301 | + | 0.0806301i | ||||
\(243\) | −13.2725 | + | 8.17566i | −0.851430 | + | 0.524469i | ||||
\(244\) | 10.7626i | 0.689003i | ||||||||
\(245\) | 5.19340 | + | 3.79237i | 0.331794 | + | 0.242286i | ||||
\(246\) | −0.764033 | + | 16.3621i | −0.0487129 | + | 1.04321i | ||||
\(247\) | 3.14211 | − | 3.14211i | 0.199927 | − | 0.199927i | ||||
\(248\) | −7.63947 | + | 7.63947i | −0.485107 | + | 0.485107i | ||||
\(249\) | 0.351019 | − | 7.51724i | 0.0222450 | − | 0.476386i | ||||
\(250\) | −5.00364 | − | 9.99818i | −0.316458 | − | 0.632340i | ||||
\(251\) | − | 11.1326i | − | 0.702686i | −0.936247 | − | 0.351343i | \(-0.885725\pi\) | ||
0.936247 | − | 0.351343i | \(-0.114275\pi\) | |||||||
\(252\) | 4.69066 | − | 3.88777i | 0.295484 | − | 0.244906i | ||||
\(253\) | 2.14781 | + | 2.14781i | 0.135031 | + | 0.135031i | ||||
\(254\) | −8.94538 | −0.561283 | ||||||||
\(255\) | −0.0986190 | + | 0.122607i | −0.00617576 | + | 0.00767794i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0.426761 | + | 0.426761i | 0.0266206 | + | 0.0266206i | 0.720292 | − | 0.693671i | \(-0.244008\pi\) |
−0.693671 | + | 0.720292i | \(0.744008\pi\) | |||||||
\(258\) | −0.179709 | − | 0.197314i | −0.0111882 | − | 0.0122843i | ||||
\(259\) | 1.14815i | 0.0713426i | ||||||||
\(260\) | −0.634373 | − | 4.06869i | −0.0393421 | − | 0.252329i | ||||
\(261\) | −2.32766 | + | 24.8696i | −0.144079 | + | 1.53939i | ||||
\(262\) | 6.06468 | − | 6.06468i | 0.374677 | − | 0.374677i | ||||
\(263\) | 13.9902 | − | 13.9902i | 0.862670 | − | 0.862670i | −0.128977 | − | 0.991648i | \(-0.541169\pi\) |
0.991648 | + | 0.128977i | \(0.0411694\pi\) | |||||||
\(264\) | −5.25530 | − | 0.245398i | −0.323441 | − | 0.0151032i | ||||
\(265\) | 0.0587283 | + | 0.376667i | 0.00360765 | + | 0.0231385i | ||||
\(266\) | 4.90023i | 0.300452i | ||||||||
\(267\) | −15.4357 | + | 14.0584i | −0.944649 | + | 0.860363i | ||||
\(268\) | −6.68856 | − | 6.68856i | −0.408569 | − | 0.408569i | ||||
\(269\) | −15.5476 | −0.947954 | −0.473977 | − | 0.880537i | \(-0.657182\pi\) | ||||
−0.473977 | + | 0.880537i | \(0.657182\pi\) | |||||||
\(270\) | −8.33561 | − | 8.09430i | −0.507289 | − | 0.492603i | ||||
\(271\) | 3.09413 | 0.187955 | 0.0939775 | − | 0.995574i | \(-0.470042\pi\) | ||||
0.0939775 | + | 0.995574i | \(0.470042\pi\) | |||||||
\(272\) | 0.0287275 | + | 0.0287275i | 0.00174186 | + | 0.00174186i | ||||
\(273\) | −4.78898 | + | 4.36169i | −0.289843 | + | 0.263982i | ||||
\(274\) | 16.4626i | 0.994543i | ||||||||
\(275\) | 14.4664 | − | 4.62348i | 0.872357 | − | 0.278806i | ||||
\(276\) | 1.73017 | + | 0.0807905i | 0.104144 | + | 0.00486302i | ||||
\(277\) | 4.78402 | − | 4.78402i | 0.287444 | − | 0.287444i | −0.548625 | − | 0.836069i | \(-0.684849\pi\) |
0.836069 | + | 0.548625i | \(0.184849\pi\) | |||||||
\(278\) | −0.158605 | + | 0.158605i | −0.00951249 | + | 0.00951249i | ||||
\(279\) | 3.02034 | − | 32.2705i | 0.180823 | − | 1.93198i | ||||
\(280\) | 3.66730 | + | 2.67797i | 0.219163 | + | 0.160039i | ||||
\(281\) | 6.07800i | 0.362583i | 0.983429 | + | 0.181292i | \(0.0580278\pi\) | ||||
−0.983429 | + | 0.181292i | \(0.941972\pi\) | |||||||
\(282\) | −0.562525 | − | 0.617633i | −0.0334979 | − | 0.0367795i | ||||
\(283\) | 1.63214 | + | 1.63214i | 0.0970206 | + | 0.0970206i | 0.753951 | − | 0.656931i | \(-0.228146\pi\) |
−0.656931 | + | 0.753951i | \(0.728146\pi\) | |||||||
\(284\) | −5.69670 | −0.338037 | ||||||||
\(285\) | 9.29091 | − | 1.00742i | 0.550346 | − | 0.0596746i | ||||
\(286\) | 5.59364 | 0.330759 | ||||||||
\(287\) | 13.5801 | + | 13.5801i | 0.801606 | + | 0.801606i | ||||
\(288\) | −2.30977 | + | 1.91441i | −0.136104 | + | 0.112808i | ||||
\(289\) | − | 16.9983i | − | 0.999903i | ||||||
\(290\) | −18.3955 | + | 2.86815i | −1.08022 | + | 0.168423i | ||||
\(291\) | 0.843392 | − | 18.0616i | 0.0494405 | − | 1.05879i | ||||
\(292\) | −6.43032 | + | 6.43032i | −0.376306 | + | 0.376306i | ||||
\(293\) | 9.90593 | − | 9.90593i | 0.578711 | − | 0.578711i | −0.355837 | − | 0.934548i | \(-0.615804\pi\) |
0.934548 | + | 0.355837i | \(0.115804\pi\) | |||||||
\(294\) | −0.232344 | + | 4.97575i | −0.0135506 | + | 0.290192i | ||||
\(295\) | −2.77695 | + | 3.80284i | −0.161680 | + | 0.221410i | ||||
\(296\) | − | 0.565371i | − | 0.0328615i | ||||||
\(297\) | 12.6083 | − | 9.49399i | 0.731609 | − | 0.550897i | ||||
\(298\) | −3.88640 | − | 3.88640i | −0.225133 | − | 0.225133i | ||||
\(299\) | −1.84156 | −0.106500 | ||||||||
\(300\) | 4.32352 | − | 7.50381i | 0.249619 | − | 0.433233i | ||||
\(301\) | −0.312919 | −0.0180363 | ||||||||
\(302\) | −6.68091 | − | 6.68091i | −0.384443 | − | 0.384443i | ||||
\(303\) | 18.3700 | + | 20.1696i | 1.05533 | + | 1.15871i | ||||
\(304\) | − | 2.41296i | − | 0.138393i | ||||||
\(305\) | 14.1924 | − | 19.4355i | 0.812655 | − | 1.11288i | ||||
\(306\) | −0.121350 | − | 0.0113577i | −0.00693713 | − | 0.000649278i | ||||
\(307\) | 22.4079 | − | 22.4079i | 1.27889 | − | 1.27889i | 0.337594 | − | 0.941292i | \(-0.390387\pi\) |
0.941292 | − | 0.337594i | \(-0.109613\pi\) | |||||||
\(308\) | −4.36175 | + | 4.36175i | −0.248534 | + | 0.248534i | ||||
\(309\) | −24.3233 | − | 1.13578i | −1.38371 | − | 0.0646125i | ||||
\(310\) | 23.8697 | − | 3.72167i | 1.35571 | − | 0.211377i | ||||
\(311\) | 22.1020i | 1.25329i | 0.779304 | + | 0.626646i | \(0.215573\pi\) | ||||
−0.779304 | + | 0.626646i | \(0.784427\pi\) | |||||||
\(312\) | 2.35818 | − | 2.14778i | 0.133506 | − | 0.121594i | ||||
\(313\) | 3.23645 | + | 3.23645i | 0.182935 | + | 0.182935i | 0.792633 | − | 0.609698i | \(-0.208709\pi\) |
−0.609698 | + | 0.792633i | \(0.708709\pi\) | |||||||
\(314\) | 22.1348 | 1.24914 | ||||||||
\(315\) | −13.5973 | + | 0.835215i | −0.766124 | + | 0.0470590i | ||||
\(316\) | 5.14788 | 0.289591 | ||||||||
\(317\) | −11.0713 | − | 11.0713i | −0.621826 | − | 0.621826i | 0.324172 | − | 0.945998i | \(-0.394914\pi\) |
−0.945998 | + | 0.324172i | \(0.894914\pi\) | |||||||
\(318\) | −0.218314 | + | 0.198835i | −0.0122424 | + | 0.0111501i | ||||
\(319\) | − | 25.2902i | − | 1.41598i | ||||||
\(320\) | −1.80585 | − | 1.31868i | −0.100950 | − | 0.0737166i | ||||
\(321\) | −20.2637 | − | 0.946218i | −1.13101 | − | 0.0528128i | ||||
\(322\) | 1.43599 | − | 1.43599i | 0.0800244 | − | 0.0800244i | ||||
\(323\) | 0.0693185 | − | 0.0693185i | 0.00385699 | − | 0.00385699i | ||||
\(324\) | 1.67007 | − | 8.84369i | 0.0927818 | − | 0.491316i | ||||
\(325\) | −4.21973 | + | 8.18396i | −0.234068 | + | 0.453964i | ||||
\(326\) | 3.81744i | 0.211429i | ||||||||
\(327\) | 6.01997 | + | 6.60971i | 0.332905 | + | 0.365518i | ||||
\(328\) | −6.68708 | − | 6.68708i | −0.369232 | − | 0.369232i | ||||
\(329\) | −0.979497 | −0.0540014 | ||||||||
\(330\) | 9.16666 | + | 7.37322i | 0.504608 | + | 0.405883i | ||||
\(331\) | 27.5838 | 1.51614 | 0.758070 | − | 0.652173i | \(-0.226142\pi\) | ||||
0.758070 | + | 0.652173i | \(0.226142\pi\) | |||||||
\(332\) | 3.07224 | + | 3.07224i | 0.168611 | + | 0.168611i | ||||
\(333\) | 1.08235 | + | 1.30588i | 0.0593125 | + | 0.0715616i | ||||
\(334\) | 7.06036i | 0.386326i | ||||||||
\(335\) | 3.25842 | + | 20.8986i | 0.178026 | + | 1.14181i | ||||
\(336\) | −0.164069 | + | 3.51361i | −0.00895069 | + | 0.191683i | ||||
\(337\) | 16.5924 | − | 16.5924i | 0.903845 | − | 0.903845i | −0.0919212 | − | 0.995766i | \(-0.529301\pi\) |
0.995766 | + | 0.0919212i | \(0.0293008\pi\) | |||||||
\(338\) | 6.79436 | − | 6.79436i | 0.369564 | − | 0.369564i | ||||
\(339\) | −1.17618 | + | 25.1884i | −0.0638812 | + | 1.36804i | ||||
\(340\) | −0.0139950 | − | 0.0897600i | −0.000758986 | − | 0.00486792i | ||||
\(341\) | 32.8162i | 1.77710i | ||||||||
\(342\) | 4.61940 | + | 5.57339i | 0.249789 | + | 0.301375i | ||||
\(343\) | 14.1816 | + | 14.1816i | 0.765737 | + | 0.765737i | ||||
\(344\) | 0.154087 | 0.00830781 | ||||||||
\(345\) | −3.01787 | − | 2.42743i | −0.162477 | − | 0.130689i | ||||
\(346\) | −7.18189 | −0.386101 | ||||||||
\(347\) | 9.47770 | + | 9.47770i | 0.508789 | + | 0.508789i | 0.914155 | − | 0.405365i | \(-0.132856\pi\) |
−0.405365 | + | 0.914155i | \(0.632856\pi\) | |||||||
\(348\) | −9.71061 | − | 10.6619i | −0.520543 | − | 0.571538i | ||||
\(349\) | 17.3941i | 0.931085i | 0.885025 | + | 0.465543i | \(0.154141\pi\) | ||||
−0.885025 | + | 0.465543i | \(0.845859\pi\) | |||||||
\(350\) | −3.09118 | − | 9.67200i | −0.165231 | − | 0.516990i | ||||
\(351\) | −1.33514 | + | 9.47540i | −0.0712644 | + | 0.505760i | ||||
\(352\) | 2.14781 | − | 2.14781i | 0.114478 | − | 0.114478i | ||||
\(353\) | −21.9958 | + | 21.9958i | −1.17072 | + | 1.17072i | −0.188681 | + | 0.982038i | \(0.560421\pi\) |
−0.982038 | + | 0.188681i | \(0.939579\pi\) | |||||||
\(354\) | −3.64347 | − | 0.170133i | −0.193648 | − | 0.00904247i | ||||
\(355\) | 10.2874 | + | 7.51214i | 0.545997 | + | 0.398703i | ||||
\(356\) | − | 12.0540i | − | 0.638863i | ||||||
\(357\) | −0.105651 | + | 0.0962240i | −0.00559162 | + | 0.00509271i | ||||
\(358\) | −6.43407 | − | 6.43407i | −0.340051 | − | 0.340051i | ||||
\(359\) | 23.7395 | 1.25292 | 0.626461 | − | 0.779453i | \(-0.284503\pi\) | ||||
0.626461 | + | 0.779453i | \(0.284503\pi\) | |||||||
\(360\) | 6.69558 | − | 0.411275i | 0.352888 | − | 0.0216761i | ||||
\(361\) | 13.1776 | 0.693558 | ||||||||
\(362\) | −18.0249 | − | 18.0249i | −0.947367 | − | 0.947367i | ||||
\(363\) | 2.27150 | − | 2.06883i | 0.119223 | − | 0.108585i | ||||
\(364\) | − | 3.73982i | − | 0.196020i | ||||||
\(365\) | 20.0917 | − | 3.13261i | 1.05165 | − | 0.163969i | ||||
\(366\) | 18.6210 | + | 0.869514i | 0.973337 | + | 0.0454502i | ||||
\(367\) | 20.2624 | − | 20.2624i | 1.05769 | − | 1.05769i | 0.0594601 | − | 0.998231i | \(-0.481062\pi\) |
0.998231 | − | 0.0594601i | \(-0.0189379\pi\) | |||||||
\(368\) | −0.707107 | + | 0.707107i | −0.0368605 | + | 0.0368605i | ||||
\(369\) | 28.2474 | + | 2.64381i | 1.47050 | + | 0.137631i | ||||
\(370\) | −0.745544 | + | 1.02097i | −0.0387590 | + | 0.0530778i | ||||
\(371\) | 0.346221i | 0.0179749i | ||||||||
\(372\) | 12.6004 | + | 13.8347i | 0.653298 | + | 0.717298i | ||||
\(373\) | 17.2579 | + | 17.2579i | 0.893581 | + | 0.893581i | 0.994858 | − | 0.101277i | \(-0.0322930\pi\) |
−0.101277 | + | 0.994858i | \(0.532293\pi\) | |||||||
\(374\) | 0.123402 | 0.00638098 | ||||||||
\(375\) | −17.7028 | + | 7.84937i | −0.914166 | + | 0.405340i | ||||
\(376\) | 0.482323 | 0.0248739 | ||||||||
\(377\) | 10.8421 | + | 10.8421i | 0.558395 | + | 0.558395i | ||||
\(378\) | −6.34752 | − | 8.42972i | −0.326481 | − | 0.433578i | ||||
\(379\) | − | 15.5004i | − | 0.796200i | −0.917342 | − | 0.398100i | \(-0.869670\pi\) | ||
0.917342 | − | 0.398100i | \(-0.130330\pi\) | |||||||
\(380\) | −3.18193 | + | 4.35744i | −0.163230 | + | 0.223532i | ||||
\(381\) | −0.722702 | + | 15.4770i | −0.0370252 | + | 0.792911i | ||||
\(382\) | 11.3461 | − | 11.3461i | 0.580514 | − | 0.580514i | ||||
\(383\) | 24.7143 | − | 24.7143i | 1.26284 | − | 1.26284i | 0.313131 | − | 0.949710i | \(-0.398622\pi\) |
0.949710 | − | 0.313131i | \(-0.101378\pi\) | |||||||
\(384\) | 0.0807905 | − | 1.73017i | 0.00412283 | − | 0.0882921i | ||||
\(385\) | 13.6284 | − | 2.12488i | 0.694568 | − | 0.108294i | ||||
\(386\) | − | 7.31479i | − | 0.372313i | ||||||
\(387\) | −0.355906 | + | 0.294986i | −0.0180917 | + | 0.0149950i | ||||
\(388\) | 7.38166 | + | 7.38166i | 0.374747 | + | 0.374747i | ||||
\(389\) | 12.7778 | 0.647858 | 0.323929 | − | 0.946081i | \(-0.394996\pi\) | ||||
0.323929 | + | 0.946081i | \(0.394996\pi\) | |||||||
\(390\) | −7.09075 | + | 0.768858i | −0.359054 | + | 0.0389327i | ||||
\(391\) | −0.0406269 | −0.00205459 | ||||||||
\(392\) | −2.03356 | − | 2.03356i | −0.102710 | − | 0.102710i | ||||
\(393\) | −10.0029 | − | 10.9829i | −0.504582 | − | 0.554013i | ||||
\(394\) | 20.5538i | 1.03548i | ||||||||
\(395\) | −9.29628 | − | 6.78842i | −0.467747 | − | 0.341563i | ||||
\(396\) | −0.849157 | + | 9.07272i | −0.0426718 | + | 0.455921i | ||||
\(397\) | −20.0396 | + | 20.0396i | −1.00576 | + | 1.00576i | −0.00577503 | + | 0.999983i | \(0.501838\pi\) |
−0.999983 | + | 0.00577503i | \(0.998162\pi\) | |||||||
\(398\) | 9.08981 | − | 9.08981i | 0.455631 | − | 0.455631i | ||||
\(399\) | 8.47821 | + | 0.395892i | 0.424441 | + | 0.0198194i | ||||
\(400\) | 1.52216 | + | 4.76267i | 0.0761078 | + | 0.238134i | ||||
\(401\) | − | 3.91057i | − | 0.195284i | −0.995222 | − | 0.0976422i | \(-0.968870\pi\) | ||
0.995222 | − | 0.0976422i | \(-0.0311301\pi\) | |||||||
\(402\) | −12.1127 | + | 11.0319i | −0.604126 | + | 0.550223i | ||||
\(403\) | −14.0685 | − | 14.0685i | −0.700803 | − | 0.700803i | ||||
\(404\) | −15.7509 | −0.783635 | ||||||||
\(405\) | −14.6779 | + | 13.7680i | −0.729351 | + | 0.684139i | ||||
\(406\) | −16.9086 | −0.839160 | ||||||||
\(407\) | −1.21431 | − | 1.21431i | −0.0601909 | − | 0.0601909i | ||||
\(408\) | 0.0520243 | − | 0.0473825i | 0.00257559 | − | 0.00234578i | ||||
\(409\) | 8.76129i | 0.433218i | 0.976258 | + | 0.216609i | \(0.0694996\pi\) | ||||
−0.976258 | + | 0.216609i | \(0.930500\pi\) | |||||||
\(410\) | 3.25770 | + | 20.8940i | 0.160886 | + | 1.03188i | ||||
\(411\) | 28.4830 | + | 1.33002i | 1.40497 | + | 0.0656052i | ||||
\(412\) | 9.94078 | − | 9.94078i | 0.489747 | − | 0.489747i | ||||
\(413\) | −3.02398 | + | 3.02398i | −0.148800 | + | 0.148800i | ||||
\(414\) | 0.279562 | − | 2.98695i | 0.0137397 | − | 0.146800i | ||||
\(415\) | −1.49668 | − | 9.59931i | −0.0734693 | − | 0.471212i | ||||
\(416\) | 1.84156i | 0.0902897i | ||||||||
\(417\) | 0.261599 | + | 0.287227i | 0.0128106 | + | 0.0140655i | ||||
\(418\) | −5.18258 | − | 5.18258i | −0.253488 | − | 0.253488i | ||||
\(419\) | −14.3441 | −0.700754 | −0.350377 | − | 0.936609i | \(-0.613946\pi\) | ||||
−0.350377 | + | 0.936609i | \(0.613946\pi\) | |||||||
\(420\) | 4.92961 | − | 6.12868i | 0.240541 | − | 0.299049i | ||||
\(421\) | −8.54877 | −0.416641 | −0.208321 | − | 0.978061i | \(-0.566800\pi\) | ||||
−0.208321 | + | 0.978061i | \(0.566800\pi\) | |||||||
\(422\) | −17.5433 | − | 17.5433i | −0.853996 | − | 0.853996i | ||||
\(423\) | −1.11405 | + | 0.923363i | −0.0541672 | + | 0.0448955i | ||||
\(424\) | − | 0.170486i | − | 0.00827952i | ||||||
\(425\) | −0.0930921 | + | 0.180548i | −0.00451563 | + | 0.00875785i | ||||
\(426\) | −0.460240 | + | 9.85624i | −0.0222987 | + | 0.477536i | ||||
\(427\) | 15.4549 | − | 15.4549i | 0.747916 | − | 0.747916i | ||||
\(428\) | 8.28163 | − | 8.28163i | 0.400308 | − | 0.400308i | ||||
\(429\) | 0.451914 | − | 9.67793i | 0.0218186 | − | 0.467255i | ||||
\(430\) | −0.278257 | − | 0.203192i | −0.0134188 | − | 0.00979878i | ||||
\(431\) | − | 34.3396i | − | 1.65408i | −0.562141 | − | 0.827041i | \(-0.690022\pi\) | ||
0.562141 | − | 0.827041i | \(-0.309978\pi\) | |||||||
\(432\) | 3.12564 | + | 4.15095i | 0.150382 | + | 0.199713i | ||||
\(433\) | −12.5838 | − | 12.5838i | −0.604740 | − | 0.604740i | 0.336827 | − | 0.941567i | \(-0.390646\pi\) |
−0.941567 | + | 0.336827i | \(0.890646\pi\) | |||||||
\(434\) | 21.9404 | 1.05317 | ||||||||
\(435\) | 3.47619 | + | 32.0590i | 0.166671 | + | 1.53711i | ||||
\(436\) | −5.16166 | −0.247199 | ||||||||
\(437\) | 1.70622 | + | 1.70622i | 0.0816197 | + | 0.0816197i | ||||
\(438\) | 10.6060 | + | 11.6450i | 0.506774 | + | 0.556421i | ||||
\(439\) | 15.6542i | 0.747133i | 0.927603 | + | 0.373567i | \(0.121865\pi\) | ||||
−0.927603 | + | 0.373567i | \(0.878135\pi\) | |||||||
\(440\) | −6.71088 | + | 1.04633i | −0.319929 | + | 0.0498819i | ||||
\(441\) | 8.59010 | + | 0.803987i | 0.409052 | + | 0.0382851i | ||||
\(442\) | −0.0529034 | + | 0.0529034i | −0.00251636 | + | 0.00251636i | ||||
\(443\) | 21.4453 | − | 21.4453i | 1.01890 | − | 1.01890i | 0.0190784 | − | 0.999818i | \(-0.493927\pi\) |
0.999818 | − | 0.0190784i | \(-0.00607322\pi\) | |||||||
\(444\) | −0.978185 | − | 0.0456766i | −0.0464226 | − | 0.00216772i | ||||
\(445\) | −15.8955 | + | 21.7677i | −0.753517 | + | 1.03189i | ||||
\(446\) | 9.38220i | 0.444260i | ||||||||
\(447\) | −7.03810 | + | 6.41013i | −0.332891 | + | 0.303189i | ||||
\(448\) | −1.43599 | − | 1.43599i | −0.0678440 | − | 0.0678440i | ||||
\(449\) | −19.2237 | −0.907224 | −0.453612 | − | 0.891199i | \(-0.649865\pi\) | ||||
−0.453612 | + | 0.891199i | \(0.649865\pi\) | |||||||
\(450\) | −12.6335 | − | 8.08665i | −0.595550 | − | 0.381208i | ||||
\(451\) | −28.7251 | −1.35261 | ||||||||
\(452\) | −10.2943 | − | 10.2943i | −0.484204 | − | 0.484204i | ||||
\(453\) | −12.0988 | + | 11.0193i | −0.568453 | + | 0.517733i | ||||
\(454\) | − | 7.00820i | − | 0.328911i | ||||||
\(455\) | −4.93163 | + | 6.75353i | −0.231198 | + | 0.316611i | ||||
\(456\) | −4.17483 | − | 0.194945i | −0.195504 | − | 0.00912912i | ||||
\(457\) | −11.6854 | + | 11.6854i | −0.546620 | + | 0.546620i | −0.925461 | − | 0.378842i | \(-0.876322\pi\) |
0.378842 | + | 0.925461i | \(0.376322\pi\) | |||||||
\(458\) | −7.97242 | + | 7.97242i | −0.372527 | + | 0.372527i | ||||
\(459\) | −0.0294547 | + | 0.209038i | −0.00137483 | + | 0.00975708i | ||||
\(460\) | 2.20937 | − | 0.344476i | 0.103013 | − | 0.0160613i | ||||
\(461\) | − | 30.4595i | − | 1.41864i | −0.704886 | − | 0.709320i | \(-0.749002\pi\) | ||
0.704886 | − | 0.709320i | \(-0.250998\pi\) | |||||||
\(462\) | 7.19416 | + | 7.89893i | 0.334703 | + | 0.367492i | ||||
\(463\) | 9.14602 | + | 9.14602i | 0.425052 | + | 0.425052i | 0.886939 | − | 0.461887i | \(-0.152827\pi\) |
−0.461887 | + | 0.886939i | \(0.652827\pi\) | |||||||
\(464\) | 8.32611 | 0.386530 | ||||||||
\(465\) | −4.51066 | − | 41.5993i | −0.209177 | − | 1.92912i | ||||
\(466\) | 17.7490 | 0.822206 | ||||||||
\(467\) | −27.1900 | − | 27.1900i | −1.25820 | − | 1.25820i | −0.951951 | − | 0.306251i | \(-0.900925\pi\) |
−0.306251 | − | 0.951951i | \(-0.599075\pi\) | |||||||
\(468\) | −3.52549 | − | 4.25357i | −0.162966 | − | 0.196621i | ||||
\(469\) | 19.2094i | 0.887006i | ||||||||
\(470\) | −0.871000 | − | 0.636030i | −0.0401762 | − | 0.0293379i | ||||
\(471\) | 1.78828 | − | 38.2969i | 0.0823998 | − | 1.76463i | ||||
\(472\) | 1.48906 | − | 1.48906i | 0.0685397 | − | 0.0685397i | ||||
\(473\) | 0.330949 | − | 0.330949i | 0.0152170 | − | 0.0152170i | ||||
\(474\) | 0.415900 | − | 8.90669i | 0.0191029 | − | 0.409098i | ||||
\(475\) | 11.4922 | − | 3.67291i | 0.527296 | − | 0.168524i | ||||
\(476\) | − | 0.0825048i | − | 0.00378160i | ||||||
\(477\) | 0.326380 | + | 0.393783i | 0.0149439 | + | 0.0180301i | ||||
\(478\) | 0.871438 | + | 0.871438i | 0.0398586 | + | 0.0398586i | ||||
\(479\) | −7.60429 | −0.347449 | −0.173724 | − | 0.984794i | \(-0.555580\pi\) | ||||
−0.173724 | + | 0.984794i | \(0.555580\pi\) | |||||||
\(480\) | −2.42743 | + | 3.01787i | −0.110797 | + | 0.137746i | ||||
\(481\) | 1.04116 | 0.0474729 | ||||||||
\(482\) | −7.09816 | − | 7.09816i | −0.323312 | − | 0.323312i | ||||
\(483\) | −2.36848 | − | 2.60051i | −0.107770 | − | 0.118327i | ||||
\(484\) | 1.77386i | 0.0806301i | ||||||||
\(485\) | −3.59607 | − | 23.0642i | −0.163289 | − | 1.04729i | ||||
\(486\) | −15.1661 | − | 3.60399i | −0.687949 | − | 0.163480i | ||||
\(487\) | 18.0300 | − | 18.0300i | 0.817017 | − | 0.817017i | −0.168658 | − | 0.985675i | \(-0.553943\pi\) |
0.985675 | + | 0.168658i | \(0.0539433\pi\) | |||||||
\(488\) | −7.61029 | + | 7.61029i | −0.344502 | + | 0.344502i | ||||
\(489\) | 6.60481 | + | 0.308413i | 0.298680 | + | 0.0139469i | ||||
\(490\) | 0.990673 | + | 6.35390i | 0.0447541 | + | 0.287040i | ||||
\(491\) | 4.29319i | 0.193749i | 0.995297 | + | 0.0968745i | \(0.0308845\pi\) | ||||
−0.995297 | + | 0.0968745i | \(0.969115\pi\) | |||||||
\(492\) | −12.1100 | + | 11.0295i | −0.545961 | + | 0.497248i | ||||
\(493\) | 0.239189 | + | 0.239189i | 0.0107725 | + | 0.0107725i | ||||
\(494\) | 4.44361 | 0.199927 | ||||||||
\(495\) | 13.4975 | − | 15.2642i | 0.606666 | − | 0.686073i | ||||
\(496\) | −10.8038 | −0.485107 | ||||||||
\(497\) | 8.18039 | + | 8.18039i | 0.366941 | + | 0.366941i | ||||
\(498\) | 5.56370 | − | 5.06728i | 0.249315 | − | 0.227070i | ||||
\(499\) | 11.6589i | 0.521925i | 0.965349 | + | 0.260963i | \(0.0840399\pi\) | ||||
−0.965349 | + | 0.260963i | \(0.915960\pi\) | |||||||
\(500\) | 3.53167 | − | 10.6079i | 0.157941 | − | 0.474399i | ||||
\(501\) | 12.2156 | + | 0.570410i | 0.545753 | + | 0.0254841i | ||||
\(502\) | 7.87197 | − | 7.87197i | 0.351343 | − | 0.351343i | ||||
\(503\) | −21.7405 | + | 21.7405i | −0.969360 | + | 0.969360i | −0.999544 | − | 0.0301846i | \(-0.990390\pi\) |
0.0301846 | + | 0.999544i | \(0.490390\pi\) | |||||||
\(504\) | 6.06587 | + | 0.567733i | 0.270195 | + | 0.0252888i | ||||
\(505\) | 28.4436 | + | 20.7704i | 1.26572 | + | 0.924270i | ||||
\(506\) | 3.03746i | 0.135031i | ||||||||
\(507\) | −11.2064 | − | 12.3043i | −0.497696 | − | 0.546452i | ||||
\(508\) | −6.32534 | − | 6.32534i | −0.280642 | − | 0.280642i | ||||
\(509\) | 36.4307 | 1.61476 | 0.807381 | − | 0.590031i | \(-0.200884\pi\) | ||||
0.807381 | + | 0.590031i | \(0.200884\pi\) | |||||||
\(510\) | −0.156430 | + | 0.0169619i | −0.00692685 | + | 0.000751086i | ||||
\(511\) | 18.4677 | 0.816963 | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 10.0161 | − | 7.54205i | 0.442221 | − | 0.332990i | ||||
\(514\) | 0.603532i | 0.0266206i | ||||||||
\(515\) | −31.0602 | + | 4.84278i | −1.36868 | + | 0.213398i | ||||
\(516\) | 0.0124488 | − | 0.266596i | 0.000548027 | − | 0.0117362i | ||||
\(517\) | 1.03594 | − | 1.03594i | 0.0455604 | − | 0.0455604i | ||||
\(518\) | −0.811865 | + | 0.811865i | −0.0356713 | + | 0.0356713i | ||||
\(519\) | −0.580229 | + | 12.4259i | −0.0254692 | + | 0.545435i | ||||
\(520\) | 2.42843 | − | 3.32557i | 0.106494 | − | 0.145836i | ||||
\(521\) | − | 40.9950i | − | 1.79602i | −0.439972 | − | 0.898012i | \(-0.645011\pi\) | ||
0.439972 | − | 0.898012i | \(-0.354989\pi\) | |||||||
\(522\) | −19.2314 | + | 15.9396i | −0.841735 | + | 0.697657i | ||||
\(523\) | −11.8550 | − | 11.8550i | −0.518381 | − | 0.518381i | 0.398700 | − | 0.917081i | \(-0.369461\pi\) |
−0.917081 | + | 0.398700i | \(0.869461\pi\) | |||||||
\(524\) | 8.57676 | 0.374677 | ||||||||
\(525\) | −16.9839 | + | 4.56685i | −0.741238 | + | 0.199314i | ||||
\(526\) | 19.7851 | 0.862670 | ||||||||
\(527\) | −0.310368 | − | 0.310368i | −0.0135198 | − | 0.0135198i | ||||
\(528\) | −3.54254 | − | 3.88958i | −0.154169 | − | 0.169272i | ||||
\(529\) | − | 1.00000i | − | 0.0434783i | ||||||
\(530\) | −0.224817 | + | 0.307871i | −0.00976541 | + | 0.0133731i | ||||
\(531\) | −0.588717 | + | 6.29007i | −0.0255481 | + | 0.272966i | ||||
\(532\) | −3.46499 | + | 3.46499i | −0.150226 | + | 0.150226i | ||||
\(533\) | 12.3146 | − | 12.3146i | 0.533406 | − | 0.533406i | ||||
\(534\) | −20.8555 | − | 0.973853i | −0.902506 | − | 0.0421427i | ||||
\(535\) | −25.8762 | + | 4.03451i | −1.11872 | + | 0.174427i | ||||
\(536\) | − | 9.45905i | − | 0.408569i | ||||||
\(537\) | −11.6518 | + | 10.6122i | −0.502813 | + | 0.457950i | ||||
\(538\) | −10.9938 | − | 10.9938i | −0.473977 | − | 0.473977i | ||||
\(539\) | −8.73536 | −0.376259 | ||||||||
\(540\) | −0.170634 | − | 11.6177i | −0.00734294 | − | 0.499946i | ||||
\(541\) | −18.7415 | −0.805758 | −0.402879 | − | 0.915253i | \(-0.631991\pi\) | ||||
−0.402879 | + | 0.915253i | \(0.631991\pi\) | |||||||
\(542\) | 2.18788 | + | 2.18788i | 0.0939775 | + | 0.0939775i | ||||
\(543\) | −32.6423 | + | 29.7298i | −1.40081 | + | 1.27583i | ||||
\(544\) | 0.0406269i | 0.00174186i | ||||||||
\(545\) | 9.32117 | + | 6.80659i | 0.399275 | + | 0.291562i | ||||
\(546\) | −6.47051 | − | 0.302142i | −0.276912 | − | 0.0129305i | ||||
\(547\) | 3.00042 | − | 3.00042i | 0.128288 | − | 0.128288i | −0.640047 | − | 0.768336i | \(-0.721085\pi\) |
0.768336 | + | 0.640047i | \(0.221085\pi\) | |||||||
\(548\) | −11.6408 | + | 11.6408i | −0.497271 | + | 0.497271i | ||||
\(549\) | 3.00881 | − | 32.1472i | 0.128413 | − | 1.37201i | ||||
\(550\) | 13.4986 | + | 6.96000i | 0.575582 | + | 0.296775i | ||||
\(551\) | − | 20.0906i | − | 0.855888i | ||||||
\(552\) | 1.16628 | + | 1.28054i | 0.0496404 | + | 0.0545034i | ||||
\(553\) | −7.39230 | − | 7.39230i | −0.314352 | − | 0.314352i | ||||
\(554\) | 6.76562 | 0.287444 | ||||||||
\(555\) | 1.70622 | + | 1.37240i | 0.0724249 | + | 0.0582551i | ||||
\(556\) | −0.224301 | −0.00951249 | ||||||||
\(557\) | 21.5167 | + | 21.5167i | 0.911692 | + | 0.911692i | 0.996405 | − | 0.0847134i | \(-0.0269975\pi\) |
−0.0847134 | + | 0.996405i | \(0.526997\pi\) | |||||||
\(558\) | 24.9544 | − | 20.6830i | 1.05640 | − | 0.875580i | ||||
\(559\) | 0.283760i | 0.0120018i | ||||||||
\(560\) | 0.699560 | + | 4.48678i | 0.0295618 | + | 0.189601i | ||||
\(561\) | 0.00996974 | − | 0.213506i | 0.000420923 | − | 0.00901425i | ||||
\(562\) | −4.29779 | + | 4.29779i | −0.181292 | + | 0.181292i | ||||
\(563\) | 5.98181 | − | 5.98181i | 0.252103 | − | 0.252103i | −0.569729 | − | 0.821832i | \(-0.692952\pi\) |
0.821832 | + | 0.569729i | \(0.192952\pi\) | |||||||
\(564\) | 0.0389671 | − | 0.834498i | 0.00164081 | − | 0.0351387i | ||||
\(565\) | 5.01501 | + | 32.1649i | 0.210983 | + | 1.35319i | ||||
\(566\) | 2.30819i | 0.0970206i | ||||||||
\(567\) | −15.0976 | + | 10.3012i | −0.634041 | + | 0.432611i | ||||
\(568\) | −4.02818 | − | 4.02818i | −0.169019 | − | 0.169019i | ||||
\(569\) | −20.4479 | −0.857222 | −0.428611 | − | 0.903489i | \(-0.640997\pi\) | ||||
−0.428611 | + | 0.903489i | \(0.640997\pi\) | |||||||
\(570\) | 7.28202 | + | 5.85731i | 0.305010 | + | 0.245336i | ||||
\(571\) | −24.0739 | −1.00746 | −0.503730 | − | 0.863861i | \(-0.668039\pi\) | ||||
−0.503730 | + | 0.863861i | \(0.668039\pi\) | |||||||
\(572\) | 3.95530 | + | 3.95530i | 0.165380 | + | 0.165380i | ||||
\(573\) | −18.7139 | − | 20.5472i | −0.781784 | − | 0.858372i | ||||
\(574\) | 19.2051i | 0.801606i | ||||||||
\(575\) | −4.44404 | − | 2.29139i | −0.185329 | − | 0.0955576i | ||||
\(576\) | −2.98695 | − | 0.279562i | −0.124456 | − | 0.0116484i | ||||
\(577\) | −8.20948 | + | 8.20948i | −0.341765 | + | 0.341765i | −0.857031 | − | 0.515266i | \(-0.827693\pi\) |
0.515266 | + | 0.857031i | \(0.327693\pi\) | |||||||
\(578\) | 12.0196 | − | 12.0196i | 0.499951 | − | 0.499951i | ||||
\(579\) | −12.6558 | − | 0.590966i | −0.525957 | − | 0.0245597i | ||||
\(580\) | −15.0357 | − | 10.9795i | −0.624322 | − | 0.455899i | ||||
\(581\) | − | 8.82341i | − | 0.366057i | ||||||
\(582\) | 13.3679 | − | 12.1751i | 0.554116 | − | 0.504675i | ||||
\(583\) | −0.366170 | − | 0.366170i | −0.0151652 | − | 0.0151652i | ||||
\(584\) | −9.09384 | −0.376306 | ||||||||
\(585\) | 0.757387 | + | 12.3303i | 0.0313141 | + | 0.509795i | ||||
\(586\) | 14.0091 | 0.578711 | ||||||||
\(587\) | −29.6663 | − | 29.6663i | −1.22446 | − | 1.22446i | −0.966031 | − | 0.258426i | \(-0.916796\pi\) |
−0.258426 | − | 0.966031i | \(-0.583204\pi\) | |||||||
\(588\) | −3.68268 | + | 3.35409i | −0.151871 | + | 0.138321i | ||||
\(589\) | 26.0693i | 1.07417i | ||||||||
\(590\) | −4.65262 | + | 0.725417i | −0.191545 | + | 0.0298649i | ||||
\(591\) | 35.5614 | + | 1.66055i | 1.46280 | + | 0.0683058i | ||||
\(592\) | 0.399778 | − | 0.399778i | 0.0164308 | − | 0.0164308i | ||||
\(593\) | −28.7282 | + | 28.7282i | −1.17972 | + | 1.17972i | −0.199911 | + | 0.979814i | \(0.564065\pi\) |
−0.979814 | + | 0.199911i | \(0.935935\pi\) | |||||||
\(594\) | 15.6287 | + | 2.20217i | 0.641253 | + | 0.0903562i | ||||
\(595\) | −0.108798 | + | 0.148991i | −0.00446026 | + | 0.00610803i | ||||
\(596\) | − | 5.49620i | − | 0.225133i | ||||||
\(597\) | −14.9925 | − | 16.4613i | −0.613603 | − | 0.673714i | ||||
\(598\) | −1.30218 | − | 1.30218i | −0.0532500 | − | 0.0532500i | ||||
\(599\) | 46.9570 | 1.91861 | 0.959305 | − | 0.282371i | \(-0.0911211\pi\) | ||||
0.959305 | + | 0.282371i | \(0.0911211\pi\) | |||||||
\(600\) | 8.36319 | − | 2.24880i | 0.341426 | − | 0.0918069i | ||||
\(601\) | −18.4761 | −0.753656 | −0.376828 | − | 0.926283i | \(-0.622985\pi\) | ||||
−0.376828 | + | 0.926283i | \(0.622985\pi\) | |||||||
\(602\) | −0.221267 | − | 0.221267i | −0.00901817 | − | 0.00901817i | ||||
\(603\) | 18.1085 | + | 21.8482i | 0.737435 | + | 0.889728i | ||||
\(604\) | − | 9.44824i | − | 0.384443i | ||||||
\(605\) | 2.33916 | − | 3.20332i | 0.0951004 | − | 0.130234i | ||||
\(606\) | −1.27252 | + | 27.2516i | −0.0516926 | + | 1.10702i | ||||
\(607\) | −29.6024 | + | 29.6024i | −1.20152 | + | 1.20152i | −0.227821 | + | 0.973703i | \(0.573160\pi\) |
−0.973703 | + | 0.227821i | \(0.926840\pi\) | |||||||
\(608\) | 1.70622 | − | 1.70622i | 0.0691965 | − | 0.0691965i | ||||
\(609\) | −1.36606 | + | 29.2547i | −0.0553553 | + | 1.18546i | ||||
\(610\) | 23.7786 | − | 3.70745i | 0.962766 | − | 0.150110i | ||||
\(611\) | 0.888224i | 0.0359337i | ||||||||
\(612\) | −0.0777765 | − | 0.0938387i | −0.00314393 | − | 0.00379321i | ||||
\(613\) | −26.0428 | − | 26.0428i | −1.05186 | − | 1.05186i | −0.998580 | − | 0.0532791i | \(-0.983033\pi\) |
−0.0532791 | − | 0.998580i | \(-0.516967\pi\) | |||||||
\(614\) | 31.6895 | 1.27889 | ||||||||
\(615\) | 36.4132 | − | 3.94832i | 1.46832 | − | 0.159212i | ||||
\(616\) | −6.16844 | −0.248534 | ||||||||
\(617\) | −9.82533 | − | 9.82533i | −0.395553 | − | 0.395553i | 0.481108 | − | 0.876661i | \(-0.340234\pi\) |
−0.876661 | + | 0.481108i | \(0.840234\pi\) | |||||||
\(618\) | −16.3961 | − | 18.0023i | −0.659547 | − | 0.724159i | ||||
\(619\) | 11.5924i | 0.465937i | 0.972484 | + | 0.232968i | \(0.0748438\pi\) | ||||
−0.972484 | + | 0.232968i | \(0.925156\pi\) | |||||||
\(620\) | 19.5101 | + | 14.2468i | 0.783543 | + | 0.572167i | ||||
\(621\) | −5.14532 | − | 0.725006i | −0.206475 | − | 0.0290935i | ||||
\(622\) | −15.6285 | + | 15.6285i | −0.626646 | + | 0.626646i | ||||
\(623\) | −17.3095 | + | 17.3095i | −0.693489 | + | 0.693489i | ||||
\(624\) | 3.18620 | + | 0.148780i | 0.127550 | + | 0.00595598i | ||||
\(625\) | −20.3661 | + | 14.4991i | −0.814644 | + | 0.579962i | ||||
\(626\) | 4.57703i | 0.182935i | ||||||||
\(627\) | −9.38542 | + | 8.54801i | −0.374818 | + | 0.341375i | ||||
\(628\) | 15.6517 | + | 15.6517i | 0.624570 | + | 0.624570i | ||||
\(629\) | 0.0229693 | 0.000915844 | ||||||||
\(630\) | −10.2054 | − | 9.02419i | −0.406591 | − | 0.359532i | ||||
\(631\) | −24.8506 | −0.989288 | −0.494644 | − | 0.869096i | \(-0.664702\pi\) | ||||
−0.494644 | + | 0.869096i | \(0.664702\pi\) | |||||||
\(632\) | 3.64010 | + | 3.64010i | 0.144796 | + | 0.144796i | ||||
\(633\) | −31.7702 | + | 28.9355i | −1.26275 | + | 1.15008i | ||||
\(634\) | − | 15.6572i | − | 0.621826i | ||||||
\(635\) | 3.08147 | + | 19.7637i | 0.122285 | + | 0.784299i | ||||
\(636\) | −0.294969 | − | 0.0137736i | −0.0116963 | − | 0.000546160i | ||||
\(637\) | 3.74491 | − | 3.74491i | 0.148379 | − | 0.148379i | ||||
\(638\) | 17.8829 | − | 17.8829i | 0.707989 | − | 0.707989i | ||||
\(639\) | 17.0157 | + | 1.59258i | 0.673132 | + | 0.0630016i | ||||
\(640\) | −0.344476 | − | 2.20937i | −0.0136166 | − | 0.0873332i | ||||
\(641\) | − | 43.6697i | − | 1.72485i | −0.506186 | − | 0.862424i | \(-0.668945\pi\) | ||
0.506186 | − | 0.862424i | \(-0.331055\pi\) | |||||||
\(642\) | −13.6595 | − | 14.9977i | −0.539098 | − | 0.591911i | ||||
\(643\) | 4.13381 | + | 4.13381i | 0.163021 | + | 0.163021i | 0.783904 | − | 0.620882i | \(-0.213226\pi\) |
−0.620882 | + | 0.783904i | \(0.713226\pi\) | |||||||
\(644\) | 2.03079 | 0.0800244 | ||||||||
\(645\) | −0.374036 | + | 0.465015i | −0.0147277 | + | 0.0183100i | ||||
\(646\) | 0.0980312 | 0.00385699 | ||||||||
\(647\) | −24.4013 | − | 24.4013i | −0.959316 | − | 0.959316i | 0.0398886 | − | 0.999204i | \(-0.487300\pi\) |
−0.999204 | + | 0.0398886i | \(0.987300\pi\) | |||||||
\(648\) | 7.43435 | − | 5.07251i | 0.292049 | − | 0.199267i | ||||
\(649\) | − | 6.39644i | − | 0.251082i | ||||||
\(650\) | −8.77073 | + | 2.80313i | −0.344016 | + | 0.109948i | ||||
\(651\) | 1.77257 | − | 37.9605i | 0.0694727 | − | 1.48779i | ||||
\(652\) | −2.69934 | + | 2.69934i | −0.105714 | + | 0.105714i | ||||
\(653\) | −3.78364 | + | 3.78364i | −0.148065 | + | 0.148065i | −0.777253 | − | 0.629188i | \(-0.783388\pi\) |
0.629188 | + | 0.777253i | \(0.283388\pi\) | |||||||
\(654\) | −0.417014 | + | 8.93053i | −0.0163065 | + | 0.349211i | ||||
\(655\) | −15.4883 | − | 11.3100i | −0.605178 | − | 0.441919i | ||||
\(656\) | − | 9.45696i | − | 0.369232i | ||||||
\(657\) | 21.0047 | − | 17.4093i | 0.819471 | − | 0.679203i | ||||
\(658\) | −0.692609 | − | 0.692609i | −0.0270007 | − | 0.0270007i | ||||
\(659\) | 21.1564 | 0.824137 | 0.412069 | − | 0.911153i | \(-0.364806\pi\) | ||||
0.412069 | + | 0.911153i | \(0.364806\pi\) | |||||||
\(660\) | 1.26815 | + | 11.6955i | 0.0493628 | + | 0.455245i | ||||
\(661\) | −13.6642 | −0.531475 | −0.265737 | − | 0.964045i | \(-0.585615\pi\) | ||||
−0.265737 | + | 0.964045i | \(0.585615\pi\) | |||||||
\(662\) | 19.5047 | + | 19.5047i | 0.758070 | + | 0.758070i | ||||
\(663\) | 0.0872575 | + | 0.0958057i | 0.00338880 | + | 0.00372078i | ||||
\(664\) | 4.34481i | 0.168611i | ||||||||
\(665\) | 10.8264 | − | 1.68801i | 0.419831 | − | 0.0654584i | ||||
\(666\) | −0.158056 | + | 1.68873i | −0.00612455 | + | 0.0654370i | ||||
\(667\) | −5.88745 | + | 5.88745i | −0.227963 | + | 0.227963i | ||||
\(668\) | −4.99243 | + | 4.99243i | −0.193163 | + | 0.193163i | ||||
\(669\) | 16.2328 | + | 0.757993i | 0.627595 | + | 0.0293057i | ||||
\(670\) | −12.4735 | + | 17.0816i | −0.481892 | + | 0.659919i | ||||
\(671\) | 32.6908i | 1.26202i | ||||||||
\(672\) | −2.60051 | + | 2.36848i | −0.100317 | + | 0.0913662i | ||||
\(673\) | −17.2276 | − | 17.2276i | −0.664074 | − | 0.664074i | 0.292264 | − | 0.956338i | \(-0.405592\pi\) |
−0.956338 | + | 0.292264i | \(0.905592\pi\) | |||||||
\(674\) | 23.4652 | 0.903845 | ||||||||
\(675\) | −15.0119 | + | 21.2048i | −0.577809 | + | 0.816172i | ||||
\(676\) | 9.60867 | 0.369564 | ||||||||
\(677\) | 8.11519 | + | 8.11519i | 0.311892 | + | 0.311892i | 0.845642 | − | 0.533750i | \(-0.179218\pi\) |
−0.533750 | + | 0.845642i | \(0.679218\pi\) | |||||||
\(678\) | −18.6425 | + | 16.9792i | −0.715963 | + | 0.652082i | ||||
\(679\) | − | 21.1999i | − | 0.813579i | ||||||
\(680\) | 0.0535739 | − | 0.0733659i | 0.00205447 | − | 0.00281345i | ||||
\(681\) | −12.1253 | − | 0.566196i | −0.464644 | − | 0.0216967i | ||||
\(682\) | −23.2046 | + | 23.2046i | −0.888548 | + | 0.888548i | ||||
\(683\) | −14.2948 | + | 14.2948i | −0.546975 | + | 0.546975i | −0.925565 | − | 0.378589i | \(-0.876409\pi\) |
0.378589 | + | 0.925565i | \(0.376409\pi\) | |||||||
\(684\) | −0.674573 | + | 7.20739i | −0.0257929 | + | 0.275582i | ||||
\(685\) | 36.3721 | − | 5.67098i | 1.38971 | − | 0.216677i | ||||
\(686\) | 20.0559i | 0.765737i | ||||||||
\(687\) | 13.1495 | + | 14.4377i | 0.501685 | + | 0.550833i | ||||
\(688\) | 0.108956 | + | 0.108956i | 0.00415391 | + | 0.00415391i | ||||
\(689\) | 0.313959 | 0.0119609 | ||||||||
\(690\) | −0.417505 | − | 3.85041i | −0.0158941 | − | 0.146583i | ||||
\(691\) | 5.32354 | 0.202517 | 0.101258 | − | 0.994860i | \(-0.467713\pi\) | ||||
0.101258 | + | 0.994860i | \(0.467713\pi\) | |||||||
\(692\) | −5.07836 | − | 5.07836i | −0.193050 | − | 0.193050i | ||||
\(693\) | 14.2477 | − | 11.8089i | 0.541225 | − | 0.448584i | ||||
\(694\) | 13.4035i | 0.508789i | ||||||||
\(695\) | 0.405053 | + | 0.295782i | 0.0153646 | + | 0.0112197i | ||||
\(696\) | 0.672671 | − | 14.4055i | 0.0254975 | − | 0.546041i | ||||
\(697\) | 0.271675 | − | 0.271675i | 0.0102904 | − | 0.0102904i | ||||
\(698\) | −12.2995 | + | 12.2995i | −0.465543 | + | 0.465543i | ||||
\(699\) | 1.43395 | − | 30.7087i | 0.0542370 | − | 1.16151i | ||||
\(700\) | 4.65334 | − | 9.02493i | 0.175880 | − | 0.341110i | ||||
\(701\) | 37.7240i | 1.42482i | 0.701765 | + | 0.712408i | \(0.252396\pi\) | ||||
−0.701765 | + | 0.712408i | \(0.747604\pi\) | |||||||
\(702\) | −7.64421 | + | 5.75604i | −0.288512 | + | 0.217248i | ||||
\(703\) | −0.964649 | − | 0.964649i | −0.0363824 | − | 0.0363824i | ||||
\(704\) | 3.03746 | 0.114478 | ||||||||
\(705\) | −1.17081 | + | 1.45559i | −0.0440951 | + | 0.0548207i | ||||
\(706\) | −31.1068 | −1.17072 | ||||||||
\(707\) | 22.6180 | + | 22.6180i | 0.850639 | + | 0.850639i | ||||
\(708\) | −2.45602 | − | 2.69663i | −0.0923030 | − | 0.101345i | ||||
\(709\) | 17.6180i | 0.661657i | 0.943691 | + | 0.330828i | \(0.107328\pi\) | ||||
−0.943691 | + | 0.330828i | \(0.892672\pi\) | |||||||
\(710\) | 1.96238 | + | 12.5862i | 0.0736468 | + | 0.472350i | ||||
\(711\) | −15.3764 | − | 1.43915i | −0.576662 | − | 0.0539724i | ||||
\(712\) | 8.52350 | − | 8.52350i | 0.319432 | − | 0.319432i | ||||
\(713\) | 7.63947 | − | 7.63947i | 0.286100 | − | 0.286100i | ||||
\(714\) | −0.142747 | − | 0.00666560i | −0.00534217 | − | 0.000249454i | ||||
\(715\) | −1.92688 | − | 12.3585i | −0.0720612 | − | 0.462180i | ||||
\(716\) | − | 9.09915i | − | 0.340051i | ||||||
\(717\) | 1.57814 | − | 1.43733i | 0.0589366 | − | 0.0536780i | ||||
\(718\) | 16.7863 | + | 16.7863i | 0.626461 | + | 0.626461i | ||||
\(719\) | 23.4101 | 0.873050 | 0.436525 | − | 0.899692i | \(-0.356209\pi\) | ||||
0.436525 | + | 0.899692i | \(0.356209\pi\) | |||||||
\(720\) | 5.02531 | + | 4.44368i | 0.187282 | + | 0.165606i | ||||
\(721\) | −28.5497 | −1.06325 | ||||||||
\(722\) | 9.31797 | + | 9.31797i | 0.346779 | + | 0.346779i | ||||
\(723\) | −12.8545 | + | 11.7075i | −0.478062 | + | 0.435408i | ||||
\(724\) | − | 25.4910i | − | 0.947367i | ||||||
\(725\) | 12.6736 | + | 39.6545i | 0.470687 | + | 1.47273i | ||||
\(726\) | 3.06908 | + | 0.143311i | 0.113904 | + | 0.00531878i | ||||
\(727\) | −1.31281 | + | 1.31281i | −0.0486893 | + | 0.0486893i | −0.731032 | − | 0.682343i | \(-0.760961\pi\) |
0.682343 | + | 0.731032i | \(0.260961\pi\) | |||||||
\(728\) | 2.64445 | − | 2.64445i | 0.0980099 | − | 0.0980099i | ||||
\(729\) | −7.46078 | + | 25.9487i | −0.276325 | + | 0.961064i | ||||
\(730\) | 16.4221 | + | 11.9919i | 0.607808 | + | 0.443840i | ||||
\(731\) | 0.00626007i | 0.000231537i | ||||||||
\(732\) | 12.5522 | + | 13.7819i | 0.463944 | + | 0.509394i | ||||
\(733\) | 33.1490 | + | 33.1490i | 1.22439 | + | 1.22439i | 0.966056 | + | 0.258332i | \(0.0831728\pi\) |
0.258332 | + | 0.966056i | \(0.416827\pi\) | |||||||
\(734\) | 28.6554 | 1.05769 | ||||||||
\(735\) | 11.0733 | − | 1.20069i | 0.408446 | − | 0.0442883i | ||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −20.3162 | − | 20.3162i | −0.748357 | − | 0.748357i | ||||
\(738\) | 18.1045 | + | 21.8434i | 0.666435 | + | 0.804066i | ||||
\(739\) | − | 20.5449i | − | 0.755758i | −0.925855 | − | 0.377879i | \(-0.876654\pi\) | ||
0.925855 | − | 0.377879i | \(-0.123346\pi\) | |||||||
\(740\) | −1.24912 | + | 0.194757i | −0.0459184 | + | 0.00715941i | ||||
\(741\) | 0.359002 | − | 7.68818i | 0.0131883 | − | 0.282432i | ||||
\(742\) | −0.244815 | + | 0.244815i | −0.00898746 | + | 0.00898746i | ||||
\(743\) | 23.4804 | − | 23.4804i | 0.861411 | − | 0.861411i | −0.130091 | − | 0.991502i | \(-0.541527\pi\) |
0.991502 | + | 0.130091i | \(0.0415269\pi\) | |||||||
\(744\) | −0.872848 | + | 18.6924i | −0.0320002 | + | 0.685298i | ||||
\(745\) | −7.24774 | + | 9.92529i | −0.265537 | + | 0.363635i | ||||
\(746\) | 24.4064i | 0.893581i | ||||||||
\(747\) | −8.31774 | − | 10.0355i | −0.304330 | − | 0.367180i | ||||
\(748\) | 0.0872586 | + | 0.0872586i | 0.00319049 | + | 0.00319049i | ||||
\(749\) | −23.7846 | −0.869072 | ||||||||
\(750\) | −18.0681 | − | 6.96740i | −0.659753 | − | 0.254413i | ||||
\(751\) | 9.33331 | 0.340577 | 0.170289 | − | 0.985394i | \(-0.445530\pi\) | ||||
0.170289 | + | 0.985394i | \(0.445530\pi\) | |||||||
\(752\) | 0.341054 | + | 0.341054i | 0.0124369 | + | 0.0124369i | ||||
\(753\) | −12.9838 | − | 14.2558i | −0.473157 | − | 0.519510i | ||||
\(754\) | 15.3330i | 0.558395i | ||||||||
\(755\) | −12.4592 | + | 17.0621i | −0.453437 | + | 0.620952i | ||||
\(756\) | 1.47234 | − | 10.4491i | 0.0535483 | − | 0.380030i | ||||
\(757\) | −7.70849 | + | 7.70849i | −0.280170 | + | 0.280170i | −0.833177 | − | 0.553007i | \(-0.813480\pi\) |
0.553007 | + | 0.833177i | \(0.313480\pi\) | |||||||
\(758\) | 10.9604 | − | 10.9604i | 0.398100 | − | 0.398100i | ||||
\(759\) | 5.25530 | + | 0.245398i | 0.190755 | + | 0.00890737i | ||||
\(760\) | −5.33114 | + | 0.831209i | −0.193381 | + | 0.0301511i | ||||
\(761\) | 5.80591i | 0.210464i | 0.994448 | + | 0.105232i | \(0.0335586\pi\) | ||||
−0.994448 | + | 0.105232i | \(0.966441\pi\) | |||||||
\(762\) | −11.4549 | + | 10.4329i | −0.414968 | + | 0.377943i | ||||
\(763\) | 7.41208 | + | 7.41208i | 0.268335 | + | 0.268335i | ||||
\(764\) | 16.0457 | 0.580514 | ||||||||
\(765\) | 0.0167088 | + | 0.272021i | 0.000604109 | + | 0.00983493i | ||||
\(766\) | 34.9513 | 1.26284 | ||||||||
\(767\) | 2.74219 | + | 2.74219i | 0.0990148 | + | 0.0990148i | ||||
\(768\) | 1.28054 | − | 1.16628i | 0.0462075 | − | 0.0420847i | ||||
\(769\) | 9.81402i | 0.353903i | 0.984220 | + | 0.176951i | \(0.0566235\pi\) | ||||
−0.984220 | + | 0.176951i | \(0.943376\pi\) | |||||||
\(770\) | 11.1393 | + | 8.13422i | 0.401431 | + | 0.293137i | ||||
\(771\) | 1.04421 | + | 0.0487597i | 0.0376063 | + | 0.00175604i | ||||
\(772\) | 5.17234 | − | 5.17234i | 0.186156 | − | 0.186156i | ||||
\(773\) | 4.72645 | − | 4.72645i | 0.169999 | − | 0.169999i | −0.616980 | − | 0.786979i | \(-0.711644\pi\) |
0.786979 | + | 0.616980i | \(0.211644\pi\) | |||||||
\(774\) | −0.460250 | − | 0.0430769i | −0.0165433 | − | 0.00154837i | ||||
\(775\) | −16.4451 | − | 51.4552i | −0.590726 | − | 1.84832i | ||||
\(776\) | 10.4392i | 0.374747i | ||||||||
\(777\) | 1.33907 | + | 1.47025i | 0.0480389 | + | 0.0527450i | ||||
\(778\) | 9.03524 | + | 9.03524i | 0.323929 | + | 0.323929i | ||||
\(779\) | −22.8193 | −0.817586 | ||||||||
\(780\) | −5.55758 | − | 4.47026i | −0.198993 | − | 0.160061i | ||||
\(781\) | −17.3035 | −0.619167 | ||||||||
\(782\) | −0.0287275 | − | 0.0287275i | −0.00102729 | − | 0.00102729i | ||||
\(783\) | 26.0244 | + | 34.5613i | 0.930036 | + | 1.23512i | ||||
\(784\) | − | 2.87588i | − | 0.102710i | ||||||
\(785\) | −7.62492 | − | 48.9041i | −0.272145 | − | 1.74546i | ||||
\(786\) | 0.692921 | − | 14.8392i | 0.0247157 | − | 0.529297i | ||||
\(787\) | −36.7991 | + | 36.7991i | −1.31175 | + | 1.31175i | −0.391619 | + | 0.920127i | \(0.628085\pi\) |
−0.920127 | + | 0.391619i | \(0.871915\pi\) | |||||||
\(788\) | −14.5337 | + | 14.5337i | −0.517741 | + | 0.517741i | ||||
\(789\) | 1.59845 | − | 34.2315i | 0.0569062 | − | 1.21867i | ||||
\(790\) | −1.77332 | − | 11.3736i | −0.0630921 | − | 0.404655i | ||||
\(791\) | 29.5650i | 1.05121i | ||||||||
\(792\) | −7.01582 | + | 5.81493i | −0.249296 | + | 0.206625i | ||||
\(793\) | −14.0148 | − | 14.0148i | −0.497679 | − | 0.497679i | ||||
\(794\) | −28.3403 | −1.00576 | ||||||||
\(795\) | 0.514505 | + | 0.413843i | 0.0182476 | + | 0.0146775i | ||||
\(796\) | 12.8549 | 0.455631 | ||||||||
\(797\) | −16.3453 | − | 16.3453i | −0.578980 | − | 0.578980i | 0.355642 | − | 0.934622i | \(-0.384262\pi\) |
−0.934622 | + | 0.355642i | \(0.884262\pi\) | |||||||
\(798\) | 5.71506 | + | 6.27494i | 0.202311 | + | 0.222130i | ||||
\(799\) | 0.0195953i | 0.000693231i | ||||||||
\(800\) | −2.29139 | + | 4.44404i | −0.0810129 | + | 0.157121i | ||||
\(801\) | −3.36985 | + | 36.0048i | −0.119068 | + | 1.27217i | ||||
\(802\) | 2.76519 | − | 2.76519i | 0.0976422 | − | 0.0976422i | ||||
\(803\) | −19.5318 | + | 19.5318i | −0.689262 | + | 0.689262i | ||||
\(804\) | −16.3657 | − | 0.764202i | −0.577174 | − | 0.0269513i | ||||
\(805\) | −3.66730 | − | 2.67797i | −0.129255 | − | 0.0943860i | ||||
\(806\) | − | 19.8959i | − | 0.700803i | ||||||
\(807\) | −19.9093 | + | 18.1329i | −0.700841 | + | 0.638309i | ||||
\(808\) | −11.1375 | − | 11.1375i | −0.391817 | − | 0.391817i | ||||
\(809\) | −45.2033 | −1.58926 | −0.794632 | − | 0.607091i | \(-0.792336\pi\) | ||||
−0.794632 | + | 0.607091i | \(0.792336\pi\) | |||||||
\(810\) | −20.1143 | − | 0.643374i | −0.706745 | − | 0.0226059i | ||||
\(811\) | 7.65829 | 0.268919 | 0.134460 | − | 0.990919i | \(-0.457070\pi\) | ||||
0.134460 | + | 0.990919i | \(0.457070\pi\) | |||||||
\(812\) | −11.9562 | − | 11.9562i | −0.419580 | − | 0.419580i | ||||
\(813\) | 3.96215 | − | 3.60863i | 0.138959 | − | 0.126560i | ||||
\(814\) | − | 1.71729i | − | 0.0601909i | ||||||
\(815\) | 8.43416 | − | 1.31502i | 0.295436 | − | 0.0460631i | ||||
\(816\) | 0.0702912 | + | 0.00328227i | 0.00246068 | + | 0.000114902i | ||||
\(817\) | 0.262907 | − | 0.262907i | 0.00919795 | − | 0.00919795i | ||||
\(818\) | −6.19516 | + | 6.19516i | −0.216609 | + | 0.216609i | ||||
\(819\) | −1.04551 | + | 11.1706i | −0.0365331 | + | 0.390334i | ||||
\(820\) | −12.4707 | + | 17.0778i | −0.435496 | + | 0.596383i | ||||
\(821\) | − | 6.24113i | − | 0.217817i | −0.994052 | − | 0.108909i | \(-0.965264\pi\) | ||
0.994052 | − | 0.108909i | \(-0.0347356\pi\) | |||||||
\(822\) | 19.2001 | + | 21.0810i | 0.669680 | + | 0.735285i | ||||
\(823\) | 14.4815 | + | 14.4815i | 0.504792 | + | 0.504792i | 0.912923 | − | 0.408131i | \(-0.133819\pi\) |
−0.408131 | + | 0.912923i | \(0.633819\pi\) | |||||||
\(824\) | 14.0584 | 0.489747 | ||||||||
\(825\) | 13.1325 | − | 22.7925i | 0.457215 | − | 0.793533i | ||||
\(826\) | −4.27655 | −0.148800 | ||||||||
\(827\) | −3.32709 | − | 3.32709i | −0.115694 | − | 0.115694i | 0.646890 | − | 0.762584i | \(-0.276069\pi\) |
−0.762584 | + | 0.646890i | \(0.776069\pi\) | |||||||
\(828\) | 2.30977 | − | 1.91441i | 0.0802700 | − | 0.0665303i | ||||
\(829\) | − | 41.4160i | − | 1.43844i | −0.694784 | − | 0.719219i | \(-0.744500\pi\) | ||
0.694784 | − | 0.719219i | \(-0.255500\pi\) | |||||||
\(830\) | 5.72942 | − | 7.84605i | 0.198871 | − | 0.272340i | ||||
\(831\) | 0.546598 | − | 11.7056i | 0.0189613 | − | 0.406064i | ||||
\(832\) | −1.30218 | + | 1.30218i | −0.0451449 | + | 0.0451449i | ||||
\(833\) | 0.0826170 | − | 0.0826170i | 0.00286251 | − | 0.00286251i | ||||
\(834\) | −0.0181214 | + | 0.388078i | −0.000627493 | + | 0.0134381i | ||||
\(835\) | 15.5990 | − | 2.43213i | 0.539825 | − | 0.0841673i | ||||
\(836\) | − | 7.32927i | − | 0.253488i | ||||||
\(837\) | −33.7689 | − | 44.8462i | −1.16722 | − | 1.55011i | ||||
\(838\) | −10.1428 | − | 10.1428i | −0.350377 | − | 0.350377i | ||||
\(839\) | 6.74222 | 0.232767 | 0.116384 | − | 0.993204i | \(-0.462870\pi\) | ||||
0.116384 | + | 0.993204i | \(0.462870\pi\) | |||||||
\(840\) | 7.81939 | − | 0.847866i | 0.269795 | − | 0.0292541i | ||||
\(841\) | 40.3241 | 1.39049 | ||||||||
\(842\) | −6.04489 | − | 6.04489i | −0.208321 | − | 0.208321i | ||||
\(843\) | 7.08868 | + | 7.78312i | 0.244147 | + | 0.268065i | ||||
\(844\) | − | 24.8100i | − | 0.853996i | ||||||
\(845\) | −17.3518 | − | 12.6708i | −0.596919 | − | 0.435888i | ||||
\(846\) | −1.44067 | − | 0.134839i | −0.0495313 | − | 0.00463586i | ||||
\(847\) | 2.54724 | − | 2.54724i | 0.0875244 | − | 0.0875244i | ||||
\(848\) | 0.120552 | − | 0.120552i | 0.00413976 | − | 0.00413976i | ||||
\(849\) | 3.99356 | + | 0.186480i | 0.137059 | + | 0.00639999i | ||||
\(850\) | −0.193492 | + | 0.0618404i | −0.00663674 | + | 0.00212111i | ||||
\(851\) | 0.565371i | 0.0193807i | ||||||||
\(852\) | −7.29485 | + | 6.64397i | −0.249918 | + | 0.227619i | ||||
\(853\) | −37.0320 | − | 37.0320i | −1.26795 | − | 1.26795i | −0.947145 | − | 0.320805i | \(-0.896047\pi\) |
−0.320805 | − | 0.947145i | \(-0.603953\pi\) | |||||||
\(854\) | 21.8566 | 0.747916 | ||||||||
\(855\) | 10.7224 | − | 12.1259i | 0.366700 | − | 0.414697i | ||||
\(856\) | 11.7120 | 0.400308 | ||||||||
\(857\) | −3.66827 | − | 3.66827i | −0.125306 | − | 0.125306i | 0.641673 | − | 0.766979i | \(-0.278241\pi\) |
−0.766979 | + | 0.641673i | \(0.778241\pi\) | |||||||
\(858\) | 7.16288 | − | 6.52378i | 0.244537 | − | 0.222718i | ||||
\(859\) | 7.96847i | 0.271881i | 0.990717 | + | 0.135940i | \(0.0434056\pi\) | ||||
−0.990717 | + | 0.135940i | \(0.956594\pi\) | |||||||
\(860\) | −0.0530793 | − | 0.340436i | −0.00180999 | − | 0.0116088i | ||||
\(861\) | 33.2280 | + | 1.55159i | 1.13241 | + | 0.0528781i | ||||
\(862\) | 24.2818 | − | 24.2818i | 0.827041 | − | 0.827041i | ||||
\(863\) | 3.16578 | − | 3.16578i | 0.107764 | − | 0.107764i | −0.651169 | − | 0.758933i | \(-0.725721\pi\) |
0.758933 | + | 0.651169i | \(0.225721\pi\) | |||||||
\(864\) | −0.725006 | + | 5.14532i | −0.0246652 | + | 0.175048i | ||||
\(865\) | 2.47399 | + | 15.8675i | 0.0841183 | + | 0.539511i | ||||
\(866\) | − | 17.7962i | − | 0.604740i | ||||||
\(867\) | −19.8249 | − | 21.7671i | −0.673289 | − | 0.739248i | ||||
\(868\) | 15.5142 | + | 15.5142i | 0.526586 | + | 0.526586i | ||||
\(869\) | 15.6365 | 0.530431 | ||||||||
\(870\) | −20.2111 | + | 25.1272i | −0.685220 | + | 0.851890i | ||||
\(871\) | 17.4194 | 0.590233 | ||||||||
\(872\) | −3.64985 | − | 3.64985i | −0.123599 | − | 0.123599i | ||||
\(873\) | −19.9850 | − | 24.1122i | −0.676389 | − | 0.816076i | ||||
\(874\) | 2.41296i | 0.0816197i | ||||||||
\(875\) | −20.3042 | + | 10.1614i | −0.686408 | + | 0.343516i | ||||
\(876\) | −0.734696 | + | 15.7338i | −0.0248231 | + | 0.531598i | ||||
\(877\) | 31.0507 | − | 31.0507i | 1.04851 | − | 1.04851i | 0.0497443 | − | 0.998762i | \(-0.484159\pi\) |
0.998762 | − | 0.0497443i | \(-0.0158406\pi\) | |||||||
\(878\) | −11.0692 | + | 11.0692i | −0.373567 | + | 0.373567i | ||||
\(879\) | 1.13180 | − | 24.2381i | 0.0381748 | − | 0.817530i | ||||
\(880\) | −5.48518 | − | 4.00544i | −0.184905 | − | 0.135023i | ||||
\(881\) | − | 12.9732i | − | 0.437080i | −0.975828 | − | 0.218540i | \(-0.929871\pi\) | ||
0.975828 | − | 0.218540i | \(-0.0701294\pi\) | |||||||
\(882\) | 5.50561 | + | 6.64262i | 0.185384 | + | 0.223669i | ||||
\(883\) | −15.5946 | − | 15.5946i | −0.524800 | − | 0.524800i | 0.394217 | − | 0.919017i | \(-0.371016\pi\) |
−0.919017 | + | 0.394217i | \(0.871016\pi\) | |||||||
\(884\) | −0.0748167 | −0.00251636 | ||||||||
\(885\) | 0.879204 | + | 8.10841i | 0.0295541 | + | 0.272561i | ||||
\(886\) | 30.3282 | 1.01890 | ||||||||
\(887\) | 31.5863 | + | 31.5863i | 1.06056 | + | 1.06056i | 0.998044 | + | 0.0625206i | \(0.0199139\pi\) |
0.0625206 | + | 0.998044i | \(0.480086\pi\) | |||||||
\(888\) | −0.659383 | − | 0.723980i | −0.0221275 | − | 0.0242952i | ||||
\(889\) | 18.1662i | 0.609276i | ||||||||
\(890\) | −26.6319 | + | 4.15234i | −0.892704 | + | 0.139187i | ||||
\(891\) | 5.07277 | − | 26.8623i | 0.169944 | − | 0.899921i | ||||
\(892\) | −6.63422 | + | 6.63422i | −0.222130 | + | 0.222130i | ||||
\(893\) | 0.822950 | − | 0.822950i | 0.0275390 | − | 0.0275390i | ||||
\(894\) | −9.50934 | − | 0.444041i | −0.318040 | − | 0.0148510i | ||||
\(895\) | −11.9989 | + | 16.4317i | −0.401079 | + | 0.549250i | ||||
\(896\) | − | 2.03079i | − | 0.0678440i | ||||||
\(897\) | −2.35818 | + | 2.14778i | −0.0787375 | + | 0.0717122i | ||||
\(898\) | −13.5932 | − | 13.5932i | −0.453612 | − | 0.453612i | ||||
\(899\) | −89.9540 | −3.00013 | ||||||||
\(900\) | −3.21513 | − | 14.6514i | −0.107171 | − | 0.488379i | ||||
\(901\) | 0.00692630 | 0.000230749 | ||||||||
\(902\) | −20.3117 | − | 20.3117i | −0.676306 | − | 0.676306i | ||||
\(903\) | −0.400705 | + | 0.364952i | −0.0133346 | + | 0.0121449i | ||||
\(904\) | − | 14.5584i | − | 0.484204i | ||||||
\(905\) | −33.6146 | + | 46.0329i | −1.11739 | + | 1.53018i | ||||
\(906\) | −16.3470 | − | 0.763328i | −0.543093 | − | 0.0253599i | ||||
\(907\) | −7.13670 | + | 7.13670i | −0.236970 | + | 0.236970i | −0.815594 | − | 0.578624i | \(-0.803590\pi\) |
0.578624 | + | 0.815594i | \(0.303590\pi\) | |||||||
\(908\) | 4.95555 | − | 4.95555i | 0.164456 | − | 0.164456i | ||||
\(909\) | 47.0470 | + | 4.40334i | 1.56045 | + | 0.146050i | ||||
\(910\) | −8.26266 | + | 1.28828i | −0.273905 | + | 0.0427060i | ||||
\(911\) | 16.6340i | 0.551109i | 0.961285 | + | 0.275554i | \(0.0888614\pi\) | ||||
−0.961285 | + | 0.275554i | \(0.911139\pi\) | |||||||
\(912\) | −2.81420 | − | 3.08990i | −0.0931875 | − | 0.102317i | ||||
\(913\) | 9.33180 | + | 9.33180i | 0.308838 | + | 0.308838i | ||||
\(914\) | −16.5256 | −0.546620 | ||||||||
\(915\) | −4.49343 | − | 41.4404i | −0.148548 | − | 1.36998i | ||||
\(916\) | −11.2747 | −0.372527 | ||||||||
\(917\) | −12.3161 | − | 12.3161i | −0.406714 | − | 0.406714i | ||||
\(918\) | −0.168640 | + | 0.126985i | −0.00556595 | + | 0.00419113i | ||||
\(919\) | 41.3582i | 1.36428i | 0.731221 | + | 0.682141i | \(0.238951\pi\) | ||||
−0.731221 | + | 0.682141i | \(0.761049\pi\) | |||||||
\(920\) | 1.80585 | + | 1.31868i | 0.0595370 | + | 0.0434757i | ||||
\(921\) | 2.56022 | − | 54.8282i | 0.0843620 | − | 1.80665i | ||||
\(922\) | 21.5381 | − | 21.5381i | 0.709320 | − | 0.709320i | ||||
\(923\) | 7.41811 | − | 7.41811i | 0.244170 | − | 0.244170i | ||||
\(924\) | −0.498352 | + | 10.6724i | −0.0163946 | + | 0.351097i | ||||
\(925\) | 2.51253 | + | 1.29549i | 0.0826116 | + | 0.0425953i | ||||
\(926\) | 12.9344i | 0.425052i | ||||||||
\(927\) | −32.4716 | + | 26.9135i | −1.06651 | + | 0.883955i | ||||
\(928\) | 5.88745 | + | 5.88745i | 0.193265 | + | 0.193265i | ||||
\(929\) | −0.182246 | −0.00597931 | −0.00298966 | − | 0.999996i | \(-0.500952\pi\) | ||||
−0.00298966 | + | 0.999996i | \(0.500952\pi\) | |||||||
\(930\) | 26.2256 | − | 32.6046i | 0.859972 | − | 1.06915i | ||||
\(931\) | −6.93940 | −0.227430 | ||||||||
\(932\) | 12.5504 | + | 12.5504i | 0.411103 | + | 0.411103i | ||||
\(933\) | 25.7773 | + | 28.3025i | 0.843910 | + | 0.926583i | ||||
\(934\) | − | 38.4524i | − | 1.25820i | ||||||
\(935\) | −0.0425092 | − | 0.272642i | −0.00139020 | − | 0.00891635i | ||||
\(936\) | 0.514829 | − | 5.50063i | 0.0168277 | − | 0.179794i | ||||
\(937\) | 39.5274 | − | 39.5274i | 1.29130 | − | 1.29130i | 0.357322 | − | 0.933981i | \(-0.383690\pi\) |
0.933981 | − | 0.357322i | \(-0.116310\pi\) | |||||||
\(938\) | −13.5831 | + | 13.5831i | −0.443503 | + | 0.443503i | ||||
\(939\) | 7.91902 | + | 0.369781i | 0.258428 | + | 0.0120673i | ||||
\(940\) | −0.166149 | − | 1.06563i | −0.00541918 | − | 0.0347571i | ||||
\(941\) | − | 21.9646i | − | 0.716025i | −0.933717 | − | 0.358013i | \(-0.883454\pi\) | ||
0.933717 | − | 0.358013i | \(-0.116546\pi\) | |||||||
\(942\) | 28.3445 | − | 25.8155i | 0.923514 | − | 0.841114i | ||||
\(943\) | 6.68708 | + | 6.68708i | 0.217761 | + | 0.217761i | ||||
\(944\) | 2.10585 | 0.0685397 | ||||||||
\(945\) | −16.4378 | + | 16.9279i | −0.534723 | + | 0.550664i | ||||
\(946\) | 0.468032 | 0.0152170 | ||||||||
\(947\) | 2.78553 | + | 2.78553i | 0.0905177 | + | 0.0905177i | 0.750916 | − | 0.660398i | \(-0.229612\pi\) |
−0.660398 | + | 0.750916i | \(0.729612\pi\) | |||||||
\(948\) | 6.59207 | − | 6.00390i | 0.214100 | − | 0.194997i | ||||
\(949\) | − | 16.7468i | − | 0.543625i | ||||||
\(950\) | 10.7233 | + | 5.52905i | 0.347910 | + | 0.179386i | ||||
\(951\) | −27.0895 | − | 1.26495i | −0.878438 | − | 0.0410189i | ||||
\(952\) | 0.0583397 | − | 0.0583397i | 0.00189080 | − | 0.00189080i | ||||
\(953\) | −5.12116 | + | 5.12116i | −0.165891 | + | 0.165891i | −0.785170 | − | 0.619280i | \(-0.787425\pi\) |
0.619280 | + | 0.785170i | \(0.287425\pi\) | |||||||
\(954\) | −0.0476613 | + | 0.509232i | −0.00154309 | + | 0.0164870i | ||||
\(955\) | −28.9761 | − | 21.1592i | −0.937645 | − | 0.684697i | ||||
\(956\) | 1.23240i | 0.0398586i | ||||||||
\(957\) | −29.4955 | − | 32.3851i | −0.953456 | − | 1.04686i | ||||
\(958\) | −5.37704 | − | 5.37704i | −0.173724 | − | 0.173724i | ||||
\(959\) | 33.4322 | 1.07958 | ||||||||
\(960\) | −3.85041 | + | 0.417505i | −0.124272 | + | 0.0134749i | ||||
\(961\) | 85.7231 | 2.76526 | ||||||||
\(962\) | 0.736213 | + | 0.736213i | 0.0237365 | + | 0.0237365i | ||||
\(963\) | −27.0520 | + | 22.4216i | −0.871739 | + | 0.722524i | ||||
\(964\) | − | 10.0383i | − | 0.323312i | ||||||
\(965\) | −16.1611 | + | 2.51977i | −0.520244 | + | 0.0811143i | ||||
\(966\) | 0.164069 | − | 3.51361i | 0.00527883 | − | 0.113048i | ||||
\(967\) | −8.28190 | + | 8.28190i | −0.266328 | + | 0.266328i | −0.827619 | − | 0.561291i | \(-0.810305\pi\) |
0.561291 | + | 0.827619i | \(0.310305\pi\) | |||||||
\(968\) | −1.25431 | + | 1.25431i | −0.0403151 | + | 0.0403151i | ||||
\(969\) | 0.00791999 | − | 0.169610i | 0.000254427 | − | 0.00544866i | ||||
\(970\) | 13.7660 | − | 18.8517i | 0.442001 | − | 0.605290i | ||||
\(971\) | 41.0986i | 1.31892i | 0.751741 | + | 0.659459i | \(0.229215\pi\) | ||||
−0.751741 | + | 0.659459i | \(0.770785\pi\) | |||||||
\(972\) | −8.17566 | − | 13.2725i | −0.262234 | − | 0.425715i | ||||
\(973\) | 0.322094 | + | 0.322094i | 0.0103259 | + | 0.0103259i | ||||
\(974\) | 25.4983 | 0.817017 | ||||||||
\(975\) | 4.14129 | + | 15.4013i | 0.132628 | + | 0.493236i | ||||
\(976\) | −10.7626 | −0.344502 | ||||||||
\(977\) | −5.84940 | − | 5.84940i | −0.187139 | − | 0.187139i | 0.607319 | − | 0.794458i | \(-0.292245\pi\) |
−0.794458 | + | 0.607319i | \(0.792245\pi\) | |||||||
\(978\) | 4.45222 | + | 4.88838i | 0.142366 | + | 0.156313i | ||||
\(979\) | − | 36.6136i | − | 1.17018i | ||||||
\(980\) | −3.79237 | + | 5.19340i | −0.121143 | + | 0.165897i | ||||
\(981\) | 15.4176 | + | 1.44301i | 0.492246 | + | 0.0460716i | ||||
\(982\) | −3.03574 | + | 3.03574i | −0.0968745 | + | 0.0968745i | ||||
\(983\) | 14.6133 | − | 14.6133i | 0.466092 | − | 0.466092i | −0.434554 | − | 0.900646i | \(-0.643094\pi\) |
0.900646 | + | 0.434554i | \(0.143094\pi\) | |||||||
\(984\) | −16.3621 | − | 0.764033i | −0.521605 | − | 0.0243565i | ||||
\(985\) | 45.4109 | − | 7.08028i | 1.44691 | − | 0.225597i | ||||
\(986\) | 0.338264i | 0.0107725i | ||||||||
\(987\) | −1.25429 | + | 1.14237i | −0.0399243 | + | 0.0363621i | ||||
\(988\) | 3.14211 | + | 3.14211i | 0.0999637 | + | 0.0999637i | ||||
\(989\) | −0.154087 | −0.00489968 | ||||||||
\(990\) | 20.3375 | − | 1.24923i | 0.646369 | − | 0.0397032i | ||||
\(991\) | 9.65620 | 0.306739 | 0.153370 | − | 0.988169i | \(-0.450988\pi\) | ||||
0.153370 | + | 0.988169i | \(0.450988\pi\) | |||||||
\(992\) | −7.63947 | − | 7.63947i | −0.242553 | − | 0.242553i | ||||
\(993\) | 35.3221 | − | 32.1705i | 1.12091 | − | 1.02090i | ||||
\(994\) | 11.5688i | 0.366941i | ||||||||
\(995\) | −23.2140 | − | 16.9516i | −0.735934 | − | 0.537401i | ||||
\(996\) | 7.51724 | + | 0.351019i | 0.238193 | + | 0.0111225i | ||||
\(997\) | −6.06407 | + | 6.06407i | −0.192051 | + | 0.192051i | −0.796582 | − | 0.604531i | \(-0.793361\pi\) |
0.604531 | + | 0.796582i | \(0.293361\pi\) | |||||||
\(998\) | −8.24410 | + | 8.24410i | −0.260963 | + | 0.260963i | ||||
\(999\) | 2.90902 | + | 0.409897i | 0.0920372 | + | 0.0129686i |
(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 | 690.2.i.f.323.13 | yes | 32 | |
3.2 | odd | 2 | inner | 690.2.i.f.323.3 | yes | 32 | |
5.2 | odd | 4 | inner | 690.2.i.f.47.3 | ✓ | 32 | |
15.2 | even | 4 | inner | 690.2.i.f.47.13 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.i.f.47.3 | ✓ | 32 | 5.2 | odd | 4 | inner | |
690.2.i.f.47.13 | yes | 32 | 15.2 | even | 4 | inner | |
690.2.i.f.323.3 | yes | 32 | 3.2 | odd | 2 | inner | |
690.2.i.f.323.13 | yes | 32 | 1.1 | even | 1 | trivial |