Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [48,3,Mod(5,48)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(48, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("48.5");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.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: | \(1.30790526893\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.629407744.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{6} + 2x^{4} - 8x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 5.2 | ||
Root | \(0.767178 + 1.18804i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 48.5 |
Dual form | 48.3.i.a.29.2 |
$q$-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 \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(31\) | \(37\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.420861 | + | 1.95522i | −0.210431 | + | 0.977609i | ||||
\(3\) | −2.77809 | − | 1.13234i | −0.926031 | − | 0.377447i | ||||
\(4\) | −3.64575 | − | 1.64575i | −0.911438 | − | 0.411438i | ||||
\(5\) | −6.28651 | + | 6.28651i | −1.25730 | + | 1.25730i | −0.304927 | + | 0.952376i | \(0.598632\pi\) |
−0.952376 | + | 0.304927i | \(0.901368\pi\) | |||||||
\(6\) | 3.38317 | − | 4.95522i | 0.563861 | − | 0.825870i | ||||
\(7\) | 1.64575i | 0.235107i | 0.993067 | + | 0.117554i | \(0.0375052\pi\) | ||||
−0.993067 | + | 0.117554i | \(0.962495\pi\) | |||||||
\(8\) | 4.75216 | − | 6.43560i | 0.594020 | − | 0.804450i | ||||
\(9\) | 6.43560 | + | 6.29150i | 0.715067 | + | 0.699056i | ||||
\(10\) | −9.64575 | − | 14.9373i | −0.964575 | − | 1.49373i | ||||
\(11\) | 4.75216 | − | 4.75216i | 0.432014 | − | 0.432014i | −0.457299 | − | 0.889313i | \(-0.651183\pi\) |
0.889313 | + | 0.457299i | \(0.151183\pi\) | |||||||
\(12\) | 8.26468 | + | 8.70029i | 0.688724 | + | 0.725024i | ||||
\(13\) | −9.35425 | + | 9.35425i | −0.719558 | + | 0.719558i | −0.968515 | − | 0.248957i | \(-0.919912\pi\) |
0.248957 | + | 0.968515i | \(0.419912\pi\) | |||||||
\(14\) | −3.21780 | − | 0.692633i | −0.229843 | − | 0.0494738i | ||||
\(15\) | 24.5830 | − | 10.3460i | 1.63887 | − | 0.689736i | ||||
\(16\) | 10.5830 | + | 12.0000i | 0.661438 | + | 0.750000i | ||||
\(17\) | 11.4859i | 0.675644i | 0.941210 | + | 0.337822i | \(0.109690\pi\) | ||||
−0.941210 | + | 0.337822i | \(0.890310\pi\) | |||||||
\(18\) | −15.0098 | + | 9.93515i | −0.833875 | + | 0.551953i | ||||
\(19\) | −8.58301 | + | 8.58301i | −0.451737 | + | 0.451737i | −0.895931 | − | 0.444194i | \(-0.853490\pi\) |
0.444194 | + | 0.895931i | \(0.353490\pi\) | |||||||
\(20\) | 33.2651 | − | 12.5730i | 1.66326 | − | 0.628651i | ||||
\(21\) | 1.86355 | − | 4.57205i | 0.0887406 | − | 0.217717i | ||||
\(22\) | 7.29150 | + | 11.2915i | 0.331432 | + | 0.513250i | ||||
\(23\) | −16.2381 | −0.706004 | −0.353002 | − | 0.935623i | \(-0.614839\pi\) | ||||
−0.353002 | + | 0.935623i | \(0.614839\pi\) | |||||||
\(24\) | −20.4892 | + | 12.4976i | −0.853718 | + | 0.520735i | ||||
\(25\) | − | 54.0405i | − | 2.16162i | ||||||
\(26\) | −14.3527 | − | 22.2264i | −0.552029 | − | 0.854863i | ||||
\(27\) | −10.7546 | − | 24.7657i | −0.398318 | − | 0.917248i | ||||
\(28\) | 2.70850 | − | 6.00000i | 0.0967320 | − | 0.214286i | ||||
\(29\) | 10.7405 | + | 10.7405i | 0.370362 | + | 0.370362i | 0.867609 | − | 0.497247i | \(-0.165656\pi\) |
−0.497247 | + | 0.867609i | \(0.665656\pi\) | |||||||
\(30\) | 9.88272 | + | 52.4194i | 0.329424 | + | 1.74731i | ||||
\(31\) | 6.35425 | 0.204976 | 0.102488 | − | 0.994734i | \(-0.467320\pi\) | ||||
0.102488 | + | 0.994734i | \(0.467320\pi\) | |||||||
\(32\) | −27.9166 | + | 15.6417i | −0.872393 | + | 0.488804i | ||||
\(33\) | −18.5830 | + | 7.82087i | −0.563121 | + | 0.236996i | ||||
\(34\) | −22.4575 | − | 4.83399i | −0.660515 | − | 0.142176i | ||||
\(35\) | −10.3460 | − | 10.3460i | −0.295601 | − | 0.295601i | ||||
\(36\) | −13.1084 | − | 33.5287i | −0.364121 | − | 0.931352i | ||||
\(37\) | 27.2288 | + | 27.2288i | 0.735912 | + | 0.735912i | 0.971784 | − | 0.235872i | \(-0.0757946\pi\) |
−0.235872 | + | 0.971784i | \(0.575795\pi\) | |||||||
\(38\) | −13.1694 | − | 20.3939i | −0.346563 | − | 0.536682i | ||||
\(39\) | 36.5792 | − | 15.3948i | 0.937928 | − | 0.394738i | ||||
\(40\) | 10.5830 | + | 70.3320i | 0.264575 | + | 1.75830i | ||||
\(41\) | −1.98162 | −0.0483323 | −0.0241662 | − | 0.999708i | \(-0.507693\pi\) | ||||
−0.0241662 | + | 0.999708i | \(0.507693\pi\) | |||||||
\(42\) | 8.15506 | + | 5.56785i | 0.194168 | + | 0.132568i | ||||
\(43\) | −19.4170 | − | 19.4170i | −0.451558 | − | 0.451558i | 0.444313 | − | 0.895871i | \(-0.353448\pi\) |
−0.895871 | + | 0.444313i | \(0.853448\pi\) | |||||||
\(44\) | −25.1461 | + | 9.50432i | −0.571501 | + | 0.216007i | ||||
\(45\) | −80.0091 | + | 0.905893i | −1.77798 | + | 0.0201310i | ||||
\(46\) | 6.83399 | − | 31.7490i | 0.148565 | − | 0.690196i | ||||
\(47\) | 74.9474i | 1.59463i | 0.603566 | + | 0.797313i | \(0.293746\pi\) | ||||
−0.603566 | + | 0.797313i | \(0.706254\pi\) | |||||||
\(48\) | −15.8125 | − | 45.3207i | −0.329427 | − | 0.944181i | ||||
\(49\) | 46.2915 | 0.944725 | ||||||||
\(50\) | 105.661 | + | 22.7436i | 2.11322 | + | 0.454871i | ||||
\(51\) | 13.0060 | − | 31.9090i | 0.255020 | − | 0.625667i | ||||
\(52\) | 49.4980 | − | 18.7085i | 0.951885 | − | 0.359779i | ||||
\(53\) | −4.00671 | + | 4.00671i | −0.0755983 | + | 0.0755983i | −0.743895 | − | 0.668297i | \(-0.767024\pi\) |
0.668297 | + | 0.743895i | \(0.267024\pi\) | |||||||
\(54\) | 52.9485 | − | 10.6046i | 0.980528 | − | 0.196382i | ||||
\(55\) | 59.7490i | 1.08635i | ||||||||
\(56\) | 10.5914 | + | 7.82087i | 0.189132 | + | 0.139658i | ||||
\(57\) | 33.5633 | − | 14.1255i | 0.588830 | − | 0.247816i | ||||
\(58\) | −25.5203 | + | 16.4797i | −0.440004 | + | 0.284133i | ||||
\(59\) | 27.9694 | − | 27.9694i | 0.474058 | − | 0.474058i | −0.429167 | − | 0.903225i | \(-0.641193\pi\) |
0.903225 | + | 0.429167i | \(0.141193\pi\) | |||||||
\(60\) | −106.651 | − | 2.73843i | −1.77751 | − | 0.0456405i | ||||
\(61\) | 39.2288 | − | 39.2288i | 0.643094 | − | 0.643094i | −0.308221 | − | 0.951315i | \(-0.599733\pi\) |
0.951315 | + | 0.308221i | \(0.0997335\pi\) | |||||||
\(62\) | −2.67426 | + | 12.4239i | −0.0431332 | + | 0.200386i | ||||
\(63\) | −10.3542 | + | 10.5914i | −0.164353 | + | 0.168118i | ||||
\(64\) | −18.8340 | − | 61.1660i | −0.294281 | − | 0.955719i | ||||
\(65\) | − | 117.611i | − | 1.80940i | ||||||
\(66\) | −7.47063 | − | 39.6253i | −0.113191 | − | 0.600384i | ||||
\(67\) | −68.6863 | + | 68.6863i | −1.02517 | + | 1.02517i | −0.0254932 | + | 0.999675i | \(0.508116\pi\) |
−0.999675 | + | 0.0254932i | \(0.991884\pi\) | |||||||
\(68\) | 18.9030 | − | 41.8749i | 0.277985 | − | 0.615807i | ||||
\(69\) | 45.1110 | + | 18.3871i | 0.653782 | + | 0.266479i | ||||
\(70\) | 24.5830 | − | 15.8745i | 0.351186 | − | 0.226779i | ||||
\(71\) | −40.6822 | −0.572988 | −0.286494 | − | 0.958082i | \(-0.592490\pi\) | ||||
−0.286494 | + | 0.958082i | \(0.592490\pi\) | |||||||
\(72\) | 71.0726 | − | 11.5188i | 0.987120 | − | 0.159983i | ||||
\(73\) | 59.0405i | 0.808774i | 0.914588 | + | 0.404387i | \(0.132515\pi\) | ||||
−0.914588 | + | 0.404387i | \(0.867485\pi\) | |||||||
\(74\) | −64.6977 | + | 41.7786i | −0.874293 | + | 0.564576i | ||||
\(75\) | −61.1923 | + | 150.130i | −0.815898 | + | 2.00173i | ||||
\(76\) | 45.4170 | − | 17.1660i | 0.597592 | − | 0.225869i | ||||
\(77\) | 7.82087 | + | 7.82087i | 0.101570 | + | 0.101570i | ||||
\(78\) | 14.7054 | + | 77.9993i | 0.188530 | + | 0.999991i | ||||
\(79\) | 17.3948 | 0.220187 | 0.110093 | − | 0.993921i | \(-0.464885\pi\) | ||||
0.110093 | + | 0.993921i | \(0.464885\pi\) | |||||||
\(80\) | −141.968 | − | 8.90796i | −1.77460 | − | 0.111349i | ||||
\(81\) | 1.83399 | + | 80.9792i | 0.0226418 | + | 0.999744i | ||||
\(82\) | 0.833990 | − | 3.87451i | 0.0101706 | − | 0.0472501i | ||||
\(83\) | 75.1400 | + | 75.1400i | 0.905301 | + | 0.905301i | 0.995889 | − | 0.0905874i | \(-0.0288745\pi\) |
−0.0905874 | + | 0.995889i | \(0.528874\pi\) | |||||||
\(84\) | −14.3185 | + | 13.6016i | −0.170458 | + | 0.161924i | ||||
\(85\) | −72.2065 | − | 72.2065i | −0.849489 | − | 0.849489i | ||||
\(86\) | 46.1363 | − | 29.7926i | 0.536469 | − | 0.346425i | ||||
\(87\) | −17.6762 | − | 42.0000i | −0.203174 | − | 0.482759i | ||||
\(88\) | −8.00000 | − | 53.1660i | −0.0909091 | − | 0.604159i | ||||
\(89\) | −78.8051 | −0.885450 | −0.442725 | − | 0.896657i | \(-0.645988\pi\) | ||||
−0.442725 | + | 0.896657i | \(0.645988\pi\) | |||||||
\(90\) | 31.9015 | − | 156.817i | 0.354462 | − | 1.74241i | ||||
\(91\) | −15.3948 | − | 15.3948i | −0.169173 | − | 0.169173i | ||||
\(92\) | 59.2001 | + | 26.7239i | 0.643479 | + | 0.290477i | ||||
\(93\) | −17.6527 | − | 7.19518i | −0.189814 | − | 0.0773675i | ||||
\(94\) | −146.539 | − | 31.5425i | −1.55892 | − | 0.335558i | ||||
\(95\) | − | 107.914i | − | 1.13594i | ||||||
\(96\) | 95.2667 | − | 11.8431i | 0.992361 | − | 0.123366i | ||||
\(97\) | −38.8340 | −0.400350 | −0.200175 | − | 0.979760i | \(-0.564151\pi\) | ||||
−0.200175 | + | 0.979760i | \(0.564151\pi\) | |||||||
\(98\) | −19.4823 | + | 90.5100i | −0.198799 | + | 0.923571i | ||||
\(99\) | 60.4812 | − | 0.684791i | 0.610921 | − | 0.00691708i | ||||
\(100\) | −88.9373 | + | 197.018i | −0.889373 | + | 1.97018i | ||||
\(101\) | 41.5332 | − | 41.5332i | 0.411220 | − | 0.411220i | −0.470943 | − | 0.882164i | \(-0.656086\pi\) |
0.882164 | + | 0.470943i | \(0.156086\pi\) | |||||||
\(102\) | 56.9153 | + | 38.8589i | 0.557993 | + | 0.380969i | ||||
\(103\) | − | 98.8118i | − | 0.959337i | −0.877450 | − | 0.479669i | \(-0.840757\pi\) | ||
0.877450 | − | 0.479669i | \(-0.159243\pi\) | |||||||
\(104\) | 15.7474 | + | 104.653i | 0.151417 | + | 1.00628i | ||||
\(105\) | 17.0270 | + | 40.4575i | 0.162162 | + | 0.385310i | ||||
\(106\) | −6.14772 | − | 9.52026i | −0.0579974 | − | 0.0898138i | ||||
\(107\) | 98.8480 | − | 98.8480i | 0.923813 | − | 0.923813i | −0.0734837 | − | 0.997296i | \(-0.523412\pi\) |
0.997296 | + | 0.0734837i | \(0.0234117\pi\) | |||||||
\(108\) | −1.54965 | + | 107.989i | −0.0143486 | + | 0.999897i | ||||
\(109\) | 68.8523 | − | 68.8523i | 0.631672 | − | 0.631672i | −0.316815 | − | 0.948487i | \(-0.602613\pi\) |
0.948487 | + | 0.316815i | \(0.102613\pi\) | |||||||
\(110\) | −116.822 | − | 25.1461i | −1.06202 | − | 0.228601i | ||||
\(111\) | −44.8118 | − | 106.476i | −0.403710 | − | 0.959246i | ||||
\(112\) | −19.7490 | + | 17.4170i | −0.176330 | + | 0.155509i | ||||
\(113\) | 8.31160i | 0.0735540i | 0.999323 | + | 0.0367770i | \(0.0117091\pi\) | ||||
−0.999323 | + | 0.0367770i | \(0.988291\pi\) | |||||||
\(114\) | 13.4929 | + | 71.5684i | 0.118359 | + | 0.627793i | ||||
\(115\) | 102.081 | − | 102.081i | 0.887661 | − | 0.887661i | ||||
\(116\) | −21.4810 | − | 56.8333i | −0.185181 | − | 0.489943i | ||||
\(117\) | −119.053 | + | 1.34796i | −1.01754 | + | 0.0115210i | ||||
\(118\) | 42.9150 | + | 66.4575i | 0.363687 | + | 0.563199i | ||||
\(119\) | −18.9030 | −0.158849 | ||||||||
\(120\) | 50.2393 | − | 207.372i | 0.418661 | − | 1.72810i | ||||
\(121\) | 75.8340i | 0.626727i | ||||||||
\(122\) | 60.1909 | + | 93.2106i | 0.493368 | + | 0.764022i | ||||
\(123\) | 5.50514 | + | 2.24388i | 0.0447572 | + | 0.0182429i | ||||
\(124\) | −23.1660 | − | 10.4575i | −0.186823 | − | 0.0843348i | ||||
\(125\) | 182.564 | + | 182.564i | 1.46051 | + | 1.46051i | ||||
\(126\) | −16.3508 | − | 24.7023i | −0.129768 | − | 0.196050i | ||||
\(127\) | −195.933 | −1.54278 | −0.771391 | − | 0.636361i | \(-0.780439\pi\) | ||||
−0.771391 | + | 0.636361i | \(0.780439\pi\) | |||||||
\(128\) | 127.519 | − | 11.0821i | 0.996245 | − | 0.0865792i | ||||
\(129\) | 31.9555 | + | 75.9289i | 0.247717 | + | 0.588596i | ||||
\(130\) | 229.956 | + | 49.4980i | 1.76889 | + | 0.380754i | ||||
\(131\) | −142.127 | − | 142.127i | −1.08494 | − | 1.08494i | −0.996041 | − | 0.0888967i | \(-0.971666\pi\) |
−0.0888967 | − | 0.996041i | \(-0.528334\pi\) | |||||||
\(132\) | 80.6202 | + | 2.07006i | 0.610759 | + | 0.0156823i | ||||
\(133\) | −14.1255 | − | 14.1255i | −0.106207 | − | 0.106207i | ||||
\(134\) | −105.389 | − | 163.204i | −0.786487 | − | 1.21794i | ||||
\(135\) | 223.299 | + | 88.0810i | 1.65406 | + | 0.652452i | ||||
\(136\) | 73.9190 | + | 54.5830i | 0.543522 | + | 0.401346i | ||||
\(137\) | 50.4847 | 0.368501 | 0.184251 | − | 0.982879i | \(-0.441014\pi\) | ||||
0.184251 | + | 0.982879i | \(0.441014\pi\) | |||||||
\(138\) | −54.9362 | + | 80.4633i | −0.398088 | + | 0.583067i | ||||
\(139\) | 171.727 | + | 171.727i | 1.23544 | + | 1.23544i | 0.961843 | + | 0.273601i | \(0.0882149\pi\) |
0.273601 | + | 0.961843i | \(0.411785\pi\) | |||||||
\(140\) | 20.6921 | + | 54.7461i | 0.147801 | + | 0.391044i | ||||
\(141\) | 84.8661 | − | 208.211i | 0.601887 | − | 1.47667i | ||||
\(142\) | 17.1216 | − | 79.5425i | 0.120574 | − | 0.560158i | ||||
\(143\) | 88.9057i | 0.621718i | ||||||||
\(144\) | −7.39000 | + | 143.810i | −0.0513195 | + | 0.998682i | ||||
\(145\) | −135.041 | −0.931314 | ||||||||
\(146\) | −115.437 | − | 24.8479i | −0.790665 | − | 0.170191i | ||||
\(147\) | −128.602 | − | 52.4178i | −0.874844 | − | 0.356584i | ||||
\(148\) | −54.4575 | − | 144.081i | −0.367956 | − | 0.973521i | ||||
\(149\) | −84.4952 | + | 84.4952i | −0.567082 | + | 0.567082i | −0.931310 | − | 0.364228i | \(-0.881333\pi\) |
0.364228 | + | 0.931310i | \(0.381333\pi\) | |||||||
\(150\) | −267.783 | − | 182.828i | −1.78522 | − | 1.21885i | ||||
\(151\) | 30.1033i | 0.199359i | 0.995020 | + | 0.0996797i | \(0.0317818\pi\) | ||||
−0.995020 | + | 0.0996797i | \(0.968218\pi\) | |||||||
\(152\) | 14.4490 | + | 96.0246i | 0.0950594 | + | 0.631741i | ||||
\(153\) | −72.2638 | + | 73.9190i | −0.472313 | + | 0.483130i | ||||
\(154\) | −18.5830 | + | 12.0000i | −0.120669 | + | 0.0779221i | ||||
\(155\) | −39.9461 | + | 39.9461i | −0.257717 | + | 0.257717i | ||||
\(156\) | −158.695 | − | 4.07475i | −1.01727 | − | 0.0261202i | ||||
\(157\) | −181.265 | + | 181.265i | −1.15456 | + | 1.15456i | −0.168928 | + | 0.985628i | \(0.554030\pi\) |
−0.985628 | + | 0.168928i | \(0.945970\pi\) | |||||||
\(158\) | −7.32079 | + | 34.0106i | −0.0463341 | + | 0.215257i | ||||
\(159\) | 15.6680 | − | 6.59405i | 0.0985407 | − | 0.0414720i | ||||
\(160\) | 77.1660 | − | 273.830i | 0.482288 | − | 1.71144i | ||||
\(161\) | − | 26.7239i | − | 0.165987i | ||||||
\(162\) | −159.104 | − | 30.4952i | −0.982123 | − | 0.188242i | ||||
\(163\) | 200.081 | − | 200.081i | 1.22749 | − | 1.22749i | 0.262581 | − | 0.964910i | \(-0.415426\pi\) |
0.964910 | − | 0.262581i | \(-0.0845737\pi\) | |||||||
\(164\) | 7.22451 | + | 3.26126i | 0.0440519 | + | 0.0198857i | ||||
\(165\) | 67.6563 | − | 165.988i | 0.410038 | − | 1.00599i | ||||
\(166\) | −178.539 | + | 115.292i | −1.07553 | + | 0.694527i | ||||
\(167\) | −172.656 | −1.03387 | −0.516933 | − | 0.856026i | \(-0.672926\pi\) | ||||
−0.516933 | + | 0.856026i | \(0.672926\pi\) | |||||||
\(168\) | −20.5680 | − | 33.7202i | −0.122429 | − | 0.200715i | ||||
\(169\) | − | 6.00394i | − | 0.0355263i | ||||||
\(170\) | 171.568 | − | 110.791i | 1.00923 | − | 0.651709i | ||||
\(171\) | −109.237 | + | 1.23682i | −0.638812 | + | 0.00723287i | ||||
\(172\) | 38.8340 | + | 102.745i | 0.225779 | + | 0.597355i | ||||
\(173\) | −40.8313 | − | 40.8313i | −0.236019 | − | 0.236019i | 0.579181 | − | 0.815199i | \(-0.303373\pi\) |
−0.815199 | + | 0.579181i | \(0.803373\pi\) | |||||||
\(174\) | 89.5584 | − | 16.8846i | 0.514703 | − | 0.0970379i | ||||
\(175\) | 88.9373 | 0.508213 | ||||||||
\(176\) | 107.318 | + | 6.73378i | 0.609761 | + | 0.0382601i | ||||
\(177\) | −109.373 | + | 46.0307i | −0.617924 | + | 0.260060i | ||||
\(178\) | 33.1660 | − | 154.081i | 0.186326 | − | 0.865624i | ||||
\(179\) | 152.613 | + | 152.613i | 0.852584 | + | 0.852584i | 0.990451 | − | 0.137866i | \(-0.0440245\pi\) |
−0.137866 | + | 0.990451i | \(0.544024\pi\) | |||||||
\(180\) | 293.184 | + | 128.372i | 1.62880 | + | 0.713180i | ||||
\(181\) | 166.601 | + | 166.601i | 0.920449 | + | 0.920449i | 0.997061 | − | 0.0766118i | \(-0.0244102\pi\) |
−0.0766118 | + | 0.997061i | \(0.524410\pi\) | |||||||
\(182\) | 36.5792 | − | 23.6211i | 0.200985 | − | 0.129786i | ||||
\(183\) | −153.402 | + | 64.5608i | −0.838260 | + | 0.352791i | ||||
\(184\) | −77.1660 | + | 104.502i | −0.419380 | + | 0.567945i | ||||
\(185\) | −342.348 | −1.85053 | ||||||||
\(186\) | 21.4975 | − | 31.4867i | 0.115578 | − | 0.169283i | ||||
\(187\) | 54.5830 | + | 54.5830i | 0.291888 | + | 0.291888i | ||||
\(188\) | 123.345 | − | 273.240i | 0.656090 | − | 1.45340i | ||||
\(189\) | 40.7582 | − | 17.6994i | 0.215652 | − | 0.0936474i | ||||
\(190\) | 210.996 | + | 45.4170i | 1.11051 | + | 0.239037i | ||||
\(191\) | − | 14.3434i | − | 0.0750963i | −0.999295 | − | 0.0375482i | \(-0.988045\pi\) | ||
0.999295 | − | 0.0375482i | \(-0.0119548\pi\) | |||||||
\(192\) | −16.9383 | + | 191.251i | −0.0882201 | + | 0.996101i | ||||
\(193\) | 207.373 | 1.07447 | 0.537235 | − | 0.843433i | \(-0.319469\pi\) | ||||
0.537235 | + | 0.843433i | \(0.319469\pi\) | |||||||
\(194\) | 16.3437 | − | 75.9289i | 0.0842460 | − | 0.391386i | ||||
\(195\) | −133.176 | + | 326.735i | −0.682954 | + | 1.67556i | ||||
\(196\) | −168.767 | − | 76.1843i | −0.861058 | − | 0.388695i | ||||
\(197\) | 97.2608 | − | 97.2608i | 0.493710 | − | 0.493710i | −0.415763 | − | 0.909473i | \(-0.636486\pi\) |
0.909473 | + | 0.415763i | \(0.136486\pi\) | |||||||
\(198\) | −24.1153 | + | 118.542i | −0.121794 | + | 0.598698i | ||||
\(199\) | − | 82.7673i | − | 0.415916i | −0.978138 | − | 0.207958i | \(-0.933318\pi\) | ||
0.978138 | − | 0.207958i | \(-0.0666818\pi\) | |||||||
\(200\) | −347.783 | − | 256.809i | −1.73892 | − | 1.28405i | ||||
\(201\) | 268.593 | − | 113.041i | 1.33628 | − | 0.562391i | ||||
\(202\) | 63.7268 | + | 98.6863i | 0.315479 | + | 0.488546i | ||||
\(203\) | −17.6762 | + | 17.6762i | −0.0870748 | + | 0.0870748i | ||||
\(204\) | −99.9310 | + | 94.9277i | −0.489858 | + | 0.465332i | ||||
\(205\) | 12.4575 | − | 12.4575i | 0.0607684 | − | 0.0607684i | ||||
\(206\) | 193.198 | + | 41.5861i | 0.937857 | + | 0.201874i | ||||
\(207\) | −104.502 | − | 102.162i | −0.504840 | − | 0.493536i | ||||
\(208\) | −211.247 | − | 13.2549i | −1.01561 | − | 0.0637256i | ||||
\(209\) | 81.5756i | 0.390314i | ||||||||
\(210\) | −86.2693 | + | 16.2645i | −0.410806 | + | 0.0774500i | ||||
\(211\) | −201.646 | + | 201.646i | −0.955667 | + | 0.955667i | −0.999058 | − | 0.0433911i | \(-0.986184\pi\) |
0.0433911 | + | 0.999058i | \(0.486184\pi\) | |||||||
\(212\) | 21.2015 | − | 8.01342i | 0.100007 | − | 0.0377992i | ||||
\(213\) | 113.019 | + | 46.0661i | 0.530605 | + | 0.216273i | ||||
\(214\) | 151.668 | + | 234.871i | 0.708729 | + | 1.09753i | ||||
\(215\) | 244.130 | 1.13549 | ||||||||
\(216\) | −210.490 | − | 48.4783i | −0.974489 | − | 0.224436i | ||||
\(217\) | 10.4575i | 0.0481913i | ||||||||
\(218\) | 105.644 | + | 163.598i | 0.484605 | + | 0.750452i | ||||
\(219\) | 66.8541 | − | 164.020i | 0.305270 | − | 0.748950i | ||||
\(220\) | 98.3320 | − | 217.830i | 0.446964 | − | 0.990137i | ||||
\(221\) | −107.442 | − | 107.442i | −0.486164 | − | 0.486164i | ||||
\(222\) | 227.044 | − | 42.8050i | 1.02272 | − | 0.192815i | ||||
\(223\) | 233.261 | 1.04602 | 0.523008 | − | 0.852328i | \(-0.324810\pi\) | ||||
0.523008 | + | 0.852328i | \(0.324810\pi\) | |||||||
\(224\) | −25.7424 | − | 45.9438i | −0.114921 | − | 0.205106i | ||||
\(225\) | 339.996 | − | 347.783i | 1.51109 | − | 1.54570i | ||||
\(226\) | −16.2510 | − | 3.49803i | −0.0719070 | − | 0.0154780i | ||||
\(227\) | 94.3599 | + | 94.3599i | 0.415682 | + | 0.415682i | 0.883712 | − | 0.468030i | \(-0.155036\pi\) |
−0.468030 | + | 0.883712i | \(0.655036\pi\) | |||||||
\(228\) | −145.610 | − | 3.73879i | −0.638642 | − | 0.0163982i | ||||
\(229\) | −138.063 | − | 138.063i | −0.602894 | − | 0.602894i | 0.338185 | − | 0.941080i | \(-0.390187\pi\) |
−0.941080 | + | 0.338185i | \(0.890187\pi\) | |||||||
\(230\) | 156.629 | + | 242.553i | 0.680994 | + | 1.05458i | ||||
\(231\) | −12.8712 | − | 30.5830i | −0.0557195 | − | 0.132394i | ||||
\(232\) | 120.162 | − | 18.0810i | 0.517940 | − | 0.0779355i | ||||
\(233\) | 396.796 | 1.70299 | 0.851493 | − | 0.524366i | \(-0.175697\pi\) | ||||
0.851493 | + | 0.524366i | \(0.175697\pi\) | |||||||
\(234\) | 47.4691 | − | 233.341i | 0.202859 | − | 0.997183i | ||||
\(235\) | −471.158 | − | 471.158i | −2.00493 | − | 2.00493i | ||||
\(236\) | −148.000 | + | 55.9388i | −0.627119 | + | 0.237029i | ||||
\(237\) | −48.3243 | − | 19.6968i | −0.203900 | − | 0.0831090i | ||||
\(238\) | 7.95554 | − | 36.9595i | 0.0334267 | − | 0.155292i | ||||
\(239\) | 284.813i | 1.19168i | 0.803102 | + | 0.595842i | \(0.203182\pi\) | ||||
−0.803102 | + | 0.595842i | \(0.796818\pi\) | |||||||
\(240\) | 384.315 | + | 185.504i | 1.60131 | + | 0.772933i | ||||
\(241\) | −266.531 | −1.10594 | −0.552968 | − | 0.833202i | \(-0.686505\pi\) | ||||
−0.552968 | + | 0.833202i | \(0.686505\pi\) | |||||||
\(242\) | −148.272 | − | 31.9156i | −0.612694 | − | 0.131883i | ||||
\(243\) | 86.6012 | − | 227.045i | 0.356383 | − | 0.934340i | ||||
\(244\) | −207.579 | + | 78.4575i | −0.850734 | + | 0.321547i | ||||
\(245\) | −291.012 | + | 291.012i | −1.18780 | + | 1.18780i | ||||
\(246\) | −6.70417 | + | 9.81938i | −0.0272527 | + | 0.0399162i | ||||
\(247\) | − | 160.575i | − | 0.650102i | ||||||
\(248\) | 30.1964 | − | 40.8934i | 0.121760 | − | 0.164893i | ||||
\(249\) | −123.662 | − | 293.830i | −0.496633 | − | 1.18004i | ||||
\(250\) | −433.786 | + | 280.118i | −1.73514 | + | 1.12047i | ||||
\(251\) | −153.945 | + | 153.945i | −0.613327 | + | 0.613327i | −0.943811 | − | 0.330485i | \(-0.892788\pi\) |
0.330485 | + | 0.943811i | \(0.392788\pi\) | |||||||
\(252\) | 55.1798 | − | 21.5731i | 0.218968 | − | 0.0856076i | ||||
\(253\) | −77.1660 | + | 77.1660i | −0.305004 | + | 0.305004i | ||||
\(254\) | 82.4608 | − | 383.092i | 0.324649 | − | 1.50824i | ||||
\(255\) | 118.834 | + | 282.359i | 0.466016 | + | 1.10729i | ||||
\(256\) | −32.0000 | + | 253.992i | −0.125000 | + | 0.992157i | ||||
\(257\) | − | 240.167i | − | 0.934503i | −0.884125 | − | 0.467251i | \(-0.845244\pi\) | ||
0.884125 | − | 0.467251i | \(-0.154756\pi\) | |||||||
\(258\) | −161.906 | + | 30.5245i | −0.627544 | + | 0.118312i | ||||
\(259\) | −44.8118 | + | 44.8118i | −0.173018 | + | 0.173018i | ||||
\(260\) | −193.559 | + | 428.781i | −0.744457 | + | 1.64916i | ||||
\(261\) | 1.54772 | + | 136.695i | 0.00592995 | + | 0.523737i | ||||
\(262\) | 337.705 | − | 218.073i | 1.28895 | − | 0.832340i | ||||
\(263\) | −140.707 | −0.535009 | −0.267505 | − | 0.963557i | \(-0.586199\pi\) | ||||
−0.267505 | + | 0.963557i | \(0.586199\pi\) | |||||||
\(264\) | −37.9774 | + | 156.759i | −0.143854 | + | 0.593784i | ||||
\(265\) | − | 50.3765i | − | 0.190100i | ||||||
\(266\) | 33.5633 | − | 21.6735i | 0.126178 | − | 0.0814795i | ||||
\(267\) | 218.928 | + | 89.2343i | 0.819954 | + | 0.334211i | ||||
\(268\) | 363.454 | − | 137.373i | 1.35617 | − | 0.512584i | ||||
\(269\) | −229.830 | − | 229.830i | −0.854388 | − | 0.854388i | 0.136282 | − | 0.990670i | \(-0.456485\pi\) |
−0.990670 | + | 0.136282i | \(0.956485\pi\) | |||||||
\(270\) | −266.195 | + | 399.527i | −0.985909 | + | 1.47973i | ||||
\(271\) | 228.731 | 0.844025 | 0.422012 | − | 0.906590i | \(-0.361324\pi\) | ||||
0.422012 | + | 0.906590i | \(0.361324\pi\) | |||||||
\(272\) | −137.831 | + | 121.556i | −0.506733 | + | 0.446896i | ||||
\(273\) | 25.3360 | + | 60.2002i | 0.0928057 | + | 0.220514i | ||||
\(274\) | −21.2470 | + | 98.7085i | −0.0775440 | + | 0.360250i | ||||
\(275\) | −256.809 | − | 256.809i | −0.933851 | − | 0.933851i | ||||
\(276\) | −134.203 | − | 141.276i | −0.486242 | − | 0.511870i | ||||
\(277\) | −103.265 | − | 103.265i | −0.372799 | − | 0.372799i | 0.495697 | − | 0.868496i | \(-0.334913\pi\) |
−0.868496 | + | 0.495697i | \(0.834913\pi\) | |||||||
\(278\) | −408.036 | + | 263.490i | −1.46776 | + | 0.947806i | ||||
\(279\) | 40.8934 | + | 39.9778i | 0.146571 | + | 0.143290i | ||||
\(280\) | −115.749 | + | 17.4170i | −0.413389 | + | 0.0622036i | ||||
\(281\) | 283.552 | 1.00908 | 0.504540 | − | 0.863388i | \(-0.331662\pi\) | ||||
0.504540 | + | 0.863388i | \(0.331662\pi\) | |||||||
\(282\) | 371.381 | + | 253.560i | 1.31695 | + | 0.899148i | ||||
\(283\) | 23.4758 | + | 23.4758i | 0.0829534 | + | 0.0829534i | 0.747366 | − | 0.664413i | \(-0.231318\pi\) |
−0.664413 | + | 0.747366i | \(0.731318\pi\) | |||||||
\(284\) | 148.317 | + | 66.9527i | 0.522243 | + | 0.235749i | ||||
\(285\) | −122.196 | + | 299.796i | −0.428758 | + | 1.05192i | ||||
\(286\) | −173.830 | − | 37.4170i | −0.607797 | − | 0.130829i | ||||
\(287\) | − | 3.26126i | − | 0.0113633i | ||||||
\(288\) | −278.070 | − | 74.9733i | −0.965521 | − | 0.260324i | ||||
\(289\) | 157.073 | 0.543506 | ||||||||
\(290\) | 56.8333 | − | 264.034i | 0.195977 | − | 0.910461i | ||||
\(291\) | 107.884 | + | 43.9734i | 0.370737 | + | 0.151111i | ||||
\(292\) | 97.1660 | − | 215.247i | 0.332760 | − | 0.737147i | ||||
\(293\) | 381.409 | − | 381.409i | 1.30174 | − | 1.30174i | 0.374516 | − | 0.927220i | \(-0.377809\pi\) |
0.927220 | − | 0.374516i | \(-0.122191\pi\) | |||||||
\(294\) | 156.612 | − | 229.384i | 0.532693 | − | 0.780219i | ||||
\(295\) | 351.660i | 1.19207i | ||||||||
\(296\) | 304.629 | − | 45.8381i | 1.02915 | − | 0.154859i | ||||
\(297\) | −168.798 | − | 66.5830i | −0.568343 | − | 0.224185i | ||||
\(298\) | −129.646 | − | 200.767i | −0.435053 | − | 0.673716i | ||||
\(299\) | 151.895 | − | 151.895i | 0.508011 | − | 0.508011i | ||||
\(300\) | 470.168 | − | 446.628i | 1.56723 | − | 1.48876i | ||||
\(301\) | 31.9555 | − | 31.9555i | 0.106165 | − | 0.106165i | ||||
\(302\) | −58.8584 | − | 12.6693i | −0.194895 | − | 0.0419513i | ||||
\(303\) | −162.413 | + | 68.3534i | −0.536017 | + | 0.225589i | ||||
\(304\) | −193.830 | − | 12.1621i | −0.637599 | − | 0.0400068i | ||||
\(305\) | 493.224i | 1.61713i | ||||||||
\(306\) | −114.115 | − | 172.401i | −0.372924 | − | 0.563402i | ||||
\(307\) | −209.055 | + | 209.055i | −0.680960 | + | 0.680960i | −0.960217 | − | 0.279256i | \(-0.909912\pi\) |
0.279256 | + | 0.960217i | \(0.409912\pi\) | |||||||
\(308\) | −15.6417 | − | 41.3842i | −0.0507849 | − | 0.134364i | ||||
\(309\) | −111.889 | + | 274.508i | −0.362099 | + | 0.888376i | ||||
\(310\) | −61.2915 | − | 94.9150i | −0.197715 | − | 0.306178i | ||||
\(311\) | 111.176 | 0.357478 | 0.178739 | − | 0.983897i | \(-0.442798\pi\) | ||||
0.178739 | + | 0.983897i | \(0.442798\pi\) | |||||||
\(312\) | 74.7554 | − | 308.567i | 0.239601 | − | 0.988998i | ||||
\(313\) | − | 282.280i | − | 0.901852i | −0.892561 | − | 0.450926i | \(-0.851094\pi\) | ||
0.892561 | − | 0.450926i | \(-0.148906\pi\) | |||||||
\(314\) | −278.126 | − | 430.701i | −0.885750 | − | 1.37166i | ||||
\(315\) | −1.49088 | − | 131.675i | −0.00473294 | − | 0.418016i | ||||
\(316\) | −63.4170 | − | 28.6275i | −0.200687 | − | 0.0905932i | ||||
\(317\) | 206.983 | + | 206.983i | 0.652943 | + | 0.652943i | 0.953701 | − | 0.300758i | \(-0.0972395\pi\) |
−0.300758 | + | 0.953701i | \(0.597240\pi\) | |||||||
\(318\) | 6.29875 | + | 33.4095i | 0.0198074 | + | 0.105061i | ||||
\(319\) | 102.081 | 0.320003 | ||||||||
\(320\) | 502.921 | + | 266.121i | 1.57163 | + | 0.831628i | ||||
\(321\) | −386.539 | + | 162.679i | −1.20417 | + | 0.506789i | ||||
\(322\) | 52.2510 | + | 11.2470i | 0.162270 | + | 0.0349287i | ||||
\(323\) | −98.5839 | − | 98.5839i | −0.305213 | − | 0.305213i | ||||
\(324\) | 126.585 | − | 298.248i | 0.390696 | − | 0.920520i | ||||
\(325\) | 505.508 | + | 505.508i | 1.55541 | + | 1.55541i | ||||
\(326\) | 306.996 | + | 475.408i | 0.941704 | + | 1.45831i | ||||
\(327\) | −269.242 | + | 113.314i | −0.823371 | + | 0.346525i | ||||
\(328\) | −9.41699 | + | 12.7530i | −0.0287103 | + | 0.0388810i | ||||
\(329\) | −123.345 | −0.374908 | ||||||||
\(330\) | 296.069 | + | 202.141i | 0.897180 | + | 0.612548i | ||||
\(331\) | 127.431 | + | 127.431i | 0.384989 | + | 0.384989i | 0.872896 | − | 0.487907i | \(-0.162239\pi\) |
−0.487907 | + | 0.872896i | \(0.662239\pi\) | |||||||
\(332\) | −150.280 | − | 397.603i | −0.452651 | − | 1.19760i | ||||
\(333\) | 3.92369 | + | 346.543i | 0.0117829 | + | 1.04067i | ||||
\(334\) | 72.6640 | − | 337.579i | 0.217557 | − | 1.01072i | ||||
\(335\) | − | 863.594i | − | 2.57789i | ||||||
\(336\) | 74.5866 | − | 26.0234i | 0.221984 | − | 0.0774506i | ||||
\(337\) | 68.9595 | 0.204628 | 0.102314 | − | 0.994752i | \(-0.467375\pi\) | ||||
0.102314 | + | 0.994752i | \(0.467375\pi\) | |||||||
\(338\) | 11.7390 | + | 2.52683i | 0.0347308 | + | 0.00747582i | ||||
\(339\) | 9.41157 | − | 23.0904i | 0.0277627 | − | 0.0681133i | ||||
\(340\) | 144.413 | + | 382.081i | 0.424744 | + | 1.12377i | ||||
\(341\) | 30.1964 | − | 30.1964i | 0.0885525 | − | 0.0885525i | ||||
\(342\) | 43.5553 | − | 214.102i | 0.127355 | − | 0.626030i | ||||
\(343\) | 156.826i | 0.457219i | ||||||||
\(344\) | −217.233 | + | 32.6875i | −0.631490 | + | 0.0950217i | ||||
\(345\) | −399.181 | + | 168.000i | −1.15705 | + | 0.486957i | ||||
\(346\) | 97.0183 | − | 62.6497i | 0.280400 | − | 0.181068i | ||||
\(347\) | −54.0628 | + | 54.0628i | −0.155801 | + | 0.155801i | −0.780703 | − | 0.624902i | \(-0.785139\pi\) |
0.624902 | + | 0.780703i | \(0.285139\pi\) | |||||||
\(348\) | −4.67860 | + | 182.212i | −0.0134442 | + | 0.523598i | ||||
\(349\) | 0.107201 | − | 0.107201i | 0.000307168 | − | 0.000307168i | −0.706953 | − | 0.707260i | \(-0.749931\pi\) |
0.707260 | + | 0.706953i | \(0.249931\pi\) | |||||||
\(350\) | −37.4303 | + | 173.892i | −0.106944 | + | 0.496833i | ||||
\(351\) | 332.265 | + | 131.063i | 0.946625 | + | 0.373400i | ||||
\(352\) | −58.3320 | + | 206.996i | −0.165716 | + | 0.588057i | ||||
\(353\) | 194.223i | 0.550208i | 0.961414 | + | 0.275104i | \(0.0887123\pi\) | ||||
−0.961414 | + | 0.275104i | \(0.911288\pi\) | |||||||
\(354\) | −43.9693 | − | 233.220i | −0.124207 | − | 0.658813i | ||||
\(355\) | 255.749 | − | 255.749i | 0.720420 | − | 0.720420i | ||||
\(356\) | 287.304 | + | 129.694i | 0.807033 | + | 0.364308i | ||||
\(357\) | 52.5143 | + | 21.4047i | 0.147099 | + | 0.0599570i | ||||
\(358\) | −362.620 | + | 234.162i | −1.01290 | + | 0.654084i | ||||
\(359\) | 437.689 | 1.21919 | 0.609595 | − | 0.792713i | \(-0.291332\pi\) | ||||
0.609595 | + | 0.792713i | \(0.291332\pi\) | |||||||
\(360\) | −374.386 | + | 519.212i | −1.03996 | + | 1.44226i | ||||
\(361\) | 213.664i | 0.591867i | ||||||||
\(362\) | −395.858 | + | 255.626i | −1.09353 | + | 0.706148i | ||||
\(363\) | 85.8700 | − | 210.674i | 0.236556 | − | 0.580369i | ||||
\(364\) | 30.7895 | + | 81.4615i | 0.0845866 | + | 0.223795i | ||||
\(365\) | −371.159 | − | 371.159i | −1.01687 | − | 1.01687i | ||||
\(366\) | −61.6696 | − | 327.104i | −0.168496 | − | 0.893728i | ||||
\(367\) | −246.678 | −0.672148 | −0.336074 | − | 0.941836i | \(-0.609099\pi\) | ||||
−0.336074 | + | 0.941836i | \(0.609099\pi\) | |||||||
\(368\) | −171.848 | − | 194.857i | −0.466978 | − | 0.529503i | ||||
\(369\) | −12.7530 | − | 12.4674i | −0.0345608 | − | 0.0337870i | ||||
\(370\) | 144.081 | − | 669.365i | 0.389408 | − | 1.80909i | ||||
\(371\) | −6.59405 | − | 6.59405i | −0.0177737 | − | 0.0177737i | ||||
\(372\) | 52.5159 | + | 55.2838i | 0.141172 | + | 0.148612i | ||||
\(373\) | −349.678 | − | 349.678i | −0.937476 | − | 0.937476i | 0.0606816 | − | 0.998157i | \(-0.480673\pi\) |
−0.998157 | + | 0.0606816i | \(0.980673\pi\) | |||||||
\(374\) | −129.694 | + | 83.7498i | −0.346774 | + | 0.223930i | ||||
\(375\) | −300.454 | − | 713.903i | −0.801212 | − | 1.90374i | ||||
\(376\) | 482.332 | + | 356.162i | 1.28280 | + | 0.947240i | ||||
\(377\) | −200.938 | −0.532993 | ||||||||
\(378\) | 17.4526 | + | 87.1400i | 0.0461708 | + | 0.230529i | ||||
\(379\) | 235.668 | + | 235.668i | 0.621815 | + | 0.621815i | 0.945995 | − | 0.324180i | \(-0.105088\pi\) |
−0.324180 | + | 0.945995i | \(0.605088\pi\) | |||||||
\(380\) | −177.600 | + | 393.429i | −0.467369 | + | 1.03534i | ||||
\(381\) | 544.321 | + | 221.864i | 1.42866 | + | 0.582319i | ||||
\(382\) | 28.0445 | + | 6.03658i | 0.0734148 | + | 0.0158026i | ||||
\(383\) | 64.2130i | 0.167658i | 0.996480 | + | 0.0838290i | \(0.0267149\pi\) | ||||
−0.996480 | + | 0.0838290i | \(0.973285\pi\) | |||||||
\(384\) | −366.809 | − | 113.608i | −0.955233 | − | 0.295855i | ||||
\(385\) | −98.3320 | −0.255408 | ||||||||
\(386\) | −87.2751 | + | 405.458i | −0.226101 | + | 1.05041i | ||||
\(387\) | −2.79801 | − | 247.122i | −0.00723000 | − | 0.638559i | ||||
\(388\) | 141.579 | + | 63.9111i | 0.364895 | + | 0.164719i | ||||
\(389\) | −273.321 | + | 273.321i | −0.702624 | + | 0.702624i | −0.964973 | − | 0.262349i | \(-0.915503\pi\) |
0.262349 | + | 0.964973i | \(0.415503\pi\) | |||||||
\(390\) | −582.789 | − | 397.898i | −1.49433 | − | 1.02025i | ||||
\(391\) | − | 186.510i | − | 0.477007i | ||||||
\(392\) | 219.985 | − | 297.914i | 0.561185 | − | 0.759984i | ||||
\(393\) | 233.905 | + | 555.778i | 0.595179 | + | 1.41419i | ||||
\(394\) | 149.233 | + | 231.099i | 0.378763 | + | 0.586547i | ||||
\(395\) | −109.352 | + | 109.352i | −0.276842 | + | 0.276842i | ||||
\(396\) | −221.626 | − | 97.0405i | −0.559663 | − | 0.245052i | ||||
\(397\) | 141.678 | − | 141.678i | 0.356873 | − | 0.356873i | −0.505786 | − | 0.862659i | \(-0.668798\pi\) |
0.862659 | + | 0.505786i | \(0.168798\pi\) | |||||||
\(398\) | 161.828 | + | 34.8336i | 0.406603 | + | 0.0875215i | ||||
\(399\) | 23.2470 | + | 55.2368i | 0.0582633 | + | 0.138438i | ||||
\(400\) | 648.486 | − | 571.911i | 1.62122 | − | 1.42978i | ||||
\(401\) | 194.801i | 0.485788i | 0.970053 | + | 0.242894i | \(0.0780967\pi\) | ||||
−0.970053 | + | 0.242894i | \(0.921903\pi\) | |||||||
\(402\) | 107.978 | + | 572.733i | 0.268603 | + | 1.42471i | ||||
\(403\) | −59.4392 | + | 59.4392i | −0.147492 | + | 0.147492i | ||||
\(404\) | −219.773 | + | 83.0665i | −0.543993 | + | 0.205610i | ||||
\(405\) | −520.607 | − | 497.548i | −1.28545 | − | 1.22851i | ||||
\(406\) | −27.1216 | − | 42.0000i | −0.0668019 | − | 0.103448i | ||||
\(407\) | 258.791 | 0.635849 | ||||||||
\(408\) | −143.547 | − | 235.338i | −0.351831 | − | 0.576809i | ||||
\(409\) | − | 420.826i | − | 1.02891i | −0.857516 | − | 0.514457i | \(-0.827993\pi\) | ||
0.857516 | − | 0.514457i | \(-0.172007\pi\) | |||||||
\(410\) | 19.1143 | + | 29.6000i | 0.0466201 | + | 0.0721952i | ||||
\(411\) | −140.251 | − | 57.1659i | −0.341244 | − | 0.139090i | ||||
\(412\) | −162.620 | + | 360.243i | −0.394708 | + | 0.874376i | ||||
\(413\) | 46.0307 | + | 46.0307i | 0.111454 | + | 0.111454i | ||||
\(414\) | 243.730 | − | 161.328i | 0.588719 | − | 0.389681i | ||||
\(415\) | −944.737 | −2.27648 | ||||||||
\(416\) | 114.822 | − | 407.455i | 0.276014 | − | 0.979460i | ||||
\(417\) | −282.620 | − | 671.526i | −0.677745 | − | 1.61038i | ||||
\(418\) | −159.498 | − | 34.3320i | −0.381574 | − | 0.0821340i | ||||
\(419\) | 186.421 | + | 186.421i | 0.444919 | + | 0.444919i | 0.893661 | − | 0.448742i | \(-0.148128\pi\) |
−0.448742 | + | 0.893661i | \(0.648128\pi\) | |||||||
\(420\) | 4.50677 | − | 175.520i | 0.0107304 | − | 0.417905i | ||||
\(421\) | −186.889 | − | 186.889i | −0.443917 | − | 0.443917i | 0.449409 | − | 0.893326i | \(-0.351634\pi\) |
−0.893326 | + | 0.449409i | \(0.851634\pi\) | |||||||
\(422\) | −309.396 | − | 479.126i | −0.733167 | − | 1.13537i | ||||
\(423\) | −471.532 | + | 482.332i | −1.11473 | + | 1.14026i | ||||
\(424\) | 6.74508 | + | 44.8261i | 0.0159082 | + | 0.105722i | ||||
\(425\) | 620.706 | 1.46049 | ||||||||
\(426\) | −137.635 | + | 201.589i | −0.323086 | + | 0.473214i | ||||
\(427\) | 64.5608 | + | 64.5608i | 0.151196 | + | 0.151196i | ||||
\(428\) | −523.054 | + | 197.696i | −1.22209 | + | 0.461906i | ||||
\(429\) | 100.672 | − | 246.988i | 0.234666 | − | 0.575731i | ||||
\(430\) | −102.745 | + | 477.328i | −0.238942 | + | 1.11007i | ||||
\(431\) | 128.395i | 0.297901i | 0.988845 | + | 0.148950i | \(0.0475895\pi\) | ||||
−0.988845 | + | 0.148950i | \(0.952411\pi\) | |||||||
\(432\) | 183.372 | − | 391.150i | 0.424473 | − | 0.905440i | ||||
\(433\) | 684.737 | 1.58138 | 0.790690 | − | 0.612217i | \(-0.209722\pi\) | ||||
0.790690 | + | 0.612217i | \(0.209722\pi\) | |||||||
\(434\) | −20.4467 | − | 4.40116i | −0.0471122 | − | 0.0101409i | ||||
\(435\) | 375.155 | + | 152.912i | 0.862426 | + | 0.351522i | ||||
\(436\) | −364.332 | + | 137.705i | −0.835624 | + | 0.315836i | ||||
\(437\) | 139.372 | − | 139.372i | 0.318928 | − | 0.318928i | ||||
\(438\) | 292.559 | + | 199.744i | 0.667942 | + | 0.456036i | ||||
\(439\) | 239.107i | 0.544663i | 0.962203 | + | 0.272332i | \(0.0877948\pi\) | ||||
−0.962203 | + | 0.272332i | \(0.912205\pi\) | |||||||
\(440\) | 384.521 | + | 283.937i | 0.873911 | + | 0.645311i | ||||
\(441\) | 297.914 | + | 291.243i | 0.675541 | + | 0.660415i | ||||
\(442\) | 255.292 | − | 164.855i | 0.577583 | − | 0.372975i | ||||
\(443\) | −310.189 | + | 310.189i | −0.700200 | + | 0.700200i | −0.964453 | − | 0.264253i | \(-0.914875\pi\) |
0.264253 | + | 0.964453i | \(0.414875\pi\) | |||||||
\(444\) | −11.8609 | + | 461.935i | −0.0267138 | + | 1.04039i | ||||
\(445\) | 495.409 | − | 495.409i | 1.11328 | − | 1.11328i | ||||
\(446\) | −98.1707 | + | 456.077i | −0.220114 | + | 1.02259i | ||||
\(447\) | 330.413 | − | 139.058i | 0.739179 | − | 0.311092i | ||||
\(448\) | 100.664 | − | 30.9961i | 0.224697 | − | 0.0691876i | ||||
\(449\) | − | 545.902i | − | 1.21582i | −0.794007 | − | 0.607908i | \(-0.792009\pi\) | ||
0.794007 | − | 0.607908i | \(-0.207991\pi\) | |||||||
\(450\) | 536.901 | + | 811.135i | 1.19311 | + | 1.80252i | ||||
\(451\) | −9.41699 | + | 9.41699i | −0.0208803 | + | 0.0208803i | ||||
\(452\) | 13.6788 | − | 30.3020i | 0.0302629 | − | 0.0670399i | ||||
\(453\) | 34.0872 | − | 83.6297i | 0.0752477 | − | 0.184613i | ||||
\(454\) | −224.207 | + | 144.782i | −0.493847 | + | 0.318902i | ||||
\(455\) | 193.559 | 0.425404 | ||||||||
\(456\) | 68.5920 | − | 283.127i | 0.150421 | − | 0.620892i | ||||
\(457\) | 289.579i | 0.633652i | 0.948484 | + | 0.316826i | \(0.102617\pi\) | ||||
−0.948484 | + | 0.316826i | \(0.897383\pi\) | |||||||
\(458\) | 328.048 | − | 211.837i | 0.716262 | − | 0.462527i | ||||
\(459\) | 284.457 | − | 123.526i | 0.619732 | − | 0.269121i | ||||
\(460\) | −540.162 | + | 204.162i | −1.17427 | + | 0.443831i | ||||
\(461\) | −160.511 | − | 160.511i | −0.348180 | − | 0.348180i | 0.511251 | − | 0.859431i | \(-0.329182\pi\) |
−0.859431 | + | 0.511251i | \(0.829182\pi\) | |||||||
\(462\) | 65.2134 | − | 12.2948i | 0.141155 | − | 0.0266121i | ||||
\(463\) | −197.573 | −0.426723 | −0.213361 | − | 0.976973i | \(-0.568441\pi\) | ||||
−0.213361 | + | 0.976973i | \(0.568441\pi\) | |||||||
\(464\) | −15.2192 | + | 242.553i | −0.0328000 | + | 0.522743i | ||||
\(465\) | 156.207 | − | 65.7413i | 0.335928 | − | 0.141379i | ||||
\(466\) | −166.996 | + | 775.822i | −0.358361 | + | 1.66485i | ||||
\(467\) | −52.7645 | − | 52.7645i | −0.112986 | − | 0.112986i | 0.648353 | − | 0.761339i | \(-0.275458\pi\) |
−0.761339 | + | 0.648353i | \(0.775458\pi\) | |||||||
\(468\) | 436.254 | + | 191.017i | 0.932167 | + | 0.408155i | ||||
\(469\) | −113.041 | − | 113.041i | −0.241025 | − | 0.241025i | ||||
\(470\) | 1119.51 | − | 722.924i | 2.38193 | − | 1.53814i | ||||
\(471\) | 708.826 | − | 298.318i | 1.50494 | − | 0.633371i | ||||
\(472\) | −47.0850 | − | 312.915i | −0.0997563 | − | 0.662956i | ||||
\(473\) | −184.545 | −0.390159 | ||||||||
\(474\) | 58.8494 | − | 86.1949i | 0.124155 | − | 0.181846i | ||||
\(475\) | 463.830 | + | 463.830i | 0.976484 | + | 0.976484i | ||||
\(476\) | 68.9156 | + | 31.1096i | 0.144781 | + | 0.0653564i | ||||
\(477\) | −50.9938 | + | 0.577371i | −0.106905 | + | 0.00121042i | ||||
\(478\) | −556.871 | − | 119.867i | −1.16500 | − | 0.250767i | ||||
\(479\) | − | 175.985i | − | 0.367401i | −0.982982 | − | 0.183700i | \(-0.941192\pi\) | ||
0.982982 | − | 0.183700i | \(-0.0588076\pi\) | |||||||
\(480\) | −524.444 | + | 673.347i | −1.09259 | + | 1.40281i | ||||
\(481\) | −509.409 | −1.05906 | ||||||||
\(482\) | 112.172 | − | 521.125i | 0.232723 | − | 1.08117i | ||||
\(483\) | −30.2606 | + | 74.2414i | −0.0626513 | + | 0.153709i | ||||
\(484\) | 124.804 | − | 276.472i | 0.257859 | − | 0.571223i | ||||
\(485\) | 244.130 | − | 244.130i | 0.503362 | − | 0.503362i | ||||
\(486\) | 407.474 | + | 264.878i | 0.838425 | + | 0.545017i | ||||
\(487\) | − | 965.217i | − | 1.98196i | −0.133991 | − | 0.990982i | \(-0.542779\pi\) | ||
0.133991 | − | 0.990982i | \(-0.457221\pi\) | |||||||
\(488\) | −66.0395 | − | 438.882i | −0.135327 | − | 0.899348i | ||||
\(489\) | −782.404 | + | 329.284i | −1.60001 | + | 0.673382i | ||||
\(490\) | −446.516 | − | 691.468i | −0.911258 | − | 1.41116i | ||||
\(491\) | −600.614 | + | 600.614i | −1.22325 | + | 1.22325i | −0.256775 | + | 0.966471i | \(0.582660\pi\) |
−0.966471 | + | 0.256775i | \(0.917340\pi\) | |||||||
\(492\) | −16.3775 | − | 17.2407i | −0.0332876 | − | 0.0350421i | ||||
\(493\) | −123.365 | + | 123.365i | −0.250233 | + | 0.250233i | ||||
\(494\) | 313.959 | + | 67.5799i | 0.635545 | + | 0.136801i | ||||
\(495\) | −375.911 | + | 384.521i | −0.759416 | + | 0.776810i | ||||
\(496\) | 67.2470 | + | 76.2510i | 0.135579 | + | 0.153732i | ||||
\(497\) | − | 66.9527i | − | 0.134714i | ||||||
\(498\) | 626.546 | − | 118.124i | 1.25812 | − | 0.237197i | ||||
\(499\) | −51.6092 | + | 51.6092i | −0.103425 | + | 0.103425i | −0.756926 | − | 0.653501i | \(-0.773300\pi\) |
0.653501 | + | 0.756926i | \(0.273300\pi\) | |||||||
\(500\) | −365.127 | − | 966.036i | −0.730255 | − | 1.93207i | ||||
\(501\) | 479.653 | + | 195.505i | 0.957391 | + | 0.390230i | ||||
\(502\) | −236.207 | − | 365.786i | −0.470531 | − | 0.728657i | ||||
\(503\) | −847.530 | −1.68495 | −0.842475 | − | 0.538735i | \(-0.818902\pi\) | ||||
−0.842475 | + | 0.538735i | \(0.818902\pi\) | |||||||
\(504\) | 18.9570 | + | 116.968i | 0.0376132 | + | 0.232079i | ||||
\(505\) | 522.199i | 1.03406i | ||||||||
\(506\) | −118.400 | − | 183.353i | −0.233992 | − | 0.362357i | ||||
\(507\) | −6.79851 | + | 16.6795i | −0.0134093 | + | 0.0328984i | ||||
\(508\) | 714.324 | + | 322.458i | 1.40615 | + | 0.634759i | ||||
\(509\) | 128.457 | + | 128.457i | 0.252372 | + | 0.252372i | 0.821942 | − | 0.569570i | \(-0.192890\pi\) |
−0.569570 | + | 0.821942i | \(0.692890\pi\) | |||||||
\(510\) | −602.086 | + | 113.512i | −1.18056 | + | 0.222573i | ||||
\(511\) | −97.1660 | −0.190149 | ||||||||
\(512\) | −483.142 | − | 169.462i | −0.943637 | − | 0.330981i | ||||
\(513\) | 304.871 | + | 120.257i | 0.594290 | + | 0.234420i | ||||
\(514\) | 469.579 | + | 101.077i | 0.913578 | + | 0.196648i | ||||
\(515\) | 621.182 | + | 621.182i | 1.20618 | + | 1.20618i | ||||
\(516\) | 8.45811 | − | 329.409i | 0.0163917 | − | 0.638389i | ||||
\(517\) | 356.162 | + | 356.162i | 0.688901 | + | 0.688901i | ||||
\(518\) | −68.7572 | − | 106.476i | −0.132736 | − | 0.205553i | ||||
\(519\) | 67.1981 | + | 159.668i | 0.129476 | + | 0.307645i | ||||
\(520\) | −756.899 | − | 558.907i | −1.45558 | − | 1.07482i | ||||
\(521\) | −676.366 | −1.29821 | −0.649103 | − | 0.760700i | \(-0.724856\pi\) | ||||
−0.649103 | + | 0.760700i | \(0.724856\pi\) | |||||||
\(522\) | −267.921 | − | 54.5037i | −0.513258 | − | 0.104413i | ||||
\(523\) | −600.494 | − | 600.494i | −1.14817 | − | 1.14817i | −0.986912 | − | 0.161260i | \(-0.948444\pi\) |
−0.161260 | − | 0.986912i | \(-0.551556\pi\) | |||||||
\(524\) | 284.254 | + | 752.064i | 0.542469 | + | 1.43524i | ||||
\(525\) | −247.076 | − | 100.707i | −0.470621 | − | 0.191824i | ||||
\(526\) | 59.2183 | − | 275.114i | 0.112582 | − | 0.523030i | ||||
\(527\) | 72.9845i | 0.138491i | ||||||||
\(528\) | −290.514 | − | 140.228i | −0.550217 | − | 0.265583i | ||||
\(529\) | −265.324 | −0.501558 | ||||||||
\(530\) | 98.4970 | + | 21.2015i | 0.185843 | + | 0.0400029i | ||||
\(531\) | 355.970 | − | 4.03042i | 0.670376 | − | 0.00759025i | ||||
\(532\) | 28.2510 | + | 74.7451i | 0.0531034 | + | 0.140498i | ||||
\(533\) | 18.5366 | − | 18.5366i | 0.0347779 | − | 0.0347779i | ||||
\(534\) | −266.611 | + | 390.496i | −0.499271 | + | 0.731266i | ||||
\(535\) | 1242.82i | 2.32302i | ||||||||
\(536\) | 115.630 | + | 768.446i | 0.215727 | + | 1.43367i | ||||
\(537\) | −251.162 | − | 596.782i | −0.467714 | − | 1.11133i | ||||
\(538\) | 546.095 | − | 352.642i | 1.01505 | − | 0.655468i | ||||
\(539\) | 219.985 | − | 219.985i | 0.408135 | − | 0.408135i | ||||
\(540\) | −669.132 | − | 688.616i | −1.23913 | − | 1.27521i | ||||
\(541\) | 43.4797 | − | 43.4797i | 0.0803692 | − | 0.0803692i | −0.665779 | − | 0.746149i | \(-0.731901\pi\) |
0.746149 | + | 0.665779i | \(0.231901\pi\) | |||||||
\(542\) | −96.2639 | + | 447.218i | −0.177609 | + | 0.825126i | ||||
\(543\) | −274.184 | − | 651.484i | −0.504943 | − | 1.19979i | ||||
\(544\) | −179.660 | − | 320.648i | −0.330258 | − | 0.589427i | ||||
\(545\) | 865.682i | 1.58841i | ||||||||
\(546\) | −128.367 | + | 24.2014i | −0.235105 | + | 0.0443248i | ||||
\(547\) | −125.498 | + | 125.498i | −0.229430 | + | 0.229430i | −0.812454 | − | 0.583025i | \(-0.801869\pi\) |
0.583025 | + | 0.812454i | \(0.301869\pi\) | |||||||
\(548\) | −184.055 | − | 83.0852i | −0.335866 | − | 0.151615i | ||||
\(549\) | 499.269 | − | 5.65291i | 0.909414 | − | 0.0102967i | ||||
\(550\) | 610.199 | − | 394.037i | 1.10945 | − | 0.716430i | ||||
\(551\) | −184.371 | −0.334612 | ||||||||
\(552\) | 332.706 | − | 202.938i | 0.602729 | − | 0.367641i | ||||
\(553\) | 28.6275i | 0.0517676i | ||||||||
\(554\) | 245.367 | − | 158.446i | 0.442900 | − | 0.286003i | ||||
\(555\) | 951.074 | + | 387.655i | 1.71365 | + | 0.698477i | ||||
\(556\) | −343.454 | − | 908.693i | −0.617722 | − | 1.63434i | ||||
\(557\) | 184.272 | + | 184.272i | 0.330829 | + | 0.330829i | 0.852901 | − | 0.522072i | \(-0.174841\pi\) |
−0.522072 | + | 0.852901i | \(0.674841\pi\) | |||||||
\(558\) | −95.3757 | + | 63.1304i | −0.170924 | + | 0.113137i | ||||
\(559\) | 363.263 | 0.649844 | ||||||||
\(560\) | 14.6603 | − | 233.645i | 0.0261791 | − | 0.417223i | ||||
\(561\) | −89.8301 | − | 213.443i | −0.160125 | − | 0.380469i | ||||
\(562\) | −119.336 | + | 554.405i | −0.212342 | + | 0.986486i | ||||
\(563\) | −523.489 | − | 523.489i | −0.929820 | − | 0.929820i | 0.0678736 | − | 0.997694i | \(-0.478379\pi\) |
−0.997694 | + | 0.0678736i | \(0.978379\pi\) | |||||||
\(564\) | −652.064 | + | 619.417i | −1.15614 | + | 1.09826i | ||||
\(565\) | −52.2510 | − | 52.2510i | −0.0924796 | − | 0.0924796i | ||||
\(566\) | −55.7804 | + | 36.0202i | −0.0985519 | + | 0.0636400i | ||||
\(567\) | −133.272 | + | 3.01829i | −0.235047 | + | 0.00532326i | ||||
\(568\) | −193.328 | + | 261.814i | −0.340366 | + | 0.460941i | ||||
\(569\) | 52.6214 | 0.0924805 | 0.0462403 | − | 0.998930i | \(-0.485276\pi\) | ||||
0.0462403 | + | 0.998930i | \(0.485276\pi\) | |||||||
\(570\) | −534.739 | − | 365.092i | −0.938139 | − | 0.640513i | ||||
\(571\) | −114.561 | − | 114.561i | −0.200632 | − | 0.200632i | 0.599639 | − | 0.800271i | \(-0.295311\pi\) |
−0.800271 | + | 0.599639i | \(0.795311\pi\) | |||||||
\(572\) | 146.317 | − | 324.128i | 0.255798 | − | 0.566658i | ||||
\(573\) | −16.2416 | + | 39.8473i | −0.0283449 | + | 0.0695415i | ||||
\(574\) | 6.37648 | + | 1.37254i | 0.0111088 | + | 0.00239118i | ||||
\(575\) | 877.515i | 1.52611i | ||||||||
\(576\) | 263.618 | − | 512.134i | 0.457670 | − | 0.889122i | ||||
\(577\) | 496.442 | 0.860384 | 0.430192 | − | 0.902737i | \(-0.358446\pi\) | ||||
0.430192 | + | 0.902737i | \(0.358446\pi\) | |||||||
\(578\) | −66.1060 | + | 307.112i | −0.114370 | + | 0.531336i | ||||
\(579\) | −576.100 | − | 234.817i | −0.994992 | − | 0.405555i | ||||
\(580\) | 492.324 | + | 222.243i | 0.848835 | + | 0.383178i | ||||
\(581\) | −123.662 | + | 123.662i | −0.212843 | + | 0.212843i | ||||
\(582\) | −131.382 | + | 192.431i | −0.225742 | + | 0.330637i | ||||
\(583\) | 38.0810i | 0.0653191i | ||||||||
\(584\) | 379.961 | + | 280.570i | 0.650619 | + | 0.480428i | ||||
\(585\) | 739.951 | − | 756.899i | 1.26487 | − | 1.29384i | ||||
\(586\) | 585.217 | + | 906.257i | 0.998664 | + | 1.54651i | ||||
\(587\) | −115.260 | + | 115.260i | −0.196354 | + | 0.196354i | −0.798435 | − | 0.602081i | \(-0.794338\pi\) |
0.602081 | + | 0.798435i | \(0.294338\pi\) | |||||||
\(588\) | 382.585 | + | 402.749i | 0.650654 | + | 0.684948i | ||||
\(589\) | −54.5385 | + | 54.5385i | −0.0925952 | + | 0.0925952i | ||||
\(590\) | −687.572 | − | 148.000i | −1.16538 | − | 0.250848i | ||||
\(591\) | −380.332 | + | 160.067i | −0.643540 | + | 0.270841i | ||||
\(592\) | −38.5830 | + | 614.907i | −0.0651740 | + | 1.03869i | ||||
\(593\) | 227.756i | 0.384074i | 0.981388 | + | 0.192037i | \(0.0615094\pi\) | ||||
−0.981388 | + | 0.192037i | \(0.938491\pi\) | |||||||
\(594\) | 201.225 | − | 302.014i | 0.338762 | − | 0.508442i | ||||
\(595\) | 118.834 | − | 118.834i | 0.199721 | − | 0.199721i | ||||
\(596\) | 447.107 | − | 168.990i | 0.750179 | − | 0.283541i | ||||
\(597\) | −93.7209 | + | 229.935i | −0.156986 | + | 0.385151i | ||||
\(598\) | 233.061 | + | 360.915i | 0.389735 | + | 0.603537i | ||||
\(599\) | 760.308 | 1.26930 | 0.634648 | − | 0.772802i | \(-0.281145\pi\) | ||||
0.634648 | + | 0.772802i | \(0.281145\pi\) | |||||||
\(600\) | 675.379 | + | 1107.25i | 1.12563 | + | 1.84542i | ||||
\(601\) | 85.7856i | 0.142738i | 0.997450 | + | 0.0713690i | \(0.0227368\pi\) | ||||
−0.997450 | + | 0.0713690i | \(0.977263\pi\) | |||||||
\(602\) | 49.0312 | + | 75.9289i | 0.0814472 | + | 0.126128i | ||||
\(603\) | −874.177 | + | 9.89776i | −1.44971 | + | 0.0164142i | ||||
\(604\) | 49.5425 | − | 109.749i | 0.0820240 | − | 0.181704i | ||||
\(605\) | −476.731 | − | 476.731i | −0.787986 | − | 0.787986i | ||||
\(606\) | −65.2924 | − | 346.320i | −0.107743 | − | 0.571485i | ||||
\(607\) | 685.217 | 1.12886 | 0.564429 | − | 0.825482i | \(-0.309096\pi\) | ||||
0.564429 | + | 0.825482i | \(0.309096\pi\) | |||||||
\(608\) | 105.355 | − | 373.861i | 0.173281 | − | 0.614904i | ||||
\(609\) | 69.1216 | − | 29.0906i | 0.113500 | − | 0.0477678i | ||||
\(610\) | −964.361 | − | 207.579i | −1.58092 | − | 0.340294i | ||||
\(611\) | −701.077 | − | 701.077i | −1.14743 | − | 1.14743i | ||||
\(612\) | 385.108 | − | 150.562i | 0.629262 | − | 0.246016i | ||||
\(613\) | −544.727 | − | 544.727i | −0.888624 | − | 0.888624i | 0.105767 | − | 0.994391i | \(-0.466270\pi\) |
−0.994391 | + | 0.105767i | \(0.966270\pi\) | |||||||
\(614\) | −320.765 | − | 496.731i | −0.522418 | − | 0.809008i | ||||
\(615\) | −48.7143 | + | 20.5020i | −0.0792102 | + | 0.0333365i | ||||
\(616\) | 87.4980 | − | 13.1660i | 0.142042 | − | 0.0213734i | ||||
\(617\) | 383.577 | 0.621681 | 0.310840 | − | 0.950462i | \(-0.399390\pi\) | ||||
0.310840 | + | 0.950462i | \(0.399390\pi\) | |||||||
\(618\) | −489.634 | − | 334.297i | −0.792288 | − | 0.540933i | ||||
\(619\) | 81.7634 | + | 81.7634i | 0.132089 | + | 0.132089i | 0.770060 | − | 0.637971i | \(-0.220226\pi\) |
−0.637971 | + | 0.770060i | \(0.720226\pi\) | |||||||
\(620\) | 211.375 | − | 79.8921i | 0.340927 | − | 0.128858i | ||||
\(621\) | 174.634 | + | 402.148i | 0.281214 | + | 0.647581i | ||||
\(622\) | −46.7895 | + | 217.373i | −0.0752243 | + | 0.349474i | ||||
\(623\) | − | 129.694i | − | 0.208176i | ||||||
\(624\) | 571.855 | + | 276.027i | 0.916434 | + | 0.442351i | ||||
\(625\) | −944.365 | −1.51098 | ||||||||
\(626\) | 551.918 | + | 118.801i | 0.881658 | + | 0.189777i | ||||
\(627\) | 92.3715 | − | 226.625i | 0.147323 | − | 0.361443i | ||||
\(628\) | 959.166 | − | 362.531i | 1.52733 | − | 0.577278i | ||||
\(629\) | −312.748 | + | 312.748i | −0.497214 | + | 0.497214i | ||||
\(630\) | 258.081 | + | 52.5020i | 0.409652 | + | 0.0833365i | ||||
\(631\) | − | 944.242i | − | 1.49642i | −0.663461 | − | 0.748211i | \(-0.730913\pi\) | ||
0.663461 | − | 0.748211i | \(-0.269087\pi\) | |||||||
\(632\) | 82.6627 | − | 111.946i | 0.130795 | − | 0.177129i | ||||
\(633\) | 788.523 | − | 331.859i | 1.24569 | − | 0.524263i | ||||
\(634\) | −491.808 | + | 317.586i | −0.775722 | + | 0.500924i | ||||
\(635\) | 1231.74 | − | 1231.74i | 1.93974 | − | 1.93974i | ||||
\(636\) | −67.9737 | − | 1.74534i | −0.106877 | − | 0.00274424i | ||||
\(637\) | −433.022 | + | 433.022i | −0.679784 | + | 0.679784i | ||||
\(638\) | −42.9620 | + | 199.591i | −0.0673385 | + | 0.312838i | ||||
\(639\) | −261.814 | − | 255.952i | −0.409725 | − | 0.400551i | ||||
\(640\) | −731.984 | + | 871.320i | −1.14373 | + | 1.36144i | ||||
\(641\) | − | 1102.48i | − | 1.71994i | −0.510344 | − | 0.859970i | \(-0.670482\pi\) | ||
0.510344 | − | 0.859970i | \(-0.329518\pi\) | |||||||
\(642\) | −155.394 | − | 824.232i | −0.242047 | − | 1.28385i | ||||
\(643\) | 794.664 | − | 794.664i | 1.23587 | − | 1.23587i | 0.274195 | − | 0.961674i | \(-0.411588\pi\) |
0.961674 | − | 0.274195i | \(-0.0884115\pi\) | |||||||
\(644\) | −43.9808 | + | 97.4286i | −0.0682932 | + | 0.151287i | ||||
\(645\) | −678.217 | − | 276.439i | −1.05150 | − | 0.428588i | ||||
\(646\) | 234.243 | − | 151.263i | 0.362605 | − | 0.234153i | ||||
\(647\) | 768.446 | 1.18771 | 0.593853 | − | 0.804574i | \(-0.297606\pi\) | ||||
0.593853 | + | 0.804574i | \(0.297606\pi\) | |||||||
\(648\) | 529.866 | + | 373.023i | 0.817694 | + | 0.575653i | ||||
\(649\) | − | 265.830i | − | 0.409599i | ||||||
\(650\) | −1201.13 | + | 775.630i | −1.84789 | + | 1.19328i | ||||
\(651\) | 11.8415 | − | 29.0519i | 0.0181897 | − | 0.0446266i | ||||
\(652\) | −1058.73 | + | 400.162i | −1.62382 | + | 0.613746i | ||||
\(653\) | 829.478 | + | 829.478i | 1.27026 | + | 1.27026i | 0.945953 | + | 0.324305i | \(0.105130\pi\) |
0.324305 | + | 0.945953i | \(0.394870\pi\) | |||||||
\(654\) | −108.239 | − | 574.117i | −0.165503 | − | 0.877854i | ||||
\(655\) | 1786.96 | 2.72819 | ||||||||
\(656\) | −20.9715 | − | 23.7795i | −0.0319688 | − | 0.0362492i | ||||
\(657\) | −371.454 | + | 379.961i | −0.565378 | + | 0.578328i | ||||
\(658\) | 51.9111 | − | 241.166i | 0.0788922 | − | 0.366514i | ||||
\(659\) | 653.956 | + | 653.956i | 0.992346 | + | 0.992346i | 0.999971 | − | 0.00762509i | \(-0.00242716\pi\) |
−0.00762509 | + | 0.999971i | \(0.502427\pi\) | |||||||
\(660\) | −519.834 | + | 493.807i | −0.787627 | + | 0.748192i | ||||
\(661\) | 734.342 | + | 734.342i | 1.11096 | + | 1.11096i | 0.993021 | + | 0.117936i | \(0.0376276\pi\) |
0.117936 | + | 0.993021i | \(0.462372\pi\) | |||||||
\(662\) | −302.787 | + | 195.525i | −0.457382 | + | 0.295355i | ||||
\(663\) | 176.823 | + | 420.146i | 0.266702 | + | 0.633705i | ||||
\(664\) | 840.648 | − | 126.494i | 1.26604 | − | 0.190503i | ||||
\(665\) | 177.600 | 0.267068 | ||||||||
\(666\) | −679.219 | − | 138.175i | −1.01985 | − | 0.207470i | ||||
\(667\) | −174.405 | − | 174.405i | −0.261477 | − | 0.261477i | ||||
\(668\) | 629.459 | + | 284.148i | 0.942304 | + | 0.425371i | ||||
\(669\) | −648.022 | − | 264.132i | −0.968643 | − | 0.394816i | ||||
\(670\) | 1688.51 | + | 363.454i | 2.52017 | + | 0.542468i | ||||
\(671\) | − | 372.842i | − | 0.555652i | ||||||
\(672\) | 19.4908 | + | 156.785i | 0.0290041 | + | 0.233311i | ||||
\(673\) | 514.259 | 0.764129 | 0.382065 | − | 0.924136i | \(-0.375213\pi\) | ||||
0.382065 | + | 0.924136i | \(0.375213\pi\) | |||||||
\(674\) | −29.0224 | + | 134.831i | −0.0430599 | + | 0.200046i | ||||
\(675\) | −1338.35 | + | 581.183i | −1.98274 | + | 0.861012i | ||||
\(676\) | −9.88099 | + | 21.8889i | −0.0146168 | + | 0.0323800i | ||||
\(677\) | −662.519 | + | 662.519i | −0.978610 | + | 0.978610i | −0.999776 | − | 0.0211661i | \(-0.993262\pi\) |
0.0211661 | + | 0.999776i | \(0.493262\pi\) | |||||||
\(678\) | 41.1858 | + | 28.1195i | 0.0607460 | + | 0.0414742i | ||||
\(679\) | − | 63.9111i | − | 0.0941253i | ||||||
\(680\) | −807.829 | + | 121.556i | −1.18798 | + | 0.178758i | ||||
\(681\) | −155.293 | − | 368.988i | −0.228037 | − | 0.541833i | ||||
\(682\) | 46.3320 | + | 71.7490i | 0.0679355 | + | 0.105204i | ||||
\(683\) | 280.446 | − | 280.446i | 0.410608 | − | 0.410608i | −0.471342 | − | 0.881950i | \(-0.656230\pi\) |
0.881950 | + | 0.471342i | \(0.156230\pi\) | |||||||
\(684\) | 400.286 | + | 175.268i | 0.585213 | + | 0.256239i | ||||
\(685\) | −317.373 | + | 317.373i | −0.463318 | + | 0.463318i | ||||
\(686\) | −306.629 | − | 66.0021i | −0.446981 | − | 0.0962129i | ||||
\(687\) | 227.217 | + | 539.885i | 0.330738 | + | 0.785859i | ||||
\(688\) | 27.5138 | − | 438.494i | 0.0399910 | − | 0.637346i | ||||
\(689\) | − | 74.9595i | − | 0.108795i | ||||||
\(690\) | −160.477 | − | 851.191i | −0.232575 | − | 1.23361i | ||||
\(691\) | −631.830 | + | 631.830i | −0.914371 | + | 0.914371i | −0.996612 | − | 0.0822418i | \(-0.973792\pi\) |
0.0822418 | + | 0.996612i | \(0.473792\pi\) | |||||||
\(692\) | 81.6625 | + | 216.059i | 0.118009 | + | 0.312224i | ||||
\(693\) | 1.12700 | + | 99.5370i | 0.00162626 | + | 0.143632i | ||||
\(694\) | −82.9516 | − | 128.458i | −0.119527 | − | 0.185097i | ||||
\(695\) | −2159.13 | −3.10666 | ||||||||
\(696\) | −354.295 | − | 85.8337i | −0.509045 | − | 0.123324i | ||||
\(697\) | − | 22.7608i | − | 0.0326554i | ||||||
\(698\) | 0.164485 | + | 0.254719i | 0.000235652 | + | 0.000364927i | ||||
\(699\) | −1102.34 | − | 449.309i | −1.57702 | − | 0.642788i | ||||
\(700\) | −324.243 | − | 146.369i | −0.463204 | − | 0.209098i | ||||
\(701\) | −160.480 | − | 160.480i | −0.228930 | − | 0.228930i | 0.583315 | − | 0.812246i | \(-0.301755\pi\) |
−0.812246 | + | 0.583315i | \(0.801755\pi\) | |||||||
\(702\) | −396.095 | + | 594.491i | −0.564238 | + | 0.846854i | ||||
\(703\) | −467.409 | −0.664878 | ||||||||
\(704\) | −380.173 | − | 201.168i | −0.540018 | − | 0.285751i | ||||
\(705\) | 775.409 | + | 1842.43i | 1.09987 | + | 2.61338i | ||||
\(706\) | −379.749 | − | 81.7411i | −0.537888 | − | 0.115781i | ||||
\(707\) | 68.3534 | + | 68.3534i | 0.0966809 | + | 0.0966809i | ||||
\(708\) | 474.500 | + | 12.1836i | 0.670198 | + | 0.0172084i | ||||
\(709\) | −410.261 | − | 410.261i | −0.578648 | − | 0.578648i | 0.355883 | − | 0.934531i | \(-0.384180\pi\) |
−0.934531 | + | 0.355883i | \(0.884180\pi\) | |||||||
\(710\) | 392.410 | + | 607.680i | 0.552690 | + | 0.855887i | ||||
\(711\) | 111.946 | + | 109.439i | 0.157448 | + | 0.153923i | ||||
\(712\) | −374.494 | + | 507.158i | −0.525975 | + | 0.712301i | ||||
\(713\) | −103.181 | −0.144714 | ||||||||
\(714\) | −63.9520 | + | 93.6685i | −0.0895686 | + | 0.131188i | ||||
\(715\) | −558.907 | − | 558.907i | −0.781688 | − | 0.781688i | ||||
\(716\) | −305.225 | − | 807.550i | −0.426292 | − | 1.12786i | ||||
\(717\) | 322.505 | − | 791.236i | 0.449798 | − | 1.10354i | ||||
\(718\) | −184.207 | + | 855.778i | −0.256555 | + | 1.19189i | ||||
\(719\) | − | 1069.18i | − | 1.48704i | −0.668716 | − | 0.743518i | \(-0.733156\pi\) | ||
0.668716 | − | 0.743518i | \(-0.266844\pi\) | |||||||
\(720\) | −857.608 | − | 950.523i | −1.19112 | − | 1.32017i | ||||
\(721\) | 162.620 | 0.225547 | ||||||||
\(722\) | −417.760 | − | 89.9230i | −0.578615 | − | 0.124547i | ||||
\(723\) | 740.447 | + | 301.804i | 1.02413 | + | 0.417433i | ||||
\(724\) | −333.203 | − | 881.571i | −0.460225 | − | 1.21764i | ||||
\(725\) | 580.422 | − | 580.422i | 0.800582 | − | 0.800582i | ||||
\(726\) | 375.774 | + | 256.559i | 0.517595 | + | 0.353387i | ||||
\(727\) | − | 148.864i | − | 0.204765i | −0.994745 | − | 0.102382i | \(-0.967353\pi\) | ||
0.994745 | − | 0.102382i | \(-0.0326466\pi\) | |||||||
\(728\) | −172.233 | + | 25.9163i | −0.236584 | + | 0.0355993i | ||||
\(729\) | −497.678 | + | 532.689i | −0.682686 | + | 0.730712i | ||||
\(730\) | 881.903 | − | 569.490i | 1.20809 | − | 0.780124i | ||||
\(731\) | 223.022 | − | 223.022i | 0.305092 | − | 0.305092i | ||||
\(732\) | 665.515 | + | 17.0882i | 0.909173 | + | 0.0233445i | ||||
\(733\) | −690.136 | + | 690.136i | −0.941522 | + | 0.941522i | −0.998382 | − | 0.0568598i | \(-0.981891\pi\) |
0.0568598 | + | 0.998382i | \(0.481891\pi\) | |||||||
\(734\) | 103.817 | − | 482.310i | 0.141441 | − | 0.657098i | ||||
\(735\) | 1137.98 | − | 478.934i | 1.54828 | − | 0.651610i | ||||
\(736\) | 453.312 | − | 253.992i | 0.615913 | − | 0.345098i | ||||
\(737\) | 652.816i | 0.885775i | ||||||||
\(738\) | 29.7437 | − | 19.6877i | 0.0403031 | − | 0.0266772i | ||||
\(739\) | −535.593 | + | 535.593i | −0.724754 | + | 0.724754i | −0.969570 | − | 0.244815i | \(-0.921273\pi\) |
0.244815 | + | 0.969570i | \(0.421273\pi\) | |||||||
\(740\) | 1248.12 | + | 563.420i | 1.68664 | + | 0.761378i | ||||
\(741\) | −181.826 | + | 446.093i | −0.245379 | + | 0.602014i | ||||
\(742\) | 15.6680 | − | 10.1176i | 0.0211159 | − | 0.0136356i | ||||
\(743\) | −20.5116 | −0.0276065 | −0.0138032 | − | 0.999905i | \(-0.504394\pi\) | ||||
−0.0138032 | + | 0.999905i | \(0.504394\pi\) | |||||||
\(744\) | −130.194 | + | 79.4131i | −0.174992 | + | 0.106738i | ||||
\(745\) | − | 1062.36i | − | 1.42599i | ||||||
\(746\) | 830.863 | − | 536.531i | 1.11376 | − | 0.719211i | ||||
\(747\) | 10.8278 | + | 956.315i | 0.0144950 | + | 1.28021i | ||||
\(748\) | −109.166 | − | 288.826i | −0.145944 | − | 0.386131i | ||||
\(749\) | 162.679 | + | 162.679i | 0.217195 | + | 0.217195i | ||||
\(750\) | 1522.29 | − | 286.999i | 2.02971 | − | 0.382666i | ||||
\(751\) | −15.8000 | −0.0210385 | −0.0105193 | − | 0.999945i | \(-0.503348\pi\) | ||||
−0.0105193 | + | 0.999945i | \(0.503348\pi\) | |||||||
\(752\) | −899.369 | + | 793.169i | −1.19597 | + | 1.05475i | ||||
\(753\) | 601.992 | − | 253.355i | 0.799458 | − | 0.336461i | ||||
\(754\) | 84.5673 | − | 392.878i | 0.112158 | − | 0.521059i | ||||
\(755\) | −189.245 | − | 189.245i | −0.250655 | − | 0.250655i | ||||
\(756\) | −177.723 | − | 2.55034i | −0.235083 | − | 0.00337347i | ||||
\(757\) | 810.497 | + | 810.497i | 1.07067 | + | 1.07067i | 0.997305 | + | 0.0733640i | \(0.0233735\pi\) |
0.0733640 | + | 0.997305i | \(0.476627\pi\) | |||||||
\(758\) | −559.966 | + | 361.599i | −0.738741 | + | 0.477043i | ||||
\(759\) | 301.753 | − | 126.996i | 0.397566 | − | 0.167320i | ||||
\(760\) | −694.494 | − | 512.826i | −0.913808 | − | 0.674771i | ||||
\(761\) | −212.194 | −0.278836 | −0.139418 | − | 0.990234i | \(-0.544523\pi\) | ||||
−0.139418 | + | 0.990234i | \(0.544523\pi\) | |||||||
\(762\) | −662.875 | + | 970.892i | −0.869915 | + | 1.27414i | ||||
\(763\) | 113.314 | + | 113.314i | 0.148511 | + | 0.148511i | ||||
\(764\) | −23.6057 | + | 52.2924i | −0.0308975 | + | 0.0684456i | ||||
\(765\) | −10.4050 | − | 918.980i | −0.0136014 | − | 1.20128i | ||||
\(766\) | −125.550 | − | 27.0248i | −0.163904 | − | 0.0352804i | ||||
\(767\) | 523.266i | 0.682224i | ||||||||
\(768\) | 376.505 | − | 669.379i | 0.490241 | − | 0.871587i | ||||
\(769\) | −883.681 | −1.14913 | −0.574565 | − | 0.818459i | \(-0.694829\pi\) | ||||
−0.574565 | + | 0.818459i | \(0.694829\pi\) | |||||||
\(770\) | 41.3842 | − | 192.260i | 0.0537457 | − | 0.249689i | ||||
\(771\) | −271.951 | + | 667.207i | −0.352725 | + | 0.865378i | ||||
\(772\) | −756.029 | − | 341.284i | −0.979312 | − | 0.442077i | ||||
\(773\) | 515.805 | − | 515.805i | 0.667277 | − | 0.667277i | −0.289808 | − | 0.957085i | \(-0.593591\pi\) |
0.957085 | + | 0.289808i | \(0.0935914\pi\) | |||||||
\(774\) | 484.355 | + | 98.5335i | 0.625782 | + | 0.127304i | ||||
\(775\) | − | 343.387i | − | 0.443080i | ||||||
\(776\) | −184.545 | + | 249.920i | −0.237816 | + | 0.322062i | ||||
\(777\) | 175.233 | − | 73.7490i | 0.225526 | − | 0.0949151i | ||||
\(778\) | −419.371 | − | 649.431i | −0.539037 | − | 0.834745i | ||||
\(779\) | 17.0083 | − | 17.0083i | 0.0218335 | − | 0.0218335i | ||||
\(780\) | 1023.25 | − | 972.020i | 1.31186 | − | 1.24618i | ||||
\(781\) | −193.328 | + | 193.328i | −0.247539 | + | 0.247539i | ||||
\(782\) | 364.667 | + | 78.4948i | 0.466326 | + | 0.100377i | ||||
\(783\) | 150.486 | − | 381.505i | 0.192192 | − | 0.487235i | ||||
\(784\) | 489.903 | + | 555.498i | 0.624877 | + | 0.708543i | ||||
\(785\) | − | 2279.05i | − | 2.90325i | ||||||
\(786\) | −1185.11 | + | 223.431i | −1.50777 | + | 0.284263i | ||||
\(787\) | 279.150 | − | 279.150i | 0.354702 | − | 0.354702i | −0.507154 | − | 0.861856i | \(-0.669302\pi\) |
0.861856 | + | 0.507154i | \(0.169302\pi\) | |||||||
\(788\) | −514.656 | + | 194.522i | −0.653116 | + | 0.246855i | ||||
\(789\) | 390.898 | + | 159.329i | 0.495435 | + | 0.201938i | ||||
\(790\) | −167.786 | − | 259.830i | −0.212387 | − | 0.328899i | ||||
\(791\) | −13.6788 | −0.0172931 | ||||||||
\(792\) | 283.009 | − | 392.487i | 0.357335 | − | 0.495565i | ||||
\(793\) | 733.911i | 0.925487i | ||||||||
\(794\) | 217.385 | + | 336.639i | 0.273785 | + | 0.423979i | ||||
\(795\) | −57.0434 | + | 139.951i | −0.0717527 | + | 0.176038i | ||||
\(796\) | −136.214 | + | 301.749i | −0.171124 | + | 0.379082i | ||||
\(797\) | 409.431 | + | 409.431i | 0.513715 | + | 0.513715i | 0.915663 | − | 0.401947i | \(-0.131667\pi\) |
−0.401947 | + | 0.915663i | \(0.631667\pi\) | |||||||
\(798\) | −117.784 | + | 22.2060i | −0.147599 | + | 0.0278271i | ||||
\(799\) | −860.842 | −1.07740 | ||||||||
\(800\) | 845.288 | + | 1508.63i | 1.05661 | + | 1.88578i | ||||
\(801\) | −507.158 | − | 495.802i | −0.633156 | − | 0.618979i | ||||
\(802\) | −380.878 | − | 81.9843i | −0.474911 | − | 0.102225i | ||||
\(803\) | 280.570 | + | 280.570i | 0.349402 | + | 0.349402i | ||||
\(804\) | −1165.26 | − | 29.9200i | −1.44933 | − | 0.0372139i | ||||
\(805\) | 168.000 | + | 168.000i | 0.208696 | + | 0.208696i | ||||
\(806\) | −91.2009 | − | 141.232i | −0.113153 | − | 0.175226i | ||||
\(807\) | 378.244 | + | 898.737i | 0.468704 | + | 1.11368i | ||||
\(808\) | −69.9190 | − | 464.664i | −0.0865334 | − | 0.575079i | ||||
\(809\) | −285.148 | −0.352470 | −0.176235 | − | 0.984348i | \(-0.556392\pi\) | ||||
−0.176235 | + | 0.984348i | \(0.556392\pi\) | |||||||
\(810\) | 1191.92 | − | 808.500i | 1.47150 | − | 0.998149i | ||||
\(811\) | 819.150 | + | 819.150i | 1.01005 | + | 1.01005i | 0.999949 | + | 0.0101007i | \(0.00321519\pi\) |
0.0101007 | + | 0.999949i | \(0.496785\pi\) | |||||||
\(812\) | 93.5336 | − | 35.3524i | 0.115189 | − | 0.0435374i | ||||
\(813\) | −635.435 | − | 259.001i | −0.781593 | − | 0.318575i | ||||
\(814\) | −108.915 | + | 505.992i | −0.133802 | + | 0.621612i | ||||
\(815\) | 2515.62i | 3.08666i | ||||||||
\(816\) | 520.551 | − | 181.621i | 0.637930 | − | 0.222575i | ||||
\(817\) | 333.312 | 0.407971 | ||||||||
\(818\) | 822.807 | + | 177.109i | 1.00588 | + | 0.216515i | ||||
\(819\) | −2.21840 | − | 195.931i | −0.00270867 | − | 0.239232i | ||||
\(820\) | −65.9190 | + | 24.9150i | −0.0803890 | + | 0.0303842i | ||||
\(821\) | −116.499 | + | 116.499i | −0.141899 | + | 0.141899i | −0.774488 | − | 0.632589i | \(-0.781992\pi\) |
0.632589 | + | 0.774488i | \(0.281992\pi\) | |||||||
\(822\) | 170.798 | − | 250.162i | 0.207784 | − | 0.304334i | ||||
\(823\) | 1551.22i | 1.88484i | 0.334429 | + | 0.942421i | \(0.391457\pi\) | ||||
−0.334429 | + | 0.942421i | \(0.608543\pi\) | |||||||
\(824\) | −635.913 | − | 469.569i | −0.771739 | − | 0.569865i | ||||
\(825\) | 422.644 | + | 1004.24i | 0.512296 | + | 1.21725i | ||||
\(826\) | −109.373 | + | 70.6275i | −0.132412 | + | 0.0855054i | ||||
\(827\) | −139.847 | + | 139.847i | −0.169102 | + | 0.169102i | −0.786584 | − | 0.617483i | \(-0.788153\pi\) |
0.617483 | + | 0.786584i | \(0.288153\pi\) | |||||||
\(828\) | 212.855 | + | 544.442i | 0.257071 | + | 0.657538i | ||||
\(829\) | −454.593 | + | 454.593i | −0.548364 | + | 0.548364i | −0.925967 | − | 0.377604i | \(-0.876748\pi\) |
0.377604 | + | 0.925967i | \(0.376748\pi\) | |||||||
\(830\) | 397.603 | − | 1847.17i | 0.479040 | − | 2.22550i | ||||
\(831\) | 169.949 | + | 403.812i | 0.204512 | + | 0.485936i | ||||
\(832\) | 748.340 | + | 395.984i | 0.899447 | + | 0.475943i | ||||
\(833\) | 531.701i | 0.638297i | ||||||||
\(834\) | 1431.92 | − | 269.963i | 1.71694 | − | 0.323697i | ||||
\(835\) | 1085.40 | − | 1085.40i | 1.29988 | − | 1.29988i | ||||
\(836\) | 134.253 | − | 297.404i | 0.160590 | − | 0.355747i | ||||
\(837\) | −68.3372 | − | 157.367i | −0.0816455 | − | 0.188014i | ||||
\(838\) | −442.952 | + | 286.037i | −0.528582 | + | 0.341332i | ||||
\(839\) | −34.1596 | −0.0407147 | −0.0203574 | − | 0.999793i | \(-0.506480\pi\) | ||||
−0.0203574 | + | 0.999793i | \(0.506480\pi\) | |||||||
\(840\) | 341.284 | + | 82.6814i | 0.406290 | + | 0.0984303i | ||||
\(841\) | − | 610.284i | − | 0.725664i | ||||||
\(842\) | 444.063 | − | 286.754i | 0.527390 | − | 0.340563i | ||||
\(843\) | −787.733 | − | 321.077i | −0.934440 | − | 0.380875i | ||||
\(844\) | 1067.01 | − | 403.292i | 1.26423 | − | 0.477834i | ||||
\(845\) | 37.7438 | + | 37.7438i | 0.0446673 | + | 0.0446673i | ||||
\(846\) | −744.614 | − | 1124.94i | −0.880159 | − | 1.32972i | ||||
\(847\) | −124.804 | −0.147348 | ||||||||
\(848\) | −90.4836 | − | 5.67749i | −0.106702 | − | 0.00669515i | ||||
\(849\) | −38.6353 | − | 91.8006i | −0.0455069 | − | 0.108128i | ||||
\(850\) | −261.231 | + | 1213.62i | −0.307331 | + | 1.42778i | ||||
\(851\) | −442.143 | − | 442.143i | −0.519557 | − | 0.519557i | ||||
\(852\) | −336.225 | − | 353.947i | −0.394631 | − | 0.415430i | ||||
\(853\) | −514.933 | − | 514.933i | −0.603673 | − | 0.603673i | 0.337612 | − | 0.941285i | \(-0.390381\pi\) |
−0.941285 | + | 0.337612i | \(0.890381\pi\) | |||||||
\(854\) | −153.402 | + | 99.0592i | −0.179627 | + | 0.115994i | ||||
\(855\) | 678.944 | − | 694.494i | 0.794086 | − | 0.812274i | ||||
\(856\) | −166.405 | − | 1105.89i | −0.194399 | − | 1.29192i | ||||
\(857\) | 1165.96 | 1.36051 | 0.680254 | − | 0.732976i | \(-0.261869\pi\) | ||||
0.680254 | + | 0.732976i | \(0.261869\pi\) | |||||||
\(858\) | 440.547 | + | 300.783i | 0.513458 | + | 0.350563i | ||||
\(859\) | 246.162 | + | 246.162i | 0.286568 | + | 0.286568i | 0.835722 | − | 0.549153i | \(-0.185050\pi\) |
−0.549153 | + | 0.835722i | \(0.685050\pi\) | |||||||
\(860\) | −890.039 | − | 401.778i | −1.03493 | − | 0.467184i | ||||
\(861\) | −3.69286 | + | 9.06009i | −0.00428904 | + | 0.0105228i | ||||
\(862\) | −251.041 | − | 54.0366i | −0.291230 | − | 0.0626874i | ||||
\(863\) | 196.851i | 0.228101i | 0.993475 | + | 0.114050i | \(0.0363825\pi\) | ||||
−0.993475 | + | 0.114050i | \(0.963617\pi\) | |||||||
\(864\) | 687.609 | + | 523.153i | 0.795844 | + | 0.605501i | ||||
\(865\) | 513.373 | 0.593494 | ||||||||
\(866\) | −288.179 | + | 1338.81i | −0.332771 | + | 1.54597i | ||||
\(867\) | −436.364 | − | 177.861i | −0.503303 | − | 0.205145i | ||||
\(868\) | 17.2105 | − | 38.1255i | 0.0198277 | − | 0.0439234i | ||||
\(869\) | 82.6627 | − | 82.6627i | 0.0951239 | − | 0.0951239i | ||||
\(870\) | −456.865 | + | 669.155i | −0.525132 | + | 0.769144i | ||||
\(871\) | − | 1285.02i | − | 1.47534i | ||||||
\(872\) | −115.909 | − | 770.303i | −0.132923 | − | 0.883375i | ||||
\(873\) | −249.920 | − | 244.324i | −0.286277 | − | 0.279867i | ||||
\(874\) | 213.846 | + | 331.158i | 0.244675 | + | 0.378899i | ||||
\(875\) | −300.454 | + | 300.454i | −0.343376 | + | 0.343376i | ||||
\(876\) | −513.669 | + | 487.951i | −0.586381 | + | 0.557022i | ||||
\(877\) | 1123.93 | − | 1123.93i | 1.28156 | − | 1.28156i | 0.341782 | − | 0.939779i | \(-0.388969\pi\) |
0.939779 | − | 0.341782i | \(-0.111031\pi\) | |||||||
\(878\) | −467.507 | − | 100.631i | −0.532468 | − | 0.114614i | ||||
\(879\) | −1491.47 | + | 627.704i | −1.69679 | + | 0.714112i | ||||
\(880\) | −716.988 | + | 632.324i | −0.814759 | + | 0.718550i | ||||
\(881\) | − | 776.024i | − | 0.880845i | −0.897791 | − | 0.440422i | \(-0.854829\pi\) | ||
0.897791 | − | 0.440422i | \(-0.145171\pi\) | |||||||
\(882\) | −694.824 | + | 459.913i | −0.787782 | + | 0.521444i | ||||
\(883\) | −157.587 | + | 157.587i | −0.178468 | + | 0.178468i | −0.790688 | − | 0.612220i | \(-0.790277\pi\) |
0.612220 | + | 0.790688i | \(0.290277\pi\) | |||||||
\(884\) | 214.885 | + | 568.531i | 0.243082 | + | 0.643135i | ||||
\(885\) | 398.199 | − | 976.945i | 0.449943 | − | 1.10389i | ||||
\(886\) | −475.940 | − | 737.033i | −0.537178 | − | 0.831865i | ||||
\(887\) | 469.259 | 0.529040 | 0.264520 | − | 0.964380i | \(-0.414786\pi\) | ||||
0.264520 | + | 0.964380i | \(0.414786\pi\) | |||||||
\(888\) | −898.192 | − | 217.601i | −1.01148 | − | 0.245047i | ||||
\(889\) | − | 322.458i | − | 0.362719i | ||||||
\(890\) | 760.134 | + | 1177.13i | 0.854083 | + | 1.32262i | ||||
\(891\) | 393.542 | + | 376.111i | 0.441685 | + | 0.422122i | ||||
\(892\) | −850.413 | − | 383.890i | −0.953378 | − | 0.430370i | ||||
\(893\) | −643.274 | − | 643.274i | −0.720352 | − | 0.720352i | ||||
\(894\) | 132.831 | + | 704.554i | 0.148580 | + | 0.788091i | ||||
\(895\) | −1918.80 | −2.14391 | ||||||||
\(896\) | 18.2384 | + | 209.865i | 0.0203554 | + | 0.234224i | ||||
\(897\) | −593.976 | + | 249.982i | −0.662181 | + | 0.278686i | ||||
\(898\) | 1067.36 | + | 229.749i | 1.18859 | + | 0.255845i | ||||
\(899\) | 68.2478 | + | 68.2478i | 0.0759152 | + | 0.0759152i | ||||
\(900\) | −1811.91 | + | 708.383i | −2.01323 | + | 0.787092i | ||||
\(901\) | −46.0208 | − | 46.0208i | −0.0510775 | − | 0.0510775i | ||||
\(902\) | −14.4490 | − | 22.3755i | −0.0160189 | − | 0.0248066i | ||||
\(903\) | −124.960 | + | 52.5909i | −0.138383 | + | 0.0582402i | ||||
\(904\) | 53.4902 | + | 39.4980i | 0.0591705 | + | 0.0436925i | ||||
\(905\) | −2094.68 | −2.31457 | ||||||||
\(906\) | 149.168 | + | 101.844i | 0.164645 | + | 0.112411i | ||||
\(907\) | −684.081 | − | 684.081i | −0.754224 | − | 0.754224i | 0.221041 | − | 0.975265i | \(-0.429055\pi\) |
−0.975265 | + | 0.221041i | \(0.929055\pi\) | |||||||
\(908\) | −188.720 | − | 499.306i | −0.207841 | − | 0.549896i | ||||
\(909\) | 528.598 | − | 5.98498i | 0.581516 | − | 0.00658414i | ||||
\(910\) | −81.4615 | + | 378.450i | −0.0895181 | + | 0.415879i | ||||
\(911\) | − | 1109.61i | − | 1.21802i | −0.793164 | − | 0.609008i | \(-0.791568\pi\) | ||
0.793164 | − | 0.609008i | \(-0.208432\pi\) | |||||||
\(912\) | 524.706 | + | 253.269i | 0.575336 | + | 0.277708i | ||||
\(913\) | 714.154 | 0.782206 | ||||||||
\(914\) | −566.190 | − | 121.873i | −0.619464 | − | 0.133340i | ||||
\(915\) | 558.498 | − | 1370.22i | 0.610381 | − | 1.49751i | ||||
\(916\) | 276.125 | + | 730.559i | 0.301447 | + | 0.797554i | ||||
\(917\) | 233.905 | − | 233.905i | 0.255077 | − | 0.255077i | ||||
\(918\) | 121.804 | + | 608.163i | 0.132684 | + | 0.662487i | ||||
\(919\) | 740.861i | 0.806160i | 0.915165 | + | 0.403080i | \(0.132060\pi\) | ||||
−0.915165 | + | 0.403080i | \(0.867940\pi\) | |||||||
\(920\) | −171.848 | − | 1142.06i | −0.186791 | − | 1.24137i | ||||
\(921\) | 817.496 | − | 344.052i | 0.887617 | − | 0.373564i | ||||
\(922\) | 381.387 | − | 246.281i | 0.413652 | − | 0.267116i | ||||
\(923\) | 380.551 | − | 380.551i | 0.412298 | − | 0.412298i | ||||
\(924\) | −3.40680 | + | 132.681i | −0.00368701 | + | 0.143594i | ||||
\(925\) | 1471.46 | − | 1471.46i | 1.59076 | − | 1.59076i | ||||
\(926\) | 83.1507 | − | 386.297i | 0.0897956 | − | 0.417168i | ||||
\(927\) | 621.674 | − | 635.913i | 0.670630 | − | 0.685991i | ||||
\(928\) | −467.838 | − | 131.838i | −0.504136 | − | 0.142067i | ||||
\(929\) | 621.861i | 0.669388i | 0.942327 | + | 0.334694i | \(0.108633\pi\) | ||||
−0.942327 | + | 0.334694i | \(0.891367\pi\) | |||||||
\(930\) | 62.7972 | + | 333.086i | 0.0675239 | + | 0.358157i | ||||
\(931\) | −397.320 | + | 397.320i | −0.426767 | + | 0.426767i | ||||
\(932\) | −1446.62 | − | 653.027i | −1.55217 | − | 0.700673i | ||||
\(933\) | −308.856 | − | 125.889i | −0.331036 | − | 0.134929i | ||||
\(934\) | 125.373 | − | 80.9595i | 0.134232 | − | 0.0866804i | ||||
\(935\) | −686.274 | −0.733983 | ||||||||
\(936\) | −557.081 | + | 772.581i | −0.595172 | + | 0.825407i | ||||
\(937\) | 1036.08i | 1.10574i | 0.833267 | + | 0.552871i | \(0.186468\pi\) | ||||
−0.833267 | + | 0.552871i | \(0.813532\pi\) | |||||||
\(938\) | 268.593 | − | 173.444i | 0.286347 | − | 0.184909i | ||||
\(939\) | −319.637 | + | 784.199i | −0.340402 | + | 0.835143i | ||||
\(940\) | 942.316 | + | 2493.13i | 1.00246 | + | 2.65227i | ||||
\(941\) | 904.283 | + | 904.283i | 0.960980 | + | 0.960980i | 0.999267 | − | 0.0382864i | \(-0.0121899\pi\) |
−0.0382864 | + | 0.999267i | \(0.512190\pi\) | |||||||
\(942\) | 284.958 | + | 1511.46i | 0.302503 | + | 1.60452i | ||||
\(943\) | 32.1778 | 0.0341228 | ||||||||
\(944\) | 631.633 | + | 39.6325i | 0.669103 | + | 0.0419836i | ||||
\(945\) | −144.959 | + | 367.494i | −0.153396 | + | 0.388883i | ||||
\(946\) | 77.6680 | − | 360.826i | 0.0821015 | − | 0.381423i | ||||
\(947\) | 895.943 | + | 895.943i | 0.946085 | + | 0.946085i | 0.998619 | − | 0.0525337i | \(-0.0167297\pi\) |
−0.0525337 | + | 0.998619i | \(0.516730\pi\) | |||||||
\(948\) | 143.762 | + | 151.339i | 0.151648 | + | 0.159641i | ||||
\(949\) | −552.280 | − | 552.280i | −0.581960 | − | 0.581960i | ||||
\(950\) | −1102.10 | + | 711.680i | −1.16010 | + | 0.749137i | ||||
\(951\) | −340.642 | − | 809.393i | −0.358194 | − | 0.851097i | ||||
\(952\) | −89.8301 | + | 121.652i | −0.0943593 | + | 0.127786i | ||||
\(953\) | −1165.12 | −1.22259 | −0.611293 | − | 0.791405i | \(-0.709350\pi\) | ||||
−0.611293 | + | 0.791405i | \(0.709350\pi\) | |||||||
\(954\) | 20.3324 | − | 99.9470i | 0.0213128 | − | 0.104766i | ||||
\(955\) | 90.1699 | + | 90.1699i | 0.0944188 | + | 0.0944188i | ||||
\(956\) | 468.731 | − | 1038.36i | 0.490304 | − | 1.08615i | ||||
\(957\) | −283.591 | − | 115.591i | −0.296333 | − | 0.120784i | ||||
\(958\) | 344.089 | + | 74.0653i | 0.359174 | + | 0.0773124i | ||||
\(959\) | 83.0852i | 0.0866373i | ||||||||
\(960\) | −1095.82 | − | 1308.79i | −1.14148 | − | 1.36332i | ||||
\(961\) | −920.624 | −0.957985 | ||||||||
\(962\) | 214.391 | − | 996.006i | 0.222859 | − | 1.03535i | ||||
\(963\) | 1258.05 | − | 14.2441i | 1.30638 | − | 0.0147914i | ||||
\(964\) | 971.705 | + | 438.643i | 1.00799 | + | 0.455024i | ||||
\(965\) | −1303.65 | + | 1303.65i | −1.35093 | + | 1.35093i | ||||
\(966\) | −132.423 | − | 90.4113i | −0.137083 | − | 0.0935935i | ||||
\(967\) | − | 453.248i | − | 0.468716i | −0.972150 | − | 0.234358i | \(-0.924701\pi\) | ||
0.972150 | − | 0.234358i | \(-0.0752988\pi\) | |||||||
\(968\) | 488.038 | + | 360.375i | 0.504171 | + | 0.372288i | ||||
\(969\) | 162.245 | + | 385.506i | 0.167435 | + | 0.397839i | ||||
\(970\) | 374.583 | + | 580.073i | 0.386168 | + | 0.598014i | ||||
\(971\) | 678.155 | − | 678.155i | 0.698408 | − | 0.698408i | −0.265659 | − | 0.964067i | \(-0.585589\pi\) |
0.964067 | + | 0.265659i | \(0.0855894\pi\) | |||||||
\(972\) | −689.385 | + | 685.224i | −0.709244 | + | 0.704963i | ||||
\(973\) | −282.620 | + | 282.620i | −0.290462 | + | 0.290462i | ||||
\(974\) | 1887.21 | + | 406.223i | 1.93759 | + | 0.417066i | ||||
\(975\) | −831.941 | − | 1976.76i | −0.853273 | − | 2.02744i | ||||
\(976\) | 885.903 | + | 55.5869i | 0.907688 | + | 0.0569538i | ||||
\(977\) | 544.399i | 0.557215i | 0.960405 | + | 0.278607i | \(0.0898728\pi\) | ||||
−0.960405 | + | 0.278607i | \(0.910127\pi\) | |||||||
\(978\) | −314.537 | − | 1668.35i | −0.321613 | − | 1.70588i | ||||
\(979\) | −374.494 | + | 374.494i | −0.382527 | + | 0.382527i | ||||
\(980\) | 1539.89 | − | 582.024i | 1.57132 | − | 0.593902i | ||||
\(981\) | 876.290 | − | 9.92169i | 0.893262 | − | 0.0101138i | ||||
\(982\) | −921.555 | − | 1427.11i | −0.938448 | − | 1.45326i | ||||
\(983\) | 514.630 | 0.523530 | 0.261765 | − | 0.965132i | \(-0.415695\pi\) | ||||
0.261765 | + | 0.965132i | \(0.415695\pi\) | |||||||
\(984\) | 40.6020 | − | 24.7656i | 0.0412622 | − | 0.0251683i | ||||
\(985\) | 1222.86i | 1.24148i | ||||||||
\(986\) | −189.285 | − | 293.124i | −0.191973 | − | 0.297286i | ||||
\(987\) | 342.663 | + | 139.669i | 0.347177 | + | 0.141508i | ||||
\(988\) | −264.267 | + | 585.417i | −0.267476 | + | 0.592527i | ||||
\(989\) | 315.295 | + | 315.295i | 0.318802 | + | 0.318802i | ||||
\(990\) | −593.616 | − | 896.818i | −0.599612 | − | 0.905877i | ||||
\(991\) | 939.282 | 0.947813 | 0.473906 | − | 0.880575i | \(-0.342844\pi\) | ||||
0.473906 | + | 0.880575i | \(0.342844\pi\) | |||||||
\(992\) | −177.389 | + | 99.3915i | −0.178820 | + | 0.100193i | ||||
\(993\) | −209.720 | − | 498.312i | −0.211199 | − | 0.501825i | ||||
\(994\) | 130.907 | + | 28.1778i | 0.131697 | + | 0.0283479i | ||||
\(995\) | 520.318 | + | 520.318i | 0.522932 | + | 0.522932i | ||||
\(996\) | −32.7313 | + | 1274.75i | −0.0328627 | + | 1.27987i | ||||
\(997\) | 165.885 | + | 165.885i | 0.166384 | + | 0.166384i | 0.785388 | − | 0.619004i | \(-0.212463\pi\) |
−0.619004 | + | 0.785388i | \(0.712463\pi\) | |||||||
\(998\) | −79.1868 | − | 122.627i | −0.0793455 | − | 0.122873i | ||||
\(999\) | 381.505 | − | 967.172i | 0.381887 | − | 0.968141i |
(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 | 48.3.i.a.5.2 | ✓ | 8 | |
3.2 | odd | 2 | inner | 48.3.i.a.5.3 | yes | 8 | |
4.3 | odd | 2 | 192.3.i.a.113.4 | 8 | |||
8.3 | odd | 2 | 384.3.i.b.353.1 | 8 | |||
8.5 | even | 2 | 384.3.i.a.353.4 | 8 | |||
12.11 | even | 2 | 192.3.i.a.113.2 | 8 | |||
16.3 | odd | 4 | 192.3.i.a.17.2 | 8 | |||
16.5 | even | 4 | 384.3.i.a.161.2 | 8 | |||
16.11 | odd | 4 | 384.3.i.b.161.3 | 8 | |||
16.13 | even | 4 | inner | 48.3.i.a.29.3 | yes | 8 | |
24.5 | odd | 2 | 384.3.i.a.353.2 | 8 | |||
24.11 | even | 2 | 384.3.i.b.353.3 | 8 | |||
48.5 | odd | 4 | 384.3.i.a.161.4 | 8 | |||
48.11 | even | 4 | 384.3.i.b.161.1 | 8 | |||
48.29 | odd | 4 | inner | 48.3.i.a.29.2 | yes | 8 | |
48.35 | even | 4 | 192.3.i.a.17.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.3.i.a.5.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
48.3.i.a.5.3 | yes | 8 | 3.2 | odd | 2 | inner | |
48.3.i.a.29.2 | yes | 8 | 48.29 | odd | 4 | inner | |
48.3.i.a.29.3 | yes | 8 | 16.13 | even | 4 | inner | |
192.3.i.a.17.2 | 8 | 16.3 | odd | 4 | |||
192.3.i.a.17.4 | 8 | 48.35 | even | 4 | |||
192.3.i.a.113.2 | 8 | 12.11 | even | 2 | |||
192.3.i.a.113.4 | 8 | 4.3 | odd | 2 | |||
384.3.i.a.161.2 | 8 | 16.5 | even | 4 | |||
384.3.i.a.161.4 | 8 | 48.5 | odd | 4 | |||
384.3.i.a.353.2 | 8 | 24.5 | odd | 2 | |||
384.3.i.a.353.4 | 8 | 8.5 | even | 2 | |||
384.3.i.b.161.1 | 8 | 48.11 | even | 4 | |||
384.3.i.b.161.3 | 8 | 16.11 | odd | 4 | |||
384.3.i.b.353.1 | 8 | 8.3 | odd | 2 | |||
384.3.i.b.353.3 | 8 | 24.11 | even | 2 |