Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [280,2,Mod(141,280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("280.141");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 280 = 2^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 280.b (of order \(2\), degree \(1\), 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: | \(2.23581125660\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.18939904.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 141.1 | ||
Root | \(0.500000 + 0.0297061i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 280.141 |
Dual form | 280.2.b.c.141.2 |
$q$-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 \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).
\(n\) | \(57\) | \(71\) | \(141\) | \(241\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.874559 | − | 1.11137i | −0.618406 | − | 0.785858i | ||||
\(3\) | 2.41421i | 1.39385i | 0.717146 | + | 0.696923i | \(0.245448\pi\) | ||||
−0.717146 | + | 0.696923i | \(0.754552\pi\) | |||||||
\(4\) | −0.470294 | + | 1.94392i | −0.235147 | + | 0.971960i | ||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 2.68309 | − | 2.11137i | 1.09537 | − | 0.861964i | ||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.57172 | − | 1.17740i | 0.909239 | − | 0.416274i | ||||
\(9\) | −2.82843 | −0.942809 | ||||||||
\(10\) | 1.11137 | − | 0.874559i | 0.351447 | − | 0.276560i | ||||
\(11\) | 1.66981i | 0.503466i | 0.967797 | + | 0.251733i | \(0.0810005\pi\) | ||||
−0.967797 | + | 0.251733i | \(0.919000\pi\) | |||||||
\(12\) | −4.69304 | − | 1.13539i | −1.35476 | − | 0.327759i | ||||
\(13\) | − | 0.143434i | − | 0.0397814i | −0.999802 | − | 0.0198907i | \(-0.993668\pi\) | ||
0.999802 | − | 0.0198907i | \(-0.00633182\pi\) | |||||||
\(14\) | 0.874559 | + | 1.11137i | 0.233736 | + | 0.297027i | ||||
\(15\) | −2.41421 | −0.623347 | ||||||||
\(16\) | −3.55765 | − | 1.82843i | −0.889412 | − | 0.457107i | ||||
\(17\) | −6.03127 | −1.46280 | −0.731399 | − | 0.681949i | \(-0.761132\pi\) | ||||
−0.731399 | + | 0.681949i | \(0.761132\pi\) | |||||||
\(18\) | 2.47363 | + | 3.14343i | 0.583039 | + | 0.740914i | ||||
\(19\) | 6.64167i | 1.52370i | 0.647752 | + | 0.761852i | \(0.275709\pi\) | ||||
−0.647752 | + | 0.761852i | \(0.724291\pi\) | |||||||
\(20\) | −1.94392 | − | 0.470294i | −0.434674 | − | 0.105161i | ||||
\(21\) | − | 2.41421i | − | 0.526825i | ||||||
\(22\) | 1.85578 | − | 1.46035i | 0.395653 | − | 0.311347i | ||||
\(23\) | −5.30205 | −1.10555 | −0.552777 | − | 0.833329i | \(-0.686432\pi\) | ||||
−0.552777 | + | 0.833329i | \(0.686432\pi\) | |||||||
\(24\) | 2.84250 | + | 6.20867i | 0.580222 | + | 1.26734i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −0.159408 | + | 0.125441i | −0.0312625 | + | 0.0246010i | ||||
\(27\) | 0.414214i | 0.0797154i | ||||||||
\(28\) | 0.470294 | − | 1.94392i | 0.0888772 | − | 0.367366i | ||||
\(29\) | − | 3.67647i | − | 0.682704i | −0.939936 | − | 0.341352i | \(-0.889115\pi\) | ||
0.939936 | − | 0.341352i | \(-0.110885\pi\) | |||||||
\(30\) | 2.11137 | + | 2.68309i | 0.385482 | + | 0.489863i | ||||
\(31\) | 6.80029 | 1.22137 | 0.610684 | − | 0.791874i | \(-0.290895\pi\) | ||||
0.610684 | + | 0.791874i | \(0.290895\pi\) | |||||||
\(32\) | 1.07931 | + | 5.55294i | 0.190797 | + | 0.981630i | ||||
\(33\) | −4.03127 | −0.701755 | ||||||||
\(34\) | 5.27470 | + | 6.70299i | 0.904604 | + | 1.14955i | ||||
\(35\) | − | 1.00000i | − | 0.169031i | ||||||
\(36\) | 1.33019 | − | 5.49824i | 0.221699 | − | 0.916373i | ||||
\(37\) | − | 4.35480i | − | 0.715925i | −0.933736 | − | 0.357962i | \(-0.883472\pi\) | ||
0.933736 | − | 0.357962i | \(-0.116528\pi\) | |||||||
\(38\) | 7.38136 | − | 5.80853i | 1.19742 | − | 0.942268i | ||||
\(39\) | 0.346280 | 0.0554491 | ||||||||
\(40\) | 1.17740 | + | 2.57172i | 0.186163 | + | 0.406624i | ||||
\(41\) | 8.64167 | 1.34960 | 0.674801 | − | 0.738000i | \(-0.264229\pi\) | ||||
0.674801 | + | 0.738000i | \(0.264229\pi\) | |||||||
\(42\) | −2.68309 | + | 2.11137i | −0.414010 | + | 0.325792i | ||||
\(43\) | 8.80029i | 1.34203i | 0.741443 | + | 0.671016i | \(0.234142\pi\) | ||||
−0.741443 | + | 0.671016i | \(0.765858\pi\) | |||||||
\(44\) | −3.24597 | − | 0.785301i | −0.489349 | − | 0.118389i | ||||
\(45\) | − | 2.82843i | − | 0.421637i | ||||||
\(46\) | 4.63696 | + | 5.89255i | 0.683682 | + | 0.868809i | ||||
\(47\) | 7.13048 | 1.04009 | 0.520044 | − | 0.854140i | \(-0.325916\pi\) | ||||
0.520044 | + | 0.854140i | \(0.325916\pi\) | |||||||
\(48\) | 4.41421 | − | 8.58892i | 0.637137 | − | 1.23970i | ||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0.874559 | + | 1.11137i | 0.123681 | + | 0.157172i | ||||
\(51\) | − | 14.5608i | − | 2.03892i | ||||||
\(52\) | 0.278824 | + | 0.0674560i | 0.0386659 | + | 0.00935447i | ||||
\(53\) | − | 5.11529i | − | 0.702640i | −0.936255 | − | 0.351320i | \(-0.885733\pi\) | ||
0.936255 | − | 0.351320i | \(-0.114267\pi\) | |||||||
\(54\) | 0.460345 | − | 0.362254i | 0.0626450 | − | 0.0492965i | ||||
\(55\) | −1.66981 | −0.225157 | ||||||||
\(56\) | −2.57172 | + | 1.17740i | −0.343660 | + | 0.157337i | ||||
\(57\) | −16.0344 | −2.12381 | ||||||||
\(58\) | −4.08593 | + | 3.21529i | −0.536508 | + | 0.422188i | ||||
\(59\) | − | 8.40569i | − | 1.09433i | −0.837025 | − | 0.547164i | \(-0.815707\pi\) | ||
0.837025 | − | 0.547164i | \(-0.184293\pi\) | |||||||
\(60\) | 1.13539 | − | 4.69304i | 0.146578 | − | 0.605868i | ||||
\(61\) | 13.8664i | 1.77541i | 0.460417 | + | 0.887703i | \(0.347700\pi\) | ||||
−0.460417 | + | 0.887703i | \(0.652300\pi\) | |||||||
\(62\) | −5.94725 | − | 7.55765i | −0.755302 | − | 0.959822i | ||||
\(63\) | 2.82843 | 0.356348 | ||||||||
\(64\) | 5.22746 | − | 6.05588i | 0.653432 | − | 0.756985i | ||||
\(65\) | 0.143434 | 0.0177908 | ||||||||
\(66\) | 3.52559 | + | 4.48024i | 0.433970 | + | 0.551480i | ||||
\(67\) | 9.11529i | 1.11361i | 0.830643 | + | 0.556805i | \(0.187973\pi\) | ||||
−0.830643 | + | 0.556805i | \(0.812027\pi\) | |||||||
\(68\) | 2.83647 | − | 11.7243i | 0.343973 | − | 1.42178i | ||||
\(69\) | − | 12.8003i | − | 1.54097i | ||||||
\(70\) | −1.11137 | + | 0.874559i | −0.132834 | + | 0.104530i | ||||
\(71\) | −3.89450 | −0.462192 | −0.231096 | − | 0.972931i | \(-0.574231\pi\) | ||||
−0.231096 | + | 0.972931i | \(0.574231\pi\) | |||||||
\(72\) | −7.27391 | + | 3.33019i | −0.857239 | + | 0.392467i | ||||
\(73\) | −1.89450 | −0.221735 | −0.110867 | − | 0.993835i | \(-0.535363\pi\) | ||||
−0.110867 | + | 0.993835i | \(0.535363\pi\) | |||||||
\(74\) | −4.83980 | + | 3.80853i | −0.562616 | + | 0.442733i | ||||
\(75\) | − | 2.41421i | − | 0.278769i | ||||||
\(76\) | −12.9109 | − | 3.12354i | −1.48098 | − | 0.358294i | ||||
\(77\) | − | 1.66981i | − | 0.190292i | ||||||
\(78\) | −0.302842 | − | 0.384845i | −0.0342901 | − | 0.0435752i | ||||
\(79\) | 11.8351 | 1.33155 | 0.665776 | − | 0.746152i | \(-0.268101\pi\) | ||||
0.665776 | + | 0.746152i | \(0.268101\pi\) | |||||||
\(80\) | 1.82843 | − | 3.55765i | 0.204424 | − | 0.397757i | ||||
\(81\) | −9.48528 | −1.05392 | ||||||||
\(82\) | −7.55765 | − | 9.60411i | −0.834603 | − | 1.06060i | ||||
\(83\) | 1.77568i | 0.194906i | 0.995240 | + | 0.0974530i | \(0.0310696\pi\) | ||||
−0.995240 | + | 0.0974530i | \(0.968930\pi\) | |||||||
\(84\) | 4.69304 | + | 1.13539i | 0.512052 | + | 0.123881i | ||||
\(85\) | − | 6.03127i | − | 0.654183i | ||||||
\(86\) | 9.78039 | − | 7.69637i | 1.05465 | − | 0.829921i | ||||
\(87\) | 8.87579 | 0.951584 | ||||||||
\(88\) | 1.96603 | + | 4.29427i | 0.209580 | + | 0.457771i | ||||
\(89\) | 7.13401 | 0.756204 | 0.378102 | − | 0.925764i | \(-0.376577\pi\) | ||||
0.378102 | + | 0.925764i | \(0.376577\pi\) | |||||||
\(90\) | −3.14343 | + | 2.47363i | −0.331347 | + | 0.260743i | ||||
\(91\) | 0.143434i | 0.0150359i | ||||||||
\(92\) | 2.49352 | − | 10.3068i | 0.259968 | − | 1.07455i | ||||
\(93\) | 16.4173i | 1.70240i | ||||||||
\(94\) | −6.23602 | − | 7.92461i | −0.643197 | − | 0.817361i | ||||
\(95\) | −6.64167 | −0.681421 | ||||||||
\(96\) | −13.4060 | + | 2.60568i | −1.36824 | + | 0.265941i | ||||
\(97\) | 5.23322 | 0.531353 | 0.265676 | − | 0.964062i | \(-0.414405\pi\) | ||||
0.265676 | + | 0.964062i | \(0.414405\pi\) | |||||||
\(98\) | −0.874559 | − | 1.11137i | −0.0883438 | − | 0.112265i | ||||
\(99\) | − | 4.72293i | − | 0.474672i | ||||||
\(100\) | 0.470294 | − | 1.94392i | 0.0470294 | − | 0.194392i | ||||
\(101\) | 10.8628i | 1.08089i | 0.841379 | + | 0.540446i | \(0.181745\pi\) | ||||
−0.841379 | + | 0.540446i | \(0.818255\pi\) | |||||||
\(102\) | −16.1824 | + | 12.7343i | −1.60230 | + | 1.26088i | ||||
\(103\) | 12.1966 | 1.20176 | 0.600881 | − | 0.799338i | \(-0.294816\pi\) | ||||
0.600881 | + | 0.799338i | \(0.294816\pi\) | |||||||
\(104\) | −0.168879 | − | 0.368871i | −0.0165599 | − | 0.0361708i | ||||
\(105\) | 2.41421 | 0.235603 | ||||||||
\(106\) | −5.68499 | + | 4.47363i | −0.552175 | + | 0.434517i | ||||
\(107\) | − | 10.6533i | − | 1.02990i | −0.857221 | − | 0.514948i | \(-0.827811\pi\) | ||
0.857221 | − | 0.514948i | \(-0.172189\pi\) | |||||||
\(108\) | −0.805198 | − | 0.194802i | −0.0774802 | − | 0.0187448i | ||||
\(109\) | − | 0.927634i | − | 0.0888512i | −0.999013 | − | 0.0444256i | \(-0.985854\pi\) | ||
0.999013 | − | 0.0444256i | \(-0.0141458\pi\) | |||||||
\(110\) | 1.46035 | + | 1.85578i | 0.139238 | + | 0.176941i | ||||
\(111\) | 10.5134 | 0.997890 | ||||||||
\(112\) | 3.55765 | + | 1.82843i | 0.336166 | + | 0.172770i | ||||
\(113\) | 8.96833 | 0.843670 | 0.421835 | − | 0.906673i | \(-0.361386\pi\) | ||||
0.421835 | + | 0.906673i | \(0.361386\pi\) | |||||||
\(114\) | 14.0230 | + | 17.8202i | 1.31338 | + | 1.66901i | ||||
\(115\) | − | 5.30205i | − | 0.494419i | ||||||
\(116\) | 7.14677 | + | 1.72902i | 0.663561 | + | 0.160536i | ||||
\(117\) | 0.405692i | 0.0375062i | ||||||||
\(118\) | −9.34185 | + | 7.35127i | −0.859987 | + | 0.676739i | ||||
\(119\) | 6.03127 | 0.552886 | ||||||||
\(120\) | −6.20867 | + | 2.84250i | −0.566772 | + | 0.259483i | ||||
\(121\) | 8.21174 | 0.746522 | ||||||||
\(122\) | 15.4107 | − | 12.1270i | 1.39522 | − | 1.09792i | ||||
\(123\) | 20.8628i | 1.88114i | ||||||||
\(124\) | −3.19813 | + | 13.2192i | −0.287201 | + | 1.18712i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | −2.47363 | − | 3.14343i | −0.220368 | − | 0.280039i | ||||
\(127\) | 0.168043 | 0.0149114 | 0.00745571 | − | 0.999972i | \(-0.497627\pi\) | ||||
0.00745571 | + | 0.999972i | \(0.497627\pi\) | |||||||
\(128\) | −11.3021 | − | 0.513421i | −0.998970 | − | 0.0453804i | ||||
\(129\) | −21.2458 | −1.87059 | ||||||||
\(130\) | −0.125441 | − | 0.159408i | −0.0110019 | − | 0.0139810i | ||||
\(131\) | 14.7909i | 1.29228i | 0.763217 | + | 0.646142i | \(0.223619\pi\) | ||||
−0.763217 | + | 0.646142i | \(0.776381\pi\) | |||||||
\(132\) | 1.89588 | − | 7.83647i | 0.165015 | − | 0.682077i | ||||
\(133\) | − | 6.64167i | − | 0.575906i | ||||||
\(134\) | 10.1305 | − | 7.97186i | 0.875140 | − | 0.688664i | ||||
\(135\) | −0.414214 | −0.0356498 | ||||||||
\(136\) | −15.5107 | + | 7.10123i | −1.33003 | + | 0.608925i | ||||
\(137\) | −5.85304 | −0.500059 | −0.250029 | − | 0.968238i | \(-0.580440\pi\) | ||||
−0.250029 | + | 0.968238i | \(0.580440\pi\) | |||||||
\(138\) | −14.2259 | + | 11.1946i | −1.21099 | + | 0.952948i | ||||
\(139\) | − | 7.41921i | − | 0.629289i | −0.949210 | − | 0.314644i | \(-0.898115\pi\) | ||
0.949210 | − | 0.314644i | \(-0.101885\pi\) | |||||||
\(140\) | 1.94392 | + | 0.470294i | 0.164291 | + | 0.0397471i | ||||
\(141\) | 17.2145i | 1.44972i | ||||||||
\(142\) | 3.40597 | + | 4.32824i | 0.285823 | + | 0.363218i | ||||
\(143\) | 0.239507 | 0.0200286 | ||||||||
\(144\) | 10.0625 | + | 5.17157i | 0.838546 | + | 0.430964i | ||||
\(145\) | 3.67647 | 0.305314 | ||||||||
\(146\) | 1.65685 | + | 2.10550i | 0.137122 | + | 0.174252i | ||||
\(147\) | 2.41421i | 0.199121i | ||||||||
\(148\) | 8.46538 | + | 2.04804i | 0.695850 | + | 0.168348i | ||||
\(149\) | 7.16451i | 0.586940i | 0.955968 | + | 0.293470i | \(0.0948100\pi\) | ||||
−0.955968 | + | 0.293470i | \(0.905190\pi\) | |||||||
\(150\) | −2.68309 | + | 2.11137i | −0.219073 | + | 0.172393i | ||||
\(151\) | −19.8843 | −1.61816 | −0.809081 | − | 0.587697i | \(-0.800035\pi\) | ||||
−0.809081 | + | 0.587697i | \(0.800035\pi\) | |||||||
\(152\) | 7.81991 | + | 17.0805i | 0.634278 | + | 1.38541i | ||||
\(153\) | 17.0590 | 1.37914 | ||||||||
\(154\) | −1.85578 | + | 1.46035i | −0.149543 | + | 0.117678i | ||||
\(155\) | 6.80029i | 0.546212i | ||||||||
\(156\) | −0.162853 | + | 0.673140i | −0.0130387 | + | 0.0538943i | ||||
\(157\) | − | 4.77215i | − | 0.380859i | −0.981701 | − | 0.190429i | \(-0.939012\pi\) | ||
0.981701 | − | 0.190429i | \(-0.0609880\pi\) | |||||||
\(158\) | −10.3505 | − | 13.1532i | −0.823440 | − | 1.04641i | ||||
\(159\) | 12.3494 | 0.979372 | ||||||||
\(160\) | −5.55294 | + | 1.07931i | −0.438998 | + | 0.0853269i | ||||
\(161\) | 5.30205 | 0.417860 | ||||||||
\(162\) | 8.29544 | + | 10.5417i | 0.651751 | + | 0.828232i | ||||
\(163\) | 14.9043i | 1.16739i | 0.811971 | + | 0.583697i | \(0.198395\pi\) | ||||
−0.811971 | + | 0.583697i | \(0.801605\pi\) | |||||||
\(164\) | −4.06412 | + | 16.7987i | −0.317355 | + | 1.31176i | ||||
\(165\) | − | 4.03127i | − | 0.313834i | ||||||
\(166\) | 1.97344 | − | 1.55294i | 0.153169 | − | 0.120531i | ||||
\(167\) | −15.1930 | −1.17567 | −0.587836 | − | 0.808980i | \(-0.700020\pi\) | ||||
−0.587836 | + | 0.808980i | \(0.700020\pi\) | |||||||
\(168\) | −2.84250 | − | 6.20867i | −0.219303 | − | 0.479010i | ||||
\(169\) | 12.9794 | 0.998417 | ||||||||
\(170\) | −6.70299 | + | 5.27470i | −0.514096 | + | 0.404551i | ||||
\(171\) | − | 18.7855i | − | 1.43656i | ||||||
\(172\) | −17.1071 | − | 4.13872i | −1.30440 | − | 0.315575i | ||||
\(173\) | − | 17.2328i | − | 1.31019i | −0.755548 | − | 0.655094i | \(-0.772629\pi\) | ||
0.755548 | − | 0.655094i | \(-0.227371\pi\) | |||||||
\(174\) | −7.76240 | − | 9.86430i | −0.588466 | − | 0.747811i | ||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 3.05312 | − | 5.94059i | 0.230138 | − | 0.447789i | ||||
\(177\) | 20.2931 | 1.52533 | ||||||||
\(178\) | −6.23911 | − | 7.92854i | −0.467641 | − | 0.594269i | ||||
\(179\) | − | 17.4325i | − | 1.30297i | −0.758662 | − | 0.651484i | \(-0.774147\pi\) | ||
0.758662 | − | 0.651484i | \(-0.225853\pi\) | |||||||
\(180\) | 5.49824 | + | 1.33019i | 0.409814 | + | 0.0991467i | ||||
\(181\) | − | 4.22432i | − | 0.313991i | −0.987599 | − | 0.156996i | \(-0.949819\pi\) | ||
0.987599 | − | 0.156996i | \(-0.0501809\pi\) | |||||||
\(182\) | 0.159408 | − | 0.125441i | 0.0118161 | − | 0.00929832i | ||||
\(183\) | −33.4764 | −2.47464 | ||||||||
\(184\) | −13.6354 | + | 6.24264i | −1.00521 | + | 0.460214i | ||||
\(185\) | 4.35480 | 0.320171 | ||||||||
\(186\) | 18.2458 | − | 14.3579i | 1.33785 | − | 1.05277i | ||||
\(187\) | − | 10.0711i | − | 0.736469i | ||||||
\(188\) | −3.35342 | + | 13.8611i | −0.244573 | + | 1.01092i | ||||
\(189\) | − | 0.414214i | − | 0.0301296i | ||||||
\(190\) | 5.80853 | + | 7.38136i | 0.421395 | + | 0.535500i | ||||
\(191\) | −11.8976 | −0.860883 | −0.430441 | − | 0.902619i | \(-0.641642\pi\) | ||||
−0.430441 | + | 0.902619i | \(0.641642\pi\) | |||||||
\(192\) | 14.6202 | + | 12.6202i | 1.05512 | + | 0.910784i | ||||
\(193\) | 24.8495 | 1.78871 | 0.894353 | − | 0.447361i | \(-0.147636\pi\) | ||||
0.894353 | + | 0.447361i | \(0.147636\pi\) | |||||||
\(194\) | −4.57676 | − | 5.81605i | −0.328592 | − | 0.417568i | ||||
\(195\) | 0.346280i | 0.0247976i | ||||||||
\(196\) | −0.470294 | + | 1.94392i | −0.0335924 | + | 0.138851i | ||||
\(197\) | − | 4.39404i | − | 0.313062i | −0.987673 | − | 0.156531i | \(-0.949969\pi\) | ||
0.987673 | − | 0.156531i | \(-0.0500311\pi\) | |||||||
\(198\) | −5.24893 | + | 4.13048i | −0.373025 | + | 0.293540i | ||||
\(199\) | −20.1118 | −1.42569 | −0.712843 | − | 0.701324i | \(-0.752593\pi\) | ||||
−0.712843 | + | 0.701324i | \(0.752593\pi\) | |||||||
\(200\) | −2.57172 | + | 1.17740i | −0.181848 | + | 0.0832548i | ||||
\(201\) | −22.0063 | −1.55220 | ||||||||
\(202\) | 12.0726 | − | 9.50019i | 0.849428 | − | 0.668431i | ||||
\(203\) | 3.67647i | 0.258038i | ||||||||
\(204\) | 28.3050 | + | 6.84785i | 1.98175 | + | 0.479445i | ||||
\(205\) | 8.64167i | 0.603560i | ||||||||
\(206\) | −10.6666 | − | 13.5549i | −0.743178 | − | 0.944415i | ||||
\(207\) | 14.9965 | 1.04233 | ||||||||
\(208\) | −0.262258 | + | 0.510287i | −0.0181843 | + | 0.0353820i | ||||
\(209\) | −11.0903 | −0.767133 | ||||||||
\(210\) | −2.11137 | − | 2.68309i | −0.145698 | − | 0.185151i | ||||
\(211\) | − | 6.49824i | − | 0.447357i | −0.974663 | − | 0.223678i | \(-0.928193\pi\) | ||
0.974663 | − | 0.223678i | \(-0.0718066\pi\) | |||||||
\(212\) | 9.94372 | + | 2.40569i | 0.682938 | + | 0.165224i | ||||
\(213\) | − | 9.40216i | − | 0.644226i | ||||||
\(214\) | −11.8398 | + | 9.31696i | −0.809352 | + | 0.636894i | ||||
\(215\) | −8.80029 | −0.600175 | ||||||||
\(216\) | 0.487695 | + | 1.06524i | 0.0331835 | + | 0.0724804i | ||||
\(217\) | −6.80029 | −0.461634 | ||||||||
\(218\) | −1.03095 | + | 0.811271i | −0.0698245 | + | 0.0549462i | ||||
\(219\) | − | 4.57373i | − | 0.309064i | ||||||
\(220\) | 0.785301 | − | 3.24597i | 0.0529449 | − | 0.218843i | ||||
\(221\) | 0.865088i | 0.0581921i | ||||||||
\(222\) | −9.19460 | − | 11.6843i | −0.617101 | − | 0.784200i | ||||
\(223\) | 10.1036 | 0.676590 | 0.338295 | − | 0.941040i | \(-0.390150\pi\) | ||||
0.338295 | + | 0.941040i | \(0.390150\pi\) | |||||||
\(224\) | −1.07931 | − | 5.55294i | −0.0721144 | − | 0.371021i | ||||
\(225\) | 2.82843 | 0.188562 | ||||||||
\(226\) | −7.84333 | − | 9.96715i | −0.521731 | − | 0.663005i | ||||
\(227\) | 10.2954i | 0.683329i | 0.939822 | + | 0.341664i | \(0.110991\pi\) | ||||
−0.939822 | + | 0.341664i | \(0.889009\pi\) | |||||||
\(228\) | 7.54088 | − | 31.1696i | 0.499407 | − | 2.06426i | ||||
\(229\) | − | 27.3740i | − | 1.80893i | −0.426552 | − | 0.904463i | \(-0.640272\pi\) | ||
0.426552 | − | 0.904463i | \(-0.359728\pi\) | |||||||
\(230\) | −5.89255 | + | 4.63696i | −0.388543 | + | 0.305752i | ||||
\(231\) | 4.03127 | 0.265238 | ||||||||
\(232\) | −4.32868 | − | 9.45484i | −0.284192 | − | 0.620741i | ||||
\(233\) | 11.2574 | 0.737499 | 0.368749 | − | 0.929529i | \(-0.379786\pi\) | ||||
0.368749 | + | 0.929529i | \(0.379786\pi\) | |||||||
\(234\) | 0.450874 | − | 0.354801i | 0.0294746 | − | 0.0231941i | ||||
\(235\) | 7.13048i | 0.465141i | ||||||||
\(236\) | 16.3400 | + | 3.95315i | 1.06364 | + | 0.257328i | ||||
\(237\) | 28.5724i | 1.85598i | ||||||||
\(238\) | −5.27470 | − | 6.70299i | −0.341908 | − | 0.434490i | ||||
\(239\) | −28.7886 | −1.86218 | −0.931090 | − | 0.364789i | \(-0.881141\pi\) | ||||
−0.931090 | + | 0.364789i | \(0.881141\pi\) | |||||||
\(240\) | 8.58892 | + | 4.41421i | 0.554412 | + | 0.284936i | ||||
\(241\) | −28.7275 | −1.85050 | −0.925251 | − | 0.379355i | \(-0.876146\pi\) | ||||
−0.925251 | + | 0.379355i | \(0.876146\pi\) | |||||||
\(242\) | −7.18165 | − | 9.12630i | −0.461654 | − | 0.586661i | ||||
\(243\) | − | 21.6569i | − | 1.38929i | ||||||
\(244\) | −26.9551 | − | 6.52127i | −1.72562 | − | 0.417481i | ||||
\(245\) | 1.00000i | 0.0638877i | ||||||||
\(246\) | 23.1864 | − | 18.2458i | 1.47831 | − | 1.16331i | ||||
\(247\) | 0.952639 | 0.0606150 | ||||||||
\(248\) | 17.4884 | − | 8.00666i | 1.11052 | − | 0.508424i | ||||
\(249\) | −4.28687 | −0.271669 | ||||||||
\(250\) | −1.11137 | + | 0.874559i | −0.0702893 | + | 0.0553120i | ||||
\(251\) | − | 6.65332i | − | 0.419954i | −0.977706 | − | 0.209977i | \(-0.932661\pi\) | ||
0.977706 | − | 0.209977i | \(-0.0673389\pi\) | |||||||
\(252\) | −1.33019 | + | 5.49824i | −0.0837942 | + | 0.346356i | ||||
\(253\) | − | 8.85341i | − | 0.556609i | ||||||
\(254\) | −0.146964 | − | 0.186758i | −0.00922131 | − | 0.0117183i | ||||
\(255\) | 14.5608 | 0.911831 | ||||||||
\(256\) | 9.31371 | + | 13.0098i | 0.582107 | + | 0.813112i | ||||
\(257\) | 19.5702 | 1.22076 | 0.610378 | − | 0.792110i | \(-0.291018\pi\) | ||||
0.610378 | + | 0.792110i | \(0.291018\pi\) | |||||||
\(258\) | 18.5807 | + | 23.6120i | 1.15678 | + | 1.47002i | ||||
\(259\) | 4.35480i | 0.270594i | ||||||||
\(260\) | −0.0674560 | + | 0.278824i | −0.00418344 | + | 0.0172919i | ||||
\(261\) | 10.3986i | 0.643659i | ||||||||
\(262\) | 16.4381 | − | 12.9355i | 1.01555 | − | 0.799157i | ||||
\(263\) | 5.22079 | 0.321928 | 0.160964 | − | 0.986960i | \(-0.448540\pi\) | ||||
0.160964 | + | 0.986960i | \(0.448540\pi\) | |||||||
\(264\) | −10.3673 | + | 4.74642i | −0.638063 | + | 0.292122i | ||||
\(265\) | 5.11529 | 0.314230 | ||||||||
\(266\) | −7.38136 | + | 5.80853i | −0.452580 | + | 0.356144i | ||||
\(267\) | 17.2230i | 1.05403i | ||||||||
\(268\) | −17.7194 | − | 4.28687i | −1.08238 | − | 0.261862i | ||||
\(269\) | 16.7721i | 1.02262i | 0.859398 | + | 0.511308i | \(0.170839\pi\) | ||||
−0.859398 | + | 0.511308i | \(0.829161\pi\) | |||||||
\(270\) | 0.362254 | + | 0.460345i | 0.0220461 | + | 0.0280157i | ||||
\(271\) | 8.30795 | 0.504672 | 0.252336 | − | 0.967640i | \(-0.418801\pi\) | ||||
0.252336 | + | 0.967640i | \(0.418801\pi\) | |||||||
\(272\) | 21.4571 | + | 11.0277i | 1.30103 | + | 0.668655i | ||||
\(273\) | −0.346280 | −0.0209578 | ||||||||
\(274\) | 5.11882 | + | 6.50490i | 0.309239 | + | 0.392975i | ||||
\(275\) | − | 1.66981i | − | 0.100693i | ||||||
\(276\) | 24.8827 | + | 6.01990i | 1.49776 | + | 0.362355i | ||||
\(277\) | 5.88744i | 0.353742i | 0.984234 | + | 0.176871i | \(0.0565976\pi\) | ||||
−0.984234 | + | 0.176871i | \(0.943402\pi\) | |||||||
\(278\) | −8.24549 | + | 6.48853i | −0.494532 | + | 0.389156i | ||||
\(279\) | −19.2341 | −1.15152 | ||||||||
\(280\) | −1.17740 | − | 2.57172i | −0.0703631 | − | 0.153689i | ||||
\(281\) | 2.70607 | 0.161431 | 0.0807154 | − | 0.996737i | \(-0.474280\pi\) | ||||
0.0807154 | + | 0.996737i | \(0.474280\pi\) | |||||||
\(282\) | 19.1317 | − | 15.0551i | 1.13928 | − | 0.896518i | ||||
\(283\) | 22.5001i | 1.33749i | 0.743492 | + | 0.668745i | \(0.233168\pi\) | ||||
−0.743492 | + | 0.668745i | \(0.766832\pi\) | |||||||
\(284\) | 1.83156 | − | 7.57060i | 0.108683 | − | 0.449233i | ||||
\(285\) | − | 16.0344i | − | 0.949796i | ||||||
\(286\) | −0.209463 | − | 0.266181i | −0.0123858 | − | 0.0157396i | ||||
\(287\) | −8.64167 | −0.510102 | ||||||||
\(288\) | −3.05275 | − | 15.7061i | −0.179885 | − | 0.925489i | ||||
\(289\) | 19.3763 | 1.13978 | ||||||||
\(290\) | −3.21529 | − | 4.08593i | −0.188808 | − | 0.239934i | ||||
\(291\) | 12.6341i | 0.740624i | ||||||||
\(292\) | 0.890973 | − | 3.68276i | 0.0521403 | − | 0.215517i | ||||
\(293\) | 9.41344i | 0.549939i | 0.961453 | + | 0.274970i | \(0.0886678\pi\) | ||||
−0.961453 | + | 0.274970i | \(0.911332\pi\) | |||||||
\(294\) | 2.68309 | − | 2.11137i | 0.156481 | − | 0.123138i | ||||
\(295\) | 8.40569 | 0.489398 | ||||||||
\(296\) | −5.12735 | − | 11.1993i | −0.298021 | − | 0.650947i | ||||
\(297\) | −0.691657 | −0.0401340 | ||||||||
\(298\) | 7.96244 | − | 6.26579i | 0.461252 | − | 0.362967i | ||||
\(299\) | 0.760493i | 0.0439805i | ||||||||
\(300\) | 4.69304 | + | 1.13539i | 0.270953 | + | 0.0655518i | ||||
\(301\) | − | 8.80029i | − | 0.507240i | ||||||
\(302\) | 17.3900 | + | 22.0989i | 1.00068 | + | 1.27165i | ||||
\(303\) | −26.2252 | −1.50660 | ||||||||
\(304\) | 12.1438 | − | 23.6287i | 0.696495 | − | 1.35520i | ||||
\(305\) | −13.8664 | −0.793986 | ||||||||
\(306\) | −14.9191 | − | 18.9589i | −0.852869 | − | 1.08381i | ||||
\(307\) | − | 23.2185i | − | 1.32515i | −0.748995 | − | 0.662576i | \(-0.769463\pi\) | ||
0.748995 | − | 0.662576i | \(-0.230537\pi\) | |||||||
\(308\) | 3.24597 | + | 0.785301i | 0.184956 | + | 0.0447466i | ||||
\(309\) | 29.4451i | 1.67507i | ||||||||
\(310\) | 7.55765 | − | 5.94725i | 0.429246 | − | 0.337781i | ||||
\(311\) | 26.2517 | 1.48860 | 0.744298 | − | 0.667848i | \(-0.232784\pi\) | ||||
0.744298 | + | 0.667848i | \(0.232784\pi\) | |||||||
\(312\) | 0.890533 | − | 0.407710i | 0.0504165 | − | 0.0230820i | ||||
\(313\) | −8.25559 | −0.466634 | −0.233317 | − | 0.972401i | \(-0.574958\pi\) | ||||
−0.233317 | + | 0.972401i | \(0.574958\pi\) | |||||||
\(314\) | −5.30363 | + | 4.17352i | −0.299301 | + | 0.235526i | ||||
\(315\) | 2.82843i | 0.159364i | ||||||||
\(316\) | −5.56597 | + | 23.0065i | −0.313110 | + | 1.29421i | ||||
\(317\) | 28.1610i | 1.58168i | 0.612024 | + | 0.790839i | \(0.290356\pi\) | ||||
−0.612024 | + | 0.790839i | \(0.709644\pi\) | |||||||
\(318\) | −10.8003 | − | 13.7248i | −0.605650 | − | 0.769648i | ||||
\(319\) | 6.13900 | 0.343718 | ||||||||
\(320\) | 6.05588 | + | 5.22746i | 0.338534 | + | 0.292224i | ||||
\(321\) | 25.7194 | 1.43552 | ||||||||
\(322\) | −4.63696 | − | 5.89255i | −0.258408 | − | 0.328379i | ||||
\(323\) | − | 40.0577i | − | 2.22887i | ||||||
\(324\) | 4.46087 | − | 18.4386i | 0.247826 | − | 1.02437i | ||||
\(325\) | 0.143434i | 0.00795627i | ||||||||
\(326\) | 16.5642 | − | 13.0347i | 0.917407 | − | 0.721925i | ||||
\(327\) | 2.23951 | 0.123845 | ||||||||
\(328\) | 22.2239 | − | 10.1747i | 1.22711 | − | 0.561804i | ||||
\(329\) | −7.13048 | −0.393116 | ||||||||
\(330\) | −4.48024 | + | 3.52559i | −0.246629 | + | 0.194077i | ||||
\(331\) | − | 19.9670i | − | 1.09749i | −0.835991 | − | 0.548744i | \(-0.815106\pi\) | ||
0.835991 | − | 0.548744i | \(-0.184894\pi\) | |||||||
\(332\) | −3.45178 | − | 0.835091i | −0.189441 | − | 0.0458316i | ||||
\(333\) | 12.3172i | 0.674981i | ||||||||
\(334\) | 13.2872 | + | 16.8851i | 0.727043 | + | 0.923911i | ||||
\(335\) | −9.11529 | −0.498022 | ||||||||
\(336\) | −4.41421 | + | 8.58892i | −0.240815 | + | 0.468564i | ||||
\(337\) | −33.2896 | −1.81340 | −0.906700 | − | 0.421776i | \(-0.861407\pi\) | ||||
−0.906700 | + | 0.421776i | \(0.861407\pi\) | |||||||
\(338\) | −11.3513 | − | 14.4250i | −0.617428 | − | 0.784615i | ||||
\(339\) | 21.6515i | 1.17595i | ||||||||
\(340\) | 11.7243 | + | 2.83647i | 0.635840 | + | 0.153829i | ||||
\(341\) | 11.3552i | 0.614917i | ||||||||
\(342\) | −20.8776 | + | 16.4290i | −1.12893 | + | 0.888379i | ||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 10.3615 | + | 22.6318i | 0.558653 | + | 1.22023i | ||||
\(345\) | 12.8003 | 0.689144 | ||||||||
\(346\) | −19.1521 | + | 15.0711i | −1.02962 | + | 0.810228i | ||||
\(347\) | − | 27.1005i | − | 1.45483i | −0.686198 | − | 0.727415i | \(-0.740722\pi\) | ||
0.686198 | − | 0.727415i | \(-0.259278\pi\) | |||||||
\(348\) | −4.17423 | + | 17.2538i | −0.223762 | + | 0.924902i | ||||
\(349\) | 4.55266i | 0.243698i | 0.992549 | + | 0.121849i | \(0.0388824\pi\) | ||||
−0.992549 | + | 0.121849i | \(0.961118\pi\) | |||||||
\(350\) | −0.874559 | − | 1.11137i | −0.0467471 | − | 0.0594053i | ||||
\(351\) | 0.0594122 | 0.00317119 | ||||||||
\(352\) | −9.27234 | + | 1.80224i | −0.494217 | + | 0.0960597i | ||||
\(353\) | 8.85970 | 0.471554 | 0.235777 | − | 0.971807i | \(-0.424236\pi\) | ||||
0.235777 | + | 0.971807i | \(0.424236\pi\) | |||||||
\(354\) | −17.7475 | − | 22.5532i | −0.943271 | − | 1.19869i | ||||
\(355\) | − | 3.89450i | − | 0.206699i | ||||||
\(356\) | −3.35508 | + | 13.8679i | −0.177819 | + | 0.734999i | ||||
\(357\) | 14.5608i | 0.770638i | ||||||||
\(358\) | −19.3740 | + | 15.2458i | −1.02395 | + | 0.805764i | ||||
\(359\) | −21.9804 | −1.16008 | −0.580040 | − | 0.814588i | \(-0.696963\pi\) | ||||
−0.580040 | + | 0.814588i | \(0.696963\pi\) | |||||||
\(360\) | −3.33019 | − | 7.27391i | −0.175517 | − | 0.383369i | ||||
\(361\) | −25.1118 | −1.32167 | ||||||||
\(362\) | −4.69479 | + | 3.69442i | −0.246753 | + | 0.194174i | ||||
\(363\) | 19.8249i | 1.04054i | ||||||||
\(364\) | −0.278824 | − | 0.0674560i | −0.0146143 | − | 0.00353566i | ||||
\(365\) | − | 1.89450i | − | 0.0991628i | ||||||
\(366\) | 29.2770 | + | 37.2047i | 1.53034 | + | 1.94472i | ||||
\(367\) | −5.77754 | −0.301585 | −0.150792 | − | 0.988565i | \(-0.548183\pi\) | ||||
−0.150792 | + | 0.988565i | \(0.548183\pi\) | |||||||
\(368\) | 18.8628 | + | 9.69442i | 0.983293 | + | 0.505356i | ||||
\(369\) | −24.4423 | −1.27242 | ||||||||
\(370\) | −3.80853 | − | 4.83980i | −0.197996 | − | 0.251609i | ||||
\(371\) | 5.11529i | 0.265573i | ||||||||
\(372\) | −31.9140 | − | 7.72098i | −1.65466 | − | 0.400314i | ||||
\(373\) | − | 18.9285i | − | 0.980082i | −0.871699 | − | 0.490041i | \(-0.836982\pi\) | ||
0.871699 | − | 0.490041i | \(-0.163018\pi\) | |||||||
\(374\) | −11.1927 | + | 8.80774i | −0.578761 | + | 0.455437i | ||||
\(375\) | 2.41421 | 0.124669 | ||||||||
\(376\) | 18.3376 | − | 8.39543i | 0.945688 | − | 0.432961i | ||||
\(377\) | −0.527330 | −0.0271589 | ||||||||
\(378\) | −0.460345 | + | 0.362254i | −0.0236776 | + | 0.0186323i | ||||
\(379\) | − | 5.11529i | − | 0.262755i | −0.991332 | − | 0.131378i | \(-0.958060\pi\) | ||
0.991332 | − | 0.131378i | \(-0.0419400\pi\) | |||||||
\(380\) | 3.12354 | − | 12.9109i | 0.160234 | − | 0.662314i | ||||
\(381\) | 0.405692i | 0.0207842i | ||||||||
\(382\) | 10.4052 | + | 13.2227i | 0.532375 | + | 0.676532i | ||||
\(383\) | −19.6927 | −1.00625 | −0.503126 | − | 0.864213i | \(-0.667817\pi\) | ||||
−0.503126 | + | 0.864213i | \(0.667817\pi\) | |||||||
\(384\) | 1.23951 | − | 27.2856i | 0.0632533 | − | 1.39241i | ||||
\(385\) | 1.66981 | 0.0851013 | ||||||||
\(386\) | −21.7324 | − | 27.6170i | −1.10615 | − | 1.40567i | ||||
\(387\) | − | 24.8910i | − | 1.26528i | ||||||
\(388\) | −2.46115 | + | 10.1730i | −0.124946 | + | 0.516453i | ||||
\(389\) | − | 9.25745i | − | 0.469371i | −0.972071 | − | 0.234686i | \(-0.924594\pi\) | ||
0.972071 | − | 0.234686i | \(-0.0754061\pi\) | |||||||
\(390\) | 0.384845 | − | 0.302842i | 0.0194874 | − | 0.0153350i | ||||
\(391\) | 31.9781 | 1.61720 | ||||||||
\(392\) | 2.57172 | − | 1.17740i | 0.129891 | − | 0.0594677i | ||||
\(393\) | −35.7083 | −1.80125 | ||||||||
\(394\) | −4.88341 | + | 3.84284i | −0.246023 | + | 0.193600i | ||||
\(395\) | 11.8351i | 0.595488i | ||||||||
\(396\) | 9.18100 | + | 2.22117i | 0.461362 | + | 0.111618i | ||||
\(397\) | 16.1871i | 0.812409i | 0.913782 | + | 0.406204i | \(0.133148\pi\) | ||||
−0.913782 | + | 0.406204i | \(0.866852\pi\) | |||||||
\(398\) | 17.5889 | + | 22.3516i | 0.881653 | + | 1.12039i | ||||
\(399\) | 16.0344 | 0.802724 | ||||||||
\(400\) | 3.55765 | + | 1.82843i | 0.177882 | + | 0.0914214i | ||||
\(401\) | −29.1914 | −1.45775 | −0.728873 | − | 0.684649i | \(-0.759956\pi\) | ||||
−0.728873 | + | 0.684649i | \(0.759956\pi\) | |||||||
\(402\) | 19.2458 | + | 24.4571i | 0.959892 | + | 1.21981i | ||||
\(403\) | − | 0.975391i | − | 0.0485877i | ||||||
\(404\) | −21.1165 | − | 5.10872i | −1.05058 | − | 0.254169i | ||||
\(405\) | − | 9.48528i | − | 0.471327i | ||||||
\(406\) | 4.08593 | − | 3.21529i | 0.202781 | − | 0.159572i | ||||
\(407\) | 7.27168 | 0.360444 | ||||||||
\(408\) | −17.1439 | − | 37.4462i | −0.848748 | − | 1.85386i | ||||
\(409\) | 16.5908 | 0.820361 | 0.410181 | − | 0.912004i | \(-0.365466\pi\) | ||||
0.410181 | + | 0.912004i | \(0.365466\pi\) | |||||||
\(410\) | 9.60411 | − | 7.55765i | 0.474313 | − | 0.373246i | ||||
\(411\) | − | 14.1305i | − | 0.697005i | ||||||
\(412\) | −5.73597 | + | 23.7091i | −0.282591 | + | 1.16806i | ||||
\(413\) | 8.40569i | 0.413617i | ||||||||
\(414\) | −13.1153 | − | 16.6667i | −0.644582 | − | 0.819121i | ||||
\(415\) | −1.77568 | −0.0871646 | ||||||||
\(416\) | 0.796478 | − | 0.154809i | 0.0390506 | − | 0.00759016i | ||||
\(417\) | 17.9115 | 0.877132 | ||||||||
\(418\) | 9.69913 | + | 12.3255i | 0.474400 | + | 0.602858i | ||||
\(419\) | − | 8.11176i | − | 0.396286i | −0.980173 | − | 0.198143i | \(-0.936509\pi\) | ||
0.980173 | − | 0.198143i | \(-0.0634910\pi\) | |||||||
\(420\) | −1.13539 | + | 4.69304i | −0.0554014 | + | 0.228997i | ||||
\(421\) | − | 33.1886i | − | 1.61751i | −0.588144 | − | 0.808757i | \(-0.700141\pi\) | ||
0.588144 | − | 0.808757i | \(-0.299859\pi\) | |||||||
\(422\) | −7.22195 | + | 5.68309i | −0.351559 | + | 0.276648i | ||||
\(423\) | −20.1680 | −0.980604 | ||||||||
\(424\) | −6.02275 | − | 13.1551i | −0.292491 | − | 0.638868i | ||||
\(425\) | 6.03127 | 0.292560 | ||||||||
\(426\) | −10.4493 | + | 8.22274i | −0.506270 | + | 0.398393i | ||||
\(427\) | − | 13.8664i | − | 0.671040i | ||||||
\(428\) | 20.7092 | + | 5.01019i | 1.00102 | + | 0.242177i | ||||
\(429\) | 0.578221i | 0.0279168i | ||||||||
\(430\) | 7.69637 | + | 9.78039i | 0.371152 | + | 0.471652i | ||||
\(431\) | 14.5277 | 0.699772 | 0.349886 | − | 0.936792i | \(-0.386220\pi\) | ||||
0.349886 | + | 0.936792i | \(0.386220\pi\) | |||||||
\(432\) | 0.757359 | − | 1.47363i | 0.0364385 | − | 0.0708999i | ||||
\(433\) | 10.7488 | 0.516556 | 0.258278 | − | 0.966071i | \(-0.416845\pi\) | ||||
0.258278 | + | 0.966071i | \(0.416845\pi\) | |||||||
\(434\) | 5.94725 | + | 7.55765i | 0.285477 | + | 0.362779i | ||||
\(435\) | 8.87579i | 0.425561i | ||||||||
\(436\) | 1.80325 | + | 0.436261i | 0.0863598 | + | 0.0208931i | ||||
\(437\) | − | 35.2145i | − | 1.68454i | ||||||
\(438\) | −5.08312 | + | 4.00000i | −0.242881 | + | 0.191127i | ||||
\(439\) | 23.1386 | 1.10435 | 0.552173 | − | 0.833730i | \(-0.313799\pi\) | ||||
0.552173 | + | 0.833730i | \(0.313799\pi\) | |||||||
\(440\) | −4.29427 | + | 1.96603i | −0.204721 | + | 0.0937269i | ||||
\(441\) | −2.82843 | −0.134687 | ||||||||
\(442\) | 0.961434 | − | 0.756570i | 0.0457308 | − | 0.0359864i | ||||
\(443\) | 19.6983i | 0.935895i | 0.883756 | + | 0.467948i | \(0.155006\pi\) | ||||
−0.883756 | + | 0.467948i | \(0.844994\pi\) | |||||||
\(444\) | −4.94440 | + | 20.4372i | −0.234651 | + | 0.969909i | ||||
\(445\) | 7.13401i | 0.338184i | ||||||||
\(446\) | −8.83623 | − | 11.2289i | −0.418407 | − | 0.531704i | ||||
\(447\) | −17.2967 | −0.818104 | ||||||||
\(448\) | −5.22746 | + | 6.05588i | −0.246974 | + | 0.286114i | ||||
\(449\) | 32.9500 | 1.55501 | 0.777503 | − | 0.628879i | \(-0.216486\pi\) | ||||
0.777503 | + | 0.628879i | \(0.216486\pi\) | |||||||
\(450\) | −2.47363 | − | 3.14343i | −0.116608 | − | 0.148183i | ||||
\(451\) | 14.4299i | 0.679479i | ||||||||
\(452\) | −4.21775 | + | 17.4337i | −0.198386 | + | 0.820013i | ||||
\(453\) | − | 48.0050i | − | 2.25547i | ||||||
\(454\) | 11.4420 | − | 9.00392i | 0.537000 | − | 0.422575i | ||||
\(455\) | −0.143434 | −0.00672428 | ||||||||
\(456\) | −41.2360 | + | 18.8789i | −1.93105 | + | 0.884087i | ||||
\(457\) | 33.7538 | 1.57894 | 0.789468 | − | 0.613791i | \(-0.210356\pi\) | ||||
0.789468 | + | 0.613791i | \(0.210356\pi\) | |||||||
\(458\) | −30.4227 | + | 23.9402i | −1.42156 | + | 1.11865i | ||||
\(459\) | − | 2.49824i | − | 0.116608i | ||||||
\(460\) | 10.3068 | + | 2.49352i | 0.480555 | + | 0.116261i | ||||
\(461\) | 23.9626i | 1.11605i | 0.829825 | + | 0.558024i | \(0.188440\pi\) | ||||
−0.829825 | + | 0.558024i | \(0.811560\pi\) | |||||||
\(462\) | −3.52559 | − | 4.48024i | −0.164025 | − | 0.208440i | ||||
\(463\) | 2.77382 | 0.128910 | 0.0644552 | − | 0.997921i | \(-0.479469\pi\) | ||||
0.0644552 | + | 0.997921i | \(0.479469\pi\) | |||||||
\(464\) | −6.72216 | + | 13.0796i | −0.312068 | + | 0.607205i | ||||
\(465\) | −16.4173 | −0.761336 | ||||||||
\(466\) | −9.84528 | − | 12.5112i | −0.456074 | − | 0.579570i | ||||
\(467\) | 25.1301i | 1.16288i | 0.813589 | + | 0.581441i | \(0.197511\pi\) | ||||
−0.813589 | + | 0.581441i | \(0.802489\pi\) | |||||||
\(468\) | −0.788632 | − | 0.190794i | −0.0364545 | − | 0.00881947i | ||||
\(469\) | − | 9.11529i | − | 0.420905i | ||||||
\(470\) | 7.92461 | − | 6.23602i | 0.365535 | − | 0.287646i | ||||
\(471\) | 11.5210 | 0.530859 | ||||||||
\(472\) | −9.89687 | − | 21.6171i | −0.455540 | − | 0.995006i | ||||
\(473\) | −14.6948 | −0.675667 | ||||||||
\(474\) | 31.7546 | − | 24.9883i | 1.45854 | − | 1.14775i | ||||
\(475\) | − | 6.64167i | − | 0.304741i | ||||||
\(476\) | −2.83647 | + | 11.7243i | −0.130009 | + | 0.537383i | ||||
\(477\) | 14.4682i | 0.662455i | ||||||||
\(478\) | 25.1773 | + | 31.9948i | 1.15158 | + | 1.46341i | ||||
\(479\) | −17.0568 | −0.779344 | −0.389672 | − | 0.920954i | \(-0.627412\pi\) | ||||
−0.389672 | + | 0.920954i | \(0.627412\pi\) | |||||||
\(480\) | −2.60568 | − | 13.4060i | −0.118933 | − | 0.611896i | ||||
\(481\) | −0.624625 | −0.0284805 | ||||||||
\(482\) | 25.1239 | + | 31.9270i | 1.14436 | + | 1.45423i | ||||
\(483\) | 12.8003i | 0.582433i | ||||||||
\(484\) | −3.86193 | + | 15.9630i | −0.175542 | + | 0.725589i | ||||
\(485\) | 5.23322i | 0.237628i | ||||||||
\(486\) | −24.0688 | + | 18.9402i | −1.09178 | + | 0.859145i | ||||
\(487\) | 40.3790 | 1.82975 | 0.914873 | − | 0.403741i | \(-0.132290\pi\) | ||||
0.914873 | + | 0.403741i | \(0.132290\pi\) | |||||||
\(488\) | 16.3263 | + | 35.6604i | 0.739055 | + | 1.61427i | ||||
\(489\) | −35.9822 | −1.62717 | ||||||||
\(490\) | 1.11137 | − | 0.874559i | 0.0502067 | − | 0.0395085i | ||||
\(491\) | 16.9968i | 0.767057i | 0.923529 | + | 0.383528i | \(0.125291\pi\) | ||||
−0.923529 | + | 0.383528i | \(0.874709\pi\) | |||||||
\(492\) | −40.5557 | − | 9.81166i | −1.82839 | − | 0.442344i | ||||
\(493\) | 22.1738i | 0.998658i | ||||||||
\(494\) | −0.833139 | − | 1.05874i | −0.0374847 | − | 0.0476348i | ||||
\(495\) | 4.72293 | 0.212280 | ||||||||
\(496\) | −24.1930 | − | 12.4338i | −1.08630 | − | 0.558295i | ||||
\(497\) | 3.89450 | 0.174692 | ||||||||
\(498\) | 3.74912 | + | 4.76430i | 0.168002 | + | 0.213494i | ||||
\(499\) | − | 10.6600i | − | 0.477208i | −0.971117 | − | 0.238604i | \(-0.923310\pi\) | ||
0.971117 | − | 0.238604i | \(-0.0766897\pi\) | |||||||
\(500\) | 1.94392 | + | 0.470294i | 0.0869347 | + | 0.0210322i | ||||
\(501\) | − | 36.6792i | − | 1.63871i | ||||||
\(502\) | −7.39432 | + | 5.81872i | −0.330024 | + | 0.259702i | ||||
\(503\) | 5.00167 | 0.223014 | 0.111507 | − | 0.993764i | \(-0.464432\pi\) | ||||
0.111507 | + | 0.993764i | \(0.464432\pi\) | |||||||
\(504\) | 7.27391 | − | 3.33019i | 0.324006 | − | 0.148339i | ||||
\(505\) | −10.8628 | −0.483390 | ||||||||
\(506\) | −9.83943 | + | 7.74283i | −0.437416 | + | 0.344211i | ||||
\(507\) | 31.3351i | 1.39164i | ||||||||
\(508\) | −0.0790296 | + | 0.326662i | −0.00350637 | + | 0.0144933i | ||||
\(509\) | 16.8284i | 0.745907i | 0.927850 | + | 0.372953i | \(0.121655\pi\) | ||||
−0.927850 | + | 0.372953i | \(0.878345\pi\) | |||||||
\(510\) | −12.7343 | − | 16.1824i | −0.563882 | − | 0.716570i | ||||
\(511\) | 1.89450 | 0.0838079 | ||||||||
\(512\) | 6.31333 | − | 21.7288i | 0.279013 | − | 0.960287i | ||||
\(513\) | −2.75107 | −0.121463 | ||||||||
\(514\) | −17.1153 | − | 21.7498i | −0.754923 | − | 0.959341i | ||||
\(515\) | 12.1966i | 0.537444i | ||||||||
\(516\) | 9.99176 | − | 41.3001i | 0.439863 | − | 1.81813i | ||||
\(517\) | 11.9065i | 0.523649i | ||||||||
\(518\) | 4.83980 | − | 3.80853i | 0.212649 | − | 0.167337i | ||||
\(519\) | 41.6037 | 1.82620 | ||||||||
\(520\) | 0.368871 | − | 0.168879i | 0.0161761 | − | 0.00740583i | ||||
\(521\) | 30.1742 | 1.32195 | 0.660977 | − | 0.750406i | \(-0.270142\pi\) | ||||
0.660977 | + | 0.750406i | \(0.270142\pi\) | |||||||
\(522\) | 11.5567 | − | 9.09422i | 0.505825 | − | 0.398043i | ||||
\(523\) | 8.92686i | 0.390345i | 0.980769 | + | 0.195172i | \(0.0625266\pi\) | ||||
−0.980769 | + | 0.195172i | \(0.937473\pi\) | |||||||
\(524\) | −28.7523 | − | 6.95605i | −1.25605 | − | 0.303877i | ||||
\(525\) | 2.41421i | 0.105365i | ||||||||
\(526\) | −4.56589 | − | 5.80224i | −0.199082 | − | 0.252990i | ||||
\(527\) | −41.0144 | −1.78662 | ||||||||
\(528\) | 14.3418 | + | 7.37089i | 0.624149 | + | 0.320777i | ||||
\(529\) | 5.11176 | 0.222251 | ||||||||
\(530\) | −4.47363 | − | 5.68499i | −0.194322 | − | 0.246940i | ||||
\(531\) | 23.7749i | 1.03174i | ||||||||
\(532\) | 12.9109 | + | 3.12354i | 0.559757 | + | 0.135422i | ||||
\(533\) | − | 1.23951i | − | 0.0536890i | ||||||
\(534\) | 19.1412 | − | 15.0625i | 0.828320 | − | 0.651820i | ||||
\(535\) | 10.6533 | 0.460583 | ||||||||
\(536\) | 10.7324 | + | 23.4420i | 0.463567 | + | 1.01254i | ||||
\(537\) | 42.0859 | 1.81614 | ||||||||
\(538\) | 18.6401 | − | 14.6682i | 0.803631 | − | 0.632392i | ||||
\(539\) | 1.66981i | 0.0719237i | ||||||||
\(540\) | 0.194802 | − | 0.805198i | 0.00838295 | − | 0.0346502i | ||||
\(541\) | − | 12.8973i | − | 0.554497i | −0.960798 | − | 0.277248i | \(-0.910578\pi\) | ||
0.960798 | − | 0.277248i | \(-0.0894225\pi\) | |||||||
\(542\) | −7.26579 | − | 9.23322i | −0.312092 | − | 0.396601i | ||||
\(543\) | 10.1984 | 0.437656 | ||||||||
\(544\) | −6.50961 | − | 33.4913i | −0.279097 | − | 1.43593i | ||||
\(545\) | 0.927634 | 0.0397355 | ||||||||
\(546\) | 0.302842 | + | 0.384845i | 0.0129604 | + | 0.0164699i | ||||
\(547\) | 20.0415i | 0.856911i | 0.903563 | + | 0.428456i | \(0.140942\pi\) | ||||
−0.903563 | + | 0.428456i | \(0.859058\pi\) | |||||||
\(548\) | 2.75265 | − | 11.3778i | 0.117587 | − | 0.486037i | ||||
\(549\) | − | 39.2200i | − | 1.67387i | ||||||
\(550\) | −1.85578 | + | 1.46035i | −0.0791306 | + | 0.0622693i | ||||
\(551\) | 24.4179 | 1.04024 | ||||||||
\(552\) | −15.0711 | − | 32.9187i | −0.641467 | − | 1.40111i | ||||
\(553\) | −11.8351 | −0.503279 | ||||||||
\(554\) | 6.54314 | − | 5.14892i | 0.277991 | − | 0.218756i | ||||
\(555\) | 10.5134i | 0.446270i | ||||||||
\(556\) | 14.4223 | + | 3.48921i | 0.611643 | + | 0.147975i | ||||
\(557\) | − | 35.9670i | − | 1.52397i | −0.647593 | − | 0.761986i | \(-0.724224\pi\) | ||
0.647593 | − | 0.761986i | \(-0.275776\pi\) | |||||||
\(558\) | 16.8214 | + | 21.3763i | 0.712105 | + | 0.904929i | ||||
\(559\) | 1.26226 | 0.0533878 | ||||||||
\(560\) | −1.82843 | + | 3.55765i | −0.0772651 | + | 0.150338i | ||||
\(561\) | 24.3137 | 1.02653 | ||||||||
\(562\) | −2.36662 | − | 3.00745i | −0.0998298 | − | 0.126862i | ||||
\(563\) | 6.97943i | 0.294148i | 0.989126 | + | 0.147074i | \(0.0469855\pi\) | ||||
−0.989126 | + | 0.147074i | \(0.953014\pi\) | |||||||
\(564\) | −33.4636 | − | 8.09588i | −1.40907 | − | 0.340898i | ||||
\(565\) | 8.96833i | 0.377301i | ||||||||
\(566\) | 25.0059 | − | 19.6776i | 1.05108 | − | 0.827113i | ||||
\(567\) | 9.48528 | 0.398344 | ||||||||
\(568\) | −10.0156 | + | 4.58539i | −0.420244 | + | 0.192399i | ||||
\(569\) | 37.3459 | 1.56562 | 0.782810 | − | 0.622260i | \(-0.213785\pi\) | ||||
0.782810 | + | 0.622260i | \(0.213785\pi\) | |||||||
\(570\) | −17.8202 | + | 14.0230i | −0.746405 | + | 0.587360i | ||||
\(571\) | − | 33.4888i | − | 1.40146i | −0.713425 | − | 0.700732i | \(-0.752857\pi\) | ||
0.713425 | − | 0.700732i | \(-0.247143\pi\) | |||||||
\(572\) | −0.112639 | + | 0.465582i | −0.00470966 | + | 0.0194670i | ||||
\(573\) | − | 28.7234i | − | 1.19994i | ||||||
\(574\) | 7.55765 | + | 9.60411i | 0.315450 | + | 0.400868i | ||||
\(575\) | 5.30205 | 0.221111 | ||||||||
\(576\) | −14.7855 | + | 17.1286i | −0.616062 | + | 0.713693i | ||||
\(577\) | −21.4638 | −0.893550 | −0.446775 | − | 0.894646i | \(-0.647428\pi\) | ||||
−0.446775 | + | 0.894646i | \(0.647428\pi\) | |||||||
\(578\) | −16.9457 | − | 21.5342i | −0.704847 | − | 0.895705i | ||||
\(579\) | 59.9920i | 2.49318i | ||||||||
\(580\) | −1.72902 | + | 7.14677i | −0.0717937 | + | 0.296753i | ||||
\(581\) | − | 1.77568i | − | 0.0736676i | ||||||
\(582\) | 14.0412 | − | 11.0493i | 0.582026 | − | 0.458007i | ||||
\(583\) | 8.54156 | 0.353755 | ||||||||
\(584\) | −4.87213 | + | 2.23059i | −0.201610 | + | 0.0923024i | ||||
\(585\) | −0.405692 | −0.0167733 | ||||||||
\(586\) | 10.4618 | − | 8.23261i | 0.432174 | − | 0.340086i | ||||
\(587\) | − | 21.9804i | − | 0.907227i | −0.891199 | − | 0.453613i | \(-0.850135\pi\) | ||
0.891199 | − | 0.453613i | \(-0.149865\pi\) | |||||||
\(588\) | −4.69304 | − | 1.13539i | −0.193538 | − | 0.0468227i | ||||
\(589\) | 45.1653i | 1.86100i | ||||||||
\(590\) | −7.35127 | − | 9.34185i | −0.302647 | − | 0.384598i | ||||
\(591\) | 10.6081 | 0.436361 | ||||||||
\(592\) | −7.96244 | + | 15.4928i | −0.327254 | + | 0.636752i | ||||
\(593\) | −19.1566 | −0.786665 | −0.393333 | − | 0.919396i | \(-0.628678\pi\) | ||||
−0.393333 | + | 0.919396i | \(0.628678\pi\) | |||||||
\(594\) | 0.604895 | + | 0.768688i | 0.0248191 | + | 0.0315397i | ||||
\(595\) | 6.03127i | 0.247258i | ||||||||
\(596\) | −13.9272 | − | 3.36943i | −0.570482 | − | 0.138017i | ||||
\(597\) | − | 48.5541i | − | 1.98719i | ||||||
\(598\) | 0.845191 | − | 0.665096i | 0.0345624 | − | 0.0271978i | ||||
\(599\) | 15.5715 | 0.636236 | 0.318118 | − | 0.948051i | \(-0.396949\pi\) | ||||
0.318118 | + | 0.948051i | \(0.396949\pi\) | |||||||
\(600\) | −2.84250 | − | 6.20867i | −0.116044 | − | 0.253468i | ||||
\(601\) | −25.7194 | −1.04912 | −0.524558 | − | 0.851375i | \(-0.675769\pi\) | ||||
−0.524558 | + | 0.851375i | \(0.675769\pi\) | |||||||
\(602\) | −9.78039 | + | 7.69637i | −0.398619 | + | 0.313681i | ||||
\(603\) | − | 25.7819i | − | 1.04992i | ||||||
\(604\) | 9.35147 | − | 38.6535i | 0.380506 | − | 1.57279i | ||||
\(605\) | 8.21174i | 0.333855i | ||||||||
\(606\) | 22.9355 | + | 29.1459i | 0.931690 | + | 1.18397i | ||||
\(607\) | −20.5227 | −0.832989 | −0.416495 | − | 0.909138i | \(-0.636741\pi\) | ||||
−0.416495 | + | 0.909138i | \(0.636741\pi\) | |||||||
\(608\) | −36.8808 | + | 7.16842i | −1.49571 | + | 0.290718i | ||||
\(609\) | −8.87579 | −0.359665 | ||||||||
\(610\) | 12.1270 | + | 15.4107i | 0.491006 | + | 0.623960i | ||||
\(611\) | − | 1.02275i | − | 0.0413761i | ||||||
\(612\) | −8.02275 | + | 33.1614i | −0.324301 | + | 1.34047i | ||||
\(613\) | 9.40216i | 0.379750i | 0.981808 | + | 0.189875i | \(0.0608082\pi\) | ||||
−0.981808 | + | 0.189875i | \(0.939192\pi\) | |||||||
\(614\) | −25.8044 | + | 20.3060i | −1.04138 | + | 0.819482i | ||||
\(615\) | −20.8628 | −0.841271 | ||||||||
\(616\) | −1.96603 | − | 4.29427i | −0.0792137 | − | 0.173021i | ||||
\(617\) | −20.0814 | −0.808446 | −0.404223 | − | 0.914660i | \(-0.632458\pi\) | ||||
−0.404223 | + | 0.914660i | \(0.632458\pi\) | |||||||
\(618\) | 32.7244 | − | 25.7515i | 1.31637 | − | 1.03588i | ||||
\(619\) | 18.6972i | 0.751502i | 0.926721 | + | 0.375751i | \(0.122615\pi\) | ||||
−0.926721 | + | 0.375751i | \(0.877385\pi\) | |||||||
\(620\) | −13.2192 | − | 3.19813i | −0.530896 | − | 0.128440i | ||||
\(621\) | − | 2.19618i | − | 0.0881298i | ||||||
\(622\) | −22.9586 | − | 29.1754i | −0.920557 | − | 1.16983i | ||||
\(623\) | −7.13401 | −0.285818 | ||||||||
\(624\) | −1.23194 | − | 0.633147i | −0.0493171 | − | 0.0253462i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 7.22000 | + | 9.17503i | 0.288569 | + | 0.366708i | ||||
\(627\) | − | 26.7744i | − | 1.06927i | ||||||
\(628\) | 9.27667 | + | 2.24431i | 0.370180 | + | 0.0895578i | ||||
\(629\) | 26.2650i | 1.04725i | ||||||||
\(630\) | 3.14343 | − | 2.47363i | 0.125237 | − | 0.0985516i | ||||
\(631\) | −8.24630 | −0.328280 | −0.164140 | − | 0.986437i | \(-0.552485\pi\) | ||||
−0.164140 | + | 0.986437i | \(0.552485\pi\) | |||||||
\(632\) | 30.4365 | − | 13.9346i | 1.21070 | − | 0.554290i | ||||
\(633\) | 15.6881 | 0.623547 | ||||||||
\(634\) | 31.2973 | − | 24.6284i | 1.24298 | − | 0.978120i | ||||
\(635\) | 0.168043i | 0.00666859i | ||||||||
\(636\) | −5.80785 | + | 24.0063i | −0.230296 | + | 0.951910i | ||||
\(637\) | − | 0.143434i | − | 0.00568305i | ||||||
\(638\) | −5.36892 | − | 6.82271i | −0.212557 | − | 0.270114i | ||||
\(639\) | 11.0153 | 0.435759 | ||||||||
\(640\) | 0.513421 | − | 11.3021i | 0.0202947 | − | 0.446753i | ||||
\(641\) | 13.2208 | 0.522190 | 0.261095 | − | 0.965313i | \(-0.415916\pi\) | ||||
0.261095 | + | 0.965313i | \(0.415916\pi\) | |||||||
\(642\) | −22.4931 | − | 28.5838i | −0.887733 | − | 1.12811i | ||||
\(643\) | − | 27.0942i | − | 1.06849i | −0.845329 | − | 0.534245i | \(-0.820596\pi\) | ||
0.845329 | − | 0.534245i | \(-0.179404\pi\) | |||||||
\(644\) | −2.49352 | + | 10.3068i | −0.0982586 | + | 0.406143i | ||||
\(645\) | − | 21.2458i | − | 0.836552i | ||||||
\(646\) | −44.5190 | + | 35.0328i | −1.75158 | + | 1.37835i | ||||
\(647\) | −2.06807 | −0.0813041 | −0.0406520 | − | 0.999173i | \(-0.512944\pi\) | ||||
−0.0406520 | + | 0.999173i | \(0.512944\pi\) | |||||||
\(648\) | −24.3935 | + | 11.1680i | −0.958266 | + | 0.438720i | ||||
\(649\) | 14.0359 | 0.550957 | ||||||||
\(650\) | 0.159408 | − | 0.125441i | 0.00625250 | − | 0.00492021i | ||||
\(651\) | − | 16.4173i | − | 0.643447i | ||||||
\(652\) | −28.9728 | − | 7.00940i | −1.13466 | − | 0.274509i | ||||
\(653\) | − | 27.6256i | − | 1.08107i | −0.841321 | − | 0.540536i | \(-0.818222\pi\) | ||
0.841321 | − | 0.540536i | \(-0.181778\pi\) | |||||||
\(654\) | −1.95858 | − | 2.48892i | −0.0765866 | − | 0.0973246i | ||||
\(655\) | −14.7909 | −0.577927 | ||||||||
\(656\) | −30.7440 | − | 15.8007i | −1.20035 | − | 0.616912i | ||||
\(657\) | 5.35846 | 0.209054 | ||||||||
\(658\) | 6.23602 | + | 7.92461i | 0.243106 | + | 0.308934i | ||||
\(659\) | − | 34.8798i | − | 1.35873i | −0.733803 | − | 0.679363i | \(-0.762256\pi\) | ||
0.733803 | − | 0.679363i | \(-0.237744\pi\) | |||||||
\(660\) | 7.83647 | + | 1.89588i | 0.305034 | + | 0.0737972i | ||||
\(661\) | − | 26.0492i | − | 1.01320i | −0.862182 | − | 0.506599i | \(-0.830903\pi\) | ||
0.862182 | − | 0.506599i | \(-0.169097\pi\) | |||||||
\(662\) | −22.1908 | + | 17.4623i | −0.862470 | + | 0.678693i | ||||
\(663\) | −2.08851 | −0.0811109 | ||||||||
\(664\) | 2.09069 | + | 4.56654i | 0.0811343 | + | 0.177216i | ||||
\(665\) | 6.64167 | 0.257553 | ||||||||
\(666\) | 13.6890 | − | 10.7721i | 0.530439 | − | 0.417412i | ||||
\(667\) | 19.4928i | 0.754766i | ||||||||
\(668\) | 7.14519 | − | 29.5340i | 0.276456 | − | 1.14271i | ||||
\(669\) | 24.3923i | 0.943062i | ||||||||
\(670\) | 7.97186 | + | 10.1305i | 0.307980 | + | 0.391375i | ||||
\(671\) | −23.1542 | −0.893857 | ||||||||
\(672\) | 13.4060 | − | 2.60568i | 0.517147 | − | 0.100516i | ||||
\(673\) | 41.5669 | 1.60229 | 0.801143 | − | 0.598472i | \(-0.204225\pi\) | ||||
0.801143 | + | 0.598472i | \(0.204225\pi\) | |||||||
\(674\) | 29.1137 | + | 36.9971i | 1.12142 | + | 1.42508i | ||||
\(675\) | − | 0.414214i | − | 0.0159431i | ||||||
\(676\) | −6.10415 | + | 25.2310i | −0.234775 | + | 0.970422i | ||||
\(677\) | 20.8530i | 0.801447i | 0.916199 | + | 0.400724i | \(0.131241\pi\) | ||||
−0.916199 | + | 0.400724i | \(0.868759\pi\) | |||||||
\(678\) | 24.0628 | − | 18.9355i | 0.924127 | − | 0.727213i | ||||
\(679\) | −5.23322 | −0.200832 | ||||||||
\(680\) | −7.10123 | − | 15.5107i | −0.272320 | − | 0.594809i | ||||
\(681\) | −24.8553 | −0.952456 | ||||||||
\(682\) | 12.6198 | − | 9.93077i | 0.483238 | − | 0.380269i | ||||
\(683\) | − | 3.74308i | − | 0.143225i | −0.997433 | − | 0.0716124i | \(-0.977186\pi\) | ||
0.997433 | − | 0.0716124i | \(-0.0228145\pi\) | |||||||
\(684\) | 36.5175 | + | 8.83469i | 1.39628 | + | 0.337803i | ||||
\(685\) | − | 5.85304i | − | 0.223633i | ||||||
\(686\) | 0.874559 | + | 1.11137i | 0.0333908 | + | 0.0424324i | ||||
\(687\) | 66.0867 | 2.52137 | ||||||||
\(688\) | 16.0907 | − | 31.3083i | 0.613452 | − | 1.19362i | ||||
\(689\) | −0.733706 | −0.0279520 | ||||||||
\(690\) | −11.1946 | − | 14.2259i | −0.426171 | − | 0.541570i | ||||
\(691\) | 26.3665i | 1.00303i | 0.865150 | + | 0.501514i | \(0.167223\pi\) | ||||
−0.865150 | + | 0.501514i | \(0.832777\pi\) | |||||||
\(692\) | 33.4992 | + | 8.10449i | 1.27345 | + | 0.308087i | ||||
\(693\) | 4.72293i | 0.179409i | ||||||||
\(694\) | −30.1187 | + | 23.7010i | −1.14329 | + | 0.899676i | ||||
\(695\) | 7.41921 | 0.281427 | ||||||||
\(696\) | 22.8260 | − | 10.4504i | 0.865218 | − | 0.396120i | ||||
\(697\) | −52.1203 | −1.97420 | ||||||||
\(698\) | 5.05969 | − | 3.98156i | 0.191512 | − | 0.150704i | ||||
\(699\) | 27.1778i | 1.02796i | ||||||||
\(700\) | −0.470294 | + | 1.94392i | −0.0177754 | + | 0.0734733i | ||||
\(701\) | 11.3145i | 0.427342i | 0.976906 | + | 0.213671i | \(0.0685420\pi\) | ||||
−0.976906 | + | 0.213671i | \(0.931458\pi\) | |||||||
\(702\) | −0.0519595 | − | 0.0660290i | −0.00196108 | − | 0.00249211i | ||||
\(703\) | 28.9231 | 1.09086 | ||||||||
\(704\) | 10.1122 | + | 8.72885i | 0.381116 | + | 0.328981i | ||||
\(705\) | −17.2145 | −0.648336 | ||||||||
\(706\) | −7.74833 | − | 9.84642i | −0.291612 | − | 0.370575i | ||||
\(707\) | − | 10.8628i | − | 0.408539i | ||||||
\(708\) | −9.54374 | + | 39.4482i | −0.358676 | + | 1.48256i | ||||
\(709\) | 5.83119i | 0.218995i | 0.993987 | + | 0.109497i | \(0.0349241\pi\) | ||||
−0.993987 | + | 0.109497i | \(0.965076\pi\) | |||||||
\(710\) | −4.32824 | + | 3.40597i | −0.162436 | + | 0.127824i | ||||
\(711\) | −33.4747 | −1.25540 | ||||||||
\(712\) | 18.3467 | − | 8.39959i | 0.687570 | − | 0.314788i | ||||
\(713\) | −36.0555 | −1.35029 | ||||||||
\(714\) | 16.1824 | − | 12.7343i | 0.605613 | − | 0.476568i | ||||
\(715\) | 0.239507i | 0.00895705i | ||||||||
\(716\) | 33.8874 | + | 8.19841i | 1.26643 | + | 0.306389i | ||||
\(717\) | − | 69.5019i | − | 2.59559i | ||||||
\(718\) | 19.2231 | + | 24.4283i | 0.717400 | + | 0.911658i | ||||
\(719\) | 22.6903 | 0.846206 | 0.423103 | − | 0.906081i | \(-0.360941\pi\) | ||||
0.423103 | + | 0.906081i | \(0.360941\pi\) | |||||||
\(720\) | −5.17157 | + | 10.0625i | −0.192733 | + | 0.375009i | ||||
\(721\) | −12.1966 | −0.454223 | ||||||||
\(722\) | 21.9617 | + | 27.9085i | 0.817330 | + | 1.03865i | ||||
\(723\) | − | 69.3544i | − | 2.57932i | ||||||
\(724\) | 8.21174 | + | 1.98667i | 0.305187 | + | 0.0738341i | ||||
\(725\) | 3.67647i | 0.136541i | ||||||||
\(726\) | 22.0328 | − | 17.3380i | 0.817715 | − | 0.643475i | ||||
\(727\) | −1.09198 | −0.0404994 | −0.0202497 | − | 0.999795i | \(-0.506446\pi\) | ||||
−0.0202497 | + | 0.999795i | \(0.506446\pi\) | |||||||
\(728\) | 0.168879 | + | 0.368871i | 0.00625907 | + | 0.0136713i | ||||
\(729\) | 23.8284 | 0.882534 | ||||||||
\(730\) | −2.10550 | + | 1.65685i | −0.0779279 | + | 0.0613229i | ||||
\(731\) | − | 53.0769i | − | 1.96312i | ||||||
\(732\) | 15.7437 | − | 65.0754i | 0.581905 | − | 2.40525i | ||||
\(733\) | − | 17.7777i | − | 0.656635i | −0.944567 | − | 0.328318i | \(-0.893518\pi\) | ||
0.944567 | − | 0.328318i | \(-0.106482\pi\) | |||||||
\(734\) | 5.05280 | + | 6.42099i | 0.186502 | + | 0.237003i | ||||
\(735\) | −2.41421 | −0.0890496 | ||||||||
\(736\) | −5.72256 | − | 29.4420i | −0.210936 | − | 1.08524i | ||||
\(737\) | −15.2208 | −0.560665 | ||||||||
\(738\) | 21.3763 | + | 27.1645i | 0.786871 | + | 0.999940i | ||||
\(739\) | 12.3302i | 0.453573i | 0.973944 | + | 0.226787i | \(0.0728220\pi\) | ||||
−0.973944 | + | 0.226787i | \(0.927178\pi\) | |||||||
\(740\) | −2.04804 | + | 8.46538i | −0.0752873 | + | 0.311194i | ||||
\(741\) | 2.29987i | 0.0844880i | ||||||||
\(742\) | 5.68499 | − | 4.47363i | 0.208703 | − | 0.164232i | ||||
\(743\) | 23.2253 | 0.852052 | 0.426026 | − | 0.904711i | \(-0.359913\pi\) | ||||
0.426026 | + | 0.904711i | \(0.359913\pi\) | |||||||
\(744\) | 19.3298 | + | 42.2208i | 0.708665 | + | 1.54789i | ||||
\(745\) | −7.16451 | −0.262487 | ||||||||
\(746\) | −21.0366 | + | 16.5541i | −0.770206 | + | 0.606089i | ||||
\(747\) | − | 5.02238i | − | 0.183759i | ||||||
\(748\) | 19.5773 | + | 4.73636i | 0.715819 | + | 0.173179i | ||||
\(749\) | 10.6533i | 0.389264i | ||||||||
\(750\) | −2.11137 | − | 2.68309i | −0.0770964 | − | 0.0979725i | ||||
\(751\) | −33.1614 | −1.21008 | −0.605038 | − | 0.796197i | \(-0.706842\pi\) | ||||
−0.605038 | + | 0.796197i | \(0.706842\pi\) | |||||||
\(752\) | −25.3677 | − | 13.0376i | −0.925066 | − | 0.475431i | ||||
\(753\) | 16.0625 | 0.585352 | ||||||||
\(754\) | 0.461181 | + | 0.586060i | 0.0167952 | + | 0.0213430i | ||||
\(755\) | − | 19.8843i | − | 0.723664i | ||||||
\(756\) | 0.805198 | + | 0.194802i | 0.0292848 | + | 0.00708488i | ||||
\(757\) | 15.6531i | 0.568923i | 0.958687 | + | 0.284461i | \(0.0918148\pi\) | ||||
−0.958687 | + | 0.284461i | \(0.908185\pi\) | |||||||
\(758\) | −5.68499 | + | 4.47363i | −0.206488 | + | 0.162489i | ||||
\(759\) | 21.3740 | 0.775828 | ||||||||
\(760\) | −17.0805 | + | 7.81991i | −0.619575 | + | 0.283658i | ||||
\(761\) | −28.8105 | −1.04438 | −0.522189 | − | 0.852830i | \(-0.674885\pi\) | ||||
−0.522189 | + | 0.852830i | \(0.674885\pi\) | |||||||
\(762\) | 0.450874 | − | 0.354801i | 0.0163335 | − | 0.0128531i | ||||
\(763\) | 0.927634i | 0.0335826i | ||||||||
\(764\) | 5.59539 | − | 23.1281i | 0.202434 | − | 0.836743i | ||||
\(765\) | 17.0590i | 0.616770i | ||||||||
\(766\) | 17.2225 | + | 21.8860i | 0.622273 | + | 0.790772i | ||||
\(767\) | −1.20566 | −0.0435338 | ||||||||
\(768\) | −31.4084 | + | 22.4853i | −1.13335 | + | 0.811368i | ||||
\(769\) | −23.1419 | −0.834520 | −0.417260 | − | 0.908787i | \(-0.637010\pi\) | ||||
−0.417260 | + | 0.908787i | \(0.637010\pi\) | |||||||
\(770\) | −1.46035 | − | 1.85578i | −0.0526272 | − | 0.0668776i | ||||
\(771\) | 47.2467i | 1.70155i | ||||||||
\(772\) | −11.6866 | + | 48.3054i | −0.420609 | + | 1.73855i | ||||
\(773\) | 4.49285i | 0.161596i | 0.996730 | + | 0.0807982i | \(0.0257469\pi\) | ||||
−0.996730 | + | 0.0807982i | \(0.974253\pi\) | |||||||
\(774\) | −27.6631 | + | 21.7686i | −0.994330 | + | 0.782457i | ||||
\(775\) | −6.80029 | −0.244274 | ||||||||
\(776\) | 13.4584 | − | 6.16159i | 0.483127 | − | 0.221188i | ||||
\(777\) | −10.5134 | −0.377167 | ||||||||
\(778\) | −10.2885 | + | 8.09619i | −0.368860 | + | 0.290262i | ||||
\(779\) | 57.3951i | 2.05639i | ||||||||
\(780\) | −0.673140 | − | 0.162853i | −0.0241023 | − | 0.00583108i | ||||
\(781\) | − | 6.50307i | − | 0.232698i | ||||||
\(782\) | −27.9668 | − | 35.5396i | −1.00009 | − | 1.27089i | ||||
\(783\) | 1.52284 | 0.0544220 | ||||||||
\(784\) | −3.55765 | − | 1.82843i | −0.127059 | − | 0.0653010i | ||||
\(785\) | 4.77215 | 0.170325 | ||||||||
\(786\) | 31.2290 | + | 39.6852i | 1.11390 | + | 1.41552i | ||||
\(787\) | 21.5832i | 0.769358i | 0.923050 | + | 0.384679i | \(0.125688\pi\) | ||||
−0.923050 | + | 0.384679i | \(0.874312\pi\) | |||||||
\(788\) | 8.54165 | + | 2.06649i | 0.304284 | + | 0.0736156i | ||||
\(789\) | 12.6041i | 0.448718i | ||||||||
\(790\) | 13.1532 | − | 10.3505i | 0.467969 | − | 0.368254i | ||||
\(791\) | −8.96833 | −0.318877 | ||||||||
\(792\) | −5.56078 | − | 12.1460i | −0.197594 | − | 0.431591i | ||||
\(793\) | 1.98890 | 0.0706281 | ||||||||
\(794\) | 17.9899 | − | 14.1566i | 0.638438 | − | 0.502399i | ||||
\(795\) | 12.3494i | 0.437989i | ||||||||
\(796\) | 9.45844 | − | 39.0957i | 0.335246 | − | 1.38571i | ||||
\(797\) | 30.2740i | 1.07236i | 0.844103 | + | 0.536181i | \(0.180134\pi\) | ||||
−0.844103 | + | 0.536181i | \(0.819866\pi\) | |||||||
\(798\) | −14.0230 | − | 17.8202i | −0.496410 | − | 0.630828i | ||||
\(799\) | −43.0059 | −1.52144 | ||||||||
\(800\) | −1.07931 | − | 5.55294i | −0.0381594 | − | 0.196326i | ||||
\(801\) | −20.1780 | −0.712956 | ||||||||
\(802\) | 25.5296 | + | 32.4424i | 0.901480 | + | 1.14558i | ||||
\(803\) | − | 3.16346i | − | 0.111636i | ||||||
\(804\) | 10.3494 | − | 42.7784i | 0.364996 | − | 1.50868i | ||||
\(805\) | 5.30205i | 0.186873i | ||||||||
\(806\) | −1.08402 | + | 0.853036i | −0.0381830 | + | 0.0300469i | ||||
\(807\) | −40.4915 | −1.42537 | ||||||||
\(808\) | 12.7899 | + | 27.9361i | 0.449947 | + | 0.982790i | ||||
\(809\) | −10.9670 | −0.385580 | −0.192790 | − | 0.981240i | \(-0.561754\pi\) | ||||
−0.192790 | + | 0.981240i | \(0.561754\pi\) | |||||||
\(810\) | −10.5417 | + | 8.29544i | −0.370397 | + | 0.291472i | ||||
\(811\) | 6.39683i | 0.224623i | 0.993673 | + | 0.112312i | \(0.0358254\pi\) | ||||
−0.993673 | + | 0.112312i | \(0.964175\pi\) | |||||||
\(812\) | −7.14677 | − | 1.72902i | −0.250802 | − | 0.0606768i | ||||
\(813\) | 20.0572i | 0.703435i | ||||||||
\(814\) | −6.35951 | − | 8.08154i | −0.222901 | − | 0.283258i | ||||
\(815\) | −14.9043 | −0.522075 | ||||||||
\(816\) | −26.6233 | + | 51.8021i | −0.932003 | + | 1.81344i | ||||
\(817\) | −58.4486 | −2.04486 | ||||||||
\(818\) | −14.5096 | − | 18.4385i | −0.507317 | − | 0.644688i | ||||
\(819\) | − | 0.405692i | − | 0.0141760i | ||||||
\(820\) | −16.7987 | − | 4.06412i | −0.586636 | − | 0.141925i | ||||
\(821\) | 36.7455i | 1.28243i | 0.767363 | + | 0.641213i | \(0.221568\pi\) | ||||
−0.767363 | + | 0.641213i | \(0.778432\pi\) | |||||||
\(822\) | −15.7042 | + | 12.3579i | −0.547747 | + | 0.431032i | ||||
\(823\) | 23.4701 | 0.818116 | 0.409058 | − | 0.912508i | \(-0.365857\pi\) | ||||
0.409058 | + | 0.912508i | \(0.365857\pi\) | |||||||
\(824\) | 31.3661 | − | 14.3602i | 1.09269 | − | 0.500262i | ||||
\(825\) | 4.03127 | 0.140351 | ||||||||
\(826\) | 9.34185 | − | 7.35127i | 0.325044 | − | 0.255783i | ||||
\(827\) | − | 30.1914i | − | 1.04986i | −0.851147 | − | 0.524928i | \(-0.824092\pi\) | ||
0.851147 | − | 0.524928i | \(-0.175908\pi\) | |||||||
\(828\) | −7.05275 | + | 29.1519i | −0.245100 | + | 1.01310i | ||||
\(829\) | − | 20.8995i | − | 0.725869i | −0.931815 | − | 0.362934i | \(-0.881775\pi\) | ||
0.931815 | − | 0.362934i | \(-0.118225\pi\) | |||||||
\(830\) | 1.55294 | + | 1.97344i | 0.0539032 | + | 0.0684991i | ||||
\(831\) | −14.2135 | −0.493062 | ||||||||
\(832\) | −0.868618 | − | 0.749793i | −0.0301139 | − | 0.0259944i | ||||
\(833\) | −6.03127 | −0.208971 | ||||||||
\(834\) | −15.6647 | − | 19.9064i | −0.542424 | − | 0.689302i | ||||
\(835\) | − | 15.1930i | − | 0.525776i | ||||||
\(836\) | 5.21571 | − | 21.5587i | 0.180389 | − | 0.745622i | ||||
\(837\) | 2.81677i | 0.0973619i | ||||||||
\(838\) | −9.01519 | + | 7.09422i | −0.311424 | + | 0.245066i | ||||
\(839\) | 0.562639 | 0.0194245 | 0.00971223 | − | 0.999953i | \(-0.496908\pi\) | ||||
0.00971223 | + | 0.999953i | \(0.496908\pi\) | |||||||
\(840\) | 6.20867 | − | 2.84250i | 0.214220 | − | 0.0980755i | ||||
\(841\) | 15.4836 | 0.533916 | ||||||||
\(842\) | −36.8849 | + | 29.0254i | −1.27114 | + | 1.00028i | ||||
\(843\) | 6.53304i | 0.225010i | ||||||||
\(844\) | 12.6320 | + | 3.05608i | 0.434813 | + | 0.105195i | ||||
\(845\) | 12.9794i | 0.446506i | ||||||||
\(846\) | 17.6381 | + | 22.4142i | 0.606412 | + | 0.770616i | ||||
\(847\) | −8.21174 | −0.282159 | ||||||||
\(848\) | −9.35294 | + | 18.1984i | −0.321181 | + | 0.624936i | ||||
\(849\) | −54.3200 | −1.86426 | ||||||||
\(850\) | −5.27470 | − | 6.70299i | −0.180921 | − | 0.229911i | ||||
\(851\) | 23.0894i | 0.791494i | ||||||||
\(852\) | 18.2770 | + | 4.42178i | 0.626161 | + | 0.151488i | ||||
\(853\) | − | 11.8757i | − | 0.406615i | −0.979115 | − | 0.203307i | \(-0.934831\pi\) | ||
0.979115 | − | 0.203307i | \(-0.0651691\pi\) | |||||||
\(854\) | −15.4107 | + | 12.1270i | −0.527343 | + | 0.414976i | ||||
\(855\) | 18.7855 | 0.642450 | ||||||||
\(856\) | −12.5432 | − | 27.3973i | −0.428719 | − | 0.936422i | ||||
\(857\) | 41.8715 | 1.43030 | 0.715152 | − | 0.698969i | \(-0.246357\pi\) | ||||
0.715152 | + | 0.698969i | \(0.246357\pi\) | |||||||
\(858\) | 0.642618 | − | 0.505688i | 0.0219386 | − | 0.0172639i | ||||
\(859\) | 1.02684i | 0.0350354i | 0.999847 | + | 0.0175177i | \(0.00557634\pi\) | ||||
−0.999847 | + | 0.0175177i | \(0.994424\pi\) | |||||||
\(860\) | 4.13872 | − | 17.1071i | 0.141129 | − | 0.583346i | ||||
\(861\) | − | 20.8628i | − | 0.711003i | ||||||
\(862\) | −12.7053 | − | 16.1456i | −0.432744 | − | 0.549922i | ||||
\(863\) | 23.4327 | 0.797657 | 0.398829 | − | 0.917025i | \(-0.369417\pi\) | ||||
0.398829 | + | 0.917025i | \(0.369417\pi\) | |||||||
\(864\) | −2.30010 | + | 0.447065i | −0.0782510 | + | 0.0152094i | ||||
\(865\) | 17.2328 | 0.585933 | ||||||||
\(866\) | −9.40049 | − | 11.9460i | −0.319442 | − | 0.405940i | ||||
\(867\) | 46.7784i | 1.58868i | ||||||||
\(868\) | 3.19813 | − | 13.2192i | 0.108552 | − | 0.448689i | ||||
\(869\) | 19.7623i | 0.670391i | ||||||||
\(870\) | 9.86430 | − | 7.76240i | 0.334431 | − | 0.263170i | ||||
\(871\) | 1.30744 | 0.0443009 | ||||||||
\(872\) | −1.09220 | − | 2.38561i | −0.0369865 | − | 0.0807870i | ||||
\(873\) | −14.8018 | −0.500964 | ||||||||
\(874\) | −39.1364 | + | 30.7971i | −1.32381 | + | 1.04173i | ||||
\(875\) | 1.00000i | 0.0338062i | ||||||||
\(876\) | 8.89097 | + | 2.15100i | 0.300398 | + | 0.0726755i | ||||
\(877\) | 26.9911i | 0.911424i | 0.890127 | + | 0.455712i | \(0.150615\pi\) | ||||
−0.890127 | + | 0.455712i | \(0.849385\pi\) | |||||||
\(878\) | −20.2361 | − | 25.7156i | −0.682934 | − | 0.867859i | ||||
\(879\) | −22.7261 | −0.766531 | ||||||||
\(880\) | 5.94059 | + | 3.05312i | 0.200257 | + | 0.102921i | ||||
\(881\) | 45.9037 | 1.54653 | 0.773267 | − | 0.634080i | \(-0.218621\pi\) | ||||
0.773267 | + | 0.634080i | \(0.218621\pi\) | |||||||
\(882\) | 2.47363 | + | 3.14343i | 0.0832913 | + | 0.105845i | ||||
\(883\) | − | 24.4946i | − | 0.824308i | −0.911114 | − | 0.412154i | \(-0.864777\pi\) | ||
0.911114 | − | 0.412154i | \(-0.135223\pi\) | |||||||
\(884\) | −1.68166 | − | 0.406846i | −0.0565604 | − | 0.0136837i | ||||
\(885\) | 20.2931i | 0.682146i | ||||||||
\(886\) | 21.8922 | − | 17.2273i | 0.735481 | − | 0.578764i | ||||
\(887\) | −54.5944 | −1.83310 | −0.916551 | − | 0.399918i | \(-0.869039\pi\) | ||||
−0.916551 | + | 0.399918i | \(0.869039\pi\) | |||||||
\(888\) | 27.0375 | − | 12.3785i | 0.907320 | − | 0.415396i | ||||
\(889\) | −0.168043 | −0.00563598 | ||||||||
\(890\) | 7.92854 | − | 6.23911i | 0.265765 | − | 0.209135i | ||||
\(891\) | − | 15.8386i | − | 0.530613i | ||||||
\(892\) | −4.75168 | + | 19.6407i | −0.159098 | + | 0.657618i | ||||
\(893\) | 47.3583i | 1.58478i | ||||||||
\(894\) | 15.1270 | + | 19.2230i | 0.505921 | + | 0.642914i | ||||
\(895\) | 17.4325 | 0.582705 | ||||||||
\(896\) | 11.3021 | + | 0.513421i | 0.377575 | + | 0.0171522i | ||||
\(897\) | −1.83599 | −0.0613020 | ||||||||
\(898\) | −28.8167 | − | 36.6197i | −0.961626 | − | 1.22201i | ||||
\(899\) | − | 25.0011i | − | 0.833832i | ||||||
\(900\) | −1.33019 | + | 5.49824i | −0.0443397 | + | 0.183275i | ||||
\(901\) | 30.8517i | 1.02782i | ||||||||
\(902\) | 16.0370 | − | 12.6198i | 0.533974 | − | 0.420194i | ||||
\(903\) | 21.2458 | 0.707015 | ||||||||
\(904\) | 23.0640 | − | 10.5593i | 0.767098 | − | 0.351198i | ||||
\(905\) | 4.22432 | 0.140421 | ||||||||
\(906\) | −53.3514 | + | 41.9832i | −1.77248 | + | 1.39480i | ||||
\(907\) | 9.90305i | 0.328825i | 0.986392 | + | 0.164413i | \(0.0525729\pi\) | ||||
−0.986392 | + | 0.164413i | \(0.947427\pi\) | |||||||
\(908\) | −20.0134 | − | 4.84186i | −0.664168 | − | 0.160683i | ||||
\(909\) | − | 30.7247i | − | 1.01908i | ||||||
\(910\) | 0.125441 | + | 0.159408i | 0.00415834 | + | 0.00528433i | ||||
\(911\) | −15.0912 | −0.499993 | −0.249997 | − | 0.968247i | \(-0.580430\pi\) | ||||
−0.249997 | + | 0.968247i | \(0.580430\pi\) | |||||||
\(912\) | 57.0448 | + | 29.3177i | 1.88894 | + | 0.970808i | ||||
\(913\) | −2.96504 | −0.0981286 | ||||||||
\(914\) | −29.5197 | − | 37.5130i | −0.976425 | − | 1.24082i | ||||
\(915\) | − | 33.4764i | − | 1.10669i | ||||||
\(916\) | 53.2129 | + | 12.8738i | 1.75820 | + | 0.425364i | ||||
\(917\) | − | 14.7909i | − | 0.488437i | ||||||
\(918\) | −2.77647 | + | 2.18485i | −0.0916371 | + | 0.0721109i | ||||
\(919\) | 34.0961 | 1.12472 | 0.562362 | − | 0.826891i | \(-0.309893\pi\) | ||||
0.562362 | + | 0.826891i | \(0.309893\pi\) | |||||||
\(920\) | −6.24264 | − | 13.6354i | −0.205814 | − | 0.449545i | ||||
\(921\) | 56.0545 | 1.84706 | ||||||||
\(922\) | 26.6313 | − | 20.9567i | 0.877056 | − | 0.690171i | ||||
\(923\) | 0.558603i | 0.0183866i | ||||||||
\(924\) | −1.89588 | + | 7.83647i | −0.0623700 | + | 0.257801i | ||||
\(925\) | 4.35480i | 0.143185i | ||||||||
\(926\) | −2.42587 | − | 3.08275i | −0.0797190 | − | 0.101305i | ||||
\(927\) | −34.4971 | −1.13303 | ||||||||
\(928\) | 20.4152 | − | 3.96805i | 0.670162 | − | 0.130258i | ||||
\(929\) | −24.7981 | −0.813598 | −0.406799 | − | 0.913518i | \(-0.633355\pi\) | ||||
−0.406799 | + | 0.913518i | \(0.633355\pi\) | |||||||
\(930\) | 14.3579 | + | 18.2458i | 0.470815 | + | 0.598303i | ||||
\(931\) | 6.64167i | 0.217672i | ||||||||
\(932\) | −5.29430 | + | 21.8835i | −0.173421 | + | 0.716819i | ||||
\(933\) | 63.3771i | 2.07487i | ||||||||
\(934\) | 27.9289 | − | 21.9777i | 0.913860 | − | 0.719133i | ||||
\(935\) | 10.0711 | 0.329359 | ||||||||
\(936\) | 0.477662 | + | 1.04332i | 0.0156129 | + | 0.0341021i | ||||
\(937\) | −8.60501 | −0.281113 | −0.140557 | − | 0.990073i | \(-0.544889\pi\) | ||||
−0.140557 | + | 0.990073i | \(0.544889\pi\) | |||||||
\(938\) | −10.1305 | + | 7.97186i | −0.330772 | + | 0.260290i | ||||
\(939\) | − | 19.9308i | − | 0.650416i | ||||||
\(940\) | −13.8611 | − | 3.35342i | −0.452099 | − | 0.109377i | ||||
\(941\) | 54.3509i | 1.77179i | 0.463889 | + | 0.885894i | \(0.346454\pi\) | ||||
−0.463889 | + | 0.885894i | \(0.653546\pi\) | |||||||
\(942\) | −10.0758 | − | 12.8041i | −0.328287 | − | 0.417180i | ||||
\(943\) | −45.8186 | −1.49206 | ||||||||
\(944\) | −15.3692 | + | 29.9045i | −0.500225 | + | 0.973308i | ||||
\(945\) | 0.414214 | 0.0134744 | ||||||||
\(946\) | 12.8515 | + | 16.3314i | 0.417837 | + | 0.530979i | ||||
\(947\) | 6.40713i | 0.208204i | 0.994567 | + | 0.104102i | \(0.0331968\pi\) | ||||
−0.994567 | + | 0.104102i | \(0.966803\pi\) | |||||||
\(948\) | −55.5425 | − | 13.4374i | −1.80394 | − | 0.436428i | ||||
\(949\) | 0.271736i | 0.00882091i | ||||||||
\(950\) | −7.38136 | + | 5.80853i | −0.239483 | + | 0.188454i | ||||
\(951\) | −67.9866 | −2.20462 | ||||||||
\(952\) | 15.5107 | − | 7.10123i | 0.502706 | − | 0.230152i | ||||
\(953\) | 7.99852 | 0.259097 | 0.129549 | − | 0.991573i | \(-0.458647\pi\) | ||||
0.129549 | + | 0.991573i | \(0.458647\pi\) | |||||||
\(954\) | 16.0796 | − | 12.6533i | 0.520596 | − | 0.409667i | ||||
\(955\) | − | 11.8976i | − | 0.384998i | ||||||
\(956\) | 13.5391 | − | 55.9627i | 0.437886 | − | 1.80996i | ||||
\(957\) | 14.8209i | 0.479090i | ||||||||
\(958\) | 14.9172 | + | 18.9564i | 0.481952 | + | 0.612454i | ||||
\(959\) | 5.85304 | 0.189004 | ||||||||
\(960\) | −12.6202 | + | 14.6202i | −0.407315 | + | 0.471865i | ||||
\(961\) | 15.2439 | 0.491739 | ||||||||
\(962\) | 0.546272 | + | 0.694191i | 0.0176125 | + | 0.0223816i | ||||
\(963\) | 30.1322i | 0.970995i | ||||||||
\(964\) | 13.5104 | − | 55.8440i | 0.435140 | − | 1.79861i | ||||
\(965\) | 24.8495i | 0.799934i | ||||||||
\(966\) | 14.2259 | − | 11.1946i | 0.457710 | − | 0.360180i | ||||
\(967\) | 47.6749 | 1.53312 | 0.766561 | − | 0.642172i | \(-0.221966\pi\) | ||||
0.766561 | + | 0.642172i | \(0.221966\pi\) | |||||||
\(968\) | 21.1183 | − | 9.66851i | 0.678767 | − | 0.310758i | ||||
\(969\) | 96.7079 | 3.10670 | ||||||||
\(970\) | 5.81605 | − | 4.57676i | 0.186742 | − | 0.146951i | ||||
\(971\) | 34.8989i | 1.11996i | 0.828506 | + | 0.559980i | \(0.189191\pi\) | ||||
−0.828506 | + | 0.559980i | \(0.810809\pi\) | |||||||
\(972\) | 42.0992 | + | 10.1851i | 1.35033 | + | 0.326687i | ||||
\(973\) | 7.41921i | 0.237849i | ||||||||
\(974\) | −35.3138 | − | 44.8761i | −1.13153 | − | 1.43792i | ||||
\(975\) | −0.346280 | −0.0110898 | ||||||||
\(976\) | 25.3536 | − | 49.3316i | 0.811550 | − | 1.57907i | ||||
\(977\) | −10.2946 | −0.329354 | −0.164677 | − | 0.986348i | \(-0.552658\pi\) | ||||
−0.164677 | + | 0.986348i | \(0.552658\pi\) | |||||||
\(978\) | 31.4685 | + | 39.9896i | 1.00625 | + | 1.27873i | ||||
\(979\) | 11.9124i | 0.380723i | ||||||||
\(980\) | −1.94392 | − | 0.470294i | −0.0620962 | − | 0.0150230i | ||||
\(981\) | 2.62375i | 0.0837697i | ||||||||
\(982\) | 18.8898 | − | 14.8647i | 0.602798 | − | 0.474353i | ||||
\(983\) | −16.6648 | −0.531524 | −0.265762 | − | 0.964039i | \(-0.585624\pi\) | ||||
−0.265762 | + | 0.964039i | \(0.585624\pi\) | |||||||
\(984\) | 24.5639 | + | 53.6533i | 0.783069 | + | 1.71040i | ||||
\(985\) | 4.39404 | 0.140006 | ||||||||
\(986\) | 24.6433 | − | 19.3923i | 0.784804 | − | 0.617576i | ||||
\(987\) | − | 17.2145i | − | 0.547944i | ||||||
\(988\) | −0.448020 | + | 1.85185i | −0.0142534 | + | 0.0589153i | ||||
\(989\) | − | 46.6596i | − | 1.48369i | ||||||
\(990\) | −4.13048 | − | 5.24893i | −0.131275 | − | 0.166822i | ||||
\(991\) | −19.1012 | −0.606769 | −0.303384 | − | 0.952868i | \(-0.598117\pi\) | ||||
−0.303384 | + | 0.952868i | \(0.598117\pi\) | |||||||
\(992\) | 7.33962 | + | 37.7616i | 0.233033 | + | 1.19893i | ||||
\(993\) | 48.2047 | 1.52973 | ||||||||
\(994\) | −3.40597 | − | 4.32824i | −0.108031 | − | 0.137283i | ||||
\(995\) | − | 20.1118i | − | 0.637586i | ||||||
\(996\) | 2.01609 | − | 8.33333i | 0.0638822 | − | 0.264052i | ||||
\(997\) | 21.8103i | 0.690738i | 0.938467 | + | 0.345369i | \(0.112246\pi\) | ||||
−0.938467 | + | 0.345369i | \(0.887754\pi\) | |||||||
\(998\) | −11.8472 | + | 9.32281i | −0.375018 | + | 0.295108i | ||||
\(999\) | 1.80382 | 0.0570703 |
(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 | 280.2.b.c.141.1 | ✓ | 8 | |
4.3 | odd | 2 | 1120.2.b.c.561.1 | 8 | |||
8.3 | odd | 2 | 1120.2.b.c.561.8 | 8 | |||
8.5 | even | 2 | inner | 280.2.b.c.141.2 | yes | 8 | |
16.3 | odd | 4 | 8960.2.a.bv.1.3 | 4 | |||
16.5 | even | 4 | 8960.2.a.bu.1.3 | 4 | |||
16.11 | odd | 4 | 8960.2.a.bs.1.2 | 4 | |||
16.13 | even | 4 | 8960.2.a.bt.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.b.c.141.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
280.2.b.c.141.2 | yes | 8 | 8.5 | even | 2 | inner | |
1120.2.b.c.561.1 | 8 | 4.3 | odd | 2 | |||
1120.2.b.c.561.8 | 8 | 8.3 | odd | 2 | |||
8960.2.a.bs.1.2 | 4 | 16.11 | odd | 4 | |||
8960.2.a.bt.1.2 | 4 | 16.13 | even | 4 | |||
8960.2.a.bu.1.3 | 4 | 16.5 | even | 4 | |||
8960.2.a.bv.1.3 | 4 | 16.3 | odd | 4 |