Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [567,2,Mod(26,567)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(567, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("567.26");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 567 = 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 567.s (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.52751779461\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 9x^{10} + 59x^{8} - 180x^{6} + 403x^{4} - 198x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | no (minimal twist has level 189) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 458.3 | ||
Root | \(1.65604 + 0.956115i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 567.458 |
Dual form | 567.2.s.f.26.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.568650 | − | 0.328310i | −0.402096 | − | 0.232150i | 0.285292 | − | 0.958441i | \(-0.407909\pi\) |
−0.687388 | + | 0.726290i | \(0.741243\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.784425 | − | 1.35866i | −0.392212 | − | 0.679332i | ||||
\(5\) | −3.31208 | −1.48121 | −0.740603 | − | 0.671943i | \(-0.765460\pi\) | ||||
−0.740603 | + | 0.671943i | \(0.765460\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.799494 | + | 2.52206i | 0.302180 | + | 0.953251i | ||||
\(8\) | 2.34338i | 0.828510i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.88341 | + | 1.08739i | 0.595588 | + | 0.343863i | ||||
\(11\) | − | 2.34338i | − | 0.706556i | −0.935518 | − | 0.353278i | \(-0.885067\pi\) | ||
0.935518 | − | 0.353278i | \(-0.114933\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.36834 | + | 0.790014i | 0.379510 | + | 0.219110i | 0.677605 | − | 0.735426i | \(-0.263018\pi\) |
−0.298095 | + | 0.954536i | \(0.596351\pi\) | |||||||
\(14\) | 0.373387 | − | 1.69665i | 0.0997919 | − | 0.453450i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.799494 | + | 1.38476i | −0.199874 | + | 0.346191i | ||||
\(17\) | 0.568650 | − | 0.984931i | 0.137918 | − | 0.238881i | −0.788790 | − | 0.614662i | \(-0.789292\pi\) |
0.926708 | + | 0.375781i | \(0.122626\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.85327 | − | 2.22469i | 0.884002 | − | 0.510379i | 0.0120260 | − | 0.999928i | \(-0.496172\pi\) |
0.871976 | + | 0.489549i | \(0.162839\pi\) | |||||||
\(20\) | 2.59808 | + | 4.50000i | 0.580948 | + | 1.00623i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.769355 | + | 1.33256i | −0.164027 | + | 0.284103i | ||||
\(23\) | 9.39331i | 1.95864i | 0.202317 | + | 0.979320i | \(0.435153\pi\) | ||||
−0.202317 | + | 0.979320i | \(0.564847\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.96986 | 1.19397 | ||||||||
\(26\) | −0.518739 | − | 0.898482i | −0.101733 | − | 0.176207i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.79949 | − | 3.06461i | 0.529055 | − | 0.579158i | ||||
\(29\) | 3.16673 | − | 1.82831i | 0.588046 | − | 0.339509i | −0.176278 | − | 0.984340i | \(-0.556406\pi\) |
0.764325 | + | 0.644832i | \(0.223073\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.33821 | − | 3.65936i | 1.13838 | − | 0.657241i | 0.192347 | − | 0.981327i | \(-0.438390\pi\) |
0.946028 | + | 0.324086i | \(0.105057\pi\) | |||||||
\(32\) | 4.96812 | − | 2.86834i | 0.878247 | − | 0.507056i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.646726 | + | 0.373387i | −0.110913 | + | 0.0640354i | ||||
\(35\) | −2.64799 | − | 8.35327i | −0.447592 | − | 1.41196i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.58392 | + | 4.47548i | 0.424794 | + | 0.735764i | 0.996401 | − | 0.0847630i | \(-0.0270133\pi\) |
−0.571607 | + | 0.820527i | \(0.693680\pi\) | |||||||
\(38\) | −2.92155 | −0.473938 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 7.76146i | − | 1.22719i | ||||||
\(41\) | 4.82277 | − | 8.35327i | 0.753189 | − | 1.30456i | −0.193080 | − | 0.981183i | \(-0.561848\pi\) |
0.946269 | − | 0.323379i | \(-0.104819\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.08392 | + | 1.87740i | 0.165296 | + | 0.286301i | 0.936760 | − | 0.349971i | \(-0.113809\pi\) |
−0.771464 | + | 0.636273i | \(0.780475\pi\) | |||||||
\(44\) | −3.18386 | + | 1.83821i | −0.479986 | + | 0.277120i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.08392 | − | 5.34150i | 0.454699 | − | 0.787562i | ||||
\(47\) | −2.79334 | + | 4.83821i | −0.407450 | + | 0.705725i | −0.994603 | − | 0.103751i | \(-0.966915\pi\) |
0.587153 | + | 0.809476i | \(0.300249\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.72162 | + | 4.03275i | −0.817374 | + | 0.576107i | ||||
\(50\) | −3.39476 | − | 1.95997i | −0.480092 | − | 0.277181i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 2.47883i | − | 0.343751i | ||||||
\(53\) | 8.70349 | + | 5.02496i | 1.19552 | + | 0.690232i | 0.959552 | − | 0.281530i | \(-0.0908418\pi\) |
0.235964 | + | 0.971762i | \(0.424175\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.76146i | 1.04655i | ||||||||
\(56\) | −5.91015 | + | 1.87352i | −0.789778 | + | 0.250359i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.40101 | −0.315268 | ||||||||
\(59\) | 1.08739 | + | 1.88341i | 0.141566 | + | 0.245200i | 0.928087 | − | 0.372365i | \(-0.121453\pi\) |
−0.786521 | + | 0.617564i | \(0.788120\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.46986 | − | 2.00333i | −0.444270 | − | 0.256500i | 0.261137 | − | 0.965302i | \(-0.415903\pi\) |
−0.705407 | + | 0.708802i | \(0.749236\pi\) | |||||||
\(62\) | −4.80563 | −0.610315 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.568850 | −0.0711062 | ||||||||
\(65\) | −4.53206 | − | 2.61659i | −0.562133 | − | 0.324548i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.38341 | + | 9.32435i | 0.657689 | + | 1.13915i | 0.981213 | + | 0.192930i | \(0.0617990\pi\) |
−0.323524 | + | 0.946220i | \(0.604868\pi\) | |||||||
\(68\) | −1.78425 | −0.216372 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.23669 | + | 5.61945i | −0.147812 | + | 0.671653i | ||||
\(71\) | 6.39331i | 0.758746i | 0.925244 | + | 0.379373i | \(0.123860\pi\) | ||||
−0.925244 | + | 0.379373i | \(0.876140\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.25176 | − | 5.34150i | −1.08284 | − | 0.625176i | −0.151176 | − | 0.988507i | \(-0.548306\pi\) |
−0.931660 | + | 0.363331i | \(0.881639\pi\) | |||||||
\(74\) | − | 3.39331i | − | 0.394464i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.04521 | − | 3.49020i | −0.693433 | − | 0.400354i | ||||
\(77\) | 5.91015 | − | 1.87352i | 0.673525 | − | 0.213507i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.616587 | + | 1.06796i | −0.0693714 | + | 0.120155i | −0.898625 | − | 0.438718i | \(-0.855433\pi\) |
0.829253 | + | 0.558873i | \(0.188766\pi\) | |||||||
\(80\) | 2.64799 | − | 4.58645i | 0.296054 | − | 0.512780i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.48493 | + | 3.16673i | −0.605709 | + | 0.349706i | ||||
\(83\) | −0.518739 | − | 0.898482i | −0.0569390 | − | 0.0986213i | 0.836151 | − | 0.548499i | \(-0.184801\pi\) |
−0.893090 | + | 0.449878i | \(0.851467\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.88341 | + | 3.26217i | −0.204285 | + | 0.353832i | ||||
\(86\) | − | 1.42345i | − | 0.153494i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.49143 | 0.585388 | ||||||||
\(89\) | 3.73538 | + | 6.46986i | 0.395949 | + | 0.685804i | 0.993222 | − | 0.116234i | \(-0.0370823\pi\) |
−0.597273 | + | 0.802038i | \(0.703749\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.898482 | + | 4.08266i | −0.0941866 | + | 0.427979i | ||||
\(92\) | 12.7623 | − | 7.36834i | 1.33057 | − | 0.768203i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.17686 | − | 1.83416i | 0.327669 | − | 0.189180i | ||||
\(95\) | −12.7623 | + | 7.36834i | −1.30939 | + | 0.755976i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.7367 | + | 6.77618i | −1.19168 | + | 0.688017i | −0.958687 | − | 0.284462i | \(-0.908185\pi\) |
−0.232993 | + | 0.972478i | \(0.574852\pi\) | |||||||
\(98\) | 4.57759 | − | 0.414758i | 0.462407 | − | 0.0418969i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.68291 | − | 8.11103i | −0.468291 | − | 0.811103i | ||||
\(101\) | 13.7044 | 1.36364 | 0.681819 | − | 0.731521i | \(-0.261189\pi\) | ||||
0.681819 | + | 0.731521i | \(0.261189\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.89211i | 0.482033i | 0.970521 | + | 0.241017i | \(0.0774809\pi\) | ||||
−0.970521 | + | 0.241017i | \(0.922519\pi\) | |||||||
\(104\) | −1.85130 | + | 3.20655i | −0.181535 | + | 0.314428i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.29949 | − | 5.71489i | −0.320475 | − | 0.555079i | ||||
\(107\) | 2.12487 | − | 1.22679i | 0.205419 | − | 0.118599i | −0.393762 | − | 0.919213i | \(-0.628827\pi\) |
0.599180 | + | 0.800614i | \(0.295493\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.16784 | + | 3.75481i | −0.207641 | + | 0.359645i | −0.950971 | − | 0.309280i | \(-0.899912\pi\) |
0.743330 | + | 0.668925i | \(0.233245\pi\) | |||||||
\(110\) | 2.54817 | − | 4.41355i | 0.242958 | − | 0.420816i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.13166 | − | 0.909265i | −0.390405 | − | 0.0859174i | ||||
\(113\) | −6.20086 | − | 3.58007i | −0.583328 | − | 0.336784i | 0.179127 | − | 0.983826i | \(-0.442673\pi\) |
−0.762455 | + | 0.647042i | \(0.776006\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 31.1114i | − | 2.90115i | ||||||
\(116\) | −4.96812 | − | 2.86834i | −0.461278 | − | 0.266319i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 1.42800i | − | 0.131458i | ||||||
\(119\) | 2.93869 | + | 0.646726i | 0.269389 | + | 0.0592852i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.50857 | 0.500779 | ||||||||
\(122\) | 1.31542 | + | 2.27838i | 0.119093 | + | 0.206275i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −9.94369 | − | 5.74099i | −0.892970 | − | 0.515556i | ||||
\(125\) | −3.21226 | −0.287313 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.7065 | −1.57120 | −0.785601 | − | 0.618733i | \(-0.787646\pi\) | ||||
−0.785601 | + | 0.618733i | \(0.787646\pi\) | |||||||
\(128\) | −9.61276 | − | 5.54993i | −0.849656 | − | 0.490549i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.71810 | + | 2.97584i | 0.150688 | + | 0.260999i | ||||
\(131\) | 13.6046 | 1.18864 | 0.594318 | − | 0.804230i | \(-0.297422\pi\) | ||||
0.594318 | + | 0.804230i | \(0.297422\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.69148 | + | 7.93958i | 0.753647 | + | 0.688449i | ||||
\(134\) | − | 7.06972i | − | 0.610731i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.30807 | + | 1.33256i | 0.197915 | + | 0.114266i | ||||
\(137\) | 10.1601i | 0.868039i | 0.900904 | + | 0.434019i | \(0.142905\pi\) | ||||
−0.900904 | + | 0.434019i | \(0.857095\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.33821 | − | 1.92731i | −0.283143 | − | 0.163473i | 0.351703 | − | 0.936112i | \(-0.385603\pi\) |
−0.634845 | + | 0.772639i | \(0.718936\pi\) | |||||||
\(140\) | −9.27214 | + | 10.1502i | −0.783639 | + | 0.857852i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.09899 | − | 3.63555i | 0.176143 | − | 0.305089i | ||||
\(143\) | 1.85130 | − | 3.20655i | 0.154814 | − | 0.268145i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.4884 | + | 6.05551i | −0.871018 | + | 0.502882i | ||||
\(146\) | 3.50734 | + | 6.07489i | 0.290270 | + | 0.502762i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.05378 | − | 7.02135i | 0.333219 | − | 0.577152i | ||||
\(149\) | − | 5.08007i | − | 0.416175i | −0.978110 | − | 0.208088i | \(-0.933276\pi\) | ||
0.978110 | − | 0.208088i | \(-0.0667239\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.3055 | 1.48968 | 0.744842 | − | 0.667241i | \(-0.232525\pi\) | ||||
0.744842 | + | 0.667241i | \(0.232525\pi\) | |||||||
\(152\) | 5.21329 | + | 9.02968i | 0.422854 | + | 0.732404i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.97590 | − | 0.874988i | −0.320387 | − | 0.0705085i | ||||
\(155\) | −20.9926 | + | 12.1201i | −1.68617 | + | 0.973510i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.86834 | + | 1.65604i | −0.228919 | + | 0.132166i | −0.610073 | − | 0.792345i | \(-0.708860\pi\) |
0.381154 | + | 0.924511i | \(0.375527\pi\) | |||||||
\(158\) | 0.701244 | − | 0.404864i | 0.0557880 | − | 0.0322092i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −16.4548 | + | 9.50018i | −1.30087 | + | 0.751055i | ||||
\(161\) | −23.6905 | + | 7.50989i | −1.86708 | + | 0.591863i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.14673 | + | 1.98619i | 0.0898185 | + | 0.155570i | 0.907434 | − | 0.420194i | \(-0.138038\pi\) |
−0.817616 | + | 0.575764i | \(0.804705\pi\) | |||||||
\(164\) | −15.1324 | −1.18164 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.681229i | 0.0528737i | ||||||||
\(167\) | 1.33256 | − | 2.30807i | 0.103117 | − | 0.178604i | −0.809850 | − | 0.586636i | \(-0.800452\pi\) |
0.912967 | + | 0.408033i | \(0.133785\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.25176 | − | 9.09631i | −0.403981 | − | 0.699716i | ||||
\(170\) | 2.14201 | − | 1.23669i | 0.164284 | − | 0.0948496i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.70051 | − | 2.94536i | 0.129662 | − | 0.224582i | ||||
\(173\) | 1.28265 | − | 2.22162i | 0.0975182 | − | 0.168907i | −0.813139 | − | 0.582070i | \(-0.802243\pi\) |
0.910657 | + | 0.413164i | \(0.135576\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.77287 | + | 15.0564i | 0.360795 | + | 1.13815i | ||||
\(176\) | 3.24503 | + | 1.87352i | 0.244603 | + | 0.141222i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 4.90545i | − | 0.367679i | ||||||
\(179\) | −11.9828 | − | 6.91827i | −0.895636 | − | 0.517096i | −0.0198545 | − | 0.999803i | \(-0.506320\pi\) |
−0.875782 | + | 0.482707i | \(0.839654\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 4.74008i | − | 0.352328i | −0.984361 | − | 0.176164i | \(-0.943631\pi\) | ||
0.984361 | − | 0.176164i | \(-0.0563688\pi\) | |||||||
\(182\) | 1.85130 | − | 2.02662i | 0.137228 | − | 0.150223i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −22.0121 | −1.62275 | ||||||||
\(185\) | −8.55814 | − | 14.8231i | −0.629207 | − | 1.08982i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.30807 | − | 1.33256i | −0.168783 | − | 0.0974466i | ||||
\(188\) | 8.76466 | 0.639228 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 9.67641 | 0.702001 | ||||||||
\(191\) | 7.22558 | + | 4.17169i | 0.522825 | + | 0.301853i | 0.738090 | − | 0.674703i | \(-0.235728\pi\) |
−0.215265 | + | 0.976556i | \(0.569062\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.92212 | + | 15.4536i | 0.642229 | + | 1.11237i | 0.984934 | + | 0.172930i | \(0.0553233\pi\) |
−0.342706 | + | 0.939443i | \(0.611343\pi\) | |||||||
\(194\) | 8.89876 | 0.638893 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.96733 | + | 4.61036i | 0.711952 | + | 0.329312i | ||||
\(197\) | − | 15.1102i | − | 1.07656i | −0.842767 | − | 0.538279i | \(-0.819075\pi\) | ||
0.842767 | − | 0.538279i | \(-0.180925\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.50000 | − | 4.33013i | −0.531661 | − | 0.306955i | 0.210032 | − | 0.977695i | \(-0.432643\pi\) |
−0.741693 | + | 0.670740i | \(0.765977\pi\) | |||||||
\(200\) | 13.9897i | 0.989218i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.79300 | − | 4.49929i | −0.548313 | − | 0.316569i | ||||
\(203\) | 7.14290 | + | 6.52496i | 0.501333 | + | 0.457963i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.9734 | + | 27.6667i | −1.11563 | + | 1.93233i | ||||
\(206\) | 1.60613 | − | 2.78190i | 0.111904 | − | 0.193824i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.18797 | + | 1.26322i | −0.151708 | + | 0.0875887i | ||||
\(209\) | −5.21329 | − | 9.02968i | −0.360611 | − | 0.624596i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.29047 | − | 12.6275i | 0.501897 | − | 0.869310i | −0.498101 | − | 0.867119i | \(-0.665969\pi\) |
0.999998 | − | 0.00219128i | \(-0.000697506\pi\) | |||||||
\(212\) | − | 15.7668i | − | 1.08287i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.61107 | −0.110131 | ||||||||
\(215\) | −3.59002 | − | 6.21810i | −0.244838 | − | 0.424071i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.2965 | + | 13.0597i | 0.970510 | + | 0.886552i | ||||
\(218\) | 2.46548 | − | 1.42345i | 0.166984 | − | 0.0964080i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 10.5452 | − | 6.08828i | 0.710958 | − | 0.410472i | ||||
\(221\) | 1.55622 | − | 0.898482i | 0.104683 | − | 0.0604385i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.16531 | − | 5.29159i | 0.613754 | − | 0.354351i | −0.160679 | − | 0.987007i | \(-0.551368\pi\) |
0.774433 | + | 0.632655i | \(0.218035\pi\) | |||||||
\(224\) | 11.2061 | + | 10.2367i | 0.748741 | + | 0.683967i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.35075 | + | 4.07161i | 0.156369 | + | 0.270839i | ||||
\(227\) | 6.72398 | 0.446286 | 0.223143 | − | 0.974786i | \(-0.428368\pi\) | ||||
0.223143 | + | 0.974786i | \(0.428368\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 12.2630i | − | 0.810364i | −0.914236 | − | 0.405182i | \(-0.867208\pi\) | ||
0.914236 | − | 0.405182i | \(-0.132792\pi\) | |||||||
\(230\) | −10.2142 | + | 17.6915i | −0.673503 | + | 1.16654i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.28442 | + | 7.42084i | 0.281286 | + | 0.487202i | ||||
\(233\) | 4.87268 | − | 2.81324i | 0.319220 | − | 0.184302i | −0.331825 | − | 0.943341i | \(-0.607664\pi\) |
0.651045 | + | 0.759039i | \(0.274331\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.25176 | − | 16.0245i | 0.603518 | − | 1.04532i | ||||
\(236\) | 1.70595 | − | 2.95479i | 0.111048 | − | 0.192341i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.45876 | − | 1.33256i | −0.0945574 | − | 0.0863772i | ||||
\(239\) | 13.8213 | + | 7.97976i | 0.894028 | + | 0.516168i | 0.875258 | − | 0.483656i | \(-0.160692\pi\) |
0.0187704 | + | 0.999824i | \(0.494025\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.58806i | 0.295543i | 0.989022 | + | 0.147771i | \(0.0472100\pi\) | ||||
−0.989022 | + | 0.147771i | \(0.952790\pi\) | |||||||
\(242\) | −3.13245 | − | 1.80852i | −0.201361 | − | 0.116256i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.28583i | 0.402409i | ||||||||
\(245\) | 18.9504 | − | 13.3568i | 1.21070 | − | 0.853334i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.03014 | 0.447317 | ||||||||
\(248\) | 8.57528 | + | 14.8528i | 0.544531 | + | 0.943155i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.82665 | + | 1.05462i | 0.115527 | + | 0.0666998i | ||||
\(251\) | 13.8042 | 0.871314 | 0.435657 | − | 0.900113i | \(-0.356516\pi\) | ||||
0.435657 | + | 0.900113i | \(0.356516\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 22.0121 | 1.38389 | ||||||||
\(254\) | 10.0688 | + | 5.81324i | 0.631774 | + | 0.364755i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.21305 | + | 7.29721i | 0.263315 | + | 0.456076i | ||||
\(257\) | −8.96430 | −0.559178 | −0.279589 | − | 0.960120i | \(-0.590198\pi\) | ||||
−0.279589 | + | 0.960120i | \(0.590198\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.22162 | + | 10.0949i | −0.573003 | + | 0.627268i | ||||
\(260\) | 8.21006i | 0.509166i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.73623 | − | 4.46652i | −0.477946 | − | 0.275942i | ||||
\(263\) | − | 28.5534i | − | 1.76068i | −0.474343 | − | 0.880340i | \(-0.657314\pi\) | ||
0.474343 | − | 0.880340i | \(-0.342686\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −28.8266 | − | 16.6431i | −1.77081 | − | 1.02238i | ||||
\(266\) | −2.33576 | − | 7.36834i | −0.143215 | − | 0.451782i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.44577 | − | 14.6285i | 0.515907 | − | 0.893578i | ||||
\(269\) | −11.9657 | + | 20.7251i | −0.729559 | + | 1.26363i | 0.227510 | + | 0.973776i | \(0.426941\pi\) |
−0.957070 | + | 0.289858i | \(0.906392\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.6467 | − | 7.30159i | 0.768234 | − | 0.443540i | −0.0640103 | − | 0.997949i | \(-0.520389\pi\) |
0.832244 | + | 0.554409i | \(0.187056\pi\) | |||||||
\(272\) | 0.909265 | + | 1.57489i | 0.0551323 | + | 0.0954919i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.33568 | − | 5.77756i | 0.201516 | − | 0.349035i | ||||
\(275\) | − | 13.9897i | − | 0.843608i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.3830 | 1.34486 | 0.672431 | − | 0.740160i | \(-0.265250\pi\) | ||||
0.672431 | + | 0.740160i | \(0.265250\pi\) | |||||||
\(278\) | 1.26551 | + | 2.19193i | 0.0759005 | + | 0.131463i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 19.5749 | − | 6.20524i | 1.16982 | − | 0.370834i | ||||
\(281\) | −10.0517 | + | 5.80335i | −0.599634 | + | 0.346199i | −0.768897 | − | 0.639372i | \(-0.779194\pi\) |
0.169264 | + | 0.985571i | \(0.445861\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.9849 | − | 7.49685i | 0.771874 | − | 0.445642i | −0.0616687 | − | 0.998097i | \(-0.519642\pi\) |
0.833543 | + | 0.552455i | \(0.186309\pi\) | |||||||
\(284\) | 8.68635 | − | 5.01507i | 0.515440 | − | 0.297590i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.10549 | + | 1.21560i | −0.124500 | + | 0.0718801i | ||||
\(287\) | 24.9233 | + | 5.48493i | 1.47117 | + | 0.323765i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.85327 | + | 13.6023i | 0.461957 | + | 0.800134i | ||||
\(290\) | 7.95234 | 0.466977 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 16.7600i | 0.980807i | ||||||||
\(293\) | −8.16762 | + | 14.1467i | −0.477157 | + | 0.826461i | −0.999657 | − | 0.0261787i | \(-0.991666\pi\) |
0.522500 | + | 0.852639i | \(0.324999\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.60152 | − | 6.23801i | −0.209688 | − | 0.363191i | ||||
\(296\) | −10.4877 | + | 6.05510i | −0.609588 | + | 0.351946i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.66784 | + | 2.88878i | −0.0966153 | + | 0.167343i | ||||
\(299\) | −7.42084 | + | 12.8533i | −0.429158 | + | 0.743324i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.86834 | + | 4.23469i | −0.222968 | + | 0.244083i | ||||
\(302\) | −10.4094 | − | 6.00989i | −0.598996 | − | 0.345831i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.11450i | 0.408045i | ||||||||
\(305\) | 11.4925 | + | 6.63517i | 0.658056 | + | 0.379929i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 3.17340i | − | 0.181115i | −0.995891 | − | 0.0905577i | \(-0.971135\pi\) | ||
0.995891 | − | 0.0905577i | \(-0.0288650\pi\) | |||||||
\(308\) | −7.18155 | − | 6.56028i | −0.409207 | − | 0.373806i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 15.9166 | 0.904003 | ||||||||
\(311\) | −12.5671 | − | 21.7668i | −0.712614 | − | 1.23428i | −0.963873 | − | 0.266364i | \(-0.914178\pi\) |
0.251259 | − | 0.967920i | \(-0.419155\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.1463 | + | 9.32205i | 0.912641 | + | 0.526914i | 0.881280 | − | 0.472594i | \(-0.156682\pi\) |
0.0313612 | + | 0.999508i | \(0.490016\pi\) | |||||||
\(314\) | 2.17478 | 0.122730 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.93466 | 0.108833 | ||||||||
\(317\) | 6.91924 | + | 3.99483i | 0.388623 | + | 0.224372i | 0.681563 | − | 0.731759i | \(-0.261300\pi\) |
−0.292940 | + | 0.956131i | \(0.594634\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.28442 | − | 7.42084i | −0.239882 | − | 0.415487i | ||||
\(320\) | 1.88407 | 0.105323 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 15.9372 | + | 3.50734i | 0.888145 | + | 0.195456i | ||||
\(323\) | − | 5.06028i | − | 0.281561i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.16882 | + | 4.71627i | 0.453125 | + | 0.261612i | ||||
\(326\) | − | 1.50593i | − | 0.0834056i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 19.5749 | + | 11.3016i | 1.08084 | + | 0.624025i | ||||
\(329\) | −14.4355 | − | 3.17686i | −0.795856 | − | 0.175146i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.46733 | − | 7.73765i | 0.245547 | − | 0.425299i | −0.716738 | − | 0.697342i | \(-0.754366\pi\) |
0.962285 | + | 0.272043i | \(0.0876992\pi\) | |||||||
\(332\) | −0.813824 | + | 1.40958i | −0.0446644 | + | 0.0773610i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.51552 | + | 0.874988i | −0.0829258 | + | 0.0478772i | ||||
\(335\) | −17.8303 | − | 30.8830i | −0.974173 | − | 1.68732i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.12263 | + | 3.67650i | −0.115627 | + | 0.200272i | −0.918030 | − | 0.396510i | \(-0.870221\pi\) |
0.802403 | + | 0.596782i | \(0.203554\pi\) | |||||||
\(338\) | 6.89682i | 0.375138i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.90958 | 0.320492 | ||||||||
\(341\) | −8.57528 | − | 14.8528i | −0.464377 | − | 0.804325i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.7453 | − | 11.2061i | −0.796169 | − | 0.605074i | ||||
\(344\) | −4.39947 | + | 2.54003i | −0.237203 | + | 0.136949i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.45876 | + | 0.842215i | −0.0784234 | + | 0.0452778i | ||||
\(347\) | 2.27460 | − | 1.31324i | 0.122107 | − | 0.0704985i | −0.437702 | − | 0.899120i | \(-0.644208\pi\) |
0.559809 | + | 0.828621i | \(0.310874\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.1387 | + | 16.2459i | −1.50623 | + | 0.869622i | −0.506255 | + | 0.862384i | \(0.668971\pi\) |
−0.999974 | + | 0.00723825i | \(0.997696\pi\) | |||||||
\(350\) | 2.22907 | − | 10.1288i | 0.119149 | − | 0.541407i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.72162 | − | 11.6422i | −0.358263 | − | 0.620531i | ||||
\(353\) | −23.3842 | −1.24461 | −0.622307 | − | 0.782773i | \(-0.713805\pi\) | ||||
−0.622307 | + | 0.782773i | \(0.713805\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 21.1751i | − | 1.12386i | ||||||
\(356\) | 5.86024 | − | 10.1502i | 0.310592 | − | 0.537962i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.54268 | + | 7.86815i | 0.240088 | + | 0.415845i | ||||
\(359\) | −18.4900 | + | 10.6752i | −0.975865 | + | 0.563416i | −0.901019 | − | 0.433779i | \(-0.857180\pi\) |
−0.0748455 | + | 0.997195i | \(0.523846\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.398482 | − | 0.690192i | 0.0209728 | − | 0.0363259i | ||||
\(362\) | −1.55622 | + | 2.69545i | −0.0817930 | + | 0.141670i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.25176 | − | 1.98181i | 0.327681 | − | 0.103875i | ||||
\(365\) | 30.6425 | + | 17.6915i | 1.60390 | + | 0.926014i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 15.5229i | − | 0.810289i | −0.914253 | − | 0.405145i | \(-0.867221\pi\) | ||
0.914253 | − | 0.405145i | \(-0.132779\pi\) | |||||||
\(368\) | −13.0075 | − | 7.50989i | −0.678064 | − | 0.391480i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 11.2389i | 0.584283i | ||||||||
\(371\) | −5.71489 | + | 25.9682i | −0.296702 | + | 1.34820i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.3528 | −1.20916 | −0.604582 | − | 0.796543i | \(-0.706660\pi\) | ||||
−0.604582 | + | 0.796543i | \(0.706660\pi\) | |||||||
\(374\) | 0.874988 | + | 1.51552i | 0.0452445 | + | 0.0783659i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −11.3378 | − | 6.54585i | −0.584700 | − | 0.337577i | ||||
\(377\) | 5.77756 | 0.297559 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.53871 | 0.130405 | 0.0652024 | − | 0.997872i | \(-0.479231\pi\) | ||||
0.0652024 | + | 0.997872i | \(0.479231\pi\) | |||||||
\(380\) | 20.0222 | + | 11.5598i | 1.02712 | + | 0.593006i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.73922 | − | 4.74446i | −0.140151 | − | 0.242748i | ||||
\(383\) | −16.2041 | −0.827993 | −0.413996 | − | 0.910278i | \(-0.635867\pi\) | ||||
−0.413996 | + | 0.910278i | \(0.635867\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −19.5749 | + | 6.20524i | −0.997629 | + | 0.316248i | ||||
\(386\) | − | 11.7169i | − | 0.596374i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 18.4131 | + | 10.6308i | 0.934783 | + | 0.539697i | ||||
\(389\) | 22.3330i | 1.13233i | 0.824292 | + | 0.566165i | \(0.191573\pi\) | ||||
−0.824292 | + | 0.566165i | \(0.808427\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.25176 | + | 5.34150i | 0.467881 | + | 0.270131i | ||||
\(392\) | −9.45027 | − | 13.4079i | −0.477311 | − | 0.677202i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.96083 | + | 8.59242i | −0.249923 | + | 0.432880i | ||||
\(395\) | 2.04218 | − | 3.53717i | 0.102753 | − | 0.177974i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.3116 | − | 16.3457i | 1.42092 | − | 0.820367i | 0.424540 | − | 0.905409i | \(-0.360436\pi\) |
0.996377 | + | 0.0850420i | \(0.0271025\pi\) | |||||||
\(398\) | 2.84325 | + | 4.92465i | 0.142519 | + | 0.246851i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.77287 | + | 8.26685i | −0.238643 | + | 0.413343i | ||||
\(401\) | 28.9270i | 1.44454i | 0.691609 | + | 0.722272i | \(0.256902\pi\) | ||||
−0.691609 | + | 0.722272i | \(0.743098\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.5638 | 0.576033 | ||||||||
\(404\) | −10.7501 | − | 18.6196i | −0.534835 | − | 0.926362i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.91959 | − | 6.05551i | −0.0952679 | − | 0.300530i | ||||
\(407\) | 10.4877 | − | 6.05510i | 0.519858 | − | 0.300140i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.910038 | + | 0.525411i | −0.0449985 | + | 0.0259799i | −0.522330 | − | 0.852743i | \(-0.674937\pi\) |
0.477332 | + | 0.878723i | \(0.341604\pi\) | |||||||
\(410\) | 18.1665 | − | 10.4884i | 0.897180 | − | 0.517987i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.64673 | − | 3.83749i | 0.327461 | − | 0.189060i | ||||
\(413\) | −3.88073 | + | 4.24824i | −0.190958 | + | 0.209042i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.71810 | + | 2.97584i | 0.0843384 | + | 0.146078i | ||||
\(416\) | 9.06412 | 0.444405 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.84631i | 0.334864i | ||||||||
\(419\) | 1.56060 | − | 2.70304i | 0.0762402 | − | 0.132052i | −0.825385 | − | 0.564571i | \(-0.809042\pi\) |
0.901625 | + | 0.432519i | \(0.142375\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.35327 | + | 7.54009i | 0.212166 | + | 0.367482i | 0.952392 | − | 0.304876i | \(-0.0986150\pi\) |
−0.740226 | + | 0.672358i | \(0.765282\pi\) | |||||||
\(422\) | −8.29145 | + | 4.78707i | −0.403621 | + | 0.233031i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −11.7754 | + | 20.3956i | −0.571864 | + | 0.990497i | ||||
\(425\) | 3.39476 | − | 5.87990i | 0.164670 | − | 0.285217i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.27838 | − | 10.3529i | 0.110259 | − | 0.501010i | ||||
\(428\) | −3.33360 | − | 1.92465i | −0.161136 | − | 0.0930316i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.71457i | 0.227357i | ||||||||
\(431\) | 23.6279 | + | 13.6416i | 1.13811 | + | 0.657090i | 0.945963 | − | 0.324275i | \(-0.105120\pi\) |
0.192151 | + | 0.981365i | \(0.438454\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 12.8711i | − | 0.618547i | −0.950973 | − | 0.309274i | \(-0.899914\pi\) | ||
0.950973 | − | 0.309274i | \(-0.100086\pi\) | |||||||
\(434\) | −3.84207 | − | 12.1201i | −0.184425 | − | 0.581783i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.80202 | 0.325758 | ||||||||
\(437\) | 20.8972 | + | 36.1950i | 0.999648 | + | 1.73144i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.9734 | − | 9.22223i | −0.762368 | − | 0.440153i | 0.0677776 | − | 0.997700i | \(-0.478409\pi\) |
−0.830145 | + | 0.557547i | \(0.811743\pi\) | |||||||
\(440\) | −18.1880 | −0.867081 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.17992 | −0.0561233 | ||||||||
\(443\) | 2.48550 | + | 1.43500i | 0.118090 | + | 0.0681790i | 0.557881 | − | 0.829921i | \(-0.311614\pi\) |
−0.439792 | + | 0.898100i | \(0.644948\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.3719 | − | 21.4287i | −0.586482 | − | 1.01582i | ||||
\(446\) | −6.94914 | −0.329051 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.454792 | − | 1.43468i | −0.0214869 | − | 0.0677820i | ||||
\(449\) | − | 1.81675i | − | 0.0857380i | −0.999081 | − | 0.0428690i | \(-0.986350\pi\) | ||
0.999081 | − | 0.0428690i | \(-0.0136498\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.5749 | − | 11.3016i | −0.921746 | − | 0.532170i | ||||
\(452\) | 11.2332i | 0.528364i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.82359 | − | 2.20755i | −0.179450 | − | 0.103605i | ||||
\(455\) | 2.97584 | − | 13.5221i | 0.139510 | − | 0.633926i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.07788 | + | 5.33104i | −0.143977 | + | 0.249375i | −0.928991 | − | 0.370103i | \(-0.879322\pi\) |
0.785014 | + | 0.619478i | \(0.212656\pi\) | |||||||
\(458\) | −4.02608 | + | 6.97338i | −0.188126 | + | 0.325844i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −42.2699 | + | 24.4045i | −1.97084 | + | 1.13787i | ||||
\(461\) | 8.52537 | + | 14.7664i | 0.397066 | + | 0.687739i | 0.993363 | − | 0.115026i | \(-0.0366951\pi\) |
−0.596296 | + | 0.802764i | \(0.703362\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.7065 | + | 25.4725i | −0.683471 | + | 1.18381i | 0.290443 | + | 0.956892i | \(0.406197\pi\) |
−0.973915 | + | 0.226915i | \(0.927136\pi\) | |||||||
\(464\) | 5.84689i | 0.271435i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.69446 | −0.171143 | ||||||||
\(467\) | −13.5590 | − | 23.4849i | −0.627437 | − | 1.08675i | −0.988064 | − | 0.154043i | \(-0.950771\pi\) |
0.360627 | − | 0.932710i | \(-0.382563\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −19.2126 | + | 21.0321i | −0.887155 | + | 0.971171i | ||||
\(470\) | −10.5220 | + | 6.07489i | −0.485345 | + | 0.280214i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.41355 | + | 2.54817i | −0.203150 | + | 0.117289i | ||||
\(473\) | 4.39947 | − | 2.54003i | 0.202288 | − | 0.116791i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 23.0035 | − | 13.2811i | 1.05547 | − | 0.609378i | ||||
\(476\) | −1.42650 | − | 4.50000i | −0.0653835 | − | 0.206257i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5.23967 | − | 9.07538i | −0.239657 | − | 0.415098i | ||||
\(479\) | 21.5569 | 0.984960 | 0.492480 | − | 0.870324i | \(-0.336090\pi\) | ||||
0.492480 | + | 0.870324i | \(0.336090\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.16532i | 0.372307i | ||||||||
\(482\) | 1.50631 | − | 2.60900i | 0.0686104 | − | 0.118837i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.32106 | − | 7.48430i | −0.196412 | − | 0.340195i | ||||
\(485\) | 38.8728 | − | 22.4432i | 1.76512 | − | 1.01909i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.29047 | − | 12.6275i | 0.330363 | − | 0.572205i | −0.652220 | − | 0.758029i | \(-0.726162\pi\) |
0.982583 | + | 0.185825i | \(0.0594956\pi\) | |||||||
\(488\) | 4.69455 | − | 8.13120i | 0.212512 | − | 0.368082i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −15.1613 | + | 1.37371i | −0.684920 | + | 0.0620580i | ||||
\(491\) | 0.245174 | + | 0.141551i | 0.0110645 | + | 0.00638811i | 0.505522 | − | 0.862814i | \(-0.331300\pi\) |
−0.494458 | + | 0.869202i | \(0.664633\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 4.15867i | − | 0.187297i | ||||||
\(494\) | −3.99769 | − | 2.30807i | −0.179864 | − | 0.103845i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 11.7026i | 0.525461i | ||||||||
\(497\) | −16.1243 | + | 5.11141i | −0.723275 | + | 0.229278i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.3055 | 0.550871 | 0.275436 | − | 0.961319i | \(-0.411178\pi\) | ||||
0.275436 | + | 0.961319i | \(0.411178\pi\) | |||||||
\(500\) | 2.51977 | + | 4.36438i | 0.112688 | + | 0.195181i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −7.84976 | − | 4.53206i | −0.350352 | − | 0.202276i | ||||
\(503\) | −1.78425 | −0.0795559 | −0.0397779 | − | 0.999209i | \(-0.512665\pi\) | ||||
−0.0397779 | + | 0.999209i | \(0.512665\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −45.3900 | −2.01983 | ||||||||
\(506\) | −12.5172 | − | 7.22679i | −0.556456 | − | 0.321270i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.8895 | + | 24.0572i | 0.616245 | + | 1.06737i | ||||
\(509\) | −39.0725 | −1.73186 | −0.865928 | − | 0.500168i | \(-0.833272\pi\) | ||||
−0.865928 | + | 0.500168i | \(0.833272\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.07489 | − | 27.6040i | 0.268737 | − | 1.22113i | ||||
\(512\) | 16.6670i | 0.736583i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.09755 | + | 2.94307i | 0.224843 | + | 0.129813i | ||||
\(515\) | − | 16.2030i | − | 0.713991i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.3378 | + | 6.54585i | 0.498634 | + | 0.287886i | ||||
\(518\) | 8.55814 | − | 2.71293i | 0.376023 | − | 0.119199i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6.13166 | − | 10.6203i | 0.268891 | − | 0.465733i | ||||
\(521\) | −10.1814 | + | 17.6347i | −0.446056 | + | 0.772591i | −0.998125 | − | 0.0612072i | \(-0.980505\pi\) |
0.552070 | + | 0.833798i | \(0.313838\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.24066 | − | 0.716293i | 0.0542501 | − | 0.0313213i | −0.472630 | − | 0.881261i | \(-0.656695\pi\) |
0.526880 | + | 0.849940i | \(0.323362\pi\) | |||||||
\(524\) | −10.6718 | − | 18.4840i | −0.466198 | − | 0.807478i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.37439 | + | 16.2369i | −0.408743 | + | 0.707963i | ||||
\(527\) | − | 8.32359i | − | 0.362581i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −65.2342 | −2.83627 | ||||||||
\(530\) | 10.9282 | + | 18.9282i | 0.474690 | + | 0.822187i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.96941 | − | 18.0368i | 0.172096 | − | 0.781994i | ||||
\(533\) | 13.1984 | − | 7.62010i | 0.571686 | − | 0.330063i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.03773 | + | 4.06323i | −0.304267 | + | 0.175669i | ||||
\(536\) | −21.8505 | + | 12.6154i | −0.943797 | + | 0.544901i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 13.6085 | − | 7.85690i | 0.586706 | − | 0.338735i | ||||
\(539\) | 9.45027 | + | 13.4079i | 0.407052 | + | 0.577520i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.04521 | + | 8.73856i | 0.216910 | + | 0.375700i | 0.953862 | − | 0.300246i | \(-0.0970687\pi\) |
−0.736951 | + | 0.675946i | \(0.763735\pi\) | |||||||
\(542\) | −9.58875 | −0.411872 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 6.52433i | − | 0.279729i | ||||||
\(545\) | 7.18005 | − | 12.4362i | 0.307559 | − | 0.532709i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.65024 | − | 6.32240i | −0.156073 | − | 0.270326i | 0.777376 | − | 0.629036i | \(-0.216550\pi\) |
−0.933449 | + | 0.358710i | \(0.883217\pi\) | |||||||
\(548\) | 13.8042 | − | 7.96986i | 0.589686 | − | 0.340456i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.59295 | + | 7.95521i | −0.195844 | + | 0.339211i | ||||
\(551\) | 8.13484 | − | 14.0900i | 0.346556 | − | 0.600253i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.18642 | − | 0.701244i | −0.135500 | − | 0.0298199i | ||||
\(554\) | −12.7281 | − | 7.34855i | −0.540764 | − | 0.312210i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.04733i | 0.256464i | ||||||||
\(557\) | −19.7970 | − | 11.4298i | −0.838828 | − | 0.484297i | 0.0180379 | − | 0.999837i | \(-0.494258\pi\) |
−0.856866 | + | 0.515540i | \(0.827591\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.42524i | 0.144872i | ||||||||
\(560\) | 13.6844 | + | 3.01156i | 0.578270 | + | 0.127261i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.62119 | 0.321481 | ||||||||
\(563\) | −10.5548 | − | 18.2814i | −0.444832 | − | 0.770471i | 0.553209 | − | 0.833043i | \(-0.313403\pi\) |
−0.998040 | + | 0.0625717i | \(0.980070\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 20.5377 | + | 11.8575i | 0.864029 | + | 0.498847i | ||||
\(566\) | −9.84517 | −0.413824 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −14.9819 | −0.628629 | ||||||||
\(569\) | −22.9095 | − | 13.2268i | −0.960415 | − | 0.554496i | −0.0641144 | − | 0.997943i | \(-0.520422\pi\) |
−0.896301 | + | 0.443447i | \(0.853756\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.01507 | − | 10.4184i | −0.251723 | − | 0.435997i | 0.712277 | − | 0.701898i | \(-0.247664\pi\) |
−0.964000 | + | 0.265901i | \(0.914330\pi\) | |||||||
\(572\) | −5.80883 | −0.242879 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −12.3719 | − | 11.3016i | −0.516391 | − | 0.471718i | ||||
\(575\) | 56.0767i | 2.33856i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.9055 | − | 18.4207i | −1.32824 | − | 0.766862i | −0.343216 | − | 0.939257i | \(-0.611516\pi\) |
−0.985028 | + | 0.172395i | \(0.944850\pi\) | |||||||
\(578\) | − | 10.3132i | − | 0.428974i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 16.4548 | + | 9.50018i | 0.683248 | + | 0.394473i | ||||
\(581\) | 1.85130 | − | 2.02662i | 0.0768049 | − | 0.0840786i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.7754 | − | 20.3956i | 0.487687 | − | 0.844699i | ||||
\(584\) | 12.5172 | − | 21.6804i | 0.517964 | − | 0.897140i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.28903 | − | 5.36302i | 0.383726 | − | 0.221544i | ||||
\(587\) | 14.3856 | + | 24.9166i | 0.593758 | + | 1.02842i | 0.993721 | + | 0.111887i | \(0.0356896\pi\) |
−0.399963 | + | 0.916531i | \(0.630977\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.2819 | − | 28.2011i | 0.670884 | − | 1.16200i | ||||
\(590\) | 4.72966i | 0.194717i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −8.26331 | −0.339620 | ||||||||
\(593\) | 5.29159 | + | 9.16531i | 0.217300 | + | 0.376374i | 0.953982 | − | 0.299865i | \(-0.0969418\pi\) |
−0.736682 | + | 0.676240i | \(0.763608\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.73317 | − | 2.14201i | −0.399021 | − | 0.0878137i | ||||
\(596\) | −6.90210 | + | 3.98493i | −0.282721 | + | 0.163229i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 8.43972 | − | 4.87268i | 0.345126 | − | 0.199259i | ||||
\(599\) | −15.7553 | + | 9.09634i | −0.643745 | + | 0.371666i | −0.786056 | − | 0.618156i | \(-0.787880\pi\) |
0.142311 | + | 0.989822i | \(0.454547\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.8719 | − | 13.2051i | 0.932963 | − | 0.538646i | 0.0452152 | − | 0.998977i | \(-0.485603\pi\) |
0.887747 | + | 0.460331i | \(0.152269\pi\) | |||||||
\(602\) | 3.59002 | − | 1.13804i | 0.146318 | − | 0.0463829i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −14.3593 | − | 24.8711i | −0.584272 | − | 1.01199i | ||||
\(605\) | −18.2448 | −0.741757 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 24.9776i | − | 1.01381i | −0.862003 | − | 0.506904i | \(-0.830790\pi\) | ||
0.862003 | − | 0.506904i | \(-0.169210\pi\) | |||||||
\(608\) | 12.7623 | − | 22.1050i | 0.517581 | − | 0.896477i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.35679 | − | 7.54618i | −0.176401 | − | 0.305536i | ||||
\(611\) | −7.64450 | + | 4.41355i | −0.309263 | + | 0.178553i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.05631 | − | 12.2219i | 0.285002 | − | 0.493637i | −0.687608 | − | 0.726082i | \(-0.741339\pi\) |
0.972610 | + | 0.232445i | \(0.0746725\pi\) | |||||||
\(614\) | −1.04186 | + | 1.80455i | −0.0420460 | + | 0.0728258i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.39036 | + | 13.8497i | 0.176893 | + | 0.558022i | ||||
\(617\) | −12.6669 | − | 7.31324i | −0.509950 | − | 0.294420i | 0.222863 | − | 0.974850i | \(-0.428460\pi\) |
−0.732813 | + | 0.680430i | \(0.761793\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26.5442i | 1.06690i | 0.845831 | + | 0.533452i | \(0.179105\pi\) | ||||
−0.845831 | + | 0.533452i | \(0.820895\pi\) | |||||||
\(620\) | 32.9343 | + | 19.0146i | 1.32267 | + | 0.763645i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 16.5036i | 0.661734i | ||||||||
\(623\) | −13.3310 | + | 14.5935i | −0.534095 | + | 0.584675i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.2101 | −0.768403 | ||||||||
\(626\) | −6.12105 | − | 10.6020i | −0.244646 | − | 0.423740i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.50000 | + | 2.59808i | 0.179570 | + | 0.103675i | ||||
\(629\) | 5.87738 | 0.234347 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.20304 | −0.326558 | −0.163279 | − | 0.986580i | \(-0.552207\pi\) | ||||
−0.163279 | + | 0.986580i | \(0.552207\pi\) | |||||||
\(632\) | −2.50264 | − | 1.44490i | −0.0995495 | − | 0.0574749i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.62308 | − | 4.54331i | −0.104176 | − | 0.180438i | ||||
\(635\) | 58.6455 | 2.32727 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.0151 | + | 0.998034i | −0.436433 | + | 0.0395436i | ||||
\(638\) | 5.62648i | 0.222755i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 31.8382 | + | 18.3818i | 1.25852 | + | 0.726604i | ||||
\(641\) | − | 16.0499i | − | 0.633934i | −0.948437 | − | 0.316967i | \(-0.897336\pi\) | ||
0.948437 | − | 0.316967i | \(-0.102664\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.8719 | + | 13.2051i | 0.901978 | + | 0.520757i | 0.877841 | − | 0.478951i | \(-0.158983\pi\) |
0.0241366 | + | 0.999709i | \(0.492316\pi\) | |||||||
\(644\) | 28.7869 | + | 26.2965i | 1.13436 | + | 1.03623i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.66134 | + | 2.87753i | −0.0653646 | + | 0.113215i | ||||
\(647\) | 15.8508 | − | 27.4543i | 0.623158 | − | 1.07934i | −0.365736 | − | 0.930719i | \(-0.619183\pi\) |
0.988894 | − | 0.148623i | \(-0.0474840\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.41355 | − | 2.54817i | 0.173247 | − | 0.100024i | ||||
\(650\) | −3.09680 | − | 5.36382i | −0.121467 | − | 0.210386i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.79904 | − | 3.11603i | 0.0704558 | − | 0.122033i | ||||
\(653\) | − | 13.2901i | − | 0.520083i | −0.965597 | − | 0.260041i | \(-0.916264\pi\) | ||
0.965597 | − | 0.260041i | \(-0.0837362\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −45.0594 | −1.76062 | ||||||||
\(656\) | 7.71155 | + | 13.3568i | 0.301085 | + | 0.521495i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 7.16576 | + | 6.54585i | 0.279351 | + | 0.255184i | ||||
\(659\) | 31.3609 | − | 18.1062i | 1.22165 | − | 0.705319i | 0.256379 | − | 0.966576i | \(-0.417470\pi\) |
0.965269 | + | 0.261257i | \(0.0841372\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −43.9880 | + | 25.3965i | −1.71093 | + | 0.987809i | −0.777630 | + | 0.628722i | \(0.783578\pi\) |
−0.933304 | + | 0.359087i | \(0.883088\pi\) | |||||||
\(662\) | −5.08070 | + | 2.93334i | −0.197467 | + | 0.114008i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.10549 | − | 1.21560i | 0.0817087 | − | 0.0471745i | ||||
\(665\) | −28.7869 | − | 26.2965i | −1.11631 | − | 1.01973i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17.1739 | + | 29.7460i | 0.664975 | + | 1.15177i | ||||
\(668\) | −4.18118 | −0.161775 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 23.4155i | 0.904618i | ||||||||
\(671\) | −4.69455 | + | 8.13120i | −0.181231 | + | 0.313902i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.66432 | − | 2.88269i | −0.0641550 | − | 0.111120i | 0.832164 | − | 0.554530i | \(-0.187102\pi\) |
−0.896319 | + | 0.443410i | \(0.853769\pi\) | |||||||
\(674\) | 2.41407 | − | 1.39376i | 0.0929864 | − | 0.0536857i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.23922 | + | 14.2707i | −0.316893 | + | 0.548875i | ||||
\(677\) | 9.96901 | − | 17.2668i | 0.383140 | − | 0.663618i | −0.608369 | − | 0.793654i | \(-0.708176\pi\) |
0.991509 | + | 0.130036i | \(0.0415093\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −26.4734 | − | 24.1832i | −1.01595 | − | 0.928065i | ||||
\(680\) | −7.64450 | − | 4.41355i | −0.293153 | − | 0.169252i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 11.2614i | 0.431222i | ||||||||
\(683\) | −24.8234 | − | 14.3318i | −0.949843 | − | 0.548392i | −0.0568107 | − | 0.998385i | \(-0.518093\pi\) |
−0.893032 | + | 0.449993i | \(0.851426\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 33.6512i | − | 1.28574i | ||||||
\(686\) | 4.70581 | + | 11.2134i | 0.179668 | + | 0.428129i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.46635 | −0.132153 | ||||||||
\(689\) | 7.93958 | + | 13.7518i | 0.302474 | + | 0.523900i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.6387 | + | 10.1837i | 0.671007 | + | 0.387406i | 0.796458 | − | 0.604694i | \(-0.206704\pi\) |
−0.125451 | + | 0.992100i | \(0.540038\pi\) | |||||||
\(692\) | −4.02458 | −0.152991 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.72460 | −0.0654650 | ||||||||
\(695\) | 11.0564 | + | 6.38341i | 0.419393 | + | 0.242137i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.48493 | − | 9.50018i | −0.207757 | − | 0.359845i | ||||
\(698\) | 21.3347 | 0.807532 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 16.7126 | − | 18.2953i | 0.631677 | − | 0.691498i | ||||
\(701\) | − | 49.1172i | − | 1.85513i | −0.373659 | − | 0.927566i | \(-0.621897\pi\) | ||
0.373659 | − | 0.927566i | \(-0.378103\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.9131 | + | 11.4968i | 0.751037 | + | 0.433611i | ||||
\(704\) | 1.33303i | 0.0502405i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13.2974 | + | 7.67727i | 0.500455 | + | 0.288938i | ||||
\(707\) | 10.9566 | + | 34.5633i | 0.412064 | + | 1.29989i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.6829 | + | 20.2354i | −0.438761 | + | 0.759956i | −0.997594 | − | 0.0693240i | \(-0.977916\pi\) |
0.558833 | + | 0.829280i | \(0.311249\pi\) | |||||||
\(710\) | −6.95201 | + | 12.0412i | −0.260904 | + | 0.451900i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −15.1613 | + | 8.75340i | −0.568195 | + | 0.328048i | ||||
\(713\) | 34.3735 | + | 59.5367i | 1.28730 | + | 2.22967i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.13166 | + | 10.6203i | −0.229311 | + | 0.397178i | ||||
\(716\) | 21.7075i | 0.811246i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 14.0191 | 0.523189 | ||||||||
\(719\) | 6.33345 | + | 10.9699i | 0.236198 | + | 0.409107i | 0.959620 | − | 0.281299i | \(-0.0907653\pi\) |
−0.723422 | + | 0.690406i | \(0.757432\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.3382 | + | 3.91121i | −0.459499 | + | 0.145661i | ||||
\(722\) | −0.453194 | + | 0.261652i | −0.0168661 | + | 0.00973767i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6.44018 | + | 3.71824i | −0.239347 | + | 0.138187i | ||||
\(725\) | 18.9049 | − | 10.9148i | 0.702111 | − | 0.405364i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.34172 | + | 1.35199i | −0.0868495 | + | 0.0501426i | −0.542796 | − | 0.839865i | \(-0.682634\pi\) |
0.455946 | + | 0.890007i | \(0.349301\pi\) | |||||||
\(728\) | −9.56723 | − | 2.10549i | −0.354585 | − | 0.0780345i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −11.6166 | − | 20.1205i | −0.429949 | − | 0.744694i | ||||
\(731\) | 2.46548 | 0.0911891 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.8087i | 0.805524i | 0.915305 | + | 0.402762i | \(0.131950\pi\) | ||||
−0.915305 | + | 0.402762i | \(0.868050\pi\) | |||||||
\(734\) | −5.09633 | + | 8.82710i | −0.188109 | + | 0.325814i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 26.9432 | + | 46.6671i | 0.993141 | + | 1.72017i | ||||
\(737\) | 21.8505 | − | 12.6154i | 0.804873 | − | 0.464694i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.0633 | + | 27.8225i | −0.590899 | + | 1.02347i | 0.403212 | + | 0.915107i | \(0.367894\pi\) |
−0.994112 | + | 0.108361i | \(0.965440\pi\) | |||||||
\(740\) | −13.4264 | + | 23.2553i | −0.493566 | + | 0.854881i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 11.7754 | − | 12.8906i | 0.432288 | − | 0.473227i | ||||
\(743\) | −35.7433 | − | 20.6364i | −1.31129 | − | 0.757075i | −0.328983 | − | 0.944336i | \(-0.606706\pi\) |
−0.982310 | + | 0.187261i | \(0.940039\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.8256i | 0.616442i | ||||||||
\(746\) | 13.2796 | + | 7.66697i | 0.486200 | + | 0.280708i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.18118i | 0.152879i | ||||||||
\(749\) | 4.79287 | + | 4.37824i | 0.175128 | + | 0.159977i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 45.8091 | 1.67160 | 0.835798 | − | 0.549037i | \(-0.185005\pi\) | ||||
0.835798 | + | 0.549037i | \(0.185005\pi\) | |||||||
\(752\) | −4.46652 | − | 7.73623i | −0.162877 | − | 0.282111i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.28541 | − | 1.89683i | −0.119648 | − | 0.0690785i | ||||
\(755\) | −60.6294 | −2.20653 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 50.3427 | 1.82974 | 0.914868 | − | 0.403752i | \(-0.132294\pi\) | ||||
0.914868 | + | 0.403752i | \(0.132294\pi\) | |||||||
\(758\) | −1.44364 | − | 0.833485i | −0.0524353 | − | 0.0302735i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −17.2668 | − | 29.9070i | −0.626334 | − | 1.08484i | ||||
\(761\) | 30.3646 | 1.10072 | 0.550358 | − | 0.834929i | \(-0.314491\pi\) | ||||
0.550358 | + | 0.834929i | \(0.314491\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.2030 | − | 2.46548i | −0.405577 | − | 0.0892564i | ||||
\(764\) | − | 13.0895i | − | 0.473562i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.21448 | + | 5.31999i | 0.332933 | + | 0.192219i | ||||
\(767\) | 3.43621i | 0.124074i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35.8000 | − | 20.6692i | −1.29098 | − | 0.745349i | −0.312154 | − | 0.950032i | \(-0.601050\pi\) |
−0.978828 | + | 0.204683i | \(0.934384\pi\) | |||||||
\(770\) | 13.1685 | + | 2.89803i | 0.474560 | + | 0.104438i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 13.9975 | − | 24.2443i | 0.503780 | − | 0.872573i | ||||
\(773\) | −6.99754 | + | 12.1201i | −0.251684 | + | 0.435930i | −0.963990 | − | 0.265940i | \(-0.914318\pi\) |
0.712305 | + | 0.701870i | \(0.247651\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 37.8382 | − | 21.8459i | 1.35919 | − | 0.784728i | ||||
\(776\) | −15.8792 | − | 27.5035i | −0.570029 | − | 0.987319i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.33216 | − | 12.6997i | 0.262871 | − | 0.455305i | ||||
\(779\) | − | 42.9166i | − | 1.53765i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.9819 | 0.536096 | ||||||||
\(782\) | −3.50734 | − | 6.07489i | −0.125422 | − | 0.217238i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.01001 | − | 11.1473i | −0.0360718 | − | 0.398116i | ||||
\(785\) | 9.50018 | − | 5.48493i | 0.339076 | − | 0.195766i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.6799 | + | 6.74341i | −0.416344 | + | 0.240377i | −0.693512 | − | 0.720445i | \(-0.743938\pi\) |
0.277168 | + | 0.960822i | \(0.410604\pi\) | |||||||
\(788\) | −20.5297 | + | 11.8528i | −0.731340 | + | 0.422239i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.32258 | + | 1.34094i | −0.0826335 | + | 0.0477085i | ||||
\(791\) | 4.07161 | − | 18.5012i | 0.144770 | − | 0.657827i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.16531 | − | 5.48248i | −0.112403 | − | 0.194688i | ||||
\(794\) | −21.4658 | −0.761794 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13.5866i | 0.481566i | ||||||||
\(797\) | 4.15867 | − | 7.20304i | 0.147308 | − | 0.255145i | −0.782924 | − | 0.622118i | \(-0.786273\pi\) |
0.930232 | + | 0.366973i | \(0.119606\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.17686 | + | 5.50249i | 0.112389 | + | 0.194664i | ||||
\(800\) | 29.6590 | − | 17.1236i | 1.04860 | − | 0.605411i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.49702 | − | 16.4493i | 0.335351 | − | 0.580846i | ||||
\(803\) | −12.5172 | + | 21.6804i | −0.441721 | + | 0.765084i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 78.4649 | − | 24.8734i | 2.76552 | − | 0.876671i | ||||
\(806\) | −6.57575 | − | 3.79651i | −0.231621 | − | 0.133726i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 32.1146i | 1.12979i | ||||||||
\(809\) | −12.5955 | − | 7.27200i | −0.442833 | − | 0.255670i | 0.261965 | − | 0.965077i | \(-0.415629\pi\) |
−0.704799 | + | 0.709407i | \(0.748963\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 41.8287i | − | 1.46880i | −0.678715 | − | 0.734401i | \(-0.737463\pi\) | ||
0.678715 | − | 0.734401i | \(-0.262537\pi\) | |||||||
\(812\) | 3.26217 | − | 14.8231i | 0.114480 | − | 0.520190i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −7.95181 | −0.278711 | ||||||||
\(815\) | −3.79804 | − | 6.57841i | −0.133040 | − | 0.230432i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.35327 | + | 4.82277i | 0.292244 | + | 0.168727i | ||||
\(818\) | 0.689991 | 0.0241250 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 50.1196 | 1.75025 | ||||||||
\(821\) | −40.2553 | − | 23.2414i | −1.40492 | − | 0.811131i | −0.410027 | − | 0.912073i | \(-0.634481\pi\) |
−0.994892 | + | 0.100942i | \(0.967814\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.86834 | − | 6.70017i | −0.134842 | − | 0.233553i | 0.790695 | − | 0.612210i | \(-0.209719\pi\) |
−0.925537 | + | 0.378657i | \(0.876386\pi\) | |||||||
\(824\) | −11.4641 | −0.399369 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.60152 | − | 1.14168i | 0.125313 | − | 0.0397242i | ||||
\(827\) | 20.8898i | 0.726409i | 0.931709 | + | 0.363205i | \(0.118317\pi\) | ||||
−0.931709 | + | 0.363205i | \(0.881683\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 41.2282 | + | 23.8031i | 1.43191 | + | 0.826716i | 0.997267 | − | 0.0738846i | \(-0.0235396\pi\) |
0.434647 | + | 0.900601i | \(0.356873\pi\) | |||||||
\(830\) | − | 2.25628i | − | 0.0783168i | ||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.778382 | − | 0.449399i | −0.0269855 | − | 0.0155801i | ||||
\(833\) | 0.718383 | + | 7.92862i | 0.0248905 | + | 0.274710i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.41355 | + | 7.64450i | −0.152737 | + | 0.264549i | ||||
\(836\) | −8.17887 | + | 14.1662i | −0.282872 | + | 0.489949i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.77487 | + | 1.02472i | −0.0613118 | + | 0.0353984i | ||||
\(839\) | 11.2017 | + | 19.4020i | 0.386727 | + | 0.669831i | 0.992007 | − | 0.126181i | \(-0.0402721\pi\) |
−0.605280 | + | 0.796013i | \(0.706939\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.81456 | + | 13.5352i | −0.269468 | + | 0.466732i | ||||
\(842\) | − | 5.71690i | − | 0.197017i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −22.8753 | −0.787400 | ||||||||
\(845\) | 17.3942 | + | 30.1277i | 0.598380 | + | 1.03642i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.40407 | + | 13.8930i | 0.151326 | + | 0.477368i | ||||
\(848\) | −13.9168 | + | 8.03486i | −0.477904 | + | 0.275918i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.86086 | + | 2.22907i | −0.132426 | + | 0.0764565i | ||||
\(851\) | −42.0396 | + | 24.2715i | −1.44110 | + | 0.832018i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 41.9393 | − | 24.2136i | 1.43597 | − | 0.829060i | 0.438406 | − | 0.898777i | \(-0.355543\pi\) |
0.997567 | + | 0.0697173i | \(0.0222097\pi\) | |||||||
\(854\) | −4.69455 | + | 5.13914i | −0.160644 | + | 0.175858i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.87484 | + | 4.97937i | 0.0982600 | + | 0.170191i | ||||
\(857\) | −49.0655 | −1.67605 | −0.838023 | − | 0.545636i | \(-0.816288\pi\) | ||||
−0.838023 | + | 0.545636i | \(0.816288\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 12.0245i | − | 0.410272i | −0.978733 | − | 0.205136i | \(-0.934236\pi\) | ||
0.978733 | − | 0.205136i | \(-0.0657636\pi\) | |||||||
\(860\) | −5.63221 | + | 9.75527i | −0.192057 | + | 0.332652i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.95732 | − | 15.5145i | −0.305088 | − | 0.528427i | ||||
\(863\) | −39.8804 | + | 23.0250i | −1.35754 | + | 0.783779i | −0.989292 | − | 0.145947i | \(-0.953377\pi\) |
−0.368252 | + | 0.929726i | \(0.620044\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.24824 | + | 7.35817i | −0.144445 | + | 0.250185i | ||||
\(866\) | −4.22572 | + | 7.31917i | −0.143596 | + | 0.248715i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6.52923 | − | 29.6685i | 0.221617 | − | 1.00702i | ||||
\(869\) | 2.50264 | + | 1.44490i | 0.0848961 | + | 0.0490148i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.0119i | 0.576426i | ||||||||
\(872\) | −8.79893 | − | 5.08007i | −0.297970 | − | 0.172033i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 27.4430i | − | 0.928275i | ||||||
\(875\) | −2.56818 | − | 8.10152i | −0.0868203 | − | 0.273881i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.4734 | 0.454964 | 0.227482 | − | 0.973782i | \(-0.426951\pi\) | ||||
0.227482 | + | 0.973782i | \(0.426951\pi\) | |||||||
\(878\) | 6.05551 | + | 10.4884i | 0.204363 | + | 0.353968i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −10.7478 | − | 6.20524i | −0.362308 | − | 0.209179i | ||||
\(881\) | 25.5247 | 0.859949 | 0.429974 | − | 0.902841i | \(-0.358523\pi\) | ||||
0.429974 | + | 0.902841i | \(0.358523\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.45532 | 0.217239 | 0.108619 | − | 0.994083i | \(-0.465357\pi\) | ||||
0.108619 | + | 0.994083i | \(0.465357\pi\) | |||||||
\(884\) | −2.44147 | − | 1.40958i | −0.0821156 | − | 0.0474094i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.942252 | − | 1.63203i | −0.0316556 | − | 0.0548291i | ||||
\(887\) | −33.1208 | −1.11209 | −0.556043 | − | 0.831153i | \(-0.687681\pi\) | ||||
−0.556043 | + | 0.831153i | \(0.687681\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.1563 | − | 44.6571i | −0.474786 | − | 1.49775i | ||||
\(890\) | 16.2472i | 0.544608i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −14.3790 | − | 8.30171i | −0.481444 | − | 0.277962i | ||||
\(893\) | 24.8572i | 0.831816i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 39.6880 | + | 22.9139i | 1.32662 | + | 0.765926i | ||||
\(896\) | 6.31193 | − | 28.6811i | 0.210867 | − | 0.958169i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.596459 | + | 1.03310i | −0.0199041 | + | 0.0344749i | ||||
\(899\) | 13.3809 | − | 23.1764i | 0.446278 | − | 0.772977i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.89848 | − | 5.71489i | 0.329766 | − | 0.190391i | ||||
\(902\) | 7.42084 | + | 12.8533i | 0.247087 | + | 0.427967i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.38946 | − | 14.5310i | 0.279029 | − | 0.483293i | ||||
\(905\) | 15.6995i | 0.521870i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.21512 | 0.206370 | 0.103185 | − | 0.994662i | \(-0.467097\pi\) | ||||
0.103185 | + | 0.994662i | \(0.467097\pi\) | |||||||
\(908\) | −5.27446 | − | 9.13562i | −0.175039 | − | 0.303176i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −6.13166 | + | 6.71234i | −0.203262 | + | 0.222512i | ||||
\(911\) | 15.6296 | − | 9.02376i | 0.517832 | − | 0.298970i | −0.218215 | − | 0.975901i | \(-0.570023\pi\) |
0.736047 | + | 0.676930i | \(0.236690\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.10549 | + | 1.21560i | −0.0696814 | + | 0.0402306i | ||||
\(914\) | 3.50047 | − | 2.02100i | 0.115785 | − | 0.0668486i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16.6613 | + | 9.61943i | −0.550506 | + | 0.317835i | ||||
\(917\) | 10.8768 | + | 34.3116i | 0.359182 | + | 1.13307i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.12913 | + | 7.15186i | 0.136207 | + | 0.235918i | 0.926058 | − | 0.377381i | \(-0.123175\pi\) |
−0.789851 | + | 0.613299i | \(0.789842\pi\) | |||||||
\(920\) | 72.9057 | 2.40363 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 11.1959i | − | 0.368716i | ||||||
\(923\) | −5.05080 | + | 8.74824i | −0.166249 | + | 0.287952i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.4256 | + | 26.7180i | 0.507192 | + | 0.878482i | ||||
\(926\) | 16.7258 | − | 9.65662i | 0.549642 | − | 0.317336i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 10.4884 | − | 18.1665i | 0.344300 | − | 0.596345i | ||||
\(929\) | 17.3855 | − | 30.1125i | 0.570399 | − | 0.987960i | −0.426126 | − | 0.904664i | \(-0.640122\pi\) |
0.996525 | − | 0.0832958i | \(-0.0265446\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.0753 | + | 28.2681i | −0.428527 | + | 0.926450i | ||||
\(932\) | −7.64450 | − | 4.41355i | −0.250404 | − | 0.144571i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 17.8063i | 0.582639i | ||||||||
\(935\) | 7.64450 | + | 4.41355i | 0.250002 | + | 0.144339i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 51.0703i | 1.66839i | 0.551466 | + | 0.834197i | \(0.314069\pi\) | ||||
−0.551466 | + | 0.834197i | \(0.685931\pi\) | |||||||
\(938\) | 17.8303 | − | 5.65220i | 0.582179 | − | 0.184551i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −29.0292 | −0.946829 | ||||||||
\(941\) | −1.73872 | − | 3.01156i | −0.0566807 | − | 0.0981739i | 0.836293 | − | 0.548283i | \(-0.184718\pi\) |
−0.892974 | + | 0.450109i | \(0.851385\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 78.4649 | + | 45.3017i | 2.55517 | + | 1.47523i | ||||
\(944\) | −3.47744 | −0.113181 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.33568 | −0.108452 | ||||||||
\(947\) | −12.4189 | − | 7.17003i | −0.403559 | − | 0.232995i | 0.284460 | − | 0.958688i | \(-0.408186\pi\) |
−0.688018 | + | 0.725693i | \(0.741519\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.43972 | − | 14.6180i | −0.273965 | − | 0.474521i | ||||
\(950\) | −17.4413 | −0.565869 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.51552 | + | 6.88647i | −0.0491184 | + | 0.223192i | ||||
\(953\) | 7.53697i | 0.244147i | 0.992521 | + | 0.122073i | \(0.0389543\pi\) | ||||
−0.992521 | + | 0.122073i | \(0.961046\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −23.9317 | − | 13.8170i | −0.774411 | − | 0.447106i | ||||
\(956\) | − | 25.0381i | − | 0.809789i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −12.2583 | − | 7.07735i | −0.396049 | − | 0.228659i | ||||
\(959\) | −25.6245 | + | 8.12297i | −0.827459 | + | 0.262304i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.2819 | − | 19.5408i | 0.363932 | − | 0.630349i | ||||
\(962\) | 2.68076 | − | 4.64321i | 0.0864312 | − | 0.149703i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 6.23363 | − | 3.59899i | 0.200772 | − | 0.115916i | ||||
\(965\) | −29.5508 | − | 51.1834i | −0.951273 | − | 1.64765i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.80807 | − | 10.0599i | 0.186775 | − | 0.323503i | −0.757398 | − | 0.652953i | \(-0.773530\pi\) |
0.944173 | + | 0.329450i | \(0.106863\pi\) | |||||||
\(968\) | 12.9087i | 0.414901i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −29.4734 | −0.946333 | ||||||||
\(971\) | 17.7476 | + | 30.7397i | 0.569548 | + | 0.986485i | 0.996611 | + | 0.0822636i | \(0.0262149\pi\) |
−0.427063 | + | 0.904222i | \(0.640452\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.19193 | − | 9.96004i | 0.0702702 | − | 0.319304i | ||||
\(974\) | −8.29145 | + | 4.78707i | −0.265675 | + | 0.153388i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.54827 | − | 3.20329i | 0.177596 | − | 0.102535i | ||||
\(977\) | 27.7210 | − | 16.0047i | 0.886873 | − | 0.512036i | 0.0139546 | − | 0.999903i | \(-0.495558\pi\) |
0.872918 | + | 0.487866i | \(0.162225\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.1613 | − | 8.75340i | 0.484559 | − | 0.279760i | ||||
\(980\) | −33.0126 | − | 15.2699i | −1.05455 | − | 0.487779i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.0929453 | − | 0.160986i | −0.00296600 | − | 0.00513727i | ||||
\(983\) | 49.4648 | 1.57768 | 0.788841 | − | 0.614598i | \(-0.210682\pi\) | ||||
0.788841 | + | 0.614598i | \(0.210682\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 50.0462i | 1.59460i | ||||||||
\(986\) | −1.36534 | + | 2.36483i | −0.0434811 | + | 0.0753115i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.51462 | − | 9.55159i | −0.175443 | − | 0.303877i | ||||
\(989\) | −17.6350 | + | 10.1816i | −0.560761 | + | 0.323756i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.97590 | + | 15.5467i | −0.285129 | + | 0.493858i | −0.972640 | − | 0.232316i | \(-0.925370\pi\) |
0.687511 | + | 0.726174i | \(0.258703\pi\) | |||||||
\(992\) | 20.9926 | − | 36.3603i | 0.666517 | − | 1.15444i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 10.8472 | + | 2.38718i | 0.344053 | + | 0.0757167i | ||||
\(995\) | 24.8406 | + | 14.3417i | 0.787500 | + | 0.454663i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33.5037i | 1.06107i | 0.847662 | + | 0.530537i | \(0.178010\pi\) | ||||
−0.847662 | + | 0.530537i | \(0.821990\pi\) | |||||||
\(998\) | −6.99754 | − | 4.04003i | −0.221503 | − | 0.127885i | ||||
\(999\) | 0 | 0 |
(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 | 567.2.s.f.458.3 | 12 | ||
3.2 | odd | 2 | inner | 567.2.s.f.458.4 | 12 | ||
7.5 | odd | 6 | 567.2.i.f.215.4 | 12 | |||
9.2 | odd | 6 | 567.2.i.f.269.3 | 12 | |||
9.4 | even | 3 | 189.2.p.d.80.4 | yes | 12 | ||
9.5 | odd | 6 | 189.2.p.d.80.3 | yes | 12 | ||
9.7 | even | 3 | 567.2.i.f.269.4 | 12 | |||
21.5 | even | 6 | 567.2.i.f.215.3 | 12 | |||
63.4 | even | 3 | 1323.2.c.d.1322.7 | 12 | |||
63.5 | even | 6 | 189.2.p.d.26.4 | yes | 12 | ||
63.31 | odd | 6 | 1323.2.c.d.1322.8 | 12 | |||
63.32 | odd | 6 | 1323.2.c.d.1322.6 | 12 | |||
63.40 | odd | 6 | 189.2.p.d.26.3 | ✓ | 12 | ||
63.47 | even | 6 | inner | 567.2.s.f.26.3 | 12 | ||
63.59 | even | 6 | 1323.2.c.d.1322.5 | 12 | |||
63.61 | odd | 6 | inner | 567.2.s.f.26.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
189.2.p.d.26.3 | ✓ | 12 | 63.40 | odd | 6 | ||
189.2.p.d.26.4 | yes | 12 | 63.5 | even | 6 | ||
189.2.p.d.80.3 | yes | 12 | 9.5 | odd | 6 | ||
189.2.p.d.80.4 | yes | 12 | 9.4 | even | 3 | ||
567.2.i.f.215.3 | 12 | 21.5 | even | 6 | |||
567.2.i.f.215.4 | 12 | 7.5 | odd | 6 | |||
567.2.i.f.269.3 | 12 | 9.2 | odd | 6 | |||
567.2.i.f.269.4 | 12 | 9.7 | even | 3 | |||
567.2.s.f.26.3 | 12 | 63.47 | even | 6 | inner | ||
567.2.s.f.26.4 | 12 | 63.61 | odd | 6 | inner | ||
567.2.s.f.458.3 | 12 | 1.1 | even | 1 | trivial | ||
567.2.s.f.458.4 | 12 | 3.2 | odd | 2 | inner | ||
1323.2.c.d.1322.5 | 12 | 63.59 | even | 6 | |||
1323.2.c.d.1322.6 | 12 | 63.32 | odd | 6 | |||
1323.2.c.d.1322.7 | 12 | 63.4 | even | 3 | |||
1323.2.c.d.1322.8 | 12 | 63.31 | odd | 6 |