Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [287,2,Mod(165,287)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(287, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("287.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 287 = 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 287.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.29170653801\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} + 7x^{8} + 4x^{7} + 32x^{6} + 3x^{5} + 30x^{4} - 7x^{3} + 26x^{2} - 5x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 247.2 | ||
Root | \(-0.580000 + 1.00459i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 287.247 |
Dual form | 287.2.e.c.165.2 |
$q$-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 \(\left(\mathbb{Z}/287\mathbb{Z}\right)^\times\).
\(n\) | \(206\) | \(211\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.678233 | + | 1.17473i | −0.479583 | + | 0.830662i | −0.999726 | − | 0.0234171i | \(-0.992545\pi\) |
0.520143 | + | 0.854079i | \(0.325879\pi\) | |||||||
\(3\) | 1.11395 | + | 1.92942i | 0.643139 | + | 1.11395i | 0.984728 | + | 0.174100i | \(0.0557017\pi\) |
−0.341589 | + | 0.939850i | \(0.610965\pi\) | |||||||
\(4\) | 0.0800004 | + | 0.138565i | 0.0400002 | + | 0.0692824i | ||||
\(5\) | −1.11395 | + | 1.92942i | −0.498173 | + | 0.862862i | −0.999998 | − | 0.00210783i | \(-0.999329\pi\) |
0.501824 | + | 0.864970i | \(0.332662\pi\) | |||||||
\(6\) | −3.02207 | −1.23375 | ||||||||
\(7\) | 2.60927 | − | 0.437865i | 0.986210 | − | 0.165497i | ||||
\(8\) | −2.92997 | −1.03590 | ||||||||
\(9\) | −0.981768 | + | 1.70047i | −0.327256 | + | 0.566824i | ||||
\(10\) | −1.51103 | − | 2.61719i | −0.477831 | − | 0.827628i | ||||
\(11\) | 0.564283 | + | 0.977367i | 0.170138 | + | 0.294687i | 0.938468 | − | 0.345367i | \(-0.112245\pi\) |
−0.768330 | + | 0.640054i | \(0.778912\pi\) | |||||||
\(12\) | −0.178233 | + | 0.308708i | −0.0514514 | + | 0.0891164i | ||||
\(13\) | 2.22790 | 0.617908 | 0.308954 | − | 0.951077i | \(-0.400021\pi\) | ||||
0.308954 | + | 0.951077i | \(0.400021\pi\) | |||||||
\(14\) | −1.25532 | + | 3.36217i | −0.335497 | + | 0.898577i | ||||
\(15\) | −4.96354 | −1.28158 | ||||||||
\(16\) | 1.82720 | − | 3.16480i | 0.456800 | − | 0.791200i | ||||
\(17\) | −2.02675 | − | 3.51044i | −0.491560 | − | 0.851406i | 0.508393 | − | 0.861125i | \(-0.330240\pi\) |
−0.999953 | + | 0.00971895i | \(0.996906\pi\) | |||||||
\(18\) | −1.33173 | − | 2.30663i | −0.313893 | − | 0.543678i | ||||
\(19\) | 1.80790 | − | 3.13137i | 0.414761 | − | 0.718387i | −0.580643 | − | 0.814159i | \(-0.697199\pi\) |
0.995403 | + | 0.0957720i | \(0.0305320\pi\) | |||||||
\(20\) | −0.356466 | −0.0797082 | ||||||||
\(21\) | 3.75142 | + | 4.54661i | 0.818626 | + | 0.992151i | ||||
\(22\) | −1.53086 | −0.326381 | ||||||||
\(23\) | 1.34292 | − | 2.32600i | 0.280017 | − | 0.485004i | −0.691371 | − | 0.722500i | \(-0.742993\pi\) |
0.971389 | + | 0.237495i | \(0.0763264\pi\) | |||||||
\(24\) | −3.26384 | − | 5.65313i | −0.666228 | − | 1.15394i | ||||
\(25\) | 0.0182320 | + | 0.0315788i | 0.00364641 | + | 0.00631577i | ||||
\(26\) | −1.51103 | + | 2.61719i | −0.296338 | + | 0.513273i | ||||
\(27\) | 2.30914 | 0.444394 | ||||||||
\(28\) | 0.269415 | + | 0.326523i | 0.0509147 | + | 0.0617071i | ||||
\(29\) | −3.72230 | −0.691213 | −0.345607 | − | 0.938380i | \(-0.612327\pi\) | ||||
−0.345607 | + | 0.938380i | \(0.612327\pi\) | |||||||
\(30\) | 3.36643 | − | 5.83083i | 0.614624 | − | 1.06456i | ||||
\(31\) | −0.172630 | − | 0.299004i | −0.0310053 | − | 0.0537027i | 0.850106 | − | 0.526611i | \(-0.176538\pi\) |
−0.881112 | + | 0.472908i | \(0.843204\pi\) | |||||||
\(32\) | −0.451434 | − | 0.781907i | −0.0798030 | − | 0.138223i | ||||
\(33\) | −1.25717 | + | 2.17748i | −0.218845 | + | 0.379050i | ||||
\(34\) | 5.49844 | 0.942974 | ||||||||
\(35\) | −2.06177 | + | 5.52212i | −0.348502 | + | 0.933409i | ||||
\(36\) | −0.314167 | −0.0523612 | ||||||||
\(37\) | −1.67465 | + | 2.90058i | −0.275311 | + | 0.476852i | −0.970214 | − | 0.242251i | \(-0.922114\pi\) |
0.694903 | + | 0.719104i | \(0.255447\pi\) | |||||||
\(38\) | 2.45235 | + | 4.24760i | 0.397824 | + | 0.689052i | ||||
\(39\) | 2.48177 | + | 4.29855i | 0.397401 | + | 0.688319i | ||||
\(40\) | 3.26384 | − | 5.65313i | 0.516058 | − | 0.893838i | ||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | −7.88539 | + | 1.32326i | −1.21674 | + | 0.204183i | ||||
\(43\) | −12.6805 | −1.93376 | −0.966880 | − | 0.255232i | \(-0.917848\pi\) | ||||
−0.966880 | + | 0.255232i | \(0.917848\pi\) | |||||||
\(44\) | −0.0902858 | + | 0.156380i | −0.0136111 | + | 0.0235751i | ||||
\(45\) | −2.18728 | − | 3.78848i | −0.326060 | − | 0.564753i | ||||
\(46\) | 1.82162 | + | 3.15514i | 0.268583 | + | 0.465200i | ||||
\(47\) | 3.65642 | − | 6.33310i | 0.533344 | − | 0.923778i | −0.465898 | − | 0.884838i | \(-0.654269\pi\) |
0.999242 | − | 0.0389396i | \(-0.0123980\pi\) | |||||||
\(48\) | 8.14163 | 1.17514 | ||||||||
\(49\) | 6.61655 | − | 2.28501i | 0.945221 | − | 0.326430i | ||||
\(50\) | −0.0494623 | −0.00699502 | ||||||||
\(51\) | 4.51540 | − | 7.82090i | 0.632282 | − | 1.09515i | ||||
\(52\) | 0.178233 | + | 0.308708i | 0.0247164 | + | 0.0428101i | ||||
\(53\) | 4.17809 | + | 7.23666i | 0.573904 | + | 0.994031i | 0.996160 | + | 0.0875544i | \(0.0279052\pi\) |
−0.422256 | + | 0.906477i | \(0.638762\pi\) | |||||||
\(54\) | −1.56613 | + | 2.71262i | −0.213124 | + | 0.369141i | ||||
\(55\) | −2.51433 | −0.339032 | ||||||||
\(56\) | −7.64507 | + | 1.28293i | −1.02161 | + | 0.171439i | ||||
\(57\) | 8.05564 | 1.06700 | ||||||||
\(58\) | 2.52458 | − | 4.37271i | 0.331494 | − | 0.574165i | ||||
\(59\) | 2.61250 | + | 4.52499i | 0.340119 | + | 0.589103i | 0.984455 | − | 0.175640i | \(-0.0561994\pi\) |
−0.644336 | + | 0.764743i | \(0.722866\pi\) | |||||||
\(60\) | −0.397085 | − | 0.687771i | −0.0512634 | − | 0.0887909i | ||||
\(61\) | −2.80432 | + | 4.85722i | −0.359056 | + | 0.621903i | −0.987803 | − | 0.155706i | \(-0.950235\pi\) |
0.628747 | + | 0.777610i | \(0.283568\pi\) | |||||||
\(62\) | 0.468334 | 0.0594785 | ||||||||
\(63\) | −1.81712 | + | 4.86687i | −0.228935 | + | 0.613168i | ||||
\(64\) | 8.53351 | 1.06669 | ||||||||
\(65\) | −2.48177 | + | 4.29855i | −0.307825 | + | 0.533169i | ||||
\(66\) | −1.70530 | − | 2.95367i | −0.209908 | − | 0.363572i | ||||
\(67\) | 4.41625 | + | 7.64916i | 0.539530 | + | 0.934494i | 0.998929 | + | 0.0462640i | \(0.0147315\pi\) |
−0.459399 | + | 0.888230i | \(0.651935\pi\) | |||||||
\(68\) | 0.324282 | − | 0.561673i | 0.0393250 | − | 0.0681128i | ||||
\(69\) | 5.98377 | 0.720361 | ||||||||
\(70\) | −5.08867 | − | 6.16732i | −0.608212 | − | 0.737135i | ||||
\(71\) | 9.92933 | 1.17839 | 0.589197 | − | 0.807989i | \(-0.299444\pi\) | ||||
0.589197 | + | 0.807989i | \(0.299444\pi\) | |||||||
\(72\) | 2.87655 | − | 4.98233i | 0.339004 | − | 0.587173i | ||||
\(73\) | −0.407898 | − | 0.706500i | −0.0477408 | − | 0.0826895i | 0.841168 | − | 0.540775i | \(-0.181869\pi\) |
−0.888908 | + | 0.458085i | \(0.848535\pi\) | |||||||
\(74\) | −2.27161 | − | 3.93454i | −0.264069 | − | 0.457381i | ||||
\(75\) | −0.0406192 | + | 0.0703545i | −0.00469030 | + | 0.00812383i | ||||
\(76\) | 0.578531 | 0.0663620 | ||||||||
\(77\) | 1.90032 | + | 2.30313i | 0.216562 | + | 0.262466i | ||||
\(78\) | −6.73287 | −0.762347 | ||||||||
\(79\) | 4.42092 | − | 7.65726i | 0.497392 | − | 0.861509i | −0.502603 | − | 0.864517i | \(-0.667624\pi\) |
0.999995 | + | 0.00300848i | \(0.000957632\pi\) | |||||||
\(80\) | 4.07082 | + | 7.05086i | 0.455131 | + | 0.788310i | ||||
\(81\) | 5.51757 | + | 9.55671i | 0.613063 | + | 1.06186i | ||||
\(82\) | 0.678233 | − | 1.17473i | 0.0748983 | − | 0.129728i | ||||
\(83\) | −7.48907 | −0.822033 | −0.411016 | − | 0.911628i | \(-0.634826\pi\) | ||||
−0.411016 | + | 0.911628i | \(0.634826\pi\) | |||||||
\(84\) | −0.329885 | + | 0.883544i | −0.0359934 | + | 0.0964026i | ||||
\(85\) | 9.03080 | 0.979528 | ||||||||
\(86\) | 8.60034 | − | 14.8962i | 0.927398 | − | 1.60630i | ||||
\(87\) | −4.14645 | − | 7.18186i | −0.444546 | − | 0.769977i | ||||
\(88\) | −1.65333 | − | 2.86365i | −0.176246 | − | 0.305266i | ||||
\(89\) | 7.88183 | − | 13.6517i | 0.835473 | − | 1.44708i | −0.0581725 | − | 0.998307i | \(-0.518527\pi\) |
0.893645 | − | 0.448774i | \(-0.148139\pi\) | |||||||
\(90\) | 5.93394 | 0.625492 | ||||||||
\(91\) | 5.81318 | − | 0.975519i | 0.609387 | − | 0.102262i | ||||
\(92\) | 0.429735 | 0.0448030 | ||||||||
\(93\) | 0.384603 | − | 0.666151i | 0.0398814 | − | 0.0690767i | ||||
\(94\) | 4.95981 | + | 8.59064i | 0.511565 | + | 0.886057i | ||||
\(95\) | 4.02782 | + | 6.97639i | 0.413246 | + | 0.715762i | ||||
\(96\) | 1.00575 | − | 1.74201i | 0.102649 | − | 0.177793i | ||||
\(97\) | −2.10829 | −0.214064 | −0.107032 | − | 0.994256i | \(-0.534135\pi\) | ||||
−0.107032 | + | 0.994256i | \(0.534135\pi\) | |||||||
\(98\) | −1.80328 | + | 9.32245i | −0.182159 | + | 0.941710i | ||||
\(99\) | −2.21598 | −0.222714 | ||||||||
\(100\) | −0.00291714 | + | 0.00505264i | −0.000291714 | + | 0.000505264i | ||||
\(101\) | −3.92090 | − | 6.79119i | −0.390144 | − | 0.675749i | 0.602324 | − | 0.798251i | \(-0.294241\pi\) |
−0.992468 | + | 0.122503i | \(0.960908\pi\) | |||||||
\(102\) | 6.12498 | + | 10.6088i | 0.606464 | + | 1.05043i | ||||
\(103\) | 3.45455 | − | 5.98346i | 0.340387 | − | 0.589568i | −0.644118 | − | 0.764927i | \(-0.722775\pi\) |
0.984505 | + | 0.175359i | \(0.0561086\pi\) | |||||||
\(104\) | −6.52767 | −0.640091 | ||||||||
\(105\) | −12.9512 | + | 2.17336i | −1.26391 | + | 0.212098i | ||||
\(106\) | −11.3349 | −1.10094 | ||||||||
\(107\) | −9.78377 | + | 16.9460i | −0.945833 | + | 1.63823i | −0.191758 | + | 0.981442i | \(0.561419\pi\) |
−0.754075 | + | 0.656788i | \(0.771915\pi\) | |||||||
\(108\) | 0.184732 | + | 0.319965i | 0.0177758 | + | 0.0307887i | ||||
\(109\) | −1.96105 | − | 3.39664i | −0.187835 | − | 0.325339i | 0.756693 | − | 0.653770i | \(-0.226814\pi\) |
−0.944528 | + | 0.328431i | \(0.893480\pi\) | |||||||
\(110\) | 1.70530 | − | 2.95367i | 0.162594 | − | 0.281621i | ||||
\(111\) | −7.46191 | −0.708253 | ||||||||
\(112\) | 3.38190 | − | 9.05788i | 0.319559 | − | 0.855889i | ||||
\(113\) | −5.10800 | −0.480520 | −0.240260 | − | 0.970709i | \(-0.577233\pi\) | ||||
−0.240260 | + | 0.970709i | \(0.577233\pi\) | |||||||
\(114\) | −5.46360 | + | 9.46323i | −0.511713 | + | 0.886313i | ||||
\(115\) | 2.99188 | + | 5.18209i | 0.278994 | + | 0.483233i | ||||
\(116\) | −0.297785 | − | 0.515779i | −0.0276487 | − | 0.0478889i | ||||
\(117\) | −2.18728 | + | 3.78848i | −0.202214 | + | 0.350245i | ||||
\(118\) | −7.08754 | −0.652461 | ||||||||
\(119\) | −6.82543 | − | 8.27222i | −0.625686 | − | 0.758314i | ||||
\(120\) | 14.5430 | 1.32759 | ||||||||
\(121\) | 4.86317 | − | 8.42326i | 0.442106 | − | 0.765751i | ||||
\(122\) | −3.80396 | − | 6.58865i | −0.344394 | − | 0.596509i | ||||
\(123\) | −1.11395 | − | 1.92942i | −0.100441 | − | 0.173970i | ||||
\(124\) | 0.0276210 | − | 0.0478409i | 0.00248044 | − | 0.00429624i | ||||
\(125\) | −11.2207 | −1.00361 | ||||||||
\(126\) | −4.48484 | − | 5.43550i | −0.399542 | − | 0.484233i | ||||
\(127\) | −19.3732 | −1.71909 | −0.859547 | − | 0.511056i | \(-0.829254\pi\) | ||||
−0.859547 | + | 0.511056i | \(0.829254\pi\) | |||||||
\(128\) | −4.88484 | + | 8.46078i | −0.431763 | + | 0.747835i | ||||
\(129\) | −14.1254 | − | 24.4660i | −1.24368 | − | 2.15411i | ||||
\(130\) | −3.36643 | − | 5.83083i | −0.295256 | − | 0.511398i | ||||
\(131\) | 0.154545 | − | 0.267680i | 0.0135027 | − | 0.0233873i | −0.859195 | − | 0.511648i | \(-0.829035\pi\) |
0.872698 | + | 0.488261i | \(0.162368\pi\) | |||||||
\(132\) | −0.402295 | −0.0350153 | ||||||||
\(133\) | 3.34617 | − | 8.96221i | 0.290150 | − | 0.777122i | ||||
\(134\) | −11.9810 | −1.03500 | ||||||||
\(135\) | −2.57226 | + | 4.45529i | −0.221385 | + | 0.383450i | ||||
\(136\) | 5.93832 | + | 10.2855i | 0.509206 | + | 0.881971i | ||||
\(137\) | 8.68377 | + | 15.0407i | 0.741905 | + | 1.28502i | 0.951627 | + | 0.307256i | \(0.0994107\pi\) |
−0.209722 | + | 0.977761i | \(0.567256\pi\) | |||||||
\(138\) | −4.05839 | + | 7.02933i | −0.345473 | + | 0.598376i | ||||
\(139\) | −15.1514 | −1.28512 | −0.642562 | − | 0.766233i | \(-0.722129\pi\) | ||||
−0.642562 | + | 0.766233i | \(0.722129\pi\) | |||||||
\(140\) | −0.930114 | + | 0.156084i | −0.0786090 | + | 0.0131915i | ||||
\(141\) | 16.2923 | 1.37206 | ||||||||
\(142\) | −6.73440 | + | 11.6643i | −0.565138 | + | 0.978848i | ||||
\(143\) | 1.25717 | + | 2.17748i | 0.105130 | + | 0.182090i | ||||
\(144\) | 3.58777 | + | 6.21420i | 0.298981 | + | 0.517850i | ||||
\(145\) | 4.14645 | − | 7.18186i | 0.344344 | − | 0.596421i | ||||
\(146\) | 1.10660 | 0.0915828 | ||||||||
\(147\) | 11.7792 | + | 10.2207i | 0.971536 | + | 0.842989i | ||||
\(148\) | −0.535891 | −0.0440500 | ||||||||
\(149\) | 5.24670 | − | 9.08756i | 0.429827 | − | 0.744482i | −0.567031 | − | 0.823697i | \(-0.691908\pi\) |
0.996858 | + | 0.0792148i | \(0.0252413\pi\) | |||||||
\(150\) | −0.0550985 | − | 0.0954334i | −0.00449877 | − | 0.00779211i | ||||
\(151\) | 2.55975 | + | 4.43361i | 0.208309 | + | 0.360802i | 0.951182 | − | 0.308630i | \(-0.0998706\pi\) |
−0.742873 | + | 0.669433i | \(0.766537\pi\) | |||||||
\(152\) | −5.29709 | + | 9.17482i | −0.429650 | + | 0.744176i | ||||
\(153\) | 7.95920 | 0.643463 | ||||||||
\(154\) | −3.99443 | + | 0.670310i | −0.321880 | + | 0.0540151i | ||||
\(155\) | 0.769205 | 0.0617841 | ||||||||
\(156\) | −0.397085 | + | 0.687771i | −0.0317922 | + | 0.0550658i | ||||
\(157\) | −7.54790 | − | 13.0733i | −0.602388 | − | 1.04337i | −0.992458 | − | 0.122582i | \(-0.960883\pi\) |
0.390070 | − | 0.920785i | \(-0.372451\pi\) | |||||||
\(158\) | 5.99683 | + | 10.3868i | 0.477082 | + | 0.826330i | ||||
\(159\) | −9.30835 | + | 16.1225i | −0.738201 | + | 1.27860i | ||||
\(160\) | 2.01150 | 0.159023 | ||||||||
\(161\) | 2.48555 | − | 6.65717i | 0.195889 | − | 0.524658i | ||||
\(162\) | −14.9688 | −1.17606 | ||||||||
\(163\) | −3.80812 | + | 6.59586i | −0.298275 | + | 0.516628i | −0.975741 | − | 0.218926i | \(-0.929745\pi\) |
0.677466 | + | 0.735554i | \(0.263078\pi\) | |||||||
\(164\) | −0.0800004 | − | 0.138565i | −0.00624698 | − | 0.0108201i | ||||
\(165\) | −2.80084 | − | 4.85120i | −0.218045 | − | 0.377665i | ||||
\(166\) | 5.07934 | − | 8.79767i | 0.394233 | − | 0.682831i | ||||
\(167\) | 8.24963 | 0.638375 | 0.319188 | − | 0.947692i | \(-0.396590\pi\) | ||||
0.319188 | + | 0.947692i | \(0.396590\pi\) | |||||||
\(168\) | −10.9915 | − | 13.3214i | −0.848015 | − | 1.02777i | ||||
\(169\) | −8.03646 | −0.618190 | ||||||||
\(170\) | −6.12498 | + | 10.6088i | −0.469765 | + | 0.813657i | ||||
\(171\) | 3.54988 | + | 6.14857i | 0.271466 | + | 0.470193i | ||||
\(172\) | −1.01445 | − | 1.75707i | −0.0773508 | − | 0.133975i | ||||
\(173\) | 11.8690 | − | 20.5578i | 0.902386 | − | 1.56298i | 0.0779974 | − | 0.996954i | \(-0.475147\pi\) |
0.824388 | − | 0.566025i | \(-0.191519\pi\) | |||||||
\(174\) | 11.2490 | 0.852787 | ||||||||
\(175\) | 0.0613995 | + | 0.0744144i | 0.00464137 | + | 0.00562520i | ||||
\(176\) | 4.12423 | 0.310876 | ||||||||
\(177\) | −5.82039 | + | 10.0812i | −0.437487 | + | 0.757750i | ||||
\(178\) | 10.6914 | + | 18.5181i | 0.801357 | + | 1.38799i | ||||
\(179\) | −5.72773 | − | 9.92072i | −0.428111 | − | 0.741509i | 0.568595 | − | 0.822618i | \(-0.307487\pi\) |
−0.996705 | + | 0.0811086i | \(0.974154\pi\) | |||||||
\(180\) | 0.349967 | − | 0.606160i | 0.0260850 | − | 0.0451805i | ||||
\(181\) | 17.7517 | 1.31948 | 0.659738 | − | 0.751495i | \(-0.270667\pi\) | ||||
0.659738 | + | 0.751495i | \(0.270667\pi\) | |||||||
\(182\) | −2.79672 | + | 7.49057i | −0.207307 | + | 0.555238i | ||||
\(183\) | −12.4955 | −0.923692 | ||||||||
\(184\) | −3.93470 | + | 6.81510i | −0.290070 | + | 0.502416i | ||||
\(185\) | −3.73095 | − | 6.46220i | −0.274305 | − | 0.475111i | ||||
\(186\) | 0.521700 | + | 0.903612i | 0.0382529 | + | 0.0662560i | ||||
\(187\) | 2.28732 | − | 3.96176i | 0.167266 | − | 0.289713i | ||||
\(188\) | 1.17006 | 0.0853354 | ||||||||
\(189\) | 6.02516 | − | 1.01109i | 0.438266 | − | 0.0735460i | ||||
\(190\) | −10.9272 | −0.792742 | ||||||||
\(191\) | −8.22890 | + | 14.2529i | −0.595423 | + | 1.03130i | 0.398065 | + | 0.917357i | \(0.369682\pi\) |
−0.993487 | + | 0.113945i | \(0.963651\pi\) | |||||||
\(192\) | 9.50590 | + | 16.4647i | 0.686029 | + | 1.18824i | ||||
\(193\) | −9.85481 | − | 17.0690i | −0.709365 | − | 1.22866i | −0.965093 | − | 0.261907i | \(-0.915649\pi\) |
0.255729 | − | 0.966749i | \(-0.417685\pi\) | |||||||
\(194\) | 1.42991 | − | 2.47668i | 0.102662 | − | 0.177815i | ||||
\(195\) | −11.0583 | −0.791898 | ||||||||
\(196\) | 0.845949 | + | 0.734019i | 0.0604249 | + | 0.0524299i | ||||
\(197\) | 12.9492 | 0.922592 | 0.461296 | − | 0.887246i | \(-0.347385\pi\) | ||||
0.461296 | + | 0.887246i | \(0.347385\pi\) | |||||||
\(198\) | 1.50295 | − | 2.60319i | 0.106810 | − | 0.185000i | ||||
\(199\) | −12.8566 | − | 22.2682i | −0.911378 | − | 1.57855i | −0.812119 | − | 0.583492i | \(-0.801686\pi\) |
−0.0992595 | − | 0.995062i | \(-0.531647\pi\) | |||||||
\(200\) | −0.0534193 | − | 0.0925249i | −0.00377731 | − | 0.00654250i | ||||
\(201\) | −9.83895 | + | 17.0416i | −0.693986 | + | 1.20202i | ||||
\(202\) | 10.6371 | 0.748425 | ||||||||
\(203\) | −9.71247 | + | 1.62986i | −0.681681 | + | 0.114394i | ||||
\(204\) | 1.44494 | 0.101166 | ||||||||
\(205\) | 1.11395 | − | 1.92942i | 0.0778016 | − | 0.134756i | ||||
\(206\) | 4.68598 | + | 8.11636i | 0.326488 | + | 0.565493i | ||||
\(207\) | 2.63686 | + | 4.56718i | 0.183275 | + | 0.317441i | ||||
\(208\) | 4.07082 | − | 7.05086i | 0.282260 | − | 0.488889i | ||||
\(209\) | 4.08067 | 0.282266 | ||||||||
\(210\) | 6.23081 | − | 16.6882i | 0.429967 | − | 1.15160i | ||||
\(211\) | 13.4799 | 0.927993 | 0.463996 | − | 0.885837i | \(-0.346415\pi\) | ||||
0.463996 | + | 0.885837i | \(0.346415\pi\) | |||||||
\(212\) | −0.668497 | + | 1.15787i | −0.0459126 | + | 0.0795229i | ||||
\(213\) | 11.0608 | + | 19.1578i | 0.757872 | + | 1.31267i | ||||
\(214\) | −13.2713 | − | 22.9867i | −0.907211 | − | 1.57134i | ||||
\(215\) | 14.1254 | − | 24.4660i | 0.963348 | − | 1.66857i | ||||
\(216\) | −6.76570 | −0.460347 | ||||||||
\(217\) | −0.581362 | − | 0.704593i | −0.0394654 | − | 0.0478309i | ||||
\(218\) | 5.32019 | 0.360329 | ||||||||
\(219\) | 0.908755 | − | 1.57401i | 0.0614080 | − | 0.106362i | ||||
\(220\) | −0.201148 | − | 0.348398i | −0.0135614 | − | 0.0234890i | ||||
\(221\) | −4.51540 | − | 7.82090i | −0.303739 | − | 0.526091i | ||||
\(222\) | 5.06091 | − | 8.76575i | 0.339666 | − | 0.588319i | ||||
\(223\) | −2.59701 | −0.173909 | −0.0869544 | − | 0.996212i | \(-0.527713\pi\) | ||||
−0.0869544 | + | 0.996212i | \(0.527713\pi\) | |||||||
\(224\) | −1.52028 | − | 1.84254i | −0.101578 | − | 0.123110i | ||||
\(225\) | −0.0715986 | −0.00477324 | ||||||||
\(226\) | 3.46441 | − | 6.00053i | 0.230449 | − | 0.399150i | ||||
\(227\) | 5.05559 | + | 8.75653i | 0.335551 | + | 0.581192i | 0.983591 | − | 0.180415i | \(-0.0577441\pi\) |
−0.648039 | + | 0.761607i | \(0.724411\pi\) | |||||||
\(228\) | 0.644454 | + | 1.11623i | 0.0426800 | + | 0.0739240i | ||||
\(229\) | 6.79492 | − | 11.7691i | 0.449021 | − | 0.777727i | −0.549302 | − | 0.835624i | \(-0.685106\pi\) |
0.998323 | + | 0.0578971i | \(0.0184395\pi\) | |||||||
\(230\) | −8.11677 | −0.535204 | ||||||||
\(231\) | −2.32684 | + | 6.23208i | −0.153095 | + | 0.410041i | ||||
\(232\) | 10.9062 | 0.716028 | ||||||||
\(233\) | −4.63114 | + | 8.02136i | −0.303396 | + | 0.525497i | −0.976903 | − | 0.213684i | \(-0.931454\pi\) |
0.673507 | + | 0.739181i | \(0.264787\pi\) | |||||||
\(234\) | −2.96697 | − | 5.13894i | −0.193957 | − | 0.335943i | ||||
\(235\) | 8.14613 | + | 14.1095i | 0.531395 | + | 0.920403i | ||||
\(236\) | −0.418002 | + | 0.724001i | −0.0272096 | + | 0.0471285i | ||||
\(237\) | 19.6987 | 1.27957 | ||||||||
\(238\) | 14.3469 | − | 2.40757i | 0.929971 | − | 0.156060i | ||||
\(239\) | −10.5580 | −0.682942 | −0.341471 | − | 0.939892i | \(-0.610925\pi\) | ||||
−0.341471 | + | 0.939892i | \(0.610925\pi\) | |||||||
\(240\) | −9.06937 | + | 15.7086i | −0.585425 | + | 1.01399i | ||||
\(241\) | −4.50762 | − | 7.80743i | −0.290362 | − | 0.502921i | 0.683534 | − | 0.729919i | \(-0.260442\pi\) |
−0.973895 | + | 0.226998i | \(0.927109\pi\) | |||||||
\(242\) | 6.59672 | + | 11.4259i | 0.424053 | + | 0.734482i | ||||
\(243\) | −8.82888 | + | 15.2921i | −0.566373 | + | 0.980986i | ||||
\(244\) | −0.897386 | −0.0574493 | ||||||||
\(245\) | −2.96176 | + | 15.3115i | −0.189220 | + | 0.978214i | ||||
\(246\) | 3.02207 | 0.192680 | ||||||||
\(247\) | 4.02782 | − | 6.97639i | 0.256284 | − | 0.443897i | ||||
\(248\) | 0.505801 | + | 0.876073i | 0.0321184 | + | 0.0556307i | ||||
\(249\) | −8.34245 | − | 14.4495i | −0.528681 | − | 0.915703i | ||||
\(250\) | 7.61027 | − | 13.1814i | 0.481316 | − | 0.833663i | ||||
\(251\) | 21.2912 | 1.34389 | 0.671945 | − | 0.740601i | \(-0.265459\pi\) | ||||
0.671945 | + | 0.740601i | \(0.265459\pi\) | |||||||
\(252\) | −0.819746 | + | 0.137563i | −0.0516392 | + | 0.00866564i | ||||
\(253\) | 3.03114 | 0.190566 | ||||||||
\(254\) | 13.1395 | − | 22.7584i | 0.824449 | − | 1.42799i | ||||
\(255\) | 10.0599 | + | 17.4242i | 0.629973 | + | 1.09114i | ||||
\(256\) | 1.90739 | + | 3.30370i | 0.119212 | + | 0.206481i | ||||
\(257\) | −4.22897 | + | 7.32479i | −0.263796 | + | 0.456908i | −0.967247 | − | 0.253836i | \(-0.918308\pi\) |
0.703452 | + | 0.710743i | \(0.251641\pi\) | |||||||
\(258\) | 38.3214 | 2.38578 | ||||||||
\(259\) | −3.09955 | + | 8.30166i | −0.192597 | + | 0.515840i | ||||
\(260\) | −0.794170 | −0.0492523 | ||||||||
\(261\) | 3.65443 | − | 6.32966i | 0.226204 | − | 0.391796i | ||||
\(262\) | 0.209635 | + | 0.363099i | 0.0129513 | + | 0.0224323i | ||||
\(263\) | 1.36129 | + | 2.35782i | 0.0839405 | + | 0.145389i | 0.904939 | − | 0.425541i | \(-0.139916\pi\) |
−0.820999 | + | 0.570930i | \(0.806583\pi\) | |||||||
\(264\) | 3.68346 | − | 6.37993i | 0.226701 | − | 0.392658i | ||||
\(265\) | −18.6167 | −1.14362 | ||||||||
\(266\) | 8.25872 | + | 10.0093i | 0.506375 | + | 0.613711i | ||||
\(267\) | 35.1199 | 2.14930 | ||||||||
\(268\) | −0.706603 | + | 1.22387i | −0.0431627 | + | 0.0747599i | ||||
\(269\) | −14.7894 | − | 25.6160i | −0.901726 | − | 1.56183i | −0.825253 | − | 0.564763i | \(-0.808968\pi\) |
−0.0764725 | − | 0.997072i | \(-0.524366\pi\) | |||||||
\(270\) | −3.48919 | − | 6.04345i | −0.212345 | − | 0.367793i | ||||
\(271\) | −4.05801 | + | 7.02867i | −0.246506 | + | 0.426961i | −0.962554 | − | 0.271090i | \(-0.912616\pi\) |
0.716048 | + | 0.698051i | \(0.245949\pi\) | |||||||
\(272\) | −14.8131 | −0.898177 | ||||||||
\(273\) | 8.35778 | + | 10.1294i | 0.505836 | + | 0.613058i | ||||
\(274\) | −23.5585 | −1.42322 | ||||||||
\(275\) | −0.0205761 | + | 0.0356388i | −0.00124078 | + | 0.00214910i | ||||
\(276\) | 0.478704 | + | 0.829139i | 0.0288146 | + | 0.0499083i | ||||
\(277\) | 0.546971 | + | 0.947382i | 0.0328643 | + | 0.0569226i | 0.881990 | − | 0.471269i | \(-0.156204\pi\) |
−0.849125 | + | 0.528191i | \(0.822870\pi\) | |||||||
\(278\) | 10.2762 | − | 17.7989i | 0.616324 | − | 1.06750i | ||||
\(279\) | 0.677931 | 0.0405867 | ||||||||
\(280\) | 6.04091 | − | 16.1796i | 0.361014 | − | 0.966919i | ||||
\(281\) | 7.95015 | 0.474266 | 0.237133 | − | 0.971477i | \(-0.423792\pi\) | ||||
0.237133 | + | 0.971477i | \(0.423792\pi\) | |||||||
\(282\) | −11.0500 | + | 19.1391i | −0.658015 | + | 1.13972i | ||||
\(283\) | 13.8297 | + | 23.9537i | 0.822089 | + | 1.42390i | 0.904124 | + | 0.427271i | \(0.140525\pi\) |
−0.0820341 | + | 0.996630i | \(0.526142\pi\) | |||||||
\(284\) | 0.794350 | + | 1.37586i | 0.0471360 | + | 0.0816420i | ||||
\(285\) | −8.97358 | + | 15.5427i | −0.531549 | + | 0.920669i | ||||
\(286\) | −3.41061 | −0.201673 | ||||||||
\(287\) | −2.60927 | + | 0.437865i | −0.154020 | + | 0.0258463i | ||||
\(288\) | 1.77281 | 0.104464 | ||||||||
\(289\) | 0.284554 | − | 0.492862i | 0.0167385 | − | 0.0289919i | ||||
\(290\) | 5.62452 | + | 9.74195i | 0.330283 | + | 0.572067i | ||||
\(291\) | −2.34853 | − | 4.06777i | −0.137673 | − | 0.238457i | ||||
\(292\) | 0.0652640 | − | 0.113041i | 0.00381929 | − | 0.00661520i | ||||
\(293\) | −9.57574 | −0.559421 | −0.279710 | − | 0.960084i | \(-0.590238\pi\) | ||||
−0.279710 | + | 0.960084i | \(0.590238\pi\) | |||||||
\(294\) | −19.9957 | + | 6.90546i | −1.16617 | + | 0.402735i | ||||
\(295\) | −11.6408 | −0.677753 | ||||||||
\(296\) | 4.90667 | − | 8.49860i | 0.285195 | − | 0.493971i | ||||
\(297\) | 1.30301 | + | 2.25688i | 0.0756082 | + | 0.130957i | ||||
\(298\) | 7.11697 | + | 12.3270i | 0.412275 | + | 0.714082i | ||||
\(299\) | 2.99188 | − | 5.18209i | 0.173025 | − | 0.299688i | ||||
\(300\) | −0.0129982 | −0.000750451 | ||||||||
\(301\) | −33.0868 | + | 5.55235i | −1.90709 | + | 0.320032i | ||||
\(302\) | −6.94442 | −0.399606 | ||||||||
\(303\) | 8.73536 | − | 15.1301i | 0.501833 | − | 0.869201i | ||||
\(304\) | −6.60679 | − | 11.4433i | −0.378925 | − | 0.656318i | ||||
\(305\) | −6.24774 | − | 10.8214i | −0.357744 | − | 0.619632i | ||||
\(306\) | −5.39819 | + | 9.34994i | −0.308594 | + | 0.534501i | ||||
\(307\) | 8.24141 | 0.470362 | 0.235181 | − | 0.971952i | \(-0.424432\pi\) | ||||
0.235181 | + | 0.971952i | \(0.424432\pi\) | |||||||
\(308\) | −0.167107 | + | 0.447569i | −0.00952178 | + | 0.0255026i | ||||
\(309\) | 15.3928 | 0.875665 | ||||||||
\(310\) | −0.521700 | + | 0.903612i | −0.0296306 | + | 0.0513217i | ||||
\(311\) | 5.83211 | + | 10.1015i | 0.330709 | + | 0.572804i | 0.982651 | − | 0.185464i | \(-0.0593789\pi\) |
−0.651942 | + | 0.758269i | \(0.726046\pi\) | |||||||
\(312\) | −7.27150 | − | 12.5946i | −0.411668 | − | 0.713029i | ||||
\(313\) | −15.3091 | + | 26.5161i | −0.865319 | + | 1.49878i | 0.00141158 | + | 0.999999i | \(0.499551\pi\) |
−0.866730 | + | 0.498777i | \(0.833783\pi\) | |||||||
\(314\) | 20.4769 | 1.15558 | ||||||||
\(315\) | −7.36604 | − | 8.92742i | −0.415029 | − | 0.503003i | ||||
\(316\) | 1.41470 | 0.0795832 | ||||||||
\(317\) | 10.4058 | − | 18.0234i | 0.584450 | − | 1.01230i | −0.410494 | − | 0.911863i | \(-0.634644\pi\) |
0.994944 | − | 0.100434i | \(-0.0320231\pi\) | |||||||
\(318\) | −12.6265 | − | 21.8697i | −0.708057 | − | 1.22639i | ||||
\(319\) | −2.10043 | − | 3.63805i | −0.117601 | − | 0.203692i | ||||
\(320\) | −9.50590 | + | 16.4647i | −0.531396 | + | 0.920404i | ||||
\(321\) | −43.5945 | −2.43321 | ||||||||
\(322\) | 6.13462 | + | 7.43498i | 0.341869 | + | 0.414335i | ||||
\(323\) | −14.6567 | −0.815518 | ||||||||
\(324\) | −0.882815 | + | 1.52908i | −0.0490453 | + | 0.0849489i | ||||
\(325\) | 0.0406192 | + | 0.0703545i | 0.00225315 | + | 0.00390256i | ||||
\(326\) | −5.16559 | − | 8.94706i | −0.286095 | − | 0.495532i | ||||
\(327\) | 4.36902 | − | 7.56737i | 0.241607 | − | 0.418476i | ||||
\(328\) | 2.92997 | 0.161780 | ||||||||
\(329\) | 6.76753 | − | 18.1258i | 0.373106 | − | 0.999306i | ||||
\(330\) | 7.59849 | 0.418283 | ||||||||
\(331\) | 0.333500 | − | 0.577639i | 0.0183308 | − | 0.0317499i | −0.856714 | − | 0.515791i | \(-0.827498\pi\) |
0.875045 | + | 0.484041i | \(0.160831\pi\) | |||||||
\(332\) | −0.599129 | − | 1.03772i | −0.0328815 | − | 0.0569524i | ||||
\(333\) | −3.28824 | − | 5.69539i | −0.180194 | − | 0.312106i | ||||
\(334\) | −5.59517 | + | 9.69112i | −0.306154 | + | 0.530274i | ||||
\(335\) | −19.6779 | −1.07512 | ||||||||
\(336\) | 21.2437 | − | 3.56493i | 1.15894 | − | 0.194483i | ||||
\(337\) | 0.0671610 | 0.00365849 | 0.00182925 | − | 0.999998i | \(-0.499418\pi\) | ||||
0.00182925 | + | 0.999998i | \(0.499418\pi\) | |||||||
\(338\) | 5.45059 | − | 9.44071i | 0.296473 | − | 0.513507i | ||||
\(339\) | −5.69005 | − | 9.85546i | −0.309041 | − | 0.535275i | ||||
\(340\) | 0.722468 | + | 1.25135i | 0.0391813 | + | 0.0678640i | ||||
\(341\) | 0.194825 | − | 0.337446i | 0.0105503 | − | 0.0182737i | ||||
\(342\) | −9.63057 | −0.520762 | ||||||||
\(343\) | 16.2638 | − | 8.85936i | 0.878164 | − | 0.478360i | ||||
\(344\) | 37.1535 | 2.00318 | ||||||||
\(345\) | −6.66561 | + | 11.5452i | −0.358865 | + | 0.621572i | ||||
\(346\) | 16.0999 | + | 27.8859i | 0.865538 | + | 1.49916i | ||||
\(347\) | −14.2567 | − | 24.6933i | −0.765338 | − | 1.32560i | −0.940068 | − | 0.340988i | \(-0.889238\pi\) |
0.174729 | − | 0.984617i | \(-0.444095\pi\) | |||||||
\(348\) | 0.663436 | − | 1.14910i | 0.0355639 | − | 0.0615984i | ||||
\(349\) | 30.8596 | 1.65188 | 0.825938 | − | 0.563761i | \(-0.190646\pi\) | ||||
0.825938 | + | 0.563761i | \(0.190646\pi\) | |||||||
\(350\) | −0.129060 | + | 0.0216578i | −0.00689856 | + | 0.00115766i | ||||
\(351\) | 5.14453 | 0.274595 | ||||||||
\(352\) | 0.509473 | − | 0.882434i | 0.0271550 | − | 0.0470339i | ||||
\(353\) | −9.43292 | − | 16.3383i | −0.502064 | − | 0.869600i | −0.999997 | − | 0.00238442i | \(-0.999241\pi\) |
0.497934 | − | 0.867215i | \(-0.334092\pi\) | |||||||
\(354\) | −7.89516 | − | 13.6748i | −0.419623 | − | 0.726809i | ||||
\(355\) | −11.0608 | + | 19.1578i | −0.587045 | + | 1.01679i | ||||
\(356\) | 2.52220 | 0.133676 | ||||||||
\(357\) | 8.35739 | − | 22.3840i | 0.442320 | − | 1.18468i | ||||
\(358\) | 15.5389 | 0.821258 | ||||||||
\(359\) | 0.323788 | − | 0.560817i | 0.0170889 | − | 0.0295988i | −0.857355 | − | 0.514726i | \(-0.827894\pi\) |
0.874443 | + | 0.485128i | \(0.161227\pi\) | |||||||
\(360\) | 6.40866 | + | 11.1001i | 0.337766 | + | 0.585028i | ||||
\(361\) | 2.96300 | + | 5.13206i | 0.155947 | + | 0.270108i | ||||
\(362\) | −12.0398 | + | 20.8536i | −0.632799 | + | 1.09604i | ||||
\(363\) | 21.6693 | 1.13734 | ||||||||
\(364\) | 0.600230 | + | 0.727461i | 0.0314606 | + | 0.0381293i | ||||
\(365\) | 1.81751 | 0.0951329 | ||||||||
\(366\) | 8.47484 | − | 14.6789i | 0.442987 | − | 0.767276i | ||||
\(367\) | 5.08183 | + | 8.80199i | 0.265269 | + | 0.459460i | 0.967634 | − | 0.252357i | \(-0.0812058\pi\) |
−0.702365 | + | 0.711817i | \(0.747872\pi\) | |||||||
\(368\) | −4.90755 | − | 8.50013i | −0.255824 | − | 0.443100i | ||||
\(369\) | 0.981768 | − | 1.70047i | 0.0511088 | − | 0.0885230i | ||||
\(370\) | 10.1218 | 0.526208 | ||||||||
\(371\) | 14.0704 | + | 17.0529i | 0.730500 | + | 0.885344i | ||||
\(372\) | 0.123073 | 0.00638106 | ||||||||
\(373\) | −3.48449 | + | 6.03531i | −0.180420 | + | 0.312496i | −0.942024 | − | 0.335547i | \(-0.891079\pi\) |
0.761604 | + | 0.648043i | \(0.224412\pi\) | |||||||
\(374\) | 3.10268 | + | 5.37399i | 0.160436 | + | 0.277883i | ||||
\(375\) | −12.4993 | − | 21.6495i | −0.645463 | − | 1.11797i | ||||
\(376\) | −10.7132 | + | 18.5558i | −0.552490 | + | 0.956941i | ||||
\(377\) | −8.29290 | −0.427106 | ||||||||
\(378\) | −2.89870 | + | 7.76371i | −0.149093 | + | 0.399322i | ||||
\(379\) | −36.4593 | −1.87279 | −0.936394 | − | 0.350950i | \(-0.885859\pi\) | ||||
−0.936394 | + | 0.350950i | \(0.885859\pi\) | |||||||
\(380\) | −0.644454 | + | 1.11623i | −0.0330598 | + | 0.0572613i | ||||
\(381\) | −21.5808 | − | 37.3790i | −1.10562 | − | 1.91498i | ||||
\(382\) | −11.1622 | − | 19.3335i | −0.571109 | − | 0.989190i | ||||
\(383\) | 10.0892 | − | 17.4750i | 0.515534 | − | 0.892932i | −0.484303 | − | 0.874900i | \(-0.660927\pi\) |
0.999837 | − | 0.0180314i | \(-0.00573989\pi\) | |||||||
\(384\) | −21.7658 | −1.11073 | ||||||||
\(385\) | −6.56056 | + | 1.10094i | −0.334357 | + | 0.0561090i | ||||
\(386\) | 26.7354 | 1.36080 | ||||||||
\(387\) | 12.4493 | − | 21.5628i | 0.632834 | − | 1.09610i | ||||
\(388\) | −0.168664 | − | 0.292135i | −0.00856262 | − | 0.0148309i | ||||
\(389\) | 9.11942 | + | 15.7953i | 0.462373 | + | 0.800853i | 0.999079 | − | 0.0429163i | \(-0.0136649\pi\) |
−0.536706 | + | 0.843769i | \(0.680332\pi\) | |||||||
\(390\) | 7.50007 | − | 12.9905i | 0.379781 | − | 0.657800i | ||||
\(391\) | −10.8870 | −0.550581 | ||||||||
\(392\) | −19.3863 | + | 6.69501i | −0.979154 | + | 0.338149i | ||||
\(393\) | 0.688623 | 0.0347364 | ||||||||
\(394\) | −8.78257 | + | 15.2119i | −0.442460 | + | 0.766362i | ||||
\(395\) | 9.84936 | + | 17.0596i | 0.495575 | + | 0.858362i | ||||
\(396\) | −0.177279 | − | 0.307057i | −0.00890862 | − | 0.0154302i | ||||
\(397\) | −18.8370 | + | 32.6266i | −0.945400 | + | 1.63748i | −0.190452 | + | 0.981697i | \(0.560995\pi\) |
−0.754948 | + | 0.655784i | \(0.772338\pi\) | |||||||
\(398\) | 34.8790 | 1.74833 | ||||||||
\(399\) | 21.0193 | − | 3.52728i | 1.05228 | − | 0.176585i | ||||
\(400\) | 0.133254 | 0.00666272 | ||||||||
\(401\) | 12.8116 | − | 22.1903i | 0.639780 | − | 1.10813i | −0.345701 | − | 0.938345i | \(-0.612359\pi\) |
0.985481 | − | 0.169787i | \(-0.0543080\pi\) | |||||||
\(402\) | −13.3462 | − | 23.1163i | −0.665648 | − | 1.15294i | ||||
\(403\) | −0.384603 | − | 0.666151i | −0.0191584 | − | 0.0331834i | ||||
\(404\) | 0.627347 | − | 1.08660i | 0.0312117 | − | 0.0540602i | ||||
\(405\) | −24.5852 | −1.22165 | ||||||||
\(406\) | 4.67266 | − | 12.5150i | 0.231900 | − | 0.621108i | ||||
\(407\) | −3.77991 | −0.187363 | ||||||||
\(408\) | −13.2300 | + | 22.9150i | −0.654981 | + | 1.13446i | ||||
\(409\) | 2.04568 | + | 3.54322i | 0.101152 | + | 0.175201i | 0.912160 | − | 0.409835i | \(-0.134414\pi\) |
−0.811007 | + | 0.585036i | \(0.801080\pi\) | |||||||
\(410\) | 1.51103 | + | 2.61719i | 0.0746247 | + | 0.129254i | ||||
\(411\) | −19.3466 | + | 33.5092i | −0.954296 | + | 1.65289i | ||||
\(412\) | 1.10546 | 0.0544622 | ||||||||
\(413\) | 8.79805 | + | 10.6630i | 0.432924 | + | 0.524691i | ||||
\(414\) | −7.15363 | −0.351582 | ||||||||
\(415\) | 8.34245 | − | 14.4495i | 0.409515 | − | 0.709300i | ||||
\(416\) | −1.00575 | − | 1.74201i | −0.0493109 | − | 0.0854091i | ||||
\(417\) | −16.8779 | − | 29.2334i | −0.826514 | − | 1.43156i | ||||
\(418\) | −2.76764 | + | 4.79370i | −0.135370 | + | 0.234468i | ||||
\(419\) | −33.7334 | −1.64798 | −0.823992 | − | 0.566602i | \(-0.808258\pi\) | ||||
−0.823992 | + | 0.566602i | \(0.808258\pi\) | |||||||
\(420\) | −1.33725 | − | 1.62071i | −0.0652512 | − | 0.0790825i | ||||
\(421\) | 0.804296 | 0.0391990 | 0.0195995 | − | 0.999808i | \(-0.493761\pi\) | ||||
0.0195995 | + | 0.999808i | \(0.493761\pi\) | |||||||
\(422\) | −9.14250 | + | 15.8353i | −0.445050 | + | 0.770849i | ||||
\(423\) | 7.17951 | + | 12.4353i | 0.349080 | + | 0.604624i | ||||
\(424\) | −12.2417 | − | 21.2032i | −0.594507 | − | 1.02972i | ||||
\(425\) | 0.0739037 | − | 0.128005i | 0.00358485 | − | 0.00620915i | ||||
\(426\) | −30.0071 | −1.45385 | ||||||||
\(427\) | −5.19041 | + | 13.9017i | −0.251181 | + | 0.672750i | ||||
\(428\) | −3.13082 | −0.151334 | ||||||||
\(429\) | −2.80084 | + | 4.85120i | −0.135226 | + | 0.234218i | ||||
\(430\) | 19.1607 | + | 33.1873i | 0.924010 | + | 1.60043i | ||||
\(431\) | 19.9140 | + | 34.4920i | 0.959221 | + | 1.66142i | 0.724398 | + | 0.689382i | \(0.242118\pi\) |
0.234824 | + | 0.972038i | \(0.424549\pi\) | |||||||
\(432\) | 4.21925 | − | 7.30796i | 0.202999 | − | 0.351605i | ||||
\(433\) | −6.07965 | −0.292169 | −0.146085 | − | 0.989272i | \(-0.546667\pi\) | ||||
−0.146085 | + | 0.989272i | \(0.546667\pi\) | |||||||
\(434\) | 1.22201 | − | 0.205067i | 0.0586583 | − | 0.00984353i | ||||
\(435\) | 18.4758 | 0.885845 | ||||||||
\(436\) | 0.313770 | − | 0.543465i | 0.0150268 | − | 0.0260272i | ||||
\(437\) | −4.85572 | − | 8.41035i | −0.232280 | − | 0.402321i | ||||
\(438\) | 1.23270 | + | 2.13509i | 0.0589005 | + | 0.102019i | ||||
\(439\) | −20.0450 | + | 34.7189i | −0.956694 | + | 1.65704i | −0.226252 | + | 0.974069i | \(0.572647\pi\) |
−0.730442 | + | 0.682974i | \(0.760686\pi\) | |||||||
\(440\) | 7.36691 | 0.351204 | ||||||||
\(441\) | −2.61032 | + | 13.4946i | −0.124301 | + | 0.642600i | ||||
\(442\) | 12.2500 | 0.582672 | ||||||||
\(443\) | −9.04105 | + | 15.6595i | −0.429553 | + | 0.744008i | −0.996834 | − | 0.0795170i | \(-0.974662\pi\) |
0.567280 | + | 0.823525i | \(0.307996\pi\) | |||||||
\(444\) | −0.596956 | − | 1.03396i | −0.0283303 | − | 0.0490694i | ||||
\(445\) | 17.5599 | + | 30.4147i | 0.832421 | + | 1.44179i | ||||
\(446\) | 1.76138 | − | 3.05080i | 0.0834037 | − | 0.144459i | ||||
\(447\) | 23.3783 | 1.10575 | ||||||||
\(448\) | 22.2662 | − | 3.73652i | 1.05198 | − | 0.176534i | ||||
\(449\) | −11.4042 | −0.538200 | −0.269100 | − | 0.963112i | \(-0.586726\pi\) | ||||
−0.269100 | + | 0.963112i | \(0.586726\pi\) | |||||||
\(450\) | 0.0485605 | − | 0.0841092i | 0.00228916 | − | 0.00396495i | ||||
\(451\) | −0.564283 | − | 0.977367i | −0.0265711 | − | 0.0460224i | ||||
\(452\) | −0.408642 | − | 0.707788i | −0.0192209 | − | 0.0332916i | ||||
\(453\) | −5.70286 | + | 9.87764i | −0.267944 | + | 0.464092i | ||||
\(454\) | −13.7155 | −0.643698 | ||||||||
\(455\) | −4.59341 | + | 12.3027i | −0.215343 | + | 0.576761i | ||||
\(456\) | −23.6028 | −1.10530 | ||||||||
\(457\) | −14.0878 | + | 24.4008i | −0.658999 | + | 1.14142i | 0.321876 | + | 0.946782i | \(0.395687\pi\) |
−0.980875 | + | 0.194638i | \(0.937647\pi\) | |||||||
\(458\) | 9.21707 | + | 15.9644i | 0.430686 | + | 0.745969i | ||||
\(459\) | −4.68005 | − | 8.10608i | −0.218446 | − | 0.378360i | ||||
\(460\) | −0.478704 | + | 0.829139i | −0.0223197 | + | 0.0386588i | ||||
\(461\) | 29.6306 | 1.38003 | 0.690017 | − | 0.723793i | \(-0.257603\pi\) | ||||
0.690017 | + | 0.723793i | \(0.257603\pi\) | |||||||
\(462\) | −5.74290 | − | 6.96022i | −0.267184 | − | 0.323819i | ||||
\(463\) | 29.1404 | 1.35427 | 0.677135 | − | 0.735859i | \(-0.263221\pi\) | ||||
0.677135 | + | 0.735859i | \(0.263221\pi\) | |||||||
\(464\) | −6.80138 | + | 11.7803i | −0.315746 | + | 0.546888i | ||||
\(465\) | 0.856856 | + | 1.48412i | 0.0397358 | + | 0.0688243i | ||||
\(466\) | −6.28198 | − | 10.8807i | −0.291007 | − | 0.504039i | ||||
\(467\) | −7.92955 | + | 13.7344i | −0.366936 | + | 0.635551i | −0.989085 | − | 0.147348i | \(-0.952926\pi\) |
0.622149 | + | 0.782899i | \(0.286260\pi\) | |||||||
\(468\) | −0.699933 | −0.0323544 | ||||||||
\(469\) | 14.8725 | + | 18.0250i | 0.686747 | + | 0.832317i | ||||
\(470\) | −22.0999 | −1.01939 | ||||||||
\(471\) | 16.8160 | − | 29.1261i | 0.774839 | − | 1.34206i | ||||
\(472\) | −7.65455 | − | 13.2581i | −0.352329 | − | 0.610252i | ||||
\(473\) | −7.15540 | − | 12.3935i | −0.329006 | − | 0.569854i | ||||
\(474\) | −13.3603 | + | 23.1408i | −0.613660 | + | 1.06289i | ||||
\(475\) | 0.131847 | 0.00604955 | ||||||||
\(476\) | 0.600201 | − | 1.60755i | 0.0275102 | − | 0.0736817i | ||||
\(477\) | −16.4076 | −0.751254 | ||||||||
\(478\) | 7.16080 | − | 12.4029i | 0.327527 | − | 0.567294i | ||||
\(479\) | −1.83916 | − | 3.18552i | −0.0840333 | − | 0.145550i | 0.820946 | − | 0.571006i | \(-0.193447\pi\) |
−0.904979 | + | 0.425456i | \(0.860114\pi\) | |||||||
\(480\) | 2.24071 | + | 3.88102i | 0.102274 | + | 0.177144i | ||||
\(481\) | −3.73095 | + | 6.46220i | −0.170117 | + | 0.294651i | ||||
\(482\) | 12.2289 | 0.557010 | ||||||||
\(483\) | 15.6132 | − | 2.62008i | 0.710427 | − | 0.119218i | ||||
\(484\) | 1.55622 | 0.0707374 | ||||||||
\(485\) | 2.34853 | − | 4.06777i | 0.106641 | − | 0.184708i | ||||
\(486\) | −11.9761 | − | 20.7432i | −0.543246 | − | 0.940929i | ||||
\(487\) | −14.4907 | − | 25.0987i | −0.656638 | − | 1.13733i | −0.981480 | − | 0.191563i | \(-0.938644\pi\) |
0.324842 | − | 0.945768i | \(-0.394689\pi\) | |||||||
\(488\) | 8.21656 | − | 14.2315i | 0.371946 | − | 0.644230i | ||||
\(489\) | −16.9682 | −0.767330 | ||||||||
\(490\) | −15.9781 | − | 13.8640i | −0.721819 | − | 0.626313i | ||||
\(491\) | −39.5204 | −1.78353 | −0.891766 | − | 0.452496i | \(-0.850534\pi\) | ||||
−0.891766 | + | 0.452496i | \(0.850534\pi\) | |||||||
\(492\) | 0.178233 | − | 0.308708i | 0.00803536 | − | 0.0139176i | ||||
\(493\) | 7.54417 | + | 13.0669i | 0.339772 | + | 0.588503i | ||||
\(494\) | 5.46360 | + | 9.46323i | 0.245819 | + | 0.425771i | ||||
\(495\) | 2.46849 | − | 4.27555i | 0.110950 | − | 0.192172i | ||||
\(496\) | −1.26172 | −0.0566528 | ||||||||
\(497\) | 25.9083 | − | 4.34770i | 1.16215 | − | 0.195021i | ||||
\(498\) | 22.6325 | 1.01419 | ||||||||
\(499\) | −2.69095 | + | 4.66086i | −0.120463 | + | 0.208649i | −0.919950 | − | 0.392035i | \(-0.871771\pi\) |
0.799487 | + | 0.600683i | \(0.205105\pi\) | |||||||
\(500\) | −0.897663 | − | 1.55480i | −0.0401447 | − | 0.0695327i | ||||
\(501\) | 9.18967 | + | 15.9170i | 0.410564 | + | 0.711118i | ||||
\(502\) | −14.4404 | + | 25.0115i | −0.644507 | + | 1.11632i | ||||
\(503\) | 3.46954 | 0.154699 | 0.0773495 | − | 0.997004i | \(-0.475354\pi\) | ||||
0.0773495 | + | 0.997004i | \(0.475354\pi\) | |||||||
\(504\) | 5.32410 | − | 14.2598i | 0.237154 | − | 0.635180i | ||||
\(505\) | 17.4707 | 0.777437 | ||||||||
\(506\) | −2.05582 | + | 3.56078i | −0.0913923 | + | 0.158296i | ||||
\(507\) | −8.95222 | − | 15.5057i | −0.397582 | − | 0.688632i | ||||
\(508\) | −1.54986 | − | 2.68444i | −0.0687641 | − | 0.119103i | ||||
\(509\) | 16.8620 | − | 29.2059i | 0.747397 | − | 1.29453i | −0.201670 | − | 0.979453i | \(-0.564637\pi\) |
0.949067 | − | 0.315075i | \(-0.102030\pi\) | |||||||
\(510\) | −27.2917 | −1.20850 | ||||||||
\(511\) | −1.37367 | − | 1.66484i | −0.0607674 | − | 0.0736483i | ||||
\(512\) | −24.7140 | −1.09221 | ||||||||
\(513\) | 4.17469 | − | 7.23077i | 0.184317 | − | 0.319247i | ||||
\(514\) | −5.73645 | − | 9.93582i | −0.253024 | − | 0.438250i | ||||
\(515\) | 7.69639 | + | 13.3305i | 0.339144 | + | 0.587414i | ||||
\(516\) | 2.26008 | − | 3.91458i | 0.0994946 | − | 0.172330i | ||||
\(517\) | 8.25302 | 0.362967 | ||||||||
\(518\) | −7.65002 | − | 9.27160i | −0.336123 | − | 0.407371i | ||||
\(519\) | 52.8860 | 2.32144 | ||||||||
\(520\) | 7.27150 | − | 12.5946i | 0.318876 | − | 0.552310i | ||||
\(521\) | −4.17464 | − | 7.23069i | −0.182894 | − | 0.316782i | 0.759971 | − | 0.649957i | \(-0.225213\pi\) |
−0.942865 | + | 0.333175i | \(0.891880\pi\) | |||||||
\(522\) | 4.95711 | + | 8.58597i | 0.216967 | + | 0.375798i | ||||
\(523\) | 6.49731 | − | 11.2537i | 0.284107 | − | 0.492089i | −0.688285 | − | 0.725441i | \(-0.741636\pi\) |
0.972392 | + | 0.233352i | \(0.0749694\pi\) | |||||||
\(524\) | 0.0494548 | 0.00216044 | ||||||||
\(525\) | −0.0751805 | + | 0.201359i | −0.00328115 | + | 0.00878804i | ||||
\(526\) | −3.69307 | −0.161026 | ||||||||
\(527\) | −0.699757 | + | 1.21201i | −0.0304819 | + | 0.0527962i | ||||
\(528\) | 4.59419 | + | 7.95736i | 0.199936 | + | 0.346300i | ||||
\(529\) | 7.89315 | + | 13.6713i | 0.343180 | + | 0.594406i | ||||
\(530\) | 12.6265 | − | 21.8697i | 0.548459 | − | 0.949958i | ||||
\(531\) | −10.2595 | −0.445224 | ||||||||
\(532\) | 1.50954 | − | 0.253318i | 0.0654469 | − | 0.0109827i | ||||
\(533\) | −2.22790 | −0.0965010 | ||||||||
\(534\) | −23.8194 | + | 41.2565i | −1.03077 | + | 1.78534i | ||||
\(535\) | −21.7973 | − | 37.7540i | −0.942378 | − | 1.63225i | ||||
\(536\) | −12.9395 | − | 22.4118i | −0.558899 | − | 0.968042i | ||||
\(537\) | 12.7608 | − | 22.1024i | 0.550669 | − | 0.953787i | ||||
\(538\) | 40.1226 | 1.72981 | ||||||||
\(539\) | 5.96690 | + | 5.17740i | 0.257013 | + | 0.223007i | ||||
\(540\) | −0.823128 | −0.0354218 | ||||||||
\(541\) | 17.9257 | − | 31.0483i | 0.770687 | − | 1.33487i | −0.166500 | − | 0.986042i | \(-0.553246\pi\) |
0.937187 | − | 0.348828i | \(-0.113420\pi\) | |||||||
\(542\) | −5.50455 | − | 9.53415i | −0.236440 | − | 0.409527i | ||||
\(543\) | 19.7746 | + | 34.2505i | 0.848607 | + | 1.46983i | ||||
\(544\) | −1.82989 | + | 3.16946i | −0.0784559 | + | 0.135890i | ||||
\(545\) | 8.73804 | 0.374297 | ||||||||
\(546\) | −17.5678 | + | 2.94808i | −0.751834 | + | 0.126166i | ||||
\(547\) | −37.4317 | −1.60046 | −0.800232 | − | 0.599691i | \(-0.795290\pi\) | ||||
−0.800232 | + | 0.599691i | \(0.795290\pi\) | |||||||
\(548\) | −1.38941 | + | 2.40653i | −0.0593527 | + | 0.102802i | ||||
\(549\) | −5.50638 | − | 9.53733i | −0.235007 | − | 0.407043i | ||||
\(550\) | −0.0279107 | − | 0.0483428i | −0.00119012 | − | 0.00206134i | ||||
\(551\) | −6.72954 | + | 11.6559i | −0.286688 | + | 0.496558i | ||||
\(552\) | −17.5322 | −0.746221 | ||||||||
\(553\) | 8.18252 | − | 21.9156i | 0.347956 | − | 0.931946i | ||||
\(554\) | −1.48389 | −0.0630447 | ||||||||
\(555\) | 8.31219 | − | 14.3971i | 0.352833 | − | 0.611124i | ||||
\(556\) | −1.21212 | − | 2.09945i | −0.0514052 | − | 0.0890365i | ||||
\(557\) | 7.22341 | + | 12.5113i | 0.306066 | + | 0.530121i | 0.977498 | − | 0.210945i | \(-0.0676539\pi\) |
−0.671432 | + | 0.741066i | \(0.734321\pi\) | |||||||
\(558\) | −0.459795 | + | 0.796389i | −0.0194647 | + | 0.0337138i | ||||
\(559\) | −28.2509 | −1.19489 | ||||||||
\(560\) | 13.7092 | + | 16.6151i | 0.579318 | + | 0.702117i | ||||
\(561\) | 10.1919 | 0.430300 | ||||||||
\(562\) | −5.39205 | + | 9.33931i | −0.227450 | + | 0.393955i | ||||
\(563\) | 2.86790 | + | 4.96736i | 0.120868 | + | 0.209349i | 0.920110 | − | 0.391660i | \(-0.128099\pi\) |
−0.799242 | + | 0.601009i | \(0.794766\pi\) | |||||||
\(564\) | 1.30339 | + | 2.25753i | 0.0548825 | + | 0.0950593i | ||||
\(565\) | 5.69005 | − | 9.85546i | 0.239382 | − | 0.414622i | ||||
\(566\) | −37.5190 | −1.57704 | ||||||||
\(567\) | 18.5814 | + | 22.5201i | 0.780343 | + | 0.945753i | ||||
\(568\) | −29.0926 | −1.22070 | ||||||||
\(569\) | −5.86822 | + | 10.1641i | −0.246009 | + | 0.426099i | −0.962415 | − | 0.271584i | \(-0.912452\pi\) |
0.716406 | + | 0.697684i | \(0.245786\pi\) | |||||||
\(570\) | −12.1723 | − | 21.0831i | −0.509844 | − | 0.883075i | ||||
\(571\) | −3.58127 | − | 6.20294i | −0.149872 | − | 0.259585i | 0.781308 | − | 0.624145i | \(-0.214553\pi\) |
−0.931180 | + | 0.364560i | \(0.881219\pi\) | |||||||
\(572\) | −0.201148 | + | 0.348398i | −0.00841040 | + | 0.0145672i | ||||
\(573\) | −36.6663 | −1.53176 | ||||||||
\(574\) | 1.25532 | − | 3.36217i | 0.0523959 | − | 0.140334i | ||||
\(575\) | 0.0979365 | 0.00408423 | ||||||||
\(576\) | −8.37792 | + | 14.5110i | −0.349080 | + | 0.604625i | ||||
\(577\) | 14.5204 | + | 25.1500i | 0.604491 | + | 1.04701i | 0.992132 | + | 0.125198i | \(0.0399566\pi\) |
−0.387641 | + | 0.921810i | \(0.626710\pi\) | |||||||
\(578\) | 0.385988 | + | 0.668550i | 0.0160550 | + | 0.0278080i | ||||
\(579\) | 21.9555 | − | 38.0281i | 0.912440 | − | 1.58039i | ||||
\(580\) | 1.32687 | 0.0550953 | ||||||||
\(581\) | −19.5410 | + | 3.27920i | −0.810697 | + | 0.136044i | ||||
\(582\) | 6.37140 | 0.264103 | ||||||||
\(583\) | −4.71525 | + | 8.16705i | −0.195286 | + | 0.338245i | ||||
\(584\) | 1.19513 | + | 2.07002i | 0.0494547 | + | 0.0856581i | ||||
\(585\) | −4.87304 | − | 8.44035i | −0.201475 | − | 0.348966i | ||||
\(586\) | 6.49458 | − | 11.2489i | 0.268289 | − | 0.464690i | ||||
\(587\) | 8.38291 | 0.346000 | 0.173000 | − | 0.984922i | \(-0.444654\pi\) | ||||
0.173000 | + | 0.984922i | \(0.444654\pi\) | |||||||
\(588\) | −0.473884 | + | 2.44985i | −0.0195426 | + | 0.101030i | ||||
\(589\) | −1.24839 | −0.0514391 | ||||||||
\(590\) | 7.89516 | − | 13.6748i | 0.325039 | − | 0.562984i | ||||
\(591\) | 14.4248 | + | 24.9844i | 0.593355 | + | 1.02772i | ||||
\(592\) | 6.11984 | + | 10.5999i | 0.251524 | + | 0.435652i | ||||
\(593\) | −1.14553 | + | 1.98411i | −0.0470412 | + | 0.0814778i | −0.888587 | − | 0.458708i | \(-0.848313\pi\) |
0.841546 | + | 0.540185i | \(0.181646\pi\) | |||||||
\(594\) | −3.53497 | −0.145042 | ||||||||
\(595\) | 23.5638 | − | 3.95427i | 0.966020 | − | 0.162109i | ||||
\(596\) | 1.67895 | 0.0687726 | ||||||||
\(597\) | 28.6432 | − | 49.6114i | 1.17229 | − | 2.03046i | ||||
\(598\) | 4.05839 | + | 7.02933i | 0.165960 | + | 0.287451i | ||||
\(599\) | −3.38508 | − | 5.86313i | −0.138311 | − | 0.239561i | 0.788547 | − | 0.614975i | \(-0.210834\pi\) |
−0.926857 | + | 0.375414i | \(0.877501\pi\) | |||||||
\(600\) | 0.119013 | − | 0.206136i | 0.00485868 | − | 0.00841548i | ||||
\(601\) | −41.3732 | −1.68765 | −0.843824 | − | 0.536619i | \(-0.819701\pi\) | ||||
−0.843824 | + | 0.536619i | \(0.819701\pi\) | |||||||
\(602\) | 15.9180 | − | 42.6340i | 0.648771 | − | 1.73763i | ||||
\(603\) | −17.3429 | −0.706258 | ||||||||
\(604\) | −0.409562 | + | 0.709382i | −0.0166648 | + | 0.0288643i | ||||
\(605\) | 10.8347 | + | 18.7662i | 0.440491 | + | 0.762953i | ||||
\(606\) | 11.8492 | + | 20.5234i | 0.481342 | + | 0.833708i | ||||
\(607\) | 8.78391 | − | 15.2142i | 0.356528 | − | 0.617525i | −0.630850 | − | 0.775905i | \(-0.717294\pi\) |
0.987378 | + | 0.158380i | \(0.0506271\pi\) | |||||||
\(608\) | −3.26459 | −0.132397 | ||||||||
\(609\) | −13.9639 | − | 16.9238i | −0.565845 | − | 0.685788i | ||||
\(610\) | 16.9497 | 0.686273 | ||||||||
\(611\) | 8.14613 | − | 14.1095i | 0.329557 | − | 0.570810i | ||||
\(612\) | 0.636739 | + | 1.10286i | 0.0257387 | + | 0.0445807i | ||||
\(613\) | 7.79078 | + | 13.4940i | 0.314666 | + | 0.545018i | 0.979367 | − | 0.202092i | \(-0.0647740\pi\) |
−0.664700 | + | 0.747110i | \(0.731441\pi\) | |||||||
\(614\) | −5.58959 | + | 9.68146i | −0.225578 | + | 0.390712i | ||||
\(615\) | 4.96354 | 0.200149 | ||||||||
\(616\) | −5.56787 | − | 6.74810i | −0.224336 | − | 0.271889i | ||||
\(617\) | 3.07666 | 0.123862 | 0.0619309 | − | 0.998080i | \(-0.480274\pi\) | ||||
0.0619309 | + | 0.998080i | \(0.480274\pi\) | |||||||
\(618\) | −10.4399 | + | 18.0824i | −0.419954 | + | 0.727382i | ||||
\(619\) | 23.4870 | + | 40.6806i | 0.944021 | + | 1.63509i | 0.757699 | + | 0.652604i | \(0.226324\pi\) |
0.186322 | + | 0.982489i | \(0.440343\pi\) | |||||||
\(620\) | 0.0615367 | + | 0.106585i | 0.00247137 | + | 0.00428055i | ||||
\(621\) | 3.10098 | − | 5.37105i | 0.124438 | − | 0.215533i | ||||
\(622\) | −15.8221 | −0.634409 | ||||||||
\(623\) | 14.5882 | − | 39.0722i | 0.584464 | − | 1.56539i | ||||
\(624\) | 18.1387 | 0.726131 | ||||||||
\(625\) | 12.4082 | − | 21.4916i | 0.496327 | − | 0.859664i | ||||
\(626\) | −20.7662 | − | 35.9681i | −0.829984 | − | 1.43758i | ||||
\(627\) | 4.54566 | + | 7.87332i | 0.181536 | + | 0.314430i | ||||
\(628\) | 1.20767 | − | 2.09175i | 0.0481913 | − | 0.0834698i | ||||
\(629\) | 13.5764 | 0.541327 | ||||||||
\(630\) | 15.4832 | − | 2.59826i | 0.616867 | − | 0.103517i | ||||
\(631\) | 4.85357 | 0.193218 | 0.0966089 | − | 0.995322i | \(-0.469200\pi\) | ||||
0.0966089 | + | 0.995322i | \(0.469200\pi\) | |||||||
\(632\) | −12.9531 | + | 22.4355i | −0.515249 | + | 0.892437i | ||||
\(633\) | 15.0159 | + | 26.0083i | 0.596829 | + | 1.03374i | ||||
\(634\) | 14.1152 | + | 24.4482i | 0.560585 | + | 0.970961i | ||||
\(635\) | 21.5808 | − | 37.3790i | 0.856407 | − | 1.48334i | ||||
\(636\) | −2.97869 | −0.118113 | ||||||||
\(637\) | 14.7410 | − | 5.09078i | 0.584060 | − | 0.201704i | ||||
\(638\) | 5.69832 | 0.225599 | ||||||||
\(639\) | −9.74830 | + | 16.8845i | −0.385637 | + | 0.667942i | ||||
\(640\) | −10.8829 | − | 18.8498i | −0.430185 | − | 0.745103i | ||||
\(641\) | 4.78914 | + | 8.29503i | 0.189160 | + | 0.327634i | 0.944970 | − | 0.327156i | \(-0.106090\pi\) |
−0.755811 | + | 0.654790i | \(0.772757\pi\) | |||||||
\(642\) | 29.5672 | − | 51.2119i | 1.16693 | − | 2.02117i | ||||
\(643\) | 8.31243 | 0.327810 | 0.163905 | − | 0.986476i | \(-0.447591\pi\) | ||||
0.163905 | + | 0.986476i | \(0.447591\pi\) | |||||||
\(644\) | 1.12129 | − | 0.188166i | 0.0441852 | − | 0.00741478i | ||||
\(645\) | 62.9402 | 2.47827 | ||||||||
\(646\) | 9.94063 | − | 17.2177i | 0.391109 | − | 0.677420i | ||||
\(647\) | −10.1951 | − | 17.6584i | −0.400810 | − | 0.694223i | 0.593014 | − | 0.805192i | \(-0.297938\pi\) |
−0.993824 | + | 0.110969i | \(0.964605\pi\) | |||||||
\(648\) | −16.1663 | − | 28.0008i | −0.635072 | − | 1.09998i | ||||
\(649\) | −2.94838 | + | 5.10675i | −0.115734 | + | 0.200457i | ||||
\(650\) | −0.110197 | −0.00432228 | ||||||||
\(651\) | 0.711847 | − | 1.90657i | 0.0278995 | − | 0.0747244i | ||||
\(652\) | −1.21860 | −0.0477243 | ||||||||
\(653\) | −7.81289 | + | 13.5323i | −0.305742 | + | 0.529561i | −0.977426 | − | 0.211277i | \(-0.932238\pi\) |
0.671684 | + | 0.740838i | \(0.265571\pi\) | |||||||
\(654\) | 5.92643 | + | 10.2649i | 0.231742 | + | 0.401388i | ||||
\(655\) | 0.344311 | + | 0.596365i | 0.0134534 | + | 0.0233019i | ||||
\(656\) | −1.82720 | + | 3.16480i | −0.0713401 | + | 0.123565i | ||||
\(657\) | 1.60184 | 0.0624939 | ||||||||
\(658\) | 16.7030 | + | 20.2435i | 0.651151 | + | 0.789175i | ||||
\(659\) | 19.6929 | 0.767127 | 0.383564 | − | 0.923514i | \(-0.374697\pi\) | ||||
0.383564 | + | 0.923514i | \(0.374697\pi\) | |||||||
\(660\) | 0.448137 | − | 0.776195i | 0.0174437 | − | 0.0302134i | ||||
\(661\) | 16.4263 | + | 28.4512i | 0.638910 | + | 1.10662i | 0.985672 | + | 0.168672i | \(0.0539478\pi\) |
−0.346762 | + | 0.937953i | \(0.612719\pi\) | |||||||
\(662\) | 0.452381 | + | 0.783548i | 0.0175823 | + | 0.0304534i | ||||
\(663\) | 10.0599 | − | 17.4242i | 0.390692 | − | 0.676699i | ||||
\(664\) | 21.9427 | 0.851543 | ||||||||
\(665\) | 13.5644 | + | 16.4396i | 0.526004 | + | 0.637501i | ||||
\(666\) | 8.92076 | 0.345673 | ||||||||
\(667\) | −4.99873 | + | 8.65806i | −0.193552 | + | 0.335241i | ||||
\(668\) | 0.659973 | + | 1.14311i | 0.0255351 | + | 0.0442282i | ||||
\(669\) | −2.89294 | − | 5.01072i | −0.111848 | − | 0.193726i | ||||
\(670\) | 13.3462 | − | 23.1163i | 0.515609 | − | 0.893061i | ||||
\(671\) | −6.32972 | −0.244356 | ||||||||
\(672\) | 1.86151 | − | 4.98575i | 0.0718091 | − | 0.192330i | ||||
\(673\) | −2.56402 | −0.0988358 | −0.0494179 | − | 0.998778i | \(-0.515737\pi\) | ||||
−0.0494179 | + | 0.998778i | \(0.515737\pi\) | |||||||
\(674\) | −0.0455508 | + | 0.0788963i | −0.00175455 | + | 0.00303897i | ||||
\(675\) | 0.0421003 | + | 0.0729199i | 0.00162044 | + | 0.00280669i | ||||
\(676\) | −0.642920 | − | 1.11357i | −0.0247277 | − | 0.0428296i | ||||
\(677\) | −11.3542 | + | 19.6660i | −0.436377 | + | 0.755826i | −0.997407 | − | 0.0719689i | \(-0.977072\pi\) |
0.561030 | + | 0.827795i | \(0.310405\pi\) | |||||||
\(678\) | 15.4367 | 0.592844 | ||||||||
\(679\) | −5.50109 | + | 0.923146i | −0.211113 | + | 0.0354271i | ||||
\(680\) | −26.4599 | −1.01469 | ||||||||
\(681\) | −11.2633 | + | 19.5087i | −0.431612 | + | 0.747574i | ||||
\(682\) | 0.264273 | + | 0.457734i | 0.0101195 | + | 0.0175275i | ||||
\(683\) | −19.7307 | − | 34.1745i | −0.754972 | − | 1.30765i | −0.945388 | − | 0.325947i | \(-0.894317\pi\) |
0.190416 | − | 0.981704i | \(-0.439016\pi\) | |||||||
\(684\) | −0.567983 | + | 0.983776i | −0.0217174 | + | 0.0376156i | ||||
\(685\) | −38.6931 | −1.47839 | ||||||||
\(686\) | −0.623265 | + | 25.1144i | −0.0237964 | + | 0.958871i | ||||
\(687\) | 30.2768 | 1.15513 | ||||||||
\(688\) | −23.1698 | + | 40.1313i | −0.883341 | + | 1.52999i | ||||
\(689\) | 9.30835 | + | 16.1225i | 0.354620 | + | 0.614220i | ||||
\(690\) | −9.04168 | − | 15.6606i | −0.344211 | − | 0.596190i | ||||
\(691\) | −12.7937 | + | 22.1593i | −0.486694 | + | 0.842978i | −0.999883 | − | 0.0152972i | \(-0.995131\pi\) |
0.513189 | + | 0.858275i | \(0.328464\pi\) | |||||||
\(692\) | 3.79811 | 0.144382 | ||||||||
\(693\) | −5.78208 | + | 0.970300i | −0.219643 | + | 0.0368586i | ||||
\(694\) | 38.6774 | 1.46817 | ||||||||
\(695\) | 16.8779 | − | 29.2334i | 0.640215 | − | 1.10888i | ||||
\(696\) | 12.1490 | + | 21.0426i | 0.460505 | + | 0.797619i | ||||
\(697\) | 2.02675 | + | 3.51044i | 0.0767687 | + | 0.132967i | ||||
\(698\) | −20.9300 | + | 36.2518i | −0.792212 | + | 1.37215i | ||||
\(699\) | −20.6354 | −0.780503 | ||||||||
\(700\) | −0.00539923 | + | 0.0144610i | −0.000204072 | + | 0.000546574i | ||||
\(701\) | −28.4667 | −1.07517 | −0.537586 | − | 0.843209i | \(-0.680664\pi\) | ||||
−0.537586 | + | 0.843209i | \(0.680664\pi\) | |||||||
\(702\) | −3.48919 | + | 6.04345i | −0.131691 | + | 0.228095i | ||||
\(703\) | 6.05520 | + | 10.4879i | 0.228376 | + | 0.395559i | ||||
\(704\) | 4.81531 | + | 8.34037i | 0.181484 | + | 0.314339i | ||||
\(705\) | −18.1488 | + | 31.4346i | −0.683522 | + | 1.18389i | ||||
\(706\) | 25.5909 | 0.963125 | ||||||||
\(707\) | −13.2043 | − | 16.0032i | −0.496598 | − | 0.601863i | ||||
\(708\) | −1.86253 | −0.0699983 | ||||||||
\(709\) | 9.29445 | − | 16.0985i | 0.349061 | − | 0.604591i | −0.637022 | − | 0.770845i | \(-0.719834\pi\) |
0.986083 | + | 0.166255i | \(0.0531674\pi\) | |||||||
\(710\) | −15.0036 | − | 25.9869i | −0.563074 | − | 0.975272i | ||||
\(711\) | 8.68063 | + | 15.0353i | 0.325549 | + | 0.563868i | ||||
\(712\) | −23.0935 | + | 39.9991i | −0.865466 | + | 1.49903i | ||||
\(713\) | −0.927312 | −0.0347281 | ||||||||
\(714\) | 20.6269 | + | 24.9992i | 0.771944 | + | 0.935573i | ||||
\(715\) | −5.60168 | −0.209491 | ||||||||
\(716\) | 0.916441 | − | 1.58732i | 0.0342490 | − | 0.0593210i | ||||
\(717\) | −11.7611 | − | 20.3708i | −0.439227 | − | 0.760763i | ||||
\(718\) | 0.439207 | + | 0.760729i | 0.0163911 | + | 0.0283902i | ||||
\(719\) | −8.31292 | + | 14.3984i | −0.310020 | + | 0.536970i | −0.978366 | − | 0.206880i | \(-0.933669\pi\) |
0.668347 | + | 0.743850i | \(0.267002\pi\) | |||||||
\(720\) | −15.9864 | −0.595777 | ||||||||
\(721\) | 6.39390 | − | 17.1251i | 0.238121 | − | 0.637771i | ||||
\(722\) | −8.03841 | −0.299158 | ||||||||
\(723\) | 10.0425 | − | 17.3942i | 0.373486 | − | 0.646896i | ||||
\(724\) | 1.42015 | + | 2.45977i | 0.0527793 | + | 0.0914165i | ||||
\(725\) | −0.0678651 | − | 0.117546i | −0.00252045 | − | 0.00436554i | ||||
\(726\) | −14.6968 | + | 25.4557i | −0.545451 | + | 0.944748i | ||||
\(727\) | −13.5357 | −0.502010 | −0.251005 | − | 0.967986i | \(-0.580761\pi\) | ||||
−0.251005 | + | 0.967986i | \(0.580761\pi\) | |||||||
\(728\) | −17.0324 | + | 2.85824i | −0.631264 | + | 0.105933i | ||||
\(729\) | −6.23430 | −0.230900 | ||||||||
\(730\) | −1.23270 | + | 2.13509i | −0.0456241 | + | 0.0790233i | ||||
\(731\) | 25.7002 | + | 44.5141i | 0.950558 | + | 1.64641i | ||||
\(732\) | −0.999643 | − | 1.73143i | −0.0369479 | − | 0.0639956i | ||||
\(733\) | −1.84531 | + | 3.19616i | −0.0681579 | + | 0.118053i | −0.898090 | − | 0.439811i | \(-0.855046\pi\) |
0.829933 | + | 0.557864i | \(0.188379\pi\) | |||||||
\(734\) | −13.7867 | −0.508875 | ||||||||
\(735\) | −32.8415 | + | 11.3417i | −1.21138 | + | 0.418346i | ||||
\(736\) | −2.42495 | −0.0893850 | ||||||||
\(737\) | −4.98403 | + | 8.63259i | −0.183589 | + | 0.317985i | ||||
\(738\) | 1.33173 | + | 2.30663i | 0.0490218 | + | 0.0849083i | ||||
\(739\) | −15.1284 | − | 26.2031i | −0.556505 | − | 0.963896i | −0.997785 | − | 0.0665258i | \(-0.978809\pi\) |
0.441279 | − | 0.897370i | \(-0.354525\pi\) | |||||||
\(740\) | 0.596956 | − | 1.03396i | 0.0219445 | − | 0.0380090i | ||||
\(741\) | 17.9472 | 0.659305 | ||||||||
\(742\) | −29.5757 | + | 4.96314i | −1.08576 | + | 0.182202i | ||||
\(743\) | −42.1181 | −1.54516 | −0.772581 | − | 0.634917i | \(-0.781034\pi\) | ||||
−0.772581 | + | 0.634917i | \(0.781034\pi\) | |||||||
\(744\) | −1.12687 | + | 1.95180i | −0.0413132 | + | 0.0715565i | ||||
\(745\) | 11.6891 | + | 20.2462i | 0.428257 | + | 0.741762i | ||||
\(746\) | −4.72659 | − | 8.18669i | −0.173053 | − | 0.299736i | ||||
\(747\) | 7.35253 | − | 12.7350i | 0.269015 | − | 0.465948i | ||||
\(748\) | 0.731947 | 0.0267626 | ||||||||
\(749\) | −18.1084 | + | 48.5006i | −0.661667 | + | 1.77217i | ||||
\(750\) | 33.9098 | 1.23821 | ||||||||
\(751\) | 9.61308 | − | 16.6503i | 0.350786 | − | 0.607580i | −0.635601 | − | 0.772018i | \(-0.719248\pi\) |
0.986387 | + | 0.164438i | \(0.0525810\pi\) | |||||||
\(752\) | −13.3620 | − | 23.1437i | −0.487262 | − | 0.843963i | ||||
\(753\) | 23.7173 | + | 41.0796i | 0.864308 | + | 1.49703i | ||||
\(754\) | 5.62452 | − | 9.74195i | 0.204833 | − | 0.354781i | ||||
\(755\) | −11.4057 | −0.415097 | ||||||||
\(756\) | 0.622116 | + | 0.753987i | 0.0226262 | + | 0.0274222i | ||||
\(757\) | 6.23128 | 0.226480 | 0.113240 | − | 0.993568i | \(-0.463877\pi\) | ||||
0.113240 | + | 0.993568i | \(0.463877\pi\) | |||||||
\(758\) | 24.7279 | − | 42.8300i | 0.898157 | − | 1.55565i | ||||
\(759\) | 3.37654 | + | 5.84833i | 0.122561 | + | 0.212281i | ||||
\(760\) | −11.8014 | − | 20.4406i | −0.428081 | − | 0.741458i | ||||
\(761\) | 14.2602 | − | 24.6995i | 0.516933 | − | 0.895355i | −0.482873 | − | 0.875690i | \(-0.660407\pi\) |
0.999807 | − | 0.0196647i | \(-0.00625987\pi\) | |||||||
\(762\) | 58.5472 | 2.12094 | ||||||||
\(763\) | −6.60417 | − | 8.00406i | −0.239087 | − | 0.289766i | ||||
\(764\) | −2.63326 | −0.0952681 | ||||||||
\(765\) | −8.86615 | + | 15.3566i | −0.320556 | + | 0.555220i | ||||
\(766\) | 13.6857 | + | 23.7043i | 0.494483 | + | 0.856470i | ||||
\(767\) | 5.82039 | + | 10.0812i | 0.210162 | + | 0.364012i | ||||
\(768\) | −4.24948 | + | 7.36032i | −0.153340 | + | 0.265593i | ||||
\(769\) | 13.9303 | 0.502340 | 0.251170 | − | 0.967943i | \(-0.419185\pi\) | ||||
0.251170 | + | 0.967943i | \(0.419185\pi\) | |||||||
\(770\) | 3.15628 | − | 8.45361i | 0.113744 | − | 0.304647i | ||||
\(771\) | −18.8434 | −0.678629 | ||||||||
\(772\) | 1.57678 | − | 2.73106i | 0.0567495 | − | 0.0982929i | ||||
\(773\) | −19.8972 | − | 34.4630i | −0.715654 | − | 1.23955i | −0.962707 | − | 0.270547i | \(-0.912795\pi\) |
0.247053 | − | 0.969002i | \(-0.420538\pi\) | |||||||
\(774\) | 16.8871 | + | 29.2493i | 0.606993 | + | 1.05134i | ||||
\(775\) | 0.00629480 | − | 0.0109029i | 0.000226116 | − | 0.000391644i | ||||
\(776\) | 6.17722 | 0.221749 | ||||||||
\(777\) | −19.4701 | + | 3.26731i | −0.698486 | + | 0.117214i | ||||
\(778\) | −24.7403 | −0.886984 | ||||||||
\(779\) | −1.80790 | + | 3.13137i | −0.0647747 | + | 0.112193i | ||||
\(780\) | −0.884665 | − | 1.53228i | −0.0316761 | − | 0.0548646i | ||||
\(781\) | 5.60295 | + | 9.70460i | 0.200489 | + | 0.347258i | ||||
\(782\) | 7.38394 | − | 12.7894i | 0.264049 | − | 0.457347i | ||||
\(783\) | −8.59530 | −0.307171 | ||||||||
\(784\) | 4.85814 | − | 25.1152i | 0.173505 | − | 0.896973i | ||||
\(785\) | 33.6319 | 1.20038 | ||||||||
\(786\) | −0.467047 | + | 0.808949i | −0.0166590 | + | 0.0288542i | ||||
\(787\) | 11.0350 | + | 19.1131i | 0.393354 | + | 0.681309i | 0.992890 | − | 0.119039i | \(-0.0379814\pi\) |
−0.599536 | + | 0.800348i | \(0.704648\pi\) | |||||||
\(788\) | 1.03594 | + | 1.79430i | 0.0369039 | + | 0.0639194i | ||||
\(789\) | −3.03281 | + | 5.25298i | −0.107971 | + | 0.187011i | ||||
\(790\) | −26.7206 | −0.950678 | ||||||||
\(791\) | −13.3281 | + | 2.23661i | −0.473894 | + | 0.0795247i | ||||
\(792\) | 6.49275 | 0.230710 | ||||||||
\(793\) | −6.24774 | + | 10.8214i | −0.221864 | + | 0.384279i | ||||
\(794\) | −25.5517 | − | 44.2568i | −0.906796 | − | 1.57062i | ||||
\(795\) | −20.7381 | − | 35.9194i | −0.735504 | − | 1.27393i | ||||
\(796\) | 2.05706 | − | 3.56294i | 0.0729106 | − | 0.126285i | ||||
\(797\) | 13.9948 | 0.495720 | 0.247860 | − | 0.968796i | \(-0.420273\pi\) | ||||
0.247860 | + | 0.968796i | \(0.420273\pi\) | |||||||
\(798\) | −10.1124 | + | 27.0844i | −0.357974 | + | 0.958778i | ||||
\(799\) | −29.6426 | −1.04868 | ||||||||
\(800\) | 0.0164611 | − | 0.0285115i | 0.000581989 | − | 0.00100803i | ||||
\(801\) | 15.4763 | + | 26.8057i | 0.546827 | + | 0.947132i | ||||
\(802\) | 17.3785 | + | 30.1004i | 0.613656 | + | 1.06288i | ||||
\(803\) | 0.460340 | − | 0.797332i | 0.0162450 | − | 0.0281372i | ||||
\(804\) | −3.14848 | −0.111038 | ||||||||
\(805\) | 10.0757 | + | 12.2114i | 0.355121 | + | 0.430396i | ||||
\(806\) | 1.04340 | 0.0367522 | ||||||||
\(807\) | 32.9493 | − | 57.0699i | 1.15987 | − | 2.00895i | ||||
\(808\) | 11.4881 | + | 19.8980i | 0.404150 | + | 0.700008i | ||||
\(809\) | 2.64582 | + | 4.58269i | 0.0930219 | + | 0.161119i | 0.908781 | − | 0.417273i | \(-0.137014\pi\) |
−0.815759 | + | 0.578391i | \(0.803681\pi\) | |||||||
\(810\) | 16.6745 | − | 28.8810i | 0.585881 | − | 1.01478i | ||||
\(811\) | −19.4147 | −0.681744 | −0.340872 | − | 0.940110i | \(-0.610722\pi\) | ||||
−0.340872 | + | 0.940110i | \(0.610722\pi\) | |||||||
\(812\) | −1.00284 | − | 1.21542i | −0.0351929 | − | 0.0426527i | ||||
\(813\) | −18.0817 | −0.634151 | ||||||||
\(814\) | 2.56366 | − | 4.44039i | 0.0898562 | − | 0.155635i | ||||
\(815\) | −8.48411 | − | 14.6949i | −0.297185 | − | 0.514740i | ||||
\(816\) | −16.5011 | − | 28.5807i | −0.577653 | − | 1.00052i | ||||
\(817\) | −22.9251 | + | 39.7074i | −0.802047 | + | 1.38919i | ||||
\(818\) | −5.54979 | −0.194044 | ||||||||
\(819\) | −4.04836 | + | 10.8429i | −0.141461 | + | 0.378881i | ||||
\(820\) | 0.356466 | 0.0124483 | ||||||||
\(821\) | 1.72340 | − | 2.98501i | 0.0601470 | − | 0.104178i | −0.834384 | − | 0.551184i | \(-0.814176\pi\) |
0.894531 | + | 0.447006i | \(0.147510\pi\) | |||||||
\(822\) | −26.2430 | − | 45.4541i | −0.915328 | − | 1.58540i | ||||
\(823\) | −19.8568 | − | 34.3931i | −0.692166 | − | 1.19887i | −0.971127 | − | 0.238564i | \(-0.923323\pi\) |
0.278961 | − | 0.960303i | \(-0.410010\pi\) | |||||||
\(824\) | −10.1217 | + | 17.5313i | −0.352607 | + | 0.610733i | ||||
\(825\) | −0.0916828 | −0.00319199 | ||||||||
\(826\) | −18.4933 | + | 3.10338i | −0.643464 | + | 0.107981i | ||||
\(827\) | 3.66589 | 0.127475 | 0.0637377 | − | 0.997967i | \(-0.479698\pi\) | ||||
0.0637377 | + | 0.997967i | \(0.479698\pi\) | |||||||
\(828\) | −0.421900 | + | 0.730753i | −0.0146621 | + | 0.0253954i | ||||
\(829\) | −2.88177 | − | 4.99138i | −0.100088 | − | 0.173358i | 0.811633 | − | 0.584168i | \(-0.198579\pi\) |
−0.911721 | + | 0.410810i | \(0.865246\pi\) | |||||||
\(830\) | 11.3162 | + | 19.6003i | 0.392793 | + | 0.680337i | ||||
\(831\) | −1.21860 | + | 2.11067i | −0.0422726 | + | 0.0732184i | ||||
\(832\) | 19.0118 | 0.659115 | ||||||||
\(833\) | −21.4315 | − | 18.5958i | −0.742557 | − | 0.644307i | ||||
\(834\) | 45.7886 | 1.58553 | ||||||||
\(835\) | −9.18967 | + | 15.9170i | −0.318022 | + | 0.550830i | ||||
\(836\) | 0.326455 | + | 0.565437i | 0.0112907 | + | 0.0195560i | ||||
\(837\) | −0.398627 | − | 0.690442i | −0.0137786 | − | 0.0238652i | ||||
\(838\) | 22.8791 | − | 39.6277i | 0.790345 | − | 1.36892i | ||||
\(839\) | 2.49460 | 0.0861232 | 0.0430616 | − | 0.999072i | \(-0.486289\pi\) | ||||
0.0430616 | + | 0.999072i | \(0.486289\pi\) | |||||||
\(840\) | 37.9466 | − | 6.36787i | 1.30928 | − | 0.219712i | ||||
\(841\) | −15.1445 | −0.522224 | ||||||||
\(842\) | −0.545500 | + | 0.944834i | −0.0187992 | + | 0.0325611i | ||||
\(843\) | 8.85607 | + | 15.3392i | 0.305019 | + | 0.528309i | ||||
\(844\) | 1.07840 | + | 1.86784i | 0.0371199 | + | 0.0642936i | ||||
\(845\) | 8.95222 | − | 15.5057i | 0.307966 | − | 0.533412i | ||||
\(846\) | −19.4775 | −0.669651 | ||||||||
\(847\) | 9.00106 | − | 24.1079i | 0.309280 | − | 0.828358i | ||||
\(848\) | 30.5368 | 1.04864 | ||||||||
\(849\) | −30.8111 | + | 53.3665i | −1.05744 | + | 1.83153i | ||||
\(850\) | 0.100248 | + | 0.173634i | 0.00343847 | + | 0.00595561i | ||||
\(851\) | 4.49783 | + | 7.79047i | 0.154184 | + | 0.267054i | ||||
\(852\) | −1.76973 | + | 3.06527i | −0.0606301 | + | 0.105014i | ||||
\(853\) | 34.6227 | 1.18546 | 0.592729 | − | 0.805402i | \(-0.298051\pi\) | ||||
0.592729 | + | 0.805402i | \(0.298051\pi\) | |||||||
\(854\) | −12.8105 | − | 15.5259i | −0.438366 | − | 0.531287i | ||||
\(855\) | −15.8175 | −0.540948 | ||||||||
\(856\) | 28.6661 | − | 49.6512i | 0.979788 | − | 1.69704i | ||||
\(857\) | −1.21181 | − | 2.09891i | −0.0413946 | − | 0.0716975i | 0.844586 | − | 0.535420i | \(-0.179847\pi\) |
−0.885980 | + | 0.463723i | \(0.846513\pi\) | |||||||
\(858\) | −3.79924 | − | 6.58048i | −0.129704 | − | 0.224654i | ||||
\(859\) | 21.0938 | − | 36.5355i | 0.719711 | − | 1.24658i | −0.241403 | − | 0.970425i | \(-0.577608\pi\) |
0.961114 | − | 0.276151i | \(-0.0890591\pi\) | |||||||
\(860\) | 4.52017 | 0.154136 | ||||||||
\(861\) | −3.75142 | − | 4.54661i | −0.127848 | − | 0.154948i | ||||
\(862\) | −54.0252 | −1.84011 | ||||||||
\(863\) | −25.1325 | + | 43.5307i | −0.855519 | + | 1.48180i | 0.0206436 | + | 0.999787i | \(0.493428\pi\) |
−0.876163 | + | 0.482016i | \(0.839905\pi\) | |||||||
\(864\) | −1.04242 | − | 1.80553i | −0.0354640 | − | 0.0614254i | ||||
\(865\) | 26.4430 | + | 45.8006i | 0.899089 | + | 1.55727i | ||||
\(866\) | 4.12342 | − | 7.14197i | 0.140119 | − | 0.242694i | ||||
\(867\) | 1.26791 | 0.0430606 | ||||||||
\(868\) | 0.0511226 | − | 0.136924i | 0.00173522 | − | 0.00464750i | ||||
\(869\) | 9.97860 | 0.338501 | ||||||||
\(870\) | −12.5309 | + | 21.7041i | −0.424836 | + | 0.735838i | ||||
\(871\) | 9.83895 | + | 17.0416i | 0.333380 | + | 0.577432i | ||||
\(872\) | 5.74581 | + | 9.95204i | 0.194578 | + | 0.337019i | ||||
\(873\) | 2.06985 | − | 3.58509i | 0.0700539 | − | 0.121337i | ||||
\(874\) | 13.1732 | 0.445591 | ||||||||
\(875\) | −29.2779 | + | 4.91316i | −0.989774 | + | 0.166095i | ||||
\(876\) | 0.290803 | 0.00982533 | ||||||||
\(877\) | −5.30500 | + | 9.18854i | −0.179137 | + | 0.310275i | −0.941585 | − | 0.336775i | \(-0.890664\pi\) |
0.762448 | + | 0.647049i | \(0.223997\pi\) | |||||||
\(878\) | −27.1903 | − | 47.0950i | −0.917629 | − | 1.58938i | ||||
\(879\) | −10.6669 | − | 18.4756i | −0.359785 | − | 0.623166i | ||||
\(880\) | −4.59419 | + | 7.95736i | −0.154870 | + | 0.268243i | ||||
\(881\) | 2.45538 | 0.0827238 | 0.0413619 | − | 0.999144i | \(-0.486830\pi\) | ||||
0.0413619 | + | 0.999144i | \(0.486830\pi\) | |||||||
\(882\) | −14.0822 | − | 12.2189i | −0.474171 | − | 0.411432i | ||||
\(883\) | −47.5296 | −1.59950 | −0.799750 | − | 0.600333i | \(-0.795035\pi\) | ||||
−0.799750 | + | 0.600333i | \(0.795035\pi\) | |||||||
\(884\) | 0.722468 | − | 1.25135i | 0.0242992 | − | 0.0420875i | ||||
\(885\) | −12.9672 | − | 22.4599i | −0.435889 | − | 0.754982i | ||||
\(886\) | −12.2639 | − | 21.2416i | −0.412013 | − | 0.713627i | ||||
\(887\) | 2.17409 | − | 3.76563i | 0.0729988 | − | 0.126438i | −0.827215 | − | 0.561885i | \(-0.810076\pi\) |
0.900214 | + | 0.435447i | \(0.143410\pi\) | |||||||
\(888\) | 21.8631 | 0.733679 | ||||||||
\(889\) | −50.5499 | + | 8.48285i | −1.69539 | + | 0.284506i | ||||
\(890\) | −47.6389 | −1.59686 | ||||||||
\(891\) | −6.22694 | + | 10.7854i | −0.208610 | + | 0.361324i | ||||
\(892\) | −0.207762 | − | 0.359854i | −0.00695638 | − | 0.0120488i | ||||
\(893\) | −13.2209 | − | 22.8992i | −0.442420 | − | 0.766294i | ||||
\(894\) | −15.8559 | + | 27.4632i | −0.530301 | + | 0.918508i | ||||
\(895\) | 25.5216 | 0.853093 | ||||||||
\(896\) | −9.04116 | + | 24.2153i | −0.302044 | + | 0.808978i | ||||
\(897\) | 13.3312 | 0.445117 | ||||||||
\(898\) | 7.73473 | − | 13.3970i | 0.258111 | − | 0.447062i | ||||
\(899\) | 0.642581 | + | 1.11298i | 0.0214313 | + | 0.0371200i | ||||
\(900\) | −0.00572791 | − | 0.00992104i | −0.000190930 | − | 0.000330701i | ||||
\(901\) | 16.9359 | − | 29.3338i | 0.564216 | − | 0.977251i | ||||
\(902\) | 1.53086 | 0.0509721 | ||||||||
\(903\) | −47.5699 | − | 57.6533i | −1.58303 | − | 1.91858i | ||||
\(904\) | 14.9663 | 0.497770 | ||||||||
\(905\) | −19.7746 | + | 34.2505i | −0.657328 | + | 1.13853i | ||||
\(906\) | −7.73573 | − | 13.3987i | −0.257003 | − | 0.445141i | ||||
\(907\) | −6.49434 | − | 11.2485i | −0.215641 | − | 0.373501i | 0.737830 | − | 0.674987i | \(-0.235851\pi\) |
−0.953471 | + | 0.301486i | \(0.902517\pi\) | |||||||
\(908\) | −0.808898 | + | 1.40105i | −0.0268442 | + | 0.0464956i | ||||
\(909\) | 15.3976 | 0.510707 | ||||||||
\(910\) | −11.3370 | − | 13.7402i | −0.375819 | − | 0.455482i | ||||
\(911\) | −15.4395 | −0.511535 | −0.255767 | − | 0.966738i | \(-0.582328\pi\) | ||||
−0.255767 | + | 0.966738i | \(0.582328\pi\) | |||||||
\(912\) | 14.7193 | − | 25.4945i | 0.487403 | − | 0.844207i | ||||
\(913\) | −4.22596 | − | 7.31957i | −0.139859 | − | 0.242243i | ||||
\(914\) | −19.1096 | − | 33.0988i | −0.632090 | − | 1.09481i | ||||
\(915\) | 13.9193 | − | 24.1090i | 0.460159 | − | 0.797019i | ||||
\(916\) | 2.17438 | 0.0718437 | ||||||||
\(917\) | 0.286042 | − | 0.766120i | 0.00944595 | − | 0.0252995i | ||||
\(918\) | 12.6967 | 0.419052 | ||||||||
\(919\) | −20.1114 | + | 34.8340i | −0.663415 | + | 1.14907i | 0.316298 | + | 0.948660i | \(0.397560\pi\) |
−0.979712 | + | 0.200408i | \(0.935773\pi\) | |||||||
\(920\) | −8.76612 | − | 15.1834i | −0.289010 | − | 0.500581i | ||||
\(921\) | 9.18051 | + | 15.9011i | 0.302508 | + | 0.523960i | ||||
\(922\) | −20.0964 | + | 34.8081i | −0.661841 | + | 1.14634i | ||||
\(923\) | 22.1216 | 0.728140 | ||||||||
\(924\) | −1.04970 | + | 0.176151i | −0.0345324 | + | 0.00579494i | ||||
\(925\) | −0.122129 | −0.00401559 | ||||||||
\(926\) | −19.7640 | + | 34.2322i | −0.649485 | + | 1.12494i | ||||
\(927\) | 6.78313 | + | 11.7487i | 0.222787 | + | 0.385879i | ||||
\(928\) | 1.68037 | + | 2.91049i | 0.0551609 | + | 0.0955415i | ||||
\(929\) | −6.75514 | + | 11.7003i | −0.221629 | + | 0.383873i | −0.955303 | − | 0.295629i | \(-0.904471\pi\) |
0.733674 | + | 0.679502i | \(0.237804\pi\) | |||||||
\(930\) | −2.32459 | −0.0762264 | ||||||||
\(931\) | 4.80683 | − | 24.8500i | 0.157537 | − | 0.814425i | ||||
\(932\) | −1.48197 | −0.0485436 | ||||||||
\(933\) | −12.9934 | + | 22.5052i | −0.425384 | + | 0.736786i | ||||
\(934\) | −10.7562 | − | 18.6302i | −0.351952 | − | 0.609599i | ||||
\(935\) | 5.09593 | + | 8.82641i | 0.166655 | + | 0.288654i | ||||
\(936\) | 6.40866 | − | 11.1001i | 0.209474 | − | 0.362819i | ||||
\(937\) | −35.6590 | −1.16493 | −0.582465 | − | 0.812856i | \(-0.697912\pi\) | ||||
−0.582465 | + | 0.812856i | \(0.697912\pi\) | |||||||
\(938\) | −31.2616 | + | 5.24605i | −1.02073 | + | 0.171289i | ||||
\(939\) | −68.2141 | −2.22608 | ||||||||
\(940\) | −1.30339 | + | 2.25753i | −0.0425118 | + | 0.0736326i | ||||
\(941\) | 6.90672 | + | 11.9628i | 0.225153 | + | 0.389976i | 0.956365 | − | 0.292174i | \(-0.0943786\pi\) |
−0.731213 | + | 0.682150i | \(0.761045\pi\) | |||||||
\(942\) | 22.8103 | + | 39.5086i | 0.743199 | + | 1.28726i | ||||
\(943\) | −1.34292 | + | 2.32600i | −0.0437314 | + | 0.0757450i | ||||
\(944\) | 19.0942 | 0.621465 | ||||||||
\(945\) | −4.76091 | + | 12.7513i | −0.154872 | + | 0.414801i | ||||
\(946\) | 19.4121 | 0.631142 | ||||||||
\(947\) | −26.7218 | + | 46.2836i | −0.868343 | + | 1.50401i | −0.00465353 | + | 0.999989i | \(0.501481\pi\) |
−0.863689 | + | 0.504025i | \(0.831852\pi\) | |||||||
\(948\) | 1.57591 | + | 2.72955i | 0.0511831 | + | 0.0886516i | ||||
\(949\) | −0.908755 | − | 1.57401i | −0.0294994 | − | 0.0510945i | ||||
\(950\) | −0.0894229 | + | 0.154885i | −0.00290126 | + | 0.00502513i | ||||
\(951\) | 46.3663 | 1.50353 | ||||||||
\(952\) | 19.9983 | + | 24.2373i | 0.648148 | + | 0.785537i | ||||
\(953\) | 43.4781 | 1.40840 | 0.704198 | − | 0.710004i | \(-0.251307\pi\) | ||||
0.704198 | + | 0.710004i | \(0.251307\pi\) | |||||||
\(954\) | 11.1282 | − | 19.2746i | 0.360289 | − | 0.624039i | ||||
\(955\) | −18.3332 | − | 31.7540i | −0.593247 | − | 1.02753i | ||||
\(956\) | −0.844646 | − | 1.46297i | −0.0273178 | − | 0.0473158i | ||||
\(957\) | 4.67955 | − | 8.10521i | 0.151268 | − | 0.262004i | ||||
\(958\) | 4.98951 | 0.161204 | ||||||||
\(959\) | 29.2441 | + | 35.4430i | 0.944341 | + | 1.14451i | ||||
\(960\) | −42.3564 | −1.36705 | ||||||||
\(961\) | 15.4404 | − | 26.7436i | 0.498077 | − | 0.862695i | ||||
\(962\) | −5.06091 | − | 8.76575i | −0.163170 | − | 0.282619i | ||||
\(963\) | −19.2108 | − | 33.2741i | −0.619059 | − | 1.07224i | ||||
\(964\) | 0.721223 | − | 1.24920i | 0.0232290 | − | 0.0402339i | ||||
\(965\) | 43.9110 | 1.41355 | ||||||||
\(966\) | −7.51152 | + | 20.1184i | −0.241679 | + | 0.647300i | ||||
\(967\) | −60.5248 | −1.94635 | −0.973173 | − | 0.230075i | \(-0.926103\pi\) | ||||
−0.973173 | + | 0.230075i | \(0.926103\pi\) | |||||||
\(968\) | −14.2489 | + | 24.6799i | −0.457978 | + | 0.793241i | ||||
\(969\) | −16.3268 | − | 28.2788i | −0.524492 | − | 0.908446i | ||||
\(970\) | 3.18570 | + | 5.51779i | 0.102287 | + | 0.177166i | ||||
\(971\) | −8.15874 | + | 14.1314i | −0.261826 | + | 0.453497i | −0.966727 | − | 0.255809i | \(-0.917658\pi\) |
0.704901 | + | 0.709306i | \(0.250991\pi\) | |||||||
\(972\) | −2.82526 | −0.0906201 | ||||||||
\(973\) | −39.5340 | + | 6.63426i | −1.26740 | + | 0.212685i | ||||
\(974\) | 39.3124 | 1.25965 | ||||||||
\(975\) | −0.0904954 | + | 0.156743i | −0.00289817 | + | 0.00501978i | ||||
\(976\) | 10.2481 | + | 17.7502i | 0.328033 | + | 0.568171i | ||||
\(977\) | 7.07755 | + | 12.2587i | 0.226431 | + | 0.392190i | 0.956748 | − | 0.290919i | \(-0.0939609\pi\) |
−0.730317 | + | 0.683109i | \(0.760628\pi\) | |||||||
\(978\) | 11.5084 | − | 19.9331i | 0.367998 | − | 0.637392i | ||||
\(979\) | 17.7903 | 0.568582 | ||||||||
\(980\) | −2.35857 | + | 0.814528i | −0.0753418 | + | 0.0260192i | ||||
\(981\) | 7.70118 | 0.245880 | ||||||||
\(982\) | 26.8041 | − | 46.4260i | 0.855352 | − | 1.48151i | ||||
\(983\) | −12.6583 | − | 21.9249i | −0.403738 | − | 0.699295i | 0.590436 | − | 0.807085i | \(-0.298956\pi\) |
−0.994174 | + | 0.107790i | \(0.965623\pi\) | |||||||
\(984\) | 3.26384 | + | 5.65313i | 0.104047 | + | 0.180215i | ||||
\(985\) | −14.4248 | + | 24.9844i | −0.459611 | + | 0.796070i | ||||
\(986\) | −20.4668 | −0.651796 | ||||||||
\(987\) | 42.5109 | − | 7.13381i | 1.35314 | − | 0.227072i | ||||
\(988\) | 1.28891 | 0.0410056 | ||||||||
\(989\) | −17.0289 | + | 29.4949i | −0.541486 | + | 0.937882i | ||||
\(990\) | 3.34842 | + | 5.79964i | 0.106420 | + | 0.184325i | ||||
\(991\) | 17.9260 | + | 31.0487i | 0.569437 | + | 0.986294i | 0.996622 | + | 0.0821299i | \(0.0261722\pi\) |
−0.427184 | + | 0.904165i | \(0.640494\pi\) | |||||||
\(992\) | −0.155862 | + | 0.269961i | −0.00494863 | + | 0.00857128i | ||||
\(993\) | 1.48601 | 0.0471571 | ||||||||
\(994\) | −12.4644 | + | 33.3841i | −0.395348 | + | 1.05888i | ||||
\(995\) | 57.2863 | 1.81610 | ||||||||
\(996\) | 1.33480 | − | 2.31194i | 0.0422947 | − | 0.0732566i | ||||
\(997\) | −11.7124 | − | 20.2865i | −0.370937 | − | 0.642481i | 0.618773 | − | 0.785570i | \(-0.287630\pi\) |
−0.989710 | + | 0.143089i | \(0.954297\pi\) | |||||||
\(998\) | −3.65018 | − | 6.32229i | −0.115544 | − | 0.200129i | ||||
\(999\) | −3.86700 | + | 6.69784i | −0.122346 | + | 0.211910i |
(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 | 287.2.e.c.247.2 | yes | 10 | |
7.2 | even | 3 | 2009.2.a.l.1.4 | 5 | |||
7.4 | even | 3 | inner | 287.2.e.c.165.2 | ✓ | 10 | |
7.5 | odd | 6 | 2009.2.a.m.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
287.2.e.c.165.2 | ✓ | 10 | 7.4 | even | 3 | inner | |
287.2.e.c.247.2 | yes | 10 | 1.1 | even | 1 | trivial | |
2009.2.a.l.1.4 | 5 | 7.2 | even | 3 | |||
2009.2.a.m.1.4 | 5 | 7.5 | odd | 6 |