Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [605,2,Mod(9,605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(605, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("605.9");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.j (of order \(10\), degree \(4\), 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: | \(4.83094932229\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | 16.0.6879707136000000000000.7 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4x^{14} + 15x^{12} - 56x^{10} + 209x^{8} - 56x^{6} + 15x^{4} - 4x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 124.2 | ||
Root | \(0.492303 - 0.159959i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 605.124 |
Dual form | 605.2.j.e.444.2 |
$q$-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 \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(486\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{4}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.304260 | − | 0.418778i | −0.215144 | − | 0.296121i | 0.687781 | − | 0.725918i | \(-0.258585\pi\) |
−0.902925 | + | 0.429797i | \(0.858585\pi\) | |||||||
\(3\) | 1.83730 | − | 0.596975i | 1.06077 | − | 0.344664i | 0.273881 | − | 0.961764i | \(-0.411693\pi\) |
0.786885 | + | 0.617100i | \(0.211693\pi\) | |||||||
\(4\) | 0.535233 | − | 1.64728i | 0.267617 | − | 0.823639i | ||||
\(5\) | −0.570005 | − | 2.16220i | −0.254914 | − | 0.966964i | ||||
\(6\) | −0.809017 | − | 0.587785i | −0.330280 | − | 0.239962i | ||||
\(7\) | −3.18230 | − | 1.03399i | −1.20280 | − | 0.390812i | −0.362007 | − | 0.932175i | \(-0.617908\pi\) |
−0.840789 | + | 0.541364i | \(0.817908\pi\) | |||||||
\(8\) | −1.83730 | + | 0.596975i | −0.649584 | + | 0.211063i | ||||
\(9\) | 0.592242 | − | 0.430289i | 0.197414 | − | 0.143430i | ||||
\(10\) | −0.732051 | + | 0.896575i | −0.231495 | + | 0.283522i | ||||
\(11\) | 0 | 0 | ||||||||
\(12\) | − | 3.34607i | − | 0.965926i | ||||||
\(13\) | 2.49376 | + | 3.43237i | 0.691645 | + | 0.951968i | 1.00000 | 0.000696272i | \(0.000221630\pi\) | |
−0.308355 | + | 0.951271i | \(0.599778\pi\) | |||||||
\(14\) | 0.535233 | + | 1.64728i | 0.143047 | + | 0.440254i | ||||
\(15\) | −2.33805 | − | 3.63233i | −0.603681 | − | 0.937862i | ||||
\(16\) | −1.99350 | − | 1.44836i | −0.498375 | − | 0.362091i | ||||
\(17\) | 2.27103 | − | 3.12580i | 0.550805 | − | 0.758118i | −0.439316 | − | 0.898333i | \(-0.644779\pi\) |
0.990121 | + | 0.140214i | \(0.0447792\pi\) | |||||||
\(18\) | −0.360391 | − | 0.117098i | −0.0849449 | − | 0.0276003i | ||||
\(19\) | −1.29668 | − | 3.99078i | −0.297479 | − | 0.915547i | −0.982377 | − | 0.186908i | \(-0.940153\pi\) |
0.684898 | − | 0.728639i | \(-0.259847\pi\) | |||||||
\(20\) | −3.86682 | − | 0.218323i | −0.864648 | − | 0.0488185i | ||||
\(21\) | −6.46410 | −1.41058 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.48477i | 0.726624i | 0.931668 | + | 0.363312i | \(0.118354\pi\) | ||||
−0.931668 | + | 0.363312i | \(0.881646\pi\) | |||||||
\(24\) | −3.01929 | + | 2.19364i | −0.616311 | + | 0.447776i | ||||
\(25\) | −4.35019 | + | 2.46492i | −0.870038 | + | 0.492985i | ||||
\(26\) | 0.678648 | − | 2.08867i | 0.133094 | − | 0.409621i | ||||
\(27\) | −2.57529 | + | 3.54458i | −0.495614 | + | 0.682155i | ||||
\(28\) | −3.40654 | + | 4.68870i | −0.643776 | + | 0.886081i | ||||
\(29\) | 2.14093 | − | 6.58911i | 0.397561 | − | 1.22357i | −0.529388 | − | 0.848380i | \(-0.677578\pi\) |
0.926949 | − | 0.375188i | \(-0.122422\pi\) | |||||||
\(30\) | −0.809764 | + | 2.08429i | −0.147842 | + | 0.380538i | ||||
\(31\) | 7.06438 | − | 5.13257i | 1.26880 | − | 0.921837i | 0.269646 | − | 0.962960i | \(-0.413093\pi\) |
0.999154 | + | 0.0411227i | \(0.0130935\pi\) | |||||||
\(32\) | 5.13922i | 0.908494i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.00000 | −0.342997 | ||||||||
\(35\) | −0.421768 | + | 7.47013i | −0.0712918 | + | 1.26268i | ||||
\(36\) | −0.391818 | − | 1.20589i | −0.0653030 | − | 0.200982i | ||||
\(37\) | −1.70539 | − | 0.554114i | −0.280364 | − | 0.0910958i | 0.165460 | − | 0.986217i | \(-0.447089\pi\) |
−0.445824 | + | 0.895121i | \(0.647089\pi\) | |||||||
\(38\) | −1.27672 | + | 1.75726i | −0.207112 | + | 0.285065i | ||||
\(39\) | 6.63083 | + | 4.81758i | 1.06178 | + | 0.771430i | ||||
\(40\) | 2.33805 | + | 3.63233i | 0.369678 | + | 0.574321i | ||||
\(41\) | −0.535233 | − | 1.64728i | −0.0835894 | − | 0.257262i | 0.900523 | − | 0.434808i | \(-0.143184\pi\) |
−0.984112 | + | 0.177547i | \(0.943184\pi\) | |||||||
\(42\) | 1.96677 | + | 2.70702i | 0.303479 | + | 0.417703i | ||||
\(43\) | 6.45189i | 0.983905i | 0.870622 | + | 0.491952i | \(0.163717\pi\) | ||||
−0.870622 | + | 0.491952i | \(0.836283\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.26795 | − | 1.03528i | −0.189015 | − | 0.154330i | ||||
\(46\) | 1.45934 | − | 1.06028i | 0.215168 | − | 0.156329i | ||||
\(47\) | 10.8919 | − | 3.53899i | 1.58875 | − | 0.516215i | 0.624455 | − | 0.781061i | \(-0.285321\pi\) |
0.964291 | + | 0.264846i | \(0.0853213\pi\) | |||||||
\(48\) | −4.52729 | − | 1.47101i | −0.653459 | − | 0.212322i | ||||
\(49\) | 3.39476 | + | 2.46644i | 0.484966 | + | 0.352348i | ||||
\(50\) | 2.35584 | + | 1.07179i | 0.333167 | + | 0.151573i | ||||
\(51\) | 2.30653 | − | 7.09878i | 0.322979 | − | 0.994028i | ||||
\(52\) | 6.98881 | − | 2.27080i | 0.969174 | − | 0.314904i | ||||
\(53\) | −1.27672 | − | 1.75726i | −0.175371 | − | 0.241378i | 0.712279 | − | 0.701897i | \(-0.247663\pi\) |
−0.887650 | + | 0.460519i | \(0.847663\pi\) | |||||||
\(54\) | 2.26795 | 0.308629 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 6.46410 | 0.863802 | ||||||||
\(57\) | −4.76479 | − | 6.55817i | −0.631112 | − | 0.868651i | ||||
\(58\) | −3.41078 | + | 1.10823i | −0.447857 | + | 0.145517i | ||||
\(59\) | 0.391818 | − | 1.20589i | 0.0510103 | − | 0.156994i | −0.922306 | − | 0.386459i | \(-0.873698\pi\) |
0.973317 | + | 0.229466i | \(0.0736979\pi\) | |||||||
\(60\) | −7.23485 | + | 1.90727i | −0.934015 | + | 0.246228i | ||||
\(61\) | −9.49143 | − | 6.89593i | −1.21525 | − | 0.882933i | −0.219556 | − | 0.975600i | \(-0.570461\pi\) |
−0.995697 | + | 0.0926671i | \(0.970461\pi\) | |||||||
\(62\) | −4.29882 | − | 1.39677i | −0.545950 | − | 0.177390i | ||||
\(63\) | −2.32960 | + | 0.756934i | −0.293502 | + | 0.0953647i | ||||
\(64\) | −1.83481 | + | 1.33307i | −0.229351 | + | 0.166633i | ||||
\(65\) | 6.00000 | − | 7.34847i | 0.744208 | − | 0.911465i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 2.20925i | − | 0.269903i | −0.990852 | − | 0.134952i | \(-0.956912\pi\) | ||
0.990852 | − | 0.134952i | \(-0.0430879\pi\) | |||||||
\(68\) | −3.93354 | − | 5.41405i | −0.477011 | − | 0.656550i | ||||
\(69\) | 2.08032 | + | 6.40256i | 0.250441 | + | 0.770778i | ||||
\(70\) | 3.25665 | − | 2.09624i | 0.389245 | − | 0.250548i | ||||
\(71\) | 6.63083 | + | 4.81758i | 0.786934 | + | 0.571741i | 0.907052 | − | 0.421018i | \(-0.138327\pi\) |
−0.120118 | + | 0.992760i | \(0.538327\pi\) | |||||||
\(72\) | −0.831254 | + | 1.14412i | −0.0979642 | + | 0.134836i | ||||
\(73\) | 4.65921 | + | 1.51387i | 0.545319 | + | 0.177185i | 0.568705 | − | 0.822542i | \(-0.307445\pi\) |
−0.0233860 | + | 0.999727i | \(0.507445\pi\) | |||||||
\(74\) | 0.286831 | + | 0.882774i | 0.0333434 | + | 0.102620i | ||||
\(75\) | −6.52111 | + | 7.12576i | −0.752992 | + | 0.822812i | ||||
\(76\) | −7.26795 | −0.833691 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − | 4.24264i | − | 0.480384i | ||||||
\(79\) | −1.18448 | + | 0.860577i | −0.133265 | + | 0.0968225i | −0.652421 | − | 0.757857i | \(-0.726246\pi\) |
0.519156 | + | 0.854680i | \(0.326246\pi\) | |||||||
\(80\) | −1.99534 | + | 5.13591i | −0.223086 | + | 0.574213i | ||||
\(81\) | −3.29420 | + | 10.1385i | −0.366022 | + | 1.12650i | ||||
\(82\) | −0.526994 | + | 0.725345i | −0.0581967 | + | 0.0801009i | ||||
\(83\) | 5.81878 | − | 8.00886i | 0.638694 | − | 0.879087i | −0.359851 | − | 0.933010i | \(-0.617173\pi\) |
0.998545 | + | 0.0539231i | \(0.0171726\pi\) | |||||||
\(84\) | −3.45980 | + | 10.6482i | −0.377495 | + | 1.16181i | ||||
\(85\) | −8.05309 | − | 3.12869i | −0.873481 | − | 0.339354i | ||||
\(86\) | 2.70191 | − | 1.96305i | 0.291355 | − | 0.211681i | ||||
\(87\) | − | 13.3843i | − | 1.43494i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.464102 | −0.0491947 | −0.0245973 | − | 0.999697i | \(-0.507830\pi\) | ||||
−0.0245973 | + | 0.999697i | \(0.507830\pi\) | |||||||
\(90\) | −0.0477646 | + | 0.845982i | −0.00503483 | + | 0.0891744i | ||||
\(91\) | −4.38685 | − | 13.5013i | −0.459867 | − | 1.41533i | ||||
\(92\) | 5.74038 | + | 1.86516i | 0.598476 | + | 0.194457i | ||||
\(93\) | 9.91537 | − | 13.6473i | 1.02818 | − | 1.41516i | ||||
\(94\) | −4.79602 | − | 3.48451i | −0.494671 | − | 0.359400i | ||||
\(95\) | −7.88973 | + | 5.07844i | −0.809469 | + | 0.521037i | ||||
\(96\) | 3.06798 | + | 9.44228i | 0.313125 | + | 0.963699i | ||||
\(97\) | −5.37331 | − | 7.39573i | −0.545577 | − | 0.750922i | 0.443827 | − | 0.896113i | \(-0.353621\pi\) |
−0.989404 | + | 0.145190i | \(0.953621\pi\) | |||||||
\(98\) | − | 2.17209i | − | 0.219414i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.73205 | + | 8.48528i | 0.173205 | + | 0.848528i | ||||
\(101\) | 15.6887 | − | 11.3985i | 1.56108 | − | 1.13419i | 0.625971 | − | 0.779847i | \(-0.284703\pi\) |
0.935114 | − | 0.354348i | \(-0.115297\pi\) | |||||||
\(102\) | −3.67460 | + | 1.19395i | −0.363840 | + | 0.118219i | ||||
\(103\) | 4.03499 | + | 1.31105i | 0.397579 | + | 0.129181i | 0.500981 | − | 0.865458i | \(-0.332973\pi\) |
−0.103401 | + | 0.994640i | \(0.532973\pi\) | |||||||
\(104\) | −6.63083 | − | 4.81758i | −0.650206 | − | 0.472402i | ||||
\(105\) | 3.68457 | + | 13.9767i | 0.359577 | + | 1.36398i | ||||
\(106\) | −0.347445 | + | 1.06933i | −0.0337468 | + | 0.103862i | ||||
\(107\) | −2.82191 | + | 0.916893i | −0.272804 | + | 0.0886394i | −0.442224 | − | 0.896905i | \(-0.645810\pi\) |
0.169420 | + | 0.985544i | \(0.445810\pi\) | |||||||
\(108\) | 4.46053 | + | 6.13939i | 0.429215 | + | 0.590763i | ||||
\(109\) | 9.19615 | 0.880832 | 0.440416 | − | 0.897794i | \(-0.354831\pi\) | ||||
0.440416 | + | 0.897794i | \(0.354831\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.46410 | −0.328798 | ||||||||
\(112\) | 4.84632 | + | 6.67038i | 0.457934 | + | 0.630292i | ||||
\(113\) | −2.68999 | + | 0.874032i | −0.253053 | + | 0.0822220i | −0.432797 | − | 0.901492i | \(-0.642473\pi\) |
0.179743 | + | 0.983714i | \(0.442473\pi\) | |||||||
\(114\) | −1.29668 | + | 3.99078i | −0.121445 | + | 0.373771i | ||||
\(115\) | 7.53475 | − | 1.98633i | 0.702619 | − | 0.185226i | ||||
\(116\) | −9.70820 | − | 7.05342i | −0.901384 | − | 0.654894i | ||||
\(117\) | 2.95382 | + | 0.959754i | 0.273081 | + | 0.0887293i | ||||
\(118\) | −0.624215 | + | 0.202820i | −0.0574637 | + | 0.0186711i | ||||
\(119\) | −10.4591 | + | 7.59901i | −0.958787 | + | 0.696600i | ||||
\(120\) | 6.46410 | + | 5.27792i | 0.590089 | + | 0.481806i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 6.07296i | 0.549820i | ||||||||
\(123\) | −1.96677 | − | 2.70702i | −0.177337 | − | 0.244084i | ||||
\(124\) | −4.67368 | − | 14.3841i | −0.419709 | − | 1.29173i | ||||
\(125\) | 7.80928 | + | 8.00095i | 0.698483 | + | 0.715626i | ||||
\(126\) | 1.02579 | + | 0.745282i | 0.0913849 | + | 0.0663950i | ||||
\(127\) | −0.526994 | + | 0.725345i | −0.0467631 | + | 0.0643639i | −0.831758 | − | 0.555138i | \(-0.812665\pi\) |
0.784995 | + | 0.619502i | \(0.212665\pi\) | |||||||
\(128\) | 10.8919 | + | 3.53899i | 0.962716 | + | 0.312805i | ||||
\(129\) | 3.85162 | + | 11.8541i | 0.339116 | + | 1.04369i | ||||
\(130\) | −4.90294 | − | 0.276823i | −0.430016 | − | 0.0242789i | ||||
\(131\) | 3.12436 | 0.272976 | 0.136488 | − | 0.990642i | \(-0.456418\pi\) | ||||
0.136488 | + | 0.990642i | \(0.456418\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.0406i | 1.21747i | ||||||||
\(134\) | −0.925187 | + | 0.672187i | −0.0799239 | + | 0.0580681i | ||||
\(135\) | 9.13200 | + | 3.54785i | 0.785958 | + | 0.305350i | ||||
\(136\) | −2.30653 | + | 7.09878i | −0.197784 | + | 0.608716i | ||||
\(137\) | 5.21026 | − | 7.17130i | 0.445142 | − | 0.612686i | −0.526203 | − | 0.850359i | \(-0.676385\pi\) |
0.971345 | + | 0.237673i | \(0.0763847\pi\) | |||||||
\(138\) | 2.04829 | − | 2.81923i | 0.174362 | − | 0.239989i | ||||
\(139\) | −4.50808 | + | 13.8744i | −0.382370 | + | 1.17682i | 0.555999 | + | 0.831183i | \(0.312336\pi\) |
−0.938370 | + | 0.345633i | \(0.887664\pi\) | |||||||
\(140\) | 12.0796 | + | 4.69303i | 1.02092 | + | 0.396634i | ||||
\(141\) | 17.8990 | − | 13.0044i | 1.50737 | − | 1.09517i | ||||
\(142\) | − | 4.24264i | − | 0.356034i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.80385 | −0.150321 | ||||||||
\(145\) | −15.4673 | − | 0.873292i | −1.28449 | − | 0.0725230i | ||||
\(146\) | −0.783636 | − | 2.41178i | −0.0648542 | − | 0.199601i | ||||
\(147\) | 7.70959 | + | 2.50500i | 0.635876 | + | 0.206609i | ||||
\(148\) | −1.82556 | + | 2.51267i | −0.150060 | + | 0.206540i | ||||
\(149\) | 8.30695 | + | 6.03535i | 0.680531 | + | 0.494435i | 0.873534 | − | 0.486763i | \(-0.161823\pi\) |
−0.193002 | + | 0.981198i | \(0.561823\pi\) | |||||||
\(150\) | 4.96822 | + | 0.562811i | 0.405654 | + | 0.0459534i | ||||
\(151\) | −1.29668 | − | 3.99078i | −0.105523 | − | 0.324765i | 0.884330 | − | 0.466862i | \(-0.154616\pi\) |
−0.989853 | + | 0.142097i | \(0.954616\pi\) | |||||||
\(152\) | 4.76479 | + | 6.55817i | 0.386475 | + | 0.531938i | ||||
\(153\) | − | 2.82843i | − | 0.228665i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.1244 | − | 12.3490i | −1.21482 | − | 0.991894i | ||||
\(156\) | 11.4849 | − | 8.34429i | 0.919530 | − | 0.668078i | ||||
\(157\) | −20.7992 | + | 6.75806i | −1.65995 | + | 0.539352i | −0.980863 | − | 0.194701i | \(-0.937626\pi\) |
−0.679092 | + | 0.734053i | \(0.737626\pi\) | |||||||
\(158\) | 0.720782 | + | 0.234196i | 0.0573423 | + | 0.0186316i | ||||
\(159\) | −3.39476 | − | 2.46644i | −0.269222 | − | 0.195601i | ||||
\(160\) | 11.1120 | − | 2.92938i | 0.878480 | − | 0.231588i | ||||
\(161\) | 3.60322 | − | 11.0896i | 0.283973 | − | 0.873980i | ||||
\(162\) | 5.24808 | − | 1.70520i | 0.412328 | − | 0.133973i | ||||
\(163\) | 3.02076 | + | 4.15771i | 0.236604 | + | 0.325657i | 0.910763 | − | 0.412928i | \(-0.135494\pi\) |
−0.674160 | + | 0.738586i | \(0.735494\pi\) | |||||||
\(164\) | −3.00000 | −0.234261 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.12436 | −0.397727 | ||||||||
\(167\) | −0.304260 | − | 0.418778i | −0.0235443 | − | 0.0324060i | 0.797083 | − | 0.603870i | \(-0.206376\pi\) |
−0.820627 | + | 0.571464i | \(0.806376\pi\) | |||||||
\(168\) | 11.8765 | − | 3.85891i | 0.916291 | − | 0.297721i | ||||
\(169\) | −1.54508 | + | 4.75528i | −0.118853 | + | 0.365791i | ||||
\(170\) | 1.14001 | + | 4.32439i | 0.0874347 | + | 0.331666i | ||||
\(171\) | −2.48514 | − | 1.80556i | −0.190043 | − | 0.138074i | ||||
\(172\) | 10.6281 | + | 3.45327i | 0.810382 | + | 0.263309i | ||||
\(173\) | 20.7026 | − | 6.72668i | 1.57399 | − | 0.511420i | 0.613490 | − | 0.789702i | \(-0.289765\pi\) |
0.960499 | + | 0.278282i | \(0.0897649\pi\) | |||||||
\(174\) | −5.60503 | + | 4.07230i | −0.424917 | + | 0.308720i | ||||
\(175\) | 16.3923 | − | 3.34607i | 1.23914 | − | 0.252939i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 2.44949i | − | 0.184115i | ||||||
\(178\) | 0.141208 | + | 0.194356i | 0.0105840 | + | 0.0145676i | ||||
\(179\) | 4.77867 | + | 14.7072i | 0.357175 | + | 1.09927i | 0.954738 | + | 0.297449i | \(0.0961357\pi\) |
−0.597563 | + | 0.801822i | \(0.703864\pi\) | |||||||
\(180\) | −2.38404 | + | 1.53455i | −0.177696 | + | 0.114379i | ||||
\(181\) | 14.0707 | + | 10.2229i | 1.04586 | + | 0.759865i | 0.971422 | − | 0.237360i | \(-0.0762821\pi\) |
0.0744429 | + | 0.997225i | \(0.476282\pi\) | |||||||
\(182\) | −4.31932 | + | 5.94504i | −0.320169 | + | 0.440675i | ||||
\(183\) | −21.5553 | − | 7.00374i | −1.59341 | − | 0.517731i | ||||
\(184\) | −2.08032 | − | 6.40256i | −0.153363 | − | 0.472003i | ||||
\(185\) | −0.226025 | + | 4.00323i | −0.0166177 | + | 0.294323i | ||||
\(186\) | −8.73205 | −0.640265 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 19.8362i | − | 1.44670i | ||||||
\(189\) | 11.8604 | − | 8.61708i | 0.862717 | − | 0.626800i | ||||
\(190\) | 4.52727 | + | 1.75888i | 0.328443 | + | 0.127602i | ||||
\(191\) | −2.24592 | + | 6.91223i | −0.162509 | + | 0.500151i | −0.998844 | − | 0.0480672i | \(-0.984694\pi\) |
0.836335 | + | 0.548219i | \(0.184694\pi\) | |||||||
\(192\) | −2.57529 | + | 3.54458i | −0.185855 | + | 0.255808i | ||||
\(193\) | −8.92106 | + | 12.2788i | −0.642152 | + | 0.883846i | −0.998728 | − | 0.0504200i | \(-0.983944\pi\) |
0.356576 | + | 0.934266i | \(0.383944\pi\) | |||||||
\(194\) | −1.46228 | + | 4.50045i | −0.104986 | + | 0.323113i | ||||
\(195\) | 6.63695 | − | 17.0832i | 0.475282 | − | 1.22335i | ||||
\(196\) | 5.87989 | − | 4.27199i | 0.419992 | − | 0.305142i | ||||
\(197\) | 17.2480i | 1.22887i | 0.788969 | + | 0.614433i | \(0.210615\pi\) | ||||
−0.788969 | + | 0.614433i | \(0.789385\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.00000 | 0.141776 | 0.0708881 | − | 0.997484i | \(-0.477417\pi\) | ||||
0.0708881 | + | 0.997484i | \(0.477417\pi\) | |||||||
\(200\) | 6.52111 | − | 7.12576i | 0.461112 | − | 0.503867i | ||||
\(201\) | −1.31887 | − | 4.05906i | −0.0930258 | − | 0.286304i | ||||
\(202\) | −9.54689 | − | 3.10197i | −0.671717 | − | 0.218254i | ||||
\(203\) | −13.6262 | + | 18.7548i | −0.956369 | + | 1.31633i | ||||
\(204\) | −10.4591 | − | 7.59901i | −0.732286 | − | 0.532037i | ||||
\(205\) | −3.25665 | + | 2.09624i | −0.227455 | + | 0.146407i | ||||
\(206\) | −0.678648 | − | 2.08867i | −0.0472837 | − | 0.145524i | ||||
\(207\) | 1.49946 | + | 2.06382i | 0.104219 | + | 0.143446i | ||||
\(208\) | − | 10.4543i | − | 0.724875i | ||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 4.73205 | − | 5.79555i | 0.326543 | − | 0.399931i | ||||
\(211\) | −10.6178 | + | 7.71430i | −0.730961 | + | 0.531074i | −0.889867 | − | 0.456219i | \(-0.849203\pi\) |
0.158906 | + | 0.987294i | \(0.449203\pi\) | |||||||
\(212\) | −3.57803 | + | 1.16257i | −0.245740 | + | 0.0798459i | ||||
\(213\) | 15.0588 | + | 4.89290i | 1.03181 | + | 0.335256i | ||||
\(214\) | 1.24257 | + | 0.902778i | 0.0849402 | + | 0.0617127i | ||||
\(215\) | 13.9503 | − | 3.67761i | 0.951400 | − | 0.250811i | ||||
\(216\) | 2.61555 | − | 8.04984i | 0.177966 | − | 0.547722i | ||||
\(217\) | −27.7880 | + | 9.02886i | −1.88637 | + | 0.612919i | ||||
\(218\) | −2.79802 | − | 3.85115i | −0.189506 | − | 0.260833i | ||||
\(219\) | 9.46410 | 0.639525 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.3923 | 1.10267 | ||||||||
\(222\) | 1.05399 | + | 1.45069i | 0.0707390 | + | 0.0973639i | ||||
\(223\) | −1.47691 | + | 0.479877i | −0.0989012 | + | 0.0321349i | −0.358050 | − | 0.933703i | \(-0.616558\pi\) |
0.259148 | + | 0.965838i | \(0.416558\pi\) | |||||||
\(224\) | 5.31390 | − | 16.3545i | 0.355050 | − | 1.09273i | ||||
\(225\) | −1.51573 | + | 3.33167i | −0.101049 | + | 0.222111i | ||||
\(226\) | 1.18448 | + | 0.860577i | 0.0787906 | + | 0.0572448i | ||||
\(227\) | 19.1291 | + | 6.21543i | 1.26964 | + | 0.412533i | 0.864922 | − | 0.501907i | \(-0.167368\pi\) |
0.404723 | + | 0.914439i | \(0.367368\pi\) | |||||||
\(228\) | −13.3534 | + | 4.33878i | −0.884351 | + | 0.287343i | ||||
\(229\) | −3.29415 | + | 2.39334i | −0.217684 | + | 0.158156i | −0.691283 | − | 0.722584i | \(-0.742954\pi\) |
0.473600 | + | 0.880740i | \(0.342954\pi\) | |||||||
\(230\) | −3.12436 | − | 2.55103i | −0.206014 | − | 0.168210i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 13.3843i | 0.878720i | ||||||||
\(233\) | 0.994306 | + | 1.36855i | 0.0651392 | + | 0.0896564i | 0.840344 | − | 0.542054i | \(-0.182353\pi\) |
−0.775204 | + | 0.631710i | \(0.782353\pi\) | |||||||
\(234\) | −0.496805 | − | 1.52901i | −0.0324772 | − | 0.0999544i | ||||
\(235\) | −13.8604 | − | 21.5332i | −0.904154 | − | 1.40467i | ||||
\(236\) | −1.77672 | − | 1.29087i | −0.115655 | − | 0.0840282i | ||||
\(237\) | −1.66251 | + | 2.28825i | −0.107991 | + | 0.148638i | ||||
\(238\) | 6.36459 | + | 2.06798i | 0.412555 | + | 0.134047i | ||||
\(239\) | 1.74911 | + | 5.38322i | 0.113141 | + | 0.348212i | 0.991555 | − | 0.129689i | \(-0.0413979\pi\) |
−0.878414 | + | 0.477901i | \(0.841398\pi\) | |||||||
\(240\) | −0.600028 | + | 10.6274i | −0.0387316 | + | 0.685995i | ||||
\(241\) | −14.1244 | −0.909830 | −0.454915 | − | 0.890535i | \(-0.650330\pi\) | ||||
−0.454915 | + | 0.890535i | \(0.650330\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.45001i | 0.477918i | ||||||||
\(244\) | −16.4396 | + | 11.9441i | −1.05244 | + | 0.764642i | ||||
\(245\) | 3.39789 | − | 8.74602i | 0.217083 | − | 0.558762i | ||||
\(246\) | −0.535233 | + | 1.64728i | −0.0341252 | + | 0.105027i | ||||
\(247\) | 10.4642 | − | 14.4027i | 0.665821 | − | 0.916424i | ||||
\(248\) | −9.91537 | + | 13.6473i | −0.629626 | + | 0.866606i | ||||
\(249\) | 5.90975 | − | 18.1883i | 0.374515 | − | 1.15264i | ||||
\(250\) | 0.974569 | − | 5.70472i | 0.0616371 | − | 0.360798i | ||||
\(251\) | 3.07738 | − | 2.23585i | 0.194242 | − | 0.141125i | −0.486413 | − | 0.873729i | \(-0.661695\pi\) |
0.680656 | + | 0.732604i | \(0.261695\pi\) | |||||||
\(252\) | 4.24264i | 0.267261i | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0.464102 | 0.0291203 | ||||||||
\(255\) | −16.6637 | − | 0.940842i | −1.04352 | − | 0.0589178i | ||||
\(256\) | −0.430246 | − | 1.32416i | −0.0268904 | − | 0.0827600i | ||||
\(257\) | −14.0742 | − | 4.57298i | −0.877924 | − | 0.285255i | −0.164829 | − | 0.986322i | \(-0.552707\pi\) |
−0.713095 | + | 0.701068i | \(0.752707\pi\) | |||||||
\(258\) | 3.79233 | − | 5.21969i | 0.236100 | − | 0.324964i | ||||
\(259\) | 4.85410 | + | 3.52671i | 0.301619 | + | 0.219139i | ||||
\(260\) | −8.89357 | − | 13.8168i | −0.551556 | − | 0.856882i | ||||
\(261\) | −1.56727 | − | 4.82357i | −0.0970117 | − | 0.298571i | ||||
\(262\) | −0.950617 | − | 1.30841i | −0.0587293 | − | 0.0808339i | ||||
\(263\) | 6.79367i | 0.418915i | 0.977818 | + | 0.209458i | \(0.0671699\pi\) | ||||
−0.977818 | + | 0.209458i | \(0.932830\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.07180 | + | 3.76217i | −0.188699 | + | 0.231108i | ||||
\(266\) | 5.87989 | − | 4.27199i | 0.360519 | − | 0.261933i | ||||
\(267\) | −0.852694 | + | 0.277057i | −0.0521840 | + | 0.0169556i | ||||
\(268\) | −3.63925 | − | 1.18247i | −0.222303 | − | 0.0722306i | ||||
\(269\) | −13.1610 | − | 9.56206i | −0.802443 | − | 0.583009i | 0.109187 | − | 0.994021i | \(-0.465175\pi\) |
−0.911630 | + | 0.411012i | \(0.865175\pi\) | |||||||
\(270\) | −1.29274 | − | 4.90375i | −0.0786737 | − | 0.298433i | ||||
\(271\) | −3.54260 | + | 10.9030i | −0.215198 | + | 0.662311i | 0.783942 | + | 0.620834i | \(0.213206\pi\) |
−0.999139 | + | 0.0414762i | \(0.986794\pi\) | |||||||
\(272\) | −9.05459 | + | 2.94201i | −0.549015 | + | 0.178386i | ||||
\(273\) | −16.1199 | − | 22.1872i | −0.975622 | − | 1.34283i | ||||
\(274\) | −4.58846 | −0.277199 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 11.6603 | 0.701865 | ||||||||
\(277\) | 18.3313 | + | 25.2308i | 1.10142 | + | 1.51597i | 0.833489 | + | 0.552536i | \(0.186340\pi\) |
0.267930 | + | 0.963438i | \(0.413660\pi\) | |||||||
\(278\) | 7.18194 | − | 2.33355i | 0.430744 | − | 0.139957i | ||||
\(279\) | 1.97533 | − | 6.07944i | 0.118260 | − | 0.363967i | ||||
\(280\) | −3.68457 | − | 13.9767i | −0.220195 | − | 0.835265i | ||||
\(281\) | −14.0126 | − | 10.1807i | −0.835921 | − | 0.607332i | 0.0853074 | − | 0.996355i | \(-0.472813\pi\) |
−0.921228 | + | 0.389023i | \(0.872813\pi\) | |||||||
\(282\) | −10.8919 | − | 3.53899i | −0.648603 | − | 0.210744i | ||||
\(283\) | −7.67425 | + | 2.49351i | −0.456187 | + | 0.148224i | −0.528091 | − | 0.849187i | \(-0.677092\pi\) |
0.0719049 | + | 0.997411i | \(0.477092\pi\) | |||||||
\(284\) | 11.4849 | − | 8.34429i | 0.681505 | − | 0.495142i | ||||
\(285\) | −11.4641 | + | 14.0406i | −0.679075 | + | 0.831693i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.79555i | 0.342101i | ||||||||
\(288\) | 2.21135 | + | 3.04366i | 0.130305 | + | 0.179349i | ||||
\(289\) | 0.640220 | + | 1.97040i | 0.0376600 | + | 0.115906i | ||||
\(290\) | 4.34037 | + | 6.74307i | 0.254875 | + | 0.395967i | ||||
\(291\) | −14.2874 | − | 10.3804i | −0.837545 | − | 0.608512i | ||||
\(292\) | 4.98752 | − | 6.86474i | 0.291873 | − | 0.401728i | ||||
\(293\) | −14.3380 | − | 4.65870i | −0.837635 | − | 0.272164i | −0.141377 | − | 0.989956i | \(-0.545153\pi\) |
−0.696258 | + | 0.717792i | \(0.745153\pi\) | |||||||
\(294\) | −1.29668 | − | 3.99078i | −0.0756241 | − | 0.232747i | ||||
\(295\) | −2.83071 | − | 0.159824i | −0.164810 | − | 0.00930529i | ||||
\(296\) | 3.46410 | 0.201347 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 5.31508i | − | 0.307894i | ||||||
\(299\) | −11.9610 | + | 8.69018i | −0.691723 | + | 0.502566i | ||||
\(300\) | 8.24780 | + | 14.5560i | 0.476187 | + | 0.840392i | ||||
\(301\) | 6.67120 | − | 20.5318i | 0.384522 | − | 1.18344i | ||||
\(302\) | −1.27672 | + | 1.75726i | −0.0734671 | + | 0.101119i | ||||
\(303\) | 22.0202 | − | 30.3082i | 1.26503 | − | 1.74116i | ||||
\(304\) | −3.19516 | + | 9.83368i | −0.183255 | + | 0.564000i | ||||
\(305\) | −9.50019 | + | 24.4530i | −0.543979 | + | 1.40018i | ||||
\(306\) | −1.18448 | + | 0.860577i | −0.0677124 | + | 0.0491959i | ||||
\(307\) | − | 7.82894i | − | 0.446821i | −0.974724 | − | 0.223411i | \(-0.928281\pi\) | ||
0.974724 | − | 0.223411i | \(-0.0717191\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.19615 | 0.466263 | ||||||||
\(310\) | −0.569746 | + | 10.0911i | −0.0323594 | + | 0.573133i | ||||
\(311\) | 3.10641 | + | 9.56055i | 0.176148 | + | 0.542129i | 0.999684 | − | 0.0251354i | \(-0.00800169\pi\) |
−0.823536 | + | 0.567265i | \(0.808002\pi\) | |||||||
\(312\) | −15.0588 | − | 4.89290i | −0.852536 | − | 0.277006i | ||||
\(313\) | −10.0784 | + | 13.8718i | −0.569666 | + | 0.784078i | −0.992515 | − | 0.122122i | \(-0.961030\pi\) |
0.422849 | + | 0.906200i | \(0.361030\pi\) | |||||||
\(314\) | 9.15848 | + | 6.65403i | 0.516843 | + | 0.375509i | ||||
\(315\) | 2.96452 | + | 4.60560i | 0.167032 | + | 0.259496i | ||||
\(316\) | 0.783636 | + | 2.41178i | 0.0440830 | + | 0.135673i | ||||
\(317\) | −7.42160 | − | 10.2150i | −0.416839 | − | 0.573729i | 0.548031 | − | 0.836458i | \(-0.315378\pi\) |
−0.964870 | + | 0.262729i | \(0.915378\pi\) | |||||||
\(318\) | 2.17209i | 0.121805i | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 3.92820 | + | 3.20736i | 0.219593 | + | 0.179297i | ||||
\(321\) | −4.63733 | + | 3.36921i | −0.258830 | + | 0.188051i | ||||
\(322\) | −5.74038 | + | 1.86516i | −0.319899 | + | 0.103941i | ||||
\(323\) | −15.4192 | − | 5.01000i | −0.857946 | − | 0.278764i | ||||
\(324\) | 14.9378 | + | 10.8529i | 0.829876 | + | 0.602940i | ||||
\(325\) | −19.3089 | − | 8.78452i | −1.07106 | − | 0.487277i | ||||
\(326\) | 0.822064 | − | 2.53005i | 0.0455299 | − | 0.140127i | ||||
\(327\) | 16.8961 | − | 5.48987i | 0.934356 | − | 0.303591i | ||||
\(328\) | 1.96677 | + | 2.70702i | 0.108597 | + | 0.149470i | ||||
\(329\) | −38.3205 | −2.11268 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.1962 | −1.00015 | −0.500075 | − | 0.865982i | \(-0.666694\pi\) | ||||
−0.500075 | + | 0.865982i | \(0.666694\pi\) | |||||||
\(332\) | −10.0784 | − | 13.8718i | −0.553125 | − | 0.761311i | ||||
\(333\) | −1.24843 | + | 0.405640i | −0.0684136 | + | 0.0222289i | ||||
\(334\) | −0.0828009 | + | 0.254835i | −0.00453066 | + | 0.0139439i | ||||
\(335\) | −4.77684 | + | 1.25928i | −0.260987 | + | 0.0688021i | ||||
\(336\) | 12.8862 | + | 9.36236i | 0.702999 | + | 0.510759i | ||||
\(337\) | −16.7642 | − | 5.44701i | −0.913203 | − | 0.296718i | −0.185527 | − | 0.982639i | \(-0.559399\pi\) |
−0.727676 | + | 0.685921i | \(0.759399\pi\) | |||||||
\(338\) | 2.46152 | − | 0.799795i | 0.133889 | − | 0.0435031i | ||||
\(339\) | −4.42055 | + | 3.21172i | −0.240091 | + | 0.174437i | ||||
\(340\) | −9.46410 | + | 11.5911i | −0.513263 | + | 0.628616i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 1.59008i | 0.0859816i | ||||||||
\(343\) | 5.51452 | + | 7.59008i | 0.297756 | + | 0.409826i | ||||
\(344\) | −3.85162 | − | 11.8541i | −0.207665 | − | 0.639128i | ||||
\(345\) | 12.6578 | − | 8.14755i | 0.681473 | − | 0.438649i | ||||
\(346\) | −9.11596 | − | 6.62313i | −0.490077 | − | 0.356062i | ||||
\(347\) | −2.57529 | + | 3.54458i | −0.138249 | + | 0.190283i | −0.872527 | − | 0.488565i | \(-0.837521\pi\) |
0.734279 | + | 0.678848i | \(0.237521\pi\) | |||||||
\(348\) | −22.0476 | − | 7.16370i | −1.18188 | − | 0.384015i | ||||
\(349\) | −2.26216 | − | 6.96222i | −0.121091 | − | 0.372679i | 0.872078 | − | 0.489367i | \(-0.162772\pi\) |
−0.993169 | + | 0.116688i | \(0.962772\pi\) | |||||||
\(350\) | −6.38878 | − | 5.84666i | −0.341495 | − | 0.312517i | ||||
\(351\) | −18.5885 | −0.992178 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 13.0053i | − | 0.692204i | −0.938197 | − | 0.346102i | \(-0.887505\pi\) | ||
0.938197 | − | 0.346102i | \(-0.112495\pi\) | |||||||
\(354\) | −1.02579 | + | 0.745282i | −0.0545203 | + | 0.0396113i | ||||
\(355\) | 6.63695 | − | 17.0832i | 0.352253 | − | 0.906682i | ||||
\(356\) | −0.248403 | + | 0.764504i | −0.0131653 | + | 0.0405187i | ||||
\(357\) | −14.6802 | + | 20.2055i | −0.776956 | + | 1.06939i | ||||
\(358\) | 4.70511 | − | 6.47603i | 0.248673 | − | 0.342269i | ||||
\(359\) | 11.0196 | − | 33.9149i | 0.581594 | − | 1.78996i | −0.0309462 | − | 0.999521i | \(-0.509852\pi\) |
0.612540 | − | 0.790440i | \(-0.290148\pi\) | |||||||
\(360\) | 2.94764 | + | 1.14518i | 0.155354 | + | 0.0603562i | ||||
\(361\) | 1.12640 | − | 0.818376i | 0.0592841 | − | 0.0430724i | ||||
\(362\) | − | 9.00292i | − | 0.473183i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −24.5885 | −1.28879 | ||||||||
\(365\) | 0.617511 | − | 10.9370i | 0.0323220 | − | 0.572470i | ||||
\(366\) | 3.62540 | + | 11.1578i | 0.189503 | + | 0.583230i | ||||
\(367\) | 16.0787 | + | 5.22430i | 0.839304 | + | 0.272706i | 0.696959 | − | 0.717111i | \(-0.254536\pi\) |
0.142345 | + | 0.989817i | \(0.454536\pi\) | |||||||
\(368\) | 5.04720 | − | 6.94688i | 0.263104 | − | 0.362131i | ||||
\(369\) | −1.02579 | − | 0.745282i | −0.0534006 | − | 0.0387978i | ||||
\(370\) | 1.74524 | − | 1.12337i | 0.0907305 | − | 0.0584012i | ||||
\(371\) | 2.24592 | + | 6.91223i | 0.116602 | + | 0.358865i | ||||
\(372\) | −17.1739 | − | 23.6379i | −0.890426 | − | 1.22557i | ||||
\(373\) | − | 0.175865i | − | 0.00910597i | −0.999990 | − | 0.00455298i | \(-0.998551\pi\) | ||
0.999990 | − | 0.00455298i | \(-0.00144926\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 19.1244 | + | 10.0382i | 0.987577 | + | 0.518370i | ||||
\(376\) | −17.8990 | + | 13.0044i | −0.923069 | + | 0.670649i | ||||
\(377\) | 27.9552 | − | 9.08321i | 1.43977 | − | 0.467809i | ||||
\(378\) | −7.21729 | − | 2.34504i | −0.371217 | − | 0.120616i | ||||
\(379\) | 1.18448 | + | 0.860577i | 0.0608428 | + | 0.0442049i | 0.617791 | − | 0.786342i | \(-0.288028\pi\) |
−0.556948 | + | 0.830547i | \(0.688028\pi\) | |||||||
\(380\) | 4.14276 | + | 15.7147i | 0.212519 | + | 0.806149i | ||||
\(381\) | −0.535233 | + | 1.64728i | −0.0274208 | + | 0.0843926i | ||||
\(382\) | 3.57803 | − | 1.16257i | 0.183068 | − | 0.0594824i | ||||
\(383\) | 22.6069 | + | 31.1157i | 1.15516 | + | 1.58994i | 0.727684 | + | 0.685913i | \(0.240597\pi\) |
0.427475 | + | 0.904027i | \(0.359403\pi\) | |||||||
\(384\) | 22.1244 | 1.12903 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.85641 | 0.399881 | ||||||||
\(387\) | 2.77618 | + | 3.82108i | 0.141121 | + | 0.194236i | ||||
\(388\) | −15.0588 | + | 4.89290i | −0.764494 | + | 0.248399i | ||||
\(389\) | −1.89253 | + | 5.82461i | −0.0959551 | + | 0.295319i | −0.987501 | − | 0.157610i | \(-0.949621\pi\) |
0.891546 | + | 0.452929i | \(0.149621\pi\) | |||||||
\(390\) | −9.17342 | + | 2.41832i | −0.464514 | + | 0.122457i | ||||
\(391\) | 10.8927 | + | 7.91400i | 0.550867 | + | 0.400228i | ||||
\(392\) | −7.70959 | − | 2.50500i | −0.389393 | − | 0.126522i | ||||
\(393\) | 5.74038 | − | 1.86516i | 0.289564 | − | 0.0940850i | ||||
\(394\) | 7.22307 | − | 5.24787i | 0.363893 | − | 0.264384i | ||||
\(395\) | 2.53590 | + | 2.07055i | 0.127595 | + | 0.104181i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 32.9802i | − | 1.65523i | −0.561298 | − | 0.827614i | \(-0.689698\pi\) | ||
0.561298 | − | 0.827614i | \(-0.310302\pi\) | |||||||
\(398\) | −0.608520 | − | 0.837556i | −0.0305024 | − | 0.0419829i | ||||
\(399\) | 8.38189 | + | 25.7968i | 0.419619 | + | 1.29146i | ||||
\(400\) | 12.2422 | + | 1.38682i | 0.612110 | + | 0.0693412i | ||||
\(401\) | −1.87733 | − | 1.36396i | −0.0937494 | − | 0.0681129i | 0.539923 | − | 0.841714i | \(-0.318453\pi\) |
−0.633673 | + | 0.773601i | \(0.718453\pi\) | |||||||
\(402\) | −1.29857 | + | 1.78732i | −0.0647666 | + | 0.0891436i | ||||
\(403\) | 35.2337 | + | 11.4481i | 1.75512 | + | 0.570272i | ||||
\(404\) | −10.3794 | − | 31.9445i | −0.516395 | − | 1.58930i | ||||
\(405\) | 23.7991 | + | 1.34371i | 1.18259 | + | 0.0667696i | ||||
\(406\) | 12.0000 | 0.595550 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 14.4195i | 0.713873i | ||||||||
\(409\) | 21.1350 | − | 15.3555i | 1.04506 | − | 0.759281i | 0.0737938 | − | 0.997274i | \(-0.476489\pi\) |
0.971267 | + | 0.237992i | \(0.0764893\pi\) | |||||||
\(410\) | 1.86873 | + | 0.726014i | 0.0922899 | + | 0.0358553i | ||||
\(411\) | 5.29172 | − | 16.2862i | 0.261021 | − | 0.803340i | ||||
\(412\) | 4.31932 | − | 5.94504i | 0.212798 | − | 0.292891i | ||||
\(413\) | −2.49376 | + | 3.43237i | −0.122710 | + | 0.168896i | ||||
\(414\) | 0.408059 | − | 1.25588i | 0.0200550 | − | 0.0617230i | ||||
\(415\) | −20.6335 | − | 8.01625i | −1.01286 | − | 0.393502i | ||||
\(416\) | −17.6397 | + | 12.8160i | −0.864857 | + | 0.628355i | ||||
\(417\) | 28.1827i | 1.38011i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.3397 | 0.602836 | 0.301418 | − | 0.953492i | \(-0.402540\pi\) | ||||
0.301418 | + | 0.953492i | \(0.402540\pi\) | |||||||
\(420\) | 24.9955 | + | 1.41126i | 1.21966 | + | 0.0688626i | ||||
\(421\) | −5.26953 | − | 16.2179i | −0.256821 | − | 0.790414i | −0.993465 | − | 0.114134i | \(-0.963591\pi\) |
0.736644 | − | 0.676281i | \(-0.236409\pi\) | |||||||
\(422\) | 6.46116 | + | 2.09936i | 0.314524 | + | 0.102195i | ||||
\(423\) | 4.92784 | − | 6.78259i | 0.239600 | − | 0.329781i | ||||
\(424\) | 3.39476 | + | 2.46644i | 0.164864 | + | 0.119781i | ||||
\(425\) | −2.17454 | + | 19.1957i | −0.105481 | + | 0.931130i | ||||
\(426\) | −2.53275 | − | 7.79500i | −0.122712 | − | 0.377669i | ||||
\(427\) | 23.0742 | + | 31.7589i | 1.11664 | + | 1.53692i | ||||
\(428\) | 5.13922i | 0.248413i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.78461 | − | 4.72311i | −0.278959 | − | 0.227769i | ||||
\(431\) | −4.10317 | + | 2.98113i | −0.197643 | + | 0.143596i | −0.682205 | − | 0.731161i | \(-0.738979\pi\) |
0.484562 | + | 0.874757i | \(0.338979\pi\) | |||||||
\(432\) | 10.2677 | − | 3.33617i | 0.494004 | − | 0.160512i | ||||
\(433\) | −27.3310 | − | 8.88039i | −1.31345 | − | 0.426764i | −0.433206 | − | 0.901295i | \(-0.642618\pi\) |
−0.880239 | + | 0.474531i | \(0.842618\pi\) | |||||||
\(434\) | 12.2359 | + | 8.88987i | 0.587340 | + | 0.426728i | ||||
\(435\) | −28.9394 | + | 7.62909i | −1.38754 | + | 0.365787i | ||||
\(436\) | 4.92209 | − | 15.1486i | 0.235725 | − | 0.725487i | ||||
\(437\) | 13.9069 | − | 4.51863i | 0.665259 | − | 0.216156i | ||||
\(438\) | −2.87955 | − | 3.96336i | −0.137590 | − | 0.189377i | ||||
\(439\) | 28.2487 | 1.34824 | 0.674119 | − | 0.738623i | \(-0.264524\pi\) | ||||
0.674119 | + | 0.738623i | \(0.264524\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.07180 | 0.146276 | ||||||||
\(442\) | −4.98752 | − | 6.86474i | −0.237232 | − | 0.326522i | ||||
\(443\) | −26.2145 | + | 8.51761i | −1.24549 | + | 0.404684i | −0.856302 | − | 0.516475i | \(-0.827244\pi\) |
−0.389187 | + | 0.921159i | \(0.627244\pi\) | |||||||
\(444\) | −1.85410 | + | 5.70634i | −0.0879918 | + | 0.270811i | ||||
\(445\) | 0.264540 | + | 1.00348i | 0.0125404 | + | 0.0475695i | ||||
\(446\) | 0.650326 | + | 0.472490i | 0.0307938 | + | 0.0223730i | ||||
\(447\) | 18.8653 | + | 6.12971i | 0.892298 | + | 0.289925i | ||||
\(448\) | 7.21729 | − | 2.34504i | 0.340985 | − | 0.110793i | ||||
\(449\) | 27.9246 | − | 20.2884i | 1.31784 | − | 0.957468i | 0.317885 | − | 0.948129i | \(-0.397027\pi\) |
0.999956 | − | 0.00933886i | \(-0.00297270\pi\) | |||||||
\(450\) | 1.85641 | − | 0.378937i | 0.0875118 | − | 0.0178633i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 4.89898i | 0.230429i | ||||||||
\(453\) | −4.76479 | − | 6.55817i | −0.223869 | − | 0.308130i | ||||
\(454\) | −3.21734 | − | 9.90197i | −0.150997 | − | 0.464722i | ||||
\(455\) | −26.6920 | + | 17.1811i | −1.25134 | + | 0.805461i | ||||
\(456\) | 12.6694 | + | 9.20487i | 0.593300 | + | 0.431057i | ||||
\(457\) | −12.4688 | + | 17.1618i | −0.583266 | + | 0.802797i | −0.994049 | − | 0.108936i | \(-0.965256\pi\) |
0.410782 | + | 0.911733i | \(0.365256\pi\) | |||||||
\(458\) | 2.00456 | + | 0.651320i | 0.0936668 | + | 0.0304342i | ||||
\(459\) | 5.23110 | + | 16.0997i | 0.244167 | + | 0.751469i | ||||
\(460\) | 0.760805 | − | 13.4750i | 0.0354727 | − | 0.628274i | ||||
\(461\) | 33.0000 | 1.53696 | 0.768482 | − | 0.639872i | \(-0.221013\pi\) | ||||
0.768482 | + | 0.639872i | \(0.221013\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 20.3166i | − | 0.944194i | −0.881547 | − | 0.472097i | \(-0.843497\pi\) | ||
0.881547 | − | 0.472097i | \(-0.156503\pi\) | |||||||
\(464\) | −13.8114 | + | 10.0346i | −0.641177 | + | 0.465842i | ||||
\(465\) | −35.1600 | − | 13.6599i | −1.63051 | − | 0.633464i | ||||
\(466\) | 0.270589 | − | 0.832787i | 0.0125348 | − | 0.0385781i | ||||
\(467\) | 0.363941 | − | 0.500922i | 0.0168412 | − | 0.0231799i | −0.800513 | − | 0.599315i | \(-0.795440\pi\) |
0.817355 | + | 0.576135i | \(0.195440\pi\) | |||||||
\(468\) | 3.16196 | − | 4.35207i | 0.146162 | − | 0.201174i | ||||
\(469\) | −2.28435 | + | 7.03050i | −0.105481 | + | 0.324638i | ||||
\(470\) | −4.80044 | + | 12.3561i | −0.221428 | + | 0.569945i | ||||
\(471\) | −34.1799 | + | 24.8332i | −1.57493 | + | 1.14425i | ||||
\(472\) | 2.44949i | 0.112747i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 1.46410 | 0.0672484 | ||||||||
\(475\) | 15.4778 | + | 14.1644i | 0.710169 | + | 0.649908i | ||||
\(476\) | 6.91960 | + | 21.2963i | 0.317159 | + | 0.976116i | ||||
\(477\) | −1.51226 | − | 0.491361i | −0.0692414 | − | 0.0224979i | ||||
\(478\) | 1.72219 | − | 2.37039i | 0.0787711 | − | 0.108419i | ||||
\(479\) | −2.05158 | − | 1.49056i | −0.0937393 | − | 0.0681056i | 0.539928 | − | 0.841711i | \(-0.318451\pi\) |
−0.633668 | + | 0.773605i | \(0.718451\pi\) | |||||||
\(480\) | 18.6673 | − | 12.0157i | 0.852042 | − | 0.548440i | ||||
\(481\) | −2.35091 | − | 7.23535i | −0.107192 | − | 0.329903i | ||||
\(482\) | 4.29748 | + | 5.91497i | 0.195745 | + | 0.269419i | ||||
\(483\) | − | 22.5259i | − | 1.02496i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.9282 | + | 15.8338i | −0.587039 | + | 0.718974i | ||||
\(486\) | 3.11990 | − | 2.26674i | 0.141521 | − | 0.102821i | ||||
\(487\) | 12.1050 | − | 3.93314i | 0.548529 | − | 0.178228i | −0.0216245 | − | 0.999766i | \(-0.506884\pi\) |
0.570153 | + | 0.821538i | \(0.306884\pi\) | |||||||
\(488\) | 21.5553 | + | 7.00374i | 0.975762 | + | 0.317044i | ||||
\(489\) | 8.03209 | + | 5.83565i | 0.363223 | + | 0.263897i | ||||
\(490\) | −4.69648 | + | 1.23810i | −0.212165 | + | 0.0559317i | ||||
\(491\) | −12.2719 | + | 37.7691i | −0.553825 | + | 1.70450i | 0.145203 | + | 0.989402i | \(0.453617\pi\) |
−0.699027 | + | 0.715095i | \(0.746383\pi\) | |||||||
\(492\) | −5.51190 | + | 1.79092i | −0.248496 | + | 0.0807411i | ||||
\(493\) | −15.7341 | − | 21.6562i | −0.708630 | − | 0.975346i | ||||
\(494\) | −9.21539 | −0.414620 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −21.5167 | −0.966127 | ||||||||
\(497\) | −16.1199 | − | 22.1872i | −0.723078 | − | 0.995231i | ||||
\(498\) | −9.41498 | + | 3.05911i | −0.421895 | + | 0.137082i | ||||
\(499\) | −5.44108 | + | 16.7459i | −0.243576 | + | 0.749650i | 0.752291 | + | 0.658831i | \(0.228949\pi\) |
−0.995867 | + | 0.0908194i | \(0.971051\pi\) | |||||||
\(500\) | 17.3596 | − | 8.58168i | 0.776344 | − | 0.383785i | ||||
\(501\) | −0.809017 | − | 0.587785i | −0.0361442 | − | 0.0262603i | ||||
\(502\) | −1.87265 | − | 0.608460i | −0.0835803 | − | 0.0271569i | ||||
\(503\) | −7.02416 | + | 2.28229i | −0.313192 | + | 0.101762i | −0.461395 | − | 0.887195i | \(-0.652651\pi\) |
0.148204 | + | 0.988957i | \(0.452651\pi\) | |||||||
\(504\) | 3.82831 | − | 2.78143i | 0.170526 | − | 0.123895i | ||||
\(505\) | −33.5885 | − | 27.4249i | −1.49467 | − | 1.22039i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.65926i | 0.428983i | ||||||||
\(508\) | 0.912780 | + | 1.25633i | 0.0404981 | + | 0.0557408i | ||||
\(509\) | 2.49432 | + | 7.67673i | 0.110559 | + | 0.340265i | 0.990995 | − | 0.133900i | \(-0.0427500\pi\) |
−0.880436 | + | 0.474165i | \(0.842750\pi\) | |||||||
\(510\) | 4.67609 | + | 7.26465i | 0.207061 | + | 0.321684i | ||||
\(511\) | −13.2617 | − | 9.63516i | −0.586661 | − | 0.426234i | ||||
\(512\) | 13.0395 | − | 17.9473i | 0.576270 | − | 0.793167i | ||||
\(513\) | 17.4850 | + | 5.68121i | 0.771980 | + | 0.250831i | ||||
\(514\) | 2.36715 | + | 7.28533i | 0.104410 | + | 0.321342i | ||||
\(515\) | 0.534780 | − | 9.47175i | 0.0235652 | − | 0.417375i | ||||
\(516\) | 21.5885 | 0.950379 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | − | 3.10583i | − | 0.136462i | ||||||
\(519\) | 34.0212 | − | 24.7179i | 1.49337 | − | 1.08499i | ||||
\(520\) | −6.63695 | + | 17.0832i | −0.291049 | + | 0.749148i | ||||
\(521\) | −2.85801 | + | 8.79605i | −0.125212 | + | 0.385362i | −0.993940 | − | 0.109928i | \(-0.964938\pi\) |
0.868728 | + | 0.495290i | \(0.164938\pi\) | |||||||
\(522\) | −1.54315 | + | 2.12396i | −0.0675416 | + | 0.0929631i | ||||
\(523\) | −15.0659 | + | 20.7365i | −0.658788 | + | 0.906743i | −0.999441 | − | 0.0334458i | \(-0.989352\pi\) |
0.340653 | + | 0.940189i | \(0.389352\pi\) | |||||||
\(524\) | 1.67226 | − | 5.14668i | 0.0730530 | − | 0.224834i | ||||
\(525\) | 28.1201 | − | 15.9335i | 1.22726 | − | 0.695396i | ||||
\(526\) | 2.84504 | − | 2.06704i | 0.124050 | − | 0.0901273i | ||||
\(527\) | − | 33.7381i | − | 1.46965i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.8564 | 0.472018 | ||||||||
\(530\) | 2.51014 | + | 0.141724i | 0.109033 | + | 0.00615609i | ||||
\(531\) | −0.286831 | − | 0.882774i | −0.0124474 | − | 0.0383091i | ||||
\(532\) | 23.1288 | + | 7.51499i | 1.00276 | + | 0.325816i | ||||
\(533\) | 4.31932 | − | 5.94504i | 0.187091 | − | 0.257508i | ||||
\(534\) | 0.375466 | + | 0.272792i | 0.0162480 | + | 0.0118049i | ||||
\(535\) | 3.59100 | + | 5.57888i | 0.155253 | + | 0.241196i | ||||
\(536\) | 1.31887 | + | 4.05906i | 0.0569665 | + | 0.175325i | ||||
\(537\) | 17.5597 | + | 24.1689i | 0.757757 | + | 1.04296i | ||||
\(538\) | 8.42091i | 0.363051i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 10.7321 | − | 13.1440i | 0.461834 | − | 0.565629i | ||||
\(541\) | −2.10967 | + | 1.53276i | −0.0907018 | + | 0.0658987i | −0.632212 | − | 0.774796i | \(-0.717853\pi\) |
0.541510 | + | 0.840694i | \(0.317853\pi\) | |||||||
\(542\) | 5.64381 | − | 1.83379i | 0.242423 | − | 0.0787678i | ||||
\(543\) | 31.9549 | + | 10.3828i | 1.37132 | + | 0.445567i | ||||
\(544\) | 16.0642 | + | 11.6713i | 0.688746 | + | 0.500403i | ||||
\(545\) | −5.24185 | − | 19.8839i | −0.224536 | − | 0.851732i | ||||
\(546\) | −4.38685 | + | 13.5013i | −0.187740 | + | 0.577804i | ||||
\(547\) | 27.3310 | − | 8.88039i | 1.16859 | − | 0.379698i | 0.340474 | − | 0.940254i | \(-0.389413\pi\) |
0.828116 | + | 0.560556i | \(0.189413\pi\) | |||||||
\(548\) | −9.02443 | − | 12.4211i | −0.385505 | − | 0.530601i | ||||
\(549\) | −8.58846 | −0.366546 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −29.0718 | −1.23850 | ||||||||
\(552\) | −7.64434 | − | 10.5215i | −0.325365 | − | 0.447826i | ||||
\(553\) | 4.65921 | − | 1.51387i | 0.198130 | − | 0.0643762i | ||||
\(554\) | 4.98864 | − | 15.3535i | 0.211947 | − | 0.652306i | ||||
\(555\) | 1.97455 | + | 7.49007i | 0.0838152 | + | 0.317936i | ||||
\(556\) | 20.4422 | + | 14.8521i | 0.866942 | + | 0.629871i | ||||
\(557\) | −35.7614 | − | 11.6196i | −1.51526 | − | 0.492337i | −0.570834 | − | 0.821065i | \(-0.693380\pi\) |
−0.944425 | + | 0.328728i | \(0.893380\pi\) | |||||||
\(558\) | −3.14695 | + | 1.02251i | −0.133221 | + | 0.0432862i | ||||
\(559\) | −22.1453 | + | 16.0895i | −0.936645 | + | 0.680513i | ||||
\(560\) | 11.6603 | − | 14.2808i | 0.492736 | − | 0.603475i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.96575i | 0.378198i | ||||||||
\(563\) | 9.38837 | + | 12.9220i | 0.395673 | + | 0.544597i | 0.959651 | − | 0.281193i | \(-0.0907300\pi\) |
−0.563979 | + | 0.825789i | \(0.690730\pi\) | |||||||
\(564\) | −11.8417 | − | 36.4450i | −0.498625 | − | 1.53461i | ||||
\(565\) | 3.42314 | + | 5.31809i | 0.144013 | + | 0.223734i | ||||
\(566\) | 3.37919 | + | 2.45513i | 0.142038 | + | 0.103197i | ||||
\(567\) | 20.9662 | − | 28.8576i | 0.880499 | − | 1.21190i | ||||
\(568\) | −15.0588 | − | 4.89290i | −0.631853 | − | 0.205301i | ||||
\(569\) | 9.30894 | + | 28.6500i | 0.390251 | + | 1.20107i | 0.932599 | + | 0.360915i | \(0.117536\pi\) |
−0.542348 | + | 0.840154i | \(0.682464\pi\) | |||||||
\(570\) | 9.36796 | + | 0.528920i | 0.392381 | + | 0.0221540i | ||||
\(571\) | 19.7128 | 0.824956 | 0.412478 | − | 0.910968i | \(-0.364663\pi\) | ||||
0.412478 | + | 0.910968i | \(0.364663\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.0406i | 0.586554i | ||||||||
\(574\) | 2.42705 | − | 1.76336i | 0.101303 | − | 0.0736010i | ||||
\(575\) | −8.58968 | − | 15.1594i | −0.358215 | − | 0.632190i | ||||
\(576\) | −0.513047 | + | 1.57900i | −0.0213769 | + | 0.0657915i | ||||
\(577\) | 2.21135 | − | 3.04366i | 0.0920596 | − | 0.126709i | −0.760503 | − | 0.649335i | \(-0.775047\pi\) |
0.852562 | + | 0.522626i | \(0.175047\pi\) | |||||||
\(578\) | 0.630365 | − | 0.867623i | 0.0262197 | − | 0.0360884i | ||||
\(579\) | −9.06054 | + | 27.8855i | −0.376543 | + | 1.15888i | ||||
\(580\) | −9.71717 | + | 25.0115i | −0.403483 | + | 1.03855i | ||||
\(581\) | −26.7982 | + | 19.4700i | −1.11178 | + | 0.807752i | ||||
\(582\) | 9.14162i | 0.378932i | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −9.46410 | −0.391627 | ||||||||
\(585\) | 0.391486 | − | 6.93380i | 0.0161860 | − | 0.286677i | ||||
\(586\) | 2.41152 | + | 7.42190i | 0.0996190 | + | 0.306596i | ||||
\(587\) | 19.3930 | + | 6.30115i | 0.800433 | + | 0.260076i | 0.680540 | − | 0.732711i | \(-0.261745\pi\) |
0.119892 | + | 0.992787i | \(0.461745\pi\) | |||||||
\(588\) | 8.25286 | − | 11.3591i | 0.340342 | − | 0.468441i | ||||
\(589\) | −29.6432 | − | 21.5370i | −1.22143 | − | 0.887419i | ||||
\(590\) | 0.794342 | + | 1.23407i | 0.0327025 | + | 0.0508058i | ||||
\(591\) | 10.2966 | + | 31.6897i | 0.423546 | + | 1.30354i | ||||
\(592\) | 2.59713 | + | 3.57465i | 0.106741 | + | 0.146917i | ||||
\(593\) | − | 0.859411i | − | 0.0352918i | −0.999844 | − | 0.0176459i | \(-0.994383\pi\) | ||
0.999844 | − | 0.0176459i | \(-0.00561715\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 22.3923 | + | 18.2832i | 0.917995 | + | 0.749540i | ||||
\(596\) | 14.3881 | − | 10.4535i | 0.589358 | − | 0.428193i | ||||
\(597\) | 3.67460 | − | 1.19395i | 0.150391 | − | 0.0488651i | ||||
\(598\) | 7.27851 | + | 2.36493i | 0.297640 | + | 0.0967092i | ||||
\(599\) | −31.1025 | − | 22.5973i | −1.27082 | − | 0.923302i | −0.271581 | − | 0.962416i | \(-0.587546\pi\) |
−0.999235 | + | 0.0391140i | \(0.987546\pi\) | |||||||
\(600\) | 7.72733 | − | 16.9851i | 0.315467 | − | 0.693414i | ||||
\(601\) | −6.18034 | + | 19.0211i | −0.252101 | + | 0.775888i | 0.742286 | + | 0.670084i | \(0.233742\pi\) |
−0.994387 | + | 0.105804i | \(0.966258\pi\) | |||||||
\(602\) | −10.6281 | + | 3.45327i | −0.433168 | + | 0.140745i | ||||
\(603\) | −0.950617 | − | 1.30841i | −0.0387121 | − | 0.0532826i | ||||
\(604\) | −7.26795 | −0.295729 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −19.3923 | −0.787759 | ||||||||
\(607\) | −21.3899 | − | 29.4406i | −0.868188 | − | 1.19496i | −0.979555 | − | 0.201179i | \(-0.935523\pi\) |
0.111367 | − | 0.993779i | \(-0.464477\pi\) | |||||||
\(608\) | 20.5095 | − | 6.66393i | 0.831769 | − | 0.270258i | ||||
\(609\) | −13.8392 | + | 42.5927i | −0.560793 | + | 1.72594i | ||||
\(610\) | 13.1309 | − | 3.46161i | 0.531656 | − | 0.140157i | ||||
\(611\) | 39.3089 | + | 28.5596i | 1.59027 | + | 1.15540i | ||||
\(612\) | −4.65921 | − | 1.51387i | −0.188337 | − | 0.0611945i | ||||
\(613\) | 1.70539 | − | 0.554114i | 0.0688800 | − | 0.0223805i | −0.274374 | − | 0.961623i | \(-0.588471\pi\) |
0.343254 | + | 0.939243i | \(0.388471\pi\) | |||||||
\(614\) | −3.27859 | + | 2.38203i | −0.132313 | + | 0.0961311i | ||||
\(615\) | −4.73205 | + | 5.79555i | −0.190815 | + | 0.233699i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 13.0053i | − | 0.523575i | −0.965126 | − | 0.261787i | \(-0.915688\pi\) | ||
0.965126 | − | 0.261787i | \(-0.0843119\pi\) | |||||||
\(618\) | −2.49376 | − | 3.43237i | −0.100314 | − | 0.138070i | ||||
\(619\) | −3.95066 | − | 12.1589i | −0.158790 | − | 0.488707i | 0.839735 | − | 0.542997i | \(-0.182710\pi\) |
−0.998525 | + | 0.0542900i | \(0.982710\pi\) | |||||||
\(620\) | −28.4373 | + | 18.3044i | −1.14207 | + | 0.735124i | ||||
\(621\) | −12.3520 | − | 8.97428i | −0.495670 | − | 0.360125i | ||||
\(622\) | 3.05859 | − | 4.20979i | 0.122638 | − | 0.168797i | ||||
\(623\) | 1.47691 | + | 0.479877i | 0.0591711 | + | 0.0192259i | ||||
\(624\) | −6.24095 | − | 19.2077i | −0.249838 | − | 0.768923i | ||||
\(625\) | 12.8483 | − | 21.4458i | 0.513932 | − | 0.857831i | ||||
\(626\) | 8.87564 | 0.354742 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 37.8792i | 1.51154i | ||||||||
\(629\) | −5.60503 | + | 4.07230i | −0.223487 | + | 0.162373i | ||||
\(630\) | 1.02674 | − | 2.64278i | 0.0409063 | − | 0.105291i | ||||
\(631\) | −4.73430 | + | 14.5707i | −0.188469 | + | 0.580049i | −0.999991 | − | 0.00427343i | \(-0.998640\pi\) |
0.811521 | + | 0.584323i | \(0.198640\pi\) | |||||||
\(632\) | 1.66251 | − | 2.28825i | 0.0661310 | − | 0.0910215i | ||||
\(633\) | −14.9029 | + | 20.5121i | −0.592337 | + | 0.815281i | ||||
\(634\) | −2.01970 | + | 6.21601i | −0.0802127 | + | 0.246869i | ||||
\(635\) | 1.86873 | + | 0.726014i | 0.0741582 | + | 0.0288110i | ||||
\(636\) | −5.87989 | + | 4.27199i | −0.233153 | + | 0.169396i | ||||
\(637\) | 17.8028i | 0.705371i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.00000 | 0.237356 | ||||||||
\(640\) | 1.44356 | − | 25.5676i | 0.0570619 | − | 1.01065i | ||||
\(641\) | −2.42776 | − | 7.47189i | −0.0958909 | − | 0.295122i | 0.891594 | − | 0.452836i | \(-0.149588\pi\) |
−0.987485 | + | 0.157714i | \(0.949588\pi\) | |||||||
\(642\) | 2.82191 | + | 0.916893i | 0.111372 | + | 0.0361869i | ||||
\(643\) | −6.18272 | + | 8.50978i | −0.243823 | + | 0.335593i | −0.913336 | − | 0.407207i | \(-0.866503\pi\) |
0.669513 | + | 0.742800i | \(0.266503\pi\) | |||||||
\(644\) | −16.3390 | − | 11.8710i | −0.643848 | − | 0.467783i | ||||
\(645\) | 23.4354 | − | 15.0848i | 0.922767 | − | 0.593965i | ||||
\(646\) | 2.59336 | + | 7.98156i | 0.102035 | + | 0.314030i | ||||
\(647\) | −21.9606 | − | 30.2261i | −0.863358 | − | 1.18831i | −0.980758 | − | 0.195226i | \(-0.937456\pi\) |
0.117400 | − | 0.993085i | \(-0.462544\pi\) | |||||||
\(648\) | − | 20.5940i | − | 0.809010i | ||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2.19615 | + | 10.7589i | 0.0861402 | + | 0.421999i | ||||
\(651\) | −45.6649 | + | 33.1775i | −1.78975 | + | 1.30033i | ||||
\(652\) | 8.46572 | − | 2.75068i | 0.331543 | − | 0.107725i | ||||
\(653\) | 11.5514 | + | 3.75329i | 0.452043 | + | 0.146878i | 0.526185 | − | 0.850370i | \(-0.323622\pi\) |
−0.0741421 | + | 0.997248i | \(0.523622\pi\) | |||||||
\(654\) | −7.43984 | − | 5.40536i | −0.290921 | − | 0.211366i | ||||
\(655\) | −1.78090 | − | 6.75547i | −0.0695854 | − | 0.263958i | ||||
\(656\) | −1.31887 | + | 4.05906i | −0.0514932 | + | 0.158480i | ||||
\(657\) | 3.41078 | − | 1.10823i | 0.133067 | − | 0.0432361i | ||||
\(658\) | 11.6594 | + | 16.0478i | 0.454531 | + | 0.625608i | ||||
\(659\) | −23.3205 | −0.908438 | −0.454219 | − | 0.890890i | \(-0.650082\pi\) | ||||
−0.454219 | + | 0.890890i | \(0.650082\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.5885 | 1.15086 | 0.575429 | − | 0.817852i | \(-0.304835\pi\) | ||||
0.575429 | + | 0.817852i | \(0.304835\pi\) | |||||||
\(662\) | 5.53636 | + | 7.62015i | 0.215177 | + | 0.296165i | ||||
\(663\) | 30.1176 | − | 9.78580i | 1.16967 | − | 0.380049i | ||||
\(664\) | −5.90975 | + | 18.1883i | −0.229343 | + | 0.705845i | ||||
\(665\) | 30.3585 | − | 8.00321i | 1.17725 | − | 0.310351i | ||||
\(666\) | 0.549721 | + | 0.399395i | 0.0213012 | + | 0.0154763i | ||||
\(667\) | 22.9615 | + | 7.46065i | 0.889073 | + | 0.288877i | ||||
\(668\) | −0.852694 | + | 0.277057i | −0.0329917 | + | 0.0107197i | ||||
\(669\) | −2.42705 | + | 1.76336i | −0.0938352 | + | 0.0681753i | ||||
\(670\) | 1.98076 | + | 1.61729i | 0.0765235 | + | 0.0624812i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | − | 33.2204i | − | 1.28151i | ||||||
\(673\) | −23.9870 | − | 33.0153i | −0.924631 | − | 1.27265i | −0.961917 | − | 0.273341i | \(-0.911871\pi\) |
0.0372864 | − | 0.999305i | \(-0.488129\pi\) | |||||||
\(674\) | 2.81958 | + | 8.67778i | 0.108606 | + | 0.334256i | ||||
\(675\) | 2.46587 | − | 21.7675i | 0.0949113 | − | 0.837831i | ||||
\(676\) | 7.00629 | + | 5.09037i | 0.269473 | + | 0.195783i | ||||
\(677\) | 11.9637 | − | 16.4666i | 0.459801 | − | 0.632861i | −0.514667 | − | 0.857390i | \(-0.672084\pi\) |
0.974467 | + | 0.224529i | \(0.0720843\pi\) | |||||||
\(678\) | 2.68999 | + | 0.874032i | 0.103309 | + | 0.0335670i | ||||
\(679\) | 9.45235 | + | 29.0914i | 0.362748 | + | 1.11642i | ||||
\(680\) | 16.6637 | + | 0.940842i | 0.639024 | + | 0.0360796i | ||||
\(681\) | 38.8564 | 1.48898 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.8372i | 1.14169i | 0.821058 | + | 0.570844i | \(0.193384\pi\) | ||||
−0.821058 | + | 0.570844i | \(0.806616\pi\) | |||||||
\(684\) | −4.30438 | + | 3.12732i | −0.164582 | + | 0.119576i | ||||
\(685\) | −18.4756 | − | 7.17792i | −0.705918 | − | 0.274254i | ||||
\(686\) | 1.50071 | − | 4.61872i | 0.0572975 | − | 0.176343i | ||||
\(687\) | −4.62358 | + | 6.36381i | −0.176401 | + | 0.242795i | ||||
\(688\) | 9.34468 | − | 12.8619i | 0.356263 | − | 0.490353i | ||||
\(689\) | 2.84771 | − | 8.76436i | 0.108489 | − | 0.333895i | ||||
\(690\) | −7.26328 | − | 2.82184i | −0.276508 | − | 0.107426i | ||||
\(691\) | −30.6690 | + | 22.2823i | −1.16670 | + | 0.847660i | −0.990611 | − | 0.136714i | \(-0.956346\pi\) |
−0.176093 | + | 0.984374i | \(0.556346\pi\) | |||||||
\(692\) | − | 37.7033i | − | 1.43326i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.26795 | 0.0860902 | ||||||||
\(695\) | 32.5689 | + | 1.83886i | 1.23541 | + | 0.0697519i | ||||
\(696\) | 7.99007 | + | 24.5909i | 0.302863 | + | 0.932116i | ||||
\(697\) | −6.36459 | − | 2.06798i | −0.241076 | − | 0.0783304i | ||||
\(698\) | −2.22734 | + | 3.06567i | −0.0843060 | + | 0.116037i | ||||
\(699\) | 2.64383 | + | 1.92085i | 0.0999987 | + | 0.0726533i | ||||
\(700\) | 3.26180 | − | 28.7936i | 0.123285 | − | 1.08830i | ||||
\(701\) | −11.6983 | − | 36.0036i | −0.441838 | − | 1.35984i | −0.885915 | − | 0.463848i | \(-0.846468\pi\) |
0.444077 | − | 0.895989i | \(-0.353532\pi\) | |||||||
\(702\) | 5.65572 | + | 7.78444i | 0.213462 | + | 0.293805i | ||||
\(703\) | 7.52433i | 0.283786i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −38.3205 | − | 31.2886i | −1.44323 | − | 1.17840i | ||||
\(706\) | −5.44634 | + | 3.95700i | −0.204976 | + | 0.148924i | ||||
\(707\) | −61.7121 | + | 20.0515i | −2.32092 | + | 0.754113i | ||||
\(708\) | −4.03499 | − | 1.31105i | −0.151644 | − | 0.0492722i | ||||
\(709\) | 2.10967 | + | 1.53276i | 0.0792303 | + | 0.0575642i | 0.626695 | − | 0.779264i | \(-0.284407\pi\) |
−0.547465 | + | 0.836829i | \(0.684407\pi\) | |||||||
\(710\) | −9.17342 | + | 2.41832i | −0.344272 | + | 0.0907581i | ||||
\(711\) | −0.331203 | + | 1.01934i | −0.0124211 | + | 0.0382282i | ||||
\(712\) | 0.852694 | − | 0.277057i | 0.0319561 | − | 0.0103832i | ||||
\(713\) | 17.8858 | + | 24.6177i | 0.669829 | + | 0.921940i | ||||
\(714\) | 12.9282 | 0.483826 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 26.7846 | 1.00099 | ||||||||
\(717\) | 6.42730 | + | 8.84642i | 0.240032 | + | 0.330375i | ||||
\(718\) | −17.5557 | + | 5.70418i | −0.655171 | + | 0.212878i | ||||
\(719\) | 15.5115 | − | 47.7394i | 0.578480 | − | 1.78038i | −0.0455311 | − | 0.998963i | \(-0.514498\pi\) |
0.624011 | − | 0.781415i | \(-0.285502\pi\) | |||||||
\(720\) | 1.02820 | + | 3.90027i | 0.0383188 | + | 0.145355i | ||||
\(721\) | −11.4849 | − | 8.34429i | −0.427721 | − | 0.310758i | ||||
\(722\) | −0.685436 | − | 0.222712i | −0.0255093 | − | 0.00828847i | ||||
\(723\) | −25.9507 | + | 8.43189i | −0.965116 | + | 0.313585i | ||||
\(724\) | 24.3711 | − | 17.7067i | 0.905745 | − | 0.658063i | ||||
\(725\) | 6.92820 | + | 33.9411i | 0.257307 | + | 1.26054i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.24504i | 0.305792i | 0.988242 | + | 0.152896i | \(0.0488599\pi\) | ||||
−0.988242 | + | 0.152896i | \(0.951140\pi\) | |||||||
\(728\) | 16.1199 | + | 22.1872i | 0.597444 | + | 0.822312i | ||||
\(729\) | −5.43513 | − | 16.7276i | −0.201301 | − | 0.619541i | ||||
\(730\) | −4.76807 | + | 3.06910i | −0.176474 | + | 0.113593i | ||||
\(731\) | 20.1673 | + | 14.6524i | 0.745916 | + | 0.541940i | ||||
\(732\) | −23.0742 | + | 31.7589i | −0.852848 | + | 1.17384i | ||||
\(733\) | 8.86146 | + | 2.87926i | 0.327305 | + | 0.106348i | 0.468060 | − | 0.883697i | \(-0.344953\pi\) |
−0.140755 | + | 0.990044i | \(0.544953\pi\) | |||||||
\(734\) | −2.70430 | − | 8.32297i | −0.0998174 | − | 0.307206i | ||||
\(735\) | 1.02180 | − | 18.0975i | 0.0376895 | − | 0.667537i | ||||
\(736\) | −17.9090 | −0.660133 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0.656339i | 0.0241602i | ||||||||
\(739\) | 31.4936 | − | 22.8814i | 1.15851 | − | 0.841707i | 0.168921 | − | 0.985630i | \(-0.445972\pi\) |
0.989589 | + | 0.143923i | \(0.0459717\pi\) | |||||||
\(740\) | 6.47346 | + | 2.51499i | 0.237969 | + | 0.0924528i | ||||
\(741\) | 10.6278 | − | 32.7090i | 0.390422 | − | 1.20160i | ||||
\(742\) | 2.21135 | − | 3.04366i | 0.0811811 | − | 0.111736i | ||||
\(743\) | −25.5083 | + | 35.1092i | −0.935809 | + | 1.28803i | 0.0217414 | + | 0.999764i | \(0.493079\pi\) |
−0.957550 | + | 0.288267i | \(0.906921\pi\) | |||||||
\(744\) | −10.0704 | + | 30.9935i | −0.369198 | + | 1.13628i | ||||
\(745\) | 8.31461 | − | 21.4014i | 0.304624 | − | 0.784088i | ||||
\(746\) | −0.0736486 | + | 0.0535088i | −0.00269647 | + | 0.00195910i | ||||
\(747\) | − | 7.24693i | − | 0.265151i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.92820 | 0.362769 | ||||||||
\(750\) | −1.61500 | − | 11.0631i | −0.0589715 | − | 0.403967i | ||||
\(751\) | 15.0309 | + | 46.2604i | 0.548485 | + | 1.68806i | 0.712556 | + | 0.701616i | \(0.247538\pi\) |
−0.164070 | + | 0.986449i | \(0.552462\pi\) | |||||||
\(752\) | −26.8387 | − | 8.72043i | −0.978707 | − | 0.318001i | ||||
\(753\) | 4.31932 | − | 5.94504i | 0.157405 | − | 0.216649i | ||||
\(754\) | −12.3095 | − | 8.94338i | −0.448286 | − | 0.325699i | ||||
\(755\) | −7.88973 | + | 5.07844i | −0.287137 | + | 0.184824i | ||||
\(756\) | −7.84665 | − | 24.1495i | −0.285380 | − | 0.878309i | ||||
\(757\) | −29.2569 | − | 40.2687i | −1.06336 | − | 1.46359i | −0.876621 | − | 0.481182i | \(-0.840207\pi\) |
−0.186741 | − | 0.982409i | \(-0.559793\pi\) | |||||||
\(758\) | − | 0.757875i | − | 0.0275273i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 11.4641 | − | 14.0406i | 0.415847 | − | 0.509306i | ||||
\(761\) | −16.0642 | + | 11.6713i | −0.582326 | + | 0.423084i | −0.839562 | − | 0.543264i | \(-0.817188\pi\) |
0.257236 | + | 0.966349i | \(0.417188\pi\) | |||||||
\(762\) | 0.852694 | − | 0.277057i | 0.0308898 | − | 0.0100367i | ||||
\(763\) | −29.2649 | − | 9.50874i | −1.05946 | − | 0.344239i | ||||
\(764\) | 10.1843 | + | 7.39931i | 0.368454 | + | 0.267698i | ||||
\(765\) | −6.11562 | + | 1.61222i | −0.221111 | + | 0.0582898i | ||||
\(766\) | 6.15221 | − | 18.9346i | 0.222288 | − | 0.684133i | ||||
\(767\) | 5.11616 | − | 1.66234i | 0.184734 | − | 0.0600237i | ||||
\(768\) | −1.58098 | − | 2.17603i | −0.0570488 | − | 0.0785209i | ||||
\(769\) | −9.85641 | −0.355431 | −0.177716 | − | 0.984082i | \(-0.556871\pi\) | ||||
−0.177716 | + | 0.984082i | \(0.556871\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −28.5885 | −1.02959 | ||||||||
\(772\) | 15.4517 | + | 21.2675i | 0.556120 | + | 0.765433i | ||||
\(773\) | 11.4549 | − | 3.72192i | 0.412004 | − | 0.133868i | −0.0956791 | − | 0.995412i | \(-0.530502\pi\) |
0.507683 | + | 0.861544i | \(0.330502\pi\) | |||||||
\(774\) | 0.755504 | − | 2.32520i | 0.0271560 | − | 0.0835777i | ||||
\(775\) | −18.0800 | + | 39.7408i | −0.649452 | + | 1.42753i | ||||
\(776\) | 14.2874 | + | 10.3804i | 0.512889 | + | 0.372636i | ||||
\(777\) | 11.0238 | + | 3.58185i | 0.395477 | + | 0.128498i | ||||
\(778\) | 3.01504 | − | 0.979646i | 0.108094 | − | 0.0351220i | ||||
\(779\) | −5.87989 | + | 4.27199i | −0.210669 | + | 0.153060i | ||||
\(780\) | −24.5885 | − | 20.0764i | −0.880408 | − | 0.718850i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | − | 6.96953i | − | 0.249230i | ||||||
\(783\) | 17.8421 | + | 24.5576i | 0.637625 | + | 0.877616i | ||||
\(784\) | −3.19516 | − | 9.83368i | −0.114113 | − | 0.351203i | ||||
\(785\) | 26.4679 | + | 41.1198i | 0.944679 | + | 1.46763i | ||||
\(786\) | −2.52766 | − | 1.83645i | −0.0901585 | − | 0.0655040i | ||||
\(787\) | −10.2196 | + | 14.0661i | −0.364290 | + | 0.501403i | −0.951338 | − | 0.308150i | \(-0.900290\pi\) |
0.587048 | + | 0.809552i | \(0.300290\pi\) | |||||||
\(788\) | 28.4122 | + | 9.23168i | 1.01214 | + | 0.328865i | ||||
\(789\) | 4.05565 | + | 12.4820i | 0.144385 | + | 0.444371i | ||||
\(790\) | 0.0955293 | − | 1.69196i | 0.00339878 | − | 0.0601974i | ||||
\(791\) | 9.46410 | 0.336505 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 49.7749i | − | 1.76756i | ||||||
\(794\) | −13.8114 | + | 10.0346i | −0.490147 | + | 0.356113i | ||||
\(795\) | −3.39789 | + | 8.74602i | −0.120511 | + | 0.310189i | ||||
\(796\) | 1.07047 | − | 3.29456i | 0.0379417 | − | 0.116772i | ||||
\(797\) | −21.2705 | + | 29.2763i | −0.753440 | + | 1.03702i | 0.244292 | + | 0.969702i | \(0.421445\pi\) |
−0.997731 | + | 0.0673193i | \(0.978555\pi\) | |||||||
\(798\) | 8.25286 | − | 11.3591i | 0.292148 | − | 0.402107i | ||||
\(799\) | 13.6736 | − | 42.0830i | 0.483737 | − | 1.48879i | ||||
\(800\) | −12.6678 | − | 22.3566i | −0.447874 | − | 0.790424i | ||||
\(801\) | −0.274860 | + | 0.199698i | −0.00971171 | + | 0.00705597i | ||||
\(802\) | 1.20118i | 0.0424153i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −7.39230 | −0.260706 | ||||||||
\(805\) | −26.0317 | − | 1.46976i | −0.917496 | − | 0.0518023i | ||||
\(806\) | −5.92599 | − | 18.2383i | −0.208734 | − | 0.642418i | ||||
\(807\) | −29.8891 | − | 9.71156i | −1.05215 | − | 0.341863i | ||||
\(808\) | −22.0202 | + | 30.3082i | −0.774669 | + | 1.06624i | ||||
\(809\) | 11.7598 | + | 8.54399i | 0.413452 | + | 0.300391i | 0.774998 | − | 0.631964i | \(-0.217751\pi\) |
−0.361546 | + | 0.932354i | \(0.617751\pi\) | |||||||
\(810\) | −6.67841 | − | 10.3754i | −0.234655 | − | 0.364554i | ||||
\(811\) | −5.86538 | − | 18.0518i | −0.205961 | − | 0.633884i | −0.999673 | − | 0.0255890i | \(-0.991854\pi\) |
0.793711 | − | 0.608295i | \(-0.208146\pi\) | |||||||
\(812\) | 23.6012 | + | 32.4843i | 0.828240 | + | 1.13997i | ||||
\(813\) | 22.1469i | 0.776727i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.26795 | − | 8.90138i | 0.254585 | − | 0.311802i | ||||
\(816\) | −14.8797 | + | 10.8107i | −0.520893 | + | 0.378451i | ||||
\(817\) | 25.7481 | − | 8.36606i | 0.900811 | − | 0.292691i | ||||
\(818\) | −12.8611 | − | 4.17882i | −0.449678 | − | 0.146109i | ||||
\(819\) | −8.40755 | − | 6.10844i | −0.293784 | − | 0.213446i | ||||
\(820\) | 1.71001 | + | 6.48659i | 0.0597163 | + | 0.226522i | ||||
\(821\) | −9.02211 | + | 27.7672i | −0.314874 | + | 0.969082i | 0.660933 | + | 0.750445i | \(0.270161\pi\) |
−0.975806 | + | 0.218636i | \(0.929839\pi\) | |||||||
\(822\) | −8.43037 | + | 2.73919i | −0.294043 | + | 0.0955404i | ||||
\(823\) | 3.97137 | + | 5.46612i | 0.138433 | + | 0.190537i | 0.872605 | − | 0.488427i | \(-0.162429\pi\) |
−0.734171 | + | 0.678964i | \(0.762429\pi\) | |||||||
\(824\) | −8.19615 | −0.285526 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.19615 | 0.0764139 | ||||||||
\(827\) | 20.0316 | + | 27.5712i | 0.696568 | + | 0.958743i | 0.999983 | + | 0.00588462i | \(0.00187314\pi\) |
−0.303415 | + | 0.952858i | \(0.598127\pi\) | |||||||
\(828\) | 4.20225 | − | 1.36539i | 0.146038 | − | 0.0474507i | ||||
\(829\) | 3.08423 | − | 9.49227i | 0.107120 | − | 0.329680i | −0.883103 | − | 0.469180i | \(-0.844550\pi\) |
0.990222 | + | 0.139500i | \(0.0445495\pi\) | |||||||
\(830\) | 2.92091 | + | 11.0799i | 0.101386 | + | 0.384588i | ||||
\(831\) | 48.7422 | + | 35.4133i | 1.69085 | + | 1.22847i | ||||
\(832\) | −9.15115 | − | 2.97339i | −0.317259 | − | 0.103084i | ||||
\(833\) | 15.4192 | − | 5.01000i | 0.534243 | − | 0.173586i | ||||
\(834\) | 11.8023 | − | 8.57488i | 0.408681 | − | 0.296924i | ||||
\(835\) | −0.732051 | + | 0.896575i | −0.0253337 | + | 0.0310273i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 38.2581i | 1.32239i | ||||||||
\(838\) | −3.75449 | − | 5.16761i | −0.129697 | − | 0.178512i | ||||
\(839\) | 11.9851 | + | 36.8864i | 0.413772 | + | 1.27346i | 0.913345 | + | 0.407187i | \(0.133490\pi\) |
−0.499573 | + | 0.866272i | \(0.666510\pi\) | |||||||
\(840\) | −15.1134 | − | 23.4797i | −0.521461 | − | 0.810127i | ||||
\(841\) | −15.3713 | − | 11.1679i | −0.530046 | − | 0.385101i | ||||
\(842\) | −5.18841 | + | 7.14124i | −0.178804 | + | 0.246103i | ||||
\(843\) | −31.8230 | − | 10.3399i | −1.09604 | − | 0.356125i | ||||
\(844\) | 7.02459 | + | 21.6195i | 0.241796 | + | 0.744173i | ||||
\(845\) | 11.1626 | + | 0.630244i | 0.384004 | + | 0.0216811i | ||||
\(846\) | −4.33975 | −0.149204 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 5.35225i | 0.183797i | ||||||||
\(849\) | −12.6113 | + | 9.16267i | −0.432820 | + | 0.314462i | ||||
\(850\) | 8.70038 | − | 4.92985i | 0.298421 | − | 0.169092i | ||||
\(851\) | 1.93096 | − | 5.94288i | 0.0661924 | − | 0.203719i | ||||
\(852\) | 16.1199 | − | 22.1872i | 0.552260 | − | 0.760120i | ||||
\(853\) | 27.2523 | − | 37.5096i | 0.933102 | − | 1.28430i | −0.0255350 | − | 0.999674i | \(-0.508129\pi\) |
0.958637 | − | 0.284631i | \(-0.0918711\pi\) | |||||||
\(854\) | 6.27938 | − | 19.3260i | 0.214876 | − | 0.661320i | ||||
\(855\) | −2.48743 | + | 6.40253i | −0.0850683 | + | 0.218962i | ||||
\(856\) | 4.63733 | − | 3.36921i | 0.158501 | − | 0.115157i | ||||
\(857\) | 29.3195i | 1.00154i | 0.865581 | + | 0.500768i | \(0.166949\pi\) | ||||
−0.865581 | + | 0.500768i | \(0.833051\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.1962 | 0.757323 | 0.378661 | − | 0.925535i | \(-0.376384\pi\) | ||||
0.378661 | + | 0.925535i | \(0.376384\pi\) | |||||||
\(860\) | 1.40860 | − | 24.9483i | 0.0480328 | − | 0.850731i | ||||
\(861\) | 3.45980 | + | 10.6482i | 0.117910 | + | 0.362889i | ||||
\(862\) | 2.49686 | + | 0.811279i | 0.0850434 | + | 0.0276323i | ||||
\(863\) | 10.0566 | − | 13.8417i | 0.342330 | − | 0.471176i | −0.602790 | − | 0.797900i | \(-0.705944\pi\) |
0.945120 | + | 0.326723i | \(0.105944\pi\) | |||||||
\(864\) | −18.2164 | − | 13.2350i | −0.619733 | − | 0.450263i | ||||
\(865\) | −26.3450 | − | 40.9289i | −0.895757 | − | 1.39162i | ||||
\(866\) | 4.59683 | + | 14.1476i | 0.156207 | + | 0.480754i | ||||
\(867\) | 2.35255 | + | 3.23801i | 0.0798969 | + | 0.109969i | ||||
\(868\) | 50.6071i | 1.71772i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 12.0000 | + | 9.79796i | 0.406838 | + | 0.332182i | ||||
\(871\) | 7.58297 | − | 5.50935i | 0.256939 | − | 0.186677i | ||||
\(872\) | −16.8961 | + | 5.48987i | −0.572174 | + | 0.185911i | ||||
\(873\) | −6.36459 | − | 2.06798i | −0.215409 | − | 0.0699906i | ||||
\(874\) | −6.12363 | − | 4.44908i | −0.207135 | − | 0.150492i | ||||
\(875\) | −16.5785 | − | 33.5361i | −0.560457 | − | 1.13373i | ||||
\(876\) | 5.06550 | − | 15.5900i | 0.171147 | − | 0.526738i | ||||
\(877\) | −11.3135 | + | 3.67598i | −0.382030 | + | 0.124129i | −0.493735 | − | 0.869612i | \(-0.664369\pi\) |
0.111705 | + | 0.993741i | \(0.464369\pi\) | |||||||
\(878\) | −8.59495 | − | 11.8299i | −0.290066 | − | 0.399241i | ||||
\(879\) | −29.1244 | −0.982340 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.9090 | −0.906586 | −0.453293 | − | 0.891362i | \(-0.649751\pi\) | ||||
−0.453293 | + | 0.891362i | \(0.649751\pi\) | |||||||
\(882\) | −0.934625 | − | 1.28640i | −0.0314705 | − | 0.0433154i | ||||
\(883\) | 20.5095 | − | 6.66393i | 0.690199 | − | 0.224259i | 0.0571437 | − | 0.998366i | \(-0.481801\pi\) |
0.633055 | + | 0.774107i | \(0.281801\pi\) | |||||||
\(884\) | 8.77370 | − | 27.0027i | 0.295092 | − | 0.908199i | ||||
\(885\) | −5.29628 | + | 1.39622i | −0.178032 | + | 0.0469334i | ||||
\(886\) | 11.5430 | + | 8.38649i | 0.387795 | + | 0.281750i | ||||
\(887\) | 14.9269 | + | 4.85004i | 0.501196 | + | 0.162848i | 0.548694 | − | 0.836023i | \(-0.315125\pi\) |
−0.0474989 | + | 0.998871i | \(0.515125\pi\) | |||||||
\(888\) | 6.36459 | − | 2.06798i | 0.213582 | − | 0.0693969i | ||||
\(889\) | 2.42705 | − | 1.76336i | 0.0814007 | − | 0.0591411i | ||||
\(890\) | 0.339746 | − | 0.416102i | 0.0113883 | − | 0.0139478i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.68973i | 0.0900587i | ||||||||
\(893\) | −28.2466 | − | 38.8782i | −0.945238 | − | 1.30101i | ||||
\(894\) | −3.17297 | − | 9.76540i | −0.106120 | − | 0.326604i | ||||
\(895\) | 29.0761 | − | 18.7156i | 0.971906 | − | 0.625594i | ||||
\(896\) | −31.0019 | − | 22.5242i | −1.03570 | − | 0.752482i | ||||
\(897\) | −16.7881 | + | 23.1069i | −0.560539 | + | 0.771516i | ||||
\(898\) | −16.9927 | − | 5.52125i | −0.567052 | − | 0.184246i | ||||
\(899\) | −18.6947 | − | 57.5365i | −0.623504 | − | 1.91895i | ||||
\(900\) | 4.67691 | + | 4.28005i | 0.155897 | + | 0.142668i | ||||
\(901\) | −8.39230 | −0.279588 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 41.7057i | − | 1.38788i | ||||||
\(904\) | 4.42055 | − | 3.21172i | 0.147025 | − | 0.106820i | ||||
\(905\) | 14.0837 | − | 36.2507i | 0.468157 | − | 1.20501i | ||||
\(906\) | −1.29668 | + | 3.99078i | −0.0430794 | + | 0.132585i | ||||
\(907\) | 17.7009 | − | 24.3632i | 0.587749 | − | 0.808967i | −0.406769 | − | 0.913531i | \(-0.633345\pi\) |
0.994518 | + | 0.104564i | \(0.0333446\pi\) | |||||||
\(908\) | 20.4771 | − | 28.1843i | 0.679556 | − | 0.935329i | ||||
\(909\) | 4.38685 | − | 13.5013i | 0.145503 | − | 0.447811i | ||||
\(910\) | 15.3164 | + | 5.95053i | 0.507733 | + | 0.197258i | ||||
\(911\) | 24.4717 | − | 17.7797i | 0.810784 | − | 0.589069i | −0.103274 | − | 0.994653i | \(-0.532932\pi\) |
0.914058 | + | 0.405584i | \(0.132932\pi\) | |||||||
\(912\) | 19.9749i | 0.661434i | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 10.9808 | 0.363211 | ||||||||
\(915\) | −2.85685 | + | 50.5990i | −0.0944444 | + | 1.67275i | ||||
\(916\) | 2.17936 | + | 6.70738i | 0.0720081 | + | 0.221618i | ||||
\(917\) | −9.94263 | − | 3.23056i | −0.328335 | − | 0.106682i | ||||
\(918\) | 5.15058 | − | 7.08916i | 0.169994 | − | 0.233977i | ||||
\(919\) | 15.3558 | + | 11.1566i | 0.506540 | + | 0.368023i | 0.811509 | − | 0.584339i | \(-0.198646\pi\) |
−0.304970 | + | 0.952362i | \(0.598646\pi\) | |||||||
\(920\) | −12.6578 | + | 8.14755i | −0.417315 | + | 0.268617i | ||||
\(921\) | −4.67368 | − | 14.3841i | −0.154003 | − | 0.473973i | ||||
\(922\) | −10.0406 | − | 13.8197i | −0.330669 | − | 0.455127i | ||||
\(923\) | 34.7733i | 1.14458i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.78461 | − | 1.79315i | 0.288836 | − | 0.0589584i | ||||
\(926\) | −8.50816 | + | 6.18154i | −0.279595 | + | 0.203138i | ||||
\(927\) | 2.95382 | − | 0.959754i | 0.0970161 | − | 0.0315225i | ||||
\(928\) | 33.8629 | + | 11.0027i | 1.11160 | + | 0.361182i | ||||
\(929\) | −35.4806 | − | 25.7781i | −1.16408 | − | 0.845754i | −0.173792 | − | 0.984782i | \(-0.555602\pi\) |
−0.990288 | + | 0.139029i | \(0.955602\pi\) | |||||||
\(930\) | 4.97731 | + | 18.8804i | 0.163212 | + | 0.619113i | ||||
\(931\) | 5.44108 | − | 16.7459i | 0.178324 | − | 0.548825i | ||||
\(932\) | 2.78656 | − | 0.905408i | 0.0912768 | − | 0.0296576i | ||||
\(933\) | 11.4148 | + | 15.7112i | 0.373704 | + | 0.514360i | ||||
\(934\) | −0.320508 | −0.0104873 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6.00000 | −0.196116 | ||||||||
\(937\) | 18.3313 | + | 25.2308i | 0.598857 | + | 0.824255i | 0.995603 | − | 0.0936728i | \(-0.0298608\pi\) |
−0.396746 | + | 0.917928i | \(0.629861\pi\) | |||||||
\(938\) | 3.63925 | − | 1.18247i | 0.118826 | − | 0.0386089i | ||||
\(939\) | −10.2360 | + | 31.5031i | −0.334039 | + | 1.02807i | ||||
\(940\) | −42.8897 | + | 11.3067i | −1.39891 | + | 0.368784i | ||||
\(941\) | −21.8435 | − | 15.8702i | −0.712076 | − | 0.517354i | 0.171766 | − | 0.985138i | \(-0.445053\pi\) |
−0.883843 | + | 0.467784i | \(0.845053\pi\) | |||||||
\(942\) | 20.7992 | + | 6.75806i | 0.677674 | + | 0.220190i | ||||
\(943\) | 5.74038 | − | 1.86516i | 0.186932 | − | 0.0607380i | ||||
\(944\) | −2.52766 | + | 1.83645i | −0.0822682 | + | 0.0597714i | ||||
\(945\) | −25.3923 | − | 20.7327i | −0.826012 | − | 0.674436i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.9749i | 0.649096i | 0.945869 | + | 0.324548i | \(0.105212\pi\) | ||||
−0.945869 | + | 0.324548i | \(0.894788\pi\) | |||||||
\(948\) | 2.87955 | + | 3.96336i | 0.0935234 | + | 0.128724i | ||||
\(949\) | 6.42280 | + | 19.7673i | 0.208493 | + | 0.641675i | ||||
\(950\) | 1.22248 | − | 10.7914i | 0.0396624 | − | 0.350120i | ||||
\(951\) | −19.7338 | − | 14.3374i | −0.639912 | − | 0.464923i | ||||
\(952\) | 14.6802 | − | 20.2055i | 0.475787 | − | 0.654864i | ||||
\(953\) | −15.8761 | − | 5.15847i | −0.514279 | − | 0.167099i | 0.0403686 | − | 0.999185i | \(-0.487147\pi\) |
−0.554647 | + | 0.832086i | \(0.687147\pi\) | |||||||
\(954\) | 0.254347 | + | 0.782801i | 0.00823480 | + | 0.0253441i | ||||
\(955\) | 16.2258 | + | 0.916117i | 0.525054 | + | 0.0296448i | ||||
\(956\) | 9.80385 | 0.317079 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.31268i | 0.0424107i | ||||||||
\(959\) | −23.9956 | + | 17.4339i | −0.774860 | + | 0.562969i | ||||
\(960\) | 9.13200 | + | 3.54785i | 0.294734 | + | 0.114506i | ||||
\(961\) | 13.9826 | − | 43.0341i | 0.451052 | − | 1.38820i | ||||
\(962\) | −2.31472 | + | 3.18594i | −0.0746295 | + | 0.102719i | ||||
\(963\) | −1.27672 | + | 1.75726i | −0.0411418 | + | 0.0566268i | ||||
\(964\) | −7.55982 | + | 23.2667i | −0.243486 | + | 0.749371i | ||||
\(965\) | 31.6342 | + | 12.2901i | 1.01834 | + | 0.395633i | ||||
\(966\) | −9.43334 | + | 6.85373i | −0.303513 | + | 0.220515i | ||||
\(967\) | 4.24264i | 0.136434i | 0.997671 | + | 0.0682171i | \(0.0217310\pi\) | ||||
−0.997671 | + | 0.0682171i | \(0.978269\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −31.3205 | −1.00616 | ||||||||
\(970\) | 10.5644 | + | 0.596470i | 0.339201 | + | 0.0191515i | ||||
\(971\) | −7.70324 | − | 23.7081i | −0.247209 | − | 0.760830i | −0.995265 | − | 0.0971952i | \(-0.969013\pi\) |
0.748057 | − | 0.663635i | \(-0.230987\pi\) | |||||||
\(972\) | 12.2722 | + | 3.98749i | 0.393632 | + | 0.127899i | ||||
\(973\) | 28.6921 | − | 39.4913i | 0.919827 | − | 1.26603i | ||||
\(974\) | −5.33017 | − | 3.87260i | −0.170790 | − | 0.124086i | ||||
\(975\) | −40.7203 | − | 4.61289i | −1.30409 | − | 0.147731i | ||||
\(976\) | 8.93336 | + | 27.4941i | 0.285950 | + | 0.880063i | ||||
\(977\) | −17.1142 | − | 23.5557i | −0.547533 | − | 0.753614i | 0.442142 | − | 0.896945i | \(-0.354219\pi\) |
−0.989675 | + | 0.143331i | \(0.954219\pi\) | |||||||
\(978\) | − | 5.13922i | − | 0.164334i | ||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −12.5885 | − | 10.2784i | −0.402124 | − | 0.328332i | ||||
\(981\) | 5.44634 | − | 3.95700i | 0.173888 | − | 0.126337i | ||||
\(982\) | 19.5507 | − | 6.35242i | 0.623889 | − | 0.202714i | ||||
\(983\) | −53.2817 | − | 17.3123i | −1.69942 | − | 0.552176i | −0.710906 | − | 0.703287i | \(-0.751715\pi\) |
−0.988517 | + | 0.151112i | \(0.951715\pi\) | |||||||
\(984\) | 5.22957 | + | 3.79950i | 0.166713 | + | 0.121124i | ||||
\(985\) | 37.2935 | − | 9.83142i | 1.18827 | − | 0.313255i | ||||
\(986\) | −4.28187 | + | 13.1782i | −0.136362 | + | 0.419680i | ||||
\(987\) | −70.4063 | + | 22.8764i | −2.24106 | + | 0.728163i | ||||
\(988\) | −18.1245 | − | 24.9463i | −0.576618 | − | 0.793647i | ||||
\(989\) | −22.4833 | −0.714929 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.9090 | 0.632429 | 0.316215 | − | 0.948688i | \(-0.397588\pi\) | ||||
0.316215 | + | 0.948688i | \(0.397588\pi\) | |||||||
\(992\) | 26.3774 | + | 36.3054i | 0.837483 | + | 1.15270i | ||||
\(993\) | −33.4318 | + | 10.8626i | −1.06093 | + | 0.344716i | ||||
\(994\) | −4.38685 | + | 13.5013i | −0.139143 | + | 0.428237i | ||||
\(995\) | −1.14001 | − | 4.32439i | −0.0361407 | − | 0.137092i | ||||
\(996\) | −26.7982 | − | 19.4700i | −0.849132 | − | 0.616931i | ||||
\(997\) | −32.4472 | − | 10.5427i | −1.02761 | − | 0.333892i | −0.253767 | − | 0.967265i | \(-0.581670\pi\) |
−0.773846 | + | 0.633374i | \(0.781670\pi\) | |||||||
\(998\) | 8.66832 | − | 2.81651i | 0.274391 | − | 0.0891550i | ||||
\(999\) | 6.35597 | − | 4.61788i | 0.201094 | − | 0.146103i |
(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 | 605.2.j.e.124.2 | 16 | ||
5.4 | even | 2 | inner | 605.2.j.e.124.3 | 16 | ||
11.2 | odd | 10 | 605.2.b.d.364.2 | ✓ | 4 | ||
11.3 | even | 5 | inner | 605.2.j.e.269.2 | 16 | ||
11.4 | even | 5 | inner | 605.2.j.e.444.3 | 16 | ||
11.5 | even | 5 | inner | 605.2.j.e.9.3 | 16 | ||
11.6 | odd | 10 | 605.2.j.f.9.2 | 16 | |||
11.7 | odd | 10 | 605.2.j.f.444.2 | 16 | |||
11.8 | odd | 10 | 605.2.j.f.269.3 | 16 | |||
11.9 | even | 5 | 605.2.b.e.364.3 | yes | 4 | ||
11.10 | odd | 2 | 605.2.j.f.124.3 | 16 | |||
55.2 | even | 20 | 3025.2.a.y.1.3 | 4 | |||
55.4 | even | 10 | inner | 605.2.j.e.444.2 | 16 | ||
55.9 | even | 10 | 605.2.b.e.364.2 | yes | 4 | ||
55.13 | even | 20 | 3025.2.a.y.1.2 | 4 | |||
55.14 | even | 10 | inner | 605.2.j.e.269.3 | 16 | ||
55.19 | odd | 10 | 605.2.j.f.269.2 | 16 | |||
55.24 | odd | 10 | 605.2.b.d.364.3 | yes | 4 | ||
55.29 | odd | 10 | 605.2.j.f.444.3 | 16 | |||
55.39 | odd | 10 | 605.2.j.f.9.3 | 16 | |||
55.42 | odd | 20 | 3025.2.a.z.1.2 | 4 | |||
55.49 | even | 10 | inner | 605.2.j.e.9.2 | 16 | ||
55.53 | odd | 20 | 3025.2.a.z.1.3 | 4 | |||
55.54 | odd | 2 | 605.2.j.f.124.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
605.2.b.d.364.2 | ✓ | 4 | 11.2 | odd | 10 | ||
605.2.b.d.364.3 | yes | 4 | 55.24 | odd | 10 | ||
605.2.b.e.364.2 | yes | 4 | 55.9 | even | 10 | ||
605.2.b.e.364.3 | yes | 4 | 11.9 | even | 5 | ||
605.2.j.e.9.2 | 16 | 55.49 | even | 10 | inner | ||
605.2.j.e.9.3 | 16 | 11.5 | even | 5 | inner | ||
605.2.j.e.124.2 | 16 | 1.1 | even | 1 | trivial | ||
605.2.j.e.124.3 | 16 | 5.4 | even | 2 | inner | ||
605.2.j.e.269.2 | 16 | 11.3 | even | 5 | inner | ||
605.2.j.e.269.3 | 16 | 55.14 | even | 10 | inner | ||
605.2.j.e.444.2 | 16 | 55.4 | even | 10 | inner | ||
605.2.j.e.444.3 | 16 | 11.4 | even | 5 | inner | ||
605.2.j.f.9.2 | 16 | 11.6 | odd | 10 | |||
605.2.j.f.9.3 | 16 | 55.39 | odd | 10 | |||
605.2.j.f.124.2 | 16 | 55.54 | odd | 2 | |||
605.2.j.f.124.3 | 16 | 11.10 | odd | 2 | |||
605.2.j.f.269.2 | 16 | 55.19 | odd | 10 | |||
605.2.j.f.269.3 | 16 | 11.8 | odd | 10 | |||
605.2.j.f.444.2 | 16 | 11.7 | odd | 10 | |||
605.2.j.f.444.3 | 16 | 55.29 | odd | 10 | |||
3025.2.a.y.1.2 | 4 | 55.13 | even | 20 | |||
3025.2.a.y.1.3 | 4 | 55.2 | even | 20 | |||
3025.2.a.z.1.2 | 4 | 55.42 | odd | 20 | |||
3025.2.a.z.1.3 | 4 | 55.53 | odd | 20 |