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 | 444.3 | ||
Root | \(-0.492303 - 0.159959i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 605.444 |
Dual form | 605.2.j.e.124.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(486\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{5}\right)\) |
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 | \(-0.741415\pi\) |
0.902925 | + | 0.429797i | \(0.141415\pi\) | |||||||
\(3\) | −1.83730 | − | 0.596975i | −1.06077 | − | 0.344664i | −0.273881 | − | 0.961764i | \(-0.588307\pi\) |
−0.786885 | + | 0.617100i | \(0.788307\pi\) | |||||||
\(4\) | 0.535233 | + | 1.64728i | 0.267617 | + | 0.823639i | ||||
\(5\) | −2.23251 | − | 0.126049i | −0.998410 | − | 0.0563708i | ||||
\(6\) | −0.809017 | + | 0.587785i | −0.330280 | + | 0.239962i | ||||
\(7\) | 3.18230 | − | 1.03399i | 1.20280 | − | 0.390812i | 0.362007 | − | 0.932175i | \(-0.382092\pi\) |
0.840789 | + | 0.541364i | \(0.182092\pi\) | |||||||
\(8\) | 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 | 0.308355 | + | 0.951271i | \(0.400222\pi\) |
−1.00000 | 0.000696272i | \(0.999778\pi\) | ||||||||
\(14\) | 0.535233 | − | 1.64728i | 0.143047 | − | 0.440254i | ||||
\(15\) | 4.02655 | + | 1.56434i | 1.03965 | + | 0.403912i | ||||
\(16\) | −1.99350 | + | 1.44836i | −0.498375 | + | 0.362091i | ||||
\(17\) | −2.27103 | − | 3.12580i | −0.550805 | − | 0.758118i | 0.439316 | − | 0.898333i | \(-0.355221\pi\) |
−0.990121 | + | 0.140214i | \(0.955221\pi\) | |||||||
\(18\) | 0.360391 | − | 0.117098i | 0.0849449 | − | 0.0276003i | ||||
\(19\) | −1.29668 | + | 3.99078i | −0.297479 | + | 0.915547i | 0.684898 | + | 0.728639i | \(0.259847\pi\) |
−0.982377 | + | 0.186908i | \(0.940153\pi\) | |||||||
\(20\) | −0.987277 | − | 3.74503i | −0.220762 | − | 0.837415i | ||||
\(21\) | −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 | ||||
\(25\) | 4.96822 | + | 0.562811i | 0.993645 | + | 0.112562i | ||||
\(26\) | 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 | 0.926949 | + | 0.375188i | \(0.122422\pi\) |
−0.529388 | + | 0.848380i | \(0.677578\pi\) | |||||||
\(30\) | 1.88023 | − | 1.21026i | 0.343281 | − | 0.220963i | ||||
\(31\) | 7.06438 | + | 5.13257i | 1.26880 | + | 0.921837i | 0.999154 | − | 0.0411227i | \(-0.0130935\pi\) |
0.269646 | + | 0.962960i | \(0.413093\pi\) | |||||||
\(32\) | 5.13922i | 0.908494i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.00000 | −0.342997 | ||||||||
\(35\) | −7.23485 | + | 1.90727i | −1.22291 | + | 0.322388i | ||||
\(36\) | −0.391818 | + | 1.20589i | −0.0653030 | + | 0.200982i | ||||
\(37\) | 1.70539 | − | 0.554114i | 0.280364 | − | 0.0910958i | −0.165460 | − | 0.986217i | \(-0.552911\pi\) |
0.445824 | + | 0.895121i | \(0.352911\pi\) | |||||||
\(38\) | 1.27672 | + | 1.75726i | 0.207112 | + | 0.285065i | ||||
\(39\) | 6.63083 | − | 4.81758i | 1.06178 | − | 0.771430i | ||||
\(40\) | −4.02655 | − | 1.56434i | −0.636653 | − | 0.247344i | ||||
\(41\) | −0.535233 | + | 1.64728i | −0.0835894 | + | 0.257262i | −0.984112 | − | 0.177547i | \(-0.943184\pi\) |
0.900523 | + | 0.434808i | \(0.143184\pi\) | |||||||
\(42\) | −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 | \(-0.714679\pi\) |
−0.964291 | + | 0.264846i | \(0.914679\pi\) | |||||||
\(48\) | 4.52729 | − | 1.47101i | 0.653459 | − | 0.212322i | ||||
\(49\) | 3.39476 | − | 2.46644i | 0.484966 | − | 0.352348i | ||||
\(50\) | 1.74732 | − | 1.90934i | 0.247109 | − | 0.270022i | ||||
\(51\) | 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 | \(-0.752337\pi\) |
0.887650 | + | 0.460519i | \(0.152337\pi\) | |||||||
\(54\) | 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 | 0.973317 | − | 0.229466i | \(-0.0736979\pi\) |
−0.922306 | + | 0.386459i | \(0.873698\pi\) | |||||||
\(60\) | −0.421768 | + | 7.47013i | −0.0544500 | + | 0.964390i | ||||
\(61\) | −9.49143 | + | 6.89593i | −1.21525 | + | 0.882933i | −0.995697 | − | 0.0926671i | \(-0.970461\pi\) |
−0.219556 | + | 0.975600i | \(0.570461\pi\) | |||||||
\(62\) | 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 | ||||
\(70\) | −1.40255 | + | 3.61010i | −0.167637 | + | 0.431490i | ||||
\(71\) | 6.63083 | − | 4.81758i | 0.786934 | − | 0.571741i | −0.120118 | − | 0.992760i | \(-0.538327\pi\) |
0.907052 | + | 0.421018i | \(0.138327\pi\) | |||||||
\(72\) | 0.831254 | + | 1.14412i | 0.0979642 | + | 0.134836i | ||||
\(73\) | −4.65921 | + | 1.51387i | −0.545319 | + | 0.177185i | −0.568705 | − | 0.822542i | \(-0.692555\pi\) |
0.0233860 | + | 0.999727i | \(0.492555\pi\) | |||||||
\(74\) | 0.286831 | − | 0.882774i | 0.0333434 | − | 0.102620i | ||||
\(75\) | −8.79213 | − | 3.99996i | −1.01523 | − | 0.461875i | ||||
\(76\) | −7.26795 | −0.833691 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − | 4.24264i | − | 0.480384i | ||||||
\(79\) | −1.18448 | − | 0.860577i | −0.133265 | − | 0.0968225i | 0.519156 | − | 0.854680i | \(-0.326246\pi\) |
−0.652421 | + | 0.757857i | \(0.726246\pi\) | |||||||
\(80\) | 4.63308 | − | 2.98221i | 0.517994 | − | 0.333421i | ||||
\(81\) | −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 | \(-0.382827\pi\) |
−0.998545 | + | 0.0539231i | \(0.982827\pi\) | |||||||
\(84\) | −3.45980 | − | 10.6482i | −0.377495 | − | 1.16181i | ||||
\(85\) | 4.67609 | + | 7.26465i | 0.507194 | + | 0.787962i | ||||
\(86\) | 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 | \(0.507830\pi\) | |||||||
\(90\) | −0.819337 | + | 0.215996i | −0.0863657 | + | 0.0227680i | ||||
\(91\) | −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 | ||||
\(95\) | 3.39789 | − | 8.74602i | 0.348616 | − | 0.897322i | ||||
\(96\) | 3.06798 | − | 9.44228i | 0.313125 | − | 0.963699i | ||||
\(97\) | 5.37331 | − | 7.39573i | 0.545577 | − | 0.750922i | −0.443827 | − | 0.896113i | \(-0.646379\pi\) |
0.989404 | + | 0.145190i | \(0.0463795\pi\) | |||||||
\(98\) | − | 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 | 0.935114 | + | 0.354348i | \(0.115297\pi\) |
0.625971 | + | 0.779847i | \(0.284703\pi\) | |||||||
\(102\) | 3.67460 | + | 1.19395i | 0.363840 | + | 0.118219i | ||||
\(103\) | −4.03499 | + | 1.31105i | −0.397579 | + | 0.129181i | −0.500981 | − | 0.865458i | \(-0.667027\pi\) |
0.103401 | + | 0.994640i | \(0.467027\pi\) | |||||||
\(104\) | −6.63083 | + | 4.81758i | −0.650206 | + | 0.472402i | ||||
\(105\) | 14.4312 | + | 0.814793i | 1.40834 | + | 0.0795156i | ||||
\(106\) | −0.347445 | − | 1.06933i | −0.0337468 | − | 0.103862i | ||||
\(107\) | 2.82191 | + | 0.916893i | 0.272804 | + | 0.0886394i | 0.442224 | − | 0.896905i | \(-0.354190\pi\) |
−0.169420 | + | 0.985544i | \(0.554190\pi\) | |||||||
\(108\) | −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 | \(-0.357527\pi\) |
−0.179743 | + | 0.983714i | \(0.557527\pi\) | |||||||
\(114\) | −1.29668 | − | 3.99078i | −0.121445 | − | 0.373771i | ||||
\(115\) | 0.439251 | − | 7.77978i | 0.0409604 | − | 0.725469i | ||||
\(116\) | −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 | ||||
\(125\) | −11.0207 | − | 1.88272i | −0.985719 | − | 0.168396i | ||||
\(126\) | 1.02579 | − | 0.745282i | 0.0913849 | − | 0.0663950i | ||||
\(127\) | 0.526994 | + | 0.725345i | 0.0467631 | + | 0.0643639i | 0.831758 | − | 0.555138i | \(-0.187335\pi\) |
−0.784995 | + | 0.619502i | \(0.787335\pi\) | |||||||
\(128\) | −10.8919 | + | 3.53899i | −0.962716 | + | 0.312805i | ||||
\(129\) | 3.85162 | − | 11.8541i | 0.339116 | − | 1.04369i | ||||
\(130\) | −1.25182 | − | 4.74851i | −0.109792 | − | 0.416472i | ||||
\(131\) | 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 | ||||
\(135\) | −5.30257 | − | 8.23793i | −0.456373 | − | 0.709008i | ||||
\(136\) | −2.30653 | − | 7.09878i | −0.197784 | − | 0.608716i | ||||
\(137\) | −5.21026 | − | 7.17130i | −0.445142 | − | 0.612686i | 0.526203 | − | 0.850359i | \(-0.323615\pi\) |
−0.971345 | + | 0.237673i | \(0.923615\pi\) | |||||||
\(138\) | −2.04829 | − | 2.81923i | −0.174362 | − | 0.239989i | ||||
\(139\) | −4.50808 | − | 13.8744i | −0.382370 | − | 1.17682i | −0.938370 | − | 0.345633i | \(-0.887664\pi\) |
0.555999 | − | 0.831183i | \(-0.312336\pi\) | |||||||
\(140\) | −7.01414 | − | 10.8970i | −0.592803 | − | 0.920963i | ||||
\(141\) | 17.8990 | + | 13.0044i | 1.50737 | + | 1.09517i | ||||
\(142\) | − | 4.24264i | − | 0.356034i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.80385 | −0.150321 | ||||||||
\(145\) | −3.94911 | − | 14.9801i | −0.327956 | − | 1.24403i | ||||
\(146\) | −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 | −0.193002 | − | 0.981198i | \(-0.561823\pi\) |
0.873534 | + | 0.486763i | \(0.161823\pi\) | |||||||
\(150\) | −4.35019 | + | 2.46492i | −0.355191 | + | 0.201260i | ||||
\(151\) | −1.29668 | + | 3.99078i | −0.105523 | + | 0.324765i | −0.989853 | − | 0.142097i | \(-0.954616\pi\) |
0.884330 | + | 0.466862i | \(0.154616\pi\) | |||||||
\(152\) | −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 | \(-0.0623737\pi\) |
0.679092 | + | 0.734053i | \(0.262374\pi\) | |||||||
\(158\) | −0.720782 | + | 0.234196i | −0.0573423 | + | 0.0186316i | ||||
\(159\) | −3.39476 | + | 2.46644i | −0.269222 | + | 0.195601i | ||||
\(160\) | 0.647792 | − | 11.4734i | 0.0512125 | − | 0.907049i | ||||
\(161\) | 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 | \(-0.864506\pi\) |
0.674160 | + | 0.738586i | \(0.264506\pi\) | |||||||
\(164\) | −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 | \(-0.793624\pi\) |
0.820627 | + | 0.571464i | \(0.193624\pi\) | |||||||
\(168\) | −11.8765 | − | 3.85891i | −0.916291 | − | 0.297721i | ||||
\(169\) | −1.54508 | − | 4.75528i | −0.118853 | − | 0.365791i | ||||
\(170\) | 4.46502 | + | 0.252098i | 0.342452 | + | 0.0193350i | ||||
\(171\) | −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 | \(-0.710235\pi\) |
−0.960499 | + | 0.278282i | \(0.910235\pi\) | |||||||
\(174\) | −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 | −0.597563 | − | 0.801822i | \(-0.703864\pi\) |
0.954738 | − | 0.297449i | \(-0.0961357\pi\) | |||||||
\(180\) | 1.02674 | − | 2.64278i | 0.0765286 | − | 0.196981i | ||||
\(181\) | 14.0707 | − | 10.2229i | 1.04586 | − | 0.759865i | 0.0744429 | − | 0.997225i | \(-0.476282\pi\) |
0.971422 | + | 0.237360i | \(0.0762821\pi\) | |||||||
\(182\) | 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 | ||||
\(185\) | −3.87715 | + | 1.02210i | −0.285053 | + | 0.0751466i | ||||
\(186\) | −8.73205 | −0.640265 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 19.8362i | − | 1.44670i | ||||||
\(189\) | 11.8604 | + | 8.61708i | 0.862717 | + | 0.626800i | ||||
\(190\) | −2.62880 | − | 4.08403i | −0.190713 | − | 0.296286i | ||||
\(191\) | −2.24592 | − | 6.91223i | −0.162509 | − | 0.500151i | 0.836335 | − | 0.548219i | \(-0.184694\pi\) |
−0.998844 | + | 0.0480672i | \(0.984694\pi\) | |||||||
\(192\) | 2.57529 | + | 3.54458i | 0.185855 | + | 0.255808i | ||||
\(193\) | 8.92106 | + | 12.2788i | 0.642152 | + | 0.883846i | 0.998728 | − | 0.0504200i | \(-0.0160560\pi\) |
−0.356576 | + | 0.934266i | \(0.616056\pi\) | |||||||
\(194\) | −1.46228 | − | 4.50045i | −0.104986 | − | 0.323113i | ||||
\(195\) | −15.4107 | + | 9.91949i | −1.10358 | + | 0.710350i | ||||
\(196\) | 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 | \(0.477417\pi\) | |||||||
\(200\) | 8.79213 | + | 3.99996i | 0.621698 | + | 0.282840i | ||||
\(201\) | −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 | ||||
\(205\) | 1.40255 | − | 3.61010i | 0.0979585 | − | 0.252141i | ||||
\(206\) | −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 | 0.158906 | − | 0.987294i | \(-0.449203\pi\) |
−0.889867 | + | 0.456219i | \(0.849203\pi\) | |||||||
\(212\) | 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 | ||||
\(215\) | 0.813254 | − | 14.4039i | 0.0554635 | − | 0.982340i | ||||
\(216\) | 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 | \(-0.383442\pi\) |
−0.259148 | + | 0.965838i | \(0.583442\pi\) | |||||||
\(224\) | 5.31390 | + | 16.3545i | 0.355050 | + | 1.09273i | ||||
\(225\) | 2.70022 | + | 2.47109i | 0.180014 | + | 0.164739i | ||||
\(226\) | 1.18448 | − | 0.860577i | 0.0787906 | − | 0.0572448i | ||||
\(227\) | −19.1291 | + | 6.21543i | −1.26964 | + | 0.412533i | −0.864922 | − | 0.501907i | \(-0.832632\pi\) |
−0.404723 | + | 0.914439i | \(0.632632\pi\) | |||||||
\(228\) | 13.3534 | + | 4.33878i | 0.884351 | + | 0.287343i | ||||
\(229\) | −3.29415 | − | 2.39334i | −0.217684 | − | 0.158156i | 0.473600 | − | 0.880740i | \(-0.342954\pi\) |
−0.691283 | + | 0.722584i | \(0.742954\pi\) | |||||||
\(230\) | −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 | \(-0.817647\pi\) |
0.775204 | + | 0.631710i | \(0.217647\pi\) | |||||||
\(234\) | −0.496805 | + | 1.52901i | −0.0324772 | + | 0.0999544i | ||||
\(235\) | 23.8702 | + | 9.27375i | 1.55712 | + | 0.604953i | ||||
\(236\) | −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 | −0.878414 | − | 0.477901i | \(-0.841398\pi\) |
0.991555 | + | 0.129689i | \(0.0413979\pi\) | |||||||
\(240\) | −10.2927 | + | 2.71338i | −0.664388 | + | 0.175148i | ||||
\(241\) | −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 | ||||
\(245\) | −7.88973 | + | 5.07844i | −0.504057 | + | 0.324450i | ||||
\(246\) | −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 | ||||
\(250\) | −4.14159 | + | 4.04238i | −0.261937 | + | 0.255663i | ||||
\(251\) | 3.07738 | + | 2.23585i | 0.194242 | + | 0.141125i | 0.680656 | − | 0.732604i | \(-0.261695\pi\) |
−0.486413 | + | 0.873729i | \(0.661695\pi\) | |||||||
\(252\) | 4.24264i | 0.267261i | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0.464102 | 0.0291203 | ||||||||
\(255\) | −4.25457 | − | 16.1389i | −0.266432 | − | 1.01065i | ||||
\(256\) | −0.430246 | + | 1.32416i | −0.0268904 | + | 0.0827600i | ||||
\(257\) | 14.0742 | − | 4.57298i | 0.877924 | − | 0.285255i | 0.164829 | − | 0.986322i | \(-0.447293\pi\) |
0.713095 | + | 0.701068i | \(0.247293\pi\) | |||||||
\(258\) | −3.79233 | − | 5.21969i | −0.236100 | − | 0.324964i | ||||
\(259\) | 4.85410 | − | 3.52671i | 0.301619 | − | 0.219139i | ||||
\(260\) | 15.3164 | + | 5.95053i | 0.949881 | + | 0.369036i | ||||
\(261\) | −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 | −0.911630 | − | 0.411012i | \(-0.865175\pi\) |
0.109187 | + | 0.994021i | \(0.465175\pi\) | |||||||
\(270\) | −5.06322 | − | 0.285872i | −0.308138 | − | 0.0173976i | ||||
\(271\) | −3.54260 | − | 10.9030i | −0.215198 | − | 0.662311i | −0.999139 | − | 0.0414762i | \(-0.986794\pi\) |
0.783942 | − | 0.620834i | \(-0.213206\pi\) | |||||||
\(272\) | 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 | −0.267930 | + | 0.963438i | \(0.586340\pi\) |
−0.833489 | + | 0.552536i | \(0.813660\pi\) | |||||||
\(278\) | −7.18194 | − | 2.33355i | −0.430744 | − | 0.139957i | ||||
\(279\) | 1.97533 | + | 6.07944i | 0.118260 | + | 0.363967i | ||||
\(280\) | −14.4312 | − | 0.814793i | −0.862428 | − | 0.0486932i | ||||
\(281\) | −14.0126 | + | 10.1807i | −0.835921 | + | 0.607332i | −0.921228 | − | 0.389023i | \(-0.872813\pi\) |
0.0853074 | + | 0.996355i | \(0.472813\pi\) | |||||||
\(282\) | 10.8919 | − | 3.53899i | 0.648603 | − | 0.210744i | ||||
\(283\) | 7.67425 | + | 2.49351i | 0.456187 | + | 0.148224i | 0.528091 | − | 0.849187i | \(-0.322908\pi\) |
−0.0719049 | + | 0.997411i | \(0.522908\pi\) | |||||||
\(284\) | 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 | ||||
\(290\) | −7.47491 | − | 2.90406i | −0.438942 | − | 0.170532i | ||||
\(291\) | −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 | \(-0.454847\pi\) |
0.696258 | + | 0.717792i | \(0.254847\pi\) | |||||||
\(294\) | −1.29668 | + | 3.99078i | −0.0756241 | + | 0.232747i | ||||
\(295\) | −0.722737 | − | 2.74156i | −0.0420794 | − | 0.159620i | ||||
\(296\) | 3.46410 | 0.201347 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 5.31508i | − | 0.307894i | ||||||
\(299\) | −11.9610 | − | 8.69018i | −0.691723 | − | 0.502566i | ||||
\(300\) | 1.88320 | − | 16.6240i | 0.108727 | − | 0.959787i | ||||
\(301\) | 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 | ||||
\(305\) | 22.0590 | − | 14.1989i | 1.26309 | − | 0.813024i | ||||
\(306\) | −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 | ||||||||
\(310\) | −9.77322 | + | 2.57645i | −0.555082 | + | 0.146332i | ||||
\(311\) | 3.10641 | − | 9.56055i | 0.176148 | − | 0.542129i | −0.823536 | − | 0.567265i | \(-0.808002\pi\) |
0.999684 | + | 0.0251354i | \(0.00800169\pi\) | |||||||
\(312\) | 15.0588 | − | 4.89290i | 0.852536 | − | 0.277006i | ||||
\(313\) | 10.0784 | + | 13.8718i | 0.569666 | + | 0.784078i | 0.992515 | − | 0.122122i | \(-0.0389700\pi\) |
−0.422849 | + | 0.906200i | \(0.638970\pi\) | |||||||
\(314\) | 9.15848 | − | 6.65403i | 0.516843 | − | 0.375509i | ||||
\(315\) | −5.10546 | − | 1.98351i | −0.287660 | − | 0.111758i | ||||
\(316\) | 0.783636 | − | 2.41178i | 0.0440830 | − | 0.135673i | ||||
\(317\) | 7.42160 | − | 10.2150i | 0.416839 | − | 0.573729i | −0.548031 | − | 0.836458i | \(-0.684622\pi\) |
0.964870 | + | 0.262729i | \(0.0846224\pi\) | |||||||
\(318\) | 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 | ||||
\(325\) | −14.3213 | + | 15.6493i | −0.794405 | + | 0.868065i | ||||
\(326\) | 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 | ||||
\(335\) | −0.278474 | + | 4.93218i | −0.0152147 | + | 0.269474i | ||||
\(336\) | 12.8862 | − | 9.36236i | 0.702999 | − | 0.510759i | ||||
\(337\) | 16.7642 | − | 5.44701i | 0.913203 | − | 0.296718i | 0.185527 | − | 0.982639i | \(-0.440601\pi\) |
0.727676 | + | 0.685921i | \(0.240601\pi\) | |||||||
\(338\) | −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 | ||||
\(345\) | −5.45137 | + | 14.0316i | −0.293492 | + | 0.755435i | ||||
\(346\) | −9.11596 | + | 6.62313i | −0.490077 | + | 0.356062i | ||||
\(347\) | 2.57529 | + | 3.54458i | 0.138249 | + | 0.190283i | 0.872527 | − | 0.488565i | \(-0.162479\pi\) |
−0.734279 | + | 0.678848i | \(0.762479\pi\) | |||||||
\(348\) | 22.0476 | − | 7.16370i | 1.18188 | − | 0.384015i | ||||
\(349\) | −2.26216 | + | 6.96222i | −0.121091 | + | 0.372679i | −0.993169 | − | 0.116688i | \(-0.962772\pi\) |
0.872078 | + | 0.489367i | \(0.162772\pi\) | |||||||
\(350\) | 3.58626 | − | 7.88281i | 0.191694 | − | 0.421354i | ||||
\(351\) | −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 | ||||
\(355\) | −15.4107 | + | 9.91949i | −0.817913 | + | 0.526472i | ||||
\(356\) | −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 | 0.612540 | + | 0.790440i | \(0.290148\pi\) |
−0.0309462 | + | 0.999521i | \(0.509852\pi\) | |||||||
\(360\) | −1.71157 | − | 2.65905i | −0.0902076 | − | 0.140144i | ||||
\(361\) | 1.12640 | + | 0.818376i | 0.0592841 | + | 0.0430724i | ||||
\(362\) | − | 9.00292i | − | 0.473183i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −24.5885 | −1.28879 | ||||||||
\(365\) | 10.5926 | − | 2.79244i | 0.554440 | − | 0.146163i | ||||
\(366\) | 3.62540 | − | 11.1578i | 0.189503 | − | 0.583230i | ||||
\(367\) | −16.0787 | + | 5.22430i | −0.839304 | + | 0.272706i | −0.696959 | − | 0.717111i | \(-0.745464\pi\) |
−0.142345 | + | 0.989817i | \(0.545464\pi\) | |||||||
\(368\) | −5.04720 | − | 6.94688i | −0.263104 | − | 0.362131i | ||||
\(369\) | −1.02579 | + | 0.745282i | −0.0534006 | + | 0.0387978i | ||||
\(370\) | −0.751625 | + | 1.93465i | −0.0390751 | + | 0.100578i | ||||
\(371\) | 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 | −0.556948 | − | 0.830547i | \(-0.688028\pi\) |
0.617791 | + | 0.786342i | \(0.288028\pi\) | |||||||
\(380\) | 16.2258 | + | 0.916117i | 0.832365 | + | 0.0469958i | ||||
\(381\) | −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 | −0.427475 | + | 0.904027i | \(0.640597\pi\) |
−0.727684 | + | 0.685913i | \(0.759403\pi\) | |||||||
\(384\) | 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 | 0.891546 | − | 0.452929i | \(-0.149621\pi\) |
−0.987501 | + | 0.157610i | \(0.949621\pi\) | |||||||
\(390\) | −0.534780 | + | 9.47175i | −0.0270796 | + | 0.479621i | ||||
\(391\) | 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 | ||||
\(400\) | −10.7193 | + | 6.07382i | −0.535965 | + | 0.303691i | ||||
\(401\) | −1.87733 | + | 1.36396i | −0.0937494 | + | 0.0681129i | −0.633673 | − | 0.773601i | \(-0.718453\pi\) |
0.539923 | + | 0.841714i | \(0.318453\pi\) | |||||||
\(402\) | 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 | ||||
\(405\) | 6.07639 | + | 23.0496i | 0.301938 | + | 1.14534i | ||||
\(406\) | 12.0000 | 0.595550 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 14.4195i | 0.713873i | ||||||||
\(409\) | 21.1350 | + | 15.3555i | 1.04506 | + | 0.759281i | 0.971267 | − | 0.237992i | \(-0.0764893\pi\) |
0.0737938 | + | 0.997274i | \(0.476489\pi\) | |||||||
\(410\) | −1.08509 | − | 1.68577i | −0.0535888 | − | 0.0832542i | ||||
\(411\) | 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 | ||||
\(415\) | 11.9810 | + | 18.6133i | 0.588123 | + | 0.913692i | ||||
\(416\) | −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 | \(0.402540\pi\) | |||||||
\(420\) | 6.38186 | + | 24.2083i | 0.311403 | + | 1.18124i | ||||
\(421\) | −5.26953 | + | 16.2179i | −0.256821 | + | 0.790414i | 0.736644 | + | 0.676281i | \(0.236409\pi\) |
−0.993465 | + | 0.114134i | \(0.963591\pi\) | |||||||
\(422\) | −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 | ||||
\(425\) | −9.52374 | − | 16.8078i | −0.461969 | − | 0.815300i | ||||
\(426\) | −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 | 0.484562 | − | 0.874757i | \(-0.338979\pi\) |
−0.682205 | + | 0.731161i | \(0.738979\pi\) | |||||||
\(432\) | −10.2677 | − | 3.33617i | −0.494004 | − | 0.160512i | ||||
\(433\) | 27.3310 | − | 8.88039i | 1.31345 | − | 0.426764i | 0.433206 | − | 0.901295i | \(-0.357382\pi\) |
0.880239 | + | 0.474531i | \(0.157382\pi\) | |||||||
\(434\) | 12.2359 | − | 8.88987i | 0.587340 | − | 0.426728i | ||||
\(435\) | −1.68707 | + | 29.8805i | −0.0808889 | + | 1.43266i | ||||
\(436\) | 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 | \(-0.172756\pi\) |
0.389187 | + | 0.921159i | \(0.372756\pi\) | |||||||
\(444\) | −1.85410 | − | 5.70634i | −0.0879918 | − | 0.270811i | ||||
\(445\) | 1.03611 | + | 0.0584995i | 0.0491164 | + | 0.00277314i | ||||
\(446\) | 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 | 0.999956 | + | 0.00933886i | \(0.00297270\pi\) |
0.317885 | + | 0.948129i | \(0.397027\pi\) | |||||||
\(450\) | 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 | ||||
\(455\) | 11.4955 | − | 29.5890i | 0.538919 | − | 1.38715i | ||||
\(456\) | 12.6694 | − | 9.20487i | 0.593300 | − | 0.431057i | ||||
\(457\) | 12.4688 | + | 17.1618i | 0.583266 | + | 0.802797i | 0.994049 | − | 0.108936i | \(-0.0347444\pi\) |
−0.410782 | + | 0.911733i | \(0.634744\pi\) | |||||||
\(458\) | −2.00456 | + | 0.651320i | −0.0936668 | + | 0.0304342i | ||||
\(459\) | 5.23110 | − | 16.0997i | 0.244167 | − | 0.751469i | ||||
\(460\) | 13.0506 | − | 3.44043i | 0.608486 | − | 0.160411i | ||||
\(461\) | 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 | ||||
\(465\) | 20.4159 | + | 31.7177i | 0.946767 | + | 1.47087i | ||||
\(466\) | 0.270589 | + | 0.832787i | 0.0125348 | + | 0.0385781i | ||||
\(467\) | −0.363941 | − | 0.500922i | −0.0168412 | − | 0.0231799i | 0.800513 | − | 0.599315i | \(-0.204560\pi\) |
−0.817355 | + | 0.576135i | \(0.804560\pi\) | |||||||
\(468\) | −3.16196 | − | 4.35207i | −0.146162 | − | 0.201174i | ||||
\(469\) | −2.28435 | − | 7.03050i | −0.105481 | − | 0.324638i | ||||
\(470\) | 11.1464 | − | 7.17468i | 0.514144 | − | 0.330943i | ||||
\(471\) | −34.1799 | − | 24.8332i | −1.57493 | − | 1.14425i | ||||
\(472\) | 2.44949i | 0.112747i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 1.46410 | 0.0672484 | ||||||||
\(475\) | −8.68826 | + | 19.0973i | −0.398645 | + | 0.876244i | ||||
\(476\) | 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 | −0.633668 | − | 0.773605i | \(-0.718451\pi\) |
0.539928 | + | 0.841711i | \(0.318451\pi\) | |||||||
\(480\) | −8.03950 | + | 20.6933i | −0.366951 | + | 0.944515i | ||||
\(481\) | −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 | \(-0.493116\pi\) |
−0.570153 | + | 0.821538i | \(0.693116\pi\) | |||||||
\(488\) | −21.5553 | + | 7.00374i | −0.975762 | + | 0.317044i | ||||
\(489\) | 8.03209 | − | 5.83565i | 0.363223 | − | 0.263897i | ||||
\(490\) | −0.273789 | + | 4.84921i | −0.0123685 | + | 0.219065i | ||||
\(491\) | −12.2719 | − | 37.7691i | −0.553825 | − | 1.70450i | −0.699027 | − | 0.715095i | \(-0.746383\pi\) |
0.145203 | − | 0.989402i | \(-0.453617\pi\) | |||||||
\(492\) | 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 | −0.995867 | − | 0.0908194i | \(-0.971051\pi\) |
0.752291 | − | 0.658831i | \(-0.228949\pi\) | |||||||
\(500\) | −2.79726 | − | 19.1618i | −0.125097 | − | 0.856943i | ||||
\(501\) | −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 | \(-0.347349\pi\) |
−0.148204 | + | 0.988957i | \(0.547349\pi\) | |||||||
\(504\) | 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 | −0.880436 | − | 0.474165i | \(-0.842750\pi\) |
0.990995 | + | 0.133900i | \(0.0427500\pi\) | |||||||
\(510\) | −8.05309 | − | 3.12869i | −0.356597 | − | 0.138541i | ||||
\(511\) | −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 | ||||
\(515\) | 9.17342 | − | 2.41832i | 0.404229 | − | 0.106564i | ||||
\(516\) | 21.5885 | 0.950379 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | − | 3.10583i | − | 0.136462i | ||||||
\(519\) | 34.0212 | + | 24.7179i | 1.49337 | + | 1.08499i | ||||
\(520\) | 15.4107 | − | 9.91949i | 0.675802 | − | 0.434999i | ||||
\(521\) | −2.85801 | − | 8.79605i | −0.125212 | − | 0.385362i | 0.868728 | − | 0.495290i | \(-0.164938\pi\) |
−0.993940 | + | 0.109928i | \(0.964938\pi\) | |||||||
\(522\) | 1.54315 | + | 2.12396i | 0.0675416 | + | 0.0929631i | ||||
\(523\) | 15.0659 | + | 20.7365i | 0.658788 | + | 0.906743i | 0.999441 | − | 0.0334458i | \(-0.0106481\pi\) |
−0.340653 | + | 0.940189i | \(0.610648\pi\) | |||||||
\(524\) | 1.67226 | + | 5.14668i | 0.0730530 | + | 0.224834i | ||||
\(525\) | −32.1151 | − | 3.63807i | −1.40162 | − | 0.158778i | ||||
\(526\) | 2.84504 | + | 2.06704i | 0.124050 | + | 0.0901273i | ||||
\(527\) | − | 33.7381i | − | 1.46965i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.8564 | 0.472018 | ||||||||
\(530\) | 0.640888 | + | 2.43108i | 0.0278384 | + | 0.105599i | ||||
\(531\) | −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 | ||||
\(535\) | −6.18437 | − | 2.40267i | −0.267374 | − | 0.103877i | ||||
\(536\) | 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 | 0.541510 | − | 0.840694i | \(-0.317853\pi\) |
−0.632212 | + | 0.774796i | \(0.717853\pi\) | |||||||
\(542\) | −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 | ||||
\(545\) | −20.5305 | − | 1.15916i | −0.879431 | − | 0.0496532i | ||||
\(546\) | −4.38685 | − | 13.5013i | −0.187740 | − | 0.577804i | ||||
\(547\) | −27.3310 | − | 8.88039i | −1.16859 | − | 0.379698i | −0.340474 | − | 0.940254i | \(-0.610587\pi\) |
−0.828116 | + | 0.560556i | \(0.810587\pi\) | |||||||
\(548\) | 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 | ||||
\(555\) | 7.73365 | + | 0.436646i | 0.328275 | + | 0.0185346i | ||||
\(556\) | 20.4422 | − | 14.8521i | 0.866942 | − | 0.629871i | ||||
\(557\) | 35.7614 | − | 11.6196i | 1.51526 | − | 0.492337i | 0.570834 | − | 0.821065i | \(-0.306620\pi\) |
0.944425 | + | 0.328728i | \(0.106620\pi\) | |||||||
\(558\) | 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 | \(-0.909270\pi\) |
0.563979 | + | 0.825789i | \(0.309270\pi\) | |||||||
\(564\) | −11.8417 | + | 36.4450i | −0.498625 | + | 1.53461i | ||||
\(565\) | −5.89527 | − | 2.29036i | −0.248016 | − | 0.0963561i | ||||
\(566\) | 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 | −0.542348 | − | 0.840154i | \(-0.682464\pi\) |
0.932599 | − | 0.360915i | \(-0.117536\pi\) | |||||||
\(570\) | 2.39183 | + | 9.07291i | 0.100183 | + | 0.380022i | ||||
\(571\) | 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 | ||||
\(575\) | −1.96127 | + | 17.3131i | −0.0817904 | + | 0.722006i | ||||
\(576\) | −0.513047 | − | 1.57900i | −0.0213769 | − | 0.0657915i | ||||
\(577\) | −2.21135 | − | 3.04366i | −0.0920596 | − | 0.126709i | 0.760503 | − | 0.649335i | \(-0.224953\pi\) |
−0.852562 | + | 0.522626i | \(0.824953\pi\) | |||||||
\(578\) | −0.630365 | − | 0.867623i | −0.0262197 | − | 0.0360884i | ||||
\(579\) | −9.06054 | − | 27.8855i | −0.376543 | − | 1.15888i | ||||
\(580\) | 22.5628 | − | 14.5231i | 0.936868 | − | 0.603041i | ||||
\(581\) | −26.7982 | − | 19.4700i | −1.11178 | − | 0.807752i | ||||
\(582\) | 9.14162i | 0.378932i | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −9.46410 | −0.391627 | ||||||||
\(585\) | 6.71541 | − | 1.77034i | 0.277648 | − | 0.0731944i | ||||
\(586\) | 2.41152 | − | 7.42190i | 0.0996190 | − | 0.306596i | ||||
\(587\) | −19.3930 | + | 6.30115i | −0.800433 | + | 0.260076i | −0.680540 | − | 0.732711i | \(-0.738255\pi\) |
−0.119892 | + | 0.992787i | \(0.538255\pi\) | |||||||
\(588\) | −8.25286 | − | 11.3591i | −0.340342 | − | 0.468441i | ||||
\(589\) | −29.6432 | + | 21.5370i | −1.22143 | + | 0.887419i | ||||
\(590\) | −1.36800 | − | 0.531479i | −0.0563198 | − | 0.0218807i | ||||
\(591\) | 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 | −0.999235 | − | 0.0391140i | \(-0.987546\pi\) |
−0.271581 | + | 0.962416i | \(0.587546\pi\) | |||||||
\(600\) | −13.7659 | − | 12.5978i | −0.561991 | − | 0.514303i | ||||
\(601\) | −6.18034 | − | 19.0211i | −0.252101 | − | 0.775888i | −0.994387 | − | 0.105804i | \(-0.966258\pi\) |
0.742286 | − | 0.670084i | \(-0.233742\pi\) | |||||||
\(602\) | 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 | −0.111367 | − | 0.993779i | \(-0.535523\pi\) |
0.979555 | − | 0.201179i | \(-0.0644772\pi\) | |||||||
\(608\) | −20.5095 | − | 6.66393i | −0.831769 | − | 0.270258i | ||||
\(609\) | −13.8392 | − | 42.5927i | −0.560793 | − | 1.72594i | ||||
\(610\) | 0.765489 | − | 13.5580i | 0.0309938 | − | 0.548945i | ||||
\(611\) | 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 | \(-0.411529\pi\) |
−0.343254 | + | 0.939243i | \(0.611529\pi\) | |||||||
\(614\) | −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 | −0.998525 | − | 0.0542900i | \(-0.982710\pi\) |
0.839735 | + | 0.542997i | \(0.182710\pi\) | |||||||
\(620\) | 12.2472 | − | 31.5236i | 0.491858 | − | 1.26602i | ||||
\(621\) | −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 | ||||
\(625\) | 24.3665 | + | 5.59235i | 0.974659 | + | 0.223694i | ||||
\(626\) | 8.87564 | 0.354742 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 37.8792i | 1.51154i | ||||||||
\(629\) | −5.60503 | − | 4.07230i | −0.223487 | − | 0.162373i | ||||
\(630\) | −2.38404 | + | 1.53455i | −0.0949823 | + | 0.0611380i | ||||
\(631\) | −4.73430 | − | 14.5707i | −0.188469 | − | 0.580049i | 0.811521 | − | 0.584323i | \(-0.198640\pi\) |
−0.999991 | + | 0.00427343i | \(0.998640\pi\) | |||||||
\(632\) | −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 | ||||
\(635\) | −1.08509 | − | 1.68577i | −0.0430605 | − | 0.0668977i | ||||
\(636\) | −5.87989 | − | 4.27199i | −0.233153 | − | 0.169396i | ||||
\(637\) | 17.8028i | 0.705371i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.00000 | 0.237356 | ||||||||
\(640\) | 24.7624 | − | 6.52793i | 0.978818 | − | 0.258039i | ||||
\(641\) | −2.42776 | + | 7.47189i | −0.0958909 | + | 0.295122i | −0.987485 | − | 0.157714i | \(-0.949588\pi\) |
0.891594 | + | 0.452836i | \(0.149588\pi\) | |||||||
\(642\) | −2.82191 | + | 0.916893i | −0.111372 | + | 0.0361869i | ||||
\(643\) | 6.18272 | + | 8.50978i | 0.243823 | + | 0.335593i | 0.913336 | − | 0.407207i | \(-0.133497\pi\) |
−0.669513 | + | 0.742800i | \(0.733497\pi\) | |||||||
\(644\) | −16.3390 | + | 11.8710i | −0.643848 | + | 0.467783i | ||||
\(645\) | −10.0930 | + | 25.9789i | −0.397411 | + | 1.02292i | ||||
\(646\) | 2.59336 | − | 7.98156i | 0.102035 | − | 0.314030i | ||||
\(647\) | 21.9606 | − | 30.2261i | 0.863358 | − | 1.18831i | −0.117400 | − | 0.993085i | \(-0.537456\pi\) |
0.980758 | − | 0.195226i | \(-0.0625441\pi\) | |||||||
\(648\) | − | 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 | \(-0.676378\pi\) |
0.0741421 | + | 0.997248i | \(0.476378\pi\) | |||||||
\(654\) | −7.43984 | + | 5.40536i | −0.290921 | + | 0.211366i | ||||
\(655\) | −6.97516 | − | 0.393822i | −0.272542 | − | 0.0153879i | ||||
\(656\) | −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 | ||||
\(665\) | 1.76980 | − | 31.3458i | 0.0686300 | − | 1.21554i | ||||
\(666\) | 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 | −0.0372864 | − | 0.999305i | \(-0.511871\pi\) |
0.961917 | − | 0.273341i | \(-0.0881286\pi\) | |||||||
\(674\) | 2.81958 | − | 8.67778i | 0.108606 | − | 0.334256i | ||||
\(675\) | 10.7997 | + | 19.0597i | 0.415680 | + | 0.733607i | ||||
\(676\) | 7.00629 | − | 5.09037i | 0.269473 | − | 0.195783i | ||||
\(677\) | −11.9637 | − | 16.4666i | −0.459801 | − | 0.632861i | 0.514667 | − | 0.857390i | \(-0.327916\pi\) |
−0.974467 | + | 0.224529i | \(0.927916\pi\) | |||||||
\(678\) | −2.68999 | + | 0.874032i | −0.103309 | + | 0.0335670i | ||||
\(679\) | 9.45235 | − | 29.0914i | 0.362748 | − | 1.11642i | ||||
\(680\) | 4.25457 | + | 16.1389i | 0.163155 | + | 0.618897i | ||||
\(681\) | 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 | ||||
\(685\) | 10.7280 | + | 16.6668i | 0.409897 | + | 0.636805i | ||||
\(686\) | 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 | ||||
\(690\) | 4.21748 | + | 6.55216i | 0.160557 | + | 0.249437i | ||||
\(691\) | −30.6690 | − | 22.2823i | −1.16670 | − | 0.847660i | −0.176093 | − | 0.984374i | \(-0.556346\pi\) |
−0.990611 | + | 0.136714i | \(0.956346\pi\) | |||||||
\(692\) | − | 37.7033i | − | 1.43326i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.26795 | 0.0860902 | ||||||||
\(695\) | 8.31549 | + | 31.5431i | 0.315424 | + | 1.19650i | ||||
\(696\) | 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 | ||||
\(700\) | 14.2856 | + | 25.2118i | 0.539945 | + | 0.952915i | ||||
\(701\) | −11.6983 | + | 36.0036i | −0.441838 | + | 1.35984i | 0.444077 | + | 0.895989i | \(0.353532\pi\) |
−0.885915 | + | 0.463848i | \(0.846468\pi\) | |||||||
\(702\) | −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 | −0.547465 | − | 0.836829i | \(-0.684407\pi\) |
0.626695 | + | 0.779264i | \(0.284407\pi\) | |||||||
\(710\) | −0.534780 | + | 9.47175i | −0.0200699 | + | 0.355468i | ||||
\(711\) | −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 | 0.624011 | + | 0.781415i | \(0.285502\pi\) |
−0.0455311 | + | 0.998963i | \(0.514498\pi\) | |||||||
\(720\) | 4.02711 | + | 0.227373i | 0.150082 | + | 0.00847369i | ||||
\(721\) | −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 | ||||
\(730\) | 2.05348 | − | 5.28556i | 0.0760027 | − | 0.195627i | ||||
\(731\) | 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 | \(-0.655047\pi\) |
0.140755 | + | 0.990044i | \(0.455047\pi\) | |||||||
\(734\) | −2.70430 | + | 8.32297i | −0.0998174 | + | 0.307206i | ||||
\(735\) | 17.5275 | − | 4.62065i | 0.646512 | − | 0.170435i | ||||
\(736\) | −17.9090 | −0.660133 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0.656339i | 0.0241602i | ||||||||
\(739\) | 31.4936 | + | 22.8814i | 1.15851 | + | 0.841707i | 0.989589 | − | 0.143923i | \(-0.0459717\pi\) |
0.168921 | + | 0.985630i | \(0.445972\pi\) | |||||||
\(740\) | −3.75887 | − | 5.83967i | −0.138179 | − | 0.214671i | ||||
\(741\) | 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 | 0.957550 | + | 0.288267i | \(0.0930789\pi\) |
−0.0217414 | + | 0.999764i | \(0.506921\pi\) | |||||||
\(744\) | −10.0704 | − | 30.9935i | −0.369198 | − | 1.13628i | ||||
\(745\) | −19.3061 | + | 12.4269i | −0.707321 | + | 0.455287i | ||||
\(746\) | −0.0736486 | − | 0.0535088i | −0.00269647 | − | 0.00195910i | ||||
\(747\) | − | 7.24693i | − | 0.265151i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.92820 | 0.362769 | ||||||||
\(750\) | 10.0226 | − | 4.95464i | 0.365972 | − | 0.180918i | ||||
\(751\) | 15.0309 | − | 46.2604i | 0.548485 | − | 1.68806i | −0.164070 | − | 0.986449i | \(-0.552462\pi\) |
0.712556 | − | 0.701616i | \(-0.247538\pi\) | |||||||
\(752\) | 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 | ||||
\(755\) | 3.39789 | − | 8.74602i | 0.123662 | − | 0.318300i | ||||
\(756\) | −7.84665 | + | 24.1495i | −0.285380 | + | 0.878309i | ||||
\(757\) | 29.2569 | − | 40.2687i | 1.06336 | − | 1.46359i | 0.186741 | − | 0.982409i | \(-0.440207\pi\) |
0.876621 | − | 0.481182i | \(-0.159793\pi\) | |||||||
\(758\) | − | 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 | 0.257236 | − | 0.966349i | \(-0.417188\pi\) |
−0.839562 | + | 0.543264i | \(0.817188\pi\) | |||||||
\(762\) | −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 | ||||
\(765\) | −0.356520 | + | 6.31450i | −0.0128900 | + | 0.228301i | ||||
\(766\) | 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 | \(-0.469498\pi\) |
−0.507683 | + | 0.861544i | \(0.669498\pi\) | |||||||
\(774\) | 0.755504 | + | 2.32520i | 0.0271560 | + | 0.0835777i | ||||
\(775\) | 32.2087 | + | 29.4757i | 1.15697 | + | 1.05880i | ||||
\(776\) | 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 | ||||
\(785\) | −45.5826 | − | 17.7092i | −1.62691 | − | 0.632067i | ||||
\(786\) | −2.52766 | + | 1.83645i | −0.0901585 | + | 0.0655040i | ||||
\(787\) | 10.2196 | + | 14.0661i | 0.364290 | + | 0.501403i | 0.951338 | − | 0.308150i | \(-0.0997098\pi\) |
−0.587048 | + | 0.809552i | \(0.699710\pi\) | |||||||
\(788\) | −28.4122 | + | 9.23168i | −1.01214 | + | 0.328865i | ||||
\(789\) | 4.05565 | − | 12.4820i | 0.144385 | − | 0.444371i | ||||
\(790\) | 1.63867 | − | 0.431992i | 0.0583014 | − | 0.0153696i | ||||
\(791\) | 9.46410 | 0.336505 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 49.7749i | − | 1.76756i | ||||||
\(794\) | −13.8114 | − | 10.0346i | −0.490147 | − | 0.356113i | ||||
\(795\) | 7.88973 | − | 5.07844i | 0.279820 | − | 0.180114i | ||||
\(796\) | 1.07047 | + | 3.29456i | 0.0379417 | + | 0.116772i | ||||
\(797\) | 21.2705 | + | 29.2763i | 0.753440 | + | 1.03702i | 0.997731 | + | 0.0673193i | \(0.0214446\pi\) |
−0.244292 | + | 0.969702i | \(0.578555\pi\) | |||||||
\(798\) | −8.25286 | − | 11.3591i | −0.292148 | − | 0.402107i | ||||
\(799\) | 13.6736 | + | 42.0830i | 0.483737 | + | 1.48879i | ||||
\(800\) | −2.89241 | + | 25.5328i | −0.102262 | + | 0.902720i | ||||
\(801\) | −0.274860 | − | 0.199698i | −0.00971171 | − | 0.00705597i | ||||
\(802\) | 1.20118i | 0.0424153i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −7.39230 | −0.260706 | ||||||||
\(805\) | −6.64640 | − | 25.2118i | −0.234255 | − | 0.888598i | ||||
\(806\) | −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 | −0.361546 | − | 0.932354i | \(-0.617751\pi\) |
0.774998 | + | 0.631964i | \(0.217751\pi\) | |||||||
\(810\) | 11.5015 | + | 4.46840i | 0.404120 | + | 0.157004i | ||||
\(811\) | −5.86538 | + | 18.0518i | −0.205961 | + | 0.633884i | 0.793711 | + | 0.608295i | \(0.208146\pi\) |
−0.999673 | + | 0.0255890i | \(0.991854\pi\) | |||||||
\(812\) | −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 | ||||
\(820\) | 6.69754 | + | 0.378147i | 0.233888 | + | 0.0132055i | ||||
\(821\) | −9.02211 | − | 27.7672i | −0.314874 | − | 0.969082i | −0.975806 | − | 0.218636i | \(-0.929839\pi\) |
0.660933 | − | 0.750445i | \(-0.270161\pi\) | |||||||
\(822\) | 8.43037 | + | 2.73919i | 0.294043 | + | 0.0955404i | ||||
\(823\) | −3.97137 | + | 5.46612i | −0.138433 | + | 0.190537i | −0.872605 | − | 0.488427i | \(-0.837571\pi\) |
0.734171 | + | 0.678964i | \(0.237571\pi\) | |||||||
\(824\) | −8.19615 | −0.285526 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.19615 | 0.0764139 | ||||||||
\(827\) | −20.0316 | + | 27.5712i | −0.696568 | + | 0.958743i | 0.303415 | + | 0.952858i | \(0.401873\pi\) |
−0.999983 | + | 0.00588462i | \(0.998127\pi\) | |||||||
\(828\) | −4.20225 | − | 1.36539i | −0.146038 | − | 0.0474507i | ||||
\(829\) | 3.08423 | + | 9.49227i | 0.107120 | + | 0.329680i | 0.990222 | − | 0.139500i | \(-0.0445495\pi\) |
−0.883103 | + | 0.469180i | \(0.844550\pi\) | |||||||
\(830\) | 11.4402 | + | 0.645919i | 0.397095 | + | 0.0224202i | ||||
\(831\) | 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 | −0.499573 | − | 0.866272i | \(-0.666510\pi\) |
0.913345 | − | 0.407187i | \(-0.133490\pi\) | |||||||
\(840\) | 26.0280 | + | 10.1121i | 0.898052 | + | 0.348900i | ||||
\(841\) | −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 | ||||
\(845\) | 2.85002 | + | 10.8110i | 0.0980438 | + | 0.371909i | ||||
\(846\) | −4.33975 | −0.149204 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 5.35225i | 0.183797i | ||||||||
\(849\) | −12.6113 | − | 9.16267i | −0.432820 | − | 0.314462i | ||||
\(850\) | −9.93645 | − | 1.12562i | −0.340817 | − | 0.0386085i | ||||
\(851\) | 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 | −0.958637 | − | 0.284631i | \(-0.908129\pi\) |
0.0255350 | − | 0.999674i | \(-0.491871\pi\) | |||||||
\(854\) | 6.27938 | + | 19.3260i | 0.214876 | + | 0.661320i | ||||
\(855\) | 5.77568 | − | 3.71768i | 0.197524 | − | 0.127142i | ||||
\(856\) | 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 | \(0.376384\pi\) | |||||||
\(860\) | 24.1626 | − | 6.36981i | 0.823937 | − | 0.217209i | ||||
\(861\) | 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 | \(-0.294056\pi\) |
−0.945120 | + | 0.326723i | \(0.894056\pi\) | |||||||
\(864\) | −18.2164 | + | 13.2350i | −0.619733 | + | 0.450263i | ||||
\(865\) | 45.3709 | + | 17.6269i | 1.54266 | + | 0.599334i | ||||
\(866\) | 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 | ||||
\(875\) | −37.0178 | + | 5.40390i | −1.25143 | + | 0.182685i | ||||
\(876\) | 5.06550 | + | 15.5900i | 0.171147 | + | 0.526738i | ||||
\(877\) | 11.3135 | + | 3.67598i | 0.382030 | + | 0.124129i | 0.493735 | − | 0.869612i | \(-0.335631\pi\) |
−0.111705 | + | 0.993741i | \(0.535631\pi\) | |||||||
\(878\) | 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 | \(-0.518199\pi\) |
−0.633055 | + | 0.774107i | \(0.718199\pi\) | |||||||
\(884\) | 8.77370 | + | 27.0027i | 0.295092 | + | 0.908199i | ||||
\(885\) | −0.308755 | + | 5.46852i | −0.0103787 | + | 0.183822i | ||||
\(886\) | 11.5430 | − | 8.38649i | 0.387795 | − | 0.281750i | ||||
\(887\) | −14.9269 | + | 4.85004i | −0.501196 | + | 0.162848i | −0.548694 | − | 0.836023i | \(-0.684875\pi\) |
0.0474989 | + | 0.998871i | \(0.484875\pi\) | |||||||
\(888\) | −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 | ||||
\(895\) | −12.5223 | + | 32.2317i | −0.418573 | + | 1.07739i | ||||
\(896\) | −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 | ||||
\(900\) | −2.62533 | + | 5.77062i | −0.0875109 | + | 0.192354i | ||||
\(901\) | −8.39230 | −0.279588 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 41.7057i | − | 1.38788i | ||||||
\(904\) | 4.42055 | + | 3.21172i | 0.147025 | + | 0.106820i | ||||
\(905\) | −32.7015 | + | 21.0492i | −1.08704 | + | 0.699701i | ||||
\(906\) | −1.29668 | − | 3.99078i | −0.0430794 | − | 0.132585i | ||||
\(907\) | −17.7009 | − | 24.3632i | −0.587749 | − | 0.808967i | 0.406769 | − | 0.913531i | \(-0.366655\pi\) |
−0.994518 | + | 0.104564i | \(0.966655\pi\) | |||||||
\(908\) | −20.4771 | − | 28.1843i | −0.679556 | − | 0.935329i | ||||
\(909\) | 4.38685 | + | 13.5013i | 0.145503 | + | 0.447811i | ||||
\(910\) | −8.89357 | − | 13.8168i | −0.294819 | − | 0.458023i | ||||
\(911\) | 24.4717 | + | 17.7797i | 0.810784 | + | 0.589069i | 0.914058 | − | 0.405584i | \(-0.132932\pi\) |
−0.103274 | + | 0.994653i | \(0.532932\pi\) | |||||||
\(912\) | 19.9749i | 0.661434i | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 10.9808 | 0.363211 | ||||||||
\(915\) | −49.0053 | + | 12.9189i | −1.62006 | + | 0.427086i | ||||
\(916\) | 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 | −0.304970 | − | 0.952362i | \(-0.598646\pi\) |
0.811509 | + | 0.584339i | \(0.198646\pi\) | |||||||
\(920\) | 5.45137 | − | 14.0316i | 0.179726 | − | 0.462607i | ||||
\(921\) | −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 | −0.990288 | − | 0.139029i | \(-0.955602\pi\) |
−0.173792 | + | 0.984782i | \(0.555602\pi\) | |||||||
\(930\) | 19.4944 | + | 1.10067i | 0.639247 | + | 0.0360922i | ||||
\(931\) | 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 | \(-0.970139\pi\) |
0.396746 | + | 0.917928i | \(0.370139\pi\) | |||||||
\(938\) | −3.63925 | − | 1.18247i | −0.118826 | − | 0.0386089i | ||||
\(939\) | −10.2360 | − | 31.5031i | −0.334039 | − | 1.02807i | ||||
\(940\) | −2.50033 | + | 44.2845i | −0.0815516 | + | 1.44440i | ||||
\(941\) | −21.8435 | + | 15.8702i | −0.712076 | + | 0.517354i | −0.883843 | − | 0.467784i | \(-0.845053\pi\) |
0.171766 | + | 0.985138i | \(0.445053\pi\) | |||||||
\(942\) | −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 | ||||
\(950\) | 5.35403 | + | 9.44900i | 0.173708 | + | 0.306566i | ||||
\(951\) | −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 | \(-0.512853\pi\) |
0.554647 | + | 0.832086i | \(0.312853\pi\) | |||||||
\(954\) | 0.254347 | − | 0.782801i | 0.00823480 | − | 0.0253441i | ||||
\(955\) | 4.14276 | + | 15.7147i | 0.134057 | + | 0.508517i | ||||
\(956\) | 9.80385 | 0.317079 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.31268i | 0.0424107i | ||||||||
\(959\) | −23.9956 | − | 17.4339i | −0.774860 | − | 0.562969i | ||||
\(960\) | −5.30257 | − | 8.23793i | −0.171140 | − | 0.265878i | ||||
\(961\) | 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 | ||||
\(965\) | −18.3686 | − | 28.5370i | −0.591308 | − | 0.918639i | ||||
\(966\) | −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 | ||||||||
\(970\) | 2.69729 | + | 10.2316i | 0.0866048 | + | 0.328518i | ||||
\(971\) | −7.70324 | + | 23.7081i | −0.247209 | + | 0.760830i | 0.748057 | + | 0.663635i | \(0.230987\pi\) |
−0.995265 | + | 0.0971952i | \(0.969013\pi\) | |||||||
\(972\) | −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 | ||||
\(975\) | 35.6548 | − | 20.2029i | 1.14187 | − | 0.647010i | ||||
\(976\) | 8.93336 | − | 27.4941i | 0.285950 | − | 0.880063i | ||||
\(977\) | 17.1142 | − | 23.5557i | 0.547533 | − | 0.753614i | −0.442142 | − | 0.896945i | \(-0.645781\pi\) |
0.989675 | + | 0.143331i | \(0.0457813\pi\) | |||||||
\(978\) | − | 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 | \(-0.248285\pi\) |
0.988517 | + | 0.151112i | \(0.0482853\pi\) | |||||||
\(984\) | 5.22957 | − | 3.79950i | 0.166713 | − | 0.121124i | ||||
\(985\) | 2.17409 | − | 38.5063i | 0.0692722 | − | 1.22691i | ||||
\(986\) | −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 | ||||
\(995\) | −4.46502 | − | 0.252098i | −0.141551 | − | 0.00799204i | ||||
\(996\) | −26.7982 | + | 19.4700i | −0.849132 | + | 0.616931i | ||||
\(997\) | 32.4472 | − | 10.5427i | 1.02761 | − | 0.333892i | 0.253767 | − | 0.967265i | \(-0.418330\pi\) |
0.773846 | + | 0.633374i | \(0.218330\pi\) | |||||||
\(998\) | −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.444.3 | 16 | ||
5.4 | even | 2 | inner | 605.2.j.e.444.2 | 16 | ||
11.2 | odd | 10 | 605.2.j.f.269.3 | 16 | |||
11.3 | even | 5 | inner | 605.2.j.e.124.2 | 16 | ||
11.4 | even | 5 | inner | 605.2.j.e.9.3 | 16 | ||
11.5 | even | 5 | 605.2.b.e.364.3 | yes | 4 | ||
11.6 | odd | 10 | 605.2.b.d.364.2 | ✓ | 4 | ||
11.7 | odd | 10 | 605.2.j.f.9.2 | 16 | |||
11.8 | odd | 10 | 605.2.j.f.124.3 | 16 | |||
11.9 | even | 5 | inner | 605.2.j.e.269.2 | 16 | ||
11.10 | odd | 2 | 605.2.j.f.444.2 | 16 | |||
55.4 | even | 10 | inner | 605.2.j.e.9.2 | 16 | ||
55.9 | even | 10 | inner | 605.2.j.e.269.3 | 16 | ||
55.14 | even | 10 | inner | 605.2.j.e.124.3 | 16 | ||
55.17 | even | 20 | 3025.2.a.y.1.3 | 4 | |||
55.19 | odd | 10 | 605.2.j.f.124.2 | 16 | |||
55.24 | odd | 10 | 605.2.j.f.269.2 | 16 | |||
55.27 | odd | 20 | 3025.2.a.z.1.2 | 4 | |||
55.28 | even | 20 | 3025.2.a.y.1.2 | 4 | |||
55.29 | odd | 10 | 605.2.j.f.9.3 | 16 | |||
55.38 | odd | 20 | 3025.2.a.z.1.3 | 4 | |||
55.39 | odd | 10 | 605.2.b.d.364.3 | yes | 4 | ||
55.49 | even | 10 | 605.2.b.e.364.2 | yes | 4 | ||
55.54 | odd | 2 | 605.2.j.f.444.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
605.2.b.d.364.2 | ✓ | 4 | 11.6 | odd | 10 | ||
605.2.b.d.364.3 | yes | 4 | 55.39 | odd | 10 | ||
605.2.b.e.364.2 | yes | 4 | 55.49 | even | 10 | ||
605.2.b.e.364.3 | yes | 4 | 11.5 | even | 5 | ||
605.2.j.e.9.2 | 16 | 55.4 | even | 10 | inner | ||
605.2.j.e.9.3 | 16 | 11.4 | even | 5 | inner | ||
605.2.j.e.124.2 | 16 | 11.3 | even | 5 | inner | ||
605.2.j.e.124.3 | 16 | 55.14 | even | 10 | inner | ||
605.2.j.e.269.2 | 16 | 11.9 | even | 5 | inner | ||
605.2.j.e.269.3 | 16 | 55.9 | even | 10 | inner | ||
605.2.j.e.444.2 | 16 | 5.4 | even | 2 | inner | ||
605.2.j.e.444.3 | 16 | 1.1 | even | 1 | trivial | ||
605.2.j.f.9.2 | 16 | 11.7 | odd | 10 | |||
605.2.j.f.9.3 | 16 | 55.29 | odd | 10 | |||
605.2.j.f.124.2 | 16 | 55.19 | odd | 10 | |||
605.2.j.f.124.3 | 16 | 11.8 | odd | 10 | |||
605.2.j.f.269.2 | 16 | 55.24 | odd | 10 | |||
605.2.j.f.269.3 | 16 | 11.2 | odd | 10 | |||
605.2.j.f.444.2 | 16 | 11.10 | odd | 2 | |||
605.2.j.f.444.3 | 16 | 55.54 | odd | 2 | |||
3025.2.a.y.1.2 | 4 | 55.28 | even | 20 | |||
3025.2.a.y.1.3 | 4 | 55.17 | even | 20 | |||
3025.2.a.z.1.2 | 4 | 55.27 | odd | 20 | |||
3025.2.a.z.1.3 | 4 | 55.38 | odd | 20 |