Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,2,Mod(239,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.239");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.f (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.04841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 239.19 | ||
Character | \(\chi\) | \(=\) | 507.239 |
Dual form | 507.2.f.g.437.20 |
$q$-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 \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.38407 | + | 1.38407i | 0.978684 | + | 0.978684i | 0.999778 | − | 0.0210936i | \(-0.00671481\pi\) |
−0.0210936 | + | 0.999778i | \(0.506715\pi\) | |||||||
\(3\) | 0.526444 | − | 1.65011i | 0.303943 | − | 0.952690i | ||||
\(4\) | 1.83129i | 0.915644i | ||||||||
\(5\) | −1.04664 | − | 1.04664i | −0.468071 | − | 0.468071i | 0.433218 | − | 0.901289i | \(-0.357378\pi\) |
−0.901289 | + | 0.433218i | \(0.857378\pi\) | |||||||
\(6\) | 3.01250 | − | 1.55523i | 1.22985 | − | 0.634919i | ||||
\(7\) | −3.17096 | − | 3.17096i | −1.19851 | − | 1.19851i | −0.974613 | − | 0.223896i | \(-0.928122\pi\) |
−0.223896 | − | 0.974613i | \(-0.571878\pi\) | |||||||
\(8\) | 0.233508 | − | 0.233508i | 0.0825576 | − | 0.0825576i | ||||
\(9\) | −2.44571 | − | 1.73738i | −0.815238 | − | 0.579127i | ||||
\(10\) | − | 2.89724i | − | 0.916188i | ||||||
\(11\) | −0.108328 | + | 0.108328i | −0.0326623 | + | 0.0326623i | −0.723249 | − | 0.690587i | \(-0.757352\pi\) |
0.690587 | + | 0.723249i | \(0.257352\pi\) | |||||||
\(12\) | 3.02182 | + | 0.964071i | 0.872325 | + | 0.278303i | ||||
\(13\) | 0 | 0 | ||||||||
\(14\) | − | 8.77764i | − | 2.34592i | ||||||
\(15\) | −2.27806 | + | 1.17607i | −0.588194 | + | 0.303660i | ||||
\(16\) | 4.30896 | 1.07724 | ||||||||
\(17\) | 3.16727 | 0.768177 | 0.384088 | − | 0.923296i | \(-0.374516\pi\) | ||||
0.384088 | + | 0.923296i | \(0.374516\pi\) | |||||||
\(18\) | −0.980382 | − | 5.78968i | −0.231078 | − | 1.36464i | ||||
\(19\) | −0.846216 | + | 0.846216i | −0.194135 | + | 0.194135i | −0.797480 | − | 0.603345i | \(-0.793834\pi\) |
0.603345 | + | 0.797480i | \(0.293834\pi\) | |||||||
\(20\) | 1.91670 | − | 1.91670i | 0.428587 | − | 0.428587i | ||||
\(21\) | −6.90175 | + | 3.56309i | −1.50609 | + | 0.777530i | ||||
\(22\) | −0.299868 | −0.0639321 | ||||||||
\(23\) | 6.70271 | 1.39761 | 0.698805 | − | 0.715312i | \(-0.253715\pi\) | ||||
0.698805 | + | 0.715312i | \(0.253715\pi\) | |||||||
\(24\) | −0.262385 | − | 0.508243i | −0.0535590 | − | 0.103745i | ||||
\(25\) | − | 2.80909i | − | 0.561819i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.15440 | + | 3.12106i | −0.799514 | + | 0.600648i | ||||
\(28\) | 5.80694 | − | 5.80694i | 1.09741 | − | 1.09741i | ||||
\(29\) | 1.98510i | 0.368624i | 0.982868 | + | 0.184312i | \(0.0590058\pi\) | ||||
−0.982868 | + | 0.184312i | \(0.940994\pi\) | |||||||
\(30\) | −4.78076 | − | 1.52523i | −0.872843 | − | 0.278469i | ||||
\(31\) | −3.64859 | + | 3.64859i | −0.655306 | + | 0.655306i | −0.954266 | − | 0.298960i | \(-0.903360\pi\) |
0.298960 | + | 0.954266i | \(0.403360\pi\) | |||||||
\(32\) | 5.49688 | + | 5.49688i | 0.971720 | + | 0.971720i | ||||
\(33\) | 0.121725 | + | 0.235783i | 0.0211896 | + | 0.0410445i | ||||
\(34\) | 4.38372 | + | 4.38372i | 0.751802 | + | 0.751802i | ||||
\(35\) | 6.63770i | 1.12198i | ||||||||
\(36\) | 3.18164 | − | 4.47881i | 0.530274 | − | 0.746468i | ||||
\(37\) | −2.31488 | − | 2.31488i | −0.380563 | − | 0.380563i | 0.490742 | − | 0.871305i | \(-0.336726\pi\) |
−0.871305 | + | 0.490742i | \(0.836726\pi\) | |||||||
\(38\) | −2.34244 | −0.379994 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.488797 | −0.0772856 | ||||||||
\(41\) | 5.91863 | + | 5.91863i | 0.924334 | + | 0.924334i | 0.997332 | − | 0.0729976i | \(-0.0232566\pi\) |
−0.0729976 | + | 0.997332i | \(0.523257\pi\) | |||||||
\(42\) | −14.4841 | − | 4.62094i | −2.23494 | − | 0.713026i | ||||
\(43\) | − | 2.78318i | − | 0.424432i | −0.977223 | − | 0.212216i | \(-0.931932\pi\) | ||
0.977223 | − | 0.212216i | \(-0.0680680\pi\) | |||||||
\(44\) | −0.198381 | − | 0.198381i | −0.0299070 | − | 0.0299070i | ||||
\(45\) | 0.741369 | + | 4.37819i | 0.110517 | + | 0.652662i | ||||
\(46\) | 9.27700 | + | 9.27700i | 1.36782 | + | 1.36782i | ||||
\(47\) | 4.06533 | − | 4.06533i | 0.592990 | − | 0.592990i | −0.345448 | − | 0.938438i | \(-0.612273\pi\) |
0.938438 | + | 0.345448i | \(0.112273\pi\) | |||||||
\(48\) | 2.26843 | − | 7.11025i | 0.327419 | − | 1.02628i | ||||
\(49\) | 13.1099i | 1.87285i | ||||||||
\(50\) | 3.88798 | − | 3.88798i | 0.549843 | − | 0.549843i | ||||
\(51\) | 1.66739 | − | 5.22634i | 0.233482 | − | 0.731835i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.628103i | 0.0862766i | 0.999069 | + | 0.0431383i | \(0.0137356\pi\) | ||||
−0.999069 | + | 0.0431383i | \(0.986264\pi\) | |||||||
\(54\) | −10.0697 | − | 1.43021i | −1.37032 | − | 0.194627i | ||||
\(55\) | 0.226762 | 0.0305765 | ||||||||
\(56\) | −1.48089 | −0.197892 | ||||||||
\(57\) | 0.950863 | + | 1.84183i | 0.125945 | + | 0.243957i | ||||
\(58\) | −2.74752 | + | 2.74752i | −0.360767 | + | 0.360767i | ||||
\(59\) | 6.20927 | − | 6.20927i | 0.808378 | − | 0.808378i | −0.176011 | − | 0.984388i | \(-0.556319\pi\) |
0.984388 | + | 0.176011i | \(0.0563193\pi\) | |||||||
\(60\) | −2.15372 | − | 4.17179i | −0.278045 | − | 0.538576i | ||||
\(61\) | 5.83263 | 0.746792 | 0.373396 | − | 0.927672i | \(-0.378193\pi\) | ||||
0.373396 | + | 0.927672i | \(0.378193\pi\) | |||||||
\(62\) | −10.0998 | −1.28267 | ||||||||
\(63\) | 2.24610 | + | 13.2644i | 0.282981 | + | 1.67116i | ||||
\(64\) | 6.59818i | 0.824773i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.157864 | + | 0.494815i | −0.0194317 | + | 0.0609075i | ||||
\(67\) | −0.475547 | + | 0.475547i | −0.0580973 | + | 0.0580973i | −0.735558 | − | 0.677461i | \(-0.763080\pi\) |
0.677461 | + | 0.735558i | \(0.263080\pi\) | |||||||
\(68\) | 5.80019i | 0.703377i | ||||||||
\(69\) | 3.52860 | − | 11.0602i | 0.424794 | − | 1.33149i | ||||
\(70\) | −9.18702 | + | 9.18702i | −1.09806 | + | 1.09806i | ||||
\(71\) | −8.09127 | − | 8.09127i | −0.960257 | − | 0.960257i | 0.0389831 | − | 0.999240i | \(-0.487588\pi\) |
−0.999240 | + | 0.0389831i | \(0.987588\pi\) | |||||||
\(72\) | −0.976786 | + | 0.165402i | −0.115115 | + | 0.0194928i | ||||
\(73\) | 3.92370 | + | 3.92370i | 0.459235 | + | 0.459235i | 0.898404 | − | 0.439169i | \(-0.144727\pi\) |
−0.439169 | + | 0.898404i | \(0.644727\pi\) | |||||||
\(74\) | − | 6.40789i | − | 0.744902i | ||||||
\(75\) | −4.63531 | − | 1.47883i | −0.535239 | − | 0.170761i | ||||
\(76\) | −1.54967 | − | 1.54967i | −0.177759 | − | 0.177759i | ||||
\(77\) | 0.687010 | 0.0782921 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.46386 | −0.614733 | −0.307366 | − | 0.951591i | \(-0.599448\pi\) | ||||
−0.307366 | + | 0.951591i | \(0.599448\pi\) | |||||||
\(80\) | −4.50993 | − | 4.50993i | −0.504225 | − | 0.504225i | ||||
\(81\) | 2.96302 | + | 8.49826i | 0.329225 | + | 0.944252i | ||||
\(82\) | 16.3836i | 1.80926i | ||||||||
\(83\) | 6.40765 | + | 6.40765i | 0.703331 | + | 0.703331i | 0.965124 | − | 0.261793i | \(-0.0843139\pi\) |
−0.261793 | + | 0.965124i | \(0.584314\pi\) | |||||||
\(84\) | −6.52505 | − | 12.6391i | −0.711941 | − | 1.37904i | ||||
\(85\) | −3.31499 | − | 3.31499i | −0.359561 | − | 0.359561i | ||||
\(86\) | 3.85212 | − | 3.85212i | 0.415384 | − | 0.415384i | ||||
\(87\) | 3.27563 | + | 1.04505i | 0.351185 | + | 0.112041i | ||||
\(88\) | 0.0505912i | 0.00539304i | ||||||||
\(89\) | −3.75466 | + | 3.75466i | −0.397993 | + | 0.397993i | −0.877525 | − | 0.479532i | \(-0.840807\pi\) |
0.479532 | + | 0.877525i | \(0.340807\pi\) | |||||||
\(90\) | −5.03360 | + | 7.08582i | −0.530588 | + | 0.746911i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 12.2746i | 1.27971i | ||||||||
\(93\) | 4.09979 | + | 7.94134i | 0.425128 | + | 0.823479i | ||||
\(94\) | 11.2534 | 1.16070 | ||||||||
\(95\) | 1.77137 | 0.181738 | ||||||||
\(96\) | 11.9642 | − | 6.17664i | 1.22110 | − | 0.630401i | ||||
\(97\) | −3.16443 | + | 3.16443i | −0.321299 | + | 0.321299i | −0.849265 | − | 0.527966i | \(-0.822955\pi\) |
0.527966 | + | 0.849265i | \(0.322955\pi\) | |||||||
\(98\) | −18.1451 | + | 18.1451i | −1.83293 | + | 1.83293i | ||||
\(99\) | 0.453148 | − | 0.0767327i | 0.0455431 | − | 0.00771193i | ||||
\(100\) | 5.14426 | 0.514426 | ||||||||
\(101\) | 1.68098 | 0.167263 | 0.0836317 | − | 0.996497i | \(-0.473348\pi\) | ||||
0.0836317 | + | 0.996497i | \(0.473348\pi\) | |||||||
\(102\) | 9.54140 | − | 4.92583i | 0.944740 | − | 0.487730i | ||||
\(103\) | 4.41524i | 0.435046i | 0.976055 | + | 0.217523i | \(0.0697977\pi\) | ||||
−0.976055 | + | 0.217523i | \(0.930202\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 10.9529 | + | 3.49438i | 1.06890 | + | 0.341016i | ||||
\(106\) | −0.869337 | + | 0.869337i | −0.0844375 | + | 0.0844375i | ||||
\(107\) | − | 15.4776i | − | 1.49628i | −0.663541 | − | 0.748140i | \(-0.730947\pi\) | ||
0.663541 | − | 0.748140i | \(-0.269053\pi\) | |||||||
\(108\) | −5.71556 | − | 7.60790i | −0.549980 | − | 0.732070i | ||||
\(109\) | 8.78130 | − | 8.78130i | 0.841096 | − | 0.841096i | −0.147905 | − | 0.989002i | \(-0.547253\pi\) |
0.989002 | + | 0.147905i | \(0.0472531\pi\) | |||||||
\(110\) | 0.313854 | + | 0.313854i | 0.0299248 | + | 0.0299248i | ||||
\(111\) | −5.03845 | + | 2.60114i | −0.478228 | + | 0.246889i | ||||
\(112\) | −13.6635 | − | 13.6635i | −1.29108 | − | 1.29108i | ||||
\(113\) | 4.79085i | 0.450685i | 0.974280 | + | 0.225343i | \(0.0723502\pi\) | ||||
−0.974280 | + | 0.225343i | \(0.927650\pi\) | |||||||
\(114\) | −1.23316 | + | 3.86528i | −0.115496 | + | 0.362017i | ||||
\(115\) | −7.01531 | − | 7.01531i | −0.654181 | − | 0.654181i | ||||
\(116\) | −3.63530 | −0.337529 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 17.1881 | 1.58229 | ||||||||
\(119\) | −10.0433 | − | 10.0433i | −0.920667 | − | 0.920667i | ||||
\(120\) | −0.257325 | + | 0.806568i | −0.0234904 | + | 0.0736293i | ||||
\(121\) | 10.9765i | 0.997866i | ||||||||
\(122\) | 8.07276 | + | 8.07276i | 0.730873 | + | 0.730873i | ||||
\(123\) | 12.8822 | − | 6.65055i | 1.16155 | − | 0.599660i | ||||
\(124\) | −6.68162 | − | 6.68162i | −0.600027 | − | 0.600027i | ||||
\(125\) | −8.17330 | + | 8.17330i | −0.731042 | + | 0.731042i | ||||
\(126\) | −15.2501 | + | 21.4676i | −1.35859 | + | 1.91249i | ||||
\(127\) | − | 15.9755i | − | 1.41759i | −0.705413 | − | 0.708796i | \(-0.749239\pi\) | ||
0.705413 | − | 0.708796i | \(-0.250761\pi\) | |||||||
\(128\) | 1.86142 | − | 1.86142i | 0.164528 | − | 0.164528i | ||||
\(129\) | −4.59255 | − | 1.46519i | −0.404352 | − | 0.129003i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.7681i | 1.63978i | 0.572524 | + | 0.819888i | \(0.305965\pi\) | ||||
−0.572524 | + | 0.819888i | \(0.694035\pi\) | |||||||
\(132\) | −0.431786 | + | 0.222913i | −0.0375821 | + | 0.0194021i | ||||
\(133\) | 5.36663 | 0.465346 | ||||||||
\(134\) | −1.31638 | −0.113718 | ||||||||
\(135\) | 7.61477 | + | 1.08153i | 0.655375 | + | 0.0930835i | ||||
\(136\) | 0.739584 | − | 0.739584i | 0.0634188 | − | 0.0634188i | ||||
\(137\) | 4.18839 | − | 4.18839i | 0.357838 | − | 0.357838i | −0.505177 | − | 0.863016i | \(-0.668573\pi\) |
0.863016 | + | 0.505177i | \(0.168573\pi\) | |||||||
\(138\) | 20.1919 | − | 10.4242i | 1.71885 | − | 0.887369i | ||||
\(139\) | −14.9698 | −1.26972 | −0.634859 | − | 0.772628i | \(-0.718942\pi\) | ||||
−0.634859 | + | 0.772628i | \(0.718942\pi\) | |||||||
\(140\) | −12.1555 | −1.02733 | ||||||||
\(141\) | −4.56807 | − | 8.84841i | −0.384701 | − | 0.745170i | ||||
\(142\) | − | 22.3977i | − | 1.87958i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −10.5385 | − | 7.48630i | −0.878206 | − | 0.623858i | ||||
\(145\) | 2.07769 | − | 2.07769i | 0.172542 | − | 0.172542i | ||||
\(146\) | 10.8613i | 0.898891i | ||||||||
\(147\) | 21.6328 | + | 6.90165i | 1.78424 | + | 0.569239i | ||||
\(148\) | 4.23920 | − | 4.23920i | 0.348460 | − | 0.348460i | ||||
\(149\) | −12.4536 | − | 12.4536i | −1.02024 | − | 1.02024i | −0.999791 | − | 0.0204461i | \(-0.993491\pi\) |
−0.0204461 | − | 0.999791i | \(-0.506509\pi\) | |||||||
\(150\) | −4.36878 | − | 8.46238i | −0.356709 | − | 0.690951i | ||||
\(151\) | 7.85127 | + | 7.85127i | 0.638928 | + | 0.638928i | 0.950291 | − | 0.311363i | \(-0.100786\pi\) |
−0.311363 | + | 0.950291i | \(0.600786\pi\) | |||||||
\(152\) | 0.395197i | 0.0320547i | ||||||||
\(153\) | −7.74624 | − | 5.50276i | −0.626247 | − | 0.444872i | ||||
\(154\) | 0.950869 | + | 0.950869i | 0.0766232 | + | 0.0766232i | ||||
\(155\) | 7.63751 | 0.613459 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.4654 | 0.835227 | 0.417614 | − | 0.908625i | \(-0.362867\pi\) | ||||
0.417614 | + | 0.908625i | \(0.362867\pi\) | |||||||
\(158\) | −7.56236 | − | 7.56236i | −0.601629 | − | 0.601629i | ||||
\(159\) | 1.03644 | + | 0.330661i | 0.0821948 | + | 0.0262231i | ||||
\(160\) | − | 11.5065i | − | 0.909668i | ||||||
\(161\) | −21.2540 | − | 21.2540i | −1.67505 | − | 1.67505i | ||||
\(162\) | −7.66115 | + | 15.8632i | −0.601917 | + | 1.24633i | ||||
\(163\) | 1.37114 | + | 1.37114i | 0.107396 | + | 0.107396i | 0.758763 | − | 0.651367i | \(-0.225804\pi\) |
−0.651367 | + | 0.758763i | \(0.725804\pi\) | |||||||
\(164\) | −10.8387 | + | 10.8387i | −0.846362 | + | 0.846362i | ||||
\(165\) | 0.119377 | − | 0.374181i | 0.00929351 | − | 0.0291300i | ||||
\(166\) | 17.7372i | 1.37668i | ||||||||
\(167\) | −9.88695 | + | 9.88695i | −0.765075 | + | 0.765075i | −0.977235 | − | 0.212160i | \(-0.931950\pi\) |
0.212160 | + | 0.977235i | \(0.431950\pi\) | |||||||
\(168\) | −0.779605 | + | 2.44363i | −0.0601478 | + | 0.188530i | ||||
\(169\) | 0 | 0 | ||||||||
\(170\) | − | 9.17635i | − | 0.703794i | ||||||
\(171\) | 3.53980 | − | 0.599403i | 0.270695 | − | 0.0458375i | ||||
\(172\) | 5.09681 | 0.388628 | ||||||||
\(173\) | −17.9530 | −1.36494 | −0.682471 | − | 0.730912i | \(-0.739095\pi\) | ||||
−0.682471 | + | 0.730912i | \(0.739095\pi\) | |||||||
\(174\) | 3.08729 | + | 5.98012i | 0.234047 | + | 0.453351i | ||||
\(175\) | −8.90752 | + | 8.90752i | −0.673345 | + | 0.673345i | ||||
\(176\) | −0.466783 | + | 0.466783i | −0.0351851 | + | 0.0351851i | ||||
\(177\) | −6.97713 | − | 13.5148i | −0.524433 | − | 1.01583i | ||||
\(178\) | −10.3934 | −0.779018 | ||||||||
\(179\) | −1.76719 | −0.132086 | −0.0660431 | − | 0.997817i | \(-0.521037\pi\) | ||||
−0.0660431 | + | 0.997817i | \(0.521037\pi\) | |||||||
\(180\) | −8.01773 | + | 1.35766i | −0.597606 | + | 0.101194i | ||||
\(181\) | 16.9949i | 1.26322i | 0.775286 | + | 0.631611i | \(0.217606\pi\) | ||||
−0.775286 | + | 0.631611i | \(0.782394\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.07055 | − | 9.62447i | 0.226982 | − | 0.711461i | ||||
\(184\) | 1.56514 | − | 1.56514i | 0.115383 | − | 0.115383i | ||||
\(185\) | 4.84568i | 0.356261i | ||||||||
\(186\) | −5.31697 | + | 16.6657i | −0.389859 | + | 1.22199i | ||||
\(187\) | −0.343106 | + | 0.343106i | −0.0250904 | + | 0.0250904i | ||||
\(188\) | 7.44479 | + | 7.44479i | 0.542967 | + | 0.542967i | ||||
\(189\) | 23.0702 | + | 3.27667i | 1.67811 | + | 0.238343i | ||||
\(190\) | 2.45169 | + | 2.45169i | 0.177864 | + | 0.177864i | ||||
\(191\) | − | 22.3761i | − | 1.61908i | −0.587066 | − | 0.809539i | \(-0.699717\pi\) | ||
0.587066 | − | 0.809539i | \(-0.300283\pi\) | |||||||
\(192\) | 10.8877 | + | 3.47358i | 0.785753 | + | 0.250684i | ||||
\(193\) | 13.9367 | + | 13.9367i | 1.00318 | + | 1.00318i | 0.999995 | + | 0.00318807i | \(0.00101480\pi\) |
0.00318807 | + | 0.999995i | \(0.498985\pi\) | |||||||
\(194\) | −8.75956 | −0.628900 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −24.0081 | −1.71486 | ||||||||
\(197\) | 1.05277 | + | 1.05277i | 0.0750064 | + | 0.0750064i | 0.743615 | − | 0.668608i | \(-0.233110\pi\) |
−0.668608 | + | 0.743615i | \(0.733110\pi\) | |||||||
\(198\) | 0.733391 | + | 0.520985i | 0.0521198 | + | 0.0370248i | ||||
\(199\) | − | 19.6776i | − | 1.39491i | −0.716629 | − | 0.697454i | \(-0.754316\pi\) | ||
0.716629 | − | 0.697454i | \(-0.245684\pi\) | |||||||
\(200\) | −0.655946 | − | 0.655946i | −0.0463824 | − | 0.0463824i | ||||
\(201\) | 0.534355 | + | 1.03505i | 0.0376905 | + | 0.0730070i | ||||
\(202\) | 2.32659 | + | 2.32659i | 0.163698 | + | 0.163698i | ||||
\(203\) | 6.29468 | − | 6.29468i | 0.441800 | − | 0.441800i | ||||
\(204\) | 9.57095 | + | 3.05348i | 0.670100 | + | 0.213786i | ||||
\(205\) | − | 12.3893i | − | 0.865309i | ||||||
\(206\) | −6.11099 | + | 6.11099i | −0.425773 | + | 0.425773i | ||||
\(207\) | −16.3929 | − | 11.6451i | −1.13938 | − | 0.809393i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 0.183339i | − | 0.0126818i | ||||||
\(210\) | 10.3231 | + | 19.9960i | 0.712363 | + | 1.37986i | ||||
\(211\) | −23.5891 | −1.62394 | −0.811969 | − | 0.583700i | \(-0.801604\pi\) | ||||
−0.811969 | + | 0.583700i | \(0.801604\pi\) | |||||||
\(212\) | −1.15024 | −0.0789986 | ||||||||
\(213\) | −17.6111 | + | 9.09186i | −1.20669 | + | 0.622964i | ||||
\(214\) | 21.4221 | − | 21.4221i | 1.46438 | − | 1.46438i | ||||
\(215\) | −2.91299 | + | 2.91299i | −0.198664 | + | 0.198664i | ||||
\(216\) | −0.241293 | + | 1.69888i | −0.0164179 | + | 0.115594i | ||||
\(217\) | 23.1390 | 1.57078 | ||||||||
\(218\) | 24.3078 | 1.64633 | ||||||||
\(219\) | 8.54015 | − | 4.40892i | 0.577090 | − | 0.297927i | ||||
\(220\) | 0.415266i | 0.0279972i | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −10.5737 | − | 3.37340i | −0.709661 | − | 0.226408i | ||||
\(223\) | 8.91990 | − | 8.91990i | 0.597321 | − | 0.597321i | −0.342278 | − | 0.939599i | \(-0.611198\pi\) |
0.939599 | + | 0.342278i | \(0.111198\pi\) | |||||||
\(224\) | − | 34.8607i | − | 2.32923i | ||||||
\(225\) | −4.88046 | + | 6.87024i | −0.325364 | + | 0.458016i | ||||
\(226\) | −6.63086 | + | 6.63086i | −0.441079 | + | 0.441079i | ||||
\(227\) | 15.7094 | + | 15.7094i | 1.04267 | + | 1.04267i | 0.999048 | + | 0.0436223i | \(0.0138898\pi\) |
0.0436223 | + | 0.999048i | \(0.486110\pi\) | |||||||
\(228\) | −3.37293 | + | 1.74130i | −0.223378 | + | 0.115321i | ||||
\(229\) | 7.05247 | + | 7.05247i | 0.466040 | + | 0.466040i | 0.900629 | − | 0.434589i | \(-0.143106\pi\) |
−0.434589 | + | 0.900629i | \(0.643106\pi\) | |||||||
\(230\) | − | 19.4193i | − | 1.28047i | ||||||
\(231\) | 0.361672 | − | 1.13364i | 0.0237963 | − | 0.0745881i | ||||
\(232\) | 0.463538 | + | 0.463538i | 0.0304327 | + | 0.0304327i | ||||
\(233\) | 22.9574 | 1.50399 | 0.751996 | − | 0.659168i | \(-0.229091\pi\) | ||||
0.751996 | + | 0.659168i | \(0.229091\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.50987 | −0.555123 | ||||||||
\(236\) | 11.3710 | + | 11.3710i | 0.740186 | + | 0.740186i | ||||
\(237\) | −2.87642 | + | 9.01596i | −0.186844 | + | 0.585650i | ||||
\(238\) | − | 27.8012i | − | 1.80208i | ||||||
\(239\) | 12.6819 | + | 12.6819i | 0.820323 | + | 0.820323i | 0.986154 | − | 0.165831i | \(-0.0530305\pi\) |
−0.165831 | + | 0.986154i | \(0.553031\pi\) | |||||||
\(240\) | −9.81609 | + | 5.06764i | −0.633626 | + | 0.327115i | ||||
\(241\) | 1.99604 | + | 1.99604i | 0.128576 | + | 0.128576i | 0.768466 | − | 0.639890i | \(-0.221020\pi\) |
−0.639890 | + | 0.768466i | \(0.721020\pi\) | |||||||
\(242\) | −15.1923 | + | 15.1923i | −0.976596 | + | 0.976596i | ||||
\(243\) | 15.5829 | − | 0.415449i | 0.999645 | − | 0.0266510i | ||||
\(244\) | 10.6812i | 0.683796i | ||||||||
\(245\) | 13.7214 | − | 13.7214i | 0.876627 | − | 0.876627i | ||||
\(246\) | 27.0347 | + | 8.62503i | 1.72367 | + | 0.549912i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1.70395i | 0.108201i | ||||||||
\(249\) | 13.9466 | − | 7.20004i | 0.883828 | − | 0.456284i | ||||
\(250\) | −22.6248 | −1.43092 | ||||||||
\(251\) | 17.1932 | 1.08522 | 0.542612 | − | 0.839984i | \(-0.317435\pi\) | ||||
0.542612 | + | 0.839984i | \(0.317435\pi\) | |||||||
\(252\) | −24.2910 | + | 4.11325i | −1.53019 | + | 0.259110i | ||||
\(253\) | −0.726094 | + | 0.726094i | −0.0456491 | + | 0.0456491i | ||||
\(254\) | 22.1111 | − | 22.1111i | 1.38738 | − | 1.38738i | ||||
\(255\) | −7.21526 | + | 3.72494i | −0.451837 | + | 0.233265i | ||||
\(256\) | 18.3490 | 1.14681 | ||||||||
\(257\) | 9.50799 | 0.593092 | 0.296546 | − | 0.955019i | \(-0.404165\pi\) | ||||
0.296546 | + | 0.955019i | \(0.404165\pi\) | |||||||
\(258\) | −4.32848 | − | 8.38433i | −0.269480 | − | 0.521986i | ||||
\(259\) | 14.6807i | 0.912217i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.44888 | − | 4.85499i | 0.213480 | − | 0.300517i | ||||
\(262\) | −25.9763 | + | 25.9763i | −1.60482 | + | 1.60482i | ||||
\(263\) | 7.24943i | 0.447019i | 0.974702 | + | 0.223510i | \(0.0717514\pi\) | ||||
−0.974702 | + | 0.223510i | \(0.928249\pi\) | |||||||
\(264\) | 0.0834809 | + | 0.0266334i | 0.00513789 | + | 0.00163917i | ||||
\(265\) | 0.657397 | − | 0.657397i | 0.0403836 | − | 0.0403836i | ||||
\(266\) | 7.42778 | + | 7.42778i | 0.455427 | + | 0.455427i | ||||
\(267\) | 4.21897 | + | 8.17221i | 0.258197 | + | 0.500131i | ||||
\(268\) | −0.870863 | − | 0.870863i | −0.0531964 | − | 0.0531964i | ||||
\(269\) | 26.7779i | 1.63268i | 0.577573 | + | 0.816339i | \(0.304000\pi\) | ||||
−0.577573 | + | 0.816339i | \(0.696000\pi\) | |||||||
\(270\) | 9.04245 | + | 12.0363i | 0.550306 | + | 0.732505i | ||||
\(271\) | 1.19552 | + | 1.19552i | 0.0726228 | + | 0.0726228i | 0.742485 | − | 0.669862i | \(-0.233647\pi\) |
−0.669862 | + | 0.742485i | \(0.733647\pi\) | |||||||
\(272\) | 13.6477 | 0.827511 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.5940 | 0.700421 | ||||||||
\(275\) | 0.304305 | + | 0.304305i | 0.0183503 | + | 0.0183503i | ||||
\(276\) | 20.2544 | + | 6.46189i | 1.21917 | + | 0.388960i | ||||
\(277\) | 24.9616i | 1.49980i | 0.661552 | + | 0.749899i | \(0.269898\pi\) | ||||
−0.661552 | + | 0.749899i | \(0.730102\pi\) | |||||||
\(278\) | −20.7192 | − | 20.7192i | −1.24265 | − | 1.24265i | ||||
\(279\) | 15.2624 | − | 2.58442i | 0.913735 | − | 0.154725i | ||||
\(280\) | 1.54996 | + | 1.54996i | 0.0926276 | + | 0.0926276i | ||||
\(281\) | 2.53054 | − | 2.53054i | 0.150959 | − | 0.150959i | −0.627587 | − | 0.778546i | \(-0.715957\pi\) |
0.778546 | + | 0.627587i | \(0.215957\pi\) | |||||||
\(282\) | 5.92428 | − | 18.5693i | 0.352786 | − | 1.10579i | ||||
\(283\) | 5.11893i | 0.304289i | 0.988358 | + | 0.152144i | \(0.0486179\pi\) | ||||
−0.988358 | + | 0.152144i | \(0.951382\pi\) | |||||||
\(284\) | 14.8174 | − | 14.8174i | 0.879254 | − | 0.879254i | ||||
\(285\) | 0.932525 | − | 2.92295i | 0.0552380 | − | 0.173140i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 37.5354i | − | 2.21565i | ||||||
\(288\) | −3.89362 | − | 22.9939i | −0.229434 | − | 1.35493i | ||||
\(289\) | −6.96837 | −0.409904 | ||||||||
\(290\) | 5.75132 | 0.337729 | ||||||||
\(291\) | 3.55575 | + | 6.88754i | 0.208442 | + | 0.403755i | ||||
\(292\) | −7.18543 | + | 7.18543i | −0.420496 | + | 0.420496i | ||||
\(293\) | 0.198293 | − | 0.198293i | 0.0115844 | − | 0.0115844i | −0.701291 | − | 0.712875i | \(-0.747393\pi\) |
0.712875 | + | 0.701291i | \(0.247393\pi\) | |||||||
\(294\) | 20.3889 | + | 39.4937i | 1.18911 | + | 2.30332i | ||||
\(295\) | −12.9977 | −0.756757 | ||||||||
\(296\) | −1.08108 | −0.0628367 | ||||||||
\(297\) | 0.111940 | − | 0.788139i | 0.00649542 | − | 0.0457325i | ||||
\(298\) | − | 34.4732i | − | 1.99698i | ||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 2.70817 | − | 8.48859i | 0.156356 | − | 0.490089i | ||||
\(301\) | −8.82536 | + | 8.82536i | −0.508685 | + | 0.508685i | ||||
\(302\) | 21.7334i | 1.25062i | ||||||||
\(303\) | 0.884941 | − | 2.77379i | 0.0508385 | − | 0.159350i | ||||
\(304\) | −3.64631 | + | 3.64631i | −0.209130 | + | 0.209130i | ||||
\(305\) | −6.10466 | − | 6.10466i | −0.349552 | − | 0.349552i | ||||
\(306\) | −3.10514 | − | 18.3375i | −0.177509 | − | 1.04829i | ||||
\(307\) | −12.9424 | − | 12.9424i | −0.738660 | − | 0.738660i | 0.233659 | − | 0.972319i | \(-0.424930\pi\) |
−0.972319 | + | 0.233659i | \(0.924930\pi\) | |||||||
\(308\) | 1.25811i | 0.0716877i | ||||||||
\(309\) | 7.28562 | + | 2.32438i | 0.414464 | + | 0.132229i | ||||
\(310\) | 10.5708 | + | 10.5708i | 0.600383 | + | 0.600383i | ||||
\(311\) | −6.76425 | −0.383565 | −0.191783 | − | 0.981437i | \(-0.561427\pi\) | ||||
−0.191783 | + | 0.981437i | \(0.561427\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.3673 | −1.43385 | −0.716923 | − | 0.697153i | \(-0.754450\pi\) | ||||
−0.716923 | + | 0.697153i | \(0.754450\pi\) | |||||||
\(314\) | 14.4848 | + | 14.4848i | 0.817424 | + | 0.817424i | ||||
\(315\) | 11.5322 | − | 16.2339i | 0.649766 | − | 0.914677i | ||||
\(316\) | − | 10.0059i | − | 0.562876i | ||||||
\(317\) | 5.65535 | + | 5.65535i | 0.317636 | + | 0.317636i | 0.847859 | − | 0.530222i | \(-0.177892\pi\) |
−0.530222 | + | 0.847859i | \(0.677892\pi\) | |||||||
\(318\) | 0.976843 | + | 1.89216i | 0.0547786 | + | 0.106107i | ||||
\(319\) | −0.215043 | − | 0.215043i | −0.0120401 | − | 0.0120401i | ||||
\(320\) | 6.90592 | − | 6.90592i | 0.386052 | − | 0.386052i | ||||
\(321\) | −25.5398 | − | 8.14811i | −1.42549 | − | 0.454783i | ||||
\(322\) | − | 58.8339i | − | 3.27869i | ||||||
\(323\) | −2.68020 | + | 2.68020i | −0.149130 | + | 0.149130i | ||||
\(324\) | −15.5628 | + | 5.42615i | −0.864599 | + | 0.301453i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.79550i | 0.210214i | ||||||||
\(327\) | −9.86723 | − | 19.1130i | −0.545659 | − | 1.05695i | ||||
\(328\) | 2.76410 | 0.152622 | ||||||||
\(329\) | −25.7820 | −1.42141 | ||||||||
\(330\) | 0.683119 | − | 0.352666i | 0.0376044 | − | 0.0194136i | ||||
\(331\) | 16.6395 | − | 16.6395i | 0.914589 | − | 0.914589i | −0.0820401 | − | 0.996629i | \(-0.526144\pi\) |
0.996629 | + | 0.0820401i | \(0.0261436\pi\) | |||||||
\(332\) | −11.7343 | + | 11.7343i | −0.644001 | + | 0.644001i | ||||
\(333\) | 1.63970 | + | 9.68334i | 0.0898552 | + | 0.530644i | ||||
\(334\) | −27.3684 | −1.49753 | ||||||||
\(335\) | 0.995452 | 0.0543873 | ||||||||
\(336\) | −29.7394 | + | 15.3532i | −1.62242 | + | 0.837586i | ||||
\(337\) | 8.25174i | 0.449501i | 0.974416 | + | 0.224750i | \(0.0721567\pi\) | ||||
−0.974416 | + | 0.224750i | \(0.927843\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.90542 | + | 2.52212i | 0.429364 | + | 0.136983i | ||||
\(340\) | 6.07071 | − | 6.07071i | 0.329230 | − | 0.329230i | ||||
\(341\) | − | 0.790492i | − | 0.0428075i | ||||||
\(342\) | 5.72894 | + | 4.06971i | 0.309786 | + | 0.220065i | ||||
\(343\) | 19.3744 | − | 19.3744i | 1.04612 | − | 1.04612i | ||||
\(344\) | −0.649896 | − | 0.649896i | −0.0350400 | − | 0.0350400i | ||||
\(345\) | −15.2692 | + | 7.88285i | −0.822066 | + | 0.424399i | ||||
\(346\) | −24.8482 | − | 24.8482i | −1.33585 | − | 1.33585i | ||||
\(347\) | 3.83606i | 0.205930i | 0.994685 | + | 0.102965i | \(0.0328330\pi\) | ||||
−0.994685 | + | 0.102965i | \(0.967167\pi\) | |||||||
\(348\) | −1.91378 | + | 5.99863i | −0.102589 | + | 0.321560i | ||||
\(349\) | −8.17613 | − | 8.17613i | −0.437658 | − | 0.437658i | 0.453565 | − | 0.891223i | \(-0.350152\pi\) |
−0.891223 | + | 0.453565i | \(0.850152\pi\) | |||||||
\(350\) | −24.6572 | −1.31798 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.19094 | −0.0634771 | ||||||||
\(353\) | 7.24062 | + | 7.24062i | 0.385379 | + | 0.385379i | 0.873036 | − | 0.487656i | \(-0.162148\pi\) |
−0.487656 | + | 0.873036i | \(0.662148\pi\) | |||||||
\(354\) | 9.04857 | − | 28.3622i | 0.480926 | − | 1.50743i | ||||
\(355\) | 16.9373i | 0.898937i | ||||||||
\(356\) | −6.87586 | − | 6.87586i | −0.364420 | − | 0.364420i | ||||
\(357\) | −21.8598 | + | 11.2853i | −1.15694 | + | 0.597281i | ||||
\(358\) | −2.44592 | − | 2.44592i | −0.129271 | − | 0.129271i | ||||
\(359\) | 7.50270 | − | 7.50270i | 0.395977 | − | 0.395977i | −0.480834 | − | 0.876812i | \(-0.659666\pi\) |
0.876812 | + | 0.480834i | \(0.159666\pi\) | |||||||
\(360\) | 1.19546 | + | 0.849227i | 0.0630062 | + | 0.0447582i | ||||
\(361\) | 17.5678i | 0.924623i | ||||||||
\(362\) | −23.5221 | + | 23.5221i | −1.23629 | + | 1.23629i | ||||
\(363\) | 18.1125 | + | 5.77853i | 0.950658 | + | 0.303294i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 8.21340i | − | 0.429909i | ||||||
\(366\) | 17.5708 | − | 9.07107i | 0.918439 | − | 0.474152i | ||||
\(367\) | −14.0058 | −0.731096 | −0.365548 | − | 0.930792i | \(-0.619118\pi\) | ||||
−0.365548 | + | 0.930792i | \(0.619118\pi\) | |||||||
\(368\) | 28.8817 | 1.50556 | ||||||||
\(369\) | −4.19236 | − | 24.7582i | −0.218246 | − | 1.28886i | ||||
\(370\) | −6.70675 | + | 6.70675i | −0.348667 | + | 0.348667i | ||||
\(371\) | 1.99169 | − | 1.99169i | 0.103403 | − | 0.103403i | ||||
\(372\) | −14.5429 | + | 7.50789i | −0.754014 | + | 0.389266i | ||||
\(373\) | −19.9776 | −1.03440 | −0.517200 | − | 0.855865i | \(-0.673026\pi\) | ||||
−0.517200 | + | 0.855865i | \(0.673026\pi\) | |||||||
\(374\) | −0.949764 | −0.0491111 | ||||||||
\(375\) | 9.18404 | + | 17.7896i | 0.474262 | + | 0.918652i | ||||
\(376\) | − | 1.89858i | − | 0.0979116i | ||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 27.3955 | + | 36.4658i | 1.40907 | + | 1.87560i | ||||
\(379\) | −6.29483 | + | 6.29483i | −0.323344 | + | 0.323344i | −0.850048 | − | 0.526705i | \(-0.823427\pi\) |
0.526705 | + | 0.850048i | \(0.323427\pi\) | |||||||
\(380\) | 3.24388i | 0.166408i | ||||||||
\(381\) | −26.3612 | − | 8.41019i | −1.35053 | − | 0.430867i | ||||
\(382\) | 30.9701 | − | 30.9701i | 1.58457 | − | 1.58457i | ||||
\(383\) | 16.5930 | + | 16.5930i | 0.847862 | + | 0.847862i | 0.989866 | − | 0.142004i | \(-0.0453545\pi\) |
−0.142004 | + | 0.989866i | \(0.545355\pi\) | |||||||
\(384\) | −2.09161 | − | 4.05147i | −0.106737 | − | 0.206751i | ||||
\(385\) | −0.719052 | − | 0.719052i | −0.0366463 | − | 0.0366463i | ||||
\(386\) | 38.5786i | 1.96360i | ||||||||
\(387\) | −4.83545 | + | 6.80687i | −0.245800 | + | 0.346013i | ||||
\(388\) | −5.79498 | − | 5.79498i | −0.294195 | − | 0.294195i | ||||
\(389\) | −33.0750 | −1.67697 | −0.838484 | − | 0.544926i | \(-0.816558\pi\) | ||||
−0.838484 | + | 0.544926i | \(0.816558\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.2293 | 1.07361 | ||||||||
\(392\) | 3.06128 | + | 3.06128i | 0.154618 | + | 0.154618i | ||||
\(393\) | 30.9694 | + | 9.88036i | 1.56220 | + | 0.498398i | ||||
\(394\) | 2.91420i | 0.146815i | ||||||||
\(395\) | 5.71869 | + | 5.71869i | 0.287739 | + | 0.287739i | ||||
\(396\) | 0.140520 | + | 0.829845i | 0.00706138 | + | 0.0417013i | ||||
\(397\) | −23.6911 | − | 23.6911i | −1.18902 | − | 1.18902i | −0.977338 | − | 0.211684i | \(-0.932105\pi\) |
−0.211684 | − | 0.977338i | \(-0.567895\pi\) | |||||||
\(398\) | 27.2351 | − | 27.2351i | 1.36517 | − | 1.36517i | ||||
\(399\) | 2.82523 | − | 8.85552i | 0.141438 | − | 0.443331i | ||||
\(400\) | − | 12.1043i | − | 0.605213i | ||||||
\(401\) | 12.1119 | − | 12.1119i | 0.604838 | − | 0.604838i | −0.336755 | − | 0.941592i | \(-0.609329\pi\) |
0.941592 | + | 0.336755i | \(0.109329\pi\) | |||||||
\(402\) | −0.693000 | + | 2.17217i | −0.0345637 | + | 0.108338i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 3.07835i | 0.153154i | ||||||||
\(405\) | 5.79340 | − | 11.9958i | 0.287876 | − | 0.596078i | ||||
\(406\) | 17.4245 | 0.864765 | ||||||||
\(407\) | 0.501534 | 0.0248601 | ||||||||
\(408\) | −0.831044 | − | 1.60974i | −0.0411428 | − | 0.0796942i | ||||
\(409\) | 8.69291 | − | 8.69291i | 0.429837 | − | 0.429837i | −0.458736 | − | 0.888573i | \(-0.651698\pi\) |
0.888573 | + | 0.458736i | \(0.151698\pi\) | |||||||
\(410\) | 17.1477 | − | 17.1477i | 0.846864 | − | 0.846864i | ||||
\(411\) | −4.70634 | − | 9.11625i | −0.232147 | − | 0.449672i | ||||
\(412\) | −8.08557 | −0.398348 | ||||||||
\(413\) | −39.3786 | −1.93770 | ||||||||
\(414\) | −6.57121 | − | 38.8066i | −0.322957 | − | 1.90724i | ||||
\(415\) | − | 13.4130i | − | 0.658418i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.88074 | + | 24.7017i | −0.385922 | + | 1.20965i | ||||
\(418\) | 0.253753 | − | 0.253753i | 0.0124115 | − | 0.0124115i | ||||
\(419\) | − | 18.0119i | − | 0.879940i | −0.898012 | − | 0.439970i | \(-0.854989\pi\) | ||
0.898012 | − | 0.439970i | \(-0.145011\pi\) | |||||||
\(420\) | −6.39921 | + | 20.0579i | −0.312250 | + | 0.978728i | ||||
\(421\) | −15.2469 | + | 15.2469i | −0.743088 | + | 0.743088i | −0.973171 | − | 0.230083i | \(-0.926100\pi\) |
0.230083 | + | 0.973171i | \(0.426100\pi\) | |||||||
\(422\) | −32.6489 | − | 32.6489i | −1.58932 | − | 1.58932i | ||||
\(423\) | −17.0057 | + | 2.87961i | −0.826843 | + | 0.140011i | ||||
\(424\) | 0.146667 | + | 0.146667i | 0.00712278 | + | 0.00712278i | ||||
\(425\) | − | 8.89717i | − | 0.431576i | ||||||
\(426\) | −36.9587 | − | 11.7912i | −1.79065 | − | 0.571283i | ||||
\(427\) | −18.4950 | − | 18.4950i | −0.895037 | − | 0.895037i | ||||
\(428\) | 28.3440 | 1.37006 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.06355 | −0.388859 | ||||||||
\(431\) | −21.3784 | − | 21.3784i | −1.02976 | − | 1.02976i | −0.999543 | − | 0.0302162i | \(-0.990380\pi\) |
−0.0302162 | − | 0.999543i | \(-0.509620\pi\) | |||||||
\(432\) | −17.9011 | + | 13.4485i | −0.861268 | + | 0.647042i | ||||
\(433\) | − | 19.2897i | − | 0.927005i | −0.886096 | − | 0.463503i | \(-0.846592\pi\) | ||
0.886096 | − | 0.463503i | \(-0.153408\pi\) | |||||||
\(434\) | 32.0260 | + | 32.0260i | 1.53730 | + | 1.53730i | ||||
\(435\) | −2.33462 | − | 4.52219i | −0.111937 | − | 0.216823i | ||||
\(436\) | 16.0811 | + | 16.0811i | 0.770145 | + | 0.770145i | ||||
\(437\) | −5.67194 | + | 5.67194i | −0.271326 | + | 0.271326i | ||||
\(438\) | 17.9224 | + | 5.71789i | 0.856365 | + | 0.273211i | ||||
\(439\) | 17.3861i | 0.829793i | 0.909869 | + | 0.414896i | \(0.136182\pi\) | ||||
−0.909869 | + | 0.414896i | \(0.863818\pi\) | |||||||
\(440\) | 0.0529507 | − | 0.0529507i | 0.00252432 | − | 0.00252432i | ||||
\(441\) | 22.7769 | − | 32.0632i | 1.08462 | − | 1.52682i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.43321i | 0.0680940i | 0.999420 | + | 0.0340470i | \(0.0108396\pi\) | ||||
−0.999420 | + | 0.0340470i | \(0.989160\pi\) | |||||||
\(444\) | −4.76344 | − | 9.22685i | −0.226063 | − | 0.437887i | ||||
\(445\) | 7.85954 | 0.372578 | ||||||||
\(446\) | 24.6915 | 1.16918 | ||||||||
\(447\) | −27.1059 | + | 13.9936i | −1.28206 | + | 0.661876i | ||||
\(448\) | 20.9226 | − | 20.9226i | 0.988498 | − | 0.988498i | ||||
\(449\) | −27.3135 | + | 27.3135i | −1.28900 | + | 1.28900i | −0.353610 | + | 0.935393i | \(0.615046\pi\) |
−0.935393 | + | 0.353610i | \(0.884954\pi\) | |||||||
\(450\) | −16.2638 | + | 2.75398i | −0.766681 | + | 0.129824i | ||||
\(451\) | −1.28231 | −0.0603817 | ||||||||
\(452\) | −8.77343 | −0.412667 | ||||||||
\(453\) | 17.0887 | − | 8.82219i | 0.802898 | − | 0.414503i | ||||
\(454\) | 43.4858i | 2.04089i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.652117 | + | 0.208049i | 0.0305382 | + | 0.00974279i | ||||
\(457\) | −3.28879 | + | 3.28879i | −0.153843 | + | 0.153843i | −0.779832 | − | 0.625989i | \(-0.784696\pi\) |
0.625989 | + | 0.779832i | \(0.284696\pi\) | |||||||
\(458\) | 19.5222i | 0.912212i | ||||||||
\(459\) | −13.1581 | + | 9.88524i | −0.614168 | + | 0.461404i | ||||
\(460\) | 12.8471 | − | 12.8471i | 0.598997 | − | 0.598997i | ||||
\(461\) | −5.76221 | − | 5.76221i | −0.268373 | − | 0.268373i | 0.560072 | − | 0.828444i | \(-0.310774\pi\) |
−0.828444 | + | 0.560072i | \(0.810774\pi\) | |||||||
\(462\) | 2.06962 | − | 1.06846i | 0.0962872 | − | 0.0497091i | ||||
\(463\) | 4.68191 | + | 4.68191i | 0.217587 | + | 0.217587i | 0.807481 | − | 0.589894i | \(-0.200830\pi\) |
−0.589894 | + | 0.807481i | \(0.700830\pi\) | |||||||
\(464\) | 8.55373i | 0.397097i | ||||||||
\(465\) | 4.02072 | − | 12.6027i | 0.186456 | − | 0.584437i | ||||
\(466\) | 31.7747 | + | 31.7747i | 1.47193 | + | 1.47193i | ||||
\(467\) | −15.0964 | −0.698578 | −0.349289 | − | 0.937015i | \(-0.613577\pi\) | ||||
−0.349289 | + | 0.937015i | \(0.613577\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.01588 | 0.139260 | ||||||||
\(470\) | −11.7782 | − | 11.7782i | −0.543290 | − | 0.543290i | ||||
\(471\) | 5.50943 | − | 17.2690i | 0.253861 | − | 0.795713i | ||||
\(472\) | − | 2.89983i | − | 0.133475i | ||||||
\(473\) | 0.301498 | + | 0.301498i | 0.0138629 | + | 0.0138629i | ||||
\(474\) | −16.4599 | + | 8.49755i | −0.756027 | + | 0.390305i | ||||
\(475\) | 2.37710 | + | 2.37710i | 0.109069 | + | 0.109069i | ||||
\(476\) | 18.3922 | − | 18.3922i | 0.843004 | − | 0.843004i | ||||
\(477\) | 1.09125 | − | 1.53616i | 0.0499650 | − | 0.0703359i | ||||
\(478\) | 35.1052i | 1.60567i | ||||||||
\(479\) | 13.0148 | − | 13.0148i | 0.594660 | − | 0.594660i | −0.344227 | − | 0.938886i | \(-0.611859\pi\) |
0.938886 | + | 0.344227i | \(0.111859\pi\) | |||||||
\(480\) | −18.9870 | − | 6.05753i | −0.866632 | − | 0.276487i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 5.52530i | 0.251671i | ||||||||
\(483\) | −46.2604 | + | 23.8823i | −2.10492 | + | 1.08668i | ||||
\(484\) | −20.1012 | −0.913691 | ||||||||
\(485\) | 6.62402 | 0.300781 | ||||||||
\(486\) | 22.1428 | + | 20.9928i | 1.00442 | + | 0.952253i | ||||
\(487\) | −20.1793 | + | 20.1793i | −0.914411 | + | 0.914411i | −0.996615 | − | 0.0822048i | \(-0.973804\pi\) |
0.0822048 | + | 0.996615i | \(0.473804\pi\) | |||||||
\(488\) | 1.36197 | − | 1.36197i | 0.0616533 | − | 0.0616533i | ||||
\(489\) | 2.98436 | − | 1.54070i | 0.134957 | − | 0.0696729i | ||||
\(490\) | 37.9826 | 1.71588 | ||||||||
\(491\) | 37.9959 | 1.71473 | 0.857366 | − | 0.514708i | \(-0.172100\pi\) | ||||
0.857366 | + | 0.514708i | \(0.172100\pi\) | |||||||
\(492\) | 12.1791 | + | 23.5910i | 0.549075 | + | 1.06357i | ||||
\(493\) | 6.28737i | 0.283169i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.554594 | − | 0.393971i | −0.0249271 | − | 0.0177077i | ||||
\(496\) | −15.7216 | + | 15.7216i | −0.705921 | + | 0.705921i | ||||
\(497\) | 51.3141i | 2.30175i | ||||||||
\(498\) | 29.2684 | + | 9.33767i | 1.31155 | + | 0.418431i | ||||
\(499\) | 11.2432 | − | 11.2432i | 0.503315 | − | 0.503315i | −0.409152 | − | 0.912466i | \(-0.634175\pi\) |
0.912466 | + | 0.409152i | \(0.134175\pi\) | |||||||
\(500\) | −14.9677 | − | 14.9677i | −0.669375 | − | 0.669375i | ||||
\(501\) | 11.1096 | + | 21.5195i | 0.496341 | + | 0.961419i | ||||
\(502\) | 23.7965 | + | 23.7965i | 1.06209 | + | 1.06209i | ||||
\(503\) | − | 4.11260i | − | 0.183372i | −0.995788 | − | 0.0916859i | \(-0.970774\pi\) | ||
0.995788 | − | 0.0916859i | \(-0.0292256\pi\) | |||||||
\(504\) | 3.62183 | + | 2.57287i | 0.161329 | + | 0.114605i | ||||
\(505\) | −1.75938 | − | 1.75938i | −0.0782912 | − | 0.0782912i | ||||
\(506\) | −2.00993 | −0.0893521 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 29.2557 | 1.29801 | ||||||||
\(509\) | 17.2162 | + | 17.2162i | 0.763093 | + | 0.763093i | 0.976880 | − | 0.213787i | \(-0.0685799\pi\) |
−0.213787 | + | 0.976880i | \(0.568580\pi\) | |||||||
\(510\) | −15.1420 | − | 4.83084i | −0.670498 | − | 0.213913i | ||||
\(511\) | − | 24.8838i | − | 1.10079i | ||||||
\(512\) | 21.6735 | + | 21.6735i | 0.957841 | + | 0.957841i | ||||
\(513\) | 0.874427 | − | 6.15661i | 0.0386069 | − | 0.271821i | ||||
\(514\) | 13.1597 | + | 13.1597i | 0.580450 | + | 0.580450i | ||||
\(515\) | 4.62116 | − | 4.62116i | 0.203633 | − | 0.203633i | ||||
\(516\) | 2.68319 | − | 8.41029i | 0.118121 | − | 0.370242i | ||||
\(517\) | 0.880782i | 0.0387368i | ||||||||
\(518\) | −20.3191 | + | 20.3191i | −0.892772 | + | 0.892772i | ||||
\(519\) | −9.45126 | + | 29.6244i | −0.414864 | + | 1.30037i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.5577i | 0.637784i | 0.947791 | + | 0.318892i | \(0.103311\pi\) | ||||
−0.947791 | + | 0.318892i | \(0.896689\pi\) | |||||||
\(522\) | 11.4931 | − | 1.94616i | 0.503040 | − | 0.0851811i | ||||
\(523\) | −3.71977 | −0.162654 | −0.0813270 | − | 0.996687i | \(-0.525916\pi\) | ||||
−0.0813270 | + | 0.996687i | \(0.525916\pi\) | |||||||
\(524\) | −34.3698 | −1.50145 | ||||||||
\(525\) | 10.0091 | + | 19.3877i | 0.436831 | + | 0.846147i | ||||
\(526\) | −10.0337 | + | 10.0337i | −0.437491 | + | 0.437491i | ||||
\(527\) | −11.5561 | + | 11.5561i | −0.503391 | + | 0.503391i | ||||
\(528\) | 0.524507 | + | 1.01598i | 0.0228262 | + | 0.0442148i | ||||
\(529\) | 21.9263 | 0.953316 | ||||||||
\(530\) | 1.81976 | 0.0790455 | ||||||||
\(531\) | −25.9739 | + | 4.39823i | −1.12717 | + | 0.190867i | ||||
\(532\) | 9.82785i | 0.426091i | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −5.47155 | + | 17.1502i | −0.236777 | + | 0.742163i | ||||
\(535\) | −16.1995 | + | 16.1995i | −0.700365 | + | 0.700365i | ||||
\(536\) | 0.222088i | 0.00959274i | ||||||||
\(537\) | −0.930329 | + | 2.91606i | −0.0401467 | + | 0.125837i | ||||
\(538\) | −37.0624 | + | 37.0624i | −1.59788 | + | 1.59788i | ||||
\(539\) | −1.42018 | − | 1.42018i | −0.0611715 | − | 0.0611715i | ||||
\(540\) | −1.98060 | + | 13.9448i | −0.0852313 | + | 0.600091i | ||||
\(541\) | 2.30265 | + | 2.30265i | 0.0989985 | + | 0.0989985i | 0.754871 | − | 0.655873i | \(-0.227699\pi\) |
−0.655873 | + | 0.754871i | \(0.727699\pi\) | |||||||
\(542\) | 3.30937i | 0.142150i | ||||||||
\(543\) | 28.0434 | + | 8.94687i | 1.20346 | + | 0.383947i | ||||
\(544\) | 17.4101 | + | 17.4101i | 0.746453 | + | 0.746453i | ||||
\(545\) | −18.3817 | −0.787386 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.9324 | −1.10879 | −0.554395 | − | 0.832253i | \(-0.687050\pi\) | ||||
−0.554395 | + | 0.832253i | \(0.687050\pi\) | |||||||
\(548\) | 7.67015 | + | 7.67015i | 0.327653 | + | 0.327653i | ||||
\(549\) | −14.2649 | − | 10.1335i | −0.608813 | − | 0.432487i | ||||
\(550\) | 0.842357i | 0.0359182i | ||||||||
\(551\) | −1.67983 | − | 1.67983i | −0.0715630 | − | 0.0715630i | ||||
\(552\) | −1.75869 | − | 3.40660i | −0.0748547 | − | 0.144995i | ||||
\(553\) | 17.3257 | + | 17.3257i | 0.736763 | + | 0.736763i | ||||
\(554\) | −34.5486 | + | 34.5486i | −1.46783 | + | 1.46783i | ||||
\(555\) | 7.99589 | + | 2.55098i | 0.339407 | + | 0.108283i | ||||
\(556\) | − | 27.4140i | − | 1.16261i | ||||||
\(557\) | 6.37725 | − | 6.37725i | 0.270213 | − | 0.270213i | −0.558973 | − | 0.829186i | \(-0.688805\pi\) |
0.829186 | + | 0.558973i | \(0.188805\pi\) | |||||||
\(558\) | 24.7012 | + | 17.5472i | 1.04568 | + | 0.742831i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 28.6016i | 1.20864i | ||||||||
\(561\) | 0.385536 | + | 0.746788i | 0.0162773 | + | 0.0315294i | ||||
\(562\) | 7.00488 | 0.295483 | ||||||||
\(563\) | −8.75049 | −0.368789 | −0.184395 | − | 0.982852i | \(-0.559032\pi\) | ||||
−0.184395 | + | 0.982852i | \(0.559032\pi\) | |||||||
\(564\) | 16.2040 | − | 8.36545i | 0.682311 | − | 0.352249i | ||||
\(565\) | 5.01429 | − | 5.01429i | 0.210953 | − | 0.210953i | ||||
\(566\) | −7.08494 | + | 7.08494i | −0.297802 | + | 0.297802i | ||||
\(567\) | 17.5520 | − | 36.3433i | 0.737115 | − | 1.52627i | ||||
\(568\) | −3.77875 | −0.158553 | ||||||||
\(569\) | −31.5099 | −1.32096 | −0.660481 | − | 0.750843i | \(-0.729648\pi\) | ||||
−0.660481 | + | 0.750843i | \(0.729648\pi\) | |||||||
\(570\) | 5.33623 | − | 2.75488i | 0.223510 | − | 0.115389i | ||||
\(571\) | − | 34.4177i | − | 1.44034i | −0.693799 | − | 0.720169i | \(-0.744064\pi\) | ||
0.693799 | − | 0.720169i | \(-0.255936\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −36.9230 | − | 11.7798i | −1.54248 | − | 0.492107i | ||||
\(574\) | 51.9516 | − | 51.9516i | 2.16842 | − | 2.16842i | ||||
\(575\) | − | 18.8285i | − | 0.785204i | ||||||
\(576\) | 11.4635 | − | 16.1373i | 0.477648 | − | 0.672386i | ||||
\(577\) | −27.5186 | + | 27.5186i | −1.14562 | + | 1.14562i | −0.158211 | + | 0.987405i | \(0.550573\pi\) |
−0.987405 | + | 0.158211i | \(0.949427\pi\) | |||||||
\(578\) | −9.64470 | − | 9.64470i | −0.401167 | − | 0.401167i | ||||
\(579\) | 30.3339 | − | 15.6601i | 1.26063 | − | 0.650813i | ||||
\(580\) | 3.80484 | + | 3.80484i | 0.157988 | + | 0.157988i | ||||
\(581\) | − | 40.6368i | − | 1.68590i | ||||||
\(582\) | −4.61142 | + | 14.4542i | −0.191150 | + | 0.599147i | ||||
\(583\) | −0.0680414 | − | 0.0680414i | −0.00281799 | − | 0.00281799i | ||||
\(584\) | 1.83243 | 0.0758266 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.548902 | 0.0226749 | ||||||||
\(587\) | 2.80955 | + | 2.80955i | 0.115963 | + | 0.115963i | 0.762707 | − | 0.646744i | \(-0.223870\pi\) |
−0.646744 | + | 0.762707i | \(0.723870\pi\) | |||||||
\(588\) | −12.6389 | + | 39.6159i | −0.521220 | + | 1.63373i | ||||
\(589\) | − | 6.17499i | − | 0.254436i | ||||||
\(590\) | −17.9897 | − | 17.9897i | −0.740625 | − | 0.740625i | ||||
\(591\) | 2.29140 | − | 1.18295i | 0.0942555 | − | 0.0486602i | ||||
\(592\) | −9.97470 | − | 9.97470i | −0.409958 | − | 0.409958i | ||||
\(593\) | 11.5666 | − | 11.5666i | 0.474985 | − | 0.474985i | −0.428539 | − | 0.903523i | \(-0.640971\pi\) |
0.903523 | + | 0.428539i | \(0.140971\pi\) | |||||||
\(594\) | 1.24577 | − | 0.935905i | 0.0511146 | − | 0.0384007i | ||||
\(595\) | 21.0234i | 0.861876i | ||||||||
\(596\) | 22.8061 | − | 22.8061i | 0.934174 | − | 0.934174i | ||||
\(597\) | −32.4702 | − | 10.3592i | −1.32892 | − | 0.423972i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.33031i | 0.0952139i | 0.998866 | + | 0.0476069i | \(0.0151595\pi\) | ||||
−0.998866 | + | 0.0476069i | \(0.984841\pi\) | |||||||
\(600\) | −1.42770 | + | 0.737063i | −0.0582856 | + | 0.0300905i | ||||
\(601\) | −3.90549 | −0.159308 | −0.0796542 | − | 0.996823i | \(-0.525382\pi\) | ||||
−0.0796542 | + | 0.996823i | \(0.525382\pi\) | |||||||
\(602\) | −24.4298 | −0.995684 | ||||||||
\(603\) | 1.98926 | − | 0.336846i | 0.0810088 | − | 0.0137174i | ||||
\(604\) | −14.3779 | + | 14.3779i | −0.585030 | + | 0.585030i | ||||
\(605\) | 11.4885 | − | 11.4885i | 0.467073 | − | 0.467073i | ||||
\(606\) | 5.06394 | − | 2.61430i | 0.205708 | − | 0.106199i | ||||
\(607\) | 27.1575 | 1.10229 | 0.551144 | − | 0.834410i | \(-0.314192\pi\) | ||||
0.551144 | + | 0.834410i | \(0.314192\pi\) | |||||||
\(608\) | −9.30309 | −0.377290 | ||||||||
\(609\) | −7.07310 | − | 13.7007i | −0.286617 | − | 0.555180i | ||||
\(610\) | − | 16.8985i | − | 0.684201i | ||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 10.0771 | − | 14.1856i | 0.407344 | − | 0.573419i | ||||
\(613\) | 4.38429 | − | 4.38429i | 0.177080 | − | 0.177080i | −0.613002 | − | 0.790082i | \(-0.710038\pi\) |
0.790082 | + | 0.613002i | \(0.210038\pi\) | |||||||
\(614\) | − | 35.8262i | − | 1.44583i | ||||||
\(615\) | −20.4437 | − | 6.52229i | −0.824371 | − | 0.263004i | ||||
\(616\) | 0.160422 | − | 0.160422i | 0.00646360 | − | 0.00646360i | ||||
\(617\) | 29.0963 | + | 29.0963i | 1.17137 | + | 1.17137i | 0.981882 | + | 0.189492i | \(0.0606842\pi\) |
0.189492 | + | 0.981882i | \(0.439316\pi\) | |||||||
\(618\) | 6.86670 | + | 13.3009i | 0.276219 | + | 0.535040i | ||||
\(619\) | −7.15152 | − | 7.15152i | −0.287444 | − | 0.287444i | 0.548625 | − | 0.836069i | \(-0.315152\pi\) |
−0.836069 | + | 0.548625i | \(0.815152\pi\) | |||||||
\(620\) | 13.9865i | 0.561711i | ||||||||
\(621\) | −27.8457 | + | 20.9195i | −1.11741 | + | 0.839472i | ||||
\(622\) | −9.36218 | − | 9.36218i | −0.375389 | − | 0.375389i | ||||
\(623\) | 23.8117 | 0.953996 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.06353 | 0.122541 | ||||||||
\(626\) | −35.1101 | − | 35.1101i | −1.40328 | − | 1.40328i | ||||
\(627\) | −0.302529 | − | 0.0965176i | −0.0120818 | − | 0.00385454i | ||||
\(628\) | 19.1651i | 0.764771i | ||||||||
\(629\) | −7.33185 | − | 7.33185i | −0.292340 | − | 0.292340i | ||||
\(630\) | 38.4302 | − | 6.50748i | 1.53109 | − | 0.259264i | ||||
\(631\) | −8.97854 | − | 8.97854i | −0.357430 | − | 0.357430i | 0.505435 | − | 0.862865i | \(-0.331332\pi\) |
−0.862865 | + | 0.505435i | \(0.831332\pi\) | |||||||
\(632\) | −1.27586 | + | 1.27586i | −0.0507508 | + | 0.0507508i | ||||
\(633\) | −12.4183 | + | 38.9245i | −0.493584 | + | 1.54711i | ||||
\(634\) | 15.6548i | 0.621731i | ||||||||
\(635\) | −16.7205 | + | 16.7205i | −0.663534 | + | 0.663534i | ||||
\(636\) | −0.605536 | + | 1.89802i | −0.0240111 | + | 0.0752612i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 0.595269i | − | 0.0235669i | ||||||
\(639\) | 5.73132 | + | 33.8465i | 0.226727 | + | 1.33895i | ||||
\(640\) | −3.89647 | −0.154021 | ||||||||
\(641\) | 30.3342 | 1.19813 | 0.599065 | − | 0.800700i | \(-0.295539\pi\) | ||||
0.599065 | + | 0.800700i | \(0.295539\pi\) | |||||||
\(642\) | −24.0712 | − | 46.6263i | −0.950016 | − | 1.84019i | ||||
\(643\) | −33.4616 | + | 33.4616i | −1.31960 | + | 1.31960i | −0.405502 | + | 0.914094i | \(0.632903\pi\) |
−0.914094 | + | 0.405502i | \(0.867097\pi\) | |||||||
\(644\) | 38.9222 | − | 38.9222i | 1.53375 | − | 1.53375i | ||||
\(645\) | 3.27322 | + | 6.34027i | 0.128883 | + | 0.249648i | ||||
\(646\) | −7.41916 | −0.291903 | ||||||||
\(647\) | −19.2475 | −0.756696 | −0.378348 | − | 0.925663i | \(-0.623508\pi\) | ||||
−0.378348 | + | 0.925663i | \(0.623508\pi\) | |||||||
\(648\) | 2.67630 | + | 1.29252i | 0.105135 | + | 0.0507751i | ||||
\(649\) | 1.34528i | 0.0528069i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.1814 | − | 38.1819i | 0.477427 | − | 1.49647i | ||||
\(652\) | −2.51095 | + | 2.51095i | −0.0983366 | + | 0.0983366i | ||||
\(653\) | − | 9.85148i | − | 0.385518i | −0.981246 | − | 0.192759i | \(-0.938256\pi\) | ||
0.981246 | − | 0.192759i | \(-0.0617436\pi\) | |||||||
\(654\) | 12.7967 | − | 40.1106i | 0.500391 | − | 1.56845i | ||||
\(655\) | 19.6434 | − | 19.6434i | 0.767532 | − | 0.767532i | ||||
\(656\) | 25.5031 | + | 25.5031i | 0.995730 | + | 0.995730i | ||||
\(657\) | −2.77929 | − | 16.4132i | −0.108430 | − | 0.640341i | ||||
\(658\) | −35.6840 | − | 35.6840i | −1.39111 | − | 1.39111i | ||||
\(659\) | − | 4.63004i | − | 0.180361i | −0.995925 | − | 0.0901805i | \(-0.971256\pi\) | ||
0.995925 | − | 0.0901805i | \(-0.0287444\pi\) | |||||||
\(660\) | 0.685234 | + | 0.218614i | 0.0266727 | + | 0.00850955i | ||||
\(661\) | −21.7120 | − | 21.7120i | −0.844498 | − | 0.844498i | 0.144942 | − | 0.989440i | \(-0.453700\pi\) |
−0.989440 | + | 0.144942i | \(0.953700\pi\) | |||||||
\(662\) | 46.0604 | 1.79019 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.99247 | 0.116131 | ||||||||
\(665\) | −5.61693 | − | 5.61693i | −0.217815 | − | 0.217815i | ||||
\(666\) | −11.1329 | + | 15.6719i | −0.431393 | + | 0.607272i | ||||
\(667\) | 13.3056i | 0.515193i | ||||||||
\(668\) | −18.1059 | − | 18.1059i | −0.700537 | − | 0.700537i | ||||
\(669\) | −10.0230 | − | 19.4146i | −0.387510 | − | 0.750613i | ||||
\(670\) | 1.37777 | + | 1.37777i | 0.0532280 | + | 0.0532280i | ||||
\(671\) | −0.631840 | + | 0.631840i | −0.0243919 | + | 0.0243919i | ||||
\(672\) | −57.5240 | − | 18.3522i | −2.21903 | − | 0.707952i | ||||
\(673\) | − | 36.0212i | − | 1.38851i | −0.719727 | − | 0.694257i | \(-0.755733\pi\) | ||
0.719727 | − | 0.694257i | \(-0.244267\pi\) | |||||||
\(674\) | −11.4210 | + | 11.4210i | −0.439919 | + | 0.439919i | ||||
\(675\) | 8.76734 | + | 11.6701i | 0.337455 | + | 0.449182i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.60187i | 0.215297i | 0.994189 | + | 0.107649i | \(0.0343322\pi\) | ||||
−0.994189 | + | 0.107649i | \(0.965668\pi\) | |||||||
\(678\) | 7.45086 | + | 14.4324i | 0.286149 | + | 0.554274i | ||||
\(679\) | 20.0685 | 0.770159 | ||||||||
\(680\) | −1.54816 | −0.0593690 | ||||||||
\(681\) | 34.1924 | − | 17.6521i | 1.31025 | − | 0.676430i | ||||
\(682\) | 1.09409 | − | 1.09409i | 0.0418950 | − | 0.0418950i | ||||
\(683\) | 1.82603 | − | 1.82603i | 0.0698711 | − | 0.0698711i | −0.671308 | − | 0.741179i | \(-0.734267\pi\) |
0.741179 | + | 0.671308i | \(0.234267\pi\) | |||||||
\(684\) | 1.09768 | + | 6.48240i | 0.0419709 | + | 0.247861i | ||||
\(685\) | −8.76747 | −0.334988 | ||||||||
\(686\) | 53.6309 | 2.04764 | ||||||||
\(687\) | 15.3501 | − | 7.92460i | 0.585642 | − | 0.302343i | ||||
\(688\) | − | 11.9926i | − | 0.457215i | ||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −32.0440 | − | 10.2232i | −1.21989 | − | 0.389191i | ||||
\(691\) | 17.7451 | − | 17.7451i | 0.675054 | − | 0.675054i | −0.283823 | − | 0.958877i | \(-0.591603\pi\) |
0.958877 | + | 0.283823i | \(0.0916027\pi\) | |||||||
\(692\) | − | 32.8772i | − | 1.24980i | ||||||
\(693\) | −1.68023 | − | 1.19360i | −0.0638266 | − | 0.0453410i | ||||
\(694\) | −5.30936 | + | 5.30936i | −0.201541 | + | 0.201541i | ||||
\(695\) | 15.6679 | + | 15.6679i | 0.594319 | + | 0.594319i | ||||
\(696\) | 1.00891 | − | 0.520860i | 0.0382428 | − | 0.0197432i | ||||
\(697\) | 18.7459 | + | 18.7459i | 0.710052 | + | 0.710052i | ||||
\(698\) | − | 22.6327i | − | 0.856659i | ||||||
\(699\) | 12.0858 | − | 37.8823i | 0.457127 | − | 1.43284i | ||||
\(700\) | −16.3122 | − | 16.3122i | −0.616544 | − | 0.616544i | ||||
\(701\) | −0.474084 | −0.0179059 | −0.00895296 | − | 0.999960i | \(-0.502850\pi\) | ||||
−0.00895296 | + | 0.999960i | \(0.502850\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.91777 | 0.147761 | ||||||||
\(704\) | −0.714771 | − | 0.714771i | −0.0269390 | − | 0.0269390i | ||||
\(705\) | −4.47997 | + | 14.0422i | −0.168725 | + | 0.528860i | ||||
\(706\) | 20.0430i | 0.754329i | ||||||||
\(707\) | −5.33031 | − | 5.33031i | −0.200467 | − | 0.200467i | ||||
\(708\) | 24.7495 | − | 12.7771i | 0.930143 | − | 0.480194i | ||||
\(709\) | −35.1122 | − | 35.1122i | −1.31867 | − | 1.31867i | −0.914832 | − | 0.403834i | \(-0.867677\pi\) |
−0.403834 | − | 0.914832i | \(-0.632323\pi\) | |||||||
\(710\) | −23.4423 | + | 23.4423i | −0.879775 | + | 0.879775i | ||||
\(711\) | 13.3630 | + | 9.49280i | 0.501153 | + | 0.356008i | ||||
\(712\) | 1.75349i | 0.0657147i | ||||||||
\(713\) | −24.4554 | + | 24.4554i | −0.915862 | + | 0.915862i | ||||
\(714\) | −45.8750 | − | 14.6358i | −1.71683 | − | 0.547730i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 3.23624i | − | 0.120944i | ||||||
\(717\) | 27.6028 | − | 14.2502i | 1.03085 | − | 0.532183i | ||||
\(718\) | 20.7685 | 0.775074 | ||||||||
\(719\) | 1.69544 | 0.0632292 | 0.0316146 | − | 0.999500i | \(-0.489935\pi\) | ||||
0.0316146 | + | 0.999500i | \(0.489935\pi\) | |||||||
\(720\) | 3.19453 | + | 18.8654i | 0.119053 | + | 0.703073i | ||||
\(721\) | 14.0005 | − | 14.0005i | 0.521407 | − | 0.521407i | ||||
\(722\) | −24.3151 | + | 24.3151i | −0.904914 | + | 0.904914i | ||||
\(723\) | 4.34448 | − | 2.24287i | 0.161573 | − | 0.0834134i | ||||
\(724\) | −31.1226 | −1.15666 | ||||||||
\(725\) | 5.57634 | 0.207100 | ||||||||
\(726\) | 17.0710 | + | 33.0668i | 0.633564 | + | 1.22722i | ||||
\(727\) | − | 20.3423i | − | 0.754455i | −0.926121 | − | 0.377227i | \(-0.876878\pi\) | ||
0.926121 | − | 0.377227i | \(-0.123122\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.51800 | − | 25.9322i | 0.278445 | − | 0.960452i | ||||
\(730\) | 11.3679 | − | 11.3679i | 0.420745 | − | 0.420745i | ||||
\(731\) | − | 8.81511i | − | 0.326038i | ||||||
\(732\) | 17.6252 | + | 5.62307i | 0.651446 | + | 0.207835i | ||||
\(733\) | 3.64797 | − | 3.64797i | 0.134741 | − | 0.134741i | −0.636520 | − | 0.771261i | \(-0.719627\pi\) |
0.771261 | + | 0.636520i | \(0.219627\pi\) | |||||||
\(734\) | −19.3850 | − | 19.3850i | −0.715512 | − | 0.715512i | ||||
\(735\) | −15.4182 | − | 29.8653i | −0.568709 | − | 1.10160i | ||||
\(736\) | 36.8439 | + | 36.8439i | 1.35809 | + | 1.35809i | ||||
\(737\) | − | 0.103031i | − | 0.00379518i | ||||||
\(738\) | 28.4645 | − | 40.0695i | 1.04779 | − | 1.47498i | ||||
\(739\) | 26.5480 | + | 26.5480i | 0.976584 | + | 0.976584i | 0.999732 | − | 0.0231482i | \(-0.00736897\pi\) |
−0.0231482 | + | 0.999732i | \(0.507369\pi\) | |||||||
\(740\) | −8.87383 | −0.326209 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.51326 | 0.202398 | ||||||||
\(743\) | 6.45650 | + | 6.45650i | 0.236866 | + | 0.236866i | 0.815551 | − | 0.578685i | \(-0.196434\pi\) |
−0.578685 | + | 0.815551i | \(0.696434\pi\) | |||||||
\(744\) | 2.81170 | + | 0.897034i | 0.103082 | + | 0.0328869i | ||||
\(745\) | 26.0688i | 0.955087i | ||||||||
\(746\) | −27.6503 | − | 27.6503i | −1.01235 | − | 1.01235i | ||||
\(747\) | −4.53875 | − | 26.8038i | −0.166064 | − | 0.980699i | ||||
\(748\) | −0.628326 | − | 0.628326i | −0.0229739 | − | 0.0229739i | ||||
\(749\) | −49.0789 | + | 49.0789i | −1.79330 | + | 1.79330i | ||||
\(750\) | −11.9107 | + | 37.3334i | −0.434917 | + | 1.36322i | ||||
\(751\) | − | 23.1057i | − | 0.843137i | −0.906796 | − | 0.421569i | \(-0.861480\pi\) | ||
0.906796 | − | 0.421569i | \(-0.138520\pi\) | |||||||
\(752\) | 17.5173 | − | 17.5173i | 0.638792 | − | 0.638792i | ||||
\(753\) | 9.05125 | − | 28.3706i | 0.329846 | − | 1.03388i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 16.4349i | − | 0.598127i | ||||||
\(756\) | −6.00053 | + | 42.2481i | −0.218237 | + | 1.53655i | ||||
\(757\) | 37.9154 | 1.37806 | 0.689029 | − | 0.724734i | \(-0.258037\pi\) | ||||
0.689029 | + | 0.724734i | \(0.258037\pi\) | |||||||
\(758\) | −17.4249 | −0.632902 | ||||||||
\(759\) | 0.815886 | + | 1.58038i | 0.0296148 | + | 0.0573642i | ||||
\(760\) | 0.413628 | − | 0.413628i | 0.0150039 | − | 0.0150039i | ||||
\(761\) | −33.0810 | + | 33.0810i | −1.19919 | + | 1.19919i | −0.224774 | + | 0.974411i | \(0.572165\pi\) |
−0.974411 | + | 0.224774i | \(0.927835\pi\) | |||||||
\(762\) | −24.8455 | − | 48.1260i | −0.900056 | − | 1.74342i | ||||
\(763\) | −55.6903 | −2.01612 | ||||||||
\(764\) | 40.9771 | 1.48250 | ||||||||
\(765\) | 2.34812 | + | 13.8669i | 0.0848965 | + | 0.501360i | ||||
\(766\) | 45.9317i | 1.65958i | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 9.65974 | − | 30.2779i | 0.348566 | − | 1.09256i | ||||
\(769\) | −21.6783 | + | 21.6783i | −0.781738 | + | 0.781738i | −0.980124 | − | 0.198386i | \(-0.936430\pi\) |
0.198386 | + | 0.980124i | \(0.436430\pi\) | |||||||
\(770\) | − | 1.99043i | − | 0.0717302i | ||||||
\(771\) | 5.00543 | − | 15.6892i | 0.180266 | − | 0.565033i | ||||
\(772\) | −25.5221 | + | 25.5221i | −0.918559 | + | 0.918559i | ||||
\(773\) | 1.91473 | + | 1.91473i | 0.0688681 | + | 0.0688681i | 0.740702 | − | 0.671834i | \(-0.234493\pi\) |
−0.671834 | + | 0.740702i | \(0.734493\pi\) | |||||||
\(774\) | −16.1138 | + | 2.72858i | −0.579197 | + | 0.0980769i | ||||
\(775\) | 10.2492 | + | 10.2492i | 0.368163 | + | 0.368163i | ||||
\(776\) | 1.47784i | 0.0530513i | ||||||||
\(777\) | 24.2248 | + | 7.72859i | 0.869060 | + | 0.277262i | ||||
\(778\) | −45.7780 | − | 45.7780i | −1.64122 | − | 1.64122i | ||||
\(779\) | −10.0169 | −0.358892 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.75303 | 0.0627283 | ||||||||
\(782\) | 29.3828 | + | 29.3828i | 1.05073 | + | 1.05073i | ||||
\(783\) | −6.19562 | − | 8.24690i | −0.221413 | − | 0.294720i | ||||
\(784\) | 56.4902i | 2.01751i | ||||||||
\(785\) | −10.9535 | − | 10.9535i | −0.390946 | − | 0.390946i | ||||
\(786\) | 29.1887 | + | 56.5388i | 1.04113 | + | 2.01667i | ||||
\(787\) | 37.8082 | + | 37.8082i | 1.34772 | + | 1.34772i | 0.888137 | + | 0.459578i | \(0.151999\pi\) |
0.459578 | + | 0.888137i | \(0.348001\pi\) | |||||||
\(788\) | −1.92792 | + | 1.92792i | −0.0686792 | + | 0.0686792i | ||||
\(789\) | 11.9623 | + | 3.81642i | 0.425871 | + | 0.135868i | ||||
\(790\) | 15.8301i | 0.563210i | ||||||||
\(791\) | 15.1916 | − | 15.1916i | 0.540151 | − | 0.540151i | ||||
\(792\) | 0.0878960 | − | 0.123731i | 0.00312325 | − | 0.00439661i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | − | 65.5802i | − | 2.32735i | ||||||
\(795\) | −0.738693 | − | 1.43086i | −0.0261987 | − | 0.0507473i | ||||
\(796\) | 36.0354 | 1.27724 | ||||||||
\(797\) | −36.4286 | −1.29037 | −0.645183 | − | 0.764028i | \(-0.723219\pi\) | ||||
−0.645183 | + | 0.764028i | \(0.723219\pi\) | |||||||
\(798\) | 16.1670 | − | 8.34633i | 0.572304 | − | 0.295457i | ||||
\(799\) | 12.8760 | − | 12.8760i | 0.455521 | − | 0.455521i | ||||
\(800\) | 15.4412 | − | 15.4412i | 0.545930 | − | 0.545930i | ||||
\(801\) | 15.7061 | − | 2.65955i | 0.554947 | − | 0.0939706i | ||||
\(802\) | 33.5273 | 1.18389 | ||||||||
\(803\) | −0.850098 | −0.0299993 | ||||||||
\(804\) | −1.89548 | + | 0.978558i | −0.0668484 | + | 0.0345111i | ||||
\(805\) | 44.4905i | 1.56808i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 44.1864 | + | 14.0971i | 1.55544 | + | 0.496241i | ||||
\(808\) | 0.392522 | − | 0.392522i | 0.0138089 | − | 0.0138089i | ||||
\(809\) | 27.9069i | 0.981154i | 0.871398 | + | 0.490577i | \(0.163214\pi\) | ||||
−0.871398 | + | 0.490577i | \(0.836786\pi\) | |||||||
\(810\) | 24.6215 | − | 8.58459i | 0.865111 | − | 0.301632i | ||||
\(811\) | 9.41030 | − | 9.41030i | 0.330440 | − | 0.330440i | −0.522313 | − | 0.852754i | \(-0.674931\pi\) |
0.852754 | + | 0.522313i | \(0.174931\pi\) | |||||||
\(812\) | 11.5274 | + | 11.5274i | 0.404531 | + | 0.404531i | ||||
\(813\) | 2.60212 | − | 1.34337i | 0.0912602 | − | 0.0471139i | ||||
\(814\) | 0.694157 | + | 0.694157i | 0.0243302 | + | 0.0243302i | ||||
\(815\) | − | 2.87018i | − | 0.100538i | ||||||
\(816\) | 7.18473 | − | 22.5201i | 0.251516 | − | 0.788361i | ||||
\(817\) | 2.35518 | + | 2.35518i | 0.0823971 | + | 0.0823971i | ||||
\(818\) | 24.0632 | 0.841349 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 22.6884 | 0.792315 | ||||||||
\(821\) | −9.06140 | − | 9.06140i | −0.316245 | − | 0.316245i | 0.531078 | − | 0.847323i | \(-0.321787\pi\) |
−0.847323 | + | 0.531078i | \(0.821787\pi\) | |||||||
\(822\) | 6.10361 | − | 19.1314i | 0.212888 | − | 0.667285i | ||||
\(823\) | 20.7304i | 0.722615i | 0.932447 | + | 0.361308i | \(0.117670\pi\) | ||||
−0.932447 | + | 0.361308i | \(0.882330\pi\) | |||||||
\(824\) | 1.03099 | + | 1.03099i | 0.0359164 | + | 0.0359164i | ||||
\(825\) | 0.662335 | − | 0.341936i | 0.0230596 | − | 0.0119047i | ||||
\(826\) | −54.5027 | − | 54.5027i | −1.89639 | − | 1.89639i | ||||
\(827\) | −30.0036 | + | 30.0036i | −1.04333 | + | 1.04333i | −0.0443105 | + | 0.999018i | \(0.514109\pi\) |
−0.999018 | + | 0.0443105i | \(0.985891\pi\) | |||||||
\(828\) | 21.3256 | − | 30.0201i | 0.741116 | − | 1.04327i | ||||
\(829\) | 1.86550i | 0.0647914i | 0.999475 | + | 0.0323957i | \(0.0103137\pi\) | ||||
−0.999475 | + | 0.0323957i | \(0.989686\pi\) | |||||||
\(830\) | 18.5645 | − | 18.5645i | 0.644383 | − | 0.644383i | ||||
\(831\) | 41.1894 | + | 13.1409i | 1.42884 | + | 0.455853i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 41.5228i | 1.43868i | ||||||||
\(834\) | −45.0964 | + | 23.2814i | −1.56156 | + | 0.806168i | ||||
\(835\) | 20.6961 | 0.716219 | ||||||||
\(836\) | 0.335746 | 0.0116120 | ||||||||
\(837\) | 3.77022 | − | 26.5451i | 0.130318 | − | 0.917534i | ||||
\(838\) | 24.9297 | − | 24.9297i | 0.861183 | − | 0.861183i | ||||
\(839\) | 18.7951 | − | 18.7951i | 0.648880 | − | 0.648880i | −0.303843 | − | 0.952722i | \(-0.598270\pi\) |
0.952722 | + | 0.303843i | \(0.0982697\pi\) | |||||||
\(840\) | 3.37356 | − | 1.74163i | 0.116399 | − | 0.0600919i | ||||
\(841\) | 25.0594 | 0.864116 | ||||||||
\(842\) | −42.2055 | −1.45450 | ||||||||
\(843\) | −2.84348 | − | 5.50785i | −0.0979346 | − | 0.189701i | ||||
\(844\) | − | 43.1984i | − | 1.48695i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −27.5226 | − | 19.5514i | −0.946245 | − | 0.672191i | ||||
\(847\) | 34.8061 | − | 34.8061i | 1.19595 | − | 1.19595i | ||||
\(848\) | 2.70647i | 0.0929405i | ||||||||
\(849\) | 8.44678 | + | 2.69483i | 0.289893 | + | 0.0924863i | ||||
\(850\) | 12.3143 | − | 12.3143i | 0.422377 | − | 0.422377i | ||||
\(851\) | −15.5159 | − | 15.5159i | −0.531879 | − | 0.531879i | ||||
\(852\) | −16.6498 | − | 32.2509i | −0.570414 | − | 1.10490i | ||||
\(853\) | −15.8825 | − | 15.8825i | −0.543806 | − | 0.543806i | 0.380837 | − | 0.924642i | \(-0.375636\pi\) |
−0.924642 | + | 0.380837i | \(0.875636\pi\) | |||||||
\(854\) | − | 51.1967i | − | 1.75192i | ||||||
\(855\) | −4.33225 | − | 3.07753i | −0.148160 | − | 0.105249i | ||||
\(856\) | −3.61415 | − | 3.61415i | −0.123529 | − | 0.123529i | ||||
\(857\) | 48.2304 | 1.64752 | 0.823759 | − | 0.566941i | \(-0.191873\pi\) | ||||
0.823759 | + | 0.566941i | \(0.191873\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.5416 | −0.700870 | −0.350435 | − | 0.936587i | \(-0.613966\pi\) | ||||
−0.350435 | + | 0.936587i | \(0.613966\pi\) | |||||||
\(860\) | −5.33452 | − | 5.33452i | −0.181906 | − | 0.181906i | ||||
\(861\) | −61.9375 | − | 19.7603i | −2.11083 | − | 0.673430i | ||||
\(862\) | − | 59.1782i | − | 2.01562i | ||||||
\(863\) | −3.75723 | − | 3.75723i | −0.127898 | − | 0.127898i | 0.640260 | − | 0.768158i | \(-0.278826\pi\) |
−0.768158 | + | 0.640260i | \(0.778826\pi\) | |||||||
\(864\) | −39.9923 | − | 5.68013i | −1.36056 | − | 0.193242i | ||||
\(865\) | 18.7903 | + | 18.7903i | 0.638890 | + | 0.638890i | ||||
\(866\) | 26.6983 | − | 26.6983i | 0.907245 | − | 0.907245i | ||||
\(867\) | −3.66846 | + | 11.4986i | −0.124587 | + | 0.390512i | ||||
\(868\) | 42.3742i | 1.43828i | ||||||||
\(869\) | 0.591892 | − | 0.591892i | 0.0200786 | − | 0.0200786i | ||||
\(870\) | 3.02775 | − | 9.49030i | 0.102650 | − | 0.321751i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | − | 4.10101i | − | 0.138878i | ||||||
\(873\) | 13.2371 | − | 2.24147i | 0.448008 | − | 0.0758622i | ||||
\(874\) | −15.7007 | −0.531084 | ||||||||
\(875\) | 51.8344 | 1.75232 | ||||||||
\(876\) | 8.07401 | + | 15.6395i | 0.272796 | + | 0.528409i | ||||
\(877\) | 33.7528 | − | 33.7528i | 1.13975 | − | 1.13975i | 0.151257 | − | 0.988494i | \(-0.451668\pi\) |
0.988494 | − | 0.151257i | \(-0.0483322\pi\) | |||||||
\(878\) | −24.0635 | + | 24.0635i | −0.812105 | + | 0.812105i | ||||
\(879\) | −0.222815 | − | 0.431595i | −0.00751535 | − | 0.0145573i | ||||
\(880\) | 0.977107 | 0.0329383 | ||||||||
\(881\) | 22.4226 | 0.755437 | 0.377718 | − | 0.925920i | \(-0.376709\pi\) | ||||
0.377718 | + | 0.925920i | \(0.376709\pi\) | |||||||
\(882\) | 75.9024 | − | 12.8527i | 2.55577 | − | 0.432774i | ||||
\(883\) | 21.7280i | 0.731205i | 0.930771 | + | 0.365602i | \(0.119137\pi\) | ||||
−0.930771 | + | 0.365602i | \(0.880863\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.84257 | + | 21.4476i | −0.230011 | + | 0.720955i | ||||
\(886\) | −1.98366 | + | 1.98366i | −0.0666425 | + | 0.0666425i | ||||
\(887\) | − | 24.1403i | − | 0.810553i | −0.914194 | − | 0.405276i | \(-0.867175\pi\) | ||
0.914194 | − | 0.405276i | \(-0.132825\pi\) | |||||||
\(888\) | −0.569131 | + | 1.78391i | −0.0190988 | + | 0.0598640i | ||||
\(889\) | −50.6575 | + | 50.6575i | −1.69900 | + | 1.69900i | ||||
\(890\) | 10.8781 | + | 10.8781i | 0.364636 | + | 0.364636i | ||||
\(891\) | −1.24158 | − | 0.599624i | −0.0415946 | − | 0.0200882i | ||||
\(892\) | 16.3349 | + | 16.3349i | 0.546933 | + | 0.546933i | ||||
\(893\) | 6.88030i | 0.230240i | ||||||||
\(894\) | −56.8845 | − | 18.1482i | −1.90250 | − | 0.606967i | ||||
\(895\) | 1.84961 | + | 1.84961i | 0.0618258 | + | 0.0618258i | ||||
\(896\) | −11.8050 | −0.394376 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −75.6075 | −2.52305 | ||||||||
\(899\) | −7.24282 | − | 7.24282i | −0.241562 | − | 0.241562i | ||||
\(900\) | −12.5814 | − | 8.93753i | −0.419379 | − | 0.297918i | ||||
\(901\) | 1.98937i | 0.0662757i | ||||||||
\(902\) | −1.77481 | − | 1.77481i | −0.0590946 | − | 0.0590946i | ||||
\(903\) | 9.91673 | + | 19.2088i | 0.330008 | + | 0.639230i | ||||
\(904\) | 1.11870 | + | 1.11870i | 0.0372075 | + | 0.0372075i | ||||
\(905\) | 17.7875 | − | 17.7875i | 0.591277 | − | 0.591277i | ||||
\(906\) | 35.8624 | + | 11.4414i | 1.19145 | + | 0.380116i | ||||
\(907\) | 23.1138i | 0.767481i | 0.923441 | + | 0.383741i | \(0.125364\pi\) | ||||
−0.923441 | + | 0.383741i | \(0.874636\pi\) | |||||||
\(908\) | −28.7685 | + | 28.7685i | −0.954715 | + | 0.954715i | ||||
\(909\) | −4.11119 | − | 2.92050i | −0.136359 | − | 0.0968667i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.77371i | 0.290686i | 0.989381 | + | 0.145343i | \(0.0464286\pi\) | ||||
−0.989381 | + | 0.145343i | \(0.953571\pi\) | |||||||
\(912\) | 4.09723 | + | 7.93639i | 0.135673 | + | 0.262800i | ||||
\(913\) | −1.38826 | −0.0459447 | ||||||||
\(914\) | −9.10382 | −0.301128 | ||||||||
\(915\) | −13.2871 | + | 6.85958i | −0.439258 | + | 0.226771i | ||||
\(916\) | −12.9151 | + | 12.9151i | −0.426727 | + | 0.426727i | ||||
\(917\) | 59.5128 | − | 59.5128i | 1.96529 | − | 1.96529i | ||||
\(918\) | −31.8936 | − | 4.52987i | −1.05264 | − | 0.149508i | ||||
\(919\) | −0.279814 | −0.00923020 | −0.00461510 | − | 0.999989i | \(-0.501469\pi\) | ||||
−0.00461510 | + | 0.999989i | \(0.501469\pi\) | |||||||
\(920\) | −3.27626 | −0.108015 | ||||||||
\(921\) | −28.1697 | + | 14.5429i | −0.928224 | + | 0.479204i | ||||
\(922\) | − | 15.9506i | − | 0.525304i | ||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 2.07602 | + | 0.662327i | 0.0682962 | + | 0.0217889i | ||||
\(925\) | −6.50270 | + | 6.50270i | −0.213807 | + | 0.213807i | ||||
\(926\) | 12.9602i | 0.425898i | ||||||||
\(927\) | 7.67094 | − | 10.7984i | 0.251947 | − | 0.354666i | ||||
\(928\) | −10.9119 | + | 10.9119i | −0.358200 | + | 0.358200i | ||||
\(929\) | −13.0263 | − | 13.0263i | −0.427378 | − | 0.427378i | 0.460357 | − | 0.887734i | \(-0.347722\pi\) |
−0.887734 | + | 0.460357i | \(0.847722\pi\) | |||||||
\(930\) | 23.0080 | − | 11.8781i | 0.754461 | − | 0.389497i | ||||
\(931\) | −11.0938 | − | 11.0938i | −0.363586 | − | 0.363586i | ||||
\(932\) | 42.0417i | 1.37712i | ||||||||
\(933\) | −3.56100 | + | 11.1617i | −0.116582 | + | 0.365419i | ||||
\(934\) | −20.8945 | − | 20.8945i | −0.683687 | − | 0.683687i | ||||
\(935\) | 0.718216 | 0.0234882 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 58.7234 | 1.91841 | 0.959205 | − | 0.282712i | \(-0.0912341\pi\) | ||||
0.959205 | + | 0.282712i | \(0.0912341\pi\) | |||||||
\(938\) | 4.17418 | + | 4.17418i | 0.136292 | + | 0.136292i | ||||
\(939\) | −13.3545 | + | 41.8588i | −0.435807 | + | 1.36601i | ||||
\(940\) | − | 15.5840i | − | 0.508295i | ||||||
\(941\) | 21.2364 | + | 21.2364i | 0.692286 | + | 0.692286i | 0.962734 | − | 0.270448i | \(-0.0871720\pi\) |
−0.270448 | + | 0.962734i | \(0.587172\pi\) | |||||||
\(942\) | 31.5269 | − | 16.2760i | 1.02720 | − | 0.530302i | ||||
\(943\) | 39.6708 | + | 39.6708i | 1.29186 | + | 1.29186i | ||||
\(944\) | 26.7555 | − | 26.7555i | 0.870817 | − | 0.870817i | ||||
\(945\) | −20.7166 | − | 27.5756i | −0.673912 | − | 0.897035i | ||||
\(946\) | 0.834588i | 0.0271348i | ||||||||
\(947\) | −25.2698 | + | 25.2698i | −0.821159 | + | 0.821159i | −0.986274 | − | 0.165115i | \(-0.947200\pi\) |
0.165115 | + | 0.986274i | \(0.447200\pi\) | |||||||
\(948\) | −16.5108 | − | 5.26755i | −0.536247 | − | 0.171082i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 6.58014i | 0.213488i | ||||||||
\(951\) | 12.3092 | − | 6.35472i | 0.399152 | − | 0.206066i | ||||
\(952\) | −4.69038 | −0.152016 | ||||||||
\(953\) | 20.1011 | 0.651140 | 0.325570 | − | 0.945518i | \(-0.394444\pi\) | ||||
0.325570 | + | 0.945518i | \(0.394444\pi\) | |||||||
\(954\) | 3.63652 | − | 0.615780i | 0.117737 | − | 0.0199366i | ||||
\(955\) | −23.4197 | + | 23.4197i | −0.757844 | + | 0.757844i | ||||
\(956\) | −23.2242 | + | 23.2242i | −0.751124 | + | 0.751124i | ||||
\(957\) | −0.468053 | + | 0.241636i | −0.0151300 | + | 0.00781099i | ||||
\(958\) | 36.0266 | 1.16397 | ||||||||
\(959\) | −26.5624 | −0.857745 | ||||||||
\(960\) | −7.75993 | − | 15.0311i | −0.250451 | − | 0.485126i | ||||
\(961\) | 4.37562i | 0.141149i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −26.8905 | + | 37.8538i | −0.866535 | + | 1.21982i | ||||
\(964\) | −3.65532 | + | 3.65532i | −0.117730 | + | 0.117730i | ||||
\(965\) | − | 29.1733i | − | 0.939122i | ||||||
\(966\) | −97.0824 | − | 30.9728i | −3.12357 | − | 0.996533i | ||||
\(967\) | 4.09441 | − | 4.09441i | 0.131667 | − | 0.131667i | −0.638202 | − | 0.769869i | \(-0.720321\pi\) |
0.769869 | + | 0.638202i | \(0.220321\pi\) | |||||||
\(968\) | 2.56311 | + | 2.56311i | 0.0823814 | + | 0.0823814i | ||||
\(969\) | 3.01164 | + | 5.83359i | 0.0967479 | + | 0.187402i | ||||
\(970\) | 9.16810 | + | 9.16810i | 0.294370 | + | 0.294370i | ||||
\(971\) | − | 36.5458i | − | 1.17281i | −0.810018 | − | 0.586405i | \(-0.800543\pi\) | ||
0.810018 | − | 0.586405i | \(-0.199457\pi\) | |||||||
\(972\) | 0.760806 | + | 28.5368i | 0.0244029 | + | 0.915319i | ||||
\(973\) | 47.4685 | + | 47.4685i | 1.52177 | + | 1.52177i | ||||
\(974\) | −55.8590 | −1.78984 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 25.1326 | 0.804474 | ||||||||
\(977\) | −1.85263 | − | 1.85263i | −0.0592709 | − | 0.0592709i | 0.676850 | − | 0.736121i | \(-0.263345\pi\) |
−0.736121 | + | 0.676850i | \(0.763345\pi\) | |||||||
\(978\) | 6.26299 | + | 1.99812i | 0.200268 | + | 0.0638929i | ||||
\(979\) | − | 0.813473i | − | 0.0259987i | ||||||
\(980\) | 25.1278 | + | 25.1278i | 0.802678 | + | 0.802678i | ||||
\(981\) | −36.7330 | + | 6.22009i | −1.17279 | + | 0.198592i | ||||
\(982\) | 52.5889 | + | 52.5889i | 1.67818 | + | 1.67818i | ||||
\(983\) | −6.87065 | + | 6.87065i | −0.219140 | + | 0.219140i | −0.808136 | − | 0.588996i | \(-0.799523\pi\) |
0.588996 | + | 0.808136i | \(0.299523\pi\) | |||||||
\(984\) | 1.45514 | − | 4.56106i | 0.0463882 | − | 0.145401i | ||||
\(985\) | − | 2.20373i | − | 0.0702167i | ||||||
\(986\) | −8.70214 | + | 8.70214i | −0.277133 | + | 0.277133i | ||||
\(987\) | −13.5728 | + | 42.5431i | −0.432026 | + | 1.35416i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 18.6549i | − | 0.593190i | ||||||
\(990\) | −0.222313 | − | 1.31288i | −0.00706557 | − | 0.0417260i | ||||
\(991\) | −29.0606 | −0.923141 | −0.461570 | − | 0.887104i | \(-0.652714\pi\) | ||||
−0.461570 | + | 0.887104i | \(0.652714\pi\) | |||||||
\(992\) | −40.1117 | −1.27355 | ||||||||
\(993\) | −18.6972 | − | 36.2167i | −0.593337 | − | 1.14930i | ||||
\(994\) | −71.0222 | + | 71.0222i | −2.25269 | + | 2.25269i | ||||
\(995\) | −20.5954 | + | 20.5954i | −0.652916 | + | 0.652916i | ||||
\(996\) | 13.1854 | + | 25.5402i | 0.417794 | + | 0.809273i | ||||
\(997\) | 23.4421 | 0.742418 | 0.371209 | − | 0.928549i | \(-0.378943\pi\) | ||||
0.371209 | + | 0.928549i | \(0.378943\pi\) | |||||||
\(998\) | 31.1227 | 0.985172 | ||||||||
\(999\) | 16.8418 | + | 2.39205i | 0.532850 | + | 0.0756811i |
(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 | 507.2.f.g.239.19 | yes | 48 | |
3.2 | odd | 2 | inner | 507.2.f.g.239.6 | yes | 48 | |
13.2 | odd | 12 | 507.2.k.k.488.20 | 96 | |||
13.3 | even | 3 | 507.2.k.k.188.6 | 96 | |||
13.4 | even | 6 | 507.2.k.k.80.5 | 96 | |||
13.5 | odd | 4 | inner | 507.2.f.g.437.19 | yes | 48 | |
13.6 | odd | 12 | 507.2.k.k.89.5 | 96 | |||
13.7 | odd | 12 | 507.2.k.k.89.19 | 96 | |||
13.8 | odd | 4 | inner | 507.2.f.g.437.5 | yes | 48 | |
13.9 | even | 3 | 507.2.k.k.80.19 | 96 | |||
13.10 | even | 6 | 507.2.k.k.188.20 | 96 | |||
13.11 | odd | 12 | 507.2.k.k.488.6 | 96 | |||
13.12 | even | 2 | inner | 507.2.f.g.239.5 | ✓ | 48 | |
39.2 | even | 12 | 507.2.k.k.488.5 | 96 | |||
39.5 | even | 4 | inner | 507.2.f.g.437.6 | yes | 48 | |
39.8 | even | 4 | inner | 507.2.f.g.437.20 | yes | 48 | |
39.11 | even | 12 | 507.2.k.k.488.19 | 96 | |||
39.17 | odd | 6 | 507.2.k.k.80.20 | 96 | |||
39.20 | even | 12 | 507.2.k.k.89.6 | 96 | |||
39.23 | odd | 6 | 507.2.k.k.188.5 | 96 | |||
39.29 | odd | 6 | 507.2.k.k.188.19 | 96 | |||
39.32 | even | 12 | 507.2.k.k.89.20 | 96 | |||
39.35 | odd | 6 | 507.2.k.k.80.6 | 96 | |||
39.38 | odd | 2 | inner | 507.2.f.g.239.20 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.2.f.g.239.5 | ✓ | 48 | 13.12 | even | 2 | inner | |
507.2.f.g.239.6 | yes | 48 | 3.2 | odd | 2 | inner | |
507.2.f.g.239.19 | yes | 48 | 1.1 | even | 1 | trivial | |
507.2.f.g.239.20 | yes | 48 | 39.38 | odd | 2 | inner | |
507.2.f.g.437.5 | yes | 48 | 13.8 | odd | 4 | inner | |
507.2.f.g.437.6 | yes | 48 | 39.5 | even | 4 | inner | |
507.2.f.g.437.19 | yes | 48 | 13.5 | odd | 4 | inner | |
507.2.f.g.437.20 | yes | 48 | 39.8 | even | 4 | inner | |
507.2.k.k.80.5 | 96 | 13.4 | even | 6 | |||
507.2.k.k.80.6 | 96 | 39.35 | odd | 6 | |||
507.2.k.k.80.19 | 96 | 13.9 | even | 3 | |||
507.2.k.k.80.20 | 96 | 39.17 | odd | 6 | |||
507.2.k.k.89.5 | 96 | 13.6 | odd | 12 | |||
507.2.k.k.89.6 | 96 | 39.20 | even | 12 | |||
507.2.k.k.89.19 | 96 | 13.7 | odd | 12 | |||
507.2.k.k.89.20 | 96 | 39.32 | even | 12 | |||
507.2.k.k.188.5 | 96 | 39.23 | odd | 6 | |||
507.2.k.k.188.6 | 96 | 13.3 | even | 3 | |||
507.2.k.k.188.19 | 96 | 39.29 | odd | 6 | |||
507.2.k.k.188.20 | 96 | 13.10 | even | 6 | |||
507.2.k.k.488.5 | 96 | 39.2 | even | 12 | |||
507.2.k.k.488.6 | 96 | 13.11 | odd | 12 | |||
507.2.k.k.488.19 | 96 | 39.11 | even | 12 | |||
507.2.k.k.488.20 | 96 | 13.2 | odd | 12 |