Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(191,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.u (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: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 401.10 | ||
Character | \(\chi\) | \(=\) | 1110.401 |
Dual form | 1110.2.u.f.191.10 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 0.707107i | −0.500000 | + | 0.500000i | ||||
\(3\) | −1.55108 | − | 0.770820i | −0.895514 | − | 0.445033i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 0.707107 | + | 0.707107i | 0.316228 | + | 0.316228i | ||||
\(6\) | 1.64183 | − | 0.551724i | 0.670274 | − | 0.225241i | ||||
\(7\) | 4.38167 | 1.65611 | 0.828057 | − | 0.560643i | \(-0.189446\pi\) | ||||
0.828057 | + | 0.560643i | \(0.189446\pi\) | |||||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | 1.81167 | + | 2.39120i | 0.603891 | + | 0.797067i | ||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 4.49999 | 1.35680 | 0.678399 | − | 0.734694i | \(-0.262674\pi\) | ||||
0.678399 | + | 0.734694i | \(0.262674\pi\) | |||||||
\(12\) | −0.770820 | + | 1.55108i | −0.222517 | + | 0.447757i | ||||
\(13\) | 1.45588 | − | 1.45588i | 0.403789 | − | 0.403789i | −0.475777 | − | 0.879566i | \(-0.657833\pi\) |
0.879566 | + | 0.475777i | \(0.157833\pi\) | |||||||
\(14\) | −3.09831 | + | 3.09831i | −0.828057 | + | 0.828057i | ||||
\(15\) | −0.551724 | − | 1.64183i | −0.142455 | − | 0.423918i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 1.09123 | + | 1.09123i | 0.264662 | + | 0.264662i | 0.826945 | − | 0.562283i | \(-0.190077\pi\) |
−0.562283 | + | 0.826945i | \(0.690077\pi\) | |||||||
\(18\) | −2.97188 | − | 0.409787i | −0.700479 | − | 0.0965878i | ||||
\(19\) | −0.737671 | + | 0.737671i | −0.169233 | + | 0.169233i | −0.786642 | − | 0.617409i | \(-0.788182\pi\) |
0.617409 | + | 0.786642i | \(0.288182\pi\) | |||||||
\(20\) | 0.707107 | − | 0.707107i | 0.158114 | − | 0.158114i | ||||
\(21\) | −6.79630 | − | 3.37748i | −1.48307 | − | 0.737026i | ||||
\(22\) | −3.18197 | + | 3.18197i | −0.678399 | + | 0.678399i | ||||
\(23\) | −1.56045 | − | 1.56045i | −0.325376 | − | 0.325376i | 0.525449 | − | 0.850825i | \(-0.323897\pi\) |
−0.850825 | + | 0.525449i | \(0.823897\pi\) | |||||||
\(24\) | −0.551724 | − | 1.64183i | −0.112620 | − | 0.335137i | ||||
\(25\) | 1.00000i | 0.200000i | ||||||||
\(26\) | 2.05893i | 0.403789i | ||||||||
\(27\) | −0.966859 | − | 5.10541i | −0.186072 | − | 0.982536i | ||||
\(28\) | − | 4.38167i | − | 0.828057i | ||||||
\(29\) | −3.68128 | + | 3.68128i | −0.683597 | + | 0.683597i | −0.960809 | − | 0.277212i | \(-0.910590\pi\) |
0.277212 | + | 0.960809i | \(0.410590\pi\) | |||||||
\(30\) | 1.55108 | + | 0.770820i | 0.283186 | + | 0.140732i | ||||
\(31\) | −0.303265 | − | 0.303265i | −0.0544680 | − | 0.0544680i | 0.679348 | − | 0.733816i | \(-0.262263\pi\) |
−0.733816 | + | 0.679348i | \(0.762263\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | −6.97982 | − | 3.46868i | −1.21503 | − | 0.603820i | ||||
\(34\) | −1.54323 | −0.264662 | ||||||||
\(35\) | 3.09831 | + | 3.09831i | 0.523709 | + | 0.523709i | ||||
\(36\) | 2.39120 | − | 1.81167i | 0.398533 | − | 0.301946i | ||||
\(37\) | 0.167677 | + | 6.08045i | 0.0275659 | + | 0.999620i | ||||
\(38\) | − | 1.04322i | − | 0.169233i | ||||||
\(39\) | −3.38041 | + | 1.13596i | −0.541298 | + | 0.181899i | ||||
\(40\) | 1.00000i | 0.158114i | ||||||||
\(41\) | −1.99260 | −0.311192 | −0.155596 | − | 0.987821i | \(-0.549730\pi\) | ||||
−0.155596 | + | 0.987821i | \(0.549730\pi\) | |||||||
\(42\) | 7.19395 | − | 2.41747i | 1.11005 | − | 0.373024i | ||||
\(43\) | 0.568955 | − | 0.568955i | 0.0867648 | − | 0.0867648i | −0.662392 | − | 0.749157i | \(-0.730459\pi\) |
0.749157 | + | 0.662392i | \(0.230459\pi\) | |||||||
\(44\) | − | 4.49999i | − | 0.678399i | ||||||
\(45\) | −0.409787 | + | 2.97188i | −0.0610875 | + | 0.443022i | ||||
\(46\) | 2.20681 | 0.325376 | ||||||||
\(47\) | − | 8.83045i | − | 1.28805i | −0.765003 | − | 0.644027i | \(-0.777262\pi\) | ||
0.765003 | − | 0.644027i | \(-0.222738\pi\) | |||||||
\(48\) | 1.55108 | + | 0.770820i | 0.223879 | + | 0.111258i | ||||
\(49\) | 12.1990 | 1.74272 | ||||||||
\(50\) | −0.707107 | − | 0.707107i | −0.100000 | − | 0.100000i | ||||
\(51\) | −0.851438 | − | 2.53372i | −0.119225 | − | 0.354791i | ||||
\(52\) | −1.45588 | − | 1.45588i | −0.201894 | − | 0.201894i | ||||
\(53\) | − | 8.07611i | − | 1.10934i | −0.832071 | − | 0.554670i | \(-0.812845\pi\) | ||
0.832071 | − | 0.554670i | \(-0.187155\pi\) | |||||||
\(54\) | 4.29374 | + | 2.92640i | 0.584304 | + | 0.398232i | ||||
\(55\) | 3.18197 | + | 3.18197i | 0.429057 | + | 0.429057i | ||||
\(56\) | 3.09831 | + | 3.09831i | 0.414029 | + | 0.414029i | ||||
\(57\) | 1.71280 | − | 0.575573i | 0.226865 | − | 0.0762365i | ||||
\(58\) | − | 5.20612i | − | 0.683597i | ||||||
\(59\) | 9.81764 | + | 9.81764i | 1.27815 | + | 1.27815i | 0.941703 | + | 0.336445i | \(0.109224\pi\) |
0.336445 | + | 0.941703i | \(0.390776\pi\) | |||||||
\(60\) | −1.64183 | + | 0.551724i | −0.211959 | + | 0.0712273i | ||||
\(61\) | 0.496818 | + | 0.496818i | 0.0636110 | + | 0.0636110i | 0.738197 | − | 0.674586i | \(-0.235678\pi\) |
−0.674586 | + | 0.738197i | \(0.735678\pi\) | |||||||
\(62\) | 0.428882 | 0.0544680 | ||||||||
\(63\) | 7.93815 | + | 10.4774i | 1.00011 | + | 1.32003i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 2.05893 | 0.255378 | ||||||||
\(66\) | 7.38821 | − | 2.48275i | 0.909425 | − | 0.305606i | ||||
\(67\) | 7.31837i | 0.894081i | 0.894514 | + | 0.447040i | \(0.147522\pi\) | ||||
−0.894514 | + | 0.447040i | \(0.852478\pi\) | |||||||
\(68\) | 1.09123 | − | 1.09123i | 0.132331 | − | 0.132331i | ||||
\(69\) | 1.21755 | + | 3.62320i | 0.146576 | + | 0.436182i | ||||
\(70\) | −4.38167 | −0.523709 | ||||||||
\(71\) | 13.3890i | 1.58898i | 0.607280 | + | 0.794488i | \(0.292261\pi\) | ||||
−0.607280 | + | 0.794488i | \(0.707739\pi\) | |||||||
\(72\) | −0.409787 | + | 2.97188i | −0.0482939 | + | 0.350239i | ||||
\(73\) | − | 12.3051i | − | 1.44021i | −0.693867 | − | 0.720104i | \(-0.744094\pi\) | ||
0.693867 | − | 0.720104i | \(-0.255906\pi\) | |||||||
\(74\) | −4.41809 | − | 4.18096i | −0.513593 | − | 0.486027i | ||||
\(75\) | 0.770820 | − | 1.55108i | 0.0890066 | − | 0.179103i | ||||
\(76\) | 0.737671 | + | 0.737671i | 0.0846167 | + | 0.0846167i | ||||
\(77\) | 19.7174 | 2.24701 | ||||||||
\(78\) | 1.58706 | − | 3.19355i | 0.179699 | − | 0.361599i | ||||
\(79\) | −2.04760 | + | 2.04760i | −0.230373 | + | 0.230373i | −0.812848 | − | 0.582475i | \(-0.802084\pi\) |
0.582475 | + | 0.812848i | \(0.302084\pi\) | |||||||
\(80\) | −0.707107 | − | 0.707107i | −0.0790569 | − | 0.0790569i | ||||
\(81\) | −2.43568 | + | 8.66415i | −0.270631 | + | 0.962683i | ||||
\(82\) | 1.40898 | − | 1.40898i | 0.155596 | − | 0.155596i | ||||
\(83\) | − | 10.2732i | − | 1.12763i | −0.825903 | − | 0.563813i | \(-0.809334\pi\) | ||
0.825903 | − | 0.563813i | \(-0.190666\pi\) | |||||||
\(84\) | −3.37748 | + | 6.79630i | −0.368513 | + | 0.741537i | ||||
\(85\) | 1.54323i | 0.167387i | ||||||||
\(86\) | 0.804623i | 0.0867648i | ||||||||
\(87\) | 8.54756 | − | 2.87234i | 0.916394 | − | 0.307948i | ||||
\(88\) | 3.18197 | + | 3.18197i | 0.339199 | + | 0.339199i | ||||
\(89\) | 11.8187 | − | 11.8187i | 1.25278 | − | 1.25278i | 0.298316 | − | 0.954467i | \(-0.403575\pi\) |
0.954467 | − | 0.298316i | \(-0.0964250\pi\) | |||||||
\(90\) | −1.81167 | − | 2.39120i | −0.190967 | − | 0.252055i | ||||
\(91\) | 6.37919 | − | 6.37919i | 0.668721 | − | 0.668721i | ||||
\(92\) | −1.56045 | + | 1.56045i | −0.162688 | + | 0.162688i | ||||
\(93\) | 0.236625 | + | 0.704150i | 0.0245368 | + | 0.0730170i | ||||
\(94\) | 6.24407 | + | 6.24407i | 0.644027 | + | 0.644027i | ||||
\(95\) | −1.04322 | −0.107033 | ||||||||
\(96\) | −1.64183 | + | 0.551724i | −0.167568 | + | 0.0563101i | ||||
\(97\) | −0.766039 | + | 0.766039i | −0.0777795 | + | 0.0777795i | −0.744926 | − | 0.667147i | \(-0.767515\pi\) |
0.667147 | + | 0.744926i | \(0.267515\pi\) | |||||||
\(98\) | −8.62600 | + | 8.62600i | −0.871358 | + | 0.871358i | ||||
\(99\) | 8.15251 | + | 10.7604i | 0.819358 | + | 1.08146i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −12.5125 | −1.24504 | −0.622519 | − | 0.782604i | \(-0.713891\pi\) | ||||
−0.622519 | + | 0.782604i | \(0.713891\pi\) | |||||||
\(102\) | 2.39367 | + | 1.18955i | 0.237008 | + | 0.117783i | ||||
\(103\) | 6.46547 | + | 6.46547i | 0.637062 | + | 0.637062i | 0.949830 | − | 0.312768i | \(-0.101256\pi\) |
−0.312768 | + | 0.949830i | \(0.601256\pi\) | |||||||
\(104\) | 2.05893 | 0.201894 | ||||||||
\(105\) | −2.41747 | − | 7.19395i | −0.235921 | − | 0.702057i | ||||
\(106\) | 5.71067 | + | 5.71067i | 0.554670 | + | 0.554670i | ||||
\(107\) | 0.550155i | 0.0531855i | 0.999646 | + | 0.0265928i | \(0.00846573\pi\) | ||||
−0.999646 | + | 0.0265928i | \(0.991534\pi\) | |||||||
\(108\) | −5.10541 | + | 0.966859i | −0.491268 | + | 0.0930361i | ||||
\(109\) | −6.68407 | + | 6.68407i | −0.640217 | + | 0.640217i | −0.950609 | − | 0.310391i | \(-0.899540\pi\) |
0.310391 | + | 0.950609i | \(0.399540\pi\) | |||||||
\(110\) | −4.49999 | −0.429057 | ||||||||
\(111\) | 4.42685 | − | 9.56049i | 0.420178 | − | 0.907442i | ||||
\(112\) | −4.38167 | −0.414029 | ||||||||
\(113\) | −6.11267 | + | 6.11267i | −0.575032 | + | 0.575032i | −0.933530 | − | 0.358499i | \(-0.883289\pi\) |
0.358499 | + | 0.933530i | \(0.383289\pi\) | |||||||
\(114\) | −0.804138 | + | 1.61812i | −0.0753145 | + | 0.151551i | ||||
\(115\) | − | 2.20681i | − | 0.205786i | ||||||
\(116\) | 3.68128 | + | 3.68128i | 0.341799 | + | 0.341799i | ||||
\(117\) | 6.11889 | + | 0.843722i | 0.565691 | + | 0.0780021i | ||||
\(118\) | −13.8842 | −1.27815 | ||||||||
\(119\) | 4.78140 | + | 4.78140i | 0.438310 | + | 0.438310i | ||||
\(120\) | 0.770820 | − | 1.55108i | 0.0703659 | − | 0.141593i | ||||
\(121\) | 9.24988 | 0.840898 | ||||||||
\(122\) | −0.702607 | −0.0636110 | ||||||||
\(123\) | 3.09068 | + | 1.53594i | 0.278677 | + | 0.138491i | ||||
\(124\) | −0.303265 | + | 0.303265i | −0.0272340 | + | 0.0272340i | ||||
\(125\) | −0.707107 | + | 0.707107i | −0.0632456 | + | 0.0632456i | ||||
\(126\) | −13.0218 | − | 1.79555i | −1.16007 | − | 0.159960i | ||||
\(127\) | 18.8279 | 1.67070 | 0.835352 | − | 0.549716i | \(-0.185264\pi\) | ||||
0.835352 | + | 0.549716i | \(0.185264\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | −1.32105 | + | 0.443930i | −0.116312 | + | 0.0390859i | ||||
\(130\) | −1.45588 | + | 1.45588i | −0.127689 | + | 0.127689i | ||||
\(131\) | −6.50740 | + | 6.50740i | −0.568554 | + | 0.568554i | −0.931723 | − | 0.363169i | \(-0.881695\pi\) |
0.363169 | + | 0.931723i | \(0.381695\pi\) | |||||||
\(132\) | −3.46868 | + | 6.97982i | −0.301910 | + | 0.607516i | ||||
\(133\) | −3.23223 | + | 3.23223i | −0.280270 | + | 0.280270i | ||||
\(134\) | −5.17487 | − | 5.17487i | −0.447040 | − | 0.447040i | ||||
\(135\) | 2.92640 | − | 4.29374i | 0.251864 | − | 0.369546i | ||||
\(136\) | 1.54323i | 0.132331i | ||||||||
\(137\) | − | 19.5068i | − | 1.66658i | −0.552838 | − | 0.833289i | \(-0.686455\pi\) | ||
0.552838 | − | 0.833289i | \(-0.313545\pi\) | |||||||
\(138\) | −3.42293 | − | 1.70105i | −0.291379 | − | 0.144803i | ||||
\(139\) | 17.7979i | 1.50960i | 0.655954 | + | 0.754801i | \(0.272266\pi\) | ||||
−0.655954 | + | 0.754801i | \(0.727734\pi\) | |||||||
\(140\) | 3.09831 | − | 3.09831i | 0.261855 | − | 0.261855i | ||||
\(141\) | −6.80669 | + | 13.6967i | −0.573227 | + | 1.15347i | ||||
\(142\) | −9.46742 | − | 9.46742i | −0.794488 | − | 0.794488i | ||||
\(143\) | 6.55145 | − | 6.55145i | 0.547860 | − | 0.547860i | ||||
\(144\) | −1.81167 | − | 2.39120i | −0.150973 | − | 0.199267i | ||||
\(145\) | −5.20612 | −0.432345 | ||||||||
\(146\) | 8.70104 | + | 8.70104i | 0.720104 | + | 0.720104i | ||||
\(147\) | −18.9216 | − | 9.40324i | −1.56063 | − | 0.775566i | ||||
\(148\) | 6.08045 | − | 0.167677i | 0.499810 | − | 0.0137830i | ||||
\(149\) | − | 19.3712i | − | 1.58695i | −0.608602 | − | 0.793476i | \(-0.708269\pi\) | ||
0.608602 | − | 0.793476i | \(-0.291731\pi\) | |||||||
\(150\) | 0.551724 | + | 1.64183i | 0.0450481 | + | 0.134055i | ||||
\(151\) | − | 12.1984i | − | 0.992693i | −0.868124 | − | 0.496347i | \(-0.834675\pi\) | ||
0.868124 | − | 0.496347i | \(-0.165325\pi\) | |||||||
\(152\) | −1.04322 | −0.0846167 | ||||||||
\(153\) | −0.632396 | + | 4.58629i | −0.0511262 | + | 0.370780i | ||||
\(154\) | −13.9423 | + | 13.9423i | −1.12351 | + | 1.12351i | ||||
\(155\) | − | 0.428882i | − | 0.0344486i | ||||||
\(156\) | 1.13596 | + | 3.38041i | 0.0909496 | + | 0.270649i | ||||
\(157\) | −7.11091 | −0.567512 | −0.283756 | − | 0.958896i | \(-0.591581\pi\) | ||||
−0.283756 | + | 0.958896i | \(0.591581\pi\) | |||||||
\(158\) | − | 2.89575i | − | 0.230373i | ||||||
\(159\) | −6.22523 | + | 12.5267i | −0.493692 | + | 0.993429i | ||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −6.83737 | − | 6.83737i | −0.538860 | − | 0.538860i | ||||
\(162\) | −4.40419 | − | 7.84876i | −0.346026 | − | 0.616657i | ||||
\(163\) | −3.95330 | − | 3.95330i | −0.309646 | − | 0.309646i | 0.535126 | − | 0.844772i | \(-0.320264\pi\) |
−0.844772 | + | 0.535126i | \(0.820264\pi\) | |||||||
\(164\) | 1.99260i | 0.155596i | ||||||||
\(165\) | −2.48275 | − | 7.38821i | −0.193282 | − | 0.575171i | ||||
\(166\) | 7.26422 | + | 7.26422i | 0.563813 | + | 0.563813i | ||||
\(167\) | −1.00757 | − | 1.00757i | −0.0779683 | − | 0.0779683i | 0.667047 | − | 0.745015i | \(-0.267558\pi\) |
−0.745015 | + | 0.667047i | \(0.767558\pi\) | |||||||
\(168\) | −2.41747 | − | 7.19395i | −0.186512 | − | 0.555025i | ||||
\(169\) | 8.76082i | 0.673909i | ||||||||
\(170\) | −1.09123 | − | 1.09123i | −0.0836934 | − | 0.0836934i | ||||
\(171\) | −3.10034 | − | 0.427500i | −0.237089 | − | 0.0326918i | ||||
\(172\) | −0.568955 | − | 0.568955i | −0.0433824 | − | 0.0433824i | ||||
\(173\) | −1.51433 | −0.115132 | −0.0575660 | − | 0.998342i | \(-0.518334\pi\) | ||||
−0.0575660 | + | 0.998342i | \(0.518334\pi\) | |||||||
\(174\) | −4.01298 | + | 8.07509i | −0.304223 | + | 0.612171i | ||||
\(175\) | 4.38167i | 0.331223i | ||||||||
\(176\) | −4.49999 | −0.339199 | ||||||||
\(177\) | −7.66027 | − | 22.7955i | −0.575782 | − | 1.71342i | ||||
\(178\) | 16.7142i | 1.25278i | ||||||||
\(179\) | 2.61668 | − | 2.61668i | 0.195580 | − | 0.195580i | −0.602522 | − | 0.798102i | \(-0.705838\pi\) |
0.798102 | + | 0.602522i | \(0.205838\pi\) | |||||||
\(180\) | 2.97188 | + | 0.409787i | 0.221511 | + | 0.0305437i | ||||
\(181\) | −8.02378 | −0.596403 | −0.298201 | − | 0.954503i | \(-0.596387\pi\) | ||||
−0.298201 | + | 0.954503i | \(0.596387\pi\) | |||||||
\(182\) | 9.02154i | 0.668721i | ||||||||
\(183\) | −0.387645 | − | 1.15356i | −0.0286556 | − | 0.0852736i | ||||
\(184\) | − | 2.20681i | − | 0.162688i | ||||||
\(185\) | −4.18096 | + | 4.41809i | −0.307390 | + | 0.324825i | ||||
\(186\) | −0.665228 | − | 0.330591i | −0.0487769 | − | 0.0242401i | ||||
\(187\) | 4.91051 | + | 4.91051i | 0.359092 | + | 0.359092i | ||||
\(188\) | −8.83045 | −0.644027 | ||||||||
\(189\) | −4.23646 | − | 22.3702i | −0.308157 | − | 1.62719i | ||||
\(190\) | 0.737671 | − | 0.737671i | 0.0535163 | − | 0.0535163i | ||||
\(191\) | −3.71929 | − | 3.71929i | −0.269118 | − | 0.269118i | 0.559627 | − | 0.828745i | \(-0.310945\pi\) |
−0.828745 | + | 0.559627i | \(0.810945\pi\) | |||||||
\(192\) | 0.770820 | − | 1.55108i | 0.0556291 | − | 0.111939i | ||||
\(193\) | 11.4367 | − | 11.4367i | 0.823235 | − | 0.823235i | −0.163336 | − | 0.986571i | \(-0.552225\pi\) |
0.986571 | + | 0.163336i | \(0.0522253\pi\) | |||||||
\(194\) | − | 1.08334i | − | 0.0777795i | ||||||
\(195\) | −3.19355 | − | 1.58706i | −0.228695 | − | 0.113652i | ||||
\(196\) | − | 12.1990i | − | 0.871358i | ||||||
\(197\) | 12.8748i | 0.917293i | 0.888619 | + | 0.458646i | \(0.151666\pi\) | ||||
−0.888619 | + | 0.458646i | \(0.848334\pi\) | |||||||
\(198\) | −13.3734 | − | 1.84404i | −0.950408 | − | 0.131050i | ||||
\(199\) | 16.5646 | + | 16.5646i | 1.17423 | + | 1.17423i | 0.981190 | + | 0.193044i | \(0.0618359\pi\) |
0.193044 | + | 0.981190i | \(0.438164\pi\) | |||||||
\(200\) | −0.707107 | + | 0.707107i | −0.0500000 | + | 0.0500000i | ||||
\(201\) | 5.64114 | − | 11.3513i | 0.397895 | − | 0.800662i | ||||
\(202\) | 8.84766 | − | 8.84766i | 0.622519 | − | 0.622519i | ||||
\(203\) | −16.1302 | + | 16.1302i | −1.13212 | + | 1.13212i | ||||
\(204\) | −2.53372 | + | 0.851438i | −0.177396 | + | 0.0596126i | ||||
\(205\) | −1.40898 | − | 1.40898i | −0.0984076 | − | 0.0984076i | ||||
\(206\) | −9.14355 | −0.637062 | ||||||||
\(207\) | 0.904321 | − | 6.55837i | 0.0628547 | − | 0.455838i | ||||
\(208\) | −1.45588 | + | 1.45588i | −0.100947 | + | 0.100947i | ||||
\(209\) | −3.31951 | + | 3.31951i | −0.229615 | + | 0.229615i | ||||
\(210\) | 6.79630 | + | 3.37748i | 0.468989 | + | 0.233068i | ||||
\(211\) | −9.22945 | −0.635382 | −0.317691 | − | 0.948194i | \(-0.602907\pi\) | ||||
−0.317691 | + | 0.948194i | \(0.602907\pi\) | |||||||
\(212\) | −8.07611 | −0.554670 | ||||||||
\(213\) | 10.3205 | − | 20.7673i | 0.707147 | − | 1.42295i | ||||
\(214\) | −0.389018 | − | 0.389018i | −0.0265928 | − | 0.0265928i | ||||
\(215\) | 0.804623 | 0.0548749 | ||||||||
\(216\) | 2.92640 | − | 4.29374i | 0.199116 | − | 0.292152i | ||||
\(217\) | −1.32881 | − | 1.32881i | −0.0902053 | − | 0.0902053i | ||||
\(218\) | − | 9.45270i | − | 0.640217i | ||||||
\(219\) | −9.48504 | + | 19.0862i | −0.640940 | + | 1.28973i | ||||
\(220\) | 3.18197 | − | 3.18197i | 0.214528 | − | 0.214528i | ||||
\(221\) | 3.17740 | 0.213735 | ||||||||
\(222\) | 3.63003 | + | 9.89054i | 0.243632 | + | 0.663810i | ||||
\(223\) | −21.7378 | −1.45567 | −0.727837 | − | 0.685750i | \(-0.759474\pi\) | ||||
−0.727837 | + | 0.685750i | \(0.759474\pi\) | |||||||
\(224\) | 3.09831 | − | 3.09831i | 0.207014 | − | 0.207014i | ||||
\(225\) | −2.39120 | + | 1.81167i | −0.159413 | + | 0.120778i | ||||
\(226\) | − | 8.64462i | − | 0.575032i | ||||||
\(227\) | 11.6318 | + | 11.6318i | 0.772032 | + | 0.772032i | 0.978462 | − | 0.206429i | \(-0.0661843\pi\) |
−0.206429 | + | 0.978462i | \(0.566184\pi\) | |||||||
\(228\) | −0.575573 | − | 1.71280i | −0.0381182 | − | 0.113433i | ||||
\(229\) | 10.0261 | 0.662545 | 0.331272 | − | 0.943535i | \(-0.392522\pi\) | ||||
0.331272 | + | 0.943535i | \(0.392522\pi\) | |||||||
\(230\) | 1.56045 | + | 1.56045i | 0.102893 | + | 0.102893i | ||||
\(231\) | −30.5833 | − | 15.1986i | −2.01223 | − | 0.999994i | ||||
\(232\) | −5.20612 | −0.341799 | ||||||||
\(233\) | −14.0316 | −0.919243 | −0.459622 | − | 0.888115i | \(-0.652015\pi\) | ||||
−0.459622 | + | 0.888115i | \(0.652015\pi\) | |||||||
\(234\) | −4.92331 | + | 3.73010i | −0.321847 | + | 0.243845i | ||||
\(235\) | 6.24407 | − | 6.24407i | 0.407318 | − | 0.407318i | ||||
\(236\) | 9.81764 | − | 9.81764i | 0.639074 | − | 0.639074i | ||||
\(237\) | 4.75432 | − | 1.59765i | 0.308826 | − | 0.103779i | ||||
\(238\) | −6.76192 | −0.438310 | ||||||||
\(239\) | −1.89394 | − | 1.89394i | −0.122509 | − | 0.122509i | 0.643194 | − | 0.765703i | \(-0.277609\pi\) |
−0.765703 | + | 0.643194i | \(0.777609\pi\) | |||||||
\(240\) | 0.551724 | + | 1.64183i | 0.0356137 | + | 0.105980i | ||||
\(241\) | 11.7784 | − | 11.7784i | 0.758715 | − | 0.758715i | −0.217373 | − | 0.976089i | \(-0.569749\pi\) |
0.976089 | + | 0.217373i | \(0.0697489\pi\) | |||||||
\(242\) | −6.54065 | + | 6.54065i | −0.420449 | + | 0.420449i | ||||
\(243\) | 10.4564 | − | 11.5613i | 0.670780 | − | 0.741657i | ||||
\(244\) | 0.496818 | − | 0.496818i | 0.0318055 | − | 0.0318055i | ||||
\(245\) | 8.62600 | + | 8.62600i | 0.551095 | + | 0.551095i | ||||
\(246\) | −3.27151 | + | 1.09937i | −0.208584 | + | 0.0700931i | ||||
\(247\) | 2.14792i | 0.136669i | ||||||||
\(248\) | − | 0.428882i | − | 0.0272340i | ||||||
\(249\) | −7.91876 | + | 15.9345i | −0.501831 | + | 1.00980i | ||||
\(250\) | − | 1.00000i | − | 0.0632456i | ||||||
\(251\) | 10.9133 | − | 10.9133i | 0.688839 | − | 0.688839i | −0.273136 | − | 0.961975i | \(-0.588061\pi\) |
0.961975 | + | 0.273136i | \(0.0880610\pi\) | |||||||
\(252\) | 10.4774 | − | 7.93815i | 0.660017 | − | 0.500057i | ||||
\(253\) | −7.02200 | − | 7.02200i | −0.441469 | − | 0.441469i | ||||
\(254\) | −13.3133 | + | 13.3133i | −0.835352 | + | 0.835352i | ||||
\(255\) | 1.18955 | − | 2.39367i | 0.0744926 | − | 0.149897i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −16.7640 | − | 16.7640i | −1.04571 | − | 1.04571i | −0.998904 | − | 0.0468078i | \(-0.985095\pi\) |
−0.0468078 | − | 0.998904i | \(-0.514905\pi\) | |||||||
\(258\) | 0.620220 | − | 1.24803i | 0.0386132 | − | 0.0776991i | ||||
\(259\) | 0.734705 | + | 26.6425i | 0.0456524 | + | 1.65549i | ||||
\(260\) | − | 2.05893i | − | 0.127689i | ||||||
\(261\) | −15.4720 | − | 2.13340i | −0.957691 | − | 0.132054i | ||||
\(262\) | − | 9.20286i | − | 0.568554i | ||||||
\(263\) | 16.2544 | 1.00229 | 0.501145 | − | 0.865363i | \(-0.332912\pi\) | ||||
0.501145 | + | 0.865363i | \(0.332912\pi\) | |||||||
\(264\) | −2.48275 | − | 7.38821i | −0.152803 | − | 0.454713i | ||||
\(265\) | 5.71067 | − | 5.71067i | 0.350804 | − | 0.350804i | ||||
\(266\) | − | 4.57106i | − | 0.280270i | ||||||
\(267\) | −27.4419 | + | 9.22164i | −1.67942 | + | 0.564355i | ||||
\(268\) | 7.31837 | 0.447040 | ||||||||
\(269\) | 14.2889i | 0.871212i | 0.900137 | + | 0.435606i | \(0.143466\pi\) | ||||
−0.900137 | + | 0.435606i | \(0.856534\pi\) | |||||||
\(270\) | 0.966859 | + | 5.10541i | 0.0588412 | + | 0.310705i | ||||
\(271\) | 20.3803 | 1.23802 | 0.619008 | − | 0.785385i | \(-0.287535\pi\) | ||||
0.619008 | + | 0.785385i | \(0.287535\pi\) | |||||||
\(272\) | −1.09123 | − | 1.09123i | −0.0661654 | − | 0.0661654i | ||||
\(273\) | −14.8118 | + | 4.97740i | −0.896452 | + | 0.301246i | ||||
\(274\) | 13.7934 | + | 13.7934i | 0.833289 | + | 0.833289i | ||||
\(275\) | 4.49999i | 0.271359i | ||||||||
\(276\) | 3.62320 | − | 1.21755i | 0.218091 | − | 0.0732879i | ||||
\(277\) | −17.5786 | − | 17.5786i | −1.05619 | − | 1.05619i | −0.998324 | − | 0.0578693i | \(-0.981569\pi\) |
−0.0578693 | − | 0.998324i | \(-0.518431\pi\) | |||||||
\(278\) | −12.5850 | − | 12.5850i | −0.754801 | − | 0.754801i | ||||
\(279\) | 0.175750 | − | 1.27459i | 0.0105219 | − | 0.0763074i | ||||
\(280\) | 4.38167i | 0.261855i | ||||||||
\(281\) | 1.34583 | + | 1.34583i | 0.0802855 | + | 0.0802855i | 0.746109 | − | 0.665824i | \(-0.231920\pi\) |
−0.665824 | + | 0.746109i | \(0.731920\pi\) | |||||||
\(282\) | −4.87198 | − | 14.4981i | −0.290122 | − | 0.863349i | ||||
\(283\) | 0.275222 | + | 0.275222i | 0.0163602 | + | 0.0163602i | 0.715240 | − | 0.698879i | \(-0.246318\pi\) |
−0.698879 | + | 0.715240i | \(0.746318\pi\) | |||||||
\(284\) | 13.3890 | 0.794488 | ||||||||
\(285\) | 1.61812 | + | 0.804138i | 0.0958492 | + | 0.0476330i | ||||
\(286\) | 9.26515i | 0.547860i | ||||||||
\(287\) | −8.73092 | −0.515370 | ||||||||
\(288\) | 2.97188 | + | 0.409787i | 0.175120 | + | 0.0241469i | ||||
\(289\) | − | 14.6184i | − | 0.859908i | ||||||
\(290\) | 3.68128 | − | 3.68128i | 0.216172 | − | 0.216172i | ||||
\(291\) | 1.77866 | − | 0.597707i | 0.104267 | − | 0.0350382i | ||||
\(292\) | −12.3051 | −0.720104 | ||||||||
\(293\) | 3.04158i | 0.177691i | 0.996045 | + | 0.0888455i | \(0.0283178\pi\) | ||||
−0.996045 | + | 0.0888455i | \(0.971682\pi\) | |||||||
\(294\) | 20.0287 | − | 6.73049i | 1.16810 | − | 0.392530i | ||||
\(295\) | 13.8842i | 0.808372i | ||||||||
\(296\) | −4.18096 | + | 4.41809i | −0.243014 | + | 0.256796i | ||||
\(297\) | −4.35085 | − | 22.9743i | −0.252462 | − | 1.33310i | ||||
\(298\) | 13.6975 | + | 13.6975i | 0.793476 | + | 0.793476i | ||||
\(299\) | −4.54366 | −0.262766 | ||||||||
\(300\) | −1.55108 | − | 0.770820i | −0.0895514 | − | 0.0445033i | ||||
\(301\) | 2.49297 | − | 2.49297i | 0.143692 | − | 0.143692i | ||||
\(302\) | 8.62559 | + | 8.62559i | 0.496347 | + | 0.496347i | ||||
\(303\) | 19.4078 | + | 9.64487i | 1.11495 | + | 0.554083i | ||||
\(304\) | 0.737671 | − | 0.737671i | 0.0423084 | − | 0.0423084i | ||||
\(305\) | 0.702607i | 0.0402311i | ||||||||
\(306\) | −2.79583 | − | 3.69017i | −0.159827 | − | 0.210953i | ||||
\(307\) | 13.1974i | 0.753217i | 0.926373 | + | 0.376608i | \(0.122910\pi\) | ||||
−0.926373 | + | 0.376608i | \(0.877090\pi\) | |||||||
\(308\) | − | 19.7174i | − | 1.12351i | ||||||
\(309\) | −5.04472 | − | 15.0121i | −0.286984 | − | 0.854011i | ||||
\(310\) | 0.303265 | + | 0.303265i | 0.0172243 | + | 0.0172243i | ||||
\(311\) | 16.5296 | − | 16.5296i | 0.937307 | − | 0.937307i | −0.0608406 | − | 0.998147i | \(-0.519378\pi\) |
0.998147 | + | 0.0608406i | \(0.0193781\pi\) | |||||||
\(312\) | −3.19355 | − | 1.58706i | −0.180799 | − | 0.0898497i | ||||
\(313\) | 4.43787 | − | 4.43787i | 0.250843 | − | 0.250843i | −0.570473 | − | 0.821316i | \(-0.693240\pi\) |
0.821316 | + | 0.570473i | \(0.193240\pi\) | |||||||
\(314\) | 5.02817 | − | 5.02817i | 0.283756 | − | 0.283756i | ||||
\(315\) | −1.79555 | + | 13.0218i | −0.101168 | + | 0.733695i | ||||
\(316\) | 2.04760 | + | 2.04760i | 0.115187 | + | 0.115187i | ||||
\(317\) | −3.18702 | −0.179001 | −0.0895003 | − | 0.995987i | \(-0.528527\pi\) | ||||
−0.0895003 | + | 0.995987i | \(0.528527\pi\) | |||||||
\(318\) | −4.45579 | − | 13.2596i | −0.249868 | − | 0.743561i | ||||
\(319\) | −16.5657 | + | 16.5657i | −0.927503 | + | 0.927503i | ||||
\(320\) | −0.707107 | + | 0.707107i | −0.0395285 | + | 0.0395285i | ||||
\(321\) | 0.424070 | − | 0.853332i | 0.0236693 | − | 0.0476284i | ||||
\(322\) | 9.66950 | 0.538860 | ||||||||
\(323\) | −1.60994 | −0.0895792 | ||||||||
\(324\) | 8.66415 | + | 2.43568i | 0.481342 | + | 0.135315i | ||||
\(325\) | 1.45588 | + | 1.45588i | 0.0807578 | + | 0.0807578i | ||||
\(326\) | 5.59081 | 0.309646 | ||||||||
\(327\) | 15.5197 | − | 5.21528i | 0.858242 | − | 0.288406i | ||||
\(328\) | −1.40898 | − | 1.40898i | −0.0777981 | − | 0.0777981i | ||||
\(329\) | − | 38.6921i | − | 2.13317i | ||||||
\(330\) | 6.97982 | + | 3.46868i | 0.384227 | + | 0.190944i | ||||
\(331\) | −13.9140 | + | 13.9140i | −0.764780 | + | 0.764780i | −0.977182 | − | 0.212402i | \(-0.931871\pi\) |
0.212402 | + | 0.977182i | \(0.431871\pi\) | |||||||
\(332\) | −10.2732 | −0.563813 | ||||||||
\(333\) | −14.2358 | + | 11.4167i | −0.780117 | + | 0.625634i | ||||
\(334\) | 1.42492 | 0.0779683 | ||||||||
\(335\) | −5.17487 | + | 5.17487i | −0.282733 | + | 0.282733i | ||||
\(336\) | 6.79630 | + | 3.37748i | 0.370769 | + | 0.184256i | ||||
\(337\) | 22.2998i | 1.21475i | 0.794416 | + | 0.607374i | \(0.207777\pi\) | ||||
−0.794416 | + | 0.607374i | \(0.792223\pi\) | |||||||
\(338\) | −6.19483 | − | 6.19483i | −0.336955 | − | 0.336955i | ||||
\(339\) | 14.1930 | − | 4.76945i | 0.770857 | − | 0.259041i | ||||
\(340\) | 1.54323 | 0.0836934 | ||||||||
\(341\) | −1.36469 | − | 1.36469i | −0.0739021 | − | 0.0739021i | ||||
\(342\) | 2.49456 | − | 1.88998i | 0.134890 | − | 0.102199i | ||||
\(343\) | 22.7803 | 1.23002 | ||||||||
\(344\) | 0.804623 | 0.0433824 | ||||||||
\(345\) | −1.70105 | + | 3.42293i | −0.0915815 | + | 0.184284i | ||||
\(346\) | 1.07079 | − | 1.07079i | 0.0575660 | − | 0.0575660i | ||||
\(347\) | −8.92530 | + | 8.92530i | −0.479135 | + | 0.479135i | −0.904855 | − | 0.425720i | \(-0.860021\pi\) |
0.425720 | + | 0.904855i | \(0.360021\pi\) | |||||||
\(348\) | −2.87234 | − | 8.54756i | −0.153974 | − | 0.458197i | ||||
\(349\) | −7.54456 | −0.403851 | −0.201926 | − | 0.979401i | \(-0.564720\pi\) | ||||
−0.201926 | + | 0.979401i | \(0.564720\pi\) | |||||||
\(350\) | −3.09831 | − | 3.09831i | −0.165611 | − | 0.165611i | ||||
\(351\) | −8.84050 | − | 6.02524i | −0.471871 | − | 0.321603i | ||||
\(352\) | 3.18197 | − | 3.18197i | 0.169600 | − | 0.169600i | ||||
\(353\) | −4.41933 | + | 4.41933i | −0.235217 | + | 0.235217i | −0.814866 | − | 0.579649i | \(-0.803190\pi\) |
0.579649 | + | 0.814866i | \(0.303190\pi\) | |||||||
\(354\) | 21.5355 | + | 10.7022i | 1.14460 | + | 0.568818i | ||||
\(355\) | −9.46742 | + | 9.46742i | −0.502478 | + | 0.502478i | ||||
\(356\) | −11.8187 | − | 11.8187i | −0.626392 | − | 0.626392i | ||||
\(357\) | −3.73072 | − | 11.1019i | −0.197450 | − | 0.587575i | ||||
\(358\) | 3.70055i | 0.195580i | ||||||||
\(359\) | − | 24.0431i | − | 1.26895i | −0.772944 | − | 0.634474i | \(-0.781217\pi\) | ||
0.772944 | − | 0.634474i | \(-0.218783\pi\) | |||||||
\(360\) | −2.39120 | + | 1.81167i | −0.126027 | + | 0.0954836i | ||||
\(361\) | 17.9117i | 0.942720i | ||||||||
\(362\) | 5.67367 | − | 5.67367i | 0.298201 | − | 0.298201i | ||||
\(363\) | −14.3473 | − | 7.12999i | −0.753036 | − | 0.374228i | ||||
\(364\) | −6.37919 | − | 6.37919i | −0.334360 | − | 0.334360i | ||||
\(365\) | 8.70104 | − | 8.70104i | 0.455433 | − | 0.455433i | ||||
\(366\) | 1.08980 | + | 0.541583i | 0.0569646 | + | 0.0283090i | ||||
\(367\) | −23.6025 | −1.23204 | −0.616020 | − | 0.787730i | \(-0.711256\pi\) | ||||
−0.616020 | + | 0.787730i | \(0.711256\pi\) | |||||||
\(368\) | 1.56045 | + | 1.56045i | 0.0813440 | + | 0.0813440i | ||||
\(369\) | −3.60995 | − | 4.76471i | −0.187926 | − | 0.248041i | ||||
\(370\) | −0.167677 | − | 6.08045i | −0.00871712 | − | 0.316108i | ||||
\(371\) | − | 35.3868i | − | 1.83719i | ||||||
\(372\) | 0.704150 | − | 0.236625i | 0.0365085 | − | 0.0122684i | ||||
\(373\) | − | 36.5693i | − | 1.89349i | −0.321991 | − | 0.946743i | \(-0.604352\pi\) | ||
0.321991 | − | 0.946743i | \(-0.395648\pi\) | |||||||
\(374\) | −6.94451 | −0.359092 | ||||||||
\(375\) | 1.64183 | − | 0.551724i | 0.0847836 | − | 0.0284909i | ||||
\(376\) | 6.24407 | − | 6.24407i | 0.322014 | − | 0.322014i | ||||
\(377\) | 10.7190i | 0.552058i | ||||||||
\(378\) | 18.8137 | + | 12.8225i | 0.967675 | + | 0.659518i | ||||
\(379\) | −36.7825 | −1.88939 | −0.944695 | − | 0.327950i | \(-0.893642\pi\) | ||||
−0.944695 | + | 0.327950i | \(0.893642\pi\) | |||||||
\(380\) | 1.04322i | 0.0535163i | ||||||||
\(381\) | −29.2035 | − | 14.5129i | −1.49614 | − | 0.743518i | ||||
\(382\) | 5.25987 | 0.269118 | ||||||||
\(383\) | 7.74910 | + | 7.74910i | 0.395960 | + | 0.395960i | 0.876806 | − | 0.480845i | \(-0.159670\pi\) |
−0.480845 | + | 0.876806i | \(0.659670\pi\) | |||||||
\(384\) | 0.551724 | + | 1.64183i | 0.0281551 | + | 0.0837842i | ||||
\(385\) | 13.9423 | + | 13.9423i | 0.710567 | + | 0.710567i | ||||
\(386\) | 16.1740i | 0.823235i | ||||||||
\(387\) | 2.39124 | + | 0.329724i | 0.121554 | + | 0.0167608i | ||||
\(388\) | 0.766039 | + | 0.766039i | 0.0388897 | + | 0.0388897i | ||||
\(389\) | 16.8656 | + | 16.8656i | 0.855119 | + | 0.855119i | 0.990758 | − | 0.135640i | \(-0.0433089\pi\) |
−0.135640 | + | 0.990758i | \(0.543309\pi\) | |||||||
\(390\) | 3.38041 | − | 1.13596i | 0.171173 | − | 0.0575216i | ||||
\(391\) | − | 3.40561i | − | 0.172229i | ||||||
\(392\) | 8.62600 | + | 8.62600i | 0.435679 | + | 0.435679i | ||||
\(393\) | 15.1095 | − | 5.07744i | 0.762174 | − | 0.256123i | ||||
\(394\) | −9.10387 | − | 9.10387i | −0.458646 | − | 0.458646i | ||||
\(395\) | −2.89575 | −0.145701 | ||||||||
\(396\) | 10.7604 | − | 8.15251i | 0.540729 | − | 0.409679i | ||||
\(397\) | − | 2.62029i | − | 0.131509i | −0.997836 | − | 0.0657543i | \(-0.979055\pi\) | ||
0.997836 | − | 0.0657543i | \(-0.0209453\pi\) | |||||||
\(398\) | −23.4259 | −1.17423 | ||||||||
\(399\) | 7.50490 | − | 2.52197i | 0.375715 | − | 0.126256i | ||||
\(400\) | − | 1.00000i | − | 0.0500000i | ||||||
\(401\) | −23.7337 | + | 23.7337i | −1.18521 | + | 1.18521i | −0.206830 | + | 0.978377i | \(0.566315\pi\) |
−0.978377 | + | 0.206830i | \(0.933685\pi\) | |||||||
\(402\) | 4.03772 | + | 12.0155i | 0.201383 | + | 0.599279i | ||||
\(403\) | −0.883036 | −0.0439872 | ||||||||
\(404\) | 12.5125i | 0.622519i | ||||||||
\(405\) | −7.84876 | + | 4.40419i | −0.390008 | + | 0.218846i | ||||
\(406\) | − | 22.8115i | − | 1.13212i | ||||||
\(407\) | 0.754545 | + | 27.3619i | 0.0374014 | + | 1.35628i | ||||
\(408\) | 1.18955 | − | 2.39367i | 0.0588916 | − | 0.118504i | ||||
\(409\) | −8.35272 | − | 8.35272i | −0.413015 | − | 0.413015i | 0.469772 | − | 0.882788i | \(-0.344336\pi\) |
−0.882788 | + | 0.469772i | \(0.844336\pi\) | |||||||
\(410\) | 1.99260 | 0.0984076 | ||||||||
\(411\) | −15.0362 | + | 30.2565i | −0.741682 | + | 1.49244i | ||||
\(412\) | 6.46547 | − | 6.46547i | 0.318531 | − | 0.318531i | ||||
\(413\) | 43.0176 | + | 43.0176i | 2.11676 | + | 2.11676i | ||||
\(414\) | 3.99801 | + | 5.27692i | 0.196492 | + | 0.259346i | ||||
\(415\) | 7.26422 | − | 7.26422i | 0.356587 | − | 0.356587i | ||||
\(416\) | − | 2.05893i | − | 0.100947i | ||||||
\(417\) | 13.7190 | − | 27.6060i | 0.671823 | − | 1.35187i | ||||
\(418\) | − | 4.69450i | − | 0.229615i | ||||||
\(419\) | − | 21.3828i | − | 1.04462i | −0.852757 | − | 0.522309i | \(-0.825071\pi\) | ||
0.852757 | − | 0.522309i | \(-0.174929\pi\) | |||||||
\(420\) | −7.19395 | + | 2.41747i | −0.351029 | + | 0.117961i | ||||
\(421\) | −24.9099 | − | 24.9099i | −1.21404 | − | 1.21404i | −0.969688 | − | 0.244348i | \(-0.921426\pi\) |
−0.244348 | − | 0.969688i | \(-0.578574\pi\) | |||||||
\(422\) | 6.52621 | − | 6.52621i | 0.317691 | − | 0.317691i | ||||
\(423\) | 21.1154 | − | 15.9979i | 1.02667 | − | 0.777845i | ||||
\(424\) | 5.71067 | − | 5.71067i | 0.277335 | − | 0.277335i | ||||
\(425\) | −1.09123 | + | 1.09123i | −0.0529323 | + | 0.0529323i | ||||
\(426\) | 7.38701 | + | 21.9824i | 0.357902 | + | 1.06505i | ||||
\(427\) | 2.17689 | + | 2.17689i | 0.105347 | + | 0.105347i | ||||
\(428\) | 0.550155 | 0.0265928 | ||||||||
\(429\) | −15.2118 | + | 5.11181i | −0.734432 | + | 0.246800i | ||||
\(430\) | −0.568955 | + | 0.568955i | −0.0274374 | + | 0.0274374i | ||||
\(431\) | −13.1558 | + | 13.1558i | −0.633692 | + | 0.633692i | −0.948992 | − | 0.315300i | \(-0.897895\pi\) |
0.315300 | + | 0.948992i | \(0.397895\pi\) | |||||||
\(432\) | 0.966859 | + | 5.10541i | 0.0465180 | + | 0.245634i | ||||
\(433\) | 40.5145 | 1.94700 | 0.973502 | − | 0.228679i | \(-0.0734405\pi\) | ||||
0.973502 | + | 0.228679i | \(0.0734405\pi\) | |||||||
\(434\) | 1.87922 | 0.0902053 | ||||||||
\(435\) | 8.07509 | + | 4.01298i | 0.387171 | + | 0.192408i | ||||
\(436\) | 6.68407 | + | 6.68407i | 0.320109 | + | 0.320109i | ||||
\(437\) | 2.30220 | 0.110129 | ||||||||
\(438\) | −6.78904 | − | 20.2029i | −0.324393 | − | 0.965333i | ||||
\(439\) | −16.5074 | − | 16.5074i | −0.787857 | − | 0.787857i | 0.193285 | − | 0.981143i | \(-0.438086\pi\) |
−0.981143 | + | 0.193285i | \(0.938086\pi\) | |||||||
\(440\) | 4.49999i | 0.214528i | ||||||||
\(441\) | 22.1006 | + | 29.1703i | 1.05241 | + | 1.38906i | ||||
\(442\) | −2.24676 | + | 2.24676i | −0.106867 | + | 0.106867i | ||||
\(443\) | −17.2944 | −0.821681 | −0.410841 | − | 0.911707i | \(-0.634765\pi\) | ||||
−0.410841 | + | 0.911707i | \(0.634765\pi\) | |||||||
\(444\) | −9.56049 | − | 4.42685i | −0.453721 | − | 0.210089i | ||||
\(445\) | 16.7142 | 0.792330 | ||||||||
\(446\) | 15.3710 | − | 15.3710i | 0.727837 | − | 0.727837i | ||||
\(447\) | −14.9317 | + | 30.0462i | −0.706246 | + | 1.42114i | ||||
\(448\) | 4.38167i | 0.207014i | ||||||||
\(449\) | 5.59586 | + | 5.59586i | 0.264085 | + | 0.264085i | 0.826711 | − | 0.562626i | \(-0.190209\pi\) |
−0.562626 | + | 0.826711i | \(0.690209\pi\) | |||||||
\(450\) | 0.409787 | − | 2.97188i | 0.0193176 | − | 0.140096i | ||||
\(451\) | −8.96669 | −0.422225 | ||||||||
\(452\) | 6.11267 | + | 6.11267i | 0.287516 | + | 0.287516i | ||||
\(453\) | −9.40278 | + | 18.9207i | −0.441781 | + | 0.888971i | ||||
\(454\) | −16.4499 | −0.772032 | ||||||||
\(455\) | 9.02154 | 0.422936 | ||||||||
\(456\) | 1.61812 | + | 0.804138i | 0.0757755 | + | 0.0376572i | ||||
\(457\) | −21.3020 | + | 21.3020i | −0.996467 | + | 0.996467i | −0.999994 | − | 0.00352675i | \(-0.998877\pi\) |
0.00352675 | + | 0.999994i | \(0.498877\pi\) | |||||||
\(458\) | −7.08954 | + | 7.08954i | −0.331272 | + | 0.331272i | ||||
\(459\) | 4.51610 | − | 6.62623i | 0.210794 | − | 0.309286i | ||||
\(460\) | −2.20681 | −0.102893 | ||||||||
\(461\) | 15.6647 | + | 15.6647i | 0.729576 | + | 0.729576i | 0.970535 | − | 0.240959i | \(-0.0774620\pi\) |
−0.240959 | + | 0.970535i | \(0.577462\pi\) | |||||||
\(462\) | 32.3727 | − | 10.8786i | 1.50611 | − | 0.506118i | ||||
\(463\) | 12.1234 | − | 12.1234i | 0.563420 | − | 0.563420i | −0.366857 | − | 0.930277i | \(-0.619566\pi\) |
0.930277 | + | 0.366857i | \(0.119566\pi\) | |||||||
\(464\) | 3.68128 | − | 3.68128i | 0.170899 | − | 0.170899i | ||||
\(465\) | −0.330591 | + | 0.665228i | −0.0153308 | + | 0.0308492i | ||||
\(466\) | 9.92187 | − | 9.92187i | 0.459622 | − | 0.459622i | ||||
\(467\) | 12.9695 | + | 12.9695i | 0.600158 | + | 0.600158i | 0.940355 | − | 0.340196i | \(-0.110493\pi\) |
−0.340196 | + | 0.940355i | \(0.610493\pi\) | |||||||
\(468\) | 0.843722 | − | 6.11889i | 0.0390011 | − | 0.282846i | ||||
\(469\) | 32.0667i | 1.48070i | ||||||||
\(470\) | 8.83045i | 0.407318i | ||||||||
\(471\) | 11.0296 | + | 5.48123i | 0.508215 | + | 0.252562i | ||||
\(472\) | 13.8842i | 0.639074i | ||||||||
\(473\) | 2.56029 | − | 2.56029i | 0.117722 | − | 0.117722i | ||||
\(474\) | −2.23210 | + | 4.49152i | −0.102524 | + | 0.206303i | ||||
\(475\) | −0.737671 | − | 0.737671i | −0.0338467 | − | 0.0338467i | ||||
\(476\) | 4.78140 | − | 4.78140i | 0.219155 | − | 0.219155i | ||||
\(477\) | 19.3116 | − | 14.6313i | 0.884217 | − | 0.669920i | ||||
\(478\) | 2.67843 | 0.122509 | ||||||||
\(479\) | 20.6435 | + | 20.6435i | 0.943226 | + | 0.943226i | 0.998473 | − | 0.0552467i | \(-0.0175945\pi\) |
−0.0552467 | + | 0.998473i | \(0.517595\pi\) | |||||||
\(480\) | −1.55108 | − | 0.770820i | −0.0707966 | − | 0.0351829i | ||||
\(481\) | 9.09653 | + | 8.60830i | 0.414766 | + | 0.392505i | ||||
\(482\) | 16.6572i | 0.758715i | ||||||||
\(483\) | 5.33490 | + | 15.8757i | 0.242746 | + | 0.722367i | ||||
\(484\) | − | 9.24988i | − | 0.420449i | ||||||
\(485\) | −1.08334 | −0.0491921 | ||||||||
\(486\) | 0.781259 | + | 15.5689i | 0.0354386 | + | 0.706218i | ||||
\(487\) | −20.1438 | + | 20.1438i | −0.912801 | + | 0.912801i | −0.996492 | − | 0.0836904i | \(-0.973329\pi\) |
0.0836904 | + | 0.996492i | \(0.473329\pi\) | |||||||
\(488\) | 0.702607i | 0.0318055i | ||||||||
\(489\) | 3.08458 | + | 9.17914i | 0.139490 | + | 0.415095i | ||||
\(490\) | −12.1990 | −0.551095 | ||||||||
\(491\) | − | 35.5626i | − | 1.60492i | −0.596707 | − | 0.802460i | \(-0.703524\pi\) | ||
0.596707 | − | 0.802460i | \(-0.296476\pi\) | |||||||
\(492\) | 1.53594 | − | 3.09068i | 0.0692454 | − | 0.139339i | ||||
\(493\) | −8.03424 | −0.361844 | ||||||||
\(494\) | −1.51881 | − | 1.51881i | −0.0683346 | − | 0.0683346i | ||||
\(495\) | −1.84404 | + | 13.3734i | −0.0828833 | + | 0.601091i | ||||
\(496\) | 0.303265 | + | 0.303265i | 0.0136170 | + | 0.0136170i | ||||
\(497\) | 58.6659i | 2.63153i | ||||||||
\(498\) | −5.66795 | − | 16.8668i | −0.253987 | − | 0.755818i | ||||
\(499\) | −5.43817 | − | 5.43817i | −0.243446 | − | 0.243446i | 0.574828 | − | 0.818274i | \(-0.305069\pi\) |
−0.818274 | + | 0.574828i | \(0.805069\pi\) | |||||||
\(500\) | 0.707107 | + | 0.707107i | 0.0316228 | + | 0.0316228i | ||||
\(501\) | 0.786165 | + | 2.33948i | 0.0351233 | + | 0.104520i | ||||
\(502\) | 15.4337i | 0.688839i | ||||||||
\(503\) | 18.5290 | + | 18.5290i | 0.826166 | + | 0.826166i | 0.986984 | − | 0.160818i | \(-0.0514133\pi\) |
−0.160818 | + | 0.986984i | \(0.551413\pi\) | |||||||
\(504\) | −1.79555 | + | 13.0218i | −0.0799802 | + | 0.580037i | ||||
\(505\) | −8.84766 | − | 8.84766i | −0.393716 | − | 0.393716i | ||||
\(506\) | 9.93060 | 0.441469 | ||||||||
\(507\) | 6.75301 | − | 13.5887i | 0.299912 | − | 0.603495i | ||||
\(508\) | − | 18.8279i | − | 0.835352i | ||||||
\(509\) | −29.5711 | −1.31072 | −0.655358 | − | 0.755318i | \(-0.727482\pi\) | ||||
−0.655358 | + | 0.755318i | \(0.727482\pi\) | |||||||
\(510\) | 0.851438 | + | 2.53372i | 0.0377023 | + | 0.112195i | ||||
\(511\) | − | 53.9170i | − | 2.38515i | ||||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 4.47934 | + | 3.05289i | 0.197768 | + | 0.134788i | ||||
\(514\) | 23.7079 | 1.04571 | ||||||||
\(515\) | 9.14355i | 0.402913i | ||||||||
\(516\) | 0.443930 | + | 1.32105i | 0.0195429 | + | 0.0581561i | ||||
\(517\) | − | 39.7369i | − | 1.74763i | ||||||
\(518\) | −19.3586 | − | 18.3196i | −0.850569 | − | 0.804917i | ||||
\(519\) | 2.34883 | + | 1.16727i | 0.103102 | + | 0.0512376i | ||||
\(520\) | 1.45588 | + | 1.45588i | 0.0638446 | + | 0.0638446i | ||||
\(521\) | 3.80161 | 0.166552 | 0.0832759 | − | 0.996527i | \(-0.473462\pi\) | ||||
0.0832759 | + | 0.996527i | \(0.473462\pi\) | |||||||
\(522\) | 12.4489 | − | 9.43179i | 0.544873 | − | 0.412818i | ||||
\(523\) | −18.5143 | + | 18.5143i | −0.809573 | + | 0.809573i | −0.984569 | − | 0.174996i | \(-0.944009\pi\) |
0.174996 | + | 0.984569i | \(0.444009\pi\) | |||||||
\(524\) | 6.50740 | + | 6.50740i | 0.284277 | + | 0.284277i | ||||
\(525\) | 3.37748 | − | 6.79630i | 0.147405 | − | 0.296615i | ||||
\(526\) | −11.4936 | + | 11.4936i | −0.501145 | + | 0.501145i | ||||
\(527\) | − | 0.661863i | − | 0.0288312i | ||||||
\(528\) | 6.97982 | + | 3.46868i | 0.303758 | + | 0.150955i | ||||
\(529\) | − | 18.1300i | − | 0.788261i | ||||||
\(530\) | 8.07611i | 0.350804i | ||||||||
\(531\) | −5.68958 | + | 41.2623i | −0.246907 | + | 1.79063i | ||||
\(532\) | 3.23223 | + | 3.23223i | 0.140135 | + | 0.140135i | ||||
\(533\) | −2.90099 | + | 2.90099i | −0.125656 | + | 0.125656i | ||||
\(534\) | 12.8836 | − | 25.9250i | 0.557530 | − | 1.12189i | ||||
\(535\) | −0.389018 | + | 0.389018i | −0.0168187 | + | 0.0168187i | ||||
\(536\) | −5.17487 | + | 5.17487i | −0.223520 | + | 0.223520i | ||||
\(537\) | −6.07566 | + | 2.04168i | −0.262184 | + | 0.0881051i | ||||
\(538\) | −10.1038 | − | 10.1038i | −0.435606 | − | 0.435606i | ||||
\(539\) | 54.8954 | 2.36451 | ||||||||
\(540\) | −4.29374 | − | 2.92640i | −0.184773 | − | 0.125932i | ||||
\(541\) | −26.4175 | + | 26.4175i | −1.13578 | + | 1.13578i | −0.146576 | + | 0.989199i | \(0.546825\pi\) |
−0.989199 | + | 0.146576i | \(0.953175\pi\) | |||||||
\(542\) | −14.4111 | + | 14.4111i | −0.619008 | + | 0.619008i | ||||
\(543\) | 12.4455 | + | 6.18489i | 0.534087 | + | 0.265419i | ||||
\(544\) | 1.54323 | 0.0661654 | ||||||||
\(545\) | −9.45270 | −0.404909 | ||||||||
\(546\) | 6.95398 | − | 13.9931i | 0.297603 | − | 0.598849i | ||||
\(547\) | 13.2147 | + | 13.2147i | 0.565018 | + | 0.565018i | 0.930729 | − | 0.365710i | \(-0.119174\pi\) |
−0.365710 | + | 0.930729i | \(0.619174\pi\) | |||||||
\(548\) | −19.5068 | −0.833289 | ||||||||
\(549\) | −0.287919 | + | 2.08806i | −0.0122881 | + | 0.0891164i | ||||
\(550\) | −3.18197 | − | 3.18197i | −0.135680 | − | 0.135680i | ||||
\(551\) | − | 5.43115i | − | 0.231375i | ||||||
\(552\) | −1.70105 | + | 3.42293i | −0.0724015 | + | 0.145689i | ||||
\(553\) | −8.97191 | + | 8.97191i | −0.381525 | + | 0.381525i | ||||
\(554\) | 24.8598 | 1.05619 | ||||||||
\(555\) | 9.89054 | − | 3.63003i | 0.419830 | − | 0.154086i | ||||
\(556\) | 17.7979 | 0.754801 | ||||||||
\(557\) | −17.3259 | + | 17.3259i | −0.734123 | + | 0.734123i | −0.971434 | − | 0.237311i | \(-0.923734\pi\) |
0.237311 | + | 0.971434i | \(0.423734\pi\) | |||||||
\(558\) | 0.776994 | + | 1.02554i | 0.0328928 | + | 0.0434147i | ||||
\(559\) | − | 1.65666i | − | 0.0700693i | ||||||
\(560\) | −3.09831 | − | 3.09831i | −0.130927 | − | 0.130927i | ||||
\(561\) | −3.83146 | − | 11.4017i | −0.161764 | − | 0.481380i | ||||
\(562\) | −1.90329 | −0.0802855 | ||||||||
\(563\) | 12.6771 | + | 12.6771i | 0.534276 | + | 0.534276i | 0.921842 | − | 0.387566i | \(-0.126684\pi\) |
−0.387566 | + | 0.921842i | \(0.626684\pi\) | |||||||
\(564\) | 13.6967 | + | 6.80669i | 0.576735 | + | 0.286613i | ||||
\(565\) | −8.64462 | −0.363682 | ||||||||
\(566\) | −0.389222 | −0.0163602 | ||||||||
\(567\) | −10.6723 | + | 37.9634i | −0.448196 | + | 1.59431i | ||||
\(568\) | −9.46742 | + | 9.46742i | −0.397244 | + | 0.397244i | ||||
\(569\) | −19.4272 | + | 19.4272i | −0.814430 | + | 0.814430i | −0.985295 | − | 0.170864i | \(-0.945344\pi\) |
0.170864 | + | 0.985295i | \(0.445344\pi\) | |||||||
\(570\) | −1.71280 | + | 0.575573i | −0.0717411 | + | 0.0241081i | ||||
\(571\) | 18.7824 | 0.786020 | 0.393010 | − | 0.919534i | \(-0.371434\pi\) | ||||
0.393010 | + | 0.919534i | \(0.371434\pi\) | |||||||
\(572\) | −6.55145 | − | 6.55145i | −0.273930 | − | 0.273930i | ||||
\(573\) | 2.90200 | + | 8.63580i | 0.121233 | + | 0.360766i | ||||
\(574\) | 6.17369 | − | 6.17369i | 0.257685 | − | 0.257685i | ||||
\(575\) | 1.56045 | − | 1.56045i | 0.0650752 | − | 0.0650752i | ||||
\(576\) | −2.39120 | + | 1.81167i | −0.0996333 | + | 0.0754864i | ||||
\(577\) | 15.0730 | − | 15.0730i | 0.627496 | − | 0.627496i | −0.319941 | − | 0.947437i | \(-0.603663\pi\) |
0.947437 | + | 0.319941i | \(0.103663\pi\) | |||||||
\(578\) | 10.3368 | + | 10.3368i | 0.429954 | + | 0.429954i | ||||
\(579\) | −26.5549 | + | 8.92359i | −1.10359 | + | 0.370852i | ||||
\(580\) | 5.20612i | 0.216172i | ||||||||
\(581\) | − | 45.0136i | − | 1.86748i | ||||||
\(582\) | −0.835062 | + | 1.68035i | −0.0346144 | + | 0.0696526i | ||||
\(583\) | − | 36.3424i | − | 1.50515i | ||||||
\(584\) | 8.70104 | − | 8.70104i | 0.360052 | − | 0.360052i | ||||
\(585\) | 3.73010 | + | 4.92331i | 0.154221 | + | 0.203554i | ||||
\(586\) | −2.15072 | − | 2.15072i | −0.0888455 | − | 0.0888455i | ||||
\(587\) | −28.6854 | + | 28.6854i | −1.18397 | + | 1.18397i | −0.205266 | + | 0.978706i | \(0.565806\pi\) |
−0.978706 | + | 0.205266i | \(0.934194\pi\) | |||||||
\(588\) | −9.40324 | + | 18.9216i | −0.387783 | + | 0.780313i | ||||
\(589\) | 0.447420 | 0.0184356 | ||||||||
\(590\) | −9.81764 | − | 9.81764i | −0.404186 | − | 0.404186i | ||||
\(591\) | 9.92416 | − | 19.9698i | 0.408226 | − | 0.821449i | ||||
\(592\) | −0.167677 | − | 6.08045i | −0.00689149 | − | 0.249905i | ||||
\(593\) | 19.5396i | 0.802396i | 0.915991 | + | 0.401198i | \(0.131406\pi\) | ||||
−0.915991 | + | 0.401198i | \(0.868594\pi\) | |||||||
\(594\) | 19.3218 | + | 13.1687i | 0.792782 | + | 0.540320i | ||||
\(595\) | 6.76192i | 0.277212i | ||||||||
\(596\) | −19.3712 | −0.793476 | ||||||||
\(597\) | −12.9246 | − | 38.4613i | −0.528970 | − | 1.57412i | ||||
\(598\) | 3.21285 | − | 3.21285i | 0.131383 | − | 0.131383i | ||||
\(599\) | − | 19.5959i | − | 0.800668i | −0.916369 | − | 0.400334i | \(-0.868894\pi\) | ||
0.916369 | − | 0.400334i | \(-0.131106\pi\) | |||||||
\(600\) | 1.64183 | − | 0.551724i | 0.0670274 | − | 0.0225241i | ||||
\(601\) | −21.1149 | −0.861294 | −0.430647 | − | 0.902520i | \(-0.641715\pi\) | ||||
−0.430647 | + | 0.902520i | \(0.641715\pi\) | |||||||
\(602\) | 3.52559i | 0.143692i | ||||||||
\(603\) | −17.4997 | + | 13.2585i | −0.712642 | + | 0.539928i | ||||
\(604\) | −12.1984 | −0.496347 | ||||||||
\(605\) | 6.54065 | + | 6.54065i | 0.265915 | + | 0.265915i | ||||
\(606\) | −20.5433 | + | 6.90344i | −0.834516 | + | 0.280433i | ||||
\(607\) | −26.0839 | − | 26.0839i | −1.05871 | − | 1.05871i | −0.998165 | − | 0.0605486i | \(-0.980715\pi\) |
−0.0605486 | − | 0.998165i | \(-0.519285\pi\) | |||||||
\(608\) | 1.04322i | 0.0423084i | ||||||||
\(609\) | 37.4526 | − | 12.5857i | 1.51765 | − | 0.509997i | ||||
\(610\) | −0.496818 | − | 0.496818i | −0.0201156 | − | 0.0201156i | ||||
\(611\) | −12.8561 | − | 12.8561i | −0.520102 | − | 0.520102i | ||||
\(612\) | 4.58629 | + | 0.632396i | 0.185390 | + | 0.0255631i | ||||
\(613\) | − | 8.19734i | − | 0.331087i | −0.986202 | − | 0.165544i | \(-0.947062\pi\) | ||
0.986202 | − | 0.165544i | \(-0.0529379\pi\) | |||||||
\(614\) | −9.33199 | − | 9.33199i | −0.376608 | − | 0.376608i | ||||
\(615\) | 1.09937 | + | 3.27151i | 0.0443308 | + | 0.131920i | ||||
\(616\) | 13.9423 | + | 13.9423i | 0.561753 | + | 0.561753i | ||||
\(617\) | 25.5042 | 1.02676 | 0.513379 | − | 0.858162i | \(-0.328393\pi\) | ||||
0.513379 | + | 0.858162i | \(0.328393\pi\) | |||||||
\(618\) | 14.1823 | + | 7.04803i | 0.570498 | + | 0.283513i | ||||
\(619\) | − | 29.5707i | − | 1.18855i | −0.804262 | − | 0.594274i | \(-0.797439\pi\) | ||
0.804262 | − | 0.594274i | \(-0.202561\pi\) | |||||||
\(620\) | −0.428882 | −0.0172243 | ||||||||
\(621\) | −6.45799 | + | 9.47546i | −0.259150 | + | 0.380237i | ||||
\(622\) | 23.3764i | 0.937307i | ||||||||
\(623\) | 51.7858 | − | 51.7858i | 2.07475 | − | 2.07475i | ||||
\(624\) | 3.38041 | − | 1.13596i | 0.135325 | − | 0.0454748i | ||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 6.27610i | 0.250843i | ||||||||
\(627\) | 7.70756 | − | 2.59007i | 0.307810 | − | 0.103437i | ||||
\(628\) | 7.11091i | 0.283756i | ||||||||
\(629\) | −6.45219 | + | 6.81813i | −0.257265 | + | 0.271857i | ||||
\(630\) | −7.93815 | − | 10.4774i | −0.316264 | − | 0.417431i | ||||
\(631\) | −2.03316 | − | 2.03316i | −0.0809387 | − | 0.0809387i | 0.665478 | − | 0.746417i | \(-0.268228\pi\) |
−0.746417 | + | 0.665478i | \(0.768228\pi\) | |||||||
\(632\) | −2.89575 | −0.115187 | ||||||||
\(633\) | 14.3156 | + | 7.11424i | 0.568993 | + | 0.282766i | ||||
\(634\) | 2.25356 | − | 2.25356i | 0.0895003 | − | 0.0895003i | ||||
\(635\) | 13.3133 | + | 13.3133i | 0.528323 | + | 0.528323i | ||||
\(636\) | 12.5267 | + | 6.22523i | 0.496714 | + | 0.246846i | ||||
\(637\) | 17.7603 | − | 17.7603i | 0.703689 | − | 0.703689i | ||||
\(638\) | − | 23.4275i | − | 0.927503i | ||||||
\(639\) | −32.0157 | + | 24.2564i | −1.26652 | + | 0.959569i | ||||
\(640\) | − | 1.00000i | − | 0.0395285i | ||||||
\(641\) | 6.05439i | 0.239134i | 0.992826 | + | 0.119567i | \(0.0381507\pi\) | ||||
−0.992826 | + | 0.119567i | \(0.961849\pi\) | |||||||
\(642\) | 0.303534 | + | 0.903260i | 0.0119795 | + | 0.0356488i | ||||
\(643\) | −13.8840 | − | 13.8840i | −0.547530 | − | 0.547530i | 0.378196 | − | 0.925726i | \(-0.376545\pi\) |
−0.925726 | + | 0.378196i | \(0.876545\pi\) | |||||||
\(644\) | −6.83737 | + | 6.83737i | −0.269430 | + | 0.269430i | ||||
\(645\) | −1.24803 | − | 0.620220i | −0.0491412 | − | 0.0244211i | ||||
\(646\) | 1.13840 | − | 1.13840i | 0.0447896 | − | 0.0447896i | ||||
\(647\) | 15.4482 | − | 15.4482i | 0.607330 | − | 0.607330i | −0.334917 | − | 0.942248i | \(-0.608708\pi\) |
0.942248 | + | 0.334917i | \(0.108708\pi\) | |||||||
\(648\) | −7.84876 | + | 4.40419i | −0.308329 | + | 0.173013i | ||||
\(649\) | 44.1793 | + | 44.1793i | 1.73419 | + | 1.73419i | ||||
\(650\) | −2.05893 | −0.0807578 | ||||||||
\(651\) | 1.03681 | + | 3.08535i | 0.0406358 | + | 0.120924i | ||||
\(652\) | −3.95330 | + | 3.95330i | −0.154823 | + | 0.154823i | ||||
\(653\) | 14.5821 | − | 14.5821i | 0.570642 | − | 0.570642i | −0.361666 | − | 0.932308i | \(-0.617792\pi\) |
0.932308 | + | 0.361666i | \(0.117792\pi\) | |||||||
\(654\) | −7.28633 | + | 14.6619i | −0.284918 | + | 0.573324i | ||||
\(655\) | −9.20286 | −0.359585 | ||||||||
\(656\) | 1.99260 | 0.0777981 | ||||||||
\(657\) | 29.4240 | − | 22.2929i | 1.14794 | − | 0.869728i | ||||
\(658\) | 27.3595 | + | 27.3595i | 1.06658 | + | 1.06658i | ||||
\(659\) | 14.6678 | 0.571375 | 0.285688 | − | 0.958323i | \(-0.407778\pi\) | ||||
0.285688 | + | 0.958323i | \(0.407778\pi\) | |||||||
\(660\) | −7.38821 | + | 2.48275i | −0.287586 | + | 0.0966410i | ||||
\(661\) | −32.3272 | − | 32.3272i | −1.25738 | − | 1.25738i | −0.952338 | − | 0.305044i | \(-0.901329\pi\) |
−0.305044 | − | 0.952338i | \(-0.598671\pi\) | |||||||
\(662\) | − | 19.6773i | − | 0.764780i | ||||||
\(663\) | −4.92839 | − | 2.44920i | −0.191403 | − | 0.0951191i | ||||
\(664\) | 7.26422 | − | 7.26422i | 0.281906 | − | 0.281906i | ||||
\(665\) | −4.57106 | −0.177258 | ||||||||
\(666\) | 1.99337 | − | 18.1391i | 0.0772417 | − | 0.702875i | ||||
\(667\) | 11.4889 | 0.444852 | ||||||||
\(668\) | −1.00757 | + | 1.00757i | −0.0389842 | + | 0.0389842i | ||||
\(669\) | 33.7171 | + | 16.7560i | 1.30358 | + | 0.647823i | ||||
\(670\) | − | 7.31837i | − | 0.282733i | ||||||
\(671\) | 2.23567 | + | 2.23567i | 0.0863073 | + | 0.0863073i | ||||
\(672\) | −7.19395 | + | 2.41747i | −0.277512 | + | 0.0932561i | ||||
\(673\) | −11.1901 | −0.431345 | −0.215673 | − | 0.976466i | \(-0.569194\pi\) | ||||
−0.215673 | + | 0.976466i | \(0.569194\pi\) | |||||||
\(674\) | −15.7683 | − | 15.7683i | −0.607374 | − | 0.607374i | ||||
\(675\) | 5.10541 | − | 0.966859i | 0.196507 | − | 0.0372144i | ||||
\(676\) | 8.76082 | 0.336955 | ||||||||
\(677\) | 13.6262 | 0.523699 | 0.261850 | − | 0.965109i | \(-0.415668\pi\) | ||||
0.261850 | + | 0.965109i | \(0.415668\pi\) | |||||||
\(678\) | −6.66344 | + | 13.4085i | −0.255908 | + | 0.514949i | ||||
\(679\) | −3.35653 | + | 3.35653i | −0.128812 | + | 0.128812i | ||||
\(680\) | −1.09123 | + | 1.09123i | −0.0418467 | + | 0.0418467i | ||||
\(681\) | −9.07582 | − | 27.0079i | −0.347786 | − | 1.03495i | ||||
\(682\) | 1.92996 | 0.0739021 | ||||||||
\(683\) | −19.9135 | − | 19.9135i | −0.761970 | − | 0.761970i | 0.214708 | − | 0.976678i | \(-0.431120\pi\) |
−0.976678 | + | 0.214708i | \(0.931120\pi\) | |||||||
\(684\) | −0.427500 | + | 3.10034i | −0.0163459 | + | 0.118544i | ||||
\(685\) | 13.7934 | − | 13.7934i | 0.527018 | − | 0.527018i | ||||
\(686\) | −16.1081 | + | 16.1081i | −0.615012 | + | 0.615012i | ||||
\(687\) | −15.5513 | − | 7.72833i | −0.593318 | − | 0.294854i | ||||
\(688\) | −0.568955 | + | 0.568955i | −0.0216912 | + | 0.0216912i | ||||
\(689\) | −11.7579 | − | 11.7579i | −0.447939 | − | 0.447939i | ||||
\(690\) | −1.21755 | − | 3.62320i | −0.0463513 | − | 0.137933i | ||||
\(691\) | − | 18.2283i | − | 0.693436i | −0.937969 | − | 0.346718i | \(-0.887296\pi\) | ||
0.937969 | − | 0.346718i | \(-0.112704\pi\) | |||||||
\(692\) | 1.51433i | 0.0575660i | ||||||||
\(693\) | 35.7216 | + | 47.1484i | 1.35695 | + | 1.79102i | ||||
\(694\) | − | 12.6223i | − | 0.479135i | ||||||
\(695\) | −12.5850 | + | 12.5850i | −0.477378 | + | 0.477378i | ||||
\(696\) | 8.07509 | + | 4.01298i | 0.306085 | + | 0.152112i | ||||
\(697\) | −2.17438 | − | 2.17438i | −0.0823607 | − | 0.0823607i | ||||
\(698\) | 5.33481 | − | 5.33481i | 0.201926 | − | 0.201926i | ||||
\(699\) | 21.7641 | + | 10.8159i | 0.823195 | + | 0.409094i | ||||
\(700\) | 4.38167 | 0.165611 | ||||||||
\(701\) | 17.6579 | + | 17.6579i | 0.666930 | + | 0.666930i | 0.957004 | − | 0.290074i | \(-0.0936799\pi\) |
−0.290074 | + | 0.957004i | \(0.593680\pi\) | |||||||
\(702\) | 10.5117 | − | 1.99069i | 0.396737 | − | 0.0751338i | ||||
\(703\) | −4.60906 | − | 4.36168i | −0.173834 | − | 0.164504i | ||||
\(704\) | 4.49999i | 0.169600i | ||||||||
\(705\) | −14.4981 | + | 4.87198i | −0.546030 | + | 0.183489i | ||||
\(706\) | − | 6.24988i | − | 0.235217i | ||||||
\(707\) | −54.8255 | −2.06193 | ||||||||
\(708\) | −22.7955 | + | 7.66027i | −0.856709 | + | 0.287891i | ||||
\(709\) | 8.86406 | − | 8.86406i | 0.332897 | − | 0.332897i | −0.520789 | − | 0.853686i | \(-0.674362\pi\) |
0.853686 | + | 0.520789i | \(0.174362\pi\) | |||||||
\(710\) | − | 13.3890i | − | 0.502478i | ||||||
\(711\) | −8.60581 | − | 1.18664i | −0.322743 | − | 0.0445025i | ||||
\(712\) | 16.7142 | 0.626392 | ||||||||
\(713\) | 0.946460i | 0.0354452i | ||||||||
\(714\) | 10.4883 | + | 5.21222i | 0.392513 | + | 0.195062i | ||||
\(715\) | 9.26515 | 0.346497 | ||||||||
\(716\) | −2.61668 | − | 2.61668i | −0.0977900 | − | 0.0977900i | ||||
\(717\) | 1.47776 | + | 4.39753i | 0.0551879 | + | 0.164229i | ||||
\(718\) | 17.0011 | + | 17.0011i | 0.634474 | + | 0.634474i | ||||
\(719\) | − | 36.0585i | − | 1.34476i | −0.740208 | − | 0.672378i | \(-0.765273\pi\) | ||
0.740208 | − | 0.672378i | \(-0.234727\pi\) | |||||||
\(720\) | 0.409787 | − | 2.97188i | 0.0152719 | − | 0.110755i | ||||
\(721\) | 28.3295 | + | 28.3295i | 1.05505 | + | 1.05505i | ||||
\(722\) | −12.6655 | − | 12.6655i | −0.471360 | − | 0.471360i | ||||
\(723\) | −27.3483 | + | 9.19019i | −1.01709 | + | 0.341787i | ||||
\(724\) | 8.02378i | 0.298201i | ||||||||
\(725\) | −3.68128 | − | 3.68128i | −0.136719 | − | 0.136719i | ||||
\(726\) | 15.1867 | − | 5.10339i | 0.563632 | − | 0.189404i | ||||
\(727\) | −4.79330 | − | 4.79330i | −0.177774 | − | 0.177774i | 0.612611 | − | 0.790385i | \(-0.290119\pi\) |
−0.790385 | + | 0.612611i | \(0.790119\pi\) | |||||||
\(728\) | 9.02154 | 0.334360 | ||||||||
\(729\) | −25.1304 | + | 9.87242i | −0.930754 | + | 0.365645i | ||||
\(730\) | 12.3051i | 0.455433i | ||||||||
\(731\) | 1.24172 | 0.0459266 | ||||||||
\(732\) | −1.15356 | + | 0.387645i | −0.0426368 | + | 0.0143278i | ||||
\(733\) | 3.58673i | 0.132479i | 0.997804 | + | 0.0662394i | \(0.0211001\pi\) | ||||
−0.997804 | + | 0.0662394i | \(0.978900\pi\) | |||||||
\(734\) | 16.6895 | − | 16.6895i | 0.616020 | − | 0.616020i | ||||
\(735\) | −6.73049 | − | 20.0287i | −0.248258 | − | 0.738769i | ||||
\(736\) | −2.20681 | −0.0813440 | ||||||||
\(737\) | 32.9326i | 1.21309i | ||||||||
\(738\) | 5.92178 | + | 0.816543i | 0.217984 | + | 0.0300574i | ||||
\(739\) | 38.9164i | 1.43156i | 0.698324 | + | 0.715781i | \(0.253929\pi\) | ||||
−0.698324 | + | 0.715781i | \(0.746071\pi\) | |||||||
\(740\) | 4.41809 | + | 4.18096i | 0.162412 | + | 0.153695i | ||||
\(741\) | 1.65566 | − | 3.33159i | 0.0608223 | − | 0.122389i | ||||
\(742\) | 25.0223 | + | 25.0223i | 0.918596 | + | 0.918596i | ||||
\(743\) | −25.3462 | −0.929863 | −0.464931 | − | 0.885347i | \(-0.653921\pi\) | ||||
−0.464931 | + | 0.885347i | \(0.653921\pi\) | |||||||
\(744\) | −0.330591 | + | 0.665228i | −0.0121200 | + | 0.0243885i | ||||
\(745\) | 13.6975 | − | 13.6975i | 0.501838 | − | 0.501838i | ||||
\(746\) | 25.8584 | + | 25.8584i | 0.946743 | + | 0.946743i | ||||
\(747\) | 24.5652 | − | 18.6116i | 0.898793 | − | 0.680963i | ||||
\(748\) | 4.91051 | − | 4.91051i | 0.179546 | − | 0.179546i | ||||
\(749\) | 2.41060i | 0.0880813i | ||||||||
\(750\) | −0.770820 | + | 1.55108i | −0.0281464 | + | 0.0566373i | ||||
\(751\) | − | 12.8037i | − | 0.467215i | −0.972331 | − | 0.233608i | \(-0.924947\pi\) | ||
0.972331 | − | 0.233608i | \(-0.0750531\pi\) | |||||||
\(752\) | 8.83045i | 0.322014i | ||||||||
\(753\) | −25.3395 | + | 8.51514i | −0.923421 | + | 0.310309i | ||||
\(754\) | −7.57950 | − | 7.57950i | −0.276029 | − | 0.276029i | ||||
\(755\) | 8.62559 | − | 8.62559i | 0.313917 | − | 0.313917i | ||||
\(756\) | −22.3702 | + | 4.23646i | −0.813596 | + | 0.154078i | ||||
\(757\) | 0.841475 | − | 0.841475i | 0.0305839 | − | 0.0305839i | −0.691649 | − | 0.722233i | \(-0.743116\pi\) |
0.722233 | + | 0.691649i | \(0.243116\pi\) | |||||||
\(758\) | 26.0092 | − | 26.0092i | 0.944695 | − | 0.944695i | ||||
\(759\) | 5.47896 | + | 16.3043i | 0.198874 | + | 0.591810i | ||||
\(760\) | −0.737671 | − | 0.737671i | −0.0267582 | − | 0.0267582i | ||||
\(761\) | 45.4549 | 1.64774 | 0.823870 | − | 0.566779i | \(-0.191811\pi\) | ||||
0.823870 | + | 0.566779i | \(0.191811\pi\) | |||||||
\(762\) | 30.9121 | − | 10.3878i | 1.11983 | − | 0.376310i | ||||
\(763\) | −29.2874 | + | 29.2874i | −1.06027 | + | 1.06027i | ||||
\(764\) | −3.71929 | + | 3.71929i | −0.134559 | + | 0.134559i | ||||
\(765\) | −3.69017 | + | 2.79583i | −0.133418 | + | 0.101083i | ||||
\(766\) | −10.9589 | −0.395960 | ||||||||
\(767\) | 28.5866 | 1.03220 | ||||||||
\(768\) | −1.55108 | − | 0.770820i | −0.0559696 | − | 0.0278146i | ||||
\(769\) | −35.9501 | − | 35.9501i | −1.29639 | − | 1.29639i | −0.930759 | − | 0.365634i | \(-0.880852\pi\) |
−0.365634 | − | 0.930759i | \(-0.619148\pi\) | |||||||
\(770\) | −19.7174 | −0.710567 | ||||||||
\(771\) | 13.0802 | + | 38.9243i | 0.471073 | + | 1.40183i | ||||
\(772\) | −11.4367 | − | 11.4367i | −0.411617 | − | 0.411617i | ||||
\(773\) | 3.80731i | 0.136939i | 0.997653 | + | 0.0684697i | \(0.0218116\pi\) | ||||
−0.997653 | + | 0.0684697i | \(0.978188\pi\) | |||||||
\(774\) | −1.92402 | + | 1.45772i | −0.0691573 | + | 0.0523965i | ||||
\(775\) | 0.303265 | − | 0.303265i | 0.0108936 | − | 0.0108936i | ||||
\(776\) | −1.08334 | −0.0388897 | ||||||||
\(777\) | 19.3970 | − | 41.8909i | 0.695863 | − | 1.50283i | ||||
\(778\) | −23.8515 | −0.855119 | ||||||||
\(779\) | 1.46989 | − | 1.46989i | 0.0526641 | − | 0.0526641i | ||||
\(780\) | −1.58706 | + | 3.19355i | −0.0568259 | + | 0.114348i | ||||
\(781\) | 60.2501i | 2.15592i | ||||||||
\(782\) | 2.40813 | + | 2.40813i | 0.0861146 | + | 0.0861146i | ||||
\(783\) | 22.3537 | + | 15.2352i | 0.798857 | + | 0.544461i | ||||
\(784\) | −12.1990 | −0.435679 | ||||||||
\(785\) | −5.02817 | − | 5.02817i | −0.179463 | − | 0.179463i | ||||
\(786\) | −7.09374 | + | 14.2743i | −0.253025 | + | 0.509148i | ||||
\(787\) | 2.17346 | 0.0774755 | 0.0387378 | − | 0.999249i | \(-0.487666\pi\) | ||||
0.0387378 | + | 0.999249i | \(0.487666\pi\) | |||||||
\(788\) | 12.8748 | 0.458646 | ||||||||
\(789\) | −25.2118 | − | 12.5292i | −0.897565 | − | 0.446052i | ||||
\(790\) | 2.04760 | − | 2.04760i | 0.0728504 | − | 0.0728504i | ||||
\(791\) | −26.7837 | + | 26.7837i | −0.952318 | + | 0.952318i | ||||
\(792\) | −1.84404 | + | 13.3734i | −0.0655250 | + | 0.475204i | ||||
\(793\) | 1.44662 | 0.0513708 | ||||||||
\(794\) | 1.85282 | + | 1.85282i | 0.0657543 | + | 0.0657543i | ||||
\(795\) | −13.2596 | + | 4.45579i | −0.470269 | + | 0.158030i | ||||
\(796\) | 16.5646 | − | 16.5646i | 0.587117 | − | 0.587117i | ||||
\(797\) | −11.8159 | + | 11.8159i | −0.418540 | + | 0.418540i | −0.884700 | − | 0.466160i | \(-0.845637\pi\) |
0.466160 | + | 0.884700i | \(0.345637\pi\) | |||||||
\(798\) | −3.52347 | + | 7.09007i | −0.124729 | + | 0.250986i | ||||
\(799\) | 9.63604 | − | 9.63604i | 0.340899 | − | 0.340899i | ||||
\(800\) | 0.707107 | + | 0.707107i | 0.0250000 | + | 0.0250000i | ||||
\(801\) | 49.6726 | + | 6.84927i | 1.75510 | + | 0.242007i | ||||
\(802\) | − | 33.5646i | − | 1.18521i | ||||||
\(803\) | − | 55.3729i | − | 1.95407i | ||||||
\(804\) | −11.3513 | − | 5.64114i | −0.400331 | − | 0.198948i | ||||
\(805\) | − | 9.66950i | − | 0.340805i | ||||||
\(806\) | 0.624401 | − | 0.624401i | 0.0219936 | − | 0.0219936i | ||||
\(807\) | 11.0142 | − | 22.1632i | 0.387718 | − | 0.780183i | ||||
\(808\) | −8.84766 | − | 8.84766i | −0.311260 | − | 0.311260i | ||||
\(809\) | −10.9733 | + | 10.9733i | −0.385800 | + | 0.385800i | −0.873186 | − | 0.487386i | \(-0.837950\pi\) |
0.487386 | + | 0.873186i | \(0.337950\pi\) | |||||||
\(810\) | 2.43568 | − | 8.66415i | 0.0855810 | − | 0.304427i | ||||
\(811\) | 10.1575 | 0.356678 | 0.178339 | − | 0.983969i | \(-0.442928\pi\) | ||||
0.178339 | + | 0.983969i | \(0.442928\pi\) | |||||||
\(812\) | 16.1302 | + | 16.1302i | 0.566058 | + | 0.566058i | ||||
\(813\) | −31.6114 | − | 15.7096i | −1.10866 | − | 0.550958i | ||||
\(814\) | −19.8814 | − | 18.8143i | −0.696841 | − | 0.659440i | ||||
\(815\) | − | 5.59081i | − | 0.195837i | ||||||
\(816\) | 0.851438 | + | 2.53372i | 0.0298063 | + | 0.0886979i | ||||
\(817\) | 0.839403i | 0.0293670i | ||||||||
\(818\) | 11.8125 | 0.413015 | ||||||||
\(819\) | 26.8109 | + | 3.69691i | 0.936850 | + | 0.129180i | ||||
\(820\) | −1.40898 | + | 1.40898i | −0.0492038 | + | 0.0492038i | ||||
\(821\) | − | 44.8407i | − | 1.56495i | −0.622681 | − | 0.782476i | \(-0.713957\pi\) | ||
0.622681 | − | 0.782476i | \(-0.286043\pi\) | |||||||
\(822\) | −10.7624 | − | 32.0268i | −0.375381 | − | 1.11706i | ||||
\(823\) | 31.0456 | 1.08218 | 0.541090 | − | 0.840965i | \(-0.318012\pi\) | ||||
0.541090 | + | 0.840965i | \(0.318012\pi\) | |||||||
\(824\) | 9.14355i | 0.318531i | ||||||||
\(825\) | 3.46868 | − | 6.97982i | 0.120764 | − | 0.243006i | ||||
\(826\) | −60.8361 | −2.11676 | ||||||||
\(827\) | −28.1012 | − | 28.1012i | −0.977176 | − | 0.977176i | 0.0225692 | − | 0.999745i | \(-0.492815\pi\) |
−0.999745 | + | 0.0225692i | \(0.992815\pi\) | |||||||
\(828\) | −6.55837 | − | 0.904321i | −0.227919 | − | 0.0314273i | ||||
\(829\) | −5.40746 | − | 5.40746i | −0.187809 | − | 0.187809i | 0.606939 | − | 0.794748i | \(-0.292397\pi\) |
−0.794748 | + | 0.606939i | \(0.792397\pi\) | |||||||
\(830\) | 10.2732i | 0.356587i | ||||||||
\(831\) | 13.7158 | + | 40.8156i | 0.475795 | + | 1.41588i | ||||
\(832\) | 1.45588 | + | 1.45588i | 0.0504736 | + | 0.0504736i | ||||
\(833\) | 13.3119 | + | 13.3119i | 0.461230 | + | 0.461230i | ||||
\(834\) | 9.81956 | + | 29.2212i | 0.340024 | + | 1.01185i | ||||
\(835\) | − | 1.42492i | − | 0.0493115i | ||||||
\(836\) | 3.31951 | + | 3.31951i | 0.114808 | + | 0.114808i | ||||
\(837\) | −1.25508 | + | 1.84151i | −0.0433818 | + | 0.0636518i | ||||
\(838\) | 15.1199 | + | 15.1199i | 0.522309 | + | 0.522309i | ||||
\(839\) | 7.42372 | 0.256295 | 0.128148 | − | 0.991755i | \(-0.459097\pi\) | ||||
0.128148 | + | 0.991755i | \(0.459097\pi\) | |||||||
\(840\) | 3.37748 | − | 6.79630i | 0.116534 | − | 0.234495i | ||||
\(841\) | 1.89630i | 0.0653897i | ||||||||
\(842\) | 35.2280 | 1.21404 | ||||||||
\(843\) | −1.05009 | − | 3.12488i | −0.0361671 | − | 0.107626i | ||||
\(844\) | 9.22945i | 0.317691i | ||||||||
\(845\) | −6.19483 | + | 6.19483i | −0.213109 | + | 0.213109i | ||||
\(846\) | −3.61861 | + | 26.2431i | −0.124410 | + | 0.902255i | ||||
\(847\) | 40.5299 | 1.39262 | ||||||||
\(848\) | 8.07611i | 0.277335i | ||||||||
\(849\) | −0.214743 | − | 0.639036i | −0.00736997 | − | 0.0219317i | ||||
\(850\) | − | 1.54323i | − | 0.0529323i | ||||||
\(851\) | 9.22658 | − | 9.74988i | 0.316283 | − | 0.334222i | ||||
\(852\) | −20.7673 | − | 10.3205i | −0.711475 | − | 0.353573i | ||||
\(853\) | −0.927344 | − | 0.927344i | −0.0317516 | − | 0.0317516i | 0.691053 | − | 0.722804i | \(-0.257147\pi\) |
−0.722804 | + | 0.691053i | \(0.757147\pi\) | |||||||
\(854\) | −3.07859 | −0.105347 | ||||||||
\(855\) | −1.88998 | − | 2.49456i | −0.0646360 | − | 0.0853121i | ||||
\(856\) | −0.389018 | + | 0.389018i | −0.0132964 | + | 0.0132964i | ||||
\(857\) | −23.2850 | − | 23.2850i | −0.795402 | − | 0.795402i | 0.186965 | − | 0.982367i | \(-0.440135\pi\) |
−0.982367 | + | 0.186965i | \(0.940135\pi\) | |||||||
\(858\) | 7.14176 | − | 14.3709i | 0.243816 | − | 0.490616i | ||||
\(859\) | 21.9971 | − | 21.9971i | 0.750532 | − | 0.750532i | −0.224047 | − | 0.974578i | \(-0.571927\pi\) |
0.974578 | + | 0.224047i | \(0.0719268\pi\) | |||||||
\(860\) | − | 0.804623i | − | 0.0274374i | ||||||
\(861\) | 13.5423 | + | 6.72997i | 0.461521 | + | 0.229357i | ||||
\(862\) | − | 18.6051i | − | 0.633692i | ||||||
\(863\) | 7.25558i | 0.246983i | 0.992346 | + | 0.123491i | \(0.0394092\pi\) | ||||
−0.992346 | + | 0.123491i | \(0.960591\pi\) | |||||||
\(864\) | −4.29374 | − | 2.92640i | −0.146076 | − | 0.0995580i | ||||
\(865\) | −1.07079 | − | 1.07079i | −0.0364079 | − | 0.0364079i | ||||
\(866\) | −28.6481 | + | 28.6481i | −0.973502 | + | 0.973502i | ||||
\(867\) | −11.2682 | + | 22.6743i | −0.382688 | + | 0.770060i | ||||
\(868\) | −1.32881 | + | 1.32881i | −0.0451027 | + | 0.0451027i | ||||
\(869\) | −9.21418 | + | 9.21418i | −0.312570 | + | 0.312570i | ||||
\(870\) | −8.54756 | + | 2.87234i | −0.289789 | + | 0.0973816i | ||||
\(871\) | 10.6547 | + | 10.6547i | 0.361020 | + | 0.361020i | ||||
\(872\) | −9.45270 | −0.320109 | ||||||||
\(873\) | −3.21957 | − | 0.443940i | −0.108966 | − | 0.0150251i | ||||
\(874\) | −1.62790 | + | 1.62790i | −0.0550645 | + | 0.0550645i | ||||
\(875\) | −3.09831 | + | 3.09831i | −0.104742 | + | 0.104742i | ||||
\(876\) | 19.0862 | + | 9.48504i | 0.644863 | + | 0.320470i | ||||
\(877\) | −46.4154 | −1.56734 | −0.783668 | − | 0.621179i | \(-0.786654\pi\) | ||||
−0.783668 | + | 0.621179i | \(0.786654\pi\) | |||||||
\(878\) | 23.3451 | 0.787857 | ||||||||
\(879\) | 2.34451 | − | 4.71772i | 0.0790784 | − | 0.159125i | ||||
\(880\) | −3.18197 | − | 3.18197i | −0.107264 | − | 0.107264i | ||||
\(881\) | −23.1046 | −0.778413 | −0.389206 | − | 0.921151i | \(-0.627251\pi\) | ||||
−0.389206 | + | 0.921151i | \(0.627251\pi\) | |||||||
\(882\) | −36.2540 | − | 4.99900i | −1.22074 | − | 0.168325i | ||||
\(883\) | −39.2707 | − | 39.2707i | −1.32156 | − | 1.32156i | −0.912511 | − | 0.409052i | \(-0.865859\pi\) |
−0.409052 | − | 0.912511i | \(-0.634141\pi\) | |||||||
\(884\) | − | 3.17740i | − | 0.106867i | ||||||
\(885\) | 10.7022 | − | 21.5355i | 0.359752 | − | 0.723908i | ||||
\(886\) | 12.2290 | − | 12.2290i | 0.410841 | − | 0.410841i | ||||
\(887\) | −28.2672 | −0.949120 | −0.474560 | − | 0.880223i | \(-0.657393\pi\) | ||||
−0.474560 | + | 0.880223i | \(0.657393\pi\) | |||||||
\(888\) | 9.89054 | − | 3.63003i | 0.331905 | − | 0.121816i | ||||
\(889\) | 82.4975 | 2.76688 | ||||||||
\(890\) | −11.8187 | + | 11.8187i | −0.396165 | + | 0.396165i | ||||
\(891\) | −10.9605 | + | 38.9886i | −0.367191 | + | 1.30617i | ||||
\(892\) | 21.7378i | 0.727837i | ||||||||
\(893\) | 6.51397 | + | 6.51397i | 0.217982 | + | 0.217982i | ||||
\(894\) | −10.6876 | − | 31.8042i | −0.357446 | − | 1.06369i | ||||
\(895\) | 3.70055 | 0.123696 | ||||||||
\(896\) | −3.09831 | − | 3.09831i | −0.103507 | − | 0.103507i | ||||
\(897\) | 7.04756 | + | 3.50234i | 0.235311 | + | 0.116940i | ||||
\(898\) | −7.91374 | −0.264085 | ||||||||
\(899\) | 2.23281 | 0.0744684 | ||||||||
\(900\) | 1.81167 | + | 2.39120i | 0.0603891 | + | 0.0797067i | ||||
\(901\) | 8.81288 | − | 8.81288i | 0.293600 | − | 0.293600i | ||||
\(902\) | 6.34040 | − | 6.34040i | 0.211112 | − | 0.211112i | ||||
\(903\) | −5.78842 | + | 1.94516i | −0.192626 | + | 0.0647307i | ||||
\(904\) | −8.64462 | −0.287516 | ||||||||
\(905\) | −5.67367 | − | 5.67367i | −0.188599 | − | 0.188599i | ||||
\(906\) | −6.73017 | − | 20.0277i | −0.223595 | − | 0.665376i | ||||
\(907\) | −12.3328 | + | 12.3328i | −0.409504 | + | 0.409504i | −0.881566 | − | 0.472061i | \(-0.843510\pi\) |
0.472061 | + | 0.881566i | \(0.343510\pi\) | |||||||
\(908\) | 11.6318 | − | 11.6318i | 0.386016 | − | 0.386016i | ||||
\(909\) | −22.6685 | − | 29.9199i | −0.751868 | − | 0.992379i | ||||
\(910\) | −6.37919 | + | 6.37919i | −0.211468 | + | 0.211468i | ||||
\(911\) | −1.77565 | − | 1.77565i | −0.0588297 | − | 0.0588297i | 0.677080 | − | 0.735910i | \(-0.263245\pi\) |
−0.735910 | + | 0.677080i | \(0.763245\pi\) | |||||||
\(912\) | −1.71280 | + | 0.575573i | −0.0567163 | + | 0.0190591i | ||||
\(913\) | − | 46.2291i | − | 1.52996i | ||||||
\(914\) | − | 30.1256i | − | 0.996467i | ||||||
\(915\) | 0.541583 | − | 1.08980i | 0.0179042 | − | 0.0360276i | ||||
\(916\) | − | 10.0261i | − | 0.331272i | ||||||
\(917\) | −28.5133 | + | 28.5133i | −0.941591 | + | 0.941591i | ||||
\(918\) | 1.49209 | + | 7.87882i | 0.0492462 | + | 0.260040i | ||||
\(919\) | −22.7873 | − | 22.7873i | −0.751682 | − | 0.751682i | 0.223111 | − | 0.974793i | \(-0.428379\pi\) |
−0.974793 | + | 0.223111i | \(0.928379\pi\) | |||||||
\(920\) | 1.56045 | − | 1.56045i | 0.0514465 | − | 0.0514465i | ||||
\(921\) | 10.1728 | − | 20.4702i | 0.335206 | − | 0.674516i | ||||
\(922\) | −22.1532 | −0.729576 | ||||||||
\(923\) | 19.4927 | + | 19.4927i | 0.641611 | + | 0.641611i | ||||
\(924\) | −15.1986 | + | 30.5833i | −0.499997 | + | 1.00612i | ||||
\(925\) | −6.08045 | + | 0.167677i | −0.199924 | + | 0.00551319i | ||||
\(926\) | 17.1450i | 0.563420i | ||||||||
\(927\) | −3.74691 | + | 27.1736i | −0.123065 | + | 0.892497i | ||||
\(928\) | 5.20612i | 0.170899i | ||||||||
\(929\) | −45.6654 | −1.49823 | −0.749116 | − | 0.662439i | \(-0.769522\pi\) | ||||
−0.749116 | + | 0.662439i | \(0.769522\pi\) | |||||||
\(930\) | −0.236625 | − | 0.704150i | −0.00775923 | − | 0.0230900i | ||||
\(931\) | −8.99886 | + | 8.99886i | −0.294926 | + | 0.294926i | ||||
\(932\) | 14.0316i | 0.459622i | ||||||||
\(933\) | −38.3800 | + | 12.8973i | −1.25650 | + | 0.422239i | ||||
\(934\) | −18.3417 | −0.600158 | ||||||||
\(935\) | 6.94451i | 0.227110i | ||||||||
\(936\) | 3.73010 | + | 4.92331i | 0.121922 | + | 0.160923i | ||||
\(937\) | 19.6515 | 0.641988 | 0.320994 | − | 0.947081i | \(-0.395983\pi\) | ||||
0.320994 | + | 0.947081i | \(0.395983\pi\) | |||||||
\(938\) | −22.6745 | − | 22.6745i | −0.740350 | − | 0.740350i | ||||
\(939\) | −10.3043 | + | 3.46268i | −0.336268 | + | 0.113000i | ||||
\(940\) | −6.24407 | − | 6.24407i | −0.203659 | − | 0.203659i | ||||
\(941\) | 17.0041i | 0.554317i | 0.960824 | + | 0.277159i | \(0.0893927\pi\) | ||||
−0.960824 | + | 0.277159i | \(0.910607\pi\) | |||||||
\(942\) | −11.6749 | + | 3.92326i | −0.380388 | + | 0.127827i | ||||
\(943\) | 3.10935 | + | 3.10935i | 0.101254 | + | 0.101254i | ||||
\(944\) | −9.81764 | − | 9.81764i | −0.319537 | − | 0.319537i | ||||
\(945\) | 12.8225 | − | 18.8137i | 0.417116 | − | 0.612011i | ||||
\(946\) | 3.62079i | 0.117722i | ||||||||
\(947\) | 3.04029 | + | 3.04029i | 0.0987962 | + | 0.0987962i | 0.754777 | − | 0.655981i | \(-0.227745\pi\) |
−0.655981 | + | 0.754777i | \(0.727745\pi\) | |||||||
\(948\) | −1.59765 | − | 4.75432i | −0.0518894 | − | 0.154413i | ||||
\(949\) | −17.9148 | − | 17.9148i | −0.581540 | − | 0.581540i | ||||
\(950\) | 1.04322 | 0.0338467 | ||||||||
\(951\) | 4.94330 | + | 2.45662i | 0.160298 | + | 0.0796612i | ||||
\(952\) | 6.76192i | 0.219155i | ||||||||
\(953\) | 7.48439 | 0.242443 | 0.121222 | − | 0.992625i | \(-0.461319\pi\) | ||||
0.121222 | + | 0.992625i | \(0.461319\pi\) | |||||||
\(954\) | −3.30949 | + | 24.0012i | −0.107149 | + | 0.777069i | ||||
\(955\) | − | 5.25987i | − | 0.170205i | ||||||
\(956\) | −1.89394 | + | 1.89394i | −0.0612544 | + | 0.0612544i | ||||
\(957\) | 38.4639 | − | 12.9255i | 1.24336 | − | 0.417822i | ||||
\(958\) | −29.1943 | −0.943226 | ||||||||
\(959\) | − | 85.4723i | − | 2.76004i | ||||||
\(960\) | 1.64183 | − | 0.551724i | 0.0529898 | − | 0.0178068i | ||||
\(961\) | − | 30.8161i | − | 0.994066i | ||||||
\(962\) | −12.5192 | + | 0.345235i | −0.403635 | + | 0.0111308i | ||||
\(963\) | −1.31553 | + | 0.996702i | −0.0423924 | + | 0.0321183i | ||||
\(964\) | −11.7784 | − | 11.7784i | −0.379358 | − | 0.379358i | ||||
\(965\) | 16.1740 | 0.520659 | ||||||||
\(966\) | −14.9981 | − | 7.45344i | −0.482557 | − | 0.239810i | ||||
\(967\) | −16.0066 | + | 16.0066i | −0.514738 | + | 0.514738i | −0.915974 | − | 0.401237i | \(-0.868581\pi\) |
0.401237 | + | 0.915974i | \(0.368581\pi\) | |||||||
\(968\) | 6.54065 | + | 6.54065i | 0.210225 | + | 0.210225i | ||||
\(969\) | 2.49713 | + | 1.24097i | 0.0802194 | + | 0.0398657i | ||||
\(970\) | 0.766039 | − | 0.766039i | 0.0245960 | − | 0.0245960i | ||||
\(971\) | − | 13.5254i | − | 0.434049i | −0.976166 | − | 0.217025i | \(-0.930365\pi\) | ||
0.976166 | − | 0.217025i | \(-0.0696352\pi\) | |||||||
\(972\) | −11.5613 | − | 10.4564i | −0.370828 | − | 0.335390i | ||||
\(973\) | 77.9847i | 2.50007i | ||||||||
\(974\) | − | 28.4876i | − | 0.912801i | ||||||
\(975\) | −1.13596 | − | 3.38041i | −0.0363799 | − | 0.108260i | ||||
\(976\) | −0.496818 | − | 0.496818i | −0.0159028 | − | 0.0159028i | ||||
\(977\) | 23.7197 | − | 23.7197i | 0.758861 | − | 0.758861i | −0.217254 | − | 0.976115i | \(-0.569710\pi\) |
0.976115 | + | 0.217254i | \(0.0697101\pi\) | |||||||
\(978\) | −8.67177 | − | 4.30950i | −0.277292 | − | 0.137803i | ||||
\(979\) | 53.1841 | − | 53.1841i | 1.69977 | − | 1.69977i | ||||
\(980\) | 8.62600 | − | 8.62600i | 0.275548 | − | 0.275548i | ||||
\(981\) | −28.0923 | − | 3.87359i | −0.896918 | − | 0.123674i | ||||
\(982\) | 25.1466 | + | 25.1466i | 0.802460 | + | 0.802460i | ||||
\(983\) | 10.5567 | 0.336707 | 0.168353 | − | 0.985727i | \(-0.446155\pi\) | ||||
0.168353 | + | 0.985727i | \(0.446155\pi\) | |||||||
\(984\) | 1.09937 | + | 3.27151i | 0.0350466 | + | 0.104292i | ||||
\(985\) | −9.10387 | + | 9.10387i | −0.290073 | + | 0.290073i | ||||
\(986\) | 5.68107 | − | 5.68107i | 0.180922 | − | 0.180922i | ||||
\(987\) | −29.8247 | + | 60.0144i | −0.949329 | + | 1.91028i | ||||
\(988\) | 2.14792 | 0.0683346 | ||||||||
\(989\) | −1.77565 | −0.0564623 | ||||||||
\(990\) | −8.15251 | − | 10.7604i | −0.259104 | − | 0.341987i | ||||
\(991\) | 20.8171 | + | 20.8171i | 0.661278 | + | 0.661278i | 0.955681 | − | 0.294403i | \(-0.0951208\pi\) |
−0.294403 | + | 0.955681i | \(0.595121\pi\) | |||||||
\(992\) | −0.428882 | −0.0136170 | ||||||||
\(993\) | 32.3068 | − | 10.8564i | 1.02522 | − | 0.344519i | ||||
\(994\) | −41.4831 | − | 41.4831i | −1.31576 | − | 1.31576i | ||||
\(995\) | 23.4259i | 0.742651i | ||||||||
\(996\) | 15.9345 | + | 7.91876i | 0.504902 | + | 0.250915i | ||||
\(997\) | −18.2060 | + | 18.2060i | −0.576588 | + | 0.576588i | −0.933962 | − | 0.357373i | \(-0.883672\pi\) |
0.357373 | + | 0.933962i | \(0.383672\pi\) | |||||||
\(998\) | 7.69073 | 0.243446 | ||||||||
\(999\) | 30.8811 | − | 6.73500i | 0.977033 | − | 0.213086i |
(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 | 1110.2.u.f.401.10 | yes | 40 | |
3.2 | odd | 2 | inner | 1110.2.u.f.401.17 | yes | 40 | |
37.6 | odd | 4 | inner | 1110.2.u.f.191.17 | yes | 40 | |
111.80 | even | 4 | inner | 1110.2.u.f.191.10 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.u.f.191.10 | ✓ | 40 | 111.80 | even | 4 | inner | |
1110.2.u.f.191.17 | yes | 40 | 37.6 | odd | 4 | inner | |
1110.2.u.f.401.10 | yes | 40 | 1.1 | even | 1 | trivial | |
1110.2.u.f.401.17 | yes | 40 | 3.2 | odd | 2 | inner |