Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,2,Mod(277,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("483.277");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.85677441763\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 3 x^{19} + 22 x^{18} - 43 x^{17} + 245 x^{16} - 416 x^{15} + 1707 x^{14} - 2021 x^{13} + \cdots + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 277.6 | ||
Root | \(-0.0131282 + 0.0227388i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 483.277 |
Dual form | 483.2.i.h.415.6 |
$q$-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 \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(346\) | \(442\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0131282 | + | 0.0227388i | 0.00928307 | + | 0.0160788i | 0.870630 | − | 0.491939i | \(-0.163712\pi\) |
−0.861347 | + | 0.508018i | \(0.830378\pi\) | |||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | 0.999655 | − | 1.73145i | 0.499828 | − | 0.865727i | ||||
\(5\) | −1.38914 | − | 2.40606i | −0.621243 | − | 1.07602i | −0.989255 | − | 0.146203i | \(-0.953295\pi\) |
0.368012 | − | 0.929821i | \(-0.380039\pi\) | |||||||
\(6\) | 0.0262565 | 0.0107192 | ||||||||
\(7\) | −2.58821 | + | 0.548771i | −0.978253 | + | 0.207416i | ||||
\(8\) | 0.105008 | 0.0371259 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0.0364740 | − | 0.0631748i | 0.0115341 | − | 0.0199776i | ||||
\(11\) | −0.330078 | + | 0.571712i | −0.0995223 | + | 0.172378i | −0.911487 | − | 0.411329i | \(-0.865065\pi\) |
0.811965 | + | 0.583706i | \(0.198398\pi\) | |||||||
\(12\) | −0.999655 | − | 1.73145i | −0.288576 | − | 0.499828i | ||||
\(13\) | 4.12488 | 1.14404 | 0.572018 | − | 0.820241i | \(-0.306161\pi\) | ||||
0.572018 | + | 0.820241i | \(0.306161\pi\) | |||||||
\(14\) | −0.0464571 | − | 0.0516484i | −0.0124162 | − | 0.0138036i | ||||
\(15\) | −2.77828 | −0.717349 | ||||||||
\(16\) | −1.99793 | − | 3.46052i | −0.499483 | − | 0.865130i | ||||
\(17\) | −2.06190 | + | 3.57132i | −0.500085 | + | 0.866173i | 0.499915 | + | 0.866074i | \(0.333365\pi\) |
−1.00000 | 9.81912e-5i | \(0.999969\pi\) | ||||||||
\(18\) | 0.0131282 | − | 0.0227388i | 0.00309436 | − | 0.00535958i | ||||
\(19\) | −2.38414 | − | 4.12946i | −0.546960 | − | 0.947363i | −0.998481 | − | 0.0551022i | \(-0.982452\pi\) |
0.451520 | − | 0.892261i | \(-0.350882\pi\) | |||||||
\(20\) | −5.55465 | −1.24206 | ||||||||
\(21\) | −0.818857 | + | 2.51584i | −0.178689 | + | 0.549002i | ||||
\(22\) | −0.0173334 | −0.00369549 | ||||||||
\(23\) | −0.500000 | − | 0.866025i | −0.104257 | − | 0.180579i | ||||
\(24\) | 0.0525039 | − | 0.0909395i | 0.0107173 | − | 0.0185629i | ||||
\(25\) | −1.35943 | + | 2.35460i | −0.271885 | + | 0.470919i | ||||
\(26\) | 0.0541524 | + | 0.0937947i | 0.0106202 | + | 0.0183947i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.63715 | + | 5.02995i | −0.309392 | + | 0.950572i | ||||
\(29\) | −1.78025 | −0.330583 | −0.165292 | − | 0.986245i | \(-0.552857\pi\) | ||||
−0.165292 | + | 0.986245i | \(0.552857\pi\) | |||||||
\(30\) | −0.0364740 | − | 0.0631748i | −0.00665921 | − | 0.0115341i | ||||
\(31\) | 1.81214 | − | 3.13872i | 0.325471 | − | 0.563732i | −0.656137 | − | 0.754642i | \(-0.727811\pi\) |
0.981607 | + | 0.190910i | \(0.0611440\pi\) | |||||||
\(32\) | 0.157467 | − | 0.272740i | 0.0278364 | − | 0.0482141i | ||||
\(33\) | 0.330078 | + | 0.571712i | 0.0574592 | + | 0.0995223i | ||||
\(34\) | −0.108277 | −0.0185693 | ||||||||
\(35\) | 4.91577 | + | 5.46509i | 0.830917 | + | 0.923768i | ||||
\(36\) | −1.99931 | −0.333218 | ||||||||
\(37\) | 4.03105 | + | 6.98199i | 0.662701 | + | 1.14783i | 0.979903 | + | 0.199474i | \(0.0639233\pi\) |
−0.317202 | + | 0.948358i | \(0.602743\pi\) | |||||||
\(38\) | 0.0625993 | − | 0.108425i | 0.0101549 | − | 0.0175889i | ||||
\(39\) | 2.06244 | − | 3.57225i | 0.330254 | − | 0.572018i | ||||
\(40\) | −0.145871 | − | 0.252656i | −0.0230642 | − | 0.0399484i | ||||
\(41\) | −7.99969 | −1.24934 | −0.624671 | − | 0.780888i | \(-0.714767\pi\) | ||||
−0.624671 | + | 0.780888i | \(0.714767\pi\) | |||||||
\(42\) | −0.0679574 | + | 0.0144088i | −0.0104861 | + | 0.00222333i | ||||
\(43\) | 12.5842 | 1.91907 | 0.959536 | − | 0.281585i | \(-0.0908601\pi\) | ||||
0.959536 | + | 0.281585i | \(0.0908601\pi\) | |||||||
\(44\) | 0.659929 | + | 1.14303i | 0.0994880 | + | 0.172318i | ||||
\(45\) | −1.38914 | + | 2.40606i | −0.207081 | + | 0.358675i | ||||
\(46\) | 0.0131282 | − | 0.0227388i | 0.00193565 | − | 0.00335265i | ||||
\(47\) | −5.88109 | − | 10.1864i | −0.857846 | − | 1.48583i | −0.873980 | − | 0.485962i | \(-0.838469\pi\) |
0.0161343 | − | 0.999870i | \(-0.494864\pi\) | |||||||
\(48\) | −3.99586 | −0.576753 | ||||||||
\(49\) | 6.39770 | − | 2.84067i | 0.913957 | − | 0.405811i | ||||
\(50\) | −0.0713876 | −0.0100957 | ||||||||
\(51\) | 2.06190 | + | 3.57132i | 0.288724 | + | 0.500085i | ||||
\(52\) | 4.12346 | − | 7.14203i | 0.571820 | − | 0.990422i | ||||
\(53\) | 0.0304128 | − | 0.0526766i | 0.00417752 | − | 0.00723568i | −0.863929 | − | 0.503613i | \(-0.832004\pi\) |
0.868107 | + | 0.496378i | \(0.165337\pi\) | |||||||
\(54\) | −0.0131282 | − | 0.0227388i | −0.00178653 | − | 0.00309436i | ||||
\(55\) | 1.83410 | 0.247310 | ||||||||
\(56\) | −0.271783 | + | 0.0576253i | −0.0363185 | + | 0.00770050i | ||||
\(57\) | −4.76829 | −0.631575 | ||||||||
\(58\) | −0.0233715 | − | 0.0404806i | −0.00306883 | − | 0.00531537i | ||||
\(59\) | 4.49359 | − | 7.78312i | 0.585015 | − | 1.01328i | −0.409859 | − | 0.912149i | \(-0.634422\pi\) |
0.994874 | − | 0.101127i | \(-0.0322447\pi\) | |||||||
\(60\) | −2.77732 | + | 4.81047i | −0.358551 | + | 0.621029i | ||||
\(61\) | −1.35633 | − | 2.34924i | −0.173661 | − | 0.300789i | 0.766036 | − | 0.642797i | \(-0.222226\pi\) |
−0.939697 | + | 0.342008i | \(0.888893\pi\) | |||||||
\(62\) | 0.0951611 | 0.0120855 | ||||||||
\(63\) | 1.76936 | + | 1.96707i | 0.222918 | + | 0.247828i | ||||
\(64\) | −7.98346 | −0.997932 | ||||||||
\(65\) | −5.73004 | − | 9.92471i | −0.710724 | − | 1.23101i | ||||
\(66\) | −0.00866669 | + | 0.0150112i | −0.00106680 | + | 0.00184774i | ||||
\(67\) | 1.34291 | − | 2.32600i | 0.164063 | − | 0.284166i | −0.772259 | − | 0.635308i | \(-0.780873\pi\) |
0.936322 | + | 0.351142i | \(0.114207\pi\) | |||||||
\(68\) | 4.12239 | + | 7.14018i | 0.499913 | + | 0.865874i | ||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | −0.0597339 | + | 0.183526i | −0.00713957 | + | 0.0219355i | ||||
\(71\) | 12.4462 | 1.47709 | 0.738545 | − | 0.674205i | \(-0.235513\pi\) | ||||
0.738545 | + | 0.674205i | \(0.235513\pi\) | |||||||
\(72\) | −0.0525039 | − | 0.0909395i | −0.00618765 | − | 0.0107173i | ||||
\(73\) | 7.14354 | − | 12.3730i | 0.836088 | − | 1.44815i | −0.0570543 | − | 0.998371i | \(-0.518171\pi\) |
0.893142 | − | 0.449775i | \(-0.148496\pi\) | |||||||
\(74\) | −0.105841 | + | 0.183323i | −0.0123038 | + | 0.0213108i | ||||
\(75\) | 1.35943 | + | 2.35460i | 0.156973 | + | 0.271885i | ||||
\(76\) | −9.53329 | −1.09354 | ||||||||
\(77\) | 0.540574 | − | 1.66085i | 0.0616041 | − | 0.189271i | ||||
\(78\) | 0.108305 | 0.0122631 | ||||||||
\(79\) | 3.47399 | + | 6.01712i | 0.390854 | + | 0.676979i | 0.992562 | − | 0.121737i | \(-0.0388464\pi\) |
−0.601708 | + | 0.798716i | \(0.705513\pi\) | |||||||
\(80\) | −5.55082 | + | 9.61430i | −0.620600 | + | 1.07491i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −0.105022 | − | 0.181903i | −0.0115977 | − | 0.0200879i | ||||
\(83\) | 9.40856 | 1.03272 | 0.516362 | − | 0.856371i | \(-0.327286\pi\) | ||||
0.516362 | + | 0.856371i | \(0.327286\pi\) | |||||||
\(84\) | 3.53749 | + | 3.93279i | 0.385972 | + | 0.429103i | ||||
\(85\) | 11.4571 | 1.24270 | ||||||||
\(86\) | 0.165208 | + | 0.286150i | 0.0178149 | + | 0.0308563i | ||||
\(87\) | −0.890123 | + | 1.54174i | −0.0954312 | + | 0.165292i | ||||
\(88\) | −0.0346608 | + | 0.0600343i | −0.00369485 | + | 0.00639967i | ||||
\(89\) | 2.96215 | + | 5.13060i | 0.313987 | + | 0.543842i | 0.979222 | − | 0.202793i | \(-0.0650017\pi\) |
−0.665234 | + | 0.746635i | \(0.731668\pi\) | |||||||
\(90\) | −0.0729480 | −0.00768939 | ||||||||
\(91\) | −10.6761 | + | 2.26361i | −1.11916 | + | 0.237291i | ||||
\(92\) | −1.99931 | −0.208443 | ||||||||
\(93\) | −1.81214 | − | 3.13872i | −0.187911 | − | 0.325471i | ||||
\(94\) | 0.154417 | − | 0.267458i | 0.0159269 | − | 0.0275862i | ||||
\(95\) | −6.62383 | + | 11.4728i | −0.679590 | + | 1.17708i | ||||
\(96\) | −0.157467 | − | 0.272740i | −0.0160714 | − | 0.0278364i | ||||
\(97\) | 2.53740 | 0.257634 | 0.128817 | − | 0.991668i | \(-0.458882\pi\) | ||||
0.128817 | + | 0.991668i | \(0.458882\pi\) | |||||||
\(98\) | 0.148584 | + | 0.108183i | 0.0150093 | + | 0.0109281i | ||||
\(99\) | 0.660156 | 0.0663482 | ||||||||
\(100\) | 2.71792 | + | 4.70757i | 0.271792 | + | 0.470757i | ||||
\(101\) | −3.35589 | + | 5.81257i | −0.333923 | + | 0.578372i | −0.983277 | − | 0.182114i | \(-0.941706\pi\) |
0.649354 | + | 0.760486i | \(0.275039\pi\) | |||||||
\(102\) | −0.0541384 | + | 0.0937704i | −0.00536050 | + | 0.00928465i | ||||
\(103\) | −5.37391 | − | 9.30788i | −0.529507 | − | 0.917132i | −0.999408 | − | 0.0344133i | \(-0.989044\pi\) |
0.469901 | − | 0.882719i | \(-0.344290\pi\) | |||||||
\(104\) | 0.433145 | 0.0424733 | ||||||||
\(105\) | 7.19079 | − | 1.52464i | 0.701749 | − | 0.148790i | ||||
\(106\) | 0.00159707 | 0.000155121 | ||||||||
\(107\) | 0.242278 | + | 0.419638i | 0.0234219 | + | 0.0405679i | 0.877499 | − | 0.479579i | \(-0.159211\pi\) |
−0.854077 | + | 0.520147i | \(0.825877\pi\) | |||||||
\(108\) | −0.999655 | + | 1.73145i | −0.0961919 | + | 0.166609i | ||||
\(109\) | −6.23260 | + | 10.7952i | −0.596975 | + | 1.03399i | 0.396290 | + | 0.918126i | \(0.370298\pi\) |
−0.993265 | + | 0.115866i | \(0.963036\pi\) | |||||||
\(110\) | 0.0240785 | + | 0.0417052i | 0.00229580 | + | 0.00397644i | ||||
\(111\) | 8.06211 | 0.765221 | ||||||||
\(112\) | 7.07011 | + | 7.86016i | 0.668062 | + | 0.742715i | ||||
\(113\) | 9.28875 | 0.873812 | 0.436906 | − | 0.899507i | \(-0.356074\pi\) | ||||
0.436906 | + | 0.899507i | \(0.356074\pi\) | |||||||
\(114\) | −0.0625993 | − | 0.108425i | −0.00586296 | − | 0.0101549i | ||||
\(115\) | −1.38914 | + | 2.40606i | −0.129538 | + | 0.224367i | ||||
\(116\) | −1.77963 | + | 3.08241i | −0.165235 | + | 0.286195i | ||||
\(117\) | −2.06244 | − | 3.57225i | −0.190673 | − | 0.330254i | ||||
\(118\) | 0.235972 | 0.0217229 | ||||||||
\(119\) | 3.37681 | − | 10.3749i | 0.309552 | − | 0.951062i | ||||
\(120\) | −0.291742 | −0.0266322 | ||||||||
\(121\) | 5.28210 | + | 9.14886i | 0.480191 | + | 0.831715i | ||||
\(122\) | 0.0356126 | − | 0.0616828i | 0.00322421 | − | 0.00558450i | ||||
\(123\) | −3.99984 | + | 6.92793i | −0.360654 | + | 0.624671i | ||||
\(124\) | −3.62304 | − | 6.27529i | −0.325358 | − | 0.563537i | ||||
\(125\) | −6.33767 | −0.566858 | ||||||||
\(126\) | −0.0215003 | + | 0.0660573i | −0.00191540 | + | 0.00588485i | ||||
\(127\) | 2.40074 | 0.213031 | 0.106515 | − | 0.994311i | \(-0.466031\pi\) | ||||
0.106515 | + | 0.994311i | \(0.466031\pi\) | |||||||
\(128\) | −0.419742 | − | 0.727014i | −0.0371003 | − | 0.0642596i | ||||
\(129\) | 6.29210 | − | 10.8982i | 0.553989 | − | 0.959536i | ||||
\(130\) | 0.150451 | − | 0.260588i | 0.0131954 | − | 0.0228551i | ||||
\(131\) | 10.0752 | + | 17.4508i | 0.880278 | + | 1.52469i | 0.851032 | + | 0.525114i | \(0.175977\pi\) |
0.0292458 | + | 0.999572i | \(0.490689\pi\) | |||||||
\(132\) | 1.31986 | 0.114879 | ||||||||
\(133\) | 8.43680 | + | 9.37957i | 0.731564 | + | 0.813312i | ||||
\(134\) | 0.0705204 | 0.00609204 | ||||||||
\(135\) | 1.38914 | + | 2.40606i | 0.119558 | + | 0.207081i | ||||
\(136\) | −0.216516 | + | 0.375017i | −0.0185661 | + | 0.0321574i | ||||
\(137\) | −3.50329 | + | 6.06788i | −0.299306 | + | 0.518414i | −0.975977 | − | 0.217872i | \(-0.930089\pi\) |
0.676671 | + | 0.736285i | \(0.263422\pi\) | |||||||
\(138\) | −0.0131282 | − | 0.0227388i | −0.00111755 | − | 0.00193565i | ||||
\(139\) | −2.88510 | −0.244711 | −0.122356 | − | 0.992486i | \(-0.539045\pi\) | ||||
−0.122356 | + | 0.992486i | \(0.539045\pi\) | |||||||
\(140\) | 14.3766 | − | 3.04823i | 1.21505 | − | 0.257623i | ||||
\(141\) | −11.7622 | −0.990555 | ||||||||
\(142\) | 0.163396 | + | 0.283011i | 0.0137119 | + | 0.0237497i | ||||
\(143\) | −1.36153 | + | 2.35824i | −0.113857 | + | 0.197206i | ||||
\(144\) | −1.99793 | + | 3.46052i | −0.166494 | + | 0.288377i | ||||
\(145\) | 2.47301 | + | 4.28338i | 0.205373 | + | 0.355716i | ||||
\(146\) | 0.375128 | 0.0310458 | ||||||||
\(147\) | 0.738754 | − | 6.96091i | 0.0609314 | − | 0.574126i | ||||
\(148\) | 16.1187 | 1.32495 | ||||||||
\(149\) | −9.53041 | − | 16.5072i | −0.780762 | − | 1.35232i | −0.931498 | − | 0.363745i | \(-0.881498\pi\) |
0.150737 | − | 0.988574i | \(-0.451835\pi\) | |||||||
\(150\) | −0.0356938 | + | 0.0618234i | −0.00291438 | + | 0.00504786i | ||||
\(151\) | 2.53145 | − | 4.38460i | 0.206006 | − | 0.356813i | −0.744447 | − | 0.667682i | \(-0.767287\pi\) |
0.950453 | + | 0.310869i | \(0.100620\pi\) | |||||||
\(152\) | −0.250354 | − | 0.433626i | −0.0203064 | − | 0.0351717i | ||||
\(153\) | 4.12381 | 0.333390 | ||||||||
\(154\) | 0.0448625 | − | 0.00951206i | 0.00361512 | − | 0.000766504i | ||||
\(155\) | −10.0693 | −0.808785 | ||||||||
\(156\) | −4.12346 | − | 7.14203i | −0.330141 | − | 0.571820i | ||||
\(157\) | 1.37194 | − | 2.37627i | 0.109493 | − | 0.189647i | −0.806072 | − | 0.591817i | \(-0.798411\pi\) |
0.915565 | + | 0.402170i | \(0.131744\pi\) | |||||||
\(158\) | −0.0912147 | + | 0.157988i | −0.00725665 | + | 0.0125689i | ||||
\(159\) | −0.0304128 | − | 0.0526766i | −0.00241189 | − | 0.00417752i | ||||
\(160\) | −0.874973 | −0.0691727 | ||||||||
\(161\) | 1.76936 | + | 1.96707i | 0.139445 | + | 0.155027i | ||||
\(162\) | −0.0262565 | −0.00206290 | ||||||||
\(163\) | −7.65440 | − | 13.2578i | −0.599539 | − | 1.03843i | −0.992889 | − | 0.119043i | \(-0.962017\pi\) |
0.393350 | − | 0.919389i | \(-0.371316\pi\) | |||||||
\(164\) | −7.99693 | + | 13.8511i | −0.624455 | + | 1.08159i | ||||
\(165\) | 0.917050 | − | 1.58838i | 0.0713923 | − | 0.123655i | ||||
\(166\) | 0.123518 | + | 0.213939i | 0.00958685 | + | 0.0166049i | ||||
\(167\) | 13.0016 | 1.00610 | 0.503049 | − | 0.864258i | \(-0.332212\pi\) | ||||
0.503049 | + | 0.864258i | \(0.332212\pi\) | |||||||
\(168\) | −0.0859864 | + | 0.264183i | −0.00663400 | + | 0.0203822i | ||||
\(169\) | 4.01461 | 0.308816 | ||||||||
\(170\) | 0.150412 | + | 0.260521i | 0.0115360 | + | 0.0199810i | ||||
\(171\) | −2.38414 | + | 4.12946i | −0.182320 | + | 0.315788i | ||||
\(172\) | 12.5799 | − | 21.7890i | 0.959206 | − | 1.66139i | ||||
\(173\) | 5.21101 | + | 9.02574i | 0.396186 | + | 0.686214i | 0.993252 | − | 0.115978i | \(-0.0370002\pi\) |
−0.597066 | + | 0.802192i | \(0.703667\pi\) | |||||||
\(174\) | −0.0467430 | −0.00354358 | ||||||||
\(175\) | 2.22635 | − | 6.84021i | 0.168296 | − | 0.517071i | ||||
\(176\) | 2.63789 | 0.198839 | ||||||||
\(177\) | −4.49359 | − | 7.78312i | −0.337759 | − | 0.585015i | ||||
\(178\) | −0.0777757 | + | 0.134711i | −0.00582953 | + | 0.0100971i | ||||
\(179\) | −9.61157 | + | 16.6477i | −0.718402 | + | 1.24431i | 0.243230 | + | 0.969969i | \(0.421793\pi\) |
−0.961633 | + | 0.274341i | \(0.911540\pi\) | |||||||
\(180\) | 2.77732 | + | 4.81047i | 0.207010 | + | 0.358551i | ||||
\(181\) | −11.1552 | −0.829162 | −0.414581 | − | 0.910012i | \(-0.636072\pi\) | ||||
−0.414581 | + | 0.910012i | \(0.636072\pi\) | |||||||
\(182\) | −0.191630 | − | 0.213043i | −0.0142045 | − | 0.0157918i | ||||
\(183\) | −2.71267 | −0.200526 | ||||||||
\(184\) | −0.0525039 | − | 0.0909395i | −0.00387064 | − | 0.00670415i | ||||
\(185\) | 11.1994 | − | 19.3979i | 0.823397 | − | 1.42616i | ||||
\(186\) | 0.0475805 | − | 0.0824119i | 0.00348877 | − | 0.00604273i | ||||
\(187\) | −1.36118 | − | 2.35763i | −0.0995392 | − | 0.172407i | ||||
\(188\) | −23.5163 | −1.71510 | ||||||||
\(189\) | 2.58821 | − | 0.548771i | 0.188265 | − | 0.0399172i | ||||
\(190\) | −0.347837 | −0.0252347 | ||||||||
\(191\) | −9.61731 | − | 16.6577i | −0.695884 | − | 1.20531i | −0.969882 | − | 0.243576i | \(-0.921679\pi\) |
0.273998 | − | 0.961730i | \(-0.411654\pi\) | |||||||
\(192\) | −3.99173 | + | 6.91388i | −0.288078 | + | 0.498966i | ||||
\(193\) | −8.72634 | + | 15.1145i | −0.628136 | + | 1.08796i | 0.359790 | + | 0.933033i | \(0.382849\pi\) |
−0.987925 | + | 0.154930i | \(0.950485\pi\) | |||||||
\(194\) | 0.0333116 | + | 0.0576974i | 0.00239163 | + | 0.00414243i | ||||
\(195\) | −11.4601 | −0.820673 | ||||||||
\(196\) | 1.47700 | − | 13.9170i | 0.105500 | − | 0.994073i | ||||
\(197\) | −1.16239 | −0.0828168 | −0.0414084 | − | 0.999142i | \(-0.513184\pi\) | ||||
−0.0414084 | + | 0.999142i | \(0.513184\pi\) | |||||||
\(198\) | 0.00866669 | + | 0.0150112i | 0.000615915 | + | 0.00106680i | ||||
\(199\) | −8.48842 | + | 14.7024i | −0.601728 | + | 1.04222i | 0.390831 | + | 0.920462i | \(0.372188\pi\) |
−0.992559 | + | 0.121761i | \(0.961146\pi\) | |||||||
\(200\) | −0.142751 | + | 0.247251i | −0.0100940 | + | 0.0174833i | ||||
\(201\) | −1.34291 | − | 2.32600i | −0.0947219 | − | 0.164063i | ||||
\(202\) | −0.176228 | −0.0123993 | ||||||||
\(203\) | 4.60766 | − | 0.976948i | 0.323394 | − | 0.0685683i | ||||
\(204\) | 8.24477 | 0.577249 | ||||||||
\(205\) | 11.1127 | + | 19.2478i | 0.776145 | + | 1.34432i | ||||
\(206\) | 0.141100 | − | 0.244392i | 0.00983090 | − | 0.0170276i | ||||
\(207\) | −0.500000 | + | 0.866025i | −0.0347524 | + | 0.0601929i | ||||
\(208\) | −8.24122 | − | 14.2742i | −0.571426 | − | 0.989739i | ||||
\(209\) | 3.14782 | 0.217739 | ||||||||
\(210\) | 0.129071 | + | 0.143494i | 0.00890674 | + | 0.00990202i | ||||
\(211\) | 11.6924 | 0.804938 | 0.402469 | − | 0.915434i | \(-0.368152\pi\) | ||||
0.402469 | + | 0.915434i | \(0.368152\pi\) | |||||||
\(212\) | −0.0608047 | − | 0.105317i | −0.00417608 | − | 0.00723319i | ||||
\(213\) | 6.22309 | − | 10.7787i | 0.426399 | − | 0.738545i | ||||
\(214\) | −0.00636137 | + | 0.0110182i | −0.000434854 | + | 0.000753189i | ||||
\(215\) | −17.4812 | − | 30.2784i | −1.19221 | − | 2.06497i | ||||
\(216\) | −0.105008 | −0.00714488 | ||||||||
\(217\) | −2.96777 | + | 9.11814i | −0.201466 | + | 0.618980i | ||||
\(218\) | −0.327293 | −0.0221671 | ||||||||
\(219\) | −7.14354 | − | 12.3730i | −0.482715 | − | 0.836088i | ||||
\(220\) | 1.83347 | − | 3.17566i | 0.123612 | − | 0.214103i | ||||
\(221\) | −8.50510 | + | 14.7313i | −0.572115 | + | 0.990932i | ||||
\(222\) | 0.105841 | + | 0.183323i | 0.00710360 | + | 0.0123038i | ||||
\(223\) | −15.5087 | −1.03854 | −0.519270 | − | 0.854610i | \(-0.673796\pi\) | ||||
−0.519270 | + | 0.854610i | \(0.673796\pi\) | |||||||
\(224\) | −0.257885 | + | 0.792323i | −0.0172307 | + | 0.0529393i | ||||
\(225\) | 2.71885 | 0.181257 | ||||||||
\(226\) | 0.121945 | + | 0.211215i | 0.00811166 | + | 0.0140498i | ||||
\(227\) | 7.66648 | − | 13.2787i | 0.508842 | − | 0.881340i | −0.491105 | − | 0.871100i | \(-0.663407\pi\) |
0.999948 | − | 0.0102402i | \(-0.00325962\pi\) | |||||||
\(228\) | −4.76665 | + | 8.25607i | −0.315679 | + | 0.546772i | ||||
\(229\) | 3.20242 | + | 5.54675i | 0.211622 | + | 0.366540i | 0.952222 | − | 0.305406i | \(-0.0987922\pi\) |
−0.740600 | + | 0.671946i | \(0.765459\pi\) | |||||||
\(230\) | −0.0729480 | −0.00481005 | ||||||||
\(231\) | −1.16805 | − | 1.29858i | −0.0768522 | − | 0.0854400i | ||||
\(232\) | −0.186940 | −0.0122732 | ||||||||
\(233\) | 13.0715 | + | 22.6405i | 0.856344 | + | 1.48323i | 0.875393 | + | 0.483413i | \(0.160603\pi\) |
−0.0190487 | + | 0.999819i | \(0.506064\pi\) | |||||||
\(234\) | 0.0541524 | − | 0.0937947i | 0.00354005 | − | 0.00613155i | ||||
\(235\) | −16.3393 | + | 28.3006i | −1.06586 | + | 1.84613i | ||||
\(236\) | −8.98407 | − | 15.5609i | −0.584813 | − | 1.01293i | ||||
\(237\) | 6.94797 | 0.451319 | ||||||||
\(238\) | 0.280243 | − | 0.0594191i | 0.0181655 | − | 0.00385157i | ||||
\(239\) | 17.6773 | 1.14345 | 0.571724 | − | 0.820446i | \(-0.306275\pi\) | ||||
0.571724 | + | 0.820446i | \(0.306275\pi\) | |||||||
\(240\) | 5.55082 | + | 9.61430i | 0.358304 | + | 0.620600i | ||||
\(241\) | −2.87985 | + | 4.98804i | −0.185507 | + | 0.321308i | −0.943747 | − | 0.330668i | \(-0.892726\pi\) |
0.758240 | + | 0.651975i | \(0.226059\pi\) | |||||||
\(242\) | −0.138689 | + | 0.240217i | −0.00891529 | + | 0.0154417i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | −5.42347 | −0.347202 | ||||||||
\(245\) | −15.7222 | − | 11.4472i | −1.00445 | − | 0.731333i | ||||
\(246\) | −0.210044 | −0.0133919 | ||||||||
\(247\) | −9.83430 | − | 17.0335i | −0.625742 | − | 1.08382i | ||||
\(248\) | 0.190289 | − | 0.329591i | 0.0120834 | − | 0.0209290i | ||||
\(249\) | 4.70428 | − | 8.14805i | 0.298122 | − | 0.516362i | ||||
\(250\) | −0.0832025 | − | 0.144111i | −0.00526219 | − | 0.00911438i | ||||
\(251\) | −10.3866 | −0.655597 | −0.327798 | − | 0.944748i | \(-0.606307\pi\) | ||||
−0.327798 | + | 0.944748i | \(0.606307\pi\) | |||||||
\(252\) | 5.17464 | − | 1.09716i | 0.325972 | − | 0.0691148i | ||||
\(253\) | 0.660156 | 0.0415037 | ||||||||
\(254\) | 0.0315175 | + | 0.0545898i | 0.00197758 | + | 0.00342527i | ||||
\(255\) | 5.72855 | − | 9.92214i | 0.358736 | − | 0.621348i | ||||
\(256\) | −7.97244 | + | 13.8087i | −0.498277 | + | 0.863042i | ||||
\(257\) | 1.34924 | + | 2.33695i | 0.0841633 | + | 0.145775i | 0.905034 | − | 0.425338i | \(-0.139845\pi\) |
−0.820871 | + | 0.571114i | \(0.806512\pi\) | |||||||
\(258\) | 0.330417 | 0.0205709 | ||||||||
\(259\) | −14.2647 | − | 15.8588i | −0.886368 | − | 0.985415i | ||||
\(260\) | −22.9122 | −1.42096 | ||||||||
\(261\) | 0.890123 | + | 1.54174i | 0.0550972 | + | 0.0954312i | ||||
\(262\) | −0.264540 | + | 0.458198i | −0.0163434 | + | 0.0283075i | ||||
\(263\) | 10.5745 | − | 18.3156i | 0.652053 | − | 1.12939i | −0.330571 | − | 0.943781i | \(-0.607241\pi\) |
0.982624 | − | 0.185607i | \(-0.0594253\pi\) | |||||||
\(264\) | 0.0346608 | + | 0.0600343i | 0.00213322 | + | 0.00369485i | ||||
\(265\) | −0.168991 | −0.0103810 | ||||||||
\(266\) | −0.102520 | + | 0.314980i | −0.00628589 | + | 0.0193127i | ||||
\(267\) | 5.92430 | 0.362561 | ||||||||
\(268\) | −2.68490 | − | 4.65039i | −0.164007 | − | 0.284068i | ||||
\(269\) | 14.2705 | − | 24.7173i | 0.870090 | − | 1.50704i | 0.00818685 | − | 0.999966i | \(-0.497394\pi\) |
0.861903 | − | 0.507073i | \(-0.169273\pi\) | |||||||
\(270\) | −0.0364740 | + | 0.0631748i | −0.00221974 | + | 0.00384469i | ||||
\(271\) | −7.57362 | − | 13.1179i | −0.460065 | − | 0.796856i | 0.538899 | − | 0.842371i | \(-0.318841\pi\) |
−0.998964 | + | 0.0455148i | \(0.985507\pi\) | |||||||
\(272\) | 16.4782 | 0.999136 | ||||||||
\(273\) | −3.37768 | + | 10.3775i | −0.204427 | + | 0.628078i | ||||
\(274\) | −0.183968 | −0.0111139 | ||||||||
\(275\) | −0.897434 | − | 1.55440i | −0.0541173 | − | 0.0937339i | ||||
\(276\) | −0.999655 | + | 1.73145i | −0.0601722 | + | 0.104221i | ||||
\(277\) | −2.11859 | + | 3.66950i | −0.127294 | + | 0.220479i | −0.922627 | − | 0.385693i | \(-0.873962\pi\) |
0.795334 | + | 0.606172i | \(0.207296\pi\) | |||||||
\(278\) | −0.0378764 | − | 0.0656038i | −0.00227167 | − | 0.00393465i | ||||
\(279\) | −3.62429 | −0.216980 | ||||||||
\(280\) | 0.516195 | + | 0.573877i | 0.0308485 | + | 0.0342957i | ||||
\(281\) | 0.762123 | 0.0454645 | 0.0227322 | − | 0.999742i | \(-0.492763\pi\) | ||||
0.0227322 | + | 0.999742i | \(0.492763\pi\) | |||||||
\(282\) | −0.154417 | − | 0.267458i | −0.00919539 | − | 0.0159269i | ||||
\(283\) | −8.58570 | + | 14.8709i | −0.510367 | + | 0.883981i | 0.489561 | + | 0.871969i | \(0.337157\pi\) |
−0.999928 | + | 0.0120120i | \(0.996176\pi\) | |||||||
\(284\) | 12.4419 | − | 21.5500i | 0.738290 | − | 1.27876i | ||||
\(285\) | 6.62383 | + | 11.4728i | 0.392362 | + | 0.679590i | ||||
\(286\) | −0.0714981 | −0.00422777 | ||||||||
\(287\) | 20.7049 | − | 4.39000i | 1.22217 | − | 0.259133i | ||||
\(288\) | −0.314933 | −0.0185576 | ||||||||
\(289\) | −0.00289139 | − | 0.00500804i | −0.000170082 | − | 0.000294590i | ||||
\(290\) | −0.0649327 | + | 0.112467i | −0.00381298 | + | 0.00660427i | ||||
\(291\) | 1.26870 | − | 2.19745i | 0.0743724 | − | 0.128817i | ||||
\(292\) | −14.2821 | − | 24.7374i | −0.835799 | − | 1.44765i | ||||
\(293\) | −1.15566 | −0.0675144 | −0.0337572 | − | 0.999430i | \(-0.510747\pi\) | ||||
−0.0337572 | + | 0.999430i | \(0.510747\pi\) | |||||||
\(294\) | 0.167981 | − | 0.0745861i | 0.00979686 | − | 0.00434995i | ||||
\(295\) | −24.9689 | −1.45375 | ||||||||
\(296\) | 0.423292 | + | 0.733164i | 0.0246034 | + | 0.0426143i | ||||
\(297\) | 0.330078 | − | 0.571712i | 0.0191531 | − | 0.0331741i | ||||
\(298\) | 0.250235 | − | 0.433420i | 0.0144957 | − | 0.0251074i | ||||
\(299\) | −2.06244 | − | 3.57225i | −0.119274 | − | 0.206588i | ||||
\(300\) | 5.43583 | 0.313838 | ||||||||
\(301\) | −32.5706 | + | 6.90585i | −1.87734 | + | 0.398046i | ||||
\(302\) | 0.132934 | 0.00764949 | ||||||||
\(303\) | 3.35589 | + | 5.81257i | 0.192791 | + | 0.333923i | ||||
\(304\) | −9.52672 | + | 16.5008i | −0.546395 | + | 0.946383i | ||||
\(305\) | −3.76828 | + | 6.52685i | −0.215771 | + | 0.373727i | ||||
\(306\) | 0.0541384 | + | 0.0937704i | 0.00309488 | + | 0.00536050i | ||||
\(307\) | 31.0365 | 1.77135 | 0.885673 | − | 0.464310i | \(-0.153698\pi\) | ||||
0.885673 | + | 0.464310i | \(0.153698\pi\) | |||||||
\(308\) | −2.33530 | − | 2.59626i | −0.133066 | − | 0.147935i | ||||
\(309\) | −10.7478 | −0.611422 | ||||||||
\(310\) | −0.132192 | − | 0.228964i | −0.00750801 | − | 0.0130043i | ||||
\(311\) | −8.80703 | + | 15.2542i | −0.499401 | + | 0.864987i | −1.00000 | 0.000691900i | \(-0.999780\pi\) | |
0.500599 | + | 0.865679i | \(0.333113\pi\) | |||||||
\(312\) | 0.216572 | − | 0.375114i | 0.0122610 | − | 0.0212367i | ||||
\(313\) | −7.87031 | − | 13.6318i | −0.444856 | − | 0.770514i | 0.553186 | − | 0.833058i | \(-0.313412\pi\) |
−0.998042 | + | 0.0625441i | \(0.980079\pi\) | |||||||
\(314\) | 0.0720446 | 0.00406571 | ||||||||
\(315\) | 2.27502 | − | 6.98973i | 0.128183 | − | 0.393826i | ||||
\(316\) | 13.8912 | 0.781438 | ||||||||
\(317\) | 2.61070 | + | 4.52186i | 0.146631 | + | 0.253973i | 0.929980 | − | 0.367609i | \(-0.119824\pi\) |
−0.783349 | + | 0.621582i | \(0.786490\pi\) | |||||||
\(318\) | 0.000798534 | − | 0.00138310i | 4.47796e−5 | − | 7.75605e-5i | ||||
\(319\) | 0.587620 | − | 1.01779i | 0.0329004 | − | 0.0569852i | ||||
\(320\) | 11.0902 | + | 19.2087i | 0.619958 | + | 1.07380i | ||||
\(321\) | 0.484556 | 0.0270453 | ||||||||
\(322\) | −0.0215003 | + | 0.0660573i | −0.00119817 | + | 0.00368123i | ||||
\(323\) | 19.6635 | 1.09411 | ||||||||
\(324\) | 0.999655 | + | 1.73145i | 0.0555364 | + | 0.0961919i | ||||
\(325\) | −5.60747 | + | 9.71242i | −0.311046 | + | 0.538748i | ||||
\(326\) | 0.200978 | − | 0.348104i | 0.0111311 | − | 0.0192797i | ||||
\(327\) | 6.23260 | + | 10.7952i | 0.344664 | + | 0.596975i | ||||
\(328\) | −0.840030 | −0.0463829 | ||||||||
\(329\) | 20.8115 | + | 23.1371i | 1.14738 | + | 1.27559i | ||||
\(330\) | 0.0481570 | 0.00265096 | ||||||||
\(331\) | 6.97246 | + | 12.0767i | 0.383241 | + | 0.663793i | 0.991524 | − | 0.129927i | \(-0.0414744\pi\) |
−0.608282 | + | 0.793721i | \(0.708141\pi\) | |||||||
\(332\) | 9.40532 | − | 16.2905i | 0.516184 | − | 0.894057i | ||||
\(333\) | 4.03105 | − | 6.98199i | 0.220900 | − | 0.382611i | ||||
\(334\) | 0.170689 | + | 0.295642i | 0.00933967 | + | 0.0161768i | ||||
\(335\) | −7.46199 | −0.407692 | ||||||||
\(336\) | 10.3422 | − | 2.19282i | 0.564211 | − | 0.119628i | ||||
\(337\) | 9.28645 | 0.505865 | 0.252933 | − | 0.967484i | \(-0.418605\pi\) | ||||
0.252933 | + | 0.967484i | \(0.418605\pi\) | |||||||
\(338\) | 0.0527048 | + | 0.0912874i | 0.00286676 | + | 0.00496538i | ||||
\(339\) | 4.64438 | − | 8.04429i | 0.252248 | − | 0.436906i | ||||
\(340\) | 11.4532 | − | 19.8374i | 0.621134 | − | 1.07584i | ||||
\(341\) | 1.19630 | + | 2.07205i | 0.0647832 | + | 0.112208i | ||||
\(342\) | −0.125199 | −0.00676996 | ||||||||
\(343\) | −14.9997 | + | 10.8631i | −0.809910 | + | 0.586555i | ||||
\(344\) | 1.32144 | 0.0712473 | ||||||||
\(345\) | 1.38914 | + | 2.40606i | 0.0747888 | + | 0.129538i | ||||
\(346\) | −0.136823 | + | 0.236984i | −0.00735565 | + | 0.0127404i | ||||
\(347\) | −3.83747 | + | 6.64670i | −0.206006 | + | 0.356813i | −0.950453 | − | 0.310869i | \(-0.899380\pi\) |
0.744447 | + | 0.667682i | \(0.232713\pi\) | |||||||
\(348\) | 1.77963 | + | 3.08241i | 0.0953983 | + | 0.165235i | ||||
\(349\) | 5.71924 | 0.306144 | 0.153072 | − | 0.988215i | \(-0.451083\pi\) | ||||
0.153072 | + | 0.988215i | \(0.451083\pi\) | |||||||
\(350\) | 0.184766 | − | 0.0391754i | 0.00987617 | − | 0.00209401i | ||||
\(351\) | −4.12488 | −0.220170 | ||||||||
\(352\) | 0.103953 | + | 0.180051i | 0.00554069 | + | 0.00959675i | ||||
\(353\) | −6.70980 | + | 11.6217i | −0.357127 | + | 0.618561i | −0.987480 | − | 0.157747i | \(-0.949577\pi\) |
0.630353 | + | 0.776309i | \(0.282910\pi\) | |||||||
\(354\) | 0.117986 | − | 0.204357i | 0.00627087 | − | 0.0108615i | ||||
\(355\) | −17.2895 | − | 29.9463i | −0.917631 | − | 1.58938i | ||||
\(356\) | 11.8445 | 0.627758 | ||||||||
\(357\) | −7.29649 | − | 8.11183i | −0.386171 | − | 0.429324i | ||||
\(358\) | −0.504732 | −0.0266759 | ||||||||
\(359\) | −8.93291 | − | 15.4723i | −0.471461 | − | 0.816594i | 0.528006 | − | 0.849241i | \(-0.322940\pi\) |
−0.999467 | + | 0.0326463i | \(0.989607\pi\) | |||||||
\(360\) | −0.145871 | + | 0.252656i | −0.00768806 | + | 0.0133161i | ||||
\(361\) | −1.86829 | + | 3.23597i | −0.0983311 | + | 0.170314i | ||||
\(362\) | −0.146449 | − | 0.253656i | −0.00769717 | − | 0.0133319i | ||||
\(363\) | 10.5642 | 0.554476 | ||||||||
\(364\) | −6.75304 | + | 20.7479i | −0.353956 | + | 1.08749i | ||||
\(365\) | −39.6935 | −2.07765 | ||||||||
\(366\) | −0.0356126 | − | 0.0616828i | −0.00186150 | − | 0.00322421i | ||||
\(367\) | −13.0761 | + | 22.6484i | −0.682566 | + | 1.18224i | 0.291630 | + | 0.956531i | \(0.405803\pi\) |
−0.974195 | + | 0.225707i | \(0.927531\pi\) | |||||||
\(368\) | −1.99793 | + | 3.46052i | −0.104149 | + | 0.180392i | ||||
\(369\) | 3.99984 | + | 6.92793i | 0.208224 | + | 0.360654i | ||||
\(370\) | 0.588114 | 0.0305746 | ||||||||
\(371\) | −0.0498075 | + | 0.153028i | −0.00258588 | + | 0.00794481i | ||||
\(372\) | −7.24608 | −0.375692 | ||||||||
\(373\) | −10.0650 | − | 17.4331i | −0.521147 | − | 0.902653i | −0.999698 | − | 0.0245929i | \(-0.992171\pi\) |
0.478551 | − | 0.878060i | \(-0.341162\pi\) | |||||||
\(374\) | 0.0357398 | − | 0.0619031i | 0.00184806 | − | 0.00320093i | ||||
\(375\) | −3.16883 | + | 5.48858i | −0.163638 | + | 0.283429i | ||||
\(376\) | −0.617561 | − | 1.06965i | −0.0318483 | − | 0.0551628i | ||||
\(377\) | −7.34330 | −0.378199 | ||||||||
\(378\) | 0.0464571 | + | 0.0516484i | 0.00238950 | + | 0.00265651i | ||||
\(379\) | 8.04896 | 0.413447 | 0.206724 | − | 0.978399i | \(-0.433720\pi\) | ||||
0.206724 | + | 0.978399i | \(0.433720\pi\) | |||||||
\(380\) | 13.2431 | + | 22.9377i | 0.679356 | + | 1.17668i | ||||
\(381\) | 1.20037 | − | 2.07910i | 0.0614967 | − | 0.106515i | ||||
\(382\) | 0.252517 | − | 0.437372i | 0.0129199 | − | 0.0223779i | ||||
\(383\) | −10.0347 | − | 17.3806i | −0.512749 | − | 0.888107i | −0.999891 | − | 0.0147842i | \(-0.995294\pi\) |
0.487142 | − | 0.873323i | \(-0.338039\pi\) | |||||||
\(384\) | −0.839484 | −0.0428397 | ||||||||
\(385\) | −4.74704 | + | 1.00650i | −0.241932 | + | 0.0512961i | ||||
\(386\) | −0.458246 | −0.0233241 | ||||||||
\(387\) | −6.29210 | − | 10.8982i | −0.319845 | − | 0.553989i | ||||
\(388\) | 2.53652 | − | 4.39339i | 0.128772 | − | 0.223040i | ||||
\(389\) | −6.22581 | + | 10.7834i | −0.315661 | + | 0.546741i | −0.979578 | − | 0.201066i | \(-0.935560\pi\) |
0.663917 | + | 0.747806i | \(0.268893\pi\) | |||||||
\(390\) | −0.150451 | − | 0.260588i | −0.00761837 | − | 0.0131954i | ||||
\(391\) | 4.12381 | 0.208550 | ||||||||
\(392\) | 0.671809 | − | 0.298293i | 0.0339315 | − | 0.0150661i | ||||
\(393\) | 20.1505 | 1.01646 | ||||||||
\(394\) | −0.0152601 | − | 0.0264313i | −0.000768795 | − | 0.00133159i | ||||
\(395\) | 9.65171 | − | 16.7173i | 0.485630 | − | 0.841137i | ||||
\(396\) | 0.659929 | − | 1.14303i | 0.0331627 | − | 0.0574394i | ||||
\(397\) | 3.46764 | + | 6.00613i | 0.174036 | + | 0.301439i | 0.939827 | − | 0.341650i | \(-0.110986\pi\) |
−0.765791 | + | 0.643089i | \(0.777652\pi\) | |||||||
\(398\) | −0.445752 | −0.0223435 | ||||||||
\(399\) | 12.3414 | − | 2.61670i | 0.617840 | − | 0.130999i | ||||
\(400\) | 10.8642 | 0.543208 | ||||||||
\(401\) | 7.20807 | + | 12.4847i | 0.359954 | + | 0.623458i | 0.987953 | − | 0.154756i | \(-0.0494591\pi\) |
−0.627999 | + | 0.778214i | \(0.716126\pi\) | |||||||
\(402\) | 0.0352602 | − | 0.0610725i | 0.00175862 | − | 0.00304602i | ||||
\(403\) | 7.47487 | − | 12.9469i | 0.372350 | − | 0.644929i | ||||
\(404\) | 6.70946 | + | 11.6211i | 0.333808 | + | 0.578173i | ||||
\(405\) | 2.77828 | 0.138054 | ||||||||
\(406\) | 0.0827051 | + | 0.0919469i | 0.00410458 | + | 0.00456325i | ||||
\(407\) | −5.32225 | −0.263814 | ||||||||
\(408\) | 0.216516 | + | 0.375017i | 0.0107191 | + | 0.0185661i | ||||
\(409\) | −12.0132 | + | 20.8075i | −0.594016 | + | 1.02887i | 0.399668 | + | 0.916660i | \(0.369125\pi\) |
−0.993685 | + | 0.112207i | \(0.964208\pi\) | |||||||
\(410\) | −0.291780 | + | 0.505379i | −0.0144100 | + | 0.0249589i | ||||
\(411\) | 3.50329 | + | 6.06788i | 0.172805 | + | 0.299306i | ||||
\(412\) | −21.4882 | −1.05865 | ||||||||
\(413\) | −7.35921 | + | 22.6103i | −0.362123 | + | 1.11258i | ||||
\(414\) | −0.0262565 | −0.00129044 | ||||||||
\(415\) | −13.0698 | − | 22.6376i | −0.641572 | − | 1.11124i | ||||
\(416\) | 0.649530 | − | 1.12502i | 0.0318458 | − | 0.0551586i | ||||
\(417\) | −1.44255 | + | 2.49857i | −0.0706421 | + | 0.122356i | ||||
\(418\) | 0.0413253 | + | 0.0715775i | 0.00202129 | + | 0.00350097i | ||||
\(419\) | 31.8946 | 1.55815 | 0.779076 | − | 0.626930i | \(-0.215689\pi\) | ||||
0.779076 | + | 0.626930i | \(0.215689\pi\) | |||||||
\(420\) | 4.54846 | − | 13.9746i | 0.221942 | − | 0.681892i | ||||
\(421\) | −18.8400 | −0.918205 | −0.459102 | − | 0.888383i | \(-0.651829\pi\) | ||||
−0.459102 | + | 0.888383i | \(0.651829\pi\) | |||||||
\(422\) | 0.153501 | + | 0.265871i | 0.00747230 | + | 0.0129424i | ||||
\(423\) | −5.88109 | + | 10.1864i | −0.285949 | + | 0.495277i | ||||
\(424\) | 0.00319359 | − | 0.00553145i | 0.000155094 | − | 0.000268631i | ||||
\(425\) | −5.60601 | − | 9.70990i | −0.271932 | − | 0.470999i | ||||
\(426\) | 0.326793 | 0.0158332 | ||||||||
\(427\) | 4.79968 | + | 5.33602i | 0.232273 | + | 0.258228i | ||||
\(428\) | 0.968777 | 0.0468276 | ||||||||
\(429\) | 1.36153 | + | 2.35824i | 0.0657354 | + | 0.113857i | ||||
\(430\) | 0.458996 | − | 0.795004i | 0.0221347 | − | 0.0383385i | ||||
\(431\) | 18.1715 | − | 31.4740i | 0.875292 | − | 1.51605i | 0.0188408 | − | 0.999822i | \(-0.494002\pi\) |
0.856451 | − | 0.516228i | \(-0.172664\pi\) | |||||||
\(432\) | 1.99793 | + | 3.46052i | 0.0961255 | + | 0.166494i | ||||
\(433\) | 21.5486 | 1.03556 | 0.517780 | − | 0.855514i | \(-0.326759\pi\) | ||||
0.517780 | + | 0.855514i | \(0.326759\pi\) | |||||||
\(434\) | −0.246297 | + | 0.0522217i | −0.0118226 | + | 0.00250672i | ||||
\(435\) | 4.94603 | 0.237144 | ||||||||
\(436\) | 12.4609 | + | 21.5829i | 0.596769 | + | 1.03363i | ||||
\(437\) | −2.38414 | + | 4.12946i | −0.114049 | + | 0.197539i | ||||
\(438\) | 0.187564 | − | 0.324871i | 0.00896216 | − | 0.0155229i | ||||
\(439\) | 5.36875 | + | 9.29896i | 0.256237 | + | 0.443815i | 0.965231 | − | 0.261400i | \(-0.0841840\pi\) |
−0.708994 | + | 0.705215i | \(0.750851\pi\) | |||||||
\(440\) | 0.192595 | 0.00918160 | ||||||||
\(441\) | −5.65895 | − | 4.12023i | −0.269474 | − | 0.196202i | ||||
\(442\) | −0.446628 | −0.0212439 | ||||||||
\(443\) | 16.9765 | + | 29.4042i | 0.806580 | + | 1.39704i | 0.915219 | + | 0.402957i | \(0.132017\pi\) |
−0.108639 | + | 0.994081i | \(0.534649\pi\) | |||||||
\(444\) | 8.05933 | − | 13.9592i | 0.382479 | − | 0.662473i | ||||
\(445\) | 8.22969 | − | 14.2542i | 0.390125 | − | 0.675716i | ||||
\(446\) | −0.203602 | − | 0.352649i | −0.00964083 | − | 0.0166984i | ||||
\(447\) | −19.0608 | −0.901546 | ||||||||
\(448\) | 20.6629 | − | 4.38109i | 0.976230 | − | 0.206987i | ||||
\(449\) | 6.94219 | 0.327622 | 0.163811 | − | 0.986492i | \(-0.447621\pi\) | ||||
0.163811 | + | 0.986492i | \(0.447621\pi\) | |||||||
\(450\) | 0.0356938 | + | 0.0618234i | 0.00168262 | + | 0.00291438i | ||||
\(451\) | 2.64052 | − | 4.57352i | 0.124337 | − | 0.215359i | ||||
\(452\) | 9.28555 | − | 16.0830i | 0.436755 | − | 0.756483i | ||||
\(453\) | −2.53145 | − | 4.38460i | −0.118938 | − | 0.206006i | ||||
\(454\) | 0.402590 | 0.0188945 | ||||||||
\(455\) | 20.2770 | + | 22.5428i | 0.950598 | + | 1.05682i | ||||
\(456\) | −0.500708 | −0.0234478 | ||||||||
\(457\) | 19.7755 | + | 34.2521i | 0.925057 | + | 1.60225i | 0.791470 | + | 0.611208i | \(0.209316\pi\) |
0.133587 | + | 0.991037i | \(0.457350\pi\) | |||||||
\(458\) | −0.0840843 | + | 0.145638i | −0.00392900 | + | 0.00680523i | ||||
\(459\) | 2.06190 | − | 3.57132i | 0.0962414 | − | 0.166695i | ||||
\(460\) | 2.77732 | + | 4.81047i | 0.129493 | + | 0.224289i | ||||
\(461\) | −4.90582 | −0.228487 | −0.114243 | − | 0.993453i | \(-0.536444\pi\) | ||||
−0.114243 | + | 0.993453i | \(0.536444\pi\) | |||||||
\(462\) | 0.0141936 | − | 0.0436081i | 0.000660344 | − | 0.00202883i | ||||
\(463\) | −0.772106 | −0.0358828 | −0.0179414 | − | 0.999839i | \(-0.505711\pi\) | ||||
−0.0179414 | + | 0.999839i | \(0.505711\pi\) | |||||||
\(464\) | 3.55681 | + | 6.16058i | 0.165121 | + | 0.285998i | ||||
\(465\) | −5.03465 | + | 8.72026i | −0.233476 | + | 0.404393i | ||||
\(466\) | −0.343212 | + | 0.594461i | −0.0158990 | + | 0.0275379i | ||||
\(467\) | 9.59886 | + | 16.6257i | 0.444182 | + | 0.769347i | 0.997995 | − | 0.0632949i | \(-0.0201609\pi\) |
−0.553812 | + | 0.832641i | \(0.686828\pi\) | |||||||
\(468\) | −8.24691 | −0.381214 | ||||||||
\(469\) | −2.19931 | + | 6.75713i | −0.101555 | + | 0.312015i | ||||
\(470\) | −0.858027 | −0.0395778 | ||||||||
\(471\) | −1.37194 | − | 2.37627i | −0.0632156 | − | 0.109493i | ||||
\(472\) | 0.471862 | − | 0.817289i | 0.0217192 | − | 0.0376188i | ||||
\(473\) | −4.15377 | + | 7.19454i | −0.190990 | + | 0.330805i | ||||
\(474\) | 0.0912147 | + | 0.157988i | 0.00418963 | + | 0.00725665i | ||||
\(475\) | 12.9643 | 0.594842 | ||||||||
\(476\) | −14.5879 | − | 16.2181i | −0.668637 | − | 0.743354i | ||||
\(477\) | −0.0608257 | −0.00278502 | ||||||||
\(478\) | 0.232072 | + | 0.401960i | 0.0106147 | + | 0.0183852i | ||||
\(479\) | 9.10522 | − | 15.7707i | 0.416028 | − | 0.720582i | −0.579508 | − | 0.814967i | \(-0.696755\pi\) |
0.995536 | + | 0.0943848i | \(0.0300884\pi\) | |||||||
\(480\) | −0.437487 | + | 0.757749i | −0.0199684 | + | 0.0345864i | ||||
\(481\) | 16.6276 | + | 28.7998i | 0.758153 | + | 1.31316i | ||||
\(482\) | −0.151229 | −0.00688830 | ||||||||
\(483\) | 2.58821 | − | 0.548771i | 0.117768 | − | 0.0249700i | ||||
\(484\) | 21.1211 | 0.960050 | ||||||||
\(485\) | −3.52480 | − | 6.10514i | −0.160053 | − | 0.277220i | ||||
\(486\) | −0.0131282 | + | 0.0227388i | −0.000595509 | + | 0.00103145i | ||||
\(487\) | 14.4406 | − | 25.0119i | 0.654367 | − | 1.13340i | −0.327684 | − | 0.944787i | \(-0.606268\pi\) |
0.982052 | − | 0.188611i | \(-0.0603984\pi\) | |||||||
\(488\) | −0.142426 | − | 0.246689i | −0.00644731 | − | 0.0111671i | ||||
\(489\) | −15.3088 | −0.692288 | ||||||||
\(490\) | 0.0538906 | − | 0.507784i | 0.00243453 | − | 0.0229393i | ||||
\(491\) | −23.6817 | −1.06874 | −0.534369 | − | 0.845251i | \(-0.679451\pi\) | ||||
−0.534369 | + | 0.845251i | \(0.679451\pi\) | |||||||
\(492\) | 7.99693 | + | 13.8511i | 0.360530 | + | 0.624455i | ||||
\(493\) | 3.67070 | − | 6.35783i | 0.165320 | − | 0.286342i | ||||
\(494\) | 0.258214 | − | 0.447240i | 0.0116176 | − | 0.0201223i | ||||
\(495\) | −0.917050 | − | 1.58838i | −0.0412183 | − | 0.0713923i | ||||
\(496\) | −14.4822 | −0.650268 | ||||||||
\(497\) | −32.2134 | + | 6.83010i | −1.44497 | + | 0.306372i | ||||
\(498\) | 0.247036 | 0.0110699 | ||||||||
\(499\) | −12.6849 | − | 21.9710i | −0.567856 | − | 0.983556i | −0.996778 | − | 0.0802139i | \(-0.974440\pi\) |
0.428922 | − | 0.903342i | \(-0.358894\pi\) | |||||||
\(500\) | −6.33548 | + | 10.9734i | −0.283332 | + | 0.490745i | ||||
\(501\) | 6.50082 | − | 11.2598i | 0.290435 | − | 0.503049i | ||||
\(502\) | −0.136358 | − | 0.236179i | −0.00608595 | − | 0.0105412i | ||||
\(503\) | −29.2636 | −1.30480 | −0.652400 | − | 0.757874i | \(-0.726238\pi\) | ||||
−0.652400 | + | 0.757874i | \(0.726238\pi\) | |||||||
\(504\) | 0.185796 | + | 0.206558i | 0.00827603 | + | 0.00920083i | ||||
\(505\) | 18.6472 | 0.829790 | ||||||||
\(506\) | 0.00866669 | + | 0.0150112i | 0.000385281 | + | 0.000667327i | ||||
\(507\) | 2.00731 | − | 3.47676i | 0.0891476 | − | 0.154408i | ||||
\(508\) | 2.39991 | − | 4.15676i | 0.106479 | − | 0.184427i | ||||
\(509\) | 20.3431 | + | 35.2353i | 0.901692 | + | 1.56178i | 0.825297 | + | 0.564699i | \(0.191008\pi\) |
0.0763952 | + | 0.997078i | \(0.475659\pi\) | |||||||
\(510\) | 0.300823 | 0.0133207 | ||||||||
\(511\) | −11.6991 | + | 35.9440i | −0.517536 | + | 1.59007i | ||||
\(512\) | −2.09762 | −0.0927028 | ||||||||
\(513\) | 2.38414 | + | 4.12946i | 0.105263 | + | 0.182320i | ||||
\(514\) | −0.0354263 | + | 0.0613602i | −0.00156259 | + | 0.00270648i | ||||
\(515\) | −14.9302 | + | 25.8599i | −0.657904 | + | 1.13952i | ||||
\(516\) | −12.5799 | − | 21.7890i | −0.553798 | − | 0.959206i | ||||
\(517\) | 7.76488 | 0.341499 | ||||||||
\(518\) | 0.173338 | − | 0.532561i | 0.00761603 | − | 0.0233994i | ||||
\(519\) | 10.4220 | 0.457476 | ||||||||
\(520\) | −0.601699 | − | 1.04217i | −0.0263862 | − | 0.0457023i | ||||
\(521\) | 16.8982 | − | 29.2686i | 0.740326 | − | 1.28228i | −0.212021 | − | 0.977265i | \(-0.568005\pi\) |
0.952347 | − | 0.305017i | \(-0.0986621\pi\) | |||||||
\(522\) | −0.0233715 | + | 0.0404806i | −0.00102294 | + | 0.00177179i | ||||
\(523\) | −6.42837 | − | 11.1343i | −0.281093 | − | 0.486867i | 0.690561 | − | 0.723274i | \(-0.257364\pi\) |
−0.971654 | + | 0.236407i | \(0.924030\pi\) | |||||||
\(524\) | 40.2871 | 1.75995 | ||||||||
\(525\) | −4.81062 | − | 5.34818i | −0.209953 | − | 0.233414i | ||||
\(526\) | 0.555300 | 0.0242122 | ||||||||
\(527\) | 7.47293 | + | 12.9435i | 0.325526 | + | 0.563827i | ||||
\(528\) | 1.31895 | − | 2.28448i | 0.0573998 | − | 0.0994194i | ||||
\(529\) | −0.500000 | + | 0.866025i | −0.0217391 | + | 0.0376533i | ||||
\(530\) | −0.00221855 | − | 0.00384265i | −9.63678e−5 | − | 0.000166914i | ||||
\(531\) | −8.98717 | −0.390010 | ||||||||
\(532\) | 24.6742 | − | 5.23160i | 1.06976 | − | 0.226818i | ||||
\(533\) | −32.9977 | −1.42929 | ||||||||
\(534\) | 0.0777757 | + | 0.134711i | 0.00336568 | + | 0.00582953i | ||||
\(535\) | 0.673116 | − | 1.16587i | 0.0291014 | − | 0.0504050i | ||||
\(536\) | 0.141017 | − | 0.244248i | 0.00609099 | − | 0.0105499i | ||||
\(537\) | 9.61157 | + | 16.6477i | 0.414770 | + | 0.718402i | ||||
\(538\) | 0.749388 | 0.0323084 | ||||||||
\(539\) | −0.487693 | + | 4.59529i | −0.0210064 | + | 0.197933i | ||||
\(540\) | 5.55465 | 0.239034 | ||||||||
\(541\) | 5.75329 | + | 9.96499i | 0.247353 | + | 0.428428i | 0.962791 | − | 0.270248i | \(-0.0871059\pi\) |
−0.715437 | + | 0.698677i | \(0.753773\pi\) | |||||||
\(542\) | 0.198857 | − | 0.344430i | 0.00854163 | − | 0.0147945i | ||||
\(543\) | −5.57762 | + | 9.66071i | −0.239358 | + | 0.414581i | ||||
\(544\) | 0.649362 | + | 1.12473i | 0.0278412 | + | 0.0482223i | ||||
\(545\) | 34.6319 | 1.48347 | ||||||||
\(546\) | −0.280316 | + | 0.0594346i | −0.0119964 | + | 0.00254356i | ||||
\(547\) | 8.26280 | 0.353292 | 0.176646 | − | 0.984274i | \(-0.443475\pi\) | ||||
0.176646 | + | 0.984274i | \(0.443475\pi\) | |||||||
\(548\) | 7.00417 | + | 12.1316i | 0.299203 | + | 0.518235i | ||||
\(549\) | −1.35633 | + | 2.34924i | −0.0578869 | + | 0.100263i | ||||
\(550\) | 0.0235635 | − | 0.0408131i | 0.00100475 | − | 0.00174028i | ||||
\(551\) | 4.24436 | + | 7.35145i | 0.180816 | + | 0.313182i | ||||
\(552\) | −0.105008 | −0.00446943 | ||||||||
\(553\) | −12.2934 | − | 13.6672i | −0.522770 | − | 0.581187i | ||||
\(554\) | −0.111253 | −0.00472670 | ||||||||
\(555\) | −11.1994 | − | 19.3979i | −0.475388 | − | 0.823397i | ||||
\(556\) | −2.88411 | + | 4.99542i | −0.122314 | + | 0.211853i | ||||
\(557\) | 11.3001 | − | 19.5724i | 0.478802 | − | 0.829309i | −0.520903 | − | 0.853616i | \(-0.674405\pi\) |
0.999705 | + | 0.0243068i | \(0.00773785\pi\) | |||||||
\(558\) | −0.0475805 | − | 0.0824119i | −0.00201424 | − | 0.00348877i | ||||
\(559\) | 51.9083 | 2.19549 | ||||||||
\(560\) | 9.09066 | − | 27.9300i | 0.384150 | − | 1.18026i | ||||
\(561\) | −2.72236 | −0.114938 | ||||||||
\(562\) | 0.0100053 | + | 0.0173298i | 0.000422050 | + | 0.000731012i | ||||
\(563\) | 5.07518 | − | 8.79046i | 0.213893 | − | 0.370474i | −0.739036 | − | 0.673665i | \(-0.764719\pi\) |
0.952930 | + | 0.303192i | \(0.0980522\pi\) | |||||||
\(564\) | −11.7581 | + | 20.3657i | −0.495107 | + | 0.857550i | ||||
\(565\) | −12.9034 | − | 22.3493i | −0.542850 | − | 0.940243i | ||||
\(566\) | −0.450860 | −0.0189511 | ||||||||
\(567\) | 0.818857 | − | 2.51584i | 0.0343888 | − | 0.105656i | ||||
\(568\) | 1.30695 | 0.0548382 | ||||||||
\(569\) | −18.2877 | − | 31.6752i | −0.766659 | − | 1.32789i | −0.939365 | − | 0.342918i | \(-0.888585\pi\) |
0.172707 | − | 0.984973i | \(-0.444749\pi\) | |||||||
\(570\) | −0.173918 | + | 0.301236i | −0.00728464 | + | 0.0126174i | ||||
\(571\) | −4.07243 | + | 7.05365i | −0.170426 | + | 0.295186i | −0.938569 | − | 0.345092i | \(-0.887848\pi\) |
0.768143 | + | 0.640278i | \(0.221181\pi\) | |||||||
\(572\) | 2.72212 | + | 4.71486i | 0.113818 | + | 0.197138i | ||||
\(573\) | −19.2346 | −0.803538 | ||||||||
\(574\) | 0.371642 | + | 0.413172i | 0.0155121 | + | 0.0172454i | ||||
\(575\) | 2.71885 | 0.113384 | ||||||||
\(576\) | 3.99173 | + | 6.91388i | 0.166322 | + | 0.288078i | ||||
\(577\) | 3.65944 | − | 6.33833i | 0.152344 | − | 0.263868i | −0.779745 | − | 0.626098i | \(-0.784651\pi\) |
0.932089 | + | 0.362230i | \(0.117984\pi\) | |||||||
\(578\) | 7.59178e−5 | 0 | 0.000131493i | 3.15776e−6 | 0 | 5.46941e-6i | ||||
\(579\) | 8.72634 | + | 15.1145i | 0.362654 | + | 0.628136i | ||||
\(580\) | 9.88864 | 0.410604 | ||||||||
\(581\) | −24.3514 | + | 5.16315i | −1.01026 | + | 0.214203i | ||||
\(582\) | 0.0666232 | 0.00276162 | ||||||||
\(583\) | 0.0200772 | + | 0.0347748i | 0.000831513 | + | 0.00144022i | ||||
\(584\) | 0.750127 | − | 1.29926i | 0.0310405 | − | 0.0537637i | ||||
\(585\) | −5.73004 | + | 9.92471i | −0.236908 | + | 0.410336i | ||||
\(586\) | −0.0151718 | − | 0.0262783i | −0.000626741 | − | 0.00108555i | ||||
\(587\) | −46.8386 | −1.93324 | −0.966618 | − | 0.256223i | \(-0.917522\pi\) | ||||
−0.966618 | + | 0.256223i | \(0.917522\pi\) | |||||||
\(588\) | −11.3140 | − | 8.23763i | −0.466581 | − | 0.339714i | ||||
\(589\) | −17.2816 | −0.712078 | ||||||||
\(590\) | −0.327798 | − | 0.567763i | −0.0134952 | − | 0.0233744i | ||||
\(591\) | −0.581195 | + | 1.00666i | −0.0239072 | + | 0.0414084i | ||||
\(592\) | 16.1075 | − | 27.8991i | 0.662016 | − | 1.14664i | ||||
\(593\) | 8.03777 | + | 13.9218i | 0.330072 | + | 0.571701i | 0.982526 | − | 0.186128i | \(-0.0595938\pi\) |
−0.652454 | + | 0.757828i | \(0.726260\pi\) | |||||||
\(594\) | 0.0173334 | 0.000711197 | ||||||||
\(595\) | −29.6534 | + | 6.28733i | −1.21567 | + | 0.257755i | ||||
\(596\) | −38.1085 | −1.56099 | ||||||||
\(597\) | 8.48842 | + | 14.7024i | 0.347408 | + | 0.601728i | ||||
\(598\) | 0.0541524 | − | 0.0937947i | 0.00221446 | − | 0.00383555i | ||||
\(599\) | 13.7899 | − | 23.8848i | 0.563439 | − | 0.975905i | −0.433754 | − | 0.901031i | \(-0.642811\pi\) |
0.997193 | − | 0.0748736i | \(-0.0238553\pi\) | |||||||
\(600\) | 0.142751 | + | 0.247251i | 0.00582776 | + | 0.0100940i | ||||
\(601\) | −32.9659 | −1.34471 | −0.672353 | − | 0.740231i | \(-0.734716\pi\) | ||||
−0.672353 | + | 0.740231i | \(0.734716\pi\) | |||||||
\(602\) | −0.584625 | − | 0.649954i | −0.0238276 | − | 0.0264902i | ||||
\(603\) | −2.68583 | −0.109375 | ||||||||
\(604\) | −5.06115 | − | 8.76617i | −0.205935 | − | 0.356690i | ||||
\(605\) | 14.6752 | − | 25.4181i | 0.596630 | − | 1.03339i | ||||
\(606\) | −0.0881139 | + | 0.152618i | −0.00357938 | + | 0.00619967i | ||||
\(607\) | 18.4202 | + | 31.9047i | 0.747653 | + | 1.29497i | 0.948945 | + | 0.315442i | \(0.102153\pi\) |
−0.201292 | + | 0.979531i | \(0.564514\pi\) | |||||||
\(608\) | −1.50169 | −0.0609017 | ||||||||
\(609\) | 1.45777 | − | 4.47882i | 0.0590717 | − | 0.181491i | ||||
\(610\) | −0.197884 | −0.00801208 | ||||||||
\(611\) | −24.2588 | − | 42.0174i | −0.981405 | − | 1.69984i | ||||
\(612\) | 4.12239 | − | 7.14018i | 0.166638 | − | 0.288625i | ||||
\(613\) | −11.0658 | + | 19.1665i | −0.446943 | + | 0.774129i | −0.998185 | − | 0.0602168i | \(-0.980821\pi\) |
0.551242 | + | 0.834345i | \(0.314154\pi\) | |||||||
\(614\) | 0.407455 | + | 0.705732i | 0.0164435 | + | 0.0284810i | ||||
\(615\) | 22.2254 | 0.896214 | ||||||||
\(616\) | 0.0567645 | − | 0.174402i | 0.00228711 | − | 0.00702687i | ||||
\(617\) | 25.5349 | 1.02800 | 0.513998 | − | 0.857792i | \(-0.328164\pi\) | ||||
0.513998 | + | 0.857792i | \(0.328164\pi\) | |||||||
\(618\) | −0.141100 | − | 0.244392i | −0.00567587 | − | 0.00983090i | ||||
\(619\) | −15.1917 | + | 26.3129i | −0.610607 | + | 1.05760i | 0.380531 | + | 0.924768i | \(0.375741\pi\) |
−0.991138 | + | 0.132835i | \(0.957592\pi\) | |||||||
\(620\) | −10.0658 | + | 17.4345i | −0.404253 | + | 0.700187i | ||||
\(621\) | 0.500000 | + | 0.866025i | 0.0200643 | + | 0.0347524i | ||||
\(622\) | −0.462483 | −0.0185439 | ||||||||
\(623\) | −10.4822 | − | 11.6535i | −0.419961 | − | 0.466889i | ||||
\(624\) | −16.4824 | −0.659826 | ||||||||
\(625\) | 15.6011 | + | 27.0218i | 0.624042 | + | 1.08087i | ||||
\(626\) | 0.206647 | − | 0.357923i | 0.00825927 | − | 0.0143055i | ||||
\(627\) | 1.57391 | − | 2.72609i | 0.0628558 | − | 0.108869i | ||||
\(628\) | −2.74293 | − | 4.75090i | −0.109455 | − | 0.189581i | ||||
\(629\) | −33.2466 | −1.32563 | ||||||||
\(630\) | 0.188805 | − | 0.0400317i | 0.00752217 | − | 0.00159490i | ||||
\(631\) | −23.5164 | −0.936175 | −0.468087 | − | 0.883682i | \(-0.655057\pi\) | ||||
−0.468087 | + | 0.883682i | \(0.655057\pi\) | |||||||
\(632\) | 0.364796 | + | 0.631845i | 0.0145108 | + | 0.0251334i | ||||
\(633\) | 5.84620 | − | 10.1259i | 0.232366 | − | 0.402469i | ||||
\(634\) | −0.0685477 | + | 0.118728i | −0.00272238 | + | 0.00471530i | ||||
\(635\) | −3.33496 | − | 5.77632i | −0.132344 | − | 0.229226i | ||||
\(636\) | −0.121609 | −0.00482213 | ||||||||
\(637\) | 26.3897 | − | 11.7174i | 1.04560 | − | 0.464262i | ||||
\(638\) | 0.0308577 | 0.00122167 | ||||||||
\(639\) | −6.22309 | − | 10.7787i | −0.246182 | − | 0.426399i | ||||
\(640\) | −1.16616 | + | 2.01985i | −0.0460966 | + | 0.0798416i | ||||
\(641\) | −10.8055 | + | 18.7157i | −0.426793 | + | 0.739227i | −0.996586 | − | 0.0825610i | \(-0.973690\pi\) |
0.569793 | + | 0.821788i | \(0.307023\pi\) | |||||||
\(642\) | 0.00636137 | + | 0.0110182i | 0.000251063 | + | 0.000434854i | ||||
\(643\) | −12.5132 | −0.493472 | −0.246736 | − | 0.969083i | \(-0.579358\pi\) | ||||
−0.246736 | + | 0.969083i | \(0.579358\pi\) | |||||||
\(644\) | 5.17464 | − | 1.09716i | 0.203910 | − | 0.0432343i | ||||
\(645\) | −34.9625 | −1.37665 | ||||||||
\(646\) | 0.258147 | + | 0.447124i | 0.0101567 | + | 0.0175919i | ||||
\(647\) | −9.42170 | + | 16.3189i | −0.370405 | + | 0.641561i | −0.989628 | − | 0.143655i | \(-0.954115\pi\) |
0.619223 | + | 0.785216i | \(0.287448\pi\) | |||||||
\(648\) | −0.0525039 | + | 0.0909395i | −0.00206255 | + | 0.00357244i | ||||
\(649\) | 2.96647 | + | 5.13807i | 0.116444 | + | 0.201687i | ||||
\(650\) | −0.294465 | −0.0115499 | ||||||||
\(651\) | 6.41266 | + | 7.12924i | 0.251332 | + | 0.279417i | ||||
\(652\) | −30.6071 | −1.19866 | ||||||||
\(653\) | −16.3318 | − | 28.2874i | −0.639111 | − | 1.10697i | −0.985628 | − | 0.168929i | \(-0.945969\pi\) |
0.346517 | − | 0.938044i | \(-0.387364\pi\) | |||||||
\(654\) | −0.163646 | + | 0.283444i | −0.00639908 | + | 0.0110835i | ||||
\(655\) | 27.9919 | − | 48.4833i | 1.09373 | − | 1.89440i | ||||
\(656\) | 15.9828 | + | 27.6831i | 0.624025 | + | 1.08084i | ||||
\(657\) | −14.2871 | −0.557392 | ||||||||
\(658\) | −0.252891 | + | 0.776978i | −0.00985871 | + | 0.0302897i | ||||
\(659\) | −31.3480 | −1.22114 | −0.610571 | − | 0.791961i | \(-0.709060\pi\) | ||||
−0.610571 | + | 0.791961i | \(0.709060\pi\) | |||||||
\(660\) | −1.83347 | − | 3.17566i | −0.0713676 | − | 0.123612i | ||||
\(661\) | −18.9962 | + | 32.9024i | −0.738866 | + | 1.27975i | 0.214140 | + | 0.976803i | \(0.431305\pi\) |
−0.953006 | + | 0.302951i | \(0.902028\pi\) | |||||||
\(662\) | −0.183072 | + | 0.317091i | −0.00711531 | + | 0.0123241i | ||||
\(663\) | 8.50510 | + | 14.7313i | 0.330311 | + | 0.572115i | ||||
\(664\) | 0.987973 | 0.0383408 | ||||||||
\(665\) | 10.8479 | − | 33.3290i | 0.420665 | − | 1.29244i | ||||
\(666\) | 0.211683 | 0.00820253 | ||||||||
\(667\) | 0.890123 | + | 1.54174i | 0.0344657 | + | 0.0596963i | ||||
\(668\) | 12.9972 | − | 22.5117i | 0.502875 | − | 0.871006i | ||||
\(669\) | −7.75435 | + | 13.4309i | −0.299800 | + | 0.519270i | ||||
\(670\) | −0.0979629 | − | 0.169677i | −0.00378464 | − | 0.00655518i | ||||
\(671\) | 1.79079 | 0.0691325 | ||||||||
\(672\) | 0.557229 | + | 0.619496i | 0.0214956 | + | 0.0238976i | ||||
\(673\) | 10.3170 | 0.397691 | 0.198845 | − | 0.980031i | \(-0.436281\pi\) | ||||
0.198845 | + | 0.980031i | \(0.436281\pi\) | |||||||
\(674\) | 0.121915 | + | 0.211163i | 0.00469598 | + | 0.00813368i | ||||
\(675\) | 1.35943 | − | 2.35460i | 0.0523244 | − | 0.0906284i | ||||
\(676\) | 4.01323 | − | 6.95111i | 0.154355 | − | 0.267351i | ||||
\(677\) | 13.6599 | + | 23.6597i | 0.524993 | + | 0.909315i | 0.999576 | + | 0.0291045i | \(0.00926556\pi\) |
−0.474583 | + | 0.880211i | \(0.657401\pi\) | |||||||
\(678\) | 0.243890 | 0.00936654 | ||||||||
\(679\) | −6.56733 | + | 1.39245i | −0.252031 | + | 0.0534374i | ||||
\(680\) | 1.20309 | 0.0461362 | ||||||||
\(681\) | −7.66648 | − | 13.2787i | −0.293780 | − | 0.508842i | ||||
\(682\) | −0.0314106 | + | 0.0544047i | −0.00120277 | + | 0.00208326i | ||||
\(683\) | 10.6541 | − | 18.4535i | 0.407669 | − | 0.706103i | −0.586959 | − | 0.809616i | \(-0.699675\pi\) |
0.994628 | + | 0.103514i | \(0.0330085\pi\) | |||||||
\(684\) | 4.76665 | + | 8.25607i | 0.182257 | + | 0.315679i | ||||
\(685\) | 19.4663 | 0.743768 | ||||||||
\(686\) | −0.443935 | − | 0.198462i | −0.0169495 | − | 0.00757731i | ||||
\(687\) | 6.40484 | 0.244360 | ||||||||
\(688\) | −25.1424 | − | 43.5479i | −0.958544 | − | 1.66025i | ||||
\(689\) | 0.125449 | − | 0.217284i | 0.00477923 | − | 0.00827788i | ||||
\(690\) | −0.0364740 | + | 0.0631748i | −0.00138854 | + | 0.00240502i | ||||
\(691\) | 10.3351 | + | 17.9009i | 0.393166 | + | 0.680984i | 0.992865 | − | 0.119242i | \(-0.0380464\pi\) |
−0.599699 | + | 0.800226i | \(0.704713\pi\) | |||||||
\(692\) | 20.8369 | 0.792099 | ||||||||
\(693\) | −1.70863 | + | 0.362275i | −0.0649053 | + | 0.0137617i | ||||
\(694\) | −0.201517 | −0.00764949 | ||||||||
\(695\) | 4.00782 | + | 6.94174i | 0.152025 | + | 0.263315i | ||||
\(696\) | −0.0934699 | + | 0.161895i | −0.00354297 | + | 0.00613660i | ||||
\(697\) | 16.4946 | − | 28.5695i | 0.624777 | − | 1.08215i | ||||
\(698\) | 0.0750836 | + | 0.130049i | 0.00284195 | + | 0.00492241i | ||||
\(699\) | 26.1430 | 0.988821 | ||||||||
\(700\) | −9.61793 | − | 10.6927i | −0.363523 | − | 0.404145i | ||||
\(701\) | −1.93401 | −0.0730465 | −0.0365232 | − | 0.999333i | \(-0.511628\pi\) | ||||
−0.0365232 | + | 0.999333i | \(0.511628\pi\) | |||||||
\(702\) | −0.0541524 | − | 0.0937947i | −0.00204385 | − | 0.00354005i | ||||
\(703\) | 19.2212 | − | 33.2921i | 0.724942 | − | 1.25564i | ||||
\(704\) | 2.63516 | − | 4.56424i | 0.0993165 | − | 0.172021i | ||||
\(705\) | 16.3393 | + | 28.3006i | 0.615375 | + | 1.06586i | ||||
\(706\) | −0.352352 | −0.0132609 | ||||||||
\(707\) | 5.49599 | − | 16.8858i | 0.206698 | − | 0.635055i | ||||
\(708\) | −17.9681 | −0.675284 | ||||||||
\(709\) | −12.6664 | − | 21.9389i | −0.475698 | − | 0.823933i | 0.523915 | − | 0.851771i | \(-0.324471\pi\) |
−0.999612 | + | 0.0278379i | \(0.991138\pi\) | |||||||
\(710\) | 0.453961 | − | 0.786284i | 0.0170369 | − | 0.0295087i | ||||
\(711\) | 3.47399 | − | 6.01712i | 0.130285 | − | 0.225660i | ||||
\(712\) | 0.311049 | + | 0.538753i | 0.0116571 | + | 0.0201906i | ||||
\(713\) | −3.62429 | −0.135731 | ||||||||
\(714\) | 0.0886631 | − | 0.272407i | 0.00331813 | − | 0.0101946i | ||||
\(715\) | 7.56544 | 0.282931 | ||||||||
\(716\) | 19.2165 | + | 33.2840i | 0.718155 | + | 1.24388i | ||||
\(717\) | 8.83864 | − | 15.3090i | 0.330085 | − | 0.571724i | ||||
\(718\) | 0.234547 | − | 0.406247i | 0.00875321 | − | 0.0151610i | ||||
\(719\) | 5.86374 | + | 10.1563i | 0.218681 | + | 0.378766i | 0.954405 | − | 0.298515i | \(-0.0964914\pi\) |
−0.735724 | + | 0.677281i | \(0.763158\pi\) | |||||||
\(720\) | 11.1016 | 0.413734 | ||||||||
\(721\) | 19.0167 | + | 21.1417i | 0.708219 | + | 0.787359i | ||||
\(722\) | −0.0981095 | −0.00365126 | ||||||||
\(723\) | 2.87985 | + | 4.98804i | 0.107103 | + | 0.185507i | ||||
\(724\) | −11.1514 | + | 19.3148i | −0.414438 | + | 0.717828i | ||||
\(725\) | 2.42011 | − | 4.19176i | 0.0898808 | − | 0.155678i | ||||
\(726\) | 0.138689 | + | 0.240217i | 0.00514724 | + | 0.00891529i | ||||
\(727\) | 13.4547 | 0.499007 | 0.249503 | − | 0.968374i | \(-0.419733\pi\) | ||||
0.249503 | + | 0.968374i | \(0.419733\pi\) | |||||||
\(728\) | −1.12107 | + | 0.237697i | −0.0415496 | + | 0.00880965i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.521106 | − | 0.902583i | −0.0192870 | − | 0.0334061i | ||||
\(731\) | −25.9474 | + | 44.9422i | −0.959700 | + | 1.66225i | ||||
\(732\) | −2.71173 | + | 4.69686i | −0.100229 | + | 0.173601i | ||||
\(733\) | −10.3971 | − | 18.0083i | −0.384025 | − | 0.665151i | 0.607608 | − | 0.794237i | \(-0.292129\pi\) |
−0.991633 | + | 0.129086i | \(0.958796\pi\) | |||||||
\(734\) | −0.686664 | −0.0253452 | ||||||||
\(735\) | −17.7746 | + | 7.89220i | −0.655627 | + | 0.291108i | ||||
\(736\) | −0.314933 | −0.0116086 | ||||||||
\(737\) | 0.886533 | + | 1.53552i | 0.0326559 | + | 0.0565616i | ||||
\(738\) | −0.105022 | + | 0.181903i | −0.00386591 | + | 0.00669595i | ||||
\(739\) | 11.6762 | − | 20.2238i | 0.429517 | − | 0.743945i | −0.567313 | − | 0.823502i | \(-0.692017\pi\) |
0.996830 | + | 0.0795569i | \(0.0253505\pi\) | |||||||
\(740\) | −22.3911 | − | 38.7825i | −0.823113 | − | 1.42567i | ||||
\(741\) | −19.6686 | −0.722544 | ||||||||
\(742\) | −0.00413356 | 0.000876425i | −0.000151748 | 3.21746e-5i | ||||||
\(743\) | 6.11578 | 0.224366 | 0.112183 | − | 0.993688i | \(-0.464216\pi\) | ||||
0.112183 | + | 0.993688i | \(0.464216\pi\) | |||||||
\(744\) | −0.190289 | − | 0.329591i | −0.00697635 | − | 0.0120834i | ||||
\(745\) | −26.4782 | + | 45.8616i | −0.970085 | + | 1.68024i | ||||
\(746\) | 0.264272 | − | 0.457733i | 0.00967569 | − | 0.0167588i | ||||
\(747\) | −4.70428 | − | 8.14805i | −0.172121 | − | 0.298122i | ||||
\(748\) | −5.44284 | −0.199010 | ||||||||
\(749\) | −0.857352 | − | 0.953157i | −0.0313270 | − | 0.0348276i | ||||
\(750\) | −0.166405 | −0.00607625 | ||||||||
\(751\) | −12.2516 | − | 21.2204i | −0.447068 | − | 0.774344i | 0.551126 | − | 0.834422i | \(-0.314198\pi\) |
−0.998194 | + | 0.0600780i | \(0.980865\pi\) | |||||||
\(752\) | −23.5000 | + | 40.7033i | −0.856959 | + | 1.48430i | ||||
\(753\) | −5.19330 | + | 8.99506i | −0.189254 | + | 0.327798i | ||||
\(754\) | −0.0964046 | − | 0.166978i | −0.00351085 | − | 0.00608097i | ||||
\(755\) | −14.0662 | −0.511920 | ||||||||
\(756\) | 1.63715 | − | 5.02995i | 0.0595426 | − | 0.182938i | ||||
\(757\) | 23.0058 | 0.836160 | 0.418080 | − | 0.908410i | \(-0.362703\pi\) | ||||
0.418080 | + | 0.908410i | \(0.362703\pi\) | |||||||
\(758\) | 0.105669 | + | 0.183024i | 0.00383806 | + | 0.00664771i | ||||
\(759\) | 0.330078 | − | 0.571712i | 0.0119811 | − | 0.0207518i | ||||
\(760\) | −0.695554 | + | 1.20473i | −0.0252304 | + | 0.0437003i | ||||
\(761\) | 5.32349 | + | 9.22056i | 0.192976 | + | 0.334245i | 0.946235 | − | 0.323479i | \(-0.104853\pi\) |
−0.753259 | + | 0.657724i | \(0.771519\pi\) | |||||||
\(762\) | 0.0630349 | 0.00228351 | ||||||||
\(763\) | 10.2072 | − | 31.3605i | 0.369526 | − | 1.13533i | ||||
\(764\) | −38.4560 | −1.39129 | ||||||||
\(765\) | −5.72855 | − | 9.92214i | −0.207116 | − | 0.358736i | ||||
\(766\) | 0.263476 | − | 0.456354i | 0.00951977 | − | 0.0164887i | ||||
\(767\) | 18.5355 | − | 32.1044i | 0.669278 | − | 1.15922i | ||||
\(768\) | 7.97244 | + | 13.8087i | 0.287681 | + | 0.498277i | ||||
\(769\) | 17.0235 | 0.613883 | 0.306942 | − | 0.951728i | \(-0.400694\pi\) | ||||
0.306942 | + | 0.951728i | \(0.400694\pi\) | |||||||
\(770\) | −0.0852070 | − | 0.0947284i | −0.00307065 | − | 0.00341378i | ||||
\(771\) | 2.69848 | 0.0971834 | ||||||||
\(772\) | 17.4467 | + | 30.2185i | 0.627919 | + | 1.08759i | ||||
\(773\) | 3.92164 | − | 6.79247i | 0.141051 | − | 0.244308i | −0.786841 | − | 0.617155i | \(-0.788285\pi\) |
0.927893 | + | 0.372847i | \(0.121618\pi\) | |||||||
\(774\) | 0.165208 | − | 0.286150i | 0.00593830 | − | 0.0102854i | ||||
\(775\) | 4.92695 | + | 8.53373i | 0.176981 | + | 0.306541i | ||||
\(776\) | 0.266447 | 0.00956488 | ||||||||
\(777\) | −20.8665 | + | 4.42425i | −0.748580 | + | 0.158719i | ||||
\(778\) | −0.326936 | −0.0117212 | ||||||||
\(779\) | 19.0724 | + | 33.0344i | 0.683340 | + | 1.18358i | ||||
\(780\) | −11.4561 | + | 19.8426i | −0.410195 | + | 0.710479i | ||||
\(781\) | −4.10821 | + | 7.11563i | −0.147003 | + | 0.254617i | ||||
\(782\) | 0.0541384 | + | 0.0937704i | 0.00193598 | + | 0.00335322i | ||||
\(783\) | 1.78025 | 0.0636208 | ||||||||
\(784\) | −22.6124 | − | 16.4639i | −0.807585 | − | 0.587996i | ||||
\(785\) | −7.62327 | −0.272086 | ||||||||
\(786\) | 0.264540 | + | 0.458198i | 0.00943585 | + | 0.0163434i | ||||
\(787\) | 20.4790 | − | 35.4706i | 0.729997 | − | 1.26439i | −0.226887 | − | 0.973921i | \(-0.572855\pi\) |
0.956884 | − | 0.290471i | \(-0.0938119\pi\) | |||||||
\(788\) | −1.16199 | + | 2.01262i | −0.0413941 | + | 0.0716968i | ||||
\(789\) | −10.5745 | − | 18.3156i | −0.376463 | − | 0.652053i | ||||
\(790\) | 0.506840 | 0.0180326 | ||||||||
\(791\) | −24.0413 | + | 5.09740i | −0.854809 | + | 0.181243i | ||||
\(792\) | 0.0693216 | 0.00246324 | ||||||||
\(793\) | −5.59471 | − | 9.69033i | −0.198674 | − | 0.344114i | ||||
\(794\) | −0.0910481 | + | 0.157700i | −0.00323118 | + | 0.00559656i | ||||
\(795\) | −0.0844954 | + | 0.146350i | −0.00299674 | + | 0.00519051i | ||||
\(796\) | 16.9710 | + | 29.3946i | 0.601521 | + | 1.04186i | ||||
\(797\) | −11.8092 | −0.418303 | −0.209151 | − | 0.977883i | \(-0.567070\pi\) | ||||
−0.209151 | + | 0.977883i | \(0.567070\pi\) | |||||||
\(798\) | 0.221521 | + | 0.246275i | 0.00784175 | + | 0.00871803i | ||||
\(799\) | 48.5050 | 1.71598 | ||||||||
\(800\) | 0.428128 | + | 0.741540i | 0.0151366 | + | 0.0262174i | ||||
\(801\) | 2.96215 | − | 5.13060i | 0.104662 | − | 0.181281i | ||||
\(802\) | −0.189259 | + | 0.327806i | −0.00668295 | + | 0.0115752i | ||||
\(803\) | 4.71585 | + | 8.16809i | 0.166419 | + | 0.288246i | ||||
\(804\) | −5.36981 | −0.189378 | ||||||||
\(805\) | 2.27502 | − | 6.98973i | 0.0801838 | − | 0.246355i | ||||
\(806\) | 0.392528 | 0.0138262 | ||||||||
\(807\) | −14.2705 | − | 24.7173i | −0.502347 | − | 0.870090i | ||||
\(808\) | −0.352395 | + | 0.610366i | −0.0123972 | + | 0.0214726i | ||||
\(809\) | −6.52389 | + | 11.2997i | −0.229368 | + | 0.397277i | −0.957621 | − | 0.288032i | \(-0.906999\pi\) |
0.728253 | + | 0.685308i | \(0.240333\pi\) | |||||||
\(810\) | 0.0364740 | + | 0.0631748i | 0.00128156 | + | 0.00221974i | ||||
\(811\) | −51.3449 | −1.80296 | −0.901481 | − | 0.432818i | \(-0.857519\pi\) | ||||
−0.901481 | + | 0.432818i | \(0.857519\pi\) | |||||||
\(812\) | 2.91453 | − | 8.95456i | 0.102280 | − | 0.314243i | ||||
\(813\) | −15.1472 | −0.531237 | ||||||||
\(814\) | −0.0698718 | − | 0.121021i | −0.00244900 | − | 0.00424180i | ||||
\(815\) | −21.2661 | + | 36.8339i | −0.744919 | + | 1.29024i | ||||
\(816\) | 8.23909 | − | 14.2705i | 0.288426 | − | 0.499568i | ||||
\(817\) | −30.0026 | − | 51.9659i | −1.04966 | − | 1.81806i | ||||
\(818\) | −0.630851 | −0.0220572 | ||||||||
\(819\) | 7.29838 | + | 8.11394i | 0.255026 | + | 0.283524i | ||||
\(820\) | 44.4355 | 1.55175 | ||||||||
\(821\) | −28.1511 | − | 48.7591i | −0.982479 | − | 1.70170i | −0.652644 | − | 0.757665i | \(-0.726340\pi\) |
−0.329835 | − | 0.944039i | \(-0.606993\pi\) | |||||||
\(822\) | −0.0919841 | + | 0.159321i | −0.00320831 | + | 0.00555696i | ||||
\(823\) | 6.77827 | − | 11.7403i | 0.236276 | − | 0.409241i | −0.723367 | − | 0.690464i | \(-0.757407\pi\) |
0.959643 | + | 0.281222i | \(0.0907398\pi\) | |||||||
\(824\) | −0.564302 | − | 0.977400i | −0.0196584 | − | 0.0340494i | ||||
\(825\) | −1.79487 | −0.0624893 | ||||||||
\(826\) | −0.610745 | + | 0.129494i | −0.0212505 | + | 0.00450569i | ||||
\(827\) | 3.80574 | 0.132339 | 0.0661693 | − | 0.997808i | \(-0.478922\pi\) | ||||
0.0661693 | + | 0.997808i | \(0.478922\pi\) | |||||||
\(828\) | 0.999655 | + | 1.73145i | 0.0347404 | + | 0.0601722i | ||||
\(829\) | 19.4462 | − | 33.6818i | 0.675395 | − | 1.16982i | −0.300959 | − | 0.953637i | \(-0.597307\pi\) |
0.976353 | − | 0.216181i | \(-0.0693600\pi\) | |||||||
\(830\) | 0.343168 | − | 0.594384i | 0.0119115 | − | 0.0206314i | ||||
\(831\) | 2.11859 | + | 3.66950i | 0.0734929 | + | 0.127294i | ||||
\(832\) | −32.9308 | −1.14167 | ||||||||
\(833\) | −3.04648 | + | 28.7054i | −0.105554 | + | 0.994585i | ||||
\(834\) | −0.0757527 | −0.00262310 | ||||||||
\(835\) | −18.0611 | − | 31.2828i | −0.625031 | − | 1.08259i | ||||
\(836\) | 3.14673 | − | 5.45030i | 0.108832 | − | 0.188502i | ||||
\(837\) | −1.81214 | + | 3.13872i | −0.0626368 | + | 0.108490i | ||||
\(838\) | 0.418720 | + | 0.725244i | 0.0144644 | + | 0.0250531i | ||||
\(839\) | 5.77279 | 0.199299 | 0.0996495 | − | 0.995023i | \(-0.468228\pi\) | ||||
0.0996495 | + | 0.995023i | \(0.468228\pi\) | |||||||
\(840\) | 0.755089 | − | 0.160099i | 0.0260531 | − | 0.00552395i | ||||
\(841\) | −25.8307 | −0.890715 | ||||||||
\(842\) | −0.247336 | − | 0.428398i | −0.00852376 | − | 0.0147636i | ||||
\(843\) | 0.381062 | − | 0.660018i | 0.0131245 | − | 0.0227322i | ||||
\(844\) | 11.6884 | − | 20.2449i | 0.402330 | − | 0.696857i | ||||
\(845\) | −5.57686 | − | 9.65941i | −0.191850 | − | 0.332294i | ||||
\(846\) | −0.308834 | −0.0106179 | ||||||||
\(847\) | −18.6918 | − | 20.7805i | −0.642259 | − | 0.714028i | ||||
\(848\) | −0.243051 | −0.00834641 | ||||||||
\(849\) | 8.58570 | + | 14.8709i | 0.294660 | + | 0.510367i | ||||
\(850\) | 0.147194 | − | 0.254948i | 0.00504872 | − | 0.00874464i | ||||
\(851\) | 4.03105 | − | 6.98199i | 0.138183 | − | 0.239339i | ||||
\(852\) | −12.4419 | − | 21.5500i | −0.426252 | − | 0.738290i | ||||
\(853\) | 6.63846 | 0.227296 | 0.113648 | − | 0.993521i | \(-0.463746\pi\) | ||||
0.113648 | + | 0.993521i | \(0.463746\pi\) | |||||||
\(854\) | −0.0583232 | + | 0.179191i | −0.00199578 | + | 0.00613181i | ||||
\(855\) | 13.2477 | 0.453060 | ||||||||
\(856\) | 0.0254411 | + | 0.0440653i | 0.000869558 | + | 0.00150612i | ||||
\(857\) | 12.8921 | − | 22.3297i | 0.440385 | − | 0.762770i | −0.557333 | − | 0.830289i | \(-0.688175\pi\) |
0.997718 | + | 0.0675197i | \(0.0215085\pi\) | |||||||
\(858\) | −0.0357490 | + | 0.0619192i | −0.00122045 | + | 0.00211389i | ||||
\(859\) | −10.5535 | − | 18.2792i | −0.360081 | − | 0.623679i | 0.627893 | − | 0.778300i | \(-0.283918\pi\) |
−0.987974 | + | 0.154621i | \(0.950584\pi\) | |||||||
\(860\) | −69.9008 | −2.38360 | ||||||||
\(861\) | 6.55060 | − | 20.1260i | 0.223244 | − | 0.685891i | ||||
\(862\) | 0.954242 | 0.0325016 | ||||||||
\(863\) | −6.22738 | − | 10.7861i | −0.211982 | − | 0.367164i | 0.740353 | − | 0.672219i | \(-0.234659\pi\) |
−0.952335 | + | 0.305055i | \(0.901325\pi\) | |||||||
\(864\) | −0.157467 | + | 0.272740i | −0.00535712 | + | 0.00927881i | ||||
\(865\) | 14.4777 | − | 25.0761i | 0.492255 | − | 0.852612i | ||||
\(866\) | 0.282895 | + | 0.489989i | 0.00961318 | + | 0.0166505i | ||||
\(867\) | −0.00578278 | −0.000196394 | ||||||||
\(868\) | 12.8209 | + | 14.2536i | 0.435169 | + | 0.483797i | ||||
\(869\) | −4.58675 | −0.155595 | ||||||||
\(870\) | 0.0649327 | + | 0.112467i | 0.00220142 | + | 0.00381298i | ||||
\(871\) | 5.53936 | − | 9.59445i | 0.187694 | − | 0.325095i | ||||
\(872\) | −0.654472 | + | 1.13358i | −0.0221632 | + | 0.0383878i | ||||
\(873\) | −1.26870 | − | 2.19745i | −0.0429390 | − | 0.0743724i | ||||
\(874\) | −0.125199 | −0.00423490 | ||||||||
\(875\) | 16.4032 | − | 3.47793i | 0.554531 | − | 0.117576i | ||||
\(876\) | −28.5643 | −0.965098 | ||||||||
\(877\) | 22.9536 | + | 39.7568i | 0.775088 | + | 1.34249i | 0.934745 | + | 0.355319i | \(0.115628\pi\) |
−0.159657 | + | 0.987172i | \(0.551039\pi\) | |||||||
\(878\) | −0.140965 | + | 0.244158i | −0.00475733 | + | 0.00823993i | ||||
\(879\) | −0.577830 | + | 1.00083i | −0.0194897 | + | 0.0337572i | ||||
\(880\) | −3.66441 | − | 6.34694i | −0.123527 | − | 0.213955i | ||||
\(881\) | 17.7656 | 0.598539 | 0.299269 | − | 0.954169i | \(-0.403257\pi\) | ||||
0.299269 | + | 0.954169i | \(0.403257\pi\) | |||||||
\(882\) | 0.0193971 | − | 0.182769i | 0.000653134 | − | 0.00615415i | ||||
\(883\) | 8.07698 | 0.271812 | 0.135906 | − | 0.990722i | \(-0.456605\pi\) | ||||
0.135906 | + | 0.990722i | \(0.456605\pi\) | |||||||
\(884\) | 17.0043 | + | 29.4524i | 0.571918 | + | 0.990590i | ||||
\(885\) | −12.4845 | + | 21.6237i | −0.419660 | + | 0.726873i | ||||
\(886\) | −0.445745 | + | 0.772052i | −0.0149751 | + | 0.0259376i | ||||
\(887\) | 25.8359 | + | 44.7491i | 0.867484 | + | 1.50253i | 0.864559 | + | 0.502531i | \(0.167598\pi\) |
0.00292545 | + | 0.999996i | \(0.499069\pi\) | |||||||
\(888\) | 0.846585 | 0.0284095 | ||||||||
\(889\) | −6.21362 | + | 1.31745i | −0.208398 | + | 0.0441860i | ||||
\(890\) | 0.432166 | 0.0144862 | ||||||||
\(891\) | −0.330078 | − | 0.571712i | −0.0110580 | − | 0.0191531i | ||||
\(892\) | −15.5034 | + | 26.8526i | −0.519091 | + | 0.899091i | ||||
\(893\) | −28.0427 | + | 48.5715i | −0.938415 | + | 1.62538i | ||||
\(894\) | −0.250235 | − | 0.433420i | −0.00836912 | − | 0.0144957i | ||||
\(895\) | 53.4073 | 1.78521 | ||||||||
\(896\) | 1.48535 | + | 1.65133i | 0.0496219 | + | 0.0551669i | ||||
\(897\) | −4.12488 | −0.137726 | ||||||||
\(898\) | 0.0911388 | + | 0.157857i | 0.00304134 | + | 0.00526776i | ||||
\(899\) | −3.22606 | + | 5.58770i | −0.107595 | + | 0.186360i | ||||
\(900\) | 2.71792 | − | 4.70757i | 0.0905972 | − | 0.156919i | ||||
\(901\) | 0.125417 | + | 0.217228i | 0.00417823 | + | 0.00723691i | ||||
\(902\) | 0.138662 | 0.00461693 | ||||||||
\(903\) | −10.3047 | + | 31.6599i | −0.342918 | + | 1.05358i | ||||
\(904\) | 0.975392 | 0.0324411 | ||||||||
\(905\) | 15.4962 | + | 26.8402i | 0.515111 | + | 0.892198i | ||||
\(906\) | 0.0664669 | − | 0.115124i | 0.00220822 | − | 0.00382474i | ||||
\(907\) | −19.3898 | + | 33.5841i | −0.643826 | + | 1.11514i | 0.340745 | + | 0.940156i | \(0.389321\pi\) |
−0.984571 | + | 0.174984i | \(0.944013\pi\) | |||||||
\(908\) | −15.3277 | − | 26.5483i | −0.508667 | − | 0.881037i | ||||
\(909\) | 6.71178 | 0.222616 | ||||||||
\(910\) | −0.246395 | + | 0.757021i | −0.00816792 | + | 0.0250950i | ||||
\(911\) | 9.13030 | 0.302500 | 0.151250 | − | 0.988496i | \(-0.451670\pi\) | ||||
0.151250 | + | 0.988496i | \(0.451670\pi\) | |||||||
\(912\) | 9.52672 | + | 16.5008i | 0.315461 | + | 0.546395i | ||||
\(913\) | −3.10556 | + | 5.37899i | −0.102779 | + | 0.178018i | ||||
\(914\) | −0.519234 | + | 0.899340i | −0.0171747 | + | 0.0297475i | ||||
\(915\) | 3.76828 | + | 6.52685i | 0.124576 | + | 0.215771i | ||||
\(916\) | 12.8053 | 0.423098 | ||||||||
\(917\) | −35.6534 | − | 39.6375i | −1.17738 | − | 1.30894i | ||||
\(918\) | 0.108277 | 0.00357366 | ||||||||
\(919\) | −1.87461 | − | 3.24692i | −0.0618377 | − | 0.107106i | 0.833449 | − | 0.552596i | \(-0.186363\pi\) |
−0.895287 | + | 0.445490i | \(0.853029\pi\) | |||||||
\(920\) | −0.145871 | + | 0.252656i | −0.00480922 | + | 0.00832981i | ||||
\(921\) | 15.5182 | − | 26.8784i | 0.511343 | − | 0.885673i | ||||
\(922\) | −0.0644048 | − | 0.111552i | −0.00212106 | − | 0.00367378i | ||||
\(923\) | 51.3389 | 1.68984 | ||||||||
\(924\) | −3.41607 | + | 0.724300i | −0.112381 | + | 0.0238277i | ||||
\(925\) | −21.9197 | −0.720715 | ||||||||
\(926\) | −0.0101364 | − | 0.0175568i | −0.000333103 | − | 0.000576951i | ||||
\(927\) | −5.37391 | + | 9.30788i | −0.176502 | + | 0.305711i | ||||
\(928\) | −0.280329 | + | 0.485544i | −0.00920226 | + | 0.0159388i | ||||
\(929\) | −22.2160 | − | 38.4792i | −0.728883 | − | 1.26246i | −0.957355 | − | 0.288913i | \(-0.906706\pi\) |
0.228472 | − | 0.973550i | \(-0.426627\pi\) | |||||||
\(930\) | −0.264384 | −0.00866950 | ||||||||
\(931\) | −26.9835 | − | 19.6465i | −0.884348 | − | 0.643887i | ||||
\(932\) | 52.2681 | 1.71210 | ||||||||
\(933\) | 8.80703 | + | 15.2542i | 0.288329 | + | 0.499401i | ||||
\(934\) | −0.252033 | + | 0.436533i | −0.00824676 | + | 0.0142838i | ||||
\(935\) | −3.78174 | + | 6.55016i | −0.123676 | + | 0.214213i | ||||
\(936\) | −0.216572 | − | 0.375114i | −0.00707889 | − | 0.0122610i | ||||
\(937\) | 59.8482 | 1.95516 | 0.977579 | − | 0.210571i | \(-0.0675324\pi\) | ||||
0.977579 | + | 0.210571i | \(0.0675324\pi\) | |||||||
\(938\) | −0.182522 | + | 0.0386996i | −0.00595955 | + | 0.00126359i | ||||
\(939\) | −15.7406 | −0.513676 | ||||||||
\(940\) | 32.6674 | + | 56.5816i | 1.06549 | + | 1.84549i | ||||
\(941\) | −10.8539 | + | 18.7995i | −0.353827 | + | 0.612846i | −0.986916 | − | 0.161232i | \(-0.948453\pi\) |
0.633089 | + | 0.774079i | \(0.281787\pi\) | |||||||
\(942\) | 0.0360223 | − | 0.0623925i | 0.00117367 | − | 0.00203286i | ||||
\(943\) | 3.99984 | + | 6.92793i | 0.130253 | + | 0.225605i | ||||
\(944\) | −35.9115 | −1.16882 | ||||||||
\(945\) | −4.91577 | − | 5.46509i | −0.159910 | − | 0.177779i | ||||
\(946\) | −0.218127 | −0.00709191 | ||||||||
\(947\) | −8.28242 | − | 14.3456i | −0.269143 | − | 0.466169i | 0.699498 | − | 0.714635i | \(-0.253407\pi\) |
−0.968641 | + | 0.248466i | \(0.920074\pi\) | |||||||
\(948\) | 6.94558 | − | 12.0301i | 0.225582 | − | 0.390719i | ||||
\(949\) | 29.4662 | − | 51.0370i | 0.956513 | − | 1.65673i | ||||
\(950\) | 0.170198 | + | 0.294792i | 0.00552196 | + | 0.00956432i | ||||
\(951\) | 5.22139 | 0.169315 | ||||||||
\(952\) | 0.354591 | − | 1.08944i | 0.0114924 | − | 0.0353090i | ||||
\(953\) | 51.8971 | 1.68111 | 0.840555 | − | 0.541726i | \(-0.182229\pi\) | ||||
0.840555 | + | 0.541726i | \(0.182229\pi\) | |||||||
\(954\) | −0.000798534 | − | 0.00138310i | −2.58535e−5 | − | 4.47796e-5i | ||||
\(955\) | −26.7196 | + | 46.2797i | −0.864626 | + | 1.49758i | ||||
\(956\) | 17.6712 | − | 30.6074i | 0.571527 | − | 0.989913i | ||||
\(957\) | −0.587620 | − | 1.01779i | −0.0189951 | − | 0.0329004i | ||||
\(958\) | 0.478142 | 0.0154481 | ||||||||
\(959\) | 5.73739 | − | 17.6275i | 0.185270 | − | 0.569221i | ||||
\(960\) | 22.1803 | 0.715866 | ||||||||
\(961\) | 8.93227 | + | 15.4711i | 0.288138 | + | 0.499069i | ||||
\(962\) | −0.436582 | + | 0.756183i | −0.0140760 | + | 0.0243803i | ||||
\(963\) | 0.242278 | − | 0.419638i | 0.00780730 | − | 0.0135226i | ||||
\(964\) | 5.75770 | + | 9.97264i | 0.185443 | + | 0.321197i | ||||
\(965\) | 48.4885 | 1.56090 | ||||||||
\(966\) | 0.0464571 | + | 0.0516484i | 0.00149473 | + | 0.00166176i | ||||
\(967\) | −1.28492 | −0.0413202 | −0.0206601 | − | 0.999787i | \(-0.506577\pi\) | ||||
−0.0206601 | + | 0.999787i | \(0.506577\pi\) | |||||||
\(968\) | 0.554662 | + | 0.960702i | 0.0178275 | + | 0.0308781i | ||||
\(969\) | 9.83175 | − | 17.0291i | 0.315841 | − | 0.547053i | ||||
\(970\) | 0.0925490 | − | 0.160300i | 0.00297157 | − | 0.00514691i | ||||
\(971\) | 25.2486 | + | 43.7318i | 0.810266 | + | 1.40342i | 0.912678 | + | 0.408679i | \(0.134010\pi\) |
−0.102413 | + | 0.994742i | \(0.532656\pi\) | |||||||
\(972\) | 1.99931 | 0.0641279 | ||||||||
\(973\) | 7.46727 | − | 1.58326i | 0.239390 | − | 0.0507571i | ||||
\(974\) | 0.758321 | 0.0242982 | ||||||||
\(975\) | 5.60747 | + | 9.71242i | 0.179583 | + | 0.311046i | ||||
\(976\) | −5.41973 | + | 9.38725i | −0.173481 | + | 0.300478i | ||||
\(977\) | 2.88750 | − | 5.00130i | 0.0923794 | − | 0.160006i | −0.816132 | − | 0.577865i | \(-0.803886\pi\) |
0.908512 | + | 0.417859i | \(0.137219\pi\) | |||||||
\(978\) | −0.200978 | − | 0.348104i | −0.00642656 | − | 0.0111311i | ||||
\(979\) | −3.91096 | −0.124995 | ||||||||
\(980\) | −35.5370 | + | 15.7789i | −1.13519 | + | 0.504040i | ||||
\(981\) | 12.4652 | 0.397983 | ||||||||
\(982\) | −0.310899 | − | 0.538492i | −0.00992117 | − | 0.0171840i | ||||
\(983\) | −22.1534 | + | 38.3708i | −0.706584 | + | 1.22384i | 0.259532 | + | 0.965734i | \(0.416432\pi\) |
−0.966117 | + | 0.258106i | \(0.916902\pi\) | |||||||
\(984\) | −0.420015 | + | 0.727488i | −0.0133896 | + | 0.0231915i | ||||
\(985\) | 1.61472 | + | 2.79678i | 0.0514494 | + | 0.0891129i | ||||
\(986\) | 0.192759 | 0.00613870 | ||||||||
\(987\) | 30.4430 | − | 6.45475i | 0.969013 | − | 0.205457i | ||||
\(988\) | −39.3237 | −1.25105 | ||||||||
\(989\) | −6.29210 | − | 10.8982i | −0.200077 | − | 0.346544i | ||||
\(990\) | 0.0240785 | − | 0.0417052i | 0.000765266 | − | 0.00132548i | ||||
\(991\) | −4.72896 | + | 8.19080i | −0.150220 | + | 0.260189i | −0.931308 | − | 0.364232i | \(-0.881332\pi\) |
0.781088 | + | 0.624421i | \(0.214665\pi\) | |||||||
\(992\) | −0.570704 | − | 0.988488i | −0.0181199 | − | 0.0313845i | ||||
\(993\) | 13.9449 | 0.442529 | ||||||||
\(994\) | −0.578213 | − | 0.642825i | −0.0183398 | − | 0.0203892i | ||||
\(995\) | 47.1665 | 1.49528 | ||||||||
\(996\) | −9.40532 | − | 16.2905i | −0.298019 | − | 0.516184i | ||||
\(997\) | 16.7234 | − | 28.9657i | 0.529635 | − | 0.917354i | −0.469768 | − | 0.882790i | \(-0.655662\pi\) |
0.999402 | − | 0.0345640i | \(-0.0110043\pi\) | |||||||
\(998\) | 0.333062 | − | 0.576881i | 0.0105429 | − | 0.0182608i | ||||
\(999\) | −4.03105 | − | 6.98199i | −0.127537 | − | 0.220900i |
(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 | 483.2.i.h.277.6 | ✓ | 20 | |
7.2 | even | 3 | inner | 483.2.i.h.415.6 | yes | 20 | |
7.3 | odd | 6 | 3381.2.a.bj.1.5 | 10 | |||
7.4 | even | 3 | 3381.2.a.bi.1.5 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.i.h.277.6 | ✓ | 20 | 1.1 | even | 1 | trivial | |
483.2.i.h.415.6 | yes | 20 | 7.2 | even | 3 | inner | |
3381.2.a.bi.1.5 | 10 | 7.4 | even | 3 | |||
3381.2.a.bj.1.5 | 10 | 7.3 | odd | 6 |