Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,2,Mod(49,675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([14, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("675.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.u (of order \(18\), degree \(6\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.38990213644\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 27) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 274.2 | ||
Character | \(\chi\) | \(=\) | 675.274 |
Dual form | 675.2.u.b.574.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) |
\(\chi(n)\) | \(e\left(\frac{1}{9}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.274138 | + | 0.753189i | −0.193845 | + | 0.532585i | −0.998094 | − | 0.0617072i | \(-0.980346\pi\) |
0.804249 | + | 0.594292i | \(0.202568\pi\) | |||||||
\(3\) | −0.386327 | + | 1.68842i | −0.223046 | + | 0.974808i | ||||
\(4\) | 1.03995 | + | 0.872619i | 0.519974 | + | 0.436310i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.16579 | − | 0.753837i | −0.475932 | − | 0.307753i | ||||
\(7\) | 1.52780 | + | 1.82076i | 0.577454 | + | 0.688183i | 0.973143 | − | 0.230202i | \(-0.0739386\pi\) |
−0.395689 | + | 0.918385i | \(0.629494\pi\) | |||||||
\(8\) | −2.33062 | + | 1.34559i | −0.823999 | + | 0.475736i | ||||
\(9\) | −2.70150 | − | 1.30456i | −0.900501 | − | 0.434854i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.0434396 | − | 0.246358i | −0.0130975 | − | 0.0742798i | 0.977558 | − | 0.210665i | \(-0.0675628\pi\) |
−0.990656 | + | 0.136385i | \(0.956452\pi\) | |||||||
\(12\) | −1.87510 | + | 1.41875i | −0.541296 | + | 0.409557i | ||||
\(13\) | 0.893351 | + | 2.45446i | 0.247771 | + | 0.680745i | 0.999767 | + | 0.0215777i | \(0.00686892\pi\) |
−0.751996 | + | 0.659167i | \(0.770909\pi\) | |||||||
\(14\) | −1.79020 | + | 0.651581i | −0.478452 | + | 0.174142i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.0969067 | + | 0.549585i | 0.0242267 | + | 0.137396i | ||||
\(17\) | 0.254072 | + | 0.146688i | 0.0616215 | + | 0.0355772i | 0.530494 | − | 0.847689i | \(-0.322006\pi\) |
−0.468873 | + | 0.883266i | \(0.655340\pi\) | |||||||
\(18\) | 1.72317 | − | 1.67711i | 0.406154 | − | 0.395299i | ||||
\(19\) | −1.39237 | − | 2.41166i | −0.319432 | − | 0.553273i | 0.660937 | − | 0.750441i | \(-0.270159\pi\) |
−0.980370 | + | 0.197168i | \(0.936825\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.66443 | + | 1.87615i | −0.799645 | + | 0.409410i | ||||
\(22\) | 0.197463 | + | 0.0348180i | 0.0420992 | + | 0.00742323i | ||||
\(23\) | −4.30015 | + | 5.12472i | −0.896643 | + | 1.06858i | 0.100641 | + | 0.994923i | \(0.467911\pi\) |
−0.997284 | + | 0.0736543i | \(0.976534\pi\) | |||||||
\(24\) | −1.37153 | − | 4.45490i | −0.279962 | − | 0.909352i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.09357 | −0.410584 | ||||||||
\(27\) | 3.24631 | − | 4.05728i | 0.624752 | − | 0.780823i | ||||
\(28\) | 3.22668i | 0.609786i | ||||||||
\(29\) | −0.333645 | − | 0.121437i | −0.0619562 | − | 0.0225502i | 0.310856 | − | 0.950457i | \(-0.399384\pi\) |
−0.372812 | + | 0.927907i | \(0.621606\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.11847 | + | 1.77761i | 0.380488 | + | 0.319268i | 0.812894 | − | 0.582411i | \(-0.197891\pi\) |
−0.432406 | + | 0.901679i | \(0.642335\pi\) | |||||||
\(32\) | −5.74108 | − | 1.01231i | −1.01489 | − | 0.178952i | ||||
\(33\) | 0.432738 | + | 0.0218307i | 0.0753299 | + | 0.00380023i | ||||
\(34\) | −0.180135 | + | 0.151151i | −0.0308929 | + | 0.0259222i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.67103 | − | 3.71406i | −0.278506 | − | 0.619010i | ||||
\(37\) | 6.05558 | + | 3.49619i | 0.995531 | + | 0.574770i | 0.906923 | − | 0.421297i | \(-0.138425\pi\) |
0.0886080 | + | 0.996067i | \(0.471758\pi\) | |||||||
\(38\) | 2.19814 | − | 0.387591i | 0.356585 | − | 0.0628756i | ||||
\(39\) | −4.48928 | + | 0.560124i | −0.718860 | + | 0.0896917i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.13156 | − | 3.32362i | 1.42611 | − | 0.519062i | 0.490296 | − | 0.871556i | \(-0.336888\pi\) |
0.935814 | + | 0.352494i | \(0.114666\pi\) | |||||||
\(42\) | −0.408537 | − | 3.27434i | −0.0630386 | − | 0.505241i | ||||
\(43\) | 0.256746 | − | 0.0452712i | 0.0391534 | − | 0.00690379i | −0.154037 | − | 0.988065i | \(-0.549228\pi\) |
0.193191 | + | 0.981161i | \(0.438116\pi\) | |||||||
\(44\) | 0.169802 | − | 0.294106i | 0.0255986 | − | 0.0443381i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.68104 | − | 4.64370i | −0.395298 | − | 0.684677i | ||||
\(47\) | −7.34421 | − | 8.75249i | −1.07126 | − | 1.27668i | −0.959123 | − | 0.282989i | \(-0.908674\pi\) |
−0.112140 | − | 0.993692i | \(-0.535770\pi\) | |||||||
\(48\) | −0.965367 | − | 0.0487006i | −0.139339 | − | 0.00702933i | ||||
\(49\) | 0.234540 | − | 1.33014i | 0.0335057 | − | 0.190020i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.345826 | + | 0.372309i | −0.0484253 | + | 0.0521337i | ||||
\(52\) | −1.21277 | + | 3.33207i | −0.168181 | + | 0.462074i | ||||
\(53\) | − | 5.43137i | − | 0.746056i | −0.927820 | − | 0.373028i | \(-0.878320\pi\) | ||
0.927820 | − | 0.373028i | \(-0.121680\pi\) | |||||||
\(54\) | 2.16596 | + | 3.55734i | 0.294750 | + | 0.484092i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −6.01071 | − | 2.18772i | −0.803215 | − | 0.292346i | ||||
\(57\) | 4.60980 | − | 1.41922i | 0.610583 | − | 0.187980i | ||||
\(58\) | 0.182930 | − | 0.218007i | 0.0240198 | − | 0.0286257i | ||||
\(59\) | −1.03788 | + | 5.88612i | −0.135121 | + | 0.766308i | 0.839655 | + | 0.543121i | \(0.182757\pi\) |
−0.974776 | + | 0.223188i | \(0.928354\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.07515 | + | 7.61495i | −1.16195 | + | 0.974995i | −0.999930 | − | 0.0117924i | \(-0.996246\pi\) |
−0.162023 | + | 0.986787i | \(0.551802\pi\) | |||||||
\(62\) | −1.91963 | + | 1.10830i | −0.243793 | + | 0.140754i | ||||
\(63\) | −1.75206 | − | 6.91190i | −0.220739 | − | 0.870817i | ||||
\(64\) | 1.77824 | − | 3.08001i | 0.222281 | − | 0.385001i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.135073 | + | 0.319949i | −0.0166263 | + | 0.0393829i | ||||
\(67\) | −0.619160 | − | 1.70113i | −0.0756424 | − | 0.207826i | 0.896108 | − | 0.443835i | \(-0.146383\pi\) |
−0.971751 | + | 0.236010i | \(0.924160\pi\) | |||||||
\(68\) | 0.136218 | + | 0.374256i | 0.0165189 | + | 0.0453852i | ||||
\(69\) | −6.99139 | − | 9.24026i | −0.841665 | − | 1.11240i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.185255 | − | 0.320871i | 0.0219857 | − | 0.0380804i | −0.854823 | − | 0.518919i | \(-0.826334\pi\) |
0.876809 | + | 0.480839i | \(0.159668\pi\) | |||||||
\(72\) | 8.05158 | − | 0.594663i | 0.948888 | − | 0.0700817i | ||||
\(73\) | −4.35333 | + | 2.51339i | −0.509518 | + | 0.294171i | −0.732636 | − | 0.680621i | \(-0.761710\pi\) |
0.223117 | + | 0.974792i | \(0.428377\pi\) | |||||||
\(74\) | −4.29336 | + | 3.60255i | −0.499093 | + | 0.418789i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.656467 | − | 3.72301i | 0.0753019 | − | 0.427059i | ||||
\(77\) | 0.382193 | − | 0.455479i | 0.0435549 | − | 0.0519067i | ||||
\(78\) | 0.808804 | − | 3.53483i | 0.0915790 | − | 0.400240i | ||||
\(79\) | 0.754406 | + | 0.274581i | 0.0848773 | + | 0.0308928i | 0.384110 | − | 0.923287i | \(-0.374508\pi\) |
−0.299233 | + | 0.954180i | \(0.596731\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.59624 | + | 7.04855i | 0.621804 | + | 0.783173i | ||||
\(82\) | 7.78892i | 0.860143i | ||||||||
\(83\) | 0.942488 | − | 2.58947i | 0.103452 | − | 0.284231i | −0.877158 | − | 0.480201i | \(-0.840564\pi\) |
0.980610 | + | 0.195971i | \(0.0627858\pi\) | |||||||
\(84\) | −5.44798 | − | 1.24655i | −0.594424 | − | 0.136010i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.0362861 | + | 0.205789i | −0.00391283 | + | 0.0221908i | ||||
\(87\) | 0.333932 | − | 0.516417i | 0.0358012 | − | 0.0553657i | ||||
\(88\) | 0.432738 | + | 0.515717i | 0.0461300 | + | 0.0549756i | ||||
\(89\) | 5.22533 | + | 9.05054i | 0.553884 | + | 0.959356i | 0.997989 | + | 0.0633809i | \(0.0201883\pi\) |
−0.444105 | + | 0.895975i | \(0.646478\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.10412 | + | 5.37650i | −0.325401 | + | 0.563611i | ||||
\(92\) | −8.94385 | + | 1.57704i | −0.932461 | + | 0.164418i | ||||
\(93\) | −3.81976 | + | 2.89012i | −0.396091 | + | 0.299692i | ||||
\(94\) | 8.60560 | − | 3.13218i | 0.887600 | − | 0.323060i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.92713 | − | 9.30225i | 0.400811 | − | 0.949407i | ||||
\(97\) | 14.6092 | − | 2.57600i | 1.48334 | − | 0.261553i | 0.627430 | − | 0.778673i | \(-0.284107\pi\) |
0.855913 | + | 0.517120i | \(0.172996\pi\) | |||||||
\(98\) | 0.937552 | + | 0.541296i | 0.0947070 | + | 0.0546791i | ||||
\(99\) | −0.204037 | + | 0.722208i | −0.0205065 | + | 0.0725846i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.06826 | − | 2.57457i | 0.305303 | − | 0.256180i | −0.477244 | − | 0.878771i | \(-0.658364\pi\) |
0.782548 | + | 0.622591i | \(0.213920\pi\) | |||||||
\(102\) | −0.185615 | − | 0.362537i | −0.0183786 | − | 0.0358965i | ||||
\(103\) | 5.82943 | + | 1.02789i | 0.574391 | + | 0.101281i | 0.453296 | − | 0.891360i | \(-0.350248\pi\) |
0.121095 | + | 0.992641i | \(0.461359\pi\) | |||||||
\(104\) | −5.38475 | − | 4.51834i | −0.528018 | − | 0.443060i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.09085 | + | 1.48895i | 0.397338 | + | 0.144619i | ||||
\(107\) | − | 0.258978i | − | 0.0250364i | −0.999922 | − | 0.0125182i | \(-0.996015\pi\) | ||
0.999922 | − | 0.0125182i | \(-0.00398477\pi\) | |||||||
\(108\) | 6.91645 | − | 1.38656i | 0.665535 | − | 0.133422i | ||||
\(109\) | 8.55787 | 0.819695 | 0.409848 | − | 0.912154i | \(-0.365582\pi\) | ||||
0.409848 | + | 0.912154i | \(0.365582\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.24246 | + | 8.87367i | −0.782340 | + | 0.842251i | ||||
\(112\) | −0.852609 | + | 1.01610i | −0.0805640 | + | 0.0960124i | ||||
\(113\) | 3.07179 | + | 0.541640i | 0.288970 | + | 0.0509532i | 0.316254 | − | 0.948675i | \(-0.397575\pi\) |
−0.0272843 | + | 0.999628i | \(0.508686\pi\) | |||||||
\(114\) | −0.194784 | + | 3.86111i | −0.0182432 | + | 0.361626i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.241005 | − | 0.417432i | −0.0223767 | − | 0.0387576i | ||||
\(117\) | 0.788606 | − | 7.79617i | 0.0729066 | − | 0.720756i | ||||
\(118\) | −4.14884 | − | 2.39533i | −0.381932 | − | 0.220508i | ||||
\(119\) | 0.121086 | + | 0.686714i | 0.0111000 | + | 0.0629510i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.2778 | − | 3.74082i | 0.934347 | − | 0.340074i | ||||
\(122\) | −3.24765 | − | 8.92285i | −0.294029 | − | 0.807837i | ||||
\(123\) | 2.08388 | + | 16.7019i | 0.187897 | + | 1.50596i | ||||
\(124\) | 0.651922 | + | 3.69724i | 0.0585444 | + | 0.332022i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 5.68627 | + | 0.575183i | 0.506573 | + | 0.0512414i | ||||
\(127\) | −15.9821 | + | 9.22726i | −1.41818 | + | 0.818787i | −0.996139 | − | 0.0877893i | \(-0.972020\pi\) |
−0.422042 | + | 0.906576i | \(0.638686\pi\) | |||||||
\(128\) | −5.66210 | − | 6.74783i | −0.500464 | − | 0.596430i | ||||
\(129\) | −0.0227511 | + | 0.450983i | −0.00200312 | + | 0.0397069i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.8973 | + | 9.14396i | 0.952105 | + | 0.798911i | 0.979651 | − | 0.200709i | \(-0.0643246\pi\) |
−0.0275454 | + | 0.999621i | \(0.508769\pi\) | |||||||
\(132\) | 0.430974 | + | 0.400318i | 0.0375115 | + | 0.0348432i | ||||
\(133\) | 2.26379 | − | 6.21971i | 0.196295 | − | 0.539317i | ||||
\(134\) | 1.45101 | 0.125348 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.789527 | −0.0677014 | ||||||||
\(137\) | −6.73287 | + | 18.4984i | −0.575228 | + | 1.58042i | 0.220900 | + | 0.975296i | \(0.429100\pi\) |
−0.796128 | + | 0.605128i | \(0.793122\pi\) | |||||||
\(138\) | 8.87627 | − | 2.73273i | 0.755598 | − | 0.232626i | ||||
\(139\) | 13.7206 | + | 11.5129i | 1.16377 | + | 0.976515i | 0.999950 | − | 0.00997617i | \(-0.00317556\pi\) |
0.163815 | + | 0.986491i | \(0.447620\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17.6151 | − | 9.01876i | 1.48346 | − | 0.759517i | ||||
\(142\) | 0.190891 | + | 0.227495i | 0.0160192 | + | 0.0190910i | ||||
\(143\) | 0.565870 | − | 0.326705i | 0.0473205 | − | 0.0273205i | ||||
\(144\) | 0.455174 | − | 1.61113i | 0.0379312 | − | 0.134261i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.699647 | − | 3.96789i | −0.0579032 | − | 0.328385i | ||||
\(147\) | 2.15522 | + | 0.909870i | 0.177760 | + | 0.0750449i | ||||
\(148\) | 3.24664 | + | 8.92007i | 0.266872 | + | 0.733225i | ||||
\(149\) | 15.3071 | − | 5.57132i | 1.25401 | − | 0.456421i | 0.372252 | − | 0.928132i | \(-0.378586\pi\) |
0.881753 | + | 0.471711i | \(0.156363\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.47880 | + | 14.0580i | 0.201722 | + | 1.14402i | 0.902515 | + | 0.430659i | \(0.141719\pi\) |
−0.700793 | + | 0.713365i | \(0.747170\pi\) | |||||||
\(152\) | 6.49019 | + | 3.74711i | 0.526424 | + | 0.303931i | ||||
\(153\) | −0.495012 | − | 0.727731i | −0.0400193 | − | 0.0588336i | ||||
\(154\) | 0.238288 | + | 0.412728i | 0.0192018 | + | 0.0332585i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −5.15739 | − | 3.33493i | −0.412922 | − | 0.267008i | ||||
\(157\) | 0.751757 | + | 0.132555i | 0.0599968 | + | 0.0105790i | 0.203566 | − | 0.979061i | \(-0.434747\pi\) |
−0.143569 | + | 0.989640i | \(0.545858\pi\) | |||||||
\(158\) | −0.413623 | + | 0.492937i | −0.0329061 | + | 0.0392159i | ||||
\(159\) | 9.17041 | + | 2.09828i | 0.727261 | + | 0.166405i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −15.9006 | −1.25315 | ||||||||
\(162\) | −6.84304 | + | 2.28275i | −0.537640 | + | 0.179349i | ||||
\(163\) | − | 5.12834i | − | 0.401682i | −0.979624 | − | 0.200841i | \(-0.935632\pi\) | ||
0.979624 | − | 0.200841i | \(-0.0643675\pi\) | |||||||
\(164\) | 12.3966 | + | 4.51199i | 0.968011 | + | 0.352327i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.69198 | + | 1.41974i | 0.131323 | + | 0.110193i | ||||
\(167\) | 8.76590 | + | 1.54566i | 0.678325 | + | 0.119607i | 0.502188 | − | 0.864759i | \(-0.332529\pi\) |
0.176137 | + | 0.984366i | \(0.443640\pi\) | |||||||
\(168\) | 6.01588 | − | 9.30341i | 0.464135 | − | 0.717774i | ||||
\(169\) | 4.73227 | − | 3.97085i | 0.364021 | − | 0.305450i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.615340 | + | 8.33154i | 0.0470562 | + | 0.637129i | ||||
\(172\) | 0.306507 | + | 0.176962i | 0.0233709 | + | 0.0134932i | ||||
\(173\) | −6.70776 | + | 1.18276i | −0.509982 | + | 0.0899235i | −0.422717 | − | 0.906262i | \(-0.638924\pi\) |
−0.0872644 | + | 0.996185i | \(0.527812\pi\) | |||||||
\(174\) | 0.297416 | + | 0.393083i | 0.0225470 | + | 0.0297996i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.131185 | − | 0.0477476i | 0.00988847 | − | 0.00359911i | ||||
\(177\) | −9.53727 | − | 4.02635i | −0.716865 | − | 0.302639i | ||||
\(178\) | −8.24923 | + | 1.45456i | −0.618306 | + | 0.109024i | ||||
\(179\) | −9.17382 | + | 15.8895i | −0.685684 | + | 1.18764i | 0.287538 | + | 0.957769i | \(0.407163\pi\) |
−0.973221 | + | 0.229870i | \(0.926170\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.66282 | − | 9.80830i | −0.420914 | − | 0.729045i | 0.575115 | − | 0.818073i | \(-0.304957\pi\) |
−0.996029 | + | 0.0890276i | \(0.971624\pi\) | |||||||
\(182\) | −3.19856 | − | 3.81190i | −0.237093 | − | 0.282557i | ||||
\(183\) | −9.35124 | − | 18.2645i | −0.691264 | − | 1.35015i | ||||
\(184\) | 3.12628 | − | 17.7300i | 0.230472 | − | 1.30707i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.12966 | − | 3.66930i | −0.0828310 | − | 0.269046i | ||||
\(187\) | 0.0251011 | − | 0.0689648i | 0.00183558 | − | 0.00504321i | ||||
\(188\) | − | 15.5108i | − | 1.13124i | ||||||
\(189\) | 12.3470 | − | 0.287957i | 0.898115 | − | 0.0209458i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.44480 | − | 2.34571i | −0.466329 | − | 0.169730i | 0.0981596 | − | 0.995171i | \(-0.468704\pi\) |
−0.564489 | + | 0.825441i | \(0.690927\pi\) | |||||||
\(192\) | 4.51336 | + | 4.19231i | 0.325724 | + | 0.302554i | ||||
\(193\) | 13.1211 | − | 15.6371i | 0.944477 | − | 1.12558i | −0.0474627 | − | 0.998873i | \(-0.515114\pi\) |
0.991940 | − | 0.126711i | \(-0.0404420\pi\) | |||||||
\(194\) | −2.06474 | + | 11.7097i | −0.148239 | + | 0.840707i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.40462 | − | 1.17861i | 0.100330 | − | 0.0841866i | ||||
\(197\) | 2.62902 | − | 1.51786i | 0.187310 | − | 0.108143i | −0.403413 | − | 0.915018i | \(-0.632176\pi\) |
0.590723 | + | 0.806875i | \(0.298843\pi\) | |||||||
\(198\) | −0.488024 | − | 0.351663i | −0.0346824 | − | 0.0249916i | ||||
\(199\) | −1.13124 | + | 1.95936i | −0.0801912 | + | 0.138895i | −0.903332 | − | 0.428942i | \(-0.858886\pi\) |
0.823141 | + | 0.567837i | \(0.192220\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.11141 | − | 0.388209i | 0.219462 | − | 0.0273821i | ||||
\(202\) | 1.09801 | + | 3.01677i | 0.0772560 | + | 0.212259i | ||||
\(203\) | −0.288635 | − | 0.793018i | −0.0202582 | − | 0.0556589i | ||||
\(204\) | −0.684525 | + | 0.0854077i | −0.0479263 | + | 0.00597974i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.37226 | + | 4.10888i | −0.165283 | + | 0.286279i | ||||
\(207\) | 18.3024 | − | 8.23463i | 1.27210 | − | 0.572346i | ||||
\(208\) | −1.26236 | + | 0.728826i | −0.0875292 | + | 0.0505350i | ||||
\(209\) | −0.533649 | + | 0.447784i | −0.0369132 | + | 0.0309739i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.41601 | − | 25.0445i | 0.304011 | − | 1.72413i | −0.324113 | − | 0.946018i | \(-0.605066\pi\) |
0.628124 | − | 0.778113i | \(-0.283823\pi\) | |||||||
\(212\) | 4.73952 | − | 5.64834i | 0.325511 | − | 0.387929i | ||||
\(213\) | 0.470195 | + | 0.436749i | 0.0322172 | + | 0.0299255i | ||||
\(214\) | 0.195060 | + | 0.0709959i | 0.0133340 | + | 0.00485318i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.10650 | + | 13.8242i | −0.143329 | + | 0.940615i | ||||
\(217\) | 6.57305i | 0.446208i | ||||||||
\(218\) | −2.34604 | + | 6.44569i | −0.158894 | + | 0.436557i | ||||
\(219\) | −2.56185 | − | 8.32122i | −0.173114 | − | 0.562296i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.133066 | + | 0.754654i | −0.00895097 | + | 0.0507635i | ||||
\(222\) | −4.42398 | − | 8.64074i | −0.296918 | − | 0.579929i | ||||
\(223\) | 2.46274 | + | 2.93497i | 0.164917 | + | 0.196540i | 0.842174 | − | 0.539206i | \(-0.181276\pi\) |
−0.677257 | + | 0.735747i | \(0.736831\pi\) | |||||||
\(224\) | −6.92805 | − | 11.9997i | −0.462900 | − | 0.801766i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.25005 | + | 2.16515i | −0.0831523 | + | 0.144024i | ||||
\(227\) | −2.47777 | + | 0.436897i | −0.164455 | + | 0.0289979i | −0.255269 | − | 0.966870i | \(-0.582164\pi\) |
0.0908142 | + | 0.995868i | \(0.471053\pi\) | |||||||
\(228\) | 6.03238 | + | 2.54669i | 0.399504 | + | 0.168659i | ||||
\(229\) | −14.9783 | + | 5.45167i | −0.989797 | + | 0.360257i | −0.785642 | − | 0.618682i | \(-0.787667\pi\) |
−0.204155 | + | 0.978939i | \(0.565445\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.621388 | + | 0.821264i | 0.0408843 | + | 0.0540352i | ||||
\(232\) | 0.941003 | − | 0.165924i | 0.0617799 | − | 0.0108935i | ||||
\(233\) | 24.3598 | + | 14.0641i | 1.59586 | + | 0.921372i | 0.992273 | + | 0.124077i | \(0.0395971\pi\) |
0.603590 | + | 0.797295i | \(0.293736\pi\) | |||||||
\(234\) | 5.65580 | + | 2.73120i | 0.369731 | + | 0.178544i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.21569 | + | 5.21558i | −0.404607 | + | 0.339505i | ||||
\(237\) | −0.755055 | + | 1.16767i | −0.0490461 | + | 0.0758485i | ||||
\(238\) | −0.550420 | − | 0.0970539i | −0.0356784 | − | 0.00629107i | ||||
\(239\) | 11.2653 | + | 9.45270i | 0.728691 | + | 0.611444i | 0.929774 | − | 0.368130i | \(-0.120002\pi\) |
−0.201083 | + | 0.979574i | \(0.564446\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.93378 | − | 2.88766i | −0.511059 | − | 0.186010i | 0.0736022 | − | 0.997288i | \(-0.476550\pi\) |
−0.584662 | + | 0.811277i | \(0.698773\pi\) | |||||||
\(242\) | 8.76664i | 0.563541i | ||||||||
\(243\) | −14.0629 | + | 6.72574i | −0.902134 | + | 0.431456i | ||||
\(244\) | −16.0826 | −1.02958 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −13.1509 | − | 3.00907i | −0.838474 | − | 0.191851i | ||||
\(247\) | 4.67545 | − | 5.57198i | 0.297492 | − | 0.354537i | ||||
\(248\) | −7.32927 | − | 1.29235i | −0.465409 | − | 0.0820642i | ||||
\(249\) | 4.00799 | + | 2.59169i | 0.253996 | + | 0.164242i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.6102 | + | 20.1095i | 0.732832 | + | 1.26930i | 0.955668 | + | 0.294447i | \(0.0951354\pi\) |
−0.222835 | + | 0.974856i | \(0.571531\pi\) | |||||||
\(252\) | 4.20940 | − | 8.71689i | 0.265168 | − | 0.549112i | ||||
\(253\) | 1.44931 | + | 0.836762i | 0.0911176 | + | 0.0526067i | ||||
\(254\) | −2.56857 | − | 14.5671i | −0.161166 | − | 0.914020i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.3186 | − | 4.84758i | 0.832413 | − | 0.302973i | ||||
\(257\) | −2.34804 | − | 6.45118i | −0.146466 | − | 0.402413i | 0.844666 | − | 0.535294i | \(-0.179799\pi\) |
−0.991132 | + | 0.132881i | \(0.957577\pi\) | |||||||
\(258\) | −0.333439 | − | 0.140768i | −0.0207590 | − | 0.00876382i | ||||
\(259\) | 2.88598 | + | 16.3672i | 0.179326 | + | 1.01701i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.742920 | + | 0.763321i | 0.0459856 | + | 0.0472484i | ||||
\(262\) | −9.87451 | + | 5.70105i | −0.610049 | + | 0.352212i | ||||
\(263\) | −2.15523 | − | 2.56850i | −0.132897 | − | 0.158381i | 0.695492 | − | 0.718534i | \(-0.255187\pi\) |
−0.828389 | + | 0.560154i | \(0.810742\pi\) | |||||||
\(264\) | −1.03792 | + | 0.531406i | −0.0638797 | + | 0.0327058i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.06402 | + | 3.41012i | 0.249181 | + | 0.209088i | ||||
\(267\) | −17.2998 | + | 5.32607i | −1.05873 | + | 0.325950i | ||||
\(268\) | 0.840543 | − | 2.30937i | 0.0513444 | − | 0.141067i | ||||
\(269\) | −12.7416 | −0.776869 | −0.388434 | − | 0.921476i | \(-0.626984\pi\) | ||||
−0.388434 | + | 0.921476i | \(0.626984\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.5566 | −1.43096 | −0.715481 | − | 0.698632i | \(-0.753792\pi\) | ||||
−0.715481 | + | 0.698632i | \(0.753792\pi\) | |||||||
\(272\) | −0.0559965 | + | 0.153849i | −0.00339529 | + | 0.00932848i | ||||
\(273\) | −7.87857 | − | 7.31814i | −0.476833 | − | 0.442914i | ||||
\(274\) | −12.0871 | − | 10.1422i | −0.730206 | − | 0.612715i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.792545 | − | 15.7102i | 0.0477056 | − | 0.945643i | ||||
\(277\) | 2.68763 | + | 3.20300i | 0.161484 | + | 0.192450i | 0.840719 | − | 0.541472i | \(-0.182133\pi\) |
−0.679235 | + | 0.733921i | \(0.737688\pi\) | |||||||
\(278\) | −12.4328 | + | 7.17806i | −0.745667 | + | 0.430511i | ||||
\(279\) | −3.40406 | − | 7.56589i | −0.203795 | − | 0.452958i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.75705 | − | 21.3073i | −0.224127 | − | 1.27109i | −0.864347 | − | 0.502896i | \(-0.832268\pi\) |
0.640220 | − | 0.768192i | \(-0.278843\pi\) | |||||||
\(282\) | 1.96386 | + | 15.7399i | 0.116946 | + | 0.937297i | ||||
\(283\) | 1.78785 | + | 4.91209i | 0.106277 | + | 0.291993i | 0.981420 | − | 0.191870i | \(-0.0614553\pi\) |
−0.875143 | + | 0.483864i | \(0.839233\pi\) | |||||||
\(284\) | 0.472654 | − | 0.172032i | 0.0280468 | − | 0.0102082i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.0909441 | + | 0.515770i | 0.00537764 | + | 0.0304981i | ||||
\(287\) | 20.0027 | + | 11.5486i | 1.18072 | + | 0.681690i | ||||
\(288\) | 14.1889 | + | 10.2243i | 0.836090 | + | 0.602475i | ||||
\(289\) | −8.45697 | − | 14.6479i | −0.497469 | − | 0.861641i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.29457 | + | 25.6617i | −0.0758893 | + | 1.50431i | ||||
\(292\) | −6.72047 | − | 1.18500i | −0.393285 | − | 0.0693468i | ||||
\(293\) | −3.94811 | + | 4.70517i | −0.230651 | + | 0.274879i | −0.868940 | − | 0.494918i | \(-0.835198\pi\) |
0.638289 | + | 0.769797i | \(0.279643\pi\) | |||||||
\(294\) | −1.27613 | + | 1.37386i | −0.0744257 | + | 0.0801252i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −18.8177 | −1.09376 | ||||||||
\(297\) | −1.14056 | − | 0.623508i | −0.0661821 | − | 0.0361796i | ||||
\(298\) | 13.0564i | 0.756339i | ||||||||
\(299\) | −16.4200 | − | 5.97638i | −0.949591 | − | 0.345623i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.474684 | + | 0.398307i | 0.0273603 | + | 0.0229580i | ||||
\(302\) | −11.2679 | − | 1.98683i | −0.648393 | − | 0.114329i | ||||
\(303\) | 3.16160 | + | 6.17513i | 0.181629 | + | 0.354752i | ||||
\(304\) | 1.19048 | − | 0.998934i | 0.0682789 | − | 0.0572928i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.683821 | − | 0.173338i | 0.0390914 | − | 0.00990909i | ||||
\(307\) | −16.4578 | − | 9.50194i | −0.939298 | − | 0.542304i | −0.0495580 | − | 0.998771i | \(-0.515781\pi\) |
−0.889740 | + | 0.456467i | \(0.849115\pi\) | |||||||
\(308\) | 0.794920 | − | 0.140166i | 0.0452948 | − | 0.00798669i | ||||
\(309\) | −3.98757 | + | 9.44541i | −0.226845 | + | 0.537331i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.2475 | − | 7.36948i | 1.14813 | − | 0.417885i | 0.303286 | − | 0.952900i | \(-0.401916\pi\) |
0.844843 | + | 0.535015i | \(0.179694\pi\) | |||||||
\(312\) | 9.70912 | − | 7.34615i | 0.549671 | − | 0.415894i | ||||
\(313\) | −3.75568 | + | 0.662228i | −0.212284 | + | 0.0374313i | −0.278778 | − | 0.960355i | \(-0.589930\pi\) |
0.0664949 | + | 0.997787i | \(0.478818\pi\) | |||||||
\(314\) | −0.305925 | + | 0.529877i | −0.0172643 | + | 0.0299027i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.544937 | + | 0.943859i | 0.0306551 | + | 0.0530962i | ||||
\(317\) | 2.73473 | + | 3.25913i | 0.153598 | + | 0.183051i | 0.837356 | − | 0.546658i | \(-0.184100\pi\) |
−0.683758 | + | 0.729709i | \(0.739656\pi\) | |||||||
\(318\) | −4.09437 | + | 6.33183i | −0.229601 | + | 0.355072i | ||||
\(319\) | −0.0154235 | + | 0.0874713i | −0.000863553 | + | 0.00489745i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.437264 | + | 0.100050i | 0.0244057 | + | 0.00558426i | ||||
\(322\) | 4.35898 | − | 11.9762i | 0.242916 | − | 0.667407i | ||||
\(323\) | − | 0.816980i | − | 0.0454580i | ||||||
\(324\) | −0.330912 | + | 12.2135i | −0.0183840 | + | 0.678528i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.86261 | + | 1.40587i | 0.213930 | + | 0.0778642i | ||||
\(327\) | −3.30614 | + | 14.4493i | −0.182830 | + | 0.799046i | ||||
\(328\) | −16.8100 | + | 20.0334i | −0.928178 | + | 1.10616i | ||||
\(329\) | 4.71570 | − | 26.7441i | 0.259985 | − | 1.47445i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.9497 | + | 9.18787i | −0.601849 | + | 0.505011i | −0.892039 | − | 0.451958i | \(-0.850726\pi\) |
0.290191 | + | 0.956969i | \(0.406281\pi\) | |||||||
\(332\) | 3.23976 | − | 1.87047i | 0.177805 | − | 0.102656i | ||||
\(333\) | −11.7982 | − | 17.3448i | −0.646536 | − | 0.950491i | ||||
\(334\) | −3.56725 | + | 6.17865i | −0.195191 | + | 0.338081i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.38621 | − | 1.83211i | −0.0756242 | − | 0.0999496i | ||||
\(337\) | −12.2164 | − | 33.5644i | −0.665472 | − | 1.82837i | −0.550194 | − | 0.835037i | \(-0.685446\pi\) |
−0.115278 | − | 0.993333i | \(-0.536776\pi\) | |||||||
\(338\) | 1.69350 | + | 4.65286i | 0.0921143 | + | 0.253082i | ||||
\(339\) | −2.10123 | + | 4.97721i | −0.114123 | + | 0.270325i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.345903 | − | 0.599121i | 0.0187317 | − | 0.0324442i | ||||
\(342\) | −6.44391 | − | 1.82053i | −0.348447 | − | 0.0984429i | ||||
\(343\) | 17.1890 | − | 9.92407i | 0.928118 | − | 0.535849i | ||||
\(344\) | −0.537461 | + | 0.450983i | −0.0289780 | + | 0.0243154i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.948013 | − | 5.37645i | 0.0509655 | − | 0.289040i | ||||
\(347\) | 12.4968 | − | 14.8931i | 0.670862 | − | 0.799502i | −0.318039 | − | 0.948078i | \(-0.603024\pi\) |
0.988901 | + | 0.148575i | \(0.0474688\pi\) | |||||||
\(348\) | 0.797906 | − | 0.245651i | 0.0427723 | − | 0.0131683i | ||||
\(349\) | −7.53700 | − | 2.74324i | −0.403446 | − | 0.146842i | 0.132323 | − | 0.991207i | \(-0.457756\pi\) |
−0.535770 | + | 0.844364i | \(0.679978\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.8585 | + | 4.34336i | 0.686337 | + | 0.231832i | ||||
\(352\) | 1.45834i | 0.0777296i | ||||||||
\(353\) | −2.99398 | + | 8.22589i | −0.159354 | + | 0.437820i | −0.993515 | − | 0.113700i | \(-0.963730\pi\) |
0.834162 | + | 0.551520i | \(0.185952\pi\) | |||||||
\(354\) | 5.64713 | − | 6.07959i | 0.300142 | − | 0.323127i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.46361 | + | 13.9718i | −0.130571 | + | 0.740505i | ||||
\(357\) | −1.20624 | − | 0.0608521i | −0.0638409 | − | 0.00322063i | ||||
\(358\) | −9.45292 | − | 11.2656i | −0.499602 | − | 0.595403i | ||||
\(359\) | −4.13896 | − | 7.16888i | −0.218446 | − | 0.378359i | 0.735887 | − | 0.677104i | \(-0.236765\pi\) |
−0.954333 | + | 0.298745i | \(0.903432\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.62260 | − | 9.73862i | 0.295926 | − | 0.512559i | ||||
\(362\) | 8.93990 | − | 1.57635i | 0.469871 | − | 0.0828509i | ||||
\(363\) | 2.34547 | + | 18.7984i | 0.123105 | + | 0.986661i | ||||
\(364\) | −7.91977 | + | 2.88256i | −0.415108 | + | 0.151087i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 16.3201 | − | 2.03625i | 0.853068 | − | 0.106437i | ||||
\(367\) | 14.5750 | − | 2.56997i | 0.760809 | − | 0.134151i | 0.220234 | − | 0.975447i | \(-0.429318\pi\) |
0.540575 | + | 0.841296i | \(0.318207\pi\) | |||||||
\(368\) | −3.23318 | − | 1.86668i | −0.168541 | − | 0.0973074i | ||||
\(369\) | −29.0048 | − | 2.93392i | −1.50993 | − | 0.152734i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.88922 | − | 8.29804i | 0.513423 | − | 0.430813i | ||||
\(372\) | −6.49433 | − | 0.327625i | −0.336715 | − | 0.0169865i | ||||
\(373\) | −25.1455 | − | 4.43383i | −1.30198 | − | 0.229575i | −0.520694 | − | 0.853743i | \(-0.674327\pi\) |
−0.781290 | + | 0.624168i | \(0.785438\pi\) | |||||||
\(374\) | 0.0450623 | + | 0.0378118i | 0.00233012 | + | 0.00195520i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 28.8938 | + | 10.5165i | 1.49008 | + | 0.542346i | ||||
\(377\) | − | 0.927403i | − | 0.0477637i | ||||||
\(378\) | −3.16791 | + | 9.37859i | −0.162940 | + | 0.482383i | ||||
\(379\) | −20.1244 | −1.03372 | −0.516861 | − | 0.856070i | \(-0.672899\pi\) | ||||
−0.516861 | + | 0.856070i | \(0.672899\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.40516 | − | 30.5492i | −0.481841 | − | 1.56508i | ||||
\(382\) | 3.53353 | − | 4.21110i | 0.180791 | − | 0.215459i | ||||
\(383\) | 23.4987 | + | 4.14346i | 1.20073 | + | 0.211721i | 0.738014 | − | 0.674785i | \(-0.235764\pi\) |
0.462716 | + | 0.886507i | \(0.346875\pi\) | |||||||
\(384\) | 13.5806 | − | 6.95312i | 0.693031 | − | 0.354825i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.18070 | + | 14.1694i | 0.416387 | + | 0.721203i | ||||
\(387\) | −0.752659 | − | 0.212640i | −0.0382598 | − | 0.0108091i | ||||
\(388\) | 17.4407 | + | 10.0694i | 0.885418 | + | 0.511196i | ||||
\(389\) | −6.59400 | − | 37.3964i | −0.334329 | − | 1.89607i | −0.433760 | − | 0.901029i | \(-0.642813\pi\) |
0.0994307 | − | 0.995044i | \(-0.468298\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.84428 | + | 0.671264i | −0.0932694 | + | 0.0339473i | ||||
\(392\) | 1.24320 | + | 3.41565i | 0.0627908 | + | 0.172516i | ||||
\(393\) | −19.6487 | + | 14.8667i | −0.991148 | + | 0.749926i | ||||
\(394\) | 0.422524 | + | 2.39625i | 0.0212864 | + | 0.120721i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.842400 | + | 0.573011i | −0.0423322 | + | 0.0287949i | ||||
\(397\) | 17.6230 | − | 10.1747i | 0.884474 | − | 0.510651i | 0.0123433 | − | 0.999924i | \(-0.496071\pi\) |
0.872131 | + | 0.489272i | \(0.162738\pi\) | |||||||
\(398\) | −1.16565 | − | 1.38917i | −0.0584289 | − | 0.0696328i | ||||
\(399\) | 9.62690 | + | 6.22506i | 0.481948 | + | 0.311643i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.32015 | + | 4.46414i | 0.265676 | + | 0.222928i | 0.765887 | − | 0.642975i | \(-0.222300\pi\) |
−0.500212 | + | 0.865903i | \(0.666744\pi\) | |||||||
\(402\) | −0.560563 | + | 2.44990i | −0.0279583 | + | 0.122190i | ||||
\(403\) | −2.47053 | + | 6.78773i | −0.123066 | + | 0.338121i | ||||
\(404\) | 5.43745 | 0.270523 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.676418 | 0.0335701 | ||||||||
\(407\) | 0.598264 | − | 1.64372i | 0.0296548 | − | 0.0814760i | ||||
\(408\) | 0.305015 | − | 1.33305i | 0.0151005 | − | 0.0659958i | ||||
\(409\) | 8.35444 | + | 7.01021i | 0.413101 | + | 0.346633i | 0.825531 | − | 0.564356i | \(-0.190876\pi\) |
−0.412431 | + | 0.910989i | \(0.635320\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −28.6319 | − | 18.5143i | −1.41231 | − | 0.913244i | ||||
\(412\) | 5.16535 | + | 6.15582i | 0.254478 | + | 0.303276i | ||||
\(413\) | −12.3029 | + | 7.10308i | −0.605386 | + | 0.349520i | ||||
\(414\) | 1.18485 | + | 16.0426i | 0.0582322 | + | 0.788449i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.64413 | − | 14.9956i | −0.129639 | − | 0.735220i | ||||
\(417\) | −24.7393 | + | 18.7183i | −1.21149 | + | 0.916640i | ||||
\(418\) | −0.190973 | − | 0.524693i | −0.00934078 | − | 0.0256636i | ||||
\(419\) | −9.46194 | + | 3.44386i | −0.462246 | + | 0.168244i | −0.562637 | − | 0.826704i | \(-0.690213\pi\) |
0.100391 | + | 0.994948i | \(0.467991\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.539623 | − | 3.06035i | −0.0262996 | − | 0.149152i | 0.968830 | − | 0.247726i | \(-0.0796832\pi\) |
−0.995130 | + | 0.0985733i | \(0.968572\pi\) | |||||||
\(422\) | 17.6526 | + | 10.1917i | 0.859315 | + | 0.496126i | ||||
\(423\) | 8.42224 | + | 33.2258i | 0.409504 | + | 1.61550i | ||||
\(424\) | 7.30837 | + | 12.6585i | 0.354926 | + | 0.614750i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.457853 | + | 0.234416i | −0.0221830 | + | 0.0113575i | ||||
\(427\) | −27.7300 | − | 4.88955i | −1.34195 | − | 0.236622i | ||||
\(428\) | 0.225990 | − | 0.269324i | 0.0109236 | − | 0.0130183i | ||||
\(429\) | 0.333004 | + | 1.08164i | 0.0160776 | + | 0.0522221i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.0701 | −1.35209 | −0.676044 | − | 0.736862i | \(-0.736307\pi\) | ||||
−0.676044 | + | 0.736862i | \(0.736307\pi\) | |||||||
\(432\) | 2.54441 | + | 1.39095i | 0.122418 | + | 0.0669219i | ||||
\(433\) | − | 19.5251i | − | 0.938317i | −0.883114 | − | 0.469158i | \(-0.844557\pi\) | ||
0.883114 | − | 0.469158i | \(-0.155443\pi\) | |||||||
\(434\) | −4.95075 | − | 1.80193i | −0.237644 | − | 0.0864952i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.89973 | + | 7.46776i | 0.426220 | + | 0.357641i | ||||
\(437\) | 18.3465 | + | 3.23498i | 0.877631 | + | 0.154750i | ||||
\(438\) | 6.96975 | + | 0.351609i | 0.333028 | + | 0.0168005i | ||||
\(439\) | −11.2069 | + | 9.40371i | −0.534876 | + | 0.448815i | −0.869781 | − | 0.493437i | \(-0.835740\pi\) |
0.334905 | + | 0.942252i | \(0.391296\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.36886 | + | 3.28741i | −0.112803 | + | 0.156543i | ||||
\(442\) | −0.531918 | − | 0.307103i | −0.0253008 | − | 0.0146074i | ||||
\(443\) | 18.0771 | − | 3.18748i | 0.858868 | − | 0.151442i | 0.273165 | − | 0.961967i | \(-0.411930\pi\) |
0.585703 | + | 0.810526i | \(0.300818\pi\) | |||||||
\(444\) | −16.3151 | + | 2.03562i | −0.774278 | + | 0.0966062i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.88572 | + | 1.05032i | −0.136643 | + | 0.0497339i | ||||
\(447\) | 3.49318 | + | 27.9971i | 0.165222 | + | 1.32422i | ||||
\(448\) | 8.32476 | − | 1.46788i | 0.393308 | − | 0.0693508i | ||||
\(449\) | 6.92969 | − | 12.0026i | 0.327032 | − | 0.566437i | −0.654889 | − | 0.755725i | \(-0.727285\pi\) |
0.981922 | + | 0.189288i | \(0.0606180\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.21547 | − | 2.10526i | −0.0572344 | − | 0.0991328i | ||||
\(452\) | 2.72185 | + | 3.24378i | 0.128025 | + | 0.152575i | ||||
\(453\) | −24.6934 | − | 1.24573i | −1.16020 | − | 0.0585294i | ||||
\(454\) | 0.350185 | − | 1.98600i | 0.0164350 | − | 0.0932075i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8.83402 | + | 9.51053i | −0.413691 | + | 0.445372i | ||||
\(457\) | 6.03602 | − | 16.5838i | 0.282353 | − | 0.775758i | −0.714728 | − | 0.699403i | \(-0.753449\pi\) |
0.997081 | − | 0.0763555i | \(-0.0243284\pi\) | |||||||
\(458\) | − | 12.7760i | − | 0.596985i | ||||||
\(459\) | 1.41995 | − | 0.554644i | 0.0662776 | − | 0.0258886i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.0919 | − | 8.76872i | −1.12207 | − | 0.408400i | −0.286663 | − | 0.958032i | \(-0.592546\pi\) |
−0.835407 | + | 0.549631i | \(0.814768\pi\) | |||||||
\(462\) | −0.788913 | + | 0.242882i | −0.0367036 | + | 0.0112999i | ||||
\(463\) | 11.7935 | − | 14.0549i | 0.548090 | − | 0.653189i | −0.418891 | − | 0.908037i | \(-0.637581\pi\) |
0.966981 | + | 0.254848i | \(0.0820255\pi\) | |||||||
\(464\) | 0.0344074 | − | 0.195134i | 0.00159732 | − | 0.00905888i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −17.2709 | + | 14.4920i | −0.800059 | + | 0.671329i | ||||
\(467\) | −14.0832 | + | 8.13092i | −0.651692 | + | 0.376254i | −0.789104 | − | 0.614260i | \(-0.789455\pi\) |
0.137412 | + | 0.990514i | \(0.456121\pi\) | |||||||
\(468\) | 7.62319 | − | 7.41945i | 0.352382 | − | 0.342964i | ||||
\(469\) | 2.15139 | − | 3.72632i | 0.0993421 | − | 0.172066i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.514232 | + | 1.21807i | −0.0236946 | + | 0.0561257i | ||||
\(472\) | −5.50137 | − | 15.1149i | −0.253221 | − | 0.695719i | ||||
\(473\) | −0.0223059 | − | 0.0612849i | −0.00102563 | − | 0.00281788i | ||||
\(474\) | −0.672489 | − | 0.888803i | −0.0308884 | − | 0.0408241i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.473317 | + | 0.819809i | −0.0216944 | + | 0.0375759i | ||||
\(477\) | −7.08555 | + | 14.6729i | −0.324425 | + | 0.671824i | ||||
\(478\) | −10.2079 | + | 5.89354i | −0.466899 | + | 0.269564i | ||||
\(479\) | 7.25575 | − | 6.08830i | 0.331524 | − | 0.278181i | −0.461797 | − | 0.886986i | \(-0.652795\pi\) |
0.793320 | + | 0.608804i | \(0.208351\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.17151 | + | 17.9865i | −0.144608 | + | 0.820114i | ||||
\(482\) | 4.34990 | − | 5.18401i | 0.198133 | − | 0.236125i | ||||
\(483\) | 6.14284 | − | 26.8469i | 0.279509 | − | 1.22158i | ||||
\(484\) | 13.9527 | + | 5.07836i | 0.634213 | + | 0.230835i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.21058 | − | 12.4358i | −0.0549129 | − | 0.564099i | ||||
\(487\) | − | 0.467564i | − | 0.0211874i | −0.999944 | − | 0.0105937i | \(-0.996628\pi\) | ||
0.999944 | − | 0.0105937i | \(-0.00337214\pi\) | |||||||
\(488\) | 10.9042 | − | 29.9590i | 0.493608 | − | 1.35618i | ||||
\(489\) | 8.65877 | + | 1.98121i | 0.391563 | + | 0.0895936i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.34936 | − | 24.6665i | 0.196284 | − | 1.11318i | −0.714294 | − | 0.699846i | \(-0.753252\pi\) |
0.910578 | − | 0.413337i | \(-0.135637\pi\) | |||||||
\(492\) | −12.4073 | + | 19.1875i | −0.559363 | + | 0.865040i | ||||
\(493\) | −0.0669563 | − | 0.0797954i | −0.00301556 | − | 0.00359380i | ||||
\(494\) | 2.91504 | + | 5.04899i | 0.131154 | + | 0.227165i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.771653 | + | 1.33654i | −0.0346482 | + | 0.0600125i | ||||
\(497\) | 0.867261 | − | 0.152922i | 0.0389020 | − | 0.00685947i | ||||
\(498\) | −3.05078 | + | 2.30829i | −0.136709 | + | 0.103437i | ||||
\(499\) | −13.1878 | + | 4.79996i | −0.590367 | + | 0.214876i | −0.619891 | − | 0.784688i | \(-0.712823\pi\) |
0.0295240 | + | 0.999564i | \(0.490601\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.99623 | + | 14.2034i | −0.267892 | + | 0.634559i | ||||
\(502\) | −18.3291 | + | 3.23191i | −0.818068 | + | 0.144247i | ||||
\(503\) | 24.5186 | + | 14.1558i | 1.09323 | + | 0.631176i | 0.934434 | − | 0.356136i | \(-0.115906\pi\) |
0.158794 | + | 0.987312i | \(0.449239\pi\) | |||||||
\(504\) | 13.3839 | + | 13.7515i | 0.596168 | + | 0.612539i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.02755 | + | 0.862218i | −0.0456803 | + | 0.0383303i | ||||
\(507\) | 4.87624 | + | 9.52410i | 0.216562 | + | 0.422980i | ||||
\(508\) | −24.6724 | − | 4.35041i | −1.09466 | − | 0.193018i | ||||
\(509\) | 21.9759 | + | 18.4399i | 0.974063 | + | 0.817336i | 0.983183 | − | 0.182622i | \(-0.0584586\pi\) |
−0.00912008 | + | 0.999958i | \(0.502903\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.2273 | − | 4.08640i | −0.496666 | − | 0.180772i | ||||
\(512\) | − | 6.25700i | − | 0.276523i | ||||||
\(513\) | −14.3048 | − | 2.17975i | −0.631574 | − | 0.0962382i | ||||
\(514\) | 5.50264 | 0.242711 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.417197 | + | 0.449146i | −0.0183661 | + | 0.0197725i | ||||
\(517\) | −1.83722 | + | 2.18951i | −0.0808008 | + | 0.0962946i | ||||
\(518\) | −13.1188 | − | 2.31319i | −0.576406 | − | 0.101636i | ||||
\(519\) | 0.594397 | − | 11.7824i | 0.0260911 | − | 0.517191i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.4548 | + | 21.5724i | 0.545655 | + | 0.945102i | 0.998565 | + | 0.0535462i | \(0.0170525\pi\) |
−0.452910 | + | 0.891556i | \(0.649614\pi\) | |||||||
\(522\) | −0.778588 | + | 0.350304i | −0.0340779 | + | 0.0153324i | ||||
\(523\) | −22.3995 | − | 12.9324i | −0.979464 | − | 0.565494i | −0.0773554 | − | 0.997004i | \(-0.524648\pi\) |
−0.902108 | + | 0.431510i | \(0.857981\pi\) | |||||||
\(524\) | 3.35347 | + | 19.0185i | 0.146497 | + | 0.830826i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.52540 | − | 0.919169i | 0.110113 | − | 0.0400777i | ||||
\(527\) | 0.277489 | + | 0.762395i | 0.0120876 | + | 0.0332104i | ||||
\(528\) | 0.0299374 | + | 0.239942i | 0.00130286 | + | 0.0104421i | ||||
\(529\) | −3.77754 | − | 21.4235i | −0.164241 | − | 0.931456i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.4827 | − | 14.5474i | 0.454908 | − | 0.631303i | ||||
\(532\) | 7.78166 | − | 4.49274i | 0.337378 | − | 0.194785i | ||||
\(533\) | 16.3154 | + | 19.4439i | 0.706698 | + | 0.842209i | ||||
\(534\) | 0.730992 | − | 14.4901i | 0.0316331 | − | 0.627047i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.73204 | + | 3.13155i | 0.161200 | + | 0.135262i | ||||
\(537\) | −23.2841 | − | 21.6278i | −1.00478 | − | 0.933308i | ||||
\(538\) | 3.49296 | − | 9.59683i | 0.150592 | − | 0.413749i | ||||
\(539\) | −0.337880 | −0.0145535 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.9158 | −0.942232 | −0.471116 | − | 0.882071i | \(-0.656149\pi\) | ||||
−0.471116 | + | 0.882071i | \(0.656149\pi\) | |||||||
\(542\) | 6.45777 | − | 17.7426i | 0.277385 | − | 0.762109i | ||||
\(543\) | 18.7482 | − | 5.77200i | 0.804562 | − | 0.247700i | ||||
\(544\) | −1.31015 | − | 1.09935i | −0.0561723 | − | 0.0471342i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 7.67176 | − | 3.92787i | 0.328321 | − | 0.168097i | ||||
\(547\) | −6.41248 | − | 7.64210i | −0.274178 | − | 0.326752i | 0.611331 | − | 0.791375i | \(-0.290634\pi\) |
−0.885509 | + | 0.464623i | \(0.846190\pi\) | |||||||
\(548\) | −23.1439 | + | 13.3621i | −0.988658 | + | 0.570802i | ||||
\(549\) | 34.4507 | − | 8.73273i | 1.47032 | − | 0.372704i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.171694 | + | 0.973722i | 0.00731439 | + | 0.0414820i | ||||
\(552\) | 28.7278 | + | 12.1280i | 1.22274 | + | 0.516203i | ||||
\(553\) | 0.652634 | + | 1.79310i | 0.0277528 | + | 0.0762502i | ||||
\(554\) | −3.14925 | + | 1.14623i | −0.133799 | + | 0.0486987i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.22227 | + | 23.9457i | 0.179064 | + | 1.01552i | ||||
\(557\) | 16.0500 | + | 9.26650i | 0.680062 | + | 0.392634i | 0.799879 | − | 0.600162i | \(-0.204897\pi\) |
−0.119816 | + | 0.992796i | \(0.538231\pi\) | |||||||
\(558\) | 6.63172 | − | 0.489797i | 0.280743 | − | 0.0207348i | ||||
\(559\) | 0.340480 | + | 0.589729i | 0.0144008 | + | 0.0249429i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.106744 | + | 0.0690241i | 0.00450674 | + | 0.00291420i | ||||
\(562\) | 17.0784 | + | 3.01138i | 0.720408 | + | 0.127027i | ||||
\(563\) | 28.0789 | − | 33.4632i | 1.18339 | − | 1.41031i | 0.292388 | − | 0.956300i | \(-0.405550\pi\) |
0.890999 | − | 0.454005i | \(-0.150005\pi\) | |||||||
\(564\) | 26.1887 | + | 5.99225i | 1.10274 | + | 0.252319i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.18985 | −0.176113 | ||||||||
\(567\) | −4.28380 | + | 20.9582i | −0.179903 | + | 0.880161i | ||||
\(568\) | 0.997105i | 0.0418376i | ||||||||
\(569\) | 12.7485 | + | 4.64008i | 0.534446 | + | 0.194522i | 0.595122 | − | 0.803635i | \(-0.297104\pi\) |
−0.0606766 | + | 0.998157i | \(0.519326\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.1926 | + | 15.2654i | 0.761335 | + | 0.638836i | 0.938474 | − | 0.345350i | \(-0.112240\pi\) |
−0.177139 | + | 0.984186i | \(0.556684\pi\) | |||||||
\(572\) | 0.873565 | + | 0.154033i | 0.0365256 | + | 0.00644044i | ||||
\(573\) | 6.45034 | − | 9.97529i | 0.269467 | − | 0.416724i | ||||
\(574\) | −14.1818 | + | 11.8999i | −0.591935 | + | 0.496693i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −8.82200 | + | 6.00083i | −0.367583 | + | 0.250034i | ||||
\(577\) | 7.03128 | + | 4.05951i | 0.292716 | + | 0.169000i | 0.639166 | − | 0.769069i | \(-0.279280\pi\) |
−0.346450 | + | 0.938068i | \(0.612613\pi\) | |||||||
\(578\) | 13.3510 | − | 2.35414i | 0.555329 | − | 0.0979194i | ||||
\(579\) | 21.3329 | + | 28.1949i | 0.886566 | + | 1.17174i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.15473 | − | 2.24014i | 0.255341 | − | 0.0929366i | ||||
\(582\) | −18.9732 | − | 8.00990i | −0.786464 | − | 0.332021i | ||||
\(583\) | −1.33806 | + | 0.235937i | −0.0554169 | + | 0.00977150i | ||||
\(584\) | 6.76397 | − | 11.7155i | 0.279895 | − | 0.484793i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.46156 | − | 4.26354i | −0.101686 | − | 0.176125i | ||||
\(587\) | −2.37317 | − | 2.82823i | −0.0979511 | − | 0.116734i | 0.714842 | − | 0.699286i | \(-0.246499\pi\) |
−0.812793 | + | 0.582552i | \(0.802054\pi\) | |||||||
\(588\) | 1.44735 | + | 2.82691i | 0.0596877 | + | 0.116580i | ||||
\(589\) | 1.33729 | − | 7.58412i | 0.0551019 | − | 0.312498i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.54713 | + | 5.02527i | 0.0636403 | + | 0.206712i | ||||
\(592\) | −1.33463 | + | 3.66686i | −0.0548529 | + | 0.150707i | ||||
\(593\) | − | 29.4590i | − | 1.20974i | −0.796325 | − | 0.604869i | \(-0.793226\pi\) | ||
0.796325 | − | 0.604869i | \(-0.206774\pi\) | |||||||
\(594\) | 0.782291 | − | 0.688131i | 0.0320978 | − | 0.0282344i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 20.7802 | + | 7.56338i | 0.851190 | + | 0.309808i | ||||
\(597\) | −2.87119 | − | 2.66695i | −0.117510 | − | 0.109151i | ||||
\(598\) | 9.00268 | − | 10.7290i | 0.368147 | − | 0.438740i | ||||
\(599\) | 3.79862 | − | 21.5431i | 0.155207 | − | 0.880225i | −0.803388 | − | 0.595455i | \(-0.796972\pi\) |
0.958596 | − | 0.284770i | \(-0.0919172\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.9764 | − | 23.4750i | 1.14118 | − | 0.957566i | 0.141706 | − | 0.989909i | \(-0.454741\pi\) |
0.999477 | + | 0.0323424i | \(0.0102967\pi\) | |||||||
\(602\) | −0.430130 | + | 0.248335i | −0.0175308 | + | 0.0101214i | ||||
\(603\) | −0.546563 | + | 5.40333i | −0.0222578 | + | 0.220041i | ||||
\(604\) | −9.68946 | + | 16.7826i | −0.394258 | + | 0.682876i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −5.51775 | + | 0.688447i | −0.224143 | + | 0.0279662i | ||||
\(607\) | 2.25077 | + | 6.18395i | 0.0913561 | + | 0.250999i | 0.976953 | − | 0.213457i | \(-0.0684722\pi\) |
−0.885596 | + | 0.464456i | \(0.846250\pi\) | |||||||
\(608\) | 5.55238 | + | 15.2550i | 0.225179 | + | 0.618674i | ||||
\(609\) | 1.45045 | − | 0.180972i | 0.0587753 | − | 0.00733335i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.9217 | − | 25.8451i | 0.603667 | − | 1.04558i | ||||
\(612\) | 0.120247 | − | 1.18876i | 0.00486068 | − | 0.0480527i | ||||
\(613\) | 6.19093 | − | 3.57434i | 0.250049 | − | 0.144366i | −0.369737 | − | 0.929136i | \(-0.620552\pi\) |
0.619787 | + | 0.784770i | \(0.287219\pi\) | |||||||
\(614\) | 11.6685 | − | 9.79101i | 0.470901 | − | 0.395133i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.277860 | + | 1.57582i | −0.0111953 | + | 0.0634917i | ||||
\(617\) | −10.6301 | + | 12.6684i | −0.427951 | + | 0.510012i | −0.936330 | − | 0.351121i | \(-0.885800\pi\) |
0.508379 | + | 0.861133i | \(0.330245\pi\) | |||||||
\(618\) | −6.02103 | − | 5.59274i | −0.242202 | − | 0.224973i | ||||
\(619\) | −1.40893 | − | 0.512808i | −0.0566296 | − | 0.0206115i | 0.313550 | − | 0.949572i | \(-0.398482\pi\) |
−0.370180 | + | 0.928960i | \(0.620704\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.83279 | + | 34.0833i | 0.274190 | + | 1.36772i | ||||
\(622\) | 17.2704i | 0.692481i | ||||||||
\(623\) | −8.49561 | + | 23.3415i | −0.340369 | + | 0.935157i | ||||
\(624\) | −0.742878 | − | 2.41296i | −0.0297389 | − | 0.0965958i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0.530793 | − | 3.01028i | 0.0212148 | − | 0.120315i | ||||
\(627\) | −0.549884 | − | 1.07401i | −0.0219602 | − | 0.0428919i | ||||
\(628\) | 0.666118 | + | 0.793848i | 0.0265810 | + | 0.0316780i | ||||
\(629\) | 1.02570 | + | 1.77657i | 0.0408974 | + | 0.0708363i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.9456 | − | 31.0827i | 0.714404 | − | 1.23738i | −0.248785 | − | 0.968559i | \(-0.580031\pi\) |
0.963189 | − | 0.268826i | \(-0.0866356\pi\) | |||||||
\(632\) | −2.12771 | + | 0.375172i | −0.0846356 | + | 0.0149235i | ||||
\(633\) | 40.5795 | + | 17.1314i | 1.61289 | + | 0.680913i | ||||
\(634\) | −3.20443 | + | 1.16632i | −0.127264 | + | 0.0463204i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 7.70574 | + | 10.1844i | 0.305553 | + | 0.403837i | ||||
\(637\) | 3.47431 | − | 0.612614i | 0.137657 | − | 0.0242727i | ||||
\(638\) | −0.0616542 | − | 0.0355961i | −0.00244091 | − | 0.00140926i | ||||
\(639\) | −0.919063 | + | 0.625157i | −0.0363576 | + | 0.0247308i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.0504 | − | 25.2152i | 1.18692 | − | 0.995942i | 0.187010 | − | 0.982358i | \(-0.440120\pi\) |
0.999908 | − | 0.0135840i | \(-0.00432406\pi\) | |||||||
\(642\) | −0.195227 | + | 0.301914i | −0.00770501 | + | 0.0119156i | ||||
\(643\) | 10.2602 | + | 1.80915i | 0.404624 | + | 0.0713461i | 0.372256 | − | 0.928130i | \(-0.378584\pi\) |
0.0323674 | + | 0.999476i | \(0.489695\pi\) | |||||||
\(644\) | −16.5358 | − | 13.8752i | −0.651603 | − | 0.546760i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.615340 | + | 0.223965i | 0.0242102 | + | 0.00881180i | ||||
\(647\) | − | 39.1517i | − | 1.53921i | −0.638519 | − | 0.769606i | \(-0.720453\pi\) | ||
0.638519 | − | 0.769606i | \(-0.279547\pi\) | |||||||
\(648\) | −22.5271 | − | 8.89730i | −0.884950 | − | 0.349519i | ||||
\(649\) | 1.49518 | 0.0586910 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.0981 | − | 2.53935i | −0.434967 | − | 0.0995248i | ||||
\(652\) | 4.47509 | − | 5.33320i | 0.175258 | − | 0.208864i | ||||
\(653\) | −32.4099 | − | 5.71474i | −1.26830 | − | 0.223635i | −0.501294 | − | 0.865277i | \(-0.667142\pi\) |
−0.767004 | + | 0.641642i | \(0.778253\pi\) | |||||||
\(654\) | −9.97668 | − | 6.45124i | −0.390119 | − | 0.252263i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.71152 | + | 4.69649i | 0.105867 | + | 0.183367i | ||||
\(657\) | 15.0394 | − | 1.11076i | 0.586743 | − | 0.0433349i | ||||
\(658\) | 18.8506 | + | 10.8834i | 0.734873 | + | 0.424279i | ||||
\(659\) | 3.74532 | + | 21.2407i | 0.145897 | + | 0.827422i | 0.966643 | + | 0.256128i | \(0.0824470\pi\) |
−0.820746 | + | 0.571293i | \(0.806442\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.7105 | + | 8.99389i | −0.961127 | + | 0.349822i | −0.774475 | − | 0.632604i | \(-0.781986\pi\) |
−0.186652 | + | 0.982426i | \(0.559764\pi\) | |||||||
\(662\) | −3.91848 | − | 10.7659i | −0.152296 | − | 0.418430i | ||||
\(663\) | −1.22276 | − | 0.516213i | −0.0474882 | − | 0.0200481i | ||||
\(664\) | 1.28776 | + | 7.30326i | 0.0499749 | + | 0.283422i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 16.2983 | − | 4.13136i | 0.631545 | − | 0.160087i | ||||
\(667\) | 2.05705 | − | 1.18764i | 0.0796493 | − | 0.0459855i | ||||
\(668\) | 7.76729 | + | 9.25670i | 0.300526 | + | 0.358152i | ||||
\(669\) | −5.90688 | + | 3.02427i | −0.228373 | + | 0.116925i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.27023 | + | 1.90495i | 0.0876412 | + | 0.0735397i | ||||
\(672\) | 22.9370 | − | 7.06161i | 0.884815 | − | 0.272408i | ||||
\(673\) | −3.94080 | + | 10.8272i | −0.151907 | + | 0.417360i | −0.992182 | − | 0.124800i | \(-0.960171\pi\) |
0.840275 | + | 0.542160i | \(0.182393\pi\) | |||||||
\(674\) | 28.6293 | 1.10276 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.38635 | 0.322552 | ||||||||
\(677\) | −11.6030 | + | 31.8791i | −0.445941 | + | 1.22521i | 0.489585 | + | 0.871955i | \(0.337148\pi\) |
−0.935526 | + | 0.353257i | \(0.885074\pi\) | |||||||
\(678\) | −3.17275 | − | 2.94707i | −0.121849 | − | 0.113181i | ||||
\(679\) | 27.0103 | + | 22.6643i | 1.03656 | + | 0.869776i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.219563 | − | 4.35229i | 0.00841369 | − | 0.166780i | ||||
\(682\) | 0.356426 | + | 0.424772i | 0.0136483 | + | 0.0162654i | ||||
\(683\) | −31.8310 | + | 18.3777i | −1.21798 | + | 0.703201i | −0.964486 | − | 0.264135i | \(-0.914913\pi\) |
−0.253495 | + | 0.967337i | \(0.581580\pi\) | |||||||
\(684\) | −6.63034 | + | 9.20132i | −0.253518 | + | 0.351821i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.76254 | + | 15.6671i | 0.105474 | + | 0.598174i | ||||
\(687\) | −3.41816 | − | 27.3958i | −0.130411 | − | 1.04522i | ||||
\(688\) | 0.0497608 | + | 0.136717i | 0.00189711 | + | 0.00521227i | ||||
\(689\) | 13.3311 | − | 4.85212i | 0.507874 | − | 0.184851i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.32309 | + | 13.1749i | 0.0883744 | + | 0.501196i | 0.996577 | + | 0.0826660i | \(0.0263435\pi\) |
−0.908203 | + | 0.418530i | \(0.862545\pi\) | |||||||
\(692\) | −8.00781 | − | 4.62331i | −0.304411 | − | 0.175752i | ||||
\(693\) | −1.62670 | + | 0.731885i | −0.0617930 | + | 0.0278020i | ||||
\(694\) | 7.79146 | + | 13.4952i | 0.295760 | + | 0.512271i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.0833854 | + | 1.65291i | −0.00316072 | + | 0.0626532i | ||||
\(697\) | 2.80761 | + | 0.495057i | 0.106346 | + | 0.0187516i | ||||
\(698\) | 4.13236 | − | 4.92475i | 0.156412 | − | 0.186405i | ||||
\(699\) | −33.1570 | + | 35.6961i | −1.25411 | + | 1.35015i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.00452 | 0.189018 | 0.0945091 | − | 0.995524i | \(-0.469872\pi\) | ||||
0.0945091 | + | 0.995524i | \(0.469872\pi\) | |||||||
\(702\) | −6.79639 | + | 8.49421i | −0.256513 | + | 0.320593i | ||||
\(703\) | − | 19.4720i | − | 0.734400i | ||||||
\(704\) | −0.836033 | − | 0.304291i | −0.0315092 | − | 0.0114684i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.37489 | − | 4.51007i | −0.202287 | − | 0.169739i | ||||
\(707\) | 9.37537 | + | 1.65313i | 0.352597 | + | 0.0621724i | ||||
\(708\) | −6.40479 | − | 12.5096i | −0.240707 | − | 0.470139i | ||||
\(709\) | −13.1330 | + | 11.0199i | −0.493218 | + | 0.413859i | −0.855178 | − | 0.518334i | \(-0.826552\pi\) |
0.361960 | + | 0.932194i | \(0.382108\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.67982 | − | 1.72595i | −0.0629982 | − | 0.0647282i | ||||
\(712\) | −24.3566 | − | 14.0623i | −0.912800 | − | 0.527006i | ||||
\(713\) | −18.2195 | + | 3.21258i | −0.682324 | + | 0.120312i | ||||
\(714\) | 0.376509 | − | 0.891844i | 0.0140905 | − | 0.0333764i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −23.4058 | + | 8.51902i | −0.874716 | + | 0.318371i | ||||
\(717\) | −20.3122 | + | 15.3687i | −0.758572 | + | 0.573954i | ||||
\(718\) | 6.53417 | − | 1.15215i | 0.243853 | − | 0.0429979i | ||||
\(719\) | −21.6760 | + | 37.5439i | −0.808377 | + | 1.40015i | 0.105610 | + | 0.994408i | \(0.466320\pi\) |
−0.913987 | + | 0.405742i | \(0.867013\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.03467 | + | 12.1844i | 0.261985 | + | 0.453771i | ||||
\(722\) | 5.79365 | + | 6.90461i | 0.215617 | + | 0.256963i | ||||
\(723\) | 7.94060 | − | 12.2799i | 0.295314 | − | 0.456696i | ||||
\(724\) | 2.66987 | − | 15.1416i | 0.0992251 | − | 0.562733i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −14.8017 | − | 3.38679i | −0.549344 | − | 0.125695i | ||||
\(727\) | −12.4303 | + | 34.1521i | −0.461016 | + | 1.26663i | 0.463706 | + | 0.885989i | \(0.346519\pi\) |
−0.924722 | + | 0.380642i | \(0.875703\pi\) | |||||||
\(728\) | − | 16.7075i | − | 0.619220i | ||||||
\(729\) | −5.92298 | − | 26.3423i | −0.219370 | − | 0.975642i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.0718726 | + | 0.0261595i | 0.00265830 | + | 0.000967544i | ||||
\(732\) | 6.21315 | − | 27.1542i | 0.229645 | − | 1.00365i | ||||
\(733\) | 2.49119 | − | 2.96889i | 0.0920143 | − | 0.109658i | −0.718073 | − | 0.695968i | \(-0.754975\pi\) |
0.810087 | + | 0.586310i | \(0.199420\pi\) | |||||||
\(734\) | −2.05990 | + | 11.6823i | −0.0760322 | + | 0.431200i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 29.8753 | − | 25.0683i | 1.10122 | − | 0.924031i | ||||
\(737\) | −0.392191 | + | 0.226432i | −0.0144465 | + | 0.00834071i | ||||
\(738\) | 10.1611 | − | 21.0418i | 0.374036 | − | 0.774559i | ||||
\(739\) | 13.2241 | − | 22.9048i | 0.486456 | − | 0.842567i | −0.513422 | − | 0.858136i | \(-0.671623\pi\) |
0.999879 | + | 0.0155689i | \(0.00495594\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.60158 | + | 10.0467i | 0.279251 | + | 0.369075i | ||||
\(742\) | 3.53898 | + | 9.72326i | 0.129920 | + | 0.356952i | ||||
\(743\) | −4.60474 | − | 12.6514i | −0.168932 | − | 0.464136i | 0.826120 | − | 0.563494i | \(-0.190543\pi\) |
−0.995052 | + | 0.0993584i | \(0.968321\pi\) | |||||||
\(744\) | 5.01352 | − | 11.8756i | 0.183805 | − | 0.435381i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 10.2329 | − | 17.7238i | 0.374651 | − | 0.648915i | ||||
\(747\) | −5.92425 | + | 5.76591i | −0.216757 | + | 0.210964i | ||||
\(748\) | 0.0862839 | − | 0.0498160i | 0.00315485 | − | 0.00182145i | ||||
\(749\) | 0.471538 | − | 0.395667i | 0.0172296 | − | 0.0144574i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.654359 | − | 3.71106i | 0.0238779 | − | 0.135418i | −0.970538 | − | 0.240946i | \(-0.922542\pi\) |
0.994416 | + | 0.105528i | \(0.0336533\pi\) | |||||||
\(752\) | 4.09854 | − | 4.88444i | 0.149458 | − | 0.178117i | ||||
\(753\) | −38.4386 | + | 11.8341i | −1.40078 | + | 0.431258i | ||||
\(754\) | 0.698510 | + | 0.254237i | 0.0254382 | + | 0.00925876i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 13.0915 | + | 10.4748i | 0.476135 | + | 0.380965i | ||||
\(757\) | − | 33.7073i | − | 1.22511i | −0.790427 | − | 0.612556i | \(-0.790141\pi\) | ||
0.790427 | − | 0.612556i | \(-0.209859\pi\) | |||||||
\(758\) | 5.51687 | − | 15.1575i | 0.200382 | − | 0.550544i | ||||
\(759\) | −1.97271 | + | 2.12378i | −0.0716049 | + | 0.0770884i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.67665 | + | 9.50874i | −0.0607784 | + | 0.344692i | 0.939221 | + | 0.343314i | \(0.111550\pi\) |
−0.999999 | + | 0.00137744i | \(0.999562\pi\) | |||||||
\(762\) | 25.5876 | + | 1.29084i | 0.926941 | + | 0.0467621i | ||||
\(763\) | 13.0747 | + | 15.5818i | 0.473336 | + | 0.564100i | ||||
\(764\) | −4.65533 | − | 8.06327i | −0.168424 | − | 0.291719i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.56272 | + | 16.5631i | −0.345515 | + | 0.598450i | ||||
\(767\) | −15.3745 | + | 2.71093i | −0.555139 | + | 0.0978861i | ||||
\(768\) | 3.03939 | + | 24.3601i | 0.109675 | + | 0.879019i | ||||
\(769\) | 36.3764 | − | 13.2399i | 1.31177 | − | 0.477445i | 0.410957 | − | 0.911655i | \(-0.365195\pi\) |
0.900812 | + | 0.434210i | \(0.142973\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.7994 | − | 1.47220i | 0.424944 | − | 0.0530200i | ||||
\(772\) | 27.2905 | − | 4.81205i | 0.982206 | − | 0.173189i | ||||
\(773\) | 21.0478 | + | 12.1519i | 0.757036 | + | 0.437075i | 0.828231 | − | 0.560387i | \(-0.189348\pi\) |
−0.0711944 | + | 0.997462i | \(0.522681\pi\) | |||||||
\(774\) | 0.366491 | − | 0.508601i | 0.0131732 | − | 0.0182813i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −30.5824 | + | 25.6617i | −1.09784 | + | 0.921200i | ||||
\(777\) | −28.7496 | − | 1.45036i | −1.03139 | − | 0.0520312i | ||||
\(778\) | 29.9742 | + | 5.28527i | 1.07463 | + | 0.189486i | ||||
\(779\) | −20.7300 | − | 17.3945i | −0.742728 | − | 0.623223i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.0870967 | − | 0.0317006i | −0.00311656 | − | 0.00113434i | ||||
\(782\) | − | 1.57311i | − | 0.0562544i | ||||||
\(783\) | −1.57581 | + | 0.959467i | −0.0563150 | + | 0.0342886i | ||||
\(784\) | 0.753755 | 0.0269198 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −5.81096 | − | 18.8748i | −0.207270 | − | 0.673240i | ||||
\(787\) | −13.4604 | + | 16.0414i | −0.479810 | + | 0.571816i | −0.950596 | − | 0.310432i | \(-0.899526\pi\) |
0.470785 | + | 0.882248i | \(0.343971\pi\) | |||||||
\(788\) | 4.05856 | + | 0.715633i | 0.144580 | + | 0.0254934i | ||||
\(789\) | 5.16932 | − | 2.64664i | 0.184033 | − | 0.0942229i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.70688 | + | 6.42051i | 0.131802 | + | 0.228287i | ||||
\(792\) | −0.496258 | − | 1.95774i | −0.0176338 | − | 0.0695654i | ||||
\(793\) | −26.7979 | − | 15.4718i | −0.951621 | − | 0.549419i | ||||
\(794\) | 2.83229 | + | 16.0627i | 0.100514 | + | 0.570045i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.88620 | + | 1.05049i | −0.102299 | + | 0.0372337i | ||||
\(797\) | −4.08261 | − | 11.2169i | −0.144614 | − | 0.397322i | 0.846146 | − | 0.532951i | \(-0.178917\pi\) |
−0.990760 | + | 0.135628i | \(0.956695\pi\) | |||||||
\(798\) | −7.32775 | + | 5.54435i | −0.259400 | + | 0.196268i | ||||
\(799\) | −0.582068 | − | 3.30107i | −0.0205921 | − | 0.116783i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.30926 | − | 31.2668i | −0.0815939 | − | 1.10476i | ||||
\(802\) | −4.82080 | + | 2.78329i | −0.170228 | + | 0.0982814i | ||||
\(803\) | 0.808303 | + | 0.963297i | 0.0285244 | + | 0.0339940i | ||||
\(804\) | 3.57446 | + | 2.31136i | 0.126062 | + | 0.0815154i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.43518 | − | 3.72155i | −0.156222 | − | 0.131086i | ||||
\(807\) | 4.92242 | − | 21.5131i | 0.173277 | − | 0.757298i | ||||
\(808\) | −3.68664 | + | 10.1290i | −0.129696 | + | 0.356336i | ||||
\(809\) | −8.60808 | −0.302644 | −0.151322 | − | 0.988485i | \(-0.548353\pi\) | ||||
−0.151322 | + | 0.988485i | \(0.548353\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.53770 | 0.0539958 | 0.0269979 | − | 0.999635i | \(-0.491405\pi\) | ||||
0.0269979 | + | 0.999635i | \(0.491405\pi\) | |||||||
\(812\) | 0.391837 | − | 1.07656i | 0.0137508 | − | 0.0377800i | ||||
\(813\) | 9.10055 | − | 39.7734i | 0.319170 | − | 1.39491i | ||||
\(814\) | 1.07402 | + | 0.901211i | 0.0376444 | + | 0.0315874i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.238129 | − | 0.153982i | −0.00833617 | − | 0.00539043i | ||||
\(817\) | −0.466665 | − | 0.556149i | −0.0163265 | − | 0.0194572i | ||||
\(818\) | −7.57029 | + | 4.37071i | −0.264689 | + | 0.152818i | ||||
\(819\) | 15.3998 | − | 10.4751i | 0.538112 | − | 0.366030i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.03168 | + | 28.5361i | 0.175607 | + | 0.995915i | 0.937441 | + | 0.348144i | \(0.113188\pi\) |
−0.761835 | + | 0.647772i | \(0.775701\pi\) | |||||||
\(822\) | 21.7939 | − | 16.4898i | 0.760149 | − | 0.575147i | ||||
\(823\) | −3.85004 | − | 10.5779i | −0.134204 | − | 0.368722i | 0.854328 | − | 0.519734i | \(-0.173969\pi\) |
−0.988532 | + | 0.151012i | \(0.951747\pi\) | |||||||
\(824\) | −14.9693 | + | 5.44838i | −0.521481 | + | 0.189803i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.97727 | − | 11.2136i | −0.0687979 | − | 0.390172i | ||||
\(827\) | −26.7844 | − | 15.4640i | −0.931383 | − | 0.537734i | −0.0441346 | − | 0.999026i | \(-0.514053\pi\) |
−0.887249 | + | 0.461291i | \(0.847386\pi\) | |||||||
\(828\) | 26.2192 | + | 7.40742i | 0.911180 | + | 0.257426i | ||||
\(829\) | −4.91762 | − | 8.51757i | −0.170796 | − | 0.295827i | 0.767902 | − | 0.640567i | \(-0.221301\pi\) |
−0.938698 | + | 0.344739i | \(0.887967\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.44630 | + | 3.30044i | −0.223620 | + | 0.114491i | ||||
\(832\) | 9.14836 | + | 1.61310i | 0.317162 | + | 0.0559243i | ||||
\(833\) | 0.254706 | − | 0.303547i | 0.00882505 | − | 0.0105173i | ||||
\(834\) | −7.31644 | − | 23.7648i | −0.253348 | − | 0.822906i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.945711 | −0.0327081 | ||||||||
\(837\) | 14.0894 | − | 2.82456i | 0.487003 | − | 0.0976310i | ||||
\(838\) | − | 8.07072i | − | 0.278798i | ||||||
\(839\) | −12.3506 | − | 4.49524i | −0.426389 | − | 0.155193i | 0.119907 | − | 0.992785i | \(-0.461740\pi\) |
−0.546296 | + | 0.837592i | \(0.683963\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.1187 | − | 18.5598i | −0.762714 | − | 0.639993i | ||||
\(842\) | 2.45296 | + | 0.432522i | 0.0845344 | + | 0.0149057i | ||||
\(843\) | 37.4271 | + | 1.88811i | 1.28906 | + | 0.0650301i | ||||
\(844\) | 26.4467 | − | 22.1914i | 0.910333 | − | 0.763860i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −27.3342 | − | 2.76494i | −0.939769 | − | 0.0950604i | ||||
\(847\) | 22.5136 | + | 12.9982i | 0.773575 | + | 0.446624i | ||||
\(848\) | 2.98500 | − | 0.526336i | 0.102505 | − | 0.0180745i | ||||
\(849\) | −8.98435 | + | 1.12097i | −0.308342 | + | 0.0384717i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −43.9569 | + | 15.9990i | −1.50682 | + | 0.548438i | ||||
\(852\) | 0.107863 | + | 0.864497i | 0.00369531 | + | 0.0296172i | ||||
\(853\) | 15.2077 | − | 2.68153i | 0.520703 | − | 0.0918139i | 0.0928812 | − | 0.995677i | \(-0.470392\pi\) |
0.427821 | + | 0.903863i | \(0.359281\pi\) | |||||||
\(854\) | 11.2846 | − | 19.5455i | 0.386151 | − | 0.668834i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.348478 | + | 0.603581i | 0.0119107 | + | 0.0206300i | ||||
\(857\) | 14.1302 | + | 16.8398i | 0.482680 | + | 0.575235i | 0.951340 | − | 0.308143i | \(-0.0997076\pi\) |
−0.468660 | + | 0.883378i | \(0.655263\pi\) | |||||||
\(858\) | −0.905968 | − | 0.0457041i | −0.0309293 | − | 0.00156031i | ||||
\(859\) | −3.39772 | + | 19.2694i | −0.115929 | + | 0.657464i | 0.870358 | + | 0.492420i | \(0.163888\pi\) |
−0.986286 | + | 0.165044i | \(0.947223\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −27.2264 | + | 29.3114i | −0.927873 | + | 0.998929i | ||||
\(862\) | 7.69508 | − | 21.1421i | 0.262095 | − | 0.720101i | ||||
\(863\) | − | 21.8676i | − | 0.744383i | −0.928156 | − | 0.372191i | \(-0.878607\pi\) | ||
0.928156 | − | 0.372191i | \(-0.121393\pi\) | |||||||
\(864\) | −22.7445 | + | 20.0069i | −0.773784 | + | 0.680648i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 14.7061 | + | 5.35258i | 0.499733 | + | 0.181888i | ||||
\(867\) | 27.9989 | − | 8.62001i | 0.950893 | − | 0.292751i | ||||
\(868\) | −5.73577 | + | 6.83563i | −0.194685 | + | 0.232016i | ||||
\(869\) | 0.0348743 | − | 0.197782i | 0.00118303 | − | 0.00670929i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.62223 | − | 3.03941i | 0.122734 | − | 0.102986i | ||||
\(872\) | −19.9452 | + | 11.5153i | −0.675428 | + | 0.389959i | ||||
\(873\) | −42.8275 | − | 12.0996i | −1.44949 | − | 0.409508i | ||||
\(874\) | −7.46602 | + | 12.9315i | −0.252542 | + | 0.437416i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.59707 | − | 10.8891i | 0.155321 | − | 0.367910i | ||||
\(877\) | 13.3729 | + | 36.7419i | 0.451572 | + | 1.24068i | 0.931617 | + | 0.363441i | \(0.118398\pi\) |
−0.480045 | + | 0.877244i | \(0.659380\pi\) | |||||||
\(878\) | −4.01053 | − | 11.0188i | −0.135349 | − | 0.371868i | ||||
\(879\) | −6.41903 | − | 8.48379i | −0.216509 | − | 0.286151i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.65254 | − | 6.32639i | 0.123057 | − | 0.213141i | −0.797915 | − | 0.602771i | \(-0.794063\pi\) |
0.920972 | + | 0.389629i | \(0.127397\pi\) | |||||||
\(882\) | −1.82665 | − | 2.68541i | −0.0615063 | − | 0.0904223i | ||||
\(883\) | 3.02496 | − | 1.74646i | 0.101798 | − | 0.0587732i | −0.448237 | − | 0.893915i | \(-0.647948\pi\) |
0.550035 | + | 0.835142i | \(0.314614\pi\) | |||||||
\(884\) | −0.796907 | + | 0.668684i | −0.0268029 | + | 0.0224903i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.55485 | + | 14.4893i | −0.0858318 | + | 0.486776i | ||||
\(887\) | −18.2688 | + | 21.7720i | −0.613408 | + | 0.731031i | −0.979922 | − | 0.199381i | \(-0.936107\pi\) |
0.366514 | + | 0.930413i | \(0.380551\pi\) | |||||||
\(888\) | 7.26978 | − | 31.7721i | 0.243958 | − | 1.06620i | ||||
\(889\) | −41.2181 | − | 15.0021i | −1.38241 | − | 0.503156i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.49337 | − | 1.68487i | 0.0500298 | − | 0.0564452i | ||||
\(892\) | 5.20125i | 0.174151i | ||||||||
\(893\) | −10.8821 | + | 29.8985i | −0.364157 | + | 1.00051i | ||||
\(894\) | −22.0447 | − | 5.04405i | −0.737286 | − | 0.168698i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.63563 | − | 20.6187i | 0.121458 | − | 0.688821i | ||||
\(897\) | 16.4341 | − | 25.4149i | 0.548718 | − | 0.848579i | ||||
\(898\) | 7.14052 | + | 8.50974i | 0.238282 | + | 0.283974i | ||||
\(899\) | −0.490949 | − | 0.850349i | −0.0163741 | − | 0.0283607i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.796719 | − | 1.37996i | 0.0265426 | − | 0.0459731i | ||||
\(902\) | 1.91887 | − | 0.338348i | 0.0638913 | − | 0.0112658i | ||||
\(903\) | −0.855892 | + | 0.647588i | −0.0284823 | + | 0.0215504i | ||||
\(904\) | −7.88800 | + | 2.87100i | −0.262351 | + | 0.0954880i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 7.70767 | − | 18.2573i | 0.256070 | − | 0.606558i | ||||
\(907\) | −52.3097 | + | 9.22362i | −1.73692 | + | 0.306265i | −0.950337 | − | 0.311224i | \(-0.899261\pi\) |
−0.786579 | + | 0.617489i | \(0.788150\pi\) | |||||||
\(908\) | −2.95799 | − | 1.70780i | −0.0981644 | − | 0.0566753i | ||||
\(909\) | −11.6476 | + | 2.95249i | −0.386327 | + | 0.0979279i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.18649 | + | 5.19108i | −0.204968 | + | 0.171988i | −0.739493 | − | 0.673164i | \(-0.764935\pi\) |
0.534526 | + | 0.845152i | \(0.320490\pi\) | |||||||
\(912\) | 1.22670 | + | 2.39595i | 0.0406201 | + | 0.0793377i | ||||
\(913\) | −0.678878 | − | 0.119704i | −0.0224676 | − | 0.00396164i | ||||
\(914\) | 10.8360 | + | 9.09252i | 0.358424 | + | 0.300754i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −20.3339 | − | 7.40094i | −0.671852 | − | 0.244534i | ||||
\(917\) | 33.8116i | 1.11656i | ||||||||
\(918\) | 0.0284888 | + | 1.22154i | 0.000940269 | + | 0.0403168i | ||||
\(919\) | 47.9961 | 1.58325 | 0.791623 | − | 0.611009i | \(-0.209236\pi\) | ||||
0.791623 | + | 0.611009i | \(0.209236\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22.4013 | − | 24.1168i | 0.738149 | − | 0.794677i | ||||
\(922\) | 13.2090 | − | 15.7419i | 0.435016 | − | 0.518431i | ||||
\(923\) | 0.953063 | + | 0.168051i | 0.0313705 | + | 0.00553146i | ||||
\(924\) | −0.0704406 | + | 1.39631i | −0.00231732 | + | 0.0459351i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 7.35298 | + | 12.7357i | 0.241634 | + | 0.418522i | ||||
\(927\) | −14.4073 | − | 10.3817i | −0.473197 | − | 0.340979i | ||||
\(928\) | 1.79255 | + | 1.03493i | 0.0588433 | + | 0.0339732i | ||||
\(929\) | 5.03474 | + | 28.5534i | 0.165185 | + | 0.936808i | 0.948874 | + | 0.315655i | \(0.102224\pi\) |
−0.783689 | + | 0.621153i | \(0.786665\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.53442 | + | 1.28642i | −0.115836 | + | 0.0421608i | ||||
\(932\) | 13.0603 | + | 35.8828i | 0.427803 | + | 1.17538i | ||||
\(933\) | 4.62061 | + | 37.0332i | 0.151272 | + | 1.21241i | ||||
\(934\) | −2.26338 | − | 12.8363i | −0.0740602 | − | 0.420016i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 8.65246 | + | 19.2311i | 0.282815 | + | 0.628587i | ||||
\(937\) | 4.35481 | − | 2.51425i | 0.142265 | − | 0.0821369i | −0.427178 | − | 0.904168i | \(-0.640492\pi\) |
0.569443 | + | 0.822031i | \(0.307159\pi\) | |||||||
\(938\) | 2.21685 | + | 2.64193i | 0.0723826 | + | 0.0862622i | ||||
\(939\) | 0.332803 | − | 6.59699i | 0.0108606 | − | 0.215285i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −42.7767 | − | 35.8939i | −1.39448 | − | 1.17011i | −0.963487 | − | 0.267755i | \(-0.913718\pi\) |
−0.430995 | − | 0.902354i | \(-0.641837\pi\) | |||||||
\(942\) | −0.776466 | − | 0.721234i | −0.0252986 | − | 0.0234991i | ||||
\(943\) | −22.2345 | + | 61.0887i | −0.724054 | + | 1.98932i | ||||
\(944\) | −3.33551 | −0.108561 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.0522740 | 0.00169957 | ||||||||
\(947\) | 14.5459 | − | 39.9645i | 0.472678 | − | 1.29867i | −0.442914 | − | 0.896564i | \(-0.646055\pi\) |
0.915592 | − | 0.402109i | \(-0.131723\pi\) | |||||||
\(948\) | −1.80415 | + | 0.555443i | −0.0585961 | + | 0.0180400i | ||||
\(949\) | −10.0581 | − | 8.43973i | −0.326499 | − | 0.273965i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.55926 | + | 3.35828i | −0.212699 | + | 0.108900i | ||||
\(952\) | −1.20624 | − | 1.43754i | −0.0390944 | − | 0.0465909i | ||||
\(953\) | −18.8922 | + | 10.9074i | −0.611977 | + | 0.353325i | −0.773739 | − | 0.633505i | \(-0.781616\pi\) |
0.161762 | + | 0.986830i | \(0.448282\pi\) | |||||||
\(954\) | −9.10901 | − | 9.35916i | −0.294915 | − | 0.303014i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.46670 | + | 19.6606i | 0.112121 | + | 0.635870i | ||||
\(957\) | −0.141729 | − | 0.0598339i | −0.00458146 | − | 0.00193415i | ||||
\(958\) | 2.59656 | + | 7.13399i | 0.0838910 | + | 0.230489i | ||||
\(959\) | −43.9676 | + | 16.0029i | −1.41979 | + | 0.516761i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.05507 | − | 22.9974i | −0.130809 | − | 0.741852i | ||||
\(962\) | −12.6778 | − | 7.31954i | −0.408749 | − | 0.235991i | ||||
\(963\) | −0.337853 | + | 0.699631i | −0.0108872 | + | 0.0225453i | ||||
\(964\) | −5.73088 | − | 9.92618i | −0.184579 | − | 0.319701i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 18.5368 | + | 11.9865i | 0.596412 | + | 0.385659i | ||||
\(967\) | 4.55827 | + | 0.803746i | 0.146584 | + | 0.0258467i | 0.246459 | − | 0.969153i | \(-0.420733\pi\) |
−0.0998746 | + | 0.995000i | \(0.531844\pi\) | |||||||
\(968\) | −18.9201 | + | 22.5481i | −0.608115 | + | 0.724724i | ||||
\(969\) | 1.37940 | + | 0.315621i | 0.0443128 | + | 0.0101392i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.6509 | −0.694809 | −0.347405 | − | 0.937715i | \(-0.612937\pi\) | ||||
−0.347405 | + | 0.937715i | \(0.612937\pi\) | |||||||
\(972\) | −20.4937 | − | 5.27712i | −0.657334 | − | 0.169264i | ||||
\(973\) | 42.5714i | 1.36478i | ||||||||
\(974\) | 0.352164 | + | 0.128177i | 0.0112841 | + | 0.00410707i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.06451 | − | 4.24963i | −0.162111 | − | 0.136027i | ||||
\(977\) | −21.7493 | − | 3.83499i | −0.695822 | − | 0.122692i | −0.185460 | − | 0.982652i | \(-0.559377\pi\) |
−0.510362 | + | 0.859960i | \(0.670489\pi\) | |||||||
\(978\) | −3.86593 | + | 5.97856i | −0.123619 | + | 0.191173i | ||||
\(979\) | 2.00269 | − | 1.68046i | 0.0640063 | − | 0.0537076i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −23.1191 | − | 11.1643i | −0.738137 | − | 0.356448i | ||||
\(982\) | 17.3862 | + | 10.0379i | 0.554815 | + | 0.320323i | ||||
\(983\) | −13.6524 | + | 2.40729i | −0.435445 | + | 0.0767807i | −0.387074 | − | 0.922049i | \(-0.626514\pi\) |
−0.0483713 | + | 0.998829i | \(0.515403\pi\) | |||||||
\(984\) | −27.3306 | − | 36.1217i | −0.871266 | − | 1.15152i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.0784563 | − | 0.0285558i | 0.00249856 | − | 0.000909401i | ||||
\(987\) | 43.3334 | + | 18.2940i | 1.37932 | + | 0.582305i | ||||
\(988\) | 9.72444 | − | 1.71468i | 0.309376 | − | 0.0545513i | ||||
\(989\) | −0.872042 | + | 1.51042i | −0.0277293 | + | 0.0480286i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.4112 | − | 30.1570i | −0.553084 | − | 0.957970i | −0.998050 | − | 0.0624224i | \(-0.980117\pi\) |
0.444966 | − | 0.895548i | \(-0.353216\pi\) | |||||||
\(992\) | −10.3628 | − | 12.3499i | −0.329020 | − | 0.392111i | ||||
\(993\) | −11.2828 | − | 22.0371i | −0.358049 | − | 0.699328i | ||||
\(994\) | −0.122571 | + | 0.695133i | −0.00388771 | + | 0.0220483i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.90653 | + | 6.19267i | 0.0604109 | + | 0.196222i | ||||
\(997\) | −8.46492 | + | 23.2572i | −0.268087 | + | 0.736562i | 0.730475 | + | 0.682940i | \(0.239299\pi\) |
−0.998561 | + | 0.0536221i | \(0.982923\pi\) | |||||||
\(998\) | − | 11.2488i | − | 0.356073i | ||||||
\(999\) | 33.8433 | − | 13.2195i | 1.07075 | − | 0.418245i |
(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 | 675.2.u.b.274.2 | 24 | ||
5.2 | odd | 4 | 675.2.l.c.301.1 | 12 | |||
5.3 | odd | 4 | 27.2.e.a.4.2 | ✓ | 12 | ||
5.4 | even | 2 | inner | 675.2.u.b.274.3 | 24 | ||
15.8 | even | 4 | 81.2.e.a.64.1 | 12 | |||
20.3 | even | 4 | 432.2.u.c.193.2 | 12 | |||
27.7 | even | 9 | inner | 675.2.u.b.574.3 | 24 | ||
45.13 | odd | 12 | 243.2.e.d.109.1 | 12 | |||
45.23 | even | 12 | 243.2.e.a.109.2 | 12 | |||
45.38 | even | 12 | 243.2.e.b.28.2 | 12 | |||
45.43 | odd | 12 | 243.2.e.c.28.1 | 12 | |||
135.7 | odd | 36 | 675.2.l.c.601.1 | 12 | |||
135.13 | odd | 36 | 729.2.a.a.1.3 | 6 | |||
135.23 | even | 36 | 729.2.c.b.244.3 | 12 | |||
135.34 | even | 18 | inner | 675.2.u.b.574.2 | 24 | ||
135.38 | even | 36 | 243.2.e.b.217.2 | 12 | |||
135.43 | odd | 36 | 243.2.e.c.217.1 | 12 | |||
135.58 | odd | 36 | 729.2.c.e.244.4 | 12 | |||
135.68 | even | 36 | 729.2.a.d.1.4 | 6 | |||
135.83 | even | 36 | 243.2.e.a.136.2 | 12 | |||
135.88 | odd | 36 | 27.2.e.a.7.2 | yes | 12 | ||
135.103 | odd | 36 | 729.2.c.e.487.4 | 12 | |||
135.113 | even | 36 | 729.2.c.b.487.3 | 12 | |||
135.128 | even | 36 | 81.2.e.a.19.1 | 12 | |||
135.133 | odd | 36 | 243.2.e.d.136.1 | 12 | |||
540.223 | even | 36 | 432.2.u.c.385.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.2.e.a.4.2 | ✓ | 12 | 5.3 | odd | 4 | ||
27.2.e.a.7.2 | yes | 12 | 135.88 | odd | 36 | ||
81.2.e.a.19.1 | 12 | 135.128 | even | 36 | |||
81.2.e.a.64.1 | 12 | 15.8 | even | 4 | |||
243.2.e.a.109.2 | 12 | 45.23 | even | 12 | |||
243.2.e.a.136.2 | 12 | 135.83 | even | 36 | |||
243.2.e.b.28.2 | 12 | 45.38 | even | 12 | |||
243.2.e.b.217.2 | 12 | 135.38 | even | 36 | |||
243.2.e.c.28.1 | 12 | 45.43 | odd | 12 | |||
243.2.e.c.217.1 | 12 | 135.43 | odd | 36 | |||
243.2.e.d.109.1 | 12 | 45.13 | odd | 12 | |||
243.2.e.d.136.1 | 12 | 135.133 | odd | 36 | |||
432.2.u.c.193.2 | 12 | 20.3 | even | 4 | |||
432.2.u.c.385.2 | 12 | 540.223 | even | 36 | |||
675.2.l.c.301.1 | 12 | 5.2 | odd | 4 | |||
675.2.l.c.601.1 | 12 | 135.7 | odd | 36 | |||
675.2.u.b.274.2 | 24 | 1.1 | even | 1 | trivial | ||
675.2.u.b.274.3 | 24 | 5.4 | even | 2 | inner | ||
675.2.u.b.574.2 | 24 | 135.34 | even | 18 | inner | ||
675.2.u.b.574.3 | 24 | 27.7 | even | 9 | inner | ||
729.2.a.a.1.3 | 6 | 135.13 | odd | 36 | |||
729.2.a.d.1.4 | 6 | 135.68 | even | 36 | |||
729.2.c.b.244.3 | 12 | 135.23 | even | 36 | |||
729.2.c.b.487.3 | 12 | 135.113 | even | 36 | |||
729.2.c.e.244.4 | 12 | 135.58 | odd | 36 | |||
729.2.c.e.487.4 | 12 | 135.103 | odd | 36 |