Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [351,2,Mod(80,351)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(351, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("351.80");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 351 = 3^{3} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 351.bd (of order \(12\), degree \(4\), 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: | \(2.80274911095\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 88 x^{16} - 6 x^{15} + 48 x^{13} + 1980 x^{12} - 204 x^{11} + 18 x^{10} + 2076 x^{9} + \cdots + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 323.2 | ||
Root | \(1.03270 - 1.03270i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 351.323 |
Dual form | 351.2.bd.d.188.2 |
$q$-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 \(\left(\mathbb{Z}/351\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(326\) |
\(\chi(n)\) | \(e\left(\frac{7}{12}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41069 | − | 0.377994i | −0.997511 | − | 0.267282i | −0.277108 | − | 0.960839i | \(-0.589376\pi\) |
−0.720402 | + | 0.693556i | \(0.756043\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.115125 | + | 0.0664674i | 0.0575625 | + | 0.0332337i | ||||
\(5\) | 2.86027 | − | 2.86027i | 1.27915 | − | 1.27915i | 0.338012 | − | 0.941142i | \(-0.390246\pi\) |
0.941142 | − | 0.338012i | \(-0.109754\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.575104 | + | 2.14632i | 0.217369 | + | 0.811231i | 0.985319 | + | 0.170722i | \(0.0546100\pi\) |
−0.767951 | + | 0.640509i | \(0.778723\pi\) | |||||||
\(8\) | 1.92812 | + | 1.92812i | 0.681692 | + | 0.681692i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −5.11614 | + | 2.95380i | −1.61786 | + | 0.934074i | ||||
\(11\) | 1.15529 | − | 4.31160i | 0.348333 | − | 1.29999i | −0.540338 | − | 0.841448i | \(-0.681704\pi\) |
0.888670 | − | 0.458547i | \(-0.151630\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.47083 | + | 3.29191i | 0.407934 | + | 0.913011i | ||||
\(14\) | − | 3.24518i | − | 0.867311i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.12410 | − | 3.67905i | −0.531025 | − | 0.919762i | ||||
\(17\) | −2.14016 | + | 3.70687i | −0.519065 | + | 0.899048i | 0.480689 | + | 0.876891i | \(0.340387\pi\) |
−0.999755 | + | 0.0221565i | \(0.992947\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.53117 | − | 0.946174i | 0.810106 | − | 0.217067i | 0.170090 | − | 0.985429i | \(-0.445594\pi\) |
0.640016 | + | 0.768361i | \(0.278928\pi\) | |||||||
\(20\) | 0.519404 | − | 0.139174i | 0.116142 | − | 0.0311202i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.25952 | + | 5.64565i | −0.694931 | + | 1.20366i | ||||
\(23\) | −1.43709 | − | 2.48911i | −0.299653 | − | 0.519015i | 0.676403 | − | 0.736532i | \(-0.263538\pi\) |
−0.976057 | + | 0.217517i | \(0.930204\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 11.3623i | − | 2.27247i | ||||||
\(26\) | −0.830565 | − | 5.19984i | −0.162887 | − | 1.01977i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.0764513 | + | 0.285320i | −0.0144479 | + | 0.0539204i | ||||
\(29\) | 5.10882 | − | 2.94958i | 0.948685 | − | 0.547723i | 0.0560127 | − | 0.998430i | \(-0.482161\pi\) |
0.892672 | + | 0.450707i | \(0.148828\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00290 | − | 4.00290i | −0.718943 | − | 0.718943i | 0.249446 | − | 0.968389i | \(-0.419752\pi\) |
−0.968389 | + | 0.249446i | \(0.919752\pi\) | |||||||
\(32\) | 0.194314 | + | 0.725192i | 0.0343503 | + | 0.128197i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.42029 | − | 4.42029i | 0.758073 | − | 0.758073i | ||||
\(35\) | 7.78401 | + | 4.49410i | 1.31574 | + | 0.759641i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.91557 | + | 2.38892i | 1.46571 | + | 0.392736i | 0.901458 | − | 0.432866i | \(-0.142498\pi\) |
0.564253 | + | 0.825602i | \(0.309164\pi\) | |||||||
\(38\) | −5.33905 | −0.866107 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 11.0299 | 1.74398 | ||||||||
\(41\) | −2.22987 | − | 0.597493i | −0.348248 | − | 0.0933127i | 0.0804552 | − | 0.996758i | \(-0.474363\pi\) |
−0.428703 | + | 0.903446i | \(0.641029\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.75162 | − | 1.58865i | −0.419618 | − | 0.242266i | 0.275296 | − | 0.961360i | \(-0.411224\pi\) |
−0.694914 | + | 0.719093i | \(0.744557\pi\) | |||||||
\(44\) | 0.419583 | − | 0.419583i | 0.0632545 | − | 0.0632545i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.08642 | + | 4.05458i | 0.160184 | + | 0.597815i | ||||
\(47\) | −2.44807 | − | 2.44807i | −0.357088 | − | 0.357088i | 0.505650 | − | 0.862738i | \(-0.331253\pi\) |
−0.862738 | + | 0.505650i | \(0.831253\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.78625 | − | 1.03129i | 0.255179 | − | 0.147327i | ||||
\(50\) | −4.29490 | + | 16.0288i | −0.607390 | + | 2.26681i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.0494757 | + | 0.476743i | −0.00686104 | + | 0.0661123i | ||||
\(53\) | − | 5.15572i | − | 0.708193i | −0.935209 | − | 0.354096i | \(-0.884789\pi\) | ||
0.935209 | − | 0.354096i | \(-0.115211\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.02790 | − | 15.6368i | −1.21732 | − | 2.10846i | ||||
\(56\) | −3.02948 | + | 5.24721i | −0.404831 | + | 0.701188i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8.32191 | + | 2.22985i | −1.09272 | + | 0.292793i | ||||
\(59\) | −9.19205 | + | 2.46300i | −1.19670 | + | 0.320656i | −0.801532 | − | 0.597952i | \(-0.795981\pi\) |
−0.395171 | + | 0.918607i | \(0.629315\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.13769 | + | 7.16668i | −0.529777 | + | 0.917600i | 0.469620 | + | 0.882869i | \(0.344391\pi\) |
−0.999397 | + | 0.0347314i | \(0.988942\pi\) | |||||||
\(62\) | 4.13380 | + | 7.15994i | 0.524993 | + | 0.909314i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.39992i | 0.924990i | ||||||||
\(65\) | 13.6227 | + | 5.20879i | 1.68969 | + | 0.646071i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.13626 | + | 4.24057i | −0.138816 | + | 0.518068i | 0.861137 | + | 0.508373i | \(0.169753\pi\) |
−0.999953 | + | 0.00969513i | \(0.996914\pi\) | |||||||
\(68\) | −0.492772 | + | 0.284502i | −0.0597574 | + | 0.0345009i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −9.28210 | − | 9.28210i | −1.10942 | − | 1.10942i | ||||
\(71\) | −0.279146 | − | 1.04179i | −0.0331286 | − | 0.123638i | 0.947381 | − | 0.320107i | \(-0.103719\pi\) |
−0.980510 | + | 0.196470i | \(0.937052\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.70808 | + | 7.70808i | −0.902162 | + | 0.902162i | −0.995623 | − | 0.0934609i | \(-0.970207\pi\) |
0.0934609 | + | 0.995623i | \(0.470207\pi\) | |||||||
\(74\) | −11.6741 | − | 6.74007i | −1.35709 | − | 0.783517i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.469415 | + | 0.125779i | 0.0538456 | + | 0.0144279i | ||||
\(77\) | 9.91846 | 1.13031 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.13223 | 0.689929 | 0.344965 | − | 0.938616i | \(-0.387891\pi\) | ||||
0.344965 | + | 0.938616i | \(0.387891\pi\) | |||||||
\(80\) | −16.5986 | − | 4.44758i | −1.85578 | − | 0.497254i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.91982 | + | 1.68576i | 0.322440 | + | 0.186161i | ||||
\(83\) | −7.06333 | + | 7.06333i | −0.775301 | + | 0.775301i | −0.979028 | − | 0.203726i | \(-0.934695\pi\) |
0.203726 | + | 0.979028i | \(0.434695\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.48121 | + | 16.7241i | 0.486056 | + | 1.81398i | ||||
\(86\) | 3.28119 | + | 3.28119i | 0.353820 | + | 0.353820i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 10.5408 | − | 6.08573i | 1.12365 | − | 0.648741i | ||||
\(89\) | −1.91951 | + | 7.16369i | −0.203467 | + | 0.759350i | 0.786444 | + | 0.617661i | \(0.211920\pi\) |
−0.989911 | + | 0.141688i | \(0.954747\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.21960 | + | 5.05005i | −0.651991 | + | 0.529389i | ||||
\(92\) | − | 0.382078i | − | 0.0398344i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.52812 | + | 4.37884i | 0.260756 | + | 0.451642i | ||||
\(95\) | 7.39380 | − | 12.8064i | 0.758588 | − | 1.31391i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.40243 | − | 2.25142i | 0.853137 | − | 0.228597i | 0.194355 | − | 0.980931i | \(-0.437739\pi\) |
0.658782 | + | 0.752334i | \(0.271072\pi\) | |||||||
\(98\) | −2.90967 | + | 0.779645i | −0.293921 | + | 0.0787560i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.755225 | − | 1.30809i | 0.0755225 | − | 0.130809i | ||||
\(101\) | 6.90247 | + | 11.9554i | 0.686821 | + | 1.18961i | 0.972861 | + | 0.231391i | \(0.0743278\pi\) |
−0.286039 | + | 0.958218i | \(0.592339\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 0.612148i | − | 0.0603168i | −0.999545 | − | 0.0301584i | \(-0.990399\pi\) | ||
0.999545 | − | 0.0301584i | \(-0.00960117\pi\) | |||||||
\(104\) | −3.51126 | + | 9.18311i | −0.344307 | + | 0.900478i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.94883 | + | 7.27314i | −0.189287 | + | 0.706430i | ||||
\(107\) | −3.54408 | + | 2.04617i | −0.342619 | + | 0.197811i | −0.661430 | − | 0.750007i | \(-0.730050\pi\) |
0.318811 | + | 0.947818i | \(0.396717\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.22391 | + | 5.22391i | 0.500360 | + | 0.500360i | 0.911550 | − | 0.411190i | \(-0.134887\pi\) |
−0.411190 | + | 0.911550i | \(0.634887\pi\) | |||||||
\(110\) | 6.82499 | + | 25.4712i | 0.650737 | + | 2.42858i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 6.67482 | − | 6.67482i | 0.630711 | − | 0.630711i | ||||
\(113\) | 0.467679 | + | 0.270015i | 0.0439956 | + | 0.0254009i | 0.521836 | − | 0.853046i | \(-0.325247\pi\) |
−0.477841 | + | 0.878446i | \(0.658580\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.2300 | − | 3.00907i | −1.04720 | − | 0.280597i | ||||
\(116\) | 0.784204 | 0.0728115 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 13.8982 | 1.27943 | ||||||||
\(119\) | −9.18692 | − | 2.46163i | −0.842164 | − | 0.225657i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.72889 | − | 4.46227i | −0.702626 | − | 0.405661i | ||||
\(122\) | 8.54597 | − | 8.54597i | 0.773716 | − | 0.773716i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.194771 | − | 0.726897i | −0.0174910 | − | 0.0652772i | ||||
\(125\) | −18.1980 | − | 18.1980i | −1.62768 | − | 1.62768i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.11785 | − | 4.10949i | 0.631607 | − | 0.364659i | −0.149767 | − | 0.988721i | \(-0.547852\pi\) |
0.781374 | + | 0.624063i | \(0.214519\pi\) | |||||||
\(128\) | 3.18576 | − | 11.8894i | 0.281584 | − | 1.05088i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −17.2486 | − | 12.4973i | −1.51280 | − | 1.09609i | ||||
\(131\) | − | 9.99328i | − | 0.873117i | −0.899676 | − | 0.436559i | \(-0.856197\pi\) | ||
0.899676 | − | 0.436559i | \(-0.143803\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.06158 | + | 7.03486i | 0.352183 | + | 0.609999i | ||||
\(134\) | 3.20582 | − | 5.55264i | 0.276941 | − | 0.479675i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −11.2738 | + | 3.02079i | −0.966716 | + | 0.259031i | ||||
\(137\) | 9.83483 | − | 2.63523i | 0.840246 | − | 0.225143i | 0.187067 | − | 0.982347i | \(-0.440102\pi\) |
0.653179 | + | 0.757204i | \(0.273435\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.53975 | − | 2.66692i | 0.130600 | − | 0.226205i | −0.793308 | − | 0.608820i | \(-0.791643\pi\) |
0.923908 | + | 0.382615i | \(0.124976\pi\) | |||||||
\(140\) | 0.597422 | + | 1.03477i | 0.0504914 | + | 0.0874536i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.57516i | 0.132184i | ||||||||
\(143\) | 15.8926 | − | 2.53851i | 1.32901 | − | 0.212281i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.17603 | − | 23.0493i | 0.512891 | − | 1.91414i | ||||
\(146\) | 13.7873 | − | 7.96012i | 1.14105 | − | 0.658784i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.867619 | + | 0.867619i | 0.0713179 | + | 0.0713179i | ||||
\(149\) | −0.460818 | − | 1.71979i | −0.0377516 | − | 0.140891i | 0.944478 | − | 0.328575i | \(-0.106568\pi\) |
−0.982229 | + | 0.187684i | \(0.939902\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.8313 | + | 13.8313i | −1.12558 | + | 1.12558i | −0.134689 | + | 0.990888i | \(0.543003\pi\) |
−0.990888 | + | 0.134689i | \(0.956997\pi\) | |||||||
\(152\) | 8.63284 | + | 4.98417i | 0.700216 | + | 0.404270i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −13.9919 | − | 3.74912i | −1.12750 | − | 0.302113i | ||||
\(155\) | −22.8988 | −1.83928 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.12683 | −0.568783 | −0.284392 | − | 0.958708i | \(-0.591792\pi\) | ||||
−0.284392 | + | 0.958708i | \(0.591792\pi\) | |||||||
\(158\) | −8.65069 | − | 2.31795i | −0.688212 | − | 0.184406i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.63004 | + | 1.51845i | 0.207923 | + | 0.120044i | ||||
\(161\) | 4.51594 | − | 4.51594i | 0.355906 | − | 0.355906i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.25091 | + | 8.40050i | 0.176305 | + | 0.657978i | 0.996326 | + | 0.0856444i | \(0.0272949\pi\) |
−0.820021 | + | 0.572333i | \(0.806038\pi\) | |||||||
\(164\) | −0.217000 | − | 0.217000i | −0.0169449 | − | 0.0169449i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.6341 | − | 7.29430i | 0.980596 | − | 0.566147i | ||||
\(167\) | −5.60021 | + | 20.9003i | −0.433357 | + | 1.61731i | 0.311611 | + | 0.950210i | \(0.399131\pi\) |
−0.744968 | + | 0.667100i | \(0.767535\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.67333 | + | 9.68366i | −0.667179 | + | 0.744897i | ||||
\(170\) | − | 25.2865i | − | 1.93938i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.211187 | − | 0.365786i | −0.0161028 | − | 0.0278909i | ||||
\(173\) | −3.61344 | + | 6.25867i | −0.274725 | + | 0.475838i | −0.970066 | − | 0.242843i | \(-0.921920\pi\) |
0.695341 | + | 0.718680i | \(0.255254\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 24.3872 | − | 6.53452i | 1.84350 | − | 0.493963i | ||||
\(176\) | −18.3165 | + | 4.90789i | −1.38066 | + | 0.369946i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.41567 | − | 9.38021i | 0.405921 | − | 0.703076i | ||||
\(179\) | 2.28409 | + | 3.95615i | 0.170721 | + | 0.295697i | 0.938672 | − | 0.344811i | \(-0.112057\pi\) |
−0.767951 | + | 0.640508i | \(0.778724\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 24.4811i | − | 1.81967i | −0.414974 | − | 0.909833i | \(-0.636209\pi\) | ||
0.414974 | − | 0.909833i | \(-0.363791\pi\) | |||||||
\(182\) | 10.6828 | − | 4.77310i | 0.791864 | − | 0.353806i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.02842 | − | 7.57016i | 0.149537 | − | 0.558080i | ||||
\(185\) | 32.3340 | − | 18.6680i | 2.37724 | − | 1.37250i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.5100 | + | 13.5100i | 0.987950 | + | 0.987950i | ||||
\(188\) | −0.119117 | − | 0.444551i | −0.00868751 | − | 0.0324222i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −15.2711 | + | 15.2711i | −1.10788 | + | 1.10788i | ||||
\(191\) | −5.37981 | − | 3.10604i | −0.389270 | − | 0.224745i | 0.292574 | − | 0.956243i | \(-0.405488\pi\) |
−0.681844 | + | 0.731498i | \(0.738822\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.7367 | − | 3.14483i | −0.844824 | − | 0.226370i | −0.189654 | − | 0.981851i | \(-0.560737\pi\) |
−0.655170 | + | 0.755481i | \(0.727403\pi\) | |||||||
\(194\) | −12.7043 | −0.912114 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.274189 | 0.0195849 | ||||||||
\(197\) | 14.7635 | + | 3.95586i | 1.05185 | + | 0.281844i | 0.743018 | − | 0.669272i | \(-0.233394\pi\) |
0.308837 | + | 0.951115i | \(0.400060\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.6220 | + | 11.3288i | 1.39096 | + | 0.803074i | 0.993422 | − | 0.114510i | \(-0.0365297\pi\) |
0.397543 | + | 0.917584i | \(0.369863\pi\) | |||||||
\(200\) | 21.9079 | − | 21.9079i | 1.54912 | − | 1.54912i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.21818 | − | 19.4745i | −0.367150 | − | 1.37022i | ||||
\(203\) | 9.26884 | + | 9.26884i | 0.650545 | + | 0.650545i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.08704 | + | 4.66906i | −0.564823 | + | 0.326101i | ||||
\(206\) | −0.231388 | + | 0.863553i | −0.0161216 | + | 0.0601666i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 8.98690 | − | 12.4036i | 0.623130 | − | 0.860034i | ||||
\(209\) | − | 16.3181i | − | 1.12875i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.217991 | + | 0.377571i | 0.0150071 | + | 0.0259931i | 0.873431 | − | 0.486947i | \(-0.161890\pi\) |
−0.858424 | + | 0.512940i | \(0.828556\pi\) | |||||||
\(212\) | 0.342687 | − | 0.593552i | 0.0235359 | − | 0.0407653i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.77305 | − | 1.54688i | 0.394638 | − | 0.105743i | ||||
\(215\) | −12.4144 | + | 3.32642i | −0.846652 | + | 0.226860i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.28941 | − | 10.8936i | 0.426953 | − | 0.739505i | ||||
\(218\) | −5.39473 | − | 9.34395i | −0.365377 | − | 0.632852i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 2.40025i | − | 0.161824i | ||||||
\(221\) | −15.3505 | − | 1.59305i | −1.03259 | − | 0.107160i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.18517 | − | 4.42310i | 0.0793646 | − | 0.296193i | −0.914823 | − | 0.403855i | \(-0.867670\pi\) |
0.994187 | + | 0.107663i | \(0.0343366\pi\) | |||||||
\(224\) | −1.44474 | + | 0.834121i | −0.0965307 | + | 0.0557320i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.557688 | − | 0.557688i | −0.0370969 | − | 0.0370969i | ||||
\(227\) | 1.05544 | + | 3.93894i | 0.0700517 | + | 0.261437i | 0.992066 | − | 0.125720i | \(-0.0401240\pi\) |
−0.922014 | + | 0.387156i | \(0.873457\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.1451 | + | 18.1451i | −1.19906 | + | 1.19906i | −0.224615 | + | 0.974447i | \(0.572113\pi\) |
−0.974447 | + | 0.224615i | \(0.927887\pi\) | |||||||
\(230\) | 14.7047 | + | 8.48974i | 0.969597 | + | 0.559797i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 15.5375 | + | 4.16327i | 1.02009 | + | 0.273332i | ||||
\(233\) | 7.55312 | 0.494822 | 0.247411 | − | 0.968911i | \(-0.420420\pi\) | ||||
0.247411 | + | 0.968911i | \(0.420420\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.0043 | −0.913541 | ||||||||
\(236\) | −1.22194 | − | 0.327419i | −0.0795418 | − | 0.0213132i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 12.0295 | + | 6.94521i | 0.779753 | + | 0.450191i | ||||
\(239\) | −1.60180 | + | 1.60180i | −0.103612 | + | 0.103612i | −0.757012 | − | 0.653400i | \(-0.773342\pi\) |
0.653400 | + | 0.757012i | \(0.273342\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.45284 | − | 5.42207i | −0.0935856 | − | 0.349266i | 0.903216 | − | 0.429187i | \(-0.141200\pi\) |
−0.996801 | + | 0.0799209i | \(0.974533\pi\) | |||||||
\(242\) | 9.21637 | + | 9.21637i | 0.592451 | + | 0.592451i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.952702 | + | 0.550043i | −0.0609905 | + | 0.0352129i | ||||
\(245\) | 2.15939 | − | 8.05894i | 0.137958 | − | 0.514867i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.30846 | + | 10.2326i | 0.528655 | + | 0.651087i | ||||
\(248\) | − | 15.4361i | − | 0.980195i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 18.7931 | + | 32.5506i | 1.18858 | + | 2.05868i | ||||
\(251\) | −10.0864 | + | 17.4702i | −0.636648 | + | 1.10271i | 0.349516 | + | 0.936931i | \(0.386346\pi\) |
−0.986163 | + | 0.165776i | \(0.946987\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.3923 | + | 3.32050i | −0.779096 | + | 0.208758i | ||||
\(254\) | −11.5945 | + | 3.10673i | −0.727502 | + | 0.194934i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.58833 | + | 2.75106i | −0.0992704 | + | 0.171941i | ||||
\(257\) | 6.32573 | + | 10.9565i | 0.394588 | + | 0.683447i | 0.993049 | − | 0.117706i | \(-0.0375539\pi\) |
−0.598460 | + | 0.801152i | \(0.704221\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.5095i | 1.27440i | ||||||||
\(260\) | 1.22210 | + | 1.50513i | 0.0757915 | + | 0.0933442i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.77740 | + | 14.0975i | −0.233369 | + | 0.870944i | ||||
\(263\) | −21.5291 | + | 12.4299i | −1.32754 | + | 0.766458i | −0.984919 | − | 0.173014i | \(-0.944649\pi\) |
−0.342625 | + | 0.939472i | \(0.611316\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −14.7468 | − | 14.7468i | −0.905887 | − | 0.905887i | ||||
\(266\) | −3.07050 | − | 11.4593i | −0.188265 | − | 0.702613i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.412671 | + | 0.412671i | −0.0252079 | + | 0.0252079i | ||||
\(269\) | −4.13082 | − | 2.38493i | −0.251860 | − | 0.145412i | 0.368755 | − | 0.929526i | \(-0.379784\pi\) |
−0.620616 | + | 0.784115i | \(0.713117\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −29.0155 | − | 7.77469i | −1.76257 | − | 0.472279i | −0.775333 | − | 0.631552i | \(-0.782418\pi\) |
−0.987234 | + | 0.159274i | \(0.949085\pi\) | |||||||
\(272\) | 18.1837 | 1.10255 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14.8700 | −0.898331 | ||||||||
\(275\) | −48.9898 | − | 13.1268i | −2.95420 | − | 0.791575i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.95845 | − | 1.70806i | −0.177756 | − | 0.102628i | 0.408482 | − | 0.912766i | \(-0.366058\pi\) |
−0.586238 | + | 0.810139i | \(0.699392\pi\) | |||||||
\(278\) | −3.18019 | + | 3.18019i | −0.190735 | + | 0.190735i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6.34333 | + | 23.6736i | 0.379086 | + | 1.41477i | ||||
\(281\) | 2.01573 | + | 2.01573i | 0.120249 | + | 0.120249i | 0.764670 | − | 0.644422i | \(-0.222902\pi\) |
−0.644422 | + | 0.764670i | \(0.722902\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.93733 | − | 2.85057i | 0.293494 | − | 0.169449i | −0.346023 | − | 0.938226i | \(-0.612468\pi\) |
0.639516 | + | 0.768777i | \(0.279135\pi\) | |||||||
\(284\) | 0.0371083 | − | 0.138490i | 0.00220197 | − | 0.00821787i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −23.3791 | − | 2.42625i | −1.38244 | − | 0.143467i | ||||
\(287\) | − | 5.12963i | − | 0.302793i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.660581 | − | 1.14416i | −0.0388577 | − | 0.0673035i | ||||
\(290\) | −17.4250 | + | 30.1809i | −1.02323 | + | 1.77228i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.39973 | + | 0.375056i | −0.0819128 | + | 0.0219485i | ||||
\(293\) | 3.79967 | − | 1.01812i | 0.221979 | − | 0.0594791i | −0.146115 | − | 0.989268i | \(-0.546677\pi\) |
0.368094 | + | 0.929788i | \(0.380010\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −19.2469 | + | 33.3367i | −1.12060 | + | 1.94094i | ||||
\(296\) | 12.5841 | + | 21.7964i | 0.731439 | + | 1.26689i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.60029i | 0.150631i | ||||||||
\(299\) | 6.08021 | − | 8.39181i | 0.351628 | − | 0.485311i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.82727 | − | 6.81948i | 0.105322 | − | 0.393068i | ||||
\(302\) | 24.7399 | − | 14.2836i | 1.42362 | − | 0.821928i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −10.9816 | − | 10.9816i | −0.629836 | − | 0.629836i | ||||
\(305\) | 8.66376 | + | 32.3336i | 0.496086 | + | 1.85142i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.8281 | − | 18.8281i | 1.07458 | − | 1.07458i | 0.0775908 | − | 0.996985i | \(-0.475277\pi\) |
0.996985 | − | 0.0775908i | \(-0.0247228\pi\) | |||||||
\(308\) | 1.14186 | + | 0.659254i | 0.0650636 | + | 0.0375645i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 32.3032 | + | 8.65562i | 1.83470 | + | 0.491606i | ||||
\(311\) | 1.93734 | 0.109856 | 0.0549281 | − | 0.998490i | \(-0.482507\pi\) | ||||
0.0549281 | + | 0.998490i | \(0.482507\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.7914 | −1.06215 | −0.531076 | − | 0.847324i | \(-0.678212\pi\) | ||||
−0.531076 | + | 0.847324i | \(0.678212\pi\) | |||||||
\(314\) | 10.0538 | + | 2.69390i | 0.567367 | + | 0.152026i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.705972 | + | 0.407593i | 0.0397140 | + | 0.0229289i | ||||
\(317\) | −7.48853 | + | 7.48853i | −0.420598 | + | 0.420598i | −0.885410 | − | 0.464812i | \(-0.846122\pi\) |
0.464812 | + | 0.885410i | \(0.346122\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.81523 | − | 25.4348i | −0.381580 | − | 1.42408i | ||||
\(320\) | 21.1658 | + | 21.1658i | 1.18320 | + | 1.18320i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.07760 | + | 4.66360i | −0.450147 | + | 0.259893i | ||||
\(323\) | −4.04993 | + | 15.1145i | −0.225344 | + | 0.840996i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 37.4038 | − | 16.7120i | 2.07479 | − | 0.927018i | ||||
\(326\) | − | 12.7014i | − | 0.703463i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.14742 | − | 5.45149i | −0.173787 | − | 0.301008i | ||||
\(329\) | 3.84644 | − | 6.66223i | 0.212061 | − | 0.367301i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.9421 | − | 8.29091i | 1.70073 | − | 0.455710i | 0.727608 | − | 0.685993i | \(-0.240632\pi\) |
0.973124 | + | 0.230283i | \(0.0739652\pi\) | |||||||
\(332\) | −1.28265 | + | 0.343684i | −0.0703944 | + | 0.0188621i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 15.8003 | − | 27.3670i | 0.864556 | − | 1.49746i | ||||
\(335\) | 8.87918 | + | 15.3792i | 0.485122 | + | 0.840255i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.28855i | 0.0701916i | 0.999384 | + | 0.0350958i | \(0.0111736\pi\) | ||||
−0.999384 | + | 0.0350958i | \(0.988826\pi\) | |||||||
\(338\) | 15.8958 | − | 10.3822i | 0.864616 | − | 0.564718i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.595709 | + | 2.22322i | −0.0323069 | + | 0.120571i | ||||
\(341\) | −21.8834 | + | 12.6344i | −1.18505 | + | 0.684191i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.2392 | + | 14.2392i | 0.768847 | + | 0.768847i | ||||
\(344\) | −2.24234 | − | 8.36854i | −0.120899 | − | 0.451201i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.46320 | − | 7.46320i | 0.401224 | − | 0.401224i | ||||
\(347\) | −21.5811 | − | 12.4599i | −1.15854 | − | 0.668881i | −0.207583 | − | 0.978217i | \(-0.566560\pi\) |
−0.950953 | + | 0.309337i | \(0.899893\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.5349 | + | 7.91385i | 1.58097 | + | 0.423618i | 0.939225 | − | 0.343303i | \(-0.111546\pi\) |
0.641741 | + | 0.766922i | \(0.278212\pi\) | |||||||
\(350\) | −36.8728 | −1.97094 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.35122 | 0.178621 | ||||||||
\(353\) | −30.6438 | − | 8.21097i | −1.63100 | − | 0.437026i | −0.676796 | − | 0.736171i | \(-0.736632\pi\) |
−0.954208 | + | 0.299145i | \(0.903299\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.77824 | − | 2.18137i | −0.200528 | − | 0.115775i | ||||
\(356\) | −0.697135 | + | 0.697135i | −0.0369481 | + | 0.0369481i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.72674 | − | 6.44429i | −0.0912611 | − | 0.340591i | ||||
\(359\) | −25.9686 | − | 25.9686i | −1.37057 | − | 1.37057i | −0.859595 | − | 0.510976i | \(-0.829284\pi\) |
−0.510976 | − | 0.859595i | \(-0.670716\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.88057 | + | 2.81780i | −0.256872 | + | 0.148305i | ||||
\(362\) | −9.25371 | + | 34.5353i | −0.486364 | + | 1.81514i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.05169 | + | 0.167986i | −0.0551238 | + | 0.00880486i | ||||
\(365\) | 44.0944i | 2.30801i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.20126 | − | 12.4729i | −0.375903 | − | 0.651082i | 0.614559 | − | 0.788871i | \(-0.289334\pi\) |
−0.990462 | + | 0.137788i | \(0.956001\pi\) | |||||||
\(368\) | −6.10503 | + | 10.5742i | −0.318247 | + | 0.551219i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −52.6697 | + | 14.1128i | −2.73817 | + | 0.733689i | ||||
\(371\) | 11.0658 | − | 2.96507i | 0.574508 | − | 0.153939i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.83661 | − | 6.64521i | 0.198652 | − | 0.344076i | −0.749439 | − | 0.662073i | \(-0.769677\pi\) |
0.948092 | + | 0.317997i | \(0.103010\pi\) | |||||||
\(374\) | −13.9518 | − | 24.1652i | −0.721429 | − | 1.24955i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 9.44034i | − | 0.486848i | ||||||
\(377\) | 17.2240 | + | 12.4795i | 0.887079 | + | 0.642725i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.21024 | − | 11.9808i | 0.164899 | − | 0.615411i | −0.833154 | − | 0.553041i | \(-0.813467\pi\) |
0.998053 | − | 0.0623705i | \(-0.0198660\pi\) | |||||||
\(380\) | 1.70242 | − | 0.982893i | 0.0873323 | − | 0.0504213i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.41520 | + | 6.41520i | 0.328230 | + | 0.328230i | ||||
\(383\) | 4.04634 | + | 15.1012i | 0.206759 | + | 0.771633i | 0.988906 | + | 0.148540i | \(0.0474575\pi\) |
−0.782148 | + | 0.623093i | \(0.785876\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 28.3695 | − | 28.3695i | 1.44584 | − | 1.44584i | ||||
\(386\) | 15.3681 | + | 8.87279i | 0.782216 | + | 0.451613i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.11698 | + | 0.299293i | 0.0567058 | + | 0.0151943i | ||||
\(389\) | 12.2648 | 0.621852 | 0.310926 | − | 0.950434i | \(-0.399361\pi\) | ||||
0.310926 | + | 0.950434i | \(0.399361\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.3024 | 0.622159 | ||||||||
\(392\) | 5.43255 | + | 1.45565i | 0.274385 | + | 0.0735213i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −19.3315 | − | 11.1610i | −0.973904 | − | 0.562284i | ||||
\(395\) | 17.5399 | − | 17.5399i | 0.882526 | − | 0.882526i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.37885 | + | 8.87800i | 0.119391 | + | 0.445574i | 0.999578 | − | 0.0290536i | \(-0.00924934\pi\) |
−0.880187 | + | 0.474628i | \(0.842583\pi\) | |||||||
\(398\) | −23.3984 | − | 23.3984i | −1.17286 | − | 1.17286i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −41.8026 | + | 24.1347i | −2.09013 | + | 1.20674i | ||||
\(401\) | −6.40341 | + | 23.8979i | −0.319771 | + | 1.19340i | 0.599693 | + | 0.800230i | \(0.295289\pi\) |
−0.919465 | + | 0.393173i | \(0.871377\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.28961 | − | 19.0648i | 0.363121 | − | 0.949684i | ||||
\(404\) | 1.83516i | 0.0913024i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.57192 | − | 16.5790i | −0.475046 | − | 0.822804i | ||||
\(407\) | 20.6001 | − | 35.6804i | 1.02111 | − | 1.76861i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.11794 | − | 0.835449i | 0.154172 | − | 0.0413103i | −0.180907 | − | 0.983500i | \(-0.557903\pi\) |
0.335080 | + | 0.942190i | \(0.391237\pi\) | |||||||
\(410\) | 13.1732 | − | 3.52975i | 0.650578 | − | 0.174322i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.0406879 | − | 0.0704735i | 0.00200455 | − | 0.00347198i | ||||
\(413\) | −10.5728 | − | 18.3126i | −0.520252 | − | 0.901103i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 40.4061i | 1.98346i | ||||||||
\(416\) | −2.10146 | + | 1.70630i | −0.103033 | + | 0.0836581i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.16814 | + | 23.0198i | −0.301693 | + | 1.12594i | ||||
\(419\) | −1.15611 | + | 0.667483i | −0.0564799 | + | 0.0326087i | −0.527974 | − | 0.849261i | \(-0.677048\pi\) |
0.471494 | + | 0.881869i | \(0.343715\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.5788 | − | 11.5788i | −0.564318 | − | 0.564318i | 0.366213 | − | 0.930531i | \(-0.380654\pi\) |
−0.930531 | + | 0.366213i | \(0.880654\pi\) | |||||||
\(422\) | −0.164799 | − | 0.615037i | −0.00802227 | − | 0.0299395i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.94083 | − | 9.94083i | 0.482769 | − | 0.482769i | ||||
\(425\) | 42.1187 | + | 24.3172i | 2.04306 | + | 1.17956i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17.7616 | − | 4.75920i | −0.859543 | − | 0.230314i | ||||
\(428\) | −0.544016 | −0.0262960 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 18.7702 | 0.905180 | ||||||||
\(431\) | −8.56581 | − | 2.29520i | −0.412601 | − | 0.110556i | 0.0465468 | − | 0.998916i | \(-0.485178\pi\) |
−0.459147 | + | 0.888360i | \(0.651845\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.2040 | − | 15.1289i | −1.25928 | − | 0.727047i | −0.286347 | − | 0.958126i | \(-0.592441\pi\) |
−0.972935 | + | 0.231079i | \(0.925774\pi\) | |||||||
\(434\) | −12.9901 | + | 12.9901i | −0.623547 | + | 0.623547i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.254183 | + | 0.948622i | 0.0121731 | + | 0.0454308i | ||||
\(437\) | −7.42973 | − | 7.42973i | −0.355412 | − | 0.355412i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.48134 | − | 3.74201i | 0.309338 | − | 0.178596i | −0.337292 | − | 0.941400i | \(-0.609511\pi\) |
0.646630 | + | 0.762804i | \(0.276178\pi\) | |||||||
\(440\) | 12.7427 | − | 47.5564i | 0.607484 | − | 2.26716i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 21.0527 | + | 8.04970i | 1.00137 | + | 0.382885i | ||||
\(443\) | 19.3969i | 0.921574i | 0.887511 | + | 0.460787i | \(0.152433\pi\) | ||||
−0.887511 | + | 0.460787i | \(0.847567\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.9998 | + | 25.9804i | 0.711059 | + | 1.23159i | ||||
\(446\) | −3.34381 | + | 5.79165i | −0.158334 | + | 0.274243i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −15.8826 | + | 4.25572i | −0.750381 | + | 0.201064i | ||||
\(449\) | 8.28037 | − | 2.21872i | 0.390775 | − | 0.104708i | −0.0580812 | − | 0.998312i | \(-0.518498\pi\) |
0.448856 | + | 0.893604i | \(0.351832\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.15229 | + | 8.92403i | −0.242612 | + | 0.420216i | ||||
\(452\) | 0.0358944 | + | 0.0621709i | 0.00168833 | + | 0.00292427i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 5.95558i | − | 0.279509i | ||||||
\(455\) | −3.34523 | + | 32.2343i | −0.156827 | + | 1.51117i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.78836 | + | 17.8704i | −0.223990 | + | 0.835943i | 0.758816 | + | 0.651305i | \(0.225778\pi\) |
−0.982807 | + | 0.184638i | \(0.940889\pi\) | |||||||
\(458\) | 32.4559 | − | 18.7384i | 1.51657 | − | 0.875590i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.09285 | − | 1.09285i | −0.0509543 | − | 0.0509543i | ||||
\(461\) | −9.37616 | − | 34.9923i | −0.436691 | − | 1.62975i | −0.736986 | − | 0.675907i | \(-0.763752\pi\) |
0.300295 | − | 0.953846i | \(-0.402915\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.5934 | − | 29.5934i | 1.37532 | − | 1.37532i | 0.522968 | − | 0.852352i | \(-0.324825\pi\) |
0.852352 | − | 0.522968i | \(-0.175175\pi\) | |||||||
\(464\) | −21.7033 | − | 12.5304i | −1.00755 | − | 0.581709i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.6551 | − | 2.85504i | −0.493590 | − | 0.132257i | ||||
\(467\) | 21.9880 | 1.01748 | 0.508741 | − | 0.860919i | \(-0.330111\pi\) | ||||
0.508741 | + | 0.860919i | \(0.330111\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.75506 | −0.450447 | ||||||||
\(470\) | 19.7558 | + | 5.29355i | 0.911267 | + | 0.244173i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −22.4723 | − | 12.9744i | −1.03437 | − | 0.597195i | ||||
\(473\) | −10.0285 | + | 10.0285i | −0.461112 | + | 0.461112i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.7508 | − | 40.1223i | −0.493278 | − | 1.84094i | ||||
\(476\) | −0.894026 | − | 0.894026i | −0.0409776 | − | 0.0409776i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.86512 | − | 1.65418i | 0.131048 | − | 0.0756604i | ||||
\(479\) | −5.81718 | + | 21.7100i | −0.265794 | + | 0.991956i | 0.695969 | + | 0.718072i | \(0.254975\pi\) |
−0.961763 | + | 0.273884i | \(0.911692\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.24917 | + | 32.8629i | 0.239341 | + | 1.49842i | ||||
\(482\) | 8.19804i | 0.373411i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.593191 | − | 1.02744i | −0.0269632 | − | 0.0467017i | ||||
\(485\) | 17.5936 | − | 30.4729i | 0.798883 | − | 1.38371i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −27.6154 | + | 7.39953i | −1.25137 | + | 0.335305i | −0.822867 | − | 0.568234i | \(-0.807627\pi\) |
−0.428507 | + | 0.903539i | \(0.640960\pi\) | |||||||
\(488\) | −21.7961 | + | 5.84026i | −0.986665 | + | 0.264376i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6.09247 | + | 10.5525i | −0.275230 | + | 0.476712i | ||||
\(491\) | −2.96335 | − | 5.13268i | −0.133734 | − | 0.231635i | 0.791379 | − | 0.611326i | \(-0.209364\pi\) |
−0.925113 | + | 0.379691i | \(0.876030\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 25.2503i | 1.13722i | ||||||||
\(494\) | −7.85282 | − | 17.5757i | −0.353315 | − | 0.790766i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.22431 | + | 23.2294i | −0.279480 | + | 1.04303i | ||||
\(497\) | 2.07547 | − | 1.19827i | 0.0930975 | − | 0.0537499i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.0680 | + | 26.0680i | 1.16696 | + | 1.16696i | 0.982918 | + | 0.184045i | \(0.0589193\pi\) |
0.184045 | + | 0.982918i | \(0.441081\pi\) | |||||||
\(500\) | −0.885471 | − | 3.30462i | −0.0395995 | − | 0.147787i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 20.8324 | − | 20.8324i | 0.929797 | − | 0.929797i | ||||
\(503\) | −38.0063 | − | 21.9429i | −1.69462 | − | 0.978387i | −0.950698 | − | 0.310117i | \(-0.899632\pi\) |
−0.743918 | − | 0.668270i | \(-0.767035\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 53.9387 | + | 14.4528i | 2.40024 | + | 0.643143i | ||||
\(506\) | 18.7368 | 0.832954 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.09259 | 0.0484758 | ||||||||
\(509\) | −13.3019 | − | 3.56424i | −0.589598 | − | 0.157982i | −0.0483283 | − | 0.998832i | \(-0.515389\pi\) |
−0.541269 | + | 0.840849i | \(0.682056\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −20.9769 | − | 12.1110i | −0.927964 | − | 0.535760i | ||||
\(512\) | −14.1268 | + | 14.1268i | −0.624321 | + | 0.624321i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.78218 | − | 17.8473i | −0.210933 | − | 0.787212i | ||||
\(515\) | −1.75091 | − | 1.75091i | −0.0771544 | − | 0.0771544i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.3833 | + | 7.72687i | −0.588598 | + | 0.339827i | ||||
\(518\) | 7.75247 | − | 28.9326i | 0.340624 | − | 1.27123i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 16.2231 | + | 36.3094i | 0.711428 | + | 1.59227i | ||||
\(521\) | − | 41.9434i | − | 1.83758i | −0.394752 | − | 0.918788i | \(-0.629169\pi\) | ||
0.394752 | − | 0.918788i | \(-0.370831\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.7016 | − | 28.9280i | −0.730308 | − | 1.26493i | −0.956751 | − | 0.290907i | \(-0.906043\pi\) |
0.226443 | − | 0.974024i | \(-0.427290\pi\) | |||||||
\(524\) | 0.664228 | − | 1.15048i | 0.0290169 | − | 0.0502588i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 35.0694 | − | 9.39683i | 1.52910 | − | 0.409721i | ||||
\(527\) | 23.4051 | − | 6.27138i | 1.01954 | − | 0.273186i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.36956 | − | 12.7645i | 0.320416 | − | 0.554976i | ||||
\(530\) | 15.2290 | + | 26.3774i | 0.661505 | + | 1.14576i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.07985i | 0.0468174i | ||||||||
\(533\) | −1.31287 | − | 8.21935i | −0.0568666 | − | 0.356019i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.28442 | + | 15.9897i | −0.185231 | + | 0.691293i | ||||
\(536\) | −10.3671 | + | 5.98547i | −0.447792 | + | 0.258533i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.92582 | + | 4.92582i | 0.212367 | + | 0.212367i | ||||
\(539\) | −2.38288 | − | 8.89303i | −0.102638 | − | 0.383050i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.6243 | + | 18.6243i | −0.800721 | + | 0.800721i | −0.983208 | − | 0.182487i | \(-0.941585\pi\) |
0.182487 | + | 0.983208i | \(0.441585\pi\) | |||||||
\(542\) | 37.9932 | + | 21.9354i | 1.63195 | + | 0.942206i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.10405 | − | 0.831729i | −0.133085 | − | 0.0356601i | ||||
\(545\) | 29.8836 | 1.28007 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.8322 | −0.805209 | −0.402604 | − | 0.915374i | \(-0.631895\pi\) | ||||
−0.402604 | + | 0.915374i | \(0.631895\pi\) | |||||||
\(548\) | 1.30739 | + | 0.350314i | 0.0558490 | + | 0.0149647i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 64.1477 | + | 37.0357i | 2.73527 | + | 1.57921i | ||||
\(551\) | 15.2493 | − | 15.2493i | 0.649642 | − | 0.649642i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.52667 | + | 13.1617i | 0.149969 | + | 0.559692i | ||||
\(554\) | 3.52783 | + | 3.52783i | 0.149883 | + | 0.149883i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.354527 | − | 0.204686i | 0.0150353 | − | 0.00868062i | ||||
\(557\) | 4.93003 | − | 18.3991i | 0.208892 | − | 0.779596i | −0.779336 | − | 0.626607i | \(-0.784443\pi\) |
0.988228 | − | 0.152989i | \(-0.0488900\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.18253 | − | 11.3947i | 0.0500155 | − | 0.481945i | ||||
\(560\) | − | 38.1836i | − | 1.61355i | ||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.08165 | − | 3.60552i | −0.0878090 | − | 0.152090i | ||||
\(563\) | 6.37989 | − | 11.0503i | 0.268880 | − | 0.465714i | −0.699693 | − | 0.714444i | \(-0.746680\pi\) |
0.968573 | + | 0.248730i | \(0.0800130\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.11001 | − | 0.565375i | 0.0887687 | − | 0.0237855i | ||||
\(566\) | −8.04256 | + | 2.15500i | −0.338054 | + | 0.0905813i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.47046 | − | 2.54692i | 0.0616993 | − | 0.106866i | ||||
\(569\) | 4.12000 | + | 7.13605i | 0.172719 | + | 0.299159i | 0.939370 | − | 0.342906i | \(-0.111411\pi\) |
−0.766650 | + | 0.642065i | \(0.778078\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 4.04220i | − | 0.169161i | −0.996417 | − | 0.0845804i | \(-0.973045\pi\) | ||
0.996417 | − | 0.0845804i | \(-0.0269550\pi\) | |||||||
\(572\) | 1.99836 | + | 0.764095i | 0.0835558 | + | 0.0319484i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.93897 | + | 7.23634i | −0.0809311 | + | 0.302039i | ||||
\(575\) | −28.2821 | + | 16.3287i | −1.17944 | + | 0.680953i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.7434 | + | 15.7434i | 0.655405 | + | 0.655405i | 0.954289 | − | 0.298885i | \(-0.0966146\pi\) |
−0.298885 | + | 0.954289i | \(0.596615\pi\) | |||||||
\(578\) | 0.499391 | + | 1.86375i | 0.0207719 | + | 0.0775219i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.24304 | − | 2.24304i | 0.0931371 | − | 0.0931371i | ||||
\(581\) | −19.2223 | − | 11.0980i | −0.797475 | − | 0.460422i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22.2294 | − | 5.95634i | −0.920647 | − | 0.246687i | ||||
\(584\) | −29.7241 | −1.22999 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.74501 | −0.237324 | ||||||||
\(587\) | 36.8797 | + | 9.88188i | 1.52219 | + | 0.407869i | 0.920461 | − | 0.390834i | \(-0.127813\pi\) |
0.601725 | + | 0.798703i | \(0.294480\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.9224 | − | 10.3475i | −0.738479 | − | 0.426361i | ||||
\(590\) | 39.7526 | − | 39.7526i | 1.63659 | − | 1.63659i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −10.1486 | − | 37.8751i | −0.417105 | − | 1.55666i | ||||
\(593\) | 20.2965 | + | 20.2965i | 0.833477 | + | 0.833477i | 0.987991 | − | 0.154513i | \(-0.0493810\pi\) |
−0.154513 | + | 0.987991i | \(0.549381\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −33.3181 | + | 19.2362i | −1.36591 | + | 0.788607i | ||||
\(596\) | 0.0612587 | − | 0.228621i | 0.00250925 | − | 0.00936466i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −11.7494 | + | 9.53999i | −0.480467 | + | 0.390119i | ||||
\(599\) | − | 0.0830308i | − | 0.00339254i | −0.999999 | − | 0.00169627i | \(-0.999460\pi\) | ||
0.999999 | − | 0.00169627i | \(-0.000539941\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.71462 | + | 2.96981i | 0.0699408 | + | 0.121141i | 0.898875 | − | 0.438205i | \(-0.144386\pi\) |
−0.828934 | + | 0.559346i | \(0.811052\pi\) | |||||||
\(602\) | −5.15545 | + | 8.92949i | −0.210120 | + | 0.363939i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.51166 | + | 0.672998i | −0.102198 | + | 0.0273839i | ||||
\(605\) | −34.8701 | + | 9.34340i | −1.41767 | + | 0.379863i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.8585 | + | 20.5396i | −0.481323 | + | 0.833675i | −0.999770 | − | 0.0214340i | \(-0.993177\pi\) |
0.518448 | + | 0.855109i | \(0.326510\pi\) | |||||||
\(608\) | 1.37231 | + | 2.37692i | 0.0556547 | + | 0.0963968i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 48.8876i | − | 1.97940i | ||||||
\(611\) | 4.45814 | − | 11.6595i | 0.180357 | − | 0.471694i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.90062 | − | 25.7535i | 0.278713 | − | 1.04017i | −0.674598 | − | 0.738185i | \(-0.735683\pi\) |
0.953312 | − | 0.301988i | \(-0.0976502\pi\) | |||||||
\(614\) | −33.6776 | + | 19.4438i | −1.35912 | + | 0.784686i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 19.1239 | + | 19.1239i | 0.770526 | + | 0.770526i | ||||
\(617\) | 4.80711 | + | 17.9404i | 0.193527 | + | 0.722253i | 0.992643 | + | 0.121076i | \(0.0386345\pi\) |
−0.799116 | + | 0.601177i | \(0.794699\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.33810 | − | 7.33810i | 0.294943 | − | 0.294943i | −0.544086 | − | 0.839029i | \(-0.683124\pi\) |
0.839029 | + | 0.544086i | \(0.183124\pi\) | |||||||
\(620\) | −2.63622 | − | 1.52202i | −0.105873 | − | 0.0611260i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.73299 | − | 0.732302i | −0.109583 | − | 0.0293626i | ||||
\(623\) | −16.4795 | −0.660236 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −47.2911 | −1.89164 | ||||||||
\(626\) | 26.5089 | + | 7.10304i | 1.05951 | + | 0.283895i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.820476 | − | 0.473702i | −0.0327406 | − | 0.0189028i | ||||
\(629\) | −27.9362 | + | 27.9362i | −1.11389 | + | 1.11389i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.21713 | + | 12.0065i | 0.128072 | + | 0.477970i | 0.999931 | − | 0.0117870i | \(-0.00375200\pi\) |
−0.871859 | + | 0.489757i | \(0.837085\pi\) | |||||||
\(632\) | 11.8236 | + | 11.8236i | 0.470319 | + | 0.470319i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 13.3946 | − | 7.73340i | 0.531969 | − | 0.307133i | ||||
\(635\) | 8.60473 | − | 32.1133i | 0.341468 | − | 1.27438i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.02219 | + | 4.36332i | 0.238608 | + | 0.172881i | ||||
\(638\) | 38.4568i | 1.52252i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −24.8948 | − | 43.1191i | −0.984054 | − | 1.70443i | ||||
\(641\) | 14.6267 | − | 25.3341i | 0.577719 | − | 1.00064i | −0.418022 | − | 0.908437i | \(-0.637276\pi\) |
0.995740 | − | 0.0922009i | \(-0.0293902\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −31.1676 | + | 8.35133i | −1.22913 | + | 0.329344i | −0.814240 | − | 0.580528i | \(-0.802846\pi\) |
−0.414889 | + | 0.909872i | \(0.636180\pi\) | |||||||
\(644\) | 0.820060 | − | 0.219734i | 0.0323149 | − | 0.00865874i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 11.4264 | − | 19.7911i | 0.449566 | − | 0.778672i | ||||
\(647\) | −5.58844 | − | 9.67946i | −0.219704 | − | 0.380539i | 0.735013 | − | 0.678053i | \(-0.237176\pi\) |
−0.954717 | + | 0.297514i | \(0.903843\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 42.4779i | 1.66740i | ||||||||
\(650\) | −59.0823 | + | 9.43716i | −2.31740 | + | 0.370156i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.299224 | + | 1.11672i | −0.0117185 | + | 0.0437341i | ||||
\(653\) | 33.5105 | − | 19.3473i | 1.31137 | − | 0.757119i | 0.329046 | − | 0.944314i | \(-0.393273\pi\) |
0.982323 | + | 0.187195i | \(0.0599396\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −28.5835 | − | 28.5835i | −1.11685 | − | 1.11685i | ||||
\(656\) | 2.53827 | + | 9.47294i | 0.0991027 | + | 0.369856i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −7.94443 | + | 7.94443i | −0.309706 | + | 0.309706i | ||||
\(659\) | −17.2573 | − | 9.96349i | −0.672248 | − | 0.388123i | 0.124680 | − | 0.992197i | \(-0.460210\pi\) |
−0.796928 | + | 0.604074i | \(0.793543\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.1562 | + | 3.25724i | 0.472820 | + | 0.126692i | 0.487357 | − | 0.873203i | \(-0.337961\pi\) |
−0.0145373 | + | 0.999894i | \(0.504628\pi\) | |||||||
\(662\) | −46.7837 | −1.81830 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −27.2379 | −1.05703 | ||||||||
\(665\) | 31.7388 | + | 8.50440i | 1.23078 | + | 0.329786i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.6837 | − | 8.47761i | −0.568553 | − | 0.328254i | ||||
\(668\) | −2.03391 | + | 2.03391i | −0.0786943 | + | 0.0786943i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6.71256 | − | 25.0516i | −0.259329 | − | 0.967828i | ||||
\(671\) | 26.1196 | + | 26.1196i | 1.00834 | + | 1.00834i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 38.5206 | − | 22.2399i | 1.48486 | − | 0.857284i | 0.485007 | − | 0.874510i | \(-0.338817\pi\) |
0.999852 | + | 0.0172265i | \(0.00548363\pi\) | |||||||
\(674\) | 0.487063 | − | 1.81774i | 0.0187610 | − | 0.0700168i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.64216 | + | 0.538337i | −0.0631602 | + | 0.0207053i | ||||
\(677\) | 12.5077i | 0.480712i | 0.970685 | + | 0.240356i | \(0.0772641\pi\) | ||||
−0.970685 | + | 0.240356i | \(0.922736\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.66453 | + | 16.7395i | 0.370891 | + | 0.642402i | ||||
\(680\) | −23.6057 | + | 40.8863i | −0.905239 | + | 1.56792i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 35.6465 | − | 9.55145i | 1.36498 | − | 0.365744i | ||||
\(683\) | 38.3295 | − | 10.2703i | 1.46664 | − | 0.392984i | 0.564860 | − | 0.825187i | \(-0.308930\pi\) |
0.901776 | + | 0.432203i | \(0.142264\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.5928 | − | 35.6678i | 0.786811 | − | 1.36280i | ||||
\(686\) | −14.7049 | − | 25.4696i | −0.561434 | − | 0.972432i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 13.4978i | 0.514598i | ||||||||
\(689\) | 16.9722 | − | 7.58318i | 0.646588 | − | 0.288896i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.99167 | + | 14.8971i | −0.151850 | + | 0.566713i | 0.847504 | + | 0.530789i | \(0.178104\pi\) |
−0.999355 | + | 0.0359243i | \(0.988562\pi\) | |||||||
\(692\) | −0.831995 | + | 0.480352i | −0.0316277 | + | 0.0182603i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 25.7346 | + | 25.7346i | 0.976872 | + | 0.976872i | ||||
\(695\) | −3.22403 | − | 12.0322i | −0.122294 | − | 0.456409i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.98711 | − | 6.98711i | 0.264656 | − | 0.264656i | ||||
\(698\) | −38.6733 | − | 22.3280i | −1.46380 | − | 0.845128i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.24190 | + | 0.868665i | 0.122532 | + | 0.0328325i | ||||
\(701\) | 11.2283 | 0.424087 | 0.212043 | − | 0.977260i | \(-0.431988\pi\) | ||||
0.212043 | + | 0.977260i | \(0.431988\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 33.7427 | 1.27263 | ||||||||
\(704\) | 31.9055 | + | 8.54905i | 1.20248 | + | 0.322204i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 40.1253 | + | 23.1663i | 1.51013 | + | 0.871876i | ||||
\(707\) | −21.6905 | + | 21.6905i | −0.815755 | + | 0.815755i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.91587 | + | 18.3463i | 0.184619 | + | 0.689009i | 0.994712 | + | 0.102707i | \(0.0327503\pi\) |
−0.810092 | + | 0.586302i | \(0.800583\pi\) | |||||||
\(710\) | 4.50539 | + | 4.50539i | 0.169084 | + | 0.169084i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −17.5135 | + | 10.1114i | −0.656345 | + | 0.378941i | ||||
\(713\) | −4.21114 | + | 15.7162i | −0.157708 | + | 0.588576i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 38.1964 | − | 52.7181i | 1.42846 | − | 1.97154i | ||||
\(716\) | 0.607269i | 0.0226947i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 26.8178 | + | 46.4497i | 1.00083 | + | 1.73349i | ||||
\(719\) | −11.7051 | + | 20.2738i | −0.436526 | + | 0.756086i | −0.997419 | − | 0.0718029i | \(-0.977125\pi\) |
0.560893 | + | 0.827889i | \(0.310458\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.31386 | − | 0.352049i | 0.0489308 | − | 0.0131110i | ||||
\(722\) | 7.95010 | − | 2.13022i | 0.295872 | − | 0.0792787i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.62720 | − | 2.81839i | 0.0604742 | − | 0.104744i | ||||
\(725\) | −33.5141 | − | 58.0482i | −1.24468 | − | 2.15586i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 8.84565i | − | 0.328067i | −0.986455 | − | 0.164033i | \(-0.947550\pi\) | ||
0.986455 | − | 0.164033i | \(-0.0524505\pi\) | |||||||
\(728\) | −21.7292 | − | 2.25502i | −0.805338 | − | 0.0835767i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 16.6674 | − | 62.2037i | 0.616889 | − | 2.30226i | ||||
\(731\) | 11.7778 | − | 6.79992i | 0.435618 | − | 0.251504i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24.1754 | − | 24.1754i | −0.892939 | − | 0.892939i | 0.101860 | − | 0.994799i | \(-0.467521\pi\) |
−0.994799 | + | 0.101860i | \(0.967521\pi\) | |||||||
\(734\) | 5.44407 | + | 20.3175i | 0.200944 | + | 0.749934i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.52583 | − | 1.52583i | 0.0562430 | − | 0.0562430i | ||||
\(737\) | 16.9709 | + | 9.79816i | 0.625132 | + | 0.360920i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.1089 | − | 4.85226i | −0.666146 | − | 0.178493i | −0.0901281 | − | 0.995930i | \(-0.528728\pi\) |
−0.576018 | + | 0.817437i | \(0.695394\pi\) | |||||||
\(740\) | 4.96326 | 0.182453 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −16.7312 | −0.614223 | ||||||||
\(743\) | 42.3605 | + | 11.3505i | 1.55406 | + | 0.416408i | 0.930776 | − | 0.365591i | \(-0.119133\pi\) |
0.623280 | + | 0.781999i | \(0.285800\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.23715 | − | 3.60102i | −0.228511 | − | 0.131931i | ||||
\(746\) | −7.92414 | + | 7.92414i | −0.290123 | + | 0.290123i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.657364 | + | 2.45331i | 0.0240356 | + | 0.0897021i | ||||
\(749\) | −6.42995 | − | 6.42995i | −0.234945 | − | 0.234945i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 42.5665 | − | 24.5758i | 1.55328 | − | 0.896784i | 0.555403 | − | 0.831581i | \(-0.312564\pi\) |
0.997872 | − | 0.0652026i | \(-0.0207694\pi\) | |||||||
\(752\) | −3.80663 | + | 14.2065i | −0.138813 | + | 0.518058i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −19.5806 | − | 24.1152i | −0.713082 | − | 0.878225i | ||||
\(755\) | 79.1227i | 2.87957i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.66206 | + | 4.61083i | 0.0967543 | + | 0.167583i | 0.910339 | − | 0.413862i | \(-0.135821\pi\) |
−0.813585 | + | 0.581446i | \(0.802487\pi\) | |||||||
\(758\) | −9.05733 | + | 15.6878i | −0.328977 | + | 0.569805i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 38.9484 | − | 10.4362i | 1.41281 | − | 0.378560i | ||||
\(761\) | −21.6018 | + | 5.78817i | −0.783063 | + | 0.209821i | −0.628135 | − | 0.778105i | \(-0.716181\pi\) |
−0.154928 | + | 0.987926i | \(0.549515\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.20788 | + | 14.2165i | −0.297145 | + | 0.514670i | ||||
\(764\) | −0.412900 | − | 0.715164i | −0.0149382 | − | 0.0258737i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 22.8326i | − | 0.824975i | ||||||
\(767\) | −21.6279 | − | 26.6368i | −0.780939 | − | 0.961797i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.42819 | + | 27.7224i | −0.267867 | + | 0.999694i | 0.692605 | + | 0.721317i | \(0.256463\pi\) |
−0.960472 | + | 0.278377i | \(0.910204\pi\) | |||||||
\(770\) | −50.7442 | + | 29.2972i | −1.82869 | + | 1.05580i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.14215 | − | 1.14215i | −0.0411070 | − | 0.0411070i | ||||
\(773\) | −2.25051 | − | 8.39903i | −0.0809454 | − | 0.302092i | 0.913570 | − | 0.406681i | \(-0.133314\pi\) |
−0.994516 | + | 0.104589i | \(0.966647\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −45.4824 | + | 45.4824i | −1.63377 | + | 1.63377i | ||||
\(776\) | 20.5419 | + | 11.8599i | 0.737410 | + | 0.425744i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −17.3019 | − | 4.63604i | −0.620304 | − | 0.166210i | ||||
\(779\) | −8.43939 | −0.302373 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.81427 | −0.172268 | ||||||||
\(782\) | −17.3549 | − | 4.65023i | −0.620610 | − | 0.166292i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −7.58834 | − | 4.38113i | −0.271012 | − | 0.156469i | ||||
\(785\) | −20.3847 | + | 20.3847i | −0.727561 | + | 0.727561i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.33848 | − | 4.99526i | −0.0477115 | − | 0.178062i | 0.937958 | − | 0.346748i | \(-0.112714\pi\) |
−0.985670 | + | 0.168686i | \(0.946047\pi\) | |||||||
\(788\) | 1.43671 | + | 1.43671i | 0.0511806 | + | 0.0511806i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −31.3733 | + | 18.1134i | −1.11621 | + | 0.644445i | ||||
\(791\) | −0.310573 | + | 1.15907i | −0.0110427 | + | 0.0412119i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −29.6779 | − | 3.07993i | −1.05389 | − | 0.109371i | ||||
\(794\) | − | 13.4233i | − | 0.476376i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.50599 | + | 2.60844i | 0.0533782 | + | 0.0924538i | ||||
\(797\) | −10.3869 | + | 17.9906i | −0.367923 | + | 0.637261i | −0.989241 | − | 0.146297i | \(-0.953264\pi\) |
0.621318 | + | 0.783559i | \(0.286598\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.3139 | − | 3.83541i | 0.506391 | − | 0.135687i | ||||
\(800\) | 8.23987 | − | 2.20787i | 0.291323 | − | 0.0780599i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 18.0665 | − | 31.2921i | 0.637950 | − | 1.10496i | ||||
\(803\) | 24.3291 | + | 42.1392i | 0.858554 | + | 1.48706i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 25.8336i | − | 0.910516i | ||||||
\(806\) | −17.4898 | + | 24.1391i | −0.616051 | + | 0.850265i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −9.74269 | + | 36.3602i | −0.342747 | + | 1.27915i | ||||
\(809\) | 28.1672 | − | 16.2623i | 0.990304 | − | 0.571753i | 0.0849391 | − | 0.996386i | \(-0.472930\pi\) |
0.905365 | + | 0.424634i | \(0.139597\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.1138 | + | 14.1138i | 0.495604 | + | 0.495604i | 0.910066 | − | 0.414462i | \(-0.136030\pi\) |
−0.414462 | + | 0.910066i | \(0.636030\pi\) | |||||||
\(812\) | 0.450999 | + | 1.68315i | 0.0158269 | + | 0.0590670i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −42.5474 | + | 42.5474i | −1.49129 | + | 1.49129i | ||||
\(815\) | 30.4659 | + | 17.5895i | 1.06717 | + | 0.616134i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.2196 | − | 3.00627i | −0.392523 | − | 0.105176i | ||||
\(818\) | −4.71425 | −0.164830 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.24136 | −0.0433502 | ||||||||
\(821\) | −13.7815 | − | 3.69275i | −0.480979 | − | 0.128878i | 0.0101795 | − | 0.999948i | \(-0.496760\pi\) |
−0.491158 | + | 0.871070i | \(0.663426\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.88216 | + | 1.66402i | 0.100466 | + | 0.0580040i | 0.549391 | − | 0.835565i | \(-0.314860\pi\) |
−0.448925 | + | 0.893569i | \(0.648193\pi\) | |||||||
\(824\) | 1.18029 | − | 1.18029i | 0.0411175 | − | 0.0411175i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.99289 | + | 29.8299i | 0.278108 | + | 1.03791i | ||||
\(827\) | −17.1703 | − | 17.1703i | −0.597071 | − | 0.597071i | 0.342461 | − | 0.939532i | \(-0.388740\pi\) |
−0.939532 | + | 0.342461i | \(0.888740\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.0223 | + | 6.94108i | −0.417552 | + | 0.241074i | −0.694029 | − | 0.719947i | \(-0.744166\pi\) |
0.276478 | + | 0.961020i | \(0.410833\pi\) | |||||||
\(830\) | 15.2733 | − | 57.0007i | 0.530143 | − | 1.97852i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −24.3599 | + | 10.8840i | −0.844527 | + | 0.377335i | ||||
\(833\) | 8.82852i | 0.305890i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 43.7623 | + | 75.7986i | 1.51446 | + | 2.62312i | ||||
\(836\) | 1.08462 | − | 1.87862i | 0.0375124 | − | 0.0649733i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.88323 | − | 0.504609i | 0.0650550 | − | 0.0174314i | ||||
\(839\) | 6.64552 | − | 1.78066i | 0.229429 | − | 0.0614752i | −0.142273 | − | 0.989827i | \(-0.545441\pi\) |
0.371702 | + | 0.928352i | \(0.378774\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.90006 | − | 5.02305i | 0.100002 | − | 0.173209i | ||||
\(842\) | 11.9575 | + | 20.7109i | 0.412081 | + | 0.713745i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.0579572i | 0.00199497i | ||||||||
\(845\) | 2.88984 | + | 52.5060i | 0.0994134 | + | 1.80626i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.13254 | − | 19.1549i | 0.176356 | − | 0.658170i | ||||
\(848\) | −18.9681 | + | 10.9513i | −0.651369 | + | 0.376068i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −50.2248 | − | 50.2248i | −1.72270 | − | 1.72270i | ||||
\(851\) | −6.86617 | − | 25.6249i | −0.235369 | − | 0.878411i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.95752 | − | 6.95752i | 0.238221 | − | 0.238221i | −0.577892 | − | 0.816113i | \(-0.696125\pi\) |
0.816113 | + | 0.577892i | \(0.196125\pi\) | |||||||
\(854\) | 23.2572 | + | 13.4275i | 0.795844 | + | 0.459481i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.7787 | − | 2.88813i | −0.368407 | − | 0.0987144i | ||||
\(857\) | −9.91039 | −0.338533 | −0.169266 | − | 0.985570i | \(-0.554140\pi\) | ||||
−0.169266 | + | 0.985570i | \(0.554140\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.5641 | 0.838116 | 0.419058 | − | 0.907959i | \(-0.362360\pi\) | ||||
0.419058 | + | 0.907959i | \(0.362360\pi\) | |||||||
\(860\) | −1.65030 | − | 0.442196i | −0.0562747 | − | 0.0150788i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 11.2162 | + | 6.47565i | 0.382024 | + | 0.220562i | ||||
\(863\) | 13.9880 | − | 13.9880i | 0.476158 | − | 0.476158i | −0.427742 | − | 0.903901i | \(-0.640691\pi\) |
0.903901 | + | 0.427742i | \(0.140691\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.56607 | + | 28.2370i | 0.257254 | + | 0.960085i | ||||
\(866\) | 31.2471 | + | 31.2471i | 1.06182 | + | 1.06182i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.44814 | − | 0.836082i | 0.0491529 | − | 0.0283785i | ||||
\(869\) | 7.08449 | − | 26.4397i | 0.240325 | − | 0.896905i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.6308 | + | 2.49669i | −0.529630 | + | 0.0845972i | ||||
\(872\) | 20.1446i | 0.682183i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 7.67267 | + | 13.2895i | 0.259532 | + | 0.449523i | ||||
\(875\) | 28.5930 | − | 49.5245i | 0.966619 | − | 1.67423i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −50.3184 | + | 13.4828i | −1.69913 | + | 0.455281i | −0.972721 | − | 0.231979i | \(-0.925480\pi\) |
−0.726411 | + | 0.687260i | \(0.758813\pi\) | |||||||
\(878\) | −10.5576 | + | 2.82891i | −0.356303 | + | 0.0954712i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −38.3523 | + | 66.4282i | −1.29286 | + | 2.23929i | ||||
\(881\) | −11.1254 | − | 19.2698i | −0.374825 | − | 0.649215i | 0.615476 | − | 0.788155i | \(-0.288964\pi\) |
−0.990301 | + | 0.138940i | \(0.955630\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 56.9678i | 1.91712i | 0.284891 | + | 0.958560i | \(0.408042\pi\) | ||||
−0.284891 | + | 0.958560i | \(0.591958\pi\) | |||||||
\(884\) | −1.66134 | − | 1.20371i | −0.0558768 | − | 0.0404850i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7.33191 | − | 27.3631i | 0.246320 | − | 0.919280i | ||||
\(887\) | −9.04924 | + | 5.22458i | −0.303844 | + | 0.175424i | −0.644168 | − | 0.764884i | \(-0.722796\pi\) |
0.340325 | + | 0.940308i | \(0.389463\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.9138 | + | 12.9138i | 0.433114 | + | 0.433114i | ||||
\(890\) | −11.3397 | − | 42.3203i | −0.380107 | − | 1.41858i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.430434 | − | 0.430434i | 0.0144120 | − | 0.0144120i | ||||
\(893\) | −10.9609 | − | 6.32826i | −0.366791 | − | 0.211767i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17.8488 | + | 4.78257i | 0.596619 | + | 0.159864i | ||||
\(896\) | 27.3506 | 0.913718 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −12.5197 | −0.417789 | ||||||||
\(899\) | −32.2570 | − | 8.64325i | −1.07583 | − | 0.288268i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.1116 | + | 11.0341i | 0.636699 | + | 0.367598i | ||||
\(902\) | 10.6415 | − | 10.6415i | 0.354324 | − | 0.354324i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.381120 | + | 1.42236i | 0.0126759 | + | 0.0473070i | ||||
\(905\) | −70.0227 | − | 70.0227i | −2.32763 | − | 2.32763i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.72283 | − | 0.994679i | 0.0572058 | − | 0.0330278i | −0.471124 | − | 0.882067i | \(-0.656152\pi\) |
0.528330 | + | 0.849039i | \(0.322818\pi\) | |||||||
\(908\) | −0.140304 | + | 0.523622i | −0.00465615 | + | 0.0173770i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 16.9035 | − | 44.2082i | 0.560344 | − | 1.46549i | ||||
\(911\) | 33.1613i | 1.09868i | 0.835598 | + | 0.549342i | \(0.185121\pi\) | ||||
−0.835598 | + | 0.549342i | \(0.814879\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22.2940 | + | 38.6144i | 0.737825 | + | 1.27795i | ||||
\(914\) | 13.5098 | − | 23.3997i | 0.446865 | − | 0.773993i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.29501 | + | 0.882896i | −0.108870 | + | 0.0291717i | ||||
\(917\) | 21.4487 | − | 5.74717i | 0.708300 | − | 0.189788i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.40003 | − | 2.42492i | 0.0461826 | − | 0.0799906i | −0.842010 | − | 0.539462i | \(-0.818628\pi\) |
0.888193 | + | 0.459471i | \(0.151961\pi\) | |||||||
\(920\) | −15.8509 | − | 27.4546i | −0.522589 | − | 0.905150i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 52.9075i | 1.74242i | ||||||||
\(923\) | 3.01890 | − | 2.45122i | 0.0993682 | − | 0.0806828i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 27.1437 | − | 101.302i | 0.892480 | − | 3.33078i | ||||
\(926\) | −52.9333 | + | 30.5610i | −1.73950 | + | 1.00430i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.13173 | + | 3.13173i | 0.102804 | + | 0.102804i | ||||
\(929\) | −11.5525 | − | 43.1147i | −0.379027 | − | 1.41455i | −0.847371 | − | 0.531001i | \(-0.821816\pi\) |
0.468345 | − | 0.883546i | \(-0.344851\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.33177 | − | 5.33177i | 0.174742 | − | 0.174742i | ||||
\(932\) | 0.869553 | + | 0.502036i | 0.0284831 | + | 0.0164448i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −31.0183 | − | 8.31133i | −1.01495 | − | 0.271955i | ||||
\(935\) | 77.2847 | 2.52748 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.3615 | 0.599843 | 0.299922 | − | 0.953964i | \(-0.403039\pi\) | ||||
0.299922 | + | 0.953964i | \(0.403039\pi\) | |||||||
\(938\) | 13.7614 | + | 3.68736i | 0.449326 | + | 0.120396i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.61225 | − | 0.930830i | −0.0525857 | − | 0.0303603i | ||||
\(941\) | −31.9766 | + | 31.9766i | −1.04241 | + | 1.04241i | −0.0433488 | + | 0.999060i | \(0.513803\pi\) |
−0.999060 | + | 0.0433488i | \(0.986197\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.71730 | + | 6.40904i | 0.0559229 | + | 0.208707i | ||||
\(944\) | 28.5863 | + | 28.5863i | 0.930406 | + | 0.930406i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 17.9379 | − | 10.3564i | 0.583211 | − | 0.336717i | ||||
\(947\) | −5.54223 | + | 20.6839i | −0.180098 | + | 0.672136i | 0.815528 | + | 0.578717i | \(0.196446\pi\) |
−0.995627 | + | 0.0934194i | \(0.970220\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −36.7115 | − | 14.0370i | −1.19171 | − | 0.455661i | ||||
\(950\) | 60.6640i | 1.96820i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −12.9672 | − | 22.4598i | −0.420268 | − | 0.727925i | ||||
\(953\) | −5.50952 | + | 9.54276i | −0.178471 | + | 0.309120i | −0.941357 | − | 0.337412i | \(-0.890448\pi\) |
0.762886 | + | 0.646533i | \(0.223782\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24.2719 | + | 6.50362i | −0.785419 | + | 0.210452i | ||||
\(956\) | −0.290875 | + | 0.0779397i | −0.00940757 | + | 0.00252075i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 16.4125 | − | 28.4273i | 0.530264 | − | 0.918444i | ||||
\(959\) | 11.3121 | + | 19.5931i | 0.365286 | + | 0.632695i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.04649i | 0.0337578i | ||||||||
\(962\) | 5.01704 | − | 48.3437i | 0.161756 | − | 1.55866i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.193133 | − | 0.720782i | 0.00622039 | − | 0.0232148i | ||||
\(965\) | −42.5652 | + | 24.5750i | −1.37022 | + | 0.791098i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.2238 | − | 22.2238i | −0.714668 | − | 0.714668i | 0.252840 | − | 0.967508i | \(-0.418635\pi\) |
−0.967508 | + | 0.252840i | \(0.918635\pi\) | |||||||
\(968\) | −6.29841 | − | 23.5060i | −0.202438 | − | 0.755511i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −36.3377 | + | 36.3377i | −1.16673 | + | 1.16673i | ||||
\(971\) | −5.81217 | − | 3.35566i | −0.186521 | − | 0.107688i | 0.403832 | − | 0.914833i | \(-0.367678\pi\) |
−0.590353 | + | 0.807145i | \(0.701011\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.60957 | + | 1.77103i | 0.211893 | + | 0.0567766i | ||||
\(974\) | 41.7539 | 1.33788 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 35.1554 | 1.12530 | ||||||||
\(977\) | 34.6264 | + | 9.27812i | 1.10780 | + | 0.296833i | 0.765936 | − | 0.642917i | \(-0.222276\pi\) |
0.341861 | + | 0.939750i | \(0.388943\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 28.6694 | + | 16.5523i | 0.916277 | + | 0.529013i | ||||
\(980\) | 0.784256 | − | 0.784256i | 0.0250521 | − | 0.0250521i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.24026 | + | 8.36077i | 0.0714896 | + | 0.266803i | ||||
\(983\) | −13.5996 | − | 13.5996i | −0.433760 | − | 0.433760i | 0.456145 | − | 0.889905i | \(-0.349230\pi\) |
−0.889905 | + | 0.456145i | \(0.849230\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 53.5425 | − | 30.9128i | 1.70600 | − | 0.984962i | ||||
\(986\) | 9.54447 | − | 35.6205i | 0.303958 | − | 1.13439i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.276375 | + | 1.73027i | 0.00879265 | + | 0.0550473i | ||||
\(989\) | 9.13210i | 0.290384i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.3366 | − | 31.7599i | −0.582481 | − | 1.00889i | −0.995184 | − | 0.0980209i | \(-0.968749\pi\) |
0.412704 | − | 0.910865i | \(-0.364585\pi\) | |||||||
\(992\) | 2.12505 | − | 3.68069i | 0.0674704 | − | 0.116862i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.38079 | + | 0.905880i | −0.107232 | + | 0.0287328i | ||||
\(995\) | 88.5276 | − | 23.7209i | 2.80651 | − | 0.752003i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.27729 | − | 7.40849i | 0.135463 | − | 0.234629i | −0.790311 | − | 0.612706i | \(-0.790081\pi\) |
0.925774 | + | 0.378077i | \(0.123414\pi\) | |||||||
\(998\) | −26.9204 | − | 46.6275i | −0.852150 | − | 1.47597i | ||||
\(999\) | 0 | 0 |
(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 | 351.2.bd.d.323.2 | yes | 20 | |
3.2 | odd | 2 | 351.2.bd.e.323.4 | yes | 20 | ||
13.6 | odd | 12 | 351.2.bd.e.188.4 | yes | 20 | ||
39.32 | even | 12 | inner | 351.2.bd.d.188.2 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
351.2.bd.d.188.2 | ✓ | 20 | 39.32 | even | 12 | inner | |
351.2.bd.d.323.2 | yes | 20 | 1.1 | even | 1 | trivial | |
351.2.bd.e.188.4 | yes | 20 | 13.6 | odd | 12 | ||
351.2.bd.e.323.4 | yes | 20 | 3.2 | odd | 2 |