Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [403,2,Mod(216,403)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(403, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("403.216");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 403 = 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 403.i (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.21797120146\) |
Analytic rank: | \(0\) |
Dimension: | \(68\) |
Relative dimension: | \(34\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 216.6 | ||
Character | \(\chi\) | \(=\) | 403.216 |
Dual form | 403.2.i.a.278.5 |
$q$-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 \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).
\(n\) | \(249\) | \(313\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.50749 | − | 1.50749i | −1.06596 | − | 1.06596i | −0.997666 | − | 0.0682901i | \(-0.978246\pi\) |
−0.0682901 | − | 0.997666i | \(-0.521754\pi\) | |||||||
\(3\) | 1.65703i | 0.956685i | 0.878173 | + | 0.478342i | \(0.158762\pi\) | ||||
−0.878173 | + | 0.478342i | \(0.841238\pi\) | |||||||
\(4\) | 2.54505i | 1.27252i | ||||||||
\(5\) | 2.11743 | + | 2.11743i | 0.946944 | + | 0.946944i | 0.998662 | − | 0.0517174i | \(-0.0164695\pi\) |
−0.0517174 | + | 0.998662i | \(0.516470\pi\) | |||||||
\(6\) | 2.49795 | − | 2.49795i | 1.01978 | − | 1.01978i | ||||
\(7\) | −2.06359 | + | 2.06359i | −0.779964 | + | 0.779964i | −0.979824 | − | 0.199860i | \(-0.935951\pi\) |
0.199860 | + | 0.979824i | \(0.435951\pi\) | |||||||
\(8\) | 0.821650 | − | 0.821650i | 0.290497 | − | 0.290497i | ||||
\(9\) | 0.254264 | 0.0847547 | ||||||||
\(10\) | − | 6.38401i | − | 2.01880i | ||||||
\(11\) | 1.21675 | + | 1.21675i | 0.366865 | + | 0.366865i | 0.866333 | − | 0.499468i | \(-0.166471\pi\) |
−0.499468 | + | 0.866333i | \(0.666471\pi\) | |||||||
\(12\) | −4.21721 | −1.21740 | ||||||||
\(13\) | −3.49118 | − | 0.900923i | −0.968279 | − | 0.249871i | ||||
\(14\) | 6.22168 | 1.66281 | ||||||||
\(15\) | −3.50864 | + | 3.50864i | −0.905927 | + | 0.905927i | ||||
\(16\) | 2.61283 | 0.653209 | ||||||||
\(17\) | −3.51667 | −0.852918 | −0.426459 | − | 0.904507i | \(-0.640239\pi\) | ||||
−0.426459 | + | 0.904507i | \(0.640239\pi\) | |||||||
\(18\) | −0.383300 | − | 0.383300i | −0.0903448 | − | 0.0903448i | ||||
\(19\) | −2.18795 | − | 2.18795i | −0.501950 | − | 0.501950i | 0.410094 | − | 0.912043i | \(-0.365496\pi\) |
−0.912043 | + | 0.410094i | \(0.865496\pi\) | |||||||
\(20\) | −5.38896 | + | 5.38896i | −1.20501 | + | 1.20501i | ||||
\(21\) | −3.41942 | − | 3.41942i | −0.746180 | − | 0.746180i | ||||
\(22\) | − | 3.66848i | − | 0.782124i | ||||||
\(23\) | −8.25892 | −1.72210 | −0.861052 | − | 0.508516i | \(-0.830194\pi\) | ||||
−0.861052 | + | 0.508516i | \(0.830194\pi\) | |||||||
\(24\) | 1.36150 | + | 1.36150i | 0.277914 | + | 0.277914i | ||||
\(25\) | 3.96704i | 0.793407i | ||||||||
\(26\) | 3.90478 | + | 6.62105i | 0.765791 | + | 1.29849i | ||||
\(27\) | 5.39240i | 1.03777i | ||||||||
\(28\) | −5.25193 | − | 5.25193i | −0.992522 | − | 0.992522i | ||||
\(29\) | − | 5.44619i | − | 1.01133i | −0.862730 | − | 0.505666i | \(-0.831247\pi\) | ||
0.862730 | − | 0.505666i | \(-0.168753\pi\) | |||||||
\(30\) | 10.5785 | 1.93136 | ||||||||
\(31\) | 3.46978 | + | 4.35438i | 0.623192 | + | 0.782069i | ||||
\(32\) | −5.58212 | − | 5.58212i | −0.986789 | − | 0.986789i | ||||
\(33\) | −2.01619 | + | 2.01619i | −0.350974 | + | 0.350974i | ||||
\(34\) | 5.30134 | + | 5.30134i | 0.909173 | + | 0.909173i | ||||
\(35\) | −8.73903 | −1.47717 | ||||||||
\(36\) | 0.647114i | 0.107852i | ||||||||
\(37\) | 8.01045 | + | 8.01045i | 1.31691 | + | 1.31691i | 0.916209 | + | 0.400701i | \(0.131233\pi\) |
0.400701 | + | 0.916209i | \(0.368767\pi\) | |||||||
\(38\) | 6.59662i | 1.07011i | ||||||||
\(39\) | 1.49285 | − | 5.78498i | 0.239048 | − | 0.926338i | ||||
\(40\) | 3.47958 | 0.550169 | ||||||||
\(41\) | 4.30972 | + | 4.30972i | 0.673065 | + | 0.673065i | 0.958421 | − | 0.285357i | \(-0.0921120\pi\) |
−0.285357 | + | 0.958421i | \(0.592112\pi\) | |||||||
\(42\) | 10.3095i | 1.59079i | ||||||||
\(43\) | −1.42480 | −0.217280 | −0.108640 | − | 0.994081i | \(-0.534650\pi\) | ||||
−0.108640 | + | 0.994081i | \(0.534650\pi\) | |||||||
\(44\) | −3.09669 | + | 3.09669i | −0.466844 | + | 0.466844i | ||||
\(45\) | 0.538387 | + | 0.538387i | 0.0802580 | + | 0.0802580i | ||||
\(46\) | 12.4502 | + | 12.4502i | 1.83569 | + | 1.83569i | ||||
\(47\) | 6.04391 | − | 6.04391i | 0.881595 | − | 0.881595i | −0.112102 | − | 0.993697i | \(-0.535758\pi\) |
0.993697 | + | 0.112102i | \(0.0357583\pi\) | |||||||
\(48\) | 4.32954i | 0.624915i | ||||||||
\(49\) | − | 1.51682i | − | 0.216688i | ||||||
\(50\) | 5.98026 | − | 5.98026i | 0.845737 | − | 0.845737i | ||||
\(51\) | − | 5.82722i | − | 0.815974i | ||||||
\(52\) | 2.29289 | − | 8.88521i | 0.317967 | − | 1.23216i | ||||
\(53\) | − | 4.78015i | − | 0.656604i | −0.944573 | − | 0.328302i | \(-0.893524\pi\) | ||
0.944573 | − | 0.328302i | \(-0.106476\pi\) | |||||||
\(54\) | 8.12898 | − | 8.12898i | 1.10621 | − | 1.10621i | ||||
\(55\) | 5.15279i | 0.694802i | ||||||||
\(56\) | 3.39110i | 0.453155i | ||||||||
\(57\) | 3.62549 | − | 3.62549i | 0.480208 | − | 0.480208i | ||||
\(58\) | −8.21006 | + | 8.21006i | −1.07803 | + | 1.07803i | ||||
\(59\) | −9.59471 | + | 9.59471i | −1.24912 | + | 1.24912i | −0.293018 | + | 0.956107i | \(0.594660\pi\) |
−0.956107 | + | 0.293018i | \(0.905340\pi\) | |||||||
\(60\) | −8.92965 | − | 8.92965i | −1.15281 | − | 1.15281i | ||||
\(61\) | − | 4.85057i | − | 0.621052i | −0.950565 | − | 0.310526i | \(-0.899495\pi\) | ||
0.950565 | − | 0.310526i | \(-0.100505\pi\) | |||||||
\(62\) | 1.33351 | − | 11.7948i | 0.169356 | − | 1.49795i | ||||
\(63\) | −0.524697 | + | 0.524697i | −0.0661057 | + | 0.0661057i | ||||
\(64\) | 11.6043i | 1.45054i | ||||||||
\(65\) | −5.48469 | − | 9.29998i | −0.680293 | − | 1.15352i | ||||
\(66\) | 6.07878 | 0.748246 | ||||||||
\(67\) | 2.62579 | + | 2.62579i | 0.320792 | + | 0.320792i | 0.849071 | − | 0.528279i | \(-0.177162\pi\) |
−0.528279 | + | 0.849071i | \(0.677162\pi\) | |||||||
\(68\) | − | 8.95009i | − | 1.08536i | ||||||
\(69\) | − | 13.6853i | − | 1.64751i | ||||||
\(70\) | 13.1740 | + | 13.1740i | 1.57459 | + | 1.57459i | ||||
\(71\) | 4.73789 | + | 4.73789i | 0.562284 | + | 0.562284i | 0.929956 | − | 0.367672i | \(-0.119845\pi\) |
−0.367672 | + | 0.929956i | \(0.619845\pi\) | |||||||
\(72\) | 0.208916 | − | 0.208916i | 0.0246210 | − | 0.0246210i | ||||
\(73\) | 7.22387 | + | 7.22387i | 0.845490 | + | 0.845490i | 0.989567 | − | 0.144077i | \(-0.0460212\pi\) |
−0.144077 | + | 0.989567i | \(0.546021\pi\) | |||||||
\(74\) | − | 24.1513i | − | 2.80753i | ||||||
\(75\) | −6.57348 | −0.759040 | ||||||||
\(76\) | 5.56843 | − | 5.56843i | 0.638743 | − | 0.638743i | ||||
\(77\) | −5.02176 | −0.572283 | ||||||||
\(78\) | −10.9712 | + | 6.47033i | −1.24225 | + | 0.732621i | ||||
\(79\) | 14.9861i | 1.68606i | 0.537864 | + | 0.843031i | \(0.319231\pi\) | ||||
−0.537864 | + | 0.843031i | \(0.680769\pi\) | |||||||
\(80\) | 5.53250 | + | 5.53250i | 0.618552 | + | 0.618552i | ||||
\(81\) | −8.17256 | −0.908062 | ||||||||
\(82\) | − | 12.9937i | − | 1.43491i | ||||||
\(83\) | −1.67927 | + | 1.67927i | −0.184324 | + | 0.184324i | −0.793237 | − | 0.608913i | \(-0.791606\pi\) |
0.608913 | + | 0.793237i | \(0.291606\pi\) | |||||||
\(84\) | 8.70259 | − | 8.70259i | 0.949530 | − | 0.949530i | ||||
\(85\) | −7.44631 | − | 7.44631i | −0.807666 | − | 0.807666i | ||||
\(86\) | 2.14787 | + | 2.14787i | 0.231611 | + | 0.231611i | ||||
\(87\) | 9.02447 | 0.967525 | ||||||||
\(88\) | 1.99949 | 0.213146 | ||||||||
\(89\) | −10.1240 | − | 10.1240i | −1.07315 | − | 1.07315i | −0.997105 | − | 0.0760403i | \(-0.975772\pi\) |
−0.0760403 | − | 0.997105i | \(-0.524228\pi\) | |||||||
\(90\) | − | 1.62323i | − | 0.171103i | ||||||
\(91\) | 9.06350 | − | 5.34523i | 0.950113 | − | 0.560333i | ||||
\(92\) | − | 21.0193i | − | 2.19142i | ||||||
\(93\) | −7.21532 | + | 5.74952i | −0.748193 | + | 0.596198i | ||||
\(94\) | −18.2223 | −1.87948 | ||||||||
\(95\) | − | 9.26567i | − | 0.950637i | ||||||
\(96\) | 9.24972 | − | 9.24972i | 0.944045 | − | 0.944045i | ||||
\(97\) | −4.94417 | − | 4.94417i | −0.502004 | − | 0.502004i | 0.410056 | − | 0.912060i | \(-0.365509\pi\) |
−0.912060 | + | 0.410056i | \(0.865509\pi\) | |||||||
\(98\) | −2.28658 | + | 2.28658i | −0.230980 | + | 0.230980i | ||||
\(99\) | 0.309377 | + | 0.309377i | 0.0310935 | + | 0.0310935i | ||||
\(100\) | −10.0963 | −1.00963 | ||||||||
\(101\) | 5.17436i | 0.514868i | 0.966296 | + | 0.257434i | \(0.0828770\pi\) | ||||
−0.966296 | + | 0.257434i | \(0.917123\pi\) | |||||||
\(102\) | −8.78446 | + | 8.78446i | −0.869792 | + | 0.869792i | ||||
\(103\) | − | 3.68175i | − | 0.362773i | −0.983412 | − | 0.181387i | \(-0.941941\pi\) | ||
0.983412 | − | 0.181387i | \(-0.0580585\pi\) | |||||||
\(104\) | −3.60877 | + | 2.12828i | −0.353869 | + | 0.208695i | ||||
\(105\) | − | 14.4808i | − | 1.41318i | ||||||
\(106\) | −7.20602 | + | 7.20602i | −0.699910 | + | 0.699910i | ||||
\(107\) | −1.69973 | −0.164319 | −0.0821594 | − | 0.996619i | \(-0.526182\pi\) | ||||
−0.0821594 | + | 0.996619i | \(0.526182\pi\) | |||||||
\(108\) | −13.7239 | −1.32058 | ||||||||
\(109\) | 5.21508 | + | 5.21508i | 0.499514 | + | 0.499514i | 0.911287 | − | 0.411772i | \(-0.135090\pi\) |
−0.411772 | + | 0.911287i | \(0.635090\pi\) | |||||||
\(110\) | 7.76777 | − | 7.76777i | 0.740628 | − | 0.740628i | ||||
\(111\) | −13.2735 | + | 13.2735i | −1.25987 | + | 1.25987i | ||||
\(112\) | −5.39182 | + | 5.39182i | −0.509479 | + | 0.509479i | ||||
\(113\) | 5.29510 | 0.498121 | 0.249060 | − | 0.968488i | \(-0.419878\pi\) | ||||
0.249060 | + | 0.968488i | \(0.419878\pi\) | |||||||
\(114\) | −10.9308 | −1.02376 | ||||||||
\(115\) | −17.4877 | − | 17.4877i | −1.63074 | − | 1.63074i | ||||
\(116\) | 13.8608 | 1.28694 | ||||||||
\(117\) | −0.887682 | − | 0.229072i | −0.0820662 | − | 0.0211778i | ||||
\(118\) | 28.9278 | 2.66302 | ||||||||
\(119\) | 7.25697 | − | 7.25697i | 0.665245 | − | 0.665245i | ||||
\(120\) | 5.76575i | 0.526338i | ||||||||
\(121\) | − | 8.03902i | − | 0.730820i | ||||||
\(122\) | −7.31218 | + | 7.31218i | −0.662014 | + | 0.662014i | ||||
\(123\) | −7.14132 | + | 7.14132i | −0.643911 | + | 0.643911i | ||||
\(124\) | −11.0821 | + | 8.83076i | −0.995201 | + | 0.793026i | ||||
\(125\) | 2.18723 | − | 2.18723i | 0.195632 | − | 0.195632i | ||||
\(126\) | 1.58195 | 0.140931 | ||||||||
\(127\) | 18.5731 | 1.64810 | 0.824050 | − | 0.566517i | \(-0.191710\pi\) | ||||
0.824050 | + | 0.566517i | \(0.191710\pi\) | |||||||
\(128\) | 6.32911 | − | 6.32911i | 0.559419 | − | 0.559419i | ||||
\(129\) | − | 2.36093i | − | 0.207868i | ||||||
\(130\) | −5.75150 | + | 22.2877i | −0.504440 | + | 1.95476i | ||||
\(131\) | −9.27337 | −0.810218 | −0.405109 | − | 0.914268i | \(-0.632767\pi\) | ||||
−0.405109 | + | 0.914268i | \(0.632767\pi\) | |||||||
\(132\) | −5.13130 | − | 5.13130i | −0.446622 | − | 0.446622i | ||||
\(133\) | 9.03006 | 0.783006 | ||||||||
\(134\) | − | 7.91671i | − | 0.683900i | ||||||
\(135\) | −11.4180 | + | 11.4180i | −0.982709 | + | 0.982709i | ||||
\(136\) | −2.88947 | + | 2.88947i | −0.247770 | + | 0.247770i | ||||
\(137\) | 6.98388 | + | 6.98388i | 0.596673 | + | 0.596673i | 0.939426 | − | 0.342753i | \(-0.111359\pi\) |
−0.342753 | + | 0.939426i | \(0.611359\pi\) | |||||||
\(138\) | −20.6304 | + | 20.6304i | −1.75617 | + | 1.75617i | ||||
\(139\) | − | 1.45412i | − | 0.123337i | −0.998097 | − | 0.0616684i | \(-0.980358\pi\) | ||
0.998097 | − | 0.0616684i | \(-0.0196421\pi\) | |||||||
\(140\) | − | 22.2412i | − | 1.87973i | ||||||
\(141\) | 10.0149 | + | 10.0149i | 0.843408 | + | 0.843408i | ||||
\(142\) | − | 14.2846i | − | 1.19874i | ||||||
\(143\) | −3.15170 | − | 5.34411i | −0.263559 | − | 0.446897i | ||||
\(144\) | 0.664350 | 0.0553625 | ||||||||
\(145\) | 11.5319 | − | 11.5319i | 0.957674 | − | 0.957674i | ||||
\(146\) | − | 21.7798i | − | 1.80251i | ||||||
\(147\) | 2.51340 | 0.207302 | ||||||||
\(148\) | −20.3870 | + | 20.3870i | −1.67580 | + | 1.67580i | ||||
\(149\) | 2.68035 | + | 2.68035i | 0.219583 | + | 0.219583i | 0.808323 | − | 0.588740i | \(-0.200376\pi\) |
−0.588740 | + | 0.808323i | \(0.700376\pi\) | |||||||
\(150\) | 9.90945 | + | 9.90945i | 0.809103 | + | 0.809103i | ||||
\(151\) | 9.59165 | + | 9.59165i | 0.780558 | + | 0.780558i | 0.979925 | − | 0.199367i | \(-0.0638887\pi\) |
−0.199367 | + | 0.979925i | \(0.563889\pi\) | |||||||
\(152\) | −3.59546 | −0.291630 | ||||||||
\(153\) | −0.894164 | −0.0722889 | ||||||||
\(154\) | 7.57025 | + | 7.57025i | 0.610028 | + | 0.610028i | ||||
\(155\) | −1.87306 | + | 16.5671i | −0.150448 | + | 1.33070i | ||||
\(156\) | 14.7230 | + | 3.79938i | 1.17879 | + | 0.304194i | ||||
\(157\) | 16.7516 | 1.33692 | 0.668460 | − | 0.743748i | \(-0.266954\pi\) | ||||
0.668460 | + | 0.743748i | \(0.266954\pi\) | |||||||
\(158\) | 22.5913 | − | 22.5913i | 1.79727 | − | 1.79727i | ||||
\(159\) | 7.92083 | 0.628163 | ||||||||
\(160\) | − | 23.6395i | − | 1.86887i | ||||||
\(161\) | 17.0430 | − | 17.0430i | 1.34318 | − | 1.34318i | ||||
\(162\) | 12.3200 | + | 12.3200i | 0.967954 | + | 0.967954i | ||||
\(163\) | 6.79908 | − | 6.79908i | 0.532545 | − | 0.532545i | −0.388784 | − | 0.921329i | \(-0.627105\pi\) |
0.921329 | + | 0.388784i | \(0.127105\pi\) | |||||||
\(164\) | −10.9684 | + | 10.9684i | −0.856490 | + | 0.856490i | ||||
\(165\) | −8.53830 | −0.664706 | ||||||||
\(166\) | 5.06296 | 0.392962 | ||||||||
\(167\) | 3.80114 | + | 3.80114i | 0.294141 | + | 0.294141i | 0.838714 | − | 0.544572i | \(-0.183308\pi\) |
−0.544572 | + | 0.838714i | \(0.683308\pi\) | |||||||
\(168\) | −5.61914 | −0.433526 | ||||||||
\(169\) | 11.3767 | + | 6.29057i | 0.875129 | + | 0.483890i | ||||
\(170\) | 22.4505i | 1.72187i | ||||||||
\(171\) | −0.556317 | − | 0.556317i | −0.0425426 | − | 0.0425426i | ||||
\(172\) | − | 3.62618i | − | 0.276494i | ||||||
\(173\) | − | 7.36092i | − | 0.559640i | −0.960052 | − | 0.279820i | \(-0.909725\pi\) | ||
0.960052 | − | 0.279820i | \(-0.0902749\pi\) | |||||||
\(174\) | −13.6043 | − | 13.6043i | −1.03134 | − | 1.03134i | ||||
\(175\) | −8.18634 | − | 8.18634i | −0.618829 | − | 0.618829i | ||||
\(176\) | 3.17918 | + | 3.17918i | 0.239639 | + | 0.239639i | ||||
\(177\) | −15.8987 | − | 15.8987i | −1.19502 | − | 1.19502i | ||||
\(178\) | 30.5237i | 2.28785i | ||||||||
\(179\) | 4.84115 | 0.361845 | 0.180922 | − | 0.983497i | \(-0.442092\pi\) | ||||
0.180922 | + | 0.983497i | \(0.442092\pi\) | |||||||
\(180\) | −1.37022 | + | 1.37022i | −0.102130 | + | 0.102130i | ||||
\(181\) | 8.59778 | 0.639068 | 0.319534 | − | 0.947575i | \(-0.396474\pi\) | ||||
0.319534 | + | 0.947575i | \(0.396474\pi\) | |||||||
\(182\) | −21.7210 | − | 5.60525i | −1.61007 | − | 0.415489i | ||||
\(183\) | 8.03752 | 0.594151 | ||||||||
\(184\) | −6.78594 | + | 6.78594i | −0.500266 | + | 0.500266i | ||||
\(185\) | 33.9232i | 2.49408i | ||||||||
\(186\) | 19.5444 | + | 2.20967i | 1.43306 | + | 0.162021i | ||||
\(187\) | −4.27892 | − | 4.27892i | −0.312906 | − | 0.312906i | ||||
\(188\) | 15.3820 | + | 15.3820i | 1.12185 | + | 1.12185i | ||||
\(189\) | −11.1277 | − | 11.1277i | −0.809422 | − | 0.809422i | ||||
\(190\) | −13.9679 | + | 13.9679i | −1.01334 | + | 1.01334i | ||||
\(191\) | −10.0958 | −0.730504 | −0.365252 | − | 0.930909i | \(-0.619017\pi\) | ||||
−0.365252 | + | 0.930909i | \(0.619017\pi\) | |||||||
\(192\) | −19.2286 | −1.38771 | ||||||||
\(193\) | −7.73860 | + | 7.73860i | −0.557037 | + | 0.557037i | −0.928463 | − | 0.371426i | \(-0.878869\pi\) |
0.371426 | + | 0.928463i | \(0.378869\pi\) | |||||||
\(194\) | 14.9065i | 1.07023i | ||||||||
\(195\) | 15.4103 | − | 9.08828i | 1.10356 | − | 0.650825i | ||||
\(196\) | 3.86036 | 0.275740 | ||||||||
\(197\) | −1.30937 | + | 1.30937i | −0.0932884 | + | 0.0932884i | −0.752211 | − | 0.658922i | \(-0.771013\pi\) |
0.658922 | + | 0.752211i | \(0.271013\pi\) | |||||||
\(198\) | − | 0.932764i | − | 0.0662887i | ||||||
\(199\) | 8.02951 | 0.569197 | 0.284599 | − | 0.958647i | \(-0.408140\pi\) | ||||
0.284599 | + | 0.958647i | \(0.408140\pi\) | |||||||
\(200\) | 3.25951 | + | 3.25951i | 0.230482 | + | 0.230482i | ||||
\(201\) | −4.35101 | + | 4.35101i | −0.306897 | + | 0.306897i | ||||
\(202\) | 7.80029 | − | 7.80029i | 0.548826 | − | 0.548826i | ||||
\(203\) | 11.2387 | + | 11.2387i | 0.788802 | + | 0.788802i | ||||
\(204\) | 14.8305 | 1.03834 | ||||||||
\(205\) | 18.2511i | 1.27471i | ||||||||
\(206\) | −5.55019 | + | 5.55019i | −0.386700 | + | 0.386700i | ||||
\(207\) | −2.09995 | −0.145957 | ||||||||
\(208\) | −9.12188 | − | 2.35396i | −0.632488 | − | 0.163218i | ||||
\(209\) | − | 5.32439i | − | 0.368296i | ||||||
\(210\) | −21.8296 | + | 21.8296i | −1.50639 | + | 1.50639i | ||||
\(211\) | −21.7480 | −1.49720 | −0.748598 | − | 0.663024i | \(-0.769273\pi\) | ||||
−0.748598 | + | 0.663024i | \(0.769273\pi\) | |||||||
\(212\) | 12.1657 | 0.835543 | ||||||||
\(213\) | −7.85080 | + | 7.85080i | −0.537928 | + | 0.537928i | ||||
\(214\) | 2.56232 | + | 2.56232i | 0.175156 | + | 0.175156i | ||||
\(215\) | −3.01692 | − | 3.01692i | −0.205752 | − | 0.205752i | ||||
\(216\) | 4.43067 | + | 4.43067i | 0.301469 | + | 0.301469i | ||||
\(217\) | −16.1459 | − | 1.82544i | −1.09605 | − | 0.123919i | ||||
\(218\) | − | 15.7234i | − | 1.06492i | ||||||
\(219\) | −11.9701 | + | 11.9701i | −0.808867 | + | 0.808867i | ||||
\(220\) | −13.1141 | −0.884151 | ||||||||
\(221\) | 12.2773 | + | 3.16825i | 0.825863 | + | 0.213120i | ||||
\(222\) | 40.0194 | 2.68592 | ||||||||
\(223\) | −3.58291 | + | 3.58291i | −0.239930 | + | 0.239930i | −0.816821 | − | 0.576891i | \(-0.804266\pi\) |
0.576891 | + | 0.816821i | \(0.304266\pi\) | |||||||
\(224\) | 23.0384 | 1.53932 | ||||||||
\(225\) | 1.00868i | 0.0672450i | ||||||||
\(226\) | −7.98230 | − | 7.98230i | −0.530975 | − | 0.530975i | ||||
\(227\) | 2.61765 | + | 2.61765i | 0.173740 | + | 0.173740i | 0.788620 | − | 0.614881i | \(-0.210796\pi\) |
−0.614881 | + | 0.788620i | \(0.710796\pi\) | |||||||
\(228\) | 9.22703 | + | 9.22703i | 0.611075 | + | 0.611075i | ||||
\(229\) | 5.57111 | + | 5.57111i | 0.368150 | + | 0.368150i | 0.866802 | − | 0.498652i | \(-0.166172\pi\) |
−0.498652 | + | 0.866802i | \(0.666172\pi\) | |||||||
\(230\) | 52.7251i | 3.47659i | ||||||||
\(231\) | − | 8.32119i | − | 0.547494i | ||||||
\(232\) | −4.47486 | − | 4.47486i | −0.293789 | − | 0.293789i | ||||
\(233\) | 6.72600i | 0.440635i | 0.975428 | + | 0.220318i | \(0.0707094\pi\) | ||||
−0.975428 | + | 0.220318i | \(0.929291\pi\) | |||||||
\(234\) | 0.992847 | + | 1.68350i | 0.0649044 | + | 0.110054i | ||||
\(235\) | 25.5951 | 1.66964 | ||||||||
\(236\) | −24.4190 | − | 24.4190i | −1.58954 | − | 1.58954i | ||||
\(237\) | −24.8323 | −1.61303 | ||||||||
\(238\) | −21.8796 | −1.41824 | ||||||||
\(239\) | 12.3057 | − | 12.3057i | 0.795990 | − | 0.795990i | −0.186471 | − | 0.982461i | \(-0.559705\pi\) |
0.982461 | + | 0.186471i | \(0.0597049\pi\) | |||||||
\(240\) | −9.16750 | + | 9.16750i | −0.591759 | + | 0.591759i | ||||
\(241\) | −2.45355 | − | 2.45355i | −0.158047 | − | 0.158047i | 0.623654 | − | 0.781701i | \(-0.285648\pi\) |
−0.781701 | + | 0.623654i | \(0.785648\pi\) | |||||||
\(242\) | −12.1187 | + | 12.1187i | −0.779022 | + | 0.779022i | ||||
\(243\) | 2.63506i | 0.169039i | ||||||||
\(244\) | 12.3449 | 0.790303 | ||||||||
\(245\) | 3.21175 | − | 3.21175i | 0.205191 | − | 0.205191i | ||||
\(246\) | 21.5309 | 1.37276 | ||||||||
\(247\) | 5.66735 | + | 9.60970i | 0.360605 | + | 0.611450i | ||||
\(248\) | 6.42872 | + | 0.726825i | 0.408224 | + | 0.0461535i | ||||
\(249\) | −2.78260 | − | 2.78260i | −0.176340 | − | 0.176340i | ||||
\(250\) | −6.59445 | −0.417070 | ||||||||
\(251\) | 6.44780 | 0.406981 | 0.203491 | − | 0.979077i | \(-0.434771\pi\) | ||||
0.203491 | + | 0.979077i | \(0.434771\pi\) | |||||||
\(252\) | −1.33538 | − | 1.33538i | −0.0841209 | − | 0.0841209i | ||||
\(253\) | −10.0491 | − | 10.0491i | −0.631780 | − | 0.631780i | ||||
\(254\) | −27.9988 | − | 27.9988i | −1.75680 | − | 1.75680i | ||||
\(255\) | 12.3387 | − | 12.3387i | 0.772682 | − | 0.772682i | ||||
\(256\) | 4.12647 | 0.257904 | ||||||||
\(257\) | − | 30.5869i | − | 1.90796i | −0.299874 | − | 0.953979i | \(-0.596945\pi\) | ||
0.299874 | − | 0.953979i | \(-0.403055\pi\) | |||||||
\(258\) | −3.55908 | + | 3.55908i | −0.221578 | + | 0.221578i | ||||
\(259\) | −33.0606 | −2.05428 | ||||||||
\(260\) | 23.6689 | − | 13.9588i | 1.46788 | − | 0.865688i | ||||
\(261\) | − | 1.38477i | − | 0.0857151i | ||||||
\(262\) | 13.9795 | + | 13.9795i | 0.863657 | + | 0.863657i | ||||
\(263\) | 1.20149i | 0.0740869i | 0.999314 | + | 0.0370434i | \(0.0117940\pi\) | ||||
−0.999314 | + | 0.0370434i | \(0.988206\pi\) | |||||||
\(264\) | 3.31321i | 0.203914i | ||||||||
\(265\) | 10.1216 | − | 10.1216i | 0.621767 | − | 0.621767i | ||||
\(266\) | −13.6127 | − | 13.6127i | −0.834649 | − | 0.834649i | ||||
\(267\) | 16.7758 | − | 16.7758i | 1.02666 | − | 1.02666i | ||||
\(268\) | −6.68277 | + | 6.68277i | −0.408215 | + | 0.408215i | ||||
\(269\) | 15.3629i | 0.936693i | 0.883545 | + | 0.468347i | \(0.155150\pi\) | ||||
−0.883545 | + | 0.468347i | \(0.844850\pi\) | |||||||
\(270\) | 34.4251 | 2.09505 | ||||||||
\(271\) | −11.6569 | − | 11.6569i | −0.708105 | − | 0.708105i | 0.258031 | − | 0.966137i | \(-0.416926\pi\) |
−0.966137 | + | 0.258031i | \(0.916926\pi\) | |||||||
\(272\) | −9.18848 | −0.557133 | ||||||||
\(273\) | 8.85719 | + | 15.0185i | 0.536061 | + | 0.908959i | ||||
\(274\) | − | 21.0562i | − | 1.27205i | ||||||
\(275\) | −4.82691 | + | 4.82691i | −0.291073 | + | 0.291073i | ||||
\(276\) | 34.8296 | 2.09650 | ||||||||
\(277\) | 26.2008 | 1.57425 | 0.787126 | − | 0.616793i | \(-0.211568\pi\) | ||||
0.787126 | + | 0.616793i | \(0.211568\pi\) | |||||||
\(278\) | −2.19207 | + | 2.19207i | −0.131471 | + | 0.131471i | ||||
\(279\) | 0.882242 | + | 1.10716i | 0.0528184 | + | 0.0662841i | ||||
\(280\) | −7.18042 | + | 7.18042i | −0.429112 | + | 0.429112i | ||||
\(281\) | 14.7633 | − | 14.7633i | 0.880703 | − | 0.880703i | −0.112903 | − | 0.993606i | \(-0.536015\pi\) |
0.993606 | + | 0.112903i | \(0.0360150\pi\) | |||||||
\(282\) | − | 30.1948i | − | 1.79807i | ||||||
\(283\) | 31.0134i | 1.84356i | 0.387719 | + | 0.921778i | \(0.373263\pi\) | ||||
−0.387719 | + | 0.921778i | \(0.626737\pi\) | |||||||
\(284\) | −12.0581 | + | 12.0581i | −0.715519 | + | 0.715519i | ||||
\(285\) | 15.3535 | 0.909460 | ||||||||
\(286\) | −3.30502 | + | 12.8073i | −0.195430 | + | 0.757314i | ||||
\(287\) | −17.7870 | −1.04993 | ||||||||
\(288\) | −1.41933 | − | 1.41933i | −0.0836350 | − | 0.0836350i | ||||
\(289\) | −4.63302 | −0.272531 | ||||||||
\(290\) | −34.7685 | −2.04168 | ||||||||
\(291\) | 8.19261 | − | 8.19261i | 0.480259 | − | 0.480259i | ||||
\(292\) | −18.3851 | + | 18.3851i | −1.07590 | + | 1.07590i | ||||
\(293\) | −18.1666 | + | 18.1666i | −1.06131 | + | 1.06131i | −0.0633128 | + | 0.997994i | \(0.520167\pi\) |
−0.997994 | + | 0.0633128i | \(0.979833\pi\) | |||||||
\(294\) | −3.78893 | − | 3.78893i | −0.220975 | − | 0.220975i | ||||
\(295\) | −40.6323 | −2.36570 | ||||||||
\(296\) | 13.1636 | 0.765117 | ||||||||
\(297\) | −6.56122 | + | 6.56122i | −0.380721 | + | 0.380721i | ||||
\(298\) | − | 8.08121i | − | 0.468132i | ||||||
\(299\) | 28.8334 | + | 7.44065i | 1.66748 | + | 0.430304i | ||||
\(300\) | − | 16.7298i | − | 0.965896i | ||||||
\(301\) | 2.94020 | − | 2.94020i | 0.169470 | − | 0.169470i | ||||
\(302\) | − | 28.9186i | − | 1.66408i | ||||||
\(303\) | −8.57405 | −0.492566 | ||||||||
\(304\) | −5.71675 | − | 5.71675i | −0.327878 | − | 0.327878i | ||||
\(305\) | 10.2708 | − | 10.2708i | 0.588102 | − | 0.588102i | ||||
\(306\) | 1.34794 | + | 1.34794i | 0.0770567 | + | 0.0770567i | ||||
\(307\) | −12.6893 | + | 12.6893i | −0.724217 | + | 0.724217i | −0.969461 | − | 0.245244i | \(-0.921132\pi\) |
0.245244 | + | 0.969461i | \(0.421132\pi\) | |||||||
\(308\) | − | 12.7806i | − | 0.728243i | ||||||
\(309\) | 6.10075 | 0.347059 | ||||||||
\(310\) | 27.7984 | − | 22.1511i | 1.57884 | − | 1.25810i | ||||
\(311\) | − | 7.71365i | − | 0.437401i | −0.975792 | − | 0.218701i | \(-0.929818\pi\) | ||
0.975792 | − | 0.218701i | \(-0.0701818\pi\) | |||||||
\(312\) | −3.52662 | − | 5.97983i | −0.199656 | − | 0.338541i | ||||
\(313\) | − | 21.4944i | − | 1.21494i | −0.794344 | − | 0.607469i | \(-0.792185\pi\) | ||
0.794344 | − | 0.607469i | \(-0.207815\pi\) | |||||||
\(314\) | −25.2528 | − | 25.2528i | −1.42510 | − | 1.42510i | ||||
\(315\) | −2.22202 | −0.125197 | ||||||||
\(316\) | −38.1402 | −2.14555 | ||||||||
\(317\) | −3.62279 | − | 3.62279i | −0.203476 | − | 0.203476i | 0.598011 | − | 0.801488i | \(-0.295958\pi\) |
−0.801488 | + | 0.598011i | \(0.795958\pi\) | |||||||
\(318\) | −11.9406 | − | 11.9406i | −0.669593 | − | 0.669593i | ||||
\(319\) | 6.62667 | − | 6.62667i | 0.371022 | − | 0.371022i | ||||
\(320\) | −24.5713 | + | 24.5713i | −1.37358 | + | 1.37358i | ||||
\(321\) | − | 2.81649i | − | 0.157201i | ||||||
\(322\) | −51.3844 | −2.86354 | ||||||||
\(323\) | 7.69430 | + | 7.69430i | 0.428122 | + | 0.428122i | ||||
\(324\) | − | 20.7995i | − | 1.15553i | ||||||
\(325\) | 3.57399 | − | 13.8496i | 0.198249 | − | 0.768240i | ||||
\(326\) | −20.4991 | −1.13534 | ||||||||
\(327\) | −8.64153 | + | 8.64153i | −0.477878 | + | 0.477878i | ||||
\(328\) | 7.08216 | 0.391047 | ||||||||
\(329\) | 24.9443i | 1.37522i | ||||||||
\(330\) | 12.8714 | + | 12.8714i | 0.708547 | + | 0.708547i | ||||
\(331\) | 15.6782 | − | 15.6782i | 0.861751 | − | 0.861751i | −0.129790 | − | 0.991541i | \(-0.541430\pi\) |
0.991541 | + | 0.129790i | \(0.0414304\pi\) | |||||||
\(332\) | −4.27382 | − | 4.27382i | −0.234556 | − | 0.234556i | ||||
\(333\) | 2.03677 | + | 2.03677i | 0.111614 | + | 0.111614i | ||||
\(334\) | − | 11.4604i | − | 0.627083i | ||||||
\(335\) | 11.1199i | 0.607544i | ||||||||
\(336\) | −8.93439 | − | 8.93439i | −0.487411 | − | 0.487411i | ||||
\(337\) | 30.4349 | 1.65790 | 0.828948 | − | 0.559325i | \(-0.188940\pi\) | ||||
0.828948 | + | 0.559325i | \(0.188940\pi\) | |||||||
\(338\) | −7.66725 | − | 26.6332i | −0.417044 | − | 1.44865i | ||||
\(339\) | 8.77411i | 0.476544i | ||||||||
\(340\) | 18.9512 | − | 18.9512i | 1.02777 | − | 1.02777i | ||||
\(341\) | −1.07633 | + | 9.52008i | −0.0582866 | + | 0.515541i | ||||
\(342\) | 1.67728i | 0.0906971i | ||||||||
\(343\) | −11.3151 | − | 11.3151i | −0.610955 | − | 0.610955i | ||||
\(344\) | −1.17069 | + | 1.17069i | −0.0631192 | + | 0.0631192i | ||||
\(345\) | 28.9776 | − | 28.9776i | 1.56010 | − | 1.56010i | ||||
\(346\) | −11.0965 | + | 11.0965i | −0.596552 | + | 0.596552i | ||||
\(347\) | − | 11.1222i | − | 0.597074i | −0.954398 | − | 0.298537i | \(-0.903501\pi\) | ||
0.954398 | − | 0.298537i | \(-0.0964986\pi\) | |||||||
\(348\) | 22.9677i | 1.23120i | ||||||||
\(349\) | −8.01166 | + | 8.01166i | −0.428854 | + | 0.428854i | −0.888238 | − | 0.459384i | \(-0.848070\pi\) |
0.459384 | + | 0.888238i | \(0.348070\pi\) | |||||||
\(350\) | 24.6816i | 1.31929i | ||||||||
\(351\) | 4.85814 | − | 18.8258i | 0.259308 | − | 1.00485i | ||||
\(352\) | − | 13.5841i | − | 0.724036i | ||||||
\(353\) | −9.63347 | + | 9.63347i | −0.512738 | + | 0.512738i | −0.915364 | − | 0.402627i | \(-0.868097\pi\) |
0.402627 | + | 0.915364i | \(0.368097\pi\) | |||||||
\(354\) | 47.9342i | 2.54767i | ||||||||
\(355\) | 20.0643i | 1.06490i | ||||||||
\(356\) | 25.7661 | − | 25.7661i | 1.36560 | − | 1.36560i | ||||
\(357\) | 12.0250 | + | 12.0250i | 0.636430 | + | 0.636430i | ||||
\(358\) | −7.29798 | − | 7.29798i | −0.385710 | − | 0.385710i | ||||
\(359\) | 17.3436 | − | 17.3436i | 0.915360 | − | 0.915360i | −0.0813275 | − | 0.996687i | \(-0.525916\pi\) |
0.996687 | + | 0.0813275i | \(0.0259160\pi\) | |||||||
\(360\) | 0.884732 | 0.0466294 | ||||||||
\(361\) | − | 9.42576i | − | 0.496093i | ||||||
\(362\) | −12.9611 | − | 12.9611i | −0.681218 | − | 0.681218i | ||||
\(363\) | 13.3209 | 0.699164 | ||||||||
\(364\) | 13.6039 | + | 23.0670i | 0.713036 | + | 1.20904i | ||||
\(365\) | 30.5921i | 1.60126i | ||||||||
\(366\) | −12.1165 | − | 12.1165i | −0.633338 | − | 0.633338i | ||||
\(367\) | − | 25.1106i | − | 1.31076i | −0.755299 | − | 0.655381i | \(-0.772508\pi\) | ||
0.755299 | − | 0.655381i | \(-0.227492\pi\) | |||||||
\(368\) | −21.5792 | −1.12489 | ||||||||
\(369\) | 1.09581 | + | 1.09581i | 0.0570454 | + | 0.0570454i | ||||
\(370\) | 51.1388 | − | 51.1388i | 2.65858 | − | 2.65858i | ||||
\(371\) | 9.86427 | + | 9.86427i | 0.512127 | + | 0.512127i | ||||
\(372\) | −14.6328 | − | 18.3633i | −0.758675 | − | 0.952093i | ||||
\(373\) | 13.4876 | 0.698361 | 0.349181 | − | 0.937055i | \(-0.386460\pi\) | ||||
0.349181 | + | 0.937055i | \(0.386460\pi\) | |||||||
\(374\) | 12.9009i | 0.667087i | ||||||||
\(375\) | 3.62430 | + | 3.62430i | 0.187158 | + | 0.187158i | ||||
\(376\) | − | 9.93196i | − | 0.512201i | ||||||
\(377\) | −4.90659 | + | 19.0136i | −0.252702 | + | 0.979251i | ||||
\(378\) | 33.5498i | 1.72562i | ||||||||
\(379\) | −0.981863 | − | 0.981863i | −0.0504349 | − | 0.0504349i | 0.681440 | − | 0.731874i | \(-0.261354\pi\) |
−0.731874 | + | 0.681440i | \(0.761354\pi\) | |||||||
\(380\) | 23.5815 | 1.20971 | ||||||||
\(381\) | 30.7762i | 1.57671i | ||||||||
\(382\) | 15.2193 | + | 15.2193i | 0.778685 | + | 0.778685i | ||||
\(383\) | −13.9142 | + | 13.9142i | −0.710983 | + | 0.710983i | −0.966741 | − | 0.255758i | \(-0.917675\pi\) |
0.255758 | + | 0.966741i | \(0.417675\pi\) | |||||||
\(384\) | 10.4875 | + | 10.4875i | 0.535188 | + | 0.535188i | ||||
\(385\) | −10.6332 | − | 10.6332i | −0.541920 | − | 0.541920i | ||||
\(386\) | 23.3317 | 1.18755 | ||||||||
\(387\) | −0.362275 | −0.0184155 | ||||||||
\(388\) | 12.5831 | − | 12.5831i | 0.638811 | − | 0.638811i | ||||
\(389\) | −21.2617 | −1.07801 | −0.539005 | − | 0.842303i | \(-0.681199\pi\) | ||||
−0.539005 | + | 0.842303i | \(0.681199\pi\) | |||||||
\(390\) | −36.9314 | − | 9.53039i | −1.87009 | − | 0.482590i | ||||
\(391\) | 29.0439 | 1.46881 | ||||||||
\(392\) | −1.24629 | − | 1.24629i | −0.0629472 | − | 0.0629472i | ||||
\(393\) | − | 15.3662i | − | 0.775123i | ||||||
\(394\) | 3.94771 | 0.198883 | ||||||||
\(395\) | −31.7320 | + | 31.7320i | −1.59661 | + | 1.59661i | ||||
\(396\) | −0.787378 | + | 0.787378i | −0.0395672 | + | 0.0395672i | ||||
\(397\) | 7.39713 | − | 7.39713i | 0.371251 | − | 0.371251i | −0.496681 | − | 0.867933i | \(-0.665448\pi\) |
0.867933 | + | 0.496681i | \(0.165448\pi\) | |||||||
\(398\) | −12.1044 | − | 12.1044i | −0.606739 | − | 0.606739i | ||||
\(399\) | 14.9631i | 0.749089i | ||||||||
\(400\) | 10.3652i | 0.518260i | ||||||||
\(401\) | 3.14225 | + | 3.14225i | 0.156916 | + | 0.156916i | 0.781199 | − | 0.624282i | \(-0.214609\pi\) |
−0.624282 | + | 0.781199i | \(0.714609\pi\) | |||||||
\(402\) | 13.1182 | 0.654276 | ||||||||
\(403\) | −8.19068 | − | 18.3279i | −0.408007 | − | 0.912979i | ||||
\(404\) | −13.1690 | −0.655181 | ||||||||
\(405\) | −17.3048 | − | 17.3048i | −0.859884 | − | 0.859884i | ||||
\(406\) | − | 33.8844i | − | 1.68166i | ||||||
\(407\) | 19.4935i | 0.966256i | ||||||||
\(408\) | −4.78793 | − | 4.78793i | −0.237038 | − | 0.237038i | ||||
\(409\) | −17.5273 | + | 17.5273i | −0.866670 | + | 0.866670i | −0.992102 | − | 0.125432i | \(-0.959968\pi\) |
0.125432 | + | 0.992102i | \(0.459968\pi\) | |||||||
\(410\) | 27.5133 | − | 27.5133i | 1.35878 | − | 1.35878i | ||||
\(411\) | −11.5725 | + | 11.5725i | −0.570828 | + | 0.570828i | ||||
\(412\) | 9.37021 | 0.461637 | ||||||||
\(413\) | − | 39.5991i | − | 1.94854i | ||||||
\(414\) | 3.16565 | + | 3.16565i | 0.155583 | + | 0.155583i | ||||
\(415\) | −7.11148 | −0.349089 | ||||||||
\(416\) | 14.4591 | + | 24.5172i | 0.708917 | + | 1.20206i | ||||
\(417\) | 2.40951 | 0.117994 | ||||||||
\(418\) | −8.02646 | + | 8.02646i | −0.392587 | + | 0.392587i | ||||
\(419\) | 11.4521 | 0.559472 | 0.279736 | − | 0.960077i | \(-0.409753\pi\) | ||||
0.279736 | + | 0.960077i | \(0.409753\pi\) | |||||||
\(420\) | 36.8543 | 1.79830 | ||||||||
\(421\) | −22.1995 | − | 22.1995i | −1.08194 | − | 1.08194i | −0.996329 | − | 0.0856066i | \(-0.972717\pi\) |
−0.0856066 | − | 0.996329i | \(-0.527283\pi\) | |||||||
\(422\) | 32.7849 | + | 32.7849i | 1.59594 | + | 1.59594i | ||||
\(423\) | 1.53675 | − | 1.53675i | 0.0747193 | − | 0.0747193i | ||||
\(424\) | −3.92761 | − | 3.92761i | −0.190741 | − | 0.190741i | ||||
\(425\) | − | 13.9508i | − | 0.676711i | ||||||
\(426\) | 23.6700 | 1.14681 | ||||||||
\(427\) | 10.0096 | + | 10.0096i | 0.484398 | + | 0.484398i | ||||
\(428\) | − | 4.32588i | − | 0.209099i | ||||||
\(429\) | 8.85532 | − | 5.22246i | 0.427539 | − | 0.252143i | ||||
\(430\) | 9.09593i | 0.438645i | ||||||||
\(431\) | 12.2376 | + | 12.2376i | 0.589465 | + | 0.589465i | 0.937487 | − | 0.348022i | \(-0.113146\pi\) |
−0.348022 | + | 0.937487i | \(0.613146\pi\) | |||||||
\(432\) | 14.0895i | 0.677879i | ||||||||
\(433\) | −0.954373 | −0.0458643 | −0.0229321 | − | 0.999737i | \(-0.507300\pi\) | ||||
−0.0229321 | + | 0.999737i | \(0.507300\pi\) | |||||||
\(434\) | 21.5879 | + | 27.0915i | 1.03625 | + | 1.30044i | ||||
\(435\) | 19.1087 | + | 19.1087i | 0.916192 | + | 0.916192i | ||||
\(436\) | −13.2726 | + | 13.2726i | −0.635643 | + | 0.635643i | ||||
\(437\) | 18.0701 | + | 18.0701i | 0.864410 | + | 0.864410i | ||||
\(438\) | 36.0897 | 1.72443 | ||||||||
\(439\) | − | 0.294063i | − | 0.0140348i | −0.999975 | − | 0.00701742i | \(-0.997766\pi\) | ||
0.999975 | − | 0.00701742i | \(-0.00223373\pi\) | |||||||
\(440\) | 4.23379 | + | 4.23379i | 0.201838 | + | 0.201838i | ||||
\(441\) | − | 0.385672i | − | 0.0183653i | ||||||
\(442\) | −13.7318 | − | 23.2840i | −0.653157 | − | 1.10751i | ||||
\(443\) | −32.7234 | −1.55474 | −0.777368 | − | 0.629047i | \(-0.783445\pi\) | ||||
−0.777368 | + | 0.629047i | \(0.783445\pi\) | |||||||
\(444\) | −33.7817 | − | 33.7817i | −1.60321 | − | 1.60321i | ||||
\(445\) | − | 42.8739i | − | 2.03242i | ||||||
\(446\) | 10.8024 | 0.511509 | ||||||||
\(447\) | −4.44142 | + | 4.44142i | −0.210072 | + | 0.210072i | ||||
\(448\) | −23.9465 | − | 23.9465i | −1.13137 | − | 1.13137i | ||||
\(449\) | 10.8768 | + | 10.8768i | 0.513308 | + | 0.513308i | 0.915538 | − | 0.402231i | \(-0.131765\pi\) |
−0.402231 | + | 0.915538i | \(0.631765\pi\) | |||||||
\(450\) | 1.52057 | − | 1.52057i | 0.0716802 | − | 0.0716802i | ||||
\(451\) | 10.4877i | 0.493848i | ||||||||
\(452\) | 13.4763i | 0.633870i | ||||||||
\(453\) | −15.8936 | + | 15.8936i | −0.746747 | + | 0.746747i | ||||
\(454\) | − | 7.89216i | − | 0.370398i | ||||||
\(455\) | 30.5095 | + | 7.87319i | 1.43031 | + | 0.369101i | ||||
\(456\) | − | 5.95776i | − | 0.278998i | ||||||
\(457\) | −20.6990 | + | 20.6990i | −0.968258 | + | 0.968258i | −0.999511 | − | 0.0312535i | \(-0.990050\pi\) |
0.0312535 | + | 0.999511i | \(0.490050\pi\) | |||||||
\(458\) | − | 16.7968i | − | 0.784862i | ||||||
\(459\) | − | 18.9633i | − | 0.885131i | ||||||
\(460\) | 44.5070 | − | 44.5070i | 2.07515 | − | 2.07515i | ||||
\(461\) | 9.10310 | − | 9.10310i | 0.423974 | − | 0.423974i | −0.462596 | − | 0.886569i | \(-0.653082\pi\) |
0.886569 | + | 0.462596i | \(0.153082\pi\) | |||||||
\(462\) | −12.5441 | + | 12.5441i | −0.583605 | + | 0.583605i | ||||
\(463\) | −6.96711 | − | 6.96711i | −0.323789 | − | 0.323789i | 0.526430 | − | 0.850219i | \(-0.323530\pi\) |
−0.850219 | + | 0.526430i | \(0.823530\pi\) | |||||||
\(464\) | − | 14.2300i | − | 0.660610i | ||||||
\(465\) | −27.4522 | − | 3.10372i | −1.27306 | − | 0.143931i | ||||
\(466\) | 10.1394 | − | 10.1394i | 0.469698 | − | 0.469698i | ||||
\(467\) | 17.4208i | 0.806137i | 0.915170 | + | 0.403068i | \(0.132056\pi\) | ||||
−0.915170 | + | 0.403068i | \(0.867944\pi\) | |||||||
\(468\) | 0.583000 | − | 2.25919i | 0.0269492 | − | 0.104431i | ||||
\(469\) | −10.8371 | −0.500412 | ||||||||
\(470\) | −38.5844 | − | 38.5844i | −1.77976 | − | 1.77976i | ||||
\(471\) | 27.7578i | 1.27901i | ||||||||
\(472\) | 15.7670i | 0.725734i | ||||||||
\(473\) | −1.73363 | − | 1.73363i | −0.0797124 | − | 0.0797124i | ||||
\(474\) | 37.4344 | + | 37.4344i | 1.71942 | + | 1.71942i | ||||
\(475\) | 8.67967 | − | 8.67967i | 0.398251 | − | 0.398251i | ||||
\(476\) | 18.4693 | + | 18.4693i | 0.846540 | + | 0.846540i | ||||
\(477\) | − | 1.21542i | − | 0.0556503i | ||||||
\(478\) | −37.1014 | −1.69698 | ||||||||
\(479\) | 23.2726 | − | 23.2726i | 1.06335 | − | 1.06335i | 0.0655003 | − | 0.997853i | \(-0.479136\pi\) |
0.997853 | − | 0.0655003i | \(-0.0208643\pi\) | |||||||
\(480\) | 39.1713 | 1.78792 | ||||||||
\(481\) | −20.7491 | − | 35.1827i | −0.946079 | − | 1.60419i | ||||
\(482\) | 7.39741i | 0.336943i | ||||||||
\(483\) | 28.2408 | + | 28.2408i | 1.28500 | + | 1.28500i | ||||
\(484\) | 20.4597 | 0.929985 | ||||||||
\(485\) | − | 20.9379i | − | 0.950740i | ||||||
\(486\) | 3.97233 | − | 3.97233i | 0.180188 | − | 0.180188i | ||||
\(487\) | −26.8058 | + | 26.8058i | −1.21469 | + | 1.21469i | −0.245220 | + | 0.969468i | \(0.578860\pi\) |
−0.969468 | + | 0.245220i | \(0.921140\pi\) | |||||||
\(488\) | −3.98547 | − | 3.98547i | −0.180414 | − | 0.180414i | ||||
\(489\) | 11.2662 | + | 11.2662i | 0.509477 | + | 0.509477i | ||||
\(490\) | −9.68337 | −0.437450 | ||||||||
\(491\) | 31.5481 | 1.42374 | 0.711872 | − | 0.702309i | \(-0.247848\pi\) | ||||
0.711872 | + | 0.702309i | \(0.247848\pi\) | |||||||
\(492\) | −18.1750 | − | 18.1750i | −0.819391 | − | 0.819391i | ||||
\(493\) | 19.1524i | 0.862583i | ||||||||
\(494\) | 5.94304 | − | 23.0300i | 0.267390 | − | 1.03617i | ||||
\(495\) | 1.31017i | 0.0588877i | ||||||||
\(496\) | 9.06597 | + | 11.3773i | 0.407074 | + | 0.510854i | ||||
\(497\) | −19.5541 | −0.877122 | ||||||||
\(498\) | 8.38946i | 0.375941i | ||||||||
\(499\) | −12.7782 | + | 12.7782i | −0.572031 | + | 0.572031i | −0.932696 | − | 0.360665i | \(-0.882550\pi\) |
0.360665 | + | 0.932696i | \(0.382550\pi\) | |||||||
\(500\) | 5.56660 | + | 5.56660i | 0.248946 | + | 0.248946i | ||||
\(501\) | −6.29859 | + | 6.29859i | −0.281400 | + | 0.281400i | ||||
\(502\) | −9.71999 | − | 9.71999i | −0.433824 | − | 0.433824i | ||||
\(503\) | 9.57192 | 0.426791 | 0.213395 | − | 0.976966i | \(-0.431548\pi\) | ||||
0.213395 | + | 0.976966i | \(0.431548\pi\) | |||||||
\(504\) | 0.862235i | 0.0384070i | ||||||||
\(505\) | −10.9564 | + | 10.9564i | −0.487551 | + | 0.487551i | ||||
\(506\) | 30.2977i | 1.34690i | ||||||||
\(507\) | −10.4236 | + | 18.8515i | −0.462930 | + | 0.837222i | ||||
\(508\) | 47.2695i | 2.09724i | ||||||||
\(509\) | −18.5296 | + | 18.5296i | −0.821312 | + | 0.821312i | −0.986296 | − | 0.164984i | \(-0.947243\pi\) |
0.164984 | + | 0.986296i | \(0.447243\pi\) | |||||||
\(510\) | −37.2010 | −1.64729 | ||||||||
\(511\) | −29.8142 | −1.31890 | ||||||||
\(512\) | −18.8788 | − | 18.8788i | −0.834334 | − | 0.834334i | ||||
\(513\) | 11.7983 | − | 11.7983i | 0.520908 | − | 0.520908i | ||||
\(514\) | −46.1094 | + | 46.1094i | −2.03380 | + | 2.03380i | ||||
\(515\) | 7.79585 | − | 7.79585i | 0.343526 | − | 0.343526i | ||||
\(516\) | 6.00867 | 0.264517 | ||||||||
\(517\) | 14.7079 | 0.646853 | ||||||||
\(518\) | 49.8385 | + | 49.8385i | 2.18978 | + | 2.18978i | ||||
\(519\) | 12.1972 | 0.535399 | ||||||||
\(520\) | −12.1478 | − | 3.13483i | −0.532717 | − | 0.137471i | ||||
\(521\) | −39.4675 | −1.72910 | −0.864551 | − | 0.502545i | \(-0.832397\pi\) | ||||
−0.864551 | + | 0.502545i | \(0.832397\pi\) | |||||||
\(522\) | −2.08753 | + | 2.08753i | −0.0913685 | + | 0.0913685i | ||||
\(523\) | 33.4176i | 1.46125i | 0.682779 | + | 0.730625i | \(0.260771\pi\) | ||||
−0.682779 | + | 0.730625i | \(0.739229\pi\) | |||||||
\(524\) | − | 23.6012i | − | 1.03102i | ||||||
\(525\) | 13.5650 | − | 13.5650i | 0.592024 | − | 0.592024i | ||||
\(526\) | 1.81123 | − | 1.81123i | 0.0789733 | − | 0.0789733i | ||||
\(527\) | −12.2021 | − | 15.3129i | −0.531531 | − | 0.667041i | ||||
\(528\) | −5.26798 | + | 5.26798i | −0.229259 | + | 0.229259i | ||||
\(529\) | 45.2098 | 1.96565 | ||||||||
\(530\) | −30.5165 | −1.32555 | ||||||||
\(531\) | −2.43959 | + | 2.43959i | −0.105869 | + | 0.105869i | ||||
\(532\) | 22.9819i | 0.996393i | ||||||||
\(533\) | −11.1633 | − | 18.9287i | −0.483535 | − | 0.819894i | ||||
\(534\) | −50.5786 | −2.18875 | ||||||||
\(535\) | −3.59905 | − | 3.59905i | −0.155601 | − | 0.155601i | ||||
\(536\) | 4.31497 | 0.186378 | ||||||||
\(537\) | 8.02192i | 0.346171i | ||||||||
\(538\) | 23.1594 | − | 23.1594i | 0.998474 | − | 0.998474i | ||||
\(539\) | 1.84559 | − | 1.84559i | 0.0794952 | − | 0.0794952i | ||||
\(540\) | −29.0594 | − | 29.0594i | −1.25052 | − | 1.25052i | ||||
\(541\) | 19.8645 | − | 19.8645i | 0.854042 | − | 0.854042i | −0.136586 | − | 0.990628i | \(-0.543613\pi\) |
0.990628 | + | 0.136586i | \(0.0436131\pi\) | |||||||
\(542\) | 35.1452i | 1.50962i | ||||||||
\(543\) | 14.2468i | 0.611387i | ||||||||
\(544\) | 19.6305 | + | 19.6305i | 0.841650 | + | 0.841650i | ||||
\(545\) | 22.0852i | 0.946025i | ||||||||
\(546\) | 9.28805 | − | 35.9923i | 0.397492 | − | 1.54033i | ||||
\(547\) | 33.5511 | 1.43454 | 0.717270 | − | 0.696795i | \(-0.245391\pi\) | ||||
0.717270 | + | 0.696795i | \(0.245391\pi\) | |||||||
\(548\) | −17.7743 | + | 17.7743i | −0.759280 | + | 0.759280i | ||||
\(549\) | − | 1.23333i | − | 0.0526371i | ||||||
\(550\) | 14.5530 | 0.620543 | ||||||||
\(551\) | −11.9160 | + | 11.9160i | −0.507638 | + | 0.507638i | ||||
\(552\) | −11.2445 | − | 11.2445i | −0.478597 | − | 0.478597i | ||||
\(553\) | −30.9251 | − | 30.9251i | −1.31507 | − | 1.31507i | ||||
\(554\) | −39.4974 | − | 39.4974i | −1.67808 | − | 1.67808i | ||||
\(555\) | −56.2116 | −2.38605 | ||||||||
\(556\) | 3.70080 | 0.156949 | ||||||||
\(557\) | −1.43217 | − | 1.43217i | −0.0606831 | − | 0.0606831i | 0.676114 | − | 0.736797i | \(-0.263663\pi\) |
−0.736797 | + | 0.676114i | \(0.763663\pi\) | |||||||
\(558\) | 0.339065 | − | 2.99900i | 0.0143538 | − | 0.126958i | ||||
\(559\) | 4.97423 | + | 1.28363i | 0.210388 | + | 0.0542919i | ||||
\(560\) | −22.8336 | −0.964897 | ||||||||
\(561\) | 7.09029 | − | 7.09029i | 0.299352 | − | 0.299352i | ||||
\(562\) | −44.5109 | −1.87758 | ||||||||
\(563\) | − | 29.6794i | − | 1.25084i | −0.780290 | − | 0.625418i | \(-0.784928\pi\) | ||
0.780290 | − | 0.625418i | \(-0.215072\pi\) | |||||||
\(564\) | −25.4884 | + | 25.4884i | −1.07326 | + | 1.07326i | ||||
\(565\) | 11.2120 | + | 11.2120i | 0.471693 | + | 0.471693i | ||||
\(566\) | 46.7523 | − | 46.7523i | 1.96515 | − | 1.96515i | ||||
\(567\) | 16.8648 | − | 16.8648i | 0.708256 | − | 0.708256i | ||||
\(568\) | 7.78577 | 0.326684 | ||||||||
\(569\) | −2.63218 | −0.110347 | −0.0551735 | − | 0.998477i | \(-0.517571\pi\) | ||||
−0.0551735 | + | 0.998477i | \(0.517571\pi\) | |||||||
\(570\) | −23.1452 | − | 23.1452i | −0.969444 | − | 0.969444i | ||||
\(571\) | −21.6661 | −0.906698 | −0.453349 | − | 0.891333i | \(-0.649771\pi\) | ||||
−0.453349 | + | 0.891333i | \(0.649771\pi\) | |||||||
\(572\) | 13.6010 | − | 8.02123i | 0.568686 | − | 0.335385i | ||||
\(573\) | − | 16.7289i | − | 0.698862i | ||||||
\(574\) | 26.8137 | + | 26.8137i | 1.11918 | + | 1.11918i | ||||
\(575\) | − | 32.7635i | − | 1.36633i | ||||||
\(576\) | 2.95056i | 0.122940i | ||||||||
\(577\) | −20.8861 | − | 20.8861i | −0.869498 | − | 0.869498i | 0.122918 | − | 0.992417i | \(-0.460775\pi\) |
−0.992417 | + | 0.122918i | \(0.960775\pi\) | |||||||
\(578\) | 6.98423 | + | 6.98423i | 0.290506 | + | 0.290506i | ||||
\(579\) | −12.8231 | − | 12.8231i | −0.532908 | − | 0.532908i | ||||
\(580\) | 29.3493 | + | 29.3493i | 1.21866 | + | 1.21866i | ||||
\(581\) | − | 6.93066i | − | 0.287532i | ||||||
\(582\) | −24.7005 | −1.02387 | ||||||||
\(583\) | 5.81626 | − | 5.81626i | 0.240885 | − | 0.240885i | ||||
\(584\) | 11.8710 | 0.491225 | ||||||||
\(585\) | −1.39456 | − | 2.36465i | −0.0576580 | − | 0.0977663i | ||||
\(586\) | 54.7720 | 2.26261 | ||||||||
\(587\) | 19.6901 | − | 19.6901i | 0.812696 | − | 0.812696i | −0.172341 | − | 0.985037i | \(-0.555133\pi\) |
0.985037 | + | 0.172341i | \(0.0551331\pi\) | |||||||
\(588\) | 6.39672i | 0.263796i | ||||||||
\(589\) | 1.93544 | − | 17.1189i | 0.0797485 | − | 0.705371i | ||||
\(590\) | 61.2527 | + | 61.2527i | 2.52173 | + | 2.52173i | ||||
\(591\) | −2.16965 | − | 2.16965i | −0.0892476 | − | 0.0892476i | ||||
\(592\) | 20.9300 | + | 20.9300i | 0.860217 | + | 0.860217i | ||||
\(593\) | −8.48280 | + | 8.48280i | −0.348347 | + | 0.348347i | −0.859493 | − | 0.511147i | \(-0.829221\pi\) |
0.511147 | + | 0.859493i | \(0.329221\pi\) | |||||||
\(594\) | 19.7819 | 0.811663 | ||||||||
\(595\) | 30.7323 | 1.25990 | ||||||||
\(596\) | −6.82162 | + | 6.82162i | −0.279424 | + | 0.279424i | ||||
\(597\) | 13.3051i | 0.544542i | ||||||||
\(598\) | −32.2493 | − | 54.6827i | −1.31877 | − | 2.23614i | ||||
\(599\) | −10.2006 | −0.416787 | −0.208393 | − | 0.978045i | \(-0.566823\pi\) | ||||
−0.208393 | + | 0.978045i | \(0.566823\pi\) | |||||||
\(600\) | −5.40110 | + | 5.40110i | −0.220499 | + | 0.220499i | ||||
\(601\) | 28.6933i | 1.17042i | 0.810880 | + | 0.585212i | \(0.198989\pi\) | ||||
−0.810880 | + | 0.585212i | \(0.801011\pi\) | |||||||
\(602\) | −8.86465 | −0.361296 | ||||||||
\(603\) | 0.667646 | + | 0.667646i | 0.0271886 | + | 0.0271886i | ||||
\(604\) | −24.4112 | + | 24.4112i | −0.993277 | + | 0.993277i | ||||
\(605\) | 17.0221 | − | 17.0221i | 0.692046 | − | 0.692046i | ||||
\(606\) | 12.9253 | + | 12.9253i | 0.525054 | + | 0.525054i | ||||
\(607\) | −13.9213 | −0.565049 | −0.282525 | − | 0.959260i | \(-0.591172\pi\) | ||||
−0.282525 | + | 0.959260i | \(0.591172\pi\) | |||||||
\(608\) | 24.4268i | 0.990637i | ||||||||
\(609\) | −18.6228 | + | 18.6228i | −0.754635 | + | 0.754635i | ||||
\(610\) | −30.9661 | −1.25378 | ||||||||
\(611\) | −26.5455 | + | 15.6553i | −1.07391 | + | 0.633345i | ||||
\(612\) | − | 2.27569i | − | 0.0919892i | ||||||
\(613\) | 28.0860 | − | 28.0860i | 1.13438 | − | 1.13438i | 0.144943 | − | 0.989440i | \(-0.453700\pi\) |
0.989440 | − | 0.144943i | \(-0.0463000\pi\) | |||||||
\(614\) | 38.2580 | 1.54397 | ||||||||
\(615\) | −30.2425 | −1.21950 | ||||||||
\(616\) | −4.12613 | + | 4.12613i | −0.166247 | + | 0.166247i | ||||
\(617\) | 3.49162 | + | 3.49162i | 0.140568 | + | 0.140568i | 0.773889 | − | 0.633321i | \(-0.218309\pi\) |
−0.633321 | + | 0.773889i | \(0.718309\pi\) | |||||||
\(618\) | −9.19681 | − | 9.19681i | −0.369950 | − | 0.369950i | ||||
\(619\) | −30.8537 | − | 30.8537i | −1.24011 | − | 1.24011i | −0.959953 | − | 0.280160i | \(-0.909612\pi\) |
−0.280160 | − | 0.959953i | \(-0.590388\pi\) | |||||||
\(620\) | −42.1641 | − | 4.76703i | −1.69335 | − | 0.191449i | ||||
\(621\) | − | 44.5354i | − | 1.78715i | ||||||
\(622\) | −11.6282 | + | 11.6282i | −0.466250 | + | 0.466250i | ||||
\(623\) | 41.7837 | 1.67403 | ||||||||
\(624\) | 3.90058 | − | 15.1152i | 0.156148 | − | 0.605092i | ||||
\(625\) | 29.0978 | 1.16391 | ||||||||
\(626\) | −32.4026 | + | 32.4026i | −1.29507 | + | 1.29507i | ||||
\(627\) | 8.82265 | 0.352343 | ||||||||
\(628\) | 42.6335i | 1.70126i | ||||||||
\(629\) | −28.1701 | − | 28.1701i | −1.12322 | − | 1.12322i | ||||
\(630\) | 3.34967 | + | 3.34967i | 0.133454 | + | 0.133454i | ||||
\(631\) | 7.48000 | + | 7.48000i | 0.297774 | + | 0.297774i | 0.840142 | − | 0.542367i | \(-0.182472\pi\) |
−0.542367 | + | 0.840142i | \(0.682472\pi\) | |||||||
\(632\) | 12.3133 | + | 12.3133i | 0.489796 | + | 0.489796i | ||||
\(633\) | − | 36.0371i | − | 1.43234i | ||||||
\(634\) | 10.9226i | 0.433793i | ||||||||
\(635\) | 39.3274 | + | 39.3274i | 1.56066 | + | 1.56066i | ||||
\(636\) | 20.1589i | 0.799351i | ||||||||
\(637\) | −1.36653 | + | 5.29548i | −0.0541440 | + | 0.209814i | ||||
\(638\) | −19.9793 | −0.790986 | ||||||||
\(639\) | 1.20467 | + | 1.20467i | 0.0476562 | + | 0.0476562i | ||||
\(640\) | 26.8029 | 1.05948 | ||||||||
\(641\) | 2.37255 | 0.0937102 | 0.0468551 | − | 0.998902i | \(-0.485080\pi\) | ||||
0.0468551 | + | 0.998902i | \(0.485080\pi\) | |||||||
\(642\) | −4.24583 | + | 4.24583i | −0.167569 | + | 0.167569i | ||||
\(643\) | 32.2921 | − | 32.2921i | 1.27348 | − | 1.27348i | 0.329223 | − | 0.944252i | \(-0.393213\pi\) |
0.944252 | − | 0.329223i | \(-0.106787\pi\) | |||||||
\(644\) | 43.3753 | + | 43.3753i | 1.70923 | + | 1.70923i | ||||
\(645\) | 4.99911 | − | 4.99911i | 0.196840 | − | 0.196840i | ||||
\(646\) | − | 23.1981i | − | 0.912718i | ||||||
\(647\) | 19.0151 | 0.747562 | 0.373781 | − | 0.927517i | \(-0.378061\pi\) | ||||
0.373781 | + | 0.927517i | \(0.378061\pi\) | |||||||
\(648\) | −6.71498 | + | 6.71498i | −0.263789 | + | 0.263789i | ||||
\(649\) | −23.3488 | −0.916520 | ||||||||
\(650\) | −26.2659 | + | 15.4904i | −1.03023 | + | 0.607584i | ||||
\(651\) | 3.02480 | − | 26.7541i | 0.118551 | − | 1.04858i | ||||
\(652\) | 17.3040 | + | 17.3040i | 0.677675 | + | 0.677675i | ||||
\(653\) | 34.0922 | 1.33413 | 0.667066 | − | 0.744999i | \(-0.267550\pi\) | ||||
0.667066 | + | 0.744999i | \(0.267550\pi\) | |||||||
\(654\) | 26.0540 | 1.01879 | ||||||||
\(655\) | −19.6357 | − | 19.6357i | −0.767232 | − | 0.767232i | ||||
\(656\) | 11.2606 | + | 11.2606i | 0.439652 | + | 0.439652i | ||||
\(657\) | 1.83677 | + | 1.83677i | 0.0716593 | + | 0.0716593i | ||||
\(658\) | 37.6033 | − | 37.6033i | 1.46593 | − | 1.46593i | ||||
\(659\) | −37.0556 | −1.44348 | −0.721740 | − | 0.692164i | \(-0.756657\pi\) | ||||
−0.721740 | + | 0.692164i | \(0.756657\pi\) | |||||||
\(660\) | − | 21.7304i | − | 0.845853i | ||||||
\(661\) | −22.8755 | + | 22.8755i | −0.889752 | + | 0.889752i | −0.994499 | − | 0.104747i | \(-0.966597\pi\) |
0.104747 | + | 0.994499i | \(0.466597\pi\) | |||||||
\(662\) | −47.2694 | −1.83718 | ||||||||
\(663\) | −5.24987 | + | 20.3439i | −0.203888 | + | 0.790090i | ||||
\(664\) | 2.75955i | 0.107091i | ||||||||
\(665\) | 19.1205 | + | 19.1205i | 0.741463 | + | 0.741463i | ||||
\(666\) | − | 6.14082i | − | 0.237952i | ||||||
\(667\) | 44.9796i | 1.74162i | ||||||||
\(668\) | −9.67408 | + | 9.67408i | −0.374301 | + | 0.374301i | ||||
\(669\) | −5.93698 | − | 5.93698i | −0.229537 | − | 0.229537i | ||||
\(670\) | 16.7631 | − | 16.7631i | 0.647615 | − | 0.647615i | ||||
\(671\) | 5.90195 | − | 5.90195i | 0.227842 | − | 0.227842i | ||||
\(672\) | 38.1753i | 1.47264i | ||||||||
\(673\) | −13.3157 | −0.513281 | −0.256640 | − | 0.966507i | \(-0.582616\pi\) | ||||
−0.256640 | + | 0.966507i | \(0.582616\pi\) | |||||||
\(674\) | −45.8803 | − | 45.8803i | −1.76724 | − | 1.76724i | ||||
\(675\) | −21.3918 | −0.823373 | ||||||||
\(676\) | −16.0098 | + | 28.9542i | −0.615761 | + | 1.11362i | ||||
\(677\) | − | 4.46150i | − | 0.171469i | −0.996318 | − | 0.0857347i | \(-0.972676\pi\) | ||
0.996318 | − | 0.0857347i | \(-0.0273238\pi\) | |||||||
\(678\) | 13.2269 | − | 13.2269i | 0.507975 | − | 0.507975i | ||||
\(679\) | 20.4055 | 0.783090 | ||||||||
\(680\) | −12.2365 | −0.469249 | ||||||||
\(681\) | −4.33752 | + | 4.33752i | −0.166214 | + | 0.166214i | ||||
\(682\) | 15.9740 | − | 12.7289i | 0.611675 | − | 0.487413i | ||||
\(683\) | 6.46323 | − | 6.46323i | 0.247309 | − | 0.247309i | −0.572557 | − | 0.819865i | \(-0.694048\pi\) |
0.819865 | + | 0.572557i | \(0.194048\pi\) | |||||||
\(684\) | 1.41585 | − | 1.41585i | 0.0541365 | − | 0.0541365i | ||||
\(685\) | 29.5758i | 1.13003i | ||||||||
\(686\) | 34.1146i | 1.30250i | ||||||||
\(687\) | −9.23148 | + | 9.23148i | −0.352203 | + | 0.352203i | ||||
\(688\) | −3.72276 | −0.141929 | ||||||||
\(689\) | −4.30654 | + | 16.6884i | −0.164066 | + | 0.635776i | ||||
\(690\) | −87.3668 | −3.32600 | ||||||||
\(691\) | −6.61617 | − | 6.61617i | −0.251691 | − | 0.251691i | 0.569973 | − | 0.821664i | \(-0.306954\pi\) |
−0.821664 | + | 0.569973i | \(0.806954\pi\) | |||||||
\(692\) | 18.7339 | 0.712155 | ||||||||
\(693\) | −1.27685 | −0.0485037 | ||||||||
\(694\) | −16.7667 | + | 16.7667i | −0.636454 | + | 0.636454i | ||||
\(695\) | 3.07900 | − | 3.07900i | 0.116793 | − | 0.116793i | ||||
\(696\) | 7.41496 | − | 7.41496i | 0.281063 | − | 0.281063i | ||||
\(697\) | −15.1559 | − | 15.1559i | −0.574069 | − | 0.574069i | ||||
\(698\) | 24.1550 | 0.914279 | ||||||||
\(699\) | −11.1452 | −0.421549 | ||||||||
\(700\) | 20.8346 | − | 20.8346i | 0.787474 | − | 0.787474i | ||||
\(701\) | 36.8544i | 1.39197i | 0.718055 | + | 0.695986i | \(0.245033\pi\) | ||||
−0.718055 | + | 0.695986i | \(0.754967\pi\) | |||||||
\(702\) | −35.7033 | + | 21.0562i | −1.34754 | + | 0.794714i | ||||
\(703\) | − | 35.0529i | − | 1.32205i | ||||||
\(704\) | −14.1196 | + | 14.1196i | −0.532151 | + | 0.532151i | ||||
\(705\) | 42.4118i | 1.59732i | ||||||||
\(706\) | 29.0447 | 1.09311 | ||||||||
\(707\) | −10.6778 | − | 10.6778i | −0.401578 | − | 0.401578i | ||||
\(708\) | 40.4629 | − | 40.4629i | 1.52069 | − | 1.52069i | ||||
\(709\) | 32.0322 | + | 32.0322i | 1.20299 | + | 1.20299i | 0.973252 | + | 0.229742i | \(0.0737881\pi\) |
0.229742 | + | 0.973252i | \(0.426212\pi\) | |||||||
\(710\) | 30.2467 | − | 30.2467i | 1.13514 | − | 1.13514i | ||||
\(711\) | 3.81042i | 0.142902i | ||||||||
\(712\) | −16.6368 | −0.623491 | ||||||||
\(713\) | −28.6567 | − | 35.9625i | −1.07320 | − | 1.34681i | ||||
\(714\) | − | 36.2551i | − | 1.35681i | ||||||
\(715\) | 4.64226 | − | 17.9893i | 0.173611 | − | 0.672762i | ||||
\(716\) | 12.3210i | 0.460456i | ||||||||
\(717\) | 20.3909 | + | 20.3909i | 0.761511 | + | 0.761511i | ||||
\(718\) | −52.2906 | −1.95147 | ||||||||
\(719\) | 2.23887 | 0.0834957 | 0.0417478 | − | 0.999128i | \(-0.486707\pi\) | ||||
0.0417478 | + | 0.999128i | \(0.486707\pi\) | |||||||
\(720\) | 1.40672 | + | 1.40672i | 0.0524252 | + | 0.0524252i | ||||
\(721\) | 7.59762 | + | 7.59762i | 0.282950 | + | 0.282950i | ||||
\(722\) | −14.2092 | + | 14.2092i | −0.528813 | + | 0.528813i | ||||
\(723\) | 4.06560 | − | 4.06560i | 0.151201 | − | 0.151201i | ||||
\(724\) | 21.8817i | 0.813229i | ||||||||
\(725\) | 21.6052 | 0.802398 | ||||||||
\(726\) | −20.0811 | − | 20.0811i | −0.745278 | − | 0.745278i | ||||
\(727\) | − | 4.64456i | − | 0.172257i | −0.996284 | − | 0.0861286i | \(-0.972550\pi\) | ||
0.996284 | − | 0.0861286i | \(-0.0274496\pi\) | |||||||
\(728\) | 3.05512 | − | 11.8389i | 0.113230 | − | 0.438780i | ||||
\(729\) | −28.8840 | −1.06978 | ||||||||
\(730\) | 46.1172 | − | 46.1172i | 1.70688 | − | 1.70688i | ||||
\(731\) | 5.01055 | 0.185322 | ||||||||
\(732\) | 20.4559i | 0.756070i | ||||||||
\(733\) | 5.46257 | + | 5.46257i | 0.201765 | + | 0.201765i | 0.800756 | − | 0.598991i | \(-0.204432\pi\) |
−0.598991 | + | 0.800756i | \(0.704432\pi\) | |||||||
\(734\) | −37.8539 | + | 37.8539i | −1.39721 | + | 1.39721i | ||||
\(735\) | 5.32196 | + | 5.32196i | 0.196303 | + | 0.196303i | ||||
\(736\) | 46.1023 | + | 46.1023i | 1.69935 | + | 1.69935i | ||||
\(737\) | 6.38989i | 0.235375i | ||||||||
\(738\) | − | 3.30383i | − | 0.121616i | ||||||
\(739\) | −7.31568 | − | 7.31568i | −0.269112 | − | 0.269112i | 0.559631 | − | 0.828742i | \(-0.310943\pi\) |
−0.828742 | + | 0.559631i | \(0.810943\pi\) | |||||||
\(740\) | −86.3360 | −3.17377 | ||||||||
\(741\) | −15.9235 | + | 9.39095i | −0.584965 | + | 0.344985i | ||||
\(742\) | − | 29.7405i | − | 1.09181i | ||||||
\(743\) | 9.10936 | − | 9.10936i | 0.334190 | − | 0.334190i | −0.519985 | − | 0.854175i | \(-0.674063\pi\) |
0.854175 | + | 0.519985i | \(0.174063\pi\) | |||||||
\(744\) | −1.20437 | + | 10.6526i | −0.0441543 | + | 0.390542i | ||||
\(745\) | 11.3509i | 0.415866i | ||||||||
\(746\) | −20.3324 | − | 20.3324i | −0.744422 | − | 0.744422i | ||||
\(747\) | −0.426978 | + | 0.426978i | −0.0156223 | + | 0.0156223i | ||||
\(748\) | 10.8901 | − | 10.8901i | 0.398180 | − | 0.398180i | ||||
\(749\) | 3.50754 | − | 3.50754i | 0.128163 | − | 0.128163i | ||||
\(750\) | − | 10.9272i | − | 0.399004i | ||||||
\(751\) | 18.4941i | 0.674858i | 0.941351 | + | 0.337429i | \(0.109557\pi\) | ||||
−0.941351 | + | 0.337429i | \(0.890443\pi\) | |||||||
\(752\) | 15.7917 | − | 15.7917i | 0.575865 | − | 0.575865i | ||||
\(753\) | 10.6842i | 0.389353i | ||||||||
\(754\) | 36.0594 | − | 21.2662i | 1.31321 | − | 0.774469i | ||||
\(755\) | 40.6193i | 1.47829i | ||||||||
\(756\) | 28.3205 | − | 28.3205i | 1.03001 | − | 1.03001i | ||||
\(757\) | 4.34477i | 0.157913i | 0.996878 | + | 0.0789567i | \(0.0251589\pi\) | ||||
−0.996878 | + | 0.0789567i | \(0.974841\pi\) | |||||||
\(758\) | 2.96029i | 0.107523i | ||||||||
\(759\) | 16.6516 | − | 16.6516i | 0.604414 | − | 0.604414i | ||||
\(760\) | −7.61313 | − | 7.61313i | −0.276157 | − | 0.276157i | ||||
\(761\) | −14.2124 | − | 14.2124i | −0.515199 | − | 0.515199i | 0.400916 | − | 0.916115i | \(-0.368692\pi\) |
−0.916115 | + | 0.400916i | \(0.868692\pi\) | |||||||
\(762\) | 46.3948 | − | 46.3948i | 1.68070 | − | 1.68070i | ||||
\(763\) | −21.5236 | −0.779207 | ||||||||
\(764\) | − | 25.6942i | − | 0.929583i | ||||||
\(765\) | −1.89333 | − | 1.89333i | −0.0684535 | − | 0.0684535i | ||||
\(766\) | 41.9510 | 1.51575 | ||||||||
\(767\) | 42.1410 | − | 24.8528i | 1.52162 | − | 0.897381i | ||||
\(768\) | 6.83767i | 0.246733i | ||||||||
\(769\) | −1.33137 | − | 1.33137i | −0.0480106 | − | 0.0480106i | 0.682694 | − | 0.730704i | \(-0.260808\pi\) |
−0.730704 | + | 0.682694i | \(0.760808\pi\) | |||||||
\(770\) | 32.0590i | 1.15533i | ||||||||
\(771\) | 50.6833 | 1.82531 | ||||||||
\(772\) | −19.6951 | − | 19.6951i | −0.708842 | − | 0.708842i | ||||
\(773\) | 5.95385 | − | 5.95385i | 0.214145 | − | 0.214145i | −0.591881 | − | 0.806026i | \(-0.701614\pi\) |
0.806026 | + | 0.591881i | \(0.201614\pi\) | |||||||
\(774\) | 0.546126 | + | 0.546126i | 0.0196301 | + | 0.0196301i | ||||
\(775\) | −17.2740 | + | 13.7648i | −0.620499 | + | 0.494445i | ||||
\(776\) | −8.12475 | −0.291661 | ||||||||
\(777\) | − | 54.7823i | − | 1.96530i | ||||||
\(778\) | 32.0517 | + | 32.0517i | 1.14911 | + | 1.14911i | ||||
\(779\) | − | 18.8589i | − | 0.675690i | ||||||
\(780\) | 23.1301 | + | 39.2199i | 0.828190 | + | 1.40430i | ||||
\(781\) | 11.5297i | 0.412564i | ||||||||
\(782\) | −43.7834 | − | 43.7834i | −1.56569 | − | 1.56569i | ||||
\(783\) | 29.3680 | 1.04953 | ||||||||
\(784\) | − | 3.96319i | − | 0.141542i | ||||||
\(785\) | 35.4703 | + | 35.4703i | 1.26599 | + | 1.26599i | ||||
\(786\) | −23.1644 | + | 23.1644i | −0.826247 | + | 0.826247i | ||||
\(787\) | 16.4104 | + | 16.4104i | 0.584967 | + | 0.584967i | 0.936264 | − | 0.351297i | \(-0.114259\pi\) |
−0.351297 | + | 0.936264i | \(0.614259\pi\) | |||||||
\(788\) | −3.33239 | − | 3.33239i | −0.118712 | − | 0.118712i | ||||
\(789\) | −1.99090 | −0.0708778 | ||||||||
\(790\) | 95.6711 | 3.40383 | ||||||||
\(791\) | −10.9269 | + | 10.9269i | −0.388516 | + | 0.388516i | ||||
\(792\) | 0.508399 | 0.0180652 | ||||||||
\(793\) | −4.36999 | + | 16.9342i | −0.155183 | + | 0.601352i | ||||
\(794\) | −22.3022 | −0.791475 | ||||||||
\(795\) | 16.7718 | + | 16.7718i | 0.594835 | + | 0.594835i | ||||
\(796\) | 20.4355i | 0.724316i | ||||||||
\(797\) | 10.3701 | 0.367327 | 0.183664 | − | 0.982989i | \(-0.441204\pi\) | ||||
0.183664 | + | 0.982989i | \(0.441204\pi\) | |||||||
\(798\) | 22.5566 | − | 22.5566i | 0.798496 | − | 0.798496i | ||||
\(799\) | −21.2544 | + | 21.2544i | −0.751928 | + | 0.751928i | ||||
\(800\) | 22.1445 | − | 22.1445i | 0.782925 | − | 0.782925i | ||||
\(801\) | −2.57418 | − | 2.57418i | −0.0909541 | − | 0.0909541i | ||||
\(802\) | − | 9.47380i | − | 0.334531i | ||||||
\(803\) | 17.5793i | 0.620361i | ||||||||
\(804\) | −11.0735 | − | 11.0735i | −0.390533 | − | 0.390533i | ||||
\(805\) | 72.1750 | 2.54383 | ||||||||
\(806\) | −15.2818 | + | 39.9765i | −0.538277 | + | 1.40811i | ||||
\(807\) | −25.4567 | −0.896120 | ||||||||
\(808\) | 4.25151 | + | 4.25151i | 0.149568 | + | 0.149568i | ||||
\(809\) | − | 42.8130i | − | 1.50523i | −0.658464 | − | 0.752613i | \(-0.728793\pi\) | ||
0.658464 | − | 0.752613i | \(-0.271207\pi\) | |||||||
\(810\) | 52.1737i | 1.83320i | ||||||||
\(811\) | 6.70682 | + | 6.70682i | 0.235508 | + | 0.235508i | 0.814987 | − | 0.579479i | \(-0.196744\pi\) |
−0.579479 | + | 0.814987i | \(0.696744\pi\) | |||||||
\(812\) | −28.6030 | + | 28.6030i | −1.00377 | + | 1.00377i | ||||
\(813\) | 19.3158 | − | 19.3158i | 0.677433 | − | 0.677433i | ||||
\(814\) | 29.3862 | − | 29.3862i | 1.02999 | − | 1.02999i | ||||
\(815\) | 28.7932 | 1.00858 | ||||||||
\(816\) | − | 15.2256i | − | 0.533001i | ||||||
\(817\) | 3.11739 | + | 3.11739i | 0.109064 | + | 0.109064i | ||||
\(818\) | 52.8445 | 1.84766 | ||||||||
\(819\) | 2.30452 | − | 1.35910i | 0.0805266 | − | 0.0474908i | ||||
\(820\) | −46.4498 | −1.62210 | ||||||||
\(821\) | −2.65512 | + | 2.65512i | −0.0926642 | + | 0.0926642i | −0.751919 | − | 0.659255i | \(-0.770872\pi\) |
0.659255 | + | 0.751919i | \(0.270872\pi\) | |||||||
\(822\) | 34.8907 | 1.21695 | ||||||||
\(823\) | 3.06556 | 0.106859 | 0.0534293 | − | 0.998572i | \(-0.482985\pi\) | ||||
0.0534293 | + | 0.998572i | \(0.482985\pi\) | |||||||
\(824\) | −3.02511 | − | 3.02511i | −0.105385 | − | 0.105385i | ||||
\(825\) | −7.99831 | − | 7.99831i | −0.278465 | − | 0.278465i | ||||
\(826\) | −59.6952 | + | 59.6952i | −2.07706 | + | 2.07706i | ||||
\(827\) | 10.8929 | + | 10.8929i | 0.378784 | + | 0.378784i | 0.870664 | − | 0.491879i | \(-0.163690\pi\) |
−0.491879 | + | 0.870664i | \(0.663690\pi\) | |||||||
\(828\) | − | 5.34447i | − | 0.185733i | ||||||
\(829\) | −21.0765 | −0.732016 | −0.366008 | − | 0.930612i | \(-0.619276\pi\) | ||||
−0.366008 | + | 0.930612i | \(0.619276\pi\) | |||||||
\(830\) | 10.7205 | + | 10.7205i | 0.372113 | + | 0.372113i | ||||
\(831\) | 43.4153i | 1.50606i | ||||||||
\(832\) | 10.4546 | − | 40.5127i | 0.362447 | − | 1.40452i | ||||
\(833\) | 5.33414i | 0.184817i | ||||||||
\(834\) | −3.63231 | − | 3.63231i | −0.125777 | − | 0.125777i | ||||
\(835\) | 16.0973i | 0.557071i | ||||||||
\(836\) | 13.5508 | 0.468665 | ||||||||
\(837\) | −23.4805 | + | 18.7105i | −0.811606 | + | 0.646728i | ||||
\(838\) | −17.2639 | − | 17.2639i | −0.596373 | − | 0.596373i | ||||
\(839\) | −13.5288 | + | 13.5288i | −0.467067 | + | 0.467067i | −0.900963 | − | 0.433896i | \(-0.857139\pi\) |
0.433896 | + | 0.900963i | \(0.357139\pi\) | |||||||
\(840\) | −11.8981 | − | 11.8981i | −0.410525 | − | 0.410525i | ||||
\(841\) | −0.660940 | −0.0227910 | ||||||||
\(842\) | 66.9309i | 2.30659i | ||||||||
\(843\) | 24.4631 | + | 24.4631i | 0.842555 | + | 0.842555i | ||||
\(844\) | − | 55.3497i | − | 1.90522i | ||||||
\(845\) | 10.7695 | + | 37.4092i | 0.370482 | + | 1.28692i | ||||
\(846\) | −4.63327 | −0.159295 | ||||||||
\(847\) | 16.5893 | + | 16.5893i | 0.570013 | + | 0.570013i | ||||
\(848\) | − | 12.4897i | − | 0.428899i | ||||||
\(849\) | −51.3900 | −1.76370 | ||||||||
\(850\) | −21.0306 | + | 21.0306i | −0.721344 | + | 0.721344i | ||||
\(851\) | −66.1577 | − | 66.1577i | −2.26786 | − | 2.26786i | ||||
\(852\) | −19.9806 | − | 19.9806i | −0.684526 | − | 0.684526i | ||||
\(853\) | 9.14864 | − | 9.14864i | 0.313244 | − | 0.313244i | −0.532921 | − | 0.846165i | \(-0.678906\pi\) |
0.846165 | + | 0.532921i | \(0.178906\pi\) | |||||||
\(854\) | − | 30.1787i | − | 1.03269i | ||||||
\(855\) | − | 2.35593i | − | 0.0805710i | ||||||
\(856\) | −1.39658 | + | 1.39658i | −0.0477341 | + | 0.0477341i | ||||
\(857\) | − | 55.6921i | − | 1.90241i | −0.308565 | − | 0.951203i | \(-0.599849\pi\) | ||
0.308565 | − | 0.951203i | \(-0.400151\pi\) | |||||||
\(858\) | −21.2221 | − | 5.47651i | −0.724511 | − | 0.186965i | ||||
\(859\) | 30.5332i | 1.04178i | 0.853624 | + | 0.520890i | \(0.174400\pi\) | ||||
−0.853624 | + | 0.520890i | \(0.825600\pi\) | |||||||
\(860\) | 7.67819 | − | 7.67819i | 0.261824 | − | 0.261824i | ||||
\(861\) | − | 29.4735i | − | 1.00445i | ||||||
\(862\) | − | 36.8961i | − | 1.25669i | ||||||
\(863\) | 8.86753 | − | 8.86753i | 0.301854 | − | 0.301854i | −0.539885 | − | 0.841739i | \(-0.681532\pi\) |
0.841739 | + | 0.539885i | \(0.181532\pi\) | |||||||
\(864\) | 30.1010 | − | 30.1010i | 1.02406 | − | 1.02406i | ||||
\(865\) | 15.5862 | − | 15.5862i | 0.529948 | − | 0.529948i | ||||
\(866\) | 1.43871 | + | 1.43871i | 0.0488893 | + | 0.0488893i | ||||
\(867\) | − | 7.67704i | − | 0.260726i | ||||||
\(868\) | 4.64582 | − | 41.0920i | 0.157689 | − | 1.39475i | ||||
\(869\) | −18.2343 | + | 18.2343i | −0.618558 | + | 0.618558i | ||||
\(870\) | − | 57.6123i | − | 1.95324i | ||||||
\(871\) | −6.80148 | − | 11.5328i | −0.230459 | − | 0.390773i | ||||
\(872\) | 8.56995 | 0.290215 | ||||||||
\(873\) | −1.25712 | − | 1.25712i | −0.0425472 | − | 0.0425472i | ||||
\(874\) | − | 54.4810i | − | 1.84285i | ||||||
\(875\) | 9.02710i | 0.305172i | ||||||||
\(876\) | −30.4645 | − | 30.4645i | −1.02930 | − | 1.02930i | ||||
\(877\) | 16.9305 | + | 16.9305i | 0.571703 | + | 0.571703i | 0.932604 | − | 0.360901i | \(-0.117531\pi\) |
−0.360901 | + | 0.932604i | \(0.617531\pi\) | |||||||
\(878\) | −0.443296 | + | 0.443296i | −0.0149605 | + | 0.0149605i | ||||
\(879\) | −30.1026 | − | 30.1026i | −1.01534 | − | 1.01534i | ||||
\(880\) | 13.4634i | 0.453850i | ||||||||
\(881\) | −37.9068 | −1.27711 | −0.638556 | − | 0.769575i | \(-0.720468\pi\) | ||||
−0.638556 | + | 0.769575i | \(0.720468\pi\) | |||||||
\(882\) | −0.581396 | + | 0.581396i | −0.0195766 | + | 0.0195766i | ||||
\(883\) | −36.5697 | −1.23067 | −0.615334 | − | 0.788267i | \(-0.710979\pi\) | ||||
−0.615334 | + | 0.788267i | \(0.710979\pi\) | |||||||
\(884\) | −8.06334 | + | 31.2464i | −0.271199 | + | 1.05093i | ||||
\(885\) | − | 67.3288i | − | 2.26323i | ||||||
\(886\) | 49.3301 | + | 49.3301i | 1.65728 | + | 1.65728i | ||||
\(887\) | −3.07706 | −0.103317 | −0.0516587 | − | 0.998665i | \(-0.516451\pi\) | ||||
−0.0516587 | + | 0.998665i | \(0.516451\pi\) | |||||||
\(888\) | 21.8124i | 0.731976i | ||||||||
\(889\) | −38.3274 | + | 38.3274i | −1.28546 | + | 1.28546i | ||||
\(890\) | −64.6319 | + | 64.6319i | −2.16647 | + | 2.16647i | ||||
\(891\) | −9.94399 | − | 9.94399i | −0.333136 | − | 0.333136i | ||||
\(892\) | −9.11868 | − | 9.11868i | −0.305316 | − | 0.305316i | ||||
\(893\) | −26.4475 | −0.885033 | ||||||||
\(894\) | 13.3908 | 0.447854 | ||||||||
\(895\) | 10.2508 | + | 10.2508i | 0.342647 | + | 0.342647i | ||||
\(896\) | 26.1214i | 0.872654i | ||||||||
\(897\) | −12.3294 | + | 47.7777i | −0.411665 | + | 1.59525i | ||||
\(898\) | − | 32.7933i | − | 1.09433i | ||||||
\(899\) | 23.7147 | − | 18.8971i | 0.790931 | − | 0.630253i | ||||
\(900\) | −2.56712 | −0.0855708 | ||||||||
\(901\) | 16.8102i | 0.560029i | ||||||||
\(902\) | 15.8101 | − | 15.8101i | 0.526420 | − | 0.526420i | ||||
\(903\) | 4.87199 | + | 4.87199i | 0.162130 | + | 0.162130i | ||||
\(904\) | 4.35071 | − | 4.35071i | 0.144703 | − | 0.144703i | ||||
\(905\) | 18.2052 | + | 18.2052i | 0.605162 | + | 0.605162i | ||||
\(906\) | 47.9189 | 1.59200 | ||||||||
\(907\) | − | 10.9732i | − | 0.364359i | −0.983265 | − | 0.182179i | \(-0.941685\pi\) | ||
0.983265 | − | 0.182179i | \(-0.0583152\pi\) | |||||||
\(908\) | −6.66205 | + | 6.66205i | −0.221088 | + | 0.221088i | ||||
\(909\) | 1.31565i | 0.0436375i | ||||||||
\(910\) | −34.1240 | − | 57.8615i | −1.13120 | − | 1.91809i | ||||
\(911\) | − | 44.4665i | − | 1.47324i | −0.676306 | − | 0.736621i | \(-0.736420\pi\) | ||
0.676306 | − | 0.736621i | \(-0.263580\pi\) | |||||||
\(912\) | 9.47280 | − | 9.47280i | 0.313676 | − | 0.313676i | ||||
\(913\) | −4.08652 | −0.135244 | ||||||||
\(914\) | 62.4070 | 2.06424 | ||||||||
\(915\) | 17.0189 | + | 17.0189i | 0.562628 | + | 0.562628i | ||||
\(916\) | −14.1787 | + | 14.1787i | −0.468479 | + | 0.468479i | ||||
\(917\) | 19.1365 | − | 19.1365i | 0.631941 | − | 0.631941i | ||||
\(918\) | −28.5870 | + | 28.5870i | −0.943511 | + | 0.943511i | ||||
\(919\) | −3.39920 | −0.112129 | −0.0560646 | − | 0.998427i | \(-0.517855\pi\) | ||||
−0.0560646 | + | 0.998427i | \(0.517855\pi\) | |||||||
\(920\) | −28.7376 | −0.947449 | ||||||||
\(921\) | −21.0265 | − | 21.0265i | −0.692847 | − | 0.692847i | ||||
\(922\) | −27.4456 | −0.903874 | ||||||||
\(923\) | −12.2723 | − | 20.8093i | −0.403949 | − | 0.684946i | ||||
\(924\) | 21.1778 | 0.696699 | ||||||||
\(925\) | −31.7777 | + | 31.7777i | −1.04485 | + | 1.04485i | ||||
\(926\) | 21.0057i | 0.690290i | ||||||||
\(927\) | − | 0.936136i | − | 0.0307467i | ||||||
\(928\) | −30.4013 | + | 30.4013i | −0.997970 | + | 0.997970i | ||||
\(929\) | 20.0016 | − | 20.0016i | 0.656230 | − | 0.656230i | −0.298256 | − | 0.954486i | \(-0.596405\pi\) |
0.954486 | + | 0.298256i | \(0.0964048\pi\) | |||||||
\(930\) | 36.7050 | + | 46.0627i | 1.20360 | + | 1.51045i | ||||
\(931\) | −3.31871 | + | 3.31871i | −0.108766 | + | 0.108766i | ||||
\(932\) | −17.1180 | −0.560718 | ||||||||
\(933\) | 12.7817 | 0.418455 | ||||||||
\(934\) | 26.2616 | − | 26.2616i | 0.859306 | − | 0.859306i | ||||
\(935\) | − | 18.1207i | − | 0.592609i | ||||||
\(936\) | −0.917581 | + | 0.541147i | −0.0299921 | + | 0.0176879i | ||||
\(937\) | −47.9555 | −1.56664 | −0.783319 | − | 0.621620i | \(-0.786475\pi\) | ||||
−0.783319 | + | 0.621620i | \(0.786475\pi\) | |||||||
\(938\) | 16.3369 | + | 16.3369i | 0.533417 | + | 0.533417i | ||||
\(939\) | 35.6169 | 1.16231 | ||||||||
\(940\) | 65.1408i | 2.12466i | ||||||||
\(941\) | −33.4816 | + | 33.4816i | −1.09147 | + | 1.09147i | −0.0960956 | + | 0.995372i | \(0.530635\pi\) |
−0.995372 | + | 0.0960956i | \(0.969365\pi\) | |||||||
\(942\) | 41.8445 | − | 41.8445i | 1.36337 | − | 1.36337i | ||||
\(943\) | −35.5936 | − | 35.5936i | −1.15909 | − | 1.15909i | ||||
\(944\) | −25.0694 | + | 25.0694i | −0.815939 | + | 0.815939i | ||||
\(945\) | − | 47.1243i | − | 1.53295i | ||||||
\(946\) | 5.22685i | 0.169940i | ||||||||
\(947\) | −39.4820 | − | 39.4820i | −1.28299 | − | 1.28299i | −0.938956 | − | 0.344038i | \(-0.888205\pi\) |
−0.344038 | − | 0.938956i | \(-0.611795\pi\) | |||||||
\(948\) | − | 63.1993i | − | 2.05262i | ||||||
\(949\) | −18.7117 | − | 31.7280i | −0.607407 | − | 1.02993i | ||||
\(950\) | −26.1690 | −0.849035 | ||||||||
\(951\) | 6.00305 | − | 6.00305i | 0.194662 | − | 0.194662i | ||||
\(952\) | − | 11.9254i | − | 0.386504i | ||||||
\(953\) | −10.8661 | −0.351989 | −0.175994 | − | 0.984391i | \(-0.556314\pi\) | ||||
−0.175994 | + | 0.984391i | \(0.556314\pi\) | |||||||
\(954\) | −1.83223 | + | 1.83223i | −0.0593207 | + | 0.0593207i | ||||
\(955\) | −21.3771 | − | 21.3771i | −0.691746 | − | 0.691746i | ||||
\(956\) | 31.3186 | + | 31.3186i | 1.01292 | + | 1.01292i | ||||
\(957\) | 10.9806 | + | 10.9806i | 0.354951 | + | 0.354951i | ||||
\(958\) | −70.1664 | −2.26697 | ||||||||
\(959\) | −28.8237 | −0.930767 | ||||||||
\(960\) | −40.7153 | − | 40.7153i | −1.31408 | − | 1.31408i | ||||
\(961\) | −6.92119 | + | 30.2175i | −0.223264 | + | 0.974758i | ||||
\(962\) | −21.7585 | + | 84.3166i | −0.701522 | + | 2.71848i | ||||
\(963\) | −0.432180 | −0.0139268 | ||||||||
\(964\) | 6.24440 | − | 6.24440i | 0.201119 | − | 0.201119i | ||||
\(965\) | −32.7719 | −1.05497 | ||||||||
\(966\) | − | 85.1453i | − | 2.73950i | ||||||
\(967\) | 7.18480 | − | 7.18480i | 0.231048 | − | 0.231048i | −0.582082 | − | 0.813130i | \(-0.697762\pi\) |
0.813130 | + | 0.582082i | \(0.197762\pi\) | |||||||
\(968\) | −6.60526 | − | 6.60526i | −0.212301 | − | 0.212301i | ||||
\(969\) | −12.7497 | + | 12.7497i | −0.409578 | + | 0.409578i | ||||
\(970\) | −31.5636 | + | 31.5636i | −1.01345 | + | 1.01345i | ||||
\(971\) | 33.0128 | 1.05943 | 0.529716 | − | 0.848175i | \(-0.322299\pi\) | ||||
0.529716 | + | 0.848175i | \(0.322299\pi\) | |||||||
\(972\) | −6.70635 | −0.215106 | ||||||||
\(973\) | 3.00071 | + | 3.00071i | 0.0961982 | + | 0.0961982i | ||||
\(974\) | 80.8189 | 2.58961 | ||||||||
\(975\) | 22.9492 | + | 5.92220i | 0.734963 | + | 0.189662i | ||||
\(976\) | − | 12.6737i | − | 0.405677i | ||||||
\(977\) | 30.9086 | + | 30.9086i | 0.988854 | + | 0.988854i | 0.999939 | − | 0.0110843i | \(-0.00352832\pi\) |
−0.0110843 | + | 0.999939i | \(0.503528\pi\) | |||||||
\(978\) | − | 33.9675i | − | 1.08616i | ||||||
\(979\) | − | 24.6369i | − | 0.787399i | ||||||
\(980\) | 8.17406 | + | 8.17406i | 0.261111 | + | 0.261111i | ||||
\(981\) | 1.32601 | + | 1.32601i | 0.0423362 | + | 0.0423362i | ||||
\(982\) | −47.5584 | − | 47.5584i | −1.51765 | − | 1.51765i | ||||
\(983\) | −18.1326 | − | 18.1326i | −0.578340 | − | 0.578340i | 0.356106 | − | 0.934446i | \(-0.384104\pi\) |
−0.934446 | + | 0.356106i | \(0.884104\pi\) | |||||||
\(984\) | 11.7353i | 0.374108i | ||||||||
\(985\) | −5.54498 | −0.176678 | ||||||||
\(986\) | 28.8721 | − | 28.8721i | 0.919475 | − | 0.919475i | ||||
\(987\) | −41.3334 | −1.31566 | ||||||||
\(988\) | −24.4571 | + | 14.4237i | −0.778084 | + | 0.458878i | ||||
\(989\) | 11.7673 | 0.374179 | ||||||||
\(990\) | 1.97507 | − | 1.97507i | 0.0627717 | − | 0.0627717i | ||||
\(991\) | − | 34.3568i | − | 1.09138i | −0.837987 | − | 0.545690i | \(-0.816268\pi\) | ||
0.837987 | − | 0.545690i | \(-0.183732\pi\) | |||||||
\(992\) | 4.93790 | − | 43.6754i | 0.156778 | − | 1.38670i | ||||
\(993\) | 25.9792 | + | 25.9792i | 0.824424 | + | 0.824424i | ||||
\(994\) | 29.4776 | + | 29.4776i | 0.934973 | + | 0.934973i | ||||
\(995\) | 17.0020 | + | 17.0020i | 0.538998 | + | 0.538998i | ||||
\(996\) | 7.08183 | − | 7.08183i | 0.224396 | − | 0.224396i | ||||
\(997\) | 11.6282 | 0.368270 | 0.184135 | − | 0.982901i | \(-0.441052\pi\) | ||||
0.184135 | + | 0.982901i | \(0.441052\pi\) | |||||||
\(998\) | 38.5260 | 1.21952 | ||||||||
\(999\) | −43.1956 | + | 43.1956i | −1.36665 | + | 1.36665i |
(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 | 403.2.i.a.216.6 | yes | 68 | |
13.5 | odd | 4 | inner | 403.2.i.a.278.6 | yes | 68 | |
31.30 | odd | 2 | inner | 403.2.i.a.216.5 | ✓ | 68 | |
403.278 | even | 4 | inner | 403.2.i.a.278.5 | yes | 68 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
403.2.i.a.216.5 | ✓ | 68 | 31.30 | odd | 2 | inner | |
403.2.i.a.216.6 | yes | 68 | 1.1 | even | 1 | trivial | |
403.2.i.a.278.5 | yes | 68 | 403.278 | even | 4 | inner | |
403.2.i.a.278.6 | yes | 68 | 13.5 | odd | 4 | inner |