Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [722,2,Mod(429,722)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(722, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("722.429");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 722 = 2 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 722.c (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.76519902594\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.324000000.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 5x^{6} + 20x^{4} + 25x^{2} + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 429.4 | ||
Root | \(-0.951057 + 1.64728i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 722.429 |
Dual form | 722.2.c.n.653.4 |
$q$-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 \(\left(\mathbb{Z}/722\mathbb{Z}\right)^\times\).
\(n\) | \(363\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 1.39680 | − | 2.41933i | 0.806444 | − | 1.39680i | −0.108868 | − | 0.994056i | \(-0.534722\pi\) |
0.915312 | − | 0.402746i | \(-0.131944\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 1.17229 | − | 2.03046i | 0.524263 | − | 0.908051i | −0.475338 | − | 0.879803i | \(-0.657674\pi\) |
0.999601 | − | 0.0282472i | \(-0.00899255\pi\) | |||||||
\(6\) | −1.39680 | − | 2.41933i | −0.570242 | − | 0.987688i | ||||
\(7\) | −1.28408 | −0.485336 | −0.242668 | − | 0.970109i | \(-0.578023\pi\) | ||||
−0.242668 | + | 0.970109i | \(0.578023\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.40211 | − | 4.16058i | −0.800704 | − | 1.38686i | ||||
\(10\) | −1.17229 | − | 2.03046i | −0.370710 | − | 0.642089i | ||||
\(11\) | 5.75621 | 1.73556 | 0.867782 | − | 0.496945i | \(-0.165545\pi\) | ||||
0.867782 | + | 0.496945i | \(0.165545\pi\) | |||||||
\(12\) | −2.79360 | −0.806444 | ||||||||
\(13\) | 0.152141 | + | 0.263516i | 0.0421964 | + | 0.0730863i | 0.886352 | − | 0.463012i | \(-0.153231\pi\) |
−0.844156 | + | 0.536098i | \(0.819898\pi\) | |||||||
\(14\) | −0.642040 | + | 1.11205i | −0.171592 | + | 0.297207i | ||||
\(15\) | −3.27491 | − | 5.67231i | −0.845578 | − | 1.46458i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −2.09310 | + | 3.62535i | −0.507650 | + | 0.879276i | 0.492310 | + | 0.870420i | \(0.336152\pi\) |
−0.999961 | + | 0.00885651i | \(0.997181\pi\) | |||||||
\(18\) | −4.80423 | −1.13237 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −2.34458 | −0.524263 | ||||||||
\(21\) | −1.79360 | + | 3.10661i | −0.391397 | + | 0.677919i | ||||
\(22\) | 2.87811 | − | 4.98503i | 0.613615 | − | 1.06281i | ||||
\(23\) | 3.23842 | + | 5.60910i | 0.675257 | + | 1.16958i | 0.976394 | + | 0.215998i | \(0.0693005\pi\) |
−0.301137 | + | 0.953581i | \(0.597366\pi\) | |||||||
\(24\) | −1.39680 | + | 2.41933i | −0.285121 | + | 0.493844i | ||||
\(25\) | −0.248520 | − | 0.430448i | −0.0497039 | − | 0.0860897i | ||||
\(26\) | 0.304282 | 0.0596747 | ||||||||
\(27\) | −5.04029 | −0.970005 | ||||||||
\(28\) | 0.642040 | + | 1.11205i | 0.121334 | + | 0.210157i | ||||
\(29\) | −1.56378 | − | 2.70855i | −0.290387 | − | 0.502964i | 0.683515 | − | 0.729937i | \(-0.260451\pi\) |
−0.973901 | + | 0.226973i | \(0.927117\pi\) | |||||||
\(30\) | −6.54982 | −1.19583 | ||||||||
\(31\) | −6.44246 | −1.15710 | −0.578550 | − | 0.815647i | \(-0.696381\pi\) | ||||
−0.578550 | + | 0.815647i | \(0.696381\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 8.04029 | − | 13.9262i | 1.39964 | − | 2.42424i | ||||
\(34\) | 2.09310 | + | 3.62535i | 0.358963 | + | 0.621742i | ||||
\(35\) | −1.50531 | + | 2.60727i | −0.254444 | + | 0.440710i | ||||
\(36\) | −2.40211 | + | 4.16058i | −0.400352 | + | 0.693430i | ||||
\(37\) | 3.97980 | 0.654275 | 0.327137 | − | 0.944977i | \(-0.393916\pi\) | ||||
0.327137 | + | 0.944977i | \(0.393916\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.850045 | 0.136116 | ||||||||
\(40\) | −1.17229 | + | 2.03046i | −0.185355 | + | 0.321044i | ||||
\(41\) | −2.50859 | + | 4.34501i | −0.391776 | + | 0.678577i | −0.992684 | − | 0.120742i | \(-0.961473\pi\) |
0.600908 | + | 0.799319i | \(0.294806\pi\) | |||||||
\(42\) | 1.79360 | + | 3.10661i | 0.276759 | + | 0.479361i | ||||
\(43\) | 0.494689 | − | 0.856827i | 0.0754394 | − | 0.130665i | −0.825838 | − | 0.563908i | \(-0.809297\pi\) |
0.901277 | + | 0.433243i | \(0.142631\pi\) | |||||||
\(44\) | −2.87811 | − | 4.98503i | −0.433891 | − | 0.751521i | ||||
\(45\) | −11.2639 | −1.67912 | ||||||||
\(46\) | 6.47684 | 0.954957 | ||||||||
\(47\) | 2.19723 | + | 3.80571i | 0.320498 | + | 0.555119i | 0.980591 | − | 0.196065i | \(-0.0628163\pi\) |
−0.660093 | + | 0.751184i | \(0.729483\pi\) | |||||||
\(48\) | 1.39680 | + | 2.41933i | 0.201611 | + | 0.349201i | ||||
\(49\) | −5.35114 | −0.764449 | ||||||||
\(50\) | −0.497039 | −0.0702919 | ||||||||
\(51\) | 5.84728 | + | 10.1278i | 0.818783 | + | 1.41817i | ||||
\(52\) | 0.152141 | − | 0.263516i | 0.0210982 | − | 0.0365431i | ||||
\(53\) | 1.64532 | + | 2.84978i | 0.226002 | + | 0.391448i | 0.956620 | − | 0.291340i | \(-0.0941010\pi\) |
−0.730617 | + | 0.682787i | \(0.760768\pi\) | |||||||
\(54\) | −2.52015 | + | 4.36502i | −0.342949 | + | 0.594004i | ||||
\(55\) | 6.74794 | − | 11.6878i | 0.909892 | − | 1.57598i | ||||
\(56\) | 1.28408 | 0.171592 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.12756 | −0.410669 | ||||||||
\(59\) | 1.65688 | − | 2.86979i | 0.215707 | − | 0.373615i | −0.737784 | − | 0.675037i | \(-0.764128\pi\) |
0.953491 | + | 0.301421i | \(0.0974611\pi\) | |||||||
\(60\) | −3.27491 | + | 5.67231i | −0.422789 | + | 0.732292i | ||||
\(61\) | 5.48073 | + | 9.49290i | 0.701735 | + | 1.21544i | 0.967857 | + | 0.251502i | \(0.0809245\pi\) |
−0.266121 | + | 0.963940i | \(0.585742\pi\) | |||||||
\(62\) | −3.22123 | + | 5.57934i | −0.409097 | + | 0.708577i | ||||
\(63\) | 3.08450 | + | 5.34252i | 0.388611 | + | 0.673094i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.713414 | 0.0884881 | ||||||||
\(66\) | −8.04029 | − | 13.9262i | −0.989692 | − | 1.71420i | ||||
\(67\) | −2.19041 | − | 3.79390i | −0.267601 | − | 0.463498i | 0.700641 | − | 0.713514i | \(-0.252897\pi\) |
−0.968242 | + | 0.250016i | \(0.919564\pi\) | |||||||
\(68\) | 4.18619 | 0.507650 | ||||||||
\(69\) | 18.0937 | 2.17823 | ||||||||
\(70\) | 1.50531 | + | 2.60727i | 0.179919 | + | 0.311629i | ||||
\(71\) | −2.20785 | + | 3.82410i | −0.262023 | + | 0.453838i | −0.966779 | − | 0.255612i | \(-0.917723\pi\) |
0.704756 | + | 0.709450i | \(0.251056\pi\) | |||||||
\(72\) | 2.40211 | + | 4.16058i | 0.283092 | + | 0.490329i | ||||
\(73\) | 1.13345 | − | 1.96319i | 0.132660 | − | 0.229774i | −0.792041 | − | 0.610468i | \(-0.790982\pi\) |
0.924701 | + | 0.380694i | \(0.124315\pi\) | |||||||
\(74\) | 1.98990 | − | 3.44660i | 0.231321 | − | 0.400660i | ||||
\(75\) | −1.38853 | −0.160334 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.39144 | −0.842332 | ||||||||
\(78\) | 0.425022 | − | 0.736160i | 0.0481243 | − | 0.0833538i | ||||
\(79\) | 4.28829 | − | 7.42754i | 0.482471 | − | 0.835664i | −0.517327 | − | 0.855788i | \(-0.673073\pi\) |
0.999797 | + | 0.0201241i | \(0.00640614\pi\) | |||||||
\(80\) | 1.17229 | + | 2.03046i | 0.131066 | + | 0.227013i | ||||
\(81\) | 0.166045 | − | 0.287598i | 0.0184495 | − | 0.0319554i | ||||
\(82\) | 2.50859 | + | 4.34501i | 0.277028 | + | 0.479826i | ||||
\(83\) | −9.76464 | −1.07181 | −0.535904 | − | 0.844279i | \(-0.680029\pi\) | ||||
−0.535904 | + | 0.844279i | \(0.680029\pi\) | |||||||
\(84\) | 3.58721 | 0.391397 | ||||||||
\(85\) | 4.90742 | + | 8.49991i | 0.532285 | + | 0.921944i | ||||
\(86\) | −0.494689 | − | 0.856827i | −0.0533437 | − | 0.0923940i | ||||
\(87\) | −8.73716 | −0.936722 | ||||||||
\(88\) | −5.75621 | −0.613615 | ||||||||
\(89\) | −7.53827 | − | 13.0567i | −0.799055 | − | 1.38400i | −0.920232 | − | 0.391372i | \(-0.872000\pi\) |
0.121178 | − | 0.992631i | \(-0.461333\pi\) | |||||||
\(90\) | −5.63194 | + | 9.75480i | −0.593658 | + | 1.02825i | ||||
\(91\) | −0.195361 | − | 0.338376i | −0.0204794 | − | 0.0354714i | ||||
\(92\) | 3.23842 | − | 5.60910i | 0.337628 | − | 0.584790i | ||||
\(93\) | −8.99885 | + | 15.5865i | −0.933137 | + | 1.61624i | ||||
\(94\) | 4.39445 | 0.453253 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.79360 | 0.285121 | ||||||||
\(97\) | 8.67609 | − | 15.0274i | 0.880924 | − | 1.52580i | 0.0306077 | − | 0.999531i | \(-0.490256\pi\) |
0.850316 | − | 0.526273i | \(-0.176411\pi\) | |||||||
\(98\) | −2.67557 | + | 4.63422i | −0.270273 | + | 0.468127i | ||||
\(99\) | −13.8271 | − | 23.9492i | −1.38967 | − | 2.40699i | ||||
\(100\) | −0.248520 | + | 0.430448i | −0.0248520 | + | 0.0430448i | ||||
\(101\) | −1.83833 | − | 3.18409i | −0.182921 | − | 0.316828i | 0.759953 | − | 0.649978i | \(-0.225222\pi\) |
−0.942874 | + | 0.333150i | \(0.891889\pi\) | |||||||
\(102\) | 11.6946 | 1.15793 | ||||||||
\(103\) | −19.0135 | −1.87346 | −0.936729 | − | 0.350055i | \(-0.886163\pi\) | ||||
−0.936729 | + | 0.350055i | \(0.886163\pi\) | |||||||
\(104\) | −0.152141 | − | 0.263516i | −0.0149187 | − | 0.0258399i | ||||
\(105\) | 4.20524 | + | 7.28369i | 0.410390 | + | 0.710816i | ||||
\(106\) | 3.29064 | 0.319616 | ||||||||
\(107\) | −10.0373 | −0.970340 | −0.485170 | − | 0.874420i | \(-0.661242\pi\) | ||||
−0.485170 | + | 0.874420i | \(0.661242\pi\) | |||||||
\(108\) | 2.52015 | + | 4.36502i | 0.242501 | + | 0.420025i | ||||
\(109\) | −4.42174 | + | 7.65868i | −0.423526 | + | 0.733568i | −0.996282 | − | 0.0861578i | \(-0.972541\pi\) |
0.572756 | + | 0.819726i | \(0.305874\pi\) | |||||||
\(110\) | −6.74794 | − | 11.6878i | −0.643391 | − | 1.11439i | ||||
\(111\) | 5.55899 | − | 9.62845i | 0.527636 | − | 0.913892i | ||||
\(112\) | 0.642040 | − | 1.11205i | 0.0606670 | − | 0.105078i | ||||
\(113\) | 14.2502 | 1.34055 | 0.670275 | − | 0.742113i | \(-0.266176\pi\) | ||||
0.670275 | + | 0.742113i | \(0.266176\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 15.1854 | 1.41605 | ||||||||
\(116\) | −1.56378 | + | 2.70855i | −0.145193 | + | 0.251482i | ||||
\(117\) | 0.730921 | − | 1.26599i | 0.0675737 | − | 0.117041i | ||||
\(118\) | −1.65688 | − | 2.86979i | −0.152528 | − | 0.264186i | ||||
\(119\) | 2.68770 | − | 4.65523i | 0.246381 | − | 0.426745i | ||||
\(120\) | 3.27491 | + | 5.67231i | 0.298957 | + | 0.517809i | ||||
\(121\) | 22.1340 | 2.01218 | ||||||||
\(122\) | 10.9615 | 0.992404 | ||||||||
\(123\) | 7.00802 | + | 12.1382i | 0.631892 | + | 1.09447i | ||||
\(124\) | 3.22123 | + | 5.57934i | 0.289275 | + | 0.501039i | ||||
\(125\) | 10.5575 | 0.944295 | ||||||||
\(126\) | 6.16901 | 0.549579 | ||||||||
\(127\) | 1.11507 | + | 1.93136i | 0.0989467 | + | 0.171381i | 0.911249 | − | 0.411856i | \(-0.135119\pi\) |
−0.812302 | + | 0.583237i | \(0.801786\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −1.38197 | − | 2.39364i | −0.121675 | − | 0.210748i | ||||
\(130\) | 0.356707 | − | 0.617834i | 0.0312853 | − | 0.0541876i | ||||
\(131\) | −0.761327 | + | 1.31866i | −0.0665175 | + | 0.115212i | −0.897366 | − | 0.441287i | \(-0.854522\pi\) |
0.830849 | + | 0.556498i | \(0.187855\pi\) | |||||||
\(132\) | −16.0806 | −1.39964 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −4.38081 | −0.378445 | ||||||||
\(135\) | −5.90868 | + | 10.2341i | −0.508538 | + | 0.880814i | ||||
\(136\) | 2.09310 | − | 3.62535i | 0.179482 | − | 0.310871i | ||||
\(137\) | −5.35588 | − | 9.27665i | −0.457583 | − | 0.792558i | 0.541249 | − | 0.840862i | \(-0.317952\pi\) |
−0.998833 | + | 0.0483046i | \(0.984618\pi\) | |||||||
\(138\) | 9.04686 | − | 15.6696i | 0.770120 | − | 1.33389i | ||||
\(139\) | 5.40717 | + | 9.36549i | 0.458630 | + | 0.794371i | 0.998889 | − | 0.0471283i | \(-0.0150070\pi\) |
−0.540259 | + | 0.841499i | \(0.681674\pi\) | |||||||
\(140\) | 3.01062 | 0.254444 | ||||||||
\(141\) | 12.2764 | 1.03386 | ||||||||
\(142\) | 2.20785 | + | 3.82410i | 0.185278 | + | 0.320912i | ||||
\(143\) | 0.875758 | + | 1.51686i | 0.0732345 | + | 0.126846i | ||||
\(144\) | 4.80423 | 0.400352 | ||||||||
\(145\) | −7.33280 | −0.608956 | ||||||||
\(146\) | −1.13345 | − | 1.96319i | −0.0938047 | − | 0.162475i | ||||
\(147\) | −7.47449 | + | 12.9462i | −0.616485 | + | 1.06778i | ||||
\(148\) | −1.98990 | − | 3.44660i | −0.163569 | − | 0.283309i | ||||
\(149\) | 4.66692 | − | 8.08334i | 0.382329 | − | 0.662213i | −0.609066 | − | 0.793120i | \(-0.708455\pi\) |
0.991395 | + | 0.130906i | \(0.0417887\pi\) | |||||||
\(150\) | −0.694265 | + | 1.20250i | −0.0566865 | + | 0.0981839i | ||||
\(151\) | −19.8232 | −1.61319 | −0.806593 | − | 0.591107i | \(-0.798691\pi\) | ||||
−0.806593 | + | 0.591107i | \(0.798691\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 20.1114 | 1.62591 | ||||||||
\(154\) | −3.69572 | + | 6.40117i | −0.297809 | + | 0.515821i | ||||
\(155\) | −7.55242 | + | 13.0812i | −0.606625 | + | 1.05071i | ||||
\(156\) | −0.425022 | − | 0.736160i | −0.0340290 | − | 0.0589400i | ||||
\(157\) | −6.93381 | + | 12.0097i | −0.553379 | + | 0.958480i | 0.444649 | + | 0.895705i | \(0.353328\pi\) |
−0.998028 | + | 0.0627750i | \(0.980005\pi\) | |||||||
\(158\) | −4.28829 | − | 7.42754i | −0.341158 | − | 0.590904i | ||||
\(159\) | 9.19276 | 0.729033 | ||||||||
\(160\) | 2.34458 | 0.185355 | ||||||||
\(161\) | −4.15838 | − | 7.20253i | −0.327727 | − | 0.567639i | ||||
\(162\) | −0.166045 | − | 0.287598i | −0.0130457 | − | 0.0225959i | ||||
\(163\) | 14.2496 | 1.11611 | 0.558057 | − | 0.829803i | \(-0.311547\pi\) | ||||
0.558057 | + | 0.829803i | \(0.311547\pi\) | |||||||
\(164\) | 5.01719 | 0.391776 | ||||||||
\(165\) | −18.8511 | − | 32.6510i | −1.46755 | − | 2.54188i | ||||
\(166\) | −4.88232 | + | 8.45643i | −0.378942 | + | 0.656346i | ||||
\(167\) | 5.79506 | + | 10.0373i | 0.448435 | + | 0.776712i | 0.998284 | − | 0.0585517i | \(-0.0186482\pi\) |
−0.549849 | + | 0.835264i | \(0.685315\pi\) | |||||||
\(168\) | 1.79360 | − | 3.10661i | 0.138380 | − | 0.239680i | ||||
\(169\) | 6.45371 | − | 11.1781i | 0.496439 | − | 0.859857i | ||||
\(170\) | 9.81485 | 0.752764 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.989378 | −0.0754394 | ||||||||
\(173\) | 1.99176 | − | 3.44983i | 0.151431 | − | 0.262286i | −0.780323 | − | 0.625377i | \(-0.784945\pi\) |
0.931754 | + | 0.363091i | \(0.118279\pi\) | |||||||
\(174\) | −4.36858 | + | 7.56661i | −0.331181 | + | 0.573623i | ||||
\(175\) | 0.319119 | + | 0.552730i | 0.0241231 | + | 0.0417824i | ||||
\(176\) | −2.87811 | + | 4.98503i | −0.216946 | + | 0.375761i | ||||
\(177\) | −4.62866 | − | 8.01707i | −0.347911 | − | 0.602600i | ||||
\(178\) | −15.0765 | −1.13003 | ||||||||
\(179\) | 8.45089 | 0.631649 | 0.315825 | − | 0.948818i | \(-0.397719\pi\) | ||||
0.315825 | + | 0.948818i | \(0.397719\pi\) | |||||||
\(180\) | 5.63194 | + | 9.75480i | 0.419780 | + | 0.727080i | ||||
\(181\) | 4.24263 | + | 7.34845i | 0.315352 | + | 0.546206i | 0.979512 | − | 0.201384i | \(-0.0645440\pi\) |
−0.664160 | + | 0.747591i | \(0.731211\pi\) | |||||||
\(182\) | −0.390723 | −0.0289623 | ||||||||
\(183\) | 30.6220 | 2.26364 | ||||||||
\(184\) | −3.23842 | − | 5.60910i | −0.238739 | − | 0.413509i | ||||
\(185\) | 4.66547 | − | 8.08083i | 0.343012 | − | 0.594114i | ||||
\(186\) | 8.99885 | + | 15.5865i | 0.659828 | + | 1.14285i | ||||
\(187\) | −12.0483 | + | 20.8683i | −0.881060 | + | 1.52604i | ||||
\(188\) | 2.19723 | − | 3.80571i | 0.160249 | − | 0.277560i | ||||
\(189\) | 6.47214 | 0.470779 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.3790 | −1.61929 | −0.809644 | − | 0.586921i | \(-0.800340\pi\) | ||||
−0.809644 | + | 0.586921i | \(0.800340\pi\) | |||||||
\(192\) | 1.39680 | − | 2.41933i | 0.100806 | − | 0.174600i | ||||
\(193\) | 3.71406 | − | 6.43293i | 0.267344 | − | 0.463053i | −0.700831 | − | 0.713327i | \(-0.747187\pi\) |
0.968175 | + | 0.250274i | \(0.0805208\pi\) | |||||||
\(194\) | −8.67609 | − | 15.0274i | −0.622907 | − | 1.07891i | ||||
\(195\) | 0.996498 | − | 1.72598i | 0.0713607 | − | 0.123600i | ||||
\(196\) | 2.67557 | + | 4.63422i | 0.191112 | + | 0.331016i | ||||
\(197\) | 8.53554 | 0.608132 | 0.304066 | − | 0.952651i | \(-0.401656\pi\) | ||||
0.304066 | + | 0.952651i | \(0.401656\pi\) | |||||||
\(198\) | −27.6542 | −1.96530 | ||||||||
\(199\) | 3.17963 | + | 5.50728i | 0.225398 | + | 0.390400i | 0.956439 | − | 0.291933i | \(-0.0942985\pi\) |
−0.731041 | + | 0.682334i | \(0.760965\pi\) | |||||||
\(200\) | 0.248520 | + | 0.430448i | 0.0175730 | + | 0.0304373i | ||||
\(201\) | −12.2383 | −0.863220 | ||||||||
\(202\) | −3.67667 | −0.258689 | ||||||||
\(203\) | 2.00802 | + | 3.47799i | 0.140935 | + | 0.244107i | ||||
\(204\) | 5.84728 | − | 10.1278i | 0.409392 | − | 0.709087i | ||||
\(205\) | 5.88159 | + | 10.1872i | 0.410788 | + | 0.711506i | ||||
\(206\) | −9.50676 | + | 16.4662i | −0.662368 | + | 1.14725i | ||||
\(207\) | 15.5581 | − | 26.9474i | 1.08136 | − | 1.87297i | ||||
\(208\) | −0.304282 | −0.0210982 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 8.41049 | 0.580379 | ||||||||
\(211\) | −6.97890 | + | 12.0878i | −0.480447 | + | 0.832159i | −0.999748 | − | 0.0224323i | \(-0.992859\pi\) |
0.519301 | + | 0.854591i | \(0.326192\pi\) | |||||||
\(212\) | 1.64532 | − | 2.84978i | 0.113001 | − | 0.195724i | ||||
\(213\) | 6.16785 | + | 10.6830i | 0.422614 | + | 0.731990i | ||||
\(214\) | −5.01864 | + | 8.69254i | −0.343067 | + | 0.594210i | ||||
\(215\) | −1.15984 | − | 2.00890i | −0.0791002 | − | 0.137006i | ||||
\(216\) | 5.04029 | 0.342949 | ||||||||
\(217\) | 8.27263 | 0.561583 | ||||||||
\(218\) | 4.42174 | + | 7.65868i | 0.299478 | + | 0.518711i | ||||
\(219\) | −3.16640 | − | 5.48437i | −0.213966 | − | 0.370599i | ||||
\(220\) | −13.4959 | −0.909892 | ||||||||
\(221\) | −1.27378 | −0.0856840 | ||||||||
\(222\) | −5.55899 | − | 9.62845i | −0.373095 | − | 0.646219i | ||||
\(223\) | 4.46200 | − | 7.72841i | 0.298798 | − | 0.517533i | −0.677064 | − | 0.735925i | \(-0.736748\pi\) |
0.975861 | + | 0.218392i | \(0.0700811\pi\) | |||||||
\(224\) | −0.642040 | − | 1.11205i | −0.0428981 | − | 0.0743016i | ||||
\(225\) | −1.19394 | + | 2.06797i | −0.0795963 | + | 0.137865i | ||||
\(226\) | 7.12512 | − | 12.3411i | 0.473956 | − | 0.820916i | ||||
\(227\) | 0.659796 | 0.0437922 | 0.0218961 | − | 0.999760i | \(-0.493030\pi\) | ||||
0.0218961 | + | 0.999760i | \(0.493030\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.97208 | −0.460728 | −0.230364 | − | 0.973105i | \(-0.573992\pi\) | ||||
−0.230364 | + | 0.973105i | \(0.573992\pi\) | |||||||
\(230\) | 7.59272 | − | 13.1510i | 0.500649 | − | 0.867150i | ||||
\(231\) | −10.3244 | + | 17.8823i | −0.679294 | + | 1.17657i | ||||
\(232\) | 1.56378 | + | 2.70855i | 0.102667 | + | 0.177825i | ||||
\(233\) | 14.8048 | − | 25.6427i | 0.969898 | − | 1.67991i | 0.274061 | − | 0.961712i | \(-0.411633\pi\) |
0.695837 | − | 0.718200i | \(-0.255034\pi\) | |||||||
\(234\) | −0.730921 | − | 1.26599i | −0.0477818 | − | 0.0827605i | ||||
\(235\) | 10.3031 | 0.672102 | ||||||||
\(236\) | −3.31375 | −0.215707 | ||||||||
\(237\) | −11.9798 | − | 20.7496i | −0.778171 | − | 1.34783i | ||||
\(238\) | −2.68770 | − | 4.65523i | −0.174218 | − | 0.301754i | ||||
\(239\) | −24.7034 | −1.59793 | −0.798965 | − | 0.601378i | \(-0.794619\pi\) | ||||
−0.798965 | + | 0.601378i | \(0.794619\pi\) | |||||||
\(240\) | 6.54982 | 0.422789 | ||||||||
\(241\) | 13.7793 | + | 23.8665i | 0.887604 | + | 1.53738i | 0.842699 | + | 0.538384i | \(0.180965\pi\) |
0.0449048 | + | 0.998991i | \(0.485702\pi\) | |||||||
\(242\) | 11.0670 | − | 19.1686i | 0.711414 | − | 1.23221i | ||||
\(243\) | −8.02431 | − | 13.8985i | −0.514759 | − | 0.891589i | ||||
\(244\) | 5.48073 | − | 9.49290i | 0.350868 | − | 0.607721i | ||||
\(245\) | −6.27308 | + | 10.8653i | −0.400772 | + | 0.694158i | ||||
\(246\) | 14.0160 | 0.893630 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 6.44246 | 0.409097 | ||||||||
\(249\) | −13.6393 | + | 23.6239i | −0.864354 | + | 1.49711i | ||||
\(250\) | 5.27877 | − | 9.14309i | 0.333859 | − | 0.578260i | ||||
\(251\) | 1.49428 | + | 2.58816i | 0.0943179 | + | 0.163363i | 0.909324 | − | 0.416089i | \(-0.136600\pi\) |
−0.815006 | + | 0.579453i | \(0.803266\pi\) | |||||||
\(252\) | 3.08450 | − | 5.34252i | 0.194305 | − | 0.336547i | ||||
\(253\) | 18.6410 | + | 32.2872i | 1.17195 | + | 2.02988i | ||||
\(254\) | 2.23015 | 0.139932 | ||||||||
\(255\) | 27.4188 | 1.71703 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 7.06613 | + | 12.2389i | 0.440773 | + | 0.763441i | 0.997747 | − | 0.0670886i | \(-0.0213710\pi\) |
−0.556974 | + | 0.830530i | \(0.688038\pi\) | |||||||
\(258\) | −2.76393 | −0.172075 | ||||||||
\(259\) | −5.11037 | −0.317543 | ||||||||
\(260\) | −0.356707 | − | 0.617834i | −0.0221220 | − | 0.0383165i | ||||
\(261\) | −7.51275 | + | 13.0125i | −0.465028 | + | 0.805451i | ||||
\(262\) | 0.761327 | + | 1.31866i | 0.0470350 | + | 0.0814669i | ||||
\(263\) | −3.78444 | + | 6.55483i | −0.233358 | + | 0.404188i | −0.958794 | − | 0.284101i | \(-0.908305\pi\) |
0.725436 | + | 0.688290i | \(0.241638\pi\) | |||||||
\(264\) | −8.04029 | + | 13.9262i | −0.494846 | + | 0.857098i | ||||
\(265\) | 7.71517 | 0.473939 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −42.1179 | −2.57757 | ||||||||
\(268\) | −2.19041 | + | 3.79390i | −0.133800 | + | 0.231749i | ||||
\(269\) | −3.83537 | + | 6.64306i | −0.233847 | + | 0.405035i | −0.958937 | − | 0.283619i | \(-0.908465\pi\) |
0.725090 | + | 0.688654i | \(0.241798\pi\) | |||||||
\(270\) | 5.90868 | + | 10.2341i | 0.359591 | + | 0.622829i | ||||
\(271\) | −5.83245 | + | 10.1021i | −0.354296 | + | 0.613658i | −0.986997 | − | 0.160737i | \(-0.948613\pi\) |
0.632701 | + | 0.774396i | \(0.281946\pi\) | |||||||
\(272\) | −2.09310 | − | 3.62535i | −0.126913 | − | 0.219819i | ||||
\(273\) | −1.09152 | −0.0660621 | ||||||||
\(274\) | −10.7118 | −0.647121 | ||||||||
\(275\) | −1.43053 | − | 2.47775i | −0.0862643 | − | 0.149414i | ||||
\(276\) | −9.04686 | − | 15.6696i | −0.544557 | − | 0.943200i | ||||
\(277\) | 27.4405 | 1.64874 | 0.824370 | − | 0.566052i | \(-0.191530\pi\) | ||||
0.824370 | + | 0.566052i | \(0.191530\pi\) | |||||||
\(278\) | 10.8143 | 0.648601 | ||||||||
\(279\) | 15.4755 | + | 26.8044i | 0.926495 | + | 1.60474i | ||||
\(280\) | 1.50531 | − | 2.60727i | 0.0899595 | − | 0.155814i | ||||
\(281\) | 8.13574 | + | 14.0915i | 0.485338 | + | 0.840629i | 0.999858 | − | 0.0168488i | \(-0.00536339\pi\) |
−0.514520 | + | 0.857478i | \(0.672030\pi\) | |||||||
\(282\) | 6.13818 | − | 10.6316i | 0.365523 | − | 0.633105i | ||||
\(283\) | −1.69687 | + | 2.93907i | −0.100868 | + | 0.174709i | −0.912043 | − | 0.410095i | \(-0.865495\pi\) |
0.811174 | + | 0.584805i | \(0.198829\pi\) | |||||||
\(284\) | 4.41570 | 0.262023 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.75152 | 0.103569 | ||||||||
\(287\) | 3.22123 | − | 5.57934i | 0.190143 | − | 0.329338i | ||||
\(288\) | 2.40211 | − | 4.16058i | 0.141546 | − | 0.245165i | ||||
\(289\) | −0.262102 | − | 0.453974i | −0.0154178 | − | 0.0267044i | ||||
\(290\) | −3.66640 | + | 6.35039i | −0.215298 | + | 0.372908i | ||||
\(291\) | −24.2376 | − | 41.9807i | −1.42083 | − | 2.46095i | ||||
\(292\) | −2.26689 | −0.132660 | ||||||||
\(293\) | −23.3783 | −1.36578 | −0.682888 | − | 0.730523i | \(-0.739276\pi\) | ||||
−0.682888 | + | 0.730523i | \(0.739276\pi\) | |||||||
\(294\) | 7.47449 | + | 12.9462i | 0.435921 | + | 0.755037i | ||||
\(295\) | −3.88467 | − | 6.72845i | −0.226174 | − | 0.391745i | ||||
\(296\) | −3.97980 | −0.231321 | ||||||||
\(297\) | −29.0130 | −1.68351 | ||||||||
\(298\) | −4.66692 | − | 8.08334i | −0.270347 | − | 0.468256i | ||||
\(299\) | −0.985394 | + | 1.70675i | −0.0569868 | + | 0.0987040i | ||||
\(300\) | 0.694265 | + | 1.20250i | 0.0400834 | + | 0.0694265i | ||||
\(301\) | −0.635220 | + | 1.10023i | −0.0366135 | + | 0.0634164i | ||||
\(302\) | −9.91158 | + | 17.1674i | −0.570347 | + | 0.987871i | ||||
\(303\) | −10.2712 | −0.590062 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 25.7000 | 1.47158 | ||||||||
\(306\) | 10.0557 | − | 17.4170i | 0.574846 | − | 0.995663i | ||||
\(307\) | −0.694010 | + | 1.20206i | −0.0396093 | + | 0.0686052i | −0.885150 | − | 0.465305i | \(-0.845945\pi\) |
0.845541 | + | 0.533910i | \(0.179278\pi\) | |||||||
\(308\) | 3.69572 | + | 6.40117i | 0.210583 | + | 0.364741i | ||||
\(309\) | −26.5581 | + | 46.0000i | −1.51084 | + | 2.61685i | ||||
\(310\) | 7.55242 | + | 13.0812i | 0.428949 | + | 0.742961i | ||||
\(311\) | −12.1902 | −0.691246 | −0.345623 | − | 0.938374i | \(-0.612332\pi\) | ||||
−0.345623 | + | 0.938374i | \(0.612332\pi\) | |||||||
\(312\) | −0.850045 | −0.0481243 | ||||||||
\(313\) | −8.26571 | − | 14.3166i | −0.467205 | − | 0.809223i | 0.532093 | − | 0.846686i | \(-0.321406\pi\) |
−0.999298 | + | 0.0374628i | \(0.988072\pi\) | |||||||
\(314\) | 6.93381 | + | 12.0097i | 0.391298 | + | 0.677748i | ||||
\(315\) | 14.4637 | 0.814938 | ||||||||
\(316\) | −8.57659 | −0.482471 | ||||||||
\(317\) | 1.34406 | + | 2.32797i | 0.0754897 | + | 0.130752i | 0.901299 | − | 0.433197i | \(-0.142615\pi\) |
−0.825809 | + | 0.563949i | \(0.809281\pi\) | |||||||
\(318\) | 4.59638 | − | 7.96116i | 0.257752 | − | 0.446440i | ||||
\(319\) | −9.00145 | − | 15.5910i | −0.503985 | − | 0.872927i | ||||
\(320\) | 1.17229 | − | 2.03046i | 0.0655329 | − | 0.113506i | ||||
\(321\) | −14.0201 | + | 24.2835i | −0.782525 | + | 1.35537i | ||||
\(322\) | −8.31677 | −0.463475 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.332090 | −0.0184495 | ||||||||
\(325\) | 0.0756201 | − | 0.130978i | 0.00419465 | − | 0.00726535i | ||||
\(326\) | 7.12480 | − | 12.3405i | 0.394606 | − | 0.683478i | ||||
\(327\) | 12.3526 | + | 21.3953i | 0.683100 | + | 1.18316i | ||||
\(328\) | 2.50859 | − | 4.34501i | 0.138514 | − | 0.239913i | ||||
\(329\) | −2.82141 | − | 4.88683i | −0.155549 | − | 0.269420i | ||||
\(330\) | −37.7022 | −2.07544 | ||||||||
\(331\) | −5.21303 | −0.286534 | −0.143267 | − | 0.989684i | \(-0.545761\pi\) | ||||
−0.143267 | + | 0.989684i | \(0.545761\pi\) | |||||||
\(332\) | 4.88232 | + | 8.45643i | 0.267952 | + | 0.464107i | ||||
\(333\) | −9.55992 | − | 16.5583i | −0.523880 | − | 0.907388i | ||||
\(334\) | 11.5901 | 0.634183 | ||||||||
\(335\) | −10.2712 | −0.561173 | ||||||||
\(336\) | −1.79360 | − | 3.10661i | −0.0978491 | − | 0.169480i | ||||
\(337\) | −13.3637 | + | 23.1467i | −0.727969 | + | 1.26088i | 0.229771 | + | 0.973245i | \(0.426202\pi\) |
−0.957740 | + | 0.287635i | \(0.907131\pi\) | |||||||
\(338\) | −6.45371 | − | 11.1781i | −0.351035 | − | 0.608011i | ||||
\(339\) | 19.9048 | − | 34.4761i | 1.08108 | − | 1.87248i | ||||
\(340\) | 4.90742 | − | 8.49991i | 0.266142 | − | 0.460972i | ||||
\(341\) | −37.0842 | −2.00822 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.8598 | 0.856351 | ||||||||
\(344\) | −0.494689 | + | 0.856827i | −0.0266719 | + | 0.0461970i | ||||
\(345\) | 21.2111 | − | 36.7386i | 1.14196 | − | 1.97794i | ||||
\(346\) | −1.99176 | − | 3.44983i | −0.107078 | − | 0.185464i | ||||
\(347\) | 16.3341 | − | 28.2915i | 0.876860 | − | 1.51877i | 0.0220925 | − | 0.999756i | \(-0.492967\pi\) |
0.854768 | − | 0.519011i | \(-0.173699\pi\) | |||||||
\(348\) | 4.36858 | + | 7.56661i | 0.234181 | + | 0.405613i | ||||
\(349\) | −29.1058 | −1.55800 | −0.778998 | − | 0.627026i | \(-0.784272\pi\) | ||||
−0.778998 | + | 0.627026i | \(0.784272\pi\) | |||||||
\(350\) | 0.638237 | 0.0341152 | ||||||||
\(351\) | −0.766837 | − | 1.32820i | −0.0409307 | − | 0.0708941i | ||||
\(352\) | 2.87811 | + | 4.98503i | 0.153404 | + | 0.265703i | ||||
\(353\) | −14.3049 | −0.761372 | −0.380686 | − | 0.924704i | \(-0.624312\pi\) | ||||
−0.380686 | + | 0.924704i | \(0.624312\pi\) | |||||||
\(354\) | −9.25731 | −0.492021 | ||||||||
\(355\) | 5.17647 | + | 8.96591i | 0.274738 | + | 0.475861i | ||||
\(356\) | −7.53827 | + | 13.0567i | −0.399527 | + | 0.692002i | ||||
\(357\) | −7.50837 | − | 13.0049i | −0.397385 | − | 0.688291i | ||||
\(358\) | 4.22545 | − | 7.31869i | 0.223322 | − | 0.386805i | ||||
\(359\) | −9.83535 | + | 17.0353i | −0.519090 | + | 0.899090i | 0.480664 | + | 0.876905i | \(0.340396\pi\) |
−0.999754 | + | 0.0221853i | \(0.992938\pi\) | |||||||
\(360\) | 11.2639 | 0.593658 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 8.48526 | 0.445976 | ||||||||
\(363\) | 30.9168 | − | 53.5495i | 1.62271 | − | 2.81062i | ||||
\(364\) | −0.195361 | + | 0.338376i | −0.0102397 | + | 0.0177357i | ||||
\(365\) | −2.65745 | − | 4.60284i | −0.139097 | − | 0.240924i | ||||
\(366\) | 15.3110 | − | 26.5194i | 0.800318 | − | 1.38619i | ||||
\(367\) | −4.77527 | − | 8.27100i | −0.249267 | − | 0.431743i | 0.714056 | − | 0.700089i | \(-0.246856\pi\) |
−0.963323 | + | 0.268346i | \(0.913523\pi\) | |||||||
\(368\) | −6.47684 | −0.337628 | ||||||||
\(369\) | 24.1037 | 1.25479 | ||||||||
\(370\) | −4.66547 | − | 8.08083i | −0.242546 | − | 0.420102i | ||||
\(371\) | −2.11272 | − | 3.65934i | −0.109687 | − | 0.189984i | ||||
\(372\) | 17.9977 | 0.933137 | ||||||||
\(373\) | −3.64010 | −0.188477 | −0.0942387 | − | 0.995550i | \(-0.530042\pi\) | ||||
−0.0942387 | + | 0.995550i | \(0.530042\pi\) | |||||||
\(374\) | 12.0483 | + | 20.8683i | 0.623003 | + | 1.07907i | ||||
\(375\) | 14.7468 | − | 25.5422i | 0.761521 | − | 1.31899i | ||||
\(376\) | −2.19723 | − | 3.80571i | −0.113313 | − | 0.196264i | ||||
\(377\) | 0.475831 | − | 0.824163i | 0.0245065 | − | 0.0424466i | ||||
\(378\) | 3.23607 | − | 5.60503i | 0.166445 | − | 0.288292i | ||||
\(379\) | −8.34741 | −0.428778 | −0.214389 | − | 0.976748i | \(-0.568776\pi\) | ||||
−0.214389 | + | 0.976748i | \(0.568776\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.23015 | 0.319180 | ||||||||
\(382\) | −11.1895 | + | 19.3808i | −0.572505 | + | 0.991608i | ||||
\(383\) | −4.74283 | + | 8.21482i | −0.242347 | + | 0.419758i | −0.961382 | − | 0.275216i | \(-0.911251\pi\) |
0.719035 | + | 0.694974i | \(0.244584\pi\) | |||||||
\(384\) | −1.39680 | − | 2.41933i | −0.0712803 | − | 0.123461i | ||||
\(385\) | −8.66489 | + | 15.0080i | −0.441604 | + | 0.764880i | ||||
\(386\) | −3.71406 | − | 6.43293i | −0.189040 | − | 0.327428i | ||||
\(387\) | −4.75320 | −0.241619 | ||||||||
\(388\) | −17.3522 | −0.880924 | ||||||||
\(389\) | −18.0240 | − | 31.2185i | −0.913852 | − | 1.58284i | −0.808573 | − | 0.588396i | \(-0.799760\pi\) |
−0.105279 | − | 0.994443i | \(-0.533574\pi\) | |||||||
\(390\) | −0.996498 | − | 1.72598i | −0.0504596 | − | 0.0873986i | ||||
\(391\) | −27.1133 | −1.37118 | ||||||||
\(392\) | 5.35114 | 0.270273 | ||||||||
\(393\) | 2.12685 | + | 3.68381i | 0.107285 | + | 0.185823i | ||||
\(394\) | 4.26777 | − | 7.39199i | 0.215007 | − | 0.372403i | ||||
\(395\) | −10.0542 | − | 17.4144i | −0.505883 | − | 0.876216i | ||||
\(396\) | −13.8271 | + | 23.9492i | −0.694837 | + | 1.20349i | ||||
\(397\) | 3.20453 | − | 5.55041i | 0.160831 | − | 0.278567i | −0.774336 | − | 0.632775i | \(-0.781916\pi\) |
0.935167 | + | 0.354207i | \(0.115249\pi\) | |||||||
\(398\) | 6.35926 | 0.318761 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.497039 | 0.0248520 | ||||||||
\(401\) | 0.0938299 | − | 0.162518i | 0.00468564 | − | 0.00811577i | −0.863673 | − | 0.504052i | \(-0.831842\pi\) |
0.868359 | + | 0.495937i | \(0.165175\pi\) | |||||||
\(402\) | −6.11913 | + | 10.5986i | −0.305194 | + | 0.528612i | ||||
\(403\) | −0.980164 | − | 1.69769i | −0.0488255 | − | 0.0845682i | ||||
\(404\) | −1.83833 | + | 3.18409i | −0.0914605 | + | 0.158414i | ||||
\(405\) | −0.389305 | − | 0.674297i | −0.0193447 | − | 0.0335061i | ||||
\(406\) | 4.01603 | 0.199312 | ||||||||
\(407\) | 22.9086 | 1.13554 | ||||||||
\(408\) | −5.84728 | − | 10.1278i | −0.289484 | − | 0.501400i | ||||
\(409\) | 8.63314 | + | 14.9530i | 0.426881 | + | 0.739380i | 0.996594 | − | 0.0824641i | \(-0.0262790\pi\) |
−0.569713 | + | 0.821844i | \(0.692946\pi\) | |||||||
\(410\) | 11.7632 | 0.580942 | ||||||||
\(411\) | −29.9244 | −1.47606 | ||||||||
\(412\) | 9.50676 | + | 16.4662i | 0.468365 | + | 0.811231i | ||||
\(413\) | −2.12756 | + | 3.68504i | −0.104690 | + | 0.181329i | ||||
\(414\) | −15.5581 | − | 26.9474i | −0.764638 | − | 1.32439i | ||||
\(415\) | −11.4470 | + | 19.8267i | −0.561910 | + | 0.973257i | ||||
\(416\) | −0.152141 | + | 0.263516i | −0.00745934 | + | 0.0129200i | ||||
\(417\) | 30.2110 | 1.47944 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.72572 | −0.0843068 | −0.0421534 | − | 0.999111i | \(-0.513422\pi\) | ||||
−0.0421534 | + | 0.999111i | \(0.513422\pi\) | |||||||
\(420\) | 4.20524 | − | 7.28369i | 0.205195 | − | 0.355408i | ||||
\(421\) | 16.3773 | − | 28.3663i | 0.798180 | − | 1.38249i | −0.122621 | − | 0.992454i | \(-0.539130\pi\) |
0.920800 | − | 0.390034i | \(-0.127537\pi\) | |||||||
\(422\) | 6.97890 | + | 12.0878i | 0.339727 | + | 0.588425i | ||||
\(423\) | 10.5560 | − | 18.2835i | 0.513249 | − | 0.888973i | ||||
\(424\) | −1.64532 | − | 2.84978i | −0.0799039 | − | 0.138398i | ||||
\(425\) | 2.08070 | 0.100929 | ||||||||
\(426\) | 12.3357 | 0.597667 | ||||||||
\(427\) | −7.03769 | − | 12.1896i | −0.340578 | − | 0.589898i | ||||
\(428\) | 5.01864 | + | 8.69254i | 0.242585 | + | 0.420170i | ||||
\(429\) | 4.89304 | 0.236238 | ||||||||
\(430\) | −2.31967 | −0.111865 | ||||||||
\(431\) | −12.7560 | − | 22.0940i | −0.614433 | − | 1.06423i | −0.990484 | − | 0.137630i | \(-0.956051\pi\) |
0.376051 | − | 0.926599i | \(-0.377282\pi\) | |||||||
\(432\) | 2.52015 | − | 4.36502i | 0.121251 | − | 0.210012i | ||||
\(433\) | 12.2417 | + | 21.2032i | 0.588299 | + | 1.01896i | 0.994455 | + | 0.105160i | \(0.0335353\pi\) |
−0.406157 | + | 0.913803i | \(0.633131\pi\) | |||||||
\(434\) | 4.13632 | − | 7.16431i | 0.198550 | − | 0.343898i | ||||
\(435\) | −10.2425 | + | 17.7405i | −0.491089 | + | 0.850591i | ||||
\(436\) | 8.84348 | 0.423526 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −6.33280 | −0.302593 | ||||||||
\(439\) | −15.4194 | + | 26.7072i | −0.735928 | + | 1.27466i | 0.218387 | + | 0.975862i | \(0.429920\pi\) |
−0.954315 | + | 0.298802i | \(0.903413\pi\) | |||||||
\(440\) | −6.74794 | + | 11.6878i | −0.321696 | + | 0.557193i | ||||
\(441\) | 12.8540 | + | 22.2639i | 0.612097 | + | 1.06018i | ||||
\(442\) | −0.636892 | + | 1.10313i | −0.0302939 | + | 0.0524705i | ||||
\(443\) | −5.35234 | − | 9.27052i | −0.254297 | − | 0.440456i | 0.710407 | − | 0.703791i | \(-0.248511\pi\) |
−0.964704 | + | 0.263335i | \(0.915177\pi\) | |||||||
\(444\) | −11.1180 | −0.527636 | ||||||||
\(445\) | −35.3481 | −1.67566 | ||||||||
\(446\) | −4.46200 | − | 7.72841i | −0.211282 | − | 0.365951i | ||||
\(447\) | −13.0375 | − | 22.5817i | −0.616654 | − | 1.06808i | ||||
\(448\) | −1.28408 | −0.0606670 | ||||||||
\(449\) | −2.31562 | −0.109281 | −0.0546403 | − | 0.998506i | \(-0.517401\pi\) | ||||
−0.0546403 | + | 0.998506i | \(0.517401\pi\) | |||||||
\(450\) | 1.19394 | + | 2.06797i | 0.0562831 | + | 0.0974851i | ||||
\(451\) | −14.4400 | + | 25.0108i | −0.679953 | + | 1.17771i | ||||
\(452\) | −7.12512 | − | 12.3411i | −0.335137 | − | 0.580475i | ||||
\(453\) | −27.6890 | + | 47.9588i | −1.30094 | + | 2.25330i | ||||
\(454\) | 0.329898 | − | 0.571400i | 0.0154829 | − | 0.0268171i | ||||
\(455\) | −0.916079 | −0.0429465 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.0521810 | −0.00244092 | −0.00122046 | − | 0.999999i | \(-0.500388\pi\) | ||||
−0.00122046 | + | 0.999999i | \(0.500388\pi\) | |||||||
\(458\) | −3.48604 | + | 6.03800i | −0.162892 | + | 0.282137i | ||||
\(459\) | 10.5498 | − | 18.2728i | 0.492423 | − | 0.852902i | ||||
\(460\) | −7.59272 | − | 13.1510i | −0.354012 | − | 0.613167i | ||||
\(461\) | −19.7360 | + | 34.1838i | −0.919198 | + | 1.59210i | −0.118561 | + | 0.992947i | \(0.537828\pi\) |
−0.800637 | + | 0.599150i | \(0.795505\pi\) | |||||||
\(462\) | 10.3244 | + | 17.8823i | 0.480333 | + | 0.831962i | ||||
\(463\) | −6.19056 | −0.287700 | −0.143850 | − | 0.989600i | \(-0.545948\pi\) | ||||
−0.143850 | + | 0.989600i | \(0.545948\pi\) | |||||||
\(464\) | 3.12756 | 0.145193 | ||||||||
\(465\) | 21.0985 | + | 36.5437i | 0.978419 | + | 1.69467i | ||||
\(466\) | −14.8048 | − | 25.6427i | −0.685821 | − | 1.18788i | ||||
\(467\) | −20.9962 | −0.971586 | −0.485793 | − | 0.874074i | \(-0.661469\pi\) | ||||
−0.485793 | + | 0.874074i | \(0.661469\pi\) | |||||||
\(468\) | −1.46184 | −0.0675737 | ||||||||
\(469\) | 2.81266 | + | 4.87166i | 0.129876 | + | 0.224952i | ||||
\(470\) | 5.15156 | − | 8.92277i | 0.237624 | − | 0.411577i | ||||
\(471\) | 19.3703 | + | 33.5504i | 0.892538 | + | 1.54592i | ||||
\(472\) | −1.65688 | + | 2.86979i | −0.0762639 | + | 0.132093i | ||||
\(473\) | 2.84754 | − | 4.93208i | 0.130930 | − | 0.226777i | ||||
\(474\) | −23.9596 | −1.10050 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −5.37540 | −0.246381 | ||||||||
\(477\) | 7.90450 | − | 13.6910i | 0.361922 | − | 0.626867i | ||||
\(478\) | −12.3517 | + | 21.3938i | −0.564953 | + | 0.978528i | ||||
\(479\) | −7.76147 | − | 13.4433i | −0.354631 | − | 0.614238i | 0.632424 | − | 0.774622i | \(-0.282060\pi\) |
−0.987055 | + | 0.160384i | \(0.948727\pi\) | |||||||
\(480\) | 3.27491 | − | 5.67231i | 0.149478 | − | 0.258904i | ||||
\(481\) | 0.605491 | + | 1.04874i | 0.0276080 | + | 0.0478185i | ||||
\(482\) | 27.5586 | 1.25526 | ||||||||
\(483\) | −23.2338 | −1.05717 | ||||||||
\(484\) | −11.0670 | − | 19.1686i | −0.503046 | − | 0.871301i | ||||
\(485\) | −20.3418 | − | 35.2330i | −0.923672 | − | 1.59985i | ||||
\(486\) | −16.0486 | −0.727980 | ||||||||
\(487\) | 28.6065 | 1.29629 | 0.648143 | − | 0.761519i | \(-0.275546\pi\) | ||||
0.648143 | + | 0.761519i | \(0.275546\pi\) | |||||||
\(488\) | −5.48073 | − | 9.49290i | −0.248101 | − | 0.429723i | ||||
\(489\) | 19.9039 | − | 34.4745i | 0.900084 | − | 1.55899i | ||||
\(490\) | 6.27308 | + | 10.8653i | 0.283389 | + | 0.490844i | ||||
\(491\) | 15.1744 | − | 26.2829i | 0.684812 | − | 1.18613i | −0.288684 | − | 0.957424i | \(-0.593218\pi\) |
0.973496 | − | 0.228705i | \(-0.0734490\pi\) | |||||||
\(492\) | 7.00802 | − | 12.1382i | 0.315946 | − | 0.547234i | ||||
\(493\) | 13.0926 | 0.589659 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −64.8373 | −2.91422 | ||||||||
\(496\) | 3.22123 | − | 5.57934i | 0.144638 | − | 0.250520i | ||||
\(497\) | 2.83505 | − | 4.91045i | 0.127169 | − | 0.220264i | ||||
\(498\) | 13.6393 | + | 23.6239i | 0.611191 | + | 1.05861i | ||||
\(499\) | −4.38812 | + | 7.60044i | −0.196439 | + | 0.340243i | −0.947371 | − | 0.320137i | \(-0.896271\pi\) |
0.750932 | + | 0.660379i | \(0.229604\pi\) | |||||||
\(500\) | −5.27877 | − | 9.14309i | −0.236074 | − | 0.408892i | ||||
\(501\) | 32.3782 | 1.44655 | ||||||||
\(502\) | 2.98855 | 0.133386 | ||||||||
\(503\) | 10.5522 | + | 18.2769i | 0.470498 | + | 0.814926i | 0.999431 | − | 0.0337373i | \(-0.0107410\pi\) |
−0.528933 | + | 0.848664i | \(0.677408\pi\) | |||||||
\(504\) | −3.08450 | − | 5.34252i | −0.137395 | − | 0.237975i | ||||
\(505\) | −8.62023 | −0.383595 | ||||||||
\(506\) | 37.2821 | 1.65739 | ||||||||
\(507\) | −18.0291 | − | 31.2273i | −0.800701 | − | 1.38685i | ||||
\(508\) | 1.11507 | − | 1.93136i | 0.0494734 | − | 0.0856904i | ||||
\(509\) | 11.1106 | + | 19.2441i | 0.492468 | + | 0.852979i | 0.999962 | − | 0.00867561i | \(-0.00276157\pi\) |
−0.507494 | + | 0.861655i | \(0.669428\pi\) | |||||||
\(510\) | 13.7094 | − | 23.7454i | 0.607062 | − | 1.05146i | ||||
\(511\) | −1.45543 | + | 2.52089i | −0.0643846 | + | 0.111517i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 14.1323 | 0.623347 | ||||||||
\(515\) | −22.2893 | + | 38.6063i | −0.982185 | + | 1.70119i | ||||
\(516\) | −1.38197 | + | 2.39364i | −0.0608377 | + | 0.105374i | ||||
\(517\) | 12.6477 | + | 21.9065i | 0.556245 | + | 0.963445i | ||||
\(518\) | −2.55519 | + | 4.42571i | −0.112268 | + | 0.194455i | ||||
\(519\) | −5.56420 | − | 9.63747i | −0.244241 | − | 0.423038i | ||||
\(520\) | −0.713414 | −0.0312853 | ||||||||
\(521\) | −10.0332 | −0.439563 | −0.219782 | − | 0.975549i | \(-0.570534\pi\) | ||||
−0.219782 | + | 0.975549i | \(0.570534\pi\) | |||||||
\(522\) | 7.51275 | + | 13.0125i | 0.328824 | + | 0.569540i | ||||
\(523\) | 14.6411 | + | 25.3592i | 0.640212 | + | 1.10888i | 0.985385 | + | 0.170341i | \(0.0544870\pi\) |
−0.345173 | + | 0.938539i | \(0.612180\pi\) | |||||||
\(524\) | 1.52265 | 0.0665175 | ||||||||
\(525\) | 1.78298 | 0.0778158 | ||||||||
\(526\) | 3.78444 | + | 6.55483i | 0.165009 | + | 0.285804i | ||||
\(527\) | 13.4847 | − | 23.3562i | 0.587403 | − | 1.01741i | ||||
\(528\) | 8.04029 | + | 13.9262i | 0.349909 | + | 0.606060i | ||||
\(529\) | −9.47470 | + | 16.4107i | −0.411943 | + | 0.713507i | ||||
\(530\) | 3.85758 | − | 6.68153i | 0.167563 | − | 0.290227i | ||||
\(531\) | −15.9200 | −0.690870 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.52664 | −0.0661262 | ||||||||
\(534\) | −21.0589 | + | 36.4751i | −0.911309 | + | 1.57843i | ||||
\(535\) | −11.7666 | + | 20.3803i | −0.508714 | + | 0.881118i | ||||
\(536\) | 2.19041 | + | 3.79390i | 0.0946112 | + | 0.163871i | ||||
\(537\) | 11.8042 | − | 20.4455i | 0.509390 | − | 0.882289i | ||||
\(538\) | 3.83537 | + | 6.64306i | 0.165355 | + | 0.286403i | ||||
\(539\) | −30.8023 | −1.32675 | ||||||||
\(540\) | 11.8174 | 0.508538 | ||||||||
\(541\) | 18.9202 | + | 32.7707i | 0.813442 | + | 1.40892i | 0.910441 | + | 0.413638i | \(0.135742\pi\) |
−0.0969995 | + | 0.995284i | \(0.530925\pi\) | |||||||
\(542\) | 5.83245 | + | 10.1021i | 0.250525 | + | 0.433922i | ||||
\(543\) | 23.7045 | 1.01726 | ||||||||
\(544\) | −4.18619 | −0.179482 | ||||||||
\(545\) | 10.3671 | + | 17.9564i | 0.444078 | + | 0.769166i | ||||
\(546\) | −0.545762 | + | 0.945288i | −0.0233565 | + | 0.0404546i | ||||
\(547\) | −7.24878 | − | 12.5553i | −0.309936 | − | 0.536824i | 0.668412 | − | 0.743791i | \(-0.266974\pi\) |
−0.978348 | + | 0.206967i | \(0.933641\pi\) | |||||||
\(548\) | −5.35588 | + | 9.27665i | −0.228792 | + | 0.396279i | ||||
\(549\) | 26.3307 | − | 45.6060i | 1.12377 | − | 1.94642i | ||||
\(550\) | −2.86106 | −0.121996 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −18.0937 | −0.770120 | ||||||||
\(553\) | −5.50651 | + | 9.53755i | −0.234161 | + | 0.405578i | ||||
\(554\) | 13.7202 | − | 23.7642i | 0.582917 | − | 1.00964i | ||||
\(555\) | −13.0335 | − | 22.5746i | −0.553240 | − | 0.958240i | ||||
\(556\) | 5.40717 | − | 9.36549i | 0.229315 | − | 0.397185i | ||||
\(557\) | 2.16901 | + | 3.75683i | 0.0919037 | + | 0.159182i | 0.908312 | − | 0.418293i | \(-0.137371\pi\) |
−0.816408 | + | 0.577475i | \(0.804038\pi\) | |||||||
\(558\) | 30.9511 | 1.31026 | ||||||||
\(559\) | 0.301051 | 0.0127331 | ||||||||
\(560\) | −1.50531 | − | 2.60727i | −0.0636110 | − | 0.110177i | ||||
\(561\) | 33.6582 | + | 58.2977i | 1.42105 | + | 2.46133i | ||||
\(562\) | 16.2715 | 0.686371 | ||||||||
\(563\) | 27.2936 | 1.15029 | 0.575144 | − | 0.818052i | \(-0.304946\pi\) | ||||
0.575144 | + | 0.818052i | \(0.304946\pi\) | |||||||
\(564\) | −6.13818 | − | 10.6316i | −0.258464 | − | 0.447673i | ||||
\(565\) | 16.7054 | − | 28.9346i | 0.702801 | − | 1.21729i | ||||
\(566\) | 1.69687 | + | 2.93907i | 0.0713248 | + | 0.123538i | ||||
\(567\) | −0.213215 | + | 0.369299i | −0.00895419 | + | 0.0155091i | ||||
\(568\) | 2.20785 | − | 3.82410i | 0.0926392 | − | 0.160456i | ||||
\(569\) | 7.19043 | 0.301439 | 0.150719 | − | 0.988577i | \(-0.451841\pi\) | ||||
0.150719 | + | 0.988577i | \(0.451841\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 42.0134 | 1.75821 | 0.879103 | − | 0.476631i | \(-0.158142\pi\) | ||||
0.879103 | + | 0.476631i | \(0.158142\pi\) | |||||||
\(572\) | 0.875758 | − | 1.51686i | 0.0366173 | − | 0.0634230i | ||||
\(573\) | −31.2591 | + | 54.1423i | −1.30587 | + | 2.26183i | ||||
\(574\) | −3.22123 | − | 5.57934i | −0.134452 | − | 0.232877i | ||||
\(575\) | 1.60962 | − | 2.78794i | 0.0671258 | − | 0.116265i | ||||
\(576\) | −2.40211 | − | 4.16058i | −0.100088 | − | 0.173358i | ||||
\(577\) | 21.6713 | 0.902190 | 0.451095 | − | 0.892476i | \(-0.351034\pi\) | ||||
0.451095 | + | 0.892476i | \(0.351034\pi\) | |||||||
\(578\) | −0.524204 | −0.0218040 | ||||||||
\(579\) | −10.3756 | − | 17.9711i | −0.431195 | − | 0.746852i | ||||
\(580\) | 3.66640 | + | 6.35039i | 0.152239 | + | 0.263686i | ||||
\(581\) | 12.5386 | 0.520188 | ||||||||
\(582\) | −48.4751 | −2.00936 | ||||||||
\(583\) | 9.47083 | + | 16.4040i | 0.392242 | + | 0.679382i | ||||
\(584\) | −1.13345 | + | 1.96319i | −0.0469023 | + | 0.0812373i | ||||
\(585\) | −1.71370 | − | 2.96822i | −0.0708528 | − | 0.122721i | ||||
\(586\) | −11.6892 | + | 20.2462i | −0.482874 | + | 0.836363i | ||||
\(587\) | 0.634322 | − | 1.09868i | 0.0261813 | − | 0.0453473i | −0.852638 | − | 0.522502i | \(-0.824999\pi\) |
0.878819 | + | 0.477155i | \(0.158332\pi\) | |||||||
\(588\) | 14.9490 | 0.616485 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −7.76934 | −0.319859 | ||||||||
\(591\) | 11.9225 | − | 20.6503i | 0.490424 | − | 0.849440i | ||||
\(592\) | −1.98990 | + | 3.44660i | −0.0817843 | + | 0.141655i | ||||
\(593\) | −10.7800 | − | 18.6715i | −0.442682 | − | 0.766747i | 0.555206 | − | 0.831713i | \(-0.312639\pi\) |
−0.997887 | + | 0.0649660i | \(0.979306\pi\) | |||||||
\(594\) | −14.5065 | + | 25.1260i | −0.595209 | + | 1.03093i | ||||
\(595\) | −6.30152 | − | 10.9146i | −0.258337 | − | 0.447453i | ||||
\(596\) | −9.33384 | −0.382329 | ||||||||
\(597\) | 17.7652 | 0.727083 | ||||||||
\(598\) | 0.985394 | + | 1.70675i | 0.0402957 | + | 0.0697943i | ||||
\(599\) | −14.3209 | − | 24.8045i | −0.585135 | − | 1.01348i | −0.994859 | − | 0.101274i | \(-0.967708\pi\) |
0.409724 | − | 0.912210i | \(-0.365625\pi\) | |||||||
\(600\) | 1.38853 | 0.0566865 | ||||||||
\(601\) | −7.55865 | −0.308324 | −0.154162 | − | 0.988046i | \(-0.549268\pi\) | ||||
−0.154162 | + | 0.988046i | \(0.549268\pi\) | |||||||
\(602\) | 0.635220 | + | 1.10023i | 0.0258896 | + | 0.0448422i | ||||
\(603\) | −10.5232 | + | 18.2267i | −0.428538 | + | 0.742250i | ||||
\(604\) | 9.91158 | + | 17.1674i | 0.403297 | + | 0.698530i | ||||
\(605\) | 25.9474 | − | 44.9423i | 1.05491 | − | 1.82716i | ||||
\(606\) | −5.13558 | + | 8.89508i | −0.208619 | + | 0.361338i | ||||
\(607\) | −1.72737 | −0.0701117 | −0.0350558 | − | 0.999385i | \(-0.511161\pi\) | ||||
−0.0350558 | + | 0.999385i | \(0.511161\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11.2192 | 0.454625 | ||||||||
\(610\) | 12.8500 | − | 22.2568i | 0.520281 | − | 0.901153i | ||||
\(611\) | −0.668577 | + | 1.15801i | −0.0270477 | + | 0.0468481i | ||||
\(612\) | −10.0557 | − | 17.4170i | −0.406478 | − | 0.704040i | ||||
\(613\) | 13.7085 | − | 23.7438i | 0.553680 | − | 0.959002i | −0.444325 | − | 0.895866i | \(-0.646556\pi\) |
0.998005 | − | 0.0631360i | \(-0.0201102\pi\) | |||||||
\(614\) | 0.694010 | + | 1.20206i | 0.0280080 | + | 0.0485112i | ||||
\(615\) | 32.8617 | 1.32511 | ||||||||
\(616\) | 7.39144 | 0.297809 | ||||||||
\(617\) | −5.31375 | − | 9.20369i | −0.213924 | − | 0.370527i | 0.739015 | − | 0.673688i | \(-0.235291\pi\) |
−0.952939 | + | 0.303162i | \(0.901958\pi\) | |||||||
\(618\) | 26.5581 | + | 46.0000i | 1.06832 | + | 1.85039i | ||||
\(619\) | 8.36008 | 0.336020 | 0.168010 | − | 0.985785i | \(-0.446266\pi\) | ||||
0.168010 | + | 0.985785i | \(0.446266\pi\) | |||||||
\(620\) | 15.1048 | 0.606625 | ||||||||
\(621\) | −16.3226 | − | 28.2715i | −0.655002 | − | 1.13450i | ||||
\(622\) | −6.09512 | + | 10.5571i | −0.244392 | + | 0.423300i | ||||
\(623\) | 9.67973 | + | 16.7658i | 0.387810 | + | 0.671707i | ||||
\(624\) | −0.425022 | + | 0.736160i | −0.0170145 | + | 0.0294700i | ||||
\(625\) | 13.6191 | − | 23.5889i | 0.544763 | − | 0.943557i | ||||
\(626\) | −16.5314 | −0.660728 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.8676 | 0.553379 | ||||||||
\(629\) | −8.33010 | + | 14.4282i | −0.332143 | + | 0.575288i | ||||
\(630\) | 7.23185 | − | 12.5259i | 0.288124 | − | 0.499045i | ||||
\(631\) | −12.2651 | − | 21.2437i | −0.488265 | − | 0.845700i | 0.511644 | − | 0.859198i | \(-0.329037\pi\) |
−0.999909 | + | 0.0134980i | \(0.995703\pi\) | |||||||
\(632\) | −4.28829 | + | 7.42754i | −0.170579 | + | 0.295452i | ||||
\(633\) | 19.4963 | + | 33.7686i | 0.774908 | + | 1.34218i | ||||
\(634\) | 2.68811 | 0.106759 | ||||||||
\(635\) | 5.22875 | 0.207497 | ||||||||
\(636\) | −4.59638 | − | 7.96116i | −0.182258 | − | 0.315681i | ||||
\(637\) | −0.814129 | − | 1.41011i | −0.0322570 | − | 0.0558707i | ||||
\(638\) | −18.0029 | −0.712742 | ||||||||
\(639\) | 21.2140 | 0.839213 | ||||||||
\(640\) | −1.17229 | − | 2.03046i | −0.0463388 | − | 0.0802611i | ||||
\(641\) | −3.48635 | + | 6.03854i | −0.137703 | + | 0.238508i | −0.926627 | − | 0.375983i | \(-0.877305\pi\) |
0.788924 | + | 0.614491i | \(0.210638\pi\) | |||||||
\(642\) | 14.0201 | + | 24.2835i | 0.553329 | + | 0.958394i | ||||
\(643\) | 4.54512 | − | 7.87238i | 0.179242 | − | 0.310456i | −0.762379 | − | 0.647131i | \(-0.775969\pi\) |
0.941621 | + | 0.336674i | \(0.109302\pi\) | |||||||
\(644\) | −4.15838 | + | 7.20253i | −0.163863 | + | 0.283820i | ||||
\(645\) | −6.48025 | −0.255160 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 30.0074 | 1.17971 | 0.589856 | − | 0.807509i | \(-0.299185\pi\) | ||||
0.589856 | + | 0.807509i | \(0.299185\pi\) | |||||||
\(648\) | −0.166045 | + | 0.287598i | −0.00652287 | + | 0.0112979i | ||||
\(649\) | 9.53733 | − | 16.5191i | 0.374373 | − | 0.648433i | ||||
\(650\) | −0.0756201 | − | 0.130978i | −0.00296607 | − | 0.00513738i | ||||
\(651\) | 11.5552 | − | 20.0142i | 0.452885 | − | 0.784420i | ||||
\(652\) | −7.12480 | − | 12.3405i | −0.279029 | − | 0.483292i | ||||
\(653\) | 10.4191 | 0.407732 | 0.203866 | − | 0.978999i | \(-0.434649\pi\) | ||||
0.203866 | + | 0.978999i | \(0.434649\pi\) | |||||||
\(654\) | 24.7052 | 0.966049 | ||||||||
\(655\) | 1.78499 | + | 3.09169i | 0.0697453 | + | 0.120802i | ||||
\(656\) | −2.50859 | − | 4.34501i | −0.0979441 | − | 0.169644i | ||||
\(657\) | −10.8907 | −0.424885 | ||||||||
\(658\) | −5.64282 | −0.219980 | ||||||||
\(659\) | −13.1878 | − | 22.8419i | −0.513724 | − | 0.889796i | −0.999873 | − | 0.0159201i | \(-0.994932\pi\) |
0.486149 | − | 0.873876i | \(-0.338401\pi\) | |||||||
\(660\) | −18.8511 | + | 32.6510i | −0.733777 | + | 1.27094i | ||||
\(661\) | −12.3470 | − | 21.3856i | −0.480242 | − | 0.831803i | 0.519502 | − | 0.854470i | \(-0.326118\pi\) |
−0.999743 | + | 0.0226668i | \(0.992784\pi\) | |||||||
\(662\) | −2.60651 | + | 4.51462i | −0.101305 | + | 0.175466i | ||||
\(663\) | −1.77923 | + | 3.08171i | −0.0690994 | + | 0.119684i | ||||
\(664\) | 9.76464 | 0.378942 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −19.1198 | −0.740879 | ||||||||
\(667\) | 10.1283 | − | 17.5428i | 0.392171 | − | 0.679260i | ||||
\(668\) | 5.79506 | − | 10.0373i | 0.224217 | − | 0.388356i | ||||
\(669\) | −12.4651 | − | 21.5901i | −0.481927 | − | 0.834722i | ||||
\(670\) | −5.13558 | + | 8.89508i | −0.198405 | + | 0.343647i | ||||
\(671\) | 31.5483 | + | 54.6432i | 1.21791 | + | 2.10948i | ||||
\(672\) | −3.58721 | −0.138380 | ||||||||
\(673\) | 9.77380 | 0.376752 | 0.188376 | − | 0.982097i | \(-0.439678\pi\) | ||||
0.188376 | + | 0.982097i | \(0.439678\pi\) | |||||||
\(674\) | 13.3637 | + | 23.1467i | 0.514752 | + | 0.891576i | ||||
\(675\) | 1.25261 | + | 2.16959i | 0.0482130 | + | 0.0835074i | ||||
\(676\) | −12.9074 | −0.496439 | ||||||||
\(677\) | 21.5747 | 0.829184 | 0.414592 | − | 0.910007i | \(-0.363924\pi\) | ||||
0.414592 | + | 0.910007i | \(0.363924\pi\) | |||||||
\(678\) | −19.9048 | − | 34.4761i | −0.764438 | − | 1.32405i | ||||
\(679\) | −11.1408 | + | 19.2964i | −0.427544 | + | 0.740528i | ||||
\(680\) | −4.90742 | − | 8.49991i | −0.188191 | − | 0.325957i | ||||
\(681\) | 0.921604 | − | 1.59627i | 0.0353159 | − | 0.0611690i | ||||
\(682\) | −18.5421 | + | 32.1159i | −0.710014 | + | 1.22978i | ||||
\(683\) | −33.2509 | −1.27231 | −0.636155 | − | 0.771561i | \(-0.719476\pi\) | ||||
−0.636155 | + | 0.771561i | \(0.719476\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −25.1145 | −0.959576 | ||||||||
\(686\) | 7.92992 | − | 13.7350i | 0.302766 | − | 0.524406i | ||||
\(687\) | −9.73862 | + | 16.8678i | −0.371551 | + | 0.643546i | ||||
\(688\) | 0.494689 | + | 0.856827i | 0.0188598 | + | 0.0326662i | ||||
\(689\) | −0.500643 | + | 0.867138i | −0.0190730 | + | 0.0330353i | ||||
\(690\) | −21.2111 | − | 36.7386i | −0.807491 | − | 1.39862i | ||||
\(691\) | 4.80932 | 0.182955 | 0.0914776 | − | 0.995807i | \(-0.470841\pi\) | ||||
0.0914776 | + | 0.995807i | \(0.470841\pi\) | |||||||
\(692\) | −3.98353 | −0.151431 | ||||||||
\(693\) | 17.7551 | + | 30.7527i | 0.674459 | + | 1.16820i | ||||
\(694\) | −16.3341 | − | 28.2915i | −0.620034 | − | 1.07393i | ||||
\(695\) | 25.3550 | 0.961772 | ||||||||
\(696\) | 8.73716 | 0.331181 | ||||||||
\(697\) | −10.5015 | − | 18.1890i | −0.397771 | − | 0.688959i | ||||
\(698\) | −14.5529 | + | 25.2063i | −0.550835 | + | 0.954074i | ||||
\(699\) | −41.3589 | − | 71.6357i | −1.56434 | − | 2.70951i | ||||
\(700\) | 0.319119 | − | 0.552730i | 0.0120616 | − | 0.0208912i | ||||
\(701\) | −1.73233 | + | 3.00049i | −0.0654293 | + | 0.113327i | −0.896884 | − | 0.442265i | \(-0.854175\pi\) |
0.831455 | + | 0.555592i | \(0.187508\pi\) | |||||||
\(702\) | −1.53367 | −0.0578848 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 5.75621 | 0.216946 | ||||||||
\(705\) | 14.3914 | − | 24.9267i | 0.542013 | − | 0.938794i | ||||
\(706\) | −7.15244 | + | 12.3884i | −0.269186 | + | 0.466243i | ||||
\(707\) | 2.36057 | + | 4.08862i | 0.0887782 | + | 0.153768i | ||||
\(708\) | −4.62866 | + | 8.01707i | −0.173956 | + | 0.301300i | ||||
\(709\) | −10.2871 | − | 17.8179i | −0.386342 | − | 0.669164i | 0.605612 | − | 0.795760i | \(-0.292928\pi\) |
−0.991954 | + | 0.126596i | \(0.959595\pi\) | |||||||
\(710\) | 10.3529 | 0.388539 | ||||||||
\(711\) | −41.2039 | −1.54527 | ||||||||
\(712\) | 7.53827 | + | 13.0567i | 0.282508 | + | 0.489319i | ||||
\(713\) | −20.8634 | − | 36.1364i | −0.781340 | − | 1.35332i | ||||
\(714\) | −15.0167 | −0.561988 | ||||||||
\(715\) | 4.10656 | 0.153577 | ||||||||
\(716\) | −4.22545 | − | 7.31869i | −0.157912 | − | 0.273512i | ||||
\(717\) | −34.5058 | + | 59.7657i | −1.28864 | + | 2.23199i | ||||
\(718\) | 9.83535 | + | 17.0353i | 0.367052 | + | 0.635753i | ||||
\(719\) | −12.0943 | + | 20.9479i | −0.451040 | + | 0.781225i | −0.998451 | − | 0.0556395i | \(-0.982280\pi\) |
0.547411 | + | 0.836864i | \(0.315614\pi\) | |||||||
\(720\) | 5.63194 | − | 9.75480i | 0.209890 | − | 0.363540i | ||||
\(721\) | 24.4149 | 0.909257 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 76.9880 | 2.86321 | ||||||||
\(724\) | 4.24263 | − | 7.34845i | 0.157676 | − | 0.273103i | ||||
\(725\) | −0.777260 | + | 1.34625i | −0.0288667 | + | 0.0499986i | ||||
\(726\) | −30.9168 | − | 53.5495i | −1.14743 | − | 1.98741i | ||||
\(727\) | −9.06381 | + | 15.6990i | −0.336158 | + | 0.582243i | −0.983707 | − | 0.179781i | \(-0.942461\pi\) |
0.647548 | + | 0.762024i | \(0.275794\pi\) | |||||||
\(728\) | 0.195361 | + | 0.338376i | 0.00724057 | + | 0.0125410i | ||||
\(729\) | −43.8372 | −1.62360 | ||||||||
\(730\) | −5.31490 | −0.196713 | ||||||||
\(731\) | 2.07086 | + | 3.58684i | 0.0765937 | + | 0.132664i | ||||
\(732\) | −15.3110 | − | 26.5194i | −0.565910 | − | 0.980186i | ||||
\(733\) | 22.7363 | 0.839785 | 0.419893 | − | 0.907574i | \(-0.362068\pi\) | ||||
0.419893 | + | 0.907574i | \(0.362068\pi\) | |||||||
\(734\) | −9.55053 | −0.352517 | ||||||||
\(735\) | 17.5245 | + | 30.3533i | 0.646401 | + | 1.11960i | ||||
\(736\) | −3.23842 | + | 5.60910i | −0.119370 | + | 0.206754i | ||||
\(737\) | −12.6085 | − | 21.8385i | −0.464438 | − | 0.804431i | ||||
\(738\) | 12.0518 | − | 20.8744i | 0.443635 | − | 0.768398i | ||||
\(739\) | −7.58933 | + | 13.1451i | −0.279178 | + | 0.483550i | −0.971181 | − | 0.238344i | \(-0.923395\pi\) |
0.692003 | + | 0.721895i | \(0.256729\pi\) | |||||||
\(740\) | −9.33094 | −0.343012 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.22545 | −0.155121 | ||||||||
\(743\) | −1.63812 | + | 2.83732i | −0.0600970 | + | 0.104091i | −0.894509 | − | 0.447051i | \(-0.852474\pi\) |
0.834412 | + | 0.551142i | \(0.185808\pi\) | |||||||
\(744\) | 8.99885 | − | 15.5865i | 0.329914 | − | 0.571427i | ||||
\(745\) | −10.9420 | − | 18.9520i | −0.400882 | − | 0.694348i | ||||
\(746\) | −1.82005 | + | 3.15242i | −0.0666368 | + | 0.115418i | ||||
\(747\) | 23.4558 | + | 40.6266i | 0.858202 | + | 1.48645i | ||||
\(748\) | 24.0966 | 0.881060 | ||||||||
\(749\) | 12.8887 | 0.470941 | ||||||||
\(750\) | −14.7468 | − | 25.5422i | −0.538477 | − | 0.932669i | ||||
\(751\) | 26.1162 | + | 45.2345i | 0.952992 | + | 1.65063i | 0.738897 | + | 0.673818i | \(0.235347\pi\) |
0.214095 | + | 0.976813i | \(0.431320\pi\) | |||||||
\(752\) | −4.39445 | −0.160249 | ||||||||
\(753\) | 8.34884 | 0.304248 | ||||||||
\(754\) | −0.475831 | − | 0.824163i | −0.0173287 | − | 0.0300142i | ||||
\(755\) | −23.2385 | + | 40.2502i | −0.845734 | + | 1.46485i | ||||
\(756\) | −3.23607 | − | 5.60503i | −0.117695 | − | 0.203853i | ||||
\(757\) | 12.1171 | − | 20.9874i | 0.440404 | − | 0.762801i | −0.557316 | − | 0.830301i | \(-0.688169\pi\) |
0.997719 | + | 0.0674993i | \(0.0215020\pi\) | |||||||
\(758\) | −4.17371 | + | 7.22907i | −0.151596 | + | 0.262572i | ||||
\(759\) | 104.151 | 3.78045 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.8054 | −0.899195 | −0.449597 | − | 0.893231i | \(-0.648433\pi\) | ||||
−0.449597 | + | 0.893231i | \(0.648433\pi\) | |||||||
\(762\) | 3.11507 | − | 5.39546i | 0.112847 | − | 0.195457i | ||||
\(763\) | 5.67786 | − | 9.83435i | 0.205552 | − | 0.356027i | ||||
\(764\) | 11.1895 | + | 19.3808i | 0.404822 | + | 0.701173i | ||||
\(765\) | 23.5764 | − | 40.8355i | 0.852406 | − | 1.47641i | ||||
\(766\) | 4.74283 | + | 8.21482i | 0.171365 | + | 0.296814i | ||||
\(767\) | 1.00832 | 0.0364082 | ||||||||
\(768\) | −2.79360 | −0.100806 | ||||||||
\(769\) | −4.82145 | − | 8.35099i | −0.173866 | − | 0.301144i | 0.765902 | − | 0.642957i | \(-0.222293\pi\) |
−0.939768 | + | 0.341812i | \(0.888959\pi\) | |||||||
\(770\) | 8.66489 | + | 15.0080i | 0.312261 | + | 0.540852i | ||||
\(771\) | 39.4799 | 1.42184 | ||||||||
\(772\) | −7.42811 | −0.267344 | ||||||||
\(773\) | 0.643656 | + | 1.11484i | 0.0231507 | + | 0.0400982i | 0.877369 | − | 0.479817i | \(-0.159297\pi\) |
−0.854218 | + | 0.519915i | \(0.825964\pi\) | |||||||
\(774\) | −2.37660 | + | 4.11639i | −0.0854251 | + | 0.147961i | ||||
\(775\) | 1.60108 | + | 2.77315i | 0.0575124 | + | 0.0996144i | ||||
\(776\) | −8.67609 | + | 15.0274i | −0.311453 | + | 0.539453i | ||||
\(777\) | −7.13818 | + | 12.3637i | −0.256081 | + | 0.443545i | ||||
\(778\) | −36.0480 | −1.29238 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −1.99300 | −0.0713607 | ||||||||
\(781\) | −12.7088 | + | 22.0124i | −0.454758 | + | 0.787664i | ||||
\(782\) | −13.5566 | + | 23.4808i | −0.484784 | + | 0.839671i | ||||
\(783\) | 7.88191 | + | 13.6519i | 0.281676 | + | 0.487878i | ||||
\(784\) | 2.67557 | − | 4.63422i | 0.0955561 | − | 0.165508i | ||||
\(785\) | 16.2569 | + | 28.1577i | 0.580232 | + | 1.00499i | ||||
\(786\) | 4.25369 | 0.151724 | ||||||||
\(787\) | 16.3446 | 0.582624 | 0.291312 | − | 0.956628i | \(-0.405908\pi\) | ||||
0.291312 | + | 0.956628i | \(0.405908\pi\) | |||||||
\(788\) | −4.26777 | − | 7.39199i | −0.152033 | − | 0.263329i | ||||
\(789\) | 10.5722 | + | 18.3116i | 0.376381 | + | 0.651911i | ||||
\(790\) | −20.1085 | −0.715427 | ||||||||
\(791\) | −18.2984 | −0.650617 | ||||||||
\(792\) | 13.8271 | + | 23.9492i | 0.491324 | + | 0.850998i | ||||
\(793\) | −1.66769 | + | 2.88852i | −0.0592214 | + | 0.102574i | ||||
\(794\) | −3.20453 | − | 5.55041i | −0.113725 | − | 0.196977i | ||||
\(795\) | 10.7766 | − | 18.6656i | 0.382205 | − | 0.661999i | ||||
\(796\) | 3.17963 | − | 5.50728i | 0.112699 | − | 0.195200i | ||||
\(797\) | 15.6884 | 0.555712 | 0.277856 | − | 0.960623i | \(-0.410376\pi\) | ||||
0.277856 | + | 0.960623i | \(0.410376\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.3960 | −0.650804 | ||||||||
\(800\) | 0.248520 | − | 0.430448i | 0.00878649 | − | 0.0152187i | ||||
\(801\) | −36.2155 | + | 62.7271i | −1.27961 | + | 2.21635i | ||||
\(802\) | −0.0938299 | − | 0.162518i | −0.00331325 | − | 0.00573871i | ||||
\(803\) | 6.52436 | − | 11.3005i | 0.230240 | − | 0.398787i | ||||
\(804\) | 6.11913 | + | 10.5986i | 0.215805 | + | 0.373785i | ||||
\(805\) | −19.4993 | −0.687260 | ||||||||
\(806\) | −1.96033 | −0.0690496 | ||||||||
\(807\) | 10.7145 | + | 18.5581i | 0.377169 | + | 0.653275i | ||||
\(808\) | 1.83833 | + | 3.18409i | 0.0646723 | + | 0.112016i | ||||
\(809\) | −11.5248 | −0.405192 | −0.202596 | − | 0.979262i | \(-0.564938\pi\) | ||||
−0.202596 | + | 0.979262i | \(0.564938\pi\) | |||||||
\(810\) | −0.778611 | −0.0273576 | ||||||||
\(811\) | −4.15051 | − | 7.18889i | −0.145744 | − | 0.252436i | 0.783906 | − | 0.620879i | \(-0.213224\pi\) |
−0.929650 | + | 0.368443i | \(0.879891\pi\) | |||||||
\(812\) | 2.00802 | − | 3.47799i | 0.0704676 | − | 0.122053i | ||||
\(813\) | 16.2935 | + | 28.2213i | 0.571440 | + | 0.989763i | ||||
\(814\) | 11.4543 | − | 19.8394i | 0.401472 | − | 0.695371i | ||||
\(815\) | 16.7046 | − | 28.9333i | 0.585138 | − | 1.01349i | ||||
\(816\) | −11.6946 | −0.409392 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 17.2663 | 0.603701 | ||||||||
\(819\) | −0.938560 | + | 1.62563i | −0.0327959 | + | 0.0568042i | ||||
\(820\) | 5.88159 | − | 10.1872i | 0.205394 | − | 0.355753i | ||||
\(821\) | 16.8556 | + | 29.1948i | 0.588265 | + | 1.01891i | 0.994460 | + | 0.105119i | \(0.0335222\pi\) |
−0.406194 | + | 0.913787i | \(0.633144\pi\) | |||||||
\(822\) | −14.9622 | + | 25.9153i | −0.521867 | + | 0.903899i | ||||
\(823\) | −10.9339 | − | 18.9380i | −0.381131 | − | 0.660138i | 0.610093 | − | 0.792330i | \(-0.291132\pi\) |
−0.991224 | + | 0.132191i | \(0.957799\pi\) | |||||||
\(824\) | 19.0135 | 0.662368 | ||||||||
\(825\) | −7.99268 | −0.278269 | ||||||||
\(826\) | 2.12756 | + | 3.68504i | 0.0740273 | + | 0.128219i | ||||
\(827\) | 19.5847 | + | 33.9218i | 0.681028 | + | 1.17958i | 0.974667 | + | 0.223659i | \(0.0718003\pi\) |
−0.293639 | + | 0.955916i | \(0.594866\pi\) | |||||||
\(828\) | −31.1162 | −1.08136 | ||||||||
\(829\) | 14.4176 | 0.500743 | 0.250371 | − | 0.968150i | \(-0.419447\pi\) | ||||
0.250371 | + | 0.968150i | \(0.419447\pi\) | |||||||
\(830\) | 11.4470 | + | 19.8267i | 0.397330 | + | 0.688196i | ||||
\(831\) | 38.3289 | − | 66.3877i | 1.32962 | − | 2.30296i | ||||
\(832\) | 0.152141 | + | 0.263516i | 0.00527455 | + | 0.00913579i | ||||
\(833\) | 11.2005 | − | 19.3998i | 0.388073 | − | 0.672162i | ||||
\(834\) | 15.1055 | − | 26.1635i | 0.523060 | − | 0.905967i | ||||
\(835\) | 27.1739 | 0.940392 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 32.4719 | 1.12239 | ||||||||
\(838\) | −0.862859 | + | 1.49452i | −0.0298070 | + | 0.0516272i | ||||
\(839\) | 10.4766 | − | 18.1460i | 0.361693 | − | 0.626470i | −0.626547 | − | 0.779384i | \(-0.715532\pi\) |
0.988240 | + | 0.152914i | \(0.0488657\pi\) | |||||||
\(840\) | −4.20524 | − | 7.28369i | −0.145095 | − | 0.251311i | ||||
\(841\) | 9.60919 | − | 16.6436i | 0.331351 | − | 0.573917i | ||||
\(842\) | −16.3773 | − | 28.3663i | −0.564398 | − | 0.977566i | ||||
\(843\) | 45.4561 | 1.56559 | ||||||||
\(844\) | 13.9578 | 0.480447 | ||||||||
\(845\) | −15.1312 | − | 26.2080i | −0.520529 | − | 0.901583i | ||||
\(846\) | −10.5560 | − | 18.2835i | −0.362922 | − | 0.628599i | ||||
\(847\) | −28.4218 | −0.976585 | ||||||||
\(848\) | −3.29064 | −0.113001 | ||||||||
\(849\) | 4.74038 | + | 8.21059i | 0.162690 | + | 0.281787i | ||||
\(850\) | 1.04035 | − | 1.80194i | 0.0356837 | − | 0.0618060i | ||||
\(851\) | 12.8882 | + | 22.3231i | 0.441803 | + | 0.765226i | ||||
\(852\) | 6.16785 | − | 10.6830i | 0.211307 | − | 0.365995i | ||||
\(853\) | −25.9777 | + | 44.9946i | −0.889458 | + | 1.54059i | −0.0489407 | + | 0.998802i | \(0.515585\pi\) |
−0.840517 | + | 0.541785i | \(0.817749\pi\) | |||||||
\(854\) | −14.0754 | −0.481650 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10.0373 | 0.343067 | ||||||||
\(857\) | 14.5917 | − | 25.2736i | 0.498444 | − | 0.863330i | −0.501554 | − | 0.865126i | \(-0.667238\pi\) |
0.999998 | + | 0.00179580i | \(0.000571621\pi\) | |||||||
\(858\) | 2.44652 | − | 4.23750i | 0.0835228 | − | 0.144666i | ||||
\(859\) | −10.9957 | − | 19.0451i | −0.375168 | − | 0.649809i | 0.615185 | − | 0.788383i | \(-0.289081\pi\) |
−0.990352 | + | 0.138574i | \(0.955748\pi\) | |||||||
\(860\) | −1.15984 | + | 2.00890i | −0.0395501 | + | 0.0685028i | ||||
\(861\) | −8.99885 | − | 15.5865i | −0.306680 | − | 0.531185i | ||||
\(862\) | −25.5119 | −0.868939 | ||||||||
\(863\) | 35.8157 | 1.21918 | 0.609590 | − | 0.792717i | \(-0.291334\pi\) | ||||
0.609590 | + | 0.792717i | \(0.291334\pi\) | |||||||
\(864\) | −2.52015 | − | 4.36502i | −0.0857371 | − | 0.148501i | ||||
\(865\) | −4.66984 | − | 8.08840i | −0.158779 | − | 0.275014i | ||||
\(866\) | 24.4834 | 0.831980 | ||||||||
\(867\) | −1.46442 | −0.0497343 | ||||||||
\(868\) | −4.13632 | − | 7.16431i | −0.140396 | − | 0.243173i | ||||
\(869\) | 24.6843 | − | 42.7545i | 0.837359 | − | 1.45035i | ||||
\(870\) | 10.2425 | + | 17.7405i | 0.347252 | + | 0.601459i | ||||
\(871\) | 0.666502 | − | 1.15442i | 0.0225836 | − | 0.0391159i | ||||
\(872\) | 4.42174 | − | 7.65868i | 0.149739 | − | 0.259356i | ||||
\(873\) | −83.3638 | −2.82144 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13.5567 | −0.458300 | ||||||||
\(876\) | −3.16640 | + | 5.48437i | −0.106983 | + | 0.185300i | ||||
\(877\) | 3.91241 | − | 6.77650i | 0.132113 | − | 0.228826i | −0.792378 | − | 0.610030i | \(-0.791157\pi\) |
0.924491 | + | 0.381204i | \(0.124491\pi\) | |||||||
\(878\) | 15.4194 | + | 26.7072i | 0.520380 | + | 0.901324i | ||||
\(879\) | −32.6549 | + | 56.5599i | −1.10142 | + | 1.90772i | ||||
\(880\) | 6.74794 | + | 11.6878i | 0.227473 | + | 0.393995i | ||||
\(881\) | −14.4829 | −0.487941 | −0.243970 | − | 0.969783i | \(-0.578450\pi\) | ||||
−0.243970 | + | 0.969783i | \(0.578450\pi\) | |||||||
\(882\) | 25.7081 | 0.865636 | ||||||||
\(883\) | 11.7765 | + | 20.3974i | 0.396310 | + | 0.686428i | 0.993267 | − | 0.115844i | \(-0.0369574\pi\) |
−0.596958 | + | 0.802273i | \(0.703624\pi\) | |||||||
\(884\) | 0.636892 | + | 1.10313i | 0.0214210 | + | 0.0371023i | ||||
\(885\) | −21.7045 | −0.729588 | ||||||||
\(886\) | −10.7047 | −0.359631 | ||||||||
\(887\) | −7.93678 | − | 13.7469i | −0.266491 | − | 0.461576i | 0.701462 | − | 0.712707i | \(-0.252531\pi\) |
−0.967953 | + | 0.251131i | \(0.919198\pi\) | |||||||
\(888\) | −5.55899 | + | 9.62845i | −0.186547 | + | 0.323110i | ||||
\(889\) | −1.43184 | − | 2.48002i | −0.0480224 | − | 0.0831773i | ||||
\(890\) | −17.6740 | + | 30.6123i | −0.592435 | + | 1.02613i | ||||
\(891\) | 0.955791 | − | 1.65548i | 0.0320202 | − | 0.0554606i | ||||
\(892\) | −8.92400 | −0.298798 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −26.0751 | −0.872081 | ||||||||
\(895\) | 9.90688 | − | 17.1592i | 0.331151 | − | 0.573570i | ||||
\(896\) | −0.642040 | + | 1.11205i | −0.0214490 | + | 0.0371508i | ||||
\(897\) | 2.75280 | + | 4.76799i | 0.0919133 | + | 0.159199i | ||||
\(898\) | −1.15781 | + | 2.00538i | −0.0386366 | + | 0.0669205i | ||||
\(899\) | 10.0746 | + | 17.4497i | 0.336007 | + | 0.581980i | ||||
\(900\) | 2.38789 | 0.0795963 | ||||||||
\(901\) | −13.7753 | −0.458921 | ||||||||
\(902\) | 14.4400 | + | 25.0108i | 0.480799 | + | 0.832769i | ||||
\(903\) | 1.77455 | + | 3.07362i | 0.0590534 | + | 0.102284i | ||||
\(904\) | −14.2502 | −0.473956 | ||||||||
\(905\) | 19.8944 | 0.661311 | ||||||||
\(906\) | 27.6890 | + | 47.9588i | 0.919907 | + | 1.59333i | ||||
\(907\) | 22.5064 | − | 38.9821i | 0.747311 | − | 1.29438i | −0.201796 | − | 0.979428i | \(-0.564678\pi\) |
0.949107 | − | 0.314953i | \(-0.101989\pi\) | |||||||
\(908\) | −0.329898 | − | 0.571400i | −0.0109480 | − | 0.0189626i | ||||
\(909\) | −8.83177 | + | 15.2971i | −0.292931 | + | 0.507372i | ||||
\(910\) | −0.458040 | + | 0.793348i | −0.0151839 | + | 0.0262992i | ||||
\(911\) | 2.75901 | 0.0914100 | 0.0457050 | − | 0.998955i | \(-0.485447\pi\) | ||||
0.0457050 | + | 0.998955i | \(0.485447\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −56.2074 | −1.86019 | ||||||||
\(914\) | −0.0260905 | + | 0.0451900i | −0.000862996 | + | 0.00149475i | ||||
\(915\) | 35.8978 | − | 62.1768i | 1.18674 | − | 2.05550i | ||||
\(916\) | 3.48604 | + | 6.03800i | 0.115182 | + | 0.199501i | ||||
\(917\) | 0.977604 | − | 1.69326i | 0.0322833 | − | 0.0559164i | ||||
\(918\) | −10.5498 | − | 18.2728i | −0.348196 | − | 0.603093i | ||||
\(919\) | −39.3083 | −1.29666 | −0.648331 | − | 0.761359i | \(-0.724533\pi\) | ||||
−0.648331 | + | 0.761359i | \(0.724533\pi\) | |||||||
\(920\) | −15.1854 | −0.500649 | ||||||||
\(921\) | 1.93879 | + | 3.35808i | 0.0638853 | + | 0.110653i | ||||
\(922\) | 19.7360 | + | 34.1838i | 0.649971 | + | 1.12578i | ||||
\(923\) | −1.34362 | −0.0442258 | ||||||||
\(924\) | 20.6487 | 0.679294 | ||||||||
\(925\) | −0.989057 | − | 1.71310i | −0.0325200 | − | 0.0563263i | ||||
\(926\) | −3.09528 | + | 5.36119i | −0.101717 | + | 0.176180i | ||||
\(927\) | 45.6726 | + | 79.1073i | 1.50009 | + | 2.59823i | ||||
\(928\) | 1.56378 | − | 2.70855i | 0.0513336 | − | 0.0889124i | ||||
\(929\) | 14.8709 | − | 25.7571i | 0.487897 | − | 0.845063i | −0.512006 | − | 0.858982i | \(-0.671097\pi\) |
0.999903 | + | 0.0139190i | \(0.00443068\pi\) | |||||||
\(930\) | 42.1970 | 1.38369 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −29.6097 | −0.969898 | ||||||||
\(933\) | −17.0274 | + | 29.4923i | −0.557451 | + | 0.965533i | ||||
\(934\) | −10.4981 | + | 18.1832i | −0.343508 | + | 0.594973i | ||||
\(935\) | 28.2482 | + | 48.9273i | 0.923814 | + | 1.60009i | ||||
\(936\) | −0.730921 | + | 1.26599i | −0.0238909 | + | 0.0413802i | ||||
\(937\) | −18.8606 | − | 32.6674i | −0.616147 | − | 1.06720i | −0.990182 | − | 0.139784i | \(-0.955359\pi\) |
0.374035 | − | 0.927415i | \(-0.377974\pi\) | |||||||
\(938\) | 5.62531 | 0.183673 | ||||||||
\(939\) | −46.1822 | −1.50710 | ||||||||
\(940\) | −5.15156 | − | 8.92277i | −0.168026 | − | 0.291029i | ||||
\(941\) | −3.23826 | − | 5.60883i | −0.105564 | − | 0.182843i | 0.808404 | − | 0.588628i | \(-0.200332\pi\) |
−0.913969 | + | 0.405785i | \(0.866998\pi\) | |||||||
\(942\) | 38.7407 | 1.26224 | ||||||||
\(943\) | −32.4955 | −1.05820 | ||||||||
\(944\) | 1.65688 | + | 2.86979i | 0.0539267 | + | 0.0934038i | ||||
\(945\) | 7.58721 | − | 13.1414i | 0.246812 | − | 0.427491i | ||||
\(946\) | −2.84754 | − | 4.93208i | −0.0925814 | − | 0.160356i | ||||
\(947\) | −8.14564 | + | 14.1087i | −0.264698 | + | 0.458470i | −0.967484 | − | 0.252931i | \(-0.918606\pi\) |
0.702787 | + | 0.711401i | \(0.251939\pi\) | |||||||
\(948\) | −11.9798 | + | 20.7496i | −0.389086 | + | 0.673916i | ||||
\(949\) | 0.689776 | 0.0223911 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.50953 | 0.243513 | ||||||||
\(952\) | −2.68770 | + | 4.65523i | −0.0871089 | + | 0.150877i | ||||
\(953\) | −17.3107 | + | 29.9830i | −0.560748 | + | 0.971243i | 0.436684 | + | 0.899615i | \(0.356153\pi\) |
−0.997431 | + | 0.0716282i | \(0.977180\pi\) | |||||||
\(954\) | −7.90450 | − | 13.6910i | −0.255918 | − | 0.443262i | ||||
\(955\) | −26.2347 | + | 45.4398i | −0.848934 | + | 1.47040i | ||||
\(956\) | 12.3517 | + | 21.3938i | 0.399482 | + | 0.691924i | ||||
\(957\) | −50.2930 | −1.62574 | ||||||||
\(958\) | −15.5229 | −0.501523 | ||||||||
\(959\) | 6.87737 | + | 11.9119i | 0.222082 | + | 0.384657i | ||||
\(960\) | −3.27491 | − | 5.67231i | −0.105697 | − | 0.183073i | ||||
\(961\) | 10.5053 | 0.338882 | ||||||||
\(962\) | 1.21098 | 0.0390436 | ||||||||
\(963\) | 24.1107 | + | 41.7609i | 0.776956 | + | 1.34573i | ||||
\(964\) | 13.7793 | − | 23.8665i | 0.443802 | − | 0.768688i | ||||
\(965\) | −8.70789 | − | 15.0825i | −0.280317 | − | 0.485523i | ||||
\(966\) | −11.6169 | + | 20.1210i | −0.373767 | + | 0.647383i | ||||
\(967\) | 24.4552 | − | 42.3577i | 0.786428 | − | 1.36213i | −0.141715 | − | 0.989908i | \(-0.545262\pi\) |
0.928142 | − | 0.372225i | \(-0.121405\pi\) | |||||||
\(968\) | −22.1340 | −0.711414 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −40.6835 | −1.30627 | ||||||||
\(971\) | 3.03796 | − | 5.26190i | 0.0974928 | − | 0.168862i | −0.813153 | − | 0.582049i | \(-0.802251\pi\) |
0.910646 | + | 0.413187i | \(0.135584\pi\) | |||||||
\(972\) | −8.02431 | + | 13.8985i | −0.257380 | + | 0.445795i | ||||
\(973\) | −6.94323 | − | 12.0260i | −0.222590 | − | 0.385537i | ||||
\(974\) | 14.3033 | − | 24.7740i | 0.458306 | − | 0.793810i | ||||
\(975\) | −0.211253 | − | 0.365900i | −0.00676550 | − | 0.0117182i | ||||
\(976\) | −10.9615 | −0.350868 | ||||||||
\(977\) | −57.0477 | −1.82512 | −0.912559 | − | 0.408944i | \(-0.865897\pi\) | ||||
−0.912559 | + | 0.408944i | \(0.865897\pi\) | |||||||
\(978\) | −19.9039 | − | 34.4745i | −0.636455 | − | 1.10237i | ||||
\(979\) | −43.3919 | − | 75.1569i | −1.38681 | − | 2.40203i | ||||
\(980\) | 12.5462 | 0.400772 | ||||||||
\(981\) | 42.4861 | 1.35648 | ||||||||
\(982\) | −15.1744 | − | 26.2829i | −0.484235 | − | 0.838720i | ||||
\(983\) | 0.0932597 | − | 0.161531i | 0.00297452 | − | 0.00515203i | −0.864534 | − | 0.502574i | \(-0.832387\pi\) |
0.867509 | + | 0.497422i | \(0.165720\pi\) | |||||||
\(984\) | −7.00802 | − | 12.1382i | −0.223407 | − | 0.386953i | ||||
\(985\) | 10.0061 | − | 17.3311i | 0.318821 | − | 0.552215i | ||||
\(986\) | 6.54628 | − | 11.3385i | 0.208476 | − | 0.361091i | ||||
\(987\) | −15.7638 | −0.501768 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.40804 | 0.203764 | ||||||||
\(990\) | −32.4186 | + | 56.1507i | −1.03033 | + | 1.78459i | ||||
\(991\) | −23.1199 | + | 40.0449i | −0.734428 | + | 1.27207i | 0.220545 | + | 0.975377i | \(0.429216\pi\) |
−0.954974 | + | 0.296690i | \(0.904117\pi\) | |||||||
\(992\) | −3.22123 | − | 5.57934i | −0.102274 | − | 0.177144i | ||||
\(993\) | −7.28157 | + | 12.6121i | −0.231074 | + | 0.400231i | ||||
\(994\) | −2.83505 | − | 4.91045i | −0.0899224 | − | 0.155750i | ||||
\(995\) | 14.9098 | 0.472671 | ||||||||
\(996\) | 27.2786 | 0.864354 | ||||||||
\(997\) | 10.4245 | + | 18.0558i | 0.330147 | + | 0.571832i | 0.982541 | − | 0.186049i | \(-0.0595682\pi\) |
−0.652393 | + | 0.757881i | \(0.726235\pi\) | |||||||
\(998\) | 4.38812 | + | 7.60044i | 0.138903 | + | 0.240588i | ||||
\(999\) | −20.0593 | −0.634650 |
(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 | 722.2.c.n.429.4 | 8 | ||
19.2 | odd | 18 | 722.2.e.r.595.1 | 24 | |||
19.3 | odd | 18 | 722.2.e.r.99.4 | 24 | |||
19.4 | even | 9 | 722.2.e.s.423.1 | 24 | |||
19.5 | even | 9 | 722.2.e.s.389.1 | 24 | |||
19.6 | even | 9 | 722.2.e.s.415.4 | 24 | |||
19.7 | even | 3 | inner | 722.2.c.n.653.4 | 8 | ||
19.8 | odd | 6 | 722.2.a.n.1.4 | yes | 4 | ||
19.9 | even | 9 | 722.2.e.s.245.1 | 24 | |||
19.10 | odd | 18 | 722.2.e.r.245.4 | 24 | |||
19.11 | even | 3 | 722.2.a.m.1.1 | ✓ | 4 | ||
19.12 | odd | 6 | 722.2.c.m.653.1 | 8 | |||
19.13 | odd | 18 | 722.2.e.r.415.1 | 24 | |||
19.14 | odd | 18 | 722.2.e.r.389.4 | 24 | |||
19.15 | odd | 18 | 722.2.e.r.423.4 | 24 | |||
19.16 | even | 9 | 722.2.e.s.99.1 | 24 | |||
19.17 | even | 9 | 722.2.e.s.595.4 | 24 | |||
19.18 | odd | 2 | 722.2.c.m.429.1 | 8 | |||
57.8 | even | 6 | 6498.2.a.bx.1.3 | 4 | |||
57.11 | odd | 6 | 6498.2.a.ca.1.3 | 4 | |||
76.11 | odd | 6 | 5776.2.a.bv.1.4 | 4 | |||
76.27 | even | 6 | 5776.2.a.bt.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
722.2.a.m.1.1 | ✓ | 4 | 19.11 | even | 3 | ||
722.2.a.n.1.4 | yes | 4 | 19.8 | odd | 6 | ||
722.2.c.m.429.1 | 8 | 19.18 | odd | 2 | |||
722.2.c.m.653.1 | 8 | 19.12 | odd | 6 | |||
722.2.c.n.429.4 | 8 | 1.1 | even | 1 | trivial | ||
722.2.c.n.653.4 | 8 | 19.7 | even | 3 | inner | ||
722.2.e.r.99.4 | 24 | 19.3 | odd | 18 | |||
722.2.e.r.245.4 | 24 | 19.10 | odd | 18 | |||
722.2.e.r.389.4 | 24 | 19.14 | odd | 18 | |||
722.2.e.r.415.1 | 24 | 19.13 | odd | 18 | |||
722.2.e.r.423.4 | 24 | 19.15 | odd | 18 | |||
722.2.e.r.595.1 | 24 | 19.2 | odd | 18 | |||
722.2.e.s.99.1 | 24 | 19.16 | even | 9 | |||
722.2.e.s.245.1 | 24 | 19.9 | even | 9 | |||
722.2.e.s.389.1 | 24 | 19.5 | even | 9 | |||
722.2.e.s.415.4 | 24 | 19.6 | even | 9 | |||
722.2.e.s.423.1 | 24 | 19.4 | even | 9 | |||
722.2.e.s.595.4 | 24 | 19.17 | even | 9 | |||
5776.2.a.bt.1.1 | 4 | 76.27 | even | 6 | |||
5776.2.a.bv.1.4 | 4 | 76.11 | odd | 6 | |||
6498.2.a.bx.1.3 | 4 | 57.8 | even | 6 | |||
6498.2.a.ca.1.3 | 4 | 57.11 | odd | 6 |