Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [966,2,Mod(229,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("966.229");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.k (of order \(6\), 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: | \(7.71354883526\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 229.1 | ||
Character | \(\chi\) | \(=\) | 966.229 |
Dual form | 966.2.k.b.367.1 |
$q$-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 \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(829\) | \(925\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | −0.866025 | + | 0.500000i | −0.500000 | + | 0.288675i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −2.02969 | + | 3.51552i | −0.907703 | + | 1.57219i | −0.0904552 | + | 0.995901i | \(0.528832\pi\) |
−0.817248 | + | 0.576287i | \(0.804501\pi\) | |||||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | 2.03303 | + | 1.69316i | 0.768412 | + | 0.639956i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 2.02969 | + | 3.51552i | 0.641843 | + | 1.11170i | ||||
\(11\) | −4.89939 | + | 2.82867i | −1.47722 | + | 0.852875i | −0.999669 | − | 0.0257278i | \(-0.991810\pi\) |
−0.477554 | + | 0.878603i | \(0.658476\pi\) | |||||||
\(12\) | 0.866025 | + | 0.500000i | 0.250000 | + | 0.144338i | ||||
\(13\) | − | 1.68666i | − | 0.467795i | −0.972261 | − | 0.233897i | \(-0.924852\pi\) | ||
0.972261 | − | 0.233897i | \(-0.0751480\pi\) | |||||||
\(14\) | 2.48284 | − | 0.914071i | 0.663566 | − | 0.244296i | ||||
\(15\) | − | 4.05937i | − | 1.04812i | ||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −0.577549 | − | 1.00034i | −0.140076 | − | 0.242619i | 0.787449 | − | 0.616380i | \(-0.211401\pi\) |
−0.927525 | + | 0.373761i | \(0.878068\pi\) | |||||||
\(18\) | −0.500000 | − | 0.866025i | −0.117851 | − | 0.204124i | ||||
\(19\) | 3.27848 | − | 5.67849i | 0.752134 | − | 1.30273i | −0.194653 | − | 0.980872i | \(-0.562358\pi\) |
0.946787 | − | 0.321862i | \(-0.104309\pi\) | |||||||
\(20\) | 4.05937 | 0.907703 | ||||||||
\(21\) | −2.60723 | − | 0.449810i | −0.568945 | − | 0.0981565i | ||||
\(22\) | 5.65733i | 1.20615i | ||||||||
\(23\) | −3.50171 | − | 3.27690i | −0.730156 | − | 0.683280i | ||||
\(24\) | 0.866025 | − | 0.500000i | 0.176777 | − | 0.102062i | ||||
\(25\) | −5.73924 | − | 9.94066i | −1.14785 | − | 1.98813i | ||||
\(26\) | −1.46069 | − | 0.843329i | −0.286465 | − | 0.165390i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0.449810 | − | 2.60723i | 0.0850061 | − | 0.492721i | ||||
\(29\) | −6.42612 | −1.19330 | −0.596651 | − | 0.802501i | \(-0.703502\pi\) | ||||
−0.596651 | + | 0.802501i | \(0.703502\pi\) | |||||||
\(30\) | −3.51552 | − | 2.02969i | −0.641843 | − | 0.370568i | ||||
\(31\) | −2.49704 | + | 1.44167i | −0.448482 | + | 0.258931i | −0.707189 | − | 0.707025i | \(-0.750037\pi\) |
0.258707 | + | 0.965956i | \(0.416704\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 2.82867 | − | 4.89939i | 0.492408 | − | 0.852875i | ||||
\(34\) | −1.15510 | −0.198098 | ||||||||
\(35\) | −10.0788 | + | 3.71055i | −1.70362 | + | 0.627198i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 1.89767 | + | 1.09562i | 0.311975 | + | 0.180119i | 0.647810 | − | 0.761802i | \(-0.275685\pi\) |
−0.335835 | + | 0.941921i | \(0.609018\pi\) | |||||||
\(38\) | −3.27848 | − | 5.67849i | −0.531839 | − | 0.921172i | ||||
\(39\) | 0.843329 | + | 1.46069i | 0.135041 | + | 0.233897i | ||||
\(40\) | 2.02969 | − | 3.51552i | 0.320921 | − | 0.555852i | ||||
\(41\) | − | 5.70186i | − | 0.890480i | −0.895411 | − | 0.445240i | \(-0.853118\pi\) | ||
0.895411 | − | 0.445240i | \(-0.146882\pi\) | |||||||
\(42\) | −1.69316 | + | 2.03303i | −0.261261 | + | 0.313703i | ||||
\(43\) | 1.32493i | 0.202049i | 0.994884 | + | 0.101025i | \(0.0322121\pi\) | ||||
−0.994884 | + | 0.101025i | \(0.967788\pi\) | |||||||
\(44\) | 4.89939 | + | 2.82867i | 0.738611 | + | 0.426437i | ||||
\(45\) | 2.02969 | + | 3.51552i | 0.302568 | + | 0.524062i | ||||
\(46\) | −4.58873 | + | 1.39412i | −0.676571 | + | 0.205551i | ||||
\(47\) | 3.82275 | + | 2.20707i | 0.557606 | + | 0.321934i | 0.752184 | − | 0.658953i | \(-0.229000\pi\) |
−0.194578 | + | 0.980887i | \(0.562334\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | 1.26639 | + | 6.88449i | 0.180913 | + | 0.983499i | ||||
\(50\) | −11.4785 | −1.62330 | ||||||||
\(51\) | 1.00034 | + | 0.577549i | 0.140076 | + | 0.0808731i | ||||
\(52\) | −1.46069 | + | 0.843329i | −0.202561 | + | 0.116949i | ||||
\(53\) | −1.85774 | + | 1.07256i | −0.255180 | + | 0.147328i | −0.622134 | − | 0.782911i | \(-0.713734\pi\) |
0.366954 | + | 0.930239i | \(0.380401\pi\) | |||||||
\(54\) | 0.866025 | + | 0.500000i | 0.117851 | + | 0.0680414i | ||||
\(55\) | − | 22.9652i | − | 3.09663i | ||||||
\(56\) | −2.03303 | − | 1.69316i | −0.271675 | − | 0.226259i | ||||
\(57\) | 6.55695i | 0.868489i | ||||||||
\(58\) | −3.21306 | + | 5.56519i | −0.421896 | + | 0.730745i | ||||
\(59\) | 6.54465 | − | 3.77855i | 0.852041 | − | 0.491926i | −0.00929818 | − | 0.999957i | \(-0.502960\pi\) |
0.861339 | + | 0.508031i | \(0.169626\pi\) | |||||||
\(60\) | −3.51552 | + | 2.02969i | −0.453851 | + | 0.262031i | ||||
\(61\) | −5.20534 | + | 9.01591i | −0.666476 | + | 1.15437i | 0.312407 | + | 0.949948i | \(0.398865\pi\) |
−0.978883 | + | 0.204421i | \(0.934469\pi\) | |||||||
\(62\) | 2.88334i | 0.366184i | ||||||||
\(63\) | 2.48284 | − | 0.914071i | 0.312808 | − | 0.115162i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.92947 | + | 3.42338i | 0.735461 | + | 0.424618i | ||||
\(66\) | −2.82867 | − | 4.89939i | −0.348185 | − | 0.603074i | ||||
\(67\) | −4.92805 | + | 2.84521i | −0.602057 | + | 0.347598i | −0.769851 | − | 0.638224i | \(-0.779669\pi\) |
0.167793 | + | 0.985822i | \(0.446336\pi\) | |||||||
\(68\) | −0.577549 | + | 1.00034i | −0.0700381 | + | 0.121310i | ||||
\(69\) | 4.67101 | + | 1.08702i | 0.562324 | + | 0.130862i | ||||
\(70\) | −1.82594 | + | 10.5837i | −0.218242 | + | 1.26500i | ||||
\(71\) | −7.18784 | −0.853040 | −0.426520 | − | 0.904478i | \(-0.640261\pi\) | ||||
−0.426520 | + | 0.904478i | \(0.640261\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | −9.62590 | + | 5.55752i | −1.12663 | + | 0.650458i | −0.943084 | − | 0.332554i | \(-0.892090\pi\) |
−0.183542 | + | 0.983012i | \(0.558756\pi\) | |||||||
\(74\) | 1.89767 | − | 1.09562i | 0.220600 | − | 0.127363i | ||||
\(75\) | 9.94066 | + | 5.73924i | 1.14785 | + | 0.662711i | ||||
\(76\) | −6.55695 | −0.752134 | ||||||||
\(77\) | −14.7500 | − | 2.54472i | −1.68092 | − | 0.289998i | ||||
\(78\) | 1.68666 | 0.190976 | ||||||||
\(79\) | −9.79501 | − | 5.65515i | −1.10202 | − | 0.636254i | −0.165272 | − | 0.986248i | \(-0.552850\pi\) |
−0.936752 | + | 0.349994i | \(0.886184\pi\) | |||||||
\(80\) | −2.02969 | − | 3.51552i | −0.226926 | − | 0.393047i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −4.93795 | − | 2.85093i | −0.545306 | − | 0.314832i | ||||
\(83\) | −0.847910 | −0.0930702 | −0.0465351 | − | 0.998917i | \(-0.514818\pi\) | ||||
−0.0465351 | + | 0.998917i | \(0.514818\pi\) | |||||||
\(84\) | 0.914071 | + | 2.48284i | 0.0997333 | + | 0.270900i | ||||
\(85\) | 4.68897 | 0.508591 | ||||||||
\(86\) | 1.14742 | + | 0.662464i | 0.123730 | + | 0.0714353i | ||||
\(87\) | 5.56519 | − | 3.21306i | 0.596651 | − | 0.344476i | ||||
\(88\) | 4.89939 | − | 2.82867i | 0.522277 | − | 0.301537i | ||||
\(89\) | 6.80960 | − | 11.7946i | 0.721817 | − | 1.25022i | −0.238454 | − | 0.971154i | \(-0.576641\pi\) |
0.960271 | − | 0.279069i | \(-0.0900259\pi\) | |||||||
\(90\) | 4.05937 | 0.427895 | ||||||||
\(91\) | 2.85579 | − | 3.42902i | 0.299368 | − | 0.359459i | ||||
\(92\) | −1.08702 | + | 4.67101i | −0.113330 | + | 0.486987i | ||||
\(93\) | 1.44167 | − | 2.49704i | 0.149494 | − | 0.258931i | ||||
\(94\) | 3.82275 | − | 2.20707i | 0.394287 | − | 0.227642i | ||||
\(95\) | 13.3085 | + | 23.0511i | 1.36543 | + | 2.36499i | ||||
\(96\) | −0.866025 | − | 0.500000i | −0.0883883 | − | 0.0510310i | ||||
\(97\) | 4.92590 | 0.500149 | 0.250075 | − | 0.968227i | \(-0.419545\pi\) | ||||
0.250075 | + | 0.968227i | \(0.419545\pi\) | |||||||
\(98\) | 6.59534 | + | 2.34552i | 0.666230 | + | 0.236933i | ||||
\(99\) | 5.65733i | 0.568583i | ||||||||
\(100\) | −5.73924 | + | 9.94066i | −0.573924 | + | 0.994066i | ||||
\(101\) | −6.94536 | + | 4.00991i | −0.691089 | + | 0.399001i | −0.804020 | − | 0.594602i | \(-0.797310\pi\) |
0.112931 | + | 0.993603i | \(0.463976\pi\) | |||||||
\(102\) | 1.00034 | − | 0.577549i | 0.0990489 | − | 0.0571859i | ||||
\(103\) | 3.81453 | − | 6.60696i | 0.375857 | − | 0.651003i | −0.614598 | − | 0.788841i | \(-0.710682\pi\) |
0.990455 | + | 0.137837i | \(0.0440150\pi\) | |||||||
\(104\) | 1.68666i | 0.165390i | ||||||||
\(105\) | 6.87318 | − | 8.25281i | 0.670754 | − | 0.805391i | ||||
\(106\) | 2.14513i | 0.208353i | ||||||||
\(107\) | 6.14656 | + | 3.54872i | 0.594210 | + | 0.343067i | 0.766761 | − | 0.641933i | \(-0.221867\pi\) |
−0.172550 | + | 0.985001i | \(0.555201\pi\) | |||||||
\(108\) | 0.866025 | − | 0.500000i | 0.0833333 | − | 0.0481125i | ||||
\(109\) | −15.1271 | + | 8.73364i | −1.44891 | + | 0.836531i | −0.998417 | − | 0.0562469i | \(-0.982087\pi\) |
−0.450497 | + | 0.892778i | \(0.648753\pi\) | |||||||
\(110\) | −19.8884 | − | 11.4826i | −1.89629 | − | 1.09482i | ||||
\(111\) | −2.19124 | −0.207983 | ||||||||
\(112\) | −2.48284 | + | 0.914071i | −0.234606 | + | 0.0863715i | ||||
\(113\) | 8.83766i | 0.831377i | 0.909507 | + | 0.415688i | \(0.136459\pi\) | ||||
−0.909507 | + | 0.415688i | \(0.863541\pi\) | |||||||
\(114\) | 5.67849 | + | 3.27848i | 0.531839 | + | 0.307057i | ||||
\(115\) | 18.6274 | − | 5.65923i | 1.73701 | − | 0.527726i | ||||
\(116\) | 3.21306 | + | 5.56519i | 0.298325 | + | 0.516715i | ||||
\(117\) | −1.46069 | − | 0.843329i | −0.135041 | − | 0.0779658i | ||||
\(118\) | − | 7.55711i | − | 0.695688i | ||||||
\(119\) | 0.519575 | − | 3.01161i | 0.0476293 | − | 0.276074i | ||||
\(120\) | 4.05937i | 0.370568i | ||||||||
\(121\) | 10.5027 | − | 18.1912i | 0.954791 | − | 1.65375i | ||||
\(122\) | 5.20534 | + | 9.01591i | 0.471269 | + | 0.816262i | ||||
\(123\) | 2.85093 | + | 4.93795i | 0.257060 | + | 0.445240i | ||||
\(124\) | 2.49704 | + | 1.44167i | 0.224241 | + | 0.129466i | ||||
\(125\) | 26.2986 | 2.35222 | ||||||||
\(126\) | 0.449810 | − | 2.60723i | 0.0400722 | − | 0.232271i | ||||
\(127\) | −6.74682 | −0.598683 | −0.299342 | − | 0.954146i | \(-0.596767\pi\) | ||||
−0.299342 | + | 0.954146i | \(0.596767\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −0.662464 | − | 1.14742i | −0.0583267 | − | 0.101025i | ||||
\(130\) | 5.92947 | − | 3.42338i | 0.520049 | − | 0.300251i | ||||
\(131\) | 4.79326 | + | 2.76739i | 0.418789 | + | 0.241788i | 0.694559 | − | 0.719436i | \(-0.255600\pi\) |
−0.275770 | + | 0.961224i | \(0.588933\pi\) | |||||||
\(132\) | −5.65733 | −0.492408 | ||||||||
\(133\) | 16.2798 | − | 5.99352i | 1.41164 | − | 0.519704i | ||||
\(134\) | 5.69042i | 0.491578i | ||||||||
\(135\) | −3.51552 | − | 2.02969i | −0.302568 | − | 0.174687i | ||||
\(136\) | 0.577549 | + | 1.00034i | 0.0495244 | + | 0.0857789i | ||||
\(137\) | −15.9415 | + | 9.20385i | −1.36198 | + | 0.786338i | −0.989887 | − | 0.141859i | \(-0.954692\pi\) |
−0.372090 | + | 0.928197i | \(0.621359\pi\) | |||||||
\(138\) | 3.27690 | − | 3.50171i | 0.278948 | − | 0.298085i | ||||
\(139\) | 20.4754i | 1.73670i | 0.495950 | + | 0.868351i | \(0.334820\pi\) | ||||
−0.495950 | + | 0.868351i | \(0.665180\pi\) | |||||||
\(140\) | 8.25281 | + | 6.87318i | 0.697489 | + | 0.580890i | ||||
\(141\) | −4.41413 | −0.371737 | ||||||||
\(142\) | −3.59392 | + | 6.22486i | −0.301595 | + | 0.522378i | ||||
\(143\) | 4.77099 | + | 8.26360i | 0.398970 | + | 0.691037i | ||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | 13.0430 | − | 22.5912i | 1.08316 | − | 1.87609i | ||||
\(146\) | 11.1150i | 0.919887i | ||||||||
\(147\) | −4.53897 | − | 5.32895i | −0.374368 | − | 0.439524i | ||||
\(148\) | − | 2.19124i | − | 0.180119i | ||||||
\(149\) | −13.7082 | − | 7.91446i | −1.12302 | − | 0.648378i | −0.180852 | − | 0.983510i | \(-0.557886\pi\) |
−0.942171 | + | 0.335132i | \(0.891219\pi\) | |||||||
\(150\) | 9.94066 | − | 5.73924i | 0.811652 | − | 0.468607i | ||||
\(151\) | 7.74316 | + | 13.4115i | 0.630129 | + | 1.09142i | 0.987525 | + | 0.157463i | \(0.0503314\pi\) |
−0.357396 | + | 0.933953i | \(0.616335\pi\) | |||||||
\(152\) | −3.27848 | + | 5.67849i | −0.265919 | + | 0.460586i | ||||
\(153\) | −1.15510 | −0.0933842 | ||||||||
\(154\) | −9.57879 | + | 11.5015i | −0.771881 | + | 0.926818i | ||||
\(155\) | − | 11.7045i | − | 0.940130i | ||||||
\(156\) | 0.843329 | − | 1.46069i | 0.0675203 | − | 0.116949i | ||||
\(157\) | 2.07407 | + | 3.59239i | 0.165529 | + | 0.286704i | 0.936843 | − | 0.349750i | \(-0.113734\pi\) |
−0.771314 | + | 0.636455i | \(0.780400\pi\) | |||||||
\(158\) | −9.79501 | + | 5.65515i | −0.779249 | + | 0.449900i | ||||
\(159\) | 1.07256 | − | 1.85774i | 0.0850599 | − | 0.147328i | ||||
\(160\) | −4.05937 | −0.320921 | ||||||||
\(161\) | −1.57073 | − | 12.5910i | −0.123791 | − | 0.992308i | ||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 10.4256 | − | 18.0576i | 0.816593 | − | 1.41438i | −0.0915851 | − | 0.995797i | \(-0.529193\pi\) |
0.908178 | − | 0.418584i | \(-0.137473\pi\) | |||||||
\(164\) | −4.93795 | + | 2.85093i | −0.385589 | + | 0.222620i | ||||
\(165\) | 11.4826 | + | 19.8884i | 0.893919 | + | 1.54831i | ||||
\(166\) | −0.423955 | + | 0.734312i | −0.0329053 | + | 0.0569936i | ||||
\(167\) | − | 10.9872i | − | 0.850212i | −0.905144 | − | 0.425106i | \(-0.860237\pi\) | ||
0.905144 | − | 0.425106i | \(-0.139763\pi\) | |||||||
\(168\) | 2.60723 | + | 0.449810i | 0.201153 | + | 0.0347036i | ||||
\(169\) | 10.1552 | 0.781168 | ||||||||
\(170\) | 2.34449 | − | 4.06077i | 0.179814 | − | 0.311447i | ||||
\(171\) | −3.27848 | − | 5.67849i | −0.250711 | − | 0.434245i | ||||
\(172\) | 1.14742 | − | 0.662464i | 0.0874900 | − | 0.0505124i | ||||
\(173\) | 1.79243 | + | 1.03486i | 0.136276 | + | 0.0786789i | 0.566588 | − | 0.824001i | \(-0.308263\pi\) |
−0.430312 | + | 0.902680i | \(0.641596\pi\) | |||||||
\(174\) | − | 6.42612i | − | 0.487163i | ||||||
\(175\) | 5.16313 | − | 29.9271i | 0.390296 | − | 2.26228i | ||||
\(176\) | − | 5.65733i | − | 0.426437i | ||||||
\(177\) | −3.77855 | + | 6.54465i | −0.284014 | + | 0.491926i | ||||
\(178\) | −6.80960 | − | 11.7946i | −0.510401 | − | 0.884041i | ||||
\(179\) | 2.79957 | + | 4.84900i | 0.209250 | + | 0.362431i | 0.951478 | − | 0.307715i | \(-0.0995645\pi\) |
−0.742229 | + | 0.670147i | \(0.766231\pi\) | |||||||
\(180\) | 2.02969 | − | 3.51552i | 0.151284 | − | 0.262031i | ||||
\(181\) | −22.5958 | −1.67954 | −0.839768 | − | 0.542946i | \(-0.817309\pi\) | ||||
−0.839768 | + | 0.542946i | \(0.817309\pi\) | |||||||
\(182\) | −1.54172 | − | 4.18769i | −0.114280 | − | 0.310413i | ||||
\(183\) | − | 10.4107i | − | 0.769580i | ||||||
\(184\) | 3.50171 | + | 3.27690i | 0.258149 | + | 0.241576i | ||||
\(185\) | −7.70334 | + | 4.44753i | −0.566361 | + | 0.326989i | ||||
\(186\) | −1.44167 | − | 2.49704i | −0.105708 | − | 0.183092i | ||||
\(187\) | 5.65928 | + | 3.26739i | 0.413848 | + | 0.238935i | ||||
\(188\) | − | 4.41413i | − | 0.321934i | ||||||
\(189\) | −1.69316 | + | 2.03303i | −0.123160 | + | 0.147881i | ||||
\(190\) | 26.6171 | 1.93101 | ||||||||
\(191\) | 4.57461 | + | 2.64115i | 0.331007 | + | 0.191107i | 0.656288 | − | 0.754510i | \(-0.272126\pi\) |
−0.325281 | + | 0.945617i | \(0.605459\pi\) | |||||||
\(192\) | −0.866025 | + | 0.500000i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | −13.3588 | − | 23.1381i | −0.961587 | − | 1.66552i | −0.718517 | − | 0.695510i | \(-0.755179\pi\) |
−0.243071 | − | 0.970009i | \(-0.578155\pi\) | |||||||
\(194\) | 2.46295 | − | 4.26595i | 0.176829 | − | 0.306278i | ||||
\(195\) | −6.84677 | −0.490307 | ||||||||
\(196\) | 5.32895 | − | 4.53897i | 0.380639 | − | 0.324212i | ||||
\(197\) | 14.1605 | 1.00889 | 0.504447 | − | 0.863443i | \(-0.331696\pi\) | ||||
0.504447 | + | 0.863443i | \(0.331696\pi\) | |||||||
\(198\) | 4.89939 | + | 2.82867i | 0.348185 | + | 0.201025i | ||||
\(199\) | −11.6374 | − | 20.1566i | −0.824955 | − | 1.42886i | −0.901954 | − | 0.431832i | \(-0.857867\pi\) |
0.0769991 | − | 0.997031i | \(-0.475466\pi\) | |||||||
\(200\) | 5.73924 | + | 9.94066i | 0.405826 | + | 0.702911i | ||||
\(201\) | 2.84521 | − | 4.92805i | 0.200686 | − | 0.347598i | ||||
\(202\) | 8.01981i | 0.564272i | ||||||||
\(203\) | −13.0645 | − | 10.8805i | −0.916947 | − | 0.763660i | ||||
\(204\) | − | 1.15510i | − | 0.0808731i | ||||||
\(205\) | 20.0450 | + | 11.5730i | 1.40000 | + | 0.808292i | ||||
\(206\) | −3.81453 | − | 6.60696i | −0.265771 | − | 0.460329i | ||||
\(207\) | −4.58873 | + | 1.39412i | −0.318939 | + | 0.0968978i | ||||
\(208\) | 1.46069 | + | 0.843329i | 0.101281 | + | 0.0584743i | ||||
\(209\) | 37.0948i | 2.56590i | ||||||||
\(210\) | −3.71055 | − | 10.0788i | −0.256052 | − | 0.695500i | ||||
\(211\) | −2.59509 | −0.178653 | −0.0893266 | − | 0.996002i | \(-0.528471\pi\) | ||||
−0.0893266 | + | 0.996002i | \(0.528471\pi\) | |||||||
\(212\) | 1.85774 | + | 1.07256i | 0.127590 | + | 0.0736640i | ||||
\(213\) | 6.22486 | − | 3.59392i | 0.426520 | − | 0.246251i | ||||
\(214\) | 6.14656 | − | 3.54872i | 0.420170 | − | 0.242585i | ||||
\(215\) | −4.65780 | − | 2.68918i | −0.317660 | − | 0.183401i | ||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | −7.51753 | − | 1.29695i | −0.510323 | − | 0.0880429i | ||||
\(218\) | 17.4673i | 1.18303i | ||||||||
\(219\) | 5.55752 | − | 9.62590i | 0.375542 | − | 0.650458i | ||||
\(220\) | −19.8884 | + | 11.4826i | −1.34088 | + | 0.774157i | ||||
\(221\) | −1.68724 | + | 0.974128i | −0.113496 | + | 0.0655269i | ||||
\(222\) | −1.09562 | + | 1.89767i | −0.0735332 | + | 0.127363i | ||||
\(223\) | 11.5831i | 0.775664i | 0.921730 | + | 0.387832i | \(0.126776\pi\) | ||||
−0.921730 | + | 0.387832i | \(0.873224\pi\) | |||||||
\(224\) | −0.449810 | + | 2.60723i | −0.0300542 | + | 0.174203i | ||||
\(225\) | −11.4785 | −0.765232 | ||||||||
\(226\) | 7.65364 | + | 4.41883i | 0.509112 | + | 0.293936i | ||||
\(227\) | 3.86164 | + | 6.68855i | 0.256306 | + | 0.443935i | 0.965249 | − | 0.261330i | \(-0.0841612\pi\) |
−0.708943 | + | 0.705265i | \(0.750828\pi\) | |||||||
\(228\) | 5.67849 | − | 3.27848i | 0.376067 | − | 0.217122i | ||||
\(229\) | −11.0002 | + | 19.0529i | −0.726912 | + | 1.25905i | 0.231271 | + | 0.972889i | \(0.425712\pi\) |
−0.958182 | + | 0.286158i | \(0.907622\pi\) | |||||||
\(230\) | 4.41263 | − | 18.9614i | 0.290961 | − | 1.25028i | ||||
\(231\) | 14.0462 | − | 5.17120i | 0.924174 | − | 0.340240i | ||||
\(232\) | 6.42612 | 0.421896 | ||||||||
\(233\) | −11.7283 | + | 20.3141i | −0.768350 | + | 1.33082i | 0.170108 | + | 0.985425i | \(0.445588\pi\) |
−0.938457 | + | 0.345395i | \(0.887745\pi\) | |||||||
\(234\) | −1.46069 | + | 0.843329i | −0.0954882 | + | 0.0551301i | ||||
\(235\) | −15.5180 | + | 8.95930i | −1.01228 | + | 0.584440i | ||||
\(236\) | −6.54465 | − | 3.77855i | −0.426020 | − | 0.245963i | ||||
\(237\) | 11.3103 | 0.734683 | ||||||||
\(238\) | −2.34835 | − | 1.95577i | −0.152221 | − | 0.126774i | ||||
\(239\) | 14.2154 | 0.919516 | 0.459758 | − | 0.888044i | \(-0.347936\pi\) | ||||
0.459758 | + | 0.888044i | \(0.347936\pi\) | |||||||
\(240\) | 3.51552 | + | 2.02969i | 0.226926 | + | 0.131016i | ||||
\(241\) | 8.10166 | + | 14.0325i | 0.521874 | + | 0.903912i | 0.999676 | + | 0.0254449i | \(0.00810022\pi\) |
−0.477802 | + | 0.878467i | \(0.658566\pi\) | |||||||
\(242\) | −10.5027 | − | 18.1912i | −0.675139 | − | 1.16938i | ||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | 10.4107 | 0.666476 | ||||||||
\(245\) | −26.7729 | − | 9.52133i | −1.71046 | − | 0.608295i | ||||
\(246\) | 5.70186 | 0.363537 | ||||||||
\(247\) | −9.57766 | − | 5.52967i | −0.609412 | − | 0.351844i | ||||
\(248\) | 2.49704 | − | 1.44167i | 0.158562 | − | 0.0915460i | ||||
\(249\) | 0.734312 | − | 0.423955i | 0.0465351 | − | 0.0268671i | ||||
\(250\) | 13.1493 | − | 22.7752i | 0.831634 | − | 1.44043i | ||||
\(251\) | 10.0678 | 0.635475 | 0.317737 | − | 0.948179i | \(-0.397077\pi\) | ||||
0.317737 | + | 0.948179i | \(0.397077\pi\) | |||||||
\(252\) | −2.03303 | − | 1.69316i | −0.128069 | − | 0.106659i | ||||
\(253\) | 26.4255 | + | 6.14966i | 1.66136 | + | 0.386626i | ||||
\(254\) | −3.37341 | + | 5.84292i | −0.211667 | + | 0.366617i | ||||
\(255\) | −4.06077 | + | 2.34449i | −0.254295 | + | 0.146817i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −17.1515 | − | 9.90240i | −1.06988 | − | 0.617695i | −0.141730 | − | 0.989905i | \(-0.545267\pi\) |
−0.928148 | + | 0.372211i | \(0.878600\pi\) | |||||||
\(258\) | −1.32493 | −0.0824864 | ||||||||
\(259\) | 2.00295 | + | 5.44049i | 0.124457 | + | 0.338055i | ||||
\(260\) | − | 6.84677i | − | 0.424618i | ||||||
\(261\) | −3.21306 | + | 5.56519i | −0.198884 | + | 0.344476i | ||||
\(262\) | 4.79326 | − | 2.76739i | 0.296128 | − | 0.170970i | ||||
\(263\) | −11.6562 | + | 6.72970i | −0.718750 | + | 0.414971i | −0.814293 | − | 0.580455i | \(-0.802875\pi\) |
0.0955421 | + | 0.995425i | \(0.469542\pi\) | |||||||
\(264\) | −2.82867 | + | 4.89939i | −0.174092 | + | 0.301537i | ||||
\(265\) | − | 8.70787i | − | 0.534920i | ||||||
\(266\) | 2.94938 | − | 17.0955i | 0.180838 | − | 1.04819i | ||||
\(267\) | 13.6192i | 0.833482i | ||||||||
\(268\) | 4.92805 | + | 2.84521i | 0.301029 | + | 0.173799i | ||||
\(269\) | −14.9189 | + | 8.61345i | −0.909624 | + | 0.525171i | −0.880310 | − | 0.474399i | \(-0.842665\pi\) |
−0.0293136 | + | 0.999570i | \(0.509332\pi\) | |||||||
\(270\) | −3.51552 | + | 2.02969i | −0.213948 | + | 0.123523i | ||||
\(271\) | 17.3001 | + | 9.98824i | 1.05091 | + | 0.606743i | 0.922904 | − | 0.385031i | \(-0.125809\pi\) |
0.128005 | + | 0.991773i | \(0.459143\pi\) | |||||||
\(272\) | 1.15510 | 0.0700381 | ||||||||
\(273\) | −0.758675 | + | 4.39751i | −0.0459171 | + | 0.266150i | ||||
\(274\) | 18.4077i | 1.11205i | ||||||||
\(275\) | 56.2376 | + | 32.4688i | 3.39126 | + | 1.95794i | ||||
\(276\) | −1.39412 | − | 4.58873i | −0.0839160 | − | 0.276209i | ||||
\(277\) | −4.94088 | − | 8.55786i | −0.296869 | − | 0.514192i | 0.678549 | − | 0.734555i | \(-0.262609\pi\) |
−0.975418 | + | 0.220363i | \(0.929276\pi\) | |||||||
\(278\) | 17.7322 | + | 10.2377i | 1.06351 | + | 0.614017i | ||||
\(279\) | 2.88334i | 0.172621i | ||||||||
\(280\) | 10.0788 | − | 3.71055i | 0.602321 | − | 0.221748i | ||||
\(281\) | − | 19.4586i | − | 1.16080i | −0.814331 | − | 0.580400i | \(-0.802896\pi\) | ||
0.814331 | − | 0.580400i | \(-0.197104\pi\) | |||||||
\(282\) | −2.20707 | + | 3.82275i | −0.131429 | + | 0.227642i | ||||
\(283\) | 15.2174 | + | 26.3573i | 0.904581 | + | 1.56678i | 0.821479 | + | 0.570239i | \(0.193149\pi\) |
0.0831017 | + | 0.996541i | \(0.473517\pi\) | |||||||
\(284\) | 3.59392 | + | 6.22486i | 0.213260 | + | 0.369377i | ||||
\(285\) | −23.0511 | − | 13.3085i | −1.36543 | − | 0.788330i | ||||
\(286\) | 9.54198 | 0.564229 | ||||||||
\(287\) | 9.65418 | − | 11.5920i | 0.569868 | − | 0.684256i | ||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 7.83287 | − | 13.5669i | 0.460757 | − | 0.798055i | ||||
\(290\) | −13.0430 | − | 22.5912i | −0.765912 | − | 1.32660i | ||||
\(291\) | −4.26595 | + | 2.46295i | −0.250075 | + | 0.144381i | ||||
\(292\) | 9.62590 | + | 5.55752i | 0.563313 | + | 0.325229i | ||||
\(293\) | −15.7604 | −0.920733 | −0.460367 | − | 0.887729i | \(-0.652282\pi\) | ||||
−0.460367 | + | 0.887729i | \(0.652282\pi\) | |||||||
\(294\) | −6.88449 | + | 1.26639i | −0.401512 | + | 0.0738575i | ||||
\(295\) | 30.6771i | 1.78609i | ||||||||
\(296\) | −1.89767 | − | 1.09562i | −0.110300 | − | 0.0636816i | ||||
\(297\) | −2.82867 | − | 4.89939i | −0.164136 | − | 0.284292i | ||||
\(298\) | −13.7082 | + | 7.91446i | −0.794097 | + | 0.458472i | ||||
\(299\) | −5.52701 | + | 5.90618i | −0.319635 | + | 0.341563i | ||||
\(300\) | − | 11.4785i | − | 0.662711i | ||||||
\(301\) | −2.24332 | + | 2.69361i | −0.129303 | + | 0.155257i | ||||
\(302\) | 15.4863 | 0.891137 | ||||||||
\(303\) | 4.00991 | − | 6.94536i | 0.230363 | − | 0.399001i | ||||
\(304\) | 3.27848 | + | 5.67849i | 0.188033 | + | 0.325684i | ||||
\(305\) | −21.1304 | − | 36.5989i | −1.20992 | − | 2.09565i | ||||
\(306\) | −0.577549 | + | 1.00034i | −0.0330163 | + | 0.0571859i | ||||
\(307\) | − | 7.88200i | − | 0.449849i | −0.974376 | − | 0.224925i | \(-0.927786\pi\) | ||
0.974376 | − | 0.224925i | \(-0.0722136\pi\) | |||||||
\(308\) | 5.17120 | + | 14.0462i | 0.294656 | + | 0.800358i | ||||
\(309\) | 7.62906i | 0.434002i | ||||||||
\(310\) | −10.1364 | − | 5.85226i | −0.575710 | − | 0.332386i | ||||
\(311\) | 15.8777 | − | 9.16702i | 0.900345 | − | 0.519814i | 0.0230326 | − | 0.999735i | \(-0.492668\pi\) |
0.877312 | + | 0.479921i | \(0.159335\pi\) | |||||||
\(312\) | −0.843329 | − | 1.46069i | −0.0477441 | − | 0.0826952i | ||||
\(313\) | −6.20167 | + | 10.7416i | −0.350539 | + | 0.607152i | −0.986344 | − | 0.164698i | \(-0.947335\pi\) |
0.635805 | + | 0.771850i | \(0.280668\pi\) | |||||||
\(314\) | 4.14814 | 0.234093 | ||||||||
\(315\) | −1.82594 | + | 10.5837i | −0.102880 | + | 0.596326i | ||||
\(316\) | 11.3103i | 0.636254i | ||||||||
\(317\) | 1.83984 | − | 3.18670i | 0.103336 | − | 0.178983i | −0.809721 | − | 0.586815i | \(-0.800382\pi\) |
0.913057 | + | 0.407832i | \(0.133715\pi\) | |||||||
\(318\) | −1.07256 | − | 1.85774i | −0.0601464 | − | 0.104177i | ||||
\(319\) | 31.4841 | − | 18.1774i | 1.76277 | − | 1.01774i | ||||
\(320\) | −2.02969 | + | 3.51552i | −0.113463 | + | 0.196523i | ||||
\(321\) | −7.09744 | −0.396140 | ||||||||
\(322\) | −11.6895 | − | 4.93520i | −0.651429 | − | 0.275028i | ||||
\(323\) | −7.57393 | −0.421424 | ||||||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | −16.7665 | + | 9.68014i | −0.930038 | + | 0.536957i | ||||
\(326\) | −10.4256 | − | 18.0576i | −0.577419 | − | 1.00012i | ||||
\(327\) | 8.73364 | − | 15.1271i | 0.482971 | − | 0.836531i | ||||
\(328\) | 5.70186i | 0.314832i | ||||||||
\(329\) | 4.03483 | + | 10.9596i | 0.222447 | + | 0.604221i | ||||
\(330\) | 22.9652 | 1.26419 | ||||||||
\(331\) | −2.45413 | + | 4.25068i | −0.134891 | + | 0.233638i | −0.925556 | − | 0.378611i | \(-0.876402\pi\) |
0.790665 | + | 0.612249i | \(0.209735\pi\) | |||||||
\(332\) | 0.423955 | + | 0.734312i | 0.0232676 | + | 0.0403006i | ||||
\(333\) | 1.89767 | − | 1.09562i | 0.103992 | − | 0.0600396i | ||||
\(334\) | −9.51516 | − | 5.49358i | −0.520647 | − | 0.300595i | ||||
\(335\) | − | 23.0995i | − | 1.26206i | ||||||
\(336\) | 1.69316 | − | 2.03303i | 0.0923697 | − | 0.110911i | ||||
\(337\) | − | 17.4280i | − | 0.949365i | −0.880157 | − | 0.474682i | \(-0.842563\pi\) | ||
0.880157 | − | 0.474682i | \(-0.157437\pi\) | |||||||
\(338\) | 5.07759 | − | 8.79465i | 0.276185 | − | 0.478366i | ||||
\(339\) | −4.41883 | − | 7.65364i | −0.239998 | − | 0.415688i | ||||
\(340\) | −2.34449 | − | 4.06077i | −0.127148 | − | 0.220226i | ||||
\(341\) | 8.15599 | − | 14.1266i | 0.441672 | − | 0.764998i | ||||
\(342\) | −6.55695 | −0.354559 | ||||||||
\(343\) | −9.08197 | + | 16.1406i | −0.490380 | + | 0.871509i | ||||
\(344\) | − | 1.32493i | − | 0.0714353i | ||||||
\(345\) | −13.3021 | + | 14.2147i | −0.716163 | + | 0.765295i | ||||
\(346\) | 1.79243 | − | 1.03486i | 0.0963615 | − | 0.0556344i | ||||
\(347\) | 5.46035 | + | 9.45761i | 0.293127 | + | 0.507711i | 0.974547 | − | 0.224181i | \(-0.0719708\pi\) |
−0.681420 | + | 0.731892i | \(0.738637\pi\) | |||||||
\(348\) | −5.56519 | − | 3.21306i | −0.298325 | − | 0.172238i | ||||
\(349\) | 35.9929i | 1.92665i | 0.268332 | + | 0.963327i | \(0.413528\pi\) | ||||
−0.268332 | + | 0.963327i | \(0.586472\pi\) | |||||||
\(350\) | −23.3361 | − | 19.4350i | −1.24737 | − | 1.03884i | ||||
\(351\) | 1.68666 | 0.0900271 | ||||||||
\(352\) | −4.89939 | − | 2.82867i | −0.261139 | − | 0.150768i | ||||
\(353\) | −4.71527 | + | 2.72237i | −0.250969 | + | 0.144897i | −0.620208 | − | 0.784438i | \(-0.712952\pi\) |
0.369239 | + | 0.929334i | \(0.379618\pi\) | |||||||
\(354\) | 3.77855 | + | 6.54465i | 0.200828 | + | 0.347844i | ||||
\(355\) | 14.5891 | − | 25.2690i | 0.774307 | − | 1.34114i | ||||
\(356\) | −13.6192 | −0.721817 | ||||||||
\(357\) | 1.05584 | + | 2.86792i | 0.0558811 | + | 0.151786i | ||||
\(358\) | 5.59914 | 0.295924 | ||||||||
\(359\) | 11.5930 | + | 6.69322i | 0.611855 | + | 0.353255i | 0.773691 | − | 0.633563i | \(-0.218408\pi\) |
−0.161836 | + | 0.986818i | \(0.551742\pi\) | |||||||
\(360\) | −2.02969 | − | 3.51552i | −0.106974 | − | 0.185284i | ||||
\(361\) | −11.9968 | − | 20.7791i | −0.631411 | − | 1.09364i | ||||
\(362\) | −11.2979 | + | 19.5686i | −0.593805 | + | 1.02850i | ||||
\(363\) | 21.0054i | 1.10250i | ||||||||
\(364\) | −4.39751 | − | 0.758675i | −0.230492 | − | 0.0397654i | ||||
\(365\) | − | 45.1200i | − | 2.36169i | ||||||
\(366\) | −9.01591 | − | 5.20534i | −0.471269 | − | 0.272087i | ||||
\(367\) | 6.26456 | + | 10.8505i | 0.327007 | + | 0.566393i | 0.981917 | − | 0.189314i | \(-0.0606265\pi\) |
−0.654909 | + | 0.755708i | \(0.727293\pi\) | |||||||
\(368\) | 4.58873 | − | 1.39412i | 0.239204 | − | 0.0726733i | ||||
\(369\) | −4.93795 | − | 2.85093i | −0.257060 | − | 0.148413i | ||||
\(370\) | 8.89505i | 0.462432i | ||||||||
\(371\) | −5.59285 | − | 0.964899i | −0.290366 | − | 0.0500951i | ||||
\(372\) | −2.88334 | −0.149494 | ||||||||
\(373\) | −8.52214 | − | 4.92026i | −0.441260 | − | 0.254761i | 0.262872 | − | 0.964831i | \(-0.415330\pi\) |
−0.704132 | + | 0.710069i | \(0.748664\pi\) | |||||||
\(374\) | 5.65928 | − | 3.26739i | 0.292635 | − | 0.168953i | ||||
\(375\) | −22.7752 | + | 13.1493i | −1.17611 | + | 0.679026i | ||||
\(376\) | −3.82275 | − | 2.20707i | −0.197143 | − | 0.113821i | ||||
\(377\) | 10.8387i | 0.558220i | ||||||||
\(378\) | 0.914071 | + | 2.48284i | 0.0470147 | + | 0.127703i | ||||
\(379\) | 10.2772i | 0.527903i | 0.964536 | + | 0.263951i | \(0.0850258\pi\) | ||||
−0.964536 | + | 0.263951i | \(0.914974\pi\) | |||||||
\(380\) | 13.3085 | − | 23.0511i | 0.682714 | − | 1.18250i | ||||
\(381\) | 5.84292 | − | 3.37341i | 0.299342 | − | 0.172825i | ||||
\(382\) | 4.57461 | − | 2.64115i | 0.234057 | − | 0.135133i | ||||
\(383\) | −8.84461 | + | 15.3193i | −0.451939 | + | 0.782781i | −0.998506 | − | 0.0546341i | \(-0.982601\pi\) |
0.546568 | + | 0.837415i | \(0.315934\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | 38.8839 | − | 46.6889i | 1.98170 | − | 2.37948i | ||||
\(386\) | −26.7176 | −1.35989 | ||||||||
\(387\) | 1.14742 | + | 0.662464i | 0.0583267 | + | 0.0336749i | ||||
\(388\) | −2.46295 | − | 4.26595i | −0.125037 | − | 0.216571i | ||||
\(389\) | −27.8127 | + | 16.0577i | −1.41016 | + | 0.814156i | −0.995403 | − | 0.0957759i | \(-0.969467\pi\) |
−0.414757 | + | 0.909932i | \(0.636133\pi\) | |||||||
\(390\) | −3.42338 | + | 5.92947i | −0.173350 | + | 0.300251i | ||||
\(391\) | −1.25562 | + | 5.39548i | −0.0634995 | + | 0.272861i | ||||
\(392\) | −1.26639 | − | 6.88449i | −0.0639625 | − | 0.347719i | ||||
\(393\) | −5.53478 | −0.279193 | ||||||||
\(394\) | 7.08025 | − | 12.2634i | 0.356698 | − | 0.617819i | ||||
\(395\) | 39.7616 | − | 22.9563i | 2.00062 | − | 1.15506i | ||||
\(396\) | 4.89939 | − | 2.82867i | 0.246204 | − | 0.142146i | ||||
\(397\) | −16.1963 | − | 9.35091i | −0.812867 | − | 0.469309i | 0.0350835 | − | 0.999384i | \(-0.488830\pi\) |
−0.847950 | + | 0.530075i | \(0.822164\pi\) | |||||||
\(398\) | −23.2748 | −1.16666 | ||||||||
\(399\) | −11.1020 | + | 13.3305i | −0.555795 | + | 0.667357i | ||||
\(400\) | 11.4785 | 0.573924 | ||||||||
\(401\) | −14.8691 | − | 8.58467i | −0.742527 | − | 0.428698i | 0.0804605 | − | 0.996758i | \(-0.474361\pi\) |
−0.822987 | + | 0.568060i | \(0.807694\pi\) | |||||||
\(402\) | −2.84521 | − | 4.92805i | −0.141906 | − | 0.245789i | ||||
\(403\) | 2.43160 | + | 4.21165i | 0.121127 | + | 0.209797i | ||||
\(404\) | 6.94536 | + | 4.00991i | 0.345545 | + | 0.199500i | ||||
\(405\) | 4.05937 | 0.201712 | ||||||||
\(406\) | −15.9550 | + | 5.87393i | −0.791834 | + | 0.291518i | ||||
\(407\) | −12.3966 | −0.614475 | ||||||||
\(408\) | −1.00034 | − | 0.577549i | −0.0495244 | − | 0.0285930i | ||||
\(409\) | −8.69664 | + | 5.02101i | −0.430021 | + | 0.248273i | −0.699356 | − | 0.714774i | \(-0.746530\pi\) |
0.269334 | + | 0.963047i | \(0.413196\pi\) | |||||||
\(410\) | 20.0450 | − | 11.5730i | 0.989951 | − | 0.571548i | ||||
\(411\) | 9.20385 | − | 15.9415i | 0.453992 | − | 0.786338i | ||||
\(412\) | −7.62906 | −0.375857 | ||||||||
\(413\) | 19.7032 | + | 3.39926i | 0.969529 | + | 0.167267i | ||||
\(414\) | −1.08702 | + | 4.67101i | −0.0534243 | + | 0.229568i | ||||
\(415\) | 1.72099 | − | 2.98084i | 0.0844801 | − | 0.146324i | ||||
\(416\) | 1.46069 | − | 0.843329i | 0.0716161 | − | 0.0413476i | ||||
\(417\) | −10.2377 | − | 17.7322i | −0.501343 | − | 0.868351i | ||||
\(418\) | 32.1251 | + | 18.5474i | 1.57129 | + | 0.907184i | ||||
\(419\) | 36.7063 | 1.79322 | 0.896610 | − | 0.442821i | \(-0.146022\pi\) | ||||
0.896610 | + | 0.442821i | \(0.146022\pi\) | |||||||
\(420\) | −10.5837 | − | 1.82594i | −0.516433 | − | 0.0890970i | ||||
\(421\) | 1.74437i | 0.0850155i | 0.999096 | + | 0.0425077i | \(0.0135347\pi\) | ||||
−0.999096 | + | 0.0425077i | \(0.986465\pi\) | |||||||
\(422\) | −1.29754 | + | 2.24741i | −0.0631634 | + | 0.109402i | ||||
\(423\) | 3.82275 | − | 2.20707i | 0.185869 | − | 0.107311i | ||||
\(424\) | 1.85774 | − | 1.07256i | 0.0902196 | − | 0.0520883i | ||||
\(425\) | −6.62939 | + | 11.4824i | −0.321573 | + | 0.556980i | ||||
\(426\) | − | 7.18784i | − | 0.348252i | ||||||
\(427\) | −25.8480 | + | 9.51610i | −1.25087 | + | 0.460516i | ||||
\(428\) | − | 7.09744i | − | 0.343067i | ||||||
\(429\) | −8.26360 | − | 4.77099i | −0.398970 | − | 0.230346i | ||||
\(430\) | −4.65780 | + | 2.68918i | −0.224619 | + | 0.129684i | ||||
\(431\) | −12.3926 | + | 7.15487i | −0.596931 | + | 0.344638i | −0.767833 | − | 0.640650i | \(-0.778665\pi\) |
0.170903 | + | 0.985288i | \(0.445332\pi\) | |||||||
\(432\) | −0.866025 | − | 0.500000i | −0.0416667 | − | 0.0240563i | ||||
\(433\) | 17.9359 | 0.861943 | 0.430972 | − | 0.902365i | \(-0.358171\pi\) | ||||
0.430972 | + | 0.902365i | \(0.358171\pi\) | |||||||
\(434\) | −4.88196 | + | 5.86190i | −0.234342 | + | 0.281380i | ||||
\(435\) | 26.0860i | 1.25073i | ||||||||
\(436\) | 15.1271 | + | 8.73364i | 0.724457 | + | 0.418265i | ||||
\(437\) | −30.0881 | + | 9.14115i | −1.43931 | + | 0.437281i | ||||
\(438\) | −5.55752 | − | 9.62590i | −0.265548 | − | 0.459943i | ||||
\(439\) | −28.0581 | − | 16.1994i | −1.33914 | − | 0.773154i | −0.352462 | − | 0.935826i | \(-0.614655\pi\) |
−0.986680 | + | 0.162672i | \(0.947989\pi\) | |||||||
\(440\) | 22.9652i | 1.09482i | ||||||||
\(441\) | 6.59534 | + | 2.34552i | 0.314064 | + | 0.111691i | ||||
\(442\) | 1.94826i | 0.0926691i | ||||||||
\(443\) | −19.0976 | + | 33.0780i | −0.907355 | + | 1.57159i | −0.0896309 | + | 0.995975i | \(0.528569\pi\) |
−0.817724 | + | 0.575610i | \(0.804765\pi\) | |||||||
\(444\) | 1.09562 | + | 1.89767i | 0.0519958 | + | 0.0900594i | ||||
\(445\) | 27.6427 | + | 47.8786i | 1.31039 | + | 2.26966i | ||||
\(446\) | 10.0313 | + | 5.79156i | 0.474995 | + | 0.274239i | ||||
\(447\) | 15.8289 | 0.748682 | ||||||||
\(448\) | 2.03303 | + | 1.69316i | 0.0960515 | + | 0.0799945i | ||||
\(449\) | 14.0922 | 0.665052 | 0.332526 | − | 0.943094i | \(-0.392099\pi\) | ||||
0.332526 | + | 0.943094i | \(0.392099\pi\) | |||||||
\(450\) | −5.73924 | + | 9.94066i | −0.270551 | + | 0.468607i | ||||
\(451\) | 16.1286 | + | 27.9356i | 0.759468 | + | 1.31544i | ||||
\(452\) | 7.65364 | − | 4.41883i | 0.359997 | − | 0.207844i | ||||
\(453\) | −13.4115 | − | 7.74316i | −0.630129 | − | 0.363805i | ||||
\(454\) | 7.72328 | 0.362471 | ||||||||
\(455\) | 6.25843 | + | 16.9994i | 0.293400 | + | 0.796944i | ||||
\(456\) | − | 6.55695i | − | 0.307057i | ||||||
\(457\) | −3.70638 | − | 2.13988i | −0.173377 | − | 0.100099i | 0.410800 | − | 0.911725i | \(-0.365249\pi\) |
−0.584177 | + | 0.811626i | \(0.698583\pi\) | |||||||
\(458\) | 11.0002 | + | 19.0529i | 0.514004 | + | 0.890281i | ||||
\(459\) | 1.00034 | − | 0.577549i | 0.0466921 | − | 0.0269577i | ||||
\(460\) | −14.2147 | − | 13.3021i | −0.662765 | − | 0.620216i | ||||
\(461\) | 7.14597i | 0.332821i | 0.986057 | + | 0.166410i | \(0.0532177\pi\) | ||||
−0.986057 | + | 0.166410i | \(0.946782\pi\) | |||||||
\(462\) | 2.54472 | − | 14.7500i | 0.118391 | − | 0.686232i | ||||
\(463\) | 2.83540 | 0.131772 | 0.0658861 | − | 0.997827i | \(-0.479013\pi\) | ||||
0.0658861 | + | 0.997827i | \(0.479013\pi\) | |||||||
\(464\) | 3.21306 | − | 5.56519i | 0.149163 | − | 0.258357i | ||||
\(465\) | 5.85226 | + | 10.1364i | 0.271392 | + | 0.470065i | ||||
\(466\) | 11.7283 | + | 20.3141i | 0.543305 | + | 0.941032i | ||||
\(467\) | 12.7367 | − | 22.0606i | 0.589384 | − | 1.02084i | −0.404929 | − | 0.914348i | \(-0.632704\pi\) |
0.994313 | − | 0.106495i | \(-0.0339628\pi\) | |||||||
\(468\) | 1.68666i | 0.0779658i | ||||||||
\(469\) | −14.8363 | − | 2.55961i | −0.685075 | − | 0.118192i | ||||
\(470\) | 17.9186i | 0.826523i | ||||||||
\(471\) | −3.59239 | − | 2.07407i | −0.165529 | − | 0.0955680i | ||||
\(472\) | −6.54465 | + | 3.77855i | −0.301242 | + | 0.173922i | ||||
\(473\) | −3.74778 | − | 6.49134i | −0.172323 | − | 0.298472i | ||||
\(474\) | 5.65515 | − | 9.79501i | 0.259750 | − | 0.449900i | ||||
\(475\) | −75.2639 | −3.45334 | ||||||||
\(476\) | −2.86792 | + | 1.05584i | −0.131451 | + | 0.0483944i | ||||
\(477\) | 2.14513i | 0.0982187i | ||||||||
\(478\) | 7.10768 | − | 12.3109i | 0.325098 | − | 0.563086i | ||||
\(479\) | 9.60900 | + | 16.6433i | 0.439046 | + | 0.760450i | 0.997616 | − | 0.0690070i | \(-0.0219831\pi\) |
−0.558570 | + | 0.829457i | \(0.688650\pi\) | |||||||
\(480\) | 3.51552 | − | 2.02969i | 0.160461 | − | 0.0926420i | ||||
\(481\) | 1.84794 | − | 3.20072i | 0.0842586 | − | 0.145940i | ||||
\(482\) | 16.2033 | 0.738041 | ||||||||
\(483\) | 7.65579 | + | 10.1187i | 0.348350 | + | 0.460419i | ||||
\(484\) | −21.0054 | −0.954791 | ||||||||
\(485\) | −9.99802 | + | 17.3171i | −0.453987 | + | 0.786328i | ||||
\(486\) | 0.866025 | − | 0.500000i | 0.0392837 | − | 0.0226805i | ||||
\(487\) | −15.1812 | − | 26.2947i | −0.687927 | − | 1.19152i | −0.972507 | − | 0.232872i | \(-0.925188\pi\) |
0.284580 | − | 0.958652i | \(-0.408146\pi\) | |||||||
\(488\) | 5.20534 | − | 9.01591i | 0.235635 | − | 0.408131i | ||||
\(489\) | 20.8511i | 0.942921i | ||||||||
\(490\) | −21.6322 | + | 18.4254i | −0.977242 | + | 0.832374i | ||||
\(491\) | 8.50669 | 0.383902 | 0.191951 | − | 0.981405i | \(-0.438519\pi\) | ||||
0.191951 | + | 0.981405i | \(0.438519\pi\) | |||||||
\(492\) | 2.85093 | − | 4.93795i | 0.128530 | − | 0.222620i | ||||
\(493\) | 3.71140 | + | 6.42834i | 0.167153 | + | 0.289518i | ||||
\(494\) | −9.57766 | + | 5.52967i | −0.430919 | + | 0.248791i | ||||
\(495\) | −19.8884 | − | 11.4826i | −0.893919 | − | 0.516105i | ||||
\(496\) | − | 2.88334i | − | 0.129466i | ||||||
\(497\) | −14.6131 | − | 12.1702i | −0.655486 | − | 0.545908i | ||||
\(498\) | − | 0.847910i | − | 0.0379958i | ||||||
\(499\) | −6.28157 | + | 10.8800i | −0.281202 | + | 0.487056i | −0.971681 | − | 0.236297i | \(-0.924066\pi\) |
0.690479 | + | 0.723352i | \(0.257400\pi\) | |||||||
\(500\) | −13.1493 | − | 22.7752i | −0.588054 | − | 1.01854i | ||||
\(501\) | 5.49358 | + | 9.51516i | 0.245435 | + | 0.425106i | ||||
\(502\) | 5.03391 | − | 8.71899i | 0.224674 | − | 0.389147i | ||||
\(503\) | −5.00925 | −0.223351 | −0.111676 | − | 0.993745i | \(-0.535622\pi\) | ||||
−0.111676 | + | 0.993745i | \(0.535622\pi\) | |||||||
\(504\) | −2.48284 | + | 0.914071i | −0.110594 | + | 0.0407159i | ||||
\(505\) | − | 32.5554i | − | 1.44870i | ||||||
\(506\) | 18.5385 | − | 19.8103i | 0.824137 | − | 0.880676i | ||||
\(507\) | −8.79465 | + | 5.07759i | −0.390584 | + | 0.225504i | ||||
\(508\) | 3.37341 | + | 5.84292i | 0.149671 | + | 0.259238i | ||||
\(509\) | 16.2344 | + | 9.37291i | 0.719575 | + | 0.415447i | 0.814596 | − | 0.580028i | \(-0.196958\pi\) |
−0.0950210 | + | 0.995475i | \(0.530292\pi\) | |||||||
\(510\) | 4.68897i | 0.207631i | ||||||||
\(511\) | −28.9795 | − | 4.99965i | −1.28198 | − | 0.221172i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 5.67849 | + | 3.27848i | 0.250711 | + | 0.144748i | ||||
\(514\) | −17.1515 | + | 9.90240i | −0.756518 | + | 0.436776i | ||||
\(515\) | 15.4846 | + | 26.8201i | 0.682333 | + | 1.18184i | ||||
\(516\) | −0.662464 | + | 1.14742i | −0.0291633 | + | 0.0505124i | ||||
\(517\) | −24.9722 | −1.09828 | ||||||||
\(518\) | 5.71307 | + | 0.985641i | 0.251018 | + | 0.0433066i | ||||
\(519\) | −2.06972 | −0.0908505 | ||||||||
\(520\) | −5.92947 | − | 3.42338i | −0.260025 | − | 0.150125i | ||||
\(521\) | −2.62697 | − | 4.55004i | −0.115090 | − | 0.199341i | 0.802726 | − | 0.596348i | \(-0.203382\pi\) |
−0.917816 | + | 0.397007i | \(0.870049\pi\) | |||||||
\(522\) | 3.21306 | + | 5.56519i | 0.140632 | + | 0.243582i | ||||
\(523\) | 9.66808 | − | 16.7456i | 0.422755 | − | 0.732234i | −0.573452 | − | 0.819239i | \(-0.694396\pi\) |
0.996208 | + | 0.0870049i | \(0.0277296\pi\) | |||||||
\(524\) | − | 5.53478i | − | 0.241788i | ||||||
\(525\) | 10.4921 | + | 28.4992i | 0.457915 | + | 1.24381i | ||||
\(526\) | 13.4594i | 0.586857i | ||||||||
\(527\) | 2.88433 | + | 1.66527i | 0.125643 | + | 0.0725402i | ||||
\(528\) | 2.82867 | + | 4.89939i | 0.123102 | + | 0.213219i | ||||
\(529\) | 1.52388 | + | 22.9495i | 0.0662555 | + | 0.997803i | ||||
\(530\) | −7.54124 | − | 4.35393i | −0.327570 | − | 0.189123i | ||||
\(531\) | − | 7.55711i | − | 0.327951i | ||||||
\(532\) | −13.3305 | − | 11.1020i | −0.577948 | − | 0.481332i | ||||
\(533\) | −9.61708 | −0.416562 | ||||||||
\(534\) | 11.7946 | + | 6.80960i | 0.510401 | + | 0.294680i | ||||
\(535\) | −24.9512 | + | 14.4056i | −1.07873 | + | 0.622807i | ||||
\(536\) | 4.92805 | − | 2.84521i | 0.212859 | − | 0.122894i | ||||
\(537\) | −4.84900 | − | 2.79957i | −0.209250 | − | 0.120810i | ||||
\(538\) | 17.2269i | 0.742705i | ||||||||
\(539\) | −25.6785 | − | 30.1476i | −1.10605 | − | 1.29855i | ||||
\(540\) | 4.05937i | 0.174687i | ||||||||
\(541\) | −4.36382 | + | 7.55835i | −0.187615 | + | 0.324959i | −0.944455 | − | 0.328642i | \(-0.893409\pi\) |
0.756840 | + | 0.653601i | \(0.226742\pi\) | |||||||
\(542\) | 17.3001 | − | 9.98824i | 0.743105 | − | 0.429032i | ||||
\(543\) | 19.5686 | − | 11.2979i | 0.839768 | − | 0.484840i | ||||
\(544\) | 0.577549 | − | 1.00034i | 0.0247622 | − | 0.0428894i | ||||
\(545\) | − | 70.9062i | − | 3.03729i | ||||||
\(546\) | 3.42902 | + | 2.85579i | 0.146748 | + | 0.122216i | ||||
\(547\) | −25.3827 | −1.08529 | −0.542643 | − | 0.839963i | \(-0.682577\pi\) | ||||
−0.542643 | + | 0.839963i | \(0.682577\pi\) | |||||||
\(548\) | 15.9415 | + | 9.20385i | 0.680988 | + | 0.393169i | ||||
\(549\) | 5.20534 | + | 9.01591i | 0.222159 | + | 0.384790i | ||||
\(550\) | 56.2376 | − | 32.4688i | 2.39798 | − | 1.38447i | ||||
\(551\) | −21.0679 | + | 36.4907i | −0.897522 | + | 1.55455i | ||||
\(552\) | −4.67101 | − | 1.08702i | −0.198812 | − | 0.0462668i | ||||
\(553\) | −10.3384 | − | 28.0816i | −0.439634 | − | 1.19415i | ||||
\(554\) | −9.88176 | −0.419836 | ||||||||
\(555\) | 4.44753 | − | 7.70334i | 0.188787 | − | 0.326989i | ||||
\(556\) | 17.7322 | − | 10.2377i | 0.752014 | − | 0.434176i | ||||
\(557\) | −0.975085 | + | 0.562966i | −0.0413157 | + | 0.0238536i | −0.520516 | − | 0.853852i | \(-0.674260\pi\) |
0.479200 | + | 0.877706i | \(0.340927\pi\) | |||||||
\(558\) | 2.49704 | + | 1.44167i | 0.105708 | + | 0.0610307i | ||||
\(559\) | 2.23470 | 0.0945177 | ||||||||
\(560\) | 1.82594 | − | 10.5837i | 0.0771602 | − | 0.447244i | ||||
\(561\) | −6.53478 | −0.275898 | ||||||||
\(562\) | −16.8516 | − | 9.72928i | −0.710842 | − | 0.410405i | ||||
\(563\) | −21.1487 | − | 36.6307i | −0.891313 | − | 1.54380i | −0.838302 | − | 0.545206i | \(-0.816452\pi\) |
−0.0530108 | − | 0.998594i | \(-0.516882\pi\) | |||||||
\(564\) | 2.20707 | + | 3.82275i | 0.0929343 | + | 0.160967i | ||||
\(565\) | −31.0689 | − | 17.9377i | −1.30708 | − | 0.754643i | ||||
\(566\) | 30.4348 | 1.27927 | ||||||||
\(567\) | 0.449810 | − | 2.60723i | 0.0188902 | − | 0.109494i | ||||
\(568\) | 7.18784 | 0.301595 | ||||||||
\(569\) | 25.2638 | + | 14.5861i | 1.05911 | + | 0.611479i | 0.925187 | − | 0.379512i | \(-0.123908\pi\) |
0.133926 | + | 0.990991i | \(0.457242\pi\) | |||||||
\(570\) | −23.0511 | + | 13.3085i | −0.965503 | + | 0.557434i | ||||
\(571\) | 11.9062 | − | 6.87403i | 0.498257 | − | 0.287669i | −0.229736 | − | 0.973253i | \(-0.573786\pi\) |
0.727994 | + | 0.685584i | \(0.240453\pi\) | |||||||
\(572\) | 4.77099 | − | 8.26360i | 0.199485 | − | 0.345518i | ||||
\(573\) | −5.28230 | −0.220671 | ||||||||
\(574\) | −5.21190 | − | 14.1568i | −0.217540 | − | 0.590892i | ||||
\(575\) | −12.4774 | + | 53.6162i | −0.520343 | + | 2.23595i | ||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | 24.2748 | − | 14.0150i | 1.01057 | − | 0.583454i | 0.0992124 | − | 0.995066i | \(-0.468368\pi\) |
0.911359 | + | 0.411613i | \(0.135034\pi\) | |||||||
\(578\) | −7.83287 | − | 13.5669i | −0.325805 | − | 0.564310i | ||||
\(579\) | 23.1381 | + | 13.3588i | 0.961587 | + | 0.555173i | ||||
\(580\) | −26.0860 | −1.08316 | ||||||||
\(581\) | −1.72382 | − | 1.43565i | −0.0715163 | − | 0.0595608i | ||||
\(582\) | 4.92590i | 0.204185i | ||||||||
\(583\) | 6.06785 | − | 10.5098i | 0.251305 | − | 0.435272i | ||||
\(584\) | 9.62590 | − | 5.55752i | 0.398323 | − | 0.229972i | ||||
\(585\) | 5.92947 | − | 3.42338i | 0.245154 | − | 0.141539i | ||||
\(586\) | −7.88021 | + | 13.6489i | −0.325528 | + | 0.563832i | ||||
\(587\) | 1.89303i | 0.0781337i | 0.999237 | + | 0.0390668i | \(0.0124385\pi\) | ||||
−0.999237 | + | 0.0390668i | \(0.987561\pi\) | |||||||
\(588\) | −2.34552 | + | 6.59534i | −0.0967276 | + | 0.271987i | ||||
\(589\) | 18.9059i | 0.779004i | ||||||||
\(590\) | 26.5672 | + | 15.3386i | 1.09375 | + | 0.631478i | ||||
\(591\) | −12.2634 | + | 7.08025i | −0.504447 | + | 0.291243i | ||||
\(592\) | −1.89767 | + | 1.09562i | −0.0779937 | + | 0.0450297i | ||||
\(593\) | 6.51640 | + | 3.76224i | 0.267596 | + | 0.154497i | 0.627795 | − | 0.778379i | \(-0.283958\pi\) |
−0.360198 | + | 0.932876i | \(0.617291\pi\) | |||||||
\(594\) | −5.65733 | −0.232123 | ||||||||
\(595\) | 9.53281 | + | 7.93920i | 0.390807 | + | 0.325475i | ||||
\(596\) | 15.8289i | 0.648378i | ||||||||
\(597\) | 20.1566 | + | 11.6374i | 0.824955 | + | 0.476288i | ||||
\(598\) | 2.35140 | + | 7.73962i | 0.0961558 | + | 0.316496i | ||||
\(599\) | 23.1928 | + | 40.1711i | 0.947631 | + | 1.64135i | 0.750395 | + | 0.660990i | \(0.229863\pi\) |
0.197236 | + | 0.980356i | \(0.436803\pi\) | |||||||
\(600\) | −9.94066 | − | 5.73924i | −0.405826 | − | 0.234304i | ||||
\(601\) | 5.74340i | 0.234278i | 0.993116 | + | 0.117139i | \(0.0373723\pi\) | ||||
−0.993116 | + | 0.117139i | \(0.962628\pi\) | |||||||
\(602\) | 1.21108 | + | 3.28958i | 0.0493598 | + | 0.134073i | ||||
\(603\) | 5.69042i | 0.231732i | ||||||||
\(604\) | 7.74316 | − | 13.4115i | 0.315065 | − | 0.545708i | ||||
\(605\) | 42.6344 | + | 73.8449i | 1.73333 | + | 3.00222i | ||||
\(606\) | −4.00991 | − | 6.94536i | −0.162891 | − | 0.282136i | ||||
\(607\) | 20.9112 | + | 12.0731i | 0.848761 | + | 0.490033i | 0.860233 | − | 0.509902i | \(-0.170318\pi\) |
−0.0114715 | + | 0.999934i | \(0.503652\pi\) | |||||||
\(608\) | 6.55695 | 0.265919 | ||||||||
\(609\) | 16.7544 | + | 2.89053i | 0.678923 | + | 0.117130i | ||||
\(610\) | −42.2608 | −1.71109 | ||||||||
\(611\) | 3.72257 | − | 6.44767i | 0.150599 | − | 0.260845i | ||||
\(612\) | 0.577549 | + | 1.00034i | 0.0233460 | + | 0.0404365i | ||||
\(613\) | 2.02156 | − | 1.16715i | 0.0816501 | − | 0.0471407i | −0.458619 | − | 0.888633i | \(-0.651656\pi\) |
0.540269 | + | 0.841492i | \(0.318322\pi\) | |||||||
\(614\) | −6.82601 | − | 3.94100i | −0.275475 | − | 0.159046i | ||||
\(615\) | −23.1459 | −0.933335 | ||||||||
\(616\) | 14.7500 | + | 2.54472i | 0.594294 | + | 0.102530i | ||||
\(617\) | 3.06512i | 0.123397i | 0.998095 | + | 0.0616986i | \(0.0196518\pi\) | ||||
−0.998095 | + | 0.0616986i | \(0.980348\pi\) | |||||||
\(618\) | 6.60696 | + | 3.81453i | 0.265771 | + | 0.153443i | ||||
\(619\) | −4.41751 | − | 7.65135i | −0.177555 | − | 0.307534i | 0.763488 | − | 0.645822i | \(-0.223485\pi\) |
−0.941042 | + | 0.338289i | \(0.890152\pi\) | |||||||
\(620\) | −10.1364 | + | 5.85226i | −0.407088 | + | 0.235033i | ||||
\(621\) | 3.27690 | − | 3.50171i | 0.131497 | − | 0.140519i | ||||
\(622\) | − | 18.3340i | − | 0.735128i | ||||||
\(623\) | 33.8143 | − | 12.4489i | 1.35474 | − | 0.498755i | ||||
\(624\) | −1.68666 | −0.0675203 | ||||||||
\(625\) | −24.6816 | + | 42.7498i | −0.987264 | + | 1.70999i | ||||
\(626\) | 6.20167 | + | 10.7416i | 0.247869 | + | 0.429321i | ||||
\(627\) | −18.5474 | − | 32.1251i | −0.740713 | − | 1.28295i | ||||
\(628\) | 2.07407 | − | 3.59239i | 0.0827643 | − | 0.143352i | ||||
\(629\) | − | 2.53110i | − | 0.100921i | ||||||
\(630\) | 8.25281 | + | 6.87318i | 0.328800 | + | 0.273834i | ||||
\(631\) | − | 5.70623i | − | 0.227162i | −0.993529 | − | 0.113581i | \(-0.963768\pi\) | ||
0.993529 | − | 0.113581i | \(-0.0362321\pi\) | |||||||
\(632\) | 9.79501 | + | 5.65515i | 0.389624 | + | 0.224950i | ||||
\(633\) | 2.24741 | − | 1.29754i | 0.0893266 | − | 0.0515727i | ||||
\(634\) | −1.83984 | − | 3.18670i | −0.0730696 | − | 0.126560i | ||||
\(635\) | 13.6939 | − | 23.7186i | 0.543427 | − | 0.941242i | ||||
\(636\) | −2.14513 | −0.0850599 | ||||||||
\(637\) | 11.6118 | − | 2.13597i | 0.460076 | − | 0.0846302i | ||||
\(638\) | − | 36.3547i | − | 1.43930i | ||||||
\(639\) | −3.59392 | + | 6.22486i | −0.142173 | + | 0.246251i | ||||
\(640\) | 2.02969 | + | 3.51552i | 0.0802303 | + | 0.138963i | ||||
\(641\) | 5.46662 | − | 3.15616i | 0.215919 | − | 0.124661i | −0.388140 | − | 0.921600i | \(-0.626882\pi\) |
0.604059 | + | 0.796940i | \(0.293549\pi\) | |||||||
\(642\) | −3.54872 | + | 6.14656i | −0.140057 | + | 0.242585i | ||||
\(643\) | −29.5677 | −1.16604 | −0.583019 | − | 0.812458i | \(-0.698129\pi\) | ||||
−0.583019 | + | 0.812458i | \(0.698129\pi\) | |||||||
\(644\) | −10.1187 | + | 7.65579i | −0.398734 | + | 0.301680i | ||||
\(645\) | 5.37837 | 0.211773 | ||||||||
\(646\) | −3.78696 | + | 6.55921i | −0.148996 | + | 0.258069i | ||||
\(647\) | 38.1119 | − | 22.0039i | 1.49833 | − | 0.865063i | 0.498335 | − | 0.866984i | \(-0.333945\pi\) |
0.999998 | + | 0.00192095i | \(0.000611456\pi\) | |||||||
\(648\) | 0.500000 | + | 0.866025i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | −21.3765 | + | 37.0252i | −0.839102 | + | 1.45337i | ||||
\(650\) | 19.3603i | 0.759372i | ||||||||
\(651\) | 7.15885 | − | 2.63557i | 0.280577 | − | 0.103296i | ||||
\(652\) | −20.8511 | −0.816593 | ||||||||
\(653\) | −8.76586 | + | 15.1829i | −0.343035 | + | 0.594154i | −0.984995 | − | 0.172585i | \(-0.944788\pi\) |
0.641960 | + | 0.766738i | \(0.278122\pi\) | |||||||
\(654\) | −8.73364 | − | 15.1271i | −0.341512 | − | 0.591517i | ||||
\(655\) | −19.4576 | + | 11.2339i | −0.760271 | + | 0.438943i | ||||
\(656\) | 4.93795 | + | 2.85093i | 0.192795 | + | 0.111310i | ||||
\(657\) | 11.1150i | 0.433639i | ||||||||
\(658\) | 11.5087 | + | 1.98552i | 0.448655 | + | 0.0774036i | ||||
\(659\) | − | 46.8252i | − | 1.82405i | −0.410132 | − | 0.912026i | \(-0.634517\pi\) | ||
0.410132 | − | 0.912026i | \(-0.365483\pi\) | |||||||
\(660\) | 11.4826 | − | 19.8884i | 0.446960 | − | 0.774157i | ||||
\(661\) | −19.0305 | − | 32.9619i | −0.740202 | − | 1.28207i | −0.952403 | − | 0.304842i | \(-0.901396\pi\) |
0.212201 | − | 0.977226i | \(-0.431937\pi\) | |||||||
\(662\) | 2.45413 | + | 4.25068i | 0.0953824 | + | 0.165207i | ||||
\(663\) | 0.974128 | − | 1.68724i | 0.0378320 | − | 0.0655269i | ||||
\(664\) | 0.847910 | 0.0329053 | ||||||||
\(665\) | −11.9726 | + | 69.3970i | −0.464279 | + | 2.69110i | ||||
\(666\) | − | 2.19124i | − | 0.0849088i | ||||||
\(667\) | 22.5024 | + | 21.0578i | 0.871296 | + | 0.815360i | ||||
\(668\) | −9.51516 | + | 5.49358i | −0.368153 | + | 0.212553i | ||||
\(669\) | −5.79156 | − | 10.0313i | −0.223915 | − | 0.387832i | ||||
\(670\) | −20.0048 | − | 11.5498i | −0.772852 | − | 0.446206i | ||||
\(671\) | − | 58.8967i | − | 2.27368i | ||||||
\(672\) | −0.914071 | − | 2.48284i | −0.0352610 | − | 0.0957775i | ||||
\(673\) | −45.8997 | −1.76930 | −0.884651 | − | 0.466254i | \(-0.845603\pi\) | ||||
−0.884651 | + | 0.466254i | \(0.845603\pi\) | |||||||
\(674\) | −15.0931 | − | 8.71401i | −0.581365 | − | 0.335651i | ||||
\(675\) | 9.94066 | − | 5.73924i | 0.382616 | − | 0.220904i | ||||
\(676\) | −5.07759 | − | 8.79465i | −0.195292 | − | 0.338256i | ||||
\(677\) | 7.26567 | − | 12.5845i | 0.279242 | − | 0.483662i | −0.691954 | − | 0.721941i | \(-0.743250\pi\) |
0.971197 | + | 0.238279i | \(0.0765834\pi\) | |||||||
\(678\) | −8.83766 | −0.339408 | ||||||||
\(679\) | 10.0145 | + | 8.34035i | 0.384320 | + | 0.320073i | ||||
\(680\) | −4.68897 | −0.179814 | ||||||||
\(681\) | −6.68855 | − | 3.86164i | −0.256306 | − | 0.147978i | ||||
\(682\) | −8.15599 | − | 14.1266i | −0.312309 | − | 0.540935i | ||||
\(683\) | −23.3505 | − | 40.4443i | −0.893482 | − | 1.54756i | −0.835672 | − | 0.549229i | \(-0.814921\pi\) |
−0.0578106 | − | 0.998328i | \(-0.518412\pi\) | |||||||
\(684\) | −3.27848 | + | 5.67849i | −0.125356 | + | 0.217122i | ||||
\(685\) | − | 74.7236i | − | 2.85504i | ||||||
\(686\) | 9.43716 | + | 15.9355i | 0.360312 | + | 0.608420i | ||||
\(687\) | − | 22.0003i | − | 0.839365i | ||||||
\(688\) | −1.14742 | − | 0.662464i | −0.0437450 | − | 0.0252562i | ||||
\(689\) | 1.80905 | + | 3.13336i | 0.0689192 | + | 0.119372i | ||||
\(690\) | 5.65923 | + | 18.6274i | 0.215443 | + | 0.709131i | ||||
\(691\) | −0.0941465 | − | 0.0543555i | −0.00358150 | − | 0.00206778i | 0.498208 | − | 0.867057i | \(-0.333992\pi\) |
−0.501790 | + | 0.864990i | \(0.667325\pi\) | |||||||
\(692\) | − | 2.06972i | − | 0.0786789i | ||||||
\(693\) | −9.57879 | + | 11.5015i | −0.363868 | + | 0.436906i | ||||
\(694\) | 10.9207 | 0.414544 | ||||||||
\(695\) | −71.9817 | − | 41.5587i | −2.73042 | − | 1.57641i | ||||
\(696\) | −5.56519 | + | 3.21306i | −0.210948 | + | 0.121791i | ||||
\(697\) | −5.70382 | + | 3.29310i | −0.216048 | + | 0.124735i | ||||
\(698\) | 31.1707 | + | 17.9964i | 1.17983 | + | 0.681175i | ||||
\(699\) | − | 23.4567i | − | 0.887214i | ||||||
\(700\) | −28.4992 | + | 10.4921i | −1.07717 | + | 0.396566i | ||||
\(701\) | − | 21.6443i | − | 0.817495i | −0.912648 | − | 0.408747i | \(-0.865966\pi\) | ||
0.912648 | − | 0.408747i | \(-0.134034\pi\) | |||||||
\(702\) | 0.843329 | − | 1.46069i | 0.0318294 | − | 0.0551301i | ||||
\(703\) | 12.4429 | − | 7.18392i | 0.469294 | − | 0.270947i | ||||
\(704\) | −4.89939 | + | 2.82867i | −0.184653 | + | 0.106609i | ||||
\(705\) | 8.95930 | − | 15.5180i | 0.337427 | − | 0.584440i | ||||
\(706\) | 5.44473i | 0.204915i | ||||||||
\(707\) | −20.9095 | − | 3.60739i | −0.786384 | − | 0.135670i | ||||
\(708\) | 7.55711 | 0.284014 | ||||||||
\(709\) | 13.6161 | + | 7.86128i | 0.511365 | + | 0.295237i | 0.733394 | − | 0.679803i | \(-0.237935\pi\) |
−0.222030 | + | 0.975040i | \(0.571268\pi\) | |||||||
\(710\) | −14.5891 | − | 25.2690i | −0.547518 | − | 0.948328i | ||||
\(711\) | −9.79501 | + | 5.65515i | −0.367341 | + | 0.212085i | ||||
\(712\) | −6.80960 | + | 11.7946i | −0.255201 | + | 0.442021i | ||||
\(713\) | 13.4681 | + | 3.13426i | 0.504384 | + | 0.117379i | ||||
\(714\) | 3.01161 | + | 0.519575i | 0.112707 | + | 0.0194446i | ||||
\(715\) | −38.7344 | −1.44859 | ||||||||
\(716\) | 2.79957 | − | 4.84900i | 0.104625 | − | 0.181216i | ||||
\(717\) | −12.3109 | + | 7.10768i | −0.459758 | + | 0.265441i | ||||
\(718\) | 11.5930 | − | 6.69322i | 0.432647 | − | 0.249789i | ||||
\(719\) | 19.1661 | + | 11.0655i | 0.714775 | + | 0.412675i | 0.812826 | − | 0.582506i | \(-0.197928\pi\) |
−0.0980518 | + | 0.995181i | \(0.531261\pi\) | |||||||
\(720\) | −4.05937 | −0.151284 | ||||||||
\(721\) | 18.9417 | − | 6.97350i | 0.705426 | − | 0.259707i | ||||
\(722\) | −23.9936 | −0.892950 | ||||||||
\(723\) | −14.0325 | − | 8.10166i | −0.521874 | − | 0.301304i | ||||
\(724\) | 11.2979 | + | 19.5686i | 0.419884 | + | 0.727260i | ||||
\(725\) | 36.8811 | + | 63.8799i | 1.36973 | + | 2.37244i | ||||
\(726\) | 18.1912 | + | 10.5027i | 0.675139 | + | 0.389792i | ||||
\(727\) | −5.61811 | −0.208364 | −0.104182 | − | 0.994558i | \(-0.533222\pi\) | ||||
−0.104182 | + | 0.994558i | \(0.533222\pi\) | |||||||
\(728\) | −2.85579 | + | 3.42902i | −0.105843 | + | 0.127088i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −39.0751 | − | 22.5600i | −1.44623 | − | 0.834984i | ||||
\(731\) | 1.32538 | − | 0.765211i | 0.0490211 | − | 0.0283023i | ||||
\(732\) | −9.01591 | + | 5.20534i | −0.333238 | + | 0.192395i | ||||
\(733\) | 13.2866 | − | 23.0130i | 0.490751 | − | 0.850006i | −0.509192 | − | 0.860653i | \(-0.670056\pi\) |
0.999943 | + | 0.0106469i | \(0.00338909\pi\) | |||||||
\(734\) | 12.5291 | 0.462458 | ||||||||
\(735\) | 27.9467 | − | 5.14076i | 1.03083 | − | 0.189620i | ||||
\(736\) | 1.08702 | − | 4.67101i | 0.0400683 | − | 0.172176i | ||||
\(737\) | 16.0963 | − | 27.8796i | 0.592915 | − | 1.02696i | ||||
\(738\) | −4.93795 | + | 2.85093i | −0.181769 | + | 0.104944i | ||||
\(739\) | −9.73154 | − | 16.8555i | −0.357981 | − | 0.620041i | 0.629643 | − | 0.776885i | \(-0.283201\pi\) |
−0.987623 | + | 0.156844i | \(0.949868\pi\) | |||||||
\(740\) | 7.70334 | + | 4.44753i | 0.283180 | + | 0.163494i | ||||
\(741\) | 11.0593 | 0.406275 | ||||||||
\(742\) | −3.63205 | + | 4.36110i | −0.133337 | + | 0.160101i | ||||
\(743\) | − | 45.3501i | − | 1.66373i | −0.554975 | − | 0.831867i | \(-0.687272\pi\) | ||
0.554975 | − | 0.831867i | \(-0.312728\pi\) | |||||||
\(744\) | −1.44167 | + | 2.49704i | −0.0528541 | + | 0.0915460i | ||||
\(745\) | 55.6468 | − | 32.1277i | 2.03874 | − | 1.17707i | ||||
\(746\) | −8.52214 | + | 4.92026i | −0.312018 | + | 0.180144i | ||||
\(747\) | −0.423955 | + | 0.734312i | −0.0155117 | + | 0.0268671i | ||||
\(748\) | − | 6.53478i | − | 0.238935i | ||||||
\(749\) | 6.48756 | + | 17.6218i | 0.237050 | + | 0.643885i | ||||
\(750\) | 26.2986i | 0.960288i | ||||||||
\(751\) | 29.0897 | + | 16.7950i | 1.06150 | + | 0.612857i | 0.925847 | − | 0.377900i | \(-0.123354\pi\) |
0.135652 | + | 0.990756i | \(0.456687\pi\) | |||||||
\(752\) | −3.82275 | + | 2.20707i | −0.139401 | + | 0.0804834i | ||||
\(753\) | −8.71899 | + | 5.03391i | −0.317737 | + | 0.183446i | ||||
\(754\) | 9.38657 | + | 5.41934i | 0.341839 | + | 0.197361i | ||||
\(755\) | −62.8647 | −2.28788 | ||||||||
\(756\) | 2.60723 | + | 0.449810i | 0.0948242 | + | 0.0163594i | ||||
\(757\) | 12.3995i | 0.450669i | 0.974281 | + | 0.225335i | \(0.0723475\pi\) | ||||
−0.974281 | + | 0.225335i | \(0.927652\pi\) | |||||||
\(758\) | 8.90029 | + | 5.13858i | 0.323273 | + | 0.186642i | ||||
\(759\) | −25.9600 | + | 7.88698i | −0.942287 | + | 0.286279i | ||||
\(760\) | −13.3085 | − | 23.0511i | −0.482752 | − | 0.836150i | ||||
\(761\) | −3.23071 | − | 1.86525i | −0.117113 | − | 0.0676152i | 0.440299 | − | 0.897851i | \(-0.354872\pi\) |
−0.557412 | + | 0.830236i | \(0.688206\pi\) | |||||||
\(762\) | − | 6.74682i | − | 0.244411i | ||||||
\(763\) | −45.5413 | − | 7.85695i | −1.64871 | − | 0.284441i | ||||
\(764\) | − | 5.28230i | − | 0.191107i | ||||||
\(765\) | 2.34449 | − | 4.06077i | 0.0847651 | − | 0.146817i | ||||
\(766\) | 8.84461 | + | 15.3193i | 0.319569 | + | 0.553510i | ||||
\(767\) | −6.37313 | − | 11.0386i | −0.230120 | − | 0.398580i | ||||
\(768\) | 0.866025 | + | 0.500000i | 0.0312500 | + | 0.0180422i | ||||
\(769\) | 22.5407 | 0.812837 | 0.406418 | − | 0.913687i | \(-0.366778\pi\) | ||||
0.406418 | + | 0.913687i | \(0.366778\pi\) | |||||||
\(770\) | −20.9918 | − | 57.0188i | −0.756493 | − | 2.05482i | ||||
\(771\) | 19.8048 | 0.713252 | ||||||||
\(772\) | −13.3588 | + | 23.1381i | −0.480794 | + | 0.832759i | ||||
\(773\) | −1.13116 | − | 1.95922i | −0.0406850 | − | 0.0704684i | 0.844966 | − | 0.534820i | \(-0.179621\pi\) |
−0.885651 | + | 0.464352i | \(0.846287\pi\) | |||||||
\(774\) | 1.14742 | − | 0.662464i | 0.0412432 | − | 0.0238118i | ||||
\(775\) | 28.6623 | + | 16.5482i | 1.02958 | + | 0.594428i | ||||
\(776\) | −4.92590 | −0.176829 | ||||||||
\(777\) | −4.45485 | − | 3.71013i | −0.159817 | − | 0.133100i | ||||
\(778\) | 32.1153i | 1.15139i | ||||||||
\(779\) | −32.3779 | − | 18.6934i | −1.16006 | − | 0.669761i | ||||
\(780\) | 3.42338 | + | 5.92947i | 0.122577 | + | 0.212309i | ||||
\(781\) | 35.2161 | − | 20.3320i | 1.26013 | − | 0.727536i | ||||
\(782\) | 4.04481 | + | 3.78514i | 0.144642 | + | 0.135356i | ||||
\(783\) | − | 6.42612i | − | 0.229651i | ||||||
\(784\) | −6.59534 | − | 2.34552i | −0.235548 | − | 0.0837685i | ||||
\(785\) | −16.8388 | −0.601003 | ||||||||
\(786\) | −2.76739 | + | 4.79326i | −0.0987095 | + | 0.170970i | ||||
\(787\) | −5.09861 | − | 8.83105i | −0.181746 | − | 0.314793i | 0.760729 | − | 0.649069i | \(-0.224841\pi\) |
−0.942475 | + | 0.334276i | \(0.891508\pi\) | |||||||
\(788\) | −7.08025 | − | 12.2634i | −0.252224 | − | 0.436864i | ||||
\(789\) | 6.72970 | − | 11.6562i | 0.239583 | − | 0.414971i | ||||
\(790\) | − | 45.9127i | − | 1.63350i | ||||||
\(791\) | −14.9636 | + | 17.9672i | −0.532045 | + | 0.638840i | ||||
\(792\) | − | 5.65733i | − | 0.201025i | ||||||
\(793\) | 15.2068 | + | 8.77963i | 0.540008 | + | 0.311774i | ||||
\(794\) | −16.1963 | + | 9.35091i | −0.574784 | + | 0.331852i | ||||
\(795\) | 4.35393 | + | 7.54124i | 0.154418 | + | 0.267460i | ||||
\(796\) | −11.6374 | + | 20.1566i | −0.412477 | + | 0.714432i | ||||
\(797\) | −42.3104 | −1.49871 | −0.749355 | − | 0.662168i | \(-0.769636\pi\) | ||||
−0.749355 | + | 0.662168i | \(0.769636\pi\) | |||||||
\(798\) | 5.99352 | + | 16.2798i | 0.212168 | + | 0.576300i | ||||
\(799\) | − | 5.09876i | − | 0.180381i | ||||||
\(800\) | 5.73924 | − | 9.94066i | 0.202913 | − | 0.351455i | ||||
\(801\) | −6.80960 | − | 11.7946i | −0.240606 | − | 0.416741i | ||||
\(802\) | −14.8691 | + | 8.58467i | −0.525046 | + | 0.303135i | ||||
\(803\) | 31.4407 | − | 54.4569i | 1.10952 | − | 1.92174i | ||||
\(804\) | −5.69042 | −0.200686 | ||||||||
\(805\) | 47.4519 | + | 20.0338i | 1.67246 | + | 0.706098i | ||||
\(806\) | 4.86320 | 0.171299 | ||||||||
\(807\) | 8.61345 | − | 14.9189i | 0.303208 | − | 0.525171i | ||||
\(808\) | 6.94536 | − | 4.00991i | 0.244337 | − | 0.141068i | ||||
\(809\) | 5.12273 | + | 8.87283i | 0.180106 | + | 0.311952i | 0.941916 | − | 0.335848i | \(-0.109023\pi\) |
−0.761811 | + | 0.647800i | \(0.775689\pi\) | |||||||
\(810\) | 2.02969 | − | 3.51552i | 0.0713159 | − | 0.123523i | ||||
\(811\) | − | 0.00263642i | − | 9.25771e-5i | −1.00000 | 4.62885e-5i | \(-0.999985\pi\) | |||
1.00000 | 4.62885e-5i | \(-1.47341e-5\pi\) | ||||||||
\(812\) | −2.89053 | + | 16.7544i | −0.101438 | + | 0.587965i | ||||
\(813\) | −19.9765 | −0.700606 | ||||||||
\(814\) | −6.19828 | + | 10.7357i | −0.217250 | + | 0.376288i | ||||
\(815\) | 42.3212 | + | 73.3025i | 1.48245 | + | 2.56767i | ||||
\(816\) | −1.00034 | + | 0.577549i | −0.0350191 | + | 0.0202183i | ||||
\(817\) | 7.52358 | + | 4.34374i | 0.263217 | + | 0.151968i | ||||
\(818\) | 10.0420i | 0.351111i | ||||||||
\(819\) | −1.54172 | − | 4.18769i | −0.0538722 | − | 0.146330i | ||||
\(820\) | − | 23.1459i | − | 0.808292i | ||||||
\(821\) | 15.5493 | − | 26.9322i | 0.542675 | − | 0.939941i | −0.456074 | − | 0.889942i | \(-0.650745\pi\) |
0.998749 | − | 0.0499989i | \(-0.0159218\pi\) | |||||||
\(822\) | −9.20385 | − | 15.9415i | −0.321021 | − | 0.556025i | ||||
\(823\) | 11.5987 | + | 20.0896i | 0.404306 | + | 0.700278i | 0.994240 | − | 0.107173i | \(-0.0341799\pi\) |
−0.589935 | + | 0.807451i | \(0.700847\pi\) | |||||||
\(824\) | −3.81453 | + | 6.60696i | −0.132886 | + | 0.230164i | ||||
\(825\) | −64.9376 | −2.26084 | ||||||||
\(826\) | 12.7954 | − | 15.3638i | 0.445210 | − | 0.534575i | ||||
\(827\) | − | 50.8112i | − | 1.76688i | −0.468547 | − | 0.883439i | \(-0.655222\pi\) | ||
0.468547 | − | 0.883439i | \(-0.344778\pi\) | |||||||
\(828\) | 3.50171 | + | 3.27690i | 0.121693 | + | 0.113880i | ||||
\(829\) | 32.1953 | − | 18.5880i | 1.11819 | − | 0.645587i | 0.177252 | − | 0.984166i | \(-0.443279\pi\) |
0.940938 | + | 0.338578i | \(0.109946\pi\) | |||||||
\(830\) | −1.72099 | − | 2.98084i | −0.0597365 | − | 0.103467i | ||||
\(831\) | 8.55786 | + | 4.94088i | 0.296869 | + | 0.171397i | ||||
\(832\) | − | 1.68666i | − | 0.0584743i | ||||||
\(833\) | 6.15546 | − | 5.24296i | 0.213274 | − | 0.181658i | ||||
\(834\) | −20.4754 | −0.709006 | ||||||||
\(835\) | 38.6256 | + | 22.3005i | 1.33669 | + | 0.771740i | ||||
\(836\) | 32.1251 | − | 18.5474i | 1.11107 | − | 0.641476i | ||||
\(837\) | −1.44167 | − | 2.49704i | −0.0498313 | − | 0.0863104i | ||||
\(838\) | 18.3532 | − | 31.7886i | 0.633999 | − | 1.09812i | ||||
\(839\) | 32.6237 | 1.12629 | 0.563147 | − | 0.826357i | \(-0.309590\pi\) | ||||
0.563147 | + | 0.826357i | \(0.309590\pi\) | |||||||
\(840\) | −6.87318 | + | 8.25281i | −0.237147 | + | 0.284749i | ||||
\(841\) | 12.2951 | 0.423968 | ||||||||
\(842\) | 1.51067 | + | 0.872186i | 0.0520611 | + | 0.0300575i | ||||
\(843\) | 9.72928 | + | 16.8516i | 0.335094 | + | 0.580400i | ||||
\(844\) | 1.29754 | + | 2.24741i | 0.0446633 | + | 0.0773591i | ||||
\(845\) | −20.6118 | + | 35.7007i | −0.709069 | + | 1.22814i | ||||
\(846\) | − | 4.41413i | − | 0.151761i | ||||||
\(847\) | 52.1530 | − | 19.2004i | 1.79200 | − | 0.659734i | ||||
\(848\) | − | 2.14513i | − | 0.0736640i | ||||||
\(849\) | −26.3573 | − | 15.2174i | −0.904581 | − | 0.522260i | ||||
\(850\) | 6.62939 | + | 11.4824i | 0.227386 | + | 0.393845i | ||||
\(851\) | −3.05484 | − | 10.0550i | −0.104719 | − | 0.344681i | ||||
\(852\) | −6.22486 | − | 3.59392i | −0.213260 | − | 0.123126i | ||||
\(853\) | 19.3294i | 0.661828i | 0.943661 | + | 0.330914i | \(0.107357\pi\) | ||||
−0.943661 | + | 0.330914i | \(0.892643\pi\) | |||||||
\(854\) | −4.68283 | + | 27.1431i | −0.160243 | + | 0.928817i | ||||
\(855\) | 26.6171 | 0.910285 | ||||||||
\(856\) | −6.14656 | − | 3.54872i | −0.210085 | − | 0.121293i | ||||
\(857\) | 0.785476 | − | 0.453495i | 0.0268314 | − | 0.0154911i | −0.486524 | − | 0.873667i | \(-0.661736\pi\) |
0.513356 | + | 0.858176i | \(0.328402\pi\) | |||||||
\(858\) | −8.26360 | + | 4.77099i | −0.282115 | + | 0.162879i | ||||
\(859\) | −40.8309 | − | 23.5737i | −1.39313 | − | 0.804324i | −0.399470 | − | 0.916746i | \(-0.630806\pi\) |
−0.993661 | + | 0.112422i | \(0.964139\pi\) | |||||||
\(860\) | 5.37837i | 0.183401i | ||||||||
\(861\) | −2.56475 | + | 14.8661i | −0.0874065 | + | 0.506635i | ||||
\(862\) | 14.3097i | 0.487392i | ||||||||
\(863\) | −7.34726 | + | 12.7258i | −0.250104 | + | 0.433192i | −0.963554 | − | 0.267513i | \(-0.913798\pi\) |
0.713450 | + | 0.700706i | \(0.247131\pi\) | |||||||
\(864\) | −0.866025 | + | 0.500000i | −0.0294628 | + | 0.0170103i | ||||
\(865\) | −7.27613 | + | 4.20088i | −0.247396 | + | 0.142834i | ||||
\(866\) | 8.96794 | − | 15.5329i | 0.304743 | − | 0.527830i | ||||
\(867\) | 15.6657i | 0.532037i | ||||||||
\(868\) | 2.63557 | + | 7.15885i | 0.0894572 | + | 0.242987i | ||||
\(869\) | 63.9861 | 2.17058 | ||||||||
\(870\) | 22.5912 | + | 13.0430i | 0.765912 | + | 0.442199i | ||||
\(871\) | 4.79890 | + | 8.31194i | 0.162604 | + | 0.281639i | ||||
\(872\) | 15.1271 | − | 8.73364i | 0.512268 | − | 0.295758i | ||||
\(873\) | 2.46295 | − | 4.26595i | 0.0833582 | − | 0.144381i | ||||
\(874\) | −7.12757 | + | 30.6276i | −0.241094 | + | 1.03599i | ||||
\(875\) | 53.4657 | + | 44.5278i | 1.80747 | + | 1.50531i | ||||
\(876\) | −11.1150 | −0.375542 | ||||||||
\(877\) | 9.56932 | − | 16.5746i | 0.323133 | − | 0.559683i | −0.658000 | − | 0.753018i | \(-0.728597\pi\) |
0.981133 | + | 0.193335i | \(0.0619305\pi\) | |||||||
\(878\) | −28.0581 | + | 16.1994i | −0.946916 | + | 0.546702i | ||||
\(879\) | 13.6489 | − | 7.88021i | 0.460367 | − | 0.265793i | ||||
\(880\) | 19.8884 | + | 11.4826i | 0.670439 | + | 0.387078i | ||||
\(881\) | 0.0981784 | 0.00330771 | 0.00165386 | − | 0.999999i | \(-0.499474\pi\) | ||||
0.00165386 | + | 0.999999i | \(0.499474\pi\) | |||||||
\(882\) | 5.32895 | − | 4.53897i | 0.179435 | − | 0.152835i | ||||
\(883\) | −27.4328 | −0.923186 | −0.461593 | − | 0.887092i | \(-0.652722\pi\) | ||||
−0.461593 | + | 0.887092i | \(0.652722\pi\) | |||||||
\(884\) | 1.68724 | + | 0.974128i | 0.0567480 | + | 0.0327635i | ||||
\(885\) | −15.3386 | − | 26.5672i | −0.515600 | − | 0.893045i | ||||
\(886\) | 19.0976 | + | 33.0780i | 0.641597 | + | 1.11128i | ||||
\(887\) | −29.6506 | − | 17.1188i | −0.995571 | − | 0.574793i | −0.0886359 | − | 0.996064i | \(-0.528251\pi\) |
−0.906935 | + | 0.421271i | \(0.861584\pi\) | |||||||
\(888\) | 2.19124 | 0.0735332 | ||||||||
\(889\) | −13.7165 | − | 11.4235i | −0.460035 | − | 0.383131i | ||||
\(890\) | 55.2854 | 1.85317 | ||||||||
\(891\) | 4.89939 | + | 2.82867i | 0.164136 | + | 0.0947639i | ||||
\(892\) | 10.0313 | − | 5.79156i | 0.335872 | − | 0.193916i | ||||
\(893\) | 25.0656 | − | 14.4716i | 0.838788 | − | 0.484275i | ||||
\(894\) | 7.91446 | − | 13.7082i | 0.264699 | − | 0.458472i | ||||
\(895\) | −22.7290 | −0.759746 | ||||||||
\(896\) | 2.48284 | − | 0.914071i | 0.0829457 | − | 0.0305370i | ||||
\(897\) | 1.83344 | − | 7.87840i | 0.0612167 | − | 0.263052i | ||||
\(898\) | 7.04610 | − | 12.2042i | 0.235131 | − | 0.407259i | ||||
\(899\) | 16.0463 | − | 9.26434i | 0.535174 | − | 0.308983i | ||||
\(900\) | 5.73924 | + | 9.94066i | 0.191308 | + | 0.331355i | ||||
\(901\) | 2.14587 | + | 1.23892i | 0.0714892 | + | 0.0412743i | ||||
\(902\) | 32.2573 | 1.07405 | ||||||||
\(903\) | 0.595965 | − | 3.45440i | 0.0198325 | − | 0.114955i | ||||
\(904\) | − | 8.83766i | − | 0.293936i | ||||||
\(905\) | 45.8624 | − | 79.4361i | 1.52452 | − | 2.64054i | ||||
\(906\) | −13.4115 | + | 7.74316i | −0.445569 | + | 0.257249i | ||||
\(907\) | −28.9373 | + | 16.7069i | −0.960846 | + | 0.554745i | −0.896433 | − | 0.443179i | \(-0.853851\pi\) |
−0.0644125 | + | 0.997923i | \(0.520517\pi\) | |||||||
\(908\) | 3.86164 | − | 6.68855i | 0.128153 | − | 0.221967i | ||||
\(909\) | 8.01981i | 0.266000i | ||||||||
\(910\) | 17.8511 | + | 3.07974i | 0.591759 | + | 0.102092i | ||||
\(911\) | − | 15.0207i | − | 0.497659i | −0.968547 | − | 0.248830i | \(-0.919954\pi\) | ||
0.968547 | − | 0.248830i | \(-0.0800460\pi\) | |||||||
\(912\) | −5.67849 | − | 3.27848i | −0.188033 | − | 0.108561i | ||||
\(913\) | 4.15424 | − | 2.39845i | 0.137485 | − | 0.0793773i | ||||
\(914\) | −3.70638 | + | 2.13988i | −0.122596 | + | 0.0707809i | ||||
\(915\) | 36.5989 | + | 21.1304i | 1.20992 | + | 0.698550i | ||||
\(916\) | 22.0003 | 0.726912 | ||||||||
\(917\) | 5.05918 | + | 13.7419i | 0.167069 | + | 0.453799i | ||||
\(918\) | − | 1.15510i | − | 0.0381239i | ||||||
\(919\) | 41.5218 | + | 23.9726i | 1.36968 | + | 0.790784i | 0.990887 | − | 0.134698i | \(-0.0430064\pi\) |
0.378792 | + | 0.925482i | \(0.376340\pi\) | |||||||
\(920\) | −18.6274 | + | 5.65923i | −0.614126 | + | 0.186579i | ||||
\(921\) | 3.94100 | + | 6.82601i | 0.129860 | + | 0.224925i | ||||
\(922\) | 6.18859 | + | 3.57298i | 0.203810 | + | 0.117670i | ||||
\(923\) | 12.1234i | 0.399048i | ||||||||
\(924\) | −11.5015 | − | 9.57879i | −0.378372 | − | 0.315119i | ||||
\(925\) | − | 25.1521i | − | 0.826996i | ||||||
\(926\) | 1.41770 | − | 2.45553i | 0.0465885 | − | 0.0806937i | ||||
\(927\) | −3.81453 | − | 6.60696i | −0.125286 | − | 0.217001i | ||||
\(928\) | −3.21306 | − | 5.56519i | −0.105474 | − | 0.182686i | ||||
\(929\) | 35.9751 | + | 20.7702i | 1.18030 | + | 0.681449i | 0.956085 | − | 0.293090i | \(-0.0946836\pi\) |
0.224219 | + | 0.974539i | \(0.428017\pi\) | |||||||
\(930\) | 11.7045 | 0.383807 | ||||||||
\(931\) | 43.2453 | + | 15.3795i | 1.41731 | + | 0.504041i | ||||
\(932\) | 23.4567 | 0.768350 | ||||||||
\(933\) | −9.16702 | + | 15.8777i | −0.300115 | + | 0.519814i | ||||
\(934\) | −12.7367 | − | 22.0606i | −0.416757 | − | 0.721845i | ||||
\(935\) | −22.9731 | + | 13.2635i | −0.751301 | + | 0.433764i | ||||
\(936\) | 1.46069 | + | 0.843329i | 0.0477441 | + | 0.0275651i | ||||
\(937\) | 1.07710 | 0.0351873 | 0.0175937 | − | 0.999845i | \(-0.494399\pi\) | ||||
0.0175937 | + | 0.999845i | \(0.494399\pi\) | |||||||
\(938\) | −9.63482 | + | 11.5688i | −0.314588 | + | 0.377734i | ||||
\(939\) | − | 12.4033i | − | 0.404768i | ||||||
\(940\) | 15.5180 | + | 8.95930i | 0.506140 | + | 0.292220i | ||||
\(941\) | 8.11695 | + | 14.0590i | 0.264605 | + | 0.458309i | 0.967460 | − | 0.253024i | \(-0.0814251\pi\) |
−0.702855 | + | 0.711333i | \(0.748092\pi\) | |||||||
\(942\) | −3.59239 | + | 2.07407i | −0.117046 | + | 0.0675768i | ||||
\(943\) | −18.6844 | + | 19.9662i | −0.608448 | + | 0.650190i | ||||
\(944\) | 7.55711i | 0.245963i | ||||||||
\(945\) | −3.71055 | − | 10.0788i | −0.120704 | − | 0.327862i | ||||
\(946\) | −7.49555 | −0.243701 | ||||||||
\(947\) | −2.86317 | + | 4.95916i | −0.0930405 | + | 0.161151i | −0.908789 | − | 0.417256i | \(-0.862992\pi\) |
0.815749 | + | 0.578407i | \(0.196325\pi\) | |||||||
\(948\) | −5.65515 | − | 9.79501i | −0.183671 | − | 0.318127i | ||||
\(949\) | 9.37363 | + | 16.2356i | 0.304281 | + | 0.527030i | ||||
\(950\) | −37.6319 | + | 65.1804i | −1.22094 | + | 2.11473i | ||||
\(951\) | 3.67969i | 0.119322i | ||||||||
\(952\) | −0.519575 | + | 3.01161i | −0.0168395 | + | 0.0976069i | ||||
\(953\) | 6.77880i | 0.219587i | 0.993954 | + | 0.109793i | \(0.0350189\pi\) | ||||
−0.993954 | + | 0.109793i | \(0.964981\pi\) | |||||||
\(954\) | 1.85774 | + | 1.07256i | 0.0601464 | + | 0.0347255i | ||||
\(955\) | −18.5700 | + | 10.7214i | −0.600912 | + | 0.346936i | ||||
\(956\) | −7.10768 | − | 12.3109i | −0.229879 | − | 0.398162i | ||||
\(957\) | −18.1774 | + | 31.4841i | −0.587591 | + | 1.01774i | ||||
\(958\) | 19.2180 | 0.620905 | ||||||||
\(959\) | −47.9932 | − | 8.27996i | −1.54978 | − | 0.267374i | ||||
\(960\) | − | 4.05937i | − | 0.131016i | ||||||
\(961\) | −11.3432 | + | 19.6470i | −0.365909 | + | 0.633773i | ||||
\(962\) | −1.84794 | − | 3.20072i | −0.0595798 | − | 0.103195i | ||||
\(963\) | 6.14656 | − | 3.54872i | 0.198070 | − | 0.114356i | ||||
\(964\) | 8.10166 | − | 14.0325i | 0.260937 | − | 0.451956i | ||||
\(965\) | 108.457 | 3.49134 | ||||||||
\(966\) | 12.5910 | − | 1.57073i | 0.405108 | − | 0.0505375i | ||||
\(967\) | −14.4508 | −0.464705 | −0.232353 | − | 0.972632i | \(-0.574642\pi\) | ||||
−0.232353 | + | 0.972632i | \(0.574642\pi\) | |||||||
\(968\) | −10.5027 | + | 18.1912i | −0.337570 | + | 0.584688i | ||||
\(969\) | 6.55921 | − | 3.78696i | 0.210712 | − | 0.121655i | ||||
\(970\) | 9.99802 | + | 17.3171i | 0.321017 | + | 0.556018i | ||||
\(971\) | −8.92641 | + | 15.4610i | −0.286462 | + | 0.496167i | −0.972963 | − | 0.230962i | \(-0.925813\pi\) |
0.686501 | + | 0.727129i | \(0.259146\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | −34.6682 | + | 41.6271i | −1.11141 | + | 1.33450i | ||||
\(974\) | −30.3625 | −0.972876 | ||||||||
\(975\) | 9.68014 | − | 16.7665i | 0.310013 | − | 0.536957i | ||||
\(976\) | −5.20534 | − | 9.01591i | −0.166619 | − | 0.288592i | ||||
\(977\) | −39.1189 | + | 22.5853i | −1.25152 | + | 0.722568i | −0.971412 | − | 0.237400i | \(-0.923705\pi\) |
−0.280112 | + | 0.959967i | \(0.590372\pi\) | |||||||
\(978\) | 18.0576 | + | 10.4256i | 0.577419 | + | 0.333373i | ||||
\(979\) | 77.0484i | 2.46248i | ||||||||
\(980\) | 5.14076 | + | 27.9467i | 0.164215 | + | 0.892725i | ||||
\(981\) | 17.4673i | 0.557687i | ||||||||
\(982\) | 4.25335 | − | 7.36701i | 0.135730 | − | 0.235091i | ||||
\(983\) | −10.9144 | − | 18.9044i | −0.348117 | − | 0.602956i | 0.637798 | − | 0.770204i | \(-0.279845\pi\) |
−0.985915 | + | 0.167248i | \(0.946512\pi\) | |||||||
\(984\) | −2.85093 | − | 4.93795i | −0.0908843 | − | 0.157416i | ||||
\(985\) | −28.7414 | + | 49.7815i | −0.915776 | + | 1.58617i | ||||
\(986\) | 7.42281 | 0.236390 | ||||||||
\(987\) | −8.97405 | − | 7.47385i | −0.285647 | − | 0.237895i | ||||
\(988\) | 11.0593i | 0.351844i | ||||||||
\(989\) | 4.34165 | − | 4.63950i | 0.138056 | − | 0.147528i | ||||
\(990\) | −19.8884 | + | 11.4826i | −0.632096 | + | 0.364941i | ||||
\(991\) | −10.9207 | − | 18.9151i | −0.346906 | − | 0.600859i | 0.638792 | − | 0.769379i | \(-0.279434\pi\) |
−0.985698 | + | 0.168520i | \(0.946101\pi\) | |||||||
\(992\) | −2.49704 | − | 1.44167i | −0.0792812 | − | 0.0457730i | ||||
\(993\) | − | 4.90826i | − | 0.155759i | ||||||
\(994\) | −17.8462 | + | 6.57020i | −0.566048 | + | 0.208394i | ||||
\(995\) | 94.4812 | 2.99525 | ||||||||
\(996\) | −0.734312 | − | 0.423955i | −0.0232676 | − | 0.0134335i | ||||
\(997\) | 49.4147 | − | 28.5296i | 1.56498 | − | 0.903542i | 0.568240 | − | 0.822863i | \(-0.307624\pi\) |
0.996740 | − | 0.0806791i | \(-0.0257089\pi\) | |||||||
\(998\) | 6.28157 | + | 10.8800i | 0.198840 | + | 0.344400i | ||||
\(999\) | −1.09562 | + | 1.89767i | −0.0346639 | + | 0.0600396i |
(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 | 966.2.k.b.229.1 | ✓ | 32 | |
7.3 | odd | 6 | inner | 966.2.k.b.367.8 | yes | 32 | |
23.22 | odd | 2 | inner | 966.2.k.b.229.8 | yes | 32 | |
161.45 | even | 6 | inner | 966.2.k.b.367.1 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.k.b.229.1 | ✓ | 32 | 1.1 | even | 1 | trivial | |
966.2.k.b.229.8 | yes | 32 | 23.22 | odd | 2 | inner | |
966.2.k.b.367.1 | yes | 32 | 161.45 | even | 6 | inner | |
966.2.k.b.367.8 | yes | 32 | 7.3 | odd | 6 | inner |