Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [670,2,Mod(171,670)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(670, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("670.171");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 670 = 2 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 670.e (of order \(3\), 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: | \(5.34997693543\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 431.2 | ||
Root | \(-1.22474 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 670.431 |
Dual form | 670.2.e.f.171.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/670\mathbb{Z}\right)^\times\).
\(n\) | \(471\) | \(537\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||
\(3\) | 3.44949 | 1.99156 | 0.995782 | − | 0.0917517i | \(-0.0292466\pi\) | ||||
0.995782 | + | 0.0917517i | \(0.0292466\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.72474 | + | 2.98735i | −0.704124 | + | 1.21958i | ||||
\(7\) | −2.22474 | − | 3.85337i | −0.840875 | − | 1.45644i | −0.889156 | − | 0.457604i | \(-0.848708\pi\) |
0.0482818 | − | 0.998834i | \(-0.484625\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 8.89898 | 2.96633 | ||||||||
\(10\) | 0.500000 | − | 0.866025i | 0.158114 | − | 0.273861i | ||||
\(11\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(12\) | −1.72474 | − | 2.98735i | −0.497891 | − | 0.862372i | ||||
\(13\) | 2.00000 | − | 3.46410i | 0.554700 | − | 0.960769i | −0.443227 | − | 0.896410i | \(-0.646166\pi\) |
0.997927 | − | 0.0643593i | \(-0.0205004\pi\) | |||||||
\(14\) | 4.44949 | 1.18918 | ||||||||
\(15\) | −3.44949 | −0.890654 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −2.22474 | + | 3.85337i | −0.539580 | + | 0.934580i | 0.459347 | + | 0.888257i | \(0.348084\pi\) |
−0.998927 | + | 0.0463227i | \(0.985250\pi\) | |||||||
\(18\) | −4.44949 | + | 7.70674i | −1.04875 | + | 1.81650i | ||||
\(19\) | 3.44949 | − | 5.97469i | 0.791367 | − | 1.37069i | −0.133753 | − | 0.991015i | \(-0.542703\pi\) |
0.925121 | − | 0.379674i | \(-0.123964\pi\) | |||||||
\(20\) | 0.500000 | + | 0.866025i | 0.111803 | + | 0.193649i | ||||
\(21\) | −7.67423 | − | 13.2922i | −1.67466 | − | 2.90059i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.22474 | + | 2.12132i | −0.255377 | + | 0.442326i | −0.964998 | − | 0.262258i | \(-0.915533\pi\) |
0.709621 | + | 0.704584i | \(0.248866\pi\) | |||||||
\(24\) | 3.44949 | 0.704124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.00000 | + | 3.46410i | 0.392232 | + | 0.679366i | ||||
\(27\) | 20.3485 | 3.91606 | ||||||||
\(28\) | −2.22474 | + | 3.85337i | −0.420437 | + | 0.728219i | ||||
\(29\) | 3.00000 | + | 5.19615i | 0.557086 | + | 0.964901i | 0.997738 | + | 0.0672232i | \(0.0214140\pi\) |
−0.440652 | + | 0.897678i | \(0.645253\pi\) | |||||||
\(30\) | 1.72474 | − | 2.98735i | 0.314894 | − | 0.545412i | ||||
\(31\) | 0.275255 | + | 0.476756i | 0.0494373 | + | 0.0856279i | 0.889685 | − | 0.456575i | \(-0.150924\pi\) |
−0.840248 | + | 0.542203i | \(0.817591\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.22474 | − | 3.85337i | −0.381541 | − | 0.660848i | ||||
\(35\) | 2.22474 | + | 3.85337i | 0.376051 | + | 0.651339i | ||||
\(36\) | −4.44949 | − | 7.70674i | −0.741582 | − | 1.28446i | ||||
\(37\) | −2.94949 | + | 5.10867i | −0.484893 | + | 0.839860i | −0.999849 | − | 0.0173569i | \(-0.994475\pi\) |
0.514956 | + | 0.857216i | \(0.327808\pi\) | |||||||
\(38\) | 3.44949 | + | 5.97469i | 0.559581 | + | 0.969223i | ||||
\(39\) | 6.89898 | − | 11.9494i | 1.10472 | − | 1.91343i | ||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 1.05051 | + | 1.81954i | 0.164062 | + | 0.284164i | 0.936322 | − | 0.351143i | \(-0.114207\pi\) |
−0.772260 | + | 0.635307i | \(0.780874\pi\) | |||||||
\(42\) | 15.3485 | 2.36832 | ||||||||
\(43\) | 4.00000 | 0.609994 | 0.304997 | − | 0.952353i | \(-0.401344\pi\) | ||||
0.304997 | + | 0.952353i | \(0.401344\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −8.89898 | −1.32658 | ||||||||
\(46\) | −1.22474 | − | 2.12132i | −0.180579 | − | 0.312772i | ||||
\(47\) | −3.67423 | − | 6.36396i | −0.535942 | − | 0.928279i | −0.999117 | − | 0.0420122i | \(-0.986623\pi\) |
0.463175 | − | 0.886267i | \(-0.346710\pi\) | |||||||
\(48\) | −1.72474 | + | 2.98735i | −0.248945 | + | 0.431186i | ||||
\(49\) | −6.39898 | + | 11.0834i | −0.914140 | + | 1.58334i | ||||
\(50\) | −0.500000 | + | 0.866025i | −0.0707107 | + | 0.122474i | ||||
\(51\) | −7.67423 | + | 13.2922i | −1.07461 | + | 1.86128i | ||||
\(52\) | −4.00000 | −0.554700 | ||||||||
\(53\) | −7.00000 | −0.961524 | −0.480762 | − | 0.876851i | \(-0.659640\pi\) | ||||
−0.480762 | + | 0.876851i | \(0.659640\pi\) | |||||||
\(54\) | −10.1742 | + | 17.6223i | −1.38454 | + | 2.39809i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.22474 | − | 3.85337i | −0.297294 | − | 0.514928i | ||||
\(57\) | 11.8990 | − | 20.6096i | 1.57606 | − | 2.72981i | ||||
\(58\) | −6.00000 | −0.787839 | ||||||||
\(59\) | −6.89898 | −0.898171 | −0.449085 | − | 0.893489i | \(-0.648250\pi\) | ||||
−0.449085 | + | 0.893489i | \(0.648250\pi\) | |||||||
\(60\) | 1.72474 | + | 2.98735i | 0.222664 | + | 0.385665i | ||||
\(61\) | −2.22474 | + | 3.85337i | −0.284849 | + | 0.493374i | −0.972573 | − | 0.232599i | \(-0.925277\pi\) |
0.687723 | + | 0.725973i | \(0.258610\pi\) | |||||||
\(62\) | −0.550510 | −0.0699149 | ||||||||
\(63\) | −19.7980 | − | 34.2911i | −2.49431 | − | 4.32027i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.00000 | + | 3.46410i | −0.248069 | + | 0.429669i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.174235 | + | 8.18350i | −0.0212861 | + | 0.999773i | ||||
\(68\) | 4.44949 | 0.539580 | ||||||||
\(69\) | −4.22474 | + | 7.31747i | −0.508600 | + | 0.880920i | ||||
\(70\) | −4.44949 | −0.531816 | ||||||||
\(71\) | −0.174235 | − | 0.301783i | −0.0206778 | − | 0.0358151i | 0.855501 | − | 0.517801i | \(-0.173249\pi\) |
−0.876179 | + | 0.481986i | \(0.839916\pi\) | |||||||
\(72\) | 8.89898 | 1.04875 | ||||||||
\(73\) | 4.22474 | − | 7.31747i | 0.494469 | − | 0.856445i | −0.505511 | − | 0.862820i | \(-0.668696\pi\) |
0.999980 | + | 0.00637493i | \(0.00202922\pi\) | |||||||
\(74\) | −2.94949 | − | 5.10867i | −0.342871 | − | 0.593870i | ||||
\(75\) | 3.44949 | 0.398313 | ||||||||
\(76\) | −6.89898 | −0.791367 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 6.89898 | + | 11.9494i | 0.781156 | + | 1.35300i | ||||
\(79\) | −1.00000 | − | 1.73205i | −0.112509 | − | 0.194871i | 0.804272 | − | 0.594261i | \(-0.202555\pi\) |
−0.916781 | + | 0.399390i | \(0.869222\pi\) | |||||||
\(80\) | 0.500000 | − | 0.866025i | 0.0559017 | − | 0.0968246i | ||||
\(81\) | 43.4949 | 4.83277 | ||||||||
\(82\) | −2.10102 | −0.232019 | ||||||||
\(83\) | −6.17423 | + | 10.6941i | −0.677710 | + | 1.17383i | 0.297958 | + | 0.954579i | \(0.403694\pi\) |
−0.975669 | + | 0.219250i | \(0.929639\pi\) | |||||||
\(84\) | −7.67423 | + | 13.2922i | −0.837328 | + | 1.45029i | ||||
\(85\) | 2.22474 | − | 3.85337i | 0.241307 | − | 0.417957i | ||||
\(86\) | −2.00000 | + | 3.46410i | −0.215666 | + | 0.373544i | ||||
\(87\) | 10.3485 | + | 17.9241i | 1.10947 | + | 1.92166i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.10102 | −0.222708 | −0.111354 | − | 0.993781i | \(-0.535519\pi\) | ||||
−0.111354 | + | 0.993781i | \(0.535519\pi\) | |||||||
\(90\) | 4.44949 | − | 7.70674i | 0.469017 | − | 0.812362i | ||||
\(91\) | −17.7980 | −1.86573 | ||||||||
\(92\) | 2.44949 | 0.255377 | ||||||||
\(93\) | 0.949490 | + | 1.64456i | 0.0984575 | + | 0.170533i | ||||
\(94\) | 7.34847 | 0.757937 | ||||||||
\(95\) | −3.44949 | + | 5.97469i | −0.353910 | + | 0.612990i | ||||
\(96\) | −1.72474 | − | 2.98735i | −0.176031 | − | 0.304895i | ||||
\(97\) | −7.89898 | + | 13.6814i | −0.802020 | + | 1.38914i | 0.116265 | + | 0.993218i | \(0.462908\pi\) |
−0.918285 | + | 0.395921i | \(0.870425\pi\) | |||||||
\(98\) | −6.39898 | − | 11.0834i | −0.646395 | − | 1.11959i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | 6.12372 | + | 10.6066i | 0.609333 | + | 1.05540i | 0.991350 | + | 0.131241i | \(0.0418962\pi\) |
−0.382017 | + | 0.924155i | \(0.624770\pi\) | |||||||
\(102\) | −7.67423 | − | 13.2922i | −0.759862 | − | 1.31612i | ||||
\(103\) | −2.77526 | − | 4.80688i | −0.273454 | − | 0.473636i | 0.696290 | − | 0.717761i | \(-0.254833\pi\) |
−0.969744 | + | 0.244124i | \(0.921499\pi\) | |||||||
\(104\) | 2.00000 | − | 3.46410i | 0.196116 | − | 0.339683i | ||||
\(105\) | 7.67423 | + | 13.2922i | 0.748929 | + | 1.29718i | ||||
\(106\) | 3.50000 | − | 6.06218i | 0.339950 | − | 0.588811i | ||||
\(107\) | 15.4495 | 1.49356 | 0.746779 | − | 0.665072i | \(-0.231599\pi\) | ||||
0.746779 | + | 0.665072i | \(0.231599\pi\) | |||||||
\(108\) | −10.1742 | − | 17.6223i | −0.979016 | − | 1.69571i | ||||
\(109\) | 10.4495 | 1.00088 | 0.500440 | − | 0.865771i | \(-0.333172\pi\) | ||||
0.500440 | + | 0.865771i | \(0.333172\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.1742 | + | 17.6223i | −0.965696 | + | 1.67263i | ||||
\(112\) | 4.44949 | 0.420437 | ||||||||
\(113\) | −2.00000 | − | 3.46410i | −0.188144 | − | 0.325875i | 0.756487 | − | 0.654008i | \(-0.226914\pi\) |
−0.944632 | + | 0.328133i | \(0.893581\pi\) | |||||||
\(114\) | 11.8990 | + | 20.6096i | 1.11444 | + | 1.93027i | ||||
\(115\) | 1.22474 | − | 2.12132i | 0.114208 | − | 0.197814i | ||||
\(116\) | 3.00000 | − | 5.19615i | 0.278543 | − | 0.482451i | ||||
\(117\) | 17.7980 | − | 30.8270i | 1.64542 | − | 2.84995i | ||||
\(118\) | 3.44949 | − | 5.97469i | 0.317551 | − | 0.550015i | ||||
\(119\) | 19.7980 | 1.81488 | ||||||||
\(120\) | −3.44949 | −0.314894 | ||||||||
\(121\) | 5.50000 | − | 9.52628i | 0.500000 | − | 0.866025i | ||||
\(122\) | −2.22474 | − | 3.85337i | −0.201419 | − | 0.348868i | ||||
\(123\) | 3.62372 | + | 6.27647i | 0.326740 | + | 0.565931i | ||||
\(124\) | 0.275255 | − | 0.476756i | 0.0247186 | − | 0.0428139i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 39.5959 | 3.52748 | ||||||||
\(127\) | −3.44949 | − | 5.97469i | −0.306093 | − | 0.530168i | 0.671411 | − | 0.741085i | \(-0.265688\pi\) |
−0.977504 | + | 0.210917i | \(0.932355\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 13.7980 | 1.21484 | ||||||||
\(130\) | −2.00000 | − | 3.46410i | −0.175412 | − | 0.303822i | ||||
\(131\) | −10.2474 | −0.895324 | −0.447662 | − | 0.894203i | \(-0.647743\pi\) | ||||
−0.447662 | + | 0.894203i | \(0.647743\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −30.6969 | −2.66176 | ||||||||
\(134\) | −7.00000 | − | 4.24264i | −0.604708 | − | 0.366508i | ||||
\(135\) | −20.3485 | −1.75132 | ||||||||
\(136\) | −2.22474 | + | 3.85337i | −0.190770 | + | 0.330424i | ||||
\(137\) | −0.449490 | −0.0384025 | −0.0192013 | − | 0.999816i | \(-0.506112\pi\) | ||||
−0.0192013 | + | 0.999816i | \(0.506112\pi\) | |||||||
\(138\) | −4.22474 | − | 7.31747i | −0.359634 | − | 0.622905i | ||||
\(139\) | −9.79796 | −0.831052 | −0.415526 | − | 0.909581i | \(-0.636402\pi\) | ||||
−0.415526 | + | 0.909581i | \(0.636402\pi\) | |||||||
\(140\) | 2.22474 | − | 3.85337i | 0.188025 | − | 0.325669i | ||||
\(141\) | −12.6742 | − | 21.9524i | −1.06736 | − | 1.84873i | ||||
\(142\) | 0.348469 | 0.0292429 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.44949 | + | 7.70674i | −0.370791 | + | 0.642229i | ||||
\(145\) | −3.00000 | − | 5.19615i | −0.249136 | − | 0.431517i | ||||
\(146\) | 4.22474 | + | 7.31747i | 0.349642 | + | 0.605598i | ||||
\(147\) | −22.0732 | + | 38.2319i | −1.82057 | + | 3.15332i | ||||
\(148\) | 5.89898 | 0.484893 | ||||||||
\(149\) | 18.2474 | 1.49489 | 0.747445 | − | 0.664324i | \(-0.231281\pi\) | ||||
0.747445 | + | 0.664324i | \(0.231281\pi\) | |||||||
\(150\) | −1.72474 | + | 2.98735i | −0.140825 | + | 0.243916i | ||||
\(151\) | −3.27526 | + | 5.67291i | −0.266536 | + | 0.461655i | −0.967965 | − | 0.251085i | \(-0.919213\pi\) |
0.701429 | + | 0.712740i | \(0.252546\pi\) | |||||||
\(152\) | 3.44949 | − | 5.97469i | 0.279791 | − | 0.484611i | ||||
\(153\) | −19.7980 | + | 34.2911i | −1.60057 | + | 2.77227i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.275255 | − | 0.476756i | −0.0221090 | − | 0.0382940i | ||||
\(156\) | −13.7980 | −1.10472 | ||||||||
\(157\) | −10.7980 | + | 18.7026i | −0.861771 | + | 1.49263i | 0.00844713 | + | 0.999964i | \(0.497311\pi\) |
−0.870218 | + | 0.492667i | \(0.836022\pi\) | |||||||
\(158\) | 2.00000 | 0.159111 | ||||||||
\(159\) | −24.1464 | −1.91494 | ||||||||
\(160\) | 0.500000 | + | 0.866025i | 0.0395285 | + | 0.0684653i | ||||
\(161\) | 10.8990 | 0.858960 | ||||||||
\(162\) | −21.7474 | + | 37.6677i | −1.70864 | + | 2.95945i | ||||
\(163\) | 3.72474 | + | 6.45145i | 0.291745 | + | 0.505316i | 0.974222 | − | 0.225590i | \(-0.0724310\pi\) |
−0.682478 | + | 0.730906i | \(0.739098\pi\) | |||||||
\(164\) | 1.05051 | − | 1.81954i | 0.0820311 | − | 0.142082i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.17423 | − | 10.6941i | −0.479214 | − | 0.830022i | ||||
\(167\) | −7.12372 | − | 12.3387i | −0.551250 | − | 0.954794i | −0.998185 | − | 0.0602269i | \(-0.980818\pi\) |
0.446934 | − | 0.894567i | \(-0.352516\pi\) | |||||||
\(168\) | −7.67423 | − | 13.2922i | −0.592080 | − | 1.02551i | ||||
\(169\) | −1.50000 | − | 2.59808i | −0.115385 | − | 0.199852i | ||||
\(170\) | 2.22474 | + | 3.85337i | 0.170630 | + | 0.295540i | ||||
\(171\) | 30.6969 | − | 53.1687i | 2.34745 | − | 4.06591i | ||||
\(172\) | −2.00000 | − | 3.46410i | −0.152499 | − | 0.264135i | ||||
\(173\) | 4.50000 | − | 7.79423i | 0.342129 | − | 0.592584i | −0.642699 | − | 0.766119i | \(-0.722185\pi\) |
0.984828 | + | 0.173534i | \(0.0555188\pi\) | |||||||
\(174\) | −20.6969 | −1.56903 | ||||||||
\(175\) | −2.22474 | − | 3.85337i | −0.168175 | − | 0.291287i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −23.7980 | −1.78876 | ||||||||
\(178\) | 1.05051 | − | 1.81954i | 0.0787391 | − | 0.136380i | ||||
\(179\) | 12.2474 | 0.915417 | 0.457709 | − | 0.889102i | \(-0.348670\pi\) | ||||
0.457709 | + | 0.889102i | \(0.348670\pi\) | |||||||
\(180\) | 4.44949 | + | 7.70674i | 0.331645 | + | 0.574427i | ||||
\(181\) | 1.67423 | + | 2.89986i | 0.124445 | + | 0.215545i | 0.921516 | − | 0.388341i | \(-0.126952\pi\) |
−0.797071 | + | 0.603886i | \(0.793618\pi\) | |||||||
\(182\) | 8.89898 | − | 15.4135i | 0.659636 | − | 1.14252i | ||||
\(183\) | −7.67423 | + | 13.2922i | −0.567296 | + | 0.982585i | ||||
\(184\) | −1.22474 | + | 2.12132i | −0.0902894 | + | 0.156386i | ||||
\(185\) | 2.94949 | − | 5.10867i | 0.216851 | − | 0.375597i | ||||
\(186\) | −1.89898 | −0.139240 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −3.67423 | + | 6.36396i | −0.267971 | + | 0.464140i | ||||
\(189\) | −45.2702 | − | 78.4102i | −3.29292 | − | 5.70350i | ||||
\(190\) | −3.44949 | − | 5.97469i | −0.250252 | − | 0.433450i | ||||
\(191\) | −9.72474 | + | 16.8438i | −0.703658 | + | 1.21877i | 0.263516 | + | 0.964655i | \(0.415118\pi\) |
−0.967174 | + | 0.254116i | \(0.918215\pi\) | |||||||
\(192\) | 3.44949 | 0.248945 | ||||||||
\(193\) | −20.4495 | −1.47199 | −0.735993 | − | 0.676989i | \(-0.763285\pi\) | ||||
−0.735993 | + | 0.676989i | \(0.763285\pi\) | |||||||
\(194\) | −7.89898 | − | 13.6814i | −0.567114 | − | 0.982270i | ||||
\(195\) | −6.89898 | + | 11.9494i | −0.494046 | + | 0.855713i | ||||
\(196\) | 12.7980 | 0.914140 | ||||||||
\(197\) | −0.449490 | − | 0.778539i | −0.0320248 | − | 0.0554686i | 0.849569 | − | 0.527478i | \(-0.176862\pi\) |
−0.881594 | + | 0.472009i | \(0.843529\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.17423 | − | 10.6941i | 0.437680 | − | 0.758084i | −0.559830 | − | 0.828607i | \(-0.689134\pi\) |
0.997510 | + | 0.0705235i | \(0.0224670\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −0.601021 | + | 28.2289i | −0.0423927 | + | 1.99111i | ||||
\(202\) | −12.2474 | −0.861727 | ||||||||
\(203\) | 13.3485 | − | 23.1202i | 0.936879 | − | 1.62272i | ||||
\(204\) | 15.3485 | 1.07461 | ||||||||
\(205\) | −1.05051 | − | 1.81954i | −0.0733708 | − | 0.127082i | ||||
\(206\) | 5.55051 | 0.386722 | ||||||||
\(207\) | −10.8990 | + | 18.8776i | −0.757531 | + | 1.31208i | ||||
\(208\) | 2.00000 | + | 3.46410i | 0.138675 | + | 0.240192i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −15.3485 | −1.05915 | ||||||||
\(211\) | 7.67423 | − | 13.2922i | 0.528316 | − | 0.915070i | −0.471139 | − | 0.882059i | \(-0.656157\pi\) |
0.999455 | − | 0.0330113i | \(-0.0105097\pi\) | |||||||
\(212\) | 3.50000 | + | 6.06218i | 0.240381 | + | 0.416352i | ||||
\(213\) | −0.601021 | − | 1.04100i | −0.0411812 | − | 0.0713280i | ||||
\(214\) | −7.72474 | + | 13.3797i | −0.528053 | + | 0.914614i | ||||
\(215\) | −4.00000 | −0.272798 | ||||||||
\(216\) | 20.3485 | 1.38454 | ||||||||
\(217\) | 1.22474 | − | 2.12132i | 0.0831411 | − | 0.144005i | ||||
\(218\) | −5.22474 | + | 9.04952i | −0.353864 | + | 0.612911i | ||||
\(219\) | 14.5732 | − | 25.2415i | 0.984767 | − | 1.70567i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.89898 | + | 15.4135i | 0.598610 | + | 1.03682i | ||||
\(222\) | −10.1742 | − | 17.6223i | −0.682850 | − | 1.18273i | ||||
\(223\) | 9.10102 | 0.609449 | 0.304725 | − | 0.952440i | \(-0.401436\pi\) | ||||
0.304725 | + | 0.952440i | \(0.401436\pi\) | |||||||
\(224\) | −2.22474 | + | 3.85337i | −0.148647 | + | 0.257464i | ||||
\(225\) | 8.89898 | 0.593265 | ||||||||
\(226\) | 4.00000 | 0.266076 | ||||||||
\(227\) | −11.1742 | − | 19.3543i | −0.741660 | − | 1.28459i | −0.951739 | − | 0.306908i | \(-0.900705\pi\) |
0.210079 | − | 0.977684i | \(-0.432628\pi\) | |||||||
\(228\) | −23.7980 | −1.57606 | ||||||||
\(229\) | −1.12372 | + | 1.94635i | −0.0742578 | + | 0.128618i | −0.900763 | − | 0.434310i | \(-0.856992\pi\) |
0.826505 | + | 0.562929i | \(0.190325\pi\) | |||||||
\(230\) | 1.22474 | + | 2.12132i | 0.0807573 | + | 0.139876i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.00000 | + | 5.19615i | 0.196960 | + | 0.341144i | ||||
\(233\) | 1.77526 | + | 3.07483i | 0.116301 | + | 0.201439i | 0.918299 | − | 0.395888i | \(-0.129563\pi\) |
−0.801998 | + | 0.597326i | \(0.796230\pi\) | |||||||
\(234\) | 17.7980 | + | 30.8270i | 1.16349 | + | 2.01522i | ||||
\(235\) | 3.67423 | + | 6.36396i | 0.239681 | + | 0.415139i | ||||
\(236\) | 3.44949 | + | 5.97469i | 0.224543 | + | 0.388919i | ||||
\(237\) | −3.44949 | − | 5.97469i | −0.224068 | − | 0.388098i | ||||
\(238\) | −9.89898 | + | 17.1455i | −0.641656 | + | 1.11138i | ||||
\(239\) | 12.8990 | + | 22.3417i | 0.834366 | + | 1.44516i | 0.894546 | + | 0.446976i | \(0.147499\pi\) |
−0.0601803 | + | 0.998188i | \(0.519168\pi\) | |||||||
\(240\) | 1.72474 | − | 2.98735i | 0.111332 | − | 0.192832i | ||||
\(241\) | −27.8990 | −1.79713 | −0.898566 | − | 0.438839i | \(-0.855390\pi\) | ||||
−0.898566 | + | 0.438839i | \(0.855390\pi\) | |||||||
\(242\) | 5.50000 | + | 9.52628i | 0.353553 | + | 0.612372i | ||||
\(243\) | 88.9898 | 5.70870 | ||||||||
\(244\) | 4.44949 | 0.284849 | ||||||||
\(245\) | 6.39898 | − | 11.0834i | 0.408816 | − | 0.708090i | ||||
\(246\) | −7.24745 | −0.462080 | ||||||||
\(247\) | −13.7980 | − | 23.8988i | −0.877943 | − | 1.52064i | ||||
\(248\) | 0.275255 | + | 0.476756i | 0.0174787 | + | 0.0302740i | ||||
\(249\) | −21.2980 | + | 36.8891i | −1.34970 | + | 2.33775i | ||||
\(250\) | 0.500000 | − | 0.866025i | 0.0316228 | − | 0.0547723i | ||||
\(251\) | −6.32577 | + | 10.9565i | −0.399279 | + | 0.691571i | −0.993637 | − | 0.112629i | \(-0.964073\pi\) |
0.594358 | + | 0.804200i | \(0.297406\pi\) | |||||||
\(252\) | −19.7980 | + | 34.2911i | −1.24715 | + | 2.16013i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 6.89898 | 0.432880 | ||||||||
\(255\) | 7.67423 | − | 13.2922i | 0.480579 | − | 0.832388i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −1.89898 | − | 3.28913i | −0.118455 | − | 0.205170i | 0.800701 | − | 0.599065i | \(-0.204461\pi\) |
−0.919156 | + | 0.393895i | \(0.871127\pi\) | |||||||
\(258\) | −6.89898 | + | 11.9494i | −0.429512 | + | 0.743936i | ||||
\(259\) | 26.2474 | 1.63094 | ||||||||
\(260\) | 4.00000 | 0.248069 | ||||||||
\(261\) | 26.6969 | + | 46.2405i | 1.65250 | + | 2.86221i | ||||
\(262\) | 5.12372 | − | 8.87455i | 0.316545 | − | 0.548272i | ||||
\(263\) | −14.8990 | −0.918710 | −0.459355 | − | 0.888253i | \(-0.651919\pi\) | ||||
−0.459355 | + | 0.888253i | \(0.651919\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.00000 | 0.430007 | ||||||||
\(266\) | 15.3485 | − | 26.5843i | 0.941075 | − | 1.62999i | ||||
\(267\) | −7.24745 | −0.443537 | ||||||||
\(268\) | 7.17423 | − | 3.94086i | 0.438236 | − | 0.240726i | ||||
\(269\) | −7.59592 | −0.463131 | −0.231566 | − | 0.972819i | \(-0.574385\pi\) | ||||
−0.231566 | + | 0.972819i | \(0.574385\pi\) | |||||||
\(270\) | 10.1742 | − | 17.6223i | 0.619184 | − | 1.07246i | ||||
\(271\) | 32.1464 | 1.95276 | 0.976378 | − | 0.216068i | \(-0.0693234\pi\) | ||||
0.976378 | + | 0.216068i | \(0.0693234\pi\) | |||||||
\(272\) | −2.22474 | − | 3.85337i | −0.134895 | − | 0.233645i | ||||
\(273\) | −61.3939 | −3.71573 | ||||||||
\(274\) | 0.224745 | − | 0.389270i | 0.0135773 | − | 0.0235166i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 8.44949 | 0.508600 | ||||||||
\(277\) | −16.1010 | −0.967417 | −0.483708 | − | 0.875229i | \(-0.660710\pi\) | ||||
−0.483708 | + | 0.875229i | \(0.660710\pi\) | |||||||
\(278\) | 4.89898 | − | 8.48528i | 0.293821 | − | 0.508913i | ||||
\(279\) | 2.44949 | + | 4.24264i | 0.146647 | + | 0.254000i | ||||
\(280\) | 2.22474 | + | 3.85337i | 0.132954 | + | 0.230283i | ||||
\(281\) | 8.74745 | − | 15.1510i | 0.521829 | − | 0.903834i | −0.477849 | − | 0.878442i | \(-0.658583\pi\) |
0.999678 | − | 0.0253922i | \(-0.00808345\pi\) | |||||||
\(282\) | 25.3485 | 1.50948 | ||||||||
\(283\) | 11.7980 | 0.701316 | 0.350658 | − | 0.936504i | \(-0.385958\pi\) | ||||
0.350658 | + | 0.936504i | \(0.385958\pi\) | |||||||
\(284\) | −0.174235 | + | 0.301783i | −0.0103389 | + | 0.0179075i | ||||
\(285\) | −11.8990 | + | 20.6096i | −0.704835 | + | 1.22081i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.67423 | − | 8.09601i | 0.275911 | − | 0.477892i | ||||
\(288\) | −4.44949 | − | 7.70674i | −0.262189 | − | 0.454124i | ||||
\(289\) | −1.39898 | − | 2.42310i | −0.0822929 | − | 0.142536i | ||||
\(290\) | 6.00000 | 0.352332 | ||||||||
\(291\) | −27.2474 | + | 47.1940i | −1.59727 | + | 2.76656i | ||||
\(292\) | −8.44949 | −0.494469 | ||||||||
\(293\) | −14.7980 | −0.864506 | −0.432253 | − | 0.901752i | \(-0.642281\pi\) | ||||
−0.432253 | + | 0.901752i | \(0.642281\pi\) | |||||||
\(294\) | −22.0732 | − | 38.2319i | −1.28734 | − | 2.22973i | ||||
\(295\) | 6.89898 | 0.401674 | ||||||||
\(296\) | −2.94949 | + | 5.10867i | −0.171436 | + | 0.296935i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9.12372 | + | 15.8028i | −0.528523 | + | 0.915429i | ||||
\(299\) | 4.89898 | + | 8.48528i | 0.283315 | + | 0.490716i | ||||
\(300\) | −1.72474 | − | 2.98735i | −0.0995782 | − | 0.172474i | ||||
\(301\) | −8.89898 | − | 15.4135i | −0.512929 | − | 0.888418i | ||||
\(302\) | −3.27526 | − | 5.67291i | −0.188470 | − | 0.326439i | ||||
\(303\) | 21.1237 | + | 36.5874i | 1.21353 | + | 2.10189i | ||||
\(304\) | 3.44949 | + | 5.97469i | 0.197842 | + | 0.342672i | ||||
\(305\) | 2.22474 | − | 3.85337i | 0.127389 | − | 0.220643i | ||||
\(306\) | −19.7980 | − | 34.2911i | −1.13177 | − | 1.96029i | ||||
\(307\) | −2.17423 | + | 3.76588i | −0.124090 | + | 0.214930i | −0.921377 | − | 0.388670i | \(-0.872935\pi\) |
0.797287 | + | 0.603601i | \(0.206268\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.57321 | − | 16.5813i | −0.544601 | − | 0.943277i | ||||
\(310\) | 0.550510 | 0.0312669 | ||||||||
\(311\) | 6.55051 | 0.371445 | 0.185723 | − | 0.982602i | \(-0.440537\pi\) | ||||
0.185723 | + | 0.982602i | \(0.440537\pi\) | |||||||
\(312\) | 6.89898 | − | 11.9494i | 0.390578 | − | 0.676501i | ||||
\(313\) | −6.00000 | −0.339140 | −0.169570 | − | 0.985518i | \(-0.554238\pi\) | ||||
−0.169570 | + | 0.985518i | \(0.554238\pi\) | |||||||
\(314\) | −10.7980 | − | 18.7026i | −0.609364 | − | 1.05545i | ||||
\(315\) | 19.7980 | + | 34.2911i | 1.11549 | + | 1.93208i | ||||
\(316\) | −1.00000 | + | 1.73205i | −0.0562544 | + | 0.0974355i | ||||
\(317\) | 13.8485 | − | 23.9863i | 0.777808 | − | 1.34720i | −0.155395 | − | 0.987852i | \(-0.549665\pi\) |
0.933203 | − | 0.359350i | \(-0.117002\pi\) | |||||||
\(318\) | 12.0732 | − | 20.9114i | 0.677032 | − | 1.17265i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 53.2929 | 2.97452 | ||||||||
\(322\) | −5.44949 | + | 9.43879i | −0.303688 | + | 0.526003i | ||||
\(323\) | 15.3485 | + | 26.5843i | 0.854012 | + | 1.47919i | ||||
\(324\) | −21.7474 | − | 37.6677i | −1.20819 | − | 2.09265i | ||||
\(325\) | 2.00000 | − | 3.46410i | 0.110940 | − | 0.192154i | ||||
\(326\) | −7.44949 | −0.412589 | ||||||||
\(327\) | 36.0454 | 1.99332 | ||||||||
\(328\) | 1.05051 | + | 1.81954i | 0.0580047 | + | 0.100467i | ||||
\(329\) | −16.3485 | + | 28.3164i | −0.901320 | + | 1.56113i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.44949 | − | 2.51059i | −0.0796712 | − | 0.137994i | 0.823437 | − | 0.567408i | \(-0.192054\pi\) |
−0.903108 | + | 0.429413i | \(0.858720\pi\) | |||||||
\(332\) | 12.3485 | 0.677710 | ||||||||
\(333\) | −26.2474 | + | 45.4619i | −1.43835 | + | 2.49130i | ||||
\(334\) | 14.2474 | 0.779586 | ||||||||
\(335\) | 0.174235 | − | 8.18350i | 0.00951945 | − | 0.447112i | ||||
\(336\) | 15.3485 | 0.837328 | ||||||||
\(337\) | −0.224745 | + | 0.389270i | −0.0122426 | + | 0.0212049i | −0.872082 | − | 0.489360i | \(-0.837230\pi\) |
0.859839 | + | 0.510565i | \(0.170564\pi\) | |||||||
\(338\) | 3.00000 | 0.163178 | ||||||||
\(339\) | −6.89898 | − | 11.9494i | −0.374701 | − | 0.649001i | ||||
\(340\) | −4.44949 | −0.241307 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 30.6969 | + | 53.1687i | 1.65990 | + | 2.87503i | ||||
\(343\) | 25.7980 | 1.39296 | ||||||||
\(344\) | 4.00000 | 0.215666 | ||||||||
\(345\) | 4.22474 | − | 7.31747i | 0.227453 | − | 0.393959i | ||||
\(346\) | 4.50000 | + | 7.79423i | 0.241921 | + | 0.419020i | ||||
\(347\) | −9.34847 | − | 16.1920i | −0.501852 | − | 0.869233i | −0.999998 | − | 0.00213997i | \(-0.999319\pi\) |
0.498146 | − | 0.867093i | \(-0.334015\pi\) | |||||||
\(348\) | 10.3485 | − | 17.9241i | 0.554736 | − | 0.960831i | ||||
\(349\) | 5.79796 | 0.310358 | 0.155179 | − | 0.987886i | \(-0.450405\pi\) | ||||
0.155179 | + | 0.987886i | \(0.450405\pi\) | |||||||
\(350\) | 4.44949 | 0.237835 | ||||||||
\(351\) | 40.6969 | − | 70.4892i | 2.17224 | − | 3.76243i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.224745 | + | 0.389270i | −0.0119620 | + | 0.0207187i | −0.871944 | − | 0.489605i | \(-0.837141\pi\) |
0.859982 | + | 0.510324i | \(0.170474\pi\) | |||||||
\(354\) | 11.8990 | − | 20.6096i | 0.632424 | − | 1.09539i | ||||
\(355\) | 0.174235 | + | 0.301783i | 0.00924741 | + | 0.0160170i | ||||
\(356\) | 1.05051 | + | 1.81954i | 0.0556769 | + | 0.0964353i | ||||
\(357\) | 68.2929 | 3.61444 | ||||||||
\(358\) | −6.12372 | + | 10.6066i | −0.323649 | + | 0.560576i | ||||
\(359\) | 14.1464 | 0.746620 | 0.373310 | − | 0.927707i | \(-0.378223\pi\) | ||||
0.373310 | + | 0.927707i | \(0.378223\pi\) | |||||||
\(360\) | −8.89898 | −0.469017 | ||||||||
\(361\) | −14.2980 | − | 24.7648i | −0.752524 | − | 1.30341i | ||||
\(362\) | −3.34847 | −0.175992 | ||||||||
\(363\) | 18.9722 | − | 32.8608i | 0.995782 | − | 1.72474i | ||||
\(364\) | 8.89898 | + | 15.4135i | 0.466433 | + | 0.807886i | ||||
\(365\) | −4.22474 | + | 7.31747i | −0.221133 | + | 0.383014i | ||||
\(366\) | −7.67423 | − | 13.2922i | −0.401139 | − | 0.694793i | ||||
\(367\) | −3.12372 | − | 5.41045i | −0.163057 | − | 0.282423i | 0.772907 | − | 0.634520i | \(-0.218802\pi\) |
−0.935964 | + | 0.352097i | \(0.885469\pi\) | |||||||
\(368\) | −1.22474 | − | 2.12132i | −0.0638442 | − | 0.110581i | ||||
\(369\) | 9.34847 | + | 16.1920i | 0.486662 | + | 0.842923i | ||||
\(370\) | 2.94949 | + | 5.10867i | 0.153337 | + | 0.265587i | ||||
\(371\) | 15.5732 | + | 26.9736i | 0.808521 | + | 1.40040i | ||||
\(372\) | 0.949490 | − | 1.64456i | 0.0492287 | − | 0.0852667i | ||||
\(373\) | 7.50000 | + | 12.9904i | 0.388335 | + | 0.672616i | 0.992226 | − | 0.124451i | \(-0.0397169\pi\) |
−0.603890 | + | 0.797067i | \(0.706384\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.44949 | −0.178131 | ||||||||
\(376\) | −3.67423 | − | 6.36396i | −0.189484 | − | 0.328196i | ||||
\(377\) | 24.0000 | 1.23606 | ||||||||
\(378\) | 90.5403 | 4.65689 | ||||||||
\(379\) | −6.89898 | + | 11.9494i | −0.354377 | + | 0.613799i | −0.987011 | − | 0.160652i | \(-0.948640\pi\) |
0.632634 | + | 0.774451i | \(0.281974\pi\) | |||||||
\(380\) | 6.89898 | 0.353910 | ||||||||
\(381\) | −11.8990 | − | 20.6096i | −0.609603 | − | 1.05586i | ||||
\(382\) | −9.72474 | − | 16.8438i | −0.497561 | − | 0.861801i | ||||
\(383\) | 4.34847 | − | 7.53177i | 0.222196 | − | 0.384855i | −0.733278 | − | 0.679929i | \(-0.762011\pi\) |
0.955475 | + | 0.295073i | \(0.0953441\pi\) | |||||||
\(384\) | −1.72474 | + | 2.98735i | −0.0880155 | + | 0.152447i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10.2247 | − | 17.7098i | 0.520426 | − | 0.901404i | ||||
\(387\) | 35.5959 | 1.80944 | ||||||||
\(388\) | 15.7980 | 0.802020 | ||||||||
\(389\) | 9.22474 | − | 15.9777i | 0.467713 | − | 0.810103i | −0.531606 | − | 0.846992i | \(-0.678411\pi\) |
0.999319 | + | 0.0368887i | \(0.0117447\pi\) | |||||||
\(390\) | −6.89898 | − | 11.9494i | −0.349343 | − | 0.605081i | ||||
\(391\) | −5.44949 | − | 9.43879i | −0.275593 | − | 0.477340i | ||||
\(392\) | −6.39898 | + | 11.0834i | −0.323197 | + | 0.559794i | ||||
\(393\) | −35.3485 | −1.78309 | ||||||||
\(394\) | 0.898979 | 0.0452899 | ||||||||
\(395\) | 1.00000 | + | 1.73205i | 0.0503155 | + | 0.0871489i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.00000 | −0.351320 | −0.175660 | − | 0.984451i | \(-0.556206\pi\) | ||||
−0.175660 | + | 0.984451i | \(0.556206\pi\) | |||||||
\(398\) | 6.17423 | + | 10.6941i | 0.309486 | + | 0.536046i | ||||
\(399\) | −105.889 | −5.30107 | ||||||||
\(400\) | −0.500000 | + | 0.866025i | −0.0250000 | + | 0.0433013i | ||||
\(401\) | 4.89898 | 0.244643 | 0.122322 | − | 0.992491i | \(-0.460966\pi\) | ||||
0.122322 | + | 0.992491i | \(0.460966\pi\) | |||||||
\(402\) | −24.1464 | − | 14.6349i | −1.20431 | − | 0.729925i | ||||
\(403\) | 2.20204 | 0.109691 | ||||||||
\(404\) | 6.12372 | − | 10.6066i | 0.304667 | − | 0.527698i | ||||
\(405\) | −43.4949 | −2.16128 | ||||||||
\(406\) | 13.3485 | + | 23.1202i | 0.662473 | + | 1.14744i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −7.67423 | + | 13.2922i | −0.379931 | + | 0.658060i | ||||
\(409\) | 18.9495 | + | 32.8215i | 0.936992 | + | 1.62292i | 0.771043 | + | 0.636783i | \(0.219735\pi\) |
0.165949 | + | 0.986134i | \(0.446931\pi\) | |||||||
\(410\) | 2.10102 | 0.103762 | ||||||||
\(411\) | −1.55051 | −0.0764810 | ||||||||
\(412\) | −2.77526 | + | 4.80688i | −0.136727 | + | 0.236818i | ||||
\(413\) | 15.3485 | + | 26.5843i | 0.755249 | + | 1.30813i | ||||
\(414\) | −10.8990 | − | 18.8776i | −0.535656 | − | 0.927783i | ||||
\(415\) | 6.17423 | − | 10.6941i | 0.303081 | − | 0.524952i | ||||
\(416\) | −4.00000 | −0.196116 | ||||||||
\(417\) | −33.7980 | −1.65509 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.79796 | + | 10.0424i | −0.283249 | + | 0.490601i | −0.972183 | − | 0.234223i | \(-0.924746\pi\) |
0.688934 | + | 0.724824i | \(0.258079\pi\) | |||||||
\(420\) | 7.67423 | − | 13.2922i | 0.374464 | − | 0.648591i | ||||
\(421\) | −3.89898 | + | 6.75323i | −0.190025 | + | 0.329132i | −0.945258 | − | 0.326324i | \(-0.894190\pi\) |
0.755234 | + | 0.655456i | \(0.227523\pi\) | |||||||
\(422\) | 7.67423 | + | 13.2922i | 0.373576 | + | 0.647052i | ||||
\(423\) | −32.6969 | − | 56.6328i | −1.58978 | − | 2.75358i | ||||
\(424\) | −7.00000 | −0.339950 | ||||||||
\(425\) | −2.22474 | + | 3.85337i | −0.107916 | + | 0.186916i | ||||
\(426\) | 1.20204 | 0.0582391 | ||||||||
\(427\) | 19.7980 | 0.958090 | ||||||||
\(428\) | −7.72474 | − | 13.3797i | −0.373390 | − | 0.646730i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.00000 | − | 3.46410i | 0.0964486 | − | 0.167054i | ||||
\(431\) | −8.17423 | − | 14.1582i | −0.393739 | − | 0.681976i | 0.599200 | − | 0.800599i | \(-0.295485\pi\) |
−0.992939 | + | 0.118623i | \(0.962152\pi\) | |||||||
\(432\) | −10.1742 | + | 17.6223i | −0.489508 | + | 0.847853i | ||||
\(433\) | −9.02270 | − | 15.6278i | −0.433603 | − | 0.751023i | 0.563577 | − | 0.826064i | \(-0.309425\pi\) |
−0.997181 | + | 0.0750403i | \(0.976091\pi\) | |||||||
\(434\) | 1.22474 | + | 2.12132i | 0.0587896 | + | 0.101827i | ||||
\(435\) | −10.3485 | − | 17.9241i | −0.496171 | − | 0.859394i | ||||
\(436\) | −5.22474 | − | 9.04952i | −0.250220 | − | 0.433394i | ||||
\(437\) | 8.44949 | + | 14.6349i | 0.404194 | + | 0.700084i | ||||
\(438\) | 14.5732 | + | 25.2415i | 0.696335 | + | 1.20609i | ||||
\(439\) | 0.275255 | − | 0.476756i | 0.0131372 | − | 0.0227543i | −0.859382 | − | 0.511334i | \(-0.829152\pi\) |
0.872519 | + | 0.488580i | \(0.162485\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −56.9444 | + | 98.6306i | −2.71164 | + | 4.69669i | ||||
\(442\) | −17.7980 | −0.846563 | ||||||||
\(443\) | −5.62372 | − | 9.74058i | −0.267191 | − | 0.462789i | 0.700944 | − | 0.713216i | \(-0.252762\pi\) |
−0.968135 | + | 0.250427i | \(0.919429\pi\) | |||||||
\(444\) | 20.3485 | 0.965696 | ||||||||
\(445\) | 2.10102 | 0.0995979 | ||||||||
\(446\) | −4.55051 | + | 7.88171i | −0.215473 | + | 0.373210i | ||||
\(447\) | 62.9444 | 2.97717 | ||||||||
\(448\) | −2.22474 | − | 3.85337i | −0.105109 | − | 0.182055i | ||||
\(449\) | −2.05051 | − | 3.55159i | −0.0967696 | − | 0.167610i | 0.813576 | − | 0.581458i | \(-0.197518\pi\) |
−0.910346 | + | 0.413849i | \(0.864184\pi\) | |||||||
\(450\) | −4.44949 | + | 7.70674i | −0.209751 | + | 0.363299i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −2.00000 | + | 3.46410i | −0.0940721 | + | 0.162938i | ||||
\(453\) | −11.2980 | + | 19.5686i | −0.530824 | + | 0.919415i | ||||
\(454\) | 22.3485 | 1.04887 | ||||||||
\(455\) | 17.7980 | 0.834381 | ||||||||
\(456\) | 11.8990 | − | 20.6096i | 0.557221 | − | 0.965135i | ||||
\(457\) | −15.7753 | − | 27.3235i | −0.737935 | − | 1.27814i | −0.953423 | − | 0.301635i | \(-0.902468\pi\) |
0.215488 | − | 0.976506i | \(-0.430866\pi\) | |||||||
\(458\) | −1.12372 | − | 1.94635i | −0.0525082 | − | 0.0909469i | ||||
\(459\) | −45.2702 | + | 78.4102i | −2.11303 | + | 3.65987i | ||||
\(460\) | −2.44949 | −0.114208 | ||||||||
\(461\) | −38.7423 | −1.80441 | −0.902205 | − | 0.431306i | \(-0.858053\pi\) | ||||
−0.902205 | + | 0.431306i | \(0.858053\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.67423 | − | 8.09601i | 0.217230 | − | 0.376254i | −0.736730 | − | 0.676187i | \(-0.763631\pi\) |
0.953960 | + | 0.299933i | \(0.0969645\pi\) | |||||||
\(464\) | −6.00000 | −0.278543 | ||||||||
\(465\) | −0.949490 | − | 1.64456i | −0.0440315 | − | 0.0762649i | ||||
\(466\) | −3.55051 | −0.164474 | ||||||||
\(467\) | −10.9722 | + | 19.0044i | −0.507733 | + | 0.879419i | 0.492227 | + | 0.870467i | \(0.336183\pi\) |
−0.999960 | + | 0.00895193i | \(0.997150\pi\) | |||||||
\(468\) | −35.5959 | −1.64542 | ||||||||
\(469\) | 31.9217 | − | 17.5348i | 1.47401 | − | 0.809682i | ||||
\(470\) | −7.34847 | −0.338960 | ||||||||
\(471\) | −37.2474 | + | 64.5145i | −1.71627 | + | 2.97267i | ||||
\(472\) | −6.89898 | −0.317551 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 6.89898 | 0.316881 | ||||||||
\(475\) | 3.44949 | − | 5.97469i | 0.158273 | − | 0.274138i | ||||
\(476\) | −9.89898 | − | 17.1455i | −0.453719 | − | 0.785864i | ||||
\(477\) | −62.2929 | −2.85219 | ||||||||
\(478\) | −25.7980 | −1.17997 | ||||||||
\(479\) | 4.65153 | − | 8.05669i | 0.212534 | − | 0.368119i | −0.739973 | − | 0.672637i | \(-0.765162\pi\) |
0.952507 | + | 0.304517i | \(0.0984951\pi\) | |||||||
\(480\) | 1.72474 | + | 2.98735i | 0.0787235 | + | 0.136353i | ||||
\(481\) | 11.7980 | + | 20.4347i | 0.537941 | + | 0.931740i | ||||
\(482\) | 13.9495 | − | 24.1612i | 0.635382 | − | 1.10051i | ||||
\(483\) | 37.5959 | 1.71067 | ||||||||
\(484\) | −11.0000 | −0.500000 | ||||||||
\(485\) | 7.89898 | − | 13.6814i | 0.358674 | − | 0.621242i | ||||
\(486\) | −44.4949 | + | 77.0674i | −2.01833 | + | 3.49585i | ||||
\(487\) | 2.12372 | − | 3.67840i | 0.0962351 | − | 0.166684i | −0.813888 | − | 0.581021i | \(-0.802653\pi\) |
0.910123 | + | 0.414337i | \(0.135987\pi\) | |||||||
\(488\) | −2.22474 | + | 3.85337i | −0.100709 | + | 0.174434i | ||||
\(489\) | 12.8485 | + | 22.2542i | 0.581028 | + | 1.00637i | ||||
\(490\) | 6.39898 | + | 11.0834i | 0.289076 | + | 0.500695i | ||||
\(491\) | 13.3485 | 0.602408 | 0.301204 | − | 0.953560i | \(-0.402611\pi\) | ||||
0.301204 | + | 0.953560i | \(0.402611\pi\) | |||||||
\(492\) | 3.62372 | − | 6.27647i | 0.163370 | − | 0.282965i | ||||
\(493\) | −26.6969 | −1.20237 | ||||||||
\(494\) | 27.5959 | 1.24160 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.550510 | −0.0247186 | ||||||||
\(497\) | −0.775255 | + | 1.34278i | −0.0347749 | + | 0.0602320i | ||||
\(498\) | −21.2980 | − | 36.8891i | −0.954384 | − | 1.65304i | ||||
\(499\) | 2.89898 | − | 5.02118i | 0.129776 | − | 0.224779i | −0.793814 | − | 0.608161i | \(-0.791907\pi\) |
0.923590 | + | 0.383382i | \(0.125241\pi\) | |||||||
\(500\) | 0.500000 | + | 0.866025i | 0.0223607 | + | 0.0387298i | ||||
\(501\) | −24.5732 | − | 42.5621i | −1.09785 | − | 1.90153i | ||||
\(502\) | −6.32577 | − | 10.9565i | −0.282333 | − | 0.489015i | ||||
\(503\) | 7.79796 | + | 13.5065i | 0.347694 | + | 0.602223i | 0.985839 | − | 0.167692i | \(-0.0536315\pi\) |
−0.638146 | + | 0.769916i | \(0.720298\pi\) | |||||||
\(504\) | −19.7980 | − | 34.2911i | −0.881871 | − | 1.52745i | ||||
\(505\) | −6.12372 | − | 10.6066i | −0.272502 | − | 0.471988i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.17423 | − | 8.96204i | −0.229796 | − | 0.398018i | ||||
\(508\) | −3.44949 | + | 5.97469i | −0.153046 | + | 0.265084i | ||||
\(509\) | 9.55051 | 0.423319 | 0.211659 | − | 0.977343i | \(-0.432113\pi\) | ||||
0.211659 | + | 0.977343i | \(0.432113\pi\) | |||||||
\(510\) | 7.67423 | + | 13.2922i | 0.339821 | + | 0.588587i | ||||
\(511\) | −37.5959 | −1.66315 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 70.1918 | − | 121.576i | 3.09905 | − | 5.36770i | ||||
\(514\) | 3.79796 | 0.167521 | ||||||||
\(515\) | 2.77526 | + | 4.80688i | 0.122292 | + | 0.211817i | ||||
\(516\) | −6.89898 | − | 11.9494i | −0.303711 | − | 0.526042i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −13.1237 | + | 22.7310i | −0.576623 | + | 0.998741i | ||||
\(519\) | 15.5227 | − | 26.8861i | 0.681371 | − | 1.18017i | ||||
\(520\) | −2.00000 | + | 3.46410i | −0.0877058 | + | 0.151911i | ||||
\(521\) | −24.0000 | −1.05146 | −0.525730 | − | 0.850652i | \(-0.676208\pi\) | ||||
−0.525730 | + | 0.850652i | \(0.676208\pi\) | |||||||
\(522\) | −53.3939 | −2.33699 | ||||||||
\(523\) | 21.9722 | − | 38.0570i | 0.960777 | − | 1.66411i | 0.240220 | − | 0.970718i | \(-0.422780\pi\) |
0.720557 | − | 0.693396i | \(-0.243886\pi\) | |||||||
\(524\) | 5.12372 | + | 8.87455i | 0.223831 | + | 0.387687i | ||||
\(525\) | −7.67423 | − | 13.2922i | −0.334931 | − | 0.580118i | ||||
\(526\) | 7.44949 | − | 12.9029i | 0.324813 | − | 0.562593i | ||||
\(527\) | −2.44949 | −0.106701 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.50000 | + | 14.7224i | 0.369565 | + | 0.640106i | ||||
\(530\) | −3.50000 | + | 6.06218i | −0.152030 | + | 0.263324i | ||||
\(531\) | −61.3939 | −2.66427 | ||||||||
\(532\) | 15.3485 | + | 26.5843i | 0.665441 | + | 1.15258i | ||||
\(533\) | 8.40408 | 0.364021 | ||||||||
\(534\) | 3.62372 | − | 6.27647i | 0.156814 | − | 0.271610i | ||||
\(535\) | −15.4495 | −0.667940 | ||||||||
\(536\) | −0.174235 | + | 8.18350i | −0.00752579 | + | 0.353473i | ||||
\(537\) | 42.2474 | 1.82311 | ||||||||
\(538\) | 3.79796 | − | 6.57826i | 0.163742 | − | 0.283609i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 10.1742 | + | 17.6223i | 0.437829 | + | 0.758343i | ||||
\(541\) | 33.5959 | 1.44440 | 0.722201 | − | 0.691684i | \(-0.243131\pi\) | ||||
0.722201 | + | 0.691684i | \(0.243131\pi\) | |||||||
\(542\) | −16.0732 | + | 27.8396i | −0.690404 | + | 1.19581i | ||||
\(543\) | 5.77526 | + | 10.0030i | 0.247840 | + | 0.429271i | ||||
\(544\) | 4.44949 | 0.190770 | ||||||||
\(545\) | −10.4495 | −0.447607 | ||||||||
\(546\) | 30.6969 | − | 53.1687i | 1.31371 | − | 2.27541i | ||||
\(547\) | 22.3207 | + | 38.6605i | 0.954363 | + | 1.65300i | 0.735820 | + | 0.677177i | \(0.236797\pi\) |
0.218543 | + | 0.975827i | \(0.429870\pi\) | |||||||
\(548\) | 0.224745 | + | 0.389270i | 0.00960063 | + | 0.0166288i | ||||
\(549\) | −19.7980 | + | 34.2911i | −0.844956 | + | 1.46351i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 41.3939 | 1.76344 | ||||||||
\(552\) | −4.22474 | + | 7.31747i | −0.179817 | + | 0.311452i | ||||
\(553\) | −4.44949 | + | 7.70674i | −0.189212 | + | 0.327724i | ||||
\(554\) | 8.05051 | − | 13.9439i | 0.342033 | − | 0.592419i | ||||
\(555\) | 10.1742 | − | 17.6223i | 0.431872 | − | 0.748025i | ||||
\(556\) | 4.89898 | + | 8.48528i | 0.207763 | + | 0.359856i | ||||
\(557\) | 19.1969 | + | 33.2501i | 0.813400 | + | 1.40885i | 0.910471 | + | 0.413573i | \(0.135719\pi\) |
−0.0970704 | + | 0.995278i | \(0.530947\pi\) | |||||||
\(558\) | −4.89898 | −0.207390 | ||||||||
\(559\) | 8.00000 | − | 13.8564i | 0.338364 | − | 0.586064i | ||||
\(560\) | −4.44949 | −0.188025 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.74745 | + | 15.1510i | 0.368989 | + | 0.639107i | ||||
\(563\) | −27.4495 | −1.15686 | −0.578429 | − | 0.815733i | \(-0.696334\pi\) | ||||
−0.578429 | + | 0.815733i | \(0.696334\pi\) | |||||||
\(564\) | −12.6742 | + | 21.9524i | −0.533682 | + | 0.924364i | ||||
\(565\) | 2.00000 | + | 3.46410i | 0.0841406 | + | 0.145736i | ||||
\(566\) | −5.89898 | + | 10.2173i | −0.247953 | + | 0.429467i | ||||
\(567\) | −96.7650 | − | 167.602i | −4.06375 | − | 7.03862i | ||||
\(568\) | −0.174235 | − | 0.301783i | −0.00731072 | − | 0.0126625i | ||||
\(569\) | 0.949490 | + | 1.64456i | 0.0398047 | + | 0.0689437i | 0.885241 | − | 0.465132i | \(-0.153993\pi\) |
−0.845437 | + | 0.534076i | \(0.820660\pi\) | |||||||
\(570\) | −11.8990 | − | 20.6096i | −0.498393 | − | 0.863243i | ||||
\(571\) | 14.3485 | + | 24.8523i | 0.600465 | + | 1.04004i | 0.992751 | + | 0.120192i | \(0.0383511\pi\) |
−0.392286 | + | 0.919843i | \(0.628316\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −33.5454 | + | 58.1024i | −1.40138 | + | 2.42726i | ||||
\(574\) | 4.67423 | + | 8.09601i | 0.195099 | + | 0.337921i | ||||
\(575\) | −1.22474 | + | 2.12132i | −0.0510754 | + | 0.0884652i | ||||
\(576\) | 8.89898 | 0.370791 | ||||||||
\(577\) | 10.2247 | + | 17.7098i | 0.425662 | + | 0.737268i | 0.996482 | − | 0.0838073i | \(-0.0267080\pi\) |
−0.570820 | + | 0.821075i | \(0.693375\pi\) | |||||||
\(578\) | 2.79796 | 0.116380 | ||||||||
\(579\) | −70.5403 | −2.93156 | ||||||||
\(580\) | −3.00000 | + | 5.19615i | −0.124568 | + | 0.215758i | ||||
\(581\) | 54.9444 | 2.27948 | ||||||||
\(582\) | −27.2474 | − | 47.1940i | −1.12944 | − | 1.95625i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 4.22474 | − | 7.31747i | 0.174821 | − | 0.302799i | ||||
\(585\) | −17.7980 | + | 30.8270i | −0.735855 | + | 1.27454i | ||||
\(586\) | 7.39898 | − | 12.8154i | 0.305649 | − | 0.529400i | ||||
\(587\) | 5.72474 | − | 9.91555i | 0.236286 | − | 0.409259i | −0.723360 | − | 0.690471i | \(-0.757403\pi\) |
0.959645 | + | 0.281213i | \(0.0907366\pi\) | |||||||
\(588\) | 44.1464 | 1.82057 | ||||||||
\(589\) | 3.79796 | 0.156492 | ||||||||
\(590\) | −3.44949 | + | 5.97469i | −0.142013 | + | 0.245974i | ||||
\(591\) | −1.55051 | − | 2.68556i | −0.0637795 | − | 0.110469i | ||||
\(592\) | −2.94949 | − | 5.10867i | −0.121223 | − | 0.209965i | ||||
\(593\) | 14.6969 | − | 25.4558i | 0.603531 | − | 1.04535i | −0.388751 | − | 0.921343i | \(-0.627093\pi\) |
0.992282 | − | 0.124003i | \(-0.0395733\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −19.7980 | −0.811637 | ||||||||
\(596\) | −9.12372 | − | 15.8028i | −0.373722 | − | 0.647306i | ||||
\(597\) | 21.2980 | − | 36.8891i | 0.871667 | − | 1.50977i | ||||
\(598\) | −9.79796 | −0.400668 | ||||||||
\(599\) | 15.1464 | + | 26.2344i | 0.618866 | + | 1.07191i | 0.989693 | + | 0.143206i | \(0.0457411\pi\) |
−0.370827 | + | 0.928702i | \(0.620926\pi\) | |||||||
\(600\) | 3.44949 | 0.140825 | ||||||||
\(601\) | −7.34847 | + | 12.7279i | −0.299750 | + | 0.519183i | −0.976079 | − | 0.217417i | \(-0.930237\pi\) |
0.676328 | + | 0.736600i | \(0.263570\pi\) | |||||||
\(602\) | 17.7980 | 0.725391 | ||||||||
\(603\) | −1.55051 | + | 72.8248i | −0.0631417 | + | 2.96565i | ||||
\(604\) | 6.55051 | 0.266536 | ||||||||
\(605\) | −5.50000 | + | 9.52628i | −0.223607 | + | 0.387298i | ||||
\(606\) | −42.2474 | −1.71619 | ||||||||
\(607\) | 8.34847 | + | 14.4600i | 0.338854 | + | 0.586912i | 0.984217 | − | 0.176963i | \(-0.0566274\pi\) |
−0.645364 | + | 0.763876i | \(0.723294\pi\) | |||||||
\(608\) | −6.89898 | −0.279791 | ||||||||
\(609\) | 46.0454 | − | 79.7530i | 1.86585 | − | 3.23175i | ||||
\(610\) | 2.22474 | + | 3.85337i | 0.0900773 | + | 0.156018i | ||||
\(611\) | −29.3939 | −1.18915 | ||||||||
\(612\) | 39.5959 | 1.60057 | ||||||||
\(613\) | 14.5000 | − | 25.1147i | 0.585649 | − | 1.01437i | −0.409145 | − | 0.912470i | \(-0.634173\pi\) |
0.994794 | − | 0.101905i | \(-0.0324938\pi\) | |||||||
\(614\) | −2.17423 | − | 3.76588i | −0.0877450 | − | 0.151979i | ||||
\(615\) | −3.62372 | − | 6.27647i | −0.146123 | − | 0.253092i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31.3485 | −1.26204 | −0.631021 | − | 0.775766i | \(-0.717364\pi\) | ||||
−0.631021 | + | 0.775766i | \(0.717364\pi\) | |||||||
\(618\) | 19.1464 | 0.770182 | ||||||||
\(619\) | 9.77526 | − | 16.9312i | 0.392901 | − | 0.680524i | −0.599930 | − | 0.800052i | \(-0.704805\pi\) |
0.992831 | + | 0.119528i | \(0.0381383\pi\) | |||||||
\(620\) | −0.275255 | + | 0.476756i | −0.0110545 | + | 0.0191470i | ||||
\(621\) | −24.9217 | + | 43.1656i | −1.00007 | + | 1.73218i | ||||
\(622\) | −3.27526 | + | 5.67291i | −0.131326 | + | 0.227463i | ||||
\(623\) | 4.67423 | + | 8.09601i | 0.187269 | + | 0.324360i | ||||
\(624\) | 6.89898 | + | 11.9494i | 0.276180 | + | 0.478358i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 3.00000 | − | 5.19615i | 0.119904 | − | 0.207680i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 21.5959 | 0.861771 | ||||||||
\(629\) | −13.1237 | − | 22.7310i | −0.523277 | − | 0.906343i | ||||
\(630\) | −39.5959 | −1.57754 | ||||||||
\(631\) | −4.89898 | + | 8.48528i | −0.195025 | + | 0.337794i | −0.946909 | − | 0.321502i | \(-0.895812\pi\) |
0.751884 | + | 0.659296i | \(0.229146\pi\) | |||||||
\(632\) | −1.00000 | − | 1.73205i | −0.0397779 | − | 0.0688973i | ||||
\(633\) | 26.4722 | − | 45.8512i | 1.05218 | − | 1.82242i | ||||
\(634\) | 13.8485 | + | 23.9863i | 0.549993 | + | 0.952616i | ||||
\(635\) | 3.44949 | + | 5.97469i | 0.136889 | + | 0.237098i | ||||
\(636\) | 12.0732 | + | 20.9114i | 0.478734 | + | 0.829192i | ||||
\(637\) | 25.5959 | + | 44.3334i | 1.01415 | + | 1.75655i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.55051 | − | 2.68556i | −0.0613372 | − | 0.106239i | ||||
\(640\) | 0.500000 | − | 0.866025i | 0.0197642 | − | 0.0342327i | ||||
\(641\) | −15.3485 | − | 26.5843i | −0.606228 | − | 1.05002i | −0.991856 | − | 0.127364i | \(-0.959349\pi\) |
0.385628 | − | 0.922654i | \(-0.373985\pi\) | |||||||
\(642\) | −26.6464 | + | 46.1530i | −1.05165 | + | 1.82151i | ||||
\(643\) | −1.04541 | −0.0412269 | −0.0206134 | − | 0.999788i | \(-0.506562\pi\) | ||||
−0.0206134 | + | 0.999788i | \(0.506562\pi\) | |||||||
\(644\) | −5.44949 | − | 9.43879i | −0.214740 | − | 0.371941i | ||||
\(645\) | −13.7980 | −0.543294 | ||||||||
\(646\) | −30.6969 | −1.20775 | ||||||||
\(647\) | −16.3485 | + | 28.3164i | −0.642725 | + | 1.11323i | 0.342097 | + | 0.939665i | \(0.388863\pi\) |
−0.984822 | + | 0.173567i | \(0.944471\pi\) | |||||||
\(648\) | 43.4949 | 1.70864 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2.00000 | + | 3.46410i | 0.0784465 | + | 0.135873i | ||||
\(651\) | 4.22474 | − | 7.31747i | 0.165581 | − | 0.286794i | ||||
\(652\) | 3.72474 | − | 6.45145i | 0.145872 | − | 0.252658i | ||||
\(653\) | 20.7474 | − | 35.9356i | 0.811910 | − | 1.40627i | −0.0996149 | − | 0.995026i | \(-0.531761\pi\) |
0.911525 | − | 0.411244i | \(-0.134906\pi\) | |||||||
\(654\) | −18.0227 | + | 31.2162i | −0.704743 | + | 1.22065i | ||||
\(655\) | 10.2474 | 0.400401 | ||||||||
\(656\) | −2.10102 | −0.0820311 | ||||||||
\(657\) | 37.5959 | − | 65.1180i | 1.46676 | − | 2.54050i | ||||
\(658\) | −16.3485 | − | 28.3164i | −0.637330 | − | 1.10389i | ||||
\(659\) | −16.8990 | − | 29.2699i | −0.658291 | − | 1.14019i | −0.981058 | − | 0.193715i | \(-0.937946\pi\) |
0.322767 | − | 0.946478i | \(-0.395387\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −43.1464 | −1.67820 | −0.839101 | − | 0.543976i | \(-0.816918\pi\) | ||||
−0.839101 | + | 0.543976i | \(0.816918\pi\) | |||||||
\(662\) | 2.89898 | 0.112672 | ||||||||
\(663\) | 30.6969 | + | 53.1687i | 1.19217 | + | 2.06490i | ||||
\(664\) | −6.17423 | + | 10.6941i | −0.239607 | + | 0.415011i | ||||
\(665\) | 30.6969 | 1.19038 | ||||||||
\(666\) | −26.2474 | − | 45.4619i | −1.01707 | − | 1.76161i | ||||
\(667\) | −14.6969 | −0.569068 | ||||||||
\(668\) | −7.12372 | + | 12.3387i | −0.275625 | + | 0.477397i | ||||
\(669\) | 31.3939 | 1.21376 | ||||||||
\(670\) | 7.00000 | + | 4.24264i | 0.270434 | + | 0.163908i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −7.67423 | + | 13.2922i | −0.296040 | + | 0.512756i | ||||
\(673\) | −14.0000 | −0.539660 | −0.269830 | − | 0.962908i | \(-0.586968\pi\) | ||||
−0.269830 | + | 0.962908i | \(0.586968\pi\) | |||||||
\(674\) | −0.224745 | − | 0.389270i | −0.00865685 | − | 0.0149941i | ||||
\(675\) | 20.3485 | 0.783213 | ||||||||
\(676\) | −1.50000 | + | 2.59808i | −0.0576923 | + | 0.0999260i | ||||
\(677\) | −14.0505 | − | 24.3362i | −0.540005 | − | 0.935316i | −0.998903 | − | 0.0468271i | \(-0.985089\pi\) |
0.458898 | − | 0.888489i | \(-0.348244\pi\) | |||||||
\(678\) | 13.7980 | 0.529907 | ||||||||
\(679\) | 70.2929 | 2.69759 | ||||||||
\(680\) | 2.22474 | − | 3.85337i | 0.0853151 | − | 0.147770i | ||||
\(681\) | −38.5454 | − | 66.7626i | −1.47706 | − | 2.55835i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.92679 | + | 10.2655i | −0.226782 | + | 0.392798i | −0.956853 | − | 0.290574i | \(-0.906154\pi\) |
0.730070 | + | 0.683372i | \(0.239487\pi\) | |||||||
\(684\) | −61.3939 | −2.34745 | ||||||||
\(685\) | 0.449490 | 0.0171741 | ||||||||
\(686\) | −12.8990 | + | 22.3417i | −0.492485 | + | 0.853010i | ||||
\(687\) | −3.87628 | + | 6.71391i | −0.147889 | + | 0.256152i | ||||
\(688\) | −2.00000 | + | 3.46410i | −0.0762493 | + | 0.132068i | ||||
\(689\) | −14.0000 | + | 24.2487i | −0.533358 | + | 0.923802i | ||||
\(690\) | 4.22474 | + | 7.31747i | 0.160833 | + | 0.278571i | ||||
\(691\) | 3.24745 | + | 5.62475i | 0.123539 | + | 0.213975i | 0.921161 | − | 0.389182i | \(-0.127242\pi\) |
−0.797622 | + | 0.603158i | \(0.793909\pi\) | |||||||
\(692\) | −9.00000 | −0.342129 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 18.6969 | 0.709726 | ||||||||
\(695\) | 9.79796 | 0.371658 | ||||||||
\(696\) | 10.3485 | + | 17.9241i | 0.392258 | + | 0.679410i | ||||
\(697\) | −9.34847 | −0.354099 | ||||||||
\(698\) | −2.89898 | + | 5.02118i | −0.109728 | + | 0.190054i | ||||
\(699\) | 6.12372 | + | 10.6066i | 0.231621 | + | 0.401179i | ||||
\(700\) | −2.22474 | + | 3.85337i | −0.0840875 | + | 0.145644i | ||||
\(701\) | 11.7980 | + | 20.4347i | 0.445603 | + | 0.771807i | 0.998094 | − | 0.0617121i | \(-0.0196561\pi\) |
−0.552491 | + | 0.833519i | \(0.686323\pi\) | |||||||
\(702\) | 40.6969 | + | 70.4892i | 1.53601 | + | 2.66044i | ||||
\(703\) | 20.3485 | + | 35.2446i | 0.767457 | + | 1.32927i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 12.6742 | + | 21.9524i | 0.477339 | + | 0.826776i | ||||
\(706\) | −0.224745 | − | 0.389270i | −0.00845838 | − | 0.0146504i | ||||
\(707\) | 27.2474 | − | 47.1940i | 1.02475 | − | 1.77491i | ||||
\(708\) | 11.8990 | + | 20.6096i | 0.447191 | + | 0.774558i | ||||
\(709\) | 13.7980 | − | 23.8988i | 0.518193 | − | 0.897537i | −0.481583 | − | 0.876400i | \(-0.659938\pi\) |
0.999777 | − | 0.0211367i | \(-0.00672853\pi\) | |||||||
\(710\) | −0.348469 | −0.0130778 | ||||||||
\(711\) | −8.89898 | − | 15.4135i | −0.333738 | − | 0.578051i | ||||
\(712\) | −2.10102 | −0.0787391 | ||||||||
\(713\) | −1.34847 | −0.0505006 | ||||||||
\(714\) | −34.1464 | + | 59.1433i | −1.27790 | + | 2.21338i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.12372 | − | 10.6066i | −0.228854 | − | 0.396387i | ||||
\(717\) | 44.4949 | + | 77.0674i | 1.66169 | + | 2.87814i | ||||
\(718\) | −7.07321 | + | 12.2512i | −0.263970 | + | 0.457209i | ||||
\(719\) | −7.82577 | + | 13.5546i | −0.291852 | + | 0.505502i | −0.974248 | − | 0.225481i | \(-0.927605\pi\) |
0.682396 | + | 0.730983i | \(0.260938\pi\) | |||||||
\(720\) | 4.44949 | − | 7.70674i | 0.165823 | − | 0.287213i | ||||
\(721\) | −12.3485 | + | 21.3882i | −0.459881 | + | 0.796537i | ||||
\(722\) | 28.5959 | 1.06423 | ||||||||
\(723\) | −96.2372 | −3.57910 | ||||||||
\(724\) | 1.67423 | − | 2.89986i | 0.0622224 | − | 0.107772i | ||||
\(725\) | 3.00000 | + | 5.19615i | 0.111417 | + | 0.192980i | ||||
\(726\) | 18.9722 | + | 32.8608i | 0.704124 | + | 1.21958i | ||||
\(727\) | −15.2474 | + | 26.4094i | −0.565497 | + | 0.979469i | 0.431507 | + | 0.902110i | \(0.357982\pi\) |
−0.997003 | + | 0.0773591i | \(0.975351\pi\) | |||||||
\(728\) | −17.7980 | −0.659636 | ||||||||
\(729\) | 176.485 | 6.53647 | ||||||||
\(730\) | −4.22474 | − | 7.31747i | −0.156365 | − | 0.270832i | ||||
\(731\) | −8.89898 | + | 15.4135i | −0.329141 | + | 0.570088i | ||||
\(732\) | 15.3485 | 0.567296 | ||||||||
\(733\) | −13.7474 | − | 23.8113i | −0.507774 | − | 0.879490i | −0.999960 | − | 0.00899957i | \(-0.997135\pi\) |
0.492186 | − | 0.870490i | \(-0.336198\pi\) | |||||||
\(734\) | 6.24745 | 0.230598 | ||||||||
\(735\) | 22.0732 | − | 38.2319i | 0.814183 | − | 1.41021i | ||||
\(736\) | 2.44949 | 0.0902894 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −18.6969 | −0.688244 | ||||||||
\(739\) | 23.0454 | − | 39.9158i | 0.847739 | − | 1.46833i | −0.0354821 | − | 0.999370i | \(-0.511297\pi\) |
0.883221 | − | 0.468957i | \(-0.155370\pi\) | |||||||
\(740\) | −5.89898 | −0.216851 | ||||||||
\(741\) | −47.5959 | − | 82.4385i | −1.74848 | − | 3.02846i | ||||
\(742\) | −31.1464 | −1.14342 | ||||||||
\(743\) | 5.10102 | − | 8.83523i | 0.187138 | − | 0.324133i | −0.757157 | − | 0.653233i | \(-0.773412\pi\) |
0.944295 | + | 0.329100i | \(0.106745\pi\) | |||||||
\(744\) | 0.949490 | + | 1.64456i | 0.0348100 | + | 0.0602927i | ||||
\(745\) | −18.2474 | −0.668535 | ||||||||
\(746\) | −15.0000 | −0.549189 | ||||||||
\(747\) | −54.9444 | + | 95.1665i | −2.01031 | + | 3.48196i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −34.3712 | − | 59.5326i | −1.25590 | − | 2.17527i | ||||
\(750\) | 1.72474 | − | 2.98735i | 0.0629788 | − | 0.109082i | ||||
\(751\) | 14.3485 | 0.523583 | 0.261792 | − | 0.965124i | \(-0.415687\pi\) | ||||
0.261792 | + | 0.965124i | \(0.415687\pi\) | |||||||
\(752\) | 7.34847 | 0.267971 | ||||||||
\(753\) | −21.8207 | + | 37.7945i | −0.795189 | + | 1.37731i | ||||
\(754\) | −12.0000 | + | 20.7846i | −0.437014 | + | 0.756931i | ||||
\(755\) | 3.27526 | − | 5.67291i | 0.119199 | − | 0.206458i | ||||
\(756\) | −45.2702 | + | 78.4102i | −1.64646 | + | 2.85175i | ||||
\(757\) | −22.0505 | − | 38.1926i | −0.801439 | − | 1.38813i | −0.918669 | − | 0.395029i | \(-0.870735\pi\) |
0.117229 | − | 0.993105i | \(-0.462599\pi\) | |||||||
\(758\) | −6.89898 | − | 11.9494i | −0.250582 | − | 0.434021i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.44949 | + | 5.97469i | −0.125126 | + | 0.216725i | ||||
\(761\) | 25.4949 | 0.924189 | 0.462095 | − | 0.886831i | \(-0.347098\pi\) | ||||
0.462095 | + | 0.886831i | \(0.347098\pi\) | |||||||
\(762\) | 23.7980 | 0.862109 | ||||||||
\(763\) | −23.2474 | − | 40.2658i | −0.841614 | − | 1.45772i | ||||
\(764\) | 19.4495 | 0.703658 | ||||||||
\(765\) | 19.7980 | − | 34.2911i | 0.715797 | − | 1.23980i | ||||
\(766\) | 4.34847 | + | 7.53177i | 0.157117 | + | 0.272134i | ||||
\(767\) | −13.7980 | + | 23.8988i | −0.498215 | + | 0.862934i | ||||
\(768\) | −1.72474 | − | 2.98735i | −0.0622364 | − | 0.107797i | ||||
\(769\) | −9.14643 | − | 15.8421i | −0.329829 | − | 0.571280i | 0.652649 | − | 0.757660i | \(-0.273658\pi\) |
−0.982478 | + | 0.186380i | \(0.940324\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.55051 | − | 11.3458i | −0.235911 | − | 0.408610i | ||||
\(772\) | 10.2247 | + | 17.7098i | 0.367997 | + | 0.637389i | ||||
\(773\) | 8.84847 | + | 15.3260i | 0.318257 | + | 0.551238i | 0.980125 | − | 0.198383i | \(-0.0635691\pi\) |
−0.661867 | + | 0.749621i | \(0.730236\pi\) | |||||||
\(774\) | −17.7980 | + | 30.8270i | −0.639734 | + | 1.10805i | ||||
\(775\) | 0.275255 | + | 0.476756i | 0.00988746 | + | 0.0171256i | ||||
\(776\) | −7.89898 | + | 13.6814i | −0.283557 | + | 0.491135i | ||||
\(777\) | 90.5403 | 3.24812 | ||||||||
\(778\) | 9.22474 | + | 15.9777i | 0.330723 | + | 0.572829i | ||||
\(779\) | 14.4949 | 0.519334 | ||||||||
\(780\) | 13.7980 | 0.494046 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 10.8990 | 0.389747 | ||||||||
\(783\) | 61.0454 | + | 105.734i | 2.18158 | + | 3.77862i | ||||
\(784\) | −6.39898 | − | 11.0834i | −0.228535 | − | 0.395834i | ||||
\(785\) | 10.7980 | − | 18.7026i | 0.385396 | − | 0.667525i | ||||
\(786\) | 17.6742 | − | 30.6127i | 0.630419 | − | 1.09192i | ||||
\(787\) | 18.4217 | − | 31.9073i | 0.656662 | − | 1.13737i | −0.324812 | − | 0.945779i | \(-0.605301\pi\) |
0.981474 | − | 0.191594i | \(-0.0613656\pi\) | |||||||
\(788\) | −0.449490 | + | 0.778539i | −0.0160124 | + | 0.0277343i | ||||
\(789\) | −51.3939 | −1.82967 | ||||||||
\(790\) | −2.00000 | −0.0711568 | ||||||||
\(791\) | −8.89898 | + | 15.4135i | −0.316411 | + | 0.548040i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.89898 | + | 15.4135i | 0.316012 | + | 0.547349i | ||||
\(794\) | 3.50000 | − | 6.06218i | 0.124210 | − | 0.215139i | ||||
\(795\) | 24.1464 | 0.856386 | ||||||||
\(796\) | −12.3485 | −0.437680 | ||||||||
\(797\) | −15.1969 | − | 26.3219i | −0.538303 | − | 0.932368i | −0.998996 | − | 0.0448086i | \(-0.985732\pi\) |
0.460692 | − | 0.887560i | \(-0.347601\pi\) | |||||||
\(798\) | 52.9444 | − | 91.7024i | 1.87421 | − | 3.24623i | ||||
\(799\) | 32.6969 | 1.15673 | ||||||||
\(800\) | −0.500000 | − | 0.866025i | −0.0176777 | − | 0.0306186i | ||||
\(801\) | −18.6969 | −0.660624 | ||||||||
\(802\) | −2.44949 | + | 4.24264i | −0.0864945 | + | 0.149813i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 24.7474 | − | 13.5939i | 0.872775 | − | 0.479422i | ||||
\(805\) | −10.8990 | −0.384139 | ||||||||
\(806\) | −1.10102 | + | 1.90702i | −0.0387818 | + | 0.0671720i | ||||
\(807\) | −26.2020 | −0.922356 | ||||||||
\(808\) | 6.12372 | + | 10.6066i | 0.215432 | + | 0.373139i | ||||
\(809\) | −22.6969 | −0.797982 | −0.398991 | − | 0.916955i | \(-0.630640\pi\) | ||||
−0.398991 | + | 0.916955i | \(0.630640\pi\) | |||||||
\(810\) | 21.7474 | − | 37.6677i | 0.764127 | − | 1.32351i | ||||
\(811\) | −11.3712 | − | 19.6954i | −0.399296 | − | 0.691601i | 0.594343 | − | 0.804211i | \(-0.297412\pi\) |
−0.993639 | + | 0.112611i | \(0.964079\pi\) | |||||||
\(812\) | −26.6969 | −0.936879 | ||||||||
\(813\) | 110.889 | 3.88904 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.72474 | − | 6.45145i | −0.130472 | − | 0.225984i | ||||
\(816\) | −7.67423 | − | 13.2922i | −0.268652 | − | 0.465319i | ||||
\(817\) | 13.7980 | − | 23.8988i | 0.482729 | − | 0.836112i | ||||
\(818\) | −37.8990 | −1.32511 | ||||||||
\(819\) | −158.384 | −5.53437 | ||||||||
\(820\) | −1.05051 | + | 1.81954i | −0.0366854 | + | 0.0635410i | ||||
\(821\) | −15.1237 | + | 26.1951i | −0.527822 | + | 0.914214i | 0.471652 | + | 0.881785i | \(0.343658\pi\) |
−0.999474 | + | 0.0324293i | \(0.989676\pi\) | |||||||
\(822\) | 0.775255 | − | 1.34278i | 0.0270401 | − | 0.0468349i | ||||
\(823\) | 12.1464 | − | 21.0382i | 0.423398 | − | 0.733347i | −0.572871 | − | 0.819645i | \(-0.694171\pi\) |
0.996269 | + | 0.0862986i | \(0.0275039\pi\) | |||||||
\(824\) | −2.77526 | − | 4.80688i | −0.0966806 | − | 0.167456i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −30.6969 | −1.06808 | ||||||||
\(827\) | 15.1464 | − | 26.2344i | 0.526693 | − | 0.912259i | −0.472823 | − | 0.881157i | \(-0.656765\pi\) |
0.999516 | − | 0.0311016i | \(-0.00990155\pi\) | |||||||
\(828\) | 21.7980 | 0.757531 | ||||||||
\(829\) | −19.8434 | −0.689189 | −0.344594 | − | 0.938752i | \(-0.611984\pi\) | ||||
−0.344594 | + | 0.938752i | \(0.611984\pi\) | |||||||
\(830\) | 6.17423 | + | 10.6941i | 0.214311 | + | 0.371197i | ||||
\(831\) | −55.5403 | −1.92667 | ||||||||
\(832\) | 2.00000 | − | 3.46410i | 0.0693375 | − | 0.120096i | ||||
\(833\) | −28.4722 | − | 49.3153i | −0.986503 | − | 1.70867i | ||||
\(834\) | 16.8990 | − | 29.2699i | 0.585164 | − | 1.01353i | ||||
\(835\) | 7.12372 | + | 12.3387i | 0.246527 | + | 0.426997i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.60102 | + | 9.70125i | 0.193600 | + | 0.335324i | ||||
\(838\) | −5.79796 | − | 10.0424i | −0.200287 | − | 0.346908i | ||||
\(839\) | −15.0732 | − | 26.1076i | −0.520385 | − | 0.901334i | −0.999719 | − | 0.0237009i | \(-0.992455\pi\) |
0.479334 | − | 0.877633i | \(-0.340878\pi\) | |||||||
\(840\) | 7.67423 | + | 13.2922i | 0.264786 | + | 0.458623i | ||||
\(841\) | −3.50000 | + | 6.06218i | −0.120690 | + | 0.209041i | ||||
\(842\) | −3.89898 | − | 6.75323i | −0.134368 | − | 0.232732i | ||||
\(843\) | 30.1742 | − | 52.2633i | 1.03926 | − | 1.80004i | ||||
\(844\) | −15.3485 | −0.528316 | ||||||||
\(845\) | 1.50000 | + | 2.59808i | 0.0516016 | + | 0.0893765i | ||||
\(846\) | 65.3939 | 2.24829 | ||||||||
\(847\) | −48.9444 | −1.68175 | ||||||||
\(848\) | 3.50000 | − | 6.06218i | 0.120190 | − | 0.208176i | ||||
\(849\) | 40.6969 | 1.39672 | ||||||||
\(850\) | −2.22474 | − | 3.85337i | −0.0763081 | − | 0.132170i | ||||
\(851\) | −7.22474 | − | 12.5136i | −0.247661 | − | 0.428962i | ||||
\(852\) | −0.601021 | + | 1.04100i | −0.0205906 | + | 0.0356640i | ||||
\(853\) | −4.05051 | + | 7.01569i | −0.138687 | + | 0.240213i | −0.927000 | − | 0.375062i | \(-0.877621\pi\) |
0.788313 | + | 0.615274i | \(0.210955\pi\) | |||||||
\(854\) | −9.89898 | + | 17.1455i | −0.338736 | + | 0.586708i | ||||
\(855\) | −30.6969 | + | 53.1687i | −1.04981 | + | 1.81833i | ||||
\(856\) | 15.4495 | 0.528053 | ||||||||
\(857\) | −53.6413 | −1.83235 | −0.916176 | − | 0.400775i | \(-0.868741\pi\) | ||||
−0.916176 | + | 0.400775i | \(0.868741\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.44949 | − | 9.43879i | −0.185934 | − | 0.322047i | 0.757957 | − | 0.652305i | \(-0.226198\pi\) |
−0.943891 | + | 0.330257i | \(0.892864\pi\) | |||||||
\(860\) | 2.00000 | + | 3.46410i | 0.0681994 | + | 0.118125i | ||||
\(861\) | 16.1237 | − | 27.9271i | 0.549495 | − | 0.951753i | ||||
\(862\) | 16.3485 | 0.556831 | ||||||||
\(863\) | 27.7526 | 0.944708 | 0.472354 | − | 0.881409i | \(-0.343404\pi\) | ||||
0.472354 | + | 0.881409i | \(0.343404\pi\) | |||||||
\(864\) | −10.1742 | − | 17.6223i | −0.346134 | − | 0.599523i | ||||
\(865\) | −4.50000 | + | 7.79423i | −0.153005 | + | 0.265012i | ||||
\(866\) | 18.0454 | 0.613208 | ||||||||
\(867\) | −4.82577 | − | 8.35847i | −0.163892 | − | 0.283869i | ||||
\(868\) | −2.44949 | −0.0831411 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 20.6969 | 0.701692 | ||||||||
\(871\) | 28.0000 | + | 16.9706i | 0.948744 | + | 0.575026i | ||||
\(872\) | 10.4495 | 0.353864 | ||||||||
\(873\) | −70.2929 | + | 121.751i | −2.37905 | + | 4.12064i | ||||
\(874\) | −16.8990 | −0.571617 | ||||||||
\(875\) | 2.22474 | + | 3.85337i | 0.0752101 | + | 0.130268i | ||||
\(876\) | −29.1464 | −0.984767 | ||||||||
\(877\) | −20.0000 | + | 34.6410i | −0.675352 | + | 1.16974i | 0.301014 | + | 0.953620i | \(0.402675\pi\) |
−0.976366 | + | 0.216124i | \(0.930658\pi\) | |||||||
\(878\) | 0.275255 | + | 0.476756i | 0.00928941 | + | 0.0160897i | ||||
\(879\) | −51.0454 | −1.72172 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.3990 | − | 18.0116i | 0.350351 | − | 0.606825i | −0.635960 | − | 0.771722i | \(-0.719396\pi\) |
0.986311 | + | 0.164897i | \(0.0527291\pi\) | |||||||
\(882\) | −56.9444 | − | 98.6306i | −1.91742 | − | 3.32106i | ||||
\(883\) | −2.89898 | − | 5.02118i | −0.0975584 | − | 0.168976i | 0.813115 | − | 0.582103i | \(-0.197770\pi\) |
−0.910674 | + | 0.413127i | \(0.864437\pi\) | |||||||
\(884\) | 8.89898 | − | 15.4135i | 0.299305 | − | 0.518412i | ||||
\(885\) | 23.7980 | 0.799960 | ||||||||
\(886\) | 11.2474 | 0.377865 | ||||||||
\(887\) | 8.22474 | − | 14.2457i | 0.276160 | − | 0.478323i | −0.694267 | − | 0.719717i | \(-0.744271\pi\) |
0.970427 | + | 0.241394i | \(0.0776047\pi\) | |||||||
\(888\) | −10.1742 | + | 17.6223i | −0.341425 | + | 0.591365i | ||||
\(889\) | −15.3485 | + | 26.5843i | −0.514771 | + | 0.891610i | ||||
\(890\) | −1.05051 | + | 1.81954i | −0.0352132 | + | 0.0609910i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.55051 | − | 7.88171i | −0.152362 | − | 0.263899i | ||||
\(893\) | −50.6969 | −1.69651 | ||||||||
\(894\) | −31.4722 | + | 54.5114i | −1.05259 | + | 1.82314i | ||||
\(895\) | −12.2474 | −0.409387 | ||||||||
\(896\) | 4.44949 | 0.148647 | ||||||||
\(897\) | 16.8990 | + | 29.2699i | 0.564241 | + | 0.977293i | ||||
\(898\) | 4.10102 | 0.136853 | ||||||||
\(899\) | −1.65153 | + | 2.86054i | −0.0550816 | + | 0.0954042i | ||||
\(900\) | −4.44949 | − | 7.70674i | −0.148316 | − | 0.256891i | ||||
\(901\) | 15.5732 | − | 26.9736i | 0.518819 | − | 0.898621i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −30.6969 | − | 53.1687i | −1.02153 | − | 1.76934i | ||||
\(904\) | −2.00000 | − | 3.46410i | −0.0665190 | − | 0.115214i | ||||
\(905\) | −1.67423 | − | 2.89986i | −0.0556534 | − | 0.0963946i | ||||
\(906\) | −11.2980 | − | 19.5686i | −0.375350 | − | 0.650124i | ||||
\(907\) | 9.87117 | + | 17.0974i | 0.327767 | + | 0.567709i | 0.982068 | − | 0.188525i | \(-0.0603706\pi\) |
−0.654302 | + | 0.756234i | \(0.727037\pi\) | |||||||
\(908\) | −11.1742 | + | 19.3543i | −0.370830 | + | 0.642296i | ||||
\(909\) | 54.4949 | + | 94.3879i | 1.80748 | + | 3.13065i | ||||
\(910\) | −8.89898 | + | 15.4135i | −0.294998 | + | 0.510952i | ||||
\(911\) | 40.8434 | 1.35320 | 0.676601 | − | 0.736350i | \(-0.263452\pi\) | ||||
0.676601 | + | 0.736350i | \(0.263452\pi\) | |||||||
\(912\) | 11.8990 | + | 20.6096i | 0.394015 | + | 0.682453i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 31.5505 | 1.04360 | ||||||||
\(915\) | 7.67423 | − | 13.2922i | 0.253702 | − | 0.439425i | ||||
\(916\) | 2.24745 | 0.0742578 | ||||||||
\(917\) | 22.7980 | + | 39.4872i | 0.752855 | + | 1.30398i | ||||
\(918\) | −45.2702 | − | 78.4102i | −1.49414 | − | 2.58792i | ||||
\(919\) | −7.17423 | + | 12.4261i | −0.236656 | + | 0.409900i | −0.959753 | − | 0.280846i | \(-0.909385\pi\) |
0.723097 | + | 0.690747i | \(0.242718\pi\) | |||||||
\(920\) | 1.22474 | − | 2.12132i | 0.0403786 | − | 0.0699379i | ||||
\(921\) | −7.50000 | + | 12.9904i | −0.247133 | + | 0.428048i | ||||
\(922\) | 19.3712 | − | 33.5519i | 0.637956 | − | 1.10497i | ||||
\(923\) | −1.39388 | −0.0458800 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.94949 | + | 5.10867i | −0.0969786 | + | 0.167972i | ||||
\(926\) | 4.67423 | + | 8.09601i | 0.153605 | + | 0.266051i | ||||
\(927\) | −24.6969 | − | 42.7764i | −0.811154 | − | 1.40496i | ||||
\(928\) | 3.00000 | − | 5.19615i | 0.0984798 | − | 0.170572i | ||||
\(929\) | −28.8990 | −0.948145 | −0.474072 | − | 0.880486i | \(-0.657216\pi\) | ||||
−0.474072 | + | 0.880486i | \(0.657216\pi\) | |||||||
\(930\) | 1.89898 | 0.0622700 | ||||||||
\(931\) | 44.1464 | + | 76.4639i | 1.44684 | + | 2.50600i | ||||
\(932\) | 1.77526 | − | 3.07483i | 0.0581504 | − | 0.100719i | ||||
\(933\) | 22.5959 | 0.739757 | ||||||||
\(934\) | −10.9722 | − | 19.0044i | −0.359021 | − | 0.621843i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 17.7980 | − | 30.8270i | 0.581744 | − | 1.00761i | ||||
\(937\) | −9.34847 | −0.305401 | −0.152701 | − | 0.988272i | \(-0.548797\pi\) | ||||
−0.152701 | + | 0.988272i | \(0.548797\pi\) | |||||||
\(938\) | −0.775255 | + | 36.4124i | −0.0253130 | + | 1.18891i | ||||
\(939\) | −20.6969 | −0.675419 | ||||||||
\(940\) | 3.67423 | − | 6.36396i | 0.119840 | − | 0.207570i | ||||
\(941\) | −47.5959 | −1.55158 | −0.775791 | − | 0.630990i | \(-0.782649\pi\) | ||||
−0.775791 | + | 0.630990i | \(0.782649\pi\) | |||||||
\(942\) | −37.2474 | − | 64.5145i | −1.21359 | − | 2.10200i | ||||
\(943\) | −5.14643 | −0.167591 | ||||||||
\(944\) | 3.44949 | − | 5.97469i | 0.112271 | − | 0.194460i | ||||
\(945\) | 45.2702 | + | 78.4102i | 1.47264 | + | 2.55068i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −24.4949 | −0.795977 | −0.397989 | − | 0.917390i | \(-0.630292\pi\) | ||||
−0.397989 | + | 0.917390i | \(0.630292\pi\) | |||||||
\(948\) | −3.44949 | + | 5.97469i | −0.112034 | + | 0.194049i | ||||
\(949\) | −16.8990 | − | 29.2699i | −0.548564 | − | 0.950141i | ||||
\(950\) | 3.44949 | + | 5.97469i | 0.111916 | + | 0.193845i | ||||
\(951\) | 47.7702 | − | 82.7403i | 1.54905 | − | 2.68304i | ||||
\(952\) | 19.7980 | 0.641656 | ||||||||
\(953\) | 0.202041 | 0.00654475 | 0.00327238 | − | 0.999995i | \(-0.498958\pi\) | ||||
0.00327238 | + | 0.999995i | \(0.498958\pi\) | |||||||
\(954\) | 31.1464 | − | 53.9472i | 1.00840 | − | 1.74660i | ||||
\(955\) | 9.72474 | − | 16.8438i | 0.314685 | − | 0.545051i | ||||
\(956\) | 12.8990 | − | 22.3417i | 0.417183 | − | 0.722582i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.65153 | + | 8.05669i | 0.150284 | + | 0.260300i | ||||
\(959\) | 1.00000 | + | 1.73205i | 0.0322917 | + | 0.0559308i | ||||
\(960\) | −3.44949 | −0.111332 | ||||||||
\(961\) | 15.3485 | − | 26.5843i | 0.495112 | − | 0.857559i | ||||
\(962\) | −23.5959 | −0.760763 | ||||||||
\(963\) | 137.485 | 4.43038 | ||||||||
\(964\) | 13.9495 | + | 24.1612i | 0.449283 | + | 0.778181i | ||||
\(965\) | 20.4495 | 0.658292 | ||||||||
\(966\) | −18.7980 | + | 32.5590i | −0.604814 | + | 1.04757i | ||||
\(967\) | −8.47219 | − | 14.6743i | −0.272447 | − | 0.471893i | 0.697041 | − | 0.717032i | \(-0.254500\pi\) |
−0.969488 | + | 0.245139i | \(0.921166\pi\) | |||||||
\(968\) | 5.50000 | − | 9.52628i | 0.176777 | − | 0.306186i | ||||
\(969\) | 52.9444 | + | 91.7024i | 1.70082 | + | 2.94590i | ||||
\(970\) | 7.89898 | + | 13.6814i | 0.253621 | + | 0.439284i | ||||
\(971\) | 3.79796 | + | 6.57826i | 0.121882 | + | 0.211106i | 0.920510 | − | 0.390719i | \(-0.127774\pi\) |
−0.798628 | + | 0.601825i | \(0.794440\pi\) | |||||||
\(972\) | −44.4949 | − | 77.0674i | −1.42717 | − | 2.47194i | ||||
\(973\) | 21.7980 | + | 37.7552i | 0.698810 | + | 1.21038i | ||||
\(974\) | 2.12372 | + | 3.67840i | 0.0680485 | + | 0.117863i | ||||
\(975\) | 6.89898 | − | 11.9494i | 0.220944 | − | 0.382687i | ||||
\(976\) | −2.22474 | − | 3.85337i | −0.0712123 | − | 0.123343i | ||||
\(977\) | −24.2702 | + | 42.0371i | −0.776471 | + | 1.34489i | 0.157493 | + | 0.987520i | \(0.449659\pi\) |
−0.933964 | + | 0.357367i | \(0.883675\pi\) | |||||||
\(978\) | −25.6969 | −0.821697 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −12.7980 | −0.408816 | ||||||||
\(981\) | 92.9898 | 2.96894 | ||||||||
\(982\) | −6.67423 | + | 11.5601i | −0.212983 | + | 0.368898i | ||||
\(983\) | −27.1464 | −0.865837 | −0.432918 | − | 0.901433i | \(-0.642516\pi\) | ||||
−0.432918 | + | 0.901433i | \(0.642516\pi\) | |||||||
\(984\) | 3.62372 | + | 6.27647i | 0.115520 | + | 0.200087i | ||||
\(985\) | 0.449490 | + | 0.778539i | 0.0143219 | + | 0.0248063i | ||||
\(986\) | 13.3485 | − | 23.1202i | 0.425102 | − | 0.736298i | ||||
\(987\) | −56.3939 | + | 97.6771i | −1.79504 | + | 3.10910i | ||||
\(988\) | −13.7980 | + | 23.8988i | −0.438972 | + | 0.760321i | ||||
\(989\) | −4.89898 | + | 8.48528i | −0.155778 | + | 0.269816i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −49.7423 | −1.58012 | −0.790059 | − | 0.613031i | \(-0.789950\pi\) | ||||
−0.790059 | + | 0.613031i | \(0.789950\pi\) | |||||||
\(992\) | 0.275255 | − | 0.476756i | 0.00873936 | − | 0.0151370i | ||||
\(993\) | −5.00000 | − | 8.66025i | −0.158670 | − | 0.274825i | ||||
\(994\) | −0.775255 | − | 1.34278i | −0.0245896 | − | 0.0425904i | ||||
\(995\) | −6.17423 | + | 10.6941i | −0.195736 | + | 0.339025i | ||||
\(996\) | 42.5959 | 1.34970 | ||||||||
\(997\) | −16.3939 | −0.519199 | −0.259600 | − | 0.965716i | \(-0.583591\pi\) | ||||
−0.259600 | + | 0.965716i | \(0.583591\pi\) | |||||||
\(998\) | 2.89898 | + | 5.02118i | 0.0917656 | + | 0.158943i | ||||
\(999\) | −60.0176 | + | 103.954i | −1.89887 | + | 3.28894i |
(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 | 670.2.e.f.431.2 | yes | 4 | |
67.37 | even | 3 | inner | 670.2.e.f.171.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
670.2.e.f.171.2 | ✓ | 4 | 67.37 | even | 3 | inner | |
670.2.e.f.431.2 | yes | 4 | 1.1 | even | 1 | trivial |