Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [38,3,Mod(27,38)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(38, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("38.27");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 38 = 2 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 38.d (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: | \(1.03542500457\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
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: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 31.2 | ||
Root | \(1.22474 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 38.31 |
Dual form | 38.3.d.a.27.2 |
$q$-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 \(\left(\mathbb{Z}/38\mathbb{Z}\right)^\times\).
\(n\) | \(21\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.22474 | − | 0.707107i | 0.612372 | − | 0.353553i | ||||
\(3\) | 0.275255 | − | 0.158919i | 0.0917517 | − | 0.0529729i | −0.453422 | − | 0.891296i | \(-0.649797\pi\) |
0.545174 | + | 0.838323i | \(0.316464\pi\) | |||||||
\(4\) | 1.00000 | − | 1.73205i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | 0.911684 | − | 0.410891i | \(-0.134782\pi\) |
−0.811684 | + | 0.584096i | \(0.801449\pi\) | |||||||
\(6\) | 0.224745 | − | 0.389270i | 0.0374575 | − | 0.0648783i | ||||
\(7\) | −2.89898 | −0.414140 | −0.207070 | − | 0.978326i | \(-0.566393\pi\) | ||||
−0.207070 | + | 0.978326i | \(0.566393\pi\) | |||||||
\(8\) | − | 2.82843i | − | 0.353553i | ||||||
\(9\) | −4.44949 | + | 7.70674i | −0.494388 | + | 0.856305i | ||||
\(10\) | 1.22474 | + | 0.707107i | 0.122474 | + | 0.0707107i | ||||
\(11\) | −5.10102 | −0.463729 | −0.231865 | − | 0.972748i | \(-0.574483\pi\) | ||||
−0.231865 | + | 0.972748i | \(0.574483\pi\) | |||||||
\(12\) | − | 0.635674i | − | 0.0529729i | ||||||
\(13\) | −0.151531 | − | 0.0874863i | −0.0116562 | − | 0.00672972i | 0.494161 | − | 0.869371i | \(-0.335475\pi\) |
−0.505817 | + | 0.862641i | \(0.668809\pi\) | |||||||
\(14\) | −3.55051 | + | 2.04989i | −0.253608 | + | 0.146421i | ||||
\(15\) | 0.275255 | + | 0.158919i | 0.0183503 | + | 0.0105946i | ||||
\(16\) | −2.00000 | − | 3.46410i | −0.125000 | − | 0.216506i | ||||
\(17\) | 5.94949 | + | 10.3048i | 0.349970 | + | 0.606166i | 0.986244 | − | 0.165298i | \(-0.0528584\pi\) |
−0.636274 | + | 0.771463i | \(0.719525\pi\) | |||||||
\(18\) | 12.5851i | 0.699170i | ||||||||
\(19\) | −3.34847 | − | 18.7026i | −0.176235 | − | 0.984348i | ||||
\(20\) | 2.00000 | 0.100000 | ||||||||
\(21\) | −0.797959 | + | 0.460702i | −0.0379980 | + | 0.0219382i | ||||
\(22\) | −6.24745 | + | 3.60697i | −0.283975 | + | 0.163953i | ||||
\(23\) | 8.52270 | − | 14.7618i | 0.370552 | − | 0.641815i | −0.619098 | − | 0.785314i | \(-0.712502\pi\) |
0.989651 | + | 0.143498i | \(0.0458351\pi\) | |||||||
\(24\) | −0.449490 | − | 0.778539i | −0.0187287 | − | 0.0324391i | ||||
\(25\) | 12.0000 | − | 20.7846i | 0.480000 | − | 0.831384i | ||||
\(26\) | −0.247449 | −0.00951726 | ||||||||
\(27\) | 5.68896i | 0.210702i | ||||||||
\(28\) | −2.89898 | + | 5.02118i | −0.103535 | + | 0.179328i | ||||
\(29\) | 38.5454 | + | 22.2542i | 1.32915 | + | 0.767386i | 0.985169 | − | 0.171589i | \(-0.0548903\pi\) |
0.343983 | + | 0.938976i | \(0.388224\pi\) | |||||||
\(30\) | 0.449490 | 0.0149830 | ||||||||
\(31\) | − | 31.1769i | − | 1.00571i | −0.864372 | − | 0.502853i | \(-0.832284\pi\) | ||
0.864372 | − | 0.502853i | \(-0.167716\pi\) | |||||||
\(32\) | −4.89898 | − | 2.82843i | −0.153093 | − | 0.0883883i | ||||
\(33\) | −1.40408 | + | 0.810647i | −0.0425479 | + | 0.0245651i | ||||
\(34\) | 14.5732 | + | 8.41385i | 0.428624 | + | 0.247466i | ||||
\(35\) | −1.44949 | − | 2.51059i | −0.0414140 | − | 0.0717311i | ||||
\(36\) | 8.89898 | + | 15.4135i | 0.247194 | + | 0.428152i | ||||
\(37\) | 21.9917i | 0.594371i | 0.954820 | + | 0.297186i | \(0.0960480\pi\) | ||||
−0.954820 | + | 0.297186i | \(0.903952\pi\) | |||||||
\(38\) | −17.3258 | − | 20.5382i | −0.455941 | − | 0.540479i | ||||
\(39\) | −0.0556128 | −0.00142597 | ||||||||
\(40\) | 2.44949 | − | 1.41421i | 0.0612372 | − | 0.0353553i | ||||
\(41\) | −46.9393 | + | 27.1004i | −1.14486 | + | 0.660986i | −0.947630 | − | 0.319371i | \(-0.896528\pi\) |
−0.197231 | + | 0.980357i | \(0.563195\pi\) | |||||||
\(42\) | −0.651531 | + | 1.12848i | −0.0155126 | + | 0.0268687i | ||||
\(43\) | −18.6691 | − | 32.3359i | −0.434166 | − | 0.751997i | 0.563061 | − | 0.826415i | \(-0.309623\pi\) |
−0.997227 | + | 0.0744178i | \(0.976290\pi\) | |||||||
\(44\) | −5.10102 | + | 8.83523i | −0.115932 | + | 0.200801i | ||||
\(45\) | −8.89898 | −0.197755 | ||||||||
\(46\) | − | 24.1058i | − | 0.524040i | ||||||
\(47\) | −40.7702 | + | 70.6160i | −0.867450 | + | 1.50247i | −0.00285637 | + | 0.999996i | \(0.500909\pi\) |
−0.864594 | + | 0.502472i | \(0.832424\pi\) | |||||||
\(48\) | −1.10102 | − | 0.635674i | −0.0229379 | − | 0.0132432i | ||||
\(49\) | −40.5959 | −0.828488 | ||||||||
\(50\) | − | 33.9411i | − | 0.678823i | ||||||
\(51\) | 3.27526 | + | 1.89097i | 0.0642207 | + | 0.0370778i | ||||
\(52\) | −0.303062 | + | 0.174973i | −0.00582811 | + | 0.00336486i | ||||
\(53\) | 48.2878 | + | 27.8789i | 0.911090 | + | 0.526018i | 0.880782 | − | 0.473523i | \(-0.157018\pi\) |
0.0303081 | + | 0.999541i | \(0.490351\pi\) | |||||||
\(54\) | 4.02270 | + | 6.96753i | 0.0744945 | + | 0.129028i | ||||
\(55\) | −2.55051 | − | 4.41761i | −0.0463729 | − | 0.0803202i | ||||
\(56\) | 8.19955i | 0.146421i | ||||||||
\(57\) | −3.89388 | − | 4.61586i | −0.0683136 | − | 0.0809799i | ||||
\(58\) | 62.9444 | 1.08525 | ||||||||
\(59\) | −29.9166 | + | 17.2723i | −0.507061 | + | 0.292752i | −0.731625 | − | 0.681708i | \(-0.761238\pi\) |
0.224564 | + | 0.974459i | \(0.427904\pi\) | |||||||
\(60\) | 0.550510 | − | 0.317837i | 0.00917517 | − | 0.00529729i | ||||
\(61\) | 38.0959 | − | 65.9841i | 0.624523 | − | 1.08171i | −0.364110 | − | 0.931356i | \(-0.618627\pi\) |
0.988633 | − | 0.150350i | \(-0.0480400\pi\) | |||||||
\(62\) | −22.0454 | − | 38.1838i | −0.355571 | − | 0.615867i | ||||
\(63\) | 12.8990 | − | 22.3417i | 0.204746 | − | 0.354630i | ||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | − | 0.174973i | − | 0.00269189i | ||||||
\(66\) | −1.14643 | + | 1.98567i | −0.0173701 | + | 0.0300859i | ||||
\(67\) | 102.659 | + | 59.2702i | 1.53222 | + | 0.884629i | 0.999259 | + | 0.0384912i | \(0.0122552\pi\) |
0.532964 | + | 0.846138i | \(0.321078\pi\) | |||||||
\(68\) | 23.7980 | 0.349970 | ||||||||
\(69\) | − | 5.41767i | − | 0.0785169i | ||||||
\(70\) | −3.55051 | − | 2.04989i | −0.0507216 | − | 0.0292841i | ||||
\(71\) | 65.4773 | − | 37.8033i | 0.922215 | − | 0.532441i | 0.0378743 | − | 0.999283i | \(-0.487941\pi\) |
0.884341 | + | 0.466841i | \(0.154608\pi\) | |||||||
\(72\) | 21.7980 | + | 12.5851i | 0.302749 | + | 0.174792i | ||||
\(73\) | −14.6918 | − | 25.4470i | −0.201258 | − | 0.348589i | 0.747676 | − | 0.664064i | \(-0.231170\pi\) |
−0.948934 | + | 0.315475i | \(0.897836\pi\) | |||||||
\(74\) | 15.5505 | + | 26.9343i | 0.210142 | + | 0.363977i | ||||
\(75\) | − | 7.62809i | − | 0.101708i | ||||||
\(76\) | −35.7423 | − | 12.9029i | −0.470294 | − | 0.169775i | ||||
\(77\) | 14.7878 | 0.192049 | ||||||||
\(78\) | −0.0681115 | + | 0.0393242i | −0.000873225 | + | 0.000504157i | ||||
\(79\) | −57.2196 | + | 33.0358i | −0.724299 | + | 0.418174i | −0.816333 | − | 0.577582i | \(-0.803997\pi\) |
0.0920338 | + | 0.995756i | \(0.470663\pi\) | |||||||
\(80\) | 2.00000 | − | 3.46410i | 0.0250000 | − | 0.0433013i | ||||
\(81\) | −39.1413 | − | 67.7948i | −0.483226 | − | 0.836972i | ||||
\(82\) | −38.3258 | + | 66.3822i | −0.467387 | + | 0.809539i | ||||
\(83\) | −30.6969 | −0.369843 | −0.184921 | − | 0.982753i | \(-0.559203\pi\) | ||||
−0.184921 | + | 0.982753i | \(0.559203\pi\) | |||||||
\(84\) | 1.84281i | 0.0219382i | ||||||||
\(85\) | −5.94949 | + | 10.3048i | −0.0699940 | + | 0.121233i | ||||
\(86\) | −45.7298 | − | 26.4021i | −0.531742 | − | 0.307002i | ||||
\(87\) | 14.1464 | 0.162603 | ||||||||
\(88\) | 14.4279i | 0.163953i | ||||||||
\(89\) | −8.84847 | − | 5.10867i | −0.0994210 | − | 0.0574007i | 0.449465 | − | 0.893298i | \(-0.351615\pi\) |
−0.548886 | + | 0.835897i | \(0.684948\pi\) | |||||||
\(90\) | −10.8990 | + | 6.29253i | −0.121100 | + | 0.0699170i | ||||
\(91\) | 0.439285 | + | 0.253621i | 0.00482730 | + | 0.00278704i | ||||
\(92\) | −17.0454 | − | 29.5235i | −0.185276 | − | 0.320908i | ||||
\(93\) | −4.95459 | − | 8.58161i | −0.0532752 | − | 0.0922753i | ||||
\(94\) | 115.315i | 1.22676i | ||||||||
\(95\) | 14.5227 | − | 12.2512i | 0.152871 | − | 0.128960i | ||||
\(96\) | −1.79796 | −0.0187287 | ||||||||
\(97\) | −128.848 | + | 74.3907i | −1.32833 | + | 0.766914i | −0.985042 | − | 0.172314i | \(-0.944876\pi\) |
−0.343293 | + | 0.939228i | \(0.611542\pi\) | |||||||
\(98\) | −49.7196 | + | 28.7056i | −0.507343 | + | 0.292915i | ||||
\(99\) | 22.6969 | − | 39.3123i | 0.229262 | − | 0.397093i | ||||
\(100\) | −24.0000 | − | 41.5692i | −0.240000 | − | 0.415692i | ||||
\(101\) | 70.2423 | − | 121.663i | 0.695469 | − | 1.20459i | −0.274554 | − | 0.961572i | \(-0.588530\pi\) |
0.970022 | − | 0.243015i | \(-0.0781366\pi\) | |||||||
\(102\) | 5.34847 | 0.0524360 | ||||||||
\(103\) | 113.965i | 1.10646i | 0.833028 | + | 0.553230i | \(0.186605\pi\) | ||||
−0.833028 | + | 0.553230i | \(0.813395\pi\) | |||||||
\(104\) | −0.247449 | + | 0.428594i | −0.00237931 | + | 0.00412109i | ||||
\(105\) | −0.797959 | − | 0.460702i | −0.00759961 | − | 0.00438764i | ||||
\(106\) | 78.8536 | 0.743902 | ||||||||
\(107\) | 113.965i | 1.06510i | 0.846399 | + | 0.532549i | \(0.178766\pi\) | ||||
−0.846399 | + | 0.532549i | \(0.821234\pi\) | |||||||
\(108\) | 9.85357 | + | 5.68896i | 0.0912368 | + | 0.0526756i | ||||
\(109\) | 59.2423 | − | 34.2036i | 0.543508 | − | 0.313794i | −0.202992 | − | 0.979180i | \(-0.565066\pi\) |
0.746499 | + | 0.665386i | \(0.231733\pi\) | |||||||
\(110\) | −6.24745 | − | 3.60697i | −0.0567950 | − | 0.0327906i | ||||
\(111\) | 3.49490 | + | 6.05334i | 0.0314856 | + | 0.0545346i | ||||
\(112\) | 5.79796 | + | 10.0424i | 0.0517675 | + | 0.0896639i | ||||
\(113\) | − | 81.9313i | − | 0.725056i | −0.931973 | − | 0.362528i | \(-0.881914\pi\) | ||
0.931973 | − | 0.362528i | \(-0.118086\pi\) | |||||||
\(114\) | −8.03291 | − | 2.89986i | −0.0704641 | − | 0.0254374i | ||||
\(115\) | 17.0454 | 0.148221 | ||||||||
\(116\) | 77.0908 | − | 44.5084i | 0.664576 | − | 0.383693i | ||||
\(117\) | 1.34847 | − | 0.778539i | 0.0115254 | − | 0.00665418i | ||||
\(118\) | −24.4268 | + | 42.3084i | −0.207007 | + | 0.358546i | ||||
\(119\) | −17.2474 | − | 29.8735i | −0.144937 | − | 0.251037i | ||||
\(120\) | 0.449490 | − | 0.778539i | 0.00374575 | − | 0.00648783i | ||||
\(121\) | −94.9796 | −0.784955 | ||||||||
\(122\) | − | 107.752i | − | 0.883209i | ||||||
\(123\) | −8.61352 | + | 14.9191i | −0.0700286 | + | 0.121293i | ||||
\(124\) | −54.0000 | − | 31.1769i | −0.435484 | − | 0.251427i | ||||
\(125\) | 49.0000 | 0.392000 | ||||||||
\(126\) | − | 36.4838i | − | 0.289554i | ||||||
\(127\) | 116.174 | + | 67.0732i | 0.914758 | + | 0.528136i | 0.881959 | − | 0.471326i | \(-0.156225\pi\) |
0.0327989 | + | 0.999462i | \(0.489558\pi\) | |||||||
\(128\) | −9.79796 | + | 5.65685i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | −10.2775 | − | 5.93375i | −0.0796709 | − | 0.0459980i | ||||
\(130\) | −0.123724 | − | 0.214297i | −0.000951726 | − | 0.00164844i | ||||
\(131\) | −41.3763 | − | 71.6658i | −0.315849 | − | 0.547067i | 0.663768 | − | 0.747938i | \(-0.268956\pi\) |
−0.979618 | + | 0.200871i | \(0.935623\pi\) | |||||||
\(132\) | 3.24259i | 0.0245651i | ||||||||
\(133\) | 9.70714 | + | 54.2185i | 0.0729860 | + | 0.407658i | ||||
\(134\) | 167.641 | 1.25105 | ||||||||
\(135\) | −4.92679 | + | 2.84448i | −0.0364947 | + | 0.0210702i | ||||
\(136\) | 29.1464 | − | 16.8277i | 0.214312 | − | 0.123733i | ||||
\(137\) | 5.94949 | − | 10.3048i | 0.0434269 | − | 0.0752177i | −0.843495 | − | 0.537137i | \(-0.819506\pi\) |
0.886922 | + | 0.461919i | \(0.152839\pi\) | |||||||
\(138\) | −3.83087 | − | 6.63526i | −0.0277599 | − | 0.0480816i | ||||
\(139\) | −20.8712 | + | 36.1499i | −0.150152 | + | 0.260071i | −0.931283 | − | 0.364296i | \(-0.881310\pi\) |
0.781131 | + | 0.624367i | \(0.214643\pi\) | |||||||
\(140\) | −5.79796 | −0.0414140 | ||||||||
\(141\) | 25.9165i | 0.183805i | ||||||||
\(142\) | 53.4620 | − | 92.5989i | 0.376493 | − | 0.652105i | ||||
\(143\) | 0.772962 | + | 0.446270i | 0.00540533 | + | 0.00312077i | ||||
\(144\) | 35.5959 | 0.247194 | ||||||||
\(145\) | 44.5084i | 0.306955i | ||||||||
\(146\) | −35.9875 | − | 20.7774i | −0.246490 | − | 0.142311i | ||||
\(147\) | −11.1742 | + | 6.45145i | −0.0760152 | + | 0.0438874i | ||||
\(148\) | 38.0908 | + | 21.9917i | 0.257370 | + | 0.148593i | ||||
\(149\) | 17.8383 | + | 30.8968i | 0.119720 | + | 0.207361i | 0.919657 | − | 0.392723i | \(-0.128467\pi\) |
−0.799937 | + | 0.600084i | \(0.795134\pi\) | |||||||
\(150\) | −5.39388 | − | 9.34247i | −0.0359592 | − | 0.0622831i | ||||
\(151\) | − | 85.5527i | − | 0.566574i | −0.959035 | − | 0.283287i | \(-0.908575\pi\) | ||
0.959035 | − | 0.283287i | \(-0.0914249\pi\) | |||||||
\(152\) | −52.8990 | + | 9.47090i | −0.348020 | + | 0.0623086i | ||||
\(153\) | −105.889 | −0.692083 | ||||||||
\(154\) | 18.1112 | − | 10.4565i | 0.117605 | − | 0.0678995i | ||||
\(155\) | 27.0000 | − | 15.5885i | 0.174194 | − | 0.100571i | ||||
\(156\) | −0.0556128 | + | 0.0963242i | −0.000356492 | + | 0.000617463i | ||||
\(157\) | 100.076 | + | 173.336i | 0.637424 | + | 1.10405i | 0.985996 | + | 0.166768i | \(0.0533332\pi\) |
−0.348573 | + | 0.937282i | \(0.613333\pi\) | |||||||
\(158\) | −46.7196 | + | 80.9208i | −0.295694 | + | 0.512157i | ||||
\(159\) | 17.7219 | 0.111459 | ||||||||
\(160\) | − | 5.65685i | − | 0.0353553i | ||||||
\(161\) | −24.7071 | + | 42.7940i | −0.153461 | + | 0.265801i | ||||
\(162\) | −95.8763 | − | 55.3542i | −0.591829 | − | 0.341693i | ||||
\(163\) | −127.303 | −0.781000 | −0.390500 | − | 0.920603i | \(-0.627698\pi\) | ||||
−0.390500 | + | 0.920603i | \(0.627698\pi\) | |||||||
\(164\) | 108.402i | 0.660986i | ||||||||
\(165\) | −1.40408 | − | 0.810647i | −0.00850959 | − | 0.00491301i | ||||
\(166\) | −37.5959 | + | 21.7060i | −0.226481 | + | 0.130759i | ||||
\(167\) | −158.917 | − | 91.7505i | −0.951596 | − | 0.549404i | −0.0580198 | − | 0.998315i | \(-0.518479\pi\) |
−0.893576 | + | 0.448911i | \(0.851812\pi\) | |||||||
\(168\) | 1.30306 | + | 2.25697i | 0.00775632 | + | 0.0134343i | ||||
\(169\) | −84.4847 | − | 146.332i | −0.499909 | − | 0.865869i | ||||
\(170\) | 16.8277i | 0.0989865i | ||||||||
\(171\) | 159.035 | + | 57.4113i | 0.930030 | + | 0.335739i | ||||
\(172\) | −74.6765 | −0.434166 | ||||||||
\(173\) | −57.6214 | + | 33.2677i | −0.333072 | + | 0.192299i | −0.657204 | − | 0.753713i | \(-0.728261\pi\) |
0.324132 | + | 0.946012i | \(0.394928\pi\) | |||||||
\(174\) | 17.3258 | − | 10.0030i | 0.0995734 | − | 0.0574887i | ||||
\(175\) | −34.7878 | + | 60.2542i | −0.198787 | + | 0.344309i | ||||
\(176\) | 10.2020 | + | 17.6705i | 0.0579661 | + | 0.100400i | ||||
\(177\) | −5.48979 | + | 9.50860i | −0.0310158 | + | 0.0537209i | ||||
\(178\) | −14.4495 | −0.0811769 | ||||||||
\(179\) | − | 24.2134i | − | 0.135270i | −0.997710 | − | 0.0676351i | \(-0.978455\pi\) | ||
0.997710 | − | 0.0676351i | \(-0.0215454\pi\) | |||||||
\(180\) | −8.89898 | + | 15.4135i | −0.0494388 | + | 0.0856305i | ||||
\(181\) | 30.8939 | + | 17.8366i | 0.170684 | + | 0.0985447i | 0.582909 | − | 0.812538i | \(-0.301915\pi\) |
−0.412224 | + | 0.911082i | \(0.635248\pi\) | |||||||
\(182\) | 0.717349 | 0.00394148 | ||||||||
\(183\) | − | 24.2166i | − | 0.132331i | ||||||
\(184\) | −41.7526 | − | 24.1058i | −0.226916 | − | 0.131010i | ||||
\(185\) | −19.0454 | + | 10.9959i | −0.102948 | + | 0.0594371i | ||||
\(186\) | −12.1362 | − | 7.00685i | −0.0652485 | − | 0.0376712i | ||||
\(187\) | −30.3485 | − | 52.5651i | −0.162291 | − | 0.281097i | ||||
\(188\) | 81.5403 | + | 141.232i | 0.433725 | + | 0.751234i | ||||
\(189\) | − | 16.4922i | − | 0.0872602i | ||||||
\(190\) | 9.12372 | − | 25.2737i | 0.0480196 | − | 0.133019i | ||||
\(191\) | −180.252 | −0.943728 | −0.471864 | − | 0.881671i | \(-0.656419\pi\) | ||||
−0.471864 | + | 0.881671i | \(0.656419\pi\) | |||||||
\(192\) | −2.20204 | + | 1.27135i | −0.0114690 | + | 0.00662161i | ||||
\(193\) | 188.985 | − | 109.110i | 0.979195 | − | 0.565339i | 0.0771682 | − | 0.997018i | \(-0.475412\pi\) |
0.902027 | + | 0.431679i | \(0.142079\pi\) | |||||||
\(194\) | −105.204 | + | 182.219i | −0.542290 | + | 0.939274i | ||||
\(195\) | −0.0278064 | − | 0.0481621i | −0.000142597 | − | 0.000246985i | ||||
\(196\) | −40.5959 | + | 70.3142i | −0.207122 | + | 0.358746i | ||||
\(197\) | 340.091 | 1.72635 | 0.863175 | − | 0.504905i | \(-0.168473\pi\) | ||||
0.863175 | + | 0.504905i | \(0.168473\pi\) | |||||||
\(198\) | − | 64.1966i | − | 0.324225i | ||||||
\(199\) | 166.694 | − | 288.723i | 0.837659 | − | 1.45087i | −0.0541881 | − | 0.998531i | \(-0.517257\pi\) |
0.891847 | − | 0.452337i | \(-0.149410\pi\) | |||||||
\(200\) | −58.7878 | − | 33.9411i | −0.293939 | − | 0.169706i | ||||
\(201\) | 37.6765 | 0.187445 | ||||||||
\(202\) | − | 198.675i | − | 0.983541i | ||||||
\(203\) | −111.742 | − | 64.5145i | −0.550455 | − | 0.317805i | ||||
\(204\) | 6.55051 | − | 3.78194i | 0.0321103 | − | 0.0185389i | ||||
\(205\) | −46.9393 | − | 27.1004i | −0.228972 | − | 0.132197i | ||||
\(206\) | 80.5857 | + | 139.579i | 0.391193 | + | 0.677566i | ||||
\(207\) | 75.8434 | + | 131.365i | 0.366393 | + | 0.634611i | ||||
\(208\) | 0.699891i | 0.00336486i | ||||||||
\(209\) | 17.0806 | + | 95.4024i | 0.0817254 | + | 0.456471i | ||||
\(210\) | −1.30306 | −0.00620505 | ||||||||
\(211\) | 302.750 | − | 174.793i | 1.43483 | − | 0.828401i | 0.437349 | − | 0.899292i | \(-0.355918\pi\) |
0.997484 | + | 0.0708908i | \(0.0225842\pi\) | |||||||
\(212\) | 96.5755 | − | 55.7579i | 0.455545 | − | 0.263009i | ||||
\(213\) | 12.0153 | − | 20.8111i | 0.0564099 | − | 0.0977048i | ||||
\(214\) | 80.5857 | + | 139.579i | 0.376569 | + | 0.652236i | ||||
\(215\) | 18.6691 | − | 32.3359i | 0.0868332 | − | 0.150399i | ||||
\(216\) | 16.0908 | 0.0744945 | ||||||||
\(217\) | 90.3812i | 0.416503i | ||||||||
\(218\) | 48.3712 | − | 83.7813i | 0.221886 | − | 0.384318i | ||||
\(219\) | −8.08801 | − | 4.66961i | −0.0369315 | − | 0.0213224i | ||||
\(220\) | −10.2020 | −0.0463729 | ||||||||
\(221\) | − | 2.08200i | − | 0.00942080i | ||||||
\(222\) | 8.56072 | + | 4.94253i | 0.0385618 | + | 0.0222637i | ||||
\(223\) | −27.5227 | + | 15.8902i | −0.123420 | + | 0.0712567i | −0.560439 | − | 0.828196i | \(-0.689368\pi\) |
0.437019 | + | 0.899452i | \(0.356034\pi\) | |||||||
\(224\) | 14.2020 | + | 8.19955i | 0.0634020 | + | 0.0366051i | ||||
\(225\) | 106.788 | + | 184.962i | 0.474612 | + | 0.822053i | ||||
\(226\) | −57.9342 | − | 100.345i | −0.256346 | − | 0.444004i | ||||
\(227\) | − | 249.730i | − | 1.10013i | −0.835121 | − | 0.550066i | \(-0.814603\pi\) | ||
0.835121 | − | 0.550066i | \(-0.185397\pi\) | |||||||
\(228\) | −11.8888 | + | 2.12854i | −0.0521437 | + | 0.00933569i | ||||
\(229\) | −259.687 | −1.13400 | −0.567002 | − | 0.823717i | \(-0.691897\pi\) | ||||
−0.567002 | + | 0.823717i | \(0.691897\pi\) | |||||||
\(230\) | 20.8763 | − | 12.0529i | 0.0907664 | − | 0.0524040i | ||||
\(231\) | 4.07041 | − | 2.35005i | 0.0176208 | − | 0.0101734i | ||||
\(232\) | 62.9444 | − | 109.023i | 0.271312 | − | 0.469926i | ||||
\(233\) | 195.141 | + | 337.995i | 0.837516 | + | 1.45062i | 0.891965 | + | 0.452104i | \(0.149327\pi\) |
−0.0544486 | + | 0.998517i | \(0.517340\pi\) | |||||||
\(234\) | 1.10102 | − | 1.90702i | 0.00470522 | − | 0.00814967i | ||||
\(235\) | −81.5403 | −0.346980 | ||||||||
\(236\) | 69.0894i | 0.292752i | ||||||||
\(237\) | −10.5000 | + | 18.1865i | −0.0443038 | + | 0.0767364i | ||||
\(238\) | −42.2474 | − | 24.3916i | −0.177510 | − | 0.102486i | ||||
\(239\) | −296.677 | −1.24132 | −0.620662 | − | 0.784078i | \(-0.713136\pi\) | ||||
−0.620662 | + | 0.784078i | \(0.713136\pi\) | |||||||
\(240\) | − | 1.27135i | − | 0.00529729i | ||||||
\(241\) | −99.7270 | − | 57.5774i | −0.413805 | − | 0.238911i | 0.278618 | − | 0.960402i | \(-0.410124\pi\) |
−0.692423 | + | 0.721491i | \(0.743457\pi\) | |||||||
\(242\) | −116.326 | + | 67.1607i | −0.480685 | + | 0.277524i | ||||
\(243\) | −65.8888 | − | 38.0409i | −0.271147 | − | 0.156547i | ||||
\(244\) | −76.1918 | − | 131.968i | −0.312262 | − | 0.540853i | ||||
\(245\) | −20.2980 | − | 35.1571i | −0.0828488 | − | 0.143498i | ||||
\(246\) | 24.3627i | 0.0990354i | ||||||||
\(247\) | −1.12883 | + | 3.12697i | −0.00457015 | + | 0.0126598i | ||||
\(248\) | −88.1816 | −0.355571 | ||||||||
\(249\) | −8.44949 | + | 4.87832i | −0.0339337 | + | 0.0195916i | ||||
\(250\) | 60.0125 | − | 34.6482i | 0.240050 | − | 0.138593i | ||||
\(251\) | −244.962 | + | 424.287i | −0.975944 | + | 1.69038i | −0.299161 | + | 0.954203i | \(0.596707\pi\) |
−0.676783 | + | 0.736182i | \(0.736627\pi\) | |||||||
\(252\) | −25.7980 | − | 44.6834i | −0.102373 | − | 0.177315i | ||||
\(253\) | −43.4745 | + | 75.3000i | −0.171836 | + | 0.297629i | ||||
\(254\) | 189.712 | 0.746897 | ||||||||
\(255\) | 3.78194i | 0.0148311i | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −197.379 | − | 113.957i | −0.768010 | − | 0.443411i | 0.0641543 | − | 0.997940i | \(-0.479565\pi\) |
−0.832164 | + | 0.554529i | \(0.812898\pi\) | |||||||
\(258\) | −16.7832 | −0.0650510 | ||||||||
\(259\) | − | 63.7536i | − | 0.246153i | ||||||
\(260\) | −0.303062 | − | 0.174973i | −0.00116562 | − | 0.000672972i | ||||
\(261\) | −343.015 | + | 198.040i | −1.31423 | + | 0.758773i | ||||
\(262\) | −101.351 | − | 58.5149i | −0.386835 | − | 0.223339i | ||||
\(263\) | −67.9620 | − | 117.714i | −0.258411 | − | 0.447580i | 0.707406 | − | 0.706808i | \(-0.249865\pi\) |
−0.965816 | + | 0.259227i | \(0.916532\pi\) | |||||||
\(264\) | 2.29286 | + | 3.97134i | 0.00868506 | + | 0.0150430i | ||||
\(265\) | 55.7579i | 0.210407i | ||||||||
\(266\) | 50.2270 | + | 59.5398i | 0.188823 | + | 0.223834i | ||||
\(267\) | −3.24745 | −0.0121627 | ||||||||
\(268\) | 205.318 | − | 118.540i | 0.766111 | − | 0.442315i | ||||
\(269\) | 225.090 | − | 129.956i | 0.836767 | − | 0.483108i | −0.0193970 | − | 0.999812i | \(-0.506175\pi\) |
0.856164 | + | 0.516704i | \(0.172841\pi\) | |||||||
\(270\) | −4.02270 | + | 6.96753i | −0.0148989 | + | 0.0258057i | ||||
\(271\) | 116.492 | + | 201.770i | 0.429860 | + | 0.744540i | 0.996860 | − | 0.0791780i | \(-0.0252295\pi\) |
−0.567000 | + | 0.823718i | \(0.691896\pi\) | |||||||
\(272\) | 23.7980 | − | 41.2193i | 0.0874925 | − | 0.151541i | ||||
\(273\) | 0.161220 | 0.000590551 | ||||||||
\(274\) | − | 16.8277i | − | 0.0614150i | ||||||
\(275\) | −61.2122 | + | 106.023i | −0.222590 | + | 0.385537i | ||||
\(276\) | −9.38367 | − | 5.41767i | −0.0339988 | − | 0.0196292i | ||||
\(277\) | −9.44387 | −0.0340934 | −0.0170467 | − | 0.999855i | \(-0.505426\pi\) | ||||
−0.0170467 | + | 0.999855i | \(0.505426\pi\) | |||||||
\(278\) | 59.0326i | 0.212347i | ||||||||
\(279\) | 240.272 | + | 138.721i | 0.861192 | + | 0.497209i | ||||
\(280\) | −7.10102 | + | 4.09978i | −0.0253608 | + | 0.0146421i | ||||
\(281\) | 135.591 | + | 78.2834i | 0.482530 | + | 0.278589i | 0.721470 | − | 0.692446i | \(-0.243467\pi\) |
−0.238940 | + | 0.971034i | \(0.576800\pi\) | |||||||
\(282\) | 18.3258 | + | 31.7412i | 0.0649850 | + | 0.112557i | ||||
\(283\) | −1.46709 | − | 2.54108i | −0.00518407 | − | 0.00897907i | 0.863422 | − | 0.504483i | \(-0.168317\pi\) |
−0.868606 | + | 0.495504i | \(0.834983\pi\) | |||||||
\(284\) | − | 151.213i | − | 0.532441i | ||||||
\(285\) | 2.05051 | − | 5.68012i | 0.00719477 | − | 0.0199303i | ||||
\(286\) | 1.26224 | 0.00441343 | ||||||||
\(287\) | 136.076 | − | 78.5635i | 0.474132 | − | 0.273741i | ||||
\(288\) | 43.5959 | − | 25.1701i | 0.151375 | − | 0.0873962i | ||||
\(289\) | 73.7071 | − | 127.665i | 0.255042 | − | 0.441746i | ||||
\(290\) | 31.4722 | + | 54.5114i | 0.108525 | + | 0.187970i | ||||
\(291\) | −23.6441 | + | 40.9528i | −0.0812513 | + | 0.140731i | ||||
\(292\) | −58.7673 | −0.201258 | ||||||||
\(293\) | − | 332.361i | − | 1.13434i | −0.823601 | − | 0.567169i | \(-0.808039\pi\) | ||
0.823601 | − | 0.567169i | \(-0.191961\pi\) | |||||||
\(294\) | −9.12372 | + | 15.8028i | −0.0310331 | + | 0.0537509i | ||||
\(295\) | −29.9166 | − | 17.2723i | −0.101412 | − | 0.0585503i | ||||
\(296\) | 62.2020 | 0.210142 | ||||||||
\(297\) | − | 29.0195i | − | 0.0977088i | ||||||
\(298\) | 43.6946 | + | 25.2271i | 0.146626 | + | 0.0846547i | ||||
\(299\) | −2.58290 | + | 1.49124i | −0.00863847 | + | 0.00498743i | ||||
\(300\) | −13.2122 | − | 7.62809i | −0.0440408 | − | 0.0254270i | ||||
\(301\) | 54.1214 | + | 93.7411i | 0.179805 | + | 0.311432i | ||||
\(302\) | −60.4949 | − | 104.780i | −0.200314 | − | 0.346954i | ||||
\(303\) | − | 44.6513i | − | 0.147364i | ||||||
\(304\) | −58.0908 | + | 49.0047i | −0.191088 | + | 0.161200i | ||||
\(305\) | 76.1918 | 0.249809 | ||||||||
\(306\) | −129.687 | + | 74.8747i | −0.423813 | + | 0.244688i | ||||
\(307\) | 222.962 | − | 128.727i | 0.726261 | − | 0.419307i | −0.0907920 | − | 0.995870i | \(-0.528940\pi\) |
0.817053 | + | 0.576563i | \(0.195607\pi\) | |||||||
\(308\) | 14.7878 | − | 25.6131i | 0.0480122 | − | 0.0831595i | ||||
\(309\) | 18.1112 | + | 31.3696i | 0.0586124 | + | 0.101520i | ||||
\(310\) | 22.0454 | − | 38.1838i | 0.0711142 | − | 0.123173i | ||||
\(311\) | 217.666 | 0.699892 | 0.349946 | − | 0.936770i | \(-0.386200\pi\) | ||||
0.349946 | + | 0.936770i | \(0.386200\pi\) | |||||||
\(312\) | 0.157297i | 0.000504157i | ||||||||
\(313\) | 155.121 | − | 268.677i | 0.495594 | − | 0.858394i | −0.504393 | − | 0.863474i | \(-0.668284\pi\) |
0.999987 | + | 0.00508018i | \(0.00161708\pi\) | |||||||
\(314\) | 245.134 | + | 141.528i | 0.780681 | + | 0.450727i | ||||
\(315\) | 25.7980 | 0.0818983 | ||||||||
\(316\) | 132.143i | 0.418174i | ||||||||
\(317\) | −298.939 | − | 172.593i | −0.943026 | − | 0.544456i | −0.0521185 | − | 0.998641i | \(-0.516597\pi\) |
−0.890908 | + | 0.454185i | \(0.849931\pi\) | |||||||
\(318\) | 21.7049 | − | 12.5313i | 0.0682542 | − | 0.0394066i | ||||
\(319\) | −196.621 | − | 113.519i | −0.616367 | − | 0.355859i | ||||
\(320\) | −4.00000 | − | 6.92820i | −0.0125000 | − | 0.0216506i | ||||
\(321\) | 18.1112 | + | 31.3696i | 0.0564213 | + | 0.0977245i | ||||
\(322\) | 69.8824i | 0.217026i | ||||||||
\(323\) | 172.805 | − | 145.776i | 0.535001 | − | 0.451320i | ||||
\(324\) | −156.565 | −0.483226 | ||||||||
\(325\) | −3.63674 | + | 2.09967i | −0.0111900 | + | 0.00646053i | ||||
\(326\) | −155.914 | + | 90.0169i | −0.478263 | + | 0.276125i | ||||
\(327\) | 10.8712 | − | 18.8294i | 0.0332452 | − | 0.0575823i | ||||
\(328\) | 76.6515 | + | 132.764i | 0.233694 | + | 0.404769i | ||||
\(329\) | 118.192 | − | 204.714i | 0.359246 | − | 0.622232i | ||||
\(330\) | −2.29286 | −0.00694805 | ||||||||
\(331\) | 487.318i | 1.47226i | 0.676841 | + | 0.736130i | \(0.263349\pi\) | ||||
−0.676841 | + | 0.736130i | \(0.736651\pi\) | |||||||
\(332\) | −30.6969 | + | 53.1687i | −0.0924607 | + | 0.160147i | ||||
\(333\) | −169.485 | − | 97.8520i | −0.508963 | − | 0.293850i | ||||
\(334\) | −259.510 | −0.776975 | ||||||||
\(335\) | 118.540i | 0.353852i | ||||||||
\(336\) | 3.19184 | + | 1.84281i | 0.00949951 | + | 0.00548455i | ||||
\(337\) | 144.393 | − | 83.3655i | 0.428467 | − | 0.247376i | −0.270226 | − | 0.962797i | \(-0.587099\pi\) |
0.698693 | + | 0.715421i | \(0.253765\pi\) | |||||||
\(338\) | −206.944 | − | 119.479i | −0.612262 | − | 0.353489i | ||||
\(339\) | −13.0204 | − | 22.5520i | −0.0384083 | − | 0.0665251i | ||||
\(340\) | 11.8990 | + | 20.6096i | 0.0349970 | + | 0.0606166i | ||||
\(341\) | 159.034i | 0.466376i | ||||||||
\(342\) | 235.373 | − | 42.1407i | 0.688227 | − | 0.123218i | ||||
\(343\) | 259.737 | 0.757250 | ||||||||
\(344\) | −91.4597 | + | 52.8043i | −0.265871 | + | 0.153501i | ||||
\(345\) | 4.69184 | − | 2.70883i | 0.0135995 | − | 0.00785169i | ||||
\(346\) | −47.0477 | + | 81.4890i | −0.135976 | + | 0.235517i | ||||
\(347\) | −188.871 | − | 327.134i | −0.544297 | − | 0.942751i | −0.998651 | − | 0.0519291i | \(-0.983463\pi\) |
0.454353 | − | 0.890822i | \(-0.349870\pi\) | |||||||
\(348\) | 14.1464 | − | 24.5023i | 0.0406507 | − | 0.0704090i | ||||
\(349\) | −586.434 | −1.68033 | −0.840163 | − | 0.542334i | \(-0.817541\pi\) | ||||
−0.840163 | + | 0.542334i | \(0.817541\pi\) | |||||||
\(350\) | 98.3946i | 0.281128i | ||||||||
\(351\) | 0.497706 | − | 0.862053i | 0.00141797 | − | 0.00245599i | ||||
\(352\) | 24.9898 | + | 14.4279i | 0.0709937 | + | 0.0409883i | ||||
\(353\) | 476.817 | 1.35076 | 0.675379 | − | 0.737471i | \(-0.263980\pi\) | ||||
0.675379 | + | 0.737471i | \(0.263980\pi\) | |||||||
\(354\) | 15.5275i | 0.0438630i | ||||||||
\(355\) | 65.4773 | + | 37.8033i | 0.184443 | + | 0.106488i | ||||
\(356\) | −17.6969 | + | 10.2173i | −0.0497105 | + | 0.0287004i | ||||
\(357\) | −9.49490 | − | 5.48188i | −0.0265964 | − | 0.0153554i | ||||
\(358\) | −17.1214 | − | 29.6552i | −0.0478252 | − | 0.0828357i | ||||
\(359\) | 123.704 | + | 214.262i | 0.344580 | + | 0.596831i | 0.985277 | − | 0.170963i | \(-0.0546879\pi\) |
−0.640697 | + | 0.767794i | \(0.721355\pi\) | |||||||
\(360\) | 25.1701i | 0.0699170i | ||||||||
\(361\) | −338.576 | + | 125.250i | −0.937882 | + | 0.346954i | ||||
\(362\) | 50.4495 | 0.139363 | ||||||||
\(363\) | −26.1436 | + | 15.0940i | −0.0720210 | + | 0.0415813i | ||||
\(364\) | 0.878569 | − | 0.507242i | 0.00241365 | − | 0.00139352i | ||||
\(365\) | 14.6918 | − | 25.4470i | 0.0402516 | − | 0.0697178i | ||||
\(366\) | −17.1237 | − | 29.6592i | −0.0467861 | − | 0.0810360i | ||||
\(367\) | −241.962 | + | 419.090i | −0.659297 | + | 1.14194i | 0.321501 | + | 0.946909i | \(0.395813\pi\) |
−0.980798 | + | 0.195027i | \(0.937521\pi\) | |||||||
\(368\) | −68.1816 | −0.185276 | ||||||||
\(369\) | − | 482.332i | − | 1.30713i | ||||||
\(370\) | −15.5505 | + | 26.9343i | −0.0420284 | + | 0.0727953i | ||||
\(371\) | −139.985 | − | 80.8205i | −0.377319 | − | 0.217845i | ||||
\(372\) | −19.8184 | −0.0532752 | ||||||||
\(373\) | − | 140.908i | − | 0.377768i | −0.981999 | − | 0.188884i | \(-0.939513\pi\) | ||
0.981999 | − | 0.188884i | \(-0.0604871\pi\) | |||||||
\(374\) | −74.3383 | − | 42.9192i | −0.198765 | − | 0.114757i | ||||
\(375\) | 13.4875 | − | 7.78701i | 0.0359667 | − | 0.0207654i | ||||
\(376\) | 199.732 | + | 115.315i | 0.531203 | + | 0.306690i | ||||
\(377\) | −3.89388 | − | 6.74439i | −0.0103286 | − | 0.0178896i | ||||
\(378\) | −11.6617 | − | 20.1987i | −0.0308512 | − | 0.0534358i | ||||
\(379\) | 468.633i | 1.23650i | 0.785982 | + | 0.618249i | \(0.212158\pi\) | ||||
−0.785982 | + | 0.618249i | \(0.787842\pi\) | |||||||
\(380\) | −6.69694 | − | 37.4052i | −0.0176235 | − | 0.0984348i | ||||
\(381\) | 42.6367 | 0.111907 | ||||||||
\(382\) | −220.763 | + | 127.457i | −0.577913 | + | 0.333658i | ||||
\(383\) | −482.552 | + | 278.602i | −1.25993 | + | 0.727420i | −0.973060 | − | 0.230551i | \(-0.925947\pi\) |
−0.286867 | + | 0.957970i | \(0.592614\pi\) | |||||||
\(384\) | −1.79796 | + | 3.11416i | −0.00468218 | + | 0.00810978i | ||||
\(385\) | 7.39388 | + | 12.8066i | 0.0192049 | + | 0.0332638i | ||||
\(386\) | 154.305 | − | 267.265i | 0.399755 | − | 0.692396i | ||||
\(387\) | 332.272 | 0.858585 | ||||||||
\(388\) | 297.563i | 0.766914i | ||||||||
\(389\) | −46.5602 | + | 80.6446i | −0.119692 | + | 0.207313i | −0.919646 | − | 0.392749i | \(-0.871524\pi\) |
0.799954 | + | 0.600062i | \(0.204857\pi\) | |||||||
\(390\) | −0.0681115 | − | 0.0393242i | −0.000174645 | − | 0.000100831i | ||||
\(391\) | 202.823 | 0.518729 | ||||||||
\(392\) | 114.823i | 0.292915i | ||||||||
\(393\) | −22.7781 | − | 13.1509i | −0.0579595 | − | 0.0334629i | ||||
\(394\) | 416.524 | − | 240.481i | 1.05717 | − | 0.610357i | ||||
\(395\) | −57.2196 | − | 33.0358i | −0.144860 | − | 0.0836349i | ||||
\(396\) | −45.3939 | − | 78.6245i | −0.114631 | − | 0.198547i | ||||
\(397\) | −129.682 | − | 224.615i | −0.326654 | − | 0.565781i | 0.655192 | − | 0.755463i | \(-0.272588\pi\) |
−0.981846 | + | 0.189681i | \(0.939255\pi\) | |||||||
\(398\) | − | 471.482i | − | 1.18463i | ||||||
\(399\) | 11.2883 | + | 13.3813i | 0.0282914 | + | 0.0335370i | ||||
\(400\) | −96.0000 | −0.240000 | ||||||||
\(401\) | −389.484 | + | 224.869i | −0.971282 | + | 0.560770i | −0.899627 | − | 0.436659i | \(-0.856161\pi\) |
−0.0716553 | + | 0.997429i | \(0.522828\pi\) | |||||||
\(402\) | 46.1441 | − | 26.6413i | 0.114786 | − | 0.0662720i | ||||
\(403\) | −2.72755 | + | 4.72426i | −0.00676812 | + | 0.0117227i | ||||
\(404\) | −140.485 | − | 243.327i | −0.347734 | − | 0.602294i | ||||
\(405\) | 39.1413 | − | 67.7948i | 0.0966452 | − | 0.167394i | ||||
\(406\) | −182.474 | −0.449445 | ||||||||
\(407\) | − | 112.180i | − | 0.275627i | ||||||
\(408\) | 5.34847 | − | 9.26382i | 0.0131090 | − | 0.0227054i | ||||
\(409\) | 90.8326 | + | 52.4423i | 0.222085 | + | 0.128221i | 0.606915 | − | 0.794767i | \(-0.292407\pi\) |
−0.384830 | + | 0.922987i | \(0.625740\pi\) | |||||||
\(410\) | −76.6515 | −0.186955 | ||||||||
\(411\) | − | 3.78194i | − | 0.00920180i | ||||||
\(412\) | 197.394 | + | 113.965i | 0.479111 | + | 0.276615i | ||||
\(413\) | 86.7276 | − | 50.0722i | 0.209994 | − | 0.121240i | ||||
\(414\) | 185.778 | + | 107.259i | 0.448738 | + | 0.259079i | ||||
\(415\) | −15.3485 | − | 26.5843i | −0.0369843 | − | 0.0640586i | ||||
\(416\) | 0.494897 | + | 0.857187i | 0.00118966 | + | 0.00206055i | ||||
\(417\) | 13.2673i | 0.0318160i | ||||||||
\(418\) | 88.3791 | + | 104.766i | 0.211433 | + | 0.250636i | ||||
\(419\) | 463.121 | 1.10530 | 0.552651 | − | 0.833413i | \(-0.313616\pi\) | ||||
0.552651 | + | 0.833413i | \(0.313616\pi\) | |||||||
\(420\) | −1.59592 | + | 0.921404i | −0.00379980 | + | 0.00219382i | ||||
\(421\) | −418.711 | + | 241.743i | −0.994563 | + | 0.574211i | −0.906635 | − | 0.421915i | \(-0.861358\pi\) |
−0.0879282 | + | 0.996127i | \(0.528025\pi\) | |||||||
\(422\) | 247.194 | − | 428.153i | 0.585768 | − | 1.01458i | ||||
\(423\) | −362.813 | − | 628.410i | −0.857713 | − | 1.48560i | ||||
\(424\) | 78.8536 | − | 136.578i | 0.185975 | − | 0.322119i | ||||
\(425\) | 285.576 | 0.671942 | ||||||||
\(426\) | − | 33.9844i | − | 0.0797756i | ||||||
\(427\) | −110.439 | + | 191.286i | −0.258640 | + | 0.447978i | ||||
\(428\) | 197.394 | + | 113.965i | 0.461201 | + | 0.266274i | ||||
\(429\) | 0.283682 | 0.000661264 | ||||||||
\(430\) | − | 52.8043i | − | 0.122801i | ||||||
\(431\) | 392.447 | + | 226.579i | 0.910549 | + | 0.525706i | 0.880608 | − | 0.473846i | \(-0.157135\pi\) |
0.0299413 | + | 0.999552i | \(0.490468\pi\) | |||||||
\(432\) | 19.7071 | − | 11.3779i | 0.0456184 | − | 0.0263378i | ||||
\(433\) | 650.651 | + | 375.654i | 1.50266 | + | 0.867560i | 0.999995 | + | 0.00307767i | \(0.000979653\pi\) |
0.502663 | + | 0.864482i | \(0.332354\pi\) | |||||||
\(434\) | 63.9092 | + | 110.694i | 0.147256 | + | 0.255055i | ||||
\(435\) | 7.07321 | + | 12.2512i | 0.0162603 | + | 0.0281636i | ||||
\(436\) | − | 136.814i | − | 0.313794i | ||||||
\(437\) | −304.621 | − | 109.968i | −0.697074 | − | 0.251642i | ||||
\(438\) | −13.2077 | −0.0301545 | ||||||||
\(439\) | 543.325 | − | 313.689i | 1.23764 | − | 0.714553i | 0.269031 | − | 0.963132i | \(-0.413297\pi\) |
0.968612 | + | 0.248578i | \(0.0799632\pi\) | |||||||
\(440\) | −12.4949 | + | 7.21393i | −0.0283975 | + | 0.0163953i | ||||
\(441\) | 180.631 | − | 312.862i | 0.409594 | − | 0.709438i | ||||
\(442\) | −1.47219 | − | 2.54991i | −0.00333075 | − | 0.00576904i | ||||
\(443\) | −220.628 | + | 382.139i | −0.498032 | + | 0.862617i | −0.999997 | − | 0.00227061i | \(-0.999277\pi\) |
0.501965 | + | 0.864888i | \(0.332611\pi\) | |||||||
\(444\) | 13.9796 | 0.0314856 | ||||||||
\(445\) | − | 10.2173i | − | 0.0229603i | ||||||
\(446\) | −22.4722 | + | 38.9230i | −0.0503861 | + | 0.0872713i | ||||
\(447\) | 9.82015 | + | 5.66966i | 0.0219690 | + | 0.0126838i | ||||
\(448\) | 23.1918 | 0.0517675 | ||||||||
\(449\) | 347.932i | 0.774904i | 0.921890 | + | 0.387452i | \(0.126645\pi\) | ||||
−0.921890 | + | 0.387452i | \(0.873355\pi\) | |||||||
\(450\) | 261.576 | + | 151.021i | 0.581279 | + | 0.335602i | ||||
\(451\) | 239.438 | − | 138.240i | 0.530905 | − | 0.306518i | ||||
\(452\) | −141.909 | − | 81.9313i | −0.313958 | − | 0.181264i | ||||
\(453\) | −13.5959 | − | 23.5488i | −0.0300131 | − | 0.0519842i | ||||
\(454\) | −176.586 | − | 305.855i | −0.388955 | − | 0.673690i | ||||
\(455\) | 0.507242i | 0.00111482i | ||||||||
\(456\) | −13.0556 | + | 11.0135i | −0.0286307 | + | 0.0241525i | ||||
\(457\) | 443.576 | 0.970625 | 0.485312 | − | 0.874341i | \(-0.338706\pi\) | ||||
0.485312 | + | 0.874341i | \(0.338706\pi\) | |||||||
\(458\) | −318.050 | + | 183.626i | −0.694432 | + | 0.400931i | ||||
\(459\) | −58.6237 | + | 33.8464i | −0.127721 | + | 0.0737395i | ||||
\(460\) | 17.0454 | − | 29.5235i | 0.0370552 | − | 0.0641815i | ||||
\(461\) | −97.8076 | − | 169.408i | −0.212164 | − | 0.367479i | 0.740227 | − | 0.672357i | \(-0.234718\pi\) |
−0.952392 | + | 0.304878i | \(0.901384\pi\) | |||||||
\(462\) | 3.32347 | − | 5.75642i | 0.00719366 | − | 0.0124598i | ||||
\(463\) | −720.958 | −1.55715 | −0.778573 | − | 0.627555i | \(-0.784056\pi\) | ||||
−0.778573 | + | 0.627555i | \(0.784056\pi\) | |||||||
\(464\) | − | 178.034i | − | 0.383693i | ||||||
\(465\) | 4.95459 | − | 8.58161i | 0.0106550 | − | 0.0184551i | ||||
\(466\) | 477.997 | + | 275.972i | 1.02574 | + | 0.592214i | ||||
\(467\) | 271.889 | 0.582203 | 0.291101 | − | 0.956692i | \(-0.405978\pi\) | ||||
0.291101 | + | 0.956692i | \(0.405978\pi\) | |||||||
\(468\) | − | 3.11416i | − | 0.00665418i | ||||||
\(469\) | −297.606 | − | 171.823i | −0.634555 | − | 0.366360i | ||||
\(470\) | −99.8661 | + | 57.6577i | −0.212481 | + | 0.122676i | ||||
\(471\) | 55.0926 | + | 31.8077i | 0.116969 | + | 0.0675323i | ||||
\(472\) | 48.8536 | + | 84.6169i | 0.103503 | + | 0.179273i | ||||
\(473\) | 95.2316 | + | 164.946i | 0.201335 | + | 0.348723i | ||||
\(474\) | 29.6985i | 0.0626550i | ||||||||
\(475\) | −428.908 | − | 154.835i | −0.902965 | − | 0.325968i | ||||
\(476\) | −68.9898 | −0.144937 | ||||||||
\(477\) | −429.712 | + | 248.094i | −0.900863 | + | 0.520114i | ||||
\(478\) | −363.353 | + | 209.782i | −0.760153 | + | 0.438874i | ||||
\(479\) | −173.599 | + | 300.682i | −0.362419 | + | 0.627728i | −0.988358 | − | 0.152144i | \(-0.951382\pi\) |
0.625939 | + | 0.779872i | \(0.284716\pi\) | |||||||
\(480\) | −0.898979 | − | 1.55708i | −0.00187287 | − | 0.00324391i | ||||
\(481\) | 1.92398 | − | 3.33243i | 0.00399995 | − | 0.00692812i | ||||
\(482\) | −162.854 | −0.337870 | ||||||||
\(483\) | 15.7057i | 0.0325170i | ||||||||
\(484\) | −94.9796 | + | 164.509i | −0.196239 | + | 0.339896i | ||||
\(485\) | −128.848 | − | 74.3907i | −0.265667 | − | 0.153383i | ||||
\(486\) | −107.596 | −0.221391 | ||||||||
\(487\) | − | 495.960i | − | 1.01840i | −0.860648 | − | 0.509200i | \(-0.829942\pi\) | ||
0.860648 | − | 0.509200i | \(-0.170058\pi\) | |||||||
\(488\) | −186.631 | − | 107.752i | −0.382441 | − | 0.220802i | ||||
\(489\) | −35.0408 | + | 20.2308i | −0.0716581 | + | 0.0413718i | ||||
\(490\) | −49.7196 | − | 28.7056i | −0.101469 | − | 0.0585830i | ||||
\(491\) | −267.174 | − | 462.759i | −0.544143 | − | 0.942483i | −0.998660 | − | 0.0517455i | \(-0.983522\pi\) |
0.454517 | − | 0.890738i | \(-0.349812\pi\) | |||||||
\(492\) | 17.2270 | + | 29.8381i | 0.0350143 | + | 0.0606466i | ||||
\(493\) | 529.605i | 1.07425i | ||||||||
\(494\) | 0.828574 | + | 4.62794i | 0.00167728 | + | 0.00936829i | ||||
\(495\) | 45.3939 | 0.0917048 | ||||||||
\(496\) | −108.000 | + | 62.3538i | −0.217742 | + | 0.125713i | ||||
\(497\) | −189.817 | + | 109.591i | −0.381926 | + | 0.220505i | ||||
\(498\) | −6.89898 | + | 11.9494i | −0.0138534 | + | 0.0239947i | ||||
\(499\) | −395.457 | − | 684.951i | −0.792499 | − | 1.37265i | −0.924415 | − | 0.381387i | \(-0.875446\pi\) |
0.131917 | − | 0.991261i | \(-0.457887\pi\) | |||||||
\(500\) | 49.0000 | − | 84.8705i | 0.0980000 | − | 0.169741i | ||||
\(501\) | −58.3235 | −0.116414 | ||||||||
\(502\) | 692.857i | 1.38019i | ||||||||
\(503\) | −209.841 | + | 363.455i | −0.417178 | + | 0.722574i | −0.995654 | − | 0.0931256i | \(-0.970314\pi\) |
0.578476 | + | 0.815699i | \(0.303648\pi\) | |||||||
\(504\) | −63.1918 | − | 36.4838i | −0.125381 | − | 0.0723885i | ||||
\(505\) | 140.485 | 0.278188 | ||||||||
\(506\) | 122.964i | 0.243013i | ||||||||
\(507\) | −46.5097 | − | 26.8524i | −0.0917351 | − | 0.0529633i | ||||
\(508\) | 232.348 | − | 134.146i | 0.457379 | − | 0.264068i | ||||
\(509\) | 695.515 | + | 401.556i | 1.36643 | + | 0.788911i | 0.990471 | − | 0.137724i | \(-0.0439786\pi\) |
0.375963 | + | 0.926635i | \(0.377312\pi\) | |||||||
\(510\) | 2.67423 | + | 4.63191i | 0.00524360 | + | 0.00908218i | ||||
\(511\) | 42.5913 | + | 73.7703i | 0.0833490 | + | 0.144365i | ||||
\(512\) | 22.6274i | 0.0441942i | ||||||||
\(513\) | 106.398 | − | 19.0493i | 0.207404 | − | 0.0371332i | ||||
\(514\) | −322.318 | −0.627078 | ||||||||
\(515\) | −98.6969 | + | 56.9827i | −0.191645 | + | 0.110646i | ||||
\(516\) | −20.5551 | + | 11.8675i | −0.0398355 | + | 0.0229990i | ||||
\(517\) | 207.969 | − | 360.214i | 0.402262 | − | 0.696738i | ||||
\(518\) | −45.0806 | − | 78.0819i | −0.0870282 | − | 0.150737i | ||||
\(519\) | −10.5737 | + | 18.3142i | −0.0203733 | + | 0.0352875i | ||||
\(520\) | −0.494897 | −0.000951726 | ||||||||
\(521\) | − | 413.663i | − | 0.793979i | −0.917823 | − | 0.396990i | \(-0.870055\pi\) | ||
0.917823 | − | 0.396990i | \(-0.129945\pi\) | |||||||
\(522\) | −280.070 | + | 485.096i | −0.536533 | + | 0.929303i | ||||
\(523\) | 434.144 | + | 250.653i | 0.830103 | + | 0.479260i | 0.853888 | − | 0.520457i | \(-0.174238\pi\) |
−0.0237853 | + | 0.999717i | \(0.507572\pi\) | |||||||
\(524\) | −165.505 | −0.315849 | ||||||||
\(525\) | 22.1137i | 0.0421213i | ||||||||
\(526\) | −166.472 | − | 96.1128i | −0.316487 | − | 0.182724i | ||||
\(527\) | 321.272 | − | 185.487i | 0.609625 | − | 0.351967i | ||||
\(528\) | 5.61633 | + | 3.24259i | 0.0106370 | + | 0.00614127i | ||||
\(529\) | 119.227 | + | 206.507i | 0.225382 | + | 0.390373i | ||||
\(530\) | 39.4268 | + | 68.2892i | 0.0743902 | + | 0.128848i | ||||
\(531\) | − | 307.413i | − | 0.578931i | ||||||
\(532\) | 103.616 | + | 37.4052i | 0.194768 | + | 0.0703106i | ||||
\(533\) | 9.48366 | 0.0177930 | ||||||||
\(534\) | −3.97730 | + | 2.29629i | −0.00744812 | + | 0.00430017i | ||||
\(535\) | −98.6969 | + | 56.9827i | −0.184480 | + | 0.106510i | ||||
\(536\) | 167.641 | − | 290.363i | 0.312764 | − | 0.541723i | ||||
\(537\) | −3.84795 | − | 6.66485i | −0.00716565 | − | 0.0124113i | ||||
\(538\) | 183.785 | − | 318.326i | 0.341609 | − | 0.591684i | ||||
\(539\) | 207.081 | 0.384194 | ||||||||
\(540\) | 11.3779i | 0.0210702i | ||||||||
\(541\) | 196.576 | − | 340.480i | 0.363357 | − | 0.629352i | −0.625154 | − | 0.780501i | \(-0.714964\pi\) |
0.988511 | + | 0.151149i | \(0.0482973\pi\) | |||||||
\(542\) | 285.346 | + | 164.745i | 0.526469 | + | 0.303957i | ||||
\(543\) | 11.3383 | 0.0208808 | ||||||||
\(544\) | − | 67.3108i | − | 0.123733i | ||||||
\(545\) | 59.2423 | + | 34.2036i | 0.108702 | + | 0.0627589i | ||||
\(546\) | 0.197454 | − | 0.114000i | 0.000361637 | − | 0.000208791i | ||||
\(547\) | −418.159 | − | 241.424i | −0.764460 | − | 0.441361i | 0.0664350 | − | 0.997791i | \(-0.478838\pi\) |
−0.830895 | + | 0.556430i | \(0.812171\pi\) | |||||||
\(548\) | −11.8990 | − | 20.6096i | −0.0217135 | − | 0.0376088i | ||||
\(549\) | 339.015 | + | 587.191i | 0.617513 | + | 1.06956i | ||||
\(550\) | 173.134i | 0.314790i | ||||||||
\(551\) | 287.144 | − | 795.417i | 0.521132 | − | 1.44359i | ||||
\(552\) | −15.3235 | −0.0277599 | ||||||||
\(553\) | 165.879 | − | 95.7700i | 0.299961 | − | 0.173183i | ||||
\(554\) | −11.5663 | + | 6.67783i | −0.0208779 | + | 0.0120538i | ||||
\(555\) | −3.49490 | + | 6.05334i | −0.00629711 | + | 0.0109069i | ||||
\(556\) | 41.7423 | + | 72.2999i | 0.0750762 | + | 0.130036i | ||||
\(557\) | 75.8531 | − | 131.381i | 0.136181 | − | 0.235873i | −0.789867 | − | 0.613279i | \(-0.789850\pi\) |
0.926048 | + | 0.377405i | \(0.123184\pi\) | |||||||
\(558\) | 392.363 | 0.703160 | ||||||||
\(559\) | 6.53318i | 0.0116873i | ||||||||
\(560\) | −5.79796 | + | 10.0424i | −0.0103535 | + | 0.0179328i | ||||
\(561\) | −16.7071 | − | 9.64587i | −0.0297810 | − | 0.0171941i | ||||
\(562\) | 221.419 | 0.393984 | ||||||||
\(563\) | − | 176.634i | − | 0.313737i | −0.987620 | − | 0.156868i | \(-0.949860\pi\) | ||
0.987620 | − | 0.156868i | \(-0.0501399\pi\) | |||||||
\(564\) | 44.8888 | + | 25.9165i | 0.0795900 | + | 0.0459513i | ||||
\(565\) | 70.9546 | − | 40.9657i | 0.125583 | − | 0.0725056i | ||||
\(566\) | −3.59362 | − | 2.07478i | −0.00634916 | − | 0.00366569i | ||||
\(567\) | 113.470 | + | 196.536i | 0.200123 | + | 0.346624i | ||||
\(568\) | −106.924 | − | 185.198i | −0.188246 | − | 0.326052i | ||||
\(569\) | 957.928i | 1.68353i | 0.539844 | + | 0.841765i | \(0.318483\pi\) | ||||
−0.539844 | + | 0.841765i | \(0.681517\pi\) | |||||||
\(570\) | −1.50510 | − | 8.40663i | −0.00264053 | − | 0.0147485i | ||||
\(571\) | 833.242 | 1.45927 | 0.729634 | − | 0.683838i | \(-0.239691\pi\) | ||||
0.729634 | + | 0.683838i | \(0.239691\pi\) | |||||||
\(572\) | 1.54592 | − | 0.892539i | 0.00270266 | − | 0.00156038i | ||||
\(573\) | −49.6153 | + | 28.6454i | −0.0865887 | + | 0.0499920i | ||||
\(574\) | 111.106 | − | 192.441i | 0.193564 | − | 0.335262i | ||||
\(575\) | −204.545 | − | 354.282i | −0.355730 | − | 0.616143i | ||||
\(576\) | 35.5959 | − | 61.6539i | 0.0617985 | − | 0.107038i | ||||
\(577\) | −484.595 | −0.839852 | −0.419926 | − | 0.907558i | \(-0.637944\pi\) | ||||
−0.419926 | + | 0.907558i | \(0.637944\pi\) | |||||||
\(578\) | − | 208.475i | − | 0.360684i | ||||||
\(579\) | 34.6793 | − | 60.0664i | 0.0598952 | − | 0.103742i | ||||
\(580\) | 77.0908 | + | 44.5084i | 0.132915 | + | 0.0767386i | ||||
\(581\) | 88.9898 | 0.153167 | ||||||||
\(582\) | 66.8757i | 0.114907i | ||||||||
\(583\) | −246.317 | − | 142.211i | −0.422499 | − | 0.243930i | ||||
\(584\) | −71.9750 | + | 41.5548i | −0.123245 | + | 0.0711555i | ||||
\(585\) | 1.34847 | + | 0.778539i | 0.00230508 | + | 0.00133084i | ||||
\(586\) | −235.015 | − | 407.058i | −0.401049 | − | 0.694637i | ||||
\(587\) | 309.432 | + | 535.952i | 0.527141 | + | 0.913035i | 0.999500 | + | 0.0316288i | \(0.0100694\pi\) |
−0.472358 | + | 0.881407i | \(0.656597\pi\) | |||||||
\(588\) | 25.8058i | 0.0438874i | ||||||||
\(589\) | −583.090 | + | 104.395i | −0.989966 | + | 0.177241i | ||||
\(590\) | −48.8536 | −0.0828027 | ||||||||
\(591\) | 93.6117 | − | 54.0468i | 0.158396 | − | 0.0914497i | ||||
\(592\) | 76.1816 | − | 43.9835i | 0.128685 | − | 0.0742964i | ||||
\(593\) | 93.9699 | − | 162.761i | 0.158465 | − | 0.274470i | −0.775850 | − | 0.630917i | \(-0.782679\pi\) |
0.934315 | + | 0.356447i | \(0.116012\pi\) | |||||||
\(594\) | −20.5199 | − | 35.5415i | −0.0345453 | − | 0.0598342i | ||||
\(595\) | 17.2474 | − | 29.8735i | 0.0289873 | − | 0.0502075i | ||||
\(596\) | 71.3531 | 0.119720 | ||||||||
\(597\) | − | 105.963i | − | 0.177493i | ||||||
\(598\) | −2.10893 | + | 3.65278i | −0.00352664 | + | 0.00610832i | ||||
\(599\) | −69.5533 | − | 40.1566i | −0.116116 | − | 0.0670394i | 0.440817 | − | 0.897597i | \(-0.354689\pi\) |
−0.556933 | + | 0.830557i | \(0.688022\pi\) | |||||||
\(600\) | −21.5755 | −0.0359592 | ||||||||
\(601\) | − | 665.929i | − | 1.10804i | −0.832505 | − | 0.554018i | \(-0.813094\pi\) | ||
0.832505 | − | 0.554018i | \(-0.186906\pi\) | |||||||
\(602\) | 132.570 | + | 76.5393i | 0.220216 | + | 0.127142i | ||||
\(603\) | −913.560 | + | 527.444i | −1.51502 | + | 0.874700i | ||||
\(604\) | −148.182 | − | 85.5527i | −0.245334 | − | 0.141644i | ||||
\(605\) | −47.4898 | − | 82.2547i | −0.0784955 | − | 0.135958i | ||||
\(606\) | −31.5732 | − | 54.6864i | −0.0521010 | − | 0.0902416i | ||||
\(607\) | 105.952i | 0.174550i | 0.996184 | + | 0.0872751i | \(0.0278159\pi\) | ||||
−0.996184 | + | 0.0872751i | \(0.972184\pi\) | |||||||
\(608\) | −36.4949 | + | 101.095i | −0.0600245 | + | 0.166274i | ||||
\(609\) | −41.0102 | −0.0673402 | ||||||||
\(610\) | 93.3156 | − | 53.8758i | 0.152976 | − | 0.0883209i | ||||
\(611\) | 12.3559 | − | 7.13366i | 0.0202224 | − | 0.0116754i | ||||
\(612\) | −105.889 | + | 183.405i | −0.173021 | + | 0.299681i | ||||
\(613\) | 569.171 | + | 985.833i | 0.928501 | + | 1.60821i | 0.785832 | + | 0.618440i | \(0.212235\pi\) |
0.142668 | + | 0.989771i | \(0.454432\pi\) | |||||||
\(614\) | 182.048 | − | 315.316i | 0.296495 | − | 0.513544i | ||||
\(615\) | −17.2270 | −0.0280114 | ||||||||
\(616\) | − | 41.8261i | − | 0.0678995i | ||||||
\(617\) | −459.131 | + | 795.238i | −0.744135 | + | 1.28888i | 0.206463 | + | 0.978454i | \(0.433805\pi\) |
−0.950598 | + | 0.310425i | \(0.899529\pi\) | |||||||
\(618\) | 44.3633 | + | 25.6131i | 0.0717852 | + | 0.0414452i | ||||
\(619\) | −1123.85 | −1.81559 | −0.907793 | − | 0.419418i | \(-0.862234\pi\) | ||||
−0.907793 | + | 0.419418i | \(0.862234\pi\) | |||||||
\(620\) | − | 62.3538i | − | 0.100571i | ||||||
\(621\) | 83.9791 | + | 48.4853i | 0.135232 | + | 0.0780762i | ||||
\(622\) | 266.586 | − | 153.913i | 0.428594 | − | 0.247449i | ||||
\(623\) | 25.6515 | + | 14.8099i | 0.0411742 | + | 0.0237719i | ||||
\(624\) | 0.111226 | + | 0.192648i | 0.000178246 | + | 0.000308732i | ||||
\(625\) | −275.500 | − | 477.180i | −0.440800 | − | 0.763488i | ||||
\(626\) | − | 438.748i | − | 0.700876i | ||||||
\(627\) | 19.8627 | + | 23.5456i | 0.0316790 | + | 0.0375528i | ||||
\(628\) | 400.302 | 0.637424 | ||||||||
\(629\) | −226.621 | + | 130.840i | −0.360288 | + | 0.208012i | ||||
\(630\) | 31.5959 | − | 18.2419i | 0.0501523 | − | 0.0289554i | ||||
\(631\) | −40.2753 | + | 69.7588i | −0.0638277 | + | 0.110553i | −0.896173 | − | 0.443704i | \(-0.853664\pi\) |
0.832346 | + | 0.554257i | \(0.186997\pi\) | |||||||
\(632\) | 93.4393 | + | 161.842i | 0.147847 | + | 0.256078i | ||||
\(633\) | 55.5556 | − | 96.2251i | 0.0877656 | − | 0.152014i | ||||
\(634\) | −488.166 | −0.769978 | ||||||||
\(635\) | 134.146i | 0.211254i | ||||||||
\(636\) | 17.7219 | − | 30.6953i | 0.0278647 | − | 0.0482630i | ||||
\(637\) | 6.15153 | + | 3.55159i | 0.00965703 | + | 0.00557549i | ||||
\(638\) | −321.081 | −0.503261 | ||||||||
\(639\) | 672.822i | 1.05293i | ||||||||
\(640\) | −9.79796 | − | 5.65685i | −0.0153093 | − | 0.00883883i | ||||
\(641\) | −428.893 | + | 247.621i | −0.669100 | + | 0.386305i | −0.795735 | − | 0.605644i | \(-0.792915\pi\) |
0.126636 | + | 0.991949i | \(0.459582\pi\) | |||||||
\(642\) | 44.3633 | + | 25.6131i | 0.0691017 | + | 0.0398959i | ||||
\(643\) | −245.123 | − | 424.566i | −0.381218 | − | 0.660289i | 0.610019 | − | 0.792387i | \(-0.291162\pi\) |
−0.991237 | + | 0.132098i | \(0.957829\pi\) | |||||||
\(644\) | 49.4143 | + | 85.5881i | 0.0767303 | + | 0.132901i | ||||
\(645\) | − | 11.8675i | − | 0.0183992i | ||||||
\(646\) | 108.563 | − | 300.731i | 0.168054 | − | 0.465527i | ||||
\(647\) | −494.132 | −0.763727 | −0.381864 | − | 0.924219i | \(-0.624718\pi\) | ||||
−0.381864 | + | 0.924219i | \(0.624718\pi\) | |||||||
\(648\) | −191.753 | + | 110.708i | −0.295914 | + | 0.170846i | ||||
\(649\) | 152.605 | − | 88.1066i | 0.235139 | − | 0.135757i | ||||
\(650\) | −2.96938 | + | 5.14312i | −0.00456828 | + | 0.00791250i | ||||
\(651\) | 14.3633 | + | 24.8779i | 0.0220634 | + | 0.0382149i | ||||
\(652\) | −127.303 | + | 220.495i | −0.195250 | + | 0.338183i | ||||
\(653\) | 475.383 | 0.727998 | 0.363999 | − | 0.931399i | \(-0.381411\pi\) | ||||
0.363999 | + | 0.931399i | \(0.381411\pi\) | |||||||
\(654\) | − | 30.7483i | − | 0.0470158i | ||||||
\(655\) | 41.3763 | − | 71.6658i | 0.0631699 | − | 0.109413i | ||||
\(656\) | 187.757 | + | 108.402i | 0.286215 | + | 0.165246i | ||||
\(657\) | 261.485 | 0.397998 | ||||||||
\(658\) | − | 334.297i | − | 0.508050i | ||||||
\(659\) | 494.082 | + | 285.259i | 0.749746 | + | 0.432866i | 0.825602 | − | 0.564253i | \(-0.190836\pi\) |
−0.0758563 | + | 0.997119i | \(0.524169\pi\) | |||||||
\(660\) | −2.80816 | + | 1.62129i | −0.00425479 | + | 0.00245651i | ||||
\(661\) | −18.6964 | − | 10.7944i | −0.0282851 | − | 0.0163304i | 0.485791 | − | 0.874075i | \(-0.338532\pi\) |
−0.514076 | + | 0.857745i | \(0.671865\pi\) | |||||||
\(662\) | 344.586 | + | 596.840i | 0.520522 | + | 0.901571i | ||||
\(663\) | −0.330868 | − | 0.573080i | −0.000499047 | − | 0.000864374i | ||||
\(664\) | 86.8241i | 0.130759i | ||||||||
\(665\) | −42.1010 | + | 35.5159i | −0.0633098 | + | 0.0534073i | ||||
\(666\) | −276.767 | −0.415567 | ||||||||
\(667\) | 657.022 | − | 379.332i | 0.985041 | − | 0.568714i | ||||
\(668\) | −317.833 | + | 183.501i | −0.475798 | + | 0.274702i | ||||
\(669\) | −5.05051 | + | 8.74774i | −0.00754934 | + | 0.0130758i | ||||
\(670\) | 83.8207 | + | 145.182i | 0.125105 | + | 0.216689i | ||||
\(671\) | −194.328 | + | 336.586i | −0.289610 | + | 0.501619i | ||||
\(672\) | 5.21225 | 0.00775632 | ||||||||
\(673\) | 256.395i | 0.380973i | 0.981690 | + | 0.190486i | \(0.0610065\pi\) | ||||
−0.981690 | + | 0.190486i | \(0.938993\pi\) | |||||||
\(674\) | 117.897 | − | 204.203i | 0.174921 | − | 0.302972i | ||||
\(675\) | 118.243 | + | 68.2675i | 0.175175 | + | 0.101137i | ||||
\(676\) | −337.939 | −0.499909 | ||||||||
\(677\) | − | 662.815i | − | 0.979048i | −0.871990 | − | 0.489524i | \(-0.837171\pi\) | ||
0.871990 | − | 0.489524i | \(-0.162829\pi\) | |||||||
\(678\) | −31.8934 | − | 18.4136i | −0.0470404 | − | 0.0271588i | ||||
\(679\) | 373.529 | − | 215.657i | 0.550116 | − | 0.317610i | ||||
\(680\) | 29.1464 | + | 16.8277i | 0.0428624 | + | 0.0247466i | ||||
\(681\) | −39.6867 | − | 68.7394i | −0.0582771 | − | 0.100939i | ||||
\(682\) | 112.454 | + | 194.776i | 0.164889 | + | 0.285596i | ||||
\(683\) | − | 310.334i | − | 0.454369i | −0.973852 | − | 0.227184i | \(-0.927048\pi\) | ||
0.973852 | − | 0.227184i | \(-0.0729520\pi\) | |||||||
\(684\) | 258.474 | − | 218.046i | 0.377887 | − | 0.318780i | ||||
\(685\) | 11.8990 | 0.0173708 | ||||||||
\(686\) | 318.111 | − | 183.662i | 0.463719 | − | 0.267728i | ||||
\(687\) | −71.4801 | + | 41.2691i | −0.104047 | + | 0.0600714i | ||||
\(688\) | −74.6765 | + | 129.344i | −0.108541 | + | 0.187999i | ||||
\(689\) | −4.87805 | − | 8.44904i | −0.00707990 | − | 0.0122628i | ||||
\(690\) | 3.83087 | − | 6.63526i | 0.00555198 | − | 0.00961632i | ||||
\(691\) | 187.789 | 0.271764 | 0.135882 | − | 0.990725i | \(-0.456613\pi\) | ||||
0.135882 | + | 0.990725i | \(0.456613\pi\) | |||||||
\(692\) | 133.071i | 0.192299i | ||||||||
\(693\) | −65.7980 | + | 113.965i | −0.0949465 | + | 0.164452i | ||||
\(694\) | −462.638 | − | 267.104i | −0.666625 | − | 0.384876i | ||||
\(695\) | −41.7423 | −0.0600609 | ||||||||
\(696\) | − | 40.0121i | − | 0.0574887i | ||||||
\(697\) | −558.530 | − | 322.467i | −0.801334 | − | 0.462650i | ||||
\(698\) | −718.232 | + | 414.671i | −1.02899 | + | 0.594085i | ||||
\(699\) | 107.427 | + | 62.0232i | 0.153687 | + | 0.0887313i | ||||
\(700\) | 69.5755 | + | 120.508i | 0.0993936 | + | 0.172155i | ||||
\(701\) | −270.818 | − | 469.070i | −0.386331 | − | 0.669144i | 0.605622 | − | 0.795752i | \(-0.292924\pi\) |
−0.991953 | + | 0.126608i | \(0.959591\pi\) | |||||||
\(702\) | − | 1.40773i | − | 0.00200531i | ||||||
\(703\) | 411.303 | − | 73.6387i | 0.585068 | − | 0.104749i | ||||
\(704\) | 40.8082 | 0.0579661 | ||||||||
\(705\) | −22.4444 | + | 12.9583i | −0.0318360 | + | 0.0183805i | ||||
\(706\) | 583.980 | − | 337.161i | 0.827167 | − | 0.477565i | ||||
\(707\) | −203.631 | + | 352.699i | −0.288021 | + | 0.498868i | ||||
\(708\) | 10.9796 | + | 19.0172i | 0.0155079 | + | 0.0268605i | ||||
\(709\) | 245.621 | − | 425.429i | 0.346434 | − | 0.600041i | −0.639180 | − | 0.769058i | \(-0.720726\pi\) |
0.985613 | + | 0.169017i | \(0.0540593\pi\) | |||||||
\(710\) | 106.924 | 0.150597 | ||||||||
\(711\) | − | 587.969i | − | 0.826961i | ||||||
\(712\) | −14.4495 | + | 25.0273i | −0.0202942 | + | 0.0351506i | ||||
\(713\) | −460.226 | − | 265.712i | −0.645478 | − | 0.372667i | ||||
\(714\) | −15.5051 | −0.0217158 | ||||||||
\(715\) | 0.892539i | 0.00124831i | ||||||||
\(716\) | −41.9388 | − | 24.2134i | −0.0585737 | − | 0.0338175i | ||||
\(717\) | −81.6617 | + | 47.1474i | −0.113894 | + | 0.0657565i | ||||
\(718\) | 303.012 | + | 174.944i | 0.422023 | + | 0.243655i | ||||
\(719\) | 287.734 | + | 498.370i | 0.400186 | + | 0.693143i | 0.993748 | − | 0.111645i | \(-0.0356121\pi\) |
−0.593562 | + | 0.804788i | \(0.702279\pi\) | |||||||
\(720\) | 17.7980 | + | 30.8270i | 0.0247194 | + | 0.0428152i | ||||
\(721\) | − | 330.383i | − | 0.458229i | ||||||
\(722\) | −326.103 | + | 392.809i | −0.451667 | + | 0.544056i | ||||
\(723\) | −36.6005 | −0.0506231 | ||||||||
\(724\) | 61.7878 | − | 35.6732i | 0.0853422 | − | 0.0492723i | ||||
\(725\) | 925.090 | − | 534.101i | 1.27599 | − | 0.736691i | ||||
\(726\) | −21.3462 | + | 36.9727i | −0.0294024 | + | 0.0509265i | ||||
\(727\) | 409.552 | + | 709.365i | 0.563346 | + | 0.975743i | 0.997201 | + | 0.0747610i | \(0.0238194\pi\) |
−0.433856 | + | 0.900982i | \(0.642847\pi\) | |||||||
\(728\) | 0.717349 | − | 1.24248i | 0.000985369 | − | 0.00170671i | ||||
\(729\) | 680.362 | 0.933282 | ||||||||
\(730\) | − | 41.5548i | − | 0.0569244i | ||||||
\(731\) | 222.144 | − | 384.764i | 0.303890 | − | 0.526353i | ||||
\(732\) | −41.9444 | − | 24.2166i | −0.0573011 | − | 0.0330828i | ||||
\(733\) | 804.332 | 1.09731 | 0.548657 | − | 0.836047i | \(-0.315139\pi\) | ||||
0.548657 | + | 0.836047i | \(0.315139\pi\) | |||||||
\(734\) | 684.372i | 0.932387i | ||||||||
\(735\) | −11.1742 | − | 6.45145i | −0.0152030 | − | 0.00877748i | ||||
\(736\) | −83.5051 | + | 48.2117i | −0.113458 | + | 0.0655050i | ||||
\(737\) | −523.665 | − | 302.338i | −0.710536 | − | 0.410228i | ||||
\(738\) | −341.060 | − | 590.734i | −0.462141 | − | 0.800452i | ||||
\(739\) | −37.9314 | − | 65.6991i | −0.0513280 | − | 0.0889027i | 0.839220 | − | 0.543792i | \(-0.183012\pi\) |
−0.890548 | + | 0.454890i | \(0.849679\pi\) | |||||||
\(740\) | 43.9835i | 0.0594371i | ||||||||
\(741\) | 0.186218 | + | 1.04011i | 0.000251306 | + | 0.00140365i | ||||
\(742\) | −228.595 | −0.308079 | ||||||||
\(743\) | 505.810 | − | 292.030i | 0.680767 | − | 0.393041i | −0.119377 | − | 0.992849i | \(-0.538090\pi\) |
0.800144 | + | 0.599808i | \(0.204756\pi\) | |||||||
\(744\) | −24.2724 | + | 14.0137i | −0.0326243 | + | 0.0188356i | ||||
\(745\) | −17.8383 | + | 30.8968i | −0.0239440 | + | 0.0414722i | ||||
\(746\) | −99.6367 | − | 172.576i | −0.133561 | − | 0.231335i | ||||
\(747\) | 136.586 | − | 236.573i | 0.182846 | − | 0.316698i | ||||
\(748\) | −121.394 | −0.162291 | ||||||||
\(749\) | − | 330.383i | − | 0.441099i | ||||||
\(750\) | 11.0125 | − | 19.0742i | 0.0146833 | − | 0.0254323i | ||||
\(751\) | 513.931 | + | 296.718i | 0.684329 | + | 0.395098i | 0.801484 | − | 0.598016i | \(-0.204044\pi\) |
−0.117155 | + | 0.993114i | \(0.537377\pi\) | |||||||
\(752\) | 326.161 | 0.433725 | ||||||||
\(753\) | 155.716i | 0.206794i | ||||||||
\(754\) | −9.53801 | − | 5.50677i | −0.0126499 | − | 0.00730341i | ||||
\(755\) | 74.0908 | − | 42.7764i | 0.0981335 | − | 0.0566574i | ||||
\(756\) | −28.5653 | − | 16.4922i | −0.0377848 | − | 0.0218151i | ||||
\(757\) | 278.257 | + | 481.956i | 0.367579 | + | 0.636665i | 0.989186 | − | 0.146664i | \(-0.0468535\pi\) |
−0.621608 | + | 0.783329i | \(0.713520\pi\) | |||||||
\(758\) | 331.373 | + | 573.956i | 0.437168 | + | 0.757197i | ||||
\(759\) | 27.6356i | 0.0364106i | ||||||||
\(760\) | −34.6515 | − | 41.0764i | −0.0455941 | − | 0.0540479i | ||||
\(761\) | −1211.85 | −1.59244 | −0.796219 | − | 0.605008i | \(-0.793170\pi\) | ||||
−0.796219 | + | 0.605008i | \(0.793170\pi\) | |||||||
\(762\) | 52.2191 | − | 30.1487i | 0.0685290 | − | 0.0395653i | ||||
\(763\) | −171.742 | + | 99.1555i | −0.225088 | + | 0.129955i | ||||
\(764\) | −180.252 | + | 312.206i | −0.235932 | + | 0.408646i | ||||
\(765\) | −52.9444 | − | 91.7024i | −0.0692083 | − | 0.119872i | ||||
\(766\) | −394.002 | + | 682.432i | −0.514363 | + | 0.890903i | ||||
\(767\) | 6.04438 | 0.00788054 | ||||||||
\(768\) | 5.08540i | 0.00662161i | ||||||||
\(769\) | 479.115 | − | 829.852i | 0.623037 | − | 1.07913i | −0.365880 | − | 0.930662i | \(-0.619232\pi\) |
0.988917 | − | 0.148469i | \(-0.0474347\pi\) | |||||||
\(770\) | 18.1112 | + | 10.4565i | 0.0235211 | + | 0.0135799i | ||||
\(771\) | −72.4393 | −0.0939550 | ||||||||
\(772\) | − | 436.441i | − | 0.565339i | ||||||
\(773\) | −404.409 | − | 233.486i | −0.523168 | − | 0.302051i | 0.215062 | − | 0.976600i | \(-0.431005\pi\) |
−0.738230 | + | 0.674549i | \(0.764338\pi\) | |||||||
\(774\) | 406.949 | − | 234.952i | 0.525774 | − | 0.303556i | ||||
\(775\) | −648.000 | − | 374.123i | −0.836129 | − | 0.482739i | ||||
\(776\) | 210.409 | + | 364.439i | 0.271145 | + | 0.469637i | ||||
\(777\) | −10.1316 | − | 17.5485i | −0.0130394 | − | 0.0225850i | ||||
\(778\) | 131.692i | 0.169270i | ||||||||
\(779\) | 664.023 | + | 787.142i | 0.852405 | + | 1.01045i | ||||
\(780\) | −0.111226 | −0.000142597 | ||||||||
\(781\) | −334.001 | + | 192.836i | −0.427658 | + | 0.246909i | ||||
\(782\) | 248.406 | − | 143.417i | 0.317655 | − | 0.183398i | ||||
\(783\) | −126.603 | + | 219.283i | −0.161690 | + | 0.280055i | ||||
\(784\) | 81.1918 | + | 140.628i | 0.103561 | + | 0.179373i | ||||
\(785\) | −100.076 | + | 173.336i | −0.127485 | + | 0.220810i | ||||
\(786\) | −37.1964 | −0.0473237 | ||||||||
\(787\) | 1410.48i | 1.79223i | 0.443824 | + | 0.896114i | \(0.353621\pi\) | ||||
−0.443824 | + | 0.896114i | \(0.646379\pi\) | |||||||
\(788\) | 340.091 | − | 589.055i | 0.431587 | − | 0.747531i | ||||
\(789\) | −37.4138 | − | 21.6009i | −0.0474192 | − | 0.0273775i | ||||
\(790\) | −93.4393 | −0.118278 | ||||||||
\(791\) | 237.517i | 0.300275i | ||||||||
\(792\) | −111.192 | − | 64.1966i | −0.140394 | − | 0.0810564i | ||||
\(793\) | −11.5454 | + | 6.66574i | −0.0145592 | + | 0.00840573i | ||||
\(794\) | −317.654 | − | 183.398i | −0.400068 | − | 0.230979i | ||||
\(795\) | 8.86097 | + | 15.3476i | 0.0111459 | + | 0.0193052i | ||||
\(796\) | −333.388 | − | 577.445i | −0.418829 | − | 0.725434i | ||||
\(797\) | − | 774.540i | − | 0.971819i | −0.874009 | − | 0.485909i | \(-0.838489\pi\) | ||
0.874009 | − | 0.485909i | \(-0.161511\pi\) | |||||||
\(798\) | 23.2872 | + | 8.40663i | 0.0291820 | + | 0.0105346i | ||||
\(799\) | −970.246 | −1.21433 | ||||||||
\(800\) | −117.576 | + | 67.8823i | −0.146969 | + | 0.0848528i | ||||
\(801\) | 78.7423 | − | 45.4619i | 0.0983051 | − | 0.0567564i | ||||
\(802\) | −318.012 | + | 550.814i | −0.396524 | + | 0.686800i | ||||
\(803\) | 74.9434 | + | 129.806i | 0.0933292 | + | 0.161651i | ||||
\(804\) | 37.6765 | − | 65.2577i | 0.0468614 | − | 0.0811662i | ||||
\(805\) | −49.4143 | −0.0613842 | ||||||||
\(806\) | 7.71469i | 0.00957157i | ||||||||
\(807\) | 41.3048 | − | 71.5421i | 0.0511832 | − | 0.0886519i | ||||
\(808\) | −344.116 | − | 198.675i | −0.425886 | − | 0.245885i | ||||
\(809\) | −1114.09 | −1.37712 | −0.688559 | − | 0.725180i | \(-0.741756\pi\) | ||||
−0.688559 | + | 0.725180i | \(0.741756\pi\) | |||||||
\(810\) | − | 110.708i | − | 0.136677i | ||||||
\(811\) | −13.7656 | − | 7.94755i | −0.0169736 | − | 0.00979970i | 0.491489 | − | 0.870884i | \(-0.336453\pi\) |
−0.508463 | + | 0.861084i | \(0.669786\pi\) | |||||||
\(812\) | −223.485 | + | 129.029i | −0.275227 | + | 0.158903i | ||||
\(813\) | 64.1301 | + | 37.0255i | 0.0788808 | + | 0.0455419i | ||||
\(814\) | −79.3235 | − | 137.392i | −0.0974490 | − | 0.168787i | ||||
\(815\) | −63.6515 | − | 110.248i | −0.0781000 | − | 0.135273i | ||||
\(816\) | − | 15.1278i | − | 0.0185389i | ||||||
\(817\) | −542.253 | + | 457.437i | −0.663712 | + | 0.559899i | ||||
\(818\) | 148.329 | 0.181331 | ||||||||
\(819\) | −3.90918 | + | 2.25697i | −0.00477312 | + | 0.00275576i | ||||
\(820\) | −93.8786 | + | 54.2008i | −0.114486 | + | 0.0660986i | ||||
\(821\) | 102.444 | − | 177.439i | 0.124780 | − | 0.216125i | −0.796867 | − | 0.604155i | \(-0.793511\pi\) |
0.921647 | + | 0.388030i | \(0.126844\pi\) | |||||||
\(822\) | −2.67423 | − | 4.63191i | −0.00325333 | − | 0.00563493i | ||||
\(823\) | −621.052 | + | 1075.69i | −0.754619 | + | 1.30704i | 0.190944 | + | 0.981601i | \(0.438845\pi\) |
−0.945563 | + | 0.325438i | \(0.894488\pi\) | |||||||
\(824\) | 322.343 | 0.391193 | ||||||||
\(825\) | 38.9111i | 0.0471649i | ||||||||
\(826\) | 70.8128 | − | 122.651i | 0.0857297 | − | 0.148488i | ||||
\(827\) | −990.128 | − | 571.651i | −1.19725 | − | 0.691234i | −0.237311 | − | 0.971434i | \(-0.576266\pi\) |
−0.959942 | + | 0.280200i | \(0.909599\pi\) | |||||||
\(828\) | 303.373 | 0.366393 | ||||||||
\(829\) | 1080.66i | 1.30357i | 0.758404 | + | 0.651784i | \(0.225979\pi\) | ||||
−0.758404 | + | 0.651784i | \(0.774021\pi\) | |||||||
\(830\) | −37.5959 | − | 21.7060i | −0.0452963 | − | 0.0261518i | ||||
\(831\) | −2.59947 | + | 1.50081i | −0.00312813 | + | 0.00180603i | ||||
\(832\) | 1.21225 | + | 0.699891i | 0.00145703 | + | 0.000841215i | ||||
\(833\) | −241.525 | − | 418.334i | −0.289946 | − | 0.502201i | ||||
\(834\) | 9.38138 | + | 16.2490i | 0.0112487 | + | 0.0194832i | ||||
\(835\) | − | 183.501i | − | 0.219762i | ||||||
\(836\) | 182.322 | + | 65.8179i | 0.218089 | + | 0.0787296i | ||||
\(837\) | 177.364 | 0.211905 | ||||||||
\(838\) | 567.206 | − | 327.476i | 0.676856 | − | 0.390783i | ||||
\(839\) | 582.598 | − | 336.363i | 0.694395 | − | 0.400909i | −0.110861 | − | 0.993836i | \(-0.535361\pi\) |
0.805257 | + | 0.592927i | \(0.202028\pi\) | |||||||
\(840\) | −1.30306 | + | 2.25697i | −0.00155126 | + | 0.00268687i | ||||
\(841\) | 569.999 | + | 987.267i | 0.677763 | + | 1.17392i | ||||
\(842\) | −341.876 | + | 592.147i | −0.406029 | + | 0.703263i | ||||
\(843\) | 49.7628 | 0.0590306 | ||||||||
\(844\) | − | 699.171i | − | 0.828401i | ||||||
\(845\) | 84.4847 | − | 146.332i | 0.0999819 | − | 0.173174i | ||||
\(846\) | −888.706 | − | 513.095i | −1.05048 | − | 0.606495i | ||||
\(847\) | 275.344 | 0.325081 | ||||||||
\(848\) | − | 223.032i | − | 0.263009i | ||||||
\(849\) | −0.807649 | − | 0.466296i | −0.000951294 | − | 0.000549230i | ||||
\(850\) | 349.757 | − | 201.932i | 0.411479 | − | 0.237568i | ||||
\(851\) | 324.637 | + | 187.429i | 0.381477 | + | 0.220246i | ||||
\(852\) | −24.0306 | − | 41.6222i | −0.0282049 | − | 0.0488524i | ||||
\(853\) | −123.620 | − | 214.117i | −0.144924 | − | 0.251016i | 0.784420 | − | 0.620229i | \(-0.212961\pi\) |
−0.929345 | + | 0.369213i | \(0.879627\pi\) | |||||||
\(854\) | 312.369i | 0.365772i | ||||||||
\(855\) | 29.7980 | + | 166.434i | 0.0348514 | + | 0.194660i | ||||
\(856\) | 322.343 | 0.376569 | ||||||||
\(857\) | −615.227 | + | 355.201i | −0.717884 | + | 0.414470i | −0.813973 | − | 0.580902i | \(-0.802700\pi\) |
0.0960894 | + | 0.995373i | \(0.469367\pi\) | |||||||
\(858\) | 0.347438 | − | 0.200594i | 0.000404940 | − | 0.000233792i | ||||
\(859\) | −505.183 | + | 875.003i | −0.588106 | + | 1.01863i | 0.406374 | + | 0.913707i | \(0.366793\pi\) |
−0.994480 | + | 0.104923i | \(0.966540\pi\) | |||||||
\(860\) | −37.3383 | − | 64.6718i | −0.0434166 | − | 0.0751997i | ||||
\(861\) | 24.9704 | − | 43.2500i | 0.0290016 | − | 0.0502323i | ||||
\(862\) | 640.863 | 0.743460 | ||||||||
\(863\) | − | 455.826i | − | 0.528188i | −0.964497 | − | 0.264094i | \(-0.914927\pi\) | ||
0.964497 | − | 0.264094i | \(-0.0850729\pi\) | |||||||
\(864\) | 16.0908 | − | 27.8701i | 0.0186236 | − | 0.0322571i | ||||
\(865\) | −57.6214 | − | 33.2677i | −0.0666144 | − | 0.0384598i | ||||
\(866\) | 1062.51 | 1.22692 | ||||||||
\(867\) | − | 46.8538i | − | 0.0540412i | ||||||
\(868\) | 156.545 | + | 90.3812i | 0.180351 | + | 0.104126i | ||||
\(869\) | 291.879 | − | 168.516i | 0.335879 | − | 0.193920i | ||||
\(870\) | 17.3258 | + | 10.0030i | 0.0199147 | + | 0.0114977i | ||||
\(871\) | −10.3707 | − | 17.9625i | −0.0119066 | − | 0.0206229i | ||||
\(872\) | −96.7423 | − | 167.563i | −0.110943 | − | 0.192159i | ||||
\(873\) | − | 1324.00i | − | 1.51661i | ||||||
\(874\) | −450.842 | + | 80.7177i | −0.515838 | + | 0.0923543i | ||||
\(875\) | −142.050 | −0.162343 | ||||||||
\(876\) | −16.1760 | + | 9.33923i | −0.0184658 | + | 0.0106612i | ||||
\(877\) | 564.060 | − | 325.660i | 0.643170 | − | 0.371334i | −0.142665 | − | 0.989771i | \(-0.545567\pi\) |
0.785834 | + | 0.618437i | \(0.212234\pi\) | |||||||
\(878\) | 443.623 | − | 768.378i | 0.505266 | − | 0.875146i | ||||
\(879\) | −52.8184 | − | 91.4841i | −0.0600892 | − | 0.104077i | ||||
\(880\) | −10.2020 | + | 17.6705i | −0.0115932 | + | 0.0200801i | ||||
\(881\) | −518.293 | −0.588301 | −0.294150 | − | 0.955759i | \(-0.595037\pi\) | ||||
−0.294150 | + | 0.955759i | \(0.595037\pi\) | |||||||
\(882\) | − | 510.902i | − | 0.579254i | ||||||
\(883\) | 336.532 | − | 582.890i | 0.381123 | − | 0.660125i | −0.610100 | − | 0.792325i | \(-0.708871\pi\) |
0.991223 | + | 0.132200i | \(0.0422040\pi\) | |||||||
\(884\) | −3.60612 | − | 2.08200i | −0.00407932 | − | 0.00235520i | ||||
\(885\) | −10.9796 | −0.0124063 | ||||||||
\(886\) | 624.031i | 0.704324i | ||||||||
\(887\) | 1296.33 | + | 748.434i | 1.46147 | + | 0.843781i | 0.999080 | − | 0.0428947i | \(-0.0136580\pi\) |
0.462392 | + | 0.886676i | \(0.346991\pi\) | |||||||
\(888\) | 17.1214 | − | 9.88506i | 0.0192809 | − | 0.0111318i | ||||
\(889\) | −336.787 | − | 194.444i | −0.378838 | − | 0.218722i | ||||
\(890\) | −7.22474 | − | 12.5136i | −0.00811769 | − | 0.0140603i | ||||
\(891\) | 199.661 | + | 345.822i | 0.224086 | + | 0.388128i | ||||
\(892\) | 63.5610i | 0.0712567i | ||||||||
\(893\) | 1457.22 | + | 526.053i | 1.63183 | + | 0.589085i | ||||
\(894\) | 16.0362 | 0.0179376 | ||||||||
\(895\) | 20.9694 | − | 12.1067i | 0.0234295 | − | 0.0135270i | ||||
\(896\) | 28.4041 | − | 16.3991i | 0.0317010 | − | 0.0183026i | ||||
\(897\) | −0.473972 | + | 0.820943i | −0.000528397 | + | 0.000915210i | ||||
\(898\) | 246.025 | + | 426.128i | 0.273970 | + | 0.474530i | ||||
\(899\) | 693.817 | − | 1201.73i | 0.771766 | − | 1.33674i | ||||
\(900\) | 427.151 | 0.474612 | ||||||||
\(901\) | 663.462i | 0.736362i | ||||||||
\(902\) | 195.501 | − | 338.617i | 0.216741 | − | 0.375407i | ||||
\(903\) | 29.7944 | + | 17.2018i | 0.0329949 | + | 0.0190496i | ||||
\(904\) | −231.737 | −0.256346 | ||||||||
\(905\) | 35.6732i | 0.0394179i | ||||||||
\(906\) | −33.3031 | − | 19.2275i | −0.0367583 | − | 0.0212224i | ||||
\(907\) | 243.114 | − | 140.362i | 0.268042 | − | 0.154754i | −0.359956 | − | 0.932969i | \(-0.617208\pi\) |
0.627997 | + | 0.778215i | \(0.283875\pi\) | |||||||
\(908\) | −432.545 | − | 249.730i | −0.476371 | − | 0.275033i | ||||
\(909\) | 625.085 | + | 1082.68i | 0.687662 | + | 1.19107i | ||||
\(910\) | 0.358674 | + | 0.621242i | 0.000394148 | + | 0.000682684i | ||||
\(911\) | − | 783.689i | − | 0.860252i | −0.902769 | − | 0.430126i | \(-0.858469\pi\) | ||
0.902769 | − | 0.430126i | \(-0.141531\pi\) | |||||||
\(912\) | −8.20204 | + | 22.7205i | −0.00899347 | + | 0.0249128i | ||||
\(913\) | 156.586 | 0.171507 | ||||||||
\(914\) | 543.267 | − | 313.655i | 0.594384 | − | 0.343168i | ||||
\(915\) | 20.9722 | − | 12.1083i | 0.0229204 | − | 0.0132331i | ||||
\(916\) | −259.687 | + | 449.791i | −0.283501 | + | 0.491038i | ||||
\(917\) | 119.949 | + | 207.758i | 0.130806 | + | 0.226562i | ||||
\(918\) | −47.8661 | + | 82.9065i | −0.0521417 | + | 0.0903121i | ||||
\(919\) | −220.334 | −0.239754 | −0.119877 | − | 0.992789i | \(-0.538250\pi\) | ||||
−0.119877 | + | 0.992789i | \(0.538250\pi\) | |||||||
\(920\) | − | 48.2117i | − | 0.0524040i | ||||||
\(921\) | 40.9143 | − | 70.8656i | 0.0444238 | − | 0.0769442i | ||||
\(922\) | −239.579 | − | 138.321i | −0.259847 | − | 0.150023i | ||||
\(923\) | −13.2291 | −0.0143327 | ||||||||
\(924\) | − | 9.40020i | − | 0.0101734i | ||||||
\(925\) | 457.090 | + | 263.901i | 0.494151 | + | 0.285298i | ||||
\(926\) | −882.990 | + | 509.794i | −0.953553 | + | 0.550534i | ||||
\(927\) | −878.302 | − | 507.088i | −0.947467 | − | 0.547020i | ||||
\(928\) | −125.889 | − | 218.046i | −0.135656 | − | 0.234963i | ||||
\(929\) | −614.742 | − | 1064.76i | −0.661724 | − | 1.14614i | −0.980162 | − | 0.198196i | \(-0.936492\pi\) |
0.318438 | − | 0.947944i | \(-0.396842\pi\) | |||||||
\(930\) | − | 14.0137i | − | 0.0150685i | ||||||
\(931\) | 135.934 | + | 759.250i | 0.146009 | + | 0.815521i | ||||
\(932\) | 780.565 | 0.837516 | ||||||||
\(933\) | 59.9138 | − | 34.5912i | 0.0642163 | − | 0.0370753i | ||||
\(934\) | 332.994 | − | 192.254i | 0.356525 | − | 0.205840i | ||||
\(935\) | 30.3485 | − | 52.5651i | 0.0324583 | − | 0.0562193i | ||||
\(936\) | −2.20204 | − | 3.81405i | −0.00235261 | − | 0.00407484i | ||||
\(937\) | 67.1061 | − | 116.231i | 0.0716181 | − | 0.124046i | −0.827993 | − | 0.560739i | \(-0.810517\pi\) |
0.899611 | + | 0.436693i | \(0.143850\pi\) | |||||||
\(938\) | −485.989 | −0.518112 | ||||||||
\(939\) | − | 98.6064i | − | 0.105012i | ||||||
\(940\) | −81.5403 | + | 141.232i | −0.0867450 | + | 0.150247i | ||||
\(941\) | −518.348 | − | 299.268i | −0.550848 | − | 0.318032i | 0.198616 | − | 0.980077i | \(-0.436355\pi\) |
−0.749464 | + | 0.662045i | \(0.769689\pi\) | |||||||
\(942\) | 89.9658 | 0.0955051 | ||||||||
\(943\) | 923.875i | 0.979719i | ||||||||
\(944\) | 119.666 | + | 69.0894i | 0.126765 | + | 0.0731879i | ||||
\(945\) | 14.2827 | − | 8.24609i | 0.0151139 | − | 0.00872602i | ||||
\(946\) | 233.269 | + | 134.678i | 0.246584 | + | 0.142366i | ||||
\(947\) | −410.265 | − | 710.600i | −0.433226 | − | 0.750369i | 0.563923 | − | 0.825827i | \(-0.309291\pi\) |
−0.997149 | + | 0.0754579i | \(0.975958\pi\) | |||||||
\(948\) | 21.0000 | + | 36.3731i | 0.0221519 | + | 0.0383682i | ||||
\(949\) | 5.14134i | 0.00541764i | ||||||||
\(950\) | −634.788 | + | 113.651i | −0.668198 | + | 0.119632i | ||||
\(951\) | −109.713 | −0.115366 | ||||||||
\(952\) | −84.4949 | + | 48.7832i | −0.0887551 | + | 0.0512428i | ||||
\(953\) | −68.1367 | + | 39.3388i | −0.0714971 | + | 0.0412789i | −0.535322 | − | 0.844648i | \(-0.679810\pi\) |
0.463825 | + | 0.885927i | \(0.346477\pi\) | |||||||
\(954\) | −350.858 | + | 607.704i | −0.367776 | + | 0.637006i | ||||
\(955\) | −90.1260 | − | 156.103i | −0.0943728 | − | 0.163458i | ||||
\(956\) | −296.677 | + | 513.859i | −0.310331 | + | 0.537509i | ||||
\(957\) | −72.1612 | −0.0754036 | ||||||||
\(958\) | 491.011i | 0.512538i | ||||||||
\(959\) | −17.2474 | + | 29.8735i | −0.0179848 | + | 0.0311506i | ||||
\(960\) | −2.20204 | − | 1.27135i | −0.00229379 | − | 0.00132432i | ||||
\(961\) | −11.0000 | −0.0114464 | ||||||||
\(962\) | − | 5.44183i | − | 0.00565679i | ||||||
\(963\) | −878.302 | − | 507.088i | −0.912048 | − | 0.526571i | ||||
\(964\) | −199.454 | + | 115.155i | −0.206903 | + | 0.119455i | ||||
\(965\) | 188.985 | + | 109.110i | 0.195839 | + | 0.113068i | ||||
\(966\) | 11.1056 | + | 19.2355i | 0.0114965 | + | 0.0199125i | ||||
\(967\) | −664.628 | − | 1151.17i | −0.687310 | − | 1.19046i | −0.972705 | − | 0.232045i | \(-0.925458\pi\) |
0.285395 | − | 0.958410i | \(-0.407875\pi\) | |||||||
\(968\) | 268.643i | 0.277524i | ||||||||
\(969\) | 24.3990 | − | 67.5877i | 0.0251795 | − | 0.0697499i | ||||
\(970\) | −210.409 | −0.216916 | ||||||||
\(971\) | −492.584 | + | 284.393i | −0.507296 | + | 0.292887i | −0.731721 | − | 0.681604i | \(-0.761283\pi\) |
0.224426 | + | 0.974491i | \(0.427949\pi\) | |||||||
\(972\) | −131.778 | + | 76.0818i | −0.135574 | + | 0.0782735i | ||||
\(973\) | 60.5051 | − | 104.798i | 0.0621841 | − | 0.107706i | ||||
\(974\) | −350.697 | − | 607.425i | −0.360058 | − | 0.623640i | ||||
\(975\) | −0.667354 | + | 1.15589i | −0.000684466 | + | 0.00118553i | ||||
\(976\) | −304.767 | −0.312262 | ||||||||
\(977\) | 884.903i | 0.905735i | 0.891578 | + | 0.452867i | \(0.149599\pi\) | ||||
−0.891578 | + | 0.452867i | \(0.850401\pi\) | |||||||
\(978\) | −28.6107 | + | 49.5552i | −0.0292543 | + | 0.0506699i | ||||
\(979\) | 45.1362 | + | 26.0594i | 0.0461044 | + | 0.0266184i | ||||
\(980\) | −81.1918 | −0.0828488 | ||||||||
\(981\) | 608.754i | 0.620544i | ||||||||
\(982\) | −654.441 | − | 377.841i | −0.666436 | − | 0.384767i | ||||
\(983\) | 290.842 | − | 167.917i | 0.295871 | − | 0.170821i | −0.344715 | − | 0.938707i | \(-0.612025\pi\) |
0.640587 | + | 0.767886i | \(0.278691\pi\) | |||||||
\(984\) | 42.1975 | + | 24.3627i | 0.0428836 | + | 0.0247589i | ||||
\(985\) | 170.045 | + | 294.527i | 0.172635 | + | 0.299012i | ||||
\(986\) | 374.487 | + | 648.630i | 0.379804 | + | 0.657840i | ||||
\(987\) | − | 75.1315i | − | 0.0761211i | ||||||
\(988\) | 4.28724 | + | 5.08215i | 0.00433931 | + | 0.00514388i | ||||
\(989\) | −636.446 | −0.643525 | ||||||||
\(990\) | 55.5959 | − | 32.0983i | 0.0561575 | − | 0.0324225i | ||||
\(991\) | −491.433 | + | 283.729i | −0.495896 | + | 0.286306i | −0.727017 | − | 0.686619i | \(-0.759094\pi\) |
0.231121 | + | 0.972925i | \(0.425761\pi\) | |||||||
\(992\) | −88.1816 | + | 152.735i | −0.0888928 | + | 0.153967i | ||||
\(993\) | 77.4439 | + | 134.137i | 0.0779898 | + | 0.135082i | ||||
\(994\) | −154.985 | + | 268.442i | −0.155921 | + | 0.270063i | ||||
\(995\) | 333.388 | 0.335064 | ||||||||
\(996\) | 19.5133i | 0.0195916i | ||||||||
\(997\) | 217.379 | − | 376.511i | 0.218033 | − | 0.377644i | −0.736174 | − | 0.676793i | \(-0.763369\pi\) |
0.954206 | + | 0.299149i | \(0.0967027\pi\) | |||||||
\(998\) | −968.668 | − | 559.260i | −0.970609 | − | 0.560381i | ||||
\(999\) | −125.110 | −0.125235 |
(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 | 38.3.d.a.31.2 | yes | 4 | |
3.2 | odd | 2 | 342.3.m.a.145.1 | 4 | |||
4.3 | odd | 2 | 304.3.r.a.145.2 | 4 | |||
19.7 | even | 3 | 722.3.b.b.721.4 | 4 | |||
19.8 | odd | 6 | inner | 38.3.d.a.27.2 | ✓ | 4 | |
19.12 | odd | 6 | 722.3.b.b.721.1 | 4 | |||
57.8 | even | 6 | 342.3.m.a.217.1 | 4 | |||
76.27 | even | 6 | 304.3.r.a.65.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.3.d.a.27.2 | ✓ | 4 | 19.8 | odd | 6 | inner | |
38.3.d.a.31.2 | yes | 4 | 1.1 | even | 1 | trivial | |
304.3.r.a.65.2 | 4 | 76.27 | even | 6 | |||
304.3.r.a.145.2 | 4 | 4.3 | odd | 2 | |||
342.3.m.a.145.1 | 4 | 3.2 | odd | 2 | |||
342.3.m.a.217.1 | 4 | 57.8 | even | 6 | |||
722.3.b.b.721.1 | 4 | 19.12 | odd | 6 | |||
722.3.b.b.721.4 | 4 | 19.7 | even | 3 |