Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(229,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.229");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.u (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(36\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 229.19 | ||
Character | \(\chi\) | \(=\) | 912.229 |
Dual form | 912.2.u.a.685.19 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0417641 | − | 1.41360i | −0.0295317 | − | 0.999564i | ||||
\(3\) | 0.707107 | − | 0.707107i | 0.408248 | − | 0.408248i | ||||
\(4\) | −1.99651 | + | 0.118075i | −0.998256 | + | 0.0590376i | ||||
\(5\) | 1.69566 | + | 1.69566i | 0.758322 | + | 0.758322i | 0.976017 | − | 0.217695i | \(-0.0698537\pi\) |
−0.217695 | + | 0.976017i | \(0.569854\pi\) | |||||||
\(6\) | −1.02910 | − | 0.970032i | −0.420126 | − | 0.396014i | ||||
\(7\) | − | 4.01648i | − | 1.51809i | −0.651040 | − | 0.759044i | \(-0.725667\pi\) | ||
0.651040 | − | 0.759044i | \(-0.274333\pi\) | |||||||
\(8\) | 0.250293 | + | 2.81733i | 0.0884920 | + | 0.996077i | ||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 2.32616 | − | 2.46780i | 0.735597 | − | 0.780386i | ||||
\(11\) | 3.12754 | + | 3.12754i | 0.942989 | + | 0.942989i | 0.998460 | − | 0.0554715i | \(-0.0176662\pi\) |
−0.0554715 | + | 0.998460i | \(0.517666\pi\) | |||||||
\(12\) | −1.32826 | + | 1.49524i | −0.383434 | + | 0.431638i | ||||
\(13\) | 3.31631 | − | 3.31631i | 0.919780 | − | 0.919780i | −0.0772334 | − | 0.997013i | \(-0.524609\pi\) |
0.997013 | + | 0.0772334i | \(0.0246087\pi\) | |||||||
\(14\) | −5.67769 | + | 0.167745i | −1.51743 | + | 0.0448317i | ||||
\(15\) | 2.39803 | 0.619168 | ||||||||
\(16\) | 3.97212 | − | 0.471477i | 0.993029 | − | 0.117869i | ||||
\(17\) | 1.28627 | 0.311967 | 0.155984 | − | 0.987760i | \(-0.450145\pi\) | ||||
0.155984 | + | 0.987760i | \(0.450145\pi\) | |||||||
\(18\) | −1.41360 | + | 0.0417641i | −0.333188 | + | 0.00984389i | ||||
\(19\) | −0.707107 | + | 0.707107i | −0.162221 | + | 0.162221i | ||||
\(20\) | −3.58562 | − | 3.18519i | −0.801769 | − | 0.712230i | ||||
\(21\) | −2.84008 | − | 2.84008i | −0.619757 | − | 0.619757i | ||||
\(22\) | 4.29046 | − | 4.55170i | 0.914729 | − | 0.970426i | ||||
\(23\) | 8.95781i | 1.86783i | 0.357492 | + | 0.933916i | \(0.383632\pi\) | ||||
−0.357492 | + | 0.933916i | \(0.616368\pi\) | |||||||
\(24\) | 2.16914 | + | 1.81517i | 0.442773 | + | 0.370520i | ||||
\(25\) | 0.750527i | 0.150105i | ||||||||
\(26\) | −4.82643 | − | 4.54943i | −0.946541 | − | 0.892216i | ||||
\(27\) | −0.707107 | − | 0.707107i | −0.136083 | − | 0.136083i | ||||
\(28\) | 0.474247 | + | 8.01895i | 0.0896243 | + | 1.51544i | ||||
\(29\) | 3.81503 | − | 3.81503i | 0.708432 | − | 0.708432i | −0.257773 | − | 0.966205i | \(-0.582989\pi\) |
0.966205 | + | 0.257773i | \(0.0829887\pi\) | |||||||
\(30\) | −0.100151 | − | 3.38984i | −0.0182851 | − | 0.618898i | ||||
\(31\) | −3.28373 | −0.589776 | −0.294888 | − | 0.955532i | \(-0.595282\pi\) | ||||
−0.294888 | + | 0.955532i | \(0.595282\pi\) | |||||||
\(32\) | −0.832370 | − | 5.59528i | −0.147144 | − | 0.989115i | ||||
\(33\) | 4.42301 | 0.769947 | ||||||||
\(34\) | −0.0537201 | − | 1.81827i | −0.00921292 | − | 0.311831i | ||||
\(35\) | 6.81059 | − | 6.81059i | 1.15120 | − | 1.15120i | ||||
\(36\) | 0.118075 | + | 1.99651i | 0.0196792 | + | 0.332752i | ||||
\(37\) | −2.41733 | − | 2.41733i | −0.397407 | − | 0.397407i | 0.479911 | − | 0.877317i | \(-0.340669\pi\) |
−0.877317 | + | 0.479911i | \(0.840669\pi\) | |||||||
\(38\) | 1.02910 | + | 0.970032i | 0.166941 | + | 0.157360i | ||||
\(39\) | − | 4.68997i | − | 0.750997i | ||||||
\(40\) | −4.35282 | + | 5.20165i | −0.688242 | + | 0.822453i | ||||
\(41\) | − | 11.8121i | − | 1.84475i | −0.386300 | − | 0.922373i | \(-0.626247\pi\) | ||
0.386300 | − | 0.922373i | \(-0.373753\pi\) | |||||||
\(42\) | −3.89612 | + | 4.13334i | −0.601184 | + | 0.637789i | ||||
\(43\) | 0.432575 | + | 0.432575i | 0.0659671 | + | 0.0659671i | 0.739321 | − | 0.673354i | \(-0.235147\pi\) |
−0.673354 | + | 0.739321i | \(0.735147\pi\) | |||||||
\(44\) | −6.61345 | − | 5.87488i | −0.997016 | − | 0.885672i | ||||
\(45\) | 1.69566 | − | 1.69566i | 0.252774 | − | 0.252774i | ||||
\(46\) | 12.6627 | − | 0.374115i | 1.86702 | − | 0.0551602i | ||||
\(47\) | −5.81260 | −0.847855 | −0.423927 | − | 0.905696i | \(-0.639349\pi\) | ||||
−0.423927 | + | 0.905696i | \(0.639349\pi\) | |||||||
\(48\) | 2.47533 | − | 3.14210i | 0.357283 | − | 0.453522i | ||||
\(49\) | −9.13213 | −1.30459 | ||||||||
\(50\) | 1.06094 | − | 0.0313451i | 0.150040 | − | 0.00443287i | ||||
\(51\) | 0.909533 | − | 0.909533i | 0.127360 | − | 0.127360i | ||||
\(52\) | −6.22948 | + | 7.01263i | −0.863874 | + | 0.972477i | ||||
\(53\) | −8.37304 | − | 8.37304i | −1.15013 | − | 1.15013i | −0.986527 | − | 0.163599i | \(-0.947690\pi\) |
−0.163599 | − | 0.986527i | \(-0.552310\pi\) | |||||||
\(54\) | −0.970032 | + | 1.02910i | −0.132005 | + | 0.140042i | ||||
\(55\) | 10.6065i | 1.43018i | ||||||||
\(56\) | 11.3158 | − | 1.00530i | 1.51213 | − | 0.134339i | ||||
\(57\) | 1.00000i | 0.132453i | ||||||||
\(58\) | −5.55224 | − | 5.23358i | −0.729045 | − | 0.687202i | ||||
\(59\) | 6.07068 | + | 6.07068i | 0.790335 | + | 0.790335i | 0.981548 | − | 0.191214i | \(-0.0612424\pi\) |
−0.191214 | + | 0.981548i | \(0.561242\pi\) | |||||||
\(60\) | −4.78769 | + | 0.283147i | −0.618088 | + | 0.0365542i | ||||
\(61\) | 9.39559 | − | 9.39559i | 1.20298 | − | 1.20298i | 0.229728 | − | 0.973255i | \(-0.426216\pi\) |
0.973255 | − | 0.229728i | \(-0.0737836\pi\) | |||||||
\(62\) | 0.137142 | + | 4.64188i | 0.0174171 | + | 0.589519i | ||||
\(63\) | −4.01648 | −0.506029 | ||||||||
\(64\) | −7.87471 | + | 1.41032i | −0.984338 | + | 0.176290i | ||||
\(65\) | 11.2467 | 1.39498 | ||||||||
\(66\) | −0.184723 | − | 6.25235i | −0.0227378 | − | 0.769611i | ||||
\(67\) | −4.53509 | + | 4.53509i | −0.554049 | + | 0.554049i | −0.927607 | − | 0.373558i | \(-0.878138\pi\) |
0.373558 | + | 0.927607i | \(0.378138\pi\) | |||||||
\(68\) | −2.56806 | + | 0.151877i | −0.311423 | + | 0.0184178i | ||||
\(69\) | 6.33413 | + | 6.33413i | 0.762539 | + | 0.762539i | ||||
\(70\) | −9.91187 | − | 9.34299i | −1.18469 | − | 1.11670i | ||||
\(71\) | − | 0.435690i | − | 0.0517069i | −0.999666 | − | 0.0258534i | \(-0.991770\pi\) | ||
0.999666 | − | 0.0258534i | \(-0.00823032\pi\) | |||||||
\(72\) | 2.81733 | − | 0.250293i | 0.332026 | − | 0.0294973i | ||||
\(73\) | 6.52722i | 0.763954i | 0.924172 | + | 0.381977i | \(0.124757\pi\) | ||||
−0.924172 | + | 0.381977i | \(0.875243\pi\) | |||||||
\(74\) | −3.31617 | + | 3.51809i | −0.385497 | + | 0.408970i | ||||
\(75\) | 0.530703 | + | 0.530703i | 0.0612803 | + | 0.0612803i | ||||
\(76\) | 1.32826 | − | 1.49524i | 0.152361 | − | 0.171516i | ||||
\(77\) | 12.5617 | − | 12.5617i | 1.43154 | − | 1.43154i | ||||
\(78\) | −6.62973 | + | 0.195873i | −0.750669 | + | 0.0221782i | ||||
\(79\) | 5.60770 | 0.630916 | 0.315458 | − | 0.948940i | \(-0.397842\pi\) | ||||
0.315458 | + | 0.948940i | \(0.397842\pi\) | |||||||
\(80\) | 7.53482 | + | 5.93590i | 0.842419 | + | 0.663653i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −16.6976 | + | 0.493323i | −1.84394 | + | 0.0544785i | ||||
\(83\) | 1.87477 | − | 1.87477i | 0.205783 | − | 0.205783i | −0.596689 | − | 0.802472i | \(-0.703518\pi\) |
0.802472 | + | 0.596689i | \(0.203518\pi\) | |||||||
\(84\) | 6.00560 | + | 5.33491i | 0.655265 | + | 0.582087i | ||||
\(85\) | 2.18108 | + | 2.18108i | 0.236572 | + | 0.236572i | ||||
\(86\) | 0.593421 | − | 0.629553i | 0.0639902 | − | 0.0678864i | ||||
\(87\) | − | 5.39526i | − | 0.578433i | ||||||
\(88\) | −8.02851 | + | 9.59412i | −0.855842 | + | 1.02274i | ||||
\(89\) | 16.5092i | 1.74998i | 0.484145 | + | 0.874988i | \(0.339131\pi\) | ||||
−0.484145 | + | 0.874988i | \(0.660869\pi\) | |||||||
\(90\) | −2.46780 | − | 2.32616i | −0.260129 | − | 0.245199i | ||||
\(91\) | −13.3199 | − | 13.3199i | −1.39631 | − | 1.39631i | ||||
\(92\) | −1.05770 | − | 17.8844i | −0.110272 | − | 1.86457i | ||||
\(93\) | −2.32195 | + | 2.32195i | −0.240775 | + | 0.240775i | ||||
\(94\) | 0.242758 | + | 8.21667i | 0.0250386 | + | 0.847485i | ||||
\(95\) | −2.39803 | −0.246032 | ||||||||
\(96\) | −4.54504 | − | 3.36789i | −0.463876 | − | 0.343733i | ||||
\(97\) | −5.55954 | −0.564486 | −0.282243 | − | 0.959343i | \(-0.591078\pi\) | ||||
−0.282243 | + | 0.959343i | \(0.591078\pi\) | |||||||
\(98\) | 0.381395 | + | 12.9092i | 0.0385267 | + | 1.30402i | ||||
\(99\) | 3.12754 | − | 3.12754i | 0.314330 | − | 0.314330i | ||||
\(100\) | −0.0886186 | − | 1.49844i | −0.00886186 | − | 0.149844i | ||||
\(101\) | 12.0505 | + | 12.0505i | 1.19907 | + | 1.19907i | 0.974447 | + | 0.224619i | \(0.0721136\pi\) |
0.224619 | + | 0.974447i | \(0.427886\pi\) | |||||||
\(102\) | −1.32370 | − | 1.24773i | −0.131066 | − | 0.123543i | ||||
\(103\) | 0.764345i | 0.0753131i | 0.999291 | + | 0.0376566i | \(0.0119893\pi\) | ||||
−0.999291 | + | 0.0376566i | \(0.988011\pi\) | |||||||
\(104\) | 10.1732 | + | 8.51310i | 0.997564 | + | 0.834778i | ||||
\(105\) | − | 9.63163i | − | 0.939951i | ||||||
\(106\) | −11.4864 | + | 12.1858i | −1.11566 | + | 1.18359i | ||||
\(107\) | −2.31480 | − | 2.31480i | −0.223781 | − | 0.223781i | 0.586308 | − | 0.810088i | \(-0.300581\pi\) |
−0.810088 | + | 0.586308i | \(0.800581\pi\) | |||||||
\(108\) | 1.49524 | + | 1.32826i | 0.143879 | + | 0.127811i | ||||
\(109\) | −10.8167 | + | 10.8167i | −1.03606 | + | 1.03606i | −0.0367303 | + | 0.999325i | \(0.511694\pi\) |
−0.999325 | + | 0.0367303i | \(0.988306\pi\) | |||||||
\(110\) | 14.9933 | − | 0.442971i | 1.42956 | − | 0.0422356i | ||||
\(111\) | −3.41862 | −0.324481 | ||||||||
\(112\) | −1.89368 | − | 15.9539i | −0.178936 | − | 1.50751i | ||||
\(113\) | −17.7886 | −1.67341 | −0.836703 | − | 0.547656i | \(-0.815520\pi\) | ||||
−0.836703 | + | 0.547656i | \(0.815520\pi\) | |||||||
\(114\) | 1.41360 | − | 0.0417641i | 0.132395 | − | 0.00391157i | ||||
\(115\) | −15.1894 | + | 15.1894i | −1.41642 | + | 1.41642i | ||||
\(116\) | −7.16628 | + | 8.06720i | −0.665373 | + | 0.749021i | ||||
\(117\) | −3.31631 | − | 3.31631i | −0.306593 | − | 0.306593i | ||||
\(118\) | 8.32795 | − | 8.83502i | 0.766650 | − | 0.813330i | ||||
\(119\) | − | 5.16630i | − | 0.473594i | ||||||
\(120\) | 0.600210 | + | 6.75603i | 0.0547914 | + | 0.616739i | ||||
\(121\) | 8.56301i | 0.778456i | ||||||||
\(122\) | −13.6740 | − | 12.8892i | −1.23798 | − | 1.16693i | ||||
\(123\) | −8.35245 | − | 8.35245i | −0.753115 | − | 0.753115i | ||||
\(124\) | 6.55601 | − | 0.387728i | 0.588747 | − | 0.0348190i | ||||
\(125\) | 7.20566 | − | 7.20566i | 0.644494 | − | 0.644494i | ||||
\(126\) | 0.167745 | + | 5.67769i | 0.0149439 | + | 0.505809i | ||||
\(127\) | 14.8617 | 1.31876 | 0.659381 | − | 0.751809i | \(-0.270818\pi\) | ||||
0.659381 | + | 0.751809i | \(0.270818\pi\) | |||||||
\(128\) | 2.32250 | + | 11.0728i | 0.205282 | + | 0.978703i | ||||
\(129\) | 0.611754 | 0.0538619 | ||||||||
\(130\) | −0.469707 | − | 15.8983i | −0.0411961 | − | 1.39437i | ||||
\(131\) | −6.76043 | + | 6.76043i | −0.590661 | + | 0.590661i | −0.937810 | − | 0.347149i | \(-0.887150\pi\) |
0.347149 | + | 0.937810i | \(0.387150\pi\) | |||||||
\(132\) | −8.83059 | + | 0.522248i | −0.768604 | + | 0.0454558i | ||||
\(133\) | 2.84008 | + | 2.84008i | 0.246266 | + | 0.246266i | ||||
\(134\) | 6.60019 | + | 6.22138i | 0.570170 | + | 0.537445i | ||||
\(135\) | − | 2.39803i | − | 0.206389i | ||||||
\(136\) | 0.321946 | + | 3.62386i | 0.0276066 | + | 0.310743i | ||||
\(137\) | 6.81085i | 0.581890i | 0.956740 | + | 0.290945i | \(0.0939696\pi\) | ||||
−0.956740 | + | 0.290945i | \(0.906030\pi\) | |||||||
\(138\) | 8.68936 | − | 9.21844i | 0.739688 | − | 0.784726i | ||||
\(139\) | 3.63392 | + | 3.63392i | 0.308225 | + | 0.308225i | 0.844221 | − | 0.535996i | \(-0.180064\pi\) |
−0.535996 | + | 0.844221i | \(0.680064\pi\) | |||||||
\(140\) | −12.7933 | + | 14.4016i | −1.08123 | + | 1.21716i | ||||
\(141\) | −4.11013 | + | 4.11013i | −0.346135 | + | 0.346135i | ||||
\(142\) | −0.615890 | + | 0.0181962i | −0.0516843 | + | 0.00152699i | ||||
\(143\) | 20.7438 | 1.73468 | ||||||||
\(144\) | −0.471477 | − | 3.97212i | −0.0392897 | − | 0.331010i | ||||
\(145\) | 12.9380 | 1.07444 | ||||||||
\(146\) | 9.22686 | − | 0.272604i | 0.763620 | − | 0.0225608i | ||||
\(147\) | −6.45739 | + | 6.45739i | −0.532597 | + | 0.532597i | ||||
\(148\) | 5.11166 | + | 4.54080i | 0.420176 | + | 0.373252i | ||||
\(149\) | −1.29352 | − | 1.29352i | −0.105969 | − | 0.105969i | 0.652134 | − | 0.758104i | \(-0.273874\pi\) |
−0.758104 | + | 0.652134i | \(0.773874\pi\) | |||||||
\(150\) | 0.728035 | − | 0.772364i | 0.0594438 | − | 0.0630633i | ||||
\(151\) | − | 8.77728i | − | 0.714285i | −0.934050 | − | 0.357142i | \(-0.883751\pi\) | ||
0.934050 | − | 0.357142i | \(-0.116249\pi\) | |||||||
\(152\) | −2.16914 | − | 1.81517i | −0.175940 | − | 0.147230i | ||||
\(153\) | − | 1.28627i | − | 0.103989i | ||||||
\(154\) | −18.2818 | − | 17.2326i | −1.47319 | − | 1.38864i | ||||
\(155\) | −5.56810 | − | 5.56810i | −0.447240 | − | 0.447240i | ||||
\(156\) | 0.553770 | + | 9.36359i | 0.0443371 | + | 0.749687i | ||||
\(157\) | −4.54898 | + | 4.54898i | −0.363048 | + | 0.363048i | −0.864934 | − | 0.501886i | \(-0.832640\pi\) |
0.501886 | + | 0.864934i | \(0.332640\pi\) | |||||||
\(158\) | −0.234201 | − | 7.92703i | −0.0186320 | − | 0.630641i | ||||
\(159\) | −11.8413 | −0.939074 | ||||||||
\(160\) | 8.07628 | − | 10.8991i | 0.638486 | − | 0.861650i | ||||
\(161\) | 35.9789 | 2.83553 | ||||||||
\(162\) | 0.0417641 | + | 1.41360i | 0.00328130 | + | 0.111063i | ||||
\(163\) | −10.7494 | + | 10.7494i | −0.841960 | + | 0.841960i | −0.989114 | − | 0.147153i | \(-0.952989\pi\) |
0.147153 | + | 0.989114i | \(0.452989\pi\) | |||||||
\(164\) | 1.39472 | + | 23.5831i | 0.108909 | + | 1.84153i | ||||
\(165\) | 7.49992 | + | 7.49992i | 0.583868 | + | 0.583868i | ||||
\(166\) | −2.72847 | − | 2.57188i | −0.211770 | − | 0.199616i | ||||
\(167\) | 1.36066i | 0.105291i | 0.998613 | + | 0.0526454i | \(0.0167653\pi\) | ||||
−0.998613 | + | 0.0526454i | \(0.983235\pi\) | |||||||
\(168\) | 7.29060 | − | 8.71230i | 0.562482 | − | 0.672169i | ||||
\(169\) | − | 8.99586i | − | 0.691989i | ||||||
\(170\) | 2.99208 | − | 3.17426i | 0.229482 | − | 0.243455i | ||||
\(171\) | 0.707107 | + | 0.707107i | 0.0540738 | + | 0.0540738i | ||||
\(172\) | −0.914718 | − | 0.812565i | −0.0697466 | − | 0.0619575i | ||||
\(173\) | −7.34626 | + | 7.34626i | −0.558526 | + | 0.558526i | −0.928888 | − | 0.370362i | \(-0.879234\pi\) |
0.370362 | + | 0.928888i | \(0.379234\pi\) | |||||||
\(174\) | −7.62672 | + | 0.225328i | −0.578180 | + | 0.0170821i | ||||
\(175\) | 3.01448 | 0.227873 | ||||||||
\(176\) | 13.8975 | + | 10.9484i | 1.04756 | + | 0.825266i | ||||
\(177\) | 8.58523 | 0.645305 | ||||||||
\(178\) | 23.3374 | − | 0.689493i | 1.74921 | − | 0.0516797i | ||||
\(179\) | −6.72145 | + | 6.72145i | −0.502385 | + | 0.502385i | −0.912178 | − | 0.409794i | \(-0.865601\pi\) |
0.409794 | + | 0.912178i | \(0.365601\pi\) | |||||||
\(180\) | −3.18519 | + | 3.58562i | −0.237410 | + | 0.267256i | ||||
\(181\) | 5.39298 | + | 5.39298i | 0.400857 | + | 0.400857i | 0.878535 | − | 0.477678i | \(-0.158521\pi\) |
−0.477678 | + | 0.878535i | \(0.658521\pi\) | |||||||
\(182\) | −18.2727 | + | 19.3853i | −1.35446 | + | 1.43693i | ||||
\(183\) | − | 13.2874i | − | 0.982231i | ||||||
\(184\) | −25.2371 | + | 2.24208i | −1.86050 | + | 0.165288i | ||||
\(185\) | − | 8.19794i | − | 0.602725i | ||||||
\(186\) | 3.37928 | + | 3.18533i | 0.247781 | + | 0.233560i | ||||
\(187\) | 4.02287 | + | 4.02287i | 0.294182 | + | 0.294182i | ||||
\(188\) | 11.6049 | − | 0.686324i | 0.846376 | − | 0.0500553i | ||||
\(189\) | −2.84008 | + | 2.84008i | −0.206586 | + | 0.206586i | ||||
\(190\) | 0.100151 | + | 3.38984i | 0.00726575 | + | 0.245925i | ||||
\(191\) | 23.2786 | 1.68438 | 0.842190 | − | 0.539180i | \(-0.181266\pi\) | ||||
0.842190 | + | 0.539180i | \(0.181266\pi\) | |||||||
\(192\) | −4.57101 | + | 6.56550i | −0.329884 | + | 0.473824i | ||||
\(193\) | −1.03215 | −0.0742961 | −0.0371481 | − | 0.999310i | \(-0.511827\pi\) | ||||
−0.0371481 | + | 0.999310i | \(0.511827\pi\) | |||||||
\(194\) | 0.232189 | + | 7.85895i | 0.0166702 | + | 0.564240i | ||||
\(195\) | 7.95260 | − | 7.95260i | 0.569498 | − | 0.569498i | ||||
\(196\) | 18.2324 | − | 1.07828i | 1.30231 | − | 0.0770199i | ||||
\(197\) | −0.216314 | − | 0.216314i | −0.0154117 | − | 0.0154117i | 0.699359 | − | 0.714771i | \(-0.253469\pi\) |
−0.714771 | + | 0.699359i | \(0.753469\pi\) | |||||||
\(198\) | −4.55170 | − | 4.29046i | −0.323475 | − | 0.304910i | ||||
\(199\) | − | 4.75556i | − | 0.337113i | −0.985692 | − | 0.168556i | \(-0.946089\pi\) | ||
0.985692 | − | 0.168556i | \(-0.0539105\pi\) | |||||||
\(200\) | −2.11448 | + | 0.187852i | −0.149517 | + | 0.0132831i | ||||
\(201\) | 6.41358i | 0.452379i | ||||||||
\(202\) | 16.5312 | − | 17.5378i | 1.16313 | − | 1.23395i | ||||
\(203\) | −15.3230 | − | 15.3230i | −1.07546 | − | 1.07546i | ||||
\(204\) | −1.70850 | + | 1.92329i | −0.119619 | + | 0.134657i | ||||
\(205\) | 20.0294 | − | 20.0294i | 1.39891 | − | 1.39891i | ||||
\(206\) | 1.08047 | − | 0.0319222i | 0.0752803 | − | 0.00222412i | ||||
\(207\) | 8.95781 | 0.622611 | ||||||||
\(208\) | 11.6092 | − | 14.7363i | 0.804954 | − | 1.02178i | ||||
\(209\) | −4.42301 | −0.305946 | ||||||||
\(210\) | −13.6152 | + | 0.402256i | −0.939541 | + | 0.0277583i | ||||
\(211\) | −4.44485 | + | 4.44485i | −0.305996 | + | 0.305996i | −0.843354 | − | 0.537358i | \(-0.819422\pi\) |
0.537358 | + | 0.843354i | \(0.319422\pi\) | |||||||
\(212\) | 17.7055 | + | 15.7282i | 1.21602 | + | 1.08022i | ||||
\(213\) | −0.308079 | − | 0.308079i | −0.0211092 | − | 0.0211092i | ||||
\(214\) | −3.17552 | + | 3.36888i | −0.217074 | + | 0.230292i | ||||
\(215\) | 1.46700i | 0.100049i | ||||||||
\(216\) | 1.81517 | − | 2.16914i | 0.123507 | − | 0.147591i | ||||
\(217\) | 13.1891i | 0.895332i | ||||||||
\(218\) | 15.7423 | + | 14.8388i | 1.06620 | + | 1.00501i | ||||
\(219\) | 4.61544 | + | 4.61544i | 0.311883 | + | 0.311883i | ||||
\(220\) | −1.25236 | − | 21.1760i | −0.0844343 | − | 1.42768i | ||||
\(221\) | 4.26569 | − | 4.26569i | 0.286941 | − | 0.286941i | ||||
\(222\) | 0.142776 | + | 4.83255i | 0.00958248 | + | 0.324340i | ||||
\(223\) | 24.8496 | 1.66405 | 0.832026 | − | 0.554736i | \(-0.187181\pi\) | ||||
0.832026 | + | 0.554736i | \(0.187181\pi\) | |||||||
\(224\) | −22.4733 | + | 3.34320i | −1.50156 | + | 0.223377i | ||||
\(225\) | 0.750527 | 0.0500351 | ||||||||
\(226\) | 0.742923 | + | 25.1458i | 0.0494185 | + | 1.67268i | ||||
\(227\) | −8.39340 | + | 8.39340i | −0.557089 | + | 0.557089i | −0.928478 | − | 0.371388i | \(-0.878882\pi\) |
0.371388 | + | 0.928478i | \(0.378882\pi\) | |||||||
\(228\) | −0.118075 | − | 1.99651i | −0.00781972 | − | 0.132222i | ||||
\(229\) | 7.87664 | + | 7.87664i | 0.520503 | + | 0.520503i | 0.917723 | − | 0.397220i | \(-0.130025\pi\) |
−0.397220 | + | 0.917723i | \(0.630025\pi\) | |||||||
\(230\) | 22.1061 | + | 20.8373i | 1.45763 | + | 1.37397i | ||||
\(231\) | − | 17.7649i | − | 1.16885i | ||||||
\(232\) | 11.7031 | + | 9.79331i | 0.768344 | + | 0.642962i | ||||
\(233\) | − | 0.905760i | − | 0.0593383i | −0.999560 | − | 0.0296691i | \(-0.990555\pi\) | ||
0.999560 | − | 0.0296691i | \(-0.00944537\pi\) | |||||||
\(234\) | −4.54943 | + | 4.82643i | −0.297405 | + | 0.315514i | ||||
\(235\) | −9.85619 | − | 9.85619i | −0.642947 | − | 0.642947i | ||||
\(236\) | −12.8370 | − | 11.4034i | −0.835615 | − | 0.742297i | ||||
\(237\) | 3.96524 | − | 3.96524i | 0.257570 | − | 0.257570i | ||||
\(238\) | −7.30306 | + | 0.215766i | −0.473387 | + | 0.0139860i | ||||
\(239\) | −15.2167 | −0.984287 | −0.492143 | − | 0.870514i | \(-0.663786\pi\) | ||||
−0.492143 | + | 0.870514i | \(0.663786\pi\) | |||||||
\(240\) | 9.52524 | − | 1.13061i | 0.614851 | − | 0.0729808i | ||||
\(241\) | 25.0035 | 1.61062 | 0.805309 | − | 0.592855i | \(-0.201999\pi\) | ||||
0.805309 | + | 0.592855i | \(0.201999\pi\) | |||||||
\(242\) | 12.1046 | − | 0.357627i | 0.778116 | − | 0.0229891i | ||||
\(243\) | −0.707107 | + | 0.707107i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | −17.6490 | + | 19.8678i | −1.12986 | + | 1.27191i | ||||
\(245\) | −15.4850 | − | 15.4850i | −0.989300 | − | 0.989300i | ||||
\(246\) | −11.4582 | + | 12.1558i | −0.730545 | + | 0.775027i | ||||
\(247\) | 4.68997i | 0.298416i | ||||||||
\(248\) | −0.821896 | − | 9.25137i | −0.0521905 | − | 0.587462i | ||||
\(249\) | − | 2.65133i | − | 0.168021i | ||||||
\(250\) | −10.4868 | − | 9.88496i | −0.663246 | − | 0.625180i | ||||
\(251\) | −1.36247 | − | 1.36247i | −0.0859986 | − | 0.0859986i | 0.662799 | − | 0.748797i | \(-0.269368\pi\) |
−0.748797 | + | 0.662799i | \(0.769368\pi\) | |||||||
\(252\) | 8.01895 | − | 0.474247i | 0.505147 | − | 0.0298748i | ||||
\(253\) | −28.0159 | + | 28.0159i | −1.76134 | + | 1.76134i | ||||
\(254\) | −0.620686 | − | 21.0085i | −0.0389453 | − | 1.31819i | ||||
\(255\) | 3.08452 | 0.193160 | ||||||||
\(256\) | 15.5554 | − | 3.74552i | 0.972214 | − | 0.234095i | ||||
\(257\) | 5.87061 | 0.366198 | 0.183099 | − | 0.983094i | \(-0.441387\pi\) | ||||
0.183099 | + | 0.983094i | \(0.441387\pi\) | |||||||
\(258\) | −0.0255493 | − | 0.864773i | −0.00159063 | − | 0.0538384i | ||||
\(259\) | −9.70917 | + | 9.70917i | −0.603298 | + | 0.603298i | ||||
\(260\) | −22.4541 | + | 1.32795i | −1.39255 | + | 0.0823562i | ||||
\(261\) | −3.81503 | − | 3.81503i | −0.236144 | − | 0.236144i | ||||
\(262\) | 9.83886 | + | 9.27418i | 0.607847 | + | 0.572961i | ||||
\(263\) | − | 1.32677i | − | 0.0818119i | −0.999163 | − | 0.0409060i | \(-0.986976\pi\) | ||
0.999163 | − | 0.0409060i | \(-0.0130244\pi\) | |||||||
\(264\) | 1.10705 | + | 12.4611i | 0.0681342 | + | 0.766927i | ||||
\(265\) | − | 28.3957i | − | 1.74433i | ||||||
\(266\) | 3.89612 | − | 4.13334i | 0.238886 | − | 0.253432i | ||||
\(267\) | 11.6738 | + | 11.6738i | 0.714425 | + | 0.714425i | ||||
\(268\) | 8.51887 | − | 9.58984i | 0.520373 | − | 0.585792i | ||||
\(269\) | 20.2148 | − | 20.2148i | 1.23252 | − | 1.23252i | 0.269523 | − | 0.962994i | \(-0.413134\pi\) |
0.962994 | − | 0.269523i | \(-0.0868659\pi\) | |||||||
\(270\) | −3.38984 | + | 0.100151i | −0.206299 | + | 0.00609502i | ||||
\(271\) | −12.8145 | −0.778424 | −0.389212 | − | 0.921148i | \(-0.627253\pi\) | ||||
−0.389212 | + | 0.921148i | \(0.627253\pi\) | |||||||
\(272\) | 5.10923 | − | 0.606449i | 0.309793 | − | 0.0367713i | ||||
\(273\) | −18.8372 | −1.14008 | ||||||||
\(274\) | 9.62779 | − | 0.284449i | 0.581636 | − | 0.0171842i | ||||
\(275\) | −2.34730 | + | 2.34730i | −0.141548 | + | 0.141548i | ||||
\(276\) | −13.3941 | − | 11.8983i | −0.806228 | − | 0.716191i | ||||
\(277\) | −20.6791 | − | 20.6791i | −1.24249 | − | 1.24249i | −0.958966 | − | 0.283521i | \(-0.908497\pi\) |
−0.283521 | − | 0.958966i | \(-0.591503\pi\) | |||||||
\(278\) | 4.98513 | − | 5.28867i | 0.298988 | − | 0.317193i | ||||
\(279\) | 3.28373i | 0.196592i | ||||||||
\(280\) | 20.8923 | + | 17.4830i | 1.24856 | + | 1.04481i | ||||
\(281\) | 15.8593i | 0.946085i | 0.881040 | + | 0.473043i | \(0.156844\pi\) | ||||
−0.881040 | + | 0.473043i | \(0.843156\pi\) | |||||||
\(282\) | 5.98172 | + | 5.63841i | 0.356206 | + | 0.335762i | ||||
\(283\) | −19.1613 | − | 19.1613i | −1.13902 | − | 1.13902i | −0.988626 | − | 0.150393i | \(-0.951946\pi\) |
−0.150393 | − | 0.988626i | \(-0.548054\pi\) | |||||||
\(284\) | 0.0514442 | + | 0.869860i | 0.00305265 | + | 0.0516167i | ||||
\(285\) | −1.69566 | + | 1.69566i | −0.100442 | + | 0.100442i | ||||
\(286\) | −0.866346 | − | 29.3234i | −0.0512281 | − | 1.73393i | ||||
\(287\) | −47.4433 | −2.80049 | ||||||||
\(288\) | −5.59528 | + | 0.832370i | −0.329705 | + | 0.0490479i | ||||
\(289\) | −15.3455 | −0.902676 | ||||||||
\(290\) | −0.540343 | − | 18.2891i | −0.0317300 | − | 1.07397i | ||||
\(291\) | −3.93119 | + | 3.93119i | −0.230450 | + | 0.230450i | ||||
\(292\) | −0.770703 | − | 13.0317i | −0.0451020 | − | 0.762621i | ||||
\(293\) | −11.8736 | − | 11.8736i | −0.693664 | − | 0.693664i | 0.269372 | − | 0.963036i | \(-0.413184\pi\) |
−0.963036 | + | 0.269372i | \(0.913184\pi\) | |||||||
\(294\) | 9.39784 | + | 8.85846i | 0.548093 | + | 0.516636i | ||||
\(295\) | 20.5876i | 1.19866i | ||||||||
\(296\) | 6.20538 | − | 7.41546i | 0.360680 | − | 0.431015i | ||||
\(297\) | − | 4.42301i | − | 0.256649i | ||||||
\(298\) | −1.77450 | + | 1.88254i | −0.102794 | + | 0.109053i | ||||
\(299\) | 29.7069 | + | 29.7069i | 1.71799 | + | 1.71799i | ||||
\(300\) | −1.12222 | − | 0.996891i | −0.0647912 | − | 0.0575556i | ||||
\(301\) | 1.73743 | − | 1.73743i | 0.100144 | − | 0.100144i | ||||
\(302\) | −12.4075 | + | 0.366575i | −0.713973 | + | 0.0210940i | ||||
\(303\) | 17.0419 | 0.979033 | ||||||||
\(304\) | −2.47533 | + | 3.14210i | −0.141970 | + | 0.180212i | ||||
\(305\) | 31.8635 | 1.82450 | ||||||||
\(306\) | −1.81827 | + | 0.0537201i | −0.103944 | + | 0.00307097i | ||||
\(307\) | −18.6128 | + | 18.6128i | −1.06229 | + | 1.06229i | −0.0643625 | + | 0.997927i | \(0.520501\pi\) |
−0.997927 | + | 0.0643625i | \(0.979499\pi\) | |||||||
\(308\) | −23.5964 | + | 26.5628i | −1.34453 | + | 1.51356i | ||||
\(309\) | 0.540473 | + | 0.540473i | 0.0307464 | + | 0.0307464i | ||||
\(310\) | −7.63850 | + | 8.10359i | −0.433838 | + | 0.460253i | ||||
\(311\) | 13.1304i | 0.744557i | 0.928121 | + | 0.372278i | \(0.121423\pi\) | ||||
−0.928121 | + | 0.372278i | \(0.878577\pi\) | |||||||
\(312\) | 13.2132 | − | 1.17387i | 0.748051 | − | 0.0664572i | ||||
\(313\) | 27.7167i | 1.56664i | 0.621618 | + | 0.783320i | \(0.286476\pi\) | ||||
−0.621618 | + | 0.783320i | \(0.713524\pi\) | |||||||
\(314\) | 6.62040 | + | 6.24043i | 0.373611 | + | 0.352168i | ||||
\(315\) | −6.81059 | − | 6.81059i | −0.383733 | − | 0.383733i | ||||
\(316\) | −11.1958 | + | 0.662131i | −0.629815 | + | 0.0372478i | ||||
\(317\) | 17.1979 | − | 17.1979i | 0.965932 | − | 0.965932i | −0.0335063 | − | 0.999439i | \(-0.510667\pi\) |
0.999439 | + | 0.0335063i | \(0.0106674\pi\) | |||||||
\(318\) | 0.494540 | + | 16.7388i | 0.0277324 | + | 0.938664i | ||||
\(319\) | 23.8633 | 1.33609 | ||||||||
\(320\) | −15.7442 | − | 10.9614i | −0.880130 | − | 0.612761i | ||||
\(321\) | −3.27363 | −0.182716 | ||||||||
\(322\) | −1.50263 | − | 50.8596i | −0.0837381 | − | 2.83430i | ||||
\(323\) | −0.909533 | + | 0.909533i | −0.0506078 | + | 0.0506078i | ||||
\(324\) | 1.99651 | − | 0.118075i | 0.110917 | − | 0.00655973i | ||||
\(325\) | 2.48898 | + | 2.48898i | 0.138064 | + | 0.138064i | ||||
\(326\) | 15.6443 | + | 14.7464i | 0.866458 | + | 0.816729i | ||||
\(327\) | 15.2972i | 0.845936i | ||||||||
\(328\) | 33.2787 | − | 2.95650i | 1.83751 | − | 0.163245i | ||||
\(329\) | 23.3462i | 1.28712i | ||||||||
\(330\) | 10.2886 | − | 10.9151i | 0.566371 | − | 0.600856i | ||||
\(331\) | 15.8401 | + | 15.8401i | 0.870648 | + | 0.870648i | 0.992543 | − | 0.121895i | \(-0.0388970\pi\) |
−0.121895 | + | 0.992543i | \(0.538897\pi\) | |||||||
\(332\) | −3.52164 | + | 3.96437i | −0.193275 | + | 0.217573i | ||||
\(333\) | −2.41733 | + | 2.41733i | −0.132469 | + | 0.132469i | ||||
\(334\) | 1.92342 | − | 0.0568266i | 0.105245 | − | 0.00310941i | ||||
\(335\) | −15.3799 | −0.840296 | ||||||||
\(336\) | −12.6202 | − | 9.94210i | −0.688487 | − | 0.542386i | ||||
\(337\) | −7.95821 | −0.433512 | −0.216756 | − | 0.976226i | \(-0.569548\pi\) | ||||
−0.216756 | + | 0.976226i | \(0.569548\pi\) | |||||||
\(338\) | −12.7165 | + | 0.375704i | −0.691687 | + | 0.0204356i | ||||
\(339\) | −12.5784 | + | 12.5784i | −0.683165 | + | 0.683165i | ||||
\(340\) | −4.61209 | − | 4.09703i | −0.250126 | − | 0.222192i | ||||
\(341\) | −10.2700 | − | 10.2700i | −0.556152 | − | 0.556152i | ||||
\(342\) | 0.970032 | − | 1.02910i | 0.0524533 | − | 0.0556471i | ||||
\(343\) | 8.56367i | 0.462395i | ||||||||
\(344\) | −1.11044 | + | 1.32698i | −0.0598707 | + | 0.0715459i | ||||
\(345\) | 21.4811i | 1.15650i | ||||||||
\(346\) | 10.6915 | + | 10.0778i | 0.574776 | + | 0.541788i | ||||
\(347\) | 10.8017 | + | 10.8017i | 0.579868 | + | 0.579868i | 0.934867 | − | 0.354999i | \(-0.115519\pi\) |
−0.354999 | + | 0.934867i | \(0.615519\pi\) | |||||||
\(348\) | 0.637046 | + | 10.7717i | 0.0341493 | + | 0.577424i | ||||
\(349\) | 1.23770 | − | 1.23770i | 0.0662523 | − | 0.0662523i | −0.673204 | − | 0.739457i | \(-0.735083\pi\) |
0.739457 | + | 0.673204i | \(0.235083\pi\) | |||||||
\(350\) | −0.125897 | − | 4.26126i | −0.00672948 | − | 0.227774i | ||||
\(351\) | −4.68997 | −0.250332 | ||||||||
\(352\) | 14.8962 | − | 20.1027i | 0.793970 | − | 1.07148i | ||||
\(353\) | −22.3824 | −1.19130 | −0.595648 | − | 0.803245i | \(-0.703105\pi\) | ||||
−0.595648 | + | 0.803245i | \(0.703105\pi\) | |||||||
\(354\) | −0.358554 | − | 12.1361i | −0.0190570 | − | 0.645024i | ||||
\(355\) | 0.738782 | − | 0.738782i | 0.0392105 | − | 0.0392105i | ||||
\(356\) | −1.94933 | − | 32.9609i | −0.103314 | − | 1.74692i | ||||
\(357\) | −3.65312 | − | 3.65312i | −0.193344 | − | 0.193344i | ||||
\(358\) | 9.78213 | + | 9.22070i | 0.517002 | + | 0.487329i | ||||
\(359\) | − | 13.9486i | − | 0.736180i | −0.929790 | − | 0.368090i | \(-0.880012\pi\) | ||
0.929790 | − | 0.368090i | \(-0.119988\pi\) | |||||||
\(360\) | 5.20165 | + | 4.35282i | 0.274151 | + | 0.229414i | ||||
\(361\) | − | 1.00000i | − | 0.0526316i | ||||||
\(362\) | 7.39827 | − | 7.84874i | 0.388844 | − | 0.412520i | ||||
\(363\) | 6.05496 | + | 6.05496i | 0.317803 | + | 0.317803i | ||||
\(364\) | 28.1661 | + | 25.0206i | 1.47631 | + | 1.31144i | ||||
\(365\) | −11.0680 | + | 11.0680i | −0.579323 | + | 0.579323i | ||||
\(366\) | −18.7830 | + | 0.554935i | −0.981803 | + | 0.0290069i | ||||
\(367\) | 4.51862 | 0.235870 | 0.117935 | − | 0.993021i | \(-0.462373\pi\) | ||||
0.117935 | + | 0.993021i | \(0.462373\pi\) | |||||||
\(368\) | 4.22340 | + | 35.5815i | 0.220160 | + | 1.85481i | ||||
\(369\) | −11.8121 | −0.614916 | ||||||||
\(370\) | −11.5886 | + | 0.342380i | −0.602462 | + | 0.0177995i | ||||
\(371\) | −33.6302 | + | 33.6302i | −1.74599 | + | 1.74599i | ||||
\(372\) | 4.36164 | − | 4.90997i | 0.226140 | − | 0.254570i | ||||
\(373\) | 4.30193 | + | 4.30193i | 0.222745 | + | 0.222745i | 0.809654 | − | 0.586908i | \(-0.199655\pi\) |
−0.586908 | + | 0.809654i | \(0.699655\pi\) | |||||||
\(374\) | 5.51871 | − | 5.85473i | 0.285366 | − | 0.302741i | ||||
\(375\) | − | 10.1903i | − | 0.526227i | ||||||
\(376\) | −1.45485 | − | 16.3760i | −0.0750284 | − | 0.844529i | ||||
\(377\) | − | 25.3036i | − | 1.30320i | ||||||
\(378\) | 4.13334 | + | 3.89612i | 0.212596 | + | 0.200395i | ||||
\(379\) | −11.6200 | − | 11.6200i | −0.596881 | − | 0.596881i | 0.342600 | − | 0.939481i | \(-0.388692\pi\) |
−0.939481 | + | 0.342600i | \(0.888692\pi\) | |||||||
\(380\) | 4.78769 | − | 0.283147i | 0.245603 | − | 0.0145252i | ||||
\(381\) | 10.5088 | − | 10.5088i | 0.538383 | − | 0.538383i | ||||
\(382\) | −0.972210 | − | 32.9066i | −0.0497426 | − | 1.68365i | ||||
\(383\) | −32.1857 | −1.64461 | −0.822307 | − | 0.569044i | \(-0.807313\pi\) | ||||
−0.822307 | + | 0.569044i | \(0.807313\pi\) | |||||||
\(384\) | 9.47188 | + | 6.18737i | 0.483360 | + | 0.315748i | ||||
\(385\) | 42.6008 | 2.17114 | ||||||||
\(386\) | 0.0431070 | + | 1.45905i | 0.00219409 | + | 0.0742637i | ||||
\(387\) | 0.432575 | − | 0.432575i | 0.0219890 | − | 0.0219890i | ||||
\(388\) | 11.0997 | − | 0.656444i | 0.563502 | − | 0.0333259i | ||||
\(389\) | 2.93023 | + | 2.93023i | 0.148569 | + | 0.148569i | 0.777478 | − | 0.628910i | \(-0.216499\pi\) |
−0.628910 | + | 0.777478i | \(0.716499\pi\) | |||||||
\(390\) | −11.5739 | − | 10.9096i | −0.586068 | − | 0.552431i | ||||
\(391\) | 11.5222i | 0.582702i | ||||||||
\(392\) | −2.28571 | − | 25.7282i | −0.115446 | − | 1.29947i | ||||
\(393\) | 9.56069i | 0.482273i | ||||||||
\(394\) | −0.296746 | + | 0.314814i | −0.0149499 | + | 0.0158601i | ||||
\(395\) | 9.50876 | + | 9.50876i | 0.478438 | + | 0.478438i | ||||
\(396\) | −5.87488 | + | 6.61345i | −0.295224 | + | 0.332339i | ||||
\(397\) | −22.9846 | + | 22.9846i | −1.15356 | + | 1.15356i | −0.167732 | + | 0.985833i | \(0.553644\pi\) |
−0.985833 | + | 0.167732i | \(0.946356\pi\) | |||||||
\(398\) | −6.72244 | + | 0.198612i | −0.336966 | + | 0.00995550i | ||||
\(399\) | 4.01648 | 0.201076 | ||||||||
\(400\) | 0.353856 | + | 2.98118i | 0.0176928 | + | 0.149059i | ||||
\(401\) | 24.6947 | 1.23319 | 0.616597 | − | 0.787279i | \(-0.288511\pi\) | ||||
0.616597 | + | 0.787279i | \(0.288511\pi\) | |||||||
\(402\) | 9.06622 | − | 0.267858i | 0.452182 | − | 0.0133595i | ||||
\(403\) | −10.8899 | + | 10.8899i | −0.542464 | + | 0.542464i | ||||
\(404\) | −25.4817 | − | 22.6360i | −1.26776 | − | 1.12618i | ||||
\(405\) | −1.69566 | − | 1.69566i | −0.0842580 | − | 0.0842580i | ||||
\(406\) | −21.0206 | + | 22.3005i | −1.04323 | + | 1.10675i | ||||
\(407\) | − | 15.1206i | − | 0.749500i | ||||||
\(408\) | 2.79011 | + | 2.33481i | 0.138131 | + | 0.115590i | ||||
\(409\) | − | 10.9815i | − | 0.543003i | −0.962438 | − | 0.271501i | \(-0.912480\pi\) | ||
0.962438 | − | 0.271501i | \(-0.0875201\pi\) | |||||||
\(410\) | −29.1500 | − | 27.4770i | −1.43961 | − | 1.35699i | ||||
\(411\) | 4.81600 | + | 4.81600i | 0.237556 | + | 0.237556i | ||||
\(412\) | −0.0902501 | − | 1.52602i | −0.00444631 | − | 0.0751817i | ||||
\(413\) | 24.3828 | − | 24.3828i | 1.19980 | − | 1.19980i | ||||
\(414\) | −0.374115 | − | 12.6627i | −0.0183867 | − | 0.622339i | ||||
\(415\) | 6.35796 | 0.312100 | ||||||||
\(416\) | −21.3161 | − | 15.7953i | −1.04511 | − | 0.774428i | ||||
\(417\) | 5.13914 | 0.251665 | ||||||||
\(418\) | 0.184723 | + | 6.25235i | 0.00903510 | + | 0.305813i | ||||
\(419\) | −10.6608 | + | 10.6608i | −0.520812 | + | 0.520812i | −0.917817 | − | 0.397004i | \(-0.870050\pi\) |
0.397004 | + | 0.917817i | \(0.370050\pi\) | |||||||
\(420\) | 1.13726 | + | 19.2297i | 0.0554924 | + | 0.938311i | ||||
\(421\) | −16.4338 | − | 16.4338i | −0.800936 | − | 0.800936i | 0.182306 | − | 0.983242i | \(-0.441644\pi\) |
−0.983242 | + | 0.182306i | \(0.941644\pi\) | |||||||
\(422\) | 6.46886 | + | 6.09759i | 0.314899 | + | 0.296826i | ||||
\(423\) | 5.81260i | 0.282618i | ||||||||
\(424\) | 21.4939 | − | 25.6853i | 1.04384 | − | 1.24739i | ||||
\(425\) | 0.965383i | 0.0468280i | ||||||||
\(426\) | −0.422633 | + | 0.448366i | −0.0204766 | + | 0.0217234i | ||||
\(427\) | −37.7372 | − | 37.7372i | −1.82623 | − | 1.82623i | ||||
\(428\) | 4.89485 | + | 4.34821i | 0.236602 | + | 0.210179i | ||||
\(429\) | 14.6681 | − | 14.6681i | 0.708182 | − | 0.708182i | ||||
\(430\) | 2.07375 | − | 0.0612680i | 0.100005 | − | 0.00295460i | ||||
\(431\) | −13.4823 | −0.649421 | −0.324711 | − | 0.945813i | \(-0.605267\pi\) | ||||
−0.324711 | + | 0.945813i | \(0.605267\pi\) | |||||||
\(432\) | −3.14210 | − | 2.47533i | −0.151174 | − | 0.119094i | ||||
\(433\) | −8.44894 | −0.406030 | −0.203015 | − | 0.979176i | \(-0.565074\pi\) | ||||
−0.203015 | + | 0.979176i | \(0.565074\pi\) | |||||||
\(434\) | 18.6440 | − | 0.550829i | 0.894941 | − | 0.0264407i | ||||
\(435\) | 9.14853 | − | 9.14853i | 0.438638 | − | 0.438638i | ||||
\(436\) | 20.3186 | − | 22.8729i | 0.973082 | − | 1.09541i | ||||
\(437\) | −6.33413 | − | 6.33413i | −0.303002 | − | 0.303002i | ||||
\(438\) | 6.33162 | − | 6.71714i | 0.302536 | − | 0.320957i | ||||
\(439\) | − | 16.1013i | − | 0.768472i | −0.923235 | − | 0.384236i | \(-0.874465\pi\) | ||
0.923235 | − | 0.384236i | \(-0.125535\pi\) | |||||||
\(440\) | −29.8820 | + | 2.65473i | −1.42457 | + | 0.126559i | ||||
\(441\) | 9.13213i | 0.434863i | ||||||||
\(442\) | −6.20811 | − | 5.85181i | −0.295290 | − | 0.278342i | ||||
\(443\) | 0.593689 | + | 0.593689i | 0.0282070 | + | 0.0282070i | 0.721070 | − | 0.692863i | \(-0.243651\pi\) |
−0.692863 | + | 0.721070i | \(0.743651\pi\) | |||||||
\(444\) | 6.82532 | − | 0.403655i | 0.323915 | − | 0.0191566i | ||||
\(445\) | −27.9941 | + | 27.9941i | −1.32705 | + | 1.32705i | ||||
\(446\) | −1.03782 | − | 35.1273i | −0.0491423 | − | 1.66333i | ||||
\(447\) | −1.82932 | −0.0865237 | ||||||||
\(448\) | 5.66452 | + | 31.6286i | 0.267623 | + | 1.49431i | ||||
\(449\) | −0.130798 | −0.00617274 | −0.00308637 | − | 0.999995i | \(-0.500982\pi\) | ||||
−0.00308637 | + | 0.999995i | \(0.500982\pi\) | |||||||
\(450\) | −0.0313451 | − | 1.06094i | −0.00147762 | − | 0.0500133i | ||||
\(451\) | 36.9429 | − | 36.9429i | 1.73958 | − | 1.73958i | ||||
\(452\) | 35.5151 | − | 2.10039i | 1.67049 | − | 0.0987939i | ||||
\(453\) | −6.20647 | − | 6.20647i | −0.291606 | − | 0.291606i | ||||
\(454\) | 12.2154 | + | 11.5143i | 0.573298 | + | 0.540395i | ||||
\(455\) | − | 45.1721i | − | 2.11770i | ||||||
\(456\) | −2.81733 | + | 0.250293i | −0.131934 | + | 0.0117211i | ||||
\(457\) | 26.9457i | 1.26047i | 0.776405 | + | 0.630234i | \(0.217041\pi\) | ||||
−0.776405 | + | 0.630234i | \(0.782959\pi\) | |||||||
\(458\) | 10.8054 | − | 11.4634i | 0.504905 | − | 0.535647i | ||||
\(459\) | −0.909533 | − | 0.909533i | −0.0424534 | − | 0.0424534i | ||||
\(460\) | 28.5323 | − | 32.1193i | 1.33033 | − | 1.49757i | ||||
\(461\) | −24.3607 | + | 24.3607i | −1.13459 | + | 1.13459i | −0.145186 | + | 0.989404i | \(0.546378\pi\) |
−0.989404 | + | 0.145186i | \(0.953622\pi\) | |||||||
\(462\) | −25.1125 | + | 0.741937i | −1.16834 | + | 0.0345180i | ||||
\(463\) | 0.882356 | 0.0410066 | 0.0205033 | − | 0.999790i | \(-0.493473\pi\) | ||||
0.0205033 | + | 0.999790i | \(0.493473\pi\) | |||||||
\(464\) | 13.3550 | − | 16.9524i | 0.619992 | − | 0.786996i | ||||
\(465\) | −7.87448 | −0.365170 | ||||||||
\(466\) | −1.28038 | + | 0.0378282i | −0.0593124 | + | 0.00175236i | ||||
\(467\) | 6.15276 | − | 6.15276i | 0.284716 | − | 0.284716i | −0.550271 | − | 0.834986i | \(-0.685475\pi\) |
0.834986 | + | 0.550271i | \(0.185475\pi\) | |||||||
\(468\) | 7.01263 | + | 6.22948i | 0.324159 | + | 0.287958i | ||||
\(469\) | 18.2151 | + | 18.2151i | 0.841095 | + | 0.841095i | ||||
\(470\) | −13.5210 | + | 14.3443i | −0.623680 | + | 0.661654i | ||||
\(471\) | 6.43322i | 0.296427i | ||||||||
\(472\) | −15.5837 | + | 18.6225i | −0.717296 | + | 0.857172i | ||||
\(473\) | 2.70579i | 0.124412i | ||||||||
\(474\) | −5.77086 | − | 5.43965i | −0.265064 | − | 0.249851i | ||||
\(475\) | −0.530703 | − | 0.530703i | −0.0243503 | − | 0.0243503i | ||||
\(476\) | 0.610011 | + | 10.3146i | 0.0279598 | + | 0.472768i | ||||
\(477\) | −8.37304 | + | 8.37304i | −0.383375 | + | 0.383375i | ||||
\(478\) | 0.635512 | + | 21.5103i | 0.0290676 | + | 0.983858i | ||||
\(479\) | 6.39674 | 0.292274 | 0.146137 | − | 0.989264i | \(-0.453316\pi\) | ||||
0.146137 | + | 0.989264i | \(0.453316\pi\) | |||||||
\(480\) | −1.99605 | − | 13.4176i | −0.0911066 | − | 0.612428i | ||||
\(481\) | −16.0333 | −0.731053 | ||||||||
\(482\) | −1.04425 | − | 35.3449i | −0.0475643 | − | 1.60992i | ||||
\(483\) | 25.4409 | − | 25.4409i | 1.15760 | − | 1.15760i | ||||
\(484\) | −1.01108 | − | 17.0962i | −0.0459582 | − | 0.777098i | ||||
\(485\) | −9.42710 | − | 9.42710i | −0.428062 | − | 0.428062i | ||||
\(486\) | 1.02910 | + | 0.970032i | 0.0466807 | + | 0.0440016i | ||||
\(487\) | − | 9.88627i | − | 0.447990i | −0.974590 | − | 0.223995i | \(-0.928090\pi\) | ||
0.974590 | − | 0.223995i | \(-0.0719099\pi\) | |||||||
\(488\) | 28.8222 | + | 24.1188i | 1.30472 | + | 1.09181i | ||||
\(489\) | 15.2020i | 0.687458i | ||||||||
\(490\) | −21.2428 | + | 22.5363i | −0.959653 | + | 1.01808i | ||||
\(491\) | −22.5224 | − | 22.5224i | −1.01642 | − | 1.01642i | −0.999863 | − | 0.0165575i | \(-0.994729\pi\) |
−0.0165575 | − | 0.999863i | \(-0.505271\pi\) | |||||||
\(492\) | 17.6620 | + | 15.6895i | 0.796263 | + | 0.707339i | ||||
\(493\) | 4.90717 | − | 4.90717i | 0.221008 | − | 0.221008i | ||||
\(494\) | 6.62973 | − | 0.195873i | 0.298286 | − | 0.00881272i | ||||
\(495\) | 10.6065 | 0.476726 | ||||||||
\(496\) | −13.0434 | + | 1.54821i | −0.585665 | + | 0.0695165i | ||||
\(497\) | −1.74994 | −0.0784956 | ||||||||
\(498\) | −3.74791 | + | 0.110730i | −0.167948 | + | 0.00496195i | ||||
\(499\) | 4.34873 | − | 4.34873i | 0.194676 | − | 0.194676i | −0.603037 | − | 0.797713i | \(-0.706043\pi\) |
0.797713 | + | 0.603037i | \(0.206043\pi\) | |||||||
\(500\) | −13.5354 | + | 15.2370i | −0.605320 | + | 0.681419i | ||||
\(501\) | 0.962130 | + | 0.962130i | 0.0429848 | + | 0.0429848i | ||||
\(502\) | −1.86909 | + | 1.98289i | −0.0834214 | + | 0.0885008i | ||||
\(503\) | 20.8300i | 0.928764i | 0.885635 | + | 0.464382i | \(0.153724\pi\) | ||||
−0.885635 | + | 0.464382i | \(0.846276\pi\) | |||||||
\(504\) | −1.00530 | − | 11.3158i | −0.0447795 | − | 0.504044i | ||||
\(505\) | 40.8670i | 1.81856i | ||||||||
\(506\) | 40.7733 | + | 38.4331i | 1.81259 | + | 1.70856i | ||||
\(507\) | −6.36103 | − | 6.36103i | −0.282503 | − | 0.282503i | ||||
\(508\) | −29.6716 | + | 1.75480i | −1.31646 | + | 0.0778566i | ||||
\(509\) | 27.4431 | − | 27.4431i | 1.21639 | − | 1.21639i | 0.247509 | − | 0.968885i | \(-0.420388\pi\) |
0.968885 | − | 0.247509i | \(-0.0796121\pi\) | |||||||
\(510\) | −0.128822 | − | 4.36026i | −0.00570434 | − | 0.193076i | ||||
\(511\) | 26.2165 | 1.15975 | ||||||||
\(512\) | −5.94432 | − | 21.8327i | −0.262704 | − | 0.964876i | ||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | −0.245181 | − | 8.29867i | −0.0108145 | − | 0.366039i | ||||
\(515\) | −1.29607 | + | 1.29607i | −0.0571116 | + | 0.0571116i | ||||
\(516\) | −1.22137 | + | 0.0722329i | −0.0537680 | + | 0.00317988i | ||||
\(517\) | −18.1791 | − | 18.1791i | −0.799518 | − | 0.799518i | ||||
\(518\) | 14.1303 | + | 13.3194i | 0.620852 | + | 0.585219i | ||||
\(519\) | 10.3892i | 0.456034i | ||||||||
\(520\) | 2.81497 | + | 31.6856i | 0.123444 | + | 1.38951i | ||||
\(521\) | − | 3.86912i | − | 0.169509i | −0.996402 | − | 0.0847545i | \(-0.972989\pi\) | ||
0.996402 | − | 0.0847545i | \(-0.0270106\pi\) | |||||||
\(522\) | −5.23358 | + | 5.55224i | −0.229067 | + | 0.243015i | ||||
\(523\) | −21.4819 | − | 21.4819i | −0.939339 | − | 0.939339i | 0.0589238 | − | 0.998262i | \(-0.481233\pi\) |
−0.998262 | + | 0.0589238i | \(0.981233\pi\) | |||||||
\(524\) | 12.6990 | − | 14.2955i | 0.554760 | − | 0.624502i | ||||
\(525\) | 2.13156 | − | 2.13156i | 0.0930288 | − | 0.0930288i | ||||
\(526\) | −1.87551 | + | 0.0554112i | −0.0817763 | + | 0.00241604i | ||||
\(527\) | −4.22378 | −0.183991 | ||||||||
\(528\) | 17.5687 | − | 2.08535i | 0.764580 | − | 0.0907531i | ||||
\(529\) | −57.2423 | −2.48880 | ||||||||
\(530\) | −40.1400 | + | 1.18592i | −1.74357 | + | 0.0515131i | ||||
\(531\) | 6.07068 | − | 6.07068i | 0.263445 | − | 0.263445i | ||||
\(532\) | −6.00560 | − | 5.33491i | −0.260376 | − | 0.231298i | ||||
\(533\) | −39.1728 | − | 39.1728i | −1.69676 | − | 1.69676i | ||||
\(534\) | 16.0145 | − | 16.9896i | 0.693015 | − | 0.735211i | ||||
\(535\) | − | 7.85024i | − | 0.339396i | ||||||
\(536\) | −13.9119 | − | 11.6417i | −0.600904 | − | 0.502847i | ||||
\(537\) | 9.50556i | 0.410195i | ||||||||
\(538\) | −29.4198 | − | 27.7313i | −1.26838 | − | 1.19558i | ||||
\(539\) | −28.5611 | − | 28.5611i | −1.23021 | − | 1.23021i | ||||
\(540\) | 0.283147 | + | 4.78769i | 0.0121847 | + | 0.206029i | ||||
\(541\) | −11.1589 | + | 11.1589i | −0.479758 | + | 0.479758i | −0.905054 | − | 0.425296i | \(-0.860170\pi\) |
0.425296 | + | 0.905054i | \(0.360170\pi\) | |||||||
\(542\) | 0.535185 | + | 18.1145i | 0.0229882 | + | 0.778085i | ||||
\(543\) | 7.62683 | 0.327299 | ||||||||
\(544\) | −1.07066 | − | 7.19706i | −0.0459040 | − | 0.308572i | ||||
\(545\) | −36.6830 | −1.57133 | ||||||||
\(546\) | 0.786719 | + | 26.6282i | 0.0336685 | + | 1.13958i | ||||
\(547\) | 19.5951 | − | 19.5951i | 0.837828 | − | 0.837828i | −0.150745 | − | 0.988573i | \(-0.548167\pi\) |
0.988573 | + | 0.150745i | \(0.0481672\pi\) | |||||||
\(548\) | −0.804192 | − | 13.5979i | −0.0343534 | − | 0.580875i | ||||
\(549\) | −9.39559 | − | 9.39559i | −0.400994 | − | 0.400994i | ||||
\(550\) | 3.41617 | + | 3.22011i | 0.145666 | + | 0.137306i | ||||
\(551\) | 5.39526i | 0.229846i | ||||||||
\(552\) | −16.2599 | + | 19.4307i | −0.692069 | + | 0.827026i | ||||
\(553\) | − | 22.5232i | − | 0.957786i | ||||||
\(554\) | −28.3683 | + | 30.0956i | −1.20525 | + | 1.27864i | ||||
\(555\) | −5.79682 | − | 5.79682i | −0.246061 | − | 0.246061i | ||||
\(556\) | −7.68425 | − | 6.82609i | −0.325885 | − | 0.289491i | ||||
\(557\) | 16.7111 | − | 16.7111i | 0.708072 | − | 0.708072i | −0.258058 | − | 0.966130i | \(-0.583082\pi\) |
0.966130 | + | 0.258058i | \(0.0830824\pi\) | |||||||
\(558\) | 4.64188 | − | 0.137142i | 0.196506 | − | 0.00580569i | ||||
\(559\) | 2.86911 | 0.121350 | ||||||||
\(560\) | 23.8414 | − | 30.2635i | 1.00748 | − | 1.27887i | ||||
\(561\) | 5.68920 | 0.240198 | ||||||||
\(562\) | 22.4186 | − | 0.662349i | 0.945673 | − | 0.0279395i | ||||
\(563\) | −3.31748 | + | 3.31748i | −0.139815 | + | 0.139815i | −0.773550 | − | 0.633735i | \(-0.781521\pi\) |
0.633735 | + | 0.773550i | \(0.281521\pi\) | |||||||
\(564\) | 7.72062 | − | 8.69122i | 0.325097 | − | 0.365967i | ||||
\(565\) | −30.1633 | − | 30.1633i | −1.26898 | − | 1.26898i | ||||
\(566\) | −26.2861 | + | 27.8866i | −1.10489 | + | 1.17216i | ||||
\(567\) | 4.01648i | 0.168676i | ||||||||
\(568\) | 1.22748 | − | 0.109050i | 0.0515040 | − | 0.00457565i | ||||
\(569\) | − | 13.1634i | − | 0.551838i | −0.961181 | − | 0.275919i | \(-0.911018\pi\) | ||
0.961181 | − | 0.275919i | \(-0.0889821\pi\) | |||||||
\(570\) | 2.46780 | + | 2.32616i | 0.103365 | + | 0.0974322i | ||||
\(571\) | −3.02144 | − | 3.02144i | −0.126443 | − | 0.126443i | 0.641053 | − | 0.767497i | \(-0.278498\pi\) |
−0.767497 | + | 0.641053i | \(0.778498\pi\) | |||||||
\(572\) | −41.4152 | + | 2.44933i | −1.73166 | + | 0.102412i | ||||
\(573\) | 16.4605 | − | 16.4605i | 0.687646 | − | 0.687646i | ||||
\(574\) | 1.98143 | + | 67.0656i | 0.0827031 | + | 2.79927i | ||||
\(575\) | −6.72308 | −0.280372 | ||||||||
\(576\) | 1.41032 | + | 7.87471i | 0.0587632 | + | 0.328113i | ||||
\(577\) | 19.6283 | 0.817138 | 0.408569 | − | 0.912727i | \(-0.366028\pi\) | ||||
0.408569 | + | 0.912727i | \(0.366028\pi\) | |||||||
\(578\) | 0.640891 | + | 21.6923i | 0.0266576 | + | 0.902283i | ||||
\(579\) | −0.729844 | + | 0.729844i | −0.0303313 | + | 0.0303313i | ||||
\(580\) | −25.8308 | + | 1.52765i | −1.07257 | + | 0.0634324i | ||||
\(581\) | −7.52999 | − | 7.52999i | −0.312397 | − | 0.312397i | ||||
\(582\) | 5.72130 | + | 5.39294i | 0.237156 | + | 0.223544i | ||||
\(583\) | − | 52.3740i | − | 2.16911i | ||||||
\(584\) | −18.3893 | + | 1.63372i | −0.760957 | + | 0.0676038i | ||||
\(585\) | − | 11.2467i | − | 0.464993i | ||||||
\(586\) | −16.2886 | + | 17.2804i | −0.672877 | + | 0.713847i | ||||
\(587\) | 6.02246 | + | 6.02246i | 0.248573 | + | 0.248573i | 0.820385 | − | 0.571812i | \(-0.193759\pi\) |
−0.571812 | + | 0.820385i | \(0.693759\pi\) | |||||||
\(588\) | 12.1298 | − | 13.6547i | 0.500224 | − | 0.563111i | ||||
\(589\) | 2.32195 | − | 2.32195i | 0.0956743 | − | 0.0956743i | ||||
\(590\) | 29.1026 | − | 0.859823i | 1.19813 | − | 0.0353983i | ||||
\(591\) | −0.305914 | −0.0125836 | ||||||||
\(592\) | −10.7416 | − | 8.46220i | −0.441479 | − | 0.347794i | ||||
\(593\) | 16.3953 | 0.673276 | 0.336638 | − | 0.941634i | \(-0.390710\pi\) | ||||
0.336638 | + | 0.941634i | \(0.390710\pi\) | |||||||
\(594\) | −6.25235 | + | 0.184723i | −0.256537 | + | 0.00757928i | ||||
\(595\) | 8.76028 | − | 8.76028i | 0.359137 | − | 0.359137i | ||||
\(596\) | 2.73526 | + | 2.42980i | 0.112041 | + | 0.0995284i | ||||
\(597\) | −3.36269 | − | 3.36269i | −0.137626 | − | 0.137626i | ||||
\(598\) | 40.7529 | − | 43.2343i | 1.66651 | − | 1.76798i | ||||
\(599\) | 42.0979i | 1.72007i | 0.510233 | + | 0.860036i | \(0.329559\pi\) | ||||
−0.510233 | + | 0.860036i | \(0.670441\pi\) | |||||||
\(600\) | −1.36233 | + | 1.62800i | −0.0556171 | + | 0.0664627i | ||||
\(601\) | − | 9.90486i | − | 0.404028i | −0.979383 | − | 0.202014i | \(-0.935251\pi\) | ||
0.979383 | − | 0.202014i | \(-0.0647486\pi\) | |||||||
\(602\) | −2.52859 | − | 2.38346i | −0.103058 | − | 0.0971427i | ||||
\(603\) | 4.53509 | + | 4.53509i | 0.184683 | + | 0.184683i | ||||
\(604\) | 1.03638 | + | 17.5239i | 0.0421697 | + | 0.713039i | ||||
\(605\) | −14.5200 | + | 14.5200i | −0.590320 | + | 0.590320i | ||||
\(606\) | −0.711740 | − | 24.0904i | −0.0289125 | − | 0.978606i | ||||
\(607\) | −31.9170 | −1.29547 | −0.647736 | − | 0.761865i | \(-0.724284\pi\) | ||||
−0.647736 | + | 0.761865i | \(0.724284\pi\) | |||||||
\(608\) | 4.54504 | + | 3.36789i | 0.184326 | + | 0.136586i | ||||
\(609\) | −21.6700 | −0.878111 | ||||||||
\(610\) | −1.33075 | − | 45.0421i | −0.0538805 | − | 1.82370i | ||||
\(611\) | −19.2764 | + | 19.2764i | −0.779840 | + | 0.779840i | ||||
\(612\) | 0.151877 | + | 2.56806i | 0.00613927 | + | 0.103808i | ||||
\(613\) | 7.28805 | + | 7.28805i | 0.294362 | + | 0.294362i | 0.838801 | − | 0.544439i | \(-0.183257\pi\) |
−0.544439 | + | 0.838801i | \(0.683257\pi\) | |||||||
\(614\) | 27.0884 | + | 25.5337i | 1.09320 | + | 1.03045i | ||||
\(615\) | − | 28.3258i | − | 1.14221i | ||||||
\(616\) | 38.5346 | + | 32.2464i | 1.55260 | + | 1.29924i | ||||
\(617\) | 24.2635i | 0.976811i | 0.872617 | + | 0.488406i | \(0.162421\pi\) | ||||
−0.872617 | + | 0.488406i | \(0.837579\pi\) | |||||||
\(618\) | 0.741439 | − | 0.786584i | 0.0298250 | − | 0.0316410i | ||||
\(619\) | −23.3844 | − | 23.3844i | −0.939898 | − | 0.939898i | 0.0583957 | − | 0.998294i | \(-0.481401\pi\) |
−0.998294 | + | 0.0583957i | \(0.981401\pi\) | |||||||
\(620\) | 11.7742 | + | 10.4593i | 0.472864 | + | 0.420056i | ||||
\(621\) | 6.33413 | − | 6.33413i | 0.254180 | − | 0.254180i | ||||
\(622\) | 18.5611 | − | 0.548379i | 0.744232 | − | 0.0219880i | ||||
\(623\) | 66.3091 | 2.65662 | ||||||||
\(624\) | −2.21122 | − | 18.6291i | −0.0885194 | − | 0.745762i | ||||
\(625\) | 28.1893 | 1.12757 | ||||||||
\(626\) | 39.1802 | − | 1.15756i | 1.56596 | − | 0.0462655i | ||||
\(627\) | −3.12754 | + | 3.12754i | −0.124902 | + | 0.124902i | ||||
\(628\) | 8.54496 | − | 9.61921i | 0.340981 | − | 0.383848i | ||||
\(629\) | −3.10935 | − | 3.10935i | −0.123978 | − | 0.123978i | ||||
\(630\) | −9.34299 | + | 9.91187i | −0.372234 | + | 0.394898i | ||||
\(631\) | 18.7187i | 0.745179i | 0.927996 | + | 0.372589i | \(0.121530\pi\) | ||||
−0.927996 | + | 0.372589i | \(0.878470\pi\) | |||||||
\(632\) | 1.40357 | + | 15.7988i | 0.0558310 | + | 0.628441i | ||||
\(633\) | 6.28597i | 0.249845i | ||||||||
\(634\) | −25.0292 | − | 23.5927i | −0.994036 | − | 0.936985i | ||||
\(635\) | 25.2004 | + | 25.2004i | 1.00005 | + | 1.00005i | ||||
\(636\) | 23.6412 | − | 1.39816i | 0.937436 | − | 0.0554407i | ||||
\(637\) | −30.2850 | + | 30.2850i | −1.19994 | + | 1.19994i | ||||
\(638\) | −0.996629 | − | 33.7331i | −0.0394569 | − | 1.33550i | ||||
\(639\) | −0.435690 | −0.0172356 | ||||||||
\(640\) | −14.8375 | + | 22.7138i | −0.586502 | + | 0.897842i | ||||
\(641\) | 25.7211 | 1.01592 | 0.507961 | − | 0.861380i | \(-0.330399\pi\) | ||||
0.507961 | + | 0.861380i | \(0.330399\pi\) | |||||||
\(642\) | 0.136720 | + | 4.62759i | 0.00539591 | + | 0.182636i | ||||
\(643\) | 0.280088 | − | 0.280088i | 0.0110456 | − | 0.0110456i | −0.701562 | − | 0.712608i | \(-0.747514\pi\) |
0.712608 | + | 0.701562i | \(0.247514\pi\) | |||||||
\(644\) | −71.8323 | + | 4.24821i | −2.83059 | + | 0.167403i | ||||
\(645\) | 1.03733 | + | 1.03733i | 0.0408447 | + | 0.0408447i | ||||
\(646\) | 1.32370 | + | 1.24773i | 0.0520802 | + | 0.0490912i | ||||
\(647\) | 15.8259i | 0.622182i | 0.950380 | + | 0.311091i | \(0.100694\pi\) | ||||
−0.950380 | + | 0.311091i | \(0.899306\pi\) | |||||||
\(648\) | −0.250293 | − | 2.81733i | −0.00983245 | − | 0.110675i | ||||
\(649\) | 37.9726i | 1.49055i | ||||||||
\(650\) | 3.41447 | − | 3.62237i | 0.133926 | − | 0.142081i | ||||
\(651\) | 9.32607 | + | 9.32607i | 0.365518 | + | 0.365518i | ||||
\(652\) | 20.1921 | − | 22.7306i | 0.790784 | − | 0.890199i | ||||
\(653\) | −33.1534 | + | 33.1534i | −1.29739 | + | 1.29739i | −0.367282 | + | 0.930109i | \(0.619712\pi\) |
−0.930109 | + | 0.367282i | \(0.880288\pi\) | |||||||
\(654\) | 21.6240 | − | 0.638873i | 0.845567 | − | 0.0249819i | ||||
\(655\) | −22.9268 | −0.895824 | ||||||||
\(656\) | −5.56915 | − | 46.9192i | −0.217439 | − | 1.83189i | ||||
\(657\) | 6.52722 | 0.254651 | ||||||||
\(658\) | 33.0021 | − | 0.975033i | 1.28656 | − | 0.0380108i | ||||
\(659\) | 11.0625 | − | 11.0625i | 0.430935 | − | 0.430935i | −0.458011 | − | 0.888946i | \(-0.651438\pi\) |
0.888946 | + | 0.458011i | \(0.151438\pi\) | |||||||
\(660\) | −15.8592 | − | 14.0881i | −0.617320 | − | 0.548379i | ||||
\(661\) | 25.4579 | + | 25.4579i | 0.990197 | + | 0.990197i | 0.999952 | − | 0.00975499i | \(-0.00310516\pi\) |
−0.00975499 | + | 0.999952i | \(0.503105\pi\) | |||||||
\(662\) | 21.7299 | − | 23.0530i | 0.844557 | − | 0.895980i | ||||
\(663\) | − | 6.03259i | − | 0.234286i | ||||||
\(664\) | 5.75110 | + | 4.81261i | 0.223186 | + | 0.186766i | ||||
\(665\) | 9.63163i | 0.373499i | ||||||||
\(666\) | 3.51809 | + | 3.31617i | 0.136323 | + | 0.128499i | ||||
\(667\) | 34.1743 | + | 34.1743i | 1.32323 | + | 1.32323i | ||||
\(668\) | −0.160660 | − | 2.71657i | −0.00621612 | − | 0.105107i | ||||
\(669\) | 17.5713 | − | 17.5713i | 0.679347 | − | 0.679347i | ||||
\(670\) | 0.642329 | + | 21.7410i | 0.0248153 | + | 0.839929i | ||||
\(671\) | 58.7702 | 2.26880 | ||||||||
\(672\) | −13.5271 | + | 18.2551i | −0.521817 | + | 0.704204i | ||||
\(673\) | 38.3367 | 1.47777 | 0.738885 | − | 0.673831i | \(-0.235352\pi\) | ||||
0.738885 | + | 0.673831i | \(0.235352\pi\) | |||||||
\(674\) | 0.332368 | + | 11.2497i | 0.0128023 | + | 0.433322i | ||||
\(675\) | 0.530703 | − | 0.530703i | 0.0204268 | − | 0.0204268i | ||||
\(676\) | 1.06219 | + | 17.9603i | 0.0408534 | + | 0.690782i | ||||
\(677\) | 5.32310 | + | 5.32310i | 0.204583 | + | 0.204583i | 0.801960 | − | 0.597377i | \(-0.203790\pi\) |
−0.597377 | + | 0.801960i | \(0.703790\pi\) | |||||||
\(678\) | 18.3061 | + | 17.2555i | 0.703042 | + | 0.662692i | ||||
\(679\) | 22.3298i | 0.856939i | ||||||||
\(680\) | −5.59892 | + | 6.69074i | −0.214709 | + | 0.256578i | ||||
\(681\) | 11.8701i | 0.454862i | ||||||||
\(682\) | −14.0887 | + | 14.9466i | −0.539486 | + | 0.572334i | ||||
\(683\) | 19.6537 | + | 19.6537i | 0.752027 | + | 0.752027i | 0.974857 | − | 0.222830i | \(-0.0715295\pi\) |
−0.222830 | + | 0.974857i | \(0.571529\pi\) | |||||||
\(684\) | −1.49524 | − | 1.32826i | −0.0571719 | − | 0.0507871i | ||||
\(685\) | −11.5489 | + | 11.5489i | −0.441260 | + | 0.441260i | ||||
\(686\) | 12.1056 | − | 0.357654i | 0.462193 | − | 0.0136553i | ||||
\(687\) | 11.1393 | 0.424989 | ||||||||
\(688\) | 1.92219 | + | 1.51429i | 0.0732827 | + | 0.0577318i | ||||
\(689\) | −55.5353 | −2.11572 | ||||||||
\(690\) | 30.3655 | − | 0.897137i | 1.15600 | − | 0.0341534i | ||||
\(691\) | −10.8763 | + | 10.8763i | −0.413756 | + | 0.413756i | −0.883045 | − | 0.469289i | \(-0.844510\pi\) |
0.469289 | + | 0.883045i | \(0.344510\pi\) | |||||||
\(692\) | 13.7995 | − | 15.5343i | 0.524578 | − | 0.590526i | ||||
\(693\) | −12.5617 | − | 12.5617i | −0.477180 | − | 0.477180i | ||||
\(694\) | 14.8182 | − | 15.7204i | 0.562491 | − | 0.596740i | ||||
\(695\) | 12.3238i | 0.467468i | ||||||||
\(696\) | 15.2002 | − | 1.35040i | 0.576163 | − | 0.0511867i | ||||
\(697\) | − | 15.1936i | − | 0.575500i | ||||||
\(698\) | −1.80129 | − | 1.69791i | −0.0681799 | − | 0.0642669i | ||||
\(699\) | −0.640469 | − | 0.640469i | −0.0242248 | − | 0.0242248i | ||||
\(700\) | −6.01844 | + | 0.355935i | −0.227476 | + | 0.0134531i | ||||
\(701\) | 8.26463 | − | 8.26463i | 0.312151 | − | 0.312151i | −0.533592 | − | 0.845742i | \(-0.679158\pi\) |
0.845742 | + | 0.533592i | \(0.179158\pi\) | |||||||
\(702\) | 0.195873 | + | 6.62973i | 0.00739273 | + | 0.250223i | ||||
\(703\) | 3.41862 | 0.128936 | ||||||||
\(704\) | −29.0393 | − | 20.2176i | −1.09446 | − | 0.761981i | ||||
\(705\) | −13.9388 | −0.524964 | ||||||||
\(706\) | 0.934782 | + | 31.6397i | 0.0351810 | + | 1.19078i | ||||
\(707\) | 48.4004 | − | 48.4004i | 1.82029 | − | 1.82029i | ||||
\(708\) | −17.1405 | + | 1.01370i | −0.644180 | + | 0.0380973i | ||||
\(709\) | 16.3112 | + | 16.3112i | 0.612578 | + | 0.612578i | 0.943617 | − | 0.331039i | \(-0.107399\pi\) |
−0.331039 | + | 0.943617i | \(0.607399\pi\) | |||||||
\(710\) | −1.07519 | − | 1.01349i | −0.0403513 | − | 0.0380354i | ||||
\(711\) | − | 5.60770i | − | 0.210305i | ||||||
\(712\) | −46.5120 | + | 4.13215i | −1.74311 | + | 0.154859i | ||||
\(713\) | − | 29.4151i | − | 1.10160i | ||||||
\(714\) | −5.01147 | + | 5.31661i | −0.187550 | + | 0.198969i | ||||
\(715\) | 35.1744 | + | 35.1744i | 1.31545 | + | 1.31545i | ||||
\(716\) | 12.6258 | − | 14.2131i | 0.471849 | − | 0.531168i | ||||
\(717\) | −10.7598 | + | 10.7598i | −0.401833 | + | 0.401833i | ||||
\(718\) | −19.7177 | + | 0.582552i | −0.735859 | + | 0.0217406i | ||||
\(719\) | 0.245598 | 0.00915926 | 0.00457963 | − | 0.999990i | \(-0.498542\pi\) | ||||
0.00457963 | + | 0.999990i | \(0.498542\pi\) | |||||||
\(720\) | 5.93590 | − | 7.53482i | 0.221218 | − | 0.280806i | ||||
\(721\) | 3.06998 | 0.114332 | ||||||||
\(722\) | −1.41360 | + | 0.0417641i | −0.0526086 | + | 0.00155430i | ||||
\(723\) | 17.6802 | − | 17.6802i | 0.657532 | − | 0.657532i | ||||
\(724\) | −11.4039 | − | 10.1304i | −0.423824 | − | 0.376492i | ||||
\(725\) | 2.86328 | + | 2.86328i | 0.106340 | + | 0.106340i | ||||
\(726\) | 8.30640 | − | 8.81216i | 0.308279 | − | 0.327050i | ||||
\(727\) | 38.3023i | 1.42055i | 0.703922 | + | 0.710277i | \(0.251431\pi\) | ||||
−0.703922 | + | 0.710277i | \(0.748569\pi\) | |||||||
\(728\) | 34.1927 | − | 40.8605i | 1.26727 | − | 1.51439i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 16.1079 | + | 15.1834i | 0.596179 | + | 0.561962i | ||||
\(731\) | 0.556410 | + | 0.556410i | 0.0205796 | + | 0.0205796i | ||||
\(732\) | 1.56891 | + | 26.5284i | 0.0579886 | + | 0.980518i | ||||
\(733\) | 0.600974 | − | 0.600974i | 0.0221975 | − | 0.0221975i | −0.695921 | − | 0.718118i | \(-0.745004\pi\) |
0.718118 | + | 0.695921i | \(0.245004\pi\) | |||||||
\(734\) | −0.188716 | − | 6.38750i | −0.00696564 | − | 0.235767i | ||||
\(735\) | −21.8991 | −0.807760 | ||||||||
\(736\) | 50.1214 | − | 7.45621i | 1.84750 | − | 0.274840i | ||||
\(737\) | −28.3673 | −1.04492 | ||||||||
\(738\) | 0.493323 | + | 16.6976i | 0.0181595 | + | 0.614647i | ||||
\(739\) | 12.1952 | − | 12.1952i | 0.448608 | − | 0.448608i | −0.446284 | − | 0.894892i | \(-0.647253\pi\) |
0.894892 | + | 0.446284i | \(0.147253\pi\) | |||||||
\(740\) | 0.967974 | + | 16.3673i | 0.0355834 | + | 0.601674i | ||||
\(741\) | 3.31631 | + | 3.31631i | 0.121828 | + | 0.121828i | ||||
\(742\) | 48.9440 | + | 46.1350i | 1.79679 | + | 1.69367i | ||||
\(743\) | 4.20499i | 0.154266i | 0.997021 | + | 0.0771330i | \(0.0245766\pi\) | ||||
−0.997021 | + | 0.0771330i | \(0.975423\pi\) | |||||||
\(744\) | −7.12287 | − | 5.96054i | −0.261137 | − | 0.218524i | ||||
\(745\) | − | 4.38675i | − | 0.160718i | ||||||
\(746\) | 5.90153 | − | 6.26086i | 0.216070 | − | 0.229226i | ||||
\(747\) | −1.87477 | − | 1.87477i | −0.0685944 | − | 0.0685944i | ||||
\(748\) | −8.50671 | − | 7.55671i | −0.311036 | − | 0.276301i | ||||
\(749\) | −9.29737 | + | 9.29737i | −0.339719 | + | 0.339719i | ||||
\(750\) | −14.4050 | + | 0.425591i | −0.525998 | + | 0.0155404i | ||||
\(751\) | 30.0536 | 1.09667 | 0.548336 | − | 0.836258i | \(-0.315262\pi\) | ||||
0.548336 | + | 0.836258i | \(0.315262\pi\) | |||||||
\(752\) | −23.0883 | + | 2.74051i | −0.841945 | + | 0.0999360i | ||||
\(753\) | −1.92683 | −0.0702176 | ||||||||
\(754\) | −35.7691 | + | 1.05678i | −1.30263 | + | 0.0384858i | ||||
\(755\) | 14.8833 | − | 14.8833i | 0.541658 | − | 0.541658i | ||||
\(756\) | 5.33491 | − | 6.00560i | 0.194029 | − | 0.218422i | ||||
\(757\) | 8.70096 | + | 8.70096i | 0.316242 | + | 0.316242i | 0.847322 | − | 0.531080i | \(-0.178214\pi\) |
−0.531080 | + | 0.847322i | \(0.678214\pi\) | |||||||
\(758\) | −15.9407 | + | 16.9113i | −0.578994 | + | 0.614248i | ||||
\(759\) | 39.6205i | 1.43813i | ||||||||
\(760\) | −0.600210 | − | 6.75603i | −0.0217719 | − | 0.245067i | ||||
\(761\) | − | 37.3646i | − | 1.35447i | −0.735768 | − | 0.677233i | \(-0.763179\pi\) | ||
0.735768 | − | 0.677233i | \(-0.236821\pi\) | |||||||
\(762\) | −15.2941 | − | 14.4163i | −0.554047 | − | 0.522248i | ||||
\(763\) | 43.4452 | + | 43.4452i | 1.57282 | + | 1.57282i | ||||
\(764\) | −46.4760 | + | 2.74863i | −1.68144 | + | 0.0994418i | ||||
\(765\) | 2.18108 | − | 2.18108i | 0.0788572 | − | 0.0788572i | ||||
\(766\) | 1.34421 | + | 45.4977i | 0.0485682 | + | 1.64390i | ||||
\(767\) | 40.2645 | 1.45387 | ||||||||
\(768\) | 8.35086 | − | 13.6478i | 0.301336 | − | 0.492474i | ||||
\(769\) | 20.1253 | 0.725738 | 0.362869 | − | 0.931840i | \(-0.381797\pi\) | ||||
0.362869 | + | 0.931840i | \(0.381797\pi\) | |||||||
\(770\) | −1.77918 | − | 60.2203i | −0.0641173 | − | 2.17019i | ||||
\(771\) | 4.15114 | − | 4.15114i | 0.149500 | − | 0.149500i | ||||
\(772\) | 2.06071 | − | 0.121872i | 0.0741665 | − | 0.00438627i | ||||
\(773\) | 5.22606 | + | 5.22606i | 0.187968 | + | 0.187968i | 0.794817 | − | 0.606849i | \(-0.207567\pi\) |
−0.606849 | + | 0.794817i | \(0.707567\pi\) | |||||||
\(774\) | −0.629553 | − | 0.593421i | −0.0226288 | − | 0.0213301i | ||||
\(775\) | − | 2.46453i | − | 0.0885286i | ||||||
\(776\) | −1.39152 | − | 15.6631i | −0.0499525 | − | 0.562272i | ||||
\(777\) | 13.7308i | 0.492591i | ||||||||
\(778\) | 4.01979 | − | 4.26454i | 0.144116 | − | 0.152891i | ||||
\(779\) | 8.35245 | + | 8.35245i | 0.299257 | + | 0.299257i | ||||
\(780\) | −14.9385 | + | 16.8165i | −0.534883 | + | 0.602126i | ||||
\(781\) | 1.36264 | − | 1.36264i | 0.0487590 | − | 0.0487590i | ||||
\(782\) | 16.2877 | − | 0.481214i | 0.582448 | − | 0.0172082i | ||||
\(783\) | −5.39526 | −0.192811 | ||||||||
\(784\) | −36.2739 | + | 4.30559i | −1.29550 | + | 0.153771i | ||||
\(785\) | −15.4270 | −0.550615 | ||||||||
\(786\) | 13.5150 | − | 0.399294i | 0.482063 | − | 0.0142423i | ||||
\(787\) | 20.5710 | − | 20.5710i | 0.733275 | − | 0.733275i | −0.237992 | − | 0.971267i | \(-0.576489\pi\) |
0.971267 | + | 0.237992i | \(0.0764891\pi\) | |||||||
\(788\) | 0.457414 | + | 0.406331i | 0.0162947 | + | 0.0144750i | ||||
\(789\) | −0.938166 | − | 0.938166i | −0.0333996 | − | 0.0333996i | ||||
\(790\) | 13.0444 | − | 13.8387i | 0.464100 | − | 0.492358i | ||||
\(791\) | 71.4474i | 2.54038i | ||||||||
\(792\) | 9.59412 | + | 8.02851i | 0.340912 | + | 0.285281i | ||||
\(793\) | − | 62.3175i | − | 2.21296i | ||||||
\(794\) | 33.4509 | + | 31.5310i | 1.18713 | + | 1.11899i | ||||
\(795\) | −20.0788 | − | 20.0788i | −0.712121 | − | 0.712121i | ||||
\(796\) | 0.561514 | + | 9.49453i | 0.0199023 | + | 0.336525i | ||||
\(797\) | −13.2341 | + | 13.2341i | −0.468774 | + | 0.468774i | −0.901517 | − | 0.432743i | \(-0.857546\pi\) |
0.432743 | + | 0.901517i | \(0.357546\pi\) | |||||||
\(798\) | −0.167745 | − | 5.67769i | −0.00593810 | − | 0.200988i | ||||
\(799\) | −7.47660 | −0.264503 | ||||||||
\(800\) | 4.19941 | − | 0.624716i | 0.148472 | − | 0.0220871i | ||||
\(801\) | 16.5092 | 0.583325 | ||||||||
\(802\) | −1.03135 | − | 34.9084i | −0.0364183 | − | 1.23266i | ||||
\(803\) | −20.4142 | + | 20.4142i | −0.720400 | + | 0.720400i | ||||
\(804\) | −0.757285 | − | 12.8048i | −0.0267074 | − | 0.451590i | ||||
\(805\) | 61.0080 | + | 61.0080i | 2.15025 | + | 2.15025i | ||||
\(806\) | 15.8487 | + | 14.9391i | 0.558247 | + | 0.526208i | ||||
\(807\) | − | 28.5880i | − | 1.00635i | ||||||
\(808\) | −30.9340 | + | 36.9663i | −1.08825 | + | 1.30047i | ||||
\(809\) | 52.0893i | 1.83136i | 0.401906 | + | 0.915681i | \(0.368348\pi\) | ||||
−0.401906 | + | 0.915681i | \(0.631652\pi\) | |||||||
\(810\) | −2.32616 | + | 2.46780i | −0.0817330 | + | 0.0867096i | ||||
\(811\) | −26.8313 | − | 26.8313i | −0.942173 | − | 0.942173i | 0.0562438 | − | 0.998417i | \(-0.482088\pi\) |
−0.998417 | + | 0.0562438i | \(0.982088\pi\) | |||||||
\(812\) | 32.4018 | + | 28.7832i | 1.13708 | + | 1.01009i | ||||
\(813\) | −9.06121 | + | 9.06121i | −0.317790 | + | 0.317790i | ||||
\(814\) | −21.3744 | + | 0.631498i | −0.749173 | + | 0.0221340i | ||||
\(815\) | −36.4548 | −1.27695 | ||||||||
\(816\) | 3.18395 | − | 4.04159i | 0.111460 | − | 0.141484i | ||||
\(817\) | −0.611754 | −0.0214026 | ||||||||
\(818\) | −15.5235 | + | 0.458634i | −0.542766 | + | 0.0160358i | ||||
\(819\) | −13.3199 | + | 13.3199i | −0.465435 | + | 0.465435i | ||||
\(820\) | −37.6239 | + | 42.3539i | −1.31388 | + | 1.47906i | ||||
\(821\) | −23.7140 | − | 23.7140i | −0.827626 | − | 0.827626i | 0.159562 | − | 0.987188i | \(-0.448992\pi\) |
−0.987188 | + | 0.159562i | \(0.948992\pi\) | |||||||
\(822\) | 6.60674 | − | 7.00901i | 0.230437 | − | 0.244467i | ||||
\(823\) | − | 41.1179i | − | 1.43328i | −0.697444 | − | 0.716640i | \(-0.745679\pi\) | ||
0.697444 | − | 0.716640i | \(-0.254321\pi\) | |||||||
\(824\) | −2.15341 | + | 0.191310i | −0.0750176 | + | 0.00666461i | ||||
\(825\) | 3.31959i | 0.115573i | ||||||||
\(826\) | −35.4857 | − | 33.4491i | −1.23471 | − | 1.16384i | ||||
\(827\) | 11.7188 | + | 11.7188i | 0.407502 | + | 0.407502i | 0.880867 | − | 0.473364i | \(-0.156961\pi\) |
−0.473364 | + | 0.880867i | \(0.656961\pi\) | |||||||
\(828\) | −17.8844 | + | 1.05770i | −0.621525 | + | 0.0367574i | ||||
\(829\) | −2.46585 | + | 2.46585i | −0.0856426 | + | 0.0856426i | −0.748630 | − | 0.662988i | \(-0.769288\pi\) |
0.662988 | + | 0.748630i | \(0.269288\pi\) | |||||||
\(830\) | −0.265534 | − | 8.98759i | −0.00921683 | − | 0.311964i | ||||
\(831\) | −29.2447 | −1.01449 | ||||||||
\(832\) | −21.4379 | + | 30.7920i | −0.743227 | + | 1.06752i | ||||
\(833\) | −11.7464 | −0.406989 | ||||||||
\(834\) | −0.214632 | − | 7.26468i | −0.00743209 | − | 0.251555i | ||||
\(835\) | −2.30721 | + | 2.30721i | −0.0798444 | + | 0.0798444i | ||||
\(836\) | 8.83059 | − | 0.522248i | 0.305412 | − | 0.0180623i | ||||
\(837\) | 2.32195 | + | 2.32195i | 0.0802584 | + | 0.0802584i | ||||
\(838\) | 15.5153 | + | 14.6248i | 0.535966 | + | 0.505205i | ||||
\(839\) | − | 44.0220i | − | 1.51981i | −0.650035 | − | 0.759904i | \(-0.725246\pi\) | ||
0.650035 | − | 0.759904i | \(-0.274754\pi\) | |||||||
\(840\) | 27.1355 | − | 2.41073i | 0.936263 | − | 0.0831781i | ||||
\(841\) | − | 0.108832i | − | 0.00375284i | ||||||
\(842\) | −22.5445 | + | 23.9172i | −0.776934 | + | 0.824240i | ||||
\(843\) | 11.2142 | + | 11.2142i | 0.386238 | + | 0.386238i | ||||
\(844\) | 8.34937 | − | 9.39903i | 0.287397 | − | 0.323528i | ||||
\(845\) | 15.2539 | − | 15.2539i | 0.524751 | − | 0.524751i | ||||
\(846\) | 8.21667 | − | 0.242758i | 0.282495 | − | 0.00834619i | ||||
\(847\) | 34.3932 | 1.18176 | ||||||||
\(848\) | −37.2064 | − | 29.3110i | −1.27767 | − | 1.00654i | ||||
\(849\) | −27.0981 | −0.930006 | ||||||||
\(850\) | 1.36466 | − | 0.0403184i | 0.0468075 | − | 0.00138291i | ||||
\(851\) | 21.6540 | − | 21.6540i | 0.742289 | − | 0.742289i | ||||
\(852\) | 0.651460 | + | 0.578707i | 0.0223187 | + | 0.0198262i | ||||
\(853\) | −29.1868 | − | 29.1868i | −0.999338 | − | 0.999338i | 0.000661680 | − | 1.00000i | \(-0.499789\pi\) |
−1.00000 | 0.000661680i | \(0.999789\pi\) | ||||||||
\(854\) | −51.7692 | + | 54.9213i | −1.77150 | + | 1.87937i | ||||
\(855\) | 2.39803i | 0.0820107i | ||||||||
\(856\) | 5.94219 | − | 7.10095i | 0.203100 | − | 0.242705i | ||||
\(857\) | − | 16.2847i | − | 0.556273i | −0.960541 | − | 0.278137i | \(-0.910283\pi\) | ||
0.960541 | − | 0.278137i | \(-0.0897168\pi\) | |||||||
\(858\) | −21.3474 | − | 20.1222i | −0.728787 | − | 0.686959i | ||||
\(859\) | −5.05121 | − | 5.05121i | −0.172345 | − | 0.172345i | 0.615664 | − | 0.788009i | \(-0.288888\pi\) |
−0.788009 | + | 0.615664i | \(0.788888\pi\) | |||||||
\(860\) | −0.173216 | − | 2.92888i | −0.00590663 | − | 0.0998741i | ||||
\(861\) | −33.5474 | + | 33.5474i | −1.14329 | + | 1.14329i | ||||
\(862\) | 0.563077 | + | 19.0586i | 0.0191785 | + | 0.649138i | ||||
\(863\) | −21.4536 | −0.730290 | −0.365145 | − | 0.930951i | \(-0.618981\pi\) | ||||
−0.365145 | + | 0.930951i | \(0.618981\pi\) | |||||||
\(864\) | −3.36789 | + | 4.54504i | −0.114578 | + | 0.154625i | ||||
\(865\) | −24.9135 | −0.847085 | ||||||||
\(866\) | 0.352862 | + | 11.9434i | 0.0119907 | + | 0.405853i | ||||
\(867\) | −10.8509 | + | 10.8509i | −0.368516 | + | 0.368516i | ||||
\(868\) | −1.55730 | − | 26.3321i | −0.0528582 | − | 0.893770i | ||||
\(869\) | 17.5383 | + | 17.5383i | 0.594947 | + | 0.594947i | ||||
\(870\) | −13.3144 | − | 12.5502i | −0.451401 | − | 0.425493i | ||||
\(871\) | 30.0795i | 1.01921i | ||||||||
\(872\) | −33.1817 | − | 27.7670i | −1.12367 | − | 0.940308i | ||||
\(873\) | 5.55954i | 0.188162i | ||||||||
\(874\) | −8.68936 | + | 9.21844i | −0.293922 | + | 0.311818i | ||||
\(875\) | −28.9414 | − | 28.9414i | −0.978398 | − | 0.978398i | ||||
\(876\) | −9.75976 | − | 8.66982i | −0.329752 | − | 0.292926i | ||||
\(877\) | −14.2382 | + | 14.2382i | −0.480788 | + | 0.480788i | −0.905383 | − | 0.424595i | \(-0.860416\pi\) |
0.424595 | + | 0.905383i | \(0.360416\pi\) | |||||||
\(878\) | −22.7607 | + | 0.672455i | −0.768137 | + | 0.0226943i | ||||
\(879\) | −16.7918 | −0.566374 | ||||||||
\(880\) | 5.00072 | + | 42.1302i | 0.168574 | + | 1.42021i | ||||
\(881\) | −2.11101 | −0.0711218 | −0.0355609 | − | 0.999368i | \(-0.511322\pi\) | ||||
−0.0355609 | + | 0.999368i | \(0.511322\pi\) | |||||||
\(882\) | 12.9092 | − | 0.381395i | 0.434674 | − | 0.0128422i | ||||
\(883\) | 20.1411 | − | 20.1411i | 0.677803 | − | 0.677803i | −0.281699 | − | 0.959503i | \(-0.590898\pi\) |
0.959503 | + | 0.281699i | \(0.0908981\pi\) | |||||||
\(884\) | −8.01282 | + | 9.02016i | −0.269500 | + | 0.303381i | ||||
\(885\) | 14.5576 | + | 14.5576i | 0.489350 | + | 0.489350i | ||||
\(886\) | 0.814442 | − | 0.864032i | 0.0273617 | − | 0.0290277i | ||||
\(887\) | − | 11.4072i | − | 0.383015i | −0.981491 | − | 0.191507i | \(-0.938662\pi\) | ||
0.981491 | − | 0.191507i | \(-0.0613376\pi\) | |||||||
\(888\) | −0.855658 | − | 9.63139i | −0.0287140 | − | 0.323208i | ||||
\(889\) | − | 59.6918i | − | 2.00200i | ||||||
\(890\) | 40.7415 | + | 38.4032i | 1.36566 | + | 1.28728i | ||||
\(891\) | −3.12754 | − | 3.12754i | −0.104777 | − | 0.104777i | ||||
\(892\) | −49.6125 | + | 2.93412i | −1.66115 | + | 0.0982417i | ||||
\(893\) | 4.11013 | − | 4.11013i | 0.137540 | − | 0.137540i | ||||
\(894\) | 0.0763998 | + | 2.58592i | 0.00255519 | + | 0.0864860i | ||||
\(895\) | −22.7946 | −0.761939 | ||||||||
\(896\) | 44.4735 | − | 9.32828i | 1.48576 | − | 0.311636i | ||||
\(897\) | 42.0119 | 1.40274 | ||||||||
\(898\) | 0.00546266 | + | 0.184896i | 0.000182291 | + | 0.00617005i | ||||
\(899\) | −12.5275 | + | 12.5275i | −0.417816 | + | 0.417816i | ||||
\(900\) | −1.49844 | + | 0.0886186i | −0.0499479 | + | 0.00295395i | ||||
\(901\) | −10.7700 | − | 10.7700i | −0.358802 | − | 0.358802i | ||||
\(902\) | −53.7653 | − | 50.6795i | −1.79019 | − | 1.68744i | ||||
\(903\) | − | 2.45710i | − | 0.0817671i | ||||||
\(904\) | −4.45236 | − | 50.1162i | −0.148083 | − | 1.66684i | ||||
\(905\) | 18.2893i | 0.607958i | ||||||||
\(906\) | −8.51424 | + | 9.03266i | −0.282867 | + | 0.300090i | ||||
\(907\) | −8.90535 | − | 8.90535i | −0.295697 | − | 0.295697i | 0.543629 | − | 0.839326i | \(-0.317050\pi\) |
−0.839326 | + | 0.543629i | \(0.817050\pi\) | |||||||
\(908\) | 15.7665 | − | 17.7486i | 0.523229 | − | 0.589007i | ||||
\(909\) | 12.0505 | − | 12.0505i | 0.399688 | − | 0.399688i | ||||
\(910\) | −63.8551 | + | 1.88657i | −2.11678 | + | 0.0625392i | ||||
\(911\) | −27.3847 | −0.907297 | −0.453649 | − | 0.891181i | \(-0.649878\pi\) | ||||
−0.453649 | + | 0.891181i | \(0.649878\pi\) | |||||||
\(912\) | 0.471477 | + | 3.97212i | 0.0156122 | + | 0.131530i | ||||
\(913\) | 11.7269 | 0.388102 | ||||||||
\(914\) | 38.0904 | − | 1.12537i | 1.25992 | − | 0.0372238i | ||||
\(915\) | 22.5309 | − | 22.5309i | 0.744848 | − | 0.744848i | ||||
\(916\) | −16.6558 | − | 14.7958i | −0.550324 | − | 0.488866i | ||||
\(917\) | 27.1531 | + | 27.1531i | 0.896676 | + | 0.896676i | ||||
\(918\) | −1.24773 | + | 1.32370i | −0.0411811 | + | 0.0436886i | ||||
\(919\) | 16.7701i | 0.553195i | 0.960986 | + | 0.276597i | \(0.0892068\pi\) | ||||
−0.960986 | + | 0.276597i | \(0.910793\pi\) | |||||||
\(920\) | −46.5954 | − | 38.9918i | −1.53620 | − | 1.28552i | ||||
\(921\) | 26.3225i | 0.867355i | ||||||||
\(922\) | 35.4536 | + | 33.4188i | 1.16760 | + | 1.10059i | ||||
\(923\) | −1.44488 | − | 1.44488i | −0.0475589 | − | 0.0475589i | ||||
\(924\) | 2.09760 | + | 35.4679i | 0.0690059 | + | 1.16681i | ||||
\(925\) | 1.81427 | − | 1.81427i | 0.0596529 | − | 0.0596529i | ||||
\(926\) | −0.0368508 | − | 1.24730i | −0.00121099 | − | 0.0409887i | ||||
\(927\) | 0.764345 | 0.0251044 | ||||||||
\(928\) | −24.5216 | − | 18.1706i | −0.804963 | − | 0.596480i | ||||
\(929\) | −14.2388 | −0.467159 | −0.233580 | − | 0.972338i | \(-0.575044\pi\) | ||||
−0.233580 | + | 0.972338i | \(0.575044\pi\) | |||||||
\(930\) | 0.328871 | + | 11.1313i | 0.0107841 | + | 0.365011i | ||||
\(931\) | 6.45739 | − | 6.45739i | 0.211632 | − | 0.211632i | ||||
\(932\) | 0.106948 | + | 1.80836i | 0.00350319 | + | 0.0592348i | ||||
\(933\) | 9.28460 | + | 9.28460i | 0.303964 | + | 0.303964i | ||||
\(934\) | −8.95448 | − | 8.44055i | −0.293000 | − | 0.276183i | ||||
\(935\) | 13.6429i | 0.446169i | ||||||||
\(936\) | 8.51310 | − | 10.1732i | 0.278259 | − | 0.332521i | ||||
\(937\) | 6.09698i | 0.199180i | 0.995029 | + | 0.0995899i | \(0.0317531\pi\) | ||||
−0.995029 | + | 0.0995899i | \(0.968247\pi\) | |||||||
\(938\) | 24.9881 | − | 26.5095i | 0.815889 | − | 0.865567i | ||||
\(939\) | 19.5987 | + | 19.5987i | 0.639578 | + | 0.639578i | ||||
\(940\) | 20.8418 | + | 18.5142i | 0.679784 | + | 0.603868i | ||||
\(941\) | 32.6743 | − | 32.6743i | 1.06515 | − | 1.06515i | 0.0674282 | − | 0.997724i | \(-0.478521\pi\) |
0.997724 | − | 0.0674282i | \(-0.0214794\pi\) | |||||||
\(942\) | 9.09399 | − | 0.268678i | 0.296298 | − | 0.00875400i | ||||
\(943\) | 105.811 | 3.44568 | ||||||||
\(944\) | 26.9756 | + | 21.2512i | 0.877981 | + | 0.691669i | ||||
\(945\) | −9.63163 | −0.313317 | ||||||||
\(946\) | 3.82490 | − | 0.113005i | 0.124358 | − | 0.00367411i | ||||
\(947\) | −1.79605 | + | 1.79605i | −0.0583638 | + | 0.0583638i | −0.735686 | − | 0.677322i | \(-0.763140\pi\) |
0.677322 | + | 0.735686i | \(0.263140\pi\) | |||||||
\(948\) | −7.44846 | + | 8.38485i | −0.241915 | + | 0.272327i | ||||
\(949\) | 21.6463 | + | 21.6463i | 0.702669 | + | 0.702669i | ||||
\(950\) | −0.728035 | + | 0.772364i | −0.0236206 | + | 0.0250588i | ||||
\(951\) | − | 24.3216i | − | 0.788680i | ||||||
\(952\) | 14.5552 | − | 1.29309i | 0.471736 | − | 0.0419093i | ||||
\(953\) | − | 11.4900i | − | 0.372198i | −0.982531 | − | 0.186099i | \(-0.940415\pi\) | ||
0.982531 | − | 0.186099i | \(-0.0595846\pi\) | |||||||
\(954\) | 12.1858 | + | 11.4864i | 0.394530 | + | 0.371886i | ||||
\(955\) | 39.4726 | + | 39.4726i | 1.27730 | + | 1.27730i | ||||
\(956\) | 30.3803 | − | 1.79672i | 0.982570 | − | 0.0581099i | ||||
\(957\) | 16.8739 | − | 16.8739i | 0.545455 | − | 0.545455i | ||||
\(958\) | −0.267154 | − | 9.04241i | −0.00863136 | − | 0.292147i | ||||
\(959\) | 27.3556 | 0.883360 | ||||||||
\(960\) | −18.8837 | + | 3.38198i | −0.609470 | + | 0.109153i | ||||
\(961\) | −20.2171 | −0.652164 | ||||||||
\(962\) | 0.669614 | + | 22.6646i | 0.0215892 | + | 0.730735i | ||||
\(963\) | −2.31480 | + | 2.31480i | −0.0745935 | + | 0.0745935i | ||||
\(964\) | −49.9198 | + | 2.95230i | −1.60781 | + | 0.0950871i | ||||
\(965\) | −1.75018 | − | 1.75018i | −0.0563404 | − | 0.0563404i | ||||
\(966\) | −37.0257 | − | 34.9007i | −1.19128 | − | 1.12291i | ||||
\(967\) | − | 55.1485i | − | 1.77346i | −0.462290 | − | 0.886729i | \(-0.652972\pi\) | ||
0.462290 | − | 0.886729i | \(-0.347028\pi\) | |||||||
\(968\) | −24.1248 | + | 2.14326i | −0.775402 | + | 0.0688871i | ||||
\(969\) | 1.28627i | 0.0413211i | ||||||||
\(970\) | −12.9324 | + | 13.7198i | −0.415234 | + | 0.440517i | ||||
\(971\) | 3.12816 | + | 3.12816i | 0.100387 | + | 0.100387i | 0.755517 | − | 0.655129i | \(-0.227386\pi\) |
−0.655129 | + | 0.755517i | \(0.727386\pi\) | |||||||
\(972\) | 1.32826 | − | 1.49524i | 0.0426038 | − | 0.0479598i | ||||
\(973\) | 14.5956 | − | 14.5956i | 0.467913 | − | 0.467913i | ||||
\(974\) | −13.9752 | + | 0.412891i | −0.447794 | + | 0.0132299i | ||||
\(975\) | 3.51995 | 0.112729 | ||||||||
\(976\) | 32.8906 | − | 41.7502i | 1.05280 | − | 1.33639i | ||||
\(977\) | −28.6613 | −0.916957 | −0.458479 | − | 0.888705i | \(-0.651605\pi\) | ||||
−0.458479 | + | 0.888705i | \(0.651605\pi\) | |||||||
\(978\) | 21.4895 | − | 0.634897i | 0.687158 | − | 0.0203018i | ||||
\(979\) | −51.6333 | + | 51.6333i | −1.65021 | + | 1.65021i | ||||
\(980\) | 32.7444 | + | 29.0876i | 1.04598 | + | 0.929168i | ||||
\(981\) | 10.8167 | + | 10.8167i | 0.345352 | + | 0.345352i | ||||
\(982\) | −30.8969 | + | 32.7782i | −0.985960 | + | 1.04599i | ||||
\(983\) | − | 25.4672i | − | 0.812278i | −0.913811 | − | 0.406139i | \(-0.866875\pi\) | ||
0.913811 | − | 0.406139i | \(-0.133125\pi\) | |||||||
\(984\) | 21.4410 | − | 25.6222i | 0.683515 | − | 0.816805i | ||||
\(985\) | − | 0.733589i | − | 0.0233741i | ||||||
\(986\) | −7.14170 | − | 6.73181i | −0.227438 | − | 0.214385i | ||||
\(987\) | 16.5083 | + | 16.5083i | 0.525464 | + | 0.525464i | ||||
\(988\) | −0.553770 | − | 9.36359i | −0.0176178 | − | 0.297895i | ||||
\(989\) | −3.87493 | + | 3.87493i | −0.123215 | + | 0.123215i | ||||
\(990\) | −0.442971 | − | 14.9933i | −0.0140785 | − | 0.476518i | ||||
\(991\) | 49.6542 | 1.57732 | 0.788659 | − | 0.614831i | \(-0.210776\pi\) | ||||
0.788659 | + | 0.614831i | \(0.210776\pi\) | |||||||
\(992\) | 2.73328 | + | 18.3734i | 0.0867818 | + | 0.583356i | ||||
\(993\) | 22.4012 | 0.710881 | ||||||||
\(994\) | 0.0730847 | + | 2.47371i | 0.00231811 | + | 0.0784613i | ||||
\(995\) | 8.06381 | − | 8.06381i | 0.255640 | − | 0.255640i | ||||
\(996\) | 0.313056 | + | 5.29341i | 0.00991957 | + | 0.167728i | ||||
\(997\) | 15.3984 | + | 15.3984i | 0.487672 | + | 0.487672i | 0.907571 | − | 0.419899i | \(-0.137934\pi\) |
−0.419899 | + | 0.907571i | \(0.637934\pi\) | |||||||
\(998\) | −6.32898 | − | 5.96574i | −0.200340 | − | 0.188842i | ||||
\(999\) | 3.41862i | 0.108160i |
(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 | 912.2.u.a.229.19 | ✓ | 72 | |
16.13 | even | 4 | inner | 912.2.u.a.685.19 | yes | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
912.2.u.a.229.19 | ✓ | 72 | 1.1 | even | 1 | trivial | |
912.2.u.a.685.19 | yes | 72 | 16.13 | even | 4 | inner |