Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(424,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.424");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.r (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 499.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.499 |
Dual form | 525.2.r.d.424.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.73205 | − | 1.00000i | −1.22474 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | 1.00000 | + | 1.73205i | 0.500000 | + | 0.866025i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.00000 | −0.816497 | ||||||||
\(7\) | −2.59808 | + | 0.500000i | −0.981981 | + | 0.188982i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.00000 | + | 5.19615i | 0.904534 | + | 1.56670i | 0.821541 | + | 0.570149i | \(0.193114\pi\) |
0.0829925 | + | 0.996550i | \(0.473552\pi\) | |||||||
\(12\) | 1.73205 | + | 1.00000i | 0.500000 | + | 0.288675i | ||||
\(13\) | − | 3.00000i | − | 0.832050i | −0.909353 | − | 0.416025i | \(-0.863423\pi\) | ||
0.909353 | − | 0.416025i | \(-0.136577\pi\) | |||||||
\(14\) | 5.00000 | + | 1.73205i | 1.33631 | + | 0.462910i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | − | 3.46410i | 0.500000 | − | 0.866025i | ||||
\(17\) | 3.46410 | − | 2.00000i | 0.840168 | − | 0.485071i | −0.0171533 | − | 0.999853i | \(-0.505460\pi\) |
0.857321 | + | 0.514782i | \(0.172127\pi\) | |||||||
\(18\) | −1.73205 | + | 1.00000i | −0.408248 | + | 0.235702i | ||||
\(19\) | 0.500000 | − | 0.866025i | 0.114708 | − | 0.198680i | −0.802955 | − | 0.596040i | \(-0.796740\pi\) |
0.917663 | + | 0.397360i | \(0.130073\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.00000 | + | 1.73205i | −0.436436 | + | 0.377964i | ||||
\(22\) | − | 12.0000i | − | 2.55841i | ||||||
\(23\) | 3.46410 | + | 2.00000i | 0.722315 | + | 0.417029i | 0.815604 | − | 0.578610i | \(-0.196405\pi\) |
−0.0932891 | + | 0.995639i | \(0.529738\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.00000 | + | 5.19615i | −0.588348 | + | 1.01905i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −3.46410 | − | 4.00000i | −0.654654 | − | 0.755929i | ||||
\(29\) | 8.00000 | 1.48556 | 0.742781 | − | 0.669534i | \(-0.233506\pi\) | ||||
0.742781 | + | 0.669534i | \(0.233506\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.500000 | − | 0.866025i | −0.0898027 | − | 0.155543i | 0.817625 | − | 0.575751i | \(-0.195290\pi\) |
−0.907428 | + | 0.420208i | \(0.861957\pi\) | |||||||
\(32\) | −6.92820 | + | 4.00000i | −1.22474 | + | 0.707107i | ||||
\(33\) | 5.19615 | + | 3.00000i | 0.904534 | + | 0.522233i | ||||
\(34\) | −8.00000 | −1.37199 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.00000 | 0.333333 | ||||||||
\(37\) | 6.06218 | + | 3.50000i | 0.996616 | + | 0.575396i | 0.907245 | − | 0.420602i | \(-0.138181\pi\) |
0.0893706 | + | 0.995998i | \(0.471514\pi\) | |||||||
\(38\) | −1.73205 | + | 1.00000i | −0.280976 | + | 0.162221i | ||||
\(39\) | −1.50000 | − | 2.59808i | −0.240192 | − | 0.416025i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 5.19615 | − | 1.00000i | 0.801784 | − | 0.154303i | ||||
\(43\) | 1.00000i | 0.152499i | 0.997089 | + | 0.0762493i | \(0.0242945\pi\) | ||||
−0.997089 | + | 0.0762493i | \(0.975706\pi\) | |||||||
\(44\) | −6.00000 | + | 10.3923i | −0.904534 | + | 1.56670i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.00000 | − | 6.92820i | −0.589768 | − | 1.02151i | ||||
\(47\) | 1.73205 | + | 1.00000i | 0.252646 | + | 0.145865i | 0.620975 | − | 0.783830i | \(-0.286737\pi\) |
−0.368329 | + | 0.929695i | \(0.620070\pi\) | |||||||
\(48\) | − | 4.00000i | − | 0.577350i | ||||||
\(49\) | 6.50000 | − | 2.59808i | 0.928571 | − | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.00000 | − | 3.46410i | 0.280056 | − | 0.485071i | ||||
\(52\) | 5.19615 | − | 3.00000i | 0.720577 | − | 0.416025i | ||||
\(53\) | 3.46410 | − | 2.00000i | 0.475831 | − | 0.274721i | −0.242846 | − | 0.970065i | \(-0.578081\pi\) |
0.718677 | + | 0.695344i | \(0.244748\pi\) | |||||||
\(54\) | −1.00000 | + | 1.73205i | −0.136083 | + | 0.235702i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 1.00000i | − | 0.132453i | ||||||
\(58\) | −13.8564 | − | 8.00000i | −1.81944 | − | 1.05045i | ||||
\(59\) | −4.00000 | − | 6.92820i | −0.520756 | − | 0.901975i | −0.999709 | − | 0.0241347i | \(-0.992317\pi\) |
0.478953 | − | 0.877841i | \(-0.341016\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.00000 | − | 12.1244i | 0.896258 | − | 1.55236i | 0.0640184 | − | 0.997949i | \(-0.479608\pi\) |
0.832240 | − | 0.554416i | \(-0.187058\pi\) | |||||||
\(62\) | 2.00000i | 0.254000i | ||||||||
\(63\) | −0.866025 | + | 2.50000i | −0.109109 | + | 0.314970i | ||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.00000 | − | 10.3923i | −0.738549 | − | 1.27920i | ||||
\(67\) | −6.06218 | + | 3.50000i | −0.740613 | + | 0.427593i | −0.822292 | − | 0.569066i | \(-0.807305\pi\) |
0.0816792 | + | 0.996659i | \(0.473972\pi\) | |||||||
\(68\) | 6.92820 | + | 4.00000i | 0.840168 | + | 0.485071i | ||||
\(69\) | 4.00000 | 0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.00000 | 0.712069 | 0.356034 | − | 0.934473i | \(-0.384129\pi\) | ||||
0.356034 | + | 0.934473i | \(0.384129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.866025 | − | 0.500000i | 0.101361 | − | 0.0585206i | −0.448463 | − | 0.893801i | \(-0.648028\pi\) |
0.549823 | + | 0.835281i | \(0.314695\pi\) | |||||||
\(74\) | −7.00000 | − | 12.1244i | −0.813733 | − | 1.40943i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00000 | 0.229416 | ||||||||
\(77\) | −10.3923 | − | 12.0000i | −1.18431 | − | 1.36753i | ||||
\(78\) | 6.00000i | 0.679366i | ||||||||
\(79\) | −0.500000 | + | 0.866025i | −0.0562544 | + | 0.0974355i | −0.892781 | − | 0.450490i | \(-0.851249\pi\) |
0.836527 | + | 0.547926i | \(0.184582\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 10.3923 | + | 6.00000i | 1.14764 | + | 0.662589i | ||||
\(83\) | 2.00000i | 0.219529i | 0.993958 | + | 0.109764i | \(0.0350096\pi\) | ||||
−0.993958 | + | 0.109764i | \(0.964990\pi\) | |||||||
\(84\) | −5.00000 | − | 1.73205i | −0.545545 | − | 0.188982i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.00000 | − | 1.73205i | 0.107833 | − | 0.186772i | ||||
\(87\) | 6.92820 | − | 4.00000i | 0.742781 | − | 0.428845i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.00000 | + | 10.3923i | −0.635999 | + | 1.10158i | 0.350304 | + | 0.936636i | \(0.386078\pi\) |
−0.986303 | + | 0.164946i | \(0.947255\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.50000 | + | 7.79423i | 0.157243 | + | 0.817057i | ||||
\(92\) | 8.00000i | 0.834058i | ||||||||
\(93\) | −0.866025 | − | 0.500000i | −0.0898027 | − | 0.0518476i | ||||
\(94\) | −2.00000 | − | 3.46410i | −0.206284 | − | 0.357295i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.00000 | + | 6.92820i | −0.408248 | + | 0.707107i | ||||
\(97\) | 6.00000i | 0.609208i | 0.952479 | + | 0.304604i | \(0.0985241\pi\) | ||||
−0.952479 | + | 0.304604i | \(0.901476\pi\) | |||||||
\(98\) | −13.8564 | − | 2.00000i | −1.39971 | − | 0.202031i | ||||
\(99\) | 6.00000 | 0.603023 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.00000 | + | 8.66025i | 0.497519 | + | 0.861727i | 0.999996 | − | 0.00286291i | \(-0.000911295\pi\) |
−0.502477 | + | 0.864590i | \(0.667578\pi\) | |||||||
\(102\) | −6.92820 | + | 4.00000i | −0.685994 | + | 0.396059i | ||||
\(103\) | 16.4545 | + | 9.50000i | 1.62131 | + | 0.936063i | 0.986571 | + | 0.163335i | \(0.0522252\pi\) |
0.634738 | + | 0.772728i | \(0.281108\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.00000 | −0.777029 | ||||||||
\(107\) | 10.3923 | + | 6.00000i | 1.00466 | + | 0.580042i | 0.909624 | − | 0.415432i | \(-0.136370\pi\) |
0.0950377 | + | 0.995474i | \(0.469703\pi\) | |||||||
\(108\) | 1.73205 | − | 1.00000i | 0.166667 | − | 0.0962250i | ||||
\(109\) | −7.50000 | − | 12.9904i | −0.718370 | − | 1.24425i | −0.961645 | − | 0.274296i | \(-0.911555\pi\) |
0.243276 | − | 0.969957i | \(-0.421778\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.00000 | 0.664411 | ||||||||
\(112\) | −3.46410 | + | 10.0000i | −0.327327 | + | 0.944911i | ||||
\(113\) | − | 6.00000i | − | 0.564433i | −0.959351 | − | 0.282216i | \(-0.908930\pi\) | ||
0.959351 | − | 0.282216i | \(-0.0910696\pi\) | |||||||
\(114\) | −1.00000 | + | 1.73205i | −0.0936586 | + | 0.162221i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 8.00000 | + | 13.8564i | 0.742781 | + | 1.28654i | ||||
\(117\) | −2.59808 | − | 1.50000i | −0.240192 | − | 0.138675i | ||||
\(118\) | 16.0000i | 1.47292i | ||||||||
\(119\) | −8.00000 | + | 6.92820i | −0.733359 | + | 0.635107i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.5000 | + | 21.6506i | −1.13636 | + | 1.96824i | ||||
\(122\) | −24.2487 | + | 14.0000i | −2.19538 | + | 1.26750i | ||||
\(123\) | −5.19615 | + | 3.00000i | −0.468521 | + | 0.270501i | ||||
\(124\) | 1.00000 | − | 1.73205i | 0.0898027 | − | 0.155543i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4.00000 | − | 3.46410i | 0.356348 | − | 0.308607i | ||||
\(127\) | − | 5.00000i | − | 0.443678i | −0.975083 | − | 0.221839i | \(-0.928794\pi\) | ||
0.975083 | − | 0.221839i | \(-0.0712060\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.500000 | + | 0.866025i | 0.0440225 | + | 0.0762493i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.00000 | + | 1.73205i | −0.0873704 | + | 0.151330i | −0.906399 | − | 0.422423i | \(-0.861180\pi\) |
0.819028 | + | 0.573753i | \(0.194513\pi\) | |||||||
\(132\) | 12.0000i | 1.04447i | ||||||||
\(133\) | −0.866025 | + | 2.50000i | −0.0750939 | + | 0.216777i | ||||
\(134\) | 14.0000 | 1.20942 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.92820 | + | 4.00000i | −0.591916 | + | 0.341743i | −0.765855 | − | 0.643013i | \(-0.777684\pi\) |
0.173939 | + | 0.984757i | \(0.444351\pi\) | |||||||
\(138\) | −6.92820 | − | 4.00000i | −0.589768 | − | 0.340503i | ||||
\(139\) | −21.0000 | −1.78120 | −0.890598 | − | 0.454791i | \(-0.849714\pi\) | ||||
−0.890598 | + | 0.454791i | \(0.849714\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.00000 | 0.168430 | ||||||||
\(142\) | −10.3923 | − | 6.00000i | −0.872103 | − | 0.503509i | ||||
\(143\) | 15.5885 | − | 9.00000i | 1.30357 | − | 0.752618i | ||||
\(144\) | −2.00000 | − | 3.46410i | −0.166667 | − | 0.288675i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.00000 | −0.165521 | ||||||||
\(147\) | 4.33013 | − | 5.50000i | 0.357143 | − | 0.453632i | ||||
\(148\) | 14.0000i | 1.15079i | ||||||||
\(149\) | −2.00000 | + | 3.46410i | −0.163846 | + | 0.283790i | −0.936245 | − | 0.351348i | \(-0.885723\pi\) |
0.772399 | + | 0.635138i | \(0.219057\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.00000 | − | 6.92820i | −0.325515 | − | 0.563809i | 0.656101 | − | 0.754673i | \(-0.272204\pi\) |
−0.981617 | + | 0.190864i | \(0.938871\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 4.00000i | − | 0.323381i | ||||||
\(154\) | 6.00000 | + | 31.1769i | 0.483494 | + | 2.51231i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.00000 | − | 5.19615i | 0.240192 | − | 0.416025i | ||||
\(157\) | −8.66025 | + | 5.00000i | −0.691164 | + | 0.399043i | −0.804048 | − | 0.594565i | \(-0.797324\pi\) |
0.112884 | + | 0.993608i | \(0.463991\pi\) | |||||||
\(158\) | 1.73205 | − | 1.00000i | 0.137795 | − | 0.0795557i | ||||
\(159\) | 2.00000 | − | 3.46410i | 0.158610 | − | 0.274721i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.0000 | − | 3.46410i | −0.788110 | − | 0.273009i | ||||
\(162\) | 2.00000i | 0.157135i | ||||||||
\(163\) | 10.3923 | + | 6.00000i | 0.813988 | + | 0.469956i | 0.848339 | − | 0.529454i | \(-0.177603\pi\) |
−0.0343508 | + | 0.999410i | \(0.510936\pi\) | |||||||
\(164\) | −6.00000 | − | 10.3923i | −0.468521 | − | 0.811503i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.00000 | − | 3.46410i | 0.155230 | − | 0.268866i | ||||
\(167\) | 10.0000i | 0.773823i | 0.922117 | + | 0.386912i | \(0.126458\pi\) | ||||
−0.922117 | + | 0.386912i | \(0.873542\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.00000 | 0.307692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.500000 | − | 0.866025i | −0.0382360 | − | 0.0662266i | ||||
\(172\) | −1.73205 | + | 1.00000i | −0.132068 | + | 0.0762493i | ||||
\(173\) | −20.7846 | − | 12.0000i | −1.58022 | − | 0.912343i | −0.994826 | − | 0.101598i | \(-0.967605\pi\) |
−0.585399 | − | 0.810745i | \(-0.699062\pi\) | |||||||
\(174\) | −16.0000 | −1.21296 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 24.0000 | 1.80907 | ||||||||
\(177\) | −6.92820 | − | 4.00000i | −0.520756 | − | 0.300658i | ||||
\(178\) | 20.7846 | − | 12.0000i | 1.55787 | − | 0.899438i | ||||
\(179\) | 9.00000 | + | 15.5885i | 0.672692 | + | 1.16514i | 0.977138 | + | 0.212607i | \(0.0681952\pi\) |
−0.304446 | + | 0.952529i | \(0.598471\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.0000 | 0.966282 | 0.483141 | − | 0.875542i | \(-0.339496\pi\) | ||||
0.483141 | + | 0.875542i | \(0.339496\pi\) | |||||||
\(182\) | 5.19615 | − | 15.0000i | 0.385164 | − | 1.11187i | ||||
\(183\) | − | 14.0000i | − | 1.03491i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.00000 | + | 1.73205i | 0.0733236 | + | 0.127000i | ||||
\(187\) | 20.7846 | + | 12.0000i | 1.51992 | + | 0.877527i | ||||
\(188\) | 4.00000i | 0.291730i | ||||||||
\(189\) | 0.500000 | + | 2.59808i | 0.0363696 | + | 0.188982i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.00000 | + | 8.66025i | −0.361787 | + | 0.626634i | −0.988255 | − | 0.152813i | \(-0.951167\pi\) |
0.626468 | + | 0.779447i | \(0.284500\pi\) | |||||||
\(192\) | 6.92820 | − | 4.00000i | 0.500000 | − | 0.288675i | ||||
\(193\) | −7.79423 | + | 4.50000i | −0.561041 | + | 0.323917i | −0.753563 | − | 0.657376i | \(-0.771667\pi\) |
0.192522 | + | 0.981293i | \(0.438333\pi\) | |||||||
\(194\) | 6.00000 | − | 10.3923i | 0.430775 | − | 0.746124i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.0000 | + | 8.66025i | 0.785714 | + | 0.618590i | ||||
\(197\) | − | 12.0000i | − | 0.854965i | −0.904024 | − | 0.427482i | \(-0.859401\pi\) | ||
0.904024 | − | 0.427482i | \(-0.140599\pi\) | |||||||
\(198\) | −10.3923 | − | 6.00000i | −0.738549 | − | 0.426401i | ||||
\(199\) | 4.00000 | + | 6.92820i | 0.283552 | + | 0.491127i | 0.972257 | − | 0.233915i | \(-0.0751537\pi\) |
−0.688705 | + | 0.725042i | \(0.741820\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.50000 | + | 6.06218i | −0.246871 | + | 0.427593i | ||||
\(202\) | − | 20.0000i | − | 1.40720i | ||||||
\(203\) | −20.7846 | + | 4.00000i | −1.45879 | + | 0.280745i | ||||
\(204\) | 8.00000 | 0.560112 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −19.0000 | − | 32.9090i | −1.32379 | − | 2.29288i | ||||
\(207\) | 3.46410 | − | 2.00000i | 0.240772 | − | 0.139010i | ||||
\(208\) | −10.3923 | − | 6.00000i | −0.720577 | − | 0.416025i | ||||
\(209\) | 6.00000 | 0.415029 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.0000 | −1.37686 | −0.688428 | − | 0.725304i | \(-0.741699\pi\) | ||||
−0.688428 | + | 0.725304i | \(0.741699\pi\) | |||||||
\(212\) | 6.92820 | + | 4.00000i | 0.475831 | + | 0.274721i | ||||
\(213\) | 5.19615 | − | 3.00000i | 0.356034 | − | 0.205557i | ||||
\(214\) | −12.0000 | − | 20.7846i | −0.820303 | − | 1.42081i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.73205 | + | 2.00000i | 0.117579 | + | 0.135769i | ||||
\(218\) | 30.0000i | 2.03186i | ||||||||
\(219\) | 0.500000 | − | 0.866025i | 0.0337869 | − | 0.0585206i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.00000 | − | 10.3923i | −0.403604 | − | 0.699062i | ||||
\(222\) | −12.1244 | − | 7.00000i | −0.813733 | − | 0.469809i | ||||
\(223\) | − | 24.0000i | − | 1.60716i | −0.595198 | − | 0.803579i | \(-0.702926\pi\) | ||
0.595198 | − | 0.803579i | \(-0.297074\pi\) | |||||||
\(224\) | 16.0000 | − | 13.8564i | 1.06904 | − | 0.925820i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.00000 | + | 10.3923i | −0.399114 | + | 0.691286i | ||||
\(227\) | 8.66025 | − | 5.00000i | 0.574801 | − | 0.331862i | −0.184263 | − | 0.982877i | \(-0.558990\pi\) |
0.759065 | + | 0.651015i | \(0.225657\pi\) | |||||||
\(228\) | 1.73205 | − | 1.00000i | 0.114708 | − | 0.0662266i | ||||
\(229\) | 6.50000 | − | 11.2583i | 0.429532 | − | 0.743971i | −0.567300 | − | 0.823511i | \(-0.692012\pi\) |
0.996832 | + | 0.0795401i | \(0.0253452\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −15.0000 | − | 5.19615i | −0.986928 | − | 0.341882i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.19615 | − | 3.00000i | −0.340411 | − | 0.196537i | 0.320043 | − | 0.947403i | \(-0.396303\pi\) |
−0.660454 | + | 0.750867i | \(0.729636\pi\) | |||||||
\(234\) | 3.00000 | + | 5.19615i | 0.196116 | + | 0.339683i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 8.00000 | − | 13.8564i | 0.520756 | − | 0.901975i | ||||
\(237\) | 1.00000i | 0.0649570i | ||||||||
\(238\) | 20.7846 | − | 4.00000i | 1.34727 | − | 0.259281i | ||||
\(239\) | −14.0000 | −0.905585 | −0.452792 | − | 0.891616i | \(-0.649572\pi\) | ||||
−0.452792 | + | 0.891616i | \(0.649572\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.00000 | + | 15.5885i | 0.579741 | + | 1.00414i | 0.995509 | + | 0.0946700i | \(0.0301796\pi\) |
−0.415768 | + | 0.909471i | \(0.636487\pi\) | |||||||
\(242\) | 43.3013 | − | 25.0000i | 2.78351 | − | 1.60706i | ||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | 28.0000 | 1.79252 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 12.0000 | 0.765092 | ||||||||
\(247\) | −2.59808 | − | 1.50000i | −0.165312 | − | 0.0954427i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.00000 | + | 1.73205i | 0.0633724 | + | 0.109764i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | −5.19615 | + | 1.00000i | −0.327327 | + | 0.0629941i | ||||
\(253\) | 24.0000i | 1.50887i | ||||||||
\(254\) | −5.00000 | + | 8.66025i | −0.313728 | + | 0.543393i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | −15.5885 | − | 9.00000i | −0.972381 | − | 0.561405i | −0.0724199 | − | 0.997374i | \(-0.523072\pi\) |
−0.899961 | + | 0.435970i | \(0.856405\pi\) | |||||||
\(258\) | − | 2.00000i | − | 0.124515i | ||||||
\(259\) | −17.5000 | − | 6.06218i | −1.08740 | − | 0.376685i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.00000 | − | 6.92820i | 0.247594 | − | 0.428845i | ||||
\(262\) | 3.46410 | − | 2.00000i | 0.214013 | − | 0.123560i | ||||
\(263\) | 3.46410 | − | 2.00000i | 0.213606 | − | 0.123325i | −0.389380 | − | 0.921077i | \(-0.627311\pi\) |
0.602986 | + | 0.797752i | \(0.293977\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.00000 | − | 3.46410i | 0.245256 | − | 0.212398i | ||||
\(267\) | 12.0000i | 0.734388i | ||||||||
\(268\) | −12.1244 | − | 7.00000i | −0.740613 | − | 0.427593i | ||||
\(269\) | −5.00000 | − | 8.66025i | −0.304855 | − | 0.528025i | 0.672374 | − | 0.740212i | \(-0.265275\pi\) |
−0.977229 | + | 0.212187i | \(0.931941\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.0000 | − | 20.7846i | 0.728948 | − | 1.26258i | −0.228380 | − | 0.973572i | \(-0.573343\pi\) |
0.957328 | − | 0.289003i | \(-0.0933238\pi\) | |||||||
\(272\) | − | 16.0000i | − | 0.970143i | ||||||
\(273\) | 5.19615 | + | 6.00000i | 0.314485 | + | 0.363137i | ||||
\(274\) | 16.0000 | 0.966595 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.00000 | + | 6.92820i | 0.240772 | + | 0.417029i | ||||
\(277\) | 6.06218 | − | 3.50000i | 0.364241 | − | 0.210295i | −0.306699 | − | 0.951807i | \(-0.599224\pi\) |
0.670940 | + | 0.741512i | \(0.265891\pi\) | |||||||
\(278\) | 36.3731 | + | 21.0000i | 2.18151 | + | 1.25950i | ||||
\(279\) | −1.00000 | −0.0598684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.0000 | −0.715860 | −0.357930 | − | 0.933748i | \(-0.616517\pi\) | ||||
−0.357930 | + | 0.933748i | \(0.616517\pi\) | |||||||
\(282\) | −3.46410 | − | 2.00000i | −0.206284 | − | 0.119098i | ||||
\(283\) | −6.06218 | + | 3.50000i | −0.360359 | + | 0.208053i | −0.669238 | − | 0.743048i | \(-0.733379\pi\) |
0.308879 | + | 0.951101i | \(0.400046\pi\) | |||||||
\(284\) | 6.00000 | + | 10.3923i | 0.356034 | + | 0.616670i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −36.0000 | −2.12872 | ||||||||
\(287\) | 15.5885 | − | 3.00000i | 0.920158 | − | 0.177084i | ||||
\(288\) | 8.00000i | 0.471405i | ||||||||
\(289\) | −0.500000 | + | 0.866025i | −0.0294118 | + | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.00000 | + | 5.19615i | 0.175863 | + | 0.304604i | ||||
\(292\) | 1.73205 | + | 1.00000i | 0.101361 | + | 0.0585206i | ||||
\(293\) | − | 16.0000i | − | 0.934730i | −0.884064 | − | 0.467365i | \(-0.845203\pi\) | ||
0.884064 | − | 0.467365i | \(-0.154797\pi\) | |||||||
\(294\) | −13.0000 | + | 5.19615i | −0.758175 | + | 0.303046i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.19615 | − | 3.00000i | 0.301511 | − | 0.174078i | ||||
\(298\) | 6.92820 | − | 4.00000i | 0.401340 | − | 0.231714i | ||||
\(299\) | 6.00000 | − | 10.3923i | 0.346989 | − | 0.601003i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.500000 | − | 2.59808i | −0.0288195 | − | 0.149751i | ||||
\(302\) | 16.0000i | 0.920697i | ||||||||
\(303\) | 8.66025 | + | 5.00000i | 0.497519 | + | 0.287242i | ||||
\(304\) | −2.00000 | − | 3.46410i | −0.114708 | − | 0.198680i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −4.00000 | + | 6.92820i | −0.228665 | + | 0.396059i | ||||
\(307\) | − | 3.00000i | − | 0.171219i | −0.996329 | − | 0.0856095i | \(-0.972716\pi\) | ||
0.996329 | − | 0.0856095i | \(-0.0272838\pi\) | |||||||
\(308\) | 10.3923 | − | 30.0000i | 0.592157 | − | 1.70941i | ||||
\(309\) | 19.0000 | 1.08087 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.00000 | − | 5.19615i | −0.170114 | − | 0.294647i | 0.768345 | − | 0.640036i | \(-0.221080\pi\) |
−0.938460 | + | 0.345389i | \(0.887747\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.52628 | − | 5.50000i | −0.538457 | − | 0.310878i | 0.205996 | − | 0.978553i | \(-0.433957\pi\) |
−0.744453 | + | 0.667674i | \(0.767290\pi\) | |||||||
\(314\) | 20.0000 | 1.12867 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.00000 | −0.112509 | ||||||||
\(317\) | 17.3205 | + | 10.0000i | 0.972817 | + | 0.561656i | 0.900094 | − | 0.435696i | \(-0.143498\pi\) |
0.0727229 | + | 0.997352i | \(0.476831\pi\) | |||||||
\(318\) | −6.92820 | + | 4.00000i | −0.388514 | + | 0.224309i | ||||
\(319\) | 24.0000 | + | 41.5692i | 1.34374 | + | 2.32743i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.0000 | 0.669775 | ||||||||
\(322\) | 13.8564 | + | 16.0000i | 0.772187 | + | 0.891645i | ||||
\(323\) | − | 4.00000i | − | 0.222566i | ||||||
\(324\) | 1.00000 | − | 1.73205i | 0.0555556 | − | 0.0962250i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −12.0000 | − | 20.7846i | −0.664619 | − | 1.15115i | ||||
\(327\) | −12.9904 | − | 7.50000i | −0.718370 | − | 0.414751i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.00000 | − | 1.73205i | −0.275659 | − | 0.0954911i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.50000 | − | 7.79423i | 0.247342 | − | 0.428410i | −0.715445 | − | 0.698669i | \(-0.753776\pi\) |
0.962788 | + | 0.270259i | \(0.0871094\pi\) | |||||||
\(332\) | −3.46410 | + | 2.00000i | −0.190117 | + | 0.109764i | ||||
\(333\) | 6.06218 | − | 3.50000i | 0.332205 | − | 0.191799i | ||||
\(334\) | 10.0000 | − | 17.3205i | 0.547176 | − | 0.947736i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.00000 | + | 10.3923i | 0.109109 | + | 0.566947i | ||||
\(337\) | − | 25.0000i | − | 1.36184i | −0.732359 | − | 0.680918i | \(-0.761581\pi\) | ||
0.732359 | − | 0.680918i | \(-0.238419\pi\) | |||||||
\(338\) | −6.92820 | − | 4.00000i | −0.376845 | − | 0.217571i | ||||
\(339\) | −3.00000 | − | 5.19615i | −0.162938 | − | 0.282216i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.00000 | − | 5.19615i | 0.162459 | − | 0.281387i | ||||
\(342\) | 2.00000i | 0.108148i | ||||||||
\(343\) | −15.5885 | + | 10.0000i | −0.841698 | + | 0.539949i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 24.0000 | + | 41.5692i | 1.29025 | + | 2.23478i | ||||
\(347\) | −13.8564 | + | 8.00000i | −0.743851 | + | 0.429463i | −0.823468 | − | 0.567363i | \(-0.807964\pi\) |
0.0796169 | + | 0.996826i | \(0.474630\pi\) | |||||||
\(348\) | 13.8564 | + | 8.00000i | 0.742781 | + | 0.428845i | ||||
\(349\) | −2.00000 | −0.107058 | −0.0535288 | − | 0.998566i | \(-0.517047\pi\) | ||||
−0.0535288 | + | 0.998566i | \(0.517047\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.00000 | −0.160128 | ||||||||
\(352\) | −41.5692 | − | 24.0000i | −2.21565 | − | 1.27920i | ||||
\(353\) | −15.5885 | + | 9.00000i | −0.829690 | + | 0.479022i | −0.853746 | − | 0.520689i | \(-0.825675\pi\) |
0.0240566 | + | 0.999711i | \(0.492342\pi\) | |||||||
\(354\) | 8.00000 | + | 13.8564i | 0.425195 | + | 0.736460i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −24.0000 | −1.27200 | ||||||||
\(357\) | −3.46410 | + | 10.0000i | −0.183340 | + | 0.529256i | ||||
\(358\) | − | 36.0000i | − | 1.90266i | ||||||
\(359\) | −12.0000 | + | 20.7846i | −0.633336 | + | 1.09697i | 0.353529 | + | 0.935423i | \(0.384981\pi\) |
−0.986865 | + | 0.161546i | \(0.948352\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | + | 15.5885i | 0.473684 | + | 0.820445i | ||||
\(362\) | −22.5167 | − | 13.0000i | −1.18345 | − | 0.683265i | ||||
\(363\) | 25.0000i | 1.31216i | ||||||||
\(364\) | −12.0000 | + | 10.3923i | −0.628971 | + | 0.544705i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −14.0000 | + | 24.2487i | −0.731792 | + | 1.26750i | ||||
\(367\) | −16.4545 | + | 9.50000i | −0.858917 | + | 0.495896i | −0.863649 | − | 0.504093i | \(-0.831827\pi\) |
0.00473247 | + | 0.999989i | \(0.498494\pi\) | |||||||
\(368\) | 13.8564 | − | 8.00000i | 0.722315 | − | 0.417029i | ||||
\(369\) | −3.00000 | + | 5.19615i | −0.156174 | + | 0.270501i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.00000 | + | 6.92820i | −0.415339 | + | 0.359694i | ||||
\(372\) | − | 2.00000i | − | 0.103695i | ||||||
\(373\) | −9.52628 | − | 5.50000i | −0.493252 | − | 0.284779i | 0.232671 | − | 0.972556i | \(-0.425254\pi\) |
−0.725923 | + | 0.687776i | \(0.758587\pi\) | |||||||
\(374\) | −24.0000 | − | 41.5692i | −1.24101 | − | 2.14949i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 24.0000i | − | 1.23606i | ||||||
\(378\) | 1.73205 | − | 5.00000i | 0.0890871 | − | 0.257172i | ||||
\(379\) | −11.0000 | −0.565032 | −0.282516 | − | 0.959263i | \(-0.591169\pi\) | ||||
−0.282516 | + | 0.959263i | \(0.591169\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.50000 | − | 4.33013i | −0.128079 | − | 0.221839i | ||||
\(382\) | 17.3205 | − | 10.0000i | 0.886194 | − | 0.511645i | ||||
\(383\) | −24.2487 | − | 14.0000i | −1.23905 | − | 0.715367i | −0.270151 | − | 0.962818i | \(-0.587074\pi\) |
−0.968900 | + | 0.247451i | \(0.920407\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 18.0000 | 0.916176 | ||||||||
\(387\) | 0.866025 | + | 0.500000i | 0.0440225 | + | 0.0254164i | ||||
\(388\) | −10.3923 | + | 6.00000i | −0.527589 | + | 0.304604i | ||||
\(389\) | 3.00000 | + | 5.19615i | 0.152106 | + | 0.263455i | 0.932002 | − | 0.362454i | \(-0.118061\pi\) |
−0.779895 | + | 0.625910i | \(0.784728\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.0000 | 0.809155 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.00000i | 0.100887i | ||||||||
\(394\) | −12.0000 | + | 20.7846i | −0.604551 | + | 1.04711i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 6.00000 | + | 10.3923i | 0.301511 | + | 0.522233i | ||||
\(397\) | −32.0429 | − | 18.5000i | −1.60819 | − | 0.928488i | −0.989775 | − | 0.142636i | \(-0.954442\pi\) |
−0.618414 | − | 0.785853i | \(-0.712224\pi\) | |||||||
\(398\) | − | 16.0000i | − | 0.802008i | ||||||
\(399\) | 0.500000 | + | 2.59808i | 0.0250313 | + | 0.130066i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.00000 | − | 10.3923i | 0.299626 | − | 0.518967i | −0.676425 | − | 0.736512i | \(-0.736472\pi\) |
0.976050 | + | 0.217545i | \(0.0698049\pi\) | |||||||
\(402\) | 12.1244 | − | 7.00000i | 0.604708 | − | 0.349128i | ||||
\(403\) | −2.59808 | + | 1.50000i | −0.129419 | + | 0.0747203i | ||||
\(404\) | −10.0000 | + | 17.3205i | −0.497519 | + | 0.861727i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 40.0000 | + | 13.8564i | 1.98517 | + | 0.687682i | ||||
\(407\) | 42.0000i | 2.08186i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.50000 | + | 4.33013i | 0.123617 | + | 0.214111i | 0.921192 | − | 0.389109i | \(-0.127217\pi\) |
−0.797574 | + | 0.603220i | \(0.793884\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.00000 | + | 6.92820i | −0.197305 | + | 0.341743i | ||||
\(412\) | 38.0000i | 1.87213i | ||||||||
\(413\) | 13.8564 | + | 16.0000i | 0.681829 | + | 0.787309i | ||||
\(414\) | −8.00000 | −0.393179 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 12.0000 | + | 20.7846i | 0.588348 | + | 1.01905i | ||||
\(417\) | −18.1865 | + | 10.5000i | −0.890598 | + | 0.514187i | ||||
\(418\) | −10.3923 | − | 6.00000i | −0.508304 | − | 0.293470i | ||||
\(419\) | −6.00000 | −0.293119 | −0.146560 | − | 0.989202i | \(-0.546820\pi\) | ||||
−0.146560 | + | 0.989202i | \(0.546820\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.00000 | 0.0487370 | 0.0243685 | − | 0.999703i | \(-0.492242\pi\) | ||||
0.0243685 | + | 0.999703i | \(0.492242\pi\) | |||||||
\(422\) | 34.6410 | + | 20.0000i | 1.68630 | + | 0.973585i | ||||
\(423\) | 1.73205 | − | 1.00000i | 0.0842152 | − | 0.0486217i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −12.0000 | −0.581402 | ||||||||
\(427\) | −12.1244 | + | 35.0000i | −0.586739 | + | 1.69377i | ||||
\(428\) | 24.0000i | 1.16008i | ||||||||
\(429\) | 9.00000 | − | 15.5885i | 0.434524 | − | 0.752618i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.00000 | + | 1.73205i | 0.0481683 | + | 0.0834300i | 0.889104 | − | 0.457705i | \(-0.151328\pi\) |
−0.840936 | + | 0.541135i | \(0.817995\pi\) | |||||||
\(432\) | −3.46410 | − | 2.00000i | −0.166667 | − | 0.0962250i | ||||
\(433\) | − | 5.00000i | − | 0.240285i | −0.992757 | − | 0.120142i | \(-0.961665\pi\) | ||
0.992757 | − | 0.120142i | \(-0.0383351\pi\) | |||||||
\(434\) | −1.00000 | − | 5.19615i | −0.0480015 | − | 0.249423i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 15.0000 | − | 25.9808i | 0.718370 | − | 1.24425i | ||||
\(437\) | 3.46410 | − | 2.00000i | 0.165710 | − | 0.0956730i | ||||
\(438\) | −1.73205 | + | 1.00000i | −0.0827606 | + | 0.0477818i | ||||
\(439\) | 8.00000 | − | 13.8564i | 0.381819 | − | 0.661330i | −0.609503 | − | 0.792784i | \(-0.708631\pi\) |
0.991322 | + | 0.131453i | \(0.0419644\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | − | 6.92820i | 0.0476190 | − | 0.329914i | ||||
\(442\) | 24.0000i | 1.14156i | ||||||||
\(443\) | 31.1769 | + | 18.0000i | 1.48126 | + | 0.855206i | 0.999774 | − | 0.0212481i | \(-0.00676401\pi\) |
0.481486 | + | 0.876454i | \(0.340097\pi\) | |||||||
\(444\) | 7.00000 | + | 12.1244i | 0.332205 | + | 0.575396i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −24.0000 | + | 41.5692i | −1.13643 | + | 1.96836i | ||||
\(447\) | 4.00000i | 0.189194i | ||||||||
\(448\) | −20.7846 | + | 4.00000i | −0.981981 | + | 0.188982i | ||||
\(449\) | −30.0000 | −1.41579 | −0.707894 | − | 0.706319i | \(-0.750354\pi\) | ||||
−0.707894 | + | 0.706319i | \(0.750354\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.0000 | − | 31.1769i | −0.847587 | − | 1.46806i | ||||
\(452\) | 10.3923 | − | 6.00000i | 0.488813 | − | 0.282216i | ||||
\(453\) | −6.92820 | − | 4.00000i | −0.325515 | − | 0.187936i | ||||
\(454\) | −20.0000 | −0.938647 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.9904 | − | 7.50000i | −0.607664 | − | 0.350835i | 0.164386 | − | 0.986396i | \(-0.447436\pi\) |
−0.772051 | + | 0.635561i | \(0.780769\pi\) | |||||||
\(458\) | −22.5167 | + | 13.0000i | −1.05213 | + | 0.607450i | ||||
\(459\) | −2.00000 | − | 3.46410i | −0.0933520 | − | 0.161690i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.00000 | −0.372597 | −0.186299 | − | 0.982493i | \(-0.559649\pi\) | ||||
−0.186299 | + | 0.982493i | \(0.559649\pi\) | |||||||
\(462\) | 20.7846 | + | 24.0000i | 0.966988 | + | 1.11658i | ||||
\(463\) | 3.00000i | 0.139422i | 0.997567 | + | 0.0697109i | \(0.0222077\pi\) | ||||
−0.997567 | + | 0.0697109i | \(0.977792\pi\) | |||||||
\(464\) | 16.0000 | − | 27.7128i | 0.742781 | − | 1.28654i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.00000 | + | 10.3923i | 0.277945 | + | 0.481414i | ||||
\(467\) | 19.0526 | + | 11.0000i | 0.881647 | + | 0.509019i | 0.871201 | − | 0.490926i | \(-0.163342\pi\) |
0.0104461 | + | 0.999945i | \(0.496675\pi\) | |||||||
\(468\) | − | 6.00000i | − | 0.277350i | ||||||
\(469\) | 14.0000 | − | 12.1244i | 0.646460 | − | 0.559851i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.00000 | + | 8.66025i | −0.230388 | + | 0.399043i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.19615 | + | 3.00000i | −0.238919 | + | 0.137940i | ||||
\(474\) | 1.00000 | − | 1.73205i | 0.0459315 | − | 0.0795557i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −20.0000 | − | 6.92820i | −0.916698 | − | 0.317554i | ||||
\(477\) | − | 4.00000i | − | 0.183147i | ||||||
\(478\) | 24.2487 | + | 14.0000i | 1.10911 | + | 0.640345i | ||||
\(479\) | −2.00000 | − | 3.46410i | −0.0913823 | − | 0.158279i | 0.816711 | − | 0.577047i | \(-0.195795\pi\) |
−0.908093 | + | 0.418769i | \(0.862462\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.5000 | − | 18.1865i | 0.478759 | − | 0.829235i | ||||
\(482\) | − | 36.0000i | − | 1.63976i | ||||||
\(483\) | −10.3923 | + | 2.00000i | −0.472866 | + | 0.0910032i | ||||
\(484\) | −50.0000 | −2.27273 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | + | 1.73205i | 0.0453609 | + | 0.0785674i | ||||
\(487\) | 11.2583 | − | 6.50000i | 0.510164 | − | 0.294543i | −0.222737 | − | 0.974879i | \(-0.571499\pi\) |
0.732901 | + | 0.680335i | \(0.238166\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.0000 | 0.542659 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.0000 | −0.541552 | −0.270776 | − | 0.962642i | \(-0.587280\pi\) | ||||
−0.270776 | + | 0.962642i | \(0.587280\pi\) | |||||||
\(492\) | −10.3923 | − | 6.00000i | −0.468521 | − | 0.270501i | ||||
\(493\) | 27.7128 | − | 16.0000i | 1.24812 | − | 0.720604i | ||||
\(494\) | 3.00000 | + | 5.19615i | 0.134976 | + | 0.233786i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | −15.5885 | + | 3.00000i | −0.699238 | + | 0.134568i | ||||
\(498\) | − | 4.00000i | − | 0.179244i | ||||||
\(499\) | 14.5000 | − | 25.1147i | 0.649109 | − | 1.12429i | −0.334227 | − | 0.942493i | \(-0.608475\pi\) |
0.983336 | − | 0.181797i | \(-0.0581915\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.00000 | + | 8.66025i | 0.223384 | + | 0.386912i | ||||
\(502\) | −20.7846 | − | 12.0000i | −0.927663 | − | 0.535586i | ||||
\(503\) | − | 2.00000i | − | 0.0891756i | −0.999005 | − | 0.0445878i | \(-0.985803\pi\) | ||
0.999005 | − | 0.0445878i | \(-0.0141974\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 24.0000 | − | 41.5692i | 1.06693 | − | 1.84798i | ||||
\(507\) | 3.46410 | − | 2.00000i | 0.153846 | − | 0.0888231i | ||||
\(508\) | 8.66025 | − | 5.00000i | 0.384237 | − | 0.221839i | ||||
\(509\) | 5.00000 | − | 8.66025i | 0.221621 | − | 0.383859i | −0.733679 | − | 0.679496i | \(-0.762199\pi\) |
0.955300 | + | 0.295637i | \(0.0955319\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.00000 | + | 1.73205i | −0.0884748 | + | 0.0766214i | ||||
\(512\) | 32.0000i | 1.41421i | ||||||||
\(513\) | −0.866025 | − | 0.500000i | −0.0382360 | − | 0.0220755i | ||||
\(514\) | 18.0000 | + | 31.1769i | 0.793946 | + | 1.37515i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.00000 | + | 1.73205i | −0.0440225 | + | 0.0762493i | ||||
\(517\) | 12.0000i | 0.527759i | ||||||||
\(518\) | 24.2487 | + | 28.0000i | 1.06543 | + | 1.23025i | ||||
\(519\) | −24.0000 | −1.05348 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.00000 | − | 3.46410i | −0.0876216 | − | 0.151765i | 0.818884 | − | 0.573959i | \(-0.194593\pi\) |
−0.906505 | + | 0.422194i | \(0.861260\pi\) | |||||||
\(522\) | −13.8564 | + | 8.00000i | −0.606478 | + | 0.350150i | ||||
\(523\) | −9.52628 | − | 5.50000i | −0.416555 | − | 0.240498i | 0.277047 | − | 0.960856i | \(-0.410644\pi\) |
−0.693602 | + | 0.720358i | \(0.743977\pi\) | |||||||
\(524\) | −4.00000 | −0.174741 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.00000 | −0.348817 | ||||||||
\(527\) | −3.46410 | − | 2.00000i | −0.150899 | − | 0.0871214i | ||||
\(528\) | 20.7846 | − | 12.0000i | 0.904534 | − | 0.522233i | ||||
\(529\) | −3.50000 | − | 6.06218i | −0.152174 | − | 0.263573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.00000 | −0.347170 | ||||||||
\(532\) | −5.19615 | + | 1.00000i | −0.225282 | + | 0.0433555i | ||||
\(533\) | 18.0000i | 0.779667i | ||||||||
\(534\) | 12.0000 | − | 20.7846i | 0.519291 | − | 0.899438i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.5885 | + | 9.00000i | 0.672692 | + | 0.388379i | ||||
\(538\) | 20.0000i | 0.862261i | ||||||||
\(539\) | 33.0000 | + | 25.9808i | 1.42141 | + | 1.11907i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.50000 | − | 2.59808i | 0.0644900 | − | 0.111700i | −0.831978 | − | 0.554809i | \(-0.812791\pi\) |
0.896468 | + | 0.443109i | \(0.146125\pi\) | |||||||
\(542\) | −41.5692 | + | 24.0000i | −1.78555 | + | 1.03089i | ||||
\(543\) | 11.2583 | − | 6.50000i | 0.483141 | − | 0.278942i | ||||
\(544\) | −16.0000 | + | 27.7128i | −0.685994 | + | 1.18818i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3.00000 | − | 15.5885i | −0.128388 | − | 0.667124i | ||||
\(547\) | − | 36.0000i | − | 1.53925i | −0.638497 | − | 0.769624i | \(-0.720443\pi\) | ||
0.638497 | − | 0.769624i | \(-0.279557\pi\) | |||||||
\(548\) | −13.8564 | − | 8.00000i | −0.591916 | − | 0.341743i | ||||
\(549\) | −7.00000 | − | 12.1244i | −0.298753 | − | 0.517455i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.00000 | − | 6.92820i | 0.170406 | − | 0.295151i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.866025 | − | 2.50000i | 0.0368271 | − | 0.106311i | ||||
\(554\) | −14.0000 | −0.594803 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −21.0000 | − | 36.3731i | −0.890598 | − | 1.54256i | ||||
\(557\) | 8.66025 | − | 5.00000i | 0.366947 | − | 0.211857i | −0.305177 | − | 0.952296i | \(-0.598716\pi\) |
0.672124 | + | 0.740439i | \(0.265382\pi\) | |||||||
\(558\) | 1.73205 | + | 1.00000i | 0.0733236 | + | 0.0423334i | ||||
\(559\) | 3.00000 | 0.126886 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 24.0000 | 1.01328 | ||||||||
\(562\) | 20.7846 | + | 12.0000i | 0.876746 | + | 0.506189i | ||||
\(563\) | −22.5167 | + | 13.0000i | −0.948964 | + | 0.547885i | −0.892759 | − | 0.450535i | \(-0.851233\pi\) |
−0.0562051 | + | 0.998419i | \(0.517900\pi\) | |||||||
\(564\) | 2.00000 | + | 3.46410i | 0.0842152 | + | 0.145865i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 14.0000 | 0.588464 | ||||||||
\(567\) | 1.73205 | + | 2.00000i | 0.0727393 | + | 0.0839921i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.00000 | − | 15.5885i | 0.377300 | − | 0.653502i | −0.613369 | − | 0.789797i | \(-0.710186\pi\) |
0.990668 | + | 0.136295i | \(0.0435194\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.50000 | + | 2.59808i | 0.0627730 | + | 0.108726i | 0.895704 | − | 0.444651i | \(-0.146672\pi\) |
−0.832931 | + | 0.553377i | \(0.813339\pi\) | |||||||
\(572\) | 31.1769 | + | 18.0000i | 1.30357 | + | 0.752618i | ||||
\(573\) | 10.0000i | 0.417756i | ||||||||
\(574\) | −30.0000 | − | 10.3923i | −1.25218 | − | 0.433766i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4.00000 | − | 6.92820i | 0.166667 | − | 0.288675i | ||||
\(577\) | 25.1147 | − | 14.5000i | 1.04554 | − | 0.603643i | 0.124143 | − | 0.992264i | \(-0.460382\pi\) |
0.921397 | + | 0.388621i | \(0.127049\pi\) | |||||||
\(578\) | 1.73205 | − | 1.00000i | 0.0720438 | − | 0.0415945i | ||||
\(579\) | −4.50000 | + | 7.79423i | −0.187014 | + | 0.323917i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.00000 | − | 5.19615i | −0.0414870 | − | 0.215573i | ||||
\(582\) | − | 12.0000i | − | 0.497416i | ||||||
\(583\) | 20.7846 | + | 12.0000i | 0.860811 | + | 0.496989i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.0000 | + | 27.7128i | −0.660954 | + | 1.14481i | ||||
\(587\) | − | 12.0000i | − | 0.495293i | −0.968850 | − | 0.247647i | \(-0.920343\pi\) | ||
0.968850 | − | 0.247647i | \(-0.0796572\pi\) | |||||||
\(588\) | 13.8564 | + | 2.00000i | 0.571429 | + | 0.0824786i | ||||
\(589\) | −1.00000 | −0.0412043 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.00000 | − | 10.3923i | −0.246807 | − | 0.427482i | ||||
\(592\) | 24.2487 | − | 14.0000i | 0.996616 | − | 0.575396i | ||||
\(593\) | 15.5885 | + | 9.00000i | 0.640141 | + | 0.369586i | 0.784669 | − | 0.619915i | \(-0.212833\pi\) |
−0.144528 | + | 0.989501i | \(0.546166\pi\) | |||||||
\(594\) | −12.0000 | −0.492366 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.00000 | −0.327693 | ||||||||
\(597\) | 6.92820 | + | 4.00000i | 0.283552 | + | 0.163709i | ||||
\(598\) | −20.7846 | + | 12.0000i | −0.849946 | + | 0.490716i | ||||
\(599\) | −2.00000 | − | 3.46410i | −0.0817178 | − | 0.141539i | 0.822270 | − | 0.569097i | \(-0.192707\pi\) |
−0.903988 | + | 0.427558i | \(0.859374\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.0000 | −1.34610 | −0.673049 | − | 0.739598i | \(-0.735016\pi\) | ||||
−0.673049 | + | 0.739598i | \(0.735016\pi\) | |||||||
\(602\) | −1.73205 | + | 5.00000i | −0.0705931 | + | 0.203785i | ||||
\(603\) | 7.00000i | 0.285062i | ||||||||
\(604\) | 8.00000 | − | 13.8564i | 0.325515 | − | 0.563809i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −10.0000 | − | 17.3205i | −0.406222 | − | 0.703598i | ||||
\(607\) | 30.3109 | + | 17.5000i | 1.23028 | + | 0.710303i | 0.967088 | − | 0.254440i | \(-0.0818912\pi\) |
0.263193 | + | 0.964743i | \(0.415225\pi\) | |||||||
\(608\) | 8.00000i | 0.324443i | ||||||||
\(609\) | −16.0000 | + | 13.8564i | −0.648353 | + | 0.561490i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.00000 | − | 5.19615i | 0.121367 | − | 0.210214i | ||||
\(612\) | 6.92820 | − | 4.00000i | 0.280056 | − | 0.161690i | ||||
\(613\) | −25.9808 | + | 15.0000i | −1.04935 | + | 0.605844i | −0.922468 | − | 0.386073i | \(-0.873831\pi\) |
−0.126885 | + | 0.991917i | \(0.540498\pi\) | |||||||
\(614\) | −3.00000 | + | 5.19615i | −0.121070 | + | 0.209700i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 18.0000i | − | 0.724653i | −0.932051 | − | 0.362326i | \(-0.881983\pi\) | ||
0.932051 | − | 0.362326i | \(-0.118017\pi\) | |||||||
\(618\) | −32.9090 | − | 19.0000i | −1.32379 | − | 0.764292i | ||||
\(619\) | 1.50000 | + | 2.59808i | 0.0602901 | + | 0.104425i | 0.894595 | − | 0.446878i | \(-0.147464\pi\) |
−0.834305 | + | 0.551303i | \(0.814131\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.00000 | − | 3.46410i | 0.0802572 | − | 0.139010i | ||||
\(622\) | 12.0000i | 0.481156i | ||||||||
\(623\) | 10.3923 | − | 30.0000i | 0.416359 | − | 1.20192i | ||||
\(624\) | −12.0000 | −0.480384 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 11.0000 | + | 19.0526i | 0.439648 | + | 0.761493i | ||||
\(627\) | 5.19615 | − | 3.00000i | 0.207514 | − | 0.119808i | ||||
\(628\) | −17.3205 | − | 10.0000i | −0.691164 | − | 0.399043i | ||||
\(629\) | 28.0000 | 1.11643 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.0000 | 0.955425 | 0.477712 | − | 0.878516i | \(-0.341466\pi\) | ||||
0.477712 | + | 0.878516i | \(0.341466\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −17.3205 | + | 10.0000i | −0.688428 | + | 0.397464i | ||||
\(634\) | −20.0000 | − | 34.6410i | −0.794301 | − | 1.37577i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 8.00000 | 0.317221 | ||||||||
\(637\) | −7.79423 | − | 19.5000i | −0.308819 | − | 0.772618i | ||||
\(638\) | − | 96.0000i | − | 3.80068i | ||||||
\(639\) | 3.00000 | − | 5.19615i | 0.118678 | − | 0.205557i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.00000 | − | 10.3923i | −0.236986 | − | 0.410471i | 0.722862 | − | 0.690992i | \(-0.242826\pi\) |
−0.959848 | + | 0.280521i | \(0.909493\pi\) | |||||||
\(642\) | −20.7846 | − | 12.0000i | −0.820303 | − | 0.473602i | ||||
\(643\) | 1.00000i | 0.0394362i | 0.999806 | + | 0.0197181i | \(0.00627687\pi\) | ||||
−0.999806 | + | 0.0197181i | \(0.993723\pi\) | |||||||
\(644\) | −4.00000 | − | 20.7846i | −0.157622 | − | 0.819028i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.00000 | + | 6.92820i | −0.157378 | + | 0.272587i | ||||
\(647\) | −25.9808 | + | 15.0000i | −1.02141 | + | 0.589711i | −0.914512 | − | 0.404559i | \(-0.867425\pi\) |
−0.106897 | + | 0.994270i | \(0.534092\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.0000 | − | 41.5692i | 0.942082 | − | 1.63173i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.50000 | + | 0.866025i | 0.0979827 | + | 0.0339422i | ||||
\(652\) | 24.0000i | 0.939913i | ||||||||
\(653\) | −12.1244 | − | 7.00000i | −0.474463 | − | 0.273931i | 0.243643 | − | 0.969865i | \(-0.421657\pi\) |
−0.718106 | + | 0.695934i | \(0.754991\pi\) | |||||||
\(654\) | 15.0000 | + | 25.9808i | 0.586546 | + | 1.01593i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −12.0000 | + | 20.7846i | −0.468521 | + | 0.811503i | ||||
\(657\) | − | 1.00000i | − | 0.0390137i | ||||||
\(658\) | 6.92820 | + | 8.00000i | 0.270089 | + | 0.311872i | ||||
\(659\) | 12.0000 | 0.467454 | 0.233727 | − | 0.972302i | \(-0.424908\pi\) | ||||
0.233727 | + | 0.972302i | \(0.424908\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.5000 | − | 19.9186i | −0.447298 | − | 0.774743i | 0.550911 | − | 0.834564i | \(-0.314280\pi\) |
−0.998209 | + | 0.0598209i | \(0.980947\pi\) | |||||||
\(662\) | −15.5885 | + | 9.00000i | −0.605863 | + | 0.349795i | ||||
\(663\) | −10.3923 | − | 6.00000i | −0.403604 | − | 0.233021i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −14.0000 | −0.542489 | ||||||||
\(667\) | 27.7128 | + | 16.0000i | 1.07304 | + | 0.619522i | ||||
\(668\) | −17.3205 | + | 10.0000i | −0.670151 | + | 0.386912i | ||||
\(669\) | −12.0000 | − | 20.7846i | −0.463947 | − | 0.803579i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 84.0000 | 3.24278 | ||||||||
\(672\) | 6.92820 | − | 20.0000i | 0.267261 | − | 0.771517i | ||||
\(673\) | − | 37.0000i | − | 1.42625i | −0.701039 | − | 0.713123i | \(-0.747280\pi\) | ||
0.701039 | − | 0.713123i | \(-0.252720\pi\) | |||||||
\(674\) | −25.0000 | + | 43.3013i | −0.962964 | + | 1.66790i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.00000 | + | 6.92820i | 0.153846 | + | 0.266469i | ||||
\(677\) | 13.8564 | + | 8.00000i | 0.532545 | + | 0.307465i | 0.742052 | − | 0.670342i | \(-0.233853\pi\) |
−0.209507 | + | 0.977807i | \(0.567186\pi\) | |||||||
\(678\) | 12.0000i | 0.460857i | ||||||||
\(679\) | −3.00000 | − | 15.5885i | −0.115129 | − | 0.598230i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.00000 | − | 8.66025i | 0.191600 | − | 0.331862i | ||||
\(682\) | −10.3923 | + | 6.00000i | −0.397942 | + | 0.229752i | ||||
\(683\) | −41.5692 | + | 24.0000i | −1.59060 | + | 0.918334i | −0.597398 | + | 0.801945i | \(0.703799\pi\) |
−0.993204 | + | 0.116390i | \(0.962868\pi\) | |||||||
\(684\) | 1.00000 | − | 1.73205i | 0.0382360 | − | 0.0662266i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 37.0000 | − | 1.73205i | 1.41267 | − | 0.0661300i | ||||
\(687\) | − | 13.0000i | − | 0.495981i | ||||||
\(688\) | 3.46410 | + | 2.00000i | 0.132068 | + | 0.0762493i | ||||
\(689\) | −6.00000 | − | 10.3923i | −0.228582 | − | 0.395915i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.5000 | + | 23.3827i | −0.513564 | + | 0.889519i | 0.486312 | + | 0.873785i | \(0.338342\pi\) |
−0.999876 | + | 0.0157341i | \(0.994991\pi\) | |||||||
\(692\) | − | 48.0000i | − | 1.82469i | ||||||
\(693\) | −15.5885 | + | 3.00000i | −0.592157 | + | 0.113961i | ||||
\(694\) | 32.0000 | 1.21470 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.7846 | + | 12.0000i | −0.787273 | + | 0.454532i | ||||
\(698\) | 3.46410 | + | 2.00000i | 0.131118 | + | 0.0757011i | ||||
\(699\) | −6.00000 | −0.226941 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −44.0000 | −1.66186 | −0.830929 | − | 0.556379i | \(-0.812190\pi\) | ||||
−0.830929 | + | 0.556379i | \(0.812190\pi\) | |||||||
\(702\) | 5.19615 | + | 3.00000i | 0.196116 | + | 0.113228i | ||||
\(703\) | 6.06218 | − | 3.50000i | 0.228639 | − | 0.132005i | ||||
\(704\) | 24.0000 | + | 41.5692i | 0.904534 | + | 1.56670i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 36.0000 | 1.35488 | ||||||||
\(707\) | −17.3205 | − | 20.0000i | −0.651405 | − | 0.752177i | ||||
\(708\) | − | 16.0000i | − | 0.601317i | ||||||
\(709\) | −13.0000 | + | 22.5167i | −0.488225 | + | 0.845631i | −0.999908 | − | 0.0135434i | \(-0.995689\pi\) |
0.511683 | + | 0.859174i | \(0.329022\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.500000 | + | 0.866025i | 0.0187515 | + | 0.0324785i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 4.00000i | − | 0.149801i | ||||||
\(714\) | 16.0000 | − | 13.8564i | 0.598785 | − | 0.518563i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −18.0000 | + | 31.1769i | −0.672692 | + | 1.16514i | ||||
\(717\) | −12.1244 | + | 7.00000i | −0.452792 | + | 0.261420i | ||||
\(718\) | 41.5692 | − | 24.0000i | 1.55135 | − | 0.895672i | ||||
\(719\) | −17.0000 | + | 29.4449i | −0.633993 | + | 1.09811i | 0.352735 | + | 0.935723i | \(0.385252\pi\) |
−0.986728 | + | 0.162385i | \(0.948081\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −47.5000 | − | 16.4545i | −1.76899 | − | 0.612797i | ||||
\(722\) | − | 36.0000i | − | 1.33978i | ||||||
\(723\) | 15.5885 | + | 9.00000i | 0.579741 | + | 0.334714i | ||||
\(724\) | 13.0000 | + | 22.5167i | 0.483141 | + | 0.836825i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 25.0000 | − | 43.3013i | 0.927837 | − | 1.60706i | ||||
\(727\) | − | 7.00000i | − | 0.259616i | −0.991539 | − | 0.129808i | \(-0.958564\pi\) | ||
0.991539 | − | 0.129808i | \(-0.0414360\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.00000 | + | 3.46410i | 0.0739727 | + | 0.128124i | ||||
\(732\) | 24.2487 | − | 14.0000i | 0.896258 | − | 0.517455i | ||||
\(733\) | 37.2391 | + | 21.5000i | 1.37546 | + | 0.794121i | 0.991609 | − | 0.129275i | \(-0.0412651\pi\) |
0.383849 | + | 0.923396i | \(0.374598\pi\) | |||||||
\(734\) | 38.0000 | 1.40261 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −32.0000 | −1.17954 | ||||||||
\(737\) | −36.3731 | − | 21.0000i | −1.33982 | − | 0.773545i | ||||
\(738\) | 10.3923 | − | 6.00000i | 0.382546 | − | 0.220863i | ||||
\(739\) | 20.5000 | + | 35.5070i | 0.754105 | + | 1.30615i | 0.945818 | + | 0.324697i | \(0.105262\pi\) |
−0.191714 | + | 0.981451i | \(0.561404\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.00000 | −0.110208 | ||||||||
\(742\) | 20.7846 | − | 4.00000i | 0.763027 | − | 0.146845i | ||||
\(743\) | 6.00000i | 0.220119i | 0.993925 | + | 0.110059i | \(0.0351041\pi\) | ||||
−0.993925 | + | 0.110059i | \(0.964896\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 11.0000 | + | 19.0526i | 0.402739 | + | 0.697564i | ||||
\(747\) | 1.73205 | + | 1.00000i | 0.0633724 | + | 0.0365881i | ||||
\(748\) | 48.0000i | 1.75505i | ||||||||
\(749\) | −30.0000 | − | 10.3923i | −1.09618 | − | 0.379727i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.5000 | + | 25.1147i | −0.529113 | + | 0.916450i | 0.470311 | + | 0.882501i | \(0.344142\pi\) |
−0.999424 | + | 0.0339490i | \(0.989192\pi\) | |||||||
\(752\) | 6.92820 | − | 4.00000i | 0.252646 | − | 0.145865i | ||||
\(753\) | 10.3923 | − | 6.00000i | 0.378717 | − | 0.218652i | ||||
\(754\) | −24.0000 | + | 41.5692i | −0.874028 | + | 1.51386i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.00000 | + | 3.46410i | −0.145479 | + | 0.125988i | ||||
\(757\) | 22.0000i | 0.799604i | 0.916602 | + | 0.399802i | \(0.130921\pi\) | ||||
−0.916602 | + | 0.399802i | \(0.869079\pi\) | |||||||
\(758\) | 19.0526 | + | 11.0000i | 0.692020 | + | 0.399538i | ||||
\(759\) | 12.0000 | + | 20.7846i | 0.435572 | + | 0.754434i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.00000 | − | 10.3923i | 0.217500 | − | 0.376721i | −0.736543 | − | 0.676391i | \(-0.763543\pi\) |
0.954043 | + | 0.299670i | \(0.0968765\pi\) | |||||||
\(762\) | 10.0000i | 0.362262i | ||||||||
\(763\) | 25.9808 | + | 30.0000i | 0.940567 | + | 1.08607i | ||||
\(764\) | −20.0000 | −0.723575 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 28.0000 | + | 48.4974i | 1.01168 | + | 1.75228i | ||||
\(767\) | −20.7846 | + | 12.0000i | −0.750489 | + | 0.433295i | ||||
\(768\) | −13.8564 | − | 8.00000i | −0.500000 | − | 0.288675i | ||||
\(769\) | 49.0000 | 1.76699 | 0.883493 | − | 0.468445i | \(-0.155186\pi\) | ||||
0.883493 | + | 0.468445i | \(0.155186\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.0000 | −0.648254 | ||||||||
\(772\) | −15.5885 | − | 9.00000i | −0.561041 | − | 0.323917i | ||||
\(773\) | 15.5885 | − | 9.00000i | 0.560678 | − | 0.323708i | −0.192740 | − | 0.981250i | \(-0.561737\pi\) |
0.753418 | + | 0.657542i | \(0.228404\pi\) | |||||||
\(774\) | −1.00000 | − | 1.73205i | −0.0359443 | − | 0.0622573i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −18.1865 | + | 3.50000i | −0.652438 | + | 0.125562i | ||||
\(778\) | − | 12.0000i | − | 0.430221i | ||||||
\(779\) | −3.00000 | + | 5.19615i | −0.107486 | + | 0.186171i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.0000 | + | 31.1769i | 0.644091 | + | 1.11560i | ||||
\(782\) | −27.7128 | − | 16.0000i | −0.991008 | − | 0.572159i | ||||
\(783\) | − | 8.00000i | − | 0.285897i | ||||||
\(784\) | 4.00000 | − | 27.7128i | 0.142857 | − | 0.989743i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2.00000 | − | 3.46410i | 0.0713376 | − | 0.123560i | ||||
\(787\) | 27.7128 | − | 16.0000i | 0.987855 | − | 0.570338i | 0.0832226 | − | 0.996531i | \(-0.473479\pi\) |
0.904632 | + | 0.426193i | \(0.140145\pi\) | |||||||
\(788\) | 20.7846 | − | 12.0000i | 0.740421 | − | 0.427482i | ||||
\(789\) | 2.00000 | − | 3.46410i | 0.0712019 | − | 0.123325i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.00000 | + | 15.5885i | 0.106668 | + | 0.554262i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −36.3731 | − | 21.0000i | −1.29165 | − | 0.745732i | ||||
\(794\) | 37.0000 | + | 64.0859i | 1.31308 | + | 2.27432i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.00000 | + | 13.8564i | −0.283552 | + | 0.491127i | ||||
\(797\) | 36.0000i | 1.27519i | 0.770374 | + | 0.637593i | \(0.220070\pi\) | ||||
−0.770374 | + | 0.637593i | \(0.779930\pi\) | |||||||
\(798\) | 1.73205 | − | 5.00000i | 0.0613139 | − | 0.176998i | ||||
\(799\) | 8.00000 | 0.283020 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.00000 | + | 10.3923i | 0.212000 | + | 0.367194i | ||||
\(802\) | −20.7846 | + | 12.0000i | −0.733930 | + | 0.423735i | ||||
\(803\) | 5.19615 | + | 3.00000i | 0.183368 | + | 0.105868i | ||||
\(804\) | −14.0000 | −0.493742 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.00000 | 0.211341 | ||||||||
\(807\) | −8.66025 | − | 5.00000i | −0.304855 | − | 0.176008i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −21.0000 | − | 36.3731i | −0.738321 | − | 1.27881i | −0.953251 | − | 0.302180i | \(-0.902286\pi\) |
0.214930 | − | 0.976629i | \(-0.431048\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −48.0000 | −1.68551 | −0.842754 | − | 0.538299i | \(-0.819067\pi\) | ||||
−0.842754 | + | 0.538299i | \(0.819067\pi\) | |||||||
\(812\) | −27.7128 | − | 32.0000i | −0.972529 | − | 1.12298i | ||||
\(813\) | − | 24.0000i | − | 0.841717i | ||||||
\(814\) | 42.0000 | − | 72.7461i | 1.47210 | − | 2.54975i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −8.00000 | − | 13.8564i | −0.280056 | − | 0.485071i | ||||
\(817\) | 0.866025 | + | 0.500000i | 0.0302984 | + | 0.0174928i | ||||
\(818\) | − | 10.0000i | − | 0.349642i | ||||||
\(819\) | 7.50000 | + | 2.59808i | 0.262071 | + | 0.0907841i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.0000 | + | 46.7654i | −0.942306 | + | 1.63212i | −0.181250 | + | 0.983437i | \(0.558014\pi\) |
−0.761056 | + | 0.648686i | \(0.775319\pi\) | |||||||
\(822\) | 13.8564 | − | 8.00000i | 0.483298 | − | 0.279032i | ||||
\(823\) | 6.92820 | − | 4.00000i | 0.241502 | − | 0.139431i | −0.374365 | − | 0.927281i | \(-0.622139\pi\) |
0.615867 | + | 0.787850i | \(0.288806\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.00000 | − | 41.5692i | −0.278356 | − | 1.44638i | ||||
\(827\) | 30.0000i | 1.04320i | 0.853189 | + | 0.521601i | \(0.174665\pi\) | ||||
−0.853189 | + | 0.521601i | \(0.825335\pi\) | |||||||
\(828\) | 6.92820 | + | 4.00000i | 0.240772 | + | 0.139010i | ||||
\(829\) | 28.5000 | + | 49.3634i | 0.989846 | + | 1.71446i | 0.618024 | + | 0.786159i | \(0.287934\pi\) |
0.371822 | + | 0.928304i | \(0.378733\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.50000 | − | 6.06218i | 0.121414 | − | 0.210295i | ||||
\(832\) | − | 24.0000i | − | 0.832050i | ||||||
\(833\) | 17.3205 | − | 22.0000i | 0.600120 | − | 0.762255i | ||||
\(834\) | 42.0000 | 1.45434 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.00000 | + | 10.3923i | 0.207514 | + | 0.359425i | ||||
\(837\) | −0.866025 | + | 0.500000i | −0.0299342 | + | 0.0172825i | ||||
\(838\) | 10.3923 | + | 6.00000i | 0.358996 | + | 0.207267i | ||||
\(839\) | −24.0000 | −0.828572 | −0.414286 | − | 0.910147i | \(-0.635969\pi\) | ||||
−0.414286 | + | 0.910147i | \(0.635969\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 35.0000 | 1.20690 | ||||||||
\(842\) | −1.73205 | − | 1.00000i | −0.0596904 | − | 0.0344623i | ||||
\(843\) | −10.3923 | + | 6.00000i | −0.357930 | + | 0.206651i | ||||
\(844\) | −20.0000 | − | 34.6410i | −0.688428 | − | 1.19239i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.00000 | −0.137523 | ||||||||
\(847\) | 21.6506 | − | 62.5000i | 0.743925 | − | 2.14753i | ||||
\(848\) | − | 16.0000i | − | 0.549442i | ||||||
\(849\) | −3.50000 | + | 6.06218i | −0.120120 | + | 0.208053i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.0000 | + | 24.2487i | 0.479914 | + | 0.831235i | ||||
\(852\) | 10.3923 | + | 6.00000i | 0.356034 | + | 0.205557i | ||||
\(853\) | − | 9.00000i | − | 0.308154i | −0.988059 | − | 0.154077i | \(-0.950760\pi\) | ||
0.988059 | − | 0.154077i | \(-0.0492404\pi\) | |||||||
\(854\) | 56.0000 | − | 48.4974i | 1.91628 | − | 1.65955i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.3923 | − | 6.00000i | 0.354994 | − | 0.204956i | −0.311888 | − | 0.950119i | \(-0.600962\pi\) |
0.666883 | + | 0.745163i | \(0.267628\pi\) | |||||||
\(858\) | −31.1769 | + | 18.0000i | −1.06436 | + | 0.614510i | ||||
\(859\) | −20.0000 | + | 34.6410i | −0.682391 | + | 1.18194i | 0.291858 | + | 0.956462i | \(0.405727\pi\) |
−0.974249 | + | 0.225475i | \(0.927607\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.0000 | − | 10.3923i | 0.408959 | − | 0.354169i | ||||
\(862\) | − | 4.00000i | − | 0.136241i | ||||||
\(863\) | 5.19615 | + | 3.00000i | 0.176879 | + | 0.102121i | 0.585826 | − | 0.810437i | \(-0.300770\pi\) |
−0.408946 | + | 0.912558i | \(0.634104\pi\) | |||||||
\(864\) | 4.00000 | + | 6.92820i | 0.136083 | + | 0.235702i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −5.00000 | + | 8.66025i | −0.169907 | + | 0.294287i | ||||
\(867\) | 1.00000i | 0.0339618i | ||||||||
\(868\) | −1.73205 | + | 5.00000i | −0.0587896 | + | 0.169711i | ||||
\(869\) | −6.00000 | −0.203536 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.5000 | + | 18.1865i | 0.355779 | + | 0.616227i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.19615 | + | 3.00000i | 0.175863 | + | 0.101535i | ||||
\(874\) | −8.00000 | −0.270604 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.00000 | 0.0675737 | ||||||||
\(877\) | −19.0526 | − | 11.0000i | −0.643359 | − | 0.371444i | 0.142548 | − | 0.989788i | \(-0.454470\pi\) |
−0.785907 | + | 0.618344i | \(0.787804\pi\) | |||||||
\(878\) | −27.7128 | + | 16.0000i | −0.935262 | + | 0.539974i | ||||
\(879\) | −8.00000 | − | 13.8564i | −0.269833 | − | 0.467365i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | −8.66025 | + | 11.0000i | −0.291606 | + | 0.370389i | ||||
\(883\) | 7.00000i | 0.235569i | 0.993039 | + | 0.117784i | \(0.0375792\pi\) | ||||
−0.993039 | + | 0.117784i | \(0.962421\pi\) | |||||||
\(884\) | 12.0000 | − | 20.7846i | 0.403604 | − | 0.699062i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −36.0000 | − | 62.3538i | −1.20944 | − | 2.09482i | ||||
\(887\) | 8.66025 | + | 5.00000i | 0.290783 | + | 0.167884i | 0.638295 | − | 0.769792i | \(-0.279640\pi\) |
−0.347512 | + | 0.937676i | \(0.612973\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.50000 | + | 12.9904i | 0.0838473 | + | 0.435683i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.00000 | − | 5.19615i | 0.100504 | − | 0.174078i | ||||
\(892\) | 41.5692 | − | 24.0000i | 1.39184 | − | 0.803579i | ||||
\(893\) | 1.73205 | − | 1.00000i | 0.0579609 | − | 0.0334637i | ||||
\(894\) | 4.00000 | − | 6.92820i | 0.133780 | − | 0.231714i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 12.0000i | − | 0.400668i | ||||||
\(898\) | 51.9615 | + | 30.0000i | 1.73398 | + | 1.00111i | ||||
\(899\) | −4.00000 | − | 6.92820i | −0.133407 | − | 0.231069i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.00000 | − | 13.8564i | 0.266519 | − | 0.461624i | ||||
\(902\) | 72.0000i | 2.39734i | ||||||||
\(903\) | −1.73205 | − | 2.00000i | −0.0576390 | − | 0.0665558i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 8.00000 | + | 13.8564i | 0.265782 | + | 0.460348i | ||||
\(907\) | −26.8468 | + | 15.5000i | −0.891433 | + | 0.514669i | −0.874411 | − | 0.485186i | \(-0.838752\pi\) |
−0.0170220 | + | 0.999855i | \(0.505419\pi\) | |||||||
\(908\) | 17.3205 | + | 10.0000i | 0.574801 | + | 0.331862i | ||||
\(909\) | 10.0000 | 0.331679 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.0000 | 0.397578 | 0.198789 | − | 0.980042i | \(-0.436299\pi\) | ||||
0.198789 | + | 0.980042i | \(0.436299\pi\) | |||||||
\(912\) | −3.46410 | − | 2.00000i | −0.114708 | − | 0.0662266i | ||||
\(913\) | −10.3923 | + | 6.00000i | −0.343935 | + | 0.198571i | ||||
\(914\) | 15.0000 | + | 25.9808i | 0.496156 | + | 0.859367i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 26.0000 | 0.859064 | ||||||||
\(917\) | 1.73205 | − | 5.00000i | 0.0571974 | − | 0.165115i | ||||
\(918\) | 8.00000i | 0.264039i | ||||||||
\(919\) | −4.50000 | + | 7.79423i | −0.148441 | + | 0.257108i | −0.930652 | − | 0.365907i | \(-0.880759\pi\) |
0.782210 | + | 0.623015i | \(0.214092\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.50000 | − | 2.59808i | −0.0494267 | − | 0.0856095i | ||||
\(922\) | 13.8564 | + | 8.00000i | 0.456336 | + | 0.263466i | ||||
\(923\) | − | 18.0000i | − | 0.592477i | ||||||
\(924\) | −6.00000 | − | 31.1769i | −0.197386 | − | 1.02565i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.00000 | − | 5.19615i | 0.0985861 | − | 0.170756i | ||||
\(927\) | 16.4545 | − | 9.50000i | 0.540436 | − | 0.312021i | ||||
\(928\) | −55.4256 | + | 32.0000i | −1.81944 | + | 1.05045i | ||||
\(929\) | −7.00000 | + | 12.1244i | −0.229663 | + | 0.397787i | −0.957708 | − | 0.287742i | \(-0.907096\pi\) |
0.728046 | + | 0.685529i | \(0.240429\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.00000 | − | 6.92820i | 0.0327737 | − | 0.227063i | ||||
\(932\) | − | 12.0000i | − | 0.393073i | ||||||
\(933\) | −5.19615 | − | 3.00000i | −0.170114 | − | 0.0982156i | ||||
\(934\) | −22.0000 | − | 38.1051i | −0.719862 | − | 1.24684i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.0000i | 0.947389i | 0.880689 | + | 0.473694i | \(0.157080\pi\) | ||||
−0.880689 | + | 0.473694i | \(0.842920\pi\) | |||||||
\(938\) | −36.3731 | + | 7.00000i | −1.18762 | + | 0.228558i | ||||
\(939\) | −11.0000 | −0.358971 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(942\) | 17.3205 | − | 10.0000i | 0.564333 | − | 0.325818i | ||||
\(943\) | −20.7846 | − | 12.0000i | −0.676840 | − | 0.390774i | ||||
\(944\) | −32.0000 | −1.04151 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.0000 | 0.390154 | ||||||||
\(947\) | 22.5167 | + | 13.0000i | 0.731693 | + | 0.422443i | 0.819041 | − | 0.573735i | \(-0.194506\pi\) |
−0.0873481 | + | 0.996178i | \(0.527839\pi\) | |||||||
\(948\) | −1.73205 | + | 1.00000i | −0.0562544 | + | 0.0324785i | ||||
\(949\) | −1.50000 | − | 2.59808i | −0.0486921 | − | 0.0843371i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20.0000 | 0.648544 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.00000i | 0.129573i | 0.997899 | + | 0.0647864i | \(0.0206366\pi\) | ||||
−0.997899 | + | 0.0647864i | \(0.979363\pi\) | |||||||
\(954\) | −4.00000 | + | 6.92820i | −0.129505 | + | 0.224309i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −14.0000 | − | 24.2487i | −0.452792 | − | 0.784259i | ||||
\(957\) | 41.5692 | + | 24.0000i | 1.34374 | + | 0.775810i | ||||
\(958\) | 8.00000i | 0.258468i | ||||||||
\(959\) | 16.0000 | − | 13.8564i | 0.516667 | − | 0.447447i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.0000 | − | 25.9808i | 0.483871 | − | 0.838089i | ||||
\(962\) | −36.3731 | + | 21.0000i | −1.17271 | + | 0.677067i | ||||
\(963\) | 10.3923 | − | 6.00000i | 0.334887 | − | 0.193347i | ||||
\(964\) | −18.0000 | + | 31.1769i | −0.579741 | + | 1.00414i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 20.0000 | + | 6.92820i | 0.643489 | + | 0.222911i | ||||
\(967\) | − | 55.0000i | − | 1.76868i | −0.466843 | − | 0.884340i | \(-0.654609\pi\) | ||
0.466843 | − | 0.884340i | \(-0.345391\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.00000 | − | 3.46410i | −0.0642493 | − | 0.111283i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.0000 | − | 45.0333i | 0.834380 | − | 1.44519i | −0.0601548 | − | 0.998189i | \(-0.519159\pi\) |
0.894534 | − | 0.446999i | \(-0.147507\pi\) | |||||||
\(972\) | − | 2.00000i | − | 0.0641500i | ||||||
\(973\) | 54.5596 | − | 10.5000i | 1.74910 | − | 0.336615i | ||||
\(974\) | −26.0000 | −0.833094 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −28.0000 | − | 48.4974i | −0.896258 | − | 1.55236i | ||||
\(977\) | 19.0526 | − | 11.0000i | 0.609545 | − | 0.351921i | −0.163242 | − | 0.986586i | \(-0.552195\pi\) |
0.772787 | + | 0.634665i | \(0.218862\pi\) | |||||||
\(978\) | −20.7846 | − | 12.0000i | −0.664619 | − | 0.383718i | ||||
\(979\) | −72.0000 | −2.30113 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.0000 | −0.478913 | ||||||||
\(982\) | 20.7846 | + | 12.0000i | 0.663264 | + | 0.382935i | ||||
\(983\) | 27.7128 | − | 16.0000i | 0.883901 | − | 0.510321i | 0.0119587 | − | 0.999928i | \(-0.496193\pi\) |
0.871943 | + | 0.489608i | \(0.162860\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −64.0000 | −2.03818 | ||||||||
\(987\) | −5.19615 | + | 1.00000i | −0.165395 | + | 0.0318304i | ||||
\(988\) | − | 6.00000i | − | 0.190885i | ||||||
\(989\) | −2.00000 | + | 3.46410i | −0.0635963 | + | 0.110152i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.50000 | + | 12.9904i | 0.238245 | + | 0.412653i | 0.960211 | − | 0.279276i | \(-0.0900944\pi\) |
−0.721966 | + | 0.691929i | \(0.756761\pi\) | |||||||
\(992\) | 6.92820 | + | 4.00000i | 0.219971 | + | 0.127000i | ||||
\(993\) | − | 9.00000i | − | 0.285606i | ||||||
\(994\) | 30.0000 | + | 10.3923i | 0.951542 | + | 0.329624i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.00000 | + | 3.46410i | −0.0633724 | + | 0.109764i | ||||
\(997\) | 21.6506 | − | 12.5000i | 0.685682 | − | 0.395879i | −0.116310 | − | 0.993213i | \(-0.537107\pi\) |
0.801993 | + | 0.597334i | \(0.203773\pi\) | |||||||
\(998\) | −50.2295 | + | 29.0000i | −1.58999 | + | 0.917979i | ||||
\(999\) | 3.50000 | − | 6.06218i | 0.110735 | − | 0.191799i |
(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 | 525.2.r.d.499.1 | 4 | ||
5.2 | odd | 4 | 105.2.i.b.16.1 | ✓ | 2 | ||
5.3 | odd | 4 | 525.2.i.a.226.1 | 2 | |||
5.4 | even | 2 | inner | 525.2.r.d.499.2 | 4 | ||
7.4 | even | 3 | inner | 525.2.r.d.424.2 | 4 | ||
15.2 | even | 4 | 315.2.j.a.226.1 | 2 | |||
20.7 | even | 4 | 1680.2.bg.l.961.1 | 2 | |||
35.2 | odd | 12 | 735.2.a.b.1.1 | 1 | |||
35.4 | even | 6 | inner | 525.2.r.d.424.1 | 4 | ||
35.12 | even | 12 | 735.2.a.a.1.1 | 1 | |||
35.17 | even | 12 | 735.2.i.f.361.1 | 2 | |||
35.18 | odd | 12 | 525.2.i.a.151.1 | 2 | |||
35.23 | odd | 12 | 3675.2.a.o.1.1 | 1 | |||
35.27 | even | 4 | 735.2.i.f.226.1 | 2 | |||
35.32 | odd | 12 | 105.2.i.b.46.1 | yes | 2 | ||
35.33 | even | 12 | 3675.2.a.p.1.1 | 1 | |||
105.2 | even | 12 | 2205.2.a.k.1.1 | 1 | |||
105.32 | even | 12 | 315.2.j.a.46.1 | 2 | |||
105.47 | odd | 12 | 2205.2.a.m.1.1 | 1 | |||
140.67 | even | 12 | 1680.2.bg.l.1201.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.i.b.16.1 | ✓ | 2 | 5.2 | odd | 4 | ||
105.2.i.b.46.1 | yes | 2 | 35.32 | odd | 12 | ||
315.2.j.a.46.1 | 2 | 105.32 | even | 12 | |||
315.2.j.a.226.1 | 2 | 15.2 | even | 4 | |||
525.2.i.a.151.1 | 2 | 35.18 | odd | 12 | |||
525.2.i.a.226.1 | 2 | 5.3 | odd | 4 | |||
525.2.r.d.424.1 | 4 | 35.4 | even | 6 | inner | ||
525.2.r.d.424.2 | 4 | 7.4 | even | 3 | inner | ||
525.2.r.d.499.1 | 4 | 1.1 | even | 1 | trivial | ||
525.2.r.d.499.2 | 4 | 5.4 | even | 2 | inner | ||
735.2.a.a.1.1 | 1 | 35.12 | even | 12 | |||
735.2.a.b.1.1 | 1 | 35.2 | odd | 12 | |||
735.2.i.f.226.1 | 2 | 35.27 | even | 4 | |||
735.2.i.f.361.1 | 2 | 35.17 | even | 12 | |||
1680.2.bg.l.961.1 | 2 | 20.7 | even | 4 | |||
1680.2.bg.l.1201.1 | 2 | 140.67 | even | 12 | |||
2205.2.a.k.1.1 | 1 | 105.2 | even | 12 | |||
2205.2.a.m.1.1 | 1 | 105.47 | odd | 12 | |||
3675.2.a.o.1.1 | 1 | 35.23 | odd | 12 | |||
3675.2.a.p.1.1 | 1 | 35.33 | even | 12 |