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 | 499.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.499 |
Dual form | 525.2.r.d.424.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(3\) | −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 | \(0.136577\pi\) | ||||
−0.909353 | + | 0.416025i | \(0.863423\pi\) | |||||||
\(14\) | 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 | −0.857321 | − | 0.514782i | \(-0.827873\pi\) |
0.0171533 | + | 0.999853i | \(0.494540\pi\) | |||||||
\(18\) | 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 | 0.0932891 | − | 0.995639i | \(-0.470262\pi\) |
−0.815604 | + | 0.578610i | \(0.803595\pi\) | |||||||
\(24\) | 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 | −0.0893706 | − | 0.995998i | \(-0.528486\pi\) |
−0.907245 | + | 0.420602i | \(0.861819\pi\) | |||||||
\(38\) | 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 | \(-0.975706\pi\) | ||
0.997089 | − | 0.0762493i | \(-0.0242945\pi\) | |||||||
\(44\) | −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 | 0.368329 | − | 0.929695i | \(-0.379930\pi\) |
−0.620975 | + | 0.783830i | \(0.713263\pi\) | |||||||
\(48\) | 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 | −0.718677 | − | 0.695344i | \(-0.755252\pi\) |
0.242846 | + | 0.970065i | \(0.421919\pi\) | |||||||
\(54\) | −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 | −0.0816792 | − | 0.996659i | \(-0.526028\pi\) |
0.822292 | + | 0.569066i | \(0.192695\pi\) | |||||||
\(68\) | −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 | −0.549823 | − | 0.835281i | \(-0.685305\pi\) |
0.448463 | + | 0.893801i | \(0.351972\pi\) | |||||||
\(74\) | −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 | \(-0.964990\pi\) | ||
0.993958 | − | 0.109764i | \(-0.0350096\pi\) | |||||||
\(84\) | −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 | \(-0.901476\pi\) | ||
0.952479 | − | 0.304604i | \(-0.0985241\pi\) | |||||||
\(98\) | 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 | \(-0.947775\pi\) |
−0.634738 | − | 0.772728i | \(-0.718892\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.00000 | −0.777029 | ||||||||
\(107\) | −10.3923 | − | 6.00000i | −1.00466 | − | 0.580042i | −0.0950377 | − | 0.995474i | \(-0.530297\pi\) |
−0.909624 | + | 0.415432i | \(0.863630\pi\) | |||||||
\(108\) | −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 | \(0.0910696\pi\) | ||||
−0.959351 | + | 0.282216i | \(0.908930\pi\) | |||||||
\(114\) | −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 | \(0.0712060\pi\) | ||||
−0.975083 | + | 0.221839i | \(0.928794\pi\) | |||||||
\(128\) | 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 | −0.173939 | − | 0.984757i | \(-0.555649\pi\) |
0.765855 | + | 0.643013i | \(0.222316\pi\) | |||||||
\(138\) | 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 | −0.112884 | − | 0.993608i | \(-0.536009\pi\) |
0.804048 | + | 0.594565i | \(0.202676\pi\) | |||||||
\(158\) | −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 | 0.0343508 | − | 0.999410i | \(-0.489064\pi\) |
−0.848339 | + | 0.529454i | \(0.822397\pi\) | |||||||
\(164\) | −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 | \(-0.873542\pi\) | ||
0.922117 | − | 0.386912i | \(-0.126458\pi\) | |||||||
\(168\) | 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 | \(0.0323955\pi\) |
0.585399 | + | 0.810745i | \(0.300938\pi\) | |||||||
\(174\) | −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 | −0.192522 | − | 0.981293i | \(-0.561667\pi\) |
0.753563 | + | 0.657376i | \(0.228333\pi\) | |||||||
\(194\) | 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 | \(0.140599\pi\) | ||||
−0.904024 | + | 0.427482i | \(0.859401\pi\) | |||||||
\(198\) | 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 | \(0.297074\pi\) | ||||
−0.595198 | + | 0.803579i | \(0.702926\pi\) | |||||||
\(224\) | 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 | −0.759065 | − | 0.651015i | \(-0.774343\pi\) |
0.184263 | + | 0.982877i | \(0.441010\pi\) | |||||||
\(228\) | −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 | 0.660454 | − | 0.750867i | \(-0.270364\pi\) |
−0.320043 | + | 0.947403i | \(0.603697\pi\) | |||||||
\(234\) | 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 | 0.899961 | − | 0.435970i | \(-0.143595\pi\) |
0.0724199 | + | 0.997374i | \(0.476928\pi\) | |||||||
\(258\) | 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 | −0.602986 | − | 0.797752i | \(-0.706023\pi\) |
0.389380 | + | 0.921077i | \(0.372689\pi\) | |||||||
\(264\) | 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 | −0.670940 | − | 0.741512i | \(-0.734109\pi\) |
0.306699 | + | 0.951807i | \(0.400776\pi\) | |||||||
\(278\) | −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 | −0.308879 | − | 0.951101i | \(-0.599954\pi\) |
0.669238 | + | 0.743048i | \(0.266621\pi\) | |||||||
\(284\) | 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 | \(0.154797\pi\) | ||||
−0.884064 | + | 0.467365i | \(0.845203\pi\) | |||||||
\(294\) | −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 | \(0.0272838\pi\) | ||||
−0.996329 | + | 0.0856095i | \(0.972716\pi\) | |||||||
\(308\) | −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 | 0.744453 | − | 0.667674i | \(-0.232710\pi\) |
−0.205996 | + | 0.978553i | \(0.566043\pi\) | |||||||
\(314\) | 20.0000 | 1.12867 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.00000 | −0.112509 | ||||||||
\(317\) | −17.3205 | − | 10.0000i | −0.972817 | − | 0.561656i | −0.0727229 | − | 0.997352i | \(-0.523169\pi\) |
−0.900094 | + | 0.435696i | \(0.856502\pi\) | |||||||
\(318\) | 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 | \(0.238419\pi\) | ||||
−0.732359 | + | 0.680918i | \(0.761581\pi\) | |||||||
\(338\) | 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 | −0.0796169 | − | 0.996826i | \(-0.525370\pi\) |
0.823468 | + | 0.567363i | \(0.192036\pi\) | |||||||
\(348\) | −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 | −0.0240566 | − | 0.999711i | \(-0.507658\pi\) |
0.853746 | + | 0.520689i | \(0.174325\pi\) | |||||||
\(354\) | 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 | −0.00473247 | − | 0.999989i | \(-0.501506\pi\) |
0.863649 | + | 0.504093i | \(0.168173\pi\) | |||||||
\(368\) | −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 | 0.725923 | − | 0.687776i | \(-0.241413\pi\) |
−0.232671 | + | 0.972556i | \(0.574746\pi\) | |||||||
\(374\) | −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 | 0.968900 | − | 0.247451i | \(-0.0795931\pi\) |
0.270151 | + | 0.962818i | \(0.412926\pi\) | |||||||
\(384\) | 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 | \(0.0455577\pi\) |
0.618414 | + | 0.785853i | \(0.287776\pi\) | |||||||
\(398\) | 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 | \(0.0383351\pi\) | ||||
−0.992757 | + | 0.120142i | \(0.961665\pi\) | |||||||
\(434\) | −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 | −0.481486 | − | 0.876454i | \(-0.659903\pi\) |
−0.999774 | + | 0.0212481i | \(0.993236\pi\) | |||||||
\(444\) | 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 | 0.772051 | − | 0.635561i | \(-0.219231\pi\) |
−0.164386 | + | 0.986396i | \(0.552564\pi\) | |||||||
\(458\) | 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 | \(-0.977792\pi\) | ||
0.997567 | − | 0.0697109i | \(-0.0222077\pi\) | |||||||
\(464\) | 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 | −0.0104461 | − | 0.999945i | \(-0.503325\pi\) |
−0.871201 | + | 0.490926i | \(0.836658\pi\) | |||||||
\(468\) | 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 | −0.732901 | − | 0.680335i | \(-0.761834\pi\) |
0.222737 | + | 0.974879i | \(0.428501\pi\) | |||||||
\(488\) | 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 | \(0.0141974\pi\) | ||||
−0.999005 | + | 0.0445878i | \(0.985803\pi\) | |||||||
\(504\) | 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 | 0.693602 | − | 0.720358i | \(-0.256023\pi\) |
−0.277047 | + | 0.960856i | \(0.589356\pi\) | |||||||
\(524\) | −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 | \(0.279557\pi\) | ||||
−0.638497 | + | 0.769624i | \(0.720443\pi\) | |||||||
\(548\) | 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 | −0.672124 | − | 0.740439i | \(-0.734618\pi\) |
0.305177 | + | 0.952296i | \(0.401284\pi\) | |||||||
\(558\) | −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 | 0.0562051 | − | 0.998419i | \(-0.482100\pi\) |
0.892759 | + | 0.450535i | \(0.148767\pi\) | |||||||
\(564\) | 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 | −0.921397 | − | 0.388621i | \(-0.872951\pi\) |
−0.124143 | + | 0.992264i | \(0.539618\pi\) | |||||||
\(578\) | −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 | \(0.0796572\pi\) | ||||
−0.968850 | + | 0.247647i | \(0.920343\pi\) | |||||||
\(588\) | −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 | 0.144528 | − | 0.989501i | \(-0.453834\pi\) |
−0.784669 | + | 0.619915i | \(0.787167\pi\) | |||||||
\(594\) | −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 | −0.263193 | − | 0.964743i | \(-0.584775\pi\) |
−0.967088 | + | 0.254440i | \(0.918109\pi\) | |||||||
\(608\) | − | 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 | 0.126885 | − | 0.991917i | \(-0.459502\pi\) |
0.922468 | + | 0.386073i | \(0.126169\pi\) | |||||||
\(614\) | −3.00000 | + | 5.19615i | −0.121070 | + | 0.209700i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.0000i | 0.724653i | 0.932051 | + | 0.362326i | \(0.118017\pi\) | ||||
−0.932051 | + | 0.362326i | \(0.881983\pi\) | |||||||
\(618\) | 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 | \(-0.993723\pi\) | ||
0.999806 | − | 0.0197181i | \(-0.00627687\pi\) | |||||||
\(644\) | −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 | 0.106897 | − | 0.994270i | \(-0.465908\pi\) |
0.914512 | + | 0.404559i | \(0.132575\pi\) | |||||||
\(648\) | 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 | 0.718106 | − | 0.695934i | \(-0.245009\pi\) |
−0.243643 | + | 0.969865i | \(0.578343\pi\) | |||||||
\(654\) | 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 | \(0.252720\pi\) | ||||
−0.701039 | + | 0.713123i | \(0.747280\pi\) | |||||||
\(674\) | −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 | 0.209507 | − | 0.977807i | \(-0.432814\pi\) |
−0.742052 | + | 0.670342i | \(0.766147\pi\) | |||||||
\(678\) | − | 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 | \(-0.296201\pi\) |
0.993204 | − | 0.116390i | \(-0.0371322\pi\) | |||||||
\(684\) | 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 | \(0.0414360\pi\) | ||||
−0.991539 | + | 0.129808i | \(0.958564\pi\) | |||||||
\(728\) | 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 | −0.383849 | − | 0.923396i | \(-0.625402\pi\) |
−0.991609 | + | 0.129275i | \(0.958735\pi\) | |||||||
\(734\) | 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 | \(-0.964896\pi\) | ||
0.993925 | − | 0.110059i | \(-0.0351041\pi\) | |||||||
\(744\) | 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 | \(-0.869079\pi\) | ||
0.916602 | − | 0.399802i | \(-0.130921\pi\) | |||||||
\(758\) | −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 | −0.753418 | − | 0.657542i | \(-0.771596\pi\) |
0.192740 | + | 0.981250i | \(0.438263\pi\) | |||||||
\(774\) | −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 | −0.904632 | − | 0.426193i | \(-0.859855\pi\) |
−0.0832226 | + | 0.996531i | \(0.526521\pi\) | |||||||
\(788\) | −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 | \(-0.779930\pi\) | ||
0.770374 | − | 0.637593i | \(-0.220070\pi\) | |||||||
\(798\) | −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 | −0.615867 | − | 0.787850i | \(-0.711194\pi\) |
0.374365 | + | 0.927281i | \(0.377861\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.00000 | − | 41.5692i | −0.278356 | − | 1.44638i | ||||
\(827\) | − | 30.0000i | − | 1.04320i | −0.853189 | − | 0.521601i | \(-0.825335\pi\) | ||
0.853189 | − | 0.521601i | \(-0.174665\pi\) | |||||||
\(828\) | −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 | \(0.0492404\pi\) | ||||
−0.988059 | + | 0.154077i | \(0.950760\pi\) | |||||||
\(854\) | 56.0000 | − | 48.4974i | 1.91628 | − | 1.65955i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.3923 | + | 6.00000i | −0.354994 | + | 0.204956i | −0.666883 | − | 0.745163i | \(-0.732372\pi\) |
0.311888 | + | 0.950119i | \(0.399038\pi\) | |||||||
\(858\) | 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 | 0.408946 | − | 0.912558i | \(-0.365896\pi\) |
−0.585826 | + | 0.810437i | \(0.699230\pi\) | |||||||
\(864\) | 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 | 0.785907 | − | 0.618344i | \(-0.212196\pi\) |
−0.142548 | + | 0.989788i | \(0.545530\pi\) | |||||||
\(878\) | 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 | \(-0.962421\pi\) | ||
0.993039 | − | 0.117784i | \(-0.0375792\pi\) | |||||||
\(884\) | 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 | 0.347512 | − | 0.937676i | \(-0.387027\pi\) |
−0.638295 | + | 0.769792i | \(0.720360\pi\) | |||||||
\(888\) | 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 | 0.0170220 | − | 0.999855i | \(-0.494581\pi\) |
0.874411 | + | 0.485186i | \(0.161248\pi\) | |||||||
\(908\) | −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 | \(-0.842920\pi\) | ||
0.880689 | − | 0.473694i | \(-0.157080\pi\) | |||||||
\(938\) | 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 | 0.0873481 | − | 0.996178i | \(-0.472161\pi\) |
−0.819041 | + | 0.573735i | \(0.805494\pi\) | |||||||
\(948\) | 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 | \(-0.979363\pi\) | ||
0.997899 | − | 0.0647864i | \(-0.0206366\pi\) | |||||||
\(954\) | −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 | \(0.345391\pi\) | ||||
−0.466843 | + | 0.884340i | \(0.654609\pi\) | |||||||
\(968\) | 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 | −0.772787 | − | 0.634665i | \(-0.781138\pi\) |
0.163242 | + | 0.986586i | \(0.447805\pi\) | |||||||
\(978\) | 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 | −0.871943 | − | 0.489608i | \(-0.837140\pi\) |
−0.0119587 | + | 0.999928i | \(0.503807\pi\) | |||||||
\(984\) | 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 | −0.801993 | − | 0.597334i | \(-0.796227\pi\) |
0.116310 | + | 0.993213i | \(0.462893\pi\) | |||||||
\(998\) | 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.499.2 | 4 | ||
5.2 | odd | 4 | 525.2.i.a.226.1 | 2 | |||
5.3 | odd | 4 | 105.2.i.b.16.1 | ✓ | 2 | ||
5.4 | even | 2 | inner | 525.2.r.d.499.1 | 4 | ||
7.4 | even | 3 | inner | 525.2.r.d.424.1 | 4 | ||
15.8 | even | 4 | 315.2.j.a.226.1 | 2 | |||
20.3 | even | 4 | 1680.2.bg.l.961.1 | 2 | |||
35.2 | odd | 12 | 3675.2.a.o.1.1 | 1 | |||
35.3 | even | 12 | 735.2.i.f.361.1 | 2 | |||
35.4 | even | 6 | inner | 525.2.r.d.424.2 | 4 | ||
35.12 | even | 12 | 3675.2.a.p.1.1 | 1 | |||
35.13 | even | 4 | 735.2.i.f.226.1 | 2 | |||
35.18 | odd | 12 | 105.2.i.b.46.1 | yes | 2 | ||
35.23 | odd | 12 | 735.2.a.b.1.1 | 1 | |||
35.32 | odd | 12 | 525.2.i.a.151.1 | 2 | |||
35.33 | even | 12 | 735.2.a.a.1.1 | 1 | |||
105.23 | even | 12 | 2205.2.a.k.1.1 | 1 | |||
105.53 | even | 12 | 315.2.j.a.46.1 | 2 | |||
105.68 | odd | 12 | 2205.2.a.m.1.1 | 1 | |||
140.123 | 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 | 5.3 | odd | 4 | ||
105.2.i.b.46.1 | yes | 2 | 35.18 | odd | 12 | ||
315.2.j.a.46.1 | 2 | 105.53 | even | 12 | |||
315.2.j.a.226.1 | 2 | 15.8 | even | 4 | |||
525.2.i.a.151.1 | 2 | 35.32 | odd | 12 | |||
525.2.i.a.226.1 | 2 | 5.2 | odd | 4 | |||
525.2.r.d.424.1 | 4 | 7.4 | even | 3 | inner | ||
525.2.r.d.424.2 | 4 | 35.4 | even | 6 | inner | ||
525.2.r.d.499.1 | 4 | 5.4 | even | 2 | inner | ||
525.2.r.d.499.2 | 4 | 1.1 | even | 1 | trivial | ||
735.2.a.a.1.1 | 1 | 35.33 | even | 12 | |||
735.2.a.b.1.1 | 1 | 35.23 | odd | 12 | |||
735.2.i.f.226.1 | 2 | 35.13 | even | 4 | |||
735.2.i.f.361.1 | 2 | 35.3 | even | 12 | |||
1680.2.bg.l.961.1 | 2 | 20.3 | even | 4 | |||
1680.2.bg.l.1201.1 | 2 | 140.123 | even | 12 | |||
2205.2.a.k.1.1 | 1 | 105.23 | even | 12 | |||
2205.2.a.m.1.1 | 1 | 105.68 | odd | 12 | |||
3675.2.a.o.1.1 | 1 | 35.2 | odd | 12 | |||
3675.2.a.p.1.1 | 1 | 35.12 | even | 12 |