Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(79,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.79");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.n (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: | \(11.7380090971\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 949.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.949 |
Dual form | 1470.2.n.f.79.1 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | 0.866025 | + | 0.500000i | 0.500000 | + | 0.288675i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | −1.23205 | + | 1.86603i | −0.550990 | + | 0.834512i | ||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0.133975 | − | 2.23205i | 0.0423665 | − | 0.705836i | ||||
\(11\) | −1.00000 | + | 1.73205i | −0.301511 | + | 0.522233i | −0.976478 | − | 0.215615i | \(-0.930824\pi\) |
0.674967 | + | 0.737848i | \(0.264158\pi\) | |||||||
\(12\) | 0.866025 | − | 0.500000i | 0.250000 | − | 0.144338i | ||||
\(13\) | − | 6.00000i | − | 1.66410i | −0.554700 | − | 0.832050i | \(-0.687167\pi\) | ||
0.554700 | − | 0.832050i | \(-0.312833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.00000 | + | 1.00000i | −0.516398 | + | 0.258199i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −3.46410 | − | 2.00000i | −0.840168 | − | 0.485071i | 0.0171533 | − | 0.999853i | \(-0.494540\pi\) |
−0.857321 | + | 0.514782i | \(0.827873\pi\) | |||||||
\(18\) | −0.866025 | − | 0.500000i | −0.204124 | − | 0.117851i | ||||
\(19\) | 3.00000 | + | 5.19615i | 0.688247 | + | 1.19208i | 0.972404 | + | 0.233301i | \(0.0749529\pi\) |
−0.284157 | + | 0.958778i | \(0.591714\pi\) | |||||||
\(20\) | 1.00000 | + | 2.00000i | 0.223607 | + | 0.447214i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 2.00000i | − | 0.426401i | ||||||
\(23\) | −6.92820 | + | 4.00000i | −1.44463 | + | 0.834058i | −0.998154 | − | 0.0607377i | \(-0.980655\pi\) |
−0.446476 | + | 0.894795i | \(0.647321\pi\) | |||||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | −1.96410 | − | 4.59808i | −0.392820 | − | 0.919615i | ||||
\(26\) | 3.00000 | + | 5.19615i | 0.588348 | + | 1.01905i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 1.23205 | − | 1.86603i | 0.224941 | − | 0.340688i | ||||
\(31\) | −1.00000 | + | 1.73205i | −0.179605 | + | 0.311086i | −0.941745 | − | 0.336327i | \(-0.890815\pi\) |
0.762140 | + | 0.647412i | \(0.224149\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | −1.73205 | + | 1.00000i | −0.301511 | + | 0.174078i | ||||
\(34\) | 4.00000 | 0.685994 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −3.46410 | + | 2.00000i | −0.569495 | + | 0.328798i | −0.756948 | − | 0.653476i | \(-0.773310\pi\) |
0.187453 | + | 0.982274i | \(0.439977\pi\) | |||||||
\(38\) | −5.19615 | − | 3.00000i | −0.842927 | − | 0.486664i | ||||
\(39\) | 3.00000 | − | 5.19615i | 0.480384 | − | 0.832050i | ||||
\(40\) | −1.86603 | − | 1.23205i | −0.295045 | − | 0.194804i | ||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000i | 0.609994i | 0.952353 | + | 0.304997i | \(0.0986555\pi\) | ||||
−0.952353 | + | 0.304997i | \(0.901344\pi\) | |||||||
\(44\) | 1.00000 | + | 1.73205i | 0.150756 | + | 0.261116i | ||||
\(45\) | −2.23205 | − | 0.133975i | −0.332734 | − | 0.0199718i | ||||
\(46\) | 4.00000 | − | 6.92820i | 0.589768 | − | 1.02151i | ||||
\(47\) | 6.92820 | − | 4.00000i | 1.01058 | − | 0.583460i | 0.0992202 | − | 0.995066i | \(-0.468365\pi\) |
0.911362 | + | 0.411606i | \(0.135032\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.00000 | + | 3.00000i | 0.565685 | + | 0.424264i | ||||
\(51\) | −2.00000 | − | 3.46410i | −0.280056 | − | 0.485071i | ||||
\(52\) | −5.19615 | − | 3.00000i | −0.720577 | − | 0.416025i | ||||
\(53\) | −5.19615 | − | 3.00000i | −0.713746 | − | 0.412082i | 0.0987002 | − | 0.995117i | \(-0.468532\pi\) |
−0.812447 | + | 0.583036i | \(0.801865\pi\) | |||||||
\(54\) | −0.500000 | − | 0.866025i | −0.0680414 | − | 0.117851i | ||||
\(55\) | −2.00000 | − | 4.00000i | −0.269680 | − | 0.539360i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.00000i | 0.794719i | ||||||||
\(58\) | 5.19615 | − | 3.00000i | 0.682288 | − | 0.393919i | ||||
\(59\) | 4.00000 | − | 6.92820i | 0.520756 | − | 0.901975i | −0.478953 | − | 0.877841i | \(-0.658984\pi\) |
0.999709 | − | 0.0241347i | \(-0.00768307\pi\) | |||||||
\(60\) | −0.133975 | + | 2.23205i | −0.0172960 | + | 0.288157i | ||||
\(61\) | −5.00000 | − | 8.66025i | −0.640184 | − | 1.10883i | −0.985391 | − | 0.170305i | \(-0.945525\pi\) |
0.345207 | − | 0.938527i | \(-0.387809\pi\) | |||||||
\(62\) | − | 2.00000i | − | 0.254000i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 11.1962 | + | 7.39230i | 1.38871 | + | 0.916903i | ||||
\(66\) | 1.00000 | − | 1.73205i | 0.123091 | − | 0.213201i | ||||
\(67\) | 6.92820 | + | 4.00000i | 0.846415 | + | 0.488678i | 0.859440 | − | 0.511237i | \(-0.170813\pi\) |
−0.0130248 | + | 0.999915i | \(0.504146\pi\) | |||||||
\(68\) | −3.46410 | + | 2.00000i | −0.420084 | + | 0.242536i | ||||
\(69\) | −8.00000 | −0.963087 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.00000 | −0.712069 | −0.356034 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356034 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(72\) | −0.866025 | + | 0.500000i | −0.102062 | + | 0.0589256i | ||||
\(73\) | −12.1244 | − | 7.00000i | −1.41905 | − | 0.819288i | −0.422833 | − | 0.906208i | \(-0.638964\pi\) |
−0.996215 | + | 0.0869195i | \(0.972298\pi\) | |||||||
\(74\) | 2.00000 | − | 3.46410i | 0.232495 | − | 0.402694i | ||||
\(75\) | 0.598076 | − | 4.96410i | 0.0690599 | − | 0.573205i | ||||
\(76\) | 6.00000 | 0.688247 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 6.00000i | 0.679366i | ||||||||
\(79\) | −6.00000 | − | 10.3923i | −0.675053 | − | 1.16923i | −0.976453 | − | 0.215728i | \(-0.930788\pi\) |
0.301401 | − | 0.953498i | \(-0.402546\pi\) | |||||||
\(80\) | 2.23205 | + | 0.133975i | 0.249551 | + | 0.0149788i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 1.73205 | − | 1.00000i | 0.191273 | − | 0.110432i | ||||
\(83\) | 8.00000i | 0.878114i | 0.898459 | + | 0.439057i | \(0.144687\pi\) | ||||
−0.898459 | + | 0.439057i | \(0.855313\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.00000 | − | 4.00000i | 0.867722 | − | 0.433861i | ||||
\(86\) | −2.00000 | − | 3.46410i | −0.215666 | − | 0.373544i | ||||
\(87\) | −5.19615 | − | 3.00000i | −0.557086 | − | 0.321634i | ||||
\(88\) | −1.73205 | − | 1.00000i | −0.184637 | − | 0.106600i | ||||
\(89\) | 5.00000 | + | 8.66025i | 0.529999 | + | 0.917985i | 0.999388 | + | 0.0349934i | \(0.0111410\pi\) |
−0.469389 | + | 0.882992i | \(0.655526\pi\) | |||||||
\(90\) | 2.00000 | − | 1.00000i | 0.210819 | − | 0.105409i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 8.00000i | 0.834058i | ||||||||
\(93\) | −1.73205 | + | 1.00000i | −0.179605 | + | 0.103695i | ||||
\(94\) | −4.00000 | + | 6.92820i | −0.412568 | + | 0.714590i | ||||
\(95\) | −13.3923 | − | 0.803848i | −1.37402 | − | 0.0824730i | ||||
\(96\) | 0.500000 | + | 0.866025i | 0.0510310 | + | 0.0883883i | ||||
\(97\) | − | 10.0000i | − | 1.01535i | −0.861550 | − | 0.507673i | \(-0.830506\pi\) | ||
0.861550 | − | 0.507673i | \(-0.169494\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | −4.96410 | − | 0.598076i | −0.496410 | − | 0.0598076i | ||||
\(101\) | 5.00000 | − | 8.66025i | 0.497519 | − | 0.861727i | −0.502477 | − | 0.864590i | \(-0.667578\pi\) |
0.999996 | + | 0.00286291i | \(0.000911295\pi\) | |||||||
\(102\) | 3.46410 | + | 2.00000i | 0.342997 | + | 0.198030i | ||||
\(103\) | −6.92820 | + | 4.00000i | −0.682656 | + | 0.394132i | −0.800855 | − | 0.598858i | \(-0.795621\pi\) |
0.118199 | + | 0.992990i | \(0.462288\pi\) | |||||||
\(104\) | 6.00000 | 0.588348 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | −10.3923 | + | 6.00000i | −1.00466 | + | 0.580042i | −0.909624 | − | 0.415432i | \(-0.863630\pi\) |
−0.0950377 | + | 0.995474i | \(0.530297\pi\) | |||||||
\(108\) | 0.866025 | + | 0.500000i | 0.0833333 | + | 0.0481125i | ||||
\(109\) | −7.00000 | + | 12.1244i | −0.670478 | + | 1.16130i | 0.307290 | + | 0.951616i | \(0.400578\pi\) |
−0.977769 | + | 0.209687i | \(0.932756\pi\) | |||||||
\(110\) | 3.73205 | + | 2.46410i | 0.355837 | + | 0.234943i | ||||
\(111\) | −4.00000 | −0.379663 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000i | 0.564433i | 0.959351 | + | 0.282216i | \(0.0910696\pi\) | ||||
−0.959351 | + | 0.282216i | \(0.908930\pi\) | |||||||
\(114\) | −3.00000 | − | 5.19615i | −0.280976 | − | 0.486664i | ||||
\(115\) | 1.07180 | − | 17.8564i | 0.0999456 | − | 1.66512i | ||||
\(116\) | −3.00000 | + | 5.19615i | −0.278543 | + | 0.482451i | ||||
\(117\) | 5.19615 | − | 3.00000i | 0.480384 | − | 0.277350i | ||||
\(118\) | 8.00000i | 0.736460i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.00000 | − | 2.00000i | −0.0912871 | − | 0.182574i | ||||
\(121\) | 3.50000 | + | 6.06218i | 0.318182 | + | 0.551107i | ||||
\(122\) | 8.66025 | + | 5.00000i | 0.784063 | + | 0.452679i | ||||
\(123\) | −1.73205 | − | 1.00000i | −0.156174 | − | 0.0901670i | ||||
\(124\) | 1.00000 | + | 1.73205i | 0.0898027 | + | 0.155543i | ||||
\(125\) | 11.0000 | + | 2.00000i | 0.983870 | + | 0.178885i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 4.00000i | − | 0.354943i | −0.984126 | − | 0.177471i | \(-0.943208\pi\) | ||
0.984126 | − | 0.177471i | \(-0.0567917\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | −2.00000 | + | 3.46410i | −0.176090 | + | 0.304997i | ||||
\(130\) | −13.3923 | − | 0.803848i | −1.17458 | − | 0.0705021i | ||||
\(131\) | −6.00000 | − | 10.3923i | −0.524222 | − | 0.907980i | −0.999602 | − | 0.0281993i | \(-0.991023\pi\) |
0.475380 | − | 0.879781i | \(-0.342311\pi\) | |||||||
\(132\) | 2.00000i | 0.174078i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −8.00000 | −0.691095 | ||||||||
\(135\) | −1.86603 | − | 1.23205i | −0.160602 | − | 0.106038i | ||||
\(136\) | 2.00000 | − | 3.46410i | 0.171499 | − | 0.297044i | ||||
\(137\) | −5.19615 | − | 3.00000i | −0.443937 | − | 0.256307i | 0.261329 | − | 0.965250i | \(-0.415839\pi\) |
−0.705266 | + | 0.708942i | \(0.749173\pi\) | |||||||
\(138\) | 6.92820 | − | 4.00000i | 0.589768 | − | 0.340503i | ||||
\(139\) | −14.0000 | −1.18746 | −0.593732 | − | 0.804663i | \(-0.702346\pi\) | ||||
−0.593732 | + | 0.804663i | \(0.702346\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.00000 | 0.673722 | ||||||||
\(142\) | 5.19615 | − | 3.00000i | 0.436051 | − | 0.251754i | ||||
\(143\) | 10.3923 | + | 6.00000i | 0.869048 | + | 0.501745i | ||||
\(144\) | 0.500000 | − | 0.866025i | 0.0416667 | − | 0.0721688i | ||||
\(145\) | 7.39230 | − | 11.1962i | 0.613898 | − | 0.929790i | ||||
\(146\) | 14.0000 | 1.15865 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.00000i | 0.328798i | ||||||||
\(149\) | 5.00000 | + | 8.66025i | 0.409616 | + | 0.709476i | 0.994847 | − | 0.101391i | \(-0.0323294\pi\) |
−0.585231 | + | 0.810867i | \(0.698996\pi\) | |||||||
\(150\) | 1.96410 | + | 4.59808i | 0.160368 | + | 0.375431i | ||||
\(151\) | 4.00000 | − | 6.92820i | 0.325515 | − | 0.563809i | −0.656101 | − | 0.754673i | \(-0.727796\pi\) |
0.981617 | + | 0.190864i | \(0.0611289\pi\) | |||||||
\(152\) | −5.19615 | + | 3.00000i | −0.421464 | + | 0.243332i | ||||
\(153\) | − | 4.00000i | − | 0.323381i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.00000 | − | 4.00000i | −0.160644 | − | 0.321288i | ||||
\(156\) | −3.00000 | − | 5.19615i | −0.240192 | − | 0.416025i | ||||
\(157\) | 19.0526 | + | 11.0000i | 1.52056 | + | 0.877896i | 0.999706 | + | 0.0242497i | \(0.00771967\pi\) |
0.520854 | + | 0.853646i | \(0.325614\pi\) | |||||||
\(158\) | 10.3923 | + | 6.00000i | 0.826767 | + | 0.477334i | ||||
\(159\) | −3.00000 | − | 5.19615i | −0.237915 | − | 0.412082i | ||||
\(160\) | −2.00000 | + | 1.00000i | −0.158114 | + | 0.0790569i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | −3.46410 | + | 2.00000i | −0.271329 | + | 0.156652i | −0.629492 | − | 0.777007i | \(-0.716737\pi\) |
0.358162 | + | 0.933659i | \(0.383403\pi\) | |||||||
\(164\) | −1.00000 | + | 1.73205i | −0.0780869 | + | 0.135250i | ||||
\(165\) | 0.267949 | − | 4.46410i | 0.0208598 | − | 0.347530i | ||||
\(166\) | −4.00000 | − | 6.92820i | −0.310460 | − | 0.537733i | ||||
\(167\) | − | 12.0000i | − | 0.928588i | −0.885681 | − | 0.464294i | \(-0.846308\pi\) | ||
0.885681 | − | 0.464294i | \(-0.153692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −23.0000 | −1.76923 | ||||||||
\(170\) | −4.92820 | + | 7.46410i | −0.377976 | + | 0.572470i | ||||
\(171\) | −3.00000 | + | 5.19615i | −0.229416 | + | 0.397360i | ||||
\(172\) | 3.46410 | + | 2.00000i | 0.264135 | + | 0.152499i | ||||
\(173\) | −6.92820 | + | 4.00000i | −0.526742 | + | 0.304114i | −0.739689 | − | 0.672949i | \(-0.765027\pi\) |
0.212947 | + | 0.977064i | \(0.431694\pi\) | |||||||
\(174\) | 6.00000 | 0.454859 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.00000 | 0.150756 | ||||||||
\(177\) | 6.92820 | − | 4.00000i | 0.520756 | − | 0.300658i | ||||
\(178\) | −8.66025 | − | 5.00000i | −0.649113 | − | 0.374766i | ||||
\(179\) | 5.00000 | − | 8.66025i | 0.373718 | − | 0.647298i | −0.616417 | − | 0.787420i | \(-0.711416\pi\) |
0.990134 | + | 0.140122i | \(0.0447496\pi\) | |||||||
\(180\) | −1.23205 | + | 1.86603i | −0.0918316 | + | 0.139085i | ||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 10.0000i | − | 0.739221i | ||||||
\(184\) | −4.00000 | − | 6.92820i | −0.294884 | − | 0.510754i | ||||
\(185\) | 0.535898 | − | 8.92820i | 0.0394000 | − | 0.656415i | ||||
\(186\) | 1.00000 | − | 1.73205i | 0.0733236 | − | 0.127000i | ||||
\(187\) | 6.92820 | − | 4.00000i | 0.506640 | − | 0.292509i | ||||
\(188\) | − | 8.00000i | − | 0.583460i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 12.0000 | − | 6.00000i | 0.870572 | − | 0.435286i | ||||
\(191\) | 9.00000 | + | 15.5885i | 0.651217 | + | 1.12794i | 0.982828 | + | 0.184525i | \(0.0590746\pi\) |
−0.331611 | + | 0.943416i | \(0.607592\pi\) | |||||||
\(192\) | −0.866025 | − | 0.500000i | −0.0625000 | − | 0.0360844i | ||||
\(193\) | 6.92820 | + | 4.00000i | 0.498703 | + | 0.287926i | 0.728178 | − | 0.685388i | \(-0.240368\pi\) |
−0.229475 | + | 0.973315i | \(0.573701\pi\) | |||||||
\(194\) | 5.00000 | + | 8.66025i | 0.358979 | + | 0.621770i | ||||
\(195\) | 6.00000 | + | 12.0000i | 0.429669 | + | 0.859338i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 2.00000i | − | 0.142494i | −0.997459 | − | 0.0712470i | \(-0.977302\pi\) | ||
0.997459 | − | 0.0712470i | \(-0.0226979\pi\) | |||||||
\(198\) | 1.73205 | − | 1.00000i | 0.123091 | − | 0.0710669i | ||||
\(199\) | −3.00000 | + | 5.19615i | −0.212664 | + | 0.368345i | −0.952548 | − | 0.304390i | \(-0.901547\pi\) |
0.739883 | + | 0.672735i | \(0.234881\pi\) | |||||||
\(200\) | 4.59808 | − | 1.96410i | 0.325133 | − | 0.138883i | ||||
\(201\) | 4.00000 | + | 6.92820i | 0.282138 | + | 0.488678i | ||||
\(202\) | 10.0000i | 0.703598i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −4.00000 | −0.280056 | ||||||||
\(205\) | 2.46410 | − | 3.73205i | 0.172100 | − | 0.260658i | ||||
\(206\) | 4.00000 | − | 6.92820i | 0.278693 | − | 0.482711i | ||||
\(207\) | −6.92820 | − | 4.00000i | −0.481543 | − | 0.278019i | ||||
\(208\) | −5.19615 | + | 3.00000i | −0.360288 | + | 0.208013i | ||||
\(209\) | −12.0000 | −0.830057 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(212\) | −5.19615 | + | 3.00000i | −0.356873 | + | 0.206041i | ||||
\(213\) | −5.19615 | − | 3.00000i | −0.356034 | − | 0.205557i | ||||
\(214\) | 6.00000 | − | 10.3923i | 0.410152 | − | 0.710403i | ||||
\(215\) | −7.46410 | − | 4.92820i | −0.509048 | − | 0.336101i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 14.0000i | − | 0.948200i | ||||||
\(219\) | −7.00000 | − | 12.1244i | −0.473016 | − | 0.819288i | ||||
\(220\) | −4.46410 | − | 0.267949i | −0.300970 | − | 0.0180651i | ||||
\(221\) | −12.0000 | + | 20.7846i | −0.807207 | + | 1.39812i | ||||
\(222\) | 3.46410 | − | 2.00000i | 0.232495 | − | 0.134231i | ||||
\(223\) | 8.00000i | 0.535720i | 0.963458 | + | 0.267860i | \(0.0863164\pi\) | ||||
−0.963458 | + | 0.267860i | \(0.913684\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.00000 | − | 4.00000i | 0.200000 | − | 0.266667i | ||||
\(226\) | −3.00000 | − | 5.19615i | −0.199557 | − | 0.345643i | ||||
\(227\) | 6.92820 | + | 4.00000i | 0.459841 | + | 0.265489i | 0.711977 | − | 0.702202i | \(-0.247800\pi\) |
−0.252136 | + | 0.967692i | \(0.581133\pi\) | |||||||
\(228\) | 5.19615 | + | 3.00000i | 0.344124 | + | 0.198680i | ||||
\(229\) | −7.00000 | − | 12.1244i | −0.462573 | − | 0.801200i | 0.536515 | − | 0.843891i | \(-0.319740\pi\) |
−0.999088 | + | 0.0426906i | \(0.986407\pi\) | |||||||
\(230\) | 8.00000 | + | 16.0000i | 0.527504 | + | 1.05501i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 6.00000i | − | 0.393919i | ||||||
\(233\) | −8.66025 | + | 5.00000i | −0.567352 | + | 0.327561i | −0.756091 | − | 0.654466i | \(-0.772893\pi\) |
0.188739 | + | 0.982027i | \(0.439560\pi\) | |||||||
\(234\) | −3.00000 | + | 5.19615i | −0.196116 | + | 0.339683i | ||||
\(235\) | −1.07180 | + | 17.8564i | −0.0699163 | + | 1.16482i | ||||
\(236\) | −4.00000 | − | 6.92820i | −0.260378 | − | 0.450988i | ||||
\(237\) | − | 12.0000i | − | 0.779484i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −26.0000 | −1.68180 | −0.840900 | − | 0.541190i | \(-0.817974\pi\) | ||||
−0.840900 | + | 0.541190i | \(0.817974\pi\) | |||||||
\(240\) | 1.86603 | + | 1.23205i | 0.120451 | + | 0.0795285i | ||||
\(241\) | −13.0000 | + | 22.5167i | −0.837404 | + | 1.45043i | 0.0546547 | + | 0.998505i | \(0.482594\pi\) |
−0.892058 | + | 0.451920i | \(0.850739\pi\) | |||||||
\(242\) | −6.06218 | − | 3.50000i | −0.389692 | − | 0.224989i | ||||
\(243\) | −0.866025 | + | 0.500000i | −0.0555556 | + | 0.0320750i | ||||
\(244\) | −10.0000 | −0.640184 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.00000 | 0.127515 | ||||||||
\(247\) | 31.1769 | − | 18.0000i | 1.98374 | − | 1.14531i | ||||
\(248\) | −1.73205 | − | 1.00000i | −0.109985 | − | 0.0635001i | ||||
\(249\) | −4.00000 | + | 6.92820i | −0.253490 | + | 0.439057i | ||||
\(250\) | −10.5263 | + | 3.76795i | −0.665740 | + | 0.238306i | ||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 16.0000i | − | 1.00591i | ||||||
\(254\) | 2.00000 | + | 3.46410i | 0.125491 | + | 0.217357i | ||||
\(255\) | 8.92820 | + | 0.535898i | 0.559106 | + | 0.0335593i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(258\) | − | 4.00000i | − | 0.249029i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 12.0000 | − | 6.00000i | 0.744208 | − | 0.372104i | ||||
\(261\) | −3.00000 | − | 5.19615i | −0.185695 | − | 0.321634i | ||||
\(262\) | 10.3923 | + | 6.00000i | 0.642039 | + | 0.370681i | ||||
\(263\) | −13.8564 | − | 8.00000i | −0.854423 | − | 0.493301i | 0.00771799 | − | 0.999970i | \(-0.497543\pi\) |
−0.862141 | + | 0.506669i | \(0.830877\pi\) | |||||||
\(264\) | −1.00000 | − | 1.73205i | −0.0615457 | − | 0.106600i | ||||
\(265\) | 12.0000 | − | 6.00000i | 0.737154 | − | 0.368577i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.0000i | 0.611990i | ||||||||
\(268\) | 6.92820 | − | 4.00000i | 0.423207 | − | 0.244339i | ||||
\(269\) | −9.00000 | + | 15.5885i | −0.548740 | + | 0.950445i | 0.449622 | + | 0.893219i | \(0.351559\pi\) |
−0.998361 | + | 0.0572259i | \(0.981774\pi\) | |||||||
\(270\) | 2.23205 | + | 0.133975i | 0.135838 | + | 0.00815343i | ||||
\(271\) | 5.00000 | + | 8.66025i | 0.303728 | + | 0.526073i | 0.976977 | − | 0.213343i | \(-0.0684351\pi\) |
−0.673249 | + | 0.739416i | \(0.735102\pi\) | |||||||
\(272\) | 4.00000i | 0.242536i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.00000 | 0.362473 | ||||||||
\(275\) | 9.92820 | + | 1.19615i | 0.598693 | + | 0.0721307i | ||||
\(276\) | −4.00000 | + | 6.92820i | −0.240772 | + | 0.417029i | ||||
\(277\) | 24.2487 | + | 14.0000i | 1.45696 | + | 0.841178i | 0.998861 | − | 0.0477206i | \(-0.0151957\pi\) |
0.458103 | + | 0.888899i | \(0.348529\pi\) | |||||||
\(278\) | 12.1244 | − | 7.00000i | 0.727171 | − | 0.419832i | ||||
\(279\) | −2.00000 | −0.119737 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 30.0000 | 1.78965 | 0.894825 | − | 0.446417i | \(-0.147300\pi\) | ||||
0.894825 | + | 0.446417i | \(0.147300\pi\) | |||||||
\(282\) | −6.92820 | + | 4.00000i | −0.412568 | + | 0.238197i | ||||
\(283\) | 17.3205 | + | 10.0000i | 1.02960 | + | 0.594438i | 0.916869 | − | 0.399188i | \(-0.130708\pi\) |
0.112728 | + | 0.993626i | \(0.464041\pi\) | |||||||
\(284\) | −3.00000 | + | 5.19615i | −0.178017 | + | 0.308335i | ||||
\(285\) | −11.1962 | − | 7.39230i | −0.663203 | − | 0.437882i | ||||
\(286\) | −12.0000 | −0.709575 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | −0.500000 | − | 0.866025i | −0.0294118 | − | 0.0509427i | ||||
\(290\) | −0.803848 | + | 13.3923i | −0.0472036 | + | 0.786423i | ||||
\(291\) | 5.00000 | − | 8.66025i | 0.293105 | − | 0.507673i | ||||
\(292\) | −12.1244 | + | 7.00000i | −0.709524 | + | 0.409644i | ||||
\(293\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.00000 | + | 16.0000i | 0.465778 | + | 0.931556i | ||||
\(296\) | −2.00000 | − | 3.46410i | −0.116248 | − | 0.201347i | ||||
\(297\) | −1.73205 | − | 1.00000i | −0.100504 | − | 0.0580259i | ||||
\(298\) | −8.66025 | − | 5.00000i | −0.501675 | − | 0.289642i | ||||
\(299\) | 24.0000 | + | 41.5692i | 1.38796 | + | 2.40401i | ||||
\(300\) | −4.00000 | − | 3.00000i | −0.230940 | − | 0.173205i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 8.00000i | 0.460348i | ||||||||
\(303\) | 8.66025 | − | 5.00000i | 0.497519 | − | 0.287242i | ||||
\(304\) | 3.00000 | − | 5.19615i | 0.172062 | − | 0.298020i | ||||
\(305\) | 22.3205 | + | 1.33975i | 1.27807 | + | 0.0767136i | ||||
\(306\) | 2.00000 | + | 3.46410i | 0.114332 | + | 0.198030i | ||||
\(307\) | − | 12.0000i | − | 0.684876i | −0.939540 | − | 0.342438i | \(-0.888747\pi\) | ||
0.939540 | − | 0.342438i | \(-0.111253\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.00000 | −0.455104 | ||||||||
\(310\) | 3.73205 | + | 2.46410i | 0.211966 | + | 0.139952i | ||||
\(311\) | 12.0000 | − | 20.7846i | 0.680458 | − | 1.17859i | −0.294384 | − | 0.955687i | \(-0.595114\pi\) |
0.974841 | − | 0.222900i | \(-0.0715523\pi\) | |||||||
\(312\) | 5.19615 | + | 3.00000i | 0.294174 | + | 0.169842i | ||||
\(313\) | 1.73205 | − | 1.00000i | 0.0979013 | − | 0.0565233i | −0.450250 | − | 0.892903i | \(-0.648665\pi\) |
0.548151 | + | 0.836379i | \(0.315332\pi\) | |||||||
\(314\) | −22.0000 | −1.24153 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.0000 | −0.675053 | ||||||||
\(317\) | 1.73205 | − | 1.00000i | 0.0972817 | − | 0.0561656i | −0.450570 | − | 0.892741i | \(-0.648779\pi\) |
0.547852 | + | 0.836576i | \(0.315446\pi\) | |||||||
\(318\) | 5.19615 | + | 3.00000i | 0.291386 | + | 0.168232i | ||||
\(319\) | 6.00000 | − | 10.3923i | 0.335936 | − | 0.581857i | ||||
\(320\) | 1.23205 | − | 1.86603i | 0.0688737 | − | 0.104314i | ||||
\(321\) | −12.0000 | −0.669775 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 24.0000i | − | 1.33540i | ||||||
\(324\) | 0.500000 | + | 0.866025i | 0.0277778 | + | 0.0481125i | ||||
\(325\) | −27.5885 | + | 11.7846i | −1.53033 | + | 0.653693i | ||||
\(326\) | 2.00000 | − | 3.46410i | 0.110770 | − | 0.191859i | ||||
\(327\) | −12.1244 | + | 7.00000i | −0.670478 | + | 0.387101i | ||||
\(328\) | − | 2.00000i | − | 0.110432i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2.00000 | + | 4.00000i | 0.110096 | + | 0.220193i | ||||
\(331\) | 4.00000 | + | 6.92820i | 0.219860 | + | 0.380808i | 0.954765 | − | 0.297361i | \(-0.0961066\pi\) |
−0.734905 | + | 0.678170i | \(0.762773\pi\) | |||||||
\(332\) | 6.92820 | + | 4.00000i | 0.380235 | + | 0.219529i | ||||
\(333\) | −3.46410 | − | 2.00000i | −0.189832 | − | 0.109599i | ||||
\(334\) | 6.00000 | + | 10.3923i | 0.328305 | + | 0.568642i | ||||
\(335\) | −16.0000 | + | 8.00000i | −0.874173 | + | 0.437087i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.00000i | 0.435788i | 0.975972 | + | 0.217894i | \(0.0699187\pi\) | ||||
−0.975972 | + | 0.217894i | \(0.930081\pi\) | |||||||
\(338\) | 19.9186 | − | 11.5000i | 1.08343 | − | 0.625518i | ||||
\(339\) | −3.00000 | + | 5.19615i | −0.162938 | + | 0.282216i | ||||
\(340\) | 0.535898 | − | 8.92820i | 0.0290632 | − | 0.484200i | ||||
\(341\) | −2.00000 | − | 3.46410i | −0.108306 | − | 0.187592i | ||||
\(342\) | − | 6.00000i | − | 0.324443i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −4.00000 | −0.215666 | ||||||||
\(345\) | 9.85641 | − | 14.9282i | 0.530651 | − | 0.803707i | ||||
\(346\) | 4.00000 | − | 6.92820i | 0.215041 | − | 0.372463i | ||||
\(347\) | 31.1769 | + | 18.0000i | 1.67366 | + | 0.966291i | 0.965559 | + | 0.260184i | \(0.0837832\pi\) |
0.708105 | + | 0.706107i | \(0.249550\pi\) | |||||||
\(348\) | −5.19615 | + | 3.00000i | −0.278543 | + | 0.160817i | ||||
\(349\) | −26.0000 | −1.39175 | −0.695874 | − | 0.718164i | \(-0.744983\pi\) | ||||
−0.695874 | + | 0.718164i | \(0.744983\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.00000 | 0.320256 | ||||||||
\(352\) | −1.73205 | + | 1.00000i | −0.0923186 | + | 0.0533002i | ||||
\(353\) | 17.3205 | + | 10.0000i | 0.921878 | + | 0.532246i | 0.884234 | − | 0.467045i | \(-0.154681\pi\) |
0.0376440 | + | 0.999291i | \(0.488015\pi\) | |||||||
\(354\) | −4.00000 | + | 6.92820i | −0.212598 | + | 0.368230i | ||||
\(355\) | 7.39230 | − | 11.1962i | 0.392343 | − | 0.594230i | ||||
\(356\) | 10.0000 | 0.529999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10.0000i | 0.528516i | ||||||||
\(359\) | 3.00000 | + | 5.19615i | 0.158334 | + | 0.274242i | 0.934268 | − | 0.356572i | \(-0.116054\pi\) |
−0.775934 | + | 0.630814i | \(0.782721\pi\) | |||||||
\(360\) | 0.133975 | − | 2.23205i | 0.00706108 | − | 0.117639i | ||||
\(361\) | −8.50000 | + | 14.7224i | −0.447368 | + | 0.774865i | ||||
\(362\) | 1.73205 | − | 1.00000i | 0.0910346 | − | 0.0525588i | ||||
\(363\) | 7.00000i | 0.367405i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 28.0000 | − | 14.0000i | 1.46559 | − | 0.732793i | ||||
\(366\) | 5.00000 | + | 8.66025i | 0.261354 | + | 0.452679i | ||||
\(367\) | 27.7128 | + | 16.0000i | 1.44660 | + | 0.835193i | 0.998277 | − | 0.0586798i | \(-0.0186891\pi\) |
0.448320 | + | 0.893873i | \(0.352022\pi\) | |||||||
\(368\) | 6.92820 | + | 4.00000i | 0.361158 | + | 0.208514i | ||||
\(369\) | −1.00000 | − | 1.73205i | −0.0520579 | − | 0.0901670i | ||||
\(370\) | 4.00000 | + | 8.00000i | 0.207950 | + | 0.415900i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.00000i | 0.103695i | ||||||||
\(373\) | −20.7846 | + | 12.0000i | −1.07619 | + | 0.621336i | −0.929865 | − | 0.367901i | \(-0.880077\pi\) |
−0.146321 | + | 0.989237i | \(0.546743\pi\) | |||||||
\(374\) | −4.00000 | + | 6.92820i | −0.206835 | + | 0.358249i | ||||
\(375\) | 8.52628 | + | 7.23205i | 0.440295 | + | 0.373461i | ||||
\(376\) | 4.00000 | + | 6.92820i | 0.206284 | + | 0.357295i | ||||
\(377\) | 36.0000i | 1.85409i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.0000 | −1.02733 | −0.513665 | − | 0.857991i | \(-0.671713\pi\) | ||||
−0.513665 | + | 0.857991i | \(0.671713\pi\) | |||||||
\(380\) | −7.39230 | + | 11.1962i | −0.379217 | + | 0.574351i | ||||
\(381\) | 2.00000 | − | 3.46410i | 0.102463 | − | 0.177471i | ||||
\(382\) | −15.5885 | − | 9.00000i | −0.797575 | − | 0.460480i | ||||
\(383\) | −17.3205 | + | 10.0000i | −0.885037 | + | 0.510976i | −0.872316 | − | 0.488943i | \(-0.837383\pi\) |
−0.0127209 | + | 0.999919i | \(0.504049\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.00000 | −0.407189 | ||||||||
\(387\) | −3.46410 | + | 2.00000i | −0.176090 | + | 0.101666i | ||||
\(388\) | −8.66025 | − | 5.00000i | −0.439658 | − | 0.253837i | ||||
\(389\) | 1.00000 | − | 1.73205i | 0.0507020 | − | 0.0878185i | −0.839561 | − | 0.543266i | \(-0.817187\pi\) |
0.890263 | + | 0.455448i | \(0.150521\pi\) | |||||||
\(390\) | −11.1962 | − | 7.39230i | −0.566939 | − | 0.374324i | ||||
\(391\) | 32.0000 | 1.61831 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 12.0000i | − | 0.605320i | ||||||
\(394\) | 1.00000 | + | 1.73205i | 0.0503793 | + | 0.0872595i | ||||
\(395\) | 26.7846 | + | 1.60770i | 1.34768 | + | 0.0808919i | ||||
\(396\) | −1.00000 | + | 1.73205i | −0.0502519 | + | 0.0870388i | ||||
\(397\) | −1.73205 | + | 1.00000i | −0.0869291 | + | 0.0501886i | −0.542834 | − | 0.839840i | \(-0.682649\pi\) |
0.455905 | + | 0.890028i | \(0.349316\pi\) | |||||||
\(398\) | − | 6.00000i | − | 0.300753i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.00000 | + | 4.00000i | −0.150000 | + | 0.200000i | ||||
\(401\) | 7.00000 | + | 12.1244i | 0.349563 | + | 0.605461i | 0.986172 | − | 0.165726i | \(-0.0529966\pi\) |
−0.636609 | + | 0.771187i | \(0.719663\pi\) | |||||||
\(402\) | −6.92820 | − | 4.00000i | −0.345547 | − | 0.199502i | ||||
\(403\) | 10.3923 | + | 6.00000i | 0.517678 | + | 0.298881i | ||||
\(404\) | −5.00000 | − | 8.66025i | −0.248759 | − | 0.430864i | ||||
\(405\) | −1.00000 | − | 2.00000i | −0.0496904 | − | 0.0993808i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 8.00000i | − | 0.396545i | ||||||
\(408\) | 3.46410 | − | 2.00000i | 0.171499 | − | 0.0990148i | ||||
\(409\) | −13.0000 | + | 22.5167i | −0.642809 | + | 1.11338i | 0.341994 | + | 0.939702i | \(0.388898\pi\) |
−0.984803 | + | 0.173675i | \(0.944436\pi\) | |||||||
\(410\) | −0.267949 | + | 4.46410i | −0.0132331 | + | 0.220466i | ||||
\(411\) | −3.00000 | − | 5.19615i | −0.147979 | − | 0.256307i | ||||
\(412\) | 8.00000i | 0.394132i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 8.00000 | 0.393179 | ||||||||
\(415\) | −14.9282 | − | 9.85641i | −0.732797 | − | 0.483832i | ||||
\(416\) | 3.00000 | − | 5.19615i | 0.147087 | − | 0.254762i | ||||
\(417\) | −12.1244 | − | 7.00000i | −0.593732 | − | 0.342791i | ||||
\(418\) | 10.3923 | − | 6.00000i | 0.508304 | − | 0.293470i | ||||
\(419\) | 20.0000 | 0.977064 | 0.488532 | − | 0.872546i | \(-0.337533\pi\) | ||||
0.488532 | + | 0.872546i | \(0.337533\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.0000 | 1.65706 | 0.828529 | − | 0.559946i | \(-0.189178\pi\) | ||||
0.828529 | + | 0.559946i | \(0.189178\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.92820 | + | 4.00000i | 0.336861 | + | 0.194487i | ||||
\(424\) | 3.00000 | − | 5.19615i | 0.145693 | − | 0.252347i | ||||
\(425\) | −2.39230 | + | 19.8564i | −0.116044 | + | 0.963177i | ||||
\(426\) | 6.00000 | 0.290701 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 12.0000i | 0.580042i | ||||||||
\(429\) | 6.00000 | + | 10.3923i | 0.289683 | + | 0.501745i | ||||
\(430\) | 8.92820 | + | 0.535898i | 0.430556 | + | 0.0258433i | ||||
\(431\) | −1.00000 | + | 1.73205i | −0.0481683 | + | 0.0834300i | −0.889104 | − | 0.457705i | \(-0.848672\pi\) |
0.840936 | + | 0.541135i | \(0.182005\pi\) | |||||||
\(432\) | 0.866025 | − | 0.500000i | 0.0416667 | − | 0.0240563i | ||||
\(433\) | 26.0000i | 1.24948i | 0.780833 | + | 0.624740i | \(0.214795\pi\) | ||||
−0.780833 | + | 0.624740i | \(0.785205\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 12.0000 | − | 6.00000i | 0.575356 | − | 0.287678i | ||||
\(436\) | 7.00000 | + | 12.1244i | 0.335239 | + | 0.580651i | ||||
\(437\) | −41.5692 | − | 24.0000i | −1.98853 | − | 1.14808i | ||||
\(438\) | 12.1244 | + | 7.00000i | 0.579324 | + | 0.334473i | ||||
\(439\) | 9.00000 | + | 15.5885i | 0.429547 | + | 0.743996i | 0.996833 | − | 0.0795241i | \(-0.0253401\pi\) |
−0.567286 | + | 0.823521i | \(0.692007\pi\) | |||||||
\(440\) | 4.00000 | − | 2.00000i | 0.190693 | − | 0.0953463i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 24.0000i | − | 1.14156i | ||||||
\(443\) | −10.3923 | + | 6.00000i | −0.493753 | + | 0.285069i | −0.726130 | − | 0.687557i | \(-0.758683\pi\) |
0.232377 | + | 0.972626i | \(0.425350\pi\) | |||||||
\(444\) | −2.00000 | + | 3.46410i | −0.0949158 | + | 0.164399i | ||||
\(445\) | −22.3205 | − | 1.33975i | −1.05809 | − | 0.0635100i | ||||
\(446\) | −4.00000 | − | 6.92820i | −0.189405 | − | 0.328060i | ||||
\(447\) | 10.0000i | 0.472984i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.00000 | 0.283158 | 0.141579 | − | 0.989927i | \(-0.454782\pi\) | ||||
0.141579 | + | 0.989927i | \(0.454782\pi\) | |||||||
\(450\) | −0.598076 | + | 4.96410i | −0.0281936 | + | 0.234010i | ||||
\(451\) | 2.00000 | − | 3.46410i | 0.0941763 | − | 0.163118i | ||||
\(452\) | 5.19615 | + | 3.00000i | 0.244406 | + | 0.141108i | ||||
\(453\) | 6.92820 | − | 4.00000i | 0.325515 | − | 0.187936i | ||||
\(454\) | −8.00000 | −0.375459 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.00000 | −0.280976 | ||||||||
\(457\) | −24.2487 | + | 14.0000i | −1.13431 | + | 0.654892i | −0.945015 | − | 0.327028i | \(-0.893953\pi\) |
−0.189292 | + | 0.981921i | \(0.560619\pi\) | |||||||
\(458\) | 12.1244 | + | 7.00000i | 0.566534 | + | 0.327089i | ||||
\(459\) | 2.00000 | − | 3.46410i | 0.0933520 | − | 0.161690i | ||||
\(460\) | −14.9282 | − | 9.85641i | −0.696031 | − | 0.459557i | ||||
\(461\) | 18.0000 | 0.838344 | 0.419172 | − | 0.907907i | \(-0.362320\pi\) | ||||
0.419172 | + | 0.907907i | \(0.362320\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 36.0000i | 1.67306i | 0.547920 | + | 0.836531i | \(0.315420\pi\) | ||||
−0.547920 | + | 0.836531i | \(0.684580\pi\) | |||||||
\(464\) | 3.00000 | + | 5.19615i | 0.139272 | + | 0.241225i | ||||
\(465\) | 0.267949 | − | 4.46410i | 0.0124258 | − | 0.207018i | ||||
\(466\) | 5.00000 | − | 8.66025i | 0.231621 | − | 0.401179i | ||||
\(467\) | −20.7846 | + | 12.0000i | −0.961797 | + | 0.555294i | −0.896726 | − | 0.442587i | \(-0.854061\pi\) |
−0.0650714 | + | 0.997881i | \(0.520728\pi\) | |||||||
\(468\) | − | 6.00000i | − | 0.277350i | ||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −8.00000 | − | 16.0000i | −0.369012 | − | 0.738025i | ||||
\(471\) | 11.0000 | + | 19.0526i | 0.506853 | + | 0.877896i | ||||
\(472\) | 6.92820 | + | 4.00000i | 0.318896 | + | 0.184115i | ||||
\(473\) | −6.92820 | − | 4.00000i | −0.318559 | − | 0.183920i | ||||
\(474\) | 6.00000 | + | 10.3923i | 0.275589 | + | 0.477334i | ||||
\(475\) | 18.0000 | − | 24.0000i | 0.825897 | − | 1.10120i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 6.00000i | − | 0.274721i | ||||||
\(478\) | 22.5167 | − | 13.0000i | 1.02989 | − | 0.594606i | ||||
\(479\) | −4.00000 | + | 6.92820i | −0.182765 | + | 0.316558i | −0.942821 | − | 0.333300i | \(-0.891838\pi\) |
0.760056 | + | 0.649857i | \(0.225171\pi\) | |||||||
\(480\) | −2.23205 | − | 0.133975i | −0.101879 | − | 0.00611508i | ||||
\(481\) | 12.0000 | + | 20.7846i | 0.547153 | + | 0.947697i | ||||
\(482\) | − | 26.0000i | − | 1.18427i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.00000 | 0.318182 | ||||||||
\(485\) | 18.6603 | + | 12.3205i | 0.847318 | + | 0.559445i | ||||
\(486\) | 0.500000 | − | 0.866025i | 0.0226805 | − | 0.0392837i | ||||
\(487\) | 10.3923 | + | 6.00000i | 0.470920 | + | 0.271886i | 0.716625 | − | 0.697459i | \(-0.245686\pi\) |
−0.245705 | + | 0.969345i | \(0.579019\pi\) | |||||||
\(488\) | 8.66025 | − | 5.00000i | 0.392031 | − | 0.226339i | ||||
\(489\) | −4.00000 | −0.180886 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.0000 | −1.35388 | −0.676941 | − | 0.736038i | \(-0.736695\pi\) | ||||
−0.676941 | + | 0.736038i | \(0.736695\pi\) | |||||||
\(492\) | −1.73205 | + | 1.00000i | −0.0780869 | + | 0.0450835i | ||||
\(493\) | 20.7846 | + | 12.0000i | 0.936092 | + | 0.540453i | ||||
\(494\) | −18.0000 | + | 31.1769i | −0.809858 | + | 1.40272i | ||||
\(495\) | 2.46410 | − | 3.73205i | 0.110753 | − | 0.167743i | ||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | − | 8.00000i | − | 0.358489i | ||||||
\(499\) | −6.00000 | − | 10.3923i | −0.268597 | − | 0.465223i | 0.699903 | − | 0.714238i | \(-0.253227\pi\) |
−0.968500 | + | 0.249015i | \(0.919893\pi\) | |||||||
\(500\) | 7.23205 | − | 8.52628i | 0.323427 | − | 0.381307i | ||||
\(501\) | 6.00000 | − | 10.3923i | 0.268060 | − | 0.464294i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.0000i | 0.535054i | 0.963550 | + | 0.267527i | \(0.0862064\pi\) | ||||
−0.963550 | + | 0.267527i | \(0.913794\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.0000 | + | 20.0000i | 0.444994 | + | 0.889988i | ||||
\(506\) | 8.00000 | + | 13.8564i | 0.355643 | + | 0.615992i | ||||
\(507\) | −19.9186 | − | 11.5000i | −0.884615 | − | 0.510733i | ||||
\(508\) | −3.46410 | − | 2.00000i | −0.153695 | − | 0.0887357i | ||||
\(509\) | −15.0000 | − | 25.9808i | −0.664863 | − | 1.15158i | −0.979322 | − | 0.202306i | \(-0.935156\pi\) |
0.314459 | − | 0.949271i | \(-0.398177\pi\) | |||||||
\(510\) | −8.00000 | + | 4.00000i | −0.354246 | + | 0.177123i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −5.19615 | + | 3.00000i | −0.229416 | + | 0.132453i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.07180 | − | 17.8564i | 0.0472290 | − | 0.786847i | ||||
\(516\) | 2.00000 | + | 3.46410i | 0.0880451 | + | 0.152499i | ||||
\(517\) | 16.0000i | 0.703679i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.00000 | −0.351161 | ||||||||
\(520\) | −7.39230 | + | 11.1962i | −0.324174 | + | 0.490984i | ||||
\(521\) | −13.0000 | + | 22.5167i | −0.569540 | + | 0.986473i | 0.427071 | + | 0.904218i | \(0.359545\pi\) |
−0.996611 | + | 0.0822547i | \(0.973788\pi\) | |||||||
\(522\) | 5.19615 | + | 3.00000i | 0.227429 | + | 0.131306i | ||||
\(523\) | 24.2487 | − | 14.0000i | 1.06032 | − | 0.612177i | 0.134801 | − | 0.990873i | \(-0.456961\pi\) |
0.925521 | + | 0.378695i | \(0.123627\pi\) | |||||||
\(524\) | −12.0000 | −0.524222 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.0000 | 0.697633 | ||||||||
\(527\) | 6.92820 | − | 4.00000i | 0.301797 | − | 0.174243i | ||||
\(528\) | 1.73205 | + | 1.00000i | 0.0753778 | + | 0.0435194i | ||||
\(529\) | 20.5000 | − | 35.5070i | 0.891304 | − | 1.54378i | ||||
\(530\) | −7.39230 | + | 11.1962i | −0.321101 | + | 0.486330i | ||||
\(531\) | 8.00000 | 0.347170 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.0000i | 0.519778i | ||||||||
\(534\) | −5.00000 | − | 8.66025i | −0.216371 | − | 0.374766i | ||||
\(535\) | 1.60770 | − | 26.7846i | 0.0695067 | − | 1.15800i | ||||
\(536\) | −4.00000 | + | 6.92820i | −0.172774 | + | 0.299253i | ||||
\(537\) | 8.66025 | − | 5.00000i | 0.373718 | − | 0.215766i | ||||
\(538\) | − | 18.0000i | − | 0.776035i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.00000 | + | 1.00000i | −0.0860663 | + | 0.0430331i | ||||
\(541\) | −11.0000 | − | 19.0526i | −0.472927 | − | 0.819133i | 0.526593 | − | 0.850118i | \(-0.323469\pi\) |
−0.999520 | + | 0.0309841i | \(0.990136\pi\) | |||||||
\(542\) | −8.66025 | − | 5.00000i | −0.371990 | − | 0.214768i | ||||
\(543\) | −1.73205 | − | 1.00000i | −0.0743294 | − | 0.0429141i | ||||
\(544\) | −2.00000 | − | 3.46410i | −0.0857493 | − | 0.148522i | ||||
\(545\) | −14.0000 | − | 28.0000i | −0.599694 | − | 1.19939i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 40.0000i | − | 1.71028i | −0.518400 | − | 0.855138i | \(-0.673472\pi\) | ||
0.518400 | − | 0.855138i | \(-0.326528\pi\) | |||||||
\(548\) | −5.19615 | + | 3.00000i | −0.221969 | + | 0.128154i | ||||
\(549\) | 5.00000 | − | 8.66025i | 0.213395 | − | 0.369611i | ||||
\(550\) | −9.19615 | + | 3.92820i | −0.392125 | + | 0.167499i | ||||
\(551\) | −18.0000 | − | 31.1769i | −0.766826 | − | 1.32818i | ||||
\(552\) | − | 8.00000i | − | 0.340503i | ||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −28.0000 | −1.18961 | ||||||||
\(555\) | 4.92820 | − | 7.46410i | 0.209191 | − | 0.316833i | ||||
\(556\) | −7.00000 | + | 12.1244i | −0.296866 | + | 0.514187i | ||||
\(557\) | −36.3731 | − | 21.0000i | −1.54118 | − | 0.889799i | −0.998765 | − | 0.0496855i | \(-0.984178\pi\) |
−0.542411 | − | 0.840113i | \(-0.682489\pi\) | |||||||
\(558\) | 1.73205 | − | 1.00000i | 0.0733236 | − | 0.0423334i | ||||
\(559\) | 24.0000 | 1.01509 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.00000 | 0.337760 | ||||||||
\(562\) | −25.9808 | + | 15.0000i | −1.09593 | + | 0.632737i | ||||
\(563\) | −3.46410 | − | 2.00000i | −0.145994 | − | 0.0842900i | 0.425223 | − | 0.905088i | \(-0.360196\pi\) |
−0.571218 | + | 0.820798i | \(0.693529\pi\) | |||||||
\(564\) | 4.00000 | − | 6.92820i | 0.168430 | − | 0.291730i | ||||
\(565\) | −11.1962 | − | 7.39230i | −0.471026 | − | 0.310997i | ||||
\(566\) | −20.0000 | −0.840663 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 6.00000i | − | 0.251754i | ||||||
\(569\) | −23.0000 | − | 39.8372i | −0.964210 | − | 1.67006i | −0.711722 | − | 0.702461i | \(-0.752085\pi\) |
−0.252488 | − | 0.967600i | \(-0.581249\pi\) | |||||||
\(570\) | 13.3923 | + | 0.803848i | 0.560942 | + | 0.0336695i | ||||
\(571\) | −2.00000 | + | 3.46410i | −0.0836974 | + | 0.144968i | −0.904835 | − | 0.425762i | \(-0.860006\pi\) |
0.821138 | + | 0.570730i | \(0.193340\pi\) | |||||||
\(572\) | 10.3923 | − | 6.00000i | 0.434524 | − | 0.250873i | ||||
\(573\) | 18.0000i | 0.751961i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 32.0000 | + | 24.0000i | 1.33449 | + | 1.00087i | ||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 22.5167 | + | 13.0000i | 0.937381 | + | 0.541197i | 0.889138 | − | 0.457639i | \(-0.151305\pi\) |
0.0482425 | + | 0.998836i | \(0.484638\pi\) | |||||||
\(578\) | 0.866025 | + | 0.500000i | 0.0360219 | + | 0.0207973i | ||||
\(579\) | 4.00000 | + | 6.92820i | 0.166234 | + | 0.287926i | ||||
\(580\) | −6.00000 | − | 12.0000i | −0.249136 | − | 0.498273i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 10.0000i | 0.414513i | ||||||||
\(583\) | 10.3923 | − | 6.00000i | 0.430405 | − | 0.248495i | ||||
\(584\) | 7.00000 | − | 12.1244i | 0.289662 | − | 0.501709i | ||||
\(585\) | −0.803848 | + | 13.3923i | −0.0332350 | + | 0.553704i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 12.0000i | − | 0.495293i | −0.968850 | − | 0.247647i | \(-0.920343\pi\) | ||
0.968850 | − | 0.247647i | \(-0.0796572\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.0000 | −0.494451 | ||||||||
\(590\) | −14.9282 | − | 9.85641i | −0.614584 | − | 0.405782i | ||||
\(591\) | 1.00000 | − | 1.73205i | 0.0411345 | − | 0.0712470i | ||||
\(592\) | 3.46410 | + | 2.00000i | 0.142374 | + | 0.0821995i | ||||
\(593\) | −10.3923 | + | 6.00000i | −0.426761 | + | 0.246390i | −0.697966 | − | 0.716131i | \(-0.745911\pi\) |
0.271205 | + | 0.962522i | \(0.412578\pi\) | |||||||
\(594\) | 2.00000 | 0.0820610 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.0000 | 0.409616 | ||||||||
\(597\) | −5.19615 | + | 3.00000i | −0.212664 | + | 0.122782i | ||||
\(598\) | −41.5692 | − | 24.0000i | −1.69989 | − | 0.981433i | ||||
\(599\) | 15.0000 | − | 25.9808i | 0.612883 | − | 1.06155i | −0.377869 | − | 0.925859i | \(-0.623343\pi\) |
0.990752 | − | 0.135686i | \(-0.0433238\pi\) | |||||||
\(600\) | 4.96410 | + | 0.598076i | 0.202659 | + | 0.0244164i | ||||
\(601\) | −38.0000 | −1.55005 | −0.775026 | − | 0.631929i | \(-0.782263\pi\) | ||||
−0.775026 | + | 0.631929i | \(0.782263\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.00000i | 0.325785i | ||||||||
\(604\) | −4.00000 | − | 6.92820i | −0.162758 | − | 0.281905i | ||||
\(605\) | −15.6244 | − | 0.937822i | −0.635220 | − | 0.0381279i | ||||
\(606\) | −5.00000 | + | 8.66025i | −0.203111 | + | 0.351799i | ||||
\(607\) | 6.92820 | − | 4.00000i | 0.281207 | − | 0.162355i | −0.352763 | − | 0.935713i | \(-0.614758\pi\) |
0.633970 | + | 0.773358i | \(0.281424\pi\) | |||||||
\(608\) | 6.00000i | 0.243332i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −20.0000 | + | 10.0000i | −0.809776 | + | 0.404888i | ||||
\(611\) | −24.0000 | − | 41.5692i | −0.970936 | − | 1.68171i | ||||
\(612\) | −3.46410 | − | 2.00000i | −0.140028 | − | 0.0808452i | ||||
\(613\) | −24.2487 | − | 14.0000i | −0.979396 | − | 0.565455i | −0.0773084 | − | 0.997007i | \(-0.524633\pi\) |
−0.902088 | + | 0.431553i | \(0.857966\pi\) | |||||||
\(614\) | 6.00000 | + | 10.3923i | 0.242140 | + | 0.419399i | ||||
\(615\) | 4.00000 | − | 2.00000i | 0.161296 | − | 0.0806478i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.0000i | 1.04672i | 0.852111 | + | 0.523360i | \(0.175322\pi\) | ||||
−0.852111 | + | 0.523360i | \(0.824678\pi\) | |||||||
\(618\) | 6.92820 | − | 4.00000i | 0.278693 | − | 0.160904i | ||||
\(619\) | 11.0000 | − | 19.0526i | 0.442127 | − | 0.765787i | −0.555720 | − | 0.831370i | \(-0.687557\pi\) |
0.997847 | + | 0.0655827i | \(0.0208906\pi\) | |||||||
\(620\) | −4.46410 | − | 0.267949i | −0.179283 | − | 0.0107611i | ||||
\(621\) | −4.00000 | − | 6.92820i | −0.160514 | − | 0.278019i | ||||
\(622\) | 24.0000i | 0.962312i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −6.00000 | −0.240192 | ||||||||
\(625\) | −17.2846 | + | 18.0622i | −0.691384 | + | 0.722487i | ||||
\(626\) | −1.00000 | + | 1.73205i | −0.0399680 | + | 0.0692267i | ||||
\(627\) | −10.3923 | − | 6.00000i | −0.415029 | − | 0.239617i | ||||
\(628\) | 19.0526 | − | 11.0000i | 0.760280 | − | 0.438948i | ||||
\(629\) | 16.0000 | 0.637962 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.00000 | −0.159237 | −0.0796187 | − | 0.996825i | \(-0.525370\pi\) | ||||
−0.0796187 | + | 0.996825i | \(0.525370\pi\) | |||||||
\(632\) | 10.3923 | − | 6.00000i | 0.413384 | − | 0.238667i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.00000 | + | 1.73205i | −0.0397151 | + | 0.0687885i | ||||
\(635\) | 7.46410 | + | 4.92820i | 0.296204 | + | 0.195570i | ||||
\(636\) | −6.00000 | −0.237915 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 12.0000i | 0.475085i | ||||||||
\(639\) | −3.00000 | − | 5.19615i | −0.118678 | − | 0.205557i | ||||
\(640\) | −0.133975 | + | 2.23205i | −0.00529581 | + | 0.0882296i | ||||
\(641\) | −7.00000 | + | 12.1244i | −0.276483 | + | 0.478883i | −0.970508 | − | 0.241068i | \(-0.922502\pi\) |
0.694025 | + | 0.719951i | \(0.255836\pi\) | |||||||
\(642\) | 10.3923 | − | 6.00000i | 0.410152 | − | 0.236801i | ||||
\(643\) | − | 12.0000i | − | 0.473234i | −0.971603 | − | 0.236617i | \(-0.923961\pi\) | ||
0.971603 | − | 0.236617i | \(-0.0760386\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.00000 | − | 8.00000i | −0.157500 | − | 0.315000i | ||||
\(646\) | 12.0000 | + | 20.7846i | 0.472134 | + | 0.817760i | ||||
\(647\) | −31.1769 | − | 18.0000i | −1.22569 | − | 0.707653i | −0.259565 | − | 0.965726i | \(-0.583579\pi\) |
−0.966126 | + | 0.258073i | \(0.916913\pi\) | |||||||
\(648\) | −0.866025 | − | 0.500000i | −0.0340207 | − | 0.0196419i | ||||
\(649\) | 8.00000 | + | 13.8564i | 0.314027 | + | 0.543912i | ||||
\(650\) | 18.0000 | − | 24.0000i | 0.706018 | − | 0.941357i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.00000i | 0.156652i | ||||||||
\(653\) | 29.4449 | − | 17.0000i | 1.15227 | − | 0.665261i | 0.202828 | − | 0.979214i | \(-0.434987\pi\) |
0.949439 | + | 0.313953i | \(0.101653\pi\) | |||||||
\(654\) | 7.00000 | − | 12.1244i | 0.273722 | − | 0.474100i | ||||
\(655\) | 26.7846 | + | 1.60770i | 1.04656 | + | 0.0628178i | ||||
\(656\) | 1.00000 | + | 1.73205i | 0.0390434 | + | 0.0676252i | ||||
\(657\) | − | 14.0000i | − | 0.546192i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26.0000 | 1.01282 | 0.506408 | − | 0.862294i | \(-0.330973\pi\) | ||||
0.506408 | + | 0.862294i | \(0.330973\pi\) | |||||||
\(660\) | −3.73205 | − | 2.46410i | −0.145270 | − | 0.0959150i | ||||
\(661\) | 19.0000 | − | 32.9090i | 0.739014 | − | 1.28001i | −0.213925 | − | 0.976850i | \(-0.568625\pi\) |
0.952940 | − | 0.303160i | \(-0.0980418\pi\) | |||||||
\(662\) | −6.92820 | − | 4.00000i | −0.269272 | − | 0.155464i | ||||
\(663\) | −20.7846 | + | 12.0000i | −0.807207 | + | 0.466041i | ||||
\(664\) | −8.00000 | −0.310460 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.00000 | 0.154997 | ||||||||
\(667\) | 41.5692 | − | 24.0000i | 1.60957 | − | 0.929284i | ||||
\(668\) | −10.3923 | − | 6.00000i | −0.402090 | − | 0.232147i | ||||
\(669\) | −4.00000 | + | 6.92820i | −0.154649 | + | 0.267860i | ||||
\(670\) | 9.85641 | − | 14.9282i | 0.380786 | − | 0.576727i | ||||
\(671\) | 20.0000 | 0.772091 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.0000i | 0.462566i | 0.972887 | + | 0.231283i | \(0.0742923\pi\) | ||||
−0.972887 | + | 0.231283i | \(0.925708\pi\) | |||||||
\(674\) | −4.00000 | − | 6.92820i | −0.154074 | − | 0.266864i | ||||
\(675\) | 4.59808 | − | 1.96410i | 0.176980 | − | 0.0755983i | ||||
\(676\) | −11.5000 | + | 19.9186i | −0.442308 | + | 0.766099i | ||||
\(677\) | 34.6410 | − | 20.0000i | 1.33136 | − | 0.768662i | 0.345854 | − | 0.938288i | \(-0.387589\pi\) |
0.985509 | + | 0.169626i | \(0.0542560\pi\) | |||||||
\(678\) | − | 6.00000i | − | 0.230429i | ||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4.00000 | + | 8.00000i | 0.153393 | + | 0.306786i | ||||
\(681\) | 4.00000 | + | 6.92820i | 0.153280 | + | 0.265489i | ||||
\(682\) | 3.46410 | + | 2.00000i | 0.132647 | + | 0.0765840i | ||||
\(683\) | −3.46410 | − | 2.00000i | −0.132550 | − | 0.0765279i | 0.432259 | − | 0.901750i | \(-0.357717\pi\) |
−0.564809 | + | 0.825222i | \(0.691050\pi\) | |||||||
\(684\) | 3.00000 | + | 5.19615i | 0.114708 | + | 0.198680i | ||||
\(685\) | 12.0000 | − | 6.00000i | 0.458496 | − | 0.229248i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 14.0000i | − | 0.534133i | ||||||
\(688\) | 3.46410 | − | 2.00000i | 0.132068 | − | 0.0762493i | ||||
\(689\) | −18.0000 | + | 31.1769i | −0.685745 | + | 1.18775i | ||||
\(690\) | −1.07180 | + | 17.8564i | −0.0408026 | + | 0.679782i | ||||
\(691\) | −1.00000 | − | 1.73205i | −0.0380418 | − | 0.0658903i | 0.846378 | − | 0.532583i | \(-0.178779\pi\) |
−0.884419 | + | 0.466693i | \(0.845445\pi\) | |||||||
\(692\) | 8.00000i | 0.304114i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −36.0000 | −1.36654 | ||||||||
\(695\) | 17.2487 | − | 26.1244i | 0.654281 | − | 0.990953i | ||||
\(696\) | 3.00000 | − | 5.19615i | 0.113715 | − | 0.196960i | ||||
\(697\) | 6.92820 | + | 4.00000i | 0.262424 | + | 0.151511i | ||||
\(698\) | 22.5167 | − | 13.0000i | 0.852268 | − | 0.492057i | ||||
\(699\) | −10.0000 | −0.378235 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −34.0000 | −1.28416 | −0.642081 | − | 0.766637i | \(-0.721929\pi\) | ||||
−0.642081 | + | 0.766637i | \(0.721929\pi\) | |||||||
\(702\) | −5.19615 | + | 3.00000i | −0.196116 | + | 0.113228i | ||||
\(703\) | −20.7846 | − | 12.0000i | −0.783906 | − | 0.452589i | ||||
\(704\) | 1.00000 | − | 1.73205i | 0.0376889 | − | 0.0652791i | ||||
\(705\) | −9.85641 | + | 14.9282i | −0.371214 | + | 0.562229i | ||||
\(706\) | −20.0000 | −0.752710 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | − | 8.00000i | − | 0.300658i | ||||||
\(709\) | −3.00000 | − | 5.19615i | −0.112667 | − | 0.195146i | 0.804178 | − | 0.594389i | \(-0.202606\pi\) |
−0.916845 | + | 0.399244i | \(0.869273\pi\) | |||||||
\(710\) | −0.803848 | + | 13.3923i | −0.0301679 | + | 0.502604i | ||||
\(711\) | 6.00000 | − | 10.3923i | 0.225018 | − | 0.389742i | ||||
\(712\) | −8.66025 | + | 5.00000i | −0.324557 | + | 0.187383i | ||||
\(713\) | − | 16.0000i | − | 0.599205i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −24.0000 | + | 12.0000i | −0.897549 | + | 0.448775i | ||||
\(716\) | −5.00000 | − | 8.66025i | −0.186859 | − | 0.323649i | ||||
\(717\) | −22.5167 | − | 13.0000i | −0.840900 | − | 0.485494i | ||||
\(718\) | −5.19615 | − | 3.00000i | −0.193919 | − | 0.111959i | ||||
\(719\) | 2.00000 | + | 3.46410i | 0.0745874 | + | 0.129189i | 0.900907 | − | 0.434013i | \(-0.142903\pi\) |
−0.826319 | + | 0.563202i | \(0.809569\pi\) | |||||||
\(720\) | 1.00000 | + | 2.00000i | 0.0372678 | + | 0.0745356i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 17.0000i | − | 0.632674i | ||||||
\(723\) | −22.5167 | + | 13.0000i | −0.837404 | + | 0.483475i | ||||
\(724\) | −1.00000 | + | 1.73205i | −0.0371647 | + | 0.0643712i | ||||
\(725\) | 11.7846 | + | 27.5885i | 0.437669 | + | 1.02461i | ||||
\(726\) | −3.50000 | − | 6.06218i | −0.129897 | − | 0.224989i | ||||
\(727\) | 24.0000i | 0.890111i | 0.895503 | + | 0.445055i | \(0.146816\pi\) | ||||
−0.895503 | + | 0.445055i | \(0.853184\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −17.2487 | + | 26.1244i | −0.638403 | + | 0.966906i | ||||
\(731\) | 8.00000 | − | 13.8564i | 0.295891 | − | 0.512498i | ||||
\(732\) | −8.66025 | − | 5.00000i | −0.320092 | − | 0.184805i | ||||
\(733\) | −12.1244 | + | 7.00000i | −0.447823 | + | 0.258551i | −0.706910 | − | 0.707303i | \(-0.749912\pi\) |
0.259087 | + | 0.965854i | \(0.416578\pi\) | |||||||
\(734\) | −32.0000 | −1.18114 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.00000 | −0.294884 | ||||||||
\(737\) | −13.8564 | + | 8.00000i | −0.510407 | + | 0.294684i | ||||
\(738\) | 1.73205 | + | 1.00000i | 0.0637577 | + | 0.0368105i | ||||
\(739\) | −22.0000 | + | 38.1051i | −0.809283 | + | 1.40172i | 0.104078 | + | 0.994569i | \(0.466811\pi\) |
−0.913361 | + | 0.407150i | \(0.866523\pi\) | |||||||
\(740\) | −7.46410 | − | 4.92820i | −0.274386 | − | 0.181164i | ||||
\(741\) | 36.0000 | 1.32249 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 48.0000i | − | 1.76095i | −0.474093 | − | 0.880475i | \(-0.657224\pi\) | ||
0.474093 | − | 0.880475i | \(-0.342776\pi\) | |||||||
\(744\) | −1.00000 | − | 1.73205i | −0.0366618 | − | 0.0635001i | ||||
\(745\) | −22.3205 | − | 1.33975i | −0.817760 | − | 0.0490845i | ||||
\(746\) | 12.0000 | − | 20.7846i | 0.439351 | − | 0.760979i | ||||
\(747\) | −6.92820 | + | 4.00000i | −0.253490 | + | 0.146352i | ||||
\(748\) | − | 8.00000i | − | 0.292509i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −11.0000 | − | 2.00000i | −0.401663 | − | 0.0730297i | ||||
\(751\) | −10.0000 | − | 17.3205i | −0.364905 | − | 0.632034i | 0.623856 | − | 0.781540i | \(-0.285565\pi\) |
−0.988761 | + | 0.149505i | \(0.952232\pi\) | |||||||
\(752\) | −6.92820 | − | 4.00000i | −0.252646 | − | 0.145865i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −18.0000 | − | 31.1769i | −0.655521 | − | 1.13540i | ||||
\(755\) | 8.00000 | + | 16.0000i | 0.291150 | + | 0.582300i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.0000i | 1.16306i | 0.813525 | + | 0.581530i | \(0.197546\pi\) | ||||
−0.813525 | + | 0.581530i | \(0.802454\pi\) | |||||||
\(758\) | 17.3205 | − | 10.0000i | 0.629109 | − | 0.363216i | ||||
\(759\) | 8.00000 | − | 13.8564i | 0.290382 | − | 0.502956i | ||||
\(760\) | 0.803848 | − | 13.3923i | 0.0291586 | − | 0.485790i | ||||
\(761\) | −3.00000 | − | 5.19615i | −0.108750 | − | 0.188360i | 0.806514 | − | 0.591215i | \(-0.201351\pi\) |
−0.915264 | + | 0.402854i | \(0.868018\pi\) | |||||||
\(762\) | 4.00000i | 0.144905i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 18.0000 | 0.651217 | ||||||||
\(765\) | 7.46410 | + | 4.92820i | 0.269865 | + | 0.178180i | ||||
\(766\) | 10.0000 | − | 17.3205i | 0.361315 | − | 0.625815i | ||||
\(767\) | −41.5692 | − | 24.0000i | −1.50098 | − | 0.866590i | ||||
\(768\) | −0.866025 | + | 0.500000i | −0.0312500 | + | 0.0180422i | ||||
\(769\) | 30.0000 | 1.08183 | 0.540914 | − | 0.841078i | \(-0.318079\pi\) | ||||
0.540914 | + | 0.841078i | \(0.318079\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.92820 | − | 4.00000i | 0.249351 | − | 0.143963i | ||||
\(773\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(774\) | 2.00000 | − | 3.46410i | 0.0718885 | − | 0.124515i | ||||
\(775\) | 9.92820 | + | 1.19615i | 0.356632 | + | 0.0429671i | ||||
\(776\) | 10.0000 | 0.358979 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.00000i | 0.0717035i | ||||||||
\(779\) | −6.00000 | − | 10.3923i | −0.214972 | − | 0.372343i | ||||
\(780\) | 13.3923 | + | 0.803848i | 0.479521 | + | 0.0287824i | ||||
\(781\) | 6.00000 | − | 10.3923i | 0.214697 | − | 0.371866i | ||||
\(782\) | −27.7128 | + | 16.0000i | −0.991008 | + | 0.572159i | ||||
\(783\) | − | 6.00000i | − | 0.214423i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −44.0000 | + | 22.0000i | −1.57043 | + | 0.785214i | ||||
\(786\) | 6.00000 | + | 10.3923i | 0.214013 | + | 0.370681i | ||||
\(787\) | −24.2487 | − | 14.0000i | −0.864373 | − | 0.499046i | 0.00110111 | − | 0.999999i | \(-0.499650\pi\) |
−0.865474 | + | 0.500953i | \(0.832983\pi\) | |||||||
\(788\) | −1.73205 | − | 1.00000i | −0.0617018 | − | 0.0356235i | ||||
\(789\) | −8.00000 | − | 13.8564i | −0.284808 | − | 0.493301i | ||||
\(790\) | −24.0000 | + | 12.0000i | −0.853882 | + | 0.426941i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − | 2.00000i | − | 0.0710669i | ||||||
\(793\) | −51.9615 | + | 30.0000i | −1.84521 | + | 1.06533i | ||||
\(794\) | 1.00000 | − | 1.73205i | 0.0354887 | − | 0.0614682i | ||||
\(795\) | 13.3923 | + | 0.803848i | 0.474976 | + | 0.0285095i | ||||
\(796\) | 3.00000 | + | 5.19615i | 0.106332 | + | 0.184173i | ||||
\(797\) | − | 8.00000i | − | 0.283375i | −0.989911 | − | 0.141687i | \(-0.954747\pi\) | ||
0.989911 | − | 0.141687i | \(-0.0452527\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32.0000 | −1.13208 | ||||||||
\(800\) | 0.598076 | − | 4.96410i | 0.0211452 | − | 0.175507i | ||||
\(801\) | −5.00000 | + | 8.66025i | −0.176666 | + | 0.305995i | ||||
\(802\) | −12.1244 | − | 7.00000i | −0.428126 | − | 0.247179i | ||||
\(803\) | 24.2487 | − | 14.0000i | 0.855718 | − | 0.494049i | ||||
\(804\) | 8.00000 | 0.282138 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −12.0000 | −0.422682 | ||||||||
\(807\) | −15.5885 | + | 9.00000i | −0.548740 | + | 0.316815i | ||||
\(808\) | 8.66025 | + | 5.00000i | 0.304667 | + | 0.175899i | ||||
\(809\) | 15.0000 | − | 25.9808i | 0.527372 | − | 0.913435i | −0.472119 | − | 0.881535i | \(-0.656511\pi\) |
0.999491 | − | 0.0319002i | \(-0.0101559\pi\) | |||||||
\(810\) | 1.86603 | + | 1.23205i | 0.0655654 | + | 0.0432899i | ||||
\(811\) | 14.0000 | 0.491606 | 0.245803 | − | 0.969320i | \(-0.420948\pi\) | ||||
0.245803 | + | 0.969320i | \(0.420948\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.0000i | 0.350715i | ||||||||
\(814\) | 4.00000 | + | 6.92820i | 0.140200 | + | 0.242833i | ||||
\(815\) | 0.535898 | − | 8.92820i | 0.0187717 | − | 0.312741i | ||||
\(816\) | −2.00000 | + | 3.46410i | −0.0700140 | + | 0.121268i | ||||
\(817\) | −20.7846 | + | 12.0000i | −0.727161 | + | 0.419827i | ||||
\(818\) | − | 26.0000i | − | 0.909069i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.00000 | − | 4.00000i | −0.0698430 | − | 0.139686i | ||||
\(821\) | −11.0000 | − | 19.0526i | −0.383903 | − | 0.664939i | 0.607714 | − | 0.794156i | \(-0.292087\pi\) |
−0.991616 | + | 0.129217i | \(0.958754\pi\) | |||||||
\(822\) | 5.19615 | + | 3.00000i | 0.181237 | + | 0.104637i | ||||
\(823\) | −10.3923 | − | 6.00000i | −0.362253 | − | 0.209147i | 0.307816 | − | 0.951446i | \(-0.400402\pi\) |
−0.670069 | + | 0.742299i | \(0.733735\pi\) | |||||||
\(824\) | −4.00000 | − | 6.92820i | −0.139347 | − | 0.241355i | ||||
\(825\) | 8.00000 | + | 6.00000i | 0.278524 | + | 0.208893i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.0000i | 0.695468i | 0.937593 | + | 0.347734i | \(0.113049\pi\) | ||||
−0.937593 | + | 0.347734i | \(0.886951\pi\) | |||||||
\(828\) | −6.92820 | + | 4.00000i | −0.240772 | + | 0.139010i | ||||
\(829\) | −9.00000 | + | 15.5885i | −0.312583 | + | 0.541409i | −0.978921 | − | 0.204240i | \(-0.934528\pi\) |
0.666338 | + | 0.745650i | \(0.267861\pi\) | |||||||
\(830\) | 17.8564 | + | 1.07180i | 0.619805 | + | 0.0372026i | ||||
\(831\) | 14.0000 | + | 24.2487i | 0.485655 | + | 0.841178i | ||||
\(832\) | 6.00000i | 0.208013i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 14.0000 | 0.484780 | ||||||||
\(835\) | 22.3923 | + | 14.7846i | 0.774918 | + | 0.511643i | ||||
\(836\) | −6.00000 | + | 10.3923i | −0.207514 | + | 0.359425i | ||||
\(837\) | −1.73205 | − | 1.00000i | −0.0598684 | − | 0.0345651i | ||||
\(838\) | −17.3205 | + | 10.0000i | −0.598327 | + | 0.345444i | ||||
\(839\) | −20.0000 | −0.690477 | −0.345238 | − | 0.938515i | \(-0.612202\pi\) | ||||
−0.345238 | + | 0.938515i | \(0.612202\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | −29.4449 | + | 17.0000i | −1.01474 | + | 0.585859i | ||||
\(843\) | 25.9808 | + | 15.0000i | 0.894825 | + | 0.516627i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 28.3372 | − | 42.9186i | 0.974828 | − | 1.47644i | ||||
\(846\) | −8.00000 | −0.275046 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6.00000i | 0.206041i | ||||||||
\(849\) | 10.0000 | + | 17.3205i | 0.343199 | + | 0.594438i | ||||
\(850\) | −7.85641 | − | 18.3923i | −0.269473 | − | 0.630851i | ||||
\(851\) | 16.0000 | − | 27.7128i | 0.548473 | − | 0.949983i | ||||
\(852\) | −5.19615 | + | 3.00000i | −0.178017 | + | 0.102778i | ||||
\(853\) | − | 38.0000i | − | 1.30110i | −0.759465 | − | 0.650548i | \(-0.774539\pi\) | ||
0.759465 | − | 0.650548i | \(-0.225461\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.00000 | − | 12.0000i | −0.205196 | − | 0.410391i | ||||
\(856\) | −6.00000 | − | 10.3923i | −0.205076 | − | 0.355202i | ||||
\(857\) | −20.7846 | − | 12.0000i | −0.709989 | − | 0.409912i | 0.101068 | − | 0.994880i | \(-0.467774\pi\) |
−0.811057 | + | 0.584967i | \(0.801107\pi\) | |||||||
\(858\) | −10.3923 | − | 6.00000i | −0.354787 | − | 0.204837i | ||||
\(859\) | 5.00000 | + | 8.66025i | 0.170598 | + | 0.295484i | 0.938629 | − | 0.344928i | \(-0.112097\pi\) |
−0.768031 | + | 0.640412i | \(0.778763\pi\) | |||||||
\(860\) | −8.00000 | + | 4.00000i | −0.272798 | + | 0.136399i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 2.00000i | − | 0.0681203i | ||||||
\(863\) | −41.5692 | + | 24.0000i | −1.41503 | + | 0.816970i | −0.995857 | − | 0.0909355i | \(-0.971014\pi\) |
−0.419176 | + | 0.907905i | \(0.637681\pi\) | |||||||
\(864\) | −0.500000 | + | 0.866025i | −0.0170103 | + | 0.0294628i | ||||
\(865\) | 1.07180 | − | 17.8564i | 0.0364422 | − | 0.607136i | ||||
\(866\) | −13.0000 | − | 22.5167i | −0.441758 | − | 0.765147i | ||||
\(867\) | − | 1.00000i | − | 0.0339618i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.0000 | 0.814144 | ||||||||
\(870\) | −7.39230 | + | 11.1962i | −0.250623 | + | 0.379585i | ||||
\(871\) | 24.0000 | − | 41.5692i | 0.813209 | − | 1.40852i | ||||
\(872\) | −12.1244 | − | 7.00000i | −0.410582 | − | 0.237050i | ||||
\(873\) | 8.66025 | − | 5.00000i | 0.293105 | − | 0.169224i | ||||
\(874\) | 48.0000 | 1.62362 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −14.0000 | −0.473016 | ||||||||
\(877\) | 24.2487 | − | 14.0000i | 0.818821 | − | 0.472746i | −0.0311889 | − | 0.999514i | \(-0.509929\pi\) |
0.850010 | + | 0.526767i | \(0.176596\pi\) | |||||||
\(878\) | −15.5885 | − | 9.00000i | −0.526085 | − | 0.303735i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.46410 | + | 3.73205i | −0.0830648 | + | 0.125807i | ||||
\(881\) | −30.0000 | −1.01073 | −0.505363 | − | 0.862907i | \(-0.668641\pi\) | ||||
−0.505363 | + | 0.862907i | \(0.668641\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.0000i | 0.807664i | 0.914833 | + | 0.403832i | \(0.132322\pi\) | ||||
−0.914833 | + | 0.403832i | \(0.867678\pi\) | |||||||
\(884\) | 12.0000 | + | 20.7846i | 0.403604 | + | 0.699062i | ||||
\(885\) | −1.07180 | + | 17.8564i | −0.0360281 | + | 0.600237i | ||||
\(886\) | 6.00000 | − | 10.3923i | 0.201574 | − | 0.349136i | ||||
\(887\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(888\) | − | 4.00000i | − | 0.134231i | ||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 20.0000 | − | 10.0000i | 0.670402 | − | 0.335201i | ||||
\(891\) | −1.00000 | − | 1.73205i | −0.0335013 | − | 0.0580259i | ||||
\(892\) | 6.92820 | + | 4.00000i | 0.231973 | + | 0.133930i | ||||
\(893\) | 41.5692 | + | 24.0000i | 1.39106 | + | 0.803129i | ||||
\(894\) | −5.00000 | − | 8.66025i | −0.167225 | − | 0.289642i | ||||
\(895\) | 10.0000 | + | 20.0000i | 0.334263 | + | 0.668526i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 48.0000i | 1.60267i | ||||||||
\(898\) | −5.19615 | + | 3.00000i | −0.173398 | + | 0.100111i | ||||
\(899\) | 6.00000 | − | 10.3923i | 0.200111 | − | 0.346603i | ||||
\(900\) | −1.96410 | − | 4.59808i | −0.0654701 | − | 0.153269i | ||||
\(901\) | 12.0000 | + | 20.7846i | 0.399778 | + | 0.692436i | ||||
\(902\) | 4.00000i | 0.133185i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.00000 | −0.199557 | ||||||||
\(905\) | 2.46410 | − | 3.73205i | 0.0819095 | − | 0.124058i | ||||
\(906\) | −4.00000 | + | 6.92820i | −0.132891 | + | 0.230174i | ||||
\(907\) | 20.7846 | + | 12.0000i | 0.690142 | + | 0.398453i | 0.803665 | − | 0.595082i | \(-0.202880\pi\) |
−0.113523 | + | 0.993535i | \(0.536214\pi\) | |||||||
\(908\) | 6.92820 | − | 4.00000i | 0.229920 | − | 0.132745i | ||||
\(909\) | 10.0000 | 0.331679 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.00000 | 0.198789 | 0.0993944 | − | 0.995048i | \(-0.468309\pi\) | ||||
0.0993944 | + | 0.995048i | \(0.468309\pi\) | |||||||
\(912\) | 5.19615 | − | 3.00000i | 0.172062 | − | 0.0993399i | ||||
\(913\) | −13.8564 | − | 8.00000i | −0.458580 | − | 0.264761i | ||||
\(914\) | 14.0000 | − | 24.2487i | 0.463079 | − | 0.802076i | ||||
\(915\) | 18.6603 | + | 12.3205i | 0.616889 | + | 0.407303i | ||||
\(916\) | −14.0000 | −0.462573 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 4.00000i | 0.132020i | ||||||||
\(919\) | 30.0000 | + | 51.9615i | 0.989609 | + | 1.71405i | 0.619327 | + | 0.785133i | \(0.287405\pi\) |
0.370281 | + | 0.928920i | \(0.379261\pi\) | |||||||
\(920\) | 17.8564 | + | 1.07180i | 0.588708 | + | 0.0353361i | ||||
\(921\) | 6.00000 | − | 10.3923i | 0.197707 | − | 0.342438i | ||||
\(922\) | −15.5885 | + | 9.00000i | −0.513378 | + | 0.296399i | ||||
\(923\) | 36.0000i | 1.18495i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16.0000 | + | 12.0000i | 0.526077 | + | 0.394558i | ||||
\(926\) | −18.0000 | − | 31.1769i | −0.591517 | − | 1.02454i | ||||
\(927\) | −6.92820 | − | 4.00000i | −0.227552 | − | 0.131377i | ||||
\(928\) | −5.19615 | − | 3.00000i | −0.170572 | − | 0.0984798i | ||||
\(929\) | 15.0000 | + | 25.9808i | 0.492134 | + | 0.852401i | 0.999959 | − | 0.00905914i | \(-0.00288365\pi\) |
−0.507825 | + | 0.861460i | \(0.669550\pi\) | |||||||
\(930\) | 2.00000 | + | 4.00000i | 0.0655826 | + | 0.131165i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 10.0000i | 0.327561i | ||||||||
\(933\) | 20.7846 | − | 12.0000i | 0.680458 | − | 0.392862i | ||||
\(934\) | 12.0000 | − | 20.7846i | 0.392652 | − | 0.680093i | ||||
\(935\) | −1.07180 | + | 17.8564i | −0.0350515 | + | 0.583967i | ||||
\(936\) | 3.00000 | + | 5.19615i | 0.0980581 | + | 0.169842i | ||||
\(937\) | 26.0000i | 0.849383i | 0.905338 | + | 0.424691i | \(0.139617\pi\) | ||||
−0.905338 | + | 0.424691i | \(0.860383\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.00000 | 0.0652675 | ||||||||
\(940\) | 14.9282 | + | 9.85641i | 0.486904 | + | 0.321481i | ||||
\(941\) | −5.00000 | + | 8.66025i | −0.162995 | + | 0.282316i | −0.935942 | − | 0.352155i | \(-0.885449\pi\) |
0.772946 | + | 0.634472i | \(0.218782\pi\) | |||||||
\(942\) | −19.0526 | − | 11.0000i | −0.620766 | − | 0.358399i | ||||
\(943\) | 13.8564 | − | 8.00000i | 0.451227 | − | 0.260516i | ||||
\(944\) | −8.00000 | −0.260378 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.00000 | 0.260102 | ||||||||
\(947\) | 10.3923 | − | 6.00000i | 0.337705 | − | 0.194974i | −0.321552 | − | 0.946892i | \(-0.604204\pi\) |
0.659256 | + | 0.751918i | \(0.270871\pi\) | |||||||
\(948\) | −10.3923 | − | 6.00000i | −0.337526 | − | 0.194871i | ||||
\(949\) | −42.0000 | + | 72.7461i | −1.36338 | + | 2.36144i | ||||
\(950\) | −3.58846 | + | 29.7846i | −0.116425 | + | 0.966340i | ||||
\(951\) | 2.00000 | 0.0648544 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 10.0000i | − | 0.323932i | −0.986796 | − | 0.161966i | \(-0.948217\pi\) | ||
0.986796 | − | 0.161966i | \(-0.0517835\pi\) | |||||||
\(954\) | 3.00000 | + | 5.19615i | 0.0971286 | + | 0.168232i | ||||
\(955\) | −40.1769 | − | 2.41154i | −1.30009 | − | 0.0780357i | ||||
\(956\) | −13.0000 | + | 22.5167i | −0.420450 | + | 0.728241i | ||||
\(957\) | 10.3923 | − | 6.00000i | 0.335936 | − | 0.193952i | ||||
\(958\) | − | 8.00000i | − | 0.258468i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.00000 | − | 1.00000i | 0.0645497 | − | 0.0322749i | ||||
\(961\) | 13.5000 | + | 23.3827i | 0.435484 | + | 0.754280i | ||||
\(962\) | −20.7846 | − | 12.0000i | −0.670123 | − | 0.386896i | ||||
\(963\) | −10.3923 | − | 6.00000i | −0.334887 | − | 0.193347i | ||||
\(964\) | 13.0000 | + | 22.5167i | 0.418702 | + | 0.725213i | ||||
\(965\) | −16.0000 | + | 8.00000i | −0.515058 | + | 0.257529i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 56.0000i | − | 1.80084i | −0.435023 | − | 0.900419i | \(-0.643260\pi\) | ||
0.435023 | − | 0.900419i | \(-0.356740\pi\) | |||||||
\(968\) | −6.06218 | + | 3.50000i | −0.194846 | + | 0.112494i | ||||
\(969\) | 12.0000 | − | 20.7846i | 0.385496 | − | 0.667698i | ||||
\(970\) | −22.3205 | − | 1.33975i | −0.716668 | − | 0.0430167i | ||||
\(971\) | −12.0000 | − | 20.7846i | −0.385098 | − | 0.667010i | 0.606685 | − | 0.794943i | \(-0.292499\pi\) |
−0.991783 | + | 0.127933i | \(0.959166\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −12.0000 | −0.384505 | ||||||||
\(975\) | −29.7846 | − | 3.58846i | −0.953871 | − | 0.114923i | ||||
\(976\) | −5.00000 | + | 8.66025i | −0.160046 | + | 0.277208i | ||||
\(977\) | −15.5885 | − | 9.00000i | −0.498719 | − | 0.287936i | 0.229465 | − | 0.973317i | \(-0.426302\pi\) |
−0.728184 | + | 0.685381i | \(0.759636\pi\) | |||||||
\(978\) | 3.46410 | − | 2.00000i | 0.110770 | − | 0.0639529i | ||||
\(979\) | −20.0000 | −0.639203 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.0000 | −0.446986 | ||||||||
\(982\) | 25.9808 | − | 15.0000i | 0.829079 | − | 0.478669i | ||||
\(983\) | −13.8564 | − | 8.00000i | −0.441951 | − | 0.255160i | 0.262474 | − | 0.964939i | \(-0.415462\pi\) |
−0.704425 | + | 0.709779i | \(0.748795\pi\) | |||||||
\(984\) | 1.00000 | − | 1.73205i | 0.0318788 | − | 0.0552158i | ||||
\(985\) | 3.73205 | + | 2.46410i | 0.118913 | + | 0.0785128i | ||||
\(986\) | −24.0000 | −0.764316 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 36.0000i | − | 1.14531i | ||||||
\(989\) | −16.0000 | − | 27.7128i | −0.508770 | − | 0.881216i | ||||
\(990\) | −0.267949 | + | 4.46410i | −0.00851598 | + | 0.141878i | ||||
\(991\) | −2.00000 | + | 3.46410i | −0.0635321 | + | 0.110041i | −0.896042 | − | 0.443969i | \(-0.853570\pi\) |
0.832510 | + | 0.554010i | \(0.186903\pi\) | |||||||
\(992\) | −1.73205 | + | 1.00000i | −0.0549927 | + | 0.0317500i | ||||
\(993\) | 8.00000i | 0.253872i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.00000 | − | 12.0000i | −0.190213 | − | 0.380426i | ||||
\(996\) | 4.00000 | + | 6.92820i | 0.126745 | + | 0.219529i | ||||
\(997\) | 36.3731 | + | 21.0000i | 1.15195 | + | 0.665077i | 0.949361 | − | 0.314188i | \(-0.101732\pi\) |
0.202586 | + | 0.979265i | \(0.435066\pi\) | |||||||
\(998\) | 10.3923 | + | 6.00000i | 0.328963 | + | 0.189927i | ||||
\(999\) | −2.00000 | − | 3.46410i | −0.0632772 | − | 0.109599i |
(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 | 1470.2.n.f.949.1 | 4 | ||
5.4 | even | 2 | inner | 1470.2.n.f.949.2 | 4 | ||
7.2 | even | 3 | inner | 1470.2.n.f.79.2 | 4 | ||
7.3 | odd | 6 | 210.2.g.b.169.1 | ✓ | 2 | ||
7.4 | even | 3 | 1470.2.g.b.589.1 | 2 | |||
7.5 | odd | 6 | 1470.2.n.b.79.2 | 4 | |||
7.6 | odd | 2 | 1470.2.n.b.949.1 | 4 | |||
21.17 | even | 6 | 630.2.g.c.379.2 | 2 | |||
28.3 | even | 6 | 1680.2.t.e.1009.1 | 2 | |||
35.3 | even | 12 | 1050.2.a.d.1.1 | 1 | |||
35.4 | even | 6 | 1470.2.g.b.589.2 | 2 | |||
35.9 | even | 6 | inner | 1470.2.n.f.79.1 | 4 | ||
35.17 | even | 12 | 1050.2.a.p.1.1 | 1 | |||
35.18 | odd | 12 | 7350.2.a.bk.1.1 | 1 | |||
35.19 | odd | 6 | 1470.2.n.b.79.1 | 4 | |||
35.24 | odd | 6 | 210.2.g.b.169.2 | yes | 2 | ||
35.32 | odd | 12 | 7350.2.a.bz.1.1 | 1 | |||
35.34 | odd | 2 | 1470.2.n.b.949.2 | 4 | |||
84.59 | odd | 6 | 5040.2.t.h.1009.1 | 2 | |||
105.17 | odd | 12 | 3150.2.a.d.1.1 | 1 | |||
105.38 | odd | 12 | 3150.2.a.bk.1.1 | 1 | |||
105.59 | even | 6 | 630.2.g.c.379.1 | 2 | |||
140.3 | odd | 12 | 8400.2.a.bp.1.1 | 1 | |||
140.59 | even | 6 | 1680.2.t.e.1009.2 | 2 | |||
140.87 | odd | 12 | 8400.2.a.w.1.1 | 1 | |||
420.59 | odd | 6 | 5040.2.t.h.1009.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.g.b.169.1 | ✓ | 2 | 7.3 | odd | 6 | ||
210.2.g.b.169.2 | yes | 2 | 35.24 | odd | 6 | ||
630.2.g.c.379.1 | 2 | 105.59 | even | 6 | |||
630.2.g.c.379.2 | 2 | 21.17 | even | 6 | |||
1050.2.a.d.1.1 | 1 | 35.3 | even | 12 | |||
1050.2.a.p.1.1 | 1 | 35.17 | even | 12 | |||
1470.2.g.b.589.1 | 2 | 7.4 | even | 3 | |||
1470.2.g.b.589.2 | 2 | 35.4 | even | 6 | |||
1470.2.n.b.79.1 | 4 | 35.19 | odd | 6 | |||
1470.2.n.b.79.2 | 4 | 7.5 | odd | 6 | |||
1470.2.n.b.949.1 | 4 | 7.6 | odd | 2 | |||
1470.2.n.b.949.2 | 4 | 35.34 | odd | 2 | |||
1470.2.n.f.79.1 | 4 | 35.9 | even | 6 | inner | ||
1470.2.n.f.79.2 | 4 | 7.2 | even | 3 | inner | ||
1470.2.n.f.949.1 | 4 | 1.1 | even | 1 | trivial | ||
1470.2.n.f.949.2 | 4 | 5.4 | even | 2 | inner | ||
1680.2.t.e.1009.1 | 2 | 28.3 | even | 6 | |||
1680.2.t.e.1009.2 | 2 | 140.59 | even | 6 | |||
3150.2.a.d.1.1 | 1 | 105.17 | odd | 12 | |||
3150.2.a.bk.1.1 | 1 | 105.38 | odd | 12 | |||
5040.2.t.h.1009.1 | 2 | 84.59 | odd | 6 | |||
5040.2.t.h.1009.2 | 2 | 420.59 | odd | 6 | |||
7350.2.a.bk.1.1 | 1 | 35.18 | odd | 12 | |||
7350.2.a.bz.1.1 | 1 | 35.32 | odd | 12 | |||
8400.2.a.w.1.1 | 1 | 140.87 | odd | 12 | |||
8400.2.a.bp.1.1 | 1 | 140.3 | odd | 12 |