Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1274,2,Mod(79,1274)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1274, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1274.79");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1274 = 2 \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1274.f (of order \(3\), 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: | \(10.1729412175\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 182) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1145.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1274.1145 |
Dual form | 1274.2.f.b.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 \(\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(885\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | −1.50000 | + | 2.59808i | −0.866025 | + | 1.50000i | 1.00000i | \(0.5\pi\) | ||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 2.00000 | + | 3.46410i | 0.894427 | + | 1.54919i | 0.834512 | + | 0.550990i | \(0.185750\pi\) |
0.0599153 | + | 0.998203i | \(0.480917\pi\) | |||||||
\(6\) | 3.00000 | 1.22474 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −3.00000 | − | 5.19615i | −1.00000 | − | 1.73205i | ||||
\(10\) | 2.00000 | − | 3.46410i | 0.632456 | − | 1.09545i | ||||
\(11\) | −0.500000 | + | 0.866025i | −0.150756 | + | 0.261116i | −0.931505 | − | 0.363727i | \(-0.881504\pi\) |
0.780750 | + | 0.624844i | \(0.214837\pi\) | |||||||
\(12\) | −1.50000 | − | 2.59808i | −0.433013 | − | 0.750000i | ||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −12.0000 | −3.09839 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(18\) | −3.00000 | + | 5.19615i | −0.707107 | + | 1.22474i | ||||
\(19\) | 3.00000 | + | 5.19615i | 0.688247 | + | 1.19208i | 0.972404 | + | 0.233301i | \(0.0749529\pi\) |
−0.284157 | + | 0.958778i | \(0.591714\pi\) | |||||||
\(20\) | −4.00000 | −0.894427 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 3.50000 | + | 6.06218i | 0.729800 | + | 1.26405i | 0.956967 | + | 0.290196i | \(0.0937204\pi\) |
−0.227167 | + | 0.973856i | \(0.572946\pi\) | |||||||
\(24\) | −1.50000 | + | 2.59808i | −0.306186 | + | 0.530330i | ||||
\(25\) | −5.50000 | + | 9.52628i | −1.10000 | + | 1.90526i | ||||
\(26\) | 0.500000 | + | 0.866025i | 0.0980581 | + | 0.169842i | ||||
\(27\) | 9.00000 | 1.73205 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.00000 | −0.742781 | −0.371391 | − | 0.928477i | \(-0.621119\pi\) | ||||
−0.371391 | + | 0.928477i | \(0.621119\pi\) | |||||||
\(30\) | 6.00000 | + | 10.3923i | 1.09545 | + | 1.89737i | ||||
\(31\) | −3.50000 | + | 6.06218i | −0.628619 | + | 1.08880i | 0.359211 | + | 0.933257i | \(0.383046\pi\) |
−0.987829 | + | 0.155543i | \(0.950287\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −1.50000 | − | 2.59808i | −0.261116 | − | 0.452267i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.00000 | 1.00000 | ||||||||
\(37\) | −4.50000 | − | 7.79423i | −0.739795 | − | 1.28136i | −0.952587 | − | 0.304266i | \(-0.901589\pi\) |
0.212792 | − | 0.977098i | \(-0.431744\pi\) | |||||||
\(38\) | 3.00000 | − | 5.19615i | 0.486664 | − | 0.842927i | ||||
\(39\) | 1.50000 | − | 2.59808i | 0.240192 | − | 0.416025i | ||||
\(40\) | 2.00000 | + | 3.46410i | 0.316228 | + | 0.547723i | ||||
\(41\) | −3.00000 | −0.468521 | −0.234261 | − | 0.972174i | \(-0.575267\pi\) | ||||
−0.234261 | + | 0.972174i | \(0.575267\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000 | 0.609994 | 0.304997 | − | 0.952353i | \(-0.401344\pi\) | ||||
0.304997 | + | 0.952353i | \(0.401344\pi\) | |||||||
\(44\) | −0.500000 | − | 0.866025i | −0.0753778 | − | 0.130558i | ||||
\(45\) | 12.0000 | − | 20.7846i | 1.78885 | − | 3.09839i | ||||
\(46\) | 3.50000 | − | 6.06218i | 0.516047 | − | 0.893819i | ||||
\(47\) | −3.50000 | − | 6.06218i | −0.510527 | − | 0.884260i | −0.999926 | − | 0.0121990i | \(-0.996117\pi\) |
0.489398 | − | 0.872060i | \(-0.337217\pi\) | |||||||
\(48\) | 3.00000 | 0.433013 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 11.0000 | 1.55563 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.500000 | − | 0.866025i | 0.0693375 | − | 0.120096i | ||||
\(53\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(54\) | −4.50000 | − | 7.79423i | −0.612372 | − | 1.06066i | ||||
\(55\) | −4.00000 | −0.539360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −18.0000 | −2.38416 | ||||||||
\(58\) | 2.00000 | + | 3.46410i | 0.262613 | + | 0.454859i | ||||
\(59\) | 5.00000 | − | 8.66025i | 0.650945 | − | 1.12747i | −0.331949 | − | 0.943297i | \(-0.607706\pi\) |
0.982894 | − | 0.184172i | \(-0.0589603\pi\) | |||||||
\(60\) | 6.00000 | − | 10.3923i | 0.774597 | − | 1.34164i | ||||
\(61\) | −0.500000 | − | 0.866025i | −0.0640184 | − | 0.110883i | 0.832240 | − | 0.554416i | \(-0.187058\pi\) |
−0.896258 | + | 0.443533i | \(0.853725\pi\) | |||||||
\(62\) | 7.00000 | 0.889001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.00000 | − | 3.46410i | −0.248069 | − | 0.429669i | ||||
\(66\) | −1.50000 | + | 2.59808i | −0.184637 | + | 0.319801i | ||||
\(67\) | −0.500000 | + | 0.866025i | −0.0610847 | + | 0.105802i | −0.894951 | − | 0.446165i | \(-0.852789\pi\) |
0.833866 | + | 0.551967i | \(0.186123\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −21.0000 | −2.52810 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.0000 | 1.89885 | 0.949425 | − | 0.313993i | \(-0.101667\pi\) | ||||
0.949425 | + | 0.313993i | \(0.101667\pi\) | |||||||
\(72\) | −3.00000 | − | 5.19615i | −0.353553 | − | 0.612372i | ||||
\(73\) | −2.50000 | + | 4.33013i | −0.292603 | + | 0.506803i | −0.974424 | − | 0.224716i | \(-0.927855\pi\) |
0.681822 | + | 0.731519i | \(0.261188\pi\) | |||||||
\(74\) | −4.50000 | + | 7.79423i | −0.523114 | + | 0.906061i | ||||
\(75\) | −16.5000 | − | 28.5788i | −1.90526 | − | 3.30000i | ||||
\(76\) | −6.00000 | −0.688247 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.00000 | −0.339683 | ||||||||
\(79\) | −5.50000 | − | 9.52628i | −0.618798 | − | 1.07179i | −0.989705 | − | 0.143120i | \(-0.954286\pi\) |
0.370907 | − | 0.928670i | \(-0.379047\pi\) | |||||||
\(80\) | 2.00000 | − | 3.46410i | 0.223607 | − | 0.387298i | ||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | 1.50000 | + | 2.59808i | 0.165647 | + | 0.286910i | ||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.00000 | − | 3.46410i | −0.215666 | − | 0.373544i | ||||
\(87\) | 6.00000 | − | 10.3923i | 0.643268 | − | 1.11417i | ||||
\(88\) | −0.500000 | + | 0.866025i | −0.0533002 | + | 0.0923186i | ||||
\(89\) | 3.00000 | + | 5.19615i | 0.317999 | + | 0.550791i | 0.980071 | − | 0.198650i | \(-0.0636557\pi\) |
−0.662071 | + | 0.749441i | \(0.730322\pi\) | |||||||
\(90\) | −24.0000 | −2.52982 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −7.00000 | −0.729800 | ||||||||
\(93\) | −10.5000 | − | 18.1865i | −1.08880 | − | 1.88586i | ||||
\(94\) | −3.50000 | + | 6.06218i | −0.360997 | + | 0.625266i | ||||
\(95\) | −12.0000 | + | 20.7846i | −1.23117 | + | 2.13246i | ||||
\(96\) | −1.50000 | − | 2.59808i | −0.153093 | − | 0.265165i | ||||
\(97\) | −1.00000 | −0.101535 | −0.0507673 | − | 0.998711i | \(-0.516167\pi\) | ||||
−0.0507673 | + | 0.998711i | \(0.516167\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.00000 | 0.603023 | ||||||||
\(100\) | −5.50000 | − | 9.52628i | −0.550000 | − | 0.952628i | ||||
\(101\) | 2.50000 | − | 4.33013i | 0.248759 | − | 0.430864i | −0.714423 | − | 0.699715i | \(-0.753311\pi\) |
0.963182 | + | 0.268851i | \(0.0866439\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.00000 | + | 12.1244i | 0.689730 | + | 1.19465i | 0.971925 | + | 0.235291i | \(0.0756043\pi\) |
−0.282194 | + | 0.959357i | \(0.591062\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.00000 | + | 3.46410i | 0.193347 | + | 0.334887i | 0.946357 | − | 0.323122i | \(-0.104732\pi\) |
−0.753010 | + | 0.658009i | \(0.771399\pi\) | |||||||
\(108\) | −4.50000 | + | 7.79423i | −0.433013 | + | 0.750000i | ||||
\(109\) | 7.00000 | − | 12.1244i | 0.670478 | − | 1.16130i | −0.307290 | − | 0.951616i | \(-0.599422\pi\) |
0.977769 | − | 0.209687i | \(-0.0672444\pi\) | |||||||
\(110\) | 2.00000 | + | 3.46410i | 0.190693 | + | 0.330289i | ||||
\(111\) | 27.0000 | 2.56273 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.00000 | −0.658505 | −0.329252 | − | 0.944242i | \(-0.606797\pi\) | ||||
−0.329252 | + | 0.944242i | \(0.606797\pi\) | |||||||
\(114\) | 9.00000 | + | 15.5885i | 0.842927 | + | 1.45999i | ||||
\(115\) | −14.0000 | + | 24.2487i | −1.30551 | + | 2.26120i | ||||
\(116\) | 2.00000 | − | 3.46410i | 0.185695 | − | 0.321634i | ||||
\(117\) | 3.00000 | + | 5.19615i | 0.277350 | + | 0.480384i | ||||
\(118\) | −10.0000 | −0.920575 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −12.0000 | −1.09545 | ||||||||
\(121\) | 5.00000 | + | 8.66025i | 0.454545 | + | 0.787296i | ||||
\(122\) | −0.500000 | + | 0.866025i | −0.0452679 | + | 0.0784063i | ||||
\(123\) | 4.50000 | − | 7.79423i | 0.405751 | − | 0.702782i | ||||
\(124\) | −3.50000 | − | 6.06218i | −0.314309 | − | 0.544400i | ||||
\(125\) | −24.0000 | −2.14663 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.0000 | −0.976092 | −0.488046 | − | 0.872818i | \(-0.662290\pi\) | ||||
−0.488046 | + | 0.872818i | \(0.662290\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | −6.00000 | + | 10.3923i | −0.528271 | + | 0.914991i | ||||
\(130\) | −2.00000 | + | 3.46410i | −0.175412 | + | 0.303822i | ||||
\(131\) | −4.00000 | − | 6.92820i | −0.349482 | − | 0.605320i | 0.636676 | − | 0.771132i | \(-0.280309\pi\) |
−0.986157 | + | 0.165812i | \(0.946976\pi\) | |||||||
\(132\) | 3.00000 | 0.261116 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.00000 | 0.0863868 | ||||||||
\(135\) | 18.0000 | + | 31.1769i | 1.54919 | + | 2.68328i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.00000 | − | 5.19615i | 0.256307 | − | 0.443937i | −0.708942 | − | 0.705266i | \(-0.750827\pi\) |
0.965250 | + | 0.261329i | \(0.0841608\pi\) | |||||||
\(138\) | 10.5000 | + | 18.1865i | 0.893819 | + | 1.54814i | ||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 21.0000 | 1.76852 | ||||||||
\(142\) | −8.00000 | − | 13.8564i | −0.671345 | − | 1.16280i | ||||
\(143\) | 0.500000 | − | 0.866025i | 0.0418121 | − | 0.0724207i | ||||
\(144\) | −3.00000 | + | 5.19615i | −0.250000 | + | 0.433013i | ||||
\(145\) | −8.00000 | − | 13.8564i | −0.664364 | − | 1.15071i | ||||
\(146\) | 5.00000 | 0.413803 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.00000 | 0.739795 | ||||||||
\(149\) | −4.50000 | − | 7.79423i | −0.368654 | − | 0.638528i | 0.620701 | − | 0.784047i | \(-0.286848\pi\) |
−0.989355 | + | 0.145519i | \(0.953515\pi\) | |||||||
\(150\) | −16.5000 | + | 28.5788i | −1.34722 | + | 2.33345i | ||||
\(151\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(152\) | 3.00000 | + | 5.19615i | 0.243332 | + | 0.421464i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −28.0000 | −2.24901 | ||||||||
\(156\) | 1.50000 | + | 2.59808i | 0.120096 | + | 0.208013i | ||||
\(157\) | −2.50000 | + | 4.33013i | −0.199522 | + | 0.345582i | −0.948373 | − | 0.317156i | \(-0.897272\pi\) |
0.748852 | + | 0.662738i | \(0.230606\pi\) | |||||||
\(158\) | −5.50000 | + | 9.52628i | −0.437557 | + | 0.757870i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.00000 | −0.316228 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 9.00000 | 0.707107 | ||||||||
\(163\) | 2.00000 | + | 3.46410i | 0.156652 | + | 0.271329i | 0.933659 | − | 0.358162i | \(-0.116597\pi\) |
−0.777007 | + | 0.629492i | \(0.783263\pi\) | |||||||
\(164\) | 1.50000 | − | 2.59808i | 0.117130 | − | 0.202876i | ||||
\(165\) | 6.00000 | − | 10.3923i | 0.467099 | − | 0.809040i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 18.0000 | − | 31.1769i | 1.37649 | − | 2.38416i | ||||
\(172\) | −2.00000 | + | 3.46410i | −0.152499 | + | 0.264135i | ||||
\(173\) | −1.00000 | − | 1.73205i | −0.0760286 | − | 0.131685i | 0.825505 | − | 0.564396i | \(-0.190891\pi\) |
−0.901533 | + | 0.432710i | \(0.857557\pi\) | |||||||
\(174\) | −12.0000 | −0.909718 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 15.0000 | + | 25.9808i | 1.12747 | + | 1.95283i | ||||
\(178\) | 3.00000 | − | 5.19615i | 0.224860 | − | 0.389468i | ||||
\(179\) | 3.00000 | − | 5.19615i | 0.224231 | − | 0.388379i | −0.731858 | − | 0.681457i | \(-0.761346\pi\) |
0.956088 | + | 0.293079i | \(0.0946798\pi\) | |||||||
\(180\) | 12.0000 | + | 20.7846i | 0.894427 | + | 1.54919i | ||||
\(181\) | 15.0000 | 1.11494 | 0.557471 | − | 0.830197i | \(-0.311772\pi\) | ||||
0.557471 | + | 0.830197i | \(0.311772\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.00000 | 0.221766 | ||||||||
\(184\) | 3.50000 | + | 6.06218i | 0.258023 | + | 0.446910i | ||||
\(185\) | 18.0000 | − | 31.1769i | 1.32339 | − | 2.29217i | ||||
\(186\) | −10.5000 | + | 18.1865i | −0.769897 | + | 1.33350i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 7.00000 | 0.510527 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 24.0000 | 1.74114 | ||||||||
\(191\) | 4.00000 | + | 6.92820i | 0.289430 | + | 0.501307i | 0.973674 | − | 0.227946i | \(-0.0732010\pi\) |
−0.684244 | + | 0.729253i | \(0.739868\pi\) | |||||||
\(192\) | −1.50000 | + | 2.59808i | −0.108253 | + | 0.187500i | ||||
\(193\) | −10.0000 | + | 17.3205i | −0.719816 | + | 1.24676i | 0.241257 | + | 0.970461i | \(0.422440\pi\) |
−0.961073 | + | 0.276296i | \(0.910893\pi\) | |||||||
\(194\) | 0.500000 | + | 0.866025i | 0.0358979 | + | 0.0621770i | ||||
\(195\) | 12.0000 | 0.859338 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −27.0000 | −1.92367 | −0.961835 | − | 0.273629i | \(-0.911776\pi\) | ||||
−0.961835 | + | 0.273629i | \(0.911776\pi\) | |||||||
\(198\) | −3.00000 | − | 5.19615i | −0.213201 | − | 0.369274i | ||||
\(199\) | 2.00000 | − | 3.46410i | 0.141776 | − | 0.245564i | −0.786389 | − | 0.617731i | \(-0.788052\pi\) |
0.928166 | + | 0.372168i | \(0.121385\pi\) | |||||||
\(200\) | −5.50000 | + | 9.52628i | −0.388909 | + | 0.673610i | ||||
\(201\) | −1.50000 | − | 2.59808i | −0.105802 | − | 0.183254i | ||||
\(202\) | −5.00000 | −0.351799 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.00000 | − | 10.3923i | −0.419058 | − | 0.725830i | ||||
\(206\) | 7.00000 | − | 12.1244i | 0.487713 | − | 0.844744i | ||||
\(207\) | 21.0000 | − | 36.3731i | 1.45960 | − | 2.52810i | ||||
\(208\) | 0.500000 | + | 0.866025i | 0.0346688 | + | 0.0600481i | ||||
\(209\) | −6.00000 | −0.415029 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.0000 | −0.688428 | −0.344214 | − | 0.938891i | \(-0.611855\pi\) | ||||
−0.344214 | + | 0.938891i | \(0.611855\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −24.0000 | + | 41.5692i | −1.64445 | + | 2.84828i | ||||
\(214\) | 2.00000 | − | 3.46410i | 0.136717 | − | 0.236801i | ||||
\(215\) | 8.00000 | + | 13.8564i | 0.545595 | + | 0.944999i | ||||
\(216\) | 9.00000 | 0.612372 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −14.0000 | −0.948200 | ||||||||
\(219\) | −7.50000 | − | 12.9904i | −0.506803 | − | 0.877809i | ||||
\(220\) | 2.00000 | − | 3.46410i | 0.134840 | − | 0.233550i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −13.5000 | − | 23.3827i | −0.906061 | − | 1.56934i | ||||
\(223\) | 21.0000 | 1.40626 | 0.703132 | − | 0.711059i | \(-0.251784\pi\) | ||||
0.703132 | + | 0.711059i | \(0.251784\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 66.0000 | 4.40000 | ||||||||
\(226\) | 3.50000 | + | 6.06218i | 0.232817 | + | 0.403250i | ||||
\(227\) | −12.0000 | + | 20.7846i | −0.796468 | + | 1.37952i | 0.125435 | + | 0.992102i | \(0.459967\pi\) |
−0.921903 | + | 0.387421i | \(0.873366\pi\) | |||||||
\(228\) | 9.00000 | − | 15.5885i | 0.596040 | − | 1.03237i | ||||
\(229\) | 12.0000 | + | 20.7846i | 0.792982 | + | 1.37349i | 0.924113 | + | 0.382121i | \(0.124806\pi\) |
−0.131130 | + | 0.991365i | \(0.541861\pi\) | |||||||
\(230\) | 28.0000 | 1.84627 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.00000 | −0.262613 | ||||||||
\(233\) | 2.50000 | + | 4.33013i | 0.163780 | + | 0.283676i | 0.936222 | − | 0.351410i | \(-0.114298\pi\) |
−0.772441 | + | 0.635086i | \(0.780964\pi\) | |||||||
\(234\) | 3.00000 | − | 5.19615i | 0.196116 | − | 0.339683i | ||||
\(235\) | 14.0000 | − | 24.2487i | 0.913259 | − | 1.58181i | ||||
\(236\) | 5.00000 | + | 8.66025i | 0.325472 | + | 0.563735i | ||||
\(237\) | 33.0000 | 2.14358 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.00000 | 0.388108 | 0.194054 | − | 0.980991i | \(-0.437836\pi\) | ||||
0.194054 | + | 0.980991i | \(0.437836\pi\) | |||||||
\(240\) | 6.00000 | + | 10.3923i | 0.387298 | + | 0.670820i | ||||
\(241\) | 9.00000 | − | 15.5885i | 0.579741 | − | 1.00414i | −0.415768 | − | 0.909471i | \(-0.636487\pi\) |
0.995509 | − | 0.0946700i | \(-0.0301796\pi\) | |||||||
\(242\) | 5.00000 | − | 8.66025i | 0.321412 | − | 0.556702i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.00000 | 0.0640184 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −9.00000 | −0.573819 | ||||||||
\(247\) | −3.00000 | − | 5.19615i | −0.190885 | − | 0.330623i | ||||
\(248\) | −3.50000 | + | 6.06218i | −0.222250 | + | 0.384949i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 12.0000 | + | 20.7846i | 0.758947 | + | 1.31453i | ||||
\(251\) | 3.00000 | 0.189358 | 0.0946792 | − | 0.995508i | \(-0.469817\pi\) | ||||
0.0946792 | + | 0.995508i | \(0.469817\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.00000 | −0.440086 | ||||||||
\(254\) | 5.50000 | + | 9.52628i | 0.345101 | + | 0.597732i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −12.0000 | − | 20.7846i | −0.748539 | − | 1.29651i | −0.948523 | − | 0.316709i | \(-0.897422\pi\) |
0.199983 | − | 0.979799i | \(-0.435911\pi\) | |||||||
\(258\) | 12.0000 | 0.747087 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.00000 | 0.248069 | ||||||||
\(261\) | 12.0000 | + | 20.7846i | 0.742781 | + | 1.28654i | ||||
\(262\) | −4.00000 | + | 6.92820i | −0.247121 | + | 0.428026i | ||||
\(263\) | −12.0000 | + | 20.7846i | −0.739952 | + | 1.28163i | 0.212565 | + | 0.977147i | \(0.431818\pi\) |
−0.952517 | + | 0.304487i | \(0.901515\pi\) | |||||||
\(264\) | −1.50000 | − | 2.59808i | −0.0923186 | − | 0.159901i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −18.0000 | −1.10158 | ||||||||
\(268\) | −0.500000 | − | 0.866025i | −0.0305424 | − | 0.0529009i | ||||
\(269\) | −4.50000 | + | 7.79423i | −0.274370 | + | 0.475223i | −0.969976 | − | 0.243201i | \(-0.921803\pi\) |
0.695606 | + | 0.718423i | \(0.255136\pi\) | |||||||
\(270\) | 18.0000 | − | 31.1769i | 1.09545 | − | 1.89737i | ||||
\(271\) | 11.5000 | + | 19.9186i | 0.698575 | + | 1.20997i | 0.968960 | + | 0.247216i | \(0.0795156\pi\) |
−0.270385 | + | 0.962752i | \(0.587151\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.00000 | −0.362473 | ||||||||
\(275\) | −5.50000 | − | 9.52628i | −0.331662 | − | 0.574456i | ||||
\(276\) | 10.5000 | − | 18.1865i | 0.632026 | − | 1.09470i | ||||
\(277\) | 9.00000 | − | 15.5885i | 0.540758 | − | 0.936620i | −0.458103 | − | 0.888899i | \(-0.651471\pi\) |
0.998861 | − | 0.0477206i | \(-0.0151957\pi\) | |||||||
\(278\) | −2.00000 | − | 3.46410i | −0.119952 | − | 0.207763i | ||||
\(279\) | 42.0000 | 2.51447 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.00000 | −0.477240 | −0.238620 | − | 0.971113i | \(-0.576695\pi\) | ||||
−0.238620 | + | 0.971113i | \(0.576695\pi\) | |||||||
\(282\) | −10.5000 | − | 18.1865i | −0.625266 | − | 1.08299i | ||||
\(283\) | −9.50000 | + | 16.4545i | −0.564716 | + | 0.978117i | 0.432360 | + | 0.901701i | \(0.357681\pi\) |
−0.997076 | + | 0.0764162i | \(0.975652\pi\) | |||||||
\(284\) | −8.00000 | + | 13.8564i | −0.474713 | + | 0.822226i | ||||
\(285\) | −36.0000 | − | 62.3538i | −2.13246 | − | 3.69352i | ||||
\(286\) | −1.00000 | −0.0591312 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 6.00000 | 0.353553 | ||||||||
\(289\) | 8.50000 | + | 14.7224i | 0.500000 | + | 0.866025i | ||||
\(290\) | −8.00000 | + | 13.8564i | −0.469776 | + | 0.813676i | ||||
\(291\) | 1.50000 | − | 2.59808i | 0.0879316 | − | 0.152302i | ||||
\(292\) | −2.50000 | − | 4.33013i | −0.146301 | − | 0.253402i | ||||
\(293\) | −26.0000 | −1.51894 | −0.759468 | − | 0.650545i | \(-0.774541\pi\) | ||||
−0.759468 | + | 0.650545i | \(0.774541\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 40.0000 | 2.32889 | ||||||||
\(296\) | −4.50000 | − | 7.79423i | −0.261557 | − | 0.453030i | ||||
\(297\) | −4.50000 | + | 7.79423i | −0.261116 | + | 0.452267i | ||||
\(298\) | −4.50000 | + | 7.79423i | −0.260678 | + | 0.451508i | ||||
\(299\) | −3.50000 | − | 6.06218i | −0.202410 | − | 0.350585i | ||||
\(300\) | 33.0000 | 1.90526 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.50000 | + | 12.9904i | 0.430864 | + | 0.746278i | ||||
\(304\) | 3.00000 | − | 5.19615i | 0.172062 | − | 0.298020i | ||||
\(305\) | 2.00000 | − | 3.46410i | 0.114520 | − | 0.198354i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.00000 | −0.228292 | −0.114146 | − | 0.993464i | \(-0.536413\pi\) | ||||
−0.114146 | + | 0.993464i | \(0.536413\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −42.0000 | −2.38930 | ||||||||
\(310\) | 14.0000 | + | 24.2487i | 0.795147 | + | 1.37723i | ||||
\(311\) | −15.0000 | + | 25.9808i | −0.850572 | + | 1.47323i | 0.0301210 | + | 0.999546i | \(0.490411\pi\) |
−0.880693 | + | 0.473688i | \(0.842923\pi\) | |||||||
\(312\) | 1.50000 | − | 2.59808i | 0.0849208 | − | 0.147087i | ||||
\(313\) | −7.00000 | − | 12.1244i | −0.395663 | − | 0.685309i | 0.597522 | − | 0.801852i | \(-0.296152\pi\) |
−0.993186 | + | 0.116543i | \(0.962819\pi\) | |||||||
\(314\) | 5.00000 | 0.282166 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.0000 | 0.618798 | ||||||||
\(317\) | −10.5000 | − | 18.1865i | −0.589739 | − | 1.02146i | −0.994266 | − | 0.106932i | \(-0.965897\pi\) |
0.404528 | − | 0.914526i | \(-0.367436\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.00000 | − | 3.46410i | 0.111979 | − | 0.193952i | ||||
\(320\) | 2.00000 | + | 3.46410i | 0.111803 | + | 0.193649i | ||||
\(321\) | −12.0000 | −0.669775 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −4.50000 | − | 7.79423i | −0.250000 | − | 0.433013i | ||||
\(325\) | 5.50000 | − | 9.52628i | 0.305085 | − | 0.528423i | ||||
\(326\) | 2.00000 | − | 3.46410i | 0.110770 | − | 0.191859i | ||||
\(327\) | 21.0000 | + | 36.3731i | 1.16130 | + | 2.01144i | ||||
\(328\) | −3.00000 | −0.165647 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −12.0000 | −0.660578 | ||||||||
\(331\) | 3.50000 | + | 6.06218i | 0.192377 | + | 0.333207i | 0.946038 | − | 0.324057i | \(-0.105047\pi\) |
−0.753660 | + | 0.657264i | \(0.771714\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −27.0000 | + | 46.7654i | −1.47959 | + | 2.56273i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.00000 | −0.218543 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.0000 | 0.926049 | 0.463025 | − | 0.886345i | \(-0.346764\pi\) | ||||
0.463025 | + | 0.886345i | \(0.346764\pi\) | |||||||
\(338\) | −0.500000 | − | 0.866025i | −0.0271964 | − | 0.0471056i | ||||
\(339\) | 10.5000 | − | 18.1865i | 0.570282 | − | 0.987757i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.50000 | − | 6.06218i | −0.189536 | − | 0.328285i | ||||
\(342\) | −36.0000 | −1.94666 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4.00000 | 0.215666 | ||||||||
\(345\) | −42.0000 | − | 72.7461i | −2.26120 | − | 3.91652i | ||||
\(346\) | −1.00000 | + | 1.73205i | −0.0537603 | + | 0.0931156i | ||||
\(347\) | 12.0000 | − | 20.7846i | 0.644194 | − | 1.11578i | −0.340293 | − | 0.940319i | \(-0.610526\pi\) |
0.984487 | − | 0.175457i | \(-0.0561403\pi\) | |||||||
\(348\) | 6.00000 | + | 10.3923i | 0.321634 | + | 0.557086i | ||||
\(349\) | −26.0000 | −1.39175 | −0.695874 | − | 0.718164i | \(-0.744983\pi\) | ||||
−0.695874 | + | 0.718164i | \(0.744983\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.00000 | −0.480384 | ||||||||
\(352\) | −0.500000 | − | 0.866025i | −0.0266501 | − | 0.0461593i | ||||
\(353\) | −12.5000 | + | 21.6506i | −0.665308 | + | 1.15235i | 0.313894 | + | 0.949458i | \(0.398366\pi\) |
−0.979202 | + | 0.202889i | \(0.934967\pi\) | |||||||
\(354\) | 15.0000 | − | 25.9808i | 0.797241 | − | 1.38086i | ||||
\(355\) | 32.0000 | + | 55.4256i | 1.69838 | + | 2.94169i | ||||
\(356\) | −6.00000 | −0.317999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.00000 | −0.317110 | ||||||||
\(359\) | −6.00000 | − | 10.3923i | −0.316668 | − | 0.548485i | 0.663123 | − | 0.748511i | \(-0.269231\pi\) |
−0.979791 | + | 0.200026i | \(0.935897\pi\) | |||||||
\(360\) | 12.0000 | − | 20.7846i | 0.632456 | − | 1.09545i | ||||
\(361\) | −8.50000 | + | 14.7224i | −0.447368 | + | 0.774865i | ||||
\(362\) | −7.50000 | − | 12.9904i | −0.394191 | − | 0.682759i | ||||
\(363\) | −30.0000 | −1.57459 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −20.0000 | −1.04685 | ||||||||
\(366\) | −1.50000 | − | 2.59808i | −0.0784063 | − | 0.135804i | ||||
\(367\) | −16.0000 | + | 27.7128i | −0.835193 | + | 1.44660i | 0.0586798 | + | 0.998277i | \(0.481311\pi\) |
−0.893873 | + | 0.448320i | \(0.852022\pi\) | |||||||
\(368\) | 3.50000 | − | 6.06218i | 0.182450 | − | 0.316013i | ||||
\(369\) | 9.00000 | + | 15.5885i | 0.468521 | + | 0.811503i | ||||
\(370\) | −36.0000 | −1.87155 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 21.0000 | 1.08880 | ||||||||
\(373\) | 8.00000 | + | 13.8564i | 0.414224 | + | 0.717458i | 0.995347 | − | 0.0963587i | \(-0.0307196\pi\) |
−0.581122 | + | 0.813816i | \(0.697386\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 36.0000 | − | 62.3538i | 1.85903 | − | 3.21994i | ||||
\(376\) | −3.50000 | − | 6.06218i | −0.180499 | − | 0.312633i | ||||
\(377\) | 4.00000 | 0.206010 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.00000 | −0.410932 | −0.205466 | − | 0.978664i | \(-0.565871\pi\) | ||||
−0.205466 | + | 0.978664i | \(0.565871\pi\) | |||||||
\(380\) | −12.0000 | − | 20.7846i | −0.615587 | − | 1.06623i | ||||
\(381\) | 16.5000 | − | 28.5788i | 0.845321 | − | 1.46414i | ||||
\(382\) | 4.00000 | − | 6.92820i | 0.204658 | − | 0.354478i | ||||
\(383\) | 7.50000 | + | 12.9904i | 0.383232 | + | 0.663777i | 0.991522 | − | 0.129937i | \(-0.0414776\pi\) |
−0.608290 | + | 0.793715i | \(0.708144\pi\) | |||||||
\(384\) | 3.00000 | 0.153093 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 20.0000 | 1.01797 | ||||||||
\(387\) | −12.0000 | − | 20.7846i | −0.609994 | − | 1.05654i | ||||
\(388\) | 0.500000 | − | 0.866025i | 0.0253837 | − | 0.0439658i | ||||
\(389\) | 18.0000 | − | 31.1769i | 0.912636 | − | 1.58073i | 0.102311 | − | 0.994753i | \(-0.467376\pi\) |
0.810326 | − | 0.585980i | \(-0.199290\pi\) | |||||||
\(390\) | −6.00000 | − | 10.3923i | −0.303822 | − | 0.526235i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 24.0000 | 1.21064 | ||||||||
\(394\) | 13.5000 | + | 23.3827i | 0.680120 | + | 1.17800i | ||||
\(395\) | 22.0000 | − | 38.1051i | 1.10694 | − | 1.91728i | ||||
\(396\) | −3.00000 | + | 5.19615i | −0.150756 | + | 0.261116i | ||||
\(397\) | 14.0000 | + | 24.2487i | 0.702640 | + | 1.21701i | 0.967537 | + | 0.252731i | \(0.0813288\pi\) |
−0.264897 | + | 0.964277i | \(0.585338\pi\) | |||||||
\(398\) | −4.00000 | −0.200502 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 11.0000 | 0.550000 | ||||||||
\(401\) | −6.00000 | − | 10.3923i | −0.299626 | − | 0.518967i | 0.676425 | − | 0.736512i | \(-0.263528\pi\) |
−0.976050 | + | 0.217545i | \(0.930195\pi\) | |||||||
\(402\) | −1.50000 | + | 2.59808i | −0.0748132 | + | 0.129580i | ||||
\(403\) | 3.50000 | − | 6.06218i | 0.174347 | − | 0.301979i | ||||
\(404\) | 2.50000 | + | 4.33013i | 0.124380 | + | 0.215432i | ||||
\(405\) | −36.0000 | −1.78885 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.00000 | 0.446113 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.0000 | − | 22.5167i | 0.642809 | − | 1.11338i | −0.341994 | − | 0.939702i | \(-0.611102\pi\) |
0.984803 | − | 0.173675i | \(-0.0555643\pi\) | |||||||
\(410\) | −6.00000 | + | 10.3923i | −0.296319 | + | 0.513239i | ||||
\(411\) | 9.00000 | + | 15.5885i | 0.443937 | + | 0.768922i | ||||
\(412\) | −14.0000 | −0.689730 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −42.0000 | −2.06419 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.500000 | − | 0.866025i | 0.0245145 | − | 0.0424604i | ||||
\(417\) | −6.00000 | + | 10.3923i | −0.293821 | + | 0.508913i | ||||
\(418\) | 3.00000 | + | 5.19615i | 0.146735 | + | 0.254152i | ||||
\(419\) | 15.0000 | 0.732798 | 0.366399 | − | 0.930458i | \(-0.380591\pi\) | ||||
0.366399 | + | 0.930458i | \(0.380591\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.0000 | 0.926003 | 0.463002 | − | 0.886357i | \(-0.346772\pi\) | ||||
0.463002 | + | 0.886357i | \(0.346772\pi\) | |||||||
\(422\) | 5.00000 | + | 8.66025i | 0.243396 | + | 0.421575i | ||||
\(423\) | −21.0000 | + | 36.3731i | −1.02105 | + | 1.76852i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 48.0000 | 2.32561 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −4.00000 | −0.193347 | ||||||||
\(429\) | 1.50000 | + | 2.59808i | 0.0724207 | + | 0.125436i | ||||
\(430\) | 8.00000 | − | 13.8564i | 0.385794 | − | 0.668215i | ||||
\(431\) | −9.00000 | + | 15.5885i | −0.433515 | + | 0.750870i | −0.997173 | − | 0.0751385i | \(-0.976060\pi\) |
0.563658 | + | 0.826008i | \(0.309393\pi\) | |||||||
\(432\) | −4.50000 | − | 7.79423i | −0.216506 | − | 0.375000i | ||||
\(433\) | 34.0000 | 1.63394 | 0.816968 | − | 0.576683i | \(-0.195653\pi\) | ||||
0.816968 | + | 0.576683i | \(0.195653\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 48.0000 | 2.30142 | ||||||||
\(436\) | 7.00000 | + | 12.1244i | 0.335239 | + | 0.580651i | ||||
\(437\) | −21.0000 | + | 36.3731i | −1.00457 | + | 1.73996i | ||||
\(438\) | −7.50000 | + | 12.9904i | −0.358364 | + | 0.620704i | ||||
\(439\) | −1.00000 | − | 1.73205i | −0.0477274 | − | 0.0826663i | 0.841175 | − | 0.540763i | \(-0.181865\pi\) |
−0.888902 | + | 0.458097i | \(0.848531\pi\) | |||||||
\(440\) | −4.00000 | −0.190693 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.00000 | − | 10.3923i | −0.285069 | − | 0.493753i | 0.687557 | − | 0.726130i | \(-0.258683\pi\) |
−0.972626 | + | 0.232377i | \(0.925350\pi\) | |||||||
\(444\) | −13.5000 | + | 23.3827i | −0.640682 | + | 1.10969i | ||||
\(445\) | −12.0000 | + | 20.7846i | −0.568855 | + | 0.985285i | ||||
\(446\) | −10.5000 | − | 18.1865i | −0.497189 | − | 0.861157i | ||||
\(447\) | 27.0000 | 1.27706 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.00000 | −0.0943858 | −0.0471929 | − | 0.998886i | \(-0.515028\pi\) | ||||
−0.0471929 | + | 0.998886i | \(0.515028\pi\) | |||||||
\(450\) | −33.0000 | − | 57.1577i | −1.55563 | − | 2.69444i | ||||
\(451\) | 1.50000 | − | 2.59808i | 0.0706322 | − | 0.122339i | ||||
\(452\) | 3.50000 | − | 6.06218i | 0.164626 | − | 0.285141i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 24.0000 | 1.12638 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −18.0000 | −0.842927 | ||||||||
\(457\) | 13.0000 | + | 22.5167i | 0.608114 | + | 1.05328i | 0.991551 | + | 0.129718i | \(0.0414071\pi\) |
−0.383437 | + | 0.923567i | \(0.625260\pi\) | |||||||
\(458\) | 12.0000 | − | 20.7846i | 0.560723 | − | 0.971201i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −14.0000 | − | 24.2487i | −0.652753 | − | 1.13060i | ||||
\(461\) | 12.0000 | 0.558896 | 0.279448 | − | 0.960161i | \(-0.409849\pi\) | ||||
0.279448 | + | 0.960161i | \(0.409849\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.0000 | 0.743583 | 0.371792 | − | 0.928316i | \(-0.378744\pi\) | ||||
0.371792 | + | 0.928316i | \(0.378744\pi\) | |||||||
\(464\) | 2.00000 | + | 3.46410i | 0.0928477 | + | 0.160817i | ||||
\(465\) | 42.0000 | − | 72.7461i | 1.94770 | − | 3.37352i | ||||
\(466\) | 2.50000 | − | 4.33013i | 0.115810 | − | 0.200589i | ||||
\(467\) | 2.00000 | + | 3.46410i | 0.0925490 | + | 0.160300i | 0.908583 | − | 0.417704i | \(-0.137165\pi\) |
−0.816034 | + | 0.578004i | \(0.803832\pi\) | |||||||
\(468\) | −6.00000 | −0.277350 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −28.0000 | −1.29154 | ||||||||
\(471\) | −7.50000 | − | 12.9904i | −0.345582 | − | 0.598565i | ||||
\(472\) | 5.00000 | − | 8.66025i | 0.230144 | − | 0.398621i | ||||
\(473\) | −2.00000 | + | 3.46410i | −0.0919601 | + | 0.159280i | ||||
\(474\) | −16.5000 | − | 28.5788i | −0.757870 | − | 1.31267i | ||||
\(475\) | −66.0000 | −3.02829 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.00000 | − | 5.19615i | −0.137217 | − | 0.237666i | ||||
\(479\) | −12.0000 | + | 20.7846i | −0.548294 | + | 0.949673i | 0.450098 | + | 0.892979i | \(0.351389\pi\) |
−0.998392 | + | 0.0566937i | \(0.981944\pi\) | |||||||
\(480\) | 6.00000 | − | 10.3923i | 0.273861 | − | 0.474342i | ||||
\(481\) | 4.50000 | + | 7.79423i | 0.205182 | + | 0.355386i | ||||
\(482\) | −18.0000 | −0.819878 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.0000 | −0.454545 | ||||||||
\(485\) | −2.00000 | − | 3.46410i | −0.0908153 | − | 0.157297i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.0000 | + | 32.9090i | −0.860972 | + | 1.49125i | 0.0100195 | + | 0.999950i | \(0.496811\pi\) |
−0.870992 | + | 0.491298i | \(0.836523\pi\) | |||||||
\(488\) | −0.500000 | − | 0.866025i | −0.0226339 | − | 0.0392031i | ||||
\(489\) | −12.0000 | −0.542659 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.0000 | 0.722070 | 0.361035 | − | 0.932552i | \(-0.382424\pi\) | ||||
0.361035 | + | 0.932552i | \(0.382424\pi\) | |||||||
\(492\) | 4.50000 | + | 7.79423i | 0.202876 | + | 0.351391i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −3.00000 | + | 5.19615i | −0.134976 | + | 0.233786i | ||||
\(495\) | 12.0000 | + | 20.7846i | 0.539360 | + | 0.934199i | ||||
\(496\) | 7.00000 | 0.314309 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.50000 | + | 4.33013i | 0.111915 | + | 0.193843i | 0.916542 | − | 0.399937i | \(-0.130968\pi\) |
−0.804627 | + | 0.593780i | \(0.797635\pi\) | |||||||
\(500\) | 12.0000 | − | 20.7846i | 0.536656 | − | 0.929516i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.50000 | − | 2.59808i | −0.0669483 | − | 0.115958i | ||||
\(503\) | −20.0000 | −0.891756 | −0.445878 | − | 0.895094i | \(-0.647108\pi\) | ||||
−0.445878 | + | 0.895094i | \(0.647108\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.0000 | 0.889988 | ||||||||
\(506\) | 3.50000 | + | 6.06218i | 0.155594 | + | 0.269497i | ||||
\(507\) | −1.50000 | + | 2.59808i | −0.0666173 | + | 0.115385i | ||||
\(508\) | 5.50000 | − | 9.52628i | 0.244023 | − | 0.422660i | ||||
\(509\) | −5.00000 | − | 8.66025i | −0.221621 | − | 0.383859i | 0.733679 | − | 0.679496i | \(-0.237801\pi\) |
−0.955300 | + | 0.295637i | \(0.904468\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 27.0000 | + | 46.7654i | 1.19208 | + | 2.06474i | ||||
\(514\) | −12.0000 | + | 20.7846i | −0.529297 | + | 0.916770i | ||||
\(515\) | −28.0000 | + | 48.4974i | −1.23383 | + | 2.13705i | ||||
\(516\) | −6.00000 | − | 10.3923i | −0.264135 | − | 0.457496i | ||||
\(517\) | 7.00000 | 0.307860 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.00000 | 0.263371 | ||||||||
\(520\) | −2.00000 | − | 3.46410i | −0.0877058 | − | 0.151911i | ||||
\(521\) | 9.00000 | − | 15.5885i | 0.394297 | − | 0.682943i | −0.598714 | − | 0.800963i | \(-0.704321\pi\) |
0.993011 | + | 0.118020i | \(0.0376547\pi\) | |||||||
\(522\) | 12.0000 | − | 20.7846i | 0.525226 | − | 0.909718i | ||||
\(523\) | −13.5000 | − | 23.3827i | −0.590314 | − | 1.02245i | −0.994190 | − | 0.107640i | \(-0.965671\pi\) |
0.403876 | − | 0.914814i | \(-0.367663\pi\) | |||||||
\(524\) | 8.00000 | 0.349482 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.0000 | 1.04645 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −1.50000 | + | 2.59808i | −0.0652791 | + | 0.113067i | ||||
\(529\) | −13.0000 | + | 22.5167i | −0.565217 | + | 0.978985i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −60.0000 | −2.60378 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.00000 | 0.129944 | ||||||||
\(534\) | 9.00000 | + | 15.5885i | 0.389468 | + | 0.674579i | ||||
\(535\) | −8.00000 | + | 13.8564i | −0.345870 | + | 0.599065i | ||||
\(536\) | −0.500000 | + | 0.866025i | −0.0215967 | + | 0.0374066i | ||||
\(537\) | 9.00000 | + | 15.5885i | 0.388379 | + | 0.672692i | ||||
\(538\) | 9.00000 | 0.388018 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −36.0000 | −1.54919 | ||||||||
\(541\) | 5.00000 | + | 8.66025i | 0.214967 | + | 0.372333i | 0.953262 | − | 0.302144i | \(-0.0977023\pi\) |
−0.738296 | + | 0.674477i | \(0.764369\pi\) | |||||||
\(542\) | 11.5000 | − | 19.9186i | 0.493967 | − | 0.855576i | ||||
\(543\) | −22.5000 | + | 38.9711i | −0.965567 | + | 1.67241i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 56.0000 | 2.39878 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.0000 | 1.19719 | 0.598597 | − | 0.801050i | \(-0.295725\pi\) | ||||
0.598597 | + | 0.801050i | \(0.295725\pi\) | |||||||
\(548\) | 3.00000 | + | 5.19615i | 0.128154 | + | 0.221969i | ||||
\(549\) | −3.00000 | + | 5.19615i | −0.128037 | + | 0.221766i | ||||
\(550\) | −5.50000 | + | 9.52628i | −0.234521 | + | 0.406202i | ||||
\(551\) | −12.0000 | − | 20.7846i | −0.511217 | − | 0.885454i | ||||
\(552\) | −21.0000 | −0.893819 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −18.0000 | −0.764747 | ||||||||
\(555\) | 54.0000 | + | 93.5307i | 2.29217 | + | 3.97016i | ||||
\(556\) | −2.00000 | + | 3.46410i | −0.0848189 | + | 0.146911i | ||||
\(557\) | −4.50000 | + | 7.79423i | −0.190671 | + | 0.330252i | −0.945473 | − | 0.325701i | \(-0.894400\pi\) |
0.754802 | + | 0.655953i | \(0.227733\pi\) | |||||||
\(558\) | −21.0000 | − | 36.3731i | −0.889001 | − | 1.53979i | ||||
\(559\) | −4.00000 | −0.169182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.00000 | + | 6.92820i | 0.168730 | + | 0.292249i | ||||
\(563\) | −5.50000 | + | 9.52628i | −0.231797 | + | 0.401485i | −0.958337 | − | 0.285640i | \(-0.907794\pi\) |
0.726540 | + | 0.687124i | \(0.241127\pi\) | |||||||
\(564\) | −10.5000 | + | 18.1865i | −0.442130 | + | 0.765791i | ||||
\(565\) | −14.0000 | − | 24.2487i | −0.588984 | − | 1.02015i | ||||
\(566\) | 19.0000 | 0.798630 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 16.0000 | 0.671345 | ||||||||
\(569\) | 17.5000 | + | 30.3109i | 0.733638 | + | 1.27070i | 0.955318 | + | 0.295579i | \(0.0955126\pi\) |
−0.221680 | + | 0.975119i | \(0.571154\pi\) | |||||||
\(570\) | −36.0000 | + | 62.3538i | −1.50787 | + | 2.61171i | ||||
\(571\) | −3.00000 | + | 5.19615i | −0.125546 | + | 0.217452i | −0.921946 | − | 0.387318i | \(-0.873402\pi\) |
0.796400 | + | 0.604770i | \(0.206735\pi\) | |||||||
\(572\) | 0.500000 | + | 0.866025i | 0.0209061 | + | 0.0362103i | ||||
\(573\) | −24.0000 | −1.00261 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −77.0000 | −3.21112 | ||||||||
\(576\) | −3.00000 | − | 5.19615i | −0.125000 | − | 0.216506i | ||||
\(577\) | −15.0000 | + | 25.9808i | −0.624458 | + | 1.08159i | 0.364187 | + | 0.931326i | \(0.381347\pi\) |
−0.988645 | + | 0.150268i | \(0.951987\pi\) | |||||||
\(578\) | 8.50000 | − | 14.7224i | 0.353553 | − | 0.612372i | ||||
\(579\) | −30.0000 | − | 51.9615i | −1.24676 | − | 2.15945i | ||||
\(580\) | 16.0000 | 0.664364 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −3.00000 | −0.124354 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −2.50000 | + | 4.33013i | −0.103451 | + | 0.179182i | ||||
\(585\) | −12.0000 | + | 20.7846i | −0.496139 | + | 0.859338i | ||||
\(586\) | 13.0000 | + | 22.5167i | 0.537025 | + | 0.930155i | ||||
\(587\) | 14.0000 | 0.577842 | 0.288921 | − | 0.957353i | \(-0.406704\pi\) | ||||
0.288921 | + | 0.957353i | \(0.406704\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −42.0000 | −1.73058 | ||||||||
\(590\) | −20.0000 | − | 34.6410i | −0.823387 | − | 1.42615i | ||||
\(591\) | 40.5000 | − | 70.1481i | 1.66595 | − | 2.88551i | ||||
\(592\) | −4.50000 | + | 7.79423i | −0.184949 | + | 0.320341i | ||||
\(593\) | −7.00000 | − | 12.1244i | −0.287456 | − | 0.497888i | 0.685746 | − | 0.727841i | \(-0.259476\pi\) |
−0.973202 | + | 0.229953i | \(0.926143\pi\) | |||||||
\(594\) | 9.00000 | 0.369274 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.00000 | 0.368654 | ||||||||
\(597\) | 6.00000 | + | 10.3923i | 0.245564 | + | 0.425329i | ||||
\(598\) | −3.50000 | + | 6.06218i | −0.143126 | + | 0.247901i | ||||
\(599\) | 14.5000 | − | 25.1147i | 0.592454 | − | 1.02616i | −0.401447 | − | 0.915882i | \(-0.631493\pi\) |
0.993901 | − | 0.110278i | \(-0.0351741\pi\) | |||||||
\(600\) | −16.5000 | − | 28.5788i | −0.673610 | − | 1.16673i | ||||
\(601\) | −26.0000 | −1.06056 | −0.530281 | − | 0.847822i | \(-0.677914\pi\) | ||||
−0.530281 | + | 0.847822i | \(0.677914\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.00000 | 0.244339 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −20.0000 | + | 34.6410i | −0.813116 | + | 1.40836i | ||||
\(606\) | 7.50000 | − | 12.9904i | 0.304667 | − | 0.527698i | ||||
\(607\) | −3.00000 | − | 5.19615i | −0.121766 | − | 0.210905i | 0.798698 | − | 0.601732i | \(-0.205522\pi\) |
−0.920464 | + | 0.390827i | \(0.872189\pi\) | |||||||
\(608\) | −6.00000 | −0.243332 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.00000 | −0.161955 | ||||||||
\(611\) | 3.50000 | + | 6.06218i | 0.141595 | + | 0.245249i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.5000 | − | 42.4352i | 0.989546 | − | 1.71394i | 0.369875 | − | 0.929082i | \(-0.379401\pi\) |
0.619671 | − | 0.784862i | \(-0.287266\pi\) | |||||||
\(614\) | 2.00000 | + | 3.46410i | 0.0807134 | + | 0.139800i | ||||
\(615\) | 36.0000 | 1.45166 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.0000 | 0.885687 | 0.442843 | − | 0.896599i | \(-0.353970\pi\) | ||||
0.442843 | + | 0.896599i | \(0.353970\pi\) | |||||||
\(618\) | 21.0000 | + | 36.3731i | 0.844744 | + | 1.46314i | ||||
\(619\) | −11.0000 | + | 19.0526i | −0.442127 | + | 0.765787i | −0.997847 | − | 0.0655827i | \(-0.979109\pi\) |
0.555720 | + | 0.831370i | \(0.312443\pi\) | |||||||
\(620\) | 14.0000 | − | 24.2487i | 0.562254 | − | 0.973852i | ||||
\(621\) | 31.5000 | + | 54.5596i | 1.26405 | + | 2.18940i | ||||
\(622\) | 30.0000 | 1.20289 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3.00000 | −0.120096 | ||||||||
\(625\) | −20.5000 | − | 35.5070i | −0.820000 | − | 1.42028i | ||||
\(626\) | −7.00000 | + | 12.1244i | −0.279776 | + | 0.484587i | ||||
\(627\) | 9.00000 | − | 15.5885i | 0.359425 | − | 0.622543i | ||||
\(628\) | −2.50000 | − | 4.33013i | −0.0997609 | − | 0.172791i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.00000 | −0.0796187 | −0.0398094 | − | 0.999207i | \(-0.512675\pi\) | ||||
−0.0398094 | + | 0.999207i | \(0.512675\pi\) | |||||||
\(632\) | −5.50000 | − | 9.52628i | −0.218778 | − | 0.378935i | ||||
\(633\) | 15.0000 | − | 25.9808i | 0.596196 | − | 1.03264i | ||||
\(634\) | −10.5000 | + | 18.1865i | −0.417008 | + | 0.722280i | ||||
\(635\) | −22.0000 | − | 38.1051i | −0.873043 | − | 1.51216i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4.00000 | −0.158362 | ||||||||
\(639\) | −48.0000 | − | 83.1384i | −1.89885 | − | 3.28891i | ||||
\(640\) | 2.00000 | − | 3.46410i | 0.0790569 | − | 0.136931i | ||||
\(641\) | −3.50000 | + | 6.06218i | −0.138242 | + | 0.239442i | −0.926831 | − | 0.375478i | \(-0.877478\pi\) |
0.788589 | + | 0.614920i | \(0.210812\pi\) | |||||||
\(642\) | 6.00000 | + | 10.3923i | 0.236801 | + | 0.410152i | ||||
\(643\) | −16.0000 | −0.630978 | −0.315489 | − | 0.948929i | \(-0.602169\pi\) | ||||
−0.315489 | + | 0.948929i | \(0.602169\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −48.0000 | −1.89000 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.00000 | − | 6.92820i | 0.157256 | − | 0.272376i | −0.776622 | − | 0.629967i | \(-0.783068\pi\) |
0.933878 | + | 0.357591i | \(0.116402\pi\) | |||||||
\(648\) | −4.50000 | + | 7.79423i | −0.176777 | + | 0.306186i | ||||
\(649\) | 5.00000 | + | 8.66025i | 0.196267 | + | 0.339945i | ||||
\(650\) | −11.0000 | −0.431455 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.00000 | −0.156652 | ||||||||
\(653\) | 18.0000 | + | 31.1769i | 0.704394 | + | 1.22005i | 0.966910 | + | 0.255119i | \(0.0821147\pi\) |
−0.262515 | + | 0.964928i | \(0.584552\pi\) | |||||||
\(654\) | 21.0000 | − | 36.3731i | 0.821165 | − | 1.42230i | ||||
\(655\) | 16.0000 | − | 27.7128i | 0.625172 | − | 1.08283i | ||||
\(656\) | 1.50000 | + | 2.59808i | 0.0585652 | + | 0.101438i | ||||
\(657\) | 30.0000 | 1.17041 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.0000 | −0.701180 | −0.350590 | − | 0.936529i | \(-0.614019\pi\) | ||||
−0.350590 | + | 0.936529i | \(0.614019\pi\) | |||||||
\(660\) | 6.00000 | + | 10.3923i | 0.233550 | + | 0.404520i | ||||
\(661\) | 2.00000 | − | 3.46410i | 0.0777910 | − | 0.134738i | −0.824506 | − | 0.565854i | \(-0.808547\pi\) |
0.902297 | + | 0.431116i | \(0.141880\pi\) | |||||||
\(662\) | 3.50000 | − | 6.06218i | 0.136031 | − | 0.235613i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 54.0000 | 2.09246 | ||||||||
\(667\) | −14.0000 | − | 24.2487i | −0.542082 | − | 0.938914i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −31.5000 | + | 54.5596i | −1.21786 | + | 2.10940i | ||||
\(670\) | 2.00000 | + | 3.46410i | 0.0772667 | + | 0.133830i | ||||
\(671\) | 1.00000 | 0.0386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.00000 | 0.269830 | 0.134915 | − | 0.990857i | \(-0.456924\pi\) | ||||
0.134915 | + | 0.990857i | \(0.456924\pi\) | |||||||
\(674\) | −8.50000 | − | 14.7224i | −0.327408 | − | 0.567087i | ||||
\(675\) | −49.5000 | + | 85.7365i | −1.90526 | + | 3.30000i | ||||
\(676\) | −0.500000 | + | 0.866025i | −0.0192308 | + | 0.0333087i | ||||
\(677\) | −19.5000 | − | 33.7750i | −0.749446 | − | 1.29808i | −0.948089 | − | 0.318006i | \(-0.896987\pi\) |
0.198643 | − | 0.980072i | \(-0.436347\pi\) | |||||||
\(678\) | −21.0000 | −0.806500 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −36.0000 | − | 62.3538i | −1.37952 | − | 2.38940i | ||||
\(682\) | −3.50000 | + | 6.06218i | −0.134022 | + | 0.232133i | ||||
\(683\) | −0.500000 | + | 0.866025i | −0.0191320 | + | 0.0331375i | −0.875433 | − | 0.483340i | \(-0.839424\pi\) |
0.856301 | + | 0.516477i | \(0.172757\pi\) | |||||||
\(684\) | 18.0000 | + | 31.1769i | 0.688247 | + | 1.19208i | ||||
\(685\) | 24.0000 | 0.916993 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −72.0000 | −2.74697 | ||||||||
\(688\) | −2.00000 | − | 3.46410i | −0.0762493 | − | 0.132068i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −42.0000 | + | 72.7461i | −1.59891 | + | 2.76940i | ||||
\(691\) | 16.0000 | + | 27.7128i | 0.608669 | + | 1.05425i | 0.991460 | + | 0.130410i | \(0.0416295\pi\) |
−0.382791 | + | 0.923835i | \(0.625037\pi\) | |||||||
\(692\) | 2.00000 | 0.0760286 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −24.0000 | −0.911028 | ||||||||
\(695\) | 8.00000 | + | 13.8564i | 0.303457 | + | 0.525603i | ||||
\(696\) | 6.00000 | − | 10.3923i | 0.227429 | − | 0.393919i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 13.0000 | + | 22.5167i | 0.492057 | + | 0.852268i | ||||
\(699\) | −15.0000 | −0.567352 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 4.50000 | + | 7.79423i | 0.169842 | + | 0.294174i | ||||
\(703\) | 27.0000 | − | 46.7654i | 1.01832 | − | 1.76379i | ||||
\(704\) | −0.500000 | + | 0.866025i | −0.0188445 | + | 0.0326396i | ||||
\(705\) | 42.0000 | + | 72.7461i | 1.58181 | + | 2.73978i | ||||
\(706\) | 25.0000 | 0.940887 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −30.0000 | −1.12747 | ||||||||
\(709\) | 6.50000 | + | 11.2583i | 0.244113 | + | 0.422815i | 0.961882 | − | 0.273466i | \(-0.0881700\pi\) |
−0.717769 | + | 0.696281i | \(0.754837\pi\) | |||||||
\(710\) | 32.0000 | − | 55.4256i | 1.20094 | − | 2.08009i | ||||
\(711\) | −33.0000 | + | 57.1577i | −1.23760 | + | 2.14358i | ||||
\(712\) | 3.00000 | + | 5.19615i | 0.112430 | + | 0.194734i | ||||
\(713\) | −49.0000 | −1.83506 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.00000 | 0.149592 | ||||||||
\(716\) | 3.00000 | + | 5.19615i | 0.112115 | + | 0.194189i | ||||
\(717\) | −9.00000 | + | 15.5885i | −0.336111 | + | 0.582162i | ||||
\(718\) | −6.00000 | + | 10.3923i | −0.223918 | + | 0.387837i | ||||
\(719\) | −1.00000 | − | 1.73205i | −0.0372937 | − | 0.0645946i | 0.846776 | − | 0.531949i | \(-0.178540\pi\) |
−0.884070 | + | 0.467355i | \(0.845207\pi\) | |||||||
\(720\) | −24.0000 | −0.894427 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 17.0000 | 0.632674 | ||||||||
\(723\) | 27.0000 | + | 46.7654i | 1.00414 | + | 1.73922i | ||||
\(724\) | −7.50000 | + | 12.9904i | −0.278735 | + | 0.482784i | ||||
\(725\) | 22.0000 | − | 38.1051i | 0.817059 | − | 1.41519i | ||||
\(726\) | 15.0000 | + | 25.9808i | 0.556702 | + | 0.964237i | ||||
\(727\) | −26.0000 | −0.964287 | −0.482143 | − | 0.876092i | \(-0.660142\pi\) | ||||
−0.482143 | + | 0.876092i | \(0.660142\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 10.0000 | + | 17.3205i | 0.370117 | + | 0.641061i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −1.50000 | + | 2.59808i | −0.0554416 | + | 0.0960277i | ||||
\(733\) | 2.00000 | + | 3.46410i | 0.0738717 | + | 0.127950i | 0.900595 | − | 0.434659i | \(-0.143131\pi\) |
−0.826723 | + | 0.562609i | \(0.809798\pi\) | |||||||
\(734\) | 32.0000 | 1.18114 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.00000 | −0.258023 | ||||||||
\(737\) | −0.500000 | − | 0.866025i | −0.0184177 | − | 0.0319005i | ||||
\(738\) | 9.00000 | − | 15.5885i | 0.331295 | − | 0.573819i | ||||
\(739\) | −12.0000 | + | 20.7846i | −0.441427 | + | 0.764574i | −0.997796 | − | 0.0663614i | \(-0.978861\pi\) |
0.556369 | + | 0.830936i | \(0.312194\pi\) | |||||||
\(740\) | 18.0000 | + | 31.1769i | 0.661693 | + | 1.14609i | ||||
\(741\) | 18.0000 | 0.661247 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.0000 | 0.586983 | 0.293492 | − | 0.955962i | \(-0.405183\pi\) | ||||
0.293492 | + | 0.955962i | \(0.405183\pi\) | |||||||
\(744\) | −10.5000 | − | 18.1865i | −0.384949 | − | 0.666751i | ||||
\(745\) | 18.0000 | − | 31.1769i | 0.659469 | − | 1.14223i | ||||
\(746\) | 8.00000 | − | 13.8564i | 0.292901 | − | 0.507319i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −72.0000 | −2.62907 | ||||||||
\(751\) | 13.5000 | + | 23.3827i | 0.492622 | + | 0.853246i | 0.999964 | − | 0.00849853i | \(-0.00270520\pi\) |
−0.507342 | + | 0.861745i | \(0.669372\pi\) | |||||||
\(752\) | −3.50000 | + | 6.06218i | −0.127632 | + | 0.221065i | ||||
\(753\) | −4.50000 | + | 7.79423i | −0.163989 | + | 0.284037i | ||||
\(754\) | −2.00000 | − | 3.46410i | −0.0728357 | − | 0.126155i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 54.0000 | 1.96266 | 0.981332 | − | 0.192323i | \(-0.0616021\pi\) | ||||
0.981332 | + | 0.192323i | \(0.0616021\pi\) | |||||||
\(758\) | 4.00000 | + | 6.92820i | 0.145287 | + | 0.251644i | ||||
\(759\) | 10.5000 | − | 18.1865i | 0.381126 | − | 0.660129i | ||||
\(760\) | −12.0000 | + | 20.7846i | −0.435286 | + | 0.753937i | ||||
\(761\) | −22.5000 | − | 38.9711i | −0.815624 | − | 1.41270i | −0.908879 | − | 0.417061i | \(-0.863060\pi\) |
0.0932544 | − | 0.995642i | \(-0.470273\pi\) | |||||||
\(762\) | −33.0000 | −1.19546 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −8.00000 | −0.289430 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.50000 | − | 12.9904i | 0.270986 | − | 0.469362i | ||||
\(767\) | −5.00000 | + | 8.66025i | −0.180540 | + | 0.312704i | ||||
\(768\) | −1.50000 | − | 2.59808i | −0.0541266 | − | 0.0937500i | ||||
\(769\) | 21.0000 | 0.757279 | 0.378640 | − | 0.925544i | \(-0.376392\pi\) | ||||
0.378640 | + | 0.925544i | \(0.376392\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 72.0000 | 2.59302 | ||||||||
\(772\) | −10.0000 | − | 17.3205i | −0.359908 | − | 0.623379i | ||||
\(773\) | −7.00000 | + | 12.1244i | −0.251773 | + | 0.436083i | −0.964014 | − | 0.265852i | \(-0.914347\pi\) |
0.712241 | + | 0.701935i | \(0.247680\pi\) | |||||||
\(774\) | −12.0000 | + | 20.7846i | −0.431331 | + | 0.747087i | ||||
\(775\) | −38.5000 | − | 66.6840i | −1.38296 | − | 2.39536i | ||||
\(776\) | −1.00000 | −0.0358979 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −36.0000 | −1.29066 | ||||||||
\(779\) | −9.00000 | − | 15.5885i | −0.322458 | − | 0.558514i | ||||
\(780\) | −6.00000 | + | 10.3923i | −0.214834 | + | 0.372104i | ||||
\(781\) | −8.00000 | + | 13.8564i | −0.286263 | + | 0.495821i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −36.0000 | −1.28654 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20.0000 | −0.713831 | ||||||||
\(786\) | −12.0000 | − | 20.7846i | −0.428026 | − | 0.741362i | ||||
\(787\) | −16.0000 | + | 27.7128i | −0.570338 | + | 0.987855i | 0.426193 | + | 0.904632i | \(0.359855\pi\) |
−0.996531 | + | 0.0832226i | \(0.973479\pi\) | |||||||
\(788\) | 13.5000 | − | 23.3827i | 0.480918 | − | 0.832974i | ||||
\(789\) | −36.0000 | − | 62.3538i | −1.28163 | − | 2.21986i | ||||
\(790\) | −44.0000 | −1.56545 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 6.00000 | 0.213201 | ||||||||
\(793\) | 0.500000 | + | 0.866025i | 0.0177555 | + | 0.0307535i | ||||
\(794\) | 14.0000 | − | 24.2487i | 0.496841 | − | 0.860555i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.00000 | + | 3.46410i | 0.0708881 | + | 0.122782i | ||||
\(797\) | 15.0000 | 0.531327 | 0.265664 | − | 0.964066i | \(-0.414409\pi\) | ||||
0.265664 | + | 0.964066i | \(0.414409\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −5.50000 | − | 9.52628i | −0.194454 | − | 0.336805i | ||||
\(801\) | 18.0000 | − | 31.1769i | 0.635999 | − | 1.10158i | ||||
\(802\) | −6.00000 | + | 10.3923i | −0.211867 | + | 0.366965i | ||||
\(803\) | −2.50000 | − | 4.33013i | −0.0882231 | − | 0.152807i | ||||
\(804\) | 3.00000 | 0.105802 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.00000 | −0.246564 | ||||||||
\(807\) | −13.5000 | − | 23.3827i | −0.475223 | − | 0.823110i | ||||
\(808\) | 2.50000 | − | 4.33013i | 0.0879497 | − | 0.152333i | ||||
\(809\) | −3.00000 | + | 5.19615i | −0.105474 | + | 0.182687i | −0.913932 | − | 0.405868i | \(-0.866969\pi\) |
0.808458 | + | 0.588555i | \(0.200303\pi\) | |||||||
\(810\) | 18.0000 | + | 31.1769i | 0.632456 | + | 1.09545i | ||||
\(811\) | −28.0000 | −0.983213 | −0.491606 | − | 0.870817i | \(-0.663590\pi\) | ||||
−0.491606 | + | 0.870817i | \(0.663590\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −69.0000 | −2.41994 | ||||||||
\(814\) | −4.50000 | − | 7.79423i | −0.157725 | − | 0.273188i | ||||
\(815\) | −8.00000 | + | 13.8564i | −0.280228 | + | 0.485369i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.0000 | + | 20.7846i | 0.419827 | + | 0.727161i | ||||
\(818\) | −26.0000 | −0.909069 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 12.0000 | 0.419058 | ||||||||
\(821\) | 23.0000 | + | 39.8372i | 0.802706 | + | 1.39033i | 0.917829 | + | 0.396976i | \(0.129940\pi\) |
−0.115124 | + | 0.993351i | \(0.536726\pi\) | |||||||
\(822\) | 9.00000 | − | 15.5885i | 0.313911 | − | 0.543710i | ||||
\(823\) | 1.50000 | − | 2.59808i | 0.0522867 | − | 0.0905632i | −0.838697 | − | 0.544598i | \(-0.816682\pi\) |
0.890984 | + | 0.454034i | \(0.150016\pi\) | |||||||
\(824\) | 7.00000 | + | 12.1244i | 0.243857 | + | 0.422372i | ||||
\(825\) | 33.0000 | 1.14891 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.0000 | −0.417281 | −0.208640 | − | 0.977992i | \(-0.566904\pi\) | ||||
−0.208640 | + | 0.977992i | \(0.566904\pi\) | |||||||
\(828\) | 21.0000 | + | 36.3731i | 0.729800 | + | 1.26405i | ||||
\(829\) | 7.00000 | − | 12.1244i | 0.243120 | − | 0.421096i | −0.718481 | − | 0.695546i | \(-0.755162\pi\) |
0.961601 | + | 0.274450i | \(0.0884958\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 27.0000 | + | 46.7654i | 0.936620 | + | 1.62227i | ||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 12.0000 | 0.415526 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.00000 | − | 5.19615i | 0.103757 | − | 0.179713i | ||||
\(837\) | −31.5000 | + | 54.5596i | −1.08880 | + | 1.88586i | ||||
\(838\) | −7.50000 | − | 12.9904i | −0.259083 | − | 0.448745i | ||||
\(839\) | 17.0000 | 0.586905 | 0.293453 | − | 0.955974i | \(-0.405196\pi\) | ||||
0.293453 | + | 0.955974i | \(0.405196\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0000 | −0.448276 | ||||||||
\(842\) | −9.50000 | − | 16.4545i | −0.327392 | − | 0.567059i | ||||
\(843\) | 12.0000 | − | 20.7846i | 0.413302 | − | 0.715860i | ||||
\(844\) | 5.00000 | − | 8.66025i | 0.172107 | − | 0.298098i | ||||
\(845\) | 2.00000 | + | 3.46410i | 0.0688021 | + | 0.119169i | ||||
\(846\) | 42.0000 | 1.44399 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −28.5000 | − | 49.3634i | −0.978117 | − | 1.69415i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 31.5000 | − | 54.5596i | 1.07981 | − | 1.87028i | ||||
\(852\) | −24.0000 | − | 41.5692i | −0.822226 | − | 1.42414i | ||||
\(853\) | 16.0000 | 0.547830 | 0.273915 | − | 0.961754i | \(-0.411681\pi\) | ||||
0.273915 | + | 0.961754i | \(0.411681\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 144.000 | 4.92470 | ||||||||
\(856\) | 2.00000 | + | 3.46410i | 0.0683586 | + | 0.118401i | ||||
\(857\) | −11.0000 | + | 19.0526i | −0.375753 | + | 0.650823i | −0.990439 | − | 0.137948i | \(-0.955949\pi\) |
0.614687 | + | 0.788771i | \(0.289283\pi\) | |||||||
\(858\) | 1.50000 | − | 2.59808i | 0.0512092 | − | 0.0886969i | ||||
\(859\) | −2.50000 | − | 4.33013i | −0.0852989 | − | 0.147742i | 0.820220 | − | 0.572049i | \(-0.193851\pi\) |
−0.905519 | + | 0.424307i | \(0.860518\pi\) | |||||||
\(860\) | −16.0000 | −0.545595 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 18.0000 | 0.613082 | ||||||||
\(863\) | −14.0000 | − | 24.2487i | −0.476566 | − | 0.825436i | 0.523074 | − | 0.852287i | \(-0.324785\pi\) |
−0.999639 | + | 0.0268516i | \(0.991452\pi\) | |||||||
\(864\) | −4.50000 | + | 7.79423i | −0.153093 | + | 0.265165i | ||||
\(865\) | 4.00000 | − | 6.92820i | 0.136004 | − | 0.235566i | ||||
\(866\) | −17.0000 | − | 29.4449i | −0.577684 | − | 1.00058i | ||||
\(867\) | −51.0000 | −1.73205 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.0000 | 0.373149 | ||||||||
\(870\) | −24.0000 | − | 41.5692i | −0.813676 | − | 1.40933i | ||||
\(871\) | 0.500000 | − | 0.866025i | 0.0169419 | − | 0.0293442i | ||||
\(872\) | 7.00000 | − | 12.1244i | 0.237050 | − | 0.410582i | ||||
\(873\) | 3.00000 | + | 5.19615i | 0.101535 | + | 0.175863i | ||||
\(874\) | 42.0000 | 1.42067 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 15.0000 | 0.506803 | ||||||||
\(877\) | 22.5000 | + | 38.9711i | 0.759771 | + | 1.31596i | 0.942967 | + | 0.332886i | \(0.108022\pi\) |
−0.183196 | + | 0.983076i | \(0.558644\pi\) | |||||||
\(878\) | −1.00000 | + | 1.73205i | −0.0337484 | + | 0.0584539i | ||||
\(879\) | 39.0000 | − | 67.5500i | 1.31544 | − | 2.27840i | ||||
\(880\) | 2.00000 | + | 3.46410i | 0.0674200 | + | 0.116775i | ||||
\(881\) | 18.0000 | 0.606435 | 0.303218 | − | 0.952921i | \(-0.401939\pi\) | ||||
0.303218 | + | 0.952921i | \(0.401939\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.0000 | −0.471138 | −0.235569 | − | 0.971858i | \(-0.575695\pi\) | ||||
−0.235569 | + | 0.971858i | \(0.575695\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −60.0000 | + | 103.923i | −2.01688 | + | 3.49334i | ||||
\(886\) | −6.00000 | + | 10.3923i | −0.201574 | + | 0.349136i | ||||
\(887\) | 19.0000 | + | 32.9090i | 0.637958 | + | 1.10497i | 0.985880 | + | 0.167452i | \(0.0535538\pi\) |
−0.347923 | + | 0.937523i | \(0.613113\pi\) | |||||||
\(888\) | 27.0000 | 0.906061 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 24.0000 | 0.804482 | ||||||||
\(891\) | −4.50000 | − | 7.79423i | −0.150756 | − | 0.261116i | ||||
\(892\) | −10.5000 | + | 18.1865i | −0.351566 | + | 0.608930i | ||||
\(893\) | 21.0000 | − | 36.3731i | 0.702738 | − | 1.21718i | ||||
\(894\) | −13.5000 | − | 23.3827i | −0.451508 | − | 0.782034i | ||||
\(895\) | 24.0000 | 0.802232 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 21.0000 | 0.701170 | ||||||||
\(898\) | 1.00000 | + | 1.73205i | 0.0333704 | + | 0.0577993i | ||||
\(899\) | 14.0000 | − | 24.2487i | 0.466926 | − | 0.808740i | ||||
\(900\) | −33.0000 | + | 57.1577i | −1.10000 | + | 1.90526i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −3.00000 | −0.0998891 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7.00000 | −0.232817 | ||||||||
\(905\) | 30.0000 | + | 51.9615i | 0.997234 | + | 1.72726i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.0000 | − | 25.9808i | 0.498067 | − | 0.862677i | −0.501931 | − | 0.864908i | \(-0.667377\pi\) |
0.999998 | + | 0.00223080i | \(0.000710087\pi\) | |||||||
\(908\) | −12.0000 | − | 20.7846i | −0.398234 | − | 0.689761i | ||||
\(909\) | −30.0000 | −0.995037 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 36.0000 | 1.19273 | 0.596367 | − | 0.802712i | \(-0.296610\pi\) | ||||
0.596367 | + | 0.802712i | \(0.296610\pi\) | |||||||
\(912\) | 9.00000 | + | 15.5885i | 0.298020 | + | 0.516185i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 13.0000 | − | 22.5167i | 0.430002 | − | 0.744785i | ||||
\(915\) | 6.00000 | + | 10.3923i | 0.198354 | + | 0.343559i | ||||
\(916\) | −24.0000 | −0.792982 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.5000 | − | 23.3827i | −0.445324 | − | 0.771324i | 0.552751 | − | 0.833347i | \(-0.313578\pi\) |
−0.998075 | + | 0.0620230i | \(0.980245\pi\) | |||||||
\(920\) | −14.0000 | + | 24.2487i | −0.461566 | + | 0.799456i | ||||
\(921\) | 6.00000 | − | 10.3923i | 0.197707 | − | 0.342438i | ||||
\(922\) | −6.00000 | − | 10.3923i | −0.197599 | − | 0.342252i | ||||
\(923\) | −16.0000 | −0.526646 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 99.0000 | 3.25510 | ||||||||
\(926\) | −8.00000 | − | 13.8564i | −0.262896 | − | 0.455350i | ||||
\(927\) | 42.0000 | − | 72.7461i | 1.37946 | − | 2.38930i | ||||
\(928\) | 2.00000 | − | 3.46410i | 0.0656532 | − | 0.113715i | ||||
\(929\) | 7.50000 | + | 12.9904i | 0.246067 | + | 0.426201i | 0.962431 | − | 0.271526i | \(-0.0875283\pi\) |
−0.716364 | + | 0.697727i | \(0.754195\pi\) | |||||||
\(930\) | −84.0000 | −2.75447 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −5.00000 | −0.163780 | ||||||||
\(933\) | −45.0000 | − | 77.9423i | −1.47323 | − | 2.55172i | ||||
\(934\) | 2.00000 | − | 3.46410i | 0.0654420 | − | 0.113349i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.00000 | + | 5.19615i | 0.0980581 | + | 0.169842i | ||||
\(937\) | −36.0000 | −1.17607 | −0.588034 | − | 0.808836i | \(-0.700098\pi\) | ||||
−0.588034 | + | 0.808836i | \(0.700098\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 42.0000 | 1.37062 | ||||||||
\(940\) | 14.0000 | + | 24.2487i | 0.456630 | + | 0.790906i | ||||
\(941\) | 25.0000 | − | 43.3013i | 0.814977 | − | 1.41158i | −0.0943679 | − | 0.995537i | \(-0.530083\pi\) |
0.909345 | − | 0.416044i | \(-0.136584\pi\) | |||||||
\(942\) | −7.50000 | + | 12.9904i | −0.244363 | + | 0.423249i | ||||
\(943\) | −10.5000 | − | 18.1865i | −0.341927 | − | 0.592235i | ||||
\(944\) | −10.0000 | −0.325472 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.00000 | 0.130051 | ||||||||
\(947\) | −12.0000 | − | 20.7846i | −0.389948 | − | 0.675409i | 0.602494 | − | 0.798123i | \(-0.294174\pi\) |
−0.992442 | + | 0.122714i | \(0.960840\pi\) | |||||||
\(948\) | −16.5000 | + | 28.5788i | −0.535895 | + | 0.928198i | ||||
\(949\) | 2.50000 | − | 4.33013i | 0.0811534 | − | 0.140562i | ||||
\(950\) | 33.0000 | + | 57.1577i | 1.07066 | + | 1.85444i | ||||
\(951\) | 63.0000 | 2.04291 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −34.0000 | −1.10137 | −0.550684 | − | 0.834714i | \(-0.685633\pi\) | ||||
−0.550684 | + | 0.834714i | \(0.685633\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.0000 | + | 27.7128i | −0.517748 | + | 0.896766i | ||||
\(956\) | −3.00000 | + | 5.19615i | −0.0970269 | + | 0.168056i | ||||
\(957\) | 6.00000 | + | 10.3923i | 0.193952 | + | 0.335936i | ||||
\(958\) | 24.0000 | 0.775405 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −12.0000 | −0.387298 | ||||||||
\(961\) | −9.00000 | − | 15.5885i | −0.290323 | − | 0.502853i | ||||
\(962\) | 4.50000 | − | 7.79423i | 0.145086 | − | 0.251296i | ||||
\(963\) | 12.0000 | − | 20.7846i | 0.386695 | − | 0.669775i | ||||
\(964\) | 9.00000 | + | 15.5885i | 0.289870 | + | 0.502070i | ||||
\(965\) | −80.0000 | −2.57529 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.0000 | −0.707472 | −0.353736 | − | 0.935345i | \(-0.615089\pi\) | ||||
−0.353736 | + | 0.935345i | \(0.615089\pi\) | |||||||
\(968\) | 5.00000 | + | 8.66025i | 0.160706 | + | 0.278351i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.00000 | + | 3.46410i | −0.0642161 | + | 0.111226i | ||||
\(971\) | 7.50000 | + | 12.9904i | 0.240686 | + | 0.416881i | 0.960910 | − | 0.276861i | \(-0.0892941\pi\) |
−0.720224 | + | 0.693742i | \(0.755961\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 38.0000 | 1.21760 | ||||||||
\(975\) | 16.5000 | + | 28.5788i | 0.528423 | + | 0.915255i | ||||
\(976\) | −0.500000 | + | 0.866025i | −0.0160046 | + | 0.0277208i | ||||
\(977\) | −21.0000 | + | 36.3731i | −0.671850 | + | 1.16368i | 0.305530 | + | 0.952183i | \(0.401167\pi\) |
−0.977379 | + | 0.211495i | \(0.932167\pi\) | |||||||
\(978\) | 6.00000 | + | 10.3923i | 0.191859 | + | 0.332309i | ||||
\(979\) | −6.00000 | −0.191761 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −84.0000 | −2.68191 | ||||||||
\(982\) | −8.00000 | − | 13.8564i | −0.255290 | − | 0.442176i | ||||
\(983\) | 20.0000 | − | 34.6410i | 0.637901 | − | 1.10488i | −0.347992 | − | 0.937498i | \(-0.613136\pi\) |
0.985893 | − | 0.167379i | \(-0.0535304\pi\) | |||||||
\(984\) | 4.50000 | − | 7.79423i | 0.143455 | − | 0.248471i | ||||
\(985\) | −54.0000 | − | 93.5307i | −1.72058 | − | 2.98014i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.00000 | 0.190885 | ||||||||
\(989\) | 14.0000 | + | 24.2487i | 0.445174 | + | 0.771064i | ||||
\(990\) | 12.0000 | − | 20.7846i | 0.381385 | − | 0.660578i | ||||
\(991\) | 28.5000 | − | 49.3634i | 0.905332 | − | 1.56808i | 0.0848618 | − | 0.996393i | \(-0.472955\pi\) |
0.820470 | − | 0.571689i | \(-0.193712\pi\) | |||||||
\(992\) | −3.50000 | − | 6.06218i | −0.111125 | − | 0.192474i | ||||
\(993\) | −21.0000 | −0.666415 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.0000 | 0.507234 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.50000 | + | 4.33013i | −0.0791758 | + | 0.137136i | −0.902895 | − | 0.429862i | \(-0.858562\pi\) |
0.823719 | + | 0.566999i | \(0.191896\pi\) | |||||||
\(998\) | 2.50000 | − | 4.33013i | 0.0791361 | − | 0.137068i | ||||
\(999\) | −40.5000 | − | 70.1481i | −1.28136 | − | 2.21939i |
(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 | 1274.2.f.b.1145.1 | 2 | ||
7.2 | even | 3 | inner | 1274.2.f.b.79.1 | 2 | ||
7.3 | odd | 6 | 1274.2.a.h.1.1 | 1 | |||
7.4 | even | 3 | 182.2.a.e.1.1 | ✓ | 1 | ||
7.5 | odd | 6 | 1274.2.f.k.79.1 | 2 | |||
7.6 | odd | 2 | 1274.2.f.k.1145.1 | 2 | |||
21.11 | odd | 6 | 1638.2.a.j.1.1 | 1 | |||
28.11 | odd | 6 | 1456.2.a.a.1.1 | 1 | |||
35.4 | even | 6 | 4550.2.a.a.1.1 | 1 | |||
56.11 | odd | 6 | 5824.2.a.bf.1.1 | 1 | |||
56.53 | even | 6 | 5824.2.a.b.1.1 | 1 | |||
91.18 | odd | 12 | 2366.2.d.j.337.1 | 2 | |||
91.25 | even | 6 | 2366.2.a.h.1.1 | 1 | |||
91.60 | odd | 12 | 2366.2.d.j.337.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
182.2.a.e.1.1 | ✓ | 1 | 7.4 | even | 3 | ||
1274.2.a.h.1.1 | 1 | 7.3 | odd | 6 | |||
1274.2.f.b.79.1 | 2 | 7.2 | even | 3 | inner | ||
1274.2.f.b.1145.1 | 2 | 1.1 | even | 1 | trivial | ||
1274.2.f.k.79.1 | 2 | 7.5 | odd | 6 | |||
1274.2.f.k.1145.1 | 2 | 7.6 | odd | 2 | |||
1456.2.a.a.1.1 | 1 | 28.11 | odd | 6 | |||
1638.2.a.j.1.1 | 1 | 21.11 | odd | 6 | |||
2366.2.a.h.1.1 | 1 | 91.25 | even | 6 | |||
2366.2.d.j.337.1 | 2 | 91.18 | odd | 12 | |||
2366.2.d.j.337.2 | 2 | 91.60 | odd | 12 | |||
4550.2.a.a.1.1 | 1 | 35.4 | even | 6 | |||
5824.2.a.b.1.1 | 1 | 56.53 | even | 6 | |||
5824.2.a.bf.1.1 | 1 | 56.11 | odd | 6 |