Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(55,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.55");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.b (of order \(2\), degree \(1\), 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: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{12} - 4x^{10} - 4x^{8} - 16x^{6} - 16x^{4} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 55.1 | ||
Root | \(1.41109 - 0.0939769i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 756.55 |
Dual form | 756.2.b.f.55.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41109 | − | 0.0939769i | −0.997790 | − | 0.0664517i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.98234 | + | 0.265219i | 0.991168 | + | 0.132610i | ||||
\(5\) | − | 2.91758i | − | 1.30478i | −0.757883 | − | 0.652391i | \(-0.773766\pi\) | ||
0.757883 | − | 0.652391i | \(-0.226234\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.63542 | − | 2.07976i | 0.618132 | − | 0.786074i | ||||
\(8\) | −2.77233 | − | 0.560541i | −0.980165 | − | 0.198181i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.274185 | + | 4.11696i | −0.0867049 | + | 1.30190i | ||||
\(11\) | − | 2.40700i | − | 0.725737i | −0.931840 | − | 0.362868i | \(-0.881797\pi\) | ||
0.931840 | − | 0.362868i | \(-0.118203\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.28591i | − | 0.356648i | −0.983972 | − | 0.178324i | \(-0.942932\pi\) | ||
0.983972 | − | 0.178324i | \(-0.0570676\pi\) | |||||||
\(14\) | −2.50318 | + | 2.78103i | −0.669002 | + | 0.743261i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.85932 | + | 1.05151i | 0.964829 | + | 0.262877i | ||||
\(17\) | − | 5.02059i | − | 1.21767i | −0.793296 | − | 0.608836i | \(-0.791637\pi\) | ||
0.793296 | − | 0.608836i | \(-0.208363\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.84850 | −1.11232 | −0.556161 | − | 0.831075i | \(-0.687726\pi\) | ||||
−0.556161 | + | 0.831075i | \(0.687726\pi\) | |||||||
\(20\) | 0.773798 | − | 5.78362i | 0.173026 | − | 1.29326i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.226202 | + | 3.39648i | −0.0482264 | + | 0.724133i | ||||
\(23\) | 8.04597i | 1.67770i | 0.544363 | + | 0.838850i | \(0.316772\pi\) | ||||
−0.544363 | + | 0.838850i | \(0.683228\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.51227 | −0.702454 | ||||||||
\(26\) | −0.120846 | + | 1.81454i | −0.0236999 | + | 0.355860i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.79355 | − | 3.68903i | 0.716914 | − | 0.697162i | ||||
\(29\) | −2.57469 | −0.478108 | −0.239054 | − | 0.971006i | \(-0.576837\pi\) | ||||
−0.239054 | + | 0.971006i | \(0.576837\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.34051 | 1.13879 | 0.569394 | − | 0.822065i | \(-0.307178\pi\) | ||||
0.569394 | + | 0.822065i | \(0.307178\pi\) | |||||||
\(32\) | −5.34702 | − | 1.84646i | −0.945228 | − | 0.326410i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.471820 | + | 7.08450i | −0.0809164 | + | 1.21498i | ||||
\(35\) | −6.06786 | − | 4.77148i | −1.02565 | − | 0.806527i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.71864 | −1.10454 | −0.552268 | − | 0.833666i | \(-0.686238\pi\) | ||||
−0.552268 | + | 0.833666i | \(0.686238\pi\) | |||||||
\(38\) | 6.84165 | + | 0.455647i | 1.10986 | + | 0.0739156i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.63542 | + | 8.08848i | −0.258583 | + | 1.27890i | ||||
\(41\) | 2.30281i | 0.359639i | 0.983700 | + | 0.179819i | \(0.0575513\pi\) | ||||
−0.983700 | + | 0.179819i | \(0.942449\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.79488i | 1.49370i | 0.664990 | + | 0.746852i | \(0.268436\pi\) | ||||
−0.664990 | + | 0.746852i | \(0.731564\pi\) | |||||||
\(44\) | 0.638382 | − | 4.77148i | 0.0962397 | − | 0.719327i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.756135 | − | 11.3536i | 0.111486 | − | 1.67399i | ||||
\(47\) | 1.21071 | 0.176600 | 0.0883002 | − | 0.996094i | \(-0.471857\pi\) | ||||
0.0883002 | + | 0.996094i | \(0.471857\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.65078 | − | 6.80257i | −0.235826 | − | 0.971795i | ||||
\(50\) | 4.95612 | + | 0.330072i | 0.700901 | + | 0.0466792i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.341049 | − | 2.54912i | 0.0472950 | − | 0.353499i | ||||
\(53\) | −5.54465 | −0.761617 | −0.380808 | − | 0.924654i | \(-0.624354\pi\) | ||||
−0.380808 | + | 0.924654i | \(0.624354\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.02260 | −0.946928 | ||||||||
\(56\) | −5.69972 | + | 4.84904i | −0.761657 | + | 0.647981i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.63312 | + | 0.241961i | 0.477051 | + | 0.0317711i | ||||
\(59\) | 12.2309 | 1.59233 | 0.796164 | − | 0.605081i | \(-0.206859\pi\) | ||||
0.796164 | + | 0.605081i | \(0.206859\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 8.95597i | − | 1.14669i | −0.819312 | − | 0.573347i | \(-0.805645\pi\) | ||
0.819312 | − | 0.573347i | \(-0.194355\pi\) | |||||||
\(62\) | −8.94701 | − | 0.595861i | −1.13627 | − | 0.0756744i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.37159 | + | 3.10801i | 0.921448 | + | 0.388501i | ||||
\(65\) | −3.75176 | −0.465348 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 7.32341i | − | 0.894696i | −0.894360 | − | 0.447348i | \(-0.852368\pi\) | ||
0.894360 | − | 0.447348i | \(-0.147632\pi\) | |||||||
\(68\) | 1.33156 | − | 9.95251i | 0.161475 | − | 1.20692i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 8.11387 | + | 7.30321i | 0.969793 | + | 0.872901i | ||||
\(71\) | − | 8.42187i | − | 0.999493i | −0.866172 | − | 0.499746i | \(-0.833427\pi\) | ||
0.866172 | − | 0.499746i | \(-0.166573\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 14.7329i | − | 1.72435i | −0.506610 | − | 0.862175i | \(-0.669102\pi\) | ||
0.506610 | − | 0.862175i | \(-0.330898\pi\) | |||||||
\(74\) | 9.48058 | + | 0.631396i | 1.10210 | + | 0.0733983i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −9.61135 | − | 1.28591i | −1.10250 | − | 0.147504i | ||||
\(77\) | −5.00597 | − | 3.93646i | −0.570483 | − | 0.448601i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.53235i | 0.397420i | 0.980058 | + | 0.198710i | \(0.0636752\pi\) | ||||
−0.980058 | + | 0.198710i | \(0.936325\pi\) | |||||||
\(80\) | 3.06786 | − | 11.2599i | 0.342997 | − | 1.25889i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.216411 | − | 3.24947i | 0.0238986 | − | 0.358844i | ||||
\(83\) | −10.4416 | −1.14612 | −0.573058 | − | 0.819515i | \(-0.694243\pi\) | ||||
−0.573058 | + | 0.819515i | \(0.694243\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −14.6480 | −1.58880 | ||||||||
\(86\) | 0.920492 | − | 13.8214i | 0.0992592 | − | 1.49040i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.34922 | + | 6.67298i | −0.143827 | + | 0.711342i | ||||
\(89\) | 9.97593i | 1.05745i | 0.848794 | + | 0.528723i | \(0.177329\pi\) | ||||
−0.848794 | + | 0.528723i | \(0.822671\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.67439 | − | 2.10301i | −0.280352 | − | 0.220456i | ||||
\(92\) | −2.13394 | + | 15.9498i | −0.222479 | + | 1.66288i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.70842 | − | 0.113779i | −0.176210 | − | 0.0117354i | ||||
\(95\) | 14.1459i | 1.45134i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 11.8187i | − | 1.20001i | −0.799998 | − | 0.600003i | \(-0.795166\pi\) | ||
0.799998 | − | 0.600003i | \(-0.204834\pi\) | |||||||
\(98\) | 1.69011 | + | 9.75415i | 0.170727 | + | 0.985318i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −6.96250 | − | 0.931521i | −0.696250 | − | 0.0931521i | ||||
\(101\) | 0.614768i | 0.0611717i | 0.999532 | + | 0.0305858i | \(0.00973730\pi\) | ||||
−0.999532 | + | 0.0305858i | \(0.990263\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.91816 | −0.780199 | −0.390100 | − | 0.920773i | \(-0.627559\pi\) | ||||
−0.390100 | + | 0.920773i | \(0.627559\pi\) | |||||||
\(104\) | −0.720808 | + | 3.56497i | −0.0706810 | + | 0.349574i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.82399 | + | 0.521069i | 0.759933 | + | 0.0506107i | ||||
\(107\) | 7.67670i | 0.742135i | 0.928606 | + | 0.371067i | \(0.121008\pi\) | ||||
−0.928606 | + | 0.371067i | \(0.878992\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.71864 | −0.643529 | −0.321764 | − | 0.946820i | \(-0.604276\pi\) | ||||
−0.321764 | + | 0.946820i | \(0.604276\pi\) | |||||||
\(110\) | 9.90951 | + | 0.659962i | 0.944835 | + | 0.0629249i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 8.49850 | − | 6.30678i | 0.803033 | − | 0.595935i | ||||
\(113\) | 3.25679 | 0.306373 | 0.153187 | − | 0.988197i | \(-0.451046\pi\) | ||||
0.153187 | + | 0.988197i | \(0.451046\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 23.4747 | 2.18903 | ||||||||
\(116\) | −5.10391 | − | 0.682858i | −0.473886 | − | 0.0634017i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −17.2589 | − | 1.14942i | −1.58881 | − | 0.105813i | ||||
\(119\) | −10.4416 | − | 8.21080i | −0.957181 | − | 0.752683i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.20637 | 0.473306 | ||||||||
\(122\) | −0.841654 | + | 12.6377i | −0.0761998 | + | 1.14416i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 12.5690 | + | 1.68162i | 1.12873 | + | 0.151014i | ||||
\(125\) | − | 4.34057i | − | 0.388233i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 12.9588i | − | 1.14990i | −0.818187 | − | 0.574952i | \(-0.805021\pi\) | ||
0.818187 | − | 0.574952i | \(-0.194979\pi\) | |||||||
\(128\) | −10.1099 | − | 5.07843i | −0.893595 | − | 0.448874i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.29406 | + | 0.352578i | 0.464320 | + | 0.0309232i | ||||
\(131\) | 19.5773 | 1.71048 | 0.855240 | − | 0.518233i | \(-0.173410\pi\) | ||||
0.855240 | + | 0.518233i | \(0.173410\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.92935 | + | 10.0837i | −0.687562 | + | 0.874367i | ||||
\(134\) | −0.688231 | + | 10.3340i | −0.0594541 | + | 0.892719i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.81425 | + | 13.9187i | −0.241320 | + | 1.19352i | ||||
\(137\) | 18.4269 | 1.57431 | 0.787156 | − | 0.616754i | \(-0.211553\pi\) | ||||
0.787156 | + | 0.616754i | \(0.211553\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.2935 | −0.873079 | −0.436540 | − | 0.899685i | \(-0.643796\pi\) | ||||
−0.436540 | + | 0.899685i | \(0.643796\pi\) | |||||||
\(140\) | −10.7630 | − | 11.0680i | −0.909643 | − | 0.935416i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.791461 | + | 11.8840i | −0.0664180 | + | 0.997283i | ||||
\(143\) | −3.09519 | −0.258833 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.51187i | 0.623827i | ||||||||
\(146\) | −1.38455 | + | 20.7894i | −0.114586 | + | 1.72054i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −13.3186 | − | 1.78191i | −1.09478 | − | 0.146472i | ||||
\(149\) | 14.6452 | 1.19978 | 0.599890 | − | 0.800082i | \(-0.295211\pi\) | ||||
0.599890 | + | 0.800082i | \(0.295211\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.0196i | 1.14090i | 0.821331 | + | 0.570451i | \(0.193232\pi\) | ||||
−0.821331 | + | 0.570451i | \(0.806768\pi\) | |||||||
\(152\) | 13.4416 | + | 2.71778i | 1.09026 | + | 0.220441i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.69392 | + | 6.02513i | 0.539412 | + | 0.485519i | ||||
\(155\) | − | 18.4989i | − | 1.48587i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.158192i | 0.0126251i | 0.999980 | + | 0.00631255i | \(0.00200936\pi\) | ||||
−0.999980 | + | 0.00631255i | \(0.997991\pi\) | |||||||
\(158\) | 0.331959 | − | 4.98445i | 0.0264092 | − | 0.396542i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.38718 | + | 15.6003i | −0.425894 | + | 1.23332i | ||||
\(161\) | 16.7337 | + | 13.1586i | 1.31880 | + | 1.03704i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 6.64972i | − | 0.520847i | −0.965495 | − | 0.260423i | \(-0.916138\pi\) | ||
0.965495 | − | 0.260423i | \(-0.0838621\pi\) | |||||||
\(164\) | −0.610750 | + | 4.56495i | −0.0476915 | + | 0.356463i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 14.7340 | + | 0.981270i | 1.14358 | + | 0.0761613i | ||||
\(167\) | −4.11552 | −0.318468 | −0.159234 | − | 0.987241i | \(-0.550903\pi\) | ||||
−0.159234 | + | 0.987241i | \(0.550903\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.3464 | 0.872802 | ||||||||
\(170\) | 20.6696 | + | 1.37657i | 1.58528 | + | 0.105578i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.59779 | + | 19.4167i | −0.198080 | + | 1.48051i | ||||
\(173\) | − | 9.82601i | − | 0.747058i | −0.927619 | − | 0.373529i | \(-0.878148\pi\) | ||
0.927619 | − | 0.373529i | \(-0.121852\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.74405 | + | 7.30467i | −0.434209 | + | 0.552181i | ||||
\(176\) | 2.53098 | − | 9.28937i | 0.190779 | − | 0.700212i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.937507 | − | 14.0769i | 0.0702691 | − | 1.05511i | ||||
\(179\) | 2.45324i | 0.183364i | 0.995788 | + | 0.0916819i | \(0.0292243\pi\) | ||||
−0.995788 | + | 0.0916819i | \(0.970776\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.5661i | 1.60299i | 0.597999 | + | 0.801497i | \(0.295963\pi\) | ||||
−0.597999 | + | 0.801497i | \(0.704037\pi\) | |||||||
\(182\) | 3.57616 | + | 3.21887i | 0.265083 | + | 0.238598i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.51010 | − | 22.3060i | 0.332489 | − | 1.64442i | ||||
\(185\) | 19.6022i | 1.44118i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.0846 | −0.883710 | ||||||||
\(188\) | 2.40004 | + | 0.321104i | 0.175041 | + | 0.0234189i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.32938 | − | 19.9611i | 0.0964437 | − | 1.44813i | ||||
\(191\) | − | 0.329664i | − | 0.0238536i | −0.999929 | − | 0.0119268i | \(-0.996203\pi\) | ||
0.999929 | − | 0.0119268i | \(-0.00379651\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.9539 | 1.14839 | 0.574193 | − | 0.818720i | \(-0.305316\pi\) | ||||
0.574193 | + | 0.818720i | \(0.305316\pi\) | |||||||
\(194\) | −1.11068 | + | 16.6772i | −0.0797423 | + | 1.19735i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.46823 | − | 13.9228i | −0.104873 | − | 0.994486i | ||||
\(197\) | 3.16936 | 0.225807 | 0.112904 | − | 0.993606i | \(-0.463985\pi\) | ||||
0.112904 | + | 0.993606i | \(0.463985\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 27.0253 | 1.91577 | 0.957887 | − | 0.287146i | \(-0.0927064\pi\) | ||||
0.957887 | + | 0.287146i | \(0.0927064\pi\) | |||||||
\(200\) | 9.73716 | + | 1.96877i | 0.688521 | + | 0.139213i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.0577740 | − | 0.867491i | 0.00406496 | − | 0.0610365i | ||||
\(203\) | −4.21071 | + | 5.35473i | −0.295534 | + | 0.375829i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.71864 | 0.469250 | ||||||||
\(206\) | 11.1732 | + | 0.744123i | 0.778475 | + | 0.0518455i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.35215 | − | 4.96275i | 0.0937546 | − | 0.344105i | ||||
\(209\) | 11.6703i | 0.807253i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.12613i | 0.0775260i | 0.999248 | + | 0.0387630i | \(0.0123417\pi\) | ||||
−0.999248 | + | 0.0387630i | \(0.987658\pi\) | |||||||
\(212\) | −10.9914 | − | 1.47055i | −0.754890 | − | 0.100998i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.721432 | − | 10.8325i | 0.0493161 | − | 0.740494i | ||||
\(215\) | 28.5773 | 1.94896 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.3694 | − | 13.1867i | 0.703922 | − | 0.895172i | ||||
\(218\) | 9.48058 | + | 0.631396i | 0.642106 | + | 0.0427635i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −13.9212 | − | 1.86253i | −0.938565 | − | 0.125572i | ||||
\(221\) | −6.45605 | −0.434281 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.78994 | −0.186828 | −0.0934140 | − | 0.995627i | \(-0.529778\pi\) | ||||
−0.0934140 | + | 0.995627i | \(0.529778\pi\) | |||||||
\(224\) | −12.5848 | + | 8.10076i | −0.840859 | + | 0.541255i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.59562 | − | 0.306063i | −0.305696 | − | 0.0203590i | ||||
\(227\) | −5.02019 | −0.333202 | −0.166601 | − | 0.986024i | \(-0.553279\pi\) | ||||
−0.166601 | + | 0.986024i | \(0.553279\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.12772i | 0.0745220i | 0.999306 | + | 0.0372610i | \(0.0118633\pi\) | ||||
−0.999306 | + | 0.0372610i | \(0.988137\pi\) | |||||||
\(230\) | −33.1249 | − | 2.20608i | −2.18419 | − | 0.145465i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.13789 | + | 1.44322i | 0.468625 | + | 0.0947521i | ||||
\(233\) | −4.15055 | −0.271911 | −0.135956 | − | 0.990715i | \(-0.543410\pi\) | ||||
−0.135956 | + | 0.990715i | \(0.543410\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 3.53235i | − | 0.230425i | ||||||
\(236\) | 24.2458 | + | 3.24387i | 1.57827 | + | 0.211158i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 13.9624 | + | 12.5674i | 0.905049 | + | 0.814625i | ||||
\(239\) | 14.8977i | 0.963651i | 0.876267 | + | 0.481826i | \(0.160026\pi\) | ||||
−0.876267 | + | 0.481826i | \(0.839974\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.2961i | 1.56505i | 0.622620 | + | 0.782524i | \(0.286068\pi\) | ||||
−0.622620 | + | 0.782524i | \(0.713932\pi\) | |||||||
\(242\) | −7.34664 | − | 0.489278i | −0.472260 | − | 0.0314520i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.37530 | − | 17.7538i | 0.152063 | − | 1.13657i | ||||
\(245\) | −19.8470 | + | 4.81628i | −1.26798 | + | 0.307701i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.23475i | 0.396708i | ||||||||
\(248\) | −17.5780 | − | 3.55412i | −1.11620 | − | 0.225687i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.407913 | + | 6.12493i | −0.0257987 | + | 0.387374i | ||||
\(251\) | −22.5773 | −1.42507 | −0.712534 | − | 0.701637i | \(-0.752453\pi\) | ||||
−0.712534 | + | 0.701637i | \(0.752453\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.3666 | 1.21757 | ||||||||
\(254\) | −1.21782 | + | 18.2860i | −0.0764131 | + | 1.14736i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.7887 | + | 8.11620i | 0.861792 | + | 0.507263i | ||||
\(257\) | − | 8.61820i | − | 0.537588i | −0.963198 | − | 0.268794i | \(-0.913375\pi\) | ||
0.963198 | − | 0.268794i | \(-0.0866251\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.9878 | + | 13.9731i | −0.682750 | + | 0.868248i | ||||
\(260\) | −7.43725 | − | 0.995038i | −0.461238 | − | 0.0617096i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −27.6253 | − | 1.83982i | −1.70670 | − | 0.113664i | ||||
\(263\) | − | 24.1043i | − | 1.48634i | −0.669104 | − | 0.743169i | \(-0.733322\pi\) | ||
0.669104 | − | 0.743169i | \(-0.266678\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.1770i | 0.993743i | ||||||||
\(266\) | 12.1366 | − | 13.4838i | 0.744145 | − | 0.826745i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.94231 | − | 14.5175i | 0.118645 | − | 0.886795i | ||||
\(269\) | − | 11.1901i | − | 0.682272i | −0.940014 | − | 0.341136i | \(-0.889188\pi\) | ||
0.940014 | − | 0.341136i | \(-0.110812\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.4251 | −1.11924 | −0.559621 | − | 0.828748i | \(-0.689053\pi\) | ||||
−0.559621 | + | 0.828748i | \(0.689053\pi\) | |||||||
\(272\) | 5.27919 | − | 19.3761i | 0.320098 | − | 1.17485i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −26.0019 | − | 1.73170i | −1.57083 | − | 0.104616i | ||||
\(275\) | 8.45402i | 0.509797i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.11552 | −0.127109 | −0.0635546 | − | 0.997978i | \(-0.520244\pi\) | ||||
−0.0635546 | + | 0.997978i | \(0.520244\pi\) | |||||||
\(278\) | 14.5250 | + | 0.967346i | 0.871149 | + | 0.0580176i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 14.1475 | + | 16.6294i | 0.845473 | + | 0.993795i | ||||
\(281\) | 9.03075 | 0.538729 | 0.269365 | − | 0.963038i | \(-0.413186\pi\) | ||||
0.269365 | + | 0.963038i | \(0.413186\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.9368 | 1.48234 | 0.741171 | − | 0.671316i | \(-0.234271\pi\) | ||||
0.741171 | + | 0.671316i | \(0.234271\pi\) | |||||||
\(284\) | 2.23364 | − | 16.6950i | 0.132542 | − | 0.990665i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.36759 | + | 0.290876i | 0.258261 | + | 0.0171999i | ||||
\(287\) | 4.78929 | + | 3.76607i | 0.282703 | + | 0.222304i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.20637 | −0.482727 | ||||||||
\(290\) | 0.705942 | − | 10.5999i | 0.0414543 | − | 0.622448i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.90744 | − | 29.2055i | 0.228665 | − | 1.70912i | ||||
\(293\) | − | 4.95534i | − | 0.289494i | −0.989469 | − | 0.144747i | \(-0.953763\pi\) | ||
0.989469 | − | 0.144747i | \(-0.0462368\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 35.6846i | − | 2.07764i | ||||||
\(296\) | 18.6262 | + | 3.76607i | 1.08263 | + | 0.218899i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −20.6656 | − | 1.37631i | −1.19713 | − | 0.0797274i | ||||
\(299\) | 10.3464 | 0.598349 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.3710 | + | 16.0188i | 1.17416 | + | 0.923307i | ||||
\(302\) | 1.31752 | − | 19.7829i | 0.0758149 | − | 1.13838i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −18.7119 | − | 5.09823i | −1.07320 | − | 0.292404i | ||||
\(305\) | −26.1298 | −1.49619 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.4907 | 1.16947 | 0.584734 | − | 0.811225i | \(-0.301199\pi\) | ||||
0.584734 | + | 0.811225i | \(0.301199\pi\) | |||||||
\(308\) | −8.87949 | − | 9.13107i | −0.505956 | − | 0.520291i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.73847 | + | 26.1036i | −0.0987385 | + | 1.48259i | ||||
\(311\) | −7.69410 | −0.436292 | −0.218146 | − | 0.975916i | \(-0.570001\pi\) | ||||
−0.218146 | + | 0.975916i | \(0.570001\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.8765i | 1.12349i | 0.827311 | + | 0.561744i | \(0.189869\pi\) | ||||
−0.827311 | + | 0.561744i | \(0.810131\pi\) | |||||||
\(314\) | 0.0148664 | − | 0.223223i | 0.000838959 | − | 0.0125972i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.936846 | + | 7.00230i | −0.0527017 | + | 0.393910i | ||||
\(317\) | −20.4069 | −1.14616 | −0.573082 | − | 0.819498i | \(-0.694252\pi\) | ||||
−0.573082 | + | 0.819498i | \(0.694252\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.19727i | 0.346981i | ||||||||
\(320\) | 9.06786 | − | 21.5072i | 0.506909 | − | 1.20229i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −22.3761 | − | 20.1405i | −1.24697 | − | 1.12238i | ||||
\(323\) | 24.3423i | 1.35444i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.51648i | 0.250529i | ||||||||
\(326\) | −0.624920 | + | 9.38334i | −0.0346111 | + | 0.519695i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.29082 | − | 6.38414i | 0.0712737 | − | 0.352505i | ||||
\(329\) | 1.98003 | − | 2.51799i | 0.109162 | − | 0.138821i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 18.9813i | − | 1.04331i | −0.853157 | − | 0.521654i | \(-0.825315\pi\) | ||
0.853157 | − | 0.521654i | \(-0.174685\pi\) | |||||||
\(332\) | −20.6988 | − | 2.76932i | −1.13599 | − | 0.151986i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.80736 | + | 0.386764i | 0.317765 | + | 0.0211628i | ||||
\(335\) | −21.3666 | −1.16738 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −25.4865 | −1.38834 | −0.694169 | − | 0.719812i | \(-0.744228\pi\) | ||||
−0.694169 | + | 0.719812i | \(0.744228\pi\) | |||||||
\(338\) | −16.0108 | − | 1.06630i | −0.870873 | − | 0.0579991i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −29.0372 | − | 3.88493i | −1.57477 | − | 0.210690i | ||||
\(341\) | − | 15.2616i | − | 0.826461i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.8474 | − | 7.69186i | −0.909675 | − | 0.415321i | ||||
\(344\) | 5.49043 | − | 27.1546i | 0.296024 | − | 1.46408i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.923418 | + | 13.8654i | −0.0496433 | + | 0.745407i | ||||
\(347\) | − | 10.5446i | − | 0.566066i | −0.959110 | − | 0.283033i | \(-0.908659\pi\) | ||
0.959110 | − | 0.283033i | \(-0.0913405\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 34.5639i | − | 1.85017i | −0.379765 | − | 0.925083i | \(-0.623995\pi\) | ||
0.379765 | − | 0.925083i | \(-0.376005\pi\) | |||||||
\(350\) | 8.79183 | − | 9.76772i | 0.469943 | − | 0.522106i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.44441 | + | 12.8703i | −0.236888 | + | 0.685987i | ||||
\(353\) | 6.44359i | 0.342958i | 0.985188 | + | 0.171479i | \(0.0548545\pi\) | ||||
−0.985188 | + | 0.171479i | \(0.945146\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −24.5715 | −1.30412 | ||||||||
\(356\) | −2.64581 | + | 19.7757i | −0.140228 | + | 1.04811i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.230548 | − | 3.46174i | 0.0121848 | − | 0.182959i | ||||
\(359\) | − | 30.0663i | − | 1.58684i | −0.608674 | − | 0.793420i | \(-0.708298\pi\) | ||
0.608674 | − | 0.793420i | \(-0.291702\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.50792 | 0.237259 | ||||||||
\(362\) | 2.02671 | − | 30.4316i | 0.106522 | − | 1.59945i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.74378 | − | 4.87818i | −0.248642 | − | 0.255686i | ||||
\(365\) | −42.9843 | −2.24990 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.55113 | 0.237567 | 0.118784 | − | 0.992920i | \(-0.462101\pi\) | ||||
0.118784 | + | 0.992920i | \(0.462101\pi\) | |||||||
\(368\) | −8.46039 | + | 31.0519i | −0.441028 | + | 1.61869i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.84215 | − | 27.6604i | 0.0957687 | − | 1.43799i | ||||
\(371\) | −9.06786 | + | 11.5315i | −0.470780 | + | 0.598687i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.81383 | 0.0939164 | 0.0469582 | − | 0.998897i | \(-0.485047\pi\) | ||||
0.0469582 | + | 0.998897i | \(0.485047\pi\) | |||||||
\(374\) | 17.0524 | + | 1.13567i | 0.881757 | + | 0.0587240i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.35649 | − | 0.678654i | −0.173098 | − | 0.0349989i | ||||
\(377\) | 3.31083i | 0.170517i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33.5629i | 1.72401i | 0.506900 | + | 0.862005i | \(0.330791\pi\) | ||||
−0.506900 | + | 0.862005i | \(0.669209\pi\) | |||||||
\(380\) | −3.75176 | + | 28.0419i | −0.192461 | + | 1.43852i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.0309808 | + | 0.465184i | −0.00158511 | + | 0.0238009i | ||||
\(383\) | 25.6725 | 1.31180 | 0.655902 | − | 0.754846i | \(-0.272288\pi\) | ||||
0.655902 | + | 0.754846i | \(0.272288\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.4849 | + | 14.6053i | −0.585326 | + | 0.744356i | ||||
\(386\) | −22.5123 | − | 1.49930i | −1.14585 | − | 0.0763122i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.13454 | − | 23.4286i | 0.159132 | − | 1.18941i | ||||
\(389\) | 14.5542 | 0.737929 | 0.368964 | − | 0.929443i | \(-0.379712\pi\) | ||||
0.368964 | + | 0.929443i | \(0.379712\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 40.3955 | 2.04289 | ||||||||
\(392\) | 0.763378 | + | 19.7843i | 0.0385564 | + | 0.999256i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.47224 | − | 0.297846i | −0.225308 | − | 0.0150053i | ||||
\(395\) | 10.3059 | 0.518546 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.27138i | 0.314752i | 0.987539 | + | 0.157376i | \(0.0503034\pi\) | ||||
−0.987539 | + | 0.157376i | \(0.949697\pi\) | |||||||
\(398\) | −38.1351 | − | 2.53975i | −1.91154 | − | 0.127306i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −13.5550 | − | 3.69318i | −0.677748 | − | 0.184659i | ||||
\(401\) | 22.8730 | 1.14222 | 0.571111 | − | 0.820873i | \(-0.306513\pi\) | ||||
0.571111 | + | 0.820873i | \(0.306513\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 8.15335i | − | 0.406147i | ||||||
\(404\) | −0.163048 | + | 1.21868i | −0.00811195 | + | 0.0606314i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.44490 | − | 7.16029i | 0.319855 | − | 0.355359i | ||||
\(407\) | 16.1717i | 0.801603i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 18.4324i | − | 0.911424i | −0.890127 | − | 0.455712i | \(-0.849385\pi\) | ||
0.890127 | − | 0.455712i | \(-0.150615\pi\) | |||||||
\(410\) | −9.48058 | − | 0.631396i | −0.468213 | − | 0.0311824i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −15.6965 | − | 2.10005i | −0.773309 | − | 0.103462i | ||||
\(413\) | 20.0027 | − | 25.4373i | 0.984269 | − | 1.25169i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 30.4642i | 1.49543i | ||||||||
\(416\) | −2.37438 | + | 6.87581i | −0.116414 | + | 0.337114i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.09674 | − | 16.4678i | 0.0536433 | − | 0.805468i | ||||
\(419\) | 15.1357 | 0.739428 | 0.369714 | − | 0.929146i | \(-0.379456\pi\) | ||||
0.369714 | + | 0.929146i | \(0.379456\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.8126 | 1.59919 | 0.799594 | − | 0.600541i | \(-0.205048\pi\) | ||||
0.799594 | + | 0.600541i | \(0.205048\pi\) | |||||||
\(422\) | 0.105830 | − | 1.58907i | 0.00515174 | − | 0.0773547i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 15.3716 | + | 3.10801i | 0.746510 | + | 0.150938i | ||||
\(425\) | 17.6337i | 0.855359i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −18.6262 | − | 14.6468i | −0.901387 | − | 0.708809i | ||||
\(428\) | −2.03601 | + | 15.2178i | −0.0984141 | + | 0.735580i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −40.3251 | − | 2.68561i | −1.94465 | − | 0.129512i | ||||
\(431\) | 4.81399i | 0.231882i | 0.993256 | + | 0.115941i | \(0.0369883\pi\) | ||||
−0.993256 | + | 0.115941i | \(0.963012\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.8325i | 1.38560i | 0.721129 | + | 0.692801i | \(0.243623\pi\) | ||||
−0.721129 | + | 0.692801i | \(0.756377\pi\) | |||||||
\(434\) | −15.8714 | + | 17.6331i | −0.761851 | + | 0.846417i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −13.3186 | − | 1.78191i | −0.637845 | − | 0.0853381i | ||||
\(437\) | − | 39.0108i | − | 1.86614i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.0795 | −1.10152 | −0.550762 | − | 0.834663i | \(-0.685663\pi\) | ||||
−0.550762 | + | 0.834663i | \(0.685663\pi\) | |||||||
\(440\) | 19.4690 | + | 3.93646i | 0.928146 | + | 0.187663i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9.11006 | + | 0.606720i | 0.433321 | + | 0.0288587i | ||||
\(443\) | − | 28.7475i | − | 1.36583i | −0.730496 | − | 0.682916i | \(-0.760711\pi\) | ||
0.730496 | − | 0.682916i | \(-0.239289\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 29.1056 | 1.37974 | ||||||||
\(446\) | 3.93685 | + | 0.262190i | 0.186415 | + | 0.0124150i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 18.5196 | − | 10.2482i | 0.874967 | − | 0.484182i | ||||
\(449\) | 35.0643 | 1.65479 | 0.827394 | − | 0.561622i | \(-0.189822\pi\) | ||||
0.827394 | + | 0.561622i | \(0.189822\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.54286 | 0.261003 | ||||||||
\(452\) | 6.45605 | + | 0.863763i | 0.303667 | + | 0.0406280i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.08393 | + | 0.471782i | 0.332465 | + | 0.0221418i | ||||
\(455\) | −6.13571 | + | 7.80274i | −0.287647 | + | 0.365798i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.1646 | 0.802926 | 0.401463 | − | 0.915875i | \(-0.368502\pi\) | ||||
0.401463 | + | 0.915875i | \(0.368502\pi\) | |||||||
\(458\) | 0.105980 | − | 1.59132i | 0.00495211 | − | 0.0743573i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 46.5349 | + | 6.22595i | 2.16970 | + | 0.290287i | ||||
\(461\) | − | 34.9394i | − | 1.62729i | −0.581363 | − | 0.813644i | \(-0.697480\pi\) | ||
0.581363 | − | 0.813644i | \(-0.302520\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.1288i | 0.563674i | 0.959462 | + | 0.281837i | \(0.0909438\pi\) | ||||
−0.959462 | + | 0.281837i | \(0.909056\pi\) | |||||||
\(464\) | −9.93655 | − | 2.70731i | −0.461293 | − | 0.125684i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.85679 | + | 0.390056i | 0.271310 | + | 0.0180690i | ||||
\(467\) | −21.7143 | −1.00482 | −0.502409 | − | 0.864630i | \(-0.667553\pi\) | ||||
−0.502409 | + | 0.864630i | \(0.667553\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.2309 | − | 11.9769i | −0.703298 | − | 0.553041i | ||||
\(470\) | −0.331959 | + | 4.98445i | −0.0153121 | + | 0.229916i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −33.9081 | − | 6.85593i | −1.56074 | − | 0.315570i | ||||
\(473\) | 23.5762 | 1.08404 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 17.0292 | 0.781355 | ||||||||
\(476\) | −18.5211 | − | 19.0459i | −0.848915 | − | 0.872967i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.40004 | − | 21.0219i | 0.0640363 | − | 0.961521i | ||||
\(479\) | −13.2107 | −0.603613 | −0.301806 | − | 0.953369i | \(-0.597590\pi\) | ||||
−0.301806 | + | 0.953369i | \(0.597590\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.63959i | 0.393931i | ||||||||
\(482\) | 2.28327 | − | 34.2839i | 0.104000 | − | 1.56159i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.3208 | + | 1.38083i | 0.469126 | + | 0.0627649i | ||||
\(485\) | −34.4819 | −1.56574 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.3925i | 0.606871i | 0.952852 | + | 0.303436i | \(0.0981337\pi\) | ||||
−0.952852 | + | 0.303436i | \(0.901866\pi\) | |||||||
\(488\) | −5.02019 | + | 24.8289i | −0.227253 | + | 1.12395i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 28.4585 | − | 4.93103i | 1.28562 | − | 0.222761i | ||||
\(491\) | 17.7604i | 0.801515i | 0.916184 | + | 0.400758i | \(0.131253\pi\) | ||||
−0.916184 | + | 0.400758i | \(0.868747\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.9265i | 0.582179i | ||||||||
\(494\) | 0.585922 | − | 8.79778i | 0.0263619 | − | 0.395831i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 24.4700 | + | 6.66709i | 1.09874 | + | 0.299361i | ||||
\(497\) | −17.5155 | − | 13.7733i | −0.785675 | − | 0.617818i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 26.4052i | − | 1.18206i | −0.806651 | − | 0.591029i | \(-0.798722\pi\) | ||
0.806651 | − | 0.591029i | \(-0.201278\pi\) | |||||||
\(500\) | 1.15120 | − | 8.60448i | 0.0514834 | − | 0.384804i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 31.8586 | + | 2.12175i | 1.42192 | + | 0.0946982i | ||||
\(503\) | −4.30590 | −0.191991 | −0.0959954 | − | 0.995382i | \(-0.530603\pi\) | ||||
−0.0959954 | + | 0.995382i | \(0.530603\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.79363 | 0.0798157 | ||||||||
\(506\) | −27.3280 | − | 1.82001i | −1.21488 | − | 0.0809095i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.43691 | − | 25.6886i | 0.152488 | − | 1.13975i | ||||
\(509\) | 5.30102i | 0.234964i | 0.993075 | + | 0.117482i | \(0.0374822\pi\) | ||||
−0.993075 | + | 0.117482i | \(0.962518\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −30.6408 | − | 24.0945i | −1.35547 | − | 1.06588i | ||||
\(512\) | −18.6943 | − | 12.7485i | −0.826178 | − | 0.563409i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −0.809911 | + | 12.1610i | −0.0357236 | + | 0.536400i | ||||
\(515\) | 23.1018i | 1.01799i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 2.91418i | − | 0.128165i | ||||||
\(518\) | 16.8179 | − | 18.6847i | 0.738937 | − | 0.820959i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 10.4011 | + | 2.10301i | 0.456118 | + | 0.0922233i | ||||
\(521\) | 22.7952i | 0.998674i | 0.866408 | + | 0.499337i | \(0.166423\pi\) | ||||
−0.866408 | + | 0.499337i | \(0.833577\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.25087 | 0.229605 | 0.114802 | − | 0.993388i | \(-0.463377\pi\) | ||||
0.114802 | + | 0.993388i | \(0.463377\pi\) | |||||||
\(524\) | 38.8089 | + | 5.19228i | 1.69537 | + | 0.226826i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.26525 | + | 34.0133i | −0.0987696 | + | 1.48305i | ||||
\(527\) | − | 31.8331i | − | 1.38667i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −41.7376 | −1.81468 | ||||||||
\(530\) | 1.52026 | − | 22.8271i | 0.0660359 | − | 0.991546i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −18.3930 | + | 17.8863i | −0.797439 | + | 0.775468i | ||||
\(533\) | 2.96122 | 0.128265 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 22.3974 | 0.968323 | ||||||||
\(536\) | −4.10507 | + | 20.3029i | −0.177312 | + | 0.876950i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.05161 | + | 15.7902i | −0.0453381 | + | 0.680764i | ||||
\(539\) | −16.3738 | + | 3.97342i | −0.705268 | + | 0.171147i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.0607 | 1.33540 | 0.667702 | − | 0.744428i | \(-0.267278\pi\) | ||||
0.667702 | + | 0.744428i | \(0.267278\pi\) | |||||||
\(542\) | 25.9994 | + | 1.73153i | 1.11677 | + | 0.0743756i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −9.27030 | + | 26.8452i | −0.397461 | + | 1.15098i | ||||
\(545\) | 19.6022i | 0.839664i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.3068i | 1.08204i | 0.841009 | + | 0.541020i | \(0.181962\pi\) | ||||
−0.841009 | + | 0.541020i | \(0.818038\pi\) | |||||||
\(548\) | 36.5282 | + | 4.88715i | 1.56041 | + | 0.208769i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.794482 | − | 11.9294i | 0.0338768 | − | 0.508670i | ||||
\(551\) | 12.4834 | 0.531810 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.34642 | + | 5.77688i | 0.312402 | + | 0.245658i | ||||
\(554\) | 2.98518 | + | 0.198810i | 0.126828 | + | 0.00844662i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −20.4051 | − | 2.73002i | −0.865368 | − | 0.115779i | ||||
\(557\) | −36.4584 | −1.54479 | −0.772397 | − | 0.635140i | \(-0.780942\pi\) | ||||
−0.772397 | + | 0.635140i | \(0.780942\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.5954 | 0.532727 | ||||||||
\(560\) | −18.4005 | − | 24.7950i | −0.777565 | − | 1.04778i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12.7432 | − | 0.848681i | −0.537538 | − | 0.0357995i | ||||
\(563\) | 13.5989 | 0.573125 | 0.286563 | − | 0.958061i | \(-0.407487\pi\) | ||||
0.286563 | + | 0.958061i | \(0.407487\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 9.50194i | − | 0.399750i | ||||||
\(566\) | −35.1881 | − | 2.34349i | −1.47907 | − | 0.0985041i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.72081 | + | 23.3482i | −0.198081 | + | 0.979668i | ||||
\(569\) | 15.7437 | 0.660011 | 0.330006 | − | 0.943979i | \(-0.392949\pi\) | ||||
0.330006 | + | 0.943979i | \(0.392949\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 12.8845i | − | 0.539199i | −0.962973 | − | 0.269599i | \(-0.913109\pi\) | ||
0.962973 | − | 0.269599i | \(-0.0868912\pi\) | |||||||
\(572\) | −6.13571 | − | 0.820904i | −0.256547 | − | 0.0343237i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6.40418 | − | 5.76434i | −0.267305 | − | 0.240599i | ||||
\(575\) | − | 28.2596i | − | 1.17851i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.59877i | 0.233080i | 0.993186 | + | 0.116540i | \(0.0371803\pi\) | ||||
−0.993186 | + | 0.116540i | \(0.962820\pi\) | |||||||
\(578\) | 11.5799 | + | 0.771208i | 0.481660 | + | 0.0320780i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.99229 | + | 14.8911i | −0.0827254 | + | 0.618317i | ||||
\(581\) | −17.0765 | + | 21.7160i | −0.708451 | + | 0.900933i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.3460i | 0.552733i | ||||||||
\(584\) | −8.25838 | + | 40.8443i | −0.341734 | + | 1.69015i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.465687 | + | 6.99242i | −0.0192374 | + | 0.288854i | ||||
\(587\) | 22.6725 | 0.935795 | 0.467898 | − | 0.883783i | \(-0.345012\pi\) | ||||
0.467898 | + | 0.883783i | \(0.345012\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −30.7419 | −1.26670 | ||||||||
\(590\) | −3.35353 | + | 50.3541i | −0.138063 | + | 2.07305i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −25.9293 | − | 7.06469i | −1.06569 | − | 0.290357i | ||||
\(593\) | − | 0.749311i | − | 0.0307705i | −0.999882 | − | 0.0153852i | \(-0.995103\pi\) | ||
0.999882 | − | 0.0153852i | \(-0.00489747\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −23.9557 | + | 30.4642i | −0.982086 | + | 1.24891i | ||||
\(596\) | 29.0317 | + | 3.88418i | 1.18918 | + | 0.159102i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −14.5997 | − | 0.972324i | −0.597027 | − | 0.0397613i | ||||
\(599\) | 17.9701i | 0.734237i | 0.930174 | + | 0.367118i | \(0.119656\pi\) | ||||
−0.930174 | + | 0.367118i | \(0.880344\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.11913i | 0.331186i | 0.986194 | + | 0.165593i | \(0.0529538\pi\) | ||||
−0.986194 | + | 0.165593i | \(0.947046\pi\) | |||||||
\(602\) | −27.2398 | − | 24.5183i | −1.11021 | − | 0.999291i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.71828 | + | 27.7917i | −0.151295 | + | 1.13083i | ||||
\(605\) | − | 15.1900i | − | 0.617561i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.4587 | 0.627449 | 0.313724 | − | 0.949514i | \(-0.398423\pi\) | ||||
0.313724 | + | 0.949514i | \(0.398423\pi\) | |||||||
\(608\) | 25.9250 | + | 8.95253i | 1.05140 | + | 0.363073i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 36.8714 | + | 2.45559i | 1.49288 | + | 0.0994241i | ||||
\(611\) | − | 1.55687i | − | 0.0629843i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.00000 | 0.0807792 | 0.0403896 | − | 0.999184i | \(-0.487140\pi\) | ||||
0.0403896 | + | 0.999184i | \(0.487140\pi\) | |||||||
\(614\) | −28.9142 | − | 1.92565i | −1.16688 | − | 0.0777131i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11.6716 | + | 13.7192i | 0.470263 | + | 0.552762i | ||||
\(617\) | −9.96087 | −0.401009 | −0.200505 | − | 0.979693i | \(-0.564258\pi\) | ||||
−0.200505 | + | 0.979693i | \(0.564258\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.1653 | 0.649739 | 0.324869 | − | 0.945759i | \(-0.394680\pi\) | ||||
0.324869 | + | 0.945759i | \(0.394680\pi\) | |||||||
\(620\) | 4.90627 | − | 36.6711i | 0.197041 | − | 1.47275i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 10.8570 | + | 0.723067i | 0.435328 | + | 0.0289923i | ||||
\(623\) | 20.7475 | + | 16.3149i | 0.831232 | + | 0.653642i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.2253 | −1.20901 | ||||||||
\(626\) | 1.86793 | − | 28.0475i | 0.0746576 | − | 1.12100i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.0419556 | + | 0.313590i | −0.00167421 | + | 0.0125136i | ||||
\(629\) | 33.7315i | 1.34496i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 10.7815i | − | 0.429203i | −0.976702 | − | 0.214602i | \(-0.931155\pi\) | ||
0.976702 | − | 0.214602i | \(-0.0688453\pi\) | |||||||
\(632\) | 1.98003 | − | 9.79282i | 0.0787612 | − | 0.389537i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 28.7959 | + | 1.91777i | 1.14363 | + | 0.0761646i | ||||
\(635\) | −37.8082 | −1.50037 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.74752 | + | 2.12276i | −0.346589 | + | 0.0841068i | ||||
\(638\) | 0.582400 | − | 8.74490i | 0.0230575 | − | 0.346214i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −14.8167 | + | 29.4964i | −0.585682 | + | 1.16595i | ||||
\(641\) | 8.70174 | 0.343698 | 0.171849 | − | 0.985123i | \(-0.445026\pi\) | ||||
0.171849 | + | 0.985123i | \(0.445026\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.75116 | −0.226803 | −0.113402 | − | 0.993549i | \(-0.536175\pi\) | ||||
−0.113402 | + | 0.993549i | \(0.536175\pi\) | |||||||
\(644\) | 29.6818 | + | 30.5228i | 1.16963 | + | 1.20277i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.28762 | − | 34.3492i | 0.0900051 | − | 1.35145i | ||||
\(647\) | 9.55700 | 0.375724 | 0.187862 | − | 0.982195i | \(-0.439844\pi\) | ||||
0.187862 | + | 0.982195i | \(0.439844\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 29.4397i | − | 1.15561i | ||||||
\(650\) | 0.424444 | − | 6.37315i | 0.0166481 | − | 0.249975i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.76363 | − | 13.1820i | 0.0690692 | − | 0.516247i | ||||
\(653\) | 21.4789 | 0.840533 | 0.420267 | − | 0.907401i | \(-0.361937\pi\) | ||||
0.420267 | + | 0.907401i | \(0.361937\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 57.1184i | − | 2.23180i | ||||||
\(656\) | −2.42142 | + | 8.88728i | −0.0945407 | + | 0.346990i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.03062 | + | 3.36702i | −0.118146 | + | 0.131260i | ||||
\(659\) | − | 1.35908i | − | 0.0529421i | −0.999650 | − | 0.0264710i | \(-0.991573\pi\) | ||
0.999650 | − | 0.0264710i | \(-0.00842698\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.78646i | 0.0694851i | 0.999396 | + | 0.0347426i | \(0.0110611\pi\) | ||||
−0.999396 | + | 0.0347426i | \(0.988939\pi\) | |||||||
\(662\) | −1.78381 | + | 26.7843i | −0.0693296 | + | 1.04100i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 28.9476 | + | 5.85296i | 1.12338 | + | 0.227139i | ||||
\(665\) | 29.4200 | + | 23.1345i | 1.14086 | + | 0.897117i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 20.7159i | − | 0.802122i | ||||||
\(668\) | −8.15835 | − | 1.09151i | −0.315656 | − | 0.0422320i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 30.1502 | + | 2.00797i | 1.16480 | + | 0.0775746i | ||||
\(671\) | −21.5570 | −0.832199 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.1646 | 0.661647 | 0.330823 | − | 0.943693i | \(-0.392674\pi\) | ||||
0.330823 | + | 0.943693i | \(0.392674\pi\) | |||||||
\(674\) | 35.9637 | + | 2.39514i | 1.38527 | + | 0.0922573i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 22.4924 | + | 3.00929i | 0.865094 | + | 0.115742i | ||||
\(677\) | − | 4.28166i | − | 0.164557i | −0.996609 | − | 0.0822787i | \(-0.973780\pi\) | ||
0.996609 | − | 0.0822787i | \(-0.0262198\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −24.5800 | − | 19.3285i | −0.943293 | − | 0.741762i | ||||
\(680\) | 40.6090 | + | 8.21080i | 1.55728 | + | 0.314870i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.43424 | + | 21.5354i | −0.0549197 | + | 0.824634i | ||||
\(683\) | − | 22.0539i | − | 0.843870i | −0.906626 | − | 0.421935i | \(-0.861351\pi\) | ||
0.906626 | − | 0.421935i | \(-0.138649\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 53.7618i | − | 2.05413i | ||||||
\(686\) | 23.0503 | + | 12.4372i | 0.880065 | + | 0.474853i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −10.2994 | + | 37.8015i | −0.392660 | + | 1.44117i | ||||
\(689\) | 7.12995i | 0.271629i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.60142 | −0.289172 | −0.144586 | − | 0.989492i | \(-0.546185\pi\) | ||||
−0.144586 | + | 0.989492i | \(0.546185\pi\) | |||||||
\(692\) | 2.60605 | − | 19.4785i | 0.0990671 | − | 0.740460i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.990952 | + | 14.8794i | −0.0376160 | + | 0.564814i | ||||
\(695\) | 30.0320i | 1.13918i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.5615 | 0.437922 | ||||||||
\(698\) | −3.24821 | + | 48.7728i | −0.122947 | + | 1.84608i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −13.3240 | + | 12.9569i | −0.503599 | + | 0.489724i | ||||
\(701\) | 5.13174 | 0.193823 | 0.0969116 | − | 0.995293i | \(-0.469104\pi\) | ||||
0.0969116 | + | 0.995293i | \(0.469104\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 32.5753 | 1.22860 | ||||||||
\(704\) | 7.48096 | − | 17.7434i | 0.281949 | − | 0.668729i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.605548 | − | 9.09247i | 0.0227901 | − | 0.342199i | ||||
\(707\) | 1.27857 | + | 1.00541i | 0.0480855 | + | 0.0378122i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.2756 | −1.06191 | −0.530957 | − | 0.847399i | \(-0.678167\pi\) | ||||
−0.530957 | + | 0.847399i | \(0.678167\pi\) | |||||||
\(710\) | 34.6725 | + | 2.30915i | 1.30124 | + | 0.0866609i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.59192 | − | 27.6565i | 0.209566 | − | 1.03647i | ||||
\(713\) | 51.0155i | 1.91055i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.03047i | 0.337720i | ||||||||
\(716\) | −0.650646 | + | 4.86315i | −0.0243158 | + | 0.181744i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2.82554 | + | 42.4262i | −0.105448 | + | 1.58333i | ||||
\(719\) | −19.6725 | −0.733661 | −0.366831 | − | 0.930288i | \(-0.619557\pi\) | ||||
−0.366831 | + | 0.930288i | \(0.619557\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.9495 | + | 16.4678i | −0.482266 | + | 0.613294i | ||||
\(722\) | −6.36108 | − | 0.423640i | −0.236735 | − | 0.0157663i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5.71974 | + | 42.7512i | −0.212572 | + | 1.58884i | ||||
\(725\) | 9.04301 | 0.335849 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.895551 | 0.0332142 | 0.0166071 | − | 0.999862i | \(-0.494714\pi\) | ||||
0.0166071 | + | 0.999862i | \(0.494714\pi\) | |||||||
\(728\) | 6.23545 | + | 7.32935i | 0.231101 | + | 0.271644i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 60.6546 | + | 4.03953i | 2.24493 | + | 0.149510i | ||||
\(731\) | 49.1761 | 1.81884 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 6.22595i | − | 0.229961i | −0.993368 | − | 0.114980i | \(-0.963319\pi\) | ||
0.993368 | − | 0.114980i | \(-0.0366805\pi\) | |||||||
\(734\) | −6.42205 | − | 0.427701i | −0.237042 | − | 0.0157867i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 14.8565 | − | 43.0219i | 0.547619 | − | 1.58581i | ||||
\(737\) | −17.6274 | −0.649314 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.85866i | 0.105158i | 0.998617 | + | 0.0525788i | \(0.0167441\pi\) | ||||
−0.998617 | + | 0.0525788i | \(0.983256\pi\) | |||||||
\(740\) | −5.19887 | + | 38.8581i | −0.191114 | + | 1.42845i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 13.8792 | − | 15.4198i | 0.509523 | − | 0.566080i | ||||
\(743\) | − | 15.8280i | − | 0.580672i | −0.956925 | − | 0.290336i | \(-0.906233\pi\) | ||
0.956925 | − | 0.290336i | \(-0.0937671\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 42.7285i | − | 1.56545i | ||||||
\(746\) | −2.55947 | − | 0.170458i | −0.0937088 | − | 0.00624090i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −23.9557 | − | 3.20506i | −0.875906 | − | 0.117188i | ||||
\(749\) | 15.9657 | + | 12.5547i | 0.583373 | + | 0.458737i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 50.6346i | 1.84768i | 0.382773 | + | 0.923842i | \(0.374969\pi\) | ||||
−0.382773 | + | 0.923842i | \(0.625031\pi\) | |||||||
\(752\) | 4.67252 | + | 1.27307i | 0.170389 | + | 0.0464242i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.311142 | − | 4.67188i | 0.0113311 | − | 0.170140i | ||||
\(755\) | 40.9034 | 1.48863 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37.1804 | −1.35135 | −0.675673 | − | 0.737201i | \(-0.736147\pi\) | ||||
−0.675673 | + | 0.737201i | \(0.736147\pi\) | |||||||
\(758\) | 3.15413 | − | 47.3602i | 0.114563 | − | 1.72020i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7.92935 | − | 39.2170i | 0.287628 | − | 1.42255i | ||||
\(761\) | 34.3898i | 1.24663i | 0.781970 | + | 0.623315i | \(0.214215\pi\) | ||||
−0.781970 | + | 0.623315i | \(0.785785\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.9878 | + | 13.9731i | −0.397786 | + | 0.505861i | ||||
\(764\) | 0.0874331 | − | 0.653504i | 0.00316322 | − | 0.0236430i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −36.2262 | − | 2.41262i | −1.30890 | − | 0.0871716i | ||||
\(767\) | − | 15.7279i | − | 0.567901i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 32.6448i | − | 1.17720i | −0.808424 | − | 0.588601i | \(-0.799679\pi\) | ||
0.808424 | − | 0.588601i | \(-0.200321\pi\) | |||||||
\(770\) | 17.5788 | − | 19.5301i | 0.633496 | − | 0.703814i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 31.6260 | + | 4.23128i | 1.13824 | + | 0.152287i | ||||
\(773\) | 39.6845i | 1.42735i | 0.700475 | + | 0.713677i | \(0.252971\pi\) | ||||
−0.700475 | + | 0.713677i | \(0.747029\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −22.2696 | −0.799946 | ||||||||
\(776\) | −6.62486 | + | 32.7652i | −0.237819 | + | 1.17620i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −20.5373 | − | 1.36776i | −0.736298 | − | 0.0490366i | ||||
\(779\) | − | 11.1652i | − | 0.400034i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.2714 | −0.725369 | ||||||||
\(782\) | −57.0016 | − | 3.79625i | −2.03837 | − | 0.135753i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.782071 | − | 27.9891i | 0.0279311 | − | 0.999610i | ||||
\(785\) | 0.461538 | 0.0164730 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.0860 | −0.787282 | −0.393641 | − | 0.919264i | \(-0.628785\pi\) | ||||
−0.393641 | + | 0.919264i | \(0.628785\pi\) | |||||||
\(788\) | 6.28273 | + | 0.840574i | 0.223813 | + | 0.0299442i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −14.5425 | − | 0.968516i | −0.517400 | − | 0.0344583i | ||||
\(791\) | 5.32623 | − | 6.77333i | 0.189379 | − | 0.240832i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.5166 | −0.408967 | ||||||||
\(794\) | 0.589365 | − | 8.84947i | 0.0209158 | − | 0.314056i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 53.5733 | + | 7.16763i | 1.89885 | + | 0.254050i | ||||
\(797\) | − | 35.9370i | − | 1.27295i | −0.771296 | − | 0.636477i | \(-0.780391\pi\) | ||
0.771296 | − | 0.636477i | \(-0.219609\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 6.07849i | − | 0.215042i | ||||||
\(800\) | 18.7802 | + | 6.48525i | 0.663979 | + | 0.229288i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −32.2758 | − | 2.14953i | −1.13970 | − | 0.0759026i | ||||
\(803\) | −35.4619 | −1.25142 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 38.3912 | − | 48.8218i | 1.35311 | − | 1.72074i | ||||
\(806\) | −0.766226 | + | 11.5051i | −0.0269892 | + | 0.405249i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.344603 | − | 1.70434i | 0.0121231 | − | 0.0599584i | ||||
\(809\) | 32.2780 | 1.13483 | 0.567417 | − | 0.823431i | \(-0.307943\pi\) | ||||
0.567417 | + | 0.823431i | \(0.307943\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 33.7682 | 1.18576 | 0.592881 | − | 0.805290i | \(-0.297990\pi\) | ||||
0.592881 | + | 0.805290i | \(0.297990\pi\) | |||||||
\(812\) | −9.76723 | + | 9.49812i | −0.342762 | + | 0.333319i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.51977 | − | 22.8197i | 0.0532679 | − | 0.799831i | ||||
\(815\) | −19.4011 | −0.679591 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 47.4904i | − | 1.66148i | ||||||
\(818\) | −1.73222 | + | 26.0097i | −0.0605656 | + | 0.909409i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 13.3186 | + | 1.78191i | 0.465106 | + | 0.0622270i | ||||
\(821\) | 4.46728 | 0.155909 | 0.0779547 | − | 0.996957i | \(-0.475161\pi\) | ||||
0.0779547 | + | 0.996957i | \(0.475161\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 52.2387i | 1.82093i | 0.413590 | + | 0.910463i | \(0.364275\pi\) | ||||
−0.413590 | + | 0.910463i | \(0.635725\pi\) | |||||||
\(824\) | 21.9517 | + | 4.43845i | 0.764724 | + | 0.154621i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −30.6161 | + | 34.0145i | −1.06527 | + | 1.18352i | ||||
\(827\) | 9.64827i | 0.335503i | 0.985829 | + | 0.167752i | \(0.0536506\pi\) | ||||
−0.985829 | + | 0.167752i | \(0.946349\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 36.3958i | − | 1.26408i | −0.774936 | − | 0.632040i | \(-0.782218\pi\) | ||
0.774936 | − | 0.632040i | \(-0.217782\pi\) | |||||||
\(830\) | 2.86293 | − | 42.9877i | 0.0993739 | − | 1.49213i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.99663 | − | 9.47923i | 0.138558 | − | 0.328633i | ||||
\(833\) | −34.1529 | + | 8.28789i | −1.18333 | + | 0.287158i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.0074i | 0.415532i | ||||||||
\(836\) | −3.09519 | + | 23.1345i | −0.107049 | + | 0.800123i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −21.3578 | − | 1.42241i | −0.737794 | − | 0.0491362i | ||||
\(839\) | 31.9439 | 1.10283 | 0.551414 | − | 0.834232i | \(-0.314089\pi\) | ||||
0.551414 | + | 0.834232i | \(0.314089\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.3710 | −0.771413 | ||||||||
\(842\) | −46.3014 | − | 3.08362i | −1.59565 | − | 0.106269i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.298671 | + | 2.23237i | −0.0102807 | + | 0.0768414i | ||||
\(845\) | − | 33.1041i | − | 1.13882i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.51461 | − | 10.8280i | 0.292566 | − | 0.372054i | ||||
\(848\) | −21.3986 | − | 5.83024i | −0.734830 | − | 0.200211i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.65716 | − | 24.8827i | 0.0568400 | − | 0.853468i | ||||
\(851\) | − | 54.0579i | − | 1.85308i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.8116i | 0.883772i | 0.897071 | + | 0.441886i | \(0.145690\pi\) | ||||
−0.897071 | + | 0.441886i | \(0.854310\pi\) | |||||||
\(854\) | 24.9068 | + | 22.4184i | 0.852293 | + | 0.767141i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.30311 | − | 21.2823i | 0.147077 | − | 0.727415i | ||||
\(857\) | − | 11.8918i | − | 0.406217i | −0.979156 | − | 0.203109i | \(-0.934896\pi\) | ||
0.979156 | − | 0.203109i | \(-0.0651045\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.2839 | −1.03327 | −0.516637 | − | 0.856205i | \(-0.672816\pi\) | ||||
−0.516637 | + | 0.856205i | \(0.672816\pi\) | |||||||
\(860\) | 56.6499 | + | 7.57926i | 1.93175 | + | 0.258450i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.452404 | − | 6.79297i | 0.0154089 | − | 0.231369i | ||||
\(863\) | 56.2350i | 1.91426i | 0.289658 | + | 0.957130i | \(0.406459\pi\) | ||||
−0.289658 | + | 0.957130i | \(0.593541\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −28.6682 | −0.974747 | ||||||||
\(866\) | 2.70959 | − | 40.6852i | 0.0920755 | − | 1.38254i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 24.0530 | − | 23.3903i | 0.816413 | − | 0.793920i | ||||
\(869\) | 8.50235 | 0.288422 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.41727 | −0.319092 | ||||||||
\(872\) | 18.6262 | + | 3.76607i | 0.630764 | + | 0.127535i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.66612 | + | 55.0477i | −0.124008 | + | 1.86202i | ||||
\(875\) | −9.02734 | − | 7.09867i | −0.305180 | − | 0.239979i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −47.5932 | −1.60711 | −0.803554 | − | 0.595232i | \(-0.797060\pi\) | ||||
−0.803554 | + | 0.595232i | \(0.797060\pi\) | |||||||
\(878\) | 32.5672 | + | 2.16894i | 1.09909 | + | 0.0731981i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −27.1025 | − | 7.38432i | −0.913624 | − | 0.248925i | ||||
\(881\) | − | 54.1981i | − | 1.82598i | −0.407980 | − | 0.912991i | \(-0.633767\pi\) | ||
0.407980 | − | 0.912991i | \(-0.366233\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 45.0923i | − | 1.51748i | −0.651395 | − | 0.758739i | \(-0.725816\pi\) | ||
0.651395 | − | 0.758739i | \(-0.274184\pi\) | |||||||
\(884\) | −12.7981 | − | 1.71227i | −0.430446 | − | 0.0575899i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.70160 | + | 40.5652i | −0.0907619 | + | 1.36281i | ||||
\(887\) | −44.4058 | −1.49100 | −0.745500 | − | 0.666506i | \(-0.767789\pi\) | ||||
−0.745500 | + | 0.666506i | \(0.767789\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −26.9511 | − | 21.1931i | −0.903911 | − | 0.710793i | ||||
\(890\) | −41.0705 | − | 2.73525i | −1.37669 | − | 0.0916858i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5.53060 | − | 0.739945i | −0.185178 | − | 0.0247752i | ||||
\(893\) | −5.87013 | −0.196436 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.15752 | 0.239250 | ||||||||
\(896\) | −27.0958 | + | 12.7207i | −0.905208 | + | 0.424969i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −49.4788 | − | 3.29524i | −1.65113 | − | 0.109963i | ||||
\(899\) | −16.3248 | −0.544464 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 27.8375i | 0.927400i | ||||||||
\(902\) | −7.82146 | − | 0.520901i | −0.260426 | − | 0.0173441i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.02888 | − | 1.82557i | −0.300296 | − | 0.0607174i | ||||
\(905\) | 62.9207 | 2.09156 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 47.2418i | 1.56864i | 0.620357 | + | 0.784320i | \(0.286988\pi\) | ||||
−0.620357 | + | 0.784320i | \(0.713012\pi\) | |||||||
\(908\) | −9.95171 | − | 1.33145i | −0.330259 | − | 0.0441858i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 9.39131 | − | 10.4337i | 0.311319 | − | 0.345875i | ||||
\(911\) | 40.2417i | 1.33327i | 0.745386 | + | 0.666634i | \(0.232265\pi\) | ||||
−0.745386 | + | 0.666634i | \(0.767735\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.1329i | 0.831779i | ||||||||
\(914\) | −24.2208 | − | 1.61307i | −0.801151 | − | 0.0533558i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.299094 | + | 2.23553i | −0.00988233 | + | 0.0738638i | ||||
\(917\) | 32.0172 | − | 40.7161i | 1.05730 | − | 1.34456i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 22.6252i | − | 0.746335i | −0.927764 | − | 0.373168i | \(-0.878272\pi\) | ||
0.927764 | − | 0.373168i | \(-0.121728\pi\) | |||||||
\(920\) | −65.0797 | − | 13.1586i | −2.14561 | − | 0.433825i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.28349 | + | 49.3025i | −0.108136 | + | 1.62369i | ||||
\(923\) | −10.8298 | −0.356468 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 23.5977 | 0.775886 | ||||||||
\(926\) | 1.13983 | − | 17.1148i | 0.0374571 | − | 0.562428i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 13.7669 | + | 4.75405i | 0.451921 | + | 0.156059i | ||||
\(929\) | 16.7562i | 0.549752i | 0.961480 | + | 0.274876i | \(0.0886368\pi\) | ||||
−0.961480 | + | 0.274876i | \(0.911363\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.00380 | + | 32.9822i | 0.262314 | + | 1.08095i | ||||
\(932\) | −8.22778 | − | 1.10081i | −0.269510 | − | 0.0360581i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 30.6408 | + | 2.04064i | 1.00260 | + | 0.0667718i | ||||
\(935\) | 35.2576i | 1.15305i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 8.34871i | − | 0.272741i | −0.990658 | − | 0.136370i | \(-0.956456\pi\) | ||
0.990658 | − | 0.136370i | \(-0.0435437\pi\) | |||||||
\(938\) | 20.3666 | + | 18.3318i | 0.664993 | + | 0.598553i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.936846 | − | 7.00230i | 0.0305566 | − | 0.228390i | ||||
\(941\) | − | 17.7578i | − | 0.578889i | −0.957195 | − | 0.289445i | \(-0.906529\pi\) | ||
0.957195 | − | 0.289445i | \(-0.0934706\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.5283 | −0.603366 | ||||||||
\(944\) | 47.2029 | + | 12.8609i | 1.53632 | + | 0.418586i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −33.2681 | − | 2.21562i | −1.08164 | − | 0.0720360i | ||||
\(947\) | 30.1863i | 0.980924i | 0.871463 | + | 0.490462i | \(0.163172\pi\) | ||||
−0.871463 | + | 0.490462i | \(0.836828\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.9452 | −0.614987 | ||||||||
\(950\) | −24.0297 | − | 1.60035i | −0.779627 | − | 0.0519223i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 24.3451 | + | 28.6160i | 0.789028 | + | 0.927449i | ||||
\(953\) | 32.3987 | 1.04950 | 0.524748 | − | 0.851257i | \(-0.324159\pi\) | ||||
0.524748 | + | 0.851257i | \(0.324159\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.961820 | −0.0311238 | ||||||||
\(956\) | −3.95115 | + | 29.5322i | −0.127789 | + | 0.955141i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 18.6415 | + | 1.24150i | 0.602279 | + | 0.0401111i | ||||
\(959\) | 30.1357 | − | 38.3234i | 0.973133 | − | 1.23753i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.20202 | 0.296839 | ||||||||
\(962\) | 0.811921 | − | 12.1912i | 0.0261774 | − | 0.393061i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −6.44379 | + | 48.1630i | −0.207540 | + | 1.55123i | ||||
\(965\) | − | 46.5467i | − | 1.49839i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 8.90900i | − | 0.286494i | −0.989687 | − | 0.143247i | \(-0.954246\pi\) | ||
0.989687 | − | 0.143247i | \(-0.0457543\pi\) | |||||||
\(968\) | −14.4337 | − | 2.91838i | −0.463918 | − | 0.0938004i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 48.6570 | + | 3.24050i | 1.56228 | + | 0.104046i | ||||
\(971\) | 13.5238 | 0.433998 | 0.216999 | − | 0.976172i | \(-0.430373\pi\) | ||||
0.216999 | + | 0.976172i | \(0.430373\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.8342 | + | 21.4079i | −0.539678 | + | 0.686305i | ||||
\(974\) | 1.25858 | − | 18.8980i | 0.0403276 | − | 0.605530i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.41727 | − | 34.5639i | 0.301440 | − | 1.10636i | ||||
\(977\) | −26.8330 | −0.858465 | −0.429232 | − | 0.903194i | \(-0.641216\pi\) | ||||
−0.429232 | + | 0.903194i | \(0.641216\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.0120 | 0.767428 | ||||||||
\(980\) | −40.6209 | + | 4.28367i | −1.29759 | + | 0.136837i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.66907 | − | 25.0615i | 0.0532620 | − | 0.799744i | ||||
\(983\) | −20.3679 | −0.649634 | −0.324817 | − | 0.945777i | \(-0.605303\pi\) | ||||
−0.324817 | + | 0.945777i | \(0.605303\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 9.24685i | − | 0.294629i | ||||||
\(986\) | 1.21479 | − | 18.2404i | 0.0386868 | − | 0.580893i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.65358 | + | 12.3594i | −0.0526073 | + | 0.393204i | ||||
\(989\) | −78.8092 | −2.50599 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 15.9105i | − | 0.505413i | −0.967543 | − | 0.252706i | \(-0.918679\pi\) | ||
0.967543 | − | 0.252706i | \(-0.0813206\pi\) | |||||||
\(992\) | −33.9028 | − | 11.7075i | −1.07642 | − | 0.371712i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 23.4215 | + | 21.0814i | 0.742884 | + | 0.668662i | ||||
\(995\) | − | 78.8485i | − | 2.49967i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 5.88360i | − | 0.186336i | −0.995650 | − | 0.0931678i | \(-0.970301\pi\) | ||
0.995650 | − | 0.0931678i | \(-0.0296993\pi\) | |||||||
\(998\) | −2.48147 | + | 37.2600i | −0.0785497 | + | 1.17944i | ||||
\(999\) | 0 | 0 |
(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 | 756.2.b.f.55.1 | yes | 16 | |
3.2 | odd | 2 | 756.2.b.e.55.16 | yes | 16 | ||
4.3 | odd | 2 | 756.2.b.e.55.2 | yes | 16 | ||
7.6 | odd | 2 | 756.2.b.e.55.1 | ✓ | 16 | ||
12.11 | even | 2 | inner | 756.2.b.f.55.15 | yes | 16 | |
21.20 | even | 2 | inner | 756.2.b.f.55.16 | yes | 16 | |
28.27 | even | 2 | inner | 756.2.b.f.55.2 | yes | 16 | |
84.83 | odd | 2 | 756.2.b.e.55.15 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.2.b.e.55.1 | ✓ | 16 | 7.6 | odd | 2 | ||
756.2.b.e.55.2 | yes | 16 | 4.3 | odd | 2 | ||
756.2.b.e.55.15 | yes | 16 | 84.83 | odd | 2 | ||
756.2.b.e.55.16 | yes | 16 | 3.2 | odd | 2 | ||
756.2.b.f.55.1 | yes | 16 | 1.1 | even | 1 | trivial | |
756.2.b.f.55.2 | yes | 16 | 28.27 | even | 2 | inner | |
756.2.b.f.55.15 | yes | 16 | 12.11 | even | 2 | inner | |
756.2.b.f.55.16 | yes | 16 | 21.20 | even | 2 | inner |