Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [117,2,Mod(8,117)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(117, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("117.8");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 117 = 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 117.i (of order \(4\), degree \(2\), 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: | \(0.934249703649\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 16x^{10} + 103x^{8} - 260x^{6} + 259x^{4} + 356x^{2} + 169 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 8.1 | ||
Root | \(-1.64111 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 117.8 |
Dual form | 117.2.i.a.44.1 |
$q$-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 \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(92\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.77776 | + | 1.77776i | −1.25707 | + | 1.25707i | −0.304583 | + | 0.952486i | \(0.598517\pi\) |
−0.952486 | + | 0.304583i | \(0.901483\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 4.32088i | − | 2.16044i | ||||||
\(5\) | 2.34822 | − | 2.34822i | 1.05016 | − | 1.05016i | 0.0514820 | − | 0.998674i | \(-0.483606\pi\) |
0.998674 | − | 0.0514820i | \(-0.0163945\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.51414 | − | 1.51414i | 0.572290 | − | 0.572290i | −0.360478 | − | 0.932768i | \(-0.617386\pi\) |
0.932768 | + | 0.360478i | \(0.117386\pi\) | |||||||
\(8\) | 4.12598 | + | 4.12598i | 1.45876 | + | 1.45876i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 8.34916i | 2.64024i | ||||||||
\(11\) | −2.34822 | − | 2.34822i | −0.708015 | − | 0.708015i | 0.258103 | − | 0.966118i | \(-0.416903\pi\) |
−0.966118 | + | 0.258103i | \(0.916903\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.806748 | + | 3.51414i | −0.223752 | + | 0.974646i | ||||
\(14\) | 5.38355i | 1.43882i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −6.02827 | −1.50707 | ||||||||
\(17\) | 4.24264 | 1.02899 | 0.514496 | − | 0.857493i | \(-0.327979\pi\) | ||||
0.514496 | + | 0.857493i | \(0.327979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.193252 | − | 0.193252i | −0.0443351 | − | 0.0443351i | 0.684592 | − | 0.728927i | \(-0.259981\pi\) |
−0.728927 | + | 0.684592i | \(0.759981\pi\) | |||||||
\(20\) | −10.1464 | − | 10.1464i | −2.26880 | − | 2.26880i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 8.34916 | 1.78005 | ||||||||
\(23\) | 2.41461 | 0.503482 | 0.251741 | − | 0.967795i | \(-0.418997\pi\) | ||||
0.251741 | + | 0.967795i | \(0.418997\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 6.02827i | − | 1.20565i | ||||||
\(26\) | −4.81310 | − | 7.68151i | −0.943926 | − | 1.50647i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −6.54241 | − | 6.54241i | −1.23640 | − | 1.23640i | ||||
\(29\) | 7.56485i | 1.40476i | 0.711803 | + | 0.702379i | \(0.247879\pi\) | ||||
−0.711803 | + | 0.702379i | \(0.752121\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.83502 | − | 4.83502i | −0.868395 | − | 0.868395i | 0.123899 | − | 0.992295i | \(-0.460460\pi\) |
−0.992295 | + | 0.123899i | \(0.960460\pi\) | |||||||
\(32\) | 2.46488 | − | 2.46488i | 0.435733 | − | 0.435733i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.54241 | + | 7.54241i | −1.29351 | + | 1.29351i | ||||
\(35\) | − | 7.11105i | − | 1.20199i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000 | − | 1.00000i | 0.164399 | − | 0.164399i | −0.620113 | − | 0.784512i | \(-0.712913\pi\) |
0.784512 | + | 0.620113i | \(0.212913\pi\) | |||||||
\(38\) | 0.687114 | 0.111465 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 19.3774 | 3.06384 | ||||||||
\(41\) | −1.89442 | + | 1.89442i | −0.295859 | + | 0.295859i | −0.839389 | − | 0.543531i | \(-0.817087\pi\) |
0.543531 | + | 0.839389i | \(0.317087\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.67004i | 0.864673i | 0.901712 | + | 0.432337i | \(0.142311\pi\) | ||||
−0.901712 | + | 0.432337i | \(0.857689\pi\) | |||||||
\(44\) | −10.1464 | + | 10.1464i | −1.52963 | + | 1.52963i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.29261 | + | 4.29261i | −0.632911 | + | 0.632911i | ||||
\(47\) | −2.34822 | − | 2.34822i | −0.342523 | − | 0.342523i | 0.514792 | − | 0.857315i | \(-0.327869\pi\) |
−0.857315 | + | 0.514792i | \(0.827869\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.41478i | 0.344968i | ||||||||
\(50\) | 10.7168 | + | 10.7168i | 1.51559 | + | 1.51559i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 15.1842 | + | 3.48586i | 2.10567 | + | 0.483402i | ||||
\(53\) | 1.96081i | 0.269339i | 0.990891 | + | 0.134669i | \(0.0429972\pi\) | ||||
−0.990891 | + | 0.134669i | \(0.957003\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11.0283 | −1.48705 | ||||||||
\(56\) | 12.4946 | 1.66966 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −13.4485 | − | 13.4485i | −1.76588 | − | 1.76588i | ||||
\(59\) | −0.753507 | − | 0.753507i | −0.0980983 | − | 0.0980983i | 0.656354 | − | 0.754453i | \(-0.272098\pi\) |
−0.754453 | + | 0.656354i | \(0.772098\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.61350 | −0.206587 | −0.103293 | − | 0.994651i | \(-0.532938\pi\) | ||||
−0.103293 | + | 0.994651i | \(0.532938\pi\) | |||||||
\(62\) | 17.1910 | 2.18327 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 3.29261i | − | 0.411576i | ||||||
\(65\) | 6.35755 | + | 10.1464i | 0.788556 | + | 1.25850i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.51414 | + | 7.51414i | 0.917998 | + | 0.917998i | 0.996884 | − | 0.0788857i | \(-0.0251362\pi\) |
−0.0788857 | + | 0.996884i | \(0.525136\pi\) | |||||||
\(68\) | − | 18.3320i | − | 2.22308i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 12.6418 | + | 12.6418i | 1.51098 | + | 1.51098i | ||||
\(71\) | −1.66111 | + | 1.66111i | −0.197137 | + | 0.197137i | −0.798772 | − | 0.601635i | \(-0.794516\pi\) |
0.601635 | + | 0.798772i | \(0.294516\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.34916 | − | 7.34916i | 0.860154 | − | 0.860154i | −0.131202 | − | 0.991356i | \(-0.541884\pi\) |
0.991356 | + | 0.131202i | \(0.0418836\pi\) | |||||||
\(74\) | 3.55553i | 0.413322i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.835021 | + | 0.835021i | −0.0957835 | + | 0.0957835i | ||||
\(77\) | −7.11105 | −0.810380 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.6983 | −1.87871 | −0.939354 | − | 0.342950i | \(-0.888574\pi\) | ||||
−0.939354 | + | 0.342950i | \(0.888574\pi\) | |||||||
\(80\) | −14.1557 | + | 14.1557i | −1.58266 | + | 1.58266i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 6.73566i | − | 0.743830i | ||||||
\(83\) | −7.73177 | + | 7.73177i | −0.848672 | + | 0.848672i | −0.989968 | − | 0.141295i | \(-0.954873\pi\) |
0.141295 | + | 0.989968i | \(0.454873\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.96265 | − | 9.96265i | 1.08060 | − | 1.08060i | ||||
\(86\) | −10.0800 | − | 10.0800i | −1.08695 | − | 1.08695i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 19.3774i | − | 2.06564i | ||||||
\(89\) | −4.76283 | − | 4.76283i | −0.504859 | − | 0.504859i | 0.408085 | − | 0.912944i | \(-0.366197\pi\) |
−0.912944 | + | 0.408085i | \(0.866197\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.09936 | + | 6.54241i | 0.429730 | + | 0.685831i | ||||
\(92\) | − | 10.4333i | − | 1.08774i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.34916 | 0.861150 | ||||||||
\(95\) | −0.907598 | −0.0931176 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.707389 | − | 0.707389i | −0.0718245 | − | 0.0718245i | 0.670282 | − | 0.742106i | \(-0.266173\pi\) |
−0.742106 | + | 0.670282i | \(0.766173\pi\) | |||||||
\(98\) | −4.29290 | − | 4.29290i | −0.433649 | − | 0.433649i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −26.0475 | −2.60475 | ||||||||
\(101\) | 1.82803 | 0.181896 | 0.0909478 | − | 0.995856i | \(-0.471010\pi\) | ||||
0.0909478 | + | 0.995856i | \(0.471010\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.2553i | 1.40461i | 0.711875 | + | 0.702306i | \(0.247846\pi\) | ||||
−0.711875 | + | 0.702306i | \(0.752154\pi\) | |||||||
\(104\) | −17.8279 | + | 11.1706i | −1.74817 | + | 1.09537i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.48586 | − | 3.48586i | −0.338577 | − | 0.338577i | ||||
\(107\) | − | 18.0109i | − | 1.74118i | −0.492006 | − | 0.870592i | \(-0.663736\pi\) | ||
0.492006 | − | 0.870592i | \(-0.336264\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.34916 | + | 7.34916i | 0.703922 | + | 0.703922i | 0.965250 | − | 0.261328i | \(-0.0841605\pi\) |
−0.261328 | + | 0.965250i | \(0.584161\pi\) | |||||||
\(110\) | 19.6057 | − | 19.6057i | 1.86933 | − | 1.86933i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −9.12763 | + | 9.12763i | −0.862480 | + | 0.862480i | ||||
\(113\) | 7.56485i | 0.711641i | 0.934554 | + | 0.355821i | \(0.115799\pi\) | ||||
−0.934554 | + | 0.355821i | \(0.884201\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.67004 | − | 5.67004i | 0.528734 | − | 0.528734i | ||||
\(116\) | 32.6869 | 3.03490 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.67912 | 0.246633 | ||||||||
\(119\) | 6.42394 | − | 6.42394i | 0.588882 | − | 0.588882i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.0282739i | 0.00257035i | ||||||||
\(122\) | 2.86841 | − | 2.86841i | 0.259694 | − | 0.259694i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −20.8916 | + | 20.8916i | −1.87612 | + | 1.87612i | ||||
\(125\) | −2.41461 | − | 2.41461i | −0.215970 | − | 0.215970i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.61350i | 0.320646i | 0.987065 | + | 0.160323i | \(0.0512536\pi\) | ||||
−0.987065 | + | 0.160323i | \(0.948746\pi\) | |||||||
\(128\) | 10.7832 | + | 10.7832i | 0.953113 | + | 0.953113i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −29.3401 | − | 6.73566i | −2.57330 | − | 0.590757i | ||||
\(131\) | 11.8075i | 1.03163i | 0.856701 | + | 0.515813i | \(0.172510\pi\) | ||||
−0.856701 | + | 0.515813i | \(0.827490\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.585221 | −0.0507451 | ||||||||
\(134\) | −26.7167 | −2.30797 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 17.5051 | + | 17.5051i | 1.50105 | + | 1.50105i | ||||
\(137\) | 1.89442 | + | 1.89442i | 0.161851 | + | 0.161851i | 0.783386 | − | 0.621535i | \(-0.213491\pi\) |
−0.621535 | + | 0.783386i | \(0.713491\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.9253 | 1.35077 | 0.675383 | − | 0.737467i | \(-0.263978\pi\) | ||||
0.675383 | + | 0.737467i | \(0.263978\pi\) | |||||||
\(140\) | −30.7260 | −2.59682 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 5.90611i | − | 0.495629i | ||||||
\(143\) | 10.1464 | − | 6.35755i | 0.848484 | − | 0.531645i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 17.7639 | + | 17.7639i | 1.47521 | + | 1.47521i | ||||
\(146\) | 26.1301i | 2.16254i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.32088 | − | 4.32088i | −0.355175 | − | 0.355175i | ||||
\(149\) | −1.89442 | + | 1.89442i | −0.155197 | + | 0.155197i | −0.780435 | − | 0.625238i | \(-0.785002\pi\) |
0.625238 | + | 0.780435i | \(0.285002\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.2498 | − | 16.2498i | 1.32239 | − | 1.32239i | 0.410553 | − | 0.911837i | \(-0.365336\pi\) |
0.911837 | − | 0.410553i | \(-0.134664\pi\) | |||||||
\(152\) | − | 1.59471i | − | 0.129348i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 12.6418 | − | 12.6418i | 1.01870 | − | 1.01870i | ||||
\(155\) | −22.7074 | −1.82390 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.47133 | −0.755894 | −0.377947 | − | 0.925827i | \(-0.623370\pi\) | ||||
−0.377947 | + | 0.925827i | \(0.623370\pi\) | |||||||
\(158\) | 29.6857 | − | 29.6857i | 2.36166 | − | 2.36166i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 11.5761i | − | 0.915175i | ||||||
\(161\) | 3.65605 | − | 3.65605i | 0.288137 | − | 0.288137i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.5051 | + | 16.5051i | −1.29278 | + | 1.29278i | −0.359714 | + | 0.933063i | \(0.617126\pi\) |
−0.933063 | + | 0.359714i | \(0.882874\pi\) | |||||||
\(164\) | 8.18557 | + | 8.18557i | 0.639186 | + | 0.639186i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 27.4905i | − | 2.13368i | ||||||
\(167\) | −8.41889 | − | 8.41889i | −0.651473 | − | 0.651473i | 0.301875 | − | 0.953348i | \(-0.402388\pi\) |
−0.953348 | + | 0.301875i | \(0.902388\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.6983 | − | 5.67004i | −0.899871 | − | 0.436157i | ||||
\(170\) | 35.4225i | 2.71678i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 24.4996 | 1.86808 | ||||||||
\(173\) | 23.1612 | 1.76091 | 0.880456 | − | 0.474127i | \(-0.157236\pi\) | ||||
0.880456 | + | 0.474127i | \(0.157236\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.12763 | − | 9.12763i | −0.689984 | − | 0.689984i | ||||
\(176\) | 14.1557 | + | 14.1557i | 1.06703 | + | 1.06703i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 16.9344 | 1.26929 | ||||||||
\(179\) | −8.48528 | −0.634220 | −0.317110 | − | 0.948389i | \(-0.602712\pi\) | ||||
−0.317110 | + | 0.948389i | \(0.602712\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 19.9253i | − | 1.48104i | −0.672036 | − | 0.740518i | \(-0.734580\pi\) | ||
0.672036 | − | 0.740518i | \(-0.265420\pi\) | |||||||
\(182\) | −18.9185 | − | 4.34317i | −1.40234 | − | 0.321937i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 9.96265 | + | 9.96265i | 0.734457 | + | 0.734457i | ||||
\(185\) | − | 4.69644i | − | 0.345289i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.96265 | − | 9.96265i | −0.728541 | − | 0.728541i | ||||
\(188\) | −10.1464 | + | 10.1464i | −0.740001 | + | 0.740001i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.61350 | − | 1.61350i | 0.117055 | − | 0.117055i | ||||
\(191\) | − | 2.28183i | − | 0.165107i | −0.996587 | − | 0.0825536i | \(-0.973692\pi\) | ||
0.996587 | − | 0.0825536i | \(-0.0263076\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.2835 | + | 14.2835i | −1.02815 | + | 1.02815i | −0.0285595 | + | 0.999592i | \(0.509092\pi\) |
−0.999592 | + | 0.0285595i | \(0.990908\pi\) | |||||||
\(194\) | 2.51514 | 0.180577 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10.4340 | 0.745284 | ||||||||
\(197\) | −3.72245 | + | 3.72245i | −0.265213 | + | 0.265213i | −0.827168 | − | 0.561955i | \(-0.810050\pi\) |
0.561955 | + | 0.827168i | \(0.310050\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 16.3118i | − | 1.15631i | −0.815926 | − | 0.578157i | \(-0.803772\pi\) | ||
0.815926 | − | 0.578157i | \(-0.196228\pi\) | |||||||
\(200\) | 24.8726 | − | 24.8726i | 1.75876 | − | 1.75876i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.24980 | + | 3.24980i | −0.228655 | + | 0.228655i | ||||
\(203\) | 11.4542 | + | 11.4542i | 0.803929 | + | 0.803929i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.89703i | 0.621396i | ||||||||
\(206\) | −25.3425 | − | 25.3425i | −1.76569 | − | 1.76569i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.86330 | − | 21.1842i | 0.337209 | − | 1.46886i | ||||
\(209\) | 0.907598i | 0.0627799i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.22699 | 0.222155 | 0.111078 | − | 0.993812i | \(-0.464570\pi\) | ||||
0.111078 | + | 0.993812i | \(0.464570\pi\) | |||||||
\(212\) | 8.47245 | 0.581890 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 32.0192 | + | 32.0192i | 2.18879 | + | 2.18879i | ||||
\(215\) | 13.3145 | + | 13.3145i | 0.908042 | + | 0.908042i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −14.6418 | −0.993948 | ||||||||
\(218\) | −26.1301 | −1.76976 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 47.6519i | 3.21269i | ||||||||
\(221\) | −3.42274 | + | 14.9092i | −0.230238 | + | 1.00290i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.77847 | − | 2.77847i | −0.186060 | − | 0.186060i | 0.607930 | − | 0.793991i | \(-0.292000\pi\) |
−0.793991 | + | 0.607930i | \(0.792000\pi\) | |||||||
\(224\) | − | 7.46432i | − | 0.498731i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.4485 | − | 13.4485i | −0.894582 | − | 0.894582i | ||||
\(227\) | −14.1557 | + | 14.1557i | −0.939548 | + | 0.939548i | −0.998274 | − | 0.0587264i | \(-0.981296\pi\) |
0.0587264 | + | 0.998274i | \(0.481296\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.32088 | + | 4.32088i | −0.285532 | + | 0.285532i | −0.835311 | − | 0.549778i | \(-0.814712\pi\) |
0.549778 | + | 0.835311i | \(0.314712\pi\) | |||||||
\(230\) | 20.1600i | 1.32931i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −31.2125 | + | 31.2125i | −2.04920 | + | 2.04920i | ||||
\(233\) | 3.00120 | 0.196615 | 0.0983075 | − | 0.995156i | \(-0.468657\pi\) | ||||
0.0983075 | + | 0.995156i | \(0.468657\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.0283 | −0.719405 | ||||||||
\(236\) | −3.25582 | + | 3.25582i | −0.211936 | + | 0.211936i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 22.8405i | 1.48053i | ||||||||
\(239\) | 17.2574 | − | 17.2574i | 1.11629 | − | 1.11629i | 0.124010 | − | 0.992281i | \(-0.460424\pi\) |
0.992281 | − | 0.124010i | \(-0.0395755\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.70739 | − | 8.70739i | 0.560892 | − | 0.560892i | −0.368669 | − | 0.929561i | \(-0.620186\pi\) |
0.929561 | + | 0.368669i | \(0.120186\pi\) | |||||||
\(242\) | −0.0502642 | − | 0.0502642i | −0.00323111 | − | 0.00323111i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.97173i | 0.446319i | ||||||||
\(245\) | 5.67043 | + | 5.67043i | 0.362271 | + | 0.362271i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.835021 | − | 0.523210i | 0.0531311 | − | 0.0332910i | ||||
\(248\) | − | 39.8984i | − | 2.53355i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 8.58522 | 0.542977 | ||||||||
\(251\) | 14.0893 | 0.889310 | 0.444655 | − | 0.895702i | \(-0.353326\pi\) | ||||
0.444655 | + | 0.895702i | \(0.353326\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.67004 | − | 5.67004i | −0.356473 | − | 0.356473i | ||||
\(254\) | −6.42394 | − | 6.42394i | −0.403074 | − | 0.403074i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −31.7549 | −1.98468 | ||||||||
\(257\) | 6.65725 | 0.415268 | 0.207634 | − | 0.978207i | \(-0.433424\pi\) | ||||
0.207634 | + | 0.978207i | \(0.433424\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 3.02827i | − | 0.188168i | ||||||
\(260\) | 43.8414 | − | 27.4702i | 2.71893 | − | 1.70363i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −20.9909 | − | 20.9909i | −1.29682 | − | 1.29682i | ||||
\(263\) | − | 24.8564i | − | 1.53271i | −0.642416 | − | 0.766356i | \(-0.722068\pi\) | ||
0.642416 | − | 0.766356i | \(-0.277932\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.60442 | + | 4.60442i | 0.282847 | + | 0.282847i | ||||
\(266\) | 1.04038 | − | 1.04038i | 0.0637901 | − | 0.0637901i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 32.4677 | − | 32.4677i | 1.98328 | − | 1.98328i | ||||
\(269\) | − | 22.2536i | − | 1.35683i | −0.734681 | − | 0.678413i | \(-0.762668\pi\) | ||
0.734681 | − | 0.678413i | \(-0.237332\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.54241 | − | 8.54241i | 0.518915 | − | 0.518915i | −0.398328 | − | 0.917243i | \(-0.630410\pi\) |
0.917243 | + | 0.398328i | \(0.130410\pi\) | |||||||
\(272\) | −25.5758 | −1.55076 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.73566 | −0.406916 | ||||||||
\(275\) | −14.1557 | + | 14.1557i | −0.853622 | + | 0.853622i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 9.41478i | − | 0.565679i | −0.959167 | − | 0.282840i | \(-0.908724\pi\) | ||
0.959167 | − | 0.282840i | \(-0.0912764\pi\) | |||||||
\(278\) | −28.3114 | + | 28.3114i | −1.69801 | + | 1.69801i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 29.3401 | − | 29.3401i | 1.75341 | − | 1.75341i | ||||
\(281\) | −20.6802 | − | 20.6802i | −1.23368 | − | 1.23368i | −0.962541 | − | 0.271135i | \(-0.912601\pi\) |
−0.271135 | − | 0.962541i | \(-0.587399\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.8013i | 0.701513i | 0.936467 | + | 0.350757i | \(0.114076\pi\) | ||||
−0.936467 | + | 0.350757i | \(0.885924\pi\) | |||||||
\(284\) | 7.17745 | + | 7.17745i | 0.425903 | + | 0.425903i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.73566 | + | 29.3401i | −0.398288 | + | 1.73492i | ||||
\(287\) | 5.73682i | 0.338634i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −63.1601 | −3.70889 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −31.7549 | − | 31.7549i | −1.85831 | − | 1.85831i | ||||
\(293\) | −8.53884 | − | 8.53884i | −0.498845 | − | 0.498845i | 0.412234 | − | 0.911078i | \(-0.364749\pi\) |
−0.911078 | + | 0.412234i | \(0.864749\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.53880 | −0.206037 | ||||||||
\(296\) | 8.25197 | 0.479636 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 6.73566i | − | 0.390186i | ||||||
\(299\) | −1.94798 | + | 8.48528i | −0.112655 | + | 0.490716i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.58522 | + | 8.58522i | 0.494844 | + | 0.494844i | ||||
\(302\) | 57.7766i | 3.32467i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.16498 | + | 1.16498i | 0.0668161 | + | 0.0668161i | ||||
\(305\) | −3.78884 | + | 3.78884i | −0.216948 | + | 0.216948i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.54241 | + | 6.54241i | −0.373395 | + | 0.373395i | −0.868712 | − | 0.495317i | \(-0.835052\pi\) |
0.495317 | + | 0.868712i | \(0.335052\pi\) | |||||||
\(308\) | 30.7260i | 1.75078i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 40.3684 | − | 40.3684i | 2.29277 | − | 2.29277i | ||||
\(311\) | 13.6227 | 0.772472 | 0.386236 | − | 0.922400i | \(-0.373775\pi\) | ||||
0.386236 | + | 0.922400i | \(0.373775\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.311812 | 0.0176246 | 0.00881232 | − | 0.999961i | \(-0.497195\pi\) | ||||
0.00881232 | + | 0.999961i | \(0.497195\pi\) | |||||||
\(314\) | 16.8378 | − | 16.8378i | 0.950211 | − | 0.950211i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 72.1515i | 4.05884i | ||||||||
\(317\) | 15.6627 | − | 15.6627i | 0.879706 | − | 0.879706i | −0.113798 | − | 0.993504i | \(-0.536302\pi\) |
0.993504 | + | 0.113798i | \(0.0363015\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.7639 | − | 17.7639i | 0.994590 | − | 0.994590i | ||||
\(320\) | −7.73177 | − | 7.73177i | −0.432219 | − | 0.432219i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 12.9992i | 0.724417i | ||||||||
\(323\) | −0.819901 | − | 0.819901i | −0.0456205 | − | 0.0456205i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 21.1842 | + | 4.86330i | 1.17509 | + | 0.269767i | ||||
\(326\) | − | 58.6842i | − | 3.25022i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −15.6327 | −0.863171 | ||||||||
\(329\) | −7.11105 | −0.392045 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.25887 | + | 5.25887i | 0.289054 | + | 0.289054i | 0.836706 | − | 0.547652i | \(-0.184478\pi\) |
−0.547652 | + | 0.836706i | \(0.684478\pi\) | |||||||
\(332\) | 33.4081 | + | 33.4081i | 1.83351 | + | 1.83351i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 29.9336 | 1.63789 | ||||||||
\(335\) | 35.2897 | 1.92808 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 18.3684i | − | 1.00059i | −0.865856 | − | 0.500294i | \(-0.833225\pi\) | ||
0.865856 | − | 0.500294i | \(-0.166775\pi\) | |||||||
\(338\) | 30.8768 | − | 10.7168i | 1.67948 | − | 0.582919i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −43.0475 | − | 43.0475i | −2.33458 | − | 2.33458i | ||||
\(341\) | 22.7074i | 1.22967i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.2553 | + | 14.2553i | 0.769712 | + | 0.769712i | ||||
\(344\) | −23.3945 | + | 23.3945i | −1.26135 | + | 1.26135i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −41.1751 | + | 41.1751i | −2.21359 | + | 2.21359i | ||||
\(347\) | 6.20345i | 0.333019i | 0.986040 | + | 0.166509i | \(0.0532496\pi\) | ||||
−0.986040 | + | 0.166509i | \(0.946750\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.0283 | + | 24.0283i | −1.28620 | + | 1.28620i | −0.349130 | + | 0.937074i | \(0.613523\pi\) |
−0.937074 | + | 0.349130i | \(0.886477\pi\) | |||||||
\(350\) | 32.4535 | 1.73471 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −11.5761 | −0.617011 | ||||||||
\(353\) | −4.30903 | + | 4.30903i | −0.229347 | + | 0.229347i | −0.812420 | − | 0.583073i | \(-0.801850\pi\) |
0.583073 | + | 0.812420i | \(0.301850\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.80128i | 0.414049i | ||||||||
\(356\) | −20.5797 | + | 20.5797i | −1.09072 | + | 1.09072i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 15.0848 | − | 15.0848i | 0.797258 | − | 0.797258i | ||||
\(359\) | 10.9663 | + | 10.9663i | 0.578779 | + | 0.578779i | 0.934567 | − | 0.355788i | \(-0.115788\pi\) |
−0.355788 | + | 0.934567i | \(0.615788\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 18.9253i | − | 0.996069i | ||||||
\(362\) | 35.4225 | + | 35.4225i | 1.86176 | + | 1.86176i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 28.2690 | − | 17.7129i | 1.48170 | − | 0.928406i | ||||
\(365\) | − | 34.5149i | − | 1.80659i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.69832 | 0.454048 | 0.227024 | − | 0.973889i | \(-0.427100\pi\) | ||||
0.227024 | + | 0.973889i | \(0.427100\pi\) | |||||||
\(368\) | −14.5559 | −0.758781 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8.34916 | + | 8.34916i | 0.434052 | + | 0.434052i | ||||
\(371\) | 2.96894 | + | 2.96894i | 0.154140 | + | 0.154140i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.311812 | 0.0161450 | 0.00807250 | − | 0.999967i | \(-0.497430\pi\) | ||||
0.00807250 | + | 0.999967i | \(0.497430\pi\) | |||||||
\(374\) | 35.4225 | 1.83165 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 19.3774i | − | 0.999315i | ||||||
\(377\) | −26.5839 | − | 6.10293i | −1.36914 | − | 0.314317i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.42024 | + | 3.42024i | 0.175686 | + | 0.175686i | 0.789472 | − | 0.613786i | \(-0.210354\pi\) |
−0.613786 | + | 0.789472i | \(0.710354\pi\) | |||||||
\(380\) | 3.92163i | 0.201175i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.05655 | + | 4.05655i | 0.207551 | + | 0.207551i | ||||
\(383\) | 16.4375 | − | 16.4375i | 0.839919 | − | 0.839919i | −0.148929 | − | 0.988848i | \(-0.547583\pi\) |
0.988848 | + | 0.148929i | \(0.0475825\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.6983 | + | 16.6983i | −0.851025 | + | 0.851025i | ||||
\(386\) | − | 50.7855i | − | 2.58491i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.05655 | + | 3.05655i | −0.155173 | + | 0.155173i | ||||
\(389\) | −25.1092 | −1.27309 | −0.636543 | − | 0.771241i | \(-0.719636\pi\) | ||||
−0.636543 | + | 0.771241i | \(0.719636\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.2443 | 0.518078 | ||||||||
\(392\) | −9.96334 | + | 9.96334i | −0.503224 | + | 0.503224i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 13.2353i | − | 0.666783i | ||||||
\(395\) | −39.2113 | + | 39.2113i | −1.97294 | + | 1.97294i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.301683 | − | 0.301683i | 0.0151410 | − | 0.0151410i | −0.699496 | − | 0.714637i | \(-0.746592\pi\) |
0.714637 | + | 0.699496i | \(0.246592\pi\) | |||||||
\(398\) | 28.9985 | + | 28.9985i | 1.45357 | + | 1.45357i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 36.3401i | 1.81700i | ||||||||
\(401\) | −7.17745 | − | 7.17745i | −0.358425 | − | 0.358425i | 0.504807 | − | 0.863232i | \(-0.331564\pi\) |
−0.863232 | + | 0.504807i | \(0.831564\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.8916 | − | 13.0903i | 1.04068 | − | 0.652074i | ||||
\(404\) | − | 7.89870i | − | 0.392975i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −40.7258 | −2.02119 | ||||||||
\(407\) | −4.69644 | −0.232794 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.93438 | + | 9.93438i | 0.491223 | + | 0.491223i | 0.908692 | − | 0.417468i | \(-0.137082\pi\) |
−0.417468 | + | 0.908692i | \(0.637082\pi\) | |||||||
\(410\) | −15.8168 | − | 15.8168i | −0.781137 | − | 0.781137i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 61.5953 | 3.03459 | ||||||||
\(413\) | −2.28183 | −0.112281 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 36.3118i | 1.78248i | ||||||||
\(416\) | 6.67338 | + | 10.6505i | 0.327190 | + | 0.522181i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.61350 | − | 1.61350i | −0.0789186 | − | 0.0789186i | ||||
\(419\) | − | 5.16307i | − | 0.252232i | −0.992015 | − | 0.126116i | \(-0.959749\pi\) | ||
0.992015 | − | 0.126116i | \(-0.0402512\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.4057 | − | 25.4057i | −1.23820 | − | 1.23820i | −0.960737 | − | 0.277462i | \(-0.910507\pi\) |
−0.277462 | − | 0.960737i | \(-0.589493\pi\) | |||||||
\(422\) | −5.73682 | + | 5.73682i | −0.279264 | + | 0.279264i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −8.09029 | + | 8.09029i | −0.392899 | + | 0.392899i | ||||
\(425\) | − | 25.5758i | − | 1.24061i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.44305 | + | 2.44305i | −0.118228 | + | 0.118228i | ||||
\(428\) | −77.8232 | −3.76173 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −47.3401 | −2.28294 | ||||||||
\(431\) | −16.5703 | + | 16.5703i | −0.798165 | + | 0.798165i | −0.982806 | − | 0.184641i | \(-0.940888\pi\) |
0.184641 | + | 0.982806i | \(0.440888\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 3.61350i | − | 0.173653i | −0.996223 | − | 0.0868267i | \(-0.972327\pi\) | ||
0.996223 | − | 0.0868267i | \(-0.0276727\pi\) | |||||||
\(434\) | 26.0296 | − | 26.0296i | 1.24946 | − | 1.24946i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 31.7549 | − | 31.7549i | 1.52078 | − | 1.52078i | ||||
\(437\) | −0.466630 | − | 0.466630i | −0.0223219 | − | 0.0223219i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.67004i | 0.270616i | 0.990804 | + | 0.135308i | \(0.0432025\pi\) | ||||
−0.990804 | + | 0.135308i | \(0.956798\pi\) | |||||||
\(440\) | −45.5025 | − | 45.5025i | −2.16925 | − | 2.16925i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −20.4202 | − | 32.5899i | −0.971292 | − | 1.55014i | ||||
\(443\) | 10.1677i | 0.483082i | 0.970391 | + | 0.241541i | \(0.0776528\pi\) | ||||
−0.970391 | + | 0.241541i | \(0.922347\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −22.3684 | −1.06036 | ||||||||
\(446\) | 9.87894 | 0.467781 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.98546 | − | 4.98546i | −0.235541 | − | 0.235541i | ||||
\(449\) | 16.5703 | + | 16.5703i | 0.782002 | + | 0.782002i | 0.980168 | − | 0.198166i | \(-0.0634986\pi\) |
−0.198166 | + | 0.980168i | \(0.563499\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.89703 | 0.418945 | ||||||||
\(452\) | 32.6869 | 1.53746 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 50.3310i | − | 2.36215i | ||||||
\(455\) | 24.9892 | + | 5.73682i | 1.17151 | + | 0.268946i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.13310 | + | 4.13310i | 0.193338 | + | 0.193338i | 0.797137 | − | 0.603799i | \(-0.206347\pi\) |
−0.603799 | + | 0.797137i | \(0.706347\pi\) | |||||||
\(458\) | − | 15.3630i | − | 0.717867i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −24.4996 | − | 24.4996i | −1.14230 | − | 1.14230i | ||||
\(461\) | −1.30784 | + | 1.30784i | −0.0609120 | + | 0.0609120i | −0.736907 | − | 0.675995i | \(-0.763714\pi\) |
0.675995 | + | 0.736907i | \(0.263714\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.7129 | − | 13.7129i | 0.637290 | − | 0.637290i | −0.312596 | − | 0.949886i | \(-0.601199\pi\) |
0.949886 | + | 0.312596i | \(0.101199\pi\) | |||||||
\(464\) | − | 45.6030i | − | 2.11707i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.33542 | + | 5.33542i | −0.247159 | + | 0.247159i | ||||
\(467\) | −2.88124 | −0.133328 | −0.0666640 | − | 0.997775i | \(-0.521236\pi\) | ||||
−0.0666640 | + | 0.997775i | \(0.521236\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 22.7549 | 1.05072 | ||||||||
\(470\) | 19.6057 | − | 19.6057i | 0.904342 | − | 0.904342i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 6.21792i | − | 0.286203i | ||||||
\(473\) | 13.3145 | − | 13.3145i | 0.612202 | − | 0.612202i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.16498 | + | 1.16498i | −0.0534529 | + | 0.0534529i | ||||
\(476\) | −27.7571 | − | 27.7571i | −1.27224 | − | 1.27224i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 61.3593i | 2.80651i | ||||||||
\(479\) | −1.52832 | − | 1.52832i | −0.0698307 | − | 0.0698307i | 0.671329 | − | 0.741160i | \(-0.265724\pi\) |
−0.741160 | + | 0.671329i | \(0.765724\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.70739 | + | 4.32088i | 0.123446 | + | 0.197015i | ||||
\(482\) | 30.9594i | 1.41016i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.122168 | 0.00555309 | ||||||||
\(485\) | −3.32221 | −0.150854 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.5798 | − | 14.5798i | −0.660672 | − | 0.660672i | 0.294867 | − | 0.955538i | \(-0.404725\pi\) |
−0.955538 | + | 0.294867i | \(0.904725\pi\) | |||||||
\(488\) | −6.65725 | − | 6.65725i | −0.301360 | − | 0.301360i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −20.1614 | −0.910798 | ||||||||
\(491\) | −35.8891 | −1.61965 | −0.809826 | − | 0.586670i | \(-0.800439\pi\) | ||||
−0.809826 | + | 0.586670i | \(0.800439\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 32.0950i | 1.44548i | ||||||||
\(494\) | −0.554328 | + | 2.41461i | −0.0249404 | + | 0.108639i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 29.1468 | + | 29.1468i | 1.30873 | + | 1.30873i | ||||
\(497\) | 5.03028i | 0.225639i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.287147 | + | 0.287147i | 0.0128544 | + | 0.0128544i | 0.713505 | − | 0.700650i | \(-0.247107\pi\) |
−0.700650 | + | 0.713505i | \(0.747107\pi\) | |||||||
\(500\) | −10.4333 | + | 10.4333i | −0.466590 | + | 0.466590i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −25.0475 | + | 25.0475i | −1.11792 | + | 1.11792i | ||||
\(503\) | 35.6235i | 1.58837i | 0.607673 | + | 0.794187i | \(0.292103\pi\) | ||||
−0.607673 | + | 0.794187i | \(0.707897\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.29261 | − | 4.29261i | 0.191019 | − | 0.191019i | ||||
\(506\) | 20.1600 | 0.896221 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 15.6135 | 0.692737 | ||||||||
\(509\) | −20.2264 | + | 20.2264i | −0.896519 | + | 0.896519i | −0.995126 | − | 0.0986078i | \(-0.968561\pi\) |
0.0986078 | + | 0.995126i | \(0.468561\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 22.2553i | − | 0.984515i | ||||||
\(512\) | 34.8862 | − | 34.8862i | 1.54176 | − | 1.54176i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −11.8350 | + | 11.8350i | −0.522020 | + | 0.522020i | ||||
\(515\) | 33.4745 | + | 33.4745i | 1.47506 | + | 1.47506i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.0283i | 0.485023i | ||||||||
\(518\) | 5.38355 | + | 5.38355i | 0.236540 | + | 0.236540i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −15.6327 | + | 68.0950i | −0.685539 | + | 2.98616i | ||||
\(521\) | 7.56485i | 0.331422i | 0.986174 | + | 0.165711i | \(0.0529919\pi\) | ||||
−0.986174 | + | 0.165711i | \(0.947008\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23.2270 | −1.01565 | −0.507823 | − | 0.861462i | \(-0.669549\pi\) | ||||
−0.507823 | + | 0.861462i | \(0.669549\pi\) | |||||||
\(524\) | 51.0188 | 2.22877 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 44.1888 | + | 44.1888i | 1.92673 | + | 1.92673i | ||||
\(527\) | −20.5133 | − | 20.5133i | −0.893572 | − | 0.893572i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.1696 | −0.746506 | ||||||||
\(530\) | −16.3711 | −0.711117 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.52867i | 0.109632i | ||||||||
\(533\) | −5.12893 | − | 8.18557i | −0.222159 | − | 0.354557i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −42.2937 | − | 42.2937i | −1.82851 | − | 1.82851i | ||||
\(536\) | 62.0064i | 2.67827i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 39.5616 | + | 39.5616i | 1.70562 | + | 1.70562i | ||||
\(539\) | 5.67043 | − | 5.67043i | 0.244243 | − | 0.244243i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.6508 | + | 10.6508i | −0.457915 | + | 0.457915i | −0.897971 | − | 0.440055i | \(-0.854959\pi\) |
0.440055 | + | 0.897971i | \(0.354959\pi\) | |||||||
\(542\) | 30.3728i | 1.30462i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 10.4576 | − | 10.4576i | 0.448365 | − | 0.448365i | ||||
\(545\) | 34.5149 | 1.47846 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.9253 | 1.19400 | 0.597000 | − | 0.802241i | \(-0.296359\pi\) | ||||
0.597000 | + | 0.802241i | \(0.296359\pi\) | |||||||
\(548\) | 8.18557 | − | 8.18557i | 0.349670 | − | 0.349670i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | − | 50.3310i | − | 2.14612i | ||||||
\(551\) | 1.46193 | − | 1.46193i | 0.0622801 | − | 0.0622801i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −25.2835 | + | 25.2835i | −1.07517 | + | 1.07517i | ||||
\(554\) | 16.7372 | + | 16.7372i | 0.711098 | + | 0.711098i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 68.8114i | − | 2.91825i | ||||||
\(557\) | −10.2469 | − | 10.2469i | −0.434176 | − | 0.434176i | 0.455870 | − | 0.890046i | \(-0.349328\pi\) |
−0.890046 | + | 0.455870i | \(0.849328\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.9253 | − | 4.57429i | −0.842751 | − | 0.193472i | ||||
\(560\) | 42.8674i | 1.81148i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 73.5289 | 3.10163 | ||||||||
\(563\) | −26.1624 | −1.10261 | −0.551307 | − | 0.834303i | \(-0.685871\pi\) | ||||
−0.551307 | + | 0.834303i | \(0.685871\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.7639 | + | 17.7639i | 0.747334 | + | 0.747334i | ||||
\(566\) | −20.9799 | − | 20.9799i | −0.881850 | − | 0.881850i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −13.7074 | −0.575149 | ||||||||
\(569\) | −34.8359 | −1.46040 | −0.730198 | − | 0.683235i | \(-0.760572\pi\) | ||||
−0.730198 | + | 0.683235i | \(0.760572\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.2726i | 0.722836i | 0.932404 | + | 0.361418i | \(0.117707\pi\) | ||||
−0.932404 | + | 0.361418i | \(0.882293\pi\) | |||||||
\(572\) | −27.4702 | − | 43.8414i | −1.14859 | − | 1.83310i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −10.1987 | − | 10.1987i | −0.425686 | − | 0.425686i | ||||
\(575\) | − | 14.5559i | − | 0.607025i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.84049 | − | 3.84049i | −0.159882 | − | 0.159882i | 0.622633 | − | 0.782514i | \(-0.286063\pi\) |
−0.782514 | + | 0.622633i | \(0.786063\pi\) | |||||||
\(578\) | −1.77776 | + | 1.77776i | −0.0739452 | + | 0.0739452i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 76.7559 | − | 76.7559i | 3.18712 | − | 3.18712i | ||||
\(581\) | 23.4139i | 0.971373i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.60442 | − | 4.60442i | 0.190696 | − | 0.190696i | ||||
\(584\) | 60.6450 | 2.50951 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 30.3601 | 1.25416 | ||||||||
\(587\) | 28.9321 | − | 28.9321i | 1.19416 | − | 1.19416i | 0.218269 | − | 0.975889i | \(-0.429959\pi\) |
0.975889 | − | 0.218269i | \(-0.0700410\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.86876i | 0.0770009i | ||||||||
\(590\) | 6.29115 | − | 6.29115i | 0.259003 | − | 0.259003i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.02827 | + | 6.02827i | −0.247761 | + | 0.247761i | ||||
\(593\) | 22.1744 | + | 22.1744i | 0.910592 | + | 0.910592i | 0.996319 | − | 0.0857267i | \(-0.0273212\pi\) |
−0.0857267 | + | 0.996319i | \(0.527321\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 30.1696i | − | 1.23683i | ||||||
\(596\) | 8.18557 | + | 8.18557i | 0.335294 | + | 0.335294i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −11.6218 | − | 18.5479i | −0.475249 | − | 0.758479i | ||||
\(599\) | − | 20.7337i | − | 0.847158i | −0.905859 | − | 0.423579i | \(-0.860774\pi\) | ||
0.905859 | − | 0.423579i | \(-0.139226\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.14217 | 0.250544 | 0.125272 | − | 0.992122i | \(-0.460020\pi\) | ||||
0.125272 | + | 0.992122i | \(0.460020\pi\) | |||||||
\(602\) | −30.5250 | −1.24411 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −70.2135 | − | 70.2135i | −2.85695 | − | 2.85695i | ||||
\(605\) | 0.0663932 | + | 0.0663932i | 0.00269927 | + | 0.00269927i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.1523 | −0.777368 | −0.388684 | − | 0.921371i | \(-0.627070\pi\) | ||||
−0.388684 | + | 0.921371i | \(0.627070\pi\) | |||||||
\(608\) | −0.952687 | −0.0386366 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 13.4713i | − | 0.545438i | ||||||
\(611\) | 10.1464 | − | 6.35755i | 0.410479 | − | 0.257199i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.9253 | − | 18.9253i | −0.764386 | − | 0.764386i | 0.212726 | − | 0.977112i | \(-0.431766\pi\) |
−0.977112 | + | 0.212726i | \(0.931766\pi\) | |||||||
\(614\) | − | 23.2617i | − | 0.938766i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −29.3401 | − | 29.3401i | −1.18215 | − | 1.18215i | ||||
\(617\) | 0.986822 | − | 0.986822i | 0.0397280 | − | 0.0397280i | −0.686964 | − | 0.726692i | \(-0.741057\pi\) |
0.726692 | + | 0.686964i | \(0.241057\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.5141 | − | 19.5141i | 0.784339 | − | 0.784339i | −0.196220 | − | 0.980560i | \(-0.562867\pi\) |
0.980560 | + | 0.196220i | \(0.0628668\pi\) | |||||||
\(620\) | 98.1160i | 3.94043i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −24.2179 | + | 24.2179i | −0.971050 | + | 0.971050i | ||||
\(623\) | −14.4232 | −0.577852 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.8013 | 0.752051 | ||||||||
\(626\) | −0.554328 | + | 0.554328i | −0.0221554 | + | 0.0221554i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 40.9245i | 1.63307i | ||||||||
\(629\) | 4.24264 | − | 4.24264i | 0.169165 | − | 0.169165i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.64723 | − | 4.64723i | 0.185003 | − | 0.185003i | −0.608529 | − | 0.793532i | \(-0.708240\pi\) |
0.793532 | + | 0.608529i | \(0.208240\pi\) | |||||||
\(632\) | −68.8970 | − | 68.8970i | −2.74057 | − | 2.74057i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 55.6892i | 2.21170i | ||||||||
\(635\) | 8.48528 | + | 8.48528i | 0.336728 | + | 0.336728i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.48586 | − | 1.94812i | −0.336222 | − | 0.0771872i | ||||
\(638\) | 63.1601i | 2.50053i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 50.6428 | 2.00183 | ||||||||
\(641\) | 32.8879 | 1.29899 | 0.649497 | − | 0.760364i | \(-0.274979\pi\) | ||||
0.649497 | + | 0.760364i | \(0.274979\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27.4394 | + | 27.4394i | 1.08211 | + | 1.08211i | 0.996313 | + | 0.0857931i | \(0.0273424\pi\) |
0.0857931 | + | 0.996313i | \(0.472658\pi\) | |||||||
\(644\) | −15.7974 | − | 15.7974i | −0.622504 | − | 0.622504i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.91518 | 0.114696 | ||||||||
\(647\) | −24.0560 | −0.945737 | −0.472869 | − | 0.881133i | \(-0.656781\pi\) | ||||
−0.472869 | + | 0.881133i | \(0.656781\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.53880i | 0.138910i | ||||||||
\(650\) | −46.3062 | + | 29.0147i | −1.81628 | + | 1.13805i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 71.3165 | + | 71.3165i | 2.79297 | + | 2.79297i | ||||
\(653\) | − | 26.6162i | − | 1.04157i | −0.853687 | − | 0.520786i | \(-0.825639\pi\) | ||
0.853687 | − | 0.520786i | \(-0.174361\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 27.7266 | + | 27.7266i | 1.08337 | + | 1.08337i | ||||
\(656\) | 11.4201 | − | 11.4201i | 0.445879 | − | 0.445879i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 12.6418 | − | 12.6418i | 0.492827 | − | 0.492827i | ||||
\(659\) | − | 10.7671i | − | 0.419427i | −0.977763 | − | 0.209713i | \(-0.932747\pi\) | ||
0.977763 | − | 0.209713i | \(-0.0672531\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.4996 | − | 31.4996i | 1.22519 | − | 1.22519i | 0.259431 | − | 0.965762i | \(-0.416465\pi\) |
0.965762 | − | 0.259431i | \(-0.0835349\pi\) | |||||||
\(662\) | −18.6981 | −0.726721 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −63.8023 | −2.47601 | ||||||||
\(665\) | −1.37423 | + | 1.37423i | −0.0532903 | + | 0.0532903i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.2662i | 0.707270i | ||||||||
\(668\) | −36.3770 | + | 36.3770i | −1.40747 | + | 1.40747i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −62.7367 | + | 62.7367i | −2.42373 | + | 2.42373i | ||||
\(671\) | 3.78884 | + | 3.78884i | 0.146267 | + | 0.146267i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 39.5844i | − | 1.52587i | −0.646477 | − | 0.762934i | \(-0.723758\pi\) | ||
0.646477 | − | 0.762934i | \(-0.276242\pi\) | |||||||
\(674\) | 32.6546 | + | 32.6546i | 1.25781 | + | 1.25781i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −24.4996 | + | 50.5471i | −0.942292 | + | 1.94412i | ||||
\(677\) | − | 2.40178i | − | 0.0923080i | −0.998934 | − | 0.0461540i | \(-0.985304\pi\) | ||
0.998934 | − | 0.0461540i | \(-0.0146965\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.14217 | −0.0822089 | ||||||||
\(680\) | 82.2115 | 3.15267 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −40.3684 | − | 40.3684i | −1.54578 | − | 1.54578i | ||||
\(683\) | 5.20380 | + | 5.20380i | 0.199118 | + | 0.199118i | 0.799622 | − | 0.600504i | \(-0.205033\pi\) |
−0.600504 | + | 0.799622i | \(0.705033\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.89703 | 0.339938 | ||||||||
\(686\) | −50.6850 | −1.93516 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 34.1806i | − | 1.30312i | ||||||
\(689\) | −6.89057 | − | 1.58188i | −0.262510 | − | 0.0602649i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.8825 | + | 13.8825i | 0.528115 | + | 0.528115i | 0.920010 | − | 0.391895i | \(-0.128180\pi\) |
−0.391895 | + | 0.920010i | \(0.628180\pi\) | |||||||
\(692\) | − | 100.077i | − | 3.80435i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −11.0283 | − | 11.0283i | −0.418628 | − | 0.418628i | ||||
\(695\) | 37.3961 | − | 37.3961i | 1.41852 | − | 1.41852i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.03735 | + | 8.03735i | −0.304436 | + | 0.304436i | ||||
\(698\) | − | 85.4332i | − | 3.23369i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −39.4394 | + | 39.4394i | −1.49067 | + | 1.49067i | ||||
\(701\) | 29.6985 | 1.12170 | 0.560848 | − | 0.827919i | \(-0.310475\pi\) | ||||
0.560848 | + | 0.827919i | \(0.310475\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.386505 | −0.0145773 | ||||||||
\(704\) | −7.73177 | + | 7.73177i | −0.291402 | + | 0.291402i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 15.3209i | − | 0.576609i | ||||||
\(707\) | 2.76788 | − | 2.76788i | 0.104097 | − | 0.104097i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.45213 | + | 4.45213i | −0.167203 | + | 0.167203i | −0.785749 | − | 0.618546i | \(-0.787722\pi\) |
0.618546 | + | 0.785749i | \(0.287722\pi\) | |||||||
\(710\) | −13.8688 | − | 13.8688i | −0.520488 | − | 0.520488i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 39.3027i | − | 1.47293i | ||||||
\(713\) | −11.6747 | − | 11.6747i | −0.437221 | − | 0.437221i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.89703 | − | 38.7549i | 0.332730 | − | 1.44935i | ||||
\(716\) | 36.6639i | 1.37020i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −38.9909 | −1.45513 | ||||||||
\(719\) | 20.0917 | 0.749295 | 0.374647 | − | 0.927167i | \(-0.377764\pi\) | ||||
0.374647 | + | 0.927167i | \(0.377764\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 21.5844 | + | 21.5844i | 0.803846 | + | 0.803846i | ||||
\(722\) | 33.6447 | + | 33.6447i | 1.25213 | + | 1.25213i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −86.0950 | −3.19969 | ||||||||
\(725\) | 45.6030 | 1.69365 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.9717i | 0.629446i | 0.949183 | + | 0.314723i | \(0.101912\pi\) | ||||
−0.949183 | + | 0.314723i | \(0.898088\pi\) | |||||||
\(728\) | −10.0800 | + | 43.9078i | −0.373589 | + | 1.62733i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 61.3593 | + | 61.3593i | 2.27101 | + | 2.27101i | ||||
\(731\) | 24.0560i | 0.889742i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.4623 | − | 27.4623i | −1.01434 | − | 1.01434i | −0.999896 | − | 0.0144458i | \(-0.995402\pi\) |
−0.0144458 | − | 0.999896i | \(-0.504598\pi\) | |||||||
\(734\) | −15.4635 | + | 15.4635i | −0.570770 | + | 0.570770i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.95173 | − | 5.95173i | 0.219384 | − | 0.219384i | ||||
\(737\) | − | 35.2897i | − | 1.29991i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27.1660 | + | 27.1660i | −0.999319 | + | 0.999319i | −1.00000 | 0.000681035i | \(-0.999783\pi\) | |
0.000681035 | 1.00000i | \(0.499783\pi\) | ||||||||
\(740\) | −20.2928 | −0.745977 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −10.5561 | −0.387528 | ||||||||
\(743\) | −9.67976 | + | 9.67976i | −0.355116 | + | 0.355116i | −0.862009 | − | 0.506893i | \(-0.830794\pi\) |
0.506893 | + | 0.862009i | \(0.330794\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.89703i | 0.325962i | ||||||||
\(746\) | −0.554328 | + | 0.554328i | −0.0202954 | + | 0.0202954i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −43.0475 | + | 43.0475i | −1.57397 | + | 1.57397i | ||||
\(749\) | −27.2710 | − | 27.2710i | −0.996462 | − | 0.996462i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 15.9144i | − | 0.580724i | −0.956917 | − | 0.290362i | \(-0.906224\pi\) | ||
0.956917 | − | 0.290362i | \(-0.0937757\pi\) | |||||||
\(752\) | 14.1557 | + | 14.1557i | 0.516206 | + | 0.516206i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 58.1095 | − | 36.4104i | 2.11622 | − | 1.32599i | ||||
\(755\) | − | 76.3162i | − | 2.77743i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 46.5561 | 1.69211 | 0.846056 | − | 0.533094i | \(-0.178971\pi\) | ||||
0.846056 | + | 0.533094i | \(0.178971\pi\) | |||||||
\(758\) | −12.1608 | −0.441699 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.74474 | − | 3.74474i | −0.135836 | − | 0.135836i | ||||
\(761\) | 24.0024 | + | 24.0024i | 0.870086 | + | 0.870086i | 0.992481 | − | 0.122395i | \(-0.0390576\pi\) |
−0.122395 | + | 0.992481i | \(0.539058\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 22.2553 | 0.805695 | ||||||||
\(764\) | −9.85951 | −0.356705 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 58.4441i | 2.11167i | ||||||||
\(767\) | 3.25582 | − | 2.04004i | 0.117561 | − | 0.0736615i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.25526 | − | 7.25526i | −0.261632 | − | 0.261632i | 0.564085 | − | 0.825717i | \(-0.309229\pi\) |
−0.825717 | + | 0.564085i | \(0.809229\pi\) | |||||||
\(770\) | − | 59.3713i | − | 2.13959i | ||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 61.7175 | + | 61.7175i | 2.22126 | + | 2.22126i | ||||
\(773\) | 1.76163 | − | 1.76163i | 0.0633616 | − | 0.0633616i | −0.674716 | − | 0.738078i | \(-0.735734\pi\) |
0.738078 | + | 0.674716i | \(0.235734\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −29.1468 | + | 29.1468i | −1.04699 | + | 1.04699i | ||||
\(776\) | − | 5.83735i | − | 0.209549i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 44.6382 | − | 44.6382i | 1.60036 | − | 1.60036i | ||||
\(779\) | 0.732203 | 0.0262339 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.80128 | 0.279152 | ||||||||
\(782\) | −18.2120 | + | 18.2120i | −0.651260 | + | 0.651260i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 14.5569i | − | 0.519891i | ||||||
\(785\) | −22.2408 | + | 22.2408i | −0.793807 | + | 0.793807i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.2125 | + | 24.2125i | −0.863081 | + | 0.863081i | −0.991695 | − | 0.128614i | \(-0.958947\pi\) |
0.128614 | + | 0.991695i | \(0.458947\pi\) | |||||||
\(788\) | 16.0843 | + | 16.0843i | 0.572978 | + | 0.572978i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 139.417i | − | 4.96023i | ||||||
\(791\) | 11.4542 | + | 11.4542i | 0.407265 | + | 0.407265i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.30168 | − | 5.67004i | 0.0462241 | − | 0.201349i | ||||
\(794\) | 1.07264i | 0.0380667i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −70.4815 | −2.49815 | ||||||||
\(797\) | −28.7652 | −1.01892 | −0.509458 | − | 0.860495i | \(-0.670154\pi\) | ||||
−0.509458 | + | 0.860495i | \(0.670154\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.96265 | − | 9.96265i | −0.352453 | − | 0.352453i | ||||
\(800\) | −14.8590 | − | 14.8590i | −0.525343 | − | 0.525343i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 25.5196 | 0.901128 | ||||||||
\(803\) | −34.5149 | −1.21800 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 17.1704i | − | 0.605179i | ||||||
\(806\) | −13.8688 | + | 60.4117i | −0.488509 | + | 2.12791i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.54241 | + | 7.54241i | 0.265341 | + | 0.265341i | ||||
\(809\) | 11.6875i | 0.410912i | 0.978666 | + | 0.205456i | \(0.0658677\pi\) | ||||
−0.978666 | + | 0.205456i | \(0.934132\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.72193 | + | 2.72193i | 0.0955797 | + | 0.0955797i | 0.753280 | − | 0.657700i | \(-0.228471\pi\) |
−0.657700 | + | 0.753280i | \(0.728471\pi\) | |||||||
\(812\) | 49.4924 | − | 49.4924i | 1.73684 | − | 1.73684i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8.34916 | − | 8.34916i | 0.292638 | − | 0.292638i | ||||
\(815\) | 77.5150i | 2.71523i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.09575 | − | 1.09575i | 0.0383354 | − | 0.0383354i | ||||
\(818\) | −35.3220 | −1.23500 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 38.4431 | 1.34249 | ||||||||
\(821\) | −12.7943 | + | 12.7943i | −0.446525 | + | 0.446525i | −0.894197 | − | 0.447673i | \(-0.852253\pi\) |
0.447673 | + | 0.894197i | \(0.352253\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 35.8397i | − | 1.24929i | −0.780908 | − | 0.624646i | \(-0.785243\pi\) | ||
0.780908 | − | 0.624646i | \(-0.214757\pi\) | |||||||
\(824\) | −58.8170 | + | 58.8170i | −2.04899 | + | 2.04899i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.05655 | − | 4.05655i | 0.141145 | − | 0.141145i | ||||
\(827\) | −10.3669 | − | 10.3669i | −0.360491 | − | 0.360491i | 0.503502 | − | 0.863994i | \(-0.332045\pi\) |
−0.863994 | + | 0.503502i | \(0.832045\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 41.5388i | − | 1.44270i | −0.692570 | − | 0.721351i | \(-0.743521\pi\) | ||
0.692570 | − | 0.721351i | \(-0.256479\pi\) | |||||||
\(830\) | −64.5538 | − | 64.5538i | −2.24070 | − | 2.24070i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 11.5707 | + | 2.65631i | 0.401141 | + | 0.0920908i | ||||
\(833\) | 10.2450i | 0.354970i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −39.5388 | −1.36830 | ||||||||
\(836\) | 3.92163 | 0.135632 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 9.17872 | + | 9.17872i | 0.317073 | + | 0.317073i | ||||
\(839\) | −12.8948 | − | 12.8948i | −0.445179 | − | 0.445179i | 0.448569 | − | 0.893748i | \(-0.351934\pi\) |
−0.893748 | + | 0.448569i | \(0.851934\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.2270 | −0.973344 | ||||||||
\(842\) | 90.3307 | 3.11300 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 13.9435i | − | 0.479953i | ||||||
\(845\) | −40.7847 | + | 14.1557i | −1.40304 | + | 0.486971i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.0428105 | + | 0.0428105i | 0.00147099 | + | 0.00147099i | ||||
\(848\) | − | 11.8203i | − | 0.405912i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 45.4677 | + | 45.4677i | 1.55953 | + | 1.55953i | ||||
\(851\) | 2.41461 | − | 2.41461i | 0.0827719 | − | 0.0827719i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31.4249 | + | 31.4249i | −1.07597 | + | 1.07597i | −0.0791018 | + | 0.996867i | \(0.525205\pi\) |
−0.996867 | + | 0.0791018i | \(0.974795\pi\) | |||||||
\(854\) | − | 8.68634i | − | 0.297240i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 74.3129 | − | 74.3129i | 2.53996 | − | 2.53996i | ||||
\(857\) | 51.3398 | 1.75374 | 0.876868 | − | 0.480732i | \(-0.159629\pi\) | ||||
0.876868 | + | 0.480732i | \(0.159629\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.4713 | 0.459636 | 0.229818 | − | 0.973234i | \(-0.426187\pi\) | ||||
0.229818 | + | 0.973234i | \(0.426187\pi\) | |||||||
\(860\) | 57.5305 | − | 57.5305i | 1.96177 | − | 1.96177i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 58.9162i | − | 2.00669i | ||||||
\(863\) | −6.60369 | + | 6.60369i | −0.224792 | + | 0.224792i | −0.810513 | − | 0.585721i | \(-0.800812\pi\) |
0.585721 | + | 0.810513i | \(0.300812\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 54.3876 | − | 54.3876i | 1.84923 | − | 1.84923i | ||||
\(866\) | 6.42394 | + | 6.42394i | 0.218294 | + | 0.218294i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 63.2654i | 2.14737i | ||||||||
\(869\) | 39.2113 | + | 39.2113i | 1.33015 | + | 1.33015i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −32.4677 | + | 20.3437i | −1.10013 | + | 0.689320i | ||||
\(872\) | 60.6450i | 2.05370i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.65911 | 0.0561204 | ||||||||
\(875\) | −7.31211 | −0.247194 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.489472 | − | 0.489472i | −0.0165283 | − | 0.0165283i | 0.698794 | − | 0.715323i | \(-0.253720\pi\) |
−0.715323 | + | 0.698794i | \(0.753720\pi\) | |||||||
\(878\) | −10.0800 | − | 10.0800i | −0.340183 | − | 0.340183i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 66.4815 | 2.24109 | ||||||||
\(881\) | 25.1774 | 0.848250 | 0.424125 | − | 0.905604i | \(-0.360582\pi\) | ||||
0.424125 | + | 0.905604i | \(0.360582\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 16.3118i | − | 0.548936i | −0.961596 | − | 0.274468i | \(-0.911498\pi\) | ||
0.961596 | − | 0.274468i | \(-0.0885018\pi\) | |||||||
\(884\) | 64.4210 | + | 14.7893i | 2.16671 | + | 0.497417i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −18.0757 | − | 18.0757i | −0.607267 | − | 0.607267i | ||||
\(887\) | − | 3.92163i | − | 0.131675i | −0.997830 | − | 0.0658377i | \(-0.979028\pi\) | ||
0.997830 | − | 0.0658377i | \(-0.0209720\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.47133 | + | 5.47133i | 0.183502 | + | 0.183502i | ||||
\(890\) | 39.7656 | − | 39.7656i | 1.33295 | − | 1.33295i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −12.0055 | + | 12.0055i | −0.401973 | + | 0.401973i | ||||
\(893\) | 0.907598i | 0.0303716i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19.9253 | + | 19.9253i | −0.666030 | + | 0.666030i | ||||
\(896\) | 32.6546 | 1.09091 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −58.9162 | −1.96606 | ||||||||
\(899\) | 36.5762 | − | 36.5762i | 1.21989 | − | 1.21989i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.31903i | 0.277147i | ||||||||
\(902\) | −15.8168 | + | 15.8168i | −0.526642 | + | 0.526642i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −31.2125 | + | 31.2125i | −1.03811 | + | 1.03811i | ||||
\(905\) | −46.7890 | − | 46.7890i | −1.55532 | − | 1.55532i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 40.6127i | 1.34852i | 0.738493 | + | 0.674261i | \(0.235538\pi\) | ||||
−0.738493 | + | 0.674261i | \(0.764462\pi\) | |||||||
\(908\) | 61.1652 | + | 61.1652i | 2.02984 | + | 2.02984i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −54.6236 | + | 34.2262i | −1.81076 | + | 1.13459i | ||||
\(911\) | 30.0195i | 0.994590i | 0.867581 | + | 0.497295i | \(0.165673\pi\) | ||||
−0.867581 | + | 0.497295i | \(0.834327\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 36.3118 | 1.20175 | ||||||||
\(914\) | −14.6953 | −0.486078 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18.6700 | + | 18.6700i | 0.616876 | + | 0.616876i | ||||
\(917\) | 17.8782 | + | 17.8782i | 0.590389 | + | 0.590389i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −46.8680 | −1.54603 | −0.773016 | − | 0.634387i | \(-0.781253\pi\) | ||||
−0.773016 | + | 0.634387i | \(0.781253\pi\) | |||||||
\(920\) | 46.7890 | 1.54259 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 4.65004i | − | 0.153141i | ||||||
\(923\) | −4.49726 | − | 7.17745i | −0.148029 | − | 0.236249i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.02827 | − | 6.02827i | −0.198208 | − | 0.198208i | ||||
\(926\) | 48.7564i | 1.60224i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 18.6464 | + | 18.6464i | 0.612099 | + | 0.612099i | ||||
\(929\) | −34.1275 | + | 34.1275i | −1.11969 | + | 1.11969i | −0.127899 | + | 0.991787i | \(0.540823\pi\) |
−0.991787 | + | 0.127899i | \(0.959177\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.466662 | − | 0.466662i | 0.0152942 | − | 0.0152942i | ||||
\(932\) | − | 12.9678i | − | 0.424776i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5.12217 | − | 5.12217i | 0.167602 | − | 0.167602i | ||||
\(935\) | −46.7890 | −1.53016 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41.4641 | −1.35457 | −0.677287 | − | 0.735719i | \(-0.736844\pi\) | ||||
−0.677287 | + | 0.735719i | \(0.736844\pi\) | |||||||
\(938\) | −40.4528 | + | 40.4528i | −1.32083 | + | 1.32083i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 47.6519i | 1.55423i | ||||||||
\(941\) | 25.0428 | − | 25.0428i | 0.816371 | − | 0.816371i | −0.169209 | − | 0.985580i | \(-0.554121\pi\) |
0.985580 | + | 0.169209i | \(0.0541213\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.57429 | + | 4.57429i | −0.148959 | + | 0.148959i | ||||
\(944\) | 4.54235 | + | 4.54235i | 0.147841 | + | 0.147841i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 47.3401i | 1.53916i | ||||||||
\(947\) | 13.8024 | + | 13.8024i | 0.448519 | + | 0.448519i | 0.894862 | − | 0.446343i | \(-0.147274\pi\) |
−0.446343 | + | 0.894862i | \(0.647274\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.8970 | + | 31.7549i | 0.645885 | + | 1.03081i | ||||
\(950\) | − | 4.14211i | − | 0.134388i | ||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 53.0101 | 1.71807 | ||||||||
\(953\) | −38.0253 | −1.23176 | −0.615880 | − | 0.787840i | \(-0.711200\pi\) | ||||
−0.615880 | + | 0.787840i | \(0.711200\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.35823 | − | 5.35823i | −0.173388 | − | 0.173388i | ||||
\(956\) | −74.5674 | − | 74.5674i | −2.41168 | − | 2.41168i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 5.43398 | 0.175564 | ||||||||
\(959\) | 5.73682 | 0.185252 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.7549i | 0.508221i | ||||||||
\(962\) | −12.4946 | − | 2.86841i | −0.402842 | − | 0.0924813i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −37.6236 | − | 37.6236i | −1.21178 | − | 1.21178i | ||||
\(965\) | 67.0818i | 2.15944i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.4021 | + | 19.4021i | 0.623929 | + | 0.623929i | 0.946534 | − | 0.322604i | \(-0.104558\pi\) |
−0.322604 | + | 0.946534i | \(0.604558\pi\) | |||||||
\(968\) | −0.116657 | + | 0.116657i | −0.00374951 | + | 0.00374951i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.90611 | − | 5.90611i | 0.189634 | − | 0.189634i | ||||
\(971\) | − | 53.4334i | − | 1.71476i | −0.514684 | − | 0.857380i | \(-0.672091\pi\) | ||
0.514684 | − | 0.857380i | \(-0.327909\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 24.1131 | − | 24.1131i | 0.773030 | − | 0.773030i | ||||
\(974\) | 51.8387 | 1.66102 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.72659 | 0.311341 | ||||||||
\(977\) | −40.3181 | + | 40.3181i | −1.28989 | + | 1.28989i | −0.355039 | + | 0.934852i | \(0.615532\pi\) |
−0.934852 | + | 0.355039i | \(0.884468\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22.3684i | 0.714896i | ||||||||
\(980\) | 24.5013 | − | 24.5013i | 0.782665 | − | 0.782665i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 63.8023 | − | 63.8023i | 2.03601 | − | 2.03601i | ||||
\(983\) | 5.31716 | + | 5.31716i | 0.169591 | + | 0.169591i | 0.786800 | − | 0.617209i | \(-0.211737\pi\) |
−0.617209 | + | 0.786800i | \(0.711737\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.4823i | 0.557031i | ||||||||
\(986\) | −57.0572 | − | 57.0572i | −1.81707 | − | 1.81707i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.26073 | − | 3.60803i | −0.0719233 | − | 0.114787i | ||||
\(989\) | 13.6910i | 0.435347i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.31903 | −0.200731 | −0.100365 | − | 0.994951i | \(-0.532001\pi\) | ||||
−0.100365 | + | 0.994951i | \(0.532001\pi\) | |||||||
\(992\) | −23.8355 | −0.756777 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −8.94265 | − | 8.94265i | −0.283644 | − | 0.283644i | ||||
\(995\) | −38.3037 | − | 38.3037i | −1.21431 | − | 1.21431i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.77301 | 0.214503 | 0.107252 | − | 0.994232i | \(-0.465795\pi\) | ||||
0.107252 | + | 0.994232i | \(0.465795\pi\) | |||||||
\(998\) | −1.02096 | −0.0323178 | ||||||||
\(999\) | 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 | 117.2.i.a.8.1 | ✓ | 12 | |
3.2 | odd | 2 | inner | 117.2.i.a.8.6 | yes | 12 | |
4.3 | odd | 2 | 1872.2.bi.f.593.6 | 12 | |||
12.11 | even | 2 | 1872.2.bi.f.593.1 | 12 | |||
13.5 | odd | 4 | inner | 117.2.i.a.44.6 | yes | 12 | |
13.8 | odd | 4 | 1521.2.i.g.746.1 | 12 | |||
13.12 | even | 2 | 1521.2.i.g.944.6 | 12 | |||
39.5 | even | 4 | inner | 117.2.i.a.44.1 | yes | 12 | |
39.8 | even | 4 | 1521.2.i.g.746.6 | 12 | |||
39.38 | odd | 2 | 1521.2.i.g.944.1 | 12 | |||
52.31 | even | 4 | 1872.2.bi.f.161.1 | 12 | |||
156.83 | odd | 4 | 1872.2.bi.f.161.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
117.2.i.a.8.1 | ✓ | 12 | 1.1 | even | 1 | trivial | |
117.2.i.a.8.6 | yes | 12 | 3.2 | odd | 2 | inner | |
117.2.i.a.44.1 | yes | 12 | 39.5 | even | 4 | inner | |
117.2.i.a.44.6 | yes | 12 | 13.5 | odd | 4 | inner | |
1521.2.i.g.746.1 | 12 | 13.8 | odd | 4 | |||
1521.2.i.g.746.6 | 12 | 39.8 | even | 4 | |||
1521.2.i.g.944.1 | 12 | 39.38 | odd | 2 | |||
1521.2.i.g.944.6 | 12 | 13.12 | even | 2 | |||
1872.2.bi.f.161.1 | 12 | 52.31 | even | 4 | |||
1872.2.bi.f.161.6 | 12 | 156.83 | odd | 4 | |||
1872.2.bi.f.593.1 | 12 | 12.11 | even | 2 | |||
1872.2.bi.f.593.6 | 12 | 4.3 | odd | 2 |