Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [560,2,Mod(17,560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(560, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("560.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 560 = 2^{4} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 560.ci (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.47162251319\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 35) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 17.1 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 560.17 |
Dual form | 560.2.ci.b.33.1 |
$q$-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 \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(351\) | \(421\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.86603 | − | 0.500000i | 1.07735 | − | 0.288675i | 0.323840 | − | 0.946112i | \(-0.395026\pi\) |
0.753510 | + | 0.657437i | \(0.228359\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.86603 | + | 1.23205i | 0.834512 | + | 0.550990i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.50000 | − | 0.866025i | 0.944911 | − | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.633975 | − | 0.366025i | 0.211325 | − | 0.122008i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.366025 | − | 0.633975i | 0.110361 | − | 0.191151i | −0.805555 | − | 0.592521i | \(-0.798133\pi\) |
0.915916 | + | 0.401371i | \(0.131466\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | − | 2.00000i | −0.554700 | − | 0.554700i | 0.373094 | − | 0.927794i | \(-0.378297\pi\) |
−0.927794 | + | 0.373094i | \(0.878297\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.09808 | + | 1.36603i | 1.05812 | + | 0.352706i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.267949 | + | 1.00000i | 0.0649872 | + | 0.242536i | 0.990777 | − | 0.135503i | \(-0.0432652\pi\) |
−0.925790 | + | 0.378039i | \(0.876599\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.36603 | + | 2.36603i | 0.313388 | + | 0.542803i | 0.979093 | − | 0.203411i | \(-0.0652027\pi\) |
−0.665706 | + | 0.746214i | \(0.731869\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.23205 | − | 2.86603i | 0.923509 | − | 0.625418i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.96410 | − | 1.86603i | −1.45212 | − | 0.389093i | −0.555357 | − | 0.831612i | \(-0.687418\pi\) |
−0.896759 | + | 0.442519i | \(0.854085\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.96410 | + | 4.59808i | 0.392820 | + | 0.919615i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.09808 | + | 3.09808i | −0.596225 | + | 0.596225i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 3.00000i | − | 0.557086i | −0.960424 | − | 0.278543i | \(-0.910149\pi\) | ||
0.960424 | − | 0.278543i | \(-0.0898515\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.464102 | − | 0.267949i | −0.0833551 | − | 0.0481251i | 0.457743 | − | 0.889085i | \(-0.348658\pi\) |
−0.541098 | + | 0.840959i | \(0.681991\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.366025 | − | 1.36603i | 0.0637168 | − | 0.237795i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.73205 | + | 1.46410i | 0.968893 | + | 0.247478i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.26795 | + | 4.73205i | −0.208450 | + | 0.777944i | 0.779921 | + | 0.625878i | \(0.215259\pi\) |
−0.988370 | + | 0.152066i | \(0.951407\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.73205 | − | 2.73205i | −0.757735 | − | 0.437478i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.464102i | 0.0724805i | 0.999343 | + | 0.0362402i | \(0.0115382\pi\) | ||||
−0.999343 | + | 0.0362402i | \(0.988462\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.83013 | − | 5.83013i | 0.889086 | − | 0.889086i | −0.105349 | − | 0.994435i | \(-0.533596\pi\) |
0.994435 | + | 0.105349i | \(0.0335960\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.63397 | + | 0.0980762i | 0.243579 | + | 0.0146203i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.633975 | − | 0.169873i | −0.0924747 | − | 0.0247785i | 0.212285 | − | 0.977208i | \(-0.431909\pi\) |
−0.304760 | + | 0.952429i | \(0.598576\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.50000 | − | 4.33013i | 0.785714 | − | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.00000 | + | 1.73205i | 0.140028 | + | 0.242536i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.83013 | − | 6.83013i | −0.251387 | − | 0.938190i | −0.970065 | − | 0.242846i | \(-0.921919\pi\) |
0.718677 | − | 0.695344i | \(-0.244748\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.46410 | − | 0.732051i | 0.197419 | − | 0.0987097i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.73205 | + | 3.73205i | 0.494322 | + | 0.494322i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.09808 | + | 1.90192i | −0.142957 | + | 0.247609i | −0.928609 | − | 0.371060i | \(-0.878995\pi\) |
0.785652 | + | 0.618669i | \(0.212328\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.33013 | + | 4.23205i | −0.938527 | + | 0.541859i | −0.889498 | − | 0.456939i | \(-0.848946\pi\) |
−0.0490285 | + | 0.998797i | \(0.515613\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.26795 | − | 1.46410i | 0.159747 | − | 0.184459i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.26795 | − | 6.19615i | −0.157270 | − | 0.768538i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.13397 | + | 0.303848i | −0.138537 | + | 0.0371209i | −0.327421 | − | 0.944878i | \(-0.606180\pi\) |
0.188884 | + | 0.981999i | \(0.439513\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −13.9282 | −1.67676 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.73205 | −0.561591 | −0.280796 | − | 0.959768i | \(-0.590598\pi\) | ||||
−0.280796 | + | 0.959768i | \(0.590598\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.46410 | − | 0.928203i | 0.405442 | − | 0.108638i | −0.0503336 | − | 0.998732i | \(-0.516028\pi\) |
0.455776 | + | 0.890094i | \(0.349362\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.96410 | + | 7.59808i | 0.688675 | + | 0.877350i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.366025 | − | 1.90192i | 0.0417125 | − | 0.216744i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.83013 | − | 3.36603i | 0.655941 | − | 0.378707i | −0.134788 | − | 0.990874i | \(-0.543035\pi\) |
0.790728 | + | 0.612167i | \(0.209702\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.33013 | + | 9.23205i | −0.592236 | + | 1.02578i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.09808 | − | 3.09808i | −0.340058 | − | 0.340058i | 0.516331 | − | 0.856389i | \(-0.327297\pi\) |
−0.856389 | + | 0.516331i | \(0.827297\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.732051 | + | 2.19615i | −0.0794021 | + | 0.238206i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.50000 | − | 5.59808i | −0.160817 | − | 0.600177i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.33013 | + | 14.4282i | 0.882992 | + | 1.52939i | 0.847998 | + | 0.529999i | \(0.177808\pi\) |
0.0349934 | + | 0.999388i | \(0.488859\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.73205 | − | 3.26795i | −0.705711 | − | 0.342574i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.00000 | − | 0.267949i | −0.103695 | − | 0.0277850i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.366025 | + | 6.09808i | −0.0375534 | + | 0.625649i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.92820 | − | 7.92820i | 0.804987 | − | 0.804987i | −0.178883 | − | 0.983870i | \(-0.557248\pi\) |
0.983870 | + | 0.178883i | \(0.0572484\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 0.535898i | − | 0.0538598i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.1603 | − | 5.86603i | −1.01098 | − | 0.583691i | −0.0995037 | − | 0.995037i | \(-0.531726\pi\) |
−0.911479 | + | 0.411346i | \(0.865059\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.598076 | − | 2.23205i | 0.0589302 | − | 0.219931i | −0.930181 | − | 0.367102i | \(-0.880350\pi\) |
0.989111 | + | 0.147171i | \(0.0470168\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 11.4282 | − | 0.133975i | 1.11528 | − | 0.0130746i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.30385 | + | 8.59808i | −0.222721 | + | 0.831207i | 0.760583 | + | 0.649240i | \(0.224913\pi\) |
−0.983305 | + | 0.181967i | \(0.941754\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.2321 | − | 7.06218i | −1.17162 | − | 0.676434i | −0.217557 | − | 0.976048i | \(-0.569809\pi\) |
−0.954061 | + | 0.299614i | \(0.903142\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.46410i | 0.898293i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.26795 | + | 4.26795i | −0.401495 | + | 0.401495i | −0.878760 | − | 0.477265i | \(-0.841628\pi\) |
0.477265 | + | 0.878760i | \(0.341628\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.6962 | − | 12.0622i | −0.997421 | − | 1.12480i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.00000 | − | 0.535898i | −0.184900 | − | 0.0495438i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.53590 | + | 2.26795i | 0.140796 | + | 0.207903i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.23205 | + | 9.06218i | 0.475641 | + | 0.823834i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.232051 | + | 0.866025i | 0.0209233 | + | 0.0780869i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.00000 | + | 11.0000i | −0.178885 | + | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.46410 | + | 6.46410i | 0.573596 | + | 0.573596i | 0.933132 | − | 0.359535i | \(-0.117065\pi\) |
−0.359535 | + | 0.933132i | \(0.617065\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.96410 | − | 13.7942i | 0.701200 | − | 1.21451i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.39230 | + | 4.26795i | −0.645869 | + | 0.372892i | −0.786872 | − | 0.617117i | \(-0.788301\pi\) |
0.141003 | + | 0.990009i | \(0.454967\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.46410 | + | 4.73205i | 0.473798 | + | 0.410321i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −9.59808 | + | 1.96410i | −0.826071 | + | 0.169043i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.4641 | + | 2.80385i | −0.894009 | + | 0.239549i | −0.676441 | − | 0.736496i | \(-0.736479\pi\) |
−0.217567 | + | 0.976045i | \(0.569812\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.6603 | −0.989010 | −0.494505 | − | 0.869175i | \(-0.664651\pi\) | ||||
−0.494505 | + | 0.869175i | \(0.664651\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.26795 | −0.106781 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.00000 | + | 0.535898i | −0.167248 | + | 0.0448141i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.69615 | − | 5.59808i | 0.306949 | − | 0.464895i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.09808 | − | 10.8301i | 0.667918 | − | 0.893254i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.69615 | + | 5.59808i | −0.794340 | + | 0.458612i | −0.841488 | − | 0.540276i | \(-0.818320\pi\) |
0.0471484 | + | 0.998888i | \(0.484987\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.92820 | + | 12.0000i | −0.563809 | + | 0.976546i | 0.433350 | + | 0.901226i | \(0.357331\pi\) |
−0.997159 | + | 0.0753205i | \(0.976002\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.535898 | + | 0.535898i | 0.0433248 | + | 0.0433248i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.535898 | − | 1.07180i | −0.0430444 | − | 0.0860888i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.36603 | − | 23.7583i | −0.508064 | − | 1.89612i | −0.438948 | − | 0.898513i | \(-0.644649\pi\) |
−0.0691164 | − | 0.997609i | \(-0.522018\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.83013 | − | 11.8301i | −0.541664 | − | 0.938190i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19.0263 | + | 1.36603i | −1.49948 | + | 0.107658i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.36603 | + | 1.43782i | 0.420300 | + | 0.112619i | 0.462769 | − | 0.886479i | \(-0.346856\pi\) |
−0.0424696 | + | 0.999098i | \(0.513523\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.36603 | − | 2.09808i | 0.184195 | − | 0.163335i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.7583 | − | 10.7583i | 0.832505 | − | 0.832505i | −0.155354 | − | 0.987859i | \(-0.549652\pi\) |
0.987859 | + | 0.155354i | \(0.0496519\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 5.00000i | − | 0.384615i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.73205 | + | 1.00000i | 0.132453 | + | 0.0764719i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.07180 | − | 22.6603i | 0.461630 | − | 1.72283i | −0.206197 | − | 0.978511i | \(-0.566109\pi\) |
0.667827 | − | 0.744317i | \(-0.267225\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.89230 | + | 9.79423i | 0.672195 | + | 0.740374i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.09808 | + | 4.09808i | −0.0825365 | + | 0.308030i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −17.1962 | − | 9.92820i | −1.28530 | − | 0.742069i | −0.307488 | − | 0.951552i | \(-0.599489\pi\) |
−0.977812 | + | 0.209483i | \(0.932822\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.19615i | 0.683545i | 0.939783 | + | 0.341772i | \(0.111027\pi\) | ||||
−0.939783 | + | 0.341772i | \(0.888973\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.5622 | + | 11.5622i | −0.854701 | + | 0.854701i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.19615 | + | 7.26795i | −0.602593 | + | 0.534350i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.732051 | + | 0.196152i | 0.0535329 | + | 0.0143441i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.06218 | + | 10.4282i | −0.368219 | + | 0.758540i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.36603 | + | 14.4904i | 0.605344 | + | 1.04849i | 0.991997 | + | 0.126262i | \(0.0402979\pi\) |
−0.386653 | + | 0.922225i | \(0.626369\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.830127 | + | 3.09808i | 0.0597539 | + | 0.223004i | 0.989346 | − | 0.145587i | \(-0.0465070\pi\) |
−0.929592 | + | 0.368591i | \(0.879840\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.46410 | − | 10.9282i | −0.391292 | − | 0.782585i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.1244 | + | 14.1244i | 1.00632 | + | 1.00632i | 0.999980 | + | 0.00633876i | \(0.00201770\pi\) |
0.00633876 | + | 0.999980i | \(0.497982\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.4641 | − | 21.5885i | 0.883557 | − | 1.53037i | 0.0361978 | − | 0.999345i | \(-0.488475\pi\) |
0.847359 | − | 0.531021i | \(-0.178191\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.96410 | + | 1.13397i | −0.138537 | + | 0.0799844i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.59808 | − | 7.50000i | −0.182349 | − | 0.526397i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.571797 | + | 0.866025i | −0.0399360 | + | 0.0604858i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.09808 | + | 1.36603i | −0.354341 | + | 0.0949453i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.00000 | 0.138343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.1962 | −0.701932 | −0.350966 | − | 0.936388i | \(-0.614147\pi\) | ||||
−0.350966 | + | 0.936388i | \(0.614147\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.83013 | + | 2.36603i | −0.605030 | + | 0.162117i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 18.0622 | − | 3.69615i | 1.23183 | − | 0.252076i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.39230 | − | 0.267949i | −0.0945158 | − | 0.0181896i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.00000 | − | 3.46410i | 0.405442 | − | 0.234082i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.46410 | − | 2.53590i | 0.0984861 | − | 0.170583i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.12436 | + | 6.12436i | 0.410117 | + | 0.410117i | 0.881779 | − | 0.471662i | \(-0.156346\pi\) |
−0.471662 | + | 0.881779i | \(0.656346\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.92820 | + | 2.19615i | 0.195214 | + | 0.146410i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.0262794 | − | 0.0980762i | −0.00174423 | − | 0.00650955i | 0.965048 | − | 0.262072i | \(-0.0844059\pi\) |
−0.966792 | + | 0.255563i | \(0.917739\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.19615 | + | 2.07180i | 0.0790440 | + | 0.136908i | 0.902838 | − | 0.429981i | \(-0.141480\pi\) |
−0.823794 | + | 0.566890i | \(0.808147\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.267949 | − | 3.73205i | −0.0176298 | − | 0.245551i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.73205 | + | 0.464102i | 0.113470 | + | 0.0304043i | 0.315107 | − | 0.949056i | \(-0.397959\pi\) |
−0.201637 | + | 0.979460i | \(0.564626\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.973721 | − | 1.09808i | −0.0635185 | − | 0.0716306i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.19615 | − | 9.19615i | 0.597354 | − | 0.597354i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.3923i | 1.18970i | 0.803837 | + | 0.594850i | \(0.202788\pi\) | ||||
−0.803837 | + | 0.594850i | \(0.797212\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.5359 | + | 8.39230i | 0.936340 | + | 0.540596i | 0.888811 | − | 0.458274i | \(-0.151532\pi\) |
0.0475286 | + | 0.998870i | \(0.484865\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.92820 | + | 7.19615i | −0.123694 | + | 0.461633i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 15.5981 | − | 1.30385i | 0.996525 | − | 0.0832998i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.00000 | − | 7.46410i | 0.127257 | − | 0.474929i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.33013 | − | 4.23205i | −0.464528 | − | 0.268195i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.85641i | 0.369653i | 0.982771 | + | 0.184827i | \(0.0591723\pi\) | ||||
−0.982771 | + | 0.184827i | \(0.940828\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.73205 | + | 3.73205i | −0.234632 | + | 0.234632i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.267949 | + | 4.46410i | −0.0167796 | + | 0.279553i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.73205 | + | 0.732051i | 0.170421 | + | 0.0456641i | 0.343020 | − | 0.939328i | \(-0.388550\pi\) |
−0.172600 | + | 0.984992i | \(0.555217\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.928203 | + | 12.9282i | 0.0576757 | + | 0.803319i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.09808 | − | 1.90192i | −0.0679692 | − | 0.117726i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.16025 | − | 8.06218i | −0.133207 | − | 0.497135i | 0.866792 | − | 0.498670i | \(-0.166178\pi\) |
−0.999999 | + | 0.00153494i | \(0.999511\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.00000 | − | 15.0000i | 0.307148 | − | 0.921443i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 22.7583 | + | 22.7583i | 1.39279 | + | 1.39279i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.42820 | + | 4.20577i | −0.148050 | + | 0.256430i | −0.930507 | − | 0.366275i | \(-0.880633\pi\) |
0.782457 | + | 0.622705i | \(0.213966\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.4186 | − | 12.3660i | 1.30109 | − | 0.751183i | 0.320496 | − | 0.947250i | \(-0.396150\pi\) |
0.980590 | + | 0.196067i | \(0.0628171\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −14.1962 | − | 2.73205i | −0.859190 | − | 0.165351i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.63397 | + | 0.437822i | 0.219137 | + | 0.0264017i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.3923 | − | 5.19615i | 1.16517 | − | 0.312207i | 0.376141 | − | 0.926562i | \(-0.377251\pi\) |
0.789029 | + | 0.614356i | \(0.210584\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.392305 | −0.0234867 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.9282 | 0.771232 | 0.385616 | − | 0.922659i | \(-0.373989\pi\) | ||||
0.385616 | + | 0.922659i | \(0.373989\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.4904 | − | 7.09808i | 1.57469 | − | 0.421937i | 0.637413 | − | 0.770523i | \(-0.280005\pi\) |
0.937277 | + | 0.348586i | \(0.113338\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.36603 | + | 11.5622i | 0.140151 | + | 0.684884i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.401924 | + | 1.16025i | 0.0237248 | + | 0.0684876i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.7942 | − | 7.96410i | 0.811425 | − | 0.468477i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.8301 | − | 18.7583i | 0.634873 | − | 1.09963i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.3923 | + | 18.3923i | 1.07449 | + | 1.07449i | 0.996993 | + | 0.0774974i | \(0.0246929\pi\) |
0.0774974 | + | 0.996993i | \(0.475307\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.39230 | + | 2.19615i | −0.255730 | + | 0.127865i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.830127 | + | 3.09808i | 0.0481689 | + | 0.179769i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.1962 | + | 17.6603i | 0.589659 | + | 1.02132i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.52628 | − | 19.6244i | 0.549086 | − | 1.13113i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −21.8923 | − | 5.86603i | −1.25768 | − | 0.336994i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −18.8923 | − | 1.13397i | −1.08177 | − | 0.0649312i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.29423 | − | 9.29423i | 0.530450 | − | 0.530450i | −0.390257 | − | 0.920706i | \(-0.627614\pi\) |
0.920706 | + | 0.390257i | \(0.127614\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 4.46410i | − | 0.253954i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.2224 | − | 9.36603i | −0.919890 | − | 0.531099i | −0.0362898 | − | 0.999341i | \(-0.511554\pi\) |
−0.883600 | + | 0.468243i | \(0.844887\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.19615 | − | 19.3923i | 0.293704 | − | 1.09612i | −0.648537 | − | 0.761183i | \(-0.724619\pi\) |
0.942241 | − | 0.334935i | \(-0.108714\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.16987 | − | 1.16987i | 0.234946 | − | 0.0659149i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.19615 | + | 4.46410i | −0.0671826 | + | 0.250729i | −0.991347 | − | 0.131265i | \(-0.958096\pi\) |
0.924165 | + | 0.381994i | \(0.124763\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.90192 | − | 1.09808i | −0.106487 | − | 0.0614805i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 17.1962i | 0.959796i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.00000 | + | 2.00000i | −0.111283 | + | 0.111283i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.26795 | − | 13.1244i | 0.292213 | − | 0.728008i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −26.3564 | − | 7.06218i | −1.45751 | − | 0.390539i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.73205 | + | 0.124356i | −0.0954911 | + | 0.00685595i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.9282 | + | 22.3923i | 0.710598 | + | 1.23079i | 0.964633 | + | 0.263597i | \(0.0849090\pi\) |
−0.254035 | + | 0.967195i | \(0.581758\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.928203 | + | 3.46410i | 0.0508652 | + | 0.189832i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.49038 | − | 0.830127i | −0.136064 | − | 0.0453547i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.4641 | + | 16.4641i | 0.896857 | + | 0.896857i | 0.995157 | − | 0.0983001i | \(-0.0313405\pi\) |
−0.0983001 | + | 0.995157i | \(0.531340\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.83013 | + | 10.0981i | −0.316649 | + | 0.548452i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.339746 | + | 0.196152i | −0.0183983 | + | 0.0106222i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | − | 15.5885i | 0.539949 | − | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −25.9904 | − | 17.1603i | −1.39928 | − | 0.923877i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.79423 | + | 2.08846i | −0.418416 | + | 0.112114i | −0.461884 | − | 0.886941i | \(-0.652826\pi\) |
0.0434674 | + | 0.999055i | \(0.486160\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.73205 | 0.520945 | 0.260472 | − | 0.965481i | \(-0.416122\pi\) | ||||
0.260472 | + | 0.965481i | \(0.416122\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.3923 | 0.661452 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.36603 | − | 1.43782i | 0.285605 | − | 0.0765276i | −0.113173 | − | 0.993575i | \(-0.536101\pi\) |
0.398777 | + | 0.917048i | \(0.369435\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.83013 | − | 5.83013i | −0.468654 | − | 0.309431i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.00000 | + | 3.46410i | 0.211702 | + | 0.183340i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.3397 | + | 7.12436i | −0.651267 | + | 0.376009i | −0.788941 | − | 0.614468i | \(-0.789371\pi\) |
0.137675 | + | 0.990478i | \(0.456037\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.76795 | − | 9.99038i | 0.303576 | − | 0.525810i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 14.2942 | + | 14.2942i | 0.750252 | + | 0.750252i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.60770 | + | 2.53590i | 0.398205 | + | 0.132735i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.500000 | − | 1.86603i | −0.0260998 | − | 0.0974057i | 0.951647 | − | 0.307193i | \(-0.0993896\pi\) |
−0.977747 | + | 0.209787i | \(0.932723\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.169873 | + | 0.294229i | 0.00884323 | + | 0.0153169i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.4904 | − | 15.4904i | −0.544633 | − | 0.804221i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.9282 | + | 4.26795i | 0.824731 | + | 0.220986i | 0.646414 | − | 0.762987i | \(-0.276268\pi\) |
0.178317 | + | 0.983973i | \(0.442935\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.76795 | + | 21.5263i | 0.0912965 | + | 1.11161i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.00000 | + | 6.00000i | −0.309016 | + | 0.309016i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 19.6603i | − | 1.00988i | −0.863155 | − | 0.504940i | \(-0.831515\pi\) | ||
0.863155 | − | 0.504940i | \(-0.168485\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.2942 | + | 8.83013i | 0.783547 | + | 0.452381i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.55256 | − | 28.1865i | 0.385918 | − | 1.44026i | −0.450797 | − | 0.892626i | \(-0.648860\pi\) |
0.836715 | − | 0.547638i | \(-0.184473\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.02628 | − | 3.09808i | 0.154233 | − | 0.157893i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.56218 | − | 5.83013i | 0.0794100 | − | 0.296362i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.73205 | − | 4.46410i | −0.392031 | − | 0.226339i | 0.291009 | − | 0.956720i | \(-0.406009\pi\) |
−0.683040 | + | 0.730381i | \(0.739342\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 7.46410i | − | 0.377476i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.6603 | + | 11.6603i | −0.588182 | + | 0.588182i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 15.0263 | + | 0.901924i | 0.756054 | + | 0.0453807i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.0263 | − | 5.36603i | −1.00509 | − | 0.269313i | −0.281514 | − | 0.959557i | \(-0.590836\pi\) |
−0.723577 | + | 0.690244i | \(0.757503\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12.5622 | + | 6.09808i | 0.628896 | + | 0.305286i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.50000 | − | 9.52628i | −0.274657 | − | 0.475720i | 0.695392 | − | 0.718631i | \(-0.255231\pi\) |
−0.970049 | + | 0.242911i | \(0.921898\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.392305 | + | 1.46410i | 0.0195421 | + | 0.0729321i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −21.3205 | + | 10.6603i | −1.05942 | + | 0.529712i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.53590 | + | 2.53590i | 0.125700 | + | 0.125700i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.42820 | − | 5.93782i | 0.169514 | − | 0.293606i | −0.768735 | − | 0.639567i | \(-0.779114\pi\) |
0.938249 | + | 0.345961i | \(0.112447\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.1244 | + | 10.4641i | −0.894009 | + | 0.516156i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.09808 | + | 5.70577i | −0.0540328 | + | 0.280763i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.96410 | − | 9.59808i | −0.0964140 | − | 0.471151i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −21.7583 | + | 5.83013i | −1.06551 | + | 0.285503i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.85641 | 0.188398 | 0.0941989 | − | 0.995553i | \(-0.469971\pi\) | ||||
0.0941989 | + | 0.995553i | \(0.469971\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.6603 | −1.68924 | −0.844619 | − | 0.535368i | \(-0.820173\pi\) | ||||
−0.844619 | + | 0.535368i | \(0.820173\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.464102 | + | 0.124356i | −0.0225654 | + | 0.00604638i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.07180 | + | 3.19615i | −0.197511 | + | 0.155036i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.6603 | + | 16.9282i | −0.709459 | + | 0.819213i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.46410 | + | 2.00000i | −0.167248 | + | 0.0965609i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.09808 | + | 3.63397i | −0.101061 | + | 0.175042i | −0.912122 | − | 0.409919i | \(-0.865557\pi\) |
0.811061 | + | 0.584961i | \(0.198890\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −24.4641 | − | 24.4641i | −1.17567 | − | 1.17567i | −0.980836 | − | 0.194833i | \(-0.937583\pi\) |
−0.194833 | − | 0.980836i | \(-0.562417\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.09808 | − | 12.2942i | 0.196488 | − | 0.589463i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.09808 | − | 19.0263i | −0.243874 | − | 0.910150i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.6603 | + | 27.1244i | 0.747423 | + | 1.29457i | 0.949054 | + | 0.315113i | \(0.102043\pi\) |
−0.201631 | + | 0.979462i | \(0.564624\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.90192 | − | 4.75833i | 0.0905678 | − | 0.226587i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.50000 | + | 0.937822i | 0.166290 | + | 0.0445573i | 0.341003 | − | 0.940062i | \(-0.389233\pi\) |
−0.174713 | + | 0.984619i | \(0.555900\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.23205 | + | 37.1865i | −0.105809 | + | 1.76281i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15.2942 | + | 15.2942i | −0.723392 | + | 0.723392i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.05256i | 0.238445i | 0.992868 | + | 0.119222i | \(0.0380402\pi\) | ||||
−0.992868 | + | 0.119222i | \(0.961960\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.294229 | + | 0.169873i | 0.0138547 | + | 0.00799901i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.92820 | + | 25.8564i | −0.325515 | + | 1.21484i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.53590 | − | 14.3923i | −0.400169 | − | 0.674722i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.26795 | + | 30.8564i | −0.386758 | + | 1.44340i | 0.448618 | + | 0.893724i | \(0.351916\pi\) |
−0.835376 | + | 0.549678i | \(0.814750\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.92820 | − | 2.26795i | −0.183353 | − | 0.105859i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 26.3923i | − | 1.22921i | −0.788834 | − | 0.614606i | \(-0.789315\pi\) | ||
0.788834 | − | 0.614606i | \(-0.210685\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.7583 | + | 17.7583i | −0.825300 | + | 0.825300i | −0.986862 | − | 0.161563i | \(-0.948347\pi\) |
0.161563 | + | 0.986862i | \(0.448347\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.53590 | − | 1.73205i | −0.0712256 | − | 0.0803219i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −31.3564 | − | 8.40192i | −1.45100 | − | 0.388795i | −0.554629 | − | 0.832097i | \(-0.687140\pi\) |
−0.896372 | + | 0.443303i | \(0.853807\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.57180 | + | 1.74167i | −0.118755 | + | 0.0804228i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −23.7583 | − | 41.1506i | −1.09473 | − | 1.89612i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.56218 | − | 5.83013i | −0.0718290 | − | 0.268070i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.19615 | + | 10.9282i | −0.376065 | + | 0.501420i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.66025 | − | 3.66025i | −0.167592 | − | 0.167592i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13.4641 | + | 23.3205i | −0.615191 | + | 1.06554i | 0.375161 | + | 0.926960i | \(0.377588\pi\) |
−0.990351 | + | 0.138581i | \(0.955746\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.0000 | − | 6.92820i | 0.547153 | − | 0.315899i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −34.8205 | + | 12.0622i | −1.58439 | + | 0.548848i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 24.5622 | − | 5.02628i | 1.11531 | − | 0.228232i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.29423 | − | 2.22243i | 0.375847 | − | 0.100708i | −0.0659498 | − | 0.997823i | \(-0.521008\pi\) |
0.441797 | + | 0.897115i | \(0.354341\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.7321 | 0.485320 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.7128 | 0.799368 | 0.399684 | − | 0.916653i | \(-0.369120\pi\) | ||||
0.399684 | + | 0.916653i | \(0.369120\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.00000 | − | 0.803848i | 0.135113 | − | 0.0362035i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.660254 | − | 1.00000i | 0.0296762 | − | 0.0449467i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −11.8301 | + | 4.09808i | −0.530654 | + | 0.183824i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.0263 | − | 16.7583i | 1.29939 | − | 0.750206i | 0.319095 | − | 0.947723i | \(-0.396621\pi\) |
0.980300 | + | 0.197517i | \(0.0632877\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.6962 | − | 25.4545i | 0.656576 | − | 1.13722i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.3660 | + | 19.3660i | 0.863488 | + | 0.863488i | 0.991741 | − | 0.128253i | \(-0.0409370\pi\) |
−0.128253 | + | 0.991741i | \(0.540937\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.7321 | − | 23.4641i | −0.522069 | − | 1.04414i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.50000 | − | 9.33013i | −0.111029 | − | 0.414365i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.4545 | + | 23.3038i | 0.596359 | + | 1.03292i | 0.993353 | + | 0.115104i | \(0.0367200\pi\) |
−0.396994 | + | 0.917821i | \(0.629947\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.85641 | − | 5.32051i | 0.347547 | − | 0.235365i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −11.5622 | − | 3.09808i | −0.510483 | − | 0.136783i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.86603 | − | 3.42820i | 0.170357 | − | 0.151065i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.339746 | + | 0.339746i | −0.0149420 | + | 0.0149420i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 45.3205i | − | 1.98935i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.33975 | − | 1.92820i | −0.146317 | − | 0.0844761i | 0.425054 | − | 0.905168i | \(-0.360255\pi\) |
−0.571371 | + | 0.820692i | \(0.693588\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.88269 | + | 14.4904i | −0.169778 | + | 0.633620i | 0.827604 | + | 0.561312i | \(0.189703\pi\) |
−0.997382 | + | 0.0723082i | \(0.976963\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 21.4904 | + | 13.8301i | 0.937917 | + | 0.603596i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.143594 | − | 0.535898i | 0.00625503 | − | 0.0233441i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25.0981 | + | 14.4904i | 1.09122 | + | 0.630017i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.60770i | 0.0697680i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.928203 | − | 0.928203i | 0.0402049 | − | 0.0402049i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.8923 | + | 13.2058i | −0.643850 | + | 0.570935i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −37.0526 | − | 9.92820i | −1.59894 | − | 0.428434i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.732051 | − | 5.07180i | −0.0315317 | − | 0.218458i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.35641 | + | 16.2058i | 0.402263 | + | 0.696741i | 0.993999 | − | 0.109392i | \(-0.0348903\pi\) |
−0.591735 | + | 0.806132i | \(0.701557\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.59808 | + | 17.1603i | 0.197322 | + | 0.736417i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.1244 | − | 28.2487i | −0.605021 | − | 1.21004i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.75833 | − | 5.75833i | −0.246208 | − | 0.246208i | 0.573204 | − | 0.819413i | \(-0.305700\pi\) |
−0.819413 | + | 0.573204i | \(0.805700\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.09808 | + | 5.36603i | −0.132223 | + | 0.229016i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.09808 | − | 4.09808i | 0.302388 | − | 0.174584i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.6603 | − | 13.4641i | 0.495844 | − | 0.572552i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −11.6603 | + | 17.6603i | −0.494950 | + | 0.749636i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.63397 | − | 1.77757i | 0.281091 | − | 0.0753180i | −0.115519 | − | 0.993305i | \(-0.536853\pi\) |
0.396610 | + | 0.917987i | \(0.370187\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −23.3205 | −0.986352 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.46410 | 0.0618144 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.3564 | + | 5.72243i | −0.900065 | + | 0.241172i | −0.679044 | − | 0.734097i | \(-0.737606\pi\) |
−0.221021 | + | 0.975269i | \(0.570939\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.2224 | + | 2.70577i | −0.556272 | + | 0.113833i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.33013 | + | 27.6962i | −0.223844 | + | 1.16313i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.0526 | − | 7.53590i | 0.547192 | − | 0.315921i | −0.200797 | − | 0.979633i | \(-0.564353\pi\) |
0.747989 | + | 0.663712i | \(0.231020\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.0263 | − | 17.3660i | 0.419587 | − | 0.726746i | −0.576311 | − | 0.817230i | \(-0.695508\pi\) |
0.995898 | + | 0.0904849i | \(0.0288417\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 22.8564 | + | 22.8564i | 0.954840 | + | 0.954840i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.09808 | − | 35.6865i | −0.212604 | − | 1.48823i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.36603 | + | 27.4904i | 0.306652 | + | 1.14444i | 0.931514 | + | 0.363705i | \(0.118488\pi\) |
−0.624863 | + | 0.780735i | \(0.714845\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.09808 | + | 5.36603i | 0.128752 | + | 0.223004i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.4282 | − | 5.06218i | −0.432635 | − | 0.210015i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.00000 | − | 1.33975i | −0.207079 | − | 0.0554866i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.07180 | − | 3.46410i | −0.127003 | − | 0.143223i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 25.7846 | − | 25.7846i | 1.06424 | − | 1.06424i | 0.0664553 | − | 0.997789i | \(-0.478831\pi\) |
0.997789 | − | 0.0664553i | \(-0.0211690\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 1.46410i | − | 0.0603273i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 33.4186 | + | 19.2942i | 1.37466 | + | 0.793659i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.75833 | + | 6.56218i | −0.0722060 | + | 0.269476i | −0.992585 | − | 0.121550i | \(-0.961213\pi\) |
0.920379 | + | 0.391027i | \(0.127880\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.0717968 | + | 6.12436i | 0.00294338 | + | 0.251074i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.4641 | − | 46.5167i | 0.510122 | − | 1.90380i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.6603 | + | 18.8564i | 1.33446 | + | 0.770452i | 0.985980 | − | 0.166864i | \(-0.0533640\pi\) |
0.348482 | + | 0.937316i | \(0.386697\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.1769i | 0.863824i | 0.901916 | + | 0.431912i | \(0.142161\pi\) | ||||
−0.901916 | + | 0.431912i | \(0.857839\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.607695 | + | 0.607695i | −0.0247473 | + | 0.0247473i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.40192 | + | 23.3564i | −0.0569963 | + | 0.949573i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.59808 | − | 2.30385i | −0.348985 | − | 0.0935103i | 0.0800683 | − | 0.996789i | \(-0.474486\pi\) |
−0.429053 | + | 0.903279i | \(0.641153\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.59808 | − | 12.6962i | −0.348412 | − | 0.514474i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.928203 | + | 1.60770i | 0.0375511 | + | 0.0650404i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.60770 | + | 13.4641i | 0.145713 | + | 0.543810i | 0.999723 | + | 0.0235520i | \(0.00749753\pi\) |
−0.854009 | + | 0.520258i | \(0.825836\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.633975 | + | 1.90192i | −0.0255643 | + | 0.0766930i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31.9090 | − | 31.9090i | −1.28461 | − | 1.28461i | −0.938017 | − | 0.346590i | \(-0.887340\pi\) |
−0.346590 | − | 0.938017i | \(-0.612660\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.0980762 | − | 0.169873i | 0.00394202 | − | 0.00682777i | −0.864048 | − | 0.503410i | \(-0.832079\pi\) |
0.867990 | + | 0.496582i | \(0.165412\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 27.3564 | − | 15.7942i | 1.09777 | − | 0.633801i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 33.3205 | + | 28.8564i | 1.33496 | + | 1.15611i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.2846 | + | 18.0622i | −0.691384 | + | 0.722487i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.73205 | − | 1.00000i | 0.149044 | − | 0.0399362i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.07180 | −0.202226 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.5885 | −1.05847 | −0.529235 | − | 0.848475i | \(-0.677521\pi\) | ||||
−0.529235 | + | 0.848475i | \(0.677521\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −19.0263 | + | 5.09808i | −0.756227 | + | 0.202630i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.09808 | + | 20.0263i | 0.162627 | + | 0.794719i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19.6603 | − | 2.33975i | −0.778968 | − | 0.0927041i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.00000 | + | 1.73205i | −0.118678 | + | 0.0685189i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.33013 | − | 5.76795i | 0.131532 | − | 0.227820i | −0.792735 | − | 0.609566i | \(-0.791344\pi\) |
0.924267 | + | 0.381746i | \(0.124677\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.4641 | − | 24.4641i | −0.964770 | − | 0.964770i | 0.0346302 | − | 0.999400i | \(-0.488975\pi\) |
−0.999400 | + | 0.0346302i | \(0.988975\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 31.8564 | − | 15.9282i | 1.25434 | − | 0.627172i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.44744 | − | 5.40192i | −0.0569048 | − | 0.212372i | 0.931619 | − | 0.363436i | \(-0.118397\pi\) |
−0.988524 | + | 0.151065i | \(0.951730\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.803848 | + | 1.39230i | 0.0315538 | + | 0.0546527i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.73205 | + | 0.196152i | −0.107078 | + | 0.00768782i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.73205 | − | 2.33975i | −0.341712 | − | 0.0915613i | 0.0838822 | − | 0.996476i | \(-0.473268\pi\) |
−0.425594 | + | 0.904914i | \(0.639935\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −19.0526 | − | 1.14359i | −0.744445 | − | 0.0446839i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.85641 | − | 1.85641i | 0.0724253 | − | 0.0724253i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.3397i | 0.402779i | 0.979511 | + | 0.201390i | \(0.0645457\pi\) | ||||
−0.979511 | + | 0.201390i | \(0.935454\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.2776 | − | 7.08846i | −0.477542 | − | 0.275709i | 0.241850 | − | 0.970314i | \(-0.422246\pi\) |
−0.719392 | + | 0.694605i | \(0.755579\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.46410 | − | 5.46410i | 0.0568610 | − | 0.212208i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.36603 | + | 15.5622i | 0.169307 | + | 0.603475i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.59808 | + | 20.8923i | −0.216758 | + | 0.808953i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.4904 | + | 8.36603i | 0.560230 | + | 0.323449i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.19615i | 0.239200i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.3923 | + | 16.3923i | −0.631877 | + | 0.631877i | −0.948539 | − | 0.316662i | \(-0.897438\pi\) |
0.316662 | + | 0.948539i | \(0.397438\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −20.3301 | − | 8.16025i | −0.782507 | − | 0.314088i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.92820 | + | 1.85641i | 0.266272 | + | 0.0713475i | 0.389485 | − | 0.921033i | \(-0.372653\pi\) |
−0.123213 | + | 0.992380i | \(0.539320\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.9545 | − | 26.6865i | 0.497147 | − | 1.02414i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.0980762 | − | 0.169873i | −0.00375829 | − | 0.00650955i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.93782 | − | 18.4282i | −0.188941 | − | 0.705136i | −0.993753 | − | 0.111606i | \(-0.964401\pi\) |
0.804812 | − | 0.593530i | \(-0.202266\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22.9808 | − | 7.66025i | −0.878050 | − | 0.292683i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.26795 | + | 3.26795i | 0.124680 | + | 0.124680i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.0000 | + | 17.3205i | −0.380970 | + | 0.659859i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.9737 | − | 14.4186i | 0.950045 | − | 0.548509i | 0.0569502 | − | 0.998377i | \(-0.481862\pi\) |
0.893095 | + | 0.449868i | \(0.148529\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.464102 | − | 1.33975i | −0.0176298 | − | 0.0508927i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −21.7583 | − | 14.3660i | −0.825341 | − | 0.544934i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.464102 | + | 0.124356i | −0.0175791 | + | 0.00471031i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.46410 | 0.131024 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.7321 | −0.896347 | −0.448174 | − | 0.893947i | \(-0.647925\pi\) | ||||
−0.448174 | + | 0.893947i | \(0.647925\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.9282 | + | 3.46410i | −0.487596 | + | 0.130651i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.36603 | − | 1.56218i | −0.0891097 | − | 0.0588350i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −30.4808 | − | 5.86603i | −1.14635 | − | 0.220615i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.99038 | + | 4.03590i | −0.262529 | + | 0.151571i | −0.625488 | − | 0.780234i | \(-0.715100\pi\) |
0.362959 | + | 0.931805i | \(0.381767\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.46410 | − | 4.26795i | 0.0924110 | − | 0.160061i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.73205 | + | 2.73205i | 0.102316 | + | 0.102316i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.39230 | − | 1.46410i | −0.164263 | − | 0.0547543i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.19615 | + | 34.3205i | 0.343437 | + | 1.28172i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.70577 | − | 6.41858i | −0.138202 | − | 0.239373i | 0.788614 | − | 0.614888i | \(-0.210799\pi\) |
−0.926816 | + | 0.375516i | \(0.877466\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.437822 | − | 6.09808i | −0.0163053 | − | 0.227104i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 31.3205 | + | 8.39230i | 1.16482 | + | 0.312113i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13.7942 | − | 5.89230i | 0.512305 | − | 0.218835i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.90192 | − | 4.90192i | 0.181802 | − | 0.181802i | −0.610338 | − | 0.792141i | \(-0.708967\pi\) |
0.792141 | + | 0.610338i | \(0.208967\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 17.5885i | − | 0.651424i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.39230 | + | 4.26795i | 0.273414 | + | 0.157856i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.63397 | + | 9.83013i | −0.0972881 | + | 0.363084i | −0.997356 | − | 0.0726647i | \(-0.976850\pi\) |
0.900068 | + | 0.435749i | \(0.143516\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 28.4545 | − | 10.2321i | 1.04956 | − | 0.377415i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.222432 | + | 0.830127i | −0.00819338 | + | 0.0305781i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.43782 | + | 4.29423i | 0.273605 | + | 0.157966i | 0.630525 | − | 0.776169i | \(-0.282840\pi\) |
−0.356920 | + | 0.934135i | \(0.616173\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 14.9282i | − | 0.548401i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.8301 | − | 14.8301i | 0.544065 | − | 0.544065i | −0.380653 | − | 0.924718i | \(-0.624301\pi\) |
0.924718 | + | 0.380653i | \(0.124301\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −24.9904 | − | 1.50000i | −0.915577 | − | 0.0549557i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.09808 | − | 0.830127i | −0.113353 | − | 0.0303728i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.68653 | + | 23.4904i | 0.0616246 | + | 0.858320i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.19615 | + | 12.4641i | 0.262591 | + | 0.454822i | 0.966930 | − | 0.255043i | \(-0.0820896\pi\) |
−0.704338 | + | 0.709864i | \(0.748756\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.92820 | + | 10.9282i | 0.106710 | + | 0.398246i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −27.7128 | + | 13.8564i | −1.00857 | + | 0.504286i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.26795 | + | 9.26795i | 0.336849 | + | 0.336849i | 0.855180 | − | 0.518331i | \(-0.173446\pi\) |
−0.518331 | + | 0.855180i | \(0.673446\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.09808 | + | 8.83013i | −0.185048 | + | 0.320513i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.0718 | − | 6.39230i | 0.401352 | − | 0.231721i | −0.285715 | − | 0.958315i | \(-0.592231\pi\) |
0.687067 | + | 0.726594i | \(0.258898\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −36.6962 | − | 7.06218i | −1.32849 | − | 0.255668i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.339746 | + | 1.66025i | 0.0122835 | + | 0.0600266i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.00000 | − | 1.60770i | 0.216647 | − | 0.0580505i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −47.1769 | −1.70124 | −0.850622 | − | 0.525778i | \(-0.823774\pi\) | ||||
−0.850622 | + | 0.525778i | \(0.823774\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.46410 | 0.196785 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.9282 | − | 4.80385i | 0.644833 | − | 0.172782i | 0.0784412 | − | 0.996919i | \(-0.475006\pi\) |
0.566391 | + | 0.824136i | \(0.308339\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.320508 | − | 2.66025i | 0.0115130 | − | 0.0955591i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.19615 | + | 23.6603i | 0.294035 | + | 0.848807i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.09808 | + | 0.633975i | −0.0393427 | + | 0.0227145i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.73205 | + | 3.00000i | −0.0619777 | + | 0.107348i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.29423 | + | 9.29423i | 0.332149 | + | 0.332149i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17.3923 | − | 52.1769i | 0.620758 | − | 1.86227i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.18653 | + | 19.3564i | 0.184880 | + | 0.689981i | 0.994656 | + | 0.103243i | \(0.0329218\pi\) |
−0.809776 | + | 0.586739i | \(0.800412\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.06218 | − | 13.9641i | −0.287021 | − | 0.497135i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.97372 | + | 14.3660i | −0.247957 | + | 0.510797i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 23.1244 | + | 6.19615i | 0.821170 | + | 0.220032i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.83013 | − | 30.4904i | 0.0649079 | − | 1.08138i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 29.4641 | − | 29.4641i | 1.04367 | − | 1.04367i | 0.0446702 | − | 0.999002i | \(-0.485776\pi\) |
0.999002 | − | 0.0446702i | \(-0.0142237\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 0.679492i | − | 0.0240387i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.5622 | + | 6.09808i | 0.373196 | + | 0.215465i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.679492 | − | 2.53590i | 0.0239787 | − | 0.0894899i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −37.1865 | − | 20.8923i | −1.31065 | − | 0.736357i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.42820 | + | 9.06218i | −0.0854768 | + | 0.319004i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.9904 | + | 12.6962i | 0.773141 | + | 0.446373i | 0.833994 | − | 0.551774i | \(-0.186049\pi\) |
−0.0608532 | + | 0.998147i | \(0.519382\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 29.0718i | − | 1.02085i | −0.859923 | − | 0.510424i | \(-0.829488\pi\) | ||
0.859923 | − | 0.510424i | \(-0.170512\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 33.7846 | − | 33.7846i | 1.18488 | − | 1.18488i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.24167 | + | 9.29423i | 0.288693 | + | 0.325563i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21.7583 | + | 5.83013i | 0.761228 | + | 0.203970i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.46410 | + | 0.392305i | −0.190931 | + | 0.0137082i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.33975 | + | 12.7128i | 0.256159 | + | 0.443680i | 0.965210 | − | 0.261477i | \(-0.0842096\pi\) |
−0.709051 | + | 0.705157i | \(0.750876\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.61731 | + | 24.6962i | 0.230665 | + | 0.860854i | 0.980055 | + | 0.198725i | \(0.0636801\pi\) |
−0.749390 | + | 0.662129i | \(0.769653\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.00000 | − | 1.00000i | 0.243709 | − | 0.0348155i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.77757 | + | 3.77757i | 0.131359 | + | 0.131359i | 0.769729 | − | 0.638370i | \(-0.220391\pi\) |
−0.638370 | + | 0.769729i | \(0.720391\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.7321 | + | 18.5885i | −0.372740 | + | 0.645604i | −0.989986 | − | 0.141166i | \(-0.954915\pi\) |
0.617246 | + | 0.786770i | \(0.288248\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 33.5885 | − | 19.3923i | 1.16517 | − | 0.672712i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.80385 | + | 4.33975i | 0.201091 | + | 0.150363i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 33.3301 | − | 6.82051i | 1.15344 | − | 0.236033i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.26795 | − | 0.607695i | 0.0783918 | − | 0.0210050i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −31.1244 | −1.07453 | −0.537266 | − | 0.843413i | \(-0.680543\pi\) | ||||
−0.537266 | + | 0.843413i | \(0.680543\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.0000 | 0.689655 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 24.1244 | − | 6.46410i | 0.830887 | − | 0.222635i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.16025 | − | 9.33013i | 0.211919 | − | 0.320966i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.9282 | + | 18.1244i | 0.719102 | + | 0.622760i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 45.8827 | − | 26.4904i | 1.57469 | − | 0.909148i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17.6603 | − | 30.5885i | 0.605386 | − | 1.04856i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.12436 | + | 6.12436i | 0.209694 | + | 0.209694i | 0.804137 | − | 0.594443i | \(-0.202628\pi\) |
−0.594443 | + | 0.804137i | \(0.702628\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.00000 | + | 4.00000i | 0.0683986 | + | 0.136797i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.90192 | − | 22.0263i | −0.201606 | − | 0.752403i | −0.990457 | − | 0.137820i | \(-0.955991\pi\) |
0.788851 | − | 0.614584i | \(-0.210676\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.5359 | + | 18.2487i | 0.359480 | + | 0.622638i | 0.987874 | − | 0.155257i | \(-0.0496207\pi\) |
−0.628394 | + | 0.777895i | \(0.716287\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.33013 | + | 1.96410i | 0.0453306 | + | 0.0669364i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 33.3827 | + | 8.94486i | 1.13636 | + | 0.304487i | 0.777487 | − | 0.628900i | \(-0.216494\pi\) |
0.358873 | + | 0.933386i | \(0.383161\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 39.2487 | − | 34.8038i | 1.33450 | − | 1.18337i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 21.7583 | − | 21.7583i | 0.738952 | − | 0.738952i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 4.92820i | − | 0.167178i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.87564 | + | 1.66025i | 0.0974375 | + | 0.0562556i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.12436 | − | 7.92820i | 0.0718985 | − | 0.268329i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.52628 | + | 29.2321i | 0.153016 | + | 0.988224i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.15064 | − | 15.4904i | 0.140157 | − | 0.523073i | −0.859766 | − | 0.510688i | \(-0.829391\pi\) |
0.999923 | − | 0.0123853i | \(-0.00394248\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 43.5167 | + | 25.1244i | 1.46778 | + | 0.847423i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 52.8564i | 1.78078i | 0.455201 | + | 0.890389i | \(0.349567\pi\) | ||||
−0.455201 | + | 0.890389i | \(0.650433\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.9282 | + | 21.9282i | −0.737943 | + | 0.737943i | −0.972180 | − | 0.234237i | \(-0.924741\pi\) |
0.234237 | + | 0.972180i | \(0.424741\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.09808 | + | 6.29423i | −0.238599 | + | 0.211578i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 36.9186 | + | 9.89230i | 1.23960 | + | 0.332151i | 0.818312 | − | 0.574774i | \(-0.194910\pi\) |
0.421292 | + | 0.906925i | \(0.361577\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21.7583 | + | 10.5622i | 0.729751 | + | 0.354244i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.90192 | + | 6.75833i | 0.130719 | + | 0.226413i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.464102 | − | 1.73205i | −0.0155306 | − | 0.0579609i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19.8564 | − | 39.7128i | −0.663726 | − | 1.32745i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 27.8564 | + | 27.8564i | 0.930098 | + | 0.930098i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.803848 | + | 1.39230i | −0.0268098 | + | 0.0464360i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.33975 | − | 3.66025i | 0.211208 | − | 0.121941i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.96410 | − | 41.3827i | 0.265029 | − | 1.37713i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.3301 | + | 17.1603i | −0.376626 | + | 0.570426i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.69615 | + | 0.454483i | −0.0563198 | + | 0.0150908i | −0.286869 | − | 0.957970i | \(-0.592614\pi\) |
0.230549 | + | 0.973061i | \(0.425948\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.58846 | −0.284861 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37.5167 | −1.24298 | −0.621491 | − | 0.783421i | \(-0.713473\pi\) | ||||
−0.621491 | + | 0.783421i | \(0.713473\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.09808 | + | 0.830127i | −0.102531 | + | 0.0274732i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −35.8205 | + | 7.33013i | −1.18419 | + | 0.242327i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −14.7846 | + | 17.0718i | −0.488231 | + | 0.563760i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −39.6673 | + | 22.9019i | −1.30850 | + | 0.755465i | −0.981846 | − | 0.189678i | \(-0.939256\pi\) |
−0.326657 | + | 0.945143i | \(0.605922\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.6962 | − | 21.9904i | 0.418352 | − | 0.724608i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.46410 | + | 9.46410i | 0.311515 | + | 0.311515i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24.2487 | + | 3.46410i | −0.797293 | + | 0.113899i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.437822 | − | 1.63397i | −0.0143800 | − | 0.0536668i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.839746 | − | 1.45448i | −0.0275512 | − | 0.0477200i | 0.851921 | − | 0.523670i | \(-0.175438\pi\) |
−0.879472 | + | 0.475950i | \(0.842104\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17.7583 | + | 7.09808i | 0.582006 | + | 0.232630i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −34.9545 | − | 9.36603i | −1.14436 | − | 0.306630i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.12436 | + | 1.26795i | 0.0367704 | + | 0.0414664i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.9282 | − | 30.9282i | 1.01038 | − | 1.01038i | 0.0104348 | − | 0.999946i | \(-0.496678\pi\) |
0.999946 | − | 0.0104348i | \(-0.00332156\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 38.7846i | − | 1.26569i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.8038 | + | 14.3205i | 0.808582 | + | 0.466835i | 0.846463 | − | 0.532447i | \(-0.178727\pi\) |
−0.0378810 | + | 0.999282i | \(0.512061\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.866025 | − | 3.23205i | 0.0282017 | − | 0.105250i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −22.2942 | + | 13.2224i | −0.725231 | + | 0.430126i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.6962 | − | 43.6506i | 0.380074 | − | 1.41846i | −0.465714 | − | 0.884935i | \(-0.654202\pi\) |
0.845788 | − | 0.533520i | \(-0.179131\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.78461 | − | 5.07180i | −0.285160 | − | 0.164637i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.92820i | 0.289517i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10.1436 | + | 10.1436i | −0.328583 | + | 0.328583i | −0.852048 | − | 0.523464i | \(-0.824639\pi\) |
0.523464 | + | 0.852048i | \(0.324639\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.24167 | + | 37.3468i | −0.0725387 | + | 1.20851i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.09808 | − | 1.09808i | −0.132472 | − | 0.0354958i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −23.7321 | + | 16.0718i | −0.766348 | + | 0.518985i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.3564 | − | 26.5981i | −0.495368 | − | 0.858002i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.68653 | + | 6.29423i | 0.0543478 | + | 0.202829i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.26795 | + | 6.80385i | −0.0730079 | + | 0.219024i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.43782 | + | 1.43782i | 0.0462372 | + | 0.0462372i | 0.729847 | − | 0.683610i | \(-0.239591\pi\) |
−0.683610 | + | 0.729847i | \(0.739591\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.73205 | + | 4.73205i | −0.0877661 | + | 0.152015i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −42.9282 | + | 24.7846i | −1.37763 | + | 0.795376i | −0.991874 | − | 0.127224i | \(-0.959393\pi\) |
−0.385758 | + | 0.922600i | \(0.626060\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −29.1506 | + | 10.0981i | −0.934526 | + | 0.323729i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.26795 | − | 27.1244i | 0.104658 | − | 0.868675i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 43.1506 | − | 11.5622i | 1.38051 | − | 0.369907i | 0.509204 | − | 0.860646i | \(-0.329940\pi\) |
0.871307 | + | 0.490739i | \(0.163273\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.1962 | 0.389791 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.3397 | −0.330123 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −14.5000 | + | 3.88526i | −0.462478 | + | 0.123921i | −0.482532 | − | 0.875878i | \(-0.660283\pi\) |
0.0200540 | + | 0.999799i | \(0.493616\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.95448 | + | 43.7583i | 0.285314 | + | 1.39426i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.16987 | + | 1.09808i | −0.100898 | + | 0.0349522i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −51.4808 | + | 29.7224i | −1.63699 | + | 0.945118i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.8564 | + | 20.5359i | −0.376631 | + | 0.652344i | −0.990570 | − | 0.137009i | \(-0.956251\pi\) |
0.613939 | + | 0.789354i | \(0.289584\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 35.3205 | + | 35.3205i | 1.12086 | + | 1.12086i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 49.8564 | − | 24.9282i | 1.58055 | − | 0.790277i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.88269 | + | 25.6865i | 0.217977 | + | 0.813501i | 0.985097 | + | 0.171998i | \(0.0550222\pi\) |
−0.767121 | + | 0.641503i | \(0.778311\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10.7321 | − | 18.5885i | −0.339547 | − | 0.588113i |
(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 | 560.2.ci.b.17.1 | 4 | ||
4.3 | odd | 2 | 35.2.k.b.17.1 | yes | 4 | ||
5.3 | odd | 4 | 560.2.ci.a.353.1 | 4 | |||
7.5 | odd | 6 | 560.2.ci.a.257.1 | 4 | |||
12.11 | even | 2 | 315.2.bz.a.262.1 | 4 | |||
20.3 | even | 4 | 35.2.k.a.3.1 | ✓ | 4 | ||
20.7 | even | 4 | 175.2.o.b.143.1 | 4 | |||
20.19 | odd | 2 | 175.2.o.a.157.1 | 4 | |||
28.3 | even | 6 | 245.2.f.a.97.2 | 4 | |||
28.11 | odd | 6 | 245.2.f.b.97.2 | 4 | |||
28.19 | even | 6 | 35.2.k.a.12.1 | yes | 4 | ||
28.23 | odd | 6 | 245.2.l.a.117.1 | 4 | |||
28.27 | even | 2 | 245.2.l.b.227.1 | 4 | |||
35.33 | even | 12 | inner | 560.2.ci.b.33.1 | 4 | ||
60.23 | odd | 4 | 315.2.bz.b.73.1 | 4 | |||
84.47 | odd | 6 | 315.2.bz.b.82.1 | 4 | |||
140.3 | odd | 12 | 245.2.f.b.48.2 | 4 | |||
140.19 | even | 6 | 175.2.o.b.82.1 | 4 | |||
140.23 | even | 12 | 245.2.l.b.68.1 | 4 | |||
140.47 | odd | 12 | 175.2.o.a.68.1 | 4 | |||
140.83 | odd | 4 | 245.2.l.a.178.1 | 4 | |||
140.103 | odd | 12 | 35.2.k.b.33.1 | yes | 4 | ||
140.123 | even | 12 | 245.2.f.a.48.2 | 4 | |||
420.383 | even | 12 | 315.2.bz.a.208.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.2.k.a.3.1 | ✓ | 4 | 20.3 | even | 4 | ||
35.2.k.a.12.1 | yes | 4 | 28.19 | even | 6 | ||
35.2.k.b.17.1 | yes | 4 | 4.3 | odd | 2 | ||
35.2.k.b.33.1 | yes | 4 | 140.103 | odd | 12 | ||
175.2.o.a.68.1 | 4 | 140.47 | odd | 12 | |||
175.2.o.a.157.1 | 4 | 20.19 | odd | 2 | |||
175.2.o.b.82.1 | 4 | 140.19 | even | 6 | |||
175.2.o.b.143.1 | 4 | 20.7 | even | 4 | |||
245.2.f.a.48.2 | 4 | 140.123 | even | 12 | |||
245.2.f.a.97.2 | 4 | 28.3 | even | 6 | |||
245.2.f.b.48.2 | 4 | 140.3 | odd | 12 | |||
245.2.f.b.97.2 | 4 | 28.11 | odd | 6 | |||
245.2.l.a.117.1 | 4 | 28.23 | odd | 6 | |||
245.2.l.a.178.1 | 4 | 140.83 | odd | 4 | |||
245.2.l.b.68.1 | 4 | 140.23 | even | 12 | |||
245.2.l.b.227.1 | 4 | 28.27 | even | 2 | |||
315.2.bz.a.208.1 | 4 | 420.383 | even | 12 | |||
315.2.bz.a.262.1 | 4 | 12.11 | even | 2 | |||
315.2.bz.b.73.1 | 4 | 60.23 | odd | 4 | |||
315.2.bz.b.82.1 | 4 | 84.47 | odd | 6 | |||
560.2.ci.a.257.1 | 4 | 7.5 | odd | 6 | |||
560.2.ci.a.353.1 | 4 | 5.3 | odd | 4 | |||
560.2.ci.b.17.1 | 4 | 1.1 | even | 1 | trivial | ||
560.2.ci.b.33.1 | 4 | 35.33 | even | 12 | inner |