Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,2,Mod(116,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("245.116");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.95633484952\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 5x^{2} + 4x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 35) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 116.2 | ||
Root | \(1.28078 + 2.21837i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.116 |
Dual form | 245.2.e.i.226.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.28078 | + | 2.21837i | 0.905646 | + | 1.56862i | 0.820048 | + | 0.572295i | \(0.193947\pi\) |
0.0855975 | + | 0.996330i | \(0.472720\pi\) | |||||||
\(3\) | −0.780776 | + | 1.35234i | −0.450781 | + | 0.780776i | −0.998435 | − | 0.0559290i | \(-0.982188\pi\) |
0.547653 | + | 0.836705i | \(0.315521\pi\) | |||||||
\(4\) | −2.28078 | + | 3.95042i | −1.14039 | + | 1.97521i | ||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | −4.00000 | −1.63299 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −6.56155 | −2.31986 | ||||||||
\(9\) | 0.280776 | + | 0.486319i | 0.0935921 | + | 0.162106i | ||||
\(10\) | 1.28078 | − | 2.21837i | 0.405017 | − | 0.701510i | ||||
\(11\) | 0.780776 | − | 1.35234i | 0.235413 | − | 0.407747i | −0.723980 | − | 0.689821i | \(-0.757689\pi\) |
0.959393 | + | 0.282074i | \(0.0910224\pi\) | |||||||
\(12\) | −3.56155 | − | 6.16879i | −1.02813 | − | 1.78078i | ||||
\(13\) | 0.438447 | 0.121603 | 0.0608017 | − | 0.998150i | \(-0.480634\pi\) | ||||
0.0608017 | + | 0.998150i | \(0.480634\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.56155 | 0.403191 | ||||||||
\(16\) | −3.84233 | − | 6.65511i | −0.960582 | − | 1.66378i | ||||
\(17\) | 0.219224 | − | 0.379706i | 0.0531695 | − | 0.0920923i | −0.838216 | − | 0.545339i | \(-0.816401\pi\) |
0.891385 | + | 0.453247i | \(0.149734\pi\) | |||||||
\(18\) | −0.719224 | + | 1.24573i | −0.169523 | + | 0.293622i | ||||
\(19\) | 3.56155 | + | 6.16879i | 0.817076 | + | 1.41522i | 0.907827 | + | 0.419344i | \(0.137740\pi\) |
−0.0907512 | + | 0.995874i | \(0.528927\pi\) | |||||||
\(20\) | 4.56155 | 1.01999 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.00000 | 0.852803 | ||||||||
\(23\) | −1.56155 | − | 2.70469i | −0.325606 | − | 0.563967i | 0.656029 | − | 0.754736i | \(-0.272235\pi\) |
−0.981635 | + | 0.190769i | \(0.938902\pi\) | |||||||
\(24\) | 5.12311 | − | 8.87348i | 1.04575 | − | 1.81129i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0.561553 | + | 0.972638i | 0.110130 | + | 0.190750i | ||||
\(27\) | −5.56155 | −1.07032 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.68466 | 1.24131 | 0.620655 | − | 0.784084i | \(-0.286867\pi\) | ||||
0.620655 | + | 0.784084i | \(0.286867\pi\) | |||||||
\(30\) | 2.00000 | + | 3.46410i | 0.365148 | + | 0.632456i | ||||
\(31\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(32\) | 3.28078 | − | 5.68247i | 0.579965 | − | 1.00453i | ||||
\(33\) | 1.21922 | + | 2.11176i | 0.212240 | + | 0.367610i | ||||
\(34\) | 1.12311 | 0.192611 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.56155 | −0.426925 | ||||||||
\(37\) | −3.00000 | − | 5.19615i | −0.493197 | − | 0.854242i | 0.506772 | − | 0.862080i | \(-0.330838\pi\) |
−0.999969 | + | 0.00783774i | \(0.997505\pi\) | |||||||
\(38\) | −9.12311 | + | 15.8017i | −1.47996 | + | 2.56337i | ||||
\(39\) | −0.342329 | + | 0.592932i | −0.0548165 | + | 0.0949450i | ||||
\(40\) | 3.28078 | + | 5.68247i | 0.518736 | + | 0.898478i | ||||
\(41\) | 5.12311 | 0.800095 | 0.400047 | − | 0.916494i | \(-0.368994\pi\) | ||||
0.400047 | + | 0.916494i | \(0.368994\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.876894 | 0.133725 | 0.0668626 | − | 0.997762i | \(-0.478701\pi\) | ||||
0.0668626 | + | 0.997762i | \(0.478701\pi\) | |||||||
\(44\) | 3.56155 | + | 6.16879i | 0.536924 | + | 0.929980i | ||||
\(45\) | 0.280776 | − | 0.486319i | 0.0418557 | − | 0.0724962i | ||||
\(46\) | 4.00000 | − | 6.92820i | 0.589768 | − | 1.02151i | ||||
\(47\) | 4.34233 | + | 7.52113i | 0.633394 | + | 1.09707i | 0.986853 | + | 0.161620i | \(0.0516720\pi\) |
−0.353459 | + | 0.935450i | \(0.614995\pi\) | |||||||
\(48\) | 12.0000 | 1.73205 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.56155 | −0.362258 | ||||||||
\(51\) | 0.342329 | + | 0.592932i | 0.0479357 | + | 0.0830270i | ||||
\(52\) | −1.00000 | + | 1.73205i | −0.138675 | + | 0.240192i | ||||
\(53\) | 2.56155 | − | 4.43674i | 0.351856 | − | 0.609433i | −0.634718 | − | 0.772744i | \(-0.718884\pi\) |
0.986575 | + | 0.163310i | \(0.0522172\pi\) | |||||||
\(54\) | −7.12311 | − | 12.3376i | −0.969332 | − | 1.67893i | ||||
\(55\) | −1.56155 | −0.210560 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −11.1231 | −1.47329 | ||||||||
\(58\) | 8.56155 | + | 14.8290i | 1.12419 | + | 1.94715i | ||||
\(59\) | 2.00000 | − | 3.46410i | 0.260378 | − | 0.450988i | −0.705965 | − | 0.708247i | \(-0.749486\pi\) |
0.966342 | + | 0.257260i | \(0.0828195\pi\) | |||||||
\(60\) | −3.56155 | + | 6.16879i | −0.459794 | + | 0.796387i | ||||
\(61\) | −7.68466 | − | 13.3102i | −0.983920 | − | 1.70420i | −0.646642 | − | 0.762794i | \(-0.723827\pi\) |
−0.337278 | − | 0.941405i | \(-0.609506\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.43845 | 0.179806 | ||||||||
\(65\) | −0.219224 | − | 0.379706i | −0.0271913 | − | 0.0470968i | ||||
\(66\) | −3.12311 | + | 5.40938i | −0.384428 | + | 0.665848i | ||||
\(67\) | −5.12311 | + | 8.87348i | −0.625887 | + | 1.08407i | 0.362482 | + | 0.931991i | \(0.381930\pi\) |
−0.988369 | + | 0.152077i | \(0.951404\pi\) | |||||||
\(68\) | 1.00000 | + | 1.73205i | 0.121268 | + | 0.210042i | ||||
\(69\) | 4.87689 | 0.587109 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | −1.84233 | − | 3.19101i | −0.217121 | − | 0.376064i | ||||
\(73\) | 6.12311 | − | 10.6055i | 0.716655 | − | 1.24128i | −0.245662 | − | 0.969355i | \(-0.579005\pi\) |
0.962318 | − | 0.271928i | \(-0.0876612\pi\) | |||||||
\(74\) | 7.68466 | − | 13.3102i | 0.893323 | − | 1.54728i | ||||
\(75\) | −0.780776 | − | 1.35234i | −0.0901563 | − | 0.156155i | ||||
\(76\) | −32.4924 | −3.72714 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.75379 | −0.198577 | ||||||||
\(79\) | 1.21922 | + | 2.11176i | 0.137173 | + | 0.237591i | 0.926426 | − | 0.376478i | \(-0.122865\pi\) |
−0.789252 | + | 0.614069i | \(0.789532\pi\) | |||||||
\(80\) | −3.84233 | + | 6.65511i | −0.429585 | + | 0.744064i | ||||
\(81\) | 3.50000 | − | 6.06218i | 0.388889 | − | 0.673575i | ||||
\(82\) | 6.56155 | + | 11.3649i | 0.724602 | + | 1.25505i | ||||
\(83\) | 4.00000 | 0.439057 | 0.219529 | − | 0.975606i | \(-0.429548\pi\) | ||||
0.219529 | + | 0.975606i | \(0.429548\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.438447 | −0.0475563 | ||||||||
\(86\) | 1.12311 | + | 1.94528i | 0.121108 | + | 0.209765i | ||||
\(87\) | −5.21922 | + | 9.03996i | −0.559560 | + | 0.969185i | ||||
\(88\) | −5.12311 | + | 8.87348i | −0.546125 | + | 0.945916i | ||||
\(89\) | 0.561553 | + | 0.972638i | 0.0595245 | + | 0.103099i | 0.894252 | − | 0.447564i | \(-0.147708\pi\) |
−0.834728 | + | 0.550663i | \(0.814375\pi\) | |||||||
\(90\) | 1.43845 | 0.151626 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 14.2462 | 1.48527 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −11.1231 | + | 19.2658i | −1.14726 | + | 1.98711i | ||||
\(95\) | 3.56155 | − | 6.16879i | 0.365408 | − | 0.632905i | ||||
\(96\) | 5.12311 | + | 8.87348i | 0.522875 | + | 0.905646i | ||||
\(97\) | 5.80776 | 0.589689 | 0.294845 | − | 0.955545i | \(-0.404732\pi\) | ||||
0.294845 | + | 0.955545i | \(0.404732\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.876894 | 0.0881312 | ||||||||
\(100\) | −2.28078 | − | 3.95042i | −0.228078 | − | 0.395042i | ||||
\(101\) | 8.12311 | − | 14.0696i | 0.808279 | − | 1.39998i | −0.105776 | − | 0.994390i | \(-0.533733\pi\) |
0.914055 | − | 0.405591i | \(-0.132934\pi\) | |||||||
\(102\) | −0.876894 | + | 1.51883i | −0.0868255 | + | 0.150386i | ||||
\(103\) | −2.78078 | − | 4.81645i | −0.273998 | − | 0.474579i | 0.695884 | − | 0.718154i | \(-0.255013\pi\) |
−0.969882 | + | 0.243576i | \(0.921680\pi\) | |||||||
\(104\) | −2.87689 | −0.282103 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.1231 | 1.27463 | ||||||||
\(107\) | −6.68466 | − | 11.5782i | −0.646230 | − | 1.11930i | −0.984016 | − | 0.178081i | \(-0.943011\pi\) |
0.337786 | − | 0.941223i | \(-0.390322\pi\) | |||||||
\(108\) | 12.6847 | − | 21.9705i | 1.22058 | − | 2.11411i | ||||
\(109\) | −2.65767 | + | 4.60322i | −0.254559 | + | 0.440909i | −0.964776 | − | 0.263074i | \(-0.915264\pi\) |
0.710217 | + | 0.703983i | \(0.248597\pi\) | |||||||
\(110\) | −2.00000 | − | 3.46410i | −0.190693 | − | 0.330289i | ||||
\(111\) | 9.36932 | 0.889296 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.0000 | −1.31701 | −0.658505 | − | 0.752577i | \(-0.728811\pi\) | ||||
−0.658505 | + | 0.752577i | \(0.728811\pi\) | |||||||
\(114\) | −14.2462 | − | 24.6752i | −1.33428 | − | 2.31104i | ||||
\(115\) | −1.56155 | + | 2.70469i | −0.145616 | + | 0.252214i | ||||
\(116\) | −15.2462 | + | 26.4072i | −1.41558 | + | 2.45185i | ||||
\(117\) | 0.123106 | + | 0.213225i | 0.0113811 | + | 0.0197127i | ||||
\(118\) | 10.2462 | 0.943240 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −10.2462 | −0.935347 | ||||||||
\(121\) | 4.28078 | + | 7.41452i | 0.389161 | + | 0.674047i | ||||
\(122\) | 19.6847 | − | 34.0948i | 1.78217 | − | 3.08680i | ||||
\(123\) | −4.00000 | + | 6.92820i | −0.360668 | + | 0.624695i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.24621 | −0.554262 | −0.277131 | − | 0.960832i | \(-0.589384\pi\) | ||||
−0.277131 | + | 0.960832i | \(0.589384\pi\) | |||||||
\(128\) | −4.71922 | − | 8.17394i | −0.417124 | − | 0.722481i | ||||
\(129\) | −0.684658 | + | 1.18586i | −0.0602808 | + | 0.104409i | ||||
\(130\) | 0.561553 | − | 0.972638i | 0.0492514 | − | 0.0853060i | ||||
\(131\) | 0.438447 | + | 0.759413i | 0.0383073 | + | 0.0663502i | 0.884543 | − | 0.466458i | \(-0.154470\pi\) |
−0.846236 | + | 0.532808i | \(0.821137\pi\) | |||||||
\(132\) | −11.1231 | −0.968142 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −26.2462 | −2.26733 | ||||||||
\(135\) | 2.78078 | + | 4.81645i | 0.239331 | + | 0.414534i | ||||
\(136\) | −1.43845 | + | 2.49146i | −0.123346 | + | 0.213641i | ||||
\(137\) | 8.56155 | − | 14.8290i | 0.731463 | − | 1.26693i | −0.224795 | − | 0.974406i | \(-0.572171\pi\) |
0.956258 | − | 0.292525i | \(-0.0944954\pi\) | |||||||
\(138\) | 6.24621 | + | 10.8188i | 0.531713 | + | 0.920954i | ||||
\(139\) | −15.1231 | −1.28273 | −0.641363 | − | 0.767238i | \(-0.721631\pi\) | ||||
−0.641363 | + | 0.767238i | \(0.721631\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13.5616 | −1.14209 | ||||||||
\(142\) | 10.2462 | + | 17.7470i | 0.859843 | + | 1.48929i | ||||
\(143\) | 0.342329 | − | 0.592932i | 0.0286270 | − | 0.0495834i | ||||
\(144\) | 2.15767 | − | 3.73720i | 0.179806 | − | 0.311433i | ||||
\(145\) | −3.34233 | − | 5.78908i | −0.277565 | − | 0.480757i | ||||
\(146\) | 31.3693 | 2.59614 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 27.3693 | 2.24974 | ||||||||
\(149\) | −6.12311 | − | 10.6055i | −0.501624 | − | 0.868839i | −0.999998 | − | 0.00187666i | \(-0.999403\pi\) |
0.498374 | − | 0.866962i | \(-0.333931\pi\) | |||||||
\(150\) | 2.00000 | − | 3.46410i | 0.163299 | − | 0.282843i | ||||
\(151\) | 3.46543 | − | 6.00231i | 0.282013 | − | 0.488461i | −0.689867 | − | 0.723936i | \(-0.742331\pi\) |
0.971880 | + | 0.235475i | \(0.0756645\pi\) | |||||||
\(152\) | −23.3693 | − | 40.4768i | −1.89550 | − | 3.28311i | ||||
\(153\) | 0.246211 | 0.0199050 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.56155 | − | 2.70469i | −0.125024 | − | 0.216548i | ||||
\(157\) | −10.1231 | + | 17.5337i | −0.807912 | + | 1.39934i | 0.106396 | + | 0.994324i | \(0.466069\pi\) |
−0.914308 | + | 0.405020i | \(0.867264\pi\) | |||||||
\(158\) | −3.12311 | + | 5.40938i | −0.248461 | + | 0.430347i | ||||
\(159\) | 4.00000 | + | 6.92820i | 0.317221 | + | 0.549442i | ||||
\(160\) | −6.56155 | −0.518736 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 17.9309 | 1.40878 | ||||||||
\(163\) | 3.56155 | + | 6.16879i | 0.278962 | + | 0.483177i | 0.971127 | − | 0.238563i | \(-0.0766762\pi\) |
−0.692165 | + | 0.721739i | \(0.743343\pi\) | |||||||
\(164\) | −11.6847 | + | 20.2384i | −0.912419 | + | 1.58036i | ||||
\(165\) | 1.21922 | − | 2.11176i | 0.0949164 | − | 0.164400i | ||||
\(166\) | 5.12311 | + | 8.87348i | 0.397630 | + | 0.688716i | ||||
\(167\) | −6.93087 | −0.536327 | −0.268163 | − | 0.963373i | \(-0.586417\pi\) | ||||
−0.268163 | + | 0.963373i | \(0.586417\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8078 | −0.985213 | ||||||||
\(170\) | −0.561553 | − | 0.972638i | −0.0430691 | − | 0.0745979i | ||||
\(171\) | −2.00000 | + | 3.46410i | −0.152944 | + | 0.264906i | ||||
\(172\) | −2.00000 | + | 3.46410i | −0.152499 | + | 0.264135i | ||||
\(173\) | 2.21922 | + | 3.84381i | 0.168724 | + | 0.292239i | 0.937972 | − | 0.346712i | \(-0.112702\pi\) |
−0.769247 | + | 0.638951i | \(0.779369\pi\) | |||||||
\(174\) | −26.7386 | −2.02705 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −12.0000 | −0.904534 | ||||||||
\(177\) | 3.12311 | + | 5.40938i | 0.234747 | + | 0.406594i | ||||
\(178\) | −1.43845 | + | 2.49146i | −0.107816 | + | 0.186743i | ||||
\(179\) | −10.0000 | + | 17.3205i | −0.747435 | + | 1.29460i | 0.201613 | + | 0.979465i | \(0.435382\pi\) |
−0.949048 | + | 0.315130i | \(0.897952\pi\) | |||||||
\(180\) | 1.28078 | + | 2.21837i | 0.0954634 | + | 0.165348i | ||||
\(181\) | −17.6155 | −1.30935 | −0.654676 | − | 0.755910i | \(-0.727195\pi\) | ||||
−0.654676 | + | 0.755910i | \(0.727195\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 24.0000 | 1.77413 | ||||||||
\(184\) | 10.2462 | + | 17.7470i | 0.755361 | + | 1.30832i | ||||
\(185\) | −3.00000 | + | 5.19615i | −0.220564 | + | 0.382029i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.342329 | − | 0.592932i | −0.0250336 | − | 0.0433595i | ||||
\(188\) | −39.6155 | −2.88926 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 18.2462 | 1.32372 | ||||||||
\(191\) | 6.78078 | + | 11.7446i | 0.490640 | + | 0.849813i | 0.999942 | − | 0.0107748i | \(-0.00342978\pi\) |
−0.509302 | + | 0.860588i | \(0.670096\pi\) | |||||||
\(192\) | −1.12311 | + | 1.94528i | −0.0810532 | + | 0.140388i | ||||
\(193\) | −9.68466 | + | 16.7743i | −0.697117 | + | 1.20744i | 0.272345 | + | 0.962200i | \(0.412201\pi\) |
−0.969462 | + | 0.245242i | \(0.921132\pi\) | |||||||
\(194\) | 7.43845 | + | 12.8838i | 0.534049 | + | 0.925001i | ||||
\(195\) | 0.684658 | 0.0490294 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.12311 | 0.0800180 | 0.0400090 | − | 0.999199i | \(-0.487261\pi\) | ||||
0.0400090 | + | 0.999199i | \(0.487261\pi\) | |||||||
\(198\) | 1.12311 | + | 1.94528i | 0.0798156 | + | 0.138245i | ||||
\(199\) | 0.876894 | − | 1.51883i | 0.0621614 | − | 0.107667i | −0.833270 | − | 0.552866i | \(-0.813534\pi\) |
0.895431 | + | 0.445200i | \(0.146867\pi\) | |||||||
\(200\) | 3.28078 | − | 5.68247i | 0.231986 | − | 0.401811i | ||||
\(201\) | −8.00000 | − | 13.8564i | −0.564276 | − | 0.977356i | ||||
\(202\) | 41.6155 | 2.92806 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −3.12311 | −0.218661 | ||||||||
\(205\) | −2.56155 | − | 4.43674i | −0.178907 | − | 0.309875i | ||||
\(206\) | 7.12311 | − | 12.3376i | 0.496290 | − | 0.859600i | ||||
\(207\) | 0.876894 | − | 1.51883i | 0.0609484 | − | 0.105566i | ||||
\(208\) | −1.68466 | − | 2.91791i | −0.116810 | − | 0.202321i | ||||
\(209\) | 11.1231 | 0.769401 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.0540 | 0.967516 | 0.483758 | − | 0.875202i | \(-0.339272\pi\) | ||||
0.483758 | + | 0.875202i | \(0.339272\pi\) | |||||||
\(212\) | 11.6847 | + | 20.2384i | 0.802506 | + | 1.38998i | ||||
\(213\) | −6.24621 | + | 10.8188i | −0.427983 | + | 0.741289i | ||||
\(214\) | 17.1231 | − | 29.6581i | 1.17051 | − | 2.02739i | ||||
\(215\) | −0.438447 | − | 0.759413i | −0.0299018 | − | 0.0517915i | ||||
\(216\) | 36.4924 | 2.48299 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −13.6155 | −0.922160 | ||||||||
\(219\) | 9.56155 | + | 16.5611i | 0.646110 | + | 1.11910i | ||||
\(220\) | 3.56155 | − | 6.16879i | 0.240120 | − | 0.415900i | ||||
\(221\) | 0.0961180 | − | 0.166481i | 0.00646559 | − | 0.0111987i | ||||
\(222\) | 12.0000 | + | 20.7846i | 0.805387 | + | 1.39497i | ||||
\(223\) | −2.43845 | −0.163291 | −0.0816453 | − | 0.996661i | \(-0.526017\pi\) | ||||
−0.0816453 | + | 0.996661i | \(0.526017\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.561553 | −0.0374369 | ||||||||
\(226\) | −17.9309 | − | 31.0572i | −1.19274 | − | 2.06589i | ||||
\(227\) | −5.65767 | + | 9.79937i | −0.375513 | + | 0.650407i | −0.990404 | − | 0.138205i | \(-0.955867\pi\) |
0.614891 | + | 0.788612i | \(0.289200\pi\) | |||||||
\(228\) | 25.3693 | − | 43.9409i | 1.68012 | − | 2.91006i | ||||
\(229\) | −5.43845 | − | 9.41967i | −0.359383 | − | 0.622469i | 0.628475 | − | 0.777830i | \(-0.283679\pi\) |
−0.987858 | + | 0.155361i | \(0.950346\pi\) | |||||||
\(230\) | −8.00000 | −0.527504 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −43.8617 | −2.87966 | ||||||||
\(233\) | −2.56155 | − | 4.43674i | −0.167813 | − | 0.290660i | 0.769838 | − | 0.638240i | \(-0.220337\pi\) |
−0.937651 | + | 0.347579i | \(0.887004\pi\) | |||||||
\(234\) | −0.315342 | + | 0.546188i | −0.0206145 | + | 0.0357054i | ||||
\(235\) | 4.34233 | − | 7.52113i | 0.283262 | − | 0.490625i | ||||
\(236\) | 9.12311 | + | 15.8017i | 0.593864 | + | 1.02860i | ||||
\(237\) | −3.80776 | −0.247341 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.8078 | 1.28126 | 0.640629 | − | 0.767851i | \(-0.278674\pi\) | ||||
0.640629 | + | 0.767851i | \(0.278674\pi\) | |||||||
\(240\) | −6.00000 | − | 10.3923i | −0.387298 | − | 0.670820i | ||||
\(241\) | 2.12311 | − | 3.67733i | 0.136761 | − | 0.236877i | −0.789508 | − | 0.613741i | \(-0.789664\pi\) |
0.926269 | + | 0.376863i | \(0.122997\pi\) | |||||||
\(242\) | −10.9654 | + | 18.9927i | −0.704885 | + | 1.22090i | ||||
\(243\) | −2.87689 | − | 4.98293i | −0.184553 | − | 0.319655i | ||||
\(244\) | 70.1080 | 4.48820 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −20.4924 | −1.30655 | ||||||||
\(247\) | 1.56155 | + | 2.70469i | 0.0993592 | + | 0.172095i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.12311 | + | 5.40938i | −0.197919 | + | 0.342805i | ||||
\(250\) | 1.28078 | + | 2.21837i | 0.0810034 | + | 0.140302i | ||||
\(251\) | −8.87689 | −0.560305 | −0.280152 | − | 0.959956i | \(-0.590385\pi\) | ||||
−0.280152 | + | 0.959956i | \(0.590385\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.87689 | −0.306608 | ||||||||
\(254\) | −8.00000 | − | 13.8564i | −0.501965 | − | 0.869428i | ||||
\(255\) | 0.342329 | − | 0.592932i | 0.0214375 | − | 0.0371308i | ||||
\(256\) | 13.5270 | − | 23.4294i | 0.845437 | − | 1.46434i | ||||
\(257\) | 5.24621 | + | 9.08670i | 0.327250 | + | 0.566813i | 0.981965 | − | 0.189062i | \(-0.0605449\pi\) |
−0.654715 | + | 0.755875i | \(0.727212\pi\) | |||||||
\(258\) | −3.50758 | −0.218372 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.00000 | 0.124035 | ||||||||
\(261\) | 1.87689 | + | 3.25088i | 0.116177 | + | 0.201224i | ||||
\(262\) | −1.12311 | + | 1.94528i | −0.0693857 | + | 0.120180i | ||||
\(263\) | 6.43845 | − | 11.1517i | 0.397012 | − | 0.687644i | −0.596344 | − | 0.802729i | \(-0.703381\pi\) |
0.993356 | + | 0.115085i | \(0.0367139\pi\) | |||||||
\(264\) | −8.00000 | − | 13.8564i | −0.492366 | − | 0.852803i | ||||
\(265\) | −5.12311 | −0.314710 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.75379 | −0.107330 | ||||||||
\(268\) | −23.3693 | − | 40.4768i | −1.42751 | − | 2.47252i | ||||
\(269\) | 10.3693 | − | 17.9602i | 0.632228 | − | 1.09505i | −0.354867 | − | 0.934917i | \(-0.615474\pi\) |
0.987095 | − | 0.160135i | \(-0.0511929\pi\) | |||||||
\(270\) | −7.12311 | + | 12.3376i | −0.433498 | + | 0.750841i | ||||
\(271\) | 8.00000 | + | 13.8564i | 0.485965 | + | 0.841717i | 0.999870 | − | 0.0161307i | \(-0.00513477\pi\) |
−0.513905 | + | 0.857847i | \(0.671801\pi\) | |||||||
\(272\) | −3.36932 | −0.204295 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 43.8617 | 2.64978 | ||||||||
\(275\) | 0.780776 | + | 1.35234i | 0.0470826 | + | 0.0815494i | ||||
\(276\) | −11.1231 | + | 19.2658i | −0.669532 | + | 1.15966i | ||||
\(277\) | 0.123106 | − | 0.213225i | 0.00739670 | − | 0.0128115i | −0.862303 | − | 0.506392i | \(-0.830979\pi\) |
0.869700 | + | 0.493581i | \(0.164312\pi\) | |||||||
\(278\) | −19.3693 | − | 33.5486i | −1.16169 | − | 2.01211i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.4384 | 0.742016 | 0.371008 | − | 0.928630i | \(-0.379012\pi\) | ||||
0.371008 | + | 0.928630i | \(0.379012\pi\) | |||||||
\(282\) | −17.3693 | − | 30.0845i | −1.03433 | − | 1.79151i | ||||
\(283\) | 5.65767 | − | 9.79937i | 0.336314 | − | 0.582512i | −0.647423 | − | 0.762131i | \(-0.724153\pi\) |
0.983736 | + | 0.179619i | \(0.0574865\pi\) | |||||||
\(284\) | −18.2462 | + | 31.6034i | −1.08271 | + | 1.87531i | ||||
\(285\) | 5.56155 | + | 9.63289i | 0.329438 | + | 0.570603i | ||||
\(286\) | 1.75379 | 0.103704 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 3.68466 | 0.217121 | ||||||||
\(289\) | 8.40388 | + | 14.5560i | 0.494346 | + | 0.856232i | ||||
\(290\) | 8.56155 | − | 14.8290i | 0.502752 | − | 0.870791i | ||||
\(291\) | −4.53457 | + | 7.85410i | −0.265821 | + | 0.460415i | ||||
\(292\) | 27.9309 | + | 48.3777i | 1.63453 | + | 2.83109i | ||||
\(293\) | −2.68466 | −0.156839 | −0.0784197 | − | 0.996920i | \(-0.524987\pi\) | ||||
−0.0784197 | + | 0.996920i | \(0.524987\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.00000 | −0.232889 | ||||||||
\(296\) | 19.6847 | + | 34.0948i | 1.14415 | + | 1.98172i | ||||
\(297\) | −4.34233 | + | 7.52113i | −0.251967 | + | 0.436421i | ||||
\(298\) | 15.6847 | − | 27.1666i | 0.908588 | − | 1.57372i | ||||
\(299\) | −0.684658 | − | 1.18586i | −0.0395948 | − | 0.0685802i | ||||
\(300\) | 7.12311 | 0.411253 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 17.7538 | 1.02162 | ||||||||
\(303\) | 12.6847 | + | 21.9705i | 0.728715 | + | 1.26217i | ||||
\(304\) | 27.3693 | − | 47.4050i | 1.56974 | − | 2.71887i | ||||
\(305\) | −7.68466 | + | 13.3102i | −0.440022 | + | 0.762141i | ||||
\(306\) | 0.315342 | + | 0.546188i | 0.0180269 | + | 0.0312235i | ||||
\(307\) | −19.3153 | −1.10238 | −0.551192 | − | 0.834378i | \(-0.685827\pi\) | ||||
−0.551192 | + | 0.834378i | \(0.685827\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.68466 | 0.494053 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.8078 | + | 27.3799i | −0.896376 | + | 1.55257i | −0.0642838 | + | 0.997932i | \(0.520476\pi\) |
−0.832092 | + | 0.554637i | \(0.812857\pi\) | |||||||
\(312\) | 2.24621 | − | 3.89055i | 0.127167 | − | 0.220259i | ||||
\(313\) | 11.1501 | + | 19.3125i | 0.630241 | + | 1.09161i | 0.987502 | + | 0.157604i | \(0.0503771\pi\) |
−0.357262 | + | 0.934004i | \(0.616290\pi\) | |||||||
\(314\) | −51.8617 | −2.92673 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.1231 | −0.625724 | ||||||||
\(317\) | −5.24621 | − | 9.08670i | −0.294657 | − | 0.510360i | 0.680248 | − | 0.732982i | \(-0.261872\pi\) |
−0.974905 | + | 0.222622i | \(0.928539\pi\) | |||||||
\(318\) | −10.2462 | + | 17.7470i | −0.574579 | + | 0.995200i | ||||
\(319\) | 5.21922 | − | 9.03996i | 0.292220 | − | 0.506141i | ||||
\(320\) | −0.719224 | − | 1.24573i | −0.0402058 | − | 0.0696385i | ||||
\(321\) | 20.8769 | 1.16523 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.12311 | 0.173774 | ||||||||
\(324\) | 15.9654 | + | 27.6529i | 0.886969 | + | 1.53627i | ||||
\(325\) | −0.219224 | + | 0.379706i | −0.0121603 | + | 0.0210623i | ||||
\(326\) | −9.12311 | + | 15.8017i | −0.505282 | + | 0.875174i | ||||
\(327\) | −4.15009 | − | 7.18817i | −0.229501 | − | 0.397507i | ||||
\(328\) | −33.6155 | −1.85611 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 6.24621 | 0.343843 | ||||||||
\(331\) | −6.00000 | − | 10.3923i | −0.329790 | − | 0.571213i | 0.652680 | − | 0.757634i | \(-0.273645\pi\) |
−0.982470 | + | 0.186421i | \(0.940311\pi\) | |||||||
\(332\) | −9.12311 | + | 15.8017i | −0.500695 | + | 0.867230i | ||||
\(333\) | 1.68466 | − | 2.91791i | 0.0923187 | − | 0.159901i | ||||
\(334\) | −8.87689 | − | 15.3752i | −0.485722 | − | 0.841295i | ||||
\(335\) | 10.2462 | 0.559810 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.50758 | −0.0821230 | −0.0410615 | − | 0.999157i | \(-0.513074\pi\) | ||||
−0.0410615 | + | 0.999157i | \(0.513074\pi\) | |||||||
\(338\) | −16.4039 | − | 28.4124i | −0.892254 | − | 1.54543i | ||||
\(339\) | 10.9309 | − | 18.9328i | 0.593683 | − | 1.02829i | ||||
\(340\) | 1.00000 | − | 1.73205i | 0.0542326 | − | 0.0939336i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −10.2462 | −0.554052 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −5.75379 | −0.310223 | ||||||||
\(345\) | −2.43845 | − | 4.22351i | −0.131282 | − | 0.227386i | ||||
\(346\) | −5.68466 | + | 9.84612i | −0.305609 | + | 0.529331i | ||||
\(347\) | −3.56155 | + | 6.16879i | −0.191194 | + | 0.331158i | −0.945646 | − | 0.325197i | \(-0.894569\pi\) |
0.754452 | + | 0.656355i | \(0.227903\pi\) | |||||||
\(348\) | −23.8078 | − | 41.2363i | −1.27623 | − | 2.21050i | ||||
\(349\) | 10.4924 | 0.561646 | 0.280823 | − | 0.959760i | \(-0.409393\pi\) | ||||
0.280823 | + | 0.959760i | \(0.409393\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.43845 | −0.130155 | ||||||||
\(352\) | −5.12311 | − | 8.87348i | −0.273062 | − | 0.472958i | ||||
\(353\) | −2.90388 | + | 5.02967i | −0.154558 | + | 0.267702i | −0.932898 | − | 0.360141i | \(-0.882729\pi\) |
0.778340 | + | 0.627843i | \(0.216062\pi\) | |||||||
\(354\) | −8.00000 | + | 13.8564i | −0.425195 | + | 0.736460i | ||||
\(355\) | −4.00000 | − | 6.92820i | −0.212298 | − | 0.367711i | ||||
\(356\) | −5.12311 | −0.271524 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −51.2311 | −2.70765 | ||||||||
\(359\) | −4.00000 | − | 6.92820i | −0.211112 | − | 0.365657i | 0.740951 | − | 0.671559i | \(-0.234375\pi\) |
−0.952063 | + | 0.305903i | \(0.901042\pi\) | |||||||
\(360\) | −1.84233 | + | 3.19101i | −0.0970993 | + | 0.168181i | ||||
\(361\) | −15.8693 | + | 27.4865i | −0.835227 | + | 1.44666i | ||||
\(362\) | −22.5616 | − | 39.0778i | −1.18581 | − | 2.05388i | ||||
\(363\) | −13.3693 | −0.701707 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.2462 | −0.640996 | ||||||||
\(366\) | 30.7386 | + | 53.2409i | 1.60673 | + | 2.78295i | ||||
\(367\) | 4.34233 | − | 7.52113i | 0.226668 | − | 0.392600i | −0.730151 | − | 0.683286i | \(-0.760550\pi\) |
0.956818 | + | 0.290686i | \(0.0938835\pi\) | |||||||
\(368\) | −12.0000 | + | 20.7846i | −0.625543 | + | 1.08347i | ||||
\(369\) | 1.43845 | + | 2.49146i | 0.0748826 | + | 0.129700i | ||||
\(370\) | −15.3693 | −0.799013 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.31534 | − | 4.01029i | −0.119884 | − | 0.207645i | 0.799838 | − | 0.600216i | \(-0.204919\pi\) |
−0.919721 | + | 0.392572i | \(0.871586\pi\) | |||||||
\(374\) | 0.876894 | − | 1.51883i | 0.0453431 | − | 0.0785366i | ||||
\(375\) | −0.780776 | + | 1.35234i | −0.0403191 | + | 0.0698348i | ||||
\(376\) | −28.4924 | − | 49.3503i | −1.46938 | − | 2.54505i | ||||
\(377\) | 2.93087 | 0.150947 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.4924 | −0.847159 | −0.423579 | − | 0.905859i | \(-0.639227\pi\) | ||||
−0.423579 | + | 0.905859i | \(0.639227\pi\) | |||||||
\(380\) | 16.2462 | + | 28.1393i | 0.833413 | + | 1.44351i | ||||
\(381\) | 4.87689 | − | 8.44703i | 0.249851 | − | 0.432754i | ||||
\(382\) | −17.3693 | + | 30.0845i | −0.888692 | + | 1.53926i | ||||
\(383\) | −3.12311 | − | 5.40938i | −0.159583 | − | 0.276406i | 0.775135 | − | 0.631795i | \(-0.217682\pi\) |
−0.934718 | + | 0.355389i | \(0.884348\pi\) | |||||||
\(384\) | 14.7386 | 0.752128 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −49.6155 | −2.52536 | ||||||||
\(387\) | 0.246211 | + | 0.426450i | 0.0125156 | + | 0.0216777i | ||||
\(388\) | −13.2462 | + | 22.9431i | −0.672474 | + | 1.16476i | ||||
\(389\) | 12.4654 | − | 21.5908i | 0.632023 | − | 1.09470i | −0.355115 | − | 0.934823i | \(-0.615558\pi\) |
0.987138 | − | 0.159873i | \(-0.0511084\pi\) | |||||||
\(390\) | 0.876894 | + | 1.51883i | 0.0444033 | + | 0.0769087i | ||||
\(391\) | −1.36932 | −0.0692493 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.36932 | −0.0690729 | ||||||||
\(394\) | 1.43845 | + | 2.49146i | 0.0724679 | + | 0.125518i | ||||
\(395\) | 1.21922 | − | 2.11176i | 0.0613458 | − | 0.106254i | ||||
\(396\) | −2.00000 | + | 3.46410i | −0.100504 | + | 0.174078i | ||||
\(397\) | −13.7808 | − | 23.8690i | −0.691637 | − | 1.19795i | −0.971301 | − | 0.237853i | \(-0.923556\pi\) |
0.279664 | − | 0.960098i | \(-0.409777\pi\) | |||||||
\(398\) | 4.49242 | 0.225185 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.68466 | 0.384233 | ||||||||
\(401\) | −15.7808 | − | 27.3331i | −0.788054 | − | 1.36495i | −0.927157 | − | 0.374672i | \(-0.877755\pi\) |
0.139103 | − | 0.990278i | \(-0.455578\pi\) | |||||||
\(402\) | 20.4924 | − | 35.4939i | 1.02207 | − | 1.77028i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 37.0540 | + | 64.1794i | 1.84350 | + | 3.19304i | ||||
\(405\) | −7.00000 | −0.347833 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.36932 | −0.464420 | ||||||||
\(408\) | −2.24621 | − | 3.89055i | −0.111204 | − | 0.192611i | ||||
\(409\) | −3.24621 | + | 5.62260i | −0.160515 | + | 0.278020i | −0.935053 | − | 0.354507i | \(-0.884649\pi\) |
0.774539 | + | 0.632527i | \(0.217982\pi\) | |||||||
\(410\) | 6.56155 | − | 11.3649i | 0.324052 | − | 0.561275i | ||||
\(411\) | 13.3693 | + | 23.1563i | 0.659460 | + | 1.14222i | ||||
\(412\) | 25.3693 | 1.24986 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 4.49242 | 0.220791 | ||||||||
\(415\) | −2.00000 | − | 3.46410i | −0.0981761 | − | 0.170046i | ||||
\(416\) | 1.43845 | − | 2.49146i | 0.0705257 | − | 0.122154i | ||||
\(417\) | 11.8078 | − | 20.4516i | 0.578229 | − | 1.00152i | ||||
\(418\) | 14.2462 | + | 24.6752i | 0.696805 | + | 1.20690i | ||||
\(419\) | 26.2462 | 1.28221 | 0.641106 | − | 0.767453i | \(-0.278476\pi\) | ||||
0.641106 | + | 0.767453i | \(0.278476\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.68466 | −0.130842 | −0.0654211 | − | 0.997858i | \(-0.520839\pi\) | ||||
−0.0654211 | + | 0.997858i | \(0.520839\pi\) | |||||||
\(422\) | 18.0000 | + | 31.1769i | 0.876226 | + | 1.51767i | ||||
\(423\) | −2.43845 | + | 4.22351i | −0.118561 | + | 0.205354i | ||||
\(424\) | −16.8078 | + | 29.1119i | −0.816257 | + | 1.41380i | ||||
\(425\) | 0.219224 | + | 0.379706i | 0.0106339 | + | 0.0184185i | ||||
\(426\) | −32.0000 | −1.55041 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 60.9848 | 2.94781 | ||||||||
\(429\) | 0.534565 | + | 0.925894i | 0.0258090 | + | 0.0447026i | ||||
\(430\) | 1.12311 | − | 1.94528i | 0.0541610 | − | 0.0938095i | ||||
\(431\) | 9.90388 | − | 17.1540i | 0.477053 | − | 0.826280i | −0.522601 | − | 0.852577i | \(-0.675038\pi\) |
0.999654 | + | 0.0262970i | \(0.00837156\pi\) | |||||||
\(432\) | 21.3693 | + | 37.0127i | 1.02813 | + | 1.78078i | ||||
\(433\) | 8.24621 | 0.396288 | 0.198144 | − | 0.980173i | \(-0.436509\pi\) | ||||
0.198144 | + | 0.980173i | \(0.436509\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.4384 | 0.500485 | ||||||||
\(436\) | −12.1231 | − | 20.9978i | −0.580591 | − | 1.00561i | ||||
\(437\) | 11.1231 | − | 19.2658i | 0.532090 | − | 0.921607i | ||||
\(438\) | −24.4924 | + | 42.4221i | −1.17029 | + | 2.02701i | ||||
\(439\) | −4.68466 | − | 8.11407i | −0.223587 | − | 0.387263i | 0.732308 | − | 0.680974i | \(-0.238443\pi\) |
−0.955894 | + | 0.293710i | \(0.905110\pi\) | |||||||
\(440\) | 10.2462 | 0.488469 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.492423 | 0.0234221 | ||||||||
\(443\) | 1.31534 | + | 2.27824i | 0.0624938 | + | 0.108242i | 0.895580 | − | 0.444901i | \(-0.146761\pi\) |
−0.833086 | + | 0.553144i | \(0.813428\pi\) | |||||||
\(444\) | −21.3693 | + | 37.0127i | −1.01414 | + | 1.75655i | ||||
\(445\) | 0.561553 | − | 0.972638i | 0.0266202 | − | 0.0461075i | ||||
\(446\) | −3.12311 | − | 5.40938i | −0.147883 | − | 0.256141i | ||||
\(447\) | 19.1231 | 0.904492 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.80776 | −0.0853137 | −0.0426568 | − | 0.999090i | \(-0.513582\pi\) | ||||
−0.0426568 | + | 0.999090i | \(0.513582\pi\) | |||||||
\(450\) | −0.719224 | − | 1.24573i | −0.0339045 | − | 0.0587244i | ||||
\(451\) | 4.00000 | − | 6.92820i | 0.188353 | − | 0.326236i | ||||
\(452\) | 31.9309 | − | 55.3059i | 1.50190 | − | 2.60137i | ||||
\(453\) | 5.41146 | + | 9.37292i | 0.254253 | + | 0.440378i | ||||
\(454\) | −28.9848 | −1.36033 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 72.9848 | 3.41783 | ||||||||
\(457\) | 8.56155 | + | 14.8290i | 0.400493 | + | 0.693673i | 0.993785 | − | 0.111313i | \(-0.0355057\pi\) |
−0.593293 | + | 0.804987i | \(0.702172\pi\) | |||||||
\(458\) | 13.9309 | − | 24.1290i | 0.650947 | − | 1.12747i | ||||
\(459\) | −1.21922 | + | 2.11176i | −0.0569085 | + | 0.0985684i | ||||
\(460\) | −7.12311 | − | 12.3376i | −0.332117 | − | 0.575243i | ||||
\(461\) | −13.1231 | −0.611204 | −0.305602 | − | 0.952159i | \(-0.598858\pi\) | ||||
−0.305602 | + | 0.952159i | \(0.598858\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.4924 | 0.580572 | 0.290286 | − | 0.956940i | \(-0.406250\pi\) | ||||
0.290286 | + | 0.956940i | \(0.406250\pi\) | |||||||
\(464\) | −25.6847 | − | 44.4871i | −1.19238 | − | 2.06526i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.56155 | − | 11.3649i | 0.303958 | − | 0.526471i | ||||
\(467\) | −11.2192 | − | 19.4323i | −0.519164 | − | 0.899218i | −0.999752 | − | 0.0222716i | \(-0.992910\pi\) |
0.480588 | − | 0.876946i | \(-0.340423\pi\) | |||||||
\(468\) | −1.12311 | −0.0519156 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 22.2462 | 1.02614 | ||||||||
\(471\) | −15.8078 | − | 27.3799i | −0.728383 | − | 1.26160i | ||||
\(472\) | −13.1231 | + | 22.7299i | −0.604040 | + | 1.04623i | ||||
\(473\) | 0.684658 | − | 1.18586i | 0.0314806 | − | 0.0545260i | ||||
\(474\) | −4.87689 | − | 8.44703i | −0.224003 | − | 0.387985i | ||||
\(475\) | −7.12311 | −0.326831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.87689 | 0.131724 | ||||||||
\(478\) | 25.3693 | + | 43.9409i | 1.16037 | + | 2.00981i | ||||
\(479\) | −2.43845 | + | 4.22351i | −0.111415 | + | 0.192977i | −0.916341 | − | 0.400398i | \(-0.868872\pi\) |
0.804926 | + | 0.593376i | \(0.202205\pi\) | |||||||
\(480\) | 5.12311 | − | 8.87348i | 0.233837 | − | 0.405017i | ||||
\(481\) | −1.31534 | − | 2.27824i | −0.0599744 | − | 0.103879i | ||||
\(482\) | 10.8769 | 0.495429 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −39.0540 | −1.77518 | ||||||||
\(485\) | −2.90388 | − | 5.02967i | −0.131858 | − | 0.228386i | ||||
\(486\) | 7.36932 | − | 12.7640i | 0.334279 | − | 0.578988i | ||||
\(487\) | 1.56155 | − | 2.70469i | 0.0707607 | − | 0.122561i | −0.828474 | − | 0.560027i | \(-0.810791\pi\) |
0.899235 | + | 0.437466i | \(0.144124\pi\) | |||||||
\(488\) | 50.4233 | + | 87.3357i | 2.28256 | + | 3.95350i | ||||
\(489\) | −11.1231 | −0.503004 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −41.1771 | −1.85830 | −0.929148 | − | 0.369708i | \(-0.879458\pi\) | ||||
−0.929148 | + | 0.369708i | \(0.879458\pi\) | |||||||
\(492\) | −18.2462 | − | 31.6034i | −0.822603 | − | 1.42479i | ||||
\(493\) | 1.46543 | − | 2.53821i | 0.0659999 | − | 0.114315i | ||||
\(494\) | −4.00000 | + | 6.92820i | −0.179969 | + | 0.311715i | ||||
\(495\) | −0.438447 | − | 0.759413i | −0.0197067 | − | 0.0341331i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −16.0000 | −0.716977 | ||||||||
\(499\) | −20.5885 | − | 35.6604i | −0.921670 | − | 1.59638i | −0.796832 | − | 0.604202i | \(-0.793492\pi\) |
−0.124838 | − | 0.992177i | \(-0.539841\pi\) | |||||||
\(500\) | −2.28078 | + | 3.95042i | −0.101999 | + | 0.176668i | ||||
\(501\) | 5.41146 | − | 9.37292i | 0.241766 | − | 0.418751i | ||||
\(502\) | −11.3693 | − | 19.6922i | −0.507437 | − | 0.878907i | ||||
\(503\) | 38.9309 | 1.73584 | 0.867921 | − | 0.496703i | \(-0.165456\pi\) | ||||
0.867921 | + | 0.496703i | \(0.165456\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.2462 | −0.722947 | ||||||||
\(506\) | −6.24621 | − | 10.8188i | −0.277678 | − | 0.480952i | ||||
\(507\) | 10.0000 | − | 17.3205i | 0.444116 | − | 0.769231i | ||||
\(508\) | 14.2462 | − | 24.6752i | 0.632073 | − | 1.09478i | ||||
\(509\) | 5.87689 | + | 10.1791i | 0.260489 | + | 0.451180i | 0.966372 | − | 0.257149i | \(-0.0827830\pi\) |
−0.705883 | + | 0.708328i | \(0.749450\pi\) | |||||||
\(510\) | 1.75379 | 0.0776591 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 50.4233 | 2.22842 | ||||||||
\(513\) | −19.8078 | − | 34.3081i | −0.874534 | − | 1.51474i | ||||
\(514\) | −13.4384 | + | 23.2761i | −0.592744 | + | 1.02666i | ||||
\(515\) | −2.78078 | + | 4.81645i | −0.122536 | + | 0.212238i | ||||
\(516\) | −3.12311 | − | 5.40938i | −0.137487 | − | 0.238135i | ||||
\(517\) | 13.5616 | 0.596436 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.93087 | −0.304231 | ||||||||
\(520\) | 1.43845 | + | 2.49146i | 0.0630801 | + | 0.109258i | ||||
\(521\) | −5.00000 | + | 8.66025i | −0.219054 | + | 0.379413i | −0.954519 | − | 0.298150i | \(-0.903630\pi\) |
0.735465 | + | 0.677563i | \(0.236964\pi\) | |||||||
\(522\) | −4.80776 | + | 8.32729i | −0.210430 | + | 0.364476i | ||||
\(523\) | −20.2462 | − | 35.0675i | −0.885305 | − | 1.53339i | −0.845364 | − | 0.534191i | \(-0.820616\pi\) |
−0.0399413 | − | 0.999202i | \(-0.512717\pi\) | |||||||
\(524\) | −4.00000 | −0.174741 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 32.9848 | 1.43821 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 9.36932 | − | 16.2281i | 0.407747 | − | 0.706239i | ||||
\(529\) | 6.62311 | − | 11.4716i | 0.287961 | − | 0.498763i | ||||
\(530\) | −6.56155 | − | 11.3649i | −0.285016 | − | 0.493662i | ||||
\(531\) | 2.24621 | 0.0974773 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.24621 | 0.0972942 | ||||||||
\(534\) | −2.24621 | − | 3.89055i | −0.0972031 | − | 0.168361i | ||||
\(535\) | −6.68466 | + | 11.5782i | −0.289003 | + | 0.500568i | ||||
\(536\) | 33.6155 | − | 58.2238i | 1.45197 | − | 2.51489i | ||||
\(537\) | −15.6155 | − | 27.0469i | −0.673860 | − | 1.16716i | ||||
\(538\) | 53.1231 | 2.29030 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −25.3693 | −1.09172 | ||||||||
\(541\) | 18.9039 | + | 32.7425i | 0.812741 | + | 1.40771i | 0.910938 | + | 0.412542i | \(0.135359\pi\) |
−0.0981971 | + | 0.995167i | \(0.531308\pi\) | |||||||
\(542\) | −20.4924 | + | 35.4939i | −0.880225 | + | 1.52459i | ||||
\(543\) | 13.7538 | − | 23.8223i | 0.590232 | − | 1.02231i | ||||
\(544\) | −1.43845 | − | 2.49146i | −0.0616729 | − | 0.106821i | ||||
\(545\) | 5.31534 | 0.227684 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.24621 | −0.0960411 | −0.0480205 | − | 0.998846i | \(-0.515291\pi\) | ||||
−0.0480205 | + | 0.998846i | \(0.515291\pi\) | |||||||
\(548\) | 39.0540 | + | 67.6435i | 1.66830 | + | 2.88959i | ||||
\(549\) | 4.31534 | − | 7.47439i | 0.184174 | − | 0.318999i | ||||
\(550\) | −2.00000 | + | 3.46410i | −0.0852803 | + | 0.147710i | ||||
\(551\) | 23.8078 | + | 41.2363i | 1.01424 | + | 1.75672i | ||||
\(552\) | −32.0000 | −1.36201 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0.630683 | 0.0267952 | ||||||||
\(555\) | −4.68466 | − | 8.11407i | −0.198853 | − | 0.344423i | ||||
\(556\) | 34.4924 | − | 59.7426i | 1.46280 | − | 2.53365i | ||||
\(557\) | 6.56155 | − | 11.3649i | 0.278022 | − | 0.481548i | −0.692871 | − | 0.721061i | \(-0.743655\pi\) |
0.970893 | + | 0.239513i | \(0.0769879\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.384472 | 0.0162614 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.06913 | 0.0451387 | ||||||||
\(562\) | 15.9309 | + | 27.5931i | 0.672003 | + | 1.16394i | ||||
\(563\) | 14.0000 | − | 24.2487i | 0.590030 | − | 1.02196i | −0.404198 | − | 0.914671i | \(-0.632449\pi\) |
0.994228 | − | 0.107290i | \(-0.0342173\pi\) | |||||||
\(564\) | 30.9309 | − | 53.5738i | 1.30242 | − | 2.25587i | ||||
\(565\) | 7.00000 | + | 12.1244i | 0.294492 | + | 0.510075i | ||||
\(566\) | 28.9848 | 1.21832 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −52.4924 | −2.20253 | ||||||||
\(569\) | 15.4924 | + | 26.8337i | 0.649476 | + | 1.12493i | 0.983248 | + | 0.182272i | \(0.0583451\pi\) |
−0.333772 | + | 0.942654i | \(0.608322\pi\) | |||||||
\(570\) | −14.2462 | + | 24.6752i | −0.596708 | + | 1.03353i | ||||
\(571\) | −20.2462 | + | 35.0675i | −0.847278 | + | 1.46753i | 0.0363509 | + | 0.999339i | \(0.488427\pi\) |
−0.883629 | + | 0.468189i | \(0.844907\pi\) | |||||||
\(572\) | 1.56155 | + | 2.70469i | 0.0652918 | + | 0.113089i | ||||
\(573\) | −21.1771 | −0.884685 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.12311 | 0.130243 | ||||||||
\(576\) | 0.403882 | + | 0.699544i | 0.0168284 | + | 0.0291477i | ||||
\(577\) | 12.0270 | − | 20.8314i | 0.500690 | − | 0.867221i | −0.499310 | − | 0.866424i | \(-0.666413\pi\) |
1.00000 | 0.000796982i | \(-0.000253687\pi\) | ||||||||
\(578\) | −21.5270 | + | 37.2858i | −0.895405 | + | 1.55089i | ||||
\(579\) | −15.1231 | − | 26.1940i | −0.628495 | − | 1.08858i | ||||
\(580\) | 30.4924 | 1.26613 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −23.2311 | −0.962958 | ||||||||
\(583\) | −4.00000 | − | 6.92820i | −0.165663 | − | 0.286937i | ||||
\(584\) | −40.1771 | + | 69.5887i | −1.66254 | + | 2.87960i | ||||
\(585\) | 0.123106 | − | 0.213225i | 0.00508979 | − | 0.00881578i | ||||
\(586\) | −3.43845 | − | 5.95557i | −0.142041 | − | 0.246022i | ||||
\(587\) | −26.2462 | −1.08330 | −0.541649 | − | 0.840605i | \(-0.682200\pi\) | ||||
−0.541649 | + | 0.840605i | \(0.682200\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −5.12311 | − | 8.87348i | −0.210915 | − | 0.365315i | ||||
\(591\) | −0.876894 | + | 1.51883i | −0.0360706 | + | 0.0624761i | ||||
\(592\) | −23.0540 | + | 39.9307i | −0.947513 | + | 1.64114i | ||||
\(593\) | 13.7808 | + | 23.8690i | 0.565909 | + | 0.980183i | 0.996965 | + | 0.0778573i | \(0.0248079\pi\) |
−0.431056 | + | 0.902325i | \(0.641859\pi\) | |||||||
\(594\) | −22.2462 | −0.912773 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 55.8617 | 2.28819 | ||||||||
\(597\) | 1.36932 | + | 2.37173i | 0.0560424 | + | 0.0970683i | ||||
\(598\) | 1.75379 | − | 3.03765i | 0.0717178 | − | 0.124219i | ||||
\(599\) | 5.90388 | − | 10.2258i | 0.241226 | − | 0.417816i | −0.719838 | − | 0.694142i | \(-0.755784\pi\) |
0.961064 | + | 0.276327i | \(0.0891171\pi\) | |||||||
\(600\) | 5.12311 | + | 8.87348i | 0.209150 | + | 0.362258i | ||||
\(601\) | 6.49242 | 0.264831 | 0.132416 | − | 0.991194i | \(-0.457727\pi\) | ||||
0.132416 | + | 0.991194i | \(0.457727\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.75379 | −0.234312 | ||||||||
\(604\) | 15.8078 | + | 27.3799i | 0.643209 | + | 1.11407i | ||||
\(605\) | 4.28078 | − | 7.41452i | 0.174038 | − | 0.301443i | ||||
\(606\) | −32.4924 | + | 56.2785i | −1.31991 | + | 2.28616i | ||||
\(607\) | 21.0270 | + | 36.4198i | 0.853459 | + | 1.47823i | 0.878067 | + | 0.478537i | \(0.158833\pi\) |
−0.0246081 | + | 0.999697i | \(0.507834\pi\) | |||||||
\(608\) | 46.7386 | 1.89550 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −39.3693 | −1.59402 | ||||||||
\(611\) | 1.90388 | + | 3.29762i | 0.0770228 | + | 0.133407i | ||||
\(612\) | −0.561553 | + | 0.972638i | −0.0226994 | + | 0.0393166i | ||||
\(613\) | −20.3693 | + | 35.2807i | −0.822709 | + | 1.42497i | 0.0809488 | + | 0.996718i | \(0.474205\pi\) |
−0.903658 | + | 0.428255i | \(0.859128\pi\) | |||||||
\(614\) | −24.7386 | − | 42.8486i | −0.998370 | − | 1.72923i | ||||
\(615\) | 8.00000 | 0.322591 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 32.2462 | 1.29818 | 0.649092 | − | 0.760710i | \(-0.275149\pi\) | ||||
0.649092 | + | 0.760710i | \(0.275149\pi\) | |||||||
\(618\) | 11.1231 | + | 19.2658i | 0.447437 | + | 0.774983i | ||||
\(619\) | −16.0540 | + | 27.8063i | −0.645264 | + | 1.11763i | 0.338977 | + | 0.940795i | \(0.389919\pi\) |
−0.984241 | + | 0.176835i | \(0.943414\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.68466 | + | 15.0423i | 0.348503 | + | 0.603625i | ||||
\(622\) | −80.9848 | −3.24720 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 5.26137 | 0.210623 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −28.5616 | + | 49.4701i | −1.14155 | + | 1.97722i | ||||
\(627\) | −8.68466 | + | 15.0423i | −0.346832 | + | 0.600730i | ||||
\(628\) | −46.1771 | − | 79.9811i | −1.84267 | − | 3.19159i | ||||
\(629\) | −2.63068 | −0.104892 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.8078 | −0.470060 | −0.235030 | − | 0.971988i | \(-0.575519\pi\) | ||||
−0.235030 | + | 0.971988i | \(0.575519\pi\) | |||||||
\(632\) | −8.00000 | − | 13.8564i | −0.318223 | − | 0.551178i | ||||
\(633\) | −10.9730 | + | 19.0058i | −0.436138 | + | 0.755413i | ||||
\(634\) | 13.4384 | − | 23.2761i | 0.533709 | − | 0.924411i | ||||
\(635\) | 3.12311 | + | 5.40938i | 0.123937 | + | 0.214665i | ||||
\(636\) | −36.4924 | −1.44702 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 26.7386 | 1.05859 | ||||||||
\(639\) | 2.24621 | + | 3.89055i | 0.0888587 | + | 0.153908i | ||||
\(640\) | −4.71922 | + | 8.17394i | −0.186544 | + | 0.323103i | ||||
\(641\) | −1.00000 | + | 1.73205i | −0.0394976 | + | 0.0684119i | −0.885098 | − | 0.465404i | \(-0.845909\pi\) |
0.845601 | + | 0.533816i | \(0.179242\pi\) | |||||||
\(642\) | 26.7386 | + | 46.3127i | 1.05529 | + | 1.82782i | ||||
\(643\) | 1.56155 | 0.0615816 | 0.0307908 | − | 0.999526i | \(-0.490197\pi\) | ||||
0.0307908 | + | 0.999526i | \(0.490197\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.36932 | 0.0539168 | ||||||||
\(646\) | 4.00000 | + | 6.92820i | 0.157378 | + | 0.272587i | ||||
\(647\) | −18.2462 | + | 31.6034i | −0.717333 | + | 1.24246i | 0.244720 | + | 0.969594i | \(0.421304\pi\) |
−0.962053 | + | 0.272863i | \(0.912029\pi\) | |||||||
\(648\) | −22.9654 | + | 39.7773i | −0.902167 | + | 1.56260i | ||||
\(649\) | −3.12311 | − | 5.40938i | −0.122593 | − | 0.212337i | ||||
\(650\) | −1.12311 | −0.0440518 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −32.4924 | −1.27250 | ||||||||
\(653\) | 16.6155 | + | 28.7789i | 0.650216 | + | 1.12621i | 0.983070 | + | 0.183229i | \(0.0586549\pi\) |
−0.332854 | + | 0.942978i | \(0.608012\pi\) | |||||||
\(654\) | 10.6307 | − | 18.4129i | 0.415693 | − | 0.720001i | ||||
\(655\) | 0.438447 | − | 0.759413i | 0.0171315 | − | 0.0296727i | ||||
\(656\) | −19.6847 | − | 34.0948i | −0.768557 | − | 1.33118i | ||||
\(657\) | 6.87689 | 0.268293 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.17708 | 0.357488 | 0.178744 | − | 0.983896i | \(-0.442797\pi\) | ||||
0.178744 | + | 0.983896i | \(0.442797\pi\) | |||||||
\(660\) | 5.56155 | + | 9.63289i | 0.216483 | + | 0.374960i | ||||
\(661\) | 2.56155 | − | 4.43674i | 0.0996329 | − | 0.172569i | −0.811900 | − | 0.583797i | \(-0.801567\pi\) |
0.911533 | + | 0.411228i | \(0.134900\pi\) | |||||||
\(662\) | 15.3693 | − | 26.6204i | 0.597345 | − | 1.03463i | ||||
\(663\) | 0.150093 | + | 0.259969i | 0.00582914 | + | 0.0100964i | ||||
\(664\) | −26.2462 | −1.01855 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.63068 | 0.334432 | ||||||||
\(667\) | −10.4384 | − | 18.0799i | −0.404178 | − | 0.700057i | ||||
\(668\) | 15.8078 | − | 27.3799i | 0.611621 | − | 1.05936i | ||||
\(669\) | 1.90388 | − | 3.29762i | 0.0736083 | − | 0.127493i | ||||
\(670\) | 13.1231 | + | 22.7299i | 0.506990 | + | 0.878132i | ||||
\(671\) | −24.0000 | −0.926510 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.8617 | 1.22818 | 0.614090 | − | 0.789236i | \(-0.289523\pi\) | ||||
0.614090 | + | 0.789236i | \(0.289523\pi\) | |||||||
\(674\) | −1.93087 | − | 3.34436i | −0.0743743 | − | 0.128820i | ||||
\(675\) | 2.78078 | − | 4.81645i | 0.107032 | − | 0.185385i | ||||
\(676\) | 29.2116 | − | 50.5961i | 1.12352 | − | 1.94600i | ||||
\(677\) | −2.46543 | − | 4.27026i | −0.0947544 | − | 0.164119i | 0.814752 | − | 0.579810i | \(-0.196873\pi\) |
−0.909506 | + | 0.415691i | \(0.863540\pi\) | |||||||
\(678\) | 56.0000 | 2.15067 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2.87689 | 0.110324 | ||||||||
\(681\) | −8.83475 | − | 15.3022i | −0.338548 | − | 0.586383i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.36932 | − | 5.83583i | 0.128923 | − | 0.223302i | −0.794336 | − | 0.607478i | \(-0.792181\pi\) |
0.923260 | + | 0.384176i | \(0.125515\pi\) | |||||||
\(684\) | −9.12311 | − | 15.8017i | −0.348831 | − | 0.604192i | ||||
\(685\) | −17.1231 | −0.654240 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.9848 | 0.648012 | ||||||||
\(688\) | −3.36932 | − | 5.83583i | −0.128454 | − | 0.222489i | ||||
\(689\) | 1.12311 | − | 1.94528i | 0.0427869 | − | 0.0741091i | ||||
\(690\) | 6.24621 | − | 10.8188i | 0.237789 | − | 0.411863i | ||||
\(691\) | 12.2462 | + | 21.2111i | 0.465868 | + | 0.806907i | 0.999240 | − | 0.0389738i | \(-0.0124089\pi\) |
−0.533372 | + | 0.845881i | \(0.679076\pi\) | |||||||
\(692\) | −20.2462 | −0.769645 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −18.2462 | −0.692617 | ||||||||
\(695\) | 7.56155 | + | 13.0970i | 0.286826 | + | 0.496797i | ||||
\(696\) | 34.2462 | − | 59.3162i | 1.29810 | − | 2.24837i | ||||
\(697\) | 1.12311 | − | 1.94528i | 0.0425407 | − | 0.0736826i | ||||
\(698\) | 13.4384 | + | 23.2761i | 0.508653 | + | 0.881012i | ||||
\(699\) | 8.00000 | 0.302588 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.9309 | 1.09270 | 0.546352 | − | 0.837556i | \(-0.316016\pi\) | ||||
0.546352 | + | 0.837556i | \(0.316016\pi\) | |||||||
\(702\) | −3.12311 | − | 5.40938i | −0.117874 | − | 0.204164i | ||||
\(703\) | 21.3693 | − | 37.0127i | 0.805959 | − | 1.39596i | ||||
\(704\) | 1.12311 | − | 1.94528i | 0.0423286 | − | 0.0733153i | ||||
\(705\) | 6.78078 | + | 11.7446i | 0.255379 | + | 0.442329i | ||||
\(706\) | −14.8769 | −0.559899 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −28.4924 | −1.07081 | ||||||||
\(709\) | −13.5885 | − | 23.5360i | −0.510328 | − | 0.883915i | −0.999928 | − | 0.0119675i | \(-0.996191\pi\) |
0.489600 | − | 0.871947i | \(-0.337143\pi\) | |||||||
\(710\) | 10.2462 | − | 17.7470i | 0.384533 | − | 0.666031i | ||||
\(711\) | −0.684658 | + | 1.18586i | −0.0256767 | + | 0.0444733i | ||||
\(712\) | −3.68466 | − | 6.38202i | −0.138088 | − | 0.239176i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.684658 | −0.0256048 | ||||||||
\(716\) | −45.6155 | − | 79.0084i | −1.70473 | − | 2.95268i | ||||
\(717\) | −15.4654 | + | 26.7869i | −0.577567 | + | 1.00038i | ||||
\(718\) | 10.2462 | − | 17.7470i | 0.382385 | − | 0.662311i | ||||
\(719\) | −4.19224 | − | 7.26117i | −0.156344 | − | 0.270796i | 0.777204 | − | 0.629249i | \(-0.216638\pi\) |
−0.933548 | + | 0.358453i | \(0.883304\pi\) | |||||||
\(720\) | −4.31534 | −0.160823 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −81.3002 | −3.02568 | ||||||||
\(723\) | 3.31534 | + | 5.74234i | 0.123299 | + | 0.213560i | ||||
\(724\) | 40.1771 | − | 69.5887i | 1.49317 | − | 2.58625i | ||||
\(725\) | −3.34233 | + | 5.78908i | −0.124131 | + | 0.215001i | ||||
\(726\) | −17.1231 | − | 29.6581i | −0.635498 | − | 1.10071i | ||||
\(727\) | 52.4924 | 1.94684 | 0.973418 | − | 0.229035i | \(-0.0735572\pi\) | ||||
0.973418 | + | 0.229035i | \(0.0735572\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.9848 | 1.11055 | ||||||||
\(730\) | −15.6847 | − | 27.1666i | −0.580515 | − | 1.00548i | ||||
\(731\) | 0.192236 | − | 0.332962i | 0.00711010 | − | 0.0123151i | ||||
\(732\) | −54.7386 | + | 94.8101i | −2.02320 | + | 3.50428i | ||||
\(733\) | −3.34233 | − | 5.78908i | −0.123452 | − | 0.213825i | 0.797675 | − | 0.603088i | \(-0.206063\pi\) |
−0.921127 | + | 0.389263i | \(0.872730\pi\) | |||||||
\(734\) | 22.2462 | 0.821123 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −20.4924 | −0.755361 | ||||||||
\(737\) | 8.00000 | + | 13.8564i | 0.294684 | + | 0.510407i | ||||
\(738\) | −3.68466 | + | 6.38202i | −0.135634 | + | 0.234925i | ||||
\(739\) | −17.4654 | + | 30.2510i | −0.642476 | + | 1.11280i | 0.342402 | + | 0.939554i | \(0.388760\pi\) |
−0.984878 | + | 0.173248i | \(0.944574\pi\) | |||||||
\(740\) | −13.6847 | − | 23.7025i | −0.503058 | − | 0.871322i | ||||
\(741\) | −4.87689 | −0.179157 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −32.9848 | −1.21010 | −0.605048 | − | 0.796189i | \(-0.706846\pi\) | ||||
−0.605048 | + | 0.796189i | \(0.706846\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.12311 | + | 10.6055i | −0.224333 | + | 0.388557i | ||||
\(746\) | 5.93087 | − | 10.2726i | 0.217145 | − | 0.376105i | ||||
\(747\) | 1.12311 | + | 1.94528i | 0.0410923 | + | 0.0711739i | ||||
\(748\) | 3.12311 | 0.114192 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −4.00000 | −0.146059 | ||||||||
\(751\) | −8.53457 | − | 14.7823i | −0.311431 | − | 0.539414i | 0.667242 | − | 0.744841i | \(-0.267475\pi\) |
−0.978672 | + | 0.205428i | \(0.934142\pi\) | |||||||
\(752\) | 33.3693 | − | 57.7974i | 1.21685 | − | 2.10765i | ||||
\(753\) | 6.93087 | − | 12.0046i | 0.252575 | − | 0.437473i | ||||
\(754\) | 3.75379 | + | 6.50175i | 0.136705 | + | 0.236780i | ||||
\(755\) | −6.93087 | −0.252240 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.3693 | 1.43090 | 0.715451 | − | 0.698663i | \(-0.246221\pi\) | ||||
0.715451 | + | 0.698663i | \(0.246221\pi\) | |||||||
\(758\) | −21.1231 | − | 36.5863i | −0.767226 | − | 1.32887i | ||||
\(759\) | 3.80776 | − | 6.59524i | 0.138213 | − | 0.239392i | ||||
\(760\) | −23.3693 | + | 40.4768i | −0.847694 | + | 1.46825i | ||||
\(761\) | −24.1231 | − | 41.7824i | −0.874462 | − | 1.51461i | −0.857335 | − | 0.514759i | \(-0.827881\pi\) |
−0.0171270 | − | 0.999853i | \(-0.505452\pi\) | |||||||
\(762\) | 24.9848 | 0.905105 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −61.8617 | −2.23808 | ||||||||
\(765\) | −0.123106 | − | 0.213225i | −0.00445089 | − | 0.00770917i | ||||
\(766\) | 8.00000 | − | 13.8564i | 0.289052 | − | 0.500652i | ||||
\(767\) | 0.876894 | − | 1.51883i | 0.0316628 | − | 0.0548416i | ||||
\(768\) | 21.1231 | + | 36.5863i | 0.762214 | + | 1.32019i | ||||
\(769\) | −42.4924 | −1.53232 | −0.766158 | − | 0.642652i | \(-0.777834\pi\) | ||||
−0.766158 | + | 0.642652i | \(0.777834\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16.3845 | −0.590072 | ||||||||
\(772\) | −44.1771 | − | 76.5169i | −1.58997 | − | 2.75391i | ||||
\(773\) | −18.4654 | + | 31.9831i | −0.664156 | + | 1.15035i | 0.315358 | + | 0.948973i | \(0.397875\pi\) |
−0.979514 | + | 0.201378i | \(0.935458\pi\) | |||||||
\(774\) | −0.630683 | + | 1.09238i | −0.0226694 | + | 0.0392646i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −38.1080 | −1.36800 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 63.8617 | 2.28955 | ||||||||
\(779\) | 18.2462 | + | 31.6034i | 0.653738 | + | 1.13231i | ||||
\(780\) | −1.56155 | + | 2.70469i | −0.0559126 | + | 0.0968434i | ||||
\(781\) | 6.24621 | − | 10.8188i | 0.223507 | − | 0.387125i | ||||
\(782\) | −1.75379 | − | 3.03765i | −0.0627154 | − | 0.108626i | ||||
\(783\) | −37.1771 | −1.32860 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.2462 | 0.722618 | ||||||||
\(786\) | −1.75379 | − | 3.03765i | −0.0625556 | − | 0.108349i | ||||
\(787\) | 24.5885 | − | 42.5886i | 0.876487 | − | 1.51812i | 0.0213164 | − | 0.999773i | \(-0.493214\pi\) |
0.855170 | − | 0.518347i | \(-0.173452\pi\) | |||||||
\(788\) | −2.56155 | + | 4.43674i | −0.0912515 | + | 0.158052i | ||||
\(789\) | 10.0540 | + | 17.4140i | 0.357931 | + | 0.619955i | ||||
\(790\) | 6.24621 | 0.222230 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −5.75379 | −0.204452 | ||||||||
\(793\) | −3.36932 | − | 5.83583i | −0.119648 | − | 0.207236i | ||||
\(794\) | 35.3002 | − | 61.1417i | 1.25276 | − | 2.16984i | ||||
\(795\) | 4.00000 | − | 6.92820i | 0.141865 | − | 0.245718i | ||||
\(796\) | 4.00000 | + | 6.92820i | 0.141776 | + | 0.245564i | ||||
\(797\) | 24.0540 | 0.852036 | 0.426018 | − | 0.904715i | \(-0.359916\pi\) | ||||
0.426018 | + | 0.904715i | \(0.359916\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.80776 | 0.134709 | ||||||||
\(800\) | 3.28078 | + | 5.68247i | 0.115993 | + | 0.200906i | ||||
\(801\) | −0.315342 | + | 0.546188i | −0.0111420 | + | 0.0192986i | ||||
\(802\) | 40.4233 | − | 70.0152i | 1.42740 | − | 2.47232i | ||||
\(803\) | −9.56155 | − | 16.5611i | −0.337420 | − | 0.584428i | ||||
\(804\) | 72.9848 | 2.57398 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.1922 | + | 28.0458i | 0.569994 | + | 0.987258i | ||||
\(808\) | −53.3002 | + | 92.3186i | −1.87509 | + | 3.24776i | ||||
\(809\) | −8.27320 | + | 14.3296i | −0.290870 | + | 0.503802i | −0.974016 | − | 0.226480i | \(-0.927278\pi\) |
0.683146 | + | 0.730282i | \(0.260611\pi\) | |||||||
\(810\) | −8.96543 | − | 15.5286i | −0.315013 | − | 0.545619i | ||||
\(811\) | 19.6155 | 0.688794 | 0.344397 | − | 0.938824i | \(-0.388083\pi\) | ||||
0.344397 | + | 0.938824i | \(0.388083\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −24.9848 | −0.876257 | ||||||||
\(814\) | −12.0000 | − | 20.7846i | −0.420600 | − | 0.728500i | ||||
\(815\) | 3.56155 | − | 6.16879i | 0.124756 | − | 0.216083i | ||||
\(816\) | 2.63068 | − | 4.55648i | 0.0920923 | − | 0.159509i | ||||
\(817\) | 3.12311 | + | 5.40938i | 0.109264 | + | 0.189250i | ||||
\(818\) | −16.6307 | −0.581478 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 23.3693 | 0.816092 | ||||||||
\(821\) | 10.7116 | + | 18.5531i | 0.373839 | + | 0.647508i | 0.990153 | − | 0.139993i | \(-0.0447079\pi\) |
−0.616314 | + | 0.787501i | \(0.711375\pi\) | |||||||
\(822\) | −34.2462 | + | 59.3162i | −1.19447 | + | 2.06889i | ||||
\(823\) | 18.2462 | − | 31.6034i | 0.636023 | − | 1.10162i | −0.350274 | − | 0.936647i | \(-0.613912\pi\) |
0.986297 | − | 0.164977i | \(-0.0527550\pi\) | |||||||
\(824\) | 18.2462 | + | 31.6034i | 0.635637 | + | 1.10096i | ||||
\(825\) | −2.43845 | −0.0848958 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.36932 | −0.186709 | −0.0933547 | − | 0.995633i | \(-0.529759\pi\) | ||||
−0.0933547 | + | 0.995633i | \(0.529759\pi\) | |||||||
\(828\) | 4.00000 | + | 6.92820i | 0.139010 | + | 0.240772i | ||||
\(829\) | −17.4384 | + | 30.2043i | −0.605662 | + | 1.04904i | 0.386284 | + | 0.922380i | \(0.373758\pi\) |
−0.991946 | + | 0.126658i | \(0.959575\pi\) | |||||||
\(830\) | 5.12311 | − | 8.87348i | 0.177826 | − | 0.308003i | ||||
\(831\) | 0.192236 | + | 0.332962i | 0.00666859 | + | 0.0115503i | ||||
\(832\) | 0.630683 | 0.0218650 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 60.4924 | 2.09468 | ||||||||
\(835\) | 3.46543 | + | 6.00231i | 0.119926 | + | 0.207718i | ||||
\(836\) | −25.3693 | + | 43.9409i | −0.877416 | + | 1.51973i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 33.6155 | + | 58.2238i | 1.16123 | + | 2.01131i | ||||
\(839\) | −28.8769 | −0.996941 | −0.498471 | − | 0.866907i | \(-0.666105\pi\) | ||||
−0.498471 | + | 0.866907i | \(0.666105\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.6847 | 0.540850 | ||||||||
\(842\) | −3.43845 | − | 5.95557i | −0.118497 | − | 0.205242i | ||||
\(843\) | −9.71165 | + | 16.8211i | −0.334487 | + | 0.579348i | ||||
\(844\) | −32.0540 | + | 55.5191i | −1.10334 | + | 1.91105i | ||||
\(845\) | 6.40388 | + | 11.0918i | 0.220300 | + | 0.381571i | ||||
\(846\) | −12.4924 | −0.429498 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −39.3693 | −1.35195 | ||||||||
\(849\) | 8.83475 | + | 15.3022i | 0.303208 | + | 0.525171i | ||||
\(850\) | −0.561553 | + | 0.972638i | −0.0192611 | + | 0.0333612i | ||||
\(851\) | −9.36932 | + | 16.2281i | −0.321176 | + | 0.556293i | ||||
\(852\) | −28.4924 | − | 49.3503i | −0.976134 | − | 1.69071i | ||||
\(853\) | −7.26137 | −0.248624 | −0.124312 | − | 0.992243i | \(-0.539672\pi\) | ||||
−0.124312 | + | 0.992243i | \(0.539672\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.00000 | 0.136797 | ||||||||
\(856\) | 43.8617 | + | 75.9708i | 1.49916 | + | 2.59663i | ||||
\(857\) | 7.87689 | − | 13.6432i | 0.269070 | − | 0.466042i | −0.699552 | − | 0.714581i | \(-0.746617\pi\) |
0.968622 | + | 0.248539i | \(0.0799505\pi\) | |||||||
\(858\) | −1.36932 | + | 2.37173i | −0.0467477 | + | 0.0809694i | ||||
\(859\) | 8.24621 | + | 14.2829i | 0.281357 | + | 0.487325i | 0.971719 | − | 0.236139i | \(-0.0758821\pi\) |
−0.690362 | + | 0.723464i | \(0.742549\pi\) | |||||||
\(860\) | 4.00000 | 0.136399 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 50.7386 | 1.72816 | ||||||||
\(863\) | 12.8769 | + | 22.3034i | 0.438335 | + | 0.759218i | 0.997561 | − | 0.0697971i | \(-0.0222352\pi\) |
−0.559227 | + | 0.829015i | \(0.688902\pi\) | |||||||
\(864\) | −18.2462 | + | 31.6034i | −0.620749 | + | 1.07517i | ||||
\(865\) | 2.21922 | − | 3.84381i | 0.0754559 | − | 0.130693i | ||||
\(866\) | 10.5616 | + | 18.2931i | 0.358896 | + | 0.621626i | ||||
\(867\) | −26.2462 | −0.891368 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.80776 | 0.129170 | ||||||||
\(870\) | 13.3693 | + | 23.1563i | 0.453262 | + | 0.785073i | ||||
\(871\) | −2.24621 | + | 3.89055i | −0.0761100 | + | 0.131826i | ||||
\(872\) | 17.4384 | − | 30.2043i | 0.590540 | − | 1.02285i | ||||
\(873\) | 1.63068 | + | 2.82443i | 0.0551903 | + | 0.0955923i | ||||
\(874\) | 56.9848 | 1.92754 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −87.2311 | −2.94726 | ||||||||
\(877\) | 20.1231 | + | 34.8542i | 0.679509 | + | 1.17694i | 0.975129 | + | 0.221638i | \(0.0711405\pi\) |
−0.295620 | + | 0.955306i | \(0.595526\pi\) | |||||||
\(878\) | 12.0000 | − | 20.7846i | 0.404980 | − | 0.701447i | ||||
\(879\) | 2.09612 | − | 3.63058i | 0.0707003 | − | 0.122457i | ||||
\(880\) | 6.00000 | + | 10.3923i | 0.202260 | + | 0.350325i | ||||
\(881\) | −11.8617 | −0.399632 | −0.199816 | − | 0.979833i | \(-0.564034\pi\) | ||||
−0.199816 | + | 0.979833i | \(0.564034\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.49242 | −0.285793 | −0.142896 | − | 0.989738i | \(-0.545642\pi\) | ||||
−0.142896 | + | 0.989738i | \(0.545642\pi\) | |||||||
\(884\) | 0.438447 | + | 0.759413i | 0.0147466 | + | 0.0255418i | ||||
\(885\) | 3.12311 | − | 5.40938i | 0.104982 | − | 0.181834i | ||||
\(886\) | −3.36932 | + | 5.83583i | −0.113194 | + | 0.196058i | ||||
\(887\) | −10.2462 | − | 17.7470i | −0.344034 | − | 0.595885i | 0.641144 | − | 0.767421i | \(-0.278460\pi\) |
−0.985178 | + | 0.171536i | \(0.945127\pi\) | |||||||
\(888\) | −61.4773 | −2.06304 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 2.87689 | 0.0964337 | ||||||||
\(891\) | −5.46543 | − | 9.46641i | −0.183099 | − | 0.317137i | ||||
\(892\) | 5.56155 | − | 9.63289i | 0.186215 | − | 0.322533i | ||||
\(893\) | −30.9309 | + | 53.5738i | −1.03506 | + | 1.79278i | ||||
\(894\) | 24.4924 | + | 42.4221i | 0.819149 | + | 1.41881i | ||||
\(895\) | 20.0000 | 0.668526 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.13826 | 0.0713944 | ||||||||
\(898\) | −2.31534 | − | 4.01029i | −0.0772639 | − | 0.133825i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 1.28078 | − | 2.21837i | 0.0426925 | − | 0.0739457i | ||||
\(901\) | −1.12311 | − | 1.94528i | −0.0374161 | − | 0.0648065i | ||||
\(902\) | 20.4924 | 0.682323 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 91.8617 | 3.05528 | ||||||||
\(905\) | 8.80776 | + | 15.2555i | 0.292780 | + | 0.507110i | ||||
\(906\) | −13.8617 | + | 24.0092i | −0.460525 | + | 0.797653i | ||||
\(907\) | 12.0540 | − | 20.8781i | 0.400246 | − | 0.693246i | −0.593510 | − | 0.804827i | \(-0.702258\pi\) |
0.993755 | + | 0.111581i | \(0.0355915\pi\) | |||||||
\(908\) | −25.8078 | − | 44.7004i | −0.856461 | − | 1.48343i | ||||
\(909\) | 9.12311 | 0.302594 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.4924 | −0.943996 | −0.471998 | − | 0.881600i | \(-0.656467\pi\) | ||||
−0.471998 | + | 0.881600i | \(0.656467\pi\) | |||||||
\(912\) | 42.7386 | + | 74.0255i | 1.41522 | + | 2.45123i | ||||
\(913\) | 3.12311 | − | 5.40938i | 0.103360 | − | 0.179024i | ||||
\(914\) | −21.9309 | + | 37.9854i | −0.725409 | + | 1.25644i | ||||
\(915\) | −12.0000 | − | 20.7846i | −0.396708 | − | 0.687118i | ||||
\(916\) | 49.6155 | 1.63934 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −6.24621 | −0.206156 | ||||||||
\(919\) | −20.1501 | − | 34.9010i | −0.664690 | − | 1.15128i | −0.979369 | − | 0.202079i | \(-0.935230\pi\) |
0.314679 | − | 0.949198i | \(-0.398103\pi\) | |||||||
\(920\) | 10.2462 | − | 17.7470i | 0.337808 | − | 0.585100i | ||||
\(921\) | 15.0810 | − | 26.1210i | 0.496935 | − | 0.860716i | ||||
\(922\) | −16.8078 | − | 29.1119i | −0.553534 | − | 0.958749i | ||||
\(923\) | 3.50758 | 0.115453 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.00000 | 0.197279 | ||||||||
\(926\) | 16.0000 | + | 27.7128i | 0.525793 | + | 0.910700i | ||||
\(927\) | 1.56155 | − | 2.70469i | 0.0512881 | − | 0.0888336i | ||||
\(928\) | 21.9309 | − | 37.9854i | 0.719916 | − | 1.24693i | ||||
\(929\) | −11.0540 | − | 19.1460i | −0.362669 | − | 0.628161i | 0.625730 | − | 0.780040i | \(-0.284801\pi\) |
−0.988399 | + | 0.151878i | \(0.951468\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 23.3693 | 0.765487 | ||||||||
\(933\) | −24.6847 | − | 42.7551i | −0.808139 | − | 1.39974i | ||||
\(934\) | 28.7386 | − | 49.7768i | 0.940357 | − | 1.62875i | ||||
\(935\) | −0.342329 | + | 0.592932i | −0.0111954 | + | 0.0193909i | ||||
\(936\) | −0.807764 | − | 1.39909i | −0.0264026 | − | 0.0457306i | ||||
\(937\) | −55.6695 | −1.81864 | −0.909322 | − | 0.416094i | \(-0.863399\pi\) | ||||
−0.909322 | + | 0.416094i | \(0.863399\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −34.8229 | −1.13640 | ||||||||
\(940\) | 19.8078 | + | 34.3081i | 0.646058 | + | 1.11901i | ||||
\(941\) | −21.9309 | + | 37.9854i | −0.714926 | + | 1.23829i | 0.248062 | + | 0.968744i | \(0.420206\pi\) |
−0.962988 | + | 0.269544i | \(0.913127\pi\) | |||||||
\(942\) | 40.4924 | − | 70.1349i | 1.31931 | − | 2.28512i | ||||
\(943\) | −8.00000 | − | 13.8564i | −0.260516 | − | 0.451227i | ||||
\(944\) | −30.7386 | −1.00046 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.50758 | 0.114041 | ||||||||
\(947\) | −2.00000 | − | 3.46410i | −0.0649913 | − | 0.112568i | 0.831699 | − | 0.555227i | \(-0.187369\pi\) |
−0.896690 | + | 0.442659i | \(0.854035\pi\) | |||||||
\(948\) | 8.68466 | − | 15.0423i | 0.282065 | − | 0.488550i | ||||
\(949\) | 2.68466 | − | 4.64996i | 0.0871477 | − | 0.150944i | ||||
\(950\) | −9.12311 | − | 15.8017i | −0.295993 | − | 0.512674i | ||||
\(951\) | 16.3845 | 0.531303 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33.1231 | −1.07296 | −0.536481 | − | 0.843912i | \(-0.680247\pi\) | ||||
−0.536481 | + | 0.843912i | \(0.680247\pi\) | |||||||
\(954\) | 3.68466 | + | 6.38202i | 0.119295 | + | 0.206625i | ||||
\(955\) | 6.78078 | − | 11.7446i | 0.219421 | − | 0.380048i | ||||
\(956\) | −45.1771 | + | 78.2490i | −1.46113 | + | 2.53075i | ||||
\(957\) | 8.15009 | + | 14.1164i | 0.263455 | + | 0.456318i | ||||
\(958\) | −12.4924 | −0.403612 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.24621 | 0.0724962 | ||||||||
\(961\) | 15.5000 | + | 26.8468i | 0.500000 | + | 0.866025i | ||||
\(962\) | 3.36932 | − | 5.83583i | 0.108631 | − | 0.188155i | ||||
\(963\) | 3.75379 | − | 6.50175i | 0.120964 | − | 0.209516i | ||||
\(964\) | 9.68466 | + | 16.7743i | 0.311922 | + | 0.540264i | ||||
\(965\) | 19.3693 | 0.623520 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −35.1231 | −1.12948 | −0.564741 | − | 0.825268i | \(-0.691024\pi\) | ||||
−0.564741 | + | 0.825268i | \(0.691024\pi\) | |||||||
\(968\) | −28.0885 | − | 48.6508i | −0.902800 | − | 1.56370i | ||||
\(969\) | −2.43845 | + | 4.22351i | −0.0783342 | + | 0.135679i | ||||
\(970\) | 7.43845 | − | 12.8838i | 0.238834 | − | 0.413673i | ||||
\(971\) | −24.7386 | − | 42.8486i | −0.793901 | − | 1.37508i | −0.923535 | − | 0.383514i | \(-0.874714\pi\) |
0.129634 | − | 0.991562i | \(-0.458620\pi\) | |||||||
\(972\) | 26.2462 | 0.841848 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 8.00000 | 0.256337 | ||||||||
\(975\) | −0.342329 | − | 0.592932i | −0.0109633 | − | 0.0189890i | ||||
\(976\) | −59.0540 | + | 102.284i | −1.89027 | + | 3.27405i | ||||
\(977\) | −16.6155 | + | 28.7789i | −0.531578 | + | 0.920720i | 0.467743 | + | 0.883865i | \(0.345067\pi\) |
−0.999321 | + | 0.0368552i | \(0.988266\pi\) | |||||||
\(978\) | −14.2462 | − | 24.6752i | −0.455544 | − | 0.789025i | ||||
\(979\) | 1.75379 | 0.0560513 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.98485 | −0.0952988 | ||||||||
\(982\) | −52.7386 | − | 91.3460i | −1.68296 | − | 2.91497i | ||||
\(983\) | −25.7116 | + | 44.5339i | −0.820074 | + | 1.42041i | 0.0855523 | + | 0.996334i | \(0.472735\pi\) |
−0.905626 | + | 0.424076i | \(0.860599\pi\) | |||||||
\(984\) | 26.2462 | − | 45.4598i | 0.836699 | − | 1.44920i | ||||
\(985\) | −0.561553 | − | 0.972638i | −0.0178926 | − | 0.0309908i | ||||
\(986\) | 7.50758 | 0.239090 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −14.2462 | −0.453232 | ||||||||
\(989\) | −1.36932 | − | 2.37173i | −0.0435417 | − | 0.0754165i | ||||
\(990\) | 1.12311 | − | 1.94528i | 0.0356946 | − | 0.0618249i | ||||
\(991\) | −6.24621 | + | 10.8188i | −0.198417 | + | 0.343669i | −0.948015 | − | 0.318224i | \(-0.896914\pi\) |
0.749598 | + | 0.661893i | \(0.230247\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.7386 | 0.594653 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.75379 | −0.0555988 | ||||||||
\(996\) | −14.2462 | − | 24.6752i | −0.451408 | − | 0.781862i | ||||
\(997\) | 1.34233 | − | 2.32498i | 0.0425120 | − | 0.0736329i | −0.843986 | − | 0.536364i | \(-0.819797\pi\) |
0.886498 | + | 0.462732i | \(0.153131\pi\) | |||||||
\(998\) | 52.7386 | − | 91.3460i | 1.66941 | − | 2.89151i | ||||
\(999\) | 16.6847 | + | 28.8987i | 0.527879 | + | 0.914314i |
(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 | 245.2.e.i.116.2 | 4 | ||
7.2 | even | 3 | inner | 245.2.e.i.226.2 | 4 | ||
7.3 | odd | 6 | 245.2.a.d.1.1 | 2 | |||
7.4 | even | 3 | 35.2.a.b.1.1 | ✓ | 2 | ||
7.5 | odd | 6 | 245.2.e.h.226.2 | 4 | |||
7.6 | odd | 2 | 245.2.e.h.116.2 | 4 | |||
21.11 | odd | 6 | 315.2.a.e.1.2 | 2 | |||
21.17 | even | 6 | 2205.2.a.x.1.2 | 2 | |||
28.3 | even | 6 | 3920.2.a.bs.1.2 | 2 | |||
28.11 | odd | 6 | 560.2.a.i.1.1 | 2 | |||
35.3 | even | 12 | 1225.2.b.f.99.4 | 4 | |||
35.4 | even | 6 | 175.2.a.f.1.2 | 2 | |||
35.17 | even | 12 | 1225.2.b.f.99.1 | 4 | |||
35.18 | odd | 12 | 175.2.b.b.99.4 | 4 | |||
35.24 | odd | 6 | 1225.2.a.s.1.2 | 2 | |||
35.32 | odd | 12 | 175.2.b.b.99.1 | 4 | |||
56.11 | odd | 6 | 2240.2.a.bd.1.2 | 2 | |||
56.53 | even | 6 | 2240.2.a.bh.1.1 | 2 | |||
77.32 | odd | 6 | 4235.2.a.m.1.2 | 2 | |||
84.11 | even | 6 | 5040.2.a.bt.1.1 | 2 | |||
91.25 | even | 6 | 5915.2.a.l.1.2 | 2 | |||
105.32 | even | 12 | 1575.2.d.e.1324.4 | 4 | |||
105.53 | even | 12 | 1575.2.d.e.1324.1 | 4 | |||
105.74 | odd | 6 | 1575.2.a.p.1.1 | 2 | |||
140.39 | odd | 6 | 2800.2.a.bi.1.2 | 2 | |||
140.67 | even | 12 | 2800.2.g.t.449.3 | 4 | |||
140.123 | even | 12 | 2800.2.g.t.449.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.2.a.b.1.1 | ✓ | 2 | 7.4 | even | 3 | ||
175.2.a.f.1.2 | 2 | 35.4 | even | 6 | |||
175.2.b.b.99.1 | 4 | 35.32 | odd | 12 | |||
175.2.b.b.99.4 | 4 | 35.18 | odd | 12 | |||
245.2.a.d.1.1 | 2 | 7.3 | odd | 6 | |||
245.2.e.h.116.2 | 4 | 7.6 | odd | 2 | |||
245.2.e.h.226.2 | 4 | 7.5 | odd | 6 | |||
245.2.e.i.116.2 | 4 | 1.1 | even | 1 | trivial | ||
245.2.e.i.226.2 | 4 | 7.2 | even | 3 | inner | ||
315.2.a.e.1.2 | 2 | 21.11 | odd | 6 | |||
560.2.a.i.1.1 | 2 | 28.11 | odd | 6 | |||
1225.2.a.s.1.2 | 2 | 35.24 | odd | 6 | |||
1225.2.b.f.99.1 | 4 | 35.17 | even | 12 | |||
1225.2.b.f.99.4 | 4 | 35.3 | even | 12 | |||
1575.2.a.p.1.1 | 2 | 105.74 | odd | 6 | |||
1575.2.d.e.1324.1 | 4 | 105.53 | even | 12 | |||
1575.2.d.e.1324.4 | 4 | 105.32 | even | 12 | |||
2205.2.a.x.1.2 | 2 | 21.17 | even | 6 | |||
2240.2.a.bd.1.2 | 2 | 56.11 | odd | 6 | |||
2240.2.a.bh.1.1 | 2 | 56.53 | even | 6 | |||
2800.2.a.bi.1.2 | 2 | 140.39 | odd | 6 | |||
2800.2.g.t.449.2 | 4 | 140.123 | even | 12 | |||
2800.2.g.t.449.3 | 4 | 140.67 | even | 12 | |||
3920.2.a.bs.1.2 | 2 | 28.3 | even | 6 | |||
4235.2.a.m.1.2 | 2 | 77.32 | odd | 6 | |||
5040.2.a.bt.1.1 | 2 | 84.11 | even | 6 | |||
5915.2.a.l.1.2 | 2 | 91.25 | even | 6 |