Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [78,3,Mod(31,78)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(78, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("78.31");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 78 = 2 \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 78.f (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.12534606201\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
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: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 31.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 78.31 |
Dual form | 78.3.f.a.73.2 |
$q$-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 \(\left(\mathbb{Z}/78\mathbb{Z}\right)^\times\).
\(n\) | \(53\) | \(67\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.00000i | 0.500000 | − | 0.500000i | ||||
\(3\) | 1.73205 | 0.577350 | ||||||||
\(4\) | − | 2.00000i | − | 0.500000i | ||||||
\(5\) | 1.26795 | − | 1.26795i | 0.253590 | − | 0.253590i | −0.568851 | − | 0.822441i | \(-0.692612\pi\) |
0.822441 | + | 0.568851i | \(0.192612\pi\) | |||||||
\(6\) | 1.73205 | − | 1.73205i | 0.288675 | − | 0.288675i | ||||
\(7\) | 0.732051 | + | 0.732051i | 0.104579 | + | 0.104579i | 0.757460 | − | 0.652881i | \(-0.226440\pi\) |
−0.652881 | + | 0.757460i | \(0.726440\pi\) | |||||||
\(8\) | −2.00000 | − | 2.00000i | −0.250000 | − | 0.250000i | ||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | − | 2.53590i | − | 0.253590i | ||||||
\(11\) | −1.73205 | − | 1.73205i | −0.157459 | − | 0.157459i | 0.623981 | − | 0.781440i | \(-0.285514\pi\) |
−0.781440 | + | 0.623981i | \(0.785514\pi\) | |||||||
\(12\) | − | 3.46410i | − | 0.288675i | ||||||
\(13\) | −3.92820 | + | 12.3923i | −0.302169 | + | 0.953254i | ||||
\(14\) | 1.46410 | 0.104579 | ||||||||
\(15\) | 2.19615 | − | 2.19615i | 0.146410 | − | 0.146410i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | − | 5.32051i | − | 0.312971i | −0.987680 | − | 0.156486i | \(-0.949984\pi\) | ||
0.987680 | − | 0.156486i | \(-0.0500165\pi\) | |||||||
\(18\) | 3.00000 | − | 3.00000i | 0.166667 | − | 0.166667i | ||||
\(19\) | −14.7321 | + | 14.7321i | −0.775371 | + | 0.775371i | −0.979040 | − | 0.203669i | \(-0.934713\pi\) |
0.203669 | + | 0.979040i | \(0.434713\pi\) | |||||||
\(20\) | −2.53590 | − | 2.53590i | −0.126795 | − | 0.126795i | ||||
\(21\) | 1.26795 | + | 1.26795i | 0.0603785 | + | 0.0603785i | ||||
\(22\) | −3.46410 | −0.157459 | ||||||||
\(23\) | − | 5.32051i | − | 0.231326i | −0.993288 | − | 0.115663i | \(-0.963101\pi\) | ||
0.993288 | − | 0.115663i | \(-0.0368993\pi\) | |||||||
\(24\) | −3.46410 | − | 3.46410i | −0.144338 | − | 0.144338i | ||||
\(25\) | 21.7846i | 0.871384i | ||||||||
\(26\) | 8.46410 | + | 16.3205i | 0.325542 | + | 0.627712i | ||||
\(27\) | 5.19615 | 0.192450 | ||||||||
\(28\) | 1.46410 | − | 1.46410i | 0.0522893 | − | 0.0522893i | ||||
\(29\) | 4.14359 | 0.142883 | 0.0714413 | − | 0.997445i | \(-0.477240\pi\) | ||||
0.0714413 | + | 0.997445i | \(0.477240\pi\) | |||||||
\(30\) | − | 4.39230i | − | 0.146410i | ||||||
\(31\) | −24.9808 | + | 24.9808i | −0.805831 | + | 0.805831i | −0.984000 | − | 0.178169i | \(-0.942983\pi\) |
0.178169 | + | 0.984000i | \(0.442983\pi\) | |||||||
\(32\) | −4.00000 | + | 4.00000i | −0.125000 | + | 0.125000i | ||||
\(33\) | −3.00000 | − | 3.00000i | −0.0909091 | − | 0.0909091i | ||||
\(34\) | −5.32051 | − | 5.32051i | −0.156486 | − | 0.156486i | ||||
\(35\) | 1.85641 | 0.0530402 | ||||||||
\(36\) | − | 6.00000i | − | 0.166667i | ||||||
\(37\) | −3.14359 | − | 3.14359i | −0.0849620 | − | 0.0849620i | 0.663349 | − | 0.748311i | \(-0.269135\pi\) |
−0.748311 | + | 0.663349i | \(0.769135\pi\) | |||||||
\(38\) | 29.4641i | 0.775371i | ||||||||
\(39\) | −6.80385 | + | 21.4641i | −0.174458 | + | 0.550362i | ||||
\(40\) | −5.07180 | −0.126795 | ||||||||
\(41\) | 44.4449 | − | 44.4449i | 1.08402 | − | 1.08402i | 0.0878910 | − | 0.996130i | \(-0.471987\pi\) |
0.996130 | − | 0.0878910i | \(-0.0280127\pi\) | |||||||
\(42\) | 2.53590 | 0.0603785 | ||||||||
\(43\) | − | 37.1769i | − | 0.864579i | −0.901735 | − | 0.432290i | \(-0.857706\pi\) | ||
0.901735 | − | 0.432290i | \(-0.142294\pi\) | |||||||
\(44\) | −3.46410 | + | 3.46410i | −0.0787296 | + | 0.0787296i | ||||
\(45\) | 3.80385 | − | 3.80385i | 0.0845299 | − | 0.0845299i | ||||
\(46\) | −5.32051 | − | 5.32051i | −0.115663 | − | 0.115663i | ||||
\(47\) | −30.8038 | − | 30.8038i | −0.655401 | − | 0.655401i | 0.298887 | − | 0.954288i | \(-0.403385\pi\) |
−0.954288 | + | 0.298887i | \(0.903385\pi\) | |||||||
\(48\) | −6.92820 | −0.144338 | ||||||||
\(49\) | − | 47.9282i | − | 0.978127i | ||||||
\(50\) | 21.7846 | + | 21.7846i | 0.435692 | + | 0.435692i | ||||
\(51\) | − | 9.21539i | − | 0.180694i | ||||||
\(52\) | 24.7846 | + | 7.85641i | 0.476627 | + | 0.151085i | ||||
\(53\) | 57.7128 | 1.08892 | 0.544460 | − | 0.838786i | \(-0.316734\pi\) | ||||
0.544460 | + | 0.838786i | \(0.316734\pi\) | |||||||
\(54\) | 5.19615 | − | 5.19615i | 0.0962250 | − | 0.0962250i | ||||
\(55\) | −4.39230 | −0.0798601 | ||||||||
\(56\) | − | 2.92820i | − | 0.0522893i | ||||||
\(57\) | −25.5167 | + | 25.5167i | −0.447661 | + | 0.447661i | ||||
\(58\) | 4.14359 | − | 4.14359i | 0.0714413 | − | 0.0714413i | ||||
\(59\) | −66.6218 | − | 66.6218i | −1.12918 | − | 1.12918i | −0.990310 | − | 0.138872i | \(-0.955652\pi\) |
−0.138872 | − | 0.990310i | \(-0.544348\pi\) | |||||||
\(60\) | −4.39230 | − | 4.39230i | −0.0732051 | − | 0.0732051i | ||||
\(61\) | 103.426 | 1.69550 | 0.847751 | − | 0.530394i | \(-0.177956\pi\) | ||||
0.847751 | + | 0.530394i | \(0.177956\pi\) | |||||||
\(62\) | 49.9615i | 0.805831i | ||||||||
\(63\) | 2.19615 | + | 2.19615i | 0.0348596 | + | 0.0348596i | ||||
\(64\) | 8.00000i | 0.125000i | ||||||||
\(65\) | 10.7321 | + | 20.6936i | 0.165108 | + | 0.318363i | ||||
\(66\) | −6.00000 | −0.0909091 | ||||||||
\(67\) | 46.6936 | − | 46.6936i | 0.696919 | − | 0.696919i | −0.266826 | − | 0.963745i | \(-0.585975\pi\) |
0.963745 | + | 0.266826i | \(0.0859748\pi\) | |||||||
\(68\) | −10.6410 | −0.156486 | ||||||||
\(69\) | − | 9.21539i | − | 0.133556i | ||||||
\(70\) | 1.85641 | − | 1.85641i | 0.0265201 | − | 0.0265201i | ||||
\(71\) | −26.9090 | + | 26.9090i | −0.379000 | + | 0.379000i | −0.870741 | − | 0.491742i | \(-0.836360\pi\) |
0.491742 | + | 0.870741i | \(0.336360\pi\) | |||||||
\(72\) | −6.00000 | − | 6.00000i | −0.0833333 | − | 0.0833333i | ||||
\(73\) | 5.67949 | + | 5.67949i | 0.0778013 | + | 0.0778013i | 0.744937 | − | 0.667135i | \(-0.232480\pi\) |
−0.667135 | + | 0.744937i | \(0.732480\pi\) | |||||||
\(74\) | −6.28719 | −0.0849620 | ||||||||
\(75\) | 37.7321i | 0.503094i | ||||||||
\(76\) | 29.4641 | + | 29.4641i | 0.387686 | + | 0.387686i | ||||
\(77\) | − | 2.53590i | − | 0.0329337i | ||||||
\(78\) | 14.6603 | + | 28.2679i | 0.187952 | + | 0.362410i | ||||
\(79\) | 4.21024 | 0.0532941 | 0.0266471 | − | 0.999645i | \(-0.491517\pi\) | ||||
0.0266471 | + | 0.999645i | \(0.491517\pi\) | |||||||
\(80\) | −5.07180 | + | 5.07180i | −0.0633975 | + | 0.0633975i | ||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | − | 88.8897i | − | 1.08402i | ||||||
\(83\) | −109.799 | + | 109.799i | −1.32288 | + | 1.32288i | −0.411438 | + | 0.911438i | \(0.634973\pi\) |
−0.911438 | + | 0.411438i | \(0.865027\pi\) | |||||||
\(84\) | 2.53590 | − | 2.53590i | 0.0301893 | − | 0.0301893i | ||||
\(85\) | −6.74613 | − | 6.74613i | −0.0793663 | − | 0.0793663i | ||||
\(86\) | −37.1769 | − | 37.1769i | −0.432290 | − | 0.432290i | ||||
\(87\) | 7.17691 | 0.0824933 | ||||||||
\(88\) | 6.92820i | 0.0787296i | ||||||||
\(89\) | −19.5167 | − | 19.5167i | −0.219288 | − | 0.219288i | 0.588910 | − | 0.808198i | \(-0.299557\pi\) |
−0.808198 | + | 0.588910i | \(0.799557\pi\) | |||||||
\(90\) | − | 7.60770i | − | 0.0845299i | ||||||
\(91\) | −11.9474 | + | 6.19615i | −0.131291 | + | 0.0680896i | ||||
\(92\) | −10.6410 | −0.115663 | ||||||||
\(93\) | −43.2679 | + | 43.2679i | −0.465247 | + | 0.465247i | ||||
\(94\) | −61.6077 | −0.655401 | ||||||||
\(95\) | 37.3590i | 0.393252i | ||||||||
\(96\) | −6.92820 | + | 6.92820i | −0.0721688 | + | 0.0721688i | ||||
\(97\) | 4.03332 | − | 4.03332i | 0.0415806 | − | 0.0415806i | −0.686011 | − | 0.727591i | \(-0.740640\pi\) |
0.727591 | + | 0.686011i | \(0.240640\pi\) | |||||||
\(98\) | −47.9282 | − | 47.9282i | −0.489063 | − | 0.489063i | ||||
\(99\) | −5.19615 | − | 5.19615i | −0.0524864 | − | 0.0524864i | ||||
\(100\) | 43.5692 | 0.435692 | ||||||||
\(101\) | 111.464i | 1.10360i | 0.833975 | + | 0.551802i | \(0.186060\pi\) | ||||
−0.833975 | + | 0.551802i | \(0.813940\pi\) | |||||||
\(102\) | −9.21539 | − | 9.21539i | −0.0903470 | − | 0.0903470i | ||||
\(103\) | 71.3205i | 0.692432i | 0.938155 | + | 0.346216i | \(0.112534\pi\) | ||||
−0.938155 | + | 0.346216i | \(0.887466\pi\) | |||||||
\(104\) | 32.6410 | − | 16.9282i | 0.313856 | − | 0.162771i | ||||
\(105\) | 3.21539 | 0.0306228 | ||||||||
\(106\) | 57.7128 | − | 57.7128i | 0.544460 | − | 0.544460i | ||||
\(107\) | −116.536 | −1.08912 | −0.544560 | − | 0.838722i | \(-0.683303\pi\) | ||||
−0.544560 | + | 0.838722i | \(0.683303\pi\) | |||||||
\(108\) | − | 10.3923i | − | 0.0962250i | ||||||
\(109\) | −109.315 | + | 109.315i | −1.00289 | + | 1.00289i | −0.00289735 | + | 0.999996i | \(0.500922\pi\) |
−0.999996 | + | 0.00289735i | \(0.999078\pi\) | |||||||
\(110\) | −4.39230 | + | 4.39230i | −0.0399300 | + | 0.0399300i | ||||
\(111\) | −5.44486 | − | 5.44486i | −0.0490528 | − | 0.0490528i | ||||
\(112\) | −2.92820 | − | 2.92820i | −0.0261447 | − | 0.0261447i | ||||
\(113\) | 148.277 | 1.31218 | 0.656092 | − | 0.754681i | \(-0.272208\pi\) | ||||
0.656092 | + | 0.754681i | \(0.272208\pi\) | |||||||
\(114\) | 51.0333i | 0.447661i | ||||||||
\(115\) | −6.74613 | − | 6.74613i | −0.0586620 | − | 0.0586620i | ||||
\(116\) | − | 8.28719i | − | 0.0714413i | ||||||
\(117\) | −11.7846 | + | 37.1769i | −0.100723 | + | 0.317751i | ||||
\(118\) | −133.244 | −1.12918 | ||||||||
\(119\) | 3.89488 | − | 3.89488i | 0.0327301 | − | 0.0327301i | ||||
\(120\) | −8.78461 | −0.0732051 | ||||||||
\(121\) | − | 115.000i | − | 0.950413i | ||||||
\(122\) | 103.426 | − | 103.426i | 0.847751 | − | 0.847751i | ||||
\(123\) | 76.9808 | − | 76.9808i | 0.625860 | − | 0.625860i | ||||
\(124\) | 49.9615 | + | 49.9615i | 0.402916 | + | 0.402916i | ||||
\(125\) | 59.3205 | + | 59.3205i | 0.474564 | + | 0.474564i | ||||
\(126\) | 4.39230 | 0.0348596 | ||||||||
\(127\) | − | 70.0385i | − | 0.551484i | −0.961232 | − | 0.275742i | \(-0.911076\pi\) | ||
0.961232 | − | 0.275742i | \(-0.0889236\pi\) | |||||||
\(128\) | 8.00000 | + | 8.00000i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | − | 64.3923i | − | 0.499165i | ||||||
\(130\) | 31.4256 | + | 9.96152i | 0.241736 | + | 0.0766271i | ||||
\(131\) | 238.890 | 1.82359 | 0.911793 | − | 0.410650i | \(-0.134698\pi\) | ||||
0.911793 | + | 0.410650i | \(0.134698\pi\) | |||||||
\(132\) | −6.00000 | + | 6.00000i | −0.0454545 | + | 0.0454545i | ||||
\(133\) | −21.5692 | −0.162175 | ||||||||
\(134\) | − | 93.3872i | − | 0.696919i | ||||||
\(135\) | 6.58846 | − | 6.58846i | 0.0488034 | − | 0.0488034i | ||||
\(136\) | −10.6410 | + | 10.6410i | −0.0782428 | + | 0.0782428i | ||||
\(137\) | −91.9474 | − | 91.9474i | −0.671149 | − | 0.671149i | 0.286832 | − | 0.957981i | \(-0.407398\pi\) |
−0.957981 | + | 0.286832i | \(0.907398\pi\) | |||||||
\(138\) | −9.21539 | − | 9.21539i | −0.0667782 | − | 0.0667782i | ||||
\(139\) | 139.138 | 1.00100 | 0.500498 | − | 0.865738i | \(-0.333150\pi\) | ||||
0.500498 | + | 0.865738i | \(0.333150\pi\) | |||||||
\(140\) | − | 3.71281i | − | 0.0265201i | ||||||
\(141\) | −53.3538 | − | 53.3538i | −0.378396 | − | 0.378396i | ||||
\(142\) | 53.8179i | 0.379000i | ||||||||
\(143\) | 28.2679 | − | 14.6603i | 0.197678 | − | 0.102519i | ||||
\(144\) | −12.0000 | −0.0833333 | ||||||||
\(145\) | 5.25387 | − | 5.25387i | 0.0362336 | − | 0.0362336i | ||||
\(146\) | 11.3590 | 0.0778013 | ||||||||
\(147\) | − | 83.0141i | − | 0.564722i | ||||||
\(148\) | −6.28719 | + | 6.28719i | −0.0424810 | + | 0.0424810i | ||||
\(149\) | 126.224 | − | 126.224i | 0.847143 | − | 0.847143i | −0.142633 | − | 0.989776i | \(-0.545557\pi\) |
0.989776 | + | 0.142633i | \(0.0455567\pi\) | |||||||
\(150\) | 37.7321 | + | 37.7321i | 0.251547 | + | 0.251547i | ||||
\(151\) | 124.406 | + | 124.406i | 0.823883 | + | 0.823883i | 0.986663 | − | 0.162779i | \(-0.0520458\pi\) |
−0.162779 | + | 0.986663i | \(0.552046\pi\) | |||||||
\(152\) | 58.9282 | 0.387686 | ||||||||
\(153\) | − | 15.9615i | − | 0.104324i | ||||||
\(154\) | −2.53590 | − | 2.53590i | −0.0164669 | − | 0.0164669i | ||||
\(155\) | 63.3487i | 0.408701i | ||||||||
\(156\) | 42.9282 | + | 13.6077i | 0.275181 | + | 0.0872288i | ||||
\(157\) | −268.785 | −1.71200 | −0.856002 | − | 0.516973i | \(-0.827059\pi\) | ||||
−0.856002 | + | 0.516973i | \(0.827059\pi\) | |||||||
\(158\) | 4.21024 | − | 4.21024i | 0.0266471 | − | 0.0266471i | ||||
\(159\) | 99.9615 | 0.628689 | ||||||||
\(160\) | 10.1436i | 0.0633975i | ||||||||
\(161\) | 3.89488 | − | 3.89488i | 0.0241918 | − | 0.0241918i | ||||
\(162\) | 9.00000 | − | 9.00000i | 0.0555556 | − | 0.0555556i | ||||
\(163\) | −46.4449 | − | 46.4449i | −0.284938 | − | 0.284938i | 0.550137 | − | 0.835075i | \(-0.314576\pi\) |
−0.835075 | + | 0.550137i | \(0.814576\pi\) | |||||||
\(164\) | −88.8897 | − | 88.8897i | −0.542011 | − | 0.542011i | ||||
\(165\) | −7.60770 | −0.0461072 | ||||||||
\(166\) | 219.597i | 1.32288i | ||||||||
\(167\) | −119.512 | − | 119.512i | −0.715638 | − | 0.715638i | 0.252071 | − | 0.967709i | \(-0.418888\pi\) |
−0.967709 | + | 0.252071i | \(0.918888\pi\) | |||||||
\(168\) | − | 5.07180i | − | 0.0301893i | ||||||
\(169\) | −138.138 | − | 97.3590i | −0.817387 | − | 0.576089i | ||||
\(170\) | −13.4923 | −0.0793663 | ||||||||
\(171\) | −44.1962 | + | 44.1962i | −0.258457 | + | 0.258457i | ||||
\(172\) | −74.3538 | −0.432290 | ||||||||
\(173\) | 242.603i | 1.40233i | 0.713001 | + | 0.701163i | \(0.247336\pi\) | ||||
−0.713001 | + | 0.701163i | \(0.752664\pi\) | |||||||
\(174\) | 7.17691 | − | 7.17691i | 0.0412466 | − | 0.0412466i | ||||
\(175\) | −15.9474 | + | 15.9474i | −0.0911282 | + | 0.0911282i | ||||
\(176\) | 6.92820 | + | 6.92820i | 0.0393648 | + | 0.0393648i | ||||
\(177\) | −115.392 | − | 115.392i | −0.651934 | − | 0.651934i | ||||
\(178\) | −39.0333 | −0.219288 | ||||||||
\(179\) | − | 26.7180i | − | 0.149262i | −0.997211 | − | 0.0746312i | \(-0.976222\pi\) | ||
0.997211 | − | 0.0746312i | \(-0.0237780\pi\) | |||||||
\(180\) | −7.60770 | − | 7.60770i | −0.0422650 | − | 0.0422650i | ||||
\(181\) | 256.144i | 1.41516i | 0.706634 | + | 0.707579i | \(0.250213\pi\) | ||||
−0.706634 | + | 0.707579i | \(0.749787\pi\) | |||||||
\(182\) | −5.75129 | + | 18.1436i | −0.0316005 | + | 0.0996901i | ||||
\(183\) | 179.138 | 0.978899 | ||||||||
\(184\) | −10.6410 | + | 10.6410i | −0.0578316 | + | 0.0578316i | ||||
\(185\) | −7.97183 | −0.0430910 | ||||||||
\(186\) | 86.5359i | 0.465247i | ||||||||
\(187\) | −9.21539 | + | 9.21539i | −0.0492802 | + | 0.0492802i | ||||
\(188\) | −61.6077 | + | 61.6077i | −0.327701 | + | 0.327701i | ||||
\(189\) | 3.80385 | + | 3.80385i | 0.0201262 | + | 0.0201262i | ||||
\(190\) | 37.3590 | + | 37.3590i | 0.196626 | + | 0.196626i | ||||
\(191\) | −129.282 | −0.676869 | −0.338435 | − | 0.940990i | \(-0.609897\pi\) | ||||
−0.338435 | + | 0.940990i | \(0.609897\pi\) | |||||||
\(192\) | 13.8564i | 0.0721688i | ||||||||
\(193\) | −160.282 | − | 160.282i | −0.830477 | − | 0.830477i | 0.157105 | − | 0.987582i | \(-0.449784\pi\) |
−0.987582 | + | 0.157105i | \(0.949784\pi\) | |||||||
\(194\) | − | 8.06664i | − | 0.0415806i | ||||||
\(195\) | 18.5885 | + | 35.8423i | 0.0953254 | + | 0.183807i | ||||
\(196\) | −95.8564 | −0.489063 | ||||||||
\(197\) | −109.268 | + | 109.268i | −0.554660 | + | 0.554660i | −0.927782 | − | 0.373122i | \(-0.878287\pi\) |
0.373122 | + | 0.927782i | \(0.378287\pi\) | |||||||
\(198\) | −10.3923 | −0.0524864 | ||||||||
\(199\) | 25.1000i | 0.126130i | 0.998009 | + | 0.0630652i | \(0.0200876\pi\) | ||||
−0.998009 | + | 0.0630652i | \(0.979912\pi\) | |||||||
\(200\) | 43.5692 | − | 43.5692i | 0.217846 | − | 0.217846i | ||||
\(201\) | 80.8756 | − | 80.8756i | 0.402366 | − | 0.402366i | ||||
\(202\) | 111.464 | + | 111.464i | 0.551802 | + | 0.551802i | ||||
\(203\) | 3.03332 | + | 3.03332i | 0.0149425 | + | 0.0149425i | ||||
\(204\) | −18.4308 | −0.0903470 | ||||||||
\(205\) | − | 112.708i | − | 0.549793i | ||||||
\(206\) | 71.3205 | + | 71.3205i | 0.346216 | + | 0.346216i | ||||
\(207\) | − | 15.9615i | − | 0.0771088i | ||||||
\(208\) | 15.7128 | − | 49.5692i | 0.0755424 | − | 0.238314i | ||||
\(209\) | 51.0333 | 0.244179 | ||||||||
\(210\) | 3.21539 | − | 3.21539i | 0.0153114 | − | 0.0153114i | ||||
\(211\) | 206.718 | 0.979706 | 0.489853 | − | 0.871805i | \(-0.337050\pi\) | ||||
0.489853 | + | 0.871805i | \(0.337050\pi\) | |||||||
\(212\) | − | 115.426i | − | 0.544460i | ||||||
\(213\) | −46.6077 | + | 46.6077i | −0.218815 | + | 0.218815i | ||||
\(214\) | −116.536 | + | 116.536i | −0.544560 | + | 0.544560i | ||||
\(215\) | −47.1384 | − | 47.1384i | −0.219249 | − | 0.219249i | ||||
\(216\) | −10.3923 | − | 10.3923i | −0.0481125 | − | 0.0481125i | ||||
\(217\) | −36.5744 | −0.168546 | ||||||||
\(218\) | 218.631i | 1.00289i | ||||||||
\(219\) | 9.83717 | + | 9.83717i | 0.0449186 | + | 0.0449186i | ||||
\(220\) | 8.78461i | 0.0399300i | ||||||||
\(221\) | 65.9334 | + | 20.9000i | 0.298341 | + | 0.0945703i | ||||
\(222\) | −10.8897 | −0.0490528 | ||||||||
\(223\) | 139.412 | − | 139.412i | 0.625164 | − | 0.625164i | −0.321683 | − | 0.946847i | \(-0.604249\pi\) |
0.946847 | + | 0.321683i | \(0.104249\pi\) | |||||||
\(224\) | −5.85641 | −0.0261447 | ||||||||
\(225\) | 65.3538i | 0.290461i | ||||||||
\(226\) | 148.277 | − | 148.277i | 0.656092 | − | 0.656092i | ||||
\(227\) | −97.3679 | + | 97.3679i | −0.428934 | + | 0.428934i | −0.888265 | − | 0.459331i | \(-0.848089\pi\) |
0.459331 | + | 0.888265i | \(0.348089\pi\) | |||||||
\(228\) | 51.0333 | + | 51.0333i | 0.223830 | + | 0.223830i | ||||
\(229\) | 204.177 | + | 204.177i | 0.891602 | + | 0.891602i | 0.994674 | − | 0.103072i | \(-0.0328671\pi\) |
−0.103072 | + | 0.994674i | \(0.532867\pi\) | |||||||
\(230\) | −13.4923 | −0.0586620 | ||||||||
\(231\) | − | 4.39230i | − | 0.0190143i | ||||||
\(232\) | −8.28719 | − | 8.28719i | −0.0357206 | − | 0.0357206i | ||||
\(233\) | − | 231.962i | − | 0.995543i | −0.867308 | − | 0.497772i | \(-0.834152\pi\) | ||
0.867308 | − | 0.497772i | \(-0.165848\pi\) | |||||||
\(234\) | 25.3923 | + | 48.9615i | 0.108514 | + | 0.209237i | ||||
\(235\) | −78.1154 | −0.332406 | ||||||||
\(236\) | −133.244 | + | 133.244i | −0.564591 | + | 0.564591i | ||||
\(237\) | 7.29234 | 0.0307694 | ||||||||
\(238\) | − | 7.78976i | − | 0.0327301i | ||||||
\(239\) | 139.981 | − | 139.981i | 0.585694 | − | 0.585694i | −0.350769 | − | 0.936462i | \(-0.614080\pi\) |
0.936462 | + | 0.350769i | \(0.114080\pi\) | |||||||
\(240\) | −8.78461 | + | 8.78461i | −0.0366025 | + | 0.0366025i | ||||
\(241\) | 53.4589 | + | 53.4589i | 0.221821 | + | 0.221821i | 0.809265 | − | 0.587444i | \(-0.199866\pi\) |
−0.587444 | + | 0.809265i | \(0.699866\pi\) | |||||||
\(242\) | −115.000 | − | 115.000i | −0.475207 | − | 0.475207i | ||||
\(243\) | 15.5885 | 0.0641500 | ||||||||
\(244\) | − | 206.851i | − | 0.847751i | ||||||
\(245\) | −60.7705 | − | 60.7705i | −0.248043 | − | 0.248043i | ||||
\(246\) | − | 153.962i | − | 0.625860i | ||||||
\(247\) | −124.694 | − | 240.435i | −0.504832 | − | 0.973419i | ||||
\(248\) | 99.9230 | 0.402916 | ||||||||
\(249\) | −190.177 | + | 190.177i | −0.763763 | + | 0.763763i | ||||
\(250\) | 118.641 | 0.474564 | ||||||||
\(251\) | 421.377i | 1.67879i | 0.543520 | + | 0.839396i | \(0.317091\pi\) | ||||
−0.543520 | + | 0.839396i | \(0.682909\pi\) | |||||||
\(252\) | 4.39230 | − | 4.39230i | 0.0174298 | − | 0.0174298i | ||||
\(253\) | −9.21539 | + | 9.21539i | −0.0364245 | + | 0.0364245i | ||||
\(254\) | −70.0385 | − | 70.0385i | −0.275742 | − | 0.275742i | ||||
\(255\) | −11.6846 | − | 11.6846i | −0.0458221 | − | 0.0458221i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − | 249.664i | − | 0.971455i | −0.874110 | − | 0.485728i | \(-0.838555\pi\) | ||
0.874110 | − | 0.485728i | \(-0.161445\pi\) | |||||||
\(258\) | −64.3923 | − | 64.3923i | −0.249583 | − | 0.249583i | ||||
\(259\) | − | 4.60254i | − | 0.0177704i | ||||||
\(260\) | 41.3872 | − | 21.4641i | 0.159181 | − | 0.0825542i | ||||
\(261\) | 12.4308 | 0.0476275 | ||||||||
\(262\) | 238.890 | − | 238.890i | 0.911793 | − | 0.911793i | ||||
\(263\) | −94.8897 | −0.360797 | −0.180399 | − | 0.983594i | \(-0.557739\pi\) | ||||
−0.180399 | + | 0.983594i | \(0.557739\pi\) | |||||||
\(264\) | 12.0000i | 0.0454545i | ||||||||
\(265\) | 73.1769 | − | 73.1769i | 0.276139 | − | 0.276139i | ||||
\(266\) | −21.5692 | + | 21.5692i | −0.0810873 | + | 0.0810873i | ||||
\(267\) | −33.8038 | − | 33.8038i | −0.126606 | − | 0.126606i | ||||
\(268\) | −93.3872 | − | 93.3872i | −0.348460 | − | 0.348460i | ||||
\(269\) | −208.774 | −0.776113 | −0.388056 | − | 0.921636i | \(-0.626853\pi\) | ||||
−0.388056 | + | 0.921636i | \(0.626853\pi\) | |||||||
\(270\) | − | 13.1769i | − | 0.0488034i | ||||||
\(271\) | 381.047 | + | 381.047i | 1.40608 | + | 1.40608i | 0.778772 | + | 0.627307i | \(0.215843\pi\) |
0.627307 | + | 0.778772i | \(0.284157\pi\) | |||||||
\(272\) | 21.2820i | 0.0782428i | ||||||||
\(273\) | −20.6936 | + | 10.7321i | −0.0758006 | + | 0.0393115i | ||||
\(274\) | −183.895 | −0.671149 | ||||||||
\(275\) | 37.7321 | − | 37.7321i | 0.137207 | − | 0.137207i | ||||
\(276\) | −18.4308 | −0.0667782 | ||||||||
\(277\) | − | 68.7846i | − | 0.248320i | −0.992262 | − | 0.124160i | \(-0.960376\pi\) | ||
0.992262 | − | 0.124160i | \(-0.0396236\pi\) | |||||||
\(278\) | 139.138 | − | 139.138i | 0.500498 | − | 0.500498i | ||||
\(279\) | −74.9423 | + | 74.9423i | −0.268610 | + | 0.268610i | ||||
\(280\) | −3.71281 | − | 3.71281i | −0.0132600 | − | 0.0132600i | ||||
\(281\) | 69.6218 | + | 69.6218i | 0.247764 | + | 0.247764i | 0.820053 | − | 0.572288i | \(-0.193944\pi\) |
−0.572288 | + | 0.820053i | \(0.693944\pi\) | |||||||
\(282\) | −106.708 | −0.378396 | ||||||||
\(283\) | − | 425.808i | − | 1.50462i | −0.658809 | − | 0.752310i | \(-0.728939\pi\) | ||
0.658809 | − | 0.752310i | \(-0.271061\pi\) | |||||||
\(284\) | 53.8179 | + | 53.8179i | 0.189500 | + | 0.189500i | ||||
\(285\) | 64.7077i | 0.227044i | ||||||||
\(286\) | 13.6077 | − | 42.9282i | 0.0475794 | − | 0.150099i | ||||
\(287\) | 65.0718 | 0.226731 | ||||||||
\(288\) | −12.0000 | + | 12.0000i | −0.0416667 | + | 0.0416667i | ||||
\(289\) | 260.692 | 0.902049 | ||||||||
\(290\) | − | 10.5077i | − | 0.0362336i | ||||||
\(291\) | 6.98592 | − | 6.98592i | 0.0240066 | − | 0.0240066i | ||||
\(292\) | 11.3590 | − | 11.3590i | 0.0389006 | − | 0.0389006i | ||||
\(293\) | 306.042 | + | 306.042i | 1.04451 | + | 1.04451i | 0.998962 | + | 0.0455508i | \(0.0145043\pi\) |
0.0455508 | + | 0.998962i | \(0.485496\pi\) | |||||||
\(294\) | −83.0141 | − | 83.0141i | −0.282361 | − | 0.282361i | ||||
\(295\) | −168.946 | −0.572699 | ||||||||
\(296\) | 12.5744i | 0.0424810i | ||||||||
\(297\) | −9.00000 | − | 9.00000i | −0.0303030 | − | 0.0303030i | ||||
\(298\) | − | 252.449i | − | 0.847143i | ||||||
\(299\) | 65.9334 | + | 20.9000i | 0.220513 | + | 0.0698998i | ||||
\(300\) | 75.4641 | 0.251547 | ||||||||
\(301\) | 27.2154 | − | 27.2154i | 0.0904166 | − | 0.0904166i | ||||
\(302\) | 248.813 | 0.823883 | ||||||||
\(303\) | 193.061i | 0.637167i | ||||||||
\(304\) | 58.9282 | − | 58.9282i | 0.193843 | − | 0.193843i | ||||
\(305\) | 131.138 | − | 131.138i | 0.429962 | − | 0.429962i | ||||
\(306\) | −15.9615 | − | 15.9615i | −0.0521618 | − | 0.0521618i | ||||
\(307\) | 246.512 | + | 246.512i | 0.802969 | + | 0.802969i | 0.983559 | − | 0.180589i | \(-0.0578005\pi\) |
−0.180589 | + | 0.983559i | \(0.557801\pi\) | |||||||
\(308\) | −5.07180 | −0.0164669 | ||||||||
\(309\) | 123.531i | 0.399776i | ||||||||
\(310\) | 63.3487 | + | 63.3487i | 0.204351 | + | 0.204351i | ||||
\(311\) | − | 313.377i | − | 1.00764i | −0.863808 | − | 0.503821i | \(-0.831927\pi\) | ||
0.863808 | − | 0.503821i | \(-0.168073\pi\) | |||||||
\(312\) | 56.5359 | − | 29.3205i | 0.181205 | − | 0.0939760i | ||||
\(313\) | −262.841 | −0.839747 | −0.419874 | − | 0.907583i | \(-0.637926\pi\) | ||||
−0.419874 | + | 0.907583i | \(0.637926\pi\) | |||||||
\(314\) | −268.785 | + | 268.785i | −0.856002 | + | 0.856002i | ||||
\(315\) | 5.56922 | 0.0176801 | ||||||||
\(316\) | − | 8.42047i | − | 0.0266471i | ||||||
\(317\) | −148.981 | + | 148.981i | −0.469971 | + | 0.469971i | −0.901905 | − | 0.431934i | \(-0.857831\pi\) |
0.431934 | + | 0.901905i | \(0.357831\pi\) | |||||||
\(318\) | 99.9615 | − | 99.9615i | 0.314344 | − | 0.314344i | ||||
\(319\) | −7.17691 | − | 7.17691i | −0.0224982 | − | 0.0224982i | ||||
\(320\) | 10.1436 | + | 10.1436i | 0.0316987 | + | 0.0316987i | ||||
\(321\) | −201.846 | −0.628804 | ||||||||
\(322\) | − | 7.78976i | − | 0.0241918i | ||||||
\(323\) | 78.3820 | + | 78.3820i | 0.242669 | + | 0.242669i | ||||
\(324\) | − | 18.0000i | − | 0.0555556i | ||||||
\(325\) | −269.962 | − | 85.5744i | −0.830651 | − | 0.263306i | ||||
\(326\) | −92.8897 | −0.284938 | ||||||||
\(327\) | −189.340 | + | 189.340i | −0.579021 | + | 0.579021i | ||||
\(328\) | −177.779 | −0.542011 | ||||||||
\(329\) | − | 45.1000i | − | 0.137082i | ||||||
\(330\) | −7.60770 | + | 7.60770i | −0.0230536 | + | 0.0230536i | ||||
\(331\) | −295.870 | + | 295.870i | −0.893869 | + | 0.893869i | −0.994885 | − | 0.101016i | \(-0.967791\pi\) |
0.101016 | + | 0.994885i | \(0.467791\pi\) | |||||||
\(332\) | 219.597 | + | 219.597i | 0.661438 | + | 0.661438i | ||||
\(333\) | −9.43078 | − | 9.43078i | −0.0283207 | − | 0.0283207i | ||||
\(334\) | −239.023 | −0.715638 | ||||||||
\(335\) | − | 118.410i | − | 0.353463i | ||||||
\(336\) | −5.07180 | − | 5.07180i | −0.0150946 | − | 0.0150946i | ||||
\(337\) | 48.9385i | 0.145218i | 0.997360 | + | 0.0726091i | \(0.0231325\pi\) | ||||
−0.997360 | + | 0.0726091i | \(0.976867\pi\) | |||||||
\(338\) | −235.497 | + | 40.7795i | −0.696738 | + | 0.120649i | ||||
\(339\) | 256.823 | 0.757590 | ||||||||
\(340\) | −13.4923 | + | 13.4923i | −0.0396831 | + | 0.0396831i | ||||
\(341\) | 86.5359 | 0.253771 | ||||||||
\(342\) | 88.3923i | 0.258457i | ||||||||
\(343\) | 70.9564 | − | 70.9564i | 0.206870 | − | 0.206870i | ||||
\(344\) | −74.3538 | + | 74.3538i | −0.216145 | + | 0.216145i | ||||
\(345\) | −11.6846 | − | 11.6846i | −0.0338685 | − | 0.0338685i | ||||
\(346\) | 242.603 | + | 242.603i | 0.701163 | + | 0.701163i | ||||
\(347\) | −552.133 | −1.59116 | −0.795581 | − | 0.605847i | \(-0.792834\pi\) | ||||
−0.795581 | + | 0.605847i | \(0.792834\pi\) | |||||||
\(348\) | − | 14.3538i | − | 0.0412466i | ||||||
\(349\) | 189.210 | + | 189.210i | 0.542150 | + | 0.542150i | 0.924159 | − | 0.382009i | \(-0.124768\pi\) |
−0.382009 | + | 0.924159i | \(0.624768\pi\) | |||||||
\(350\) | 31.8949i | 0.0911282i | ||||||||
\(351\) | −20.4115 | + | 64.3923i | −0.0581525 | + | 0.183454i | ||||
\(352\) | 13.8564 | 0.0393648 | ||||||||
\(353\) | −51.8705 | + | 51.8705i | −0.146942 | + | 0.146942i | −0.776750 | − | 0.629809i | \(-0.783133\pi\) |
0.629809 | + | 0.776750i | \(0.283133\pi\) | |||||||
\(354\) | −230.785 | −0.651934 | ||||||||
\(355\) | 68.2384i | 0.192221i | ||||||||
\(356\) | −39.0333 | + | 39.0333i | −0.109644 | + | 0.109644i | ||||
\(357\) | 6.74613 | − | 6.74613i | 0.0188967 | − | 0.0188967i | ||||
\(358\) | −26.7180 | − | 26.7180i | −0.0746312 | − | 0.0746312i | ||||
\(359\) | −205.119 | − | 205.119i | −0.571363 | − | 0.571363i | 0.361146 | − | 0.932509i | \(-0.382385\pi\) |
−0.932509 | + | 0.361146i | \(0.882385\pi\) | |||||||
\(360\) | −15.2154 | −0.0422650 | ||||||||
\(361\) | − | 73.0666i | − | 0.202401i | ||||||
\(362\) | 256.144 | + | 256.144i | 0.707579 | + | 0.707579i | ||||
\(363\) | − | 199.186i | − | 0.548721i | ||||||
\(364\) | 12.3923 | + | 23.8949i | 0.0340448 | + | 0.0656453i | ||||
\(365\) | 14.4026 | 0.0394592 | ||||||||
\(366\) | 179.138 | − | 179.138i | 0.489449 | − | 0.489449i | ||||
\(367\) | −351.292 | −0.957200 | −0.478600 | − | 0.878033i | \(-0.658856\pi\) | ||||
−0.478600 | + | 0.878033i | \(0.658856\pi\) | |||||||
\(368\) | 21.2820i | 0.0578316i | ||||||||
\(369\) | 133.335 | − | 133.335i | 0.361340 | − | 0.361340i | ||||
\(370\) | −7.97183 | + | 7.97183i | −0.0215455 | + | 0.0215455i | ||||
\(371\) | 42.2487 | + | 42.2487i | 0.113878 | + | 0.113878i | ||||
\(372\) | 86.5359 | + | 86.5359i | 0.232623 | + | 0.232623i | ||||
\(373\) | −131.836 | −0.353447 | −0.176724 | − | 0.984261i | \(-0.556550\pi\) | ||||
−0.176724 | + | 0.984261i | \(0.556550\pi\) | |||||||
\(374\) | 18.4308i | 0.0492802i | ||||||||
\(375\) | 102.746 | + | 102.746i | 0.273990 | + | 0.273990i | ||||
\(376\) | 123.215i | 0.327701i | ||||||||
\(377\) | −16.2769 | + | 51.3487i | −0.0431747 | + | 0.136203i | ||||
\(378\) | 7.60770 | 0.0201262 | ||||||||
\(379\) | −24.7987 | + | 24.7987i | −0.0654319 | + | 0.0654319i | −0.739065 | − | 0.673634i | \(-0.764733\pi\) |
0.673634 | + | 0.739065i | \(0.264733\pi\) | |||||||
\(380\) | 74.7180 | 0.196626 | ||||||||
\(381\) | − | 121.310i | − | 0.318399i | ||||||
\(382\) | −129.282 | + | 129.282i | −0.338435 | + | 0.338435i | ||||
\(383\) | 174.555 | − | 174.555i | 0.455758 | − | 0.455758i | −0.441502 | − | 0.897260i | \(-0.645554\pi\) |
0.897260 | + | 0.441502i | \(0.145554\pi\) | |||||||
\(384\) | 13.8564 | + | 13.8564i | 0.0360844 | + | 0.0360844i | ||||
\(385\) | −3.21539 | − | 3.21539i | −0.00835166 | − | 0.00835166i | ||||
\(386\) | −320.564 | −0.830477 | ||||||||
\(387\) | − | 111.531i | − | 0.288193i | ||||||
\(388\) | −8.06664 | − | 8.06664i | −0.0207903 | − | 0.0207903i | ||||
\(389\) | − | 644.305i | − | 1.65631i | −0.560498 | − | 0.828156i | \(-0.689390\pi\) | ||
0.560498 | − | 0.828156i | \(-0.310610\pi\) | |||||||
\(390\) | 54.4308 | + | 17.2539i | 0.139566 | + | 0.0442407i | ||||
\(391\) | −28.3078 | −0.0723985 | ||||||||
\(392\) | −95.8564 | + | 95.8564i | −0.244532 | + | 0.244532i | ||||
\(393\) | 413.769 | 1.05285 | ||||||||
\(394\) | 218.536i | 0.554660i | ||||||||
\(395\) | 5.33836 | − | 5.33836i | 0.0135148 | − | 0.0135148i | ||||
\(396\) | −10.3923 | + | 10.3923i | −0.0262432 | + | 0.0262432i | ||||
\(397\) | 432.692 | + | 432.692i | 1.08990 | + | 1.08990i | 0.995537 | + | 0.0943673i | \(0.0300828\pi\) |
0.0943673 | + | 0.995537i | \(0.469917\pi\) | |||||||
\(398\) | 25.1000 | + | 25.1000i | 0.0630652 | + | 0.0630652i | ||||
\(399\) | −37.3590 | −0.0936315 | ||||||||
\(400\) | − | 87.1384i | − | 0.217846i | ||||||
\(401\) | −274.550 | − | 274.550i | −0.684663 | − | 0.684663i | 0.276384 | − | 0.961047i | \(-0.410864\pi\) |
−0.961047 | + | 0.276384i | \(0.910864\pi\) | |||||||
\(402\) | − | 161.751i | − | 0.402366i | ||||||
\(403\) | −211.440 | − | 407.699i | −0.524664 | − | 1.01166i | ||||
\(404\) | 222.928 | 0.551802 | ||||||||
\(405\) | 11.4115 | − | 11.4115i | 0.0281766 | − | 0.0281766i | ||||
\(406\) | 6.06664 | 0.0149425 | ||||||||
\(407\) | 10.8897i | 0.0267561i | ||||||||
\(408\) | −18.4308 | + | 18.4308i | −0.0451735 | + | 0.0451735i | ||||
\(409\) | 76.1872 | − | 76.1872i | 0.186277 | − | 0.186277i | −0.607808 | − | 0.794084i | \(-0.707951\pi\) |
0.794084 | + | 0.607808i | \(0.207951\pi\) | |||||||
\(410\) | −112.708 | − | 112.708i | −0.274897 | − | 0.274897i | ||||
\(411\) | −159.258 | − | 159.258i | −0.387488 | − | 0.387488i | ||||
\(412\) | 142.641 | 0.346216 | ||||||||
\(413\) | − | 97.5411i | − | 0.236177i | ||||||
\(414\) | −15.9615 | − | 15.9615i | −0.0385544 | − | 0.0385544i | ||||
\(415\) | 278.438i | 0.670936i | ||||||||
\(416\) | −33.8564 | − | 65.2820i | −0.0813856 | − | 0.156928i | ||||
\(417\) | 240.995 | 0.577925 | ||||||||
\(418\) | 51.0333 | − | 51.0333i | 0.122089 | − | 0.122089i | ||||
\(419\) | 76.8231 | 0.183349 | 0.0916743 | − | 0.995789i | \(-0.470778\pi\) | ||||
0.0916743 | + | 0.995789i | \(0.470778\pi\) | |||||||
\(420\) | − | 6.43078i | − | 0.0153114i | ||||||
\(421\) | 117.756 | − | 117.756i | 0.279707 | − | 0.279707i | −0.553285 | − | 0.832992i | \(-0.686626\pi\) |
0.832992 | + | 0.553285i | \(0.186626\pi\) | |||||||
\(422\) | 206.718 | − | 206.718i | 0.489853 | − | 0.489853i | ||||
\(423\) | −92.4115 | − | 92.4115i | −0.218467 | − | 0.218467i | ||||
\(424\) | −115.426 | − | 115.426i | −0.272230 | − | 0.272230i | ||||
\(425\) | 115.905 | 0.272718 | ||||||||
\(426\) | 93.2154i | 0.218815i | ||||||||
\(427\) | 75.7128 | + | 75.7128i | 0.177313 | + | 0.177313i | ||||
\(428\) | 233.072i | 0.544560i | ||||||||
\(429\) | 48.9615 | − | 25.3923i | 0.114129 | − | 0.0591895i | ||||
\(430\) | −94.2769 | −0.219249 | ||||||||
\(431\) | 362.478 | − | 362.478i | 0.841017 | − | 0.841017i | −0.147975 | − | 0.988991i | \(-0.547275\pi\) |
0.988991 | + | 0.147975i | \(0.0472754\pi\) | |||||||
\(432\) | −20.7846 | −0.0481125 | ||||||||
\(433\) | − | 197.292i | − | 0.455641i | −0.973703 | − | 0.227820i | \(-0.926840\pi\) | ||
0.973703 | − | 0.227820i | \(-0.0731599\pi\) | |||||||
\(434\) | −36.5744 | + | 36.5744i | −0.0842728 | + | 0.0842728i | ||||
\(435\) | 9.09996 | − | 9.09996i | 0.0209195 | − | 0.0209195i | ||||
\(436\) | 218.631 | + | 218.631i | 0.501447 | + | 0.501447i | ||||
\(437\) | 78.3820 | + | 78.3820i | 0.179364 | + | 0.179364i | ||||
\(438\) | 19.6743 | 0.0449186 | ||||||||
\(439\) | 272.238i | 0.620133i | 0.950715 | + | 0.310067i | \(0.100351\pi\) | ||||
−0.950715 | + | 0.310067i | \(0.899649\pi\) | |||||||
\(440\) | 8.78461 | + | 8.78461i | 0.0199650 | + | 0.0199650i | ||||
\(441\) | − | 143.785i | − | 0.326042i | ||||||
\(442\) | 86.8334 | − | 45.0333i | 0.196456 | − | 0.101885i | ||||
\(443\) | 74.7358 | 0.168704 | 0.0843519 | − | 0.996436i | \(-0.473118\pi\) | ||||
0.0843519 | + | 0.996436i | \(0.473118\pi\) | |||||||
\(444\) | −10.8897 | + | 10.8897i | −0.0245264 | + | 0.0245264i | ||||
\(445\) | −49.4923 | −0.111219 | ||||||||
\(446\) | − | 278.823i | − | 0.625164i | ||||||
\(447\) | 218.627 | − | 218.627i | 0.489098 | − | 0.489098i | ||||
\(448\) | −5.85641 | + | 5.85641i | −0.0130723 | + | 0.0130723i | ||||
\(449\) | 516.224 | + | 516.224i | 1.14972 | + | 1.14972i | 0.986607 | + | 0.163113i | \(0.0521534\pi\) |
0.163113 | + | 0.986607i | \(0.447847\pi\) | |||||||
\(450\) | 65.3538 | + | 65.3538i | 0.145231 | + | 0.145231i | ||||
\(451\) | −153.962 | −0.341378 | ||||||||
\(452\) | − | 296.554i | − | 0.656092i | ||||||
\(453\) | 215.478 | + | 215.478i | 0.475669 | + | 0.475669i | ||||
\(454\) | 194.736i | 0.428934i | ||||||||
\(455\) | −7.29234 | + | 23.0052i | −0.0160271 | + | 0.0505608i | ||||
\(456\) | 102.067 | 0.223830 | ||||||||
\(457\) | −50.9615 | + | 50.9615i | −0.111513 | + | 0.111513i | −0.760662 | − | 0.649149i | \(-0.775125\pi\) |
0.649149 | + | 0.760662i | \(0.275125\pi\) | |||||||
\(458\) | 408.354 | 0.891602 | ||||||||
\(459\) | − | 27.6462i | − | 0.0602313i | ||||||
\(460\) | −13.4923 | + | 13.4923i | −0.0293310 | + | 0.0293310i | ||||
\(461\) | 202.550 | − | 202.550i | 0.439371 | − | 0.439371i | −0.452429 | − | 0.891800i | \(-0.649443\pi\) |
0.891800 | + | 0.452429i | \(0.149443\pi\) | |||||||
\(462\) | −4.39230 | − | 4.39230i | −0.00950715 | − | 0.00950715i | ||||
\(463\) | −223.247 | − | 223.247i | −0.482176 | − | 0.482176i | 0.423650 | − | 0.905826i | \(-0.360749\pi\) |
−0.905826 | + | 0.423650i | \(0.860749\pi\) | |||||||
\(464\) | −16.5744 | −0.0357206 | ||||||||
\(465\) | 109.723i | 0.235964i | ||||||||
\(466\) | −231.962 | − | 231.962i | −0.497772 | − | 0.497772i | ||||
\(467\) | 161.818i | 0.346505i | 0.984877 | + | 0.173253i | \(0.0554277\pi\) | ||||
−0.984877 | + | 0.173253i | \(0.944572\pi\) | |||||||
\(468\) | 74.3538 | + | 23.5692i | 0.158876 | + | 0.0503616i | ||||
\(469\) | 68.3641 | 0.145766 | ||||||||
\(470\) | −78.1154 | + | 78.1154i | −0.166203 | + | 0.166203i | ||||
\(471\) | −465.549 | −0.988426 | ||||||||
\(472\) | 266.487i | 0.564591i | ||||||||
\(473\) | −64.3923 | + | 64.3923i | −0.136136 | + | 0.136136i | ||||
\(474\) | 7.29234 | − | 7.29234i | 0.0153847 | − | 0.0153847i | ||||
\(475\) | −320.932 | − | 320.932i | −0.675646 | − | 0.675646i | ||||
\(476\) | −7.78976 | − | 7.78976i | −0.0163651 | − | 0.0163651i | ||||
\(477\) | 173.138 | 0.362974 | ||||||||
\(478\) | − | 279.962i | − | 0.585694i | ||||||
\(479\) | −89.1295 | − | 89.1295i | −0.186074 | − | 0.186074i | 0.607922 | − | 0.793996i | \(-0.292003\pi\) |
−0.793996 | + | 0.607922i | \(0.792003\pi\) | |||||||
\(480\) | 17.5692i | 0.0366025i | ||||||||
\(481\) | 51.3050 | − | 26.6077i | 0.106663 | − | 0.0553175i | ||||
\(482\) | 106.918 | 0.221821 | ||||||||
\(483\) | 6.74613 | − | 6.74613i | 0.0139672 | − | 0.0139672i | ||||
\(484\) | −230.000 | −0.475207 | ||||||||
\(485\) | − | 10.2281i | − | 0.0210888i | ||||||
\(486\) | 15.5885 | − | 15.5885i | 0.0320750 | − | 0.0320750i | ||||
\(487\) | −527.440 | + | 527.440i | −1.08304 | + | 1.08304i | −0.0868139 | + | 0.996225i | \(0.527669\pi\) |
−0.996225 | + | 0.0868139i | \(0.972331\pi\) | |||||||
\(488\) | −206.851 | − | 206.851i | −0.423876 | − | 0.423876i | ||||
\(489\) | −80.4449 | − | 80.4449i | −0.164509 | − | 0.164509i | ||||
\(490\) | −121.541 | −0.248043 | ||||||||
\(491\) | 700.726i | 1.42714i | 0.700584 | + | 0.713570i | \(0.252923\pi\) | ||||
−0.700584 | + | 0.713570i | \(0.747077\pi\) | |||||||
\(492\) | −153.962 | − | 153.962i | −0.312930 | − | 0.312930i | ||||
\(493\) | − | 22.0460i | − | 0.0447181i | ||||||
\(494\) | −365.128 | − | 115.741i | −0.739126 | − | 0.234293i | ||||
\(495\) | −13.1769 | −0.0266200 | ||||||||
\(496\) | 99.9230 | − | 99.9230i | 0.201458 | − | 0.201458i | ||||
\(497\) | −39.3975 | −0.0792705 | ||||||||
\(498\) | 380.354i | 0.763763i | ||||||||
\(499\) | 279.065 | − | 279.065i | 0.559249 | − | 0.559249i | −0.369845 | − | 0.929094i | \(-0.620589\pi\) |
0.929094 | + | 0.369845i | \(0.120589\pi\) | |||||||
\(500\) | 118.641 | − | 118.641i | 0.237282 | − | 0.237282i | ||||
\(501\) | −207.000 | − | 207.000i | −0.413174 | − | 0.413174i | ||||
\(502\) | 421.377 | + | 421.377i | 0.839396 | + | 0.839396i | ||||
\(503\) | −23.9821 | −0.0476782 | −0.0238391 | − | 0.999716i | \(-0.507589\pi\) | ||||
−0.0238391 | + | 0.999716i | \(0.507589\pi\) | |||||||
\(504\) | − | 8.78461i | − | 0.0174298i | ||||||
\(505\) | 141.331 | + | 141.331i | 0.279863 | + | 0.279863i | ||||
\(506\) | 18.4308i | 0.0364245i | ||||||||
\(507\) | −239.263 | − | 168.631i | −0.471919 | − | 0.332605i | ||||
\(508\) | −140.077 | −0.275742 | ||||||||
\(509\) | −287.678 | + | 287.678i | −0.565183 | + | 0.565183i | −0.930775 | − | 0.365592i | \(-0.880866\pi\) |
0.365592 | + | 0.930775i | \(0.380866\pi\) | |||||||
\(510\) | −23.3693 | −0.0458221 | ||||||||
\(511\) | 8.31535i | 0.0162727i | ||||||||
\(512\) | 16.0000 | − | 16.0000i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | −76.5500 | + | 76.5500i | −0.149220 | + | 0.149220i | ||||
\(514\) | −249.664 | − | 249.664i | −0.485728 | − | 0.485728i | ||||
\(515\) | 90.4308 | + | 90.4308i | 0.175594 | + | 0.175594i | ||||
\(516\) | −128.785 | −0.249583 | ||||||||
\(517\) | 106.708i | 0.206398i | ||||||||
\(518\) | −4.60254 | − | 4.60254i | −0.00888521 | − | 0.00888521i | ||||
\(519\) | 420.200i | 0.809634i | ||||||||
\(520\) | 19.9230 | − | 62.8513i | 0.0383136 | − | 0.120868i | ||||
\(521\) | −921.349 | −1.76842 | −0.884212 | − | 0.467086i | \(-0.845304\pi\) | ||||
−0.884212 | + | 0.467086i | \(0.845304\pi\) | |||||||
\(522\) | 12.4308 | − | 12.4308i | 0.0238138 | − | 0.0238138i | ||||
\(523\) | −558.677 | −1.06822 | −0.534108 | − | 0.845416i | \(-0.679352\pi\) | ||||
−0.534108 | + | 0.845416i | \(0.679352\pi\) | |||||||
\(524\) | − | 477.779i | − | 0.911793i | ||||||
\(525\) | −27.6218 | + | 27.6218i | −0.0526129 | + | 0.0526129i | ||||
\(526\) | −94.8897 | + | 94.8897i | −0.180399 | + | 0.180399i | ||||
\(527\) | 132.910 | + | 132.910i | 0.252202 | + | 0.252202i | ||||
\(528\) | 12.0000 | + | 12.0000i | 0.0227273 | + | 0.0227273i | ||||
\(529\) | 500.692 | 0.946488 | ||||||||
\(530\) | − | 146.354i | − | 0.276139i | ||||||
\(531\) | −199.865 | − | 199.865i | −0.376394 | − | 0.376394i | ||||
\(532\) | 43.1384i | 0.0810873i | ||||||||
\(533\) | 376.186 | + | 725.363i | 0.705790 | + | 1.36091i | ||||
\(534\) | −67.6077 | −0.126606 | ||||||||
\(535\) | −147.762 | + | 147.762i | −0.276190 | + | 0.276190i | ||||
\(536\) | −186.774 | −0.348460 | ||||||||
\(537\) | − | 46.2769i | − | 0.0861767i | ||||||
\(538\) | −208.774 | + | 208.774i | −0.388056 | + | 0.388056i | ||||
\(539\) | −83.0141 | + | 83.0141i | −0.154015 | + | 0.154015i | ||||
\(540\) | −13.1769 | − | 13.1769i | −0.0244017 | − | 0.0244017i | ||||
\(541\) | −101.756 | − | 101.756i | −0.188090 | − | 0.188090i | 0.606780 | − | 0.794870i | \(-0.292461\pi\) |
−0.794870 | + | 0.606780i | \(0.792461\pi\) | |||||||
\(542\) | 762.095 | 1.40608 | ||||||||
\(543\) | 443.654i | 0.817042i | ||||||||
\(544\) | 21.2820 | + | 21.2820i | 0.0391214 | + | 0.0391214i | ||||
\(545\) | 277.213i | 0.508647i | ||||||||
\(546\) | −9.96152 | + | 31.4256i | −0.0182445 | + | 0.0575561i | ||||
\(547\) | 301.800 | 0.551737 | 0.275868 | − | 0.961195i | \(-0.411035\pi\) | ||||
0.275868 | + | 0.961195i | \(0.411035\pi\) | |||||||
\(548\) | −183.895 | + | 183.895i | −0.335575 | + | 0.335575i | ||||
\(549\) | 310.277 | 0.565167 | ||||||||
\(550\) | − | 75.4641i | − | 0.137207i | ||||||
\(551\) | −61.0436 | + | 61.0436i | −0.110787 | + | 0.110787i | ||||
\(552\) | −18.4308 | + | 18.4308i | −0.0333891 | + | 0.0333891i | ||||
\(553\) | 3.08211 | + | 3.08211i | 0.00557343 | + | 0.00557343i | ||||
\(554\) | −68.7846 | − | 68.7846i | −0.124160 | − | 0.124160i | ||||
\(555\) | −13.8076 | −0.0248786 | ||||||||
\(556\) | − | 278.277i | − | 0.500498i | ||||||
\(557\) | −285.258 | − | 285.258i | −0.512132 | − | 0.512132i | 0.403047 | − | 0.915179i | \(-0.367951\pi\) |
−0.915179 | + | 0.403047i | \(0.867951\pi\) | |||||||
\(558\) | 149.885i | 0.268610i | ||||||||
\(559\) | 460.708 | + | 146.038i | 0.824164 | + | 0.261250i | ||||
\(560\) | −7.42563 | −0.0132600 | ||||||||
\(561\) | −15.9615 | + | 15.9615i | −0.0284519 | + | 0.0284519i | ||||
\(562\) | 139.244 | 0.247764 | ||||||||
\(563\) | 863.174i | 1.53317i | 0.642143 | + | 0.766585i | \(0.278045\pi\) | ||||
−0.642143 | + | 0.766585i | \(0.721955\pi\) | |||||||
\(564\) | −106.708 | + | 106.708i | −0.189198 | + | 0.189198i | ||||
\(565\) | 188.008 | − | 188.008i | 0.332757 | − | 0.332757i | ||||
\(566\) | −425.808 | − | 425.808i | −0.752310 | − | 0.752310i | ||||
\(567\) | 6.58846 | + | 6.58846i | 0.0116199 | + | 0.0116199i | ||||
\(568\) | 107.636 | 0.189500 | ||||||||
\(569\) | 317.223i | 0.557510i | 0.960362 | + | 0.278755i | \(0.0899217\pi\) | ||||
−0.960362 | + | 0.278755i | \(0.910078\pi\) | |||||||
\(570\) | 64.7077 | + | 64.7077i | 0.113522 | + | 0.113522i | ||||
\(571\) | − | 73.2539i | − | 0.128290i | −0.997941 | − | 0.0641452i | \(-0.979568\pi\) | ||
0.997941 | − | 0.0641452i | \(-0.0204321\pi\) | |||||||
\(572\) | −29.3205 | − | 56.5359i | −0.0512596 | − | 0.0988390i | ||||
\(573\) | −223.923 | −0.390791 | ||||||||
\(574\) | 65.0718 | − | 65.0718i | 0.113365 | − | 0.113365i | ||||
\(575\) | 115.905 | 0.201574 | ||||||||
\(576\) | 24.0000i | 0.0416667i | ||||||||
\(577\) | −81.6410 | + | 81.6410i | −0.141492 | + | 0.141492i | −0.774305 | − | 0.632813i | \(-0.781900\pi\) |
0.632813 | + | 0.774305i | \(0.281900\pi\) | |||||||
\(578\) | 260.692 | − | 260.692i | 0.451025 | − | 0.451025i | ||||
\(579\) | −277.617 | − | 277.617i | −0.479476 | − | 0.479476i | ||||
\(580\) | −10.5077 | − | 10.5077i | −0.0181168 | − | 0.0181168i | ||||
\(581\) | −160.756 | −0.276689 | ||||||||
\(582\) | − | 13.9718i | − | 0.0240066i | ||||||
\(583\) | −99.9615 | − | 99.9615i | −0.171461 | − | 0.171461i | ||||
\(584\) | − | 22.7180i | − | 0.0389006i | ||||||
\(585\) | 32.1962 | + | 62.0807i | 0.0550362 | + | 0.106121i | ||||
\(586\) | 612.084 | 1.04451 | ||||||||
\(587\) | 382.219 | − | 382.219i | 0.651140 | − | 0.651140i | −0.302128 | − | 0.953268i | \(-0.597697\pi\) |
0.953268 | + | 0.302128i | \(0.0976968\pi\) | |||||||
\(588\) | −166.028 | −0.282361 | ||||||||
\(589\) | − | 736.036i | − | 1.24964i | ||||||
\(590\) | −168.946 | + | 168.946i | −0.286349 | + | 0.286349i | ||||
\(591\) | −189.258 | + | 189.258i | −0.320233 | + | 0.320233i | ||||
\(592\) | 12.5744 | + | 12.5744i | 0.0212405 | + | 0.0212405i | ||||
\(593\) | 171.355 | + | 171.355i | 0.288963 | + | 0.288963i | 0.836670 | − | 0.547707i | \(-0.184499\pi\) |
−0.547707 | + | 0.836670i | \(0.684499\pi\) | |||||||
\(594\) | −18.0000 | −0.0303030 | ||||||||
\(595\) | − | 9.87703i | − | 0.0166000i | ||||||
\(596\) | −252.449 | − | 252.449i | −0.423572 | − | 0.423572i | ||||
\(597\) | 43.4744i | 0.0728215i | ||||||||
\(598\) | 86.8334 | − | 45.0333i | 0.145206 | − | 0.0753066i | ||||
\(599\) | −109.608 | −0.182984 | −0.0914922 | − | 0.995806i | \(-0.529164\pi\) | ||||
−0.0914922 | + | 0.995806i | \(0.529164\pi\) | |||||||
\(600\) | 75.4641 | − | 75.4641i | 0.125774 | − | 0.125774i | ||||
\(601\) | 779.108 | 1.29635 | 0.648176 | − | 0.761491i | \(-0.275532\pi\) | ||||
0.648176 | + | 0.761491i | \(0.275532\pi\) | |||||||
\(602\) | − | 54.4308i | − | 0.0904166i | ||||||
\(603\) | 140.081 | − | 140.081i | 0.232306 | − | 0.232306i | ||||
\(604\) | 248.813 | − | 248.813i | 0.411942 | − | 0.411942i | ||||
\(605\) | −145.814 | − | 145.814i | −0.241015 | − | 0.241015i | ||||
\(606\) | 193.061 | + | 193.061i | 0.318583 | + | 0.318583i | ||||
\(607\) | 1144.40 | 1.88534 | 0.942669 | − | 0.333730i | \(-0.108307\pi\) | ||||
0.942669 | + | 0.333730i | \(0.108307\pi\) | |||||||
\(608\) | − | 117.856i | − | 0.193843i | ||||||
\(609\) | 5.25387 | + | 5.25387i | 0.00862704 | + | 0.00862704i | ||||
\(610\) | − | 262.277i | − | 0.429962i | ||||||
\(611\) | 502.734 | − | 260.727i | 0.822806 | − | 0.426722i | ||||
\(612\) | −31.9230 | −0.0521618 | ||||||||
\(613\) | 292.349 | − | 292.349i | 0.476915 | − | 0.476915i | −0.427229 | − | 0.904144i | \(-0.640510\pi\) |
0.904144 | + | 0.427229i | \(0.140510\pi\) | |||||||
\(614\) | 493.023 | 0.802969 | ||||||||
\(615\) | − | 195.215i | − | 0.317423i | ||||||
\(616\) | −5.07180 | + | 5.07180i | −0.00823344 | + | 0.00823344i | ||||
\(617\) | −369.391 | + | 369.391i | −0.598689 | + | 0.598689i | −0.939964 | − | 0.341275i | \(-0.889141\pi\) |
0.341275 | + | 0.939964i | \(0.389141\pi\) | |||||||
\(618\) | 123.531 | + | 123.531i | 0.199888 | + | 0.199888i | ||||
\(619\) | −446.070 | − | 446.070i | −0.720631 | − | 0.720631i | 0.248103 | − | 0.968734i | \(-0.420193\pi\) |
−0.968734 | + | 0.248103i | \(0.920193\pi\) | |||||||
\(620\) | 126.697 | 0.204351 | ||||||||
\(621\) | − | 27.6462i | − | 0.0445188i | ||||||
\(622\) | −313.377 | − | 313.377i | −0.503821 | − | 0.503821i | ||||
\(623\) | − | 28.5744i | − | 0.0458658i | ||||||
\(624\) | 27.2154 | − | 85.8564i | 0.0436144 | − | 0.137590i | ||||
\(625\) | −394.184 | −0.630695 | ||||||||
\(626\) | −262.841 | + | 262.841i | −0.419874 | + | 0.419874i | ||||
\(627\) | 88.3923 | 0.140977 | ||||||||
\(628\) | 537.569i | 0.856002i | ||||||||
\(629\) | −16.7255 | + | 16.7255i | −0.0265906 | + | 0.0265906i | ||||
\(630\) | 5.56922 | − | 5.56922i | 0.00884003 | − | 0.00884003i | ||||
\(631\) | −604.406 | − | 604.406i | −0.957855 | − | 0.957855i | 0.0412923 | − | 0.999147i | \(-0.486853\pi\) |
−0.999147 | + | 0.0412923i | \(0.986853\pi\) | |||||||
\(632\) | −8.42047 | − | 8.42047i | −0.0133235 | − | 0.0133235i | ||||
\(633\) | 358.046 | 0.565634 | ||||||||
\(634\) | 297.962i | 0.469971i | ||||||||
\(635\) | −88.8052 | − | 88.8052i | −0.139851 | − | 0.139851i | ||||
\(636\) | − | 199.923i | − | 0.314344i | ||||||
\(637\) | 593.941 | + | 188.272i | 0.932403 | + | 0.295560i | ||||
\(638\) | −14.3538 | −0.0224982 | ||||||||
\(639\) | −80.7269 | + | 80.7269i | −0.126333 | + | 0.126333i | ||||
\(640\) | 20.2872 | 0.0316987 | ||||||||
\(641\) | − | 1213.91i | − | 1.89378i | −0.321565 | − | 0.946888i | \(-0.604209\pi\) | ||
0.321565 | − | 0.946888i | \(-0.395791\pi\) | |||||||
\(642\) | −201.846 | + | 201.846i | −0.314402 | + | 0.314402i | ||||
\(643\) | 413.804 | − | 413.804i | 0.643552 | − | 0.643552i | −0.307875 | − | 0.951427i | \(-0.599618\pi\) |
0.951427 | + | 0.307875i | \(0.0996178\pi\) | |||||||
\(644\) | −7.78976 | − | 7.78976i | −0.0120959 | − | 0.0120959i | ||||
\(645\) | −81.6462 | − | 81.6462i | −0.126583 | − | 0.126583i | ||||
\(646\) | 156.764 | 0.242669 | ||||||||
\(647\) | 117.913i | 0.182245i | 0.995840 | + | 0.0911227i | \(0.0290455\pi\) | ||||
−0.995840 | + | 0.0911227i | \(0.970954\pi\) | |||||||
\(648\) | −18.0000 | − | 18.0000i | −0.0277778 | − | 0.0277778i | ||||
\(649\) | 230.785i | 0.355600i | ||||||||
\(650\) | −355.536 | + | 184.387i | −0.546978 | + | 0.283673i | ||||
\(651\) | −63.3487 | −0.0973098 | ||||||||
\(652\) | −92.8897 | + | 92.8897i | −0.142469 | + | 0.142469i | ||||
\(653\) | −1088.62 | −1.66711 | −0.833553 | − | 0.552439i | \(-0.813697\pi\) | ||||
−0.833553 | + | 0.552439i | \(0.813697\pi\) | |||||||
\(654\) | 378.679i | 0.579021i | ||||||||
\(655\) | 302.900 | − | 302.900i | 0.462443 | − | 0.462443i | ||||
\(656\) | −177.779 | + | 177.779i | −0.271005 | + | 0.271005i | ||||
\(657\) | 17.0385 | + | 17.0385i | 0.0259338 | + | 0.0259338i | ||||
\(658\) | −45.1000 | − | 45.1000i | −0.0685410 | − | 0.0685410i | ||||
\(659\) | 1222.68 | 1.85535 | 0.927676 | − | 0.373387i | \(-0.121804\pi\) | ||||
0.927676 | + | 0.373387i | \(0.121804\pi\) | |||||||
\(660\) | 15.2154i | 0.0230536i | ||||||||
\(661\) | −667.851 | − | 667.851i | −1.01036 | − | 1.01036i | −0.999946 | − | 0.0104193i | \(-0.996683\pi\) |
−0.0104193 | − | 0.999946i | \(-0.503317\pi\) | |||||||
\(662\) | 591.741i | 0.893869i | ||||||||
\(663\) | 114.200 | + | 36.1999i | 0.172247 | + | 0.0546002i | ||||
\(664\) | 439.195 | 0.661438 | ||||||||
\(665\) | −27.3487 | + | 27.3487i | −0.0411258 | + | 0.0411258i | ||||
\(666\) | −18.8616 | −0.0283207 | ||||||||
\(667\) | − | 22.0460i | − | 0.0330525i | ||||||
\(668\) | −239.023 | + | 239.023i | −0.357819 | + | 0.357819i | ||||
\(669\) | 241.468 | − | 241.468i | 0.360939 | − | 0.360939i | ||||
\(670\) | −118.410 | − | 118.410i | −0.176732 | − | 0.176732i | ||||
\(671\) | −179.138 | − | 179.138i | −0.266972 | − | 0.266972i | ||||
\(672\) | −10.1436 | −0.0150946 | ||||||||
\(673\) | 411.779i | 0.611857i | 0.952055 | + | 0.305928i | \(0.0989668\pi\) | ||||
−0.952055 | + | 0.305928i | \(0.901033\pi\) | |||||||
\(674\) | 48.9385 | + | 48.9385i | 0.0726091 | + | 0.0726091i | ||||
\(675\) | 113.196i | 0.167698i | ||||||||
\(676\) | −194.718 | + | 276.277i | −0.288044 | + | 0.408694i | ||||
\(677\) | −948.600 | −1.40118 | −0.700591 | − | 0.713563i | \(-0.747080\pi\) | ||||
−0.700591 | + | 0.713563i | \(0.747080\pi\) | |||||||
\(678\) | 256.823 | − | 256.823i | 0.378795 | − | 0.378795i | ||||
\(679\) | 5.90519 | 0.00869690 | ||||||||
\(680\) | 26.9845i | 0.0396831i | ||||||||
\(681\) | −168.646 | + | 168.646i | −0.247645 | + | 0.247645i | ||||
\(682\) | 86.5359 | − | 86.5359i | 0.126885 | − | 0.126885i | ||||
\(683\) | 101.809 | + | 101.809i | 0.149061 | + | 0.149061i | 0.777699 | − | 0.628637i | \(-0.216387\pi\) |
−0.628637 | + | 0.777699i | \(0.716387\pi\) | |||||||
\(684\) | 88.3923 | + | 88.3923i | 0.129229 | + | 0.129229i | ||||
\(685\) | −233.169 | −0.340393 | ||||||||
\(686\) | − | 141.913i | − | 0.206870i | ||||||
\(687\) | 353.645 | + | 353.645i | 0.514767 | + | 0.514767i | ||||
\(688\) | 148.708i | 0.216145i | ||||||||
\(689\) | −226.708 | + | 715.195i | −0.329039 | + | 1.03802i | ||||
\(690\) | −23.3693 | −0.0338685 | ||||||||
\(691\) | −111.135 | + | 111.135i | −0.160832 | + | 0.160832i | −0.782935 | − | 0.622103i | \(-0.786278\pi\) |
0.622103 | + | 0.782935i | \(0.286278\pi\) | |||||||
\(692\) | 485.205 | 0.701163 | ||||||||
\(693\) | − | 7.60770i | − | 0.0109779i | ||||||
\(694\) | −552.133 | + | 552.133i | −0.795581 | + | 0.795581i | ||||
\(695\) | 176.420 | − | 176.420i | 0.253842 | − | 0.253842i | ||||
\(696\) | −14.3538 | − | 14.3538i | −0.0206233 | − | 0.0206233i | ||||
\(697\) | −236.469 | − | 236.469i | −0.339267 | − | 0.339267i | ||||
\(698\) | 378.420 | 0.542150 | ||||||||
\(699\) | − | 401.769i | − | 0.574777i | ||||||
\(700\) | 31.8949 | + | 31.8949i | 0.0455641 | + | 0.0455641i | ||||
\(701\) | − | 779.520i | − | 1.11201i | −0.831178 | − | 0.556006i | \(-0.812333\pi\) | ||
0.831178 | − | 0.556006i | \(-0.187667\pi\) | |||||||
\(702\) | 43.9808 | + | 84.8038i | 0.0626507 | + | 0.120803i | ||||
\(703\) | 92.6232 | 0.131754 | ||||||||
\(704\) | 13.8564 | − | 13.8564i | 0.0196824 | − | 0.0196824i | ||||
\(705\) | −135.300 | −0.191915 | ||||||||
\(706\) | 103.741i | 0.146942i | ||||||||
\(707\) | −81.5974 | + | 81.5974i | −0.115414 | + | 0.115414i | ||||
\(708\) | −230.785 | + | 230.785i | −0.325967 | + | 0.325967i | ||||
\(709\) | 43.0179 | + | 43.0179i | 0.0606740 | + | 0.0606740i | 0.736793 | − | 0.676119i | \(-0.236339\pi\) |
−0.676119 | + | 0.736793i | \(0.736339\pi\) | |||||||
\(710\) | 68.2384 | + | 68.2384i | 0.0961104 | + | 0.0961104i | ||||
\(711\) | 12.6307 | 0.0177647 | ||||||||
\(712\) | 78.0666i | 0.109644i | ||||||||
\(713\) | 132.910 | + | 132.910i | 0.186410 | + | 0.186410i | ||||
\(714\) | − | 13.4923i | − | 0.0188967i | ||||||
\(715\) | 17.2539 | − | 54.4308i | 0.0241313 | − | 0.0761270i | ||||
\(716\) | −53.4359 | −0.0746312 | ||||||||
\(717\) | 242.454 | − | 242.454i | 0.338150 | − | 0.338150i | ||||
\(718\) | −410.238 | −0.571363 | ||||||||
\(719\) | − | 335.290i | − | 0.466328i | −0.972437 | − | 0.233164i | \(-0.925092\pi\) | ||
0.972437 | − | 0.233164i | \(-0.0749078\pi\) | |||||||
\(720\) | −15.2154 | + | 15.2154i | −0.0211325 | + | 0.0211325i | ||||
\(721\) | −52.2102 | + | 52.2102i | −0.0724136 | + | 0.0724136i | ||||
\(722\) | −73.0666 | − | 73.0666i | −0.101200 | − | 0.101200i | ||||
\(723\) | 92.5936 | + | 92.5936i | 0.128069 | + | 0.128069i | ||||
\(724\) | 512.287 | 0.707579 | ||||||||
\(725\) | 90.2666i | 0.124506i | ||||||||
\(726\) | −199.186 | − | 199.186i | −0.274361 | − | 0.274361i | ||||
\(727\) | 537.577i | 0.739445i | 0.929142 | + | 0.369723i | \(0.120547\pi\) | ||||
−0.929142 | + | 0.369723i | \(0.879453\pi\) | |||||||
\(728\) | 36.2872 | + | 11.5026i | 0.0498450 | + | 0.0158002i | ||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 14.4026 | − | 14.4026i | 0.0197296 | − | 0.0197296i | ||||
\(731\) | −197.800 | −0.270588 | ||||||||
\(732\) | − | 358.277i | − | 0.489449i | ||||||
\(733\) | −479.946 | + | 479.946i | −0.654770 | + | 0.654770i | −0.954138 | − | 0.299368i | \(-0.903224\pi\) |
0.299368 | + | 0.954138i | \(0.403224\pi\) | |||||||
\(734\) | −351.292 | + | 351.292i | −0.478600 | + | 0.478600i | ||||
\(735\) | −105.258 | − | 105.258i | −0.143208 | − | 0.143208i | ||||
\(736\) | 21.2820 | + | 21.2820i | 0.0289158 | + | 0.0289158i | ||||
\(737\) | −161.751 | −0.219473 | ||||||||
\(738\) | − | 266.669i | − | 0.361340i | ||||||
\(739\) | 512.788 | + | 512.788i | 0.693895 | + | 0.693895i | 0.963087 | − | 0.269192i | \(-0.0867565\pi\) |
−0.269192 | + | 0.963087i | \(0.586757\pi\) | |||||||
\(740\) | 15.9437i | 0.0215455i | ||||||||
\(741\) | −215.976 | − | 416.445i | −0.291465 | − | 0.562004i | ||||
\(742\) | 84.4974 | 0.113878 | ||||||||
\(743\) | 801.509 | − | 801.509i | 1.07875 | − | 1.07875i | 0.0821246 | − | 0.996622i | \(-0.473829\pi\) |
0.996622 | − | 0.0821246i | \(-0.0261705\pi\) | |||||||
\(744\) | 173.072 | 0.232623 | ||||||||
\(745\) | − | 320.092i | − | 0.429654i | ||||||
\(746\) | −131.836 | + | 131.836i | −0.176724 | + | 0.176724i | ||||
\(747\) | −329.396 | + | 329.396i | −0.440959 | + | 0.440959i | ||||
\(748\) | 18.4308 | + | 18.4308i | 0.0246401 | + | 0.0246401i | ||||
\(749\) | −85.3102 | − | 85.3102i | −0.113899 | − | 0.113899i | ||||
\(750\) | 205.492 | 0.273990 | ||||||||
\(751\) | 1384.43i | 1.84345i | 0.387849 | + | 0.921723i | \(0.373218\pi\) | ||||
−0.387849 | + | 0.921723i | \(0.626782\pi\) | |||||||
\(752\) | 123.215 | + | 123.215i | 0.163850 | + | 0.163850i | ||||
\(753\) | 729.846i | 0.969251i | ||||||||
\(754\) | 35.0718 | + | 67.6256i | 0.0465143 | + | 0.0896891i | ||||
\(755\) | 315.482 | 0.417857 | ||||||||
\(756\) | 7.60770 | − | 7.60770i | 0.0100631 | − | 0.0100631i | ||||
\(757\) | −125.836 | −0.166230 | −0.0831148 | − | 0.996540i | \(-0.526487\pi\) | ||||
−0.0831148 | + | 0.996540i | \(0.526487\pi\) | |||||||
\(758\) | 49.5974i | 0.0654319i | ||||||||
\(759\) | −15.9615 | + | 15.9615i | −0.0210297 | + | 0.0210297i | ||||
\(760\) | 74.7180 | − | 74.7180i | 0.0983131 | − | 0.0983131i | ||||
\(761\) | −3.55514 | − | 3.55514i | −0.00467166 | − | 0.00467166i | 0.704767 | − | 0.709439i | \(-0.251051\pi\) |
−0.709439 | + | 0.704767i | \(0.751051\pi\) | |||||||
\(762\) | −121.310 | − | 121.310i | −0.159200 | − | 0.159200i | ||||
\(763\) | −160.049 | −0.209762 | ||||||||
\(764\) | 258.564i | 0.338435i | ||||||||
\(765\) | −20.2384 | − | 20.2384i | −0.0264554 | − | 0.0264554i | ||||
\(766\) | − | 349.110i | − | 0.455758i | ||||||
\(767\) | 1087.30 | − | 563.894i | 1.41760 | − | 0.735194i | ||||
\(768\) | 27.7128 | 0.0360844 | ||||||||
\(769\) | −958.405 | + | 958.405i | −1.24630 | + | 1.24630i | −0.288959 | + | 0.957342i | \(0.593309\pi\) |
−0.957342 | + | 0.288959i | \(0.906691\pi\) | |||||||
\(770\) | −6.43078 | −0.00835166 | ||||||||
\(771\) | − | 432.431i | − | 0.560870i | ||||||
\(772\) | −320.564 | + | 320.564i | −0.415238 | + | 0.415238i | ||||
\(773\) | 76.8165 | − | 76.8165i | 0.0993746 | − | 0.0993746i | −0.655672 | − | 0.755046i | \(-0.727614\pi\) |
0.755046 | + | 0.655672i | \(0.227614\pi\) | |||||||
\(774\) | −111.531 | − | 111.531i | −0.144097 | − | 0.144097i | ||||
\(775\) | −544.196 | − | 544.196i | −0.702189 | − | 0.702189i | ||||
\(776\) | −16.1333 | −0.0207903 | ||||||||
\(777\) | − | 7.97183i | − | 0.0102598i | ||||||
\(778\) | −644.305 | − | 644.305i | −0.828156 | − | 0.828156i | ||||
\(779\) | 1309.53i | 1.68104i | ||||||||
\(780\) | 71.6846 | − | 37.1769i | 0.0919034 | − | 0.0476627i | ||||
\(781\) | 93.2154 | 0.119354 | ||||||||
\(782\) | −28.3078 | + | 28.3078i | −0.0361992 | + | 0.0361992i | ||||
\(783\) | 21.5307 | 0.0274978 | ||||||||
\(784\) | 191.713i | 0.244532i | ||||||||
\(785\) | −340.805 | + | 340.805i | −0.434147 | + | 0.434147i | ||||
\(786\) | 413.769 | − | 413.769i | 0.526424 | − | 0.526424i | ||||
\(787\) | −486.883 | − | 486.883i | −0.618657 | − | 0.618657i | 0.326530 | − | 0.945187i | \(-0.394121\pi\) |
−0.945187 | + | 0.326530i | \(0.894121\pi\) | |||||||
\(788\) | 218.536 | + | 218.536i | 0.277330 | + | 0.277330i | ||||
\(789\) | −164.354 | −0.208307 | ||||||||
\(790\) | − | 10.6767i | − | 0.0135148i | ||||||
\(791\) | 108.546 | + | 108.546i | 0.137227 | + | 0.137227i | ||||
\(792\) | 20.7846i | 0.0262432i | ||||||||
\(793\) | −406.277 | + | 1281.68i | −0.512329 | + | 1.61624i | ||||
\(794\) | 865.384 | 1.08990 | ||||||||
\(795\) | 126.746 | − | 126.746i | 0.159429 | − | 0.159429i | ||||
\(796\) | 50.1999 | 0.0630652 | ||||||||
\(797\) | − | 713.587i | − | 0.895341i | −0.894198 | − | 0.447671i | \(-0.852254\pi\) | ||
0.894198 | − | 0.447671i | \(-0.147746\pi\) | |||||||
\(798\) | −37.3590 | + | 37.3590i | −0.0468158 | + | 0.0468158i | ||||
\(799\) | −163.892 | + | 163.892i | −0.205122 | + | 0.205122i | ||||
\(800\) | −87.1384 | − | 87.1384i | −0.108923 | − | 0.108923i | ||||
\(801\) | −58.5500 | − | 58.5500i | −0.0730961 | − | 0.0730961i | ||||
\(802\) | −549.100 | −0.684663 | ||||||||
\(803\) | − | 19.6743i | − | 0.0245010i | ||||||
\(804\) | −161.751 | − | 161.751i | −0.201183 | − | 0.201183i | ||||
\(805\) | − | 9.87703i | − | 0.0122696i | ||||||
\(806\) | −619.138 | − | 196.259i | −0.768162 | − | 0.243498i | ||||
\(807\) | −361.608 | −0.448089 | ||||||||
\(808\) | 222.928 | − | 222.928i | 0.275901 | − | 0.275901i | ||||
\(809\) | −257.600 | −0.318418 | −0.159209 | − | 0.987245i | \(-0.550894\pi\) | ||||
−0.159209 | + | 0.987245i | \(0.550894\pi\) | |||||||
\(810\) | − | 22.8231i | − | 0.0281766i | ||||||
\(811\) | −127.258 | + | 127.258i | −0.156914 | + | 0.156914i | −0.781198 | − | 0.624283i | \(-0.785391\pi\) |
0.624283 | + | 0.781198i | \(0.285391\pi\) | |||||||
\(812\) | 6.06664 | − | 6.06664i | 0.00747123 | − | 0.00747123i | ||||
\(813\) | 659.993 | + | 659.993i | 0.811800 | + | 0.811800i | ||||
\(814\) | 10.8897 | + | 10.8897i | 0.0133780 | + | 0.0133780i | ||||
\(815\) | −117.779 | −0.144515 | ||||||||
\(816\) | 36.8616i | 0.0451735i | ||||||||
\(817\) | 547.692 | + | 547.692i | 0.670370 | + | 0.670370i | ||||
\(818\) | − | 152.374i | − | 0.186277i | ||||||
\(819\) | −35.8423 | + | 18.5885i | −0.0437635 | + | 0.0226965i | ||||
\(820\) | −225.415 | −0.274897 | ||||||||
\(821\) | 1116.87 | − | 1116.87i | 1.36038 | − | 1.36038i | 0.486953 | − | 0.873428i | \(-0.338108\pi\) |
0.873428 | − | 0.486953i | \(-0.161892\pi\) | |||||||
\(822\) | −318.515 | −0.387488 | ||||||||
\(823\) | 617.920i | 0.750814i | 0.926860 | + | 0.375407i | \(0.122497\pi\) | ||||
−0.926860 | + | 0.375407i | \(0.877503\pi\) | |||||||
\(824\) | 142.641 | − | 142.641i | 0.173108 | − | 0.173108i | ||||
\(825\) | 65.3538 | − | 65.3538i | 0.0792168 | − | 0.0792168i | ||||
\(826\) | −97.5411 | − | 97.5411i | −0.118088 | − | 0.118088i | ||||
\(827\) | 349.847 | + | 349.847i | 0.423032 | + | 0.423032i | 0.886246 | − | 0.463214i | \(-0.153304\pi\) |
−0.463214 | + | 0.886246i | \(0.653304\pi\) | |||||||
\(828\) | −31.9230 | −0.0385544 | ||||||||
\(829\) | − | 247.646i | − | 0.298729i | −0.988782 | − | 0.149364i | \(-0.952277\pi\) | ||
0.988782 | − | 0.149364i | \(-0.0477227\pi\) | |||||||
\(830\) | 278.438 | + | 278.438i | 0.335468 | + | 0.335468i | ||||
\(831\) | − | 119.138i | − | 0.143368i | ||||||
\(832\) | −99.1384 | − | 31.4256i | −0.119157 | − | 0.0377712i | ||||
\(833\) | −255.002 | −0.306125 | ||||||||
\(834\) | 240.995 | − | 240.995i | 0.288963 | − | 0.288963i | ||||
\(835\) | −303.069 | −0.362957 | ||||||||
\(836\) | − | 102.067i | − | 0.122089i | ||||||
\(837\) | −129.804 | + | 129.804i | −0.155082 | + | 0.155082i | ||||
\(838\) | 76.8231 | − | 76.8231i | 0.0916743 | − | 0.0916743i | ||||
\(839\) | −598.868 | − | 598.868i | −0.713788 | − | 0.713788i | 0.253538 | − | 0.967325i | \(-0.418406\pi\) |
−0.967325 | + | 0.253538i | \(0.918406\pi\) | |||||||
\(840\) | −6.43078 | − | 6.43078i | −0.00765569 | − | 0.00765569i | ||||
\(841\) | −823.831 | −0.979585 | ||||||||
\(842\) | − | 235.513i | − | 0.279707i | ||||||
\(843\) | 120.588 | + | 120.588i | 0.143047 | + | 0.143047i | ||||
\(844\) | − | 413.436i | − | 0.489853i | ||||||
\(845\) | −298.599 | + | 51.7063i | −0.353371 | + | 0.0611909i | ||||
\(846\) | −184.823 | −0.218467 | ||||||||
\(847\) | 84.1858 | − | 84.1858i | 0.0993930 | − | 0.0993930i | ||||
\(848\) | −230.851 | −0.272230 | ||||||||
\(849\) | − | 737.520i | − | 0.868693i | ||||||
\(850\) | 115.905 | − | 115.905i | 0.136359 | − | 0.136359i | ||||
\(851\) | −16.7255 | + | 16.7255i | −0.0196540 | + | 0.0196540i | ||||
\(852\) | 93.2154 | + | 93.2154i | 0.109408 | + | 0.109408i | ||||
\(853\) | −519.210 | − | 519.210i | −0.608687 | − | 0.608687i | 0.333916 | − | 0.942603i | \(-0.391630\pi\) |
−0.942603 | + | 0.333916i | \(0.891630\pi\) | |||||||
\(854\) | 151.426 | 0.177313 | ||||||||
\(855\) | 112.077i | 0.131084i | ||||||||
\(856\) | 233.072 | + | 233.072i | 0.272280 | + | 0.272280i | ||||
\(857\) | 226.756i | 0.264593i | 0.991210 | + | 0.132297i | \(0.0422351\pi\) | ||||
−0.991210 | + | 0.132297i | \(0.957765\pi\) | |||||||
\(858\) | 23.5692 | − | 74.3538i | 0.0274700 | − | 0.0866595i | ||||
\(859\) | 950.656 | 1.10670 | 0.553350 | − | 0.832949i | \(-0.313349\pi\) | ||||
0.553350 | + | 0.832949i | \(0.313349\pi\) | |||||||
\(860\) | −94.2769 | + | 94.2769i | −0.109624 | + | 0.109624i | ||||
\(861\) | 112.708 | 0.130903 | ||||||||
\(862\) | − | 724.956i | − | 0.841017i | ||||||
\(863\) | 773.711 | − | 773.711i | 0.896537 | − | 0.896537i | −0.0985910 | − | 0.995128i | \(-0.531434\pi\) |
0.995128 | + | 0.0985910i | \(0.0314336\pi\) | |||||||
\(864\) | −20.7846 | + | 20.7846i | −0.0240563 | + | 0.0240563i | ||||
\(865\) | 307.608 | + | 307.608i | 0.355616 | + | 0.355616i | ||||
\(866\) | −197.292 | − | 197.292i | −0.227820 | − | 0.227820i | ||||
\(867\) | 451.532 | 0.520798 | ||||||||
\(868\) | 73.1487i | 0.0842728i | ||||||||
\(869\) | −7.29234 | − | 7.29234i | −0.00839165 | − | 0.00839165i | ||||
\(870\) | − | 18.1999i | − | 0.0209195i | ||||||
\(871\) | 395.219 | + | 762.063i | 0.453753 | + | 0.874929i | ||||
\(872\) | 437.261 | 0.501447 | ||||||||
\(873\) | 12.1000 | − | 12.1000i | 0.0138602 | − | 0.0138602i | ||||
\(874\) | 156.764 | 0.179364 | ||||||||
\(875\) | 86.8513i | 0.0992586i | ||||||||
\(876\) | 19.6743 | − | 19.6743i | 0.0224593 | − | 0.0224593i | ||||
\(877\) | 646.713 | − | 646.713i | 0.737415 | − | 0.737415i | −0.234662 | − | 0.972077i | \(-0.575398\pi\) |
0.972077 | + | 0.234662i | \(0.0753984\pi\) | |||||||
\(878\) | 272.238 | + | 272.238i | 0.310067 | + | 0.310067i | ||||
\(879\) | 530.081 | + | 530.081i | 0.603050 | + | 0.603050i | ||||
\(880\) | 17.5692 | 0.0199650 | ||||||||
\(881\) | − | 783.997i | − | 0.889895i | −0.895557 | − | 0.444947i | \(-0.853222\pi\) | ||
0.895557 | − | 0.444947i | \(-0.146778\pi\) | |||||||
\(882\) | −143.785 | − | 143.785i | −0.163021 | − | 0.163021i | ||||
\(883\) | − | 1089.81i | − | 1.23421i | −0.786881 | − | 0.617105i | \(-0.788305\pi\) | ||
0.786881 | − | 0.617105i | \(-0.211695\pi\) | |||||||
\(884\) | 41.8001 | − | 131.867i | 0.0472852 | − | 0.149170i | ||||
\(885\) | −292.623 | −0.330648 | ||||||||
\(886\) | 74.7358 | − | 74.7358i | 0.0843519 | − | 0.0843519i | ||||
\(887\) | −1057.03 | −1.19169 | −0.595846 | − | 0.803099i | \(-0.703183\pi\) | ||||
−0.595846 | + | 0.803099i | \(0.703183\pi\) | |||||||
\(888\) | 21.7795i | 0.0245264i | ||||||||
\(889\) | 51.2717 | − | 51.2717i | 0.0576735 | − | 0.0576735i | ||||
\(890\) | −49.4923 | + | 49.4923i | −0.0556093 | + | 0.0556093i | ||||
\(891\) | −15.5885 | − | 15.5885i | −0.0174955 | − | 0.0174955i | ||||
\(892\) | −278.823 | − | 278.823i | −0.312582 | − | 0.312582i | ||||
\(893\) | 907.608 | 1.01636 | ||||||||
\(894\) | − | 437.254i | − | 0.489098i | ||||||
\(895\) | −33.8770 | − | 33.8770i | −0.0378514 | − | 0.0378514i | ||||
\(896\) | 11.7128i | 0.0130723i | ||||||||
\(897\) | 114.200 | + | 36.1999i | 0.127313 | + | 0.0403567i | ||||
\(898\) | 1032.45 | 1.14972 | ||||||||
\(899\) | −103.510 | + | 103.510i | −0.115139 | + | 0.115139i | ||||
\(900\) | 130.708 | 0.145231 | ||||||||
\(901\) | − | 307.061i | − | 0.340801i | ||||||
\(902\) | −153.962 | + | 153.962i | −0.170689 | + | 0.170689i | ||||
\(903\) | 47.1384 | − | 47.1384i | 0.0522020 | − | 0.0522020i | ||||
\(904\) | −296.554 | − | 296.554i | −0.328046 | − | 0.328046i | ||||
\(905\) | 324.777 | + | 324.777i | 0.358870 | + | 0.358870i | ||||
\(906\) | 430.956 | 0.475669 | ||||||||
\(907\) | 546.669i | 0.602722i | 0.953510 | + | 0.301361i | \(0.0974410\pi\) | ||||
−0.953510 | + | 0.301361i | \(0.902559\pi\) | |||||||
\(908\) | 194.736 | + | 194.736i | 0.214467 | + | 0.214467i | ||||
\(909\) | 334.392i | 0.367868i | ||||||||
\(910\) | 15.7128 | + | 30.2975i | 0.0172668 | + | 0.0332940i | ||||
\(911\) | 724.743 | 0.795547 | 0.397774 | − | 0.917484i | \(-0.369783\pi\) | ||||
0.397774 | + | 0.917484i | \(0.369783\pi\) | |||||||
\(912\) | 102.067 | − | 102.067i | 0.111915 | − | 0.111915i | ||||
\(913\) | 380.354 | 0.416598 | ||||||||
\(914\) | 101.923i | 0.111513i | ||||||||
\(915\) | 227.138 | − | 227.138i | 0.248239 | − | 0.248239i | ||||
\(916\) | 408.354 | − | 408.354i | 0.445801 | − | 0.445801i | ||||
\(917\) | 174.879 | + | 174.879i | 0.190708 | + | 0.190708i | ||||
\(918\) | −27.6462 | − | 27.6462i | −0.0301157 | − | 0.0301157i | ||||
\(919\) | −941.108 | −1.02406 | −0.512028 | − | 0.858969i | \(-0.671106\pi\) | ||||
−0.512028 | + | 0.858969i | \(0.671106\pi\) | |||||||
\(920\) | 26.9845i | 0.0293310i | ||||||||
\(921\) | 426.970 | + | 426.970i | 0.463594 | + | 0.463594i | ||||
\(922\) | − | 405.100i | − | 0.439371i | ||||||
\(923\) | −227.760 | − | 439.168i | −0.246761 | − | 0.475805i | ||||
\(924\) | −8.78461 | −0.00950715 | ||||||||
\(925\) | 68.4820 | − | 68.4820i | 0.0740345 | − | 0.0740345i | ||||
\(926\) | −446.495 | −0.482176 | ||||||||
\(927\) | 213.962i | 0.230811i | ||||||||
\(928\) | −16.5744 | + | 16.5744i | −0.0178603 | + | 0.0178603i | ||||
\(929\) | −260.130 | + | 260.130i | −0.280010 | + | 0.280010i | −0.833113 | − | 0.553103i | \(-0.813444\pi\) |
0.553103 | + | 0.833113i | \(0.313444\pi\) | |||||||
\(930\) | 109.723 | + | 109.723i | 0.117982 | + | 0.117982i | ||||
\(931\) | 706.081 | + | 706.081i | 0.758411 | + | 0.758411i | ||||
\(932\) | −463.923 | −0.497772 | ||||||||
\(933\) | − | 542.785i | − | 0.581763i | ||||||
\(934\) | 161.818 | + | 161.818i | 0.173253 | + | 0.173253i | ||||
\(935\) | 23.3693i | 0.0249939i | ||||||||
\(936\) | 97.9230 | − | 50.7846i | 0.104619 | − | 0.0542571i | ||||
\(937\) | 1387.56 | 1.48085 | 0.740426 | − | 0.672138i | \(-0.234624\pi\) | ||||
0.740426 | + | 0.672138i | \(0.234624\pi\) | |||||||
\(938\) | 68.3641 | − | 68.3641i | 0.0728829 | − | 0.0728829i | ||||
\(939\) | −455.254 | −0.484828 | ||||||||
\(940\) | 156.231i | 0.166203i | ||||||||
\(941\) | −61.6012 | + | 61.6012i | −0.0654635 | + | 0.0654635i | −0.739081 | − | 0.673617i | \(-0.764740\pi\) |
0.673617 | + | 0.739081i | \(0.264740\pi\) | |||||||
\(942\) | −465.549 | + | 465.549i | −0.494213 | + | 0.494213i | ||||
\(943\) | −236.469 | − | 236.469i | −0.250763 | − | 0.250763i | ||||
\(944\) | 266.487 | + | 266.487i | 0.282296 | + | 0.282296i | ||||
\(945\) | 9.64617 | 0.0102076 | ||||||||
\(946\) | 128.785i | 0.136136i | ||||||||
\(947\) | 54.5064 | + | 54.5064i | 0.0575569 | + | 0.0575569i | 0.735299 | − | 0.677742i | \(-0.237042\pi\) |
−0.677742 | + | 0.735299i | \(0.737042\pi\) | |||||||
\(948\) | − | 14.5847i | − | 0.0153847i | ||||||
\(949\) | −92.6922 | + | 48.0718i | −0.0976735 | + | 0.0506552i | ||||
\(950\) | −641.864 | −0.675646 | ||||||||
\(951\) | −258.042 | + | 258.042i | −0.271338 | + | 0.271338i | ||||
\(952\) | −15.5795 | −0.0163651 | ||||||||
\(953\) | 1079.56i | 1.13280i | 0.824131 | + | 0.566399i | \(0.191664\pi\) | ||||
−0.824131 | + | 0.566399i | \(0.808336\pi\) | |||||||
\(954\) | 173.138 | − | 173.138i | 0.181487 | − | 0.181487i | ||||
\(955\) | −163.923 | + | 163.923i | −0.171647 | + | 0.171647i | ||||
\(956\) | −279.962 | − | 279.962i | −0.292847 | − | 0.292847i | ||||
\(957\) | −12.4308 | − | 12.4308i | −0.0129893 | − | 0.0129893i | ||||
\(958\) | −178.259 | −0.186074 | ||||||||
\(959\) | − | 134.620i | − | 0.140376i | ||||||
\(960\) | 17.5692 | + | 17.5692i | 0.0183013 | + | 0.0183013i | ||||
\(961\) | − | 287.077i | − | 0.298727i | ||||||
\(962\) | 24.6973 | − | 77.9127i | 0.0256729 | − | 0.0809904i | ||||
\(963\) | −349.608 | −0.363040 | ||||||||
\(964\) | 106.918 | − | 106.918i | 0.110911 | − | 0.110911i | ||||
\(965\) | −406.459 | −0.421201 | ||||||||
\(966\) | − | 13.4923i | − | 0.0139672i | ||||||
\(967\) | 493.745 | − | 493.745i | 0.510594 | − | 0.510594i | −0.404114 | − | 0.914709i | \(-0.632420\pi\) |
0.914709 | + | 0.404114i | \(0.132420\pi\) | |||||||
\(968\) | −230.000 | + | 230.000i | −0.237603 | + | 0.237603i | ||||
\(969\) | 135.762 | + | 135.762i | 0.140105 | + | 0.140105i | ||||
\(970\) | −10.2281 | − | 10.2281i | −0.0105444 | − | 0.0105444i | ||||
\(971\) | −1694.52 | −1.74513 | −0.872566 | − | 0.488497i | \(-0.837545\pi\) | ||||
−0.872566 | + | 0.488497i | \(0.837545\pi\) | |||||||
\(972\) | − | 31.1769i | − | 0.0320750i | ||||||
\(973\) | 101.856 | + | 101.856i | 0.104683 | + | 0.104683i | ||||
\(974\) | 1054.88i | 1.08304i | ||||||||
\(975\) | −467.587 | − | 148.219i | −0.479576 | − | 0.152020i | ||||
\(976\) | −413.703 | −0.423876 | ||||||||
\(977\) | −390.060 | + | 390.060i | −0.399243 | + | 0.399243i | −0.877966 | − | 0.478723i | \(-0.841100\pi\) |
0.478723 | + | 0.877966i | \(0.341100\pi\) | |||||||
\(978\) | −160.890 | −0.164509 | ||||||||
\(979\) | 67.6077i | 0.0690579i | ||||||||
\(980\) | −121.541 | + | 121.541i | −0.124021 | + | 0.124021i | ||||
\(981\) | −327.946 | + | 327.946i | −0.334298 | + | 0.334298i | ||||
\(982\) | 700.726 | + | 700.726i | 0.713570 | + | 0.713570i | ||||
\(983\) | −1123.12 | − | 1123.12i | −1.14254 | − | 1.14254i | −0.987984 | − | 0.154559i | \(-0.950604\pi\) |
−0.154559 | − | 0.987984i | \(-0.549396\pi\) | |||||||
\(984\) | −307.923 | −0.312930 | ||||||||
\(985\) | 277.092i | 0.281312i | ||||||||
\(986\) | −22.0460 | − | 22.0460i | −0.0223590 | − | 0.0223590i | ||||
\(987\) | − | 78.1154i | − | 0.0791443i | ||||||
\(988\) | −480.869 | + | 249.387i | −0.486710 | + | 0.252416i | ||||
\(989\) | −197.800 | −0.200000 | ||||||||
\(990\) | −13.1769 | + | 13.1769i | −0.0133100 | + | 0.0133100i | ||||
\(991\) | 610.985 | 0.616533 | 0.308267 | − | 0.951300i | \(-0.400251\pi\) | ||||
0.308267 | + | 0.951300i | \(0.400251\pi\) | |||||||
\(992\) | − | 199.846i | − | 0.201458i | ||||||
\(993\) | −512.463 | + | 512.463i | −0.516075 | + | 0.516075i | ||||
\(994\) | −39.3975 | + | 39.3975i | −0.0396353 | + | 0.0396353i | ||||
\(995\) | 31.8255 | + | 31.8255i | 0.0319854 | + | 0.0319854i | ||||
\(996\) | 380.354 | + | 380.354i | 0.381881 | + | 0.381881i | ||||
\(997\) | −412.123 | −0.413363 | −0.206682 | − | 0.978408i | \(-0.566266\pi\) | ||||
−0.206682 | + | 0.978408i | \(0.566266\pi\) | |||||||
\(998\) | − | 558.131i | − | 0.559249i | ||||||
\(999\) | −16.3346 | − | 16.3346i | −0.0163509 | − | 0.0163509i |
(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 | 78.3.f.a.31.2 | ✓ | 4 | |
3.2 | odd | 2 | 234.3.i.b.109.2 | 4 | |||
4.3 | odd | 2 | 624.3.ba.a.577.1 | 4 | |||
13.5 | odd | 4 | 1014.3.f.a.775.2 | 4 | |||
13.8 | odd | 4 | inner | 78.3.f.a.73.2 | yes | 4 | |
13.12 | even | 2 | 1014.3.f.a.577.2 | 4 | |||
39.8 | even | 4 | 234.3.i.b.73.2 | 4 | |||
52.47 | even | 4 | 624.3.ba.a.385.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
78.3.f.a.31.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
78.3.f.a.73.2 | yes | 4 | 13.8 | odd | 4 | inner | |
234.3.i.b.73.2 | 4 | 39.8 | even | 4 | |||
234.3.i.b.109.2 | 4 | 3.2 | odd | 2 | |||
624.3.ba.a.385.1 | 4 | 52.47 | even | 4 | |||
624.3.ba.a.577.1 | 4 | 4.3 | odd | 2 | |||
1014.3.f.a.577.2 | 4 | 13.12 | even | 2 | |||
1014.3.f.a.775.2 | 4 | 13.5 | odd | 4 |