Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,4,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, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("245.116");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
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: | \(14.4554679514\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 11x^{2} + 121 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 226.2 | ||
Root | \(1.65831 - 2.87228i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.226 |
Dual form | 245.4.e.j.116.2 |
$q$-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 \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.15831 | − | 2.00626i | 0.409525 | − | 0.709319i | −0.585311 | − | 0.810809i | \(-0.699028\pi\) |
0.994837 | + | 0.101490i | \(0.0323610\pi\) | |||||||
\(3\) | −2.50000 | − | 4.33013i | −0.481125 | − | 0.833333i | 0.518640 | − | 0.854993i | \(-0.326438\pi\) |
−0.999765 | + | 0.0216593i | \(0.993105\pi\) | |||||||
\(4\) | 1.31662 | + | 2.28046i | 0.164578 | + | 0.285058i | ||||
\(5\) | −2.50000 | + | 4.33013i | −0.223607 | + | 0.387298i | ||||
\(6\) | −11.5831 | −0.788132 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 24.6332 | 1.08865 | ||||||||
\(9\) | 1.00000 | − | 1.73205i | 0.0370370 | − | 0.0641500i | ||||
\(10\) | 5.79156 | + | 10.0313i | 0.183145 | + | 0.317217i | ||||
\(11\) | −23.1332 | − | 40.0680i | −0.634085 | − | 1.09827i | −0.986708 | − | 0.162502i | \(-0.948044\pi\) |
0.352623 | − | 0.935765i | \(-0.385290\pi\) | |||||||
\(12\) | 6.58312 | − | 11.4023i | 0.158365 | − | 0.274297i | ||||
\(13\) | −61.3325 | −1.30851 | −0.654253 | − | 0.756276i | \(-0.727017\pi\) | ||||
−0.654253 | + | 0.756276i | \(0.727017\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 25.0000 | 0.430331 | ||||||||
\(16\) | 18.0000 | − | 31.1769i | 0.281250 | − | 0.487139i | ||||
\(17\) | −50.6662 | − | 87.7565i | −0.722845 | − | 1.25200i | −0.959855 | − | 0.280497i | \(-0.909501\pi\) |
0.237009 | − | 0.971507i | \(-0.423833\pi\) | |||||||
\(18\) | −2.31662 | − | 4.01251i | −0.0303352 | − | 0.0525421i | ||||
\(19\) | −1.83375 | + | 3.17615i | −0.0221417 | + | 0.0383505i | −0.876884 | − | 0.480702i | \(-0.840382\pi\) |
0.854742 | + | 0.519053i | \(0.173715\pi\) | |||||||
\(20\) | −13.1662 | −0.147203 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −107.182 | −1.03870 | ||||||||
\(23\) | −42.4327 | + | 73.4957i | −0.384689 | + | 0.666300i | −0.991726 | − | 0.128373i | \(-0.959025\pi\) |
0.607037 | + | 0.794673i | \(0.292358\pi\) | |||||||
\(24\) | −61.5831 | − | 106.665i | −0.523775 | − | 0.907205i | ||||
\(25\) | −12.5000 | − | 21.6506i | −0.100000 | − | 0.173205i | ||||
\(26\) | −71.0422 | + | 123.049i | −0.535866 | + | 0.928147i | ||||
\(27\) | −145.000 | −1.03353 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 30.1980 | 0.193366 | 0.0966832 | − | 0.995315i | \(-0.469177\pi\) | ||||
0.0966832 | + | 0.995315i | \(0.469177\pi\) | |||||||
\(30\) | 28.9578 | − | 50.1564i | 0.176232 | − | 0.305242i | ||||
\(31\) | −94.4987 | − | 163.677i | −0.547499 | − | 0.948296i | −0.998445 | − | 0.0557451i | \(-0.982247\pi\) |
0.450946 | − | 0.892551i | \(-0.351087\pi\) | |||||||
\(32\) | 56.8338 | + | 98.4389i | 0.313965 | + | 0.543803i | ||||
\(33\) | −115.666 | + | 200.340i | −0.610149 | + | 1.05681i | ||||
\(34\) | −234.749 | −1.18409 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.26650 | 0.0243819 | ||||||||
\(37\) | −9.03425 | + | 15.6478i | −0.0401411 | + | 0.0695265i | −0.885398 | − | 0.464834i | \(-0.846114\pi\) |
0.845257 | + | 0.534360i | \(0.179447\pi\) | |||||||
\(38\) | 4.24812 | + | 7.35795i | 0.0181351 | + | 0.0314110i | ||||
\(39\) | 153.331 | + | 265.577i | 0.629555 | + | 1.09042i | ||||
\(40\) | −61.5831 | + | 106.665i | −0.243429 | + | 0.421631i | ||||
\(41\) | 481.662 | 1.83471 | 0.917354 | − | 0.398072i | \(-0.130321\pi\) | ||||
0.917354 | + | 0.398072i | \(0.130321\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −97.7995 | −0.346844 | −0.173422 | − | 0.984848i | \(-0.555482\pi\) | ||||
−0.173422 | + | 0.984848i | \(0.555482\pi\) | |||||||
\(44\) | 60.9156 | − | 105.509i | 0.208713 | − | 0.361502i | ||||
\(45\) | 5.00000 | + | 8.66025i | 0.0165635 | + | 0.0286888i | ||||
\(46\) | 98.3008 | + | 170.262i | 0.315079 | + | 0.545734i | ||||
\(47\) | −58.8325 | + | 101.901i | −0.182587 | + | 0.316250i | −0.942761 | − | 0.333470i | \(-0.891781\pi\) |
0.760174 | + | 0.649720i | \(0.225114\pi\) | |||||||
\(48\) | −180.000 | −0.541266 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −57.9156 | −0.163810 | ||||||||
\(51\) | −253.331 | + | 438.783i | −0.695558 | + | 1.20474i | ||||
\(52\) | −80.7519 | − | 139.866i | −0.215351 | − | 0.373000i | ||||
\(53\) | −333.997 | − | 578.501i | −0.865624 | − | 1.49931i | −0.866426 | − | 0.499305i | \(-0.833589\pi\) |
0.000801827 | − | 1.00000i | \(-0.499745\pi\) | |||||||
\(54\) | −167.955 | + | 290.907i | −0.423256 | + | 0.733101i | ||||
\(55\) | 231.332 | 0.567143 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 18.3375 | 0.0426116 | ||||||||
\(58\) | 34.9787 | − | 60.5849i | 0.0791884 | − | 0.137158i | ||||
\(59\) | −28.6675 | − | 49.6536i | −0.0632575 | − | 0.109565i | 0.832662 | − | 0.553781i | \(-0.186816\pi\) |
−0.895920 | + | 0.444216i | \(0.853482\pi\) | |||||||
\(60\) | 32.9156 | + | 57.0115i | 0.0708231 | + | 0.122669i | ||||
\(61\) | −369.499 | + | 639.991i | −0.775565 | + | 1.34332i | 0.158911 | + | 0.987293i | \(0.449202\pi\) |
−0.934476 | + | 0.356025i | \(0.884132\pi\) | |||||||
\(62\) | −437.836 | −0.896859 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 551.325 | 1.07681 | ||||||||
\(65\) | 153.331 | − | 265.577i | 0.292591 | − | 0.506782i | ||||
\(66\) | 267.955 | + | 464.112i | 0.499743 | + | 0.865580i | ||||
\(67\) | −276.198 | − | 478.389i | −0.503626 | − | 0.872306i | −0.999991 | − | 0.00419224i | \(-0.998666\pi\) |
0.496365 | − | 0.868114i | \(-0.334668\pi\) | |||||||
\(68\) | 133.417 | − | 231.085i | 0.237929 | − | 0.412105i | ||||
\(69\) | 424.327 | 0.740334 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −740.264 | −1.23737 | −0.618684 | − | 0.785640i | \(-0.712334\pi\) | ||||
−0.618684 | + | 0.785640i | \(0.712334\pi\) | |||||||
\(72\) | 24.6332 | − | 42.6660i | 0.0403202 | − | 0.0698367i | ||||
\(73\) | −116.662 | − | 202.065i | −0.187045 | − | 0.323972i | 0.757218 | − | 0.653162i | \(-0.226558\pi\) |
−0.944264 | + | 0.329190i | \(0.893224\pi\) | |||||||
\(74\) | 20.9290 | + | 36.2501i | 0.0328776 | + | 0.0569457i | ||||
\(75\) | −62.5000 | + | 108.253i | −0.0962250 | + | 0.166667i | ||||
\(76\) | −9.65745 | −0.0145761 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 710.422 | 1.03127 | ||||||||
\(79\) | 537.593 | − | 931.138i | 0.765619 | − | 1.32609i | −0.174300 | − | 0.984693i | \(-0.555766\pi\) |
0.939919 | − | 0.341398i | \(-0.110901\pi\) | |||||||
\(80\) | 90.0000 | + | 155.885i | 0.125779 | + | 0.217855i | ||||
\(81\) | 335.500 | + | 581.103i | 0.460219 | + | 0.797124i | ||||
\(82\) | 557.916 | − | 966.338i | 0.751359 | − | 1.30139i | ||||
\(83\) | 683.325 | 0.903671 | 0.451835 | − | 0.892101i | \(-0.350769\pi\) | ||||
0.451835 | + | 0.892101i | \(0.350769\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 506.662 | 0.646532 | ||||||||
\(86\) | −113.282 | + | 196.211i | −0.142041 | + | 0.246023i | ||||
\(87\) | −75.4950 | − | 130.761i | −0.0930335 | − | 0.161139i | ||||
\(88\) | −569.847 | − | 987.004i | −0.690294 | − | 1.19562i | ||||
\(89\) | 690.159 | − | 1195.39i | 0.821985 | − | 1.42372i | −0.0822166 | − | 0.996614i | \(-0.526200\pi\) |
0.904202 | − | 0.427106i | \(-0.140467\pi\) | |||||||
\(90\) | 23.1662 | 0.0271326 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −223.472 | −0.253245 | ||||||||
\(93\) | −472.494 | + | 818.383i | −0.526831 | + | 0.912499i | ||||
\(94\) | 136.293 | + | 236.066i | 0.149548 | + | 0.259025i | ||||
\(95\) | −9.16876 | − | 15.8808i | −0.00990205 | − | 0.0171509i | ||||
\(96\) | 284.169 | − | 492.195i | 0.302113 | − | 0.523275i | ||||
\(97\) | 218.008 | 0.228199 | 0.114100 | − | 0.993469i | \(-0.463602\pi\) | ||||
0.114100 | + | 0.993469i | \(0.463602\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −92.5330 | −0.0939385 | ||||||||
\(100\) | 32.9156 | − | 57.0115i | 0.0329156 | − | 0.0570115i | ||||
\(101\) | 737.164 | + | 1276.81i | 0.726243 | + | 1.25789i | 0.958460 | + | 0.285226i | \(0.0920686\pi\) |
−0.232217 | + | 0.972664i | \(0.574598\pi\) | |||||||
\(102\) | 586.873 | + | 1016.49i | 0.569697 | + | 0.986745i | ||||
\(103\) | 405.495 | − | 702.338i | 0.387909 | − | 0.671878i | −0.604259 | − | 0.796788i | \(-0.706531\pi\) |
0.992168 | + | 0.124910i | \(0.0398642\pi\) | |||||||
\(104\) | −1510.82 | −1.42450 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1547.49 | −1.41798 | ||||||||
\(107\) | −220.330 | + | 381.623i | −0.199066 | + | 0.344793i | −0.948226 | − | 0.317596i | \(-0.897124\pi\) |
0.749160 | + | 0.662390i | \(0.230458\pi\) | |||||||
\(108\) | −190.911 | − | 330.667i | −0.170096 | − | 0.294615i | ||||
\(109\) | 953.094 | + | 1650.81i | 0.837522 | + | 1.45063i | 0.891961 | + | 0.452113i | \(0.149330\pi\) |
−0.0544393 | + | 0.998517i | \(0.517337\pi\) | |||||||
\(110\) | 267.955 | − | 464.112i | 0.232259 | − | 0.402285i | ||||
\(111\) | 90.3425 | 0.0772517 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 962.470 | 0.801252 | 0.400626 | − | 0.916242i | \(-0.368793\pi\) | ||||
0.400626 | + | 0.916242i | \(0.368793\pi\) | |||||||
\(114\) | 21.2406 | − | 36.7898i | 0.0174505 | − | 0.0302252i | ||||
\(115\) | −212.164 | − | 367.478i | −0.172038 | − | 0.297979i | ||||
\(116\) | 39.7594 | + | 68.8653i | 0.0318239 | + | 0.0551206i | ||||
\(117\) | −61.3325 | + | 106.231i | −0.0484632 | + | 0.0839407i | ||||
\(118\) | −132.824 | −0.103622 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 615.831 | 0.468479 | ||||||||
\(121\) | −404.794 | + | 701.125i | −0.304128 | + | 0.526765i | ||||
\(122\) | 855.990 | + | 1482.62i | 0.635227 | + | 1.10025i | ||||
\(123\) | −1204.16 | − | 2085.66i | −0.882724 | − | 1.52892i | ||||
\(124\) | 248.839 | − | 431.001i | 0.180213 | − | 0.312138i | ||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1621.74 | −1.13312 | −0.566558 | − | 0.824022i | \(-0.691725\pi\) | ||||
−0.566558 | + | 0.824022i | \(0.691725\pi\) | |||||||
\(128\) | 183.937 | − | 318.587i | 0.127014 | − | 0.219995i | ||||
\(129\) | 244.499 | + | 423.484i | 0.166875 | + | 0.289037i | ||||
\(130\) | −355.211 | − | 615.243i | −0.239647 | − | 0.415080i | ||||
\(131\) | 690.159 | − | 1195.39i | 0.460301 | − | 0.797265i | −0.538675 | − | 0.842514i | \(-0.681075\pi\) |
0.998976 | + | 0.0452490i | \(0.0144081\pi\) | |||||||
\(132\) | −609.156 | −0.401668 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1279.69 | −0.824991 | ||||||||
\(135\) | 362.500 | − | 627.868i | 0.231104 | − | 0.400284i | ||||
\(136\) | −1248.07 | − | 2161.73i | −0.786923 | − | 1.36299i | ||||
\(137\) | 974.829 | + | 1688.45i | 0.607921 | + | 1.05295i | 0.991582 | + | 0.129477i | \(0.0413298\pi\) |
−0.383661 | + | 0.923474i | \(0.625337\pi\) | |||||||
\(138\) | 491.504 | − | 851.309i | 0.303185 | − | 0.525132i | ||||
\(139\) | 2800.00 | 1.70858 | 0.854291 | − | 0.519795i | \(-0.173992\pi\) | ||||
0.854291 | + | 0.519795i | \(0.173992\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 588.325 | 0.351389 | ||||||||
\(142\) | −857.457 | + | 1485.16i | −0.506734 | + | 0.877689i | ||||
\(143\) | 1418.82 | + | 2457.47i | 0.829704 | + | 1.43709i | ||||
\(144\) | −36.0000 | − | 62.3538i | −0.0208333 | − | 0.0360844i | ||||
\(145\) | −75.4950 | + | 130.761i | −0.0432380 | + | 0.0748905i | ||||
\(146\) | −540.526 | −0.306399 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −47.5789 | −0.0264254 | ||||||||
\(149\) | 717.058 | − | 1241.98i | 0.394253 | − | 0.682866i | −0.598752 | − | 0.800934i | \(-0.704337\pi\) |
0.993006 | + | 0.118068i | \(0.0376700\pi\) | |||||||
\(150\) | 144.789 | + | 250.782i | 0.0788132 | + | 0.136508i | ||||
\(151\) | 992.791 | + | 1719.56i | 0.535047 | + | 0.926729i | 0.999161 | + | 0.0409537i | \(0.0130396\pi\) |
−0.464114 | + | 0.885776i | \(0.653627\pi\) | |||||||
\(152\) | −45.1713 | + | 78.2389i | −0.0241044 | + | 0.0417501i | ||||
\(153\) | −202.665 | −0.107088 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 944.987 | 0.489698 | ||||||||
\(156\) | −403.759 | + | 699.332i | −0.207222 | + | 0.358919i | ||||
\(157\) | −20.3300 | − | 35.2126i | −0.0103345 | − | 0.0178998i | 0.860812 | − | 0.508923i | \(-0.169956\pi\) |
−0.871146 | + | 0.491023i | \(0.836623\pi\) | |||||||
\(158\) | −1245.40 | − | 2157.10i | −0.627081 | − | 1.08614i | ||||
\(159\) | −1669.99 | + | 2892.50i | −0.832947 | + | 1.44271i | ||||
\(160\) | −568.338 | −0.280819 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1554.46 | 0.753886 | ||||||||
\(163\) | 1976.99 | − | 3424.25i | 0.950000 | − | 1.64545i | 0.204584 | − | 0.978849i | \(-0.434416\pi\) |
0.745416 | − | 0.666599i | \(-0.232251\pi\) | |||||||
\(164\) | 634.169 | + | 1098.41i | 0.301953 | + | 0.522998i | ||||
\(165\) | −578.331 | − | 1001.70i | −0.272867 | − | 0.472619i | ||||
\(166\) | 791.504 | − | 1370.92i | 0.370076 | − | 0.640990i | ||||
\(167\) | 3380.30 | 1.56632 | 0.783161 | − | 0.621819i | \(-0.213606\pi\) | ||||
0.783161 | + | 0.621819i | \(0.213606\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1564.68 | 0.712187 | ||||||||
\(170\) | 586.873 | − | 1016.49i | 0.264771 | − | 0.458598i | ||||
\(171\) | 3.66750 | + | 6.35230i | 0.00164012 | + | 0.00284078i | ||||
\(172\) | −128.765 | − | 223.028i | −0.0570829 | − | 0.0988705i | ||||
\(173\) | −1603.33 | + | 2777.05i | −0.704619 | + | 1.22044i | 0.262210 | + | 0.965011i | \(0.415549\pi\) |
−0.966829 | + | 0.255424i | \(0.917785\pi\) | |||||||
\(174\) | −349.787 | −0.152398 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1665.59 | −0.713346 | ||||||||
\(177\) | −143.338 | + | 248.268i | −0.0608695 | + | 0.105429i | ||||
\(178\) | −1598.84 | − | 2769.27i | −0.673247 | − | 1.16610i | ||||
\(179\) | −721.325 | − | 1249.37i | −0.301198 | − | 0.521689i | 0.675210 | − | 0.737626i | \(-0.264053\pi\) |
−0.976407 | + | 0.215936i | \(0.930720\pi\) | |||||||
\(180\) | −13.1662 | + | 22.8046i | −0.00545197 | + | 0.00944308i | ||||
\(181\) | −908.680 | −0.373158 | −0.186579 | − | 0.982440i | \(-0.559740\pi\) | ||||
−0.186579 | + | 0.982440i | \(0.559740\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3694.99 | 1.49258 | ||||||||
\(184\) | −1045.26 | + | 1810.44i | −0.418790 | + | 0.725365i | ||||
\(185\) | −45.1713 | − | 78.2389i | −0.0179517 | − | 0.0310932i | ||||
\(186\) | 1094.59 | + | 1895.89i | 0.431502 | + | 0.747383i | ||||
\(187\) | −2344.15 | + | 4060.19i | −0.916691 | + | 1.58776i | ||||
\(188\) | −309.841 | −0.120199 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −42.4812 | −0.0162206 | ||||||||
\(191\) | −1237.32 | + | 2143.10i | −0.468739 | + | 0.811881i | −0.999362 | − | 0.0357280i | \(-0.988625\pi\) |
0.530622 | + | 0.847609i | \(0.321958\pi\) | |||||||
\(192\) | −1378.31 | − | 2387.31i | −0.518079 | − | 0.897339i | ||||
\(193\) | −1766.76 | − | 3060.12i | −0.658934 | − | 1.14131i | −0.980892 | − | 0.194553i | \(-0.937674\pi\) |
0.321958 | − | 0.946754i | \(-0.395659\pi\) | |||||||
\(194\) | 252.521 | − | 437.379i | 0.0934533 | − | 0.161866i | ||||
\(195\) | −1533.31 | −0.563091 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1952.57 | −0.706165 | −0.353083 | − | 0.935592i | \(-0.614867\pi\) | ||||
−0.353083 | + | 0.935592i | \(0.614867\pi\) | |||||||
\(198\) | −107.182 | + | 185.645i | −0.0384702 | + | 0.0666324i | ||||
\(199\) | −2032.34 | − | 3520.11i | −0.723962 | − | 1.25394i | −0.959400 | − | 0.282049i | \(-0.908986\pi\) |
0.235438 | − | 0.971889i | \(-0.424348\pi\) | |||||||
\(200\) | −307.916 | − | 533.325i | −0.108865 | − | 0.188559i | ||||
\(201\) | −1380.99 | + | 2391.94i | −0.484615 | + | 0.839377i | ||||
\(202\) | 3415.46 | 1.18966 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1334.17 | −0.457895 | ||||||||
\(205\) | −1204.16 | + | 2085.66i | −0.410253 | + | 0.710579i | ||||
\(206\) | −939.380 | − | 1627.05i | −0.317717 | − | 0.550302i | ||||
\(207\) | 84.8655 | + | 146.991i | 0.0284955 | + | 0.0493556i | ||||
\(208\) | −1103.98 | + | 1912.16i | −0.368017 | + | 0.637425i | ||||
\(209\) | 169.683 | 0.0561588 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4325.34 | −1.41123 | −0.705613 | − | 0.708598i | \(-0.749328\pi\) | ||||
−0.705613 | + | 0.708598i | \(0.749328\pi\) | |||||||
\(212\) | 879.499 | − | 1523.34i | 0.284926 | − | 0.493506i | ||||
\(213\) | 1850.66 | + | 3205.44i | 0.595329 | + | 1.03114i | ||||
\(214\) | 510.422 | + | 884.077i | 0.163045 | + | 0.282403i | ||||
\(215\) | 244.499 | − | 423.484i | 0.0775566 | − | 0.134332i | ||||
\(216\) | −3571.82 | −1.12515 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4415.92 | 1.37194 | ||||||||
\(219\) | −583.312 | + | 1010.33i | −0.179984 | + | 0.311742i | ||||
\(220\) | 304.578 | + | 527.545i | 0.0933393 | + | 0.161668i | ||||
\(221\) | 3107.49 | + | 5382.33i | 0.945847 | + | 1.63826i | ||||
\(222\) | 104.645 | − | 181.250i | 0.0316365 | − | 0.0547960i | ||||
\(223\) | −982.970 | −0.295177 | −0.147589 | − | 0.989049i | \(-0.547151\pi\) | ||||
−0.147589 | + | 0.989049i | \(0.547151\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −50.0000 | −0.0148148 | ||||||||
\(226\) | 1114.84 | − | 1930.96i | 0.328133 | − | 0.568343i | ||||
\(227\) | 830.482 | + | 1438.44i | 0.242824 | + | 0.420584i | 0.961518 | − | 0.274743i | \(-0.0885929\pi\) |
−0.718694 | + | 0.695327i | \(0.755260\pi\) | |||||||
\(228\) | 24.1436 | + | 41.8180i | 0.00701294 | + | 0.0121468i | ||||
\(229\) | 287.164 | − | 497.382i | 0.0828660 | − | 0.143528i | −0.821614 | − | 0.570044i | \(-0.806926\pi\) |
0.904480 | + | 0.426516i | \(0.140259\pi\) | |||||||
\(230\) | −983.008 | −0.281816 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 743.875 | 0.210508 | ||||||||
\(233\) | 1158.24 | − | 2006.13i | 0.325660 | − | 0.564059i | −0.655986 | − | 0.754773i | \(-0.727747\pi\) |
0.981646 | + | 0.190714i | \(0.0610802\pi\) | |||||||
\(234\) | 142.084 | + | 246.097i | 0.0396938 | + | 0.0687517i | ||||
\(235\) | −294.162 | − | 509.504i | −0.0816555 | − | 0.141431i | ||||
\(236\) | 75.4887 | − | 130.750i | 0.0208216 | − | 0.0360641i | ||||
\(237\) | −5375.93 | −1.47343 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3659.31 | −0.990382 | −0.495191 | − | 0.868784i | \(-0.664902\pi\) | ||||
−0.495191 | + | 0.868784i | \(0.664902\pi\) | |||||||
\(240\) | 450.000 | − | 779.423i | 0.121031 | − | 0.209631i | ||||
\(241\) | −1223.17 | − | 2118.59i | −0.326934 | − | 0.566266i | 0.654968 | − | 0.755657i | \(-0.272682\pi\) |
−0.981902 | + | 0.189391i | \(0.939349\pi\) | |||||||
\(242\) | 937.757 | + | 1624.24i | 0.249096 | + | 0.431447i | ||||
\(243\) | −280.000 | + | 484.974i | −0.0739177 | + | 0.128029i | ||||
\(244\) | −1945.96 | −0.510564 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5579.16 | −1.44599 | ||||||||
\(247\) | 112.469 | − | 194.801i | 0.0289725 | − | 0.0501818i | ||||
\(248\) | −2327.81 | − | 4031.89i | −0.596033 | − | 1.03236i | ||||
\(249\) | −1708.31 | − | 2958.88i | −0.434779 | − | 0.753059i | ||||
\(250\) | 144.789 | − | 250.782i | 0.0366291 | − | 0.0634434i | ||||
\(251\) | −2909.29 | −0.731605 | −0.365802 | − | 0.930693i | \(-0.619205\pi\) | ||||
−0.365802 | + | 0.930693i | \(0.619205\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3926.43 | 0.975702 | ||||||||
\(254\) | −1878.48 | + | 3253.62i | −0.464040 | + | 0.803741i | ||||
\(255\) | −1266.66 | − | 2193.91i | −0.311063 | − | 0.538777i | ||||
\(256\) | 1779.19 | + | 3081.64i | 0.434372 | + | 0.752354i | ||||
\(257\) | −84.3400 | + | 146.081i | −0.0204708 | + | 0.0354564i | −0.876079 | − | 0.482167i | \(-0.839850\pi\) |
0.855609 | + | 0.517623i | \(0.173183\pi\) | |||||||
\(258\) | 1132.82 | 0.273359 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 807.519 | 0.192616 | ||||||||
\(261\) | 30.1980 | − | 52.3045i | 0.00716172 | − | 0.0124045i | ||||
\(262\) | −1598.84 | − | 2769.27i | −0.377010 | − | 0.653000i | ||||
\(263\) | 1622.24 | + | 2809.80i | 0.380347 | + | 0.658781i | 0.991112 | − | 0.133031i | \(-0.0424711\pi\) |
−0.610764 | + | 0.791812i | \(0.709138\pi\) | |||||||
\(264\) | −2849.24 | + | 4935.02i | −0.664236 | + | 1.15049i | ||||
\(265\) | 3339.97 | 0.774238 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6901.59 | −1.58191 | ||||||||
\(268\) | 727.298 | − | 1259.72i | 0.165772 | − | 0.287125i | ||||
\(269\) | 1424.33 | + | 2467.01i | 0.322836 | + | 0.559168i | 0.981072 | − | 0.193644i | \(-0.0620306\pi\) |
−0.658236 | + | 0.752811i | \(0.728697\pi\) | |||||||
\(270\) | −839.776 | − | 1454.54i | −0.189286 | − | 0.327853i | ||||
\(271\) | 1425.49 | − | 2469.02i | 0.319529 | − | 0.553440i | −0.660861 | − | 0.750508i | \(-0.729809\pi\) |
0.980390 | + | 0.197068i | \(0.0631421\pi\) | |||||||
\(272\) | −3647.97 | −0.813201 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4516.62 | 0.995837 | ||||||||
\(275\) | −578.331 | + | 1001.70i | −0.126817 | + | 0.219654i | ||||
\(276\) | 558.680 | + | 967.662i | 0.121843 | + | 0.211038i | ||||
\(277\) | −1149.31 | − | 1990.67i | −0.249298 | − | 0.431797i | 0.714033 | − | 0.700112i | \(-0.246867\pi\) |
−0.963331 | + | 0.268315i | \(0.913533\pi\) | |||||||
\(278\) | 3243.27 | − | 5617.52i | 0.699708 | − | 1.21193i | ||||
\(279\) | −377.995 | −0.0811110 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6109.20 | 1.29695 | 0.648477 | − | 0.761234i | \(-0.275406\pi\) | ||||
0.648477 | + | 0.761234i | \(0.275406\pi\) | |||||||
\(282\) | 681.464 | − | 1180.33i | 0.143903 | − | 0.249247i | ||||
\(283\) | −2927.47 | − | 5070.54i | −0.614913 | − | 1.06506i | −0.990400 | − | 0.138233i | \(-0.955858\pi\) |
0.375487 | − | 0.926828i | \(-0.377475\pi\) | |||||||
\(284\) | −974.650 | − | 1688.14i | −0.203644 | − | 0.352721i | ||||
\(285\) | −45.8438 | + | 79.4038i | −0.00952825 | + | 0.0165034i | ||||
\(286\) | 6573.75 | 1.35914 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 227.335 | 0.0465133 | ||||||||
\(289\) | −2677.64 | + | 4637.80i | −0.545011 | + | 0.943986i | ||||
\(290\) | 174.894 | + | 302.924i | 0.0354141 | + | 0.0613391i | ||||
\(291\) | −545.019 | − | 944.000i | −0.109792 | − | 0.190166i | ||||
\(292\) | 307.201 | − | 532.088i | 0.0615671 | − | 0.106637i | ||||
\(293\) | −5135.34 | −1.02392 | −0.511962 | − | 0.859008i | \(-0.671081\pi\) | ||||
−0.511962 | + | 0.859008i | \(0.671081\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 286.675 | 0.0565792 | ||||||||
\(296\) | −222.543 | + | 385.456i | −0.0436995 | + | 0.0756898i | ||||
\(297\) | 3354.32 | + | 5809.85i | 0.655345 | + | 1.13509i | ||||
\(298\) | −1661.16 | − | 2877.21i | −0.322913 | − | 0.559302i | ||||
\(299\) | 2602.51 | − | 4507.67i | 0.503367 | − | 0.871858i | ||||
\(300\) | −329.156 | −0.0633461 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 4599.85 | 0.876462 | ||||||||
\(303\) | 3685.82 | − | 6384.03i | 0.698828 | − | 1.21040i | ||||
\(304\) | 66.0151 | + | 114.341i | 0.0124547 | + | 0.0215721i | ||||
\(305\) | −1847.49 | − | 3199.95i | −0.346843 | − | 0.600750i | ||||
\(306\) | −234.749 | + | 406.598i | −0.0438553 | + | 0.0759596i | ||||
\(307\) | 2102.97 | 0.390954 | 0.195477 | − | 0.980708i | \(-0.437375\pi\) | ||||
0.195477 | + | 0.980708i | \(0.437375\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4054.95 | −0.746531 | ||||||||
\(310\) | 1094.59 | − | 1895.89i | 0.200544 | − | 0.347352i | ||||
\(311\) | 2882.15 | + | 4992.03i | 0.525504 | + | 0.910200i | 0.999559 | + | 0.0297045i | \(0.00945661\pi\) |
−0.474055 | + | 0.880495i | \(0.657210\pi\) | |||||||
\(312\) | 3777.05 | + | 6542.04i | 0.685363 | + | 1.18708i | ||||
\(313\) | 680.006 | − | 1177.81i | 0.122799 | − | 0.212695i | −0.798071 | − | 0.602563i | \(-0.794146\pi\) |
0.920871 | + | 0.389868i | \(0.127479\pi\) | |||||||
\(314\) | −94.1939 | −0.0169289 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2831.23 | 0.504017 | ||||||||
\(317\) | −2569.47 | + | 4450.46i | −0.455256 | + | 0.788526i | −0.998703 | − | 0.0509173i | \(-0.983785\pi\) |
0.543447 | + | 0.839443i | \(0.317119\pi\) | |||||||
\(318\) | 3868.73 | + | 6700.84i | 0.682226 | + | 1.18165i | ||||
\(319\) | −698.578 | − | 1209.97i | −0.122611 | − | 0.212368i | ||||
\(320\) | −1378.31 | + | 2387.31i | −0.240781 | + | 0.417045i | ||||
\(321\) | 2203.30 | 0.383103 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 371.637 | 0.0640200 | ||||||||
\(324\) | −883.455 | + | 1530.19i | −0.151484 | + | 0.262378i | ||||
\(325\) | 766.656 | + | 1327.89i | 0.130851 | + | 0.226640i | ||||
\(326\) | −4579.95 | − | 7932.71i | −0.778098 | − | 1.34771i | ||||
\(327\) | 4765.47 | − | 8254.04i | 0.805905 | − | 1.39587i | ||||
\(328\) | 11864.9 | 1.99735 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2679.55 | −0.446983 | ||||||||
\(331\) | −912.850 | + | 1581.10i | −0.151585 | + | 0.262554i | −0.931810 | − | 0.362945i | \(-0.881771\pi\) |
0.780225 | + | 0.625499i | \(0.215105\pi\) | |||||||
\(332\) | 899.683 | + | 1558.30i | 0.148724 | + | 0.257598i | ||||
\(333\) | 18.0685 | + | 31.2956i | 0.00297342 | + | 0.00515011i | ||||
\(334\) | 3915.45 | − | 6781.76i | 0.641449 | − | 1.11102i | ||||
\(335\) | 2761.98 | 0.450457 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 153.985 | 0.0248905 | 0.0124452 | − | 0.999923i | \(-0.496038\pi\) | ||||
0.0124452 | + | 0.999923i | \(0.496038\pi\) | |||||||
\(338\) | 1812.38 | − | 3139.14i | 0.291659 | − | 0.505168i | ||||
\(339\) | −2406.17 | − | 4167.62i | −0.385503 | − | 0.667710i | ||||
\(340\) | 667.084 | + | 1155.42i | 0.106405 | + | 0.184299i | ||||
\(341\) | −4372.13 | + | 7572.74i | −0.694322 | + | 1.20260i | ||||
\(342\) | 16.9925 | 0.00268669 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2409.12 | −0.377590 | ||||||||
\(345\) | −1060.82 | + | 1837.39i | −0.165544 | + | 0.286730i | ||||
\(346\) | 3714.32 | + | 6433.39i | 0.577118 | + | 0.999598i | ||||
\(347\) | −2179.69 | − | 3775.34i | −0.337211 | − | 0.584066i | 0.646696 | − | 0.762748i | \(-0.276150\pi\) |
−0.983907 | + | 0.178682i | \(0.942817\pi\) | |||||||
\(348\) | 198.797 | − | 344.327i | 0.0306225 | − | 0.0530398i | ||||
\(349\) | 1689.00 | 0.259054 | 0.129527 | − | 0.991576i | \(-0.458654\pi\) | ||||
0.129527 | + | 0.991576i | \(0.458654\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8893.21 | 1.35238 | ||||||||
\(352\) | 2629.50 | − | 4554.43i | 0.398161 | − | 0.689635i | ||||
\(353\) | 1960.68 | + | 3396.00i | 0.295627 | + | 0.512041i | 0.975131 | − | 0.221631i | \(-0.0711380\pi\) |
−0.679503 | + | 0.733672i | \(0.737805\pi\) | |||||||
\(354\) | 332.059 | + | 575.143i | 0.0498552 | + | 0.0863518i | ||||
\(355\) | 1850.66 | − | 3205.44i | 0.276684 | − | 0.479231i | ||||
\(356\) | 3634.72 | 0.541123 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3342.08 | −0.493392 | ||||||||
\(359\) | 1433.93 | − | 2483.64i | 0.210808 | − | 0.365130i | −0.741160 | − | 0.671329i | \(-0.765724\pi\) |
0.951968 | + | 0.306199i | \(0.0990572\pi\) | |||||||
\(360\) | 123.166 | + | 213.330i | 0.0180318 | + | 0.0312319i | ||||
\(361\) | 3422.77 | + | 5928.42i | 0.499019 | + | 0.864327i | ||||
\(362\) | −1052.54 | + | 1823.04i | −0.152818 | + | 0.264688i | ||||
\(363\) | 4047.94 | 0.585295 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1166.62 | 0.167298 | ||||||||
\(366\) | 4279.95 | − | 7413.09i | 0.611247 | − | 1.05871i | ||||
\(367\) | −5751.50 | − | 9961.89i | −0.818054 | − | 1.41691i | −0.907114 | − | 0.420884i | \(-0.861720\pi\) |
0.0890605 | − | 0.996026i | \(-0.471614\pi\) | |||||||
\(368\) | 1527.58 | + | 2645.84i | 0.216387 | + | 0.374794i | ||||
\(369\) | 481.662 | − | 834.264i | 0.0679522 | − | 0.117697i | ||||
\(370\) | −209.290 | −0.0294066 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −2488.39 | −0.346820 | ||||||||
\(373\) | −2543.21 | + | 4404.98i | −0.353037 | + | 0.611477i | −0.986780 | − | 0.162066i | \(-0.948184\pi\) |
0.633743 | + | 0.773543i | \(0.281518\pi\) | |||||||
\(374\) | 5430.52 | + | 9405.93i | 0.750816 | + | 1.30045i | ||||
\(375\) | −312.500 | − | 541.266i | −0.0430331 | − | 0.0745356i | ||||
\(376\) | −1449.24 | + | 2510.15i | −0.198773 | + | 0.344285i | ||||
\(377\) | −1852.12 | −0.253021 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 954.827 | 0.129409 | 0.0647047 | − | 0.997904i | \(-0.479389\pi\) | ||||
0.0647047 | + | 0.997904i | \(0.479389\pi\) | |||||||
\(380\) | 24.1436 | − | 41.8180i | 0.00325932 | − | 0.00564531i | ||||
\(381\) | 4054.34 | + | 7022.32i | 0.545171 | + | 0.944264i | ||||
\(382\) | 2866.40 | + | 4964.76i | 0.383921 | + | 0.664971i | ||||
\(383\) | −1541.95 | + | 2670.74i | −0.205719 | + | 0.356315i | −0.950361 | − | 0.311148i | \(-0.899286\pi\) |
0.744643 | + | 0.667463i | \(0.232620\pi\) | |||||||
\(384\) | −1839.37 | −0.244439 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8185.84 | −1.07940 | ||||||||
\(387\) | −97.7995 | + | 169.394i | −0.0128461 | + | 0.0222500i | ||||
\(388\) | 287.034 | + | 497.158i | 0.0375566 | + | 0.0650499i | ||||
\(389\) | 3165.57 | + | 5482.93i | 0.412599 | + | 0.714642i | 0.995173 | − | 0.0981353i | \(-0.0312878\pi\) |
−0.582574 | + | 0.812777i | \(0.697954\pi\) | |||||||
\(390\) | −1776.05 | + | 3076.22i | −0.230600 | + | 0.399411i | ||||
\(391\) | 8599.63 | 1.11228 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6901.59 | −0.885850 | ||||||||
\(394\) | −2261.68 | + | 3917.35i | −0.289193 | + | 0.500896i | ||||
\(395\) | 2687.96 | + | 4655.69i | 0.342395 | + | 0.593046i | ||||
\(396\) | −121.831 | − | 211.018i | −0.0154602 | − | 0.0267779i | ||||
\(397\) | 6066.62 | − | 10507.7i | 0.766939 | − | 1.32838i | −0.172276 | − | 0.985049i | \(-0.555112\pi\) |
0.939215 | − | 0.343329i | \(-0.111555\pi\) | |||||||
\(398\) | −9416.32 | −1.18592 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −900.000 | −0.112500 | ||||||||
\(401\) | 135.335 | − | 234.407i | 0.0168536 | − | 0.0291913i | −0.857476 | − | 0.514525i | \(-0.827968\pi\) |
0.874329 | + | 0.485333i | \(0.161302\pi\) | |||||||
\(402\) | 3199.24 | + | 5541.24i | 0.396924 | + | 0.687492i | ||||
\(403\) | 5795.84 | + | 10038.7i | 0.716406 | + | 1.24085i | ||||
\(404\) | −1941.14 | + | 3362.15i | −0.239047 | + | 0.414042i | ||||
\(405\) | −3355.00 | −0.411633 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 835.967 | 0.101812 | ||||||||
\(408\) | −6240.37 | + | 10808.6i | −0.757217 | + | 1.31154i | ||||
\(409\) | −2009.96 | − | 3481.36i | −0.242998 | − | 0.420885i | 0.718569 | − | 0.695456i | \(-0.244798\pi\) |
−0.961567 | + | 0.274571i | \(0.911464\pi\) | |||||||
\(410\) | 2789.58 | + | 4831.69i | 0.336018 | + | 0.582001i | ||||
\(411\) | 4874.14 | − | 8442.26i | 0.584973 | − | 1.01320i | ||||
\(412\) | 2135.54 | 0.255365 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 393.203 | 0.0466784 | ||||||||
\(415\) | −1708.31 | + | 2958.88i | −0.202067 | + | 0.349990i | ||||
\(416\) | −3485.76 | − | 6037.51i | −0.410825 | − | 0.711570i | ||||
\(417\) | −7000.00 | − | 12124.4i | −0.822042 | − | 1.42382i | ||||
\(418\) | 196.545 | − | 340.427i | 0.0229984 | − | 0.0398345i | ||||
\(419\) | 2437.28 | 0.284175 | 0.142087 | − | 0.989854i | \(-0.454619\pi\) | ||||
0.142087 | + | 0.989854i | \(0.454619\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4751.36 | −0.550041 | −0.275020 | − | 0.961438i | \(-0.588685\pi\) | ||||
−0.275020 | + | 0.961438i | \(0.588685\pi\) | |||||||
\(422\) | −5010.09 | + | 8677.73i | −0.577932 | + | 1.00101i | ||||
\(423\) | 117.665 | + | 203.802i | 0.0135250 | + | 0.0234260i | ||||
\(424\) | −8227.44 | − | 14250.4i | −0.942358 | − | 1.63221i | ||||
\(425\) | −1266.66 | + | 2193.91i | −0.144569 | + | 0.250401i | ||||
\(426\) | 8574.57 | 0.975210 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1160.37 | −0.131048 | ||||||||
\(429\) | 7094.10 | − | 12287.3i | 0.798383 | − | 1.38284i | ||||
\(430\) | −566.412 | − | 981.054i | −0.0635228 | − | 0.110025i | ||||
\(431\) | −3962.59 | − | 6863.41i | −0.442857 | − | 0.767051i | 0.555043 | − | 0.831822i | \(-0.312702\pi\) |
−0.997900 | + | 0.0647706i | \(0.979368\pi\) | |||||||
\(432\) | −2610.00 | + | 4520.65i | −0.290680 | + | 0.503472i | ||||
\(433\) | −11487.3 | −1.27492 | −0.637462 | − | 0.770481i | \(-0.720016\pi\) | ||||
−0.637462 | + | 0.770481i | \(0.720016\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 754.950 | 0.0832117 | ||||||||
\(436\) | −2509.73 | + | 4346.99i | −0.275675 | + | 0.477484i | ||||
\(437\) | −155.622 | − | 269.546i | −0.0170353 | − | 0.0295060i | ||||
\(438\) | 1351.32 | + | 2340.55i | 0.147416 | + | 0.255333i | ||||
\(439\) | 4573.96 | − | 7922.33i | 0.497274 | − | 0.861303i | −0.502721 | − | 0.864449i | \(-0.667668\pi\) |
0.999995 | + | 0.00314511i | \(0.00100112\pi\) | |||||||
\(440\) | 5698.47 | 0.617418 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 14397.8 | 1.54939 | ||||||||
\(443\) | −932.176 | + | 1614.58i | −0.0999752 | + | 0.173162i | −0.911674 | − | 0.410914i | \(-0.865210\pi\) |
0.811699 | + | 0.584076i | \(0.198543\pi\) | |||||||
\(444\) | 118.947 | + | 206.023i | 0.0127139 | + | 0.0220212i | ||||
\(445\) | 3450.79 | + | 5976.95i | 0.367603 | + | 0.636707i | ||||
\(446\) | −1138.59 | + | 1972.09i | −0.120883 | + | 0.209375i | ||||
\(447\) | −7170.58 | −0.758741 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4490.88 | 0.472022 | 0.236011 | − | 0.971750i | \(-0.424160\pi\) | ||||
0.236011 | + | 0.971750i | \(0.424160\pi\) | |||||||
\(450\) | −57.9156 | + | 100.313i | −0.00606704 | + | 0.0105084i | ||||
\(451\) | −11142.4 | − | 19299.2i | −1.16336 | − | 2.01500i | ||||
\(452\) | 1267.21 | + | 2194.87i | 0.131869 | + | 0.228403i | ||||
\(453\) | 4963.95 | − | 8597.82i | 0.514850 | − | 0.891746i | ||||
\(454\) | 3847.83 | 0.397770 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 451.713 | 0.0463890 | ||||||||
\(457\) | 7171.91 | − | 12422.1i | 0.734109 | − | 1.27151i | −0.221005 | − | 0.975273i | \(-0.570934\pi\) |
0.955113 | − | 0.296241i | \(-0.0957330\pi\) | |||||||
\(458\) | −665.251 | − | 1152.25i | −0.0678714 | − | 0.117557i | ||||
\(459\) | 7346.61 | + | 12724.7i | 0.747081 | + | 1.29398i | ||||
\(460\) | 558.680 | − | 967.662i | 0.0566274 | − | 0.0980815i | ||||
\(461\) | −14558.7 | −1.47086 | −0.735429 | − | 0.677602i | \(-0.763019\pi\) | ||||
−0.735429 | + | 0.677602i | \(0.763019\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1809.56 | −0.181636 | −0.0908178 | − | 0.995868i | \(-0.528948\pi\) | ||||
−0.0908178 | + | 0.995868i | \(0.528948\pi\) | |||||||
\(464\) | 543.564 | − | 941.480i | 0.0543843 | − | 0.0941964i | ||||
\(465\) | −2362.47 | − | 4091.92i | −0.235606 | − | 0.408082i | ||||
\(466\) | −2683.20 | − | 4647.45i | −0.266732 | − | 0.461993i | ||||
\(467\) | −2990.82 | + | 5180.26i | −0.296357 | + | 0.513306i | −0.975300 | − | 0.220886i | \(-0.929105\pi\) |
0.678942 | + | 0.734192i | \(0.262439\pi\) | |||||||
\(468\) | −323.008 | −0.0319039 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1362.93 | −0.133760 | ||||||||
\(471\) | −101.650 | + | 176.063i | −0.00994433 | + | 0.0172241i | ||||
\(472\) | −706.174 | − | 1223.13i | −0.0688650 | − | 0.119278i | ||||
\(473\) | 2262.42 | + | 3918.63i | 0.219929 | + | 0.380927i | ||||
\(474\) | −6227.00 | + | 10785.5i | −0.603409 | + | 1.04513i | ||||
\(475\) | 91.6876 | 0.00885666 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1335.99 | −0.128241 | ||||||||
\(478\) | −4238.63 | + | 7341.52i | −0.405586 | + | 0.702496i | ||||
\(479\) | −5763.75 | − | 9983.11i | −0.549796 | − | 0.952275i | −0.998288 | − | 0.0584884i | \(-0.981372\pi\) |
0.448492 | − | 0.893787i | \(-0.351961\pi\) | |||||||
\(480\) | 1420.84 | + | 2460.97i | 0.135109 | + | 0.234016i | ||||
\(481\) | 554.093 | − | 959.718i | 0.0525249 | − | 0.0909758i | ||||
\(482\) | −5667.23 | −0.535551 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2131.85 | −0.200211 | ||||||||
\(485\) | −545.019 | + | 944.000i | −0.0510269 | + | 0.0883811i | ||||
\(486\) | 648.655 | + | 1123.50i | 0.0605424 | + | 0.104862i | ||||
\(487\) | −7895.74 | − | 13675.8i | −0.734682 | − | 1.27251i | −0.954863 | − | 0.297048i | \(-0.903998\pi\) |
0.220180 | − | 0.975459i | \(-0.429335\pi\) | |||||||
\(488\) | −9101.95 | + | 15765.0i | −0.844316 | + | 1.46240i | ||||
\(489\) | −19769.9 | −1.82828 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13064.9 | 1.20083 | 0.600417 | − | 0.799687i | \(-0.295001\pi\) | ||||
0.600417 | + | 0.799687i | \(0.295001\pi\) | |||||||
\(492\) | 3170.84 | − | 5492.06i | 0.290554 | − | 0.503255i | ||||
\(493\) | −1530.02 | − | 2650.07i | −0.139774 | − | 0.242096i | ||||
\(494\) | −260.548 | − | 451.282i | −0.0237299 | − | 0.0411015i | ||||
\(495\) | 231.332 | − | 400.680i | 0.0210053 | − | 0.0363822i | ||||
\(496\) | −6803.91 | −0.615937 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −7915.04 | −0.712211 | ||||||||
\(499\) | 10067.9 | − | 17438.1i | 0.903209 | − | 1.56440i | 0.0799059 | − | 0.996802i | \(-0.474538\pi\) |
0.823303 | − | 0.567602i | \(-0.192129\pi\) | |||||||
\(500\) | 164.578 | + | 285.058i | 0.0147203 | + | 0.0254963i | ||||
\(501\) | −8450.76 | − | 14637.1i | −0.753597 | − | 1.30527i | ||||
\(502\) | −3369.87 | + | 5836.78i | −0.299611 | + | 0.518941i | ||||
\(503\) | 751.675 | 0.0666313 | 0.0333156 | − | 0.999445i | \(-0.489393\pi\) | ||||
0.0333156 | + | 0.999445i | \(0.489393\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7371.64 | −0.649571 | ||||||||
\(506\) | 4548.03 | − | 7877.42i | 0.399574 | − | 0.692083i | ||||
\(507\) | −3911.69 | − | 6775.24i | −0.342651 | − | 0.593489i | ||||
\(508\) | −2135.22 | − | 3698.31i | −0.186486 | − | 0.323004i | ||||
\(509\) | −6167.23 | + | 10682.0i | −0.537049 | + | 0.930196i | 0.462012 | + | 0.886874i | \(0.347128\pi\) |
−0.999061 | + | 0.0433224i | \(0.986206\pi\) | |||||||
\(510\) | −5868.73 | −0.509553 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 11186.4 | 0.965574 | ||||||||
\(513\) | 265.894 | − | 460.542i | 0.0228840 | − | 0.0396363i | ||||
\(514\) | 195.384 | + | 338.415i | 0.0167666 | + | 0.0290406i | ||||
\(515\) | 2027.47 | + | 3511.69i | 0.173478 | + | 0.300473i | ||||
\(516\) | −643.826 | + | 1115.14i | −0.0549280 | + | 0.0951382i | ||||
\(517\) | 5443.95 | 0.463104 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16033.3 | 1.35604 | ||||||||
\(520\) | 3777.05 | − | 6542.04i | 0.318528 | − | 0.551706i | ||||
\(521\) | −868.216 | − | 1503.80i | −0.0730082 | − | 0.126454i | 0.827210 | − | 0.561893i | \(-0.189927\pi\) |
−0.900218 | + | 0.435439i | \(0.856593\pi\) | |||||||
\(522\) | −69.9574 | − | 121.170i | −0.00586581 | − | 0.0101599i | ||||
\(523\) | −710.710 | + | 1230.99i | −0.0594210 | + | 0.102920i | −0.894206 | − | 0.447656i | \(-0.852259\pi\) |
0.834785 | + | 0.550577i | \(0.185592\pi\) | |||||||
\(524\) | 3634.72 | 0.303022 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7516.23 | 0.623048 | ||||||||
\(527\) | −9575.79 | + | 16585.8i | −0.791514 | + | 1.37094i | ||||
\(528\) | 4163.98 | + | 7212.23i | 0.343209 | + | 0.594455i | ||||
\(529\) | 2482.42 | + | 4299.68i | 0.204029 | + | 0.353389i | ||||
\(530\) | 3868.73 | − | 6700.84i | 0.317070 | − | 0.549181i | ||||
\(531\) | −114.670 | −0.00937148 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −29541.6 | −2.40073 | ||||||||
\(534\) | −7994.19 | + | 13846.3i | −0.647833 | + | 1.12208i | ||||
\(535\) | −1101.65 | − | 1908.11i | −0.0890252 | − | 0.154196i | ||||
\(536\) | −6803.65 | − | 11784.3i | −0.548271 | − | 0.949633i | ||||
\(537\) | −3606.62 | + | 6246.86i | −0.289827 | + | 0.501996i | ||||
\(538\) | 6599.26 | 0.528837 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1909.11 | 0.152139 | ||||||||
\(541\) | −2886.63 | + | 4999.79i | −0.229401 | + | 0.397334i | −0.957631 | − | 0.287999i | \(-0.907010\pi\) |
0.728230 | + | 0.685333i | \(0.240343\pi\) | |||||||
\(542\) | −3302.32 | − | 5719.79i | −0.261710 | − | 0.453295i | ||||
\(543\) | 2271.70 | + | 3934.70i | 0.179536 | + | 0.310965i | ||||
\(544\) | 5759.11 | − | 9975.06i | 0.453896 | − | 0.786172i | ||||
\(545\) | −9530.94 | −0.749102 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3941.30 | −0.308076 | −0.154038 | − | 0.988065i | \(-0.549228\pi\) | ||||
−0.154038 | + | 0.988065i | \(0.549228\pi\) | |||||||
\(548\) | −2566.97 | + | 4446.12i | −0.200101 | + | 0.346585i | ||||
\(549\) | 738.997 | + | 1279.98i | 0.0574493 | + | 0.0995050i | ||||
\(550\) | 1339.78 | + | 2320.56i | 0.103870 | + | 0.179907i | ||||
\(551\) | −55.3756 | + | 95.9134i | −0.00428145 | + | 0.00741570i | ||||
\(552\) | 10452.6 | 0.805961 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −5325.06 | −0.408376 | ||||||||
\(555\) | −225.856 | + | 391.195i | −0.0172740 | + | 0.0299194i | ||||
\(556\) | 3686.55 | + | 6385.29i | 0.281195 | + | 0.487044i | ||||
\(557\) | 3475.87 | + | 6020.38i | 0.264412 | + | 0.457974i | 0.967409 | − | 0.253218i | \(-0.0814889\pi\) |
−0.702998 | + | 0.711192i | \(0.748156\pi\) | |||||||
\(558\) | −437.836 | + | 758.355i | −0.0332170 | + | 0.0575335i | ||||
\(559\) | 5998.29 | 0.453847 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 23441.5 | 1.76417 | ||||||||
\(562\) | 7076.36 | − | 12256.6i | 0.531136 | − | 0.919954i | ||||
\(563\) | −12142.3 | − | 21031.1i | −0.908946 | − | 1.57434i | −0.815530 | − | 0.578714i | \(-0.803555\pi\) |
−0.0934159 | − | 0.995627i | \(-0.529779\pi\) | |||||||
\(564\) | 774.603 | + | 1341.65i | 0.0578310 | + | 0.100166i | ||||
\(565\) | −2406.17 | + | 4167.62i | −0.179165 | + | 0.310324i | ||||
\(566\) | −13563.7 | −1.00729 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −18235.1 | −1.34706 | ||||||||
\(569\) | 10781.7 | − | 18674.5i | 0.794363 | − | 1.37588i | −0.128880 | − | 0.991660i | \(-0.541138\pi\) |
0.923243 | − | 0.384217i | \(-0.125528\pi\) | |||||||
\(570\) | 106.203 | + | 183.949i | 0.00780412 | + | 0.0135171i | ||||
\(571\) | 1844.78 | + | 3195.25i | 0.135204 | + | 0.234181i | 0.925675 | − | 0.378319i | \(-0.123498\pi\) |
−0.790471 | + | 0.612499i | \(0.790164\pi\) | |||||||
\(572\) | −3736.11 | + | 6471.13i | −0.273102 | + | 0.473027i | ||||
\(573\) | 12373.2 | 0.902090 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2121.64 | 0.153875 | ||||||||
\(576\) | 551.325 | − | 954.923i | 0.0398817 | − | 0.0690772i | ||||
\(577\) | 11092.0 | + | 19211.8i | 0.800285 | + | 1.38613i | 0.919429 | + | 0.393257i | \(0.128652\pi\) |
−0.119144 | + | 0.992877i | \(0.538015\pi\) | |||||||
\(578\) | 6203.08 | + | 10744.1i | 0.446391 | + | 0.773172i | ||||
\(579\) | −8833.80 | + | 15300.6i | −0.634059 | + | 1.09822i | ||||
\(580\) | −397.594 | −0.0284641 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −2525.21 | −0.179851 | ||||||||
\(583\) | −15452.9 | + | 26765.2i | −1.09776 | + | 1.90137i | ||||
\(584\) | −2873.78 | − | 4977.53i | −0.203626 | − | 0.352691i | ||||
\(585\) | −306.662 | − | 531.155i | −0.0216734 | − | 0.0375394i | ||||
\(586\) | −5948.33 | + | 10302.8i | −0.419323 | + | 0.726289i | ||||
\(587\) | 10605.3 | 0.745705 | 0.372852 | − | 0.927891i | \(-0.378380\pi\) | ||||
0.372852 | + | 0.927891i | \(0.378380\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 693.149 | 0.0484902 | ||||||||
\(590\) | 332.059 | − | 575.143i | 0.0231706 | − | 0.0401327i | ||||
\(591\) | 4881.42 | + | 8454.86i | 0.339754 | + | 0.588471i | ||||
\(592\) | 325.233 | + | 563.320i | 0.0225794 | + | 0.0391087i | ||||
\(593\) | −3138.62 | + | 5436.26i | −0.217349 | + | 0.376459i | −0.953997 | − | 0.299817i | \(-0.903074\pi\) |
0.736648 | + | 0.676277i | \(0.236408\pi\) | |||||||
\(594\) | 15541.4 | 1.07352 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3776.39 | 0.259542 | ||||||||
\(597\) | −10161.7 | + | 17600.5i | −0.696633 | + | 1.20660i | ||||
\(598\) | −6029.03 | − | 10442.6i | −0.412283 | − | 0.714096i | ||||
\(599\) | 4985.36 | + | 8634.90i | 0.340061 | + | 0.589003i | 0.984444 | − | 0.175700i | \(-0.0562190\pi\) |
−0.644383 | + | 0.764703i | \(0.722886\pi\) | |||||||
\(600\) | −1539.58 | + | 2666.63i | −0.104755 | + | 0.181441i | ||||
\(601\) | −24619.2 | −1.67094 | −0.835472 | − | 0.549533i | \(-0.814806\pi\) | ||||
−0.835472 | + | 0.549533i | \(0.814806\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1104.79 | −0.0746113 | ||||||||
\(604\) | −2614.27 | + | 4528.04i | −0.176114 | + | 0.305039i | ||||
\(605\) | −2023.97 | − | 3505.62i | −0.136010 | − | 0.235577i | ||||
\(606\) | −8538.66 | − | 14789.4i | −0.572375 | − | 0.991383i | ||||
\(607\) | −5626.47 | + | 9745.34i | −0.376230 | + | 0.651649i | −0.990510 | − | 0.137439i | \(-0.956113\pi\) |
0.614281 | + | 0.789088i | \(0.289446\pi\) | |||||||
\(608\) | −416.876 | −0.0278068 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8559.90 | −0.568164 | ||||||||
\(611\) | 3608.34 | − | 6249.83i | 0.238916 | − | 0.413815i | ||||
\(612\) | −266.834 | − | 462.170i | −0.0176244 | − | 0.0305263i | ||||
\(613\) | 7646.61 | + | 13244.3i | 0.503824 | + | 0.872648i | 0.999990 | + | 0.00442069i | \(0.00140715\pi\) |
−0.496167 | + | 0.868227i | \(0.665260\pi\) | |||||||
\(614\) | 2435.90 | − | 4219.10i | 0.160105 | − | 0.277311i | ||||
\(615\) | 12041.6 | 0.789533 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17589.4 | −1.14769 | −0.573843 | − | 0.818966i | \(-0.694548\pi\) | ||||
−0.573843 | + | 0.818966i | \(0.694548\pi\) | |||||||
\(618\) | −4696.90 | + | 8135.27i | −0.305723 | + | 0.529528i | ||||
\(619\) | 11733.7 | + | 20323.3i | 0.761900 | + | 1.31965i | 0.941870 | + | 0.335978i | \(0.109067\pi\) |
−0.179970 | + | 0.983672i | \(0.557600\pi\) | |||||||
\(620\) | 1244.19 | + | 2155.01i | 0.0805936 | + | 0.139592i | ||||
\(621\) | 6152.75 | − | 10656.9i | 0.397587 | − | 0.688640i | ||||
\(622\) | 13353.7 | 0.860829 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 11039.8 | 0.708249 | ||||||||
\(625\) | −312.500 | + | 541.266i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −1575.32 | − | 2728.53i | −0.100579 | − | 0.174208i | ||||
\(627\) | −424.206 | − | 734.747i | −0.0270194 | − | 0.0467990i | ||||
\(628\) | 53.5339 | − | 92.7235i | 0.00340165 | − | 0.00589183i | ||||
\(629\) | 1830.93 | 0.116063 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6040.86 | −0.381114 | −0.190557 | − | 0.981676i | \(-0.561029\pi\) | ||||
−0.190557 | + | 0.981676i | \(0.561029\pi\) | |||||||
\(632\) | 13242.7 | − | 22937.0i | 0.833488 | − | 1.44364i | ||||
\(633\) | 10813.3 | + | 18729.3i | 0.678976 | + | 1.17602i | ||||
\(634\) | 5952.51 | + | 10310.0i | 0.372877 | + | 0.645843i | ||||
\(635\) | 4054.34 | − | 7022.32i | 0.253373 | − | 0.438854i | ||||
\(636\) | −8794.99 | −0.548340 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −3236.68 | −0.200849 | ||||||||
\(639\) | −740.264 | + | 1282.17i | −0.0458285 | + | 0.0793772i | ||||
\(640\) | 919.683 | + | 1592.94i | 0.0568026 | + | 0.0983849i | ||||
\(641\) | −12555.8 | − | 21747.3i | −0.773673 | − | 1.34004i | −0.935538 | − | 0.353227i | \(-0.885084\pi\) |
0.161865 | − | 0.986813i | \(-0.448249\pi\) | |||||||
\(642\) | 2552.11 | − | 4420.38i | 0.156891 | − | 0.271742i | ||||
\(643\) | 3095.03 | 0.189823 | 0.0949113 | − | 0.995486i | \(-0.469743\pi\) | ||||
0.0949113 | + | 0.995486i | \(0.469743\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2444.99 | −0.149258 | ||||||||
\(646\) | 430.472 | − | 745.600i | 0.0262178 | − | 0.0454106i | ||||
\(647\) | −4589.31 | − | 7948.93i | −0.278863 | − | 0.483005i | 0.692239 | − | 0.721668i | \(-0.256624\pi\) |
−0.971103 | + | 0.238663i | \(0.923291\pi\) | |||||||
\(648\) | 8264.46 | + | 14314.5i | 0.501016 | + | 0.867785i | ||||
\(649\) | −1326.35 | + | 2297.30i | −0.0802213 | + | 0.138947i | ||||
\(650\) | 3552.11 | 0.214346 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10411.8 | 0.625397 | ||||||||
\(653\) | 7219.19 | − | 12504.0i | 0.432632 | − | 0.749341i | −0.564467 | − | 0.825456i | \(-0.690918\pi\) |
0.997099 | + | 0.0761147i | \(0.0242515\pi\) | |||||||
\(654\) | −11039.8 | − | 19121.5i | −0.660077 | − | 1.14329i | ||||
\(655\) | 3450.79 | + | 5976.95i | 0.205853 | + | 0.356548i | ||||
\(656\) | 8669.92 | − | 15016.7i | 0.516012 | − | 0.893759i | ||||
\(657\) | −466.650 | −0.0277104 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2900.64 | −0.171461 | −0.0857305 | − | 0.996318i | \(-0.527322\pi\) | ||||
−0.0857305 | + | 0.996318i | \(0.527322\pi\) | |||||||
\(660\) | 1522.89 | − | 2637.72i | 0.0898158 | − | 0.155566i | ||||
\(661\) | −4988.26 | − | 8639.92i | −0.293526 | − | 0.508403i | 0.681115 | − | 0.732177i | \(-0.261496\pi\) |
−0.974641 | + | 0.223774i | \(0.928162\pi\) | |||||||
\(662\) | 2114.73 | + | 3662.82i | 0.124156 | + | 0.215045i | ||||
\(663\) | 15537.4 | − | 26911.6i | 0.910142 | − | 1.57641i | ||||
\(664\) | 16832.5 | 0.983777 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 83.7159 | 0.00487076 | ||||||||
\(667\) | −1281.38 | + | 2219.42i | −0.0743859 | + | 0.128840i | ||||
\(668\) | 4450.59 | + | 7708.65i | 0.257782 | + | 0.446492i | ||||
\(669\) | 2457.42 | + | 4256.38i | 0.142017 | + | 0.245981i | ||||
\(670\) | 3199.24 | − | 5541.24i | 0.184474 | − | 0.319517i | ||||
\(671\) | 34190.8 | 1.96710 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20760.8 | 1.18911 | 0.594554 | − | 0.804055i | \(-0.297329\pi\) | ||||
0.594554 | + | 0.804055i | \(0.297329\pi\) | |||||||
\(674\) | 178.363 | − | 308.933i | 0.0101933 | − | 0.0176553i | ||||
\(675\) | 1812.50 | + | 3139.34i | 0.103353 | + | 0.179012i | ||||
\(676\) | 2060.09 | + | 3568.18i | 0.117210 | + | 0.203014i | ||||
\(677\) | −1604.56 | + | 2779.19i | −0.0910907 | + | 0.157774i | −0.907970 | − | 0.419034i | \(-0.862369\pi\) |
0.816880 | + | 0.576808i | \(0.195702\pi\) | |||||||
\(678\) | −11148.4 | −0.631492 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 12480.7 | 0.703845 | ||||||||
\(681\) | 4152.41 | − | 7192.19i | 0.233658 | − | 0.404707i | ||||
\(682\) | 10128.6 | + | 17543.2i | 0.568685 | + | 0.984991i | ||||
\(683\) | −2166.79 | − | 3752.98i | −0.121391 | − | 0.210255i | 0.798926 | − | 0.601430i | \(-0.205402\pi\) |
−0.920316 | + | 0.391175i | \(0.872069\pi\) | |||||||
\(684\) | −9.65745 | + | 16.7272i | −0.000539857 | + | 0.000935059i | ||||
\(685\) | −9748.29 | −0.543741 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2871.64 | −0.159476 | ||||||||
\(688\) | −1760.39 | + | 3049.09i | −0.0975498 | + | 0.168961i | ||||
\(689\) | 20484.9 | + | 35480.9i | 1.13267 | + | 1.96185i | ||||
\(690\) | 2457.52 | + | 4256.55i | 0.135589 | + | 0.234846i | ||||
\(691\) | 7222.98 | − | 12510.6i | 0.397649 | − | 0.688748i | −0.595787 | − | 0.803143i | \(-0.703160\pi\) |
0.993435 | + | 0.114395i | \(0.0364930\pi\) | |||||||
\(692\) | −8443.94 | −0.463859 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10099.1 | −0.552385 | ||||||||
\(695\) | −7000.00 | + | 12124.4i | −0.382051 | + | 0.661731i | ||||
\(696\) | −1859.69 | − | 3221.07i | −0.101281 | − | 0.175423i | ||||
\(697\) | −24404.0 | − | 42269.0i | −1.32621 | − | 2.29706i | ||||
\(698\) | 1956.39 | − | 3388.56i | 0.106089 | − | 0.183752i | ||||
\(699\) | −11582.4 | −0.626733 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −859.801 | −0.0463256 | −0.0231628 | − | 0.999732i | \(-0.507374\pi\) | ||||
−0.0231628 | + | 0.999732i | \(0.507374\pi\) | |||||||
\(702\) | 10301.1 | − | 17842.1i | 0.553833 | − | 0.959267i | ||||
\(703\) | −33.1332 | − | 57.3883i | −0.00177758 | − | 0.00307886i | ||||
\(704\) | −12753.9 | − | 22090.5i | −0.682787 | − | 1.18262i | ||||
\(705\) | −1470.81 | + | 2547.52i | −0.0785730 | + | 0.136093i | ||||
\(706\) | 9084.31 | 0.484267 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −754.887 | −0.0400712 | ||||||||
\(709\) | 3989.56 | − | 6910.13i | 0.211327 | − | 0.366030i | −0.740803 | − | 0.671723i | \(-0.765555\pi\) |
0.952130 | + | 0.305693i | \(0.0988880\pi\) | |||||||
\(710\) | −4287.28 | − | 7425.80i | −0.226618 | − | 0.392514i | ||||
\(711\) | −1075.19 | − | 1862.28i | −0.0567125 | − | 0.0982290i | ||||
\(712\) | 17000.9 | − | 29446.3i | 0.894851 | − | 1.54993i | ||||
\(713\) | 16039.4 | 0.842467 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14188.2 | −0.742110 | ||||||||
\(716\) | 1899.43 | − | 3289.91i | 0.0991410 | − | 0.171717i | ||||
\(717\) | 9148.28 | + | 15845.3i | 0.476498 | + | 0.825318i | ||||
\(718\) | −3321.88 | − | 5753.67i | −0.172662 | − | 0.299060i | ||||
\(719\) | 16851.6 | − | 29187.9i | 0.874076 | − | 1.51394i | 0.0163313 | − | 0.999867i | \(-0.494801\pi\) |
0.857744 | − | 0.514077i | \(-0.171865\pi\) | |||||||
\(720\) | 360.000 | 0.0186339 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 15858.6 | 0.817444 | ||||||||
\(723\) | −6115.83 | + | 10592.9i | −0.314592 | + | 0.544890i | ||||
\(724\) | −1196.39 | − | 2072.21i | −0.0614137 | − | 0.106372i | ||||
\(725\) | −377.475 | − | 653.806i | −0.0193366 | − | 0.0334920i | ||||
\(726\) | 4688.78 | − | 8121.21i | 0.239693 | − | 0.415160i | ||||
\(727\) | −30277.0 | −1.54458 | −0.772290 | − | 0.635270i | \(-0.780889\pi\) | ||||
−0.772290 | + | 0.635270i | \(0.780889\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20917.0 | 1.06269 | ||||||||
\(730\) | 1351.32 | − | 2340.55i | 0.0685129 | − | 0.118668i | ||||
\(731\) | 4955.13 | + | 8582.54i | 0.250714 | + | 0.434250i | ||||
\(732\) | 4864.91 | + | 8426.27i | 0.245645 | + | 0.425470i | ||||
\(733\) | −9681.97 | + | 16769.7i | −0.487874 | + | 0.845023i | −0.999903 | − | 0.0139454i | \(-0.995561\pi\) |
0.512028 | + | 0.858968i | \(0.328894\pi\) | |||||||
\(734\) | −26648.1 | −1.34005 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9646.45 | −0.483115 | ||||||||
\(737\) | −12778.7 | + | 22133.4i | −0.638684 | + | 1.10623i | ||||
\(738\) | −1115.83 | − | 1932.68i | −0.0556563 | − | 0.0963995i | ||||
\(739\) | −12476.2 | − | 21609.4i | −0.621035 | − | 1.07566i | −0.989293 | − | 0.145940i | \(-0.953379\pi\) |
0.368259 | − | 0.929723i | \(-0.379954\pi\) | |||||||
\(740\) | 118.947 | − | 206.023i | 0.00590890 | − | 0.0102345i | ||||
\(741\) | −1124.69 | −0.0557576 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8154.54 | −0.402640 | −0.201320 | − | 0.979526i | \(-0.564523\pi\) | ||||
−0.201320 | + | 0.979526i | \(0.564523\pi\) | |||||||
\(744\) | −11639.1 | + | 20159.4i | −0.573533 | + | 0.993388i | ||||
\(745\) | 3585.29 | + | 6209.91i | 0.176315 | + | 0.305387i | ||||
\(746\) | 5891.67 | + | 10204.7i | 0.289155 | + | 0.500831i | ||||
\(747\) | 683.325 | − | 1183.55i | 0.0334693 | − | 0.0579705i | ||||
\(748\) | −12345.5 | −0.603469 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1447.89 | −0.0704926 | ||||||||
\(751\) | 2155.63 | − | 3733.66i | 0.104740 | − | 0.181416i | −0.808892 | − | 0.587958i | \(-0.799932\pi\) |
0.913632 | + | 0.406542i | \(0.133265\pi\) | |||||||
\(752\) | 2117.97 | + | 3668.43i | 0.102705 | + | 0.177891i | ||||
\(753\) | 7273.22 | + | 12597.6i | 0.351993 | + | 0.609670i | ||||
\(754\) | −2145.33 | + | 3715.82i | −0.103619 | + | 0.179473i | ||||
\(755\) | −9927.91 | −0.478561 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3624.79 | 0.174036 | 0.0870179 | − | 0.996207i | \(-0.472266\pi\) | ||||
0.0870179 | + | 0.996207i | \(0.472266\pi\) | |||||||
\(758\) | 1105.99 | − | 1915.63i | 0.0529964 | − | 0.0917925i | ||||
\(759\) | −9816.07 | − | 17001.9i | −0.469435 | − | 0.813085i | ||||
\(760\) | −225.856 | − | 391.195i | −0.0107798 | − | 0.0186712i | ||||
\(761\) | −10288.2 | + | 17819.7i | −0.490075 | + | 0.848835i | −0.999935 | − | 0.0114227i | \(-0.996364\pi\) |
0.509860 | + | 0.860258i | \(0.329697\pi\) | |||||||
\(762\) | 18784.8 | 0.893045 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −6516.34 | −0.308577 | ||||||||
\(765\) | 506.662 | − | 877.565i | 0.0239456 | − | 0.0414751i | ||||
\(766\) | 3572.13 | + | 6187.11i | 0.168494 | + | 0.291840i | ||||
\(767\) | 1758.25 | + | 3045.38i | 0.0827728 | + | 0.143367i | ||||
\(768\) | 8895.94 | − | 15408.2i | 0.417975 | − | 0.723953i | ||||
\(769\) | −3066.14 | −0.143781 | −0.0718907 | − | 0.997413i | \(-0.522903\pi\) | ||||
−0.0718907 | + | 0.997413i | \(0.522903\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 843.400 | 0.0393960 | ||||||||
\(772\) | 4652.32 | − | 8058.06i | 0.216892 | − | 0.375668i | ||||
\(773\) | 9693.52 | + | 16789.7i | 0.451037 | + | 0.781219i | 0.998451 | − | 0.0556429i | \(-0.0177208\pi\) |
−0.547413 | + | 0.836862i | \(0.684387\pi\) | |||||||
\(774\) | 226.565 | + | 392.422i | 0.0105216 | + | 0.0182239i | ||||
\(775\) | −2362.47 | + | 4091.92i | −0.109500 | + | 0.189659i | ||||
\(776\) | 5370.23 | 0.248428 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 14666.9 | 0.675879 | ||||||||
\(779\) | −883.250 | + | 1529.83i | −0.0406235 | + | 0.0703620i | ||||
\(780\) | −2018.80 | − | 3496.66i | −0.0926725 | − | 0.160513i | ||||
\(781\) | 17124.7 | + | 29660.9i | 0.784597 | + | 1.35896i | ||||
\(782\) | 9961.06 | − | 17253.1i | 0.455507 | − | 0.788962i | ||||
\(783\) | −4378.71 | −0.199850 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 203.300 | 0.00924342 | ||||||||
\(786\) | −7994.19 | + | 13846.3i | −0.362778 | + | 0.628350i | ||||
\(787\) | −21681.7 | − | 37553.8i | −0.982044 | − | 1.70095i | −0.654399 | − | 0.756150i | \(-0.727078\pi\) |
−0.327645 | − | 0.944801i | \(-0.606255\pi\) | |||||||
\(788\) | −2570.80 | − | 4452.75i | −0.116219 | − | 0.201298i | ||||
\(789\) | 8111.18 | − | 14049.0i | 0.365990 | − | 0.633912i | ||||
\(790\) | 12454.0 | 0.560878 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −2279.39 | −0.102266 | ||||||||
\(793\) | 22662.3 | − | 39252.2i | 1.01483 | − | 1.75774i | ||||
\(794\) | −14054.1 | − | 24342.4i | −0.628162 | − | 1.08801i | ||||
\(795\) | −8349.94 | − | 14462.5i | −0.372505 | − | 0.645198i | ||||
\(796\) | 5351.65 | − | 9269.32i | 0.238297 | − | 0.412742i | ||||
\(797\) | 17132.6 | 0.761439 | 0.380720 | − | 0.924691i | \(-0.375676\pi\) | ||||
0.380720 | + | 0.924691i | \(0.375676\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11923.3 | 0.527929 | ||||||||
\(800\) | 1420.84 | − | 2460.97i | 0.0627930 | − | 0.108761i | ||||
\(801\) | −1380.32 | − | 2390.78i | −0.0608878 | − | 0.105461i | ||||
\(802\) | −313.520 | − | 543.032i | −0.0138039 | − | 0.0239091i | ||||
\(803\) | −5397.56 | + | 9348.86i | −0.237205 | + | 0.410852i | ||||
\(804\) | −7272.98 | −0.319028 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 26853.6 | 1.17355 | ||||||||
\(807\) | 7121.64 | − | 12335.0i | 0.310649 | − | 0.538059i | ||||
\(808\) | 18158.7 | + | 31451.9i | 0.790622 | + | 1.36940i | ||||
\(809\) | 540.244 | + | 935.729i | 0.0234783 | + | 0.0406656i | 0.877526 | − | 0.479529i | \(-0.159193\pi\) |
−0.854048 | + | 0.520195i | \(0.825859\pi\) | |||||||
\(810\) | −3886.14 | + | 6730.99i | −0.168574 | + | 0.291979i | ||||
\(811\) | 19593.9 | 0.848378 | 0.424189 | − | 0.905574i | \(-0.360559\pi\) | ||||
0.424189 | + | 0.905574i | \(0.360559\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −14254.9 | −0.614933 | ||||||||
\(814\) | 968.311 | − | 1677.16i | 0.0416944 | − | 0.0722169i | ||||
\(815\) | 9884.96 | + | 17121.3i | 0.424853 | + | 0.735867i | ||||
\(816\) | 9119.92 | + | 15796.2i | 0.391251 | + | 0.677667i | ||||
\(817\) | 179.340 | − | 310.626i | 0.00767970 | − | 0.0133016i | ||||
\(818\) | −9312.66 | −0.398056 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6341.69 | −0.270075 | ||||||||
\(821\) | −2561.90 | + | 4437.34i | −0.108905 | + | 0.188629i | −0.915327 | − | 0.402712i | \(-0.868068\pi\) |
0.806422 | + | 0.591341i | \(0.201401\pi\) | |||||||
\(822\) | −11291.6 | − | 19557.6i | −0.479122 | − | 0.829864i | ||||
\(823\) | 6592.03 | + | 11417.7i | 0.279202 | + | 0.483593i | 0.971187 | − | 0.238320i | \(-0.0765966\pi\) |
−0.691984 | + | 0.721913i | \(0.743263\pi\) | |||||||
\(824\) | 9988.66 | − | 17300.9i | 0.422295 | − | 0.731437i | ||||
\(825\) | 5783.31 | 0.244060 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24658.7 | 1.03684 | 0.518421 | − | 0.855126i | \(-0.326520\pi\) | ||||
0.518421 | + | 0.855126i | \(0.326520\pi\) | |||||||
\(828\) | −223.472 | + | 387.065i | −0.00937946 | + | 0.0162457i | ||||
\(829\) | 14281.2 | + | 24735.7i | 0.598318 | + | 1.03632i | 0.993069 | + | 0.117529i | \(0.0374974\pi\) |
−0.394751 | + | 0.918788i | \(0.629169\pi\) | |||||||
\(830\) | 3957.52 | + | 6854.62i | 0.165503 | + | 0.286660i | ||||
\(831\) | −5746.57 | + | 9953.36i | −0.239887 | + | 0.415497i | ||||
\(832\) | −33814.1 | −1.40901 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −32432.7 | −1.34659 | ||||||||
\(835\) | −8450.76 | + | 14637.1i | −0.350240 | + | 0.606634i | ||||
\(836\) | 223.408 | + | 386.955i | 0.00924251 | + | 0.0160085i | ||||
\(837\) | 13702.3 | + | 23733.1i | 0.565856 | + | 0.980091i | ||||
\(838\) | 2823.14 | − | 4889.82i | 0.116377 | − | 0.201570i | ||||
\(839\) | 31106.0 | 1.27997 | 0.639987 | − | 0.768386i | \(-0.278940\pi\) | ||||
0.639987 | + | 0.768386i | \(0.278940\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23477.1 | −0.962609 | ||||||||
\(842\) | −5503.56 | + | 9532.45i | −0.225256 | + | 0.390154i | ||||
\(843\) | −15273.0 | − | 26453.6i | −0.623998 | − | 1.08080i | ||||
\(844\) | −5694.85 | − | 9863.76i | −0.232257 | − | 0.402281i | ||||
\(845\) | −3911.69 | + | 6775.24i | −0.159250 | + | 0.275829i | ||||
\(846\) | 545.171 | 0.0221553 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −24047.8 | −0.973827 | ||||||||
\(849\) | −14637.4 | + | 25352.7i | −0.591700 | + | 1.02485i | ||||
\(850\) | 2934.37 | + | 5082.47i | 0.118409 | + | 0.205091i | ||||
\(851\) | −766.696 | − | 1327.96i | −0.0308837 | − | 0.0534921i | ||||
\(852\) | −4873.25 | + | 8440.72i | −0.195956 | + | 0.339406i | ||||
\(853\) | −20567.9 | −0.825596 | −0.412798 | − | 0.910823i | \(-0.635448\pi\) | ||||
−0.412798 | + | 0.910823i | \(0.635448\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −36.6750 | −0.00146697 | ||||||||
\(856\) | −5427.44 | + | 9400.61i | −0.216713 | + | 0.375358i | ||||
\(857\) | 3229.72 | + | 5594.04i | 0.128734 | + | 0.222974i | 0.923186 | − | 0.384353i | \(-0.125575\pi\) |
−0.794452 | + | 0.607327i | \(0.792242\pi\) | |||||||
\(858\) | −16434.4 | − | 28465.2i | −0.653916 | − | 1.13262i | ||||
\(859\) | −24107.2 | + | 41754.9i | −0.957541 | + | 1.65851i | −0.229096 | + | 0.973404i | \(0.573577\pi\) |
−0.728444 | + | 0.685105i | \(0.759756\pi\) | |||||||
\(860\) | 1287.65 | 0.0510565 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −18359.7 | −0.725445 | ||||||||
\(863\) | 15854.7 | − | 27461.2i | 0.625378 | − | 1.08319i | −0.363089 | − | 0.931754i | \(-0.618278\pi\) |
0.988468 | − | 0.151433i | \(-0.0483887\pi\) | |||||||
\(864\) | −8240.89 | − | 14273.6i | −0.324492 | − | 0.562036i | ||||
\(865\) | −8016.66 | − | 13885.3i | −0.315115 | − | 0.545795i | ||||
\(866\) | −13305.8 | + | 23046.4i | −0.522114 | + | 0.904328i | ||||
\(867\) | 26776.4 | 1.04887 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −49745.1 | −1.94187 | ||||||||
\(870\) | 874.468 | − | 1514.62i | 0.0340773 | − | 0.0590236i | ||||
\(871\) | 16939.9 | + | 29340.8i | 0.658998 | + | 1.14142i | ||||
\(872\) | 23477.8 | + | 40664.7i | 0.911765 | + | 1.57922i | ||||
\(873\) | 218.008 | − | 377.600i | 0.00845182 | − | 0.0146390i | ||||
\(874\) | −721.037 | −0.0279055 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3072.01 | −0.118486 | ||||||||
\(877\) | −12827.4 | + | 22217.7i | −0.493900 | + | 0.855459i | −0.999975 | − | 0.00702998i | \(-0.997762\pi\) |
0.506076 | + | 0.862489i | \(0.331096\pi\) | |||||||
\(878\) | −10596.1 | − | 18353.1i | −0.407292 | − | 0.705451i | ||||
\(879\) | 12838.4 | + | 22236.7i | 0.492636 | + | 0.853271i | ||||
\(880\) | 4163.98 | − | 7212.23i | 0.159509 | − | 0.276278i | ||||
\(881\) | 11470.4 | 0.438647 | 0.219323 | − | 0.975652i | \(-0.429615\pi\) | ||||
0.219323 | + | 0.975652i | \(0.429615\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39124.0 | 1.49108 | 0.745542 | − | 0.666459i | \(-0.232191\pi\) | ||||
0.745542 | + | 0.666459i | \(0.232191\pi\) | |||||||
\(884\) | −8182.79 | + | 14173.0i | −0.311331 | + | 0.539242i | ||||
\(885\) | −716.688 | − | 1241.34i | −0.0272217 | − | 0.0471493i | ||||
\(886\) | 2159.50 | + | 3740.37i | 0.0818848 | + | 0.141829i | ||||
\(887\) | 7792.88 | − | 13497.7i | 0.294994 | − | 0.510944i | −0.679990 | − | 0.733222i | \(-0.738016\pi\) |
0.974983 | + | 0.222278i | \(0.0713491\pi\) | |||||||
\(888\) | 2225.43 | 0.0840997 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 15988.4 | 0.602171 | ||||||||
\(891\) | 15522.4 | − | 26885.6i | 0.583637 | − | 1.01089i | ||||
\(892\) | −1294.20 | − | 2241.62i | −0.0485797 | − | 0.0841425i | ||||
\(893\) | −215.768 | − | 373.722i | −0.00808557 | − | 0.0140046i | ||||
\(894\) | −8305.78 | + | 14386.0i | −0.310723 | + | 0.538189i | ||||
\(895\) | 7213.25 | 0.269399 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −26025.1 | −0.968731 | ||||||||
\(898\) | 5201.85 | − | 9009.86i | 0.193305 | − | 0.334814i | ||||
\(899\) | −2853.67 | − | 4942.71i | −0.105868 | − | 0.183369i | ||||
\(900\) | −65.8312 | − | 114.023i | −0.00243819 | − | 0.00422308i | ||||
\(901\) | −33844.8 | + | 58620.9i | −1.25142 | + | 2.16753i | ||||
\(902\) | −51625.6 | −1.90570 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 23708.8 | 0.872280 | ||||||||
\(905\) | 2271.70 | − | 3934.70i | 0.0834407 | − | 0.144524i | ||||
\(906\) | −11499.6 | − | 19917.9i | −0.421688 | − | 0.730385i | ||||
\(907\) | −13798.1 | − | 23898.9i | −0.505134 | − | 0.874918i | −0.999982 | − | 0.00593879i | \(-0.998110\pi\) |
0.494848 | − | 0.868980i | \(-0.335224\pi\) | |||||||
\(908\) | −2186.87 | + | 3787.77i | −0.0799270 | + | 0.138438i | ||||
\(909\) | 2948.65 | 0.107592 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14396.2 | −0.523565 | −0.261782 | − | 0.965127i | \(-0.584310\pi\) | ||||
−0.261782 | + | 0.965127i | \(0.584310\pi\) | |||||||
\(912\) | 330.075 | − | 571.707i | 0.0119845 | − | 0.0207578i | ||||
\(913\) | −15807.5 | − | 27379.4i | −0.573004 | − | 0.992472i | ||||
\(914\) | −16614.6 | − | 28777.4i | −0.601272 | − | 1.04143i | ||||
\(915\) | −9237.47 | + | 15999.8i | −0.333750 | + | 0.578072i | ||||
\(916\) | 1512.35 | 0.0545517 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 34038.7 | 1.22379 | ||||||||
\(919\) | −5139.78 | + | 8902.35i | −0.184489 | + | 0.319545i | −0.943404 | − | 0.331645i | \(-0.892396\pi\) |
0.758915 | + | 0.651190i | \(0.225730\pi\) | |||||||
\(920\) | −5226.28 | − | 9052.19i | −0.187289 | − | 0.324393i | ||||
\(921\) | −5257.42 | − | 9106.13i | −0.188098 | − | 0.325795i | ||||
\(922\) | −16863.5 | + | 29208.4i | −0.602353 | + | 1.04331i | ||||
\(923\) | 45402.2 | 1.61910 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 451.713 | 0.0160565 | ||||||||
\(926\) | −2096.03 | + | 3630.43i | −0.0743843 | + | 0.128837i | ||||
\(927\) | −810.990 | − | 1404.68i | −0.0287340 | − | 0.0497687i | ||||
\(928\) | 1716.27 | + | 2972.66i | 0.0607103 | + | 0.105153i | ||||
\(929\) | −3249.94 | + | 5629.06i | −0.114776 | + | 0.198798i | −0.917690 | − | 0.397297i | \(-0.869948\pi\) |
0.802914 | + | 0.596095i | \(0.203282\pi\) | |||||||
\(930\) | −10945.9 | −0.385947 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 6099.86 | 0.214386 | ||||||||
\(933\) | 14410.8 | − | 24960.2i | 0.505667 | − | 0.875840i | ||||
\(934\) | 6928.62 | + | 12000.7i | 0.242732 | + | 0.420424i | ||||
\(935\) | −11720.7 | − | 20300.9i | −0.409957 | − | 0.710066i | ||||
\(936\) | −1510.82 | + | 2616.81i | −0.0527592 | + | 0.0913817i | ||||
\(937\) | −10269.8 | −0.358056 | −0.179028 | − | 0.983844i | \(-0.557295\pi\) | ||||
−0.179028 | + | 0.983844i | \(0.557295\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6800.06 | −0.236328 | ||||||||
\(940\) | 774.603 | − | 1341.65i | 0.0268774 | − | 0.0465531i | ||||
\(941\) | −17198.1 | − | 29788.0i | −0.595794 | − | 1.03195i | −0.993434 | − | 0.114404i | \(-0.963504\pi\) |
0.397640 | − | 0.917541i | \(-0.369829\pi\) | |||||||
\(942\) | 235.485 | + | 407.871i | 0.00814491 | + | 0.0141074i | ||||
\(943\) | −20438.3 | + | 35400.1i | −0.705792 | + | 1.22247i | ||||
\(944\) | −2064.06 | −0.0711647 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10482.4 | 0.360265 | ||||||||
\(947\) | −13596.1 | + | 23549.1i | −0.466539 | + | 0.808070i | −0.999270 | − | 0.0382155i | \(-0.987833\pi\) |
0.532730 | + | 0.846285i | \(0.321166\pi\) | |||||||
\(948\) | −7078.08 | − | 12259.6i | −0.242495 | − | 0.420014i | ||||
\(949\) | 7155.20 | + | 12393.2i | 0.244750 | + | 0.423919i | ||||
\(950\) | 106.203 | − | 183.949i | 0.00362703 | − | 0.00628220i | ||||
\(951\) | 25694.7 | 0.876140 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 49965.2 | 1.69836 | 0.849178 | − | 0.528107i | \(-0.177098\pi\) | ||||
0.849178 | + | 0.528107i | \(0.177098\pi\) | |||||||
\(954\) | −1547.49 | + | 2680.34i | −0.0525178 | + | 0.0909635i | ||||
\(955\) | −6186.59 | − | 10715.5i | −0.209627 | − | 0.363084i | ||||
\(956\) | −4817.94 | − | 8344.92i | −0.162995 | − | 0.282316i | ||||
\(957\) | −3492.89 | + | 6049.86i | −0.117982 | + | 0.204351i | ||||
\(958\) | −26704.9 | −0.900622 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 13783.1 | 0.463384 | ||||||||
\(961\) | −2964.53 | + | 5134.71i | −0.0995108 | + | 0.172358i | ||||
\(962\) | −1283.63 | − | 2223.31i | −0.0430206 | − | 0.0745138i | ||||
\(963\) | 440.660 | + | 763.245i | 0.0147457 | + | 0.0255402i | ||||
\(964\) | 3220.90 | − | 5578.77i | 0.107612 | − | 0.186390i | ||||
\(965\) | 17667.6 | 0.589368 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16755.5 | −0.557208 | −0.278604 | − | 0.960406i | \(-0.589872\pi\) | ||||
−0.278604 | + | 0.960406i | \(0.589872\pi\) | |||||||
\(968\) | −9971.40 | + | 17271.0i | −0.331088 | + | 0.573461i | ||||
\(969\) | −929.093 | − | 1609.24i | −0.0308016 | − | 0.0533500i | ||||
\(970\) | 1262.60 | + | 2186.89i | 0.0417936 | + | 0.0723886i | ||||
\(971\) | 18808.7 | − | 32577.6i | 0.621626 | − | 1.07669i | −0.367557 | − | 0.930001i | \(-0.619806\pi\) |
0.989183 | − | 0.146687i | \(-0.0468611\pi\) | |||||||
\(972\) | −1474.62 | −0.0486610 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −36583.0 | −1.20348 | ||||||||
\(975\) | 3833.28 | − | 6639.44i | 0.125911 | − | 0.218084i | ||||
\(976\) | 13302.0 | + | 23039.7i | 0.436255 | + | 0.755616i | ||||
\(977\) | 13845.5 | + | 23981.1i | 0.453384 | + | 0.785284i | 0.998594 | − | 0.0530160i | \(-0.0168834\pi\) |
−0.545210 | + | 0.838300i | \(0.683550\pi\) | |||||||
\(978\) | −22899.7 | + | 39663.5i | −0.748725 | + | 1.29683i | ||||
\(979\) | −63862.5 | −2.08483 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3812.38 | 0.124077 | ||||||||
\(982\) | 15133.2 | − | 26211.5i | 0.491772 | − | 0.851774i | ||||
\(983\) | 11377.1 | + | 19705.7i | 0.369149 | + | 0.639385i | 0.989433 | − | 0.144992i | \(-0.0463158\pi\) |
−0.620283 | + | 0.784378i | \(0.712982\pi\) | |||||||
\(984\) | −29662.3 | − | 51376.6i | −0.960975 | − | 1.66446i | ||||
\(985\) | 4881.42 | − | 8454.86i | 0.157903 | − | 0.273497i | ||||
\(986\) | −7088.96 | −0.228964 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 592.316 | 0.0190729 | ||||||||
\(989\) | 4149.90 | − | 7187.84i | 0.133427 | − | 0.231102i | ||||
\(990\) | −535.911 | − | 928.224i | −0.0172044 | − | 0.0297989i | ||||
\(991\) | 27735.5 | + | 48039.2i | 0.889047 | + | 1.53987i | 0.841004 | + | 0.541030i | \(0.181965\pi\) |
0.0480435 | + | 0.998845i | \(0.484701\pi\) | |||||||
\(992\) | 10741.4 | − | 18604.7i | 0.343791 | − | 0.595464i | ||||
\(993\) | 9128.50 | 0.291726 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20323.4 | 0.647531 | ||||||||
\(996\) | 4498.41 | − | 7791.48i | 0.143110 | − | 0.247874i | ||||
\(997\) | 7590.97 | + | 13147.9i | 0.241132 | + | 0.417653i | 0.961037 | − | 0.276420i | \(-0.0891480\pi\) |
−0.719905 | + | 0.694072i | \(0.755815\pi\) | |||||||
\(998\) | −23323.6 | − | 40397.6i | −0.739774 | − | 1.28133i | ||||
\(999\) | 1309.97 | − | 2268.93i | 0.0414870 | − | 0.0718576i |
(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 | 245.4.e.j.226.2 | 4 | ||
7.2 | even | 3 | 245.4.a.j.1.1 | yes | 2 | ||
7.3 | odd | 6 | 245.4.e.k.116.2 | 4 | |||
7.4 | even | 3 | inner | 245.4.e.j.116.2 | 4 | ||
7.5 | odd | 6 | 245.4.a.i.1.1 | ✓ | 2 | ||
7.6 | odd | 2 | 245.4.e.k.226.2 | 4 | |||
21.2 | odd | 6 | 2205.4.a.w.1.2 | 2 | |||
21.5 | even | 6 | 2205.4.a.x.1.2 | 2 | |||
35.9 | even | 6 | 1225.4.a.p.1.2 | 2 | |||
35.19 | odd | 6 | 1225.4.a.q.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
245.4.a.i.1.1 | ✓ | 2 | 7.5 | odd | 6 | ||
245.4.a.j.1.1 | yes | 2 | 7.2 | even | 3 | ||
245.4.e.j.116.2 | 4 | 7.4 | even | 3 | inner | ||
245.4.e.j.226.2 | 4 | 1.1 | even | 1 | trivial | ||
245.4.e.k.116.2 | 4 | 7.3 | odd | 6 | |||
245.4.e.k.226.2 | 4 | 7.6 | odd | 2 | |||
1225.4.a.p.1.2 | 2 | 35.9 | even | 6 | |||
1225.4.a.q.1.2 | 2 | 35.19 | odd | 6 | |||
2205.4.a.w.1.2 | 2 | 21.2 | odd | 6 | |||
2205.4.a.x.1.2 | 2 | 21.5 | even | 6 |