Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1014,3,Mod(577,1014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1014, 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("1014.577");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1014 = 2 \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1014.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: | \(27.6294988061\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 2x^{6} + 82x^{5} + 5053x^{4} - 6736x^{3} + 6728x^{2} + 275384x + 5635876 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 78) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 775.3 | ||
Root | \(5.41254 + 5.41254i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1014.775 |
Dual form | 1014.3.f.h.577.3 |
$q$-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 \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(847\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(5\) | −5.04651 | − | 5.04651i | −1.00930 | − | 1.00930i | −0.999956 | − | 0.00934664i | \(-0.997025\pi\) |
−0.00934664 | − | 0.999956i | \(-0.502975\pi\) | |||||||
\(6\) | −1.73205 | − | 1.73205i | −0.288675 | − | 0.288675i | ||||
\(7\) | −3.68049 | + | 3.68049i | −0.525784 | + | 0.525784i | −0.919313 | − | 0.393528i | \(-0.871254\pi\) |
0.393528 | + | 0.919313i | \(0.371254\pi\) | |||||||
\(8\) | 2.00000 | − | 2.00000i | 0.250000 | − | 0.250000i | ||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 10.0930i | 1.00930i | ||||||||
\(11\) | 5.36098 | − | 5.36098i | 0.487362 | − | 0.487362i | −0.420111 | − | 0.907473i | \(-0.638009\pi\) |
0.907473 | + | 0.420111i | \(0.138009\pi\) | |||||||
\(12\) | 3.46410i | 0.288675i | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 7.36098 | 0.525784 | ||||||||
\(15\) | −8.74082 | − | 8.74082i | −0.582721 | − | 0.582721i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | 16.1621i | 0.950712i | 0.879794 | + | 0.475356i | \(0.157681\pi\) | ||||
−0.879794 | + | 0.475356i | \(0.842319\pi\) | |||||||
\(18\) | −3.00000 | − | 3.00000i | −0.166667 | − | 0.166667i | ||||
\(19\) | −7.23020 | − | 7.23020i | −0.380537 | − | 0.380537i | 0.490759 | − | 0.871296i | \(-0.336720\pi\) |
−0.871296 | + | 0.490759i | \(0.836720\pi\) | |||||||
\(20\) | 10.0930 | − | 10.0930i | 0.504651 | − | 0.504651i | ||||
\(21\) | −6.37479 | + | 6.37479i | −0.303562 | + | 0.303562i | ||||
\(22\) | −10.7220 | −0.487362 | ||||||||
\(23\) | − | 9.57467i | − | 0.416290i | −0.978098 | − | 0.208145i | \(-0.933257\pi\) | ||
0.978098 | − | 0.208145i | \(-0.0667426\pi\) | |||||||
\(24\) | 3.46410 | − | 3.46410i | 0.144338 | − | 0.144338i | ||||
\(25\) | 25.9346i | 1.03738i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615 | 0.192450 | ||||||||
\(28\) | −7.36098 | − | 7.36098i | −0.262892 | − | 0.262892i | ||||
\(29\) | −33.1759 | −1.14400 | −0.571999 | − | 0.820254i | \(-0.693832\pi\) | ||||
−0.571999 | + | 0.820254i | \(0.693832\pi\) | |||||||
\(30\) | 17.4816i | 0.582721i | ||||||||
\(31\) | −34.2312 | − | 34.2312i | −1.10423 | − | 1.10423i | −0.993894 | − | 0.110338i | \(-0.964807\pi\) |
−0.110338 | − | 0.993894i | \(-0.535193\pi\) | |||||||
\(32\) | 4.00000 | + | 4.00000i | 0.125000 | + | 0.125000i | ||||
\(33\) | 9.28549 | − | 9.28549i | 0.281378 | − | 0.281378i | ||||
\(34\) | 16.1621 | − | 16.1621i | 0.475356 | − | 0.475356i | ||||
\(35\) | 37.1473 | 1.06135 | ||||||||
\(36\) | 6.00000i | 0.166667i | ||||||||
\(37\) | −46.2851 | + | 46.2851i | −1.25095 | + | 1.25095i | −0.295655 | + | 0.955295i | \(0.595538\pi\) |
−0.955295 | + | 0.295655i | \(0.904462\pi\) | |||||||
\(38\) | 14.4604i | 0.380537i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −20.1861 | −0.504651 | ||||||||
\(41\) | 38.5116 | + | 38.5116i | 0.939308 | + | 0.939308i | 0.998261 | − | 0.0589525i | \(-0.0187760\pi\) |
−0.0589525 | + | 0.998261i | \(0.518776\pi\) | |||||||
\(42\) | 12.7496 | 0.303562 | ||||||||
\(43\) | 47.0461i | 1.09410i | 0.837101 | + | 0.547048i | \(0.184249\pi\) | ||||
−0.837101 | + | 0.547048i | \(0.815751\pi\) | |||||||
\(44\) | 10.7220 | + | 10.7220i | 0.243681 | + | 0.243681i | ||||
\(45\) | −15.1395 | − | 15.1395i | −0.336434 | − | 0.336434i | ||||
\(46\) | −9.57467 | + | 9.57467i | −0.208145 | + | 0.208145i | ||||
\(47\) | 47.8214 | − | 47.8214i | 1.01748 | − | 1.01748i | 0.0176317 | − | 0.999845i | \(-0.494387\pi\) |
0.999845 | − | 0.0176317i | \(-0.00561265\pi\) | |||||||
\(48\) | −6.92820 | −0.144338 | ||||||||
\(49\) | 21.9080i | 0.447102i | ||||||||
\(50\) | 25.9346 | − | 25.9346i | 0.518692 | − | 0.518692i | ||||
\(51\) | 27.9936i | 0.548894i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 67.5177 | 1.27392 | 0.636959 | − | 0.770897i | \(-0.280192\pi\) | ||||
0.636959 | + | 0.770897i | \(0.280192\pi\) | |||||||
\(54\) | −5.19615 | − | 5.19615i | −0.0962250 | − | 0.0962250i | ||||
\(55\) | −54.1085 | −0.983791 | ||||||||
\(56\) | 14.7220i | 0.262892i | ||||||||
\(57\) | −12.5231 | − | 12.5231i | −0.219703 | − | 0.219703i | ||||
\(58\) | 33.1759 | + | 33.1759i | 0.571999 | + | 0.571999i | ||||
\(59\) | −53.2525 | + | 53.2525i | −0.902584 | + | 0.902584i | −0.995659 | − | 0.0930750i | \(-0.970330\pi\) |
0.0930750 | + | 0.995659i | \(0.470330\pi\) | |||||||
\(60\) | 17.4816 | − | 17.4816i | 0.291361 | − | 0.291361i | ||||
\(61\) | 70.5195 | 1.15606 | 0.578028 | − | 0.816017i | \(-0.303822\pi\) | ||||
0.578028 | + | 0.816017i | \(0.303822\pi\) | |||||||
\(62\) | 68.4624i | 1.10423i | ||||||||
\(63\) | −11.0415 | + | 11.0415i | −0.175261 | + | 0.175261i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −18.5710 | −0.281378 | ||||||||
\(67\) | 30.5554 | + | 30.5554i | 0.456051 | + | 0.456051i | 0.897357 | − | 0.441306i | \(-0.145485\pi\) |
−0.441306 | + | 0.897357i | \(0.645485\pi\) | |||||||
\(68\) | −32.3242 | −0.475356 | ||||||||
\(69\) | − | 16.5838i | − | 0.240345i | ||||||
\(70\) | −37.1473 | − | 37.1473i | −0.530676 | − | 0.530676i | ||||
\(71\) | 78.1807 | + | 78.1807i | 1.10114 | + | 1.10114i | 0.994274 | + | 0.106862i | \(0.0340804\pi\) |
0.106862 | + | 0.994274i | \(0.465920\pi\) | |||||||
\(72\) | 6.00000 | − | 6.00000i | 0.0833333 | − | 0.0833333i | ||||
\(73\) | −36.8385 | + | 36.8385i | −0.504638 | + | 0.504638i | −0.912876 | − | 0.408238i | \(-0.866143\pi\) |
0.408238 | + | 0.912876i | \(0.366143\pi\) | |||||||
\(74\) | 92.5703 | 1.25095 | ||||||||
\(75\) | 44.9201i | 0.598934i | ||||||||
\(76\) | 14.4604 | − | 14.4604i | 0.190269 | − | 0.190269i | ||||
\(77\) | 39.4621i | 0.512494i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.3867 | −0.169452 | −0.0847259 | − | 0.996404i | \(-0.527001\pi\) | ||||
−0.0847259 | + | 0.996404i | \(0.527001\pi\) | |||||||
\(80\) | 20.1861 | + | 20.1861i | 0.252326 | + | 0.252326i | ||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | − | 77.0233i | − | 0.939308i | ||||||
\(83\) | 93.1237 | + | 93.1237i | 1.12197 | + | 1.12197i | 0.991445 | + | 0.130528i | \(0.0416671\pi\) |
0.130528 | + | 0.991445i | \(0.458333\pi\) | |||||||
\(84\) | −12.7496 | − | 12.7496i | −0.151781 | − | 0.151781i | ||||
\(85\) | 81.5623 | − | 81.5623i | 0.959556 | − | 0.959556i | ||||
\(86\) | 47.0461 | − | 47.0461i | 0.547048 | − | 0.547048i | ||||
\(87\) | −57.4624 | −0.660488 | ||||||||
\(88\) | − | 21.4439i | − | 0.243681i | ||||||
\(89\) | −35.5877 | + | 35.5877i | −0.399862 | + | 0.399862i | −0.878184 | − | 0.478322i | \(-0.841245\pi\) |
0.478322 | + | 0.878184i | \(0.341245\pi\) | |||||||
\(90\) | 30.2791i | 0.336434i | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 19.1493 | 0.208145 | ||||||||
\(93\) | −59.2902 | − | 59.2902i | −0.637529 | − | 0.637529i | ||||
\(94\) | −95.6428 | −1.01748 | ||||||||
\(95\) | 72.9747i | 0.768154i | ||||||||
\(96\) | 6.92820 | + | 6.92820i | 0.0721688 | + | 0.0721688i | ||||
\(97\) | 38.4633 | + | 38.4633i | 0.396529 | + | 0.396529i | 0.877007 | − | 0.480478i | \(-0.159537\pi\) |
−0.480478 | + | 0.877007i | \(0.659537\pi\) | |||||||
\(98\) | 21.9080 | − | 21.9080i | 0.223551 | − | 0.223551i | ||||
\(99\) | 16.0829 | − | 16.0829i | 0.162454 | − | 0.162454i | ||||
\(100\) | −51.8692 | −0.518692 | ||||||||
\(101\) | 22.5497i | 0.223264i | 0.993750 | + | 0.111632i | \(0.0356079\pi\) | ||||
−0.993750 | + | 0.111632i | \(0.964392\pi\) | |||||||
\(102\) | 27.9936 | − | 27.9936i | 0.274447 | − | 0.274447i | ||||
\(103\) | 109.385i | 1.06199i | 0.847374 | + | 0.530996i | \(0.178182\pi\) | ||||
−0.847374 | + | 0.530996i | \(0.821818\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 64.3410 | 0.612771 | ||||||||
\(106\) | −67.5177 | − | 67.5177i | −0.636959 | − | 0.636959i | ||||
\(107\) | −32.8750 | −0.307243 | −0.153621 | − | 0.988130i | \(-0.549094\pi\) | ||||
−0.153621 | + | 0.988130i | \(0.549094\pi\) | |||||||
\(108\) | 10.3923i | 0.0962250i | ||||||||
\(109\) | −150.086 | − | 150.086i | −1.37693 | − | 1.37693i | −0.849752 | − | 0.527183i | \(-0.823248\pi\) |
−0.527183 | − | 0.849752i | \(-0.676752\pi\) | |||||||
\(110\) | 54.1085 | + | 54.1085i | 0.491896 | + | 0.491896i | ||||
\(111\) | −80.1682 | + | 80.1682i | −0.722236 | + | 0.722236i | ||||
\(112\) | 14.7220 | − | 14.7220i | 0.131446 | − | 0.131446i | ||||
\(113\) | −118.788 | −1.05122 | −0.525609 | − | 0.850726i | \(-0.676163\pi\) | ||||
−0.525609 | + | 0.850726i | \(0.676163\pi\) | |||||||
\(114\) | 25.0462i | 0.219703i | ||||||||
\(115\) | −48.3187 | + | 48.3187i | −0.420163 | + | 0.420163i | ||||
\(116\) | − | 66.3519i | − | 0.571999i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 106.505 | 0.902584 | ||||||||
\(119\) | −59.4844 | − | 59.4844i | −0.499869 | − | 0.499869i | ||||
\(120\) | −34.9633 | −0.291361 | ||||||||
\(121\) | 63.5198i | 0.524957i | ||||||||
\(122\) | −70.5195 | − | 70.5195i | −0.578028 | − | 0.578028i | ||||
\(123\) | 66.7041 | + | 66.7041i | 0.542310 | + | 0.542310i | ||||
\(124\) | 68.4624 | − | 68.4624i | 0.552116 | − | 0.552116i | ||||
\(125\) | 4.71659 | − | 4.71659i | 0.0377327 | − | 0.0377327i | ||||
\(126\) | 22.0829 | 0.175261 | ||||||||
\(127\) | − | 66.4529i | − | 0.523252i | −0.965169 | − | 0.261626i | \(-0.915741\pi\) | ||
0.965169 | − | 0.261626i | \(-0.0842586\pi\) | |||||||
\(128\) | −8.00000 | + | 8.00000i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | 81.4863i | 0.631677i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −28.3277 | −0.216242 | −0.108121 | − | 0.994138i | \(-0.534483\pi\) | ||||
−0.108121 | + | 0.994138i | \(0.534483\pi\) | |||||||
\(132\) | 18.5710 | + | 18.5710i | 0.140689 | + | 0.140689i | ||||
\(133\) | 53.2214 | 0.400161 | ||||||||
\(134\) | − | 61.1108i | − | 0.456051i | ||||||
\(135\) | −26.2225 | − | 26.2225i | −0.194240 | − | 0.194240i | ||||
\(136\) | 32.3242 | + | 32.3242i | 0.237678 | + | 0.237678i | ||||
\(137\) | 35.5910 | − | 35.5910i | 0.259789 | − | 0.259789i | −0.565179 | − | 0.824968i | \(-0.691193\pi\) |
0.824968 | + | 0.565179i | \(0.191193\pi\) | |||||||
\(138\) | −16.5838 | + | 16.5838i | −0.120173 | + | 0.120173i | ||||
\(139\) | −148.284 | −1.06679 | −0.533396 | − | 0.845866i | \(-0.679084\pi\) | ||||
−0.533396 | + | 0.845866i | \(0.679084\pi\) | |||||||
\(140\) | 74.2946i | 0.530676i | ||||||||
\(141\) | 82.8291 | − | 82.8291i | 0.587440 | − | 0.587440i | ||||
\(142\) | − | 156.361i | − | 1.10114i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −12.0000 | −0.0833333 | ||||||||
\(145\) | 167.423 | + | 167.423i | 1.15464 | + | 1.15464i | ||||
\(146\) | 73.6771 | 0.504638 | ||||||||
\(147\) | 37.9458i | 0.258134i | ||||||||
\(148\) | −92.5703 | − | 92.5703i | −0.625475 | − | 0.625475i | ||||
\(149\) | 29.5935 | + | 29.5935i | 0.198614 | + | 0.198614i | 0.799406 | − | 0.600792i | \(-0.205148\pi\) |
−0.600792 | + | 0.799406i | \(0.705148\pi\) | |||||||
\(150\) | 44.9201 | − | 44.9201i | 0.299467 | − | 0.299467i | ||||
\(151\) | −2.57635 | + | 2.57635i | −0.0170619 | + | 0.0170619i | −0.715586 | − | 0.698524i | \(-0.753840\pi\) |
0.698524 | + | 0.715586i | \(0.253840\pi\) | |||||||
\(152\) | −28.9208 | −0.190269 | ||||||||
\(153\) | 48.4863i | 0.316904i | ||||||||
\(154\) | 39.4621 | − | 39.4621i | 0.256247 | − | 0.256247i | ||||
\(155\) | 345.497i | 2.22901i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 275.987 | 1.75788 | 0.878939 | − | 0.476934i | \(-0.158252\pi\) | ||||
0.878939 | + | 0.476934i | \(0.158252\pi\) | |||||||
\(158\) | 13.3867 | + | 13.3867i | 0.0847259 | + | 0.0847259i | ||||
\(159\) | 116.944 | 0.735497 | ||||||||
\(160\) | − | 40.3721i | − | 0.252326i | ||||||
\(161\) | 35.2395 | + | 35.2395i | 0.218879 | + | 0.218879i | ||||
\(162\) | −9.00000 | − | 9.00000i | −0.0555556 | − | 0.0555556i | ||||
\(163\) | −99.4028 | + | 99.4028i | −0.609833 | + | 0.609833i | −0.942902 | − | 0.333069i | \(-0.891916\pi\) |
0.333069 | + | 0.942902i | \(0.391916\pi\) | |||||||
\(164\) | −77.0233 | + | 77.0233i | −0.469654 | + | 0.469654i | ||||
\(165\) | −93.7187 | −0.567992 | ||||||||
\(166\) | − | 186.247i | − | 1.12197i | ||||||
\(167\) | −138.947 | + | 138.947i | −0.832018 | + | 0.832018i | −0.987793 | − | 0.155774i | \(-0.950213\pi\) |
0.155774 | + | 0.987793i | \(0.450213\pi\) | |||||||
\(168\) | 25.4992i | 0.151781i | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −163.125 | −0.959556 | ||||||||
\(171\) | −21.6906 | − | 21.6906i | −0.126846 | − | 0.126846i | ||||
\(172\) | −94.0923 | −0.547048 | ||||||||
\(173\) | − | 132.251i | − | 0.764456i | −0.924068 | − | 0.382228i | \(-0.875157\pi\) | ||
0.924068 | − | 0.382228i | \(-0.124843\pi\) | |||||||
\(174\) | 57.4624 | + | 57.4624i | 0.330244 | + | 0.330244i | ||||
\(175\) | −95.4521 | − | 95.4521i | −0.545441 | − | 0.545441i | ||||
\(176\) | −21.4439 | + | 21.4439i | −0.121840 | + | 0.121840i | ||||
\(177\) | −92.2360 | + | 92.2360i | −0.521107 | + | 0.521107i | ||||
\(178\) | 71.1755 | 0.399862 | ||||||||
\(179\) | 35.4311i | 0.197939i | 0.995090 | + | 0.0989697i | \(0.0315547\pi\) | ||||
−0.995090 | + | 0.0989697i | \(0.968445\pi\) | |||||||
\(180\) | 30.2791 | − | 30.2791i | 0.168217 | − | 0.168217i | ||||
\(181\) | 121.119i | 0.669163i | 0.942367 | + | 0.334582i | \(0.108595\pi\) | ||||
−0.942367 | + | 0.334582i | \(0.891405\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 122.143 | 0.667450 | ||||||||
\(184\) | −19.1493 | − | 19.1493i | −0.104072 | − | 0.104072i | ||||
\(185\) | 467.157 | 2.52517 | ||||||||
\(186\) | 118.580i | 0.637529i | ||||||||
\(187\) | 86.6447 | + | 86.6447i | 0.463341 | + | 0.463341i | ||||
\(188\) | 95.6428 | + | 95.6428i | 0.508738 | + | 0.508738i | ||||
\(189\) | −19.1244 | + | 19.1244i | −0.101187 | + | 0.101187i | ||||
\(190\) | 72.9747 | − | 72.9747i | 0.384077 | − | 0.384077i | ||||
\(191\) | 200.564 | 1.05007 | 0.525036 | − | 0.851080i | \(-0.324052\pi\) | ||||
0.525036 | + | 0.851080i | \(0.324052\pi\) | |||||||
\(192\) | − | 13.8564i | − | 0.0721688i | ||||||
\(193\) | −18.5004 | + | 18.5004i | −0.0958572 | + | 0.0958572i | −0.753409 | − | 0.657552i | \(-0.771592\pi\) |
0.657552 | + | 0.753409i | \(0.271592\pi\) | |||||||
\(194\) | − | 76.9267i | − | 0.396529i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −43.8160 | −0.223551 | ||||||||
\(197\) | −66.9799 | − | 66.9799i | −0.339999 | − | 0.339999i | 0.516368 | − | 0.856367i | \(-0.327284\pi\) |
−0.856367 | + | 0.516368i | \(0.827284\pi\) | |||||||
\(198\) | −32.1659 | −0.162454 | ||||||||
\(199\) | − | 197.199i | − | 0.990951i | −0.868622 | − | 0.495475i | \(-0.834994\pi\) | ||
0.868622 | − | 0.495475i | \(-0.165006\pi\) | |||||||
\(200\) | 51.8692 | + | 51.8692i | 0.259346 | + | 0.259346i | ||||
\(201\) | 52.9235 | + | 52.9235i | 0.263301 | + | 0.263301i | ||||
\(202\) | 22.5497 | − | 22.5497i | 0.111632 | − | 0.111632i | ||||
\(203\) | 122.104 | − | 122.104i | 0.601496 | − | 0.601496i | ||||
\(204\) | −55.9872 | −0.274447 | ||||||||
\(205\) | − | 388.699i | − | 1.89609i | ||||||
\(206\) | 109.385 | − | 109.385i | 0.530996 | − | 0.530996i | ||||
\(207\) | − | 28.7240i | − | 0.138763i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −77.5219 | −0.370918 | ||||||||
\(210\) | −64.3410 | − | 64.3410i | −0.306386 | − | 0.306386i | ||||
\(211\) | −194.835 | −0.923387 | −0.461694 | − | 0.887039i | \(-0.652758\pi\) | ||||
−0.461694 | + | 0.887039i | \(0.652758\pi\) | |||||||
\(212\) | 135.035i | 0.636959i | ||||||||
\(213\) | 135.413 | + | 135.413i | 0.635741 | + | 0.635741i | ||||
\(214\) | 32.8750 | + | 32.8750i | 0.153621 | + | 0.153621i | ||||
\(215\) | 237.419 | − | 237.419i | 1.10427 | − | 1.10427i | ||||
\(216\) | 10.3923 | − | 10.3923i | 0.0481125 | − | 0.0481125i | ||||
\(217\) | 251.975 | 1.16118 | ||||||||
\(218\) | 300.172i | 1.37693i | ||||||||
\(219\) | −63.8062 | + | 63.8062i | −0.291353 | + | 0.291353i | ||||
\(220\) | − | 108.217i | − | 0.491896i | ||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 160.336 | 0.722236 | ||||||||
\(223\) | 289.655 | + | 289.655i | 1.29890 | + | 1.29890i | 0.929119 | + | 0.369782i | \(0.120568\pi\) |
0.369782 | + | 0.929119i | \(0.379432\pi\) | |||||||
\(224\) | −29.4439 | −0.131446 | ||||||||
\(225\) | 77.8039i | 0.345795i | ||||||||
\(226\) | 118.788 | + | 118.788i | 0.525609 | + | 0.525609i | ||||
\(227\) | −176.560 | − | 176.560i | −0.777798 | − | 0.777798i | 0.201658 | − | 0.979456i | \(-0.435367\pi\) |
−0.979456 | + | 0.201658i | \(0.935367\pi\) | |||||||
\(228\) | 25.0462 | − | 25.0462i | 0.109852 | − | 0.109852i | ||||
\(229\) | −174.256 | + | 174.256i | −0.760945 | + | 0.760945i | −0.976493 | − | 0.215548i | \(-0.930846\pi\) |
0.215548 | + | 0.976493i | \(0.430846\pi\) | |||||||
\(230\) | 96.6374 | 0.420163 | ||||||||
\(231\) | 68.3503i | 0.295889i | ||||||||
\(232\) | −66.3519 | + | 66.3519i | −0.286000 | + | 0.286000i | ||||
\(233\) | − | 290.609i | − | 1.24725i | −0.781724 | − | 0.623624i | \(-0.785660\pi\) | ||
0.781724 | − | 0.623624i | \(-0.214340\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −482.663 | −2.05388 | ||||||||
\(236\) | −106.505 | − | 106.505i | −0.451292 | − | 0.451292i | ||||
\(237\) | −23.1864 | −0.0978330 | ||||||||
\(238\) | 118.969i | 0.499869i | ||||||||
\(239\) | 215.875 | + | 215.875i | 0.903243 | + | 0.903243i | 0.995715 | − | 0.0924720i | \(-0.0294769\pi\) |
−0.0924720 | + | 0.995715i | \(0.529477\pi\) | |||||||
\(240\) | 34.9633 | + | 34.9633i | 0.145680 | + | 0.145680i | ||||
\(241\) | −84.9486 | + | 84.9486i | −0.352484 | + | 0.352484i | −0.861033 | − | 0.508549i | \(-0.830182\pi\) |
0.508549 | + | 0.861033i | \(0.330182\pi\) | |||||||
\(242\) | 63.5198 | − | 63.5198i | 0.262479 | − | 0.262479i | ||||
\(243\) | 15.5885 | 0.0641500 | ||||||||
\(244\) | 141.039i | 0.578028i | ||||||||
\(245\) | 110.559 | − | 110.559i | 0.451261 | − | 0.451261i | ||||
\(246\) | − | 133.408i | − | 0.542310i | ||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −136.925 | −0.552116 | ||||||||
\(249\) | 161.295 | + | 161.295i | 0.647771 | + | 0.647771i | ||||
\(250\) | −9.43317 | −0.0377327 | ||||||||
\(251\) | 174.494i | 0.695196i | 0.937644 | + | 0.347598i | \(0.113003\pi\) | ||||
−0.937644 | + | 0.347598i | \(0.886997\pi\) | |||||||
\(252\) | −22.0829 | − | 22.0829i | −0.0876307 | − | 0.0876307i | ||||
\(253\) | −51.3296 | − | 51.3296i | −0.202884 | − | 0.202884i | ||||
\(254\) | −66.4529 | + | 66.4529i | −0.261626 | + | 0.261626i | ||||
\(255\) | 141.270 | − | 141.270i | 0.554000 | − | 0.554000i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − | 4.64878i | − | 0.0180887i | −0.999959 | − | 0.00904433i | \(-0.997121\pi\) | ||
0.999959 | − | 0.00904433i | \(-0.00287894\pi\) | |||||||
\(258\) | 81.4863 | − | 81.4863i | 0.315838 | − | 0.315838i | ||||
\(259\) | − | 340.704i | − | 1.31546i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −99.5278 | −0.381333 | ||||||||
\(262\) | 28.3277 | + | 28.3277i | 0.108121 | + | 0.108121i | ||||
\(263\) | 13.8431 | 0.0526355 | 0.0263177 | − | 0.999654i | \(-0.491622\pi\) | ||||
0.0263177 | + | 0.999654i | \(0.491622\pi\) | |||||||
\(264\) | − | 37.1420i | − | 0.140689i | ||||||
\(265\) | −340.729 | − | 340.729i | −1.28577 | − | 1.28577i | ||||
\(266\) | −53.2214 | − | 53.2214i | −0.200080 | − | 0.200080i | ||||
\(267\) | −61.6398 | + | 61.6398i | −0.230860 | + | 0.230860i | ||||
\(268\) | −61.1108 | + | 61.1108i | −0.228025 | + | 0.228025i | ||||
\(269\) | −460.252 | −1.71097 | −0.855487 | − | 0.517825i | \(-0.826742\pi\) | ||||
−0.855487 | + | 0.517825i | \(0.826742\pi\) | |||||||
\(270\) | 52.4449i | 0.194240i | ||||||||
\(271\) | −104.874 | + | 104.874i | −0.386988 | + | 0.386988i | −0.873612 | − | 0.486624i | \(-0.838228\pi\) |
0.486624 | + | 0.873612i | \(0.338228\pi\) | |||||||
\(272\) | − | 64.6484i | − | 0.237678i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −71.1821 | −0.259789 | ||||||||
\(275\) | 139.035 | + | 139.035i | 0.505582 | + | 0.505582i | ||||
\(276\) | 33.1676 | 0.120173 | ||||||||
\(277\) | − | 373.291i | − | 1.34762i | −0.738904 | − | 0.673811i | \(-0.764656\pi\) | ||
0.738904 | − | 0.673811i | \(-0.235344\pi\) | |||||||
\(278\) | 148.284 | + | 148.284i | 0.533396 | + | 0.533396i | ||||
\(279\) | −102.694 | − | 102.694i | −0.368077 | − | 0.368077i | ||||
\(280\) | 74.2946 | − | 74.2946i | 0.265338 | − | 0.265338i | ||||
\(281\) | −136.099 | + | 136.099i | −0.484337 | + | 0.484337i | −0.906514 | − | 0.422177i | \(-0.861266\pi\) |
0.422177 | + | 0.906514i | \(0.361266\pi\) | |||||||
\(282\) | −165.658 | −0.587440 | ||||||||
\(283\) | − | 380.695i | − | 1.34521i | −0.740001 | − | 0.672606i | \(-0.765175\pi\) | ||
0.740001 | − | 0.672606i | \(-0.234825\pi\) | |||||||
\(284\) | −156.361 | + | 156.361i | −0.550568 | + | 0.550568i | ||||
\(285\) | 126.396i | 0.443494i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −283.483 | −0.987747 | ||||||||
\(288\) | 12.0000 | + | 12.0000i | 0.0416667 | + | 0.0416667i | ||||
\(289\) | 27.7865 | 0.0961470 | ||||||||
\(290\) | − | 334.846i | − | 1.15464i | ||||||
\(291\) | 66.6205 | + | 66.6205i | 0.228936 | + | 0.228936i | ||||
\(292\) | −73.6771 | − | 73.6771i | −0.252319 | − | 0.252319i | ||||
\(293\) | −3.90849 | + | 3.90849i | −0.0133396 | + | 0.0133396i | −0.713745 | − | 0.700406i | \(-0.753002\pi\) |
0.700406 | + | 0.713745i | \(0.253002\pi\) | |||||||
\(294\) | 37.9458 | − | 37.9458i | 0.129067 | − | 0.129067i | ||||
\(295\) | 537.479 | 1.82196 | ||||||||
\(296\) | 185.141i | 0.625475i | ||||||||
\(297\) | 27.8565 | − | 27.8565i | 0.0937928 | − | 0.0937928i | ||||
\(298\) | − | 59.1870i | − | 0.198614i | ||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −89.8402 | −0.299467 | ||||||||
\(301\) | −173.153 | − | 173.153i | −0.575259 | − | 0.575259i | ||||
\(302\) | 5.15270 | 0.0170619 | ||||||||
\(303\) | 39.0572i | 0.128902i | ||||||||
\(304\) | 28.9208 | + | 28.9208i | 0.0951343 | + | 0.0951343i | ||||
\(305\) | −355.878 | − | 355.878i | −1.16681 | − | 1.16681i | ||||
\(306\) | 48.4863 | − | 48.4863i | 0.158452 | − | 0.158452i | ||||
\(307\) | −227.287 | + | 227.287i | −0.740349 | + | 0.740349i | −0.972645 | − | 0.232296i | \(-0.925376\pi\) |
0.232296 | + | 0.972645i | \(0.425376\pi\) | |||||||
\(308\) | −78.9241 | −0.256247 | ||||||||
\(309\) | 189.461i | 0.613141i | ||||||||
\(310\) | 345.497 | − | 345.497i | 1.11450 | − | 1.11450i | ||||
\(311\) | − | 308.864i | − | 0.993132i | −0.867999 | − | 0.496566i | \(-0.834594\pi\) | ||
0.867999 | − | 0.496566i | \(-0.165406\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.51660 | 0.00804026 | 0.00402013 | − | 0.999992i | \(-0.498720\pi\) | ||||
0.00402013 | + | 0.999992i | \(0.498720\pi\) | |||||||
\(314\) | −275.987 | − | 275.987i | −0.878939 | − | 0.878939i | ||||
\(315\) | 111.442 | 0.353784 | ||||||||
\(316\) | − | 26.7734i | − | 0.0847259i | ||||||
\(317\) | 46.8460 | + | 46.8460i | 0.147779 | + | 0.147779i | 0.777125 | − | 0.629346i | \(-0.216677\pi\) |
−0.629346 | + | 0.777125i | \(0.716677\pi\) | |||||||
\(318\) | −116.944 | − | 116.944i | −0.367749 | − | 0.367749i | ||||
\(319\) | −177.856 | + | 177.856i | −0.557541 | + | 0.557541i | ||||
\(320\) | −40.3721 | + | 40.3721i | −0.126163 | + | 0.126163i | ||||
\(321\) | −56.9412 | −0.177387 | ||||||||
\(322\) | − | 70.4789i | − | 0.218879i | ||||||
\(323\) | 116.855 | − | 116.855i | 0.361781 | − | 0.361781i | ||||
\(324\) | 18.0000i | 0.0555556i | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 198.806 | 0.609833 | ||||||||
\(327\) | −259.956 | − | 259.956i | −0.794974 | − | 0.794974i | ||||
\(328\) | 154.047 | 0.469654 | ||||||||
\(329\) | 352.012i | 1.06995i | ||||||||
\(330\) | 93.7187 | + | 93.7187i | 0.283996 | + | 0.283996i | ||||
\(331\) | −169.867 | − | 169.867i | −0.513192 | − | 0.513192i | 0.402311 | − | 0.915503i | \(-0.368207\pi\) |
−0.915503 | + | 0.402311i | \(0.868207\pi\) | |||||||
\(332\) | −186.247 | + | 186.247i | −0.560986 | + | 0.560986i | ||||
\(333\) | −138.855 | + | 138.855i | −0.416983 | + | 0.416983i | ||||
\(334\) | 277.894 | 0.832018 | ||||||||
\(335\) | − | 308.397i | − | 0.920587i | ||||||
\(336\) | 25.4992 | − | 25.4992i | 0.0758904 | − | 0.0758904i | ||||
\(337\) | − | 5.72952i | − | 0.0170015i | −0.999964 | − | 0.00850077i | \(-0.997294\pi\) | ||
0.999964 | − | 0.00850077i | \(-0.00270591\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −205.746 | −0.606921 | ||||||||
\(340\) | 163.125 | + | 163.125i | 0.479778 | + | 0.479778i | ||||
\(341\) | −367.025 | −1.07632 | ||||||||
\(342\) | 43.3812i | 0.126846i | ||||||||
\(343\) | −260.976 | − | 260.976i | −0.760863 | − | 0.760863i | ||||
\(344\) | 94.0923 | + | 94.0923i | 0.273524 | + | 0.273524i | ||||
\(345\) | −83.6905 | + | 83.6905i | −0.242581 | + | 0.242581i | ||||
\(346\) | −132.251 | + | 132.251i | −0.382228 | + | 0.382228i | ||||
\(347\) | −102.971 | −0.296747 | −0.148373 | − | 0.988931i | \(-0.547404\pi\) | ||||
−0.148373 | + | 0.988931i | \(0.547404\pi\) | |||||||
\(348\) | − | 114.925i | − | 0.330244i | ||||||
\(349\) | −342.739 | + | 342.739i | −0.982059 | + | 0.982059i | −0.999842 | − | 0.0177827i | \(-0.994339\pi\) |
0.0177827 | + | 0.999842i | \(0.494339\pi\) | |||||||
\(350\) | 190.904i | 0.545441i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 42.8878 | 0.121840 | ||||||||
\(353\) | −139.237 | − | 139.237i | −0.394439 | − | 0.394439i | 0.481827 | − | 0.876266i | \(-0.339973\pi\) |
−0.876266 | + | 0.481827i | \(0.839973\pi\) | |||||||
\(354\) | 184.472 | 0.521107 | ||||||||
\(355\) | − | 789.080i | − | 2.22276i | ||||||
\(356\) | −71.1755 | − | 71.1755i | −0.199931 | − | 0.199931i | ||||
\(357\) | −103.030 | − | 103.030i | −0.288600 | − | 0.288600i | ||||
\(358\) | 35.4311 | − | 35.4311i | 0.0989697 | − | 0.0989697i | ||||
\(359\) | −54.1215 | + | 54.1215i | −0.150756 | + | 0.150756i | −0.778456 | − | 0.627699i | \(-0.783997\pi\) |
0.627699 | + | 0.778456i | \(0.283997\pi\) | |||||||
\(360\) | −60.5582 | −0.168217 | ||||||||
\(361\) | − | 256.448i | − | 0.710383i | ||||||
\(362\) | 121.119 | − | 121.119i | 0.334582 | − | 0.334582i | ||||
\(363\) | 110.020i | 0.303084i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 371.812 | 1.01866 | ||||||||
\(366\) | −122.143 | − | 122.143i | −0.333725 | − | 0.333725i | ||||
\(367\) | −215.649 | −0.587598 | −0.293799 | − | 0.955867i | \(-0.594920\pi\) | ||||
−0.293799 | + | 0.955867i | \(0.594920\pi\) | |||||||
\(368\) | 38.2987i | 0.104072i | ||||||||
\(369\) | 115.535 | + | 115.535i | 0.313103 | + | 0.313103i | ||||
\(370\) | −467.157 | − | 467.157i | −1.26259 | − | 1.26259i | ||||
\(371\) | −248.498 | + | 248.498i | −0.669806 | + | 0.669806i | ||||
\(372\) | 118.580 | − | 118.580i | 0.318764 | − | 0.318764i | ||||
\(373\) | −631.387 | −1.69273 | −0.846363 | − | 0.532607i | \(-0.821213\pi\) | ||||
−0.846363 | + | 0.532607i | \(0.821213\pi\) | |||||||
\(374\) | − | 173.289i | − | 0.463341i | ||||||
\(375\) | 8.16937 | − | 8.16937i | 0.0217850 | − | 0.0217850i | ||||
\(376\) | − | 191.286i | − | 0.508738i | ||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 38.2488 | 0.101187 | ||||||||
\(379\) | −176.261 | − | 176.261i | −0.465069 | − | 0.465069i | 0.435244 | − | 0.900313i | \(-0.356662\pi\) |
−0.900313 | + | 0.435244i | \(0.856662\pi\) | |||||||
\(380\) | −145.949 | −0.384077 | ||||||||
\(381\) | − | 115.100i | − | 0.302099i | ||||||
\(382\) | −200.564 | − | 200.564i | −0.525036 | − | 0.525036i | ||||
\(383\) | −198.656 | − | 198.656i | −0.518684 | − | 0.518684i | 0.398489 | − | 0.917173i | \(-0.369535\pi\) |
−0.917173 | + | 0.398489i | \(0.869535\pi\) | |||||||
\(384\) | −13.8564 | + | 13.8564i | −0.0360844 | + | 0.0360844i | ||||
\(385\) | 199.146 | − | 199.146i | 0.517262 | − | 0.517262i | ||||
\(386\) | 37.0009 | 0.0958572 | ||||||||
\(387\) | 141.138i | 0.364699i | ||||||||
\(388\) | −76.9267 | + | 76.9267i | −0.198265 | + | 0.198265i | ||||
\(389\) | 265.150i | 0.681620i | 0.940132 | + | 0.340810i | \(0.110701\pi\) | ||||
−0.940132 | + | 0.340810i | \(0.889299\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 154.747 | 0.395772 | ||||||||
\(392\) | 43.8160 | + | 43.8160i | 0.111775 | + | 0.111775i | ||||
\(393\) | −49.0650 | −0.124847 | ||||||||
\(394\) | 133.960i | 0.339999i | ||||||||
\(395\) | 67.5561 | + | 67.5561i | 0.171028 | + | 0.171028i | ||||
\(396\) | 32.1659 | + | 32.1659i | 0.0812270 | + | 0.0812270i | ||||
\(397\) | −89.0047 | + | 89.0047i | −0.224193 | + | 0.224193i | −0.810262 | − | 0.586068i | \(-0.800675\pi\) |
0.586068 | + | 0.810262i | \(0.300675\pi\) | |||||||
\(398\) | −197.199 | + | 197.199i | −0.495475 | + | 0.495475i | ||||
\(399\) | 92.1821 | 0.231033 | ||||||||
\(400\) | − | 103.738i | − | 0.259346i | ||||||
\(401\) | 393.820 | − | 393.820i | 0.982095 | − | 0.982095i | −0.0177478 | − | 0.999842i | \(-0.505650\pi\) |
0.999842 | + | 0.0177478i | \(0.00564959\pi\) | |||||||
\(402\) | − | 105.847i | − | 0.263301i | ||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −45.0994 | −0.111632 | ||||||||
\(405\) | −45.4186 | − | 45.4186i | −0.112145 | − | 0.112145i | ||||
\(406\) | −244.207 | −0.601496 | ||||||||
\(407\) | 496.267i | 1.21933i | ||||||||
\(408\) | 55.9872 | + | 55.9872i | 0.137223 | + | 0.137223i | ||||
\(409\) | −146.003 | − | 146.003i | −0.356977 | − | 0.356977i | 0.505721 | − | 0.862697i | \(-0.331227\pi\) |
−0.862697 | + | 0.505721i | \(0.831227\pi\) | |||||||
\(410\) | −388.699 | + | 388.699i | −0.948047 | + | 0.948047i | ||||
\(411\) | 61.6455 | − | 61.6455i | 0.149989 | − | 0.149989i | ||||
\(412\) | −218.770 | −0.530996 | ||||||||
\(413\) | − | 391.990i | − | 0.949129i | ||||||
\(414\) | −28.7240 | + | 28.7240i | −0.0693817 | + | 0.0693817i | ||||
\(415\) | − | 939.900i | − | 2.26482i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −256.835 | −0.615912 | ||||||||
\(418\) | 77.5219 | + | 77.5219i | 0.185459 | + | 0.185459i | ||||
\(419\) | 335.412 | 0.800506 | 0.400253 | − | 0.916405i | \(-0.368922\pi\) | ||||
0.400253 | + | 0.916405i | \(0.368922\pi\) | |||||||
\(420\) | 128.682i | 0.306386i | ||||||||
\(421\) | 274.627 | + | 274.627i | 0.652321 | + | 0.652321i | 0.953551 | − | 0.301230i | \(-0.0973973\pi\) |
−0.301230 | + | 0.953551i | \(0.597397\pi\) | |||||||
\(422\) | 194.835 | + | 194.835i | 0.461694 | + | 0.461694i | ||||
\(423\) | 143.464 | − | 143.464i | 0.339159 | − | 0.339159i | ||||
\(424\) | 135.035 | − | 135.035i | 0.318480 | − | 0.318480i | ||||
\(425\) | −419.158 | −0.986254 | ||||||||
\(426\) | − | 270.826i | − | 0.635741i | ||||||
\(427\) | −259.546 | + | 259.546i | −0.607836 | + | 0.607836i | ||||
\(428\) | − | 65.7500i | − | 0.153621i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −474.838 | −1.10427 | ||||||||
\(431\) | 97.2197 | + | 97.2197i | 0.225568 | + | 0.225568i | 0.810838 | − | 0.585270i | \(-0.199012\pi\) |
−0.585270 | + | 0.810838i | \(0.699012\pi\) | |||||||
\(432\) | −20.7846 | −0.0481125 | ||||||||
\(433\) | 420.434i | 0.970980i | 0.874242 | + | 0.485490i | \(0.161359\pi\) | ||||
−0.874242 | + | 0.485490i | \(0.838641\pi\) | |||||||
\(434\) | −251.975 | − | 251.975i | −0.580588 | − | 0.580588i | ||||
\(435\) | 289.985 | + | 289.985i | 0.666632 | + | 0.666632i | ||||
\(436\) | 300.172 | − | 300.172i | 0.688467 | − | 0.688467i | ||||
\(437\) | −69.2268 | + | 69.2268i | −0.158414 | + | 0.158414i | ||||
\(438\) | 127.612 | 0.291353 | ||||||||
\(439\) | 745.361i | 1.69786i | 0.528505 | + | 0.848930i | \(0.322753\pi\) | ||||
−0.528505 | + | 0.848930i | \(0.677247\pi\) | |||||||
\(440\) | −108.217 | + | 108.217i | −0.245948 | + | 0.245948i | ||||
\(441\) | 65.7240i | 0.149034i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 661.917 | 1.49417 | 0.747084 | − | 0.664729i | \(-0.231453\pi\) | ||||
0.747084 | + | 0.664729i | \(0.231453\pi\) | |||||||
\(444\) | −160.336 | − | 160.336i | −0.361118 | − | 0.361118i | ||||
\(445\) | 359.188 | 0.807164 | ||||||||
\(446\) | − | 579.310i | − | 1.29890i | ||||||
\(447\) | 51.2574 | + | 51.2574i | 0.114670 | + | 0.114670i | ||||
\(448\) | 29.4439 | + | 29.4439i | 0.0657230 | + | 0.0657230i | ||||
\(449\) | −22.1856 | + | 22.1856i | −0.0494112 | + | 0.0494112i | −0.731381 | − | 0.681969i | \(-0.761124\pi\) |
0.681969 | + | 0.731381i | \(0.261124\pi\) | |||||||
\(450\) | 77.8039 | − | 77.8039i | 0.172897 | − | 0.172897i | ||||
\(451\) | 412.920 | 0.915566 | ||||||||
\(452\) | − | 237.575i | − | 0.525609i | ||||||
\(453\) | −4.46237 | + | 4.46237i | −0.00985070 | + | 0.00985070i | ||||
\(454\) | 353.120i | 0.777798i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −50.0923 | −0.109852 | ||||||||
\(457\) | −115.008 | − | 115.008i | −0.251659 | − | 0.251659i | 0.569991 | − | 0.821651i | \(-0.306947\pi\) |
−0.821651 | + | 0.569991i | \(0.806947\pi\) | |||||||
\(458\) | 348.513 | 0.760945 | ||||||||
\(459\) | 83.9807i | 0.182965i | ||||||||
\(460\) | −96.6374 | − | 96.6374i | −0.210081 | − | 0.210081i | ||||
\(461\) | 56.9560 | + | 56.9560i | 0.123549 | + | 0.123549i | 0.766178 | − | 0.642629i | \(-0.222156\pi\) |
−0.642629 | + | 0.766178i | \(0.722156\pi\) | |||||||
\(462\) | 68.3503 | − | 68.3503i | 0.147944 | − | 0.147944i | ||||
\(463\) | −172.856 | + | 172.856i | −0.373338 | + | 0.373338i | −0.868692 | − | 0.495353i | \(-0.835039\pi\) |
0.495353 | + | 0.868692i | \(0.335039\pi\) | |||||||
\(464\) | 132.704 | 0.286000 | ||||||||
\(465\) | 598.418i | 1.28692i | ||||||||
\(466\) | −290.609 | + | 290.609i | −0.623624 | + | 0.623624i | ||||
\(467\) | − | 649.970i | − | 1.39180i | −0.718139 | − | 0.695899i | \(-0.755006\pi\) | ||
0.718139 | − | 0.695899i | \(-0.244994\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −224.918 | −0.479569 | ||||||||
\(470\) | 482.663 | + | 482.663i | 1.02694 | + | 1.02694i | ||||
\(471\) | 478.023 | 1.01491 | ||||||||
\(472\) | 213.010i | 0.451292i | ||||||||
\(473\) | 252.213 | + | 252.213i | 0.533221 | + | 0.533221i | ||||
\(474\) | 23.1864 | + | 23.1864i | 0.0489165 | + | 0.0489165i | ||||
\(475\) | 187.513 | − | 187.513i | 0.394763 | − | 0.394763i | ||||
\(476\) | 118.969 | − | 118.969i | 0.249935 | − | 0.249935i | ||||
\(477\) | 202.553 | 0.424640 | ||||||||
\(478\) | − | 431.750i | − | 0.903243i | ||||||
\(479\) | 359.283 | − | 359.283i | 0.750068 | − | 0.750068i | −0.224423 | − | 0.974492i | \(-0.572050\pi\) |
0.974492 | + | 0.224423i | \(0.0720499\pi\) | |||||||
\(480\) | − | 69.9266i | − | 0.145680i | ||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 169.897 | 0.352484 | ||||||||
\(483\) | 61.0366 | + | 61.0366i | 0.126370 | + | 0.126370i | ||||
\(484\) | −127.040 | −0.262479 | ||||||||
\(485\) | − | 388.212i | − | 0.800436i | ||||||
\(486\) | −15.5885 | − | 15.5885i | −0.0320750 | − | 0.0320750i | ||||
\(487\) | 548.721 | + | 548.721i | 1.12674 | + | 1.12674i | 0.990704 | + | 0.136034i | \(0.0434355\pi\) |
0.136034 | + | 0.990704i | \(0.456564\pi\) | |||||||
\(488\) | 141.039 | − | 141.039i | 0.289014 | − | 0.289014i | ||||
\(489\) | −172.171 | + | 172.171i | −0.352087 | + | 0.352087i | ||||
\(490\) | −221.118 | −0.451261 | ||||||||
\(491\) | − | 125.014i | − | 0.254610i | −0.991864 | − | 0.127305i | \(-0.959367\pi\) | ||
0.991864 | − | 0.127305i | \(-0.0406327\pi\) | |||||||
\(492\) | −133.408 | + | 133.408i | −0.271155 | + | 0.271155i | ||||
\(493\) | − | 536.193i | − | 1.08761i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −162.326 | −0.327930 | ||||||||
\(496\) | 136.925 | + | 136.925i | 0.276058 | + | 0.276058i | ||||
\(497\) | −575.486 | −1.15792 | ||||||||
\(498\) | − | 322.590i | − | 0.647771i | ||||||
\(499\) | 151.406 | + | 151.406i | 0.303419 | + | 0.303419i | 0.842350 | − | 0.538931i | \(-0.181172\pi\) |
−0.538931 | + | 0.842350i | \(0.681172\pi\) | |||||||
\(500\) | 9.43317 | + | 9.43317i | 0.0188663 | + | 0.0188663i | ||||
\(501\) | −240.663 | + | 240.663i | −0.480366 | + | 0.480366i | ||||
\(502\) | 174.494 | − | 174.494i | 0.347598 | − | 0.347598i | ||||
\(503\) | 526.512 | 1.04674 | 0.523372 | − | 0.852104i | \(-0.324674\pi\) | ||||
0.523372 | + | 0.852104i | \(0.324674\pi\) | |||||||
\(504\) | 44.1659i | 0.0876307i | ||||||||
\(505\) | 113.797 | − | 113.797i | 0.225341 | − | 0.225341i | ||||
\(506\) | 102.659i | 0.202884i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 132.906 | 0.261626 | ||||||||
\(509\) | −682.053 | − | 682.053i | −1.33999 | − | 1.33999i | −0.896066 | − | 0.443920i | \(-0.853587\pi\) |
−0.443920 | − | 0.896066i | \(-0.646413\pi\) | |||||||
\(510\) | −282.540 | −0.554000 | ||||||||
\(511\) | − | 271.168i | − | 0.530661i | ||||||
\(512\) | −16.0000 | − | 16.0000i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | −37.5692 | − | 37.5692i | −0.0732344 | − | 0.0732344i | ||||
\(514\) | −4.64878 | + | 4.64878i | −0.00904433 | + | 0.00904433i | ||||
\(515\) | 552.014 | − | 552.014i | 1.07187 | − | 1.07187i | ||||
\(516\) | −162.973 | −0.315838 | ||||||||
\(517\) | − | 512.739i | − | 0.991758i | ||||||
\(518\) | −340.704 | + | 340.704i | −0.657729 | + | 0.657729i | ||||
\(519\) | − | 229.065i | − | 0.441359i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −158.382 | −0.303997 | −0.151998 | − | 0.988381i | \(-0.548571\pi\) | ||||
−0.151998 | + | 0.988381i | \(0.548571\pi\) | |||||||
\(522\) | 99.5278 | + | 99.5278i | 0.190666 | + | 0.190666i | ||||
\(523\) | −229.478 | −0.438773 | −0.219386 | − | 0.975638i | \(-0.570406\pi\) | ||||
−0.219386 | + | 0.975638i | \(0.570406\pi\) | |||||||
\(524\) | − | 56.6554i | − | 0.108121i | ||||||
\(525\) | −165.328 | − | 165.328i | −0.314910 | − | 0.314910i | ||||
\(526\) | −13.8431 | − | 13.8431i | −0.0263177 | − | 0.0263177i | ||||
\(527\) | 553.248 | − | 553.248i | 1.04981 | − | 1.04981i | ||||
\(528\) | −37.1420 | + | 37.1420i | −0.0703446 | + | 0.0703446i | ||||
\(529\) | 437.326 | 0.826703 | ||||||||
\(530\) | 681.458i | 1.28577i | ||||||||
\(531\) | −159.757 | + | 159.757i | −0.300861 | + | 0.300861i | ||||
\(532\) | 106.443i | 0.200080i | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 123.280 | 0.230860 | ||||||||
\(535\) | 165.904 | + | 165.904i | 0.310101 | + | 0.310101i | ||||
\(536\) | 122.222 | 0.228025 | ||||||||
\(537\) | 61.3685i | 0.114280i | ||||||||
\(538\) | 460.252 | + | 460.252i | 0.855487 | + | 0.855487i | ||||
\(539\) | 117.448 | + | 117.448i | 0.217900 | + | 0.217900i | ||||
\(540\) | 52.4449 | − | 52.4449i | 0.0971202 | − | 0.0971202i | ||||
\(541\) | 606.240 | − | 606.240i | 1.12059 | − | 1.12059i | 0.128938 | − | 0.991653i | \(-0.458843\pi\) |
0.991653 | − | 0.128938i | \(-0.0411569\pi\) | |||||||
\(542\) | 209.747 | 0.386988 | ||||||||
\(543\) | 209.783i | 0.386341i | ||||||||
\(544\) | −64.6484 | + | 64.6484i | −0.118839 | + | 0.118839i | ||||
\(545\) | 1514.82i | 2.77949i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −790.673 | −1.44547 | −0.722736 | − | 0.691124i | \(-0.757116\pi\) | ||||
−0.722736 | + | 0.691124i | \(0.757116\pi\) | |||||||
\(548\) | 71.1821 | + | 71.1821i | 0.129894 | + | 0.129894i | ||||
\(549\) | 211.558 | 0.385352 | ||||||||
\(550\) | − | 278.070i | − | 0.505582i | ||||||
\(551\) | 239.869 | + | 239.869i | 0.435334 | + | 0.435334i | ||||
\(552\) | −33.1676 | − | 33.1676i | −0.0600863 | − | 0.0600863i | ||||
\(553\) | 49.2696 | − | 49.2696i | 0.0890951 | − | 0.0890951i | ||||
\(554\) | −373.291 | + | 373.291i | −0.673811 | + | 0.673811i | ||||
\(555\) | 809.140 | 1.45791 | ||||||||
\(556\) | − | 296.568i | − | 0.533396i | ||||||
\(557\) | 303.574 | − | 303.574i | 0.545016 | − | 0.545016i | −0.379979 | − | 0.924995i | \(-0.624069\pi\) |
0.924995 | + | 0.379979i | \(0.124069\pi\) | |||||||
\(558\) | 205.387i | 0.368077i | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −148.589 | −0.265338 | ||||||||
\(561\) | 150.073 | + | 150.073i | 0.267510 | + | 0.267510i | ||||
\(562\) | 272.197 | 0.484337 | ||||||||
\(563\) | 319.331i | 0.567195i | 0.958943 | + | 0.283598i | \(0.0915280\pi\) | ||||
−0.958943 | + | 0.283598i | \(0.908472\pi\) | |||||||
\(564\) | 165.658 | + | 165.658i | 0.293720 | + | 0.293720i | ||||
\(565\) | 599.464 | + | 599.464i | 1.06100 | + | 1.06100i | ||||
\(566\) | −380.695 | + | 380.695i | −0.672606 | + | 0.672606i | ||||
\(567\) | −33.1244 | + | 33.1244i | −0.0584205 | + | 0.0584205i | ||||
\(568\) | 312.723 | 0.550568 | ||||||||
\(569\) | 793.301i | 1.39420i | 0.716973 | + | 0.697101i | \(0.245527\pi\) | ||||
−0.716973 | + | 0.697101i | \(0.754473\pi\) | |||||||
\(570\) | 126.396 | − | 126.396i | 0.221747 | − | 0.221747i | ||||
\(571\) | 852.111i | 1.49231i | 0.665771 | + | 0.746156i | \(0.268103\pi\) | ||||
−0.665771 | + | 0.746156i | \(0.731897\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 347.387 | 0.606259 | ||||||||
\(574\) | 283.483 | + | 283.483i | 0.493873 | + | 0.493873i | ||||
\(575\) | 248.315 | 0.431853 | ||||||||
\(576\) | − | 24.0000i | − | 0.0416667i | ||||||
\(577\) | −186.391 | − | 186.391i | −0.323035 | − | 0.323035i | 0.526895 | − | 0.849930i | \(-0.323356\pi\) |
−0.849930 | + | 0.526895i | \(0.823356\pi\) | |||||||
\(578\) | −27.7865 | − | 27.7865i | −0.0480735 | − | 0.0480735i | ||||
\(579\) | −32.0437 | + | 32.0437i | −0.0553432 | + | 0.0553432i | ||||
\(580\) | −334.846 | + | 334.846i | −0.577320 | + | 0.577320i | ||||
\(581\) | −685.482 | −1.17983 | ||||||||
\(582\) | − | 133.241i | − | 0.228936i | ||||||
\(583\) | 361.961 | − | 361.961i | 0.620859 | − | 0.620859i | ||||
\(584\) | 147.354i | 0.252319i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.81698 | 0.0133396 | ||||||||
\(587\) | 554.844 | + | 554.844i | 0.945220 | + | 0.945220i | 0.998576 | − | 0.0533553i | \(-0.0169916\pi\) |
−0.0533553 | + | 0.998576i | \(0.516992\pi\) | |||||||
\(588\) | −75.8915 | −0.129067 | ||||||||
\(589\) | 494.997i | 0.840403i | ||||||||
\(590\) | −537.479 | − | 537.479i | −0.910981 | − | 0.910981i | ||||
\(591\) | −116.013 | − | 116.013i | −0.196299 | − | 0.196299i | ||||
\(592\) | 185.141 | − | 185.141i | 0.312737 | − | 0.312737i | ||||
\(593\) | −375.307 | + | 375.307i | −0.632895 | + | 0.632895i | −0.948793 | − | 0.315898i | \(-0.897694\pi\) |
0.315898 | + | 0.948793i | \(0.397694\pi\) | |||||||
\(594\) | −55.7129 | −0.0937928 | ||||||||
\(595\) | 600.378i | 1.00904i | ||||||||
\(596\) | −59.1870 | + | 59.1870i | −0.0993070 | + | 0.0993070i | ||||
\(597\) | − | 341.559i | − | 0.572126i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 320.645 | 0.535300 | 0.267650 | − | 0.963516i | \(-0.413753\pi\) | ||||
0.267650 | + | 0.963516i | \(0.413753\pi\) | |||||||
\(600\) | 89.8402 | + | 89.8402i | 0.149734 | + | 0.149734i | ||||
\(601\) | −58.4208 | −0.0972059 | −0.0486030 | − | 0.998818i | \(-0.515477\pi\) | ||||
−0.0486030 | + | 0.998818i | \(0.515477\pi\) | |||||||
\(602\) | 346.306i | 0.575259i | ||||||||
\(603\) | 91.6662 | + | 91.6662i | 0.152017 | + | 0.152017i | ||||
\(604\) | −5.15270 | − | 5.15270i | −0.00853096 | − | 0.00853096i | ||||
\(605\) | 320.554 | − | 320.554i | 0.529841 | − | 0.529841i | ||||
\(606\) | 39.0572 | − | 39.0572i | 0.0644509 | − | 0.0644509i | ||||
\(607\) | −655.852 | −1.08048 | −0.540240 | − | 0.841511i | \(-0.681667\pi\) | ||||
−0.540240 | + | 0.841511i | \(0.681667\pi\) | |||||||
\(608\) | − | 57.8416i | − | 0.0951343i | ||||||
\(609\) | 211.490 | − | 211.490i | 0.347274 | − | 0.347274i | ||||
\(610\) | 711.755i | 1.16681i | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −96.9726 | −0.158452 | ||||||||
\(613\) | −136.104 | − | 136.104i | −0.222030 | − | 0.222030i | 0.587323 | − | 0.809353i | \(-0.300182\pi\) |
−0.809353 | + | 0.587323i | \(0.800182\pi\) | |||||||
\(614\) | 454.574 | 0.740349 | ||||||||
\(615\) | − | 673.247i | − | 1.09471i | ||||||
\(616\) | 78.9241 | + | 78.9241i | 0.128124 | + | 0.128124i | ||||
\(617\) | −14.0356 | − | 14.0356i | −0.0227481 | − | 0.0227481i | 0.695641 | − | 0.718389i | \(-0.255120\pi\) |
−0.718389 | + | 0.695641i | \(0.755120\pi\) | |||||||
\(618\) | 189.461 | − | 189.461i | 0.306571 | − | 0.306571i | ||||
\(619\) | −319.972 | + | 319.972i | −0.516917 | + | 0.516917i | −0.916637 | − | 0.399720i | \(-0.869107\pi\) |
0.399720 | + | 0.916637i | \(0.369107\pi\) | |||||||
\(620\) | −690.993 | −1.11450 | ||||||||
\(621\) | − | 49.7514i | − | 0.0801150i | ||||||
\(622\) | −308.864 | + | 308.864i | −0.496566 | + | 0.496566i | ||||
\(623\) | − | 261.961i | − | 0.420482i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 600.761 | 0.961217 | ||||||||
\(626\) | −2.51660 | − | 2.51660i | −0.00402013 | − | 0.00402013i | ||||
\(627\) | −134.272 | −0.214150 | ||||||||
\(628\) | 551.974i | 0.878939i | ||||||||
\(629\) | −748.065 | − | 748.065i | −1.18929 | − | 1.18929i | ||||
\(630\) | −111.442 | − | 111.442i | −0.176892 | − | 0.176892i | ||||
\(631\) | 309.780 | − | 309.780i | 0.490935 | − | 0.490935i | −0.417666 | − | 0.908601i | \(-0.637152\pi\) |
0.908601 | + | 0.417666i | \(0.137152\pi\) | |||||||
\(632\) | −26.7734 | + | 26.7734i | −0.0423630 | + | 0.0423630i | ||||
\(633\) | −337.464 | −0.533118 | ||||||||
\(634\) | − | 93.6921i | − | 0.147779i | ||||||
\(635\) | −335.356 | + | 335.356i | −0.528119 | + | 0.528119i | ||||
\(636\) | 233.888i | 0.367749i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 355.711 | 0.557541 | ||||||||
\(639\) | 234.542 | + | 234.542i | 0.367045 | + | 0.367045i | ||||
\(640\) | 80.7442 | 0.126163 | ||||||||
\(641\) | 619.237i | 0.966048i | 0.875607 | + | 0.483024i | \(0.160462\pi\) | ||||
−0.875607 | + | 0.483024i | \(0.839538\pi\) | |||||||
\(642\) | 56.9412 | + | 56.9412i | 0.0886934 | + | 0.0886934i | ||||
\(643\) | 285.392 | + | 285.392i | 0.443845 | + | 0.443845i | 0.893302 | − | 0.449457i | \(-0.148382\pi\) |
−0.449457 | + | 0.893302i | \(0.648382\pi\) | |||||||
\(644\) | −70.4789 | + | 70.4789i | −0.109439 | + | 0.109439i | ||||
\(645\) | 411.222 | − | 411.222i | 0.637553 | − | 0.637553i | ||||
\(646\) | −233.711 | −0.361781 | ||||||||
\(647\) | − | 250.092i | − | 0.386540i | −0.981146 | − | 0.193270i | \(-0.938091\pi\) | ||
0.981146 | − | 0.193270i | \(-0.0619094\pi\) | |||||||
\(648\) | 18.0000 | − | 18.0000i | 0.0277778 | − | 0.0277778i | ||||
\(649\) | 570.971i | 0.879770i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 436.434 | 0.670405 | ||||||||
\(652\) | −198.806 | − | 198.806i | −0.304917 | − | 0.304917i | ||||
\(653\) | −391.661 | −0.599787 | −0.299894 | − | 0.953973i | \(-0.596951\pi\) | ||||
−0.299894 | + | 0.953973i | \(0.596951\pi\) | |||||||
\(654\) | 519.913i | 0.794974i | ||||||||
\(655\) | 142.956 | + | 142.956i | 0.218254 | + | 0.218254i | ||||
\(656\) | −154.047 | − | 154.047i | −0.234827 | − | 0.234827i | ||||
\(657\) | −110.516 | + | 110.516i | −0.168213 | + | 0.168213i | ||||
\(658\) | 352.012 | − | 352.012i | 0.534973 | − | 0.534973i | ||||
\(659\) | −611.987 | −0.928661 | −0.464330 | − | 0.885662i | \(-0.653705\pi\) | ||||
−0.464330 | + | 0.885662i | \(0.653705\pi\) | |||||||
\(660\) | − | 187.437i | − | 0.283996i | ||||||
\(661\) | 428.563 | − | 428.563i | 0.648356 | − | 0.648356i | −0.304239 | − | 0.952596i | \(-0.598402\pi\) |
0.952596 | + | 0.304239i | \(0.0984023\pi\) | |||||||
\(662\) | 339.733i | 0.513192i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 372.495 | 0.560986 | ||||||||
\(665\) | −268.582 | − | 268.582i | −0.403883 | − | 0.403883i | ||||
\(666\) | 277.711 | 0.416983 | ||||||||
\(667\) | 317.649i | 0.476235i | ||||||||
\(668\) | −277.894 | − | 277.894i | −0.416009 | − | 0.416009i | ||||
\(669\) | 501.697 | + | 501.697i | 0.749920 | + | 0.749920i | ||||
\(670\) | −308.397 | + | 308.397i | −0.460293 | + | 0.460293i | ||||
\(671\) | 378.053 | − | 378.053i | 0.563418 | − | 0.563418i | ||||
\(672\) | −50.9984 | −0.0758904 | ||||||||
\(673\) | 785.253i | 1.16680i | 0.812187 | + | 0.583398i | \(0.198277\pi\) | ||||
−0.812187 | + | 0.583398i | \(0.801723\pi\) | |||||||
\(674\) | −5.72952 | + | 5.72952i | −0.00850077 | + | 0.00850077i | ||||
\(675\) | 134.760i | 0.199645i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −622.197 | −0.919051 | −0.459525 | − | 0.888165i | \(-0.651980\pi\) | ||||
−0.459525 | + | 0.888165i | \(0.651980\pi\) | |||||||
\(678\) | 205.746 | + | 205.746i | 0.303461 | + | 0.303461i | ||||
\(679\) | −283.128 | −0.416978 | ||||||||
\(680\) | − | 326.249i | − | 0.479778i | ||||||
\(681\) | −305.811 | − | 305.811i | −0.449062 | − | 0.449062i | ||||
\(682\) | 367.025 | + | 367.025i | 0.538161 | + | 0.538161i | ||||
\(683\) | 597.755 | − | 597.755i | 0.875191 | − | 0.875191i | −0.117842 | − | 0.993032i | \(-0.537598\pi\) |
0.993032 | + | 0.117842i | \(0.0375975\pi\) | |||||||
\(684\) | 43.3812 | − | 43.3812i | 0.0634228 | − | 0.0634228i | ||||
\(685\) | −359.221 | −0.524411 | ||||||||
\(686\) | 521.952i | 0.760863i | ||||||||
\(687\) | −301.821 | + | 301.821i | −0.439332 | + | 0.439332i | ||||
\(688\) | − | 188.185i | − | 0.273524i | ||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 167.381 | 0.242581 | ||||||||
\(691\) | 471.479 | + | 471.479i | 0.682314 | + | 0.682314i | 0.960521 | − | 0.278207i | \(-0.0897402\pi\) |
−0.278207 | + | 0.960521i | \(0.589740\pi\) | |||||||
\(692\) | 264.502 | 0.382228 | ||||||||
\(693\) | 118.386i | 0.170831i | ||||||||
\(694\) | 102.971 | + | 102.971i | 0.148373 | + | 0.148373i | ||||
\(695\) | 748.317 | + | 748.317i | 1.07672 | + | 1.07672i | ||||
\(696\) | −114.925 | + | 114.925i | −0.165122 | + | 0.165122i | ||||
\(697\) | −622.429 | + | 622.429i | −0.893012 | + | 0.893012i | ||||
\(698\) | 685.477 | 0.982059 | ||||||||
\(699\) | − | 503.349i | − | 0.720099i | ||||||
\(700\) | 190.904 | − | 190.904i | 0.272720 | − | 0.272720i | ||||
\(701\) | − | 299.776i | − | 0.427640i | −0.976873 | − | 0.213820i | \(-0.931409\pi\) | ||
0.976873 | − | 0.213820i | \(-0.0685907\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 669.302 | 0.952065 | ||||||||
\(704\) | −42.8878 | − | 42.8878i | −0.0609202 | − | 0.0609202i | ||||
\(705\) | −835.996 | −1.18581 | ||||||||
\(706\) | 278.474i | 0.394439i | ||||||||
\(707\) | −82.9940 | − | 82.9940i | −0.117389 | − | 0.117389i | ||||
\(708\) | −184.472 | − | 184.472i | −0.260554 | − | 0.260554i | ||||
\(709\) | −242.444 | + | 242.444i | −0.341951 | + | 0.341951i | −0.857101 | − | 0.515149i | \(-0.827737\pi\) |
0.515149 | + | 0.857101i | \(0.327737\pi\) | |||||||
\(710\) | −789.080 | + | 789.080i | −1.11138 | + | 1.11138i | ||||
\(711\) | −40.1601 | −0.0564839 | ||||||||
\(712\) | 142.351i | 0.199931i | ||||||||
\(713\) | −327.752 | + | 327.752i | −0.459681 | + | 0.459681i | ||||
\(714\) | 206.060i | 0.288600i | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −70.8623 | −0.0989697 | ||||||||
\(717\) | 373.907 | + | 373.907i | 0.521488 | + | 0.521488i | ||||
\(718\) | 108.243 | 0.150756 | ||||||||
\(719\) | − | 637.194i | − | 0.886223i | −0.896466 | − | 0.443112i | \(-0.853875\pi\) | ||
0.896466 | − | 0.443112i | \(-0.146125\pi\) | |||||||
\(720\) | 60.5582 | + | 60.5582i | 0.0841086 | + | 0.0841086i | ||||
\(721\) | −402.591 | − | 402.591i | −0.558379 | − | 0.558379i | ||||
\(722\) | −256.448 | + | 256.448i | −0.355192 | + | 0.355192i | ||||
\(723\) | −147.135 | + | 147.135i | −0.203507 | + | 0.203507i | ||||
\(724\) | −242.237 | −0.334582 | ||||||||
\(725\) | − | 860.406i | − | 1.18677i | ||||||
\(726\) | 110.020 | − | 110.020i | 0.151542 | − | 0.151542i | ||||
\(727\) | 617.181i | 0.848943i | 0.905441 | + | 0.424471i | \(0.139540\pi\) | ||||
−0.905441 | + | 0.424471i | \(0.860460\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | −371.812 | − | 371.812i | −0.509332 | − | 0.509332i | ||||
\(731\) | −760.364 | −1.04017 | ||||||||
\(732\) | 244.287i | 0.333725i | ||||||||
\(733\) | −932.866 | − | 932.866i | −1.27267 | − | 1.27267i | −0.944683 | − | 0.327985i | \(-0.893631\pi\) |
−0.327985 | − | 0.944683i | \(-0.606369\pi\) | |||||||
\(734\) | 215.649 | + | 215.649i | 0.293799 | + | 0.293799i | ||||
\(735\) | 191.494 | − | 191.494i | 0.260536 | − | 0.260536i | ||||
\(736\) | 38.2987 | − | 38.2987i | 0.0520362 | − | 0.0520362i | ||||
\(737\) | 327.614 | 0.444523 | ||||||||
\(738\) | − | 231.070i | − | 0.313103i | ||||||
\(739\) | −142.848 | + | 142.848i | −0.193299 | + | 0.193299i | −0.797120 | − | 0.603821i | \(-0.793644\pi\) |
0.603821 | + | 0.797120i | \(0.293644\pi\) | |||||||
\(740\) | 934.314i | 1.26259i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 496.996 | 0.669806 | ||||||||
\(743\) | −741.898 | − | 741.898i | −0.998517 | − | 0.998517i | 0.00148231 | − | 0.999999i | \(-0.499528\pi\) |
−0.999999 | + | 0.00148231i | \(0.999528\pi\) | |||||||
\(744\) | −237.161 | −0.318764 | ||||||||
\(745\) | − | 298.688i | − | 0.400923i | ||||||
\(746\) | 631.387 | + | 631.387i | 0.846363 | + | 0.846363i | ||||
\(747\) | 279.371 | + | 279.371i | 0.373991 | + | 0.373991i | ||||
\(748\) | −173.289 | + | 173.289i | −0.231670 | + | 0.231670i | ||||
\(749\) | 120.996 | − | 120.996i | 0.161543 | − | 0.161543i | ||||
\(750\) | −16.3387 | −0.0217850 | ||||||||
\(751\) | 1468.78i | 1.95576i | 0.209162 | + | 0.977881i | \(0.432926\pi\) | ||||
−0.209162 | + | 0.977881i | \(0.567074\pi\) | |||||||
\(752\) | −191.286 | + | 191.286i | −0.254369 | + | 0.254369i | ||||
\(753\) | 302.233i | 0.401371i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 26.0032 | 0.0344413 | ||||||||
\(756\) | −38.2488 | − | 38.2488i | −0.0505936 | − | 0.0505936i | ||||
\(757\) | −855.727 | −1.13042 | −0.565210 | − | 0.824947i | \(-0.691205\pi\) | ||||
−0.565210 | + | 0.824947i | \(0.691205\pi\) | |||||||
\(758\) | 352.522i | 0.465069i | ||||||||
\(759\) | −88.9055 | − | 88.9055i | −0.117135 | − | 0.117135i | ||||
\(760\) | 145.949 | + | 145.949i | 0.192039 | + | 0.192039i | ||||
\(761\) | 303.471 | − | 303.471i | 0.398779 | − | 0.398779i | −0.479023 | − | 0.877802i | \(-0.659009\pi\) |
0.877802 | + | 0.479023i | \(0.159009\pi\) | |||||||
\(762\) | −115.100 | + | 115.100i | −0.151050 | + | 0.151050i | ||||
\(763\) | 1104.78 | 1.44794 | ||||||||
\(764\) | 401.127i | 0.525036i | ||||||||
\(765\) | 244.687 | − | 244.687i | 0.319852 | − | 0.319852i | ||||
\(766\) | 397.312i | 0.518684i | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 27.7128 | 0.0360844 | ||||||||
\(769\) | 311.509 | + | 311.509i | 0.405083 | + | 0.405083i | 0.880020 | − | 0.474937i | \(-0.157529\pi\) |
−0.474937 | + | 0.880020i | \(0.657529\pi\) | |||||||
\(770\) | −398.292 | −0.517262 | ||||||||
\(771\) | − | 8.05193i | − | 0.0104435i | ||||||
\(772\) | −37.0009 | − | 37.0009i | −0.0479286 | − | 0.0479286i | ||||
\(773\) | −845.415 | − | 845.415i | −1.09368 | − | 1.09368i | −0.995132 | − | 0.0985477i | \(-0.968580\pi\) |
−0.0985477 | − | 0.995132i | \(-0.531420\pi\) | |||||||
\(774\) | 141.138 | − | 141.138i | 0.182349 | − | 0.182349i | ||||
\(775\) | 887.773 | − | 887.773i | 1.14551 | − | 1.14551i | ||||
\(776\) | 153.853 | 0.198265 | ||||||||
\(777\) | − | 590.116i | − | 0.759481i | ||||||
\(778\) | 265.150 | − | 265.150i | 0.340810 | − | 0.340810i | ||||
\(779\) | − | 556.894i | − | 0.714883i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 838.250 | 1.07330 | ||||||||
\(782\) | −154.747 | − | 154.747i | −0.197886 | − | 0.197886i | ||||
\(783\) | −172.387 | −0.220163 | ||||||||
\(784\) | − | 87.6320i | − | 0.111775i | ||||||
\(785\) | −1392.77 | − | 1392.77i | −1.77423 | − | 1.77423i | ||||
\(786\) | 49.0650 | + | 49.0650i | 0.0624237 | + | 0.0624237i | ||||
\(787\) | 230.179 | − | 230.179i | 0.292477 | − | 0.292477i | −0.545581 | − | 0.838058i | \(-0.683691\pi\) |
0.838058 | + | 0.545581i | \(0.183691\pi\) | |||||||
\(788\) | 133.960 | − | 133.960i | 0.170000 | − | 0.170000i | ||||
\(789\) | 23.9770 | 0.0303891 | ||||||||
\(790\) | − | 135.112i | − | 0.171028i | ||||||
\(791\) | 437.197 | − | 437.197i | 0.552714 | − | 0.552714i | ||||
\(792\) | − | 64.3317i | − | 0.0812270i | ||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 178.009 | 0.224193 | ||||||||
\(795\) | −590.160 | − | 590.160i | −0.742340 | − | 0.742340i | ||||
\(796\) | 394.398 | 0.495475 | ||||||||
\(797\) | − | 2.59745i | − | 0.00325903i | −0.999999 | − | 0.00162952i | \(-0.999481\pi\) | ||
0.999999 | − | 0.00162952i | \(-0.000518691\pi\) | |||||||
\(798\) | −92.1821 | − | 92.1821i | −0.115516 | − | 0.115516i | ||||
\(799\) | 772.894 | + | 772.894i | 0.967327 | + | 0.967327i | ||||
\(800\) | −103.738 | + | 103.738i | −0.129673 | + | 0.129673i | ||||
\(801\) | −106.763 | + | 106.763i | −0.133287 | + | 0.133287i | ||||
\(802\) | −787.640 | −0.982095 | ||||||||
\(803\) | 394.981i | 0.491882i | ||||||||
\(804\) | −105.847 | + | 105.847i | −0.131651 | + | 0.131651i | ||||
\(805\) | − | 355.673i | − | 0.441830i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −797.180 | −0.987831 | ||||||||
\(808\) | 45.0994 | + | 45.0994i | 0.0558161 | + | 0.0558161i | ||||
\(809\) | −112.480 | −0.139036 | −0.0695179 | − | 0.997581i | \(-0.522146\pi\) | ||||
−0.0695179 | + | 0.997581i | \(0.522146\pi\) | |||||||
\(810\) | 90.8373i | 0.112145i | ||||||||
\(811\) | 725.545 | + | 725.545i | 0.894630 | + | 0.894630i | 0.994955 | − | 0.100324i | \(-0.0319881\pi\) |
−0.100324 | + | 0.994955i | \(0.531988\pi\) | |||||||
\(812\) | 244.207 | + | 244.207i | 0.300748 | + | 0.300748i | ||||
\(813\) | −181.647 | + | 181.647i | −0.223428 | + | 0.223428i | ||||
\(814\) | 496.267 | − | 496.267i | 0.609665 | − | 0.609665i | ||||
\(815\) | 1003.28 | 1.23101 | ||||||||
\(816\) | − | 111.974i | − | 0.137223i | ||||||
\(817\) | 340.153 | − | 340.153i | 0.416344 | − | 0.416344i | ||||
\(818\) | 292.007i | 0.356977i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 777.398 | 0.948047 | ||||||||
\(821\) | −392.048 | − | 392.048i | −0.477525 | − | 0.477525i | 0.426815 | − | 0.904339i | \(-0.359636\pi\) |
−0.904339 | + | 0.426815i | \(0.859636\pi\) | |||||||
\(822\) | −123.291 | −0.149989 | ||||||||
\(823\) | 111.028i | 0.134907i | 0.997722 | + | 0.0674534i | \(0.0214874\pi\) | ||||
−0.997722 | + | 0.0674534i | \(0.978513\pi\) | |||||||
\(824\) | 218.770 | + | 218.770i | 0.265498 | + | 0.265498i | ||||
\(825\) | 240.816 | + | 240.816i | 0.291898 | + | 0.291898i | ||||
\(826\) | −391.990 | + | 391.990i | −0.474564 | + | 0.474564i | ||||
\(827\) | 878.475 | − | 878.475i | 1.06224 | − | 1.06224i | 0.0643137 | − | 0.997930i | \(-0.479514\pi\) |
0.997930 | − | 0.0643137i | \(-0.0204858\pi\) | |||||||
\(828\) | 57.4480 | 0.0693817 | ||||||||
\(829\) | 826.511i | 0.996998i | 0.866890 | + | 0.498499i | \(0.166115\pi\) | ||||
−0.866890 | + | 0.498499i | \(0.833885\pi\) | |||||||
\(830\) | −939.900 | + | 939.900i | −1.13241 | + | 1.13241i | ||||
\(831\) | − | 646.559i | − | 0.778050i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −354.079 | −0.425065 | ||||||||
\(834\) | 256.835 | + | 256.835i | 0.307956 | + | 0.307956i | ||||
\(835\) | 1402.40 | 1.67952 | ||||||||
\(836\) | − | 155.044i | − | 0.185459i | ||||||
\(837\) | −177.871 | − | 177.871i | −0.212510 | − | 0.212510i | ||||
\(838\) | −335.412 | − | 335.412i | −0.400253 | − | 0.400253i | ||||
\(839\) | −220.394 | + | 220.394i | −0.262686 | + | 0.262686i | −0.826144 | − | 0.563458i | \(-0.809470\pi\) |
0.563458 | + | 0.826144i | \(0.309470\pi\) | |||||||
\(840\) | 128.682 | − | 128.682i | 0.153193 | − | 0.153193i | ||||
\(841\) | 259.643 | 0.308732 | ||||||||
\(842\) | − | 549.254i | − | 0.652321i | ||||||
\(843\) | −235.730 | + | 235.730i | −0.279632 | + | 0.279632i | ||||
\(844\) | − | 389.670i | − | 0.461694i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −286.928 | −0.339159 | ||||||||
\(847\) | −233.784 | − | 233.784i | −0.276014 | − | 0.276014i | ||||
\(848\) | −270.071 | −0.318480 | ||||||||
\(849\) | − | 659.383i | − | 0.776658i | ||||||
\(850\) | 419.158 | + | 419.158i | 0.493127 | + | 0.493127i | ||||
\(851\) | 443.165 | + | 443.165i | 0.520758 | + | 0.520758i | ||||
\(852\) | −270.826 | + | 270.826i | −0.317871 | + | 0.317871i | ||||
\(853\) | 724.409 | − | 724.409i | 0.849249 | − | 0.849249i | −0.140791 | − | 0.990039i | \(-0.544964\pi\) |
0.990039 | + | 0.140791i | \(0.0449645\pi\) | |||||||
\(854\) | 519.092 | 0.607836 | ||||||||
\(855\) | 218.924i | 0.256051i | ||||||||
\(856\) | −65.7500 | + | 65.7500i | −0.0768107 | + | 0.0768107i | ||||
\(857\) | − | 49.0244i | − | 0.0572047i | −0.999591 | − | 0.0286023i | \(-0.990894\pi\) | ||
0.999591 | − | 0.0286023i | \(-0.00910565\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −584.617 | −0.680578 | −0.340289 | − | 0.940321i | \(-0.610525\pi\) | ||||
−0.340289 | + | 0.940321i | \(0.610525\pi\) | |||||||
\(860\) | 474.838 | + | 474.838i | 0.552137 | + | 0.552137i | ||||
\(861\) | −491.008 | −0.570276 | ||||||||
\(862\) | − | 194.439i | − | 0.225568i | ||||||
\(863\) | 458.022 | + | 458.022i | 0.530732 | + | 0.530732i | 0.920790 | − | 0.390058i | \(-0.127545\pi\) |
−0.390058 | + | 0.920790i | \(0.627545\pi\) | |||||||
\(864\) | 20.7846 | + | 20.7846i | 0.0240563 | + | 0.0240563i | ||||
\(865\) | −667.406 | + | 667.406i | −0.771568 | + | 0.771568i | ||||
\(866\) | 420.434 | − | 420.434i | 0.485490 | − | 0.485490i | ||||
\(867\) | 48.1276 | 0.0555105 | ||||||||
\(868\) | 503.950i | 0.580588i | ||||||||
\(869\) | −71.7658 | + | 71.7658i | −0.0825843 | + | 0.0825843i | ||||
\(870\) | − | 579.970i | − | 0.666632i | ||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −600.344 | −0.688467 | ||||||||
\(873\) | 115.390 | + | 115.390i | 0.132176 | + | 0.132176i | ||||
\(874\) | 138.454 | 0.158414 | ||||||||
\(875\) | 34.7187i | 0.0396785i | ||||||||
\(876\) | −127.612 | − | 127.612i | −0.145676 | − | 0.145676i | ||||
\(877\) | 228.121 | + | 228.121i | 0.260116 | + | 0.260116i | 0.825101 | − | 0.564985i | \(-0.191118\pi\) |
−0.564985 | + | 0.825101i | \(0.691118\pi\) | |||||||
\(878\) | 745.361 | − | 745.361i | 0.848930 | − | 0.848930i | ||||
\(879\) | −6.76970 | + | 6.76970i | −0.00770160 | + | 0.00770160i | ||||
\(880\) | 216.434 | 0.245948 | ||||||||
\(881\) | − | 1259.45i | − | 1.42957i | −0.699345 | − | 0.714785i | \(-0.746525\pi\) | ||
0.699345 | − | 0.714785i | \(-0.253475\pi\) | |||||||
\(882\) | 65.7240 | − | 65.7240i | 0.0745170 | − | 0.0745170i | ||||
\(883\) | − | 213.692i | − | 0.242007i | −0.992652 | − | 0.121003i | \(-0.961389\pi\) | ||
0.992652 | − | 0.121003i | \(-0.0386112\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 930.940 | 1.05191 | ||||||||
\(886\) | −661.917 | − | 661.917i | −0.747084 | − | 0.747084i | ||||
\(887\) | −267.572 | −0.301660 | −0.150830 | − | 0.988560i | \(-0.548195\pi\) | ||||
−0.150830 | + | 0.988560i | \(0.548195\pi\) | |||||||
\(888\) | 320.673i | 0.361118i | ||||||||
\(889\) | 244.579 | + | 244.579i | 0.275117 | + | 0.275117i | ||||
\(890\) | −359.188 | − | 359.188i | −0.403582 | − | 0.403582i | ||||
\(891\) | 48.2488 | − | 48.2488i | 0.0541513 | − | 0.0541513i | ||||
\(892\) | −579.310 | + | 579.310i | −0.649450 | + | 0.649450i | ||||
\(893\) | −691.517 | −0.774375 | ||||||||
\(894\) | − | 102.515i | − | 0.114670i | ||||||
\(895\) | 178.804 | − | 178.804i | 0.199781 | − | 0.199781i | ||||
\(896\) | − | 58.8878i | − | 0.0657230i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 44.3712 | 0.0494112 | ||||||||
\(899\) | 1135.65 | + | 1135.65i | 1.26324 | + | 1.26324i | ||||
\(900\) | −155.608 | −0.172897 | ||||||||
\(901\) | 1091.23i | 1.21113i | ||||||||
\(902\) | −412.920 | − | 412.920i | −0.457783 | − | 0.457783i | ||||
\(903\) | −299.909 | − | 299.909i | −0.332126 | − | 0.332126i | ||||
\(904\) | −237.575 | + | 237.575i | −0.262805 | + | 0.262805i | ||||
\(905\) | 611.226 | − | 611.226i | 0.675388 | − | 0.675388i | ||||
\(906\) | 8.92473 | 0.00985070 | ||||||||
\(907\) | 49.8286i | 0.0549378i | 0.999623 | + | 0.0274689i | \(0.00874473\pi\) | ||||
−0.999623 | + | 0.0274689i | \(0.991255\pi\) | |||||||
\(908\) | 353.120 | − | 353.120i | 0.388899 | − | 0.388899i | ||||
\(909\) | 67.6491i | 0.0744215i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −465.226 | −0.510676 | −0.255338 | − | 0.966852i | \(-0.582187\pi\) | ||||
−0.255338 | + | 0.966852i | \(0.582187\pi\) | |||||||
\(912\) | 50.0923 | + | 50.0923i | 0.0549258 | + | 0.0549258i | ||||
\(913\) | 998.468 | 1.09361 | ||||||||
\(914\) | 230.017i | 0.251659i | ||||||||
\(915\) | −616.398 | − | 616.398i | −0.673659 | − | 0.673659i | ||||
\(916\) | −348.513 | − | 348.513i | −0.380472 | − | 0.380472i | ||||
\(917\) | 104.260 | − | 104.260i | 0.113697 | − | 0.113697i | ||||
\(918\) | 83.9807 | − | 83.9807i | 0.0914823 | − | 0.0914823i | ||||
\(919\) | 668.804 | 0.727752 | 0.363876 | − | 0.931447i | \(-0.381453\pi\) | ||||
0.363876 | + | 0.931447i | \(0.381453\pi\) | |||||||
\(920\) | 193.275i | 0.210081i | ||||||||
\(921\) | −393.673 | + | 393.673i | −0.427440 | + | 0.427440i | ||||
\(922\) | − | 113.912i | − | 0.123549i | ||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −136.701 | −0.147944 | ||||||||
\(925\) | −1200.39 | − | 1200.39i | −1.29772 | − | 1.29772i | ||||
\(926\) | 345.711 | 0.373338 | ||||||||
\(927\) | 328.156i | 0.353997i | ||||||||
\(928\) | −132.704 | − | 132.704i | −0.143000 | − | 0.143000i | ||||
\(929\) | 480.209 | + | 480.209i | 0.516910 | + | 0.516910i | 0.916635 | − | 0.399725i | \(-0.130895\pi\) |
−0.399725 | + | 0.916635i | \(0.630895\pi\) | |||||||
\(930\) | 598.418 | − | 598.418i | 0.643460 | − | 0.643460i | ||||
\(931\) | 158.399 | − | 158.399i | 0.170139 | − | 0.170139i | ||||
\(932\) | 581.218 | 0.623624 | ||||||||
\(933\) | − | 534.968i | − | 0.573385i | ||||||
\(934\) | −649.970 | + | 649.970i | −0.695899 | + | 0.695899i | ||||
\(935\) | − | 874.507i | − | 0.935302i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −210.517 | −0.224671 | −0.112336 | − | 0.993670i | \(-0.535833\pi\) | ||||
−0.112336 | + | 0.993670i | \(0.535833\pi\) | |||||||
\(938\) | 224.918 | + | 224.918i | 0.239784 | + | 0.239784i | ||||
\(939\) | 4.35888 | 0.00464205 | ||||||||
\(940\) | − | 965.325i | − | 1.02694i | ||||||
\(941\) | 447.841 | + | 447.841i | 0.475920 | + | 0.475920i | 0.903824 | − | 0.427904i | \(-0.140748\pi\) |
−0.427904 | + | 0.903824i | \(0.640748\pi\) | |||||||
\(942\) | −478.023 | − | 478.023i | −0.507456 | − | 0.507456i | ||||
\(943\) | 368.736 | − | 368.736i | 0.391025 | − | 0.391025i | ||||
\(944\) | 213.010 | − | 213.010i | 0.225646 | − | 0.225646i | ||||
\(945\) | 193.023 | 0.204257 | ||||||||
\(946\) | − | 504.427i | − | 0.533221i | ||||||
\(947\) | −416.587 | + | 416.587i | −0.439902 | + | 0.439902i | −0.891979 | − | 0.452077i | \(-0.850683\pi\) |
0.452077 | + | 0.891979i | \(0.350683\pi\) | |||||||
\(948\) | − | 46.3729i | − | 0.0489165i | ||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −375.025 | −0.394763 | ||||||||
\(951\) | 81.1397 | + | 81.1397i | 0.0853204 | + | 0.0853204i | ||||
\(952\) | −237.938 | −0.249935 | ||||||||
\(953\) | − | 384.832i | − | 0.403811i | −0.979405 | − | 0.201906i | \(-0.935287\pi\) | ||
0.979405 | − | 0.201906i | \(-0.0647135\pi\) | |||||||
\(954\) | −202.553 | − | 202.553i | −0.212320 | − | 0.212320i | ||||
\(955\) | −1012.15 | − | 1012.15i | −1.05984 | − | 1.05984i | ||||
\(956\) | −431.750 | + | 431.750i | −0.451622 | + | 0.451622i | ||||
\(957\) | −308.055 | + | 308.055i | −0.321896 | + | 0.321896i | ||||
\(958\) | −718.565 | −0.750068 | ||||||||
\(959\) | 261.985i | 0.273186i | ||||||||
\(960\) | −69.9266 | + | 69.9266i | −0.0728402 | + | 0.0728402i | ||||
\(961\) | 1382.55i | 1.43866i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −98.6250 | −0.102414 | ||||||||
\(964\) | −169.897 | − | 169.897i | −0.176242 | − | 0.176242i | ||||
\(965\) | 186.725 | 0.193498 | ||||||||
\(966\) | − | 122.073i | − | 0.126370i | ||||||
\(967\) | 1196.08 | + | 1196.08i | 1.23690 | + | 1.23690i | 0.961262 | + | 0.275638i | \(0.0888891\pi\) |
0.275638 | + | 0.961262i | \(0.411111\pi\) | |||||||
\(968\) | 127.040 | + | 127.040i | 0.131239 | + | 0.131239i | ||||
\(969\) | 202.399 | − | 202.399i | 0.208874 | − | 0.208874i | ||||
\(970\) | −388.212 | + | 388.212i | −0.400218 | + | 0.400218i | ||||
\(971\) | 299.923 | 0.308881 | 0.154440 | − | 0.988002i | \(-0.450643\pi\) | ||||
0.154440 | + | 0.988002i | \(0.450643\pi\) | |||||||
\(972\) | 31.1769i | 0.0320750i | ||||||||
\(973\) | 545.758 | − | 545.758i | 0.560902 | − | 0.560902i | ||||
\(974\) | − | 1097.44i | − | 1.12674i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −282.078 | −0.289014 | ||||||||
\(977\) | 169.795 | + | 169.795i | 0.173792 | + | 0.173792i | 0.788643 | − | 0.614851i | \(-0.210784\pi\) |
−0.614851 | + | 0.788643i | \(0.710784\pi\) | |||||||
\(978\) | 344.341 | 0.352087 | ||||||||
\(979\) | 381.570i | 0.389755i | ||||||||
\(980\) | 221.118 | + | 221.118i | 0.225631 | + | 0.225631i | ||||
\(981\) | −450.258 | − | 450.258i | −0.458978 | − | 0.458978i | ||||
\(982\) | −125.014 | + | 125.014i | −0.127305 | + | 0.127305i | ||||
\(983\) | −503.122 | + | 503.122i | −0.511823 | + | 0.511823i | −0.915085 | − | 0.403261i | \(-0.867877\pi\) |
0.403261 | + | 0.915085i | \(0.367877\pi\) | |||||||
\(984\) | 266.816 | 0.271155 | ||||||||
\(985\) | 676.030i | 0.686325i | ||||||||
\(986\) | −536.193 | + | 536.193i | −0.543806 | + | 0.543806i | ||||
\(987\) | 609.703i | 0.617734i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 450.451 | 0.455461 | ||||||||
\(990\) | 162.326 | + | 162.326i | 0.163965 | + | 0.163965i | ||||
\(991\) | −536.965 | −0.541842 | −0.270921 | − | 0.962602i | \(-0.587328\pi\) | ||||
−0.270921 | + | 0.962602i | \(0.587328\pi\) | |||||||
\(992\) | − | 273.850i | − | 0.276058i | ||||||
\(993\) | −294.217 | − | 294.217i | −0.296291 | − | 0.296291i | ||||
\(994\) | 575.486 | + | 575.486i | 0.578960 | + | 0.578960i | ||||
\(995\) | −995.169 | + | 995.169i | −1.00017 | + | 1.00017i | ||||
\(996\) | −322.590 | + | 322.590i | −0.323886 | + | 0.323886i | ||||
\(997\) | −1019.21 | −1.02228 | −0.511139 | − | 0.859498i | \(-0.670776\pi\) | ||||
−0.511139 | + | 0.859498i | \(0.670776\pi\) | |||||||
\(998\) | − | 302.812i | − | 0.303419i | ||||||
\(999\) | −240.505 | + | 240.505i | −0.240745 | + | 0.240745i |
(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 | 1014.3.f.h.775.3 | 8 | ||
13.2 | odd | 12 | 78.3.l.c.19.1 | ✓ | 8 | ||
13.5 | odd | 4 | inner | 1014.3.f.h.577.3 | 8 | ||
13.8 | odd | 4 | 1014.3.f.j.577.4 | 8 | |||
13.9 | even | 3 | 78.3.l.c.37.1 | yes | 8 | ||
13.12 | even | 2 | 1014.3.f.j.775.4 | 8 | |||
39.2 | even | 12 | 234.3.bb.d.19.2 | 8 | |||
39.35 | odd | 6 | 234.3.bb.d.37.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
78.3.l.c.19.1 | ✓ | 8 | 13.2 | odd | 12 | ||
78.3.l.c.37.1 | yes | 8 | 13.9 | even | 3 | ||
234.3.bb.d.19.2 | 8 | 39.2 | even | 12 | |||
234.3.bb.d.37.2 | 8 | 39.35 | odd | 6 | |||
1014.3.f.h.577.3 | 8 | 13.5 | odd | 4 | inner | ||
1014.3.f.h.775.3 | 8 | 1.1 | even | 1 | trivial | ||
1014.3.f.j.577.4 | 8 | 13.8 | odd | 4 | |||
1014.3.f.j.775.4 | 8 | 13.12 | even | 2 |