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 | 775.4 | ||
Root | \(5.41254 + 5.41254i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1014.775 |
Dual form | 1014.3.f.j.577.4 |
$q$-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 | \(0.00297517\pi\) |
0.00934664 | + | 0.999956i | \(0.497025\pi\) | |||||||
\(6\) | 1.73205 | + | 1.73205i | 0.288675 | + | 0.288675i | ||||
\(7\) | 3.68049 | − | 3.68049i | 0.525784 | − | 0.525784i | −0.393528 | − | 0.919313i | \(-0.628746\pi\) |
0.919313 | + | 0.393528i | \(0.128746\pi\) | |||||||
\(8\) | −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 | −0.907473 | − | 0.420111i | \(-0.861991\pi\) |
0.420111 | + | 0.907473i | \(0.361991\pi\) | |||||||
\(12\) | 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 | 0.871296 | − | 0.490759i | \(-0.163280\pi\) |
−0.490759 | + | 0.871296i | \(0.663280\pi\) | |||||||
\(20\) | −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 | \(0.0351934\pi\) |
0.110338 | + | 0.993894i | \(0.464807\pi\) | |||||||
\(32\) | −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 | \(-0.404462\pi\) |
0.955295 | − | 0.295655i | \(-0.0955378\pi\) | |||||||
\(38\) | 14.4604i | 0.380537i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −20.1861 | −0.504651 | ||||||||
\(41\) | −38.5116 | − | 38.5116i | −0.939308 | − | 0.939308i | 0.0589525 | − | 0.998261i | \(-0.481224\pi\) |
−0.998261 | + | 0.0589525i | \(0.981224\pi\) | |||||||
\(42\) | 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 | \(0.505613\pi\) |
−0.999845 | + | 0.0176317i | \(0.994387\pi\) | |||||||
\(48\) | −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 | −0.0930750 | − | 0.995659i | \(-0.529670\pi\) |
0.995659 | + | 0.0930750i | \(0.0296696\pi\) | |||||||
\(60\) | −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 | 0.441306 | − | 0.897357i | \(-0.354515\pi\) |
−0.897357 | + | 0.441306i | \(0.854515\pi\) | |||||||
\(68\) | −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 | \(-0.965920\pi\) |
−0.106862 | − | 0.994274i | \(-0.534080\pi\) | |||||||
\(72\) | −6.00000 | + | 6.00000i | −0.0833333 | + | 0.0833333i | ||||
\(73\) | 36.8385 | − | 36.8385i | 0.504638 | − | 0.504638i | −0.408238 | − | 0.912876i | \(-0.633857\pi\) |
0.912876 | + | 0.408238i | \(0.133857\pi\) | |||||||
\(74\) | 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 | \(-0.958333\pi\) |
−0.130528 | − | 0.991445i | \(-0.541667\pi\) | |||||||
\(84\) | 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 | −0.478322 | − | 0.878184i | \(-0.658755\pi\) |
0.878184 | + | 0.478322i | \(0.158755\pi\) | |||||||
\(90\) | 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 | 0.480478 | − | 0.877007i | \(-0.340463\pi\) |
−0.877007 | + | 0.480478i | \(0.840463\pi\) | |||||||
\(98\) | −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 | \(0.176752\pi\) |
0.527183 | + | 0.849752i | \(0.323248\pi\) | |||||||
\(110\) | −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 | −0.824968 | − | 0.565179i | \(-0.808807\pi\) |
0.565179 | + | 0.824968i | \(0.308807\pi\) | |||||||
\(138\) | 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 | 0.600792 | − | 0.799406i | \(-0.294852\pi\) |
−0.799406 | + | 0.600792i | \(0.794852\pi\) | |||||||
\(150\) | −44.9201 | + | 44.9201i | −0.299467 | + | 0.299467i | ||||
\(151\) | 2.57635 | − | 2.57635i | 0.0170619 | − | 0.0170619i | −0.698524 | − | 0.715586i | \(-0.746160\pi\) |
0.715586 | + | 0.698524i | \(0.246160\pi\) | |||||||
\(152\) | −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 | −0.333069 | − | 0.942902i | \(-0.608084\pi\) |
0.942902 | + | 0.333069i | \(0.108084\pi\) | |||||||
\(164\) | 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 | −0.155774 | − | 0.987793i | \(-0.549787\pi\) |
0.987793 | + | 0.155774i | \(0.0497872\pi\) | |||||||
\(168\) | 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 | −0.657552 | − | 0.753409i | \(-0.728408\pi\) |
0.753409 | + | 0.657552i | \(0.228408\pi\) | |||||||
\(194\) | − | 76.9267i | − | 0.396529i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −43.8160 | −0.223551 | ||||||||
\(197\) | 66.9799 | + | 66.9799i | 0.339999 | + | 0.339999i | 0.856367 | − | 0.516368i | \(-0.172716\pi\) |
−0.516368 | + | 0.856367i | \(0.672716\pi\) | |||||||
\(198\) | −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 | \(-0.879432\pi\) |
−0.369782 | − | 0.929119i | \(-0.620568\pi\) | |||||||
\(224\) | −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 | 0.979456 | − | 0.201658i | \(-0.0646329\pi\) |
−0.201658 | + | 0.979456i | \(0.564633\pi\) | |||||||
\(228\) | −25.0462 | + | 25.0462i | −0.109852 | + | 0.109852i | ||||
\(229\) | 174.256 | − | 174.256i | 0.760945 | − | 0.760945i | −0.215548 | − | 0.976493i | \(-0.569154\pi\) |
0.976493 | + | 0.215548i | \(0.0691539\pi\) | |||||||
\(230\) | 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 | 0.0924720 | − | 0.995715i | \(-0.470523\pi\) |
−0.995715 | + | 0.0924720i | \(0.970523\pi\) | |||||||
\(240\) | −34.9633 | − | 34.9633i | −0.145680 | − | 0.145680i | ||||
\(241\) | 84.9486 | − | 84.9486i | 0.352484 | − | 0.352484i | −0.508549 | − | 0.861033i | \(-0.669818\pi\) |
0.861033 | + | 0.508549i | \(0.169818\pi\) | |||||||
\(242\) | −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 | −0.486624 | − | 0.873612i | \(-0.661772\pi\) |
0.873612 | + | 0.486624i | \(0.161772\pi\) | |||||||
\(272\) | − | 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 | −0.422177 | − | 0.906514i | \(-0.638734\pi\) |
0.906514 | + | 0.422177i | \(0.138734\pi\) | |||||||
\(282\) | −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 | −0.700406 | − | 0.713745i | \(-0.746998\pi\) |
0.713745 | + | 0.700406i | \(0.246998\pi\) | |||||||
\(294\) | −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 | −0.232296 | − | 0.972645i | \(-0.574624\pi\) |
0.972645 | + | 0.232296i | \(0.0746240\pi\) | |||||||
\(308\) | −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 | 0.629346 | − | 0.777125i | \(-0.283323\pi\) |
−0.777125 | + | 0.629346i | \(0.783323\pi\) | |||||||
\(318\) | 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 | 0.915503 | − | 0.402311i | \(-0.131793\pi\) |
−0.402311 | + | 0.915503i | \(0.631793\pi\) | |||||||
\(332\) | 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 | −0.0177827 | − | 0.999842i | \(-0.505661\pi\) |
0.999842 | + | 0.0177827i | \(0.00566072\pi\) | |||||||
\(350\) | 190.904i | 0.545441i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 42.8878 | 0.121840 | ||||||||
\(353\) | 139.237 | + | 139.237i | 0.394439 | + | 0.394439i | 0.876266 | − | 0.481827i | \(-0.160027\pi\) |
−0.481827 | + | 0.876266i | \(0.660027\pi\) | |||||||
\(354\) | 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 | −0.627699 | − | 0.778456i | \(-0.716003\pi\) |
0.778456 | + | 0.627699i | \(0.216003\pi\) | |||||||
\(360\) | −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 | 0.900313 | − | 0.435244i | \(-0.143338\pi\) |
−0.435244 | + | 0.900313i | \(0.643338\pi\) | |||||||
\(380\) | −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 | 0.917173 | − | 0.398489i | \(-0.130465\pi\) |
−0.398489 | + | 0.917173i | \(0.630465\pi\) | |||||||
\(384\) | 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 | −0.586068 | − | 0.810262i | \(-0.699325\pi\) |
0.810262 | + | 0.586068i | \(0.199325\pi\) | |||||||
\(398\) | 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 | −0.999842 | − | 0.0177478i | \(-0.994350\pi\) |
0.0177478 | + | 0.999842i | \(0.494350\pi\) | |||||||
\(402\) | − | 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 | 0.862697 | − | 0.505721i | \(-0.168773\pi\) |
−0.505721 | + | 0.862697i | \(0.668773\pi\) | |||||||
\(410\) | 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 | 0.301230 | − | 0.953551i | \(-0.402603\pi\) |
−0.953551 | + | 0.301230i | \(0.902603\pi\) | |||||||
\(422\) | −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 | 0.585270 | − | 0.810838i | \(-0.300988\pi\) |
−0.810838 | + | 0.585270i | \(0.800988\pi\) | |||||||
\(432\) | −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 | −0.681969 | − | 0.731381i | \(-0.738876\pi\) |
0.731381 | + | 0.681969i | \(0.238876\pi\) | |||||||
\(450\) | −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 | 0.821651 | − | 0.569991i | \(-0.193053\pi\) |
−0.569991 | + | 0.821651i | \(0.693053\pi\) | |||||||
\(458\) | 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 | 0.642629 | − | 0.766178i | \(-0.277844\pi\) |
−0.766178 | + | 0.642629i | \(0.777844\pi\) | |||||||
\(462\) | −68.3503 | + | 68.3503i | −0.147944 | + | 0.147944i | ||||
\(463\) | 172.856 | − | 172.856i | 0.373338 | − | 0.373338i | −0.495353 | − | 0.868692i | \(-0.664961\pi\) |
0.868692 | + | 0.495353i | \(0.164961\pi\) | |||||||
\(464\) | 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 | −0.974492 | − | 0.224423i | \(-0.927950\pi\) |
0.224423 | + | 0.974492i | \(0.427950\pi\) | |||||||
\(480\) | − | 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 | \(-0.956564\pi\) |
−0.136034 | − | 0.990704i | \(-0.543436\pi\) | |||||||
\(488\) | −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 | 0.538931 | − | 0.842350i | \(-0.318828\pi\) |
−0.842350 | + | 0.538931i | \(0.818828\pi\) | |||||||
\(500\) | −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 | \(0.146413\pi\) |
0.443920 | + | 0.896066i | \(0.353587\pi\) | |||||||
\(510\) | −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 | \(0.541157\pi\) |
−0.991653 | + | 0.128938i | \(0.958843\pi\) | |||||||
\(542\) | 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 | −0.924995 | − | 0.379979i | \(-0.875931\pi\) |
0.379979 | + | 0.924995i | \(0.375931\pi\) | |||||||
\(558\) | 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 | 0.849930 | − | 0.526895i | \(-0.176644\pi\) |
−0.526895 | + | 0.849930i | \(0.676644\pi\) | |||||||
\(578\) | 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 | 0.0533553 | − | 0.998576i | \(-0.483008\pi\) |
−0.998576 | + | 0.0533553i | \(0.983008\pi\) | |||||||
\(588\) | −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 | −0.315898 | − | 0.948793i | \(-0.602306\pi\) |
0.948793 | + | 0.315898i | \(0.102306\pi\) | |||||||
\(594\) | −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 | 0.809353 | − | 0.587323i | \(-0.199818\pi\) |
−0.587323 | + | 0.809353i | \(0.699818\pi\) | |||||||
\(614\) | 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 | 0.718389 | − | 0.695641i | \(-0.244880\pi\) |
−0.695641 | + | 0.718389i | \(0.744880\pi\) | |||||||
\(618\) | −189.461 | + | 189.461i | −0.306571 | + | 0.306571i | ||||
\(619\) | 319.972 | − | 319.972i | 0.516917 | − | 0.516917i | −0.399720 | − | 0.916637i | \(-0.630893\pi\) |
0.916637 | + | 0.399720i | \(0.130893\pi\) | |||||||
\(620\) | −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 | −0.908601 | − | 0.417666i | \(-0.862848\pi\) |
0.417666 | + | 0.908601i | \(0.362848\pi\) | |||||||
\(632\) | 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 | 0.449457 | − | 0.893302i | \(-0.351618\pi\) |
−0.893302 | + | 0.449457i | \(0.851618\pi\) | |||||||
\(644\) | 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 | −0.952596 | − | 0.304239i | \(-0.901598\pi\) |
0.304239 | + | 0.952596i | \(0.401598\pi\) | |||||||
\(662\) | 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 | −0.993032 | − | 0.117842i | \(-0.962402\pi\) |
0.117842 | + | 0.993032i | \(0.462402\pi\) | |||||||
\(684\) | −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 | 0.278207 | − | 0.960521i | \(-0.410260\pi\) |
−0.960521 | + | 0.278207i | \(0.910260\pi\) | |||||||
\(692\) | 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 | −0.515149 | − | 0.857101i | \(-0.672263\pi\) |
0.857101 | + | 0.515149i | \(0.172263\pi\) | |||||||
\(710\) | 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 | \(0.106369\pi\) |
0.327985 | + | 0.944683i | \(0.393631\pi\) | |||||||
\(734\) | −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 | −0.603821 | − | 0.797120i | \(-0.706356\pi\) |
0.797120 | + | 0.603821i | \(0.206356\pi\) | |||||||
\(740\) | 934.314i | 1.26259i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 496.996 | 0.669806 | ||||||||
\(743\) | 741.898 | + | 741.898i | 0.998517 | + | 0.998517i | 0.999999 | − | 0.00148231i | \(-0.000471834\pi\) |
−0.00148231 | + | 0.999999i | \(0.500472\pi\) | |||||||
\(744\) | −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 | −0.877802 | − | 0.479023i | \(-0.840991\pi\) |
0.479023 | + | 0.877802i | \(0.340991\pi\) | |||||||
\(762\) | 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 | 0.474937 | − | 0.880020i | \(-0.342471\pi\) |
−0.880020 | + | 0.474937i | \(0.842471\pi\) | |||||||
\(770\) | −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 | \(0.0314197\pi\) |
0.0985477 | + | 0.995132i | \(0.468580\pi\) | |||||||
\(774\) | −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 | −0.838058 | − | 0.545581i | \(-0.816309\pi\) |
0.545581 | + | 0.838058i | \(0.316309\pi\) | |||||||
\(788\) | −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 | 0.100324 | − | 0.994955i | \(-0.468012\pi\) |
−0.994955 | + | 0.100324i | \(0.968012\pi\) | |||||||
\(812\) | −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 | 0.904339 | − | 0.426815i | \(-0.140364\pi\) |
−0.426815 | + | 0.904339i | \(0.640364\pi\) | |||||||
\(822\) | −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 | \(0.520486\pi\) |
−0.997930 | + | 0.0643137i | \(0.979514\pi\) | |||||||
\(828\) | 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 | −0.563458 | − | 0.826144i | \(-0.690530\pi\) |
0.826144 | + | 0.563458i | \(0.190530\pi\) | |||||||
\(840\) | −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 | −0.990039 | − | 0.140791i | \(-0.955036\pi\) |
0.140791 | + | 0.990039i | \(0.455036\pi\) | |||||||
\(854\) | 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 | 0.390058 | − | 0.920790i | \(-0.372455\pi\) |
−0.920790 | + | 0.390058i | \(0.872455\pi\) | |||||||
\(864\) | −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 | 0.564985 | − | 0.825101i | \(-0.308882\pi\) |
−0.825101 | + | 0.564985i | \(0.808882\pi\) | |||||||
\(878\) | −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 | 0.399725 | − | 0.916635i | \(-0.369105\pi\) |
−0.916635 | + | 0.399725i | \(0.869105\pi\) | |||||||
\(930\) | −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 | 0.427904 | − | 0.903824i | \(-0.359252\pi\) |
−0.903824 | + | 0.427904i | \(0.859252\pi\) | |||||||
\(942\) | 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 | −0.452077 | − | 0.891979i | \(-0.649317\pi\) |
0.891979 | + | 0.452077i | \(0.149317\pi\) | |||||||
\(948\) | − | 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 | \(-0.911111\pi\) |
−0.275638 | − | 0.961262i | \(-0.588889\pi\) | |||||||
\(968\) | −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 | 0.614851 | − | 0.788643i | \(-0.289216\pi\) |
−0.788643 | + | 0.614851i | \(0.789216\pi\) | |||||||
\(978\) | 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 | −0.403261 | − | 0.915085i | \(-0.632123\pi\) |
0.915085 | + | 0.403261i | \(0.132123\pi\) | |||||||
\(984\) | 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.j.775.4 | 8 | ||
13.4 | even | 6 | 78.3.l.c.37.1 | yes | 8 | ||
13.5 | odd | 4 | inner | 1014.3.f.j.577.4 | 8 | ||
13.8 | odd | 4 | 1014.3.f.h.577.3 | 8 | |||
13.11 | odd | 12 | 78.3.l.c.19.1 | ✓ | 8 | ||
13.12 | even | 2 | 1014.3.f.h.775.3 | 8 | |||
39.11 | even | 12 | 234.3.bb.d.19.2 | 8 | |||
39.17 | 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 | 13.11 | odd | 12 | ||
78.3.l.c.37.1 | yes | 8 | 13.4 | even | 6 | ||
234.3.bb.d.19.2 | 8 | 39.11 | even | 12 | |||
234.3.bb.d.37.2 | 8 | 39.17 | odd | 6 | |||
1014.3.f.h.577.3 | 8 | 13.8 | odd | 4 | |||
1014.3.f.h.775.3 | 8 | 13.12 | even | 2 | |||
1014.3.f.j.577.4 | 8 | 13.5 | odd | 4 | inner | ||
1014.3.f.j.775.4 | 8 | 1.1 | even | 1 | trivial |