Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [45,3,Mod(28,45)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(45, 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("45.28");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 45 = 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 45.g (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: | \(1.22616118962\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 37.2 | ||
Root | \(1.58114 + 1.58114i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 45.37 |
Dual form | 45.3.g.a.28.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(37\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.58114 | + | 1.58114i | 0.790569 | + | 0.790569i | 0.981587 | − | 0.191017i | \(-0.0611786\pi\) |
−0.191017 | + | 0.981587i | \(0.561179\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000i | 0.250000i | ||||||||
\(5\) | 1.58114 | + | 4.74342i | 0.316228 | + | 0.948683i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.00000 | − | 5.00000i | −0.714286 | − | 0.714286i | 0.253143 | − | 0.967429i | \(-0.418536\pi\) |
−0.967429 | + | 0.253143i | \(0.918536\pi\) | |||||||
\(8\) | 4.74342 | − | 4.74342i | 0.592927 | − | 0.592927i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −5.00000 | + | 10.0000i | −0.500000 | + | 1.00000i | ||||
\(11\) | −15.8114 | −1.43740 | −0.718699 | − | 0.695321i | \(-0.755262\pi\) | ||||
−0.718699 | + | 0.695321i | \(0.755262\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10.0000 | − | 10.0000i | 0.769231 | − | 0.769231i | −0.208740 | − | 0.977971i | \(-0.566936\pi\) |
0.977971 | + | 0.208740i | \(0.0669363\pi\) | |||||||
\(14\) | − | 15.8114i | − | 1.12938i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 19.0000 | 1.18750 | ||||||||
\(17\) | −3.16228 | − | 3.16228i | −0.186016 | − | 0.186016i | 0.607955 | − | 0.793971i | \(-0.291990\pi\) |
−0.793971 | + | 0.607955i | \(0.791990\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 18.0000i | 0.947368i | 0.880695 | + | 0.473684i | \(0.157076\pi\) | ||||
−0.880695 | + | 0.473684i | \(0.842924\pi\) | |||||||
\(20\) | −4.74342 | + | 1.58114i | −0.237171 | + | 0.0790569i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −25.0000 | − | 25.0000i | −1.13636 | − | 1.13636i | ||||
\(23\) | −3.16228 | + | 3.16228i | −0.137490 | + | 0.137490i | −0.772502 | − | 0.635012i | \(-0.780995\pi\) |
0.635012 | + | 0.772502i | \(0.280995\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −20.0000 | + | 15.0000i | −0.800000 | + | 0.600000i | ||||
\(26\) | 31.6228 | 1.21626 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.00000 | − | 5.00000i | 0.178571 | − | 0.178571i | ||||
\(29\) | 47.4342i | 1.63566i | 0.575459 | + | 0.817830i | \(0.304823\pi\) | ||||
−0.575459 | + | 0.817830i | \(0.695177\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.00000 | 0.258065 | 0.129032 | − | 0.991640i | \(-0.458813\pi\) | ||||
0.129032 | + | 0.991640i | \(0.458813\pi\) | |||||||
\(32\) | 11.0680 | + | 11.0680i | 0.345874 | + | 0.345874i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 10.0000i | − | 0.294118i | ||||||
\(35\) | 15.8114 | − | 31.6228i | 0.451754 | − | 0.903508i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.0000 | + | 10.0000i | 0.270270 | + | 0.270270i | 0.829209 | − | 0.558939i | \(-0.188791\pi\) |
−0.558939 | + | 0.829209i | \(0.688791\pi\) | |||||||
\(38\) | −28.4605 | + | 28.4605i | −0.748960 | + | 0.748960i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 30.0000 | + | 15.0000i | 0.750000 | + | 0.375000i | ||||
\(41\) | 31.6228 | 0.771287 | 0.385644 | − | 0.922648i | \(-0.373979\pi\) | ||||
0.385644 | + | 0.922648i | \(0.373979\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.0000 | − | 10.0000i | 0.232558 | − | 0.232558i | −0.581202 | − | 0.813760i | \(-0.697417\pi\) |
0.813760 | + | 0.581202i | \(0.197417\pi\) | |||||||
\(44\) | − | 15.8114i | − | 0.359350i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −10.0000 | −0.217391 | ||||||||
\(47\) | −41.1096 | − | 41.1096i | −0.874673 | − | 0.874673i | 0.118305 | − | 0.992977i | \(-0.462254\pi\) |
−0.992977 | + | 0.118305i | \(0.962254\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000i | 0.0204082i | ||||||||
\(50\) | −55.3399 | − | 7.90569i | −1.10680 | − | 0.158114i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 10.0000 | + | 10.0000i | 0.192308 | + | 0.192308i | ||||
\(53\) | 25.2982 | − | 25.2982i | 0.477325 | − | 0.477325i | −0.426950 | − | 0.904275i | \(-0.640412\pi\) |
0.904275 | + | 0.426950i | \(0.140412\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −25.0000 | − | 75.0000i | −0.454545 | − | 1.36364i | ||||
\(56\) | −47.4342 | −0.847039 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −75.0000 | + | 75.0000i | −1.29310 | + | 1.29310i | ||||
\(59\) | − | 47.4342i | − | 0.803969i | −0.915646 | − | 0.401984i | \(-0.868321\pi\) | ||
0.915646 | − | 0.401984i | \(-0.131679\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −58.0000 | −0.950820 | −0.475410 | − | 0.879764i | \(-0.657700\pi\) | ||||
−0.475410 | + | 0.879764i | \(0.657700\pi\) | |||||||
\(62\) | 12.6491 | + | 12.6491i | 0.204018 | + | 0.204018i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 41.0000i | − | 0.640625i | ||||||
\(65\) | 63.2456 | + | 31.6228i | 0.973009 | + | 0.486504i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 70.0000 | + | 70.0000i | 1.04478 | + | 1.04478i | 0.998949 | + | 0.0458267i | \(0.0145922\pi\) |
0.0458267 | + | 0.998949i | \(0.485408\pi\) | |||||||
\(68\) | 3.16228 | − | 3.16228i | 0.0465041 | − | 0.0465041i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 75.0000 | − | 25.0000i | 1.07143 | − | 0.357143i | ||||
\(71\) | −63.2456 | −0.890782 | −0.445391 | − | 0.895336i | \(-0.646935\pi\) | ||||
−0.445391 | + | 0.895336i | \(0.646935\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 55.0000 | − | 55.0000i | 0.753425 | − | 0.753425i | −0.221692 | − | 0.975117i | \(-0.571158\pi\) |
0.975117 | + | 0.221692i | \(0.0711580\pi\) | |||||||
\(74\) | 31.6228i | 0.427335i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −18.0000 | −0.236842 | ||||||||
\(77\) | 79.0569 | + | 79.0569i | 1.02671 | + | 1.02671i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.0000i | 0.151899i | 0.997112 | + | 0.0759494i | \(0.0241987\pi\) | ||||
−0.997112 | + | 0.0759494i | \(0.975801\pi\) | |||||||
\(80\) | 30.0416 | + | 90.1249i | 0.375520 | + | 1.12656i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 50.0000 | + | 50.0000i | 0.609756 | + | 0.609756i | ||||
\(83\) | 53.7587 | − | 53.7587i | 0.647695 | − | 0.647695i | −0.304740 | − | 0.952436i | \(-0.598570\pi\) |
0.952436 | + | 0.304740i | \(0.0985696\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.0000 | − | 20.0000i | 0.117647 | − | 0.235294i | ||||
\(86\) | 31.6228 | 0.367707 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −75.0000 | + | 75.0000i | −0.852273 | + | 0.852273i | ||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −100.000 | −1.09890 | ||||||||
\(92\) | −3.16228 | − | 3.16228i | −0.0343726 | − | 0.0343726i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 130.000i | − | 1.38298i | ||||||
\(95\) | −85.3815 | + | 28.4605i | −0.898753 | + | 0.299584i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.00000 | − | 5.00000i | −0.0515464 | − | 0.0515464i | 0.680864 | − | 0.732410i | \(-0.261605\pi\) |
−0.732410 | + | 0.680864i | \(0.761605\pi\) | |||||||
\(98\) | −1.58114 | + | 1.58114i | −0.0161341 | + | 0.0161341i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −15.0000 | − | 20.0000i | −0.150000 | − | 0.200000i | ||||
\(101\) | −15.8114 | −0.156548 | −0.0782742 | − | 0.996932i | \(-0.524941\pi\) | ||||
−0.0782742 | + | 0.996932i | \(0.524941\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −35.0000 | + | 35.0000i | −0.339806 | + | 0.339806i | −0.856294 | − | 0.516488i | \(-0.827239\pi\) |
0.516488 | + | 0.856294i | \(0.327239\pi\) | |||||||
\(104\) | − | 94.8683i | − | 0.912195i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 80.0000 | 0.754717 | ||||||||
\(107\) | −60.0833 | − | 60.0833i | −0.561526 | − | 0.561526i | 0.368215 | − | 0.929741i | \(-0.379969\pi\) |
−0.929741 | + | 0.368215i | \(0.879969\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 162.000i | 1.48624i | 0.669159 | + | 0.743119i | \(0.266655\pi\) | ||||
−0.669159 | + | 0.743119i | \(0.733345\pi\) | |||||||
\(110\) | 79.0569 | − | 158.114i | 0.718699 | − | 1.43740i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −95.0000 | − | 95.0000i | −0.848214 | − | 0.848214i | ||||
\(113\) | −117.004 | + | 117.004i | −1.03544 | + | 1.03544i | −0.0360874 | + | 0.999349i | \(0.511489\pi\) |
−0.999349 | + | 0.0360874i | \(0.988511\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −20.0000 | − | 10.0000i | −0.173913 | − | 0.0869565i | ||||
\(116\) | −47.4342 | −0.408915 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 75.0000 | − | 75.0000i | 0.635593 | − | 0.635593i | ||||
\(119\) | 31.6228i | 0.265738i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 129.000 | 1.06612 | ||||||||
\(122\) | −91.7061 | − | 91.7061i | −0.751689 | − | 0.751689i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.00000i | 0.0645161i | ||||||||
\(125\) | −102.774 | − | 71.1512i | −0.822192 | − | 0.569210i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 55.0000 | + | 55.0000i | 0.433071 | + | 0.433071i | 0.889672 | − | 0.456601i | \(-0.150933\pi\) |
−0.456601 | + | 0.889672i | \(0.650933\pi\) | |||||||
\(128\) | 109.099 | − | 109.099i | 0.852333 | − | 0.852333i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 50.0000 | + | 150.000i | 0.384615 | + | 1.15385i | ||||
\(131\) | 173.925 | 1.32767 | 0.663837 | − | 0.747877i | \(-0.268927\pi\) | ||||
0.663837 | + | 0.747877i | \(0.268927\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 90.0000 | − | 90.0000i | 0.676692 | − | 0.676692i | ||||
\(134\) | 221.359i | 1.65194i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −30.0000 | −0.220588 | ||||||||
\(137\) | 15.8114 | + | 15.8114i | 0.115412 | + | 0.115412i | 0.762454 | − | 0.647042i | \(-0.223994\pi\) |
−0.647042 | + | 0.762454i | \(0.723994\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 102.000i | − | 0.733813i | −0.930258 | − | 0.366906i | \(-0.880417\pi\) | ||
0.930258 | − | 0.366906i | \(-0.119583\pi\) | |||||||
\(140\) | 31.6228 | + | 15.8114i | 0.225877 | + | 0.112938i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −100.000 | − | 100.000i | −0.704225 | − | 0.704225i | ||||
\(143\) | −158.114 | + | 158.114i | −1.10569 | + | 1.10569i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −225.000 | + | 75.0000i | −1.55172 | + | 0.517241i | ||||
\(146\) | 173.925 | 1.19127 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10.0000 | + | 10.0000i | −0.0675676 | + | 0.0675676i | ||||
\(149\) | − | 47.4342i | − | 0.318350i | −0.987250 | − | 0.159175i | \(-0.949117\pi\) | ||
0.987250 | − | 0.159175i | \(-0.0508834\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.0000 | −0.145695 | −0.0728477 | − | 0.997343i | \(-0.523209\pi\) | ||||
−0.0728477 | + | 0.997343i | \(0.523209\pi\) | |||||||
\(152\) | 85.3815 | + | 85.3815i | 0.561720 | + | 0.561720i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 250.000i | 1.62338i | ||||||||
\(155\) | 12.6491 | + | 37.9473i | 0.0816072 | + | 0.244821i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −200.000 | − | 200.000i | −1.27389 | − | 1.27389i | −0.944032 | − | 0.329853i | \(-0.893001\pi\) |
−0.329853 | − | 0.944032i | \(-0.606999\pi\) | |||||||
\(158\) | −18.9737 | + | 18.9737i | −0.120086 | + | 0.120086i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −35.0000 | + | 70.0000i | −0.218750 | + | 0.437500i | ||||
\(161\) | 31.6228 | 0.196415 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 100.000 | − | 100.000i | 0.613497 | − | 0.613497i | −0.330359 | − | 0.943856i | \(-0.607170\pi\) |
0.943856 | + | 0.330359i | \(0.107170\pi\) | |||||||
\(164\) | 31.6228i | 0.192822i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 170.000 | 1.02410 | ||||||||
\(167\) | 148.627 | + | 148.627i | 0.889982 | + | 0.889982i | 0.994521 | − | 0.104539i | \(-0.0333365\pi\) |
−0.104539 | + | 0.994521i | \(0.533337\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 31.0000i | − | 0.183432i | ||||||
\(170\) | 47.4342 | − | 15.8114i | 0.279024 | − | 0.0930082i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 10.0000 | + | 10.0000i | 0.0581395 | + | 0.0581395i | ||||
\(173\) | 110.680 | − | 110.680i | 0.639767 | − | 0.639767i | −0.310731 | − | 0.950498i | \(-0.600574\pi\) |
0.950498 | + | 0.310731i | \(0.100574\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 175.000 | + | 25.0000i | 1.00000 | + | 0.142857i | ||||
\(176\) | −300.416 | −1.70691 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 142.302i | − | 0.794986i | −0.917605 | − | 0.397493i | \(-0.869880\pi\) | ||
0.917605 | − | 0.397493i | \(-0.130120\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 218.000 | 1.20442 | 0.602210 | − | 0.798338i | \(-0.294287\pi\) | ||||
0.602210 | + | 0.798338i | \(0.294287\pi\) | |||||||
\(182\) | −158.114 | − | 158.114i | −0.868758 | − | 0.868758i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 30.0000i | 0.163043i | ||||||||
\(185\) | −31.6228 | + | 63.2456i | −0.170934 | + | 0.341868i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 50.0000 | + | 50.0000i | 0.267380 | + | 0.267380i | ||||
\(188\) | 41.1096 | − | 41.1096i | 0.218668 | − | 0.218668i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −180.000 | − | 90.0000i | −0.947368 | − | 0.473684i | ||||
\(191\) | −158.114 | −0.827821 | −0.413911 | − | 0.910317i | \(-0.635837\pi\) | ||||
−0.413911 | + | 0.910317i | \(0.635837\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −125.000 | + | 125.000i | −0.647668 | + | 0.647668i | −0.952429 | − | 0.304761i | \(-0.901424\pi\) |
0.304761 | + | 0.952429i | \(0.401424\pi\) | |||||||
\(194\) | − | 15.8114i | − | 0.0815020i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.00000 | −0.00510204 | ||||||||
\(197\) | −145.465 | − | 145.465i | −0.738400 | − | 0.738400i | 0.233868 | − | 0.972268i | \(-0.424862\pi\) |
−0.972268 | + | 0.233868i | \(0.924862\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 18.0000i | − | 0.0904523i | −0.998977 | − | 0.0452261i | \(-0.985599\pi\) | ||
0.998977 | − | 0.0452261i | \(-0.0144008\pi\) | |||||||
\(200\) | −23.7171 | + | 166.020i | −0.118585 | + | 0.830098i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −25.0000 | − | 25.0000i | −0.123762 | − | 0.123762i | ||||
\(203\) | 237.171 | − | 237.171i | 1.16833 | − | 1.16833i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 50.0000 | + | 150.000i | 0.243902 | + | 0.731707i | ||||
\(206\) | −110.680 | −0.537280 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 190.000 | − | 190.000i | 0.913462 | − | 0.913462i | ||||
\(209\) | − | 284.605i | − | 1.36175i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −298.000 | −1.41232 | −0.706161 | − | 0.708051i | \(-0.749575\pi\) | ||||
−0.706161 | + | 0.708051i | \(0.749575\pi\) | |||||||
\(212\) | 25.2982 | + | 25.2982i | 0.119331 | + | 0.119331i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 190.000i | − | 0.887850i | ||||||
\(215\) | 63.2456 | + | 31.6228i | 0.294165 | + | 0.147083i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −40.0000 | − | 40.0000i | −0.184332 | − | 0.184332i | ||||
\(218\) | −256.144 | + | 256.144i | −1.17497 | + | 1.17497i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 75.0000 | − | 25.0000i | 0.340909 | − | 0.113636i | ||||
\(221\) | −63.2456 | −0.286179 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −215.000 | + | 215.000i | −0.964126 | + | 0.964126i | −0.999378 | − | 0.0352529i | \(-0.988776\pi\) |
0.0352529 | + | 0.999378i | \(0.488776\pi\) | |||||||
\(224\) | − | 110.680i | − | 0.494106i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −370.000 | −1.63717 | ||||||||
\(227\) | 271.956 | + | 271.956i | 1.19804 | + | 1.19804i | 0.974752 | + | 0.223292i | \(0.0716803\pi\) |
0.223292 | + | 0.974752i | \(0.428320\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 78.0000i | 0.340611i | 0.985391 | + | 0.170306i | \(0.0544755\pi\) | ||||
−0.985391 | + | 0.170306i | \(0.945524\pi\) | |||||||
\(230\) | −15.8114 | − | 47.4342i | −0.0687452 | − | 0.206235i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 225.000 | + | 225.000i | 0.969828 | + | 0.969828i | ||||
\(233\) | 110.680 | − | 110.680i | 0.475020 | − | 0.475020i | −0.428515 | − | 0.903535i | \(-0.640963\pi\) |
0.903535 | + | 0.428515i | \(0.140963\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 130.000 | − | 260.000i | 0.553191 | − | 1.10638i | ||||
\(236\) | 47.4342 | 0.200992 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −50.0000 | + | 50.0000i | −0.210084 | + | 0.210084i | ||||
\(239\) | 379.473i | 1.58775i | 0.608078 | + | 0.793877i | \(0.291941\pi\) | ||||
−0.608078 | + | 0.793877i | \(0.708059\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 212.000 | 0.879668 | 0.439834 | − | 0.898079i | \(-0.355037\pi\) | ||||
0.439834 | + | 0.898079i | \(0.355037\pi\) | |||||||
\(242\) | 203.967 | + | 203.967i | 0.842838 | + | 0.842838i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 58.0000i | − | 0.237705i | ||||||
\(245\) | −4.74342 | + | 1.58114i | −0.0193609 | + | 0.00645363i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 180.000 | + | 180.000i | 0.728745 | + | 0.728745i | ||||
\(248\) | 37.9473 | − | 37.9473i | 0.153013 | − | 0.153013i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −50.0000 | − | 275.000i | −0.200000 | − | 1.10000i | ||||
\(251\) | 363.662 | 1.44885 | 0.724426 | − | 0.689352i | \(-0.242105\pi\) | ||||
0.724426 | + | 0.689352i | \(0.242105\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 50.0000 | − | 50.0000i | 0.197628 | − | 0.197628i | ||||
\(254\) | 173.925i | 0.684745i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 181.000 | 0.707031 | ||||||||
\(257\) | −306.741 | − | 306.741i | −1.19354 | − | 1.19354i | −0.976065 | − | 0.217480i | \(-0.930216\pi\) |
−0.217480 | − | 0.976065i | \(-0.569784\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 100.000i | − | 0.386100i | ||||||
\(260\) | −31.6228 | + | 63.2456i | −0.121626 | + | 0.243252i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 275.000 | + | 275.000i | 1.04962 | + | 1.04962i | ||||
\(263\) | −287.767 | + | 287.767i | −1.09417 | + | 1.09417i | −0.0990940 | + | 0.995078i | \(0.531594\pi\) |
−0.995078 | + | 0.0990940i | \(0.968406\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 160.000 | + | 80.0000i | 0.603774 | + | 0.301887i | ||||
\(266\) | 284.605 | 1.06994 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −70.0000 | + | 70.0000i | −0.261194 | + | 0.261194i | ||||
\(269\) | 142.302i | 0.529006i | 0.964385 | + | 0.264503i | \(0.0852078\pi\) | ||||
−0.964385 | + | 0.264503i | \(0.914792\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −178.000 | −0.656827 | −0.328413 | − | 0.944534i | \(-0.606514\pi\) | ||||
−0.328413 | + | 0.944534i | \(0.606514\pi\) | |||||||
\(272\) | −60.0833 | − | 60.0833i | −0.220894 | − | 0.220894i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 50.0000i | 0.182482i | ||||||||
\(275\) | 316.228 | − | 237.171i | 1.14992 | − | 0.862439i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −230.000 | − | 230.000i | −0.830325 | − | 0.830325i | 0.157236 | − | 0.987561i | \(-0.449742\pi\) |
−0.987561 | + | 0.157236i | \(0.949742\pi\) | |||||||
\(278\) | 161.276 | − | 161.276i | 0.580130 | − | 0.580130i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −75.0000 | − | 225.000i | −0.267857 | − | 0.803571i | ||||
\(281\) | −158.114 | −0.562683 | −0.281341 | − | 0.959608i | \(-0.590779\pi\) | ||||
−0.281341 | + | 0.959608i | \(0.590779\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −350.000 | + | 350.000i | −1.23675 | + | 1.23675i | −0.275427 | + | 0.961322i | \(0.588819\pi\) |
−0.961322 | + | 0.275427i | \(0.911181\pi\) | |||||||
\(284\) | − | 63.2456i | − | 0.222696i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −500.000 | −1.74825 | ||||||||
\(287\) | −158.114 | − | 158.114i | −0.550919 | − | 0.550919i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 269.000i | − | 0.930796i | ||||||
\(290\) | −474.342 | − | 237.171i | −1.63566 | − | 0.817830i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 55.0000 | + | 55.0000i | 0.188356 | + | 0.188356i | ||||
\(293\) | −202.386 | + | 202.386i | −0.690736 | + | 0.690736i | −0.962394 | − | 0.271658i | \(-0.912428\pi\) |
0.271658 | + | 0.962394i | \(0.412428\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 225.000 | − | 75.0000i | 0.762712 | − | 0.254237i | ||||
\(296\) | 94.8683 | 0.320501 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 75.0000 | − | 75.0000i | 0.251678 | − | 0.251678i | ||||
\(299\) | 63.2456i | 0.211524i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −100.000 | −0.332226 | ||||||||
\(302\) | −34.7851 | − | 34.7851i | −0.115182 | − | 0.115182i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 342.000i | 1.12500i | ||||||||
\(305\) | −91.7061 | − | 275.118i | −0.300676 | − | 0.902027i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 190.000 | + | 190.000i | 0.618893 | + | 0.618893i | 0.945247 | − | 0.326355i | \(-0.105820\pi\) |
−0.326355 | + | 0.945247i | \(0.605820\pi\) | |||||||
\(308\) | −79.0569 | + | 79.0569i | −0.256678 | + | 0.256678i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −40.0000 | + | 80.0000i | −0.129032 | + | 0.258065i | ||||
\(311\) | −252.982 | −0.813448 | −0.406724 | − | 0.913551i | \(-0.633329\pi\) | ||||
−0.406724 | + | 0.913551i | \(0.633329\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 145.000 | − | 145.000i | 0.463259 | − | 0.463259i | −0.436463 | − | 0.899722i | \(-0.643769\pi\) |
0.899722 | + | 0.436463i | \(0.143769\pi\) | |||||||
\(314\) | − | 632.456i | − | 2.01419i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.0000 | −0.0379747 | ||||||||
\(317\) | 15.8114 | + | 15.8114i | 0.0498782 | + | 0.0498782i | 0.731606 | − | 0.681728i | \(-0.238771\pi\) |
−0.681728 | + | 0.731606i | \(0.738771\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 750.000i | − | 2.35110i | ||||||
\(320\) | 194.480 | − | 64.8267i | 0.607750 | − | 0.202583i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 50.0000 | + | 50.0000i | 0.155280 | + | 0.155280i | ||||
\(323\) | 56.9210 | − | 56.9210i | 0.176226 | − | 0.176226i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −50.0000 | + | 350.000i | −0.153846 | + | 1.07692i | ||||
\(326\) | 316.228 | 0.970024 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 150.000 | − | 150.000i | 0.457317 | − | 0.457317i | ||||
\(329\) | 411.096i | 1.24953i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 482.000 | 1.45619 | 0.728097 | − | 0.685474i | \(-0.240405\pi\) | ||||
0.728097 | + | 0.685474i | \(0.240405\pi\) | |||||||
\(332\) | 53.7587 | + | 53.7587i | 0.161924 | + | 0.161924i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 470.000i | 1.40719i | ||||||||
\(335\) | −221.359 | + | 442.719i | −0.660774 | + | 1.32155i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −155.000 | − | 155.000i | −0.459941 | − | 0.459941i | 0.438695 | − | 0.898636i | \(-0.355441\pi\) |
−0.898636 | + | 0.438695i | \(0.855441\pi\) | |||||||
\(338\) | 49.0153 | − | 49.0153i | 0.145016 | − | 0.145016i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 20.0000 | + | 10.0000i | 0.0588235 | + | 0.0294118i | ||||
\(341\) | −126.491 | −0.370942 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −240.000 | + | 240.000i | −0.699708 | + | 0.699708i | ||||
\(344\) | − | 94.8683i | − | 0.275780i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 350.000 | 1.01156 | ||||||||
\(347\) | −164.438 | − | 164.438i | −0.473886 | − | 0.473886i | 0.429284 | − | 0.903170i | \(-0.358766\pi\) |
−0.903170 | + | 0.429284i | \(0.858766\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 318.000i | 0.911175i | 0.890191 | + | 0.455587i | \(0.150571\pi\) | ||||
−0.890191 | + | 0.455587i | \(0.849429\pi\) | |||||||
\(350\) | 237.171 | + | 316.228i | 0.677631 | + | 0.903508i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −175.000 | − | 175.000i | −0.497159 | − | 0.497159i | ||||
\(353\) | 224.522 | − | 224.522i | 0.636039 | − | 0.636039i | −0.313537 | − | 0.949576i | \(-0.601514\pi\) |
0.949576 | + | 0.313537i | \(0.101514\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −100.000 | − | 300.000i | −0.281690 | − | 0.845070i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 225.000 | − | 225.000i | 0.628492 | − | 0.628492i | ||||
\(359\) | 284.605i | 0.792772i | 0.918084 | + | 0.396386i | \(0.129736\pi\) | ||||
−0.918084 | + | 0.396386i | \(0.870264\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 37.0000 | 0.102493 | ||||||||
\(362\) | 344.688 | + | 344.688i | 0.952178 | + | 0.952178i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 100.000i | − | 0.274725i | ||||||
\(365\) | 347.851 | + | 173.925i | 0.953015 | + | 0.476508i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −185.000 | − | 185.000i | −0.504087 | − | 0.504087i | 0.408618 | − | 0.912705i | \(-0.366011\pi\) |
−0.912705 | + | 0.408618i | \(0.866011\pi\) | |||||||
\(368\) | −60.0833 | + | 60.0833i | −0.163270 | + | 0.163270i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −150.000 | + | 50.0000i | −0.405405 | + | 0.135135i | ||||
\(371\) | −252.982 | −0.681893 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 100.000 | − | 100.000i | 0.268097 | − | 0.268097i | −0.560236 | − | 0.828333i | \(-0.689290\pi\) |
0.828333 | + | 0.560236i | \(0.189290\pi\) | |||||||
\(374\) | 158.114i | 0.422764i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −390.000 | −1.03723 | ||||||||
\(377\) | 474.342 | + | 474.342i | 1.25820 | + | 1.25820i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 558.000i | 1.47230i | 0.676821 | + | 0.736148i | \(0.263357\pi\) | ||||
−0.676821 | + | 0.736148i | \(0.736643\pi\) | |||||||
\(380\) | −28.4605 | − | 85.3815i | −0.0748960 | − | 0.224688i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −250.000 | − | 250.000i | −0.654450 | − | 0.654450i | ||||
\(383\) | 281.443 | − | 281.443i | 0.734837 | − | 0.734837i | −0.236737 | − | 0.971574i | \(-0.576078\pi\) |
0.971574 | + | 0.236737i | \(0.0760778\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −250.000 | + | 500.000i | −0.649351 | + | 1.29870i | ||||
\(386\) | −395.285 | −1.02405 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.00000 | − | 5.00000i | 0.0128866 | − | 0.0128866i | ||||
\(389\) | − | 521.776i | − | 1.34133i | −0.741762 | − | 0.670663i | \(-0.766010\pi\) | ||
0.741762 | − | 0.670663i | \(-0.233990\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.0000 | 0.0511509 | ||||||||
\(392\) | 4.74342 | + | 4.74342i | 0.0121006 | + | 0.0121006i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 460.000i | − | 1.16751i | ||||||
\(395\) | −56.9210 | + | 18.9737i | −0.144104 | + | 0.0480346i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −260.000 | − | 260.000i | −0.654912 | − | 0.654912i | 0.299260 | − | 0.954172i | \(-0.403260\pi\) |
−0.954172 | + | 0.299260i | \(0.903260\pi\) | |||||||
\(398\) | 28.4605 | − | 28.4605i | 0.0715088 | − | 0.0715088i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −380.000 | + | 285.000i | −0.950000 | + | 0.712500i | ||||
\(401\) | −252.982 | −0.630878 | −0.315439 | − | 0.948946i | \(-0.602152\pi\) | ||||
−0.315439 | + | 0.948946i | \(0.602152\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 80.0000 | − | 80.0000i | 0.198511 | − | 0.198511i | ||||
\(404\) | − | 15.8114i | − | 0.0391371i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 750.000 | 1.84729 | ||||||||
\(407\) | −158.114 | − | 158.114i | −0.388486 | − | 0.388486i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 348.000i | 0.850856i | 0.904992 | + | 0.425428i | \(0.139876\pi\) | ||||
−0.904992 | + | 0.425428i | \(0.860124\pi\) | |||||||
\(410\) | −158.114 | + | 316.228i | −0.385644 | + | 0.771287i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −35.0000 | − | 35.0000i | −0.0849515 | − | 0.0849515i | ||||
\(413\) | −237.171 | + | 237.171i | −0.574263 | + | 0.574263i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 340.000 | + | 170.000i | 0.819277 | + | 0.409639i | ||||
\(416\) | 221.359 | 0.532114 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 450.000 | − | 450.000i | 1.07656 | − | 1.07656i | ||||
\(419\) | − | 616.644i | − | 1.47170i | −0.677142 | − | 0.735852i | \(-0.736782\pi\) | ||
0.677142 | − | 0.735852i | \(-0.263218\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 338.000 | 0.802850 | 0.401425 | − | 0.915892i | \(-0.368515\pi\) | ||||
0.401425 | + | 0.915892i | \(0.368515\pi\) | |||||||
\(422\) | −471.179 | − | 471.179i | −1.11654 | − | 1.11654i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 240.000i | − | 0.566038i | ||||||
\(425\) | 110.680 | + | 15.8114i | 0.260423 | + | 0.0372033i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 290.000 | + | 290.000i | 0.679157 | + | 0.679157i | ||||
\(428\) | 60.0833 | − | 60.0833i | 0.140381 | − | 0.140381i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 50.0000 | + | 150.000i | 0.116279 | + | 0.348837i | ||||
\(431\) | 221.359 | 0.513595 | 0.256797 | − | 0.966465i | \(-0.417333\pi\) | ||||
0.256797 | + | 0.966465i | \(0.417333\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 145.000 | − | 145.000i | 0.334873 | − | 0.334873i | −0.519561 | − | 0.854434i | \(-0.673904\pi\) |
0.854434 | + | 0.519561i | \(0.173904\pi\) | |||||||
\(434\) | − | 126.491i | − | 0.291454i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −162.000 | −0.371560 | ||||||||
\(437\) | −56.9210 | − | 56.9210i | −0.130254 | − | 0.130254i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 78.0000i | − | 0.177677i | −0.996046 | − | 0.0888383i | \(-0.971685\pi\) | ||
0.996046 | − | 0.0888383i | \(-0.0283154\pi\) | |||||||
\(440\) | −474.342 | − | 237.171i | −1.07805 | − | 0.539025i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −100.000 | − | 100.000i | −0.226244 | − | 0.226244i | ||||
\(443\) | 196.061 | − | 196.061i | 0.442576 | − | 0.442576i | −0.450301 | − | 0.892877i | \(-0.648683\pi\) |
0.892877 | + | 0.450301i | \(0.148683\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −679.890 | −1.52442 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −205.000 | + | 205.000i | −0.457589 | + | 0.457589i | ||||
\(449\) | 284.605i | 0.633864i | 0.948448 | + | 0.316932i | \(0.102653\pi\) | ||||
−0.948448 | + | 0.316932i | \(0.897347\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −500.000 | −1.10865 | ||||||||
\(452\) | −117.004 | − | 117.004i | −0.258859 | − | 0.258859i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 860.000i | 1.89427i | ||||||||
\(455\) | −158.114 | − | 474.342i | −0.347503 | − | 1.04251i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −365.000 | − | 365.000i | −0.798687 | − | 0.798687i | 0.184201 | − | 0.982889i | \(-0.441030\pi\) |
−0.982889 | + | 0.184201i | \(0.941030\pi\) | |||||||
\(458\) | −123.329 | + | 123.329i | −0.269277 | + | 0.269277i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 10.0000 | − | 20.0000i | 0.0217391 | − | 0.0434783i | ||||
\(461\) | 838.004 | 1.81780 | 0.908898 | − | 0.417019i | \(-0.136925\pi\) | ||||
0.908898 | + | 0.417019i | \(0.136925\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −35.0000 | + | 35.0000i | −0.0755940 | + | 0.0755940i | −0.743893 | − | 0.668299i | \(-0.767023\pi\) |
0.668299 | + | 0.743893i | \(0.267023\pi\) | |||||||
\(464\) | 901.249i | 1.94235i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 350.000 | 0.751073 | ||||||||
\(467\) | −117.004 | − | 117.004i | −0.250544 | − | 0.250544i | 0.570649 | − | 0.821194i | \(-0.306692\pi\) |
−0.821194 | + | 0.570649i | \(0.806692\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 700.000i | − | 1.49254i | ||||||
\(470\) | 616.644 | − | 205.548i | 1.31201 | − | 0.437336i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −225.000 | − | 225.000i | −0.476695 | − | 0.476695i | ||||
\(473\) | −158.114 | + | 158.114i | −0.334279 | + | 0.334279i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −270.000 | − | 360.000i | −0.568421 | − | 0.757895i | ||||
\(476\) | −31.6228 | −0.0664344 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −600.000 | + | 600.000i | −1.25523 | + | 1.25523i | ||||
\(479\) | − | 379.473i | − | 0.792220i | −0.918203 | − | 0.396110i | \(-0.870360\pi\) | ||
0.918203 | − | 0.396110i | \(-0.129640\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 200.000 | 0.415800 | ||||||||
\(482\) | 335.201 | + | 335.201i | 0.695439 | + | 0.695439i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 129.000i | 0.266529i | ||||||||
\(485\) | 15.8114 | − | 31.6228i | 0.0326008 | − | 0.0652016i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −125.000 | − | 125.000i | −0.256674 | − | 0.256674i | 0.567026 | − | 0.823700i | \(-0.308094\pi\) |
−0.823700 | + | 0.567026i | \(0.808094\pi\) | |||||||
\(488\) | −275.118 | + | 275.118i | −0.563767 | + | 0.563767i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −10.0000 | − | 5.00000i | −0.0204082 | − | 0.0102041i | ||||
\(491\) | 458.530 | 0.933870 | 0.466935 | − | 0.884292i | \(-0.345358\pi\) | ||||
0.466935 | + | 0.884292i | \(0.345358\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 150.000 | − | 150.000i | 0.304260 | − | 0.304260i | ||||
\(494\) | 569.210i | 1.15225i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 152.000 | 0.306452 | ||||||||
\(497\) | 316.228 | + | 316.228i | 0.636273 | + | 0.636273i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 222.000i | 0.444890i | 0.974945 | + | 0.222445i | \(0.0714037\pi\) | ||||
−0.974945 | + | 0.222445i | \(0.928596\pi\) | |||||||
\(500\) | 71.1512 | − | 102.774i | 0.142302 | − | 0.205548i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 575.000 | + | 575.000i | 1.14542 | + | 1.14542i | ||||
\(503\) | −458.530 | + | 458.530i | −0.911591 | + | 0.911591i | −0.996397 | − | 0.0848065i | \(-0.972973\pi\) |
0.0848065 | + | 0.996397i | \(0.472973\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −25.0000 | − | 75.0000i | −0.0495050 | − | 0.148515i | ||||
\(506\) | 158.114 | 0.312478 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −55.0000 | + | 55.0000i | −0.108268 | + | 0.108268i | ||||
\(509\) | 237.171i | 0.465954i | 0.972482 | + | 0.232977i | \(0.0748468\pi\) | ||||
−0.972482 | + | 0.232977i | \(0.925153\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −550.000 | −1.07632 | ||||||||
\(512\) | −150.208 | − | 150.208i | −0.293375 | − | 0.293375i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 970.000i | − | 1.88716i | ||||||
\(515\) | −221.359 | − | 110.680i | −0.429824 | − | 0.214912i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 650.000 | + | 650.000i | 1.25725 | + | 1.25725i | ||||
\(518\) | 158.114 | − | 158.114i | 0.305239 | − | 0.305239i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 450.000 | − | 150.000i | 0.865385 | − | 0.288462i | ||||
\(521\) | 790.569 | 1.51741 | 0.758704 | − | 0.651436i | \(-0.225833\pi\) | ||||
0.758704 | + | 0.651436i | \(0.225833\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 370.000 | − | 370.000i | 0.707457 | − | 0.707457i | −0.258543 | − | 0.966000i | \(-0.583242\pi\) |
0.966000 | + | 0.258543i | \(0.0832423\pi\) | |||||||
\(524\) | 173.925i | 0.331918i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −910.000 | −1.73004 | ||||||||
\(527\) | −25.2982 | − | 25.2982i | −0.0480042 | − | 0.0480042i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 509.000i | 0.962193i | ||||||||
\(530\) | 126.491 | + | 379.473i | 0.238662 | + | 0.715987i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 90.0000 | + | 90.0000i | 0.169173 | + | 0.169173i | ||||
\(533\) | 316.228 | − | 316.228i | 0.593298 | − | 0.593298i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 190.000 | − | 380.000i | 0.355140 | − | 0.710280i | ||||
\(536\) | 664.078 | 1.23895 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −225.000 | + | 225.000i | −0.418216 | + | 0.418216i | ||||
\(539\) | − | 15.8114i | − | 0.0293347i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 362.000 | 0.669131 | 0.334566 | − | 0.942372i | \(-0.391410\pi\) | ||||
0.334566 | + | 0.942372i | \(0.391410\pi\) | |||||||
\(542\) | −281.443 | − | 281.443i | −0.519267 | − | 0.519267i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 70.0000i | − | 0.128676i | ||||||
\(545\) | −768.433 | + | 256.144i | −1.40997 | + | 0.469990i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 490.000 | + | 490.000i | 0.895795 | + | 0.895795i | 0.995061 | − | 0.0992657i | \(-0.0316494\pi\) |
−0.0992657 | + | 0.995061i | \(0.531649\pi\) | |||||||
\(548\) | −15.8114 | + | 15.8114i | −0.0288529 | + | 0.0288529i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 875.000 | + | 125.000i | 1.59091 | + | 0.227273i | ||||
\(551\) | −853.815 | −1.54957 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 60.0000 | − | 60.0000i | 0.108499 | − | 0.108499i | ||||
\(554\) | − | 727.324i | − | 1.31286i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 102.000 | 0.183453 | ||||||||
\(557\) | 252.982 | + | 252.982i | 0.454187 | + | 0.454187i | 0.896742 | − | 0.442555i | \(-0.145928\pi\) |
−0.442555 | + | 0.896742i | \(0.645928\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 200.000i | − | 0.357782i | ||||||
\(560\) | 300.416 | − | 600.833i | 0.536458 | − | 1.07292i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −250.000 | − | 250.000i | −0.444840 | − | 0.444840i | ||||
\(563\) | −202.386 | + | 202.386i | −0.359477 | + | 0.359477i | −0.863620 | − | 0.504143i | \(-0.831808\pi\) |
0.504143 | + | 0.863620i | \(0.331808\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −740.000 | − | 370.000i | −1.30973 | − | 0.654867i | ||||
\(566\) | −1106.80 | −1.95547 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −300.000 | + | 300.000i | −0.528169 | + | 0.528169i | ||||
\(569\) | 189.737i | 0.333456i | 0.986003 | + | 0.166728i | \(0.0533202\pi\) | ||||
−0.986003 | + | 0.166728i | \(0.946680\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −658.000 | −1.15236 | −0.576182 | − | 0.817321i | \(-0.695458\pi\) | ||||
−0.576182 | + | 0.817321i | \(0.695458\pi\) | |||||||
\(572\) | −158.114 | − | 158.114i | −0.276423 | − | 0.276423i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 500.000i | − | 0.871080i | ||||||
\(575\) | 15.8114 | − | 110.680i | 0.0274981 | − | 0.192486i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −35.0000 | − | 35.0000i | −0.0606586 | − | 0.0606586i | 0.676127 | − | 0.736785i | \(-0.263657\pi\) |
−0.736785 | + | 0.676127i | \(0.763657\pi\) | |||||||
\(578\) | 425.326 | − | 425.326i | 0.735859 | − | 0.735859i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −75.0000 | − | 225.000i | −0.129310 | − | 0.387931i | ||||
\(581\) | −537.587 | −0.925279 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −400.000 | + | 400.000i | −0.686106 | + | 0.686106i | ||||
\(584\) | − | 521.776i | − | 0.893452i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −640.000 | −1.09215 | ||||||||
\(587\) | −154.952 | − | 154.952i | −0.263972 | − | 0.263972i | 0.562694 | − | 0.826666i | \(-0.309765\pi\) |
−0.826666 | + | 0.562694i | \(0.809765\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 144.000i | 0.244482i | ||||||||
\(590\) | 474.342 | + | 237.171i | 0.803969 | + | 0.401984i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 190.000 | + | 190.000i | 0.320946 | + | 0.320946i | ||||
\(593\) | 167.601 | − | 167.601i | 0.282632 | − | 0.282632i | −0.551526 | − | 0.834158i | \(-0.685954\pi\) |
0.834158 | + | 0.551526i | \(0.185954\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −150.000 | + | 50.0000i | −0.252101 | + | 0.0840336i | ||||
\(596\) | 47.4342 | 0.0795875 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −100.000 | + | 100.000i | −0.167224 | + | 0.167224i | ||||
\(599\) | − | 1043.55i | − | 1.74216i | −0.491144 | − | 0.871078i | \(-0.663421\pi\) | ||
0.491144 | − | 0.871078i | \(-0.336579\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −382.000 | −0.635607 | −0.317804 | − | 0.948157i | \(-0.602945\pi\) | ||||
−0.317804 | + | 0.948157i | \(0.602945\pi\) | |||||||
\(602\) | −158.114 | − | 158.114i | −0.262648 | − | 0.262648i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 22.0000i | − | 0.0364238i | ||||||
\(605\) | 203.967 | + | 611.901i | 0.337135 | + | 1.01141i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 655.000 | + | 655.000i | 1.07908 | + | 1.07908i | 0.996592 | + | 0.0824851i | \(0.0262857\pi\) |
0.0824851 | + | 0.996592i | \(0.473714\pi\) | |||||||
\(608\) | −199.223 | + | 199.223i | −0.327670 | + | 0.327670i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 290.000 | − | 580.000i | 0.475410 | − | 0.950820i | ||||
\(611\) | −822.192 | −1.34565 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −620.000 | + | 620.000i | −1.01142 | + | 1.01142i | −0.0114852 | + | 0.999934i | \(0.503656\pi\) |
−0.999934 | + | 0.0114852i | \(0.996344\pi\) | |||||||
\(614\) | 600.833i | 0.978555i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 750.000 | 1.21753 | ||||||||
\(617\) | 34.7851 | + | 34.7851i | 0.0563777 | + | 0.0563777i | 0.734734 | − | 0.678356i | \(-0.237307\pi\) |
−0.678356 | + | 0.734734i | \(0.737307\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 258.000i | − | 0.416801i | −0.978044 | − | 0.208401i | \(-0.933174\pi\) | ||
0.978044 | − | 0.208401i | \(-0.0668258\pi\) | |||||||
\(620\) | −37.9473 | + | 12.6491i | −0.0612054 | + | 0.0204018i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −400.000 | − | 400.000i | −0.643087 | − | 0.643087i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 175.000 | − | 600.000i | 0.280000 | − | 0.960000i | ||||
\(626\) | 458.530 | 0.732476 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 200.000 | − | 200.000i | 0.318471 | − | 0.318471i | ||||
\(629\) | − | 63.2456i | − | 0.100549i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 812.000 | 1.28685 | 0.643423 | − | 0.765511i | \(-0.277514\pi\) | ||||
0.643423 | + | 0.765511i | \(0.277514\pi\) | |||||||
\(632\) | 56.9210 | + | 56.9210i | 0.0900649 | + | 0.0900649i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 50.0000i | 0.0788644i | ||||||||
\(635\) | −173.925 | + | 347.851i | −0.273898 | + | 0.547796i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.0000 | + | 10.0000i | 0.0156986 | + | 0.0156986i | ||||
\(638\) | 1185.85 | − | 1185.85i | 1.85871 | − | 1.85871i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 690.000 | + | 345.000i | 1.07812 | + | 0.539062i | ||||
\(641\) | −442.719 | −0.690669 | −0.345335 | − | 0.938480i | \(-0.612235\pi\) | ||||
−0.345335 | + | 0.938480i | \(0.612235\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 820.000 | − | 820.000i | 1.27527 | − | 1.27527i | 0.331989 | − | 0.943283i | \(-0.392280\pi\) |
0.943283 | − | 0.331989i | \(-0.107720\pi\) | |||||||
\(644\) | 31.6228i | 0.0491037i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 180.000 | 0.278638 | ||||||||
\(647\) | 679.890 | + | 679.890i | 1.05083 | + | 1.05083i | 0.998637 | + | 0.0521974i | \(0.0166225\pi\) |
0.0521974 | + | 0.998637i | \(0.483378\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 750.000i | 1.15562i | ||||||||
\(650\) | −632.456 | + | 474.342i | −0.973009 | + | 0.729756i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 100.000 | + | 100.000i | 0.153374 | + | 0.153374i | ||||
\(653\) | −515.451 | + | 515.451i | −0.789359 | + | 0.789359i | −0.981389 | − | 0.192030i | \(-0.938493\pi\) |
0.192030 | + | 0.981389i | \(0.438493\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 275.000 | + | 825.000i | 0.419847 | + | 1.25954i | ||||
\(656\) | 600.833 | 0.915904 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −650.000 | + | 650.000i | −0.987842 | + | 0.987842i | ||||
\(659\) | 901.249i | 1.36760i | 0.729669 | + | 0.683801i | \(0.239674\pi\) | ||||
−0.729669 | + | 0.683801i | \(0.760326\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −802.000 | −1.21331 | −0.606657 | − | 0.794964i | \(-0.707490\pi\) | ||||
−0.606657 | + | 0.794964i | \(0.707490\pi\) | |||||||
\(662\) | 762.109 | + | 762.109i | 1.15122 | + | 1.15122i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 510.000i | − | 0.768072i | ||||||
\(665\) | 569.210 | + | 284.605i | 0.855955 | + | 0.427977i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −150.000 | − | 150.000i | −0.224888 | − | 0.224888i | ||||
\(668\) | −148.627 | + | 148.627i | −0.222496 | + | 0.222496i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1050.00 | + | 350.000i | −1.56716 | + | 0.522388i | ||||
\(671\) | 917.061 | 1.36671 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 775.000 | − | 775.000i | 1.15156 | − | 1.15156i | 0.165320 | − | 0.986240i | \(-0.447134\pi\) |
0.986240 | − | 0.165320i | \(-0.0528658\pi\) | |||||||
\(674\) | − | 490.153i | − | 0.727230i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 31.0000 | 0.0458580 | ||||||||
\(677\) | −496.478 | − | 496.478i | −0.733349 | − | 0.733349i | 0.237932 | − | 0.971282i | \(-0.423530\pi\) |
−0.971282 | + | 0.237932i | \(0.923530\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 50.0000i | 0.0736377i | ||||||||
\(680\) | −47.4342 | − | 142.302i | −0.0697561 | − | 0.209268i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −200.000 | − | 200.000i | −0.293255 | − | 0.293255i | ||||
\(683\) | −60.0833 | + | 60.0833i | −0.0879697 | + | 0.0879697i | −0.749722 | − | 0.661753i | \(-0.769813\pi\) |
0.661753 | + | 0.749722i | \(0.269813\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −50.0000 | + | 100.000i | −0.0729927 | + | 0.145985i | ||||
\(686\) | −758.947 | −1.10634 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 190.000 | − | 190.000i | 0.276163 | − | 0.276163i | ||||
\(689\) | − | 505.964i | − | 0.734346i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −562.000 | −0.813314 | −0.406657 | − | 0.913581i | \(-0.633306\pi\) | ||||
−0.406657 | + | 0.913581i | \(0.633306\pi\) | |||||||
\(692\) | 110.680 | + | 110.680i | 0.159942 | + | 0.159942i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 520.000i | − | 0.749280i | ||||||
\(695\) | 483.828 | − | 161.276i | 0.696156 | − | 0.232052i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −100.000 | − | 100.000i | −0.143472 | − | 0.143472i | ||||
\(698\) | −502.802 | + | 502.802i | −0.720347 | + | 0.720347i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −25.0000 | + | 175.000i | −0.0357143 | + | 0.250000i | ||||
\(701\) | 363.662 | 0.518776 | 0.259388 | − | 0.965773i | \(-0.416479\pi\) | ||||
0.259388 | + | 0.965773i | \(0.416479\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −180.000 | + | 180.000i | −0.256046 | + | 0.256046i | ||||
\(704\) | 648.267i | 0.920834i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 710.000 | 1.00567 | ||||||||
\(707\) | 79.0569 | + | 79.0569i | 0.111820 | + | 0.111820i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 498.000i | 0.702398i | 0.936301 | + | 0.351199i | \(0.114226\pi\) | ||||
−0.936301 | + | 0.351199i | \(0.885774\pi\) | |||||||
\(710\) | 316.228 | − | 632.456i | 0.445391 | − | 0.890782i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −25.2982 | + | 25.2982i | −0.0354814 | + | 0.0354814i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1000.00 | − | 500.000i | −1.39860 | − | 0.699301i | ||||
\(716\) | 142.302 | 0.198747 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −450.000 | + | 450.000i | −0.626741 | + | 0.626741i | ||||
\(719\) | 569.210i | 0.791669i | 0.918322 | + | 0.395834i | \(0.129545\pi\) | ||||
−0.918322 | + | 0.395834i | \(0.870455\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 350.000 | 0.485437 | ||||||||
\(722\) | 58.5021 | + | 58.5021i | 0.0810279 | + | 0.0810279i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 218.000i | 0.301105i | ||||||||
\(725\) | −711.512 | − | 948.683i | −0.981397 | − | 1.30853i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −905.000 | − | 905.000i | −1.24484 | − | 1.24484i | −0.957969 | − | 0.286873i | \(-0.907384\pi\) |
−0.286873 | − | 0.957969i | \(-0.592616\pi\) | |||||||
\(728\) | −474.342 | + | 474.342i | −0.651568 | + | 0.651568i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 275.000 | + | 825.000i | 0.376712 | + | 1.13014i | ||||
\(731\) | −63.2456 | −0.0865192 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 550.000 | − | 550.000i | 0.750341 | − | 0.750341i | −0.224202 | − | 0.974543i | \(-0.571977\pi\) |
0.974543 | + | 0.224202i | \(0.0719774\pi\) | |||||||
\(734\) | − | 585.021i | − | 0.797032i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −70.0000 | −0.0951087 | ||||||||
\(737\) | −1106.80 | − | 1106.80i | −1.50176 | − | 1.50176i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 198.000i | 0.267930i | 0.990986 | + | 0.133965i | \(0.0427709\pi\) | ||||
−0.990986 | + | 0.133965i | \(0.957229\pi\) | |||||||
\(740\) | −63.2456 | − | 31.6228i | −0.0854670 | − | 0.0427335i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −400.000 | − | 400.000i | −0.539084 | − | 0.539084i | ||||
\(743\) | 964.495 | − | 964.495i | 1.29811 | − | 1.29811i | 0.368468 | − | 0.929640i | \(-0.379882\pi\) |
0.929640 | − | 0.368468i | \(-0.120118\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 225.000 | − | 75.0000i | 0.302013 | − | 0.100671i | ||||
\(746\) | 316.228 | 0.423898 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −50.0000 | + | 50.0000i | −0.0668449 | + | 0.0668449i | ||||
\(749\) | 600.833i | 0.802180i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 728.000 | 0.969374 | 0.484687 | − | 0.874688i | \(-0.338933\pi\) | ||||
0.484687 | + | 0.874688i | \(0.338933\pi\) | |||||||
\(752\) | −781.083 | − | 781.083i | −1.03867 | − | 1.03867i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1500.00i | 1.98939i | ||||||||
\(755\) | −34.7851 | − | 104.355i | −0.0460729 | − | 0.138219i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −170.000 | − | 170.000i | −0.224571 | − | 0.224571i | 0.585849 | − | 0.810420i | \(-0.300761\pi\) |
−0.810420 | + | 0.585849i | \(0.800761\pi\) | |||||||
\(758\) | −882.275 | + | 882.275i | −1.16395 | + | 1.16395i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −270.000 | + | 540.000i | −0.355263 | + | 0.710526i | ||||
\(761\) | 31.6228 | 0.0415542 | 0.0207771 | − | 0.999784i | \(-0.493386\pi\) | ||||
0.0207771 | + | 0.999784i | \(0.493386\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 810.000 | − | 810.000i | 1.06160 | − | 1.06160i | ||||
\(764\) | − | 158.114i | − | 0.206955i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 890.000 | 1.16188 | ||||||||
\(767\) | −474.342 | − | 474.342i | −0.618438 | − | 0.618438i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 318.000i | − | 0.413524i | −0.978391 | − | 0.206762i | \(-0.933707\pi\) | ||
0.978391 | − | 0.206762i | \(-0.0662926\pi\) | |||||||
\(770\) | −1185.85 | + | 395.285i | −1.54007 | + | 0.513357i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −125.000 | − | 125.000i | −0.161917 | − | 0.161917i | ||||
\(773\) | 452.206 | − | 452.206i | 0.585001 | − | 0.585001i | −0.351272 | − | 0.936273i | \(-0.614251\pi\) |
0.936273 | + | 0.351272i | \(0.114251\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −160.000 | + | 120.000i | −0.206452 | + | 0.154839i | ||||
\(776\) | −47.4342 | −0.0611265 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 825.000 | − | 825.000i | 1.06041 | − | 1.06041i | ||||
\(779\) | 569.210i | 0.730693i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1000.00 | 1.28041 | ||||||||
\(782\) | 31.6228 | + | 31.6228i | 0.0404383 | + | 0.0404383i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 19.0000i |