Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [845,2,Mod(844,845)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(845, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("845.844");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 845 = 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 845.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.74735897080\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.49787136.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 65) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 844.8 | ||
Root | \(0.228425 - 1.39564i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 845.844 |
Dual form | 845.2.d.c.844.7 |
$q$-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 \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).
\(n\) | \(171\) | \(677\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.18890 | 1.54779 | 0.773893 | − | 0.633316i | \(-0.218307\pi\) | ||||
0.773893 | + | 0.633316i | \(0.218307\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | 0.957427 | + | 0.288675i | \(0.0932147\pi\) | ||||
−0.957427 | + | 0.288675i | \(0.906785\pi\) | |||||||
\(4\) | 2.79129 | 1.39564 | ||||||||
\(5\) | 0.456850 | − | 2.18890i | 0.204310 | − | 0.978906i | ||||
\(6\) | 2.18890i | 0.893615i | ||||||||
\(7\) | 1.73205 | 0.654654 | 0.327327 | − | 0.944911i | \(-0.393852\pi\) | ||||
0.327327 | + | 0.944911i | \(0.393852\pi\) | |||||||
\(8\) | 1.73205 | 0.612372 | ||||||||
\(9\) | 2.00000 | 0.666667 | ||||||||
\(10\) | 1.00000 | − | 4.79129i | 0.316228 | − | 1.51514i | ||||
\(11\) | 2.64575i | 0.797724i | 0.917011 | + | 0.398862i | \(0.130595\pi\) | ||||
−0.917011 | + | 0.398862i | \(0.869405\pi\) | |||||||
\(12\) | 2.79129i | 0.805775i | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 3.79129 | 1.01326 | ||||||||
\(15\) | 2.18890 | + | 0.456850i | 0.565172 | + | 0.117958i | ||||
\(16\) | −1.79129 | −0.447822 | ||||||||
\(17\) | − | 4.58258i | − | 1.11144i | −0.831370 | − | 0.555719i | \(-0.812443\pi\) | ||
0.831370 | − | 0.555719i | \(-0.187557\pi\) | |||||||
\(18\) | 4.37780 | 1.03186 | ||||||||
\(19\) | 1.73205i | 0.397360i | 0.980064 | + | 0.198680i | \(0.0636654\pi\) | ||||
−0.980064 | + | 0.198680i | \(0.936335\pi\) | |||||||
\(20\) | 1.27520 | − | 6.10985i | 0.285144 | − | 1.36620i | ||||
\(21\) | 1.73205i | 0.377964i | ||||||||
\(22\) | 5.79129i | 1.23471i | ||||||||
\(23\) | − | 4.58258i | − | 0.955533i | −0.878487 | − | 0.477767i | \(-0.841446\pi\) | ||
0.878487 | − | 0.477767i | \(-0.158554\pi\) | |||||||
\(24\) | 1.73205i | 0.353553i | ||||||||
\(25\) | −4.58258 | − | 2.00000i | −0.916515 | − | 0.400000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.00000i | 0.962250i | ||||||||
\(28\) | 4.83465 | 0.913663 | ||||||||
\(29\) | 4.58258 | 0.850963 | 0.425481 | − | 0.904967i | \(-0.360105\pi\) | ||||
0.425481 | + | 0.904967i | \(0.360105\pi\) | |||||||
\(30\) | 4.79129 | + | 1.00000i | 0.874765 | + | 0.182574i | ||||
\(31\) | 9.66930i | 1.73666i | 0.495988 | + | 0.868329i | \(0.334806\pi\) | ||||
−0.495988 | + | 0.868329i | \(0.665194\pi\) | |||||||
\(32\) | −7.38505 | −1.30551 | ||||||||
\(33\) | −2.64575 | −0.460566 | ||||||||
\(34\) | − | 10.0308i | − | 1.72027i | ||||||
\(35\) | 0.791288 | − | 3.79129i | 0.133752 | − | 0.640845i | ||||
\(36\) | 5.58258 | 0.930429 | ||||||||
\(37\) | 7.93725 | 1.30488 | 0.652438 | − | 0.757842i | \(-0.273746\pi\) | ||||
0.652438 | + | 0.757842i | \(0.273746\pi\) | |||||||
\(38\) | 3.79129i | 0.615028i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.791288 | − | 3.79129i | 0.125114 | − | 0.599455i | ||||
\(41\) | − | 2.64575i | − | 0.413197i | −0.978426 | − | 0.206598i | \(-0.933761\pi\) | ||
0.978426 | − | 0.206598i | \(-0.0662394\pi\) | |||||||
\(42\) | 3.79129i | 0.585008i | ||||||||
\(43\) | 1.41742i | 0.216155i | 0.994142 | + | 0.108078i | \(0.0344695\pi\) | ||||
−0.994142 | + | 0.108078i | \(0.965531\pi\) | |||||||
\(44\) | 7.38505i | 1.11334i | ||||||||
\(45\) | 0.913701 | − | 4.37780i | 0.136206 | − | 0.652604i | ||||
\(46\) | − | 10.0308i | − | 1.47896i | ||||||
\(47\) | −8.75560 | −1.27714 | −0.638568 | − | 0.769565i | \(-0.720473\pi\) | ||||
−0.638568 | + | 0.769565i | \(0.720473\pi\) | |||||||
\(48\) | − | 1.79129i | − | 0.258550i | ||||||
\(49\) | −4.00000 | −0.571429 | ||||||||
\(50\) | −10.0308 | − | 4.37780i | −1.41857 | − | 0.619115i | ||||
\(51\) | 4.58258 | 0.641689 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 1.58258i | − | 0.217383i | −0.994076 | − | 0.108692i | \(-0.965334\pi\) | ||
0.994076 | − | 0.108692i | \(-0.0346661\pi\) | |||||||
\(54\) | 10.9445i | 1.48936i | ||||||||
\(55\) | 5.79129 | + | 1.20871i | 0.780897 | + | 0.162983i | ||||
\(56\) | 3.00000 | 0.400892 | ||||||||
\(57\) | −1.73205 | −0.229416 | ||||||||
\(58\) | 10.0308 | 1.31711 | ||||||||
\(59\) | 3.36875i | 0.438574i | 0.975660 | + | 0.219287i | \(0.0703731\pi\) | ||||
−0.975660 | + | 0.219287i | \(0.929627\pi\) | |||||||
\(60\) | 6.10985 | + | 1.27520i | 0.788779 | + | 0.164628i | ||||
\(61\) | −10.5826 | −1.35496 | −0.677480 | − | 0.735541i | \(-0.736928\pi\) | ||||
−0.677480 | + | 0.735541i | \(0.736928\pi\) | |||||||
\(62\) | 21.1652i | 2.68798i | ||||||||
\(63\) | 3.46410 | 0.436436 | ||||||||
\(64\) | −12.5826 | −1.57282 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.79129 | −0.712858 | ||||||||
\(67\) | −14.8655 | −1.81610 | −0.908052 | − | 0.418857i | \(-0.862431\pi\) | ||||
−0.908052 | + | 0.418857i | \(0.862431\pi\) | |||||||
\(68\) | − | 12.7913i | − | 1.55117i | ||||||
\(69\) | 4.58258 | 0.551677 | ||||||||
\(70\) | 1.73205 | − | 8.29875i | 0.207020 | − | 0.991891i | ||||
\(71\) | 3.55945i | 0.422429i | 0.977440 | + | 0.211215i | \(0.0677419\pi\) | ||||
−0.977440 | + | 0.211215i | \(0.932258\pi\) | |||||||
\(72\) | 3.46410 | 0.408248 | ||||||||
\(73\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(74\) | 17.3739 | 2.01967 | ||||||||
\(75\) | 2.00000 | − | 4.58258i | 0.230940 | − | 0.529150i | ||||
\(76\) | 4.83465i | 0.554573i | ||||||||
\(77\) | 4.58258i | 0.522233i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.00000 | 0.675053 | 0.337526 | − | 0.941316i | \(-0.390410\pi\) | ||||
0.337526 | + | 0.941316i | \(0.390410\pi\) | |||||||
\(80\) | −0.818350 | + | 3.92095i | −0.0914943 | + | 0.438376i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 5.79129i | − | 0.639541i | ||||||
\(83\) | −11.3060 | −1.24100 | −0.620498 | − | 0.784208i | \(-0.713069\pi\) | ||||
−0.620498 | + | 0.784208i | \(0.713069\pi\) | |||||||
\(84\) | 4.83465i | 0.527504i | ||||||||
\(85\) | −10.0308 | − | 2.09355i | −1.08799 | − | 0.227077i | ||||
\(86\) | 3.10260i | 0.334562i | ||||||||
\(87\) | 4.58258i | 0.491304i | ||||||||
\(88\) | 4.58258i | 0.488504i | ||||||||
\(89\) | 4.28245i | 0.453939i | 0.973902 | + | 0.226969i | \(0.0728818\pi\) | ||||
−0.973902 | + | 0.226969i | \(0.927118\pi\) | |||||||
\(90\) | 2.00000 | − | 9.58258i | 0.210819 | − | 1.01009i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 12.7913i | − | 1.33358i | ||||||
\(93\) | −9.66930 | −1.00266 | ||||||||
\(94\) | −19.1652 | −1.97673 | ||||||||
\(95\) | 3.79129 | + | 0.791288i | 0.388978 | + | 0.0811844i | ||||
\(96\) | − | 7.38505i | − | 0.753734i | ||||||
\(97\) | −4.47315 | −0.454180 | −0.227090 | − | 0.973874i | \(-0.572921\pi\) | ||||
−0.227090 | + | 0.973874i | \(0.572921\pi\) | |||||||
\(98\) | −8.75560 | −0.884450 | ||||||||
\(99\) | 5.29150i | 0.531816i | ||||||||
\(100\) | −12.7913 | − | 5.58258i | −1.27913 | − | 0.558258i | ||||
\(101\) | 9.00000 | 0.895533 | 0.447767 | − | 0.894150i | \(-0.352219\pi\) | ||||
0.447767 | + | 0.894150i | \(0.352219\pi\) | |||||||
\(102\) | 10.0308 | 0.993198 | ||||||||
\(103\) | − | 15.1652i | − | 1.49427i | −0.664674 | − | 0.747133i | \(-0.731430\pi\) | ||
0.664674 | − | 0.747133i | \(-0.268570\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.79129 | + | 0.791288i | 0.369992 | + | 0.0772218i | ||||
\(106\) | − | 3.46410i | − | 0.336463i | ||||||
\(107\) | 1.41742i | 0.137028i | 0.997650 | + | 0.0685138i | \(0.0218257\pi\) | ||||
−0.997650 | + | 0.0685138i | \(0.978174\pi\) | |||||||
\(108\) | 13.9564i | 1.34296i | ||||||||
\(109\) | − | 2.74110i | − | 0.262550i | −0.991346 | − | 0.131275i | \(-0.958093\pi\) | ||
0.991346 | − | 0.131275i | \(-0.0419071\pi\) | |||||||
\(110\) | 12.6766 | + | 2.64575i | 1.20866 | + | 0.252262i | ||||
\(111\) | 7.93725i | 0.753371i | ||||||||
\(112\) | −3.10260 | −0.293168 | ||||||||
\(113\) | − | 16.5826i | − | 1.55996i | −0.625806 | − | 0.779979i | \(-0.715230\pi\) | ||
0.625806 | − | 0.779979i | \(-0.284770\pi\) | |||||||
\(114\) | −3.79129 | −0.355087 | ||||||||
\(115\) | −10.0308 | − | 2.09355i | −0.935377 | − | 0.195225i | ||||
\(116\) | 12.7913 | 1.18764 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.37386i | 0.678819i | ||||||||
\(119\) | − | 7.93725i | − | 0.727607i | ||||||
\(120\) | 3.79129 | + | 0.791288i | 0.346096 | + | 0.0722344i | ||||
\(121\) | 4.00000 | 0.363636 | ||||||||
\(122\) | −23.1642 | −2.09719 | ||||||||
\(123\) | 2.64575 | 0.238559 | ||||||||
\(124\) | 26.9898i | 2.42376i | ||||||||
\(125\) | −6.47135 | + | 9.11710i | −0.578815 | + | 0.815459i | ||||
\(126\) | 7.58258 | 0.675510 | ||||||||
\(127\) | 9.74773i | 0.864971i | 0.901641 | + | 0.432485i | \(0.142363\pi\) | ||||
−0.901641 | + | 0.432485i | \(0.857637\pi\) | |||||||
\(128\) | −12.7719 | −1.12889 | ||||||||
\(129\) | −1.41742 | −0.124797 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.58258 | 0.138270 | 0.0691351 | − | 0.997607i | \(-0.477976\pi\) | ||||
0.0691351 | + | 0.997607i | \(0.477976\pi\) | |||||||
\(132\) | −7.38505 | −0.642786 | ||||||||
\(133\) | 3.00000i | 0.260133i | ||||||||
\(134\) | −32.5390 | −2.81094 | ||||||||
\(135\) | 10.9445 | + | 2.28425i | 0.941953 | + | 0.196597i | ||||
\(136\) | − | 7.93725i | − | 0.680614i | ||||||
\(137\) | 0.0953502 | 0.00814632 | 0.00407316 | − | 0.999992i | \(-0.498703\pi\) | ||||
0.00407316 | + | 0.999992i | \(0.498703\pi\) | |||||||
\(138\) | 10.0308 | 0.853879 | ||||||||
\(139\) | −5.74773 | −0.487516 | −0.243758 | − | 0.969836i | \(-0.578380\pi\) | ||||
−0.243758 | + | 0.969836i | \(0.578380\pi\) | |||||||
\(140\) | 2.20871 | − | 10.5826i | 0.186670 | − | 0.894391i | ||||
\(141\) | − | 8.75560i | − | 0.737355i | ||||||
\(142\) | 7.79129i | 0.653830i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −3.58258 | −0.298548 | ||||||||
\(145\) | 2.09355 | − | 10.0308i | 0.173860 | − | 0.833013i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 4.00000i | − | 0.329914i | ||||||
\(148\) | 22.1552 | 1.82114 | ||||||||
\(149\) | − | 9.76465i | − | 0.799952i | −0.916526 | − | 0.399976i | \(-0.869019\pi\) | ||
0.916526 | − | 0.399976i | \(-0.130981\pi\) | |||||||
\(150\) | 4.37780 | − | 10.0308i | 0.357446 | − | 0.819012i | ||||
\(151\) | − | 6.20520i | − | 0.504972i | −0.967601 | − | 0.252486i | \(-0.918752\pi\) | ||
0.967601 | − | 0.252486i | \(-0.0812482\pi\) | |||||||
\(152\) | 3.00000i | 0.243332i | ||||||||
\(153\) | − | 9.16515i | − | 0.740959i | ||||||
\(154\) | 10.0308i | 0.808305i | ||||||||
\(155\) | 21.1652 | + | 4.41742i | 1.70003 | + | 0.354816i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.16515i | 0.731459i | 0.930721 | + | 0.365729i | \(0.119180\pi\) | ||||
−0.930721 | + | 0.365729i | \(0.880820\pi\) | |||||||
\(158\) | 13.1334 | 1.04484 | ||||||||
\(159\) | 1.58258 | 0.125506 | ||||||||
\(160\) | −3.37386 | + | 16.1652i | −0.266727 | + | 1.27797i | ||||
\(161\) | − | 7.93725i | − | 0.625543i | ||||||
\(162\) | 2.18890 | 0.171976 | ||||||||
\(163\) | 10.6784 | 0.836393 | 0.418197 | − | 0.908357i | \(-0.362662\pi\) | ||||
0.418197 | + | 0.908357i | \(0.362662\pi\) | |||||||
\(164\) | − | 7.38505i | − | 0.576676i | ||||||
\(165\) | −1.20871 | + | 5.79129i | −0.0940981 | + | 0.450851i | ||||
\(166\) | −24.7477 | −1.92080 | ||||||||
\(167\) | 4.28245 | 0.331386 | 0.165693 | − | 0.986177i | \(-0.447014\pi\) | ||||
0.165693 | + | 0.986177i | \(0.447014\pi\) | |||||||
\(168\) | 3.00000i | 0.231455i | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −21.9564 | − | 4.58258i | −1.68398 | − | 0.351468i | ||||
\(171\) | 3.46410i | 0.264906i | ||||||||
\(172\) | 3.95644i | 0.301676i | ||||||||
\(173\) | − | 7.41742i | − | 0.563936i | −0.959424 | − | 0.281968i | \(-0.909013\pi\) | ||
0.959424 | − | 0.281968i | \(-0.0909873\pi\) | |||||||
\(174\) | 10.0308i | 0.760433i | ||||||||
\(175\) | −7.93725 | − | 3.46410i | −0.600000 | − | 0.261861i | ||||
\(176\) | − | 4.73930i | − | 0.357238i | ||||||
\(177\) | −3.36875 | −0.253211 | ||||||||
\(178\) | 9.37386i | 0.702601i | ||||||||
\(179\) | 0.165151 | 0.0123440 | 0.00617200 | − | 0.999981i | \(-0.498035\pi\) | ||||
0.00617200 | + | 0.999981i | \(0.498035\pi\) | |||||||
\(180\) | 2.55040 | − | 12.2197i | 0.190096 | − | 0.910803i | ||||
\(181\) | −18.7477 | −1.39351 | −0.696754 | − | 0.717310i | \(-0.745373\pi\) | ||||
−0.696754 | + | 0.717310i | \(0.745373\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 10.5826i | − | 0.782287i | ||||||
\(184\) | − | 7.93725i | − | 0.585142i | ||||||
\(185\) | 3.62614 | − | 17.3739i | 0.266599 | − | 1.27735i | ||||
\(186\) | −21.1652 | −1.55190 | ||||||||
\(187\) | 12.1244 | 0.886621 | ||||||||
\(188\) | −24.4394 | −1.78243 | ||||||||
\(189\) | 8.66025i | 0.629941i | ||||||||
\(190\) | 8.29875 | + | 1.73205i | 0.602055 | + | 0.125656i | ||||
\(191\) | −7.41742 | −0.536706 | −0.268353 | − | 0.963321i | \(-0.586479\pi\) | ||||
−0.268353 | + | 0.963321i | \(0.586479\pi\) | |||||||
\(192\) | − | 12.5826i | − | 0.908069i | ||||||
\(193\) | 1.00905 | 0.0726331 | 0.0363165 | − | 0.999340i | \(-0.488438\pi\) | ||||
0.0363165 | + | 0.999340i | \(0.488438\pi\) | |||||||
\(194\) | −9.79129 | −0.702973 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −11.1652 | −0.797511 | ||||||||
\(197\) | 19.9663 | 1.42254 | 0.711269 | − | 0.702920i | \(-0.248121\pi\) | ||||
0.711269 | + | 0.702920i | \(0.248121\pi\) | |||||||
\(198\) | 11.5826i | 0.823138i | ||||||||
\(199\) | −1.41742 | −0.100479 | −0.0502393 | − | 0.998737i | \(-0.515998\pi\) | ||||
−0.0502393 | + | 0.998737i | \(0.515998\pi\) | |||||||
\(200\) | −7.93725 | − | 3.46410i | −0.561249 | − | 0.244949i | ||||
\(201\) | − | 14.8655i | − | 1.04853i | ||||||
\(202\) | 19.7001 | 1.38609 | ||||||||
\(203\) | 7.93725 | 0.557086 | ||||||||
\(204\) | 12.7913 | 0.895569 | ||||||||
\(205\) | −5.79129 | − | 1.20871i | −0.404481 | − | 0.0844201i | ||||
\(206\) | − | 33.1950i | − | 2.31281i | ||||||
\(207\) | − | 9.16515i | − | 0.637022i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.58258 | −0.316983 | ||||||||
\(210\) | 8.29875 | + | 1.73205i | 0.572668 | + | 0.119523i | ||||
\(211\) | 18.1652 | 1.25054 | 0.625270 | − | 0.780408i | \(-0.284989\pi\) | ||||
0.625270 | + | 0.780408i | \(0.284989\pi\) | |||||||
\(212\) | − | 4.41742i | − | 0.303390i | ||||||
\(213\) | −3.55945 | −0.243890 | ||||||||
\(214\) | 3.10260i | 0.212089i | ||||||||
\(215\) | 3.10260 | + | 0.647551i | 0.211596 | + | 0.0441626i | ||||
\(216\) | 8.66025i | 0.589256i | ||||||||
\(217\) | 16.7477i | 1.13691i | ||||||||
\(218\) | − | 6.00000i | − | 0.406371i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 16.1652 | + | 3.37386i | 1.08985 | + | 0.227466i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 17.3739i | 1.16606i | ||||||||
\(223\) | 8.66025 | 0.579934 | 0.289967 | − | 0.957037i | \(-0.406356\pi\) | ||||
0.289967 | + | 0.957037i | \(0.406356\pi\) | |||||||
\(224\) | −12.7913 | −0.854654 | ||||||||
\(225\) | −9.16515 | − | 4.00000i | −0.611010 | − | 0.266667i | ||||
\(226\) | − | 36.2976i | − | 2.41448i | ||||||
\(227\) | −6.10985 | −0.405525 | −0.202763 | − | 0.979228i | \(-0.564992\pi\) | ||||
−0.202763 | + | 0.979228i | \(0.564992\pi\) | |||||||
\(228\) | −4.83465 | −0.320183 | ||||||||
\(229\) | 5.48220i | 0.362274i | 0.983458 | + | 0.181137i | \(0.0579778\pi\) | ||||
−0.983458 | + | 0.181137i | \(0.942022\pi\) | |||||||
\(230\) | −21.9564 | − | 4.58258i | −1.44776 | − | 0.302166i | ||||
\(231\) | −4.58258 | −0.301511 | ||||||||
\(232\) | 7.93725 | 0.521106 | ||||||||
\(233\) | 21.1652i | 1.38658i | 0.720661 | + | 0.693288i | \(0.243838\pi\) | ||||
−0.720661 | + | 0.693288i | \(0.756162\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.00000 | + | 19.1652i | −0.260931 | + | 1.25020i | ||||
\(236\) | 9.40315i | 0.612093i | ||||||||
\(237\) | 6.00000i | 0.389742i | ||||||||
\(238\) | − | 17.3739i | − | 1.12618i | ||||||
\(239\) | 20.9753i | 1.35678i | 0.734702 | + | 0.678390i | \(0.237322\pi\) | ||||
−0.734702 | + | 0.678390i | \(0.762678\pi\) | |||||||
\(240\) | −3.92095 | − | 0.818350i | −0.253096 | − | 0.0528243i | ||||
\(241\) | 1.73205i | 0.111571i | 0.998443 | + | 0.0557856i | \(0.0177663\pi\) | ||||
−0.998443 | + | 0.0557856i | \(0.982234\pi\) | |||||||
\(242\) | 8.75560 | 0.562832 | ||||||||
\(243\) | 16.0000i | 1.02640i | ||||||||
\(244\) | −29.5390 | −1.89104 | ||||||||
\(245\) | −1.82740 | + | 8.75560i | −0.116748 | + | 0.559375i | ||||
\(246\) | 5.79129 | 0.369239 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 16.7477i | 1.06348i | ||||||||
\(249\) | − | 11.3060i | − | 0.716489i | ||||||
\(250\) | −14.1652 | + | 19.9564i | −0.895883 | + | 1.26216i | ||||
\(251\) | 18.1652 | 1.14657 | 0.573287 | − | 0.819355i | \(-0.305668\pi\) | ||||
0.573287 | + | 0.819355i | \(0.305668\pi\) | |||||||
\(252\) | 9.66930 | 0.609109 | ||||||||
\(253\) | 12.1244 | 0.762252 | ||||||||
\(254\) | 21.3368i | 1.33879i | ||||||||
\(255\) | 2.09355 | − | 10.0308i | 0.131103 | − | 0.628153i | ||||
\(256\) | −2.79129 | −0.174455 | ||||||||
\(257\) | − | 0.165151i | − | 0.0103019i | −0.999987 | − | 0.00515093i | \(-0.998360\pi\) | ||
0.999987 | − | 0.00515093i | \(-0.00163960\pi\) | |||||||
\(258\) | −3.10260 | −0.193160 | ||||||||
\(259\) | 13.7477 | 0.854242 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.16515 | 0.567309 | ||||||||
\(262\) | 3.46410 | 0.214013 | ||||||||
\(263\) | 9.00000i | 0.554964i | 0.960731 | + | 0.277482i | \(0.0894999\pi\) | ||||
−0.960731 | + | 0.277482i | \(0.910500\pi\) | |||||||
\(264\) | −4.58258 | −0.282038 | ||||||||
\(265\) | −3.46410 | − | 0.723000i | −0.212798 | − | 0.0444135i | ||||
\(266\) | 6.56670i | 0.402630i | ||||||||
\(267\) | −4.28245 | −0.262082 | ||||||||
\(268\) | −41.4938 | −2.53464 | ||||||||
\(269\) | 15.0000 | 0.914566 | 0.457283 | − | 0.889321i | \(-0.348823\pi\) | ||||
0.457283 | + | 0.889321i | \(0.348823\pi\) | |||||||
\(270\) | 23.9564 | + | 5.00000i | 1.45794 | + | 0.304290i | ||||
\(271\) | 8.66025i | 0.526073i | 0.964786 | + | 0.263036i | \(0.0847240\pi\) | ||||
−0.964786 | + | 0.263036i | \(0.915276\pi\) | |||||||
\(272\) | 8.20871i | 0.497726i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.208712 | 0.0126088 | ||||||||
\(275\) | 5.29150 | − | 12.1244i | 0.319090 | − | 0.731126i | ||||
\(276\) | 12.7913 | 0.769945 | ||||||||
\(277\) | 16.5826i | 0.996350i | 0.867076 | + | 0.498175i | \(0.165996\pi\) | ||||
−0.867076 | + | 0.498175i | \(0.834004\pi\) | |||||||
\(278\) | −12.5812 | −0.754571 | ||||||||
\(279\) | 19.3386i | 1.15777i | ||||||||
\(280\) | 1.37055 | − | 6.56670i | 0.0819061 | − | 0.392436i | ||||
\(281\) | 17.5112i | 1.04463i | 0.852752 | + | 0.522316i | \(0.174932\pi\) | ||||
−0.852752 | + | 0.522316i | \(0.825068\pi\) | |||||||
\(282\) | − | 19.1652i | − | 1.14127i | ||||||
\(283\) | − | 0.252273i | − | 0.0149961i | −0.999972 | − | 0.00749803i | \(-0.997613\pi\) | ||
0.999972 | − | 0.00749803i | \(-0.00238672\pi\) | |||||||
\(284\) | 9.93545i | 0.589561i | ||||||||
\(285\) | −0.791288 | + | 3.79129i | −0.0468718 | + | 0.224577i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 4.58258i | − | 0.270501i | ||||||
\(288\) | −14.7701 | −0.870337 | ||||||||
\(289\) | −4.00000 | −0.235294 | ||||||||
\(290\) | 4.58258 | − | 21.9564i | 0.269098 | − | 1.28933i | ||||
\(291\) | − | 4.47315i | − | 0.262221i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.4304 | 1.36882 | 0.684408 | − | 0.729099i | \(-0.260061\pi\) | ||||
0.684408 | + | 0.729099i | \(0.260061\pi\) | |||||||
\(294\) | − | 8.75560i | − | 0.510637i | ||||||
\(295\) | 7.37386 | + | 1.53901i | 0.429323 | + | 0.0896049i | ||||
\(296\) | 13.7477 | 0.799070 | ||||||||
\(297\) | −13.2288 | −0.767610 | ||||||||
\(298\) | − | 21.3739i | − | 1.23815i | ||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 5.58258 | − | 12.7913i | 0.322310 | − | 0.738505i | ||||
\(301\) | 2.45505i | 0.141507i | ||||||||
\(302\) | − | 13.5826i | − | 0.781589i | ||||||
\(303\) | 9.00000i | 0.517036i | ||||||||
\(304\) | − | 3.10260i | − | 0.177946i | ||||||
\(305\) | −4.83465 | + | 23.1642i | −0.276831 | + | 1.32638i | ||||
\(306\) | − | 20.0616i | − | 1.14685i | ||||||
\(307\) | 24.2487 | 1.38395 | 0.691974 | − | 0.721923i | \(-0.256741\pi\) | ||||
0.691974 | + | 0.721923i | \(0.256741\pi\) | |||||||
\(308\) | 12.7913i | 0.728851i | ||||||||
\(309\) | 15.1652 | 0.862715 | ||||||||
\(310\) | 46.3284 | + | 9.66930i | 2.63128 | + | 0.549180i | ||||
\(311\) | −1.58258 | −0.0897396 | −0.0448698 | − | 0.998993i | \(-0.514287\pi\) | ||||
−0.0448698 | + | 0.998993i | \(0.514287\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 30.7477i | − | 1.73796i | −0.494843 | − | 0.868982i | \(-0.664775\pi\) | ||
0.494843 | − | 0.868982i | \(-0.335225\pi\) | |||||||
\(314\) | 20.0616i | 1.13214i | ||||||||
\(315\) | 1.58258 | − | 7.58258i | 0.0891680 | − | 0.427230i | ||||
\(316\) | 16.7477 | 0.942133 | ||||||||
\(317\) | 20.9753 | 1.17809 | 0.589045 | − | 0.808100i | \(-0.299504\pi\) | ||||
0.589045 | + | 0.808100i | \(0.299504\pi\) | |||||||
\(318\) | 3.46410 | 0.194257 | ||||||||
\(319\) | 12.1244i | 0.678834i | ||||||||
\(320\) | −5.74835 | + | 27.5420i | −0.321343 | + | 1.53965i | ||||
\(321\) | −1.41742 | −0.0791129 | ||||||||
\(322\) | − | 17.3739i | − | 0.968208i | ||||||
\(323\) | 7.93725 | 0.441641 | ||||||||
\(324\) | 2.79129 | 0.155072 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 23.3739 | 1.29456 | ||||||||
\(327\) | 2.74110 | 0.151583 | ||||||||
\(328\) | − | 4.58258i | − | 0.253030i | ||||||
\(329\) | −15.1652 | −0.836082 | ||||||||
\(330\) | −2.64575 | + | 12.6766i | −0.145644 | + | 0.697821i | ||||
\(331\) | − | 11.4014i | − | 0.626675i | −0.949642 | − | 0.313338i | \(-0.898553\pi\) | ||
0.949642 | − | 0.313338i | \(-0.101447\pi\) | |||||||
\(332\) | −31.5583 | −1.73199 | ||||||||
\(333\) | 15.8745 | 0.869918 | ||||||||
\(334\) | 9.37386 | 0.512915 | ||||||||
\(335\) | −6.79129 | + | 32.5390i | −0.371048 | + | 1.77780i | ||||
\(336\) | − | 3.10260i | − | 0.169261i | ||||||
\(337\) | − | 3.25227i | − | 0.177163i | −0.996069 | − | 0.0885813i | \(-0.971767\pi\) | ||
0.996069 | − | 0.0885813i | \(-0.0282333\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.5826 | 0.900642 | ||||||||
\(340\) | −27.9989 | − | 5.84370i | −1.51845 | − | 0.316919i | ||||
\(341\) | −25.5826 | −1.38537 | ||||||||
\(342\) | 7.58258i | 0.410019i | ||||||||
\(343\) | −19.0526 | −1.02874 | ||||||||
\(344\) | 2.45505i | 0.132367i | ||||||||
\(345\) | 2.09355 | − | 10.0308i | 0.112713 | − | 0.540040i | ||||
\(346\) | − | 16.2360i | − | 0.872853i | ||||||
\(347\) | − | 15.3303i | − | 0.822974i | −0.911416 | − | 0.411487i | \(-0.865010\pi\) | ||
0.911416 | − | 0.411487i | \(-0.134990\pi\) | |||||||
\(348\) | 12.7913i | 0.685685i | ||||||||
\(349\) | 18.3296i | 0.981159i | 0.871396 | + | 0.490579i | \(0.163215\pi\) | ||||
−0.871396 | + | 0.490579i | \(0.836785\pi\) | |||||||
\(350\) | −17.3739 | − | 7.58258i | −0.928672 | − | 0.405306i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 19.5390i | − | 1.04143i | ||||||
\(353\) | −17.4159 | −0.926953 | −0.463476 | − | 0.886109i | \(-0.653398\pi\) | ||||
−0.463476 | + | 0.886109i | \(0.653398\pi\) | |||||||
\(354\) | −7.37386 | −0.391916 | ||||||||
\(355\) | 7.79129 | + | 1.62614i | 0.413519 | + | 0.0863064i | ||||
\(356\) | 11.9536i | 0.633537i | ||||||||
\(357\) | 7.93725 | 0.420084 | ||||||||
\(358\) | 0.361500 | 0.0191059 | ||||||||
\(359\) | − | 33.3857i | − | 1.76203i | −0.473088 | − | 0.881015i | \(-0.656861\pi\) | ||
0.473088 | − | 0.881015i | \(-0.343139\pi\) | |||||||
\(360\) | 1.58258 | − | 7.58258i | 0.0834091 | − | 0.399637i | ||||
\(361\) | 16.0000 | 0.842105 | ||||||||
\(362\) | −41.0369 | −2.15685 | ||||||||
\(363\) | 4.00000i | 0.209946i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | − | 23.1642i | − | 1.21081i | ||||||
\(367\) | − | 25.7477i | − | 1.34402i | −0.740542 | − | 0.672010i | \(-0.765431\pi\) | ||
0.740542 | − | 0.672010i | \(-0.234569\pi\) | |||||||
\(368\) | 8.20871i | 0.427909i | ||||||||
\(369\) | − | 5.29150i | − | 0.275465i | ||||||
\(370\) | 7.93725 | − | 38.0297i | 0.412638 | − | 1.97707i | ||||
\(371\) | − | 2.74110i | − | 0.142311i | ||||||
\(372\) | −26.9898 | −1.39936 | ||||||||
\(373\) | − | 13.0000i | − | 0.673114i | −0.941663 | − | 0.336557i | \(-0.890737\pi\) | ||
0.941663 | − | 0.336557i | \(-0.109263\pi\) | |||||||
\(374\) | 26.5390 | 1.37230 | ||||||||
\(375\) | −9.11710 | − | 6.47135i | −0.470805 | − | 0.334179i | ||||
\(376\) | −15.1652 | −0.782083 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 18.9564i | 0.975014i | ||||||||
\(379\) | 21.0707i | 1.08233i | 0.840917 | + | 0.541164i | \(0.182016\pi\) | ||||
−0.840917 | + | 0.541164i | \(0.817984\pi\) | |||||||
\(380\) | 10.5826 | + | 2.20871i | 0.542875 | + | 0.113305i | ||||
\(381\) | −9.74773 | −0.499391 | ||||||||
\(382\) | −16.2360 | −0.830706 | ||||||||
\(383\) | 2.83645 | 0.144936 | 0.0724680 | − | 0.997371i | \(-0.476912\pi\) | ||||
0.0724680 | + | 0.997371i | \(0.476912\pi\) | |||||||
\(384\) | − | 12.7719i | − | 0.651764i | ||||||
\(385\) | 10.0308 | + | 2.09355i | 0.511217 | + | 0.106697i | ||||
\(386\) | 2.20871 | 0.112420 | ||||||||
\(387\) | 2.83485i | 0.144103i | ||||||||
\(388\) | −12.4859 | −0.633873 | ||||||||
\(389\) | −15.1652 | −0.768904 | −0.384452 | − | 0.923145i | \(-0.625610\pi\) | ||||
−0.384452 | + | 0.923145i | \(0.625610\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.0000 | −1.06202 | ||||||||
\(392\) | −6.92820 | −0.349927 | ||||||||
\(393\) | 1.58258i | 0.0798304i | ||||||||
\(394\) | 43.7042 | 2.20178 | ||||||||
\(395\) | 2.74110 | − | 13.1334i | 0.137920 | − | 0.660813i | ||||
\(396\) | 14.7701i | 0.742226i | ||||||||
\(397\) | −27.2759 | −1.36894 | −0.684468 | − | 0.729043i | \(-0.739966\pi\) | ||||
−0.684468 | + | 0.729043i | \(0.739966\pi\) | |||||||
\(398\) | −3.10260 | −0.155519 | ||||||||
\(399\) | −3.00000 | −0.150188 | ||||||||
\(400\) | 8.20871 | + | 3.58258i | 0.410436 | + | 0.179129i | ||||
\(401\) | 12.5058i | 0.624508i | 0.949999 | + | 0.312254i | \(0.101084\pi\) | ||||
−0.949999 | + | 0.312254i | \(0.898916\pi\) | |||||||
\(402\) | − | 32.5390i | − | 1.62290i | ||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 25.1216 | 1.24985 | ||||||||
\(405\) | 0.456850 | − | 2.18890i | 0.0227011 | − | 0.108767i | ||||
\(406\) | 17.3739 | 0.862250 | ||||||||
\(407\) | 21.0000i | 1.04093i | ||||||||
\(408\) | 7.93725 | 0.392953 | ||||||||
\(409\) | − | 8.66025i | − | 0.428222i | −0.976809 | − | 0.214111i | \(-0.931315\pi\) | ||
0.976809 | − | 0.214111i | \(-0.0686854\pi\) | |||||||
\(410\) | −12.6766 | − | 2.64575i | −0.626050 | − | 0.130664i | ||||
\(411\) | 0.0953502i | 0.00470328i | ||||||||
\(412\) | − | 42.3303i | − | 2.08546i | ||||||
\(413\) | 5.83485i | 0.287114i | ||||||||
\(414\) | − | 20.0616i | − | 0.985974i | ||||||
\(415\) | −5.16515 | + | 24.7477i | −0.253547 | + | 1.21482i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 5.74773i | − | 0.281467i | ||||||
\(418\) | −10.0308 | −0.490623 | ||||||||
\(419\) | 24.1652 | 1.18054 | 0.590272 | − | 0.807204i | \(-0.299020\pi\) | ||||
0.590272 | + | 0.807204i | \(0.299020\pi\) | |||||||
\(420\) | 10.5826 | + | 2.20871i | 0.516377 | + | 0.107774i | ||||
\(421\) | 26.2668i | 1.28017i | 0.768306 | + | 0.640083i | \(0.221100\pi\) | ||||
−0.768306 | + | 0.640083i | \(0.778900\pi\) | |||||||
\(422\) | 39.7617 | 1.93557 | ||||||||
\(423\) | −17.5112 | −0.851424 | ||||||||
\(424\) | − | 2.74110i | − | 0.133120i | ||||||
\(425\) | −9.16515 | + | 21.0000i | −0.444575 | + | 1.01865i | ||||
\(426\) | −7.79129 | −0.377489 | ||||||||
\(427\) | −18.3296 | −0.887030 | ||||||||
\(428\) | 3.95644i | 0.191242i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.79129 | + | 1.41742i | 0.327505 | + | 0.0683543i | ||||
\(431\) | 29.6356i | 1.42749i | 0.700403 | + | 0.713747i | \(0.253004\pi\) | ||||
−0.700403 | + | 0.713747i | \(0.746996\pi\) | |||||||
\(432\) | − | 8.95644i | − | 0.430917i | ||||||
\(433\) | − | 17.7477i | − | 0.852901i | −0.904511 | − | 0.426451i | \(-0.859764\pi\) | ||
0.904511 | − | 0.426451i | \(-0.140236\pi\) | |||||||
\(434\) | 36.6591i | 1.75969i | ||||||||
\(435\) | 10.0308 | + | 2.09355i | 0.480940 | + | 0.100378i | ||||
\(436\) | − | 7.65120i | − | 0.366426i | ||||||
\(437\) | 7.93725 | 0.379690 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −40.4955 | −1.93274 | −0.966371 | − | 0.257151i | \(-0.917216\pi\) | ||||
−0.966371 | + | 0.257151i | \(0.917216\pi\) | |||||||
\(440\) | 10.0308 | + | 2.09355i | 0.478200 | + | 0.0998061i | ||||
\(441\) | −8.00000 | −0.380952 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 25.9129i | − | 1.23116i | −0.788075 | − | 0.615579i | \(-0.788922\pi\) | ||
0.788075 | − | 0.615579i | \(-0.211078\pi\) | |||||||
\(444\) | 22.1552i | 1.05144i | ||||||||
\(445\) | 9.37386 | + | 1.95644i | 0.444364 | + | 0.0927441i | ||||
\(446\) | 18.9564 | 0.897613 | ||||||||
\(447\) | 9.76465 | 0.461852 | ||||||||
\(448\) | −21.7937 | −1.02965 | ||||||||
\(449\) | − | 37.4775i | − | 1.76867i | −0.466852 | − | 0.884336i | \(-0.654612\pi\) | ||
0.466852 | − | 0.884336i | \(-0.345388\pi\) | |||||||
\(450\) | −20.0616 | − | 8.75560i | −0.945713 | − | 0.412743i | ||||
\(451\) | 7.00000 | 0.329617 | ||||||||
\(452\) | − | 46.2867i | − | 2.17715i | ||||||
\(453\) | 6.20520 | 0.291546 | ||||||||
\(454\) | −13.3739 | −0.627667 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.00000 | −0.140488 | ||||||||
\(457\) | −1.73205 | −0.0810219 | −0.0405110 | − | 0.999179i | \(-0.512899\pi\) | ||||
−0.0405110 | + | 0.999179i | \(0.512899\pi\) | |||||||
\(458\) | 12.0000i | 0.560723i | ||||||||
\(459\) | 22.9129 | 1.06948 | ||||||||
\(460\) | −27.9989 | − | 5.84370i | −1.30545 | − | 0.272464i | ||||
\(461\) | 1.19975i | 0.0558780i | 0.999610 | + | 0.0279390i | \(0.00889441\pi\) | ||||
−0.999610 | + | 0.0279390i | \(0.991106\pi\) | |||||||
\(462\) | −10.0308 | −0.466675 | ||||||||
\(463\) | −8.22330 | −0.382169 | −0.191085 | − | 0.981574i | \(-0.561201\pi\) | ||||
−0.191085 | + | 0.981574i | \(0.561201\pi\) | |||||||
\(464\) | −8.20871 | −0.381080 | ||||||||
\(465\) | −4.41742 | + | 21.1652i | −0.204853 | + | 0.981510i | ||||
\(466\) | 46.3284i | 2.14612i | ||||||||
\(467\) | − | 12.3303i | − | 0.570578i | −0.958441 | − | 0.285289i | \(-0.907910\pi\) | ||
0.958441 | − | 0.285289i | \(-0.0920896\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −25.7477 | −1.18892 | ||||||||
\(470\) | −8.75560 | + | 41.9506i | −0.403866 | + | 1.93504i | ||||
\(471\) | −9.16515 | −0.422308 | ||||||||
\(472\) | 5.83485i | 0.268571i | ||||||||
\(473\) | −3.75015 | −0.172432 | ||||||||
\(474\) | 13.1334i | 0.603237i | ||||||||
\(475\) | 3.46410 | − | 7.93725i | 0.158944 | − | 0.364186i | ||||
\(476\) | − | 22.1552i | − | 1.01548i | ||||||
\(477\) | − | 3.16515i | − | 0.144922i | ||||||
\(478\) | 45.9129i | 2.10001i | ||||||||
\(479\) | − | 32.3767i | − | 1.47933i | −0.672977 | − | 0.739664i | \(-0.734985\pi\) | ||
0.672977 | − | 0.739664i | \(-0.265015\pi\) | |||||||
\(480\) | −16.1652 | − | 3.37386i | −0.737835 | − | 0.153995i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 3.79129i | 0.172688i | ||||||||
\(483\) | 7.93725 | 0.361158 | ||||||||
\(484\) | 11.1652 | 0.507507 | ||||||||
\(485\) | −2.04356 | + | 9.79129i | −0.0927933 | + | 0.444599i | ||||
\(486\) | 35.0224i | 1.58865i | ||||||||
\(487\) | 21.0707 | 0.954803 | 0.477401 | − | 0.878685i | \(-0.341579\pi\) | ||||
0.477401 | + | 0.878685i | \(0.341579\pi\) | |||||||
\(488\) | −18.3296 | −0.829740 | ||||||||
\(489\) | 10.6784i | 0.482892i | ||||||||
\(490\) | −4.00000 | + | 19.1652i | −0.180702 | + | 0.865793i | ||||
\(491\) | 28.5826 | 1.28991 | 0.644957 | − | 0.764219i | \(-0.276875\pi\) | ||||
0.644957 | + | 0.764219i | \(0.276875\pi\) | |||||||
\(492\) | 7.38505 | 0.332944 | ||||||||
\(493\) | − | 21.0000i | − | 0.945792i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11.5826 | + | 2.41742i | 0.520598 | + | 0.108655i | ||||
\(496\) | − | 17.3205i | − | 0.777714i | ||||||
\(497\) | 6.16515i | 0.276545i | ||||||||
\(498\) | − | 24.7477i | − | 1.10897i | ||||||
\(499\) | − | 16.5975i | − | 0.743006i | −0.928432 | − | 0.371503i | \(-0.878842\pi\) | ||
0.928432 | − | 0.371503i | \(-0.121158\pi\) | |||||||
\(500\) | −18.0634 | + | 25.4485i | −0.807820 | + | 1.13809i | ||||
\(501\) | 4.28245i | 0.191326i | ||||||||
\(502\) | 39.7617 | 1.77465 | ||||||||
\(503\) | − | 18.1652i | − | 0.809944i | −0.914329 | − | 0.404972i | \(-0.867281\pi\) | ||
0.914329 | − | 0.404972i | \(-0.132719\pi\) | |||||||
\(504\) | 6.00000 | 0.267261 | ||||||||
\(505\) | 4.11165 | − | 19.7001i | 0.182966 | − | 0.876643i | ||||
\(506\) | 26.5390 | 1.17980 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 27.2087i | 1.20719i | ||||||||
\(509\) | − | 29.6356i | − | 1.31357i | −0.754076 | − | 0.656787i | \(-0.771915\pi\) | ||
0.754076 | − | 0.656787i | \(-0.228085\pi\) | |||||||
\(510\) | 4.58258 | − | 21.9564i | 0.202920 | − | 0.972247i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 19.4340 | 0.858868 | ||||||||
\(513\) | −8.66025 | −0.382360 | ||||||||
\(514\) | − | 0.361500i | − | 0.0159451i | ||||||
\(515\) | −33.1950 | − | 6.92820i | −1.46275 | − | 0.305293i | ||||
\(516\) | −3.95644 | −0.174173 | ||||||||
\(517\) | − | 23.1652i | − | 1.01880i | ||||||
\(518\) | 30.0924 | 1.32218 | ||||||||
\(519\) | 7.41742 | 0.325589 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.4955 | −1.20460 | −0.602299 | − | 0.798271i | \(-0.705748\pi\) | ||||
−0.602299 | + | 0.798271i | \(0.705748\pi\) | |||||||
\(522\) | 20.0616 | 0.878073 | ||||||||
\(523\) | − | 18.1652i | − | 0.794307i | −0.917752 | − | 0.397153i | \(-0.869998\pi\) | ||
0.917752 | − | 0.397153i | \(-0.130002\pi\) | |||||||
\(524\) | 4.41742 | 0.192976 | ||||||||
\(525\) | 3.46410 | − | 7.93725i | 0.151186 | − | 0.346410i | ||||
\(526\) | 19.7001i | 0.858966i | ||||||||
\(527\) | 44.3103 | 1.93019 | ||||||||
\(528\) | 4.73930 | 0.206252 | ||||||||
\(529\) | 2.00000 | 0.0869565 | ||||||||
\(530\) | −7.58258 | − | 1.58258i | −0.329366 | − | 0.0687427i | ||||
\(531\) | 6.73750i | 0.292383i | ||||||||
\(532\) | 8.37386i | 0.363053i | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −9.37386 | −0.405647 | ||||||||
\(535\) | 3.10260 | + | 0.647551i | 0.134137 | + | 0.0279961i | ||||
\(536\) | −25.7477 | −1.11213 | ||||||||
\(537\) | 0.165151i | 0.00712681i | ||||||||
\(538\) | 32.8335 | 1.41555 | ||||||||
\(539\) | − | 10.5830i | − | 0.455842i | ||||||
\(540\) | 30.5493 | + | 6.37600i | 1.31463 | + | 0.274379i | ||||
\(541\) | 10.3923i | 0.446800i | 0.974727 | + | 0.223400i | \(0.0717156\pi\) | ||||
−0.974727 | + | 0.223400i | \(0.928284\pi\) | |||||||
\(542\) | 18.9564i | 0.814249i | ||||||||
\(543\) | − | 18.7477i | − | 0.804542i | ||||||
\(544\) | 33.8426i | 1.45099i | ||||||||
\(545\) | −6.00000 | − | 1.25227i | −0.257012 | − | 0.0536415i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 1.25227i | − | 0.0535433i | −0.999642 | − | 0.0267717i | \(-0.991477\pi\) | ||
0.999642 | − | 0.0267717i | \(-0.00852270\pi\) | |||||||
\(548\) | 0.266150 | 0.0113694 | ||||||||
\(549\) | −21.1652 | −0.903307 | ||||||||
\(550\) | 11.5826 | − | 26.5390i | 0.493883 | − | 1.13163i | ||||
\(551\) | 7.93725i | 0.338138i | ||||||||
\(552\) | 7.93725 | 0.337832 | ||||||||
\(553\) | 10.3923 | 0.441926 | ||||||||
\(554\) | 36.2976i | 1.54214i | ||||||||
\(555\) | 17.3739 | + | 3.62614i | 0.737479 | + | 0.153921i | ||||
\(556\) | −16.0436 | −0.680399 | ||||||||
\(557\) | −13.0381 | −0.552440 | −0.276220 | − | 0.961094i | \(-0.589082\pi\) | ||||
−0.276220 | + | 0.961094i | \(0.589082\pi\) | |||||||
\(558\) | 42.3303i | 1.79198i | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1.41742 | + | 6.79129i | −0.0598971 | + | 0.286984i | ||||
\(561\) | 12.1244i | 0.511891i | ||||||||
\(562\) | 38.3303i | 1.61687i | ||||||||
\(563\) | − | 9.00000i | − | 0.379305i | −0.981851 | − | 0.189652i | \(-0.939264\pi\) | ||
0.981851 | − | 0.189652i | \(-0.0607361\pi\) | |||||||
\(564\) | − | 24.4394i | − | 1.02908i | ||||||
\(565\) | −36.2976 | − | 7.57575i | −1.52705 | − | 0.318714i | ||||
\(566\) | − | 0.552200i | − | 0.0232107i | ||||||
\(567\) | 1.73205 | 0.0727393 | ||||||||
\(568\) | 6.16515i | 0.258684i | ||||||||
\(569\) | 19.7477 | 0.827868 | 0.413934 | − | 0.910307i | \(-0.364154\pi\) | ||||
0.413934 | + | 0.910307i | \(0.364154\pi\) | |||||||
\(570\) | −1.73205 | + | 8.29875i | −0.0725476 | + | 0.347597i | ||||
\(571\) | 29.0780 | 1.21688 | 0.608439 | − | 0.793601i | \(-0.291796\pi\) | ||||
0.608439 | + | 0.793601i | \(0.291796\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 7.41742i | − | 0.309867i | ||||||
\(574\) | − | 10.0308i | − | 0.418678i | ||||||
\(575\) | −9.16515 | + | 21.0000i | −0.382213 | + | 0.875761i | ||||
\(576\) | −25.1652 | −1.04855 | ||||||||
\(577\) | −6.92820 | −0.288425 | −0.144212 | − | 0.989547i | \(-0.546065\pi\) | ||||
−0.144212 | + | 0.989547i | \(0.546065\pi\) | |||||||
\(578\) | −8.75560 | −0.364185 | ||||||||
\(579\) | 1.00905i | 0.0419347i | ||||||||
\(580\) | 5.84370 | − | 27.9989i | 0.242647 | − | 1.16259i | ||||
\(581\) | −19.5826 | −0.812422 | ||||||||
\(582\) | − | 9.79129i | − | 0.405862i | ||||||
\(583\) | 4.18710 | 0.173412 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 51.2867 | 2.11864 | ||||||||
\(587\) | 18.7110 | 0.772284 | 0.386142 | − | 0.922439i | \(-0.373807\pi\) | ||||
0.386142 | + | 0.922439i | \(0.373807\pi\) | |||||||
\(588\) | − | 11.1652i | − | 0.460443i | ||||||
\(589\) | −16.7477 | −0.690078 | ||||||||
\(590\) | 16.1407 | + | 3.36875i | 0.664500 | + | 0.138689i | ||||
\(591\) | 19.9663i | 0.821302i | ||||||||
\(592\) | −14.2179 | −0.584352 | ||||||||
\(593\) | 21.1660 | 0.869184 | 0.434592 | − | 0.900627i | \(-0.356893\pi\) | ||||
0.434592 | + | 0.900627i | \(0.356893\pi\) | |||||||
\(594\) | −28.9564 | −1.18810 | ||||||||
\(595\) | −17.3739 | − | 3.62614i | −0.712259 | − | 0.148657i | ||||
\(596\) | − | 27.2560i | − | 1.11645i | ||||||
\(597\) | − | 1.41742i | − | 0.0580113i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 39.4955 | 1.61374 | 0.806870 | − | 0.590729i | \(-0.201160\pi\) | ||||
0.806870 | + | 0.590729i | \(0.201160\pi\) | |||||||
\(600\) | 3.46410 | − | 7.93725i | 0.141421 | − | 0.324037i | ||||
\(601\) | −28.9129 | −1.17938 | −0.589690 | − | 0.807629i | \(-0.700750\pi\) | ||||
−0.589690 | + | 0.807629i | \(0.700750\pi\) | |||||||
\(602\) | 5.37386i | 0.219022i | ||||||||
\(603\) | −29.7309 | −1.21074 | ||||||||
\(604\) | − | 17.3205i | − | 0.704761i | ||||||
\(605\) | 1.82740 | − | 8.75560i | 0.0742944 | − | 0.355966i | ||||
\(606\) | 19.7001i | 0.800262i | ||||||||
\(607\) | 19.7477i | 0.801536i | 0.916180 | + | 0.400768i | \(0.131257\pi\) | ||||
−0.916180 | + | 0.400768i | \(0.868743\pi\) | |||||||
\(608\) | − | 12.7913i | − | 0.518755i | ||||||
\(609\) | 7.93725i | 0.321634i | ||||||||
\(610\) | −10.5826 | + | 50.7042i | −0.428476 | + | 2.05295i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | − | 25.5826i | − | 1.03411i | ||||||
\(613\) | 21.7937 | 0.880238 | 0.440119 | − | 0.897940i | \(-0.354936\pi\) | ||||
0.440119 | + | 0.897940i | \(0.354936\pi\) | |||||||
\(614\) | 53.0780 | 2.14205 | ||||||||
\(615\) | 1.20871 | − | 5.79129i | 0.0487400 | − | 0.233527i | ||||
\(616\) | 7.93725i | 0.319801i | ||||||||
\(617\) | 3.36875 | 0.135621 | 0.0678104 | − | 0.997698i | \(-0.478399\pi\) | ||||
0.0678104 | + | 0.997698i | \(0.478399\pi\) | |||||||
\(618\) | 33.1950 | 1.33530 | ||||||||
\(619\) | − | 2.01810i | − | 0.0811143i | −0.999177 | − | 0.0405572i | \(-0.987087\pi\) | ||
0.999177 | − | 0.0405572i | \(-0.0129133\pi\) | |||||||
\(620\) | 59.0780 | + | 12.3303i | 2.37263 | + | 0.495197i | ||||
\(621\) | 22.9129 | 0.919462 | ||||||||
\(622\) | −3.46410 | −0.138898 | ||||||||
\(623\) | 7.41742i | 0.297173i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.0000 | + | 18.3303i | 0.680000 | + | 0.733212i | ||||
\(626\) | − | 67.3037i | − | 2.69000i | ||||||
\(627\) | − | 4.58258i | − | 0.183010i | ||||||
\(628\) | 25.5826i | 1.02086i | ||||||||
\(629\) | − | 36.3731i | − | 1.45029i | ||||||
\(630\) | 3.46410 | − | 16.5975i | 0.138013 | − | 0.661261i | ||||
\(631\) | 21.7937i | 0.867592i | 0.901011 | + | 0.433796i | \(0.142826\pi\) | ||||
−0.901011 | + | 0.433796i | \(0.857174\pi\) | |||||||
\(632\) | 10.3923 | 0.413384 | ||||||||
\(633\) | 18.1652i | 0.722000i | ||||||||
\(634\) | 45.9129 | 1.82343 | ||||||||
\(635\) | 21.3368 | + | 4.45325i | 0.846725 | + | 0.176722i | ||||
\(636\) | 4.41742 | 0.175162 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 26.5390i | 1.05069i | ||||||||
\(639\) | 7.11890i | 0.281619i | ||||||||
\(640\) | −5.83485 | + | 27.9564i | −0.230643 | + | 1.10508i | ||||
\(641\) | −0.165151 | −0.00652309 | −0.00326154 | − | 0.999995i | \(-0.501038\pi\) | ||||
−0.00326154 | + | 0.999995i | \(0.501038\pi\) | |||||||
\(642\) | −3.10260 | −0.122450 | ||||||||
\(643\) | 5.91915 | 0.233429 | 0.116714 | − | 0.993166i | \(-0.462764\pi\) | ||||
0.116714 | + | 0.993166i | \(0.462764\pi\) | |||||||
\(644\) | − | 22.1552i | − | 0.873036i | ||||||
\(645\) | −0.647551 | + | 3.10260i | −0.0254973 | + | 0.122165i | ||||
\(646\) | 17.3739 | 0.683566 | ||||||||
\(647\) | − | 27.0000i | − | 1.06148i | −0.847535 | − | 0.530740i | \(-0.821914\pi\) | ||
0.847535 | − | 0.530740i | \(-0.178086\pi\) | |||||||
\(648\) | 1.73205 | 0.0680414 | ||||||||
\(649\) | −8.91288 | −0.349861 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16.7477 | −0.656395 | ||||||||
\(652\) | 29.8064 | 1.16731 | ||||||||
\(653\) | 48.8258i | 1.91070i | 0.295477 | + | 0.955350i | \(0.404521\pi\) | ||||
−0.295477 | + | 0.955350i | \(0.595479\pi\) | |||||||
\(654\) | 6.00000 | 0.234619 | ||||||||
\(655\) | 0.723000 | − | 3.46410i | 0.0282500 | − | 0.135354i | ||||
\(656\) | 4.73930i | 0.185039i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −33.1950 | −1.29408 | ||||||||
\(659\) | 24.4955 | 0.954207 | 0.477104 | − | 0.878847i | \(-0.341687\pi\) | ||||
0.477104 | + | 0.878847i | \(0.341687\pi\) | |||||||
\(660\) | −3.37386 | + | 16.1652i | −0.131327 | + | 0.629228i | ||||
\(661\) | 2.45505i | 0.0954904i | 0.998860 | + | 0.0477452i | \(0.0152036\pi\) | ||||
−0.998860 | + | 0.0477452i | \(0.984796\pi\) | |||||||
\(662\) | − | 24.9564i | − | 0.969960i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −19.5826 | −0.759951 | ||||||||
\(665\) | 6.56670 | + | 1.37055i | 0.254646 | + | 0.0531477i | ||||
\(666\) | 34.7477 | 1.34645 | ||||||||
\(667\) | − | 21.0000i | − | 0.813123i | ||||||
\(668\) | 11.9536 | 0.462497 | ||||||||
\(669\) | 8.66025i | 0.334825i | ||||||||
\(670\) | −14.8655 | + | 71.2247i | −0.574303 | + | 2.75165i | ||||
\(671\) | − | 27.9989i | − | 1.08088i | ||||||
\(672\) | − | 12.7913i | − | 0.493435i | ||||||
\(673\) | − | 5.83485i | − | 0.224917i | −0.993656 | − | 0.112458i | \(-0.964127\pi\) | ||
0.993656 | − | 0.112458i | \(-0.0358725\pi\) | |||||||
\(674\) | − | 7.11890i | − | 0.274210i | ||||||
\(675\) | 10.0000 | − | 22.9129i | 0.384900 | − | 0.881917i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.1652i | 0.813443i | 0.913552 | + | 0.406721i | \(0.133328\pi\) | ||||
−0.913552 | + | 0.406721i | \(0.866672\pi\) | |||||||
\(678\) | 36.2976 | 1.39400 | ||||||||
\(679\) | −7.74773 | −0.297330 | ||||||||
\(680\) | −17.3739 | − | 3.62614i | −0.666257 | − | 0.139056i | ||||
\(681\) | − | 6.10985i | − | 0.234130i | ||||||
\(682\) | −55.9977 | −2.14426 | ||||||||
\(683\) | −11.9337 | −0.456629 | −0.228314 | − | 0.973587i | \(-0.573321\pi\) | ||||
−0.228314 | + | 0.973587i | \(0.573321\pi\) | |||||||
\(684\) | 9.66930i | 0.369715i | ||||||||
\(685\) | 0.0435608 | − | 0.208712i | 0.00166437 | − | 0.00797448i | ||||
\(686\) | −41.7042 | −1.59227 | ||||||||
\(687\) | −5.48220 | −0.209159 | ||||||||
\(688\) | − | 2.53901i | − | 0.0967990i | ||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 4.58258 | − | 21.9564i | 0.174456 | − | 0.835867i | ||||
\(691\) | 35.6501i | 1.35619i | 0.734973 | + | 0.678096i | \(0.237195\pi\) | ||||
−0.734973 | + | 0.678096i | \(0.762805\pi\) | |||||||
\(692\) | − | 20.7042i | − | 0.787054i | ||||||
\(693\) | 9.16515i | 0.348155i | ||||||||
\(694\) | − | 33.5565i | − | 1.27379i | ||||||
\(695\) | −2.62585 | + | 12.5812i | −0.0996042 | + | 0.477232i | ||||
\(696\) | 7.93725i | 0.300861i | ||||||||
\(697\) | −12.1244 | −0.459243 | ||||||||
\(698\) | 40.1216i | 1.51862i | ||||||||
\(699\) | −21.1652 | −0.800540 | ||||||||
\(700\) | −22.1552 | − | 9.66930i | −0.837386 | − | 0.365465i | ||||
\(701\) | −2.83485 | −0.107071 | −0.0535354 | − | 0.998566i | \(-0.517049\pi\) | ||||
−0.0535354 | + | 0.998566i | \(0.517049\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.7477i | 0.518505i | ||||||||
\(704\) | − | 33.2904i | − | 1.25468i | ||||||
\(705\) | −19.1652 | − | 4.00000i | −0.721801 | − | 0.150649i | ||||
\(706\) | −38.1216 | −1.43472 | ||||||||
\(707\) | 15.5885 | 0.586264 | ||||||||
\(708\) | −9.40315 | −0.353392 | ||||||||
\(709\) | − | 36.3731i | − | 1.36602i | −0.730409 | − | 0.683010i | \(-0.760671\pi\) | ||
0.730409 | − | 0.683010i | \(-0.239329\pi\) | |||||||
\(710\) | 17.0544 | + | 3.55945i | 0.640039 | + | 0.133584i | ||||
\(711\) | 12.0000 | 0.450035 | ||||||||
\(712\) | 7.41742i | 0.277980i | ||||||||
\(713\) | 44.3103 | 1.65943 | ||||||||
\(714\) | 17.3739 | 0.650201 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.460985 | 0.0172278 | ||||||||
\(717\) | −20.9753 | −0.783337 | ||||||||
\(718\) | − | 73.0780i | − | 2.72725i | ||||||
\(719\) | −30.4955 | −1.13729 | −0.568644 | − | 0.822584i | \(-0.692532\pi\) | ||||
−0.568644 | + | 0.822584i | \(0.692532\pi\) | |||||||
\(720\) | −1.63670 | + | 7.84190i | −0.0609962 | + | 0.292250i | ||||
\(721\) | − | 26.2668i | − | 0.978227i | ||||||
\(722\) | 35.0224 | 1.30340 | ||||||||
\(723\) | −1.73205 | −0.0644157 | ||||||||
\(724\) | −52.3303 | −1.94484 | ||||||||
\(725\) | −21.0000 | − | 9.16515i | −0.779920 | − | 0.340385i | ||||
\(726\) | 8.75560i | 0.324951i | ||||||||
\(727\) | 42.7477i | 1.58543i | 0.609595 | + | 0.792713i | \(0.291332\pi\) | ||||
−0.609595 | + | 0.792713i | \(0.708668\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.49545 | 0.240243 | ||||||||
\(732\) | − | 29.5390i | − | 1.09179i | ||||||
\(733\) | −8.94630 | −0.330439 | −0.165220 | − | 0.986257i | \(-0.552833\pi\) | ||||
−0.165220 | + | 0.986257i | \(0.552833\pi\) | |||||||
\(734\) | − | 56.3592i | − | 2.08026i | ||||||
\(735\) | −8.75560 | − | 1.82740i | −0.322955 | − | 0.0674047i | ||||
\(736\) | 33.8426i | 1.24745i | ||||||||
\(737\) | − | 39.3303i | − | 1.44875i | ||||||
\(738\) | − | 11.5826i | − | 0.426361i | ||||||
\(739\) | − | 48.7835i | − | 1.79453i | −0.441493 | − | 0.897265i | \(-0.645551\pi\) | ||
0.441493 | − | 0.897265i | \(-0.354449\pi\) | |||||||
\(740\) | 10.1216 | − | 48.4955i | 0.372077 | − | 1.78273i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 6.00000i | − | 0.220267i | ||||||
\(743\) | −42.7690 | −1.56904 | −0.784521 | − | 0.620103i | \(-0.787091\pi\) | ||||
−0.784521 | + | 0.620103i | \(0.787091\pi\) | |||||||
\(744\) | −16.7477 | −0.614001 | ||||||||
\(745\) | −21.3739 | − | 4.46099i | −0.783078 | − | 0.163438i | ||||
\(746\) | − | 28.4557i | − | 1.04184i | ||||||
\(747\) | −22.6120 | −0.827330 | ||||||||
\(748\) | 33.8426 | 1.23741 | ||||||||
\(749\) | 2.45505i | 0.0897056i | ||||||||
\(750\) | −19.9564 | − | 14.1652i | −0.728706 | − | 0.517238i | ||||
\(751\) | −15.7477 | −0.574643 | −0.287321 | − | 0.957834i | \(-0.592765\pi\) | ||||
−0.287321 | + | 0.957834i | \(0.592765\pi\) | |||||||
\(752\) | 15.6838 | 0.571930 | ||||||||
\(753\) | 18.1652i | 0.661975i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −13.5826 | − | 2.83485i | −0.494321 | − | 0.103171i | ||||
\(756\) | 24.1733i | 0.879173i | ||||||||
\(757\) | 17.7477i | 0.645052i | 0.946561 | + | 0.322526i | \(0.104532\pi\) | ||||
−0.946561 | + | 0.322526i | \(0.895468\pi\) | |||||||
\(758\) | 46.1216i | 1.67521i | ||||||||
\(759\) | 12.1244i | 0.440086i | ||||||||
\(760\) | 6.56670 | + | 1.37055i | 0.238199 | + | 0.0497151i | ||||
\(761\) | 40.7509i | 1.47722i | 0.674134 | + | 0.738609i | \(0.264517\pi\) | ||||
−0.674134 | + | 0.738609i | \(0.735483\pi\) | |||||||
\(762\) | −21.3368 | −0.772951 | ||||||||
\(763\) | − | 4.74773i | − | 0.171879i | ||||||
\(764\) | −20.7042 | −0.749050 | ||||||||
\(765\) | −20.0616 | − | 4.18710i | −0.725329 | − | 0.151385i | ||||
\(766\) | 6.20871 | 0.224330 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | − | 2.79129i | − | 0.100722i | ||||||
\(769\) | − | 15.5885i | − | 0.562134i | −0.959688 | − | 0.281067i | \(-0.909312\pi\) | ||
0.959688 | − | 0.281067i | \(-0.0906883\pi\) | |||||||
\(770\) | 21.9564 | + | 4.58258i | 0.791255 | + | 0.165145i | ||||
\(771\) | 0.165151 | 0.00594778 | ||||||||
\(772\) | 2.81655 | 0.101370 | ||||||||
\(773\) | 34.7364 | 1.24938 | 0.624690 | − | 0.780873i | \(-0.285225\pi\) | ||||
0.624690 | + | 0.780873i | \(0.285225\pi\) | |||||||
\(774\) | 6.20520i | 0.223041i | ||||||||
\(775\) | 19.3386 | − | 44.3103i | 0.694663 | − | 1.59167i | ||||
\(776\) | −7.74773 | −0.278127 | ||||||||
\(777\) | 13.7477i | 0.493197i | ||||||||
\(778\) | −33.1950 | −1.19010 | ||||||||
\(779\) | 4.58258 | 0.164188 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.41742 | −0.336982 | ||||||||
\(782\) | −45.9669 | −1.64377 | ||||||||
\(783\) | 22.9129i | 0.818839i | ||||||||
\(784\) | 7.16515 | 0.255898 | ||||||||
\(785\) | 20.0616 | + | 4.18710i | 0.716030 | + | 0.149444i | ||||
\(786\) | 3.46410i | 0.123560i | ||||||||
\(787\) | −32.1860 | −1.14731 | −0.573653 | − | 0.819099i | \(-0.694474\pi\) | ||||
−0.573653 | + | 0.819099i | \(0.694474\pi\) | |||||||
\(788\) | 55.7316 | 1.98536 | ||||||||
\(789\) | −9.00000 | −0.320408 | ||||||||
\(790\) | 6.00000 | − | 28.7477i | 0.213470 | − | 1.02280i | ||||
\(791\) | − | 28.7219i | − | 1.02123i | ||||||
\(792\) | 9.16515i | 0.325669i | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −59.7042 | −2.11882 | ||||||||
\(795\) | 0.723000 | − | 3.46410i | 0.0256422 | − | 0.122859i | ||||
\(796\) | −3.95644 | −0.140232 | ||||||||
\(797\) | 20.0780i | 0.711200i | 0.934638 | + | 0.355600i | \(0.115724\pi\) | ||||
−0.934638 | + | 0.355600i | \(0.884276\pi\) | |||||||
\(798\) | −6.56670 | −0.232459 | ||||||||
\(799\) | 40.1232i | 1.41946i | ||||||||
\(800\) | 33.8426 | + | 14.7701i | 1.19652 | + | 0.522202i | ||||
\(801\) | 8.56490i | 0.302626i | ||||||||
\(802\) | 27.3739i | 0.966605i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | − | 41.4938i | − | 1.46337i | ||||||
\(805\) | −17.3739 | − | 3.62614i | −0.612348 | − | 0.127805i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.0000i | 0.528025i | ||||||||
\(808\) | 15.5885 | 0.548400 | ||||||||
\(809\) | −36.8258 | −1.29472 | −0.647362 | − | 0.762182i | \(-0.724128\pi\) | ||||
−0.647362 | + | 0.762182i | \(0.724128\pi\) | |||||||
\(810\) | 1.00000 | − | 4.79129i | 0.0351364 | − | 0.168349i | ||||
\(811\) | 18.7665i | 0.658981i | 0.944159 | + | 0.329491i | \(0.106877\pi\) | ||||
−0.944159 | + | 0.329491i | \(0.893123\pi\) | |||||||
\(812\) | 22.1552 | 0.777494 | ||||||||
\(813\) | −8.66025 | −0.303728 | ||||||||
\(814\) | 45.9669i | 1.61114i | ||||||||
\(815\) | 4.87841 | − | 23.3739i | 0.170883 | − | 0.818751i | ||||
\(816\) | −8.20871 | −0.287362 | ||||||||
\(817\) | −2.45505 | −0.0858914 | ||||||||
\(818\) | − | 18.9564i | − | 0.662796i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −16.1652 | − | 3.37386i | −0.564512 | − | 0.117820i | ||||
\(821\) | 23.4304i | 0.817725i | 0.912596 | + | 0.408863i | \(0.134074\pi\) | ||||
−0.912596 | + | 0.408863i | \(0.865926\pi\) | |||||||
\(822\) | 0.208712i | 0.00727967i | ||||||||
\(823\) | − | 40.5826i | − | 1.41462i | −0.706904 | − | 0.707310i | \(-0.749909\pi\) | ||
0.706904 | − | 0.707310i | \(-0.250091\pi\) | |||||||
\(824\) | − | 26.2668i | − | 0.915048i | ||||||
\(825\) | 12.1244 | + | 5.29150i | 0.422116 | + | 0.184226i | ||||
\(826\) | 12.7719i | 0.444391i | ||||||||
\(827\) | −31.5583 | −1.09739 | −0.548695 | − | 0.836023i | \(-0.684875\pi\) | ||||
−0.548695 | + | 0.836023i | \(0.684875\pi\) | |||||||
\(828\) | − | 25.5826i | − | 0.889056i | ||||||
\(829\) | −3.33030 | −0.115666 | −0.0578331 | − | 0.998326i | \(-0.518419\pi\) | ||||
−0.0578331 | + | 0.998326i | \(0.518419\pi\) | |||||||
\(830\) | −11.3060 | + | 54.1703i | −0.392437 | + | 1.88028i | ||||
\(831\) | −16.5826 | −0.575243 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.3303i | 0.635107i | ||||||||
\(834\) | − | 12.5812i | − | 0.435652i | ||||||
\(835\) | 1.95644 | − | 9.37386i | 0.0677054 | − | 0.324396i | ||||
\(836\) | −12.7913 | −0.442396 | ||||||||
\(837\) | −48.3465 | −1.67110 | ||||||||
\(838\) | 52.8951 | 1.82723 | ||||||||
\(839\) | − | 1.35065i | − | 0.0466296i | −0.999728 | − | 0.0233148i | \(-0.992578\pi\) | ||
0.999728 | − | 0.0233148i | \(-0.00742201\pi\) | |||||||
\(840\) | 6.56670 | + | 1.37055i | 0.226573 | + | 0.0472885i | ||||
\(841\) | −8.00000 | −0.275862 | ||||||||
\(842\) | 57.4955i | 1.98142i | ||||||||
\(843\) | −17.5112 | −0.603118 | ||||||||
\(844\) | 50.7042 | 1.74531 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −38.3303 | −1.31782 | ||||||||
\(847\) | 6.92820 | 0.238056 | ||||||||
\(848\) | 2.83485i | 0.0973491i | ||||||||
\(849\) | 0.252273 | 0.00865798 | ||||||||
\(850\) | −20.0616 | + | 45.9669i | −0.688108 | + | 1.57665i | ||||
\(851\) | − | 36.3731i | − | 1.24685i | ||||||
\(852\) | −9.93545 | −0.340383 | ||||||||
\(853\) | −53.2566 | −1.82347 | −0.911736 | − | 0.410777i | \(-0.865258\pi\) | ||||
−0.911736 | + | 0.410777i | \(0.865258\pi\) | |||||||
\(854\) | −40.1216 | −1.37293 | ||||||||
\(855\) | 7.58258 | + | 1.58258i | 0.259319 | + | 0.0541229i | ||||
\(856\) | 2.45505i | 0.0839119i | ||||||||
\(857\) | − | 22.7477i | − | 0.777048i | −0.921439 | − | 0.388524i | \(-0.872985\pi\) | ||
0.921439 | − | 0.388524i | \(-0.127015\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.2432 | −1.30484 | −0.652420 | − | 0.757857i | \(-0.726246\pi\) | ||||
−0.652420 | + | 0.757857i | \(0.726246\pi\) | |||||||
\(860\) | 8.66025 | + | 1.80750i | 0.295312 | + | 0.0616352i | ||||
\(861\) | 4.58258 | 0.156174 | ||||||||
\(862\) | 64.8693i | 2.20946i | ||||||||
\(863\) | 34.8317 | 1.18569 | 0.592843 | − | 0.805318i | \(-0.298006\pi\) | ||||
0.592843 | + | 0.805318i | \(0.298006\pi\) | |||||||
\(864\) | − | 36.9253i | − | 1.25622i | ||||||
\(865\) | −16.2360 | − | 3.38865i | −0.552041 | − | 0.115218i | ||||
\(866\) | − | 38.8480i | − | 1.32011i | ||||||
\(867\) | − | 4.00000i | − | 0.135847i | ||||||
\(868\) | 46.7477i | 1.58672i | ||||||||
\(869\) | 15.8745i | 0.538506i | ||||||||
\(870\) | 21.9564 | + | 4.58258i | 0.744393 | + | 0.155364i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | − | 4.74773i | − | 0.160778i | ||||||
\(873\) | −8.94630 | −0.302787 | ||||||||
\(874\) | 17.3739 | 0.587680 | ||||||||
\(875\) | −11.2087 | + | 15.7913i | −0.378924 | + | 0.533843i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.93725 | −0.268022 | −0.134011 | − | 0.990980i | \(-0.542786\pi\) | ||||
−0.134011 | + | 0.990980i | \(0.542786\pi\) | |||||||
\(878\) | −88.6405 | −2.99147 | ||||||||
\(879\) | 23.4304i | 0.790286i | ||||||||
\(880\) | −10.3739 | − | 2.16515i | −0.349703 | − | 0.0729872i | ||||
\(881\) | −18.4955 | −0.623128 | −0.311564 | − | 0.950225i | \(-0.600853\pi\) | ||||
−0.311564 | + | 0.950225i | \(0.600853\pi\) | |||||||
\(882\) | −17.5112 | −0.589633 | ||||||||
\(883\) | − | 46.2432i | − | 1.55621i | −0.628136 | − | 0.778103i | \(-0.716182\pi\) | ||
0.628136 | − | 0.778103i | \(-0.283818\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.53901 | + | 7.37386i | −0.0517334 | + | 0.247870i | ||||
\(886\) | − | 56.7207i | − | 1.90557i | ||||||
\(887\) | 0.495454i | 0.0166357i | 0.999965 | + | 0.00831786i | \(0.00264769\pi\) | ||||
−0.999965 | + | 0.00831786i | \(0.997352\pi\) | |||||||
\(888\) | 13.7477i | 0.461344i | ||||||||
\(889\) | 16.8836i | 0.566256i | ||||||||
\(890\) | 20.5185 | + | 4.28245i | 0.687780 | + | 0.143548i | ||||
\(891\) | 2.64575i | 0.0886360i | ||||||||
\(892\) | 24.1733 | 0.809381 | ||||||||
\(893\) | − | 15.1652i | − | 0.507482i | ||||||
\(894\) | 21.3739 | 0.714849 | ||||||||
\(895\) | 0.0754495 | − | 0.361500i | 0.00252200 | − | 0.0120836i | ||||
\(896\) | −22.1216 | −0.739030 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 82.0345i | − | 2.73753i | ||||||
\(899\) | 44.3103i | 1.47783i | ||||||||
\(900\) | −25.5826 | − | 11.1652i | −0.852753 | − | 0.372172i | ||||
\(901\) | −7.25227 | −0.241608 | ||||||||
\(902\) | 15.3223 | 0.510177 | ||||||||
\(903\) | −2.45505 | −0.0816990 | ||||||||
\(904\) | − | 28.7219i | − | 0.955275i | ||||||
\(905\) | −8.56490 | + | 41.0369i | −0.284707 | + | 1.36411i | ||||
\(906\) | 13.5826 | 0.451251 | ||||||||
\(907\) | 33.7477i | 1.12057i | 0.828298 | + | 0.560287i | \(0.189309\pi\) | ||||
−0.828298 | + | 0.560287i | \(0.810691\pi\) | |||||||
\(908\) | −17.0544 | −0.565969 | ||||||||
\(909\) | 18.0000 | 0.597022 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.9129 | 1.25611 | 0.628055 | − | 0.778169i | \(-0.283851\pi\) | ||||
0.628055 | + | 0.778169i | \(0.283851\pi\) | |||||||
\(912\) | 3.10260 | 0.102737 | ||||||||
\(913\) | − | 29.9129i | − | 0.989972i | ||||||
\(914\) | −3.79129 | −0.125405 | ||||||||
\(915\) | −23.1642 | − | 4.83465i | −0.765785 | − | 0.159829i | ||||
\(916\) | 15.3024i | 0.505606i | ||||||||
\(917\) | 2.74110 | 0.0905191 | ||||||||
\(918\) | 50.1540 | 1.65533 | ||||||||
\(919\) | −35.8348 | −1.18208 | −0.591041 | − | 0.806641i | \(-0.701283\pi\) | ||||
−0.591041 | + | 0.806641i | \(0.701283\pi\) | |||||||
\(920\) | −17.3739 | − | 3.62614i | −0.572799 | − | 0.119550i | ||||
\(921\) | 24.2487i | 0.799022i | ||||||||
\(922\) | 2.62614i | 0.0864872i | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −12.7913 | −0.420802 | ||||||||
\(925\) | −36.3731 | − | 15.8745i | −1.19594 | − | 0.521951i | ||||
\(926\) | −18.0000 | −0.591517 | ||||||||
\(927\) | − | 30.3303i | − | 0.996178i | ||||||
\(928\) | −33.8426 | −1.11094 | ||||||||
\(929\) | 15.9699i | 0.523954i | 0.965074 | + | 0.261977i | \(0.0843745\pi\) | ||||
−0.965074 | + | 0.261977i | \(0.915626\pi\) | |||||||
\(930\) | −9.66930 | + | 46.3284i | −0.317069 | + | 1.51917i | ||||
\(931\) | − | 6.92820i | − | 0.227063i | ||||||
\(932\) | 59.0780i | 1.93517i | ||||||||
\(933\) | − | 1.58258i | − | 0.0518112i | ||||||
\(934\) | − | 26.9898i | − | 0.883134i | ||||||
\(935\) | 5.53901 | − | 26.5390i | 0.181145 | − | 0.867919i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.4955i | 0.767563i | 0.923424 | + | 0.383782i | \(0.125378\pi\) | ||||
−0.923424 | + | 0.383782i | \(0.874622\pi\) | |||||||
\(938\) | −56.3592 | −1.84019 | ||||||||
\(939\) | 30.7477 | 1.00341 | ||||||||
\(940\) | −11.1652 | + | 53.4955i | −0.364167 | + | 1.74483i | ||||
\(941\) | − | 26.4575i | − | 0.862490i | −0.902235 | − | 0.431245i | \(-0.858074\pi\) | ||
0.902235 | − | 0.431245i | \(-0.141926\pi\) | |||||||
\(942\) | −20.0616 | −0.653643 | ||||||||
\(943\) | −12.1244 | −0.394823 | ||||||||
\(944\) | − | 6.03440i | − | 0.196403i | ||||||
\(945\) | 18.9564 | + | 3.95644i | 0.616653 | + | 0.128703i | ||||
\(946\) | −8.20871 | −0.266888 | ||||||||
\(947\) | 38.5819 | 1.25374 | 0.626871 | − | 0.779123i | \(-0.284335\pi\) | ||||
0.626871 | + | 0.779123i | \(0.284335\pi\) | |||||||
\(948\) | 16.7477i | 0.543941i | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 7.58258 | − | 17.3739i | 0.246011 | − | 0.563683i | ||||
\(951\) | 20.9753i | 0.680171i | ||||||||
\(952\) | − | 13.7477i | − | 0.445566i | ||||||
\(953\) | 56.0780i | 1.81655i | 0.418378 | + | 0.908273i | \(0.362599\pi\) | ||||
−0.418378 | + | 0.908273i | \(0.637401\pi\) | |||||||
\(954\) | − | 6.92820i | − | 0.224309i | ||||||
\(955\) | −3.38865 | + | 16.2360i | −0.109654 | + | 0.525385i | ||||
\(956\) | 58.5481i | 1.89358i | ||||||||
\(957\) | −12.1244 | −0.391925 | ||||||||
\(958\) | − | 70.8693i | − | 2.28968i | ||||||
\(959\) | 0.165151 | 0.00533302 | ||||||||
\(960\) | −27.5420 | − | 5.74835i | −0.888915 | − | 0.185527i | ||||
\(961\) | −62.4955 | −2.01598 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.83485i | 0.0913517i | ||||||||
\(964\) | 4.83465i | 0.155714i | ||||||||
\(965\) | 0.460985 | − | 2.20871i | 0.0148396 | − | 0.0711010i | ||||
\(966\) | 17.3739 | 0.558995 | ||||||||
\(967\) | −21.5076 | −0.691638 | −0.345819 | − | 0.938301i | \(-0.612399\pi\) | ||||
−0.345819 | + | 0.938301i | \(0.612399\pi\) | |||||||
\(968\) | 6.92820 | 0.222681 | ||||||||
\(969\) | 7.93725i | 0.254981i | ||||||||
\(970\) | −4.47315 | + | 21.4322i | −0.143624 | + | 0.688145i | ||||
\(971\) | 36.4955 | 1.17119 | 0.585597 | − | 0.810602i | \(-0.300860\pi\) | ||||
0.585597 | + | 0.810602i | \(0.300860\pi\) | |||||||
\(972\) | 44.6606i | 1.43249i | ||||||||
\(973\) | −9.95536 | −0.319154 | ||||||||
\(974\) | 46.1216 | 1.47783 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 18.9564 | 0.606781 | ||||||||
\(977\) | −38.7726 | −1.24044 | −0.620222 | − | 0.784426i | \(-0.712958\pi\) | ||||
−0.620222 | + | 0.784426i | \(0.712958\pi\) | |||||||
\(978\) | 23.3739i | 0.747414i | ||||||||
\(979\) | −11.3303 | −0.362118 | ||||||||
\(980\) | −5.10080 | + | 24.4394i | −0.162939 | + | 0.780688i | ||||
\(981\) | − | 5.48220i | − | 0.175033i | ||||||
\(982\) | 62.5644 | 1.99651 | ||||||||
\(983\) | −3.12250 | −0.0995924 | −0.0497962 | − | 0.998759i | \(-0.515857\pi\) | ||||
−0.0497962 | + | 0.998759i | \(0.515857\pi\) | |||||||
\(984\) | 4.58258 | 0.146087 | ||||||||
\(985\) | 9.12159 | − | 43.7042i | 0.290638 | − | 1.39253i | ||||
\(986\) | − | 45.9669i | − | 1.46389i | ||||||
\(987\) | − | 15.1652i | − | 0.482712i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.49545 | 0.206543 | ||||||||
\(990\) | 25.3531 | + | 5.29150i | 0.805775 | + | 0.168175i | ||||
\(991\) | −13.0000 | −0.412959 | −0.206479 | − | 0.978451i | \(-0.566201\pi\) | ||||
−0.206479 | + | 0.978451i | \(0.566201\pi\) | |||||||
\(992\) | − | 71.4083i | − | 2.26722i | ||||||
\(993\) | 11.4014 | 0.361811 | ||||||||
\(994\) | 13.4949i | 0.428032i | ||||||||
\(995\) | −0.647551 | + | 3.10260i | −0.0205287 | + | 0.0983591i | ||||
\(996\) | − | 31.5583i | − | 0.999963i | ||||||
\(997\) | 18.1652i | 0.575296i | 0.957736 | + | 0.287648i | \(0.0928733\pi\) | ||||
−0.957736 | + | 0.287648i | \(0.907127\pi\) | |||||||
\(998\) | − | 36.3303i | − | 1.15002i | ||||||
\(999\) | 39.6863i | 1.25562i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))