Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,2,Mod(46,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.46");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.h (of order \(5\), degree \(4\), 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: | \(1.79663404548\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.26265625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 2x^{6} + x^{4} + 8x^{2} - 24x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 181.1 | ||
Root | \(-1.21700 - 0.720348i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.181 |
Dual form | 225.2.h.c.46.1 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.655837 | − | 2.01846i | −0.463747 | − | 1.42727i | −0.860552 | − | 0.509363i | \(-0.829881\pi\) |
0.396805 | − | 0.917903i | \(-0.370119\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.02602 | + | 1.47199i | −1.01301 | + | 0.735995i | ||||
\(5\) | 2.21700 | + | 0.291365i | 0.991474 | + | 0.130303i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.35840 | 1.64732 | 0.823660 | − | 0.567083i | \(-0.191928\pi\) | ||||
0.823660 | + | 0.567083i | \(0.191928\pi\) | |||||||
\(8\) | 0.865884 | + | 0.629102i | 0.306136 | + | 0.222421i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.865884 | − | 4.66602i | −0.273817 | − | 1.47553i | ||||
\(11\) | 0.488218 | + | 1.50258i | 0.147203 | + | 0.453045i | 0.997288 | − | 0.0736014i | \(-0.0234493\pi\) |
−0.850085 | + | 0.526646i | \(0.823449\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.370184 | − | 1.13931i | 0.102670 | − | 0.315987i | −0.886506 | − | 0.462717i | \(-0.846875\pi\) |
0.989177 | + | 0.146729i | \(0.0468747\pi\) | |||||||
\(14\) | −2.85840 | − | 8.79726i | −0.763940 | − | 2.35117i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.845805 | + | 2.60312i | −0.211451 | + | 0.650780i | ||||
\(17\) | −0.907987 | − | 0.659691i | −0.220219 | − | 0.159999i | 0.472206 | − | 0.881488i | \(-0.343458\pi\) |
−0.692425 | + | 0.721490i | \(0.743458\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.21218 | − | 4.51341i | −1.42517 | − | 1.03545i | −0.990890 | − | 0.134670i | \(-0.957002\pi\) |
−0.434281 | − | 0.900777i | \(-0.642998\pi\) | |||||||
\(20\) | −4.92058 | + | 2.67310i | −1.10028 | + | 0.597722i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.71270 | − | 1.97090i | 0.578351 | − | 0.420196i | ||||
\(23\) | 0.717004 | + | 2.20671i | 0.149506 | + | 0.460131i | 0.997563 | − | 0.0697736i | \(-0.0222277\pi\) |
−0.848057 | + | 0.529905i | \(0.822228\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.83021 | + | 1.29192i | 0.966042 | + | 0.258383i | ||||
\(26\) | −2.54243 | −0.498611 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −8.83021 | + | 6.41552i | −1.66875 | + | 1.21242i | ||||
\(29\) | −4.45307 | + | 3.23535i | −0.826915 | + | 0.600789i | −0.918685 | − | 0.394992i | \(-0.870748\pi\) |
0.0917701 | + | 0.995780i | \(0.470748\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.88495 | − | 2.82258i | −0.697757 | − | 0.506950i | 0.181444 | − | 0.983401i | \(-0.441923\pi\) |
−0.879201 | + | 0.476451i | \(0.841923\pi\) | |||||||
\(32\) | 7.94959 | 1.40530 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.736068 | + | 2.26538i | −0.126235 | + | 0.388510i | ||||
\(35\) | 9.66259 | + | 1.26989i | 1.63328 | + | 0.214650i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.96915 | + | 6.06043i | −0.323727 | + | 0.996329i | 0.648285 | + | 0.761398i | \(0.275486\pi\) |
−0.972012 | + | 0.234931i | \(0.924514\pi\) | |||||||
\(38\) | −5.03596 | + | 15.4991i | −0.816941 | + | 2.51428i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.73637 | + | 1.64701i | 0.274544 | + | 0.260415i | ||||
\(41\) | 2.30902 | − | 7.10642i | 0.360608 | − | 1.10984i | −0.592078 | − | 0.805881i | \(-0.701692\pi\) |
0.952686 | − | 0.303956i | \(-0.0983077\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.24998 | −0.190620 | −0.0953102 | − | 0.995448i | \(-0.530384\pi\) | ||||
−0.0953102 | + | 0.995448i | \(0.530384\pi\) | |||||||
\(44\) | −3.20092 | − | 2.32561i | −0.482557 | − | 0.350598i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.98392 | − | 2.89449i | 0.587397 | − | 0.426769i | ||||
\(47\) | 3.33934 | − | 2.42617i | 0.487092 | − | 0.353893i | −0.316973 | − | 0.948435i | \(-0.602666\pi\) |
0.804065 | + | 0.594541i | \(0.202666\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.9957 | 1.71367 | ||||||||
\(50\) | −0.560152 | − | 10.5969i | −0.0792174 | − | 1.49862i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.927051 | + | 2.85317i | 0.128559 | + | 0.395663i | ||||
\(53\) | 3.03032 | − | 2.20166i | 0.416247 | − | 0.302421i | −0.359879 | − | 0.932999i | \(-0.617182\pi\) |
0.776126 | + | 0.630578i | \(0.217182\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.644581 | + | 3.47347i | 0.0869153 | + | 0.468363i | ||||
\(56\) | 3.77387 | + | 2.74188i | 0.504305 | + | 0.366399i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9.45090 | + | 6.86648i | 1.24096 | + | 0.901613i | ||||
\(59\) | −2.82940 | + | 8.70799i | −0.368356 | + | 1.13368i | 0.579496 | + | 0.814975i | \(0.303249\pi\) |
−0.947853 | + | 0.318709i | \(0.896751\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.431351 | + | 1.32756i | 0.0552288 | + | 0.169977i | 0.974866 | − | 0.222792i | \(-0.0715172\pi\) |
−0.919637 | + | 0.392769i | \(0.871517\pi\) | |||||||
\(62\) | −3.14937 | + | 9.69276i | −0.399970 | + | 1.23098i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.52202 | − | 10.8397i | −0.440253 | − | 1.35496i | ||||
\(65\) | 1.15265 | − | 2.41799i | 0.142969 | − | 0.299915i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.12499 | + | 2.27044i | 0.381778 | + | 0.277378i | 0.762078 | − | 0.647485i | \(-0.224179\pi\) |
−0.380300 | + | 0.924863i | \(0.624179\pi\) | |||||||
\(68\) | 2.81066 | 0.340843 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.77387 | − | 20.3364i | −0.451064 | − | 2.43066i | ||||
\(71\) | −8.57970 | + | 6.23352i | −1.01822 | + | 0.739783i | −0.965918 | − | 0.258848i | \(-0.916657\pi\) |
−0.0523057 | + | 0.998631i | \(0.516657\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.54407 | + | 4.75216i | 0.180720 | + | 0.556198i | 0.999848 | − | 0.0174117i | \(-0.00554259\pi\) |
−0.819129 | + | 0.573610i | \(0.805543\pi\) | |||||||
\(74\) | 13.5242 | 1.57215 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 19.2297 | 2.20580 | ||||||||
\(77\) | 2.12785 | + | 6.54885i | 0.242491 | + | 0.746310i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.7737 | + | 8.55407i | −1.32464 | + | 0.962408i | −0.324779 | + | 0.945790i | \(0.605290\pi\) |
−0.999862 | + | 0.0166185i | \(0.994710\pi\) | |||||||
\(80\) | −2.63361 | + | 5.52469i | −0.294447 | + | 0.617679i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −15.8584 | −1.75126 | ||||||||
\(83\) | −7.06760 | − | 5.13491i | −0.775770 | − | 0.563630i | 0.127937 | − | 0.991782i | \(-0.459165\pi\) |
−0.903706 | + | 0.428153i | \(0.859165\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.82080 | − | 1.72709i | −0.197493 | − | 0.187330i | ||||
\(86\) | 0.819784 | + | 2.52304i | 0.0883996 | + | 0.272066i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.522535 | + | 1.60820i | −0.0557025 | + | 0.171435i | ||||
\(89\) | 3.10195 | + | 9.54683i | 0.328806 | + | 1.01196i | 0.969693 | + | 0.244326i | \(0.0785668\pi\) |
−0.640887 | + | 0.767635i | \(0.721433\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.61341 | − | 4.96556i | 0.169131 | − | 0.520532i | ||||
\(92\) | −4.70092 | − | 3.41542i | −0.490105 | − | 0.356082i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.08719 | − | 5.14914i | −0.730988 | − | 0.531094i | ||||
\(95\) | −12.4574 | − | 11.8163i | −1.27810 | − | 1.21232i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.06760 | − | 4.40837i | 0.616071 | − | 0.447602i | −0.235476 | − | 0.971880i | \(-0.575665\pi\) |
0.851547 | + | 0.524278i | \(0.175665\pi\) | |||||||
\(98\) | −7.86720 | − | 24.2128i | −0.794707 | − | 2.44586i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −11.6878 | + | 4.49258i | −1.16878 | + | 0.449258i | ||||
\(101\) | 6.51821 | 0.648586 | 0.324293 | − | 0.945957i | \(-0.394874\pi\) | ||||
0.324293 | + | 0.945957i | \(0.394874\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.51158 | + | 4.73094i | −0.641605 | + | 0.466153i | −0.860401 | − | 0.509617i | \(-0.829787\pi\) |
0.218796 | + | 0.975771i | \(0.429787\pi\) | |||||||
\(104\) | 1.03728 | − | 0.753626i | 0.101713 | − | 0.0738991i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.43135 | − | 4.67265i | −0.624668 | − | 0.453848i | ||||
\(107\) | −9.47745 | −0.916220 | −0.458110 | − | 0.888896i | \(-0.651473\pi\) | ||||
−0.458110 | + | 0.888896i | \(0.651473\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.60491 | + | 11.0948i | −0.345288 | + | 1.06269i | 0.616142 | + | 0.787635i | \(0.288695\pi\) |
−0.961429 | + | 0.275052i | \(0.911305\pi\) | |||||||
\(110\) | 6.58833 | − | 3.57909i | 0.628172 | − | 0.341253i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.68636 | + | 11.3454i | −0.348328 | + | 1.07204i | ||||
\(113\) | 4.61219 | − | 14.1949i | 0.433879 | − | 1.33534i | −0.460353 | − | 0.887736i | \(-0.652277\pi\) |
0.894231 | − | 0.447605i | \(-0.147723\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.946641 | + | 5.10120i | 0.0882747 | + | 0.475689i | ||||
\(116\) | 4.25962 | − | 13.1098i | 0.395496 | − | 1.21721i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 19.4324 | 1.78889 | ||||||||
\(119\) | −3.95737 | − | 2.87520i | −0.362772 | − | 0.263569i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.87980 | − | 4.99847i | 0.625436 | − | 0.454406i | ||||
\(122\) | 2.39673 | − | 1.74133i | 0.216990 | − | 0.157652i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 12.0258 | 1.07995 | ||||||||
\(125\) | 10.3322 | + | 4.27154i | 0.924138 | + | 0.382058i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.25195 | − | 16.1638i | −0.466035 | − | 1.43431i | −0.857676 | − | 0.514190i | \(-0.828092\pi\) |
0.391641 | − | 0.920118i | \(-0.371908\pi\) | |||||||
\(128\) | −6.70686 | + | 4.87282i | −0.592809 | + | 0.430701i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.63657 | − | 0.740776i | −0.494360 | − | 0.0649703i | ||||
\(131\) | −0.266063 | − | 0.193306i | −0.0232461 | − | 0.0168892i | 0.576102 | − | 0.817378i | \(-0.304573\pi\) |
−0.599348 | + | 0.800489i | \(0.704573\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −27.0752 | − | 19.6713i | −2.34771 | − | 1.70571i | ||||
\(134\) | 2.53330 | − | 7.79670i | 0.218844 | − | 0.673533i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.371199 | − | 1.14243i | −0.0318300 | − | 0.0979628i | ||||
\(137\) | −1.40995 | + | 4.33939i | −0.120461 | + | 0.370739i | −0.993047 | − | 0.117721i | \(-0.962441\pi\) |
0.872586 | + | 0.488460i | \(0.162441\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.46289 | − | 4.50230i | −0.124080 | − | 0.381880i | 0.869652 | − | 0.493665i | \(-0.164343\pi\) |
−0.993732 | + | 0.111785i | \(0.964343\pi\) | |||||||
\(140\) | −21.4459 | + | 11.6504i | −1.81251 | + | 0.984641i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 18.2090 | + | 13.2296i | 1.52806 | + | 1.11020i | ||||
\(143\) | 1.89263 | 0.158270 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.8151 | + | 5.87530i | −0.898149 | + | 0.487917i | ||||
\(146\) | 8.57938 | − | 6.23328i | 0.710035 | − | 0.515870i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.93135 | − | 15.1771i | −0.405355 | − | 1.24755i | ||||
\(149\) | −4.67644 | −0.383109 | −0.191555 | − | 0.981482i | \(-0.561353\pi\) | ||||
−0.191555 | + | 0.981482i | \(0.561353\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.54178 | −0.532362 | −0.266181 | − | 0.963923i | \(-0.585762\pi\) | ||||
−0.266181 | + | 0.963923i | \(0.585762\pi\) | |||||||
\(152\) | −2.53963 | − | 7.81618i | −0.205991 | − | 0.633976i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 11.8231 | − | 8.58995i | 0.952729 | − | 0.692198i | ||||
\(155\) | −7.79054 | − | 7.38961i | −0.625751 | − | 0.593548i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.99404 | 0.318759 | 0.159379 | − | 0.987217i | \(-0.449051\pi\) | ||||
0.159379 | + | 0.987217i | \(0.449051\pi\) | |||||||
\(158\) | 24.9877 | + | 18.1546i | 1.98791 | + | 1.44430i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 17.6243 | + | 2.31623i | 1.39332 | + | 0.183114i | ||||
\(161\) | 3.12499 | + | 9.61773i | 0.246284 | + | 0.757984i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.48372 | − | 4.56641i | 0.116214 | − | 0.357669i | −0.875985 | − | 0.482339i | \(-0.839787\pi\) |
0.992198 | + | 0.124670i | \(0.0397873\pi\) | |||||||
\(164\) | 5.78247 | + | 17.7966i | 0.451535 | + | 1.38968i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.72941 | + | 17.6333i | −0.444689 | + | 1.36861i | ||||
\(167\) | 19.1414 | + | 13.9070i | 1.48120 | + | 1.07616i | 0.977167 | + | 0.212474i | \(0.0681522\pi\) |
0.504036 | + | 0.863682i | \(0.331848\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.35623 | + | 6.79770i | 0.719710 | + | 0.522900i | ||||
\(170\) | −2.29192 | + | 4.80790i | −0.175782 | + | 0.368749i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.53249 | − | 1.83996i | 0.193100 | − | 0.140296i | ||||
\(173\) | −4.48208 | − | 13.7944i | −0.340766 | − | 1.04877i | −0.963812 | − | 0.266584i | \(-0.914105\pi\) |
0.623046 | − | 0.782185i | \(-0.285895\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 21.0520 | + | 5.63069i | 1.59138 | + | 0.425640i | ||||
\(176\) | −4.32433 | −0.325959 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 17.2355 | − | 12.5223i | 1.29186 | − | 0.938588i | ||||
\(179\) | 0.644581 | − | 0.468315i | 0.0481782 | − | 0.0350035i | −0.563436 | − | 0.826160i | \(-0.690521\pi\) |
0.611614 | + | 0.791157i | \(0.290521\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.5030 | + | 8.35741i | 0.855010 | + | 0.621201i | 0.926523 | − | 0.376239i | \(-0.122783\pi\) |
−0.0715129 | + | 0.997440i | \(0.522783\pi\) | |||||||
\(182\) | −11.0809 | −0.821372 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.767403 | + | 2.36182i | −0.0565737 | + | 0.174116i | ||||
\(185\) | −6.13142 | + | 12.8623i | −0.450791 | + | 0.945652i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.547943 | − | 1.68640i | 0.0400696 | − | 0.123321i | ||||
\(188\) | −3.19427 | + | 9.83094i | −0.232966 | + | 0.716995i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −15.6806 | + | 32.8942i | −1.13759 | + | 2.38640i | ||||
\(191\) | 3.20441 | − | 9.86215i | 0.231863 | − | 0.713600i | −0.765659 | − | 0.643246i | \(-0.777587\pi\) |
0.997522 | − | 0.0703540i | \(-0.0224129\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.34712 | 0.312913 | 0.156456 | − | 0.987685i | \(-0.449993\pi\) | ||||
0.156456 | + | 0.987685i | \(0.449993\pi\) | |||||||
\(194\) | −12.8775 | − | 9.35603i | −0.924548 | − | 0.671724i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −24.3035 | + | 17.6575i | −1.73596 | + | 1.26125i | ||||
\(197\) | 1.52087 | − | 1.10498i | 0.108358 | − | 0.0787263i | −0.532287 | − | 0.846564i | \(-0.678667\pi\) |
0.640644 | + | 0.767838i | \(0.278667\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.26028 | 0.302003 | 0.151002 | − | 0.988534i | \(-0.451750\pi\) | ||||
0.151002 | + | 0.988534i | \(0.451750\pi\) | |||||||
\(200\) | 3.36966 | + | 4.15735i | 0.238271 | + | 0.293969i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.27489 | − | 13.1567i | −0.300780 | − | 0.925705i | ||||
\(203\) | −19.4083 | + | 14.1009i | −1.36219 | + | 0.989692i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.18967 | − | 15.0822i | 0.502148 | − | 1.05339i | ||||
\(206\) | 13.8197 | + | 10.0406i | 0.962867 | + | 0.699564i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.65265 | + | 1.92727i | 0.183928 | + | 0.133632i | ||||
\(209\) | 3.74887 | − | 11.5378i | 0.259314 | − | 0.798088i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.87284 | − | 8.84170i | −0.197775 | − | 0.608687i | −0.999933 | − | 0.0115762i | \(-0.996315\pi\) |
0.802158 | − | 0.597111i | \(-0.203685\pi\) | |||||||
\(212\) | −2.89868 | + | 8.92120i | −0.199082 | + | 0.612711i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.21566 | + | 19.1298i | 0.424894 | + | 1.30769i | ||||
\(215\) | −2.77121 | − | 0.364201i | −0.188995 | − | 0.0248383i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16.9322 | − | 12.3019i | −1.14943 | − | 0.835110i | ||||
\(218\) | 24.7586 | 1.67686 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.41886 | − | 6.08852i | −0.432759 | − | 0.410488i | ||||
\(221\) | −1.08771 | + | 0.790270i | −0.0731675 | + | 0.0531593i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.04991 | − | 3.23129i | −0.0703072 | − | 0.216383i | 0.909729 | − | 0.415203i | \(-0.136289\pi\) |
−0.980036 | + | 0.198819i | \(0.936289\pi\) | |||||||
\(224\) | 34.6475 | 2.31498 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −31.6766 | −2.10710 | ||||||||
\(227\) | −8.28083 | − | 25.4858i | −0.549618 | − | 1.69155i | −0.709750 | − | 0.704454i | \(-0.751192\pi\) |
0.160132 | − | 0.987096i | \(-0.448808\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.956255 | − | 0.694760i | 0.0631911 | − | 0.0459110i | −0.555741 | − | 0.831355i | \(-0.687565\pi\) |
0.618932 | + | 0.785444i | \(0.287565\pi\) | |||||||
\(230\) | 9.67572 | − | 5.25631i | 0.637998 | − | 0.346591i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.89121 | −0.386777 | ||||||||
\(233\) | 5.73984 | + | 4.17024i | 0.376030 | + | 0.273201i | 0.759707 | − | 0.650266i | \(-0.225342\pi\) |
−0.383677 | + | 0.923467i | \(0.625342\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.11023 | − | 4.40586i | 0.529053 | − | 0.287407i | ||||
\(236\) | −7.08566 | − | 21.8074i | −0.461237 | − | 1.41954i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.20808 | + | 9.87345i | −0.207949 | + | 0.640001i | ||||
\(239\) | −0.0132236 | − | 0.0406981i | −0.000855365 | − | 0.00263254i | 0.950628 | − | 0.310333i | \(-0.100441\pi\) |
−0.951483 | + | 0.307700i | \(0.900441\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.63746 | + | 11.1950i | −0.234310 | + | 0.721131i | 0.762903 | + | 0.646513i | \(0.223774\pi\) |
−0.997212 | + | 0.0746174i | \(0.976226\pi\) | |||||||
\(242\) | −14.6012 | − | 10.6084i | −0.938602 | − | 0.681934i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.82808 | − | 2.05472i | −0.181049 | − | 0.131540i | ||||
\(245\) | 26.5944 | + | 3.49512i | 1.69906 | + | 0.223295i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.44182 | + | 5.40680i | −0.473511 | + | 0.344026i | ||||
\(248\) | −1.58823 | − | 4.88806i | −0.100852 | − | 0.310392i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.84570 | − | 23.6565i | 0.116733 | − | 1.49617i | ||||
\(251\) | −17.4764 | −1.10310 | −0.551550 | − | 0.834142i | \(-0.685964\pi\) | ||||
−0.551550 | + | 0.834142i | \(0.685964\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.96571 | + | 2.15471i | −0.186452 | + | 0.135466i | ||||
\(254\) | −29.1816 | + | 21.2017i | −1.83102 | + | 1.33031i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.20735 | − | 3.05682i | −0.262960 | − | 0.191051i | ||||
\(257\) | −15.4671 | −0.964814 | −0.482407 | − | 0.875947i | \(-0.660237\pi\) | ||||
−0.482407 | + | 0.875947i | \(0.660237\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.58236 | + | 26.4138i | −0.533282 | + | 1.64127i | ||||
\(260\) | 1.22396 | + | 6.59560i | 0.0759068 | + | 0.409042i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.215687 | + | 0.663815i | −0.0133252 | + | 0.0410106i | ||||
\(263\) | −0.447331 | + | 1.37674i | −0.0275836 | + | 0.0848936i | −0.963901 | − | 0.266262i | \(-0.914211\pi\) |
0.936317 | + | 0.351156i | \(0.114211\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.35972 | − | 3.99815i | 0.452104 | − | 0.245604i | ||||
\(266\) | −21.9487 | + | 67.5513i | −1.34576 | + | 4.14183i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −9.67336 | −0.590895 | ||||||||
\(269\) | −7.04344 | − | 5.11736i | −0.429446 | − | 0.312011i | 0.351981 | − | 0.936007i | \(-0.385508\pi\) |
−0.781427 | + | 0.623996i | \(0.785508\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.1652 | − | 16.8305i | 1.40719 | − | 1.02238i | 0.413462 | − | 0.910521i | \(-0.364319\pi\) |
0.993724 | − | 0.111860i | \(-0.0356807\pi\) | |||||||
\(272\) | 2.48524 | − | 1.80563i | 0.150690 | − | 0.109482i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.68359 | 0.585007 | ||||||||
\(275\) | 0.416988 | + | 7.88852i | 0.0251453 | + | 0.475695i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.63844 | + | 5.04259i | 0.0984442 | + | 0.302980i | 0.988136 | − | 0.153582i | \(-0.0490808\pi\) |
−0.889692 | + | 0.456562i | \(0.849081\pi\) | |||||||
\(278\) | −8.12830 | + | 5.90555i | −0.487503 | + | 0.354192i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 7.56780 | + | 7.17833i | 0.452262 | + | 0.428987i | ||||
\(281\) | −19.4837 | − | 14.1557i | −1.16230 | − | 0.844461i | −0.172234 | − | 0.985056i | \(-0.555098\pi\) |
−0.990067 | + | 0.140595i | \(0.955098\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.9359 | + | 15.9374i | 1.30396 | + | 0.947380i | 0.999986 | − | 0.00530192i | \(-0.00168766\pi\) |
0.303970 | + | 0.952682i | \(0.401688\pi\) | |||||||
\(284\) | 8.20698 | − | 25.2585i | 0.486995 | − | 1.49882i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.24126 | − | 3.82020i | −0.0733971 | − | 0.225893i | ||||
\(287\) | 10.0636 | − | 30.9726i | 0.594037 | − | 1.82826i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.86404 | − | 14.9700i | −0.286120 | − | 0.880587i | ||||
\(290\) | 18.9520 | + | 17.9767i | 1.11290 | + | 1.05563i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −10.1234 | − | 7.35512i | −0.592430 | − | 0.430426i | ||||
\(293\) | 20.3016 | 1.18603 | 0.593017 | − | 0.805190i | \(-0.297937\pi\) | ||||
0.593017 | + | 0.805190i | \(0.297937\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.81000 | + | 18.4813i | −0.512938 | + | 1.07602i | ||||
\(296\) | −5.51769 | + | 4.00883i | −0.320709 | + | 0.233009i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.06698 | + | 9.43921i | 0.177666 | + | 0.546799i | ||||
\(299\) | 2.77955 | 0.160745 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.44792 | −0.314013 | ||||||||
\(302\) | 4.29034 | + | 13.2043i | 0.246881 | + | 0.759823i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 17.0032 | − | 12.3536i | 0.975203 | − | 0.708527i | ||||
\(305\) | 0.569501 | + | 3.06889i | 0.0326095 | + | 0.175724i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.51330 | −0.143442 | −0.0717208 | − | 0.997425i | \(-0.522849\pi\) | ||||
−0.0717208 | + | 0.997425i | \(0.522849\pi\) | |||||||
\(308\) | −13.9509 | − | 10.1359i | −0.794927 | − | 0.577548i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −9.80630 | + | 20.5713i | −0.556960 | + | 1.16837i | ||||
\(311\) | −1.49075 | − | 4.58806i | −0.0845327 | − | 0.260165i | 0.899852 | − | 0.436195i | \(-0.143674\pi\) |
−0.984385 | + | 0.176030i | \(0.943674\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.85043 | + | 5.69504i | −0.104592 | + | 0.321903i | −0.989635 | − | 0.143608i | \(-0.954129\pi\) |
0.885042 | + | 0.465511i | \(0.154129\pi\) | |||||||
\(314\) | −2.61944 | − | 8.06180i | −0.147823 | − | 0.454954i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.2622 | − | 34.6615i | 0.633548 | − | 1.94986i | ||||
\(317\) | 14.0389 | + | 10.1999i | 0.788506 | + | 0.572883i | 0.907520 | − | 0.420010i | \(-0.137973\pi\) |
−0.119014 | + | 0.992893i | \(0.537973\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.03543 | − | 5.11154i | −0.393909 | − | 0.286191i | ||||
\(320\) | −4.65003 | − | 25.0578i | −0.259945 | − | 1.40077i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 17.3635 | − | 12.6153i | 0.967631 | − | 0.703025i | ||||
\(323\) | 2.66312 | + | 8.19624i | 0.148180 | + | 0.456051i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.25996 | − | 5.02486i | 0.180830 | − | 0.278729i | ||||
\(326\) | −10.1902 | −0.564383 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.47000 | − | 4.70073i | 0.357246 | − | 0.259555i | ||||
\(329\) | 14.5542 | − | 10.5742i | 0.802398 | − | 0.582976i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.4518 | − | 11.9529i | −0.904270 | − | 0.656991i | 0.0352890 | − | 0.999377i | \(-0.488765\pi\) |
−0.939559 | + | 0.342386i | \(0.888765\pi\) | |||||||
\(332\) | 21.8776 | 1.20069 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 15.5171 | − | 47.7568i | 0.849059 | − | 2.61314i | ||||
\(335\) | 6.26659 | + | 5.94409i | 0.342380 | + | 0.324760i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.5860 | − | 32.5805i | 0.576658 | − | 1.77477i | −0.0538048 | − | 0.998551i | \(-0.517135\pi\) |
0.630463 | − | 0.776219i | \(-0.282865\pi\) | |||||||
\(338\) | 7.58472 | − | 23.3434i | 0.412554 | − | 1.26971i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.23124 | + | 0.818929i | 0.337937 | + | 0.0444127i | ||||
\(341\) | 2.34445 | − | 7.21548i | 0.126959 | − | 0.390740i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 21.7731 | 1.17564 | ||||||||
\(344\) | −1.08234 | − | 0.786366i | −0.0583558 | − | 0.0423980i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −24.9039 | + | 18.0938i | −1.33884 | + | 0.972727i | ||||
\(347\) | −0.0399344 | + | 0.0290140i | −0.00214379 | + | 0.00155756i | −0.588857 | − | 0.808238i | \(-0.700422\pi\) |
0.586713 | + | 0.809795i | \(0.300422\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.47437 | −0.400094 | −0.200047 | − | 0.979786i | \(-0.564109\pi\) | ||||
−0.200047 | + | 0.979786i | \(0.564109\pi\) | |||||||
\(350\) | −2.44137 | − | 46.1854i | −0.130497 | − | 2.46871i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.88113 | + | 11.9449i | 0.206865 | + | 0.636665i | ||||
\(353\) | −15.0194 | + | 10.9122i | −0.799401 | + | 0.580799i | −0.910738 | − | 0.412984i | \(-0.864487\pi\) |
0.111337 | + | 0.993783i | \(0.464487\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −20.8375 | + | 11.3199i | −1.10594 | + | 0.600798i | ||||
\(356\) | −20.3375 | − | 14.7760i | −1.07788 | − | 0.783128i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.36802 | − | 0.993921i | −0.0723019 | − | 0.0525304i | ||||
\(359\) | −3.27695 | + | 10.0854i | −0.172951 | + | 0.532289i | −0.999534 | − | 0.0305264i | \(-0.990282\pi\) |
0.826583 | + | 0.562815i | \(0.190282\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.3490 | + | 38.0062i | 0.649945 | + | 2.00032i | ||||
\(362\) | 9.32500 | − | 28.6994i | 0.490111 | − | 1.50841i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.04046 | + | 12.4353i | 0.211778 | + | 0.651785i | ||||
\(365\) | 2.03859 | + | 10.9854i | 0.106705 | + | 0.575004i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.39886 | + | 6.82867i | 0.490617 | + | 0.356454i | 0.805421 | − | 0.592703i | \(-0.201939\pi\) |
−0.314805 | + | 0.949156i | \(0.601939\pi\) | |||||||
\(368\) | −6.35078 | −0.331057 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 29.9832 | + | 3.94048i | 1.55875 | + | 0.204856i | ||||
\(371\) | 13.2074 | − | 9.59570i | 0.685692 | − | 0.498184i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.14671 | − | 21.9953i | −0.370043 | − | 1.13887i | −0.946763 | − | 0.321932i | \(-0.895668\pi\) |
0.576720 | − | 0.816942i | \(-0.304332\pi\) | |||||||
\(374\) | −3.76328 | −0.194595 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.41779 | 0.227830 | ||||||||
\(377\) | 2.03760 | + | 6.27109i | 0.104942 | + | 0.322978i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.1374 | + | 14.6307i | −1.03439 | + | 0.751527i | −0.969182 | − | 0.246345i | \(-0.920770\pi\) |
−0.0652058 | + | 0.997872i | \(0.520770\pi\) | |||||||
\(380\) | 42.6323 | + | 5.60287i | 2.18699 | + | 0.287421i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −22.0079 | −1.12602 | ||||||||
\(383\) | −12.7195 | − | 9.24123i | −0.649934 | − | 0.472205i | 0.213315 | − | 0.976984i | \(-0.431574\pi\) |
−0.863249 | + | 0.504779i | \(0.831574\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.80934 | + | 15.1388i | 0.143177 | + | 0.771545i | ||||
\(386\) | −2.85100 | − | 8.77449i | −0.145112 | − | 0.446610i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.80400 | + | 17.8629i | −0.294654 | + | 0.906851i | ||||
\(389\) | 2.62860 | + | 8.09000i | 0.133275 | + | 0.410179i | 0.995318 | − | 0.0966568i | \(-0.0308149\pi\) |
−0.862042 | + | 0.506836i | \(0.830815\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.804717 | − | 2.47667i | 0.0406963 | − | 0.125250i | ||||
\(392\) | 10.3869 | + | 7.54649i | 0.524615 | + | 0.381155i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.22779 | − | 2.34513i | −0.162614 | − | 0.118146i | ||||
\(395\) | −28.5946 | + | 15.5340i | −1.43875 | + | 0.781599i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.2407 | + | 15.4322i | −1.06604 | + | 0.774522i | −0.975196 | − | 0.221343i | \(-0.928956\pi\) |
−0.0908420 | + | 0.995865i | \(0.528956\pi\) | |||||||
\(398\) | −2.79405 | − | 8.59921i | −0.140053 | − | 0.431039i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7.44843 | + | 11.4809i | −0.372422 | + | 0.574046i | ||||
\(401\) | 25.2815 | 1.26250 | 0.631250 | − | 0.775579i | \(-0.282542\pi\) | ||||
0.631250 | + | 0.775579i | \(0.282542\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.65393 | + | 3.38128i | −0.231829 | + | 0.168434i | ||||
\(404\) | −13.2060 | + | 9.59475i | −0.657025 | + | 0.477356i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 41.1908 | + | 29.9269i | 2.04427 | + | 1.48525i | ||||
\(407\) | −10.0677 | −0.499035 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.4427 | − | 32.1392i | 0.516357 | − | 1.58918i | −0.264443 | − | 0.964401i | \(-0.585188\pi\) |
0.780800 | − | 0.624781i | \(-0.214812\pi\) | |||||||
\(410\) | −35.1581 | − | 4.62058i | −1.73633 | − | 0.228194i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.22870 | − | 19.1700i | 0.306866 | − | 0.944437i | ||||
\(413\) | −12.3317 | + | 37.9529i | −0.606801 | + | 1.86754i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.1728 | − | 13.4434i | −0.695713 | − | 0.659909i | ||||
\(416\) | 2.94281 | − | 9.05703i | 0.144283 | − | 0.444057i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −25.7473 | −1.25934 | ||||||||
\(419\) | 6.41819 | + | 4.66309i | 0.313549 | + | 0.227807i | 0.733418 | − | 0.679778i | \(-0.237924\pi\) |
−0.419869 | + | 0.907585i | \(0.637924\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.05788 | + | 4.40131i | −0.295243 | + | 0.214507i | −0.725539 | − | 0.688181i | \(-0.758409\pi\) |
0.430296 | + | 0.902688i | \(0.358409\pi\) | |||||||
\(422\) | −15.9625 | + | 11.5974i | −0.777042 | + | 0.564554i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.00897 | 0.194693 | ||||||||
\(425\) | −3.53350 | − | 4.35949i | −0.171400 | − | 0.211466i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.88000 | + | 5.78604i | 0.0909795 | + | 0.280006i | ||||
\(428\) | 19.2015 | − | 13.9507i | 0.928140 | − | 0.674333i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.08234 | + | 5.83244i | 0.0521950 | + | 0.281265i | ||||
\(431\) | 18.8882 | + | 13.7231i | 0.909811 | + | 0.661016i | 0.940967 | − | 0.338498i | \(-0.109919\pi\) |
−0.0311564 | + | 0.999515i | \(0.509919\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.71569 | + | 1.97306i | 0.130508 | + | 0.0948193i | 0.651124 | − | 0.758971i | \(-0.274298\pi\) |
−0.520616 | + | 0.853791i | \(0.674298\pi\) | |||||||
\(434\) | −13.7262 | + | 42.2449i | −0.658879 | + | 2.02782i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.02778 | − | 27.7846i | −0.432352 | − | 1.33064i | ||||
\(437\) | 5.50564 | − | 16.9446i | 0.263370 | − | 0.810571i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.93072 | − | 9.01984i | −0.139876 | − | 0.430493i | 0.856441 | − | 0.516245i | \(-0.172671\pi\) |
−0.996317 | + | 0.0857520i | \(0.972671\pi\) | |||||||
\(440\) | −1.62704 | + | 3.41313i | −0.0775659 | + | 0.162715i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.30849 | + | 1.67722i | 0.109804 | + | 0.0797771i | ||||
\(443\) | −9.65446 | −0.458697 | −0.229349 | − | 0.973344i | \(-0.573660\pi\) | ||||
−0.229349 | + | 0.973344i | \(0.573660\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.09542 | + | 22.0692i | 0.194142 | + | 1.04618i | ||||
\(446\) | −5.83366 | + | 4.23840i | −0.276232 | + | 0.200694i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −15.3504 | − | 47.2437i | −0.725238 | − | 2.23205i | ||||
\(449\) | −31.5260 | −1.48780 | −0.743902 | − | 0.668289i | \(-0.767027\pi\) | ||||
−0.743902 | + | 0.668289i | \(0.767027\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.8053 | 0.555888 | ||||||||
\(452\) | 11.5503 | + | 35.5482i | 0.543281 | + | 1.67205i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −46.0111 | + | 33.4290i | −2.15941 | + | 1.56890i | ||||
\(455\) | 5.02373 | − | 10.5386i | 0.235516 | − | 0.494056i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.94467 | −0.465192 | −0.232596 | − | 0.972573i | \(-0.574722\pi\) | ||||
−0.232596 | + | 0.972573i | \(0.574722\pi\) | |||||||
\(458\) | −2.02949 | − | 1.47451i | −0.0948319 | − | 0.0688994i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −9.42683 | − | 8.94169i | −0.439528 | − | 0.416908i | ||||
\(461\) | 7.31863 | + | 22.5244i | 0.340863 | + | 1.04907i | 0.963762 | + | 0.266765i | \(0.0859548\pi\) |
−0.622899 | + | 0.782302i | \(0.714045\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.54443 | − | 26.2971i | 0.397094 | − | 1.22213i | −0.530226 | − | 0.847857i | \(-0.677893\pi\) |
0.927319 | − | 0.374272i | \(-0.122107\pi\) | |||||||
\(464\) | −4.65556 | − | 14.3284i | −0.216129 | − | 0.665177i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.65306 | − | 14.3206i | 0.215549 | − | 0.663391i | ||||
\(467\) | 3.52602 | + | 2.56180i | 0.163165 | + | 0.118546i | 0.666371 | − | 0.745620i | \(-0.267847\pi\) |
−0.503207 | + | 0.864166i | \(0.667847\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.6200 | + | 9.89548i | 0.628912 | + | 0.456931i | ||||
\(470\) | −14.2120 | − | 13.4806i | −0.655553 | − | 0.621815i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7.92814 | + | 5.76013i | −0.364922 | + | 0.265132i | ||||
\(473\) | −0.610263 | − | 1.87820i | −0.0280599 | − | 0.0863596i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −24.1752 | − | 29.8264i | −1.10923 | − | 1.36853i | ||||
\(476\) | 12.2500 | 0.561477 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.0734750 | + | 0.0533827i | −0.00336067 | + | 0.00244167i | ||||
\(479\) | 10.3670 | − | 7.53204i | 0.473679 | − | 0.344148i | −0.325195 | − | 0.945647i | \(-0.605430\pi\) |
0.798873 | + | 0.601499i | \(0.205430\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.17575 | + | 4.48695i | 0.281590 | + | 0.204587i | ||||
\(482\) | 24.9822 | 1.13791 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.58092 | + | 20.2540i | −0.299133 | + | 0.920636i | ||||
\(485\) | 14.7363 | − | 8.00548i | 0.669142 | − | 0.363510i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.13904 | + | 6.58330i | −0.0969293 | + | 0.298318i | −0.987752 | − | 0.156034i | \(-0.950129\pi\) |
0.890822 | + | 0.454352i | \(0.150129\pi\) | |||||||
\(488\) | −0.461671 | + | 1.42088i | −0.0208989 | + | 0.0643201i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −10.3869 | − | 55.9720i | −0.469230 | − | 2.52856i | ||||
\(491\) | −8.28665 | + | 25.5037i | −0.373971 | + | 1.15096i | 0.570199 | + | 0.821507i | \(0.306866\pi\) |
−0.944170 | + | 0.329458i | \(0.893134\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.17766 | 0.278228 | ||||||||
\(494\) | 15.7940 | + | 11.4750i | 0.710606 | + | 0.516286i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10.6334 | − | 7.72564i | 0.477455 | − | 0.346891i | ||||
\(497\) | −37.3938 | + | 27.1682i | −1.67734 | + | 1.21866i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.75460 | 0.123313 | 0.0616565 | − | 0.998097i | \(-0.480362\pi\) | ||||
0.0616565 | + | 0.998097i | \(0.480362\pi\) | |||||||
\(500\) | −27.2209 | + | 6.55464i | −1.21735 | + | 0.293132i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 11.4617 | + | 35.2754i | 0.511559 | + | 1.57442i | ||||
\(503\) | 12.7098 | − | 9.23422i | 0.566702 | − | 0.411733i | −0.267203 | − | 0.963640i | \(-0.586100\pi\) |
0.833906 | + | 0.551907i | \(0.186100\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.4509 | + | 1.89918i | 0.643057 | + | 0.0845125i | ||||
\(506\) | 6.29422 | + | 4.57302i | 0.279812 | + | 0.203295i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 34.4336 | + | 25.0175i | 1.52774 | + | 1.10997i | ||||
\(509\) | 12.6970 | − | 39.0774i | 0.562785 | − | 1.73207i | −0.111657 | − | 0.993747i | \(-0.535616\pi\) |
0.674442 | − | 0.738328i | \(-0.264384\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.72968 | + | 20.7118i | 0.297703 | + | 0.916237i | ||||
\(512\) | −8.53432 | + | 26.2659i | −0.377167 | + | 1.16080i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10.1439 | + | 31.2198i | 0.447430 | + | 1.37705i | ||||
\(515\) | −15.8146 | + | 8.59126i | −0.696876 | + | 0.378576i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.27584 | + | 3.83312i | 0.232031 | + | 0.168580i | ||||
\(518\) | 58.9438 | 2.58984 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.51923 | − | 1.36856i | 0.110475 | − | 0.0600155i | ||||
\(521\) | 29.2630 | − | 21.2608i | 1.28203 | − | 0.931452i | 0.282421 | − | 0.959290i | \(-0.408862\pi\) |
0.999612 | + | 0.0278383i | \(0.00886235\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.66761 | + | 26.6761i | 0.379008 | + | 1.16647i | 0.940735 | + | 0.339144i | \(0.110137\pi\) |
−0.561727 | + | 0.827323i | \(0.689863\pi\) | |||||||
\(524\) | 0.823595 | 0.0359789 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.07228 | 0.133958 | ||||||||
\(527\) | 1.66545 | + | 5.12573i | 0.0725482 | + | 0.223280i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.2519 | − | 10.3546i | 0.619648 | − | 0.450201i | ||||
\(530\) | −12.8969 | − | 12.2332i | −0.560205 | − | 0.531374i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 83.8108 | 3.63366 | ||||||||
\(533\) | −7.24165 | − | 5.26137i | −0.313671 | − | 0.227895i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −21.0115 | − | 2.76140i | −0.908408 | − | 0.119386i | ||||
\(536\) | 1.27754 | + | 3.93187i | 0.0551815 | + | 0.169831i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5.70983 | + | 17.5731i | −0.246168 | + | 0.757628i | ||||
\(539\) | 5.85650 | + | 18.0244i | 0.252257 | + | 0.776368i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.06865 | − | 3.28896i | 0.0459448 | − | 0.141404i | −0.925452 | − | 0.378864i | \(-0.876315\pi\) |
0.971397 | + | 0.237460i | \(0.0763149\pi\) | |||||||
\(542\) | −49.1643 | − | 35.7200i | −2.11179 | − | 1.53430i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −7.21812 | − | 5.24427i | −0.309474 | − | 0.224846i | ||||
\(545\) | −11.2247 | + | 23.5468i | −0.480815 | + | 1.00863i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.2967 | + | 8.20751i | −0.483011 | + | 0.350928i | −0.802490 | − | 0.596665i | \(-0.796492\pi\) |
0.319479 | + | 0.947593i | \(0.396492\pi\) | |||||||
\(548\) | −3.53095 | − | 10.8671i | −0.150835 | − | 0.464221i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 15.6492 | − | 6.01525i | 0.667283 | − | 0.256491i | ||||
\(551\) | 42.2657 | 1.80058 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −51.3144 | + | 37.2821i | −2.18211 | + | 1.58540i | ||||
\(554\) | 9.10372 | − | 6.61424i | 0.386780 | − | 0.281012i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.59118 | + | 6.96840i | 0.406757 | + | 0.295526i | ||||
\(557\) | 6.59585 | 0.279475 | 0.139738 | − | 0.990189i | \(-0.455374\pi\) | ||||
0.139738 | + | 0.990189i | \(0.455374\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.462723 | + | 1.42411i | −0.0195711 | + | 0.0602336i | ||||
\(560\) | −11.4783 | + | 24.0788i | −0.485048 | + | 1.01752i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −15.7947 | + | 48.6110i | −0.666257 | + | 2.05053i | ||||
\(563\) | 4.95100 | − | 15.2376i | 0.208660 | − | 0.642189i | −0.790883 | − | 0.611967i | \(-0.790379\pi\) |
0.999543 | − | 0.0302222i | \(-0.00962148\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.3611 | − | 30.1263i | 0.604178 | − | 1.26742i | ||||
\(566\) | 17.7826 | − | 54.7291i | 0.747457 | − | 2.30044i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −11.3505 | −0.476258 | ||||||||
\(569\) | 18.6813 | + | 13.5728i | 0.783162 | + | 0.569001i | 0.905926 | − | 0.423435i | \(-0.139176\pi\) |
−0.122764 | + | 0.992436i | \(0.539176\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.5148 | − | 19.9907i | 1.15146 | − | 0.836583i | 0.162784 | − | 0.986662i | \(-0.447953\pi\) |
0.988674 | + | 0.150078i | \(0.0479526\pi\) | |||||||
\(572\) | −3.83451 | + | 2.78594i | −0.160329 | + | 0.116486i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −69.1171 | −2.88489 | ||||||||
\(575\) | 0.612394 | + | 11.5852i | 0.0255386 | + | 0.483136i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.99850 | − | 6.15074i | −0.0831985 | − | 0.256059i | 0.900800 | − | 0.434233i | \(-0.142981\pi\) |
−0.983999 | + | 0.178175i | \(0.942981\pi\) | |||||||
\(578\) | −27.0263 | + | 19.6357i | −1.12414 | + | 0.816739i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 13.2633 | − | 27.8233i | 0.550729 | − | 1.15530i | ||||
\(581\) | −30.8034 | − | 22.3800i | −1.27794 | − | 0.928479i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.78762 | + | 3.47841i | 0.198283 | + | 0.144061i | ||||
\(584\) | −1.65261 | + | 5.08620i | −0.0683853 | + | 0.210468i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −13.3146 | − | 40.9780i | −0.550019 | − | 1.69279i | ||||
\(587\) | −11.8975 | + | 36.6168i | −0.491063 | + | 1.51134i | 0.331940 | + | 0.943301i | \(0.392297\pi\) |
−0.823003 | + | 0.568037i | \(0.807703\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.3945 | + | 35.0687i | 0.469503 | + | 1.44498i | ||||
\(590\) | 43.0816 | + | 5.66192i | 1.77364 | + | 0.233097i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −14.1105 | − | 10.2519i | −0.579939 | − | 0.421350i | ||||
\(593\) | −4.93069 | −0.202479 | −0.101240 | − | 0.994862i | \(-0.532281\pi\) | ||||
−0.101240 | + | 0.994862i | \(0.532281\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.93577 | − | 7.52737i | −0.325335 | − | 0.308592i | ||||
\(596\) | 9.47457 | − | 6.88368i | 0.388093 | − | 0.281966i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.82293 | − | 5.61040i | −0.0745452 | − | 0.229426i | ||||
\(599\) | 35.0268 | 1.43116 | 0.715578 | − | 0.698533i | \(-0.246164\pi\) | ||||
0.715578 | + | 0.698533i | \(0.246164\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.90570 | −0.200108 | −0.100054 | − | 0.994982i | \(-0.531901\pi\) | ||||
−0.100054 | + | 0.994982i | \(0.531901\pi\) | |||||||
\(602\) | 3.57295 | + | 10.9964i | 0.145623 | + | 0.448180i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 13.2538 | − | 9.62943i | 0.539289 | − | 0.391816i | ||||
\(605\) | 16.7089 | − | 9.07708i | 0.679314 | − | 0.369036i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 48.6955 | 1.97649 | 0.988244 | − | 0.152884i | \(-0.0488562\pi\) | ||||
0.988244 | + | 0.152884i | \(0.0488562\pi\) | |||||||
\(608\) | −49.3842 | − | 35.8798i | −2.00280 | − | 1.45512i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5.82092 | − | 3.16220i | 0.235682 | − | 0.128034i | ||||
\(611\) | −1.52799 | − | 4.70266i | −0.0618158 | − | 0.190249i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.31938 | − | 16.3714i | 0.214848 | − | 0.661234i | −0.784317 | − | 0.620361i | \(-0.786986\pi\) |
0.999164 | − | 0.0408728i | \(-0.0130138\pi\) | |||||||
\(614\) | 1.64832 | + | 5.07299i | 0.0665206 | + | 0.204729i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.27742 | + | 7.00918i | −0.0917598 | + | 0.282408i | ||||
\(617\) | −25.5723 | − | 18.5794i | −1.02950 | − | 0.747978i | −0.0612947 | − | 0.998120i | \(-0.519523\pi\) |
−0.968209 | + | 0.250141i | \(0.919523\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.4615 | + | 13.4130i | 0.742029 | + | 0.539116i | 0.893346 | − | 0.449370i | \(-0.148351\pi\) |
−0.151317 | + | 0.988485i | \(0.548351\pi\) | |||||||
\(620\) | 26.6612 | + | 3.50390i | 1.07074 | + | 0.140720i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −8.28312 | + | 6.01804i | −0.332123 | + | 0.241301i | ||||
\(623\) | 13.5196 | + | 41.6089i | 0.541649 | + | 1.66703i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.6619 | + | 12.4805i | 0.866476 | + | 0.499219i | ||||
\(626\) | 12.7088 | 0.507945 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8.09200 | + | 5.87918i | −0.322906 | + | 0.234605i | ||||
\(629\) | 5.78598 | − | 4.20376i | 0.230702 | − | 0.167615i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.7830 | − | 22.3652i | −1.22545 | − | 0.890344i | −0.228913 | − | 0.973447i | \(-0.573517\pi\) |
−0.996541 | + | 0.0831027i | \(0.973517\pi\) | |||||||
\(632\) | −15.5760 | −0.619581 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 11.3808 | − | 35.0265i | 0.451989 | − | 1.39108i | ||||
\(635\) | −6.93401 | − | 37.3655i | −0.275168 | − | 1.48281i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.44060 | − | 13.6668i | 0.175943 | − | 0.541497i | ||||
\(638\) | −5.70334 | + | 17.5531i | −0.225797 | + | 0.694933i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −16.2889 | + | 8.84892i | −0.643876 | + | 0.349784i | ||||
\(641\) | −8.19229 | + | 25.2133i | −0.323576 | + | 0.995864i | 0.648504 | + | 0.761212i | \(0.275395\pi\) |
−0.972079 | + | 0.234652i | \(0.924605\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −36.0014 | −1.41976 | −0.709879 | − | 0.704324i | \(-0.751250\pi\) | ||||
−0.709879 | + | 0.704324i | \(0.751250\pi\) | |||||||
\(644\) | −20.4885 | − | 14.8858i | −0.807360 | − | 0.586582i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 14.7972 | − | 10.7508i | 0.582188 | − | 0.422984i | ||||
\(647\) | 33.8040 | − | 24.5600i | 1.32897 | − | 0.965554i | 0.329197 | − | 0.944261i | \(-0.393222\pi\) |
0.999773 | − | 0.0212924i | \(-0.00677811\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.4658 | −0.567833 | ||||||||
\(650\) | −12.2805 | − | 3.28460i | −0.481679 | − | 0.128833i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.71567 | + | 11.4357i | 0.145517 | + | 0.447855i | ||||
\(653\) | 17.3456 | − | 12.6023i | 0.678787 | − | 0.493168i | −0.194168 | − | 0.980968i | \(-0.562201\pi\) |
0.872955 | + | 0.487801i | \(0.162201\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.533541 | − | 0.506082i | −0.0208472 | − | 0.0197743i | ||||
\(656\) | 16.5459 | + | 12.0213i | 0.646009 | + | 0.469353i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −30.8888 | − | 22.4420i | −1.20417 | − | 0.874882i | ||||
\(659\) | 5.20135 | − | 16.0081i | 0.202616 | − | 0.623587i | −0.797187 | − | 0.603732i | \(-0.793680\pi\) |
0.999803 | − | 0.0198549i | \(-0.00632042\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.629918 | + | 1.93869i | 0.0245010 | + | 0.0754062i | 0.962559 | − | 0.271071i | \(-0.0873778\pi\) |
−0.938058 | + | 0.346477i | \(0.887378\pi\) | |||||||
\(662\) | −13.3368 | + | 41.0463i | −0.518348 | + | 1.59531i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.88934 | − | 8.89248i | −0.112128 | − | 0.345095i | ||||
\(665\) | −54.2942 | − | 51.5000i | −2.10544 | − | 1.99709i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.3323 | − | 7.50689i | −0.400070 | − | 0.290668i | ||||
\(668\) | −59.2518 | −2.29252 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 7.88803 | − | 16.5472i | 0.304741 | − | 0.639274i | ||||
\(671\) | −1.78417 | + | 1.29628i | −0.0688772 | + | 0.0500422i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.9323 | + | 33.6461i | 0.421409 | + | 1.29696i | 0.906391 | + | 0.422439i | \(0.138826\pi\) |
−0.484983 | + | 0.874524i | \(0.661174\pi\) | |||||||
\(674\) | −72.7050 | −2.80049 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −28.9621 | −1.11393 | ||||||||
\(677\) | −13.7257 | − | 42.2434i | −0.527522 | − | 1.62354i | −0.759275 | − | 0.650770i | \(-0.774446\pi\) |
0.231753 | − | 0.972775i | \(-0.425554\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 26.4450 | − | 19.2134i | 1.01487 | − | 0.737344i | ||||
\(680\) | −0.490084 | − | 2.64093i | −0.0187939 | − | 0.101275i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −16.1017 | −0.616567 | ||||||||
\(683\) | 34.3793 | + | 24.9780i | 1.31549 | + | 0.955758i | 0.999977 | + | 0.00683639i | \(0.00217611\pi\) |
0.315512 | + | 0.948922i | \(0.397824\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.39022 | + | 9.20964i | −0.167742 | + | 0.351882i | ||||
\(686\) | −14.2796 | − | 43.9481i | −0.545198 | − | 1.67795i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.05724 | − | 3.25385i | 0.0403069 | − | 0.124052i | ||||
\(689\) | −1.38659 | − | 4.26749i | −0.0528249 | − | 0.162578i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.67746 | − | 26.7065i | 0.330106 | − | 1.01596i | −0.638977 | − | 0.769226i | \(-0.720642\pi\) |
0.969083 | − | 0.246736i | \(-0.0793580\pi\) | |||||||
\(692\) | 29.3860 | + | 21.3502i | 1.11709 | + | 0.811612i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.0847541 | + | 0.0615775i | 0.00321722 | + | 0.00233745i | ||||
\(695\) | −1.93141 | − | 10.4079i | −0.0732626 | − | 0.394793i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.78460 | + | 4.92930i | −0.256985 | + | 0.186711i | ||||
\(698\) | 4.90197 | + | 15.0867i | 0.185542 | + | 0.571040i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −50.9401 | + | 19.5804i | −1.92536 | + | 0.740071i | ||||
\(701\) | −46.4314 | −1.75369 | −0.876845 | − | 0.480772i | \(-0.840356\pi\) | ||||
−0.876845 | + | 0.480772i | \(0.840356\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 39.5860 | − | 28.7609i | 1.49301 | − | 1.08474i | ||||
\(704\) | 14.5680 | − | 10.5842i | 0.549051 | − | 0.398909i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 31.8762 | + | 23.1594i | 1.19967 | + | 0.871615i | ||||
\(707\) | 28.4090 | 1.06843 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.0285 | − | 46.2529i | 0.564406 | − | 1.73706i | −0.105305 | − | 0.994440i | \(-0.533582\pi\) |
0.669710 | − | 0.742622i | \(-0.266418\pi\) | |||||||
\(710\) | 36.5148 | + | 34.6356i | 1.37037 | + | 1.29985i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.31999 | + | 10.2179i | −0.124422 | + | 0.382932i | ||||
\(713\) | 3.44310 | − | 10.5968i | 0.128945 | − | 0.396852i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.19597 | + | 0.551448i | 0.156920 | + | 0.0206230i | ||||
\(716\) | −0.616579 | + | 1.89763i | −0.0230426 | + | 0.0709179i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 22.5062 | 0.839923 | ||||||||
\(719\) | −17.1475 | − | 12.4584i | −0.639493 | − | 0.464619i | 0.220183 | − | 0.975459i | \(-0.429334\pi\) |
−0.859676 | + | 0.510840i | \(0.829334\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −28.3801 | + | 20.6193i | −1.05693 | + | 0.767904i | ||||
\(722\) | 68.6150 | − | 49.8517i | 2.55359 | − | 1.85529i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −35.6073 | −1.32333 | ||||||||
\(725\) | −25.6891 | + | 9.87441i | −0.954068 | + | 0.366726i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.19988 | + | 12.9259i | 0.155765 | + | 0.479396i | 0.998238 | − | 0.0593437i | \(-0.0189008\pi\) |
−0.842473 | + | 0.538739i | \(0.818901\pi\) | |||||||
\(728\) | 4.52087 | − | 3.28460i | 0.167555 | − | 0.121736i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 20.8367 | − | 11.3195i | 0.771200 | − | 0.418953i | ||||
\(731\) | 1.13497 | + | 0.824602i | 0.0419783 | + | 0.0304990i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.0907 | − | 10.9640i | −0.557386 | − | 0.404965i | 0.273115 | − | 0.961981i | \(-0.411946\pi\) |
−0.830501 | + | 0.557017i | \(0.811946\pi\) | |||||||
\(734\) | 7.61927 | − | 23.4497i | 0.281233 | − | 0.865545i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.69988 | + | 17.5424i | 0.210101 | + | 0.646623i | ||||
\(737\) | −1.88584 | + | 5.80402i | −0.0694658 | + | 0.213794i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.17202 | + | 25.1509i | 0.300613 | + | 0.925191i | 0.981278 | + | 0.192596i | \(0.0616907\pi\) |
−0.680665 | + | 0.732594i | \(0.738309\pi\) | |||||||
\(740\) | −6.51073 | − | 35.0846i | −0.239339 | − | 1.28974i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −28.0304 | − | 20.3653i | −1.02903 | − | 0.747633i | ||||
\(743\) | 29.0191 | 1.06461 | 0.532304 | − | 0.846553i | \(-0.321326\pi\) | ||||
0.532304 | + | 0.846553i | \(0.321326\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.3677 | − | 1.36255i | −0.379843 | − | 0.0499201i | ||||
\(746\) | −39.7096 | + | 28.8507i | −1.45387 | + | 1.05630i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.37221 | + | 4.22324i | 0.0501731 | + | 0.154417i | ||||
\(749\) | −41.3065 | −1.50931 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.9489 | 0.581985 | 0.290992 | − | 0.956725i | \(-0.406015\pi\) | ||||
0.290992 | + | 0.956725i | \(0.406015\pi\) | |||||||
\(752\) | 3.49119 | + | 10.7448i | 0.127310 | + | 0.391821i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 11.3216 | − | 8.22563i | 0.412309 | − | 0.299560i | ||||
\(755\) | −14.5031 | − | 1.90605i | −0.527824 | − | 0.0693682i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.4183 | −0.596734 | −0.298367 | − | 0.954451i | \(-0.596442\pi\) | ||||
−0.298367 | + | 0.954451i | \(0.596442\pi\) | |||||||
\(758\) | 42.7382 | + | 31.0512i | 1.55232 | + | 1.12783i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.35301 | − | 18.0685i | −0.121626 | − | 0.655412i | ||||
\(761\) | 15.2257 | + | 46.8600i | 0.551932 | + | 1.69867i | 0.703910 | + | 0.710289i | \(0.251436\pi\) |
−0.151978 | + | 0.988384i | \(0.548564\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.7117 | + | 48.3555i | −0.568800 | + | 1.75059i | ||||
\(764\) | 8.02480 | + | 24.6978i | 0.290327 | + | 0.893534i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.3111 | + | 31.7345i | −0.372557 | + | 1.14661i | ||||
\(767\) | 8.87369 | + | 6.44711i | 0.320410 | + | 0.232792i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −39.9845 | − | 29.0504i | −1.44188 | − | 1.04759i | −0.987646 | − | 0.156702i | \(-0.949914\pi\) |
−0.454232 | − | 0.890884i | \(-0.650086\pi\) | |||||||
\(770\) | 28.7146 | − | 15.5991i | 1.03480 | − | 0.562154i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8.80736 | + | 6.39892i | −0.316984 | + | 0.230302i | ||||
\(773\) | −8.00613 | − | 24.6403i | −0.287960 | − | 0.886251i | −0.985496 | − | 0.169701i | \(-0.945720\pi\) |
0.697535 | − | 0.716550i | \(-0.254280\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.1186 | − | 18.6527i | −0.543076 | − | 0.670024i | ||||
\(776\) | 8.02715 | 0.288158 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 14.6054 | − | 10.6114i | 0.523629 | − | 0.380439i | ||||
\(779\) | −46.4182 | + | 33.7248i | −1.66311 | + | 1.20832i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.5551 | − | 9.84838i | −0.485041 | − | 0.352403i | ||||
\(782\) | −5.52681 | −0.197638 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −10.1460 | + | 31.2262i | −0.362357 | + | 1.11522i | ||||
\(785\) | 8.85479 | + | 1.16372i | 0.316041 | + | 0.0415351i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.49160 | − | 29.2122i | 0.338339 | − | 1.04130i | −0.626715 | − | 0.779249i | \(-0.715601\pi\) |
0.965054 | − | 0.262052i | \(-0.0843992\pi\) | |||||||
\(788\) | −1.45480 | + | 4.47741i | −0.0518251 | + | 0.159501i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 50.1081 | + | 47.5293i | 1.78277 | + | 1.69102i | ||||
\(791\) | 20.1018 | − | 61.8670i | 0.714737 | − | 2.19974i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.67218 | 0.0593808 | ||||||||
\(794\) | 45.0798 | + | 32.7524i | 1.59982 | + | 1.16234i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.63142 | + | 6.27109i | −0.305933 | + | 0.222273i | ||||
\(797\) | −27.2753 | + | 19.8166i | −0.966140 | + | 0.701942i | −0.954569 | − | 0.297991i | \(-0.903683\pi\) |
−0.0115713 | + | 0.999933i | \(0.503683\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.63260 | −0.163890 | ||||||||
\(800\) | 38.3982 | + | 10.2702i | 1.35758 | + | 0.363106i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −16.5806 | − | 51.0298i | −0.585480 | − | 1.80192i | ||||
\(803\) | −6.38665 | + | 4.64018i | −0.225380 | + | 0.163748i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.12584 | + | 22.2331i | 0.145417 | + | 0.783613i | ||||
\(806\) | 9.87720 | + | 7.17621i | 0.347910 | + | 0.252771i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5.64402 | + | 4.10062i | 0.198556 | + | 0.144259i | ||||
\(809\) | 0.285227 | − | 0.877838i | 0.0100280 | − | 0.0308632i | −0.945917 | − | 0.324408i | \(-0.894835\pi\) |
0.955945 | + | 0.293545i | \(0.0948350\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.27593 | + | 25.4707i | 0.290607 | + | 0.894397i | 0.984662 | + | 0.174474i | \(0.0558226\pi\) |
−0.694055 | + | 0.719922i | \(0.744177\pi\) | |||||||
\(812\) | 18.5651 | − | 57.1376i | 0.651508 | − | 2.00514i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.60274 | + | 20.3212i | 0.231426 | + | 0.712256i | ||||
\(815\) | 4.61990 | − | 9.69145i | 0.161828 | − | 0.339477i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.76511 | + | 5.64168i | 0.271667 | + | 0.197377i | ||||
\(818\) | −71.7204 | −2.50765 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 7.63444 | + | 41.1400i | 0.266606 | + | 1.43667i | ||||
\(821\) | −29.8114 | + | 21.6592i | −1.04042 | + | 0.755912i | −0.970368 | − | 0.241631i | \(-0.922318\pi\) |
−0.0700559 | + | 0.997543i | \(0.522318\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.31204 | + | 19.4265i | 0.220024 | + | 0.677164i | 0.998759 | + | 0.0498106i | \(0.0158618\pi\) |
−0.778735 | + | 0.627353i | \(0.784138\pi\) | |||||||
\(824\) | −8.61452 | −0.300101 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 84.6940 | 2.94688 | ||||||||
\(827\) | −1.33810 | − | 4.11824i | −0.0465302 | − | 0.143205i | 0.925092 | − | 0.379743i | \(-0.123987\pi\) |
−0.971622 | + | 0.236537i | \(0.923987\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.497018 | − | 0.361104i | 0.0172621 | − | 0.0125417i | −0.579121 | − | 0.815242i | \(-0.696604\pi\) |
0.596383 | + | 0.802700i | \(0.296604\pi\) | |||||||
\(830\) | −17.8399 | + | 37.4238i | −0.619231 | + | 1.29900i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −13.6535 | −0.473351 | ||||||||
\(833\) | −10.8919 | − | 7.91343i | −0.377382 | − | 0.274184i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 38.3844 | + | 36.4090i | 1.32835 | + | 1.25999i | ||||
\(836\) | 9.38828 | + | 28.8942i | 0.324701 | + | 0.999325i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5.20297 | − | 16.0131i | 0.179733 | − | 0.553163i | ||||
\(839\) | −1.66863 | − | 5.13553i | −0.0576077 | − | 0.177298i | 0.918112 | − | 0.396321i | \(-0.129713\pi\) |
−0.975720 | + | 0.219023i | \(0.929713\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.400892 | − | 1.23382i | 0.0138239 | − | 0.0425455i | ||||
\(842\) | 12.8568 | + | 9.34105i | 0.443076 | + | 0.321914i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 18.8353 | + | 13.6847i | 0.648339 | + | 0.471046i | ||||
\(845\) | 18.7622 | + | 17.7966i | 0.645439 | + | 0.612222i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 29.9849 | − | 21.7853i | 1.03029 | − | 0.748552i | ||||
\(848\) | 3.16812 | + | 9.75046i | 0.108794 | + | 0.334832i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6.48205 | + | 9.99135i | −0.222333 | + | 0.342700i | ||||
\(851\) | −14.7855 | −0.506841 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32.1936 | − | 23.3900i | 1.10229 | − | 0.800860i | 0.120857 | − | 0.992670i | \(-0.461436\pi\) |
0.981432 | + | 0.191810i | \(0.0614358\pi\) | |||||||
\(854\) | 10.4459 | − | 7.58940i | 0.357452 | − | 0.259704i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.20637 | − | 5.96228i | −0.280488 | − | 0.203787i | ||||
\(857\) | 42.8643 | 1.46422 | 0.732109 | − | 0.681188i | \(-0.238536\pi\) | ||||
0.732109 | + | 0.681188i | \(0.238536\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.41064 | + | 4.34152i | −0.0481306 | + | 0.148131i | −0.972233 | − | 0.234013i | \(-0.924814\pi\) |
0.924103 | + | 0.382144i | \(0.124814\pi\) | |||||||
\(860\) | 6.15064 | − | 3.34132i | 0.209735 | − | 0.113938i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15.3119 | − | 47.1251i | 0.521524 | − | 1.60509i | ||||
\(863\) | 11.6275 | − | 35.7857i | 0.395804 | − | 1.21816i | −0.532530 | − | 0.846411i | \(-0.678759\pi\) |
0.928334 | − | 0.371747i | \(-0.121241\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.91756 | − | 31.8882i | −0.201203 | − | 1.08423i | ||||
\(866\) | 2.20150 | − | 6.77551i | 0.0748099 | − | 0.230241i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 52.4133 | 1.77902 | ||||||||
\(869\) | −18.6013 | − | 13.5146i | −0.631006 | − | 0.458452i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.74355 | − | 2.71985i | 0.126845 | − | 0.0921586i | ||||
\(872\) | −10.1012 | + | 7.33894i | −0.342069 | + | 0.248528i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −37.8128 | −1.27904 | ||||||||
\(875\) | 45.0318 | + | 18.6171i | 1.52235 | + | 0.629373i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.1938 | + | 49.8393i | 0.546825 | + | 1.68295i | 0.716612 | + | 0.697472i | \(0.245692\pi\) |
−0.169787 | + | 0.985481i | \(0.554308\pi\) | |||||||
\(878\) | −16.2841 | + | 11.8311i | −0.549562 | + | 0.399280i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −9.58706 | − | 1.25996i | −0.323180 | − | 0.0424733i | ||||
\(881\) | −6.42180 | − | 4.66571i | −0.216356 | − | 0.157192i | 0.474329 | − | 0.880348i | \(-0.342691\pi\) |
−0.690685 | + | 0.723156i | \(0.742691\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.6393 | − | 18.6280i | −0.862831 | − | 0.626883i | 0.0658227 | − | 0.997831i | \(-0.479033\pi\) |
−0.928654 | + | 0.370948i | \(0.879033\pi\) | |||||||
\(884\) | 1.04046 | − | 3.20221i | 0.0349945 | − | 0.107702i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.33175 | + | 19.4871i | 0.212719 | + | 0.654683i | ||||
\(887\) | −0.871749 | + | 2.68297i | −0.0292705 | + | 0.0900853i | −0.964625 | − | 0.263628i | \(-0.915081\pi\) |
0.935354 | + | 0.353713i | \(0.115081\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −22.8901 | − | 70.4485i | −0.767709 | − | 2.36277i | ||||
\(890\) | 41.8598 | − | 22.7402i | 1.40314 | − | 0.762254i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.88357 | + | 5.00121i | 0.230479 | + | 0.167453i | ||||
\(893\) | −31.6949 | −1.06063 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.56549 | − | 0.850448i | 0.0523285 | − | 0.0284274i | ||||
\(896\) | −29.2312 | + | 21.2377i | −0.976546 | + | 0.709502i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 20.6759 | + | 63.6340i | 0.689965 | + | 2.12349i | ||||
\(899\) | 26.4320 | 0.881556 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.20390 | −0.140052 | ||||||||
\(902\) | −7.74233 | − | 23.8285i | −0.257792 | − | 0.793401i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12.9236 | − | 9.38958i | 0.429834 | − | 0.312293i | ||||
\(905\) | 23.0671 | + | 21.8800i | 0.766776 | + | 0.727315i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −44.1799 | −1.46697 | −0.733485 | − | 0.679705i | \(-0.762108\pi\) | ||||
−0.733485 | + | 0.679705i | \(0.762108\pi\) | |||||||
\(908\) | 54.2919 | + | 39.4454i | 1.80174 | + | 1.30904i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −24.5664 | − | 3.22860i | −0.814370 | − | 0.107027i | ||||
\(911\) | 10.6691 | + | 32.8362i | 0.353484 | + | 1.08791i | 0.956883 | + | 0.290472i | \(0.0938124\pi\) |
−0.603400 | + | 0.797439i | \(0.706188\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.26509 | − | 13.1266i | 0.141154 | − | 0.434426i | ||||
\(914\) | 6.52209 | + | 20.0729i | 0.215731 | + | 0.663953i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.914713 | + | 2.81520i | −0.0302230 | + | 0.0930167i | ||||
\(917\) | −1.15961 | − | 0.842506i | −0.0382937 | − | 0.0278220i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.429648 | + | 0.312158i | 0.0141728 | + | 0.0102971i | 0.594849 | − | 0.803837i | \(-0.297212\pi\) |
−0.580676 | + | 0.814135i | \(0.697212\pi\) | |||||||
\(920\) | −2.38949 | + | 5.01258i | −0.0787792 | + | 0.165260i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 40.6648 | − | 29.5447i | 1.33922 | − | 0.973003i | ||||
\(923\) | 3.92584 | + | 12.0825i | 0.129220 | + | 0.397700i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.3410 | + | 26.7292i | −0.570169 | + | 0.878850i | ||||
\(926\) | −58.6833 | −1.92845 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −35.4001 | + | 25.7197i | −1.16206 | + | 0.844289i | ||||
\(929\) | 37.3735 | − | 27.1534i | 1.22618 | − | 0.890874i | 0.229585 | − | 0.973289i | \(-0.426263\pi\) |
0.996598 | + | 0.0824143i | \(0.0262631\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −74.5192 | − | 54.1414i | −2.44227 | − | 1.77441i | ||||
\(932\) | −17.7676 | −0.581997 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.85840 | − | 8.79726i | 0.0935298 | − | 0.287855i | ||||
\(935\) | 1.70615 | − | 3.57909i | 0.0557971 | − | 0.117049i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.30820 | + | 28.6477i | −0.304086 | + | 0.935880i | 0.675931 | + | 0.736965i | \(0.263742\pi\) |
−0.980017 | + | 0.198915i | \(0.936258\pi\) | |||||||
\(938\) | 11.0412 | − | 33.9812i | 0.360506 | − | 1.10952i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −9.94610 | + | 20.8645i | −0.324406 | + | 0.680526i | ||||
\(941\) | −17.6382 | + | 54.2847i | −0.574988 | + | 1.76963i | 0.0612315 | + | 0.998124i | \(0.480497\pi\) |
−0.636220 | + | 0.771508i | \(0.719503\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17.3374 | 0.564583 | ||||||||
\(944\) | −20.2748 | − | 14.7305i | −0.659890 | − | 0.479438i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.39083 | + | 2.46358i | −0.110245 | + | 0.0800980i | ||||
\(947\) | −33.2708 | + | 24.1727i | −1.08116 | + | 0.785506i | −0.977884 | − | 0.209147i | \(-0.932931\pi\) |
−0.103273 | + | 0.994653i | \(0.532931\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.98576 | 0.194306 | ||||||||
\(950\) | −44.3483 | + | 68.3579i | −1.43885 | + | 2.21782i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.61783 | − | 4.97918i | −0.0524343 | − | 0.161376i | ||||
\(953\) | 28.1654 | − | 20.4633i | 0.912366 | − | 0.662873i | −0.0292462 | − | 0.999572i | \(-0.509311\pi\) |
0.941612 | + | 0.336700i | \(0.109311\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.97767 | − | 20.9308i | 0.322870 | − | 0.677304i | ||||
\(956\) | 0.0866986 | + | 0.0629902i | 0.00280403 | + | 0.00203725i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −22.0022 | − | 15.9855i | −0.710857 | − | 0.516468i | ||||
\(959\) | −6.14515 | + | 18.9128i | −0.198437 | + | 0.610727i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.45366 | − | 7.55160i | −0.0791504 | − | 0.243600i | ||||
\(962\) | 5.00643 | − | 15.4082i | 0.161414 | − | 0.496781i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −9.10930 | − | 28.0355i | −0.293391 | − | 0.902964i | ||||
\(965\) | 9.63759 | + | 1.26660i | 0.310245 | + | 0.0407733i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.1519 | + | 21.9066i | 0.969618 | + | 0.704469i | 0.955365 | − | 0.295430i | \(-0.0954628\pi\) |
0.0142537 | + | 0.999898i | \(0.495463\pi\) | |||||||
\(968\) | 9.10165 | 0.292538 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −25.8234 | − | 24.4944i | −0.829138 | − | 0.786468i | ||||
\(971\) | −21.0419 | + | 15.2879i | −0.675267 | + | 0.490611i | −0.871784 | − | 0.489890i | \(-0.837037\pi\) |
0.196517 | + | 0.980500i | \(0.437037\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.37585 | − | 19.6228i | −0.204400 | − | 0.629079i | ||||
\(974\) | 14.6910 | 0.470729 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.82064 | −0.122296 | ||||||||
\(977\) | −0.141709 | − | 0.436134i | −0.00453366 | − | 0.0139532i | 0.948764 | − | 0.315985i | \(-0.102335\pi\) |
−0.953298 | + | 0.302032i | \(0.902335\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.8304 | + | 9.32186i | −0.410063 | + | 0.297928i | ||||
\(980\) | −59.0257 | + | 32.0656i | −1.88551 | + | 1.02430i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 56.9128 | 1.81616 | ||||||||
\(983\) | 7.23718 | + | 5.25812i | 0.230830 | + | 0.167708i | 0.697188 | − | 0.716888i | \(-0.254434\pi\) |
−0.466358 | + | 0.884596i | \(0.654434\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.69373 | − | 2.00661i | 0.117692 | − | 0.0639359i | ||||
\(986\) | −4.05154 | − | 12.4694i | −0.129027 | − | 0.397105i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.11852 | − | 21.9086i | 0.226470 | − | 0.697004i | ||||
\(989\) | −0.896242 | − | 2.75835i | −0.0284988 | − | 0.0877104i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.4699 | + | 53.7667i | −0.554949 | + | 1.70796i | 0.141130 | + | 0.989991i | \(0.454926\pi\) |
−0.696079 | + | 0.717965i | \(0.745074\pi\) | |||||||
\(992\) | −30.8837 | − | 22.4383i | −0.980559 | − | 0.712418i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 79.3621 | + | 57.6599i | 2.51721 | + | 1.82886i | ||||
\(995\) | 9.44506 | + | 1.24130i | 0.299429 | + | 0.0393518i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −32.0463 | + | 23.2830i | −1.01492 | + | 0.737380i | −0.965235 | − | 0.261385i | \(-0.915821\pi\) |
−0.0496816 | + | 0.998765i | \(0.515821\pi\) | |||||||
\(998\) | −1.80657 | − | 5.56005i | −0.0571860 | − | 0.176000i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 225.2.h.c.181.1 | 8 | ||
3.2 | odd | 2 | 75.2.g.b.31.2 | ✓ | 8 | ||
15.2 | even | 4 | 375.2.i.b.349.1 | 16 | |||
15.8 | even | 4 | 375.2.i.b.349.4 | 16 | |||
15.14 | odd | 2 | 375.2.g.b.151.1 | 8 | |||
25.11 | even | 5 | 5625.2.a.i.1.2 | 4 | |||
25.14 | even | 10 | 5625.2.a.n.1.3 | 4 | |||
25.21 | even | 5 | inner | 225.2.h.c.46.1 | 8 | ||
75.2 | even | 20 | 1875.2.b.c.1249.7 | 8 | |||
75.11 | odd | 10 | 1875.2.a.h.1.3 | 4 | |||
75.14 | odd | 10 | 1875.2.a.e.1.2 | 4 | |||
75.23 | even | 20 | 1875.2.b.c.1249.2 | 8 | |||
75.29 | odd | 10 | 375.2.g.b.226.1 | 8 | |||
75.47 | even | 20 | 375.2.i.b.274.4 | 16 | |||
75.53 | even | 20 | 375.2.i.b.274.1 | 16 | |||
75.71 | odd | 10 | 75.2.g.b.46.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.b.31.2 | ✓ | 8 | 3.2 | odd | 2 | ||
75.2.g.b.46.2 | yes | 8 | 75.71 | odd | 10 | ||
225.2.h.c.46.1 | 8 | 25.21 | even | 5 | inner | ||
225.2.h.c.181.1 | 8 | 1.1 | even | 1 | trivial | ||
375.2.g.b.151.1 | 8 | 15.14 | odd | 2 | |||
375.2.g.b.226.1 | 8 | 75.29 | odd | 10 | |||
375.2.i.b.274.1 | 16 | 75.53 | even | 20 | |||
375.2.i.b.274.4 | 16 | 75.47 | even | 20 | |||
375.2.i.b.349.1 | 16 | 15.2 | even | 4 | |||
375.2.i.b.349.4 | 16 | 15.8 | even | 4 | |||
1875.2.a.e.1.2 | 4 | 75.14 | odd | 10 | |||
1875.2.a.h.1.3 | 4 | 75.11 | odd | 10 | |||
1875.2.b.c.1249.2 | 8 | 75.23 | even | 20 | |||
1875.2.b.c.1249.7 | 8 | 75.2 | even | 20 | |||
5625.2.a.i.1.2 | 4 | 25.11 | even | 5 | |||
5625.2.a.n.1.3 | 4 | 25.14 | even | 10 |