Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [720,2,Mod(307,720)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(720, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("720.307");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 720.bd (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.74922894553\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(9\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 307.3 | ||
Root | \(-1.37691 - 0.322680i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 720.307 |
Dual form | 720.2.bd.g.523.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(271\) | \(577\) | \(641\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.687667 | + | 1.23576i | −0.486254 | + | 0.873818i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.05423 | − | 1.69959i | −0.527114 | − | 0.849794i | ||||
\(5\) | 2.07551 | + | 0.832020i | 0.928196 | + | 0.372091i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.83610 | + | 2.83610i | 1.07194 | + | 1.07194i | 0.997203 | + | 0.0747413i | \(0.0238131\pi\) |
0.0747413 | + | 0.997203i | \(0.476187\pi\) | |||||||
\(8\) | 2.82525 | − | 0.134028i | 0.998877 | − | 0.0473862i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.45544 | + | 1.99269i | −0.776478 | + | 0.630144i | ||||
\(11\) | −1.95928 | − | 1.95928i | −0.590745 | − | 0.590745i | 0.347088 | − | 0.937833i | \(-0.387171\pi\) |
−0.937833 | + | 0.347088i | \(0.887171\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.05493 | −0.569934 | −0.284967 | − | 0.958537i | \(-0.591983\pi\) | ||||
−0.284967 | + | 0.958537i | \(0.591983\pi\) | |||||||
\(14\) | −5.45504 | + | 1.55446i | −1.45792 | + | 0.415447i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.77720 | + | 3.58351i | −0.444301 | + | 0.895878i | ||||
\(17\) | 4.06774 | + | 4.06774i | 0.986571 | + | 0.986571i | 0.999911 | − | 0.0133401i | \(-0.00424641\pi\) |
−0.0133401 | + | 0.999911i | \(0.504246\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.683479 | + | 0.683479i | 0.156801 | + | 0.156801i | 0.781147 | − | 0.624347i | \(-0.214635\pi\) |
−0.624347 | + | 0.781147i | \(0.714635\pi\) | |||||||
\(20\) | −0.773972 | − | 4.40465i | −0.173065 | − | 0.984910i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.76854 | − | 1.07388i | 0.803455 | − | 0.228951i | ||||
\(23\) | 4.95014 | − | 4.95014i | 1.03218 | − | 1.03218i | 0.0327113 | − | 0.999465i | \(-0.489586\pi\) |
0.999465 | − | 0.0327113i | \(-0.0104142\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.61549 | + | 3.45373i | 0.723097 | + | 0.690746i | ||||
\(26\) | 1.41310 | − | 2.53941i | 0.277133 | − | 0.498018i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.83030 | − | 7.81010i | 0.345895 | − | 1.47597i | ||||
\(29\) | 0.835439 | − | 0.835439i | 0.155137 | − | 0.155137i | −0.625271 | − | 0.780408i | \(-0.715011\pi\) |
0.780408 | + | 0.625271i | \(0.215011\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2.35978i | − | 0.423829i | −0.977288 | − | 0.211915i | \(-0.932030\pi\) | ||
0.977288 | − | 0.211915i | \(-0.0679698\pi\) | |||||||
\(32\) | −3.20625 | − | 4.66047i | −0.566791 | − | 0.823862i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.82401 | + | 2.22952i | −1.34181 | + | 0.382359i | ||||
\(35\) | 3.52666 | + | 8.24604i | 0.596114 | + | 1.39384i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.54384 | −0.747002 | −0.373501 | − | 0.927630i | \(-0.621843\pi\) | ||||
−0.373501 | + | 0.927630i | \(0.621843\pi\) | |||||||
\(38\) | −1.31462 | + | 0.374613i | −0.213260 | + | 0.0607703i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.97535 | + | 2.07249i | 0.944786 | + | 0.327689i | ||||
\(41\) | 5.07255i | 0.792199i | 0.918208 | + | 0.396100i | \(0.129636\pi\) | ||||
−0.918208 | + | 0.396100i | \(0.870364\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.849753 | −0.129586 | −0.0647930 | − | 0.997899i | \(-0.520639\pi\) | ||||
−0.0647930 | + | 0.997899i | \(0.520639\pi\) | |||||||
\(44\) | −1.26444 | + | 5.39549i | −0.190621 | + | 0.813401i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.71316 | + | 9.52126i | 0.400034 | + | 1.40383i | ||||
\(47\) | −2.72646 | + | 2.72646i | −0.397696 | + | 0.397696i | −0.877419 | − | 0.479724i | \(-0.840737\pi\) |
0.479724 | + | 0.877419i | \(0.340737\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.08690i | 1.29813i | ||||||||
\(50\) | −6.75425 | + | 2.09287i | −0.955195 | + | 0.295977i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.16636 | + | 3.49253i | 0.300420 | + | 0.484327i | ||||
\(53\) | 5.17605i | 0.710985i | 0.934679 | + | 0.355492i | \(0.115687\pi\) | ||||
−0.934679 | + | 0.355492i | \(0.884313\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.43634 | − | 5.69666i | −0.328517 | − | 0.768138i | ||||
\(56\) | 8.39280 | + | 7.63257i | 1.12154 | + | 1.01994i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.457903 | + | 1.60691i | 0.0601256 | + | 0.210998i | ||||
\(59\) | −4.16328 | + | 4.16328i | −0.542013 | + | 0.542013i | −0.924119 | − | 0.382105i | \(-0.875199\pi\) |
0.382105 | + | 0.924119i | \(0.375199\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.55706 | + | 5.55706i | 0.711509 | + | 0.711509i | 0.966851 | − | 0.255342i | \(-0.0821880\pi\) |
−0.255342 | + | 0.966851i | \(0.582188\pi\) | |||||||
\(62\) | 2.91613 | + | 1.62274i | 0.370349 | + | 0.206088i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.96407 | − | 0.757328i | 0.995509 | − | 0.0946660i | ||||
\(65\) | −4.26502 | − | 1.70974i | −0.529011 | − | 0.212067i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.73609 | −0.212097 | −0.106048 | − | 0.994361i | \(-0.533820\pi\) | ||||
−0.106048 | + | 0.994361i | \(0.533820\pi\) | |||||||
\(68\) | 2.62515 | − | 11.2018i | 0.318347 | − | 1.35842i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −12.6153 | − | 1.31240i | −1.50782 | − | 0.156862i | ||||
\(71\) | −2.33526 | −0.277144 | −0.138572 | − | 0.990352i | \(-0.544251\pi\) | ||||
−0.138572 | + | 0.990352i | \(0.544251\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.39686 | + | 4.39686i | 0.514613 | + | 0.514613i | 0.915936 | − | 0.401323i | \(-0.131450\pi\) |
−0.401323 | + | 0.915936i | \(0.631450\pi\) | |||||||
\(74\) | 3.12465 | − | 5.61511i | 0.363233 | − | 0.652744i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.441090 | − | 1.88218i | 0.0505964 | − | 0.215900i | ||||
\(77\) | − | 11.1134i | − | 1.26649i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.0993 | −1.58629 | −0.793146 | − | 0.609032i | \(-0.791558\pi\) | ||||
−0.793146 | + | 0.609032i | \(0.791558\pi\) | |||||||
\(80\) | −6.67015 | + | 5.95895i | −0.745746 | + | 0.666230i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.26848 | − | 3.48822i | −0.692238 | − | 0.385210i | ||||
\(83\) | − | 2.75725i | − | 0.302648i | −0.988484 | − | 0.151324i | \(-0.951646\pi\) | ||
0.988484 | − | 0.151324i | \(-0.0483536\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.05819 | + | 11.8271i | 0.548638 | + | 1.28283i | ||||
\(86\) | 0.584347 | − | 1.05009i | 0.0630117 | − | 0.113235i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.79805 | − | 5.27285i | −0.618074 | − | 0.562088i | ||||
\(89\) | 11.6448 | 1.23435 | 0.617173 | − | 0.786828i | \(-0.288278\pi\) | ||||
0.617173 | + | 0.786828i | \(0.288278\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.82797 | − | 5.82797i | −0.610937 | − | 0.610937i | ||||
\(92\) | −13.6318 | − | 3.19462i | −1.42121 | − | 0.333062i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.49437 | − | 5.24417i | −0.154132 | − | 0.540894i | ||||
\(95\) | 0.849899 | + | 1.98724i | 0.0871978 | + | 0.203886i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.52933 | − | 3.52933i | −0.358349 | − | 0.358349i | 0.504855 | − | 0.863204i | \(-0.331546\pi\) |
−0.863204 | + | 0.504855i | \(0.831546\pi\) | |||||||
\(98\) | −11.2293 | − | 6.24876i | −1.13433 | − | 0.631220i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.05837 | − | 9.78586i | 0.205837 | − | 0.978586i | ||||
\(101\) | −7.39467 | + | 7.39467i | −0.735797 | + | 0.735797i | −0.971762 | − | 0.235964i | \(-0.924175\pi\) |
0.235964 | + | 0.971762i | \(0.424175\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.72605 | − | 3.72605i | 0.367139 | − | 0.367139i | −0.499294 | − | 0.866433i | \(-0.666407\pi\) |
0.866433 | + | 0.499294i | \(0.166407\pi\) | |||||||
\(104\) | −5.80568 | + | 0.275419i | −0.569294 | + | 0.0270070i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.39637 | − | 3.55939i | −0.621271 | − | 0.345719i | ||||
\(107\) | − | 16.4605i | − | 1.59130i | −0.605758 | − | 0.795649i | \(-0.707130\pi\) | ||
0.605758 | − | 0.795649i | \(-0.292870\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.8554 | − | 12.8554i | 1.23133 | − | 1.23133i | 0.267870 | − | 0.963455i | \(-0.413680\pi\) |
0.963455 | − | 0.267870i | \(-0.0863199\pi\) | |||||||
\(110\) | 8.71512 | + | 0.906656i | 0.830955 | + | 0.0864463i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −15.2035 | + | 5.12287i | −1.43660 | + | 0.484065i | ||||
\(113\) | −0.863630 | + | 0.863630i | −0.0812435 | + | 0.0812435i | −0.746561 | − | 0.665317i | \(-0.768296\pi\) |
0.665317 | + | 0.746561i | \(0.268296\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.3927 | − | 6.15546i | 1.34213 | − | 0.573999i | ||||
\(116\) | −2.30065 | − | 0.539159i | −0.213610 | − | 0.0500596i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.28189 | − | 8.00779i | −0.210065 | − | 0.737177i | ||||
\(119\) | 23.0730i | 2.11510i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 3.32246i | − | 0.302042i | ||||||
\(122\) | −10.6886 | + | 3.04582i | −0.967703 | + | 0.275755i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.01066 | + | 2.48775i | −0.360168 | + | 0.223406i | ||||
\(125\) | 4.63041 | + | 10.1764i | 0.414156 | + | 0.910206i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.7944 | − | 11.7944i | 1.04659 | − | 1.04659i | 0.0477265 | − | 0.998860i | \(-0.484802\pi\) |
0.998860 | − | 0.0477265i | \(-0.0151976\pi\) | |||||||
\(128\) | −4.54075 | + | 10.3625i | −0.401349 | + | 0.915925i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.04575 | − | 4.09483i | 0.442541 | − | 0.359140i | ||||
\(131\) | 15.9756 | − | 15.9756i | 1.39579 | − | 1.39579i | 0.584132 | − | 0.811659i | \(-0.301435\pi\) |
0.811659 | − | 0.584132i | \(-0.198565\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.87683i | 0.336163i | ||||||||
\(134\) | 1.19385 | − | 2.14539i | 0.103133 | − | 0.185334i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.0376 | + | 10.9472i | 1.03221 | + | 0.938713i | ||||
\(137\) | 1.29423 | − | 1.29423i | 0.110573 | − | 0.110573i | −0.649655 | − | 0.760229i | \(-0.725087\pi\) |
0.760229 | + | 0.649655i | \(0.225087\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.61413 | + | 8.61413i | −0.730641 | + | 0.730641i | −0.970747 | − | 0.240106i | \(-0.922818\pi\) |
0.240106 | + | 0.970747i | \(0.422818\pi\) | |||||||
\(140\) | 10.2970 | − | 14.6871i | 0.870253 | − | 1.24129i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.60588 | − | 2.88583i | 0.134762 | − | 0.242173i | ||||
\(143\) | 4.02617 | + | 4.02617i | 0.336685 | + | 0.336685i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.42906 | − | 1.03886i | 0.201723 | − | 0.0862727i | ||||
\(146\) | −8.45705 | + | 2.40991i | −0.699911 | + | 0.199445i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.79025 | + | 7.72265i | 0.393756 | + | 0.634798i | ||||
\(149\) | 0.0806133 | + | 0.0806133i | 0.00660410 | + | 0.00660410i | 0.710401 | − | 0.703797i | \(-0.248514\pi\) |
−0.703797 | + | 0.710401i | \(0.748514\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.25198 | −0.264643 | −0.132321 | − | 0.991207i | \(-0.542243\pi\) | ||||
−0.132321 | + | 0.991207i | \(0.542243\pi\) | |||||||
\(152\) | 2.02260 | + | 1.83939i | 0.164055 | + | 0.149194i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 13.7336 | + | 7.64232i | 1.10668 | + | 0.615836i | ||||
\(155\) | 1.96338 | − | 4.89775i | 0.157703 | − | 0.393397i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 9.06652i | − | 0.723587i | −0.932258 | − | 0.361793i | \(-0.882165\pi\) | ||
0.932258 | − | 0.361793i | \(-0.117835\pi\) | |||||||
\(158\) | 9.69559 | − | 17.4234i | 0.771340 | − | 1.38613i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.77701 | − | 12.3405i | −0.219542 | − | 0.975603i | ||||
\(161\) | 28.0782 | 2.21287 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 3.93313i | − | 0.308067i | −0.988066 | − | 0.154033i | \(-0.950774\pi\) | ||
0.988066 | − | 0.154033i | \(-0.0492263\pi\) | |||||||
\(164\) | 8.62125 | − | 5.34763i | 0.673206 | − | 0.417580i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.40731 | + | 1.89607i | 0.264459 | + | 0.147164i | ||||
\(167\) | −8.13216 | − | 8.13216i | −0.629285 | − | 0.629285i | 0.318603 | − | 0.947888i | \(-0.396786\pi\) |
−0.947888 | + | 0.318603i | \(0.896786\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.77728 | −0.675175 | ||||||||
\(170\) | −18.0938 | − | 1.88235i | −1.38773 | − | 0.144369i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.895834 | + | 1.44423i | 0.0683067 | + | 0.110121i | ||||
\(173\) | −6.86735 | −0.522115 | −0.261057 | − | 0.965323i | \(-0.584071\pi\) | ||||
−0.261057 | + | 0.965323i | \(0.584071\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.458751 | + | 20.0490i | 0.0346784 | + | 1.51556i | ||||
\(176\) | 10.5031 | − | 3.53906i | 0.791703 | − | 0.266767i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −8.00774 | + | 14.3902i | −0.600205 | + | 1.07859i | ||||
\(179\) | −15.7117 | − | 15.7117i | −1.17435 | − | 1.17435i | −0.981163 | − | 0.193183i | \(-0.938119\pi\) |
−0.193183 | − | 0.981163i | \(-0.561881\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.9112 | + | 13.9112i | −1.03401 | + | 1.03401i | −0.0346142 | + | 0.999401i | \(0.511020\pi\) |
−0.999401 | + | 0.0346142i | \(0.988980\pi\) | |||||||
\(182\) | 11.2097 | − | 3.19430i | 0.830919 | − | 0.236777i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 13.3219 | − | 14.6489i | 0.982106 | − | 1.07993i | ||||
\(185\) | −9.43078 | − | 3.78056i | −0.693365 | − | 0.277953i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 15.9397i | − | 1.16562i | ||||||
\(188\) | 7.50818 | + | 1.75955i | 0.547591 | + | 0.128328i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.04020 | − | 0.316280i | −0.220559 | − | 0.0229454i | ||||
\(191\) | 10.3393i | 0.748123i | 0.927404 | + | 0.374061i | \(0.122035\pi\) | ||||
−0.927404 | + | 0.374061i | \(0.877965\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.2080 | − | 13.2080i | 0.950734 | − | 0.950734i | −0.0481079 | − | 0.998842i | \(-0.515319\pi\) |
0.998842 | + | 0.0481079i | \(0.0153191\pi\) | |||||||
\(194\) | 6.78843 | − | 1.93442i | 0.487381 | − | 0.138883i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 15.4440 | − | 9.57968i | 1.10314 | − | 0.684263i | ||||
\(197\) | −15.2437 | −1.08607 | −0.543036 | − | 0.839709i | \(-0.682725\pi\) | ||||
−0.543036 | + | 0.839709i | \(0.682725\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.98761i | 0.353562i | 0.984250 | + | 0.176781i | \(0.0565684\pi\) | ||||
−0.984250 | + | 0.176781i | \(0.943432\pi\) | |||||||
\(200\) | 10.6775 | + | 9.27308i | 0.755017 | + | 0.655706i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.05300 | − | 14.2231i | −0.285168 | − | 1.00074i | ||||
\(203\) | 4.73878 | 0.332597 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.22046 | + | 10.5281i | −0.294770 | + | 0.735316i | ||||
\(206\) | 2.04224 | + | 7.16680i | 0.142290 | + | 0.499335i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.65202 | − | 7.36385i | 0.253222 | − | 0.510591i | ||||
\(209\) | − | 2.67825i | − | 0.185258i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.3803 | − | 10.3803i | 0.714608 | − | 0.714608i | −0.252887 | − | 0.967496i | \(-0.581380\pi\) |
0.967496 | + | 0.252887i | \(0.0813802\pi\) | |||||||
\(212\) | 8.79715 | − | 5.45674i | 0.604191 | − | 0.374770i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 20.3413 | + | 11.3193i | 1.39050 | + | 0.773774i | ||||
\(215\) | −1.76367 | − | 0.707011i | −0.120281 | − | 0.0482178i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.69257 | − | 6.69257i | 0.454321 | − | 0.454321i | ||||
\(218\) | 7.04603 | + | 24.7265i | 0.477217 | + | 1.67469i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −7.11352 | + | 10.1464i | −0.479593 | + | 0.684068i | ||||
\(221\) | −8.35890 | − | 8.35890i | −0.562280 | − | 0.562280i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.49853 | − | 1.49853i | −0.100349 | − | 0.100349i | 0.655150 | − | 0.755499i | \(-0.272605\pi\) |
−0.755499 | + | 0.655150i | \(0.772605\pi\) | |||||||
\(224\) | 4.12429 | − | 22.3108i | 0.275566 | − | 1.49070i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.473354 | − | 1.66113i | −0.0314870 | − | 0.110497i | ||||
\(227\) | 15.6346 | 1.03771 | 0.518853 | − | 0.854864i | \(-0.326359\pi\) | ||||
0.518853 | + | 0.854864i | \(0.326359\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.74097 | − | 9.74097i | −0.643702 | − | 0.643702i | 0.307762 | − | 0.951463i | \(-0.400420\pi\) |
−0.951463 | + | 0.307762i | \(0.900420\pi\) | |||||||
\(230\) | −2.29068 | + | 22.0189i | −0.151043 | + | 1.45188i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.24835 | − | 2.47230i | 0.147612 | − | 0.162314i | ||||
\(233\) | −0.509123 | − | 0.509123i | −0.0333538 | − | 0.0333538i | 0.690233 | − | 0.723587i | \(-0.257508\pi\) |
−0.723587 | + | 0.690233i | \(0.757508\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.92727 | + | 3.39033i | −0.517118 | + | 0.221161i | ||||
\(236\) | 11.4649 | + | 2.68681i | 0.746303 | + | 0.174897i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −28.5128 | − | 15.8665i | −1.84821 | − | 1.02847i | ||||
\(239\) | −8.19486 | −0.530081 | −0.265041 | − | 0.964237i | \(-0.585385\pi\) | ||||
−0.265041 | + | 0.964237i | \(0.585385\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.66775 | 0.365092 | 0.182546 | − | 0.983197i | \(-0.441566\pi\) | ||||
0.182546 | + | 0.983197i | \(0.441566\pi\) | |||||||
\(242\) | 4.10578 | + | 2.28474i | 0.263929 | + | 0.146869i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.58630 | − | 15.3031i | 0.229590 | − | 0.979683i | ||||
\(245\) | −7.56048 | + | 18.8600i | −0.483022 | + | 1.20492i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.40450 | − | 1.40450i | −0.0893661 | − | 0.0893661i | ||||
\(248\) | −0.316278 | − | 6.66697i | −0.0200837 | − | 0.423353i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −15.7598 | − | 1.27589i | −0.996739 | − | 0.0806942i | ||||
\(251\) | −14.7484 | − | 14.7484i | −0.930911 | − | 0.930911i | 0.0668521 | − | 0.997763i | \(-0.478704\pi\) |
−0.997763 | + | 0.0668521i | \(0.978704\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −19.3974 | −1.21951 | ||||||||
\(254\) | 6.46451 | + | 22.6858i | 0.405619 | + | 1.42343i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.68310 | − | 12.7373i | −0.605194 | − | 0.796078i | ||||
\(257\) | −3.61143 | − | 3.61143i | −0.225275 | − | 0.225275i | 0.585440 | − | 0.810715i | \(-0.300922\pi\) |
−0.810715 | + | 0.585440i | \(0.800922\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.8868 | − | 12.8868i | −0.800745 | − | 0.800745i | ||||
\(260\) | 1.59045 | + | 9.05124i | 0.0986358 | + | 0.561334i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.75617 | + | 30.7279i | 0.540958 | + | 1.89838i | ||||
\(263\) | 6.80041 | − | 6.80041i | 0.419331 | − | 0.419331i | −0.465642 | − | 0.884973i | \(-0.654177\pi\) |
0.884973 | + | 0.465642i | \(0.154177\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.30657 | + | 10.7429i | −0.264551 | + | 0.659933i | ||||
\(266\) | −4.79084 | − | 2.66596i | −0.293746 | − | 0.163461i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.83023 | + | 2.95063i | 0.111799 | + | 0.180238i | ||||
\(269\) | 1.20010 | − | 1.20010i | 0.0731711 | − | 0.0731711i | −0.669574 | − | 0.742745i | \(-0.733523\pi\) |
0.742745 | + | 0.669574i | \(0.233523\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 2.79591i | − | 0.169840i | −0.996388 | − | 0.0849199i | \(-0.972937\pi\) | ||
0.996388 | − | 0.0849199i | \(-0.0270634\pi\) | |||||||
\(272\) | −21.8060 | + | 7.34759i | −1.32218 | + | 0.445513i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.709364 | + | 2.48936i | 0.0428543 | + | 0.150388i | ||||
\(275\) | −0.316922 | − | 13.8506i | −0.0191111 | − | 0.835220i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.8115 | 0.829852 | 0.414926 | − | 0.909855i | \(-0.363807\pi\) | ||||
0.414926 | + | 0.909855i | \(0.363807\pi\) | |||||||
\(278\) | −4.72139 | − | 16.5687i | −0.283170 | − | 0.993724i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 11.0689 | + | 22.8244i | 0.661493 | + | 1.36402i | ||||
\(281\) | − | 7.21718i | − | 0.430541i | −0.976554 | − | 0.215270i | \(-0.930937\pi\) | ||
0.976554 | − | 0.215270i | \(-0.0690633\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.2988 | 1.50386 | 0.751930 | − | 0.659243i | \(-0.229123\pi\) | ||||
0.751930 | + | 0.659243i | \(0.229123\pi\) | |||||||
\(284\) | 2.46190 | + | 3.96898i | 0.146087 | + | 0.235515i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.74407 | + | 2.20674i | −0.457916 | + | 0.130487i | ||||
\(287\) | −14.3862 | + | 14.3862i | −0.849193 | + | 0.849193i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.0930i | 0.946644i | ||||||||
\(290\) | −0.386600 | + | 3.71614i | −0.0227019 | + | 0.218219i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.83755 | − | 12.1081i | 0.166055 | − | 0.708575i | ||||
\(293\) | − | 14.1276i | − | 0.825344i | −0.910880 | − | 0.412672i | \(-0.864596\pi\) | ||
0.910880 | − | 0.412672i | \(-0.135404\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.1049 | + | 5.17700i | −0.704773 | + | 0.301417i | ||||
\(296\) | −12.8375 | + | 0.609004i | −0.746163 | + | 0.0353976i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.155054 | + | 0.0441840i | −0.00898204 | + | 0.00255951i | ||||
\(299\) | −10.1722 | + | 10.1722i | −0.588272 | + | 0.588272i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.40998 | − | 2.40998i | −0.138909 | − | 0.138909i | ||||
\(302\) | 2.23628 | − | 4.01869i | 0.128683 | − | 0.231249i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.66393 | + | 1.23457i | −0.210141 | + | 0.0708076i | ||||
\(305\) | 6.91016 | + | 16.1573i | 0.395674 | + | 0.925166i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.6081 | −1.29031 | −0.645156 | − | 0.764051i | \(-0.723208\pi\) | ||||
−0.645156 | + | 0.764051i | \(0.723208\pi\) | |||||||
\(308\) | −18.8882 | + | 11.7161i | −1.07626 | + | 0.667586i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.70231 | + | 5.79430i | 0.267073 | + | 0.329094i | ||||
\(311\) | 10.7903 | 0.611859 | 0.305929 | − | 0.952054i | \(-0.401033\pi\) | ||||
0.305929 | + | 0.952054i | \(0.401033\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.6842 | + | 20.6842i | 1.16914 | + | 1.16914i | 0.982412 | + | 0.186727i | \(0.0597879\pi\) |
0.186727 | + | 0.982412i | \(0.440212\pi\) | |||||||
\(314\) | 11.2041 | + | 6.23474i | 0.632283 | + | 0.351847i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.8639 | + | 23.9629i | 0.836157 | + | 1.34802i | ||||
\(317\) | − | 23.8207i | − | 1.33791i | −0.743305 | − | 0.668953i | \(-0.766743\pi\) | ||
0.743305 | − | 0.668953i | \(-0.233257\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.27372 | −0.183293 | ||||||||
\(320\) | 17.1596 | + | 5.05442i | 0.959252 | + | 0.282551i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −19.3084 | + | 34.6980i | −1.07602 | + | 1.93365i | ||||
\(323\) | 5.56042i | 0.309390i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.42956 | − | 7.09716i | −0.412118 | − | 0.393680i | ||||
\(326\) | 4.86043 | + | 2.70469i | 0.269194 | + | 0.149799i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.679866 | + | 14.3312i | 0.0375393 | + | 0.791309i | ||||
\(329\) | −15.4650 | −0.852615 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.7688 | − | 19.7688i | −1.08659 | − | 1.08659i | −0.995877 | − | 0.0907155i | \(-0.971085\pi\) |
−0.0907155 | − | 0.995877i | \(-0.528915\pi\) | |||||||
\(332\) | −4.68619 | + | 2.90677i | −0.257188 | + | 0.159530i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 15.6417 | − | 4.45722i | 0.855873 | − | 0.243888i | ||||
\(335\) | −3.60326 | − | 1.44446i | −0.196867 | − | 0.0789191i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.26955 | + | 7.26955i | 0.395998 | + | 0.395998i | 0.876819 | − | 0.480821i | \(-0.159661\pi\) |
−0.480821 | + | 0.876819i | \(0.659661\pi\) | |||||||
\(338\) | 6.03584 | − | 10.8467i | 0.328307 | − | 0.589980i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 14.7687 | − | 21.0653i | 0.800943 | − | 1.14243i | ||||
\(341\) | −4.62347 | + | 4.62347i | −0.250375 | + | 0.250375i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.91866 | + | 5.91866i | −0.319578 | + | 0.319578i | ||||
\(344\) | −2.40076 | + | 0.113891i | −0.129440 | + | 0.00614059i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.72245 | − | 8.48642i | 0.253880 | − | 0.456233i | ||||
\(347\) | 23.4667i | 1.25976i | 0.776692 | + | 0.629880i | \(0.216896\pi\) | ||||
−0.776692 | + | 0.629880i | \(0.783104\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.2089 | + | 23.2089i | −1.24234 | + | 1.24234i | −0.283315 | + | 0.959027i | \(0.591434\pi\) |
−0.959027 | + | 0.283315i | \(0.908566\pi\) | |||||||
\(350\) | −25.0913 | − | 13.2201i | −1.34119 | − | 0.706645i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.84921 | + | 15.4131i | −0.151863 | + | 0.821521i | ||||
\(353\) | 13.3220 | − | 13.3220i | 0.709059 | − | 0.709059i | −0.257278 | − | 0.966337i | \(-0.582826\pi\) |
0.966337 | + | 0.257278i | \(0.0828256\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.84685 | − | 1.94298i | −0.257244 | − | 0.103123i | ||||
\(356\) | −12.2763 | − | 19.7914i | −0.650642 | − | 1.04894i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 30.2203 | − | 8.61154i | 1.59719 | − | 0.455134i | ||||
\(359\) | − | 26.9902i | − | 1.42449i | −0.701932 | − | 0.712244i | \(-0.747679\pi\) | ||
0.701932 | − | 0.712244i | \(-0.252321\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 18.0657i | − | 0.950827i | ||||||
\(362\) | −7.62473 | − | 26.7573i | −0.400747 | − | 1.40633i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.76114 | + | 16.0492i | −0.197137 | + | 0.841205i | ||||
\(365\) | 5.46745 | + | 12.7840i | 0.286179 | + | 0.669145i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.4758 | + | 19.4758i | −1.01663 | + | 1.01663i | −0.0167684 | + | 0.999859i | \(0.505338\pi\) |
−0.999859 | + | 0.0167684i | \(0.994662\pi\) | |||||||
\(368\) | 8.94148 | + | 26.5363i | 0.466107 | + | 1.38330i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 11.1571 | − | 9.05446i | 0.580031 | − | 0.470719i | ||||
\(371\) | −14.6798 | + | 14.6798i | −0.762136 | + | 0.762136i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 4.87069i | − | 0.252195i | −0.992018 | − | 0.126097i | \(-0.959755\pi\) | ||
0.992018 | − | 0.126097i | \(-0.0402452\pi\) | |||||||
\(374\) | 19.6977 | + | 10.9612i | 1.01854 | + | 0.566789i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.33752 | + | 8.06836i | −0.378404 | + | 0.416094i | ||||
\(377\) | −1.71677 | + | 1.71677i | −0.0884180 | + | 0.0884180i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.54450 | − | 2.54450i | 0.130702 | − | 0.130702i | −0.638729 | − | 0.769432i | \(-0.720540\pi\) |
0.769432 | + | 0.638729i | \(0.220540\pi\) | |||||||
\(380\) | 2.48149 | − | 3.53948i | 0.127298 | − | 0.181571i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −12.7769 | − | 7.10996i | −0.653723 | − | 0.363777i | ||||
\(383\) | −0.193238 | − | 0.193238i | −0.00987399 | − | 0.00987399i | 0.702153 | − | 0.712027i | \(-0.252222\pi\) |
−0.712027 | + | 0.702153i | \(0.752222\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.24658 | − | 23.0660i | 0.471249 | − | 1.17555i | ||||
\(386\) | 7.23929 | + | 25.4047i | 0.368470 | + | 1.29307i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.27769 | + | 9.71914i | −0.115632 | + | 0.493414i | ||||
\(389\) | −2.01528 | − | 2.01528i | −0.102179 | − | 0.102179i | 0.654169 | − | 0.756348i | \(-0.273018\pi\) |
−0.756348 | + | 0.654169i | \(0.773018\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 40.2718 | 2.03663 | ||||||||
\(392\) | 1.21790 | + | 25.6728i | 0.0615134 | + | 1.29667i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10.4826 | − | 18.8377i | 0.528107 | − | 0.949029i | ||||
\(395\) | −29.2632 | − | 11.7309i | −1.47239 | − | 0.590244i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 21.5509i | − | 1.08161i | −0.841149 | − | 0.540804i | \(-0.818120\pi\) | ||
0.841149 | − | 0.540804i | \(-0.181880\pi\) | |||||||
\(398\) | −6.16351 | − | 3.42981i | −0.308949 | − | 0.171921i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −18.8019 | + | 6.81815i | −0.940097 | + | 0.340908i | ||||
\(401\) | 10.3965 | 0.519176 | 0.259588 | − | 0.965719i | \(-0.416413\pi\) | ||||
0.259588 | + | 0.965719i | \(0.416413\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.84917i | 0.241555i | ||||||||
\(404\) | 20.3636 | + | 4.77222i | 1.01313 | + | 0.237427i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.25870 | + | 5.85601i | −0.161726 | + | 0.290629i | ||||
\(407\) | 8.90264 | + | 8.90264i | 0.441288 | + | 0.441288i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.330732 | −0.0163536 | −0.00817682 | − | 0.999967i | \(-0.502603\pi\) | ||||
−0.00817682 | + | 0.999967i | \(0.502603\pi\) | |||||||
\(410\) | −10.1080 | − | 12.4553i | −0.499199 | − | 0.615125i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −10.2609 | − | 2.40464i | −0.505516 | − | 0.118468i | ||||
\(413\) | −23.6150 | −1.16202 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.29409 | − | 5.72270i | 0.112612 | − | 0.280917i | ||||
\(416\) | 6.58861 | + | 9.57691i | 0.323033 | + | 0.469547i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.30969 | + | 1.84174i | 0.161882 | + | 0.0900826i | ||||
\(419\) | 6.71354 | + | 6.71354i | 0.327978 | + | 0.327978i | 0.851817 | − | 0.523839i | \(-0.175501\pi\) |
−0.523839 | + | 0.851817i | \(0.675501\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.99831 | − | 2.99831i | 0.146129 | − | 0.146129i | −0.630258 | − | 0.776386i | \(-0.717051\pi\) |
0.776386 | + | 0.630258i | \(0.217051\pi\) | |||||||
\(422\) | 5.68941 | + | 19.9658i | 0.276956 | + | 0.971918i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.693737 | + | 14.6236i | 0.0336909 | + | 0.710186i | ||||
\(425\) | 0.657974 | + | 28.7557i | 0.0319164 | + | 1.39486i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 31.5208i | 1.52540i | ||||||||
\(428\) | −27.9761 | + | 17.3531i | −1.35228 | + | 0.838796i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.08652 | − | 1.69329i | 0.100621 | − | 0.0816579i | ||||
\(431\) | 19.9548i | 0.961191i | 0.876942 | + | 0.480596i | \(0.159580\pi\) | ||||
−0.876942 | + | 0.480596i | \(0.840420\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.1910 | + | 16.1910i | −0.778092 | + | 0.778092i | −0.979506 | − | 0.201414i | \(-0.935446\pi\) |
0.201414 | + | 0.979506i | \(0.435446\pi\) | |||||||
\(434\) | 3.66818 | + | 12.8727i | 0.176078 | + | 0.617909i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −35.4015 | − | 8.29636i | −1.69542 | − | 0.397324i | ||||
\(437\) | 6.76664 | 0.323692 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 29.3734i | 1.40191i | 0.713204 | + | 0.700957i | \(0.247243\pi\) | ||||
−0.713204 | + | 0.700957i | \(0.752757\pi\) | |||||||
\(440\) | −7.64679 | − | 15.7679i | −0.364547 | − | 0.751708i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 16.0778 | − | 4.58150i | 0.764741 | − | 0.217920i | ||||
\(443\) | 19.8713 | 0.944115 | 0.472057 | − | 0.881568i | \(-0.343511\pi\) | ||||
0.472057 | + | 0.881568i | \(0.343511\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 24.1689 | + | 9.68870i | 1.14572 | + | 0.459288i | ||||
\(446\) | 2.88232 | − | 0.821341i | 0.136482 | − | 0.0388916i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 24.7347 | + | 20.4390i | 1.16861 | + | 0.965654i | ||||
\(449\) | 16.7577i | 0.790844i | 0.918500 | + | 0.395422i | \(0.129402\pi\) | ||||
−0.918500 | + | 0.395422i | \(0.870598\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.93854 | − | 9.93854i | 0.467987 | − | 0.467987i | ||||
\(452\) | 2.37828 | + | 0.557352i | 0.111865 | + | 0.0262156i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −10.7514 | + | 19.3207i | −0.504588 | + | 0.906766i | ||||
\(455\) | −7.24703 | − | 16.9450i | −0.339746 | − | 0.794394i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.00267 | + | 5.00267i | −0.234015 | + | 0.234015i | −0.814366 | − | 0.580351i | \(-0.802915\pi\) |
0.580351 | + | 0.814366i | \(0.302915\pi\) | |||||||
\(458\) | 18.7361 | − | 5.33901i | 0.875480 | − | 0.249475i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −25.6349 | − | 17.9724i | −1.19523 | − | 0.837967i | ||||
\(461\) | −2.71518 | − | 2.71518i | −0.126459 | − | 0.126459i | 0.641045 | − | 0.767503i | \(-0.278501\pi\) |
−0.767503 | + | 0.641045i | \(0.778501\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.18551 | + | 9.18551i | 0.426887 | + | 0.426887i | 0.887566 | − | 0.460680i | \(-0.152394\pi\) |
−0.460680 | + | 0.887566i | \(0.652394\pi\) | |||||||
\(464\) | 1.50906 | + | 4.47855i | 0.0700564 | + | 0.207912i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.979263 | − | 0.279049i | 0.0453635 | − | 0.0129267i | ||||
\(467\) | 1.06405 | 0.0492385 | 0.0246193 | − | 0.999697i | \(-0.492163\pi\) | ||||
0.0246193 | + | 0.999697i | \(0.492163\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.92371 | − | 4.92371i | −0.227356 | − | 0.227356i | ||||
\(470\) | 1.26167 | − | 12.1277i | 0.0581966 | − | 0.559407i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −11.2043 | + | 12.3203i | −0.515720 | + | 0.567088i | ||||
\(473\) | 1.66490 | + | 1.66490i | 0.0765523 | + | 0.0765523i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.110556 | + | 4.83166i | 0.00507265 | + | 0.221692i | ||||
\(476\) | 39.2146 | − | 24.3242i | 1.79740 | − | 1.11490i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.63533 | − | 10.1269i | 0.257754 | − | 0.463194i | ||||
\(479\) | −15.8658 | −0.724926 | −0.362463 | − | 0.931998i | \(-0.618064\pi\) | ||||
−0.362463 | + | 0.931998i | \(0.618064\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.33725 | 0.425742 | ||||||||
\(482\) | −3.89752 | + | 7.00400i | −0.177527 | + | 0.319024i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.64681 | + | 3.50263i | −0.256673 | + | 0.159210i | ||||
\(485\) | −4.38869 | − | 10.2616i | −0.199280 | − | 0.465957i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.7947 | − | 13.7947i | −0.625099 | − | 0.625099i | 0.321732 | − | 0.946831i | \(-0.395735\pi\) |
−0.946831 | + | 0.321732i | \(0.895735\pi\) | |||||||
\(488\) | 16.4449 | + | 14.9553i | 0.744426 | + | 0.676994i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −18.1074 | − | 22.3123i | −0.818008 | − | 1.00797i | ||||
\(491\) | −19.4471 | − | 19.4471i | −0.877637 | − | 0.877637i | 0.115652 | − | 0.993290i | \(-0.463104\pi\) |
−0.993290 | + | 0.115652i | \(0.963104\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.79669 | 0.306108 | ||||||||
\(494\) | 2.70146 | − | 0.769803i | 0.121544 | − | 0.0346351i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.45630 | + | 4.19381i | 0.379699 | + | 0.188308i | ||||
\(497\) | −6.62302 | − | 6.62302i | −0.297083 | − | 0.297083i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.0141 | + | 23.0141i | 1.03025 | + | 1.03025i | 0.999528 | + | 0.0307258i | \(0.00978185\pi\) |
0.0307258 | + | 0.999528i | \(0.490218\pi\) | |||||||
\(500\) | 12.4142 | − | 18.5981i | 0.555180 | − | 0.831730i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 28.3675 | − | 8.08357i | 1.26611 | − | 0.360787i | ||||
\(503\) | −6.63364 | + | 6.63364i | −0.295780 | + | 0.295780i | −0.839358 | − | 0.543579i | \(-0.817069\pi\) |
0.543579 | + | 0.839358i | \(0.317069\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21.5002 | + | 9.19520i | −0.956748 | + | 0.409181i | ||||
\(506\) | 13.3390 | − | 23.9706i | 0.592989 | − | 1.06562i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −32.4797 | − | 7.61165i | −1.44105 | − | 0.337712i | ||||
\(509\) | −8.04140 | + | 8.04140i | −0.356429 | + | 0.356429i | −0.862495 | − | 0.506066i | \(-0.831099\pi\) |
0.506066 | + | 0.862495i | \(0.331099\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.9398i | 1.10327i | ||||||||
\(512\) | 22.3990 | − | 3.20705i | 0.989905 | − | 0.141733i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.94634 | − | 1.97942i | 0.306390 | − | 0.0873084i | ||||
\(515\) | 10.8336 | − | 4.63331i | 0.477386 | − | 0.204168i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.6838 | 0.469873 | ||||||||
\(518\) | 24.7868 | − | 7.06321i | 1.08907 | − | 0.310340i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −12.2789 | − | 4.25881i | −0.538465 | − | 0.186761i | ||||
\(521\) | − | 32.8549i | − | 1.43940i | −0.694285 | − | 0.719700i | \(-0.744279\pi\) | ||
0.694285 | − | 0.719700i | \(-0.255721\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.46341 | −0.107717 | −0.0538587 | − | 0.998549i | \(-0.517152\pi\) | ||||
−0.0538587 | + | 0.998549i | \(0.517152\pi\) | |||||||
\(524\) | −43.9938 | − | 10.3100i | −1.92188 | − | 0.450393i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.72729 | + | 13.0801i | 0.162518 | + | 0.570321i | ||||
\(527\) | 9.59896 | − | 9.59896i | 0.418137 | − | 0.418137i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 26.0078i | − | 1.13078i | ||||||
\(530\) | −10.3143 | − | 12.7095i | −0.448023 | − | 0.552064i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.58901 | − | 4.08706i | 0.285670 | − | 0.177197i | ||||
\(533\) | − | 10.4237i | − | 0.451501i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.6955 | − | 34.1640i | 0.592107 | − | 1.47704i | ||||
\(536\) | −4.90487 | + | 0.232685i | −0.211858 | + | 0.0100505i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.657770 | + | 2.30830i | 0.0283585 | + | 0.0995180i | ||||
\(539\) | 17.8038 | − | 17.8038i | 0.766863 | − | 0.766863i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.0772 | − | 18.0772i | −0.777198 | − | 0.777198i | 0.202156 | − | 0.979353i | \(-0.435205\pi\) |
−0.979353 | + | 0.202156i | \(0.935205\pi\) | |||||||
\(542\) | 3.45509 | + | 1.92266i | 0.148409 | + | 0.0825852i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.91535 | − | 31.9997i | 0.253619 | − | 1.37198i | ||||
\(545\) | 37.3775 | − | 15.9856i | 1.60108 | − | 0.684747i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 43.6742 | 1.86738 | 0.933688 | − | 0.358089i | \(-0.116572\pi\) | ||||
0.933688 | + | 0.358089i | \(0.116572\pi\) | |||||||
\(548\) | −3.56407 | − | 0.835243i | −0.152250 | − | 0.0356798i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 17.3340 | + | 9.13293i | 0.739123 | + | 0.389429i | ||||
\(551\) | 1.14201 | 0.0486513 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −39.9869 | − | 39.9869i | −1.70042 | − | 1.70042i | ||||
\(554\) | −9.49770 | + | 17.0677i | −0.403519 | + | 0.725139i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 23.7217 | + | 5.55921i | 1.00603 | + | 0.235763i | ||||
\(557\) | 5.18948i | 0.219885i | 0.993938 | + | 0.109943i | \(0.0350667\pi\) | ||||
−0.993938 | + | 0.109943i | \(0.964933\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.74618 | 0.0738555 | ||||||||
\(560\) | −35.8174 | − | 2.01706i | −1.51356 | − | 0.0852362i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.91874 | + | 4.96301i | 0.376214 | + | 0.209352i | ||||
\(563\) | 11.3756i | 0.479423i | 0.970844 | + | 0.239711i | \(0.0770528\pi\) | ||||
−0.970844 | + | 0.239711i | \(0.922947\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.51103 | + | 1.07392i | −0.105640 | + | 0.0451800i | ||||
\(566\) | −17.3972 | + | 31.2634i | −0.731257 | + | 1.31410i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.59768 | + | 0.312991i | −0.276833 | + | 0.0131328i | ||||
\(569\) | 7.51787 | 0.315165 | 0.157583 | − | 0.987506i | \(-0.449630\pi\) | ||||
0.157583 | + | 0.987506i | \(0.449630\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.76889 | − | 7.76889i | −0.325118 | − | 0.325118i | 0.525609 | − | 0.850726i | \(-0.323838\pi\) |
−0.850726 | + | 0.525609i | \(0.823838\pi\) | |||||||
\(572\) | 2.59833 | − | 11.0873i | 0.108642 | − | 0.463585i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −7.88507 | − | 27.6710i | −0.329117 | − | 1.15496i | ||||
\(575\) | 34.9936 | − | 0.800708i | 1.45934 | − | 0.0333918i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.84819 | − | 9.84819i | −0.409986 | − | 0.409986i | 0.471748 | − | 0.881733i | \(-0.343623\pi\) |
−0.881733 | + | 0.471748i | \(0.843623\pi\) | |||||||
\(578\) | −19.8871 | − | 11.0666i | −0.827195 | − | 0.460309i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.32643 | − | 3.03321i | −0.179645 | − | 0.125947i | ||||
\(581\) | 7.81984 | − | 7.81984i | 0.324421 | − | 0.324421i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.1413 | − | 10.1413i | 0.420010 | − | 0.420010i | ||||
\(584\) | 13.0115 | + | 11.8329i | 0.538421 | + | 0.489650i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 17.4584 | + | 9.71509i | 0.721200 | + | 0.401327i | ||||
\(587\) | 33.0447i | 1.36390i | 0.731398 | + | 0.681951i | \(0.238868\pi\) | ||||
−0.731398 | + | 0.681951i | \(0.761132\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.61286 | − | 1.61286i | 0.0664567 | − | 0.0664567i | ||||
\(590\) | 1.92656 | − | 18.5188i | 0.0793152 | − | 0.762408i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.07532 | − | 16.2829i | 0.331894 | − | 0.669223i | ||||
\(593\) | −18.5424 | + | 18.5424i | −0.761445 | + | 0.761445i | −0.976584 | − | 0.215139i | \(-0.930980\pi\) |
0.215139 | + | 0.976584i | \(0.430980\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −19.1972 | + | 47.8882i | −0.787008 | + | 1.96323i | ||||
\(596\) | 0.0520245 | − | 0.221994i | 0.00213101 | − | 0.00909324i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.57535 | − | 19.5655i | −0.227993 | − | 0.800092i | ||||
\(599\) | 28.3117i | 1.15678i | 0.815759 | + | 0.578392i | \(0.196319\pi\) | ||||
−0.815759 | + | 0.578392i | \(0.803681\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 41.7630i | − | 1.70355i | −0.523909 | − | 0.851774i | \(-0.675527\pi\) | ||
0.523909 | − | 0.851774i | \(-0.324473\pi\) | |||||||
\(602\) | 4.63543 | − | 1.32091i | 0.188926 | − | 0.0538361i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.42833 | + | 5.52703i | 0.139497 | + | 0.224892i | ||||
\(605\) | 2.76435 | − | 6.89579i | 0.112387 | − | 0.280354i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.01973 | − | 4.01973i | 0.163156 | − | 0.163156i | −0.620807 | − | 0.783963i | \(-0.713195\pi\) |
0.783963 | + | 0.620807i | \(0.213195\pi\) | |||||||
\(608\) | 0.993923 | − | 5.37674i | 0.0403089 | − | 0.218055i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −24.7185 | − | 2.57153i | −1.00082 | − | 0.104118i | ||||
\(611\) | 5.60268 | − | 5.60268i | 0.226660 | − | 0.226660i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 21.5230i | − | 0.869305i | −0.900598 | − | 0.434652i | \(-0.856871\pi\) | ||
0.900598 | − | 0.434652i | \(-0.143129\pi\) | |||||||
\(614\) | 15.5468 | − | 27.9383i | 0.627419 | − | 1.12750i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.48951 | − | 31.3982i | −0.0600142 | − | 1.26507i | ||||
\(617\) | 26.4655 | − | 26.4655i | 1.06546 | − | 1.06546i | 0.0677580 | − | 0.997702i | \(-0.478415\pi\) |
0.997702 | − | 0.0677580i | \(-0.0215846\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.7935 | − | 21.7935i | 0.875955 | − | 0.875955i | −0.117158 | − | 0.993113i | \(-0.537378\pi\) |
0.993113 | + | 0.117158i | \(0.0373784\pi\) | |||||||
\(620\) | −10.3940 | + | 1.82640i | −0.417434 | + | 0.0733501i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −7.42010 | + | 13.3342i | −0.297519 | + | 0.534653i | ||||
\(623\) | 33.0258 | + | 33.0258i | 1.32315 | + | 1.32315i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.14348 | + | 24.9738i | 0.0457391 | + | 0.998953i | ||||
\(626\) | −39.7846 | + | 11.3370i | −1.59011 | + | 0.453116i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −15.4093 | + | 9.55818i | −0.614900 | + | 0.381413i | ||||
\(629\) | −18.4831 | − | 18.4831i | −0.736971 | − | 0.736971i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −42.7412 | −1.70150 | −0.850751 | − | 0.525570i | \(-0.823852\pi\) | ||||
−0.850751 | + | 0.525570i | \(0.823852\pi\) | |||||||
\(632\) | −39.8339 | + | 1.88970i | −1.58451 | + | 0.0751683i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 29.4368 | + | 16.3807i | 1.16909 | + | 0.650562i | ||||
\(635\) | 34.2927 | − | 14.6663i | 1.36086 | − | 0.582013i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 18.6729i | − | 0.739848i | ||||||
\(638\) | 2.25123 | − | 4.04554i | 0.0891269 | − | 0.160165i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −18.0462 | + | 17.7295i | −0.713338 | + | 0.700820i | ||||
\(641\) | −45.4930 | −1.79687 | −0.898433 | − | 0.439110i | \(-0.855294\pi\) | ||||
−0.898433 | + | 0.439110i | \(0.855294\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.3531i | 1.23645i | 0.786002 | + | 0.618224i | \(0.212147\pi\) | ||||
−0.786002 | + | 0.618224i | \(0.787853\pi\) | |||||||
\(644\) | −29.6008 | − | 47.7214i | −1.16644 | − | 1.88048i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.87137 | − | 3.82372i | −0.270351 | − | 0.150442i | ||||
\(647\) | 24.0355 | + | 24.0355i | 0.944932 | + | 0.944932i | 0.998561 | − | 0.0536292i | \(-0.0170789\pi\) |
−0.0536292 | + | 0.998561i | \(0.517079\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.3141 | 0.640383 | ||||||||
\(650\) | 13.8795 | − | 4.30070i | 0.544398 | − | 0.168687i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.68471 | + | 4.14642i | −0.261793 | + | 0.162387i | ||||
\(653\) | −15.4153 | −0.603248 | −0.301624 | − | 0.953427i | \(-0.597529\pi\) | ||||
−0.301624 | + | 0.953427i | \(0.597529\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 46.4494 | − | 19.8654i | 1.81493 | − | 0.776207i | ||||
\(656\) | −18.1775 | − | 9.01495i | −0.709714 | − | 0.351975i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 10.6348 | − | 19.1111i | 0.414587 | − | 0.745030i | ||||
\(659\) | 30.4355 | + | 30.4355i | 1.18560 | + | 1.18560i | 0.978272 | + | 0.207327i | \(0.0664763\pi\) |
0.207327 | + | 0.978272i | \(0.433524\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.2208 | + | 11.2208i | −0.436437 | + | 0.436437i | −0.890811 | − | 0.454374i | \(-0.849863\pi\) |
0.454374 | + | 0.890811i | \(0.349863\pi\) | |||||||
\(662\) | 38.0240 | − | 10.8352i | 1.47784 | − | 0.421124i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.369550 | − | 7.78992i | −0.0143413 | − | 0.302308i | ||||
\(665\) | −3.22560 | + | 8.04639i | −0.125083 | + | 0.312026i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 8.27109i | − | 0.320258i | ||||||
\(668\) | −5.24817 | + | 22.3945i | −0.203058 | + | 0.866469i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.26285 | − | 3.45948i | 0.164688 | − | 0.133651i | ||||
\(671\) | − | 21.7757i | − | 0.840640i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.2965 | + | 29.2965i | −1.12930 | + | 1.12930i | −0.139006 | + | 0.990291i | \(0.544391\pi\) |
−0.990291 | + | 0.139006i | \(0.955609\pi\) | |||||||
\(674\) | −13.9825 | + | 3.98443i | −0.538585 | + | 0.153474i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.25326 | + | 14.9178i | 0.355895 | + | 0.573760i | ||||
\(677\) | −2.74511 | −0.105503 | −0.0527516 | − | 0.998608i | \(-0.516799\pi\) | ||||
−0.0527516 | + | 0.998608i | \(0.516799\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 20.0191i | − | 0.768261i | ||||||
\(680\) | 15.8758 | + | 32.7365i | 0.608810 | + | 1.25539i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.53411 | − | 8.89292i | −0.0970362 | − | 0.340528i | ||||
\(683\) | 33.0796 | 1.26576 | 0.632878 | − | 0.774251i | \(-0.281873\pi\) | ||||
0.632878 | + | 0.774251i | \(0.281873\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.76301 | − | 1.60936i | 0.143777 | − | 0.0614905i | ||||
\(686\) | −3.24401 | − | 11.3841i | −0.123857 | − | 0.434648i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.51018 | − | 3.04510i | 0.0575752 | − | 0.116093i | ||||
\(689\) | − | 10.6364i | − | 0.405214i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.8216 | + | 30.8216i | −1.17251 | + | 1.17251i | −0.190899 | + | 0.981610i | \(0.561140\pi\) |
−0.981610 | + | 0.190899i | \(0.938860\pi\) | |||||||
\(692\) | 7.23976 | + | 11.6717i | 0.275214 | + | 0.443690i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −28.9994 | − | 16.1373i | −1.10080 | − | 0.612563i | ||||
\(695\) | −25.0458 | + | 10.7116i | −0.950043 | + | 0.406314i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.6338 | + | 20.6338i | −0.781561 | + | 0.781561i | ||||
\(698\) | −12.7207 | − | 44.6407i | −0.481487 | − | 1.68967i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 33.5914 | − | 21.9159i | 1.26964 | − | 0.828344i | ||||
\(701\) | 22.1242 | + | 22.1242i | 0.835619 | + | 0.835619i | 0.988279 | − | 0.152660i | \(-0.0487838\pi\) |
−0.152660 | + | 0.988279i | \(0.548784\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.10562 | − | 3.10562i | −0.117131 | − | 0.117131i | ||||
\(704\) | −17.0877 | − | 14.1200i | −0.644015 | − | 0.532168i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.30177 | + | 25.6240i | 0.274806 | + | 0.964371i | ||||
\(707\) | −41.9440 | −1.57747 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.09244 | − | 7.09244i | −0.266362 | − | 0.266362i | 0.561270 | − | 0.827632i | \(-0.310313\pi\) |
−0.827632 | + | 0.561270i | \(0.810313\pi\) | |||||||
\(710\) | 5.73408 | − | 4.65344i | 0.215196 | − | 0.174641i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 32.8995 | − | 1.56073i | 1.23296 | − | 0.0584910i | ||||
\(713\) | −11.6812 | − | 11.6812i | −0.437466 | − | 0.437466i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.00651 | + | 11.7062i | 0.187233 | + | 0.437788i | ||||
\(716\) | −10.1397 | + | 43.2671i | −0.378938 | + | 1.61697i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 33.3535 | + | 18.5603i | 1.24474 | + | 0.692663i | ||||
\(719\) | −30.2949 | −1.12981 | −0.564905 | − | 0.825156i | \(-0.691087\pi\) | ||||
−0.564905 | + | 0.825156i | \(0.691087\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 21.1349 | 0.787104 | ||||||||
\(722\) | 22.3250 | + | 12.4232i | 0.830849 | + | 0.462343i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 38.3090 | + | 8.97776i | 1.42374 | + | 0.333656i | ||||
\(725\) | 5.90590 | − | 0.135136i | 0.219340 | − | 0.00501883i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.9503 | + | 15.9503i | 0.591566 | + | 0.591566i | 0.938054 | − | 0.346489i | \(-0.112626\pi\) |
−0.346489 | + | 0.938054i | \(0.612626\pi\) | |||||||
\(728\) | −17.2466 | − | 15.6844i | −0.639201 | − | 0.581301i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −19.5578 | − | 2.03465i | −0.723866 | − | 0.0753056i | ||||
\(731\) | −3.45657 | − | 3.45657i | −0.127846 | − | 0.127846i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.8535 | 1.32428 | 0.662140 | − | 0.749380i | \(-0.269648\pi\) | ||||
0.662140 | + | 0.749380i | \(0.269648\pi\) | |||||||
\(734\) | −10.6746 | − | 37.4603i | −0.394008 | − | 1.38269i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −38.9414 | − | 7.19856i | −1.43540 | − | 0.265342i | ||||
\(737\) | 3.40147 | + | 3.40147i | 0.125295 | + | 0.125295i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21.4532 | − | 21.4532i | −0.789168 | − | 0.789168i | 0.192190 | − | 0.981358i | \(-0.438441\pi\) |
−0.981358 | + | 0.192190i | \(0.938441\pi\) | |||||||
\(740\) | 3.51680 | + | 20.0140i | 0.129280 | + | 0.735730i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.04595 | − | 28.2355i | −0.295376 | − | 1.03656i | ||||
\(743\) | −13.0311 | + | 13.0311i | −0.478063 | + | 0.478063i | −0.904512 | − | 0.426449i | \(-0.859765\pi\) |
0.426449 | + | 0.904512i | \(0.359765\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.100242 | + | 0.234385i | 0.00367258 | + | 0.00858722i | ||||
\(746\) | 6.01903 | + | 3.34941i | 0.220372 | + | 0.122631i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −27.0909 | + | 16.8040i | −0.990540 | + | 0.614417i | ||||
\(749\) | 46.6836 | − | 46.6836i | 1.70578 | − | 1.70578i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.4879i | 0.820595i | 0.911952 | + | 0.410297i | \(0.134575\pi\) | ||||
−0.911952 | + | 0.410297i | \(0.865425\pi\) | |||||||
\(752\) | −4.92483 | − | 14.6158i | −0.179590 | − | 0.532983i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.940956 | − | 3.30208i | −0.0342676 | − | 0.120255i | ||||
\(755\) | −6.74952 | − | 2.70571i | −0.245640 | − | 0.0984710i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.8781 | 0.577100 | 0.288550 | − | 0.957465i | \(-0.406827\pi\) | ||||
0.288550 | + | 0.957465i | \(0.406827\pi\) | |||||||
\(758\) | 1.39464 | + | 4.89418i | 0.0506555 | + | 0.177764i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.66752 | + | 5.50052i | 0.0967613 | + | 0.199525i | ||||
\(761\) | 19.5227i | 0.707696i | 0.935303 | + | 0.353848i | \(0.115127\pi\) | ||||
−0.935303 | + | 0.353848i | \(0.884873\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 72.9184 | 2.63982 | ||||||||
\(764\) | 17.5725 | − | 10.8999i | 0.635750 | − | 0.394346i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.371680 | − | 0.105913i | 0.0134293 | − | 0.00382680i | ||||
\(767\) | 8.55524 | − | 8.55524i | 0.308912 | − | 0.308912i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 8.03843i | − | 0.289873i | −0.989441 | − | 0.144937i | \(-0.953702\pi\) | ||
0.989441 | − | 0.144937i | \(-0.0462978\pi\) | |||||||
\(770\) | 22.1456 | + | 27.2883i | 0.798071 | + | 0.983403i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −36.3725 | − | 8.52392i | −1.30907 | − | 0.306783i | ||||
\(773\) | 40.5118i | 1.45711i | 0.684988 | + | 0.728554i | \(0.259807\pi\) | ||||
−0.684988 | + | 0.728554i | \(0.740193\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.15005 | − | 8.53175i | 0.292758 | − | 0.306470i | ||||
\(776\) | −10.4443 | − | 9.49821i | −0.374928 | − | 0.340966i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.87625 | − | 1.10457i | 0.138970 | − | 0.0396008i | ||||
\(779\) | −3.46698 | + | 3.46698i | −0.124217 | + | 0.124217i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.57542 | + | 4.57542i | 0.163721 | + | 0.163721i | ||||
\(782\) | −27.6935 | + | 49.7664i | −0.990319 | + | 1.77964i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −32.5630 | − | 16.1493i | −1.16296 | − | 0.576760i | ||||
\(785\) | 7.54352 | − | 18.8176i | 0.269240 | − | 0.671631i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.8333 | 0.564396 | 0.282198 | − | 0.959356i | \(-0.408937\pi\) | ||||
0.282198 | + | 0.959356i | \(0.408937\pi\) | |||||||
\(788\) | 16.0704 | + | 25.9081i | 0.572484 | + | 0.922938i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 34.6199 | − | 28.0955i | 1.23172 | − | 0.999592i | ||||
\(791\) | −4.89868 | −0.174177 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.4194 | − | 11.4194i | −0.405513 | − | 0.405513i | ||||
\(794\) | 26.6318 | + | 14.8198i | 0.945128 | + | 0.525936i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.47688 | − | 5.25808i | 0.300455 | − | 0.186368i | ||||
\(797\) | 10.2670i | 0.363674i | 0.983329 | + | 0.181837i | \(0.0582044\pi\) | ||||
−0.983329 | + | 0.181837i | \(0.941796\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22.1811 | −0.784710 | ||||||||
\(800\) | 4.50383 | − | 27.9234i | 0.159235 | − | 0.987241i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7.14932 | + | 12.8476i | −0.252451 | + | 0.453665i | ||||
\(803\) | − | 17.2293i | − | 0.608010i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 58.2766 | + | 23.3616i | 2.05398 | + | 0.823388i | ||||
\(806\) | −5.99244 | − | 3.33462i | −0.211075 | − | 0.117457i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −19.9007 | + | 21.8829i | −0.700104 | + | 0.769837i | ||||
\(809\) | 9.16442 | 0.322204 | 0.161102 | − | 0.986938i | \(-0.448495\pi\) | ||||
0.161102 | + | 0.986938i | \(0.448495\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.1702 | − | 22.1702i | −0.778502 | − | 0.778502i | 0.201074 | − | 0.979576i | \(-0.435557\pi\) |
−0.979576 | + | 0.201074i | \(0.935557\pi\) | |||||||
\(812\) | −4.99575 | − | 8.05397i | −0.175317 | − | 0.282639i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −17.1236 | + | 4.87952i | −0.600183 | + | 0.171027i | ||||
\(815\) | 3.27245 | − | 8.16326i | 0.114629 | − | 0.285947i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.580788 | − | 0.580788i | −0.0203192 | − | 0.0203192i | ||||
\(818\) | 0.227433 | − | 0.408707i | 0.00795202 | − | 0.0142901i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 22.3428 | − | 3.92601i | 0.780245 | − | 0.137102i | ||||
\(821\) | −13.3258 | + | 13.3258i | −0.465074 | + | 0.465074i | −0.900314 | − | 0.435240i | \(-0.856663\pi\) |
0.435240 | + | 0.900314i | \(0.356663\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −34.7796 | + | 34.7796i | −1.21234 | + | 1.21234i | −0.242084 | + | 0.970255i | \(0.577831\pi\) |
−0.970255 | + | 0.242084i | \(0.922169\pi\) | |||||||
\(824\) | 10.0276 | − | 11.0264i | 0.349329 | − | 0.384123i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 16.2392 | − | 29.1825i | 0.565035 | − | 1.01539i | ||||
\(827\) | − | 16.5717i | − | 0.576253i | −0.957592 | − | 0.288127i | \(-0.906968\pi\) | ||
0.957592 | − | 0.288127i | \(-0.0930324\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.9869 | + | 11.9869i | −0.416321 | + | 0.416321i | −0.883933 | − | 0.467613i | \(-0.845114\pi\) |
0.467613 | + | 0.883933i | \(0.345114\pi\) | |||||||
\(830\) | 5.49435 | + | 6.77027i | 0.190712 | + | 0.234999i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −16.3656 | + | 1.55625i | −0.567374 | + | 0.0539534i | ||||
\(833\) | −36.9631 | + | 36.9631i | −1.28070 | + | 1.28070i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.1123 | − | 23.6445i | −0.349949 | − | 0.818252i | ||||
\(836\) | −4.55192 | + | 2.82349i | −0.157432 | + | 0.0976524i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −12.9130 | + | 3.67968i | −0.446073 | + | 0.127112i | ||||
\(839\) | − | 4.44215i | − | 0.153360i | −0.997056 | − | 0.0766800i | \(-0.975568\pi\) | ||
0.997056 | − | 0.0766800i | \(-0.0244320\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.6041i | 0.951865i | ||||||||
\(842\) | 1.64337 | + | 5.76704i | 0.0566341 | + | 0.198745i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −28.5854 | − | 6.69902i | −0.983951 | − | 0.230590i | ||||
\(845\) | −18.2173 | − | 7.30287i | −0.626695 | − | 0.251226i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.42281 | − | 9.42281i | 0.323772 | − | 0.323772i | ||||
\(848\) | −18.5484 | − | 9.19888i | −0.636955 | − | 0.315891i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −35.9878 | − | 18.9612i | −1.23437 | − | 0.650365i | ||||
\(851\) | −22.4926 | + | 22.4926i | −0.771038 | + | 0.771038i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 35.6748i | − | 1.22148i | −0.791830 | − | 0.610742i | \(-0.790871\pi\) | ||
0.791830 | − | 0.610742i | \(-0.209129\pi\) | |||||||
\(854\) | −38.9522 | − | 21.6758i | −1.33292 | − | 0.741730i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.20618 | − | 46.5050i | −0.0754056 | − | 1.58951i | ||||
\(857\) | 13.8568 | − | 13.8568i | 0.473340 | − | 0.473340i | −0.429654 | − | 0.902994i | \(-0.641364\pi\) |
0.902994 | + | 0.429654i | \(0.141364\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.4217 | + | 19.4217i | −0.662660 | + | 0.662660i | −0.956006 | − | 0.293346i | \(-0.905231\pi\) |
0.293346 | + | 0.956006i | \(0.405231\pi\) | |||||||
\(860\) | 0.657684 | + | 3.74287i | 0.0224269 | + | 0.127631i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −24.6595 | − | 13.7223i | −0.839906 | − | 0.467383i | ||||
\(863\) | −9.22041 | − | 9.22041i | −0.313866 | − | 0.313866i | 0.532539 | − | 0.846405i | \(-0.321238\pi\) |
−0.846405 | + | 0.532539i | \(0.821238\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.2532 | − | 5.71377i | −0.484625 | − | 0.194274i | ||||
\(866\) | −8.87428 | − | 31.1424i | −0.301560 | − | 1.05826i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −18.4301 | − | 4.31911i | −0.625559 | − | 0.146600i | ||||
\(869\) | 27.6244 | + | 27.6244i | 0.937093 | + | 0.937093i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.56753 | 0.120881 | ||||||||
\(872\) | 34.5968 | − | 38.0427i | 1.17159 | − | 1.28829i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.65319 | + | 8.36197i | −0.157396 | + | 0.282848i | ||||
\(875\) | −15.7290 | + | 41.9936i | −0.531738 | + | 1.41964i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.4267i | 0.352084i | 0.984383 | + | 0.176042i | \(0.0563295\pi\) | ||||
−0.984383 | + | 0.176042i | \(0.943670\pi\) | |||||||
\(878\) | −36.2986 | − | 20.1991i | −1.22502 | − | 0.681686i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 24.7439 | + | 1.39346i | 0.834117 | + | 0.0469734i | ||||
\(881\) | 12.7405 | 0.429239 | 0.214619 | − | 0.976698i | \(-0.431149\pi\) | ||||
0.214619 | + | 0.976698i | \(0.431149\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 27.9073i | − | 0.939156i | −0.882891 | − | 0.469578i | \(-0.844406\pi\) | ||
0.882891 | − | 0.469578i | \(-0.155594\pi\) | |||||||
\(884\) | −5.39449 | + | 23.0189i | −0.181437 | + | 0.774209i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −13.6648 | + | 24.5563i | −0.459079 | + | 0.824984i | ||||
\(887\) | −41.7449 | − | 41.7449i | −1.40166 | − | 1.40166i | −0.794846 | − | 0.606811i | \(-0.792448\pi\) |
−0.606811 | − | 0.794846i | \(-0.707552\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 66.9004 | 2.24377 | ||||||||
\(890\) | −28.5931 | + | 23.2045i | −0.958443 | + | 0.777816i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.967091 | + | 4.12668i | −0.0323806 | + | 0.138171i | ||||
\(893\) | −3.72696 | −0.124718 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19.5373 | − | 45.6822i | −0.653061 | − | 1.52699i | ||||
\(896\) | −42.2671 | + | 16.5111i | −1.41204 | + | 0.551597i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −20.7086 | − | 11.5237i | −0.691053 | − | 0.384551i | ||||
\(899\) | −1.97145 | − | 1.97145i | −0.0657516 | − | 0.0657516i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.0548 | + | 21.0548i | −0.701437 | + | 0.701437i | ||||
\(902\) | 5.44729 | + | 19.1161i | 0.181375 | + | 0.636496i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.32422 | + | 2.55572i | −0.0773024 | + | 0.0850021i | ||||
\(905\) | −40.4474 | + | 17.2985i | −1.34452 | + | 0.575022i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.7614i | 0.888597i | 0.895879 | + | 0.444298i | \(0.146547\pi\) | ||||
−0.895879 | + | 0.444298i | \(0.853453\pi\) | |||||||
\(908\) | −16.4825 | − | 26.5724i | −0.546990 | − | 0.881836i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 25.9236 | + | 2.69689i | 0.859358 | + | 0.0894012i | ||||
\(911\) | − | 19.2403i | − | 0.637459i | −0.947846 | − | 0.318729i | \(-0.896744\pi\) | ||
0.947846 | − | 0.318729i | \(-0.103256\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.40222 | + | 5.40222i | −0.178787 | + | 0.178787i | ||||
\(914\) | −2.74195 | − | 9.62229i | −0.0906957 | − | 0.318277i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.28643 | + | 26.8249i | −0.207709 | + | 0.886318i | ||||
\(917\) | 90.6165 | 2.99242 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42.6903i | 1.40822i | 0.710090 | + | 0.704111i | \(0.248654\pi\) | ||||
−0.710090 | + | 0.704111i | \(0.751346\pi\) | |||||||
\(920\) | 39.8379 | − | 19.3197i | 1.31342 | − | 0.636953i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 5.22246 | − | 1.48819i | 0.171993 | − | 0.0490108i | ||||
\(923\) | 4.79878 | 0.157954 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.4282 | − | 15.6932i | −0.540155 | − | 0.515989i | ||||
\(926\) | −17.6677 | + | 5.03456i | −0.580597 | + | 0.165446i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.57217 | − | 1.21491i | −0.215742 | − | 0.0398812i | ||||
\(929\) | − | 5.58037i | − | 0.183086i | −0.995801 | − | 0.0915430i | \(-0.970820\pi\) | ||
0.995801 | − | 0.0915430i | \(-0.0291799\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.21070 | + | 6.21070i | −0.203548 | + | 0.203548i | ||||
\(932\) | −0.328567 | + | 1.40203i | −0.0107626 | + | 0.0459251i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.731714 | + | 1.31492i | −0.0239424 | + | 0.0430255i | ||||
\(935\) | 13.2621 | − | 33.0829i | 0.433717 | − | 1.08193i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41.0680 | − | 41.0680i | 1.34163 | − | 1.34163i | 0.447197 | − | 0.894435i | \(-0.352422\pi\) |
0.894435 | − | 0.447197i | \(-0.147578\pi\) | |||||||
\(938\) | 9.47042 | − | 2.69867i | 0.309220 | − | 0.0881149i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 14.1193 | + | 9.89892i | 0.460522 | + | 0.322867i | ||||
\(941\) | 31.5476 | + | 31.5476i | 1.02842 | + | 1.02842i | 0.999584 | + | 0.0288377i | \(0.00918061\pi\) |
0.0288377 | + | 0.999584i | \(0.490819\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25.1098 | + | 25.1098i | 0.817689 | + | 0.817689i | ||||
\(944\) | −7.52017 | − | 22.3182i | −0.244761 | − | 0.726394i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.20232 | + | 0.912529i | −0.104117 | + | 0.0296689i | ||||
\(947\) | 34.7892 | 1.13050 | 0.565248 | − | 0.824921i | \(-0.308780\pi\) | ||||
0.565248 | + | 0.824921i | \(0.308780\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.03522 | − | 9.03522i | −0.293296 | − | 0.293296i | ||||
\(950\) | −6.04682 | − | 3.18595i | −0.196185 | − | 0.103366i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.09244 | + | 65.1870i | 0.100227 | + | 2.11272i | ||||
\(953\) | −26.7047 | − | 26.7047i | −0.865050 | − | 0.865050i | 0.126870 | − | 0.991919i | \(-0.459507\pi\) |
−0.991919 | + | 0.126870i | \(0.959507\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.60247 | + | 21.4592i | −0.278369 | + | 0.694405i | ||||
\(956\) | 8.63926 | + | 13.9279i | 0.279413 | + | 0.450460i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 10.9104 | − | 19.6064i | 0.352498 | − | 0.633453i | ||||
\(959\) | 7.34112 | 0.237057 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.4314 | 0.820369 | ||||||||
\(962\) | −6.42092 | + | 11.5386i | −0.207019 | + | 0.372021i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.97510 | − | 9.63284i | −0.192445 | − | 0.310253i | ||||
\(965\) | 38.4027 | − | 16.4241i | 1.23623 | − | 0.528709i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.8711 | − | 12.8711i | −0.413906 | − | 0.413906i | 0.469191 | − | 0.883097i | \(-0.344546\pi\) |
−0.883097 | + | 0.469191i | \(0.844546\pi\) | |||||||
\(968\) | −0.445304 | − | 9.38677i | −0.0143126 | − | 0.301702i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 15.6989 | + | 1.63320i | 0.504062 | + | 0.0524389i | ||||
\(971\) | 23.9028 | + | 23.9028i | 0.767078 | + | 0.767078i | 0.977591 | − | 0.210513i | \(-0.0675134\pi\) |
−0.210513 | + | 0.977591i | \(0.567513\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −48.8610 | −1.56641 | ||||||||
\(974\) | 26.5332 | − | 7.56087i | 0.850179 | − | 0.242266i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −29.7898 | + | 10.0378i | −0.953549 | + | 0.321301i | ||||
\(977\) | −2.71449 | − | 2.71449i | −0.0868441 | − | 0.0868441i | 0.662350 | − | 0.749194i | \(-0.269559\pi\) |
−0.749194 | + | 0.662350i | \(0.769559\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −22.8154 | − | 22.8154i | −0.729183 | − | 0.729183i | ||||
\(980\) | 40.0247 | − | 7.03300i | 1.27854 | − | 0.224661i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 37.4053 | − | 10.6589i | 1.19365 | − | 0.340141i | ||||
\(983\) | 13.7542 | − | 13.7542i | 0.438692 | − | 0.438692i | −0.452880 | − | 0.891572i | \(-0.649603\pi\) |
0.891572 | + | 0.452880i | \(0.149603\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −31.6386 | − | 12.6831i | −1.00809 | − | 0.404117i | ||||
\(986\) | −4.67386 | + | 8.39911i | −0.148846 | + | 0.267482i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.906407 | + | 3.86773i | −0.0288366 | + | 0.123049i | ||||
\(989\) | −4.20640 | + | 4.20640i | −0.133756 | + | 0.133756i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.5971i | 0.844883i | 0.906390 | + | 0.422442i | \(0.138827\pi\) | ||||
−0.906390 | + | 0.422442i | \(0.861173\pi\) | |||||||
\(992\) | −10.9977 | + | 7.56605i | −0.349177 | + | 0.240222i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 12.7389 | − | 3.63006i | 0.404054 | − | 0.115139i | ||||
\(995\) | −4.14979 | + | 10.3518i | −0.131557 | + | 0.328175i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25.4590 | −0.806295 | −0.403148 | − | 0.915135i | \(-0.632084\pi\) | ||||
−0.403148 | + | 0.915135i | \(0.632084\pi\) | |||||||
\(998\) | −44.2661 | + | 12.6140i | −1.40122 | + | 0.399289i | ||||
\(999\) | 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 | 720.2.bd.g.307.3 | 18 | ||
3.2 | odd | 2 | 80.2.j.b.67.7 | yes | 18 | ||
5.3 | odd | 4 | 720.2.z.g.163.7 | 18 | |||
12.11 | even | 2 | 320.2.j.b.47.5 | 18 | |||
15.2 | even | 4 | 400.2.s.d.243.7 | 18 | |||
15.8 | even | 4 | 80.2.s.b.3.3 | yes | 18 | ||
15.14 | odd | 2 | 400.2.j.d.307.3 | 18 | |||
16.11 | odd | 4 | 720.2.z.g.667.7 | 18 | |||
24.5 | odd | 2 | 640.2.j.d.607.5 | 18 | |||
24.11 | even | 2 | 640.2.j.c.607.5 | 18 | |||
48.5 | odd | 4 | 320.2.s.b.207.5 | 18 | |||
48.11 | even | 4 | 80.2.s.b.27.3 | yes | 18 | ||
48.29 | odd | 4 | 640.2.s.c.287.5 | 18 | |||
48.35 | even | 4 | 640.2.s.d.287.5 | 18 | |||
60.23 | odd | 4 | 320.2.s.b.303.5 | 18 | |||
60.47 | odd | 4 | 1600.2.s.d.943.5 | 18 | |||
60.59 | even | 2 | 1600.2.j.d.1007.5 | 18 | |||
80.43 | even | 4 | inner | 720.2.bd.g.523.3 | 18 | ||
120.53 | even | 4 | 640.2.s.d.223.5 | 18 | |||
120.83 | odd | 4 | 640.2.s.c.223.5 | 18 | |||
240.53 | even | 4 | 320.2.j.b.143.5 | 18 | |||
240.59 | even | 4 | 400.2.s.d.107.7 | 18 | |||
240.83 | odd | 4 | 640.2.j.d.543.5 | 18 | |||
240.107 | odd | 4 | 400.2.j.d.43.3 | 18 | |||
240.149 | odd | 4 | 1600.2.s.d.207.5 | 18 | |||
240.173 | even | 4 | 640.2.j.c.543.5 | 18 | |||
240.197 | even | 4 | 1600.2.j.d.143.5 | 18 | |||
240.203 | odd | 4 | 80.2.j.b.43.7 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.2.j.b.43.7 | ✓ | 18 | 240.203 | odd | 4 | ||
80.2.j.b.67.7 | yes | 18 | 3.2 | odd | 2 | ||
80.2.s.b.3.3 | yes | 18 | 15.8 | even | 4 | ||
80.2.s.b.27.3 | yes | 18 | 48.11 | even | 4 | ||
320.2.j.b.47.5 | 18 | 12.11 | even | 2 | |||
320.2.j.b.143.5 | 18 | 240.53 | even | 4 | |||
320.2.s.b.207.5 | 18 | 48.5 | odd | 4 | |||
320.2.s.b.303.5 | 18 | 60.23 | odd | 4 | |||
400.2.j.d.43.3 | 18 | 240.107 | odd | 4 | |||
400.2.j.d.307.3 | 18 | 15.14 | odd | 2 | |||
400.2.s.d.107.7 | 18 | 240.59 | even | 4 | |||
400.2.s.d.243.7 | 18 | 15.2 | even | 4 | |||
640.2.j.c.543.5 | 18 | 240.173 | even | 4 | |||
640.2.j.c.607.5 | 18 | 24.11 | even | 2 | |||
640.2.j.d.543.5 | 18 | 240.83 | odd | 4 | |||
640.2.j.d.607.5 | 18 | 24.5 | odd | 2 | |||
640.2.s.c.223.5 | 18 | 120.83 | odd | 4 | |||
640.2.s.c.287.5 | 18 | 48.29 | odd | 4 | |||
640.2.s.d.223.5 | 18 | 120.53 | even | 4 | |||
640.2.s.d.287.5 | 18 | 48.35 | even | 4 | |||
720.2.z.g.163.7 | 18 | 5.3 | odd | 4 | |||
720.2.z.g.667.7 | 18 | 16.11 | odd | 4 | |||
720.2.bd.g.307.3 | 18 | 1.1 | even | 1 | trivial | ||
720.2.bd.g.523.3 | 18 | 80.43 | even | 4 | inner | ||
1600.2.j.d.143.5 | 18 | 240.197 | even | 4 | |||
1600.2.j.d.1007.5 | 18 | 60.59 | even | 2 | |||
1600.2.s.d.207.5 | 18 | 240.149 | odd | 4 | |||
1600.2.s.d.943.5 | 18 | 60.47 | odd | 4 |