Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [750,2,Mod(107,750)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(750, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([10, 13]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("750.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 750 = 2 \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 750.l (of order \(20\), degree \(8\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.98878015160\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{20})\) |
Twist minimal: | no (minimal twist has level 150) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{20}]$ |
Embedding invariants
Embedding label | 143.9 | ||
Character | \(\chi\) | \(=\) | 750.143 |
Dual form | 750.2.l.c.257.9 |
$q$-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 \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{3}{20}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.453990 | − | 0.891007i | 0.321020 | − | 0.630037i | ||||
\(3\) | 0.333634 | − | 1.69961i | 0.192624 | − | 0.981273i | ||||
\(4\) | −0.587785 | − | 0.809017i | −0.293893 | − | 0.404508i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.36290 | − | 1.06888i | −0.556402 | − | 0.436368i | ||||
\(7\) | 2.58285 | − | 2.58285i | 0.976227 | − | 0.976227i | −0.0234972 | − | 0.999724i | \(-0.507480\pi\) |
0.999724 | + | 0.0234972i | \(0.00748007\pi\) | |||||||
\(8\) | −0.987688 | + | 0.156434i | −0.349201 | + | 0.0553079i | ||||
\(9\) | −2.77738 | − | 1.13410i | −0.925792 | − | 0.378033i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.45719 | − | 0.473470i | 0.439360 | − | 0.142757i | −0.0809806 | − | 0.996716i | \(-0.525805\pi\) |
0.520340 | + | 0.853959i | \(0.325805\pi\) | |||||||
\(12\) | −1.57112 | + | 0.729092i | −0.453544 | + | 0.210471i | ||||
\(13\) | 4.48435 | − | 2.28489i | 1.24373 | − | 0.633714i | 0.296738 | − | 0.954959i | \(-0.404101\pi\) |
0.946996 | + | 0.321245i | \(0.104101\pi\) | |||||||
\(14\) | −1.12875 | − | 3.47393i | −0.301671 | − | 0.928447i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.309017 | + | 0.951057i | −0.0772542 | + | 0.237764i | ||||
\(17\) | 0.806752 | + | 5.09363i | 0.195666 | + | 1.23539i | 0.868536 | + | 0.495626i | \(0.165061\pi\) |
−0.672870 | + | 0.739761i | \(0.734939\pi\) | |||||||
\(18\) | −2.27139 | + | 1.95979i | −0.535372 | + | 0.461927i | ||||
\(19\) | 1.27450 | − | 1.75421i | 0.292391 | − | 0.402442i | −0.637398 | − | 0.770535i | \(-0.719989\pi\) |
0.929789 | + | 0.368093i | \(0.119989\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.52813 | − | 5.25158i | −0.769900 | − | 1.14599i | ||||
\(22\) | 0.239686 | − | 1.51332i | 0.0511012 | − | 0.322640i | ||||
\(23\) | −5.66723 | − | 2.88760i | −1.18170 | − | 0.602105i | −0.251034 | − | 0.967978i | \(-0.580770\pi\) |
−0.930665 | + | 0.365873i | \(0.880770\pi\) | |||||||
\(24\) | −0.0636485 | + | 1.73088i | −0.0129922 | + | 0.353315i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 5.03290i | − | 0.987033i | ||||||
\(27\) | −2.85416 | + | 4.34209i | −0.549283 | + | 0.835636i | ||||
\(28\) | −3.60774 | − | 0.571409i | −0.681798 | − | 0.107986i | ||||
\(29\) | −5.64831 | + | 4.10373i | −1.04886 | + | 0.762044i | −0.971996 | − | 0.234997i | \(-0.924492\pi\) |
−0.0768679 | + | 0.997041i | \(0.524492\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.95310 | − | 4.32518i | −1.06921 | − | 0.776825i | −0.0934378 | − | 0.995625i | \(-0.529786\pi\) |
−0.975770 | + | 0.218800i | \(0.929786\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | −0.318547 | − | 2.63463i | −0.0554520 | − | 0.458630i | ||||
\(34\) | 4.90472 | + | 1.59364i | 0.841152 | + | 0.273307i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.714995 | + | 2.91355i | 0.119166 | + | 0.485592i | ||||
\(37\) | 3.48561 | + | 6.84089i | 0.573031 | + | 1.12464i | 0.977667 | + | 0.210158i | \(0.0673979\pi\) |
−0.404637 | + | 0.914477i | \(0.632602\pi\) | |||||||
\(38\) | −0.984395 | − | 1.93198i | −0.159690 | − | 0.313409i | ||||
\(39\) | −2.38730 | − | 8.38398i | −0.382274 | − | 1.34251i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.85939 | + | 0.929072i | 0.446562 | + | 0.145097i | 0.523661 | − | 0.851927i | \(-0.324566\pi\) |
−0.0770993 | + | 0.997023i | \(0.524566\pi\) | |||||||
\(42\) | −6.28093 | + | 0.759414i | −0.969168 | + | 0.117180i | ||||
\(43\) | 3.24693 | + | 3.24693i | 0.495151 | + | 0.495151i | 0.909925 | − | 0.414773i | \(-0.136139\pi\) |
−0.414773 | + | 0.909925i | \(0.636139\pi\) | |||||||
\(44\) | −1.23956 | − | 0.900593i | −0.186871 | − | 0.135770i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.14573 | + | 3.73859i | −0.758697 | + | 0.551226i | ||||
\(47\) | 2.81716 | + | 0.446195i | 0.410925 | + | 0.0650842i | 0.358475 | − | 0.933539i | \(-0.383297\pi\) |
0.0524505 | + | 0.998624i | \(0.483297\pi\) | |||||||
\(48\) | 1.51333 | + | 0.842515i | 0.218430 | + | 0.121607i | ||||
\(49\) | − | 6.34226i | − | 0.906037i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.92637 | + | 0.328243i | 1.24994 | + | 0.0459632i | ||||
\(52\) | −4.48435 | − | 2.28489i | −0.621867 | − | 0.316857i | ||||
\(53\) | 0.161639 | − | 1.02055i | 0.0222028 | − | 0.140183i | −0.974097 | − | 0.226131i | \(-0.927392\pi\) |
0.996300 | + | 0.0859487i | \(0.0273921\pi\) | |||||||
\(54\) | 2.57307 | + | 4.51434i | 0.350151 | + | 0.614324i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.14701 | + | 2.95510i | −0.286906 | + | 0.394892i | ||||
\(57\) | −2.55625 | − | 2.75143i | −0.338584 | − | 0.364436i | ||||
\(58\) | 1.09218 | + | 6.89573i | 0.143410 | + | 0.905454i | ||||
\(59\) | 2.10801 | − | 6.48779i | 0.274439 | − | 0.844638i | −0.714928 | − | 0.699198i | \(-0.753540\pi\) |
0.989367 | − | 0.145439i | \(-0.0464596\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.78395 | + | 5.49044i | 0.228412 | + | 0.702979i | 0.997927 | + | 0.0643507i | \(0.0204976\pi\) |
−0.769516 | + | 0.638628i | \(0.779502\pi\) | |||||||
\(62\) | −6.55641 | + | 3.34066i | −0.832665 | + | 0.424264i | ||||
\(63\) | −10.1028 | + | 4.24434i | −1.27283 | + | 0.534737i | ||||
\(64\) | 0.951057 | − | 0.309017i | 0.118882 | − | 0.0386271i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.49209 | − | 0.912268i | −0.306755 | − | 0.112292i | ||||
\(67\) | −3.33029 | + | 0.527466i | −0.406859 | + | 0.0644402i | −0.356510 | − | 0.934291i | \(-0.616033\pi\) |
−0.0503493 | + | 0.998732i | \(0.516033\pi\) | |||||||
\(68\) | 3.64664 | − | 3.64664i | 0.442220 | − | 0.442220i | ||||
\(69\) | −6.79858 | + | 8.66870i | −0.818453 | + | 1.04359i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.18090 | − | 3.00175i | −0.258825 | − | 0.356242i | 0.659752 | − | 0.751483i | \(-0.270661\pi\) |
−0.918578 | + | 0.395241i | \(0.870661\pi\) | |||||||
\(72\) | 2.92059 | + | 0.685659i | 0.344195 | + | 0.0808057i | ||||
\(73\) | 0.270757 | − | 0.531390i | 0.0316897 | − | 0.0621945i | −0.874619 | − | 0.484811i | \(-0.838888\pi\) |
0.906309 | + | 0.422617i | \(0.138888\pi\) | |||||||
\(74\) | 7.67771 | 0.892516 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.16832 | −0.248723 | ||||||||
\(77\) | 2.54081 | − | 4.98661i | 0.289552 | − | 0.568277i | ||||
\(78\) | −8.55399 | − | 1.67915i | −0.968549 | − | 0.190126i | ||||
\(79\) | 0.782199 | + | 1.07660i | 0.0880042 | + | 0.121127i | 0.850749 | − | 0.525572i | \(-0.176149\pi\) |
−0.762745 | + | 0.646700i | \(0.776149\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.42764 | + | 6.29964i | 0.714182 | + | 0.699960i | ||||
\(82\) | 2.12595 | − | 2.12595i | 0.234771 | − | 0.234771i | ||||
\(83\) | 2.73356 | − | 0.432953i | 0.300047 | − | 0.0475228i | −0.00459575 | − | 0.999989i | \(-0.501463\pi\) |
0.304643 | + | 0.952467i | \(0.401463\pi\) | |||||||
\(84\) | −2.17484 | + | 5.94112i | −0.237294 | + | 0.648229i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.36710 | − | 1.41896i | 0.470917 | − | 0.153010i | ||||
\(87\) | 5.09030 | + | 10.9691i | 0.545737 | + | 1.17601i | ||||
\(88\) | −1.36518 | + | 0.695596i | −0.145529 | + | 0.0741507i | ||||
\(89\) | 1.98939 | + | 6.12272i | 0.210875 | + | 0.649007i | 0.999421 | + | 0.0340306i | \(0.0108344\pi\) |
−0.788546 | + | 0.614976i | \(0.789166\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.68088 | − | 17.4839i | 0.595518 | − | 1.83282i | ||||
\(92\) | 0.994998 | + | 6.28217i | 0.103736 | + | 0.654961i | ||||
\(93\) | −9.33729 | + | 8.67494i | −0.968232 | + | 0.899549i | ||||
\(94\) | 1.67653 | − | 2.30754i | 0.172921 | − | 0.238005i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.43772 | − | 0.965894i | 0.146737 | − | 0.0985811i | ||||
\(97\) | 2.14067 | − | 13.5156i | 0.217352 | − | 1.37230i | −0.601763 | − | 0.798675i | \(-0.705535\pi\) |
0.819114 | − | 0.573630i | \(-0.194465\pi\) | |||||||
\(98\) | −5.65100 | − | 2.87933i | −0.570837 | − | 0.290856i | ||||
\(99\) | −4.58413 | − | 0.337594i | −0.460722 | − | 0.0339295i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 0.146560i | − | 0.0145833i | −0.999973 | − | 0.00729163i | \(-0.997679\pi\) | ||
0.999973 | − | 0.00729163i | \(-0.00232102\pi\) | |||||||
\(102\) | 4.34495 | − | 7.80443i | 0.430214 | − | 0.772754i | ||||
\(103\) | 15.4311 | + | 2.44405i | 1.52047 | + | 0.240819i | 0.860103 | − | 0.510120i | \(-0.170399\pi\) |
0.660371 | + | 0.750939i | \(0.270399\pi\) | |||||||
\(104\) | −4.07170 | + | 2.95827i | −0.399263 | + | 0.290082i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.835930 | − | 0.607339i | −0.0811927 | − | 0.0589900i | ||||
\(107\) | −1.77141 | − | 1.77141i | −0.171249 | − | 0.171249i | 0.616279 | − | 0.787528i | \(-0.288639\pi\) |
−0.787528 | + | 0.616279i | \(0.788639\pi\) | |||||||
\(108\) | 5.19046 | − | 0.243156i | 0.499452 | − | 0.0233977i | ||||
\(109\) | −7.65945 | − | 2.48870i | −0.733642 | − | 0.238375i | −0.0817142 | − | 0.996656i | \(-0.526039\pi\) |
−0.651928 | + | 0.758281i | \(0.726039\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.7898 | − | 3.64183i | 1.21395 | − | 0.345668i | ||||
\(112\) | 1.65829 | + | 3.25458i | 0.156694 | + | 0.307529i | ||||
\(113\) | 4.92541 | + | 9.66667i | 0.463344 | + | 0.909364i | 0.997934 | + | 0.0642521i | \(0.0204662\pi\) |
−0.534590 | + | 0.845112i | \(0.679534\pi\) | |||||||
\(114\) | −3.61206 | + | 1.02852i | −0.338300 | + | 0.0963293i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.63998 | + | 2.15746i | 0.616507 | + | 0.200315i | ||||
\(117\) | −15.0460 | + | 1.26030i | −1.39100 | + | 0.116515i | ||||
\(118\) | −4.82364 | − | 4.82364i | −0.444052 | − | 0.444052i | ||||
\(119\) | 15.2398 | + | 11.0724i | 1.39703 | + | 1.01500i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.99996 | + | 5.08577i | −0.636360 | + | 0.462342i | ||||
\(122\) | 5.70191 | + | 0.903094i | 0.516227 | + | 0.0817623i | ||||
\(123\) | 2.53305 | − | 4.54989i | 0.228398 | − | 0.410250i | ||||
\(124\) | 7.35843i | 0.660807i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.804822 | + | 10.9285i | −0.0716992 | + | 0.973590i | ||||
\(127\) | 16.4638 | + | 8.38871i | 1.46092 | + | 0.744378i | 0.990429 | − | 0.138025i | \(-0.0440754\pi\) |
0.470495 | + | 0.882403i | \(0.344075\pi\) | |||||||
\(128\) | 0.156434 | − | 0.987688i | 0.0138270 | − | 0.0873001i | ||||
\(129\) | 6.60181 | − | 4.43523i | 0.581257 | − | 0.390501i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.79711 | + | 10.7318i | −0.681236 | + | 0.937641i | −0.999948 | − | 0.0102104i | \(-0.996750\pi\) |
0.318712 | + | 0.947852i | \(0.396750\pi\) | |||||||
\(132\) | −1.94422 | + | 1.80631i | −0.169223 | + | 0.157219i | ||||
\(133\) | −1.23900 | − | 7.82271i | −0.107435 | − | 0.678315i | ||||
\(134\) | −1.04194 | + | 3.20677i | −0.0900102 | + | 0.277023i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.59364 | − | 4.90472i | −0.136653 | − | 0.420576i | ||||
\(137\) | 8.69698 | − | 4.43133i | 0.743033 | − | 0.378594i | −0.0411262 | − | 0.999154i | \(-0.513095\pi\) |
0.784159 | + | 0.620560i | \(0.213095\pi\) | |||||||
\(138\) | 4.63737 | + | 9.99308i | 0.394760 | + | 0.850668i | ||||
\(139\) | 4.61980 | − | 1.50106i | 0.391846 | − | 0.127319i | −0.106466 | − | 0.994316i | \(-0.533953\pi\) |
0.498312 | + | 0.866998i | \(0.333953\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.69826 | − | 4.63922i | 0.143019 | − | 0.390693i | ||||
\(142\) | −3.66469 | + | 0.580430i | −0.307534 | + | 0.0487086i | ||||
\(143\) | 5.45272 | − | 5.45272i | 0.455980 | − | 0.455980i | ||||
\(144\) | 1.93685 | − | 2.29099i | 0.161404 | − | 0.190915i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.350551 | − | 0.482492i | −0.0290118 | − | 0.0399313i | ||||
\(147\) | −10.7794 | − | 2.11600i | −0.889070 | − | 0.174524i | ||||
\(148\) | 3.48561 | − | 6.84089i | 0.286515 | − | 0.562318i | ||||
\(149\) | −6.55688 | −0.537160 | −0.268580 | − | 0.963257i | \(-0.586554\pi\) | ||||
−0.268580 | + | 0.963257i | \(0.586554\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.06618 | 0.0867647 | 0.0433824 | − | 0.999059i | \(-0.486187\pi\) | ||||
0.0433824 | + | 0.999059i | \(0.486187\pi\) | |||||||
\(152\) | −0.984395 | + | 1.93198i | −0.0798450 | + | 0.156705i | ||||
\(153\) | 3.53603 | − | 15.0619i | 0.285871 | − | 1.21768i | ||||
\(154\) | −3.28960 | − | 4.52775i | −0.265084 | − | 0.364856i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −5.37956 | + | 6.85934i | −0.430710 | + | 0.549187i | ||||
\(157\) | 15.3342 | − | 15.3342i | 1.22380 | − | 1.22380i | 0.257528 | − | 0.966271i | \(-0.417092\pi\) |
0.966271 | − | 0.257528i | \(-0.0829078\pi\) | |||||||
\(158\) | 1.31437 | − | 0.208176i | 0.104566 | − | 0.0165616i | ||||
\(159\) | −1.68061 | − | 0.615212i | −0.133281 | − | 0.0487895i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −22.0958 | + | 7.17938i | −1.74140 | + | 0.565814i | ||||
\(162\) | 8.53111 | − | 2.86709i | 0.670267 | − | 0.225260i | ||||
\(163\) | 9.16108 | − | 4.66780i | 0.717551 | − | 0.365610i | −0.0567839 | − | 0.998386i | \(-0.518085\pi\) |
0.774335 | + | 0.632776i | \(0.218085\pi\) | |||||||
\(164\) | −0.929072 | − | 2.85939i | −0.0725483 | − | 0.223281i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.855246 | − | 2.63218i | 0.0663800 | − | 0.204297i | ||||
\(167\) | −3.76955 | − | 23.8000i | −0.291697 | − | 1.84170i | −0.503008 | − | 0.864282i | \(-0.667773\pi\) |
0.211311 | − | 0.977419i | \(-0.432227\pi\) | |||||||
\(168\) | 4.30622 | + | 4.63501i | 0.332232 | + | 0.357598i | ||||
\(169\) | 7.24745 | − | 9.97526i | 0.557496 | − | 0.767327i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.52922 | + | 3.42667i | −0.422830 | + | 0.262044i | ||||
\(172\) | 0.718323 | − | 4.53531i | 0.0547716 | − | 0.345814i | ||||
\(173\) | 21.3945 | + | 10.9010i | 1.62659 | + | 0.828791i | 0.998725 | + | 0.0504717i | \(0.0160725\pi\) |
0.627869 | + | 0.778319i | \(0.283928\pi\) | |||||||
\(174\) | 12.0845 | + | 0.444374i | 0.916122 | + | 0.0336879i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.53218i | 0.115492i | ||||||||
\(177\) | −10.3234 | − | 5.74735i | −0.775956 | − | 0.431997i | ||||
\(178\) | 6.35855 | + | 1.00709i | 0.476593 | + | 0.0754849i | ||||
\(179\) | 3.64757 | − | 2.65012i | 0.272632 | − | 0.198079i | −0.443065 | − | 0.896489i | \(-0.646109\pi\) |
0.715697 | + | 0.698410i | \(0.246109\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.4405 | − | 8.31202i | −0.850367 | − | 0.617828i | 0.0748802 | − | 0.997193i | \(-0.476143\pi\) |
−0.925247 | + | 0.379365i | \(0.876143\pi\) | |||||||
\(182\) | −12.9992 | − | 12.9992i | −0.963568 | − | 0.963568i | ||||
\(183\) | 9.92681 | − | 1.20023i | 0.733811 | − | 0.0887236i | ||||
\(184\) | 6.04917 | + | 1.96550i | 0.445951 | + | 0.144898i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.49039 | + | 12.2579i | 0.255928 | + | 0.898795i | ||||
\(187\) | 3.58727 | + | 7.04042i | 0.262327 | + | 0.514846i | ||||
\(188\) | −1.29491 | − | 2.54140i | −0.0944409 | − | 0.185351i | ||||
\(189\) | 3.84312 | + | 18.5869i | 0.279546 | + | 1.35200i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.1952 | + | 3.96247i | 0.882416 | + | 0.286714i | 0.714960 | − | 0.699165i | \(-0.246445\pi\) |
0.167456 | + | 0.985880i | \(0.446445\pi\) | |||||||
\(192\) | −0.207905 | − | 1.71953i | −0.0150042 | − | 0.124096i | ||||
\(193\) | −9.89879 | − | 9.89879i | −0.712531 | − | 0.712531i | 0.254533 | − | 0.967064i | \(-0.418078\pi\) |
−0.967064 | + | 0.254533i | \(0.918078\pi\) | |||||||
\(194\) | −11.0707 | − | 8.04332i | −0.794828 | − | 0.577477i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.13100 | + | 3.72789i | −0.366500 | + | 0.266278i | ||||
\(197\) | −6.72363 | − | 1.06492i | −0.479039 | − | 0.0758723i | −0.0877545 | − | 0.996142i | \(-0.527969\pi\) |
−0.391284 | + | 0.920270i | \(0.627969\pi\) | |||||||
\(198\) | −2.38195 | + | 3.93122i | −0.169278 | + | 0.279380i | ||||
\(199\) | 5.40490i | 0.383143i | 0.981479 | + | 0.191572i | \(0.0613585\pi\) | ||||
−0.981479 | + | 0.191572i | \(0.938642\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.214610 | + | 5.83618i | −0.0151374 | + | 0.411653i | ||||
\(202\) | −0.130586 | − | 0.0665368i | −0.00918799 | − | 0.00468151i | ||||
\(203\) | −3.98940 | + | 25.1881i | −0.280001 | + | 1.76786i | ||||
\(204\) | −4.98123 | − | 7.41452i | −0.348756 | − | 0.519120i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 9.18325 | − | 12.6397i | 0.639827 | − | 0.880647i | ||||
\(207\) | 12.4652 | + | 14.4471i | 0.866391 | + | 1.00415i | ||||
\(208\) | 0.787319 | + | 4.97094i | 0.0545908 | + | 0.344673i | ||||
\(209\) | 1.02663 | − | 3.15965i | 0.0710137 | − | 0.218558i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.95464 | + | 12.1711i | 0.272249 | + | 0.837896i | 0.989934 | + | 0.141529i | \(0.0452017\pi\) |
−0.717685 | + | 0.696368i | \(0.754798\pi\) | |||||||
\(212\) | −0.920647 | + | 0.469093i | −0.0632303 | + | 0.0322175i | ||||
\(213\) | −5.82944 | + | 2.70520i | −0.399427 | + | 0.185357i | ||||
\(214\) | −2.38255 | + | 0.774136i | −0.162868 | + | 0.0529189i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.13977 | − | 4.73512i | 0.145593 | − | 0.322184i | ||||
\(217\) | −26.5473 | + | 4.20467i | −1.80215 | + | 0.285432i | ||||
\(218\) | −5.69477 | + | 5.69477i | −0.385698 | + | 0.385698i | ||||
\(219\) | −0.812824 | − | 0.637472i | −0.0549256 | − | 0.0430763i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15.2561 | + | 20.9983i | 1.02624 | + | 1.41250i | ||||
\(222\) | 2.56155 | − | 13.0491i | 0.171920 | − | 0.875802i | ||||
\(223\) | −13.1811 | + | 25.8694i | −0.882673 | + | 1.73234i | −0.232437 | + | 0.972611i | \(0.574670\pi\) |
−0.650236 | + | 0.759732i | \(0.725330\pi\) | |||||||
\(224\) | 3.65271 | 0.244057 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.8492 | 0.721675 | ||||||||
\(227\) | −1.79400 | + | 3.52093i | −0.119072 | + | 0.233692i | −0.942848 | − | 0.333224i | \(-0.891864\pi\) |
0.823776 | + | 0.566916i | \(0.191864\pi\) | |||||||
\(228\) | −0.723425 | + | 3.68530i | −0.0479100 | + | 0.244065i | ||||
\(229\) | −7.75981 | − | 10.6805i | −0.512783 | − | 0.705785i | 0.471603 | − | 0.881811i | \(-0.343676\pi\) |
−0.984386 | + | 0.176026i | \(0.943676\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.62762 | − | 5.98209i | −0.501860 | − | 0.393593i | ||||
\(232\) | 4.93680 | − | 4.93680i | 0.324117 | − | 0.324117i | ||||
\(233\) | −8.65736 | + | 1.37119i | −0.567163 | + | 0.0898297i | −0.433429 | − | 0.901188i | \(-0.642697\pi\) |
−0.133733 | + | 0.991017i | \(0.542697\pi\) | |||||||
\(234\) | −5.70781 | + | 13.9783i | −0.373131 | + | 0.913787i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.48779 | + | 2.10801i | −0.422319 | + | 0.137220i | ||||
\(237\) | 2.09078 | − | 0.970244i | 0.135811 | − | 0.0630241i | ||||
\(238\) | 16.7843 | − | 8.55203i | 1.08796 | − | 0.554345i | ||||
\(239\) | 5.85405 | + | 18.0169i | 0.378667 | + | 1.16542i | 0.940971 | + | 0.338486i | \(0.109915\pi\) |
−0.562305 | + | 0.826930i | \(0.690085\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.26464 | + | 22.3583i | −0.467957 | + | 1.44022i | 0.387269 | + | 0.921967i | \(0.373418\pi\) |
−0.855226 | + | 0.518256i | \(0.826582\pi\) | |||||||
\(242\) | 1.35354 | + | 8.54590i | 0.0870087 | + | 0.549351i | ||||
\(243\) | 12.8514 | − | 8.82273i | 0.824420 | − | 0.565978i | ||||
\(244\) | 3.39328 | − | 4.67045i | 0.217232 | − | 0.298995i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.90400 | − | 4.32257i | −0.185152 | − | 0.275597i | ||||
\(247\) | 1.70716 | − | 10.7786i | 0.108624 | − | 0.685824i | ||||
\(248\) | 6.55641 | + | 3.34066i | 0.416332 | + | 0.212132i | ||||
\(249\) | 0.176156 | − | 4.79044i | 0.0111634 | − | 0.303582i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 13.6488i | − | 0.861504i | −0.902470 | − | 0.430752i | \(-0.858248\pi\) | ||
0.902470 | − | 0.430752i | \(-0.141752\pi\) | |||||||
\(252\) | 9.37200 | + | 5.67855i | 0.590381 | + | 0.357715i | ||||
\(253\) | −9.62542 | − | 1.52452i | −0.605145 | − | 0.0958455i | ||||
\(254\) | 14.9488 | − | 10.8609i | 0.937971 | − | 0.681476i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.809017 | − | 0.587785i | −0.0505636 | − | 0.0367366i | ||||
\(257\) | 14.2769 | + | 14.2769i | 0.890571 | + | 0.890571i | 0.994577 | − | 0.104006i | \(-0.0331660\pi\) |
−0.104006 | + | 0.994577i | \(0.533166\pi\) | |||||||
\(258\) | −0.954666 | − | 7.89581i | −0.0594349 | − | 0.491571i | ||||
\(259\) | 26.6718 | + | 8.66620i | 1.65731 | + | 0.538492i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 20.3415 | − | 4.99188i | 1.25911 | − | 0.308989i | ||||
\(262\) | 6.02229 | + | 11.8194i | 0.372058 | + | 0.730205i | ||||
\(263\) | −7.39734 | − | 14.5181i | −0.456139 | − | 0.895224i | −0.998483 | − | 0.0550670i | \(-0.982463\pi\) |
0.542343 | − | 0.840157i | \(-0.317537\pi\) | |||||||
\(264\) | 0.726772 | + | 2.55236i | 0.0447297 | + | 0.157087i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −7.53258 | − | 2.44748i | −0.461852 | − | 0.150065i | ||||
\(267\) | 11.0700 | − | 1.33845i | 0.677472 | − | 0.0819118i | ||||
\(268\) | 2.38422 | + | 2.38422i | 0.145640 | + | 0.145640i | ||||
\(269\) | −8.83824 | − | 6.42136i | −0.538877 | − | 0.391517i | 0.284791 | − | 0.958590i | \(-0.408076\pi\) |
−0.823668 | + | 0.567073i | \(0.808076\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.71650 | + | 1.97365i | −0.165016 | + | 0.119891i | −0.667228 | − | 0.744853i | \(-0.732519\pi\) |
0.502213 | + | 0.864744i | \(0.332519\pi\) | |||||||
\(272\) | −5.09363 | − | 0.806752i | −0.308847 | − | 0.0489165i | ||||
\(273\) | −27.8206 | − | 15.4885i | −1.68378 | − | 0.937409i | ||||
\(274\) | − | 9.76085i | − | 0.589674i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 11.0092 | + | 0.404835i | 0.662678 | + | 0.0243682i | ||||
\(277\) | −25.0088 | − | 12.7426i | −1.50263 | − | 0.765631i | −0.507269 | − | 0.861788i | \(-0.669345\pi\) |
−0.995366 | + | 0.0961574i | \(0.969345\pi\) | |||||||
\(278\) | 0.759888 | − | 4.79774i | 0.0455750 | − | 0.287749i | ||||
\(279\) | 11.6288 | + | 18.7640i | 0.696198 | + | 1.12337i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.417572 | − | 0.574739i | 0.0249103 | − | 0.0342861i | −0.796380 | − | 0.604796i | \(-0.793255\pi\) |
0.821290 | + | 0.570510i | \(0.193255\pi\) | |||||||
\(282\) | −3.36258 | − | 3.61933i | −0.200239 | − | 0.215528i | ||||
\(283\) | 1.44181 | + | 9.10320i | 0.0857064 | + | 0.541129i | 0.992760 | + | 0.120114i | \(0.0383260\pi\) |
−0.907054 | + | 0.421015i | \(0.861674\pi\) | |||||||
\(284\) | −1.14657 | + | 3.52877i | −0.0680363 | + | 0.209394i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.38293 | − | 7.33390i | −0.140905 | − | 0.433662i | ||||
\(287\) | 9.78504 | − | 4.98573i | 0.577593 | − | 0.294298i | ||||
\(288\) | −1.16197 | − | 2.76583i | −0.0684699 | − | 0.162978i | ||||
\(289\) | −9.12626 | + | 2.96530i | −0.536839 | + | 0.174430i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −22.2572 | − | 8.14759i | −1.30474 | − | 0.477620i | ||||
\(292\) | −0.589050 | + | 0.0932964i | −0.0344716 | + | 0.00545976i | ||||
\(293\) | −1.97743 | + | 1.97743i | −0.115523 | + | 0.115523i | −0.762505 | − | 0.646982i | \(-0.776031\pi\) |
0.646982 | + | 0.762505i | \(0.276031\pi\) | |||||||
\(294\) | −6.77911 | + | 8.64387i | −0.395366 | + | 0.504121i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.51285 | − | 6.21140i | −0.262304 | − | 0.361030i | ||||
\(297\) | −2.10320 | + | 7.67862i | −0.122040 | + | 0.445559i | ||||
\(298\) | −2.97676 | + | 5.84222i | −0.172439 | + | 0.338431i | ||||
\(299\) | −32.0116 | −1.85128 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.7727 | 0.966760 | ||||||||
\(302\) | 0.484037 | − | 0.949976i | 0.0278532 | − | 0.0546650i | ||||
\(303\) | −0.249095 | − | 0.0488974i | −0.0143102 | − | 0.00280908i | ||||
\(304\) | 1.27450 | + | 1.75421i | 0.0730979 | + | 0.100611i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −11.8149 | − | 9.98857i | −0.675413 | − | 0.571008i | ||||
\(307\) | −11.7511 | + | 11.7511i | −0.670673 | + | 0.670673i | −0.957871 | − | 0.287198i | \(-0.907276\pi\) |
0.287198 | + | 0.957871i | \(0.407276\pi\) | |||||||
\(308\) | −5.52770 | + | 0.875502i | −0.314970 | + | 0.0498864i | ||||
\(309\) | 9.30230 | − | 25.4115i | 0.529189 | − | 1.44561i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.30339 | + | 1.07334i | −0.187318 | + | 0.0608633i | −0.401174 | − | 0.916002i | \(-0.631398\pi\) |
0.213856 | + | 0.976865i | \(0.431398\pi\) | |||||||
\(312\) | 3.66945 | + | 7.90730i | 0.207742 | + | 0.447663i | ||||
\(313\) | −7.56390 | + | 3.85400i | −0.427537 | + | 0.217841i | −0.654499 | − | 0.756063i | \(-0.727121\pi\) |
0.226962 | + | 0.973904i | \(0.427121\pi\) | |||||||
\(314\) | −6.70127 | − | 20.6244i | −0.378175 | − | 1.16390i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.411226 | − | 1.26562i | 0.0231333 | − | 0.0711969i | ||||
\(317\) | −1.54252 | − | 9.73906i | −0.0866363 | − | 0.547000i | −0.992384 | − | 0.123183i | \(-0.960690\pi\) |
0.905748 | − | 0.423817i | \(-0.139310\pi\) | |||||||
\(318\) | −1.31114 | + | 1.21813i | −0.0735249 | + | 0.0683093i | ||||
\(319\) | −6.28766 | + | 8.65423i | −0.352042 | + | 0.484544i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.60172 | + | 2.41972i | −0.201029 | + | 0.135055i | ||||
\(322\) | −3.63443 | + | 22.9469i | −0.202539 | + | 1.27878i | ||||
\(323\) | 9.96348 | + | 5.07665i | 0.554383 | + | 0.282472i | ||||
\(324\) | 1.31844 | − | 8.90290i | 0.0732469 | − | 0.494606i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 10.2817i | − | 0.569452i | ||||||
\(327\) | −6.78529 | + | 12.1878i | −0.375227 | + | 0.673986i | ||||
\(328\) | −2.96952 | − | 0.470327i | −0.163965 | − | 0.0259694i | ||||
\(329\) | 8.42877 | − | 6.12386i | 0.464693 | − | 0.337619i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.3891 | − | 9.72777i | −0.735933 | − | 0.534687i | 0.155502 | − | 0.987836i | \(-0.450301\pi\) |
−0.891435 | + | 0.453149i | \(0.850301\pi\) | |||||||
\(332\) | −1.95701 | − | 1.95701i | −0.107405 | − | 0.107405i | ||||
\(333\) | −1.92260 | − | 22.9528i | −0.105358 | − | 1.25780i | ||||
\(334\) | −22.9173 | − | 7.44629i | −1.25398 | − | 0.407443i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 6.08480 | − | 1.73262i | 0.331953 | − | 0.0945221i | ||||
\(337\) | 11.9038 | + | 23.3624i | 0.648439 | + | 1.27263i | 0.947913 | + | 0.318528i | \(0.103189\pi\) |
−0.299475 | + | 0.954104i | \(0.596811\pi\) | |||||||
\(338\) | −5.59775 | − | 10.9862i | −0.304477 | − | 0.597570i | ||||
\(339\) | 18.0729 | − | 5.14617i | 0.981585 | − | 0.279502i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.7226 | − | 3.48400i | −0.580663 | − | 0.188669i | ||||
\(342\) | 0.542974 | + | 6.48225i | 0.0293607 | + | 0.350520i | ||||
\(343\) | 1.69884 | + | 1.69884i | 0.0917290 | + | 0.0917290i | ||||
\(344\) | −3.71488 | − | 2.69902i | −0.200293 | − | 0.145521i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 19.4258 | − | 14.1137i | 1.04434 | − | 0.758756i | ||||
\(347\) | −11.7554 | − | 1.86187i | −0.631061 | − | 0.0999502i | −0.167293 | − | 0.985907i | \(-0.553503\pi\) |
−0.463768 | + | 0.885957i | \(0.653503\pi\) | |||||||
\(348\) | 5.88218 | − | 10.5656i | 0.315318 | − | 0.566376i | ||||
\(349\) | 25.4721i | 1.36349i | 0.731591 | + | 0.681744i | \(0.238778\pi\) | ||||
−0.731591 | + | 0.681744i | \(0.761222\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.87784 | + | 25.9929i | −0.153608 | + | 1.38740i | ||||
\(352\) | 1.36518 | + | 0.695596i | 0.0727645 | + | 0.0370754i | ||||
\(353\) | 1.37767 | − | 8.69825i | 0.0733258 | − | 0.462961i | −0.923517 | − | 0.383558i | \(-0.874699\pi\) |
0.996843 | − | 0.0794030i | \(-0.0253014\pi\) | |||||||
\(354\) | −9.80767 | + | 6.58900i | −0.521272 | + | 0.350201i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.78405 | − | 5.20829i | 0.200554 | − | 0.276039i | ||||
\(357\) | 23.9033 | − | 22.2077i | 1.26510 | − | 1.17536i | ||||
\(358\) | −0.705308 | − | 4.45314i | −0.0372767 | − | 0.235356i | ||||
\(359\) | 2.11987 | − | 6.52428i | 0.111882 | − | 0.344338i | −0.879402 | − | 0.476080i | \(-0.842057\pi\) |
0.991284 | + | 0.131742i | \(0.0420571\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.41845 | + | 13.5986i | 0.232550 | + | 0.715715i | ||||
\(362\) | −12.6000 | + | 6.42000i | −0.662239 | + | 0.337428i | ||||
\(363\) | 6.30841 | + | 13.5940i | 0.331106 | + | 0.713500i | ||||
\(364\) | −17.4839 | + | 5.68088i | −0.916408 | + | 0.297759i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.43727 | − | 9.38975i | 0.179669 | − | 0.490810i | ||||
\(367\) | −14.6468 | + | 2.31983i | −0.764559 | + | 0.121094i | −0.526522 | − | 0.850162i | \(-0.676504\pi\) |
−0.238038 | + | 0.971256i | \(0.576504\pi\) | |||||||
\(368\) | 4.49754 | − | 4.49754i | 0.234450 | − | 0.234450i | ||||
\(369\) | −6.88794 | − | 5.82321i | −0.358572 | − | 0.303144i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.21843 | − | 3.05341i | −0.115175 | − | 0.158525i | ||||
\(372\) | 12.5065 | + | 2.45502i | 0.648431 | + | 0.127287i | ||||
\(373\) | 7.85384 | − | 15.4140i | 0.406656 | − | 0.798108i | −0.593320 | − | 0.804967i | \(-0.702183\pi\) |
0.999976 | + | 0.00685847i | \(0.00218314\pi\) | |||||||
\(374\) | 7.90165 | 0.408584 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.85228 | −0.147095 | ||||||||
\(377\) | −15.9524 | + | 31.3083i | −0.821590 | + | 1.61246i | ||||
\(378\) | 18.3058 | + | 5.01402i | 0.941546 | + | 0.257893i | ||||
\(379\) | 3.34257 | + | 4.60065i | 0.171696 | + | 0.236319i | 0.886190 | − | 0.463323i | \(-0.153343\pi\) |
−0.714494 | + | 0.699642i | \(0.753343\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 19.7505 | − | 25.1833i | 1.01185 | − | 1.29018i | ||||
\(382\) | 9.06711 | − | 9.06711i | 0.463914 | − | 0.463914i | ||||
\(383\) | −29.9833 | + | 4.74888i | −1.53207 | + | 0.242657i | −0.864785 | − | 0.502143i | \(-0.832545\pi\) |
−0.667289 | + | 0.744799i | \(0.732545\pi\) | |||||||
\(384\) | −1.62650 | − | 0.595405i | −0.0830018 | − | 0.0303841i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −13.3138 | + | 4.32593i | −0.677657 | + | 0.220184i | ||||
\(387\) | −5.33560 | − | 12.7003i | −0.271224 | − | 0.645591i | ||||
\(388\) | −12.1926 | + | 6.21246i | −0.618987 | + | 0.315390i | ||||
\(389\) | 0.407506 | + | 1.25417i | 0.0206613 | + | 0.0635891i | 0.960856 | − | 0.277050i | \(-0.0893567\pi\) |
−0.940194 | + | 0.340639i | \(0.889357\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.1363 | − | 31.1963i | 0.512615 | − | 1.57767i | ||||
\(392\) | 0.992148 | + | 6.26418i | 0.0501110 | + | 0.316389i | ||||
\(393\) | 15.6385 | + | 16.8326i | 0.788860 | + | 0.849091i | ||||
\(394\) | −4.00131 | + | 5.50734i | −0.201583 | + | 0.277456i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.42136 | + | 3.90707i | 0.121678 | + | 0.196338i | ||||
\(397\) | 1.73643 | − | 10.9634i | 0.0871491 | − | 0.550238i | −0.905023 | − | 0.425362i | \(-0.860147\pi\) |
0.992172 | − | 0.124876i | \(-0.0398532\pi\) | |||||||
\(398\) | 4.81580 | + | 2.45377i | 0.241394 | + | 0.122997i | ||||
\(399\) | −13.7090 | − | 0.504110i | −0.686307 | − | 0.0252371i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 38.4533i | − | 1.92026i | −0.279545 | − | 0.960132i | \(-0.590184\pi\) | ||
0.279545 | − | 0.960132i | \(-0.409816\pi\) | |||||||
\(402\) | 5.10265 | + | 2.84079i | 0.254497 | + | 0.141686i | ||||
\(403\) | −36.5783 | − | 5.79343i | −1.82209 | − | 0.288591i | ||||
\(404\) | −0.118569 | + | 0.0861458i | −0.00589905 | + | 0.00428591i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 20.6316 | + | 14.9897i | 1.02393 | + | 0.743928i | ||||
\(407\) | 8.31815 | + | 8.31815i | 0.412316 | + | 0.412316i | ||||
\(408\) | −8.86782 | + | 1.07219i | −0.439022 | + | 0.0530813i | ||||
\(409\) | −10.8096 | − | 3.51227i | −0.534502 | − | 0.173670i | 0.0293144 | − | 0.999570i | \(-0.490668\pi\) |
−0.563817 | + | 0.825900i | \(0.690668\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.62994 | − | 16.2600i | −0.228378 | − | 0.802044i | ||||
\(412\) | −7.09291 | − | 13.9206i | −0.349443 | − | 0.685820i | ||||
\(413\) | −11.3123 | − | 22.2017i | −0.556643 | − | 1.09247i | ||||
\(414\) | 18.5316 | − | 4.54771i | 0.910777 | − | 0.223508i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.78657 | + | 1.55525i | 0.234681 | + | 0.0762525i | ||||
\(417\) | −1.00991 | − | 8.35269i | −0.0494553 | − | 0.409033i | ||||
\(418\) | −2.34919 | − | 2.34919i | −0.114903 | − | 0.114903i | ||||
\(419\) | 4.06691 | + | 2.95479i | 0.198682 | + | 0.144351i | 0.682678 | − | 0.730719i | \(-0.260815\pi\) |
−0.483996 | + | 0.875070i | \(0.660815\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.36850 | + | 5.35353i | −0.359119 | + | 0.260915i | −0.752684 | − | 0.658382i | \(-0.771241\pi\) |
0.393566 | + | 0.919296i | \(0.371241\pi\) | |||||||
\(422\) | 12.6399 | + | 2.00197i | 0.615303 | + | 0.0974544i | ||||
\(423\) | −7.31829 | − | 4.43419i | −0.355828 | − | 0.215598i | ||||
\(424\) | 1.03327i | 0.0501799i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.236159 | + | 6.42221i | −0.0114420 | + | 0.311157i | ||||
\(427\) | 18.7887 | + | 9.57331i | 0.909248 | + | 0.463285i | ||||
\(428\) | −0.391893 | + | 2.47432i | −0.0189429 | + | 0.119601i | ||||
\(429\) | −7.44831 | − | 11.0867i | −0.359608 | − | 0.535273i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.5495 | − | 20.0257i | 0.700824 | − | 0.964602i | −0.299122 | − | 0.954215i | \(-0.596694\pi\) |
0.999946 | − | 0.0103868i | \(-0.00330628\pi\) | |||||||
\(432\) | −3.24759 | − | 4.05625i | −0.156250 | − | 0.195156i | ||||
\(433\) | 3.46945 | + | 21.9052i | 0.166731 | + | 1.05270i | 0.919119 | + | 0.393979i | \(0.128902\pi\) |
−0.752388 | + | 0.658720i | \(0.771098\pi\) | |||||||
\(434\) | −8.30582 | + | 25.5627i | −0.398692 | + | 1.22705i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.48870 | + | 7.65945i | 0.119187 | + | 0.366821i | ||||
\(437\) | −12.2883 | + | 6.26122i | −0.587831 | + | 0.299515i | ||||
\(438\) | −0.937006 | + | 0.434825i | −0.0447719 | + | 0.0207768i | ||||
\(439\) | −1.62057 | + | 0.526555i | −0.0773456 | + | 0.0251311i | −0.347434 | − | 0.937704i | \(-0.612947\pi\) |
0.270089 | + | 0.962835i | \(0.412947\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.19275 | + | 17.6148i | −0.342512 | + | 0.838802i | ||||
\(442\) | 25.6357 | − | 4.06030i | 1.21937 | − | 0.193129i | ||||
\(443\) | 0.713085 | − | 0.713085i | 0.0338797 | − | 0.0338797i | −0.689964 | − | 0.723844i | \(-0.742374\pi\) |
0.723844 | + | 0.689964i | \(0.242374\pi\) | |||||||
\(444\) | −10.4640 | − | 8.20655i | −0.496598 | − | 0.389465i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 17.0657 | + | 23.4889i | 0.808085 | + | 1.11223i | ||||
\(447\) | −2.18760 | + | 11.1442i | −0.103470 | + | 0.527101i | ||||
\(448\) | 1.65829 | − | 3.25458i | 0.0783470 | − | 0.153765i | ||||
\(449\) | −12.4310 | −0.586657 | −0.293329 | − | 0.956012i | \(-0.594763\pi\) | ||||
−0.293329 | + | 0.956012i | \(0.594763\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.60656 | 0.216915 | ||||||||
\(452\) | 4.92541 | − | 9.66667i | 0.231672 | − | 0.454682i | ||||
\(453\) | 0.355715 | − | 1.81210i | 0.0167130 | − | 0.0851398i | ||||
\(454\) | 2.32271 | + | 3.19694i | 0.109010 | + | 0.150040i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.95520 | + | 2.31767i | 0.138390 | + | 0.108535i | ||||
\(457\) | −25.4659 | + | 25.4659i | −1.19125 | + | 1.19125i | −0.214529 | + | 0.976718i | \(0.568822\pi\) |
−0.976718 | + | 0.214529i | \(0.931178\pi\) | |||||||
\(458\) | −13.0392 | + | 2.06521i | −0.609284 | + | 0.0965011i | ||||
\(459\) | −24.4196 | − | 11.0350i | −1.13981 | − | 0.515071i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −34.8009 | + | 11.3075i | −1.62084 | + | 0.526642i | −0.972140 | − | 0.234403i | \(-0.924686\pi\) |
−0.648699 | + | 0.761045i | \(0.724686\pi\) | |||||||
\(462\) | −8.79295 | + | 4.08044i | −0.409085 | + | 0.189839i | ||||
\(463\) | −5.89566 | + | 3.00399i | −0.273994 | + | 0.139607i | −0.585589 | − | 0.810608i | \(-0.699137\pi\) |
0.311595 | + | 0.950215i | \(0.399137\pi\) | |||||||
\(464\) | −2.15746 | − | 6.63998i | −0.100158 | − | 0.308253i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.70862 | + | 8.33627i | −0.125474 | + | 0.386170i | ||||
\(467\) | 5.97151 | + | 37.7026i | 0.276328 | + | 1.74467i | 0.601371 | + | 0.798970i | \(0.294621\pi\) |
−0.325043 | + | 0.945699i | \(0.605379\pi\) | |||||||
\(468\) | 9.86343 | + | 11.4317i | 0.455937 | + | 0.528430i | ||||
\(469\) | −7.23928 | + | 9.96401i | −0.334279 | + | 0.460095i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20.9461 | − | 31.1781i | −0.965147 | − | 1.43661i | ||||
\(472\) | −1.06714 | + | 6.73768i | −0.0491192 | + | 0.310127i | ||||
\(473\) | 6.26871 | + | 3.19407i | 0.288236 | + | 0.146863i | ||||
\(474\) | 0.0847006 | − | 2.30338i | 0.00389043 | − | 0.105798i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 18.8375i | − | 0.863413i | ||||||
\(477\) | −1.60633 | + | 2.65112i | −0.0735488 | + | 0.121387i | ||||
\(478\) | 18.7109 | + | 2.96351i | 0.855815 | + | 0.135548i | ||||
\(479\) | 9.41843 | − | 6.84289i | 0.430339 | − | 0.312660i | −0.351445 | − | 0.936208i | \(-0.614310\pi\) |
0.781785 | + | 0.623549i | \(0.214310\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 31.2614 | + | 22.7127i | 1.42540 | + | 1.03561i | ||||
\(482\) | 16.6233 | + | 16.6233i | 0.757170 | + | 0.757170i | ||||
\(483\) | 4.83024 | + | 39.9497i | 0.219783 | + | 1.81777i | ||||
\(484\) | 8.22894 | + | 2.67375i | 0.374043 | + | 0.121534i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.02668 | − | 15.4561i | −0.0919320 | − | 0.701105i | ||||
\(487\) | −16.1262 | − | 31.6495i | −0.730750 | − | 1.43418i | −0.894219 | − | 0.447629i | \(-0.852269\pi\) |
0.163470 | − | 0.986548i | \(-0.447731\pi\) | |||||||
\(488\) | −2.62088 | − | 5.14377i | −0.118642 | − | 0.232848i | ||||
\(489\) | −4.87701 | − | 17.1276i | −0.220546 | − | 0.774538i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.18688 | − | 1.03548i | −0.143822 | − | 0.0467305i | 0.236222 | − | 0.971699i | \(-0.424091\pi\) |
−0.380043 | + | 0.924969i | \(0.624091\pi\) | |||||||
\(492\) | −5.16983 | + | 0.625074i | −0.233074 | + | 0.0281805i | ||||
\(493\) | −25.4597 | − | 25.4597i | −1.14665 | − | 1.14665i | ||||
\(494\) | −8.82874 | − | 6.41446i | −0.397224 | − | 0.288600i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.95310 | − | 4.32518i | 0.267302 | − | 0.194206i | ||||
\(497\) | −13.3860 | − | 2.12014i | −0.600446 | − | 0.0951012i | ||||
\(498\) | −4.18834 | − | 2.33177i | −0.187684 | − | 0.104489i | ||||
\(499\) | − | 2.56390i | − | 0.114776i | −0.998352 | − | 0.0573880i | \(-0.981723\pi\) | ||
0.998352 | − | 0.0573880i | \(-0.0182772\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −41.7085 | − | 1.53372i | −1.86340 | − | 0.0685214i | ||||
\(502\) | −12.1612 | − | 6.19642i | −0.542779 | − | 0.276560i | ||||
\(503\) | −2.27523 | + | 14.3652i | −0.101448 | + | 0.640515i | 0.883601 | + | 0.468240i | \(0.155112\pi\) |
−0.985049 | + | 0.172275i | \(0.944888\pi\) | |||||||
\(504\) | 9.31442 | − | 5.77251i | 0.414897 | − | 0.257128i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5.72820 | + | 7.88419i | −0.254650 | + | 0.350495i | ||||
\(507\) | −14.5361 | − | 15.6460i | −0.645570 | − | 0.694861i | ||||
\(508\) | −2.89055 | − | 18.2502i | −0.128248 | − | 0.809723i | ||||
\(509\) | 2.88278 | − | 8.87228i | 0.127777 | − | 0.393257i | −0.866620 | − | 0.498969i | \(-0.833712\pi\) |
0.994397 | + | 0.105712i | \(0.0337122\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.673177 | − | 2.07183i | −0.0297796 | − | 0.0916522i | ||||
\(512\) | −0.891007 | + | 0.453990i | −0.0393773 | + | 0.0200637i | ||||
\(513\) | 3.97929 | + | 10.5408i | 0.175690 | + | 0.465388i | ||||
\(514\) | 19.2024 | − | 6.23925i | 0.846983 | − | 0.275202i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −7.46862 | − | 2.73401i | −0.328788 | − | 0.120358i | ||||
\(517\) | 4.31640 | − | 0.683651i | 0.189835 | − | 0.0300669i | ||||
\(518\) | 19.8304 | − | 19.8304i | 0.871298 | − | 0.871298i | ||||
\(519\) | 25.6655 | − | 32.7254i | 1.12659 | − | 1.43649i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.0337 | + | 26.1976i | 0.833881 | + | 1.14774i | 0.987188 | + | 0.159560i | \(0.0510075\pi\) |
−0.153308 | + | 0.988179i | \(0.548993\pi\) | |||||||
\(522\) | 4.78706 | − | 20.3907i | 0.209524 | − | 0.892476i | ||||
\(523\) | 10.0842 | − | 19.7913i | 0.440950 | − | 0.865413i | −0.558408 | − | 0.829567i | \(-0.688587\pi\) |
0.999357 | − | 0.0358458i | \(-0.0114125\pi\) | |||||||
\(524\) | 13.2652 | 0.579494 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.2940 | −0.710454 | ||||||||
\(527\) | 17.2282 | − | 33.8122i | 0.750471 | − | 1.47288i | ||||
\(528\) | 2.60412 | + | 0.511188i | 0.113330 | + | 0.0222466i | ||||
\(529\) | 10.2602 | + | 14.1219i | 0.446095 | + | 0.613997i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.2125 | + | 15.6283i | −0.573375 | + | 0.678212i | ||||
\(532\) | −5.60044 | + | 5.60044i | −0.242810 | + | 0.242810i | ||||
\(533\) | 14.9453 | − | 2.36711i | 0.647354 | − | 0.102531i | ||||
\(534\) | 3.83310 | − | 10.4711i | 0.165875 | − | 0.453128i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.20677 | − | 1.04194i | 0.138511 | − | 0.0450051i | ||||
\(537\) | −3.28722 | − | 7.08363i | −0.141854 | − | 0.305681i | ||||
\(538\) | −9.73395 | + | 4.95969i | −0.419660 | + | 0.213828i | ||||
\(539\) | −3.00287 | − | 9.24188i | −0.129343 | − | 0.398076i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.547811 | + | 1.68599i | −0.0235522 | + | 0.0724863i | −0.962142 | − | 0.272549i | \(-0.912133\pi\) |
0.938590 | + | 0.345036i | \(0.112133\pi\) | |||||||
\(542\) | 0.525272 | + | 3.31644i | 0.0225624 | + | 0.142453i | ||||
\(543\) | −17.9442 | + | 16.6713i | −0.770058 | + | 0.715434i | ||||
\(544\) | −3.03128 | + | 4.17220i | −0.129965 | + | 0.178882i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −26.4307 | + | 17.7567i | −1.13113 | + | 0.759917i | ||||
\(547\) | −1.96467 | + | 12.4044i | −0.0840033 | + | 0.530376i | 0.909420 | + | 0.415878i | \(0.136526\pi\) |
−0.993424 | + | 0.114497i | \(0.963474\pi\) | |||||||
\(548\) | −8.69698 | − | 4.43133i | −0.371517 | − | 0.189297i | ||||
\(549\) | 1.27200 | − | 17.2722i | 0.0542875 | − | 0.737159i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.1385i | 0.644922i | ||||||||
\(552\) | 5.35879 | − | 9.62550i | 0.228085 | − | 0.409689i | ||||
\(553\) | 4.80101 | + | 0.760406i | 0.204160 | + | 0.0323357i | ||||
\(554\) | −22.7075 | + | 16.4980i | −0.964751 | + | 0.700933i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.92984 | − | 2.85519i | −0.166662 | − | 0.121087i | ||||
\(557\) | −19.4225 | − | 19.4225i | −0.822959 | − | 0.822959i | 0.163573 | − | 0.986531i | \(-0.447698\pi\) |
−0.986531 | + | 0.163573i | \(0.947698\pi\) | |||||||
\(558\) | 21.9983 | − | 1.84265i | 0.931260 | − | 0.0780054i | ||||
\(559\) | 21.9792 | + | 7.14148i | 0.929621 | + | 0.302052i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.1628 | − | 3.74805i | 0.555735 | − | 0.158243i | ||||
\(562\) | −0.322522 | − | 0.632986i | −0.0136048 | − | 0.0267009i | ||||
\(563\) | −11.4362 | − | 22.4447i | −0.481977 | − | 0.945933i | −0.996101 | − | 0.0882171i | \(-0.971883\pi\) |
0.514125 | − | 0.857716i | \(-0.328117\pi\) | |||||||
\(564\) | −4.75142 | + | 1.35295i | −0.200071 | + | 0.0569693i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 8.76558 | + | 2.84811i | 0.368445 | + | 0.119715i | ||||
\(567\) | 32.8727 | − | 0.330602i | 1.38052 | − | 0.0138840i | ||||
\(568\) | 2.62363 | + | 2.62363i | 0.110085 | + | 0.110085i | ||||
\(569\) | 24.7435 | + | 17.9772i | 1.03730 | + | 0.753643i | 0.969757 | − | 0.244073i | \(-0.0784837\pi\) |
0.0675439 | + | 0.997716i | \(0.478484\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.91080 | + | 6.47408i | −0.372905 | + | 0.270932i | −0.758415 | − | 0.651772i | \(-0.774026\pi\) |
0.385509 | + | 0.922704i | \(0.374026\pi\) | |||||||
\(572\) | −7.61638 | − | 1.20632i | −0.318457 | − | 0.0504386i | ||||
\(573\) | 10.8034 | − | 19.4052i | 0.451320 | − | 0.810663i | ||||
\(574\) | − | 10.9820i | − | 0.458380i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.99190 | − | 0.220336i | −0.124662 | − | 0.00918066i | ||||
\(577\) | 3.45787 | + | 1.76187i | 0.143953 | + | 0.0733478i | 0.524483 | − | 0.851421i | \(-0.324259\pi\) |
−0.380530 | + | 0.924768i | \(0.624259\pi\) | |||||||
\(578\) | −1.50113 | + | 9.47778i | −0.0624389 | + | 0.394224i | ||||
\(579\) | −20.1267 | + | 13.5216i | −0.836437 | + | 0.561937i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.94213 | − | 8.17864i | 0.246521 | − | 0.339307i | ||||
\(582\) | −17.3641 | + | 16.1324i | −0.719765 | + | 0.668708i | ||||
\(583\) | −0.247659 | − | 1.56366i | −0.0102570 | − | 0.0647602i | ||||
\(584\) | −0.184296 | + | 0.567203i | −0.00762620 | + | 0.0234710i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.864170 | + | 2.65964i | 0.0356985 | + | 0.109869i | ||||
\(587\) | 39.5031 | − | 20.1279i | 1.63047 | − | 0.830766i | 0.632028 | − | 0.774945i | \(-0.282223\pi\) |
0.998441 | − | 0.0558204i | \(-0.0177774\pi\) | |||||||
\(588\) | 4.62409 | + | 9.96447i | 0.190694 | + | 0.410928i | ||||
\(589\) | −15.1745 | + | 4.93049i | −0.625254 | + | 0.203157i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.05318 | + | 11.0723i | −0.166726 | + | 0.455453i | ||||
\(592\) | −7.58319 | + | 1.20106i | −0.311667 | + | 0.0493632i | ||||
\(593\) | 11.0677 | − | 11.0677i | 0.454495 | − | 0.454495i | −0.442348 | − | 0.896843i | \(-0.645855\pi\) |
0.896843 | + | 0.442348i | \(0.145855\pi\) | |||||||
\(594\) | 5.88686 | + | 5.35999i | 0.241541 | + | 0.219923i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.85404 | + | 5.30463i | 0.157868 | + | 0.217286i | ||||
\(597\) | 9.18625 | + | 1.80326i | 0.375968 | + | 0.0738026i | ||||
\(598\) | −14.5330 | + | 28.5226i | −0.594298 | + | 1.16638i | ||||
\(599\) | 39.0036 | 1.59364 | 0.796822 | − | 0.604215i | \(-0.206513\pi\) | ||||
0.796822 | + | 0.604215i | \(0.206513\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.7471 | −1.05025 | −0.525123 | − | 0.851027i | \(-0.675981\pi\) | ||||
−0.525123 | + | 0.851027i | \(0.675981\pi\) | |||||||
\(602\) | 7.61463 | − | 14.9446i | 0.310349 | − | 0.609094i | ||||
\(603\) | 9.84766 | + | 2.31190i | 0.401028 | + | 0.0941480i | ||||
\(604\) | −0.626686 | − | 0.862560i | −0.0254995 | − | 0.0350971i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.156655 | + | 0.199747i | −0.00636367 | + | 0.00811415i | ||||
\(607\) | −14.3533 | + | 14.3533i | −0.582583 | + | 0.582583i | −0.935612 | − | 0.353030i | \(-0.885152\pi\) |
0.353030 | + | 0.935612i | \(0.385152\pi\) | |||||||
\(608\) | 2.14162 | − | 0.339200i | 0.0868542 | − | 0.0137564i | ||||
\(609\) | 41.4790 | + | 15.1841i | 1.68081 | + | 0.615289i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.6526 | − | 4.43601i | 0.552327 | − | 0.179462i | ||||
\(612\) | −14.2637 | + | 5.99244i | −0.576577 | + | 0.242230i | ||||
\(613\) | 25.0841 | − | 12.7810i | 1.01314 | − | 0.516219i | 0.133089 | − | 0.991104i | \(-0.457510\pi\) |
0.880048 | + | 0.474885i | \(0.157510\pi\) | |||||||
\(614\) | 5.13543 | + | 15.8052i | 0.207249 | + | 0.637848i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.72945 | + | 5.32269i | −0.0696814 | + | 0.214457i | ||||
\(617\) | −3.61324 | − | 22.8131i | −0.145464 | − | 0.918421i | −0.947177 | − | 0.320712i | \(-0.896078\pi\) |
0.801713 | − | 0.597709i | \(-0.203922\pi\) | |||||||
\(618\) | −18.4187 | − | 19.8250i | −0.740909 | − | 0.797479i | ||||
\(619\) | −5.12654 | + | 7.05608i | −0.206053 | + | 0.283608i | −0.899519 | − | 0.436882i | \(-0.856083\pi\) |
0.693466 | + | 0.720489i | \(0.256083\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 28.7134 | − | 16.3660i | 1.15223 | − | 0.656744i | ||||
\(622\) | −0.543357 | + | 3.43062i | −0.0217866 | + | 0.137555i | ||||
\(623\) | 20.9524 | + | 10.6758i | 0.839440 | + | 0.427716i | ||||
\(624\) | 8.71135 | + | 0.320336i | 0.348733 | + | 0.0128237i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 8.48916i | 0.339295i | ||||||||
\(627\) | −5.02767 | − | 2.79905i | −0.200786 | − | 0.111783i | ||||
\(628\) | −21.4188 | − | 3.39240i | −0.854702 | − | 0.135372i | ||||
\(629\) | −32.0330 | + | 23.2733i | −1.27724 | + | 0.927967i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.4095 | + | 14.8283i | 0.812488 | + | 0.590307i | 0.914551 | − | 0.404471i | \(-0.132544\pi\) |
−0.102063 | + | 0.994778i | \(0.532544\pi\) | |||||||
\(632\) | −0.940986 | − | 0.940986i | −0.0374304 | − | 0.0374304i | ||||
\(633\) | 22.0057 | − | 2.66066i | 0.874646 | − | 0.105752i | ||||
\(634\) | −9.37785 | − | 3.04705i | −0.372442 | − | 0.121014i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.490118 | + | 1.72125i | 0.0194344 | + | 0.0682520i | ||||
\(637\) | −14.4914 | − | 28.4409i | −0.574169 | − | 1.12687i | ||||
\(638\) | 4.85643 | + | 9.53128i | 0.192268 | + | 0.377347i | ||||
\(639\) | 2.65290 | + | 10.8104i | 0.104947 | + | 0.427651i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.1335 | + | 9.79096i | 1.19020 | + | 0.386720i | 0.836147 | − | 0.548505i | \(-0.184803\pi\) |
0.354054 | + | 0.935225i | \(0.384803\pi\) | |||||||
\(642\) | 0.520834 | + | 4.30769i | 0.0205557 | + | 0.170011i | ||||
\(643\) | 11.3185 | + | 11.3185i | 0.446357 | + | 0.446357i | 0.894142 | − | 0.447785i | \(-0.147787\pi\) |
−0.447785 | + | 0.894142i | \(0.647787\pi\) | |||||||
\(644\) | 18.7959 | + | 13.6560i | 0.740660 | + | 0.538121i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.04665 | − | 6.57278i | 0.355936 | − | 0.258602i | ||||
\(647\) | 30.8296 | + | 4.88293i | 1.21204 | + | 0.191968i | 0.729545 | − | 0.683933i | \(-0.239732\pi\) |
0.482491 | + | 0.875901i | \(0.339732\pi\) | |||||||
\(648\) | −7.33398 | − | 5.21658i | −0.288106 | − | 0.204926i | ||||
\(649\) | − | 10.4520i | − | 0.410278i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.71075 | + | 46.5229i | −0.0670498 | + | 1.82338i | ||||
\(652\) | −9.16108 | − | 4.66780i | −0.358775 | − | 0.182805i | ||||
\(653\) | −0.252918 | + | 1.59686i | −0.00989744 | + | 0.0624900i | −0.992143 | − | 0.125111i | \(-0.960071\pi\) |
0.982245 | + | 0.187601i | \(0.0600712\pi\) | |||||||
\(654\) | 7.77894 | + | 11.5789i | 0.304181 | + | 0.452770i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.76720 | + | 2.43234i | −0.0689976 | + | 0.0949670i | ||||
\(657\) | −1.35464 | + | 1.16880i | −0.0528496 | + | 0.0455994i | ||||
\(658\) | −1.62982 | − | 10.2903i | −0.0635369 | − | 0.401156i | ||||
\(659\) | 1.49604 | − | 4.60434i | 0.0582774 | − | 0.179360i | −0.917680 | − | 0.397320i | \(-0.869940\pi\) |
0.975958 | + | 0.217960i | \(0.0699403\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.5577 | − | 44.8040i | −0.566229 | − | 1.74267i | −0.664271 | − | 0.747492i | \(-0.731258\pi\) |
0.0980414 | − | 0.995182i | \(-0.468742\pi\) | |||||||
\(662\) | −14.7460 | + | 7.51349i | −0.573121 | + | 0.292020i | ||||
\(663\) | 40.7789 | − | 18.9238i | 1.58372 | − | 0.734940i | ||||
\(664\) | −2.63218 | + | 0.855246i | −0.102148 | + | 0.0331900i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −21.3239 | − | 8.70729i | −0.826284 | − | 0.337401i | ||||
\(667\) | 43.8601 | − | 6.94676i | 1.69827 | − | 0.268980i | ||||
\(668\) | −17.0389 | + | 17.0389i | −0.659256 | + | 0.659256i | ||||
\(669\) | 39.5703 | + | 31.0337i | 1.52988 | + | 1.19983i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.19911 | + | 7.15597i | 0.200710 | + | 0.276253i | ||||
\(672\) | 1.21867 | − | 6.20819i | 0.0470111 | − | 0.239486i | ||||
\(673\) | −11.6331 | + | 22.8312i | −0.448422 | + | 0.880077i | 0.550553 | + | 0.834800i | \(0.314417\pi\) |
−0.998974 | + | 0.0452767i | \(0.985583\pi\) | |||||||
\(674\) | 26.2203 | 1.00997 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.3301 | −0.474234 | ||||||||
\(677\) | −8.38373 | + | 16.4540i | −0.322213 | + | 0.632379i | −0.994123 | − | 0.108254i | \(-0.965474\pi\) |
0.671910 | + | 0.740633i | \(0.265474\pi\) | |||||||
\(678\) | 3.61965 | − | 18.4394i | 0.139012 | − | 0.708160i | ||||
\(679\) | −29.3799 | − | 40.4379i | −1.12750 | − | 1.55187i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.38568 | + | 4.22382i | 0.206380 | + | 0.161857i | ||||
\(682\) | −7.97224 | + | 7.97224i | −0.305273 | + | 0.305273i | ||||
\(683\) | −16.2967 | + | 2.58115i | −0.623578 | + | 0.0987650i | −0.460224 | − | 0.887803i | \(-0.652231\pi\) |
−0.163353 | + | 0.986568i | \(0.552231\pi\) | |||||||
\(684\) | 6.02223 | + | 2.45909i | 0.230266 | + | 0.0940255i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.28494 | − | 0.742422i | 0.0872394 | − | 0.0283458i | ||||
\(687\) | −20.7416 | + | 9.62532i | −0.791342 | + | 0.367229i | ||||
\(688\) | −4.09136 | + | 2.08465i | −0.155982 | + | 0.0794767i | ||||
\(689\) | −1.60699 | − | 4.94581i | −0.0612214 | − | 0.188420i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.6221 | + | 32.6914i | −0.404084 | + | 1.24364i | 0.517574 | + | 0.855638i | \(0.326835\pi\) |
−0.921658 | + | 0.388003i | \(0.873165\pi\) | |||||||
\(692\) | −3.75624 | − | 23.7160i | −0.142791 | − | 0.901547i | ||||
\(693\) | −12.7121 | + | 10.9682i | −0.482892 | + | 0.416646i | ||||
\(694\) | −6.99576 | + | 9.62884i | −0.265555 | + | 0.365506i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −6.74357 | − | 10.0377i | −0.255614 | − | 0.380480i | ||||
\(697\) | −2.42553 | + | 15.3142i | −0.0918736 | + | 0.580067i | ||||
\(698\) | 22.6958 | + | 11.5641i | 0.859048 | + | 0.437707i | ||||
\(699\) | −0.557896 | + | 15.1717i | −0.0211016 | + | 0.573845i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.8859i | 0.562232i | 0.959674 | + | 0.281116i | \(0.0907045\pi\) | ||||
−0.959674 | + | 0.281116i | \(0.909295\pi\) | |||||||
\(702\) | 21.8533 | + | 14.3647i | 0.824801 | + | 0.542161i | ||||
\(703\) | 16.4428 | + | 2.60428i | 0.620150 | + | 0.0982222i | ||||
\(704\) | 1.23956 | − | 0.900593i | 0.0467177 | − | 0.0339424i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.12475 | − | 5.17643i | −0.268143 | − | 0.194818i | ||||
\(707\) | −0.378543 | − | 0.378543i | −0.0142366 | − | 0.0142366i | ||||
\(708\) | 1.41825 | + | 11.7300i | 0.0533013 | + | 0.440842i | ||||
\(709\) | −38.5502 | − | 12.5257i | −1.44778 | − | 0.470413i | −0.523468 | − | 0.852045i | \(-0.675362\pi\) |
−0.924314 | + | 0.381632i | \(0.875362\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.951484 | − | 3.87723i | −0.0356834 | − | 0.145407i | ||||
\(712\) | −2.92270 | − | 5.73613i | −0.109533 | − | 0.214970i | ||||
\(713\) | 21.2482 | + | 41.7019i | 0.795750 | + | 1.56175i | ||||
\(714\) | −8.93533 | − | 31.3801i | −0.334396 | − | 1.17437i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.28798 | − | 1.39325i | −0.160249 | − | 0.0520681i | ||||
\(717\) | 32.5749 | − | 3.93856i | 1.21653 | − | 0.147088i | ||||
\(718\) | −4.85077 | − | 4.85077i | −0.181029 | − | 0.181029i | ||||
\(719\) | −17.9319 | − | 13.0283i | −0.668748 | − | 0.485874i | 0.200858 | − | 0.979620i | \(-0.435627\pi\) |
−0.869606 | + | 0.493746i | \(0.835627\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 46.1690 | − | 33.5437i | 1.71942 | − | 1.24923i | ||||
\(722\) | 14.1224 | + | 2.23676i | 0.525580 | + | 0.0832437i | ||||
\(723\) | 35.5767 | + | 19.8066i | 1.32311 | + | 0.736614i | ||||
\(724\) | 14.1413i | 0.525556i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 14.9763 | + | 0.550713i | 0.555823 | + | 0.0204389i | ||||
\(727\) | 16.6015 | + | 8.45889i | 0.615716 | + | 0.313723i | 0.733888 | − | 0.679270i | \(-0.237704\pi\) |
−0.118172 | + | 0.992993i | \(0.537704\pi\) | |||||||
\(728\) | −2.87585 | + | 18.1574i | −0.106586 | + | 0.672957i | ||||
\(729\) | −10.7076 | − | 24.7860i | −0.396576 | − | 0.918002i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.9192 | + | 19.1581i | −0.514819 | + | 0.708588i | ||||
\(732\) | −6.80584 | − | 7.32548i | −0.251551 | − | 0.270758i | ||||
\(733\) | 0.339633 | + | 2.14436i | 0.0125446 | + | 0.0792038i | 0.993166 | − | 0.116707i | \(-0.0372338\pi\) |
−0.980622 | + | 0.195911i | \(0.937234\pi\) | |||||||
\(734\) | −4.58254 | + | 14.1036i | −0.169145 | + | 0.520574i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.96550 | − | 6.04917i | −0.0724491 | − | 0.222975i | ||||
\(737\) | −4.60312 | + | 2.34541i | −0.169558 | + | 0.0863942i | ||||
\(738\) | −8.31558 | + | 3.49352i | −0.306101 | + | 0.128598i | ||||
\(739\) | −25.4696 | + | 8.27559i | −0.936916 | + | 0.304423i | −0.737388 | − | 0.675470i | \(-0.763941\pi\) |
−0.199528 | + | 0.979892i | \(0.563941\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −17.7498 | − | 6.49761i | −0.652057 | − | 0.238696i | ||||
\(742\) | −3.72775 | + | 0.590418i | −0.136850 | + | 0.0216749i | ||||
\(743\) | 30.8466 | − | 30.8466i | 1.13165 | − | 1.13165i | 0.141749 | − | 0.989903i | \(-0.454727\pi\) |
0.989903 | − | 0.141749i | \(-0.0452727\pi\) | |||||||
\(744\) | 7.86527 | − | 10.0288i | 0.288355 | − | 0.367674i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −10.1684 | − | 13.9956i | −0.372293 | − | 0.512417i | ||||
\(747\) | −8.08314 | − | 1.89765i | −0.295746 | − | 0.0694315i | ||||
\(748\) | 3.58727 | − | 7.04042i | 0.131164 | − | 0.257423i | ||||
\(749\) | −9.15060 | −0.334356 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 48.1007 | 1.75522 | 0.877610 | − | 0.479376i | \(-0.159137\pi\) | ||||
0.877610 | + | 0.479376i | \(0.159137\pi\) | |||||||
\(752\) | −1.29491 | + | 2.54140i | −0.0472204 | + | 0.0926753i | ||||
\(753\) | −23.1977 | − | 4.55370i | −0.845370 | − | 0.165946i | ||||
\(754\) | 20.6537 | + | 28.4274i | 0.752163 | + | 1.03526i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 12.7782 | − | 14.0342i | 0.464737 | − | 0.510420i | ||||
\(757\) | 2.64953 | − | 2.64953i | 0.0962989 | − | 0.0962989i | −0.657316 | − | 0.753615i | \(-0.728308\pi\) |
0.753615 | + | 0.657316i | \(0.228308\pi\) | |||||||
\(758\) | 5.61670 | − | 0.889598i | 0.204008 | − | 0.0323117i | ||||
\(759\) | −5.80246 | + | 15.8509i | −0.210616 | + | 0.575350i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −37.7032 | + | 12.2505i | −1.36674 | + | 0.444080i | −0.898287 | − | 0.439409i | \(-0.855188\pi\) |
−0.468452 | + | 0.883489i | \(0.655188\pi\) | |||||||
\(762\) | −13.4720 | − | 29.0308i | −0.488038 | − | 1.05167i | ||||
\(763\) | −26.2112 | + | 13.3553i | −0.948909 | + | 0.483493i | ||||
\(764\) | −3.96247 | − | 12.1952i | −0.143357 | − | 0.441208i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.38083 | + | 28.8712i | −0.338943 | + | 1.04316i | ||||
\(767\) | −5.37083 | − | 33.9101i | −0.193929 | − | 1.22442i | ||||
\(768\) | −1.26892 | + | 1.17891i | −0.0457883 | + | 0.0425403i | ||||
\(769\) | 13.8631 | − | 19.0810i | 0.499918 | − | 0.688078i | −0.482261 | − | 0.876028i | \(-0.660184\pi\) |
0.982179 | + | 0.187950i | \(0.0601843\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 29.0286 | − | 19.5020i | 1.04544 | − | 0.702348i | ||||
\(772\) | −2.18993 | + | 13.8267i | −0.0788172 | + | 0.497632i | ||||
\(773\) | −37.0692 | − | 18.8877i | −1.33329 | − | 0.679344i | −0.365429 | − | 0.930839i | \(-0.619078\pi\) |
−0.967859 | + | 0.251495i | \(0.919078\pi\) | |||||||
\(774\) | −13.7383 | − | 1.01175i | −0.493814 | − | 0.0363665i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 13.6841i | 0.491231i | ||||||||
\(777\) | 23.6278 | − | 42.4405i | 0.847644 | − | 1.52254i | ||||
\(778\) | 1.30248 | + | 0.206293i | 0.0466962 | + | 0.00739595i | ||||
\(779\) | 5.27409 | − | 3.83185i | 0.188964 | − | 0.137290i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.59923 | − | 3.34153i | −0.164573 | − | 0.119570i | ||||
\(782\) | −23.1943 | − | 23.1943i | −0.829428 | − | 0.829428i | ||||
\(783\) | −1.69764 | − | 36.2382i | −0.0606686 | − | 1.29505i | ||||
\(784\) | 6.03185 | + | 1.95987i | 0.215423 | + | 0.0699952i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 22.0977 | − | 6.29221i | 0.788198 | − | 0.224436i | ||||
\(787\) | −2.05558 | − | 4.03430i | −0.0732734 | − | 0.143807i | 0.851464 | − | 0.524413i | \(-0.175715\pi\) |
−0.924737 | + | 0.380606i | \(0.875715\pi\) | |||||||
\(788\) | 3.09051 | + | 6.06547i | 0.110095 | + | 0.216074i | ||||
\(789\) | −27.1432 | + | 7.72889i | −0.966322 | + | 0.275156i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 37.6892 | + | 12.2460i | 1.34007 | + | 0.435416i | ||||
\(792\) | 4.58050 | − | 0.383678i | 0.162761 | − | 0.0136334i | ||||
\(793\) | 20.5449 | + | 20.5449i | 0.729571 | + | 0.729571i | ||||
\(794\) | −8.98015 | − | 6.52446i | −0.318693 | − | 0.231544i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.37266 | − | 3.17692i | 0.154985 | − | 0.112603i | ||||
\(797\) | 12.9409 | + | 2.04964i | 0.458392 | + | 0.0726021i | 0.381360 | − | 0.924427i | \(-0.375456\pi\) |
0.0770316 | + | 0.997029i | \(0.475456\pi\) | |||||||
\(798\) | −6.67291 | + | 11.9859i | −0.236218 | + | 0.424297i | ||||
\(799\) | 14.7096i | 0.520387i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.41848 | − | 19.2613i | 0.0501195 | − | 0.680563i | ||||
\(802\) | −34.2621 | − | 17.4574i | −1.20984 | − | 0.616443i | ||||
\(803\) | 0.142947 | − | 0.902532i | 0.00504449 | − | 0.0318496i | ||||
\(804\) | 4.84772 | − | 3.25680i | 0.170966 | − | 0.114858i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −21.7682 | + | 29.9613i | −0.766752 | + | 1.05534i | ||||
\(807\) | −13.8626 | + | 12.8792i | −0.487985 | + | 0.453370i | ||||
\(808\) | 0.0229270 | + | 0.144756i | 0.000806570 | + | 0.00509248i | ||||
\(809\) | −10.9215 | + | 33.6130i | −0.383980 | + | 1.18177i | 0.553237 | + | 0.833024i | \(0.313392\pi\) |
−0.937217 | + | 0.348746i | \(0.886608\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.0429712 | + | 0.132252i | 0.00150892 | + | 0.00464399i | 0.951808 | − | 0.306694i | \(-0.0992228\pi\) |
−0.950299 | + | 0.311338i | \(0.899223\pi\) | |||||||
\(812\) | 22.7225 | − | 11.5777i | 0.797403 | − | 0.406297i | ||||
\(813\) | 2.44813 | + | 5.27548i | 0.0858597 | + | 0.185019i | ||||
\(814\) | 11.1879 | − | 3.63517i | 0.392135 | − | 0.127413i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3.07058 | + | 8.38805i | −0.107492 | + | 0.293640i | ||||
\(817\) | 9.83400 | − | 1.55755i | 0.344048 | − | 0.0544918i | ||||
\(818\) | −8.03693 | + | 8.03693i | −0.281005 | + | 0.281005i | ||||
\(819\) | −35.6065 | + | 42.1168i | −1.24419 | + | 1.47168i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.62196 | + | 2.23243i | 0.0566067 | + | 0.0779125i | 0.836382 | − | 0.548147i | \(-0.184667\pi\) |
−0.779775 | + | 0.626060i | \(0.784667\pi\) | |||||||
\(822\) | −16.5897 | − | 3.25655i | −0.578631 | − | 0.113585i | ||||
\(823\) | 9.20610 | − | 18.0680i | 0.320905 | − | 0.629811i | −0.673051 | − | 0.739596i | \(-0.735016\pi\) |
0.993955 | + | 0.109786i | \(0.0350164\pi\) | |||||||
\(824\) | −15.6235 | −0.544270 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −24.9175 | −0.866992 | ||||||||
\(827\) | −1.51186 | + | 2.96720i | −0.0525726 | + | 0.103180i | −0.915798 | − | 0.401639i | \(-0.868441\pi\) |
0.863225 | + | 0.504819i | \(0.168441\pi\) | |||||||
\(828\) | 4.36112 | − | 18.5764i | 0.151559 | − | 0.645574i | ||||
\(829\) | 17.4925 | + | 24.0763i | 0.607539 | + | 0.836206i | 0.996372 | − | 0.0851024i | \(-0.0271218\pi\) |
−0.388833 | + | 0.921308i | \(0.627122\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −30.0014 | + | 38.2540i | −1.04074 | + | 1.32702i | ||||
\(832\) | 3.55880 | − | 3.55880i | 0.123379 | − | 0.123379i | ||||
\(833\) | 32.3051 | − | 5.11663i | 1.11931 | − | 0.177281i | ||||
\(834\) | −7.90079 | − | 2.89221i | −0.273582 | − | 0.100149i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.15965 | + | 1.02663i | −0.109279 | + | 0.0355068i | ||||
\(837\) | 35.7714 | − | 13.5042i | 1.23644 | − | 0.466772i | ||||
\(838\) | 4.47907 | − | 2.28220i | 0.154727 | − | 0.0788374i | ||||
\(839\) | 5.16619 | + | 15.8999i | 0.178357 | + | 0.548926i | 0.999771 | − | 0.0214067i | \(-0.00681447\pi\) |
−0.821414 | + | 0.570332i | \(0.806814\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.10123 | − | 18.7776i | 0.210387 | − | 0.647505i | ||||
\(842\) | 1.42480 | + | 8.99583i | 0.0491018 | + | 0.310017i | ||||
\(843\) | −0.837518 | − | 0.901465i | −0.0288457 | − | 0.0310481i | ||||
\(844\) | 7.52218 | − | 10.3534i | 0.258924 | − | 0.356379i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7.27333 | + | 4.50757i | −0.250062 | + | 0.154973i | ||||
\(847\) | −4.94407 | + | 31.2156i | −0.169880 | + | 1.07258i | ||||
\(848\) | 0.920647 | + | 0.469093i | 0.0316152 | + | 0.0161087i | ||||
\(849\) | 15.9530 | + | 0.586627i | 0.547504 | + | 0.0201330i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 48.8339i | − | 1.67400i | ||||||
\(852\) | 5.61502 | + | 3.12604i | 0.192367 | + | 0.107096i | ||||
\(853\) | −2.82627 | − | 0.447638i | −0.0967698 | − | 0.0153268i | 0.107862 | − | 0.994166i | \(-0.465600\pi\) |
−0.204632 | + | 0.978839i | \(0.565600\pi\) | |||||||
\(854\) | 17.0598 | − | 12.3946i | 0.583773 | − | 0.424136i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.02672 | + | 1.47249i | 0.0692717 | + | 0.0503288i | ||||
\(857\) | 8.27926 | + | 8.27926i | 0.282814 | + | 0.282814i | 0.834230 | − | 0.551416i | \(-0.185912\pi\) |
−0.551416 | + | 0.834230i | \(0.685912\pi\) | |||||||
\(858\) | −13.2598 | + | 1.60322i | −0.452683 | + | 0.0547330i | ||||
\(859\) | −21.3255 | − | 6.92908i | −0.727617 | − | 0.236417i | −0.0782946 | − | 0.996930i | \(-0.524947\pi\) |
−0.649323 | + | 0.760513i | \(0.724947\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.20919 | − | 18.2942i | −0.177529 | − | 0.623465i | ||||
\(862\) | −11.2377 | − | 22.0551i | −0.382756 | − | 0.751201i | ||||
\(863\) | −8.33881 | − | 16.3658i | −0.283857 | − | 0.557100i | 0.704418 | − | 0.709785i | \(-0.251208\pi\) |
−0.988275 | + | 0.152685i | \(0.951208\pi\) | |||||||
\(864\) | −5.08852 | + | 1.05213i | −0.173115 | + | 0.0357942i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 21.0928 | + | 6.85347i | 0.716763 | + | 0.232890i | ||||
\(867\) | 1.99504 | + | 16.5004i | 0.0677550 | + | 0.560385i | ||||
\(868\) | 19.0057 | + | 19.0057i | 0.645097 | + | 0.645097i | ||||
\(869\) | 1.64955 | + | 1.19847i | 0.0559572 | + | 0.0406553i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.7290 | + | 9.97468i | −0.465188 | + | 0.337979i | ||||
\(872\) | 7.95446 | + | 1.25986i | 0.269372 | + | 0.0426644i | ||||
\(873\) | −21.2735 | + | 35.1103i | −0.719999 | + | 1.18830i | ||||
\(874\) | 13.7915i | 0.466505i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.0379595 | + | 1.03228i | −0.00128253 | + | 0.0348777i | ||||
\(877\) | 34.8578 | + | 17.7609i | 1.17706 | + | 0.599744i | 0.929390 | − | 0.369100i | \(-0.120334\pi\) |
0.247673 | + | 0.968844i | \(0.420334\pi\) | |||||||
\(878\) | −0.266559 | + | 1.68299i | −0.00899594 | + | 0.0567981i | ||||
\(879\) | 2.70113 | + | 4.02061i | 0.0911069 | + | 0.135612i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.436643 | + | 0.600988i | −0.0147109 | + | 0.0202478i | −0.816309 | − | 0.577615i | \(-0.803983\pi\) |
0.801598 | + | 0.597863i | \(0.203983\pi\) | |||||||
\(882\) | 12.4295 | + | 14.4058i | 0.418523 | + | 0.485067i | ||||
\(883\) | −4.62830 | − | 29.2220i | −0.155755 | − | 0.983397i | −0.934476 | − | 0.356027i | \(-0.884131\pi\) |
0.778721 | − | 0.627371i | \(-0.215869\pi\) | |||||||
\(884\) | 8.02063 | − | 24.6849i | 0.269763 | − | 0.830245i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.311629 | − | 0.959097i | −0.0104694 | − | 0.0322215i | ||||
\(887\) | −52.4089 | + | 26.7037i | −1.75972 | + | 0.896621i | −0.808270 | + | 0.588813i | \(0.799596\pi\) |
−0.951448 | + | 0.307809i | \(0.900404\pi\) | |||||||
\(888\) | −12.0626 | + | 5.59776i | −0.404795 | + | 0.187849i | ||||
\(889\) | 64.1903 | − | 20.8567i | 2.15287 | − | 0.699511i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 12.3490 | + | 6.13648i | 0.413707 | + | 0.205580i | ||||
\(892\) | 28.6765 | − | 4.54190i | 0.960159 | − | 0.152074i | ||||
\(893\) | 4.37321 | − | 4.37321i | 0.146344 | − | 0.146344i | ||||
\(894\) | 8.93637 | + | 7.00851i | 0.298877 | + | 0.234400i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.14701 | − | 2.95510i | −0.0717265 | − | 0.0987230i | ||||
\(897\) | −10.6802 | + | 54.4075i | −0.356601 | + | 1.81661i | ||||
\(898\) | −5.64357 | + | 11.0761i | −0.188329 | + | 0.369616i | ||||
\(899\) | 51.3743 | 1.71343 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.32868 | 0.177524 | ||||||||
\(902\) | 2.09134 | − | 4.10448i | 0.0696339 | − | 0.136664i | ||||
\(903\) | 5.59594 | − | 28.5071i | 0.186221 | − | 0.948655i | ||||
\(904\) | −6.37698 | − | 8.77715i | −0.212095 | − | 0.291924i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.45310 | − | 1.13962i | −0.0482760 | − | 0.0378613i | ||||
\(907\) | −8.72011 | + | 8.72011i | −0.289547 | + | 0.289547i | −0.836901 | − | 0.547354i | \(-0.815635\pi\) |
0.547354 | + | 0.836901i | \(0.315635\pi\) | |||||||
\(908\) | 3.90298 | − | 0.618172i | 0.129525 | − | 0.0205148i | ||||
\(909\) | −0.166213 | + | 0.407052i | −0.00551295 | + | 0.0135011i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.6554 | − | 11.5852i | 1.18132 | − | 0.383833i | 0.348461 | − | 0.937323i | \(-0.386704\pi\) |
0.832856 | + | 0.553490i | \(0.186704\pi\) | |||||||
\(912\) | 3.40669 | − | 1.58090i | 0.112807 | − | 0.0523489i | ||||
\(913\) | 3.77833 | − | 1.92515i | 0.125044 | − | 0.0637133i | ||||
\(914\) | 11.1290 | + | 34.2516i | 0.368116 | + | 1.13294i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.07958 | + | 12.5556i | −0.134793 | + | 0.414850i | ||||
\(917\) | 7.57987 | + | 47.8574i | 0.250309 | + | 1.58039i | ||||
\(918\) | −20.9186 | + | 16.7482i | −0.690416 | + | 0.552774i | ||||
\(919\) | 17.9736 | − | 24.7386i | 0.592896 | − | 0.816051i | −0.402139 | − | 0.915579i | \(-0.631733\pi\) |
0.995035 | + | 0.0995274i | \(0.0317331\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.0518 | + | 23.8930i | 0.528925 | + | 0.787300i | ||||
\(922\) | −5.72422 | + | 36.1413i | −0.188517 | + | 1.19025i | ||||
\(923\) | −16.6386 | − | 8.47779i | −0.547666 | − | 0.279050i | ||||
\(924\) | −0.356215 | + | 9.68706i | −0.0117186 | + | 0.318681i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 6.61685i | 0.217443i | ||||||||
\(927\) | −40.0863 | − | 24.2885i | −1.31661 | − | 0.797738i | ||||
\(928\) | −6.89573 | − | 1.09218i | −0.226364 | − | 0.0358525i | ||||
\(929\) | −0.652608 | + | 0.474147i | −0.0214114 | + | 0.0155563i | −0.598439 | − | 0.801168i | \(-0.704212\pi\) |
0.577028 | + | 0.816724i | \(0.304212\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.1256 | − | 8.08324i | −0.364628 | − | 0.264918i | ||||
\(932\) | 6.19799 | + | 6.19799i | 0.203022 | + | 0.203022i | ||||
\(933\) | 0.722133 | + | 5.97258i | 0.0236416 | + | 0.195534i | ||||
\(934\) | 36.3043 | + | 11.7960i | 1.18791 | + | 0.385976i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 14.6636 | − | 3.59850i | 0.479295 | − | 0.117621i | ||||
\(937\) | −3.87770 | − | 7.61042i | −0.126679 | − | 0.248622i | 0.818953 | − | 0.573861i | \(-0.194555\pi\) |
−0.945632 | + | 0.325240i | \(0.894555\pi\) | |||||||
\(938\) | 5.59143 | + | 10.9738i | 0.182567 | + | 0.358308i | ||||
\(939\) | 4.02673 | + | 14.1415i | 0.131408 | + | 0.461492i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.4242 | − | 5.66148i | −0.568014 | − | 0.184559i | 0.0109101 | − | 0.999940i | \(-0.496527\pi\) |
−0.578924 | + | 0.815382i | \(0.696527\pi\) | |||||||
\(942\) | −37.2893 | + | 4.50857i | −1.21495 | + | 0.146897i | ||||
\(943\) | −13.5220 | − | 13.5220i | −0.440338 | − | 0.440338i | ||||
\(944\) | 5.51884 | + | 4.00967i | 0.179623 | + | 0.130504i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.69187 | − | 4.13539i | 0.185059 | − | 0.134453i | ||||
\(947\) | −35.5120 | − | 5.62455i | −1.15398 | − | 0.182773i | −0.450027 | − | 0.893015i | \(-0.648586\pi\) |
−0.703958 | + | 0.710242i | \(0.748586\pi\) | |||||||
\(948\) | −2.01387 | − | 1.12118i | −0.0654076 | − | 0.0364143i | ||||
\(949\) | − | 3.00159i | − | 0.0974356i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −17.0673 | − | 0.627603i | −0.553444 | − | 0.0203514i | ||||
\(952\) | −16.7843 | − | 8.55203i | −0.543982 | − | 0.277173i | ||||
\(953\) | −1.94289 | + | 12.2669i | −0.0629365 | + | 0.397365i | 0.936030 | + | 0.351919i | \(0.114471\pi\) |
−0.998967 | + | 0.0454459i | \(0.985529\pi\) | |||||||
\(954\) | 1.63291 | + | 2.63484i | 0.0528674 | + | 0.0853060i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 11.1351 | − | 15.3261i | 0.360133 | − | 0.495681i | ||||
\(957\) | 12.6111 | + | 13.5739i | 0.407658 | + | 0.438783i | ||||
\(958\) | −1.82118 | − | 11.4985i | −0.0588397 | − | 0.371500i | ||||
\(959\) | 11.0175 | − | 33.9085i | 0.355775 | − | 1.09496i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.15266 | + | 22.0136i | 0.230731 | + | 0.710117i | ||||
\(962\) | 34.4295 | − | 17.5427i | 1.11005 | − | 0.565600i | ||||
\(963\) | 2.91092 | + | 6.92884i | 0.0938032 | + | 0.223279i | ||||
\(964\) | 22.3583 | − | 7.26464i | 0.720111 | − | 0.233978i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 37.7883 | + | 13.8330i | 1.21582 | + | 0.445070i | ||||
\(967\) | 5.27370 | − | 0.835271i | 0.169591 | − | 0.0268605i | −0.0710616 | − | 0.997472i | \(-0.522639\pi\) |
0.240652 | + | 0.970611i | \(0.422639\pi\) | |||||||
\(968\) | 6.11819 | − | 6.11819i | 0.196646 | − | 0.196646i | ||||
\(969\) | 11.9525 | − | 15.2403i | 0.383970 | − | 0.489590i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33.9216 | − | 46.6890i | −1.08859 | − | 1.49832i | −0.849693 | − | 0.527278i | \(-0.823212\pi\) |
−0.238902 | − | 0.971044i | \(-0.576788\pi\) | |||||||
\(972\) | −14.6916 | − | 5.21116i | −0.471234 | − | 0.167148i | ||||
\(973\) | 8.05524 | − | 15.8093i | 0.258239 | − | 0.506823i | ||||
\(974\) | −35.5211 | −1.13817 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.77299 | −0.184789 | ||||||||
\(977\) | −4.68324 | + | 9.19137i | −0.149830 | + | 0.294058i | −0.953707 | − | 0.300738i | \(-0.902767\pi\) |
0.803877 | + | 0.594796i | \(0.202767\pi\) | |||||||
\(978\) | −17.4750 | − | 3.43033i | −0.558787 | − | 0.109690i | ||||
\(979\) | 5.79785 | + | 7.98005i | 0.185300 | + | 0.255043i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.4507 | + | 15.5986i | 0.589086 | + | 0.498026i | ||||
\(982\) | −2.36943 | + | 2.36943i | −0.0756116 | + | 0.0756116i | ||||
\(983\) | −39.7879 | + | 6.30178i | −1.26904 | + | 0.200996i | −0.754401 | − | 0.656413i | \(-0.772073\pi\) |
−0.514635 | + | 0.857409i | \(0.672073\pi\) | |||||||
\(984\) | −1.79011 | + | 4.89013i | −0.0570666 | + | 0.155892i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −34.2432 | + | 11.1263i | −1.09053 | + | 0.354333i | ||||
\(987\) | −7.59608 | − | 16.3688i | −0.241786 | − | 0.521024i | ||||
\(988\) | −9.72349 | + | 4.95436i | −0.309345 | + | 0.157619i | ||||
\(989\) | −9.02525 | − | 27.7769i | −0.286986 | − | 0.883253i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.61373 | + | 23.4326i | −0.241858 | + | 0.744362i | 0.754279 | + | 0.656554i | \(0.227986\pi\) |
−0.996137 | + | 0.0878088i | \(0.972014\pi\) | |||||||
\(992\) | −1.15111 | − | 7.26784i | −0.0365478 | − | 0.230754i | ||||
\(993\) | −21.0005 | + | 19.5108i | −0.666432 | + | 0.619158i | ||||
\(994\) | −7.96619 | + | 10.9645i | −0.252672 | + | 0.347773i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −3.97909 | + | 2.67324i | −0.126082 | + | 0.0847048i | ||||
\(997\) | 5.80306 | − | 36.6391i | 0.183785 | − | 1.16037i | −0.707428 | − | 0.706785i | \(-0.750145\pi\) |
0.891213 | − | 0.453585i | \(-0.149855\pi\) | |||||||
\(998\) | −2.28445 | − | 1.16399i | −0.0723131 | − | 0.0368454i | ||||
\(999\) | −39.6523 | − | 4.39015i | −1.25454 | − | 0.138898i |
(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 | 750.2.l.c.143.9 | 80 | ||
3.2 | odd | 2 | inner | 750.2.l.c.143.3 | 80 | ||
5.2 | odd | 4 | 150.2.l.a.17.6 | yes | 80 | ||
5.3 | odd | 4 | 750.2.l.b.107.5 | 80 | |||
5.4 | even | 2 | 750.2.l.a.143.2 | 80 | |||
15.2 | even | 4 | 150.2.l.a.17.5 | ✓ | 80 | ||
15.8 | even | 4 | 750.2.l.b.107.6 | 80 | |||
15.14 | odd | 2 | 750.2.l.a.143.8 | 80 | |||
25.3 | odd | 20 | 750.2.l.a.257.8 | 80 | |||
25.4 | even | 10 | 750.2.l.b.743.6 | 80 | |||
25.21 | even | 5 | 150.2.l.a.53.5 | yes | 80 | ||
25.22 | odd | 20 | inner | 750.2.l.c.257.3 | 80 | ||
75.29 | odd | 10 | 750.2.l.b.743.5 | 80 | |||
75.47 | even | 20 | inner | 750.2.l.c.257.9 | 80 | ||
75.53 | even | 20 | 750.2.l.a.257.2 | 80 | |||
75.71 | odd | 10 | 150.2.l.a.53.6 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.l.a.17.5 | ✓ | 80 | 15.2 | even | 4 | ||
150.2.l.a.17.6 | yes | 80 | 5.2 | odd | 4 | ||
150.2.l.a.53.5 | yes | 80 | 25.21 | even | 5 | ||
150.2.l.a.53.6 | yes | 80 | 75.71 | odd | 10 | ||
750.2.l.a.143.2 | 80 | 5.4 | even | 2 | |||
750.2.l.a.143.8 | 80 | 15.14 | odd | 2 | |||
750.2.l.a.257.2 | 80 | 75.53 | even | 20 | |||
750.2.l.a.257.8 | 80 | 25.3 | odd | 20 | |||
750.2.l.b.107.5 | 80 | 5.3 | odd | 4 | |||
750.2.l.b.107.6 | 80 | 15.8 | even | 4 | |||
750.2.l.b.743.5 | 80 | 75.29 | odd | 10 | |||
750.2.l.b.743.6 | 80 | 25.4 | even | 10 | |||
750.2.l.c.143.3 | 80 | 3.2 | odd | 2 | inner | ||
750.2.l.c.143.9 | 80 | 1.1 | even | 1 | trivial | ||
750.2.l.c.257.3 | 80 | 25.22 | odd | 20 | inner | ||
750.2.l.c.257.9 | 80 | 75.47 | even | 20 | inner |