Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [462,2,Mod(169,462)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(462, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("462.169");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 462.j (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.68908857338\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.324000000.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 169.2 | ||
Root | \(-0.535233 + 1.64728i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.169 |
Dual form | 462.2.j.g.421.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.809017 | + | 0.587785i | 0.572061 | + | 0.415627i | ||||
\(3\) | 0.309017 | − | 0.951057i | 0.178411 | − | 0.549093i | ||||
\(4\) | 0.309017 | + | 0.951057i | 0.154508 | + | 0.475528i | ||||
\(5\) | 2.26728 | − | 1.64728i | 1.01396 | − | 0.736685i | 0.0489242 | − | 0.998802i | \(-0.484421\pi\) |
0.965036 | + | 0.262117i | \(0.0844207\pi\) | |||||||
\(6\) | 0.809017 | − | 0.587785i | 0.330280 | − | 0.239962i | ||||
\(7\) | 0.309017 | + | 0.951057i | 0.116797 | + | 0.359466i | ||||
\(8\) | −0.309017 | + | 0.951057i | −0.109254 | + | 0.336249i | ||||
\(9\) | −0.809017 | − | 0.587785i | −0.269672 | − | 0.195928i | ||||
\(10\) | 2.80252 | 0.886234 | ||||||||
\(11\) | 0.921216 | + | 3.18612i | 0.277757 | + | 0.960651i | ||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −0.706258 | − | 0.513127i | −0.195881 | − | 0.142316i | 0.485522 | − | 0.874225i | \(-0.338630\pi\) |
−0.681403 | + | 0.731909i | \(0.738630\pi\) | |||||||
\(14\) | −0.309017 | + | 0.951057i | −0.0825883 | + | 0.254181i | ||||
\(15\) | −0.866025 | − | 2.66535i | −0.223607 | − | 0.688191i | ||||
\(16\) | −0.809017 | + | 0.587785i | −0.202254 | + | 0.146946i | ||||
\(17\) | 3.92055 | − | 2.84845i | 0.950873 | − | 0.690850i | −0.000139955 | − | 1.00000i | \(-0.500045\pi\) |
0.951013 | + | 0.309150i | \(0.100045\pi\) | |||||||
\(18\) | −0.309017 | − | 0.951057i | −0.0728360 | − | 0.224166i | ||||
\(19\) | 1.10570 | − | 3.40299i | 0.253665 | − | 0.780700i | −0.740425 | − | 0.672139i | \(-0.765376\pi\) |
0.994090 | − | 0.108561i | \(-0.0346243\pi\) | |||||||
\(20\) | 2.26728 | + | 1.64728i | 0.506980 | + | 0.368343i | ||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −1.12747 | + | 3.11910i | −0.240378 | + | 0.664995i | ||||
\(23\) | −2.89765 | −0.604202 | −0.302101 | − | 0.953276i | \(-0.597688\pi\) | ||||
−0.302101 | + | 0.953276i | \(0.597688\pi\) | |||||||
\(24\) | 0.809017 | + | 0.587785i | 0.165140 | + | 0.119981i | ||||
\(25\) | 0.881966 | − | 2.71441i | 0.176393 | − | 0.542882i | ||||
\(26\) | −0.269767 | − | 0.830257i | −0.0529056 | − | 0.162827i | ||||
\(27\) | −0.809017 | + | 0.587785i | −0.155695 | + | 0.113119i | ||||
\(28\) | −0.809017 | + | 0.587785i | −0.152890 | + | 0.111081i | ||||
\(29\) | −0.687377 | − | 2.11553i | −0.127643 | − | 0.392844i | 0.866731 | − | 0.498777i | \(-0.166217\pi\) |
−0.994373 | + | 0.105933i | \(0.966217\pi\) | |||||||
\(30\) | 0.866025 | − | 2.66535i | 0.158114 | − | 0.486624i | ||||
\(31\) | −4.70378 | − | 3.41749i | −0.844823 | − | 0.613800i | 0.0788907 | − | 0.996883i | \(-0.474862\pi\) |
−0.923714 | + | 0.383083i | \(0.874862\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 3.31485 | + | 0.108436i | 0.577042 | + | 0.0188764i | ||||
\(34\) | 4.84607 | 0.831094 | ||||||||
\(35\) | 2.26728 | + | 1.64728i | 0.383241 | + | 0.278441i | ||||
\(36\) | 0.309017 | − | 0.951057i | 0.0515028 | − | 0.158509i | ||||
\(37\) | 1.83414 | + | 5.64492i | 0.301531 | + | 0.928018i | 0.980949 | + | 0.194266i | \(0.0622326\pi\) |
−0.679417 | + | 0.733752i | \(0.737767\pi\) | |||||||
\(38\) | 2.89476 | − | 2.10317i | 0.469592 | − | 0.341178i | ||||
\(39\) | −0.706258 | + | 0.513127i | −0.113092 | + | 0.0821660i | ||||
\(40\) | 0.866025 | + | 2.66535i | 0.136931 | + | 0.421429i | ||||
\(41\) | −2.18850 | + | 6.73551i | −0.341786 | + | 1.05191i | 0.621495 | + | 0.783418i | \(0.286525\pi\) |
−0.963282 | + | 0.268492i | \(0.913475\pi\) | |||||||
\(42\) | 0.809017 | + | 0.587785i | 0.124834 | + | 0.0906972i | ||||
\(43\) | 3.74009 | 0.570358 | 0.285179 | − | 0.958474i | \(-0.407947\pi\) | ||||
0.285179 | + | 0.958474i | \(0.407947\pi\) | |||||||
\(44\) | −2.74551 | + | 1.86069i | −0.413901 | + | 0.280510i | ||||
\(45\) | −2.80252 | −0.417775 | ||||||||
\(46\) | −2.34425 | − | 1.70320i | −0.345641 | − | 0.251123i | ||||
\(47\) | −3.53344 | + | 10.8748i | −0.515406 | + | 1.58626i | 0.267136 | + | 0.963659i | \(0.413923\pi\) |
−0.782542 | + | 0.622597i | \(0.786077\pi\) | |||||||
\(48\) | 0.309017 | + | 0.951057i | 0.0446028 | + | 0.137273i | ||||
\(49\) | −0.809017 | + | 0.587785i | −0.115574 | + | 0.0839693i | ||||
\(50\) | 2.30902 | − | 1.67760i | 0.326544 | − | 0.237248i | ||||
\(51\) | −1.49752 | − | 4.60888i | −0.209694 | − | 0.645373i | ||||
\(52\) | 0.269767 | − | 0.830257i | 0.0374099 | − | 0.115136i | ||||
\(53\) | −10.1109 | − | 7.34598i | −1.38883 | − | 1.00905i | −0.995992 | − | 0.0894417i | \(-0.971492\pi\) |
−0.392843 | − | 0.919606i | \(-0.628508\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 7.33708 | + | 5.70634i | 0.989332 | + | 0.769443i | ||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −2.89476 | − | 2.10317i | −0.383420 | − | 0.278571i | ||||
\(58\) | 0.687377 | − | 2.11553i | 0.0902570 | − | 0.277783i | ||||
\(59\) | 2.04467 | + | 6.29286i | 0.266194 | + | 0.819260i | 0.991416 | + | 0.130745i | \(0.0417371\pi\) |
−0.725222 | + | 0.688515i | \(0.758263\pi\) | |||||||
\(60\) | 2.26728 | − | 1.64728i | 0.292705 | − | 0.212663i | ||||
\(61\) | 8.35994 | − | 6.07385i | 1.07038 | − | 0.777677i | 0.0943996 | − | 0.995534i | \(-0.469907\pi\) |
0.975981 | + | 0.217858i | \(0.0699069\pi\) | |||||||
\(62\) | −1.79668 | − | 5.52962i | −0.228179 | − | 0.702262i | ||||
\(63\) | 0.309017 | − | 0.951057i | 0.0389325 | − | 0.119822i | ||||
\(64\) | −0.809017 | − | 0.587785i | −0.101127 | − | 0.0734732i | ||||
\(65\) | −2.44655 | −0.303457 | ||||||||
\(66\) | 2.61803 | + | 2.03615i | 0.322258 | + | 0.250632i | ||||
\(67\) | −7.98782 | −0.975868 | −0.487934 | − | 0.872881i | \(-0.662249\pi\) | ||||
−0.487934 | + | 0.872881i | \(0.662249\pi\) | |||||||
\(68\) | 3.92055 | + | 2.84845i | 0.475437 | + | 0.345425i | ||||
\(69\) | −0.895424 | + | 2.75583i | −0.107796 | + | 0.331763i | ||||
\(70\) | 0.866025 | + | 2.66535i | 0.103510 | + | 0.318571i | ||||
\(71\) | −8.26662 | + | 6.00605i | −0.981067 | + | 0.712787i | −0.957947 | − | 0.286946i | \(-0.907360\pi\) |
−0.0231203 | + | 0.999733i | \(0.507360\pi\) | |||||||
\(72\) | 0.809017 | − | 0.587785i | 0.0953436 | − | 0.0692712i | ||||
\(73\) | −4.85523 | − | 14.9428i | −0.568261 | − | 1.74893i | −0.658057 | − | 0.752968i | \(-0.728622\pi\) |
0.0897963 | − | 0.995960i | \(-0.471378\pi\) | |||||||
\(74\) | −1.83414 | + | 5.64492i | −0.213215 | + | 0.656208i | ||||
\(75\) | −2.30902 | − | 1.67760i | −0.266622 | − | 0.193712i | ||||
\(76\) | 3.57812 | 0.410438 | ||||||||
\(77\) | −2.74551 | + | 1.86069i | −0.312880 | + | 0.212046i | ||||
\(78\) | −0.872983 | −0.0988459 | ||||||||
\(79\) | 4.97106 | + | 3.61169i | 0.559288 | + | 0.406346i | 0.831198 | − | 0.555976i | \(-0.187655\pi\) |
−0.271910 | + | 0.962323i | \(0.587655\pi\) | |||||||
\(80\) | −0.866025 | + | 2.66535i | −0.0968246 | + | 0.297995i | ||||
\(81\) | 0.309017 | + | 0.951057i | 0.0343352 | + | 0.105673i | ||||
\(82\) | −5.72957 | + | 4.16277i | −0.632725 | + | 0.459702i | ||||
\(83\) | −8.08032 | + | 5.87069i | −0.886930 | + | 0.644392i | −0.935076 | − | 0.354448i | \(-0.884669\pi\) |
0.0481456 | + | 0.998840i | \(0.484669\pi\) | |||||||
\(84\) | 0.309017 | + | 0.951057i | 0.0337165 | + | 0.103769i | ||||
\(85\) | 4.19682 | − | 12.9165i | 0.455209 | − | 1.40099i | ||||
\(86\) | 3.02579 | + | 2.19837i | 0.326280 | + | 0.237056i | ||||
\(87\) | −2.22440 | −0.238481 | ||||||||
\(88\) | −3.31485 | − | 0.108436i | −0.353364 | − | 0.0115594i | ||||
\(89\) | −12.6952 | −1.34569 | −0.672844 | − | 0.739784i | \(-0.734928\pi\) | ||||
−0.672844 | + | 0.739784i | \(0.734928\pi\) | |||||||
\(90\) | −2.26728 | − | 1.64728i | −0.238993 | − | 0.173638i | ||||
\(91\) | 0.269767 | − | 0.830257i | 0.0282792 | − | 0.0870345i | ||||
\(92\) | −0.895424 | − | 2.75583i | −0.0933544 | − | 0.287315i | ||||
\(93\) | −4.70378 | + | 3.41749i | −0.487759 | + | 0.354378i | ||||
\(94\) | −9.25068 | + | 6.72101i | −0.954135 | + | 0.693219i | ||||
\(95\) | −3.09874 | − | 9.53695i | −0.317924 | − | 0.978470i | ||||
\(96\) | −0.309017 | + | 0.951057i | −0.0315389 | + | 0.0970668i | ||||
\(97\) | 2.34827 | + | 1.70612i | 0.238430 | + | 0.173230i | 0.700584 | − | 0.713570i | \(-0.252923\pi\) |
−0.462153 | + | 0.886800i | \(0.652923\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 1.12747 | − | 3.11910i | 0.113315 | − | 0.313482i | ||||
\(100\) | 2.85410 | 0.285410 | ||||||||
\(101\) | 4.82289 | + | 3.50403i | 0.479895 | + | 0.348664i | 0.801285 | − | 0.598283i | \(-0.204150\pi\) |
−0.321390 | + | 0.946947i | \(0.604150\pi\) | |||||||
\(102\) | 1.49752 | − | 4.60888i | 0.148276 | − | 0.456348i | ||||
\(103\) | −0.800288 | − | 2.46303i | −0.0788548 | − | 0.242690i | 0.903856 | − | 0.427836i | \(-0.140724\pi\) |
−0.982711 | + | 0.185146i | \(0.940724\pi\) | |||||||
\(104\) | 0.706258 | − | 0.513127i | 0.0692543 | − | 0.0503162i | ||||
\(105\) | 2.26728 | − | 1.64728i | 0.221264 | − | 0.160758i | ||||
\(106\) | −3.86201 | − | 11.8860i | −0.375111 | − | 1.15447i | ||||
\(107\) | −2.40999 | + | 7.41718i | −0.232982 | + | 0.717046i | 0.764400 | + | 0.644742i | \(0.223035\pi\) |
−0.997383 | + | 0.0723038i | \(0.976965\pi\) | |||||||
\(108\) | −0.809017 | − | 0.587785i | −0.0778477 | − | 0.0565597i | ||||
\(109\) | −11.6276 | −1.11372 | −0.556859 | − | 0.830607i | \(-0.687994\pi\) | ||||
−0.556859 | + | 0.830607i | \(0.687994\pi\) | |||||||
\(110\) | 2.58172 | + | 8.92916i | 0.246158 | + | 0.851362i | ||||
\(111\) | 5.93542 | 0.563365 | ||||||||
\(112\) | −0.809017 | − | 0.587785i | −0.0764449 | − | 0.0555405i | ||||
\(113\) | 4.40958 | − | 13.5713i | 0.414818 | − | 1.27668i | −0.497596 | − | 0.867409i | \(-0.665784\pi\) |
0.912414 | − | 0.409269i | \(-0.134216\pi\) | |||||||
\(114\) | −1.10570 | − | 3.40299i | −0.103558 | − | 0.318719i | ||||
\(115\) | −6.56980 | + | 4.77324i | −0.612637 | + | 0.445107i | ||||
\(116\) | 1.79958 | − | 1.30747i | 0.167086 | − | 0.121395i | ||||
\(117\) | 0.269767 | + | 0.830257i | 0.0249399 | + | 0.0767572i | ||||
\(118\) | −2.04467 | + | 6.29286i | −0.188227 | + | 0.579305i | ||||
\(119\) | 3.92055 | + | 2.84845i | 0.359396 | + | 0.261117i | ||||
\(120\) | 2.80252 | 0.255834 | ||||||||
\(121\) | −9.30272 | + | 5.87021i | −0.845702 | + | 0.533656i | ||||
\(122\) | 10.3334 | 0.935547 | ||||||||
\(123\) | 5.72957 | + | 4.16277i | 0.516618 | + | 0.375345i | ||||
\(124\) | 1.79668 | − | 5.52962i | 0.161347 | − | 0.496575i | ||||
\(125\) | 1.85840 | + | 5.71957i | 0.166221 | + | 0.511574i | ||||
\(126\) | 0.809017 | − | 0.587785i | 0.0720730 | − | 0.0523641i | ||||
\(127\) | 11.4463 | − | 8.31626i | 1.01570 | − | 0.737948i | 0.0503020 | − | 0.998734i | \(-0.483982\pi\) |
0.965397 | + | 0.260786i | \(0.0839816\pi\) | |||||||
\(128\) | −0.309017 | − | 0.951057i | −0.0273135 | − | 0.0840623i | ||||
\(129\) | 1.15575 | − | 3.55703i | 0.101758 | − | 0.313179i | ||||
\(130\) | −1.97930 | − | 1.43805i | −0.173596 | − | 0.126125i | ||||
\(131\) | 12.5014 | 1.09225 | 0.546124 | − | 0.837704i | \(-0.316103\pi\) | ||||
0.546124 | + | 0.837704i | \(0.316103\pi\) | |||||||
\(132\) | 0.921216 | + | 3.18612i | 0.0801816 | + | 0.277316i | ||||
\(133\) | 3.57812 | 0.310262 | ||||||||
\(134\) | −6.46228 | − | 4.69512i | −0.558256 | − | 0.405597i | ||||
\(135\) | −0.866025 | + | 2.66535i | −0.0745356 | + | 0.229397i | ||||
\(136\) | 1.49752 | + | 4.60888i | 0.128411 | + | 0.395209i | ||||
\(137\) | 3.28256 | − | 2.38492i | 0.280448 | − | 0.203757i | −0.438665 | − | 0.898651i | \(-0.644548\pi\) |
0.719113 | + | 0.694893i | \(0.244548\pi\) | |||||||
\(138\) | −2.34425 | + | 1.70320i | −0.199556 | + | 0.144986i | ||||
\(139\) | 3.48270 | + | 10.7186i | 0.295399 | + | 0.909144i | 0.983087 | + | 0.183138i | \(0.0586255\pi\) |
−0.687688 | + | 0.726006i | \(0.741374\pi\) | |||||||
\(140\) | −0.866025 | + | 2.66535i | −0.0731925 | + | 0.225263i | ||||
\(141\) | 9.25068 | + | 6.72101i | 0.779048 | + | 0.566011i | ||||
\(142\) | −10.2181 | −0.857484 | ||||||||
\(143\) | 0.984267 | − | 2.72292i | 0.0823085 | − | 0.227702i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −5.04334 | − | 3.66420i | −0.418827 | − | 0.304296i | ||||
\(146\) | 4.85523 | − | 14.9428i | 0.401821 | − | 1.23668i | ||||
\(147\) | 0.309017 | + | 0.951057i | 0.0254873 | + | 0.0784418i | ||||
\(148\) | −4.80185 | + | 3.48875i | −0.394710 | + | 0.286773i | ||||
\(149\) | 1.23607 | − | 0.898056i | 0.101263 | − | 0.0735716i | −0.536002 | − | 0.844217i | \(-0.680066\pi\) |
0.637264 | + | 0.770645i | \(0.280066\pi\) | |||||||
\(150\) | −0.881966 | − | 2.71441i | −0.0720122 | − | 0.221631i | ||||
\(151\) | 3.97797 | − | 12.2429i | 0.323723 | − | 0.996316i | −0.648291 | − | 0.761392i | \(-0.724516\pi\) |
0.972014 | − | 0.234923i | \(-0.0754839\pi\) | |||||||
\(152\) | 2.89476 | + | 2.10317i | 0.234796 | + | 0.170589i | ||||
\(153\) | −4.84607 | −0.391781 | ||||||||
\(154\) | −3.31485 | − | 0.108436i | −0.267118 | − | 0.00873806i | ||||
\(155\) | −16.2944 | −1.30879 | ||||||||
\(156\) | −0.706258 | − | 0.513127i | −0.0565459 | − | 0.0410830i | ||||
\(157\) | 0.859067 | − | 2.64394i | 0.0685610 | − | 0.211009i | −0.910906 | − | 0.412614i | \(-0.864616\pi\) |
0.979467 | + | 0.201605i | \(0.0646157\pi\) | |||||||
\(158\) | 1.89878 | + | 5.84383i | 0.151058 | + | 0.464910i | ||||
\(159\) | −10.1109 | + | 7.34598i | −0.801844 | + | 0.582574i | ||||
\(160\) | −2.26728 | + | 1.64728i | −0.179245 | + | 0.130229i | ||||
\(161\) | −0.895424 | − | 2.75583i | −0.0705693 | − | 0.217190i | ||||
\(162\) | −0.309017 | + | 0.951057i | −0.0242787 | + | 0.0747221i | ||||
\(163\) | 6.85410 | + | 4.97980i | 0.536855 | + | 0.390048i | 0.822916 | − | 0.568164i | \(-0.192346\pi\) |
−0.286061 | + | 0.958211i | \(0.592346\pi\) | |||||||
\(164\) | −7.08214 | −0.553022 | ||||||||
\(165\) | 7.69433 | − | 5.21463i | 0.599003 | − | 0.405958i | ||||
\(166\) | −9.98782 | −0.775205 | ||||||||
\(167\) | 4.02264 | + | 2.92262i | 0.311282 | + | 0.226159i | 0.732446 | − | 0.680825i | \(-0.238379\pi\) |
−0.421165 | + | 0.906984i | \(0.638379\pi\) | |||||||
\(168\) | −0.309017 | + | 0.951057i | −0.0238412 | + | 0.0733756i | ||||
\(169\) | −3.78172 | − | 11.6389i | −0.290901 | − | 0.895303i | ||||
\(170\) | 10.9874 | − | 7.98282i | 0.842696 | − | 0.612254i | ||||
\(171\) | −2.89476 | + | 2.10317i | −0.221368 | + | 0.160833i | ||||
\(172\) | 1.15575 | + | 3.55703i | 0.0881251 | + | 0.271221i | ||||
\(173\) | −2.95107 | + | 9.08247i | −0.224366 | + | 0.690527i | 0.773989 | + | 0.633199i | \(0.218258\pi\) |
−0.998355 | + | 0.0573288i | \(0.981742\pi\) | |||||||
\(174\) | −1.79958 | − | 1.30747i | −0.136426 | − | 0.0991189i | ||||
\(175\) | 2.85410 | 0.215750 | ||||||||
\(176\) | −2.61803 | − | 2.03615i | −0.197342 | − | 0.153480i | ||||
\(177\) | 6.61670 | 0.497342 | ||||||||
\(178\) | −10.2706 | − | 7.46205i | −0.769817 | − | 0.559305i | ||||
\(179\) | 3.41541 | − | 10.5116i | 0.255280 | − | 0.785670i | −0.738495 | − | 0.674259i | \(-0.764463\pi\) |
0.993774 | − | 0.111411i | \(-0.0355370\pi\) | |||||||
\(180\) | −0.866025 | − | 2.66535i | −0.0645497 | − | 0.198664i | ||||
\(181\) | 3.24083 | − | 2.35460i | 0.240889 | − | 0.175016i | −0.460790 | − | 0.887509i | \(-0.652434\pi\) |
0.701679 | + | 0.712493i | \(0.252434\pi\) | |||||||
\(182\) | 0.706258 | − | 0.513127i | 0.0523514 | − | 0.0380355i | ||||
\(183\) | −3.19321 | − | 9.82769i | −0.236049 | − | 0.726484i | ||||
\(184\) | 0.895424 | − | 2.75583i | 0.0660115 | − | 0.203163i | ||||
\(185\) | 13.4573 | + | 9.77728i | 0.989398 | + | 0.718840i | ||||
\(186\) | −5.81419 | −0.426317 | ||||||||
\(187\) | 12.6872 | + | 9.86731i | 0.927778 | + | 0.721569i | ||||
\(188\) | −11.4345 | −0.833944 | ||||||||
\(189\) | −0.809017 | − | 0.587785i | −0.0588473 | − | 0.0427551i | ||||
\(190\) | 3.09874 | − | 9.53695i | 0.224806 | − | 0.691883i | ||||
\(191\) | 2.40305 | + | 7.39582i | 0.173878 | + | 0.535143i | 0.999580 | − | 0.0289638i | \(-0.00922076\pi\) |
−0.825702 | + | 0.564106i | \(0.809221\pi\) | |||||||
\(192\) | −0.809017 | + | 0.587785i | −0.0583858 | + | 0.0424197i | ||||
\(193\) | 13.6541 | − | 9.92031i | 0.982846 | − | 0.714080i | 0.0245033 | − | 0.999700i | \(-0.492200\pi\) |
0.958343 | + | 0.285620i | \(0.0921996\pi\) | |||||||
\(194\) | 0.896958 | + | 2.76055i | 0.0643979 | + | 0.198196i | ||||
\(195\) | −0.756026 | + | 2.32681i | −0.0541401 | + | 0.166626i | ||||
\(196\) | −0.809017 | − | 0.587785i | −0.0577869 | − | 0.0419847i | ||||
\(197\) | −10.6863 | −0.761371 | −0.380685 | − | 0.924705i | \(-0.624312\pi\) | ||||
−0.380685 | + | 0.924705i | \(0.624312\pi\) | |||||||
\(198\) | 2.74551 | − | 1.86069i | 0.195115 | − | 0.132234i | ||||
\(199\) | −19.4630 | −1.37970 | −0.689849 | − | 0.723954i | \(-0.742323\pi\) | ||||
−0.689849 | + | 0.723954i | \(0.742323\pi\) | |||||||
\(200\) | 2.30902 | + | 1.67760i | 0.163272 | + | 0.118624i | ||||
\(201\) | −2.46837 | + | 7.59687i | −0.174106 | + | 0.535842i | ||||
\(202\) | 1.84218 | + | 5.66964i | 0.129615 | + | 0.398915i | ||||
\(203\) | 1.79958 | − | 1.30747i | 0.126305 | − | 0.0917663i | ||||
\(204\) | 3.92055 | − | 2.84845i | 0.274493 | − | 0.199431i | ||||
\(205\) | 6.13331 | + | 18.8764i | 0.428369 | + | 1.31838i | ||||
\(206\) | 0.800288 | − | 2.46303i | 0.0557587 | − | 0.171608i | ||||
\(207\) | 2.34425 | + | 1.70320i | 0.162937 | + | 0.118380i | ||||
\(208\) | 0.872983 | 0.0605305 | ||||||||
\(209\) | 11.8609 | + | 0.387998i | 0.820438 | + | 0.0268384i | ||||
\(210\) | 2.80252 | 0.193392 | ||||||||
\(211\) | 2.48480 | + | 1.80531i | 0.171061 | + | 0.124283i | 0.670022 | − | 0.742342i | \(-0.266285\pi\) |
−0.498961 | + | 0.866625i | \(0.666285\pi\) | |||||||
\(212\) | 3.86201 | − | 11.8860i | 0.265244 | − | 0.816337i | ||||
\(213\) | 3.15757 | + | 9.71799i | 0.216353 | + | 0.665866i | ||||
\(214\) | −6.30943 | + | 4.58407i | −0.431304 | + | 0.313360i | ||||
\(215\) | 8.47983 | − | 6.16096i | 0.578320 | − | 0.420174i | ||||
\(216\) | −0.309017 | − | 0.951057i | −0.0210259 | − | 0.0647112i | ||||
\(217\) | 1.79668 | − | 5.52962i | 0.121967 | − | 0.375375i | ||||
\(218\) | −9.40689 | − | 6.83450i | −0.637115 | − | 0.462891i | ||||
\(219\) | −15.7118 | −1.06171 | ||||||||
\(220\) | −3.15977 | + | 8.74134i | −0.213031 | + | 0.589341i | ||||
\(221\) | −4.23054 | −0.284577 | ||||||||
\(222\) | 4.80185 | + | 3.48875i | 0.322279 | + | 0.234150i | ||||
\(223\) | 4.49375 | − | 13.8304i | 0.300924 | − | 0.926149i | −0.680243 | − | 0.732987i | \(-0.738126\pi\) |
0.981167 | − | 0.193162i | \(-0.0618743\pi\) | |||||||
\(224\) | −0.309017 | − | 0.951057i | −0.0206471 | − | 0.0635451i | ||||
\(225\) | −2.30902 | + | 1.67760i | −0.153934 | + | 0.111840i | ||||
\(226\) | 11.5444 | − | 8.38751i | 0.767923 | − | 0.557929i | ||||
\(227\) | −7.93135 | − | 24.4102i | −0.526422 | − | 1.62016i | −0.761486 | − | 0.648181i | \(-0.775530\pi\) |
0.235064 | − | 0.971980i | \(-0.424470\pi\) | |||||||
\(228\) | 1.10570 | − | 3.40299i | 0.0732267 | − | 0.225369i | ||||
\(229\) | 4.40937 | + | 3.20359i | 0.291379 | + | 0.211699i | 0.723866 | − | 0.689941i | \(-0.242364\pi\) |
−0.432486 | + | 0.901641i | \(0.642364\pi\) | |||||||
\(230\) | −8.12072 | −0.535464 | ||||||||
\(231\) | 0.921216 | + | 3.18612i | 0.0606116 | + | 0.209631i | ||||
\(232\) | 2.22440 | 0.146039 | ||||||||
\(233\) | 23.4499 | + | 17.0373i | 1.53625 | + | 1.11615i | 0.952631 | + | 0.304129i | \(0.0983655\pi\) |
0.583623 | + | 0.812025i | \(0.301635\pi\) | |||||||
\(234\) | −0.269767 | + | 0.830257i | −0.0176352 | + | 0.0542756i | ||||
\(235\) | 9.90254 | + | 30.4769i | 0.645970 | + | 1.98809i | ||||
\(236\) | −5.35303 | + | 3.88920i | −0.348452 | + | 0.253165i | ||||
\(237\) | 4.97106 | − | 3.61169i | 0.322905 | − | 0.234604i | ||||
\(238\) | 1.49752 | + | 4.60888i | 0.0970696 | + | 0.298750i | ||||
\(239\) | −8.42196 | + | 25.9201i | −0.544771 | + | 1.67663i | 0.176762 | + | 0.984254i | \(0.443438\pi\) |
−0.721533 | + | 0.692380i | \(0.756562\pi\) | |||||||
\(240\) | 2.26728 | + | 1.64728i | 0.146353 | + | 0.106331i | ||||
\(241\) | 13.6089 | 0.876628 | 0.438314 | − | 0.898822i | \(-0.355576\pi\) | ||||
0.438314 | + | 0.898822i | \(0.355576\pi\) | |||||||
\(242\) | −10.9765 | − | 0.718901i | −0.705595 | − | 0.0462127i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 8.35994 | + | 6.07385i | 0.535190 | + | 0.388838i | ||||
\(245\) | −0.866025 | + | 2.66535i | −0.0553283 | + | 0.170283i | ||||
\(246\) | 2.18850 | + | 6.73551i | 0.139534 | + | 0.429441i | ||||
\(247\) | −2.52708 | + | 1.83603i | −0.160794 | + | 0.116824i | ||||
\(248\) | 4.70378 | − | 3.41749i | 0.298690 | − | 0.217011i | ||||
\(249\) | 3.08641 | + | 9.49898i | 0.195593 | + | 0.601974i | ||||
\(250\) | −1.85840 | + | 5.71957i | −0.117536 | + | 0.361738i | ||||
\(251\) | 18.2010 | + | 13.2238i | 1.14884 | + | 0.834681i | 0.988326 | − | 0.152353i | \(-0.0486851\pi\) |
0.160513 | + | 0.987034i | \(0.448685\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | −2.66936 | − | 9.23227i | −0.167822 | − | 0.580428i | ||||
\(254\) | 14.1485 | 0.887753 | ||||||||
\(255\) | −10.9874 | − | 7.98282i | −0.688058 | − | 0.499904i | ||||
\(256\) | 0.309017 | − | 0.951057i | 0.0193136 | − | 0.0594410i | ||||
\(257\) | −1.19769 | − | 3.68610i | −0.0747097 | − | 0.229933i | 0.906727 | − | 0.421717i | \(-0.138573\pi\) |
−0.981437 | + | 0.191785i | \(0.938573\pi\) | |||||||
\(258\) | 3.02579 | − | 2.19837i | 0.188378 | − | 0.136864i | ||||
\(259\) | −4.80185 | + | 3.48875i | −0.298373 | + | 0.216780i | ||||
\(260\) | −0.756026 | − | 2.32681i | −0.0468867 | − | 0.144303i | ||||
\(261\) | −0.687377 | + | 2.11553i | −0.0425476 | + | 0.130948i | ||||
\(262\) | 10.1138 | + | 7.34811i | 0.624833 | + | 0.453968i | ||||
\(263\) | 3.53672 | 0.218084 | 0.109042 | − | 0.994037i | \(-0.465222\pi\) | ||||
0.109042 | + | 0.994037i | \(0.465222\pi\) | |||||||
\(264\) | −1.12747 | + | 3.11910i | −0.0693913 | + | 0.191967i | ||||
\(265\) | −35.0251 | −2.15157 | ||||||||
\(266\) | 2.89476 | + | 2.10317i | 0.177489 | + | 0.128953i | ||||
\(267\) | −3.92303 | + | 12.0739i | −0.240086 | + | 0.738908i | ||||
\(268\) | −2.46837 | − | 7.59687i | −0.150780 | − | 0.464053i | ||||
\(269\) | 21.1862 | − | 15.3927i | 1.29175 | − | 0.938509i | 0.291908 | − | 0.956447i | \(-0.405710\pi\) |
0.999839 | + | 0.0179376i | \(0.00571002\pi\) | |||||||
\(270\) | −2.26728 | + | 1.64728i | −0.137983 | + | 0.100250i | ||||
\(271\) | 2.58528 | + | 7.95668i | 0.157045 | + | 0.483334i | 0.998362 | − | 0.0572070i | \(-0.0182195\pi\) |
−0.841318 | + | 0.540541i | \(0.818220\pi\) | |||||||
\(272\) | −1.49752 | + | 4.60888i | −0.0908003 | + | 0.279455i | ||||
\(273\) | −0.706258 | − | 0.513127i | −0.0427447 | − | 0.0310558i | ||||
\(274\) | 4.05747 | 0.245121 | ||||||||
\(275\) | 9.46092 | + | 0.309489i | 0.570515 | + | 0.0186629i | ||||
\(276\) | −2.89765 | −0.174418 | ||||||||
\(277\) | 4.24799 | + | 3.08635i | 0.255237 | + | 0.185441i | 0.708045 | − | 0.706168i | \(-0.249578\pi\) |
−0.452808 | + | 0.891608i | \(0.649578\pi\) | |||||||
\(278\) | −3.48270 | + | 10.7186i | −0.208878 | + | 0.642862i | ||||
\(279\) | 1.79668 | + | 5.52962i | 0.107565 | + | 0.331050i | ||||
\(280\) | −2.26728 | + | 1.64728i | −0.135496 | + | 0.0984437i | ||||
\(281\) | 5.53275 | − | 4.01978i | 0.330056 | − | 0.239800i | −0.410398 | − | 0.911906i | \(-0.634610\pi\) |
0.740454 | + | 0.672107i | \(0.234610\pi\) | |||||||
\(282\) | 3.53344 | + | 10.8748i | 0.210414 | + | 0.647586i | ||||
\(283\) | 1.34801 | − | 4.14876i | 0.0801311 | − | 0.246618i | −0.902963 | − | 0.429718i | \(-0.858613\pi\) |
0.983094 | + | 0.183100i | \(0.0586131\pi\) | |||||||
\(284\) | −8.26662 | − | 6.00605i | −0.490534 | − | 0.356394i | ||||
\(285\) | −10.0277 | −0.593992 | ||||||||
\(286\) | 2.39678 | − | 1.62435i | 0.141725 | − | 0.0960501i | ||||
\(287\) | −7.08214 | −0.418045 | ||||||||
\(288\) | 0.809017 | + | 0.587785i | 0.0476718 | + | 0.0346356i | ||||
\(289\) | 2.00378 | − | 6.16700i | 0.117869 | − | 0.362765i | ||||
\(290\) | −1.92639 | − | 5.92881i | −0.113121 | − | 0.348151i | ||||
\(291\) | 2.34827 | − | 1.70612i | 0.137658 | − | 0.100014i | ||||
\(292\) | 12.7111 | − | 9.23519i | 0.743863 | − | 0.540448i | ||||
\(293\) | −6.02717 | − | 18.5497i | −0.352111 | − | 1.08369i | −0.957666 | − | 0.287883i | \(-0.907049\pi\) |
0.605555 | − | 0.795804i | \(-0.292951\pi\) | |||||||
\(294\) | −0.309017 | + | 0.951057i | −0.0180222 | + | 0.0554667i | ||||
\(295\) | 15.0019 | + | 10.8996i | 0.873447 | + | 0.634596i | ||||
\(296\) | −5.93542 | −0.344989 | ||||||||
\(297\) | −2.61803 | − | 2.03615i | −0.151914 | − | 0.118149i | ||||
\(298\) | 1.52786 | 0.0885068 | ||||||||
\(299\) | 2.04649 | + | 1.48686i | 0.118352 | + | 0.0859875i | ||||
\(300\) | 0.881966 | − | 2.71441i | 0.0509203 | − | 0.156717i | ||||
\(301\) | 1.15575 | + | 3.55703i | 0.0666163 | + | 0.205024i | ||||
\(302\) | 10.4145 | − | 7.56655i | 0.599285 | − | 0.435406i | ||||
\(303\) | 4.82289 | − | 3.50403i | 0.277068 | − | 0.201301i | ||||
\(304\) | 1.10570 | + | 3.40299i | 0.0634162 | + | 0.195175i | ||||
\(305\) | 8.94903 | − | 27.5423i | 0.512420 | − | 1.57707i | ||||
\(306\) | −3.92055 | − | 2.84845i | −0.224123 | − | 0.162835i | ||||
\(307\) | 12.2886 | 0.701346 | 0.350673 | − | 0.936498i | \(-0.385953\pi\) | ||||
0.350673 | + | 0.936498i | \(0.385953\pi\) | |||||||
\(308\) | −2.61803 | − | 2.03615i | −0.149176 | − | 0.116020i | ||||
\(309\) | −2.58979 | −0.147328 | ||||||||
\(310\) | −13.1824 | − | 9.57758i | −0.748711 | − | 0.543970i | ||||
\(311\) | 9.98994 | − | 30.7459i | 0.566478 | − | 1.74344i | −0.0970425 | − | 0.995280i | \(-0.530938\pi\) |
0.663520 | − | 0.748158i | \(-0.269062\pi\) | |||||||
\(312\) | −0.269767 | − | 0.830257i | −0.0152725 | − | 0.0470040i | ||||
\(313\) | 18.2239 | − | 13.2404i | 1.03008 | − | 0.748393i | 0.0617515 | − | 0.998092i | \(-0.480331\pi\) |
0.968324 | + | 0.249698i | \(0.0803314\pi\) | |||||||
\(314\) | 2.24907 | − | 1.63404i | 0.126922 | − | 0.0922144i | ||||
\(315\) | −0.866025 | − | 2.66535i | −0.0487950 | − | 0.150176i | ||||
\(316\) | −1.89878 | + | 5.84383i | −0.106814 | + | 0.328741i | ||||
\(317\) | 2.22622 | + | 1.61744i | 0.125037 | + | 0.0908445i | 0.648546 | − | 0.761176i | \(-0.275377\pi\) |
−0.523509 | + | 0.852020i | \(0.675377\pi\) | |||||||
\(318\) | −12.4977 | −0.700837 | ||||||||
\(319\) | 6.10711 | − | 4.13893i | 0.341932 | − | 0.231735i | ||||
\(320\) | −2.80252 | −0.156665 | ||||||||
\(321\) | 6.30943 | + | 4.58407i | 0.352158 | + | 0.255858i | ||||
\(322\) | 0.895424 | − | 2.75583i | 0.0499000 | − | 0.153576i | ||||
\(323\) | −5.35829 | − | 16.4911i | −0.298143 | − | 0.917591i | ||||
\(324\) | −0.809017 | + | 0.587785i | −0.0449454 | + | 0.0326547i | ||||
\(325\) | −2.01573 | + | 1.46452i | −0.111813 | + | 0.0812367i | ||||
\(326\) | 2.61803 | + | 8.05748i | 0.144999 | + | 0.446263i | ||||
\(327\) | −3.59311 | + | 11.0585i | −0.198699 | + | 0.611534i | ||||
\(328\) | −5.72957 | − | 4.16277i | −0.316362 | − | 0.229851i | ||||
\(329\) | −11.4345 | −0.630403 | ||||||||
\(330\) | 9.28993 | + | 0.303895i | 0.511394 | + | 0.0167289i | ||||
\(331\) | −14.4366 | −0.793508 | −0.396754 | − | 0.917925i | \(-0.629863\pi\) | ||||
−0.396754 | + | 0.917925i | \(0.629863\pi\) | |||||||
\(332\) | −8.08032 | − | 5.87069i | −0.443465 | − | 0.322196i | ||||
\(333\) | 1.83414 | − | 5.64492i | 0.100510 | − | 0.309339i | ||||
\(334\) | 1.53651 | + | 4.72890i | 0.0840743 | + | 0.258754i | ||||
\(335\) | −18.1107 | + | 13.1582i | −0.989491 | + | 0.718907i | ||||
\(336\) | −0.809017 | + | 0.587785i | −0.0441355 | + | 0.0320663i | ||||
\(337\) | 6.69252 | + | 20.5975i | 0.364565 | + | 1.12201i | 0.950253 | + | 0.311478i | \(0.100824\pi\) |
−0.585689 | + | 0.810536i | \(0.699176\pi\) | |||||||
\(338\) | 3.78172 | − | 11.6389i | 0.205698 | − | 0.633075i | ||||
\(339\) | −11.5444 | − | 8.38751i | −0.627007 | − | 0.455547i | ||||
\(340\) | 13.5812 | 0.736543 | ||||||||
\(341\) | 6.55535 | − | 18.1350i | 0.354992 | − | 0.982068i | ||||
\(342\) | −3.57812 | −0.193482 | ||||||||
\(343\) | −0.809017 | − | 0.587785i | −0.0436828 | − | 0.0317374i | ||||
\(344\) | −1.15575 | + | 3.55703i | −0.0623139 | + | 0.191782i | ||||
\(345\) | 2.50944 | + | 7.72326i | 0.135104 | + | 0.415807i | ||||
\(346\) | −7.72601 | + | 5.61327i | −0.415353 | + | 0.301771i | ||||
\(347\) | −13.3245 | + | 9.68085i | −0.715299 | + | 0.519695i | −0.884879 | − | 0.465821i | \(-0.845759\pi\) |
0.169580 | + | 0.985516i | \(0.445759\pi\) | |||||||
\(348\) | −0.687377 | − | 2.11553i | −0.0368473 | − | 0.113404i | ||||
\(349\) | 3.65411 | − | 11.2462i | 0.195600 | − | 0.601995i | −0.804369 | − | 0.594130i | \(-0.797497\pi\) |
0.999969 | − | 0.00786475i | \(-0.00250345\pi\) | |||||||
\(350\) | 2.30902 | + | 1.67760i | 0.123422 | + | 0.0896714i | ||||
\(351\) | 0.872983 | 0.0465964 | ||||||||
\(352\) | −0.921216 | − | 3.18612i | −0.0491010 | − | 0.169821i | ||||
\(353\) | 23.8231 | 1.26798 | 0.633989 | − | 0.773342i | \(-0.281417\pi\) | ||||
0.633989 | + | 0.773342i | \(0.281417\pi\) | |||||||
\(354\) | 5.35303 | + | 3.88920i | 0.284510 | + | 0.206709i | ||||
\(355\) | −8.84914 | + | 27.2348i | −0.469663 | + | 1.44548i | ||||
\(356\) | −3.92303 | − | 12.0739i | −0.207920 | − | 0.639913i | ||||
\(357\) | 3.92055 | − | 2.84845i | 0.207498 | − | 0.150756i | ||||
\(358\) | 8.94166 | − | 6.49650i | 0.472581 | − | 0.343351i | ||||
\(359\) | −6.24861 | − | 19.2312i | −0.329789 | − | 1.01499i | −0.969232 | − | 0.246148i | \(-0.920835\pi\) |
0.639444 | − | 0.768838i | \(-0.279165\pi\) | |||||||
\(360\) | 0.866025 | − | 2.66535i | 0.0456435 | − | 0.140476i | ||||
\(361\) | 5.01353 | + | 3.64255i | 0.263870 | + | 0.191713i | ||||
\(362\) | 4.00588 | 0.210544 | ||||||||
\(363\) | 2.70820 | + | 10.6614i | 0.142144 | + | 0.559579i | ||||
\(364\) | 0.872983 | 0.0457568 | ||||||||
\(365\) | −35.6232 | − | 25.8818i | −1.86460 | − | 1.35471i | ||||
\(366\) | 3.19321 | − | 9.82769i | 0.166912 | − | 0.513702i | ||||
\(367\) | −3.86715 | − | 11.9019i | −0.201864 | − | 0.621272i | −0.999828 | − | 0.0185670i | \(-0.994090\pi\) |
0.797964 | − | 0.602705i | \(-0.205910\pi\) | |||||||
\(368\) | 2.34425 | − | 1.70320i | 0.122202 | − | 0.0887853i | ||||
\(369\) | 5.72957 | − | 4.16277i | 0.298269 | − | 0.216705i | ||||
\(370\) | 5.14022 | + | 15.8200i | 0.267227 | + | 0.822441i | ||||
\(371\) | 3.86201 | − | 11.8860i | 0.200505 | − | 0.617092i | ||||
\(372\) | −4.70378 | − | 3.41749i | −0.243879 | − | 0.177189i | ||||
\(373\) | −35.4217 | −1.83407 | −0.917034 | − | 0.398810i | \(-0.869423\pi\) | ||||
−0.917034 | + | 0.398810i | \(0.869423\pi\) | |||||||
\(374\) | 4.46428 | + | 15.4402i | 0.230842 | + | 0.798391i | ||||
\(375\) | 6.01392 | 0.310557 | ||||||||
\(376\) | −9.25068 | − | 6.72101i | −0.477067 | − | 0.346610i | ||||
\(377\) | −0.600069 | + | 1.84682i | −0.0309051 | + | 0.0951161i | ||||
\(378\) | −0.309017 | − | 0.951057i | −0.0158941 | − | 0.0489171i | ||||
\(379\) | −15.3611 | + | 11.1605i | −0.789045 | + | 0.573274i | −0.907680 | − | 0.419663i | \(-0.862148\pi\) |
0.118635 | + | 0.992938i | \(0.462148\pi\) | |||||||
\(380\) | 8.11261 | − | 5.89416i | 0.416168 | − | 0.302364i | ||||
\(381\) | −4.37211 | − | 13.4560i | −0.223990 | − | 0.689371i | ||||
\(382\) | −2.40305 | + | 7.39582i | −0.122951 | + | 0.378403i | ||||
\(383\) | −9.08802 | − | 6.60283i | −0.464376 | − | 0.337389i | 0.330869 | − | 0.943677i | \(-0.392658\pi\) |
−0.795245 | + | 0.606288i | \(0.792658\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −3.15977 | + | 8.74134i | −0.161037 | + | 0.445500i | ||||
\(386\) | 16.8774 | 0.859039 | ||||||||
\(387\) | −3.02579 | − | 2.19837i | −0.153810 | − | 0.111749i | ||||
\(388\) | −0.896958 | + | 2.76055i | −0.0455362 | + | 0.140146i | ||||
\(389\) | 8.22571 | + | 25.3161i | 0.417060 | + | 1.28358i | 0.910395 | + | 0.413739i | \(0.135778\pi\) |
−0.493335 | + | 0.869839i | \(0.664222\pi\) | |||||||
\(390\) | −1.97930 | + | 1.43805i | −0.100226 | + | 0.0728183i | ||||
\(391\) | −11.3604 | + | 8.25381i | −0.574520 | + | 0.417413i | ||||
\(392\) | −0.309017 | − | 0.951057i | −0.0156077 | − | 0.0480356i | ||||
\(393\) | 3.86313 | − | 11.8895i | 0.194869 | − | 0.599746i | ||||
\(394\) | −8.64544 | − | 6.28128i | −0.435551 | − | 0.316446i | ||||
\(395\) | 17.2203 | 0.866445 | ||||||||
\(396\) | 3.31485 | + | 0.108436i | 0.166578 | + | 0.00544914i | ||||
\(397\) | −19.5534 | −0.981359 | −0.490680 | − | 0.871340i | \(-0.663251\pi\) | ||||
−0.490680 | + | 0.871340i | \(0.663251\pi\) | |||||||
\(398\) | −15.7459 | − | 11.4401i | −0.789272 | − | 0.573439i | ||||
\(399\) | 1.10570 | − | 3.40299i | 0.0553542 | − | 0.170363i | ||||
\(400\) | 0.881966 | + | 2.71441i | 0.0440983 | + | 0.135721i | ||||
\(401\) | 4.10135 | − | 2.97981i | 0.204812 | − | 0.148804i | −0.480651 | − | 0.876912i | \(-0.659600\pi\) |
0.685463 | + | 0.728107i | \(0.259600\pi\) | |||||||
\(402\) | −6.46228 | + | 4.69512i | −0.322309 | + | 0.234172i | ||||
\(403\) | 1.56847 | + | 4.82727i | 0.0781312 | + | 0.240463i | ||||
\(404\) | −1.84218 | + | 5.66964i | −0.0916518 | + | 0.282075i | ||||
\(405\) | 2.26728 | + | 1.64728i | 0.112662 | + | 0.0818539i | ||||
\(406\) | 2.22440 | 0.110395 | ||||||||
\(407\) | −16.2957 | + | 11.0440i | −0.807750 | + | 0.547430i | ||||
\(408\) | 4.84607 | 0.239916 | ||||||||
\(409\) | 1.84391 | + | 1.33968i | 0.0911757 | + | 0.0662430i | 0.632439 | − | 0.774610i | \(-0.282054\pi\) |
−0.541263 | + | 0.840853i | \(0.682054\pi\) | |||||||
\(410\) | −6.13331 | + | 18.8764i | −0.302903 | + | 0.932238i | ||||
\(411\) | −1.25383 | − | 3.85888i | −0.0618467 | − | 0.190345i | ||||
\(412\) | 2.09518 | − | 1.52224i | 0.103222 | − | 0.0749953i | ||||
\(413\) | −5.35303 | + | 3.88920i | −0.263405 | + | 0.191375i | ||||
\(414\) | 0.895424 | + | 2.75583i | 0.0440077 | + | 0.135442i | ||||
\(415\) | −8.64971 | + | 26.6211i | −0.424597 | + | 1.30678i | ||||
\(416\) | 0.706258 | + | 0.513127i | 0.0346272 | + | 0.0251581i | ||||
\(417\) | 11.2703 | 0.551907 | ||||||||
\(418\) | 9.36764 | + | 7.28558i | 0.458186 | + | 0.356349i | ||||
\(419\) | −20.6719 | −1.00989 | −0.504945 | − | 0.863152i | \(-0.668487\pi\) | ||||
−0.504945 | + | 0.863152i | \(0.668487\pi\) | |||||||
\(420\) | 2.26728 | + | 1.64728i | 0.110632 | + | 0.0803789i | ||||
\(421\) | −6.18853 | + | 19.0463i | −0.301610 | + | 0.928262i | 0.679310 | + | 0.733852i | \(0.262279\pi\) |
−0.980920 | + | 0.194410i | \(0.937721\pi\) | |||||||
\(422\) | 0.949109 | + | 2.92106i | 0.0462019 | + | 0.142195i | ||||
\(423\) | 9.25068 | − | 6.72101i | 0.449783 | − | 0.326787i | ||||
\(424\) | 10.1109 | − | 7.34598i | 0.491027 | − | 0.356752i | ||||
\(425\) | −4.27407 | − | 13.1542i | −0.207323 | − | 0.638074i | ||||
\(426\) | −3.15757 | + | 9.71799i | −0.152985 | + | 0.470838i | ||||
\(427\) | 8.35994 | + | 6.07385i | 0.404566 | + | 0.293934i | ||||
\(428\) | −7.79888 | −0.376973 | ||||||||
\(429\) | −2.28550 | − | 1.77752i | −0.110345 | − | 0.0858196i | ||||
\(430\) | 10.4817 | 0.505470 | ||||||||
\(431\) | −23.5646 | − | 17.1207i | −1.13507 | − | 0.824674i | −0.148642 | − | 0.988891i | \(-0.547490\pi\) |
−0.986424 | + | 0.164217i | \(0.947490\pi\) | |||||||
\(432\) | 0.309017 | − | 0.951057i | 0.0148676 | − | 0.0457577i | ||||
\(433\) | −6.59600 | − | 20.3004i | −0.316984 | − | 0.975576i | −0.974930 | − | 0.222511i | \(-0.928575\pi\) |
0.657946 | − | 0.753065i | \(-0.271425\pi\) | |||||||
\(434\) | 4.70378 | − | 3.41749i | 0.225788 | − | 0.164045i | ||||
\(435\) | −5.04334 | + | 3.66420i | −0.241810 | + | 0.175685i | ||||
\(436\) | −3.59311 | − | 11.0585i | −0.172079 | − | 0.529604i | ||||
\(437\) | −3.20393 | + | 9.86069i | −0.153265 | + | 0.471701i | ||||
\(438\) | −12.7111 | − | 9.23519i | −0.607362 | − | 0.441274i | ||||
\(439\) | 26.9372 | 1.28564 | 0.642820 | − | 0.766017i | \(-0.277764\pi\) | ||||
0.642820 | + | 0.766017i | \(0.277764\pi\) | |||||||
\(440\) | −7.69433 | + | 5.21463i | −0.366813 | + | 0.248598i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −3.42258 | − | 2.48665i | −0.162795 | − | 0.118278i | ||||
\(443\) | −3.25160 | + | 10.0074i | −0.154488 | + | 0.475465i | −0.998109 | − | 0.0614744i | \(-0.980420\pi\) |
0.843621 | + | 0.536940i | \(0.180420\pi\) | |||||||
\(444\) | 1.83414 | + | 5.64492i | 0.0870446 | + | 0.267896i | ||||
\(445\) | −28.7836 | + | 20.9125i | −1.36448 | + | 0.991349i | ||||
\(446\) | 11.7648 | − | 8.54763i | 0.557079 | − | 0.404742i | ||||
\(447\) | −0.472136 | − | 1.45309i | −0.0223313 | − | 0.0687286i | ||||
\(448\) | 0.309017 | − | 0.951057i | 0.0145997 | − | 0.0449332i | ||||
\(449\) | 27.2327 | + | 19.7857i | 1.28519 | + | 0.933746i | 0.999697 | − | 0.0246343i | \(-0.00784212\pi\) |
0.285495 | + | 0.958380i | \(0.407842\pi\) | |||||||
\(450\) | −2.85410 | −0.134544 | ||||||||
\(451\) | −23.4762 | − | 0.767962i | −1.10545 | − | 0.0361619i | ||||
\(452\) | 14.2697 | 0.671190 | ||||||||
\(453\) | −10.4145 | − | 7.56655i | −0.489314 | − | 0.355508i | ||||
\(454\) | 7.93135 | − | 24.4102i | 0.372237 | − | 1.14563i | ||||
\(455\) | −0.756026 | − | 2.32681i | −0.0354430 | − | 0.109082i | ||||
\(456\) | 2.89476 | − | 2.10317i | 0.135559 | − | 0.0984897i | ||||
\(457\) | 0.579449 | − | 0.420994i | 0.0271055 | − | 0.0196933i | −0.574150 | − | 0.818750i | \(-0.694667\pi\) |
0.601256 | + | 0.799057i | \(0.294667\pi\) | |||||||
\(458\) | 1.68423 | + | 5.18352i | 0.0786989 | + | 0.242210i | ||||
\(459\) | −1.49752 | + | 4.60888i | −0.0698981 | + | 0.215124i | ||||
\(460\) | −6.56980 | − | 4.77324i | −0.306319 | − | 0.222553i | ||||
\(461\) | −9.64710 | −0.449310 | −0.224655 | − | 0.974438i | \(-0.572126\pi\) | ||||
−0.224655 | + | 0.974438i | \(0.572126\pi\) | |||||||
\(462\) | −1.12747 | + | 3.11910i | −0.0524549 | + | 0.145114i | ||||
\(463\) | −19.6747 | −0.914360 | −0.457180 | − | 0.889374i | \(-0.651140\pi\) | ||||
−0.457180 | + | 0.889374i | \(0.651140\pi\) | |||||||
\(464\) | 1.79958 | + | 1.30747i | 0.0835432 | + | 0.0606977i | ||||
\(465\) | −5.03523 | + | 15.4969i | −0.233503 | + | 0.718649i | ||||
\(466\) | 8.95706 | + | 27.5670i | 0.414928 | + | 1.27702i | ||||
\(467\) | 26.0857 | − | 18.9524i | 1.20710 | − | 0.877011i | 0.212137 | − | 0.977240i | \(-0.431958\pi\) |
0.994964 | + | 0.100229i | \(0.0319575\pi\) | |||||||
\(468\) | −0.706258 | + | 0.513127i | −0.0326468 | + | 0.0237193i | ||||
\(469\) | −2.46837 | − | 7.59687i | −0.113979 | − | 0.350791i | ||||
\(470\) | −9.90254 | + | 30.4769i | −0.456770 | + | 1.40579i | ||||
\(471\) | −2.24907 | − | 1.63404i | −0.103632 | − | 0.0752927i | ||||
\(472\) | −6.61670 | −0.304558 | ||||||||
\(473\) | 3.44543 | + | 11.9164i | 0.158421 | + | 0.547915i | ||||
\(474\) | 6.14457 | 0.282229 | ||||||||
\(475\) | −8.26194 | − | 6.00265i | −0.379084 | − | 0.275420i | ||||
\(476\) | −1.49752 | + | 4.60888i | −0.0686386 | + | 0.211248i | ||||
\(477\) | 3.86201 | + | 11.8860i | 0.176829 | + | 0.544224i | ||||
\(478\) | −22.0490 | + | 16.0195i | −1.00850 | + | 0.732716i | ||||
\(479\) | −1.00215 | + | 0.728107i | −0.0457895 | + | 0.0332680i | −0.610445 | − | 0.792059i | \(-0.709009\pi\) |
0.564655 | + | 0.825327i | \(0.309009\pi\) | |||||||
\(480\) | 0.866025 | + | 2.66535i | 0.0395285 | + | 0.121656i | ||||
\(481\) | 1.60118 | − | 4.92792i | 0.0730074 | − | 0.224694i | ||||
\(482\) | 11.0099 | + | 7.99913i | 0.501485 | + | 0.364350i | ||||
\(483\) | −2.89765 | −0.131848 | ||||||||
\(484\) | −8.45760 | − | 7.03342i | −0.384436 | − | 0.319701i | ||||
\(485\) | 8.13464 | 0.369375 | ||||||||
\(486\) | 0.809017 | + | 0.587785i | 0.0366978 | + | 0.0266625i | ||||
\(487\) | 8.47953 | − | 26.0973i | 0.384244 | − | 1.18258i | −0.552783 | − | 0.833326i | \(-0.686434\pi\) |
0.937027 | − | 0.349257i | \(-0.113566\pi\) | |||||||
\(488\) | 3.19321 | + | 9.82769i | 0.144550 | + | 0.444879i | ||||
\(489\) | 6.85410 | − | 4.97980i | 0.309953 | − | 0.225194i | ||||
\(490\) | −2.26728 | + | 1.64728i | −0.102425 | + | 0.0744164i | ||||
\(491\) | −6.79281 | − | 20.9061i | −0.306555 | − | 0.943480i | −0.979092 | − | 0.203417i | \(-0.934795\pi\) |
0.672537 | − | 0.740064i | \(-0.265205\pi\) | |||||||
\(492\) | −2.18850 | + | 6.73551i | −0.0986652 | + | 0.303660i | ||||
\(493\) | −8.72087 | − | 6.33608i | −0.392768 | − | 0.285363i | ||||
\(494\) | −3.12364 | −0.140539 | ||||||||
\(495\) | −2.58172 | − | 8.92916i | −0.116040 | − | 0.401336i | ||||
\(496\) | 5.81419 | 0.261065 | ||||||||
\(497\) | −8.26662 | − | 6.00605i | −0.370809 | − | 0.269408i | ||||
\(498\) | −3.08641 | + | 9.49898i | −0.138305 | + | 0.425660i | ||||
\(499\) | 9.35415 | + | 28.7891i | 0.418749 | + | 1.28878i | 0.908854 | + | 0.417114i | \(0.136958\pi\) |
−0.490105 | + | 0.871663i | \(0.663042\pi\) | |||||||
\(500\) | −4.86536 | + | 3.53489i | −0.217586 | + | 0.158085i | ||||
\(501\) | 4.02264 | − | 2.92262i | 0.179718 | − | 0.130573i | ||||
\(502\) | 6.95218 | + | 21.3966i | 0.310291 | + | 0.954977i | ||||
\(503\) | −0.123254 | + | 0.379336i | −0.00549561 | + | 0.0169137i | −0.953767 | − | 0.300548i | \(-0.902830\pi\) |
0.948271 | + | 0.317462i | \(0.102830\pi\) | |||||||
\(504\) | 0.809017 | + | 0.587785i | 0.0360365 | + | 0.0261820i | ||||
\(505\) | 16.7070 | 0.743450 | ||||||||
\(506\) | 3.26703 | − | 9.03808i | 0.145237 | − | 0.401791i | ||||
\(507\) | −12.2379 | −0.543504 | ||||||||
\(508\) | 11.4463 | + | 8.31626i | 0.507849 | + | 0.368974i | ||||
\(509\) | −4.22829 | + | 13.0133i | −0.187416 | + | 0.576806i | −0.999982 | − | 0.00606333i | \(-0.998070\pi\) |
0.812566 | + | 0.582869i | \(0.198070\pi\) | |||||||
\(510\) | −4.19682 | − | 12.9165i | −0.185838 | − | 0.571951i | ||||
\(511\) | 12.7111 | − | 9.23519i | 0.562308 | − | 0.408541i | ||||
\(512\) | 0.809017 | − | 0.587785i | 0.0357538 | − | 0.0259767i | ||||
\(513\) | 1.10570 | + | 3.40299i | 0.0488178 | + | 0.150246i | ||||
\(514\) | 1.19769 | − | 3.68610i | 0.0528277 | − | 0.162587i | ||||
\(515\) | −5.87178 | − | 4.26610i | −0.258742 | − | 0.187987i | ||||
\(516\) | 3.74009 | 0.164648 | ||||||||
\(517\) | −37.9036 | − | 1.23991i | −1.66700 | − | 0.0545313i | ||||
\(518\) | −5.93542 | −0.260787 | ||||||||
\(519\) | 7.72601 | + | 5.61327i | 0.339134 | + | 0.246395i | ||||
\(520\) | 0.756026 | − | 2.32681i | 0.0331539 | − | 0.102037i | ||||
\(521\) | 9.69973 | + | 29.8527i | 0.424953 | + | 1.30787i | 0.903039 | + | 0.429558i | \(0.141331\pi\) |
−0.478087 | + | 0.878313i | \(0.658669\pi\) | |||||||
\(522\) | −1.79958 | + | 1.30747i | −0.0787653 | + | 0.0572264i | ||||
\(523\) | 23.1950 | − | 16.8522i | 1.01425 | − | 0.736893i | 0.0491509 | − | 0.998791i | \(-0.484348\pi\) |
0.965095 | + | 0.261898i | \(0.0843485\pi\) | |||||||
\(524\) | 3.86313 | + | 11.8895i | 0.168762 | + | 0.519395i | ||||
\(525\) | 0.881966 | − | 2.71441i | 0.0384922 | − | 0.118467i | ||||
\(526\) | 2.86127 | + | 2.07883i | 0.124757 | + | 0.0906414i | ||||
\(527\) | −28.1759 | −1.22736 | ||||||||
\(528\) | −2.74551 | + | 1.86069i | −0.119483 | + | 0.0809763i | ||||
\(529\) | −14.6036 | −0.634940 | ||||||||
\(530\) | −28.3359 | − | 20.5872i | −1.23083 | − | 0.894252i | ||||
\(531\) | 2.04467 | − | 6.29286i | 0.0887313 | − | 0.273087i | ||||
\(532\) | 1.10570 | + | 3.40299i | 0.0479381 | + | 0.147538i | ||||
\(533\) | 5.00182 | − | 3.63403i | 0.216653 | − | 0.157407i | ||||
\(534\) | −10.2706 | + | 7.46205i | −0.444454 | + | 0.322915i | ||||
\(535\) | 6.75403 | + | 20.7868i | 0.292002 | + | 0.898690i | ||||
\(536\) | 2.46837 | − | 7.59687i | 0.106617 | − | 0.328135i | ||||
\(537\) | −8.94166 | − | 6.49650i | −0.385861 | − | 0.280345i | ||||
\(538\) | 26.1876 | 1.12903 | ||||||||
\(539\) | −2.61803 | − | 2.03615i | −0.112767 | − | 0.0877031i | ||||
\(540\) | −2.80252 | −0.120601 | ||||||||
\(541\) | −32.6577 | − | 23.7272i | −1.40406 | − | 1.02011i | −0.994152 | − | 0.107987i | \(-0.965560\pi\) |
−0.409912 | − | 0.912125i | \(-0.634440\pi\) | |||||||
\(542\) | −2.58528 | + | 7.95668i | −0.111047 | + | 0.341769i | ||||
\(543\) | −1.23789 | − | 3.80982i | −0.0531228 | − | 0.163495i | ||||
\(544\) | −3.92055 | + | 2.84845i | −0.168092 | + | 0.122126i | ||||
\(545\) | −26.3630 | + | 19.1538i | −1.12927 | + | 0.820459i | ||||
\(546\) | −0.269767 | − | 0.830257i | −0.0115449 | − | 0.0355317i | ||||
\(547\) | 9.02019 | − | 27.7613i | 0.385676 | − | 1.18699i | −0.550314 | − | 0.834958i | \(-0.685492\pi\) |
0.935989 | − | 0.352029i | \(-0.114508\pi\) | |||||||
\(548\) | 3.28256 | + | 2.38492i | 0.140224 | + | 0.101879i | ||||
\(549\) | −10.3334 | −0.441021 | ||||||||
\(550\) | 7.47214 | + | 5.81137i | 0.318613 | + | 0.247798i | ||||
\(551\) | −7.95916 | −0.339072 | ||||||||
\(552\) | −2.34425 | − | 1.70320i | −0.0997779 | − | 0.0724929i | ||||
\(553\) | −1.89878 | + | 5.84383i | −0.0807442 | + | 0.248505i | ||||
\(554\) | 1.62259 | + | 4.99381i | 0.0689372 | + | 0.212167i | ||||
\(555\) | 13.4573 | − | 9.77728i | 0.571229 | − | 0.415022i | ||||
\(556\) | −9.11783 | + | 6.62449i | −0.386682 | + | 0.280941i | ||||
\(557\) | 3.43719 | + | 10.5786i | 0.145638 | + | 0.448228i | 0.997093 | − | 0.0762004i | \(-0.0242789\pi\) |
−0.851454 | + | 0.524429i | \(0.824279\pi\) | |||||||
\(558\) | −1.79668 | + | 5.52962i | −0.0760596 | + | 0.234087i | ||||
\(559\) | −2.64147 | − | 1.91914i | −0.111722 | − | 0.0811709i | ||||
\(560\) | −2.80252 | −0.118428 | ||||||||
\(561\) | 13.3049 | − | 9.01705i | 0.561734 | − | 0.380700i | ||||
\(562\) | 6.83886 | 0.288480 | ||||||||
\(563\) | 12.0455 | + | 8.75157i | 0.507657 | + | 0.368834i | 0.811934 | − | 0.583749i | \(-0.198415\pi\) |
−0.304277 | + | 0.952584i | \(0.598415\pi\) | |||||||
\(564\) | −3.53344 | + | 10.8748i | −0.148785 | + | 0.457913i | ||||
\(565\) | −12.3579 | − | 38.0337i | −0.519901 | − | 1.60009i | ||||
\(566\) | 3.52914 | − | 2.56407i | 0.148341 | − | 0.107776i | ||||
\(567\) | −0.809017 | + | 0.587785i | −0.0339755 | + | 0.0246847i | ||||
\(568\) | −3.15757 | − | 9.71799i | −0.132489 | − | 0.407758i | ||||
\(569\) | 4.22539 | − | 13.0044i | 0.177138 | − | 0.545174i | −0.822587 | − | 0.568639i | \(-0.807470\pi\) |
0.999725 | + | 0.0234655i | \(0.00747000\pi\) | |||||||
\(570\) | −8.11261 | − | 5.89416i | −0.339800 | − | 0.246879i | ||||
\(571\) | −14.9587 | −0.626002 | −0.313001 | − | 0.949753i | \(-0.601334\pi\) | ||||
−0.313001 | + | 0.949753i | \(0.601334\pi\) | |||||||
\(572\) | 2.89381 | + | 0.0946632i | 0.120996 | + | 0.00395807i | ||||
\(573\) | 7.77642 | 0.324865 | ||||||||
\(574\) | −5.72957 | − | 4.16277i | −0.239148 | − | 0.173751i | ||||
\(575\) | −2.55563 | + | 7.86542i | −0.106577 | + | 0.328011i | ||||
\(576\) | 0.309017 | + | 0.951057i | 0.0128757 | + | 0.0396274i | ||||
\(577\) | 10.4493 | − | 7.59185i | 0.435009 | − | 0.316053i | −0.348639 | − | 0.937257i | \(-0.613356\pi\) |
0.783649 | + | 0.621204i | \(0.213356\pi\) | |||||||
\(578\) | 5.24597 | − | 3.81142i | 0.218203 | − | 0.158534i | ||||
\(579\) | −5.21542 | − | 16.0514i | −0.216745 | − | 0.667073i | ||||
\(580\) | 1.92639 | − | 5.92881i | 0.0799888 | − | 0.246180i | ||||
\(581\) | −8.08032 | − | 5.87069i | −0.335228 | − | 0.243557i | ||||
\(582\) | 2.90262 | 0.120317 | ||||||||
\(583\) | 14.0909 | − | 38.9817i | 0.583584 | − | 1.61446i | ||||
\(584\) | 15.7118 | 0.650161 | ||||||||
\(585\) | 1.97930 | + | 1.43805i | 0.0818340 | + | 0.0594559i | ||||
\(586\) | 6.02717 | − | 18.5497i | 0.248980 | − | 0.766282i | ||||
\(587\) | −13.6727 | − | 42.0804i | −0.564335 | − | 1.73684i | −0.669920 | − | 0.742433i | \(-0.733672\pi\) |
0.105586 | − | 0.994410i | \(-0.466328\pi\) | |||||||
\(588\) | −0.809017 | + | 0.587785i | −0.0333633 | + | 0.0242399i | ||||
\(589\) | −16.8307 | + | 12.2282i | −0.693496 | + | 0.503854i | ||||
\(590\) | 5.73023 | + | 17.6358i | 0.235910 | + | 0.726056i | ||||
\(591\) | −3.30226 | + | 10.1633i | −0.135837 | + | 0.418063i | ||||
\(592\) | −4.80185 | − | 3.48875i | −0.197355 | − | 0.143387i | ||||
\(593\) | 5.83880 | 0.239771 | 0.119885 | − | 0.992788i | \(-0.461747\pi\) | ||||
0.119885 | + | 0.992788i | \(0.461747\pi\) | |||||||
\(594\) | −0.921216 | − | 3.18612i | −0.0377980 | − | 0.130728i | ||||
\(595\) | 13.5812 | 0.556774 | ||||||||
\(596\) | 1.23607 | + | 0.898056i | 0.0506313 | + | 0.0367858i | ||||
\(597\) | −6.01441 | + | 18.5104i | −0.246153 | + | 0.757582i | ||||
\(598\) | 0.781690 | + | 2.40579i | 0.0319657 | + | 0.0983803i | ||||
\(599\) | −33.9887 | + | 24.6942i | −1.38874 | + | 1.00898i | −0.392738 | + | 0.919650i | \(0.628472\pi\) |
−0.996002 | + | 0.0893285i | \(0.971528\pi\) | |||||||
\(600\) | 2.30902 | − | 1.67760i | 0.0942652 | − | 0.0684877i | ||||
\(601\) | −5.01663 | − | 15.4396i | −0.204633 | − | 0.629795i | −0.999728 | − | 0.0233107i | \(-0.992579\pi\) |
0.795095 | − | 0.606484i | \(-0.207421\pi\) | |||||||
\(602\) | −1.15575 | + | 3.55703i | −0.0471048 | + | 0.144974i | ||||
\(603\) | 6.46228 | + | 4.69512i | 0.263165 | + | 0.191200i | ||||
\(604\) | 12.8730 | 0.523794 | ||||||||
\(605\) | −11.4220 | + | 28.6336i | −0.464372 | + | 1.16412i | ||||
\(606\) | 5.96141 | 0.242166 | ||||||||
\(607\) | 7.48294 | + | 5.43667i | 0.303723 | + | 0.220668i | 0.729198 | − | 0.684302i | \(-0.239893\pi\) |
−0.425475 | + | 0.904970i | \(0.639893\pi\) | |||||||
\(608\) | −1.10570 | + | 3.40299i | −0.0448420 | + | 0.138010i | ||||
\(609\) | −0.687377 | − | 2.11553i | −0.0278539 | − | 0.0857256i | ||||
\(610\) | 23.4289 | − | 17.0221i | 0.948607 | − | 0.689203i | ||||
\(611\) | 8.07569 | − | 5.86733i | 0.326707 | − | 0.237367i | ||||
\(612\) | −1.49752 | − | 4.60888i | −0.0605335 | − | 0.186303i | ||||
\(613\) | 15.0435 | − | 46.2991i | 0.607601 | − | 1.87000i | 0.129787 | − | 0.991542i | \(-0.458571\pi\) |
0.477814 | − | 0.878461i | \(-0.341429\pi\) | |||||||
\(614\) | 9.94166 | + | 7.22304i | 0.401213 | + | 0.291498i | ||||
\(615\) | 19.8478 | 0.800341 | ||||||||
\(616\) | −0.921216 | − | 3.18612i | −0.0371169 | − | 0.128372i | ||||
\(617\) | 36.6494 | 1.47545 | 0.737725 | − | 0.675102i | \(-0.235900\pi\) | ||||
0.737725 | + | 0.675102i | \(0.235900\pi\) | |||||||
\(618\) | −2.09518 | − | 1.52224i | −0.0842806 | − | 0.0612334i | ||||
\(619\) | −12.4835 | + | 38.4202i | −0.501753 | + | 1.54424i | 0.304408 | + | 0.952542i | \(0.401541\pi\) |
−0.806161 | + | 0.591696i | \(0.798459\pi\) | |||||||
\(620\) | −5.03523 | − | 15.4969i | −0.202220 | − | 0.622369i | ||||
\(621\) | 2.34425 | − | 1.70320i | 0.0940715 | − | 0.0683470i | ||||
\(622\) | 26.1540 | − | 19.0020i | 1.04868 | − | 0.761911i | ||||
\(623\) | −3.92303 | − | 12.0739i | −0.157173 | − | 0.483729i | ||||
\(624\) | 0.269767 | − | 0.830257i | 0.0107993 | − | 0.0332369i | ||||
\(625\) | 25.1803 | + | 18.2946i | 1.00721 | + | 0.731784i | ||||
\(626\) | 22.5260 | 0.900319 | ||||||||
\(627\) | 4.03424 | − | 11.1605i | 0.161112 | − | 0.445708i | ||||
\(628\) | 2.78000 | 0.110934 | ||||||||
\(629\) | 23.2701 | + | 16.9067i | 0.927840 | + | 0.674115i | ||||
\(630\) | 0.866025 | − | 2.66535i | 0.0345033 | − | 0.106190i | ||||
\(631\) | 5.35441 | + | 16.4792i | 0.213156 | + | 0.656026i | 0.999279 | + | 0.0379569i | \(0.0120849\pi\) |
−0.786124 | + | 0.618069i | \(0.787915\pi\) | |||||||
\(632\) | −4.97106 | + | 3.61169i | −0.197738 | + | 0.143665i | ||||
\(633\) | 2.48480 | − | 1.80531i | 0.0987620 | − | 0.0717548i | ||||
\(634\) | 0.850339 | + | 2.61707i | 0.0337713 | + | 0.103937i | ||||
\(635\) | 12.2529 | − | 37.7106i | 0.486242 | − | 1.49650i | ||||
\(636\) | −10.1109 | − | 7.34598i | −0.400922 | − | 0.291287i | ||||
\(637\) | 0.872983 | 0.0345889 | ||||||||
\(638\) | 7.37355 | + | 0.241206i | 0.291922 | + | 0.00954943i | ||||
\(639\) | 10.2181 | 0.404222 | ||||||||
\(640\) | −2.26728 | − | 1.64728i | −0.0896223 | − | 0.0651144i | ||||
\(641\) | −14.7337 | + | 45.3458i | −0.581948 | + | 1.79105i | 0.0292488 | + | 0.999572i | \(0.490688\pi\) |
−0.611197 | + | 0.791479i | \(0.709312\pi\) | |||||||
\(642\) | 2.40999 | + | 7.41718i | 0.0951146 | + | 0.292733i | ||||
\(643\) | 22.7133 | − | 16.5022i | 0.895727 | − | 0.650784i | −0.0416380 | − | 0.999133i | \(-0.513258\pi\) |
0.937365 | + | 0.348349i | \(0.113258\pi\) | |||||||
\(644\) | 2.34425 | − | 1.70320i | 0.0923764 | − | 0.0671154i | ||||
\(645\) | −3.23901 | − | 9.96864i | −0.127536 | − | 0.392515i | ||||
\(646\) | 5.35829 | − | 16.4911i | 0.210819 | − | 0.648835i | ||||
\(647\) | 14.3996 | + | 10.4620i | 0.566108 | + | 0.411302i | 0.833689 | − | 0.552233i | \(-0.186224\pi\) |
−0.267581 | + | 0.963535i | \(0.586224\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −18.1662 | + | 12.3117i | −0.713086 | + | 0.483275i | ||||
\(650\) | −2.49158 | −0.0977279 | ||||||||
\(651\) | −4.70378 | − | 3.41749i | −0.184356 | − | 0.133942i | ||||
\(652\) | −2.61803 | + | 8.05748i | −0.102530 | + | 0.315555i | ||||
\(653\) | −3.87562 | − | 11.9279i | −0.151665 | − | 0.466776i | 0.846143 | − | 0.532956i | \(-0.178919\pi\) |
−0.997808 | + | 0.0661797i | \(0.978919\pi\) | |||||||
\(654\) | −9.40689 | + | 6.83450i | −0.367838 | + | 0.267250i | ||||
\(655\) | 28.3441 | − | 20.5932i | 1.10750 | − | 0.804643i | ||||
\(656\) | −2.18850 | − | 6.73551i | −0.0854466 | − | 0.262978i | ||||
\(657\) | −4.85523 | + | 14.9428i | −0.189420 | + | 0.582976i | ||||
\(658\) | −9.25068 | − | 6.72101i | −0.360629 | − | 0.262012i | ||||
\(659\) | 31.1808 | 1.21463 | 0.607317 | − | 0.794460i | \(-0.292246\pi\) | ||||
0.607317 | + | 0.794460i | \(0.292246\pi\) | |||||||
\(660\) | 7.33708 | + | 5.70634i | 0.285596 | + | 0.222119i | ||||
\(661\) | −29.7716 | −1.15798 | −0.578990 | − | 0.815335i | \(-0.696553\pi\) | ||||
−0.578990 | + | 0.815335i | \(0.696553\pi\) | |||||||
\(662\) | −11.6795 | − | 8.48563i | −0.453936 | − | 0.329803i | ||||
\(663\) | −1.30731 | + | 4.02348i | −0.0507716 | + | 0.156259i | ||||
\(664\) | −3.08641 | − | 9.49898i | −0.119776 | − | 0.368632i | ||||
\(665\) | 8.11261 | − | 5.89416i | 0.314594 | − | 0.228566i | ||||
\(666\) | 4.80185 | − | 3.48875i | 0.186068 | − | 0.135186i | ||||
\(667\) | 1.99178 | + | 6.13007i | 0.0771220 | + | 0.237357i | ||||
\(668\) | −1.53651 | + | 4.72890i | −0.0594495 | + | 0.182967i | ||||
\(669\) | −11.7648 | − | 8.54763i | −0.454853 | − | 0.330470i | ||||
\(670\) | −22.3860 | −0.864847 | ||||||||
\(671\) | 27.0533 | + | 21.0404i | 1.04438 | + | 0.812257i | ||||
\(672\) | −1.00000 | −0.0385758 | ||||||||
\(673\) | 36.0403 | + | 26.1848i | 1.38925 | + | 1.00935i | 0.995947 | + | 0.0899431i | \(0.0286685\pi\) |
0.393305 | + | 0.919408i | \(0.371331\pi\) | |||||||
\(674\) | −6.69252 | + | 20.5975i | −0.257786 | + | 0.793384i | ||||
\(675\) | 0.881966 | + | 2.71441i | 0.0339469 | + | 0.104478i | ||||
\(676\) | 9.90067 | − | 7.19326i | 0.380795 | − | 0.276664i | ||||
\(677\) | −30.0171 | + | 21.8087i | −1.15365 | + | 0.838177i | −0.988962 | − | 0.148168i | \(-0.952662\pi\) |
−0.164690 | + | 0.986345i | \(0.552662\pi\) | |||||||
\(678\) | −4.40958 | − | 13.5713i | −0.169349 | − | 0.521202i | ||||
\(679\) | −0.896958 | + | 2.76055i | −0.0344221 | + | 0.105940i | ||||
\(680\) | 10.9874 | + | 7.98282i | 0.421348 | + | 0.306127i | ||||
\(681\) | −25.6664 | −0.983538 | ||||||||
\(682\) | 15.9629 | − | 10.8184i | 0.611251 | − | 0.414259i | ||||
\(683\) | 19.6972 | 0.753692 | 0.376846 | − | 0.926276i | \(-0.377009\pi\) | ||||
0.376846 | + | 0.926276i | \(0.377009\pi\) | |||||||
\(684\) | −2.89476 | − | 2.10317i | −0.110684 | − | 0.0804165i | ||||
\(685\) | 3.51387 | − | 10.8146i | 0.134258 | − | 0.413204i | ||||
\(686\) | −0.309017 | − | 0.951057i | −0.0117983 | − | 0.0363115i | ||||
\(687\) | 4.40937 | − | 3.20359i | 0.168228 | − | 0.122225i | ||||
\(688\) | −3.02579 | + | 2.19837i | −0.115357 | + | 0.0838120i | ||||
\(689\) | 3.37147 | + | 10.3763i | 0.128443 | + | 0.395306i | ||||
\(690\) | −2.50944 | + | 7.72326i | −0.0955328 | + | 0.294020i | ||||
\(691\) | −30.7345 | − | 22.3299i | −1.16920 | − | 0.849471i | −0.178284 | − | 0.983979i | \(-0.557055\pi\) |
−0.990913 | + | 0.134508i | \(0.957055\pi\) | |||||||
\(692\) | −9.54987 | −0.363032 | ||||||||
\(693\) | 3.31485 | + | 0.108436i | 0.125921 | + | 0.00411916i | ||||
\(694\) | −16.4700 | −0.625194 | ||||||||
\(695\) | 25.5529 | + | 18.5652i | 0.969275 | + | 0.704220i | ||||
\(696\) | 0.687377 | − | 2.11553i | 0.0260550 | − | 0.0801889i | ||||
\(697\) | 10.6056 | + | 32.6407i | 0.401717 | + | 1.23636i | ||||
\(698\) | 9.56658 | − | 6.95053i | 0.362100 | − | 0.263081i | ||||
\(699\) | 23.4499 | − | 17.0373i | 0.886957 | − | 0.644412i | ||||
\(700\) | 0.881966 | + | 2.71441i | 0.0333352 | + | 0.102595i | ||||
\(701\) | −12.0154 | + | 36.9797i | −0.453817 | + | 1.39670i | 0.418702 | + | 0.908124i | \(0.362485\pi\) |
−0.872519 | + | 0.488580i | \(0.837515\pi\) | |||||||
\(702\) | 0.706258 | + | 0.513127i | 0.0266560 | + | 0.0193667i | ||||
\(703\) | 21.2376 | 0.800992 | ||||||||
\(704\) | 1.12747 | − | 3.11910i | 0.0424933 | − | 0.117556i | ||||
\(705\) | 32.0453 | 1.20690 | ||||||||
\(706\) | 19.2733 | + | 14.0029i | 0.725361 | + | 0.527006i | ||||
\(707\) | −1.84218 | + | 5.66964i | −0.0692823 | + | 0.213229i | ||||
\(708\) | 2.04467 | + | 6.29286i | 0.0768435 | + | 0.236500i | ||||
\(709\) | 9.16949 | − | 6.66202i | 0.344367 | − | 0.250198i | −0.402135 | − | 0.915580i | \(-0.631732\pi\) |
0.746502 | + | 0.665383i | \(0.231732\pi\) | |||||||
\(710\) | −23.1673 | + | 16.8321i | −0.869455 | + | 0.631696i | ||||
\(711\) | −1.89878 | − | 5.84383i | −0.0712097 | − | 0.219161i | ||||
\(712\) | 3.92303 | − | 12.0739i | 0.147022 | − | 0.452487i | ||||
\(713\) | 13.6299 | + | 9.90271i | 0.510444 | + | 0.370859i | ||||
\(714\) | 4.84607 | 0.181360 | ||||||||
\(715\) | −2.25380 | − | 7.79500i | −0.0842874 | − | 0.291517i | ||||
\(716\) | 11.0525 | 0.413051 | ||||||||
\(717\) | 22.0490 | + | 16.0195i | 0.823434 | + | 0.598260i | ||||
\(718\) | 6.24861 | − | 19.2312i | 0.233196 | − | 0.717703i | ||||
\(719\) | 10.9500 | + | 33.7005i | 0.408365 | + | 1.25682i | 0.918053 | + | 0.396458i | \(0.129761\pi\) |
−0.509688 | + | 0.860359i | \(0.670239\pi\) | |||||||
\(720\) | 2.26728 | − | 1.64728i | 0.0844967 | − | 0.0613904i | ||||
\(721\) | 2.09518 | − | 1.52224i | 0.0780287 | − | 0.0566911i | ||||
\(722\) | 1.91500 | + | 5.89376i | 0.0712689 | + | 0.219343i | ||||
\(723\) | 4.20539 | − | 12.9429i | 0.156400 | − | 0.481350i | ||||
\(724\) | 3.24083 | + | 2.35460i | 0.120444 | + | 0.0875079i | ||||
\(725\) | −6.34866 | −0.235783 | ||||||||
\(726\) | −4.07564 | + | 10.2171i | −0.151261 | + | 0.379192i | ||||
\(727\) | 34.8985 | 1.29431 | 0.647156 | − | 0.762357i | \(-0.275958\pi\) | ||||
0.647156 | + | 0.762357i | \(0.275958\pi\) | |||||||
\(728\) | 0.706258 | + | 0.513127i | 0.0261757 | + | 0.0190177i | ||||
\(729\) | 0.309017 | − | 0.951057i | 0.0114451 | − | 0.0352243i | ||||
\(730\) | −13.6069 | − | 41.8776i | −0.503612 | − | 1.54996i | ||||
\(731\) | 14.6632 | − | 10.6534i | 0.542338 | − | 0.394032i | ||||
\(732\) | 8.35994 | − | 6.07385i | 0.308992 | − | 0.224496i | ||||
\(733\) | 6.89018 | + | 21.2058i | 0.254494 | + | 0.783253i | 0.993929 | + | 0.110025i | \(0.0350930\pi\) |
−0.739434 | + | 0.673229i | \(0.764907\pi\) | |||||||
\(734\) | 3.86715 | − | 11.9019i | 0.142739 | − | 0.439306i | ||||
\(735\) | 2.26728 | + | 1.64728i | 0.0836300 | + | 0.0607608i | ||||
\(736\) | 2.89765 | 0.106809 | ||||||||
\(737\) | −7.35851 | − | 25.4502i | −0.271054 | − | 0.937469i | ||||
\(738\) | 7.08214 | 0.260697 | ||||||||
\(739\) | 0.164779 | + | 0.119719i | 0.00606151 | + | 0.00440394i | 0.590812 | − | 0.806809i | \(-0.298808\pi\) |
−0.584750 | + | 0.811213i | \(0.698808\pi\) | |||||||
\(740\) | −5.14022 | + | 15.8200i | −0.188958 | + | 0.581554i | ||||
\(741\) | 0.965257 | + | 2.97076i | 0.0354596 | + | 0.109133i | ||||
\(742\) | 10.1109 | − | 7.34598i | 0.371182 | − | 0.269679i | ||||
\(743\) | −35.7216 | + | 25.9532i | −1.31050 | + | 0.952132i | −0.310499 | + | 0.950574i | \(0.600496\pi\) |
−0.999999 | + | 0.00155865i | \(0.999504\pi\) | |||||||
\(744\) | −1.79668 | − | 5.52962i | −0.0658696 | − | 0.202726i | ||||
\(745\) | 1.32317 | − | 4.07230i | 0.0484772 | − | 0.149197i | ||||
\(746\) | −28.6568 | − | 20.8204i | −1.04920 | − | 0.762288i | ||||
\(747\) | 9.98782 | 0.365435 | ||||||||
\(748\) | −5.46382 | + | 15.1154i | −0.199777 | + | 0.552673i | ||||
\(749\) | −7.79888 | −0.284965 | ||||||||
\(750\) | 4.86536 | + | 3.53489i | 0.177658 | + | 0.129076i | ||||
\(751\) | 7.74999 | − | 23.8520i | 0.282801 | − | 0.870373i | −0.704248 | − | 0.709954i | \(-0.748716\pi\) |
0.987049 | − | 0.160419i | \(-0.0512844\pi\) | |||||||
\(752\) | −3.53344 | − | 10.8748i | −0.128851 | − | 0.396564i | ||||
\(753\) | 18.2010 | − | 13.2238i | 0.663283 | − | 0.481903i | ||||
\(754\) | −1.57100 | + | 1.14140i | −0.0572125 | + | 0.0415673i | ||||
\(755\) | −11.1483 | − | 34.3110i | −0.405729 | − | 1.24871i | ||||
\(756\) | 0.309017 | − | 0.951057i | 0.0112388 | − | 0.0345896i | ||||
\(757\) | 41.5796 | + | 30.2093i | 1.51124 | + | 1.09798i | 0.965625 | + | 0.259939i | \(0.0837025\pi\) |
0.545611 | + | 0.838038i | \(0.316297\pi\) | |||||||
\(758\) | −18.9873 | −0.689650 | ||||||||
\(759\) | −9.60529 | − | 0.314211i | −0.348650 | − | 0.0114051i | ||||
\(760\) | 10.0277 | 0.363744 | ||||||||
\(761\) | 9.20203 | + | 6.68567i | 0.333573 | + | 0.242355i | 0.741945 | − | 0.670460i | \(-0.233903\pi\) |
−0.408372 | + | 0.912816i | \(0.633903\pi\) | |||||||
\(762\) | 4.37211 | − | 13.4560i | 0.158385 | − | 0.487459i | ||||
\(763\) | −3.59311 | − | 11.0585i | −0.130079 | − | 0.400343i | ||||
\(764\) | −6.29126 | + | 4.57087i | −0.227610 | + | 0.165368i | ||||
\(765\) | −10.9874 | + | 7.98282i | −0.397251 | + | 0.288620i | ||||
\(766\) | −3.47131 | − | 10.6836i | −0.125424 | − | 0.386014i | ||||
\(767\) | 1.78497 | − | 5.49356i | 0.0644514 | − | 0.198361i | ||||
\(768\) | −0.809017 | − | 0.587785i | −0.0291929 | − | 0.0212099i | ||||
\(769\) | −46.3417 | −1.67112 | −0.835562 | − | 0.549396i | \(-0.814858\pi\) | ||||
−0.835562 | + | 0.549396i | \(0.814858\pi\) | |||||||
\(770\) | −7.69433 | + | 5.21463i | −0.277285 | + | 0.187922i | ||||
\(771\) | −3.87580 | −0.139583 | ||||||||
\(772\) | 13.6541 | + | 9.92031i | 0.491423 | + | 0.357040i | ||||
\(773\) | 2.58533 | − | 7.95683i | 0.0929879 | − | 0.286187i | −0.893736 | − | 0.448593i | \(-0.851925\pi\) |
0.986724 | + | 0.162406i | \(0.0519253\pi\) | |||||||
\(774\) | −1.15575 | − | 3.55703i | −0.0415426 | − | 0.127855i | ||||
\(775\) | −13.4251 | + | 9.75387i | −0.482242 | + | 0.350369i | ||||
\(776\) | −2.34827 | + | 1.70612i | −0.0842979 | + | 0.0612460i | ||||
\(777\) | 1.83414 | + | 5.64492i | 0.0657996 | + | 0.202510i | ||||
\(778\) | −8.22571 | + | 25.3161i | −0.294906 | + | 0.907627i | ||||
\(779\) | 20.5011 | + | 14.8949i | 0.734527 | + | 0.533665i | ||||
\(780\) | −2.44655 | −0.0876006 | ||||||||
\(781\) | −26.7513 | − | 20.8056i | −0.957238 | − | 0.744482i | ||||
\(782\) | −14.0422 | −0.502149 | ||||||||
\(783\) | 1.79958 | + | 1.30747i | 0.0643116 | + | 0.0467251i | ||||
\(784\) | 0.309017 | − | 0.951057i | 0.0110363 | − | 0.0339663i | ||||
\(785\) | −2.40755 | − | 7.40968i | −0.0859292 | − | 0.264463i | ||||
\(786\) | 10.1138 | − | 7.34811i | 0.360748 | − | 0.262099i | ||||
\(787\) | 6.78691 | − | 4.93098i | 0.241927 | − | 0.175770i | −0.460214 | − | 0.887808i | \(-0.652227\pi\) |
0.702141 | + | 0.712038i | \(0.252227\pi\) | |||||||
\(788\) | −3.30226 | − | 10.1633i | −0.117638 | − | 0.362053i | ||||
\(789\) | 1.09291 | − | 3.36362i | 0.0389085 | − | 0.119748i | ||||
\(790\) | 13.9315 | + | 10.1218i | 0.495660 | + | 0.360118i | ||||
\(791\) | 14.2697 | 0.507372 | ||||||||
\(792\) | 2.61803 | + | 2.03615i | 0.0930278 | + | 0.0723514i | ||||
\(793\) | −9.02093 | −0.320343 | ||||||||
\(794\) | −15.8191 | − | 11.4932i | −0.561398 | − | 0.407879i | ||||
\(795\) | −10.8233 | + | 33.3108i | −0.383864 | + | 1.18141i | ||||
\(796\) | −6.01441 | − | 18.5104i | −0.213175 | − | 0.656085i | ||||
\(797\) | −7.02492 | + | 5.10390i | −0.248835 | + | 0.180790i | −0.705211 | − | 0.708998i | \(-0.749148\pi\) |
0.456375 | + | 0.889787i | \(0.349148\pi\) | |||||||
\(798\) | 2.89476 | − | 2.10317i | 0.102473 | − | 0.0744512i | ||||
\(799\) | 17.1233 | + | 52.7001i | 0.605779 | + | 1.86440i | ||||
\(800\) | −0.881966 | + | 2.71441i | −0.0311822 | + | 0.0959690i | ||||
\(801\) | 10.2706 | + | 7.46205i | 0.362895 | + | 0.263659i | ||||
\(802\) | 5.06955 | 0.179012 | ||||||||
\(803\) | 43.1370 | − | 29.2349i | 1.52227 | − | 1.03168i | ||||
\(804\) | −7.98782 | −0.281709 | ||||||||
\(805\) | −6.56980 | − | 4.77324i | −0.231555 | − | 0.168235i | ||||
\(806\) | −1.56847 | + | 4.82727i | −0.0552471 | + | 0.170033i | ||||
\(807\) | −8.09242 | − | 24.9059i | −0.284867 | − | 0.876729i | ||||
\(808\) | −4.82289 | + | 3.50403i | −0.169669 | + | 0.123271i | ||||
\(809\) | 3.70129 | − | 2.68915i | 0.130131 | − | 0.0945454i | −0.520816 | − | 0.853669i | \(-0.674372\pi\) |
0.650946 | + | 0.759124i | \(0.274372\pi\) | |||||||
\(810\) | 0.866025 | + | 2.66535i | 0.0304290 | + | 0.0936509i | ||||
\(811\) | −10.7257 | + | 33.0103i | −0.376630 | + | 1.15915i | 0.565742 | + | 0.824582i | \(0.308590\pi\) |
−0.942372 | + | 0.334566i | \(0.891410\pi\) | |||||||
\(812\) | 1.79958 | + | 1.30747i | 0.0631527 | + | 0.0458832i | ||||
\(813\) | 8.36615 | 0.293414 | ||||||||
\(814\) | −19.6750 | − | 0.643615i | −0.689609 | − | 0.0225587i | ||||
\(815\) | 23.7433 | 0.831692 | ||||||||
\(816\) | 3.92055 | + | 2.84845i | 0.137247 | + | 0.0997156i | ||||
\(817\) | 4.13541 | − | 12.7275i | 0.144680 | − | 0.445278i | ||||
\(818\) | 0.704313 | + | 2.16765i | 0.0246257 | + | 0.0757902i | ||||
\(819\) | −0.706258 | + | 0.513127i | −0.0246787 | + | 0.0179301i | ||||
\(820\) | −16.0572 | + | 11.6662i | −0.560742 | + | 0.407403i | ||||
\(821\) | 4.02861 | + | 12.3988i | 0.140599 | + | 0.432720i | 0.996419 | − | 0.0845543i | \(-0.0269466\pi\) |
−0.855820 | + | 0.517274i | \(0.826947\pi\) | |||||||
\(822\) | 1.25383 | − | 3.85888i | 0.0437322 | − | 0.134594i | ||||
\(823\) | −38.3444 | − | 27.8588i | −1.33660 | − | 0.971098i | −0.999562 | − | 0.0296079i | \(-0.990574\pi\) |
−0.337040 | − | 0.941490i | \(-0.609426\pi\) | |||||||
\(824\) | 2.58979 | 0.0902195 | ||||||||
\(825\) | 3.21793 | − | 8.90224i | 0.112034 | − | 0.309936i | ||||
\(826\) | −6.61670 | −0.230225 | ||||||||
\(827\) | −5.14034 | − | 3.73468i | −0.178747 | − | 0.129867i | 0.494814 | − | 0.868999i | \(-0.335236\pi\) |
−0.673561 | + | 0.739131i | \(0.735236\pi\) | |||||||
\(828\) | −0.895424 | + | 2.75583i | −0.0311181 | + | 0.0957718i | ||||
\(829\) | 2.80139 | + | 8.62180i | 0.0972964 | + | 0.299448i | 0.987845 | − | 0.155440i | \(-0.0496795\pi\) |
−0.890549 | + | 0.454887i | \(0.849679\pi\) | |||||||
\(830\) | −22.6452 | + | 16.4527i | −0.786027 | + | 0.571082i | ||||
\(831\) | 4.24799 | − | 3.08635i | 0.147361 | − | 0.107064i | ||||
\(832\) | 0.269767 | + | 0.830257i | 0.00935248 | + | 0.0287840i | ||||
\(833\) | −1.49752 | + | 4.60888i | −0.0518859 | + | 0.159688i | ||||
\(834\) | 9.11783 | + | 6.62449i | 0.315725 | + | 0.229387i | ||||
\(835\) | 13.9348 | 0.482235 | ||||||||
\(836\) | 3.29622 | + | 11.4003i | 0.114002 | + | 0.394288i | ||||
\(837\) | 5.81419 | 0.200968 | ||||||||
\(838\) | −16.7239 | − | 12.1507i | −0.577719 | − | 0.419737i | ||||
\(839\) | −0.0183944 | + | 0.0566121i | −0.000635045 | + | 0.00195447i | −0.951374 | − | 0.308040i | \(-0.900327\pi\) |
0.950738 | + | 0.309994i | \(0.100327\pi\) | |||||||
\(840\) | 0.866025 | + | 2.66535i | 0.0298807 | + | 0.0919634i | ||||
\(841\) | 19.4585 | − | 14.1374i | 0.670983 | − | 0.487498i | ||||
\(842\) | −16.2018 | + | 11.7713i | −0.558350 | + | 0.405665i | ||||
\(843\) | −2.11332 | − | 6.50414i | −0.0727867 | − | 0.224014i | ||||
\(844\) | −0.949109 | + | 2.92106i | −0.0326697 | + | 0.100547i | ||||
\(845\) | −27.7468 | − | 20.1592i | −0.954519 | − | 0.693498i | ||||
\(846\) | 11.4345 | 0.393125 | ||||||||
\(847\) | −8.45760 | − | 7.03342i | −0.290607 | − | 0.241671i | ||||
\(848\) | 12.4977 | 0.429174 | ||||||||
\(849\) | −3.52914 | − | 2.56407i | −0.121120 | − | 0.0879988i | ||||
\(850\) | 4.27407 | − | 13.1542i | 0.146599 | − | 0.451186i | ||||
\(851\) | −5.31471 | − | 16.3570i | −0.182186 | − | 0.560711i | ||||
\(852\) | −8.26662 | + | 6.00605i | −0.283210 | + | 0.205764i | ||||
\(853\) | −43.0804 | + | 31.2997i | −1.47504 | + | 1.07168i | −0.495932 | + | 0.868361i | \(0.665174\pi\) |
−0.979112 | + | 0.203321i | \(0.934826\pi\) | |||||||
\(854\) | 3.19321 | + | 9.82769i | 0.109269 | + | 0.336297i | ||||
\(855\) | −3.09874 | + | 9.53695i | −0.105975 | + | 0.326157i | ||||
\(856\) | −6.30943 | − | 4.58407i | −0.215652 | − | 0.156680i | ||||
\(857\) | −2.70283 | −0.0923269 | −0.0461635 | − | 0.998934i | \(-0.514700\pi\) | ||||
−0.0461635 | + | 0.998934i | \(0.514700\pi\) | |||||||
\(858\) | −0.804207 | − | 2.78143i | −0.0274552 | − | 0.0949564i | ||||
\(859\) | −4.14359 | −0.141378 | −0.0706888 | − | 0.997498i | \(-0.522520\pi\) | ||||
−0.0706888 | + | 0.997498i | \(0.522520\pi\) | |||||||
\(860\) | 8.47983 | + | 6.16096i | 0.289160 | + | 0.210087i | ||||
\(861\) | −2.18850 | + | 6.73551i | −0.0745839 | + | 0.229546i | ||||
\(862\) | −9.00087 | − | 27.7018i | −0.306571 | − | 0.943528i | ||||
\(863\) | 16.9763 | − | 12.3340i | 0.577879 | − | 0.419854i | −0.260080 | − | 0.965587i | \(-0.583749\pi\) |
0.837959 | + | 0.545733i | \(0.183749\pi\) | |||||||
\(864\) | 0.809017 | − | 0.587785i | 0.0275233 | − | 0.0199969i | ||||
\(865\) | 8.27043 | + | 25.4538i | 0.281203 | + | 0.865454i | ||||
\(866\) | 6.59600 | − | 20.3004i | 0.224141 | − | 0.689836i | ||||
\(867\) | −5.24597 | − | 3.81142i | −0.178162 | − | 0.129443i | ||||
\(868\) | 5.81419 | 0.197346 | ||||||||
\(869\) | −6.92784 | + | 19.1655i | −0.235011 | + | 0.650146i | ||||
\(870\) | −6.23392 | −0.211350 | ||||||||
\(871\) | 5.64147 | + | 4.09877i | 0.191154 | + | 0.138881i | ||||
\(872\) | 3.59311 | − | 11.0585i | 0.121678 | − | 0.374487i | ||||
\(873\) | −0.896958 | − | 2.76055i | −0.0303574 | − | 0.0934306i | ||||
\(874\) | −8.38800 | + | 6.09424i | −0.283728 | + | 0.206141i | ||||
\(875\) | −4.86536 | + | 3.53489i | −0.164479 | + | 0.119501i | ||||
\(876\) | −4.85523 | − | 14.9428i | −0.164043 | − | 0.504872i | ||||
\(877\) | −1.12348 | + | 3.45770i | −0.0379371 | + | 0.116758i | −0.968232 | − | 0.250055i | \(-0.919551\pi\) |
0.930295 | + | 0.366813i | \(0.119551\pi\) | |||||||
\(878\) | 21.7926 | + | 15.8333i | 0.735465 | + | 0.534347i | ||||
\(879\) | −19.5043 | −0.657865 | ||||||||
\(880\) | −9.28993 | − | 0.303895i | −0.313163 | − | 0.0102443i | ||||
\(881\) | 16.8954 | 0.569221 | 0.284610 | − | 0.958643i | \(-0.408136\pi\) | ||||
0.284610 | + | 0.958643i | \(0.408136\pi\) | |||||||
\(882\) | 0.809017 | + | 0.587785i | 0.0272410 | + | 0.0197918i | ||||
\(883\) | 1.80818 | − | 5.56500i | 0.0608500 | − | 0.187277i | −0.916011 | − | 0.401154i | \(-0.868609\pi\) |
0.976861 | + | 0.213877i | \(0.0686092\pi\) | |||||||
\(884\) | −1.30731 | − | 4.02348i | −0.0439695 | − | 0.135324i | ||||
\(885\) | 15.0019 | − | 10.8996i | 0.504285 | − | 0.366384i | ||||
\(886\) | −8.51279 | + | 6.18491i | −0.285993 | + | 0.207786i | ||||
\(887\) | −5.81746 | − | 17.9043i | −0.195331 | − | 0.601168i | −0.999973 | − | 0.00740663i | \(-0.997642\pi\) |
0.804641 | − | 0.593761i | \(-0.202358\pi\) | |||||||
\(888\) | −1.83414 | + | 5.64492i | −0.0615498 | + | 0.189431i | ||||
\(889\) | 11.4463 | + | 8.31626i | 0.383898 | + | 0.278918i | ||||
\(890\) | −35.5785 | −1.19259 | ||||||||
\(891\) | −2.74551 | + | 1.86069i | −0.0919780 | + | 0.0623356i | ||||
\(892\) | 14.5421 | 0.486905 | ||||||||
\(893\) | 33.1000 | + | 24.0486i | 1.10765 | + | 0.804755i | ||||
\(894\) | 0.472136 | − | 1.45309i | 0.0157906 | − | 0.0485984i | ||||
\(895\) | −9.57175 | − | 29.4588i | −0.319948 | − | 0.984699i | ||||
\(896\) | 0.809017 | − | 0.587785i | 0.0270274 | − | 0.0196365i | ||||
\(897\) | 2.04649 | − | 1.48686i | 0.0683304 | − | 0.0496449i | ||||
\(898\) | 10.4020 | + | 32.0140i | 0.347118 | + | 1.06832i | ||||
\(899\) | −3.99654 | + | 12.3001i | −0.133292 | + | 0.410231i | ||||
\(900\) | −2.30902 | − | 1.67760i | −0.0769672 | − | 0.0559200i | ||||
\(901\) | −60.5648 | −2.01771 | ||||||||
\(902\) | −18.5413 | − | 14.4203i | −0.617357 | − | 0.480143i | ||||
\(903\) | 3.74009 | 0.124462 | ||||||||
\(904\) | 11.5444 | + | 8.38751i | 0.383962 | + | 0.278964i | ||||
\(905\) | 3.46920 | − | 10.6771i | 0.115320 | − | 0.354918i | ||||
\(906\) | −3.97797 | − | 12.2429i | −0.132159 | − | 0.406744i | ||||
\(907\) | −43.1095 | + | 31.3209i | −1.43143 | + | 1.03999i | −0.441677 | + | 0.897174i | \(0.645616\pi\) |
−0.989749 | + | 0.142818i | \(0.954384\pi\) | |||||||
\(908\) | 20.7645 | − | 15.0863i | 0.689096 | − | 0.500657i | ||||
\(909\) | −1.84218 | − | 5.66964i | −0.0611012 | − | 0.188050i | ||||
\(910\) | 0.756026 | − | 2.32681i | 0.0250620 | − | 0.0771329i | ||||
\(911\) | −40.8640 | − | 29.6895i | −1.35389 | − | 0.983655i | −0.998808 | − | 0.0488188i | \(-0.984454\pi\) |
−0.355078 | − | 0.934837i | \(-0.615546\pi\) | |||||||
\(912\) | 3.57812 | 0.118483 | ||||||||
\(913\) | −26.1485 | − | 20.3367i | −0.865388 | − | 0.673046i | ||||
\(914\) | 0.716238 | 0.0236911 | ||||||||
\(915\) | −23.4289 | − | 17.0221i | −0.774534 | − | 0.562732i | ||||
\(916\) | −1.68423 | + | 5.18352i | −0.0556485 | + | 0.171268i | ||||
\(917\) | 3.86313 | + | 11.8895i | 0.127572 | + | 0.392626i | ||||
\(918\) | −3.92055 | + | 2.84845i | −0.129397 | + | 0.0940128i | ||||
\(919\) | 39.8294 | − | 28.9378i | 1.31385 | − | 0.954569i | 0.313864 | − | 0.949468i | \(-0.398376\pi\) |
0.999987 | − | 0.00510074i | \(-0.00162362\pi\) | |||||||
\(920\) | −2.50944 | − | 7.72326i | −0.0827338 | − | 0.254628i | ||||
\(921\) | 3.79738 | − | 11.6871i | 0.125128 | − | 0.385104i | ||||
\(922\) | −7.80467 | − | 5.67042i | −0.257033 | − | 0.186745i | ||||
\(923\) | 8.92023 | 0.293613 | ||||||||
\(924\) | −2.74551 | + | 1.86069i | −0.0903206 | + | 0.0612123i | ||||
\(925\) | 16.9403 | 0.556993 | ||||||||
\(926\) | −15.9171 | − | 11.5645i | −0.523070 | − | 0.380033i | ||||
\(927\) | −0.800288 | + | 2.46303i | −0.0262849 | + | 0.0808967i | ||||
\(928\) | 0.687377 | + | 2.11553i | 0.0225643 | + | 0.0694456i | ||||
\(929\) | −33.9712 | + | 24.6815i | −1.11456 | + | 0.809775i | −0.983376 | − | 0.181583i | \(-0.941878\pi\) |
−0.131184 | + | 0.991358i | \(0.541878\pi\) | |||||||
\(930\) | −13.1824 | + | 9.57758i | −0.432268 | + | 0.314061i | ||||
\(931\) | 1.10570 | + | 3.40299i | 0.0362378 | + | 0.111529i | ||||
\(932\) | −8.95706 | + | 27.5670i | −0.293398 | + | 0.902987i | ||||
\(933\) | −26.1540 | − | 19.0020i | −0.856244 | − | 0.622097i | ||||
\(934\) | 32.2437 | 1.05505 | ||||||||
\(935\) | 45.0196 | + | 1.47270i | 1.47230 | + | 0.0481623i | ||||
\(936\) | −0.872983 | −0.0285344 | ||||||||
\(937\) | 42.7479 | + | 31.0582i | 1.39651 | + | 1.01463i | 0.995115 | + | 0.0987220i | \(0.0314755\pi\) |
0.401398 | + | 0.915904i | \(0.368525\pi\) | |||||||
\(938\) | 2.46837 | − | 7.59687i | 0.0805952 | − | 0.248047i | ||||
\(939\) | −6.96091 | − | 21.4235i | −0.227161 | − | 0.699128i | ||||
\(940\) | −25.9252 | + | 18.8357i | −0.845586 | + | 0.614354i | ||||
\(941\) | −5.11725 | + | 3.71790i | −0.166817 | + | 0.121200i | −0.668062 | − | 0.744106i | \(-0.732876\pi\) |
0.501244 | + | 0.865306i | \(0.332876\pi\) | |||||||
\(942\) | −0.859067 | − | 2.64394i | −0.0279899 | − | 0.0861441i | ||||
\(943\) | 6.34151 | − | 19.5172i | 0.206508 | − | 0.635567i | ||||
\(944\) | −5.35303 | − | 3.88920i | −0.174226 | − | 0.126583i | ||||
\(945\) | −2.80252 | −0.0911659 | ||||||||
\(946\) | −4.21685 | + | 11.6657i | −0.137102 | + | 0.379285i | ||||
\(947\) | −55.0356 | −1.78842 | −0.894208 | − | 0.447651i | \(-0.852261\pi\) | ||||
−0.894208 | + | 0.447651i | \(0.852261\pi\) | |||||||
\(948\) | 4.97106 | + | 3.61169i | 0.161453 | + | 0.117302i | ||||
\(949\) | −4.23853 | + | 13.0449i | −0.137589 | + | 0.423454i | ||||
\(950\) | −3.15578 | − | 9.71249i | −0.102387 | − | 0.315115i | ||||
\(951\) | 2.22622 | − | 1.61744i | 0.0721900 | − | 0.0524491i | ||||
\(952\) | −3.92055 | + | 2.84845i | −0.127066 | + | 0.0923187i | ||||
\(953\) | 14.4068 | + | 44.3395i | 0.466681 | + | 1.43630i | 0.856856 | + | 0.515556i | \(0.172415\pi\) |
−0.390174 | + | 0.920741i | \(0.627585\pi\) | |||||||
\(954\) | −3.86201 | + | 11.8860i | −0.125037 | + | 0.384825i | ||||
\(955\) | 17.6314 | + | 12.8099i | 0.570537 | + | 0.414520i | ||||
\(956\) | −27.2540 | −0.881458 | ||||||||
\(957\) | −2.04915 | − | 7.08720i | −0.0662397 | − | 0.229097i | ||||
\(958\) | −1.23873 | −0.0400215 | ||||||||
\(959\) | 3.28256 | + | 2.38492i | 0.105999 | + | 0.0770130i | ||||
\(960\) | −0.866025 | + | 2.66535i | −0.0279508 | + | 0.0860239i | ||||
\(961\) | 0.866720 | + | 2.66749i | 0.0279587 | + | 0.0860480i | ||||
\(962\) | 4.19194 | − | 3.04562i | 0.135153 | − | 0.0981947i | ||||
\(963\) | 6.30943 | − | 4.58407i | 0.203318 | − | 0.147720i | ||||
\(964\) | 4.20539 | + | 12.9429i | 0.135446 | + | 0.416861i | ||||
\(965\) | 14.6163 | − | 44.9843i | 0.470515 | − | 1.44810i | ||||
\(966\) | −2.34425 | − | 1.70320i | −0.0754250 | − | 0.0547995i | ||||
\(967\) | −3.41562 | −0.109839 | −0.0549195 | − | 0.998491i | \(-0.517490\pi\) | ||||
−0.0549195 | + | 0.998491i | \(0.517490\pi\) | |||||||
\(968\) | −2.70820 | − | 10.6614i | −0.0870450 | − | 0.342671i | ||||
\(969\) | −17.3398 | −0.557035 | ||||||||
\(970\) | 6.58106 | + | 4.78142i | 0.211305 | + | 0.153522i | ||||
\(971\) | −7.26600 | + | 22.3625i | −0.233177 | + | 0.717645i | 0.764181 | + | 0.645002i | \(0.223144\pi\) |
−0.997358 | + | 0.0726434i | \(0.976856\pi\) | |||||||
\(972\) | 0.309017 | + | 0.951057i | 0.00991172 | + | 0.0305052i | ||||
\(973\) | −9.11783 | + | 6.62449i | −0.292304 | + | 0.212371i | ||||
\(974\) | 22.1997 | − | 16.1290i | 0.711325 | − | 0.516808i | ||||
\(975\) | 0.769942 | + | 2.36964i | 0.0246579 | + | 0.0758891i | ||||
\(976\) | −3.19321 | + | 9.82769i | −0.102212 | + | 0.314577i | ||||
\(977\) | −49.3426 | − | 35.8495i | −1.57861 | − | 1.14693i | −0.918267 | − | 0.395962i | \(-0.870411\pi\) |
−0.660342 | − | 0.750965i | \(-0.729589\pi\) | |||||||
\(978\) | 8.47214 | 0.270909 | ||||||||
\(979\) | −11.6950 | − | 40.4484i | −0.373775 | − | 1.29274i | ||||
\(980\) | −2.80252 | −0.0895231 | ||||||||
\(981\) | 9.40689 | + | 6.83450i | 0.300339 | + | 0.218209i | ||||
\(982\) | 6.79281 | − | 20.9061i | 0.216767 | − | 0.667141i | ||||
\(983\) | −11.8011 | − | 36.3201i | −0.376398 | − | 1.15843i | −0.942531 | − | 0.334119i | \(-0.891561\pi\) |
0.566133 | − | 0.824314i | \(-0.308439\pi\) | |||||||
\(984\) | −5.72957 | + | 4.16277i | −0.182652 | + | 0.132704i | ||||
\(985\) | −24.2290 | + | 17.6034i | −0.772000 | + | 0.560891i | ||||
\(986\) | −3.33108 | − | 10.2520i | −0.106083 | − | 0.326490i | ||||
\(987\) | −3.53344 | + | 10.8748i | −0.112471 | + | 0.346149i | ||||
\(988\) | −2.52708 | − | 1.83603i | −0.0803970 | − | 0.0584118i | ||||
\(989\) | −10.8375 | −0.344611 | ||||||||
\(990\) | 3.15977 | − | 8.74134i | 0.100424 | − | 0.277818i | ||||
\(991\) | 5.79183 | 0.183983 | 0.0919917 | − | 0.995760i | \(-0.470677\pi\) | ||||
0.0919917 | + | 0.995760i | \(0.470677\pi\) | |||||||
\(992\) | 4.70378 | + | 3.41749i | 0.149345 | + | 0.108506i | ||||
\(993\) | −4.46116 | + | 13.7300i | −0.141571 | + | 0.435710i | ||||
\(994\) | −3.15757 | − | 9.71799i | −0.100152 | − | 0.308236i | ||||
\(995\) | −44.1282 | + | 32.0610i | −1.39896 | + | 1.01640i | ||||
\(996\) | −8.08032 | + | 5.87069i | −0.256035 | + | 0.186020i | ||||
\(997\) | −6.67662 | − | 20.5485i | −0.211451 | − | 0.650779i | −0.999387 | − | 0.0350212i | \(-0.988850\pi\) |
0.787936 | − | 0.615757i | \(-0.211150\pi\) | |||||||
\(998\) | −9.35415 | + | 28.7891i | −0.296100 | + | 0.911303i | ||||
\(999\) | −4.80185 | − | 3.48875i | −0.151924 | − | 0.110379i |
(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 | 462.2.j.g.169.2 | ✓ | 8 | |
11.3 | even | 5 | inner | 462.2.j.g.421.2 | yes | 8 | |
11.5 | even | 5 | 5082.2.a.bz.1.1 | 4 | |||
11.6 | odd | 10 | 5082.2.a.ce.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.j.g.169.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
462.2.j.g.421.2 | yes | 8 | 11.3 | even | 5 | inner | |
5082.2.a.bz.1.1 | 4 | 11.5 | even | 5 | |||
5082.2.a.ce.1.1 | 4 | 11.6 | odd | 10 |