Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [71,2,Mod(5,71)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(71, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("71.5");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 71 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 71.c (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: | \(0.566937854351\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 6 x^{19} + 28 x^{18} - 91 x^{17} + 268 x^{16} - 604 x^{15} + 1278 x^{14} - 1990 x^{13} + \cdots + 961 \) |
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 | 54.2 | ||
Root | \(1.27286 - 0.924789i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 71.54 |
Dual form | 71.2.c.a.25.2 |
$q$-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 \(\left(\mathbb{Z}/71\mathbb{Z}\right)^\times\).
\(n\) | \(7\) |
\(\chi(n)\) | \(e\left(\frac{1}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.27286 | − | 0.924789i | −0.900050 | − | 0.653924i | 0.0384291 | − | 0.999261i | \(-0.487765\pi\) |
−0.938479 | + | 0.345337i | \(0.887765\pi\) | |||||||
\(3\) | −0.850399 | − | 0.617851i | −0.490978 | − | 0.356717i | 0.314582 | − | 0.949230i | \(-0.398136\pi\) |
−0.805560 | + | 0.592514i | \(0.798136\pi\) | |||||||
\(4\) | 0.146911 | + | 0.452144i | 0.0734553 | + | 0.226072i | ||||
\(5\) | 0.148297 | − | 0.456410i | 0.0663202 | − | 0.204113i | −0.912405 | − | 0.409289i | \(-0.865777\pi\) |
0.978725 | + | 0.205176i | \(0.0657768\pi\) | |||||||
\(6\) | 0.511060 | + | 1.57288i | 0.208639 | + | 0.642125i | ||||
\(7\) | −4.12180 | − | 2.99466i | −1.55789 | − | 1.13188i | −0.937710 | − | 0.347420i | \(-0.887058\pi\) |
−0.620184 | − | 0.784456i | \(-0.712942\pi\) | |||||||
\(8\) | −0.741239 | + | 2.28130i | −0.262068 | + | 0.806561i | ||||
\(9\) | −0.585612 | − | 1.80233i | −0.195204 | − | 0.600776i | ||||
\(10\) | −0.610844 | + | 0.443804i | −0.193166 | + | 0.140343i | ||||
\(11\) | 3.85852 | + | 2.80338i | 1.16339 | + | 0.845250i | 0.990202 | − | 0.139640i | \(-0.0445944\pi\) |
0.173184 | + | 0.984889i | \(0.444594\pi\) | |||||||
\(12\) | 0.154425 | − | 0.475272i | 0.0445788 | − | 0.137199i | ||||
\(13\) | 3.98746 | − | 2.89706i | 1.10592 | − | 0.803500i | 0.123906 | − | 0.992294i | \(-0.460458\pi\) |
0.982017 | + | 0.188794i | \(0.0604579\pi\) | |||||||
\(14\) | 2.47705 | + | 7.62359i | 0.662020 | + | 2.03749i | ||||
\(15\) | −0.408105 | + | 0.296505i | −0.105372 | + | 0.0765574i | ||||
\(16\) | 3.82245 | − | 2.77717i | 0.955613 | − | 0.694293i | ||||
\(17\) | 1.54622 | − | 1.12339i | 0.375013 | − | 0.272463i | −0.384273 | − | 0.923219i | \(-0.625548\pi\) |
0.759287 | + | 0.650756i | \(0.225548\pi\) | |||||||
\(18\) | −0.921369 | + | 2.83568i | −0.217169 | + | 0.668377i | ||||
\(19\) | −1.01097 | − | 0.734509i | −0.231931 | − | 0.168508i | 0.465750 | − | 0.884917i | \(-0.345785\pi\) |
−0.697681 | + | 0.716408i | \(0.745785\pi\) | |||||||
\(20\) | 0.228149 | 0.0510158 | ||||||||
\(21\) | 1.65492 | + | 5.09332i | 0.361133 | + | 1.11145i | ||||
\(22\) | −2.31883 | − | 7.13663i | −0.494376 | − | 1.52153i | ||||
\(23\) | −2.45752 | −0.512428 | −0.256214 | − | 0.966620i | \(-0.582475\pi\) | ||||
−0.256214 | + | 0.966620i | \(0.582475\pi\) | |||||||
\(24\) | 2.03985 | − | 1.48204i | 0.416383 | − | 0.302520i | ||||
\(25\) | 3.85877 | + | 2.80356i | 0.771753 | + | 0.560712i | ||||
\(26\) | −7.75466 | −1.52081 | ||||||||
\(27\) | −1.59004 | + | 4.89363i | −0.306003 | + | 0.941780i | ||||
\(28\) | 0.748484 | − | 2.30360i | 0.141450 | − | 0.435339i | ||||
\(29\) | 1.32106 | − | 4.06581i | 0.245315 | − | 0.755003i | −0.750269 | − | 0.661132i | \(-0.770076\pi\) |
0.995584 | − | 0.0938702i | \(-0.0299239\pi\) | |||||||
\(30\) | 0.793666 | 0.144903 | ||||||||
\(31\) | −1.22888 | − | 0.892830i | −0.220713 | − | 0.160357i | 0.471935 | − | 0.881633i | \(-0.343556\pi\) |
−0.692647 | + | 0.721276i | \(0.743556\pi\) | |||||||
\(32\) | −2.63635 | −0.466045 | ||||||||
\(33\) | −1.54921 | − | 4.76798i | −0.269683 | − | 0.829999i | ||||
\(34\) | −3.00703 | −0.515701 | ||||||||
\(35\) | −1.97804 | + | 1.43713i | −0.334350 | + | 0.242920i | ||||
\(36\) | 0.728880 | − | 0.529562i | 0.121480 | − | 0.0882604i | ||||
\(37\) | −5.25971 | −0.864691 | −0.432346 | − | 0.901708i | \(-0.642314\pi\) | ||||
−0.432346 | + | 0.901708i | \(0.642314\pi\) | |||||||
\(38\) | 0.607554 | + | 1.86986i | 0.0985583 | + | 0.303331i | ||||
\(39\) | −5.18089 | −0.829606 | ||||||||
\(40\) | 0.931285 | + | 0.676618i | 0.147249 | + | 0.106983i | ||||
\(41\) | −1.67389 | −0.261418 | −0.130709 | − | 0.991421i | \(-0.541725\pi\) | ||||
−0.130709 | + | 0.991421i | \(0.541725\pi\) | |||||||
\(42\) | 2.60376 | − | 8.01354i | 0.401769 | − | 1.23652i | ||||
\(43\) | 1.95712 | − | 6.02339i | 0.298458 | − | 0.918559i | −0.683580 | − | 0.729875i | \(-0.739578\pi\) |
0.982038 | − | 0.188683i | \(-0.0604219\pi\) | |||||||
\(44\) | −0.700674 | + | 2.15645i | −0.105631 | + | 0.325097i | ||||
\(45\) | −0.909445 | −0.135572 | ||||||||
\(46\) | 3.12808 | + | 2.27268i | 0.461211 | + | 0.335089i | ||||
\(47\) | 6.28284 | − | 4.56475i | 0.916446 | − | 0.665837i | −0.0261908 | − | 0.999657i | \(-0.508338\pi\) |
0.942637 | + | 0.333820i | \(0.108338\pi\) | |||||||
\(48\) | −4.96649 | −0.716851 | ||||||||
\(49\) | 5.85811 | + | 18.0294i | 0.836872 | + | 2.57563i | ||||
\(50\) | −2.31898 | − | 7.13709i | −0.327953 | − | 1.00934i | ||||
\(51\) | −2.00899 | −0.281316 | ||||||||
\(52\) | 1.89569 | + | 1.37730i | 0.262885 | + | 0.190997i | ||||
\(53\) | −2.81716 | + | 8.67034i | −0.386967 | + | 1.19096i | 0.548076 | + | 0.836429i | \(0.315361\pi\) |
−0.935043 | + | 0.354534i | \(0.884639\pi\) | |||||||
\(54\) | 6.54948 | − | 4.75847i | 0.891271 | − | 0.647546i | ||||
\(55\) | 1.85169 | − | 1.34533i | 0.249682 | − | 0.181405i | ||||
\(56\) | 9.88696 | − | 7.18330i | 1.32120 | − | 0.959909i | ||||
\(57\) | 0.405907 | + | 1.24925i | 0.0537637 | + | 0.165468i | ||||
\(58\) | −5.44155 | + | 3.95352i | −0.714510 | + | 0.519122i | ||||
\(59\) | −0.683986 | + | 2.10509i | −0.0890475 | + | 0.274060i | −0.985657 | − | 0.168763i | \(-0.946023\pi\) |
0.896609 | + | 0.442823i | \(0.146023\pi\) | |||||||
\(60\) | −0.194018 | − | 0.140962i | −0.0250476 | − | 0.0181982i | ||||
\(61\) | 7.83017 | − | 5.68895i | 1.00255 | − | 0.728396i | 0.0399171 | − | 0.999203i | \(-0.487291\pi\) |
0.962634 | + | 0.270807i | \(0.0872906\pi\) | |||||||
\(62\) | 0.738510 | + | 2.27290i | 0.0937909 | + | 0.288659i | ||||
\(63\) | −2.98359 | + | 9.18255i | −0.375897 | + | 1.15689i | ||||
\(64\) | −4.28919 | − | 3.11628i | −0.536149 | − | 0.389535i | ||||
\(65\) | −0.730920 | − | 2.24954i | −0.0906595 | − | 0.279021i | ||||
\(66\) | −2.43744 | + | 7.50168i | −0.300028 | + | 0.923392i | ||||
\(67\) | −0.465104 | − | 1.43144i | −0.0568215 | − | 0.174879i | 0.918618 | − | 0.395147i | \(-0.129307\pi\) |
−0.975439 | + | 0.220269i | \(0.929307\pi\) | |||||||
\(68\) | 0.735092 | + | 0.534076i | 0.0891430 | + | 0.0647662i | ||||
\(69\) | 2.08987 | + | 1.51838i | 0.251591 | + | 0.182792i | ||||
\(70\) | 3.84682 | 0.459783 | ||||||||
\(71\) | −2.21803 | + | 8.12898i | −0.263232 | + | 0.964733i | ||||
\(72\) | 4.54573 | 0.535720 | ||||||||
\(73\) | 4.29859 | + | 3.12311i | 0.503112 | + | 0.365532i | 0.810204 | − | 0.586148i | \(-0.199356\pi\) |
−0.307093 | + | 0.951680i | \(0.599356\pi\) | |||||||
\(74\) | 6.69489 | + | 4.86412i | 0.778265 | + | 0.565443i | ||||
\(75\) | −1.54931 | − | 4.76829i | −0.178899 | − | 0.550595i | ||||
\(76\) | 0.183583 | − | 0.565010i | 0.0210584 | − | 0.0648111i | ||||
\(77\) | −7.50887 | − | 23.1099i | −0.855715 | − | 2.63362i | ||||
\(78\) | 6.59456 | + | 4.79123i | 0.746687 | + | 0.542500i | ||||
\(79\) | 0.954168 | − | 2.93663i | 0.107352 | − | 0.330396i | −0.882923 | − | 0.469518i | \(-0.844428\pi\) |
0.990275 | + | 0.139121i | \(0.0444278\pi\) | |||||||
\(80\) | −0.700673 | − | 2.15645i | −0.0783376 | − | 0.241098i | ||||
\(81\) | −0.223750 | + | 0.162564i | −0.0248612 | + | 0.0180627i | ||||
\(82\) | 2.13063 | + | 1.54800i | 0.235289 | + | 0.170948i | ||||
\(83\) | −0.659424 | + | 2.02950i | −0.0723812 | + | 0.222766i | −0.980702 | − | 0.195507i | \(-0.937365\pi\) |
0.908321 | + | 0.418274i | \(0.137365\pi\) | |||||||
\(84\) | −2.05979 | + | 1.49653i | −0.224742 | + | 0.163284i | ||||
\(85\) | −0.283429 | − | 0.872305i | −0.0307422 | − | 0.0946148i | ||||
\(86\) | −8.06151 | + | 5.85703i | −0.869295 | + | 0.631580i | ||||
\(87\) | −3.63550 | + | 2.64135i | −0.389766 | + | 0.283182i | ||||
\(88\) | −9.25543 | + | 6.72446i | −0.986632 | + | 0.716830i | ||||
\(89\) | −0.424840 | + | 1.30752i | −0.0450329 | + | 0.138597i | −0.971045 | − | 0.238897i | \(-0.923214\pi\) |
0.926012 | + | 0.377494i | \(0.123214\pi\) | |||||||
\(90\) | 1.15760 | + | 0.841044i | 0.122022 | + | 0.0886538i | ||||
\(91\) | −25.1112 | −2.63237 | ||||||||
\(92\) | −0.361036 | − | 1.11115i | −0.0376406 | − | 0.115846i | ||||
\(93\) | 0.493399 | + | 1.51853i | 0.0511631 | + | 0.157464i | ||||
\(94\) | −12.2186 | −1.26025 | ||||||||
\(95\) | −0.485160 | + | 0.352489i | −0.0497764 | + | 0.0361646i | ||||
\(96\) | 2.24195 | + | 1.62887i | 0.228818 | + | 0.166246i | ||||
\(97\) | 4.29833 | 0.436429 | 0.218215 | − | 0.975901i | \(-0.429977\pi\) | ||||
0.218215 | + | 0.975901i | \(0.429977\pi\) | |||||||
\(98\) | 9.21682 | − | 28.3665i | 0.931039 | − | 2.86544i | ||||
\(99\) | 2.79301 | − | 8.59601i | 0.280708 | − | 0.863931i | ||||
\(100\) | −0.700719 | + | 2.15659i | −0.0700719 | + | 0.215659i | ||||
\(101\) | 7.80759 | 0.776884 | 0.388442 | − | 0.921473i | \(-0.373013\pi\) | ||||
0.388442 | + | 0.921473i | \(0.373013\pi\) | |||||||
\(102\) | 2.55717 | + | 1.85790i | 0.253198 | + | 0.183959i | ||||
\(103\) | 18.7205 | 1.84459 | 0.922293 | − | 0.386491i | \(-0.126313\pi\) | ||||
0.922293 | + | 0.386491i | \(0.126313\pi\) | |||||||
\(104\) | 3.65340 | + | 11.2440i | 0.358245 | + | 1.10257i | ||||
\(105\) | 2.57006 | 0.250812 | ||||||||
\(106\) | 11.6041 | − | 8.43087i | 1.12709 | − | 0.818878i | ||||
\(107\) | 3.49578 | − | 2.53983i | 0.337949 | − | 0.245535i | −0.405847 | − | 0.913941i | \(-0.633023\pi\) |
0.743796 | + | 0.668407i | \(0.233023\pi\) | |||||||
\(108\) | −2.44622 | −0.235388 | ||||||||
\(109\) | −0.573033 | − | 1.76361i | −0.0548866 | − | 0.168924i | 0.919855 | − | 0.392258i | \(-0.128306\pi\) |
−0.974742 | + | 0.223334i | \(0.928306\pi\) | |||||||
\(110\) | −3.60110 | −0.343351 | ||||||||
\(111\) | 4.47286 | + | 3.24972i | 0.424545 | + | 0.308450i | ||||
\(112\) | −24.0721 | −2.27460 | ||||||||
\(113\) | 0.412705 | − | 1.27018i | 0.0388240 | − | 0.119488i | −0.929766 | − | 0.368151i | \(-0.879991\pi\) |
0.968590 | + | 0.248663i | \(0.0799910\pi\) | |||||||
\(114\) | 0.638631 | − | 1.96551i | 0.0598133 | − | 0.184086i | ||||
\(115\) | −0.364441 | + | 1.12164i | −0.0339843 | + | 0.104593i | ||||
\(116\) | 2.03241 | 0.188705 | ||||||||
\(117\) | −7.55656 | − | 5.49016i | −0.698604 | − | 0.507566i | ||||
\(118\) | 2.81739 | − | 2.04695i | 0.259362 | − | 0.188437i | ||||
\(119\) | −9.73739 | −0.892625 | ||||||||
\(120\) | −0.373915 | − | 1.15079i | −0.0341336 | − | 0.105052i | ||||
\(121\) | 3.63005 | + | 11.1721i | 0.330004 | + | 1.01565i | ||||
\(122\) | −15.2278 | −1.37866 | ||||||||
\(123\) | 1.42348 | + | 1.03422i | 0.128351 | + | 0.0932522i | ||||
\(124\) | 0.223153 | − | 0.686796i | 0.0200398 | − | 0.0616761i | ||||
\(125\) | 3.79304 | − | 2.75581i | 0.339260 | − | 0.246487i | ||||
\(126\) | 12.2896 | − | 8.92893i | 1.09485 | − | 0.795452i | ||||
\(127\) | −2.53095 | + | 1.83884i | −0.224586 | + | 0.163171i | −0.694388 | − | 0.719600i | \(-0.744325\pi\) |
0.469803 | + | 0.882771i | \(0.344325\pi\) | |||||||
\(128\) | 4.20700 | + | 12.9478i | 0.371850 | + | 1.14444i | ||||
\(129\) | −5.38589 | + | 3.91308i | −0.474201 | + | 0.344528i | ||||
\(130\) | −1.14999 | + | 3.53930i | −0.100861 | + | 0.310417i | ||||
\(131\) | −17.1568 | − | 12.4651i | −1.49900 | − | 1.08908i | −0.970779 | − | 0.239976i | \(-0.922860\pi\) |
−0.528218 | − | 0.849109i | \(-0.677140\pi\) | |||||||
\(132\) | 1.92822 | − | 1.40093i | 0.167830 | − | 0.121936i | ||||
\(133\) | 1.96739 | + | 6.05500i | 0.170594 | + | 0.525035i | ||||
\(134\) | −0.731769 | + | 2.25215i | −0.0632152 | + | 0.194556i | ||||
\(135\) | 1.99771 | + | 1.45142i | 0.171935 | + | 0.124918i | ||||
\(136\) | 1.41668 | + | 4.36009i | 0.121479 | + | 0.373875i | ||||
\(137\) | −4.18619 | + | 12.8838i | −0.357650 | + | 1.10073i | 0.596806 | + | 0.802385i | \(0.296436\pi\) |
−0.954457 | + | 0.298349i | \(0.903564\pi\) | |||||||
\(138\) | −1.25594 | − | 3.86538i | −0.106913 | − | 0.329043i | ||||
\(139\) | 6.40078 | + | 4.65044i | 0.542907 | + | 0.394445i | 0.825163 | − | 0.564894i | \(-0.191083\pi\) |
−0.282257 | + | 0.959339i | \(0.591083\pi\) | |||||||
\(140\) | −0.940386 | − | 0.683231i | −0.0794772 | − | 0.0577435i | ||||
\(141\) | −8.16326 | −0.687470 | ||||||||
\(142\) | 10.3408 | − | 8.29587i | 0.867784 | − | 0.696174i | ||||
\(143\) | 23.5072 | 1.96577 | ||||||||
\(144\) | −7.24385 | − | 5.26297i | −0.603654 | − | 0.438580i | ||||
\(145\) | −1.65977 | − | 1.20589i | −0.137836 | − | 0.100144i | ||||
\(146\) | −2.58330 | − | 7.95057i | −0.213795 | − | 0.657994i | ||||
\(147\) | 6.15776 | − | 18.9516i | 0.507883 | − | 1.56310i | ||||
\(148\) | −0.772707 | − | 2.37815i | −0.0635162 | − | 0.195483i | ||||
\(149\) | −4.59211 | − | 3.33636i | −0.376200 | − | 0.273325i | 0.383577 | − | 0.923509i | \(-0.374692\pi\) |
−0.759777 | + | 0.650184i | \(0.774692\pi\) | |||||||
\(150\) | −2.43760 | + | 7.50216i | −0.199029 | + | 0.612549i | ||||
\(151\) | 4.17951 | + | 12.8632i | 0.340124 | + | 1.04679i | 0.964143 | + | 0.265384i | \(0.0854986\pi\) |
−0.624019 | + | 0.781409i | \(0.714501\pi\) | |||||||
\(152\) | 2.42500 | − | 1.76187i | 0.196694 | − | 0.142906i | ||||
\(153\) | −2.93021 | − | 2.12892i | −0.236893 | − | 0.172113i | ||||
\(154\) | −11.8140 | + | 36.3599i | −0.952002 | + | 2.92996i | ||||
\(155\) | −0.589735 | + | 0.428467i | −0.0473686 | + | 0.0344153i | ||||
\(156\) | −0.761127 | − | 2.34251i | −0.0609390 | − | 0.187551i | ||||
\(157\) | 4.84385 | − | 3.51926i | 0.386581 | − | 0.280868i | −0.377472 | − | 0.926021i | \(-0.623207\pi\) |
0.764053 | + | 0.645153i | \(0.223207\pi\) | |||||||
\(158\) | −3.93029 | + | 2.85552i | −0.312677 | + | 0.227173i | ||||
\(159\) | 7.75270 | − | 5.63266i | 0.614829 | − | 0.446699i | ||||
\(160\) | −0.390961 | + | 1.20326i | −0.0309082 | + | 0.0951257i | ||||
\(161\) | 10.1294 | + | 7.35944i | 0.798308 | + | 0.580005i | ||||
\(162\) | 0.435141 | 0.0341879 | ||||||||
\(163\) | 3.89351 | + | 11.9830i | 0.304963 | + | 0.938580i | 0.979691 | + | 0.200513i | \(0.0642610\pi\) |
−0.674728 | + | 0.738067i | \(0.735739\pi\) | |||||||
\(164\) | −0.245913 | − | 0.756841i | −0.0192025 | − | 0.0590994i | ||||
\(165\) | −2.40590 | −0.187299 | ||||||||
\(166\) | 2.71621 | − | 1.97344i | 0.210819 | − | 0.153169i | ||||
\(167\) | 17.5676 | + | 12.7636i | 1.35943 | + | 0.987680i | 0.998481 | + | 0.0550930i | \(0.0175455\pi\) |
0.360944 | + | 0.932587i | \(0.382454\pi\) | |||||||
\(168\) | −12.8461 | −0.991097 | ||||||||
\(169\) | 3.48967 | − | 10.7401i | 0.268436 | − | 0.826161i | ||||
\(170\) | −0.445932 | + | 1.37244i | −0.0342014 | + | 0.105261i | ||||
\(171\) | −0.731794 | + | 2.25223i | −0.0559617 | + | 0.172232i | ||||
\(172\) | 3.01096 | 0.229584 | ||||||||
\(173\) | −8.68474 | − | 6.30983i | −0.660288 | − | 0.479728i | 0.206472 | − | 0.978453i | \(-0.433802\pi\) |
−0.866760 | + | 0.498725i | \(0.833802\pi\) | |||||||
\(174\) | 7.07018 | 0.535989 | ||||||||
\(175\) | −7.50935 | − | 23.1114i | −0.567654 | − | 1.74706i | ||||
\(176\) | 22.5345 | 1.69860 | ||||||||
\(177\) | 1.88230 | − | 1.36757i | 0.141482 | − | 0.102793i | ||||
\(178\) | 1.74994 | − | 1.27141i | 0.131164 | − | 0.0952961i | ||||
\(179\) | 16.0837 | 1.20215 | 0.601077 | − | 0.799191i | \(-0.294739\pi\) | ||||
0.601077 | + | 0.799191i | \(0.294739\pi\) | |||||||
\(180\) | −0.133607 | − | 0.411200i | −0.00995848 | − | 0.0306491i | ||||
\(181\) | −20.3539 | −1.51289 | −0.756447 | − | 0.654055i | \(-0.773066\pi\) | ||||
−0.756447 | + | 0.654055i | \(0.773066\pi\) | |||||||
\(182\) | 31.9631 | + | 23.2226i | 2.36927 | + | 1.72137i | ||||
\(183\) | −10.1737 | −0.752062 | ||||||||
\(184\) | 1.82161 | − | 5.60634i | 0.134291 | − | 0.413305i | ||||
\(185\) | −0.779997 | + | 2.40058i | −0.0573465 | + | 0.176494i | ||||
\(186\) | 0.776286 | − | 2.38916i | 0.0569201 | − | 0.175182i | ||||
\(187\) | 9.11541 | 0.666585 | ||||||||
\(188\) | 2.98694 | + | 2.17014i | 0.217845 | + | 0.158274i | ||||
\(189\) | 21.2086 | − | 15.4089i | 1.54270 | − | 1.12084i | ||||
\(190\) | 0.943520 | 0.0684501 | ||||||||
\(191\) | −5.78740 | − | 17.8118i | −0.418762 | − | 1.28882i | −0.908843 | − | 0.417139i | \(-0.863033\pi\) |
0.490081 | − | 0.871677i | \(-0.336967\pi\) | |||||||
\(192\) | 1.72213 | + | 5.30016i | 0.124284 | + | 0.382506i | ||||
\(193\) | −20.8928 | −1.50390 | −0.751949 | − | 0.659222i | \(-0.770886\pi\) | ||||
−0.751949 | + | 0.659222i | \(0.770886\pi\) | |||||||
\(194\) | −5.47118 | − | 3.97505i | −0.392808 | − | 0.285392i | ||||
\(195\) | −0.768308 | + | 2.36461i | −0.0550197 | + | 0.169333i | ||||
\(196\) | −7.29127 | + | 5.29742i | −0.520805 | + | 0.378387i | ||||
\(197\) | −17.4538 | + | 12.6810i | −1.24353 | + | 0.903481i | −0.997829 | − | 0.0658638i | \(-0.979020\pi\) |
−0.245706 | + | 0.969344i | \(0.579020\pi\) | |||||||
\(198\) | −11.5046 | + | 8.35859i | −0.817597 | + | 0.594019i | ||||
\(199\) | −2.09292 | − | 6.44133i | −0.148363 | − | 0.456614i | 0.849065 | − | 0.528288i | \(-0.177166\pi\) |
−0.997428 | + | 0.0716740i | \(0.977166\pi\) | |||||||
\(200\) | −9.25603 | + | 6.72490i | −0.654500 | + | 0.475522i | ||||
\(201\) | −0.488895 | + | 1.50466i | −0.0344840 | + | 0.106131i | ||||
\(202\) | −9.93798 | − | 7.22037i | −0.699234 | − | 0.508023i | ||||
\(203\) | −17.6209 | + | 12.8023i | −1.23674 | + | 0.898547i | ||||
\(204\) | −0.295143 | − | 0.908356i | −0.0206641 | − | 0.0635976i | ||||
\(205\) | −0.248232 | + | 0.763981i | −0.0173373 | + | 0.0533588i | ||||
\(206\) | −23.8286 | − | 17.3125i | −1.66022 | − | 1.20622i | ||||
\(207\) | 1.43915 | + | 4.42926i | 0.100028 | + | 0.307855i | ||||
\(208\) | 7.19624 | − | 22.1477i | 0.498969 | − | 1.53567i | ||||
\(209\) | −1.84172 | − | 5.66823i | −0.127395 | − | 0.392080i | ||||
\(210\) | −3.27133 | − | 2.37676i | −0.225743 | − | 0.164012i | ||||
\(211\) | −0.465946 | − | 0.338529i | −0.0320770 | − | 0.0233053i | 0.571631 | − | 0.820511i | \(-0.306311\pi\) |
−0.603708 | + | 0.797205i | \(0.706311\pi\) | |||||||
\(212\) | −4.33412 | −0.297668 | ||||||||
\(213\) | 6.90871 | − | 5.54247i | 0.473377 | − | 0.379764i | ||||
\(214\) | −6.79845 | −0.464732 | ||||||||
\(215\) | −2.45890 | − | 1.78650i | −0.167696 | − | 0.121838i | ||||
\(216\) | −9.98525 | − | 7.25471i | −0.679410 | − | 0.493620i | ||||
\(217\) | 2.39145 | + | 7.36014i | 0.162342 | + | 0.499639i | ||||
\(218\) | −0.901578 | + | 2.77477i | −0.0610626 | + | 0.187931i | ||||
\(219\) | −1.72590 | − | 5.31178i | −0.116626 | − | 0.358937i | ||||
\(220\) | 0.880319 | + | 0.639589i | 0.0593511 | + | 0.0431211i | ||||
\(221\) | 2.91095 | − | 8.95898i | 0.195812 | − | 0.602646i | ||||
\(222\) | −2.68803 | − | 8.27289i | −0.180408 | − | 0.555240i | ||||
\(223\) | −4.35370 | + | 3.16315i | −0.291545 | + | 0.211820i | −0.723938 | − | 0.689866i | \(-0.757670\pi\) |
0.432392 | + | 0.901686i | \(0.357670\pi\) | |||||||
\(224\) | 10.8665 | + | 7.89498i | 0.726049 | + | 0.527505i | ||||
\(225\) | 2.79319 | − | 8.59656i | 0.186213 | − | 0.573104i | ||||
\(226\) | −1.69996 | + | 1.23509i | −0.113080 | + | 0.0821572i | ||||
\(227\) | 1.23901 | + | 3.81327i | 0.0822358 | + | 0.253096i | 0.983718 | − | 0.179721i | \(-0.0575196\pi\) |
−0.901482 | + | 0.432817i | \(0.857520\pi\) | |||||||
\(228\) | −0.505211 | + | 0.367057i | −0.0334584 | + | 0.0243089i | ||||
\(229\) | 8.83914 | − | 6.42201i | 0.584107 | − | 0.424379i | −0.256095 | − | 0.966652i | \(-0.582436\pi\) |
0.840202 | + | 0.542273i | \(0.182436\pi\) | |||||||
\(230\) | 1.50116 | − | 1.09066i | 0.0989835 | − | 0.0719157i | ||||
\(231\) | −7.89296 | + | 24.2920i | −0.519318 | + | 1.59830i | ||||
\(232\) | 8.29612 | + | 6.02748i | 0.544667 | + | 0.395724i | ||||
\(233\) | −5.67125 | −0.371536 | −0.185768 | − | 0.982594i | \(-0.559477\pi\) | ||||
−0.185768 | + | 0.982594i | \(0.559477\pi\) | |||||||
\(234\) | 4.54122 | + | 13.9764i | 0.296869 | + | 0.913669i | ||||
\(235\) | −1.15167 | − | 3.54449i | −0.0751269 | − | 0.231217i | ||||
\(236\) | −1.05229 | −0.0684983 | ||||||||
\(237\) | −2.62582 | + | 1.90777i | −0.170566 | + | 0.123923i | ||||
\(238\) | 12.3944 | + | 9.00503i | 0.803407 | + | 0.583709i | ||||
\(239\) | −21.3798 | −1.38294 | −0.691471 | − | 0.722404i | \(-0.743037\pi\) | ||||
−0.691471 | + | 0.722404i | \(0.743037\pi\) | |||||||
\(240\) | −0.736513 | + | 2.26675i | −0.0475417 | + | 0.146318i | ||||
\(241\) | 5.21881 | − | 16.0618i | 0.336173 | − | 1.03463i | −0.629968 | − | 0.776621i | \(-0.716932\pi\) |
0.966141 | − | 0.258013i | \(-0.0830678\pi\) | |||||||
\(242\) | 5.71131 | − | 17.5776i | 0.367137 | − | 1.12993i | ||||
\(243\) | 15.7271 | 1.00890 | ||||||||
\(244\) | 3.72256 | + | 2.70460i | 0.238313 | + | 0.173144i | ||||
\(245\) | 9.09753 | 0.581220 | ||||||||
\(246\) | −0.855459 | − | 2.63283i | −0.0545421 | − | 0.167863i | ||||
\(247\) | −6.15910 | −0.391894 | ||||||||
\(248\) | 2.94771 | − | 2.14163i | 0.187179 | − | 0.135994i | ||||
\(249\) | 1.81470 | − | 1.31846i | 0.115002 | − | 0.0835539i | ||||
\(250\) | −7.37656 | −0.466534 | ||||||||
\(251\) | 1.23518 | + | 3.80148i | 0.0779636 | + | 0.239947i | 0.982441 | − | 0.186575i | \(-0.0597386\pi\) |
−0.904477 | + | 0.426522i | \(0.859739\pi\) | |||||||
\(252\) | −4.59016 | −0.289153 | ||||||||
\(253\) | −9.48238 | − | 6.88935i | −0.596152 | − | 0.433130i | ||||
\(254\) | 4.92210 | 0.308840 | ||||||||
\(255\) | −0.297927 | + | 0.916925i | −0.0186569 | + | 0.0574201i | ||||
\(256\) | 3.34241 | − | 10.2869i | 0.208901 | − | 0.642931i | ||||
\(257\) | −6.27115 | + | 19.3006i | −0.391184 | + | 1.20394i | 0.540710 | + | 0.841209i | \(0.318156\pi\) |
−0.931894 | + | 0.362731i | \(0.881844\pi\) | |||||||
\(258\) | 10.4743 | 0.652100 | ||||||||
\(259\) | 21.6795 | + | 15.7511i | 1.34710 | + | 0.978723i | ||||
\(260\) | 0.909737 | − | 0.660963i | 0.0564195 | − | 0.0409912i | ||||
\(261\) | −8.10156 | −0.501474 | ||||||||
\(262\) | 10.3106 | + | 31.7328i | 0.636992 | + | 1.96046i | ||||
\(263\) | −2.99875 | − | 9.22920i | −0.184911 | − | 0.569097i | 0.815036 | − | 0.579410i | \(-0.196717\pi\) |
−0.999947 | + | 0.0103135i | \(0.996717\pi\) | |||||||
\(264\) | 12.0255 | 0.740120 | ||||||||
\(265\) | 3.53945 | + | 2.57156i | 0.217427 | + | 0.157970i | ||||
\(266\) | 3.09538 | − | 9.52660i | 0.189790 | − | 0.584113i | ||||
\(267\) | 1.16914 | − | 0.849429i | 0.0715501 | − | 0.0519842i | ||||
\(268\) | 0.578890 | − | 0.420588i | 0.0353613 | − | 0.0256915i | ||||
\(269\) | −1.69652 | + | 1.23260i | −0.103439 | + | 0.0751528i | −0.638302 | − | 0.769786i | \(-0.720363\pi\) |
0.534863 | + | 0.844938i | \(0.320363\pi\) | |||||||
\(270\) | −1.20055 | − | 3.69491i | −0.0730631 | − | 0.224865i | ||||
\(271\) | 0.120476 | − | 0.0875309i | 0.00731839 | − | 0.00531712i | −0.584120 | − | 0.811667i | \(-0.698560\pi\) |
0.591438 | + | 0.806350i | \(0.298560\pi\) | |||||||
\(272\) | 2.79049 | − | 8.58824i | 0.169198 | − | 0.520738i | ||||
\(273\) | 21.3546 | + | 15.5150i | 1.29244 | + | 0.939011i | ||||
\(274\) | 17.2432 | − | 12.5279i | 1.04170 | − | 0.756840i | ||||
\(275\) | 7.02969 | + | 21.6352i | 0.423906 | + | 1.30465i | ||||
\(276\) | −0.379503 | + | 1.16799i | −0.0228434 | + | 0.0703048i | ||||
\(277\) | 3.24494 | + | 2.35758i | 0.194969 | + | 0.141653i | 0.680987 | − | 0.732295i | \(-0.261551\pi\) |
−0.486018 | + | 0.873949i | \(0.661551\pi\) | |||||||
\(278\) | −3.84664 | − | 11.8387i | −0.230706 | − | 0.710040i | ||||
\(279\) | −0.889529 | + | 2.73769i | −0.0532547 | + | 0.163901i | ||||
\(280\) | −1.81233 | − | 5.57777i | −0.108307 | − | 0.333335i | ||||
\(281\) | 14.2647 | + | 10.3639i | 0.850959 | + | 0.618258i | 0.925410 | − | 0.378967i | \(-0.123721\pi\) |
−0.0744513 | + | 0.997225i | \(0.523721\pi\) | |||||||
\(282\) | 10.3907 | + | 7.54929i | 0.618757 | + | 0.449554i | ||||
\(283\) | 21.0156 | 1.24925 | 0.624624 | − | 0.780926i | \(-0.285252\pi\) | ||||
0.624624 | + | 0.780926i | \(0.285252\pi\) | |||||||
\(284\) | −4.00133 | + | 0.191364i | −0.237435 | + | 0.0113553i | ||||
\(285\) | 0.630366 | 0.0373397 | ||||||||
\(286\) | −29.9215 | − | 21.7392i | −1.76929 | − | 1.28547i | ||||
\(287\) | 6.89945 | + | 5.01274i | 0.407262 | + | 0.295893i | ||||
\(288\) | 1.54388 | + | 4.75157i | 0.0909739 | + | 0.279989i | ||||
\(289\) | −4.12451 | + | 12.6939i | −0.242618 | + | 0.746702i | ||||
\(290\) | 0.997461 | + | 3.06987i | 0.0585729 | + | 0.180269i | ||||
\(291\) | −3.65530 | − | 2.65573i | −0.214277 | − | 0.155682i | ||||
\(292\) | −0.780587 | + | 2.40240i | −0.0456804 | + | 0.140590i | ||||
\(293\) | −8.86229 | − | 27.2753i | −0.517741 | − | 1.59344i | −0.778240 | − | 0.627967i | \(-0.783887\pi\) |
0.260499 | − | 0.965474i | \(-0.416113\pi\) | |||||||
\(294\) | −25.3642 | + | 18.4282i | −1.47927 | + | 1.07475i | ||||
\(295\) | 0.859353 | + | 0.624356i | 0.0500334 | + | 0.0363514i | ||||
\(296\) | 3.89870 | − | 11.9990i | 0.226608 | − | 0.697427i | ||||
\(297\) | −19.8539 | + | 14.4247i | −1.15204 | + | 0.837006i | ||||
\(298\) | 2.75969 | + | 8.49345i | 0.159865 | + | 0.492013i | ||||
\(299\) | −9.79926 | + | 7.11958i | −0.566706 | + | 0.411736i | ||||
\(300\) | 1.92834 | − | 1.40102i | 0.111333 | − | 0.0808882i | ||||
\(301\) | −26.1049 | + | 18.9663i | −1.50466 | + | 1.09320i | ||||
\(302\) | 6.57581 | − | 20.2382i | 0.378395 | − | 1.16458i | ||||
\(303\) | −6.63957 | − | 4.82393i | −0.381433 | − | 0.277127i | ||||
\(304\) | −5.90422 | −0.338631 | ||||||||
\(305\) | −1.43531 | − | 4.41742i | −0.0821854 | − | 0.252941i | ||||
\(306\) | 1.76095 | + | 5.41965i | 0.100667 | + | 0.309821i | ||||
\(307\) | 22.6278 | 1.29144 | 0.645719 | − | 0.763575i | \(-0.276558\pi\) | ||||
0.645719 | + | 0.763575i | \(0.276558\pi\) | |||||||
\(308\) | 9.34589 | − | 6.79018i | 0.532531 | − | 0.386907i | ||||
\(309\) | −15.9199 | − | 11.5665i | −0.905652 | − | 0.657995i | ||||
\(310\) | 1.14689 | 0.0651391 | ||||||||
\(311\) | 0.853167 | − | 2.62578i | 0.0483786 | − | 0.148894i | −0.923949 | − | 0.382516i | \(-0.875058\pi\) |
0.972328 | + | 0.233622i | \(0.0750577\pi\) | |||||||
\(312\) | 3.84028 | − | 11.8192i | 0.217413 | − | 0.669128i | ||||
\(313\) | −3.99992 | + | 12.3105i | −0.226089 | + | 0.695829i | 0.772091 | + | 0.635512i | \(0.219211\pi\) |
−0.998179 | + | 0.0603168i | \(0.980789\pi\) | |||||||
\(314\) | −9.42013 | −0.531608 | ||||||||
\(315\) | 3.74855 | + | 2.72348i | 0.211207 | + | 0.153451i | ||||
\(316\) | 1.46796 | 0.0825791 | ||||||||
\(317\) | 6.71851 | + | 20.6775i | 0.377349 | + | 1.16136i | 0.941880 | + | 0.335950i | \(0.109057\pi\) |
−0.564531 | + | 0.825412i | \(0.690943\pi\) | |||||||
\(318\) | −15.0771 | −0.845484 | ||||||||
\(319\) | 16.4954 | − | 11.9846i | 0.923562 | − | 0.671007i | ||||
\(320\) | −2.05837 | + | 1.49550i | −0.115067 | + | 0.0836007i | ||||
\(321\) | −4.54204 | −0.253512 | ||||||||
\(322\) | −6.08740 | − | 18.7351i | −0.339238 | − | 1.04407i | ||||
\(323\) | −2.38832 | −0.132890 | ||||||||
\(324\) | −0.106374 | − | 0.0772851i | −0.00590966 | − | 0.00429362i | ||||
\(325\) | 23.5088 | 1.30403 | ||||||||
\(326\) | 6.12583 | − | 18.8534i | 0.339278 | − | 1.04419i | ||||
\(327\) | −0.602345 | + | 1.85383i | −0.0333097 | + | 0.102517i | ||||
\(328\) | 1.24076 | − | 3.81865i | 0.0685092 | − | 0.210850i | ||||
\(329\) | −39.5665 | −2.18137 | ||||||||
\(330\) | 3.06237 | + | 2.22495i | 0.168578 | + | 0.122479i | ||||
\(331\) | −12.5241 | + | 9.09928i | −0.688386 | + | 0.500141i | −0.876129 | − | 0.482077i | \(-0.839883\pi\) |
0.187743 | + | 0.982218i | \(0.439883\pi\) | |||||||
\(332\) | −1.01450 | −0.0556781 | ||||||||
\(333\) | 3.08015 | + | 9.47973i | 0.168791 | + | 0.519486i | ||||
\(334\) | −10.5575 | − | 32.4927i | −0.577682 | − | 1.77792i | ||||
\(335\) | −0.722298 | −0.0394633 | ||||||||
\(336\) | 20.4709 | + | 14.8730i | 1.11678 | + | 0.811386i | ||||
\(337\) | −8.44372 | + | 25.9871i | −0.459959 | + | 1.41561i | 0.405255 | + | 0.914204i | \(0.367183\pi\) |
−0.865213 | + | 0.501404i | \(0.832817\pi\) | |||||||
\(338\) | −14.3742 | + | 10.4435i | −0.781853 | + | 0.568049i | ||||
\(339\) | −1.13574 | + | 0.825166i | −0.0616851 | + | 0.0448169i | ||||
\(340\) | 0.352769 | − | 0.256302i | 0.0191316 | − | 0.0138999i | ||||
\(341\) | −2.23870 | − | 6.89000i | −0.121232 | − | 0.373115i | ||||
\(342\) | 3.01431 | − | 2.19002i | 0.162995 | − | 0.118423i | ||||
\(343\) | 18.8253 | − | 57.9384i | 1.01647 | − | 3.12838i | ||||
\(344\) | 12.2905 | + | 8.92955i | 0.662658 | + | 0.481449i | ||||
\(345\) | 1.00292 | − | 0.728668i | 0.0539957 | − | 0.0392301i | ||||
\(346\) | 5.21922 | + | 16.0631i | 0.280587 | + | 0.863557i | ||||
\(347\) | 0.276474 | − | 0.850901i | 0.0148419 | − | 0.0456787i | −0.943361 | − | 0.331767i | \(-0.892355\pi\) |
0.958203 | + | 0.286089i | \(0.0923551\pi\) | |||||||
\(348\) | −1.72836 | − | 1.25573i | −0.0926500 | − | 0.0673142i | ||||
\(349\) | −7.79406 | − | 23.9877i | −0.417207 | − | 1.28403i | −0.910262 | − | 0.414032i | \(-0.864120\pi\) |
0.493056 | − | 0.869998i | \(-0.335880\pi\) | |||||||
\(350\) | −11.8148 | + | 36.3622i | −0.631527 | + | 1.94364i | ||||
\(351\) | 7.83694 | + | 24.1196i | 0.418305 | + | 1.28741i | ||||
\(352\) | −10.1724 | − | 7.39068i | −0.542191 | − | 0.393925i | ||||
\(353\) | −11.9616 | − | 8.69059i | −0.636650 | − | 0.462553i | 0.222048 | − | 0.975036i | \(-0.428726\pi\) |
−0.858698 | + | 0.512483i | \(0.828726\pi\) | |||||||
\(354\) | −3.66062 | −0.194560 | ||||||||
\(355\) | 3.38122 | + | 2.21783i | 0.179457 | + | 0.117710i | ||||
\(356\) | −0.653602 | −0.0346409 | ||||||||
\(357\) | 8.28067 | + | 6.01626i | 0.438260 | + | 0.318414i | ||||
\(358\) | −20.4724 | − | 14.8740i | −1.08200 | − | 0.786117i | ||||
\(359\) | −2.11004 | − | 6.49405i | −0.111364 | − | 0.342743i | 0.879807 | − | 0.475330i | \(-0.157671\pi\) |
−0.991171 | + | 0.132588i | \(0.957671\pi\) | |||||||
\(360\) | 0.674116 | − | 2.07472i | 0.0355290 | − | 0.109347i | ||||
\(361\) | −5.38878 | − | 16.5849i | −0.283620 | − | 0.872892i | ||||
\(362\) | 25.9077 | + | 18.8231i | 1.36168 | + | 0.989318i | ||||
\(363\) | 3.81573 | − | 11.7436i | 0.200274 | − | 0.616379i | ||||
\(364\) | −3.68911 | − | 11.3539i | −0.193362 | − | 0.595106i | ||||
\(365\) | 2.06288 | − | 1.49877i | 0.107976 | − | 0.0784493i | ||||
\(366\) | 12.9497 | + | 9.40852i | 0.676893 | + | 0.491791i | ||||
\(367\) | 6.69671 | − | 20.6104i | 0.349565 | − | 1.07585i | −0.609529 | − | 0.792764i | \(-0.708641\pi\) |
0.959094 | − | 0.283088i | \(-0.0913587\pi\) | |||||||
\(368\) | −9.39374 | + | 6.82495i | −0.489683 | + | 0.355775i | ||||
\(369\) | 0.980252 | + | 3.01690i | 0.0510299 | + | 0.157054i | ||||
\(370\) | 3.21286 | − | 2.33428i | 0.167029 | − | 0.121353i | ||||
\(371\) | 37.5765 | − | 27.3009i | 1.95088 | − | 1.41739i | ||||
\(372\) | −0.614107 | + | 0.446175i | −0.0318400 | + | 0.0231331i | ||||
\(373\) | 4.04478 | − | 12.4486i | 0.209431 | − | 0.644562i | −0.790071 | − | 0.613015i | \(-0.789957\pi\) |
0.999502 | − | 0.0315470i | \(-0.0100434\pi\) | |||||||
\(374\) | −11.6027 | − | 8.42983i | −0.599959 | − | 0.435896i | ||||
\(375\) | −4.92828 | −0.254495 | ||||||||
\(376\) | 5.75648 | + | 17.7166i | 0.296868 | + | 0.913664i | ||||
\(377\) | −6.51122 | − | 20.0395i | −0.335345 | − | 1.03209i | ||||
\(378\) | −41.2457 | −2.12145 | ||||||||
\(379\) | −8.78181 | + | 6.38036i | −0.451091 | + | 0.327737i | −0.790026 | − | 0.613073i | \(-0.789933\pi\) |
0.338935 | + | 0.940810i | \(0.389933\pi\) | |||||||
\(380\) | −0.230651 | − | 0.167578i | −0.0118322 | − | 0.00859657i | ||||
\(381\) | 3.28845 | 0.168473 | ||||||||
\(382\) | −9.10558 | + | 28.0241i | −0.465882 | + | 1.43384i | ||||
\(383\) | −8.61334 | + | 26.5091i | −0.440121 | + | 1.35455i | 0.447626 | + | 0.894221i | \(0.352270\pi\) |
−0.887747 | + | 0.460332i | \(0.847730\pi\) | |||||||
\(384\) | 4.42220 | − | 13.6101i | 0.225669 | − | 0.694539i | ||||
\(385\) | −11.6611 | −0.594306 | ||||||||
\(386\) | 26.5937 | + | 19.3214i | 1.35358 | + | 0.983435i | ||||
\(387\) | −12.0022 | −0.610108 | ||||||||
\(388\) | 0.631470 | + | 1.94347i | 0.0320580 | + | 0.0986645i | ||||
\(389\) | 7.01800 | 0.355827 | 0.177913 | − | 0.984046i | \(-0.443065\pi\) | ||||
0.177913 | + | 0.984046i | \(0.443065\pi\) | |||||||
\(390\) | 3.16471 | − | 2.29930i | 0.160251 | − | 0.116429i | ||||
\(391\) | −3.79986 | + | 2.76076i | −0.192167 | + | 0.139618i | ||||
\(392\) | −45.4727 | −2.29672 | ||||||||
\(393\) | 6.88853 | + | 21.2007i | 0.347480 | + | 1.06943i | ||||
\(394\) | 33.9435 | 1.71005 | ||||||||
\(395\) | −1.19881 | − | 0.870984i | −0.0603185 | − | 0.0438239i | ||||
\(396\) | 4.29696 | 0.215930 | ||||||||
\(397\) | 2.65674 | − | 8.17660i | 0.133338 | − | 0.410372i | −0.861990 | − | 0.506925i | \(-0.830782\pi\) |
0.995328 | + | 0.0965538i | \(0.0307820\pi\) | |||||||
\(398\) | −3.29288 | + | 10.1344i | −0.165057 | + | 0.507993i | ||||
\(399\) | 2.06802 | − | 6.36472i | 0.103531 | − | 0.318635i | ||||
\(400\) | 22.5359 | 1.12680 | ||||||||
\(401\) | 17.6636 | + | 12.8334i | 0.882078 | + | 0.640867i | 0.933801 | − | 0.357794i | \(-0.116471\pi\) |
−0.0517222 | + | 0.998662i | \(0.516471\pi\) | |||||||
\(402\) | 2.01379 | − | 1.46311i | 0.100439 | − | 0.0729731i | ||||
\(403\) | −7.48668 | −0.372938 | ||||||||
\(404\) | 1.14702 | + | 3.53016i | 0.0570662 | + | 0.175632i | ||||
\(405\) | 0.0410145 | + | 0.126230i | 0.00203803 | + | 0.00627240i | ||||
\(406\) | 34.2684 | 1.70071 | ||||||||
\(407\) | −20.2947 | − | 14.7450i | −1.00597 | − | 0.730880i | ||||
\(408\) | 1.48915 | − | 4.58312i | 0.0737237 | − | 0.226898i | ||||
\(409\) | 13.0018 | − | 9.44638i | 0.642899 | − | 0.467093i | −0.217946 | − | 0.975961i | \(-0.569936\pi\) |
0.860845 | + | 0.508867i | \(0.169936\pi\) | |||||||
\(410\) | 1.02249 | − | 0.742880i | 0.0504970 | − | 0.0366882i | ||||
\(411\) | 11.5202 | − | 8.36991i | 0.568249 | − | 0.412857i | ||||
\(412\) | 2.75024 | + | 8.46437i | 0.135495 | + | 0.417010i | ||||
\(413\) | 9.12330 | − | 6.62847i | 0.448928 | − | 0.326165i | ||||
\(414\) | 2.26428 | − | 6.96874i | 0.111283 | − | 0.342495i | ||||
\(415\) | 0.828492 | + | 0.601935i | 0.0406691 | + | 0.0295478i | ||||
\(416\) | −10.5123 | + | 7.63766i | −0.515410 | + | 0.374467i | ||||
\(417\) | −2.56994 | − | 7.90946i | −0.125850 | − | 0.387328i | ||||
\(418\) | −2.89766 | + | 8.91809i | −0.141729 | + | 0.436198i | ||||
\(419\) | 16.9394 | + | 12.3072i | 0.827542 | + | 0.601244i | 0.918863 | − | 0.394577i | \(-0.129109\pi\) |
−0.0913209 | + | 0.995822i | \(0.529109\pi\) | |||||||
\(420\) | 0.377569 | + | 1.16204i | 0.0184235 | + | 0.0567017i | ||||
\(421\) | −6.52349 | + | 20.0773i | −0.317936 | + | 0.978505i | 0.656594 | + | 0.754245i | \(0.271997\pi\) |
−0.974529 | + | 0.224261i | \(0.928003\pi\) | |||||||
\(422\) | 0.280017 | + | 0.861803i | 0.0136310 | + | 0.0419519i | ||||
\(423\) | −11.9065 | − | 8.65057i | −0.578913 | − | 0.420605i | ||||
\(424\) | −17.6915 | − | 12.8536i | −0.859173 | − | 0.624226i | ||||
\(425\) | 9.11600 | 0.442191 | ||||||||
\(426\) | −13.9195 | + | 0.665698i | −0.674400 | + | 0.0322532i | ||||
\(427\) | −49.3109 | −2.38632 | ||||||||
\(428\) | 1.66194 | + | 1.20747i | 0.0803327 | + | 0.0583651i | ||||
\(429\) | −19.9905 | − | 14.5240i | −0.965153 | − | 0.701224i | ||||
\(430\) | 1.47771 | + | 4.54793i | 0.0712616 | + | 0.219321i | ||||
\(431\) | −7.30855 | + | 22.4934i | −0.352040 | + | 1.08347i | 0.605665 | + | 0.795719i | \(0.292907\pi\) |
−0.957706 | + | 0.287749i | \(0.907093\pi\) | |||||||
\(432\) | 7.51263 | + | 23.1215i | 0.361451 | + | 1.11243i | ||||
\(433\) | 6.61299 | + | 4.80462i | 0.317800 | + | 0.230895i | 0.735236 | − | 0.677811i | \(-0.237071\pi\) |
−0.417436 | + | 0.908706i | \(0.637071\pi\) | |||||||
\(434\) | 3.76258 | − | 11.5800i | 0.180610 | − | 0.555859i | ||||
\(435\) | 0.666404 | + | 2.05098i | 0.0319516 | + | 0.0983370i | ||||
\(436\) | 0.713224 | − | 0.518187i | 0.0341572 | − | 0.0248167i | ||||
\(437\) | 2.48447 | + | 1.80507i | 0.118848 | + | 0.0863482i | ||||
\(438\) | −2.71544 | + | 8.35725i | −0.129749 | + | 0.399325i | ||||
\(439\) | 1.00668 | − | 0.731398i | 0.0480463 | − | 0.0349077i | −0.563503 | − | 0.826114i | \(-0.690547\pi\) |
0.611549 | + | 0.791206i | \(0.290547\pi\) | |||||||
\(440\) | 1.69656 | + | 5.22148i | 0.0808805 | + | 0.248924i | ||||
\(441\) | 29.0643 | − | 21.1165i | 1.38402 | − | 1.00555i | ||||
\(442\) | −11.9904 | + | 8.71154i | −0.570325 | + | 0.414366i | ||||
\(443\) | 25.4672 | − | 18.5030i | 1.20999 | − | 0.879106i | 0.214756 | − | 0.976668i | \(-0.431104\pi\) |
0.995229 | + | 0.0975618i | \(0.0311044\pi\) | |||||||
\(444\) | −0.812233 | + | 2.49980i | −0.0385469 | + | 0.118635i | ||||
\(445\) | 0.533764 | + | 0.387802i | 0.0253028 | + | 0.0183836i | ||||
\(446\) | 8.46691 | 0.400920 | ||||||||
\(447\) | 1.84375 | + | 5.67448i | 0.0872064 | + | 0.268394i | ||||
\(448\) | 8.34698 | + | 25.6894i | 0.394358 | + | 1.21371i | ||||
\(449\) | 20.6146 | 0.972863 | 0.486432 | − | 0.873719i | \(-0.338298\pi\) | ||||
0.486432 | + | 0.873719i | \(0.338298\pi\) | |||||||
\(450\) | −11.5054 | + | 8.35913i | −0.542368 | + | 0.394053i | ||||
\(451\) | −6.45874 | − | 4.69255i | −0.304130 | − | 0.220964i | ||||
\(452\) | 0.634933 | 0.0298648 | ||||||||
\(453\) | 4.39330 | − | 13.5212i | 0.206415 | − | 0.635280i | ||||
\(454\) | 1.94938 | − | 5.99959i | 0.0914891 | − | 0.281575i | ||||
\(455\) | −3.72391 | + | 11.4610i | −0.174580 | + | 0.537301i | ||||
\(456\) | −3.15079 | −0.147549 | ||||||||
\(457\) | 11.1221 | + | 8.08065i | 0.520268 | + | 0.377997i | 0.816705 | − | 0.577055i | \(-0.195798\pi\) |
−0.296437 | + | 0.955053i | \(0.595798\pi\) | |||||||
\(458\) | −17.1900 | −0.803237 | ||||||||
\(459\) | 3.03893 | + | 9.35287i | 0.141845 | + | 0.436555i | ||||
\(460\) | −0.560682 | −0.0261419 | ||||||||
\(461\) | −22.1855 | + | 16.1187i | −1.03328 | + | 0.750724i | −0.968963 | − | 0.247206i | \(-0.920488\pi\) |
−0.0643196 | + | 0.997929i | \(0.520488\pi\) | |||||||
\(462\) | 32.5116 | − | 23.6211i | 1.51258 | − | 1.09895i | ||||
\(463\) | 26.0295 | 1.20969 | 0.604846 | − | 0.796343i | \(-0.293235\pi\) | ||||
0.604846 | + | 0.796343i | \(0.293235\pi\) | |||||||
\(464\) | −6.24177 | − | 19.2102i | −0.289767 | − | 0.891811i | ||||
\(465\) | 0.766239 | 0.0355335 | ||||||||
\(466\) | 7.21872 | + | 5.24471i | 0.334401 | + | 0.242956i | ||||
\(467\) | −25.0045 | −1.15707 | −0.578536 | − | 0.815657i | \(-0.696376\pi\) | ||||
−0.578536 | + | 0.815657i | \(0.696376\pi\) | |||||||
\(468\) | 1.37221 | − | 4.22322i | 0.0634303 | − | 0.195218i | ||||
\(469\) | −2.36962 | + | 7.29295i | −0.109419 | + | 0.336757i | ||||
\(470\) | −1.81198 | + | 5.57670i | −0.0835803 | + | 0.257234i | ||||
\(471\) | −6.29359 | −0.289993 | ||||||||
\(472\) | −4.29535 | − | 3.12076i | −0.197710 | − | 0.143644i | ||||
\(473\) | 24.4374 | − | 17.7548i | 1.12363 | − | 0.816367i | ||||
\(474\) | 5.10660 | 0.234554 | ||||||||
\(475\) | −1.84184 | − | 5.66860i | −0.0845094 | − | 0.260093i | ||||
\(476\) | −1.43053 | − | 4.40271i | −0.0655681 | − | 0.201798i | ||||
\(477\) | 17.2766 | 0.791040 | ||||||||
\(478\) | 27.2135 | + | 19.7718i | 1.24472 | + | 0.904339i | ||||
\(479\) | 4.07082 | − | 12.5287i | 0.186001 | − | 0.572451i | −0.813964 | − | 0.580916i | \(-0.802694\pi\) |
0.999964 | + | 0.00846486i | \(0.00269448\pi\) | |||||||
\(480\) | 1.07591 | − | 0.781692i | 0.0491082 | − | 0.0356792i | ||||
\(481\) | −20.9729 | + | 15.2377i | −0.956282 | + | 0.694779i | ||||
\(482\) | −21.4966 | + | 15.6182i | −0.979145 | + | 0.711390i | ||||
\(483\) | −4.06699 | − | 12.5169i | −0.185055 | − | 0.569540i | ||||
\(484\) | −4.51812 | + | 3.28261i | −0.205369 | + | 0.149210i | ||||
\(485\) | 0.637427 | − | 1.96180i | 0.0289441 | − | 0.0890807i | ||||
\(486\) | −20.0185 | − | 14.5443i | −0.908056 | − | 0.659742i | ||||
\(487\) | −28.6618 | + | 20.8240i | −1.29879 | + | 0.943627i | −0.999943 | − | 0.0106733i | \(-0.996603\pi\) |
−0.298849 | + | 0.954301i | \(0.596603\pi\) | |||||||
\(488\) | 7.17418 | + | 22.0798i | 0.324760 | + | 0.999508i | ||||
\(489\) | 4.09267 | − | 12.5959i | 0.185077 | − | 0.569608i | ||||
\(490\) | −11.5799 | − | 8.41329i | −0.523127 | − | 0.380074i | ||||
\(491\) | 1.81161 | + | 5.57557i | 0.0817570 | + | 0.251622i | 0.983577 | − | 0.180490i | \(-0.0577684\pi\) |
−0.901820 | + | 0.432112i | \(0.857768\pi\) | |||||||
\(492\) | −0.258491 | + | 0.795555i | −0.0116537 | + | 0.0358664i | ||||
\(493\) | −2.52486 | − | 7.77071i | −0.113714 | − | 0.349975i | ||||
\(494\) | 7.83969 | + | 5.69587i | 0.352724 | + | 0.256269i | ||||
\(495\) | −3.50911 | − | 2.54952i | −0.157723 | − | 0.114592i | ||||
\(496\) | −7.17686 | −0.322251 | ||||||||
\(497\) | 33.4858 | − | 26.8638i | 1.50204 | − | 1.20501i | ||||
\(498\) | −3.52916 | −0.158145 | ||||||||
\(499\) | −16.5384 | − | 12.0158i | −0.740359 | − | 0.537903i | 0.152464 | − | 0.988309i | \(-0.451279\pi\) |
−0.892824 | + | 0.450406i | \(0.851279\pi\) | |||||||
\(500\) | 1.80326 | + | 1.31014i | 0.0806442 | + | 0.0585915i | ||||
\(501\) | −7.05348 | − | 21.7084i | −0.315126 | − | 0.969859i | ||||
\(502\) | 1.94336 | − | 5.98104i | 0.0867363 | − | 0.266947i | ||||
\(503\) | 9.05107 | + | 27.8563i | 0.403567 | + | 1.24205i | 0.922086 | + | 0.386986i | \(0.126484\pi\) |
−0.518519 | + | 0.855066i | \(0.673516\pi\) | |||||||
\(504\) | −18.7366 | − | 13.6129i | −0.834594 | − | 0.606368i | ||||
\(505\) | 1.15784 | − | 3.56346i | 0.0515231 | − | 0.158572i | ||||
\(506\) | 5.69857 | + | 17.5384i | 0.253332 | + | 0.779676i | ||||
\(507\) | −9.60339 | + | 6.97727i | −0.426502 | + | 0.309872i | ||||
\(508\) | −1.20325 | − | 0.874210i | −0.0533855 | − | 0.0387868i | ||||
\(509\) | −9.46544 | + | 29.1316i | −0.419548 | + | 1.29124i | 0.488571 | + | 0.872524i | \(0.337518\pi\) |
−0.908119 | + | 0.418712i | \(0.862482\pi\) | |||||||
\(510\) | 1.22718 | − | 0.891600i | 0.0543405 | − | 0.0394807i | ||||
\(511\) | −8.36527 | − | 25.7456i | −0.370058 | − | 1.13892i | ||||
\(512\) | 8.26052 | − | 6.00162i | 0.365067 | − | 0.265236i | ||||
\(513\) | 5.20189 | − | 3.77940i | 0.229669 | − | 0.166864i | ||||
\(514\) | 25.8313 | − | 18.7675i | 1.13937 | − | 0.827801i | ||||
\(515\) | 2.77619 | − | 8.54422i | 0.122333 | − | 0.376503i | ||||
\(516\) | −2.56052 | − | 1.86033i | −0.112721 | − | 0.0818964i | ||||
\(517\) | 37.0391 | 1.62898 | ||||||||
\(518\) | −13.0286 | − | 40.0979i | −0.572443 | − | 1.76180i | ||||
\(519\) | 3.48696 | + | 10.7318i | 0.153060 | + | 0.471072i | ||||
\(520\) | 5.67366 | 0.248807 | ||||||||
\(521\) | 26.2726 | − | 19.0882i | 1.15102 | − | 0.836267i | 0.162406 | − | 0.986724i | \(-0.448074\pi\) |
0.988617 | + | 0.150457i | \(0.0480745\pi\) | |||||||
\(522\) | 10.3122 | + | 7.49223i | 0.451352 | + | 0.327926i | ||||
\(523\) | −2.06231 | −0.0901787 | −0.0450894 | − | 0.998983i | \(-0.514357\pi\) | ||||
−0.0450894 | + | 0.998983i | \(0.514357\pi\) | |||||||
\(524\) | 3.11553 | − | 9.58861i | 0.136103 | − | 0.418881i | ||||
\(525\) | −7.89347 | + | 24.2936i | −0.344499 | + | 1.06026i | ||||
\(526\) | −4.71806 | + | 14.5207i | −0.205717 | + | 0.633133i | ||||
\(527\) | −2.90311 | −0.126462 | ||||||||
\(528\) | −19.1633 | − | 13.9229i | −0.833975 | − | 0.605918i | ||||
\(529\) | −16.9606 | −0.737418 | ||||||||
\(530\) | −2.12708 | − | 6.54649i | −0.0923946 | − | 0.284361i | ||||
\(531\) | 4.19462 | 0.182031 | ||||||||
\(532\) | −2.44870 | + | 1.77909i | −0.106165 | + | 0.0771332i | ||||
\(533\) | −6.67458 | + | 4.84937i | −0.289108 | + | 0.210049i | ||||
\(534\) | −2.27369 | −0.0983923 | ||||||||
\(535\) | −0.640792 | − | 1.97215i | −0.0277038 | − | 0.0852637i | ||||
\(536\) | 3.61030 | 0.155941 | ||||||||
\(537\) | −13.6776 | − | 9.93735i | −0.590231 | − | 0.428828i | ||||
\(538\) | 3.29933 | 0.142244 | ||||||||
\(539\) | −27.9396 | + | 85.9892i | −1.20344 | + | 3.70382i | ||||
\(540\) | −0.362766 | + | 1.11648i | −0.0156110 | + | 0.0480457i | ||||
\(541\) | −5.13856 | + | 15.8149i | −0.220924 | + | 0.679934i | 0.777756 | + | 0.628566i | \(0.216358\pi\) |
−0.998680 | + | 0.0513674i | \(0.983642\pi\) | |||||||
\(542\) | −0.234297 | −0.0100639 | ||||||||
\(543\) | 17.3090 | + | 12.5757i | 0.742798 | + | 0.539674i | ||||
\(544\) | −4.07637 | + | 2.96166i | −0.174773 | + | 0.126980i | ||||
\(545\) | −0.889910 | −0.0381195 | ||||||||
\(546\) | −12.8333 | − | 39.4969i | −0.549216 | − | 1.69031i | ||||
\(547\) | −1.52958 | − | 4.70755i | −0.0653999 | − | 0.201280i | 0.913017 | − | 0.407922i | \(-0.133747\pi\) |
−0.978417 | + | 0.206642i | \(0.933747\pi\) | |||||||
\(548\) | −6.44032 | −0.275117 | ||||||||
\(549\) | −14.8388 | − | 10.7810i | −0.633305 | − | 0.460123i | ||||
\(550\) | 11.0601 | − | 34.0396i | 0.471605 | − | 1.45145i | ||||
\(551\) | −4.32193 | + | 3.14006i | −0.184120 | + | 0.133771i | ||||
\(552\) | −5.01298 | + | 3.64214i | −0.213367 | + | 0.155020i | ||||
\(553\) | −12.7271 | + | 9.24678i | −0.541211 | + | 0.393213i | ||||
\(554\) | −1.95009 | − | 6.00176i | −0.0828514 | − | 0.254990i | ||||
\(555\) | 2.14651 | − | 1.55953i | 0.0911144 | − | 0.0661985i | ||||
\(556\) | −1.16233 | + | 3.57727i | −0.0492936 | + | 0.151710i | ||||
\(557\) | 7.67465 | + | 5.57596i | 0.325185 | + | 0.236261i | 0.738385 | − | 0.674380i | \(-0.235589\pi\) |
−0.413200 | + | 0.910641i | \(0.635589\pi\) | |||||||
\(558\) | 3.66403 | − | 2.66208i | 0.155111 | − | 0.112695i | ||||
\(559\) | −9.64619 | − | 29.6879i | −0.407991 | − | 1.25567i | ||||
\(560\) | −3.56980 | + | 10.9867i | −0.150852 | + | 0.464274i | ||||
\(561\) | −7.75174 | − | 5.63197i | −0.327279 | − | 0.237782i | ||||
\(562\) | −8.57256 | − | 26.3836i | −0.361611 | − | 1.11293i | ||||
\(563\) | 6.60972 | − | 20.3426i | 0.278567 | − | 0.857340i | −0.709687 | − | 0.704517i | \(-0.751164\pi\) |
0.988254 | − | 0.152823i | \(-0.0488364\pi\) | |||||||
\(564\) | −1.19927 | − | 3.69097i | −0.0504984 | − | 0.155418i | ||||
\(565\) | −0.518518 | − | 0.376725i | −0.0218142 | − | 0.0158489i | ||||
\(566\) | −26.7500 | − | 19.4350i | −1.12439 | − | 0.816914i | ||||
\(567\) | 1.40908 | 0.0591758 | ||||||||
\(568\) | −16.9006 | − | 11.0855i | −0.709132 | − | 0.465138i | ||||
\(569\) | 2.76131 | 0.115760 | 0.0578800 | − | 0.998324i | \(-0.481566\pi\) | ||||
0.0578800 | + | 0.998324i | \(0.481566\pi\) | |||||||
\(570\) | −0.802369 | − | 0.582955i | −0.0336075 | − | 0.0244173i | ||||
\(571\) | −10.9168 | − | 7.93151i | −0.456853 | − | 0.331923i | 0.335442 | − | 0.942061i | \(-0.391114\pi\) |
−0.792296 | + | 0.610137i | \(0.791114\pi\) | |||||||
\(572\) | 3.45346 | + | 10.6287i | 0.144397 | + | 0.444407i | ||||
\(573\) | −6.08344 | + | 18.7229i | −0.254139 | + | 0.782160i | ||||
\(574\) | −4.14632 | − | 12.7611i | −0.173064 | − | 0.532637i | ||||
\(575\) | −9.48299 | − | 6.88980i | −0.395468 | − | 0.287324i | ||||
\(576\) | −3.10476 | + | 9.55546i | −0.129365 | + | 0.398144i | ||||
\(577\) | 9.07319 | + | 27.9244i | 0.377722 | + | 1.16251i | 0.941624 | + | 0.336667i | \(0.109300\pi\) |
−0.563902 | + | 0.825842i | \(0.690700\pi\) | |||||||
\(578\) | 16.9891 | − | 12.3433i | 0.706655 | − | 0.513415i | ||||
\(579\) | 17.7672 | + | 12.9087i | 0.738381 | + | 0.536465i | ||||
\(580\) | 0.301400 | − | 0.927613i | 0.0125149 | − | 0.0385170i | ||||
\(581\) | 8.79567 | − | 6.39043i | 0.364906 | − | 0.265120i | ||||
\(582\) | 2.19670 | + | 6.76075i | 0.0910562 | + | 0.280242i | ||||
\(583\) | −35.1763 | + | 25.5571i | −1.45685 | + | 1.05847i | ||||
\(584\) | −10.3110 | + | 7.49140i | −0.426673 | + | 0.309996i | ||||
\(585\) | −3.62638 | + | 2.63472i | −0.149932 | + | 0.108932i | ||||
\(586\) | −13.9434 | + | 42.9135i | −0.575998 | + | 1.77274i | ||||
\(587\) | −14.7046 | − | 10.6835i | −0.606924 | − | 0.440956i | 0.241406 | − | 0.970424i | \(-0.422391\pi\) |
−0.848330 | + | 0.529468i | \(0.822391\pi\) | |||||||
\(588\) | 9.47351 | 0.390681 | ||||||||
\(589\) | 0.586559 | + | 1.80524i | 0.0241687 | + | 0.0743837i | ||||
\(590\) | −0.516440 | − | 1.58944i | −0.0212615 | − | 0.0654362i | ||||
\(591\) | 22.6777 | 0.932835 | ||||||||
\(592\) | −20.1050 | + | 14.6071i | −0.826310 | + | 0.600349i | ||||
\(593\) | −15.1915 | − | 11.0372i | −0.623839 | − | 0.453245i | 0.230422 | − | 0.973091i | \(-0.425989\pi\) |
−0.854260 | + | 0.519846i | \(0.825989\pi\) | |||||||
\(594\) | 38.6111 | 1.58423 | ||||||||
\(595\) | −1.44402 | + | 4.44424i | −0.0591991 | + | 0.182196i | ||||
\(596\) | 0.833887 | − | 2.56644i | 0.0341574 | − | 0.105126i | ||||
\(597\) | −2.19997 | + | 6.77082i | −0.0900389 | + | 0.277111i | ||||
\(598\) | 19.0572 | 0.779307 | ||||||||
\(599\) | 12.5179 | + | 9.09479i | 0.511468 | + | 0.371603i | 0.813380 | − | 0.581733i | \(-0.197625\pi\) |
−0.301912 | + | 0.953336i | \(0.597625\pi\) | |||||||
\(600\) | 12.0263 | 0.490972 | ||||||||
\(601\) | 7.46527 | + | 22.9758i | 0.304515 | + | 0.937201i | 0.979858 | + | 0.199697i | \(0.0639957\pi\) |
−0.675343 | + | 0.737504i | \(0.736004\pi\) | |||||||
\(602\) | 50.7677 | 2.06914 | ||||||||
\(603\) | −2.30756 | + | 1.67654i | −0.0939711 | + | 0.0682740i | ||||
\(604\) | −5.20201 | + | 3.77948i | −0.211667 | + | 0.153785i | ||||
\(605\) | 5.63739 | 0.229193 | ||||||||
\(606\) | 3.99014 | + | 12.2804i | 0.162088 | + | 0.498857i | ||||
\(607\) | −5.07800 | −0.206110 | −0.103055 | − | 0.994676i | \(-0.532862\pi\) | ||||
−0.103055 | + | 0.994676i | \(0.532862\pi\) | |||||||
\(608\) | 2.66526 | + | 1.93642i | 0.108090 | + | 0.0785323i | ||||
\(609\) | 22.8947 | 0.927742 | ||||||||
\(610\) | −2.25823 | + | 6.95012i | −0.0914331 | + | 0.281402i | ||||
\(611\) | 11.8282 | − | 36.4035i | 0.478519 | − | 1.47273i | ||||
\(612\) | 0.532101 | − | 1.63764i | 0.0215089 | − | 0.0661976i | ||||
\(613\) | 29.9794 | 1.21085 | 0.605427 | − | 0.795900i | \(-0.293002\pi\) | ||||
0.605427 | + | 0.795900i | \(0.293002\pi\) | |||||||
\(614\) | −28.8021 | − | 20.9259i | −1.16236 | − | 0.844502i | ||||
\(615\) | 0.683124 | − | 0.496318i | 0.0275462 | − | 0.0200135i | ||||
\(616\) | 58.2865 | 2.34843 | ||||||||
\(617\) | −12.6307 | − | 38.8731i | −0.508491 | − | 1.56497i | −0.794822 | − | 0.606843i | \(-0.792436\pi\) |
0.286331 | − | 0.958131i | \(-0.407564\pi\) | |||||||
\(618\) | 9.56729 | + | 29.4451i | 0.384853 | + | 1.18446i | ||||
\(619\) | −41.7805 | −1.67930 | −0.839650 | − | 0.543129i | \(-0.817240\pi\) | ||||
−0.839650 | + | 0.543129i | \(0.817240\pi\) | |||||||
\(620\) | −0.280367 | − | 0.203699i | −0.0112598 | − | 0.00818074i | ||||
\(621\) | 3.90755 | − | 12.0262i | 0.156804 | − | 0.482595i | ||||
\(622\) | −3.51425 | + | 2.55325i | −0.140909 | + | 0.102376i | ||||
\(623\) | 5.66669 | − | 4.11709i | 0.227031 | − | 0.164948i | ||||
\(624\) | −19.8037 | + | 14.3882i | −0.792782 | + | 0.575990i | ||||
\(625\) | 6.67431 | + | 20.5414i | 0.266972 | + | 0.821656i | ||||
\(626\) | 16.4759 | − | 11.9705i | 0.658511 | − | 0.478436i | ||||
\(627\) | −1.93593 | + | 5.95817i | −0.0773135 | + | 0.237947i | ||||
\(628\) | 2.30283 | + | 1.67310i | 0.0918928 | + | 0.0667640i | ||||
\(629\) | −8.13267 | + | 5.90873i | −0.324271 | + | 0.235596i | ||||
\(630\) | −2.25274 | − | 6.93323i | −0.0897514 | − | 0.276227i | ||||
\(631\) | −9.57896 | + | 29.4810i | −0.381332 | + | 1.17362i | 0.557774 | + | 0.829993i | \(0.311656\pi\) |
−0.939106 | + | 0.343628i | \(0.888344\pi\) | |||||||
\(632\) | 5.99206 | + | 4.35349i | 0.238351 | + | 0.173172i | ||||
\(633\) | 0.187079 | + | 0.575771i | 0.00743573 | + | 0.0228848i | ||||
\(634\) | 10.5705 | − | 32.5328i | 0.419810 | − | 1.29204i | ||||
\(635\) | 0.463935 | + | 1.42785i | 0.0184107 | + | 0.0566623i | ||||
\(636\) | 3.68573 | + | 2.67784i | 0.146149 | + | 0.106183i | ||||
\(637\) | 75.5912 | + | 54.9202i | 2.99503 | + | 2.17602i | ||||
\(638\) | −32.0795 | −1.27004 | ||||||||
\(639\) | 15.9500 | − | 0.762809i | 0.630972 | − | 0.0301763i | ||||
\(640\) | 6.53340 | 0.258255 | ||||||||
\(641\) | 7.66094 | + | 5.56600i | 0.302589 | + | 0.219844i | 0.728710 | − | 0.684822i | \(-0.240120\pi\) |
−0.426121 | + | 0.904666i | \(0.640120\pi\) | |||||||
\(642\) | 5.78140 | + | 4.20043i | 0.228173 | + | 0.165778i | ||||
\(643\) | 0.220183 | + | 0.677655i | 0.00868318 | + | 0.0267241i | 0.955304 | − | 0.295624i | \(-0.0955277\pi\) |
−0.946621 | + | 0.322349i | \(0.895528\pi\) | |||||||
\(644\) | −1.83941 | + | 5.66113i | −0.0724830 | + | 0.223080i | ||||
\(645\) | 0.987259 | + | 3.03847i | 0.0388733 | + | 0.119640i | ||||
\(646\) | 3.04000 | + | 2.20869i | 0.119607 | + | 0.0868997i | ||||
\(647\) | 7.21568 | − | 22.2076i | 0.283678 | − | 0.873070i | −0.703114 | − | 0.711077i | \(-0.748208\pi\) |
0.986792 | − | 0.161993i | \(-0.0517922\pi\) | |||||||
\(648\) | −0.205005 | − | 0.630941i | −0.00805336 | − | 0.0247857i | ||||
\(649\) | −8.54054 | + | 6.20507i | −0.335246 | + | 0.243570i | ||||
\(650\) | −29.9234 | − | 21.7406i | −1.17369 | − | 0.852738i | ||||
\(651\) | 2.51378 | − | 7.73662i | 0.0985228 | − | 0.303222i | ||||
\(652\) | −4.84604 | + | 3.52086i | −0.189786 | + | 0.137887i | ||||
\(653\) | −11.7827 | − | 36.2634i | −0.461092 | − | 1.41910i | −0.863831 | − | 0.503782i | \(-0.831942\pi\) |
0.402739 | − | 0.915315i | \(-0.368058\pi\) | |||||||
\(654\) | 2.48110 | − | 1.80262i | 0.0970186 | − | 0.0704882i | ||||
\(655\) | −8.23351 | + | 5.98199i | −0.321710 | + | 0.233736i | ||||
\(656\) | −6.39837 | + | 4.64869i | −0.249814 | + | 0.181501i | ||||
\(657\) | 3.11156 | − | 9.57640i | 0.121394 | − | 0.373611i | ||||
\(658\) | 50.3627 | + | 36.5906i | 1.96334 | + | 1.42645i | ||||
\(659\) | 12.7371 | 0.496168 | 0.248084 | − | 0.968738i | \(-0.420199\pi\) | ||||
0.248084 | + | 0.968738i | \(0.420199\pi\) | |||||||
\(660\) | −0.353452 | − | 1.08781i | −0.0137581 | − | 0.0423430i | ||||
\(661\) | 2.86147 | + | 8.80669i | 0.111298 | + | 0.342541i | 0.991157 | − | 0.132695i | \(-0.0423630\pi\) |
−0.879859 | + | 0.475235i | \(0.842363\pi\) | |||||||
\(662\) | 24.3563 | 0.946636 | ||||||||
\(663\) | −8.01079 | + | 5.82018i | −0.311113 | + | 0.226037i | ||||
\(664\) | −4.14110 | − | 3.00869i | −0.160706 | − | 0.116760i | ||||
\(665\) | 3.05532 | 0.118480 | ||||||||
\(666\) | 4.84614 | − | 14.9149i | 0.187784 | − | 0.577940i | ||||
\(667\) | −3.24654 | + | 9.99181i | −0.125706 | + | 0.386884i | ||||
\(668\) | −3.19014 | + | 9.81823i | −0.123430 | + | 0.379879i | ||||
\(669\) | 5.65674 | 0.218702 | ||||||||
\(670\) | 0.919386 | + | 0.667973i | 0.0355190 | + | 0.0258060i | ||||
\(671\) | 46.1611 | 1.78203 | ||||||||
\(672\) | −4.36295 | − | 13.4278i | −0.168304 | − | 0.517987i | ||||
\(673\) | −37.0658 | −1.42878 | −0.714390 | − | 0.699748i | \(-0.753296\pi\) | ||||
−0.714390 | + | 0.699748i | \(0.753296\pi\) | |||||||
\(674\) | 34.7803 | − | 25.2693i | 1.33969 | − | 0.973339i | ||||
\(675\) | −19.8552 | + | 14.4256i | −0.764226 | + | 0.555243i | ||||
\(676\) | 5.36874 | 0.206490 | ||||||||
\(677\) | −3.12735 | − | 9.62498i | −0.120194 | − | 0.369918i | 0.872801 | − | 0.488076i | \(-0.162301\pi\) |
−0.992995 | + | 0.118158i | \(0.962301\pi\) | |||||||
\(678\) | 2.20875 | 0.0848265 | ||||||||
\(679\) | −17.7168 | − | 12.8720i | −0.679910 | − | 0.493984i | ||||
\(680\) | 2.20008 | 0.0843692 | ||||||||
\(681\) | 1.30238 | − | 4.00833i | 0.0499075 | − | 0.153599i | ||||
\(682\) | −3.52224 | + | 10.8403i | −0.134874 | + | 0.415098i | ||||
\(683\) | 8.93575 | − | 27.5014i | 0.341917 | − | 1.05231i | −0.621296 | − | 0.783576i | \(-0.713394\pi\) |
0.963214 | − | 0.268737i | \(-0.0866063\pi\) | |||||||
\(684\) | −1.12584 | −0.0430476 | ||||||||
\(685\) | 5.25948 | + | 3.82124i | 0.200954 | + | 0.146002i | ||||
\(686\) | −77.5428 | + | 56.3381i | −2.96060 | + | 2.15100i | ||||
\(687\) | −11.4847 | −0.438167 | ||||||||
\(688\) | −9.24701 | − | 28.4594i | −0.352539 | − | 1.08500i | ||||
\(689\) | 13.8852 | + | 42.7341i | 0.528983 | + | 1.62804i | ||||
\(690\) | −1.95045 | −0.0742523 | ||||||||
\(691\) | −24.0028 | − | 17.4390i | −0.913108 | − | 0.663412i | 0.0286912 | − | 0.999588i | \(-0.490866\pi\) |
−0.941799 | + | 0.336177i | \(0.890866\pi\) | |||||||
\(692\) | 1.57707 | − | 4.85374i | 0.0599514 | − | 0.184511i | ||||
\(693\) | −37.2544 | + | 27.0669i | −1.41518 | + | 1.02819i | ||||
\(694\) | −1.13882 | + | 0.827399i | −0.0432289 | + | 0.0314076i | ||||
\(695\) | 3.07172 | − | 2.23173i | 0.116517 | − | 0.0846545i | ||||
\(696\) | −3.33093 | − | 10.2515i | −0.126258 | − | 0.388583i | ||||
\(697\) | −2.58820 | + | 1.88044i | −0.0980353 | + | 0.0712268i | ||||
\(698\) | −12.2627 | + | 37.7409i | −0.464152 | + | 1.42851i | ||||
\(699\) | 4.82283 | + | 3.50399i | 0.182416 | + | 0.132533i | ||||
\(700\) | 9.34649 | − | 6.79062i | 0.353264 | − | 0.256661i | ||||
\(701\) | −4.55326 | − | 14.0135i | −0.171974 | − | 0.529283i | 0.827508 | − | 0.561454i | \(-0.189758\pi\) |
−0.999482 | + | 0.0321713i | \(0.989758\pi\) | |||||||
\(702\) | 12.3302 | − | 37.9485i | 0.465373 | − | 1.43227i | ||||
\(703\) | 5.31739 | + | 3.86331i | 0.200549 | + | 0.145707i | ||||
\(704\) | −7.81381 | − | 24.0484i | −0.294494 | − | 0.906359i | ||||
\(705\) | −1.21058 | + | 3.72579i | −0.0455932 | + | 0.140321i | ||||
\(706\) | 7.18847 | + | 22.1238i | 0.270542 | + | 0.832642i | ||||
\(707\) | −32.1813 | − | 23.3811i | −1.21030 | − | 0.879336i | ||||
\(708\) | 0.894868 | + | 0.650160i | 0.0336312 | + | 0.0244345i | ||||
\(709\) | −12.9984 | −0.488164 | −0.244082 | − | 0.969755i | \(-0.578487\pi\) | ||||
−0.244082 | + | 0.969755i | \(0.578487\pi\) | |||||||
\(710\) | −2.25280 | − | 5.94991i | −0.0845462 | − | 0.223296i | ||||
\(711\) | −5.85154 | −0.219450 | ||||||||
\(712\) | −2.66794 | − | 1.93837i | −0.0999854 | − | 0.0726436i | ||||
\(713\) | 3.01998 | + | 2.19415i | 0.113099 | + | 0.0821714i | ||||
\(714\) | −4.97639 | − | 15.3157i | −0.186237 | − | 0.573177i | ||||
\(715\) | 3.48604 | − | 10.7289i | 0.130371 | − | 0.401239i | ||||
\(716\) | 2.36287 | + | 7.27216i | 0.0883046 | + | 0.271773i | ||||
\(717\) | 18.1813 | + | 13.2095i | 0.678994 | + | 0.493318i | ||||
\(718\) | −3.31983 | + | 10.2174i | −0.123895 | + | 0.381309i | ||||
\(719\) | 3.64798 | + | 11.2273i | 0.136047 | + | 0.418708i | 0.995751 | − | 0.0920831i | \(-0.0293525\pi\) |
−0.859705 | + | 0.510791i | \(0.829353\pi\) | |||||||
\(720\) | −3.47631 | + | 2.52568i | −0.129554 | + | 0.0941267i | ||||
\(721\) | −77.1622 | − | 56.0616i | −2.87367 | − | 2.08784i | ||||
\(722\) | −8.47840 | + | 26.0938i | −0.315533 | + | 0.971112i | ||||
\(723\) | −14.3619 | + | 10.4345i | −0.534125 | + | 0.388064i | ||||
\(724\) | −2.99021 | − | 9.20291i | −0.111130 | − | 0.342023i | ||||
\(725\) | 16.4964 | − | 11.9853i | 0.612662 | − | 0.445125i | ||||
\(726\) | −15.7172 | + | 11.4193i | −0.583322 | + | 0.423808i | ||||
\(727\) | −23.3702 | + | 16.9794i | −0.866751 | + | 0.629731i | −0.929713 | − | 0.368284i | \(-0.879945\pi\) |
0.0629622 | + | 0.998016i | \(0.479945\pi\) | |||||||
\(728\) | 18.6134 | − | 57.2863i | 0.689860 | − | 2.12317i | ||||
\(729\) | −12.7031 | − | 9.22934i | −0.470485 | − | 0.341827i | ||||
\(730\) | −4.01181 | −0.148484 | ||||||||
\(731\) | −3.74051 | − | 11.5121i | −0.138348 | − | 0.425790i | ||||
\(732\) | −1.49462 | − | 4.59998i | −0.0552429 | − | 0.170020i | ||||
\(733\) | 39.3496 | 1.45341 | 0.726705 | − | 0.686949i | \(-0.241051\pi\) | ||||
0.726705 | + | 0.686949i | \(0.241051\pi\) | |||||||
\(734\) | −27.5842 | + | 20.0411i | −1.01815 | + | 0.739731i | ||||
\(735\) | −7.73654 | − | 5.62092i | −0.285366 | − | 0.207331i | ||||
\(736\) | 6.47888 | 0.238815 | ||||||||
\(737\) | 2.21826 | − | 6.82711i | 0.0817107 | − | 0.251480i | ||||
\(738\) | 1.54227 | − | 4.74663i | 0.0567719 | − | 0.174726i | ||||
\(739\) | 4.90793 | − | 15.1051i | 0.180541 | − | 0.555648i | −0.819302 | − | 0.573362i | \(-0.805639\pi\) |
0.999843 | + | 0.0177138i | \(0.00563878\pi\) | |||||||
\(740\) | −1.20000 | −0.0441129 | ||||||||
\(741\) | 5.23770 | + | 3.80541i | 0.192412 | + | 0.139795i | ||||
\(742\) | −73.0774 | −2.68275 | ||||||||
\(743\) | −2.10055 | − | 6.46482i | −0.0770616 | − | 0.237171i | 0.905104 | − | 0.425191i | \(-0.139793\pi\) |
−0.982165 | + | 0.188020i | \(0.939793\pi\) | |||||||
\(744\) | −3.82994 | −0.140412 | ||||||||
\(745\) | −2.20374 | + | 1.60111i | −0.0807388 | + | 0.0586602i | ||||
\(746\) | −16.6607 | + | 12.1047i | −0.609993 | + | 0.443186i | ||||
\(747\) | 4.04399 | 0.147962 | ||||||||
\(748\) | 1.33915 | + | 4.12148i | 0.0489642 | + | 0.150696i | ||||
\(749\) | −22.0148 | −0.804404 | ||||||||
\(750\) | 6.27302 | + | 4.55762i | 0.229058 | + | 0.166421i | ||||
\(751\) | 40.1879 | 1.46648 | 0.733238 | − | 0.679972i | \(-0.238008\pi\) | ||||
0.733238 | + | 0.679972i | \(0.238008\pi\) | |||||||
\(752\) | 11.3387 | − | 34.8971i | 0.413481 | − | 1.27256i | ||||
\(753\) | 1.29836 | − | 3.99593i | 0.0473148 | − | 0.145620i | ||||
\(754\) | −10.2444 | + | 31.5290i | −0.373079 | + | 1.14822i | ||||
\(755\) | 6.49070 | 0.236221 | ||||||||
\(756\) | 10.0828 | + | 7.32561i | 0.366709 | + | 0.266430i | ||||
\(757\) | 29.7699 | − | 21.6291i | 1.08200 | − | 0.786122i | 0.103972 | − | 0.994580i | \(-0.466845\pi\) |
0.978031 | + | 0.208458i | \(0.0668446\pi\) | |||||||
\(758\) | 17.0785 | 0.620320 | ||||||||
\(759\) | 3.80721 | + | 11.7174i | 0.138193 | + | 0.425315i | ||||
\(760\) | −0.444514 | − | 1.36807i | −0.0161242 | − | 0.0496253i | ||||
\(761\) | 27.5907 | 1.00016 | 0.500080 | − | 0.865979i | \(-0.333304\pi\) | ||||
0.500080 | + | 0.865979i | \(0.333304\pi\) | |||||||
\(762\) | −4.18575 | − | 3.04112i | −0.151634 | − | 0.110168i | ||||
\(763\) | −2.91950 | + | 8.98530i | −0.105693 | + | 0.325290i | ||||
\(764\) | 7.20327 | − | 5.23348i | 0.260605 | − | 0.189341i | ||||
\(765\) | −1.40620 | + | 1.02166i | −0.0508413 | + | 0.0369384i | ||||
\(766\) | 35.4789 | − | 25.7770i | 1.28191 | − | 0.931359i | ||||
\(767\) | 3.37121 | + | 10.3755i | 0.121727 | + | 0.374639i | ||||
\(768\) | −9.19816 | + | 6.68285i | −0.331910 | + | 0.241147i | ||||
\(769\) | −0.965564 | + | 2.97170i | −0.0348191 | + | 0.107162i | −0.966956 | − | 0.254945i | \(-0.917943\pi\) |
0.932136 | + | 0.362107i | \(0.117943\pi\) | |||||||
\(770\) | 14.8430 | + | 10.7841i | 0.534905 | + | 0.388631i | ||||
\(771\) | 17.2579 | − | 12.5386i | 0.621528 | − | 0.451567i | ||||
\(772\) | −3.06938 | − | 9.44657i | −0.110469 | − | 0.339989i | ||||
\(773\) | −0.958647 | + | 2.95041i | −0.0344801 | + | 0.106119i | −0.966815 | − | 0.255476i | \(-0.917768\pi\) |
0.932335 | + | 0.361595i | \(0.117768\pi\) | |||||||
\(774\) | 15.2772 | + | 11.0995i | 0.549128 | + | 0.398965i | ||||
\(775\) | −2.23884 | − | 6.89045i | −0.0804216 | − | 0.247512i | ||||
\(776\) | −3.18609 | + | 9.80578i | −0.114374 | + | 0.352007i | ||||
\(777\) | −8.70440 | − | 26.7894i | −0.312269 | − | 0.961064i | ||||
\(778\) | −8.93295 | − | 6.49017i | −0.320262 | − | 0.232684i | ||||
\(779\) | 1.69225 | + | 1.22949i | 0.0606311 | + | 0.0440510i | ||||
\(780\) | −1.18202 | −0.0423230 | ||||||||
\(781\) | −31.3469 | + | 25.1478i | −1.12168 | + | 0.899860i | ||||
\(782\) | 7.38982 | 0.264259 | ||||||||
\(783\) | 17.7961 | + | 12.9296i | 0.635979 | + | 0.462066i | ||||
\(784\) | 72.4631 | + | 52.6475i | 2.58797 | + | 1.88027i | ||||
\(785\) | −0.887900 | − | 2.73267i | −0.0316905 | − | 0.0975333i | ||||
\(786\) | 10.8380 | − | 33.3560i | 0.386580 | − | 1.18977i | ||||
\(787\) | 2.16069 | + | 6.64992i | 0.0770203 | + | 0.237044i | 0.982153 | − | 0.188086i | \(-0.0602284\pi\) |
−0.905132 | + | 0.425130i | \(0.860228\pi\) | |||||||
\(788\) | −8.29778 | − | 6.02869i | −0.295596 | − | 0.214763i | ||||
\(789\) | −3.15214 | + | 9.70128i | −0.112219 | + | 0.345375i | ||||
\(790\) | 0.720439 | + | 2.21728i | 0.0256321 | + | 0.0788874i | ||||
\(791\) | −5.50483 | + | 3.99950i | −0.195729 | + | 0.142206i | ||||
\(792\) | 17.5398 | + | 12.7434i | 0.623249 | + | 0.452817i | ||||
\(793\) | 14.7413 | − | 45.3690i | 0.523478 | − | 1.61110i | ||||
\(794\) | −10.9433 | + | 7.95076i | −0.388363 | + | 0.282162i | ||||
\(795\) | −1.42111 | − | 4.37371i | −0.0504014 | − | 0.155120i | ||||
\(796\) | 2.60494 | − | 1.89260i | 0.0923297 | − | 0.0670815i | ||||
\(797\) | −7.60845 | + | 5.52786i | −0.269505 | + | 0.195807i | −0.714327 | − | 0.699812i | \(-0.753267\pi\) |
0.444822 | + | 0.895619i | \(0.353267\pi\) | |||||||
\(798\) | −8.51833 | + | 6.18893i | −0.301546 | + | 0.219086i | ||||
\(799\) | 4.58663 | − | 14.1162i | 0.162263 | − | 0.499395i | ||||
\(800\) | −10.1731 | − | 7.39116i | −0.359672 | − | 0.261317i | ||||
\(801\) | 2.60538 | 0.0920564 | ||||||||
\(802\) | −10.6152 | − | 32.6702i | −0.374835 | − | 1.15363i | ||||
\(803\) | 7.83093 | + | 24.1011i | 0.276347 | + | 0.850510i | ||||
\(804\) | −0.752149 | −0.0265262 | ||||||||
\(805\) | 4.86107 | − | 3.53178i | 0.171330 | − | 0.124479i | ||||
\(806\) | 9.52951 | + | 6.92359i | 0.335663 | + | 0.243873i | ||||
\(807\) | 2.20428 | 0.0775945 | ||||||||
\(808\) | −5.78729 | + | 17.8114i | −0.203596 | + | 0.626605i | ||||
\(809\) | 4.25823 | − | 13.1055i | 0.149711 | − | 0.460764i | −0.847875 | − | 0.530196i | \(-0.822119\pi\) |
0.997587 | + | 0.0694314i | \(0.0221185\pi\) | |||||||
\(810\) | 0.0645299 | − | 0.198603i | 0.00226735 | − | 0.00697819i | ||||
\(811\) | −0.245383 | −0.00861657 | −0.00430829 | − | 0.999991i | \(-0.501371\pi\) | ||||
−0.00430829 | + | 0.999991i | \(0.501371\pi\) | |||||||
\(812\) | −8.37720 | − | 6.08639i | −0.293982 | − | 0.213590i | ||||
\(813\) | −0.156534 | −0.00548988 | ||||||||
\(814\) | 12.1964 | + | 37.5366i | 0.427483 | + | 1.31566i | ||||
\(815\) | 6.04655 | 0.211801 | ||||||||
\(816\) | −7.67928 | + | 5.57932i | −0.268829 | + | 0.195315i | ||||
\(817\) | −6.40282 | + | 4.65192i | −0.224006 | + | 0.162750i | ||||
\(818\) | −25.2854 | −0.884085 | ||||||||
\(819\) | 14.7054 | + | 45.2587i | 0.513850 | + | 1.58147i | ||||
\(820\) | −0.381898 | −0.0133364 | ||||||||
\(821\) | −23.2961 | − | 16.9256i | −0.813040 | − | 0.590708i | 0.101671 | − | 0.994818i | \(-0.467581\pi\) |
−0.914710 | + | 0.404110i | \(0.867581\pi\) | |||||||
\(822\) | −22.4040 | −0.781430 | ||||||||
\(823\) | −1.38395 | + | 4.25935i | −0.0482413 | + | 0.148472i | −0.972275 | − | 0.233838i | \(-0.924871\pi\) |
0.924034 | + | 0.382310i | \(0.124871\pi\) | |||||||
\(824\) | −13.8764 | + | 42.7071i | −0.483406 | + | 1.48777i | ||||
\(825\) | 7.38927 | − | 22.7418i | 0.257261 | − | 0.791769i | ||||
\(826\) | −17.7426 | −0.617345 | ||||||||
\(827\) | −33.4518 | − | 24.3041i | −1.16323 | − | 0.845138i | −0.173049 | − | 0.984913i | \(-0.555362\pi\) |
−0.990183 | + | 0.139775i | \(0.955362\pi\) | |||||||
\(828\) | −1.79124 | + | 1.30141i | −0.0622498 | + | 0.0452271i | ||||
\(829\) | 32.0883 | 1.11447 | 0.557236 | − | 0.830354i | \(-0.311862\pi\) | ||||
0.557236 | + | 0.830354i | \(0.311862\pi\) | |||||||
\(830\) | −0.497894 | − | 1.53236i | −0.0172822 | − | 0.0531890i | ||||
\(831\) | −1.30286 | − | 4.00978i | −0.0451955 | − | 0.139098i | ||||
\(832\) | −26.1310 | −0.905930 | ||||||||
\(833\) | 29.3120 | + | 21.2964i | 1.01560 | + | 0.737878i | ||||
\(834\) | −4.04340 | + | 12.4443i | −0.140011 | + | 0.430911i | ||||
\(835\) | 8.43067 | − | 6.12524i | 0.291756 | − | 0.211973i | ||||
\(836\) | 2.29229 | − | 1.66545i | 0.0792806 | − | 0.0576007i | ||||
\(837\) | 6.32314 | − | 4.59403i | 0.218560 | − | 0.158793i | ||||
\(838\) | −10.1799 | − | 31.3307i | −0.351660 | − | 1.08230i | ||||
\(839\) | −2.04628 | + | 1.48671i | −0.0706453 | + | 0.0513268i | −0.622547 | − | 0.782582i | \(-0.713902\pi\) |
0.551902 | + | 0.833909i | \(0.313902\pi\) | |||||||
\(840\) | −1.90503 | + | 5.86308i | −0.0657298 | + | 0.202295i | ||||
\(841\) | 8.67586 | + | 6.30338i | 0.299168 | + | 0.217358i | ||||
\(842\) | 26.8707 | − | 19.5227i | 0.926026 | − | 0.672797i | ||||
\(843\) | −5.72733 | − | 17.6269i | −0.197260 | − | 0.607102i | ||||
\(844\) | 0.0846118 | − | 0.260408i | 0.00291246 | − | 0.00896363i | ||||
\(845\) | −4.38438 | − | 3.18544i | −0.150827 | − | 0.109582i | ||||
\(846\) | 7.15537 | + | 22.0220i | 0.246007 | + | 0.757131i | ||||
\(847\) | 18.4944 | − | 56.9200i | 0.635477 | − | 1.95580i | ||||
\(848\) | 13.3106 | + | 40.9657i | 0.457087 | + | 1.40677i | ||||
\(849\) | −17.8717 | − | 12.9845i | −0.613354 | − | 0.445628i | ||||
\(850\) | −11.6034 | − | 8.43037i | −0.397994 | − | 0.289159i | ||||
\(851\) | 12.9258 | 0.443092 | ||||||||
\(852\) | 3.52096 | + | 2.30949i | 0.120626 | + | 0.0791218i | ||||
\(853\) | 19.4598 | 0.666290 | 0.333145 | − | 0.942876i | \(-0.391890\pi\) | ||||
0.333145 | + | 0.942876i | \(0.391890\pi\) | |||||||
\(854\) | 62.7660 | + | 45.6021i | 2.14781 | + | 1.56047i | ||||
\(855\) | 0.919417 | + | 0.667996i | 0.0314434 | + | 0.0228450i | ||||
\(856\) | 3.20291 | + | 9.85753i | 0.109473 | + | 0.336924i | ||||
\(857\) | −14.2179 | + | 43.7582i | −0.485675 | + | 1.49475i | 0.345326 | + | 0.938483i | \(0.387768\pi\) |
−0.831001 | + | 0.556271i | \(0.812232\pi\) | |||||||
\(858\) | 12.0136 | + | 36.9741i | 0.410137 | + | 1.26227i | ||||
\(859\) | 32.3955 | + | 23.5367i | 1.10532 | + | 0.803062i | 0.981920 | − | 0.189295i | \(-0.0606202\pi\) |
0.123400 | + | 0.992357i | \(0.460620\pi\) | |||||||
\(860\) | 0.446516 | − | 1.37423i | 0.0152261 | − | 0.0468610i | ||||
\(861\) | −2.77016 | − | 8.52567i | −0.0944067 | − | 0.290554i | ||||
\(862\) | 30.1044 | − | 21.8721i | 1.02536 | − | 0.744968i | ||||
\(863\) | 6.24299 | + | 4.53580i | 0.212514 | + | 0.154400i | 0.688950 | − | 0.724808i | \(-0.258072\pi\) |
−0.476436 | + | 0.879209i | \(0.658072\pi\) | |||||||
\(864\) | 4.19190 | − | 12.9013i | 0.142611 | − | 0.438912i | ||||
\(865\) | −4.16779 | + | 3.02807i | −0.141709 | + | 0.102958i | ||||
\(866\) | −3.97417 | − | 12.2312i | −0.135048 | − | 0.415635i | ||||
\(867\) | 11.3504 | − | 8.24658i | 0.385481 | − | 0.280069i | ||||
\(868\) | −2.97651 | + | 2.16256i | −0.101029 | + | 0.0734022i | ||||
\(869\) | 11.9141 | − | 8.65614i | 0.404160 | − | 0.293639i | ||||
\(870\) | 1.04848 | − | 3.22690i | 0.0355469 | − | 0.109402i | ||||
\(871\) | −6.00156 | − | 4.36039i | −0.203355 | − | 0.147746i | ||||
\(872\) | 4.44809 | 0.150631 | ||||||||
\(873\) | −2.51715 | − | 7.74700i | −0.0851927 | − | 0.262196i | ||||
\(874\) | −1.49307 | − | 4.59521i | −0.0505040 | − | 0.155435i | ||||
\(875\) | −23.8869 | −0.807523 | ||||||||
\(876\) | 2.14814 | − | 1.56071i | 0.0725788 | − | 0.0527316i | ||||
\(877\) | −29.5626 | − | 21.4785i | −0.998259 | − | 0.725278i | −0.0365448 | − | 0.999332i | \(-0.511635\pi\) |
−0.961714 | + | 0.274054i | \(0.911635\pi\) | |||||||
\(878\) | −1.95776 | −0.0660711 | ||||||||
\(879\) | −9.31561 | + | 28.6705i | −0.314208 | + | 0.967032i | ||||
\(880\) | 3.34178 | − | 10.2849i | 0.112651 | − | 0.346705i | ||||
\(881\) | −11.0622 | + | 34.0459i | −0.372695 | + | 1.14704i | 0.572326 | + | 0.820026i | \(0.306041\pi\) |
−0.945021 | + | 0.327010i | \(0.893959\pi\) | |||||||
\(882\) | −56.5232 | −1.90323 | ||||||||
\(883\) | −15.8729 | − | 11.5324i | −0.534167 | − | 0.388095i | 0.287747 | − | 0.957706i | \(-0.407094\pi\) |
−0.821914 | + | 0.569611i | \(0.807094\pi\) | |||||||
\(884\) | 4.47840 | 0.150625 | ||||||||
\(885\) | −0.345034 | − | 1.06190i | −0.0115982 | − | 0.0356955i | ||||
\(886\) | −49.5277 | −1.66392 | ||||||||
\(887\) | −37.9772 | + | 27.5920i | −1.27515 | + | 0.926450i | −0.999395 | − | 0.0347779i | \(-0.988928\pi\) |
−0.275754 | + | 0.961228i | \(0.588928\pi\) | |||||||
\(888\) | −10.7290 | + | 7.79511i | −0.360043 | + | 0.261587i | ||||
\(889\) | 15.9388 | 0.534570 | ||||||||
\(890\) | −0.320773 | − | 0.987237i | −0.0107523 | − | 0.0330923i | ||||
\(891\) | −1.31907 | −0.0441906 | ||||||||
\(892\) | −2.06981 | − | 1.50380i | −0.0693022 | − | 0.0503510i | ||||
\(893\) | −9.70458 | −0.324752 | ||||||||
\(894\) | 2.90085 | − | 8.92791i | 0.0970190 | − | 0.298594i | ||||
\(895\) | 2.38516 | − | 7.34077i | 0.0797271 | − | 0.245375i | ||||
\(896\) | 21.4339 | − | 65.9669i | 0.716058 | − | 2.20380i | ||||
\(897\) | 12.7321 | 0.425113 | ||||||||
\(898\) | −26.2395 | − | 19.0641i | −0.875625 | − | 0.636179i | ||||
\(899\) | −5.25350 | + | 3.81689i | −0.175214 | + | 0.127301i | ||||
\(900\) | 4.29724 | 0.143241 | ||||||||
\(901\) | 5.38425 | + | 16.5710i | 0.179376 | + | 0.552061i | ||||
\(902\) | 3.88147 | + | 11.9459i | 0.129239 | + | 0.397756i | ||||
\(903\) | 33.9179 | 1.12872 | ||||||||
\(904\) | 2.59174 | + | 1.88301i | 0.0861999 | + | 0.0626279i | ||||
\(905\) | −3.01841 | + | 9.28972i | −0.100335 | + | 0.308801i | ||||
\(906\) | −18.0963 | + | 13.1477i | −0.601209 | + | 0.436804i | ||||
\(907\) | 27.2473 | − | 19.7963i | 0.904730 | − | 0.657325i | −0.0349462 | − | 0.999389i | \(-0.511126\pi\) |
0.939677 | + | 0.342064i | \(0.111126\pi\) | |||||||
\(908\) | −1.54213 | + | 1.12042i | −0.0511772 | + | 0.0371824i | ||||
\(909\) | −4.57222 | − | 14.0718i | −0.151651 | − | 0.466733i | ||||
\(910\) | 15.3390 | − | 11.1445i | 0.508484 | − | 0.369435i | ||||
\(911\) | −13.0711 | + | 40.2287i | −0.433064 | + | 1.33283i | 0.461993 | + | 0.886884i | \(0.347135\pi\) |
−0.895057 | + | 0.445951i | \(0.852865\pi\) | |||||||
\(912\) | 5.02095 | + | 3.64793i | 0.166260 | + | 0.120795i | ||||
\(913\) | −8.23384 | + | 5.98224i | −0.272500 | + | 0.197983i | ||||
\(914\) | −6.68396 | − | 20.5711i | −0.221086 | − | 0.680432i | ||||
\(915\) | −1.50872 | + | 4.64338i | −0.0498769 | + | 0.153505i | ||||
\(916\) | 4.20224 | + | 3.05311i | 0.138846 | + | 0.100878i | ||||
\(917\) | 33.3880 | + | 102.758i | 1.10257 | + | 3.39336i | ||||
\(918\) | 4.78129 | − | 14.7153i | 0.157806 | − | 0.485677i | ||||
\(919\) | 2.62465 | + | 8.07783i | 0.0865791 | + | 0.266463i | 0.984968 | − | 0.172738i | \(-0.0552615\pi\) |
−0.898389 | + | 0.439201i | \(0.855261\pi\) | |||||||
\(920\) | −2.28865 | − | 1.66280i | −0.0754545 | − | 0.0548209i | ||||
\(921\) | −19.2427 | − | 13.9806i | −0.634068 | − | 0.460677i | ||||
\(922\) | 43.1455 | 1.42092 | ||||||||
\(923\) | 14.7058 | + | 38.8398i | 0.484049 | + | 1.27843i | ||||
\(924\) | −12.1431 | −0.399477 | ||||||||
\(925\) | −20.2960 | − | 14.7459i | −0.667328 | − | 0.484842i | ||||
\(926\) | −33.1319 | − | 24.0717i | −1.08878 | − | 0.791047i | ||||
\(927\) | −10.9630 | − | 33.7405i | −0.360071 | − | 1.10818i | ||||
\(928\) | −3.48278 | + | 10.7189i | −0.114328 | + | 0.351865i | ||||
\(929\) | −8.76846 | − | 26.9866i | −0.287684 | − | 0.885400i | −0.985581 | − | 0.169202i | \(-0.945881\pi\) |
0.697897 | − | 0.716198i | \(-0.254119\pi\) | |||||||
\(930\) | −0.975317 | − | 0.708609i | −0.0319819 | − | 0.0232362i | ||||
\(931\) | 7.32042 | − | 22.5299i | 0.239917 | − | 0.738389i | ||||
\(932\) | −0.833167 | − | 2.56422i | −0.0272913 | − | 0.0839939i | ||||
\(933\) | −2.34787 | + | 1.70583i | −0.0768659 | + | 0.0558463i | ||||
\(934\) | 31.8273 | + | 23.1239i | 1.04142 | + | 0.756637i | ||||
\(935\) | 1.35178 | − | 4.16036i | 0.0442081 | − | 0.136058i | ||||
\(936\) | 18.1259 | − | 13.1693i | 0.592464 | − | 0.430451i | ||||
\(937\) | 5.53253 | + | 17.0274i | 0.180740 | + | 0.556260i | 0.999849 | − | 0.0173778i | \(-0.00553179\pi\) |
−0.819109 | + | 0.573638i | \(0.805532\pi\) | |||||||
\(938\) | 9.76064 | − | 7.09152i | 0.318696 | − | 0.231546i | ||||
\(939\) | 11.0076 | − | 7.99747i | 0.359219 | − | 0.260988i | ||||
\(940\) | 1.43343 | − | 1.04145i | 0.0467532 | − | 0.0339682i | ||||
\(941\) | −12.7066 | + | 39.1070i | −0.414225 | + | 1.27485i | 0.498718 | + | 0.866764i | \(0.333804\pi\) |
−0.912943 | + | 0.408088i | \(0.866196\pi\) | |||||||
\(942\) | 8.01087 | + | 5.82024i | 0.261008 | + | 0.189634i | ||||
\(943\) | 4.11362 | 0.133958 | ||||||||
\(944\) | 3.23170 | + | 9.94617i | 0.105183 | + | 0.323720i | ||||
\(945\) | −3.88763 | − | 11.9649i | −0.126465 | − | 0.389218i | ||||
\(946\) | −47.5249 | −1.54517 | ||||||||
\(947\) | 16.8935 | − | 12.2739i | 0.548965 | − | 0.398847i | −0.278439 | − | 0.960454i | \(-0.589817\pi\) |
0.827404 | + | 0.561607i | \(0.189817\pi\) | |||||||
\(948\) | −1.24835 | − | 0.906980i | −0.0405445 | − | 0.0294573i | ||||
\(949\) | 26.1883 | 0.850108 | ||||||||
\(950\) | −2.89785 | + | 8.91866i | −0.0940186 | + | 0.289360i | ||||
\(951\) | 7.06218 | − | 21.7351i | 0.229007 | − | 0.704810i | ||||
\(952\) | 7.21774 | − | 22.2139i | 0.233928 | − | 0.719957i | ||||
\(953\) | −13.5140 | −0.437760 | −0.218880 | − | 0.975752i | \(-0.570240\pi\) | ||||
−0.218880 | + | 0.975752i | \(0.570240\pi\) | |||||||
\(954\) | −21.9907 | − | 15.9772i | −0.711975 | − | 0.517280i | ||||
\(955\) | −8.98773 | −0.290836 | ||||||||
\(956\) | −3.14091 | − | 9.66674i | −0.101584 | − | 0.312645i | ||||
\(957\) | −21.4323 | −0.692809 | ||||||||
\(958\) | −16.7680 | + | 12.1827i | −0.541750 | + | 0.393604i | ||||
\(959\) | 55.8372 | − | 40.5681i | 1.80308 | − | 1.31001i | ||||
\(960\) | 2.67443 | 0.0863170 | ||||||||
\(961\) | −8.86654 | − | 27.2884i | −0.286017 | − | 0.880271i | ||||
\(962\) | 40.7873 | 1.31503 | ||||||||
\(963\) | −6.62478 | − | 4.81318i | −0.213480 | − | 0.155103i | ||||
\(964\) | 8.02897 | 0.258596 | ||||||||
\(965\) | −3.09833 | + | 9.53568i | −0.0997388 | + | 0.306965i | ||||
\(966\) | −6.39878 | + | 19.6934i | −0.205877 | + | 0.633626i | ||||
\(967\) | −6.99169 | + | 21.5182i | −0.224837 | + | 0.691978i | 0.773471 | + | 0.633832i | \(0.218519\pi\) |
−0.998308 | + | 0.0581463i | \(0.981481\pi\) | |||||||
\(968\) | −28.1777 | −0.905666 | ||||||||
\(969\) | 2.03102 | + | 1.47563i | 0.0652459 | + | 0.0474039i | ||||
\(970\) | −2.62561 | + | 1.90762i | −0.0843032 | + | 0.0612498i | ||||
\(971\) | 2.40464 | 0.0771685 | 0.0385842 | − | 0.999255i | \(-0.487715\pi\) | ||||
0.0385842 | + | 0.999255i | \(0.487715\pi\) | |||||||
\(972\) | 2.31048 | + | 7.11093i | 0.0741088 | + | 0.228083i | ||||
\(973\) | −12.4562 | − | 38.3363i | −0.399328 | − | 1.22901i | ||||
\(974\) | 55.7404 | 1.78604 | ||||||||
\(975\) | −19.9918 | − | 14.5249i | −0.640251 | − | 0.465170i | ||||
\(976\) | 14.1312 | − | 43.4915i | 0.452330 | − | 1.39213i | ||||
\(977\) | 38.0133 | − | 27.6183i | 1.21615 | − | 0.883586i | 0.220377 | − | 0.975415i | \(-0.429271\pi\) |
0.995775 | + | 0.0918285i | \(0.0292712\pi\) | |||||||
\(978\) | −16.8580 | + | 12.2480i | −0.539059 | + | 0.391649i | ||||
\(979\) | −5.30473 | + | 3.85411i | −0.169540 | + | 0.123178i | ||||
\(980\) | 1.33652 | + | 4.11340i | 0.0426937 | + | 0.131398i | ||||
\(981\) | −2.84304 | + | 2.06559i | −0.0907712 | + | 0.0659491i | ||||
\(982\) | 2.85029 | − | 8.77230i | 0.0909565 | − | 0.279935i | ||||
\(983\) | −33.7912 | − | 24.5507i | −1.07777 | − | 0.783046i | −0.100478 | − | 0.994939i | \(-0.532037\pi\) |
−0.977293 | + | 0.211893i | \(0.932037\pi\) | |||||||
\(984\) | −3.41450 | + | 2.48078i | −0.108850 | + | 0.0790843i | ||||
\(985\) | 3.19937 | + | 9.84664i | 0.101940 | + | 0.313740i | ||||
\(986\) | −3.97247 | + | 12.2260i | −0.126509 | + | 0.389355i | ||||
\(987\) | 33.6473 | + | 24.4462i | 1.07101 | + | 0.778131i | ||||
\(988\) | −0.904838 | − | 2.78480i | −0.0287867 | − | 0.0885964i | ||||
\(989\) | −4.80965 | + | 14.8026i | −0.152938 | + | 0.470695i | ||||
\(990\) | 2.10885 | + | 6.49037i | 0.0670236 | + | 0.206277i | ||||
\(991\) | 16.8862 | + | 12.2686i | 0.536408 | + | 0.389723i | 0.822749 | − | 0.568404i | \(-0.192439\pi\) |
−0.286341 | + | 0.958128i | \(0.592439\pi\) | |||||||
\(992\) | 3.23975 | + | 2.35381i | 0.102862 | + | 0.0747336i | ||||
\(993\) | 16.2725 | 0.516391 | ||||||||
\(994\) | −67.4662 | + | 3.22657i | −2.13990 | + | 0.102341i | ||||
\(995\) | −3.25026 | −0.103040 | ||||||||
\(996\) | 0.862732 | + | 0.626812i | 0.0273367 | + | 0.0198613i | ||||
\(997\) | 2.90816 | + | 2.11290i | 0.0921023 | + | 0.0669162i | 0.632883 | − | 0.774247i | \(-0.281871\pi\) |
−0.540781 | + | 0.841163i | \(0.681871\pi\) | |||||||
\(998\) | 9.93897 | + | 30.5890i | 0.314613 | + | 0.968278i | ||||
\(999\) | 8.36314 | − | 25.7391i | 0.264598 | − | 0.814349i |
(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 | 71.2.c.a.54.2 | yes | 20 | |
3.2 | odd | 2 | 639.2.f.c.622.4 | 20 | |||
71.5 | even | 5 | 5041.2.a.i.1.8 | 10 | |||
71.25 | even | 5 | inner | 71.2.c.a.25.2 | ✓ | 20 | |
71.66 | odd | 10 | 5041.2.a.j.1.8 | 10 | |||
213.167 | odd | 10 | 639.2.f.c.451.4 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
71.2.c.a.25.2 | ✓ | 20 | 71.25 | even | 5 | inner | |
71.2.c.a.54.2 | yes | 20 | 1.1 | even | 1 | trivial | |
639.2.f.c.451.4 | 20 | 213.167 | odd | 10 | |||
639.2.f.c.622.4 | 20 | 3.2 | odd | 2 | |||
5041.2.a.i.1.8 | 10 | 71.5 | even | 5 | |||
5041.2.a.j.1.8 | 10 | 71.66 | odd | 10 |