Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [585,2,Mod(376,585)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(585, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("585.376");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 585 = 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 585.bt (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.67124851824\) |
Analytic rank: | \(0\) |
Dimension: | \(108\) |
Relative dimension: | \(54\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 571.39 | ||
Character | \(\chi\) | \(=\) | 585.571 |
Dual form | 585.2.bt.b.376.39 |
$q$-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 \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) | \(496\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.16682 | − | 0.673666i | 0.825069 | − | 0.476354i | −0.0270923 | − | 0.999633i | \(-0.508625\pi\) |
0.852161 | + | 0.523279i | \(0.175291\pi\) | |||||||
\(3\) | 0.619932 | + | 1.61731i | 0.357918 | + | 0.933753i | ||||
\(4\) | −0.0923480 | + | 0.159951i | −0.0461740 | + | 0.0799757i | ||||
\(5\) | −0.866025 | − | 0.500000i | −0.387298 | − | 0.223607i | ||||
\(6\) | 1.81288 | + | 1.46949i | 0.740104 | + | 0.599915i | ||||
\(7\) | 4.07352 | − | 2.35185i | 1.53965 | − | 0.888916i | 0.540788 | − | 0.841159i | \(-0.318126\pi\) |
0.998859 | − | 0.0477566i | \(-0.0152072\pi\) | |||||||
\(8\) | 2.94351i | 1.04069i | ||||||||
\(9\) | −2.23137 | + | 2.00524i | −0.743789 | + | 0.668414i | ||||
\(10\) | −1.34733 | −0.426064 | ||||||||
\(11\) | 1.11056 | − | 0.641180i | 0.334845 | − | 0.193323i | −0.323145 | − | 0.946349i | \(-0.604740\pi\) |
0.657990 | + | 0.753027i | \(0.271407\pi\) | |||||||
\(12\) | −0.315940 | − | 0.0501961i | −0.0912041 | − | 0.0144904i | ||||
\(13\) | 2.91362 | − | 2.12387i | 0.808094 | − | 0.589054i | ||||
\(14\) | 3.16872 | − | 5.48839i | 0.846877 | − | 1.46683i | ||||
\(15\) | 0.271777 | − | 1.71060i | 0.0701724 | − | 0.441674i | ||||
\(16\) | 1.79825 | + | 3.11466i | 0.449562 | + | 0.778664i | ||||
\(17\) | −0.689981 | −0.167345 | −0.0836725 | − | 0.996493i | \(-0.526665\pi\) | ||||
−0.0836725 | + | 0.996493i | \(0.526665\pi\) | |||||||
\(18\) | −1.25275 | + | 3.84296i | −0.295276 | + | 0.905795i | ||||
\(19\) | 6.46642i | 1.48350i | 0.670678 | + | 0.741749i | \(0.266003\pi\) | ||||
−0.670678 | + | 0.741749i | \(0.733997\pi\) | |||||||
\(20\) | 0.159951 | − | 0.0923480i | 0.0357662 | − | 0.0206496i | ||||
\(21\) | 6.32897 | + | 5.13015i | 1.38110 | + | 1.11949i | ||||
\(22\) | 0.863882 | − | 1.49629i | 0.184180 | − | 0.319010i | ||||
\(23\) | −2.10450 | + | 3.64510i | −0.438818 | + | 0.760056i | −0.997599 | − | 0.0692600i | \(-0.977936\pi\) |
0.558780 | + | 0.829316i | \(0.311270\pi\) | |||||||
\(24\) | −4.76056 | + | 1.82478i | −0.971746 | + | 0.372481i | ||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | 1.96891 | − | 4.44099i | 0.386135 | − | 0.870949i | ||||
\(27\) | −4.62639 | − | 2.36569i | −0.890349 | − | 0.455278i | ||||
\(28\) | 0.868754i | 0.164179i | ||||||||
\(29\) | 2.78420 | + | 4.82237i | 0.517012 | + | 0.895492i | 0.999805 | + | 0.0197568i | \(0.00628921\pi\) |
−0.482792 | + | 0.875735i | \(0.660377\pi\) | |||||||
\(30\) | −0.835255 | − | 2.17905i | −0.152496 | − | 0.397838i | ||||
\(31\) | 0.646732 | + | 0.373391i | 0.116157 | + | 0.0670630i | 0.556953 | − | 0.830544i | \(-0.311970\pi\) |
−0.440796 | + | 0.897607i | \(0.645304\pi\) | |||||||
\(32\) | −0.901834 | − | 0.520674i | −0.159423 | − | 0.0920431i | ||||
\(33\) | 1.72545 | + | 1.39862i | 0.300363 | + | 0.243469i | ||||
\(34\) | −0.805086 | + | 0.464817i | −0.138071 | + | 0.0797154i | ||||
\(35\) | −4.70370 | −0.795070 | ||||||||
\(36\) | −0.114679 | − | 0.542091i | −0.0191132 | − | 0.0903484i | ||||
\(37\) | − | 8.06746i | − | 1.32628i | −0.748494 | − | 0.663141i | \(-0.769223\pi\) | ||
0.748494 | − | 0.663141i | \(-0.230777\pi\) | |||||||
\(38\) | 4.35621 | + | 7.54517i | 0.706670 | + | 1.22399i | ||||
\(39\) | 5.24119 | + | 3.39557i | 0.839262 | + | 0.543727i | ||||
\(40\) | 1.47176 | − | 2.54916i | 0.232705 | − | 0.403057i | ||||
\(41\) | −6.39700 | − | 3.69331i | −0.999043 | − | 0.576798i | −0.0910779 | − | 0.995844i | \(-0.529031\pi\) |
−0.907965 | + | 0.419046i | \(0.862365\pi\) | |||||||
\(42\) | 10.8408 | + | 1.72237i | 1.67277 | + | 0.265767i | ||||
\(43\) | −5.42456 | − | 9.39562i | −0.827238 | − | 1.43282i | −0.900197 | − | 0.435483i | \(-0.856578\pi\) |
0.0729590 | − | 0.997335i | \(-0.476756\pi\) | |||||||
\(44\) | 0.236847i | 0.0357060i | ||||||||
\(45\) | 2.93504 | − | 0.620907i | 0.437530 | − | 0.0925594i | ||||
\(46\) | 5.67092i | 0.836131i | ||||||||
\(47\) | 6.50187 | − | 3.75385i | 0.948394 | − | 0.547556i | 0.0558127 | − | 0.998441i | \(-0.482225\pi\) |
0.892582 | + | 0.450885i | \(0.148892\pi\) | |||||||
\(48\) | −3.92257 | + | 4.83920i | −0.566174 | + | 0.698478i | ||||
\(49\) | 7.56239 | − | 13.0984i | 1.08034 | − | 1.87121i | ||||
\(50\) | 1.16682 | + | 0.673666i | 0.165014 | + | 0.0952708i | ||||
\(51\) | −0.427741 | − | 1.11591i | −0.0598958 | − | 0.156259i | ||||
\(52\) | 0.0706481 | + | 0.662173i | 0.00979712 | + | 0.0918269i | ||||
\(53\) | −5.44121 | −0.747407 | −0.373704 | − | 0.927548i | \(-0.621912\pi\) | ||||
−0.373704 | + | 0.927548i | \(0.621912\pi\) | |||||||
\(54\) | −6.99187 | + | 0.356295i | −0.951473 | + | 0.0484856i | ||||
\(55\) | −1.28236 | −0.172913 | ||||||||
\(56\) | 6.92270 | + | 11.9905i | 0.925084 | + | 1.60229i | ||||
\(57\) | −10.4582 | + | 4.00874i | −1.38522 | + | 0.530971i | ||||
\(58\) | 6.49733 | + | 3.75124i | 0.853142 | + | 0.492562i | ||||
\(59\) | −0.357947 | − | 0.206661i | −0.0466007 | − | 0.0269050i | 0.476519 | − | 0.879164i | \(-0.341898\pi\) |
−0.523119 | + | 0.852259i | \(0.675232\pi\) | |||||||
\(60\) | 0.248514 | + | 0.201441i | 0.0320830 | + | 0.0260059i | ||||
\(61\) | −2.91595 | − | 5.05058i | −0.373350 | − | 0.646661i | 0.616729 | − | 0.787176i | \(-0.288457\pi\) |
−0.990079 | + | 0.140515i | \(0.955124\pi\) | |||||||
\(62\) | 1.00616 | 0.127783 | ||||||||
\(63\) | −4.37350 | + | 13.4162i | −0.551009 | + | 1.69029i | ||||
\(64\) | −8.59603 | −1.07450 | ||||||||
\(65\) | −3.58520 | + | 0.382510i | −0.444690 | + | 0.0474445i | ||||
\(66\) | 2.95551 | + | 0.469566i | 0.363798 | + | 0.0577996i | ||||
\(67\) | 9.45733 | + | 5.46019i | 1.15540 | + | 0.667068i | 0.950196 | − | 0.311652i | \(-0.100882\pi\) |
0.205200 | + | 0.978720i | \(0.434216\pi\) | |||||||
\(68\) | 0.0637184 | − | 0.110363i | 0.00772699 | − | 0.0133835i | ||||
\(69\) | −7.19989 | − | 1.14391i | −0.866765 | − | 0.137710i | ||||
\(70\) | −5.48839 | + | 3.16872i | −0.655988 | + | 0.378735i | ||||
\(71\) | 5.80266i | 0.688649i | 0.938851 | + | 0.344325i | \(0.111892\pi\) | ||||
−0.938851 | + | 0.344325i | \(0.888108\pi\) | |||||||
\(72\) | −5.90245 | − | 6.56806i | −0.695611 | − | 0.774053i | ||||
\(73\) | − | 9.51919i | − | 1.11414i | −0.830467 | − | 0.557068i | \(-0.811926\pi\) | ||
0.830467 | − | 0.557068i | \(-0.188074\pi\) | |||||||
\(74\) | −5.43478 | − | 9.41331i | −0.631780 | − | 1.09427i | ||||
\(75\) | −1.09066 | + | 1.34553i | −0.125939 | + | 0.155369i | ||||
\(76\) | −1.03431 | − | 0.597161i | −0.118644 | − | 0.0684990i | ||||
\(77\) | 3.01592 | − | 5.22372i | 0.343695 | − | 0.595298i | ||||
\(78\) | 8.40303 | + | 0.431220i | 0.951456 | + | 0.0488261i | ||||
\(79\) | −2.41946 | − | 4.19062i | −0.272210 | − | 0.471482i | 0.697217 | − | 0.716860i | \(-0.254421\pi\) |
−0.969427 | + | 0.245378i | \(0.921088\pi\) | |||||||
\(80\) | − | 3.59650i | − | 0.402100i | ||||||
\(81\) | 0.958005 | − | 8.94887i | 0.106445 | − | 0.994319i | ||||
\(82\) | −9.95222 | −1.09904 | ||||||||
\(83\) | 2.46941 | − | 1.42572i | 0.271053 | − | 0.156493i | −0.358313 | − | 0.933602i | \(-0.616648\pi\) |
0.629366 | + | 0.777109i | \(0.283315\pi\) | |||||||
\(84\) | −1.40504 | + | 0.538569i | −0.153303 | + | 0.0587627i | ||||
\(85\) | 0.597541 | + | 0.344990i | 0.0648124 | + | 0.0374195i | ||||
\(86\) | −12.6590 | − | 7.30869i | −1.36506 | − | 0.788116i | ||||
\(87\) | −6.07324 | + | 7.49245i | −0.651120 | + | 0.803274i | ||||
\(88\) | 1.88732 | + | 3.26893i | 0.201189 | + | 0.348469i | ||||
\(89\) | − | 10.7367i | − | 1.13809i | −0.822306 | − | 0.569045i | \(-0.807313\pi\) | ||
0.822306 | − | 0.569045i | \(-0.192687\pi\) | |||||||
\(90\) | 3.00639 | − | 2.70173i | 0.316902 | − | 0.284787i | ||||
\(91\) | 6.87370 | − | 15.5040i | 0.720559 | − | 1.62526i | ||||
\(92\) | −0.388693 | − | 0.673235i | −0.0405240 | − | 0.0701896i | ||||
\(93\) | −0.202958 | + | 1.27744i | −0.0210458 | + | 0.132465i | ||||
\(94\) | 5.05769 | − | 8.76017i | 0.521661 | − | 0.903543i | ||||
\(95\) | 3.23321 | − | 5.60008i | 0.331720 | − | 0.574556i | ||||
\(96\) | 0.283014 | − | 1.78133i | 0.0288850 | − | 0.181806i | ||||
\(97\) | 1.55060 | − | 0.895240i | 0.157440 | − | 0.0908979i | −0.419210 | − | 0.907889i | \(-0.637693\pi\) |
0.576650 | + | 0.816991i | \(0.304360\pi\) | |||||||
\(98\) | − | 20.3781i | − | 2.05850i | ||||||
\(99\) | −1.19234 | + | 3.65764i | −0.119834 | + | 0.367607i | ||||
\(100\) | −0.184696 | −0.0184696 | ||||||||
\(101\) | −1.85667 | − | 3.21584i | −0.184745 | − | 0.319988i | 0.758746 | − | 0.651387i | \(-0.225813\pi\) |
−0.943491 | + | 0.331399i | \(0.892479\pi\) | |||||||
\(102\) | −1.25085 | − | 1.01392i | −0.123853 | − | 0.100393i | ||||
\(103\) | −5.29740 | + | 9.17537i | −0.521969 | + | 0.904076i | 0.477705 | + | 0.878520i | \(0.341469\pi\) |
−0.999673 | + | 0.0255558i | \(0.991864\pi\) | |||||||
\(104\) | 6.25162 | + | 8.57628i | 0.613022 | + | 0.840974i | ||||
\(105\) | −2.91598 | − | 7.60733i | −0.284570 | − | 0.742399i | ||||
\(106\) | −6.34893 | + | 3.66556i | −0.616663 | + | 0.356030i | ||||
\(107\) | −14.5036 | −1.40211 | −0.701056 | − | 0.713106i | \(-0.747288\pi\) | ||||
−0.701056 | + | 0.713106i | \(0.747288\pi\) | |||||||
\(108\) | 0.805634 | − | 0.521531i | 0.0775222 | − | 0.0501843i | ||||
\(109\) | 4.43511i | 0.424806i | 0.977182 | + | 0.212403i | \(0.0681290\pi\) | ||||
−0.977182 | + | 0.212403i | \(0.931871\pi\) | |||||||
\(110\) | −1.49629 | + | 0.863882i | −0.142665 | + | 0.0823679i | ||||
\(111\) | 13.0476 | − | 5.00128i | 1.23842 | − | 0.474701i | ||||
\(112\) | 14.6504 | + | 8.45842i | 1.38433 | + | 0.799245i | ||||
\(113\) | 3.57608 | − | 6.19396i | 0.336409 | − | 0.582678i | −0.647345 | − | 0.762197i | \(-0.724121\pi\) |
0.983755 | + | 0.179519i | \(0.0574540\pi\) | |||||||
\(114\) | −9.50231 | + | 11.7228i | −0.889973 | + | 1.09794i | ||||
\(115\) | 3.64510 | − | 2.10450i | 0.339907 | − | 0.196246i | ||||
\(116\) | −1.02846 | −0.0954901 | ||||||||
\(117\) | −2.24250 | + | 10.5816i | −0.207319 | + | 0.978273i | ||||
\(118\) | −0.556882 | −0.0512651 | ||||||||
\(119\) | −2.81065 | + | 1.62273i | −0.257652 | + | 0.148756i | ||||
\(120\) | 5.03516 | + | 0.799978i | 0.459645 | + | 0.0730276i | ||||
\(121\) | −4.67778 | + | 8.10215i | −0.425253 | + | 0.736559i | ||||
\(122\) | −6.80481 | − | 3.92876i | −0.616078 | − | 0.355693i | ||||
\(123\) | 2.00751 | − | 12.6355i | 0.181011 | − | 1.13931i | ||||
\(124\) | −0.119449 | + | 0.0689638i | −0.0107268 | + | 0.00619313i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 3.93496 | + | 18.6007i | 0.350554 | + | 1.65708i | ||||
\(127\) | 10.7582 | 0.954634 | 0.477317 | − | 0.878731i | \(-0.341609\pi\) | ||||
0.477317 | + | 0.878731i | \(0.341609\pi\) | |||||||
\(128\) | −8.22639 | + | 4.74951i | −0.727117 | + | 0.419801i | ||||
\(129\) | 11.8327 | − | 14.5978i | 1.04181 | − | 1.28527i | ||||
\(130\) | −3.92562 | + | 2.86155i | −0.344299 | + | 0.250975i | ||||
\(131\) | −8.92688 | + | 15.4618i | −0.779945 | + | 1.35090i | 0.152028 | + | 0.988376i | \(0.451420\pi\) |
−0.931973 | + | 0.362528i | \(0.881914\pi\) | |||||||
\(132\) | −0.383054 | + | 0.146829i | −0.0333406 | + | 0.0127798i | ||||
\(133\) | 15.2080 | + | 26.3411i | 1.31870 | + | 2.28406i | ||||
\(134\) | 14.7134 | 1.27104 | ||||||||
\(135\) | 2.82373 | + | 4.36195i | 0.243028 | + | 0.375417i | ||||
\(136\) | − | 2.03097i | − | 0.174154i | ||||||
\(137\) | −3.72175 | + | 2.14875i | −0.317970 | + | 0.183580i | −0.650488 | − | 0.759517i | \(-0.725435\pi\) |
0.332517 | + | 0.943097i | \(0.392102\pi\) | |||||||
\(138\) | −9.17162 | + | 3.51559i | −0.780740 | + | 0.299267i | ||||
\(139\) | 0.0771951 | − | 0.133706i | 0.00654761 | − | 0.0113408i | −0.862733 | − | 0.505660i | \(-0.831249\pi\) |
0.869281 | + | 0.494319i | \(0.164582\pi\) | |||||||
\(140\) | 0.434377 | − | 0.752363i | 0.0367116 | − | 0.0635863i | ||||
\(141\) | 10.1019 | + | 8.18838i | 0.850729 | + | 0.689586i | ||||
\(142\) | 3.90906 | + | 6.77068i | 0.328041 | + | 0.568183i | ||||
\(143\) | 1.87396 | − | 4.22683i | 0.156708 | − | 0.353465i | ||||
\(144\) | −10.2582 | − | 3.34402i | −0.854849 | − | 0.278668i | ||||
\(145\) | − | 5.56839i | − | 0.462430i | ||||||
\(146\) | −6.41276 | − | 11.1072i | −0.530723 | − | 0.919240i | ||||
\(147\) | 25.8724 | + | 4.11056i | 2.13392 | + | 0.339034i | ||||
\(148\) | 1.29040 | + | 0.745014i | 0.106070 | + | 0.0612398i | ||||
\(149\) | −8.04826 | − | 4.64667i | −0.659339 | − | 0.380670i | 0.132686 | − | 0.991158i | \(-0.457640\pi\) |
−0.792025 | + | 0.610488i | \(0.790973\pi\) | |||||||
\(150\) | −0.366173 | + | 2.30474i | −0.0298979 | + | 0.188181i | ||||
\(151\) | 6.14219 | − | 3.54620i | 0.499845 | − | 0.288585i | −0.228805 | − | 0.973472i | \(-0.573482\pi\) |
0.728649 | + | 0.684887i | \(0.240148\pi\) | |||||||
\(152\) | −19.0340 | −1.54386 | ||||||||
\(153\) | 1.53960 | − | 1.38358i | 0.124469 | − | 0.111856i | ||||
\(154\) | − | 8.12688i | − | 0.654883i | ||||||
\(155\) | −0.373391 | − | 0.646732i | −0.0299915 | − | 0.0519468i | ||||
\(156\) | −1.02714 | + | 0.524762i | −0.0822370 | + | 0.0420146i | ||||
\(157\) | −6.72039 | + | 11.6401i | −0.536345 | + | 0.928978i | 0.462751 | + | 0.886488i | \(0.346862\pi\) |
−0.999097 | + | 0.0424895i | \(0.986471\pi\) | |||||||
\(158\) | −5.64616 | − | 3.25981i | −0.449184 | − | 0.259337i | ||||
\(159\) | −3.37318 | − | 8.80011i | −0.267511 | − | 0.697894i | ||||
\(160\) | 0.520674 | + | 0.901834i | 0.0411629 | + | 0.0712963i | ||||
\(161\) | 19.7979i | 1.56029i | ||||||||
\(162\) | −4.91073 | − | 11.0871i | −0.385823 | − | 0.871087i | ||||
\(163\) | − | 4.64686i | − | 0.363970i | −0.983301 | − | 0.181985i | \(-0.941748\pi\) | ||
0.983301 | − | 0.181985i | \(-0.0582523\pi\) | |||||||
\(164\) | 1.18150 | − | 0.682139i | 0.0922596 | − | 0.0532661i | ||||
\(165\) | −0.794976 | − | 2.07397i | −0.0618888 | − | 0.161458i | ||||
\(166\) | 1.92091 | − | 3.32712i | 0.149092 | − | 0.258234i | ||||
\(167\) | −10.9080 | − | 6.29773i | −0.844086 | − | 0.487333i | 0.0145650 | − | 0.999894i | \(-0.495364\pi\) |
−0.858651 | + | 0.512561i | \(0.828697\pi\) | |||||||
\(168\) | −15.1007 | + | 18.6294i | −1.16504 | + | 1.43729i | ||||
\(169\) | 3.97839 | − | 12.3763i | 0.306030 | − | 0.952022i | ||||
\(170\) | 0.929633 | 0.0712996 | ||||||||
\(171\) | −12.9667 | − | 14.4290i | −0.991591 | − | 1.10341i | ||||
\(172\) | 2.00379 | 0.152788 | ||||||||
\(173\) | 10.8444 | + | 18.7831i | 0.824485 | + | 1.42805i | 0.902313 | + | 0.431082i | \(0.141868\pi\) |
−0.0778279 | + | 0.996967i | \(0.524798\pi\) | |||||||
\(174\) | −2.03900 | + | 12.8337i | −0.154576 | + | 0.972920i | ||||
\(175\) | 4.07352 | + | 2.35185i | 0.307929 | + | 0.177783i | ||||
\(176\) | 3.99411 | + | 2.30600i | 0.301067 | + | 0.173821i | ||||
\(177\) | 0.112331 | − | 0.707026i | 0.00844333 | − | 0.0531434i | ||||
\(178\) | −7.23297 | − | 12.5279i | −0.542134 | − | 0.939004i | ||||
\(179\) | −15.5830 | −1.16473 | −0.582364 | − | 0.812928i | \(-0.697872\pi\) | ||||
−0.582364 | + | 0.812928i | \(0.697872\pi\) | |||||||
\(180\) | −0.171730 | + | 0.526804i | −0.0128000 | + | 0.0392656i | ||||
\(181\) | −23.6483 | −1.75776 | −0.878882 | − | 0.477040i | \(-0.841710\pi\) | ||||
−0.878882 | + | 0.477040i | \(0.841710\pi\) | |||||||
\(182\) | −2.42414 | − | 22.7210i | −0.179689 | − | 1.68419i | ||||
\(183\) | 6.36065 | − | 7.84701i | 0.470193 | − | 0.580068i | ||||
\(184\) | −10.7294 | − | 6.19462i | −0.790981 | − | 0.456673i | ||||
\(185\) | −4.03373 | + | 6.98663i | −0.296566 | + | 0.513667i | ||||
\(186\) | 0.623753 | + | 1.62728i | 0.0457358 | + | 0.119318i | ||||
\(187\) | −0.766262 | + | 0.442402i | −0.0560346 | + | 0.0323516i | ||||
\(188\) | 1.38664i | 0.101131i | ||||||||
\(189\) | −24.4095 | + | 1.24387i | −1.77553 | + | 0.0904781i | ||||
\(190\) | − | 8.71241i | − | 0.632065i | ||||||
\(191\) | −0.337619 | − | 0.584773i | −0.0244292 | − | 0.0423127i | 0.853552 | − | 0.521007i | \(-0.174444\pi\) |
−0.877982 | + | 0.478694i | \(0.841110\pi\) | |||||||
\(192\) | −5.32896 | − | 13.9024i | −0.384584 | − | 1.00332i | ||||
\(193\) | 12.7236 | + | 7.34599i | 0.915867 | + | 0.528776i | 0.882314 | − | 0.470661i | \(-0.155985\pi\) |
0.0335526 | + | 0.999437i | \(0.489318\pi\) | |||||||
\(194\) | 1.20619 | − | 2.08918i | 0.0865991 | − | 0.149994i | ||||
\(195\) | −2.84122 | − | 5.56125i | −0.203464 | − | 0.398249i | ||||
\(196\) | 1.39674 | + | 2.41923i | 0.0997674 | + | 0.172802i | ||||
\(197\) | − | 2.61631i | − | 0.186404i | −0.995647 | − | 0.0932021i | \(-0.970290\pi\) | ||
0.995647 | − | 0.0932021i | \(-0.0297103\pi\) | |||||||
\(198\) | 1.07278 | + | 5.07106i | 0.0762392 | + | 0.360385i | ||||
\(199\) | 25.9577 | 1.84009 | 0.920045 | − | 0.391813i | \(-0.128152\pi\) | ||||
0.920045 | + | 0.391813i | \(0.128152\pi\) | |||||||
\(200\) | −2.54916 | + | 1.47176i | −0.180253 | + | 0.104069i | ||||
\(201\) | −2.96790 | + | 18.6804i | −0.209340 | + | 1.31761i | ||||
\(202\) | −4.33280 | − | 2.50154i | −0.304855 | − | 0.176008i | ||||
\(203\) | 22.6830 | + | 13.0960i | 1.59203 | + | 0.919161i | ||||
\(204\) | 0.217993 | + | 0.0346343i | 0.0152625 | + | 0.00242489i | ||||
\(205\) | 3.69331 | + | 6.39700i | 0.257952 | + | 0.446786i | ||||
\(206\) | 14.2747i | 0.994567i | ||||||||
\(207\) | −2.61340 | − | 12.3536i | −0.181644 | − | 0.858634i | ||||
\(208\) | 11.8545 | + | 5.25570i | 0.821963 | + | 0.364417i | ||||
\(209\) | 4.14613 | + | 7.18132i | 0.286794 | + | 0.496742i | ||||
\(210\) | −8.52723 | − | 6.91202i | −0.588435 | − | 0.476975i | ||||
\(211\) | −5.16589 | + | 8.94758i | −0.355634 | + | 0.615977i | −0.987226 | − | 0.159324i | \(-0.949069\pi\) |
0.631592 | + | 0.775301i | \(0.282402\pi\) | |||||||
\(212\) | 0.502485 | − | 0.870329i | 0.0345108 | − | 0.0597744i | ||||
\(213\) | −9.38469 | + | 3.59726i | −0.643028 | + | 0.246480i | ||||
\(214\) | −16.9231 | + | 9.77056i | −1.15684 | + | 0.667902i | ||||
\(215\) | 10.8491i | 0.739904i | ||||||||
\(216\) | 6.96345 | − | 13.6178i | 0.473802 | − | 0.926576i | ||||
\(217\) | 3.51264 | 0.238453 | ||||||||
\(218\) | 2.98778 | + | 5.17499i | 0.202358 | + | 0.350494i | ||||
\(219\) | 15.3955 | − | 5.90125i | 1.04033 | − | 0.398770i | ||||
\(220\) | 0.118423 | − | 0.205115i | 0.00798410 | − | 0.0138289i | ||||
\(221\) | −2.01034 | + | 1.46543i | −0.135230 | + | 0.0985753i | ||||
\(222\) | 11.8550 | − | 14.6253i | 0.795657 | − | 0.981587i | ||||
\(223\) | −15.3886 | + | 8.88463i | −1.03050 | + | 0.594959i | −0.917128 | − | 0.398594i | \(-0.869498\pi\) |
−0.113371 | + | 0.993553i | \(0.536165\pi\) | |||||||
\(224\) | −4.89819 | −0.327274 | ||||||||
\(225\) | −2.85227 | − | 0.929800i | −0.190152 | − | 0.0619867i | ||||
\(226\) | − | 9.63634i | − | 0.641000i | ||||||
\(227\) | 24.6734 | − | 14.2452i | 1.63763 | − | 0.945485i | 0.655981 | − | 0.754777i | \(-0.272255\pi\) |
0.981647 | − | 0.190707i | \(-0.0610782\pi\) | |||||||
\(228\) | 0.324589 | − | 2.04300i | 0.0214964 | − | 0.135301i | ||||
\(229\) | 5.24154 | + | 3.02620i | 0.346371 | + | 0.199977i | 0.663086 | − | 0.748544i | \(-0.269247\pi\) |
−0.316715 | + | 0.948521i | \(0.602580\pi\) | |||||||
\(230\) | 2.83546 | − | 4.91116i | 0.186965 | − | 0.323832i | ||||
\(231\) | 10.3180 | + | 1.63931i | 0.678876 | + | 0.107859i | ||||
\(232\) | −14.1947 | + | 8.19531i | −0.931928 | + | 0.538049i | ||||
\(233\) | 8.75020 | 0.573244 | 0.286622 | − | 0.958044i | \(-0.407468\pi\) | ||||
0.286622 | + | 0.958044i | \(0.407468\pi\) | |||||||
\(234\) | 4.51189 | + | 13.8576i | 0.294952 | + | 0.905900i | ||||
\(235\) | −7.50771 | −0.489749 | ||||||||
\(236\) | 0.0661114 | − | 0.0381694i | 0.00430349 | − | 0.00248462i | ||||
\(237\) | 5.27763 | − | 6.51091i | 0.342819 | − | 0.422929i | ||||
\(238\) | −2.18636 | + | 3.78688i | −0.141721 | + | 0.245467i | ||||
\(239\) | −24.3851 | − | 14.0788i | −1.57734 | − | 0.910679i | −0.995229 | − | 0.0975716i | \(-0.968892\pi\) |
−0.582114 | − | 0.813107i | \(-0.697774\pi\) | |||||||
\(240\) | 5.81664 | − | 2.22958i | 0.375462 | − | 0.143919i | ||||
\(241\) | 2.53789 | − | 1.46525i | 0.163480 | − | 0.0943852i | −0.416028 | − | 0.909352i | \(-0.636578\pi\) |
0.579508 | + | 0.814967i | \(0.303245\pi\) | |||||||
\(242\) | 12.6050i | 0.810283i | ||||||||
\(243\) | 15.0670 | − | 3.99830i | 0.966547 | − | 0.256491i | ||||
\(244\) | 1.07713 | 0.0689562 | ||||||||
\(245\) | −13.0984 | + | 7.56239i | −0.836829 | + | 0.483143i | ||||
\(246\) | −6.16970 | − | 16.0958i | −0.393366 | − | 1.02623i | ||||
\(247\) | 13.7338 | + | 18.8407i | 0.873861 | + | 1.19880i | ||||
\(248\) | −1.09908 | + | 1.90366i | −0.0697917 | + | 0.120883i | ||||
\(249\) | 3.83669 | + | 3.10995i | 0.243140 | + | 0.197085i | ||||
\(250\) | −0.673666 | − | 1.16682i | −0.0426064 | − | 0.0737964i | ||||
\(251\) | 14.7686 | 0.932185 | 0.466093 | − | 0.884736i | \(-0.345661\pi\) | ||||
0.466093 | + | 0.884736i | \(0.345661\pi\) | |||||||
\(252\) | −1.74206 | − | 1.93851i | −0.109740 | − | 0.122115i | ||||
\(253\) | 5.39745i | 0.339335i | ||||||||
\(254\) | 12.5529 | − | 7.24742i | 0.787639 | − | 0.454744i | ||||
\(255\) | −0.187521 | + | 1.18028i | −0.0117430 | + | 0.0739119i | ||||
\(256\) | 2.19687 | − | 3.80509i | 0.137304 | − | 0.237818i | ||||
\(257\) | −8.52231 | + | 14.7611i | −0.531607 | + | 0.920771i | 0.467712 | + | 0.883881i | \(0.345078\pi\) |
−0.999319 | + | 0.0368900i | \(0.988255\pi\) | |||||||
\(258\) | 3.97266 | − | 25.0044i | 0.247327 | − | 1.55671i | ||||
\(259\) | −18.9735 | − | 32.8630i | −1.17895 | − | 2.04201i | ||||
\(260\) | 0.269903 | − | 0.608783i | 0.0167387 | − | 0.0377551i | ||||
\(261\) | −15.8826 | − | 5.17749i | −0.983108 | − | 0.320479i | ||||
\(262\) | 24.0549i | 1.48612i | ||||||||
\(263\) | −6.10773 | − | 10.5789i | −0.376619 | − | 0.652323i | 0.613949 | − | 0.789346i | \(-0.289580\pi\) |
−0.990568 | + | 0.137023i | \(0.956247\pi\) | |||||||
\(264\) | −4.11686 | + | 5.07889i | −0.253375 | + | 0.312584i | ||||
\(265\) | 4.71222 | + | 2.72060i | 0.289470 | + | 0.167125i | ||||
\(266\) | 35.4902 | + | 20.4903i | 2.17604 | + | 1.25634i | ||||
\(267\) | 17.3646 | − | 6.65604i | 1.06270 | − | 0.407343i | ||||
\(268\) | −1.74673 | + | 1.00848i | −0.106699 | + | 0.0616024i | ||||
\(269\) | 14.2974 | 0.871727 | 0.435863 | − | 0.900013i | \(-0.356443\pi\) | ||||
0.435863 | + | 0.900013i | \(0.356443\pi\) | |||||||
\(270\) | 6.23329 | + | 3.18738i | 0.379346 | + | 0.193977i | ||||
\(271\) | − | 3.84476i | − | 0.233553i | −0.993158 | − | 0.116776i | \(-0.962744\pi\) | ||
0.993158 | − | 0.116776i | \(-0.0372561\pi\) | |||||||
\(272\) | −1.24076 | − | 2.14905i | −0.0752319 | − | 0.130306i | ||||
\(273\) | 29.3360 | + | 1.50544i | 1.77549 | + | 0.0911135i | ||||
\(274\) | −2.89508 | + | 5.01443i | −0.174898 | + | 0.302933i | ||||
\(275\) | 1.11056 | + | 0.641180i | 0.0669690 | + | 0.0386646i | ||||
\(276\) | 0.847865 | − | 1.04600i | 0.0510355 | − | 0.0629615i | ||||
\(277\) | 13.5454 | + | 23.4614i | 0.813865 | + | 1.40966i | 0.910140 | + | 0.414301i | \(0.135974\pi\) |
−0.0962743 | + | 0.995355i | \(0.530693\pi\) | |||||||
\(278\) | − | 0.208015i | − | 0.0124759i | ||||||
\(279\) | −2.19184 | + | 0.463682i | −0.131222 | + | 0.0277599i | ||||
\(280\) | − | 13.8454i | − | 0.827420i | ||||||
\(281\) | −7.02708 | + | 4.05709i | −0.419201 | + | 0.242026i | −0.694735 | − | 0.719266i | \(-0.744478\pi\) |
0.275535 | + | 0.961291i | \(0.411145\pi\) | |||||||
\(282\) | 17.3033 | + | 2.74912i | 1.03040 | + | 0.163708i | ||||
\(283\) | 12.1427 | − | 21.0317i | 0.721807 | − | 1.25021i | −0.238468 | − | 0.971150i | \(-0.576645\pi\) |
0.960275 | − | 0.279056i | \(-0.0900215\pi\) | |||||||
\(284\) | −0.928144 | − | 0.535864i | −0.0550752 | − | 0.0317977i | ||||
\(285\) | 11.0614 | + | 1.75742i | 0.655222 | + | 0.104101i | ||||
\(286\) | −0.660887 | − | 6.19438i | −0.0390791 | − | 0.366282i | ||||
\(287\) | −34.7444 | −2.05090 | ||||||||
\(288\) | 3.05640 | − | 0.646581i | 0.180100 | − | 0.0381001i | ||||
\(289\) | −16.5239 | −0.971996 | ||||||||
\(290\) | −3.75124 | − | 6.49733i | −0.220280 | − | 0.381537i | ||||
\(291\) | 2.40915 | + | 1.95281i | 0.141227 | + | 0.114476i | ||||
\(292\) | 1.52261 | + | 0.879078i | 0.0891039 | + | 0.0514442i | ||||
\(293\) | 22.8249 | + | 13.1779i | 1.33344 | + | 0.769864i | 0.985826 | − | 0.167773i | \(-0.0536575\pi\) |
0.347617 | + | 0.937637i | \(0.386991\pi\) | |||||||
\(294\) | 32.9577 | − | 12.6330i | 1.92213 | − | 0.736774i | ||||
\(295\) | 0.206661 | + | 0.357947i | 0.0120323 | + | 0.0208405i | ||||
\(296\) | 23.7467 | 1.38025 | ||||||||
\(297\) | −6.65470 | + | 0.339113i | −0.386145 | + | 0.0196773i | ||||
\(298\) | −12.5212 | −0.725334 | ||||||||
\(299\) | 1.60998 | + | 15.0901i | 0.0931077 | + | 0.872684i | ||||
\(300\) | −0.114499 | − | 0.298710i | −0.00661060 | − | 0.0172460i | ||||
\(301\) | −44.1941 | − | 25.5155i | −2.54731 | − | 1.47069i | ||||
\(302\) | 4.77791 | − | 8.27557i | 0.274938 | − | 0.476206i | ||||
\(303\) | 4.04999 | − | 4.99640i | 0.232666 | − | 0.287036i | ||||
\(304\) | −20.1407 | + | 11.6282i | −1.15515 | + | 0.666924i | ||||
\(305\) | 5.83191i | 0.333934i | ||||||||
\(306\) | 0.864373 | − | 2.65157i | 0.0494129 | − | 0.151580i | ||||
\(307\) | 17.8331i | 1.01779i | 0.860828 | + | 0.508896i | \(0.169946\pi\) | ||||
−0.860828 | + | 0.508896i | \(0.830054\pi\) | |||||||
\(308\) | 0.557028 | + | 0.964800i | 0.0317396 | + | 0.0549746i | ||||
\(309\) | −18.1234 | − | 2.87942i | −1.03101 | − | 0.163805i | ||||
\(310\) | −0.871363 | − | 0.503082i | −0.0494901 | − | 0.0285731i | ||||
\(311\) | 12.4668 | − | 21.5932i | 0.706929 | − | 1.22444i | −0.259062 | − | 0.965861i | \(-0.583413\pi\) |
0.965991 | − | 0.258576i | \(-0.0832533\pi\) | |||||||
\(312\) | −9.99490 | + | 15.4275i | −0.565850 | + | 0.873411i | ||||
\(313\) | 0.556344 | + | 0.963617i | 0.0314464 | + | 0.0544668i | 0.881320 | − | 0.472519i | \(-0.156655\pi\) |
−0.849874 | + | 0.526986i | \(0.823322\pi\) | |||||||
\(314\) | 18.1092i | 1.02196i | ||||||||
\(315\) | 10.4957 | − | 9.43206i | 0.591365 | − | 0.531436i | ||||
\(316\) | 0.893728 | 0.0502761 | ||||||||
\(317\) | −23.8124 | + | 13.7481i | −1.33744 | + | 0.772169i | −0.986427 | − | 0.164203i | \(-0.947495\pi\) |
−0.351010 | + | 0.936372i | \(0.614162\pi\) | |||||||
\(318\) | −9.86424 | − | 7.99578i | −0.553159 | − | 0.448381i | ||||
\(319\) | 6.18401 | + | 3.57034i | 0.346238 | + | 0.199901i | ||||
\(320\) | 7.44438 | + | 4.29802i | 0.416154 | + | 0.240266i | ||||
\(321\) | −8.99123 | − | 23.4567i | −0.501841 | − | 1.30923i | ||||
\(322\) | 13.3371 | + | 23.1006i | 0.743250 | + | 1.28735i | ||||
\(323\) | − | 4.46170i | − | 0.248256i | ||||||
\(324\) | 1.34291 | + | 0.979644i | 0.0746064 | + | 0.0544247i | ||||
\(325\) | 3.29613 | + | 1.46134i | 0.182837 | + | 0.0810605i | ||||
\(326\) | −3.13043 | − | 5.42207i | −0.173379 | − | 0.300301i | ||||
\(327\) | −7.17293 | + | 2.74947i | −0.396664 | + | 0.152046i | ||||
\(328\) | 10.8713 | − | 18.8296i | 0.600267 | − | 1.03969i | ||||
\(329\) | 17.6570 | − | 30.5828i | 0.973462 | − | 1.68609i | ||||
\(330\) | −2.32476 | − | 1.88441i | −0.127974 | − | 0.103733i | ||||
\(331\) | 10.6947 | − | 6.17460i | 0.587835 | − | 0.339387i | −0.176406 | − | 0.984317i | \(-0.556447\pi\) |
0.764241 | + | 0.644931i | \(0.223114\pi\) | |||||||
\(332\) | 0.526648i | 0.0289036i | ||||||||
\(333\) | 16.1772 | + | 18.0015i | 0.886506 | + | 0.986475i | ||||
\(334\) | −16.9703 | −0.928572 | ||||||||
\(335\) | −5.46019 | − | 9.45733i | −0.298322 | − | 0.516709i | ||||
\(336\) | −4.59760 | + | 28.9379i | −0.250820 | + | 1.57869i | ||||
\(337\) | −0.663331 | + | 1.14892i | −0.0361339 | + | 0.0625858i | −0.883527 | − | 0.468381i | \(-0.844838\pi\) |
0.847393 | + | 0.530966i | \(0.178171\pi\) | |||||||
\(338\) | −3.69540 | − | 17.1211i | −0.201003 | − | 0.931262i | ||||
\(339\) | 12.2345 | + | 1.94379i | 0.664485 | + | 0.105572i | ||||
\(340\) | −0.110363 | + | 0.0637184i | −0.00598530 | + | 0.00345561i | ||||
\(341\) | 0.957643 | 0.0518593 | ||||||||
\(342\) | −24.8502 | − | 8.10080i | −1.34374 | − | 0.438041i | ||||
\(343\) | − | 38.2165i | − | 2.06350i | ||||||
\(344\) | 27.6561 | − | 15.9673i | 1.49112 | − | 0.860897i | ||||
\(345\) | 5.66334 | + | 4.59060i | 0.304904 | + | 0.247150i | ||||
\(346\) | 25.3070 | + | 14.6110i | 1.36051 | + | 0.785493i | ||||
\(347\) | 12.6904 | − | 21.9804i | 0.681256 | − | 1.17997i | −0.293342 | − | 0.956008i | \(-0.594767\pi\) |
0.974598 | − | 0.223963i | \(-0.0718993\pi\) | |||||||
\(348\) | −0.637576 | − | 1.66334i | −0.0341776 | − | 0.0891642i | ||||
\(349\) | 11.4337 | − | 6.60123i | 0.612030 | − | 0.353355i | −0.161730 | − | 0.986835i | \(-0.551707\pi\) |
0.773759 | + | 0.633480i | \(0.218374\pi\) | |||||||
\(350\) | 6.33744 | 0.338751 | ||||||||
\(351\) | −18.5040 | + | 2.93309i | −0.987669 | + | 0.156557i | ||||
\(352\) | −1.33538 | −0.0711761 | ||||||||
\(353\) | −8.09353 | + | 4.67280i | −0.430775 | + | 0.248708i | −0.699677 | − | 0.714460i | \(-0.746673\pi\) |
0.268902 | + | 0.963168i | \(0.413339\pi\) | |||||||
\(354\) | −0.345229 | − | 0.900649i | −0.0183487 | − | 0.0478689i | ||||
\(355\) | 2.90133 | − | 5.02525i | 0.153987 | − | 0.266713i | ||||
\(356\) | 1.71736 | + | 0.991515i | 0.0910196 | + | 0.0525502i | ||||
\(357\) | −4.36687 | − | 3.53971i | −0.231119 | − | 0.187341i | ||||
\(358\) | −18.1826 | + | 10.4977i | −0.960981 | + | 0.554823i | ||||
\(359\) | − | 29.6022i | − | 1.56234i | −0.624315 | − | 0.781172i | \(-0.714622\pi\) | ||
0.624315 | − | 0.781172i | \(-0.285378\pi\) | |||||||
\(360\) | 1.82765 | + | 8.63933i | 0.0963254 | + | 0.455333i | ||||
\(361\) | −22.8145 | −1.20077 | ||||||||
\(362\) | −27.5934 | + | 15.9311i | −1.45028 | + | 0.837318i | ||||
\(363\) | −16.0036 | − | 2.54262i | −0.839970 | − | 0.133453i | ||||
\(364\) | 1.84512 | + | 2.53122i | 0.0967104 | + | 0.132672i | ||||
\(365\) | −4.75959 | + | 8.24386i | −0.249129 | + | 0.431503i | ||||
\(366\) | 2.13549 | − | 13.4410i | 0.111624 | − | 0.702574i | ||||
\(367\) | 9.36803 | + | 16.2259i | 0.489007 | + | 0.846985i | 0.999920 | − | 0.0126473i | \(-0.00402586\pi\) |
−0.510913 | + | 0.859633i | \(0.670693\pi\) | |||||||
\(368\) | −15.1376 | −0.789104 | ||||||||
\(369\) | 21.6800 | − | 4.58640i | 1.12862 | − | 0.238758i | ||||
\(370\) | 10.8696i | 0.565081i | ||||||||
\(371\) | −22.1649 | + | 12.7969i | −1.15074 | + | 0.664382i | ||||
\(372\) | −0.185586 | − | 0.150433i | −0.00962218 | − | 0.00779957i | ||||
\(373\) | 7.12935 | − | 12.3484i | 0.369144 | − | 0.639375i | −0.620288 | − | 0.784374i | \(-0.712984\pi\) |
0.989432 | + | 0.144998i | \(0.0463177\pi\) | |||||||
\(374\) | −0.596062 | + | 1.03241i | −0.0308216 | + | 0.0533846i | ||||
\(375\) | 1.61731 | − | 0.619932i | 0.0835174 | − | 0.0320132i | ||||
\(376\) | 11.0495 | + | 19.1383i | 0.569835 | + | 0.986983i | ||||
\(377\) | 18.3542 | + | 8.13731i | 0.945287 | + | 0.419093i | ||||
\(378\) | −27.6436 | + | 17.8952i | −1.42183 | + | 0.920430i | ||||
\(379\) | − | 2.12905i | − | 0.109362i | −0.998504 | − | 0.0546811i | \(-0.982586\pi\) | ||
0.998504 | − | 0.0546811i | \(-0.0174142\pi\) | |||||||
\(380\) | 0.597161 | + | 1.03431i | 0.0306337 | + | 0.0530591i | ||||
\(381\) | 6.66934 | + | 17.3993i | 0.341681 | + | 0.891392i | ||||
\(382\) | −0.787883 | − | 0.454885i | −0.0403116 | − | 0.0232739i | ||||
\(383\) | 10.5441 | + | 6.08761i | 0.538776 | + | 0.311063i | 0.744583 | − | 0.667530i | \(-0.232648\pi\) |
−0.205807 | + | 0.978593i | \(0.565982\pi\) | |||||||
\(384\) | −12.7812 | − | 10.3602i | −0.652239 | − | 0.528693i | ||||
\(385\) | −5.22372 | + | 3.01592i | −0.266225 | + | 0.153705i | ||||
\(386\) | 19.7950 | 1.00754 | ||||||||
\(387\) | 30.9447 | + | 10.0875i | 1.57301 | + | 0.512777i | ||||
\(388\) | 0.330695i | 0.0167885i | ||||||||
\(389\) | 12.7383 | + | 22.0634i | 0.645858 | + | 1.11866i | 0.984103 | + | 0.177600i | \(0.0568333\pi\) |
−0.338245 | + | 0.941058i | \(0.609833\pi\) | |||||||
\(390\) | −7.06163 | − | 4.57496i | −0.357579 | − | 0.231662i | ||||
\(391\) | 1.45206 | − | 2.51505i | 0.0734340 | − | 0.127191i | ||||
\(392\) | 38.5554 | + | 22.2600i | 1.94734 | + | 1.12430i | ||||
\(393\) | −30.5406 | − | 4.85223i | −1.54057 | − | 0.244763i | ||||
\(394\) | −1.76252 | − | 3.05277i | −0.0887943 | − | 0.153796i | ||||
\(395\) | 4.83891i | 0.243472i | ||||||||
\(396\) | −0.474935 | − | 0.528492i | −0.0238664 | − | 0.0265577i | ||||
\(397\) | 18.5900i | 0.933004i | 0.884520 | + | 0.466502i | \(0.154486\pi\) | ||||
−0.884520 | + | 0.466502i | \(0.845514\pi\) | |||||||
\(398\) | 30.2880 | − | 17.4868i | 1.51820 | − | 0.876534i | ||||
\(399\) | −33.1737 | + | 40.9258i | −1.66076 | + | 2.04885i | ||||
\(400\) | −1.79825 | + | 3.11466i | −0.0899124 | + | 0.155733i | ||||
\(401\) | −3.02411 | − | 1.74597i | −0.151017 | − | 0.0871897i | 0.422587 | − | 0.906322i | \(-0.361122\pi\) |
−0.573604 | + | 0.819132i | \(0.694455\pi\) | |||||||
\(402\) | 9.12130 | + | 23.7961i | 0.454929 | + | 1.18684i | ||||
\(403\) | 2.67737 | − | 0.285652i | 0.133369 | − | 0.0142293i | ||||
\(404\) | 0.685837 | 0.0341217 | ||||||||
\(405\) | −5.30409 | + | 7.27094i | −0.263562 | + | 0.361296i | ||||
\(406\) | 35.2894 | 1.75138 | ||||||||
\(407\) | −5.17269 | − | 8.95937i | −0.256401 | − | 0.444099i | ||||
\(408\) | 3.28470 | − | 1.25906i | 0.162617 | − | 0.0623328i | ||||
\(409\) | −6.29168 | − | 3.63250i | −0.311103 | − | 0.179616i | 0.336317 | − | 0.941749i | \(-0.390819\pi\) |
−0.647420 | + | 0.762133i | \(0.724152\pi\) | |||||||
\(410\) | 8.61888 | + | 4.97611i | 0.425656 | + | 0.245753i | ||||
\(411\) | −5.78242 | − | 4.68713i | −0.285226 | − | 0.231199i | ||||
\(412\) | −0.978409 | − | 1.69465i | −0.0482028 | − | 0.0834896i | ||||
\(413\) | −1.94414 | −0.0956649 | ||||||||
\(414\) | −11.3716 | − | 12.6539i | −0.558882 | − | 0.621906i | ||||
\(415\) | −2.85143 | −0.139971 | ||||||||
\(416\) | −3.73345 | + | 0.398326i | −0.183047 | + | 0.0195295i | ||||
\(417\) | 0.264099 | + | 0.0419597i | 0.0129330 | + | 0.00205477i | ||||
\(418\) | 9.67562 | + | 5.58622i | 0.473250 | + | 0.273231i | ||||
\(419\) | −8.78209 | + | 15.2110i | −0.429033 | + | 0.743107i | −0.996788 | − | 0.0800910i | \(-0.974479\pi\) |
0.567755 | + | 0.823198i | \(0.307812\pi\) | |||||||
\(420\) | 1.48609 | + | 0.236107i | 0.0725136 | + | 0.0115209i | ||||
\(421\) | −13.8198 | + | 7.97886i | −0.673536 | + | 0.388866i | −0.797415 | − | 0.603431i | \(-0.793800\pi\) |
0.123879 | + | 0.992297i | \(0.460466\pi\) | |||||||
\(422\) | 13.9203i | 0.677631i | ||||||||
\(423\) | −6.98067 | + | 21.4140i | −0.339412 | + | 1.04119i | ||||
\(424\) | − | 16.0163i | − | 0.777818i | ||||||
\(425\) | −0.344990 | − | 0.597541i | −0.0167345 | − | 0.0289850i | ||||
\(426\) | −8.52693 | + | 10.5195i | −0.413131 | + | 0.509672i | ||||
\(427\) | −23.7564 | − | 13.7158i | −1.14965 | − | 0.663753i | ||||
\(428\) | 1.33938 | − | 2.31987i | 0.0647412 | − | 0.112135i | ||||
\(429\) | 7.99781 | + | 0.410425i | 0.386138 | + | 0.0198155i | ||||
\(430\) | 7.30869 | + | 12.6590i | 0.352456 | + | 0.610472i | ||||
\(431\) | − | 2.36438i | − | 0.113888i | −0.998377 | − | 0.0569440i | \(-0.981864\pi\) | ||
0.998377 | − | 0.0569440i | \(-0.0181356\pi\) | |||||||
\(432\) | −0.951075 | − | 18.6637i | −0.0457586 | − | 0.897959i | ||||
\(433\) | −15.9227 | −0.765194 | −0.382597 | − | 0.923915i | \(-0.624970\pi\) | ||||
−0.382597 | + | 0.923915i | \(0.624970\pi\) | |||||||
\(434\) | 4.09863 | − | 2.36634i | 0.196741 | − | 0.113588i | ||||
\(435\) | 9.00580 | − | 3.45203i | 0.431795 | − | 0.165512i | ||||
\(436\) | −0.709402 | − | 0.409573i | −0.0339742 | − | 0.0196150i | ||||
\(437\) | −23.5707 | − | 13.6086i | −1.12754 | − | 0.650986i | ||||
\(438\) | 13.9883 | − | 17.2571i | 0.668387 | − | 0.824577i | ||||
\(439\) | 12.2763 | + | 21.2632i | 0.585916 | + | 1.01484i | 0.994761 | + | 0.102233i | \(0.0325986\pi\) |
−0.408844 | + | 0.912604i | \(0.634068\pi\) | |||||||
\(440\) | − | 3.77464i | − | 0.179949i | ||||||
\(441\) | 9.39108 | + | 44.3919i | 0.447195 | + | 2.11390i | ||||
\(442\) | −1.35851 | + | 3.06420i | −0.0646177 | + | 0.145749i | ||||
\(443\) | 10.9342 | + | 18.9386i | 0.519501 | + | 0.899802i | 0.999743 | + | 0.0226659i | \(0.00721539\pi\) |
−0.480242 | + | 0.877136i | \(0.659451\pi\) | |||||||
\(444\) | −0.404955 | + | 2.54884i | −0.0192183 | + | 0.120962i | ||||
\(445\) | −5.36836 | + | 9.29828i | −0.254485 | + | 0.440781i | ||||
\(446\) | −11.9705 | + | 20.7336i | −0.566822 | + | 0.981764i | ||||
\(447\) | 2.52571 | − | 15.8971i | 0.119462 | − | 0.751909i | ||||
\(448\) | −35.0161 | + | 20.2166i | −1.65436 | + | 0.955143i | ||||
\(449\) | 13.2031i | 0.623092i | 0.950231 | + | 0.311546i | \(0.100847\pi\) | ||||
−0.950231 | + | 0.311546i | \(0.899153\pi\) | |||||||
\(450\) | −3.95448 | + | 0.836568i | −0.186416 | + | 0.0394362i | ||||
\(451\) | −9.47229 | −0.446033 | ||||||||
\(452\) | 0.660488 | + | 1.14400i | 0.0310667 | + | 0.0538092i | ||||
\(453\) | 9.54304 | + | 7.73541i | 0.448371 | + | 0.363441i | ||||
\(454\) | 19.1930 | − | 33.2432i | 0.900771 | − | 1.56018i | ||||
\(455\) | −13.7048 | + | 9.99002i | −0.642491 | + | 0.468339i | ||||
\(456\) | −11.7998 | − | 30.7838i | −0.552575 | − | 1.44158i | ||||
\(457\) | −14.3166 | + | 8.26571i | −0.669704 | + | 0.386654i | −0.795964 | − | 0.605344i | \(-0.793036\pi\) |
0.126261 | + | 0.991997i | \(0.459702\pi\) | |||||||
\(458\) | 8.15460 | 0.381039 | ||||||||
\(459\) | 3.19212 | + | 1.63228i | 0.148995 | + | 0.0761885i | ||||
\(460\) | 0.777385i | 0.0362458i | ||||||||
\(461\) | 30.1732 | − | 17.4205i | 1.40531 | − | 0.811354i | 0.410375 | − | 0.911917i | \(-0.365398\pi\) |
0.994931 | + | 0.100563i | \(0.0320645\pi\) | |||||||
\(462\) | 13.1437 | − | 5.03812i | 0.611499 | − | 0.234394i | ||||
\(463\) | −28.0327 | − | 16.1847i | −1.30279 | − | 0.752167i | −0.321910 | − | 0.946770i | \(-0.604325\pi\) |
−0.980882 | + | 0.194603i | \(0.937658\pi\) | |||||||
\(464\) | −10.0134 | + | 17.3436i | −0.464858 | + | 0.805158i | ||||
\(465\) | 0.814488 | − | 1.00482i | 0.0377710 | − | 0.0465973i | ||||
\(466\) | 10.2099 | − | 5.89471i | 0.472966 | − | 0.273067i | ||||
\(467\) | 8.15829 | 0.377521 | 0.188760 | − | 0.982023i | \(-0.439553\pi\) | ||||
0.188760 | + | 0.982023i | \(0.439553\pi\) | |||||||
\(468\) | −1.48546 | − | 1.33588i | −0.0686654 | − | 0.0617513i | ||||
\(469\) | 51.3662 | 2.37187 | ||||||||
\(470\) | −8.76017 | + | 5.05769i | −0.404077 | + | 0.233294i | ||||
\(471\) | −22.9917 | − | 3.65289i | −1.05940 | − | 0.168316i | ||||
\(472\) | 0.608309 | − | 1.05362i | 0.0279997 | − | 0.0484969i | ||||
\(473\) | −12.0486 | − | 6.95624i | −0.553993 | − | 0.319848i | ||||
\(474\) | 1.77188 | − | 11.1524i | 0.0813852 | − | 0.512249i | ||||
\(475\) | −5.60008 | + | 3.23321i | −0.256949 | + | 0.148350i | ||||
\(476\) | − | 0.599424i | − | 0.0274746i | ||||||
\(477\) | 12.1413 | − | 10.9109i | 0.555914 | − | 0.499578i | ||||
\(478\) | −37.9375 | −1.73522 | ||||||||
\(479\) | 15.9891 | − | 9.23132i | 0.730561 | − | 0.421790i | −0.0880661 | − | 0.996115i | \(-0.528069\pi\) |
0.818628 | + | 0.574325i | \(0.194735\pi\) | |||||||
\(480\) | −1.13576 | + | 1.40117i | −0.0518401 | + | 0.0639542i | ||||
\(481\) | −17.1342 | − | 23.5055i | −0.781252 | − | 1.07176i | ||||
\(482\) | 1.97418 | − | 3.41938i | 0.0899215 | − | 0.155749i | ||||
\(483\) | −32.0192 | + | 12.2733i | −1.45693 | + | 0.558456i | ||||
\(484\) | −0.863967 | − | 1.49643i | −0.0392712 | − | 0.0680197i | ||||
\(485\) | −1.79048 | −0.0813015 | ||||||||
\(486\) | 14.8870 | − | 14.8154i | 0.675287 | − | 0.672041i | ||||
\(487\) | − | 36.5271i | − | 1.65520i | −0.561317 | − | 0.827601i | \(-0.689705\pi\) | ||
0.561317 | − | 0.827601i | \(-0.310295\pi\) | |||||||
\(488\) | 14.8664 | − | 8.58314i | 0.672972 | − | 0.388541i | ||||
\(489\) | 7.51540 | − | 2.88074i | 0.339858 | − | 0.130272i | ||||
\(490\) | −10.1891 | + | 17.6480i | −0.460295 | + | 0.797254i | ||||
\(491\) | −12.3472 | + | 21.3859i | −0.557220 | + | 0.965133i | 0.440508 | + | 0.897749i | \(0.354798\pi\) |
−0.997727 | + | 0.0673836i | \(0.978535\pi\) | |||||||
\(492\) | 1.83568 | + | 1.48797i | 0.0827588 | + | 0.0670828i | ||||
\(493\) | −1.92104 | − | 3.32734i | −0.0865194 | − | 0.149856i | ||||
\(494\) | 28.7173 | + | 12.7318i | 1.29205 | + | 0.572830i | ||||
\(495\) | 2.86141 | − | 2.57144i | 0.128611 | − | 0.115578i | ||||
\(496\) | 2.68580i | 0.120596i | ||||||||
\(497\) | 13.6470 | + | 23.6373i | 0.612151 | + | 1.06028i | ||||
\(498\) | 6.57181 | + | 1.04412i | 0.294490 | + | 0.0467881i | ||||
\(499\) | −6.04869 | − | 3.49221i | −0.270776 | − | 0.156333i | 0.358464 | − | 0.933544i | \(-0.383301\pi\) |
−0.629240 | + | 0.777211i | \(0.716634\pi\) | |||||||
\(500\) | 0.159951 | + | 0.0923480i | 0.00715325 | + | 0.00412993i | ||||
\(501\) | 3.42315 | − | 21.5458i | 0.152935 | − | 0.962593i | ||||
\(502\) | 17.2323 | − | 9.94910i | 0.769117 | − | 0.444050i | ||||
\(503\) | 10.0965 | 0.450179 | 0.225089 | − | 0.974338i | \(-0.427733\pi\) | ||||
0.225089 | + | 0.974338i | \(0.427733\pi\) | |||||||
\(504\) | −39.4909 | − | 12.8734i | −1.75906 | − | 0.573429i | ||||
\(505\) | 3.71333i | 0.165241i | ||||||||
\(506\) | 3.63608 | + | 6.29787i | 0.161643 | + | 0.279974i | ||||
\(507\) | 22.4826 | − | 1.23817i | 0.998487 | − | 0.0549892i | ||||
\(508\) | −0.993496 | + | 1.72079i | −0.0440793 | + | 0.0763475i | ||||
\(509\) | 25.1392 | + | 14.5141i | 1.11427 | + | 0.643326i | 0.939933 | − | 0.341359i | \(-0.110887\pi\) |
0.174341 | + | 0.984685i | \(0.444221\pi\) | |||||||
\(510\) | 0.576310 | + | 1.50350i | 0.0255194 | + | 0.0665762i | ||||
\(511\) | −22.3877 | − | 38.7766i | −0.990374 | − | 1.71538i | ||||
\(512\) | − | 24.9179i | − | 1.10122i | ||||||
\(513\) | 15.2976 | − | 29.9162i | 0.675404 | − | 1.32083i | ||||
\(514\) | 22.9648i | 1.01293i | ||||||||
\(515\) | 9.17537 | − | 5.29740i | 0.404315 | − | 0.233431i | ||||
\(516\) | 1.24221 | + | 3.24074i | 0.0546854 | + | 0.142666i | ||||
\(517\) | 4.81379 | − | 8.33773i | 0.211710 | − | 0.366693i | ||||
\(518\) | −44.2774 | − | 25.5636i | −1.94544 | − | 1.12320i | ||||
\(519\) | −23.6552 | + | 29.1830i | −1.03835 | + | 1.28099i | ||||
\(520\) | −1.12592 | − | 10.5531i | −0.0493750 | − | 0.462784i | ||||
\(521\) | 11.5657 | 0.506701 | 0.253350 | − | 0.967375i | \(-0.418467\pi\) | ||||
0.253350 | + | 0.967375i | \(0.418467\pi\) | |||||||
\(522\) | −22.0201 | + | 4.65834i | −0.963793 | + | 0.203890i | ||||
\(523\) | 6.17284 | 0.269919 | 0.134960 | − | 0.990851i | \(-0.456910\pi\) | ||||
0.134960 | + | 0.990851i | \(0.456910\pi\) | |||||||
\(524\) | −1.64876 | − | 2.85573i | −0.0720264 | − | 0.124753i | ||||
\(525\) | −1.27836 | + | 8.04613i | −0.0557920 | + | 0.351162i | ||||
\(526\) | −14.2533 | − | 8.22914i | −0.621473 | − | 0.358808i | ||||
\(527\) | −0.446233 | − | 0.257633i | −0.0194382 | − | 0.0112227i | ||||
\(528\) | −1.25343 | + | 7.88926i | −0.0545487 | + | 0.343336i | ||||
\(529\) | 2.64217 | + | 4.57637i | 0.114877 | + | 0.198973i | ||||
\(530\) | 7.33111 | 0.318443 | ||||||||
\(531\) | 1.21312 | − | 0.256634i | 0.0526448 | − | 0.0111370i | ||||
\(532\) | −5.61773 | −0.243559 | ||||||||
\(533\) | −26.4825 | + | 2.82545i | −1.14709 | + | 0.122384i | ||||
\(534\) | 15.7775 | − | 19.4644i | 0.682758 | − | 0.842306i | ||||
\(535\) | 12.5605 | + | 7.25178i | 0.543036 | + | 0.313522i | ||||
\(536\) | −16.0721 | + | 27.8377i | −0.694210 | + | 1.20241i | ||||
\(537\) | −9.66040 | − | 25.2025i | −0.416877 | − | 1.08757i | ||||
\(538\) | 16.6825 | − | 9.63166i | 0.719235 | − | 0.415250i | ||||
\(539\) | − | 19.3954i | − | 0.835419i | ||||||
\(540\) | −0.958465 | + | 0.0488419i | −0.0412458 | + | 0.00210182i | ||||
\(541\) | 10.6019i | 0.455811i | 0.973683 | + | 0.227905i | \(0.0731877\pi\) | ||||
−0.973683 | + | 0.227905i | \(0.926812\pi\) | |||||||
\(542\) | −2.59009 | − | 4.48616i | −0.111254 | − | 0.192697i | ||||
\(543\) | −14.6603 | − | 38.2466i | −0.629135 | − | 1.64132i | ||||
\(544\) | 0.622248 | + | 0.359255i | 0.0266787 | + | 0.0154029i | ||||
\(545\) | 2.21755 | − | 3.84091i | 0.0949895 | − | 0.164527i | ||||
\(546\) | 35.2441 | − | 18.0061i | 1.50831 | − | 0.770589i | ||||
\(547\) | −13.0254 | − | 22.5607i | −0.556926 | − | 0.964624i | −0.997751 | − | 0.0670308i | \(-0.978647\pi\) |
0.440825 | − | 0.897593i | \(-0.354686\pi\) | |||||||
\(548\) | − | 0.793732i | − | 0.0339065i | ||||||
\(549\) | 16.6342 | + | 5.42251i | 0.709931 | + | 0.231427i | ||||
\(550\) | 1.72776 | 0.0736721 | ||||||||
\(551\) | −31.1835 | + | 18.0038i | −1.32846 | + | 0.766987i | ||||
\(552\) | 3.36710 | − | 21.1930i | 0.143313 | − | 0.902033i | ||||
\(553\) | −19.7114 | − | 11.3804i | −0.838215 | − | 0.483944i | ||||
\(554\) | 31.6102 | + | 18.2502i | 1.34299 | + | 0.775376i | ||||
\(555\) | −13.8002 | − | 2.19255i | −0.585784 | − | 0.0930685i | ||||
\(556\) | 0.0142576 | + | 0.0246949i | 0.000604658 | + | 0.00104730i | ||||
\(557\) | 33.4373i | 1.41678i | 0.705819 | + | 0.708392i | \(0.250579\pi\) | ||||
−0.705819 | + | 0.708392i | \(0.749421\pi\) | |||||||
\(558\) | −2.24512 | + | 2.01760i | −0.0950435 | + | 0.0854119i | ||||
\(559\) | −35.7601 | − | 15.8542i | −1.51249 | − | 0.670563i | ||||
\(560\) | −8.45842 | − | 14.6504i | −0.357433 | − | 0.619093i | ||||
\(561\) | −1.19053 | − | 0.965023i | −0.0502642 | − | 0.0407433i | ||||
\(562\) | −5.46625 | + | 9.46782i | −0.230580 | + | 0.399376i | ||||
\(563\) | −6.04230 | + | 10.4656i | −0.254653 | + | 0.441071i | −0.964801 | − | 0.262981i | \(-0.915294\pi\) |
0.710148 | + | 0.704052i | \(0.248628\pi\) | |||||||
\(564\) | −2.24263 | + | 0.859625i | −0.0944317 | + | 0.0361967i | ||||
\(565\) | −6.19396 | + | 3.57608i | −0.260582 | + | 0.150447i | ||||
\(566\) | − | 32.7204i | − | 1.37534i | ||||||
\(567\) | −17.1439 | − | 38.7065i | −0.719978 | − | 1.62552i | ||||
\(568\) | −17.0802 | −0.716669 | ||||||||
\(569\) | −2.87574 | − | 4.98094i | −0.120557 | − | 0.208812i | 0.799430 | − | 0.600759i | \(-0.205135\pi\) |
−0.919988 | + | 0.391947i | \(0.871802\pi\) | |||||||
\(570\) | 14.0906 | − | 5.40111i | 0.590192 | − | 0.226227i | ||||
\(571\) | 3.34805 | − | 5.79900i | 0.140112 | − | 0.242681i | −0.787427 | − | 0.616408i | \(-0.788587\pi\) |
0.927539 | + | 0.373728i | \(0.121921\pi\) | |||||||
\(572\) | 0.503030 | + | 0.690082i | 0.0210328 | + | 0.0288538i | ||||
\(573\) | 0.736457 | − | 0.908553i | 0.0307659 | − | 0.0379553i | ||||
\(574\) | −40.5406 | + | 23.4061i | −1.69213 | + | 0.976953i | ||||
\(575\) | −4.20900 | −0.175527 | ||||||||
\(576\) | 19.1809 | − | 17.2371i | 0.799205 | − | 0.718214i | ||||
\(577\) | − | 21.0568i | − | 0.876607i | −0.898827 | − | 0.438304i | \(-0.855579\pi\) | ||
0.898827 | − | 0.438304i | \(-0.144421\pi\) | |||||||
\(578\) | −19.2805 | + | 11.1316i | −0.801964 | + | 0.463014i | ||||
\(579\) | −3.99294 | + | 25.1320i | −0.165941 | + | 1.04445i | ||||
\(580\) | 0.890673 | + | 0.514230i | 0.0369832 | + | 0.0213522i | ||||
\(581\) | 6.70614 | − | 11.6154i | 0.278217 | − | 0.481887i | ||||
\(582\) | 4.12659 | + | 0.655627i | 0.171053 | + | 0.0271766i | ||||
\(583\) | −6.04276 | + | 3.48879i | −0.250266 | + | 0.144491i | ||||
\(584\) | 28.0198 | 1.15947 | ||||||||
\(585\) | 7.23288 | − | 8.04272i | 0.299043 | − | 0.332526i | ||||
\(586\) | 35.5101 | 1.46691 | ||||||||
\(587\) | 13.1797 | − | 7.60928i | 0.543983 | − | 0.314069i | −0.202709 | − | 0.979239i | \(-0.564974\pi\) |
0.746692 | + | 0.665170i | \(0.231641\pi\) | |||||||
\(588\) | −3.04675 | + | 3.75872i | −0.125646 | + | 0.155007i | ||||
\(589\) | −2.41450 | + | 4.18204i | −0.0994878 | + | 0.172318i | ||||
\(590\) | 0.482274 | + | 0.278441i | 0.0198549 | + | 0.0114632i | ||||
\(591\) | 4.23137 | − | 1.62193i | 0.174055 | − | 0.0667174i | ||||
\(592\) | 25.1274 | − | 14.5073i | 1.03273 | − | 0.596246i | ||||
\(593\) | 31.4829i | 1.29285i | 0.762979 | + | 0.646423i | \(0.223736\pi\) | ||||
−0.762979 | + | 0.646423i | \(0.776264\pi\) | |||||||
\(594\) | −7.53641 | + | 4.87873i | −0.309223 | + | 0.200177i | ||||
\(595\) | 3.24546 | 0.133051 | ||||||||
\(596\) | 1.48648 | − | 0.858221i | 0.0608887 | − | 0.0351541i | ||||
\(597\) | 16.0920 | + | 41.9815i | 0.658601 | + | 1.71819i | ||||
\(598\) | 12.0443 | + | 16.5229i | 0.492527 | + | 0.675672i | ||||
\(599\) | −3.53079 | + | 6.11551i | −0.144264 | + | 0.249873i | −0.929098 | − | 0.369833i | \(-0.879415\pi\) |
0.784834 | + | 0.619706i | \(0.212748\pi\) | |||||||
\(600\) | −3.96059 | − | 3.21038i | −0.161690 | − | 0.131063i | ||||
\(601\) | −0.0378043 | − | 0.0654790i | −0.00154207 | − | 0.00267094i | 0.865253 | − | 0.501335i | \(-0.167158\pi\) |
−0.866795 | + | 0.498664i | \(0.833824\pi\) | |||||||
\(602\) | −68.7557 | −2.80227 | ||||||||
\(603\) | −32.0518 | + | 6.78054i | −1.30525 | + | 0.276125i | ||||
\(604\) | 1.30994i | 0.0533006i | ||||||||
\(605\) | 8.10215 | − | 4.67778i | 0.329399 | − | 0.190179i | ||||
\(606\) | 1.35972 | − | 8.55826i | 0.0552350 | − | 0.347656i | ||||
\(607\) | −22.5595 | + | 39.0742i | −0.915663 | + | 1.58597i | −0.109735 | + | 0.993961i | \(0.535000\pi\) |
−0.805928 | + | 0.592014i | \(0.798333\pi\) | |||||||
\(608\) | 3.36690 | − | 5.83164i | 0.136546 | − | 0.236504i | ||||
\(609\) | −7.11839 | + | 44.8040i | −0.288452 | + | 1.81555i | ||||
\(610\) | 3.92876 | + | 6.80481i | 0.159071 | + | 0.275519i | ||||
\(611\) | 10.9713 | − | 24.7464i | 0.443851 | − | 1.00113i | ||||
\(612\) | 0.0791264 | + | 0.374032i | 0.00319849 | + | 0.0151194i | ||||
\(613\) | 18.2482i | 0.737039i | 0.929620 | + | 0.368519i | \(0.120135\pi\) | ||||
−0.929620 | + | 0.368519i | \(0.879865\pi\) | |||||||
\(614\) | 12.0136 | + | 20.8081i | 0.484829 | + | 0.839748i | ||||
\(615\) | −8.05631 | + | 9.93892i | −0.324862 | + | 0.400776i | ||||
\(616\) | 15.3761 | + | 8.87738i | 0.619520 | + | 0.357680i | ||||
\(617\) | 6.90824 | + | 3.98847i | 0.278115 | + | 0.160570i | 0.632570 | − | 0.774503i | \(-0.282000\pi\) |
−0.354455 | + | 0.935073i | \(0.615333\pi\) | |||||||
\(618\) | −23.0866 | + | 8.84936i | −0.928680 | + | 0.355974i | ||||
\(619\) | 3.59308 | − | 2.07447i | 0.144418 | − | 0.0833799i | −0.426050 | − | 0.904700i | \(-0.640095\pi\) |
0.570468 | + | 0.821320i | \(0.306762\pi\) | |||||||
\(620\) | 0.137928 | 0.00553931 | ||||||||
\(621\) | 18.3594 | − | 11.8851i | 0.736738 | − | 0.476931i | ||||
\(622\) | − | 33.5939i | − | 1.34699i | ||||||
\(623\) | −25.2512 | − | 43.7363i | −1.01167 | − | 1.75226i | ||||
\(624\) | −1.15108 | + | 22.4306i | −0.0460799 | + | 0.897942i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 1.29831 | + | 0.749581i | 0.0518910 | + | 0.0299593i | ||||
\(627\) | −9.04407 | + | 11.1575i | −0.361186 | + | 0.445588i | ||||
\(628\) | −1.24123 | − | 2.14987i | −0.0495304 | − | 0.0857892i | ||||
\(629\) | 5.56640i | 0.221947i | ||||||||
\(630\) | 5.89256 | − | 18.0761i | 0.234765 | − | 0.720170i | ||||
\(631\) | 47.5878i | 1.89444i | 0.320586 | + | 0.947219i | \(0.396120\pi\) | ||||
−0.320586 | + | 0.947219i | \(0.603880\pi\) | |||||||
\(632\) | 12.3351 | − | 7.12170i | 0.490666 | − | 0.283286i | ||||
\(633\) | −17.6735 | − | 2.80794i | −0.702458 | − | 0.111605i | ||||
\(634\) | −18.5232 | + | 32.0832i | −0.735652 | + | 1.27419i | ||||
\(635\) | −9.31686 | − | 5.37909i | −0.369728 | − | 0.213463i | ||||
\(636\) | 1.71910 | + | 0.273127i | 0.0681666 | + | 0.0108302i | ||||
\(637\) | −5.78538 | − | 54.2254i | −0.229225 | − | 2.14849i | ||||
\(638\) | 9.62087 | 0.380894 | ||||||||
\(639\) | −11.6357 | − | 12.9479i | −0.460303 | − | 0.512210i | ||||
\(640\) | 9.49901 | 0.375482 | ||||||||
\(641\) | −22.3444 | − | 38.7016i | −0.882549 | − | 1.52862i | −0.848497 | − | 0.529200i | \(-0.822492\pi\) |
−0.0340518 | − | 0.999420i | \(-0.510841\pi\) | |||||||
\(642\) | −26.2932 | − | 21.3128i | −1.03771 | − | 0.841148i | ||||
\(643\) | 40.3294 | + | 23.2842i | 1.59043 | + | 0.918238i | 0.993232 | + | 0.116148i | \(0.0370546\pi\) |
0.597203 | + | 0.802090i | \(0.296279\pi\) | |||||||
\(644\) | −3.16670 | − | 1.82829i | −0.124785 | − | 0.0720448i | ||||
\(645\) | −17.5464 | + | 6.72572i | −0.690888 | + | 0.264825i | ||||
\(646\) | −3.00570 | − | 5.20602i | −0.118258 | − | 0.204828i | ||||
\(647\) | 9.01192 | 0.354295 | 0.177148 | − | 0.984184i | \(-0.443313\pi\) | ||||
0.177148 | + | 0.984184i | \(0.443313\pi\) | |||||||
\(648\) | 26.3411 | + | 2.81990i | 1.03478 | + | 0.110776i | ||||
\(649\) | −0.530027 | −0.0208054 | ||||||||
\(650\) | 4.83046 | − | 0.515368i | 0.189466 | − | 0.0202144i | ||||
\(651\) | 2.17760 | + | 5.68102i | 0.0853468 | + | 0.222657i | ||||
\(652\) | 0.743272 | + | 0.429128i | 0.0291088 | + | 0.0168060i | ||||
\(653\) | −1.39222 | + | 2.41140i | −0.0544820 | + | 0.0943655i | −0.891980 | − | 0.452075i | \(-0.850684\pi\) |
0.837498 | + | 0.546440i | \(0.184017\pi\) | |||||||
\(654\) | −6.51732 | + | 8.04030i | −0.254848 | + | 0.314401i | ||||
\(655\) | 15.4618 | − | 8.92688i | 0.604143 | − | 0.348802i | ||||
\(656\) | − | 26.5659i | − | 1.03722i | ||||||
\(657\) | 19.0883 | + | 21.2408i | 0.744705 | + | 0.828683i | ||||
\(658\) | − | 47.5797i | − | 1.85485i | ||||||
\(659\) | 24.3369 | + | 42.1528i | 0.948033 | + | 1.64204i | 0.749562 | + | 0.661934i | \(0.230264\pi\) |
0.198471 | + | 0.980107i | \(0.436402\pi\) | |||||||
\(660\) | 0.405149 | + | 0.0643694i | 0.0157704 | + | 0.00250557i | ||||
\(661\) | −17.4542 | − | 10.0772i | −0.678889 | − | 0.391957i | 0.120547 | − | 0.992708i | \(-0.461535\pi\) |
−0.799436 | + | 0.600751i | \(0.794868\pi\) | |||||||
\(662\) | 8.31923 | − | 14.4093i | 0.323336 | − | 0.560035i | ||||
\(663\) | −3.61632 | − | 2.34288i | −0.140446 | − | 0.0909899i | ||||
\(664\) | 4.19661 | + | 7.26874i | 0.162860 | + | 0.282082i | ||||
\(665\) | − | 30.4161i | − | 1.17948i | ||||||
\(666\) | 31.0030 | + | 10.1065i | 1.20134 | + | 0.391619i | ||||
\(667\) | −23.4374 | −0.907498 | ||||||||
\(668\) | 2.01466 | − | 1.16317i | 0.0779497 | − | 0.0450043i | ||||
\(669\) | −23.9091 | − | 19.3803i | −0.924379 | − | 0.749285i | ||||
\(670\) | −12.7422 | − | 7.35669i | −0.492273 | − | 0.284214i | ||||
\(671\) | −6.47666 | − | 3.73930i | −0.250029 | − | 0.144354i | ||||
\(672\) | −3.03655 | − | 7.92188i | −0.117137 | − | 0.305593i | ||||
\(673\) | −6.19480 | − | 10.7297i | −0.238792 | − | 0.413600i | 0.721576 | − | 0.692335i | \(-0.243418\pi\) |
−0.960368 | + | 0.278735i | \(0.910085\pi\) | |||||||
\(674\) | 1.78745i | 0.0688502i | ||||||||
\(675\) | −0.264445 | − | 5.18942i | −0.0101785 | − | 0.199741i | ||||
\(676\) | 1.61221 | + | 1.77927i | 0.0620080 | + | 0.0684336i | ||||
\(677\) | −23.2146 | − | 40.2088i | −0.892208 | − | 1.54535i | −0.837223 | − | 0.546862i | \(-0.815822\pi\) |
−0.0549850 | − | 0.998487i | \(-0.517511\pi\) | |||||||
\(678\) | 15.5849 | − | 5.97388i | 0.598536 | − | 0.229425i | ||||
\(679\) | 4.21094 | − | 7.29356i | 0.161601 | − | 0.279901i | ||||
\(680\) | −1.01548 | + | 1.75887i | −0.0389420 | + | 0.0674495i | ||||
\(681\) | 38.3346 | + | 31.0734i | 1.46899 | + | 1.19073i | ||||
\(682\) | 1.11740 | − | 0.645131i | 0.0427875 | − | 0.0247034i | ||||
\(683\) | 19.0750i | 0.729884i | 0.931030 | + | 0.364942i | \(0.118911\pi\) | ||||
−0.931030 | + | 0.364942i | \(0.881089\pi\) | |||||||
\(684\) | 3.50538 | − | 0.741563i | 0.134032 | − | 0.0283544i | ||||
\(685\) | 4.29750 | 0.164199 | ||||||||
\(686\) | −25.7452 | − | 44.5920i | −0.982956 | − | 1.70253i | ||||
\(687\) | −1.64490 | + | 10.3532i | −0.0627570 | + | 0.395000i | ||||
\(688\) | 19.5094 | − | 33.7913i | 0.743789 | − | 1.28828i | ||||
\(689\) | −15.8536 | + | 11.5564i | −0.603975 | + | 0.440263i | ||||
\(690\) | 9.70065 | + | 1.54122i | 0.369297 | + | 0.0586734i | ||||
\(691\) | −14.9252 | + | 8.61704i | −0.567779 | + | 0.327808i | −0.756262 | − | 0.654269i | \(-0.772976\pi\) |
0.188483 | + | 0.982077i | \(0.439643\pi\) | |||||||
\(692\) | −4.00584 | −0.152279 | ||||||||
\(693\) | 3.74521 | + | 17.7037i | 0.142269 | + | 0.672507i | ||||
\(694\) | − | 34.1964i | − | 1.29808i | ||||||
\(695\) | −0.133706 | + | 0.0771951i | −0.00507175 | + | 0.00292818i | ||||
\(696\) | −22.0541 | − | 17.8767i | −0.835958 | − | 0.677613i | ||||
\(697\) | 4.41380 | + | 2.54831i | 0.167185 | + | 0.0965242i | ||||
\(698\) | 8.89404 | − | 15.4049i | 0.336645 | − | 0.583085i | ||||
\(699\) | 5.42453 | + | 14.1518i | 0.205175 | + | 0.535269i | ||||
\(700\) | −0.752363 | + | 0.434377i | −0.0284367 | + | 0.0164179i | ||||
\(701\) | −37.1790 | −1.40423 | −0.702116 | − | 0.712063i | \(-0.747761\pi\) | ||||
−0.702116 | + | 0.712063i | \(0.747761\pi\) | |||||||
\(702\) | −19.6150 | + | 15.8879i | −0.740319 | + | 0.599650i | ||||
\(703\) | 52.1676 | 1.96754 | ||||||||
\(704\) | −9.54637 | + | 5.51160i | −0.359792 | + | 0.207726i | ||||
\(705\) | −4.65427 | − | 12.1423i | −0.175290 | − | 0.457304i | ||||
\(706\) | −6.29581 | + | 10.9047i | −0.236946 | + | 0.410403i | ||||
\(707\) | −15.1263 | − | 8.73319i | −0.568884 | − | 0.328446i | ||||
\(708\) | 0.102716 | + | 0.0832600i | 0.00386032 | + | 0.00312910i | ||||
\(709\) | 4.67297 | − | 2.69794i | 0.175497 | − | 0.101323i | −0.409678 | − | 0.912230i | \(-0.634359\pi\) |
0.585175 | + | 0.810907i | \(0.301026\pi\) | |||||||
\(710\) | − | 7.81811i | − | 0.293409i | ||||||
\(711\) | 13.8019 | + | 4.49922i | 0.517612 | + | 0.168734i | ||||
\(712\) | 31.6037 | 1.18440 | ||||||||
\(713\) | −2.72209 | + | 1.57160i | −0.101943 | + | 0.0588570i | ||||
\(714\) | −7.47995 | − | 1.18840i | −0.279930 | − | 0.0444748i | ||||
\(715\) | −3.73631 | + | 2.72356i | −0.139730 | + | 0.101855i | ||||
\(716\) | 1.43906 | − | 2.49252i | 0.0537801 | − | 0.0931499i | ||||
\(717\) | 7.65255 | − | 48.1661i | 0.285790 | − | 1.79880i | ||||
\(718\) | −19.9420 | − | 34.5406i | −0.744229 | − | 1.28904i | ||||
\(719\) | −13.0486 | −0.486630 | −0.243315 | − | 0.969947i | \(-0.578235\pi\) | ||||
−0.243315 | + | 0.969947i | \(0.578235\pi\) | |||||||
\(720\) | 7.21185 | + | 8.02510i | 0.268770 | + | 0.299078i | ||||
\(721\) | 49.8348i | 1.85594i | ||||||||
\(722\) | −26.6206 | + | 15.3694i | −0.990715 | + | 0.571989i | ||||
\(723\) | 3.94308 | + | 3.19619i | 0.146645 | + | 0.118868i | ||||
\(724\) | 2.18387 | − | 3.78258i | 0.0811630 | − | 0.140578i | ||||
\(725\) | −2.78420 | + | 4.82237i | −0.103402 | + | 0.179098i | ||||
\(726\) | −20.3862 | + | 7.81427i | −0.756604 | + | 0.290015i | ||||
\(727\) | 13.1337 | + | 22.7482i | 0.487102 | + | 0.843685i | 0.999890 | − | 0.0148298i | \(-0.00472065\pi\) |
−0.512788 | + | 0.858515i | \(0.671387\pi\) | |||||||
\(728\) | 45.6362 | + | 20.2328i | 1.69139 | + | 0.749878i | ||||
\(729\) | 15.8070 | + | 21.8892i | 0.585444 | + | 0.810713i | ||||
\(730\) | 12.8255i | 0.474693i | ||||||||
\(731\) | 3.74284 | + | 6.48280i | 0.138434 | + | 0.239775i | ||||
\(732\) | 0.667748 | + | 1.74205i | 0.0246807 | + | 0.0643880i | ||||
\(733\) | 0.173348 | + | 0.100083i | 0.00640277 | + | 0.00369664i | 0.503198 | − | 0.864171i | \(-0.332157\pi\) |
−0.496795 | + | 0.867868i | \(0.665490\pi\) | |||||||
\(734\) | 21.8617 | + | 12.6218i | 0.806929 | + | 0.465881i | ||||
\(735\) | −20.3509 | − | 16.4960i | −0.750653 | − | 0.608466i | ||||
\(736\) | 3.79582 | − | 2.19152i | 0.139916 | − | 0.0807804i | ||||
\(737\) | 14.0038 | 0.515838 | ||||||||
\(738\) | 22.2071 | − | 19.9566i | 0.817453 | − | 0.734613i | ||||
\(739\) | 18.4711i | 0.679469i | 0.940521 | + | 0.339734i | \(0.110337\pi\) | ||||
−0.940521 | + | 0.339734i | \(0.889663\pi\) | |||||||
\(740\) | −0.745014 | − | 1.29040i | −0.0273873 | − | 0.0474361i | ||||
\(741\) | −21.9572 | + | 33.8917i | −0.806617 | + | 1.24504i | ||||
\(742\) | −17.2417 | + | 29.8635i | −0.632962 | + | 1.09632i | ||||
\(743\) | −39.2169 | − | 22.6419i | −1.43873 | − | 0.830651i | −0.440969 | − | 0.897523i | \(-0.645365\pi\) |
−0.997762 | + | 0.0668712i | \(0.978698\pi\) | |||||||
\(744\) | −3.76017 | − | 0.597409i | −0.137854 | − | 0.0219021i | ||||
\(745\) | 4.64667 | + | 8.04826i | 0.170241 | + | 0.294865i | ||||
\(746\) | − | 19.2112i | − | 0.703372i | ||||||
\(747\) | −2.65126 | + | 8.13306i | −0.0970045 | + | 0.297573i | ||||
\(748\) | − | 0.163420i | − | 0.00597521i | ||||||
\(749\) | −59.0806 | + | 34.1102i | −2.15876 | + | 1.24636i | ||||
\(750\) | 1.46949 | − | 1.81288i | 0.0536580 | − | 0.0661969i | ||||
\(751\) | 1.17321 | − | 2.03207i | 0.0428112 | − | 0.0741511i | −0.843826 | − | 0.536617i | \(-0.819702\pi\) |
0.886637 | + | 0.462466i | \(0.153035\pi\) | |||||||
\(752\) | 23.3839 | + | 13.5007i | 0.852724 | + | 0.492320i | ||||
\(753\) | 9.15553 | + | 23.8854i | 0.333646 | + | 0.870431i | ||||
\(754\) | 26.8979 | − | 2.86977i | 0.979564 | − | 0.104511i | ||||
\(755\) | −7.09239 | −0.258119 | ||||||||
\(756\) | 2.05521 | − | 4.01920i | 0.0747471 | − | 0.146177i | ||||
\(757\) | 16.5812 | 0.602655 | 0.301328 | − | 0.953521i | \(-0.402570\pi\) | ||||
0.301328 | + | 0.953521i | \(0.402570\pi\) | |||||||
\(758\) | −1.43427 | − | 2.48423i | −0.0520951 | − | 0.0902313i | ||||
\(759\) | −8.72933 | + | 3.34605i | −0.316855 | + | 0.121454i | ||||
\(760\) | 16.4839 | + | 9.51699i | 0.597934 | + | 0.345217i | ||||
\(761\) | −33.9243 | − | 19.5862i | −1.22976 | − | 0.709999i | −0.262776 | − | 0.964857i | \(-0.584638\pi\) |
−0.966979 | + | 0.254857i | \(0.917972\pi\) | |||||||
\(762\) | 19.5033 | + | 15.8090i | 0.706528 | + | 0.572699i | ||||
\(763\) | 10.4307 | + | 18.0665i | 0.377617 | + | 0.654051i | ||||
\(764\) | 0.124714 | 0.00451198 | ||||||||
\(765\) | −2.02512 | + | 0.428414i | −0.0732185 | + | 0.0154893i | ||||
\(766\) | 16.4041 | 0.592703 | ||||||||
\(767\) | −1.48184 | + | 0.158100i | −0.0535062 | + | 0.00570865i | ||||
\(768\) | 7.51591 | + | 1.19412i | 0.271207 | + | 0.0430889i | ||||
\(769\) | 11.5984 | + | 6.69637i | 0.418251 | + | 0.241477i | 0.694329 | − | 0.719658i | \(-0.255701\pi\) |
−0.276078 | + | 0.961135i | \(0.589035\pi\) | |||||||
\(770\) | −4.06344 | + | 7.03808i | −0.146436 | + | 0.253635i | ||||
\(771\) | −29.1565 | − | 4.63233i | −1.05004 | − | 0.166829i | ||||
\(772\) | −2.35000 | + | 1.35677i | −0.0845785 | + | 0.0488314i | ||||
\(773\) | 1.74544i | 0.0627792i | 0.999507 | + | 0.0313896i | \(0.00999327\pi\) | ||||
−0.999507 | + | 0.0313896i | \(0.990007\pi\) | |||||||
\(774\) | 42.9026 | − | 9.07603i | 1.54210 | − | 0.326231i | ||||
\(775\) | 0.746782i | 0.0268252i | ||||||||
\(776\) | 2.63515 | + | 4.56421i | 0.0945964 | + | 0.163846i | ||||
\(777\) | 41.3873 | − | 51.0587i | 1.48476 | − | 1.83172i | ||||
\(778\) | 29.7267 | + | 17.1627i | 1.06575 | + | 0.615313i | ||||
\(779\) | 23.8825 | − | 41.3656i | 0.855678 | − | 1.48208i | ||||
\(780\) | 1.15191 | + | 0.0591129i | 0.0412450 | + | 0.00211658i | ||||
\(781\) | 3.72055 | + | 6.44418i | 0.133132 | + | 0.230591i | ||||
\(782\) | − | 3.91283i | − | 0.139922i | ||||||
\(783\) | −1.47253 | − | 28.8967i | −0.0526240 | − | 1.03268i | ||||
\(784\) | 54.3962 | 1.94272 | ||||||||
\(785\) | 11.6401 | − | 6.72039i | 0.415451 | − | 0.239861i | ||||
\(786\) | −38.9042 | + | 14.9124i | −1.38767 | + | 0.531909i | ||||
\(787\) | −6.26287 | − | 3.61587i | −0.223247 | − | 0.128892i | 0.384206 | − | 0.923248i | \(-0.374475\pi\) |
−0.607453 | + | 0.794356i | \(0.707809\pi\) | |||||||
\(788\) | 0.418482 | + | 0.241611i | 0.0149078 | + | 0.00860702i | ||||
\(789\) | 13.3230 | − | 16.4363i | 0.474310 | − | 0.585147i | ||||
\(790\) | 3.25981 | + | 5.64616i | 0.115979 | + | 0.200881i | ||||
\(791\) | − | 33.6416i | − | 1.19616i | ||||||
\(792\) | −10.7663 | − | 3.50966i | −0.382564 | − | 0.124710i | ||||
\(793\) | −19.2227 | − | 8.52239i | −0.682620 | − | 0.302639i | ||||
\(794\) | 12.5234 | + | 21.6912i | 0.444440 | + | 0.769792i | ||||
\(795\) | −1.47879 | + | 9.30771i | −0.0524474 | + | 0.330110i | ||||
\(796\) | −2.39714 | + | 4.15196i | −0.0849643 | + | 0.147162i | ||||
\(797\) | −0.166846 | + | 0.288986i | −0.00590999 | + | 0.0102364i | −0.868965 | − | 0.494873i | \(-0.835215\pi\) |
0.863055 | + | 0.505109i | \(0.168548\pi\) | |||||||
\(798\) | −11.1376 | + | 70.1012i | −0.394265 | + | 2.48155i | ||||
\(799\) | −4.48616 | + | 2.59009i | −0.158709 | + | 0.0916307i | ||||
\(800\) | − | 1.04135i | − | 0.0368172i | ||||||
\(801\) | 21.5297 | + | 23.9576i | 0.760716 | + | 0.846500i | ||||
\(802\) | −4.70481 | −0.166133 | ||||||||
\(803\) | −6.10351 | − | 10.5716i | −0.215388 | − | 0.373063i | ||||
\(804\) | −2.71387 | − | 2.19981i | −0.0957108 | − | 0.0775814i | ||||
\(805\) | 9.89893 | − | 17.1454i | 0.348891 | − | 0.604298i | ||||
\(806\) | 2.93158 | − | 2.13696i | 0.103261 | − | 0.0752710i | ||||
\(807\) | 8.86341 | + | 23.1233i | 0.312007 | + | 0.813977i | ||||
\(808\) | 9.46586 | − | 5.46511i | 0.333008 | − | 0.192262i | ||||
\(809\) | −21.5481 | −0.757589 | −0.378795 | − | 0.925481i | \(-0.623661\pi\) | ||||
−0.378795 | + | 0.925481i | \(0.623661\pi\) | |||||||
\(810\) | −1.29075 | + | 12.0571i | −0.0453524 | + | 0.423643i | ||||
\(811\) | 38.3145i | 1.34540i | 0.739913 | + | 0.672702i | \(0.234867\pi\) | ||||
−0.739913 | + | 0.672702i | \(0.765133\pi\) | |||||||
\(812\) | −4.18946 | + | 2.41878i | −0.147021 | + | 0.0848826i | ||||
\(813\) | 6.21816 | − | 2.38349i | 0.218081 | − | 0.0835927i | ||||
\(814\) | −12.0712 | − | 6.96933i | −0.423097 | − | 0.244275i | ||||
\(815\) | −2.32343 | + | 4.02430i | −0.0813862 | + | 0.140965i | ||||
\(816\) | 2.70650 | − | 3.33895i | 0.0947463 | − | 0.116887i | ||||
\(817\) | 60.7560 | − | 35.0775i | 2.12558 | − | 1.22721i | ||||
\(818\) | −9.78837 | −0.342242 | ||||||||
\(819\) | 15.7516 | + | 48.3786i | 0.550404 | + | 1.69048i | ||||
\(820\) | −1.36428 | −0.0476427 | ||||||||
\(821\) | 2.80704 | − | 1.62065i | 0.0979665 | − | 0.0565610i | −0.450216 | − | 0.892920i | \(-0.648653\pi\) |
0.548183 | + | 0.836359i | \(0.315320\pi\) | |||||||
\(822\) | −9.90463 | − | 1.57363i | −0.345464 | − | 0.0548867i | ||||
\(823\) | −10.2808 | + | 17.8069i | −0.358367 | + | 0.620711i | −0.987688 | − | 0.156435i | \(-0.950000\pi\) |
0.629321 | + | 0.777146i | \(0.283333\pi\) | |||||||
\(824\) | −27.0078 | − | 15.5930i | −0.940862 | − | 0.543207i | ||||
\(825\) | −0.348515 | + | 2.19360i | −0.0121337 | + | 0.0763713i | ||||
\(826\) | −2.26847 | + | 1.30970i | −0.0789302 | + | 0.0455704i | ||||
\(827\) | − | 15.8002i | − | 0.549426i | −0.961526 | − | 0.274713i | \(-0.911417\pi\) | ||
0.961526 | − | 0.274713i | \(-0.0885828\pi\) | |||||||
\(828\) | 2.21732 | + | 0.722813i | 0.0770571 | + | 0.0251195i | ||||
\(829\) | −36.2323 | −1.25840 | −0.629201 | − | 0.777243i | \(-0.716618\pi\) | ||||
−0.629201 | + | 0.777243i | \(0.716618\pi\) | |||||||
\(830\) | −3.32712 | + | 1.92091i | −0.115486 | + | 0.0666758i | ||||
\(831\) | −29.5470 | + | 36.4516i | −1.02497 | + | 1.26449i | ||||
\(832\) | −25.0456 | + | 18.2568i | −0.868300 | + | 0.632941i | ||||
\(833\) | −5.21791 | + | 9.03768i | −0.180790 | + | 0.313137i | ||||
\(834\) | 0.336424 | − | 0.128955i | 0.0116494 | − | 0.00446535i | ||||
\(835\) | 6.29773 | + | 10.9080i | 0.217942 | + | 0.377487i | ||||
\(836\) | −1.53155 | −0.0529697 | ||||||||
\(837\) | −2.10871 | − | 3.25742i | −0.0728876 | − | 0.112593i | ||||
\(838\) | 23.6648i | 0.817486i | ||||||||
\(839\) | 38.1830 | − | 22.0450i | 1.31822 | − | 0.761077i | 0.334781 | − | 0.942296i | \(-0.391338\pi\) |
0.983443 | + | 0.181219i | \(0.0580043\pi\) | |||||||
\(840\) | 22.3923 | − | 8.58321i | 0.772606 | − | 0.296149i | ||||
\(841\) | −1.00350 | + | 1.73812i | −0.0346035 | + | 0.0599350i | ||||
\(842\) | −10.7502 | + | 18.6199i | −0.370476 | + | 0.641683i | ||||
\(843\) | −10.9179 | − | 8.84984i | −0.376032 | − | 0.304805i | ||||
\(844\) | −0.954119 | − | 1.65258i | −0.0328421 | − | 0.0568842i | ||||
\(845\) | −9.63353 | + | 8.72898i | −0.331404 | + | 0.300286i | ||||
\(846\) | 6.28071 | + | 29.6891i | 0.215935 | + | 1.02073i | ||||
\(847\) | 44.0057i | 1.51205i | ||||||||
\(848\) | −9.78464 | − | 16.9475i | −0.336006 | − | 0.581979i | ||||
\(849\) | 41.5424 | + | 6.60019i | 1.42573 | + | 0.226518i | ||||
\(850\) | −0.805086 | − | 0.464817i | −0.0276142 | − | 0.0159431i | ||||
\(851\) | 29.4067 | + | 16.9780i | 1.00805 | + | 0.581997i | ||||
\(852\) | 0.291271 | − | 1.83329i | 0.00997877 | − | 0.0628076i | ||||
\(853\) | −24.3692 | + | 14.0696i | −0.834386 | + | 0.481733i | −0.855352 | − | 0.518047i | \(-0.826659\pi\) |
0.0209659 | + | 0.999780i | \(0.493326\pi\) | |||||||
\(854\) | −36.9594 | −1.26472 | ||||||||
\(855\) | 4.01504 | + | 18.9792i | 0.137312 | + | 0.649075i | ||||
\(856\) | − | 42.6914i | − | 1.45916i | ||||||
\(857\) | 22.0174 | + | 38.1353i | 0.752100 | + | 1.30268i | 0.946803 | + | 0.321813i | \(0.104292\pi\) |
−0.194703 | + | 0.980862i | \(0.562374\pi\) | |||||||
\(858\) | 9.60852 | − | 4.90896i | 0.328029 | − | 0.167589i | ||||
\(859\) | 1.83197 | − | 3.17306i | 0.0625060 | − | 0.108263i | −0.833079 | − | 0.553154i | \(-0.813424\pi\) |
0.895585 | + | 0.444891i | \(0.146757\pi\) | |||||||
\(860\) | −1.73533 | − | 1.00189i | −0.0591744 | − | 0.0341643i | ||||
\(861\) | −21.5392 | − | 56.1924i | −0.734053 | − | 1.91503i | ||||
\(862\) | −1.59280 | − | 2.75881i | −0.0542510 | − | 0.0939654i | ||||
\(863\) | − | 27.1013i | − | 0.922539i | −0.887260 | − | 0.461269i | \(-0.847394\pi\) | ||
0.887260 | − | 0.461269i | \(-0.152606\pi\) | |||||||
\(864\) | 2.94048 | + | 4.54231i | 0.100037 | + | 0.154532i | ||||
\(865\) | − | 21.6888i | − | 0.737441i | ||||||
\(866\) | −18.5789 | + | 10.7266i | −0.631338 | + | 0.364503i | ||||
\(867\) | −10.2437 | − | 26.7243i | −0.347895 | − | 0.907604i | ||||
\(868\) | −0.324385 | + | 0.561851i | −0.0110103 | + | 0.0190705i | ||||
\(869\) | −5.37388 | − | 3.10261i | −0.182296 | − | 0.105249i | ||||
\(870\) | 8.18267 | − | 10.0948i | 0.277419 | − | 0.342246i | ||||
\(871\) | 39.1518 | − | 4.17715i | 1.32661 | − | 0.141537i | ||||
\(872\) | −13.0548 | −0.442091 | ||||||||
\(873\) | −1.66479 | + | 5.10694i | −0.0563446 | + | 0.172844i | ||||
\(874\) | −36.6705 | −1.24040 | ||||||||
\(875\) | −2.35185 | − | 4.07352i | −0.0795070 | − | 0.137710i | ||||
\(876\) | −0.477826 | + | 3.00749i | −0.0161442 | + | 0.101614i | ||||
\(877\) | −21.1948 | − | 12.2368i | −0.715697 | − | 0.413208i | 0.0974701 | − | 0.995238i | \(-0.468925\pi\) |
−0.813167 | + | 0.582031i | \(0.802258\pi\) | |||||||
\(878\) | 28.6486 | + | 16.5403i | 0.966843 | + | 0.558207i | ||||
\(879\) | −7.16291 | + | 45.0843i | −0.241599 | + | 1.52065i | ||||
\(880\) | −2.30600 | − | 3.99411i | −0.0777352 | − | 0.134641i | ||||
\(881\) | 39.3187 | 1.32468 | 0.662341 | − | 0.749203i | \(-0.269563\pi\) | ||||
0.662341 | + | 0.749203i | \(0.269563\pi\) | |||||||
\(882\) | 40.8630 | + | 45.4711i | 1.37593 | + | 1.53109i | ||||
\(883\) | −19.4346 | −0.654027 | −0.327014 | − | 0.945020i | \(-0.606042\pi\) | ||||
−0.327014 | + | 0.945020i | \(0.606042\pi\) | |||||||
\(884\) | −0.0487458 | − | 0.456887i | −0.00163950 | − | 0.0153668i | ||||
\(885\) | −0.450795 | + | 0.556137i | −0.0151533 | + | 0.0186943i | ||||
\(886\) | 25.5166 | + | 14.7320i | 0.857248 | + | 0.494932i | ||||
\(887\) | 18.3946 | − | 31.8604i | 0.617631 | − | 1.06977i | −0.372285 | − | 0.928118i | \(-0.621426\pi\) |
0.989917 | − | 0.141650i | \(-0.0452409\pi\) | |||||||
\(888\) | 14.7213 | + | 38.4057i | 0.494015 | + | 1.28881i | ||||
\(889\) | 43.8237 | − | 25.3016i | 1.46980 | − | 0.848589i | ||||
\(890\) | 14.4659i | 0.484899i | ||||||||
\(891\) | −4.67391 | − | 10.5525i | −0.156582 | − | 0.353521i | ||||
\(892\) | − | 3.28191i | − | 0.109887i | ||||||
\(893\) | 24.2740 | + | 42.0438i | 0.812298 | + | 1.40694i | ||||
\(894\) | −7.76230 | − | 20.2506i | −0.259610 | − | 0.677283i | ||||
\(895\) | 13.4953 | + | 7.79150i | 0.451097 | + | 0.260441i | ||||
\(896\) | −22.3403 | + | 38.6945i | −0.746335 | + | 1.29269i | ||||
\(897\) | −23.4073 | + | 11.9587i | −0.781546 | + | 0.399289i | ||||
\(898\) | 8.89447 | + | 15.4057i | 0.296812 | + | 0.514094i | ||||
\(899\) | 4.15838i | 0.138690i | ||||||||
\(900\) | 0.412125 | − | 0.370360i | 0.0137375 | − | 0.0123453i | ||||
\(901\) | 3.75433 | 0.125075 | ||||||||
\(902\) | −11.0525 | + | 6.38116i | −0.368008 | + | 0.212469i | ||||
\(903\) | 13.8690 | − | 87.2934i | 0.461533 | − | 2.90494i | ||||
\(904\) | 18.2320 | + | 10.5262i | 0.606387 | + | 0.350097i | ||||
\(905\) | 20.4800 | + | 11.8241i | 0.680779 | + | 0.393048i | ||||
\(906\) | 16.3461 | + | 2.59705i | 0.543064 | + | 0.0862811i | ||||
\(907\) | 7.55603 | + | 13.0874i | 0.250894 | + | 0.434561i | 0.963772 | − | 0.266727i | \(-0.0859421\pi\) |
−0.712878 | + | 0.701288i | \(0.752609\pi\) | |||||||
\(908\) | 5.26205i | 0.174627i | ||||||||
\(909\) | 10.5914 | + | 3.45265i | 0.351296 | + | 0.114517i | ||||
\(910\) | −9.26115 | + | 20.8891i | −0.307004 | + | 0.692466i | ||||
\(911\) | 1.15976 | + | 2.00877i | 0.0384247 | + | 0.0665535i | 0.884598 | − | 0.466354i | \(-0.154433\pi\) |
−0.846174 | + | 0.532907i | \(0.821099\pi\) | |||||||
\(912\) | −31.2923 | − | 25.3649i | −1.03619 | − | 0.839917i | ||||
\(913\) | 1.82828 | − | 3.16667i | 0.0605072 | − | 0.104802i | ||||
\(914\) | −11.1367 | + | 19.2893i | −0.368368 | + | 0.638032i | ||||
\(915\) | −9.43199 | + | 3.61539i | −0.311812 | + | 0.119521i | ||||
\(916\) | −0.968091 | + | 0.558928i | −0.0319866 | + | 0.0184675i | ||||
\(917\) | 83.9787i | 2.77322i | ||||||||
\(918\) | 4.82426 | − | 0.245837i | 0.159224 | − | 0.00811382i | ||||
\(919\) | −2.41646 | −0.0797116 | −0.0398558 | − | 0.999205i | \(-0.512690\pi\) | ||||
−0.0398558 | + | 0.999205i | \(0.512690\pi\) | |||||||
\(920\) | 6.19462 | + | 10.7294i | 0.204230 | + | 0.353738i | ||||
\(921\) | −28.8417 | + | 11.0553i | −0.950366 | + | 0.364286i | ||||
\(922\) | 23.4712 | − | 40.6533i | 0.772983 | − | 1.33885i | ||||
\(923\) | 12.3241 | + | 16.9068i | 0.405652 | + | 0.556493i | ||||
\(924\) | −1.21506 | + | 1.49900i | −0.0399725 | + | 0.0493133i | ||||
\(925\) | 6.98663 | − | 4.03373i | 0.229719 | − | 0.132628i | ||||
\(926\) | −43.6124 | −1.43319 | ||||||||
\(927\) | −6.57839 | − | 31.0962i | −0.216063 | − | 1.02133i | ||||
\(928\) | − | 5.79864i | − | 0.190350i | ||||||
\(929\) | −14.6055 | + | 8.43250i | −0.479191 | + | 0.276661i | −0.720079 | − | 0.693892i | \(-0.755895\pi\) |
0.240888 | + | 0.970553i | \(0.422561\pi\) | |||||||
\(930\) | 0.273452 | − | 1.72114i | 0.00896684 | − | 0.0564384i | ||||
\(931\) | 84.7000 | + | 48.9016i | 2.77593 | + | 1.60268i | ||||
\(932\) | −0.808063 | + | 1.39961i | −0.0264690 | + | 0.0458456i | ||||
\(933\) | 42.6514 | + | 6.77639i | 1.39634 | + | 0.221849i | ||||
\(934\) | 9.51929 | − | 5.49596i | 0.311481 | − | 0.179833i | ||||
\(935\) | 0.884803 | 0.0289362 | ||||||||
\(936\) | −31.1472 | − | 6.60082i | −1.01808 | − | 0.215755i | ||||
\(937\) | 7.73841 | 0.252803 | 0.126401 | − | 0.991979i | \(-0.459657\pi\) | ||||
0.126401 | + | 0.991979i | \(0.459657\pi\) | |||||||
\(938\) | 59.9353 | − | 34.6036i | 1.95696 | − | 1.12985i | ||||
\(939\) | −1.21357 | + | 1.49716i | −0.0396033 | + | 0.0488579i | ||||
\(940\) | 0.693322 | − | 1.20087i | 0.0226137 | − | 0.0391680i | ||||
\(941\) | 50.6505 | + | 29.2431i | 1.65116 | + | 0.953298i | 0.976596 | + | 0.215082i | \(0.0690018\pi\) |
0.674564 | + | 0.738216i | \(0.264332\pi\) | |||||||
\(942\) | −29.2881 | + | 11.2265i | −0.954259 | + | 0.365778i | ||||
\(943\) | 26.9249 | − | 15.5451i | 0.876797 | − | 0.506219i | ||||
\(944\) | − | 1.48651i | − | 0.0483818i | ||||||
\(945\) | 21.7612 | + | 11.1275i | 0.707890 | + | 0.361978i | ||||
\(946\) | −18.7447 | −0.609443 | ||||||||
\(947\) | 4.70833 | − | 2.71836i | 0.153000 | − | 0.0883347i | −0.421545 | − | 0.906807i | \(-0.638512\pi\) |
0.574546 | + | 0.818473i | \(0.305179\pi\) | |||||||
\(948\) | 0.554051 | + | 1.44543i | 0.0179947 | + | 0.0469455i | ||||
\(949\) | −20.2175 | − | 27.7353i | −0.656287 | − | 0.900327i | ||||
\(950\) | −4.35621 | + | 7.54517i | −0.141334 | + | 0.244798i | ||||
\(951\) | −36.9969 | − | 29.9891i | −1.19971 | − | 0.972462i | ||||
\(952\) | −4.77653 | − | 8.27319i | −0.154808 | − | 0.268136i | ||||
\(953\) | −4.08765 | −0.132412 | −0.0662059 | − | 0.997806i | \(-0.521089\pi\) | ||||
−0.0662059 | + | 0.997806i | \(0.521089\pi\) | |||||||
\(954\) | 6.81647 | − | 20.9104i | 0.220691 | − | 0.676998i | ||||
\(955\) | 0.675237i | 0.0218502i | ||||||||
\(956\) | 4.50383 | − | 2.60029i | 0.145664 | − | 0.0840994i | ||||
\(957\) | −1.94067 | + | 12.2148i | −0.0627330 | + | 0.394849i | ||||
\(958\) | 12.4377 | − | 21.5427i | 0.401842 | − | 0.696011i | ||||
\(959\) | −10.1071 | + | 17.5060i | −0.326375 | + | 0.565297i | ||||
\(960\) | −2.33620 | + | 14.7043i | −0.0754006 | + | 0.474580i | ||||
\(961\) | −15.2212 | − | 26.3638i | −0.491005 | − | 0.850446i | ||||
\(962\) | −35.8275 | − | 15.8841i | −1.15512 | − | 0.512124i | ||||
\(963\) | 32.3628 | − | 29.0832i | 1.04288 | − | 0.937192i | ||||
\(964\) | 0.541253i | 0.0174326i | ||||||||
\(965\) | −7.34599 | − | 12.7236i | −0.236476 | − | 0.409588i | ||||
\(966\) | −29.0927 | + | 35.8911i | −0.936041 | + | 1.15478i | ||||
\(967\) | −22.6264 | − | 13.0634i | −0.727616 | − | 0.420089i | 0.0899337 | − | 0.995948i | \(-0.471334\pi\) |
−0.817549 | + | 0.575859i | \(0.804668\pi\) | |||||||
\(968\) | −23.8488 | − | 13.7691i | −0.766528 | − | 0.442555i | ||||
\(969\) | 7.21595 | − | 2.76595i | 0.231810 | − | 0.0888553i | ||||
\(970\) | −2.08918 | + | 1.20619i | −0.0670794 | + | 0.0387283i | ||||
\(971\) | 17.6665 | 0.566945 | 0.283473 | − | 0.958980i | \(-0.408513\pi\) | ||||
0.283473 | + | 0.958980i | \(0.408513\pi\) | |||||||
\(972\) | −0.751870 | + | 2.77922i | −0.0241162 | + | 0.0891435i | ||||
\(973\) | − | 0.726205i | − | 0.0232811i | ||||||
\(974\) | −24.6071 | − | 42.6207i | −0.788462 | − | 1.36566i | ||||
\(975\) | −0.320055 | + | 6.23679i | −0.0102500 | + | 0.199737i | ||||
\(976\) | 10.4872 | − | 18.1644i | 0.335688 | − | 0.581428i | ||||
\(977\) | −4.95084 | − | 2.85837i | −0.158391 | − | 0.0914473i | 0.418709 | − | 0.908120i | \(-0.362483\pi\) |
−0.577101 | + | 0.816673i | \(0.695816\pi\) | |||||||
\(978\) | 6.82850 | − | 8.42419i | 0.218351 | − | 0.269376i | ||||
\(979\) | −6.88417 | − | 11.9237i | −0.220019 | − | 0.381084i | ||||
\(980\) | − | 2.79349i | − | 0.0892347i | ||||||
\(981\) | −8.89346 | − | 9.89635i | −0.283946 | − | 0.315966i | ||||
\(982\) | 33.2715i | 1.06173i | ||||||||
\(983\) | 23.1189 | − | 13.3477i | 0.737380 | − | 0.425726i | −0.0837361 | − | 0.996488i | \(-0.526685\pi\) |
0.821116 | + | 0.570762i | \(0.193352\pi\) | |||||||
\(984\) | 37.1928 | + | 5.90913i | 1.18566 | + | 0.188376i | ||||
\(985\) | −1.30815 | + | 2.26579i | −0.0416812 | + | 0.0721940i | ||||
\(986\) | −4.48304 | − | 2.58828i | −0.142769 | − | 0.0824277i | ||||
\(987\) | 60.4080 | + | 9.59752i | 1.92281 | + | 0.305492i | ||||
\(988\) | −4.28189 | + | 0.456840i | −0.136225 | + | 0.0145340i | ||||
\(989\) | 45.6639 | 1.45203 | ||||||||
\(990\) | 1.60647 | − | 4.92806i | 0.0510571 | − | 0.156624i | ||||
\(991\) | 16.9888 | 0.539668 | 0.269834 | − | 0.962907i | \(-0.413031\pi\) | ||||
0.269834 | + | 0.962907i | \(0.413031\pi\) | |||||||
\(992\) | −0.388830 | − | 0.673474i | −0.0123454 | − | 0.0213828i | ||||
\(993\) | 16.6162 | + | 13.4688i | 0.527300 | + | 0.427420i | ||||
\(994\) | 31.8473 | + | 18.3870i | 1.01013 | + | 0.583201i | ||||
\(995\) | −22.4800 | − | 12.9788i | −0.712664 | − | 0.411457i | ||||
\(996\) | −0.851752 | + | 0.326486i | −0.0269888 | + | 0.0103451i | ||||
\(997\) | −6.32338 | − | 10.9524i | −0.200263 | − | 0.346867i | 0.748350 | − | 0.663304i | \(-0.230846\pi\) |
−0.948613 | + | 0.316438i | \(0.897513\pi\) | |||||||
\(998\) | −9.41034 | −0.297879 | ||||||||
\(999\) | −19.0851 | + | 37.3232i | −0.603827 | + | 1.18085i |
(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 | 585.2.bt.b.571.39 | yes | 108 | |
9.7 | even | 3 | inner | 585.2.bt.b.376.16 | ✓ | 108 | |
13.12 | even | 2 | inner | 585.2.bt.b.571.16 | yes | 108 | |
117.25 | even | 6 | inner | 585.2.bt.b.376.39 | yes | 108 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
585.2.bt.b.376.16 | ✓ | 108 | 9.7 | even | 3 | inner | |
585.2.bt.b.376.39 | yes | 108 | 117.25 | even | 6 | inner | |
585.2.bt.b.571.16 | yes | 108 | 13.12 | even | 2 | inner | |
585.2.bt.b.571.39 | yes | 108 | 1.1 | even | 1 | trivial |