Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,2,Mod(49,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.k (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.79663404548\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 12x^{14} + 102x^{12} - 406x^{10} + 1167x^{8} - 1842x^{6} + 2023x^{4} - 441x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 124.4 | ||
Root | \(-0.409850 - 0.236627i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.124 |
Dual form | 225.2.k.c.49.4 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.409850 | − | 0.236627i | −0.289808 | − | 0.167321i | 0.348047 | − | 0.937477i | \(-0.386845\pi\) |
−0.637855 | + | 0.770156i | \(0.720178\pi\) | |||||||
\(3\) | 1.64411 | − | 0.544899i | 0.949225 | − | 0.314598i | ||||
\(4\) | −0.888015 | − | 1.53809i | −0.444008 | − | 0.769044i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.802776 | − | 0.165713i | −0.327732 | − | 0.0676521i | ||||
\(7\) | −2.21967 | − | 1.28153i | −0.838956 | − | 0.484372i | 0.0179531 | − | 0.999839i | \(-0.494285\pi\) |
−0.856909 | + | 0.515467i | \(0.827618\pi\) | |||||||
\(8\) | 1.78702i | 0.631808i | ||||||||
\(9\) | 2.40617 | − | 1.79175i | 0.802056 | − | 0.597248i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.08430 | − | 5.34217i | 0.929952 | − | 1.61072i | 0.146555 | − | 0.989202i | \(-0.453181\pi\) |
0.783397 | − | 0.621522i | \(-0.213485\pi\) | |||||||
\(12\) | −2.29809 | − | 2.04490i | −0.663403 | − | 0.590312i | ||||
\(13\) | −1.84662 | + | 1.06615i | −0.512161 | + | 0.295696i | −0.733722 | − | 0.679450i | \(-0.762218\pi\) |
0.221560 | + | 0.975147i | \(0.428885\pi\) | |||||||
\(14\) | 0.606488 | + | 1.05047i | 0.162091 | + | 0.280750i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.35317 | + | 2.34376i | −0.338293 | + | 0.585941i | ||||
\(17\) | 3.16860i | 0.768500i | 0.923229 | + | 0.384250i | \(0.125540\pi\) | ||||
−0.923229 | + | 0.384250i | \(0.874460\pi\) | |||||||
\(18\) | −1.41015 | + | 0.164982i | −0.332374 | + | 0.0388867i | ||||
\(19\) | −0.356267 | −0.0817332 | −0.0408666 | − | 0.999165i | \(-0.513012\pi\) | ||||
−0.0408666 | + | 0.999165i | \(0.513012\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.34768 | − | 0.897469i | −0.948740 | − | 0.195844i | ||||
\(22\) | −2.52821 | + | 1.45966i | −0.539015 | + | 0.311201i | ||||
\(23\) | 3.64854 | − | 2.10649i | 0.760774 | − | 0.439233i | −0.0687995 | − | 0.997631i | \(-0.521917\pi\) |
0.829574 | + | 0.558397i | \(0.188584\pi\) | |||||||
\(24\) | 0.973748 | + | 2.93806i | 0.198766 | + | 0.599728i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.00912 | 0.197905 | ||||||||
\(27\) | 2.97968 | − | 4.25694i | 0.573439 | − | 0.819248i | ||||
\(28\) | 4.55206i | 0.860259i | ||||||||
\(29\) | 0.843116 | − | 1.46032i | 0.156563 | − | 0.271174i | −0.777064 | − | 0.629421i | \(-0.783292\pi\) |
0.933627 | + | 0.358247i | \(0.116625\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.12920 | + | 7.15199i | 0.741627 | + | 1.28453i | 0.951754 | + | 0.306861i | \(0.0992787\pi\) |
−0.210128 | + | 0.977674i | \(0.567388\pi\) | |||||||
\(32\) | 4.20441 | − | 2.42742i | 0.743242 | − | 0.429111i | ||||
\(33\) | 2.15998 | − | 10.4637i | 0.376003 | − | 1.82150i | ||||
\(34\) | 0.749778 | − | 1.29865i | 0.128586 | − | 0.222717i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.89257 | − | 2.10980i | −0.815429 | − | 0.351634i | ||||
\(37\) | 3.63274i | 0.597219i | 0.954375 | + | 0.298609i | \(0.0965228\pi\) | ||||
−0.954375 | + | 0.298609i | \(0.903477\pi\) | |||||||
\(38\) | 0.146016 | + | 0.0843024i | 0.0236869 | + | 0.0136757i | ||||
\(39\) | −2.45510 | + | 2.75908i | −0.393131 | + | 0.441807i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.36677 | + | 2.36731i | 0.213453 | + | 0.369711i | 0.952793 | − | 0.303621i | \(-0.0981956\pi\) |
−0.739340 | + | 0.673332i | \(0.764862\pi\) | |||||||
\(42\) | 1.56953 | + | 1.39661i | 0.242184 | + | 0.215501i | ||||
\(43\) | −6.64949 | − | 3.83908i | −1.01404 | − | 0.585455i | −0.101666 | − | 0.994819i | \(-0.532417\pi\) |
−0.912371 | + | 0.409364i | \(0.865751\pi\) | |||||||
\(44\) | −10.9556 | −1.65162 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.99381 | −0.293971 | ||||||||
\(47\) | 9.89770 | + | 5.71444i | 1.44373 | + | 0.833537i | 0.998096 | − | 0.0616792i | \(-0.0196456\pi\) |
0.445632 | + | 0.895216i | \(0.352979\pi\) | |||||||
\(48\) | −0.947643 | + | 4.59074i | −0.136780 | + | 0.662616i | ||||
\(49\) | −0.215378 | − | 0.373046i | −0.0307683 | − | 0.0532923i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.72657 | + | 5.20952i | 0.241768 | + | 0.729479i | ||||
\(52\) | 3.27966 | + | 1.89351i | 0.454807 | + | 0.262583i | ||||
\(53\) | 9.43507i | 1.29601i | 0.761637 | + | 0.648003i | \(0.224396\pi\) | ||||
−0.761637 | + | 0.648003i | \(0.775604\pi\) | |||||||
\(54\) | −2.22853 | + | 1.03964i | −0.303264 | + | 0.141477i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.29012 | − | 3.96660i | 0.306030 | − | 0.530059i | ||||
\(57\) | −0.585740 | + | 0.194129i | −0.0775832 | + | 0.0257131i | ||||
\(58\) | −0.691103 | + | 0.399008i | −0.0907462 | + | 0.0523924i | ||||
\(59\) | 5.10795 | + | 8.84723i | 0.664999 | + | 1.15181i | 0.979286 | + | 0.202484i | \(0.0649013\pi\) |
−0.314287 | + | 0.949328i | \(0.601765\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.00549659 | − | 0.00952038i | 0.000703767 | − | 0.00121896i | −0.865673 | − | 0.500609i | \(-0.833109\pi\) |
0.866377 | + | 0.499390i | \(0.166443\pi\) | |||||||
\(62\) | − | 3.90833i | − | 0.496358i | ||||||
\(63\) | −7.63707 | + | 0.893512i | −0.962180 | + | 0.112572i | ||||
\(64\) | 3.11511 | 0.389389 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.36127 | + | 3.77745i | −0.413744 | + | 0.464972i | ||||
\(67\) | 0.851145 | − | 0.491409i | 0.103984 | − | 0.0600351i | −0.447106 | − | 0.894481i | \(-0.647545\pi\) |
0.551090 | + | 0.834446i | \(0.314212\pi\) | |||||||
\(68\) | 4.87359 | − | 2.81377i | 0.591010 | − | 0.341220i | ||||
\(69\) | 4.85077 | − | 5.45138i | 0.583964 | − | 0.656269i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.43507 | −0.763703 | −0.381851 | − | 0.924224i | \(-0.624713\pi\) | ||||
−0.381851 | + | 0.924224i | \(0.624713\pi\) | |||||||
\(72\) | 3.20189 | + | 4.29988i | 0.377346 | + | 0.506746i | ||||
\(73\) | − | 6.61467i | − | 0.774189i | −0.922040 | − | 0.387094i | \(-0.873479\pi\) | ||
0.922040 | − | 0.387094i | \(-0.126521\pi\) | |||||||
\(74\) | 0.859605 | − | 1.48888i | 0.0999271 | − | 0.173079i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.316370 | + | 0.547969i | 0.0362901 | + | 0.0628564i | ||||
\(77\) | −13.6923 | + | 7.90523i | −1.56038 | + | 0.900885i | ||||
\(78\) | 1.65910 | − | 0.549868i | 0.187856 | − | 0.0622603i | ||||
\(79\) | −4.73569 | + | 8.20246i | −0.532807 | + | 0.922848i | 0.466459 | + | 0.884543i | \(0.345529\pi\) |
−0.999266 | + | 0.0383057i | \(0.987804\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.57930 | − | 8.62248i | 0.286589 | − | 0.958054i | ||||
\(82\) | − | 1.29366i | − | 0.142860i | ||||||
\(83\) | −9.02378 | − | 5.20988i | −0.990489 | − | 0.571859i | −0.0850682 | − | 0.996375i | \(-0.527111\pi\) |
−0.905420 | + | 0.424516i | \(0.860444\pi\) | |||||||
\(84\) | 2.48042 | + | 7.48407i | 0.270636 | + | 0.816579i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.81686 | + | 3.14690i | 0.195917 | + | 0.339339i | ||||
\(87\) | 0.590444 | − | 2.86033i | 0.0633023 | − | 0.306660i | ||||
\(88\) | 9.54658 | + | 5.51172i | 1.01767 | + | 0.587551i | ||||
\(89\) | 6.26940 | 0.664555 | 0.332277 | − | 0.943182i | \(-0.392183\pi\) | ||||
0.332277 | + | 0.943182i | \(0.392183\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.46519 | 0.572908 | ||||||||
\(92\) | −6.47993 | − | 3.74119i | −0.675579 | − | 0.390046i | ||||
\(93\) | 10.6860 | + | 9.50863i | 1.10808 | + | 0.985999i | ||||
\(94\) | −2.70439 | − | 4.68413i | −0.278936 | − | 0.483131i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 5.58980 | − | 6.28191i | 0.570506 | − | 0.641145i | ||||
\(97\) | −6.24126 | − | 3.60339i | −0.633704 | − | 0.365869i | 0.148481 | − | 0.988915i | \(-0.452562\pi\) |
−0.782185 | + | 0.623046i | \(0.785895\pi\) | |||||||
\(98\) | 0.203858i | 0.0205927i | ||||||||
\(99\) | −2.15045 | − | 18.3804i | −0.216128 | − | 1.84730i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.48547 | + | 6.03701i | −0.346817 | + | 0.600705i | −0.985682 | − | 0.168614i | \(-0.946071\pi\) |
0.638865 | + | 0.769319i | \(0.279404\pi\) | |||||||
\(102\) | 0.525079 | − | 2.54368i | 0.0519906 | − | 0.251862i | ||||
\(103\) | 5.29584 | − | 3.05756i | 0.521815 | − | 0.301270i | −0.215862 | − | 0.976424i | \(-0.569256\pi\) |
0.737677 | + | 0.675154i | \(0.235923\pi\) | |||||||
\(104\) | −1.90523 | − | 3.29996i | −0.186823 | − | 0.323588i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.23260 | − | 3.86697i | 0.216849 | − | 0.375593i | ||||
\(107\) | − | 14.5349i | − | 1.40514i | −0.711615 | − | 0.702570i | \(-0.752036\pi\) | ||
0.711615 | − | 0.702570i | \(-0.247964\pi\) | |||||||
\(108\) | −9.19354 | − | 0.802776i | −0.884649 | − | 0.0772471i | ||||
\(109\) | −1.90214 | −0.182192 | −0.0910958 | − | 0.995842i | \(-0.529037\pi\) | ||||
−0.0910958 | + | 0.995842i | \(0.529037\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.97948 | + | 5.97261i | 0.187884 | + | 0.566895i | ||||
\(112\) | 6.00719 | − | 3.46825i | 0.567626 | − | 0.327719i | ||||
\(113\) | 5.69780 | − | 3.28962i | 0.536004 | − | 0.309462i | −0.207454 | − | 0.978245i | \(-0.566518\pi\) |
0.743458 | + | 0.668783i | \(0.233184\pi\) | |||||||
\(114\) | 0.286002 | + | 0.0590380i | 0.0267866 | + | 0.00552942i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.99480 | −0.278060 | ||||||||
\(117\) | −2.53302 | + | 5.87401i | −0.234178 | + | 0.543053i | ||||
\(118\) | − | 4.83472i | − | 0.445072i | ||||||
\(119\) | 4.06065 | − | 7.03326i | 0.372239 | − | 0.644737i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13.5258 | − | 23.4274i | −1.22962 | − | 2.12977i | ||||
\(122\) | −0.00450556 | + | 0.00260129i | −0.000407914 | + | 0.000235509i | ||||
\(123\) | 3.53705 | + | 3.14736i | 0.318925 | + | 0.283788i | ||||
\(124\) | 7.33359 | − | 12.7021i | 0.658576 | − | 1.14069i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.34149 | + | 1.44093i | 0.297683 | + | 0.128368i | ||||
\(127\) | − | 9.25840i | − | 0.821550i | −0.911737 | − | 0.410775i | \(-0.865258\pi\) | ||
0.911737 | − | 0.410775i | \(-0.134742\pi\) | |||||||
\(128\) | −9.68555 | − | 5.59196i | −0.856090 | − | 0.494264i | ||||
\(129\) | −13.0244 | − | 2.68856i | −1.14673 | − | 0.236714i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.134698 | − | 0.233305i | −0.0117687 | − | 0.0203839i | 0.860081 | − | 0.510157i | \(-0.170413\pi\) |
−0.871850 | + | 0.489773i | \(0.837080\pi\) | |||||||
\(132\) | −18.0122 | + | 5.96972i | −1.56776 | + | 0.519597i | ||||
\(133\) | 0.790794 | + | 0.456565i | 0.0685705 | + | 0.0395892i | ||||
\(134\) | −0.465123 | −0.0401805 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.66237 | −0.485544 | ||||||||
\(137\) | −3.01046 | − | 1.73809i | −0.257201 | − | 0.148495i | 0.365856 | − | 0.930671i | \(-0.380776\pi\) |
−0.623057 | + | 0.782176i | \(0.714110\pi\) | |||||||
\(138\) | −3.27804 | + | 1.08643i | −0.279045 | + | 0.0924827i | ||||
\(139\) | 7.37393 | + | 12.7720i | 0.625448 | + | 1.08331i | 0.988454 | + | 0.151521i | \(0.0484172\pi\) |
−0.363006 | + | 0.931787i | \(0.618249\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 19.3867 | + | 4.00189i | 1.63265 | + | 0.337020i | ||||
\(142\) | 2.63742 | + | 1.52271i | 0.221327 | + | 0.127783i | ||||
\(143\) | 13.1533i | 1.09993i | ||||||||
\(144\) | 0.943464 | + | 8.06403i | 0.0786220 | + | 0.672002i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.56521 | + | 2.71103i | −0.129538 | + | 0.224366i | ||||
\(147\) | −0.557378 | − | 0.495968i | −0.0459717 | − | 0.0409068i | ||||
\(148\) | 5.58747 | − | 3.22593i | 0.459287 | − | 0.265170i | ||||
\(149\) | −5.07665 | − | 8.79301i | −0.415895 | − | 0.720352i | 0.579627 | − | 0.814882i | \(-0.303198\pi\) |
−0.995522 | + | 0.0945305i | \(0.969865\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.15811 | − | 8.93410i | 0.419761 | − | 0.727047i | −0.576155 | − | 0.817341i | \(-0.695447\pi\) |
0.995915 | + | 0.0902940i | \(0.0287807\pi\) | |||||||
\(152\) | − | 0.636657i | − | 0.0516397i | ||||||
\(153\) | 5.67733 | + | 7.62420i | 0.458985 | + | 0.616380i | ||||
\(154\) | 7.48237 | 0.602947 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.42388 | + | 1.32605i | 0.514322 | + | 0.106169i | ||||
\(157\) | 0.920247 | − | 0.531305i | 0.0734437 | − | 0.0424028i | −0.462828 | − | 0.886448i | \(-0.653165\pi\) |
0.536272 | + | 0.844045i | \(0.319832\pi\) | |||||||
\(158\) | 3.88185 | − | 2.24119i | 0.308823 | − | 0.178299i | ||||
\(159\) | 5.14117 | + | 15.5123i | 0.407721 | + | 1.23020i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.7981 | −0.851008 | ||||||||
\(162\) | −3.09744 | + | 2.92360i | −0.243358 | + | 0.229699i | ||||
\(163\) | 17.1386i | 1.34240i | 0.741278 | + | 0.671198i | \(0.234220\pi\) | ||||
−0.741278 | + | 0.671198i | \(0.765780\pi\) | |||||||
\(164\) | 2.42742 | − | 4.20441i | 0.189549 | − | 0.328309i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.46560 | + | 4.27054i | 0.191368 | + | 0.331459i | ||||
\(167\) | −3.78752 | + | 2.18672i | −0.293087 | + | 0.169214i | −0.639333 | − | 0.768930i | \(-0.720790\pi\) |
0.346246 | + | 0.938144i | \(0.387456\pi\) | |||||||
\(168\) | 1.60380 | − | 7.76940i | 0.123736 | − | 0.599422i | ||||
\(169\) | −4.22666 | + | 7.32078i | −0.325127 | + | 0.563137i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.857238 | + | 0.638339i | −0.0655546 | + | 0.0488150i | ||||
\(172\) | 13.6367i | 1.03979i | ||||||||
\(173\) | −12.6960 | − | 7.33005i | −0.965260 | − | 0.557293i | −0.0674723 | − | 0.997721i | \(-0.521493\pi\) |
−0.897788 | + | 0.440428i | \(0.854827\pi\) | |||||||
\(174\) | −0.918827 | + | 1.03259i | −0.0696561 | + | 0.0782807i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 8.34718 | + | 14.4577i | 0.629192 | + | 1.08979i | ||||
\(177\) | 13.2189 | + | 11.7625i | 0.993591 | + | 0.884121i | ||||
\(178\) | −2.56952 | − | 1.48351i | −0.192593 | − | 0.111194i | ||||
\(179\) | 6.87014 | 0.513499 | 0.256749 | − | 0.966478i | \(-0.417349\pi\) | ||||
0.256749 | + | 0.966478i | \(0.417349\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.9709 | −0.815463 | −0.407732 | − | 0.913102i | \(-0.633680\pi\) | ||||
−0.407732 | + | 0.913102i | \(0.633680\pi\) | |||||||
\(182\) | −2.23991 | − | 1.29321i | −0.166033 | − | 0.0958593i | ||||
\(183\) | 0.00384933 | − | 0.0186476i | 0.000284551 | − | 0.00137847i | ||||
\(184\) | 3.76434 | + | 6.52003i | 0.277511 | + | 0.480663i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.12965 | − | 6.42570i | −0.156153 | − | 0.471155i | ||||
\(187\) | 16.9272 | + | 9.77294i | 1.23784 | + | 0.714668i | ||||
\(188\) | − | 20.2980i | − | 1.48039i | ||||||
\(189\) | −12.0693 | + | 5.63046i | −0.877911 | + | 0.409556i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.86627 | + | 11.8927i | −0.496826 | + | 0.860528i | −0.999993 | − | 0.00366109i | \(-0.998835\pi\) |
0.503167 | + | 0.864189i | \(0.332168\pi\) | |||||||
\(192\) | 5.12158 | − | 1.69742i | 0.369618 | − | 0.122501i | ||||
\(193\) | 0.417748 | − | 0.241187i | 0.0300701 | − | 0.0173610i | −0.484890 | − | 0.874575i | \(-0.661140\pi\) |
0.514960 | + | 0.857214i | \(0.327807\pi\) | |||||||
\(194\) | 1.70532 | + | 2.95370i | 0.122435 | + | 0.212064i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.382518 | + | 0.662541i | −0.0273227 | + | 0.0473244i | ||||
\(197\) | 5.53488i | 0.394344i | 0.980369 | + | 0.197172i | \(0.0631757\pi\) | ||||
−0.980369 | + | 0.197172i | \(0.936824\pi\) | |||||||
\(198\) | −3.46795 | + | 8.04209i | −0.246457 | + | 0.571526i | ||||
\(199\) | −17.4590 | −1.23764 | −0.618818 | − | 0.785534i | \(-0.712388\pi\) | ||||
−0.618818 | + | 0.785534i | \(0.712388\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.13160 | − | 1.27172i | 0.0798172 | − | 0.0896999i | ||||
\(202\) | 2.85704 | − | 1.64951i | 0.201021 | − | 0.116059i | ||||
\(203\) | −3.74288 | + | 2.16095i | −0.262698 | + | 0.151669i | ||||
\(204\) | 6.47948 | − | 7.28175i | 0.453654 | − | 0.509825i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.89401 | −0.201635 | ||||||||
\(207\) | 5.00473 | − | 11.6058i | 0.347852 | − | 0.806661i | ||||
\(208\) | − | 5.77073i | − | 0.400128i | ||||||
\(209\) | −1.09883 | + | 1.90324i | −0.0760079 | + | 0.131650i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.818328 | + | 1.41739i | 0.0563360 | + | 0.0975769i | 0.892818 | − | 0.450417i | \(-0.148725\pi\) |
−0.836482 | + | 0.547994i | \(0.815392\pi\) | |||||||
\(212\) | 14.5120 | − | 8.37849i | 0.996686 | − | 0.575437i | ||||
\(213\) | −10.5799 | + | 3.50647i | −0.724926 | + | 0.240259i | ||||
\(214\) | −3.43935 | + | 5.95713i | −0.235109 | + | 0.407221i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 7.60725 | + | 5.32475i | 0.517608 | + | 0.362303i | ||||
\(217\) | − | 21.1667i | − | 1.43689i | ||||||
\(218\) | 0.779592 | + | 0.450098i | 0.0528006 | + | 0.0304844i | ||||
\(219\) | −3.60433 | − | 10.8752i | −0.243558 | − | 0.734879i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.37820 | − | 5.85122i | −0.227243 | − | 0.393596i | ||||
\(222\) | 0.601992 | − | 2.91628i | 0.0404031 | − | 0.195728i | ||||
\(223\) | 6.70984 | + | 3.87393i | 0.449324 | + | 0.259417i | 0.707545 | − | 0.706669i | \(-0.249803\pi\) |
−0.258221 | + | 0.966086i | \(0.583136\pi\) | |||||||
\(224\) | −12.4432 | −0.831397 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.11366 | −0.207118 | ||||||||
\(227\) | 9.75169 | + | 5.63014i | 0.647242 | + | 0.373685i | 0.787399 | − | 0.616444i | \(-0.211427\pi\) |
−0.140157 | + | 0.990129i | \(0.544761\pi\) | |||||||
\(228\) | 0.818734 | + | 0.728529i | 0.0542220 | + | 0.0482480i | ||||
\(229\) | −5.23879 | − | 9.07384i | −0.346189 | − | 0.599616i | 0.639380 | − | 0.768891i | \(-0.279191\pi\) |
−0.985569 | + | 0.169274i | \(0.945858\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −18.2040 | + | 20.4579i | −1.19773 | + | 1.34603i | ||||
\(232\) | 2.60962 | + | 1.50667i | 0.171330 | + | 0.0989176i | ||||
\(233\) | 2.90214i | 0.190125i | 0.995471 | + | 0.0950627i | \(0.0303051\pi\) | ||||
−0.995471 | + | 0.0950627i | \(0.969695\pi\) | |||||||
\(234\) | 2.42811 | − | 1.80808i | 0.158731 | − | 0.118198i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 9.07188 | − | 15.7130i | 0.590529 | − | 1.02283i | ||||
\(237\) | −3.31646 | + | 16.0662i | −0.215427 | + | 1.04361i | ||||
\(238\) | −3.32852 | + | 1.92172i | −0.215756 | + | 0.124567i | ||||
\(239\) | 8.17723 | + | 14.1634i | 0.528941 | + | 0.916153i | 0.999430 | + | 0.0337471i | \(0.0107441\pi\) |
−0.470489 | + | 0.882406i | \(0.655923\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.76194 | + | 15.1761i | −0.564406 | + | 0.977580i | 0.432698 | + | 0.901539i | \(0.357562\pi\) |
−0.997105 | + | 0.0760416i | \(0.975772\pi\) | |||||||
\(242\) | 12.8023i | 0.822965i | ||||||||
\(243\) | −0.457745 | − | 15.5817i | −0.0293644 | − | 0.999569i | ||||
\(244\) | −0.0195242 | −0.00124991 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.704913 | − | 2.12691i | −0.0449436 | − | 0.135607i | ||||
\(247\) | 0.657890 | − | 0.379833i | 0.0418605 | − | 0.0241682i | ||||
\(248\) | −12.7808 | + | 7.37898i | −0.811580 | + | 0.468566i | ||||
\(249\) | −17.6749 | − | 3.64854i | −1.12010 | − | 0.231217i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.46999 | 0.534621 | 0.267311 | − | 0.963610i | \(-0.413865\pi\) | ||||
0.267311 | + | 0.963610i | \(0.413865\pi\) | |||||||
\(252\) | 8.15613 | + | 10.9530i | 0.513788 | + | 0.689976i | ||||
\(253\) | − | 25.9882i | − | 1.63386i | ||||||
\(254\) | −2.19079 | + | 3.79456i | −0.137462 | + | 0.238092i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.468695 | − | 0.811804i | −0.0292934 | − | 0.0507377i | ||||
\(257\) | −2.48766 | + | 1.43625i | −0.155176 | + | 0.0895910i | −0.575577 | − | 0.817747i | \(-0.695223\pi\) |
0.420401 | + | 0.907338i | \(0.361889\pi\) | |||||||
\(258\) | 4.70186 | + | 4.18383i | 0.292725 | + | 0.260474i | ||||
\(259\) | 4.65545 | − | 8.06348i | 0.289276 | − | 0.501040i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.587841 | − | 5.02442i | −0.0363864 | − | 0.311004i | ||||
\(262\) | 0.127493i | 0.00787656i | ||||||||
\(263\) | 22.1909 | + | 12.8119i | 1.36835 | + | 0.790017i | 0.990717 | − | 0.135938i | \(-0.0434048\pi\) |
0.377633 | + | 0.925955i | \(0.376738\pi\) | |||||||
\(264\) | 18.6989 | + | 3.85993i | 1.15084 | + | 0.237562i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.216072 | − | 0.374247i | −0.0132482 | − | 0.0229465i | ||||
\(267\) | 10.3076 | − | 3.41619i | 0.630812 | − | 0.209068i | ||||
\(268\) | −1.51166 | − | 0.872756i | −0.0923392 | − | 0.0533121i | ||||
\(269\) | −0.337210 | −0.0205600 | −0.0102800 | − | 0.999947i | \(-0.503272\pi\) | ||||
−0.0102800 | + | 0.999947i | \(0.503272\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.5927 | 1.31166 | 0.655831 | − | 0.754908i | \(-0.272318\pi\) | ||||
0.655831 | + | 0.754908i | \(0.272318\pi\) | |||||||
\(272\) | −7.42646 | − | 4.28767i | −0.450295 | − | 0.259978i | ||||
\(273\) | 8.98535 | − | 2.97798i | 0.543818 | − | 0.180236i | ||||
\(274\) | 0.822560 | + | 1.42472i | 0.0496927 | + | 0.0860702i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −12.6923 | − | 2.62000i | −0.763984 | − | 0.157705i | ||||
\(277\) | −20.9004 | − | 12.0669i | −1.25579 | − | 0.725028i | −0.283533 | − | 0.958962i | \(-0.591507\pi\) |
−0.972252 | + | 0.233934i | \(0.924840\pi\) | |||||||
\(278\) | − | 6.97949i | − | 0.418602i | ||||||
\(279\) | 22.7501 | + | 9.81041i | 1.36201 | + | 0.587334i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.68363 | + | 2.91613i | −0.100437 | + | 0.173962i | −0.911865 | − | 0.410491i | \(-0.865357\pi\) |
0.811428 | + | 0.584453i | \(0.198691\pi\) | |||||||
\(282\) | −6.99868 | − | 6.22759i | −0.416765 | − | 0.370848i | ||||
\(283\) | −18.9224 | + | 10.9249i | −1.12482 | + | 0.649415i | −0.942627 | − | 0.333848i | \(-0.891653\pi\) |
−0.182193 | + | 0.983263i | \(0.558319\pi\) | |||||||
\(284\) | 5.71444 | + | 9.89770i | 0.339090 | + | 0.587321i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.11243 | − | 5.39088i | 0.184042 | − | 0.318770i | ||||
\(287\) | − | 7.00619i | − | 0.413562i | ||||||
\(288\) | 5.76721 | − | 13.3740i | 0.339836 | − | 0.788071i | ||||
\(289\) | 6.95994 | 0.409408 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.2248 | − | 2.52350i | −0.716629 | − | 0.147930i | ||||
\(292\) | −10.1739 | + | 5.87393i | −0.595385 | + | 0.343746i | ||||
\(293\) | −11.9114 | + | 6.87702i | −0.695869 | + | 0.401760i | −0.805807 | − | 0.592179i | \(-0.798268\pi\) |
0.109938 | + | 0.993938i | \(0.464935\pi\) | |||||||
\(294\) | 0.111082 | + | 0.335163i | 0.00647843 | + | 0.0195471i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.49179 | −0.377328 | ||||||||
\(297\) | −13.5511 | − | 29.0476i | −0.786312 | − | 1.68551i | ||||
\(298\) | 4.80509i | 0.278352i | ||||||||
\(299\) | −4.49166 | + | 7.77978i | −0.259759 | + | 0.449916i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.83978 | + | 17.0430i | 0.567155 | + | 0.982342i | ||||
\(302\) | −4.22810 | + | 2.44110i | −0.243300 | + | 0.140469i | ||||
\(303\) | −2.44092 | + | 11.8247i | −0.140227 | + | 0.679312i | ||||
\(304\) | 0.482090 | − | 0.835004i | 0.0276498 | − | 0.0478908i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.522764 | − | 4.46819i | −0.0298844 | − | 0.255430i | ||||
\(307\) | 34.2183i | 1.95294i | 0.215644 | + | 0.976472i | \(0.430815\pi\) | ||||
−0.215644 | + | 0.976472i | \(0.569185\pi\) | |||||||
\(308\) | 24.3179 | + | 14.0399i | 1.38564 | + | 0.799999i | ||||
\(309\) | 7.04087 | − | 7.91265i | 0.400541 | − | 0.450135i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.5199 | − | 19.9530i | −0.653232 | − | 1.13143i | −0.982334 | − | 0.187136i | \(-0.940079\pi\) |
0.329102 | − | 0.944294i | \(-0.393254\pi\) | |||||||
\(312\) | −4.93055 | − | 4.38732i | −0.279137 | − | 0.248383i | ||||
\(313\) | −3.11016 | − | 1.79565i | −0.175796 | − | 0.101496i | 0.409520 | − | 0.912301i | \(-0.365696\pi\) |
−0.585316 | + | 0.810805i | \(0.699030\pi\) | |||||||
\(314\) | −0.502885 | −0.0283794 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 16.8215 | 0.946281 | ||||||||
\(317\) | −11.4148 | − | 6.59033i | −0.641118 | − | 0.370150i | 0.143927 | − | 0.989588i | \(-0.454027\pi\) |
−0.785045 | + | 0.619439i | \(0.787360\pi\) | |||||||
\(318\) | 1.56351 | − | 7.57425i | 0.0876775 | − | 0.424743i | ||||
\(319\) | −5.20085 | − | 9.00813i | −0.291192 | − | 0.504359i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.92005 | − | 23.8969i | −0.442054 | − | 1.33379i | ||||
\(322\) | 4.42560 | + | 2.55512i | 0.246629 | + | 0.142391i | ||||
\(323\) | − | 1.12887i | − | 0.0628119i | ||||||
\(324\) | −15.5526 | + | 3.68971i | −0.864033 | + | 0.204984i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.05545 | − | 7.02424i | 0.224611 | − | 0.389037i | ||||
\(327\) | −3.12732 | + | 1.03647i | −0.172941 | + | 0.0573171i | ||||
\(328\) | −4.23044 | + | 2.44244i | −0.233587 | + | 0.134861i | ||||
\(329\) | −14.6464 | − | 25.3683i | −0.807483 | − | 1.39860i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.591264 | + | 1.02410i | −0.0324988 | + | 0.0562896i | −0.881817 | − | 0.471591i | \(-0.843680\pi\) |
0.849319 | + | 0.527881i | \(0.177013\pi\) | |||||||
\(332\) | 18.5058i | 1.01564i | ||||||||
\(333\) | 6.50894 | + | 8.74099i | 0.356688 | + | 0.479003i | ||||
\(334\) | 2.06975 | 0.113252 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 7.98661 | − | 8.97549i | 0.435705 | − | 0.489653i | ||||
\(337\) | −21.4770 | + | 12.3997i | −1.16993 | + | 0.675457i | −0.953662 | − | 0.300879i | \(-0.902720\pi\) |
−0.216263 | + | 0.976335i | \(0.569387\pi\) | |||||||
\(338\) | 3.46459 | − | 2.00028i | 0.188449 | − | 0.108801i | ||||
\(339\) | 7.57527 | − | 8.51322i | 0.411432 | − | 0.462375i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 50.9428 | 2.75871 | ||||||||
\(342\) | 0.502388 | − | 0.0587777i | 0.0271660 | − | 0.00317833i | ||||
\(343\) | 19.0454i | 1.02836i | ||||||||
\(344\) | 6.86053 | − | 11.8828i | 0.369895 | − | 0.640677i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.46898 | + | 6.00845i | 0.186493 | + | 0.323016i | ||||
\(347\) | 19.1991 | − | 11.0846i | 1.03066 | − | 0.595052i | 0.113486 | − | 0.993540i | \(-0.463798\pi\) |
0.917174 | + | 0.398488i | \(0.130465\pi\) | |||||||
\(348\) | −4.92376 | + | 1.63186i | −0.263941 | + | 0.0874771i | ||||
\(349\) | 7.45925 | − | 12.9198i | 0.399285 | − | 0.691581i | −0.594353 | − | 0.804204i | \(-0.702592\pi\) |
0.993638 | + | 0.112623i | \(0.0359252\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.963810 | + | 11.0377i | −0.0514444 | + | 0.589151i | ||||
\(352\) | − | 29.9476i | − | 1.59621i | ||||||
\(353\) | 14.6484 | + | 8.45726i | 0.779656 | + | 0.450134i | 0.836308 | − | 0.548260i | \(-0.184709\pi\) |
−0.0566525 | + | 0.998394i | \(0.518043\pi\) | |||||||
\(354\) | −2.63444 | − | 7.94880i | −0.140019 | − | 0.422474i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5.56732 | − | 9.64288i | −0.295067 | − | 0.511072i | ||||
\(357\) | 2.84372 | − | 13.7761i | 0.150506 | − | 0.729107i | ||||
\(358\) | −2.81573 | − | 1.62566i | −0.148816 | − | 0.0859190i | ||||
\(359\) | −0.636657 | −0.0336015 | −0.0168007 | − | 0.999859i | \(-0.505348\pi\) | ||||
−0.0168007 | + | 0.999859i | \(0.505348\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8731 | −0.993320 | ||||||||
\(362\) | 4.49644 | + | 2.59602i | 0.236328 | + | 0.136444i | ||||
\(363\) | −35.0035 | − | 31.1470i | −1.83721 | − | 1.63479i | ||||
\(364\) | −4.85317 | − | 8.40594i | −0.254375 | − | 0.440591i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.00599018 | + | 0.00673187i | −0.000313112 | + | 0.000351880i | ||||
\(367\) | −17.4053 | − | 10.0490i | −0.908550 | − | 0.524552i | −0.0285858 | − | 0.999591i | \(-0.509100\pi\) |
−0.879964 | + | 0.475040i | \(0.842434\pi\) | |||||||
\(368\) | 11.4018i | 0.594358i | ||||||||
\(369\) | 7.53028 | + | 3.24725i | 0.392011 | + | 0.169045i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.0913 | − | 20.9427i | 0.627749 | − | 1.08729i | ||||
\(372\) | 5.13580 | − | 24.8797i | 0.266279 | − | 1.28995i | ||||
\(373\) | 17.0113 | − | 9.82146i | 0.880810 | − | 0.508536i | 0.00988448 | − | 0.999951i | \(-0.496854\pi\) |
0.870925 | + | 0.491415i | \(0.163520\pi\) | |||||||
\(374\) | −4.62509 | − | 8.01088i | −0.239157 | − | 0.414233i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.2118 | + | 17.6874i | −0.526635 | + | 0.912159i | ||||
\(377\) | 3.59555i | 0.185180i | ||||||||
\(378\) | 6.27892 | + | 0.548272i | 0.322953 | + | 0.0282001i | ||||
\(379\) | 7.94219 | 0.407963 | 0.203982 | − | 0.978975i | \(-0.434612\pi\) | ||||
0.203982 | + | 0.978975i | \(0.434612\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.04490 | − | 15.2218i | −0.258458 | − | 0.779836i | ||||
\(382\) | 5.62829 | − | 3.24949i | 0.287968 | − | 0.166259i | ||||
\(383\) | 27.0103 | − | 15.5944i | 1.38016 | − | 0.796836i | 0.387983 | − | 0.921667i | \(-0.373172\pi\) |
0.992178 | + | 0.124830i | \(0.0398387\pi\) | |||||||
\(384\) | −18.9711 | − | 3.91612i | −0.968116 | − | 0.199843i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.228285 | −0.0116194 | ||||||||
\(387\) | −22.8785 | + | 2.67670i | −1.16298 | + | 0.136064i | ||||
\(388\) | 12.7995i | 0.649795i | ||||||||
\(389\) | −15.7247 | + | 27.2360i | −0.797274 | + | 1.38092i | 0.124111 | + | 0.992268i | \(0.460392\pi\) |
−0.921385 | + | 0.388650i | \(0.872941\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.67463 | + | 11.5608i | 0.337550 | + | 0.584655i | ||||
\(392\) | 0.666642 | − | 0.384886i | 0.0336705 | − | 0.0194397i | ||||
\(393\) | −0.348586 | − | 0.310180i | −0.0175838 | − | 0.0156465i | ||||
\(394\) | 1.30970 | − | 2.26847i | 0.0659819 | − | 0.114284i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −26.3611 | + | 19.6297i | −1.32469 | + | 0.986429i | ||||
\(397\) | 17.7174i | 0.889211i | 0.895726 | + | 0.444606i | \(0.146656\pi\) | ||||
−0.895726 | + | 0.444606i | \(0.853344\pi\) | |||||||
\(398\) | 7.15558 | + | 4.13128i | 0.358677 | + | 0.207082i | ||||
\(399\) | 1.54893 | + | 0.319738i | 0.0775436 | + | 0.0160069i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.57124 | + | 6.18556i | 0.178339 | + | 0.308892i | 0.941312 | − | 0.337538i | \(-0.109594\pi\) |
−0.762973 | + | 0.646431i | \(0.776261\pi\) | |||||||
\(402\) | −0.764711 | + | 0.253445i | −0.0381403 | + | 0.0126407i | ||||
\(403\) | −15.2502 | − | 8.80468i | −0.759665 | − | 0.438593i | ||||
\(404\) | 12.3806 | 0.615958 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.04536 | 0.101509 | ||||||||
\(407\) | 19.4067 | + | 11.2045i | 0.961955 | + | 0.555385i | ||||
\(408\) | −9.30954 | + | 3.08542i | −0.460891 | + | 0.152751i | ||||
\(409\) | 12.3759 | + | 21.4357i | 0.611948 | + | 1.05993i | 0.990912 | + | 0.134514i | \(0.0429472\pi\) |
−0.378964 | + | 0.925412i | \(0.623719\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.89661 | − | 1.21721i | −0.290858 | − | 0.0600404i | ||||
\(412\) | −9.40558 | − | 5.43031i | −0.463380 | − | 0.267532i | ||||
\(413\) | − | 26.1839i | − | 1.28843i | ||||||
\(414\) | −4.79744 | + | 3.57240i | −0.235782 | + | 0.175574i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −5.17598 | + | 8.96505i | −0.253773 | + | 0.439548i | ||||
\(417\) | 19.0830 | + | 16.9805i | 0.934498 | + | 0.831539i | ||||
\(418\) | 0.900715 | − | 0.520028i | 0.0440554 | − | 0.0254354i | ||||
\(419\) | −5.32956 | − | 9.23106i | −0.260366 | − | 0.450967i | 0.705973 | − | 0.708238i | \(-0.250510\pi\) |
−0.966339 | + | 0.257272i | \(0.917176\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.08931 | − | 7.08288i | 0.199301 | − | 0.345199i | −0.749001 | − | 0.662569i | \(-0.769466\pi\) |
0.948302 | + | 0.317370i | \(0.102800\pi\) | |||||||
\(422\) | − | 0.774555i | − | 0.0377048i | ||||||
\(423\) | 34.0544 | − | 3.98425i | 1.65578 | − | 0.193721i | ||||
\(424\) | −16.8607 | −0.818828 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 5.16592 | + | 1.06638i | 0.250290 | + | 0.0516660i | ||||
\(427\) | −0.0244012 | + | 0.0140881i | −0.00118086 | + | 0.000681769i | ||||
\(428\) | −22.3559 | + | 12.9072i | −1.08061 | + | 0.623893i | ||||
\(429\) | 7.16722 | + | 21.6254i | 0.346037 | + | 1.04408i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.67248 | 0.0805604 | 0.0402802 | − | 0.999188i | \(-0.487175\pi\) | ||||
0.0402802 | + | 0.999188i | \(0.487175\pi\) | |||||||
\(432\) | 5.94524 | + | 12.7440i | 0.286040 | + | 0.613147i | ||||
\(433\) | 9.95994i | 0.478644i | 0.970940 | + | 0.239322i | \(0.0769252\pi\) | ||||
−0.970940 | + | 0.239322i | \(0.923075\pi\) | |||||||
\(434\) | −5.00863 | + | 8.67519i | −0.240422 | + | 0.416423i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.68913 | + | 2.92565i | 0.0808945 | + | 0.140113i | ||||
\(437\) | −1.29985 | + | 0.750471i | −0.0621805 | + | 0.0358999i | ||||
\(438\) | −1.09614 | + | 5.31010i | −0.0523754 | + | 0.253726i | ||||
\(439\) | 6.40788 | − | 11.0988i | 0.305832 | − | 0.529716i | −0.671615 | − | 0.740901i | \(-0.734399\pi\) |
0.977446 | + | 0.211185i | \(0.0677322\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.18664 | − | 0.511709i | −0.0565067 | − | 0.0243671i | ||||
\(442\) | 3.19750i | 0.152090i | ||||||||
\(443\) | −6.71520 | − | 3.87702i | −0.319049 | − | 0.184203i | 0.331920 | − | 0.943308i | \(-0.392304\pi\) |
−0.650968 | + | 0.759105i | \(0.725637\pi\) | |||||||
\(444\) | 7.42859 | − | 8.34838i | 0.352545 | − | 0.396196i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.83335 | − | 3.17546i | −0.0868118 | − | 0.150362i | ||||
\(447\) | −13.1379 | − | 11.6904i | −0.621399 | − | 0.552936i | ||||
\(448\) | −6.91452 | − | 3.99210i | −0.326681 | − | 0.188609i | ||||
\(449\) | 33.3401 | 1.57342 | 0.786709 | − | 0.617324i | \(-0.211783\pi\) | ||||
0.786709 | + | 0.617324i | \(0.211783\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.8621 | 0.794004 | ||||||||
\(452\) | −10.1195 | − | 5.84247i | −0.475979 | − | 0.274807i | ||||
\(453\) | 3.61229 | − | 17.4993i | 0.169720 | − | 0.822187i | ||||
\(454\) | −2.66449 | − | 4.61503i | −0.125051 | − | 0.216594i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.346914 | − | 1.04673i | −0.0162457 | − | 0.0490177i | ||||
\(457\) | 33.0988 | + | 19.1096i | 1.54830 | + | 0.893910i | 0.998272 | + | 0.0587626i | \(0.0187155\pi\) |
0.550026 | + | 0.835148i | \(0.314618\pi\) | |||||||
\(458\) | 4.95856i | 0.231698i | ||||||||
\(459\) | 13.4886 | + | 9.44142i | 0.629592 | + | 0.440688i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.6517 | + | 27.1095i | −0.728971 | + | 1.26261i | 0.228348 | + | 0.973580i | \(0.426668\pi\) |
−0.957319 | + | 0.289035i | \(0.906666\pi\) | |||||||
\(462\) | 12.3018 | − | 4.07714i | 0.572332 | − | 0.189686i | ||||
\(463\) | −10.4661 | + | 6.04258i | −0.486399 | + | 0.280823i | −0.723079 | − | 0.690765i | \(-0.757274\pi\) |
0.236680 | + | 0.971588i | \(0.423941\pi\) | |||||||
\(464\) | 2.28176 | + | 3.95212i | 0.105928 | + | 0.183473i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.686725 | − | 1.18944i | 0.0318119 | − | 0.0550998i | ||||
\(467\) | − | 7.60466i | − | 0.351902i | −0.984399 | − | 0.175951i | \(-0.943700\pi\) | ||
0.984399 | − | 0.175951i | \(-0.0563000\pi\) | |||||||
\(468\) | 11.2841 | − | 1.32020i | 0.521608 | − | 0.0610264i | ||||
\(469\) | −2.51901 | −0.116317 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.22348 | − | 1.37496i | 0.0563748 | − | 0.0633550i | ||||
\(472\) | −15.8102 | + | 9.12803i | −0.727724 | + | 0.420152i | ||||
\(473\) | −41.0181 | + | 23.6818i | −1.88601 | + | 1.08889i | ||||
\(474\) | 5.16095 | − | 5.79997i | 0.237050 | − | 0.266401i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −14.4237 | −0.661108 | ||||||||
\(477\) | 16.9052 | + | 22.7024i | 0.774038 | + | 1.03947i | ||||
\(478\) | − | 7.73982i | − | 0.354011i | ||||||
\(479\) | −16.2417 | + | 28.1314i | −0.742101 | + | 1.28536i | 0.209437 | + | 0.977822i | \(0.432837\pi\) |
−0.951537 | + | 0.307534i | \(0.900496\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.87304 | − | 6.70830i | −0.176595 | − | 0.305872i | ||||
\(482\) | 7.18217 | − | 4.14663i | 0.327139 | − | 0.188874i | ||||
\(483\) | −17.7532 | + | 5.88387i | −0.807798 | + | 0.267725i | ||||
\(484\) | −24.0223 | + | 41.6079i | −1.09192 | + | 1.89127i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −3.49946 | + | 6.49450i | −0.158739 | + | 0.294596i | ||||
\(487\) | − | 4.46121i | − | 0.202157i | −0.994878 | − | 0.101078i | \(-0.967771\pi\) | ||
0.994878 | − | 0.101078i | \(-0.0322293\pi\) | |||||||
\(488\) | 0.0170131 | + | 0.00982254i | 0.000770148 | + | 0.000444645i | ||||
\(489\) | 9.33879 | + | 28.1776i | 0.422315 | + | 1.27424i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.4210 | − | 28.4420i | −0.741070 | − | 1.28357i | −0.952008 | − | 0.306072i | \(-0.900985\pi\) |
0.210938 | − | 0.977499i | \(-0.432348\pi\) | |||||||
\(492\) | 1.69995 | − | 8.23520i | 0.0766397 | − | 0.371271i | ||||
\(493\) | 4.62717 | + | 2.67150i | 0.208397 | + | 0.120318i | ||||
\(494\) | −0.359515 | −0.0161754 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −22.3501 | −1.00355 | ||||||||
\(497\) | 14.2837 | + | 8.24672i | 0.640713 | + | 0.369916i | ||||
\(498\) | 6.38073 | + | 5.67772i | 0.285927 | + | 0.254425i | ||||
\(499\) | −17.1010 | − | 29.6198i | −0.765547 | − | 1.32597i | −0.939957 | − | 0.341293i | \(-0.889135\pi\) |
0.174410 | − | 0.984673i | \(-0.444198\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.03554 | + | 5.65902i | −0.224971 | + | 0.252827i | ||||
\(502\) | −3.47143 | − | 2.00423i | −0.154938 | − | 0.0894532i | ||||
\(503\) | − | 22.1773i | − | 0.988837i | −0.869224 | − | 0.494419i | \(-0.835381\pi\) | ||
0.869224 | − | 0.494419i | \(-0.164619\pi\) | |||||||
\(504\) | −1.59673 | − | 13.6476i | −0.0711238 | − | 0.607913i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −6.14951 | + | 10.6513i | −0.273379 | + | 0.473507i | ||||
\(507\) | −2.95998 | + | 14.3392i | −0.131457 | + | 0.636828i | ||||
\(508\) | −14.2402 | + | 8.22160i | −0.631808 | + | 0.364775i | ||||
\(509\) | −10.7816 | − | 18.6743i | −0.477887 | − | 0.827724i | 0.521792 | − | 0.853073i | \(-0.325264\pi\) |
−0.999679 | + | 0.0253489i | \(0.991930\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.47688 | + | 14.6824i | −0.374995 | + | 0.649510i | ||||
\(512\) | 22.8115i | 1.00813i | ||||||||
\(513\) | −1.06156 | + | 1.51661i | −0.0468690 | + | 0.0669598i | ||||
\(514\) | 1.35943 | 0.0599617 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 7.43061 | + | 22.4201i | 0.327114 | + | 0.986990i | ||||
\(517\) | 61.0550 | − | 35.2501i | 2.68520 | − | 1.55030i | ||||
\(518\) | −3.81608 | + | 2.20321i | −0.167669 | + | 0.0968037i | ||||
\(519\) | −24.8677 | − | 5.13332i | −1.09157 | − | 0.225328i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.2626 | 0.887718 | 0.443859 | − | 0.896097i | \(-0.353609\pi\) | ||||
0.443859 | + | 0.896097i | \(0.353609\pi\) | |||||||
\(522\) | −0.947989 | + | 2.19836i | −0.0414923 | + | 0.0962196i | ||||
\(523\) | − | 31.8114i | − | 1.39101i | −0.718520 | − | 0.695507i | \(-0.755180\pi\) | ||
0.718520 | − | 0.695507i | \(-0.244820\pi\) | |||||||
\(524\) | −0.239229 | + | 0.414356i | −0.0104507 | + | 0.0181012i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.06330 | − | 10.5019i | −0.264373 | − | 0.457907i | ||||
\(527\) | −22.6618 | + | 13.0838i | −0.987164 | + | 0.569940i | ||||
\(528\) | 21.6017 | + | 19.2217i | 0.940092 | + | 0.836517i | ||||
\(529\) | −2.62541 | + | 4.54735i | −0.114148 | + | 0.197711i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 28.1426 | + | 12.1358i | 1.22128 | + | 0.526649i | ||||
\(532\) | − | 1.62175i | − | 0.0703117i | ||||||
\(533\) | −5.04780 | − | 2.91435i | −0.218645 | − | 0.126235i | ||||
\(534\) | −5.03292 | − | 1.03892i | −0.217796 | − | 0.0449585i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.878159 | + | 1.52102i | 0.0379307 | + | 0.0656978i | ||||
\(537\) | 11.2952 | − | 3.74354i | 0.487426 | − | 0.161546i | ||||
\(538\) | 0.138205 | + | 0.0797930i | 0.00595846 | + | 0.00344012i | ||||
\(539\) | −2.65717 | −0.114452 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.1315 | −0.650553 | −0.325277 | − | 0.945619i | \(-0.605457\pi\) | ||||
−0.325277 | + | 0.945619i | \(0.605457\pi\) | |||||||
\(542\) | −8.84977 | − | 5.10942i | −0.380130 | − | 0.219468i | ||||
\(543\) | −18.0374 | + | 5.97806i | −0.774058 | + | 0.256543i | ||||
\(544\) | 7.69153 | + | 13.3221i | 0.329772 | + | 0.571181i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.38732 | − | 0.905653i | −0.187760 | − | 0.0387584i | ||||
\(547\) | 3.53982 | + | 2.04372i | 0.151352 | + | 0.0873831i | 0.573763 | − | 0.819021i | \(-0.305483\pi\) |
−0.422411 | + | 0.906404i | \(0.638816\pi\) | |||||||
\(548\) | 6.17381i | 0.263732i | ||||||||
\(549\) | −0.00383236 | − | 0.0327561i | −0.000163561 | − | 0.00139800i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.300374 | + | 0.520263i | −0.0127964 | + | 0.0221639i | ||||
\(552\) | 9.74174 | + | 8.66844i | 0.414636 | + | 0.368953i | ||||
\(553\) | 21.0233 | − | 12.1378i | 0.894003 | − | 0.516153i | ||||
\(554\) | 5.71070 | + | 9.89123i | 0.242625 | + | 0.420238i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13.0963 | − | 22.6835i | 0.555408 | − | 0.961994i | ||||
\(557\) | − | 13.1425i | − | 0.556864i | −0.960456 | − | 0.278432i | \(-0.910185\pi\) | ||
0.960456 | − | 0.278432i | \(-0.0898147\pi\) | |||||||
\(558\) | −7.00273 | − | 9.40410i | −0.296449 | − | 0.398107i | ||||
\(559\) | 16.3721 | 0.692467 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 33.1554 | + | 6.84411i | 1.39982 | + | 0.288958i | ||||
\(562\) | 1.38007 | − | 0.796785i | 0.0582149 | − | 0.0336104i | ||||
\(563\) | 21.2368 | − | 12.2611i | 0.895023 | − | 0.516742i | 0.0194410 | − | 0.999811i | \(-0.493811\pi\) |
0.875582 | + | 0.483069i | \(0.160478\pi\) | |||||||
\(564\) | −11.0604 | − | 33.3721i | −0.465727 | − | 1.40522i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 10.3405 | 0.434642 | ||||||||
\(567\) | −16.7751 | + | 15.8336i | −0.704489 | + | 0.664950i | ||||
\(568\) | − | 11.4996i | − | 0.482514i | ||||||
\(569\) | 11.3649 | − | 19.6846i | 0.476442 | − | 0.825223i | −0.523193 | − | 0.852214i | \(-0.675259\pi\) |
0.999636 | + | 0.0269915i | \(0.00859271\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.247093 | + | 0.427977i | 0.0103405 | + | 0.0179103i | 0.871149 | − | 0.491018i | \(-0.163375\pi\) |
−0.860809 | + | 0.508928i | \(0.830042\pi\) | |||||||
\(572\) | 20.2309 | − | 11.6803i | 0.845897 | − | 0.488379i | ||||
\(573\) | −4.80854 | + | 23.2943i | −0.200879 | + | 0.973135i | ||||
\(574\) | −1.65786 | + | 2.87149i | −0.0691976 | + | 0.119854i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 7.49549 | − | 5.58149i | 0.312312 | − | 0.232562i | ||||
\(577\) | − | 9.41187i | − | 0.391821i | −0.980622 | − | 0.195911i | \(-0.937234\pi\) | ||
0.980622 | − | 0.195911i | \(-0.0627662\pi\) | |||||||
\(578\) | −2.85254 | − | 1.64691i | −0.118650 | − | 0.0685025i | ||||
\(579\) | 0.555399 | − | 0.624167i | 0.0230816 | − | 0.0259395i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.3532 | + | 23.1284i | 0.553984 | + | 0.959529i | ||||
\(582\) | 4.41320 | + | 3.92697i | 0.182933 | + | 0.162778i | ||||
\(583\) | 50.4037 | + | 29.1006i | 2.08751 | + | 1.20522i | ||||
\(584\) | 11.8206 | 0.489139 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.50916 | 0.268891 | ||||||||
\(587\) | −8.63705 | − | 4.98661i | −0.356489 | − | 0.205819i | 0.311050 | − | 0.950393i | \(-0.399319\pi\) |
−0.667540 | + | 0.744574i | \(0.732653\pi\) | |||||||
\(588\) | −0.267882 | + | 1.29772i | −0.0110473 | + | 0.0535172i | ||||
\(589\) | −1.47110 | − | 2.54801i | −0.0606155 | − | 0.104989i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.01595 | + | 9.09993i | 0.124060 | + | 0.374321i | ||||
\(592\) | −8.51428 | − | 4.91572i | −0.349935 | − | 0.202035i | ||||
\(593\) | − | 38.3421i | − | 1.57452i | −0.616621 | − | 0.787260i | \(-0.711499\pi\) | ||
0.616621 | − | 0.787260i | \(-0.288501\pi\) | |||||||
\(594\) | −1.31955 | + | 15.1117i | −0.0541418 | + | 0.620042i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9.01628 | + | 15.6167i | −0.369321 | + | 0.639683i | ||||
\(597\) | −28.7044 | + | 9.51340i | −1.17479 | + | 0.389358i | ||||
\(598\) | 3.68182 | − | 2.12570i | 0.150561 | − | 0.0869262i | ||||
\(599\) | −5.07665 | − | 8.79301i | −0.207426 | − | 0.359273i | 0.743477 | − | 0.668762i | \(-0.233175\pi\) |
−0.950903 | + | 0.309489i | \(0.899842\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.6371 | − | 18.4241i | 0.433898 | − | 0.751533i | −0.563307 | − | 0.826248i | \(-0.690471\pi\) |
0.997205 | + | 0.0747146i | \(0.0238046\pi\) | |||||||
\(602\) | − | 9.31344i | − | 0.379587i | ||||||
\(603\) | 1.16752 | − | 2.70745i | 0.0475450 | − | 0.110256i | ||||
\(604\) | −18.3219 | −0.745508 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.79846 | − | 4.26878i | 0.154302 | − | 0.173407i | ||||
\(607\) | −32.6799 | + | 18.8678i | −1.32644 | + | 0.765819i | −0.984747 | − | 0.173993i | \(-0.944333\pi\) |
−0.341691 | + | 0.939812i | \(0.611000\pi\) | |||||||
\(608\) | −1.49789 | + | 0.864808i | −0.0607475 | + | 0.0350726i | ||||
\(609\) | −4.97618 | + | 5.59232i | −0.201645 | + | 0.226612i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −24.3698 | −0.985895 | ||||||||
\(612\) | 6.68513 | − | 15.5026i | 0.270230 | − | 0.626657i | ||||
\(613\) | 32.2633i | 1.30310i | 0.758605 | + | 0.651551i | \(0.225881\pi\) | ||||
−0.758605 | + | 0.651551i | \(0.774119\pi\) | |||||||
\(614\) | 8.09699 | − | 14.0244i | 0.326768 | − | 0.565979i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −14.1268 | − | 24.4684i | −0.569186 | − | 0.985860i | ||||
\(617\) | −22.5321 | + | 13.0089i | −0.907108 | + | 0.523719i | −0.879499 | − | 0.475900i | \(-0.842122\pi\) |
−0.0276084 | + | 0.999619i | \(0.508789\pi\) | |||||||
\(618\) | −4.75805 | + | 1.57694i | −0.191397 | + | 0.0634339i | ||||
\(619\) | −5.94077 | + | 10.2897i | −0.238780 | + | 0.413578i | −0.960364 | − | 0.278748i | \(-0.910081\pi\) |
0.721585 | + | 0.692326i | \(0.243414\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.90429 | − | 21.8083i | 0.0764165 | − | 0.875136i | ||||
\(622\) | 10.9037i | 0.437197i | ||||||||
\(623\) | −13.9160 | − | 8.03440i | −0.557532 | − | 0.321891i | ||||
\(624\) | −3.14447 | − | 9.48769i | −0.125879 | − | 0.379811i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0.849799 | + | 1.47189i | 0.0339648 | + | 0.0588288i | ||||
\(627\) | −0.769527 | + | 3.72788i | −0.0307319 | + | 0.148877i | ||||
\(628\) | −1.63439 | − | 0.943614i | −0.0652191 | − | 0.0376543i | ||||
\(629\) | −11.5107 | −0.458962 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.2726 | −0.528372 | −0.264186 | − | 0.964472i | \(-0.585103\pi\) | ||||
−0.264186 | + | 0.964472i | \(0.585103\pi\) | |||||||
\(632\) | −14.6580 | − | 8.46279i | −0.583063 | − | 0.336632i | ||||
\(633\) | 2.11775 | + | 1.88443i | 0.0841731 | + | 0.0748992i | ||||
\(634\) | 3.11890 | + | 5.40210i | 0.123867 | + | 0.214545i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 19.2938 | − | 21.6827i | 0.765048 | − | 0.859774i | ||||
\(637\) | 0.795445 | + | 0.459251i | 0.0315167 | + | 0.0181962i | ||||
\(638\) | 4.92265i | 0.194890i | ||||||||
\(639\) | −15.4839 | + | 11.5300i | −0.612533 | + | 0.456120i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.4075 | + | 38.8109i | −0.885042 | + | 1.53294i | −0.0393765 | + | 0.999224i | \(0.512537\pi\) |
−0.845665 | + | 0.533713i | \(0.820796\pi\) | |||||||
\(642\) | −2.40862 | + | 11.6682i | −0.0950606 | + | 0.460509i | ||||
\(643\) | 12.9259 | − | 7.46275i | 0.509747 | − | 0.294302i | −0.222983 | − | 0.974822i | \(-0.571579\pi\) |
0.732729 | + | 0.680520i | \(0.238246\pi\) | |||||||
\(644\) | 9.58886 | + | 16.6084i | 0.377854 | + | 0.654462i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.267121 | + | 0.462667i | −0.0105097 | + | 0.0182034i | ||||
\(647\) | − | 41.2684i | − | 1.62243i | −0.584749 | − | 0.811214i | \(-0.698807\pi\) | ||
0.584749 | − | 0.811214i | \(-0.301193\pi\) | |||||||
\(648\) | 15.4086 | + | 4.60927i | 0.605306 | + | 0.181069i | ||||
\(649\) | 63.0179 | 2.47367 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.5337 | − | 34.8003i | −0.452043 | − | 1.36393i | ||||
\(652\) | 26.3606 | − | 15.2193i | 1.03236 | − | 0.596034i | ||||
\(653\) | −23.9241 | + | 13.8126i | −0.936223 | + | 0.540528i | −0.888774 | − | 0.458345i | \(-0.848442\pi\) |
−0.0474484 | + | 0.998874i | \(0.515109\pi\) | |||||||
\(654\) | 1.52699 | + | 0.315209i | 0.0597100 | + | 0.0123256i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −7.39788 | −0.288839 | ||||||||
\(657\) | −11.8518 | − | 15.9160i | −0.462383 | − | 0.620943i | ||||
\(658\) | 13.8630i | 0.540435i | ||||||||
\(659\) | 20.0112 | − | 34.6605i | 0.779527 | − | 1.35018i | −0.152688 | − | 0.988274i | \(-0.548793\pi\) |
0.932215 | − | 0.361905i | \(-0.117874\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.4965 | − | 21.6445i | −0.486056 | − | 0.841874i | 0.513816 | − | 0.857901i | \(-0.328232\pi\) |
−0.999872 | + | 0.0160270i | \(0.994898\pi\) | |||||||
\(662\) | 0.484659 | − | 0.279818i | 0.0188368 | − | 0.0108754i | ||||
\(663\) | −8.74245 | − | 7.77924i | −0.339529 | − | 0.302121i | ||||
\(664\) | 9.31018 | − | 16.1257i | 0.361305 | − | 0.625799i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.599338 | − | 5.12269i | −0.0232239 | − | 0.198500i | ||||
\(667\) | − | 7.10405i | − | 0.275070i | ||||||
\(668\) | 6.72675 | + | 3.88369i | 0.260266 | + | 0.150264i | ||||
\(669\) | 13.1426 | + | 2.71296i | 0.508122 | + | 0.104889i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.0339063 | − | 0.0587274i | −0.00130894 | − | 0.00226715i | ||||
\(672\) | −20.4579 | + | 6.78030i | −0.789182 | + | 0.261556i | ||||
\(673\) | −35.3380 | − | 20.4024i | −1.36218 | − | 0.786454i | −0.372265 | − | 0.928126i | \(-0.621419\pi\) |
−0.989914 | + | 0.141672i | \(0.954752\pi\) | |||||||
\(674\) | 11.7365 | 0.452072 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 15.0133 | 0.577436 | ||||||||
\(677\) | −35.6710 | − | 20.5947i | −1.37095 | − | 0.791518i | −0.379901 | − | 0.925027i | \(-0.624042\pi\) |
−0.991048 | + | 0.133509i | \(0.957375\pi\) | |||||||
\(678\) | −5.11919 | + | 1.69663i | −0.196601 | + | 0.0651587i | ||||
\(679\) | 9.23569 | + | 15.9967i | 0.354433 | + | 0.613896i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.1007 | + | 3.94286i | 0.731939 | + | 0.151091i | ||||
\(682\) | −20.8789 | − | 12.0545i | −0.799496 | − | 0.461589i | ||||
\(683\) | − | 1.33820i | − | 0.0512047i | −0.999672 | − | 0.0256023i | \(-0.991850\pi\) | ||
0.999672 | − | 0.0256023i | \(-0.00815037\pi\) | |||||||
\(684\) | 1.74306 | + | 0.751652i | 0.0666476 | + | 0.0287401i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 4.50667 | − | 7.80578i | 0.172065 | − | 0.298026i | ||||
\(687\) | −13.5574 | − | 12.0637i | −0.517249 | − | 0.460261i | ||||
\(688\) | 17.9958 | − | 10.3899i | 0.686083 | − | 0.396110i | ||||
\(689\) | −10.0592 | − | 17.4230i | −0.383225 | − | 0.663764i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.6407 | − | 21.8943i | 0.480874 | − | 0.832898i | −0.518885 | − | 0.854844i | \(-0.673653\pi\) |
0.999759 | + | 0.0219459i | \(0.00698617\pi\) | |||||||
\(692\) | 26.0368i | 0.989770i | ||||||||
\(693\) | −18.7817 | + | 43.5544i | −0.713459 | + | 1.65449i | ||||
\(694\) | −10.4917 | −0.398258 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5.11148 | + | 1.05514i | 0.193750 | + | 0.0399949i | ||||
\(697\) | −7.50106 | + | 4.33074i | −0.284123 | + | 0.164039i | ||||
\(698\) | −6.11435 | + | 3.53012i | −0.231432 | + | 0.133617i | ||||
\(699\) | 1.58137 | + | 4.77142i | 0.0598130 | + | 0.180472i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.2064 | −0.687645 | −0.343822 | − | 0.939035i | \(-0.611722\pi\) | ||||
−0.343822 | + | 0.939035i | \(0.611722\pi\) | |||||||
\(702\) | 3.00685 | − | 4.29576i | 0.113486 | − | 0.162133i | ||||
\(703\) | − | 1.29422i | − | 0.0488126i | ||||||
\(704\) | 9.60795 | − | 16.6415i | 0.362113 | − | 0.627199i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.00244 | − | 6.93242i | −0.150634 | − | 0.260905i | ||||
\(707\) | 15.4732 | − | 8.93344i | 0.581929 | − | 0.335977i | ||||
\(708\) | 6.35315 | − | 30.7770i | 0.238766 | − | 1.15667i | ||||
\(709\) | 20.9103 | − | 36.2177i | 0.785304 | − | 1.36019i | −0.143514 | − | 0.989648i | \(-0.545840\pi\) |
0.928818 | − | 0.370537i | \(-0.120826\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.30184 | + | 28.2216i | 0.123829 | + | 1.05839i | ||||
\(712\) | 11.2036i | 0.419871i | ||||||||
\(713\) | 30.1312 | + | 17.3962i | 1.12842 | + | 0.651494i | ||||
\(714\) | −4.42529 | + | 4.97322i | −0.165612 | + | 0.186118i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.10079 | − | 10.5669i | −0.227997 | − | 0.394903i | ||||
\(717\) | 21.1619 | + | 18.8303i | 0.790304 | + | 0.703231i | ||||
\(718\) | 0.260934 | + | 0.150650i | 0.00973797 | + | 0.00562222i | ||||
\(719\) | −48.9786 | −1.82660 | −0.913298 | − | 0.407293i | \(-0.866473\pi\) | ||||
−0.913298 | + | 0.407293i | \(0.866473\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.6734 | −0.583707 | ||||||||
\(722\) | 7.73514 | + | 4.46588i | 0.287872 | + | 0.166203i | ||||
\(723\) | −6.13610 | + | 29.7255i | −0.228204 | + | 1.10550i | ||||
\(724\) | 9.74236 | + | 16.8743i | 0.362072 | + | 0.627127i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 6.97598 | + | 21.0484i | 0.258903 | + | 0.781179i | ||||
\(727\) | 37.9327 | + | 21.9005i | 1.40685 | + | 0.812243i | 0.995083 | − | 0.0990474i | \(-0.0315796\pi\) |
0.411764 | + | 0.911291i | \(0.364913\pi\) | |||||||
\(728\) | 9.76642i | 0.361968i | ||||||||
\(729\) | −9.24306 | − | 25.3686i | −0.342336 | − | 0.939578i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.1645 | − | 21.0696i | 0.449922 | − | 0.779287i | ||||
\(732\) | −0.0320999 | + | 0.0106387i | −0.00118645 | + | 0.000393219i | ||||
\(733\) | 5.87740 | − | 3.39332i | 0.217087 | − | 0.125335i | −0.387514 | − | 0.921864i | \(-0.626666\pi\) |
0.604601 | + | 0.796529i | \(0.293333\pi\) | |||||||
\(734\) | 4.75572 | + | 8.23715i | 0.175537 | + | 0.304039i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10.2267 | − | 17.7131i | 0.376960 | − | 0.652913i | ||||
\(737\) | − | 6.06261i | − | 0.223319i | ||||||
\(738\) | −2.31790 | − | 3.11276i | −0.0853232 | − | 0.114582i | ||||
\(739\) | −28.7245 | −1.05665 | −0.528324 | − | 0.849043i | \(-0.677179\pi\) | ||||
−0.528324 | + | 0.849043i | \(0.677179\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.874670 | − | 0.982970i | 0.0321318 | − | 0.0361103i | ||||
\(742\) | −9.91125 | + | 5.72226i | −0.363853 | + | 0.210071i | ||||
\(743\) | 27.2385 | − | 15.7262i | 0.999284 | − | 0.576937i | 0.0912477 | − | 0.995828i | \(-0.470915\pi\) |
0.908036 | + | 0.418891i | \(0.137581\pi\) | |||||||
\(744\) | −16.9921 | + | 19.0961i | −0.622962 | + | 0.700096i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −9.29610 | −0.340354 | ||||||||
\(747\) | −31.0475 | + | 3.63246i | −1.13597 | + | 0.132905i | ||||
\(748\) | − | 34.7141i | − | 1.26927i | ||||||
\(749\) | −18.6268 | + | 32.2626i | −0.680610 | + | 1.17885i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.47659 | − | 9.48574i | −0.199844 | − | 0.346139i | 0.748634 | − | 0.662984i | \(-0.230710\pi\) |
−0.948478 | + | 0.316844i | \(0.897377\pi\) | |||||||
\(752\) | −26.7866 | + | 15.4652i | −0.976806 | + | 0.563959i | ||||
\(753\) | 13.9256 | − | 4.61530i | 0.507476 | − | 0.168191i | ||||
\(754\) | 0.850804 | − | 1.47364i | 0.0309845 | − | 0.0536667i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 19.3778 | + | 13.5637i | 0.704765 | + | 0.493306i | ||||
\(757\) | − | 45.7942i | − | 1.66442i | −0.554461 | − | 0.832210i | \(-0.687075\pi\) | ||
0.554461 | − | 0.832210i | \(-0.312925\pi\) | |||||||
\(758\) | −3.25511 | − | 1.87934i | −0.118231 | − | 0.0682607i | ||||
\(759\) | −14.1610 | − | 42.7273i | −0.514010 | − | 1.55090i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.9569 | + | 29.3702i | 0.614687 | + | 1.06467i | 0.990439 | + | 0.137948i | \(0.0440508\pi\) |
−0.375753 | + | 0.926720i | \(0.622616\pi\) | |||||||
\(762\) | −1.53424 | + | 7.43242i | −0.0555796 | + | 0.269248i | ||||
\(763\) | 4.22212 | + | 2.43764i | 0.152851 | + | 0.0882485i | ||||
\(764\) | 24.3894 | 0.882378 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −14.7602 | −0.533309 | ||||||||
\(767\) | −18.8649 | − | 10.8917i | −0.681173 | − | 0.393275i | ||||
\(768\) | −1.21294 | − | 1.07930i | −0.0437680 | − | 0.0389459i | ||||
\(769\) | 3.57986 | + | 6.20050i | 0.129093 | + | 0.223596i | 0.923325 | − | 0.384018i | \(-0.125460\pi\) |
−0.794232 | + | 0.607614i | \(0.792127\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.30737 | + | 3.71688i | −0.119112 | + | 0.133860i | ||||
\(772\) | −0.741933 | − | 0.428355i | −0.0267027 | − | 0.0154168i | ||||
\(773\) | 14.5998i | 0.525117i | 0.964916 | + | 0.262558i | \(0.0845663\pi\) | ||||
−0.964916 | + | 0.262558i | \(0.915434\pi\) | |||||||
\(774\) | 10.0101 | + | 4.31662i | 0.359806 | + | 0.155158i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.43935 | − | 11.1533i | 0.231159 | − | 0.400379i | ||||
\(777\) | 3.26027 | − | 15.7940i | 0.116962 | − | 0.566606i | ||||
\(778\) | 12.8895 | − | 7.44178i | 0.462113 | − | 0.266801i | ||||
\(779\) | −0.486933 | − | 0.843393i | −0.0174462 | − | 0.0302177i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.8477 | + | 34.3772i | −0.710207 | + | 1.23011i | ||||
\(782\) | − | 6.31760i | − | 0.225917i | ||||||
\(783\) | −3.70428 | − | 7.94037i | −0.132380 | − | 0.283766i | ||||
\(784\) | 1.16578 | 0.0416348 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.0694710 | + | 0.209613i | 0.00247795 | + | 0.00747663i | ||||
\(787\) | 15.9979 | − | 9.23638i | 0.570263 | − | 0.329242i | −0.186991 | − | 0.982362i | \(-0.559874\pi\) |
0.757254 | + | 0.653120i | \(0.226540\pi\) | |||||||
\(788\) | 8.51312 | − | 4.91505i | 0.303267 | − | 0.175092i | ||||
\(789\) | 43.4654 | + | 8.97235i | 1.54741 | + | 0.319424i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.8630 | −0.599578 | ||||||||
\(792\) | 32.8463 | − | 3.84291i | 1.16714 | − | 0.136552i | ||||
\(793\) | 0.0234407i | 0.000832405i | ||||||||
\(794\) | 4.19242 | − | 7.26149i | 0.148783 | − | 0.257700i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 15.5039 | + | 26.8535i | 0.549520 | + | 0.951796i | ||||
\(797\) | 35.5395 | − | 20.5187i | 1.25887 | − | 0.726810i | 0.286017 | − | 0.958225i | \(-0.407669\pi\) |
0.972855 | + | 0.231414i | \(0.0743353\pi\) | |||||||
\(798\) | −0.559171 | − | 0.497564i | −0.0197945 | − | 0.0176136i | ||||
\(799\) | −18.1068 | + | 31.3619i | −0.640573 | + | 1.10950i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.0852 | − | 11.2332i | 0.533010 | − | 0.396904i | ||||
\(802\) | − | 3.38021i | − | 0.119359i | ||||||
\(803\) | −35.3367 | − | 20.4016i | −1.24700 | − | 0.719958i | ||||
\(804\) | −2.96089 | − | 0.611202i | −0.104423 | − | 0.0215554i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.16686 | + | 7.21721i | 0.146771 | + | 0.254215i | ||||
\(807\) | −0.554408 | + | 0.183745i | −0.0195161 | + | 0.00646814i | ||||
\(808\) | −10.7883 | − | 6.22861i | −0.379530 | − | 0.219122i | ||||
\(809\) | −7.19375 | −0.252919 | −0.126459 | − | 0.991972i | \(-0.540361\pi\) | ||||
−0.126459 | + | 0.991972i | \(0.540361\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.2183 | 1.34203 | 0.671014 | − | 0.741445i | \(-0.265859\pi\) | ||||
0.671014 | + | 0.741445i | \(0.265859\pi\) | |||||||
\(812\) | 6.64746 | + | 3.83791i | 0.233280 | + | 0.134684i | ||||
\(813\) | 35.5007 | − | 11.7658i | 1.24506 | − | 0.412646i | ||||
\(814\) | −5.30257 | − | 9.18431i | −0.185855 | − | 0.321910i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −14.5462 | − | 3.00271i | −0.509220 | − | 0.105116i | ||||
\(817\) | 2.36899 | + | 1.36774i | 0.0828805 | + | 0.0478511i | ||||
\(818\) | − | 11.7139i | − | 0.409566i | ||||||
\(819\) | 13.1502 | − | 9.79223i | 0.459504 | − | 0.342168i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.334280 | − | 0.578990i | 0.0116665 | − | 0.0202069i | −0.860133 | − | 0.510069i | \(-0.829620\pi\) |
0.871800 | + | 0.489863i | \(0.162953\pi\) | |||||||
\(822\) | 2.12870 | + | 1.89417i | 0.0742470 | + | 0.0660668i | ||||
\(823\) | 1.23004 | − | 0.710165i | 0.0428766 | − | 0.0247548i | −0.478408 | − | 0.878137i | \(-0.658786\pi\) |
0.521285 | + | 0.853383i | \(0.325453\pi\) | |||||||
\(824\) | 5.46393 | + | 9.46380i | 0.190345 | + | 0.329687i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.19583 | + | 10.7315i | −0.215580 | + | 0.373396i | ||||
\(827\) | 49.8169i | 1.73230i | 0.499782 | + | 0.866152i | \(0.333414\pi\) | ||||
−0.499782 | + | 0.866152i | \(0.666586\pi\) | |||||||
\(828\) | −22.2950 | + | 2.60845i | −0.774807 | + | 0.0906498i | ||||
\(829\) | −36.4150 | −1.26475 | −0.632373 | − | 0.774664i | \(-0.717919\pi\) | ||||
−0.632373 | + | 0.774664i | \(0.717919\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −40.9378 | − | 8.45058i | −1.42012 | − | 0.293147i | ||||
\(832\) | −5.75244 | + | 3.32117i | −0.199430 | + | 0.115141i | ||||
\(833\) | 1.18204 | − | 0.682449i | 0.0409551 | − | 0.0236455i | ||||
\(834\) | −3.80312 | − | 11.4750i | −0.131691 | − | 0.397347i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.90312 | 0.134992 | ||||||||
\(837\) | 42.7493 | + | 3.73285i | 1.47763 | + | 0.129026i | ||||
\(838\) | 5.04447i | 0.174258i | ||||||||
\(839\) | −10.0445 | + | 17.3976i | −0.346774 | + | 0.600631i | −0.985674 | − | 0.168659i | \(-0.946056\pi\) |
0.638900 | + | 0.769290i | \(0.279390\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.0783 | + | 22.6523i | 0.450976 | + | 0.781114i | ||||
\(842\) | −3.35201 | + | 1.93528i | −0.115518 | + | 0.0666942i | ||||
\(843\) | −1.17907 | + | 5.71184i | −0.0406092 | + | 0.196726i | ||||
\(844\) | 1.45338 | − | 2.51732i | 0.0500273 | − | 0.0866498i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −14.9000 | − | 6.42525i | −0.512272 | − | 0.220905i | ||||
\(847\) | 69.3349i | 2.38238i | ||||||||
\(848\) | −22.1136 | − | 12.7673i | −0.759383 | − | 0.438430i | ||||
\(849\) | −25.1575 | + | 28.2724i | −0.863402 | + | 0.970307i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.65232 | + | 13.2542i | 0.262318 | + | 0.454349i | ||||
\(852\) | 14.7884 | + | 13.1591i | 0.506642 | + | 0.450823i | ||||
\(853\) | 23.3034 | + | 13.4542i | 0.797892 | + | 0.460663i | 0.842733 | − | 0.538331i | \(-0.180945\pi\) |
−0.0448418 | + | 0.998994i | \(0.514278\pi\) | |||||||
\(854\) | 0.0133345 | 0.000456296 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 25.9742 | 0.887779 | ||||||||
\(857\) | 42.2973 | + | 24.4204i | 1.44485 | + | 0.834184i | 0.998168 | − | 0.0605088i | \(-0.0192723\pi\) |
0.446682 | + | 0.894693i | \(0.352606\pi\) | |||||||
\(858\) | 2.17967 | − | 10.5591i | 0.0744128 | − | 0.360483i | ||||
\(859\) | −20.7047 | − | 35.8616i | −0.706435 | − | 1.22358i | −0.966171 | − | 0.257902i | \(-0.916969\pi\) |
0.259736 | − | 0.965680i | \(-0.416365\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.81767 | − | 11.5189i | −0.130106 | − | 0.392564i | ||||
\(862\) | −0.685465 | − | 0.395754i | −0.0233470 | − | 0.0134794i | ||||
\(863\) | 50.8101i | 1.72960i | 0.502119 | + | 0.864799i | \(0.332554\pi\) | ||||
−0.502119 | + | 0.864799i | \(0.667446\pi\) | |||||||
\(864\) | 2.19441 | − | 25.1308i | 0.0746555 | − | 0.854969i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.35679 | − | 4.08209i | 0.0800871 | − | 0.138715i | ||||
\(867\) | 11.4429 | − | 3.79247i | 0.388621 | − | 0.128799i | ||||
\(868\) | −32.5563 | + | 18.7964i | −1.10503 | + | 0.637991i | ||||
\(869\) | 29.2126 | + | 50.5977i | 0.990970 | + | 1.71641i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.04783 | + | 1.81489i | −0.0355043 | + | 0.0614953i | ||||
\(872\) | − | 3.39916i | − | 0.115110i | ||||||
\(873\) | −21.4739 | + | 2.51237i | −0.726781 | + | 0.0850310i | ||||
\(874\) | 0.710328 | 0.0240272 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −13.5263 | + | 15.2011i | −0.457013 | + | 0.513599i | ||||
\(877\) | −0.354715 | + | 0.204795i | −0.0119779 | + | 0.00691542i | −0.505977 | − | 0.862547i | \(-0.668868\pi\) |
0.493999 | + | 0.869462i | \(0.335535\pi\) | |||||||
\(878\) | −5.25255 | + | 3.03256i | −0.177265 | + | 0.102344i | ||||
\(879\) | −15.8362 | + | 17.7970i | −0.534143 | + | 0.600279i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.32851 | −0.179522 | −0.0897610 | − | 0.995963i | \(-0.528610\pi\) | ||||
−0.0897610 | + | 0.995963i | \(0.528610\pi\) | |||||||
\(882\) | 0.365261 | + | 0.490516i | 0.0122990 | + | 0.0165165i | ||||
\(883\) | 14.2064i | 0.478083i | 0.971009 | + | 0.239042i | \(0.0768333\pi\) | ||||
−0.971009 | + | 0.239042i | \(0.923167\pi\) | |||||||
\(884\) | −5.99979 | + | 10.3919i | −0.201795 | + | 0.349519i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.83482 | + | 3.17800i | 0.0616419 | + | 0.106767i | ||||
\(887\) | −6.26304 | + | 3.61597i | −0.210292 | + | 0.121412i | −0.601447 | − | 0.798913i | \(-0.705409\pi\) |
0.391155 | + | 0.920325i | \(0.372076\pi\) | |||||||
\(888\) | −10.6732 | + | 3.53737i | −0.358169 | + | 0.118706i | ||||
\(889\) | −11.8649 | + | 20.5506i | −0.397936 | + | 0.689245i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −38.1074 | − | 40.3734i | −1.27665 | − | 1.35256i | ||||
\(892\) | − | 13.7604i | − | 0.460733i | ||||||
\(893\) | −3.52622 | − | 2.03586i | −0.118000 | − | 0.0681276i | ||||
\(894\) | 2.61829 | + | 7.90008i | 0.0875688 | + | 0.264218i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 14.3325 | + | 24.8246i | 0.478815 | + | 0.829331i | ||||
\(897\) | −3.14556 | + | 15.2383i | −0.105027 | + | 0.508792i | ||||
\(898\) | −13.6645 | − | 7.88919i | −0.455989 | − | 0.263266i | ||||
\(899\) | 13.9256 | 0.464444 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29.8960 | −0.995981 | ||||||||
\(902\) | −6.91093 | − | 3.99003i | −0.230109 | − | 0.132853i | ||||
\(903\) | 25.4644 | + | 22.6588i | 0.847401 | + | 0.754038i | ||||
\(904\) | 5.87864 | + | 10.1821i | 0.195521 | + | 0.338651i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −5.62130 | + | 6.31731i | −0.186755 | + | 0.209879i | ||||
\(907\) | −33.6106 | − | 19.4051i | −1.11602 | − | 0.644335i | −0.175639 | − | 0.984455i | \(-0.556199\pi\) |
−0.940382 | + | 0.340120i | \(0.889532\pi\) | |||||||
\(908\) | − | 19.9986i | − | 0.663677i | ||||||
\(909\) | 2.43015 | + | 20.7711i | 0.0806031 | + | 0.688935i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.1390 | − | 34.8819i | 0.667236 | − | 1.15569i | −0.311437 | − | 0.950267i | \(-0.600810\pi\) |
0.978674 | − | 0.205421i | \(-0.0658563\pi\) | |||||||
\(912\) | 0.337614 | − | 1.63553i | 0.0111795 | − | 0.0541577i | ||||
\(913\) | −55.6641 | + | 32.1377i | −1.84221 | + | 1.06360i | ||||
\(914\) | −9.04371 | − | 15.6642i | −0.299139 | − | 0.518125i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.30424 | + | 16.1154i | −0.307421 | + | 0.532468i | ||||
\(917\) | 0.690479i | 0.0228016i | ||||||||
\(918\) | −3.29419 | − | 7.06133i | −0.108725 | − | 0.233059i | ||||
\(919\) | 13.0468 | 0.430375 | 0.215187 | − | 0.976573i | \(-0.430964\pi\) | ||||
0.215187 | + | 0.976573i | \(0.430964\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 18.6456 | + | 56.2586i | 0.614392 | + | 1.85378i | ||||
\(922\) | 12.8297 | − | 7.40722i | 0.422523 | − | 0.243944i | ||||
\(923\) | 11.8832 | − | 6.86074i | 0.391139 | − | 0.225824i | ||||
\(924\) | 47.6315 | + | 9.83234i | 1.56696 | + | 0.323460i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 5.71936 | 0.187950 | ||||||||
\(927\) | 7.26433 | − | 16.8458i | 0.238592 | − | 0.553289i | ||||
\(928\) | − | 8.18638i | − | 0.268731i | ||||||
\(929\) | 0.146912 | − | 0.254460i | 0.00482004 | − | 0.00834855i | −0.863605 | − | 0.504168i | \(-0.831799\pi\) |
0.868425 | + | 0.495820i | \(0.165132\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.0767321 | + | 0.132904i | 0.00251479 | + | 0.00435575i | ||||
\(932\) | 4.46374 | − | 2.57714i | 0.146215 | − | 0.0844171i | ||||
\(933\) | −29.8123 | − | 26.5277i | −0.976010 | − | 0.868477i | ||||
\(934\) | −1.79947 | + | 3.11678i | −0.0588805 | + | 0.101984i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −10.4970 | − | 4.52657i | −0.343105 | − | 0.147956i | ||||
\(937\) | − | 16.9141i | − | 0.552559i | −0.961077 | − | 0.276280i | \(-0.910898\pi\) | ||
0.961077 | − | 0.276280i | \(-0.0891016\pi\) | |||||||
\(938\) | 1.03242 | + | 0.596067i | 0.0337097 | + | 0.0194623i | ||||
\(939\) | −6.09187 | − | 1.25752i | −0.198801 | − | 0.0410375i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.6046 | − | 49.5447i | −0.932485 | − | 1.61511i | −0.779059 | − | 0.626951i | \(-0.784303\pi\) |
−0.153426 | − | 0.988160i | \(-0.549031\pi\) | |||||||
\(942\) | −0.826796 | + | 0.274022i | −0.0269385 | + | 0.00892811i | ||||
\(943\) | 9.97342 | + | 5.75815i | 0.324779 | + | 0.187511i | ||||
\(944\) | −27.6478 | −0.899858 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 22.4150 | 0.728775 | ||||||||
\(947\) | 33.6664 | + | 19.4373i | 1.09401 | + | 0.631627i | 0.934641 | − | 0.355592i | \(-0.115721\pi\) |
0.159369 | + | 0.987219i | \(0.449054\pi\) | |||||||
\(948\) | 27.6563 | − | 9.16600i | 0.898234 | − | 0.297698i | ||||
\(949\) | 7.05222 | + | 12.2148i | 0.228925 | + | 0.396509i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22.3582 | − | 4.61529i | −0.725013 | − | 0.149661i | ||||
\(952\) | 12.5686 | + | 7.25648i | 0.407350 | + | 0.235184i | ||||
\(953\) | 54.4516i | 1.76386i | 0.471381 | + | 0.881930i | \(0.343756\pi\) | ||||
−0.471381 | + | 0.881930i | \(0.656244\pi\) | |||||||
\(954\) | −1.55662 | − | 13.3048i | −0.0503974 | − | 0.430760i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 14.5230 | − | 25.1546i | 0.469708 | − | 0.813557i | ||||
\(957\) | −13.4593 | − | 11.9764i | −0.435076 | − | 0.387141i | ||||
\(958\) | 13.3133 | − | 7.68644i | 0.430133 | − | 0.248338i | ||||
\(959\) | 4.45482 | + | 7.71598i | 0.143854 | + | 0.249162i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18.6006 | + | 32.2172i | −0.600020 | + | 1.03926i | ||||
\(962\) | 3.66587i | 0.118192i | ||||||||
\(963\) | −26.0428 | − | 34.9734i | −0.839217 | − | 1.12700i | ||||
\(964\) | 31.1229 | 1.00240 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 8.66844 | + | 1.78938i | 0.278902 | + | 0.0575725i | ||||
\(967\) | −16.9482 | + | 9.78507i | −0.545018 | + | 0.314666i | −0.747110 | − | 0.664700i | \(-0.768559\pi\) |
0.202092 | + | 0.979367i | \(0.435226\pi\) | |||||||
\(968\) | 41.8654 | − | 24.1710i | 1.34560 | − | 0.776885i | ||||
\(969\) | −0.615120 | − | 1.85598i | −0.0197605 | − | 0.0596226i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.31009 | 0.202500 | 0.101250 | − | 0.994861i | \(-0.467716\pi\) | ||||
0.101250 | + | 0.994861i | \(0.467716\pi\) | |||||||
\(972\) | −23.5596 | + | 14.5409i | −0.755674 | + | 0.466399i | ||||
\(973\) | − | 37.7995i | − | 1.21180i | ||||||
\(974\) | −1.05564 | + | 1.82843i | −0.0338250 | + | 0.0585866i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.0148757 | + | 0.0257654i | 0.000476158 | + | 0.000824731i | ||||
\(977\) | 6.42514 | − | 3.70955i | 0.205558 | − | 0.118679i | −0.393687 | − | 0.919244i | \(-0.628801\pi\) |
0.599245 | + | 0.800565i | \(0.295467\pi\) | |||||||
\(978\) | 2.84008 | − | 13.7584i | 0.0908158 | − | 0.439946i | ||||
\(979\) | 19.3367 | − | 33.4922i | 0.618004 | − | 1.07041i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.57686 | + | 3.40814i | −0.146128 | + | 0.108814i | ||||
\(982\) | 15.5426i | 0.495986i | ||||||||
\(983\) | −9.51134 | − | 5.49137i | −0.303365 | − | 0.175148i | 0.340589 | − | 0.940212i | \(-0.389374\pi\) |
−0.643953 | + | 0.765065i | \(0.722707\pi\) | |||||||
\(984\) | −5.62440 | + | 6.32080i | −0.179299 | + | 0.201500i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.26430 | − | 2.18983i | −0.0402635 | − | 0.0697384i | ||||
\(987\) | −37.9035 | − | 33.7274i | −1.20648 | − | 1.07356i | ||||
\(988\) | −1.16843 | − | 0.674595i | −0.0371728 | − | 0.0214617i | ||||
\(989\) | −32.3479 | −1.02860 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.3721 | −0.678908 | −0.339454 | − | 0.940623i | \(-0.610242\pi\) | ||||
−0.339454 | + | 0.940623i | \(0.610242\pi\) | |||||||
\(992\) | 34.7217 | + | 20.0466i | 1.10242 | + | 0.636480i | ||||
\(993\) | −0.414069 | + | 2.00591i | −0.0131401 | + | 0.0636555i | ||||
\(994\) | −3.90280 | − | 6.75984i | −0.123789 | − | 0.214409i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 10.0838 | + | 30.4255i | 0.319518 | + | 0.964070i | ||||
\(997\) | 26.4439 | + | 15.2674i | 0.837487 | + | 0.483524i | 0.856409 | − | 0.516297i | \(-0.172690\pi\) |
−0.0189220 | + | 0.999821i | \(0.506023\pi\) | |||||||
\(998\) | 16.1863i | 0.512368i | ||||||||
\(999\) | 15.4644 | + | 10.8244i | 0.489271 | + | 0.342469i |
(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 | 225.2.k.c.124.4 | 16 | ||
3.2 | odd | 2 | 675.2.k.c.424.5 | 16 | |||
5.2 | odd | 4 | 225.2.e.c.151.3 | yes | 8 | ||
5.3 | odd | 4 | 225.2.e.e.151.2 | yes | 8 | ||
5.4 | even | 2 | inner | 225.2.k.c.124.5 | 16 | ||
9.2 | odd | 6 | 2025.2.b.o.649.4 | 8 | |||
9.4 | even | 3 | inner | 225.2.k.c.49.5 | 16 | ||
9.5 | odd | 6 | 675.2.k.c.199.4 | 16 | |||
9.7 | even | 3 | 2025.2.b.n.649.5 | 8 | |||
15.2 | even | 4 | 675.2.e.e.451.2 | 8 | |||
15.8 | even | 4 | 675.2.e.c.451.3 | 8 | |||
15.14 | odd | 2 | 675.2.k.c.424.4 | 16 | |||
45.2 | even | 12 | 2025.2.a.p.1.3 | 4 | |||
45.4 | even | 6 | inner | 225.2.k.c.49.4 | 16 | ||
45.7 | odd | 12 | 2025.2.a.y.1.2 | 4 | |||
45.13 | odd | 12 | 225.2.e.e.76.2 | yes | 8 | ||
45.14 | odd | 6 | 675.2.k.c.199.5 | 16 | |||
45.22 | odd | 12 | 225.2.e.c.76.3 | ✓ | 8 | ||
45.23 | even | 12 | 675.2.e.c.226.3 | 8 | |||
45.29 | odd | 6 | 2025.2.b.o.649.5 | 8 | |||
45.32 | even | 12 | 675.2.e.e.226.2 | 8 | |||
45.34 | even | 6 | 2025.2.b.n.649.4 | 8 | |||
45.38 | even | 12 | 2025.2.a.z.1.2 | 4 | |||
45.43 | odd | 12 | 2025.2.a.q.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
225.2.e.c.76.3 | ✓ | 8 | 45.22 | odd | 12 | ||
225.2.e.c.151.3 | yes | 8 | 5.2 | odd | 4 | ||
225.2.e.e.76.2 | yes | 8 | 45.13 | odd | 12 | ||
225.2.e.e.151.2 | yes | 8 | 5.3 | odd | 4 | ||
225.2.k.c.49.4 | 16 | 45.4 | even | 6 | inner | ||
225.2.k.c.49.5 | 16 | 9.4 | even | 3 | inner | ||
225.2.k.c.124.4 | 16 | 1.1 | even | 1 | trivial | ||
225.2.k.c.124.5 | 16 | 5.4 | even | 2 | inner | ||
675.2.e.c.226.3 | 8 | 45.23 | even | 12 | |||
675.2.e.c.451.3 | 8 | 15.8 | even | 4 | |||
675.2.e.e.226.2 | 8 | 45.32 | even | 12 | |||
675.2.e.e.451.2 | 8 | 15.2 | even | 4 | |||
675.2.k.c.199.4 | 16 | 9.5 | odd | 6 | |||
675.2.k.c.199.5 | 16 | 45.14 | odd | 6 | |||
675.2.k.c.424.4 | 16 | 15.14 | odd | 2 | |||
675.2.k.c.424.5 | 16 | 3.2 | odd | 2 | |||
2025.2.a.p.1.3 | 4 | 45.2 | even | 12 | |||
2025.2.a.q.1.3 | 4 | 45.43 | odd | 12 | |||
2025.2.a.y.1.2 | 4 | 45.7 | odd | 12 | |||
2025.2.a.z.1.2 | 4 | 45.38 | even | 12 | |||
2025.2.b.n.649.4 | 8 | 45.34 | even | 6 | |||
2025.2.b.n.649.5 | 8 | 9.7 | even | 3 | |||
2025.2.b.o.649.4 | 8 | 9.2 | odd | 6 | |||
2025.2.b.o.649.5 | 8 | 45.29 | odd | 6 |