Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,2,Mod(76,225)]
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, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.76");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.e (of order \(3\), 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: | \(1.79663404548\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.1223810289.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 8x^{6} - 2x^{5} + 23x^{4} - 8x^{3} + 37x^{2} + 15x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 151.3 | ||
Root | \(-0.236627 + 0.409850i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.151 |
Dual form | 225.2.e.c.76.3 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.236627 | − | 0.409850i | 0.167321 | − | 0.289808i | −0.770156 | − | 0.637855i | \(-0.779822\pi\) |
0.937477 | + | 0.348047i | \(0.113155\pi\) | |||||||
\(3\) | −0.544899 | − | 1.64411i | −0.314598 | − | 0.949225i | ||||
\(4\) | 0.888015 | + | 1.53809i | 0.444008 | + | 0.769044i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.802776 | − | 0.165713i | −0.327732 | − | 0.0676521i | ||||
\(7\) | 1.28153 | − | 2.21967i | 0.484372 | − | 0.838956i | −0.515467 | − | 0.856909i | \(-0.672382\pi\) |
0.999839 | + | 0.0179531i | \(0.00571495\pi\) | |||||||
\(8\) | 1.78702 | 0.631808 | ||||||||
\(9\) | −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 | \(-0.213485\pi\) | |||||||
\(12\) | 2.04490 | − | 2.29809i | 0.590312 | − | 0.663403i | ||||
\(13\) | 1.06615 | + | 1.84662i | 0.295696 | + | 0.512161i | 0.975147 | − | 0.221560i | \(-0.0711150\pi\) |
−0.679450 | + | 0.733722i | \(0.737782\pi\) | |||||||
\(14\) | −0.606488 | − | 1.05047i | −0.162091 | − | 0.280750i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.35317 | + | 2.34376i | −0.338293 | + | 0.585941i | ||||
\(17\) | −3.16860 | −0.768500 | −0.384250 | − | 0.923229i | \(-0.625540\pi\) | ||||
−0.384250 | + | 0.923229i | \(0.625540\pi\) | |||||||
\(18\) | 0.164982 | + | 1.41015i | 0.0388867 | + | 0.332374i | ||||
\(19\) | 0.356267 | 0.0817332 | 0.0408666 | − | 0.999165i | \(-0.486988\pi\) | ||||
0.0408666 | + | 0.999165i | \(0.486988\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.34768 | − | 0.897469i | −0.948740 | − | 0.195844i | ||||
\(22\) | −1.45966 | − | 2.52821i | −0.311201 | − | 0.539015i | ||||
\(23\) | −2.10649 | − | 3.64854i | −0.439233 | − | 0.760774i | 0.558397 | − | 0.829574i | \(-0.311416\pi\) |
−0.997631 | + | 0.0687995i | \(0.978083\pi\) | |||||||
\(24\) | −0.973748 | − | 2.93806i | −0.198766 | − | 0.599728i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.00912 | 0.197905 | ||||||||
\(27\) | 4.25694 | + | 2.97968i | 0.819248 | + | 0.573439i | ||||
\(28\) | 4.55206 | 0.860259 | ||||||||
\(29\) | −0.843116 | + | 1.46032i | −0.156563 | + | 0.271174i | −0.933627 | − | 0.358247i | \(-0.883375\pi\) |
0.777064 | + | 0.629421i | \(0.216708\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.12920 | + | 7.15199i | 0.741627 | + | 1.28453i | 0.951754 | + | 0.306861i | \(0.0992787\pi\) |
−0.210128 | + | 0.977674i | \(0.567388\pi\) | |||||||
\(32\) | 2.42742 | + | 4.20441i | 0.429111 | + | 0.743242i | ||||
\(33\) | −10.4637 | − | 2.15998i | −1.82150 | − | 0.376003i | ||||
\(34\) | −0.749778 | + | 1.29865i | −0.128586 | + | 0.222717i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.89257 | − | 2.10980i | −0.815429 | − | 0.351634i | ||||
\(37\) | −3.63274 | −0.597219 | −0.298609 | − | 0.954375i | \(-0.596523\pi\) | ||||
−0.298609 | + | 0.954375i | \(0.596523\pi\) | |||||||
\(38\) | 0.0843024 | − | 0.146016i | 0.0136757 | − | 0.0236869i | ||||
\(39\) | 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 | \(0.764862\pi\) | |||||||
\(42\) | −1.39661 | + | 1.56953i | −0.215501 | + | 0.242184i | ||||
\(43\) | −3.83908 | + | 6.64949i | −0.585455 | + | 1.01404i | 0.409364 | + | 0.912371i | \(0.365751\pi\) |
−0.994819 | + | 0.101666i | \(0.967583\pi\) | |||||||
\(44\) | 10.9556 | 1.65162 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.99381 | −0.293971 | ||||||||
\(47\) | −5.71444 | + | 9.89770i | −0.833537 | + | 1.44373i | 0.0616792 | + | 0.998096i | \(0.480354\pi\) |
−0.895216 | + | 0.445632i | \(0.852979\pi\) | |||||||
\(48\) | 4.59074 | + | 0.947643i | 0.662616 | + | 0.136780i | ||||
\(49\) | 0.215378 | + | 0.373046i | 0.0307683 | + | 0.0532923i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.72657 | + | 5.20952i | 0.241768 | + | 0.729479i | ||||
\(52\) | −1.89351 | + | 3.27966i | −0.262583 | + | 0.454807i | ||||
\(53\) | 9.43507 | 1.29601 | 0.648003 | − | 0.761637i | \(-0.275604\pi\) | ||||
0.648003 | + | 0.761637i | \(0.275604\pi\) | |||||||
\(54\) | 2.22853 | − | 1.03964i | 0.303264 | − | 0.141477i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.29012 | − | 3.96660i | 0.306030 | − | 0.530059i | ||||
\(57\) | −0.194129 | − | 0.585740i | −0.0257131 | − | 0.0775832i | ||||
\(58\) | 0.399008 | + | 0.691103i | 0.0523924 | + | 0.0907462i | ||||
\(59\) | −5.10795 | − | 8.84723i | −0.664999 | − | 1.15181i | −0.979286 | − | 0.202484i | \(-0.935099\pi\) |
0.314287 | − | 0.949328i | \(-0.398235\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.00549659 | − | 0.00952038i | 0.000703767 | − | 0.00121896i | −0.865673 | − | 0.500609i | \(-0.833109\pi\) |
0.866377 | + | 0.499390i | \(0.166443\pi\) | |||||||
\(62\) | 3.90833 | 0.496358 | ||||||||
\(63\) | 0.893512 | + | 7.63707i | 0.112572 | + | 0.962180i | ||||
\(64\) | −3.11511 | −0.389389 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.36127 | + | 3.77745i | −0.413744 | + | 0.464972i | ||||
\(67\) | 0.491409 | + | 0.851145i | 0.0600351 | + | 0.103984i | 0.894481 | − | 0.447106i | \(-0.147545\pi\) |
−0.834446 | + | 0.551090i | \(0.814212\pi\) | |||||||
\(68\) | −2.81377 | − | 4.87359i | −0.341220 | − | 0.591010i | ||||
\(69\) | −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 | \(0.624713\pi\) | |||||||
\(72\) | −4.29988 | + | 3.20189i | −0.506746 | + | 0.377346i | ||||
\(73\) | −6.61467 | −0.774189 | −0.387094 | − | 0.922040i | \(-0.626521\pi\) | ||||
−0.387094 | + | 0.922040i | \(0.626521\pi\) | |||||||
\(74\) | −0.859605 | + | 1.48888i | −0.0999271 | + | 0.173079i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.316370 | + | 0.547969i | 0.0362901 | + | 0.0628564i | ||||
\(77\) | −7.90523 | − | 13.6923i | −0.900885 | − | 1.56038i | ||||
\(78\) | −0.549868 | − | 1.65910i | −0.0622603 | − | 0.187856i | ||||
\(79\) | 4.73569 | − | 8.20246i | 0.532807 | − | 0.922848i | −0.466459 | − | 0.884543i | \(-0.654471\pi\) |
0.999266 | − | 0.0383057i | \(-0.0121961\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.57930 | − | 8.62248i | 0.286589 | − | 0.958054i | ||||
\(82\) | 1.29366 | 0.142860 | ||||||||
\(83\) | −5.20988 | + | 9.02378i | −0.571859 | + | 0.990489i | 0.424516 | + | 0.905420i | \(0.360444\pi\) |
−0.996375 | + | 0.0850682i | \(0.972889\pi\) | |||||||
\(84\) | −2.48042 | − | 7.48407i | −0.270636 | − | 0.816579i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.81686 | + | 3.14690i | 0.195917 | + | 0.339339i | ||||
\(87\) | 2.86033 | + | 0.590444i | 0.306660 | + | 0.0633023i | ||||
\(88\) | 5.51172 | − | 9.54658i | 0.587551 | − | 1.01767i | ||||
\(89\) | −6.26940 | −0.664555 | −0.332277 | − | 0.943182i | \(-0.607817\pi\) | ||||
−0.332277 | + | 0.943182i | \(0.607817\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.46519 | 0.572908 | ||||||||
\(92\) | 3.74119 | − | 6.47993i | 0.390046 | − | 0.675579i | ||||
\(93\) | 9.50863 | − | 10.6860i | 0.985999 | − | 1.10808i | ||||
\(94\) | 2.70439 | + | 4.68413i | 0.278936 | + | 0.483131i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 5.58980 | − | 6.28191i | 0.570506 | − | 0.641145i | ||||
\(97\) | 3.60339 | − | 6.24126i | 0.365869 | − | 0.633704i | −0.623046 | − | 0.782185i | \(-0.714105\pi\) |
0.988915 | + | 0.148481i | \(0.0474384\pi\) | |||||||
\(98\) | 0.203858 | 0.0205927 | ||||||||
\(99\) | 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 | \(0.279404\pi\) | |||||||
\(102\) | 2.54368 | + | 0.525079i | 0.251862 | + | 0.0519906i | ||||
\(103\) | −3.05756 | − | 5.29584i | −0.301270 | − | 0.521815i | 0.675154 | − | 0.737677i | \(-0.264077\pi\) |
−0.976424 | + | 0.215862i | \(0.930744\pi\) | |||||||
\(104\) | 1.90523 | + | 3.29996i | 0.186823 | + | 0.323588i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.23260 | − | 3.86697i | 0.216849 | − | 0.375593i | ||||
\(107\) | 14.5349 | 1.40514 | 0.702570 | − | 0.711615i | \(-0.252036\pi\) | ||||
0.702570 | + | 0.711615i | \(0.252036\pi\) | |||||||
\(108\) | −0.802776 | + | 9.19354i | −0.0772471 | + | 0.884649i | ||||
\(109\) | 1.90214 | 0.182192 | 0.0910958 | − | 0.995842i | \(-0.470963\pi\) | ||||
0.0910958 | + | 0.995842i | \(0.470963\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.97948 | + | 5.97261i | 0.187884 | + | 0.566895i | ||||
\(112\) | 3.46825 | + | 6.00719i | 0.327719 | + | 0.567626i | ||||
\(113\) | −3.28962 | − | 5.69780i | −0.309462 | − | 0.536004i | 0.668783 | − | 0.743458i | \(-0.266816\pi\) |
−0.978245 | + | 0.207454i | \(0.933482\pi\) | |||||||
\(114\) | −0.286002 | − | 0.0590380i | −0.0267866 | − | 0.00552942i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.99480 | −0.278060 | ||||||||
\(117\) | −5.87401 | − | 2.53302i | −0.543053 | − | 0.234178i | ||||
\(118\) | −4.83472 | −0.445072 | ||||||||
\(119\) | −4.06065 | + | 7.03326i | −0.372239 | + | 0.644737i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13.5258 | − | 23.4274i | −1.22962 | − | 2.12977i | ||||
\(122\) | −0.00260129 | − | 0.00450556i | −0.000235509 | − | 0.000407914i | ||||
\(123\) | 3.14736 | − | 3.53705i | 0.283788 | − | 0.318925i | ||||
\(124\) | −7.33359 | + | 12.7021i | −0.658576 | + | 1.14069i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.34149 | + | 1.44093i | 0.297683 | + | 0.128368i | ||||
\(127\) | 9.25840 | 0.821550 | 0.410775 | − | 0.911737i | \(-0.365258\pi\) | ||||
0.410775 | + | 0.911737i | \(0.365258\pi\) | |||||||
\(128\) | −5.59196 | + | 9.68555i | −0.494264 | + | 0.856090i | ||||
\(129\) | 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 | \(0.837080\pi\) | |||||||
\(132\) | −5.96972 | − | 18.0122i | −0.519597 | − | 1.56776i | ||||
\(133\) | 0.456565 | − | 0.790794i | 0.0395892 | − | 0.0685705i | ||||
\(134\) | 0.465123 | 0.0401805 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.66237 | −0.485544 | ||||||||
\(137\) | 1.73809 | − | 3.01046i | 0.148495 | − | 0.257201i | −0.782176 | − | 0.623057i | \(-0.785890\pi\) |
0.930671 | + | 0.365856i | \(0.119224\pi\) | |||||||
\(138\) | 1.08643 | + | 3.27804i | 0.0924827 | + | 0.279045i | ||||
\(139\) | −7.37393 | − | 12.7720i | −0.625448 | − | 1.08331i | −0.988454 | − | 0.151521i | \(-0.951583\pi\) |
0.363006 | − | 0.931787i | \(-0.381751\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 19.3867 | + | 4.00189i | 1.63265 | + | 0.337020i | ||||
\(142\) | −1.52271 | + | 2.63742i | −0.127783 | + | 0.221327i | ||||
\(143\) | 13.1533 | 1.09993 | ||||||||
\(144\) | −0.943464 | − | 8.06403i | −0.0786220 | − | 0.672002i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.56521 | + | 2.71103i | −0.129538 | + | 0.224366i | ||||
\(147\) | 0.495968 | − | 0.557378i | 0.0409068 | − | 0.0459717i | ||||
\(148\) | −3.22593 | − | 5.58747i | −0.265170 | − | 0.459287i | ||||
\(149\) | 5.07665 | + | 8.79301i | 0.415895 | + | 0.720352i | 0.995522 | − | 0.0945305i | \(-0.0301350\pi\) |
−0.579627 | + | 0.814882i | \(0.696802\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.15811 | − | 8.93410i | 0.419761 | − | 0.727047i | −0.576155 | − | 0.817341i | \(-0.695447\pi\) |
0.995915 | + | 0.0902940i | \(0.0287807\pi\) | |||||||
\(152\) | 0.636657 | 0.0516397 | ||||||||
\(153\) | 7.62420 | − | 5.67733i | 0.616380 | − | 0.458985i | ||||
\(154\) | −7.48237 | −0.602947 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.42388 | + | 1.32605i | 0.514322 | + | 0.106169i | ||||
\(157\) | 0.531305 | + | 0.920247i | 0.0424028 | + | 0.0734437i | 0.886448 | − | 0.462828i | \(-0.153165\pi\) |
−0.844045 | + | 0.536272i | \(0.819832\pi\) | |||||||
\(158\) | −2.24119 | − | 3.88185i | −0.178299 | − | 0.308823i | ||||
\(159\) | −5.14117 | − | 15.5123i | −0.407721 | − | 1.23020i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.7981 | −0.851008 | ||||||||
\(162\) | −2.92360 | − | 3.09744i | −0.229699 | − | 0.243358i | ||||
\(163\) | 17.1386 | 1.34240 | 0.671198 | − | 0.741278i | \(-0.265780\pi\) | ||||
0.671198 | + | 0.741278i | \(0.265780\pi\) | |||||||
\(164\) | −2.42742 | + | 4.20441i | −0.189549 | + | 0.328309i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.46560 | + | 4.27054i | 0.191368 | + | 0.331459i | ||||
\(167\) | −2.18672 | − | 3.78752i | −0.169214 | − | 0.293087i | 0.768930 | − | 0.639333i | \(-0.220790\pi\) |
−0.938144 | + | 0.346246i | \(0.887456\pi\) | |||||||
\(168\) | −7.76940 | − | 1.60380i | −0.599422 | − | 0.123736i | ||||
\(169\) | 4.22666 | − | 7.32078i | 0.325127 | − | 0.563137i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.857238 | + | 0.638339i | −0.0655546 | + | 0.0488150i | ||||
\(172\) | −13.6367 | −1.03979 | ||||||||
\(173\) | −7.33005 | + | 12.6960i | −0.557293 | + | 0.965260i | 0.440428 | + | 0.897788i | \(0.354827\pi\) |
−0.997721 | + | 0.0674723i | \(0.978507\pi\) | |||||||
\(174\) | 0.918827 | − | 1.03259i | 0.0696561 | − | 0.0782807i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 8.34718 | + | 14.4577i | 0.629192 | + | 1.08979i | ||||
\(177\) | −11.7625 | + | 13.2189i | −0.884121 | + | 0.993591i | ||||
\(178\) | −1.48351 | + | 2.56952i | −0.111194 | + | 0.192593i | ||||
\(179\) | −6.87014 | −0.513499 | −0.256749 | − | 0.966478i | \(-0.582651\pi\) | ||||
−0.256749 | + | 0.966478i | \(0.582651\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.9709 | −0.815463 | −0.407732 | − | 0.913102i | \(-0.633680\pi\) | ||||
−0.407732 | + | 0.913102i | \(0.633680\pi\) | |||||||
\(182\) | 1.29321 | − | 2.23991i | 0.0958593 | − | 0.166033i | ||||
\(183\) | −0.0186476 | − | 0.00384933i | −0.00137847 | − | 0.000284551i | ||||
\(184\) | −3.76434 | − | 6.52003i | −0.277511 | − | 0.480663i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.12965 | − | 6.42570i | −0.156153 | − | 0.471155i | ||||
\(187\) | −9.77294 | + | 16.9272i | −0.714668 | + | 1.23784i | ||||
\(188\) | −20.2980 | −1.48039 | ||||||||
\(189\) | 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 | \(0.332168\pi\) | |||||||
\(192\) | 1.69742 | + | 5.12158i | 0.122501 | + | 0.369618i | ||||
\(193\) | −0.241187 | − | 0.417748i | −0.0173610 | − | 0.0300701i | 0.857214 | − | 0.514960i | \(-0.172193\pi\) |
−0.874575 | + | 0.484890i | \(0.838860\pi\) | |||||||
\(194\) | −1.70532 | − | 2.95370i | −0.122435 | − | 0.212064i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.382518 | + | 0.662541i | −0.0273227 | + | 0.0473244i | ||||
\(197\) | −5.53488 | −0.394344 | −0.197172 | − | 0.980369i | \(-0.563176\pi\) | ||||
−0.197172 | + | 0.980369i | \(0.563176\pi\) | |||||||
\(198\) | 8.04209 | + | 3.46795i | 0.571526 | + | 0.246457i | ||||
\(199\) | 17.4590 | 1.23764 | 0.618818 | − | 0.785534i | \(-0.287612\pi\) | ||||
0.618818 | + | 0.785534i | \(0.287612\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.13160 | − | 1.27172i | 0.0798172 | − | 0.0896999i | ||||
\(202\) | 1.64951 | + | 2.85704i | 0.116059 | + | 0.201021i | ||||
\(203\) | 2.16095 | + | 3.74288i | 0.151669 | + | 0.262698i | ||||
\(204\) | −6.47948 | + | 7.28175i | −0.453654 | + | 0.509825i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.89401 | −0.201635 | ||||||||
\(207\) | 11.6058 | + | 5.00473i | 0.806661 | + | 0.347852i | ||||
\(208\) | −5.77073 | −0.400128 | ||||||||
\(209\) | 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 | \(0.815392\pi\) | |||||||
\(212\) | 8.37849 | + | 14.5120i | 0.575437 | + | 0.996686i | ||||
\(213\) | 3.50647 | + | 10.5799i | 0.240259 | + | 0.724926i | ||||
\(214\) | 3.43935 | − | 5.95713i | 0.235109 | − | 0.407221i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 7.60725 | + | 5.32475i | 0.517608 | + | 0.362303i | ||||
\(217\) | 21.1667 | 1.43689 | ||||||||
\(218\) | 0.450098 | − | 0.779592i | 0.0304844 | − | 0.0528006i | ||||
\(219\) | 3.60433 | + | 10.8752i | 0.243558 | + | 0.734879i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.37820 | − | 5.85122i | −0.227243 | − | 0.393596i | ||||
\(222\) | 2.91628 | + | 0.601992i | 0.195728 | + | 0.0404031i | ||||
\(223\) | 3.87393 | − | 6.70984i | 0.259417 | − | 0.449324i | −0.706669 | − | 0.707545i | \(-0.749803\pi\) |
0.966086 | + | 0.258221i | \(0.0831362\pi\) | |||||||
\(224\) | 12.4432 | 0.831397 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.11366 | −0.207118 | ||||||||
\(227\) | −5.63014 | + | 9.75169i | −0.373685 | + | 0.647242i | −0.990129 | − | 0.140157i | \(-0.955239\pi\) |
0.616444 | + | 0.787399i | \(0.288573\pi\) | |||||||
\(228\) | 0.728529 | − | 0.818734i | 0.0482480 | − | 0.0542220i | ||||
\(229\) | 5.23879 | + | 9.07384i | 0.346189 | + | 0.599616i | 0.985569 | − | 0.169274i | \(-0.0541424\pi\) |
−0.639380 | + | 0.768891i | \(0.720809\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −18.2040 | + | 20.4579i | −1.19773 | + | 1.34603i | ||||
\(232\) | −1.50667 | + | 2.60962i | −0.0989176 | + | 0.171330i | ||||
\(233\) | 2.90214 | 0.190125 | 0.0950627 | − | 0.995471i | \(-0.469695\pi\) | ||||
0.0950627 | + | 0.995471i | \(0.469695\pi\) | |||||||
\(234\) | −2.42811 | + | 1.80808i | −0.158731 | + | 0.118198i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 9.07188 | − | 15.7130i | 0.590529 | − | 1.02283i | ||||
\(237\) | −16.0662 | − | 3.31646i | −1.04361 | − | 0.215427i | ||||
\(238\) | 1.92172 | + | 3.32852i | 0.124567 | + | 0.215756i | ||||
\(239\) | −8.17723 | − | 14.1634i | −0.528941 | − | 0.916153i | −0.999430 | − | 0.0337471i | \(-0.989256\pi\) |
0.470489 | − | 0.882406i | \(-0.344077\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.76194 | + | 15.1761i | −0.564406 | + | 0.977580i | 0.432698 | + | 0.901539i | \(0.357562\pi\) |
−0.997105 | + | 0.0760416i | \(0.975772\pi\) | |||||||
\(242\) | −12.8023 | −0.822965 | ||||||||
\(243\) | −15.5817 | + | 0.457745i | −0.999569 | + | 0.0293644i | ||||
\(244\) | 0.0195242 | 0.00124991 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.704913 | − | 2.12691i | −0.0449436 | − | 0.135607i | ||||
\(247\) | 0.379833 | + | 0.657890i | 0.0241682 | + | 0.0418605i | ||||
\(248\) | 7.37898 | + | 12.7808i | 0.468566 | + | 0.811580i | ||||
\(249\) | 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 | \(0.413865\pi\) | |||||||
\(252\) | −10.9530 | + | 8.15613i | −0.689976 | + | 0.513788i | ||||
\(253\) | −25.9882 | −1.63386 | ||||||||
\(254\) | 2.19079 | − | 3.79456i | 0.137462 | − | 0.238092i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.468695 | − | 0.811804i | −0.0292934 | − | 0.0507377i | ||||
\(257\) | −1.43625 | − | 2.48766i | −0.0895910 | − | 0.155176i | 0.817747 | − | 0.575577i | \(-0.195223\pi\) |
−0.907338 | + | 0.420401i | \(0.861889\pi\) | |||||||
\(258\) | 4.18383 | − | 4.70186i | 0.260474 | − | 0.292725i | ||||
\(259\) | −4.65545 | + | 8.06348i | −0.289276 | + | 0.501040i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.587841 | − | 5.02442i | −0.0363864 | − | 0.311004i | ||||
\(262\) | −0.127493 | −0.00787656 | ||||||||
\(263\) | 12.8119 | − | 22.1909i | 0.790017 | − | 1.36835i | −0.135938 | − | 0.990717i | \(-0.543405\pi\) |
0.925955 | − | 0.377633i | \(-0.123262\pi\) | |||||||
\(264\) | −18.6989 | − | 3.85993i | −1.15084 | − | 0.237562i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.216072 | − | 0.374247i | −0.0132482 | − | 0.0229465i | ||||
\(267\) | 3.41619 | + | 10.3076i | 0.209068 | + | 0.630812i | ||||
\(268\) | −0.872756 | + | 1.51166i | −0.0533121 | + | 0.0923392i | ||||
\(269\) | 0.337210 | 0.0205600 | 0.0102800 | − | 0.999947i | \(-0.496728\pi\) | ||||
0.0102800 | + | 0.999947i | \(0.496728\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.5927 | 1.31166 | 0.655831 | − | 0.754908i | \(-0.272318\pi\) | ||||
0.655831 | + | 0.754908i | \(0.272318\pi\) | |||||||
\(272\) | 4.28767 | − | 7.42646i | 0.259978 | − | 0.450295i | ||||
\(273\) | −2.97798 | − | 8.98535i | −0.180236 | − | 0.543818i | ||||
\(274\) | −0.822560 | − | 1.42472i | −0.0496927 | − | 0.0860702i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −12.6923 | − | 2.62000i | −0.763984 | − | 0.157705i | ||||
\(277\) | 12.0669 | − | 20.9004i | 0.725028 | − | 1.25579i | −0.233934 | − | 0.972252i | \(-0.575160\pi\) |
0.958962 | − | 0.283533i | \(-0.0915067\pi\) | |||||||
\(278\) | −6.97949 | −0.418602 | ||||||||
\(279\) | −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 | \(0.198691\pi\) | |||||||
\(282\) | 6.22759 | − | 6.99868i | 0.370848 | − | 0.416765i | ||||
\(283\) | 10.9249 | + | 18.9224i | 0.649415 | + | 1.12482i | 0.983263 | + | 0.182193i | \(0.0583195\pi\) |
−0.333848 | + | 0.942627i | \(0.608347\pi\) | |||||||
\(284\) | −5.71444 | − | 9.89770i | −0.339090 | − | 0.587321i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.11243 | − | 5.39088i | 0.184042 | − | 0.318770i | ||||
\(287\) | 7.00619 | 0.413562 | ||||||||
\(288\) | −13.3740 | − | 5.76721i | −0.788071 | − | 0.339836i | ||||
\(289\) | −6.95994 | −0.409408 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.2248 | − | 2.52350i | −0.716629 | − | 0.147930i | ||||
\(292\) | −5.87393 | − | 10.1739i | −0.343746 | − | 0.595385i | ||||
\(293\) | 6.87702 | + | 11.9114i | 0.401760 | + | 0.695869i | 0.993938 | − | 0.109938i | \(-0.0350653\pi\) |
−0.592179 | + | 0.805807i | \(0.701732\pi\) | |||||||
\(294\) | −0.111082 | − | 0.335163i | −0.00647843 | − | 0.0195471i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.49179 | −0.377328 | ||||||||
\(297\) | 29.0476 | − | 13.5511i | 1.68551 | − | 0.786312i | ||||
\(298\) | 4.80509 | 0.278352 | ||||||||
\(299\) | 4.49166 | − | 7.77978i | 0.259759 | − | 0.449916i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.83978 | + | 17.0430i | 0.567155 | + | 0.982342i | ||||
\(302\) | −2.44110 | − | 4.22810i | −0.140469 | − | 0.243300i | ||||
\(303\) | 11.8247 | + | 2.44092i | 0.679312 | + | 0.140227i | ||||
\(304\) | −0.482090 | + | 0.835004i | −0.0276498 | + | 0.0478908i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.522764 | − | 4.46819i | −0.0298844 | − | 0.255430i | ||||
\(307\) | −34.2183 | −1.95294 | −0.976472 | − | 0.215644i | \(-0.930815\pi\) | ||||
−0.976472 | + | 0.215644i | \(0.930815\pi\) | |||||||
\(308\) | 14.0399 | − | 24.3179i | 0.799999 | − | 1.38564i | ||||
\(309\) | −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 | \(-0.393254\pi\) | |||||||
\(312\) | 4.38732 | − | 4.93055i | 0.248383 | − | 0.279137i | ||||
\(313\) | −1.79565 | + | 3.11016i | −0.101496 | + | 0.175796i | −0.912301 | − | 0.409520i | \(-0.865696\pi\) |
0.810805 | + | 0.585316i | \(0.199030\pi\) | |||||||
\(314\) | 0.502885 | 0.0283794 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 16.8215 | 0.946281 | ||||||||
\(317\) | 6.59033 | − | 11.4148i | 0.370150 | − | 0.641118i | −0.619439 | − | 0.785045i | \(-0.712640\pi\) |
0.989588 | + | 0.143927i | \(0.0459731\pi\) | |||||||
\(318\) | −7.57425 | − | 1.56351i | −0.424743 | − | 0.0876775i | ||||
\(319\) | 5.20085 | + | 9.00813i | 0.291192 | + | 0.504359i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.92005 | − | 23.8969i | −0.442054 | − | 1.33379i | ||||
\(322\) | −2.55512 | + | 4.42560i | −0.142391 | + | 0.246629i | ||||
\(323\) | −1.12887 | −0.0628119 | ||||||||
\(324\) | 15.5526 | − | 3.68971i | 0.864033 | − | 0.204984i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.05545 | − | 7.02424i | 0.224611 | − | 0.389037i | ||||
\(327\) | −1.03647 | − | 3.12732i | −0.0573171 | − | 0.172941i | ||||
\(328\) | 2.44244 | + | 4.23044i | 0.134861 | + | 0.233587i | ||||
\(329\) | 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 | \(0.177013\pi\) | |||||||
\(332\) | −18.5058 | −1.01564 | ||||||||
\(333\) | 8.74099 | − | 6.50894i | 0.479003 | − | 0.356688i | ||||
\(334\) | −2.06975 | −0.113252 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 7.98661 | − | 8.97549i | 0.435705 | − | 0.489653i | ||||
\(337\) | −12.3997 | − | 21.4770i | −0.675457 | − | 1.16993i | −0.976335 | − | 0.216263i | \(-0.930613\pi\) |
0.300879 | − | 0.953662i | \(-0.402720\pi\) | |||||||
\(338\) | −2.00028 | − | 3.46459i | −0.108801 | − | 0.188449i | ||||
\(339\) | −7.57527 | + | 8.51322i | −0.411432 | + | 0.462375i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 50.9428 | 2.75871 | ||||||||
\(342\) | 0.0587777 | + | 0.502388i | 0.00317833 | + | 0.0271660i | ||||
\(343\) | 19.0454 | 1.02836 | ||||||||
\(344\) | −6.86053 | + | 11.8828i | −0.369895 | + | 0.640677i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.46898 | + | 6.00845i | 0.186493 | + | 0.323016i | ||||
\(347\) | 11.0846 | + | 19.1991i | 0.595052 | + | 1.03066i | 0.993540 | + | 0.113486i | \(0.0362018\pi\) |
−0.398488 | + | 0.917174i | \(0.630465\pi\) | |||||||
\(348\) | 1.63186 | + | 4.92376i | 0.0874771 | + | 0.263941i | ||||
\(349\) | −7.45925 | + | 12.9198i | −0.399285 | + | 0.691581i | −0.993638 | − | 0.112623i | \(-0.964075\pi\) |
0.594353 | + | 0.804204i | \(0.297408\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.963810 | + | 11.0377i | −0.0514444 | + | 0.589151i | ||||
\(352\) | 29.9476 | 1.59621 | ||||||||
\(353\) | 8.45726 | − | 14.6484i | 0.450134 | − | 0.779656i | −0.548260 | − | 0.836308i | \(-0.684709\pi\) |
0.998394 | + | 0.0566525i | \(0.0180427\pi\) | |||||||
\(354\) | 2.63444 | + | 7.94880i | 0.140019 | + | 0.422474i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5.56732 | − | 9.64288i | −0.295067 | − | 0.511072i | ||||
\(357\) | 13.7761 | + | 2.84372i | 0.729107 | + | 0.150506i | ||||
\(358\) | −1.62566 | + | 2.81573i | −0.0859190 | + | 0.148816i | ||||
\(359\) | 0.636657 | 0.0336015 | 0.0168007 | − | 0.999859i | \(-0.494652\pi\) | ||||
0.0168007 | + | 0.999859i | \(0.494652\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8731 | −0.993320 | ||||||||
\(362\) | −2.59602 | + | 4.49644i | −0.136444 | + | 0.236328i | ||||
\(363\) | −31.1470 | + | 35.0035i | −1.63479 | + | 1.83721i | ||||
\(364\) | 4.85317 | + | 8.40594i | 0.254375 | + | 0.440591i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.00599018 | + | 0.00673187i | −0.000313112 | + | 0.000351880i | ||||
\(367\) | 10.0490 | − | 17.4053i | 0.524552 | − | 0.908550i | −0.475040 | − | 0.879964i | \(-0.657566\pi\) |
0.999591 | − | 0.0285858i | \(-0.00910039\pi\) | |||||||
\(368\) | 11.4018 | 0.594358 | ||||||||
\(369\) | −7.53028 | − | 3.24725i | −0.392011 | − | 0.169045i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.0913 | − | 20.9427i | 0.627749 | − | 1.08729i | ||||
\(372\) | 24.8797 | + | 5.13580i | 1.28995 | + | 0.266279i | ||||
\(373\) | −9.82146 | − | 17.0113i | −0.508536 | − | 0.880810i | −0.999951 | − | 0.00988448i | \(-0.996854\pi\) |
0.491415 | − | 0.870925i | \(-0.336480\pi\) | |||||||
\(374\) | 4.62509 | + | 8.01088i | 0.239157 | + | 0.414233i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.2118 | + | 17.6874i | −0.526635 | + | 0.912159i | ||||
\(377\) | −3.59555 | −0.185180 | ||||||||
\(378\) | 0.548272 | − | 6.27892i | 0.0282001 | − | 0.322953i | ||||
\(379\) | −7.94219 | −0.407963 | −0.203982 | − | 0.978975i | \(-0.565388\pi\) | ||||
−0.203982 | + | 0.978975i | \(0.565388\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.04490 | − | 15.2218i | −0.258458 | − | 0.779836i | ||||
\(382\) | 3.24949 | + | 5.62829i | 0.166259 | + | 0.287968i | ||||
\(383\) | −15.5944 | − | 27.0103i | −0.796836 | − | 1.38016i | −0.921667 | − | 0.387983i | \(-0.873172\pi\) |
0.124830 | − | 0.992178i | \(-0.460161\pi\) | |||||||
\(384\) | 18.9711 | + | 3.91612i | 0.968116 | + | 0.199843i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.228285 | −0.0116194 | ||||||||
\(387\) | −2.67670 | − | 22.8785i | −0.136064 | − | 1.16298i | ||||
\(388\) | 12.7995 | 0.649795 | ||||||||
\(389\) | 15.7247 | − | 27.2360i | 0.797274 | − | 1.38092i | −0.124111 | − | 0.992268i | \(-0.539608\pi\) |
0.921385 | − | 0.388650i | \(-0.127059\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.67463 | + | 11.5608i | 0.337550 | + | 0.584655i | ||||
\(392\) | 0.384886 | + | 0.666642i | 0.0194397 | + | 0.0336705i | ||||
\(393\) | −0.310180 | + | 0.348586i | −0.0156465 | + | 0.0175838i | ||||
\(394\) | −1.30970 | + | 2.26847i | −0.0659819 | + | 0.114284i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −26.3611 | + | 19.6297i | −1.32469 | + | 0.986429i | ||||
\(397\) | −17.7174 | −0.889211 | −0.444606 | − | 0.895726i | \(-0.646656\pi\) | ||||
−0.444606 | + | 0.895726i | \(0.646656\pi\) | |||||||
\(398\) | 4.13128 | − | 7.15558i | 0.207082 | − | 0.358677i | ||||
\(399\) | −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 | \(0.776261\pi\) | |||||||
\(402\) | −0.253445 | − | 0.764711i | −0.0126407 | − | 0.0381403i | ||||
\(403\) | −8.80468 | + | 15.2502i | −0.438593 | + | 0.759665i | ||||
\(404\) | −12.3806 | −0.615958 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.04536 | 0.101509 | ||||||||
\(407\) | −11.2045 | + | 19.4067i | −0.555385 | + | 0.961955i | ||||
\(408\) | 3.08542 | + | 9.30954i | 0.152751 | + | 0.460891i | ||||
\(409\) | −12.3759 | − | 21.4357i | −0.611948 | − | 1.05993i | −0.990912 | − | 0.134514i | \(-0.957053\pi\) |
0.378964 | − | 0.925412i | \(-0.376281\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.89661 | − | 1.21721i | −0.290858 | − | 0.0600404i | ||||
\(412\) | 5.43031 | − | 9.40558i | 0.267532 | − | 0.463380i | ||||
\(413\) | −26.1839 | −1.28843 | ||||||||
\(414\) | 4.79744 | − | 3.57240i | 0.235782 | − | 0.175574i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −5.17598 | + | 8.96505i | −0.253773 | + | 0.439548i | ||||
\(417\) | −16.9805 | + | 19.0830i | −0.831539 | + | 0.934498i | ||||
\(418\) | −0.520028 | − | 0.900715i | −0.0254354 | − | 0.0440554i | ||||
\(419\) | 5.32956 | + | 9.23106i | 0.260366 | + | 0.450967i | 0.966339 | − | 0.257272i | \(-0.0828235\pi\) |
−0.705973 | + | 0.708238i | \(0.749490\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.08931 | − | 7.08288i | 0.199301 | − | 0.345199i | −0.749001 | − | 0.662569i | \(-0.769466\pi\) |
0.948302 | + | 0.317370i | \(0.102800\pi\) | |||||||
\(422\) | 0.774555 | 0.0377048 | ||||||||
\(423\) | −3.98425 | − | 34.0544i | −0.193721 | − | 1.65578i | ||||
\(424\) | 16.8607 | 0.818828 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 5.16592 | + | 1.06638i | 0.250290 | + | 0.0516660i | ||||
\(427\) | −0.0140881 | − | 0.0244012i | −0.000681769 | − | 0.00118086i | ||||
\(428\) | 12.9072 | + | 22.3559i | 0.623893 | + | 1.08061i | ||||
\(429\) | −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 | \(0.487175\pi\) | |||||||
\(432\) | −12.7440 | + | 5.94524i | −0.613147 | + | 0.286040i | ||||
\(433\) | 9.95994 | 0.478644 | 0.239322 | − | 0.970940i | \(-0.423075\pi\) | ||||
0.239322 | + | 0.970940i | \(0.423075\pi\) | |||||||
\(434\) | 5.00863 | − | 8.67519i | 0.240422 | − | 0.416423i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.68913 | + | 2.92565i | 0.0808945 | + | 0.140113i | ||||
\(437\) | −0.750471 | − | 1.29985i | −0.0358999 | − | 0.0621805i | ||||
\(438\) | 5.31010 | + | 1.09614i | 0.253726 | + | 0.0523754i | ||||
\(439\) | −6.40788 | + | 11.0988i | −0.305832 | + | 0.529716i | −0.977446 | − | 0.211185i | \(-0.932268\pi\) |
0.671615 | + | 0.740901i | \(0.265601\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.18664 | − | 0.511709i | −0.0565067 | − | 0.0243671i | ||||
\(442\) | −3.19750 | −0.152090 | ||||||||
\(443\) | −3.87702 | + | 6.71520i | −0.184203 | + | 0.319049i | −0.943308 | − | 0.331920i | \(-0.892304\pi\) |
0.759105 | + | 0.650968i | \(0.225637\pi\) | |||||||
\(444\) | −7.42859 | + | 8.34838i | −0.352545 | + | 0.396196i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.83335 | − | 3.17546i | −0.0868118 | − | 0.150362i | ||||
\(447\) | 11.6904 | − | 13.1379i | 0.552936 | − | 0.621399i | ||||
\(448\) | −3.99210 | + | 6.91452i | −0.188609 | + | 0.326681i | ||||
\(449\) | −33.3401 | −1.57342 | −0.786709 | − | 0.617324i | \(-0.788217\pi\) | ||||
−0.786709 | + | 0.617324i | \(0.788217\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.8621 | 0.794004 | ||||||||
\(452\) | 5.84247 | − | 10.1195i | 0.274807 | − | 0.475979i | ||||
\(453\) | −17.4993 | − | 3.61229i | −0.822187 | − | 0.169720i | ||||
\(454\) | 2.66449 | + | 4.61503i | 0.125051 | + | 0.216594i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.346914 | − | 1.04673i | −0.0162457 | − | 0.0490177i | ||||
\(457\) | −19.1096 | + | 33.0988i | −0.893910 | + | 1.54830i | −0.0587626 | + | 0.998272i | \(0.518715\pi\) |
−0.835148 | + | 0.550026i | \(0.814618\pi\) | |||||||
\(458\) | 4.95856 | 0.231698 | ||||||||
\(459\) | −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 | \(0.906666\pi\) | |||||||
\(462\) | 4.07714 | + | 12.3018i | 0.189686 | + | 0.572332i | ||||
\(463\) | 6.04258 | + | 10.4661i | 0.280823 | + | 0.486399i | 0.971588 | − | 0.236680i | \(-0.0760594\pi\) |
−0.690765 | + | 0.723079i | \(0.742726\pi\) | |||||||
\(464\) | −2.28176 | − | 3.95212i | −0.105928 | − | 0.183473i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.686725 | − | 1.18944i | 0.0318119 | − | 0.0550998i | ||||
\(467\) | 7.60466 | 0.351902 | 0.175951 | − | 0.984399i | \(-0.443700\pi\) | ||||
0.175951 | + | 0.984399i | \(0.443700\pi\) | |||||||
\(468\) | −1.32020 | − | 11.2841i | −0.0610264 | − | 0.521608i | ||||
\(469\) | 2.51901 | 0.116317 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.22348 | − | 1.37496i | 0.0563748 | − | 0.0633550i | ||||
\(472\) | −9.12803 | − | 15.8102i | −0.420152 | − | 0.727724i | ||||
\(473\) | 23.6818 | + | 41.0181i | 1.08889 | + | 1.88601i | ||||
\(474\) | −5.16095 | + | 5.79997i | −0.237050 | + | 0.266401i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −14.4237 | −0.661108 | ||||||||
\(477\) | −22.7024 | + | 16.9052i | −1.03947 | + | 0.774038i | ||||
\(478\) | −7.73982 | −0.354011 | ||||||||
\(479\) | 16.2417 | − | 28.1314i | 0.742101 | − | 1.28536i | −0.209437 | − | 0.977822i | \(-0.567163\pi\) |
0.951537 | − | 0.307534i | \(-0.0995037\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.87304 | − | 6.70830i | −0.176595 | − | 0.305872i | ||||
\(482\) | 4.14663 | + | 7.18217i | 0.188874 | + | 0.327139i | ||||
\(483\) | 5.88387 | + | 17.7532i | 0.267725 | + | 0.807798i | ||||
\(484\) | 24.0223 | − | 41.6079i | 1.09192 | − | 1.89127i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −3.49946 | + | 6.49450i | −0.158739 | + | 0.294596i | ||||
\(487\) | 4.46121 | 0.202157 | 0.101078 | − | 0.994878i | \(-0.467771\pi\) | ||||
0.101078 | + | 0.994878i | \(0.467771\pi\) | |||||||
\(488\) | 0.00982254 | − | 0.0170131i | 0.000444645 | − | 0.000770148i | ||||
\(489\) | −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 | \(-0.432348\pi\) | |||||||
\(492\) | 8.23520 | + | 1.69995i | 0.371271 | + | 0.0766397i | ||||
\(493\) | 2.67150 | − | 4.62717i | 0.120318 | − | 0.208397i | ||||
\(494\) | 0.359515 | 0.0161754 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −22.3501 | −1.00355 | ||||||||
\(497\) | −8.24672 | + | 14.2837i | −0.369916 | + | 0.640713i | ||||
\(498\) | 5.67772 | − | 6.38073i | 0.254425 | − | 0.285927i | ||||
\(499\) | 17.1010 | + | 29.6198i | 0.765547 | + | 1.32597i | 0.939957 | + | 0.341293i | \(0.110865\pi\) |
−0.174410 | + | 0.984673i | \(0.555802\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.03554 | + | 5.65902i | −0.224971 | + | 0.252827i | ||||
\(502\) | 2.00423 | − | 3.47143i | 0.0894532 | − | 0.154938i | ||||
\(503\) | −22.1773 | −0.988837 | −0.494419 | − | 0.869224i | \(-0.664619\pi\) | ||||
−0.494419 | + | 0.869224i | \(0.664619\pi\) | |||||||
\(504\) | 1.59673 | + | 13.6476i | 0.0711238 | + | 0.607913i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −6.14951 | + | 10.6513i | −0.273379 | + | 0.473507i | ||||
\(507\) | −14.3392 | − | 2.95998i | −0.636828 | − | 0.131457i | ||||
\(508\) | 8.22160 | + | 14.2402i | 0.364775 | + | 0.631808i | ||||
\(509\) | 10.7816 | + | 18.6743i | 0.477887 | + | 0.827724i | 0.999679 | − | 0.0253489i | \(-0.00806968\pi\) |
−0.521792 | + | 0.853073i | \(0.674736\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.47688 | + | 14.6824i | −0.374995 | + | 0.649510i | ||||
\(512\) | −22.8115 | −1.00813 | ||||||||
\(513\) | 1.51661 | + | 1.06156i | 0.0669598 | + | 0.0468690i | ||||
\(514\) | −1.35943 | −0.0599617 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 7.43061 | + | 22.4201i | 0.327114 | + | 0.986990i | ||||
\(517\) | 35.2501 | + | 61.0550i | 1.55030 | + | 2.68520i | ||||
\(518\) | 2.20321 | + | 3.81608i | 0.0968037 | + | 0.167669i | ||||
\(519\) | 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 | \(0.353609\pi\) | |||||||
\(522\) | −2.19836 | − | 0.947989i | −0.0962196 | − | 0.0414923i | ||||
\(523\) | −31.8114 | −1.39101 | −0.695507 | − | 0.718520i | \(-0.744820\pi\) | ||||
−0.695507 | + | 0.718520i | \(0.744820\pi\) | |||||||
\(524\) | 0.239229 | − | 0.414356i | 0.0104507 | − | 0.0181012i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.06330 | − | 10.5019i | −0.264373 | − | 0.457907i | ||||
\(527\) | −13.0838 | − | 22.6618i | −0.569940 | − | 0.987164i | ||||
\(528\) | 19.2217 | − | 21.6017i | 0.836517 | − | 0.940092i | ||||
\(529\) | 2.62541 | − | 4.54735i | 0.114148 | − | 0.197711i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 28.1426 | + | 12.1358i | 1.22128 | + | 0.526649i | ||||
\(532\) | 1.62175 | 0.0703117 | ||||||||
\(533\) | −2.91435 | + | 5.04780i | −0.126235 | + | 0.218645i | ||||
\(534\) | 5.03292 | + | 1.03892i | 0.217796 | + | 0.0449585i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.878159 | + | 1.52102i | 0.0379307 | + | 0.0656978i | ||||
\(537\) | 3.74354 | + | 11.2952i | 0.161546 | + | 0.487426i | ||||
\(538\) | 0.0797930 | − | 0.138205i | 0.00344012 | − | 0.00595846i | ||||
\(539\) | 2.65717 | 0.114452 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.1315 | −0.650553 | −0.325277 | − | 0.945619i | \(-0.605457\pi\) | ||||
−0.325277 | + | 0.945619i | \(0.605457\pi\) | |||||||
\(542\) | 5.10942 | − | 8.84977i | 0.219468 | − | 0.380130i | ||||
\(543\) | 5.97806 | + | 18.0374i | 0.256543 | + | 0.774058i | ||||
\(544\) | −7.69153 | − | 13.3221i | −0.329772 | − | 0.571181i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.38732 | − | 0.905653i | −0.187760 | − | 0.0387584i | ||||
\(547\) | −2.04372 | + | 3.53982i | −0.0873831 | + | 0.151352i | −0.906404 | − | 0.422411i | \(-0.861184\pi\) |
0.819021 | + | 0.573763i | \(0.194517\pi\) | |||||||
\(548\) | 6.17381 | 0.263732 | ||||||||
\(549\) | 0.00383236 | + | 0.0327561i | 0.000163561 | + | 0.00139800i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.300374 | + | 0.520263i | −0.0127964 | + | 0.0221639i | ||||
\(552\) | −8.66844 | + | 9.74174i | −0.368953 | + | 0.414636i | ||||
\(553\) | −12.1378 | − | 21.0233i | −0.516153 | − | 0.894003i | ||||
\(554\) | −5.71070 | − | 9.89123i | −0.242625 | − | 0.420238i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13.0963 | − | 22.6835i | 0.555408 | − | 0.961994i | ||||
\(557\) | 13.1425 | 0.556864 | 0.278432 | − | 0.960456i | \(-0.410185\pi\) | ||||
0.278432 | + | 0.960456i | \(0.410185\pi\) | |||||||
\(558\) | −9.40410 | + | 7.00273i | −0.398107 | + | 0.296449i | ||||
\(559\) | −16.3721 | −0.692467 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 33.1554 | + | 6.84411i | 1.39982 | + | 0.288958i | ||||
\(562\) | 0.796785 | + | 1.38007i | 0.0336104 | + | 0.0582149i | ||||
\(563\) | −12.2611 | − | 21.2368i | −0.516742 | − | 0.895023i | −0.999811 | − | 0.0194410i | \(-0.993811\pi\) |
0.483069 | − | 0.875582i | \(-0.339522\pi\) | |||||||
\(564\) | 11.0604 | + | 33.3721i | 0.465727 | + | 1.40522i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 10.3405 | 0.434642 | ||||||||
\(567\) | −15.8336 | − | 16.7751i | −0.664950 | − | 0.704489i | ||||
\(568\) | −11.4996 | −0.482514 | ||||||||
\(569\) | −11.3649 | + | 19.6846i | −0.476442 | + | 0.825223i | −0.999636 | − | 0.0269915i | \(-0.991407\pi\) |
0.523193 | + | 0.852214i | \(0.324741\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.247093 | + | 0.427977i | 0.0103405 | + | 0.0179103i | 0.871149 | − | 0.491018i | \(-0.163375\pi\) |
−0.860809 | + | 0.508928i | \(0.830042\pi\) | |||||||
\(572\) | 11.6803 | + | 20.2309i | 0.488379 | + | 0.845897i | ||||
\(573\) | 23.2943 | + | 4.80854i | 0.973135 | + | 0.200879i | ||||
\(574\) | 1.65786 | − | 2.87149i | 0.0691976 | − | 0.119854i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 7.49549 | − | 5.58149i | 0.312312 | − | 0.232562i | ||||
\(577\) | 9.41187 | 0.391821 | 0.195911 | − | 0.980622i | \(-0.437234\pi\) | ||||
0.195911 | + | 0.980622i | \(0.437234\pi\) | |||||||
\(578\) | −1.64691 | + | 2.85254i | −0.0685025 | + | 0.118650i | ||||
\(579\) | −0.555399 | + | 0.624167i | −0.0230816 | + | 0.0259395i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.3532 | + | 23.1284i | 0.553984 | + | 0.959529i | ||||
\(582\) | −3.92697 | + | 4.41320i | −0.162778 | + | 0.182933i | ||||
\(583\) | 29.1006 | − | 50.4037i | 1.20522 | − | 2.08751i | ||||
\(584\) | −11.8206 | −0.489139 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.50916 | 0.268891 | ||||||||
\(587\) | 4.98661 | − | 8.63705i | 0.205819 | − | 0.356489i | −0.744574 | − | 0.667540i | \(-0.767347\pi\) |
0.950393 | + | 0.311050i | \(0.100681\pi\) | |||||||
\(588\) | 1.29772 | + | 0.267882i | 0.0535172 | + | 0.0110473i | ||||
\(589\) | 1.47110 | + | 2.54801i | 0.0606155 | + | 0.104989i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.01595 | + | 9.09993i | 0.124060 | + | 0.374321i | ||||
\(592\) | 4.91572 | − | 8.51428i | 0.202035 | − | 0.349935i | ||||
\(593\) | −38.3421 | −1.57452 | −0.787260 | − | 0.616621i | \(-0.788501\pi\) | ||||
−0.787260 | + | 0.616621i | \(0.788501\pi\) | |||||||
\(594\) | 1.31955 | − | 15.1117i | 0.0541418 | − | 0.620042i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9.01628 | + | 15.6167i | −0.369321 | + | 0.639683i | ||||
\(597\) | −9.51340 | − | 28.7044i | −0.389358 | − | 1.17479i | ||||
\(598\) | −2.12570 | − | 3.68182i | −0.0869262 | − | 0.150561i | ||||
\(599\) | 5.07665 | + | 8.79301i | 0.207426 | + | 0.359273i | 0.950903 | − | 0.309489i | \(-0.100158\pi\) |
−0.743477 | + | 0.668762i | \(0.766825\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.6371 | − | 18.4241i | 0.433898 | − | 0.751533i | −0.563307 | − | 0.826248i | \(-0.690471\pi\) |
0.997205 | + | 0.0747146i | \(0.0238046\pi\) | |||||||
\(602\) | 9.31344 | 0.379587 | ||||||||
\(603\) | −2.70745 | − | 1.16752i | −0.110256 | − | 0.0475450i | ||||
\(604\) | 18.3219 | 0.745508 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.79846 | − | 4.26878i | 0.154302 | − | 0.173407i | ||||
\(607\) | −18.8678 | − | 32.6799i | −0.765819 | − | 1.32644i | −0.939812 | − | 0.341691i | \(-0.889000\pi\) |
0.173993 | − | 0.984747i | \(-0.444333\pi\) | |||||||
\(608\) | 0.864808 | + | 1.49789i | 0.0350726 | + | 0.0607475i | ||||
\(609\) | 4.97618 | − | 5.59232i | 0.201645 | − | 0.226612i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −24.3698 | −0.985895 | ||||||||
\(612\) | 15.5026 | + | 6.68513i | 0.626657 | + | 0.270230i | ||||
\(613\) | 32.2633 | 1.30310 | 0.651551 | − | 0.758605i | \(-0.274119\pi\) | ||||
0.651551 | + | 0.758605i | \(0.274119\pi\) | |||||||
\(614\) | −8.09699 | + | 14.0244i | −0.326768 | + | 0.565979i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −14.1268 | − | 24.4684i | −0.569186 | − | 0.985860i | ||||
\(617\) | −13.0089 | − | 22.5321i | −0.523719 | − | 0.907108i | −0.999619 | − | 0.0276084i | \(-0.991211\pi\) |
0.475900 | − | 0.879499i | \(-0.342122\pi\) | |||||||
\(618\) | 1.57694 | + | 4.75805i | 0.0634339 | + | 0.191397i | ||||
\(619\) | 5.94077 | − | 10.2897i | 0.238780 | − | 0.413578i | −0.721585 | − | 0.692326i | \(-0.756586\pi\) |
0.960364 | + | 0.278748i | \(0.0899193\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.90429 | − | 21.8083i | 0.0764165 | − | 0.875136i | ||||
\(622\) | −10.9037 | −0.437197 | ||||||||
\(623\) | −8.03440 | + | 13.9160i | −0.321891 | + | 0.557532i | ||||
\(624\) | 3.14447 | + | 9.48769i | 0.125879 | + | 0.379811i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0.849799 | + | 1.47189i | 0.0339648 | + | 0.0588288i | ||||
\(627\) | −3.72788 | − | 0.769527i | −0.148877 | − | 0.0307319i | ||||
\(628\) | −0.943614 | + | 1.63439i | −0.0376543 | + | 0.0652191i | ||||
\(629\) | 11.5107 | 0.458962 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.2726 | −0.528372 | −0.264186 | − | 0.964472i | \(-0.585103\pi\) | ||||
−0.264186 | + | 0.964472i | \(0.585103\pi\) | |||||||
\(632\) | 8.46279 | − | 14.6580i | 0.336632 | − | 0.583063i | ||||
\(633\) | 1.88443 | − | 2.11775i | 0.0748992 | − | 0.0841731i | ||||
\(634\) | −3.11890 | − | 5.40210i | −0.123867 | − | 0.214545i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 19.2938 | − | 21.6827i | 0.765048 | − | 0.859774i | ||||
\(637\) | −0.459251 | + | 0.795445i | −0.0181962 | + | 0.0315167i | ||||
\(638\) | 4.92265 | 0.194890 | ||||||||
\(639\) | 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 | \(0.820796\pi\) | |||||||
\(642\) | −11.6682 | − | 2.40862i | −0.460509 | − | 0.0950606i | ||||
\(643\) | −7.46275 | − | 12.9259i | −0.294302 | − | 0.509747i | 0.680520 | − | 0.732729i | \(-0.261754\pi\) |
−0.974822 | + | 0.222983i | \(0.928421\pi\) | |||||||
\(644\) | −9.58886 | − | 16.6084i | −0.377854 | − | 0.654462i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.267121 | + | 0.462667i | −0.0105097 | + | 0.0182034i | ||||
\(647\) | 41.2684 | 1.62243 | 0.811214 | − | 0.584749i | \(-0.198807\pi\) | ||||
0.811214 | + | 0.584749i | \(0.198807\pi\) | |||||||
\(648\) | 4.60927 | − | 15.4086i | 0.181069 | − | 0.605306i | ||||
\(649\) | −63.0179 | −2.47367 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.5337 | − | 34.8003i | −0.452043 | − | 1.36393i | ||||
\(652\) | 15.2193 | + | 26.3606i | 0.596034 | + | 1.03236i | ||||
\(653\) | 13.8126 | + | 23.9241i | 0.540528 | + | 0.936223i | 0.998874 | + | 0.0474484i | \(0.0151090\pi\) |
−0.458345 | + | 0.888774i | \(0.651558\pi\) | |||||||
\(654\) | −1.52699 | − | 0.315209i | −0.0597100 | − | 0.0123256i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −7.39788 | −0.288839 | ||||||||
\(657\) | 15.9160 | − | 11.8518i | 0.620943 | − | 0.462383i | ||||
\(658\) | 13.8630 | 0.540435 | ||||||||
\(659\) | −20.0112 | + | 34.6605i | −0.779527 | + | 1.35018i | 0.152688 | + | 0.988274i | \(0.451207\pi\) |
−0.932215 | + | 0.361905i | \(0.882126\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.4965 | − | 21.6445i | −0.486056 | − | 0.841874i | 0.513816 | − | 0.857901i | \(-0.328232\pi\) |
−0.999872 | + | 0.0160270i | \(0.994898\pi\) | |||||||
\(662\) | 0.279818 | + | 0.484659i | 0.0108754 | + | 0.0188368i | ||||
\(663\) | −7.77924 | + | 8.74245i | −0.302121 | + | 0.339529i | ||||
\(664\) | −9.31018 | + | 16.1257i | −0.361305 | + | 0.625799i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.599338 | − | 5.12269i | −0.0232239 | − | 0.198500i | ||||
\(667\) | 7.10405 | 0.275070 | ||||||||
\(668\) | 3.88369 | − | 6.72675i | 0.150264 | − | 0.260266i | ||||
\(669\) | −13.1426 | − | 2.71296i | −0.508122 | − | 0.104889i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.0339063 | − | 0.0587274i | −0.00130894 | − | 0.00226715i | ||||
\(672\) | −6.78030 | − | 20.4579i | −0.261556 | − | 0.789182i | ||||
\(673\) | −20.4024 | + | 35.3380i | −0.786454 | + | 1.36218i | 0.141672 | + | 0.989914i | \(0.454752\pi\) |
−0.928126 | + | 0.372265i | \(0.878581\pi\) | |||||||
\(674\) | −11.7365 | −0.452072 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 15.0133 | 0.577436 | ||||||||
\(677\) | 20.5947 | − | 35.6710i | 0.791518 | − | 1.37095i | −0.133509 | − | 0.991048i | \(-0.542625\pi\) |
0.925027 | − | 0.379901i | \(-0.124042\pi\) | |||||||
\(678\) | 1.69663 | + | 5.11919i | 0.0651587 | + | 0.196601i | ||||
\(679\) | −9.23569 | − | 15.9967i | −0.354433 | − | 0.613896i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.1007 | + | 3.94286i | 0.731939 | + | 0.151091i | ||||
\(682\) | 12.0545 | − | 20.8789i | 0.461589 | − | 0.799496i | ||||
\(683\) | −1.33820 | −0.0512047 | −0.0256023 | − | 0.999672i | \(-0.508150\pi\) | ||||
−0.0256023 | + | 0.999672i | \(0.508150\pi\) | |||||||
\(684\) | −1.74306 | − | 0.751652i | −0.0666476 | − | 0.0287401i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 4.50667 | − | 7.80578i | 0.172065 | − | 0.298026i | ||||
\(687\) | 12.0637 | − | 13.5574i | 0.460261 | − | 0.517249i | ||||
\(688\) | −10.3899 | − | 17.9958i | −0.396110 | − | 0.686083i | ||||
\(689\) | 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 | \(0.00698617\pi\) | |||||||
\(692\) | −26.0368 | −0.989770 | ||||||||
\(693\) | 43.5544 | + | 18.7817i | 1.65449 | + | 0.713459i | ||||
\(694\) | 10.4917 | 0.398258 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5.11148 | + | 1.05514i | 0.193750 | + | 0.0399949i | ||||
\(697\) | −4.33074 | − | 7.50106i | −0.164039 | − | 0.284123i | ||||
\(698\) | 3.53012 | + | 6.11435i | 0.133617 | + | 0.231432i | ||||
\(699\) | −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 | \(0.611722\pi\) | |||||||
\(702\) | 4.29576 | + | 3.00685i | 0.162133 | + | 0.113486i | ||||
\(703\) | −1.29422 | −0.0488126 | ||||||||
\(704\) | −9.60795 | + | 16.6415i | −0.362113 | + | 0.627199i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.00244 | − | 6.93242i | −0.150634 | − | 0.260905i | ||||
\(707\) | 8.93344 | + | 15.4732i | 0.335977 | + | 0.581929i | ||||
\(708\) | −30.7770 | − | 6.35315i | −1.15667 | − | 0.238766i | ||||
\(709\) | −20.9103 | + | 36.2177i | −0.785304 | + | 1.36019i | 0.143514 | + | 0.989648i | \(0.454160\pi\) |
−0.928818 | + | 0.370537i | \(0.879174\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.30184 | + | 28.2216i | 0.123829 | + | 1.05839i | ||||
\(712\) | −11.2036 | −0.419871 | ||||||||
\(713\) | 17.3962 | − | 30.1312i | 0.651494 | − | 1.12842i | ||||
\(714\) | 4.42529 | − | 4.97322i | 0.165612 | − | 0.186118i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.10079 | − | 10.5669i | −0.227997 | − | 0.394903i | ||||
\(717\) | −18.8303 | + | 21.1619i | −0.703231 | + | 0.790304i | ||||
\(718\) | 0.150650 | − | 0.260934i | 0.00562222 | − | 0.00973797i | ||||
\(719\) | 48.9786 | 1.82660 | 0.913298 | − | 0.407293i | \(-0.133527\pi\) | ||||
0.913298 | + | 0.407293i | \(0.133527\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.6734 | −0.583707 | ||||||||
\(722\) | −4.46588 | + | 7.73514i | −0.166203 | + | 0.287872i | ||||
\(723\) | 29.7255 | + | 6.13610i | 1.10550 | + | 0.228204i | ||||
\(724\) | −9.74236 | − | 16.8743i | −0.362072 | − | 0.627127i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 6.97598 | + | 21.0484i | 0.258903 | + | 0.781179i | ||||
\(727\) | −21.9005 | + | 37.9327i | −0.812243 | + | 1.40685i | 0.0990474 | + | 0.995083i | \(0.468420\pi\) |
−0.911291 | + | 0.411764i | \(0.864913\pi\) | |||||||
\(728\) | 9.76642 | 0.361968 | ||||||||
\(729\) | 9.24306 | + | 25.3686i | 0.342336 | + | 0.939578i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.1645 | − | 21.0696i | 0.449922 | − | 0.779287i | ||||
\(732\) | −0.0106387 | − | 0.0320999i | −0.000393219 | − | 0.00118645i | ||||
\(733\) | −3.39332 | − | 5.87740i | −0.125335 | − | 0.217087i | 0.796529 | − | 0.604601i | \(-0.206667\pi\) |
−0.921864 | + | 0.387514i | \(0.873334\pi\) | |||||||
\(734\) | −4.75572 | − | 8.23715i | −0.175537 | − | 0.304039i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10.2267 | − | 17.7131i | 0.376960 | − | 0.652913i | ||||
\(737\) | 6.06261 | 0.223319 | ||||||||
\(738\) | −3.11276 | + | 2.31790i | −0.114582 | + | 0.0853232i | ||||
\(739\) | 28.7245 | 1.05665 | 0.528324 | − | 0.849043i | \(-0.322821\pi\) | ||||
0.528324 | + | 0.849043i | \(0.322821\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.874670 | − | 0.982970i | 0.0321318 | − | 0.0361103i | ||||
\(742\) | −5.72226 | − | 9.91125i | −0.210071 | − | 0.363853i | ||||
\(743\) | −15.7262 | − | 27.2385i | −0.576937 | − | 0.999284i | −0.995828 | − | 0.0912477i | \(-0.970915\pi\) |
0.418891 | − | 0.908036i | \(-0.362419\pi\) | |||||||
\(744\) | 16.9921 | − | 19.0961i | 0.622962 | − | 0.700096i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −9.29610 | −0.340354 | ||||||||
\(747\) | −3.63246 | − | 31.0475i | −0.132905 | − | 1.13597i | ||||
\(748\) | −34.7141 | −1.26927 | ||||||||
\(749\) | 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 | \(0.897377\pi\) | |||||||
\(752\) | −15.4652 | − | 26.7866i | −0.563959 | − | 0.976806i | ||||
\(753\) | −4.61530 | − | 13.9256i | −0.168191 | − | 0.507476i | ||||
\(754\) | −0.850804 | + | 1.47364i | −0.0309845 | + | 0.0536667i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 19.3778 | + | 13.5637i | 0.704765 | + | 0.493306i | ||||
\(757\) | 45.7942 | 1.66442 | 0.832210 | − | 0.554461i | \(-0.187075\pi\) | ||||
0.832210 | + | 0.554461i | \(0.187075\pi\) | |||||||
\(758\) | −1.87934 | + | 3.25511i | −0.0682607 | + | 0.118231i | ||||
\(759\) | 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 | \(0.622616\pi\) | |||||||
\(762\) | −7.43242 | − | 1.53424i | −0.269248 | − | 0.0555796i | ||||
\(763\) | 2.43764 | − | 4.22212i | 0.0882485 | − | 0.152851i | ||||
\(764\) | −24.3894 | −0.882378 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −14.7602 | −0.533309 | ||||||||
\(767\) | 10.8917 | − | 18.8649i | 0.393275 | − | 0.681173i | ||||
\(768\) | −1.07930 | + | 1.21294i | −0.0389459 | + | 0.0437680i | ||||
\(769\) | −3.57986 | − | 6.20050i | −0.129093 | − | 0.223596i | 0.794232 | − | 0.607614i | \(-0.207873\pi\) |
−0.923325 | + | 0.384018i | \(0.874540\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.30737 | + | 3.71688i | −0.119112 | + | 0.133860i | ||||
\(772\) | 0.428355 | − | 0.741933i | 0.0154168 | − | 0.0267027i | ||||
\(773\) | 14.5998 | 0.525117 | 0.262558 | − | 0.964916i | \(-0.415434\pi\) | ||||
0.262558 | + | 0.964916i | \(0.415434\pi\) | |||||||
\(774\) | −10.0101 | − | 4.31662i | −0.359806 | − | 0.155158i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.43935 | − | 11.1533i | 0.231159 | − | 0.400379i | ||||
\(777\) | 15.7940 | + | 3.26027i | 0.566606 | + | 0.116962i | ||||
\(778\) | −7.44178 | − | 12.8895i | −0.266801 | − | 0.462113i | ||||
\(779\) | 0.486933 | + | 0.843393i | 0.0174462 | + | 0.0302177i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.8477 | + | 34.3772i | −0.710207 | + | 1.23011i | ||||
\(782\) | 6.31760 | 0.225917 | ||||||||
\(783\) | −7.94037 | + | 3.70428i | −0.283766 | + | 0.132380i | ||||
\(784\) | −1.16578 | −0.0416348 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.0694710 | + | 0.209613i | 0.00247795 | + | 0.00747663i | ||||
\(787\) | 9.23638 | + | 15.9979i | 0.329242 | + | 0.570263i | 0.982362 | − | 0.186991i | \(-0.0598736\pi\) |
−0.653120 | + | 0.757254i | \(0.726540\pi\) | |||||||
\(788\) | −4.91505 | − | 8.51312i | −0.175092 | − | 0.303267i | ||||
\(789\) | −43.4654 | − | 8.97235i | −1.54741 | − | 0.319424i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.8630 | −0.599578 | ||||||||
\(792\) | 3.84291 | + | 32.8463i | 0.136552 | + | 1.16714i | ||||
\(793\) | 0.0234407 | 0.000832405 | ||||||||
\(794\) | −4.19242 | + | 7.26149i | −0.148783 | + | 0.257700i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 15.5039 | + | 26.8535i | 0.549520 | + | 0.951796i | ||||
\(797\) | 20.5187 | + | 35.5395i | 0.726810 | + | 1.25887i | 0.958225 | + | 0.286017i | \(0.0923314\pi\) |
−0.231414 | + | 0.972855i | \(0.574335\pi\) | |||||||
\(798\) | −0.497564 | + | 0.559171i | −0.0176136 | + | 0.0197945i | ||||
\(799\) | 18.1068 | − | 31.3619i | 0.640573 | − | 1.10950i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.0852 | − | 11.2332i | 0.533010 | − | 0.396904i | ||||
\(802\) | 3.38021 | 0.119359 | ||||||||
\(803\) | −20.4016 | + | 35.3367i | −0.719958 | + | 1.24700i | ||||
\(804\) | 2.96089 | + | 0.611202i | 0.104423 | + | 0.0215554i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.16686 | + | 7.21721i | 0.146771 | + | 0.254215i | ||||
\(807\) | −0.183745 | − | 0.554408i | −0.00646814 | − | 0.0195161i | ||||
\(808\) | −6.22861 | + | 10.7883i | −0.219122 | + | 0.379530i | ||||
\(809\) | 7.19375 | 0.252919 | 0.126459 | − | 0.991972i | \(-0.459639\pi\) | ||||
0.126459 | + | 0.991972i | \(0.459639\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.2183 | 1.34203 | 0.671014 | − | 0.741445i | \(-0.265859\pi\) | ||||
0.671014 | + | 0.741445i | \(0.265859\pi\) | |||||||
\(812\) | −3.83791 | + | 6.64746i | −0.134684 | + | 0.233280i | ||||
\(813\) | −11.7658 | − | 35.5007i | −0.412646 | − | 1.24506i | ||||
\(814\) | 5.30257 | + | 9.18431i | 0.185855 | + | 0.321910i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −14.5462 | − | 3.00271i | −0.509220 | − | 0.105116i | ||||
\(817\) | −1.36774 | + | 2.36899i | −0.0478511 | + | 0.0828805i | ||||
\(818\) | −11.7139 | −0.409566 | ||||||||
\(819\) | −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 | \(0.162953\pi\) | |||||||
\(822\) | −1.89417 | + | 2.12870i | −0.0660668 | + | 0.0742470i | ||||
\(823\) | −0.710165 | − | 1.23004i | −0.0247548 | − | 0.0428766i | 0.853383 | − | 0.521285i | \(-0.174547\pi\) |
−0.878137 | + | 0.478408i | \(0.841214\pi\) | |||||||
\(824\) | −5.46393 | − | 9.46380i | −0.190345 | − | 0.329687i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.19583 | + | 10.7315i | −0.215580 | + | 0.373396i | ||||
\(827\) | −49.8169 | −1.73230 | −0.866152 | − | 0.499782i | \(-0.833414\pi\) | ||||
−0.866152 | + | 0.499782i | \(0.833414\pi\) | |||||||
\(828\) | 2.60845 | + | 22.2950i | 0.0906498 | + | 0.774807i | ||||
\(829\) | 36.4150 | 1.26475 | 0.632373 | − | 0.774664i | \(-0.282081\pi\) | ||||
0.632373 | + | 0.774664i | \(0.282081\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −40.9378 | − | 8.45058i | −1.42012 | − | 0.293147i | ||||
\(832\) | −3.32117 | − | 5.75244i | −0.115141 | − | 0.199430i | ||||
\(833\) | −0.682449 | − | 1.18204i | −0.0236455 | − | 0.0409551i | ||||
\(834\) | 3.80312 | + | 11.4750i | 0.131691 | + | 0.397347i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.90312 | 0.134992 | ||||||||
\(837\) | −3.73285 | + | 42.7493i | −0.129026 | + | 1.47763i | ||||
\(838\) | 5.04447 | 0.174258 | ||||||||
\(839\) | 10.0445 | − | 17.3976i | 0.346774 | − | 0.600631i | −0.638900 | − | 0.769290i | \(-0.720610\pi\) |
0.985674 | + | 0.168659i | \(0.0539436\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.0783 | + | 22.6523i | 0.450976 | + | 0.781114i | ||||
\(842\) | −1.93528 | − | 3.35201i | −0.0666942 | − | 0.115518i | ||||
\(843\) | 5.71184 | + | 1.17907i | 0.196726 | + | 0.0406092i | ||||
\(844\) | −1.45338 | + | 2.51732i | −0.0500273 | + | 0.0866498i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −14.9000 | − | 6.42525i | −0.512272 | − | 0.220905i | ||||
\(847\) | −69.3349 | −2.38238 | ||||||||
\(848\) | −12.7673 | + | 22.1136i | −0.438430 | + | 0.759383i | ||||
\(849\) | 25.1575 | − | 28.2724i | 0.863402 | − | 0.970307i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.65232 | + | 13.2542i | 0.262318 | + | 0.454349i | ||||
\(852\) | −13.1591 | + | 14.7884i | −0.450823 | + | 0.506642i | ||||
\(853\) | 13.4542 | − | 23.3034i | 0.460663 | − | 0.797892i | −0.538331 | − | 0.842733i | \(-0.680945\pi\) |
0.998994 | + | 0.0448418i | \(0.0142784\pi\) | |||||||
\(854\) | −0.0133345 | −0.000456296 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 25.9742 | 0.887779 | ||||||||
\(857\) | −24.4204 | + | 42.2973i | −0.834184 | + | 1.44485i | 0.0605088 | + | 0.998168i | \(0.480728\pi\) |
−0.894693 | + | 0.446682i | \(0.852606\pi\) | |||||||
\(858\) | −10.5591 | − | 2.17967i | −0.360483 | − | 0.0744128i | ||||
\(859\) | 20.7047 | + | 35.8616i | 0.706435 | + | 1.22358i | 0.966171 | + | 0.257902i | \(0.0830312\pi\) |
−0.259736 | + | 0.965680i | \(0.583635\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.81767 | − | 11.5189i | −0.130106 | − | 0.392564i | ||||
\(862\) | 0.395754 | − | 0.685465i | 0.0134794 | − | 0.0233470i | ||||
\(863\) | 50.8101 | 1.72960 | 0.864799 | − | 0.502119i | \(-0.167446\pi\) | ||||
0.864799 | + | 0.502119i | \(0.167446\pi\) | |||||||
\(864\) | −2.19441 | + | 25.1308i | −0.0746555 | + | 0.854969i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.35679 | − | 4.08209i | 0.0800871 | − | 0.138715i | ||||
\(867\) | 3.79247 | + | 11.4429i | 0.128799 | + | 0.388621i | ||||
\(868\) | 18.7964 | + | 32.5563i | 0.637991 | + | 1.10503i | ||||
\(869\) | −29.2126 | − | 50.5977i | −0.990970 | − | 1.71641i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.04783 | + | 1.81489i | −0.0355043 | + | 0.0614953i | ||||
\(872\) | 3.39916 | 0.115110 | ||||||||
\(873\) | 2.51237 | + | 21.4739i | 0.0850310 | + | 0.726781i | ||||
\(874\) | −0.710328 | −0.0240272 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −13.5263 | + | 15.2011i | −0.457013 | + | 0.513599i | ||||
\(877\) | −0.204795 | − | 0.354715i | −0.00691542 | − | 0.0119779i | 0.862547 | − | 0.505977i | \(-0.168868\pi\) |
−0.869462 | + | 0.493999i | \(0.835535\pi\) | |||||||
\(878\) | 3.03256 | + | 5.25255i | 0.102344 | + | 0.177265i | ||||
\(879\) | 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 | \(0.528610\pi\) | |||||||
\(882\) | −0.490516 | + | 0.365261i | −0.0165165 | + | 0.0122990i | ||||
\(883\) | 14.2064 | 0.478083 | 0.239042 | − | 0.971009i | \(-0.423167\pi\) | ||||
0.239042 | + | 0.971009i | \(0.423167\pi\) | |||||||
\(884\) | 5.99979 | − | 10.3919i | 0.201795 | − | 0.349519i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.83482 | + | 3.17800i | 0.0616419 | + | 0.106767i | ||||
\(887\) | −3.61597 | − | 6.26304i | −0.121412 | − | 0.210292i | 0.798913 | − | 0.601447i | \(-0.205409\pi\) |
−0.920325 | + | 0.391155i | \(0.872076\pi\) | |||||||
\(888\) | 3.53737 | + | 10.6732i | 0.118706 | + | 0.358169i | ||||
\(889\) | 11.8649 | − | 20.5506i | 0.397936 | − | 0.689245i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −38.1074 | − | 40.3734i | −1.27665 | − | 1.35256i | ||||
\(892\) | 13.7604 | 0.460733 | ||||||||
\(893\) | −2.03586 | + | 3.52622i | −0.0681276 | + | 0.118000i | ||||
\(894\) | −2.61829 | − | 7.90008i | −0.0875688 | − | 0.264218i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 14.3325 | + | 24.8246i | 0.478815 | + | 0.829331i | ||||
\(897\) | −15.2383 | − | 3.14556i | −0.508792 | − | 0.105027i | ||||
\(898\) | −7.88919 | + | 13.6645i | −0.263266 | + | 0.455989i | ||||
\(899\) | −13.9256 | −0.464444 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29.8960 | −0.995981 | ||||||||
\(902\) | 3.99003 | − | 6.91093i | 0.132853 | − | 0.230109i | ||||
\(903\) | 22.6588 | − | 25.4644i | 0.754038 | − | 0.847401i | ||||
\(904\) | −5.87864 | − | 10.1821i | −0.195521 | − | 0.338651i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −5.62130 | + | 6.31731i | −0.186755 | + | 0.209879i | ||||
\(907\) | 19.4051 | − | 33.6106i | 0.644335 | − | 1.11602i | −0.340120 | − | 0.940382i | \(-0.610468\pi\) |
0.984455 | − | 0.175639i | \(-0.0561990\pi\) | |||||||
\(908\) | −19.9986 | −0.663677 | ||||||||
\(909\) | −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 | \(-0.0658563\pi\) | |||||||
\(912\) | 1.63553 | + | 0.337614i | 0.0541577 | + | 0.0111795i | ||||
\(913\) | 32.1377 | + | 55.6641i | 1.06360 | + | 1.84221i | ||||
\(914\) | 9.04371 | + | 15.6642i | 0.299139 | + | 0.518125i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.30424 | + | 16.1154i | −0.307421 | + | 0.532468i | ||||
\(917\) | −0.690479 | −0.0228016 | ||||||||
\(918\) | −7.06133 | + | 3.29419i | −0.233059 | + | 0.108725i | ||||
\(919\) | −13.0468 | −0.430375 | −0.215187 | − | 0.976573i | \(-0.569036\pi\) | ||||
−0.215187 | + | 0.976573i | \(0.569036\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 18.6456 | + | 56.2586i | 0.614392 | + | 1.85378i | ||||
\(922\) | 7.40722 | + | 12.8297i | 0.243944 | + | 0.422523i | ||||
\(923\) | −6.86074 | − | 11.8832i | −0.225824 | − | 0.391139i | ||||
\(924\) | −47.6315 | − | 9.83234i | −1.56696 | − | 0.323460i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 5.71936 | 0.187950 | ||||||||
\(927\) | 16.8458 | + | 7.26433i | 0.553289 | + | 0.238592i | ||||
\(928\) | −8.18638 | −0.268731 | ||||||||
\(929\) | −0.146912 | + | 0.254460i | −0.00482004 | + | 0.00834855i | −0.868425 | − | 0.495820i | \(-0.834868\pi\) |
0.863605 | + | 0.504168i | \(0.168201\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.0767321 | + | 0.132904i | 0.00251479 | + | 0.00435575i | ||||
\(932\) | 2.57714 | + | 4.46374i | 0.0844171 | + | 0.146215i | ||||
\(933\) | −26.5277 | + | 29.8123i | −0.868477 | + | 0.976010i | ||||
\(934\) | 1.79947 | − | 3.11678i | 0.0588805 | − | 0.101984i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −10.4970 | − | 4.52657i | −0.343105 | − | 0.147956i | ||||
\(937\) | 16.9141 | 0.552559 | 0.276280 | − | 0.961077i | \(-0.410898\pi\) | ||||
0.276280 | + | 0.961077i | \(0.410898\pi\) | |||||||
\(938\) | 0.596067 | − | 1.03242i | 0.0194623 | − | 0.0337097i | ||||
\(939\) | 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 | \(-0.549031\pi\) | |||||||
\(942\) | −0.274022 | − | 0.826796i | −0.00892811 | − | 0.0269385i | ||||
\(943\) | 5.75815 | − | 9.97342i | 0.187511 | − | 0.324779i | ||||
\(944\) | 27.6478 | 0.899858 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 22.4150 | 0.728775 | ||||||||
\(947\) | −19.4373 | + | 33.6664i | −0.631627 | + | 1.09401i | 0.355592 | + | 0.934641i | \(0.384279\pi\) |
−0.987219 | + | 0.159369i | \(0.949054\pi\) | |||||||
\(948\) | −9.16600 | − | 27.6563i | −0.297698 | − | 0.898234i | ||||
\(949\) | −7.05222 | − | 12.2148i | −0.228925 | − | 0.396509i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22.3582 | − | 4.61529i | −0.725013 | − | 0.149661i | ||||
\(952\) | −7.25648 | + | 12.5686i | −0.235184 | + | 0.407350i | ||||
\(953\) | 54.4516 | 1.76386 | 0.881930 | − | 0.471381i | \(-0.156244\pi\) | ||||
0.881930 | + | 0.471381i | \(0.156244\pi\) | |||||||
\(954\) | 1.55662 | + | 13.3048i | 0.0503974 | + | 0.430760i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 14.5230 | − | 25.1546i | 0.469708 | − | 0.813557i | ||||
\(957\) | 11.9764 | − | 13.4593i | 0.387141 | − | 0.435076i | ||||
\(958\) | −7.68644 | − | 13.3133i | −0.248338 | − | 0.430133i | ||||
\(959\) | −4.45482 | − | 7.71598i | −0.143854 | − | 0.249162i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18.6006 | + | 32.2172i | −0.600020 | + | 1.03926i | ||||
\(962\) | −3.66587 | −0.118192 | ||||||||
\(963\) | −34.9734 | + | 26.0428i | −1.12700 | + | 0.839217i | ||||
\(964\) | −31.1229 | −1.00240 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 8.66844 | + | 1.78938i | 0.278902 | + | 0.0575725i | ||||
\(967\) | −9.78507 | − | 16.9482i | −0.314666 | − | 0.545018i | 0.664700 | − | 0.747110i | \(-0.268559\pi\) |
−0.979367 | + | 0.202092i | \(0.935226\pi\) | |||||||
\(968\) | −24.1710 | − | 41.8654i | −0.776885 | − | 1.34560i | ||||
\(969\) | 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 | \(0.467716\pi\) | |||||||
\(972\) | −14.5409 | − | 23.5596i | −0.466399 | − | 0.755674i | ||||
\(973\) | −37.7995 | −1.21180 | ||||||||
\(974\) | 1.05564 | − | 1.82843i | 0.0338250 | − | 0.0585866i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.0148757 | + | 0.0257654i | 0.000476158 | + | 0.000824731i | ||||
\(977\) | 3.70955 | + | 6.42514i | 0.118679 | + | 0.205558i | 0.919244 | − | 0.393687i | \(-0.128801\pi\) |
−0.800565 | + | 0.599245i | \(0.795467\pi\) | |||||||
\(978\) | −13.7584 | − | 2.84008i | −0.439946 | − | 0.0908158i | ||||
\(979\) | −19.3367 | + | 33.4922i | −0.618004 | + | 1.07041i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.57686 | + | 3.40814i | −0.146128 | + | 0.108814i | ||||
\(982\) | −15.5426 | −0.495986 | ||||||||
\(983\) | −5.49137 | + | 9.51134i | −0.175148 | + | 0.303365i | −0.940212 | − | 0.340589i | \(-0.889374\pi\) |
0.765065 | + | 0.643953i | \(0.222707\pi\) | |||||||
\(984\) | 5.62440 | − | 6.32080i | 0.179299 | − | 0.201500i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.26430 | − | 2.18983i | −0.0402635 | − | 0.0697384i | ||||
\(987\) | 33.7274 | − | 37.9035i | 1.07356 | − | 1.20648i | ||||
\(988\) | −0.674595 | + | 1.16843i | −0.0214617 | + | 0.0371728i | ||||
\(989\) | 32.3479 | 1.02860 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.3721 | −0.678908 | −0.339454 | − | 0.940623i | \(-0.610242\pi\) | ||||
−0.339454 | + | 0.940623i | \(0.610242\pi\) | |||||||
\(992\) | −20.0466 | + | 34.7217i | −0.636480 | + | 1.10242i | ||||
\(993\) | 2.00591 | + | 0.414069i | 0.0636555 | + | 0.0131401i | ||||
\(994\) | 3.90280 | + | 6.75984i | 0.123789 | + | 0.214409i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 10.0838 | + | 30.4255i | 0.319518 | + | 0.964070i | ||||
\(997\) | −15.2674 | + | 26.4439i | −0.483524 | + | 0.837487i | −0.999821 | − | 0.0189220i | \(-0.993977\pi\) |
0.516297 | + | 0.856409i | \(0.327310\pi\) | |||||||
\(998\) | 16.1863 | 0.512368 | ||||||||
\(999\) | −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.e.c.151.3 | yes | 8 | |
3.2 | odd | 2 | 675.2.e.e.451.2 | 8 | |||
5.2 | odd | 4 | 225.2.k.c.124.5 | 16 | |||
5.3 | odd | 4 | 225.2.k.c.124.4 | 16 | |||
5.4 | even | 2 | 225.2.e.e.151.2 | yes | 8 | ||
9.2 | odd | 6 | 2025.2.a.p.1.3 | 4 | |||
9.4 | even | 3 | inner | 225.2.e.c.76.3 | ✓ | 8 | |
9.5 | odd | 6 | 675.2.e.e.226.2 | 8 | |||
9.7 | even | 3 | 2025.2.a.y.1.2 | 4 | |||
15.2 | even | 4 | 675.2.k.c.424.4 | 16 | |||
15.8 | even | 4 | 675.2.k.c.424.5 | 16 | |||
15.14 | odd | 2 | 675.2.e.c.451.3 | 8 | |||
45.2 | even | 12 | 2025.2.b.o.649.5 | 8 | |||
45.4 | even | 6 | 225.2.e.e.76.2 | yes | 8 | ||
45.7 | odd | 12 | 2025.2.b.n.649.4 | 8 | |||
45.13 | odd | 12 | 225.2.k.c.49.5 | 16 | |||
45.14 | odd | 6 | 675.2.e.c.226.3 | 8 | |||
45.22 | odd | 12 | 225.2.k.c.49.4 | 16 | |||
45.23 | even | 12 | 675.2.k.c.199.4 | 16 | |||
45.29 | odd | 6 | 2025.2.a.z.1.2 | 4 | |||
45.32 | even | 12 | 675.2.k.c.199.5 | 16 | |||
45.34 | even | 6 | 2025.2.a.q.1.3 | 4 | |||
45.38 | even | 12 | 2025.2.b.o.649.4 | 8 | |||
45.43 | odd | 12 | 2025.2.b.n.649.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
225.2.e.c.76.3 | ✓ | 8 | 9.4 | even | 3 | inner | |
225.2.e.c.151.3 | yes | 8 | 1.1 | even | 1 | trivial | |
225.2.e.e.76.2 | yes | 8 | 45.4 | even | 6 | ||
225.2.e.e.151.2 | yes | 8 | 5.4 | even | 2 | ||
225.2.k.c.49.4 | 16 | 45.22 | odd | 12 | |||
225.2.k.c.49.5 | 16 | 45.13 | odd | 12 | |||
225.2.k.c.124.4 | 16 | 5.3 | odd | 4 | |||
225.2.k.c.124.5 | 16 | 5.2 | odd | 4 | |||
675.2.e.c.226.3 | 8 | 45.14 | odd | 6 | |||
675.2.e.c.451.3 | 8 | 15.14 | odd | 2 | |||
675.2.e.e.226.2 | 8 | 9.5 | odd | 6 | |||
675.2.e.e.451.2 | 8 | 3.2 | odd | 2 | |||
675.2.k.c.199.4 | 16 | 45.23 | even | 12 | |||
675.2.k.c.199.5 | 16 | 45.32 | even | 12 | |||
675.2.k.c.424.4 | 16 | 15.2 | even | 4 | |||
675.2.k.c.424.5 | 16 | 15.8 | even | 4 | |||
2025.2.a.p.1.3 | 4 | 9.2 | odd | 6 | |||
2025.2.a.q.1.3 | 4 | 45.34 | even | 6 | |||
2025.2.a.y.1.2 | 4 | 9.7 | even | 3 | |||
2025.2.a.z.1.2 | 4 | 45.29 | odd | 6 | |||
2025.2.b.n.649.4 | 8 | 45.7 | odd | 12 | |||
2025.2.b.n.649.5 | 8 | 45.43 | odd | 12 | |||
2025.2.b.o.649.4 | 8 | 45.38 | even | 12 | |||
2025.2.b.o.649.5 | 8 | 45.2 | even | 12 |