Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,2,Mod(46,675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, base_ring=CyclotomicField(30))
chi = DirichletCharacter(H, H._module([20, 18]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("675.46");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.r (of order \(15\), degree \(8\), 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: | \(5.38990213644\) |
Analytic rank: | \(0\) |
Dimension: | \(224\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{15})\) |
Twist minimal: | no (minimal twist has level 225) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{15}]$ |
Embedding invariants
Embedding label | 46.8 | ||
Character | \(\chi\) | \(=\) | 675.46 |
Dual form | 675.2.r.a.631.8 |
$q$-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 \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{3}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.955162 | − | 1.06081i | −0.675401 | − | 0.750109i | 0.303859 | − | 0.952717i | \(-0.401725\pi\) |
−0.979260 | + | 0.202608i | \(0.935058\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.00393676 | + | 0.0374558i | −0.00196838 | + | 0.0187279i | ||||
\(5\) | −0.397449 | + | 2.20046i | −0.177745 | + | 0.984077i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.20474 | − | 2.08666i | 0.455348 | − | 0.788685i | −0.543361 | − | 0.839499i | \(-0.682848\pi\) |
0.998708 | + | 0.0508144i | \(0.0161817\pi\) | |||||||
\(8\) | −2.26620 | + | 1.64649i | −0.801221 | + | 0.582121i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.71391 | − | 1.68018i | 0.858214 | − | 0.531319i | ||||
\(11\) | 0.0211445 | + | 0.0234833i | 0.00637530 | + | 0.00708049i | 0.746324 | − | 0.665583i | \(-0.231817\pi\) |
−0.739949 | + | 0.672663i | \(0.765150\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.22250 | + | 4.68956i | −1.17111 | + | 1.30065i | −0.225914 | + | 0.974147i | \(0.572537\pi\) |
−0.945196 | + | 0.326503i | \(0.894130\pi\) | |||||||
\(14\) | −3.36428 | + | 0.715100i | −0.899142 | + | 0.191119i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.98488 | + | 0.847013i | 0.996220 | + | 0.211753i | ||||
\(17\) | −2.72065 | + | 1.97667i | −0.659854 | + | 0.479412i | −0.866614 | − | 0.498980i | \(-0.833708\pi\) |
0.206760 | + | 0.978392i | \(0.433708\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.81267 | − | 1.31698i | 0.415855 | − | 0.302136i | −0.360113 | − | 0.932909i | \(-0.617262\pi\) |
0.775968 | + | 0.630772i | \(0.217262\pi\) | |||||||
\(20\) | −0.0808554 | − | 0.0235495i | −0.0180798 | − | 0.00526582i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.00471506 | − | 0.0448608i | 0.00100525 | − | 0.00956434i | ||||
\(23\) | 1.88117 | − | 0.399856i | 0.392252 | − | 0.0833756i | −0.00756369 | − | 0.999971i | \(-0.502408\pi\) |
0.399815 | + | 0.916596i | \(0.369074\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.68407 | − | 1.74914i | −0.936814 | − | 0.349829i | ||||
\(26\) | 9.00793 | 1.76660 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.0734149 | + | 0.0533391i | 0.0138741 | + | 0.0100801i | ||||
\(29\) | −8.54224 | + | 3.80325i | −1.58625 | + | 0.706246i | −0.994966 | − | 0.100215i | \(-0.968047\pi\) |
−0.591288 | + | 0.806460i | \(0.701380\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.43471 | − | 1.52923i | −0.616893 | − | 0.274658i | 0.0744052 | − | 0.997228i | \(-0.476294\pi\) |
−0.691298 | + | 0.722570i | \(0.742961\pi\) | |||||||
\(32\) | −0.106511 | − | 0.184482i | −0.0188286 | − | 0.0326121i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.69554 | + | 0.998067i | 0.805278 | + | 0.171167i | ||||
\(35\) | 4.11281 | + | 3.48032i | 0.695191 | + | 0.588281i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.22975 | + | 9.94014i | 0.530967 | + | 1.63415i | 0.752205 | + | 0.658929i | \(0.228990\pi\) |
−0.221238 | + | 0.975220i | \(0.571010\pi\) | |||||||
\(38\) | −3.12847 | − | 0.664976i | −0.507504 | − | 0.107873i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.72234 | − | 5.64107i | −0.430439 | − | 0.891932i | ||||
\(41\) | −1.08631 | + | 1.20647i | −0.169654 | + | 0.188420i | −0.821976 | − | 0.569522i | \(-0.807128\pi\) |
0.652322 | + | 0.757942i | \(0.273795\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.58816 | + | 9.67898i | −0.852186 | + | 1.47603i | 0.0270444 | + | 0.999634i | \(0.491390\pi\) |
−0.879231 | + | 0.476396i | \(0.841943\pi\) | |||||||
\(44\) | −0.000962828 | 0 | 0.000699535i | −0.000145152 | 0 | 0.000105459i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.22100 | − | 1.61365i | −0.327468 | − | 0.237919i | ||||
\(47\) | 2.88640 | − | 1.28511i | 0.421025 | − | 0.187452i | −0.185278 | − | 0.982686i | \(-0.559319\pi\) |
0.606303 | + | 0.795234i | \(0.292652\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.597221 | + | 1.03442i | 0.0853173 | + | 0.147774i | ||||
\(50\) | 2.61853 | + | 6.63964i | 0.370316 | + | 0.938987i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.159028 | − | 0.176619i | −0.0220533 | − | 0.0244926i | ||||
\(53\) | −1.23376 | − | 0.896379i | −0.169470 | − | 0.123127i | 0.499817 | − | 0.866131i | \(-0.333400\pi\) |
−0.669287 | + | 0.743004i | \(0.733400\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.0600780 | + | 0.0371942i | −0.00810092 | + | 0.00501527i | ||||
\(56\) | 0.705499 | + | 6.71237i | 0.0942763 | + | 0.896979i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 12.1938 | + | 5.42901i | 1.60112 | + | 0.712864i | ||||
\(59\) | 8.58158 | − | 9.53081i | 1.11723 | − | 1.24081i | 0.149511 | − | 0.988760i | \(-0.452230\pi\) |
0.967715 | − | 0.252046i | \(-0.0811034\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.10677 | + | 7.89287i | 0.909929 | + | 1.01058i | 0.999893 | + | 0.0146335i | \(0.00465815\pi\) |
−0.0899640 | + | 0.995945i | \(0.528675\pi\) | |||||||
\(62\) | 1.65848 | + | 5.10426i | 0.210627 | + | 0.648242i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.42385 | − | 7.45983i | 0.302981 | − | 0.932479i | ||||
\(65\) | −8.64097 | − | 11.1553i | −1.07178 | − | 1.38365i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.07993 | − | 0.926044i | −0.254104 | − | 0.113134i | 0.275732 | − | 0.961235i | \(-0.411080\pi\) |
−0.529836 | + | 0.848100i | \(0.677746\pi\) | |||||||
\(68\) | −0.0633271 | − | 0.109686i | −0.00767954 | − | 0.0133014i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.236421 | − | 7.68719i | −0.0282577 | − | 0.918795i | ||||
\(71\) | 3.63556 | + | 2.64139i | 0.431462 | + | 0.313475i | 0.782233 | − | 0.622986i | \(-0.214081\pi\) |
−0.350771 | + | 0.936461i | \(0.614081\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.380414 | − | 1.17080i | 0.0445241 | − | 0.137031i | −0.926323 | − | 0.376730i | \(-0.877049\pi\) |
0.970847 | + | 0.239698i | \(0.0770486\pi\) | |||||||
\(74\) | 7.45971 | − | 12.9206i | 0.867174 | − | 1.50199i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.0421926 | + | 0.0730797i | 0.00483982 | + | 0.00838281i | ||||
\(77\) | 0.0744753 | − | 0.0158302i | 0.00848725 | − | 0.00180402i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.840545 | − | 0.374235i | 0.0945687 | − | 0.0421047i | −0.358907 | − | 0.933373i | \(-0.616851\pi\) |
0.453476 | + | 0.891269i | \(0.350184\pi\) | |||||||
\(80\) | −3.44761 | + | 8.43194i | −0.385454 | + | 0.942719i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.31745 | 0.255920 | ||||||||
\(83\) | 0.581163 | + | 5.52940i | 0.0637909 | + | 0.606930i | 0.978987 | + | 0.203922i | \(0.0653688\pi\) |
−0.915196 | + | 0.403008i | \(0.867965\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.26826 | − | 6.77231i | −0.354493 | − | 0.734560i | ||||
\(86\) | 15.6052 | − | 3.31699i | 1.68275 | − | 0.357680i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.0865826 | − | 0.0184037i | −0.00922973 | − | 0.00196184i | ||||
\(89\) | 0.932477 | − | 2.86987i | 0.0988424 | − | 0.304206i | −0.889394 | − | 0.457142i | \(-0.848873\pi\) |
0.988236 | + | 0.152937i | \(0.0488730\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.69854 | + | 14.4606i | 0.492541 | + | 1.51589i | ||||
\(92\) | 0.00757118 | + | 0.0720350i | 0.000789350 | + | 0.00751017i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.12024 | − | 1.83445i | −0.424971 | − | 0.189209i | ||||
\(95\) | 2.17753 | + | 4.51214i | 0.223409 | + | 0.462936i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.49506 | + | 4.22747i | −0.964077 | + | 0.429235i | −0.827544 | − | 0.561401i | \(-0.810263\pi\) |
−0.136533 | + | 0.990636i | \(0.543596\pi\) | |||||||
\(98\) | 0.526882 | − | 1.62158i | 0.0532232 | − | 0.163804i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.0839556 | − | 0.168560i | 0.00839556 | − | 0.0168560i | ||||
\(101\) | −2.74091 | + | 4.74740i | −0.272731 | + | 0.472384i | −0.969560 | − | 0.244853i | \(-0.921260\pi\) |
0.696829 | + | 0.717237i | \(0.254594\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.191572 | − | 1.82268i | 0.0188761 | − | 0.179594i | −0.981022 | − | 0.193899i | \(-0.937887\pi\) |
0.999898 | + | 0.0143043i | \(0.00455337\pi\) | |||||||
\(104\) | 1.84771 | − | 17.5798i | 0.181183 | − | 1.72384i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.227548 | + | 2.16498i | 0.0221014 | + | 0.210281i | ||||
\(107\) | −18.4750 | −1.78604 | −0.893021 | − | 0.450014i | \(-0.851419\pi\) | ||||
−0.893021 | + | 0.450014i | \(0.851419\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.39665 | + | 4.29846i | 0.133775 | + | 0.411718i | 0.995397 | − | 0.0958324i | \(-0.0305513\pi\) |
−0.861622 | + | 0.507550i | \(0.830551\pi\) | |||||||
\(110\) | 0.0968404 | + | 0.0282052i | 0.00923337 | + | 0.00268926i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 6.56816 | − | 7.29468i | 0.620633 | − | 0.689283i | ||||
\(113\) | −2.49461 | + | 2.77055i | −0.234673 | + | 0.260631i | −0.848966 | − | 0.528447i | \(-0.822775\pi\) |
0.614293 | + | 0.789078i | \(0.289441\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.132197 | + | 4.29837i | 0.0123274 | + | 0.400825i | ||||
\(116\) | −0.108825 | − | 0.334929i | −0.0101041 | − | 0.0310974i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −18.3072 | −1.68532 | ||||||||
\(119\) | 0.846976 | + | 8.05844i | 0.0776422 | + | 0.738716i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.14971 | − | 10.9387i | 0.104519 | − | 0.994432i | ||||
\(122\) | 1.58476 | − | 15.0779i | 0.143477 | − | 1.36509i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.0708003 | − | 0.122630i | 0.00635806 | − | 0.0110125i | ||||
\(125\) | 5.71060 | − | 9.61192i | 0.510772 | − | 0.859716i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.06084 | − | 9.42031i | 0.271606 | − | 0.835917i | −0.718492 | − | 0.695536i | \(-0.755167\pi\) |
0.990098 | − | 0.140381i | \(-0.0448329\pi\) | |||||||
\(128\) | −10.6179 | + | 4.72738i | −0.938496 | + | 0.417845i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.58019 | + | 19.8216i | −0.314003 | + | 1.73847i | ||||
\(131\) | −0.808980 | − | 0.360181i | −0.0706809 | − | 0.0314692i | 0.371092 | − | 0.928596i | \(-0.378984\pi\) |
−0.441773 | + | 0.897127i | \(0.645650\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.564310 | − | 5.36905i | −0.0489319 | − | 0.465556i | ||||
\(134\) | 1.00431 | + | 3.09094i | 0.0867590 | + | 0.267017i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.91097 | − | 8.95903i | 0.249613 | − | 0.768230i | ||||
\(137\) | −10.9483 | − | 2.32714i | −0.935378 | − | 0.198821i | −0.285083 | − | 0.958503i | \(-0.592021\pi\) |
−0.650295 | + | 0.759682i | \(0.725355\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.0394061 | − | 0.00837602i | 0.00334238 | − | 0.000710445i | −0.206240 | − | 0.978501i | \(-0.566123\pi\) |
0.209583 | + | 0.977791i | \(0.432789\pi\) | |||||||
\(140\) | −0.146549 | + | 0.140347i | −0.0123857 | + | 0.0118615i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.670525 | − | 6.37962i | −0.0562692 | − | 0.535365i | ||||
\(143\) | −0.199409 | −0.0166754 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.97380 | − | 20.3085i | −0.413052 | − | 1.68653i | ||||
\(146\) | −1.60535 | + | 0.714750i | −0.132860 | + | 0.0591531i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.385031 | + | 0.0818408i | −0.0316493 | + | 0.00672727i | ||||
\(149\) | −4.04741 | − | 7.01032i | −0.331577 | − | 0.574308i | 0.651245 | − | 0.758868i | \(-0.274247\pi\) |
−0.982821 | + | 0.184560i | \(0.940914\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.63305 | + | 8.02468i | −0.377032 | + | 0.653039i | −0.990629 | − | 0.136580i | \(-0.956389\pi\) |
0.613597 | + | 0.789620i | \(0.289722\pi\) | |||||||
\(152\) | −1.93947 | + | 5.96908i | −0.157312 | + | 0.484156i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.0879289 | − | 0.0638841i | −0.00708552 | − | 0.00514793i | ||||
\(155\) | 4.73014 | − | 6.95017i | 0.379934 | − | 0.558251i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.80545 | − | 10.0553i | −0.463326 | − | 0.802503i | 0.535799 | − | 0.844346i | \(-0.320011\pi\) |
−0.999124 | + | 0.0418424i | \(0.986677\pi\) | |||||||
\(158\) | −1.19985 | − | 0.534208i | −0.0954549 | − | 0.0424993i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.448277 | − | 0.161050i | 0.0354394 | − | 0.0127321i | ||||
\(161\) | 1.43195 | − | 4.40710i | 0.112854 | − | 0.347328i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.85642 | − | 5.71348i | −0.145406 | − | 0.447515i | 0.851657 | − | 0.524100i | \(-0.175598\pi\) |
−0.997063 | + | 0.0765854i | \(0.975598\pi\) | |||||||
\(164\) | −0.0409129 | − | 0.0454384i | −0.00319476 | − | 0.00354814i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.31056 | − | 5.89797i | 0.412179 | − | 0.457772i | ||||
\(167\) | −12.3524 | − | 5.49964i | −0.955857 | − | 0.425575i | −0.131293 | − | 0.991344i | \(-0.541913\pi\) |
−0.824564 | + | 0.565769i | \(0.808580\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.80361 | − | 26.6745i | −0.215662 | − | 2.05189i | ||||
\(170\) | −4.06245 | + | 9.93567i | −0.311575 | + | 0.762031i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.340535 | − | 0.247413i | −0.0259655 | − | 0.0188651i | ||||
\(173\) | 4.52702 | + | 5.02776i | 0.344183 | + | 0.382254i | 0.890238 | − | 0.455495i | \(-0.150538\pi\) |
−0.546055 | + | 0.837749i | \(0.683871\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.29294 | + | 7.66682i | −0.702480 | + | 0.579557i | ||||
\(176\) | 0.0643676 | + | 0.111488i | 0.00485189 | + | 0.00840372i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.93507 | + | 1.75200i | −0.294946 | + | 0.131318i | ||||
\(179\) | −5.82355 | − | 4.23106i | −0.435272 | − | 0.316244i | 0.348481 | − | 0.937316i | \(-0.386698\pi\) |
−0.783754 | + | 0.621072i | \(0.786698\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.56870 | + | 4.04590i | −0.413918 | + | 0.300729i | −0.775186 | − | 0.631733i | \(-0.782344\pi\) |
0.361268 | + | 0.932462i | \(0.382344\pi\) | |||||||
\(182\) | 10.8522 | − | 18.7965i | 0.804417 | − | 1.39329i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.60475 | + | 4.00348i | −0.265746 | + | 0.295140i | ||||
\(185\) | −23.1566 | + | 3.15624i | −1.70250 | + | 0.232051i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.103945 | − | 0.0220943i | −0.00760124 | − | 0.00161569i | ||||
\(188\) | 0.0367717 | + | 0.113172i | 0.00268185 | + | 0.00825389i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.70666 | − | 6.61978i | 0.196362 | − | 0.480249i | ||||
\(191\) | 11.0464 | + | 2.34798i | 0.799289 | + | 0.169894i | 0.589411 | − | 0.807834i | \(-0.299360\pi\) |
0.209878 | + | 0.977728i | \(0.432693\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.1617 | + | 19.3326i | 0.803434 | + | 1.39159i | 0.917343 | + | 0.398098i | \(0.130330\pi\) |
−0.113909 | + | 0.993491i | \(0.536337\pi\) | |||||||
\(194\) | 13.5539 | + | 6.03458i | 0.973112 | + | 0.433257i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.0410961 | + | 0.0182971i | −0.00293543 | + | 0.00130694i | ||||
\(197\) | 21.1964 | + | 15.4001i | 1.51018 | + | 1.09721i | 0.966097 | + | 0.258179i | \(0.0831224\pi\) |
0.544083 | + | 0.839031i | \(0.316878\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.6094 | −1.17741 | −0.588703 | − | 0.808349i | \(-0.700361\pi\) | ||||
−0.588703 | + | 0.808349i | \(0.700361\pi\) | |||||||
\(200\) | 13.4950 | − | 3.74836i | 0.954238 | − | 0.265049i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7.65412 | − | 1.62693i | 0.538542 | − | 0.114471i | ||||
\(203\) | −2.35504 | + | 22.4067i | −0.165291 | + | 1.57264i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.22305 | − | 2.86991i | −0.155264 | − | 0.200443i | ||||
\(206\) | −2.11651 | + | 1.53774i | −0.147464 | + | 0.107139i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −20.7983 | + | 15.1108i | −1.44210 | + | 1.04775i | ||||
\(209\) | 0.0692551 | + | 0.0147206i | 0.00479047 | + | 0.00101825i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.41180 | − | 2.00054i | 0.647935 | − | 0.137723i | 0.127791 | − | 0.991801i | \(-0.459211\pi\) |
0.520145 | + | 0.854078i | \(0.325878\pi\) | |||||||
\(212\) | 0.0384316 | − | 0.0426826i | 0.00263949 | − | 0.00293146i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 17.6466 | + | 19.5985i | 1.20630 | + | 1.33973i | ||||
\(215\) | −19.0772 | − | 16.1434i | −1.30106 | − | 1.10097i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.32892 | + | 5.32477i | −0.497520 | + | 0.361469i | ||||
\(218\) | 3.22584 | − | 5.58731i | 0.218481 | − | 0.378421i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.00115663 | − | 0.00239670i | −7.79797e−5 | − | 0.000161585i | ||||
\(221\) | 2.21824 | − | 21.1051i | 0.149215 | − | 1.41968i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.3409 | − | 19.2591i | −1.16124 | − | 1.28968i | −0.950001 | − | 0.312248i | \(-0.898918\pi\) |
−0.211235 | − | 0.977435i | \(-0.567749\pi\) | |||||||
\(224\) | −0.513268 | −0.0342942 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.32179 | 0.354000 | ||||||||
\(227\) | −13.4978 | − | 14.9908i | −0.895881 | − | 0.994977i | −1.00000 | 0.000411914i | \(-0.999869\pi\) | |
0.104119 | − | 0.994565i | \(-0.466798\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.727435 | − | 6.92109i | 0.0480703 | − | 0.457358i | −0.943839 | − | 0.330407i | \(-0.892814\pi\) |
0.991909 | − | 0.126951i | \(-0.0405193\pi\) | |||||||
\(230\) | 4.43351 | − | 4.24588i | 0.292337 | − | 0.279965i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 13.0964 | − | 22.6836i | 0.859820 | − | 1.48925i | ||||
\(233\) | 22.8409 | − | 16.5949i | 1.49636 | − | 1.08717i | 0.524551 | − | 0.851379i | \(-0.324233\pi\) |
0.971805 | − | 0.235787i | \(-0.0757666\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.68064 | + | 6.86218i | 0.109633 | + | 0.447639i | ||||
\(236\) | 0.323201 | + | 0.358951i | 0.0210386 | + | 0.0233657i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7.73951 | − | 8.59560i | 0.501678 | − | 0.557170i | ||||
\(239\) | 4.35020 | − | 0.924664i | 0.281391 | − | 0.0598115i | −0.0650541 | − | 0.997882i | \(-0.520722\pi\) |
0.346445 | + | 0.938070i | \(0.387389\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.8371 | − | 3.15373i | −0.955743 | − | 0.203149i | −0.296461 | − | 0.955045i | \(-0.595806\pi\) |
−0.659282 | + | 0.751895i | \(0.729140\pi\) | |||||||
\(242\) | −12.7021 | + | 9.22865i | −0.816525 | + | 0.593240i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.323612 | + | 0.235118i | −0.0207171 | + | 0.0150519i | ||||
\(245\) | −2.51356 | + | 0.903035i | −0.160586 | + | 0.0576928i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.47793 | + | 14.0616i | −0.0940385 | + | 0.894717i | ||||
\(248\) | 10.3016 | − | 2.18967i | 0.654152 | − | 0.139044i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −15.6510 | + | 3.12305i | −0.989857 | + | 0.197519i | ||||
\(251\) | 14.0348 | 0.885869 | 0.442935 | − | 0.896554i | \(-0.353937\pi\) | ||||
0.442935 | + | 0.896554i | \(0.353937\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.0491663 | + | 0.0357214i | 0.00309106 | + | 0.00224579i | ||||
\(254\) | −12.9168 | + | 5.75093i | −0.810472 | + | 0.360845i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.825455 | + | 0.367516i | 0.0515909 | + | 0.0229698i | ||||
\(257\) | 4.76132 | + | 8.24684i | 0.297003 | + | 0.514424i | 0.975449 | − | 0.220226i | \(-0.0706796\pi\) |
−0.678446 | + | 0.734650i | \(0.737346\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 24.6327 | + | 5.23585i | 1.53060 | + | 0.325340i | ||||
\(260\) | 0.451849 | − | 0.279739i | 0.0280225 | − | 0.0173487i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.390622 | + | 1.20221i | 0.0241327 | + | 0.0742728i | ||||
\(263\) | 23.7423 | + | 5.04659i | 1.46402 | + | 0.311186i | 0.869914 | − | 0.493204i | \(-0.164174\pi\) |
0.594101 | + | 0.804390i | \(0.297508\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.46280 | − | 2.35858i | 0.151289 | − | 0.144886i | ||||
\(266\) | −5.15656 | + | 5.72694i | −0.316169 | + | 0.351141i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.0428739 | − | 0.0742598i | 0.00261894 | − | 0.00453614i | ||||
\(269\) | 12.9182 | − | 9.38564i | 0.787638 | − | 0.572252i | −0.119624 | − | 0.992819i | \(-0.538169\pi\) |
0.907262 | + | 0.420567i | \(0.138169\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.6010 | + | 8.42860i | 0.704709 | + | 0.512001i | 0.881462 | − | 0.472254i | \(-0.156560\pi\) |
−0.176754 | + | 0.984255i | \(0.556560\pi\) | |||||||
\(272\) | −12.5157 | + | 5.57236i | −0.758877 | + | 0.337874i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.98875 | + | 13.8369i | 0.482618 | + | 0.835919i | ||||
\(275\) | −0.0579665 | − | 0.146982i | −0.00349551 | − | 0.00886336i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.5642 | − | 11.7327i | −0.634740 | − | 0.704950i | 0.336867 | − | 0.941552i | \(-0.390633\pi\) |
−0.971607 | + | 0.236602i | \(0.923966\pi\) | |||||||
\(278\) | −0.0465246 | − | 0.0338021i | −0.00279036 | − | 0.00202732i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −15.0507 | − | 1.11540i | −0.899453 | − | 0.0666580i | ||||
\(281\) | −0.154395 | − | 1.46897i | −0.00921045 | − | 0.0876316i | 0.988951 | − | 0.148243i | \(-0.0473617\pi\) |
−0.998161 | + | 0.0606112i | \(0.980695\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.4438 | − | 5.54033i | −0.739706 | − | 0.329338i | 0.00205936 | − | 0.999998i | \(-0.499344\pi\) |
−0.741765 | + | 0.670660i | \(0.766011\pi\) | |||||||
\(284\) | −0.113248 | + | 0.125774i | −0.00672002 | + | 0.00746334i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.190468 | + | 0.211536i | 0.0112626 | + | 0.0125084i | ||||
\(287\) | 1.20879 | + | 3.72026i | 0.0713523 | + | 0.219600i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.75857 | + | 5.41233i | −0.103445 | + | 0.318372i | ||||
\(290\) | −16.7927 | + | 24.6742i | −0.986104 | + | 1.44892i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.0423555 | + | 0.0188579i | 0.00247867 | + | 0.00110357i | ||||
\(293\) | 8.13530 | + | 14.0908i | 0.475270 | + | 0.823191i | 0.999599 | − | 0.0283246i | \(-0.00901721\pi\) |
−0.524329 | + | 0.851516i | \(0.675684\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.5615 | + | 22.6715i | 1.02247 | + | 1.31998i | ||||
\(296\) | −23.6856 | − | 17.2086i | −1.37669 | − | 1.00023i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.57072 | + | 10.9895i | −0.206846 | + | 0.636607i | ||||
\(299\) | −6.06810 | + | 10.5103i | −0.350927 | + | 0.607824i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.4645 | + | 23.3212i | 0.776082 | + | 1.34421i | ||||
\(302\) | 12.9380 | − | 2.75006i | 0.744499 | − | 0.158248i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 8.33877 | − | 3.71266i | 0.478262 | − | 0.212936i | ||||
\(305\) | −20.1925 | + | 12.5012i | −1.15622 | + | 0.715815i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.3507 | 0.819040 | 0.409520 | − | 0.912301i | \(-0.365696\pi\) | ||||
0.409520 | + | 0.912301i | \(0.365696\pi\) | |||||||
\(308\) | 0.000299742 | 0.00285185i | 1.70794e−5 | 0.000162499i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −11.8909 | + | 1.62073i | −0.675357 | + | 0.0920512i | ||||
\(311\) | −21.9008 | + | 4.65515i | −1.24188 | + | 0.263970i | −0.781586 | − | 0.623797i | \(-0.785589\pi\) |
−0.460293 | + | 0.887767i | \(0.652256\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.9037 | + | 5.08090i | 1.35112 | + | 0.287189i | 0.825919 | − | 0.563789i | \(-0.190657\pi\) |
0.525200 | + | 0.850979i | \(0.323990\pi\) | |||||||
\(314\) | −5.12170 | + | 15.7630i | −0.289035 | + | 0.889557i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.0107082 | + | 0.0329566i | 0.000602385 | + | 0.00185395i | ||||
\(317\) | 1.80810 | + | 17.2029i | 0.101553 | + | 0.966213i | 0.920076 | + | 0.391740i | \(0.128127\pi\) |
−0.818523 | + | 0.574474i | \(0.805207\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.269934 | − | 0.120182i | −0.0151134 | − | 0.00672892i | ||||
\(320\) | 15.4517 | + | 8.29848i | 0.863778 | + | 0.463899i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.04286 | + | 2.69045i | −0.336755 | + | 0.149933i | ||||
\(323\) | −2.32840 | + | 7.16609i | −0.129556 | + | 0.398732i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 27.9812 | − | 14.5805i | 1.55212 | − | 0.808779i | ||||
\(326\) | −4.28776 | + | 7.42662i | −0.237477 | + | 0.411323i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.475356 | − | 4.52271i | 0.0262472 | − | 0.249725i | ||||
\(329\) | 0.795762 | − | 7.57117i | 0.0438718 | − | 0.417412i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.74019 | + | 26.0711i | 0.150614 | + | 1.43300i | 0.765019 | + | 0.644008i | \(0.222730\pi\) |
−0.614404 | + | 0.788991i | \(0.710604\pi\) | |||||||
\(332\) | −0.209396 | −0.0114921 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.96444 | + | 18.3567i | 0.326360 | + | 1.00443i | ||||
\(335\) | 2.86439 | − | 4.20875i | 0.156498 | − | 0.229949i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.8044 | − | 11.9995i | 0.588553 | − | 0.653654i | −0.373143 | − | 0.927774i | \(-0.621720\pi\) |
0.961696 | + | 0.274120i | \(0.0883864\pi\) | |||||||
\(338\) | −25.6189 | + | 28.4526i | −1.39348 | + | 1.54762i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.266529 | − | 0.0957544i | 0.0144545 | − | 0.00519301i | ||||
\(341\) | −0.0367138 | − | 0.112993i | −0.00198816 | − | 0.00611893i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.7443 | 1.06609 | ||||||||
\(344\) | −3.27245 | − | 31.1353i | −0.176439 | − | 1.67870i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.00949 | − | 9.60465i | 0.0542705 | − | 0.516349i | ||||
\(347\) | −1.95974 | + | 18.6457i | −0.105205 | + | 1.00095i | 0.806814 | + | 0.590806i | \(0.201190\pi\) |
−0.912019 | + | 0.410149i | \(0.865477\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.899591 | + | 1.55814i | −0.0481540 | + | 0.0834051i | −0.889098 | − | 0.457717i | \(-0.848667\pi\) |
0.840944 | + | 0.541123i | \(0.182000\pi\) | |||||||
\(350\) | 17.0093 | + | 2.53503i | 0.909188 | + | 0.135503i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.00208013 | − | 0.00640199i | 0.000110871 | − | 0.000341227i | ||||
\(353\) | 1.67743 | − | 0.746839i | 0.0892805 | − | 0.0397502i | −0.361610 | − | 0.932329i | \(-0.617773\pi\) |
0.450891 | + | 0.892579i | \(0.351106\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.25723 | + | 6.95010i | −0.385174 | + | 0.368873i | ||||
\(356\) | 0.103822 | + | 0.0462247i | 0.00550257 | + | 0.00244990i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.07407 | + | 10.2190i | 0.0567661 | + | 0.540093i | ||||
\(359\) | 10.8516 | + | 33.3977i | 0.572724 | + | 1.76266i | 0.643802 | + | 0.765192i | \(0.277356\pi\) |
−0.0710775 | + | 0.997471i | \(0.522644\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.31999 | + | 13.2956i | −0.227368 | + | 0.699767i | ||||
\(362\) | 9.61096 | + | 2.04287i | 0.505141 | + | 0.107371i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.560131 | + | 0.119060i | −0.0293589 | + | 0.00624042i | ||||
\(365\) | 2.42510 | + | 1.30242i | 0.126935 | + | 0.0681717i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.51317 | − | 23.9112i | −0.131186 | − | 1.24815i | −0.839933 | − | 0.542690i | \(-0.817406\pi\) |
0.708747 | − | 0.705463i | \(-0.249261\pi\) | |||||||
\(368\) | 7.83493 | 0.408424 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 25.4664 | + | 21.5501i | 1.32394 | + | 1.12034i | ||||
\(371\) | −3.35680 | + | 1.49454i | −0.174276 | + | 0.0775928i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.97274 | + | 0.419319i | −0.102145 | + | 0.0217115i | −0.258700 | − | 0.965958i | \(-0.583294\pi\) |
0.156556 | + | 0.987669i | \(0.449961\pi\) | |||||||
\(374\) | 0.0758467 | + | 0.131370i | 0.00392194 | + | 0.00679300i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.42524 | + | 7.66473i | −0.228214 | + | 0.395278i | ||||
\(377\) | 18.2340 | − | 56.1186i | 0.939100 | − | 2.89025i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.2526 | − | 11.0817i | −0.783474 | − | 0.569227i | 0.122546 | − | 0.992463i | \(-0.460894\pi\) |
−0.906020 | + | 0.423236i | \(0.860894\pi\) | |||||||
\(380\) | −0.177578 | + | 0.0637977i | −0.00910958 | + | 0.00327275i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −8.06032 | − | 13.9609i | −0.412402 | − | 0.714301i | ||||
\(383\) | −10.1089 | − | 4.50077i | −0.516541 | − | 0.229979i | 0.131873 | − | 0.991267i | \(-0.457901\pi\) |
−0.648414 | + | 0.761288i | \(0.724567\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.00523367 | + | 0.170172i | 0.000266732 | + | 0.00867276i | ||||
\(386\) | 9.84708 | − | 30.3062i | 0.501203 | − | 1.54254i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.120964 | − | 0.372288i | −0.00614100 | − | 0.0189000i | ||||
\(389\) | 14.4803 | + | 16.0820i | 0.734181 | + | 0.815391i | 0.988419 | − | 0.151751i | \(-0.0484912\pi\) |
−0.254238 | + | 0.967142i | \(0.581825\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.32763 | + | 4.80632i | −0.218858 | + | 0.243066i | ||||
\(392\) | −3.05658 | − | 1.36088i | −0.154380 | − | 0.0687346i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.90935 | − | 37.1950i | −0.196950 | − | 1.87386i | ||||
\(395\) | 0.489416 | + | 1.99833i | 0.0246252 | + | 0.100547i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.42510 | + | 4.66811i | 0.322467 | + | 0.234286i | 0.737227 | − | 0.675645i | \(-0.236135\pi\) |
−0.414761 | + | 0.909931i | \(0.636135\pi\) | |||||||
\(398\) | 15.8646 | + | 17.6195i | 0.795222 | + | 0.883184i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −17.1839 | − | 10.9376i | −0.859196 | − | 0.546880i | ||||
\(401\) | −6.27204 | − | 10.8635i | −0.313211 | − | 0.542497i | 0.665845 | − | 0.746090i | \(-0.268071\pi\) |
−0.979056 | + | 0.203593i | \(0.934738\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 21.6745 | − | 9.65011i | 1.07968 | − | 0.480706i | ||||
\(404\) | −0.167027 | − | 0.121352i | −0.00830992 | − | 0.00603751i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 26.0188 | − | 18.9038i | 1.29129 | − | 0.938178i | ||||
\(407\) | −0.165136 | + | 0.286024i | −0.00818549 | + | 0.0141777i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.96912 | + | 3.29754i | −0.146813 | + | 0.163053i | −0.812066 | − | 0.583565i | \(-0.801657\pi\) |
0.665253 | + | 0.746618i | \(0.268324\pi\) | |||||||
\(410\) | −0.921069 | + | 5.09947i | −0.0454884 | + | 0.251845i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.0675159 | + | 0.0143510i | 0.00332627 | + | 0.000707021i | ||||
\(413\) | −9.54906 | − | 29.3890i | −0.469879 | − | 1.44614i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.3982 | − | 0.918825i | −0.608604 | − | 0.0451034i | ||||
\(416\) | 1.31488 | + | 0.279486i | 0.0644672 | + | 0.0137029i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.0505340 | − | 0.0875274i | −0.00247170 | − | 0.00428110i | ||||
\(419\) | 6.70380 | + | 2.98472i | 0.327502 | + | 0.145813i | 0.563900 | − | 0.825843i | \(-0.309300\pi\) |
−0.236398 | + | 0.971656i | \(0.575967\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.15154 | + | 3.18407i | −0.348545 | + | 0.155182i | −0.573540 | − | 0.819178i | \(-0.694430\pi\) |
0.224995 | + | 0.974360i | \(0.427763\pi\) | |||||||
\(422\) | −11.1120 | − | 8.07334i | −0.540924 | − | 0.393004i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.27182 | 0.207458 | ||||||||
\(425\) | 16.2012 | − | 4.50004i | 0.785872 | − | 0.218284i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 25.0316 | − | 5.32062i | 1.21136 | − | 0.257483i | ||||
\(428\) | 0.0727316 | − | 0.691995i | 0.00351562 | − | 0.0334488i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.09664 | + | 35.6570i | 0.0528845 | + | 1.71953i | ||||
\(431\) | −10.2026 | + | 7.41261i | −0.491441 | + | 0.357053i | −0.805738 | − | 0.592272i | \(-0.798231\pi\) |
0.314297 | + | 0.949325i | \(0.398231\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.3440 | − | 22.0462i | 1.45824 | − | 1.05947i | 0.474425 | − | 0.880296i | \(-0.342656\pi\) |
0.983817 | − | 0.179179i | \(-0.0573441\pi\) | |||||||
\(434\) | 12.6489 | + | 2.68861i | 0.607167 | + | 0.129057i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.166501 | + | 0.0353908i | −0.00797393 | + | 0.00169491i | ||||
\(437\) | 2.88334 | − | 3.20228i | 0.137929 | − | 0.153186i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.3463 | + | 25.9287i | 1.11426 | + | 1.23751i | 0.968721 | + | 0.248154i | \(0.0798239\pi\) |
0.145536 | + | 0.989353i | \(0.453509\pi\) | |||||||
\(440\) | 0.0749088 | − | 0.183207i | 0.00357114 | − | 0.00873406i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −24.5074 | + | 17.8057i | −1.16570 | + | 0.846929i | ||||
\(443\) | 12.2771 | − | 21.2646i | 0.583304 | − | 1.01031i | −0.411780 | − | 0.911283i | \(-0.635093\pi\) |
0.995085 | − | 0.0990295i | \(-0.0315738\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.94443 | + | 3.19251i | 0.281793 | + | 0.151339i | ||||
\(446\) | −3.86690 | + | 36.7911i | −0.183103 | + | 1.74211i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −12.6461 | − | 14.0449i | −0.597471 | − | 0.663558i | ||||
\(449\) | −5.69752 | −0.268882 | −0.134441 | − | 0.990922i | \(-0.542924\pi\) | ||||
−0.134441 | + | 0.990922i | \(0.542924\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.0513016 | −0.00241570 | ||||||||
\(452\) | −0.0939523 | − | 0.104345i | −0.00441915 | − | 0.00490796i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.00991 | + | 28.6374i | −0.141262 | + | 1.34402i | ||||
\(455\) | −33.6875 | + | 4.59160i | −1.57929 | + | 0.215258i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.9907 | + | 25.9647i | −0.701238 | + | 1.21458i | 0.266795 | + | 0.963753i | \(0.414035\pi\) |
−0.968032 | + | 0.250826i | \(0.919298\pi\) | |||||||
\(458\) | −8.03681 | + | 5.83908i | −0.375535 | + | 0.272842i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.161519 | − | 0.0119701i | −0.00753088 | − | 0.000558110i | ||||
\(461\) | 3.32317 | + | 3.69076i | 0.154776 | + | 0.171896i | 0.815546 | − | 0.578693i | \(-0.196437\pi\) |
−0.660770 | + | 0.750588i | \(0.729770\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.65307 | − | 8.49959i | 0.355668 | − | 0.395009i | −0.538585 | − | 0.842571i | \(-0.681041\pi\) |
0.894253 | + | 0.447562i | \(0.147708\pi\) | |||||||
\(464\) | −37.2612 | + | 7.92011i | −1.72981 | + | 0.367682i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −39.4208 | − | 8.37915i | −1.82613 | − | 0.388157i | ||||
\(467\) | −21.2823 | + | 15.4625i | −0.984827 | + | 0.715518i | −0.958782 | − | 0.284142i | \(-0.908291\pi\) |
−0.0260445 | + | 0.999661i | \(0.508291\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.43811 | + | 3.22447i | −0.204933 | + | 0.148892i | ||||
\(470\) | 5.67422 | − | 8.33734i | 0.261732 | − | 0.384573i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.75518 | + | 35.7282i | −0.172846 | + | 1.64452i | ||||
\(473\) | −0.345453 | + | 0.0734284i | −0.0158840 | + | 0.00337624i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.7943 | + | 2.99821i | −0.495275 | + | 0.137568i | ||||
\(476\) | −0.305170 | −0.0139874 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5.13604 | − | 3.73155i | −0.234917 | − | 0.170677i | ||||
\(479\) | −0.427614 | + | 0.190386i | −0.0195382 | + | 0.00869896i | −0.416482 | − | 0.909144i | \(-0.636737\pi\) |
0.396944 | + | 0.917843i | \(0.370071\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −60.2525 | − | 26.8261i | −2.74728 | − | 1.22317i | ||||
\(482\) | 10.8263 | + | 18.7518i | 0.493126 | + | 0.854119i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.405194 | + | 0.0861265i | 0.0184179 | + | 0.00391484i | ||||
\(485\) | −5.52859 | − | 22.5737i | −0.251041 | − | 1.02502i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.55836 | + | 4.79614i | 0.0706160 | + | 0.217334i | 0.980136 | − | 0.198326i | \(-0.0635506\pi\) |
−0.909520 | + | 0.415660i | \(0.863551\pi\) | |||||||
\(488\) | −29.1009 | − | 6.18558i | −1.31733 | − | 0.280008i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.35881 | + | 1.80388i | 0.151736 | + | 0.0814909i | ||||
\(491\) | 5.02924 | − | 5.58554i | 0.226966 | − | 0.252072i | −0.618896 | − | 0.785473i | \(-0.712420\pi\) |
0.845862 | + | 0.533401i | \(0.179086\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.7227 | − | 27.2325i | 0.708113 | − | 1.22649i | ||||
\(494\) | 16.3284 | − | 11.8633i | 0.734649 | − | 0.533754i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −12.3916 | − | 9.00306i | −0.556401 | − | 0.404249i | ||||
\(497\) | 9.89159 | − | 4.40402i | 0.443699 | − | 0.197547i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.05527 | + | 7.02394i | 0.181539 | + | 0.314435i | 0.942405 | − | 0.334474i | \(-0.108559\pi\) |
−0.760866 | + | 0.648909i | \(0.775225\pi\) | |||||||
\(500\) | 0.337541 | + | 0.251735i | 0.0150953 | + | 0.0112579i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −13.4055 | − | 14.8883i | −0.598317 | − | 0.664499i | ||||
\(503\) | 16.3455 | + | 11.8757i | 0.728812 | + | 0.529513i | 0.889187 | − | 0.457543i | \(-0.151271\pi\) |
−0.160376 | + | 0.987056i | \(0.551271\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.35710 | − | 7.91812i | −0.416385 | − | 0.352352i | ||||
\(506\) | −0.00906799 | − | 0.0862761i | −0.000403121 | − | 0.00383544i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.340795 | + | 0.151732i | 0.0151204 | + | 0.00673201i | ||||
\(509\) | −14.0043 | + | 15.5533i | −0.620728 | + | 0.689389i | −0.968733 | − | 0.248104i | \(-0.920193\pi\) |
0.348005 | + | 0.937493i | \(0.386859\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.98476 | − | 2.20430i | −0.0878005 | − | 0.0975124i | ||||
\(512\) | 6.78465 | + | 20.8810i | 0.299842 | + | 0.922819i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.20054 | − | 12.9279i | 0.185278 | − | 0.570227i | ||||
\(515\) | 3.93461 | + | 1.14597i | 0.173379 | + | 0.0504975i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.0912101 | + | 0.0406093i | 0.00401141 | + | 0.00178600i | ||||
\(518\) | −17.9740 | − | 31.1318i | −0.789731 | − | 1.36785i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 37.9492 | + | 11.0529i | 1.66418 | + | 0.484700i | ||||
\(521\) | −5.09658 | − | 3.70289i | −0.223285 | − | 0.162226i | 0.470519 | − | 0.882390i | \(-0.344067\pi\) |
−0.693804 | + | 0.720164i | \(0.744067\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.61794 | + | 20.3679i | −0.289382 | + | 0.890628i | 0.695668 | + | 0.718363i | \(0.255108\pi\) |
−0.985051 | + | 0.172264i | \(0.944892\pi\) | |||||||
\(524\) | 0.0166756 | − | 0.0288831i | 0.000728479 | − | 0.00126176i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17.3243 | − | 30.0065i | −0.755374 | − | 1.30835i | ||||
\(527\) | 12.3674 | − | 2.62878i | 0.538734 | − | 0.114511i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.6326 | + | 7.85055i | −0.766636 | + | 0.341328i | ||||
\(530\) | −4.85439 | − | 0.359756i | −0.210861 | − | 0.0156268i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.203324 | 0.00881520 | ||||||||
\(533\) | −1.07087 | − | 10.1887i | −0.0463847 | − | 0.441321i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.34286 | − | 40.6535i | 0.317459 | − | 1.75760i | ||||
\(536\) | 6.23825 | − | 1.32598i | 0.269451 | − | 0.0572736i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −22.2954 | − | 4.73904i | −0.961224 | − | 0.204314i | ||||
\(539\) | −0.0116636 | + | 0.0358970i | −0.000502388 | + | 0.00154619i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.06074 | + | 6.34232i | 0.0885983 | + | 0.272678i | 0.985533 | − | 0.169486i | \(-0.0542109\pi\) |
−0.896934 | + | 0.442164i | \(0.854211\pi\) | |||||||
\(542\) | −2.13962 | − | 20.3572i | −0.0919047 | − | 0.874415i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.654436 | + | 0.291374i | 0.0280587 | + | 0.0124925i | ||||
\(545\) | −10.0137 | + | 1.36487i | −0.428939 | + | 0.0584644i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.9519 | + | 12.8902i | −1.23790 | + | 0.551147i | −0.918103 | − | 0.396341i | \(-0.870280\pi\) |
−0.319792 | + | 0.947488i | \(0.603613\pi\) | |||||||
\(548\) | 0.130266 | − | 0.400917i | 0.00556467 | − | 0.0171263i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.100553 | + | 0.201884i | −0.00428762 | + | 0.00860834i | ||||
\(551\) | −10.4754 | + | 18.1440i | −0.446269 | + | 0.772961i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.231733 | − | 2.20479i | 0.00985427 | − | 0.0937571i | ||||
\(554\) | −2.35573 | + | 22.4133i | −0.100085 | + | 0.952248i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.000158598 | 0.00150896i | 6.72606e−6 | 6.39942e-5i | ||||||
\(557\) | 23.0896 | 0.978337 | 0.489168 | − | 0.872189i | \(-0.337300\pi\) | ||||
0.489168 | + | 0.872189i | \(0.337300\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21.7941 | − | 67.0755i | −0.921794 | − | 2.83699i | ||||
\(560\) | 13.4412 | + | 17.3523i | 0.567993 | + | 0.733267i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.41084 | + | 1.56689i | −0.0595125 | + | 0.0660953i | ||||
\(563\) | 24.5755 | − | 27.2938i | 1.03573 | − | 1.15030i | 0.0472616 | − | 0.998883i | \(-0.484951\pi\) |
0.988470 | − | 0.151414i | \(-0.0483828\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.10500 | − | 6.59045i | −0.214769 | − | 0.277262i | ||||
\(566\) | 6.00856 | + | 18.4925i | 0.252559 | + | 0.777296i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.5879 | −0.528177 | ||||||||
\(569\) | 1.66757 | + | 15.8659i | 0.0699083 | + | 0.665133i | 0.972223 | + | 0.234055i | \(0.0751997\pi\) |
−0.902315 | + | 0.431077i | \(0.858134\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.299358 | + | 2.84820i | −0.0125277 | + | 0.119193i | −0.998998 | − | 0.0447439i | \(-0.985753\pi\) |
0.986471 | + | 0.163937i | \(0.0524195\pi\) | |||||||
\(572\) | 0.000785026 | − | 0.00746903i | 3.28236e−5 | − | 0.000312296i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.79192 | − | 4.83575i | 0.116532 | − | 0.201840i | ||||
\(575\) | −9.51094 | − | 1.41749i | −0.396634 | − | 0.0591133i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.14710 | − | 6.60811i | 0.0893851 | − | 0.275099i | −0.896365 | − | 0.443318i | \(-0.853801\pi\) |
0.985750 | + | 0.168218i | \(0.0538014\pi\) | |||||||
\(578\) | 7.42120 | − | 3.30413i | 0.308681 | − | 0.137434i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.780251 | − | 0.106348i | 0.0323982 | − | 0.00441587i | ||||
\(581\) | 12.2381 | + | 5.44877i | 0.507724 | + | 0.226053i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.00503725 | − | 0.0479262i | −0.000208622 | − | 0.00198490i | ||||
\(584\) | 1.06561 | + | 3.27960i | 0.0440951 | + | 0.135711i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.17715 | − | 22.0890i | 0.296485 | − | 0.912489i | ||||
\(587\) | 0.784085 | + | 0.166662i | 0.0323626 | + | 0.00687889i | 0.224065 | − | 0.974574i | \(-0.428067\pi\) |
−0.191702 | + | 0.981453i | \(0.561401\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.23998 | + | 1.75146i | −0.339522 | + | 0.0721677i | ||||
\(590\) | 7.27619 | − | 40.2844i | 0.299556 | − | 1.65848i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.45073 | + | 42.3459i | 0.182924 | + | 1.74041i | ||||
\(593\) | −19.9879 | −0.820804 | −0.410402 | − | 0.911905i | \(-0.634612\pi\) | ||||
−0.410402 | + | 0.911905i | \(0.634612\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.0689 | − | 1.33908i | −0.740754 | − | 0.0548969i | ||||
\(596\) | 0.278511 | − | 0.124001i | 0.0114082 | − | 0.00507928i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 16.9455 | − | 3.60187i | 0.692951 | − | 0.147291i | ||||
\(599\) | −1.80743 | − | 3.13056i | −0.0738495 | − | 0.127911i | 0.826736 | − | 0.562590i | \(-0.190195\pi\) |
−0.900585 | + | 0.434679i | \(0.856862\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.5936 | − | 32.2050i | 0.758449 | − | 1.31367i | −0.185193 | − | 0.982702i | \(-0.559291\pi\) |
0.943642 | − | 0.330969i | \(-0.107376\pi\) | |||||||
\(602\) | 11.8787 | − | 36.5589i | 0.484140 | − | 1.49003i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.282332 | − | 0.205126i | −0.0114879 | − | 0.00834646i | ||||
\(605\) | 23.6134 | + | 6.87748i | 0.960019 | + | 0.279609i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.6597 | − | 28.8555i | −0.676197 | − | 1.17121i | −0.976117 | − | 0.217244i | \(-0.930293\pi\) |
0.299920 | − | 0.953964i | \(-0.403040\pi\) | |||||||
\(608\) | −0.436027 | − | 0.194132i | −0.0176832 | − | 0.00787309i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 32.5486 | + | 9.47990i | 1.31785 | + | 0.383830i | ||||
\(611\) | −6.16123 | + | 18.9623i | −0.249257 | + | 0.767134i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.94595 | + | 5.98902i | 0.0785962 | + | 0.241894i | 0.982633 | − | 0.185561i | \(-0.0594102\pi\) |
−0.904037 | + | 0.427455i | \(0.859410\pi\) | |||||||
\(614\) | −13.7073 | − | 15.2235i | −0.553181 | − | 0.614370i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.142711 | + | 0.158497i | −0.00575001 | + | 0.00638603i | ||||
\(617\) | −24.1693 | − | 10.7608i | −0.973018 | − | 0.433215i | −0.142248 | − | 0.989831i | \(-0.545433\pi\) |
−0.830770 | + | 0.556616i | \(0.812100\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.63835 | + | 15.5879i | 0.0658508 | + | 0.626529i | 0.976821 | + | 0.214057i | \(0.0686678\pi\) |
−0.910970 | + | 0.412472i | \(0.864666\pi\) | |||||||
\(620\) | 0.241703 | + | 0.204533i | 0.00970701 | + | 0.00821423i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 25.8570 | + | 18.7862i | 1.03677 | + | 0.753260i | ||||
\(623\) | −4.86507 | − | 5.40320i | −0.194915 | − | 0.216475i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.8810 | + | 16.3862i | 0.755240 | + | 0.655448i | ||||
\(626\) | −17.4420 | − | 30.2105i | −0.697124 | − | 1.20745i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.399486 | − | 0.177862i | 0.0159412 | − | 0.00709748i | ||||
\(629\) | −28.4353 | − | 20.6595i | −1.13379 | − | 0.823748i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.57126 | − | 1.14159i | 0.0625508 | − | 0.0454458i | −0.556070 | − | 0.831135i | \(-0.687692\pi\) |
0.618621 | + | 0.785689i | \(0.287692\pi\) | |||||||
\(632\) | −1.28867 | + | 2.23204i | −0.0512604 | + | 0.0887856i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 16.5221 | − | 18.3497i | 0.656176 | − | 0.728758i | ||||
\(635\) | 19.5125 | + | 10.4794i | 0.774330 | + | 0.415861i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.37273 | − | 1.56712i | −0.292118 | − | 0.0620916i | ||||
\(638\) | 0.130340 | + | 0.401144i | 0.00516019 | + | 0.0158814i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −6.18236 | − | 25.2431i | −0.244379 | − | 0.997822i | ||||
\(641\) | 16.3424 | + | 3.47368i | 0.645484 | + | 0.137202i | 0.519010 | − | 0.854768i | \(-0.326301\pi\) |
0.126474 | + | 0.991970i | \(0.459634\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.9436 | + | 27.6151i | 0.628753 | + | 1.08903i | 0.987802 | + | 0.155713i | \(0.0497676\pi\) |
−0.359050 | + | 0.933319i | \(0.616899\pi\) | |||||||
\(644\) | 0.159434 | + | 0.0709846i | 0.00628258 | + | 0.00279719i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.82589 | − | 4.37477i | 0.386595 | − | 0.172123i | ||||
\(647\) | −16.4808 | − | 11.9740i | −0.647928 | − | 0.470747i | 0.214637 | − | 0.976694i | \(-0.431143\pi\) |
−0.862565 | + | 0.505947i | \(0.831143\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.405268 | 0.0159082 | ||||||||
\(650\) | −42.1937 | − | 15.7561i | −1.65497 | − | 0.618007i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.221312 | − | 0.0470412i | 0.00866723 | − | 0.00184228i | ||||
\(653\) | 3.91951 | − | 37.2917i | 0.153382 | − | 1.45934i | −0.599074 | − | 0.800694i | \(-0.704464\pi\) |
0.752456 | − | 0.658642i | \(-0.228869\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.11409 | − | 1.63698i | 0.0435312 | − | 0.0639620i | ||||
\(656\) | −5.35073 | + | 3.88754i | −0.208911 | + | 0.151783i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −8.79169 | + | 6.38754i | −0.342736 | + | 0.249012i | ||||
\(659\) | 24.0150 | + | 5.10455i | 0.935492 | + | 0.198845i | 0.650345 | − | 0.759639i | \(-0.274624\pi\) |
0.285147 | + | 0.958484i | \(0.407958\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.52118 | − | 1.38612i | 0.253645 | − | 0.0539138i | −0.0793344 | − | 0.996848i | \(-0.525279\pi\) |
0.332979 | + | 0.942934i | \(0.391946\pi\) | |||||||
\(662\) | 25.0393 | − | 27.8090i | 0.973181 | − | 1.08083i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.4211 | − | 11.5738i | −0.404418 | − | 0.449151i | ||||
\(665\) | 12.0387 | + | 0.892180i | 0.466840 | + | 0.0345973i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.5487 | + | 10.5702i | −0.563327 | + | 0.409281i | ||||
\(668\) | 0.254622 | − | 0.441018i | 0.00985162 | − | 0.0170635i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7.20066 | + | 0.981450i | −0.278186 | + | 0.0379167i | ||||
\(671\) | −0.0350818 | + | 0.333781i | −0.00135432 | + | 0.0128855i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.06200 | + | 8.95376i | 0.310767 | + | 0.345142i | 0.878214 | − | 0.478268i | \(-0.158735\pi\) |
−0.567446 | + | 0.823410i | \(0.692069\pi\) | |||||||
\(674\) | −23.0492 | −0.887822 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.01015 | 0.0388521 | ||||||||
\(677\) | 16.8244 | + | 18.6854i | 0.646613 | + | 0.718137i | 0.973948 | − | 0.226772i | \(-0.0728172\pi\) |
−0.327335 | + | 0.944908i | \(0.606151\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.61773 | + | 24.9060i | −0.100459 | + | 0.955804i | ||||
\(680\) | 18.5570 | + | 9.96623i | 0.711630 | + | 0.382187i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.0847974 | + | 0.146873i | −0.00324706 | + | 0.00562408i | ||||
\(683\) | −29.2073 | + | 21.2203i | −1.11758 | + | 0.811973i | −0.983841 | − | 0.179043i | \(-0.942700\pi\) |
−0.133743 | + | 0.991016i | \(0.542700\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.47217 | − | 23.1664i | 0.361913 | − | 0.885144i | ||||
\(686\) | −18.8590 | − | 20.9450i | −0.720039 | − | 0.799685i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −30.4664 | + | 33.8363i | −1.16152 | + | 1.29000i | ||||
\(689\) | 9.41317 | − | 2.00083i | 0.358613 | − | 0.0762256i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.37700 | − | 1.56803i | −0.280634 | − | 0.0596506i | 0.0654442 | − | 0.997856i | \(-0.479154\pi\) |
−0.346078 | + | 0.938206i | \(0.612487\pi\) | |||||||
\(692\) | −0.206141 | + | 0.149770i | −0.00783629 | + | 0.00569340i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 21.6515 | − | 15.7308i | 0.821881 | − | 0.597131i | ||||
\(695\) | 0.00276922 | + | 0.0900406i | 0.000105042 | + | 0.00341544i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.570682 | − | 5.42968i | 0.0216161 | − | 0.205664i | ||||
\(698\) | 2.51215 | − | 0.533974i | 0.0950862 | − | 0.0202112i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.250583 | − | 0.378257i | −0.00947115 | − | 0.0142968i | ||||
\(701\) | 41.9293 | 1.58365 | 0.791824 | − | 0.610749i | \(-0.209132\pi\) | ||||
0.791824 | + | 0.610749i | \(0.209132\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.9454 | + | 13.7647i | 0.714541 | + | 0.519144i | ||||
\(704\) | 0.226433 | − | 0.100814i | 0.00853400 | − | 0.00379958i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.39447 | − | 1.06609i | −0.0901172 | − | 0.0401228i | ||||
\(707\) | 6.60415 | + | 11.4387i | 0.248375 | + | 0.430197i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.535037 | + | 0.113726i | 0.0200937 | + | 0.00427105i | 0.217948 | − | 0.975960i | \(-0.430064\pi\) |
−0.197854 | + | 0.980232i | \(0.563397\pi\) | |||||||
\(710\) | 14.3046 | + | 1.06011i | 0.536842 | + | 0.0397851i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.61203 | + | 8.03900i | 0.0978899 | + | 0.301274i | ||||
\(713\) | −7.07276 | − | 1.50336i | −0.264877 | − | 0.0563014i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.0792549 | − | 0.438792i | 0.00296397 | − | 0.0164099i | ||||
\(716\) | 0.181404 | − | 0.201469i | 0.00677937 | − | 0.00752925i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 25.0638 | − | 43.4117i | 0.935371 | − | 1.62011i | ||||
\(719\) | 23.1267 | − | 16.8026i | 0.862482 | − | 0.626630i | −0.0660771 | − | 0.997815i | \(-0.521048\pi\) |
0.928559 | + | 0.371185i | \(0.121048\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.57254 | − | 2.59560i | −0.133048 | − | 0.0966651i | ||||
\(722\) | 18.2304 | − | 8.11671i | 0.678466 | − | 0.302073i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.129620 | − | 0.224508i | −0.00481728 | − | 0.00834378i | ||||
\(725\) | 46.6649 | − | 2.87309i | 1.73309 | − | 0.106704i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.0768 | + | 28.9613i | 0.967136 | + | 1.07411i | 0.997216 | + | 0.0745661i | \(0.0237572\pi\) |
−0.0300799 | + | 0.999547i | \(0.509576\pi\) | |||||||
\(728\) | −34.4571 | − | 25.0345i | −1.27706 | − | 0.927841i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.934734 | − | 3.81660i | −0.0345960 | − | 0.141259i | ||||
\(731\) | −3.92869 | − | 37.3790i | −0.145308 | − | 1.38251i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.18772 | + | 4.09063i | 0.339356 | + | 0.151091i | 0.569337 | − | 0.822104i | \(-0.307200\pi\) |
−0.229981 | + | 0.973195i | \(0.573867\pi\) | |||||||
\(734\) | −22.9649 | + | 25.5051i | −0.847648 | + | 0.941409i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.274131 | − | 0.304453i | −0.0101046 | − | 0.0112223i | ||||
\(737\) | −0.0222324 | − | 0.0684244i | −0.000818942 | − | 0.00252044i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.4137 | + | 38.2054i | −0.456645 | + | 1.40541i | 0.412548 | + | 0.910936i | \(0.364639\pi\) |
−0.869193 | + | 0.494473i | \(0.835361\pi\) | |||||||
\(740\) | −0.0270576 | − | 0.879773i | −0.000994656 | − | 0.0323411i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.79172 | + | 2.13341i | 0.175909 | + | 0.0783199i | ||||
\(743\) | −6.57831 | − | 11.3940i | −0.241335 | − | 0.418004i | 0.719760 | − | 0.694223i | \(-0.244252\pi\) |
−0.961095 | + | 0.276219i | \(0.910919\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.0346 | − | 6.11993i | 0.624099 | − | 0.224217i | ||||
\(746\) | 2.32911 | + | 1.69220i | 0.0852747 | + | 0.0619557i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.00123677 | − | 0.00380638i | 4.52207e−5 | − | 0.000139175i | ||||
\(749\) | −22.2575 | + | 38.5511i | −0.813270 | + | 1.40863i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.07148 | + | 10.5161i | 0.221552 | + | 0.383738i | 0.955279 | − | 0.295705i | \(-0.0955546\pi\) |
−0.733728 | + | 0.679444i | \(0.762221\pi\) | |||||||
\(752\) | 12.5905 | − | 2.67619i | 0.459127 | − | 0.0975905i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −76.9478 | + | 34.2594i | −2.80228 | + | 1.24765i | ||||
\(755\) | −15.8166 | − | 13.3843i | −0.575625 | − | 0.487103i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.4368 | −0.379330 | −0.189665 | − | 0.981849i | \(-0.560740\pi\) | ||||
−0.189665 | + | 0.981849i | \(0.560740\pi\) | |||||||
\(758\) | 2.81311 | + | 26.7650i | 0.102177 | + | 0.972148i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −12.3639 | − | 6.64014i | −0.448485 | − | 0.240863i | ||||
\(761\) | −3.64738 | + | 0.775275i | −0.132218 | + | 0.0281037i | −0.273545 | − | 0.961859i | \(-0.588196\pi\) |
0.141328 | + | 0.989963i | \(0.454863\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.6520 | + | 2.26416i | 0.385630 | + | 0.0819681i | ||||
\(764\) | −0.131433 | + | 0.404508i | −0.00475507 | + | 0.0146346i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.88115 | + | 15.0226i | 0.176363 | + | 0.542790i | ||||
\(767\) | 8.45960 | + | 80.4877i | 0.305458 | + | 2.90624i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.2623 | − | 12.5832i | −1.01916 | − | 0.453761i | −0.172003 | − | 0.985097i | \(-0.555024\pi\) |
−0.847162 | + | 0.531335i | \(0.821690\pi\) | |||||||
\(770\) | 0.175522 | − | 0.168094i | 0.00632537 | − | 0.00605767i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.768058 | + | 0.341961i | −0.0276430 | + | 0.0123075i | ||||
\(773\) | 1.07567 | − | 3.31057i | 0.0386891 | − | 0.119073i | −0.929847 | − | 0.367947i | \(-0.880061\pi\) |
0.968536 | + | 0.248874i | \(0.0800607\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.4136 | + | 13.1708i | 0.481830 | + | 0.473111i | ||||
\(776\) | 14.5572 | − | 25.2138i | 0.522572 | − | 0.905122i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.22900 | − | 30.7219i | 0.115765 | − | 1.10143i | ||||
\(779\) | −0.380225 | + | 3.61760i | −0.0136230 | + | 0.129614i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.0148434 | + | 0.141226i | 0.000531140 | + | 0.00505346i | ||||
\(782\) | 9.23220 | 0.330143 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.50369 | + | 4.62788i | 0.0537032 | + | 0.165282i | ||||
\(785\) | 24.4338 | − | 8.77820i | 0.872078 | − | 0.313307i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.5111 | − | 34.9966i | 1.12325 | − | 1.24749i | 0.157640 | − | 0.987497i | \(-0.449612\pi\) |
0.965609 | − | 0.259998i | \(-0.0837218\pi\) | |||||||
\(788\) | −0.660268 | + | 0.733301i | −0.0235211 | + | 0.0261228i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.65238 | − | 2.42790i | 0.0587891 | − | 0.0863810i | ||||
\(791\) | 2.77585 | + | 8.54319i | 0.0986979 | + | 0.303761i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −67.0224 | −2.38004 | ||||||||
\(794\) | −1.18501 | − | 11.2746i | −0.0420545 | − | 0.400122i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.0653872 | − | 0.622117i | 0.00231759 | − | 0.0220504i | ||||
\(797\) | −3.29146 | + | 31.3161i | −0.116589 | + | 1.10927i | 0.767206 | + | 0.641401i | \(0.221646\pi\) |
−0.883795 | + | 0.467873i | \(0.845020\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.31265 | + | 9.20178i | −0.187948 | + | 0.325536i | ||||
\(800\) | 0.176218 | + | 1.05043i | 0.00623024 | + | 0.0371382i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −5.53334 | + | 17.0299i | −0.195389 | + | 0.601345i | ||||
\(803\) | 0.0355378 | − | 0.0158225i | 0.00125410 | − | 0.000558363i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.12852 | + | 4.90255i | 0.321738 | + | 0.172792i | ||||
\(806\) | −30.9397 | − | 13.7752i | −1.08980 | − | 0.485211i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.60509 | − | 15.2714i | −0.0564669 | − | 0.537246i | ||||
\(809\) | 8.49171 | + | 26.1348i | 0.298553 | + | 0.918851i | 0.982005 | + | 0.188856i | \(0.0604778\pi\) |
−0.683452 | + | 0.729995i | \(0.739522\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.41545 | + | 7.43400i | −0.0848180 | + | 0.261043i | −0.984467 | − | 0.175572i | \(-0.943823\pi\) |
0.899649 | + | 0.436615i | \(0.143823\pi\) | |||||||
\(812\) | −0.829990 | − | 0.176420i | −0.0291269 | − | 0.00619112i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.461150 | − | 0.0980206i | 0.0161633 | − | 0.00343562i | ||||
\(815\) | 13.3101 | − | 1.81417i | 0.466234 | − | 0.0635477i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.61755 | + | 24.9043i | 0.0915764 | + | 0.871291i | ||||
\(818\) | 6.33407 | 0.221466 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.116246 | − | 0.0719679i | 0.00405950 | − | 0.00251323i | ||||
\(821\) | 19.5212 | − | 8.69141i | 0.681295 | − | 0.303332i | −0.0367542 | − | 0.999324i | \(-0.511702\pi\) |
0.718049 | + | 0.695992i | \(0.245035\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 30.8456 | − | 6.55643i | 1.07521 | − | 0.228543i | 0.363911 | − | 0.931434i | \(-0.381441\pi\) |
0.711298 | + | 0.702891i | \(0.248108\pi\) | |||||||
\(824\) | 2.56689 | + | 4.44598i | 0.0894217 | + | 0.154883i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −22.0554 | + | 38.2010i | −0.767405 | + | 1.32918i | ||||
\(827\) | −0.0456076 | + | 0.140366i | −0.00158593 | + | 0.00488099i | −0.951846 | − | 0.306575i | \(-0.900817\pi\) |
0.950260 | + | 0.311456i | \(0.100817\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.5635 | − | 22.9322i | −1.09625 | − | 0.796469i | −0.115802 | − | 0.993272i | \(-0.536944\pi\) |
−0.980443 | + | 0.196803i | \(0.936944\pi\) | |||||||
\(830\) | 10.8676 | + | 14.0298i | 0.377220 | + | 0.486982i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 24.7486 | + | 42.8659i | 0.858005 | + | 1.48611i | ||||
\(833\) | −3.66953 | − | 1.63378i | −0.127142 | − | 0.0566071i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.0112 | − | 24.9952i | 0.588697 | − | 0.864993i | ||||
\(836\) | −0.000824014 | 0.00253605i | −2.84991e−5 | 8.77112e-5i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3.23698 | − | 9.96239i | −0.111819 | − | 0.344145i | ||||
\(839\) | −25.7166 | − | 28.5612i | −0.887836 | − | 0.986042i | 0.112135 | − | 0.993693i | \(-0.464231\pi\) |
−0.999971 | + | 0.00765121i | \(0.997565\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 39.1003 | − | 43.4253i | 1.34829 | − | 1.49743i | ||||
\(842\) | 10.2086 | + | 4.54515i | 0.351811 | + | 0.156636i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.0378798 | + | 0.360402i | 0.00130388 | + | 0.0124056i | ||||
\(845\) | 59.8106 | + | 4.43254i | 2.05755 | + | 0.152484i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.4404 | − | 15.5774i | −0.736701 | − | 0.535244i | ||||
\(848\) | −4.15714 | − | 4.61697i | −0.142757 | − | 0.158547i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −20.2485 | − | 12.8882i | −0.694516 | − | 0.442061i | ||||
\(851\) | 10.0503 | + | 17.4077i | 0.344521 | + | 0.596728i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27.6057 | + | 12.2909i | −0.945202 | + | 0.420831i | −0.820681 | − | 0.571386i | \(-0.806406\pi\) |
−0.124520 | + | 0.992217i | \(0.539739\pi\) | |||||||
\(854\) | −29.5534 | − | 21.4718i | −1.01130 | − | 0.734750i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 41.8679 | − | 30.4188i | 1.43102 | − | 1.03969i | ||||
\(857\) | 3.63200 | − | 6.29081i | 0.124067 | − | 0.214890i | −0.797301 | − | 0.603582i | \(-0.793740\pi\) |
0.921368 | + | 0.388692i | \(0.127073\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.0773 | + | 23.4088i | −0.719149 | + | 0.798696i | −0.986301 | − | 0.164958i | \(-0.947251\pi\) |
0.267151 | + | 0.963655i | \(0.413918\pi\) | |||||||
\(860\) | 0.679768 | − | 0.651000i | 0.0231799 | − | 0.0221989i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 17.6085 | + | 3.74281i | 0.599749 | + | 0.127481i | ||||
\(863\) | 14.1918 | + | 43.6780i | 0.483096 | + | 1.48682i | 0.834719 | + | 0.550675i | \(0.185630\pi\) |
−0.351623 | + | 0.936142i | \(0.614370\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.8627 | + | 7.96325i | −0.437344 | + | 0.270759i | ||||
\(866\) | −52.3705 | − | 11.1317i | −1.77962 | − | 0.378270i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.170591 | − | 0.295473i | −0.00579025 | − | 0.0100290i | ||||
\(869\) | 0.0265612 | + | 0.0118258i | 0.000901025 | + | 0.000401162i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.1252 | − | 5.84373i | 0.444732 | − | 0.198007i | ||||
\(872\) | −10.2424 | − | 7.44158i | −0.346853 | − | 0.252004i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6.15108 | −0.208063 | ||||||||
\(875\) | −13.1771 | − | 23.4959i | −0.445467 | − | 0.794308i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.3320 | + | 3.25891i | −0.517724 | + | 0.110046i | −0.459361 | − | 0.888250i | \(-0.651922\pi\) |
−0.0583633 | + | 0.998295i | \(0.518588\pi\) | |||||||
\(878\) | 5.20604 | − | 49.5321i | 0.175695 | − | 1.67163i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.270908 | + | 0.0973277i | −0.00913230 | + | 0.00328091i | ||||
\(881\) | −36.7061 | + | 26.6685i | −1.23666 | + | 0.898486i | −0.997371 | − | 0.0724624i | \(-0.976914\pi\) |
−0.239289 | + | 0.970948i | \(0.576914\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.12115 | − | 1.54110i | 0.0713823 | − | 0.0518623i | −0.551522 | − | 0.834160i | \(-0.685953\pi\) |
0.622904 | + | 0.782298i | \(0.285953\pi\) | |||||||
\(884\) | 0.781777 | + | 0.166172i | 0.0262940 | + | 0.00558896i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −34.2845 | + | 7.28739i | −1.15181 | + | 0.244825i | ||||
\(887\) | −21.0513 | + | 23.3798i | −0.706833 | + | 0.785017i | −0.984448 | − | 0.175675i | \(-0.943789\pi\) |
0.277615 | + | 0.960692i | \(0.410456\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −15.9695 | − | 17.7359i | −0.535600 | − | 0.594844i | ||||
\(890\) | −2.29123 | − | 9.35530i | −0.0768023 | − | 0.313590i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.789632 | − | 0.573701i | 0.0264388 | − | 0.0192089i | ||||
\(893\) | 3.53963 | − | 6.13082i | 0.118449 | − | 0.205160i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.6248 | − | 11.1329i | 0.388576 | − | 0.372131i | ||||
\(896\) | −2.92728 | + | 27.8512i | −0.0977935 | + | 0.930443i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 5.44205 | + | 6.04401i | 0.181604 | + | 0.201691i | ||||
\(899\) | 35.1562 | 1.17253 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.12847 | 0.170854 | ||||||||
\(902\) | 0.0490013 | + | 0.0544215i | 0.00163157 | + | 0.00181204i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.09161 | − | 10.3859i | 0.0363063 | − | 0.345431i | ||||
\(905\) | −6.68957 | − | 13.8618i | −0.222369 | − | 0.460780i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19.4248 | − | 33.6448i | 0.644991 | − | 1.11716i | −0.339312 | − | 0.940674i | \(-0.610194\pi\) |
0.984304 | − | 0.176484i | \(-0.0564724\pi\) | |||||||
\(908\) | 0.614632 | − | 0.446556i | 0.0203973 | − | 0.0148195i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 37.0478 | + | 31.3505i | 1.22812 | + | 1.03926i | ||||
\(911\) | 16.0647 | + | 17.8417i | 0.532248 | + | 0.591121i | 0.947966 | − | 0.318373i | \(-0.103136\pi\) |
−0.415718 | + | 0.909494i | \(0.636470\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.117560 | + | 0.130564i | −0.00389067 | + | 0.00432103i | ||||
\(914\) | 41.8624 | − | 8.89812i | 1.38468 | − | 0.294324i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.256371 | + | 0.0544934i | 0.00847074 | + | 0.00180051i | ||||
\(917\) | −1.72619 | + | 1.25415i | −0.0570037 | + | 0.0414156i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.1266 | − | 24.7944i | 1.12573 | − | 0.817892i | 0.140664 | − | 0.990057i | \(-0.455076\pi\) |
0.985068 | + | 0.172165i | \(0.0550762\pi\) | |||||||
\(920\) | −7.37680 | − | 9.52329i | −0.243206 | − | 0.313974i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.741042 | − | 7.05054i | 0.0244049 | − | 0.232197i | ||||
\(923\) | −27.7381 | + | 5.89592i | −0.913012 | + | 0.194067i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.25836 | − | 52.2096i | 0.0742545 | − | 1.71664i | ||||
\(926\) | −16.3264 | −0.536519 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.61147 | + | 1.17080i | 0.0528990 | + | 0.0384334i | ||||
\(929\) | −3.60542 | + | 1.60523i | −0.118290 | + | 0.0526660i | −0.465028 | − | 0.885296i | \(-0.653956\pi\) |
0.346738 | + | 0.937962i | \(0.387289\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.44487 | + | 1.08853i | 0.0801275 | + | 0.0356751i | ||||
\(932\) | 0.531655 | + | 0.920854i | 0.0174149 | + | 0.0301636i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 36.7309 | + | 7.80738i | 1.20187 | + | 0.255465i | ||||
\(935\) | 0.0899306 | − | 0.219947i | 0.00294105 | − | 0.00719302i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.87834 | + | 30.4024i | 0.322711 | + | 0.993204i | 0.972463 | + | 0.233057i | \(0.0748729\pi\) |
−0.649752 | + | 0.760147i | \(0.725127\pi\) | |||||||
\(938\) | 7.65968 | + | 1.62812i | 0.250097 | + | 0.0531599i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.263645 | + | 0.0359348i | −0.00859915 | + | 0.00117206i | ||||
\(941\) | −9.66246 | + | 10.7313i | −0.314987 | + | 0.349829i | −0.879760 | − | 0.475417i | \(-0.842297\pi\) |
0.564773 | + | 0.825246i | \(0.308964\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.56113 | + | 2.70396i | −0.0508374 | + | 0.0880529i | ||||
\(944\) | 42.2693 | − | 30.7104i | 1.37575 | − | 0.999540i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.407858 | + | 0.296326i | 0.0132606 | + | 0.00963439i | ||||
\(947\) | −43.6238 | + | 19.4226i | −1.41758 | + | 0.631149i | −0.965399 | − | 0.260776i | \(-0.916022\pi\) |
−0.452184 | + | 0.891925i | \(0.649355\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.88422 | + | 6.72766i | 0.126087 | + | 0.218389i | ||||
\(950\) | 13.4908 | + | 8.58693i | 0.437700 | + | 0.278597i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −15.1875 | − | 16.8675i | −0.492231 | − | 0.546678i | ||||
\(953\) | 14.1198 | + | 10.2587i | 0.457387 | + | 0.332311i | 0.792505 | − | 0.609865i | \(-0.208776\pi\) |
−0.335119 | + | 0.942176i | \(0.608776\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.55702 | + | 23.3740i | −0.309258 | + | 0.756364i | ||||
\(956\) | 0.0175083 | + | 0.166580i | 0.000566259 | + | 0.00538760i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.610405 | + | 0.271770i | 0.0197213 | + | 0.00878048i | ||||
\(959\) | −18.0458 | + | 20.0419i | −0.582729 | + | 0.647186i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.2843 | − | 12.5325i | −0.364011 | − | 0.404275i | ||||
\(962\) | 29.0933 | + | 89.5400i | 0.938006 | + | 2.88689i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.176536 | − | 0.543321i | 0.00568583 | − | 0.0174992i | ||||
\(965\) | −46.9768 | + | 16.8771i | −1.51224 | + | 0.543294i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.4521 | + | 10.4416i | 0.754170 | + | 0.335778i | 0.747555 | − | 0.664200i | \(-0.231228\pi\) |
0.00661483 | + | 0.999978i | \(0.497894\pi\) | |||||||
\(968\) | 15.4051 | + | 26.6823i | 0.495137 | + | 0.857603i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −18.6658 | + | 27.4264i | −0.599324 | + | 0.880608i | ||||
\(971\) | 0.505556 | + | 0.367308i | 0.0162241 | + | 0.0117875i | 0.595868 | − | 0.803083i | \(-0.296808\pi\) |
−0.579644 | + | 0.814870i | \(0.696808\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.0299960 | − | 0.0923182i | 0.000961627 | − | 0.00295958i | ||||
\(974\) | 3.59933 | − | 6.23422i | 0.115330 | − | 0.199757i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 21.6343 | + | 37.4717i | 0.692497 | + | 1.19944i | ||||
\(977\) | −36.0526 | + | 7.66322i | −1.15342 | + | 0.245168i | −0.744642 | − | 0.667464i | \(-0.767380\pi\) |
−0.408783 | + | 0.912632i | \(0.634047\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.0871108 | − | 0.0387842i | 0.00278407 | − | 0.00123955i | ||||
\(980\) | −0.0239286 | − | 0.0977025i | −0.000764371 | − | 0.00312099i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −10.7290 | −0.342375 | ||||||||
\(983\) | −2.98616 | − | 28.4114i | −0.0952436 | − | 0.906182i | −0.932937 | − | 0.360041i | \(-0.882763\pi\) |
0.837693 | − | 0.546141i | \(-0.183904\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −42.3118 | + | 40.5211i | −1.34817 | + | 1.29111i | ||||
\(986\) | −43.9063 | + | 9.33257i | −1.39826 | + | 0.297210i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.520870 | − | 0.110714i | −0.0165711 | − | 0.00352229i | ||||
\(989\) | −6.64210 | + | 20.4423i | −0.211206 | + | 0.650027i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.1246 | + | 55.7817i | 0.575746 | + | 1.77196i | 0.633626 | + | 0.773639i | \(0.281566\pi\) |
−0.0578809 | + | 0.998323i | \(0.518434\pi\) | |||||||
\(992\) | 0.0837177 | + | 0.796521i | 0.00265804 | + | 0.0252896i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −14.1199 | − | 6.28659i | −0.447857 | − | 0.199399i | ||||
\(995\) | 6.60137 | − | 36.5483i | 0.209278 | − | 1.15866i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −45.5343 | + | 20.2732i | −1.44209 | + | 0.642058i | −0.970793 | − | 0.239919i | \(-0.922879\pi\) |
−0.471293 | + | 0.881977i | \(0.656213\pi\) | |||||||
\(998\) | 3.57766 | − | 11.0109i | 0.113249 | − | 0.348544i | ||||
\(999\) | 0 | 0 |
(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 | 675.2.r.a.46.8 | 224 | ||
3.2 | odd | 2 | 225.2.q.a.196.21 | yes | 224 | ||
9.4 | even | 3 | inner | 675.2.r.a.496.21 | 224 | ||
9.5 | odd | 6 | 225.2.q.a.121.8 | yes | 224 | ||
25.6 | even | 5 | inner | 675.2.r.a.181.21 | 224 | ||
75.56 | odd | 10 | 225.2.q.a.106.8 | yes | 224 | ||
225.31 | even | 15 | inner | 675.2.r.a.631.8 | 224 | ||
225.131 | odd | 30 | 225.2.q.a.31.21 | ✓ | 224 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
225.2.q.a.31.21 | ✓ | 224 | 225.131 | odd | 30 | ||
225.2.q.a.106.8 | yes | 224 | 75.56 | odd | 10 | ||
225.2.q.a.121.8 | yes | 224 | 9.5 | odd | 6 | ||
225.2.q.a.196.21 | yes | 224 | 3.2 | odd | 2 | ||
675.2.r.a.46.8 | 224 | 1.1 | even | 1 | trivial | ||
675.2.r.a.181.21 | 224 | 25.6 | even | 5 | inner | ||
675.2.r.a.496.21 | 224 | 9.4 | even | 3 | inner | ||
675.2.r.a.631.8 | 224 | 225.31 | even | 15 | inner |