Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [375,2,Mod(76,375)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(375, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("375.76");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 375 = 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 375.g (of order \(5\), degree \(4\), 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: | \(2.99439007580\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 3x^{10} - 2x^{9} + 34x^{8} - 22x^{7} + 236x^{6} - 179x^{5} + 877x^{4} - 409x^{3} + 96x^{2} - 11x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 76.3 | ||
Root | \(-0.667650 - 2.05481i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 375.76 |
Dual form | 375.2.g.c.301.3 |
$q$-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 \(\left(\mathbb{Z}/375\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{1}{5}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.74793 | + | 1.26995i | 1.23597 | + | 0.897987i | 0.997323 | − | 0.0731189i | \(-0.0232952\pi\) |
0.238650 | + | 0.971106i | \(0.423295\pi\) | |||||||
\(3\) | 0.309017 | + | 0.951057i | 0.178411 | + | 0.549093i | ||||
\(4\) | 0.824463 | + | 2.53744i | 0.412232 | + | 1.26872i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.667650 | + | 2.05481i | −0.272567 | + | 0.838875i | ||||
\(7\) | 3.16056 | 1.19458 | 0.597290 | − | 0.802026i | \(-0.296244\pi\) | ||||
0.597290 | + | 0.802026i | \(0.296244\pi\) | |||||||
\(8\) | −0.446002 | + | 1.37265i | −0.157686 | + | 0.485307i | ||||
\(9\) | −0.809017 | + | 0.587785i | −0.269672 | + | 0.195928i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.24455 | − | 0.904220i | −0.375247 | − | 0.272633i | 0.384137 | − | 0.923276i | \(-0.374499\pi\) |
−0.759383 | + | 0.650644i | \(0.774499\pi\) | |||||||
\(12\) | −2.15847 | + | 1.56822i | −0.623097 | + | 0.452707i | ||||
\(13\) | −4.24041 | + | 3.08084i | −1.17608 | + | 0.854471i | −0.991724 | − | 0.128389i | \(-0.959019\pi\) |
−0.184355 | + | 0.982860i | \(0.559019\pi\) | |||||||
\(14\) | 5.52444 | + | 4.01374i | 1.47647 | + | 1.07272i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.79417 | − | 1.30354i | 0.448542 | − | 0.325885i | ||||
\(17\) | −0.398843 | + | 1.22751i | −0.0967337 | + | 0.297716i | −0.987702 | − | 0.156351i | \(-0.950027\pi\) |
0.890968 | + | 0.454066i | \(0.150027\pi\) | |||||||
\(18\) | −2.16056 | −0.509249 | ||||||||
\(19\) | 1.68287 | − | 5.17933i | 0.386076 | − | 1.18822i | −0.549620 | − | 0.835415i | \(-0.685228\pi\) |
0.935696 | − | 0.352806i | \(-0.114772\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.976667 | + | 3.00587i | 0.213126 | + | 0.655935i | ||||
\(22\) | −1.02708 | − | 3.16103i | −0.218974 | − | 0.673933i | ||||
\(23\) | −5.21204 | − | 3.78677i | −1.08679 | − | 0.789596i | −0.107932 | − | 0.994158i | \(-0.534423\pi\) |
−0.978854 | + | 0.204562i | \(0.934423\pi\) | |||||||
\(24\) | −1.44329 | −0.294611 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −11.3244 | −2.22090 | ||||||||
\(27\) | −0.809017 | − | 0.587785i | −0.155695 | − | 0.113119i | ||||
\(28\) | 2.60577 | + | 8.01972i | 0.492443 | + | 1.51558i | ||||
\(29\) | −0.730396 | − | 2.24793i | −0.135631 | − | 0.417430i | 0.860056 | − | 0.510199i | \(-0.170428\pi\) |
−0.995688 | + | 0.0927690i | \(0.970428\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.37989 | + | 4.24687i | −0.247836 | + | 0.762760i | 0.747321 | + | 0.664463i | \(0.231340\pi\) |
−0.995157 | + | 0.0982974i | \(0.968660\pi\) | |||||||
\(32\) | 7.67809 | 1.35731 | ||||||||
\(33\) | 0.475377 | − | 1.46306i | 0.0827525 | − | 0.254686i | ||||
\(34\) | −2.25602 | + | 1.63910i | −0.386905 | + | 0.281103i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.15847 | − | 1.56822i | −0.359745 | − | 0.261370i | ||||
\(37\) | −4.81973 | + | 3.50174i | −0.792358 | + | 0.575682i | −0.908662 | − | 0.417532i | \(-0.862895\pi\) |
0.116304 | + | 0.993214i | \(0.462895\pi\) | |||||||
\(38\) | 9.51901 | − | 6.91596i | 1.54419 | − | 1.12192i | ||||
\(39\) | −4.24041 | − | 3.08084i | −0.679009 | − | 0.493329i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.90269 | − | 5.01510i | 1.07802 | − | 0.783227i | 0.100683 | − | 0.994919i | \(-0.467897\pi\) |
0.977336 | + | 0.211692i | \(0.0678974\pi\) | |||||||
\(42\) | −2.11015 | + | 6.49436i | −0.325603 | + | 1.00210i | ||||
\(43\) | 8.48426 | 1.29384 | 0.646919 | − | 0.762559i | \(-0.276057\pi\) | ||||
0.646919 | + | 0.762559i | \(0.276057\pi\) | |||||||
\(44\) | 1.26831 | − | 3.90347i | 0.191206 | − | 0.588470i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.30129 | − | 13.2380i | −0.634191 | − | 1.95184i | ||||
\(47\) | −0.232712 | − | 0.716212i | −0.0339445 | − | 0.104470i | 0.932649 | − | 0.360786i | \(-0.117491\pi\) |
−0.966593 | + | 0.256315i | \(0.917491\pi\) | |||||||
\(48\) | 1.79417 | + | 1.30354i | 0.258966 | + | 0.188150i | ||||
\(49\) | 2.98914 | 0.427020 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.29068 | −0.180732 | ||||||||
\(52\) | −11.3135 | − | 8.21974i | −1.56890 | − | 1.13987i | ||||
\(53\) | −3.01289 | − | 9.27271i | −0.413852 | − | 1.27371i | −0.913274 | − | 0.407346i | \(-0.866454\pi\) |
0.499422 | − | 0.866359i | \(-0.333546\pi\) | |||||||
\(54\) | −0.667650 | − | 2.05481i | −0.0908556 | − | 0.279625i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.40962 | + | 4.33836i | −0.188368 | + | 0.579737i | ||||
\(57\) | 5.44587 | 0.721324 | ||||||||
\(58\) | 1.57806 | − | 4.85678i | 0.207210 | − | 0.637727i | ||||
\(59\) | −3.32724 | + | 2.41738i | −0.433170 | + | 0.314717i | −0.782915 | − | 0.622128i | \(-0.786268\pi\) |
0.349745 | + | 0.936845i | \(0.386268\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.65159 | + | 6.28574i | 1.10772 | + | 0.804807i | 0.982303 | − | 0.187297i | \(-0.0599726\pi\) |
0.125419 | + | 0.992104i | \(0.459973\pi\) | |||||||
\(62\) | −7.80525 | + | 5.67084i | −0.991267 | + | 0.720198i | ||||
\(63\) | −2.55695 | + | 1.85773i | −0.322145 | + | 0.234052i | ||||
\(64\) | 9.83243 | + | 7.14368i | 1.22905 | + | 0.892960i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.68893 | − | 1.95362i | 0.330984 | − | 0.240474i | ||||
\(67\) | 0.586713 | − | 1.80572i | 0.0716785 | − | 0.220604i | −0.908799 | − | 0.417233i | \(-0.863000\pi\) |
0.980478 | + | 0.196630i | \(0.0629997\pi\) | |||||||
\(68\) | −3.44357 | −0.417594 | ||||||||
\(69\) | 1.99082 | − | 6.12712i | 0.239667 | − | 0.737619i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.0219023 | − | 0.0674084i | −0.00259933 | − | 0.00799990i | 0.949748 | − | 0.313014i | \(-0.101339\pi\) |
−0.952348 | + | 0.305014i | \(0.901339\pi\) | |||||||
\(72\) | −0.446002 | − | 1.37265i | −0.0525619 | − | 0.161769i | ||||
\(73\) | 3.24515 | + | 2.35774i | 0.379816 | + | 0.275952i | 0.761270 | − | 0.648436i | \(-0.224576\pi\) |
−0.381454 | + | 0.924388i | \(0.624576\pi\) | |||||||
\(74\) | −12.8716 | −1.49629 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 14.5297 | 1.66667 | ||||||||
\(77\) | −3.93348 | − | 2.85784i | −0.448262 | − | 0.325681i | ||||
\(78\) | −3.49944 | − | 10.7702i | −0.396234 | − | 1.21948i | ||||
\(79\) | 0.500141 | + | 1.53928i | 0.0562703 | + | 0.173182i | 0.975242 | − | 0.221143i | \(-0.0709786\pi\) |
−0.918971 | + | 0.394325i | \(0.870979\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.309017 | − | 0.951057i | 0.0343352 | − | 0.105673i | ||||
\(82\) | 18.4343 | 2.03573 | ||||||||
\(83\) | −4.06322 | + | 12.5053i | −0.445996 | + | 1.37263i | 0.435392 | + | 0.900241i | \(0.356610\pi\) |
−0.881388 | + | 0.472393i | \(0.843390\pi\) | |||||||
\(84\) | −6.82198 | + | 4.95646i | −0.744339 | + | 0.540794i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 14.8299 | + | 10.7745i | 1.59915 | + | 1.16185i | ||||
\(87\) | 1.91220 | − | 1.38930i | 0.205010 | − | 0.148948i | ||||
\(88\) | 1.79626 | − | 1.30506i | 0.191481 | − | 0.139119i | ||||
\(89\) | −5.88638 | − | 4.27671i | −0.623955 | − | 0.453330i | 0.230345 | − | 0.973109i | \(-0.426014\pi\) |
−0.854301 | + | 0.519779i | \(0.826014\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.4021 | + | 9.73718i | −1.40492 | + | 1.02073i | ||||
\(92\) | 5.31155 | − | 16.3473i | 0.553768 | − | 1.70432i | ||||
\(93\) | −4.46542 | −0.463043 | ||||||||
\(94\) | 0.502787 | − | 1.54742i | 0.0518585 | − | 0.159604i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.37266 | + | 7.30230i | 0.242159 | + | 0.745288i | ||||
\(97\) | −3.15009 | − | 9.69499i | −0.319843 | − | 0.984377i | −0.973715 | − | 0.227771i | \(-0.926856\pi\) |
0.653871 | − | 0.756606i | \(-0.273144\pi\) | |||||||
\(98\) | 5.22480 | + | 3.79604i | 0.527785 | + | 0.383458i | ||||
\(99\) | 1.53835 | 0.154610 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.08759 | 0.108219 | 0.0541096 | − | 0.998535i | \(-0.482768\pi\) | ||||
0.0541096 | + | 0.998535i | \(0.482768\pi\) | |||||||
\(102\) | −2.25602 | − | 1.63910i | −0.223380 | − | 0.162295i | ||||
\(103\) | 1.52579 | + | 4.69590i | 0.150341 | + | 0.462701i | 0.997659 | − | 0.0683845i | \(-0.0217845\pi\) |
−0.847319 | + | 0.531085i | \(0.821784\pi\) | |||||||
\(104\) | −2.33769 | − | 7.19468i | −0.229230 | − | 0.705497i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.50952 | − | 20.0343i | 0.632261 | − | 1.94590i | ||||
\(107\) | −15.3059 | −1.47967 | −0.739837 | − | 0.672786i | \(-0.765098\pi\) | ||||
−0.739837 | + | 0.672786i | \(0.765098\pi\) | |||||||
\(108\) | 0.824463 | − | 2.53744i | 0.0793340 | − | 0.244165i | ||||
\(109\) | −5.38724 | + | 3.91406i | −0.516004 | + | 0.374899i | −0.815097 | − | 0.579325i | \(-0.803316\pi\) |
0.299092 | + | 0.954224i | \(0.403316\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.81973 | − | 3.50174i | −0.457468 | − | 0.332370i | ||||
\(112\) | 5.67058 | − | 4.11991i | 0.535819 | − | 0.389295i | ||||
\(113\) | −7.25804 | + | 5.27328i | −0.682779 | + | 0.496068i | −0.874278 | − | 0.485425i | \(-0.838665\pi\) |
0.191499 | + | 0.981493i | \(0.438665\pi\) | |||||||
\(114\) | 9.51901 | + | 6.91596i | 0.891537 | + | 0.647739i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.10179 | − | 3.70667i | 0.473689 | − | 0.344155i | ||||
\(117\) | 1.61969 | − | 4.98490i | 0.149741 | − | 0.460854i | ||||
\(118\) | −8.88573 | −0.817998 | ||||||||
\(119\) | −1.26057 | + | 3.87963i | −0.115556 | + | 0.355645i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.66789 | − | 8.21092i | −0.242536 | − | 0.746448i | ||||
\(122\) | 7.13981 | + | 21.9741i | 0.646408 | + | 1.98944i | ||||
\(123\) | 6.90269 | + | 5.01510i | 0.622395 | + | 0.452196i | ||||
\(124\) | −11.9138 | −1.06989 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −6.82858 | −0.608338 | ||||||||
\(127\) | 8.10511 | + | 5.88870i | 0.719212 | + | 0.522538i | 0.886132 | − | 0.463432i | \(-0.153382\pi\) |
−0.166920 | + | 0.985970i | \(0.553382\pi\) | |||||||
\(128\) | 3.36899 | + | 10.3687i | 0.297780 | + | 0.916471i | ||||
\(129\) | 2.62178 | + | 8.06901i | 0.230835 | + | 0.710437i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.97111 | + | 6.06645i | −0.172217 | + | 0.530029i | −0.999495 | − | 0.0317631i | \(-0.989888\pi\) |
0.827279 | + | 0.561792i | \(0.189888\pi\) | |||||||
\(132\) | 4.10435 | 0.357238 | ||||||||
\(133\) | 5.31880 | − | 16.3696i | 0.461199 | − | 1.41942i | ||||
\(134\) | 3.31870 | − | 2.41117i | 0.286692 | − | 0.208294i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.50707 | − | 1.09495i | −0.129230 | − | 0.0938910i | ||||
\(137\) | −7.42461 | + | 5.39429i | −0.634327 | + | 0.460866i | −0.857897 | − | 0.513822i | \(-0.828229\pi\) |
0.223570 | + | 0.974688i | \(0.428229\pi\) | |||||||
\(138\) | 11.2609 | − | 8.18154i | 0.958594 | − | 0.696459i | ||||
\(139\) | 7.49586 | + | 5.44606i | 0.635790 | + | 0.461929i | 0.858401 | − | 0.512979i | \(-0.171458\pi\) |
−0.222611 | + | 0.974907i | \(0.571458\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.609247 | − | 0.442644i | 0.0513078 | − | 0.0372773i | ||||
\(142\) | 0.0473213 | − | 0.145640i | 0.00397111 | − | 0.0122218i | ||||
\(143\) | 8.06317 | 0.674276 | ||||||||
\(144\) | −0.685311 | + | 2.10917i | −0.0571093 | + | 0.175764i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.67809 | + | 8.24232i | 0.221641 | + | 0.682140i | ||||
\(147\) | 0.923695 | + | 2.84284i | 0.0761850 | + | 0.234473i | ||||
\(148\) | −12.8591 | − | 9.34270i | −1.05701 | − | 0.767965i | ||||
\(149\) | −10.0817 | −0.825928 | −0.412964 | − | 0.910747i | \(-0.635506\pi\) | ||||
−0.412964 | + | 0.910747i | \(0.635506\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.7375 | 0.873804 | 0.436902 | − | 0.899509i | \(-0.356076\pi\) | ||||
0.436902 | + | 0.899509i | \(0.356076\pi\) | |||||||
\(152\) | 6.35887 | + | 4.61999i | 0.515773 | + | 0.374731i | ||||
\(153\) | −0.398843 | − | 1.22751i | −0.0322446 | − | 0.0992385i | ||||
\(154\) | −3.24615 | − | 9.99061i | −0.261582 | − | 0.805067i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 4.32137 | − | 13.2998i | 0.345987 | − | 1.06484i | ||||
\(157\) | −17.4417 | −1.39200 | −0.696001 | − | 0.718041i | \(-0.745039\pi\) | ||||
−0.696001 | + | 0.718041i | \(0.745039\pi\) | |||||||
\(158\) | −1.08058 | + | 3.32570i | −0.0859667 | + | 0.264578i | ||||
\(159\) | 7.88784 | − | 5.73085i | 0.625546 | − | 0.454486i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16.4730 | − | 11.9683i | −1.29825 | − | 0.943235i | ||||
\(162\) | 1.74793 | − | 1.26995i | 0.137330 | − | 0.0997763i | ||||
\(163\) | −13.1525 | + | 9.55586i | −1.03018 | + | 0.748473i | −0.968346 | − | 0.249613i | \(-0.919697\pi\) |
−0.0618392 | + | 0.998086i | \(0.519697\pi\) | |||||||
\(164\) | 18.4165 | + | 13.3804i | 1.43809 | + | 1.04483i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −22.9832 | + | 16.6983i | −1.78385 | + | 1.29604i | ||||
\(167\) | 3.51989 | − | 10.8331i | 0.272377 | − | 0.838290i | −0.717525 | − | 0.696533i | \(-0.754725\pi\) |
0.989902 | − | 0.141757i | \(-0.0452751\pi\) | |||||||
\(168\) | −4.56162 | −0.351936 | ||||||||
\(169\) | 4.47230 | − | 13.7643i | 0.344023 | − | 1.05879i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.68287 | + | 5.17933i | 0.128692 | + | 0.396074i | ||||
\(172\) | 6.99496 | + | 21.5283i | 0.533361 | + | 1.64152i | ||||
\(173\) | 7.65205 | + | 5.55954i | 0.581775 | + | 0.422684i | 0.839363 | − | 0.543571i | \(-0.182928\pi\) |
−0.257589 | + | 0.966255i | \(0.582928\pi\) | |||||||
\(174\) | 5.10672 | 0.387140 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.41162 | −0.257161 | ||||||||
\(177\) | −3.32724 | − | 2.41738i | −0.250091 | − | 0.181702i | ||||
\(178\) | −4.85780 | − | 14.9508i | −0.364107 | − | 1.12061i | ||||
\(179\) | 1.26001 | + | 3.87790i | 0.0941773 | + | 0.289848i | 0.987038 | − | 0.160484i | \(-0.0513056\pi\) |
−0.892861 | + | 0.450332i | \(0.851306\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.43633 | + | 10.5759i | −0.255421 | + | 0.786104i | 0.738326 | + | 0.674444i | \(0.235617\pi\) |
−0.993747 | + | 0.111660i | \(0.964383\pi\) | |||||||
\(182\) | −35.7916 | −2.65305 | ||||||||
\(183\) | −3.30461 | + | 10.1705i | −0.244284 | + | 0.751829i | ||||
\(184\) | 7.52251 | − | 5.46542i | 0.554567 | − | 0.402916i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −7.80525 | − | 5.67084i | −0.572308 | − | 0.415806i | ||||
\(187\) | 1.60632 | − | 1.16706i | 0.117466 | − | 0.0853440i | ||||
\(188\) | 1.62548 | − | 1.18098i | 0.118550 | − | 0.0861319i | ||||
\(189\) | −2.55695 | − | 1.85773i | −0.185990 | − | 0.135130i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.92164 | + | 2.12270i | −0.211403 | + | 0.153593i | −0.688448 | − | 0.725286i | \(-0.741708\pi\) |
0.477046 | + | 0.878879i | \(0.341708\pi\) | |||||||
\(192\) | −3.75565 | + | 11.5587i | −0.271041 | + | 0.834178i | ||||
\(193\) | 17.0562 | 1.22774 | 0.613868 | − | 0.789409i | \(-0.289613\pi\) | ||||
0.613868 | + | 0.789409i | \(0.289613\pi\) | |||||||
\(194\) | 6.80596 | − | 20.9466i | 0.488640 | − | 1.50388i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.46443 | + | 7.58475i | 0.176031 | + | 0.541768i | ||||
\(197\) | 1.36129 | + | 4.18963i | 0.0969880 | + | 0.298498i | 0.987767 | − | 0.155939i | \(-0.0498403\pi\) |
−0.890779 | + | 0.454437i | \(0.849840\pi\) | |||||||
\(198\) | 2.68893 | + | 1.95362i | 0.191094 | + | 0.138838i | ||||
\(199\) | 16.5956 | 1.17643 | 0.588214 | − | 0.808705i | \(-0.299831\pi\) | ||||
0.588214 | + | 0.808705i | \(0.299831\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.89864 | 0.133920 | ||||||||
\(202\) | 1.90103 | + | 1.38118i | 0.133756 | + | 0.0971795i | ||||
\(203\) | −2.30846 | − | 7.10471i | −0.162022 | − | 0.498653i | ||||
\(204\) | −1.06412 | − | 3.27503i | −0.0745034 | − | 0.229298i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.29656 | + | 10.1458i | −0.229682 | + | 0.706889i | ||||
\(207\) | 6.44244 | 0.447780 | ||||||||
\(208\) | −3.59202 | + | 11.0551i | −0.249061 | + | 0.766532i | ||||
\(209\) | −6.77768 | + | 4.92427i | −0.468822 | + | 0.340619i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.0035 | − | 10.9007i | −1.03288 | − | 0.750434i | −0.0640001 | − | 0.997950i | \(-0.520386\pi\) |
−0.968884 | + | 0.247516i | \(0.920386\pi\) | |||||||
\(212\) | 21.0449 | − | 15.2900i | 1.44537 | − | 1.05012i | ||||
\(213\) | 0.0573410 | − | 0.0416607i | 0.00392894 | − | 0.00285454i | ||||
\(214\) | −26.7536 | − | 19.4376i | −1.82884 | − | 1.32873i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.16765 | − | 0.848347i | 0.0794485 | − | 0.0577227i | ||||
\(217\) | −4.36123 | + | 13.4225i | −0.296060 | + | 0.911178i | ||||
\(218\) | −14.3872 | −0.974422 | ||||||||
\(219\) | −1.23954 | + | 3.81490i | −0.0837601 | + | 0.257787i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.09051 | − | 6.43393i | −0.140623 | − | 0.432793i | ||||
\(222\) | −3.97753 | − | 12.2416i | −0.266954 | − | 0.821601i | ||||
\(223\) | −0.624203 | − | 0.453510i | −0.0417997 | − | 0.0303693i | 0.566689 | − | 0.823932i | \(-0.308224\pi\) |
−0.608489 | + | 0.793562i | \(0.708224\pi\) | |||||||
\(224\) | 24.2671 | 1.62141 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −19.3833 | −1.28936 | ||||||||
\(227\) | 9.24817 | + | 6.71919i | 0.613823 | + | 0.445968i | 0.850758 | − | 0.525557i | \(-0.176143\pi\) |
−0.236936 | + | 0.971525i | \(0.576143\pi\) | |||||||
\(228\) | 4.48992 | + | 13.8186i | 0.297352 | + | 0.915157i | ||||
\(229\) | 3.15962 | + | 9.72432i | 0.208794 | + | 0.642601i | 0.999536 | + | 0.0304520i | \(0.00969467\pi\) |
−0.790743 | + | 0.612149i | \(0.790305\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.50246 | − | 4.62409i | 0.0988544 | − | 0.304242i | ||||
\(232\) | 3.41139 | 0.223969 | ||||||||
\(233\) | 6.95997 | − | 21.4206i | 0.455963 | − | 1.40331i | −0.414038 | − | 0.910260i | \(-0.635882\pi\) |
0.870001 | − | 0.493050i | \(-0.164118\pi\) | |||||||
\(234\) | 9.16166 | − | 6.65634i | 0.598917 | − | 0.435138i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −8.87715 | − | 6.44963i | −0.577853 | − | 0.419835i | ||||
\(237\) | −1.30939 | + | 0.951325i | −0.0850538 | + | 0.0617952i | ||||
\(238\) | −7.13030 | + | 5.18047i | −0.462189 | + | 0.335800i | ||||
\(239\) | 0.476571 | + | 0.346249i | 0.0308268 | + | 0.0223970i | 0.603092 | − | 0.797672i | \(-0.293935\pi\) |
−0.572265 | + | 0.820069i | \(0.693935\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.22110 | + | 0.887185i | −0.0786583 | + | 0.0571486i | −0.626419 | − | 0.779486i | \(-0.715480\pi\) |
0.547761 | + | 0.836635i | \(0.315480\pi\) | |||||||
\(242\) | 5.76414 | − | 17.7402i | 0.370533 | − | 1.14038i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −8.81677 | + | 27.1352i | −0.564436 | + | 1.73715i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.69652 | + | 17.5321i | 0.363197 | + | 1.11780i | ||||
\(247\) | 8.82065 | + | 27.1472i | 0.561244 | + | 1.72733i | ||||
\(248\) | −5.21405 | − | 3.78823i | −0.331093 | − | 0.240553i | ||||
\(249\) | −13.1488 | −0.833274 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.8953 | 0.750823 | 0.375412 | − | 0.926858i | \(-0.377501\pi\) | ||||
0.375412 | + | 0.926858i | \(0.377501\pi\) | |||||||
\(252\) | −6.82198 | − | 4.95646i | −0.429744 | − | 0.312228i | ||||
\(253\) | 3.06258 | + | 9.42567i | 0.192543 | + | 0.592587i | ||||
\(254\) | 6.68882 | + | 20.5861i | 0.419694 | + | 1.29169i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.232398 | − | 0.715248i | 0.0145249 | − | 0.0447030i | ||||
\(257\) | 18.0492 | 1.12588 | 0.562939 | − | 0.826498i | \(-0.309671\pi\) | ||||
0.562939 | + | 0.826498i | \(0.309671\pi\) | |||||||
\(258\) | −5.66451 | + | 17.4336i | −0.352657 | + | 1.08537i | ||||
\(259\) | −15.2330 | + | 11.0674i | −0.946534 | + | 0.687698i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.91220 | + | 1.38930i | 0.118362 | + | 0.0859953i | ||||
\(262\) | −11.1494 | + | 8.10053i | −0.688814 | + | 0.500453i | ||||
\(263\) | −15.4576 | + | 11.2306i | −0.953157 | + | 0.692509i | −0.951551 | − | 0.307490i | \(-0.900511\pi\) |
−0.00160518 | + | 0.999999i | \(0.500511\pi\) | |||||||
\(264\) | 1.79626 | + | 1.30506i | 0.110552 | + | 0.0803206i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 30.0854 | − | 21.8583i | 1.84465 | − | 1.34022i | ||||
\(267\) | 2.24840 | − | 6.91986i | 0.137600 | − | 0.423489i | ||||
\(268\) | 5.06562 | 0.309432 | ||||||||
\(269\) | −6.86791 | + | 21.1372i | −0.418744 | + | 1.28876i | 0.490115 | + | 0.871658i | \(0.336955\pi\) |
−0.908859 | + | 0.417103i | \(0.863045\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.24546 | + | 19.2216i | 0.379385 | + | 1.16763i | 0.940472 | + | 0.339870i | \(0.110383\pi\) |
−0.561088 | + | 0.827756i | \(0.689617\pi\) | |||||||
\(272\) | 0.884520 | + | 2.72227i | 0.0536319 | + | 0.165062i | ||||
\(273\) | −13.4021 | − | 9.73718i | −0.811130 | − | 0.589321i | ||||
\(274\) | −19.8281 | −1.19786 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 17.1885 | 1.03463 | ||||||||
\(277\) | −12.9777 | − | 9.42882i | −0.779752 | − | 0.566523i | 0.125153 | − | 0.992137i | \(-0.460058\pi\) |
−0.904904 | + | 0.425615i | \(0.860058\pi\) | |||||||
\(278\) | 6.18604 | + | 19.0387i | 0.371014 | + | 1.14186i | ||||
\(279\) | −1.37989 | − | 4.24687i | −0.0826120 | − | 0.254253i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.58742 | − | 7.96327i | 0.154353 | − | 0.475049i | −0.843742 | − | 0.536749i | \(-0.819652\pi\) |
0.998095 | + | 0.0617001i | \(0.0196522\pi\) | |||||||
\(282\) | 1.62705 | 0.0968896 | ||||||||
\(283\) | 0.349174 | − | 1.07465i | 0.0207562 | − | 0.0638811i | −0.940142 | − | 0.340783i | \(-0.889308\pi\) |
0.960898 | + | 0.276902i | \(0.0893078\pi\) | |||||||
\(284\) | 0.152987 | − | 0.111151i | 0.00907810 | − | 0.00659563i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 14.0939 | + | 10.2398i | 0.833387 | + | 0.605491i | ||||
\(287\) | 21.8164 | − | 15.8505i | 1.28778 | − | 0.935626i | ||||
\(288\) | −6.21171 | + | 4.51307i | −0.366028 | + | 0.265935i | ||||
\(289\) | 12.4056 | + | 9.01318i | 0.729740 | + | 0.530187i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.24705 | − | 5.99183i | 0.483451 | − | 0.351247i | ||||
\(292\) | −3.30711 | + | 10.1782i | −0.193534 | + | 0.595636i | ||||
\(293\) | 2.37857 | 0.138958 | 0.0694789 | − | 0.997583i | \(-0.477866\pi\) | ||||
0.0694789 | + | 0.997583i | \(0.477866\pi\) | |||||||
\(294\) | −1.99570 | + | 6.14212i | −0.116391 | + | 0.358216i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.65706 | − | 8.17760i | −0.154439 | − | 0.475313i | ||||
\(297\) | 0.475377 | + | 1.46306i | 0.0275842 | + | 0.0848953i | ||||
\(298\) | −17.6222 | − | 12.8032i | −1.02082 | − | 0.741672i | ||||
\(299\) | 33.7676 | 1.95283 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 26.8150 | 1.54559 | ||||||||
\(302\) | 18.7684 | + | 13.6360i | 1.08000 | + | 0.784665i | ||||
\(303\) | 0.336084 | + | 1.03436i | 0.0193075 | + | 0.0594224i | ||||
\(304\) | −3.73212 | − | 11.4863i | −0.214052 | − | 0.658783i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.861724 | − | 2.65212i | 0.0492615 | − | 0.151611i | ||||
\(307\) | −2.89366 | −0.165150 | −0.0825748 | − | 0.996585i | \(-0.526314\pi\) | ||||
−0.0825748 | + | 0.996585i | \(0.526314\pi\) | |||||||
\(308\) | 4.00858 | − | 12.3371i | 0.228410 | − | 0.702974i | ||||
\(309\) | −3.99457 | + | 2.90222i | −0.227243 | + | 0.165102i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.78079 | + | 4.19999i | 0.327799 | + | 0.238160i | 0.739496 | − | 0.673161i | \(-0.235064\pi\) |
−0.411697 | + | 0.911321i | \(0.635064\pi\) | |||||||
\(312\) | 6.12016 | − | 4.44656i | 0.346486 | − | 0.251737i | ||||
\(313\) | 18.6331 | − | 13.5378i | 1.05321 | − | 0.765200i | 0.0803879 | − | 0.996764i | \(-0.474384\pi\) |
0.972820 | + | 0.231563i | \(0.0743841\pi\) | |||||||
\(314\) | −30.4869 | − | 22.1500i | −1.72048 | − | 1.25000i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.49347 | + | 2.53815i | −0.196523 | + | 0.142782i | ||||
\(317\) | 6.41981 | − | 19.7582i | 0.360573 | − | 1.10973i | −0.592135 | − | 0.805839i | \(-0.701715\pi\) |
0.952707 | − | 0.303890i | \(-0.0982854\pi\) | |||||||
\(318\) | 21.0653 | 1.18128 | ||||||||
\(319\) | −1.12361 | + | 3.45810i | −0.0629098 | + | 0.193617i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.72978 | − | 14.5568i | −0.263990 | − | 0.812479i | ||||
\(322\) | −13.5945 | − | 41.8395i | −0.757591 | − | 2.33163i | ||||
\(323\) | 5.68650 | + | 4.13148i | 0.316405 | + | 0.229882i | ||||
\(324\) | 2.66802 | 0.148223 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −35.1251 | −1.94540 | ||||||||
\(327\) | −5.38724 | − | 3.91406i | −0.297915 | − | 0.216448i | ||||
\(328\) | 3.80538 | + | 11.7118i | 0.210117 | + | 0.646673i | ||||
\(329\) | −0.735499 | − | 2.26363i | −0.0405494 | − | 0.124798i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.94869 | + | 18.3082i | −0.326969 | + | 1.00631i | 0.643574 | + | 0.765383i | \(0.277451\pi\) |
−0.970544 | + | 0.240925i | \(0.922549\pi\) | |||||||
\(332\) | −35.0814 | −1.92534 | ||||||||
\(333\) | 1.84097 | − | 5.66593i | 0.100885 | − | 0.310491i | ||||
\(334\) | 19.9099 | − | 14.4654i | 1.08942 | − | 0.791513i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 5.67058 | + | 4.11991i | 0.309355 | + | 0.224760i | ||||
\(337\) | 17.5609 | − | 12.7587i | 0.956602 | − | 0.695012i | 0.00424305 | − | 0.999991i | \(-0.498649\pi\) |
0.952359 | + | 0.304979i | \(0.0986494\pi\) | |||||||
\(338\) | 25.2972 | − | 18.3795i | 1.37599 | − | 0.999712i | ||||
\(339\) | −7.25804 | − | 5.27328i | −0.394203 | − | 0.286405i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.55745 | − | 4.03773i | 0.300953 | − | 0.218655i | ||||
\(342\) | −3.63594 | + | 11.1903i | −0.196609 | + | 0.605100i | ||||
\(343\) | −12.6766 | −0.684470 | ||||||||
\(344\) | −3.78400 | + | 11.6460i | −0.204020 | + | 0.627908i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.31493 | + | 19.4354i | 0.339493 | + | 1.04485i | ||||
\(347\) | 0.529944 | + | 1.63100i | 0.0284489 | + | 0.0875567i | 0.964273 | − | 0.264911i | \(-0.0853426\pi\) |
−0.935824 | + | 0.352468i | \(0.885343\pi\) | |||||||
\(348\) | 5.10179 | + | 3.70667i | 0.273485 | + | 0.198698i | ||||
\(349\) | −15.5553 | −0.832654 | −0.416327 | − | 0.909215i | \(-0.636683\pi\) | ||||
−0.416327 | + | 0.909215i | \(0.636683\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.24144 | 0.279767 | ||||||||
\(352\) | −9.55579 | − | 6.94268i | −0.509325 | − | 0.370046i | ||||
\(353\) | −4.80632 | − | 14.7923i | −0.255814 | − | 0.787316i | −0.993668 | − | 0.112355i | \(-0.964161\pi\) |
0.737854 | − | 0.674961i | \(-0.235839\pi\) | |||||||
\(354\) | −2.74584 | − | 8.45083i | −0.145940 | − | 0.449157i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.99877 | − | 18.4623i | 0.317934 | − | 0.978501i | ||||
\(357\) | −4.07928 | −0.215899 | ||||||||
\(358\) | −2.72232 | + | 8.37844i | −0.143879 | + | 0.442814i | ||||
\(359\) | 19.8509 | − | 14.4225i | 1.04769 | − | 0.761191i | 0.0759181 | − | 0.997114i | \(-0.475811\pi\) |
0.971772 | + | 0.235923i | \(0.0758112\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.62214 | − | 6.26435i | −0.453797 | − | 0.329703i | ||||
\(362\) | −19.4373 | + | 14.1221i | −1.02160 | + | 0.742239i | ||||
\(363\) | 6.98463 | − | 5.07463i | 0.366598 | − | 0.266349i | ||||
\(364\) | −35.7570 | − | 25.9790i | −1.87418 | − | 1.36167i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −18.6923 | + | 13.5807i | −0.977060 | + | 0.709876i | ||||
\(367\) | −8.68548 | + | 26.7311i | −0.453378 | + | 1.39535i | 0.419651 | + | 0.907686i | \(0.362153\pi\) |
−0.873029 | + | 0.487669i | \(0.837847\pi\) | |||||||
\(368\) | −14.2875 | −0.744786 | ||||||||
\(369\) | −2.63659 | + | 8.11460i | −0.137256 | + | 0.422429i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.52241 | − | 29.3070i | −0.494379 | − | 1.52154i | ||||
\(372\) | −3.68158 | − | 11.3307i | −0.190881 | − | 0.587471i | ||||
\(373\) | −7.85414 | − | 5.70637i | −0.406672 | − | 0.295464i | 0.365581 | − | 0.930779i | \(-0.380870\pi\) |
−0.772253 | + | 0.635315i | \(0.780870\pi\) | |||||||
\(374\) | 4.28984 | 0.221823 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.08690 | 0.0560527 | ||||||||
\(377\) | 10.0227 | + | 7.28191i | 0.516195 | + | 0.375037i | ||||
\(378\) | −2.11015 | − | 6.49436i | −0.108534 | − | 0.334034i | ||||
\(379\) | −6.88071 | − | 21.1767i | −0.353438 | − | 1.08777i | −0.956909 | − | 0.290387i | \(-0.906216\pi\) |
0.603471 | − | 0.797385i | \(-0.293784\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.09587 | + | 9.52812i | −0.158606 | + | 0.488141i | ||||
\(382\) | −7.80253 | −0.399212 | ||||||||
\(383\) | 4.21189 | − | 12.9628i | 0.215217 | − | 0.662371i | −0.783921 | − | 0.620861i | \(-0.786783\pi\) |
0.999138 | − | 0.0415099i | \(-0.0132168\pi\) | |||||||
\(384\) | −8.82014 | + | 6.40820i | −0.450101 | + | 0.327017i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 29.8131 | + | 21.6605i | 1.51745 | + | 1.10249i | ||||
\(387\) | −6.86391 | + | 4.98692i | −0.348912 | + | 0.253500i | ||||
\(388\) | 22.0033 | − | 15.9863i | 1.11705 | − | 0.811582i | ||||
\(389\) | −15.5577 | − | 11.3034i | −0.788808 | − | 0.573103i | 0.118801 | − | 0.992918i | \(-0.462095\pi\) |
−0.907610 | + | 0.419815i | \(0.862095\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.72710 | − | 4.88752i | 0.340204 | − | 0.247173i | ||||
\(392\) | −1.33316 | + | 4.10305i | −0.0673349 | + | 0.207236i | ||||
\(393\) | −6.37865 | −0.321760 | ||||||||
\(394\) | −2.94115 | + | 9.05194i | −0.148173 | + | 0.456030i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.26831 | + | 3.90347i | 0.0637352 | + | 0.196157i | ||||
\(397\) | −6.86887 | − | 21.1402i | −0.344739 | − | 1.06100i | −0.961723 | − | 0.274022i | \(-0.911646\pi\) |
0.616984 | − | 0.786975i | \(-0.288354\pi\) | |||||||
\(398\) | 29.0079 | + | 21.0755i | 1.45403 | + | 1.05642i | ||||
\(399\) | 17.2120 | 0.861678 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.71728 | 0.235570 | 0.117785 | − | 0.993039i | \(-0.462421\pi\) | ||||
0.117785 | + | 0.993039i | \(0.462421\pi\) | |||||||
\(402\) | 3.31870 | + | 2.41117i | 0.165522 | + | 0.120258i | ||||
\(403\) | −7.23261 | − | 22.2597i | −0.360282 | − | 1.10883i | ||||
\(404\) | 0.896678 | + | 2.75969i | 0.0446114 | + | 0.137300i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.98757 | − | 15.3502i | 0.247529 | − | 0.761815i | ||||
\(407\) | 9.16474 | 0.454279 | ||||||||
\(408\) | 0.575648 | − | 1.77166i | 0.0284988 | − | 0.0877104i | ||||
\(409\) | 10.0971 | − | 7.33597i | 0.499269 | − | 0.362740i | −0.309469 | − | 0.950910i | \(-0.600151\pi\) |
0.808738 | + | 0.588169i | \(0.200151\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.42461 | − | 5.39429i | −0.366229 | − | 0.266081i | ||||
\(412\) | −10.6576 | + | 7.74319i | −0.525062 | + | 0.381480i | ||||
\(413\) | −10.5160 | + | 7.64029i | −0.517456 | + | 0.375954i | ||||
\(414\) | 11.2609 | + | 8.18154i | 0.553444 | + | 0.402101i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −32.5583 | + | 23.6550i | −1.59630 | + | 1.15978i | ||||
\(417\) | −2.86316 | + | 8.81191i | −0.140210 | + | 0.431521i | ||||
\(418\) | −18.1005 | −0.885322 | ||||||||
\(419\) | 10.7996 | − | 33.2379i | 0.527597 | − | 1.62378i | −0.231527 | − | 0.972829i | \(-0.574372\pi\) |
0.759123 | − | 0.650947i | \(-0.225628\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.2247 | − | 37.6239i | −0.595797 | − | 1.83368i | −0.550717 | − | 0.834692i | \(-0.685646\pi\) |
−0.0450804 | − | 0.998983i | \(-0.514354\pi\) | |||||||
\(422\) | −12.3818 | − | 38.1073i | −0.602737 | − | 1.85503i | ||||
\(423\) | 0.609247 | + | 0.442644i | 0.0296226 | + | 0.0215221i | ||||
\(424\) | 14.0720 | 0.683396 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.153135 | 0.00741940 | ||||||||
\(427\) | 27.3439 | + | 19.8665i | 1.32326 | + | 0.961406i | ||||
\(428\) | −12.6191 | − | 38.8377i | −0.609969 | − | 1.87729i | ||||
\(429\) | 2.49166 | + | 7.66853i | 0.120298 | + | 0.370240i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.34429 | + | 13.3703i | −0.209257 | + | 0.644027i | 0.790255 | + | 0.612778i | \(0.209948\pi\) |
−0.999512 | + | 0.0312481i | \(0.990052\pi\) | |||||||
\(432\) | −2.21771 | −0.106700 | ||||||||
\(433\) | 0.169860 | − | 0.522775i | 0.00816294 | − | 0.0251230i | −0.946892 | − | 0.321552i | \(-0.895796\pi\) |
0.955055 | + | 0.296429i | \(0.0957957\pi\) | |||||||
\(434\) | −24.6689 | + | 17.9230i | −1.18415 | + | 0.860333i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −14.3733 | − | 10.4428i | −0.688355 | − | 0.500119i | ||||
\(437\) | −28.3841 | + | 20.6223i | −1.35780 | + | 0.986497i | ||||
\(438\) | −7.01134 | + | 5.09404i | −0.335015 | + | 0.243402i | ||||
\(439\) | 2.40583 | + | 1.74794i | 0.114824 | + | 0.0834245i | 0.643715 | − | 0.765265i | \(-0.277392\pi\) |
−0.528891 | + | 0.848690i | \(0.677392\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.41826 | + | 1.75697i | −0.115155 | + | 0.0836653i | ||||
\(442\) | 4.51667 | − | 13.9009i | 0.214836 | − | 0.661198i | ||||
\(443\) | 36.6893 | 1.74316 | 0.871580 | − | 0.490253i | \(-0.163095\pi\) | ||||
0.871580 | + | 0.490253i | \(0.163095\pi\) | |||||||
\(444\) | 4.91175 | − | 15.1168i | 0.233101 | − | 0.717412i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −0.515130 | − | 1.58541i | −0.0243921 | − | 0.0750712i | ||||
\(447\) | −3.11543 | − | 9.58830i | −0.147355 | − | 0.453511i | ||||
\(448\) | 31.0760 | + | 22.5780i | 1.46820 | + | 1.06671i | ||||
\(449\) | −17.8432 | −0.842071 | −0.421036 | − | 0.907044i | \(-0.638333\pi\) | ||||
−0.421036 | + | 0.907044i | \(0.638333\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.1255 | −0.618056 | ||||||||
\(452\) | −19.3646 | − | 14.0692i | −0.910834 | − | 0.661759i | ||||
\(453\) | 3.31807 | + | 10.2120i | 0.155896 | + | 0.479800i | ||||
\(454\) | 7.63215 | + | 23.4893i | 0.358195 | + | 1.10241i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.42887 | + | 7.47530i | −0.113742 | + | 0.350063i | ||||
\(457\) | 24.1784 | 1.13102 | 0.565509 | − | 0.824742i | \(-0.308680\pi\) | ||||
0.565509 | + | 0.824742i | \(0.308680\pi\) | |||||||
\(458\) | −6.82655 | + | 21.0100i | −0.318984 | + | 0.981731i | ||||
\(459\) | 1.04418 | − | 0.758645i | 0.0487384 | − | 0.0354105i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.2470 | + | 21.9757i | 1.40874 | + | 1.02351i | 0.993504 | + | 0.113800i | \(0.0363024\pi\) |
0.415240 | + | 0.909712i | \(0.363698\pi\) | |||||||
\(462\) | 8.49852 | − | 6.17454i | 0.395387 | − | 0.287266i | ||||
\(463\) | 16.5294 | − | 12.0093i | 0.768186 | − | 0.558120i | −0.133224 | − | 0.991086i | \(-0.542533\pi\) |
0.901410 | + | 0.432966i | \(0.142533\pi\) | |||||||
\(464\) | −4.24072 | − | 3.08106i | −0.196870 | − | 0.143035i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 39.3685 | − | 28.6029i | 1.82371 | − | 1.32500i | ||||
\(467\) | −9.64517 | + | 29.6848i | −0.446325 | + | 1.37365i | 0.434699 | + | 0.900576i | \(0.356855\pi\) |
−0.881024 | + | 0.473072i | \(0.843145\pi\) | |||||||
\(468\) | 13.9843 | 0.646422 | ||||||||
\(469\) | 1.85434 | − | 5.70708i | 0.0856256 | − | 0.263529i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.38979 | − | 16.5881i | −0.248348 | − | 0.764338i | ||||
\(472\) | −1.83427 | − | 5.64532i | −0.0844293 | − | 0.259847i | ||||
\(473\) | −10.5591 | − | 7.67164i | −0.485508 | − | 0.352742i | ||||
\(474\) | −3.49684 | −0.160615 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −10.8836 | −0.498849 | ||||||||
\(477\) | 7.88784 | + | 5.73085i | 0.361159 | + | 0.262398i | ||||
\(478\) | 0.393295 | + | 1.21044i | 0.0179889 | + | 0.0553641i | ||||
\(479\) | 3.42915 | + | 10.5538i | 0.156682 | + | 0.482217i | 0.998327 | − | 0.0578133i | \(-0.0184128\pi\) |
−0.841646 | + | 0.540030i | \(0.818413\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.64933 | − | 29.6976i | 0.439972 | − | 1.35409i | ||||
\(482\) | −3.26108 | −0.148538 | ||||||||
\(483\) | 6.29211 | − | 19.3651i | 0.286301 | − | 0.881144i | ||||
\(484\) | 18.6351 | − | 13.5392i | 0.847051 | − | 0.615418i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.74793 | + | 1.26995i | 0.0792877 | + | 0.0576059i | ||||
\(487\) | 5.77397 | − | 4.19504i | 0.261644 | − | 0.190095i | −0.449228 | − | 0.893417i | \(-0.648301\pi\) |
0.710871 | + | 0.703322i | \(0.248301\pi\) | |||||||
\(488\) | −12.4868 | + | 9.07218i | −0.565250 | + | 0.410678i | ||||
\(489\) | −13.1525 | − | 9.55586i | −0.594777 | − | 0.432131i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.85201 | + | 4.25173i | −0.264097 | + | 0.191878i | −0.711951 | − | 0.702229i | \(-0.752188\pi\) |
0.447854 | + | 0.894107i | \(0.352188\pi\) | |||||||
\(492\) | −7.03448 | + | 21.6499i | −0.317139 | + | 0.976053i | ||||
\(493\) | 3.05067 | 0.137395 | ||||||||
\(494\) | −19.0575 | + | 58.6531i | −0.857439 | + | 2.63893i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.06020 | + | 9.41834i | 0.137407 | + | 0.422896i | ||||
\(497\) | −0.0692236 | − | 0.213048i | −0.00310510 | − | 0.00955652i | ||||
\(498\) | −22.9832 | − | 16.6983i | −1.02990 | − | 0.748269i | ||||
\(499\) | 16.0169 | 0.717014 | 0.358507 | − | 0.933527i | \(-0.383286\pi\) | ||||
0.358507 | + | 0.933527i | \(0.383286\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.3906 | 0.508894 | ||||||||
\(502\) | 20.7921 | + | 15.1063i | 0.927997 | + | 0.674229i | ||||
\(503\) | 10.4436 | + | 32.1422i | 0.465659 | + | 1.43315i | 0.858152 | + | 0.513396i | \(0.171613\pi\) |
−0.392492 | + | 0.919755i | \(0.628387\pi\) | |||||||
\(504\) | −1.40962 | − | 4.33836i | −0.0627894 | − | 0.193246i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −6.61690 | + | 20.3647i | −0.294157 | + | 0.905322i | ||||
\(507\) | 14.4727 | 0.642753 | ||||||||
\(508\) | −8.25985 | + | 25.4212i | −0.366472 | + | 1.12788i | ||||
\(509\) | 29.4701 | − | 21.4113i | 1.30624 | − | 0.949038i | 0.306243 | − | 0.951953i | \(-0.400928\pi\) |
0.999996 | + | 0.00291563i | \(0.000928074\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.2565 | + | 7.45178i | 0.453720 | + | 0.329647i | ||||
\(512\) | 18.9548 | − | 13.7715i | 0.837692 | − | 0.608619i | ||||
\(513\) | −4.40581 | + | 3.20100i | −0.194521 | + | 0.141328i | ||||
\(514\) | 31.5487 | + | 22.9215i | 1.39156 | + | 1.01102i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −18.3130 | + | 13.3052i | −0.806187 | + | 0.585729i | ||||
\(517\) | −0.357992 | + | 1.10179i | −0.0157445 | + | 0.0484565i | ||||
\(518\) | −40.6813 | −1.78743 | ||||||||
\(519\) | −2.92282 | + | 8.99552i | −0.128298 | + | 0.394860i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.87972 | + | 24.2513i | 0.345217 | + | 1.06247i | 0.961468 | + | 0.274918i | \(0.0886507\pi\) |
−0.616251 | + | 0.787550i | \(0.711349\pi\) | |||||||
\(522\) | 1.57806 | + | 4.85678i | 0.0690700 | + | 0.212576i | ||||
\(523\) | −5.68880 | − | 4.13315i | −0.248754 | − | 0.180730i | 0.456420 | − | 0.889764i | \(-0.349131\pi\) |
−0.705174 | + | 0.709034i | \(0.749131\pi\) | |||||||
\(524\) | −17.0184 | −0.743450 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −41.2811 | −1.79994 | ||||||||
\(527\) | −4.66273 | − | 3.38767i | −0.203112 | − | 0.147569i | ||||
\(528\) | −1.05425 | − | 3.24465i | −0.0458803 | − | 0.141205i | ||||
\(529\) | 5.71836 | + | 17.5993i | 0.248624 | + | 0.765187i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.27089 | − | 3.91141i | 0.0551521 | − | 0.169741i | ||||
\(532\) | 45.9220 | 1.99097 | ||||||||
\(533\) | −13.8195 | + | 42.5322i | −0.598590 | + | 1.84227i | ||||
\(534\) | 12.7179 | − | 9.24008i | 0.550357 | − | 0.399858i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.21695 | + | 1.61071i | 0.0957577 | + | 0.0695721i | ||||
\(537\) | −3.29874 | + | 2.39667i | −0.142351 | + | 0.103424i | ||||
\(538\) | −38.8478 | + | 28.2246i | −1.67485 | + | 1.21685i | ||||
\(539\) | −3.72014 | − | 2.70284i | −0.160238 | − | 0.116420i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.9629 | − | 15.9570i | 0.944258 | − | 0.686044i | −0.00518365 | − | 0.999987i | \(-0.501650\pi\) |
0.949442 | + | 0.313943i | \(0.101650\pi\) | |||||||
\(542\) | −13.4937 | + | 41.5293i | −0.579604 | + | 1.78384i | ||||
\(543\) | −11.1202 | −0.477214 | ||||||||
\(544\) | −3.06235 | + | 9.42496i | −0.131297 | + | 0.404092i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −11.0602 | − | 34.0398i | −0.473333 | − | 1.45677i | ||||
\(547\) | −13.6205 | − | 41.9196i | −0.582371 | − | 1.79235i | −0.609582 | − | 0.792723i | \(-0.708663\pi\) |
0.0272113 | − | 0.999630i | \(-0.491337\pi\) | |||||||
\(548\) | −19.8090 | − | 14.3921i | −0.846198 | − | 0.614799i | ||||
\(549\) | −10.6939 | −0.456407 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.8719 | −0.548363 | ||||||||
\(552\) | 7.52251 | + | 5.46542i | 0.320179 | + | 0.232624i | ||||
\(553\) | 1.58073 | + | 4.86497i | 0.0672193 | + | 0.206880i | ||||
\(554\) | −10.7099 | − | 32.9618i | −0.455022 | − | 1.40041i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.63897 | + | 23.5103i | −0.323965 | + | 0.997061i | ||||
\(557\) | 9.85667 | 0.417641 | 0.208820 | − | 0.977954i | \(-0.433038\pi\) | ||||
0.208820 | + | 0.977954i | \(0.433038\pi\) | |||||||
\(558\) | 2.98134 | − | 9.17562i | 0.126210 | − | 0.388435i | ||||
\(559\) | −35.9768 | + | 26.1386i | −1.52165 | + | 1.10555i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.60632 | + | 1.16706i | 0.0678190 | + | 0.0492734i | ||||
\(562\) | 14.6356 | − | 10.6334i | 0.617363 | − | 0.448541i | ||||
\(563\) | −10.0251 | + | 7.28367i | −0.422508 | + | 0.306970i | −0.778646 | − | 0.627463i | \(-0.784093\pi\) |
0.356138 | + | 0.934433i | \(0.384093\pi\) | |||||||
\(564\) | 1.62548 | + | 1.18098i | 0.0684451 | + | 0.0497283i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.97507 | − | 1.43497i | 0.0830185 | − | 0.0603165i | ||||
\(567\) | 0.976667 | − | 3.00587i | 0.0410161 | − | 0.126235i | ||||
\(568\) | 0.102297 | 0.00429228 | ||||||||
\(569\) | −3.62037 | + | 11.1424i | −0.151774 | + | 0.467112i | −0.997820 | − | 0.0659983i | \(-0.978977\pi\) |
0.846046 | + | 0.533110i | \(0.178977\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.95523 | + | 27.5614i | 0.374765 | + | 1.15341i | 0.943637 | + | 0.330982i | \(0.107380\pi\) |
−0.568872 | + | 0.822426i | \(0.692620\pi\) | |||||||
\(572\) | 6.64779 | + | 20.4598i | 0.277958 | + | 0.855467i | ||||
\(573\) | −2.92164 | − | 2.12270i | −0.122053 | − | 0.0886769i | ||||
\(574\) | 58.2628 | 2.43184 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −12.1535 | −0.506398 | ||||||||
\(577\) | −26.5377 | − | 19.2808i | −1.10478 | − | 0.802668i | −0.122945 | − | 0.992414i | \(-0.539234\pi\) |
−0.981833 | + | 0.189745i | \(0.939234\pi\) | |||||||
\(578\) | 10.2378 | + | 31.5088i | 0.425838 | + | 1.31059i | ||||
\(579\) | 5.27067 | + | 16.2215i | 0.219042 | + | 0.674141i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.8420 | + | 39.5237i | −0.532777 | + | 1.63972i | ||||
\(582\) | 22.0246 | 0.912947 | ||||||||
\(583\) | −4.63488 | + | 14.2647i | −0.191957 | + | 0.590783i | ||||
\(584\) | −4.68371 | + | 3.40291i | −0.193813 | + | 0.140813i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.15758 | + | 3.02066i | 0.171748 | + | 0.124782i | ||||
\(587\) | 15.0797 | − | 10.9560i | 0.622405 | − | 0.452203i | −0.231356 | − | 0.972869i | \(-0.574316\pi\) |
0.853761 | + | 0.520666i | \(0.174316\pi\) | |||||||
\(588\) | −6.45197 | + | 4.68763i | −0.266075 | + | 0.193315i | ||||
\(589\) | 19.6738 | + | 14.2938i | 0.810644 | + | 0.588967i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.56391 | + | 2.58933i | −0.146600 | + | 0.106511i | ||||
\(592\) | −4.08275 | + | 12.5654i | −0.167800 | + | 0.516435i | ||||
\(593\) | −1.55882 | −0.0640129 | −0.0320064 | − | 0.999488i | \(-0.510190\pi\) | ||||
−0.0320064 | + | 0.999488i | \(0.510190\pi\) | |||||||
\(594\) | −1.02708 | + | 3.16103i | −0.0421416 | + | 0.129698i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.31202 | − | 25.5818i | −0.340474 | − | 1.04787i | ||||
\(597\) | 5.12831 | + | 15.7833i | 0.209888 | + | 0.645969i | ||||
\(598\) | 59.0234 | + | 42.8830i | 2.41365 | + | 1.75362i | ||||
\(599\) | −31.5470 | −1.28898 | −0.644489 | − | 0.764614i | \(-0.722930\pi\) | ||||
−0.644489 | + | 0.764614i | \(0.722930\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −32.3999 | −1.32162 | −0.660809 | − | 0.750554i | \(-0.729787\pi\) | ||||
−0.660809 | + | 0.750554i | \(0.729787\pi\) | |||||||
\(602\) | 46.8707 | + | 34.0536i | 1.91031 | + | 1.38792i | ||||
\(603\) | 0.586713 | + | 1.80572i | 0.0238928 | + | 0.0735345i | ||||
\(604\) | 8.85266 | + | 27.2457i | 0.360210 | + | 1.10861i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.726129 | + | 2.23480i | −0.0294970 | + | 0.0907824i | ||||
\(607\) | −24.8410 | −1.00827 | −0.504133 | − | 0.863626i | \(-0.668188\pi\) | ||||
−0.504133 | + | 0.863626i | \(0.668188\pi\) | |||||||
\(608\) | 12.9212 | − | 39.7674i | 0.524024 | − | 1.61278i | ||||
\(609\) | 6.04363 | − | 4.39095i | 0.244900 | − | 0.177930i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.19333 | + | 2.32009i | 0.129188 | + | 0.0938607i | ||||
\(612\) | 2.78590 | − | 2.02408i | 0.112614 | − | 0.0818185i | ||||
\(613\) | −3.19204 | + | 2.31915i | −0.128925 | + | 0.0936697i | −0.650379 | − | 0.759610i | \(-0.725390\pi\) |
0.521454 | + | 0.853280i | \(0.325390\pi\) | |||||||
\(614\) | −5.05791 | − | 3.67478i | −0.204120 | − | 0.148302i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.67717 | − | 4.12471i | 0.228740 | − | 0.166189i | ||||
\(617\) | 5.40225 | − | 16.6264i | 0.217486 | − | 0.669354i | −0.781481 | − | 0.623929i | \(-0.785536\pi\) |
0.998968 | − | 0.0454257i | \(-0.0144644\pi\) | |||||||
\(618\) | −10.6679 | −0.429126 | ||||||||
\(619\) | −4.44581 | + | 13.6828i | −0.178692 | + | 0.549958i | −0.999783 | − | 0.0208398i | \(-0.993366\pi\) |
0.821091 | + | 0.570798i | \(0.193366\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.99082 | + | 6.12712i | 0.0798890 | + | 0.245873i | ||||
\(622\) | 4.77066 | + | 14.6826i | 0.191286 | + | 0.588718i | ||||
\(623\) | −18.6043 | − | 13.5168i | −0.745364 | − | 0.541539i | ||||
\(624\) | −11.6240 | −0.465333 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 49.7617 | 1.98888 | ||||||||
\(627\) | −6.77768 | − | 4.92427i | −0.270674 | − | 0.196656i | ||||
\(628\) | −14.3801 | − | 44.2573i | −0.573827 | − | 1.76606i | ||||
\(629\) | −2.37611 | − | 7.31292i | −0.0947418 | − | 0.291585i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.46214 | + | 16.8107i | −0.217444 | + | 0.669225i | 0.781527 | + | 0.623872i | \(0.214441\pi\) |
−0.998971 | + | 0.0453529i | \(0.985559\pi\) | |||||||
\(632\) | −2.33596 | −0.0929194 | ||||||||
\(633\) | 5.73083 | − | 17.6377i | 0.227780 | − | 0.701035i | ||||
\(634\) | 36.3132 | − | 26.3831i | 1.44218 | − | 1.04781i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 21.0449 | + | 15.2900i | 0.834485 | + | 0.606289i | ||||
\(637\) | −12.6752 | + | 9.20905i | −0.502209 | + | 0.364876i | ||||
\(638\) | −6.35559 | + | 4.61760i | −0.251620 | + | 0.182813i | ||||
\(639\) | 0.0573410 | + | 0.0416607i | 0.00226837 | + | 0.00164807i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.21774 | − | 1.61128i | 0.0875954 | − | 0.0636417i | −0.543126 | − | 0.839651i | \(-0.682759\pi\) |
0.630721 | + | 0.776010i | \(0.282759\pi\) | |||||||
\(642\) | 10.2190 | − | 31.4507i | 0.403310 | − | 1.24126i | ||||
\(643\) | −20.9276 | −0.825303 | −0.412651 | − | 0.910889i | \(-0.635397\pi\) | ||||
−0.412651 | + | 0.910889i | \(0.635397\pi\) | |||||||
\(644\) | 16.7875 | − | 51.6665i | 0.661519 | − | 2.03595i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.69284 | + | 14.4431i | 0.184637 | + | 0.568256i | ||||
\(647\) | 0.570653 | + | 1.75629i | 0.0224347 | + | 0.0690469i | 0.961647 | − | 0.274290i | \(-0.0884428\pi\) |
−0.939212 | + | 0.343337i | \(0.888443\pi\) | |||||||
\(648\) | 1.16765 | + | 0.848347i | 0.0458696 | + | 0.0333262i | ||||
\(649\) | 6.32678 | 0.248348 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14.1132 | −0.553141 | ||||||||
\(652\) | −35.0912 | − | 25.4952i | −1.37428 | − | 0.998470i | ||||
\(653\) | 5.69002 | + | 17.5121i | 0.222667 | + | 0.685300i | 0.998520 | + | 0.0543858i | \(0.0173201\pi\) |
−0.775853 | + | 0.630914i | \(0.782680\pi\) | |||||||
\(654\) | −4.44588 | − | 13.6830i | −0.173848 | − | 0.535048i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5.84721 | − | 17.9959i | 0.228295 | − | 0.702620i | ||||
\(657\) | −4.01123 | −0.156493 | ||||||||
\(658\) | 1.58909 | − | 4.89071i | 0.0619491 | − | 0.190660i | ||||
\(659\) | 10.8246 | − | 7.86455i | 0.421668 | − | 0.306360i | −0.356641 | − | 0.934242i | \(-0.616078\pi\) |
0.778308 | + | 0.627882i | \(0.216078\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.7001 | − | 23.0315i | −1.23299 | − | 0.895820i | −0.235879 | − | 0.971782i | \(-0.575797\pi\) |
−0.997111 | + | 0.0759628i | \(0.975797\pi\) | |||||||
\(662\) | −33.6483 | + | 24.4469i | −1.30778 | + | 0.950155i | ||||
\(663\) | 5.47303 | − | 3.97639i | 0.212555 | − | 0.154430i | ||||
\(664\) | −15.3532 | − | 11.1548i | −0.595821 | − | 0.432890i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10.4133 | − | 7.56571i | 0.403507 | − | 0.293165i | ||||
\(667\) | −4.70553 | + | 14.4821i | −0.182199 | + | 0.560751i | ||||
\(668\) | 30.3903 | 1.17584 | ||||||||
\(669\) | 0.238424 | − | 0.733794i | 0.00921801 | − | 0.0283701i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.08365 | − | 15.6459i | −0.196252 | − | 0.604002i | ||||
\(672\) | 7.49894 | + | 23.0794i | 0.289278 | + | 0.890305i | ||||
\(673\) | 15.6877 | + | 11.3978i | 0.604718 | + | 0.439353i | 0.847550 | − | 0.530715i | \(-0.178077\pi\) |
−0.242832 | + | 0.970068i | \(0.578077\pi\) | |||||||
\(674\) | 46.8981 | 1.80645 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 38.6133 | 1.48513 | ||||||||
\(677\) | −36.9588 | − | 26.8522i | −1.42044 | − | 1.03201i | −0.991698 | − | 0.128587i | \(-0.958956\pi\) |
−0.428746 | − | 0.903425i | \(-0.641044\pi\) | |||||||
\(678\) | −5.98977 | − | 18.4346i | −0.230036 | − | 0.707978i | ||||
\(679\) | −9.95606 | − | 30.6416i | −0.382078 | − | 1.17592i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.53249 | + | 10.8719i | −0.135365 | + | 0.416611i | ||||
\(682\) | 14.8417 | 0.568319 | ||||||||
\(683\) | −3.58128 | + | 11.0220i | −0.137034 | + | 0.421747i | −0.995901 | − | 0.0904520i | \(-0.971169\pi\) |
0.858867 | + | 0.512199i | \(0.171169\pi\) | |||||||
\(684\) | −11.7548 | + | 8.54034i | −0.449455 | + | 0.326548i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −22.1577 | − | 16.0985i | −0.845987 | − | 0.614645i | ||||
\(687\) | −8.27200 | + | 6.00996i | −0.315596 | + | 0.229294i | ||||
\(688\) | 15.2222 | − | 11.0596i | 0.580340 | − | 0.421642i | ||||
\(689\) | 41.3436 | + | 30.0379i | 1.57507 | + | 1.14435i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.5091 | − | 12.7211i | 0.666077 | − | 0.483934i | −0.202632 | − | 0.979255i | \(-0.564950\pi\) |
0.868710 | + | 0.495321i | \(0.164950\pi\) | |||||||
\(692\) | −7.79815 | + | 24.0002i | −0.296441 | + | 0.912352i | ||||
\(693\) | 4.86205 | 0.184694 | ||||||||
\(694\) | −1.14498 | + | 3.52388i | −0.0434627 | + | 0.133764i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.05418 | + | 3.24442i | 0.0399585 | + | 0.122980i | ||||
\(697\) | 3.40301 | + | 10.4734i | 0.128898 | + | 0.396707i | ||||
\(698\) | −27.1895 | − | 19.7543i | −1.02914 | − | 0.747713i | ||||
\(699\) | 22.5229 | 0.851896 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.61904 | −0.325537 | −0.162768 | − | 0.986664i | \(-0.552042\pi\) | ||||
−0.162768 | + | 0.986664i | \(0.552042\pi\) | |||||||
\(702\) | 9.16166 | + | 6.65634i | 0.345785 | + | 0.251227i | ||||
\(703\) | 10.0257 | + | 30.8559i | 0.378126 | + | 1.16375i | ||||
\(704\) | −5.77751 | − | 17.7814i | −0.217748 | − | 0.670160i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10.3843 | − | 31.9597i | 0.390820 | − | 1.20282i | ||||
\(707\) | 3.43739 | 0.129276 | ||||||||
\(708\) | 3.39077 | − | 10.4357i | 0.127433 | − | 0.392198i | ||||
\(709\) | −12.9443 | + | 9.40460i | −0.486134 | + | 0.353197i | −0.803696 | − | 0.595041i | \(-0.797136\pi\) |
0.317562 | + | 0.948238i | \(0.397136\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.30939 | − | 0.951325i | −0.0491058 | − | 0.0356775i | ||||
\(712\) | 8.49579 | − | 6.17255i | 0.318393 | − | 0.231326i | ||||
\(713\) | 23.2740 | − | 16.9095i | 0.871617 | − | 0.633267i | ||||
\(714\) | −7.13030 | − | 5.18047i | −0.266845 | − | 0.193874i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.80110 | + | 6.39437i | −0.328913 | + | 0.238969i | ||||
\(717\) | −0.182034 | + | 0.560243i | −0.00679818 | + | 0.0209226i | ||||
\(718\) | 53.0138 | 1.97846 | ||||||||
\(719\) | −15.0132 | + | 46.2060i | −0.559899 | + | 1.72319i | 0.122743 | + | 0.992438i | \(0.460831\pi\) |
−0.682642 | + | 0.730753i | \(0.739169\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.82235 | + | 14.8417i | 0.179594 | + | 0.552733i | ||||
\(722\) | −7.11551 | − | 21.8993i | −0.264812 | − | 0.815007i | ||||
\(723\) | −1.22110 | − | 0.887185i | −0.0454134 | − | 0.0329948i | ||||
\(724\) | −29.6689 | −1.10264 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 18.6531 | 0.692283 | ||||||||
\(727\) | 20.5756 | + | 14.9490i | 0.763106 | + | 0.554429i | 0.899861 | − | 0.436176i | \(-0.143667\pi\) |
−0.136755 | + | 0.990605i | \(0.543667\pi\) | |||||||
\(728\) | −7.38842 | − | 22.7392i | −0.273833 | − | 0.842772i | ||||
\(729\) | 0.309017 | + | 0.951057i | 0.0114451 | + | 0.0352243i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.38389 | + | 10.4145i | −0.125158 | + | 0.385196i | ||||
\(732\) | −28.5317 | −1.05456 | ||||||||
\(733\) | 5.75358 | − | 17.7077i | 0.212513 | − | 0.654049i | −0.786807 | − | 0.617199i | \(-0.788267\pi\) |
0.999321 | − | 0.0368505i | \(-0.0117325\pi\) | |||||||
\(734\) | −49.1287 | + | 35.6941i | −1.81337 | + | 1.31749i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −40.0185 | − | 29.0752i | −1.47510 | − | 1.07172i | ||||
\(737\) | −2.36296 | + | 1.71679i | −0.0870408 | + | 0.0632389i | ||||
\(738\) | −14.9137 | + | 10.8354i | −0.548980 | + | 0.398857i | ||||
\(739\) | −37.9326 | − | 27.5596i | −1.39537 | − | 1.01380i | −0.995252 | − | 0.0973351i | \(-0.968968\pi\) |
−0.400121 | − | 0.916462i | \(-0.631032\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −23.0927 | + | 16.7779i | −0.848333 | + | 0.616350i | ||||
\(742\) | 20.5737 | − | 63.3194i | 0.755286 | − | 2.32453i | ||||
\(743\) | 42.7061 | 1.56674 | 0.783368 | − | 0.621558i | \(-0.213500\pi\) | ||||
0.783368 | + | 0.621558i | \(0.213500\pi\) | |||||||
\(744\) | 1.99159 | − | 6.12948i | 0.0730152 | − | 0.224718i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −6.48171 | − | 19.9487i | −0.237312 | − | 0.730372i | ||||
\(747\) | −4.06322 | − | 12.5053i | −0.148665 | − | 0.457545i | ||||
\(748\) | 4.28570 | + | 3.11374i | 0.156701 | + | 0.113850i | ||||
\(749\) | −48.3751 | −1.76759 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.64893 | −0.0966608 | −0.0483304 | − | 0.998831i | \(-0.515390\pi\) | ||||
−0.0483304 | + | 0.998831i | \(0.515390\pi\) | |||||||
\(752\) | −1.35113 | − | 0.981657i | −0.0492708 | − | 0.0357973i | ||||
\(753\) | 3.67584 | + | 11.3131i | 0.133955 | + | 0.412272i | ||||
\(754\) | 8.27133 | + | 25.4565i | 0.301224 | + | 0.927072i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.60577 | − | 8.01972i | 0.0947708 | − | 0.291674i | ||||
\(757\) | −52.9153 | −1.92324 | −0.961620 | − | 0.274383i | \(-0.911526\pi\) | ||||
−0.961620 | + | 0.274383i | \(0.911526\pi\) | |||||||
\(758\) | 14.8662 | − | 45.7534i | 0.539964 | − | 1.66184i | ||||
\(759\) | −8.01795 | + | 5.82538i | −0.291033 | + | 0.211448i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −41.0808 | − | 29.8470i | −1.48918 | − | 1.08195i | −0.974451 | − | 0.224598i | \(-0.927893\pi\) |
−0.514728 | − | 0.857354i | \(-0.672107\pi\) | |||||||
\(762\) | −17.5116 | + | 12.7229i | −0.634377 | + | 0.460902i | ||||
\(763\) | −17.0267 | + | 12.3706i | −0.616408 | + | 0.447847i | ||||
\(764\) | −7.79499 | − | 5.66339i | −0.282013 | − | 0.204894i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 23.8242 | − | 17.3093i | 0.860803 | − | 0.625410i | ||||
\(767\) | 6.66131 | − | 20.5014i | 0.240526 | − | 0.740263i | ||||
\(768\) | 0.752056 | 0.0271375 | ||||||||
\(769\) | 7.59580 | − | 23.3775i | 0.273912 | − | 0.843013i | −0.715594 | − | 0.698517i | \(-0.753844\pi\) |
0.989505 | − | 0.144496i | \(-0.0461562\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.57751 | + | 17.1658i | 0.200869 | + | 0.618212i | ||||
\(772\) | 14.0622 | + | 43.2791i | 0.506111 | + | 1.55765i | ||||
\(773\) | −16.1894 | − | 11.7623i | −0.582293 | − | 0.423061i | 0.257257 | − | 0.966343i | \(-0.417181\pi\) |
−0.839550 | + | 0.543282i | \(0.817181\pi\) | |||||||
\(774\) | −18.3308 | −0.658885 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 14.7128 | 0.528159 | ||||||||
\(777\) | −15.2330 | − | 11.0674i | −0.546482 | − | 0.397042i | ||||
\(778\) | −12.8392 | − | 39.5149i | −0.460307 | − | 1.41668i | ||||
\(779\) | −14.3586 | − | 44.1911i | −0.514449 | − | 1.58331i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.0336934 | + | 0.103698i | −0.00120565 | + | 0.00371060i | ||||
\(782\) | 17.9654 | 0.642441 | ||||||||
\(783\) | −0.730396 | + | 2.24793i | −0.0261022 | + | 0.0803344i | ||||
\(784\) | 5.36302 | − | 3.89646i | 0.191536 | − | 0.139159i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −11.1494 | − | 8.10053i | −0.397687 | − | 0.288936i | ||||
\(787\) | 7.27526 | − | 5.28579i | 0.259335 | − | 0.188418i | −0.450519 | − | 0.892767i | \(-0.648761\pi\) |
0.709854 | + | 0.704349i | \(0.248761\pi\) | |||||||
\(788\) | −9.50857 | + | 6.90838i | −0.338729 | + | 0.246101i | ||||
\(789\) | −15.4576 | − | 11.2306i | −0.550305 | − | 0.399820i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −22.9395 | + | 16.6665i | −0.815634 | + | 0.592593i | ||||
\(792\) | −0.686108 | + | 2.11162i | −0.0243798 | + | 0.0750333i | ||||
\(793\) | −56.0517 | −1.99045 | ||||||||
\(794\) | 14.8406 | − | 45.6747i | 0.526674 | − | 1.62093i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13.6824 | + | 42.1102i | 0.484961 | + | 1.49256i | ||||
\(797\) | 11.6674 | + | 35.9084i | 0.413279 | + | 1.27194i | 0.913781 | + | 0.406207i | \(0.133149\pi\) |
−0.500502 | + | 0.865735i | \(0.666851\pi\) | |||||||
\(798\) | 30.0854 | + | 21.8583i | 1.06501 | + | 0.773776i | ||||
\(799\) | 0.971976 | 0.0343860 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.27597 | 0.257084 | ||||||||
\(802\) | 8.24547 | + | 5.99069i | 0.291158 | + | 0.211538i | ||||
\(803\) | −1.90684 | − | 5.86866i | −0.0672910 | − | 0.207100i | ||||
\(804\) | 1.56536 | + | 4.81769i | 0.0552061 | + | 0.169907i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 15.6265 | − | 48.0934i | 0.550420 | − | 1.69402i | ||||
\(807\) | −22.2250 | −0.782358 | ||||||||
\(808\) | −0.485068 | + | 1.49289i | −0.0170646 | + | 0.0525195i | ||||
\(809\) | 39.5610 | − | 28.7428i | 1.39089 | − | 1.01054i | 0.395124 | − | 0.918628i | \(-0.370702\pi\) |
0.995767 | − | 0.0919140i | \(-0.0292985\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.6069 | + | 10.6125i | 0.512916 | + | 0.372655i | 0.813929 | − | 0.580965i | \(-0.197325\pi\) |
−0.301013 | + | 0.953620i | \(0.597325\pi\) | |||||||
\(812\) | 16.1245 | − | 11.7151i | 0.565860 | − | 0.411121i | ||||
\(813\) | −16.3508 | + | 11.8796i | −0.573449 | + | 0.416635i | ||||
\(814\) | 16.0193 | + | 11.6387i | 0.561477 | + | 0.407937i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.31570 | + | 1.68246i | −0.0810658 | + | 0.0588978i | ||||
\(817\) | 14.2779 | − | 43.9428i | 0.499520 | − | 1.53736i | ||||
\(818\) | 26.9653 | 0.942819 | ||||||||
\(819\) | 5.11914 | − | 15.7551i | 0.178877 | − | 0.550527i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.6393 | + | 48.1327i | 0.545814 | + | 1.67984i | 0.719046 | + | 0.694962i | \(0.244579\pi\) |
−0.173232 | + | 0.984881i | \(0.555421\pi\) | |||||||
\(822\) | −6.12723 | − | 18.8577i | −0.213712 | − | 0.657737i | ||||
\(823\) | −21.6873 | − | 15.7568i | −0.755972 | − | 0.549246i | 0.141700 | − | 0.989910i | \(-0.454743\pi\) |
−0.897672 | + | 0.440664i | \(0.854743\pi\) | |||||||
\(824\) | −7.12635 | −0.248258 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −28.0839 | −0.977163 | ||||||||
\(827\) | −17.2845 | − | 12.5580i | −0.601042 | − | 0.436683i | 0.245206 | − | 0.969471i | \(-0.421144\pi\) |
−0.846249 | + | 0.532788i | \(0.821144\pi\) | |||||||
\(828\) | 5.31155 | + | 16.3473i | 0.184589 | + | 0.568107i | ||||
\(829\) | −14.8675 | − | 45.7575i | −0.516370 | − | 1.58922i | −0.780775 | − | 0.624812i | \(-0.785176\pi\) |
0.264405 | − | 0.964412i | \(-0.414824\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.95702 | − | 15.2561i | 0.171957 | − | 0.529230i | ||||
\(832\) | −63.7021 | −2.20847 | ||||||||
\(833\) | −1.19220 | + | 3.66921i | −0.0413072 | + | 0.127130i | ||||
\(834\) | −16.1953 | + | 11.7665i | −0.560796 | + | 0.407442i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −18.0830 | − | 13.1380i | −0.625412 | − | 0.454389i | ||||
\(837\) | 3.61260 | − | 2.62471i | 0.124870 | − | 0.0907232i | ||||
\(838\) | 61.0873 | − | 44.3825i | 2.11022 | − | 1.53317i | ||||
\(839\) | 33.8606 | + | 24.6012i | 1.16900 | + | 0.849327i | 0.990889 | − | 0.134684i | \(-0.0430018\pi\) |
0.178110 | + | 0.984011i | \(0.443002\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.9418 | − | 13.7620i | 0.653165 | − | 0.474552i | ||||
\(842\) | 26.4123 | − | 81.2886i | 0.910227 | − | 2.80139i | ||||
\(843\) | 8.37308 | 0.288384 | ||||||||
\(844\) | 15.2900 | − | 47.0577i | 0.526302 | − | 1.61979i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.502787 | + | 1.54742i | 0.0172862 | + | 0.0532014i | ||||
\(847\) | −8.43203 | − | 25.9511i | −0.289728 | − | 0.891691i | ||||
\(848\) | −17.4930 | − | 12.7094i | −0.600711 | − | 0.436442i | ||||
\(849\) | 1.12995 | 0.0387798 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 38.3809 | 1.31568 | ||||||||
\(852\) | 0.152987 | + | 0.111151i | 0.00524124 | + | 0.00380799i | ||||
\(853\) | 17.9855 | + | 55.3537i | 0.615812 | + | 1.89527i | 0.388485 | + | 0.921455i | \(0.372998\pi\) |
0.227327 | + | 0.973819i | \(0.427002\pi\) | |||||||
\(854\) | 22.5658 | + | 69.4504i | 0.772186 | + | 2.37654i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.82646 | − | 21.0097i | 0.233324 | − | 0.718096i | ||||
\(857\) | 3.22045 | 0.110008 | 0.0550042 | − | 0.998486i | \(-0.482483\pi\) | ||||
0.0550042 | + | 0.998486i | \(0.482483\pi\) | |||||||
\(858\) | −5.38337 | + | 16.5683i | −0.183785 | + | 0.565633i | ||||
\(859\) | −40.0003 | + | 29.0619i | −1.36479 | + | 0.991580i | −0.366669 | + | 0.930351i | \(0.619502\pi\) |
−0.998124 | + | 0.0612288i | \(0.980498\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 21.8164 | + | 15.8505i | 0.743500 | + | 0.540184i | ||||
\(862\) | −24.5731 | + | 17.8534i | −0.836963 | + | 0.608089i | ||||
\(863\) | 17.3878 | − | 12.6329i | 0.591886 | − | 0.430030i | −0.251104 | − | 0.967960i | \(-0.580793\pi\) |
0.842990 | + | 0.537930i | \(0.180793\pi\) | |||||||
\(864\) | −6.21171 | − | 4.51307i | −0.211327 | − | 0.153538i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0.960798 | − | 0.698061i | 0.0326493 | − | 0.0237211i | ||||
\(867\) | −4.73851 | + | 14.5836i | −0.160928 | + | 0.495286i | ||||
\(868\) | −37.6544 | −1.27807 | ||||||||
\(869\) | 0.769392 | − | 2.36795i | 0.0260999 | − | 0.0803271i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.07522 | + | 9.46456i | 0.104200 | + | 0.320694i | ||||
\(872\) | −2.96993 | − | 9.14051i | −0.100575 | − | 0.309537i | ||||
\(873\) | 8.24705 | + | 5.99183i | 0.279120 | + | 0.202793i | ||||
\(874\) | −75.8026 | −2.56406 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −10.7020 | −0.361588 | ||||||||
\(877\) | 12.4421 | + | 9.03971i | 0.420140 | + | 0.305249i | 0.777694 | − | 0.628643i | \(-0.216389\pi\) |
−0.357554 | + | 0.933892i | \(0.616389\pi\) | |||||||
\(878\) | 1.98544 | + | 6.11054i | 0.0670052 | + | 0.206221i | ||||
\(879\) | 0.735020 | + | 2.26216i | 0.0247916 | + | 0.0763007i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.84891 | − | 18.0011i | 0.197055 | − | 0.606472i | −0.802892 | − | 0.596125i | \(-0.796706\pi\) |
0.999946 | − | 0.0103472i | \(-0.00329367\pi\) | |||||||
\(882\) | −6.45821 | −0.217459 | ||||||||
\(883\) | −1.95208 | + | 6.00790i | −0.0656928 | + | 0.202182i | −0.978515 | − | 0.206175i | \(-0.933898\pi\) |
0.912822 | + | 0.408357i | \(0.133898\pi\) | |||||||
\(884\) | 14.6021 | − | 10.6091i | 0.491123 | − | 0.356822i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 64.1303 | + | 46.5934i | 2.15450 | + | 1.56534i | ||||
\(887\) | 0.0583776 | − | 0.0424138i | 0.00196013 | − | 0.00142412i | −0.586805 | − | 0.809728i | \(-0.699614\pi\) |
0.588765 | + | 0.808304i | \(0.299614\pi\) | |||||||
\(888\) | 6.95628 | − | 5.05404i | 0.233438 | − | 0.169602i | ||||
\(889\) | 25.6167 | + | 18.6116i | 0.859156 | + | 0.624213i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.24455 | + | 0.904220i | −0.0416941 | + | 0.0302925i | ||||
\(892\) | 0.636120 | − | 1.95778i | 0.0212989 | − | 0.0655512i | ||||
\(893\) | −4.10113 | −0.137239 | ||||||||
\(894\) | 6.73107 | − | 20.7161i | 0.225121 | − | 0.692850i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 10.6479 | + | 32.7709i | 0.355721 | + | 1.09480i | ||||
\(897\) | 10.4348 | + | 32.1149i | 0.348407 | + | 1.07229i | ||||
\(898\) | −31.1886 | − | 22.6599i | −1.04078 | − | 0.756169i | ||||
\(899\) | 10.5545 | 0.352013 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.5840 | 0.419235 | ||||||||
\(902\) | −22.9425 | − | 16.6687i | −0.763901 | − | 0.555006i | ||||
\(903\) | 8.28629 | + | 25.5026i | 0.275751 | + | 0.848673i | ||||
\(904\) | −4.00128 | − | 12.3147i | −0.133081 | − | 0.409580i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −7.16888 | + | 22.0635i | −0.238170 | + | 0.733012i | ||||
\(907\) | 25.4951 | 0.846550 | 0.423275 | − | 0.906001i | \(-0.360880\pi\) | ||||
0.423275 | + | 0.906001i | \(0.360880\pi\) | |||||||
\(908\) | −9.42474 | + | 29.0064i | −0.312771 | + | 0.962610i | ||||
\(909\) | −0.879879 | + | 0.639269i | −0.0291837 | + | 0.0212032i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.87851 | − | 2.09136i | −0.0953692 | − | 0.0692898i | 0.539079 | − | 0.842255i | \(-0.318773\pi\) |
−0.634448 | + | 0.772966i | \(0.718773\pi\) | |||||||
\(912\) | 9.77081 | − | 7.09891i | 0.323544 | − | 0.235068i | ||||
\(913\) | 16.3644 | − | 11.8894i | 0.541583 | − | 0.393483i | ||||
\(914\) | 42.2621 | + | 30.7052i | 1.39791 | + | 1.01564i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −22.0698 | + | 16.0347i | −0.729208 | + | 0.529801i | ||||
\(917\) | −6.22981 | + | 19.1734i | −0.205727 | + | 0.633161i | ||||
\(918\) | 2.78860 | 0.0920375 | ||||||||
\(919\) | 2.46277 | − | 7.57962i | 0.0812392 | − | 0.250029i | −0.902185 | − | 0.431350i | \(-0.858037\pi\) |
0.983424 | + | 0.181321i | \(0.0580374\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.894189 | − | 2.75203i | −0.0294645 | − | 0.0906825i | ||||
\(922\) | 24.9617 | + | 76.8241i | 0.822068 | + | 2.53007i | ||||
\(923\) | 0.300549 | + | 0.218362i | 0.00989270 | + | 0.00718747i | ||||
\(924\) | 12.9720 | 0.426749 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 44.1434 | 1.45064 | ||||||||
\(927\) | −3.99457 | − | 2.90222i | −0.131199 | − | 0.0953216i | ||||
\(928\) | −5.60805 | − | 17.2598i | −0.184093 | − | 0.566581i | ||||
\(929\) | 15.0004 | + | 46.1666i | 0.492149 | + | 1.51468i | 0.821354 | + | 0.570419i | \(0.193219\pi\) |
−0.329205 | + | 0.944258i | \(0.606781\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.03032 | − | 15.4817i | 0.164862 | − | 0.507394i | ||||
\(932\) | 60.0916 | 1.96837 | ||||||||
\(933\) | −2.20807 | + | 6.79573i | −0.0722888 | + | 0.222482i | ||||
\(934\) | −54.5571 | + | 39.6381i | −1.78516 | + | 1.29700i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.12016 | + | 4.44656i | 0.200044 | + | 0.145340i | ||||
\(937\) | 25.6698 | − | 18.6502i | 0.838594 | − | 0.609274i | −0.0833833 | − | 0.996518i | \(-0.526573\pi\) |
0.921978 | + | 0.387243i | \(0.126573\pi\) | |||||||
\(938\) | 10.4889 | − | 7.62066i | 0.342476 | − | 0.248823i | ||||
\(939\) | 18.6331 | + | 13.5378i | 0.608070 | + | 0.441789i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −33.1752 | + | 24.1032i | −1.08148 | + | 0.785742i | −0.977941 | − | 0.208883i | \(-0.933017\pi\) |
−0.103541 | + | 0.994625i | \(0.533017\pi\) | |||||||
\(942\) | 11.6450 | − | 35.8395i | 0.379414 | − | 1.16771i | ||||
\(943\) | −54.9681 | −1.79001 | ||||||||
\(944\) | −2.81848 | + | 8.67439i | −0.0917337 | + | 0.282327i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.71401 | − | 26.8190i | −0.283317 | − | 0.871960i | ||||
\(947\) | 3.03389 | + | 9.33737i | 0.0985883 | + | 0.303424i | 0.988172 | − | 0.153348i | \(-0.0490056\pi\) |
−0.889584 | + | 0.456772i | \(0.849006\pi\) | |||||||
\(948\) | −3.49347 | − | 2.53815i | −0.113463 | − | 0.0824353i | ||||
\(949\) | −21.0246 | −0.682487 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20.7750 | 0.673674 | ||||||||
\(952\) | −4.76317 | − | 3.46065i | −0.154375 | − | 0.112160i | ||||
\(953\) | −16.4125 | − | 50.5123i | −0.531652 | − | 1.63626i | −0.750775 | − | 0.660558i | \(-0.770320\pi\) |
0.219123 | − | 0.975697i | \(-0.429680\pi\) | |||||||
\(954\) | 6.50952 | + | 20.0343i | 0.210754 | + | 0.648633i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.485670 | + | 1.49474i | −0.0157077 | + | 0.0483433i | ||||
\(957\) | −3.63606 | −0.117537 | ||||||||
\(958\) | −7.40888 | + | 22.8022i | −0.239370 | + | 0.736705i | ||||
\(959\) | −23.4659 | + | 17.0490i | −0.757754 | + | 0.550540i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.94773 | + | 6.50090i | 0.288636 | + | 0.209707i | ||||
\(962\) | 54.5807 | − | 39.6552i | 1.75975 | − | 1.27853i | ||||
\(963\) | 12.3827 | − | 8.99657i | 0.399027 | − | 0.289910i | ||||
\(964\) | −3.25793 | − | 2.36703i | −0.104931 | − | 0.0762368i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 35.5908 | − | 25.8583i | 1.14512 | − | 0.831976i | ||||
\(967\) | 0.756262 | − | 2.32754i | 0.0243198 | − | 0.0748485i | −0.938160 | − | 0.346202i | \(-0.887471\pi\) |
0.962480 | + | 0.271353i | \(0.0874712\pi\) | |||||||
\(968\) | 12.4606 | 0.400500 | ||||||||
\(969\) | −2.17205 | + | 6.68488i | −0.0697763 | + | 0.214749i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.8230 | − | 45.6205i | −0.475693 | − | 1.46403i | −0.845021 | − | 0.534734i | \(-0.820412\pi\) |
0.369328 | − | 0.929299i | \(-0.379588\pi\) | |||||||
\(972\) | 0.824463 | + | 2.53744i | 0.0264447 | + | 0.0813883i | ||||
\(973\) | 23.6911 | + | 17.2126i | 0.759502 | + | 0.551811i | ||||
\(974\) | 15.4200 | 0.494088 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 23.7161 | 0.759134 | ||||||||
\(977\) | 19.1696 | + | 13.9276i | 0.613291 | + | 0.445582i | 0.850572 | − | 0.525859i | \(-0.176256\pi\) |
−0.237280 | + | 0.971441i | \(0.576256\pi\) | |||||||
\(978\) | −10.8543 | − | 33.4060i | −0.347081 | − | 1.06820i | ||||
\(979\) | 3.45883 | + | 10.6452i | 0.110545 | + | 0.340221i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.05774 | − | 6.33308i | 0.0656987 | − | 0.202200i | ||||
\(982\) | −15.6284 | −0.498721 | ||||||||
\(983\) | −4.00193 | + | 12.3167i | −0.127642 | + | 0.392841i | −0.994373 | − | 0.105934i | \(-0.966217\pi\) |
0.866731 | + | 0.498775i | \(0.166217\pi\) | |||||||
\(984\) | −9.96261 | + | 7.23826i | −0.317597 | + | 0.230747i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.33236 | + | 3.87419i | 0.169817 | + | 0.123379i | ||||
\(987\) | 1.92556 | − | 1.39900i | 0.0612913 | − | 0.0445307i | ||||
\(988\) | −61.6119 | + | 44.7637i | −1.96014 | + | 1.42412i | ||||
\(989\) | −44.2203 | − | 32.1279i | −1.40612 | − | 1.02161i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −35.9986 | + | 26.1545i | −1.14353 | + | 0.830826i | −0.987608 | − | 0.156943i | \(-0.949836\pi\) |
−0.155926 | + | 0.987769i | \(0.549836\pi\) | |||||||
\(992\) | −10.5949 | + | 32.6079i | −0.336389 | + | 1.03530i | ||||
\(993\) | −19.2504 | −0.610891 | ||||||||
\(994\) | 0.149562 | − | 0.460303i | 0.00474381 | − | 0.0145999i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −10.8407 | − | 33.3644i | −0.343502 | − | 1.05719i | ||||
\(997\) | 17.1663 | + | 52.8324i | 0.543662 | + | 1.67322i | 0.724150 | + | 0.689642i | \(0.242232\pi\) |
−0.180488 | + | 0.983577i | \(0.557768\pi\) | |||||||
\(998\) | 27.9964 | + | 20.3406i | 0.886209 | + | 0.643869i | ||||
\(999\) | 5.95751 | 0.188487 |
(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 | 375.2.g.c.76.3 | 12 | ||
5.2 | odd | 4 | 375.2.i.d.49.1 | 24 | |||
5.3 | odd | 4 | 375.2.i.d.49.6 | 24 | |||
5.4 | even | 2 | 75.2.g.c.16.1 | ✓ | 12 | ||
15.14 | odd | 2 | 225.2.h.d.91.3 | 12 | |||
25.2 | odd | 20 | 375.2.i.d.199.6 | 24 | |||
25.6 | even | 5 | 1875.2.a.k.1.2 | 6 | |||
25.8 | odd | 20 | 1875.2.b.f.1249.10 | 12 | |||
25.11 | even | 5 | inner | 375.2.g.c.301.3 | 12 | ||
25.14 | even | 10 | 75.2.g.c.61.1 | yes | 12 | ||
25.17 | odd | 20 | 1875.2.b.f.1249.3 | 12 | |||
25.19 | even | 10 | 1875.2.a.j.1.5 | 6 | |||
25.23 | odd | 20 | 375.2.i.d.199.1 | 24 | |||
75.14 | odd | 10 | 225.2.h.d.136.3 | 12 | |||
75.44 | odd | 10 | 5625.2.a.p.1.2 | 6 | |||
75.56 | odd | 10 | 5625.2.a.q.1.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.c.16.1 | ✓ | 12 | 5.4 | even | 2 | ||
75.2.g.c.61.1 | yes | 12 | 25.14 | even | 10 | ||
225.2.h.d.91.3 | 12 | 15.14 | odd | 2 | |||
225.2.h.d.136.3 | 12 | 75.14 | odd | 10 | |||
375.2.g.c.76.3 | 12 | 1.1 | even | 1 | trivial | ||
375.2.g.c.301.3 | 12 | 25.11 | even | 5 | inner | ||
375.2.i.d.49.1 | 24 | 5.2 | odd | 4 | |||
375.2.i.d.49.6 | 24 | 5.3 | odd | 4 | |||
375.2.i.d.199.1 | 24 | 25.23 | odd | 20 | |||
375.2.i.d.199.6 | 24 | 25.2 | odd | 20 | |||
1875.2.a.j.1.5 | 6 | 25.19 | even | 10 | |||
1875.2.a.k.1.2 | 6 | 25.6 | even | 5 | |||
1875.2.b.f.1249.3 | 12 | 25.17 | odd | 20 | |||
1875.2.b.f.1249.10 | 12 | 25.8 | odd | 20 | |||
5625.2.a.p.1.2 | 6 | 75.44 | odd | 10 | |||
5625.2.a.q.1.5 | 6 | 75.56 | odd | 10 |