Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(148,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.f (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: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} + \cdots + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | no (minimal twist has level 77) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 372.2 | ||
Root | \(0.183009 + 0.132964i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.372 |
Dual form | 847.2.f.w.148.2 |
$q$-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 \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0699031 | − | 0.215140i | 0.0494290 | − | 0.152127i | −0.923295 | − | 0.384090i | \(-0.874515\pi\) |
0.972724 | + | 0.231964i | \(0.0745151\pi\) | |||||||
\(3\) | 0.177280 | − | 0.128801i | 0.102352 | − | 0.0743634i | −0.535432 | − | 0.844578i | \(-0.679851\pi\) |
0.637784 | + | 0.770215i | \(0.279851\pi\) | |||||||
\(4\) | 1.57664 | + | 1.14549i | 0.788318 | + | 0.572746i | ||||
\(5\) | −0.771159 | − | 2.37338i | −0.344873 | − | 1.06141i | −0.961652 | − | 0.274273i | \(-0.911563\pi\) |
0.616779 | − | 0.787136i | \(-0.288437\pi\) | |||||||
\(6\) | −0.0153178 | − | 0.0471435i | −0.00625348 | − | 0.0192462i | ||||
\(7\) | −0.809017 | − | 0.587785i | −0.305780 | − | 0.222162i | ||||
\(8\) | 0.722670 | − | 0.525051i | 0.255503 | − | 0.185633i | ||||
\(9\) | −0.912213 | + | 2.80750i | −0.304071 | + | 0.935834i | ||||
\(10\) | −0.564516 | −0.178516 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0.427046 | 0.123278 | ||||||||
\(13\) | 1.58680 | − | 4.88366i | 0.440099 | − | 1.35448i | −0.447672 | − | 0.894198i | \(-0.647747\pi\) |
0.887771 | − | 0.460286i | \(-0.152253\pi\) | |||||||
\(14\) | −0.183009 | + | 0.132964i | −0.0489112 | + | 0.0355360i | ||||
\(15\) | −0.442405 | − | 0.321426i | −0.114229 | − | 0.0829919i | ||||
\(16\) | 1.14200 | + | 3.51471i | 0.285500 | + | 0.878679i | ||||
\(17\) | −0.444220 | − | 1.36717i | −0.107739 | − | 0.331587i | 0.882624 | − | 0.470079i | \(-0.155774\pi\) |
−0.990364 | + | 0.138492i | \(0.955774\pi\) | |||||||
\(18\) | 0.540239 | + | 0.392506i | 0.127336 | + | 0.0925147i | ||||
\(19\) | 4.90950 | − | 3.56696i | 1.12632 | − | 0.818317i | 0.141162 | − | 0.989986i | \(-0.454916\pi\) |
0.985155 | + | 0.171669i | \(0.0549161\pi\) | |||||||
\(20\) | 1.50286 | − | 4.62532i | 0.336049 | − | 1.03425i | ||||
\(21\) | −0.219130 | −0.0478180 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.08292 | 1.47689 | 0.738446 | − | 0.674313i | \(-0.235560\pi\) | ||||
0.738446 | + | 0.674313i | \(0.235560\pi\) | |||||||
\(24\) | 0.0604875 | − | 0.186161i | 0.0123470 | − | 0.0380001i | ||||
\(25\) | −0.993180 | + | 0.721588i | −0.198636 | + | 0.144318i | ||||
\(26\) | −0.939748 | − | 0.682767i | −0.184300 | − | 0.133902i | ||||
\(27\) | 0.403037 | + | 1.24042i | 0.0775645 | + | 0.238719i | ||||
\(28\) | −0.602221 | − | 1.85345i | −0.113809 | − | 0.350268i | ||||
\(29\) | −5.27292 | − | 3.83100i | −0.979156 | − | 0.711399i | −0.0216365 | − | 0.999766i | \(-0.506888\pi\) |
−0.957520 | + | 0.288367i | \(0.906888\pi\) | |||||||
\(30\) | −0.100077 | + | 0.0727103i | −0.0182715 | + | 0.0132750i | ||||
\(31\) | 2.37602 | − | 7.31263i | 0.426745 | − | 1.31339i | −0.474568 | − | 0.880219i | \(-0.657396\pi\) |
0.901313 | − | 0.433168i | \(-0.142604\pi\) | |||||||
\(32\) | 2.62252 | 0.463601 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.325184 | −0.0557687 | ||||||||
\(35\) | −0.771159 | + | 2.37338i | −0.130350 | + | 0.401175i | ||||
\(36\) | −4.65420 | + | 3.38147i | −0.775700 | + | 0.563579i | ||||
\(37\) | 3.22339 | + | 2.34193i | 0.529921 | + | 0.385010i | 0.820328 | − | 0.571893i | \(-0.193791\pi\) |
−0.290407 | + | 0.956903i | \(0.593791\pi\) | |||||||
\(38\) | −0.424206 | − | 1.30557i | −0.0688153 | − | 0.211792i | ||||
\(39\) | −0.347714 | − | 1.07015i | −0.0556788 | − | 0.171362i | ||||
\(40\) | −1.80344 | − | 1.31028i | −0.285149 | − | 0.207173i | ||||
\(41\) | −5.46006 | + | 3.96696i | −0.852718 | + | 0.619536i | −0.925894 | − | 0.377783i | \(-0.876686\pi\) |
0.0731765 | + | 0.997319i | \(0.476686\pi\) | |||||||
\(42\) | −0.0153178 | + | 0.0471435i | −0.00236359 | + | 0.00727440i | ||||
\(43\) | −0.802299 | −0.122349 | −0.0611747 | − | 0.998127i | \(-0.519485\pi\) | ||||
−0.0611747 | + | 0.998127i | \(0.519485\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7.36674 | 1.09817 | ||||||||
\(46\) | 0.495119 | − | 1.52382i | 0.0730012 | − | 0.224675i | ||||
\(47\) | −5.46266 | + | 3.96885i | −0.796811 | + | 0.578917i | −0.909977 | − | 0.414659i | \(-0.863901\pi\) |
0.113166 | + | 0.993576i | \(0.463901\pi\) | |||||||
\(48\) | 0.655152 | + | 0.475996i | 0.0945631 | + | 0.0687041i | ||||
\(49\) | 0.309017 | + | 0.951057i | 0.0441453 | + | 0.135865i | ||||
\(50\) | 0.0858158 | + | 0.264114i | 0.0121362 | + | 0.0373513i | ||||
\(51\) | −0.254844 | − | 0.185155i | −0.0356853 | − | 0.0259269i | ||||
\(52\) | 8.09600 | − | 5.88209i | 1.12271 | − | 0.815699i | ||||
\(53\) | 2.03385 | − | 6.25954i | 0.279371 | − | 0.859814i | −0.708659 | − | 0.705551i | \(-0.750700\pi\) |
0.988030 | − | 0.154263i | \(-0.0493004\pi\) | |||||||
\(54\) | 0.295037 | 0.0401495 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.893270 | −0.119368 | ||||||||
\(57\) | 0.410925 | − | 1.26470i | 0.0544284 | − | 0.167513i | ||||
\(58\) | −1.19279 | + | 0.866616i | −0.156622 | + | 0.113792i | ||||
\(59\) | −2.32694 | − | 1.69062i | −0.302941 | − | 0.220100i | 0.425921 | − | 0.904761i | \(-0.359950\pi\) |
−0.728862 | + | 0.684661i | \(0.759950\pi\) | |||||||
\(60\) | −0.329320 | − | 1.01354i | −0.0425151 | − | 0.130848i | ||||
\(61\) | −0.264315 | − | 0.813478i | −0.0338421 | − | 0.104155i | 0.932709 | − | 0.360631i | \(-0.117439\pi\) |
−0.966551 | + | 0.256476i | \(0.917439\pi\) | |||||||
\(62\) | −1.40715 | − | 1.02235i | −0.178708 | − | 0.129839i | ||||
\(63\) | 2.38820 | − | 1.73513i | 0.300885 | − | 0.218606i | ||||
\(64\) | −2.10068 | + | 6.46522i | −0.262585 | + | 0.808152i | ||||
\(65\) | −12.8145 | −1.58944 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.64668 | −0.201174 | −0.100587 | − | 0.994928i | \(-0.532072\pi\) | ||||
−0.100587 | + | 0.994928i | \(0.532072\pi\) | |||||||
\(68\) | 0.865708 | − | 2.66437i | 0.104982 | − | 0.323103i | ||||
\(69\) | 1.25566 | − | 0.912288i | 0.151163 | − | 0.109827i | ||||
\(70\) | 0.456703 | + | 0.331814i | 0.0545864 | + | 0.0396594i | ||||
\(71\) | 1.39700 | + | 4.29951i | 0.165793 | + | 0.510258i | 0.999094 | − | 0.0425617i | \(-0.0135519\pi\) |
−0.833301 | + | 0.552819i | \(0.813552\pi\) | |||||||
\(72\) | 0.814852 | + | 2.50786i | 0.0960312 | + | 0.295554i | ||||
\(73\) | 12.0122 | + | 8.72740i | 1.40593 | + | 1.02147i | 0.993899 | + | 0.110294i | \(0.0351792\pi\) |
0.412027 | + | 0.911171i | \(0.364821\pi\) | |||||||
\(74\) | 0.729166 | − | 0.529770i | 0.0847639 | − | 0.0615846i | ||||
\(75\) | −0.0831292 | + | 0.255845i | −0.00959894 | + | 0.0295425i | ||||
\(76\) | 11.8264 | 1.35658 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.254539 | −0.0288209 | ||||||||
\(79\) | 0.757990 | − | 2.33285i | 0.0852805 | − | 0.262466i | −0.899319 | − | 0.437294i | \(-0.855937\pi\) |
0.984599 | + | 0.174828i | \(0.0559369\pi\) | |||||||
\(80\) | 7.46110 | − | 5.42081i | 0.834177 | − | 0.606065i | ||||
\(81\) | −6.93339 | − | 5.03741i | −0.770377 | − | 0.559712i | ||||
\(82\) | 0.471776 | + | 1.45198i | 0.0520990 | + | 0.160344i | ||||
\(83\) | 0.694608 | + | 2.13778i | 0.0762431 | + | 0.234652i | 0.981913 | − | 0.189330i | \(-0.0606317\pi\) |
−0.905670 | + | 0.423983i | \(0.860632\pi\) | |||||||
\(84\) | −0.345487 | − | 0.251011i | −0.0376958 | − | 0.0273876i | ||||
\(85\) | −2.90225 | + | 2.10861i | −0.314793 | + | 0.228711i | ||||
\(86\) | −0.0560832 | + | 0.172606i | −0.00604761 | + | 0.0186126i | ||||
\(87\) | −1.42822 | −0.153121 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.73566 | 0.183980 | 0.0919898 | − | 0.995760i | \(-0.470677\pi\) | ||||
0.0919898 | + | 0.995760i | \(0.470677\pi\) | |||||||
\(90\) | 0.514958 | − | 1.58488i | 0.0542814 | − | 0.167061i | ||||
\(91\) | −4.15429 | + | 3.01827i | −0.435488 | + | 0.316401i | ||||
\(92\) | 11.1672 | + | 8.11343i | 1.16426 | + | 0.845884i | ||||
\(93\) | −0.520655 | − | 1.60241i | −0.0539895 | − | 0.166162i | ||||
\(94\) | 0.472001 | + | 1.45267i | 0.0486832 | + | 0.149832i | ||||
\(95\) | −12.2518 | − | 8.90144i | −1.25701 | − | 0.913268i | ||||
\(96\) | 0.464920 | − | 0.337784i | 0.0474507 | − | 0.0344749i | ||||
\(97\) | −3.73217 | + | 11.4864i | −0.378944 | + | 1.16627i | 0.561834 | + | 0.827250i | \(0.310096\pi\) |
−0.940779 | + | 0.339021i | \(0.889904\pi\) | |||||||
\(98\) | 0.226211 | 0.0228508 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.39246 | −0.239246 | ||||||||
\(101\) | −1.14132 | + | 3.51261i | −0.113565 | + | 0.349518i | −0.991645 | − | 0.128996i | \(-0.958825\pi\) |
0.878080 | + | 0.478514i | \(0.158825\pi\) | |||||||
\(102\) | −0.0576485 | + | 0.0418841i | −0.00570805 | + | 0.00414714i | ||||
\(103\) | 0.931634 | + | 0.676872i | 0.0917966 | + | 0.0666942i | 0.632737 | − | 0.774367i | \(-0.281931\pi\) |
−0.540940 | + | 0.841061i | \(0.681931\pi\) | |||||||
\(104\) | −1.41744 | − | 4.36243i | −0.138991 | − | 0.427771i | ||||
\(105\) | 0.168984 | + | 0.520079i | 0.0164911 | + | 0.0507545i | ||||
\(106\) | −1.20450 | − | 0.875124i | −0.116992 | − | 0.0849995i | ||||
\(107\) | −0.944233 | + | 0.686025i | −0.0912825 | + | 0.0663206i | −0.632490 | − | 0.774568i | \(-0.717967\pi\) |
0.541208 | + | 0.840889i | \(0.317967\pi\) | |||||||
\(108\) | −0.785450 | + | 2.41737i | −0.0755800 | + | 0.232611i | ||||
\(109\) | 9.30234 | 0.891003 | 0.445501 | − | 0.895281i | \(-0.353025\pi\) | ||||
0.445501 | + | 0.895281i | \(0.353025\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.873083 | 0.0828694 | ||||||||
\(112\) | 1.14200 | − | 3.51471i | 0.107909 | − | 0.332109i | ||||
\(113\) | −2.66760 | + | 1.93812i | −0.250946 | + | 0.182323i | −0.706146 | − | 0.708066i | \(-0.749568\pi\) |
0.455200 | + | 0.890389i | \(0.349568\pi\) | |||||||
\(114\) | −0.243362 | − | 0.176813i | −0.0227929 | − | 0.0165600i | ||||
\(115\) | −5.46206 | − | 16.8105i | −0.509340 | − | 1.56759i | ||||
\(116\) | −3.92509 | − | 12.0802i | −0.364435 | − | 1.12162i | ||||
\(117\) | 12.2634 | + | 8.90988i | 1.13375 | + | 0.823718i | ||||
\(118\) | −0.526379 | + | 0.382437i | −0.0484571 | + | 0.0352062i | ||||
\(119\) | −0.444220 | + | 1.36717i | −0.0407215 | + | 0.125328i | ||||
\(120\) | −0.488478 | −0.0445918 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −0.193488 | −0.0175176 | ||||||||
\(123\) | −0.457007 | + | 1.40652i | −0.0412069 | + | 0.126822i | ||||
\(124\) | 12.1227 | − | 8.80764i | 1.08865 | − | 0.790949i | ||||
\(125\) | −7.61610 | − | 5.53342i | −0.681205 | − | 0.494924i | ||||
\(126\) | −0.206353 | − | 0.635089i | −0.0183834 | − | 0.0565782i | ||||
\(127\) | −0.0893693 | − | 0.275050i | −0.00793024 | − | 0.0244068i | 0.947013 | − | 0.321195i | \(-0.104084\pi\) |
−0.954943 | + | 0.296788i | \(0.904084\pi\) | |||||||
\(128\) | 5.48741 | + | 3.98684i | 0.485023 | + | 0.352390i | ||||
\(129\) | −0.142231 | + | 0.103337i | −0.0125228 | + | 0.00909831i | ||||
\(130\) | −0.895772 | + | 2.75690i | −0.0785644 | + | 0.241796i | ||||
\(131\) | −16.5059 | −1.44212 | −0.721062 | − | 0.692871i | \(-0.756346\pi\) | ||||
−0.721062 | + | 0.692871i | \(0.756346\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.06848 | −0.526204 | ||||||||
\(134\) | −0.115108 | + | 0.354266i | −0.00994383 | + | 0.0306040i | ||||
\(135\) | 2.63319 | − | 1.91312i | 0.226629 | − | 0.164655i | ||||
\(136\) | −1.03886 | − | 0.754773i | −0.0890812 | − | 0.0647213i | ||||
\(137\) | 2.88185 | + | 8.86944i | 0.246213 | + | 0.757767i | 0.995435 | + | 0.0954470i | \(0.0304281\pi\) |
−0.749221 | + | 0.662320i | \(0.769572\pi\) | |||||||
\(138\) | −0.108495 | − | 0.333914i | −0.00923572 | − | 0.0284246i | ||||
\(139\) | −3.90471 | − | 2.83694i | −0.331193 | − | 0.240626i | 0.409744 | − | 0.912201i | \(-0.365618\pi\) |
−0.740937 | + | 0.671575i | \(0.765618\pi\) | |||||||
\(140\) | −3.93453 | + | 2.85860i | −0.332529 | + | 0.241596i | ||||
\(141\) | −0.457225 | + | 1.40719i | −0.0385053 | + | 0.118507i | ||||
\(142\) | 1.02265 | 0.0858189 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −10.9093 | −0.909109 | ||||||||
\(145\) | −5.02617 | + | 15.4690i | −0.417401 | + | 1.28463i | ||||
\(146\) | 2.71731 | − | 1.97424i | 0.224886 | − | 0.163389i | ||||
\(147\) | 0.177280 | + | 0.128801i | 0.0146218 | + | 0.0106233i | ||||
\(148\) | 2.39944 | + | 7.38473i | 0.197233 | + | 0.607021i | ||||
\(149\) | 0.284887 | + | 0.876793i | 0.0233389 | + | 0.0718297i | 0.962048 | − | 0.272882i | \(-0.0879768\pi\) |
−0.938709 | + | 0.344711i | \(0.887977\pi\) | |||||||
\(150\) | 0.0492315 | + | 0.0357688i | 0.00401974 | + | 0.00292051i | ||||
\(151\) | −14.6403 | + | 10.6368i | −1.19141 | + | 0.865611i | −0.993413 | − | 0.114591i | \(-0.963444\pi\) |
−0.197999 | + | 0.980202i | \(0.563444\pi\) | |||||||
\(152\) | 1.67512 | − | 5.15548i | 0.135870 | − | 0.418164i | ||||
\(153\) | 4.24355 | 0.343070 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −19.1880 | −1.54121 | ||||||||
\(156\) | 0.677635 | − | 2.08555i | 0.0542543 | − | 0.166977i | ||||
\(157\) | 9.92933 | − | 7.21408i | 0.792447 | − | 0.575746i | −0.116242 | − | 0.993221i | \(-0.537085\pi\) |
0.908689 | + | 0.417475i | \(0.137085\pi\) | |||||||
\(158\) | −0.448903 | − | 0.326147i | −0.0357128 | − | 0.0259469i | ||||
\(159\) | −0.445676 | − | 1.37165i | −0.0353444 | − | 0.108779i | ||||
\(160\) | −2.02238 | − | 6.22426i | −0.159883 | − | 0.492071i | ||||
\(161\) | −5.73020 | − | 4.16324i | −0.451603 | − | 0.328109i | ||||
\(162\) | −1.56841 | + | 1.13952i | −0.123226 | + | 0.0895290i | ||||
\(163\) | 2.50277 | − | 7.70273i | 0.196032 | − | 0.603324i | −0.803931 | − | 0.594723i | \(-0.797262\pi\) |
0.999963 | − | 0.00860182i | \(-0.00273808\pi\) | |||||||
\(164\) | −13.1526 | −1.02705 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.508478 | 0.0394655 | ||||||||
\(167\) | −4.03317 | + | 12.4128i | −0.312096 | + | 0.960532i | 0.664838 | + | 0.746988i | \(0.268501\pi\) |
−0.976933 | + | 0.213544i | \(0.931499\pi\) | |||||||
\(168\) | −0.158358 | + | 0.115054i | −0.0122176 | + | 0.00887662i | ||||
\(169\) | −10.8150 | − | 7.85756i | −0.831923 | − | 0.604428i | ||||
\(170\) | 0.250769 | + | 0.771787i | 0.0192331 | + | 0.0591934i | ||||
\(171\) | 5.53574 | + | 17.0373i | 0.423329 | + | 1.30287i | ||||
\(172\) | −1.26493 | − | 0.919027i | −0.0964502 | − | 0.0700752i | ||||
\(173\) | −4.78306 | + | 3.47510i | −0.363649 | + | 0.264207i | −0.754573 | − | 0.656217i | \(-0.772156\pi\) |
0.390923 | + | 0.920423i | \(0.372156\pi\) | |||||||
\(174\) | −0.0998369 | + | 0.307266i | −0.00756862 | + | 0.0232938i | ||||
\(175\) | 1.22764 | 0.0928007 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.630271 | −0.0473741 | ||||||||
\(178\) | 0.121328 | − | 0.373410i | 0.00909393 | − | 0.0279882i | ||||
\(179\) | −3.50715 | + | 2.54810i | −0.262137 | + | 0.190454i | −0.711089 | − | 0.703102i | \(-0.751798\pi\) |
0.448952 | + | 0.893556i | \(0.351798\pi\) | |||||||
\(180\) | 11.6147 | + | 8.43855i | 0.865706 | + | 0.628972i | ||||
\(181\) | 3.34687 | + | 10.3006i | 0.248771 | + | 0.765639i | 0.994993 | + | 0.0999417i | \(0.0318656\pi\) |
−0.746222 | + | 0.665697i | \(0.768134\pi\) | |||||||
\(182\) | 0.358952 | + | 1.10474i | 0.0266073 | + | 0.0818888i | ||||
\(183\) | −0.151635 | − | 0.110169i | −0.0112091 | − | 0.00814392i | ||||
\(184\) | 5.11862 | − | 3.71889i | 0.377350 | − | 0.274160i | ||||
\(185\) | 3.07255 | − | 9.45633i | 0.225898 | − | 0.695243i | ||||
\(186\) | −0.381138 | −0.0279464 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −13.1589 | −0.959713 | ||||||||
\(189\) | 0.403037 | − | 1.24042i | 0.0293166 | − | 0.0902273i | ||||
\(190\) | −2.77149 | + | 2.01361i | −0.201065 | + | 0.146082i | ||||
\(191\) | −9.42959 | − | 6.85100i | −0.682301 | − | 0.495721i | 0.191819 | − | 0.981430i | \(-0.438561\pi\) |
−0.874120 | + | 0.485710i | \(0.838561\pi\) | |||||||
\(192\) | 0.460320 | + | 1.41672i | 0.0332208 | + | 0.102243i | ||||
\(193\) | 6.93602 | + | 21.3469i | 0.499265 | + | 1.53658i | 0.810202 | + | 0.586151i | \(0.199357\pi\) |
−0.310937 | + | 0.950431i | \(0.600643\pi\) | |||||||
\(194\) | 2.21030 | + | 1.60588i | 0.158690 | + | 0.115295i | ||||
\(195\) | −2.27174 | + | 1.65052i | −0.162683 | + | 0.118196i | ||||
\(196\) | −0.602221 | + | 1.85345i | −0.0430158 | + | 0.132389i | ||||
\(197\) | 24.1022 | 1.71721 | 0.858604 | − | 0.512639i | \(-0.171332\pi\) | ||||
0.858604 | + | 0.512639i | \(0.171332\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.7205 | 1.32706 | 0.663531 | − | 0.748148i | \(-0.269057\pi\) | ||||
0.663531 | + | 0.748148i | \(0.269057\pi\) | |||||||
\(200\) | −0.338872 | + | 1.04294i | −0.0239619 | + | 0.0737470i | ||||
\(201\) | −0.291923 | + | 0.212094i | −0.0205906 | + | 0.0149600i | ||||
\(202\) | 0.675921 | + | 0.491085i | 0.0475576 | + | 0.0345527i | ||||
\(203\) | 2.01408 | + | 6.19869i | 0.141360 | + | 0.435063i | ||||
\(204\) | −0.189702 | − | 0.583843i | −0.0132818 | − | 0.0408772i | ||||
\(205\) | 13.6257 | + | 9.89965i | 0.951660 | + | 0.691422i | ||||
\(206\) | 0.210746 | − | 0.153116i | 0.0146834 | − | 0.0106681i | ||||
\(207\) | −6.46113 | + | 19.8853i | −0.449080 | + | 1.38213i | ||||
\(208\) | 18.9768 | 1.31580 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0.123702 | 0.00853625 | ||||||||
\(211\) | −2.33813 | + | 7.19603i | −0.160964 | + | 0.495395i | −0.998716 | − | 0.0506548i | \(-0.983869\pi\) |
0.837753 | + | 0.546050i | \(0.183869\pi\) | |||||||
\(212\) | 10.3769 | − | 7.53926i | 0.712688 | − | 0.517798i | ||||
\(213\) | 0.801440 | + | 0.582280i | 0.0549138 | + | 0.0398972i | ||||
\(214\) | 0.0815865 | + | 0.251097i | 0.00557714 | + | 0.0171647i | ||||
\(215\) | 0.618700 | + | 1.90416i | 0.0421950 | + | 0.129863i | ||||
\(216\) | 0.942547 | + | 0.684800i | 0.0641322 | + | 0.0465947i | ||||
\(217\) | −6.22049 | + | 4.51945i | −0.422275 | + | 0.306800i | ||||
\(218\) | 0.650263 | − | 2.00130i | 0.0440414 | − | 0.135545i | ||||
\(219\) | 3.25362 | 0.219859 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.38167 | −0.496545 | ||||||||
\(222\) | 0.0610313 | − | 0.187835i | 0.00409615 | − | 0.0126067i | ||||
\(223\) | −14.1775 | + | 10.3006i | −0.949397 | + | 0.689777i | −0.950664 | − | 0.310222i | \(-0.899597\pi\) |
0.00126729 | + | 0.999999i | \(0.499597\pi\) | |||||||
\(224\) | −2.12167 | − | 1.54148i | −0.141760 | − | 0.102995i | ||||
\(225\) | −1.11987 | − | 3.44660i | −0.0746578 | − | 0.229773i | ||||
\(226\) | 0.230494 | + | 0.709387i | 0.0153322 | + | 0.0471877i | ||||
\(227\) | 20.7733 | + | 15.0927i | 1.37877 | + | 1.00174i | 0.996993 | + | 0.0774861i | \(0.0246893\pi\) |
0.381782 | + | 0.924253i | \(0.375311\pi\) | |||||||
\(228\) | 2.09658 | − | 1.52326i | 0.138850 | − | 0.100880i | ||||
\(229\) | −6.12993 | + | 18.8660i | −0.405077 | + | 1.24670i | 0.515753 | + | 0.856737i | \(0.327512\pi\) |
−0.920831 | + | 0.389963i | \(0.872488\pi\) | |||||||
\(230\) | −3.99842 | −0.263648 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.82205 | −0.382236 | ||||||||
\(233\) | −6.24665 | + | 19.2252i | −0.409232 | + | 1.25949i | 0.508078 | + | 0.861311i | \(0.330356\pi\) |
−0.917310 | + | 0.398174i | \(0.869644\pi\) | |||||||
\(234\) | 2.77412 | − | 2.01552i | 0.181350 | − | 0.131758i | ||||
\(235\) | 13.6322 | + | 9.90437i | 0.889267 | + | 0.646090i | ||||
\(236\) | −1.73214 | − | 5.33097i | −0.112753 | − | 0.347017i | ||||
\(237\) | −0.166098 | − | 0.511197i | −0.0107892 | − | 0.0332058i | ||||
\(238\) | 0.263080 | + | 0.191139i | 0.0170529 | + | 0.0123897i | ||||
\(239\) | −13.8345 | + | 10.0514i | −0.894880 | + | 0.650168i | −0.937146 | − | 0.348938i | \(-0.886542\pi\) |
0.0422657 | + | 0.999106i | \(0.486542\pi\) | |||||||
\(240\) | 0.624495 | − | 1.92200i | 0.0403109 | − | 0.124064i | ||||
\(241\) | −24.1529 | −1.55582 | −0.777912 | − | 0.628373i | \(-0.783721\pi\) | ||||
−0.777912 | + | 0.628373i | \(0.783721\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.79074 | −0.371476 | ||||||||
\(244\) | 0.515105 | − | 1.58533i | 0.0329762 | − | 0.101490i | ||||
\(245\) | 2.01892 | − | 1.46683i | 0.128984 | − | 0.0937125i | ||||
\(246\) | 0.270653 | + | 0.196641i | 0.0172562 | + | 0.0125374i | ||||
\(247\) | −9.62945 | − | 29.6364i | −0.612707 | − | 1.88572i | ||||
\(248\) | −2.12242 | − | 6.53215i | −0.134774 | − | 0.414792i | ||||
\(249\) | 0.398489 | + | 0.289519i | 0.0252532 | + | 0.0183475i | ||||
\(250\) | −1.72285 | + | 1.25172i | −0.108962 | + | 0.0791659i | ||||
\(251\) | 3.67568 | − | 11.3126i | 0.232007 | − | 0.714044i | −0.765498 | − | 0.643439i | \(-0.777507\pi\) |
0.997504 | − | 0.0706047i | \(-0.0224929\pi\) | |||||||
\(252\) | 5.75291 | 0.362399 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −0.0654215 | −0.00410491 | ||||||||
\(255\) | −0.242918 | + | 0.747626i | −0.0152121 | + | 0.0468181i | ||||
\(256\) | −9.75797 | + | 7.08958i | −0.609873 | + | 0.443099i | ||||
\(257\) | −18.5758 | − | 13.4961i | −1.15872 | − | 0.841862i | −0.169108 | − | 0.985598i | \(-0.554089\pi\) |
−0.989616 | + | 0.143735i | \(0.954089\pi\) | |||||||
\(258\) | 0.0122895 | + | 0.0378231i | 0.000765110 | + | 0.00235477i | ||||
\(259\) | −1.23122 | − | 3.78932i | −0.0765045 | − | 0.235457i | ||||
\(260\) | −20.2038 | − | 14.6789i | −1.25298 | − | 0.910346i | ||||
\(261\) | 15.5656 | − | 11.3090i | 0.963484 | − | 0.700012i | ||||
\(262\) | −1.15381 | + | 3.55107i | −0.0712827 | + | 0.219386i | ||||
\(263\) | 1.93774 | 0.119486 | 0.0597432 | − | 0.998214i | \(-0.480972\pi\) | ||||
0.0597432 | + | 0.998214i | \(0.480972\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16.4247 | −1.00896 | ||||||||
\(266\) | −0.424206 | + | 1.30557i | −0.0260097 | + | 0.0800497i | ||||
\(267\) | 0.307697 | − | 0.223555i | 0.0188308 | − | 0.0136813i | ||||
\(268\) | −2.59621 | − | 1.88626i | −0.158589 | − | 0.115222i | ||||
\(269\) | 2.22083 | + | 6.83501i | 0.135406 | + | 0.416738i | 0.995653 | − | 0.0931402i | \(-0.0296905\pi\) |
−0.860247 | + | 0.509878i | \(0.829690\pi\) | |||||||
\(270\) | −0.227521 | − | 0.700237i | −0.0138465 | − | 0.0426151i | ||||
\(271\) | −0.963622 | − | 0.700112i | −0.0585359 | − | 0.0425288i | 0.558133 | − | 0.829752i | \(-0.311518\pi\) |
−0.616668 | + | 0.787223i | \(0.711518\pi\) | |||||||
\(272\) | 4.29790 | − | 3.12261i | 0.260599 | − | 0.189336i | ||||
\(273\) | −0.347714 | + | 1.07015i | −0.0210446 | + | 0.0647687i | ||||
\(274\) | 2.10962 | 0.127447 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.02473 | 0.182067 | ||||||||
\(277\) | 3.19531 | − | 9.83415i | 0.191988 | − | 0.590877i | −0.808011 | − | 0.589167i | \(-0.799456\pi\) |
0.999999 | − | 0.00170957i | \(-0.000544173\pi\) | |||||||
\(278\) | −0.883290 | + | 0.641748i | −0.0529762 | + | 0.0384895i | ||||
\(279\) | 18.3628 | + | 13.3413i | 1.09935 | + | 0.798725i | ||||
\(280\) | 0.688853 | + | 2.12007i | 0.0411669 | + | 0.126699i | ||||
\(281\) | −4.06398 | − | 12.5076i | −0.242437 | − | 0.746143i | −0.996047 | − | 0.0888223i | \(-0.971690\pi\) |
0.753611 | − | 0.657321i | \(-0.228310\pi\) | |||||||
\(282\) | 0.270782 | + | 0.196734i | 0.0161248 | + | 0.0117154i | ||||
\(283\) | −0.242730 | + | 0.176354i | −0.0144288 | + | 0.0104831i | −0.594976 | − | 0.803743i | \(-0.702839\pi\) |
0.580547 | + | 0.814226i | \(0.302839\pi\) | |||||||
\(284\) | −2.72250 | + | 8.37900i | −0.161551 | + | 0.497202i | ||||
\(285\) | −3.31850 | −0.196571 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.74900 | 0.398381 | ||||||||
\(288\) | −2.39230 | + | 7.36274i | −0.140968 | + | 0.433854i | ||||
\(289\) | 12.0815 | − | 8.77770i | 0.710675 | − | 0.516336i | ||||
\(290\) | 2.97665 | + | 2.16266i | 0.174795 | + | 0.126996i | ||||
\(291\) | 0.817829 | + | 2.51702i | 0.0479420 | + | 0.147550i | ||||
\(292\) | 8.94175 | + | 27.5199i | 0.523276 | + | 1.61048i | ||||
\(293\) | −13.0608 | − | 9.48926i | −0.763023 | − | 0.554369i | 0.136813 | − | 0.990597i | \(-0.456314\pi\) |
−0.899836 | + | 0.436228i | \(0.856314\pi\) | |||||||
\(294\) | 0.0401026 | − | 0.0291363i | 0.00233883 | − | 0.00169926i | ||||
\(295\) | −2.21805 | + | 6.82645i | −0.129140 | + | 0.397451i | ||||
\(296\) | 3.55908 | 0.206867 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.208548 | 0.0120808 | ||||||||
\(299\) | 11.2392 | − | 34.5906i | 0.649978 | − | 2.00043i | ||||
\(300\) | −0.424134 | + | 0.308151i | −0.0244874 | + | 0.0177911i | ||||
\(301\) | 0.649073 | + | 0.471579i | 0.0374120 | + | 0.0271814i | ||||
\(302\) | 1.26500 | + | 3.89326i | 0.0727924 | + | 0.224032i | ||||
\(303\) | 0.250096 | + | 0.769717i | 0.0143677 | + | 0.0442191i | ||||
\(304\) | 18.1435 | + | 13.1820i | 1.04060 | + | 0.756041i | ||||
\(305\) | −1.72687 | + | 1.25464i | −0.0988801 | + | 0.0718406i | ||||
\(306\) | 0.296637 | − | 0.912956i | 0.0169576 | − | 0.0521902i | ||||
\(307\) | −28.6376 | −1.63443 | −0.817217 | − | 0.576330i | \(-0.804484\pi\) | ||||
−0.817217 | + | 0.576330i | \(0.804484\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.252341 | 0.0143552 | ||||||||
\(310\) | −1.34130 | + | 4.12809i | −0.0761807 | + | 0.234460i | ||||
\(311\) | 25.7452 | − | 18.7049i | 1.45987 | − | 1.06066i | 0.476478 | − | 0.879186i | \(-0.341913\pi\) |
0.983396 | − | 0.181474i | \(-0.0580867\pi\) | |||||||
\(312\) | −0.813168 | − | 0.590801i | −0.0460366 | − | 0.0334475i | ||||
\(313\) | 0.0105756 | + | 0.0325482i | 0.000597766 | + | 0.00183974i | 0.951355 | − | 0.308097i | \(-0.0996921\pi\) |
−0.950757 | + | 0.309937i | \(0.899692\pi\) | |||||||
\(314\) | −0.857944 | − | 2.64048i | −0.0484166 | − | 0.149011i | ||||
\(315\) | −5.95982 | − | 4.33006i | −0.335798 | − | 0.243971i | ||||
\(316\) | 3.86734 | − | 2.80979i | 0.217555 | − | 0.158063i | ||||
\(317\) | 6.91871 | − | 21.2936i | 0.388594 | − | 1.19597i | −0.545246 | − | 0.838276i | \(-0.683564\pi\) |
0.933840 | − | 0.357692i | \(-0.116436\pi\) | |||||||
\(318\) | −0.326251 | −0.0182952 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 16.9644 | 0.948339 | ||||||||
\(321\) | −0.0790323 | + | 0.243237i | −0.00441115 | + | 0.0135761i | ||||
\(322\) | −1.29624 | + | 0.941771i | −0.0722365 | + | 0.0524829i | ||||
\(323\) | −7.05753 | − | 5.12760i | −0.392691 | − | 0.285307i | ||||
\(324\) | −5.16112 | − | 15.8843i | −0.286729 | − | 0.882461i | ||||
\(325\) | 1.94801 | + | 5.99537i | 0.108056 | + | 0.332563i | ||||
\(326\) | −1.48221 | − | 1.07689i | −0.0820921 | − | 0.0596434i | ||||
\(327\) | 1.64911 | − | 1.19815i | 0.0911963 | − | 0.0662580i | ||||
\(328\) | −1.86296 | + | 5.73361i | −0.102865 | + | 0.316586i | ||||
\(329\) | 6.75222 | 0.372262 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.7577 | 0.591297 | 0.295648 | − | 0.955297i | \(-0.404464\pi\) | ||||
0.295648 | + | 0.955297i | \(0.404464\pi\) | |||||||
\(332\) | −1.35367 | + | 4.16617i | −0.0742924 | + | 0.228648i | ||||
\(333\) | −9.51538 | + | 6.91333i | −0.521439 | + | 0.378848i | ||||
\(334\) | 2.38856 | + | 1.73539i | 0.130696 | + | 0.0949563i | ||||
\(335\) | 1.26985 | + | 3.90821i | 0.0693795 | + | 0.213528i | ||||
\(336\) | −0.250246 | − | 0.770178i | −0.0136520 | − | 0.0420166i | ||||
\(337\) | −6.07161 | − | 4.41128i | −0.330742 | − | 0.240298i | 0.410004 | − | 0.912084i | \(-0.365527\pi\) |
−0.740745 | + | 0.671786i | \(0.765527\pi\) | |||||||
\(338\) | −2.44648 | + | 1.77747i | −0.133071 | + | 0.0966816i | ||||
\(339\) | −0.223278 | + | 0.687178i | −0.0121268 | + | 0.0373224i | ||||
\(340\) | −6.99118 | −0.379150 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 4.05236 | 0.219126 | ||||||||
\(343\) | 0.309017 | − | 0.951057i | 0.0166853 | − | 0.0513522i | ||||
\(344\) | −0.579798 | + | 0.421248i | −0.0312606 | + | 0.0227121i | ||||
\(345\) | −3.13352 | − | 2.27664i | −0.168703 | − | 0.122570i | ||||
\(346\) | 0.413281 | + | 1.27195i | 0.0222181 | + | 0.0683803i | ||||
\(347\) | −8.55415 | − | 26.3270i | −0.459211 | − | 1.41331i | −0.866120 | − | 0.499837i | \(-0.833393\pi\) |
0.406909 | − | 0.913469i | \(-0.366607\pi\) | |||||||
\(348\) | −2.25178 | − | 1.63601i | −0.120708 | − | 0.0876995i | ||||
\(349\) | 8.94813 | − | 6.50120i | 0.478983 | − | 0.348001i | −0.321949 | − | 0.946757i | \(-0.604338\pi\) |
0.800932 | + | 0.598756i | \(0.204338\pi\) | |||||||
\(350\) | 0.0858158 | − | 0.264114i | 0.00458705 | − | 0.0141175i | ||||
\(351\) | 6.69733 | 0.357477 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 31.9202 | 1.69894 | 0.849469 | − | 0.527638i | \(-0.176922\pi\) | ||||
0.849469 | + | 0.527638i | \(0.176922\pi\) | |||||||
\(354\) | −0.0440580 | + | 0.135596i | −0.00234165 | + | 0.00720687i | ||||
\(355\) | 9.12708 | − | 6.63121i | 0.484415 | − | 0.351948i | ||||
\(356\) | 2.73650 | + | 1.98819i | 0.145034 | + | 0.105374i | ||||
\(357\) | 0.0973416 | + | 0.299587i | 0.00515186 | + | 0.0158558i | ||||
\(358\) | 0.303036 | + | 0.932648i | 0.0160159 | + | 0.0492920i | ||||
\(359\) | −2.89488 | − | 2.10325i | −0.152786 | − | 0.111005i | 0.508766 | − | 0.860905i | \(-0.330102\pi\) |
−0.661552 | + | 0.749899i | \(0.730102\pi\) | |||||||
\(360\) | 5.32373 | − | 3.86791i | 0.280585 | − | 0.203857i | ||||
\(361\) | 5.50867 | − | 16.9539i | 0.289930 | − | 0.892312i | ||||
\(362\) | 2.45003 | 0.128771 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −10.0072 | −0.524520 | ||||||||
\(365\) | 11.4501 | − | 35.2399i | 0.599327 | − | 1.84454i | ||||
\(366\) | −0.0343015 | + | 0.0249215i | −0.00179297 | + | 0.00130267i | ||||
\(367\) | −1.85586 | − | 1.34836i | −0.0968750 | − | 0.0703838i | 0.538293 | − | 0.842758i | \(-0.319069\pi\) |
−0.635168 | + | 0.772374i | \(0.719069\pi\) | |||||||
\(368\) | 8.08870 | + | 24.8944i | 0.421652 | + | 1.29771i | ||||
\(369\) | −6.15652 | − | 18.9478i | −0.320496 | − | 0.986385i | ||||
\(370\) | −1.81965 | − | 1.32205i | −0.0945992 | − | 0.0687303i | ||||
\(371\) | −5.32469 | + | 3.86861i | −0.276444 | + | 0.200848i | ||||
\(372\) | 1.01467 | − | 3.12283i | 0.0526081 | − | 0.161911i | ||||
\(373\) | 7.96856 | 0.412596 | 0.206298 | − | 0.978489i | \(-0.433858\pi\) | ||||
0.206298 | + | 0.978489i | \(0.433858\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.06289 | −0.106527 | ||||||||
\(376\) | −1.86385 | + | 5.73635i | −0.0961209 | + | 0.295830i | ||||
\(377\) | −27.0764 | + | 19.6721i | −1.39450 | + | 1.01317i | ||||
\(378\) | −0.238690 | − | 0.173419i | −0.0122769 | − | 0.00891969i | ||||
\(379\) | −3.59115 | − | 11.0524i | −0.184465 | − | 0.567724i | 0.815474 | − | 0.578794i | \(-0.196476\pi\) |
−0.999939 | + | 0.0110695i | \(0.996476\pi\) | |||||||
\(380\) | −9.12005 | − | 28.0686i | −0.467849 | − | 1.43989i | ||||
\(381\) | −0.0512701 | − | 0.0372499i | −0.00262665 | − | 0.00190837i | ||||
\(382\) | −2.13308 | + | 1.54977i | −0.109138 | + | 0.0792933i | ||||
\(383\) | 3.88696 | − | 11.9628i | 0.198614 | − | 0.611271i | −0.801301 | − | 0.598261i | \(-0.795859\pi\) |
0.999915 | − | 0.0130104i | \(-0.00414144\pi\) | |||||||
\(384\) | 1.48632 | 0.0758482 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.07741 | 0.258433 | ||||||||
\(387\) | 0.731867 | − | 2.25246i | 0.0372029 | − | 0.114499i | ||||
\(388\) | −19.0419 | + | 13.8347i | −0.966706 | + | 0.702353i | ||||
\(389\) | 0.354587 | + | 0.257623i | 0.0179783 | + | 0.0130620i | 0.596738 | − | 0.802436i | \(-0.296463\pi\) |
−0.578760 | + | 0.815498i | \(0.696463\pi\) | |||||||
\(390\) | 0.196290 | + | 0.604119i | 0.00993954 | + | 0.0305908i | ||||
\(391\) | −3.14637 | − | 9.68354i | −0.159119 | − | 0.489718i | ||||
\(392\) | 0.722670 | + | 0.525051i | 0.0365004 | + | 0.0265191i | ||||
\(393\) | −2.92615 | + | 2.12597i | −0.147605 | + | 0.107241i | ||||
\(394\) | 1.68482 | − | 5.18534i | 0.0848799 | − | 0.261233i | ||||
\(395\) | −6.12128 | −0.307995 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.8147 | 0.843905 | 0.421952 | − | 0.906618i | \(-0.361345\pi\) | ||||
0.421952 | + | 0.906618i | \(0.361345\pi\) | |||||||
\(398\) | 1.30862 | − | 4.02753i | 0.0655954 | − | 0.201882i | ||||
\(399\) | −1.07582 | + | 0.781627i | −0.0538582 | + | 0.0391303i | ||||
\(400\) | −3.67039 | − | 2.66669i | −0.183519 | − | 0.133335i | ||||
\(401\) | 11.3906 | + | 35.0568i | 0.568821 | + | 1.75065i | 0.656315 | + | 0.754487i | \(0.272114\pi\) |
−0.0874935 | + | 0.996165i | \(0.527886\pi\) | |||||||
\(402\) | 0.0252236 | + | 0.0776302i | 0.00125804 | + | 0.00387184i | ||||
\(403\) | −31.9421 | − | 23.2073i | −1.59115 | − | 1.15604i | ||||
\(404\) | −5.82311 | + | 4.23074i | −0.289711 | + | 0.210487i | ||||
\(405\) | −6.60895 | + | 20.3402i | −0.328401 | + | 1.01072i | ||||
\(406\) | 1.47437 | 0.0731720 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −0.281384 | −0.0139306 | ||||||||
\(409\) | 5.02891 | − | 15.4774i | 0.248664 | − | 0.765308i | −0.746349 | − | 0.665555i | \(-0.768195\pi\) |
0.995012 | − | 0.0997528i | \(-0.0318052\pi\) | |||||||
\(410\) | 3.08229 | − | 2.23941i | 0.152223 | − | 0.110597i | ||||
\(411\) | 1.65329 | + | 1.20118i | 0.0815506 | + | 0.0592500i | ||||
\(412\) | 0.693496 | + | 2.13436i | 0.0341661 | + | 0.105152i | ||||
\(413\) | 0.888810 | + | 2.73548i | 0.0437355 | + | 0.134604i | ||||
\(414\) | 3.82647 | + | 2.78009i | 0.188061 | + | 0.136634i | ||||
\(415\) | 4.53813 | − | 3.29714i | 0.222768 | − | 0.161850i | ||||
\(416\) | 4.16142 | − | 12.8075i | 0.204030 | − | 0.627940i | ||||
\(417\) | −1.05763 | −0.0517922 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.56352 | 0.271796 | 0.135898 | − | 0.990723i | \(-0.456608\pi\) | ||||
0.135898 | + | 0.990723i | \(0.456608\pi\) | |||||||
\(420\) | −0.329320 | + | 1.01354i | −0.0160692 | + | 0.0494559i | ||||
\(421\) | −17.3869 | + | 12.6323i | −0.847386 | + | 0.615662i | −0.924424 | − | 0.381366i | \(-0.875454\pi\) |
0.0770384 | + | 0.997028i | \(0.475454\pi\) | |||||||
\(422\) | 1.38471 | + | 1.00605i | 0.0674066 | + | 0.0489738i | ||||
\(423\) | −6.15946 | − | 18.9569i | −0.299483 | − | 0.921714i | ||||
\(424\) | −1.81678 | − | 5.59146i | −0.0882304 | − | 0.271545i | ||||
\(425\) | 1.42772 | + | 1.03730i | 0.0692547 | + | 0.0503165i | ||||
\(426\) | 0.181295 | − | 0.131718i | 0.00878376 | − | 0.00638178i | ||||
\(427\) | −0.264315 | + | 0.813478i | −0.0127911 | + | 0.0393670i | ||||
\(428\) | −2.27455 | −0.109944 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.452910 | 0.0218413 | ||||||||
\(431\) | −8.56557 | + | 26.3621i | −0.412589 | + | 1.26982i | 0.501801 | + | 0.864983i | \(0.332671\pi\) |
−0.914390 | + | 0.404835i | \(0.867329\pi\) | |||||||
\(432\) | −3.89945 | + | 2.83312i | −0.187613 | + | 0.136309i | ||||
\(433\) | −7.51424 | − | 5.45942i | −0.361112 | − | 0.262363i | 0.392404 | − | 0.919793i | \(-0.371644\pi\) |
−0.753516 | + | 0.657430i | \(0.771644\pi\) | |||||||
\(434\) | 0.537482 | + | 1.65420i | 0.0258000 | + | 0.0794041i | ||||
\(435\) | 1.10138 | + | 3.38971i | 0.0528073 | + | 0.162524i | ||||
\(436\) | 14.6664 | + | 10.6558i | 0.702393 | + | 0.510319i | ||||
\(437\) | 34.7736 | − | 25.2645i | 1.66345 | − | 1.20857i | ||||
\(438\) | 0.227439 | − | 0.699984i | 0.0108674 | − | 0.0334465i | ||||
\(439\) | −14.7118 | −0.702156 | −0.351078 | − | 0.936346i | \(-0.614185\pi\) | ||||
−0.351078 | + | 0.936346i | \(0.614185\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.95198 | −0.140571 | ||||||||
\(442\) | −0.516002 | + | 1.58809i | −0.0245437 | + | 0.0755378i | ||||
\(443\) | −1.97679 | + | 1.43622i | −0.0939202 | + | 0.0682370i | −0.633754 | − | 0.773534i | \(-0.718487\pi\) |
0.539834 | + | 0.841771i | \(0.318487\pi\) | |||||||
\(444\) | 1.37653 | + | 1.00011i | 0.0653274 | + | 0.0474631i | ||||
\(445\) | −1.33847 | − | 4.11939i | −0.0634496 | − | 0.195278i | ||||
\(446\) | 1.22501 | + | 3.77019i | 0.0580059 | + | 0.178524i | ||||
\(447\) | 0.163437 | + | 0.118744i | 0.00773029 | + | 0.00561638i | ||||
\(448\) | 5.49964 | − | 3.99573i | 0.259834 | − | 0.188780i | ||||
\(449\) | 1.47381 | − | 4.53592i | 0.0695534 | − | 0.214063i | −0.910238 | − | 0.414086i | \(-0.864101\pi\) |
0.979791 | + | 0.200022i | \(0.0641014\pi\) | |||||||
\(450\) | −0.819782 | −0.0386449 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −6.42593 | −0.302250 | ||||||||
\(453\) | −1.22539 | + | 3.77138i | −0.0575740 | + | 0.177195i | ||||
\(454\) | 4.69917 | − | 3.41414i | 0.220543 | − | 0.160234i | ||||
\(455\) | 10.3671 | + | 7.53216i | 0.486019 | + | 0.353113i | ||||
\(456\) | −0.367067 | − | 1.12972i | −0.0171895 | − | 0.0529038i | ||||
\(457\) | 9.60657 | + | 29.5660i | 0.449376 | + | 1.38304i | 0.877612 | + | 0.479371i | \(0.159135\pi\) |
−0.428236 | + | 0.903667i | \(0.640865\pi\) | |||||||
\(458\) | 3.63033 | + | 2.63759i | 0.169634 | + | 0.123246i | ||||
\(459\) | 1.51682 | − | 1.10204i | 0.0707993 | − | 0.0514387i | ||||
\(460\) | 10.6446 | − | 32.7608i | 0.496308 | − | 1.52748i | ||||
\(461\) | 29.7215 | 1.38427 | 0.692134 | − | 0.721769i | \(-0.256671\pi\) | ||||
0.692134 | + | 0.721769i | \(0.256671\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.4553 | −1.18301 | −0.591505 | − | 0.806302i | \(-0.701466\pi\) | ||||
−0.591505 | + | 0.806302i | \(0.701466\pi\) | |||||||
\(464\) | 7.44320 | − | 22.9078i | 0.345542 | − | 1.06347i | ||||
\(465\) | −3.40163 | + | 2.47143i | −0.157747 | + | 0.114610i | ||||
\(466\) | 3.69945 | + | 2.68780i | 0.171374 | + | 0.124510i | ||||
\(467\) | −0.984192 | − | 3.02903i | −0.0455430 | − | 0.140167i | 0.925699 | − | 0.378260i | \(-0.123478\pi\) |
−0.971242 | + | 0.238093i | \(0.923478\pi\) | |||||||
\(468\) | 9.12870 | + | 28.0953i | 0.421974 | + | 1.29870i | ||||
\(469\) | 1.33219 | + | 0.967895i | 0.0615149 | + | 0.0446932i | ||||
\(470\) | 3.08376 | − | 2.24048i | 0.142243 | − | 0.103346i | ||||
\(471\) | 0.831085 | − | 2.55782i | 0.0382944 | − | 0.117858i | ||||
\(472\) | −2.56927 | −0.118260 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −0.121590 | −0.00558479 | ||||||||
\(475\) | −2.30214 | + | 7.08527i | −0.105630 | + | 0.325095i | ||||
\(476\) | −2.26645 | + | 1.64667i | −0.103883 | + | 0.0754752i | ||||
\(477\) | 15.7184 | + | 11.4201i | 0.719695 | + | 0.522889i | ||||
\(478\) | 1.19537 | + | 3.67898i | 0.0546750 | + | 0.168272i | ||||
\(479\) | 0.999218 | + | 3.07528i | 0.0456554 | + | 0.140513i | 0.971286 | − | 0.237916i | \(-0.0764644\pi\) |
−0.925630 | + | 0.378429i | \(0.876464\pi\) | |||||||
\(480\) | −1.16022 | − | 0.842948i | −0.0529565 | − | 0.0384751i | ||||
\(481\) | 16.5520 | − | 12.0258i | 0.754708 | − | 0.548328i | ||||
\(482\) | −1.68836 | + | 5.19625i | −0.0769028 | + | 0.236683i | ||||
\(483\) | −1.55208 | −0.0706220 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 30.1398 | 1.36858 | ||||||||
\(486\) | −0.404791 | + | 1.24582i | −0.0183617 | + | 0.0565114i | ||||
\(487\) | −7.98577 | + | 5.80200i | −0.361870 | + | 0.262914i | −0.753832 | − | 0.657068i | \(-0.771797\pi\) |
0.391962 | + | 0.919982i | \(0.371797\pi\) | |||||||
\(488\) | −0.618130 | − | 0.449098i | −0.0279814 | − | 0.0203297i | ||||
\(489\) | −0.548430 | − | 1.68790i | −0.0248009 | − | 0.0763293i | ||||
\(490\) | −0.174445 | − | 0.536886i | −0.00788062 | − | 0.0242541i | ||||
\(491\) | −3.41891 | − | 2.48398i | −0.154293 | − | 0.112101i | 0.507960 | − | 0.861381i | \(-0.330400\pi\) |
−0.662253 | + | 0.749280i | \(0.730400\pi\) | |||||||
\(492\) | −2.33169 | + | 1.69408i | −0.105121 | + | 0.0763748i | ||||
\(493\) | −2.89528 | + | 8.91077i | −0.130397 | + | 0.401321i | ||||
\(494\) | −7.04910 | −0.317154 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 28.4152 | 1.27588 | ||||||||
\(497\) | 1.39700 | − | 4.29951i | 0.0626638 | − | 0.192859i | ||||
\(498\) | 0.0901427 | − | 0.0654925i | 0.00403939 | − | 0.00293479i | ||||
\(499\) | 16.5001 | + | 11.9880i | 0.738647 | + | 0.536658i | 0.892287 | − | 0.451468i | \(-0.149100\pi\) |
−0.153640 | + | 0.988127i | \(0.549100\pi\) | |||||||
\(500\) | −5.66932 | − | 17.4484i | −0.253540 | − | 0.780315i | ||||
\(501\) | 0.883786 | + | 2.72001i | 0.0394846 | + | 0.121521i | ||||
\(502\) | −2.17684 | − | 1.58157i | −0.0971573 | − | 0.0705889i | ||||
\(503\) | 19.3834 | − | 14.0829i | 0.864265 | − | 0.627925i | −0.0647768 | − | 0.997900i | \(-0.520634\pi\) |
0.929042 | + | 0.369974i | \(0.120634\pi\) | |||||||
\(504\) | 0.814852 | − | 2.50786i | 0.0362964 | − | 0.111709i | ||||
\(505\) | 9.21692 | 0.410147 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.92934 | −0.130097 | ||||||||
\(508\) | 0.174165 | − | 0.536026i | 0.00772734 | − | 0.0237823i | ||||
\(509\) | −2.98803 | + | 2.17093i | −0.132442 | + | 0.0962249i | −0.652034 | − | 0.758190i | \(-0.726084\pi\) |
0.519592 | + | 0.854415i | \(0.326084\pi\) | |||||||
\(510\) | 0.143863 | + | 0.104523i | 0.00637037 | + | 0.00462835i | ||||
\(511\) | −4.58827 | − | 14.1212i | −0.202973 | − | 0.624687i | ||||
\(512\) | 5.03515 | + | 15.4966i | 0.222524 | + | 0.684859i | ||||
\(513\) | 6.40324 | + | 4.65223i | 0.282710 | + | 0.205401i | ||||
\(514\) | −4.20205 | + | 3.05297i | −0.185344 | + | 0.134661i | ||||
\(515\) | 0.888038 | − | 2.73310i | 0.0391316 | − | 0.120435i | ||||
\(516\) | −0.342618 | −0.0150829 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −0.901299 | −0.0396008 | ||||||||
\(519\) | −0.400342 | + | 1.23213i | −0.0175731 | + | 0.0540844i | ||||
\(520\) | −9.26065 | + | 6.72825i | −0.406106 | + | 0.295053i | ||||
\(521\) | 0.192764 | + | 0.140051i | 0.00844515 | + | 0.00613576i | 0.592000 | − | 0.805938i | \(-0.298339\pi\) |
−0.583555 | + | 0.812074i | \(0.698339\pi\) | |||||||
\(522\) | −1.34494 | − | 4.13931i | −0.0588666 | − | 0.181173i | ||||
\(523\) | −6.79573 | − | 20.9151i | −0.297156 | − | 0.914553i | −0.982489 | − | 0.186323i | \(-0.940343\pi\) |
0.685332 | − | 0.728231i | \(-0.259657\pi\) | |||||||
\(524\) | −26.0237 | − | 18.9073i | −1.13685 | − | 0.825971i | ||||
\(525\) | 0.217635 | − | 0.158121i | 0.00949838 | − | 0.00690097i | ||||
\(526\) | 0.135454 | − | 0.416885i | 0.00590609 | − | 0.0181771i | ||||
\(527\) | −11.0531 | −0.481479 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27.1678 | 1.18121 | ||||||||
\(530\) | −1.14814 | + | 3.53361i | −0.0498720 | + | 0.153490i | ||||
\(531\) | 6.86907 | − | 4.99067i | 0.298092 | − | 0.216577i | ||||
\(532\) | −9.56778 | − | 6.95140i | −0.414816 | − | 0.301381i | ||||
\(533\) | 10.7093 | + | 32.9598i | 0.463871 | + | 1.42765i | ||||
\(534\) | −0.0265866 | − | 0.0818251i | −0.00115051 | − | 0.00354092i | ||||
\(535\) | 2.35636 | + | 1.71199i | 0.101874 | + | 0.0740159i | ||||
\(536\) | −1.19001 | + | 0.864591i | −0.0514005 | + | 0.0373446i | ||||
\(537\) | −0.293549 | + | 0.903450i | −0.0126676 | + | 0.0389868i | ||||
\(538\) | 1.62573 | 0.0700900 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 6.34305 | 0.272961 | ||||||||
\(541\) | 8.84744 | − | 27.2296i | 0.380381 | − | 1.17069i | −0.559395 | − | 0.828901i | \(-0.688966\pi\) |
0.939776 | − | 0.341791i | \(-0.111034\pi\) | |||||||
\(542\) | −0.217982 | + | 0.158373i | −0.00936314 | + | 0.00680272i | ||||
\(543\) | 1.92006 | + | 1.39501i | 0.0823978 | + | 0.0598655i | ||||
\(544\) | −1.16498 | − | 3.58543i | −0.0499479 | − | 0.153724i | ||||
\(545\) | −7.17359 | − | 22.0780i | −0.307283 | − | 0.945719i | ||||
\(546\) | 0.205926 | + | 0.149614i | 0.00881284 | + | 0.00640290i | ||||
\(547\) | −5.18456 | + | 3.76681i | −0.221676 | + | 0.161057i | −0.693081 | − | 0.720860i | \(-0.743747\pi\) |
0.471405 | + | 0.881917i | \(0.343747\pi\) | |||||||
\(548\) | −5.61624 | + | 17.2850i | −0.239914 | + | 0.738379i | ||||
\(549\) | 2.52495 | 0.107762 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −39.5524 | −1.68499 | ||||||||
\(552\) | 0.428429 | − | 1.31857i | 0.0182351 | − | 0.0561220i | ||||
\(553\) | −1.98444 | + | 1.44178i | −0.0843871 | + | 0.0613108i | ||||
\(554\) | −1.89236 | − | 1.37488i | −0.0803985 | − | 0.0584129i | ||||
\(555\) | −0.673286 | − | 2.07216i | −0.0285794 | − | 0.0879583i | ||||
\(556\) | −2.90661 | − | 8.94563i | −0.123268 | − | 0.379379i | ||||
\(557\) | 18.2185 | + | 13.2365i | 0.771941 | + | 0.560848i | 0.902550 | − | 0.430586i | \(-0.141693\pi\) |
−0.130608 | + | 0.991434i | \(0.541693\pi\) | |||||||
\(558\) | 4.15387 | − | 3.01796i | 0.175847 | − | 0.127761i | ||||
\(559\) | −1.27309 | + | 3.91816i | −0.0538458 | + | 0.165720i | ||||
\(560\) | −9.22243 | −0.389719 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.97498 | −0.125492 | ||||||||
\(563\) | −9.21696 | + | 28.3669i | −0.388449 | + | 1.19552i | 0.545499 | + | 0.838111i | \(0.316340\pi\) |
−0.933948 | + | 0.357410i | \(0.883660\pi\) | |||||||
\(564\) | −2.33281 | + | 1.69488i | −0.0982289 | + | 0.0713674i | ||||
\(565\) | 6.65705 | + | 4.83663i | 0.280064 | + | 0.203478i | ||||
\(566\) | 0.0209731 | + | 0.0645485i | 0.000881564 | + | 0.00271318i | ||||
\(567\) | 2.64832 | + | 8.15069i | 0.111219 | + | 0.342297i | ||||
\(568\) | 3.26703 | + | 2.37363i | 0.137081 | + | 0.0995955i | ||||
\(569\) | −23.6851 | + | 17.2082i | −0.992930 | + | 0.721406i | −0.960561 | − | 0.278070i | \(-0.910305\pi\) |
−0.0323695 | + | 0.999476i | \(0.510305\pi\) | |||||||
\(570\) | −0.231974 | + | 0.713942i | −0.00971632 | + | 0.0299037i | ||||
\(571\) | 37.9252 | 1.58712 | 0.793559 | − | 0.608493i | \(-0.208226\pi\) | ||||
0.793559 | + | 0.608493i | \(0.208226\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.55409 | −0.106699 | ||||||||
\(574\) | 0.471776 | − | 1.45198i | 0.0196916 | − | 0.0606044i | ||||
\(575\) | −7.03462 | + | 5.11095i | −0.293364 | + | 0.213141i | ||||
\(576\) | −16.2349 | − | 11.7953i | −0.676452 | − | 0.491471i | ||||
\(577\) | 2.71089 | + | 8.34327i | 0.112856 | + | 0.347335i | 0.991494 | − | 0.130154i | \(-0.0415471\pi\) |
−0.878638 | + | 0.477489i | \(0.841547\pi\) | |||||||
\(578\) | −1.04390 | − | 3.21279i | −0.0434205 | − | 0.133635i | ||||
\(579\) | 3.97911 | + | 2.89100i | 0.165366 | + | 0.120146i | ||||
\(580\) | −25.6440 | + | 18.6315i | −1.06481 | + | 0.773630i | ||||
\(581\) | 0.694608 | − | 2.13778i | 0.0288172 | − | 0.0886902i | ||||
\(582\) | 0.598679 | 0.0248161 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 13.2632 | 0.548836 | ||||||||
\(585\) | 11.6895 | − | 35.9767i | 0.483303 | − | 1.48745i | ||||
\(586\) | −2.95451 | + | 2.14658i | −0.122050 | + | 0.0886743i | ||||
\(587\) | −7.41878 | − | 5.39006i | −0.306206 | − | 0.222472i | 0.424061 | − | 0.905634i | \(-0.360604\pi\) |
−0.730267 | + | 0.683162i | \(0.760604\pi\) | |||||||
\(588\) | 0.131964 | + | 0.406145i | 0.00544212 | + | 0.0167491i | ||||
\(589\) | −14.4188 | − | 44.3765i | −0.594117 | − | 1.82850i | ||||
\(590\) | 1.31359 | + | 0.954380i | 0.0540797 | + | 0.0392912i | ||||
\(591\) | 4.27282 | − | 3.10439i | 0.175760 | − | 0.127697i | ||||
\(592\) | −4.55010 | + | 14.0038i | −0.187008 | + | 0.575551i | ||||
\(593\) | 7.25596 | 0.297967 | 0.148983 | − | 0.988840i | \(-0.452400\pi\) | ||||
0.148983 | + | 0.988840i | \(0.452400\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.58738 | 0.147068 | ||||||||
\(596\) | −0.555196 | + | 1.70872i | −0.0227417 | + | 0.0699919i | ||||
\(597\) | 3.31877 | − | 2.41122i | 0.135828 | − | 0.0986848i | ||||
\(598\) | −6.65616 | − | 4.83598i | −0.272191 | − | 0.197758i | ||||
\(599\) | −6.18592 | − | 19.0383i | −0.252750 | − | 0.777884i | −0.994265 | − | 0.106947i | \(-0.965892\pi\) |
0.741515 | − | 0.670936i | \(-0.234108\pi\) | |||||||
\(600\) | 0.0742568 | + | 0.228539i | 0.00303152 | + | 0.00933007i | ||||
\(601\) | 9.11808 | + | 6.62467i | 0.371934 | + | 0.270226i | 0.758013 | − | 0.652240i | \(-0.226171\pi\) |
−0.386078 | + | 0.922466i | \(0.626171\pi\) | |||||||
\(602\) | 0.146828 | − | 0.106677i | 0.00598425 | − | 0.00434781i | ||||
\(603\) | 1.50212 | − | 4.62306i | 0.0611712 | − | 0.188266i | ||||
\(604\) | −35.2668 | −1.43499 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.183079 | 0.00743709 | ||||||||
\(607\) | −4.17977 | + | 12.8640i | −0.169652 | + | 0.522135i | −0.999349 | − | 0.0360793i | \(-0.988513\pi\) |
0.829697 | + | 0.558214i | \(0.188513\pi\) | |||||||
\(608\) | 12.8753 | − | 9.35444i | 0.522162 | − | 0.379373i | ||||
\(609\) | 1.15545 | + | 0.839485i | 0.0468213 | + | 0.0340177i | ||||
\(610\) | 0.149210 | + | 0.459221i | 0.00604134 | + | 0.0185933i | ||||
\(611\) | 10.7144 | + | 32.9756i | 0.433459 | + | 1.33405i | ||||
\(612\) | 6.69053 | + | 4.86095i | 0.270449 | + | 0.196492i | ||||
\(613\) | 24.9151 | − | 18.1019i | 1.00631 | − | 0.731129i | 0.0428801 | − | 0.999080i | \(-0.486347\pi\) |
0.963432 | + | 0.267951i | \(0.0863466\pi\) | |||||||
\(614\) | −2.00186 | + | 6.16109i | −0.0807884 | + | 0.248641i | ||||
\(615\) | 3.69064 | 0.148821 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.6896 | 0.953707 | 0.476853 | − | 0.878983i | \(-0.341777\pi\) | ||||
0.476853 | + | 0.878983i | \(0.341777\pi\) | |||||||
\(618\) | 0.0176395 | − | 0.0542887i | 0.000709563 | − | 0.00218381i | ||||
\(619\) | 26.2832 | − | 19.0958i | 1.05641 | − | 0.767527i | 0.0829892 | − | 0.996550i | \(-0.473553\pi\) |
0.973421 | + | 0.229024i | \(0.0735533\pi\) | |||||||
\(620\) | −30.2524 | − | 21.9797i | −1.21497 | − | 0.882725i | ||||
\(621\) | 2.85468 | + | 8.78580i | 0.114554 | + | 0.352562i | ||||
\(622\) | −2.22451 | − | 6.84634i | −0.0891948 | − | 0.274513i | ||||
\(623\) | −1.40418 | − | 1.02020i | −0.0562573 | − | 0.0408733i | ||||
\(624\) | 3.36420 | − | 2.44423i | 0.134676 | − | 0.0978476i | ||||
\(625\) | −9.15651 | + | 28.1808i | −0.366260 | + | 1.12723i | ||||
\(626\) | 0.00774169 | 0.000309420 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 23.9186 | 0.954456 | ||||||||
\(629\) | 1.76991 | − | 5.44724i | 0.0705711 | − | 0.217196i | ||||
\(630\) | −1.34818 | + | 0.979509i | −0.0537127 | + | 0.0390246i | ||||
\(631\) | 12.2431 | + | 8.89515i | 0.487391 | + | 0.354110i | 0.804180 | − | 0.594386i | \(-0.202605\pi\) |
−0.316789 | + | 0.948496i | \(0.602605\pi\) | |||||||
\(632\) | −0.677089 | − | 2.08387i | −0.0269332 | − | 0.0828917i | ||||
\(633\) | 0.512354 | + | 1.57686i | 0.0203642 | + | 0.0626747i | ||||
\(634\) | −4.09746 | − | 2.97698i | −0.162731 | − | 0.118231i | ||||
\(635\) | −0.583882 | + | 0.424215i | −0.0231707 | + | 0.0168345i | ||||
\(636\) | 0.868547 | − | 2.67311i | 0.0344401 | − | 0.105996i | ||||
\(637\) | 5.13499 | 0.203456 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13.3452 | −0.527929 | ||||||||
\(640\) | 5.23063 | − | 16.0982i | 0.206759 | − | 0.636338i | ||||
\(641\) | 13.3894 | − | 9.72799i | 0.528850 | − | 0.384232i | −0.291077 | − | 0.956700i | \(-0.594014\pi\) |
0.819928 | + | 0.572467i | \(0.194014\pi\) | |||||||
\(642\) | 0.0468052 | + | 0.0340060i | 0.00184726 | + | 0.00134211i | ||||
\(643\) | 0.616506 | + | 1.89741i | 0.0243126 | + | 0.0748266i | 0.962477 | − | 0.271365i | \(-0.0874749\pi\) |
−0.938164 | + | 0.346191i | \(0.887475\pi\) | |||||||
\(644\) | −4.26549 | − | 13.1278i | −0.168084 | − | 0.517308i | ||||
\(645\) | 0.354941 | + | 0.257880i | 0.0139758 | + | 0.0101540i | ||||
\(646\) | −1.59649 | + | 1.15992i | −0.0628132 | + | 0.0456365i | ||||
\(647\) | 12.5003 | − | 38.4719i | 0.491436 | − | 1.51248i | −0.331002 | − | 0.943630i | \(-0.607387\pi\) |
0.822438 | − | 0.568855i | \(-0.192613\pi\) | |||||||
\(648\) | −7.65545 | −0.300735 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 1.42602 | 0.0559329 | ||||||||
\(651\) | −0.520655 | + | 1.60241i | −0.0204061 | + | 0.0628035i | ||||
\(652\) | 12.7694 | − | 9.27749i | 0.500087 | − | 0.363335i | ||||
\(653\) | 33.5626 | + | 24.3846i | 1.31341 | + | 0.954245i | 0.999989 | + | 0.00462886i | \(0.00147342\pi\) |
0.313416 | + | 0.949616i | \(0.398527\pi\) | |||||||
\(654\) | −0.142492 | − | 0.438545i | −0.00557187 | − | 0.0171485i | ||||
\(655\) | 12.7286 | + | 39.1747i | 0.497349 | + | 1.53068i | ||||
\(656\) | −20.1781 | − | 14.6603i | −0.787823 | − | 0.572387i | ||||
\(657\) | −35.4599 | + | 25.7631i | −1.38342 | + | 1.00512i | ||||
\(658\) | 0.472001 | − | 1.45267i | 0.0184005 | − | 0.0566310i | ||||
\(659\) | −51.1359 | −1.99197 | −0.995985 | − | 0.0895158i | \(-0.971468\pi\) | ||||
−0.995985 | + | 0.0895158i | \(0.971468\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −42.8840 | −1.66800 | −0.833998 | − | 0.551768i | \(-0.813954\pi\) | ||||
−0.833998 | + | 0.551768i | \(0.813954\pi\) | |||||||
\(662\) | 0.751997 | − | 2.31441i | 0.0292272 | − | 0.0899521i | ||||
\(663\) | −1.30862 | + | 0.950767i | −0.0508225 | + | 0.0369247i | ||||
\(664\) | 1.62442 | + | 1.18021i | 0.0630396 | + | 0.0458010i | ||||
\(665\) | 4.67976 | + | 14.4028i | 0.181473 | + | 0.558518i | ||||
\(666\) | 0.822177 | + | 2.53040i | 0.0318587 | + | 0.0980510i | ||||
\(667\) | −37.3477 | − | 27.1347i | −1.44611 | − | 1.05066i | ||||
\(668\) | −20.5776 | + | 14.9505i | −0.796172 | + | 0.578453i | ||||
\(669\) | −1.18666 | + | 3.65216i | −0.0458789 | + | 0.141201i | ||||
\(670\) | 0.929577 | 0.0359127 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −0.574672 | −0.0221685 | ||||||||
\(673\) | −7.72766 | + | 23.7833i | −0.297879 | + | 0.916778i | 0.684360 | + | 0.729145i | \(0.260082\pi\) |
−0.982239 | + | 0.187634i | \(0.939918\pi\) | |||||||
\(674\) | −1.37347 | + | 0.997882i | −0.0529040 | + | 0.0384370i | ||||
\(675\) | −1.29536 | − | 0.941135i | −0.0498585 | − | 0.0362243i | ||||
\(676\) | −8.05054 | − | 24.7770i | −0.309636 | − | 0.952962i | ||||
\(677\) | −3.06511 | − | 9.43343i | −0.117802 | − | 0.362556i | 0.874719 | − | 0.484630i | \(-0.161046\pi\) |
−0.992521 | + | 0.122073i | \(0.961046\pi\) | |||||||
\(678\) | 0.132232 | + | 0.0960719i | 0.00507832 | + | 0.00368962i | ||||
\(679\) | 9.77095 | − | 7.09901i | 0.374975 | − | 0.272435i | ||||
\(680\) | −0.990244 | + | 3.04766i | −0.0379741 | + | 0.116872i | ||||
\(681\) | 5.62665 | 0.215614 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −39.8980 | −1.52666 | −0.763328 | − | 0.646011i | \(-0.776436\pi\) | ||||
−0.763328 | + | 0.646011i | \(0.776436\pi\) | |||||||
\(684\) | −10.7882 | + | 33.2027i | −0.412498 | + | 1.26954i | ||||
\(685\) | 18.8282 | − | 13.6795i | 0.719389 | − | 0.522667i | ||||
\(686\) | −0.183009 | − | 0.132964i | −0.00698731 | − | 0.00507658i | ||||
\(687\) | 1.34325 | + | 4.13410i | 0.0512482 | + | 0.157726i | ||||
\(688\) | −0.916225 | − | 2.81985i | −0.0349307 | − | 0.107506i | ||||
\(689\) | −27.3422 | − | 19.8653i | −1.04165 | − | 0.756806i | ||||
\(690\) | −0.708838 | + | 0.515001i | −0.0269850 | + | 0.0196058i | ||||
\(691\) | −2.04384 | + | 6.29029i | −0.0777513 | + | 0.239294i | −0.982376 | − | 0.186915i | \(-0.940151\pi\) |
0.904625 | + | 0.426209i | \(0.140151\pi\) | |||||||
\(692\) | −11.5218 | −0.437995 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.26194 | −0.237700 | ||||||||
\(695\) | −3.72199 | + | 11.4551i | −0.141183 | + | 0.434517i | ||||
\(696\) | −1.03213 | + | 0.749887i | −0.0391228 | + | 0.0284244i | ||||
\(697\) | 7.84897 | + | 5.70261i | 0.297301 | + | 0.216002i | ||||
\(698\) | −0.773164 | − | 2.37955i | −0.0292647 | − | 0.0900674i | ||||
\(699\) | 1.36883 | + | 4.21281i | 0.0517737 | + | 0.159343i | ||||
\(700\) | 1.93554 | + | 1.40625i | 0.0731565 | + | 0.0531513i | ||||
\(701\) | −11.8130 | + | 8.58261i | −0.446169 | + | 0.324161i | −0.788081 | − | 0.615571i | \(-0.788925\pi\) |
0.341912 | + | 0.939732i | \(0.388925\pi\) | |||||||
\(702\) | 0.468165 | − | 1.44086i | 0.0176697 | − | 0.0543818i | ||||
\(703\) | 24.1788 | 0.911920 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.69240 | 0.139064 | ||||||||
\(706\) | 2.23132 | − | 6.86730i | 0.0839768 | − | 0.258454i | ||||
\(707\) | 2.98801 | − | 2.17091i | 0.112376 | − | 0.0816456i | ||||
\(708\) | −0.993708 | − | 0.721971i | −0.0373458 | − | 0.0271333i | ||||
\(709\) | −1.28058 | − | 3.94123i | −0.0480934 | − | 0.148016i | 0.924126 | − | 0.382088i | \(-0.124795\pi\) |
−0.972219 | + | 0.234072i | \(0.924795\pi\) | |||||||
\(710\) | −0.788626 | − | 2.42714i | −0.0295966 | − | 0.0910890i | ||||
\(711\) | 5.85804 | + | 4.25611i | 0.219694 | + | 0.159617i | ||||
\(712\) | 1.25431 | − | 0.911310i | 0.0470073 | − | 0.0341528i | ||||
\(713\) | 16.8291 | − | 51.7948i | 0.630256 | − | 1.93973i | ||||
\(714\) | 0.0712575 | 0.00266674 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.44832 | −0.315729 | ||||||||
\(717\) | −1.15795 | + | 3.56380i | −0.0432444 | + | 0.133093i | ||||
\(718\) | −0.654854 | + | 0.475779i | −0.0244389 | + | 0.0177559i | ||||
\(719\) | −13.7713 | − | 10.0054i | −0.513583 | − | 0.373140i | 0.300598 | − | 0.953751i | \(-0.402814\pi\) |
−0.814181 | + | 0.580611i | \(0.802814\pi\) | |||||||
\(720\) | 8.41282 | + | 25.8920i | 0.313527 | + | 0.964938i | ||||
\(721\) | −0.355853 | − | 1.09520i | −0.0132526 | − | 0.0407874i | ||||
\(722\) | −3.26239 | − | 2.37027i | −0.121414 | − | 0.0882122i | ||||
\(723\) | −4.28181 | + | 3.11092i | −0.159242 | + | 0.115696i | ||||
\(724\) | −6.52248 | + | 20.0741i | −0.242406 | + | 0.746049i | ||||
\(725\) | 8.00136 | 0.297163 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.6199 | −0.801837 | −0.400918 | − | 0.916114i | \(-0.631309\pi\) | ||||
−0.400918 | + | 0.916114i | \(0.631309\pi\) | |||||||
\(728\) | −1.41744 | + | 4.36243i | −0.0525338 | + | 0.161682i | ||||
\(729\) | 19.7736 | − | 14.3664i | 0.732356 | − | 0.532088i | ||||
\(730\) | −6.78110 | − | 4.92676i | −0.250980 | − | 0.182347i | ||||
\(731\) | 0.356397 | + | 1.09688i | 0.0131818 | + | 0.0405694i | ||||
\(732\) | −0.112875 | − | 0.347392i | −0.00417197 | − | 0.0128400i | ||||
\(733\) | 39.0210 | + | 28.3504i | 1.44127 | + | 1.04715i | 0.987775 | + | 0.155887i | \(0.0498237\pi\) |
0.453497 | + | 0.891258i | \(0.350176\pi\) | |||||||
\(734\) | −0.419816 | + | 0.305014i | −0.0154957 | + | 0.0112583i | ||||
\(735\) | 0.168984 | − | 0.520079i | 0.00623306 | − | 0.0191834i | ||||
\(736\) | 18.5751 | 0.684688 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −4.50679 | −0.165897 | ||||||||
\(739\) | −2.52265 | + | 7.76392i | −0.0927973 | + | 0.285601i | −0.986673 | − | 0.162713i | \(-0.947975\pi\) |
0.893876 | + | 0.448314i | \(0.147975\pi\) | |||||||
\(740\) | 15.6764 | − | 11.3896i | 0.576278 | − | 0.418690i | ||||
\(741\) | −5.52430 | − | 4.01364i | −0.202940 | − | 0.147445i | ||||
\(742\) | 0.460080 | + | 1.41598i | 0.0168901 | + | 0.0519822i | ||||
\(743\) | 6.04476 | + | 18.6039i | 0.221761 | + | 0.682509i | 0.998604 | + | 0.0528156i | \(0.0168195\pi\) |
−0.776844 | + | 0.629694i | \(0.783180\pi\) | |||||||
\(744\) | −1.21761 | − | 0.884646i | −0.0446398 | − | 0.0324327i | ||||
\(745\) | 1.86127 | − | 1.35229i | 0.0681918 | − | 0.0495442i | ||||
\(746\) | 0.557027 | − | 1.71435i | 0.0203942 | − | 0.0627669i | ||||
\(747\) | −6.63546 | −0.242779 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.16714 | 0.0426462 | ||||||||
\(750\) | −0.144202 | + | 0.443810i | −0.00526553 | + | 0.0162056i | ||||
\(751\) | −0.903104 | + | 0.656143i | −0.0329547 | + | 0.0239430i | −0.604141 | − | 0.796878i | \(-0.706484\pi\) |
0.571186 | + | 0.820821i | \(0.306484\pi\) | |||||||
\(752\) | −20.1877 | − | 14.6673i | −0.736171 | − | 0.534860i | ||||
\(753\) | −0.805450 | − | 2.47892i | −0.0293522 | − | 0.0903369i | ||||
\(754\) | 2.33953 | + | 7.20035i | 0.0852008 | + | 0.262221i | ||||
\(755\) | 36.5352 | + | 26.5444i | 1.32965 | + | 0.966050i | ||||
\(756\) | 2.05633 | − | 1.49401i | 0.0747882 | − | 0.0543368i | ||||
\(757\) | −8.21284 | + | 25.2765i | −0.298501 | + | 0.918691i | 0.683522 | + | 0.729930i | \(0.260447\pi\) |
−0.982023 | + | 0.188761i | \(0.939553\pi\) | |||||||
\(758\) | −2.62885 | −0.0954840 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −13.5277 | −0.490701 | ||||||||
\(761\) | 1.94682 | − | 5.99168i | 0.0705720 | − | 0.217198i | −0.909550 | − | 0.415595i | \(-0.863573\pi\) |
0.980122 | + | 0.198397i | \(0.0635734\pi\) | |||||||
\(762\) | −0.0115979 | + | 0.00842636i | −0.000420147 | + | 0.000305255i | ||||
\(763\) | −7.52575 | − | 5.46778i | −0.272451 | − | 0.197947i | ||||
\(764\) | −7.01926 | − | 21.6030i | −0.253948 | − | 0.781571i | ||||
\(765\) | −3.27245 | − | 10.0716i | −0.118316 | − | 0.364138i | ||||
\(766\) | −2.30197 | − | 1.67248i | −0.0831735 | − | 0.0604291i | ||||
\(767\) | −11.9488 | + | 8.68130i | −0.431445 | + | 0.313463i | ||||
\(768\) | −0.816743 | + | 2.51368i | −0.0294717 | + | 0.0907044i | ||||
\(769\) | 13.1916 | 0.475700 | 0.237850 | − | 0.971302i | \(-0.423557\pi\) | ||||
0.237850 | + | 0.971302i | \(0.423557\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.03141 | −0.181202 | ||||||||
\(772\) | −13.5171 | + | 41.6014i | −0.486491 | + | 1.49727i | ||||
\(773\) | −37.0674 | + | 26.9310i | −1.33322 | + | 0.968641i | −0.333556 | + | 0.942730i | \(0.608249\pi\) |
−0.999664 | + | 0.0259112i | \(0.991751\pi\) | |||||||
\(774\) | −0.433433 | − | 0.314907i | −0.0155794 | − | 0.0113191i | ||||
\(775\) | 2.91689 | + | 8.97726i | 0.104778 | + | 0.322473i | ||||
\(776\) | 3.33383 | + | 10.2605i | 0.119678 | + | 0.368330i | ||||
\(777\) | −0.706339 | − | 0.513185i | −0.0253398 | − | 0.0184104i | ||||
\(778\) | 0.0802116 | − | 0.0582772i | 0.00287573 | − | 0.00208934i | ||||
\(779\) | −12.6561 | + | 38.9516i | −0.453454 | + | 1.39559i | ||||
\(780\) | −5.47237 | −0.195942 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −2.30326 | −0.0823643 | ||||||||
\(783\) | 2.62687 | − | 8.08467i | 0.0938766 | − | 0.288923i | ||||
\(784\) | −2.98979 | + | 2.17221i | −0.106778 | + | 0.0775790i | ||||
\(785\) | −24.7789 | − | 18.0029i | −0.884396 | − | 0.642551i | ||||
\(786\) | 0.252834 | + | 0.778144i | 0.00901830 | + | 0.0277555i | ||||
\(787\) | −5.82433 | − | 17.9255i | −0.207615 | − | 0.638973i | −0.999596 | − | 0.0284274i | \(-0.990950\pi\) |
0.791981 | − | 0.610546i | \(-0.209050\pi\) | |||||||
\(788\) | 38.0003 | + | 27.6089i | 1.35371 | + | 0.983525i | ||||
\(789\) | 0.343522 | − | 0.249583i | 0.0122297 | − | 0.00888540i | ||||
\(790\) | −0.427897 | + | 1.31693i | −0.0152239 | + | 0.0468543i | ||||
\(791\) | 3.29733 | 0.117240 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.39217 | −0.155970 | ||||||||
\(794\) | 1.17540 | − | 3.61751i | 0.0417134 | − | 0.128381i | ||||
\(795\) | −2.91177 | + | 2.11552i | −0.103270 | + | 0.0750298i | ||||
\(796\) | 29.5154 | + | 21.4442i | 1.04615 | + | 0.760070i | ||||
\(797\) | −8.70234 | − | 26.7830i | −0.308253 | − | 0.948704i | −0.978443 | − | 0.206515i | \(-0.933788\pi\) |
0.670191 | − | 0.742189i | \(-0.266212\pi\) | |||||||
\(798\) | 0.0929560 | + | 0.286089i | 0.00329061 | + | 0.0101274i | ||||
\(799\) | 7.85271 | + | 5.70533i | 0.277809 | + | 0.201840i | ||||
\(800\) | −2.60464 | + | 1.89238i | −0.0920879 | + | 0.0669058i | ||||
\(801\) | −1.58329 | + | 4.87287i | −0.0559429 | + | 0.172174i | ||||
\(802\) | 8.33835 | 0.294437 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −0.703208 | −0.0248002 | ||||||||
\(805\) | −5.46206 | + | 16.8105i | −0.192512 | + | 0.592492i | ||||
\(806\) | −7.22568 | + | 5.24976i | −0.254514 | + | 0.184915i | ||||
\(807\) | 1.27406 | + | 0.925662i | 0.0448492 | + | 0.0325849i | ||||
\(808\) | 1.01950 | + | 3.13771i | 0.0358660 | + | 0.110384i | ||||
\(809\) | −2.02268 | − | 6.22516i | −0.0711135 | − | 0.218865i | 0.909183 | − | 0.416397i | \(-0.136707\pi\) |
−0.980296 | + | 0.197532i | \(0.936707\pi\) | |||||||
\(810\) | 3.91401 | + | 2.84369i | 0.137524 | + | 0.0999172i | ||||
\(811\) | −15.2133 | + | 11.0531i | −0.534210 | + | 0.388127i | −0.821930 | − | 0.569588i | \(-0.807103\pi\) |
0.287720 | + | 0.957715i | \(0.407103\pi\) | |||||||
\(812\) | −3.92509 | + | 12.0802i | −0.137744 | + | 0.423931i | ||||
\(813\) | −0.261006 | −0.00915387 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −20.2116 | −0.707980 | ||||||||
\(816\) | 0.359735 | − | 1.10715i | 0.0125932 | − | 0.0387580i | ||||
\(817\) | −3.93889 | + | 2.86177i | −0.137804 | + | 0.100121i | ||||
\(818\) | −2.97827 | − | 2.16384i | −0.104133 | − | 0.0756568i | ||||
\(819\) | −4.68420 | − | 14.4165i | −0.163679 | − | 0.503753i | ||||
\(820\) | 10.1428 | + | 31.2163i | 0.354201 | + | 1.09012i | ||||
\(821\) | 9.37489 | + | 6.81125i | 0.327186 | + | 0.237714i | 0.739236 | − | 0.673447i | \(-0.235187\pi\) |
−0.412050 | + | 0.911161i | \(0.635187\pi\) | |||||||
\(822\) | 0.373992 | − | 0.271721i | 0.0130445 | − | 0.00947737i | ||||
\(823\) | 3.81524 | − | 11.7421i | 0.132991 | − | 0.409304i | −0.862281 | − | 0.506430i | \(-0.830965\pi\) |
0.995272 | + | 0.0971256i | \(0.0309649\pi\) | |||||||
\(824\) | 1.02866 | 0.0358349 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.650640 | 0.0226387 | ||||||||
\(827\) | −1.38927 | + | 4.27575i | −0.0483098 | + | 0.148682i | −0.972301 | − | 0.233730i | \(-0.924907\pi\) |
0.923992 | + | 0.382413i | \(0.124907\pi\) | |||||||
\(828\) | −32.9653 | + | 23.9507i | −1.14562 | + | 0.832345i | ||||
\(829\) | 16.0694 | + | 11.6751i | 0.558113 | + | 0.405493i | 0.830768 | − | 0.556619i | \(-0.187902\pi\) |
−0.272655 | + | 0.962112i | \(0.587902\pi\) | |||||||
\(830\) | −0.392117 | − | 1.20681i | −0.0136106 | − | 0.0418891i | ||||
\(831\) | −0.700187 | − | 2.15495i | −0.0242892 | − | 0.0747545i | ||||
\(832\) | 28.2406 | + | 20.5180i | 0.979066 | + | 0.711333i | ||||
\(833\) | 1.16298 | − | 0.844956i | 0.0402949 | − | 0.0292760i | ||||
\(834\) | −0.0739314 | + | 0.227537i | −0.00256003 | + | 0.00787898i | ||||
\(835\) | 32.5706 | 1.12715 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.0284 | 0.346631 | ||||||||
\(838\) | 0.388908 | − | 1.19694i | 0.0134346 | − | 0.0413474i | ||||
\(839\) | 35.4777 | − | 25.7760i | 1.22483 | − | 0.889888i | 0.228334 | − | 0.973583i | \(-0.426672\pi\) |
0.996491 | + | 0.0836954i | \(0.0266723\pi\) | |||||||
\(840\) | 0.395187 | + | 0.287120i | 0.0136353 | + | 0.00990659i | ||||
\(841\) | 4.16562 | + | 12.8205i | 0.143642 | + | 0.442085i | ||||
\(842\) | 1.50232 | + | 4.62365i | 0.0517732 | + | 0.159342i | ||||
\(843\) | −2.33146 | − | 1.69390i | −0.0802997 | − | 0.0583411i | ||||
\(844\) | −11.9294 | + | 8.66721i | −0.410626 | + | 0.298338i | ||||
\(845\) | −10.3089 | + | 31.7276i | −0.354638 | + | 1.09146i | ||||
\(846\) | −4.50894 | −0.155021 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 24.3232 | 0.835261 | ||||||||
\(849\) | −0.0203165 | + | 0.0625277i | −0.000697260 | + | 0.00214595i | ||||
\(850\) | 0.322967 | − | 0.234649i | 0.0110777 | − | 0.00804840i | ||||
\(851\) | 22.8310 | + | 16.5877i | 0.782636 | + | 0.568619i | ||||
\(852\) | 0.596581 | + | 1.83609i | 0.0204385 | + | 0.0629033i | ||||
\(853\) | 12.0951 | + | 37.2250i | 0.414130 | + | 1.27456i | 0.913027 | + | 0.407899i | \(0.133738\pi\) |
−0.498897 | + | 0.866661i | \(0.666262\pi\) | |||||||
\(854\) | 0.156535 | + | 0.113729i | 0.00535652 | + | 0.00389174i | ||||
\(855\) | 36.1670 | − | 26.2769i | 1.23689 | − | 0.898651i | ||||
\(856\) | −0.322171 | + | 0.991541i | −0.0110116 | + | 0.0338902i | ||||
\(857\) | 35.0524 | 1.19737 | 0.598684 | − | 0.800986i | \(-0.295691\pi\) | ||||
0.598684 | + | 0.800986i | \(0.295691\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32.5206 | −1.10959 | −0.554794 | − | 0.831988i | \(-0.687203\pi\) | ||||
−0.554794 | + | 0.831988i | \(0.687203\pi\) | |||||||
\(860\) | −1.20574 | + | 3.71089i | −0.0411154 | + | 0.126540i | ||||
\(861\) | 1.19646 | − | 0.869279i | 0.0407752 | − | 0.0296249i | ||||
\(862\) | 5.07278 | + | 3.68559i | 0.172779 | + | 0.125532i | ||||
\(863\) | 3.92265 | + | 12.0727i | 0.133529 | + | 0.410959i | 0.995358 | − | 0.0962391i | \(-0.0306814\pi\) |
−0.861830 | + | 0.507198i | \(0.830681\pi\) | |||||||
\(864\) | 1.05697 | + | 3.25303i | 0.0359590 | + | 0.110670i | ||||
\(865\) | 11.9362 | + | 8.67219i | 0.405844 | + | 0.294863i | ||||
\(866\) | −1.69981 | + | 1.23498i | −0.0577618 | + | 0.0419664i | ||||
\(867\) | 1.01122 | − | 3.11221i | 0.0343428 | − | 0.105696i | ||||
\(868\) | −14.9844 | −0.508605 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0.806251 | 0.0273345 | ||||||||
\(871\) | −2.61295 | + | 8.04183i | −0.0885364 | + | 0.272487i | ||||
\(872\) | 6.72253 | − | 4.88420i | 0.227654 | − | 0.165400i | ||||
\(873\) | −28.8437 | − | 20.9561i | −0.976210 | − | 0.709258i | ||||
\(874\) | −3.00462 | − | 9.24726i | −0.101633 | − | 0.312793i | ||||
\(875\) | 2.90909 | + | 8.95326i | 0.0983452 | + | 0.302676i | ||||
\(876\) | 5.12978 | + | 3.72700i | 0.173319 | + | 0.125924i | ||||
\(877\) | 22.7609 | − | 16.5367i | 0.768580 | − | 0.558406i | −0.132950 | − | 0.991123i | \(-0.542445\pi\) |
0.901530 | + | 0.432717i | \(0.142445\pi\) | |||||||
\(878\) | −1.02840 | + | 3.16509i | −0.0347069 | + | 0.106817i | ||||
\(879\) | −3.53765 | −0.119322 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36.7964 | −1.23970 | −0.619850 | − | 0.784720i | \(-0.712807\pi\) | ||||
−0.619850 | + | 0.784720i | \(0.712807\pi\) | |||||||
\(882\) | −0.206353 | + | 0.635089i | −0.00694826 | + | 0.0213846i | ||||
\(883\) | 1.84795 | − | 1.34262i | 0.0621885 | − | 0.0451826i | −0.556257 | − | 0.831011i | \(-0.687763\pi\) |
0.618445 | + | 0.785828i | \(0.287763\pi\) | |||||||
\(884\) | −11.6382 | − | 8.45565i | −0.391435 | − | 0.284394i | ||||
\(885\) | 0.486040 | + | 1.49588i | 0.0163380 | + | 0.0502833i | ||||
\(886\) | 0.170805 | + | 0.525683i | 0.00573830 | + | 0.0176607i | ||||
\(887\) | −34.1952 | − | 24.8443i | −1.14816 | − | 0.834190i | −0.159928 | − | 0.987129i | \(-0.551126\pi\) |
−0.988236 | + | 0.152939i | \(0.951126\pi\) | |||||||
\(888\) | 0.630951 | − | 0.458413i | 0.0211733 | − | 0.0153833i | ||||
\(889\) | −0.0893693 | + | 0.275050i | −0.00299735 | + | 0.00922489i | ||||
\(890\) | −0.979808 | −0.0328432 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −34.1520 | −1.14349 | ||||||||
\(893\) | −12.6622 | + | 38.9702i | −0.423724 | + | 1.30409i | ||||
\(894\) | 0.0369712 | − | 0.0268612i | 0.00123650 | − | 0.000898371i | ||||
\(895\) | 8.75218 | + | 6.35883i | 0.292553 | + | 0.212552i | ||||
\(896\) | −2.09601 | − | 6.45084i | −0.0700226 | − | 0.215508i | ||||
\(897\) | −2.46283 | − | 7.57982i | −0.0822316 | − | 0.253083i | ||||
\(898\) | −0.872833 | − | 0.634151i | −0.0291268 | − | 0.0211619i | ||||
\(899\) | −40.5432 | + | 29.4564i | −1.35219 | + | 0.982425i | ||||
\(900\) | 2.18243 | − | 6.71683i | 0.0727476 | − | 0.223894i | ||||
\(901\) | −9.46132 | −0.315202 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.175807 | 0.00585050 | ||||||||
\(904\) | −0.910180 | + | 2.80125i | −0.0302721 | + | 0.0931681i | ||||
\(905\) | 21.8663 | − | 15.8868i | 0.726862 | − | 0.528096i | ||||
\(906\) | 0.725714 | + | 0.527262i | 0.0241102 | + | 0.0175171i | ||||
\(907\) | 12.2150 | + | 37.5939i | 0.405592 | + | 1.24828i | 0.920400 | + | 0.390979i | \(0.127864\pi\) |
−0.514807 | + | 0.857306i | \(0.672136\pi\) | |||||||
\(908\) | 15.4634 | + | 47.5914i | 0.513171 | + | 1.57938i | ||||
\(909\) | −8.82055 | − | 6.40850i | −0.292559 | − | 0.212557i | ||||
\(910\) | 2.34516 | − | 1.70386i | 0.0777414 | − | 0.0564824i | ||||
\(911\) | −10.8865 | + | 33.5053i | −0.360687 | + | 1.11008i | 0.591951 | + | 0.805974i | \(0.298358\pi\) |
−0.952638 | + | 0.304106i | \(0.901642\pi\) | |||||||
\(912\) | 4.91433 | 0.162730 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 7.03234 | 0.232609 | ||||||||
\(915\) | −0.144539 | + | 0.444845i | −0.00477831 | + | 0.0147061i | ||||
\(916\) | −31.2755 | + | 22.7230i | −1.03337 | + | 0.750789i | ||||
\(917\) | 13.3535 | + | 9.70190i | 0.440972 | + | 0.320385i | ||||
\(918\) | −0.131061 | − | 0.403365i | −0.00432567 | − | 0.0133130i | ||||
\(919\) | −12.2403 | − | 37.6718i | −0.403770 | − | 1.24268i | −0.921918 | − | 0.387386i | \(-0.873378\pi\) |
0.518147 | − | 0.855292i | \(-0.326622\pi\) | |||||||
\(920\) | −12.7736 | − | 9.28059i | −0.421134 | − | 0.305972i | ||||
\(921\) | −5.07686 | + | 3.68856i | −0.167288 | + | 0.121542i | ||||
\(922\) | 2.07763 | − | 6.39428i | 0.0684230 | − | 0.210584i | ||||
\(923\) | 23.2141 | 0.764101 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.89131 | −0.160825 | ||||||||
\(926\) | −1.77941 | + | 5.47645i | −0.0584750 | + | 0.179967i | ||||
\(927\) | −2.75017 | + | 1.99811i | −0.0903273 | + | 0.0656267i | ||||
\(928\) | −13.8284 | − | 10.0469i | −0.453938 | − | 0.329805i | ||||
\(929\) | 0.808565 | + | 2.48851i | 0.0265281 | + | 0.0816452i | 0.963444 | − | 0.267910i | \(-0.0863328\pi\) |
−0.936916 | + | 0.349555i | \(0.886333\pi\) | |||||||
\(930\) | 0.293918 | + | 0.904587i | 0.00963796 | + | 0.0296626i | ||||
\(931\) | 4.90950 | + | 3.56696i | 0.160902 | + | 0.116902i | ||||
\(932\) | −31.8710 | + | 23.1556i | −1.04397 | + | 0.758489i | ||||
\(933\) | 2.15487 | − | 6.63201i | 0.0705473 | − | 0.217122i | ||||
\(934\) | −0.720463 | −0.0235743 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 13.5405 | 0.442586 | ||||||||
\(937\) | 16.6375 | − | 51.2050i | 0.543523 | − | 1.67279i | −0.180952 | − | 0.983492i | \(-0.557918\pi\) |
0.724475 | − | 0.689301i | \(-0.242082\pi\) | |||||||
\(938\) | 0.301357 | − | 0.218949i | 0.00983966 | − | 0.00714893i | ||||
\(939\) | 0.00606708 | + | 0.00440799i | 0.000197992 | + | 0.000143849i | ||||
\(940\) | 10.1476 | + | 31.2312i | 0.330979 | + | 1.01865i | ||||
\(941\) | 9.16161 | + | 28.1965i | 0.298660 | + | 0.919181i | 0.981967 | + | 0.189050i | \(0.0605409\pi\) |
−0.683307 | + | 0.730131i | \(0.739459\pi\) | |||||||
\(942\) | −0.492193 | − | 0.357599i | −0.0160365 | − | 0.0116512i | ||||
\(943\) | −38.6732 | + | 28.0977i | −1.25937 | + | 0.914987i | ||||
\(944\) | 3.28468 | − | 10.1092i | 0.106907 | − | 0.329026i | ||||
\(945\) | −3.25480 | −0.105879 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.7861 | −0.512980 | −0.256490 | − | 0.966547i | \(-0.582566\pi\) | ||||
−0.256490 | + | 0.966547i | \(0.582566\pi\) | |||||||
\(948\) | 0.323696 | − | 0.996235i | 0.0105132 | − | 0.0323562i | ||||
\(949\) | 61.6827 | − | 44.8151i | 2.00230 | − | 1.45476i | ||||
\(950\) | 1.36340 | + | 0.990566i | 0.0442344 | + | 0.0321382i | ||||
\(951\) | −1.51609 | − | 4.66606i | −0.0491627 | − | 0.151307i | ||||
\(952\) | 0.396808 | + | 1.22125i | 0.0128606 | + | 0.0395809i | ||||
\(953\) | 28.4061 | + | 20.6383i | 0.920165 | + | 0.668539i | 0.943565 | − | 0.331187i | \(-0.107449\pi\) |
−0.0233999 | + | 0.999726i | \(0.507449\pi\) | |||||||
\(954\) | 3.55568 | − | 2.58335i | 0.115119 | − | 0.0836390i | ||||
\(955\) | −8.98833 | + | 27.6632i | −0.290856 | + | 0.895162i | ||||
\(956\) | −33.3257 | −1.07783 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.731463 | 0.0236325 | ||||||||
\(959\) | 2.88185 | − | 8.86944i | 0.0930599 | − | 0.286409i | ||||
\(960\) | 3.00744 | − | 2.18503i | 0.0970648 | − | 0.0705217i | ||||
\(961\) | −22.7495 | − | 16.5285i | −0.733856 | − | 0.533178i | ||||
\(962\) | −1.43018 | − | 4.40164i | −0.0461108 | − | 0.141915i | ||||
\(963\) | −1.06468 | − | 3.27674i | −0.0343087 | − | 0.105591i | ||||
\(964\) | −38.0803 | − | 27.6670i | −1.22648 | − | 0.891093i | ||||
\(965\) | 45.3155 | − | 32.9237i | 1.45876 | − | 1.05985i | ||||
\(966\) | −0.108495 | + | 0.333914i | −0.00349077 | + | 0.0107435i | ||||
\(967\) | −49.2820 | −1.58480 | −0.792401 | − | 0.610001i | \(-0.791169\pi\) | ||||
−0.792401 | + | 0.610001i | \(0.791169\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.91160 | −0.0614093 | ||||||||
\(970\) | 2.10687 | − | 6.48427i | 0.0676475 | − | 0.208198i | ||||
\(971\) | −30.2107 | + | 21.9493i | −0.969506 | + | 0.704388i | −0.955339 | − | 0.295512i | \(-0.904510\pi\) |
−0.0141673 | + | 0.999900i | \(0.504510\pi\) | |||||||
\(972\) | −9.12988 | − | 6.63325i | −0.292841 | − | 0.212761i | ||||
\(973\) | 1.49147 | + | 4.59026i | 0.0478142 | + | 0.147157i | ||||
\(974\) | 0.690011 | + | 2.12364i | 0.0221094 | + | 0.0680457i | ||||
\(975\) | 1.11755 | + | 0.811950i | 0.0357904 | + | 0.0260032i | ||||
\(976\) | 2.55730 | − | 1.85798i | 0.0818570 | − | 0.0594726i | ||||
\(977\) | 12.3757 | − | 38.0884i | 0.395932 | − | 1.21855i | −0.532301 | − | 0.846555i | \(-0.678672\pi\) |
0.928233 | − | 0.371999i | \(-0.121328\pi\) | |||||||
\(978\) | −0.401470 | −0.0128376 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 4.86335 | 0.155354 | ||||||||
\(981\) | −8.48571 | + | 26.1163i | −0.270928 | + | 0.833831i | ||||
\(982\) | −0.773396 | + | 0.561905i | −0.0246801 | + | 0.0179311i | ||||
\(983\) | 42.1024 | + | 30.5892i | 1.34286 | + | 0.975644i | 0.999334 | + | 0.0365000i | \(0.0116209\pi\) |
0.343525 | + | 0.939144i | \(0.388379\pi\) | |||||||
\(984\) | 0.408230 | + | 1.25640i | 0.0130139 | + | 0.0400527i | ||||
\(985\) | −18.5866 | − | 57.2037i | −0.592219 | − | 1.82266i | ||||
\(986\) | 1.71467 | + | 1.24578i | 0.0546062 | + | 0.0396738i | ||||
\(987\) | 1.19703 | − | 0.869693i | 0.0381019 | − | 0.0276826i | ||||
\(988\) | 18.7661 | − | 57.7562i | 0.597031 | − | 1.83747i | ||||
\(989\) | −5.68262 | −0.180697 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.4828 | 1.44481 | 0.722404 | − | 0.691471i | \(-0.243037\pi\) | ||||
0.722404 | + | 0.691471i | \(0.243037\pi\) | |||||||
\(992\) | 6.23116 | − | 19.1775i | 0.197840 | − | 0.608888i | ||||
\(993\) | 1.90712 | − | 1.38560i | 0.0605206 | − | 0.0439708i | ||||
\(994\) | −0.827341 | − | 0.601098i | −0.0262417 | − | 0.0190657i | ||||
\(995\) | −14.4365 | − | 44.4310i | −0.457668 | − | 1.40856i | ||||
\(996\) | 0.296629 | + | 0.912932i | 0.00939907 | + | 0.0289273i | ||||
\(997\) | −22.6196 | − | 16.4341i | −0.716370 | − | 0.520473i | 0.168852 | − | 0.985641i | \(-0.445994\pi\) |
−0.885222 | + | 0.465168i | \(0.845994\pi\) | |||||||
\(998\) | 3.73252 | − | 2.71183i | 0.118151 | − | 0.0858415i | ||||
\(999\) | −1.60583 | + | 4.94224i | −0.0508062 | + | 0.156365i |
(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 | 847.2.f.w.372.2 | 16 | ||
11.2 | odd | 10 | 847.2.f.x.729.2 | 16 | |||
11.3 | even | 5 | 77.2.f.b.15.3 | ✓ | 16 | ||
11.4 | even | 5 | 847.2.a.p.1.4 | 8 | |||
11.5 | even | 5 | inner | 847.2.f.w.148.2 | 16 | ||
11.6 | odd | 10 | 847.2.f.v.148.3 | 16 | |||
11.7 | odd | 10 | 847.2.a.o.1.5 | 8 | |||
11.8 | odd | 10 | 847.2.f.x.323.2 | 16 | |||
11.9 | even | 5 | 77.2.f.b.36.3 | yes | 16 | ||
11.10 | odd | 2 | 847.2.f.v.372.3 | 16 | |||
33.14 | odd | 10 | 693.2.m.i.631.2 | 16 | |||
33.20 | odd | 10 | 693.2.m.i.190.2 | 16 | |||
33.26 | odd | 10 | 7623.2.a.ct.1.5 | 8 | |||
33.29 | even | 10 | 7623.2.a.cw.1.4 | 8 | |||
77.3 | odd | 30 | 539.2.q.f.422.2 | 32 | |||
77.9 | even | 15 | 539.2.q.g.410.2 | 32 | |||
77.20 | odd | 10 | 539.2.f.e.344.3 | 16 | |||
77.25 | even | 15 | 539.2.q.g.422.2 | 32 | |||
77.31 | odd | 30 | 539.2.q.f.520.3 | 32 | |||
77.47 | odd | 30 | 539.2.q.f.312.3 | 32 | |||
77.48 | odd | 10 | 5929.2.a.bt.1.4 | 8 | |||
77.53 | even | 15 | 539.2.q.g.520.3 | 32 | |||
77.58 | even | 15 | 539.2.q.g.312.3 | 32 | |||
77.62 | even | 10 | 5929.2.a.bs.1.5 | 8 | |||
77.69 | odd | 10 | 539.2.f.e.246.3 | 16 | |||
77.75 | odd | 30 | 539.2.q.f.410.2 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.f.b.15.3 | ✓ | 16 | 11.3 | even | 5 | ||
77.2.f.b.36.3 | yes | 16 | 11.9 | even | 5 | ||
539.2.f.e.246.3 | 16 | 77.69 | odd | 10 | |||
539.2.f.e.344.3 | 16 | 77.20 | odd | 10 | |||
539.2.q.f.312.3 | 32 | 77.47 | odd | 30 | |||
539.2.q.f.410.2 | 32 | 77.75 | odd | 30 | |||
539.2.q.f.422.2 | 32 | 77.3 | odd | 30 | |||
539.2.q.f.520.3 | 32 | 77.31 | odd | 30 | |||
539.2.q.g.312.3 | 32 | 77.58 | even | 15 | |||
539.2.q.g.410.2 | 32 | 77.9 | even | 15 | |||
539.2.q.g.422.2 | 32 | 77.25 | even | 15 | |||
539.2.q.g.520.3 | 32 | 77.53 | even | 15 | |||
693.2.m.i.190.2 | 16 | 33.20 | odd | 10 | |||
693.2.m.i.631.2 | 16 | 33.14 | odd | 10 | |||
847.2.a.o.1.5 | 8 | 11.7 | odd | 10 | |||
847.2.a.p.1.4 | 8 | 11.4 | even | 5 | |||
847.2.f.v.148.3 | 16 | 11.6 | odd | 10 | |||
847.2.f.v.372.3 | 16 | 11.10 | odd | 2 | |||
847.2.f.w.148.2 | 16 | 11.5 | even | 5 | inner | ||
847.2.f.w.372.2 | 16 | 1.1 | even | 1 | trivial | ||
847.2.f.x.323.2 | 16 | 11.8 | odd | 10 | |||
847.2.f.x.729.2 | 16 | 11.2 | odd | 10 | |||
5929.2.a.bs.1.5 | 8 | 77.62 | even | 10 | |||
5929.2.a.bt.1.4 | 8 | 77.48 | odd | 10 | |||
7623.2.a.ct.1.5 | 8 | 33.26 | odd | 10 | |||
7623.2.a.cw.1.4 | 8 | 33.29 | even | 10 |