Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(106,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.106");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.51528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\zeta_{15})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 211.1 | ||
Root | \(-0.104528 + 0.994522i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 315.211 |
Dual form | 315.2.i.d.106.1 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.978148 | − | 1.69420i | −0.691655 | − | 1.19798i | −0.971295 | − | 0.237877i | \(-0.923549\pi\) |
0.279641 | − | 0.960105i | \(-0.409785\pi\) | |||||||
\(3\) | 1.72256 | − | 0.181049i | 0.994522 | − | 0.104528i | ||||
\(4\) | −0.913545 | + | 1.58231i | −0.456773 | + | 0.791154i | ||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | −1.99165 | − | 2.74128i | −0.813089 | − | 1.11912i | ||||
\(7\) | 0.500000 | + | 0.866025i | 0.188982 | + | 0.327327i | ||||
\(8\) | −0.338261 | −0.119593 | ||||||||
\(9\) | 2.93444 | − | 0.623735i | 0.978148 | − | 0.207912i | ||||
\(10\) | −1.95630 | −0.618635 | ||||||||
\(11\) | −1.97815 | − | 3.42625i | −0.596434 | − | 1.03305i | −0.993343 | − | 0.115196i | \(-0.963250\pi\) |
0.396909 | − | 0.917858i | \(-0.370083\pi\) | |||||||
\(12\) | −1.28716 | + | 2.89102i | −0.371572 | + | 0.834565i | ||||
\(13\) | 1.77366 | − | 3.07207i | 0.491925 | − | 0.852038i | −0.508032 | − | 0.861338i | \(-0.669627\pi\) |
0.999957 | + | 0.00929980i | \(0.00296026\pi\) | |||||||
\(14\) | 0.978148 | − | 1.69420i | 0.261421 | − | 0.452794i | ||||
\(15\) | 0.704489 | − | 1.58231i | 0.181898 | − | 0.408550i | ||||
\(16\) | 2.15796 | + | 3.73770i | 0.539490 | + | 0.934424i | ||||
\(17\) | −1.95630 | −0.474471 | −0.237236 | − | 0.971452i | \(-0.576241\pi\) | ||||
−0.237236 | + | 0.971452i | \(0.576241\pi\) | |||||||
\(18\) | −3.92705 | − | 4.36143i | −0.925615 | − | 1.02800i | ||||
\(19\) | 0.231398 | 0.0530862 | 0.0265431 | − | 0.999648i | \(-0.491550\pi\) | ||||
0.0265431 | + | 0.999648i | \(0.491550\pi\) | |||||||
\(20\) | 0.913545 | + | 1.58231i | 0.204275 | + | 0.353815i | ||||
\(21\) | 1.01807 | + | 1.40126i | 0.222162 | + | 0.305780i | ||||
\(22\) | −3.86984 | + | 6.70276i | −0.825053 | + | 1.42903i | ||||
\(23\) | 3.86527 | − | 6.69485i | 0.805965 | − | 1.39597i | −0.109673 | − | 0.993968i | \(-0.534980\pi\) |
0.915638 | − | 0.402005i | \(-0.131686\pi\) | |||||||
\(24\) | −0.582676 | + | 0.0612417i | −0.118938 | + | 0.0125009i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | −6.93960 | −1.36097 | ||||||||
\(27\) | 4.94183 | − | 1.60570i | 0.951057 | − | 0.309017i | ||||
\(28\) | −1.82709 | −0.345288 | ||||||||
\(29\) | 3.88791 | + | 6.73407i | 0.721968 | + | 1.25048i | 0.960210 | + | 0.279279i | \(0.0900954\pi\) |
−0.238242 | + | 0.971206i | \(0.576571\pi\) | |||||||
\(30\) | −3.36984 | + | 0.354185i | −0.615246 | + | 0.0646650i | ||||
\(31\) | −3.00973 | + | 5.21300i | −0.540563 | + | 0.936282i | 0.458309 | + | 0.888793i | \(0.348455\pi\) |
−0.998872 | + | 0.0474894i | \(0.984878\pi\) | |||||||
\(32\) | 3.88335 | − | 6.72615i | 0.686485 | − | 1.18903i | ||||
\(33\) | −4.02780 | − | 5.54379i | −0.701150 | − | 0.965050i | ||||
\(34\) | 1.91355 | + | 3.31436i | 0.328170 | + | 0.568408i | ||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | −1.69381 | + | 5.21300i | −0.282301 | + | 0.868833i | ||||
\(37\) | −7.31592 | −1.20273 | −0.601365 | − | 0.798974i | \(-0.705376\pi\) | ||||
−0.601365 | + | 0.798974i | \(0.705376\pi\) | |||||||
\(38\) | −0.226341 | − | 0.392034i | −0.0367173 | − | 0.0635963i | ||||
\(39\) | 2.49904 | − | 5.61295i | 0.400167 | − | 0.898791i | ||||
\(40\) | −0.169131 | + | 0.292943i | −0.0267419 | + | 0.0463183i | ||||
\(41\) | −4.29173 | + | 7.43350i | −0.670256 | + | 1.16092i | 0.307575 | + | 0.951524i | \(0.400482\pi\) |
−0.977831 | + | 0.209394i | \(0.932851\pi\) | |||||||
\(42\) | 1.37819 | − | 3.09546i | 0.212659 | − | 0.477640i | ||||
\(43\) | 3.72539 | + | 6.45256i | 0.568116 | + | 0.984006i | 0.996752 | + | 0.0805287i | \(0.0256609\pi\) |
−0.428636 | + | 0.903477i | \(0.641006\pi\) | |||||||
\(44\) | 7.22851 | 1.08974 | ||||||||
\(45\) | 0.927051 | − | 2.85317i | 0.138197 | − | 0.425325i | ||||
\(46\) | −15.1232 | −2.22980 | ||||||||
\(47\) | −0.124148 | − | 0.215030i | −0.0181088 | − | 0.0313654i | 0.856829 | − | 0.515601i | \(-0.172431\pi\) |
−0.874938 | + | 0.484235i | \(0.839098\pi\) | |||||||
\(48\) | 4.39393 | + | 6.04772i | 0.634209 | + | 0.872913i | ||||
\(49\) | −0.500000 | + | 0.866025i | −0.0714286 | + | 0.123718i | ||||
\(50\) | −0.978148 | + | 1.69420i | −0.138331 | + | 0.239596i | ||||
\(51\) | −3.36984 | + | 0.354185i | −0.471872 | + | 0.0495958i | ||||
\(52\) | 3.24064 | + | 5.61295i | 0.449395 | + | 0.778376i | ||||
\(53\) | −2.16982 | −0.298047 | −0.149024 | − | 0.988834i | \(-0.547613\pi\) | ||||
−0.149024 | + | 0.988834i | \(0.547613\pi\) | |||||||
\(54\) | −7.55422 | − | 6.80185i | −1.02800 | − | 0.925615i | ||||
\(55\) | −3.95630 | −0.533467 | ||||||||
\(56\) | −0.169131 | − | 0.292943i | −0.0226010 | − | 0.0391461i | ||||
\(57\) | 0.398597 | − | 0.0418942i | 0.0527954 | − | 0.00554902i | ||||
\(58\) | 7.60591 | − | 13.1738i | 0.998705 | − | 1.72981i | ||||
\(59\) | −0.323966 | + | 0.561125i | −0.0421768 | + | 0.0730523i | −0.886343 | − | 0.463029i | \(-0.846763\pi\) |
0.844166 | + | 0.536081i | \(0.180096\pi\) | |||||||
\(60\) | 1.86011 | + | 2.56023i | 0.240140 | + | 0.330524i | ||||
\(61\) | 3.83603 | + | 6.64420i | 0.491153 | + | 0.850702i | 0.999948 | − | 0.0101856i | \(-0.00324224\pi\) |
−0.508795 | + | 0.860888i | \(0.669909\pi\) | |||||||
\(62\) | 11.7758 | 1.49553 | ||||||||
\(63\) | 2.00739 | + | 2.22943i | 0.252908 | + | 0.280882i | ||||
\(64\) | −6.56210 | −0.820263 | ||||||||
\(65\) | −1.77366 | − | 3.07207i | −0.219995 | − | 0.381043i | ||||
\(66\) | −5.45252 | + | 12.2466i | −0.671158 | + | 1.50745i | ||||
\(67\) | 3.30902 | − | 5.73139i | 0.404261 | − | 0.700200i | −0.589974 | − | 0.807422i | \(-0.700862\pi\) |
0.994235 | + | 0.107222i | \(0.0341955\pi\) | |||||||
\(68\) | 1.78716 | − | 3.09546i | 0.216726 | − | 0.375380i | ||||
\(69\) | 5.44608 | − | 12.2321i | 0.655631 | − | 1.47257i | ||||
\(70\) | −0.978148 | − | 1.69420i | −0.116911 | − | 0.202496i | ||||
\(71\) | 4.05751 | 0.481538 | 0.240769 | − | 0.970582i | \(-0.422600\pi\) | ||||
0.240769 | + | 0.970582i | \(0.422600\pi\) | |||||||
\(72\) | −0.992608 | + | 0.210985i | −0.116980 | + | 0.0248649i | ||||
\(73\) | 13.5639 | 1.58753 | 0.793766 | − | 0.608223i | \(-0.208117\pi\) | ||||
0.793766 | + | 0.608223i | \(0.208117\pi\) | |||||||
\(74\) | 7.15605 | + | 12.3946i | 0.831874 | + | 1.44085i | ||||
\(75\) | −1.01807 | − | 1.40126i | −0.117557 | − | 0.161803i | ||||
\(76\) | −0.211392 | + | 0.366142i | −0.0242483 | + | 0.0419994i | ||||
\(77\) | 1.97815 | − | 3.42625i | 0.225431 | − | 0.390458i | ||||
\(78\) | −11.9539 | + | 1.25641i | −1.35351 | + | 0.142260i | ||||
\(79\) | 2.84049 | + | 4.91988i | 0.319581 | + | 0.553530i | 0.980401 | − | 0.197015i | \(-0.0631247\pi\) |
−0.660820 | + | 0.750544i | \(0.729791\pi\) | |||||||
\(80\) | 4.31592 | 0.482535 | ||||||||
\(81\) | 8.22191 | − | 3.66063i | 0.913545 | − | 0.406737i | ||||
\(82\) | 16.7918 | 1.85434 | ||||||||
\(83\) | 7.40599 | + | 12.8275i | 0.812913 | + | 1.40801i | 0.910817 | + | 0.412810i | \(0.135453\pi\) |
−0.0979041 | + | 0.995196i | \(0.531214\pi\) | |||||||
\(84\) | −3.14728 | + | 0.330792i | −0.343396 | + | 0.0360924i | ||||
\(85\) | −0.978148 | + | 1.69420i | −0.106095 | + | 0.183762i | ||||
\(86\) | 7.28795 | − | 12.6231i | 0.785880 | − | 1.36118i | ||||
\(87\) | 7.91637 | + | 10.8959i | 0.848724 | + | 1.16817i | ||||
\(88\) | 0.669131 | + | 1.15897i | 0.0713296 | + | 0.123546i | ||||
\(89\) | 6.12611 | 0.649367 | 0.324683 | − | 0.945823i | \(-0.394742\pi\) | ||||
0.324683 | + | 0.945823i | \(0.394742\pi\) | |||||||
\(90\) | −5.74064 | + | 1.22021i | −0.605116 | + | 0.128621i | ||||
\(91\) | 3.54732 | 0.371860 | ||||||||
\(92\) | 7.06220 | + | 12.2321i | 0.736286 | + | 1.27528i | ||||
\(93\) | −4.24064 | + | 9.52463i | −0.439734 | + | 0.987658i | ||||
\(94\) | −0.242870 | + | 0.420662i | −0.0250501 | + | 0.0433880i | ||||
\(95\) | 0.115699 | − | 0.200396i | 0.0118704 | − | 0.0205602i | ||||
\(96\) | 5.47155 | − | 12.2893i | 0.558437 | − | 1.25427i | ||||
\(97\) | −3.10154 | − | 5.37202i | −0.314914 | − | 0.545446i | 0.664505 | − | 0.747283i | \(-0.268642\pi\) |
−0.979419 | + | 0.201837i | \(0.935309\pi\) | |||||||
\(98\) | 1.95630 | 0.197616 | ||||||||
\(99\) | −7.94183 | − | 8.82030i | −0.798184 | − | 0.886474i | ||||
\(100\) | 1.82709 | 0.182709 | ||||||||
\(101\) | −1.53332 | − | 2.65580i | −0.152571 | − | 0.264262i | 0.779601 | − | 0.626277i | \(-0.215422\pi\) |
−0.932172 | + | 0.362015i | \(0.882089\pi\) | |||||||
\(102\) | 3.89626 | + | 5.36274i | 0.385787 | + | 0.530991i | ||||
\(103\) | 8.30507 | − | 14.3848i | 0.818323 | − | 1.41738i | −0.0885937 | − | 0.996068i | \(-0.528237\pi\) |
0.906917 | − | 0.421310i | \(-0.138429\pi\) | |||||||
\(104\) | −0.599960 | + | 1.03916i | −0.0588309 | + | 0.101898i | ||||
\(105\) | 1.72256 | − | 0.181049i | 0.168105 | − | 0.0176685i | ||||
\(106\) | 2.12240 | + | 3.67611i | 0.206146 | + | 0.357055i | ||||
\(107\) | −19.2470 | −1.86068 | −0.930338 | − | 0.366702i | \(-0.880487\pi\) | ||||
−0.930338 | + | 0.366702i | \(0.880487\pi\) | |||||||
\(108\) | −1.97388 | + | 9.28638i | −0.189937 | + | 0.893582i | ||||
\(109\) | −16.6132 | −1.59126 | −0.795630 | − | 0.605783i | \(-0.792860\pi\) | ||||
−0.795630 | + | 0.605783i | \(0.792860\pi\) | |||||||
\(110\) | 3.86984 | + | 6.70276i | 0.368975 | + | 0.639083i | ||||
\(111\) | −12.6021 | + | 1.32454i | −1.19614 | + | 0.125720i | ||||
\(112\) | −2.15796 | + | 3.73770i | −0.203908 | + | 0.353179i | ||||
\(113\) | −6.50674 | + | 11.2700i | −0.612102 | + | 1.06019i | 0.378783 | + | 0.925486i | \(0.376343\pi\) |
−0.990885 | + | 0.134707i | \(0.956991\pi\) | |||||||
\(114\) | −0.460864 | − | 0.634324i | −0.0431638 | − | 0.0594099i | ||||
\(115\) | −3.86527 | − | 6.69485i | −0.360438 | − | 0.624298i | ||||
\(116\) | −14.2071 | −1.31910 | ||||||||
\(117\) | 3.28854 | − | 10.1211i | 0.304026 | − | 0.935696i | ||||
\(118\) | 1.26755 | 0.116687 | ||||||||
\(119\) | −0.978148 | − | 1.69420i | −0.0896666 | − | 0.155307i | ||||
\(120\) | −0.238301 | + | 0.535233i | −0.0217538 | + | 0.0488599i | ||||
\(121\) | −2.32614 | + | 4.02899i | −0.211467 | + | 0.366271i | ||||
\(122\) | 7.50440 | − | 12.9980i | 0.679417 | − | 1.17678i | ||||
\(123\) | −6.04695 | + | 13.5817i | −0.545235 | + | 1.22462i | ||||
\(124\) | −5.49904 | − | 9.52463i | −0.493829 | − | 0.855337i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 1.81359 | − | 5.58164i | 0.161567 | − | 0.497252i | ||||
\(127\) | 10.8009 | 0.958428 | 0.479214 | − | 0.877698i | \(-0.340922\pi\) | ||||
0.479214 | + | 0.877698i | \(0.340922\pi\) | |||||||
\(128\) | −1.34799 | − | 2.33478i | −0.119146 | − | 0.206368i | ||||
\(129\) | 7.58544 | + | 10.4405i | 0.667860 | + | 0.919231i | ||||
\(130\) | −3.46980 | + | 6.00987i | −0.304322 | + | 0.527101i | ||||
\(131\) | −6.98186 | + | 12.0929i | −0.610008 | + | 1.05657i | 0.381230 | + | 0.924480i | \(0.375501\pi\) |
−0.991238 | + | 0.132085i | \(0.957833\pi\) | |||||||
\(132\) | 12.4516 | − | 1.30871i | 1.08377 | − | 0.113909i | ||||
\(133\) | 0.115699 | + | 0.200396i | 0.0100324 | + | 0.0173765i | ||||
\(134\) | −12.9468 | −1.11844 | ||||||||
\(135\) | 1.08034 | − | 5.08260i | 0.0929809 | − | 0.437441i | ||||
\(136\) | 0.661739 | 0.0567436 | ||||||||
\(137\) | 1.61064 | + | 2.78971i | 0.137606 | + | 0.238341i | 0.926590 | − | 0.376073i | \(-0.122726\pi\) |
−0.788984 | + | 0.614414i | \(0.789392\pi\) | |||||||
\(138\) | −26.0507 | + | 2.73804i | −2.21758 | + | 0.233077i | ||||
\(139\) | 5.39074 | − | 9.33703i | 0.457236 | − | 0.791957i | −0.541577 | − | 0.840651i | \(-0.682173\pi\) |
0.998814 | + | 0.0486942i | \(0.0155060\pi\) | |||||||
\(140\) | −0.913545 | + | 1.58231i | −0.0772087 | + | 0.133729i | ||||
\(141\) | −0.252783 | − | 0.347926i | −0.0212882 | − | 0.0293007i | ||||
\(142\) | −3.96885 | − | 6.87424i | −0.333058 | − | 0.576874i | ||||
\(143\) | −14.0342 | −1.17360 | ||||||||
\(144\) | 8.66374 | + | 9.62206i | 0.721979 | + | 0.801839i | ||||
\(145\) | 7.77583 | 0.645747 | ||||||||
\(146\) | −13.2675 | − | 22.9800i | −1.09802 | − | 1.90183i | ||||
\(147\) | −0.704489 | + | 1.58231i | −0.0581052 | + | 0.130506i | ||||
\(148\) | 6.68343 | − | 11.5760i | 0.549374 | − | 0.951544i | ||||
\(149\) | −7.08783 | + | 12.2765i | −0.580658 | + | 1.00573i | 0.414743 | + | 0.909938i | \(0.363871\pi\) |
−0.995401 | + | 0.0957908i | \(0.969462\pi\) | |||||||
\(150\) | −1.37819 | + | 3.09546i | −0.112529 | + | 0.252743i | ||||
\(151\) | −3.59523 | − | 6.22712i | −0.292575 | − | 0.506755i | 0.681843 | − | 0.731499i | \(-0.261179\pi\) |
−0.974418 | + | 0.224744i | \(0.927846\pi\) | |||||||
\(152\) | −0.0782728 | −0.00634876 | ||||||||
\(153\) | −5.74064 | + | 1.22021i | −0.464103 | + | 0.0986481i | ||||
\(154\) | −7.73968 | −0.623681 | ||||||||
\(155\) | 3.00973 | + | 5.21300i | 0.241747 | + | 0.418718i | ||||
\(156\) | 6.59841 | + | 9.08194i | 0.528296 | + | 0.727137i | ||||
\(157\) | 0.923438 | − | 1.59944i | 0.0736983 | − | 0.127649i | −0.826821 | − | 0.562465i | \(-0.809853\pi\) |
0.900519 | + | 0.434816i | \(0.143186\pi\) | |||||||
\(158\) | 5.55685 | − | 9.62474i | 0.442079 | − | 0.765703i | ||||
\(159\) | −3.73765 | + | 0.392843i | −0.296415 | + | 0.0311544i | ||||
\(160\) | −3.88335 | − | 6.72615i | −0.307005 | − | 0.531749i | ||||
\(161\) | 7.73054 | 0.609252 | ||||||||
\(162\) | −14.2441 | − | 10.3489i | −1.11912 | − | 0.813089i | ||||
\(163\) | −15.9000 | −1.24538 | −0.622691 | − | 0.782468i | \(-0.713960\pi\) | ||||
−0.622691 | + | 0.782468i | \(0.713960\pi\) | |||||||
\(164\) | −7.84139 | − | 13.5817i | −0.612309 | − | 1.06055i | ||||
\(165\) | −6.81497 | + | 0.716282i | −0.530544 | + | 0.0557625i | ||||
\(166\) | 14.4883 | − | 25.0945i | 1.12451 | − | 1.94771i | ||||
\(167\) | 0.679813 | − | 1.17747i | 0.0526055 | − | 0.0911154i | −0.838524 | − | 0.544865i | \(-0.816581\pi\) |
0.891129 | + | 0.453750i | \(0.149914\pi\) | |||||||
\(168\) | −0.344375 | − | 0.473991i | −0.0265691 | − | 0.0365692i | ||||
\(169\) | 0.208267 | + | 0.360729i | 0.0160205 | + | 0.0277484i | ||||
\(170\) | 3.82709 | 0.293524 | ||||||||
\(171\) | 0.679023 | − | 0.144331i | 0.0519262 | − | 0.0110372i | ||||
\(172\) | −13.6132 | −1.03800 | ||||||||
\(173\) | −2.49953 | − | 4.32932i | −0.190036 | − | 0.329152i | 0.755226 | − | 0.655465i | \(-0.227527\pi\) |
−0.945262 | + | 0.326313i | \(0.894194\pi\) | |||||||
\(174\) | 10.7166 | − | 24.0698i | 0.812420 | − | 1.82472i | ||||
\(175\) | 0.500000 | − | 0.866025i | 0.0377964 | − | 0.0654654i | ||||
\(176\) | 8.53753 | − | 14.7874i | 0.643540 | − | 1.11464i | ||||
\(177\) | −0.456460 | + | 1.02523i | −0.0343097 | + | 0.0770608i | ||||
\(178\) | −5.99224 | − | 10.3789i | −0.449138 | − | 0.777929i | ||||
\(179\) | 20.8475 | 1.55822 | 0.779108 | − | 0.626889i | \(-0.215672\pi\) | ||||
0.779108 | + | 0.626889i | \(0.215672\pi\) | |||||||
\(180\) | 3.66769 | + | 4.07338i | 0.273373 | + | 0.303612i | ||||
\(181\) | −7.64696 | −0.568394 | −0.284197 | − | 0.958766i | \(-0.591727\pi\) | ||||
−0.284197 | + | 0.958766i | \(0.591727\pi\) | |||||||
\(182\) | −3.46980 | − | 6.00987i | −0.257199 | − | 0.445481i | ||||
\(183\) | 7.81072 | + | 10.7505i | 0.577385 | + | 0.794702i | ||||
\(184\) | −1.30747 | + | 2.26461i | −0.0963881 | + | 0.166949i | ||||
\(185\) | −3.65796 | + | 6.33577i | −0.268939 | + | 0.465815i | ||||
\(186\) | 20.2846 | − | 2.13200i | 1.48734 | − | 0.156326i | ||||
\(187\) | 3.86984 | + | 6.70276i | 0.282991 | + | 0.490154i | ||||
\(188\) | 0.453658 | 0.0330864 | ||||||||
\(189\) | 3.86149 | + | 3.47690i | 0.280882 | + | 0.252908i | ||||
\(190\) | −0.452682 | −0.0328410 | ||||||||
\(191\) | −5.41194 | − | 9.37375i | −0.391594 | − | 0.678261i | 0.601066 | − | 0.799199i | \(-0.294743\pi\) |
−0.992660 | + | 0.120939i | \(0.961410\pi\) | |||||||
\(192\) | −11.3036 | + | 1.18806i | −0.815769 | + | 0.0857408i | ||||
\(193\) | −4.35380 | + | 7.54100i | −0.313393 | + | 0.542813i | −0.979095 | − | 0.203405i | \(-0.934799\pi\) |
0.665701 | + | 0.746218i | \(0.268133\pi\) | |||||||
\(194\) | −6.06753 | + | 10.5093i | −0.435623 | + | 0.754521i | ||||
\(195\) | −3.61143 | − | 4.97071i | −0.258620 | − | 0.355960i | ||||
\(196\) | −0.913545 | − | 1.58231i | −0.0652532 | − | 0.113022i | ||||
\(197\) | −26.1081 | −1.86013 | −0.930063 | − | 0.367400i | \(-0.880248\pi\) | ||||
−0.930063 | + | 0.367400i | \(0.880248\pi\) | |||||||
\(198\) | −7.17508 | + | 22.0826i | −0.509911 | + | 1.56934i | ||||
\(199\) | −3.79757 | −0.269202 | −0.134601 | − | 0.990900i | \(-0.542975\pi\) | ||||
−0.134601 | + | 0.990900i | \(0.542975\pi\) | |||||||
\(200\) | 0.169131 | + | 0.292943i | 0.0119593 | + | 0.0207142i | ||||
\(201\) | 4.66233 | − | 10.4718i | 0.328855 | − | 0.738621i | ||||
\(202\) | −2.99964 | + | 5.19552i | −0.211054 | + | 0.365556i | ||||
\(203\) | −3.88791 | + | 6.73407i | −0.272878 | + | 0.472639i | ||||
\(204\) | 2.51807 | − | 5.65569i | 0.176300 | − | 0.395977i | ||||
\(205\) | 4.29173 | + | 7.43350i | 0.299748 | + | 0.519178i | ||||
\(206\) | −32.4944 | −2.26399 | ||||||||
\(207\) | 7.16661 | − | 22.0566i | 0.498114 | − | 1.53304i | ||||
\(208\) | 15.3099 | 1.06155 | ||||||||
\(209\) | −0.457738 | − | 0.792826i | −0.0316624 | − | 0.0548409i | ||||
\(210\) | −1.99165 | − | 2.74128i | −0.137437 | − | 0.189166i | ||||
\(211\) | −3.75473 | + | 6.50339i | −0.258486 | + | 0.447712i | −0.965837 | − | 0.259152i | \(-0.916557\pi\) |
0.707350 | + | 0.706863i | \(0.249890\pi\) | |||||||
\(212\) | 1.98223 | − | 3.43332i | 0.136140 | − | 0.235801i | ||||
\(213\) | 6.98932 | − | 0.734607i | 0.478900 | − | 0.0503344i | ||||
\(214\) | 18.8264 | + | 32.6083i | 1.28695 | + | 2.22906i | ||||
\(215\) | 7.45077 | 0.508138 | ||||||||
\(216\) | −1.67163 | + | 0.543146i | −0.113740 | + | 0.0369564i | ||||
\(217\) | −6.01945 | −0.408627 | ||||||||
\(218\) | 16.2502 | + | 28.1462i | 1.10060 | + | 1.90630i | ||||
\(219\) | 23.3646 | − | 2.45572i | 1.57884 | − | 0.165942i | ||||
\(220\) | 3.61426 | − | 6.26007i | 0.243673 | − | 0.422054i | ||||
\(221\) | −3.46980 | + | 6.00987i | −0.233404 | + | 0.404268i | ||||
\(222\) | 14.5708 | + | 20.0550i | 0.977926 | + | 1.34600i | ||||
\(223\) | −9.16391 | − | 15.8724i | −0.613661 | − | 1.06289i | −0.990618 | − | 0.136661i | \(-0.956363\pi\) |
0.376957 | − | 0.926231i | \(-0.376970\pi\) | |||||||
\(224\) | 7.76669 | 0.518934 | ||||||||
\(225\) | −2.00739 | − | 2.22943i | −0.133826 | − | 0.148629i | ||||
\(226\) | 25.4582 | 1.69345 | ||||||||
\(227\) | −6.31293 | − | 10.9343i | −0.419004 | − | 0.725736i | 0.576836 | − | 0.816860i | \(-0.304287\pi\) |
−0.995840 | + | 0.0911241i | \(0.970954\pi\) | |||||||
\(228\) | −0.297847 | + | 0.668975i | −0.0197254 | + | 0.0443039i | ||||
\(229\) | −0.0782097 | + | 0.135463i | −0.00516824 | + | 0.00895166i | −0.868598 | − | 0.495517i | \(-0.834978\pi\) |
0.863430 | + | 0.504469i | \(0.168312\pi\) | |||||||
\(230\) | −7.56161 | + | 13.0971i | −0.498598 | + | 0.863597i | ||||
\(231\) | 2.78716 | − | 6.26007i | 0.183382 | − | 0.411883i | ||||
\(232\) | −1.31513 | − | 2.27787i | −0.0863426 | − | 0.149550i | ||||
\(233\) | 20.9785 | 1.37435 | 0.687174 | − | 0.726493i | \(-0.258851\pi\) | ||||
0.687174 | + | 0.726493i | \(0.258851\pi\) | |||||||
\(234\) | −20.3639 | + | 4.32847i | −1.33123 | + | 0.282961i | ||||
\(235\) | −0.248295 | −0.0161970 | ||||||||
\(236\) | −0.591915 | − | 1.02523i | −0.0385304 | − | 0.0667366i | ||||
\(237\) | 5.78367 | + | 7.96053i | 0.375690 | + | 0.517092i | ||||
\(238\) | −1.91355 | + | 3.31436i | −0.124037 | + | 0.214838i | ||||
\(239\) | 1.67856 | − | 2.90734i | 0.108577 | − | 0.188060i | −0.806617 | − | 0.591074i | \(-0.798704\pi\) |
0.915194 | + | 0.403014i | \(0.132037\pi\) | |||||||
\(240\) | 7.43444 | − | 0.781391i | 0.479891 | − | 0.0504386i | ||||
\(241\) | 5.36277 | + | 9.28859i | 0.345447 | + | 0.598331i | 0.985435 | − | 0.170054i | \(-0.0543941\pi\) |
−0.639988 | + | 0.768385i | \(0.721061\pi\) | |||||||
\(242\) | 9.10122 | 0.585048 | ||||||||
\(243\) | 13.5000 | − | 7.79423i | 0.866025 | − | 0.500000i | ||||
\(244\) | −14.0175 | −0.897381 | ||||||||
\(245\) | 0.500000 | + | 0.866025i | 0.0319438 | + | 0.0553283i | ||||
\(246\) | 28.9249 | − | 3.04013i | 1.84419 | − | 0.193832i | ||||
\(247\) | 0.410420 | − | 0.710869i | 0.0261144 | − | 0.0452315i | ||||
\(248\) | 1.01807 | − | 1.76336i | 0.0646478 | − | 0.111973i | ||||
\(249\) | 15.0797 | + | 20.7554i | 0.955636 | + | 1.31532i | ||||
\(250\) | 0.978148 | + | 1.69420i | 0.0618635 | + | 0.107151i | ||||
\(251\) | 9.63655 | 0.608254 | 0.304127 | − | 0.952632i | \(-0.401635\pi\) | ||||
0.304127 | + | 0.952632i | \(0.401635\pi\) | |||||||
\(252\) | −5.36149 | + | 1.13962i | −0.337742 | + | 0.0717894i | ||||
\(253\) | −30.5843 | −1.92282 | ||||||||
\(254\) | −10.5649 | − | 18.2990i | −0.662901 | − | 1.14818i | ||||
\(255\) | −1.37819 | + | 3.09546i | −0.0863055 | + | 0.193845i | ||||
\(256\) | −9.19916 | + | 15.9334i | −0.574948 | + | 0.995839i | ||||
\(257\) | −12.3196 | + | 21.3381i | −0.768473 | + | 1.33103i | 0.169918 | + | 0.985458i | \(0.445650\pi\) |
−0.938391 | + | 0.345576i | \(0.887684\pi\) | |||||||
\(258\) | 10.2686 | − | 23.0636i | 0.639293 | − | 1.43587i | ||||
\(259\) | −3.65796 | − | 6.33577i | −0.227295 | − | 0.393686i | ||||
\(260\) | 6.48127 | 0.401951 | ||||||||
\(261\) | 15.6091 | + | 17.3357i | 0.966181 | + | 1.07305i | ||||
\(262\) | 27.3172 | 1.68766 | ||||||||
\(263\) | −7.19210 | − | 12.4571i | −0.443484 | − | 0.768136i | 0.554462 | − | 0.832209i | \(-0.312924\pi\) |
−0.997945 | + | 0.0640731i | \(0.979591\pi\) | |||||||
\(264\) | 1.36245 | + | 1.87525i | 0.0838529 | + | 0.115414i | ||||
\(265\) | −1.08491 | + | 1.87912i | −0.0666454 | + | 0.115433i | ||||
\(266\) | 0.226341 | − | 0.392034i | 0.0138779 | − | 0.0240371i | ||||
\(267\) | 10.5526 | − | 1.10912i | 0.645809 | − | 0.0678773i | ||||
\(268\) | 6.04587 | + | 10.4718i | 0.369311 | + | 0.639665i | ||||
\(269\) | 13.6989 | 0.835234 | 0.417617 | − | 0.908623i | \(-0.362865\pi\) | ||||
0.417617 | + | 0.908623i | \(0.362865\pi\) | |||||||
\(270\) | −9.66769 | + | 3.14122i | −0.588357 | + | 0.191169i | ||||
\(271\) | −1.43854 | −0.0873853 | −0.0436927 | − | 0.999045i | \(-0.513912\pi\) | ||||
−0.0436927 | + | 0.999045i | \(0.513912\pi\) | |||||||
\(272\) | −4.22161 | − | 7.31204i | −0.255973 | − | 0.443357i | ||||
\(273\) | 6.11048 | − | 0.642237i | 0.369823 | − | 0.0388700i | ||||
\(274\) | 3.15089 | − | 5.45750i | 0.190352 | − | 0.329700i | ||||
\(275\) | −1.97815 | + | 3.42625i | −0.119287 | + | 0.206611i | ||||
\(276\) | 14.3797 | + | 19.7919i | 0.865556 | + | 1.19134i | ||||
\(277\) | −9.12713 | − | 15.8087i | −0.548396 | − | 0.949850i | −0.998385 | − | 0.0568155i | \(-0.981905\pi\) |
0.449989 | − | 0.893034i | \(-0.351428\pi\) | |||||||
\(278\) | −21.0917 | −1.26500 | ||||||||
\(279\) | −5.58034 | + | 17.1745i | −0.334086 | + | 1.02821i | ||||
\(280\) | −0.338261 | −0.0202150 | ||||||||
\(281\) | −2.91684 | − | 5.05211i | −0.174004 | − | 0.301383i | 0.765812 | − | 0.643064i | \(-0.222337\pi\) |
−0.939816 | + | 0.341681i | \(0.889004\pi\) | |||||||
\(282\) | −0.342198 | + | 0.768588i | −0.0203776 | + | 0.0457688i | ||||
\(283\) | 6.90764 | − | 11.9644i | 0.410616 | − | 0.711208i | −0.584341 | − | 0.811508i | \(-0.698647\pi\) |
0.994957 | + | 0.100300i | \(0.0319802\pi\) | |||||||
\(284\) | −3.70672 | + | 6.42023i | −0.219953 | + | 0.380971i | ||||
\(285\) | 0.163017 | − | 0.366142i | 0.00965629 | − | 0.0216884i | ||||
\(286\) | 13.7276 | + | 23.7768i | 0.811727 | + | 1.40595i | ||||
\(287\) | −8.58347 | −0.506666 | ||||||||
\(288\) | 7.20012 | − | 22.1597i | 0.424271 | − | 1.30577i | ||||
\(289\) | −13.1729 | −0.774877 | ||||||||
\(290\) | −7.60591 | − | 13.1738i | −0.446634 | − | 0.773593i | ||||
\(291\) | −6.31519 | − | 8.69212i | −0.370203 | − | 0.509541i | ||||
\(292\) | −12.3912 | + | 21.4622i | −0.725142 | + | 1.25598i | ||||
\(293\) | −6.92449 | + | 11.9936i | −0.404533 | + | 0.700672i | −0.994267 | − | 0.106926i | \(-0.965899\pi\) |
0.589734 | + | 0.807597i | \(0.299233\pi\) | |||||||
\(294\) | 3.36984 | − | 0.354185i | 0.196533 | − | 0.0206565i | ||||
\(295\) | 0.323966 | + | 0.561125i | 0.0188620 | + | 0.0326700i | ||||
\(296\) | 2.47469 | 0.143839 | ||||||||
\(297\) | −15.2772 | − | 13.7557i | −0.886474 | − | 0.798184i | ||||
\(298\) | 27.7318 | 1.60646 | ||||||||
\(299\) | −13.7114 | − | 23.7488i | −0.792948 | − | 1.37343i | ||||
\(300\) | 3.14728 | − | 0.330792i | 0.181708 | − | 0.0190983i | ||||
\(301\) | −3.72539 | + | 6.45256i | −0.214728 | + | 0.371919i | ||||
\(302\) | −7.03332 | + | 12.1821i | −0.404722 | + | 0.701000i | ||||
\(303\) | −3.12208 | − | 4.29717i | −0.179359 | − | 0.246866i | ||||
\(304\) | 0.499347 | + | 0.864894i | 0.0286395 | + | 0.0496051i | ||||
\(305\) | 7.67206 | 0.439301 | ||||||||
\(306\) | 7.68247 | + | 8.53225i | 0.439178 | + | 0.487756i | ||||
\(307\) | 32.4126 | 1.84988 | 0.924942 | − | 0.380108i | \(-0.124113\pi\) | ||||
0.924942 | + | 0.380108i | \(0.124113\pi\) | |||||||
\(308\) | 3.61426 | + | 6.26007i | 0.205941 | + | 0.356701i | ||||
\(309\) | 11.7017 | − | 26.2824i | 0.665684 | − | 1.49515i | ||||
\(310\) | 5.88791 | − | 10.1982i | 0.334411 | − | 0.579217i | ||||
\(311\) | 15.1887 | − | 26.3076i | 0.861273 | − | 1.49177i | −0.00942711 | − | 0.999956i | \(-0.503001\pi\) |
0.870700 | − | 0.491814i | \(-0.163666\pi\) | |||||||
\(312\) | −0.845330 | + | 1.89864i | −0.0478574 | + | 0.107489i | ||||
\(313\) | 12.3176 | + | 21.3348i | 0.696233 | + | 1.20591i | 0.969763 | + | 0.244048i | \(0.0784754\pi\) |
−0.273530 | + | 0.961863i | \(0.588191\pi\) | |||||||
\(314\) | −3.61303 | −0.203895 | ||||||||
\(315\) | 2.93444 | − | 0.623735i | 0.165337 | − | 0.0351435i | ||||
\(316\) | −10.3797 | −0.583903 | ||||||||
\(317\) | −9.54823 | − | 16.5380i | −0.536282 | − | 0.928868i | −0.999100 | − | 0.0424145i | \(-0.986495\pi\) |
0.462818 | − | 0.886453i | \(-0.346838\pi\) | |||||||
\(318\) | 4.32153 | + | 5.94807i | 0.242339 | + | 0.333551i | ||||
\(319\) | 15.3817 | − | 26.6420i | 0.861212 | − | 1.49166i | ||||
\(320\) | −3.28105 | + | 5.68295i | −0.183416 | + | 0.317686i | ||||
\(321\) | −33.1541 | + | 3.48464i | −1.85048 | + | 0.194494i | ||||
\(322\) | −7.56161 | − | 13.0971i | −0.421392 | − | 0.729873i | ||||
\(323\) | −0.452682 | −0.0251879 | ||||||||
\(324\) | −1.71885 | + | 16.3537i | −0.0954915 | + | 0.908541i | ||||
\(325\) | −3.54732 | −0.196770 | ||||||||
\(326\) | 15.5525 | + | 26.9377i | 0.861374 | + | 1.49194i | ||||
\(327\) | −28.6173 | + | 3.00780i | −1.58254 | + | 0.166332i | ||||
\(328\) | 1.45173 | − | 2.51446i | 0.0801582 | − | 0.138838i | ||||
\(329\) | 0.124148 | − | 0.215030i | 0.00684448 | − | 0.0118550i | ||||
\(330\) | 7.87957 | + | 10.8453i | 0.433756 | + | 0.597014i | ||||
\(331\) | −6.02149 | − | 10.4295i | −0.330971 | − | 0.573258i | 0.651732 | − | 0.758450i | \(-0.274043\pi\) |
−0.982702 | + | 0.185191i | \(0.940710\pi\) | |||||||
\(332\) | −27.0628 | −1.48527 | ||||||||
\(333\) | −21.4682 | + | 4.56320i | −1.17645 | + | 0.250062i | ||||
\(334\) | −2.65983 | −0.145539 | ||||||||
\(335\) | −3.30902 | − | 5.73139i | −0.180791 | − | 0.313139i | ||||
\(336\) | −3.04052 | + | 6.82911i | −0.165874 | + | 0.372559i | ||||
\(337\) | −5.50956 | + | 9.54284i | −0.300125 | + | 0.519832i | −0.976164 | − | 0.217034i | \(-0.930362\pi\) |
0.676039 | + | 0.736866i | \(0.263695\pi\) | |||||||
\(338\) | 0.407432 | − | 0.705692i | 0.0221614 | − | 0.0383846i | ||||
\(339\) | −9.16785 | + | 20.5913i | −0.497929 | + | 1.11837i | ||||
\(340\) | −1.78716 | − | 3.09546i | −0.0969226 | − | 0.167875i | ||||
\(341\) | 23.8147 | 1.28964 | ||||||||
\(342\) | −0.908710 | − | 1.00922i | −0.0491374 | − | 0.0545726i | ||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −1.26015 | − | 2.18265i | −0.0679429 | − | 0.117681i | ||||
\(345\) | −7.87027 | − | 10.8325i | −0.423721 | − | 0.583202i | ||||
\(346\) | −4.88982 | + | 8.46942i | −0.262879 | + | 0.455319i | ||||
\(347\) | −15.4307 | + | 26.7268i | −0.828364 | + | 1.43477i | 0.0709578 | + | 0.997479i | \(0.477394\pi\) |
−0.899321 | + | 0.437288i | \(0.855939\pi\) | |||||||
\(348\) | −24.4727 | + | 2.57218i | −1.31187 | + | 0.137884i | ||||
\(349\) | 3.94403 | + | 6.83127i | 0.211119 | + | 0.365669i | 0.952065 | − | 0.305896i | \(-0.0989558\pi\) |
−0.740946 | + | 0.671565i | \(0.765622\pi\) | |||||||
\(350\) | −1.95630 | −0.104568 | ||||||||
\(351\) | 3.83231 | − | 18.0296i | 0.204554 | − | 0.962350i | ||||
\(352\) | −30.7273 | −1.63777 | ||||||||
\(353\) | 13.0468 | + | 22.5977i | 0.694410 | + | 1.20275i | 0.970379 | + | 0.241588i | \(0.0776681\pi\) |
−0.275969 | + | 0.961167i | \(0.588999\pi\) | |||||||
\(354\) | 2.18343 | − | 0.229487i | 0.116048 | − | 0.0121971i | ||||
\(355\) | 2.02876 | − | 3.51391i | 0.107675 | − | 0.186499i | ||||
\(356\) | −5.59648 | + | 9.69339i | −0.296613 | + | 0.513749i | ||||
\(357\) | −1.99165 | − | 2.74128i | −0.105409 | − | 0.145084i | ||||
\(358\) | −20.3920 | − | 35.3199i | −1.07775 | − | 1.86671i | ||||
\(359\) | −26.1440 | −1.37983 | −0.689913 | − | 0.723892i | \(-0.742351\pi\) | ||||
−0.689913 | + | 0.723892i | \(0.742351\pi\) | |||||||
\(360\) | −0.313585 | + | 0.965117i | −0.0165274 | + | 0.0508661i | ||||
\(361\) | −18.9465 | −0.997182 | ||||||||
\(362\) | 7.47985 | + | 12.9555i | 0.393132 | + | 0.680925i | ||||
\(363\) | −3.27747 | + | 7.36132i | −0.172023 | + | 0.386369i | ||||
\(364\) | −3.24064 | + | 5.61295i | −0.169855 | + | 0.294198i | ||||
\(365\) | 6.78194 | − | 11.7467i | 0.354983 | − | 0.614849i | ||||
\(366\) | 10.5735 | − | 23.7485i | 0.552687 | − | 1.24136i | ||||
\(367\) | −3.20323 | − | 5.54816i | −0.167207 | − | 0.289612i | 0.770230 | − | 0.637767i | \(-0.220142\pi\) |
−0.937437 | + | 0.348155i | \(0.886808\pi\) | |||||||
\(368\) | 33.3644 | 1.73924 | ||||||||
\(369\) | −7.95731 | + | 24.4901i | −0.414241 | + | 1.27490i | ||||
\(370\) | 14.3121 | 0.744051 | ||||||||
\(371\) | −1.08491 | − | 1.87912i | −0.0563257 | − | 0.0975589i | ||||
\(372\) | −11.1969 | − | 15.4112i | −0.580531 | − | 0.799032i | ||||
\(373\) | 6.65658 | − | 11.5295i | 0.344665 | − | 0.596977i | −0.640628 | − | 0.767851i | \(-0.721326\pi\) |
0.985293 | + | 0.170875i | \(0.0546593\pi\) | |||||||
\(374\) | 7.57055 | − | 13.1126i | 0.391464 | − | 0.678035i | ||||
\(375\) | −1.72256 | + | 0.181049i | −0.0889527 | + | 0.00934931i | ||||
\(376\) | 0.0419943 | + | 0.0727363i | 0.00216569 | + | 0.00375109i | ||||
\(377\) | 27.5833 | 1.42061 | ||||||||
\(378\) | 2.11347 | − | 9.94307i | 0.108705 | − | 0.511417i | ||||
\(379\) | −9.14013 | −0.469497 | −0.234748 | − | 0.972056i | \(-0.575427\pi\) | ||||
−0.234748 | + | 0.972056i | \(0.575427\pi\) | |||||||
\(380\) | 0.211392 | + | 0.366142i | 0.0108442 | + | 0.0187827i | ||||
\(381\) | 18.6053 | − | 1.95549i | 0.953177 | − | 0.100183i | ||||
\(382\) | −10.5873 | + | 18.3378i | −0.541696 | + | 0.938245i | ||||
\(383\) | 4.83416 | − | 8.37301i | 0.247014 | − | 0.427841i | −0.715682 | − | 0.698426i | \(-0.753884\pi\) |
0.962696 | + | 0.270586i | \(0.0872173\pi\) | |||||||
\(384\) | −2.74470 | − | 3.77776i | −0.140065 | − | 0.192783i | ||||
\(385\) | −1.97815 | − | 3.42625i | −0.100816 | − | 0.174618i | ||||
\(386\) | 17.0346 | 0.867040 | ||||||||
\(387\) | 14.9566 | + | 16.6110i | 0.760288 | + | 0.844385i | ||||
\(388\) | 11.3336 | 0.575376 | ||||||||
\(389\) | −3.70041 | − | 6.40930i | −0.187618 | − | 0.324964i | 0.756837 | − | 0.653603i | \(-0.226743\pi\) |
−0.944456 | + | 0.328639i | \(0.893410\pi\) | |||||||
\(390\) | −4.88887 | + | 10.9806i | −0.247558 | + | 0.556023i | ||||
\(391\) | −7.56161 | + | 13.0971i | −0.382407 | + | 0.662349i | ||||
\(392\) | 0.169131 | − | 0.292943i | 0.00854239 | − | 0.0147958i | ||||
\(393\) | −9.83728 | + | 22.0949i | −0.496225 | + | 1.11454i | ||||
\(394\) | 25.5376 | + | 44.2324i | 1.28657 | + | 2.22840i | ||||
\(395\) | 5.68099 | 0.285842 | ||||||||
\(396\) | 21.2117 | − | 4.50868i | 1.06593 | − | 0.226569i | ||||
\(397\) | −20.6228 | −1.03503 | −0.517514 | − | 0.855675i | \(-0.673142\pi\) | ||||
−0.517514 | + | 0.855675i | \(0.673142\pi\) | |||||||
\(398\) | 3.71458 | + | 6.43384i | 0.186195 | + | 0.322499i | ||||
\(399\) | 0.235580 | + | 0.324248i | 0.0117937 | + | 0.0162327i | ||||
\(400\) | 2.15796 | − | 3.73770i | 0.107898 | − | 0.186885i | ||||
\(401\) | −5.58454 | + | 9.67271i | −0.278879 | + | 0.483032i | −0.971106 | − | 0.238647i | \(-0.923296\pi\) |
0.692228 | + | 0.721679i | \(0.256629\pi\) | |||||||
\(402\) | −22.3017 | + | 2.34401i | −1.11231 | + | 0.116908i | ||||
\(403\) | 10.6765 | + | 18.4922i | 0.531832 | + | 0.921161i | ||||
\(404\) | 5.60305 | 0.278762 | ||||||||
\(405\) | 0.940756 | − | 8.95070i | 0.0467465 | − | 0.444764i | ||||
\(406\) | 15.2118 | 0.754950 | ||||||||
\(407\) | 14.4720 | + | 25.0662i | 0.717349 | + | 1.24248i | ||||
\(408\) | 1.13989 | − | 0.119807i | 0.0564328 | − | 0.00593132i | ||||
\(409\) | 14.6875 | − | 25.4394i | 0.726248 | − | 1.25790i | −0.232210 | − | 0.972666i | \(-0.574596\pi\) |
0.958458 | − | 0.285233i | \(-0.0920711\pi\) | |||||||
\(410\) | 8.39590 | − | 14.5421i | 0.414644 | − | 0.718184i | ||||
\(411\) | 3.27951 | + | 4.51385i | 0.161766 | + | 0.222652i | ||||
\(412\) | 15.1741 | + | 26.2824i | 0.747575 | + | 1.29484i | ||||
\(413\) | −0.647932 | −0.0318826 | ||||||||
\(414\) | −44.3782 | + | 9.43289i | −2.18107 | + | 0.463601i | ||||
\(415\) | 14.8120 | 0.727091 | ||||||||
\(416\) | −13.7755 | − | 23.8598i | −0.675398 | − | 1.16982i | ||||
\(417\) | 7.59543 | − | 17.0596i | 0.371950 | − | 0.835413i | ||||
\(418\) | −0.895472 | + | 1.55100i | −0.0437989 | + | 0.0758620i | ||||
\(419\) | 6.64380 | − | 11.5074i | 0.324571 | − | 0.562173i | −0.656854 | − | 0.754017i | \(-0.728113\pi\) |
0.981425 | + | 0.191844i | \(0.0614468\pi\) | |||||||
\(420\) | −1.28716 | + | 2.89102i | −0.0628072 | + | 0.141067i | ||||
\(421\) | 8.12385 | + | 14.0709i | 0.395932 | + | 0.685774i | 0.993220 | − | 0.116253i | \(-0.0370883\pi\) |
−0.597288 | + | 0.802027i | \(0.703755\pi\) | |||||||
\(422\) | 14.6907 | 0.715133 | ||||||||
\(423\) | −0.498426 | − | 0.553558i | −0.0242343 | − | 0.0269149i | ||||
\(424\) | 0.733965 | 0.0356445 | ||||||||
\(425\) | 0.978148 | + | 1.69420i | 0.0474471 | + | 0.0821808i | ||||
\(426\) | −8.08116 | − | 11.1228i | −0.391533 | − | 0.538899i | ||||
\(427\) | −3.83603 | + | 6.64420i | −0.185638 | + | 0.321535i | ||||
\(428\) | 17.5830 | − | 30.4546i | 0.849906 | − | 1.47208i | ||||
\(429\) | −24.1749 | + | 2.54088i | −1.16717 | + | 0.122675i | ||||
\(430\) | −7.28795 | − | 12.6231i | −0.351456 | − | 0.608740i | ||||
\(431\) | −7.28753 | −0.351028 | −0.175514 | − | 0.984477i | \(-0.556159\pi\) | ||||
−0.175514 | + | 0.984477i | \(0.556159\pi\) | |||||||
\(432\) | 16.6659 | + | 15.0060i | 0.801839 | + | 0.721979i | ||||
\(433\) | −33.6740 | −1.61827 | −0.809133 | − | 0.587625i | \(-0.800063\pi\) | ||||
−0.809133 | + | 0.587625i | \(0.800063\pi\) | |||||||
\(434\) | 5.88791 | + | 10.1982i | 0.282629 | + | 0.489528i | ||||
\(435\) | 13.3944 | − | 1.40780i | 0.642210 | − | 0.0674990i | ||||
\(436\) | 15.1769 | − | 26.2872i | 0.726844 | − | 1.25893i | ||||
\(437\) | 0.894414 | − | 1.54917i | 0.0427856 | − | 0.0741069i | ||||
\(438\) | −27.0146 | − | 37.1823i | −1.29081 | − | 1.77664i | ||||
\(439\) | −18.1856 | − | 31.4984i | −0.867952 | − | 1.50334i | −0.864086 | − | 0.503345i | \(-0.832103\pi\) |
−0.00386647 | − | 0.999993i | \(-0.501231\pi\) | |||||||
\(440\) | 1.33826 | 0.0637991 | ||||||||
\(441\) | −0.927051 | + | 2.85317i | −0.0441453 | + | 0.135865i | ||||
\(442\) | 13.5759 | 0.645740 | ||||||||
\(443\) | −2.19973 | − | 3.81005i | −0.104513 | − | 0.181021i | 0.809026 | − | 0.587772i | \(-0.199995\pi\) |
−0.913539 | + | 0.406751i | \(0.866662\pi\) | |||||||
\(444\) | 9.41679 | − | 21.1505i | 0.446901 | − | 1.00376i | ||||
\(445\) | 3.06306 | − | 5.30537i | 0.145203 | − | 0.251499i | ||||
\(446\) | −17.9273 | + | 31.0510i | −0.848883 | + | 1.47031i | ||||
\(447\) | −9.98660 | + | 22.4303i | −0.472350 | + | 1.06092i | ||||
\(448\) | −3.28105 | − | 5.68295i | −0.155015 | − | 0.268494i | ||||
\(449\) | −5.79317 | −0.273397 | −0.136698 | − | 0.990613i | \(-0.543649\pi\) | ||||
−0.136698 | + | 0.990613i | \(0.543649\pi\) | |||||||
\(450\) | −1.81359 | + | 5.58164i | −0.0854932 | + | 0.263121i | ||||
\(451\) | 33.9587 | 1.59905 | ||||||||
\(452\) | −11.8884 | − | 20.5913i | −0.559183 | − | 0.968534i | ||||
\(453\) | −7.32041 | − | 10.0757i | −0.343943 | − | 0.473397i | ||||
\(454\) | −12.3500 | + | 21.3908i | −0.579612 | + | 1.00392i | ||||
\(455\) | 1.77366 | − | 3.07207i | 0.0831504 | − | 0.144021i | ||||
\(456\) | −0.134830 | + | 0.0141712i | −0.00631398 | + | 0.000663626i | ||||
\(457\) | −7.04153 | − | 12.1963i | −0.329389 | − | 0.570518i | 0.653002 | − | 0.757356i | \(-0.273509\pi\) |
−0.982391 | + | 0.186838i | \(0.940176\pi\) | |||||||
\(458\) | 0.306003 | 0.0142986 | ||||||||
\(459\) | −9.66769 | + | 3.14122i | −0.451249 | + | 0.146620i | ||||
\(460\) | 14.1244 | 0.658554 | ||||||||
\(461\) | 11.8443 | + | 20.5149i | 0.551645 | + | 0.955476i | 0.998156 | + | 0.0606986i | \(0.0193328\pi\) |
−0.446512 | + | 0.894778i | \(0.647334\pi\) | |||||||
\(462\) | −13.3321 | + | 1.40126i | −0.620265 | + | 0.0651924i | ||||
\(463\) | 7.56095 | − | 13.0959i | 0.351387 | − | 0.608620i | −0.635106 | − | 0.772425i | \(-0.719043\pi\) |
0.986493 | + | 0.163805i | \(0.0523768\pi\) | |||||||
\(464\) | −16.7799 | + | 29.0637i | −0.778989 | + | 1.34925i | ||||
\(465\) | 6.12825 | + | 8.43481i | 0.284191 | + | 0.391155i | ||||
\(466\) | −20.5201 | − | 35.5418i | −0.950574 | − | 1.64644i | ||||
\(467\) | 13.8433 | 0.640593 | 0.320296 | − | 0.947317i | \(-0.396217\pi\) | ||||
0.320296 | + | 0.947317i | \(0.396217\pi\) | |||||||
\(468\) | 13.0105 | + | 14.4496i | 0.601408 | + | 0.667932i | ||||
\(469\) | 6.61803 | 0.305592 | ||||||||
\(470\) | 0.242870 | + | 0.420662i | 0.0112027 | + | 0.0194037i | ||||
\(471\) | 1.30110 | − | 2.92232i | 0.0599516 | − | 0.134654i | ||||
\(472\) | 0.109585 | − | 0.189807i | 0.00504406 | − | 0.00873657i | ||||
\(473\) | 14.7387 | − | 25.5282i | 0.677687 | − | 1.17379i | ||||
\(474\) | 7.82947 | − | 17.5853i | 0.359619 | − | 0.807718i | ||||
\(475\) | −0.115699 | − | 0.200396i | −0.00530862 | − | 0.00919481i | ||||
\(476\) | 3.57433 | 0.163829 | ||||||||
\(477\) | −6.36721 | + | 1.35339i | −0.291534 | + | 0.0619676i | ||||
\(478\) | −6.56750 | −0.300391 | ||||||||
\(479\) | 6.78407 | + | 11.7504i | 0.309972 | + | 0.536888i | 0.978356 | − | 0.206929i | \(-0.0663469\pi\) |
−0.668384 | + | 0.743817i | \(0.733014\pi\) | |||||||
\(480\) | −7.90707 | − | 10.8831i | −0.360907 | − | 0.496745i | ||||
\(481\) | −12.9759 | + | 22.4750i | −0.591652 | + | 1.02477i | ||||
\(482\) | 10.4912 | − | 18.1712i | 0.477859 | − | 0.827677i | ||||
\(483\) | 13.3163 | − | 1.39960i | 0.605915 | − | 0.0636842i | ||||
\(484\) | −4.25006 | − | 7.36132i | −0.193185 | − | 0.334606i | ||||
\(485\) | −6.20308 | −0.281667 | ||||||||
\(486\) | −26.4100 | − | 15.2478i | −1.19798 | − | 0.691655i | ||||
\(487\) | 5.48843 | 0.248705 | 0.124352 | − | 0.992238i | \(-0.460315\pi\) | ||||
0.124352 | + | 0.992238i | \(0.460315\pi\) | |||||||
\(488\) | −1.29758 | − | 2.24747i | −0.0587387 | − | 0.101738i | ||||
\(489\) | −27.3887 | + | 2.87867i | −1.23856 | + | 0.130178i | ||||
\(490\) | 0.978148 | − | 1.69420i | 0.0441882 | − | 0.0765362i | ||||
\(491\) | 18.5490 | − | 32.1277i | 0.837103 | − | 1.44990i | −0.0552041 | − | 0.998475i | \(-0.517581\pi\) |
0.892307 | − | 0.451429i | \(-0.149086\pi\) | |||||||
\(492\) | −15.9662 | − | 21.9756i | −0.719813 | − | 0.990737i | ||||
\(493\) | −7.60591 | − | 13.1738i | −0.342553 | − | 0.593319i | ||||
\(494\) | −1.60581 | −0.0722487 | ||||||||
\(495\) | −11.6095 | + | 2.46768i | −0.521809 | + | 0.110914i | ||||
\(496\) | −25.9795 | −1.16651 | ||||||||
\(497\) | 2.02876 | + | 3.51391i | 0.0910021 | + | 0.157620i | ||||
\(498\) | 20.4137 | − | 45.8499i | 0.914759 | − | 2.05458i | ||||
\(499\) | 10.8042 | − | 18.7135i | 0.483663 | − | 0.837729i | −0.516161 | − | 0.856492i | \(-0.672639\pi\) |
0.999824 | + | 0.0187623i | \(0.00597259\pi\) | |||||||
\(500\) | 0.913545 | − | 1.58231i | 0.0408550 | − | 0.0707629i | ||||
\(501\) | 0.957841 | − | 2.15135i | 0.0427932 | − | 0.0961150i | ||||
\(502\) | −9.42597 | − | 16.3263i | −0.420702 | − | 0.728677i | ||||
\(503\) | 21.4561 | 0.956681 | 0.478340 | − | 0.878174i | \(-0.341239\pi\) | ||||
0.478340 | + | 0.878174i | \(0.341239\pi\) | |||||||
\(504\) | −0.679023 | − | 0.754131i | −0.0302461 | − | 0.0335917i | ||||
\(505\) | −3.06665 | −0.136464 | ||||||||
\(506\) | 29.9160 | + | 51.8160i | 1.32993 | + | 2.30350i | ||||
\(507\) | 0.424062 | + | 0.583672i | 0.0188333 | + | 0.0259218i | ||||
\(508\) | −9.86714 | + | 17.0904i | −0.437784 | + | 0.758263i | ||||
\(509\) | 7.45748 | − | 12.9167i | 0.330547 | − | 0.572524i | −0.652072 | − | 0.758157i | \(-0.726100\pi\) |
0.982619 | + | 0.185633i | \(0.0594335\pi\) | |||||||
\(510\) | 6.59240 | − | 0.692889i | 0.291917 | − | 0.0306817i | ||||
\(511\) | 6.78194 | + | 11.7467i | 0.300015 | + | 0.519642i | ||||
\(512\) | 30.6006 | 1.35237 | ||||||||
\(513\) | 1.14353 | − | 0.371555i | 0.0504880 | − | 0.0164045i | ||||
\(514\) | 48.2014 | 2.12607 | ||||||||
\(515\) | −8.30507 | − | 14.3848i | −0.365965 | − | 0.633870i | ||||
\(516\) | −23.4497 | + | 2.46466i | −1.03231 | + | 0.108501i | ||||
\(517\) | −0.491165 | + | 0.850723i | −0.0216014 | + | 0.0374147i | ||||
\(518\) | −7.15605 | + | 12.3946i | −0.314419 | + | 0.544589i | ||||
\(519\) | −5.08942 | − | 7.00498i | −0.223401 | − | 0.307485i | ||||
\(520\) | 0.599960 | + | 1.03916i | 0.0263100 | + | 0.0455702i | ||||
\(521\) | 22.6100 | 0.990563 | 0.495281 | − | 0.868733i | \(-0.335065\pi\) | ||||
0.495281 | + | 0.868733i | \(0.335065\pi\) | |||||||
\(522\) | 14.1021 | − | 43.4019i | 0.617233 | − | 1.89965i | ||||
\(523\) | −37.1387 | −1.62396 | −0.811982 | − | 0.583683i | \(-0.801611\pi\) | ||||
−0.811982 | + | 0.583683i | \(0.801611\pi\) | |||||||
\(524\) | −12.7565 | − | 22.0949i | −0.557270 | − | 0.965220i | ||||
\(525\) | 0.704489 | − | 1.58231i | 0.0307464 | − | 0.0690575i | ||||
\(526\) | −14.0699 | + | 24.3697i | −0.613475 | + | 1.06257i | ||||
\(527\) | 5.88791 | − | 10.1982i | 0.256482 | − | 0.444239i | ||||
\(528\) | 12.0292 | − | 27.0180i | 0.523503 | − | 1.17581i | ||||
\(529\) | −18.3807 | − | 31.8362i | −0.799159 | − | 1.38418i | ||||
\(530\) | 4.24481 | 0.184383 | ||||||||
\(531\) | −0.600666 | + | 1.84866i | −0.0260667 | + | 0.0802249i | ||||
\(532\) | −0.422784 | −0.0183300 | ||||||||
\(533\) | 15.2241 | + | 26.3690i | 0.659431 | + | 1.14217i | ||||
\(534\) | −12.2011 | − | 16.7934i | −0.527993 | − | 0.726720i | ||||
\(535\) | −9.62349 | + | 16.6684i | −0.416060 | + | 0.720637i | ||||
\(536\) | −1.11931 | + | 1.93871i | −0.0483469 | + | 0.0837393i | ||||
\(537\) | 35.9112 | − | 3.77441i | 1.54968 | − | 0.162878i | ||||
\(538\) | −13.3995 | − | 23.2086i | −0.577694 | − | 1.00060i | ||||
\(539\) | 3.95630 | 0.170410 | ||||||||
\(540\) | 7.05530 | + | 6.35262i | 0.303612 | + | 0.273373i | ||||
\(541\) | −38.7201 | −1.66471 | −0.832355 | − | 0.554244i | \(-0.813008\pi\) | ||||
−0.832355 | + | 0.554244i | \(0.813008\pi\) | |||||||
\(542\) | 1.40711 | + | 2.43718i | 0.0604405 | + | 0.104686i | ||||
\(543\) | −13.1724 | + | 1.38447i | −0.565280 | + | 0.0594133i | ||||
\(544\) | −7.59697 | + | 13.1583i | −0.325717 | + | 0.564159i | ||||
\(545\) | −8.30662 | + | 14.3875i | −0.355816 | + | 0.616292i | ||||
\(546\) | −7.06503 | − | 9.72418i | −0.302355 | − | 0.416156i | ||||
\(547\) | 8.96478 | + | 15.5275i | 0.383306 | + | 0.663906i | 0.991533 | − | 0.129858i | \(-0.0414521\pi\) |
−0.608226 | + | 0.793764i | \(0.708119\pi\) | |||||||
\(548\) | −5.88558 | −0.251419 | ||||||||
\(549\) | 15.4008 | + | 17.1043i | 0.657291 | + | 0.729996i | ||||
\(550\) | 7.73968 | 0.330021 | ||||||||
\(551\) | 0.899654 | + | 1.55825i | 0.0383265 | + | 0.0663835i | ||||
\(552\) | −1.84220 | + | 4.13764i | −0.0784091 | + | 0.176110i | ||||
\(553\) | −2.84049 | + | 4.91988i | −0.120790 | + | 0.209215i | ||||
\(554\) | −17.8554 | + | 30.9264i | −0.758602 | + | 1.31394i | ||||
\(555\) | −5.15398 | + | 11.5760i | −0.218774 | + | 0.491375i | ||||
\(556\) | 9.84937 | + | 17.0596i | 0.417706 | + | 0.723488i | ||||
\(557\) | −18.9035 | −0.800968 | −0.400484 | − | 0.916304i | \(-0.631158\pi\) | ||||
−0.400484 | + | 0.916304i | \(0.631158\pi\) | |||||||
\(558\) | 34.5555 | − | 7.34500i | 1.46285 | − | 0.310939i | ||||
\(559\) | 26.4303 | 1.11788 | ||||||||
\(560\) | 2.15796 | + | 3.73770i | 0.0911905 | + | 0.157947i | ||||
\(561\) | 7.87957 | + | 10.8453i | 0.332676 | + | 0.457889i | ||||
\(562\) | −5.70619 | + | 9.88341i | −0.240701 | + | 0.416907i | ||||
\(563\) | −17.1129 | + | 29.6405i | −0.721224 | + | 1.24920i | 0.239285 | + | 0.970949i | \(0.423087\pi\) |
−0.960509 | + | 0.278248i | \(0.910246\pi\) | |||||||
\(564\) | 0.781455 | − | 0.0821342i | 0.0329052 | − | 0.00345847i | ||||
\(565\) | 6.50674 | + | 11.2700i | 0.273741 | + | 0.474133i | ||||
\(566\) | −27.0267 | −1.13602 | ||||||||
\(567\) | 7.28115 | + | 5.29007i | 0.305780 | + | 0.222162i | ||||
\(568\) | −1.37250 | −0.0575888 | ||||||||
\(569\) | −5.87973 | − | 10.1840i | −0.246491 | − | 0.426935i | 0.716059 | − | 0.698040i | \(-0.245944\pi\) |
−0.962550 | + | 0.271105i | \(0.912611\pi\) | |||||||
\(570\) | −0.779773 | + | 0.0819574i | −0.0326611 | + | 0.00343282i | ||||
\(571\) | 9.85140 | − | 17.0631i | 0.412268 | − | 0.714070i | −0.582869 | − | 0.812566i | \(-0.698070\pi\) |
0.995137 | + | 0.0984964i | \(0.0314033\pi\) | |||||||
\(572\) | 12.8209 | − | 22.2065i | 0.536069 | − | 0.928499i | ||||
\(573\) | −11.0195 | − | 15.1670i | −0.460346 | − | 0.633612i | ||||
\(574\) | 8.39590 | + | 14.5421i | 0.350438 | + | 0.606976i | ||||
\(575\) | −7.73054 | −0.322386 | ||||||||
\(576\) | −19.2561 | + | 4.09301i | −0.802338 | + | 0.170542i | ||||
\(577\) | 21.9439 | 0.913538 | 0.456769 | − | 0.889585i | \(-0.349007\pi\) | ||||
0.456769 | + | 0.889585i | \(0.349007\pi\) | |||||||
\(578\) | 12.8850 | + | 22.3176i | 0.535947 | + | 0.928288i | ||||
\(579\) | −6.13440 | + | 13.7781i | −0.254937 | + | 0.572598i | ||||
\(580\) | −7.10357 | + | 12.3038i | −0.294960 | + | 0.510885i | ||||
\(581\) | −7.40599 | + | 12.8275i | −0.307252 | + | 0.532176i | ||||
\(582\) | −8.54901 | + | 19.2014i | −0.354368 | + | 0.795923i | ||||
\(583\) | 4.29222 | + | 7.43435i | 0.177766 | + | 0.307899i | ||||
\(584\) | −4.58814 | −0.189858 | ||||||||
\(585\) | −7.12086 | − | 7.90851i | −0.294411 | − | 0.326977i | ||||
\(586\) | 27.0927 | 1.11919 | ||||||||
\(587\) | −0.427820 | − | 0.741005i | −0.0176580 | − | 0.0305846i | 0.857061 | − | 0.515214i | \(-0.172288\pi\) |
−0.874719 | + | 0.484630i | \(0.838954\pi\) | |||||||
\(588\) | −1.86011 | − | 2.56023i | −0.0767098 | − | 0.105582i | ||||
\(589\) | −0.696443 | + | 1.20628i | −0.0286964 | + | 0.0497037i | ||||
\(590\) | 0.633773 | − | 1.09773i | 0.0260920 | − | 0.0451927i | ||||
\(591\) | −44.9729 | + | 4.72684i | −1.84994 | + | 0.194436i | ||||
\(592\) | −15.7875 | − | 27.3447i | −0.648861 | − | 1.12386i | ||||
\(593\) | 12.4833 | 0.512628 | 0.256314 | − | 0.966594i | \(-0.417492\pi\) | ||||
0.256314 | + | 0.966594i | \(0.417492\pi\) | |||||||
\(594\) | −8.36149 | + | 39.3377i | −0.343076 | + | 1.61405i | ||||
\(595\) | −1.95630 | −0.0802003 | ||||||||
\(596\) | −12.9501 | − | 22.4303i | −0.530458 | − | 0.918779i | ||||
\(597\) | −6.54155 | + | 0.687544i | −0.267728 | + | 0.0281393i | ||||
\(598\) | −26.8234 | + | 46.4596i | −1.09689 | + | 1.89987i | ||||
\(599\) | 1.86633 | − | 3.23258i | 0.0762562 | − | 0.132080i | −0.825376 | − | 0.564584i | \(-0.809037\pi\) |
0.901632 | + | 0.432504i | \(0.142370\pi\) | |||||||
\(600\) | 0.344375 | + | 0.473991i | 0.0140590 | + | 0.0193506i | ||||
\(601\) | 8.95613 | + | 15.5125i | 0.365328 | + | 0.632767i | 0.988829 | − | 0.149056i | \(-0.0476234\pi\) |
−0.623501 | + | 0.781823i | \(0.714290\pi\) | |||||||
\(602\) | 14.5759 | 0.594070 | ||||||||
\(603\) | 6.13525 | − | 18.8824i | 0.249847 | − | 0.768950i | ||||
\(604\) | 13.1376 | 0.534562 | ||||||||
\(605\) | 2.32614 | + | 4.02899i | 0.0945709 | + | 0.163802i | ||||
\(606\) | −4.22642 | + | 9.49269i | −0.171686 | + | 0.385614i | ||||
\(607\) | −22.2438 | + | 38.5274i | −0.902849 | + | 1.56378i | −0.0790694 | + | 0.996869i | \(0.525195\pi\) |
−0.823779 | + | 0.566911i | \(0.808138\pi\) | |||||||
\(608\) | 0.898597 | − | 1.55642i | 0.0364429 | − | 0.0631210i | ||||
\(609\) | −5.47798 | + | 12.3038i | −0.221979 | + | 0.498573i | ||||
\(610\) | −7.50440 | − | 12.9980i | −0.303844 | − | 0.526274i | ||||
\(611\) | −0.880783 | −0.0356327 | ||||||||
\(612\) | 3.31359 | − | 10.1982i | 0.133944 | − | 0.412236i | ||||
\(613\) | 27.1824 | 1.09789 | 0.548943 | − | 0.835860i | \(-0.315031\pi\) | ||||
0.548943 | + | 0.835860i | \(0.315031\pi\) | |||||||
\(614\) | −31.7043 | − | 54.9134i | −1.27948 | − | 2.21613i | ||||
\(615\) | 8.73860 | + | 12.0277i | 0.352374 | + | 0.485002i | ||||
\(616\) | −0.669131 | + | 1.15897i | −0.0269600 | + | 0.0466962i | ||||
\(617\) | 18.4977 | − | 32.0390i | 0.744690 | − | 1.28984i | −0.205649 | − | 0.978626i | \(-0.565930\pi\) |
0.950339 | − | 0.311216i | \(-0.100736\pi\) | |||||||
\(618\) | −55.9735 | + | 5.88306i | −2.25159 | + | 0.236651i | ||||
\(619\) | 12.7730 | + | 22.1234i | 0.513389 | + | 0.889215i | 0.999879 | + | 0.0155296i | \(0.00494344\pi\) |
−0.486491 | + | 0.873686i | \(0.661723\pi\) | |||||||
\(620\) | −10.9981 | −0.441694 | ||||||||
\(621\) | 8.35162 | − | 39.2913i | 0.335139 | − | 1.57671i | ||||
\(622\) | −59.4272 | −2.38282 | ||||||||
\(623\) | 3.06306 | + | 5.30537i | 0.122719 | + | 0.212555i | ||||
\(624\) | 26.3723 | − | 2.77184i | 1.05574 | − | 0.110963i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 24.0969 | − | 41.7371i | 0.963106 | − | 1.66815i | ||||
\(627\) | −0.932023 | − | 1.28282i | −0.0372214 | − | 0.0512309i | ||||
\(628\) | 1.68720 | + | 2.92232i | 0.0673268 | + | 0.116613i | ||||
\(629\) | 14.3121 | 0.570661 | ||||||||
\(630\) | −3.92705 | − | 4.36143i | −0.156457 | − | 0.173764i | ||||
\(631\) | −24.6348 | −0.980696 | −0.490348 | − | 0.871527i | \(-0.663130\pi\) | ||||
−0.490348 | + | 0.871527i | \(0.663130\pi\) | |||||||
\(632\) | −0.960829 | − | 1.66420i | −0.0382197 | − | 0.0661985i | ||||
\(633\) | −5.29033 | + | 11.8823i | −0.210272 | + | 0.472278i | ||||
\(634\) | −18.6792 | + | 32.3533i | −0.741844 | + | 1.28491i | ||||
\(635\) | 5.40047 | − | 9.35388i | 0.214311 | − | 0.371197i | ||||
\(636\) | 2.79291 | − | 6.27299i | 0.110746 | − | 0.248740i | ||||
\(637\) | 1.77366 | + | 3.07207i | 0.0702749 | + | 0.121720i | ||||
\(638\) | −60.1824 | −2.38265 | ||||||||
\(639\) | 11.9065 | − | 2.53081i | 0.471015 | − | 0.100117i | ||||
\(640\) | −2.69598 | −0.106568 | ||||||||
\(641\) | 20.5715 | + | 35.6309i | 0.812525 | + | 1.40734i | 0.911091 | + | 0.412205i | \(0.135241\pi\) |
−0.0985659 | + | 0.995131i | \(0.531426\pi\) | |||||||
\(642\) | 38.3333 | + | 52.7613i | 1.51290 | + | 2.08232i | ||||
\(643\) | −3.80747 | + | 6.59473i | −0.150152 | + | 0.260071i | −0.931283 | − | 0.364296i | \(-0.881310\pi\) |
0.781131 | + | 0.624367i | \(0.214643\pi\) | |||||||
\(644\) | −7.06220 | + | 12.2321i | −0.278290 | + | 0.482012i | ||||
\(645\) | 12.8344 | − | 1.34895i | 0.505355 | − | 0.0531149i | ||||
\(646\) | 0.442790 | + | 0.766934i | 0.0174213 | + | 0.0301746i | ||||
\(647\) | −22.2127 | −0.873270 | −0.436635 | − | 0.899639i | \(-0.643830\pi\) | ||||
−0.436635 | + | 0.899639i | \(0.643830\pi\) | |||||||
\(648\) | −2.78115 | + | 1.23825i | −0.109254 | + | 0.0486430i | ||||
\(649\) | 2.56341 | 0.100623 | ||||||||
\(650\) | 3.46980 | + | 6.00987i | 0.136097 | + | 0.235727i | ||||
\(651\) | −10.3689 | + | 1.08981i | −0.406389 | + | 0.0427132i | ||||
\(652\) | 14.5253 | − | 25.1586i | 0.568856 | − | 0.985288i | ||||
\(653\) | −2.17886 | + | 3.77389i | −0.0852653 | + | 0.147684i | −0.905504 | − | 0.424337i | \(-0.860507\pi\) |
0.820239 | + | 0.572021i | \(0.193840\pi\) | |||||||
\(654\) | 33.0878 | + | 45.5415i | 1.29384 | + | 1.78081i | ||||
\(655\) | 6.98186 | + | 12.0929i | 0.272804 | + | 0.472510i | ||||
\(656\) | −37.0456 | −1.44639 | ||||||||
\(657\) | 39.8024 | − | 8.46027i | 1.55284 | − | 0.330067i | ||||
\(658\) | −0.485739 | −0.0189361 | ||||||||
\(659\) | −14.8386 | − | 25.7011i | −0.578028 | − | 1.00117i | −0.995705 | − | 0.0925789i | \(-0.970489\pi\) |
0.417677 | − | 0.908596i | \(-0.362844\pi\) | |||||||
\(660\) | 5.09240 | − | 11.4377i | 0.198222 | − | 0.445213i | ||||
\(661\) | 0.458240 | − | 0.793695i | 0.0178235 | − | 0.0308711i | −0.856976 | − | 0.515356i | \(-0.827660\pi\) |
0.874800 | + | 0.484485i | \(0.160993\pi\) | |||||||
\(662\) | −11.7798 | + | 20.4032i | −0.457835 | + | 0.792994i | ||||
\(663\) | −4.88887 | + | 10.9806i | −0.189868 | + | 0.426450i | ||||
\(664\) | −2.50516 | − | 4.33906i | −0.0972190 | − | 0.168388i | ||||
\(665\) | 0.231398 | 0.00897321 | ||||||||
\(666\) | 28.7300 | + | 31.9079i | 1.11326 | + | 1.23641i | ||||
\(667\) | 60.1114 | 2.32752 | ||||||||
\(668\) | 1.24208 | + | 2.15135i | 0.0480575 | + | 0.0832380i | ||||
\(669\) | −18.6591 | − | 25.6820i | −0.721401 | − | 0.992924i | ||||
\(670\) | −6.47341 | + | 11.2123i | −0.250090 | + | 0.433168i | ||||
\(671\) | 15.1765 | − | 26.2864i | 0.585881 | − | 1.01478i | ||||
\(672\) | 13.3786 | − | 1.40615i | 0.516091 | − | 0.0542434i | ||||
\(673\) | 14.6539 | + | 25.3813i | 0.564867 | + | 0.978378i | 0.997062 | + | 0.0765981i | \(0.0244058\pi\) |
−0.432195 | + | 0.901780i | \(0.642261\pi\) | |||||||
\(674\) | 21.5567 | 0.830331 | ||||||||
\(675\) | −3.86149 | − | 3.47690i | −0.148629 | − | 0.133826i | ||||
\(676\) | −0.761046 | −0.0292710 | ||||||||
\(677\) | −13.7620 | − | 23.8364i | −0.528915 | − | 0.916108i | −0.999431 | − | 0.0337165i | \(-0.989266\pi\) |
0.470516 | − | 0.882391i | \(-0.344068\pi\) | |||||||
\(678\) | 43.8533 | − | 4.60917i | 1.68418 | − | 0.177014i | ||||
\(679\) | 3.10154 | − | 5.37202i | 0.119026 | − | 0.206159i | ||||
\(680\) | 0.330869 | − | 0.573083i | 0.0126883 | − | 0.0219767i | ||||
\(681\) | −12.8541 | − | 17.6921i | −0.492569 | − | 0.677963i | ||||
\(682\) | −23.2943 | − | 40.3470i | −0.891986 | − | 1.54496i | ||||
\(683\) | −36.1320 | −1.38255 | −0.691276 | − | 0.722591i | \(-0.742951\pi\) | ||||
−0.691276 | + | 0.722591i | \(0.742951\pi\) | |||||||
\(684\) | −0.391943 | + | 1.20628i | −0.0149863 | + | 0.0461231i | ||||
\(685\) | 3.22128 | 0.123079 | ||||||||
\(686\) | 0.978148 | + | 1.69420i | 0.0373458 | + | 0.0646849i | ||||
\(687\) | −0.110196 | + | 0.247504i | −0.00420423 | + | 0.00944285i | ||||
\(688\) | −16.0785 | + | 27.8487i | −0.612986 | + | 1.06172i | ||||
\(689\) | −3.84852 | + | 6.66583i | −0.146617 | + | 0.253948i | ||||
\(690\) | −10.6541 | + | 23.9296i | −0.405596 | + | 0.910984i | ||||
\(691\) | −13.7504 | − | 23.8163i | −0.523088 | − | 0.906015i | −0.999639 | − | 0.0268681i | \(-0.991447\pi\) |
0.476551 | − | 0.879147i | \(-0.341887\pi\) | |||||||
\(692\) | 9.13375 | 0.347213 | ||||||||
\(693\) | 3.66769 | − | 11.2880i | 0.139324 | − | 0.428795i | ||||
\(694\) | 60.3740 | 2.29177 | ||||||||
\(695\) | −5.39074 | − | 9.33703i | −0.204482 | − | 0.354174i | ||||
\(696\) | −2.67780 | − | 3.68568i | −0.101502 | − | 0.139705i | ||||
\(697\) | 8.39590 | − | 14.5421i | 0.318017 | − | 0.550822i | ||||
\(698\) | 7.71569 | − | 13.3640i | 0.292043 | − | 0.505834i | ||||
\(699\) | 36.1368 | − | 3.79813i | 1.36682 | − | 0.143658i | ||||
\(700\) | 0.913545 | + | 1.58231i | 0.0345288 | + | 0.0598056i | ||||
\(701\) | 0.206128 | 0.00778534 | 0.00389267 | − | 0.999992i | \(-0.498761\pi\) | ||||
0.00389267 | + | 0.999992i | \(0.498761\pi\) | |||||||
\(702\) | −34.2944 | + | 11.1429i | −1.29436 | + | 0.420562i | ||||
\(703\) | −1.69289 | −0.0638484 | ||||||||
\(704\) | 12.9808 | + | 22.4834i | 0.489233 | + | 0.847376i | ||||
\(705\) | −0.427704 | + | 0.0449535i | −0.0161083 | + | 0.00169305i | ||||
\(706\) | 25.5234 | − | 44.2078i | 0.960585 | − | 1.66378i | ||||
\(707\) | 1.53332 | − | 2.65580i | 0.0576666 | − | 0.0998815i | ||||
\(708\) | −1.20523 | − | 1.65885i | −0.0452952 | − | 0.0623435i | ||||
\(709\) | 23.1935 | + | 40.1723i | 0.871049 | + | 1.50870i | 0.860913 | + | 0.508753i | \(0.169893\pi\) |
0.0101367 | + | 0.999949i | \(0.496773\pi\) | |||||||
\(710\) | −7.93769 | −0.297896 | ||||||||
\(711\) | 11.4040 | + | 12.6654i | 0.427682 | + | 0.474989i | ||||
\(712\) | −2.07223 | −0.0776600 | ||||||||
\(713\) | 23.2668 | + | 40.2993i | 0.871350 | + | 1.50922i | ||||
\(714\) | −2.69614 | + | 6.05563i | −0.100901 | + | 0.226626i | ||||
\(715\) | −7.01712 | + | 12.1540i | −0.262425 | + | 0.454534i | ||||
\(716\) | −19.0452 | + | 32.9872i | −0.711751 | + | 1.23279i | ||||
\(717\) | 2.36505 | − | 5.31198i | 0.0883243 | − | 0.198380i | ||||
\(718\) | 25.5727 | + | 44.2932i | 0.954364 | + | 1.65301i | ||||
\(719\) | 18.5632 | 0.692292 | 0.346146 | − | 0.938181i | \(-0.387490\pi\) | ||||
0.346146 | + | 0.938181i | \(0.387490\pi\) | |||||||
\(720\) | 12.6648 | − | 2.69199i | 0.471990 | − | 0.100325i | ||||
\(721\) | 16.6101 | 0.618594 | ||||||||
\(722\) | 18.5324 | + | 32.0991i | 0.689706 | + | 1.19461i | ||||
\(723\) | 10.9194 | + | 15.0293i | 0.406097 | + | 0.558944i | ||||
\(724\) | 6.98584 | − | 12.0998i | 0.259627 | − | 0.449687i | ||||
\(725\) | 3.88791 | − | 6.73407i | 0.144394 | − | 0.250097i | ||||
\(726\) | 15.6774 | − | 1.64776i | 0.581843 | − | 0.0611542i | ||||
\(727\) | 17.6537 | + | 30.5770i | 0.654738 | + | 1.13404i | 0.981959 | + | 0.189091i | \(0.0605542\pi\) |
−0.327222 | + | 0.944948i | \(0.606112\pi\) | |||||||
\(728\) | −1.19992 | −0.0444720 | ||||||||
\(729\) | 21.8435 | − | 15.8702i | 0.809017 | − | 0.587785i | ||||
\(730\) | −26.5350 | −0.982103 | ||||||||
\(731\) | −7.28795 | − | 12.6231i | −0.269555 | − | 0.466882i | ||||
\(732\) | −24.1461 | + | 2.53786i | −0.892465 | + | 0.0938019i | ||||
\(733\) | −8.85865 | + | 15.3436i | −0.327202 | + | 0.566730i | −0.981955 | − | 0.189112i | \(-0.939439\pi\) |
0.654754 | + | 0.755842i | \(0.272772\pi\) | |||||||
\(734\) | −6.26647 | + | 10.8538i | −0.231300 | + | 0.400623i | ||||
\(735\) | 1.01807 | + | 1.40126i | 0.0375522 | + | 0.0516862i | ||||
\(736\) | −30.0204 | − | 51.9968i | −1.10657 | − | 1.91663i | ||||
\(737\) | −26.1829 | −0.964459 | ||||||||
\(738\) | 49.2746 | − | 10.4736i | 1.81382 | − | 0.385540i | ||||
\(739\) | 21.8311 | 0.803068 | 0.401534 | − | 0.915844i | \(-0.368477\pi\) | ||||
0.401534 | + | 0.915844i | \(0.368477\pi\) | |||||||
\(740\) | −6.68343 | − | 11.5760i | −0.245688 | − | 0.425543i | ||||
\(741\) | 0.578273 | − | 1.29882i | 0.0212434 | − | 0.0477134i | ||||
\(742\) | −2.12240 | + | 3.67611i | −0.0779159 | + | 0.134954i | ||||
\(743\) | 20.8738 | − | 36.1545i | 0.765786 | − | 1.32638i | −0.174044 | − | 0.984738i | \(-0.555683\pi\) |
0.939830 | − | 0.341642i | \(-0.110983\pi\) | |||||||
\(744\) | 1.43444 | − | 3.22181i | 0.0525892 | − | 0.118117i | ||||
\(745\) | 7.08783 | + | 12.2765i | 0.259678 | + | 0.449776i | ||||
\(746\) | −26.0445 | −0.953556 | ||||||||
\(747\) | 29.7334 | + | 33.0223i | 1.08789 | + | 1.20822i | ||||
\(748\) | −14.1411 | −0.517050 | ||||||||
\(749\) | −9.62349 | − | 16.6684i | −0.351635 | − | 0.609049i | ||||
\(750\) | 1.99165 | + | 2.74128i | 0.0727249 | + | 0.100097i | ||||
\(751\) | 3.83979 | − | 6.65070i | 0.140116 | − | 0.242688i | −0.787424 | − | 0.616411i | \(-0.788586\pi\) |
0.927540 | + | 0.373724i | \(0.121919\pi\) | |||||||
\(752\) | 0.535812 | − | 0.928053i | 0.0195390 | − | 0.0338426i | ||||
\(753\) | 16.5996 | − | 1.74468i | 0.604922 | − | 0.0635798i | ||||
\(754\) | −26.9806 | − | 46.7317i | −0.982575 | − | 1.70187i | ||||
\(755\) | −7.19045 | −0.261687 | ||||||||
\(756\) | −9.02918 | + | 2.93376i | −0.328388 | + | 0.106700i | ||||
\(757\) | 18.4236 | 0.669617 | 0.334808 | − | 0.942286i | \(-0.391328\pi\) | ||||
0.334808 | + | 0.942286i | \(0.391328\pi\) | |||||||
\(758\) | 8.94039 | + | 15.4852i | 0.324730 | + | 0.562448i | ||||
\(759\) | −52.6834 | + | 5.53725i | −1.91229 | + | 0.200989i | ||||
\(760\) | −0.0391364 | + | 0.0677862i | −0.00141963 | + | 0.00245887i | ||||
\(761\) | 19.4522 | − | 33.6921i | 0.705140 | − | 1.22134i | −0.261501 | − | 0.965203i | \(-0.584217\pi\) |
0.966641 | − | 0.256135i | \(-0.0824492\pi\) | |||||||
\(762\) | −21.5117 | − | 29.6083i | −0.779287 | − | 1.07260i | ||||
\(763\) | −8.30662 | − | 14.3875i | −0.300720 | − | 0.520862i | ||||
\(764\) | 19.7762 | 0.715478 | ||||||||
\(765\) | −1.81359 | + | 5.58164i | −0.0655703 | + | 0.201805i | ||||
\(766\) | −18.9141 | −0.683394 | ||||||||
\(767\) | 1.14921 | + | 1.99049i | 0.0414956 | + | 0.0718724i | ||||
\(768\) | −12.9614 | + | 29.1118i | −0.467705 | + | 1.05048i | ||||
\(769\) | 4.40099 | − | 7.62275i | 0.158704 | − | 0.274883i | −0.775698 | − | 0.631105i | \(-0.782602\pi\) |
0.934402 | + | 0.356221i | \(0.115935\pi\) | |||||||
\(770\) | −3.86984 | + | 6.70276i | −0.139459 | + | 0.241551i | ||||
\(771\) | −17.3580 | + | 38.9866i | −0.625132 | + | 1.40407i | ||||
\(772\) | −7.95479 | − | 13.7781i | −0.286299 | − | 0.495885i | ||||
\(773\) | −25.5896 | −0.920394 | −0.460197 | − | 0.887817i | \(-0.652221\pi\) | ||||
−0.460197 | + | 0.887817i | \(0.652221\pi\) | |||||||
\(774\) | 13.5126 | − | 41.5875i | 0.485701 | − | 1.49483i | ||||
\(775\) | 6.01945 | 0.216225 | ||||||||
\(776\) | 1.04913 | + | 1.81715i | 0.0376616 | + | 0.0652318i | ||||
\(777\) | −7.44815 | − | 10.2515i | −0.267201 | − | 0.367770i | ||||
\(778\) | −7.23909 | + | 12.5385i | −0.259534 | + | 0.449526i | ||||
\(779\) | −0.993096 | + | 1.72009i | −0.0355814 | + | 0.0616287i | ||||
\(780\) | 11.1644 | − | 1.17343i | 0.399750 | − | 0.0420154i | ||||
\(781\) | −8.02636 | − | 13.9021i | −0.287206 | − | 0.497455i | ||||
\(782\) | 29.5855 | 1.05798 | ||||||||
\(783\) | 30.0263 | + | 27.0358i | 1.07305 | + | 0.966181i | ||||
\(784\) | −4.31592 | −0.154140 | ||||||||
\(785\) | −0.923438 | − | 1.59944i | −0.0329589 | − | 0.0570865i | ||||
\(786\) | 47.0555 | − | 4.94574i | 1.67842 | − | 0.176409i | ||||
\(787\) | −1.25597 | + | 2.17541i | −0.0447705 | + | 0.0775449i | −0.887542 | − | 0.460726i | \(-0.847589\pi\) |
0.842772 | + | 0.538271i | \(0.180922\pi\) | |||||||
\(788\) | 23.8509 | − | 41.3111i | 0.849655 | − | 1.47165i | ||||
\(789\) | −14.6442 | − | 20.1560i | −0.521346 | − | 0.717572i | ||||
\(790\) | −5.55685 | − | 9.62474i | −0.197704 | − | 0.342433i | ||||
\(791\) | −13.0135 | −0.462706 | ||||||||
\(792\) | 2.68641 | + | 2.98357i | 0.0954576 | + | 0.106016i | ||||
\(793\) | 27.2152 | 0.966441 | ||||||||
\(794\) | 20.1721 | + | 34.9391i | 0.715882 | + | 1.23994i | ||||
\(795\) | −1.52861 | + | 3.43332i | −0.0542143 | + | 0.121767i | ||||
\(796\) | 3.46925 | − | 6.00892i | 0.122964 | − | 0.212980i | ||||
\(797\) | −16.9635 | + | 29.3816i | −0.600878 | + | 1.04075i | 0.391810 | + | 0.920046i | \(0.371849\pi\) |
−0.992688 | + | 0.120705i | \(0.961484\pi\) | |||||||
\(798\) | 0.318909 | − | 0.716282i | 0.0112893 | − | 0.0253561i | ||||
\(799\) | 0.242870 | + | 0.420662i | 0.00859211 | + | 0.0148820i | ||||
\(800\) | −7.76669 | −0.274594 | ||||||||
\(801\) | 17.9767 | − | 3.82107i | 0.635177 | − | 0.135011i | ||||
\(802\) | 21.8500 | 0.771552 | ||||||||
\(803\) | −26.8314 | − | 46.4733i | −0.946858 | − | 1.64001i | ||||
\(804\) | 12.3103 | + | 16.9437i | 0.434151 | + | 0.597557i | ||||
\(805\) | 3.86527 | − | 6.69485i | 0.136233 | − | 0.235962i | ||||
\(806\) | 20.8863 | − | 36.1761i | 0.735689 | − | 1.27425i | ||||
\(807\) | 23.5971 | − | 2.48016i | 0.830659 | − | 0.0873058i | ||||
\(808\) | 0.518664 | + | 0.898353i | 0.0182465 | + | 0.0316039i | ||||
\(809\) | −19.0145 | −0.668513 | −0.334256 | − | 0.942482i | \(-0.608485\pi\) | ||||
−0.334256 | + | 0.942482i | \(0.608485\pi\) | |||||||
\(810\) | −16.0845 | + | 7.16127i | −0.565151 | + | 0.251621i | ||||
\(811\) | 47.0454 | 1.65199 | 0.825994 | − | 0.563679i | \(-0.190614\pi\) | ||||
0.825994 | + | 0.563679i | \(0.190614\pi\) | |||||||
\(812\) | −7.10357 | − | 12.3038i | −0.249287 | − | 0.431777i | ||||
\(813\) | −2.47798 | + | 0.260446i | −0.0869066 | + | 0.00913426i | ||||
\(814\) | 28.3114 | − | 49.0369i | 0.992316 | − | 1.71874i | ||||
\(815\) | −7.94998 | + | 13.7698i | −0.278476 | + | 0.482334i | ||||
\(816\) | −8.59582 | − | 11.8311i | −0.300914 | − | 0.414172i | ||||
\(817\) | 0.862045 | + | 1.49311i | 0.0301591 | + | 0.0522372i | ||||
\(818\) | −57.4660 | −2.00925 | ||||||||
\(819\) | 10.4094 | − | 2.21259i | 0.363734 | − | 0.0773140i | ||||
\(820\) | −15.6828 | −0.547666 | ||||||||
\(821\) | −3.14464 | − | 5.44668i | −0.109749 | − | 0.190090i | 0.805920 | − | 0.592025i | \(-0.201671\pi\) |
−0.915668 | + | 0.401934i | \(0.868338\pi\) | |||||||
\(822\) | 4.43953 | − | 9.97136i | 0.154847 | − | 0.347791i | ||||
\(823\) | −15.9300 | + | 27.5916i | −0.555285 | + | 0.961783i | 0.442596 | + | 0.896721i | \(0.354058\pi\) |
−0.997881 | + | 0.0650614i | \(0.979276\pi\) | |||||||
\(824\) | −2.80928 | + | 4.86582i | −0.0978661 | + | 0.169509i | ||||
\(825\) | −2.78716 | + | 6.26007i | −0.0970366 | + | 0.217948i | ||||
\(826\) | 0.633773 | + | 1.09773i | 0.0220518 | + | 0.0381948i | ||||
\(827\) | −15.0182 | −0.522235 | −0.261117 | − | 0.965307i | \(-0.584091\pi\) | ||||
−0.261117 | + | 0.965307i | \(0.584091\pi\) | |||||||
\(828\) | 28.3532 | + | 31.4894i | 0.985343 | + | 1.09433i | ||||
\(829\) | −45.7077 | −1.58749 | −0.793747 | − | 0.608248i | \(-0.791873\pi\) | ||||
−0.793747 | + | 0.608248i | \(0.791873\pi\) | |||||||
\(830\) | −14.4883 | − | 25.0945i | −0.502896 | − | 0.871042i | ||||
\(831\) | −18.5842 | − | 25.5789i | −0.644678 | − | 0.887323i | ||||
\(832\) | −11.6389 | + | 20.1592i | −0.403507 | + | 0.698895i | ||||
\(833\) | 0.978148 | − | 1.69420i | 0.0338908 | − | 0.0587006i | ||||
\(834\) | −36.3319 | + | 3.81863i | −1.25807 | + | 0.132228i | ||||
\(835\) | −0.679813 | − | 1.17747i | −0.0235259 | − | 0.0407480i | ||||
\(836\) | 1.67266 | 0.0578501 | ||||||||
\(837\) | −6.50306 | + | 30.5945i | −0.224779 | + | 1.05750i | ||||
\(838\) | −25.9945 | −0.897964 | ||||||||
\(839\) | 10.7054 | + | 18.5424i | 0.369593 | + | 0.640153i | 0.989502 | − | 0.144520i | \(-0.0461639\pi\) |
−0.619909 | + | 0.784674i | \(0.712831\pi\) | |||||||
\(840\) | −0.582676 | + | 0.0612417i | −0.0201042 | + | 0.00211304i | ||||
\(841\) | −15.7318 | + | 27.2482i | −0.542474 | + | 0.939593i | ||||
\(842\) | 15.8926 | − | 27.5269i | 0.547697 | − | 0.948638i | ||||
\(843\) | −5.93911 | − | 8.17448i | −0.204554 | − | 0.281544i | ||||
\(844\) | −6.86024 | − | 11.8823i | −0.236139 | − | 0.409005i | ||||
\(845\) | 0.416534 | 0.0143292 | ||||||||
\(846\) | −0.450305 | + | 1.38590i | −0.0154818 | + | 0.0476481i | ||||
\(847\) | −4.65227 | −0.159854 | ||||||||
\(848\) | −4.68238 | − | 8.11012i | −0.160794 | − | 0.278503i | ||||
\(849\) | 9.73270 | − | 21.8600i | 0.334025 | − | 0.750233i | ||||
\(850\) | 1.91355 | − | 3.31436i | 0.0656341 | − | 0.113682i | ||||
\(851\) | −28.2780 | + | 48.9790i | −0.969358 | + | 1.67898i | ||||
\(852\) | −5.22269 | + | 11.7303i | −0.178926 | + | 0.401875i | ||||
\(853\) | −20.0193 | − | 34.6745i | −0.685448 | − | 1.18723i | −0.973296 | − | 0.229555i | \(-0.926273\pi\) |
0.287848 | − | 0.957676i | \(-0.407060\pi\) | |||||||
\(854\) | 15.0088 | 0.513591 | ||||||||
\(855\) | 0.214517 | − | 0.660216i | 0.00733634 | − | 0.0225789i | ||||
\(856\) | 6.51051 | 0.222525 | ||||||||
\(857\) | 22.9609 | + | 39.7695i | 0.784330 | + | 1.35850i | 0.929398 | + | 0.369078i | \(0.120327\pi\) |
−0.145068 | + | 0.989422i | \(0.546340\pi\) | |||||||
\(858\) | 27.9513 | + | 38.4717i | 0.954243 | + | 1.31340i | ||||
\(859\) | −25.6958 | + | 44.5065i | −0.876730 | + | 1.51854i | −0.0218212 | + | 0.999762i | \(0.506946\pi\) |
−0.854909 | + | 0.518779i | \(0.826387\pi\) | |||||||
\(860\) | −6.80662 | + | 11.7894i | −0.232104 | + | 0.402016i | ||||
\(861\) | −14.7856 | + | 1.55402i | −0.503890 | + | 0.0529610i | ||||
\(862\) | 7.12828 | + | 12.3465i | 0.242790 | + | 0.420525i | ||||
\(863\) | 33.9778 | 1.15662 | 0.578308 | − | 0.815818i | \(-0.303713\pi\) | ||||
0.578308 | + | 0.815818i | \(0.303713\pi\) | |||||||
\(864\) | 8.39067 | − | 39.4750i | 0.285457 | − | 1.34297i | ||||
\(865\) | −4.99907 | −0.169973 | ||||||||
\(866\) | 32.9381 | + | 57.0505i | 1.11928 | + | 1.93865i | ||||
\(867\) | −22.6912 | + | 2.38494i | −0.770632 | + | 0.0809967i | ||||
\(868\) | 5.49904 | − | 9.52463i | 0.186650 | − | 0.323287i | ||||
\(869\) | 11.2378 | − | 19.4645i | 0.381217 | − | 0.660288i | ||||
\(870\) | −15.4868 | − | 21.3157i | −0.525050 | − | 0.722670i | ||||
\(871\) | −11.7381 | − | 20.3310i | −0.397732 | − | 0.688891i | ||||
\(872\) | 5.61961 | 0.190304 | ||||||||
\(873\) | −12.4520 | − | 13.8294i | −0.421437 | − | 0.468053i | ||||
\(874\) | −3.49948 | −0.118372 | ||||||||
\(875\) | −0.500000 | − | 0.866025i | −0.0169031 | − | 0.0292770i | ||||
\(876\) | −17.4590 | + | 39.2135i | −0.589883 | + | 1.32490i | ||||
\(877\) | 15.7416 | − | 27.2653i | 0.531558 | − | 0.920685i | −0.467764 | − | 0.883853i | \(-0.654940\pi\) |
0.999321 | − | 0.0368314i | \(-0.0117264\pi\) | |||||||
\(878\) | −35.5764 | + | 61.6202i | −1.20065 | + | 2.07958i | ||||
\(879\) | −9.75644 | + | 21.9133i | −0.329077 | + | 0.739118i | ||||
\(880\) | −8.53753 | − | 14.7874i | −0.287800 | − | 0.498484i | ||||
\(881\) | 17.4293 | 0.587209 | 0.293605 | − | 0.955927i | \(-0.405145\pi\) | ||||
0.293605 | + | 0.955927i | \(0.405145\pi\) | |||||||
\(882\) | 5.74064 | − | 1.22021i | 0.193297 | − | 0.0410866i | ||||
\(883\) | −17.2534 | −0.580623 | −0.290312 | − | 0.956932i | \(-0.593759\pi\) | ||||
−0.290312 | + | 0.956932i | \(0.593759\pi\) | |||||||
\(884\) | −6.33964 | − | 10.9806i | −0.213225 | − | 0.369317i | ||||
\(885\) | 0.659642 | + | 0.907920i | 0.0221736 | + | 0.0305194i | ||||
\(886\) | −4.30333 | + | 7.45358i | −0.144573 | + | 0.250408i | ||||
\(887\) | 2.37120 | − | 4.10704i | 0.0796171 | − | 0.137901i | −0.823468 | − | 0.567363i | \(-0.807964\pi\) |
0.903085 | + | 0.429462i | \(0.141297\pi\) | |||||||
\(888\) | 4.26281 | − | 0.448040i | 0.143051 | − | 0.0150352i | ||||
\(889\) | 5.40047 | + | 9.35388i | 0.181126 | + | 0.313719i | ||||
\(890\) | −11.9845 | −0.401721 | ||||||||
\(891\) | −28.8064 | − | 20.9291i | −0.965050 | − | 0.701150i | ||||
\(892\) | 33.4866 | 1.12121 | ||||||||
\(893\) | −0.0287275 | − | 0.0497574i | −0.000961328 | − | 0.00166507i | ||||
\(894\) | 47.7697 | − | 5.02080i | 1.59766 | − | 0.167921i | ||||
\(895\) | 10.4238 | − | 18.0545i | 0.348428 | − | 0.603495i | ||||
\(896\) | 1.34799 | − | 2.33478i | 0.0450331 | − | 0.0779997i | ||||
\(897\) | −27.9183 | − | 38.4263i | −0.932166 | − | 1.28302i | ||||
\(898\) | 5.66657 | + | 9.81479i | 0.189096 | + | 0.327524i | ||||
\(899\) | −46.8062 | −1.56108 | ||||||||
\(900\) | 5.36149 | − | 1.13962i | 0.178716 | − | 0.0379874i | ||||
\(901\) | 4.24481 | 0.141415 | ||||||||
\(902\) | −33.2166 | − | 57.5329i | −1.10599 | − | 1.91564i | ||||
\(903\) | −5.24898 | + | 11.7894i | −0.174675 | + | 0.392327i | ||||
\(904\) | 2.20098 | − | 3.81220i | 0.0732034 | − | 0.126792i | ||||
\(905\) | −3.82348 | + | 6.62246i | −0.127097 | + | 0.220138i | ||||
\(906\) | −9.90979 | + | 22.2578i | −0.329231 | + | 0.739465i | ||||
\(907\) | −9.24073 | − | 16.0054i | −0.306833 | − | 0.531451i | 0.670835 | − | 0.741607i | \(-0.265936\pi\) |
−0.977668 | + | 0.210156i | \(0.932603\pi\) | |||||||
\(908\) | 23.0686 | 0.765558 | ||||||||
\(909\) | −6.15597 | − | 6.83689i | −0.204180 | − | 0.226765i | ||||
\(910\) | −6.93960 | −0.230046 | ||||||||
\(911\) | −4.31637 | − | 7.47618i | −0.143008 | − | 0.247697i | 0.785620 | − | 0.618709i | \(-0.212344\pi\) |
−0.928628 | + | 0.371012i | \(0.879011\pi\) | |||||||
\(912\) | 1.01674 | + | 1.39943i | 0.0336677 | + | 0.0463397i | ||||
\(913\) | 29.3003 | − | 50.7496i | 0.969698 | − | 1.67957i | ||||
\(914\) | −13.7753 | + | 23.8595i | −0.455647 | + | 0.789203i | ||||
\(915\) | 13.2156 | − | 1.38902i | 0.436894 | − | 0.0459194i | ||||
\(916\) | −0.142896 | − | 0.247504i | −0.00472143 | − | 0.00817775i | ||||
\(917\) | −13.9637 | −0.461123 | ||||||||
\(918\) | 14.7783 | + | 13.3064i | 0.487756 | + | 0.439178i | ||||
\(919\) | −10.5715 | −0.348721 | −0.174361 | − | 0.984682i | \(-0.555786\pi\) | ||||
−0.174361 | + | 0.984682i | \(0.555786\pi\) | |||||||
\(920\) | 1.30747 | + | 2.26461i | 0.0431061 | + | 0.0746619i | ||||
\(921\) | 55.8327 | − | 5.86825i | 1.83975 | − | 0.193366i | ||||
\(922\) | 23.1710 | − | 40.1333i | 0.763095 | − | 1.32172i | ||||
\(923\) | 7.19664 | − | 12.4650i | 0.236880 | − | 0.410289i | ||||
\(924\) | 7.35916 | + | 10.1290i | 0.242099 | + | 0.333220i | ||||
\(925\) | 3.65796 | + | 6.33577i | 0.120273 | + | 0.208319i | ||||
\(926\) | −29.5829 | −0.972154 | ||||||||
\(927\) | 15.3985 | − | 47.3916i | 0.505752 | − | 1.55654i | ||||
\(928\) | 60.3925 | 1.98248 | ||||||||
\(929\) | −5.86050 | − | 10.1507i | −0.192277 | − | 0.333033i | 0.753728 | − | 0.657187i | \(-0.228254\pi\) |
−0.946004 | + | 0.324154i | \(0.894921\pi\) | |||||||
\(930\) | 8.29594 | − | 18.6330i | 0.272034 | − | 0.610999i | ||||
\(931\) | −0.115699 | + | 0.200396i | −0.00379187 | + | 0.00656772i | ||||
\(932\) | −19.1648 | + | 33.1944i | −0.627765 | + | 1.08732i | ||||
\(933\) | 21.4006 | − | 48.0664i | 0.700623 | − | 1.57362i | ||||
\(934\) | −13.5408 | − | 23.4534i | −0.443069 | − | 0.767418i | ||||
\(935\) | 7.73968 | 0.253115 | ||||||||
\(936\) | −1.11239 | + | 3.42358i | −0.0363595 | + | 0.111903i | ||||
\(937\) | −20.3067 | −0.663392 | −0.331696 | − | 0.943386i | \(-0.607621\pi\) | ||||
−0.331696 | + | 0.943386i | \(0.607621\pi\) | |||||||
\(938\) | −6.47341 | − | 11.2123i | −0.211364 | − | 0.366094i | ||||
\(939\) | 25.0805 | + | 34.5204i | 0.818471 | + | 1.12653i | ||||
\(940\) | 0.226829 | − | 0.392880i | 0.00739835 | − | 0.0128143i | ||||
\(941\) | 13.0889 | − | 22.6707i | 0.426686 | − | 0.739042i | −0.569890 | − | 0.821721i | \(-0.693014\pi\) |
0.996576 | + | 0.0826786i | \(0.0263475\pi\) | |||||||
\(942\) | −6.22368 | + | 0.654135i | −0.202778 | + | 0.0213129i | ||||
\(943\) | 33.1774 | + | 57.4650i | 1.08041 | + | 1.87132i | ||||
\(944\) | −2.79642 | −0.0910158 | ||||||||
\(945\) | 4.94183 | − | 1.60570i | 0.160758 | − | 0.0522334i | ||||
\(946\) | −57.6666 | −1.87490 | ||||||||
\(947\) | 3.82695 | + | 6.62848i | 0.124359 | + | 0.215397i | 0.921482 | − | 0.388420i | \(-0.126979\pi\) |
−0.797123 | + | 0.603817i | \(0.793646\pi\) | |||||||
\(948\) | −17.8797 | + | 1.87923i | −0.580704 | + | 0.0610345i | ||||
\(949\) | 24.0577 | − | 41.6692i | 0.780946 | − | 1.35264i | ||||
\(950\) | −0.226341 | + | 0.392034i | −0.00734347 | + | 0.0127193i | ||||
\(951\) | −19.4416 | − | 26.7591i | −0.630437 | − | 0.867723i | ||||
\(952\) | 0.330869 | + | 0.573083i | 0.0107235 | + | 0.0185737i | ||||
\(953\) | −23.3548 | −0.756536 | −0.378268 | − | 0.925696i | \(-0.623480\pi\) | ||||
−0.378268 | + | 0.925696i | \(0.623480\pi\) | |||||||
\(954\) | 8.52099 | + | 9.46352i | 0.275877 | + | 0.306393i | ||||
\(955\) | −10.8239 | −0.350252 | ||||||||
\(956\) | 3.06687 | + | 5.31198i | 0.0991898 | + | 0.171802i | ||||
\(957\) | 21.6725 | − | 48.6773i | 0.700573 | − | 1.57351i | ||||
\(958\) | 13.2717 | − | 22.9872i | 0.428788 | − | 0.742682i | ||||
\(959\) | −1.61064 | + | 2.78971i | −0.0520103 | + | 0.0900846i | ||||
\(960\) | −4.62293 | + | 10.3833i | −0.149204 | + | 0.335118i | ||||
\(961\) | −2.61691 | − | 4.53263i | −0.0844166 | − | 0.146214i | ||||
\(962\) | 50.7696 | 1.63688 | ||||||||
\(963\) | −56.4792 | + | 12.0050i | −1.82002 | + | 0.386856i | ||||
\(964\) | −19.5965 | −0.631162 | ||||||||
\(965\) | 4.35380 | + | 7.54100i | 0.140154 | + | 0.242753i | ||||
\(966\) | −15.3966 | − | 21.1916i | −0.495376 | − | 0.681827i | ||||
\(967\) | 14.7240 | − | 25.5028i | 0.473493 | − | 0.820115i | −0.526046 | − | 0.850456i | \(-0.676326\pi\) |
0.999540 | + | 0.0303414i | \(0.00965946\pi\) | |||||||
\(968\) | 0.786842 | − | 1.36285i | 0.0252900 | − | 0.0438036i | ||||
\(969\) | −0.779773 | + | 0.0819574i | −0.0250499 | + | 0.00263285i | ||||
\(970\) | 6.06753 | + | 10.5093i | 0.194817 | + | 0.337432i | ||||
\(971\) | −48.9293 | −1.57022 | −0.785108 | − | 0.619359i | \(-0.787393\pi\) | ||||
−0.785108 | + | 0.619359i | \(0.787393\pi\) | |||||||
\(972\) | 28.4815i | 0.913545i | ||||||||
\(973\) | 10.7815 | 0.345638 | ||||||||
\(974\) | −5.36850 | − | 9.29851i | −0.172018 | − | 0.297943i | ||||
\(975\) | −6.11048 | + | 0.642237i | −0.195692 | + | 0.0205680i | ||||
\(976\) | −16.5560 | + | 28.6758i | −0.529944 | + | 0.917891i | ||||
\(977\) | −19.8045 | + | 34.3024i | −0.633603 | + | 1.09743i | 0.353207 | + | 0.935545i | \(0.385091\pi\) |
−0.986809 | + | 0.161887i | \(0.948242\pi\) | |||||||
\(978\) | 31.6672 | + | 43.5862i | 1.01261 | + | 1.39373i | ||||
\(979\) | −12.1184 | − | 20.9896i | −0.387304 | − | 0.670831i | ||||
\(980\) | −1.82709 | −0.0583643 | ||||||||
\(981\) | −48.7506 | + | 10.3623i | −1.55649 | + | 0.330841i | ||||
\(982\) | −72.5745 | −2.31594 | ||||||||
\(983\) | −17.3953 | − | 30.1295i | −0.554823 | − | 0.960982i | −0.997917 | − | 0.0645066i | \(-0.979453\pi\) |
0.443094 | − | 0.896475i | \(-0.353881\pi\) | |||||||
\(984\) | 2.04545 | − | 4.59416i | 0.0652066 | − | 0.146456i | ||||
\(985\) | −13.0541 | + | 22.6103i | −0.415937 | + | 0.720424i | ||||
\(986\) | −14.8794 | + | 25.7719i | −0.473857 | + | 0.820744i | ||||
\(987\) | 0.174921 | − | 0.392880i | 0.00556780 | − | 0.0125055i | ||||
\(988\) | 0.749875 | + | 1.29882i | 0.0238567 | + | 0.0413210i | ||||
\(989\) | 57.5985 | 1.83153 | ||||||||
\(990\) | 15.5366 | + | 17.2551i | 0.493785 | + | 0.548403i | ||||
\(991\) | 10.3214 | 0.327870 | 0.163935 | − | 0.986471i | \(-0.447581\pi\) | ||||
0.163935 | + | 0.986471i | \(0.447581\pi\) | |||||||
\(992\) | 23.3756 | + | 40.4878i | 0.742177 | + | 1.28549i | ||||
\(993\) | −12.2606 | − | 16.8753i | −0.389080 | − | 0.535522i | ||||
\(994\) | 3.96885 | − | 6.87424i | 0.125884 | − | 0.218038i | ||||
\(995\) | −1.89878 | + | 3.28879i | −0.0601955 | + | 0.104262i | ||||
\(996\) | −46.6174 | + | 4.89969i | −1.47713 | + | 0.155253i | ||||
\(997\) | 3.73355 | + | 6.46669i | 0.118243 | + | 0.204802i | 0.919071 | − | 0.394091i | \(-0.128941\pi\) |
−0.800829 | + | 0.598893i | \(0.795607\pi\) | |||||||
\(998\) | −42.2725 | −1.33811 | ||||||||
\(999\) | −36.1541 | + | 11.7472i | −1.14386 | + | 0.371664i |
(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 | 315.2.i.d.211.1 | yes | 8 | |
3.2 | odd | 2 | 945.2.i.c.631.4 | 8 | |||
9.2 | odd | 6 | 945.2.i.c.316.4 | 8 | |||
9.4 | even | 3 | 2835.2.a.l.1.4 | 4 | |||
9.5 | odd | 6 | 2835.2.a.q.1.1 | 4 | |||
9.7 | even | 3 | inner | 315.2.i.d.106.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.i.d.106.1 | ✓ | 8 | 9.7 | even | 3 | inner | |
315.2.i.d.211.1 | yes | 8 | 1.1 | even | 1 | trivial | |
945.2.i.c.316.4 | 8 | 9.2 | odd | 6 | |||
945.2.i.c.631.4 | 8 | 3.2 | odd | 2 | |||
2835.2.a.l.1.4 | 4 | 9.4 | even | 3 | |||
2835.2.a.q.1.1 | 4 | 9.5 | odd | 6 |