Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [731,2,Mod(307,731)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(731, base_ring=CyclotomicField(6))
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("731.307");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 731 = 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 731.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.83706438776\) |
Analytic rank: | \(0\) |
Dimension: | \(58\) |
Relative dimension: | \(29\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 307.3 | ||
Character | \(\chi\) | \(=\) | 731.307 |
Dual form | 731.2.e.b.681.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).
\(n\) | \(173\) | \(562\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.46652 | −1.74409 | −0.872047 | − | 0.489422i | \(-0.837208\pi\) | ||||
−0.872047 | + | 0.489422i | \(0.837208\pi\) | |||||||
\(3\) | 0.742625 | − | 1.28626i | 0.428755 | − | 0.742625i | −0.568008 | − | 0.823023i | \(-0.692286\pi\) |
0.996763 | + | 0.0803981i | \(0.0256192\pi\) | |||||||
\(4\) | 4.08373 | 2.04186 | ||||||||
\(5\) | 0.428499 | − | 0.742181i | 0.191630 | − | 0.331914i | −0.754160 | − | 0.656690i | \(-0.771956\pi\) |
0.945791 | + | 0.324777i | \(0.105289\pi\) | |||||||
\(6\) | −1.83170 | + | 3.17260i | −0.747788 | + | 1.29521i | ||||
\(7\) | −2.43048 | − | 4.20972i | −0.918635 | − | 1.59112i | −0.801490 | − | 0.598008i | \(-0.795959\pi\) |
−0.117145 | − | 0.993115i | \(-0.537374\pi\) | |||||||
\(8\) | −5.13956 | −1.81711 | ||||||||
\(9\) | 0.397017 | + | 0.687654i | 0.132339 | + | 0.229218i | ||||
\(10\) | −1.05690 | + | 1.83061i | −0.334221 | + | 0.578889i | ||||
\(11\) | 6.05985 | 1.82711 | 0.913556 | − | 0.406712i | \(-0.133325\pi\) | ||||
0.913556 | + | 0.406712i | \(0.133325\pi\) | |||||||
\(12\) | 3.03268 | − | 5.25275i | 0.875459 | − | 1.51634i | ||||
\(13\) | 0.875156 | + | 1.51581i | 0.242724 | + | 0.420411i | 0.961489 | − | 0.274842i | \(-0.0886256\pi\) |
−0.718765 | + | 0.695253i | \(0.755292\pi\) | |||||||
\(14\) | 5.99483 | + | 10.3834i | 1.60219 | + | 2.77507i | ||||
\(15\) | −0.636427 | − | 1.10232i | −0.164325 | − | 0.284619i | ||||
\(16\) | 4.50938 | 1.12734 | ||||||||
\(17\) | −0.500000 | − | 0.866025i | −0.121268 | − | 0.210042i | ||||
\(18\) | −0.979251 | − | 1.69611i | −0.230812 | − | 0.399777i | ||||
\(19\) | 2.26398 | − | 3.92132i | 0.519392 | − | 0.899614i | −0.480354 | − | 0.877075i | \(-0.659492\pi\) |
0.999746 | − | 0.0225388i | \(-0.00717492\pi\) | |||||||
\(20\) | 1.74987 | − | 3.03087i | 0.391283 | − | 0.677722i | ||||
\(21\) | −7.21974 | −1.57548 | ||||||||
\(22\) | −14.9467 | −3.18666 | ||||||||
\(23\) | 4.28730 | − | 7.42582i | 0.893963 | − | 1.54839i | 0.0588811 | − | 0.998265i | \(-0.481247\pi\) |
0.835082 | − | 0.550125i | \(-0.185420\pi\) | |||||||
\(24\) | −3.81676 | + | 6.61083i | −0.779094 | + | 1.34943i | ||||
\(25\) | 2.13278 | + | 3.69408i | 0.426556 | + | 0.738816i | ||||
\(26\) | −2.15859 | − | 3.73879i | −0.423334 | − | 0.733236i | ||||
\(27\) | 5.63509 | 1.08447 | ||||||||
\(28\) | −9.92542 | − | 17.1913i | −1.87573 | − | 3.24886i | ||||
\(29\) | −1.39854 | − | 2.42234i | −0.259703 | − | 0.449818i | 0.706460 | − | 0.707753i | \(-0.250291\pi\) |
−0.966162 | + | 0.257935i | \(0.916958\pi\) | |||||||
\(30\) | 1.56976 | + | 2.71891i | 0.286598 | + | 0.496402i | ||||
\(31\) | −2.36665 | + | 4.09915i | −0.425062 | + | 0.736230i | −0.996426 | − | 0.0844672i | \(-0.973081\pi\) |
0.571364 | + | 0.820697i | \(0.306415\pi\) | |||||||
\(32\) | −0.843355 | −0.149085 | ||||||||
\(33\) | 4.50019 | − | 7.79456i | 0.783383 | − | 1.35686i | ||||
\(34\) | 1.23326 | + | 2.13607i | 0.211502 | + | 0.366333i | ||||
\(35\) | −4.16583 | −0.704154 | ||||||||
\(36\) | 1.62131 | + | 2.80819i | 0.270218 | + | 0.468032i | ||||
\(37\) | −4.58473 | + | 7.94098i | −0.753725 | + | 1.30549i | 0.192281 | + | 0.981340i | \(0.438411\pi\) |
−0.946006 | + | 0.324150i | \(0.894922\pi\) | |||||||
\(38\) | −5.58415 | + | 9.67203i | −0.905869 | + | 1.56901i | ||||
\(39\) | 2.59965 | 0.416277 | ||||||||
\(40\) | −2.20229 | + | 3.81449i | −0.348213 | + | 0.603123i | ||||
\(41\) | −2.70589 | −0.422589 | −0.211294 | − | 0.977422i | \(-0.567768\pi\) | ||||
−0.211294 | + | 0.977422i | \(0.567768\pi\) | |||||||
\(42\) | 17.8076 | 2.74778 | ||||||||
\(43\) | 4.05456 | − | 5.15369i | 0.618315 | − | 0.785931i | ||||
\(44\) | 24.7468 | 3.73071 | ||||||||
\(45\) | 0.680485 | 0.101441 | ||||||||
\(46\) | −10.5747 | + | 18.3159i | −1.55916 | + | 2.70054i | ||||
\(47\) | 1.27282 | 0.185659 | 0.0928297 | − | 0.995682i | \(-0.470409\pi\) | ||||
0.0928297 | + | 0.995682i | \(0.470409\pi\) | |||||||
\(48\) | 3.34877 | − | 5.80025i | 0.483354 | − | 0.837194i | ||||
\(49\) | −8.31447 | + | 14.4011i | −1.18778 | + | 2.05730i | ||||
\(50\) | −5.26054 | − | 9.11153i | −0.743953 | − | 1.28856i | ||||
\(51\) | −1.48525 | −0.207977 | ||||||||
\(52\) | 3.57390 | + | 6.19017i | 0.495610 | + | 0.858422i | ||||
\(53\) | 4.59828 | − | 7.96446i | 0.631623 | − | 1.09400i | −0.355597 | − | 0.934639i | \(-0.615722\pi\) |
0.987220 | − | 0.159364i | \(-0.0509442\pi\) | |||||||
\(54\) | −13.8991 | −1.89142 | ||||||||
\(55\) | 2.59664 | − | 4.49751i | 0.350130 | − | 0.606444i | ||||
\(56\) | 12.4916 | + | 21.6361i | 1.66926 | + | 2.89124i | ||||
\(57\) | −3.36257 | − | 5.82415i | −0.445384 | − | 0.771427i | ||||
\(58\) | 3.44953 | + | 5.97477i | 0.452946 | + | 0.784525i | ||||
\(59\) | −7.62547 | −0.992752 | −0.496376 | − | 0.868108i | \(-0.665336\pi\) | ||||
−0.496376 | + | 0.868108i | \(0.665336\pi\) | |||||||
\(60\) | −2.59900 | − | 4.50159i | −0.335529 | − | 0.581153i | ||||
\(61\) | 2.05511 | + | 3.55956i | 0.263131 | + | 0.455755i | 0.967072 | − | 0.254502i | \(-0.0819117\pi\) |
−0.703942 | + | 0.710258i | \(0.748578\pi\) | |||||||
\(62\) | 5.83739 | − | 10.1106i | 0.741349 | − | 1.28405i | ||||
\(63\) | 1.92988 | − | 3.34266i | 0.243142 | − | 0.421135i | ||||
\(64\) | −6.93860 | −0.867325 | ||||||||
\(65\) | 1.50001 | 0.186054 | ||||||||
\(66\) | −11.0998 | + | 19.2255i | −1.36629 | + | 2.36649i | ||||
\(67\) | −5.41099 | + | 9.37210i | −0.661057 | + | 1.14498i | 0.319281 | + | 0.947660i | \(0.396559\pi\) |
−0.980338 | + | 0.197324i | \(0.936775\pi\) | |||||||
\(68\) | −2.04186 | − | 3.53661i | −0.247612 | − | 0.428877i | ||||
\(69\) | −6.36771 | − | 11.0292i | −0.766582 | − | 1.32776i | ||||
\(70\) | 10.2751 | 1.22811 | ||||||||
\(71\) | −2.66225 | − | 4.61115i | −0.315951 | − | 0.547243i | 0.663688 | − | 0.748009i | \(-0.268990\pi\) |
−0.979639 | + | 0.200767i | \(0.935657\pi\) | |||||||
\(72\) | −2.04049 | − | 3.53424i | −0.240474 | − | 0.416514i | ||||
\(73\) | −5.78506 | − | 10.0200i | −0.677090 | − | 1.17275i | −0.975853 | − | 0.218426i | \(-0.929908\pi\) |
0.298764 | − | 0.954327i | \(-0.403426\pi\) | |||||||
\(74\) | 11.3083 | − | 19.5866i | 1.31457 | − | 2.27690i | ||||
\(75\) | 6.33541 | 0.731551 | ||||||||
\(76\) | 9.24547 | − | 16.0136i | 1.06053 | − | 1.83689i | ||||
\(77\) | −14.7283 | − | 25.5102i | −1.67845 | − | 2.90716i | ||||
\(78\) | −6.41209 | −0.726026 | ||||||||
\(79\) | −3.54591 | − | 6.14170i | −0.398947 | − | 0.690996i | 0.594650 | − | 0.803985i | \(-0.297291\pi\) |
−0.993596 | + | 0.112989i | \(0.963957\pi\) | |||||||
\(80\) | 1.93226 | − | 3.34678i | 0.216033 | − | 0.374181i | ||||
\(81\) | 2.99370 | − | 5.18525i | 0.332634 | − | 0.576139i | ||||
\(82\) | 6.67413 | 0.737034 | ||||||||
\(83\) | −0.350368 | + | 0.606856i | −0.0384579 | + | 0.0666111i | −0.884614 | − | 0.466325i | \(-0.845578\pi\) |
0.846156 | + | 0.532936i | \(0.178911\pi\) | |||||||
\(84\) | −29.4834 | −3.21691 | ||||||||
\(85\) | −0.856997 | −0.0929544 | ||||||||
\(86\) | −10.0007 | + | 12.7117i | −1.07840 | + | 1.37074i | ||||
\(87\) | −4.15437 | −0.445395 | ||||||||
\(88\) | −31.1449 | −3.32006 | ||||||||
\(89\) | −4.96902 | + | 8.60659i | −0.526715 | + | 0.912297i | 0.472801 | + | 0.881169i | \(0.343243\pi\) |
−0.999515 | + | 0.0311273i | \(0.990090\pi\) | |||||||
\(90\) | −1.67843 | −0.176922 | ||||||||
\(91\) | 4.25410 | − | 7.36831i | 0.445950 | − | 0.772409i | ||||
\(92\) | 17.5082 | − | 30.3250i | 1.82535 | − | 3.16160i | ||||
\(93\) | 3.51506 | + | 6.08826i | 0.364495 | + | 0.631324i | ||||
\(94\) | −3.13943 | −0.323808 | ||||||||
\(95\) | −1.94022 | − | 3.36056i | −0.199063 | − | 0.344787i | ||||
\(96\) | −0.626296 | + | 1.08478i | −0.0639211 | + | 0.110715i | ||||
\(97\) | −4.70746 | −0.477971 | −0.238985 | − | 0.971023i | \(-0.576815\pi\) | ||||
−0.238985 | + | 0.971023i | \(0.576815\pi\) | |||||||
\(98\) | 20.5078 | − | 35.5206i | 2.07160 | − | 3.58812i | ||||
\(99\) | 2.40586 | + | 4.16707i | 0.241798 | + | 0.418807i | ||||
\(100\) | 8.70968 | + | 15.0856i | 0.870968 | + | 1.50856i | ||||
\(101\) | 1.05832 | + | 1.83307i | 0.105307 | + | 0.182397i | 0.913864 | − | 0.406021i | \(-0.133084\pi\) |
−0.808556 | + | 0.588419i | \(0.799751\pi\) | |||||||
\(102\) | 3.66340 | 0.362731 | ||||||||
\(103\) | −3.43231 | − | 5.94494i | −0.338196 | − | 0.585772i | 0.645898 | − | 0.763424i | \(-0.276483\pi\) |
−0.984093 | + | 0.177652i | \(0.943150\pi\) | |||||||
\(104\) | −4.49791 | − | 7.79061i | −0.441057 | − | 0.763933i | ||||
\(105\) | −3.09365 | + | 5.35836i | −0.301909 | + | 0.522922i | ||||
\(106\) | −11.3418 | + | 19.6445i | −1.10161 | + | 1.90804i | ||||
\(107\) | 4.90980 | 0.474649 | 0.237324 | − | 0.971430i | \(-0.423730\pi\) | ||||
0.237324 | + | 0.971430i | \(0.423730\pi\) | |||||||
\(108\) | 23.0122 | 2.21435 | ||||||||
\(109\) | 6.72905 | − | 11.6551i | 0.644526 | − | 1.11635i | −0.339884 | − | 0.940467i | \(-0.610388\pi\) |
0.984411 | − | 0.175885i | \(-0.0562788\pi\) | |||||||
\(110\) | −6.40466 | + | 11.0932i | −0.610660 | + | 1.05769i | ||||
\(111\) | 6.80947 | + | 11.7943i | 0.646326 | + | 1.11947i | ||||
\(112\) | −10.9599 | − | 18.9832i | −1.03562 | − | 1.79374i | ||||
\(113\) | −3.50120 | −0.329365 | −0.164683 | − | 0.986347i | \(-0.552660\pi\) | ||||
−0.164683 | + | 0.986347i | \(0.552660\pi\) | |||||||
\(114\) | 8.29386 | + | 14.3654i | 0.776791 | + | 1.34544i | ||||
\(115\) | −3.67420 | − | 6.36391i | −0.342621 | − | 0.593437i | ||||
\(116\) | −5.71126 | − | 9.89220i | −0.530277 | − | 0.918467i | ||||
\(117\) | −0.694903 | + | 1.20361i | −0.0642438 | + | 0.111274i | ||||
\(118\) | 18.8084 | 1.73145 | ||||||||
\(119\) | −2.43048 | + | 4.20972i | −0.222802 | + | 0.385904i | ||||
\(120\) | 3.27096 | + | 5.66546i | 0.298596 | + | 0.517184i | ||||
\(121\) | 25.7217 | 2.33834 | ||||||||
\(122\) | −5.06898 | − | 8.77974i | −0.458924 | − | 0.794880i | ||||
\(123\) | −2.00946 | + | 3.48049i | −0.181187 | + | 0.313825i | ||||
\(124\) | −9.66474 | + | 16.7398i | −0.867919 | + | 1.50328i | ||||
\(125\) | 7.94056 | 0.710225 | ||||||||
\(126\) | −4.76010 | + | 8.24473i | −0.424063 | + | 0.734499i | ||||
\(127\) | −13.7604 | −1.22103 | −0.610517 | − | 0.792003i | \(-0.709038\pi\) | ||||
−0.610517 | + | 0.792003i | \(0.709038\pi\) | |||||||
\(128\) | 18.8009 | 1.66178 | ||||||||
\(129\) | −3.61799 | − | 9.04249i | −0.318546 | − | 0.796147i | ||||
\(130\) | −3.69981 | −0.324495 | ||||||||
\(131\) | 20.7164 | 1.81000 | 0.904999 | − | 0.425413i | \(-0.139871\pi\) | ||||
0.904999 | + | 0.425413i | \(0.139871\pi\) | |||||||
\(132\) | 18.3776 | − | 31.8309i | 1.59956 | − | 2.77052i | ||||
\(133\) | −22.0102 | −1.90853 | ||||||||
\(134\) | 13.3463 | − | 23.1165i | 1.15295 | − | 1.99696i | ||||
\(135\) | 2.41463 | − | 4.18226i | 0.207818 | − | 0.359951i | ||||
\(136\) | 2.56978 | + | 4.45099i | 0.220357 | + | 0.381669i | ||||
\(137\) | −9.58510 | −0.818910 | −0.409455 | − | 0.912330i | \(-0.634281\pi\) | ||||
−0.409455 | + | 0.912330i | \(0.634281\pi\) | |||||||
\(138\) | 15.7061 | + | 27.2037i | 1.33699 | + | 2.31574i | ||||
\(139\) | −9.32195 | + | 16.1461i | −0.790678 | + | 1.36949i | 0.134870 | + | 0.990863i | \(0.456938\pi\) |
−0.925548 | + | 0.378630i | \(0.876395\pi\) | |||||||
\(140\) | −17.0121 | −1.43779 | ||||||||
\(141\) | 0.945226 | − | 1.63718i | 0.0796024 | − | 0.137875i | ||||
\(142\) | 6.56649 | + | 11.3735i | 0.551048 | + | 0.954442i | ||||
\(143\) | 5.30331 | + | 9.18560i | 0.443485 | + | 0.768138i | ||||
\(144\) | 1.79030 | + | 3.10089i | 0.149192 | + | 0.258407i | ||||
\(145\) | −2.39709 | −0.199068 | ||||||||
\(146\) | 14.2690 | + | 24.7146i | 1.18091 | + | 2.04539i | ||||
\(147\) | 12.3491 | + | 21.3892i | 1.01853 | + | 1.76415i | ||||
\(148\) | −18.7228 | + | 32.4288i | −1.53900 | + | 2.66563i | ||||
\(149\) | 3.57420 | − | 6.19070i | 0.292810 | − | 0.507162i | −0.681663 | − | 0.731666i | \(-0.738743\pi\) |
0.974473 | + | 0.224504i | \(0.0720763\pi\) | |||||||
\(150\) | −15.6264 | −1.27589 | ||||||||
\(151\) | −18.1400 | −1.47621 | −0.738107 | − | 0.674684i | \(-0.764280\pi\) | ||||
−0.738107 | + | 0.674684i | \(0.764280\pi\) | |||||||
\(152\) | −11.6358 | + | 20.1539i | −0.943792 | + | 1.63470i | ||||
\(153\) | 0.397017 | − | 0.687654i | 0.0320969 | − | 0.0555935i | ||||
\(154\) | 36.3278 | + | 62.9215i | 2.92737 | + | 5.07036i | ||||
\(155\) | 2.02821 | + | 3.51296i | 0.162910 | + | 0.282168i | ||||
\(156\) | 10.6163 | 0.849981 | ||||||||
\(157\) | −3.30807 | − | 5.72975i | −0.264013 | − | 0.457284i | 0.703292 | − | 0.710901i | \(-0.251713\pi\) |
−0.967304 | + | 0.253618i | \(0.918379\pi\) | |||||||
\(158\) | 8.74607 | + | 15.1486i | 0.695800 | + | 1.20516i | ||||
\(159\) | −6.82960 | − | 11.8292i | −0.541622 | − | 0.938118i | ||||
\(160\) | −0.361376 | + | 0.625922i | −0.0285693 | + | 0.0494835i | ||||
\(161\) | −41.6808 | −3.28490 | ||||||||
\(162\) | −7.38404 | + | 12.7895i | −0.580145 | + | 1.00484i | ||||
\(163\) | 4.09343 | + | 7.09003i | 0.320622 | + | 0.555334i | 0.980617 | − | 0.195937i | \(-0.0627747\pi\) |
−0.659994 | + | 0.751271i | \(0.729441\pi\) | |||||||
\(164\) | −11.0501 | −0.862869 | ||||||||
\(165\) | −3.85665 | − | 6.67992i | −0.300240 | − | 0.520031i | ||||
\(166\) | 0.864191 | − | 1.49682i | 0.0670742 | − | 0.116176i | ||||
\(167\) | −1.08847 | + | 1.88529i | −0.0842286 | + | 0.145888i | −0.905062 | − | 0.425279i | \(-0.860176\pi\) |
0.820834 | + | 0.571167i | \(0.193509\pi\) | |||||||
\(168\) | 37.1063 | 2.86281 | ||||||||
\(169\) | 4.96821 | − | 8.60518i | 0.382170 | − | 0.661937i | ||||
\(170\) | 2.11380 | 0.162121 | ||||||||
\(171\) | 3.59535 | 0.274943 | ||||||||
\(172\) | 16.5577 | − | 21.0463i | 1.26251 | − | 1.60476i | ||||
\(173\) | 3.77252 | 0.286819 | 0.143410 | − | 0.989663i | \(-0.454193\pi\) | ||||
0.143410 | + | 0.989663i | \(0.454193\pi\) | |||||||
\(174\) | 10.2468 | 0.776810 | ||||||||
\(175\) | 10.3673 | − | 17.9568i | 0.783698 | − | 1.35740i | ||||
\(176\) | 27.3261 | 2.05978 | ||||||||
\(177\) | −5.66287 | + | 9.80837i | −0.425647 | + | 0.737242i | ||||
\(178\) | 12.2562 | − | 21.2283i | 0.918640 | − | 1.59113i | ||||
\(179\) | 3.30603 | + | 5.72620i | 0.247104 | + | 0.427997i | 0.962721 | − | 0.270496i | \(-0.0871877\pi\) |
−0.715617 | + | 0.698493i | \(0.753854\pi\) | |||||||
\(180\) | 2.77892 | 0.207128 | ||||||||
\(181\) | 5.06434 | + | 8.77169i | 0.376429 | + | 0.651994i | 0.990540 | − | 0.137226i | \(-0.0438185\pi\) |
−0.614111 | + | 0.789220i | \(0.710485\pi\) | |||||||
\(182\) | −10.4928 | + | 18.1741i | −0.777780 | + | 1.34715i | ||||
\(183\) | 6.10472 | 0.451274 | ||||||||
\(184\) | −22.0348 | + | 38.1654i | −1.62443 | + | 2.81359i | ||||
\(185\) | 3.92910 | + | 6.80540i | 0.288873 | + | 0.500343i | ||||
\(186\) | −8.66997 | − | 15.0168i | −0.635713 | − | 1.10109i | ||||
\(187\) | −3.02992 | − | 5.24798i | −0.221570 | − | 0.383770i | ||||
\(188\) | 5.19784 | 0.379091 | ||||||||
\(189\) | −13.6960 | − | 23.7221i | −0.996235 | − | 1.72553i | ||||
\(190\) | 4.78560 | + | 8.28891i | 0.347184 | + | 0.601340i | ||||
\(191\) | 4.57251 | − | 7.91982i | 0.330855 | − | 0.573058i | −0.651824 | − | 0.758370i | \(-0.725996\pi\) |
0.982680 | + | 0.185312i | \(0.0593294\pi\) | |||||||
\(192\) | −5.15278 | + | 8.92487i | −0.371870 | + | 0.644097i | ||||
\(193\) | 5.95482 | 0.428637 | 0.214319 | − | 0.976764i | \(-0.431247\pi\) | ||||
0.214319 | + | 0.976764i | \(0.431247\pi\) | |||||||
\(194\) | 11.6111 | 0.833626 | ||||||||
\(195\) | 1.11395 | − | 1.92941i | 0.0797713 | − | 0.138168i | ||||
\(196\) | −33.9540 | + | 58.8101i | −2.42529 | + | 4.20072i | ||||
\(197\) | 12.4998 | + | 21.6502i | 0.890570 | + | 1.54251i | 0.839193 | + | 0.543834i | \(0.183028\pi\) |
0.0513776 | + | 0.998679i | \(0.483639\pi\) | |||||||
\(198\) | −5.93411 | − | 10.2782i | −0.421719 | − | 0.730438i | ||||
\(199\) | 21.9092 | 1.55310 | 0.776550 | − | 0.630055i | \(-0.216968\pi\) | ||||
0.776550 | + | 0.630055i | \(0.216968\pi\) | |||||||
\(200\) | −10.9615 | − | 18.9859i | −0.775098 | − | 1.34251i | ||||
\(201\) | 8.03666 | + | 13.9199i | 0.566863 | + | 0.981835i | ||||
\(202\) | −2.61038 | − | 4.52131i | −0.183666 | − | 0.318118i | ||||
\(203\) | −6.79825 | + | 11.7749i | −0.477144 | + | 0.826438i | ||||
\(204\) | −6.06535 | −0.424660 | ||||||||
\(205\) | −1.15947 | + | 2.00826i | −0.0809809 | + | 0.140263i | ||||
\(206\) | 8.46587 | + | 14.6633i | 0.589845 | + | 1.02164i | ||||
\(207\) | 6.80852 | 0.473225 | ||||||||
\(208\) | 3.94641 | + | 6.83537i | 0.273634 | + | 0.473948i | ||||
\(209\) | 13.7194 | − | 23.7626i | 0.948988 | − | 1.64370i | ||||
\(210\) | 7.63055 | − | 13.2165i | 0.526558 | − | 0.912025i | ||||
\(211\) | 1.70694 | 0.117511 | 0.0587553 | − | 0.998272i | \(-0.481287\pi\) | ||||
0.0587553 | + | 0.998272i | \(0.481287\pi\) | |||||||
\(212\) | 18.7781 | − | 32.5247i | 1.28969 | − | 2.23380i | ||||
\(213\) | −7.90820 | −0.541861 | ||||||||
\(214\) | −12.1101 | −0.827832 | ||||||||
\(215\) | −2.08760 | − | 5.21757i | −0.142373 | − | 0.355835i | ||||
\(216\) | −28.9619 | −1.97060 | ||||||||
\(217\) | 23.0084 | 1.56191 | ||||||||
\(218\) | −16.5974 | + | 28.7475i | −1.12411 | + | 1.94702i | ||||
\(219\) | −17.1845 | −1.16122 | ||||||||
\(220\) | 10.6040 | − | 18.3666i | 0.714919 | − | 1.23828i | ||||
\(221\) | 0.875156 | − | 1.51581i | 0.0588693 | − | 0.101965i | ||||
\(222\) | −16.7957 | − | 29.0910i | −1.12725 | − | 1.95246i | ||||
\(223\) | −19.2650 | −1.29008 | −0.645039 | − | 0.764150i | \(-0.723159\pi\) | ||||
−0.645039 | + | 0.764150i | \(0.723159\pi\) | |||||||
\(224\) | 2.04976 | + | 3.55028i | 0.136955 | + | 0.237213i | ||||
\(225\) | −1.69350 | + | 2.93322i | −0.112900 | + | 0.195548i | ||||
\(226\) | 8.63579 | 0.574444 | ||||||||
\(227\) | −13.9956 | + | 24.2410i | −0.928918 | + | 1.60893i | −0.143783 | + | 0.989609i | \(0.545927\pi\) |
−0.785135 | + | 0.619324i | \(0.787407\pi\) | |||||||
\(228\) | −13.7318 | − | 23.7842i | −0.909413 | − | 1.57515i | ||||
\(229\) | 8.72065 | + | 15.1046i | 0.576277 | + | 0.998141i | 0.995902 | + | 0.0904433i | \(0.0288284\pi\) |
−0.419625 | + | 0.907698i | \(0.637838\pi\) | |||||||
\(230\) | 9.06250 | + | 15.6967i | 0.597564 | + | 1.03501i | ||||
\(231\) | −43.7505 | −2.87857 | ||||||||
\(232\) | 7.18789 | + | 12.4498i | 0.471908 | + | 0.817368i | ||||
\(233\) | 3.43121 | + | 5.94303i | 0.224786 | + | 0.389341i | 0.956255 | − | 0.292534i | \(-0.0944984\pi\) |
−0.731469 | + | 0.681874i | \(0.761165\pi\) | |||||||
\(234\) | 1.71399 | − | 2.96872i | 0.112047 | − | 0.194072i | ||||
\(235\) | 0.545401 | − | 0.944661i | 0.0355780 | − | 0.0616229i | ||||
\(236\) | −31.1404 | −2.02706 | ||||||||
\(237\) | −10.5331 | −0.684201 | ||||||||
\(238\) | 5.99483 | − | 10.3834i | 0.388587 | − | 0.673053i | ||||
\(239\) | 1.81199 | − | 3.13845i | 0.117208 | − | 0.203009i | −0.801452 | − | 0.598058i | \(-0.795939\pi\) |
0.918660 | + | 0.395049i | \(0.129272\pi\) | |||||||
\(240\) | −2.86989 | − | 4.97080i | −0.185251 | − | 0.320864i | ||||
\(241\) | 5.94814 | + | 10.3025i | 0.383154 | + | 0.663641i | 0.991511 | − | 0.130022i | \(-0.0415047\pi\) |
−0.608358 | + | 0.793663i | \(0.708171\pi\) | |||||||
\(242\) | −63.4432 | −4.07829 | ||||||||
\(243\) | 4.00623 | + | 6.93900i | 0.257000 | + | 0.445137i | ||||
\(244\) | 8.39253 | + | 14.5363i | 0.537277 | + | 0.930590i | ||||
\(245\) | 7.12548 | + | 12.3417i | 0.455230 | + | 0.788482i | ||||
\(246\) | 4.95637 | − | 8.58469i | 0.316007 | − | 0.547340i | ||||
\(247\) | 7.92533 | 0.504277 | ||||||||
\(248\) | 12.1635 | − | 21.0678i | 0.772384 | − | 1.33781i | ||||
\(249\) | 0.520384 | + | 0.901332i | 0.0329780 | + | 0.0571196i | ||||
\(250\) | −19.5856 | −1.23870 | ||||||||
\(251\) | 8.04457 | + | 13.9336i | 0.507769 | + | 0.879482i | 0.999960 | + | 0.00899420i | \(0.00286298\pi\) |
−0.492191 | + | 0.870487i | \(0.663804\pi\) | |||||||
\(252\) | 7.88112 | − | 13.6505i | 0.496464 | − | 0.859901i | ||||
\(253\) | 25.9804 | − | 44.9993i | 1.63337 | − | 2.82908i | ||||
\(254\) | 33.9402 | 2.12960 | ||||||||
\(255\) | −0.636427 | + | 1.10232i | −0.0398546 | + | 0.0690303i | ||||
\(256\) | −32.4957 | −2.03098 | ||||||||
\(257\) | 1.90268 | 0.118686 | 0.0593429 | − | 0.998238i | \(-0.481099\pi\) | ||||
0.0593429 | + | 0.998238i | \(0.481099\pi\) | |||||||
\(258\) | 8.92385 | + | 22.3035i | 0.555574 | + | 1.38856i | ||||
\(259\) | 44.5724 | 2.76959 | ||||||||
\(260\) | 6.12564 | 0.379896 | ||||||||
\(261\) | 1.11049 | − | 1.92342i | 0.0687376 | − | 0.119057i | ||||
\(262\) | −51.0974 | −3.15681 | ||||||||
\(263\) | 1.99586 | − | 3.45692i | 0.123070 | − | 0.213163i | −0.797907 | − | 0.602780i | \(-0.794059\pi\) |
0.920977 | + | 0.389618i | \(0.127393\pi\) | |||||||
\(264\) | −23.1290 | + | 40.0606i | −1.42349 | + | 2.46556i | ||||
\(265\) | −3.94072 | − | 6.82552i | −0.242076 | − | 0.419288i | ||||
\(266\) | 54.2887 | 3.32865 | ||||||||
\(267\) | 7.38023 | + | 12.7829i | 0.451663 | + | 0.782303i | ||||
\(268\) | −22.0970 | + | 38.2731i | −1.34979 | + | 2.33790i | ||||
\(269\) | 13.3698 | 0.815172 | 0.407586 | − | 0.913167i | \(-0.366371\pi\) | ||||
0.407586 | + | 0.913167i | \(0.366371\pi\) | |||||||
\(270\) | −5.95573 | + | 10.3156i | −0.362454 | + | 0.627789i | ||||
\(271\) | −7.43452 | − | 12.8770i | −0.451615 | − | 0.782220i | 0.546872 | − | 0.837216i | \(-0.315819\pi\) |
−0.998487 | + | 0.0549967i | \(0.982485\pi\) | |||||||
\(272\) | −2.25469 | − | 3.90523i | −0.136711 | − | 0.236790i | ||||
\(273\) | −6.31839 | − | 10.9438i | −0.382407 | − | 0.662348i | ||||
\(274\) | 23.6418 | 1.42826 | ||||||||
\(275\) | 12.9243 | + | 22.3856i | 0.779365 | + | 1.34990i | ||||
\(276\) | −26.0040 | − | 45.0402i | −1.56526 | − | 2.71110i | ||||
\(277\) | −12.5897 | + | 21.8060i | −0.756442 | + | 1.31020i | 0.188212 | + | 0.982128i | \(0.439731\pi\) |
−0.944654 | + | 0.328068i | \(0.893602\pi\) | |||||||
\(278\) | 22.9928 | − | 39.8247i | 1.37902 | − | 2.38853i | ||||
\(279\) | −3.75840 | −0.225009 | ||||||||
\(280\) | 21.4105 | 1.27952 | ||||||||
\(281\) | 0.684462 | − | 1.18552i | 0.0408316 | − | 0.0707224i | −0.844887 | − | 0.534944i | \(-0.820333\pi\) |
0.885719 | + | 0.464222i | \(0.153666\pi\) | |||||||
\(282\) | −2.33142 | + | 4.03814i | −0.138834 | + | 0.240468i | ||||
\(283\) | −6.72457 | − | 11.6473i | −0.399734 | − | 0.692360i | 0.593959 | − | 0.804495i | \(-0.297564\pi\) |
−0.993693 | + | 0.112136i | \(0.964231\pi\) | |||||||
\(284\) | −10.8719 | − | 18.8307i | −0.645128 | − | 1.11739i | ||||
\(285\) | −5.76343 | −0.341396 | ||||||||
\(286\) | −13.0807 | − | 22.6565i | −0.773479 | − | 1.33971i | ||||
\(287\) | 6.57661 | + | 11.3910i | 0.388205 | + | 0.672390i | ||||
\(288\) | −0.334826 | − | 0.579936i | −0.0197298 | − | 0.0341730i | ||||
\(289\) | −0.500000 | + | 0.866025i | −0.0294118 | + | 0.0509427i | ||||
\(290\) | 5.91248 | 0.347193 | ||||||||
\(291\) | −3.49588 | + | 6.05504i | −0.204932 | + | 0.354953i | ||||
\(292\) | −23.6246 | − | 40.9190i | −1.38252 | − | 2.39460i | ||||
\(293\) | 5.61563 | 0.328068 | 0.164034 | − | 0.986455i | \(-0.447549\pi\) | ||||
0.164034 | + | 0.986455i | \(0.447549\pi\) | |||||||
\(294\) | −30.4592 | − | 52.7569i | −1.77642 | − | 3.07685i | ||||
\(295\) | −3.26751 | + | 5.65949i | −0.190242 | + | 0.329508i | ||||
\(296\) | 23.5635 | − | 40.8131i | 1.36960 | − | 2.37222i | ||||
\(297\) | 34.1478 | 1.98145 | ||||||||
\(298\) | −8.81585 | + | 15.2695i | −0.510689 | + | 0.884538i | ||||
\(299\) | 15.0082 | 0.867947 | ||||||||
\(300\) | 25.8721 | 1.49373 | ||||||||
\(301\) | −31.5501 | − | 4.54261i | −1.81852 | − | 0.261831i | ||||
\(302\) | 44.7427 | 2.57466 | ||||||||
\(303\) | 3.14375 | 0.180604 | ||||||||
\(304\) | 10.2091 | − | 17.6827i | 0.585534 | − | 1.01417i | ||||
\(305\) | 3.52246 | 0.201695 | ||||||||
\(306\) | −0.979251 | + | 1.69611i | −0.0559800 | + | 0.0969603i | ||||
\(307\) | 11.5797 | − | 20.0567i | 0.660890 | − | 1.14470i | −0.319492 | − | 0.947589i | \(-0.603512\pi\) |
0.980382 | − | 0.197106i | \(-0.0631544\pi\) | |||||||
\(308\) | −60.1465 | − | 104.177i | −3.42717 | − | 5.93603i | ||||
\(309\) | −10.1957 | −0.580012 | ||||||||
\(310\) | −5.00262 | − | 8.66480i | −0.284130 | − | 0.492128i | ||||
\(311\) | −8.72666 | + | 15.1150i | −0.494843 | + | 0.857094i | −0.999982 | − | 0.00594409i | \(-0.998108\pi\) |
0.505139 | + | 0.863038i | \(0.331441\pi\) | |||||||
\(312\) | −13.3610 | −0.756420 | ||||||||
\(313\) | −12.6106 | + | 21.8422i | −0.712793 | + | 1.23459i | 0.251012 | + | 0.967984i | \(0.419237\pi\) |
−0.963805 | + | 0.266609i | \(0.914097\pi\) | |||||||
\(314\) | 8.15943 | + | 14.1325i | 0.460463 | + | 0.797545i | ||||
\(315\) | −1.65391 | − | 2.86465i | −0.0931870 | − | 0.161405i | ||||
\(316\) | −14.4805 | − | 25.0810i | −0.814595 | − | 1.41092i | ||||
\(317\) | 12.6194 | 0.708779 | 0.354389 | − | 0.935098i | \(-0.384689\pi\) | ||||
0.354389 | + | 0.935098i | \(0.384689\pi\) | |||||||
\(318\) | 16.8454 | + | 29.1770i | 0.944640 | + | 1.63617i | ||||
\(319\) | −8.47495 | − | 14.6790i | −0.474506 | − | 0.821868i | ||||
\(320\) | −2.97318 | + | 5.14970i | −0.166206 | + | 0.287877i | ||||
\(321\) | 3.64614 | − | 6.31530i | 0.203508 | − | 0.352486i | ||||
\(322\) | 102.807 | 5.72918 | ||||||||
\(323\) | −4.52796 | −0.251942 | ||||||||
\(324\) | 12.2255 | − | 21.1751i | 0.679193 | − | 1.17640i | ||||
\(325\) | −3.73302 | + | 6.46579i | −0.207071 | + | 0.358657i | ||||
\(326\) | −10.0965 | − | 17.4877i | −0.559195 | − | 0.968555i | ||||
\(327\) | −9.99432 | − | 17.3107i | −0.552687 | − | 0.957283i | ||||
\(328\) | 13.9071 | 0.767889 | ||||||||
\(329\) | −3.09356 | − | 5.35820i | −0.170553 | − | 0.295407i | ||||
\(330\) | 9.51252 | + | 16.4762i | 0.523647 | + | 0.906983i | ||||
\(331\) | −5.12471 | − | 8.87626i | −0.281680 | − | 0.487883i | 0.690119 | − | 0.723696i | \(-0.257558\pi\) |
−0.971799 | + | 0.235813i | \(0.924225\pi\) | |||||||
\(332\) | −1.43081 | + | 2.47823i | −0.0785258 | + | 0.136011i | ||||
\(333\) | −7.28086 | −0.398989 | ||||||||
\(334\) | 2.68474 | − | 4.65011i | 0.146903 | − | 0.254443i | ||||
\(335\) | 4.63720 | + | 8.03187i | 0.253357 | + | 0.438828i | ||||
\(336\) | −32.5565 | −1.77610 | ||||||||
\(337\) | 5.14044 | + | 8.90350i | 0.280017 | + | 0.485004i | 0.971389 | − | 0.237495i | \(-0.0763264\pi\) |
−0.691371 | + | 0.722500i | \(0.742993\pi\) | |||||||
\(338\) | −12.2542 | + | 21.2249i | −0.666540 | + | 1.15448i | ||||
\(339\) | −2.60008 | + | 4.50347i | −0.141217 | + | 0.244595i | ||||
\(340\) | −3.49974 | −0.189800 | ||||||||
\(341\) | −14.3415 | + | 24.8402i | −0.776637 | + | 1.34517i | ||||
\(342\) | −8.86801 | −0.479527 | ||||||||
\(343\) | 46.8059 | 2.52728 | ||||||||
\(344\) | −20.8387 | + | 26.4877i | −1.12355 | + | 1.42812i | ||||
\(345\) | −10.9142 | −0.587602 | ||||||||
\(346\) | −9.30500 | −0.500240 | ||||||||
\(347\) | 2.91463 | − | 5.04828i | 0.156465 | − | 0.271006i | −0.777126 | − | 0.629345i | \(-0.783323\pi\) |
0.933592 | + | 0.358339i | \(0.116657\pi\) | |||||||
\(348\) | −16.9653 | −0.909436 | ||||||||
\(349\) | −8.47194 | + | 14.6738i | −0.453493 | + | 0.785472i | −0.998600 | − | 0.0528938i | \(-0.983156\pi\) |
0.545107 | + | 0.838366i | \(0.316489\pi\) | |||||||
\(350\) | −25.5713 | + | 44.2908i | −1.36684 | + | 2.36744i | ||||
\(351\) | 4.93158 | + | 8.54174i | 0.263228 | + | 0.455924i | ||||
\(352\) | −5.11060 | −0.272396 | ||||||||
\(353\) | −9.81905 | − | 17.0071i | −0.522615 | − | 0.905196i | −0.999654 | − | 0.0263138i | \(-0.991623\pi\) |
0.477038 | − | 0.878882i | \(-0.341710\pi\) | |||||||
\(354\) | 13.9676 | − | 24.1926i | 0.742369 | − | 1.28582i | ||||
\(355\) | −4.56308 | −0.242183 | ||||||||
\(356\) | −20.2921 | + | 35.1470i | −1.07548 | + | 1.86279i | ||||
\(357\) | 3.60987 | + | 6.25248i | 0.191055 | + | 0.330916i | ||||
\(358\) | −8.15438 | − | 14.1238i | −0.430973 | − | 0.746466i | ||||
\(359\) | −0.370894 | − | 0.642408i | −0.0195751 | − | 0.0339050i | 0.856072 | − | 0.516857i | \(-0.172898\pi\) |
−0.875647 | + | 0.482952i | \(0.839565\pi\) | |||||||
\(360\) | −3.49739 | −0.184329 | ||||||||
\(361\) | −0.751192 | − | 1.30110i | −0.0395364 | − | 0.0684790i | ||||
\(362\) | −12.4913 | − | 21.6356i | −0.656528 | − | 1.13714i | ||||
\(363\) | 19.1016 | − | 33.0849i | 1.00257 | − | 1.73651i | ||||
\(364\) | 17.3726 | − | 30.0902i | 0.910570 | − | 1.57715i | ||||
\(365\) | −9.91556 | −0.519004 | ||||||||
\(366\) | −15.0574 | −0.787064 | ||||||||
\(367\) | 7.65072 | − | 13.2514i | 0.399364 | − | 0.691719i | −0.594283 | − | 0.804256i | \(-0.702564\pi\) |
0.993648 | + | 0.112537i | \(0.0358975\pi\) | |||||||
\(368\) | 19.3330 | − | 33.4858i | 1.00780 | − | 1.74557i | ||||
\(369\) | −1.07428 | − | 1.86071i | −0.0559250 | − | 0.0968649i | ||||
\(370\) | −9.69121 | − | 16.7857i | −0.503822 | − | 0.872645i | ||||
\(371\) | −44.7042 | −2.32092 | ||||||||
\(372\) | 14.3546 | + | 24.8628i | 0.744249 | + | 1.28908i | ||||
\(373\) | −7.42932 | − | 12.8680i | −0.384676 | − | 0.666278i | 0.607048 | − | 0.794665i | \(-0.292353\pi\) |
−0.991724 | + | 0.128387i | \(0.959020\pi\) | |||||||
\(374\) | 7.47337 | + | 12.9443i | 0.386439 | + | 0.669332i | ||||
\(375\) | 5.89685 | − | 10.2137i | 0.304512 | − | 0.527431i | ||||
\(376\) | −6.54172 | −0.337363 | ||||||||
\(377\) | 2.44788 | − | 4.23986i | 0.126072 | − | 0.218364i | ||||
\(378\) | 33.7814 | + | 58.5111i | 1.73753 | + | 3.00949i | ||||
\(379\) | 35.4666 | 1.82180 | 0.910900 | − | 0.412628i | \(-0.135389\pi\) | ||||
0.910900 | + | 0.412628i | \(0.135389\pi\) | |||||||
\(380\) | −7.92334 | − | 13.7236i | −0.406459 | − | 0.704007i | ||||
\(381\) | −10.2188 | + | 17.6994i | −0.523524 | + | 0.906770i | ||||
\(382\) | −11.2782 | + | 19.5344i | −0.577043 | + | 0.999467i | ||||
\(383\) | −9.68269 | −0.494762 | −0.247381 | − | 0.968918i | \(-0.579570\pi\) | ||||
−0.247381 | + | 0.968918i | \(0.579570\pi\) | |||||||
\(384\) | 13.9620 | − | 24.1829i | 0.712497 | − | 1.23408i | ||||
\(385\) | −25.2443 | −1.28657 | ||||||||
\(386\) | −14.6877 | −0.747584 | ||||||||
\(387\) | 5.15368 | + | 0.742031i | 0.261976 | + | 0.0377195i | ||||
\(388\) | −19.2240 | −0.975951 | ||||||||
\(389\) | 15.2437 | 0.772887 | 0.386443 | − | 0.922313i | \(-0.373704\pi\) | ||||
0.386443 | + | 0.922313i | \(0.373704\pi\) | |||||||
\(390\) | −2.74757 | + | 4.75893i | −0.139129 | + | 0.240978i | ||||
\(391\) | −8.57460 | −0.433636 | ||||||||
\(392\) | 42.7327 | − | 74.0152i | 2.15833 | − | 3.73833i | ||||
\(393\) | 15.3845 | − | 26.6467i | 0.776045 | − | 1.34415i | ||||
\(394\) | −30.8309 | − | 53.4007i | −1.55324 | − | 2.69029i | ||||
\(395\) | −6.07768 | −0.305801 | ||||||||
\(396\) | 9.82488 | + | 17.0172i | 0.493719 | + | 0.855146i | ||||
\(397\) | 3.41766 | − | 5.91957i | 0.171528 | − | 0.297095i | −0.767427 | − | 0.641137i | \(-0.778463\pi\) |
0.938954 | + | 0.344042i | \(0.111796\pi\) | |||||||
\(398\) | −54.0394 | −2.70875 | ||||||||
\(399\) | −16.3453 | + | 28.3109i | −0.818290 | + | 1.41732i | ||||
\(400\) | 9.61750 | + | 16.6580i | 0.480875 | + | 0.832900i | ||||
\(401\) | −3.06047 | − | 5.30089i | −0.152832 | − | 0.264714i | 0.779435 | − | 0.626483i | \(-0.215506\pi\) |
−0.932268 | + | 0.361769i | \(0.882173\pi\) | |||||||
\(402\) | −19.8226 | − | 34.3338i | −0.988662 | − | 1.71241i | ||||
\(403\) | −8.28474 | −0.412692 | ||||||||
\(404\) | 4.32191 | + | 7.48576i | 0.215023 | + | 0.372431i | ||||
\(405\) | −2.56560 | − | 4.44374i | −0.127486 | − | 0.220811i | ||||
\(406\) | 16.7680 | − | 29.0431i | 0.832184 | − | 1.44138i | ||||
\(407\) | −27.7828 | + | 48.1211i | −1.37714 | + | 2.38528i | ||||
\(408\) | 7.63353 | 0.377916 | ||||||||
\(409\) | −1.11227 | −0.0549982 | −0.0274991 | − | 0.999622i | \(-0.508754\pi\) | ||||
−0.0274991 | + | 0.999622i | \(0.508754\pi\) | |||||||
\(410\) | 2.85986 | − | 4.95342i | 0.141238 | − | 0.244632i | ||||
\(411\) | −7.11813 | + | 12.3290i | −0.351111 | + | 0.608143i | ||||
\(412\) | −14.0166 | − | 24.2775i | −0.690550 | − | 1.19607i | ||||
\(413\) | 18.5336 | + | 32.1011i | 0.911977 | + | 1.57959i | ||||
\(414\) | −16.7934 | −0.825349 | ||||||||
\(415\) | 0.300265 | + | 0.520074i | 0.0147394 | + | 0.0255294i | ||||
\(416\) | −0.738066 | − | 1.27837i | −0.0361867 | − | 0.0626772i | ||||
\(417\) | 13.8454 | + | 23.9810i | 0.678013 | + | 1.17435i | ||||
\(418\) | −33.8391 | + | 58.6110i | −1.65512 | + | 2.86676i | ||||
\(419\) | −2.58513 | −0.126292 | −0.0631459 | − | 0.998004i | \(-0.520113\pi\) | ||||
−0.0631459 | + | 0.998004i | \(0.520113\pi\) | |||||||
\(420\) | −12.6336 | + | 21.8821i | −0.616457 | + | 1.06774i | ||||
\(421\) | −8.63285 | − | 14.9525i | −0.420739 | − | 0.728742i | 0.575273 | − | 0.817962i | \(-0.304896\pi\) |
−0.996012 | + | 0.0892198i | \(0.971563\pi\) | |||||||
\(422\) | −4.21020 | −0.204950 | ||||||||
\(423\) | 0.505330 | + | 0.875257i | 0.0245700 | + | 0.0425565i | ||||
\(424\) | −23.6331 | + | 40.9338i | −1.14773 | + | 1.98792i | ||||
\(425\) | 2.13278 | − | 3.69408i | 0.103455 | − | 0.179189i | ||||
\(426\) | 19.5058 | 0.945057 | ||||||||
\(427\) | 9.98983 | − | 17.3029i | 0.483442 | − | 0.837346i | ||||
\(428\) | 20.0503 | 0.969168 | ||||||||
\(429\) | 15.7535 | 0.760585 | ||||||||
\(430\) | 5.14911 | + | 12.8692i | 0.248312 | + | 0.620610i | ||||
\(431\) | −2.22097 | −0.106980 | −0.0534902 | − | 0.998568i | \(-0.517035\pi\) | ||||
−0.0534902 | + | 0.998568i | \(0.517035\pi\) | |||||||
\(432\) | 25.4107 | 1.22257 | ||||||||
\(433\) | −20.0830 | + | 34.7847i | −0.965125 | + | 1.67165i | −0.255847 | + | 0.966717i | \(0.582354\pi\) |
−0.709278 | + | 0.704929i | \(0.750979\pi\) | |||||||
\(434\) | −56.7506 | −2.72412 | ||||||||
\(435\) | −1.78014 | + | 3.08329i | −0.0853512 | + | 0.147833i | ||||
\(436\) | 27.4796 | − | 47.5961i | 1.31604 | − | 2.27944i | ||||
\(437\) | −19.4127 | − | 33.6238i | −0.928635 | − | 1.60844i | ||||
\(438\) | 42.3859 | 2.02528 | ||||||||
\(439\) | 3.54785 | + | 6.14506i | 0.169330 | + | 0.293288i | 0.938184 | − | 0.346136i | \(-0.112506\pi\) |
−0.768855 | + | 0.639424i | \(0.779173\pi\) | |||||||
\(440\) | −13.3456 | + | 23.1152i | −0.636225 | + | 1.10197i | ||||
\(441\) | −13.2039 | −0.628759 | ||||||||
\(442\) | −2.15859 | + | 3.73879i | −0.102674 | + | 0.177836i | ||||
\(443\) | −0.111399 | − | 0.192948i | −0.00529272 | − | 0.00916725i | 0.863367 | − | 0.504577i | \(-0.168351\pi\) |
−0.868660 | + | 0.495409i | \(0.835018\pi\) | |||||||
\(444\) | 27.8080 | + | 48.1649i | 1.31971 | + | 2.28580i | ||||
\(445\) | 4.25843 | + | 7.37583i | 0.201869 | + | 0.349648i | ||||
\(446\) | 47.5175 | 2.25002 | ||||||||
\(447\) | −5.30859 | − | 9.19474i | −0.251087 | − | 0.434896i | ||||
\(448\) | 16.8641 | + | 29.2095i | 0.796755 | + | 1.38002i | ||||
\(449\) | 11.0104 | − | 19.0706i | 0.519613 | − | 0.899996i | −0.480127 | − | 0.877199i | \(-0.659410\pi\) |
0.999740 | − | 0.0227970i | \(-0.00725713\pi\) | |||||||
\(450\) | 4.17705 | − | 7.23486i | 0.196908 | − | 0.341055i | ||||
\(451\) | −16.3973 | −0.772117 | ||||||||
\(452\) | −14.2980 | −0.672519 | ||||||||
\(453\) | −13.4712 | + | 23.3328i | −0.632933 | + | 1.09627i | ||||
\(454\) | 34.5204 | − | 59.7910i | 1.62012 | − | 2.80613i | ||||
\(455\) | −3.64575 | − | 6.31462i | −0.170915 | − | 0.296034i | ||||
\(456\) | 17.2821 | + | 29.9335i | 0.809310 | + | 1.40177i | ||||
\(457\) | 26.0286 | 1.21757 | 0.608784 | − | 0.793336i | \(-0.291658\pi\) | ||||
0.608784 | + | 0.793336i | \(0.291658\pi\) | |||||||
\(458\) | −21.5097 | − | 37.2559i | −1.00508 | − | 1.74085i | ||||
\(459\) | −2.81754 | − | 4.88013i | −0.131512 | − | 0.227785i | ||||
\(460\) | −15.0044 | − | 25.9885i | −0.699586 | − | 1.21172i | ||||
\(461\) | −2.47306 | + | 4.28346i | −0.115182 | + | 0.199501i | −0.917852 | − | 0.396922i | \(-0.870078\pi\) |
0.802671 | + | 0.596422i | \(0.203412\pi\) | |||||||
\(462\) | 107.912 | 5.02050 | ||||||||
\(463\) | −1.72500 | + | 2.98778i | −0.0801674 | + | 0.138854i | −0.903322 | − | 0.428964i | \(-0.858879\pi\) |
0.823154 | + | 0.567818i | \(0.192212\pi\) | |||||||
\(464\) | −6.30655 | − | 10.9233i | −0.292774 | − | 0.507100i | ||||
\(465\) | 6.02480 | 0.279393 | ||||||||
\(466\) | −8.46315 | − | 14.6586i | −0.392048 | − | 0.679047i | ||||
\(467\) | 14.0814 | − | 24.3896i | 0.651608 | − | 1.12862i | −0.331125 | − | 0.943587i | \(-0.607428\pi\) |
0.982733 | − | 0.185031i | \(-0.0592384\pi\) | |||||||
\(468\) | −2.83780 | + | 4.91521i | −0.131177 | + | 0.227205i | ||||
\(469\) | 52.6052 | 2.42908 | ||||||||
\(470\) | −1.34524 | + | 2.33003i | −0.0620514 | + | 0.107476i | ||||
\(471\) | −9.82662 | −0.452787 | ||||||||
\(472\) | 39.1916 | 1.80394 | ||||||||
\(473\) | 24.5700 | − | 31.2306i | 1.12973 | − | 1.43598i | ||||
\(474\) | 25.9802 | 1.19331 | ||||||||
\(475\) | 19.3142 | 0.886198 | ||||||||
\(476\) | −9.92542 | + | 17.1913i | −0.454931 | + | 0.787963i | ||||
\(477\) | 7.30239 | 0.334353 | ||||||||
\(478\) | −4.46930 | + | 7.74105i | −0.204421 | + | 0.354068i | ||||
\(479\) | 6.65004 | − | 11.5182i | 0.303848 | − | 0.526280i | −0.673156 | − | 0.739500i | \(-0.735062\pi\) |
0.977004 | + | 0.213220i | \(0.0683951\pi\) | |||||||
\(480\) | 0.536734 | + | 0.929651i | 0.0244984 | + | 0.0424325i | ||||
\(481\) | −16.0494 | −0.731790 | ||||||||
\(482\) | −14.6712 | − | 25.4113i | −0.668256 | − | 1.15745i | ||||
\(483\) | −30.9532 | + | 53.6125i | −1.40842 | + | 2.43945i | ||||
\(484\) | 105.041 | 4.77457 | ||||||||
\(485\) | −2.01714 | + | 3.49379i | −0.0915937 | + | 0.158645i | ||||
\(486\) | −9.88146 | − | 17.1152i | −0.448232 | − | 0.776361i | ||||
\(487\) | −7.08585 | − | 12.2731i | −0.321091 | − | 0.556145i | 0.659623 | − | 0.751597i | \(-0.270716\pi\) |
−0.980713 | + | 0.195452i | \(0.937383\pi\) | |||||||
\(488\) | −10.5624 | − | 18.2946i | −0.478137 | − | 0.828157i | ||||
\(489\) | 12.1595 | 0.549873 | ||||||||
\(490\) | −17.5751 | − | 30.4410i | −0.793964 | − | 1.37519i | ||||
\(491\) | 12.2611 | + | 21.2369i | 0.553337 | + | 0.958407i | 0.998031 | + | 0.0627246i | \(0.0199790\pi\) |
−0.444694 | + | 0.895682i | \(0.646688\pi\) | |||||||
\(492\) | −8.20608 | + | 14.2134i | −0.369959 | + | 0.640788i | ||||
\(493\) | −1.39854 | + | 2.42234i | −0.0629871 | + | 0.109097i | ||||
\(494\) | −19.5480 | −0.879506 | ||||||||
\(495\) | 4.12363 | 0.185344 | ||||||||
\(496\) | −10.6721 | + | 18.4846i | −0.479191 | + | 0.829984i | ||||
\(497\) | −12.9411 | + | 22.4146i | −0.580487 | + | 1.00543i | ||||
\(498\) | −1.28354 | − | 2.22316i | −0.0575168 | − | 0.0996220i | ||||
\(499\) | 12.4613 | + | 21.5837i | 0.557846 | + | 0.966218i | 0.997676 | + | 0.0681370i | \(0.0217055\pi\) |
−0.439830 | + | 0.898081i | \(0.644961\pi\) | |||||||
\(500\) | 32.4271 | 1.45018 | ||||||||
\(501\) | 1.61665 | + | 2.80013i | 0.0722268 | + | 0.125100i | ||||
\(502\) | −19.8421 | − | 34.3675i | −0.885597 | − | 1.53390i | ||||
\(503\) | 4.29789 | + | 7.44417i | 0.191634 | + | 0.331919i | 0.945792 | − | 0.324774i | \(-0.105288\pi\) |
−0.754158 | + | 0.656693i | \(0.771955\pi\) | |||||||
\(504\) | −9.91875 | + | 17.1798i | −0.441816 | + | 0.765248i | ||||
\(505\) | 1.81396 | 0.0807202 | ||||||||
\(506\) | −64.0811 | + | 110.992i | −2.84875 | + | 4.93419i | ||||
\(507\) | −7.37903 | − | 12.7808i | −0.327714 | − | 0.567617i | ||||
\(508\) | −56.1935 | −2.49319 | ||||||||
\(509\) | −0.525420 | − | 0.910055i | −0.0232889 | − | 0.0403375i | 0.854146 | − | 0.520033i | \(-0.174080\pi\) |
−0.877435 | + | 0.479696i | \(0.840747\pi\) | |||||||
\(510\) | 1.56976 | − | 2.71891i | 0.0695102 | − | 0.120395i | ||||
\(511\) | −28.1209 | + | 48.7069i | −1.24400 | + | 2.15467i | ||||
\(512\) | 42.5494 | 1.88044 | ||||||||
\(513\) | 12.7577 | − | 22.0970i | 0.563267 | − | 0.975607i | ||||
\(514\) | −4.69299 | −0.206999 | ||||||||
\(515\) | −5.88297 | −0.259234 | ||||||||
\(516\) | −14.7749 | − | 36.9271i | −0.650428 | − | 1.62562i | ||||
\(517\) | 7.71308 | 0.339221 | ||||||||
\(518\) | −109.939 | −4.83043 | ||||||||
\(519\) | 2.80157 | − | 4.85246i | 0.122975 | − | 0.212999i | ||||
\(520\) | −7.70940 | −0.338080 | ||||||||
\(521\) | 20.0113 | − | 34.6606i | 0.876711 | − | 1.51851i | 0.0217816 | − | 0.999763i | \(-0.493066\pi\) |
0.854929 | − | 0.518745i | \(-0.173601\pi\) | |||||||
\(522\) | −2.73905 | + | 4.74417i | −0.119885 | + | 0.207647i | ||||
\(523\) | 11.0656 | + | 19.1662i | 0.483864 | + | 0.838078i | 0.999828 | − | 0.0185327i | \(-0.00589947\pi\) |
−0.515964 | + | 0.856610i | \(0.672566\pi\) | |||||||
\(524\) | 84.6000 | 3.69577 | ||||||||
\(525\) | −15.3981 | − | 26.6703i | −0.672028 | − | 1.16399i | ||||
\(526\) | −4.92282 | + | 8.52657i | −0.214645 | + | 0.371776i | ||||
\(527\) | 4.73329 | 0.206186 | ||||||||
\(528\) | 20.2931 | − | 35.1486i | 0.883142 | − | 1.52965i | ||||
\(529\) | −25.2618 | − | 43.7548i | −1.09834 | − | 1.90238i | ||||
\(530\) | 9.71986 | + | 16.8353i | 0.422204 | + | 0.731279i | ||||
\(531\) | −3.02744 | − | 5.24368i | −0.131380 | − | 0.227557i | ||||
\(532\) | −89.8837 | −3.89695 | ||||||||
\(533\) | −2.36807 | − | 4.10162i | −0.102573 | − | 0.177661i | ||||
\(534\) | −18.2035 | − | 31.5294i | −0.787742 | − | 1.36441i | ||||
\(535\) | 2.10384 | − | 3.64397i | 0.0909571 | − | 0.157542i | ||||
\(536\) | 27.8101 | − | 48.1685i | 1.20121 | − | 2.08056i | ||||
\(537\) | 9.82055 | 0.423788 | ||||||||
\(538\) | −32.9769 | −1.42174 | ||||||||
\(539\) | −50.3844 | + | 87.2683i | −2.17021 | + | 3.75891i | ||||
\(540\) | 9.86068 | − | 17.0792i | 0.424336 | − | 0.734972i | ||||
\(541\) | 8.77806 | + | 15.2040i | 0.377398 | + | 0.653673i | 0.990683 | − | 0.136189i | \(-0.0434854\pi\) |
−0.613285 | + | 0.789862i | \(0.710152\pi\) | |||||||
\(542\) | 18.3374 | + | 31.7613i | 0.787659 | + | 1.36426i | ||||
\(543\) | 15.0436 | 0.645583 | ||||||||
\(544\) | 0.421677 | + | 0.730366i | 0.0180793 | + | 0.0313142i | ||||
\(545\) | −5.76678 | − | 9.98836i | −0.247022 | − | 0.427854i | ||||
\(546\) | 15.5845 | + | 26.9931i | 0.666953 | + | 1.15520i | ||||
\(547\) | −5.85241 | + | 10.1367i | −0.250231 | + | 0.433413i | −0.963589 | − | 0.267387i | \(-0.913840\pi\) |
0.713358 | + | 0.700799i | \(0.247173\pi\) | |||||||
\(548\) | −39.1429 | −1.67210 | ||||||||
\(549\) | −1.63183 | + | 2.82641i | −0.0696448 | + | 0.120628i | ||||
\(550\) | −31.8781 | − | 55.2144i | −1.35929 | − | 2.35435i | ||||
\(551\) | −12.6651 | −0.539550 | ||||||||
\(552\) | 32.7272 | + | 56.6852i | 1.39296 | + | 2.41268i | ||||
\(553\) | −17.2366 | + | 29.8546i | −0.732973 | + | 1.26955i | ||||
\(554\) | 31.0528 | − | 53.7850i | 1.31931 | − | 2.28511i | ||||
\(555\) | 11.6714 | 0.495423 | ||||||||
\(556\) | −38.0683 | + | 65.9362i | −1.61446 | + | 2.79632i | ||||
\(557\) | −11.9744 | −0.507370 | −0.253685 | − | 0.967287i | \(-0.581643\pi\) | ||||
−0.253685 | + | 0.967287i | \(0.581643\pi\) | |||||||
\(558\) | 9.27016 | 0.392437 | ||||||||
\(559\) | 11.3604 | + | 1.63568i | 0.480494 | + | 0.0691819i | ||||
\(560\) | −18.7853 | −0.793824 | ||||||||
\(561\) | −9.00038 | −0.379997 | ||||||||
\(562\) | −1.68824 | + | 2.92412i | −0.0712141 | + | 0.123347i | ||||
\(563\) | −10.8070 | −0.455460 | −0.227730 | − | 0.973724i | \(-0.573130\pi\) | ||||
−0.227730 | + | 0.973724i | \(0.573130\pi\) | |||||||
\(564\) | 3.86004 | − | 6.68579i | 0.162537 | − | 0.281523i | ||||
\(565\) | −1.50026 | + | 2.59853i | −0.0631164 | + | 0.109321i | ||||
\(566\) | 16.5863 | + | 28.7283i | 0.697174 | + | 1.20754i | ||||
\(567\) | −29.1046 | −1.22228 | ||||||||
\(568\) | 13.6828 | + | 23.6993i | 0.574117 | + | 0.994399i | ||||
\(569\) | 7.38597 | − | 12.7929i | 0.309636 | − | 0.536305i | −0.668647 | − | 0.743580i | \(-0.733126\pi\) |
0.978283 | + | 0.207275i | \(0.0664595\pi\) | |||||||
\(570\) | 14.2156 | 0.595427 | ||||||||
\(571\) | 0.412767 | − | 0.714934i | 0.0172738 | − | 0.0299190i | −0.857259 | − | 0.514885i | \(-0.827835\pi\) |
0.874533 | + | 0.484966i | \(0.161168\pi\) | |||||||
\(572\) | 21.6573 | + | 37.5115i | 0.905536 | + | 1.56843i | ||||
\(573\) | −6.79132 | − | 11.7629i | −0.283712 | − | 0.491403i | ||||
\(574\) | −16.2213 | − | 28.0962i | −0.677066 | − | 1.17271i | ||||
\(575\) | 36.5754 | 1.52530 | ||||||||
\(576\) | −2.75474 | − | 4.77135i | −0.114781 | − | 0.198806i | ||||
\(577\) | 18.8361 | + | 32.6250i | 0.784156 | + | 1.35820i | 0.929502 | + | 0.368817i | \(0.120237\pi\) |
−0.145346 | + | 0.989381i | \(0.546429\pi\) | |||||||
\(578\) | 1.23326 | − | 2.13607i | 0.0512969 | − | 0.0888488i | ||||
\(579\) | 4.42220 | − | 7.65947i | 0.183780 | − | 0.318317i | ||||
\(580\) | −9.78907 | −0.406469 | ||||||||
\(581\) | 3.40625 | 0.141315 | ||||||||
\(582\) | 8.62266 | − | 14.9349i | 0.357421 | − | 0.619071i | ||||
\(583\) | 27.8649 | − | 48.2634i | 1.15405 | − | 1.99887i | ||||
\(584\) | 29.7326 | + | 51.4984i | 1.23035 | + | 2.13102i | ||||
\(585\) | 0.595530 | + | 1.03149i | 0.0246221 | + | 0.0426468i | ||||
\(586\) | −13.8511 | −0.572182 | ||||||||
\(587\) | −1.02827 | − | 1.78102i | −0.0424414 | − | 0.0735107i | 0.844024 | − | 0.536305i | \(-0.180180\pi\) |
−0.886466 | + | 0.462794i | \(0.846847\pi\) | |||||||
\(588\) | 50.4302 | + | 87.3477i | 2.07971 | + | 3.60216i | ||||
\(589\) | 10.7161 | + | 18.5608i | 0.441548 | + | 0.764784i | ||||
\(590\) | 8.05937 | − | 13.9592i | 0.331799 | − | 0.574693i | ||||
\(591\) | 37.1305 | 1.52734 | ||||||||
\(592\) | −20.6743 | + | 35.8089i | −0.849707 | + | 1.47174i | ||||
\(593\) | −10.0552 | − | 17.4161i | −0.412918 | − | 0.715195i | 0.582290 | − | 0.812981i | \(-0.302157\pi\) |
−0.995207 | + | 0.0977868i | \(0.968824\pi\) | |||||||
\(594\) | −84.2262 | −3.45584 | ||||||||
\(595\) | 2.08292 | + | 3.60771i | 0.0853912 | + | 0.147902i | ||||
\(596\) | 14.5961 | − | 25.2811i | 0.597879 | − | 1.03556i | ||||
\(597\) | 16.2703 | − | 28.1810i | 0.665899 | − | 1.15337i | ||||
\(598\) | −37.0181 | −1.51378 | ||||||||
\(599\) | −9.31183 | + | 16.1286i | −0.380471 | + | 0.658995i | −0.991130 | − | 0.132899i | \(-0.957572\pi\) |
0.610658 | + | 0.791894i | \(0.290905\pi\) | |||||||
\(600\) | −32.5612 | −1.32931 | ||||||||
\(601\) | 15.4768 | 0.631312 | 0.315656 | − | 0.948874i | \(-0.397776\pi\) | ||||
0.315656 | + | 0.948874i | \(0.397776\pi\) | |||||||
\(602\) | 77.8190 | + | 11.2044i | 3.17167 | + | 0.456659i | ||||
\(603\) | −8.59301 | −0.349934 | ||||||||
\(604\) | −74.0789 | −3.01423 | ||||||||
\(605\) | 11.0217 | − | 19.0902i | 0.448097 | − | 0.776127i | ||||
\(606\) | −7.75413 | −0.314990 | ||||||||
\(607\) | −18.5792 | + | 32.1802i | −0.754107 | + | 1.30615i | 0.191710 | + | 0.981452i | \(0.438597\pi\) |
−0.945817 | + | 0.324701i | \(0.894736\pi\) | |||||||
\(608\) | −1.90934 | + | 3.30707i | −0.0774338 | + | 0.134119i | ||||
\(609\) | 10.0971 | + | 17.4887i | 0.409155 | + | 0.708678i | ||||
\(610\) | −8.68821 | −0.351775 | ||||||||
\(611\) | 1.11391 | + | 1.92935i | 0.0450641 | + | 0.0780533i | ||||
\(612\) | 1.62131 | − | 2.80819i | 0.0655375 | − | 0.113514i | ||||
\(613\) | −0.666538 | −0.0269212 | −0.0134606 | − | 0.999909i | \(-0.504285\pi\) | ||||
−0.0134606 | + | 0.999909i | \(0.504285\pi\) | |||||||
\(614\) | −28.5617 | + | 49.4702i | −1.15265 | + | 1.99646i | ||||
\(615\) | 1.72210 | + | 2.98277i | 0.0694418 | + | 0.120277i | ||||
\(616\) | 75.6972 | + | 131.111i | 3.04993 | + | 5.28263i | ||||
\(617\) | 9.02543 | + | 15.6325i | 0.363350 | + | 0.629341i | 0.988510 | − | 0.151156i | \(-0.0482995\pi\) |
−0.625160 | + | 0.780497i | \(0.714966\pi\) | |||||||
\(618\) | 25.1479 | 1.01160 | ||||||||
\(619\) | −9.90836 | − | 17.1618i | −0.398251 | − | 0.689790i | 0.595260 | − | 0.803533i | \(-0.297049\pi\) |
−0.993510 | + | 0.113743i | \(0.963716\pi\) | |||||||
\(620\) | 8.28266 | + | 14.3460i | 0.332640 | + | 0.576149i | ||||
\(621\) | 24.1593 | − | 41.8451i | 0.969479 | − | 1.67919i | ||||
\(622\) | 21.5245 | − | 37.2815i | 0.863053 | − | 1.49485i | ||||
\(623\) | 48.3084 | 1.93543 | ||||||||
\(624\) | 11.7228 | 0.469287 | ||||||||
\(625\) | −7.26137 | + | 12.5771i | −0.290455 | + | 0.503083i | ||||
\(626\) | 31.1043 | − | 53.8742i | 1.24318 | − | 2.15325i | ||||
\(627\) | −20.3767 | − | 35.2934i | −0.813766 | − | 1.40948i | ||||
\(628\) | −13.5093 | − | 23.3987i | −0.539078 | − | 0.933711i | ||||
\(629\) | 9.16946 | 0.365610 | ||||||||
\(630\) | 4.07939 | + | 7.06571i | 0.162527 | + | 0.281505i | ||||
\(631\) | 3.18978 | + | 5.52485i | 0.126983 | + | 0.219941i | 0.922506 | − | 0.385982i | \(-0.126137\pi\) |
−0.795523 | + | 0.605923i | \(0.792804\pi\) | |||||||
\(632\) | 18.2244 | + | 31.5656i | 0.724929 | + | 1.25561i | ||||
\(633\) | 1.26762 | − | 2.19558i | 0.0503832 | − | 0.0872663i | ||||
\(634\) | −31.1261 | −1.23618 | ||||||||
\(635\) | −5.89629 | + | 10.2127i | −0.233987 | + | 0.405278i | ||||
\(636\) | −27.8902 | − | 48.3073i | −1.10592 | − | 1.91551i | ||||
\(637\) | −29.1058 | −1.15321 | ||||||||
\(638\) | 20.9036 | + | 36.2062i | 0.827583 | + | 1.43342i | ||||
\(639\) | 2.11391 | − | 3.66141i | 0.0836252 | − | 0.144843i | ||||
\(640\) | 8.05617 | − | 13.9537i | 0.318448 | − | 0.551568i | ||||
\(641\) | −14.0926 | −0.556625 | −0.278312 | − | 0.960491i | \(-0.589775\pi\) | ||||
−0.278312 | + | 0.960491i | \(0.589775\pi\) | |||||||
\(642\) | −8.99329 | + | 15.5768i | −0.354937 | + | 0.614769i | ||||
\(643\) | 34.0930 | 1.34450 | 0.672248 | − | 0.740326i | \(-0.265329\pi\) | ||||
0.672248 | + | 0.740326i | \(0.265329\pi\) | |||||||
\(644\) | −170.213 | −6.70733 | ||||||||
\(645\) | −8.26148 | − | 1.18949i | −0.325295 | − | 0.0468362i | ||||
\(646\) | 11.1683 | 0.439411 | ||||||||
\(647\) | 6.82365 | 0.268265 | 0.134133 | − | 0.990963i | \(-0.457175\pi\) | ||||
0.134133 | + | 0.990963i | \(0.457175\pi\) | |||||||
\(648\) | −15.3863 | + | 26.6499i | −0.604432 | + | 1.04691i | ||||
\(649\) | −46.2092 | −1.81387 | ||||||||
\(650\) | 9.20758 | − | 15.9480i | 0.361151 | − | 0.625532i | ||||
\(651\) | 17.0866 | − | 29.5948i | 0.669676 | − | 1.15991i | ||||
\(652\) | 16.7165 | + | 28.9537i | 0.654667 | + | 1.13392i | ||||
\(653\) | 35.1241 | 1.37451 | 0.687256 | − | 0.726415i | \(-0.258815\pi\) | ||||
0.687256 | + | 0.726415i | \(0.258815\pi\) | |||||||
\(654\) | 24.6512 | + | 42.6972i | 0.963939 | + | 1.66959i | ||||
\(655\) | 8.87694 | − | 15.3753i | 0.346851 | − | 0.600763i | ||||
\(656\) | −12.2019 | −0.476403 | ||||||||
\(657\) | 4.59353 | − | 7.95623i | 0.179211 | − | 0.310402i | ||||
\(658\) | 7.63032 | + | 13.2161i | 0.297461 | + | 0.515218i | ||||
\(659\) | −5.41357 | − | 9.37658i | −0.210883 | − | 0.365260i | 0.741108 | − | 0.671385i | \(-0.234300\pi\) |
−0.951991 | + | 0.306126i | \(0.900967\pi\) | |||||||
\(660\) | −15.7495 | − | 27.2790i | −0.613049 | − | 1.06183i | ||||
\(661\) | 17.4304 | 0.677963 | 0.338981 | − | 0.940793i | \(-0.389918\pi\) | ||||
0.338981 | + | 0.940793i | \(0.389918\pi\) | |||||||
\(662\) | 12.6402 | + | 21.8935i | 0.491276 | + | 0.850915i | ||||
\(663\) | −1.29982 | − | 2.25136i | −0.0504810 | − | 0.0874356i | ||||
\(664\) | 1.80074 | − | 3.11897i | 0.0698822 | − | 0.121040i | ||||
\(665\) | −9.43135 | + | 16.3356i | −0.365732 | + | 0.633466i | ||||
\(666\) | 17.9584 | 0.695874 | ||||||||
\(667\) | −23.9839 | −0.928659 | ||||||||
\(668\) | −4.44503 | + | 7.69901i | −0.171983 | + | 0.297884i | ||||
\(669\) | −14.3066 | + | 24.7798i | −0.553127 | + | 0.958044i | ||||
\(670\) | −11.4378 | − | 19.8108i | −0.441879 | − | 0.765357i | ||||
\(671\) | 12.4537 | + | 21.5704i | 0.480769 | + | 0.832716i | ||||
\(672\) | 6.08880 | 0.234881 | ||||||||
\(673\) | −16.0682 | − | 27.8310i | −0.619385 | − | 1.07281i | −0.989598 | − | 0.143860i | \(-0.954049\pi\) |
0.370213 | − | 0.928947i | \(-0.379285\pi\) | |||||||
\(674\) | −12.6790 | − | 21.9607i | −0.488377 | − | 0.845893i | ||||
\(675\) | 12.0184 | + | 20.8165i | 0.462588 | + | 0.801226i | ||||
\(676\) | 20.2888 | − | 35.1412i | 0.780338 | − | 1.35159i | ||||
\(677\) | −36.1628 | −1.38985 | −0.694924 | − | 0.719083i | \(-0.744562\pi\) | ||||
−0.694924 | + | 0.719083i | \(0.744562\pi\) | |||||||
\(678\) | 6.41315 | − | 11.1079i | 0.246296 | − | 0.426597i | ||||
\(679\) | 11.4414 | + | 19.8171i | 0.439081 | + | 0.760510i | ||||
\(680\) | 4.40459 | 0.168908 | ||||||||
\(681\) | 20.7869 | + | 36.0040i | 0.796556 | + | 1.37968i | ||||
\(682\) | 35.3737 | − | 61.2690i | 1.35453 | − | 2.34611i | ||||
\(683\) | 5.93363 | − | 10.2773i | 0.227044 | − | 0.393252i | −0.729887 | − | 0.683568i | \(-0.760427\pi\) |
0.956931 | + | 0.290316i | \(0.0937605\pi\) | |||||||
\(684\) | 14.6824 | 0.561397 | ||||||||
\(685\) | −4.10720 | + | 7.11388i | −0.156928 | + | 0.271807i | ||||
\(686\) | −115.448 | −4.40781 | ||||||||
\(687\) | 25.9047 | 0.988326 | ||||||||
\(688\) | 18.2835 | − | 23.2399i | 0.697053 | − | 0.886014i | ||||
\(689\) | 16.0969 | 0.613241 | ||||||||
\(690\) | 26.9201 | 1.02483 | ||||||||
\(691\) | −2.57372 | + | 4.45782i | −0.0979091 | + | 0.169584i | −0.910819 | − | 0.412806i | \(-0.864549\pi\) |
0.812910 | + | 0.582389i | \(0.197882\pi\) | |||||||
\(692\) | 15.4059 | 0.585646 | ||||||||
\(693\) | 11.6948 | − | 20.2560i | 0.444249 | − | 0.769461i | ||||
\(694\) | −7.18899 | + | 12.4517i | −0.272890 | + | 0.472660i | ||||
\(695\) | 7.98889 | + | 13.8372i | 0.303036 | + | 0.524873i | ||||
\(696\) | 21.3516 | 0.809331 | ||||||||
\(697\) | 1.35294 | + | 2.34337i | 0.0512464 | + | 0.0887614i | ||||
\(698\) | 20.8962 | − | 36.1933i | 0.790934 | − | 1.36994i | ||||
\(699\) | 10.1924 | 0.385512 | ||||||||
\(700\) | 42.3374 | − | 73.3306i | 1.60020 | − | 2.77164i | ||||
\(701\) | −16.1751 | − | 28.0161i | −0.610926 | − | 1.05815i | −0.991085 | − | 0.133233i | \(-0.957464\pi\) |
0.380159 | − | 0.924921i | \(-0.375869\pi\) | |||||||
\(702\) | −12.1638 | − | 21.0684i | −0.459095 | − | 0.795175i | ||||
\(703\) | 20.7594 | + | 35.9564i | 0.782957 | + | 1.35612i | ||||
\(704\) | −42.0468 | −1.58470 | ||||||||
\(705\) | −0.810056 | − | 1.40306i | −0.0305085 | − | 0.0528422i | ||||
\(706\) | 24.2189 | + | 41.9484i | 0.911490 | + | 1.57875i | ||||
\(707\) | 5.14447 | − | 8.91049i | 0.193478 | − | 0.335113i | ||||
\(708\) | −23.1256 | + | 40.0547i | −0.869113 | + | 1.50535i | ||||
\(709\) | 4.53699 | 0.170390 | 0.0851951 | − | 0.996364i | \(-0.472849\pi\) | ||||
0.0851951 | + | 0.996364i | \(0.472849\pi\) | |||||||
\(710\) | 11.2549 | 0.422390 | ||||||||
\(711\) | 2.81558 | − | 4.87672i | 0.105592 | − | 0.182891i | ||||
\(712\) | 25.5386 | − | 44.2341i | 0.957098 | − | 1.65774i | ||||
\(713\) | 20.2930 | + | 35.1486i | 0.759980 | + | 1.31632i | ||||
\(714\) | −8.90382 | − | 15.4219i | −0.333217 | − | 0.577149i | ||||
\(715\) | 9.08984 | 0.339941 | ||||||||
\(716\) | 13.5009 | + | 23.3843i | 0.504553 | + | 0.873911i | ||||
\(717\) | −2.69125 | − | 4.66138i | −0.100507 | − | 0.174082i | ||||
\(718\) | 0.914819 | + | 1.58451i | 0.0341407 | + | 0.0591335i | ||||
\(719\) | 7.14812 | − | 12.3809i | 0.266580 | − | 0.461730i | −0.701396 | − | 0.712771i | \(-0.747440\pi\) |
0.967976 | + | 0.251041i | \(0.0807730\pi\) | |||||||
\(720\) | 3.06856 | 0.114359 | ||||||||
\(721\) | −16.6843 | + | 28.8981i | −0.621357 | + | 1.07622i | ||||
\(722\) | 1.85283 | + | 3.20920i | 0.0689552 | + | 0.119434i | ||||
\(723\) | 17.6690 | 0.657115 | ||||||||
\(724\) | 20.6814 | + | 35.8212i | 0.768617 | + | 1.33128i | ||||
\(725\) | 5.96556 | − | 10.3326i | 0.221555 | − | 0.383745i | ||||
\(726\) | −47.1145 | + | 81.6047i | −1.74858 | + | 3.02864i | ||||
\(727\) | 23.8266 | 0.883681 | 0.441840 | − | 0.897094i | \(-0.354326\pi\) | ||||
0.441840 | + | 0.897094i | \(0.354326\pi\) | |||||||
\(728\) | −21.8642 | + | 37.8699i | −0.810340 | + | 1.40355i | ||||
\(729\) | 29.8627 | 1.10603 | ||||||||
\(730\) | 24.4569 | 0.905192 | ||||||||
\(731\) | −6.49051 | − | 0.934508i | −0.240060 | − | 0.0345640i | ||||
\(732\) | 24.9300 | 0.921439 | ||||||||
\(733\) | 2.27980 | 0.0842063 | 0.0421031 | − | 0.999113i | \(-0.486594\pi\) | ||||
0.0421031 | + | 0.999113i | \(0.486594\pi\) | |||||||
\(734\) | −18.8707 | + | 32.6849i | −0.696529 | + | 1.20642i | ||||
\(735\) | 21.1662 | 0.780728 | ||||||||
\(736\) | −3.61571 | + | 6.26260i | −0.133277 | + | 0.230842i | ||||
\(737\) | −32.7897 | + | 56.7935i | −1.20783 | + | 2.09202i | ||||
\(738\) | 2.64974 | + | 4.58949i | 0.0975384 | + | 0.168941i | ||||
\(739\) | −27.6319 | −1.01646 | −0.508228 | − | 0.861222i | \(-0.669699\pi\) | ||||
−0.508228 | + | 0.861222i | \(0.669699\pi\) | |||||||
\(740\) | 16.0454 | + | 27.7914i | 0.589840 | + | 1.02163i | ||||
\(741\) | 5.88555 | − | 10.1941i | 0.216211 | − | 0.374488i | ||||
\(742\) | 110.264 | 4.04791 | ||||||||
\(743\) | 10.7834 | − | 18.6774i | 0.395605 | − | 0.685209i | −0.597573 | − | 0.801815i | \(-0.703868\pi\) |
0.993178 | + | 0.116606i | \(0.0372015\pi\) | |||||||
\(744\) | −18.0659 | − | 31.2910i | −0.662327 | − | 1.14718i | ||||
\(745\) | −3.06308 | − | 5.30542i | −0.112223 | − | 0.194375i | ||||
\(746\) | 18.3246 | + | 31.7391i | 0.670910 | + | 1.16205i | ||||
\(747\) | −0.556409 | −0.0203579 | ||||||||
\(748\) | −12.3734 | − | 21.4313i | −0.452416 | − | 0.783607i | ||||
\(749\) | −11.9332 | − | 20.6689i | −0.436029 | − | 0.755224i | ||||
\(750\) | −14.5447 | + | 25.1922i | −0.531098 | + | 0.919889i | ||||
\(751\) | 2.45618 | − | 4.25423i | 0.0896273 | − | 0.155239i | −0.817726 | − | 0.575607i | \(-0.804766\pi\) |
0.907354 | + | 0.420368i | \(0.138099\pi\) | |||||||
\(752\) | 5.73961 | 0.209302 | ||||||||
\(753\) | 23.8964 | 0.870833 | ||||||||
\(754\) | −6.03775 | + | 10.4577i | −0.219882 | + | 0.380847i | ||||
\(755\) | −7.77297 | + | 13.4632i | −0.282887 | + | 0.489976i | ||||
\(756\) | −55.9306 | − | 96.8746i | −2.03418 | − | 3.52330i | ||||
\(757\) | −14.4082 | − | 24.9557i | −0.523673 | − | 0.907029i | −0.999620 | − | 0.0275549i | \(-0.991228\pi\) |
0.475947 | − | 0.879474i | \(-0.342105\pi\) | |||||||
\(758\) | −87.4792 | −3.17739 | ||||||||
\(759\) | −38.5873 | − | 66.8352i | −1.40063 | − | 2.42596i | ||||
\(760\) | 9.97189 | + | 17.2718i | 0.361718 | + | 0.626515i | ||||
\(761\) | −16.8873 | − | 29.2497i | −0.612165 | − | 1.06030i | −0.990875 | − | 0.134786i | \(-0.956965\pi\) |
0.378709 | − | 0.925516i | \(-0.376368\pi\) | |||||||
\(762\) | 25.2048 | − | 43.6561i | 0.913075 | − | 1.58149i | ||||
\(763\) | −65.4193 | −2.36834 | ||||||||
\(764\) | 18.6729 | − | 32.3424i | 0.675562 | − | 1.17011i | ||||
\(765\) | −0.340242 | − | 0.589317i | −0.0123015 | − | 0.0213068i | ||||
\(766\) | 23.8826 | 0.862912 | ||||||||
\(767\) | −6.67348 | − | 11.5588i | −0.240965 | − | 0.417364i | ||||
\(768\) | −24.1321 | + | 41.7980i | −0.870791 | + | 1.50825i | ||||
\(769\) | −7.17339 | + | 12.4247i | −0.258679 | + | 0.448046i | −0.965888 | − | 0.258959i | \(-0.916621\pi\) |
0.707209 | + | 0.707004i | \(0.249954\pi\) | |||||||
\(770\) | 62.2656 | 2.24390 | ||||||||
\(771\) | 1.41297 | − | 2.44734i | 0.0508870 | − | 0.0881389i | ||||
\(772\) | 24.3179 | 0.875219 | ||||||||
\(773\) | −0.116741 | −0.00419887 | −0.00209943 | − | 0.999998i | \(-0.500668\pi\) | ||||
−0.00209943 | + | 0.999998i | \(0.500668\pi\) | |||||||
\(774\) | −12.7117 | − | 1.83023i | −0.456912 | − | 0.0657864i | ||||
\(775\) | −20.1901 | −0.725251 | ||||||||
\(776\) | 24.1943 | 0.868524 | ||||||||
\(777\) | 33.1005 | − | 57.3318i | 1.18748 | − | 2.05677i | ||||
\(778\) | −37.5989 | −1.34799 | ||||||||
\(779\) | −6.12607 | + | 10.6107i | −0.219489 | + | 0.380167i | ||||
\(780\) | 4.54905 | − | 7.87919i | 0.162882 | − | 0.282120i | ||||
\(781\) | −16.1328 | − | 27.9428i | −0.577277 | − | 0.999874i | ||||
\(782\) | 21.1494 | 0.756302 | ||||||||
\(783\) | −7.88090 | − | 13.6501i | −0.281640 | − | 0.487816i | ||||
\(784\) | −37.4931 | + | 64.9399i | −1.33904 | + | 2.31928i | ||||
\(785\) | −5.67002 | −0.202372 | ||||||||
\(786\) | −37.9462 | + | 65.7247i | −1.35350 | + | 2.34432i | ||||
\(787\) | −6.55228 | − | 11.3489i | −0.233564 | − | 0.404544i | 0.725291 | − | 0.688443i | \(-0.241705\pi\) |
−0.958854 | + | 0.283899i | \(0.908372\pi\) | |||||||
\(788\) | 51.0456 | + | 88.4135i | 1.81842 | + | 3.14960i | ||||
\(789\) | −2.96434 | − | 5.13439i | −0.105533 | − | 0.182789i | ||||
\(790\) | 14.9907 | 0.533346 | ||||||||
\(791\) | 8.50960 | + | 14.7391i | 0.302567 | + | 0.524061i | ||||
\(792\) | −12.3651 | − | 21.4169i | −0.439374 | − | 0.761017i | ||||
\(793\) | −3.59709 | + | 6.23034i | −0.127736 | + | 0.221246i | ||||
\(794\) | −8.42974 | + | 14.6007i | −0.299160 | + | 0.518161i | ||||
\(795\) | −11.7059 | −0.415165 | ||||||||
\(796\) | 89.4711 | 3.17122 | ||||||||
\(797\) | −11.6155 | + | 20.1186i | −0.411442 | + | 0.712638i | −0.995048 | − | 0.0993987i | \(-0.968308\pi\) |
0.583606 | + | 0.812037i | \(0.301641\pi\) | |||||||
\(798\) | 40.3161 | − | 69.8295i | 1.42717 | − | 2.47194i | ||||
\(799\) | −0.636409 | − | 1.10229i | −0.0225145 | − | 0.0389963i | ||||
\(800\) | −1.79869 | − | 3.11542i | −0.0635932 | − | 0.110147i | ||||
\(801\) | −7.89114 | −0.278820 | ||||||||
\(802\) | 7.54871 | + | 13.0747i | 0.266554 | + | 0.461685i | ||||
\(803\) | −35.0566 | − | 60.7197i | −1.23712 | − | 2.14275i | ||||
\(804\) | 32.8195 | + | 56.8451i | 1.15746 | + | 2.00477i | ||||
\(805\) | −17.8602 | + | 30.9347i | −0.629488 | + | 1.09030i | ||||
\(806\) | 20.4345 | 0.719774 | ||||||||
\(807\) | 9.92875 | − | 17.1971i | 0.349509 | − | 0.605367i | ||||
\(808\) | −5.43932 | − | 9.42118i | −0.191355 | − | 0.331436i | ||||
\(809\) | −49.8597 | −1.75297 | −0.876486 | − | 0.481427i | \(-0.840119\pi\) | ||||
−0.876486 | + | 0.481427i | \(0.840119\pi\) | |||||||
\(810\) | 6.32810 | + | 10.9606i | 0.222347 | + | 0.385116i | ||||
\(811\) | 0.311149 | − | 0.538925i | 0.0109259 | − | 0.0189242i | −0.860511 | − | 0.509432i | \(-0.829855\pi\) |
0.871437 | + | 0.490508i | \(0.163189\pi\) | |||||||
\(812\) | −27.7622 | + | 48.0856i | −0.974263 | + | 1.68747i | ||||
\(813\) | −22.0842 | −0.774528 | ||||||||
\(814\) | 68.5267 | − | 118.692i | 2.40186 | − | 4.16015i | ||||
\(815\) | 7.01612 | 0.245764 | ||||||||
\(816\) | −6.69755 | −0.234461 | ||||||||
\(817\) | −11.0299 | − | 27.5671i | −0.385886 | − | 0.964451i | ||||
\(818\) | 2.74344 | 0.0959220 | ||||||||
\(819\) | 6.75579 | 0.236067 | ||||||||
\(820\) | −4.73496 | + | 8.20119i | −0.165352 | + | 0.286398i | ||||
\(821\) | −18.0316 | −0.629306 | −0.314653 | − | 0.949207i | \(-0.601888\pi\) | ||||
−0.314653 | + | 0.949207i | \(0.601888\pi\) | |||||||
\(822\) | 17.5570 | − | 30.4096i | 0.612371 | − | 1.06066i | ||||
\(823\) | −19.7079 | + | 34.1351i | −0.686975 | + | 1.18988i | 0.285837 | + | 0.958278i | \(0.407729\pi\) |
−0.972812 | + | 0.231597i | \(0.925605\pi\) | |||||||
\(824\) | 17.6406 | + | 30.5544i | 0.614539 | + | 1.06441i | ||||
\(825\) | 38.3916 | 1.33663 | ||||||||
\(826\) | −45.7134 | − | 79.1780i | −1.59057 | − | 2.75495i | ||||
\(827\) | 13.3224 | − | 23.0751i | 0.463266 | − | 0.802401i | −0.535855 | − | 0.844310i | \(-0.680011\pi\) |
0.999121 | + | 0.0419091i | \(0.0133440\pi\) | |||||||
\(828\) | 27.8041 | 0.966261 | ||||||||
\(829\) | 6.61456 | − | 11.4568i | 0.229733 | − | 0.397910i | −0.727996 | − | 0.685582i | \(-0.759548\pi\) |
0.957729 | + | 0.287672i | \(0.0928813\pi\) | |||||||
\(830\) | −0.740609 | − | 1.28277i | −0.0257069 | − | 0.0445257i | ||||
\(831\) | 18.6989 | + | 32.3874i | 0.648656 | + | 1.12351i | ||||
\(832\) | −6.07235 | − | 10.5176i | −0.210521 | − | 0.364633i | ||||
\(833\) | 16.6289 | 0.576158 | ||||||||
\(834\) | −34.1500 | − | 59.1496i | −1.18252 | − | 2.04818i | ||||
\(835\) | 0.932819 | + | 1.61569i | 0.0322815 | + | 0.0559132i | ||||
\(836\) | 56.0261 | − | 97.0401i | 1.93770 | − | 3.35620i | ||||
\(837\) | −13.3363 | + | 23.0991i | −0.460969 | + | 0.798421i | ||||
\(838\) | 6.37627 | 0.220265 | ||||||||
\(839\) | −10.3966 | −0.358930 | −0.179465 | − | 0.983764i | \(-0.557437\pi\) | ||||
−0.179465 | + | 0.983764i | \(0.557437\pi\) | |||||||
\(840\) | 15.9000 | − | 27.5396i | 0.548602 | − | 0.950206i | ||||
\(841\) | 10.5882 | − | 18.3392i | 0.365109 | − | 0.632387i | ||||
\(842\) | 21.2931 | + | 36.8807i | 0.733809 | + | 1.27099i | ||||
\(843\) | −1.01660 | − | 1.76080i | −0.0350135 | − | 0.0606451i | ||||
\(844\) | 6.97068 | 0.239941 | ||||||||
\(845\) | −4.25774 | − | 7.37462i | −0.146471 | − | 0.253695i | ||||
\(846\) | −1.24641 | − | 2.15884i | −0.0428524 | − | 0.0742225i | ||||
\(847\) | −62.5162 | − | 108.281i | −2.14808 | − | 3.72059i | ||||
\(848\) | 20.7354 | − | 35.9147i | 0.712056 | − | 1.23332i | ||||
\(849\) | −19.9753 | −0.685551 | ||||||||
\(850\) | −5.26054 | + | 9.11153i | −0.180435 | + | 0.312523i | ||||
\(851\) | 39.3122 | + | 68.0907i | 1.34760 | + | 2.33412i | ||||
\(852\) | −32.2949 | −1.10641 | ||||||||
\(853\) | −3.67648 | − | 6.36784i | −0.125880 | − | 0.218031i | 0.796197 | − | 0.605038i | \(-0.206842\pi\) |
−0.922077 | + | 0.387007i | \(0.873509\pi\) | |||||||
\(854\) | −24.6401 | + | 42.6780i | −0.843168 | + | 1.46041i | ||||
\(855\) | 1.54060 | − | 2.66840i | 0.0526875 | − | 0.0912574i | ||||
\(856\) | −25.2342 | −0.862488 | ||||||||
\(857\) | −20.0485 | + | 34.7250i | −0.684844 | + | 1.18618i | 0.288642 | + | 0.957437i | \(0.406796\pi\) |
−0.973486 | + | 0.228748i | \(0.926537\pi\) | |||||||
\(858\) | −38.8563 | −1.32653 | ||||||||
\(859\) | 12.2536 | 0.418089 | 0.209044 | − | 0.977906i | \(-0.432965\pi\) | ||||
0.209044 | + | 0.977906i | \(0.432965\pi\) | |||||||
\(860\) | −8.52519 | − | 21.3071i | −0.290707 | − | 0.726567i | ||||
\(861\) | 19.5358 | 0.665778 | ||||||||
\(862\) | 5.47807 | 0.186584 | ||||||||
\(863\) | −1.53879 | + | 2.66526i | −0.0523810 | + | 0.0907265i | −0.891027 | − | 0.453950i | \(-0.850014\pi\) |
0.838646 | + | 0.544677i | \(0.183348\pi\) | |||||||
\(864\) | −4.75238 | −0.161679 | ||||||||
\(865\) | 1.61652 | − | 2.79989i | 0.0549633 | − | 0.0951993i | ||||
\(866\) | 49.5350 | − | 85.7972i | 1.68327 | − | 2.91551i | ||||
\(867\) | 0.742625 | + | 1.28626i | 0.0252209 | + | 0.0436838i | ||||
\(868\) | 93.9599 | 3.18921 | ||||||||
\(869\) | −21.4877 | − | 37.2178i | −0.728920 | − | 1.26253i | ||||
\(870\) | 4.39075 | − | 7.60501i | 0.148861 | − | 0.257834i | ||||
\(871\) | −18.9418 | −0.641819 | ||||||||
\(872\) | −34.5844 | + | 59.9019i | −1.17117 | + | 2.02853i | ||||
\(873\) | −1.86894 | − | 3.23710i | −0.0632541 | − | 0.109559i | ||||
\(874\) | 47.8818 | + | 82.9338i | 1.61963 | + | 2.80528i | ||||
\(875\) | −19.2994 | − | 33.4275i | −0.652438 | − | 1.13006i | ||||
\(876\) | −70.1768 | −2.37106 | ||||||||
\(877\) | −10.0383 | − | 17.3869i | −0.338970 | − | 0.587113i | 0.645269 | − | 0.763955i | \(-0.276745\pi\) |
−0.984239 | + | 0.176842i | \(0.943412\pi\) | |||||||
\(878\) | −8.75085 | − | 15.1569i | −0.295327 | − | 0.511521i | ||||
\(879\) | 4.17030 | − | 7.22318i | 0.140661 | − | 0.243632i | ||||
\(880\) | 11.7092 | − | 20.2809i | 0.394717 | − | 0.683671i | ||||
\(881\) | −43.0069 | −1.44894 | −0.724470 | − | 0.689307i | \(-0.757915\pi\) | ||||
−0.724470 | + | 0.689307i | \(0.757915\pi\) | |||||||
\(882\) | 32.5678 | 1.09661 | ||||||||
\(883\) | 0.0219248 | − | 0.0379749i | 0.000737829 | − | 0.00127796i | −0.865656 | − | 0.500639i | \(-0.833098\pi\) |
0.866394 | + | 0.499361i | \(0.166432\pi\) | |||||||
\(884\) | 3.57390 | − | 6.19017i | 0.120203 | − | 0.208198i | ||||
\(885\) | 4.85306 | + | 8.40575i | 0.163134 | + | 0.282556i | ||||
\(886\) | 0.274767 | + | 0.475911i | 0.00923099 | + | 0.0159886i | ||||
\(887\) | −3.88506 | −0.130448 | −0.0652238 | − | 0.997871i | \(-0.520776\pi\) | ||||
−0.0652238 | + | 0.997871i | \(0.520776\pi\) | |||||||
\(888\) | −34.9976 | − | 60.6177i | −1.17444 | − | 2.03420i | ||||
\(889\) | 33.4443 | + | 57.9272i | 1.12168 | + | 1.94282i | ||||
\(890\) | −10.5035 | − | 18.1926i | −0.352079 | − | 0.609818i | ||||
\(891\) | 18.1414 | − | 31.4218i | 0.607759 | − | 1.05267i | ||||
\(892\) | −78.6729 | −2.63416 | ||||||||
\(893\) | 2.88163 | − | 4.99113i | 0.0964301 | − | 0.167022i | ||||
\(894\) | 13.0937 | + | 22.6790i | 0.437920 | + | 0.758500i | ||||
\(895\) | 5.66651 | 0.189411 | ||||||||
\(896\) | −45.6952 | − | 79.1465i | −1.52657 | − | 2.64410i | ||||
\(897\) | 11.1455 | − | 19.3045i | 0.372136 | − | 0.644559i | ||||
\(898\) | −27.1574 | + | 47.0380i | −0.906254 | + | 1.56968i | ||||
\(899\) | 13.2394 | 0.441559 | ||||||||
\(900\) | −6.91578 | + | 11.9785i | −0.230526 | + | 0.399283i | ||||
\(901\) | −9.19657 | −0.306382 | ||||||||
\(902\) | 40.4442 | 1.34664 | ||||||||
\(903\) | −29.2729 | + | 37.2083i | −0.974140 | + | 1.23821i | ||||
\(904\) | 17.9946 | 0.598493 | ||||||||
\(905\) | 8.68024 | 0.288541 | ||||||||
\(906\) | 33.2271 | − | 57.5510i | 1.10390 | − | 1.91200i | ||||
\(907\) | 52.5460 | 1.74476 | 0.872381 | − | 0.488827i | \(-0.162575\pi\) | ||||
0.872381 | + | 0.488827i | \(0.162575\pi\) | |||||||
\(908\) | −57.1541 | + | 98.9937i | −1.89672 | + | 3.28522i | ||||
\(909\) | −0.840345 | + | 1.45552i | −0.0278725 | + | 0.0482766i | ||||
\(910\) | 8.99232 | + | 15.5752i | 0.298092 | + | 0.516311i | ||||
\(911\) | 37.2037 | 1.23261 | 0.616306 | − | 0.787507i | \(-0.288628\pi\) | ||||
0.616306 | + | 0.787507i | \(0.288628\pi\) | |||||||
\(912\) | −15.1631 | − | 26.2633i | −0.502100 | − | 0.869663i | ||||
\(913\) | −2.12318 | + | 3.67745i | −0.0702670 | + | 0.121706i | ||||
\(914\) | −64.2002 | −2.12355 | ||||||||
\(915\) | 2.61586 | − | 4.53081i | 0.0864778 | − | 0.149784i | ||||
\(916\) | 35.6128 | + | 61.6831i | 1.17668 | + | 2.03807i | ||||
\(917\) | −50.3507 | − | 87.2101i | −1.66273 | − | 2.87993i | ||||
\(918\) | 6.94953 | + | 12.0369i | 0.229369 | + | 0.397278i | ||||
\(919\) | 16.2799 | 0.537026 | 0.268513 | − | 0.963276i | \(-0.413468\pi\) | ||||
0.268513 | + | 0.963276i | \(0.413468\pi\) | |||||||
\(920\) | 18.8838 | + | 32.7077i | 0.622580 | + | 1.07834i | ||||
\(921\) | −17.1988 | − | 29.7892i | −0.566719 | − | 0.981587i | ||||
\(922\) | 6.09984 | − | 10.5652i | 0.200888 | − | 0.347948i | ||||
\(923\) | 4.65976 | − | 8.07094i | 0.153378 | − | 0.265658i | ||||
\(924\) | −178.665 | −5.87765 | ||||||||
\(925\) | −39.1128 | −1.28602 | ||||||||
\(926\) | 4.25474 | − | 7.36943i | 0.139819 | − | 0.242174i | ||||
\(927\) | 2.72537 | − | 4.72048i | 0.0895130 | − | 0.155041i | ||||
\(928\) | 1.17947 | + | 2.04290i | 0.0387179 | + | 0.0670613i | ||||
\(929\) | −23.3724 | − | 40.4822i | −0.766824 | − | 1.32818i | −0.939277 | − | 0.343161i | \(-0.888502\pi\) |
0.172452 | − | 0.985018i | \(-0.444831\pi\) | |||||||
\(930\) | −14.8603 | −0.487288 | ||||||||
\(931\) | 37.6475 | + | 65.2075i | 1.23385 | + | 2.13709i | ||||
\(932\) | 14.0121 | + | 24.2697i | 0.458982 | + | 0.794981i | ||||
\(933\) | 12.9613 | + | 22.4496i | 0.424333 | + | 0.734966i | ||||
\(934\) | −34.7320 | + | 60.1575i | −1.13646 | + | 1.96842i | ||||
\(935\) | −5.19327 | −0.169838 | ||||||||
\(936\) | 3.57150 | − | 6.18601i | 0.116738 | − | 0.202196i | ||||
\(937\) | 18.9089 | + | 32.7513i | 0.617728 | + | 1.06994i | 0.989899 | + | 0.141773i | \(0.0452802\pi\) |
−0.372171 | + | 0.928164i | \(0.621386\pi\) | |||||||
\(938\) | −129.752 | −4.23655 | ||||||||
\(939\) | 18.7299 | + | 32.4411i | 0.611226 | + | 1.05868i | ||||
\(940\) | 2.22727 | − | 3.85774i | 0.0726454 | − | 0.125826i | ||||
\(941\) | −14.7068 | + | 25.4730i | −0.479429 | + | 0.830395i | −0.999722 | − | 0.0235926i | \(-0.992490\pi\) |
0.520293 | + | 0.853988i | \(0.325823\pi\) | |||||||
\(942\) | 24.2376 | 0.789703 | ||||||||
\(943\) | −11.6009 | + | 20.0934i | −0.377779 | + | 0.654332i | ||||
\(944\) | −34.3861 | −1.11917 | ||||||||
\(945\) | −23.4748 | −0.763636 | ||||||||
\(946\) | −60.6025 | + | 77.0309i | −1.97036 | + | 2.50449i | ||||
\(947\) | −33.4006 | −1.08537 | −0.542687 | − | 0.839935i | \(-0.682593\pi\) | ||||
−0.542687 | + | 0.839935i | \(0.682593\pi\) | |||||||
\(948\) | −43.0145 | −1.39704 | ||||||||
\(949\) | 10.1256 | − | 17.5381i | 0.328692 | − | 0.569312i | ||||
\(950\) | −47.6390 | −1.54561 | ||||||||
\(951\) | 9.37151 | − | 16.2319i | 0.303892 | − | 0.526357i | ||||
\(952\) | 12.4916 | − | 21.6361i | 0.404855 | − | 0.701229i | ||||
\(953\) | 9.14829 | + | 15.8453i | 0.296342 | + | 0.513280i | 0.975296 | − | 0.220901i | \(-0.0708998\pi\) |
−0.678954 | + | 0.734181i | \(0.737566\pi\) | |||||||
\(954\) | −18.0115 | −0.583144 | ||||||||
\(955\) | −3.91863 | − | 6.78727i | −0.126804 | − | 0.219631i | ||||
\(956\) | 7.39965 | − | 12.8166i | 0.239322 | − | 0.414518i | ||||
\(957\) | −25.1748 | −0.813786 | ||||||||
\(958\) | −16.4025 | + | 28.4099i | −0.529940 | + | 0.917882i | ||||
\(959\) | 23.2964 | + | 40.3505i | 0.752280 | + | 1.30299i | ||||
\(960\) | 4.41592 | + | 7.64859i | 0.142523 | + | 0.246857i | ||||
\(961\) | 4.29796 | + | 7.44429i | 0.138644 | + | 0.240138i | ||||
\(962\) | 39.5862 | 1.27631 | ||||||||
\(963\) | 1.94928 | + | 3.37624i | 0.0628145 | + | 0.108798i | ||||
\(964\) | 24.2906 | + | 42.0725i | 0.782347 | + | 1.35507i | ||||
\(965\) | 2.55163 | − | 4.41956i | 0.0821399 | − | 0.142271i | ||||
\(966\) | 76.3467 | − | 132.236i | 2.45641 | − | 4.25463i | ||||
\(967\) | 16.0303 | 0.515499 | 0.257750 | − | 0.966212i | \(-0.417019\pi\) | ||||
0.257750 | + | 0.966212i | \(0.417019\pi\) | |||||||
\(968\) | −132.198 | −4.24902 | ||||||||
\(969\) | −3.36257 | + | 5.82415i | −0.108021 | + | 0.187099i | ||||
\(970\) | 4.97532 | − | 8.61752i | 0.159748 | − | 0.276692i | ||||
\(971\) | 19.0441 | + | 32.9853i | 0.611154 | + | 1.05855i | 0.991046 | + | 0.133519i | \(0.0426277\pi\) |
−0.379892 | + | 0.925031i | \(0.624039\pi\) | |||||||
\(972\) | 16.3604 | + | 28.3370i | 0.524759 | + | 0.908909i | ||||
\(973\) | 90.6273 | 2.90538 | ||||||||
\(974\) | 17.4774 | + | 30.2718i | 0.560012 | + | 0.969970i | ||||
\(975\) | 5.54447 | + | 9.60331i | 0.177565 | + | 0.307552i | ||||
\(976\) | 9.26729 | + | 16.0514i | 0.296639 | + | 0.513793i | ||||
\(977\) | −26.5719 | + | 46.0239i | −0.850111 | + | 1.47244i | 0.0309958 | + | 0.999520i | \(0.490132\pi\) |
−0.881107 | + | 0.472917i | \(0.843201\pi\) | |||||||
\(978\) | −29.9917 | −0.959030 | ||||||||
\(979\) | −30.1115 | + | 52.1546i | −0.962367 | + | 1.66687i | ||||
\(980\) | 29.0985 | + | 50.4001i | 0.929518 | + | 1.60997i | ||||
\(981\) | 10.6862 | 0.341184 | ||||||||
\(982\) | −30.2423 | − | 52.3812i | −0.965071 | − | 1.67155i | ||||
\(983\) | −17.6016 | + | 30.4869i | −0.561405 | + | 0.972381i | 0.435970 | + | 0.899961i | \(0.356406\pi\) |
−0.997374 | + | 0.0724200i | \(0.976928\pi\) | |||||||
\(984\) | 10.3277 | − | 17.8882i | 0.329236 | − | 0.570254i | ||||
\(985\) | 21.4245 | 0.682642 | ||||||||
\(986\) | 3.44953 | − | 5.97477i | 0.109855 | − | 0.190275i | ||||
\(987\) | −9.18941 | −0.292502 | ||||||||
\(988\) | 32.3649 | 1.02966 | ||||||||
\(989\) | −20.8873 | − | 52.2038i | −0.664176 | − | 1.65999i | ||||
\(990\) | −10.1710 | −0.323257 | ||||||||
\(991\) | −26.1834 | −0.831744 | −0.415872 | − | 0.909423i | \(-0.636524\pi\) | ||||
−0.415872 | + | 0.909423i | \(0.636524\pi\) | |||||||
\(992\) | 1.99592 | − | 3.45704i | 0.0633706 | − | 0.109761i | ||||
\(993\) | −15.2230 | −0.483086 | ||||||||
\(994\) | 31.9194 | − | 55.2861i | 1.01242 | − | 1.75357i | ||||
\(995\) | 9.38805 | − | 16.2606i | 0.297621 | − | 0.515495i | ||||
\(996\) | 2.12511 | + | 3.68080i | 0.0673366 | + | 0.116630i | ||||
\(997\) | −54.0745 | −1.71256 | −0.856278 | − | 0.516516i | \(-0.827229\pi\) | ||||
−0.856278 | + | 0.516516i | \(0.827229\pi\) | |||||||
\(998\) | −30.7362 | − | 53.2366i | −0.972936 | − | 1.68518i | ||||
\(999\) | −25.8353 | + | 44.7481i | −0.817394 | + | 1.41577i |
(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 | 731.2.e.b.307.3 | ✓ | 58 | |
43.36 | even | 3 | inner | 731.2.e.b.681.3 | yes | 58 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
731.2.e.b.307.3 | ✓ | 58 | 1.1 | even | 1 | trivial | |
731.2.e.b.681.3 | yes | 58 | 43.36 | even | 3 | inner |