Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,3,Mod(19,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.f (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.94278685509\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 7 x^{14} - 30 x^{13} + 76 x^{12} - 144 x^{11} + 424 x^{10} - 912 x^{9} + \cdots + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 91.8 | ||
Root | \(1.93353 + 0.511345i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.91 |
Dual form | 108.3.f.c.19.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.93353 | + | 0.511345i | 0.966763 | + | 0.255672i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.47705 | + | 1.97740i | 0.869263 | + | 0.494350i | ||||
\(5\) | 4.03104 | − | 6.98197i | 0.806209 | − | 1.39639i | −0.109263 | − | 0.994013i | \(-0.534849\pi\) |
0.915472 | − | 0.402382i | \(-0.131818\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.90254 | + | 2.25313i | −0.557506 | + | 0.321876i | −0.752144 | − | 0.658999i | \(-0.770980\pi\) |
0.194638 | + | 0.980875i | \(0.437647\pi\) | |||||||
\(8\) | 5.71184 | + | 5.60133i | 0.713980 | + | 0.700166i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 11.3643 | − | 11.4386i | 1.13643 | − | 1.14386i | ||||
\(11\) | −3.25842 | + | 1.88125i | −0.296220 | + | 0.171023i | −0.640744 | − | 0.767755i | \(-0.721374\pi\) |
0.344523 | + | 0.938778i | \(0.388041\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.52605 | + | 6.10730i | −0.271235 | + | 0.469792i | −0.969178 | − | 0.246361i | \(-0.920765\pi\) |
0.697944 | + | 0.716153i | \(0.254099\pi\) | |||||||
\(14\) | −8.69780 | + | 2.36095i | −0.621271 | + | 0.168639i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 8.17979 | + | 13.7510i | 0.511237 | + | 0.859440i | ||||
\(17\) | −0.517890 | −0.0304641 | −0.0152321 | − | 0.999884i | \(-0.504849\pi\) | ||||
−0.0152321 | + | 0.999884i | \(0.504849\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 16.4164i | 0.864023i | 0.901868 | + | 0.432012i | \(0.142196\pi\) | ||||
−0.901868 | + | 0.432012i | \(0.857804\pi\) | |||||||
\(20\) | 27.8223 | − | 16.3057i | 1.39111 | − | 0.815286i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −7.26222 | + | 1.97127i | −0.330101 | + | 0.0896033i | ||||
\(23\) | −27.7049 | − | 15.9954i | −1.20456 | − | 0.695454i | −0.242996 | − | 0.970027i | \(-0.578130\pi\) |
−0.961566 | + | 0.274573i | \(0.911463\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −19.9986 | − | 34.6387i | −0.799946 | − | 1.38555i | ||||
\(26\) | −9.94065 | + | 10.0056i | −0.382333 | + | 0.384831i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −18.0247 | + | 0.117384i | −0.643739 | + | 0.00419230i | ||||
\(29\) | −9.48394 | − | 16.4267i | −0.327032 | − | 0.566437i | 0.654889 | − | 0.755725i | \(-0.272715\pi\) |
−0.981922 | + | 0.189288i | \(0.939382\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −13.1355 | − | 7.58377i | −0.423725 | − | 0.244638i | 0.272945 | − | 0.962030i | \(-0.412002\pi\) |
−0.696670 | + | 0.717392i | \(0.745336\pi\) | |||||||
\(32\) | 8.78432 | + | 30.7707i | 0.274510 | + | 0.961584i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.00135 | − | 0.264820i | −0.0294516 | − | 0.00778884i | ||||
\(35\) | 36.3299i | 1.03800i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.592061 | 0.0160017 | 0.00800083 | − | 0.999968i | \(-0.497453\pi\) | ||||
0.00800083 | + | 0.999968i | \(0.497453\pi\) | |||||||
\(38\) | −8.39446 | + | 31.7416i | −0.220907 | + | 0.835306i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 62.1330 | − | 17.3007i | 1.55333 | − | 0.432518i | ||||
\(41\) | −12.3766 | + | 21.4369i | −0.301868 | + | 0.522850i | −0.976559 | − | 0.215250i | \(-0.930943\pi\) |
0.674691 | + | 0.738100i | \(0.264277\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 27.8686 | − | 16.0900i | 0.648107 | − | 0.374185i | −0.139623 | − | 0.990205i | \(-0.544589\pi\) |
0.787731 | + | 0.616020i | \(0.211256\pi\) | |||||||
\(44\) | −15.0497 | + | 0.0980099i | −0.342039 | + | 0.00222750i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −45.3890 | − | 45.0944i | −0.986718 | − | 0.980313i | ||||
\(47\) | 52.4682 | − | 30.2925i | 1.11634 | − | 0.644521i | 0.175879 | − | 0.984412i | \(-0.443723\pi\) |
0.940465 | + | 0.339890i | \(0.110390\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −14.3468 | + | 24.8493i | −0.292791 | + | 0.507129i | ||||
\(50\) | −20.9556 | − | 77.2010i | −0.419112 | − | 1.54402i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −24.3368 | + | 14.2630i | −0.468016 | + | 0.274288i | ||||
\(53\) | 0.664765 | 0.0125427 | 0.00627137 | − | 0.999980i | \(-0.498004\pi\) | ||||
0.00627137 | + | 0.999980i | \(0.498004\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 30.3336i | 0.551521i | ||||||||
\(56\) | −34.9113 | − | 8.98987i | −0.623415 | − | 0.160533i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −9.93776 | − | 36.6110i | −0.171341 | − | 0.631224i | ||||
\(59\) | 30.5921 | + | 17.6623i | 0.518510 | + | 0.299362i | 0.736325 | − | 0.676628i | \(-0.236560\pi\) |
−0.217815 | + | 0.975990i | \(0.569893\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 33.7750 | + | 58.5000i | 0.553688 | + | 0.959016i | 0.998004 | + | 0.0631460i | \(0.0201134\pi\) |
−0.444316 | + | 0.895870i | \(0.646553\pi\) | |||||||
\(62\) | −21.5199 | − | 21.3802i | −0.347095 | − | 0.344842i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.25029 | + | 63.9878i | 0.0195357 | + | 0.999809i | ||||
\(65\) | 28.4273 | + | 49.2376i | 0.437343 | + | 0.757501i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −74.4692 | − | 42.9948i | −1.11148 | − | 0.641714i | −0.172269 | − | 0.985050i | \(-0.555110\pi\) |
−0.939213 | + | 0.343336i | \(0.888443\pi\) | |||||||
\(68\) | −1.80073 | − | 1.02407i | −0.0264813 | − | 0.0150599i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −18.5771 | + | 70.2449i | −0.265388 | + | 1.00350i | ||||
\(71\) | − | 56.4434i | − | 0.794977i | −0.917607 | − | 0.397489i | \(-0.869882\pi\) | ||
0.917607 | − | 0.397489i | \(-0.130118\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 131.921 | 1.80713 | 0.903567 | − | 0.428447i | \(-0.140939\pi\) | ||||
0.903567 | + | 0.428447i | \(0.140939\pi\) | |||||||
\(74\) | 1.14477 | + | 0.302748i | 0.0154698 | + | 0.00409118i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −32.4618 | + | 57.0808i | −0.427129 | + | 0.751063i | ||||
\(77\) | 8.47743 | − | 14.6833i | 0.110096 | − | 0.190693i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 126.869 | − | 73.2481i | 1.60594 | − | 0.927191i | 0.615677 | − | 0.787999i | \(-0.288883\pi\) |
0.990265 | − | 0.139192i | \(-0.0444505\pi\) | |||||||
\(80\) | 128.982 | − | 1.68005i | 1.61228 | − | 0.0210006i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −34.8921 | + | 35.1201i | −0.425513 | + | 0.428293i | ||||
\(83\) | −87.1029 | + | 50.2889i | −1.04943 | + | 0.605890i | −0.922491 | − | 0.386020i | \(-0.873850\pi\) |
−0.126942 | + | 0.991910i | \(0.540516\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.08764 | + | 3.61589i | −0.0245604 | + | 0.0425399i | ||||
\(86\) | 62.1122 | − | 16.8599i | 0.722235 | − | 0.196045i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −29.1491 | − | 7.50608i | −0.331240 | − | 0.0852964i | ||||
\(89\) | 25.8362 | 0.290295 | 0.145147 | − | 0.989410i | \(-0.453634\pi\) | ||||
0.145147 | + | 0.989410i | \(0.453634\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 31.7786i | − | 0.349216i | ||||||
\(92\) | −64.7021 | − | 110.401i | −0.703284 | − | 1.20001i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 116.939 | − | 31.7420i | 1.24403 | − | 0.337681i | ||||
\(95\) | 114.619 | + | 66.1754i | 1.20652 | + | 0.696583i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −48.2534 | − | 83.5773i | −0.497457 | − | 0.861621i | 0.502538 | − | 0.864555i | \(-0.332400\pi\) |
−0.999996 | + | 0.00293363i | \(0.999066\pi\) | |||||||
\(98\) | −40.4465 | + | 40.7107i | −0.412719 | + | 0.415415i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.04189 | − | 159.986i | −0.0104189 | − | 1.59986i | ||||
\(101\) | 21.6600 | + | 37.5163i | 0.214456 | + | 0.371448i | 0.953104 | − | 0.302643i | \(-0.0978689\pi\) |
−0.738648 | + | 0.674091i | \(0.764536\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 125.439 | + | 72.4223i | 1.21786 | + | 0.703129i | 0.964459 | − | 0.264233i | \(-0.0851189\pi\) |
0.253397 | + | 0.967362i | \(0.418452\pi\) | |||||||
\(104\) | −54.3492 | + | 15.1334i | −0.522588 | + | 0.145513i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.28534 | + | 0.339924i | 0.0121259 | + | 0.00320683i | ||||
\(107\) | − | 54.9861i | − | 0.513889i | −0.966426 | − | 0.256944i | \(-0.917284\pi\) | ||
0.966426 | − | 0.256944i | \(-0.0827158\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −63.9235 | −0.586454 | −0.293227 | − | 0.956043i | \(-0.594729\pi\) | ||||
−0.293227 | + | 0.956043i | \(0.594729\pi\) | |||||||
\(110\) | −15.5110 | + | 58.6509i | −0.141009 | + | 0.533190i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −62.9049 | − | 35.2338i | −0.561651 | − | 0.314588i | ||||
\(113\) | −17.8239 | + | 30.8720i | −0.157734 | + | 0.273203i | −0.934051 | − | 0.357139i | \(-0.883752\pi\) |
0.776317 | + | 0.630342i | \(0.217086\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −223.360 | + | 128.957i | −1.94226 | + | 1.12136i | ||||
\(116\) | −0.494097 | − | 75.8699i | −0.00425945 | − | 0.654051i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 50.1190 | + | 49.7937i | 0.424738 | + | 0.421981i | ||||
\(119\) | 2.02109 | − | 1.16688i | 0.0169839 | − | 0.00980568i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −53.4218 | + | 92.5292i | −0.441502 | + | 0.764704i | ||||
\(122\) | 35.3912 | + | 130.382i | 0.290091 | + | 1.06870i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −30.6766 | − | 52.3432i | −0.247392 | − | 0.422123i | ||||
\(125\) | −120.909 | −0.967276 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 9.81219i | − | 0.0772613i | −0.999254 | − | 0.0386307i | \(-0.987700\pi\) | ||
0.999254 | − | 0.0386307i | \(-0.0122996\pi\) | |||||||
\(128\) | −30.3024 | + | 124.361i | −0.236737 | + | 0.971574i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 29.7876 | + | 109.738i | 0.229135 | + | 0.844141i | ||||
\(131\) | −101.561 | − | 58.6365i | −0.775278 | − | 0.447607i | 0.0594761 | − | 0.998230i | \(-0.481057\pi\) |
−0.834754 | + | 0.550623i | \(0.814390\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −36.9884 | − | 64.0659i | −0.278109 | − | 0.481698i | ||||
\(134\) | −122.003 | − | 121.211i | −0.910471 | − | 0.904561i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.95811 | − | 2.90087i | −0.0217508 | − | 0.0213299i | ||||
\(137\) | −125.606 | − | 217.556i | −0.916831 | − | 1.58800i | −0.804198 | − | 0.594362i | \(-0.797405\pi\) |
−0.112634 | − | 0.993637i | \(-0.535929\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −133.073 | − | 76.8298i | −0.957361 | − | 0.552732i | −0.0620009 | − | 0.998076i | \(-0.519748\pi\) |
−0.895360 | + | 0.445344i | \(0.853081\pi\) | |||||||
\(140\) | −71.8388 | + | 126.321i | −0.513134 | + | 0.902294i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 28.8620 | − | 109.135i | 0.203254 | − | 0.768555i | ||||
\(143\) | − | 26.5335i | − | 0.185549i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −152.921 | −1.05463 | ||||||||
\(146\) | 255.072 | + | 67.4570i | 1.74707 | + | 0.462034i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.05863 | + | 1.17074i | 0.0139097 | + | 0.00791041i | ||||
\(149\) | 45.8643 | − | 79.4393i | 0.307814 | − | 0.533150i | −0.670070 | − | 0.742298i | \(-0.733736\pi\) |
0.977884 | + | 0.209148i | \(0.0670691\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 36.0215 | − | 20.7970i | 0.238553 | − | 0.137729i | −0.375958 | − | 0.926637i | \(-0.622686\pi\) |
0.614512 | + | 0.788908i | \(0.289353\pi\) | |||||||
\(152\) | −91.9538 | + | 93.7681i | −0.604959 | + | 0.616895i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 23.8996 | − | 24.0557i | 0.155192 | − | 0.156206i | ||||
\(155\) | −105.899 | + | 61.1410i | −0.683222 | + | 0.394458i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 112.909 | − | 195.565i | 0.719167 | − | 1.24563i | −0.242163 | − | 0.970236i | \(-0.577857\pi\) |
0.961330 | − | 0.275399i | \(-0.0888099\pi\) | |||||||
\(158\) | 282.760 | − | 76.7531i | 1.78962 | − | 0.485779i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 250.250 | + | 62.7061i | 1.56406 | + | 0.391913i | ||||
\(161\) | 144.160 | 0.895401 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 125.175i | 0.767945i | 0.923344 | + | 0.383973i | \(0.125444\pi\) | ||||
−0.923344 | + | 0.383973i | \(0.874556\pi\) | |||||||
\(164\) | −85.4233 | + | 50.0637i | −0.520874 | + | 0.305266i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −194.131 | + | 52.6953i | −1.16946 | + | 0.317442i | ||||
\(167\) | −154.373 | − | 89.1274i | −0.924390 | − | 0.533697i | −0.0393573 | − | 0.999225i | \(-0.512531\pi\) |
−0.885033 | + | 0.465528i | \(0.845864\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 59.6340 | + | 103.289i | 0.352864 | + | 0.611178i | ||||
\(170\) | −5.88547 | + | 5.92393i | −0.0346204 | + | 0.0348466i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 128.717 | − | 0.838258i | 0.748354 | − | 0.00487359i | ||||
\(173\) | 75.5904 | + | 130.926i | 0.436939 | + | 0.756800i | 0.997452 | − | 0.0713455i | \(-0.0227293\pi\) |
−0.560513 | + | 0.828146i | \(0.689396\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 156.091 | + | 90.1193i | 0.891949 | + | 0.514967i | ||||
\(176\) | −52.5224 | − | 29.4185i | −0.298423 | − | 0.167150i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 49.9551 | + | 13.2112i | 0.280646 | + | 0.0742204i | ||||
\(179\) | 276.827i | 1.54652i | 0.634088 | + | 0.773261i | \(0.281376\pi\) | ||||
−0.634088 | + | 0.773261i | \(0.718624\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −104.729 | −0.578612 | −0.289306 | − | 0.957237i | \(-0.593425\pi\) | ||||
−0.289306 | + | 0.957237i | \(0.593425\pi\) | |||||||
\(182\) | 16.2499 | − | 61.4449i | 0.0892849 | − | 0.337609i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −68.6504 | − | 246.548i | −0.373100 | − | 1.33993i | ||||
\(185\) | 2.38663 | − | 4.13376i | 0.0129007 | − | 0.0223446i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.68751 | − | 0.974282i | 0.00902409 | − | 0.00521006i | ||||
\(188\) | 242.335 | − | 1.57819i | 1.28902 | − | 0.00839461i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 187.781 | + | 186.562i | 0.988320 | + | 0.981904i | ||||
\(191\) | 192.972 | − | 111.413i | 1.01033 | − | 0.583312i | 0.0990389 | − | 0.995084i | \(-0.468423\pi\) |
0.911287 | + | 0.411772i | \(0.135090\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 56.6790 | − | 98.1709i | 0.293674 | − | 0.508657i | −0.681002 | − | 0.732282i | \(-0.738455\pi\) |
0.974675 | + | 0.223624i | \(0.0717888\pi\) | |||||||
\(194\) | −50.5623 | − | 186.273i | −0.260631 | − | 0.960170i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −99.0215 | + | 58.0332i | −0.505212 | + | 0.296088i | ||||
\(197\) | 120.998 | 0.614201 | 0.307100 | − | 0.951677i | \(-0.400641\pi\) | ||||
0.307100 | + | 0.951677i | \(0.400641\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 82.2364i | − | 0.413248i | −0.978420 | − | 0.206624i | \(-0.933752\pi\) | ||
0.978420 | − | 0.206624i | \(-0.0662477\pi\) | |||||||
\(200\) | 79.7934 | − | 309.870i | 0.398967 | − | 1.54935i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 22.6965 | + | 83.6145i | 0.112359 | + | 0.413933i | ||||
\(203\) | 74.0230 | + | 42.7372i | 0.364645 | + | 0.210528i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 99.7811 | + | 172.826i | 0.486737 | + | 0.843053i | ||||
\(206\) | 205.507 | + | 204.173i | 0.997607 | + | 0.991132i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −112.824 | + | 1.46958i | −0.542423 | + | 0.00706527i | ||||
\(209\) | −30.8835 | − | 53.4917i | −0.147768 | − | 0.255941i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 93.5819 | + | 54.0295i | 0.443516 | + | 0.256064i | 0.705088 | − | 0.709120i | \(-0.250907\pi\) |
−0.261572 | + | 0.965184i | \(0.584241\pi\) | |||||||
\(212\) | 2.31142 | + | 1.31451i | 0.0109029 | + | 0.00620050i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 28.1169 | − | 106.317i | 0.131387 | − | 0.496809i | ||||
\(215\) | − | 259.437i | − | 1.20668i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 68.3490 | 0.314972 | ||||||||
\(218\) | −123.598 | − | 32.6870i | −0.566962 | − | 0.149940i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −59.9817 | + | 105.472i | −0.272644 | + | 0.479417i | ||||
\(221\) | 1.82611 | − | 3.16291i | 0.00826292 | − | 0.0143118i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −141.400 | + | 81.6371i | −0.634079 | + | 0.366086i | −0.782330 | − | 0.622864i | \(-0.785969\pi\) |
0.148251 | + | 0.988950i | \(0.452636\pi\) | |||||||
\(224\) | −103.612 | − | 100.292i | −0.462552 | − | 0.447731i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −50.2493 | + | 50.5776i | −0.222342 | + | 0.223795i | ||||
\(227\) | −9.56722 | + | 5.52364i | −0.0421463 | + | 0.0243332i | −0.520925 | − | 0.853602i | \(-0.674413\pi\) |
0.478779 | + | 0.877936i | \(0.341080\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.1725 | + | 28.0116i | −0.0706222 | + | 0.122321i | −0.899174 | − | 0.437591i | \(-0.855832\pi\) |
0.828552 | + | 0.559912i | \(0.189165\pi\) | |||||||
\(230\) | −497.813 | + | 135.127i | −2.16440 | + | 0.587511i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 37.8404 | − | 146.949i | 0.163105 | − | 0.633402i | ||||
\(233\) | −181.049 | −0.777036 | −0.388518 | − | 0.921441i | \(-0.627013\pi\) | ||||
−0.388518 | + | 0.921441i | \(0.627013\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 488.442i | − | 2.07848i | ||||||
\(236\) | 71.4448 | + | 121.906i | 0.302732 | + | 0.516549i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.50450 | − | 1.22271i | 0.0189265 | − | 0.00513745i | ||||
\(239\) | 39.6432 | + | 22.8880i | 0.165871 | + | 0.0957658i | 0.580638 | − | 0.814162i | \(-0.302803\pi\) |
−0.414766 | + | 0.909928i | \(0.636137\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 169.216 | + | 293.090i | 0.702140 | + | 1.21614i | 0.967714 | + | 0.252052i | \(0.0811054\pi\) |
−0.265573 | + | 0.964091i | \(0.585561\pi\) | |||||||
\(242\) | −150.607 | + | 151.591i | −0.622342 | + | 0.626408i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.75962 | + | 270.194i | 0.00721154 | + | 1.10735i | ||||
\(245\) | 115.665 | + | 200.338i | 0.472102 | + | 0.817704i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −100.260 | − | 57.8852i | −0.405911 | − | 0.234353i | ||||
\(248\) | −32.5486 | − | 116.893i | −0.131244 | − | 0.471344i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −233.782 | − | 61.8264i | −0.935127 | − | 0.247306i | ||||
\(251\) | 282.587i | 1.12585i | 0.826510 | + | 0.562923i | \(0.190323\pi\) | ||||
−0.826510 | + | 0.562923i | \(0.809677\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 120.366 | 0.475754 | ||||||||
\(254\) | 5.01741 | − | 18.9721i | 0.0197536 | − | 0.0746934i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −122.182 | + | 224.961i | −0.477274 | + | 0.878755i | ||||
\(257\) | −38.8897 | + | 67.3589i | −0.151322 | + | 0.262097i | −0.931714 | − | 0.363194i | \(-0.881686\pi\) |
0.780392 | + | 0.625291i | \(0.215020\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.31055 | + | 1.33399i | −0.00892102 | + | 0.00515056i | ||||
\(260\) | 1.48101 | + | 227.414i | 0.00569620 | + | 0.874668i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −166.388 | − | 165.308i | −0.635070 | − | 0.630947i | ||||
\(263\) | 195.201 | − | 112.700i | 0.742211 | − | 0.428516i | −0.0806619 | − | 0.996742i | \(-0.525703\pi\) |
0.822873 | + | 0.568226i | \(0.192370\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.67970 | − | 4.64138i | 0.0101121 | − | 0.0175146i | ||||
\(266\) | −38.7584 | − | 142.787i | −0.145708 | − | 0.536793i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −173.916 | − | 296.751i | −0.648939 | − | 1.10728i | ||||
\(269\) | −425.808 | −1.58293 | −0.791465 | − | 0.611214i | \(-0.790681\pi\) | ||||
−0.791465 | + | 0.611214i | \(0.790681\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 56.3665i | 0.207995i | 0.994578 | + | 0.103997i | \(0.0331633\pi\) | ||||
−0.994578 | + | 0.103997i | \(0.966837\pi\) | |||||||
\(272\) | −4.23623 | − | 7.12152i | −0.0155744 | − | 0.0261821i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −131.616 | − | 484.878i | −0.480352 | − | 1.76963i | ||||
\(275\) | 130.328 | + | 75.2450i | 0.473920 | + | 0.273618i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −209.641 | − | 363.109i | −0.756828 | − | 1.31086i | −0.944461 | − | 0.328625i | \(-0.893415\pi\) |
0.187633 | − | 0.982239i | \(-0.439918\pi\) | |||||||
\(278\) | −218.014 | − | 216.599i | −0.784223 | − | 0.779132i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −203.496 | + | 207.511i | −0.726771 | + | 0.741110i | ||||
\(281\) | 73.9638 | + | 128.109i | 0.263216 | + | 0.455904i | 0.967095 | − | 0.254416i | \(-0.0818833\pi\) |
−0.703878 | + | 0.710320i | \(0.748550\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 229.852 | + | 132.705i | 0.812198 | + | 0.468923i | 0.847719 | − | 0.530446i | \(-0.177976\pi\) |
−0.0355207 | + | 0.999369i | \(0.511309\pi\) | |||||||
\(284\) | 111.611 | − | 196.257i | 0.392997 | − | 0.691045i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 13.5678 | − | 51.3033i | 0.0474398 | − | 0.179382i | ||||
\(287\) | − | 111.544i | − | 0.388656i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −288.732 | −0.999072 | ||||||||
\(290\) | −295.676 | − | 78.1953i | −1.01957 | − | 0.269639i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 458.695 | + | 260.860i | 1.57087 | + | 0.893356i | ||||
\(293\) | −124.844 | + | 216.236i | −0.426088 | + | 0.738006i | −0.996521 | − | 0.0833379i | \(-0.973442\pi\) |
0.570433 | + | 0.821344i | \(0.306775\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 246.636 | − | 142.395i | 0.836054 | − | 0.482696i | ||||
\(296\) | 3.38176 | + | 3.31633i | 0.0114249 | + | 0.0112038i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 129.301 | − | 130.146i | 0.433895 | − | 0.436730i | ||||
\(299\) | 195.378 | − | 112.801i | 0.653438 | − | 0.377262i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −72.5056 | + | 125.583i | −0.240883 | + | 0.417221i | ||||
\(302\) | 80.2830 | − | 21.7922i | 0.265838 | − | 0.0721596i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −225.743 | + | 134.283i | −0.742576 | + | 0.441721i | ||||
\(305\) | 544.594 | 1.78555 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 259.968i | 0.846801i | 0.905943 | + | 0.423401i | \(0.139164\pi\) | ||||
−0.905943 | + | 0.423401i | \(0.860836\pi\) | |||||||
\(308\) | 58.5113 | − | 34.2915i | 0.189972 | − | 0.111336i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −236.023 | + | 64.0667i | −0.761366 | + | 0.206667i | ||||
\(311\) | 16.5959 | + | 9.58164i | 0.0533630 | + | 0.0308091i | 0.526444 | − | 0.850210i | \(-0.323525\pi\) |
−0.473081 | + | 0.881019i | \(0.656858\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.9358 | − | 37.9939i | −0.0700823 | − | 0.121386i | 0.828855 | − | 0.559464i | \(-0.188993\pi\) |
−0.898937 | + | 0.438078i | \(0.855660\pi\) | |||||||
\(314\) | 318.314 | − | 320.394i | 1.01374 | − | 1.02036i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 585.972 | − | 3.81610i | 1.85434 | − | 0.0120763i | ||||
\(317\) | −68.9690 | − | 119.458i | −0.217568 | − | 0.376838i | 0.736496 | − | 0.676442i | \(-0.236479\pi\) |
−0.954064 | + | 0.299603i | \(0.903146\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 61.8054 | + | 35.6834i | 0.193747 | + | 0.111860i | ||||
\(320\) | 451.801 | + | 249.208i | 1.41188 | + | 0.778775i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 278.736 | + | 73.7152i | 0.865641 | + | 0.228929i | ||||
\(323\) | − | 8.50191i | − | 0.0263217i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 282.065 | 0.867892 | ||||||||
\(326\) | −64.0076 | + | 242.029i | −0.196342 | + | 0.742421i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −190.768 | + | 53.1187i | −0.581610 | + | 0.161947i | ||||
\(329\) | −136.506 | + | 236.436i | −0.414912 | + | 0.718649i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −51.7490 | + | 29.8773i | −0.156341 | + | 0.0902638i | −0.576130 | − | 0.817358i | \(-0.695438\pi\) |
0.419788 | + | 0.907622i | \(0.362104\pi\) | |||||||
\(332\) | −402.303 | + | 2.61996i | −1.21176 | + | 0.00789145i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −252.910 | − | 251.268i | −0.757215 | − | 0.752300i | ||||
\(335\) | −600.378 | + | 346.628i | −1.79217 | + | 1.03471i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 224.356 | − | 388.595i | 0.665743 | − | 1.15310i | −0.313340 | − | 0.949641i | \(-0.601448\pi\) |
0.979083 | − | 0.203460i | \(-0.0652188\pi\) | |||||||
\(338\) | 62.4875 | + | 230.206i | 0.184874 | + | 0.681082i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −14.4089 | + | 8.44457i | −0.0423791 | + | 0.0248370i | ||||
\(341\) | 57.0679 | 0.167355 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 350.108i | − | 1.02072i | ||||||
\(344\) | 249.306 | + | 64.1979i | 0.724727 | + | 0.186622i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 79.2075 | + | 291.803i | 0.228924 | + | 0.843360i | ||||
\(347\) | −500.441 | − | 288.930i | −1.44219 | − | 0.832651i | −0.444198 | − | 0.895929i | \(-0.646511\pi\) |
−0.997996 | + | 0.0632779i | \(0.979845\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 66.1311 | + | 114.542i | 0.189487 | + | 0.328202i | 0.945079 | − | 0.326841i | \(-0.105984\pi\) |
−0.755592 | + | 0.655042i | \(0.772651\pi\) | |||||||
\(350\) | 255.724 | + | 254.064i | 0.730641 | + | 0.725898i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −86.5105 | − | 83.7384i | −0.245768 | − | 0.237893i | ||||
\(353\) | −270.562 | − | 468.628i | −0.766465 | − | 1.32756i | −0.939468 | − | 0.342636i | \(-0.888680\pi\) |
0.173003 | − | 0.984921i | \(-0.444653\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −394.086 | − | 227.526i | −1.11010 | − | 0.640918i | ||||
\(356\) | 89.8339 | + | 51.0885i | 0.252343 | + | 0.143507i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −141.554 | + | 535.253i | −0.395403 | + | 1.49512i | ||||
\(359\) | 292.754i | 0.815470i | 0.913100 | + | 0.407735i | \(0.133681\pi\) | ||||
−0.913100 | + | 0.407735i | \(0.866319\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 91.5006 | 0.253464 | ||||||||
\(362\) | −202.496 | − | 53.5525i | −0.559381 | − | 0.147935i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 62.8390 | − | 110.496i | 0.172635 | − | 0.303561i | ||||
\(365\) | 531.779 | − | 921.067i | 1.45693 | − | 2.52347i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −378.870 | + | 218.741i | −1.03234 | + | 0.596024i | −0.917655 | − | 0.397377i | \(-0.869920\pi\) |
−0.114689 | + | 0.993401i | \(0.536587\pi\) | |||||||
\(368\) | −6.66653 | − | 511.811i | −0.0181156 | − | 1.39079i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.72838 | − | 6.77234i | 0.0181848 | − | 0.0183036i | ||||
\(371\) | −2.59428 | + | 1.49781i | −0.00699266 | + | 0.00403721i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −352.979 | + | 611.377i | −0.946323 | + | 1.63908i | −0.193243 | + | 0.981151i | \(0.561901\pi\) |
−0.753080 | + | 0.657929i | \(0.771433\pi\) | |||||||
\(374\) | 3.76103 | − | 1.02090i | 0.0100562 | − | 0.00272969i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 469.368 | + | 120.865i | 1.24832 | + | 0.321450i | ||||
\(377\) | 133.763 | 0.354810 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 541.432i | 1.42858i | 0.699850 | + | 0.714290i | \(0.253250\pi\) | ||||
−0.699850 | + | 0.714290i | \(0.746750\pi\) | |||||||
\(380\) | 267.682 | + | 456.743i | 0.704426 | + | 1.20196i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 430.087 | − | 116.744i | 1.12588 | − | 0.305612i | ||||
\(383\) | 311.941 | + | 180.099i | 0.814467 | + | 0.470233i | 0.848505 | − | 0.529188i | \(-0.177503\pi\) |
−0.0340377 | + | 0.999421i | \(0.510837\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −68.3458 | − | 118.378i | −0.177521 | − | 0.307476i | ||||
\(386\) | 159.790 | − | 160.834i | 0.413963 | − | 0.416667i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.51391 | − | 386.019i | −0.00647916 | − | 0.994893i | ||||
\(389\) | 43.9057 | + | 76.0468i | 0.112868 | + | 0.195493i | 0.916926 | − | 0.399058i | \(-0.130663\pi\) |
−0.804057 | + | 0.594552i | \(0.797330\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.3481 | + | 8.28388i | 0.0366959 | + | 0.0211864i | ||||
\(392\) | −221.136 | + | 61.5745i | −0.564122 | + | 0.157078i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 233.952 | + | 61.8715i | 0.593787 | + | 0.157034i | ||||
\(395\) | − | 1181.07i | − | 2.99004i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −48.4128 | −0.121947 | −0.0609733 | − | 0.998139i | \(-0.519420\pi\) | ||||
−0.0609733 | + | 0.998139i | \(0.519420\pi\) | |||||||
\(398\) | 42.0512 | − | 159.006i | 0.105656 | − | 0.399513i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 312.733 | − | 558.339i | 0.781832 | − | 1.39585i | ||||
\(401\) | −217.859 | + | 377.343i | −0.543290 | + | 0.941005i | 0.455423 | + | 0.890275i | \(0.349488\pi\) |
−0.998712 | + | 0.0507299i | \(0.983845\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 92.6326 | − | 53.4815i | 0.229858 | − | 0.132708i | ||||
\(404\) | 1.12845 | + | 173.277i | 0.00279319 | + | 0.428902i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 121.272 | + | 120.485i | 0.298699 | + | 0.296761i | ||||
\(407\) | −1.92919 | + | 1.11382i | −0.00474002 | + | 0.00273665i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −27.1145 | + | 46.9636i | −0.0662945 | + | 0.114825i | −0.897267 | − | 0.441487i | \(-0.854451\pi\) |
0.830973 | + | 0.556313i | \(0.187784\pi\) | |||||||
\(410\) | 104.556 | + | 385.186i | 0.255014 | + | 0.939479i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 292.951 | + | 499.859i | 0.711045 | + | 1.21325i | ||||
\(413\) | −159.182 | −0.385430 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 810.867i | 1.95390i | ||||||||
\(416\) | −218.900 | − | 54.8505i | −0.526201 | − | 0.131852i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −32.3613 | − | 119.220i | −0.0774193 | − | 0.285215i | ||||
\(419\) | 552.029 | + | 318.714i | 1.31749 | + | 0.760655i | 0.983325 | − | 0.181859i | \(-0.0582114\pi\) |
0.334168 | + | 0.942514i | \(0.391545\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −95.7757 | − | 165.888i | −0.227496 | − | 0.394034i | 0.729570 | − | 0.683907i | \(-0.239720\pi\) |
−0.957065 | + | 0.289873i | \(0.906387\pi\) | |||||||
\(422\) | 153.315 | + | 152.320i | 0.363307 | + | 0.360948i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.79704 | + | 3.72357i | 0.00895527 | + | 0.00878200i | ||||
\(425\) | 10.3571 | + | 17.9390i | 0.0243696 | + | 0.0422095i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −263.617 | − | 152.199i | −0.617369 | − | 0.356438i | ||||
\(428\) | 108.729 | − | 191.190i | 0.254041 | − | 0.446705i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 132.662 | − | 501.629i | 0.308516 | − | 1.16658i | ||||
\(431\) | 481.190i | 1.11645i | 0.829689 | + | 0.558225i | \(0.188518\pi\) | ||||
−0.829689 | + | 0.558225i | \(0.811482\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −360.347 | −0.832209 | −0.416105 | − | 0.909317i | \(-0.636605\pi\) | ||||
−0.416105 | + | 0.909317i | \(0.636605\pi\) | |||||||
\(434\) | 132.155 | + | 34.9499i | 0.304504 | + | 0.0805297i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −222.265 | − | 126.402i | −0.509783 | − | 0.289913i | ||||
\(437\) | 262.588 | − | 454.816i | 0.600888 | − | 1.04077i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 488.267 | − | 281.901i | 1.11223 | − | 0.642144i | 0.172821 | − | 0.984953i | \(-0.444712\pi\) |
0.939405 | + | 0.342809i | \(0.111378\pi\) | |||||||
\(440\) | −169.909 | + | 173.261i | −0.386156 | + | 0.393775i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.14816 | − | 5.18180i | 0.0116474 | − | 0.0117235i | ||||
\(443\) | −569.917 | + | 329.042i | −1.28649 | + | 0.742757i | −0.978027 | − | 0.208478i | \(-0.933149\pi\) |
−0.308467 | + | 0.951235i | \(0.599816\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 104.147 | − | 180.388i | 0.234038 | − | 0.405366i | ||||
\(446\) | −315.145 | + | 85.5436i | −0.706603 | + | 0.191802i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −149.052 | − | 246.898i | −0.332706 | − | 0.551112i | ||||
\(449\) | −227.569 | −0.506836 | −0.253418 | − | 0.967357i | \(-0.581555\pi\) | ||||
−0.253418 | + | 0.967357i | \(0.581555\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 93.1339i | − | 0.206505i | ||||||
\(452\) | −123.021 | + | 72.0984i | −0.272170 | + | 0.159510i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −21.3230 | + | 5.78795i | −0.0469669 | + | 0.0127488i | ||||
\(455\) | −221.878 | − | 128.101i | −0.487643 | − | 0.281541i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −358.879 | − | 621.596i | −0.785292 | − | 1.36017i | −0.928824 | − | 0.370520i | \(-0.879179\pi\) |
0.143532 | − | 0.989646i | \(-0.454154\pi\) | |||||||
\(458\) | −45.5935 | + | 45.8914i | −0.0995492 | + | 0.100200i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1031.63 | + | 6.71842i | −2.24268 | + | 0.0146053i | ||||
\(461\) | 200.873 | + | 347.922i | 0.435733 | + | 0.754712i | 0.997355 | − | 0.0726819i | \(-0.0231558\pi\) |
−0.561622 | + | 0.827394i | \(0.689822\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −396.754 | − | 229.066i | −0.856920 | − | 0.494743i | 0.00605956 | − | 0.999982i | \(-0.498071\pi\) |
−0.862980 | + | 0.505239i | \(0.831405\pi\) | |||||||
\(464\) | 148.307 | − | 264.781i | 0.319627 | − | 0.570648i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −350.064 | − | 92.5787i | −0.751210 | − | 0.198667i | ||||
\(467\) | 204.395i | 0.437677i | 0.975761 | + | 0.218838i | \(0.0702267\pi\) | ||||
−0.975761 | + | 0.218838i | \(0.929773\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 387.493 | 0.826210 | ||||||||
\(470\) | 249.762 | − | 944.415i | 0.531409 | − | 2.00939i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 75.8045 | + | 272.241i | 0.160603 | + | 0.576781i | ||||
\(473\) | −60.5385 | + | 104.856i | −0.127988 | + | 0.221682i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 568.643 | − | 328.306i | 1.19714 | − | 0.691172i | ||||
\(476\) | 9.33481 | − | 0.0607922i | 0.0196109 | − | 0.000127715i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 64.9475 | + | 64.5259i | 0.135874 | + | 0.134992i | ||||
\(479\) | −78.4548 | + | 45.2959i | −0.163789 | + | 0.0945634i | −0.579654 | − | 0.814863i | \(-0.696812\pi\) |
0.415865 | + | 0.909426i | \(0.363479\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.08764 | + | 3.61589i | −0.00434020 | + | 0.00751745i | ||||
\(482\) | 177.313 | + | 653.226i | 0.367869 | + | 1.35524i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −368.718 | + | 216.093i | −0.761813 | + | 0.446473i | ||||
\(485\) | −778.046 | −1.60422 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 301.289i | − | 0.618663i | −0.950954 | − | 0.309332i | \(-0.899895\pi\) | ||
0.950954 | − | 0.309332i | \(-0.100105\pi\) | |||||||
\(488\) | −134.760 | + | 523.327i | −0.276148 | + | 1.07239i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 121.200 | + | 446.503i | 0.247346 | + | 0.911230i | ||||
\(491\) | −389.556 | − | 224.911i | −0.793394 | − | 0.458066i | 0.0477620 | − | 0.998859i | \(-0.484791\pi\) |
−0.841156 | + | 0.540792i | \(0.818124\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.91164 | + | 8.50721i | 0.00996276 | + | 0.0172560i | ||||
\(494\) | −164.256 | − | 163.190i | −0.332502 | − | 0.330344i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.16074 | − | 242.660i | −0.00637246 | − | 0.489234i | ||||
\(497\) | 127.175 | + | 220.273i | 0.255884 | + | 0.443205i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 552.630 | + | 319.061i | 1.10748 | + | 0.639401i | 0.938174 | − | 0.346163i | \(-0.112516\pi\) |
0.169301 | + | 0.985564i | \(0.445849\pi\) | |||||||
\(500\) | −420.409 | − | 239.086i | −0.840817 | − | 0.478172i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −144.500 | + | 546.390i | −0.287848 | + | 1.08843i | ||||
\(503\) | − | 182.179i | − | 0.362185i | −0.983466 | − | 0.181093i | \(-0.942037\pi\) | ||
0.983466 | − | 0.181093i | \(-0.0579634\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 349.250 | 0.691585 | ||||||||
\(506\) | 232.731 | + | 61.5485i | 0.459942 | + | 0.121637i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 19.4026 | − | 34.1175i | 0.0381941 | − | 0.0671604i | ||||
\(509\) | −471.123 | + | 816.009i | −0.925585 | + | 1.60316i | −0.134968 | + | 0.990850i | \(0.543093\pi\) |
−0.790617 | + | 0.612311i | \(0.790240\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −514.827 | + | 297.235i | −1.00749 | + | 0.581674i | ||||
\(512\) | −351.275 | + | 372.491i | −0.686084 | + | 0.727522i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −109.638 | + | 110.354i | −0.213303 | + | 0.214697i | ||||
\(515\) | 1011.30 | − | 583.875i | 1.96369 | − | 1.13374i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −113.976 | + | 197.412i | −0.220456 | + | 0.381841i | ||||
\(518\) | −5.14963 | + | 1.39783i | −0.00994138 | + | 0.00269851i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −113.423 | + | 440.468i | −0.218122 | + | 0.847054i | ||||
\(521\) | 634.330 | 1.21752 | 0.608762 | − | 0.793353i | \(-0.291666\pi\) | ||||
0.608762 | + | 0.793353i | \(0.291666\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 534.777i | − | 1.02252i | −0.859426 | − | 0.511259i | \(-0.829179\pi\) | ||
0.859426 | − | 0.511259i | \(-0.170821\pi\) | |||||||
\(524\) | −237.187 | − | 404.710i | −0.452646 | − | 0.772347i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 435.056 | − | 118.092i | 0.827102 | − | 0.224510i | ||||
\(527\) | 6.80273 | + | 3.92756i | 0.0129084 | + | 0.00745267i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 247.208 | + | 428.178i | 0.467313 | + | 0.809409i | ||||
\(530\) | 7.55461 | − | 7.60397i | 0.0142540 | − | 0.0143471i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.92703 | − | 295.901i | −0.00362224 | − | 0.556205i | ||||
\(533\) | −87.2809 | − | 151.175i | −0.163754 | − | 0.283630i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −383.912 | − | 221.652i | −0.717592 | − | 0.414302i | ||||
\(536\) | −184.528 | − | 662.706i | −0.344270 | − | 1.23639i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −823.312 | − | 217.735i | −1.53032 | − | 0.404712i | ||||
\(539\) | − | 107.960i | − | 0.200296i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −61.0097 | −0.112772 | −0.0563860 | − | 0.998409i | \(-0.517958\pi\) | ||||
−0.0563860 | + | 0.998409i | \(0.517958\pi\) | |||||||
\(542\) | −28.8227 | + | 108.986i | −0.0531785 | + | 0.201082i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.54931 | − | 15.9358i | −0.00836271 | − | 0.0292938i | ||||
\(545\) | −257.678 | + | 446.312i | −0.472805 | + | 0.818921i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 104.430 | − | 60.2925i | 0.190914 | − | 0.110224i | −0.401497 | − | 0.915861i | \(-0.631510\pi\) |
0.592410 | + | 0.805637i | \(0.298177\pi\) | |||||||
\(548\) | −6.54385 | − | 1004.83i | −0.0119413 | − | 1.83362i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 213.517 | + | 212.131i | 0.388212 | + | 0.385692i | ||||
\(551\) | 269.667 | − | 155.693i | 0.489415 | − | 0.282564i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −330.076 | + | 571.708i | −0.596882 | + | 1.03383i | ||||
\(554\) | −219.673 | − | 809.281i | −0.396521 | − | 1.46080i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −310.779 | − | 530.280i | −0.558955 | − | 0.953741i | ||||
\(557\) | 527.461 | 0.946968 | 0.473484 | − | 0.880802i | \(-0.342996\pi\) | ||||
0.473484 | + | 0.880802i | \(0.342996\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 226.936i | 0.405967i | ||||||||
\(560\) | −499.574 | + | 297.171i | −0.892097 | + | 0.530663i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 77.5031 | + | 285.523i | 0.137906 | + | 0.508049i | ||||
\(563\) | 595.478 | + | 343.800i | 1.05769 | + | 0.610656i | 0.924792 | − | 0.380474i | \(-0.124239\pi\) |
0.132896 | + | 0.991130i | \(0.457572\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 143.698 | + | 248.893i | 0.254333 | + | 0.440518i | ||||
\(566\) | 376.567 | + | 374.123i | 0.665313 | + | 0.660994i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 316.158 | − | 322.396i | 0.556616 | − | 0.567598i | ||||
\(569\) | −293.677 | − | 508.664i | −0.516128 | − | 0.893961i | −0.999825 | − | 0.0187248i | \(-0.994039\pi\) |
0.483696 | − | 0.875236i | \(-0.339294\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 742.245 | + | 428.535i | 1.29990 | + | 0.750500i | 0.980387 | − | 0.197081i | \(-0.0631461\pi\) |
0.319517 | + | 0.947581i | \(0.396479\pi\) | |||||||
\(572\) | 52.4674 | − | 92.2585i | 0.0917262 | − | 0.161291i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 57.0377 | − | 215.674i | 0.0993688 | − | 0.375739i | ||||
\(575\) | 1279.55i | 2.22530i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 871.732 | 1.51080 | 0.755401 | − | 0.655263i | \(-0.227442\pi\) | ||||
0.755401 | + | 0.655263i | \(0.227442\pi\) | |||||||
\(578\) | −558.271 | − | 147.642i | −0.965866 | − | 0.255435i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −531.714 | − | 302.385i | −0.916748 | − | 0.521354i | ||||
\(581\) | 226.615 | − | 392.509i | 0.390044 | − | 0.675575i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.16609 | + | 1.25059i | −0.00371542 | + | 0.00214510i | ||||
\(584\) | 753.511 | + | 738.931i | 1.29026 | + | 1.26529i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −351.960 | + | 354.259i | −0.600614 | + | 0.604538i | ||||
\(587\) | 700.071 | − | 404.186i | 1.19263 | − | 0.688563i | 0.233725 | − | 0.972303i | \(-0.424909\pi\) |
0.958901 | + | 0.283740i | \(0.0915753\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 124.498 | − | 215.638i | 0.211373 | − | 0.366108i | ||||
\(590\) | 549.690 | − | 149.209i | 0.931679 | − | 0.252897i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.84294 | + | 8.14146i | 0.00818064 | + | 0.0137525i | ||||
\(593\) | 445.123 | 0.750628 | 0.375314 | − | 0.926898i | \(-0.377535\pi\) | ||||
0.375314 | + | 0.926898i | \(0.377535\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 18.8149i | − | 0.0316217i | ||||||
\(596\) | 316.556 | − | 185.523i | 0.531134 | − | 0.311280i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 435.449 | − | 118.199i | 0.728175 | − | 0.197657i | ||||
\(599\) | −684.932 | − | 395.445i | −1.14346 | − | 0.660176i | −0.196174 | − | 0.980569i | \(-0.562852\pi\) |
−0.947285 | + | 0.320393i | \(0.896185\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 193.532 | + | 335.208i | 0.322017 | + | 0.557750i | 0.980904 | − | 0.194492i | \(-0.0623057\pi\) |
−0.658887 | + | 0.752242i | \(0.728972\pi\) | |||||||
\(602\) | −204.408 | + | 205.744i | −0.339548 | + | 0.341767i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 166.373 | − | 1.08349i | 0.275451 | − | 0.00179385i | ||||
\(605\) | 430.691 | + | 745.979i | 0.711886 | + | 1.23302i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −902.512 | − | 521.066i | −1.48684 | − | 0.858428i | −0.486953 | − | 0.873428i | \(-0.661892\pi\) |
−0.999887 | + | 0.0150003i | \(0.995225\pi\) | |||||||
\(608\) | −505.145 | + | 144.207i | −0.830831 | + | 0.237183i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1052.99 | + | 278.475i | 1.72621 | + | 0.456517i | ||||
\(611\) | 427.251i | 0.699266i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 256.336 | 0.418166 | 0.209083 | − | 0.977898i | \(-0.432952\pi\) | ||||
0.209083 | + | 0.977898i | \(0.432952\pi\) | |||||||
\(614\) | −132.933 | + | 502.655i | −0.216504 | + | 0.818657i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 130.668 | − | 36.3841i | 0.212123 | − | 0.0590650i | ||||
\(617\) | 253.519 | − | 439.108i | 0.410890 | − | 0.711683i | −0.584097 | − | 0.811684i | \(-0.698551\pi\) |
0.994987 | + | 0.100001i | \(0.0318846\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 662.787 | − | 382.660i | 1.07074 | − | 0.618191i | 0.142355 | − | 0.989816i | \(-0.454532\pi\) |
0.928383 | + | 0.371624i | \(0.121199\pi\) | |||||||
\(620\) | −489.118 | + | 3.18534i | −0.788900 | + | 0.00513764i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 27.1891 | + | 27.0126i | 0.0437123 | + | 0.0434286i | ||||
\(623\) | −100.827 | + | 58.2125i | −0.161841 | + | 0.0934390i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.5746 | − | 21.7799i | 0.0201194 | − | 0.0348479i | ||||
\(626\) | −22.9854 | − | 84.6789i | −0.0367179 | − | 0.135270i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 779.301 | − | 456.722i | 1.24092 | − | 0.727264i | ||||
\(629\) | −0.306623 | −0.000487477 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 719.756i | − | 1.14066i | −0.821416 | − | 0.570330i | \(-0.806815\pi\) | ||
0.821416 | − | 0.570330i | \(-0.193185\pi\) | |||||||
\(632\) | 1134.94 | + | 292.255i | 1.79580 | + | 0.462429i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −72.2692 | − | 266.242i | −0.113989 | − | 0.419940i | ||||
\(635\) | −68.5084 | − | 39.5534i | −0.107887 | − | 0.0622888i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −101.175 | − | 175.240i | −0.158830 | − | 0.275102i | ||||
\(638\) | 101.256 | + | 100.599i | 0.158708 | + | 0.157678i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 746.138 | + | 712.877i | 1.16584 | + | 1.11387i | ||||
\(641\) | −351.516 | − | 608.844i | −0.548388 | − | 0.949835i | −0.998385 | − | 0.0568054i | \(-0.981909\pi\) |
0.449998 | − | 0.893030i | \(-0.351425\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 507.224 | + | 292.846i | 0.788841 | + | 0.455437i | 0.839554 | − | 0.543276i | \(-0.182816\pi\) |
−0.0507136 | + | 0.998713i | \(0.516150\pi\) | |||||||
\(644\) | 501.250 | + | 285.061i | 0.778339 | + | 0.442641i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.34741 | − | 16.4387i | 0.00672973 | − | 0.0254469i | ||||
\(647\) | − | 791.553i | − | 1.22342i | −0.791082 | − | 0.611710i | \(-0.790482\pi\) | ||
0.791082 | − | 0.611710i | \(-0.209518\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −132.909 | −0.204791 | ||||||||
\(650\) | 545.380 | + | 144.232i | 0.839046 | + | 0.221896i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −247.521 | + | 435.240i | −0.379633 | + | 0.667547i | ||||
\(653\) | 196.385 | − | 340.148i | 0.300742 | − | 0.520901i | −0.675562 | − | 0.737303i | \(-0.736099\pi\) |
0.976304 | + | 0.216402i | \(0.0694323\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −818.797 | + | 472.733i | −1.25007 | + | 0.721730i | ||||
\(656\) | −396.017 | + | 5.15827i | −0.603685 | + | 0.00786322i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −384.838 | + | 387.353i | −0.584861 | + | 0.588682i | ||||
\(659\) | −372.557 | + | 215.096i | −0.565337 | + | 0.326398i | −0.755285 | − | 0.655397i | \(-0.772501\pi\) |
0.189948 | + | 0.981794i | \(0.439168\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 453.865 | − | 786.117i | 0.686633 | − | 1.18928i | −0.286287 | − | 0.958144i | \(-0.592421\pi\) |
0.972920 | − | 0.231140i | \(-0.0742456\pi\) | |||||||
\(662\) | −115.336 | + | 31.3070i | −0.174223 | + | 0.0472915i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −779.203 | − | 200.650i | −1.17350 | − | 0.302183i | ||||
\(665\) | −596.408 | −0.896854 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 606.799i | 0.909744i | ||||||||
\(668\) | −360.523 | − | 615.158i | −0.539706 | − | 0.920895i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1338.09 | + | 363.215i | −1.99715 | + | 0.542112i | ||||
\(671\) | −220.106 | − | 127.078i | −0.328027 | − | 0.189387i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −34.8528 | − | 60.3668i | −0.0517872 | − | 0.0896980i | 0.838970 | − | 0.544178i | \(-0.183158\pi\) |
−0.890757 | + | 0.454480i | \(0.849825\pi\) | |||||||
\(674\) | 632.504 | − | 636.636i | 0.938433 | − | 0.944564i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.10682 | + | 477.062i | 0.00459589 | + | 0.705712i | ||||
\(677\) | 144.502 | + | 250.285i | 0.213444 | + | 0.369697i | 0.952790 | − | 0.303629i | \(-0.0981984\pi\) |
−0.739346 | + | 0.673326i | \(0.764865\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 376.622 | + | 217.443i | 0.554671 | + | 0.320239i | ||||
\(680\) | −32.1781 | + | 8.95988i | −0.0473207 | + | 0.0131763i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 110.342 | + | 29.1814i | 0.161792 | + | 0.0427880i | ||||
\(683\) | − | 522.729i | − | 0.765343i | −0.923884 | − | 0.382672i | \(-0.875004\pi\) | ||
0.923884 | − | 0.382672i | \(-0.124996\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2025.29 | −2.95663 | ||||||||
\(686\) | 179.026 | − | 676.943i | 0.260971 | − | 0.986798i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 449.213 | + | 251.610i | 0.652926 | + | 0.365712i | ||||
\(689\) | −2.34400 | + | 4.05992i | −0.00340203 | + | 0.00589248i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −485.917 | + | 280.544i | −0.703208 | + | 0.405997i | −0.808541 | − | 0.588440i | \(-0.799742\pi\) |
0.105333 | + | 0.994437i | \(0.466409\pi\) | |||||||
\(692\) | 3.93813 | + | 604.711i | 0.00569093 | + | 0.873859i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −819.874 | − | 814.552i | −1.18137 | − | 1.17371i | ||||
\(695\) | −1072.85 | + | 619.409i | −1.54367 | + | 0.891236i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.40971 | − | 11.1019i | 0.00919614 | − | 0.0159282i | ||||
\(698\) | 69.2956 | + | 255.287i | 0.0992773 | + | 0.365740i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 364.535 | + | 622.004i | 0.520765 | + | 0.888577i | ||||
\(701\) | −1203.11 | −1.71627 | −0.858137 | − | 0.513421i | \(-0.828378\pi\) | ||||
−0.858137 | + | 0.513421i | \(0.828378\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.71954i | 0.0138258i | ||||||||
\(704\) | −124.451 | − | 206.147i | −0.176777 | − | 0.292823i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −283.509 | − | 1044.45i | −0.401571 | − | 1.47940i | ||||
\(707\) | −169.058 | − | 97.6059i | −0.239121 | − | 0.138056i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 89.2724 | + | 154.624i | 0.125913 | + | 0.218088i | 0.922090 | − | 0.386977i | \(-0.126481\pi\) |
−0.796176 | + | 0.605065i | \(0.793147\pi\) | |||||||
\(710\) | −645.632 | − | 641.441i | −0.909341 | − | 0.903439i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 147.572 | + | 144.717i | 0.207265 | + | 0.203254i | ||||
\(713\) | 242.611 | + | 420.215i | 0.340269 | + | 0.589362i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −185.257 | − | 106.958i | −0.259100 | − | 0.149591i | ||||
\(716\) | −547.398 | + | 962.543i | −0.764522 | + | 1.34433i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −149.698 | + | 566.048i | −0.208493 | + | 0.788367i | ||||
\(719\) | 53.0278i | 0.0737521i | 0.999320 | + | 0.0368760i | \(0.0117407\pi\) | ||||
−0.999320 | + | 0.0368760i | \(0.988259\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −652.709 | −0.905282 | ||||||||
\(722\) | 176.919 | + | 46.7884i | 0.245040 | + | 0.0648038i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −364.148 | − | 207.091i | −0.502966 | − | 0.286037i | ||||
\(725\) | −379.332 | + | 657.022i | −0.523216 | + | 0.906238i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −436.956 | + | 252.277i | −0.601041 | + | 0.347011i | −0.769451 | − | 0.638706i | \(-0.779470\pi\) |
0.168410 | + | 0.985717i | \(0.446137\pi\) | |||||||
\(728\) | 178.003 | − | 181.515i | 0.244509 | − | 0.249333i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1499.19 | − | 1508.99i | 2.05369 | − | 2.06710i | ||||
\(731\) | −14.4329 | + | 8.33283i | −0.0197440 | + | 0.0113992i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 410.964 | − | 711.811i | 0.560660 | − | 0.971092i | −0.436779 | − | 0.899569i | \(-0.643881\pi\) |
0.997439 | − | 0.0715233i | \(-0.0227860\pi\) | |||||||
\(734\) | −844.408 | + | 229.208i | −1.15042 | + | 0.312272i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 248.822 | − | 993.009i | 0.338073 | − | 1.34920i | ||||
\(737\) | 323.536 | 0.438991 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 190.298i | 0.257507i | 0.991677 | + | 0.128754i | \(0.0410977\pi\) | ||||
−0.991677 | + | 0.128754i | \(0.958902\pi\) | |||||||
\(740\) | 16.4725 | − | 9.65398i | 0.0222602 | − | 0.0130459i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.78200 | + | 1.56948i | −0.00779245 | + | 0.00211520i | ||||
\(743\) | 664.128 | + | 383.435i | 0.893847 | + | 0.516063i | 0.875199 | − | 0.483763i | \(-0.160730\pi\) |
0.0186481 | + | 0.999826i | \(0.494064\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −369.762 | − | 640.447i | −0.496325 | − | 0.859660i | ||||
\(746\) | −995.118 | + | 1001.62i | −1.33394 | + | 1.34265i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 7.79409 | − | 0.0507583i | 0.0104199 | − | 6.78587e-5i | ||||
\(749\) | 123.891 | + | 214.586i | 0.165409 | + | 0.286496i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 519.601 | + | 299.992i | 0.691879 | + | 0.399456i | 0.804315 | − | 0.594202i | \(-0.202532\pi\) |
−0.112437 | + | 0.993659i | \(0.535866\pi\) | |||||||
\(752\) | 845.732 | + | 473.705i | 1.12464 | + | 0.629927i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 258.635 | + | 68.3992i | 0.343017 | + | 0.0907152i | ||||
\(755\) | − | 335.335i | − | 0.444152i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −343.082 | −0.453213 | −0.226606 | − | 0.973986i | \(-0.572763\pi\) | ||||
−0.226606 | + | 0.973986i | \(0.572763\pi\) | |||||||
\(758\) | −276.858 | + | 1046.87i | −0.365249 | + | 1.38110i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 284.017 | + | 1020.00i | 0.373706 | + | 1.34211i | ||||
\(761\) | 149.365 | − | 258.708i | 0.196275 | − | 0.339958i | −0.751043 | − | 0.660253i | \(-0.770449\pi\) |
0.947318 | + | 0.320295i | \(0.103782\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 249.464 | − | 144.028i | 0.326952 | − | 0.188766i | ||||
\(764\) | 891.282 | − | 5.80440i | 1.16660 | − | 0.00759738i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 511.053 | + | 507.736i | 0.667171 | + | 0.662841i | ||||
\(767\) | −215.738 | + | 124.557i | −0.281275 | + | 0.162394i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −466.241 | + | 807.553i | −0.606295 | + | 1.05013i | 0.385550 | + | 0.922687i | \(0.374012\pi\) |
−0.991845 | + | 0.127447i | \(0.959322\pi\) | |||||||
\(770\) | −71.6162 | − | 263.836i | −0.0930081 | − | 0.342644i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 391.199 | − | 229.268i | 0.506734 | − | 0.296980i | ||||
\(773\) | 173.239 | 0.224113 | 0.112056 | − | 0.993702i | \(-0.464256\pi\) | ||||
0.112056 | + | 0.993702i | \(0.464256\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 606.660i | 0.782787i | ||||||||
\(776\) | 192.528 | − | 747.663i | 0.248103 | − | 0.963483i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 46.0066 | + | 169.490i | 0.0591345 | + | 0.217853i | ||||
\(779\) | −351.917 | − | 203.179i | −0.451755 | − | 0.260821i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 106.184 | + | 183.916i | 0.135959 | + | 0.235488i | ||||
\(782\) | 23.5065 | + | 23.3539i | 0.0300595 | + | 0.0298644i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −459.058 | + | 5.97940i | −0.585533 | + | 0.00762679i | ||||
\(785\) | −910.285 | − | 1576.66i | −1.15960 | − | 2.00848i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −43.1896 | − | 24.9355i | −0.0548788 | − | 0.0316843i | 0.472310 | − | 0.881433i | \(-0.343420\pi\) |
−0.527188 | + | 0.849748i | \(0.676754\pi\) | |||||||
\(788\) | 420.715 | + | 239.260i | 0.533902 | + | 0.303630i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 603.932 | − | 2283.62i | 0.764471 | − | 2.89066i | ||||
\(791\) | − | 160.639i | − | 0.203083i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −476.369 | −0.600717 | ||||||||
\(794\) | −93.6075 | − | 24.7557i | −0.117894 | − | 0.0311784i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 162.614 | − | 285.940i | 0.204289 | − | 0.359221i | ||||
\(797\) | 513.753 | − | 889.846i | 0.644608 | − | 1.11649i | −0.339784 | − | 0.940504i | \(-0.610354\pi\) |
0.984392 | − | 0.175991i | \(-0.0563129\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −27.1727 | + | 15.6882i | −0.0340084 | + | 0.0196348i | ||||
\(800\) | 890.181 | − | 919.649i | 1.11273 | − | 1.14956i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −614.189 | + | 618.202i | −0.765822 | + | 0.770825i | ||||
\(803\) | −429.854 | + | 248.176i | −0.535310 | + | 0.309061i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 581.114 | − | 1006.52i | 0.721880 | − | 1.25033i | ||||
\(806\) | 206.455 | − | 56.0406i | 0.256148 | − | 0.0695293i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −86.4222 | + | 335.612i | −0.106958 | + | 0.415361i | ||||
\(809\) | 637.363 | 0.787841 | 0.393920 | − | 0.919145i | \(-0.371119\pi\) | ||||
0.393920 | + | 0.919145i | \(0.371119\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1486.54i | − | 1.83298i | −0.400061 | − | 0.916489i | \(-0.631011\pi\) | ||
0.400061 | − | 0.916489i | \(-0.368989\pi\) | |||||||
\(812\) | 172.873 | + | 294.972i | 0.212898 | + | 0.363266i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.29968 | + | 1.16711i | −0.00528216 | + | 0.00143380i | ||||
\(815\) | 873.969 | + | 504.586i | 1.07235 | + | 0.619124i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 264.140 | + | 457.503i | 0.323304 | + | 0.559980i | ||||
\(818\) | −76.4412 | + | 76.9406i | −0.0934488 | + | 0.0940594i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.19842 | + | 798.232i | 0.00633954 | + | 0.973454i | ||||
\(821\) | −517.865 | − | 896.969i | −0.630773 | − | 1.09253i | −0.987394 | − | 0.158282i | \(-0.949404\pi\) |
0.356620 | − | 0.934249i | \(-0.383929\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −278.230 | − | 160.636i | −0.338068 | − | 0.195184i | 0.321349 | − | 0.946961i | \(-0.395864\pi\) |
−0.659417 | + | 0.751777i | \(0.729197\pi\) | |||||||
\(824\) | 310.827 | + | 1116.29i | 0.377218 | + | 1.35472i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −307.784 | − | 81.3972i | −0.372619 | − | 0.0985438i | ||||
\(827\) | − | 119.865i | − | 0.144939i | −0.997371 | − | 0.0724695i | \(-0.976912\pi\) | ||
0.997371 | − | 0.0724695i | \(-0.0230880\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 810.947 | 0.978223 | 0.489112 | − | 0.872221i | \(-0.337321\pi\) | ||||
0.489112 | + | 0.872221i | \(0.337321\pi\) | |||||||
\(830\) | −414.633 | + | 1567.83i | −0.499558 | + | 1.88896i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −395.201 | − | 217.988i | −0.475001 | − | 0.262005i | ||||
\(833\) | 7.43005 | − | 12.8692i | 0.00891963 | − | 0.0154492i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1244.57 | + | 718.553i | −1.49050 | + | 0.860543i | ||||
\(836\) | −1.60897 | − | 247.062i | −0.00192461 | − | 0.295529i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 904.391 | + | 898.520i | 1.07923 | + | 1.07222i | ||||
\(839\) | 51.3491 | − | 29.6464i | 0.0612027 | − | 0.0353354i | −0.469086 | − | 0.883152i | \(-0.655417\pi\) |
0.530289 | + | 0.847817i | \(0.322083\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 240.610 | − | 416.748i | 0.286100 | − | 0.495539i | ||||
\(842\) | −100.359 | − | 369.724i | −0.119191 | − | 0.439102i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 218.551 | + | 372.912i | 0.258947 | + | 0.441839i | ||||
\(845\) | 961.549 | 1.13793 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 481.466i | − | 0.568437i | ||||||
\(848\) | 5.43764 | + | 9.14121i | 0.00641231 | + | 0.0107797i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 10.8527 | + | 39.9816i | 0.0127679 | + | 0.0470372i | ||||
\(851\) | −16.4030 | − | 9.47029i | −0.0192750 | − | 0.0111284i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 547.729 | + | 948.694i | 0.642121 | + | 1.11219i | 0.984959 | + | 0.172791i | \(0.0552785\pi\) |
−0.342838 | + | 0.939395i | \(0.611388\pi\) | |||||||
\(854\) | −431.884 | − | 429.080i | −0.505718 | − | 0.502436i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 307.995 | − | 314.072i | 0.359807 | − | 0.366907i | ||||
\(857\) | 692.162 | + | 1198.86i | 0.807658 | + | 1.39890i | 0.914482 | + | 0.404626i | \(0.132598\pi\) |
−0.106825 | + | 0.994278i | \(0.534068\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −414.983 | − | 239.591i | −0.483101 | − | 0.278918i | 0.238607 | − | 0.971116i | \(-0.423309\pi\) |
−0.721708 | + | 0.692198i | \(0.756643\pi\) | |||||||
\(860\) | 513.011 | − | 902.077i | 0.596524 | − | 1.04893i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −246.054 | + | 930.394i | −0.285446 | + | 1.07934i | ||||
\(863\) | − | 4.93230i | − | 0.00571530i | −0.999996 | − | 0.00285765i | \(-0.999090\pi\) | ||
0.999996 | − | 0.00285765i | \(-0.000909619\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1218.83 | 1.40906 | ||||||||
\(866\) | −696.740 | − | 184.261i | −0.804550 | − | 0.212773i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 237.653 | + | 135.153i | 0.273794 | + | 0.155706i | ||||
\(869\) | −275.596 | + | 477.347i | −0.317142 | + | 0.549306i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 525.164 | − | 303.204i | 0.602944 | − | 0.348110i | ||||
\(872\) | −365.121 | − | 358.056i | −0.418717 | − | 0.410615i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 740.289 | − | 745.126i | 0.847013 | − | 0.852547i | ||||
\(875\) | 471.854 | − | 272.425i | 0.539262 | − | 0.311343i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −839.494 | + | 1454.05i | −0.957234 | + | 1.65798i | −0.228062 | + | 0.973647i | \(0.573239\pi\) |
−0.729172 | + | 0.684331i | \(0.760095\pi\) | |||||||
\(878\) | 1088.23 | − | 295.391i | 1.23944 | − | 0.336436i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −417.119 | + | 248.123i | −0.473999 | + | 0.281958i | ||||
\(881\) | −830.879 | −0.943109 | −0.471555 | − | 0.881837i | \(-0.656307\pi\) | ||||
−0.471555 | + | 0.881837i | \(0.656307\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1228.46i | 1.39123i | 0.718414 | + | 0.695615i | \(0.244868\pi\) | ||||
−0.718414 | + | 0.695615i | \(0.755132\pi\) | |||||||
\(884\) | 12.6038 | − | 7.38666i | 0.0142577 | − | 0.00835595i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1270.20 | + | 344.787i | −1.43364 | + | 0.389150i | ||||
\(887\) | −660.079 | − | 381.097i | −0.744170 | − | 0.429647i | 0.0794134 | − | 0.996842i | \(-0.474695\pi\) |
−0.823584 | + | 0.567195i | \(0.808029\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.1082 | + | 38.2925i | 0.0248686 | + | 0.0430737i | ||||
\(890\) | 293.612 | − | 295.530i | 0.329901 | − | 0.332056i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −653.083 | + | 4.25315i | −0.732156 | + | 0.00476810i | ||||
\(893\) | 497.295 | + | 861.340i | 0.556881 | + | 0.964547i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1932.80 | + | 1115.90i | 2.15955 | + | 1.24682i | ||||
\(896\) | −161.947 | − | 553.601i | −0.180744 | − | 0.617858i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −440.011 | − | 116.366i | −0.489990 | − | 0.129584i | ||||
\(899\) | 287.696i | 0.320018i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.344275 | −0.000382104 | ||||||||
\(902\) | 47.6235 | − | 180.077i | 0.0527977 | − | 0.199642i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −274.731 | + | 76.4981i | −0.303907 | + | 0.0846218i | ||||
\(905\) | −422.166 | + | 731.214i | −0.466482 | + | 0.807971i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 324.076 | − | 187.106i | 0.357306 | − | 0.206291i | −0.310592 | − | 0.950543i | \(-0.600527\pi\) |
0.667898 | + | 0.744253i | \(0.267194\pi\) | |||||||
\(908\) | −44.1882 | + | 0.287772i | −0.0486654 | + | 0.000316929i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −363.503 | − | 361.143i | −0.399453 | − | 0.396861i | ||||
\(911\) | 1265.50 | − | 730.639i | 1.38914 | − | 0.802018i | 0.395918 | − | 0.918286i | \(-0.370426\pi\) |
0.993218 | + | 0.116268i | \(0.0370930\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 189.212 | − | 327.725i | 0.207242 | − | 0.358954i | ||||
\(914\) | −376.051 | − | 1385.38i | −0.411435 | − | 1.51574i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −111.623 | + | 65.4183i | −0.121859 | + | 0.0714173i | ||||
\(917\) | 528.464 | 0.576296 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1112.72i | − | 1.21080i | −0.795923 | − | 0.605398i | \(-0.793014\pi\) | ||
0.795923 | − | 0.605398i | \(-0.206986\pi\) | |||||||
\(920\) | −1998.12 | − | 514.529i | −2.17187 | − | 0.559271i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 210.485 | + | 775.432i | 0.228292 | + | 0.841033i | ||||
\(923\) | 344.717 | + | 199.022i | 0.373474 | + | 0.215625i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.8404 | − | 20.5082i | −0.0128005 | − | 0.0221710i | ||||
\(926\) | −650.003 | − | 645.784i | −0.701947 | − | 0.697390i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 422.150 | − | 436.125i | 0.454903 | − | 0.469962i | ||||
\(929\) | 508.204 | + | 880.234i | 0.547044 | + | 0.947507i | 0.998475 | + | 0.0552017i | \(0.0175802\pi\) |
−0.451432 | + | 0.892306i | \(0.649086\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −407.938 | − | 235.523i | −0.438171 | − | 0.252978i | ||||
\(932\) | −629.518 | − | 358.007i | −0.675449 | − | 0.384127i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −104.516 | + | 395.203i | −0.111902 | + | 0.423130i | ||||
\(935\) | − | 15.7095i | − | 0.0168016i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 170.282 | 0.181731 | 0.0908654 | − | 0.995863i | \(-0.471037\pi\) | ||||
0.0908654 | + | 0.995863i | \(0.471037\pi\) | |||||||
\(938\) | 749.227 | + | 198.142i | 0.798750 | + | 0.211239i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 965.844 | − | 1698.34i | 1.02749 | − | 1.80674i | ||||
\(941\) | 150.929 | − | 261.417i | 0.160392 | − | 0.277808i | −0.774617 | − | 0.632430i | \(-0.782057\pi\) |
0.935009 | + | 0.354623i | \(0.115391\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 685.784 | − | 395.938i | 0.727237 | − | 0.419870i | ||||
\(944\) | 7.36126 | + | 565.147i | 0.00779794 | + | 0.598673i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −170.670 | + | 171.785i | −0.180413 | + | 0.181591i | ||||
\(947\) | −730.155 | + | 421.555i | −0.771019 | + | 0.445148i | −0.833238 | − | 0.552914i | \(-0.813516\pi\) |
0.0622189 | + | 0.998063i | \(0.480182\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −465.159 | + | 805.679i | −0.490157 | + | 0.848977i | ||||
\(950\) | 1267.37 | − | 344.016i | 1.33407 | − | 0.362123i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 18.0802 | + | 4.65576i | 0.0189918 | + | 0.00489051i | ||||
\(953\) | −306.171 | −0.321270 | −0.160635 | − | 0.987014i | \(-0.551354\pi\) | ||||
−0.160635 | + | 0.987014i | \(0.551354\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 1796.44i | − | 1.88109i | ||||||
\(956\) | 92.5828 | + | 157.973i | 0.0968439 | + | 0.165244i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −174.856 | + | 47.4634i | −0.182522 | + | 0.0495442i | ||||
\(959\) | 980.365 | + | 566.014i | 1.02228 | + | 0.590213i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −365.473 | − | 633.018i | −0.380305 | − | 0.658707i | ||||
\(962\) | −5.88547 | + | 5.92393i | −0.00611796 | + | 0.00615793i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 8.81584 | + | 1353.70i | 0.00914507 | + | 1.40425i | ||||
\(965\) | −456.951 | − | 791.462i | −0.473524 | − | 0.820168i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −103.822 | − | 59.9417i | −0.107365 | − | 0.0619873i | 0.445356 | − | 0.895354i | \(-0.353077\pi\) |
−0.552721 | + | 0.833366i | \(0.686410\pi\) | |||||||
\(968\) | −823.423 | + | 229.280i | −0.850644 | + | 0.236859i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1504.37 | − | 397.850i | −1.55090 | − | 0.410154i | ||||
\(971\) | 62.7602i | 0.0646346i | 0.999478 | + | 0.0323173i | \(0.0102887\pi\) | ||||
−0.999478 | + | 0.0323173i | \(0.989711\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 692.431 | 0.711646 | ||||||||
\(974\) | 154.063 | − | 582.551i | 0.158175 | − | 0.598101i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −528.163 | + | 942.959i | −0.541151 | + | 0.966146i | ||||
\(977\) | −618.115 | + | 1070.61i | −0.632666 | + | 1.09581i | 0.354338 | + | 0.935117i | \(0.384706\pi\) |
−0.987004 | + | 0.160693i | \(0.948627\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −84.1854 | + | 48.6045i | −0.0859912 | + | 0.0496471i | ||||
\(980\) | 6.02594 | + | 925.300i | 0.00614892 | + | 0.944184i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −638.211 | − | 634.068i | −0.649909 | − | 0.645691i | ||||
\(983\) | −490.618 | + | 283.258i | −0.499103 | + | 0.288157i | −0.728343 | − | 0.685213i | \(-0.759709\pi\) |
0.229240 | + | 0.973370i | \(0.426376\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 487.746 | − | 844.801i | 0.495174 | − | 0.857666i | ||||
\(986\) | 5.14667 | + | 18.9605i | 0.00521974 | + | 0.0192297i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −234.147 | − | 399.524i | −0.236991 | − | 0.404376i | ||||
\(989\) | −1029.46 | −1.04091 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 457.774i | 0.461931i | 0.972962 | + | 0.230966i | \(0.0741885\pi\) | ||||
−0.972962 | + | 0.230966i | \(0.925812\pi\) | |||||||
\(992\) | 117.972 | − | 470.806i | 0.118923 | − | 0.474603i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 133.260 | + | 490.933i | 0.134064 | + | 0.493897i | ||||
\(995\) | −574.172 | − | 331.498i | −0.577057 | − | 0.333164i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.3798 | + | 33.5667i | 0.0194381 | + | 0.0336677i | 0.875581 | − | 0.483072i | \(-0.160479\pi\) |
−0.856143 | + | 0.516739i | \(0.827146\pi\) | |||||||
\(998\) | 905.375 | + | 899.498i | 0.907190 | + | 0.901301i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 108.3.f.c.91.8 | 16 | ||
3.2 | odd | 2 | 36.3.f.c.31.1 | yes | 16 | ||
4.3 | odd | 2 | inner | 108.3.f.c.91.4 | 16 | ||
8.3 | odd | 2 | 1728.3.o.g.1279.2 | 16 | |||
8.5 | even | 2 | 1728.3.o.g.1279.1 | 16 | |||
9.2 | odd | 6 | 36.3.f.c.7.5 | yes | 16 | ||
9.4 | even | 3 | 324.3.d.g.163.4 | 8 | |||
9.5 | odd | 6 | 324.3.d.i.163.5 | 8 | |||
9.7 | even | 3 | inner | 108.3.f.c.19.4 | 16 | ||
12.11 | even | 2 | 36.3.f.c.31.5 | yes | 16 | ||
24.5 | odd | 2 | 576.3.o.g.319.8 | 16 | |||
24.11 | even | 2 | 576.3.o.g.319.1 | 16 | |||
36.7 | odd | 6 | inner | 108.3.f.c.19.8 | 16 | ||
36.11 | even | 6 | 36.3.f.c.7.1 | ✓ | 16 | ||
36.23 | even | 6 | 324.3.d.i.163.6 | 8 | |||
36.31 | odd | 6 | 324.3.d.g.163.3 | 8 | |||
72.11 | even | 6 | 576.3.o.g.511.8 | 16 | |||
72.29 | odd | 6 | 576.3.o.g.511.1 | 16 | |||
72.43 | odd | 6 | 1728.3.o.g.127.1 | 16 | |||
72.61 | even | 6 | 1728.3.o.g.127.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.3.f.c.7.1 | ✓ | 16 | 36.11 | even | 6 | ||
36.3.f.c.7.5 | yes | 16 | 9.2 | odd | 6 | ||
36.3.f.c.31.1 | yes | 16 | 3.2 | odd | 2 | ||
36.3.f.c.31.5 | yes | 16 | 12.11 | even | 2 | ||
108.3.f.c.19.4 | 16 | 9.7 | even | 3 | inner | ||
108.3.f.c.19.8 | 16 | 36.7 | odd | 6 | inner | ||
108.3.f.c.91.4 | 16 | 4.3 | odd | 2 | inner | ||
108.3.f.c.91.8 | 16 | 1.1 | even | 1 | trivial | ||
324.3.d.g.163.3 | 8 | 36.31 | odd | 6 | |||
324.3.d.g.163.4 | 8 | 9.4 | even | 3 | |||
324.3.d.i.163.5 | 8 | 9.5 | odd | 6 | |||
324.3.d.i.163.6 | 8 | 36.23 | even | 6 | |||
576.3.o.g.319.1 | 16 | 24.11 | even | 2 | |||
576.3.o.g.319.8 | 16 | 24.5 | odd | 2 | |||
576.3.o.g.511.1 | 16 | 72.29 | odd | 6 | |||
576.3.o.g.511.8 | 16 | 72.11 | even | 6 | |||
1728.3.o.g.127.1 | 16 | 72.43 | odd | 6 | |||
1728.3.o.g.127.2 | 16 | 72.61 | even | 6 | |||
1728.3.o.g.1279.1 | 16 | 8.5 | even | 2 | |||
1728.3.o.g.1279.2 | 16 | 8.3 | odd | 2 |