Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [850,2,Mod(107,850)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(850, base_ring=CyclotomicField(16))
chi = DirichletCharacter(H, H._module([4, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("850.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 850 = 2 \cdot 5^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 850.v (of order \(16\), degree \(8\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.78728417181\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{16})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{16}]$ |
Embedding invariants
Embedding label | 193.2 | ||
Character | \(\chi\) | \(=\) | 850.193 |
Dual form | 850.2.v.b.207.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/850\mathbb{Z}\right)^\times\).
\(n\) | \(477\) | \(751\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{15}{16}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.923880 | − | 0.382683i | 0.653281 | − | 0.270598i | ||||
\(3\) | −1.23998 | − | 0.828527i | −0.715902 | − | 0.478351i | 0.143500 | − | 0.989650i | \(-0.454164\pi\) |
−0.859402 | + | 0.511300i | \(0.829164\pi\) | |||||||
\(4\) | 0.707107 | − | 0.707107i | 0.353553 | − | 0.353553i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.46265 | − | 0.290940i | −0.597126 | − | 0.118776i | ||||
\(7\) | 3.43494 | + | 0.683252i | 1.29829 | + | 0.258245i | 0.795388 | − | 0.606101i | \(-0.207267\pi\) |
0.502898 | + | 0.864346i | \(0.332267\pi\) | |||||||
\(8\) | 0.382683 | − | 0.923880i | 0.135299 | − | 0.326641i | ||||
\(9\) | −0.296960 | − | 0.716925i | −0.0989867 | − | 0.238975i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.279207 | − | 1.40367i | 0.0841842 | − | 0.423222i | −0.915593 | − | 0.402107i | \(-0.868278\pi\) |
0.999777 | − | 0.0211159i | \(-0.00672189\pi\) | |||||||
\(12\) | −1.46265 | + | 0.290940i | −0.422232 | + | 0.0839872i | ||||
\(13\) | −0.687320 | −0.190628 | −0.0953141 | − | 0.995447i | \(-0.530386\pi\) | ||||
−0.0953141 | + | 0.995447i | \(0.530386\pi\) | |||||||
\(14\) | 3.43494 | − | 0.683252i | 0.918027 | − | 0.182607i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | − | 1.00000i | − | 0.250000i | ||||||
\(17\) | 3.97099 | + | 1.10961i | 0.963106 | + | 0.269121i | ||||
\(18\) | −0.548711 | − | 0.548711i | −0.129332 | − | 0.129332i | ||||
\(19\) | 0.0862003 | − | 0.208106i | 0.0197757 | − | 0.0477428i | −0.913683 | − | 0.406427i | \(-0.866775\pi\) |
0.933459 | + | 0.358684i | \(0.116775\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.69316 | − | 3.69316i | −0.805914 | − | 0.805914i | ||||
\(22\) | −0.279207 | − | 1.40367i | −0.0595272 | − | 0.299263i | ||||
\(23\) | 0.358556 | + | 0.536616i | 0.0747640 | + | 0.111892i | 0.866967 | − | 0.498365i | \(-0.166066\pi\) |
−0.792203 | + | 0.610257i | \(0.791066\pi\) | |||||||
\(24\) | −1.23998 | + | 0.828527i | −0.253110 | + | 0.169122i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.635001 | + | 0.263026i | −0.124534 | + | 0.0515836i | ||||
\(27\) | −1.09859 | + | 5.52298i | −0.211423 | + | 1.06290i | ||||
\(28\) | 2.91200 | − | 1.94574i | 0.550317 | − | 0.367710i | ||||
\(29\) | 3.16366 | − | 4.73475i | 0.587477 | − | 0.879222i | −0.412012 | − | 0.911178i | \(-0.635174\pi\) |
0.999489 | + | 0.0319568i | \(0.0101739\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.14661 | − | 10.7917i | −0.385542 | − | 1.93825i | −0.343548 | − | 0.939135i | \(-0.611629\pi\) |
−0.0419943 | − | 0.999118i | \(-0.513371\pi\) | |||||||
\(32\) | −0.382683 | − | 0.923880i | −0.0676495 | − | 0.163320i | ||||
\(33\) | −1.50919 | + | 1.50919i | −0.262716 | + | 0.262716i | ||||
\(34\) | 4.09335 | − | 0.494483i | 0.702003 | − | 0.0848032i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.716925 | − | 0.296960i | −0.119488 | − | 0.0494934i | ||||
\(37\) | 0.235023 | − | 0.351736i | 0.0386375 | − | 0.0578251i | −0.811648 | − | 0.584147i | \(-0.801429\pi\) |
0.850286 | + | 0.526322i | \(0.176429\pi\) | |||||||
\(38\) | − | 0.225252i | − | 0.0365408i | ||||||
\(39\) | 0.852262 | + | 0.569463i | 0.136471 | + | 0.0911871i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.49783 | − | 2.24166i | −0.233922 | − | 0.350089i | 0.695874 | − | 0.718164i | \(-0.255017\pi\) |
−0.929796 | + | 0.368075i | \(0.880017\pi\) | |||||||
\(42\) | −4.82535 | − | 1.99872i | −0.744568 | − | 0.308410i | ||||
\(43\) | 2.98993 | + | 1.23847i | 0.455960 | + | 0.188865i | 0.598829 | − | 0.800877i | \(-0.295633\pi\) |
−0.142869 | + | 0.989742i | \(0.545633\pi\) | |||||||
\(44\) | −0.795115 | − | 1.18997i | −0.119868 | − | 0.179395i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.536616 | + | 0.358556i | 0.0791198 | + | 0.0528661i | ||||
\(47\) | − | 4.97288i | − | 0.725369i | −0.931912 | − | 0.362685i | \(-0.881860\pi\) | ||
0.931912 | − | 0.362685i | \(-0.118140\pi\) | |||||||
\(48\) | −0.828527 | + | 1.23998i | −0.119588 | + | 0.178976i | ||||
\(49\) | 4.86483 | + | 2.01508i | 0.694976 | + | 0.287869i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.00460 | − | 4.66597i | −0.560756 | − | 0.653367i | ||||
\(52\) | −0.486008 | + | 0.486008i | −0.0673973 | + | 0.0673973i | ||||
\(53\) | −1.07924 | − | 2.60552i | −0.148245 | − | 0.357896i | 0.832261 | − | 0.554384i | \(-0.187046\pi\) |
−0.980506 | + | 0.196488i | \(0.937046\pi\) | |||||||
\(54\) | 1.09859 | + | 5.52298i | 0.149499 | + | 0.751582i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.94574 | − | 2.91200i | 0.260010 | − | 0.389133i | ||||
\(57\) | −0.279308 | + | 0.186628i | −0.0369953 | + | 0.0247195i | ||||
\(58\) | 1.11093 | − | 5.58502i | 0.145872 | − | 0.733349i | ||||
\(59\) | −2.73373 | + | 1.13235i | −0.355902 | + | 0.147419i | −0.553468 | − | 0.832870i | \(-0.686696\pi\) |
0.197567 | + | 0.980289i | \(0.436696\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.0227 | + | 7.36516i | −1.41132 | + | 0.943012i | −0.411821 | + | 0.911265i | \(0.635107\pi\) |
−0.999496 | + | 0.0317466i | \(0.989893\pi\) | |||||||
\(62\) | −6.11303 | − | 9.14879i | −0.776355 | − | 1.16190i | ||||
\(63\) | −0.530200 | − | 2.66550i | −0.0667989 | − | 0.335821i | ||||
\(64\) | −0.707107 | − | 0.707107i | −0.0883883 | − | 0.0883883i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.816768 | + | 1.97185i | −0.100537 | + | 0.242718i | ||||
\(67\) | 5.28482 | + | 5.28482i | 0.645644 | + | 0.645644i | 0.951937 | − | 0.306293i | \(-0.0990888\pi\) |
−0.306293 | + | 0.951937i | \(0.599089\pi\) | |||||||
\(68\) | 3.59253 | − | 2.02330i | 0.435658 | − | 0.245361i | ||||
\(69\) | − | 0.962466i | − | 0.115867i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.6099 | − | 2.11045i | 1.25917 | − | 0.250464i | 0.479995 | − | 0.877271i | \(-0.340639\pi\) |
0.779174 | + | 0.626807i | \(0.215639\pi\) | |||||||
\(72\) | −0.775994 | −0.0914518 | ||||||||
\(73\) | −9.61892 | + | 1.91332i | −1.12581 | + | 0.223937i | −0.722665 | − | 0.691199i | \(-0.757083\pi\) |
−0.403145 | + | 0.915136i | \(0.632083\pi\) | |||||||
\(74\) | 0.0825290 | − | 0.414901i | 0.00959380 | − | 0.0482313i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.0862003 | − | 0.208106i | −0.00988786 | − | 0.0238714i | ||||
\(77\) | 1.91812 | − | 4.63076i | 0.218590 | − | 0.527724i | ||||
\(78\) | 1.00531 | + | 0.199969i | 0.113829 | + | 0.0226420i | ||||
\(79\) | −1.79628 | − | 0.357303i | −0.202098 | − | 0.0401997i | 0.0930034 | − | 0.995666i | \(-0.470353\pi\) |
−0.295101 | + | 0.955466i | \(0.595353\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.29203 | − | 4.29203i | 0.476892 | − | 0.476892i | ||||
\(82\) | −2.24166 | − | 1.49783i | −0.247550 | − | 0.165408i | ||||
\(83\) | 2.36249 | − | 0.978574i | 0.259317 | − | 0.107412i | −0.249238 | − | 0.968442i | \(-0.580180\pi\) |
0.508554 | + | 0.861030i | \(0.330180\pi\) | |||||||
\(84\) | −5.22292 | −0.569867 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.23628 | 0.348977 | ||||||||
\(87\) | −7.84575 | + | 3.24981i | −0.841152 | + | 0.348417i | ||||
\(88\) | −1.18997 | − | 0.795115i | −0.126852 | − | 0.0847596i | ||||
\(89\) | 9.75720 | − | 9.75720i | 1.03426 | − | 1.03426i | 0.0348693 | − | 0.999392i | \(-0.488899\pi\) |
0.999392 | − | 0.0348693i | \(-0.0111015\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.36090 | − | 0.469613i | −0.247490 | − | 0.0492288i | ||||
\(92\) | 0.632982 | + | 0.125908i | 0.0659929 | + | 0.0131268i | ||||
\(93\) | −6.27950 | + | 15.1601i | −0.651154 | + | 1.57202i | ||||
\(94\) | −1.90304 | − | 4.59434i | −0.196284 | − | 0.473870i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.290940 | + | 1.46265i | −0.0296940 | + | 0.149282i | ||||
\(97\) | −8.64723 | + | 1.72004i | −0.877993 | + | 0.174644i | −0.613453 | − | 0.789731i | \(-0.710220\pi\) |
−0.264540 | + | 0.964375i | \(0.585220\pi\) | |||||||
\(98\) | 5.26566 | 0.531912 | ||||||||
\(99\) | −1.08924 | + | 0.216663i | −0.109473 | + | 0.0217755i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.2302i | 1.31645i | 0.752820 | + | 0.658226i | \(0.228693\pi\) | ||||
−0.752820 | + | 0.658226i | \(0.771307\pi\) | |||||||
\(102\) | −5.48536 | − | 2.77830i | −0.543131 | − | 0.275093i | ||||
\(103\) | 12.8336 | + | 12.8336i | 1.26454 | + | 1.26454i | 0.948871 | + | 0.315665i | \(0.102227\pi\) |
0.315665 | + | 0.948871i | \(0.397773\pi\) | |||||||
\(104\) | −0.263026 | + | 0.635001i | −0.0257918 | + | 0.0622669i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.99418 | − | 1.99418i | −0.193692 | − | 0.193692i | ||||
\(107\) | 2.83228 | + | 14.2388i | 0.273807 | + | 1.37652i | 0.835643 | + | 0.549273i | \(0.185095\pi\) |
−0.561836 | + | 0.827249i | \(0.689905\pi\) | |||||||
\(108\) | 3.12852 | + | 4.68215i | 0.301042 | + | 0.450540i | ||||
\(109\) | −10.7548 | + | 7.18615i | −1.03013 | + | 0.688308i | −0.951201 | − | 0.308572i | \(-0.900149\pi\) |
−0.0789251 | + | 0.996881i | \(0.525149\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.582846 | + | 0.241423i | −0.0553213 | + | 0.0229148i | ||||
\(112\) | 0.683252 | − | 3.43494i | 0.0645613 | − | 0.324571i | ||||
\(113\) | −2.50435 | + | 1.67335i | −0.235589 | + | 0.157416i | −0.667761 | − | 0.744376i | \(-0.732747\pi\) |
0.432172 | + | 0.901791i | \(0.357747\pi\) | |||||||
\(114\) | −0.186628 | + | 0.279308i | −0.0174793 | + | 0.0261596i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.11093 | − | 5.58502i | −0.103147 | − | 0.518556i | ||||
\(117\) | 0.204107 | + | 0.492757i | 0.0188697 | + | 0.0455554i | ||||
\(118\) | −2.09231 | + | 2.09231i | −0.192613 | + | 0.192613i | ||||
\(119\) | 12.8820 | + | 6.52464i | 1.18089 | + | 0.598113i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.27034 | + | 3.42569i | 0.751849 | + | 0.311426i | ||||
\(122\) | −7.36516 | + | 11.0227i | −0.666810 | + | 0.997951i | ||||
\(123\) | 4.02061i | 0.362526i | ||||||||
\(124\) | −9.14879 | − | 6.11303i | −0.821586 | − | 0.548966i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.50988 | − | 2.25970i | −0.134511 | − | 0.201310i | ||||
\(127\) | 11.5255 | + | 4.77400i | 1.02272 | + | 0.423624i | 0.830079 | − | 0.557645i | \(-0.188295\pi\) |
0.192640 | + | 0.981270i | \(0.438295\pi\) | |||||||
\(128\) | −0.923880 | − | 0.382683i | −0.0816602 | − | 0.0338248i | ||||
\(129\) | −2.68135 | − | 4.01292i | −0.236079 | − | 0.353318i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.3126 | + | 10.8997i | 1.42524 | + | 0.952314i | 0.998858 | + | 0.0477705i | \(0.0152116\pi\) |
0.426381 | + | 0.904544i | \(0.359788\pi\) | |||||||
\(132\) | 2.13432i | 0.185769i | ||||||||
\(133\) | 0.438282 | − | 0.655936i | 0.0380039 | − | 0.0568768i | ||||
\(134\) | 6.90495 | + | 2.86013i | 0.596497 | + | 0.247077i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.54478 | − | 3.24409i | 0.218213 | − | 0.278178i | ||||
\(137\) | 5.01618 | − | 5.01618i | 0.428561 | − | 0.428561i | −0.459577 | − | 0.888138i | \(-0.651999\pi\) |
0.888138 | + | 0.459577i | \(0.151999\pi\) | |||||||
\(138\) | −0.368320 | − | 0.889203i | −0.0313535 | − | 0.0756940i | ||||
\(139\) | 2.05197 | + | 10.3159i | 0.174045 | + | 0.874986i | 0.964827 | + | 0.262887i | \(0.0846745\pi\) |
−0.790781 | + | 0.612099i | \(0.790325\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.12017 | + | 6.16627i | −0.346981 | + | 0.519294i | ||||
\(142\) | 8.99468 | − | 6.01005i | 0.754817 | − | 0.504352i | ||||
\(143\) | −0.191905 | + | 0.964770i | −0.0160479 | + | 0.0806781i | ||||
\(144\) | −0.716925 | + | 0.296960i | −0.0597438 | + | 0.0247467i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.15453 | + | 5.44868i | −0.674874 | + | 0.450936i | ||||
\(147\) | −4.36274 | − | 6.52931i | −0.359833 | − | 0.538528i | ||||
\(148\) | −0.0825290 | − | 0.414901i | −0.00678384 | − | 0.0341047i | ||||
\(149\) | −3.74622 | − | 3.74622i | −0.306902 | − | 0.306902i | 0.536804 | − | 0.843707i | \(-0.319631\pi\) |
−0.843707 | + | 0.536804i | \(0.819631\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.01503 | + | 9.69314i | −0.326738 | + | 0.788816i | 0.672092 | + | 0.740468i | \(0.265396\pi\) |
−0.998831 | + | 0.0483488i | \(0.984604\pi\) | |||||||
\(152\) | −0.159277 | − | 0.159277i | −0.0129191 | − | 0.0129191i | ||||
\(153\) | −0.383716 | − | 3.17641i | −0.0310216 | − | 0.256798i | ||||
\(154\) | − | 5.01229i | − | 0.403902i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.00531 | − | 0.199969i | 0.0804894 | − | 0.0160103i | ||||
\(157\) | 15.0303 | 1.19955 | 0.599773 | − | 0.800170i | \(-0.295258\pi\) | ||||
0.599773 | + | 0.800170i | \(0.295258\pi\) | |||||||
\(158\) | −1.79628 | + | 0.357303i | −0.142905 | + | 0.0284255i | ||||
\(159\) | −0.820509 | + | 4.12498i | −0.0650706 | + | 0.327132i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.864973 | + | 2.08823i | 0.0681694 | + | 0.164576i | ||||
\(162\) | 2.32283 | − | 5.60781i | 0.182499 | − | 0.440591i | ||||
\(163\) | −14.6915 | − | 2.92232i | −1.15073 | − | 0.228894i | −0.417370 | − | 0.908736i | \(-0.637048\pi\) |
−0.733358 | + | 0.679842i | \(0.762048\pi\) | |||||||
\(164\) | −2.64422 | − | 0.525968i | −0.206479 | − | 0.0410712i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.80817 | − | 1.80817i | 0.140341 | − | 0.140341i | ||||
\(167\) | 6.33305 | + | 4.23161i | 0.490066 | + | 0.327452i | 0.775930 | − | 0.630818i | \(-0.217281\pi\) |
−0.285865 | + | 0.958270i | \(0.592281\pi\) | |||||||
\(168\) | −4.82535 | + | 1.99872i | −0.372284 | + | 0.154205i | ||||
\(169\) | −12.5276 | −0.963661 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.174795 | −0.0133669 | ||||||||
\(172\) | 2.98993 | − | 1.23847i | 0.227980 | − | 0.0944324i | ||||
\(173\) | −15.1101 | − | 10.0963i | −1.14880 | − | 0.767606i | −0.172713 | − | 0.984972i | \(-0.555253\pi\) |
−0.976090 | + | 0.217366i | \(0.930253\pi\) | |||||||
\(174\) | −6.00487 | + | 6.00487i | −0.455228 | + | 0.455228i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.40367 | − | 0.279207i | −0.105806 | − | 0.0210460i | ||||
\(177\) | 4.32795 | + | 0.860883i | 0.325309 | + | 0.0647080i | ||||
\(178\) | 5.28056 | − | 12.7484i | 0.395795 | − | 0.955533i | ||||
\(179\) | −4.94606 | − | 11.9408i | −0.369686 | − | 0.892501i | −0.993802 | − | 0.111169i | \(-0.964541\pi\) |
0.624116 | − | 0.781332i | \(-0.285459\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.11267 | + | 5.59375i | −0.0827039 | + | 0.415780i | 0.917148 | + | 0.398548i | \(0.130486\pi\) |
−0.999852 | + | 0.0172328i | \(0.994514\pi\) | |||||||
\(182\) | −2.36090 | + | 0.469613i | −0.175002 | + | 0.0348100i | ||||
\(183\) | 19.7702 | 1.46145 | ||||||||
\(184\) | 0.632982 | − | 0.125908i | 0.0466641 | − | 0.00928206i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 16.4091i | 1.20318i | ||||||||
\(187\) | 2.66626 | − | 5.26415i | 0.194976 | − | 0.384953i | ||||
\(188\) | −3.51636 | − | 3.51636i | −0.256457 | − | 0.256457i | ||||
\(189\) | −7.54717 | + | 18.2205i | −0.548976 | + | 1.32535i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.3527 | + | 15.3527i | 1.11088 | + | 1.11088i | 0.993032 | + | 0.117849i | \(0.0375997\pi\) |
0.117849 | + | 0.993032i | \(0.462400\pi\) | |||||||
\(192\) | 0.290940 | + | 1.46265i | 0.0209968 | + | 0.105558i | ||||
\(193\) | 0.326059 | + | 0.487981i | 0.0234702 | + | 0.0351257i | 0.843019 | − | 0.537883i | \(-0.180776\pi\) |
−0.819549 | + | 0.573009i | \(0.805776\pi\) | |||||||
\(194\) | −7.33077 | + | 4.89826i | −0.526318 | + | 0.351675i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.86483 | − | 2.01508i | 0.347488 | − | 0.143934i | ||||
\(197\) | −3.47533 | + | 17.4717i | −0.247607 | + | 1.24481i | 0.634190 | + | 0.773177i | \(0.281334\pi\) |
−0.881797 | + | 0.471629i | \(0.843666\pi\) | |||||||
\(198\) | −0.923413 | + | 0.617005i | −0.0656241 | + | 0.0438486i | ||||
\(199\) | −1.99127 | + | 2.98014i | −0.141157 | + | 0.211256i | −0.895311 | − | 0.445441i | \(-0.853047\pi\) |
0.754154 | + | 0.656697i | \(0.228047\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.17445 | − | 10.9317i | −0.153374 | − | 0.771062i | ||||
\(202\) | 5.06297 | + | 12.2231i | 0.356230 | + | 0.860014i | ||||
\(203\) | 14.1020 | − | 14.1020i | 0.989768 | − | 0.989768i | ||||
\(204\) | −6.13102 | − | 0.467660i | −0.429257 | − | 0.0327428i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 16.7680 | + | 6.94551i | 1.16828 | + | 0.483917i | ||||
\(207\) | 0.278237 | − | 0.416411i | 0.0193388 | − | 0.0289426i | ||||
\(208\) | 0.687320i | 0.0476571i | ||||||||
\(209\) | −0.268044 | − | 0.179102i | −0.0185410 | − | 0.0123887i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.56243 | + | 3.83494i | 0.176405 | + | 0.264008i | 0.909127 | − | 0.416520i | \(-0.136750\pi\) |
−0.732722 | + | 0.680528i | \(0.761750\pi\) | |||||||
\(212\) | −2.60552 | − | 1.07924i | −0.178948 | − | 0.0741227i | ||||
\(213\) | −14.9047 | − | 6.17372i | −1.02125 | − | 0.423016i | ||||
\(214\) | 8.06566 | + | 12.0711i | 0.551357 | + | 0.825164i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4.68215 | + | 3.12852i | 0.318580 | + | 0.212868i | ||||
\(217\) | − | 38.5357i | − | 2.61597i | ||||||
\(218\) | −7.18615 | + | 10.7548i | −0.486707 | + | 0.728409i | ||||
\(219\) | 13.5125 | + | 5.59706i | 0.913090 | + | 0.378214i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.72934 | − | 0.762659i | −0.183595 | − | 0.0513020i | ||||
\(222\) | −0.446091 | + | 0.446091i | −0.0299397 | + | 0.0299397i | ||||
\(223\) | 3.81376 | + | 9.20723i | 0.255388 | + | 0.616562i | 0.998623 | − | 0.0524694i | \(-0.0167092\pi\) |
−0.743234 | + | 0.669031i | \(0.766709\pi\) | |||||||
\(224\) | −0.683252 | − | 3.43494i | −0.0456517 | − | 0.229507i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.67335 | + | 2.50435i | −0.111310 | + | 0.166587i | ||||
\(227\) | −13.2623 | + | 8.86159i | −0.880250 | + | 0.588164i | −0.911478 | − | 0.411348i | \(-0.865058\pi\) |
0.0312282 | + | 0.999512i | \(0.490058\pi\) | |||||||
\(228\) | −0.0655350 | + | 0.329466i | −0.00434016 | + | 0.0218195i | ||||
\(229\) | −26.3976 | + | 10.9342i | −1.74440 | + | 0.722554i | −0.746004 | + | 0.665941i | \(0.768030\pi\) |
−0.998396 | + | 0.0566131i | \(0.981970\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.21514 | + | 4.15282i | −0.408926 | + | 0.273236i | ||||
\(232\) | −3.16366 | − | 4.73475i | −0.207704 | − | 0.310852i | ||||
\(233\) | −4.64291 | − | 23.3415i | −0.304167 | − | 1.52915i | −0.766383 | − | 0.642384i | \(-0.777945\pi\) |
0.462215 | − | 0.886768i | \(-0.347055\pi\) | |||||||
\(234\) | 0.377140 | + | 0.377140i | 0.0246544 | + | 0.0246544i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.13235 | + | 2.73373i | −0.0737096 | + | 0.177951i | ||||
\(237\) | 1.93132 | + | 1.93132i | 0.125453 | + | 0.125453i | ||||
\(238\) | 14.3983 | + | 1.09827i | 0.933301 | + | 0.0711901i | ||||
\(239\) | − | 22.2129i | − | 1.43683i | −0.695614 | − | 0.718416i | \(-0.744868\pi\) | ||
0.695614 | − | 0.718416i | \(-0.255132\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.55756 | + | 1.70220i | −0.551241 | + | 0.109649i | −0.462849 | − | 0.886437i | \(-0.653173\pi\) |
−0.0883919 | + | 0.996086i | \(0.528173\pi\) | |||||||
\(242\) | 8.95175 | 0.575440 | ||||||||
\(243\) | 7.69083 | − | 1.52980i | 0.493367 | − | 0.0981369i | ||||
\(244\) | −2.58630 | + | 13.0022i | −0.165571 | + | 0.832381i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.53862 | + | 3.71456i | 0.0980989 | + | 0.236832i | ||||
\(247\) | −0.0592472 | + | 0.143035i | −0.00376981 | + | 0.00910113i | ||||
\(248\) | −10.7917 | − | 2.14661i | −0.685276 | − | 0.136310i | ||||
\(249\) | −3.74021 | − | 0.743974i | −0.237026 | − | 0.0471474i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.55862 | + | 7.55862i | −0.477096 | + | 0.477096i | −0.904202 | − | 0.427106i | \(-0.859533\pi\) |
0.427106 | + | 0.904202i | \(0.359533\pi\) | |||||||
\(252\) | −2.25970 | − | 1.50988i | −0.142348 | − | 0.0951136i | ||||
\(253\) | 0.853344 | − | 0.353466i | 0.0536493 | − | 0.0222222i | ||||
\(254\) | 12.4751 | 0.782755 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.00000 | −0.0625000 | ||||||||
\(257\) | −23.1908 | + | 9.60595i | −1.44660 | + | 0.599203i | −0.961389 | − | 0.275192i | \(-0.911259\pi\) |
−0.485215 | + | 0.874395i | \(0.661259\pi\) | |||||||
\(258\) | −4.01292 | − | 2.68135i | −0.249833 | − | 0.166933i | ||||
\(259\) | 1.04761 | − | 1.04761i | 0.0650955 | − | 0.0650955i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.33395 | − | 0.862075i | −0.268264 | − | 0.0533611i | ||||
\(262\) | 19.2420 | + | 3.82748i | 1.18878 | + | 0.236462i | ||||
\(263\) | 3.53421 | − | 8.53235i | 0.217929 | − | 0.526127i | −0.776671 | − | 0.629906i | \(-0.783093\pi\) |
0.994600 | + | 0.103779i | \(0.0330934\pi\) | |||||||
\(264\) | 0.816768 | + | 1.97185i | 0.0502686 | + | 0.121359i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.153904 | − | 0.773729i | 0.00943647 | − | 0.0474404i | ||||
\(267\) | −20.1828 | + | 4.01461i | −1.23517 | + | 0.245690i | ||||
\(268\) | 7.47387 | 0.456539 | ||||||||
\(269\) | 3.39522 | − | 0.675351i | 0.207010 | − | 0.0411768i | −0.0904959 | − | 0.995897i | \(-0.528845\pi\) |
0.297506 | + | 0.954720i | \(0.403845\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 20.2345i | − | 1.22916i | −0.788855 | − | 0.614579i | \(-0.789326\pi\) | ||
0.788855 | − | 0.614579i | \(-0.210674\pi\) | |||||||
\(272\) | 1.10961 | − | 3.97099i | 0.0672802 | − | 0.240777i | ||||
\(273\) | 2.53838 | + | 2.53838i | 0.153630 | + | 0.153630i | ||||
\(274\) | 2.71474 | − | 6.55395i | 0.164003 | − | 0.395939i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.680566 | − | 0.680566i | −0.0409653 | − | 0.0409653i | ||||
\(277\) | −3.91058 | − | 19.6598i | −0.234964 | − | 1.18124i | −0.900493 | − | 0.434871i | \(-0.856794\pi\) |
0.665529 | − | 0.746372i | \(-0.268206\pi\) | |||||||
\(278\) | 5.84350 | + | 8.74542i | 0.350470 | + | 0.524515i | ||||
\(279\) | −7.09941 | + | 4.74367i | −0.425031 | + | 0.283996i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.1942 | − | 8.36471i | 1.20468 | − | 0.498997i | 0.312175 | − | 0.950025i | \(-0.398942\pi\) |
0.892510 | + | 0.451028i | \(0.148942\pi\) | |||||||
\(282\) | −1.44681 | + | 7.27361i | −0.0861563 | + | 0.433137i | ||||
\(283\) | 16.6821 | − | 11.1466i | 0.991650 | − | 0.662600i | 0.0498445 | − | 0.998757i | \(-0.484127\pi\) |
0.941806 | + | 0.336157i | \(0.109127\pi\) | |||||||
\(284\) | 6.01005 | − | 8.99468i | 0.356631 | − | 0.533736i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.191905 | + | 0.964770i | 0.0113476 | + | 0.0570481i | ||||
\(287\) | −3.61334 | − | 8.72338i | −0.213289 | − | 0.514925i | ||||
\(288\) | −0.548711 | + | 0.548711i | −0.0323331 | + | 0.0323331i | ||||
\(289\) | 14.5375 | + | 8.81252i | 0.855148 | + | 0.518384i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.1475 | + | 5.03165i | 0.712098 | + | 0.294961i | ||||
\(292\) | −5.44868 | + | 8.15453i | −0.318860 | + | 0.477208i | ||||
\(293\) | 15.9816i | 0.933653i | 0.884349 | + | 0.466826i | \(0.154603\pi\) | ||||
−0.884349 | + | 0.466826i | \(0.845397\pi\) | |||||||
\(294\) | −6.52931 | − | 4.36274i | −0.380797 | − | 0.254440i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.235023 | − | 0.351736i | −0.0136604 | − | 0.0204443i | ||||
\(297\) | 7.44570 | + | 3.08411i | 0.432044 | + | 0.178958i | ||||
\(298\) | −4.89467 | − | 2.02744i | −0.283541 | − | 0.117446i | ||||
\(299\) | −0.246442 | − | 0.368827i | −0.0142521 | − | 0.0213298i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.42405 | + | 6.29695i | 0.543193 | + | 0.362950i | ||||
\(302\) | 10.4918i | 0.603734i | ||||||||
\(303\) | 10.9616 | − | 16.4052i | 0.629726 | − | 0.942451i | ||||
\(304\) | −0.208106 | − | 0.0862003i | −0.0119357 | − | 0.00494393i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.57007 | − | 2.78778i | −0.0897548 | − | 0.159367i | ||||
\(307\) | −1.37631 | + | 1.37631i | −0.0785503 | + | 0.0785503i | −0.745290 | − | 0.666740i | \(-0.767689\pi\) |
0.666740 | + | 0.745290i | \(0.267689\pi\) | |||||||
\(308\) | −1.91812 | − | 4.63076i | −0.109295 | − | 0.263862i | ||||
\(309\) | −5.28042 | − | 26.5465i | −0.300392 | − | 1.51018i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.6826 | + | 17.4843i | −0.662461 | + | 0.991442i | 0.336304 | + | 0.941753i | \(0.390823\pi\) |
−0.998765 | + | 0.0496889i | \(0.984177\pi\) | |||||||
\(312\) | 0.852262 | − | 0.569463i | 0.0482498 | − | 0.0322395i | ||||
\(313\) | −5.54040 | + | 27.8535i | −0.313162 | + | 1.57437i | 0.428465 | + | 0.903559i | \(0.359055\pi\) |
−0.741627 | + | 0.670813i | \(0.765945\pi\) | |||||||
\(314\) | 13.8862 | − | 5.75183i | 0.783641 | − | 0.324595i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.52281 | + | 1.01751i | −0.0856650 | + | 0.0572395i | ||||
\(317\) | −15.3659 | − | 22.9967i | −0.863035 | − | 1.29162i | −0.955225 | − | 0.295882i | \(-0.904387\pi\) |
0.0921896 | − | 0.995741i | \(-0.470613\pi\) | |||||||
\(318\) | 0.820509 | + | 4.12498i | 0.0460119 | + | 0.231317i | ||||
\(319\) | −5.76271 | − | 5.76271i | −0.322650 | − | 0.322650i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.28531 | − | 20.0025i | 0.462441 | − | 1.11643i | ||||
\(322\) | 1.59826 | + | 1.59826i | 0.0890676 | + | 0.0890676i | ||||
\(323\) | 0.573218 | − | 0.730738i | 0.0318947 | − | 0.0406593i | ||||
\(324\) | − | 6.06985i | − | 0.337214i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −14.6915 | + | 2.92232i | −0.813688 | + | 0.161853i | ||||
\(327\) | 19.2897 | 1.06672 | ||||||||
\(328\) | −2.64422 | + | 0.525968i | −0.146003 | + | 0.0290418i | ||||
\(329\) | 3.39773 | − | 17.0816i | 0.187323 | − | 0.941737i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.1660 | − | 31.7855i | −0.723668 | − | 1.74709i | −0.662620 | − | 0.748955i | \(-0.730556\pi\) |
−0.0610482 | − | 0.998135i | \(-0.519444\pi\) | |||||||
\(332\) | 0.978574 | − | 2.36249i | 0.0537062 | − | 0.129658i | ||||
\(333\) | −0.321961 | − | 0.0640420i | −0.0176434 | − | 0.00350948i | ||||
\(334\) | 7.47034 | + | 1.48594i | 0.408759 | + | 0.0813072i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.69316 | + | 3.69316i | −0.201479 | + | 0.201479i | ||||
\(337\) | −10.9142 | − | 7.29265i | −0.594536 | − | 0.397256i | 0.221582 | − | 0.975142i | \(-0.428878\pi\) |
−0.816118 | + | 0.577886i | \(0.803878\pi\) | |||||||
\(338\) | −11.5740 | + | 4.79410i | −0.629542 | + | 0.260765i | ||||
\(339\) | 4.49175 | 0.243959 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.7474 | −0.852769 | ||||||||
\(342\) | −0.161489 | + | 0.0668910i | −0.00873233 | + | 0.00361705i | ||||
\(343\) | −5.05041 | − | 3.37457i | −0.272696 | − | 0.182210i | ||||
\(344\) | 2.28839 | − | 2.28839i | 0.123382 | − | 0.123382i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −17.8236 | − | 3.54534i | −0.958205 | − | 0.190599i | ||||
\(347\) | 18.8905 | + | 3.75756i | 1.01410 | + | 0.201717i | 0.674045 | − | 0.738690i | \(-0.264555\pi\) |
0.340052 | + | 0.940407i | \(0.389555\pi\) | |||||||
\(348\) | −3.24981 | + | 7.84575i | −0.174208 | + | 0.420576i | ||||
\(349\) | 8.24203 | + | 19.8980i | 0.441186 | + | 1.06512i | 0.975533 | + | 0.219852i | \(0.0705575\pi\) |
−0.534347 | + | 0.845265i | \(0.679443\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.755082 | − | 3.79605i | 0.0403033 | − | 0.202618i | ||||
\(352\) | −1.40367 | + | 0.279207i | −0.0748159 | + | 0.0148818i | ||||
\(353\) | −7.84481 | −0.417537 | −0.208768 | − | 0.977965i | \(-0.566946\pi\) | ||||
−0.208768 | + | 0.977965i | \(0.566946\pi\) | |||||||
\(354\) | 4.32795 | − | 0.860883i | 0.230028 | − | 0.0457554i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 13.7988i | − | 0.731333i | ||||||
\(357\) | −10.5675 | − | 18.7635i | −0.559293 | − | 0.993069i | ||||
\(358\) | −9.13913 | − | 9.13913i | −0.483018 | − | 0.483018i | ||||
\(359\) | −4.46689 | + | 10.7840i | −0.235753 | + | 0.569159i | −0.996835 | − | 0.0794970i | \(-0.974669\pi\) |
0.761082 | + | 0.648656i | \(0.224669\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.3992 | + | 13.3992i | 0.705218 | + | 0.705218i | ||||
\(362\) | 1.11267 | + | 5.59375i | 0.0584805 | + | 0.294001i | ||||
\(363\) | −7.41677 | − | 11.1000i | −0.389280 | − | 0.582598i | ||||
\(364\) | −2.00148 | + | 1.33734i | −0.104906 | + | 0.0700959i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 18.2653 | − | 7.56573i | 0.954741 | − | 0.395467i | ||||
\(367\) | −2.94262 | + | 14.7935i | −0.153603 | + | 0.772216i | 0.824786 | + | 0.565445i | \(0.191296\pi\) |
−0.978389 | + | 0.206771i | \(0.933704\pi\) | |||||||
\(368\) | 0.536616 | − | 0.358556i | 0.0279731 | − | 0.0186910i | ||||
\(369\) | −1.16231 | + | 1.73952i | −0.0605074 | + | 0.0905557i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.92691 | − | 9.68722i | −0.100040 | − | 0.502935i | ||||
\(372\) | 6.27950 | + | 15.1601i | 0.325577 | + | 0.786012i | ||||
\(373\) | 0.0702693 | − | 0.0702693i | 0.00363841 | − | 0.00363841i | −0.705285 | − | 0.708924i | \(-0.749181\pi\) |
0.708924 | + | 0.705285i | \(0.249181\pi\) | |||||||
\(374\) | 0.448801 | − | 5.88377i | 0.0232069 | − | 0.304243i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.59434 | − | 1.90304i | −0.236935 | − | 0.0981418i | ||||
\(377\) | −2.17445 | + | 3.25429i | −0.111990 | + | 0.167604i | ||||
\(378\) | 19.7217i | 1.01438i | ||||||||
\(379\) | −11.0779 | − | 7.40200i | −0.569032 | − | 0.380215i | 0.237516 | − | 0.971384i | \(-0.423667\pi\) |
−0.806548 | + | 0.591168i | \(0.798667\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.3359 | − | 15.4688i | −0.529526 | − | 0.792492i | ||||
\(382\) | 20.0592 | + | 8.30880i | 1.02632 | + | 0.425115i | ||||
\(383\) | 26.2569 | + | 10.8760i | 1.34167 | + | 0.555736i | 0.933960 | − | 0.357377i | \(-0.116329\pi\) |
0.407705 | + | 0.913114i | \(0.366329\pi\) | |||||||
\(384\) | 0.828527 | + | 1.23998i | 0.0422806 | + | 0.0632774i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.487981 | + | 0.326059i | 0.0248376 | + | 0.0165959i | ||||
\(387\) | − | 2.51133i | − | 0.127658i | ||||||
\(388\) | −4.89826 | + | 7.33077i | −0.248672 | + | 0.372163i | ||||
\(389\) | 28.5749 | + | 11.8361i | 1.44880 | + | 0.600115i | 0.961915 | − | 0.273349i | \(-0.0881313\pi\) |
0.486890 | + | 0.873463i | \(0.338131\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.828384 | + | 2.52876i | 0.0418932 | + | 0.127885i | ||||
\(392\) | 3.72338 | − | 3.72338i | 0.188059 | − | 0.188059i | ||||
\(393\) | −11.1966 | − | 27.0309i | −0.564792 | − | 1.36353i | ||||
\(394\) | 3.47533 | + | 17.4717i | 0.175085 | + | 0.880211i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.617005 | + | 0.923413i | −0.0310057 | + | 0.0464033i | ||||
\(397\) | −5.96544 | + | 3.98598i | −0.299397 | + | 0.200051i | −0.696190 | − | 0.717857i | \(-0.745123\pi\) |
0.396793 | + | 0.917908i | \(0.370123\pi\) | |||||||
\(398\) | −0.699239 | + | 3.51531i | −0.0350497 | + | 0.176207i | ||||
\(399\) | −1.08692 | + | 0.450218i | −0.0544141 | + | 0.0225391i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.19658 | − | 4.14042i | 0.309442 | − | 0.206763i | −0.391146 | − | 0.920329i | \(-0.627921\pi\) |
0.700588 | + | 0.713566i | \(0.252921\pi\) | |||||||
\(402\) | −6.19231 | − | 9.26744i | −0.308844 | − | 0.462218i | ||||
\(403\) | 1.47541 | + | 7.41737i | 0.0734953 | + | 0.369486i | ||||
\(404\) | 9.35515 | + | 9.35515i | 0.465436 | + | 0.465436i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.63196 | − | 18.4252i | 0.378768 | − | 0.914426i | ||||
\(407\) | −0.428102 | − | 0.428102i | −0.0212202 | − | 0.0212202i | ||||
\(408\) | −5.84329 | + | 1.91418i | −0.289286 | + | 0.0947659i | ||||
\(409\) | − | 18.1578i | − | 0.897847i | −0.893570 | − | 0.448924i | \(-0.851808\pi\) | ||
0.893570 | − | 0.448924i | \(-0.148192\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.3760 | + | 2.06391i | −0.511810 | + | 0.101805i | ||||
\(412\) | 18.1495 | 0.894162 | ||||||||
\(413\) | −10.1639 | + | 2.02172i | −0.500132 | + | 0.0994825i | ||||
\(414\) | 0.0977039 | − | 0.491190i | 0.00480188 | − | 0.0241407i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.263026 | + | 0.635001i | 0.0128959 | + | 0.0311335i | ||||
\(417\) | 6.00263 | − | 14.4916i | 0.293950 | − | 0.709659i | ||||
\(418\) | −0.316180 | − | 0.0628921i | −0.0154649 | − | 0.00307615i | ||||
\(419\) | 5.30674 | + | 1.05558i | 0.259251 | + | 0.0515683i | 0.323005 | − | 0.946397i | \(-0.395307\pi\) |
−0.0637533 | + | 0.997966i | \(0.520307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.5830 | − | 12.5830i | 0.613260 | − | 0.613260i | −0.330534 | − | 0.943794i | \(-0.607229\pi\) |
0.943794 | + | 0.330534i | \(0.107229\pi\) | |||||||
\(422\) | 3.83494 | + | 2.56243i | 0.186682 | + | 0.124737i | ||||
\(423\) | −3.56518 | + | 1.47675i | −0.173345 | + | 0.0718019i | ||||
\(424\) | −2.82020 | −0.136961 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −16.1327 | −0.781632 | ||||||||
\(427\) | −42.8947 | + | 17.7676i | −2.07582 | + | 0.859833i | ||||
\(428\) | 12.0711 | + | 8.06566i | 0.583479 | + | 0.389868i | ||||
\(429\) | 1.03730 | − | 1.03730i | 0.0500811 | − | 0.0500811i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.0155 | − | 1.99220i | −0.482429 | − | 0.0959611i | −0.0521163 | − | 0.998641i | \(-0.516597\pi\) |
−0.430313 | + | 0.902680i | \(0.641597\pi\) | |||||||
\(432\) | 5.52298 | + | 1.09859i | 0.265724 | + | 0.0528559i | ||||
\(433\) | −13.3385 | + | 32.2019i | −0.641006 | + | 1.54752i | 0.184319 | + | 0.982867i | \(0.440992\pi\) |
−0.825325 | + | 0.564658i | \(0.809008\pi\) | |||||||
\(434\) | −14.7470 | − | 35.6023i | −0.707877 | − | 1.70897i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.52344 | + | 12.6862i | −0.120851 | + | 0.607558i | ||||
\(437\) | 0.142581 | − | 0.0283611i | 0.00682056 | − | 0.00135669i | ||||
\(438\) | 14.6258 | 0.698849 | ||||||||
\(439\) | −2.63978 | + | 0.525084i | −0.125990 | + | 0.0250609i | −0.257682 | − | 0.966230i | \(-0.582959\pi\) |
0.131693 | + | 0.991291i | \(0.457959\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 4.08612i | − | 0.194577i | ||||||
\(442\) | −2.81344 | + | 0.339868i | −0.133822 | + | 0.0161659i | ||||
\(443\) | 21.5344 | + | 21.5344i | 1.02313 | + | 1.02313i | 0.999726 | + | 0.0234065i | \(0.00745121\pi\) |
0.0234065 | + | 0.999726i | \(0.492549\pi\) | |||||||
\(444\) | −0.241423 | + | 0.582846i | −0.0114574 | + | 0.0276607i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 7.04691 | + | 7.04691i | 0.333681 | + | 0.333681i | ||||
\(447\) | 1.54139 | + | 7.74908i | 0.0729052 | + | 0.366519i | ||||
\(448\) | −1.94574 | − | 2.91200i | −0.0919275 | − | 0.137579i | ||||
\(449\) | 21.9479 | − | 14.6651i | 1.03578 | − | 0.692089i | 0.0832522 | − | 0.996529i | \(-0.473469\pi\) |
0.952532 | + | 0.304440i | \(0.0984693\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.56476 | + | 1.47657i | −0.167858 | + | 0.0695291i | ||||
\(452\) | −0.587603 | + | 2.95408i | −0.0276385 | + | 0.138948i | ||||
\(453\) | 13.0096 | − | 8.69273i | 0.611244 | − | 0.408420i | ||||
\(454\) | −8.86159 | + | 13.2623i | −0.415895 | + | 0.622431i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.0655350 | + | 0.329466i | 0.00306896 | + | 0.0154287i | ||||
\(457\) | 9.81102 | + | 23.6859i | 0.458940 | + | 1.10798i | 0.968827 | + | 0.247738i | \(0.0796872\pi\) |
−0.509887 | + | 0.860241i | \(0.670313\pi\) | |||||||
\(458\) | −20.2038 | + | 20.2038i | −0.944063 | + | 0.944063i | ||||
\(459\) | −10.4908 | + | 20.7127i | −0.489671 | + | 0.966785i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.3509 | − | 5.11592i | −0.575240 | − | 0.238272i | 0.0760463 | − | 0.997104i | \(-0.475770\pi\) |
−0.651286 | + | 0.758832i | \(0.725770\pi\) | |||||||
\(462\) | −4.15282 | + | 6.21514i | −0.193207 | + | 0.289154i | ||||
\(463\) | 32.8821i | 1.52816i | 0.645121 | + | 0.764081i | \(0.276807\pi\) | ||||
−0.645121 | + | 0.764081i | \(0.723193\pi\) | |||||||
\(464\) | −4.73475 | − | 3.16366i | −0.219805 | − | 0.146869i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −13.2219 | − | 19.7880i | −0.612492 | − | 0.916660i | ||||
\(467\) | −4.42354 | − | 1.83229i | −0.204697 | − | 0.0847883i | 0.277979 | − | 0.960587i | \(-0.410335\pi\) |
−0.482676 | + | 0.875799i | \(0.660335\pi\) | |||||||
\(468\) | 0.492757 | + | 0.204107i | 0.0227777 | + | 0.00943483i | ||||
\(469\) | 14.5422 | + | 21.7639i | 0.671496 | + | 1.00496i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.6372 | − | 12.4530i | −0.858758 | − | 0.573803i | ||||
\(472\) | 2.95897i | 0.136198i | ||||||||
\(473\) | 2.57321 | − | 3.85109i | 0.118317 | − | 0.177073i | ||||
\(474\) | 2.52339 | + | 1.04522i | 0.115903 | + | 0.0480086i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 13.7225 | − | 4.49531i | 0.628972 | − | 0.206042i | ||||
\(477\) | −1.54747 | + | 1.54747i | −0.0708540 | + | 0.0708540i | ||||
\(478\) | −8.50050 | − | 20.5220i | −0.388804 | − | 0.938655i | ||||
\(479\) | −6.42297 | − | 32.2905i | −0.293473 | − | 1.47539i | −0.793070 | − | 0.609130i | \(-0.791519\pi\) |
0.499597 | − | 0.866258i | \(-0.333481\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.161536 | + | 0.241755i | −0.00736539 | + | 0.0110231i | ||||
\(482\) | −7.25475 | + | 4.84747i | −0.330445 | + | 0.220796i | ||||
\(483\) | 0.657607 | − | 3.30601i | 0.0299222 | − | 0.150429i | ||||
\(484\) | 8.27034 | − | 3.42569i | 0.375925 | − | 0.155713i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 6.51997 | − | 4.35651i | 0.295752 | − | 0.197615i | ||||
\(487\) | −16.8849 | − | 25.2701i | −0.765130 | − | 1.14510i | −0.985499 | − | 0.169681i | \(-0.945726\pi\) |
0.220369 | − | 0.975417i | \(-0.429274\pi\) | |||||||
\(488\) | 2.58630 | + | 13.0022i | 0.117076 | + | 0.588582i | ||||
\(489\) | 15.7959 | + | 15.7959i | 0.714318 | + | 0.714318i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.24928 | − | 15.0871i | 0.282026 | − | 0.680871i | −0.717857 | − | 0.696191i | \(-0.754877\pi\) |
0.999883 | + | 0.0153199i | \(0.00487666\pi\) | |||||||
\(492\) | 2.84300 | + | 2.84300i | 0.128172 | + | 0.128172i | ||||
\(493\) | 17.8166 | − | 15.2912i | 0.802420 | − | 0.688682i | ||||
\(494\) | 0.154820i | 0.00696570i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.7917 | + | 2.14661i | −0.484563 | + | 0.0963856i | ||||
\(497\) | 37.8865 | 1.69944 | ||||||||
\(498\) | −3.74021 | + | 0.743974i | −0.167603 | + | 0.0333383i | ||||
\(499\) | 4.87821 | − | 24.5244i | 0.218379 | − | 1.09786i | −0.703592 | − | 0.710604i | \(-0.748422\pi\) |
0.921971 | − | 0.387260i | \(-0.126578\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.34684 | − | 10.4942i | −0.194203 | − | 0.468847i | ||||
\(502\) | −4.09070 | + | 9.87582i | −0.182577 | + | 0.440779i | ||||
\(503\) | −4.24133 | − | 0.843653i | −0.189111 | − | 0.0376166i | 0.0996258 | − | 0.995025i | \(-0.468235\pi\) |
−0.288737 | + | 0.957408i | \(0.593235\pi\) | |||||||
\(504\) | −2.66550 | − | 0.530200i | −0.118731 | − | 0.0236170i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.653121 | − | 0.653121i | 0.0290348 | − | 0.0290348i | ||||
\(507\) | 15.5340 | + | 10.3795i | 0.689887 | + | 0.460968i | ||||
\(508\) | 11.5255 | − | 4.77400i | 0.511360 | − | 0.211812i | ||||
\(509\) | 14.6760 | 0.650503 | 0.325251 | − | 0.945628i | \(-0.394551\pi\) | ||||
0.325251 | + | 0.945628i | \(0.394551\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −34.3477 | −1.51945 | ||||||||
\(512\) | −0.923880 | + | 0.382683i | −0.0408301 | + | 0.0169124i | ||||
\(513\) | 1.05467 | + | 0.704705i | 0.0465646 | + | 0.0311135i | ||||
\(514\) | −17.7495 | + | 17.7495i | −0.782896 | + | 0.782896i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.73356 | − | 0.941563i | −0.208383 | − | 0.0414500i | ||||
\(517\) | −6.98029 | − | 1.38847i | −0.306993 | − | 0.0610646i | ||||
\(518\) | 0.566964 | − | 1.36877i | 0.0249110 | − | 0.0601404i | ||||
\(519\) | 10.3712 | + | 25.0383i | 0.455246 | + | 1.09906i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.76990 | + | 8.89788i | −0.0775406 | + | 0.389823i | 0.922452 | + | 0.386111i | \(0.126182\pi\) |
−0.999993 | + | 0.00371240i | \(0.998818\pi\) | |||||||
\(522\) | −4.33395 | + | 0.862075i | −0.189692 | + | 0.0377320i | ||||
\(523\) | −7.38904 | −0.323100 | −0.161550 | − | 0.986865i | \(-0.551649\pi\) | ||||
−0.161550 | + | 0.986865i | \(0.551649\pi\) | |||||||
\(524\) | 19.2420 | − | 3.82748i | 0.840592 | − | 0.167204i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 9.23535i | − | 0.402680i | ||||||
\(527\) | 3.45048 | − | 45.2358i | 0.150305 | − | 1.97050i | ||||
\(528\) | 1.50919 | + | 1.50919i | 0.0656791 | + | 0.0656791i | ||||
\(529\) | 8.64232 | − | 20.8644i | 0.375753 | − | 0.907149i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.62362 | + | 1.62362i | 0.0704591 | + | 0.0704591i | ||||
\(532\) | −0.153904 | − | 0.773729i | −0.00667259 | − | 0.0335454i | ||||
\(533\) | 1.02949 | + | 1.54074i | 0.0445921 | + | 0.0667368i | ||||
\(534\) | −17.1102 | + | 11.4327i | −0.740430 | + | 0.494739i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6.90495 | − | 2.86013i | 0.298249 | − | 0.123539i | ||||
\(537\) | −3.76031 | + | 18.9043i | −0.162269 | + | 0.815783i | ||||
\(538\) | 2.87833 | − | 1.92324i | 0.124093 | − | 0.0829166i | ||||
\(539\) | 4.18681 | − | 6.26600i | 0.180338 | − | 0.269896i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.09529 | − | 5.50641i | −0.0470904 | − | 0.236739i | 0.950071 | − | 0.312034i | \(-0.101010\pi\) |
−0.997161 | + | 0.0752947i | \(0.976010\pi\) | |||||||
\(542\) | −7.74341 | − | 18.6942i | −0.332608 | − | 0.802986i | ||||
\(543\) | 6.01426 | − | 6.01426i | 0.258097 | − | 0.258097i | ||||
\(544\) | −0.494483 | − | 4.09335i | −0.0212008 | − | 0.175501i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.31656 | + | 1.37376i | 0.141936 | + | 0.0587916i | ||||
\(547\) | −20.5784 | + | 30.7977i | −0.879868 | + | 1.31682i | 0.0678469 | + | 0.997696i | \(0.478387\pi\) |
−0.947715 | + | 0.319119i | \(0.896613\pi\) | |||||||
\(548\) | − | 7.09395i | − | 0.303038i | ||||||
\(549\) | 8.55358 | + | 5.71532i | 0.365058 | + | 0.243924i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.712622 | − | 1.06651i | −0.0303587 | − | 0.0454350i | ||||
\(552\) | −0.889203 | − | 0.368320i | −0.0378470 | − | 0.0156767i | ||||
\(553\) | −5.92600 | − | 2.45463i | −0.251999 | − | 0.104381i | ||||
\(554\) | −11.1364 | − | 16.6668i | −0.473140 | − | 0.708104i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.74542 | + | 5.84350i | 0.370888 | + | 0.247820i | ||||
\(557\) | − | 31.1211i | − | 1.31864i | −0.751862 | − | 0.659321i | \(-0.770844\pi\) | ||
0.751862 | − | 0.659321i | \(-0.229156\pi\) | |||||||
\(558\) | −4.74367 | + | 7.09941i | −0.200816 | + | 0.300542i | ||||
\(559\) | −2.05504 | − | 0.851225i | −0.0869189 | − | 0.0360030i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.66760 | + | 4.31836i | −0.323726 | + | 0.182321i | ||||
\(562\) | 15.4560 | − | 15.4560i | 0.651971 | − | 0.651971i | ||||
\(563\) | −11.8843 | − | 28.6912i | −0.500863 | − | 1.20919i | −0.949014 | − | 0.315233i | \(-0.897917\pi\) |
0.448151 | − | 0.893958i | \(-0.352083\pi\) | |||||||
\(564\) | 1.44681 | + | 7.27361i | 0.0609217 | + | 0.306274i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 11.1466 | − | 16.6821i | 0.468529 | − | 0.701203i | ||||
\(567\) | 17.6754 | − | 11.8103i | 0.742298 | − | 0.495988i | ||||
\(568\) | 2.11045 | − | 10.6099i | 0.0885525 | − | 0.445183i | ||||
\(569\) | 2.92191 | − | 1.21029i | 0.122493 | − | 0.0507381i | −0.320595 | − | 0.947216i | \(-0.603883\pi\) |
0.443088 | + | 0.896478i | \(0.353883\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.63933 | + | 1.09537i | −0.0686039 | + | 0.0458397i | −0.589399 | − | 0.807842i | \(-0.700635\pi\) |
0.520795 | + | 0.853682i | \(0.325635\pi\) | |||||||
\(572\) | 0.546498 | + | 0.817893i | 0.0228502 | + | 0.0341978i | ||||
\(573\) | −6.31688 | − | 31.7571i | −0.263891 | − | 1.32667i | ||||
\(574\) | −6.67659 | − | 6.67659i | −0.278675 | − | 0.278675i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.296960 | + | 0.716925i | −0.0123733 | + | 0.0298719i | ||||
\(577\) | −23.0553 | − | 23.0553i | −0.959807 | − | 0.959807i | 0.0394163 | − | 0.999223i | \(-0.487450\pi\) |
−0.999223 | + | 0.0394163i | \(0.987450\pi\) | |||||||
\(578\) | 16.8033 | + | 2.57844i | 0.698926 | + | 0.107249i | ||||
\(579\) | − | 0.875235i | − | 0.0363735i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.78362 | − | 1.74717i | 0.364406 | − | 0.0724848i | ||||
\(582\) | 13.1483 | 0.545016 | ||||||||
\(583\) | −3.95863 | + | 0.787420i | −0.163950 | + | 0.0326116i | ||||
\(584\) | −1.91332 | + | 9.61892i | −0.0791739 | + | 0.398034i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.11588 | + | 14.7650i | 0.252645 | + | 0.609938i | ||||
\(587\) | −11.7884 | + | 28.4598i | −0.486560 | + | 1.17466i | 0.469879 | + | 0.882731i | \(0.344297\pi\) |
−0.956440 | + | 0.291930i | \(0.905703\pi\) | |||||||
\(588\) | −7.70184 | − | 1.53199i | −0.317619 | − | 0.0631783i | ||||
\(589\) | −2.43086 | − | 0.483529i | −0.100162 | − | 0.0199235i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18.7851 | − | 18.7851i | 0.772716 | − | 0.772716i | ||||
\(592\) | −0.351736 | − | 0.235023i | −0.0144563 | − | 0.00965937i | ||||
\(593\) | −6.97472 | + | 2.88902i | −0.286417 | + | 0.118638i | −0.521267 | − | 0.853394i | \(-0.674540\pi\) |
0.234849 | + | 0.972032i | \(0.424540\pi\) | |||||||
\(594\) | 8.05917 | 0.330672 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.29796 | −0.217013 | ||||||||
\(597\) | 4.93825 | − | 2.04549i | 0.202109 | − | 0.0837164i | ||||
\(598\) | −0.368827 | − | 0.246442i | −0.0150825 | − | 0.0100778i | ||||
\(599\) | −0.148385 | + | 0.148385i | −0.00606283 | + | 0.00606283i | −0.710132 | − | 0.704069i | \(-0.751365\pi\) |
0.704069 | + | 0.710132i | \(0.251365\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.7537 | − | 2.53686i | −0.520233 | − | 0.103481i | −0.0720121 | − | 0.997404i | \(-0.522942\pi\) |
−0.448220 | + | 0.893923i | \(0.647942\pi\) | |||||||
\(602\) | 11.1164 | + | 2.21119i | 0.453072 | + | 0.0901216i | ||||
\(603\) | 2.21944 | − | 5.35821i | 0.0903826 | − | 0.218203i | ||||
\(604\) | 4.01503 | + | 9.69314i | 0.163369 | + | 0.394408i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.84919 | − | 19.3512i | 0.156363 | − | 0.786089i | ||||
\(607\) | 1.06561 | − | 0.211963i | 0.0432517 | − | 0.00860330i | −0.173417 | − | 0.984848i | \(-0.555481\pi\) |
0.216669 | + | 0.976245i | \(0.430481\pi\) | |||||||
\(608\) | −0.225252 | −0.00913519 | ||||||||
\(609\) | −29.1701 | + | 5.80230i | −1.18203 | + | 0.235121i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.41796i | 0.138276i | ||||||||
\(612\) | −2.51739 | − | 1.97474i | −0.101760 | − | 0.0798239i | ||||
\(613\) | −22.9407 | − | 22.9407i | −0.926565 | − | 0.926565i | 0.0709174 | − | 0.997482i | \(-0.477407\pi\) |
−0.997482 | + | 0.0709174i | \(0.977407\pi\) | |||||||
\(614\) | −0.744855 | + | 1.79824i | −0.0300599 | + | 0.0725710i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.54423 | − | 3.54423i | −0.142801 | − | 0.142801i | ||||
\(617\) | 0.407054 | + | 2.04640i | 0.0163874 | + | 0.0823850i | 0.988114 | − | 0.153726i | \(-0.0491272\pi\) |
−0.971726 | + | 0.236111i | \(0.924127\pi\) | |||||||
\(618\) | −15.0374 | − | 22.5050i | −0.604891 | − | 0.905284i | ||||
\(619\) | 29.8012 | − | 19.9126i | 1.19781 | − | 0.800353i | 0.213528 | − | 0.976937i | \(-0.431505\pi\) |
0.984286 | + | 0.176584i | \(0.0565047\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.35762 | + | 1.39077i | −0.134737 | + | 0.0558098i | ||||
\(622\) | −4.10239 | + | 20.6241i | −0.164491 | + | 0.826951i | ||||
\(623\) | 40.1820 | − | 26.8488i | 1.60986 | − | 1.07567i | ||||
\(624\) | 0.569463 | − | 0.852262i | 0.0227968 | − | 0.0341178i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 5.54040 | + | 27.8535i | 0.221439 | + | 1.11325i | ||||
\(627\) | 0.183979 | + | 0.444164i | 0.00734741 | + | 0.0177382i | ||||
\(628\) | 10.6280 | − | 10.6280i | 0.424104 | − | 0.424104i | ||||
\(629\) | 1.32356 | − | 1.13596i | 0.0527739 | − | 0.0452936i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.5925 | + | 11.0150i | 1.05863 | + | 0.438499i | 0.842965 | − | 0.537969i | \(-0.180808\pi\) |
0.215664 | + | 0.976468i | \(0.430808\pi\) | |||||||
\(632\) | −1.01751 | + | 1.52281i | −0.0404745 | + | 0.0605743i | ||||
\(633\) | − | 6.87829i | − | 0.273387i | ||||||
\(634\) | −22.9967 | − | 15.3659i | −0.913315 | − | 0.610258i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.33661 | + | 3.49699i | 0.0926527 | + | 0.138665i | ||||
\(637\) | −3.34370 | − | 1.38500i | −0.132482 | − | 0.0548759i | ||||
\(638\) | −7.52935 | − | 3.11876i | −0.298090 | − | 0.123473i | ||||
\(639\) | −4.66377 | − | 6.97982i | −0.184496 | − | 0.276117i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.5118 | + | 11.7010i | 0.691676 | + | 0.462163i | 0.851070 | − | 0.525052i | \(-0.175954\pi\) |
−0.159394 | + | 0.987215i | \(0.550954\pi\) | |||||||
\(642\) | − | 21.6505i | − | 0.854479i | ||||||
\(643\) | 10.0396 | − | 15.0254i | 0.395924 | − | 0.592542i | −0.578933 | − | 0.815375i | \(-0.696531\pi\) |
0.974857 | + | 0.222833i | \(0.0715305\pi\) | |||||||
\(644\) | 2.08823 | + | 0.864973i | 0.0822878 | + | 0.0340847i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.249943 | − | 0.894475i | 0.00983387 | − | 0.0351926i | ||||
\(647\) | 30.4615 | − | 30.4615i | 1.19756 | − | 1.19756i | 0.222671 | − | 0.974894i | \(-0.428523\pi\) |
0.974894 | − | 0.222671i | \(-0.0714774\pi\) | |||||||
\(648\) | −2.32283 | − | 5.60781i | −0.0912494 | − | 0.220296i | ||||
\(649\) | 0.826166 | + | 4.15342i | 0.0324299 | + | 0.163036i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −31.9279 | + | 47.7834i | −1.25135 | + | 1.87278i | ||||
\(652\) | −12.4549 | + | 8.32208i | −0.487770 | + | 0.325918i | ||||
\(653\) | −8.20651 | + | 41.2569i | −0.321145 | + | 1.61451i | 0.396456 | + | 0.918054i | \(0.370240\pi\) |
−0.717602 | + | 0.696454i | \(0.754760\pi\) | |||||||
\(654\) | 17.8213 | − | 7.38184i | 0.696870 | − | 0.288653i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.24166 | + | 1.49783i | −0.0875222 | + | 0.0584805i | ||||
\(657\) | 4.22815 | + | 6.32787i | 0.164956 | + | 0.246874i | ||||
\(658\) | −3.39773 | − | 17.0816i | −0.132457 | − | 0.665909i | ||||
\(659\) | −13.4187 | − | 13.4187i | −0.522718 | − | 0.522718i | 0.395673 | − | 0.918391i | \(-0.370511\pi\) |
−0.918391 | + | 0.395673i | \(0.870511\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.49648 | − | 22.9265i | 0.369370 | − | 0.891738i | −0.624484 | − | 0.781038i | \(-0.714691\pi\) |
0.993854 | − | 0.110701i | \(-0.0353094\pi\) | |||||||
\(662\) | −24.3276 | − | 24.3276i | −0.945518 | − | 0.945518i | ||||
\(663\) | 2.75244 | + | 3.20701i | 0.106896 | + | 0.124550i | ||||
\(664\) | − | 2.55714i | − | 0.0992362i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.321961 | + | 0.0640420i | −0.0124757 | + | 0.00248158i | ||||
\(667\) | 3.67509 | 0.142300 | ||||||||
\(668\) | 7.47034 | − | 1.48594i | 0.289036 | − | 0.0574929i | ||||
\(669\) | 2.89946 | − | 14.5766i | 0.112100 | − | 0.563563i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.26062 | + | 17.5287i | 0.280293 | + | 0.676688i | ||||
\(672\) | −1.99872 | + | 4.82535i | −0.0771025 | + | 0.186142i | ||||
\(673\) | −8.33039 | − | 1.65702i | −0.321113 | − | 0.0638733i | 0.0319020 | − | 0.999491i | \(-0.489844\pi\) |
−0.353015 | + | 0.935618i | \(0.614844\pi\) | |||||||
\(674\) | −12.8742 | − | 2.56084i | −0.495896 | − | 0.0986398i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.85834 | + | 8.85834i | −0.340706 | + | 0.340706i | ||||
\(677\) | 4.53636 | + | 3.03110i | 0.174347 | + | 0.116495i | 0.639682 | − | 0.768640i | \(-0.279066\pi\) |
−0.465335 | + | 0.885135i | \(0.654066\pi\) | |||||||
\(678\) | 4.14984 | − | 1.71892i | 0.159374 | − | 0.0660147i | ||||
\(679\) | −30.8779 | −1.18499 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 23.7871 | 0.911522 | ||||||||
\(682\) | −14.5487 | + | 6.02626i | −0.557098 | + | 0.230758i | ||||
\(683\) | −30.4635 | − | 20.3551i | −1.16565 | − | 0.778866i | −0.186595 | − | 0.982437i | \(-0.559745\pi\) |
−0.979060 | + | 0.203571i | \(0.934745\pi\) | |||||||
\(684\) | −0.123598 | + | 0.123598i | −0.00472590 | + | 0.00472590i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −5.95736 | − | 1.18499i | −0.227453 | − | 0.0452432i | ||||
\(687\) | 41.7917 | + | 8.31289i | 1.59445 | + | 0.317157i | ||||
\(688\) | 1.23847 | − | 2.98993i | 0.0472162 | − | 0.113990i | ||||
\(689\) | 0.741785 | + | 1.79083i | 0.0282598 | + | 0.0682251i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.37635 | + | 6.91939i | −0.0523589 | + | 0.263226i | −0.998094 | − | 0.0617127i | \(-0.980344\pi\) |
0.945735 | + | 0.324939i | \(0.105344\pi\) | |||||||
\(692\) | −17.8236 | + | 3.54534i | −0.677553 | + | 0.134774i | ||||
\(693\) | −3.88951 | −0.147750 | ||||||||
\(694\) | 18.8905 | − | 3.75756i | 0.717075 | − | 0.142635i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 8.49217i | 0.321895i | ||||||||
\(697\) | −3.46050 | − | 10.5636i | −0.131076 | − | 0.400126i | ||||
\(698\) | 15.2293 | + | 15.2293i | 0.576437 | + | 0.576437i | ||||
\(699\) | −13.5820 | + | 32.7897i | −0.513717 | + | 1.24022i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.7123 | + | 16.7123i | 0.631215 | + | 0.631215i | 0.948373 | − | 0.317158i | \(-0.102728\pi\) |
−0.317158 | + | 0.948373i | \(0.602728\pi\) | |||||||
\(702\) | −0.755082 | − | 3.79605i | −0.0284987 | − | 0.143273i | ||||
\(703\) | −0.0529394 | − | 0.0792294i | −0.00199665 | − | 0.00298819i | ||||
\(704\) | −1.18997 | + | 0.795115i | −0.0448488 | + | 0.0299670i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.24766 | + | 3.00208i | −0.272769 | + | 0.112985i | ||||
\(707\) | −9.03956 | + | 45.4449i | −0.339967 | + | 1.70913i | ||||
\(708\) | 3.66906 | − | 2.45159i | 0.137892 | − | 0.0921363i | ||||
\(709\) | −14.4329 | + | 21.6003i | −0.542038 | + | 0.811217i | −0.996845 | − | 0.0793729i | \(-0.974708\pi\) |
0.454807 | + | 0.890590i | \(0.349708\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.277265 | + | 1.39390i | 0.0103982 | + | 0.0522755i | ||||
\(712\) | −5.28056 | − | 12.7484i | −0.197897 | − | 0.477766i | ||||
\(713\) | 5.02134 | − | 5.02134i | 0.188051 | − | 0.188051i | ||||
\(714\) | −16.9436 | − | 13.2912i | −0.634098 | − | 0.497410i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −11.9408 | − | 4.94606i | −0.446250 | − | 0.184843i | ||||
\(717\) | −18.4040 | + | 27.5435i | −0.687309 | + | 1.02863i | ||||
\(718\) | 11.6725i | 0.435615i | ||||||||
\(719\) | 31.3017 | + | 20.9151i | 1.16735 | + | 0.780002i | 0.979351 | − | 0.202167i | \(-0.0647983\pi\) |
0.188004 | + | 0.982168i | \(0.439798\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 35.3142 | + | 52.8514i | 1.31517 | + | 1.96829i | ||||
\(722\) | 17.5068 | + | 7.25157i | 0.651537 | + | 0.269875i | ||||
\(723\) | 12.0215 | + | 4.97948i | 0.447085 | + | 0.185189i | ||||
\(724\) | 3.16861 | + | 4.74216i | 0.117760 | + | 0.176241i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −11.1000 | − | 7.41677i | −0.411959 | − | 0.275262i | ||||
\(727\) | − | 11.7248i | − | 0.434847i | −0.976077 | − | 0.217424i | \(-0.930235\pi\) | ||
0.976077 | − | 0.217424i | \(-0.0697653\pi\) | |||||||
\(728\) | −1.33734 | + | 2.00148i | −0.0495653 | + | 0.0741797i | ||||
\(729\) | −27.6274 | − | 11.4436i | −1.02324 | − | 0.423838i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.4988 | + | 8.23562i | 0.388311 | + | 0.304605i | ||||
\(732\) | 13.9796 | − | 13.9796i | 0.516702 | − | 0.516702i | ||||
\(733\) | 15.1940 | + | 36.6816i | 0.561203 | + | 1.35486i | 0.908805 | + | 0.417222i | \(0.136996\pi\) |
−0.347601 | + | 0.937642i | \(0.613004\pi\) | |||||||
\(734\) | 2.94262 | + | 14.7935i | 0.108614 | + | 0.546039i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.358556 | − | 0.536616i | 0.0132165 | − | 0.0197799i | ||||
\(737\) | 8.89371 | − | 5.94259i | 0.327604 | − | 0.218898i | ||||
\(738\) | −0.408149 | + | 2.05190i | −0.0150242 | + | 0.0755315i | ||||
\(739\) | −41.6307 | + | 17.2440i | −1.53141 | + | 0.634332i | −0.979838 | − | 0.199795i | \(-0.935973\pi\) |
−0.551574 | + | 0.834126i | \(0.685973\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.191974 | − | 0.128273i | 0.00705234 | − | 0.00471223i | ||||
\(742\) | −5.48737 | − | 8.21243i | −0.201448 | − | 0.301488i | ||||
\(743\) | 5.03606 | + | 25.3180i | 0.184755 | + | 0.928826i | 0.956241 | + | 0.292580i | \(0.0945137\pi\) |
−0.771486 | + | 0.636246i | \(0.780486\pi\) | |||||||
\(744\) | 11.6030 | + | 11.6030i | 0.425387 | + | 0.425387i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0.0380295 | − | 0.0918113i | 0.00139236 | − | 0.00336145i | ||||
\(747\) | −1.40313 | − | 1.40313i | −0.0513378 | − | 0.0513378i | ||||
\(748\) | −1.83698 | − | 5.60765i | −0.0671668 | − | 0.205036i | ||||
\(749\) | 50.8448i | 1.85783i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.7948 | − | 3.93743i | 0.722322 | − | 0.143679i | 0.179779 | − | 0.983707i | \(-0.442462\pi\) |
0.542543 | + | 0.840028i | \(0.317462\pi\) | |||||||
\(752\) | −4.97288 | −0.181342 | ||||||||
\(753\) | 15.6351 | − | 3.11001i | 0.569773 | − | 0.113335i | ||||
\(754\) | −0.763564 | + | 3.83870i | −0.0278074 | + | 0.139797i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 7.54717 | + | 18.2205i | 0.274488 | + | 0.662673i | ||||
\(757\) | −4.45049 | + | 10.7444i | −0.161756 | + | 0.390513i | −0.983889 | − | 0.178783i | \(-0.942784\pi\) |
0.822133 | + | 0.569296i | \(0.192784\pi\) | |||||||
\(758\) | −13.0672 | − | 2.59924i | −0.474624 | − | 0.0944086i | ||||
\(759\) | −1.35098 | − | 0.268728i | −0.0490376 | − | 0.00975419i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.7743 | + | 27.7743i | −1.00682 | + | 1.00682i | −0.00684140 | + | 0.999977i | \(0.502178\pi\) |
−0.999977 | + | 0.00684140i | \(0.997822\pi\) | |||||||
\(762\) | −15.4688 | − | 10.3359i | −0.560376 | − | 0.374431i | ||||
\(763\) | −41.8522 | + | 17.3357i | −1.51515 | + | 0.627596i | ||||
\(764\) | 21.7120 | 0.785511 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 28.4203 | 1.02687 | ||||||||
\(767\) | 1.87895 | − | 0.778286i | 0.0678449 | − | 0.0281023i | ||||
\(768\) | 1.23998 | + | 0.828527i | 0.0447439 | + | 0.0298969i | ||||
\(769\) | −4.24272 | + | 4.24272i | −0.152997 | + | 0.152997i | −0.779455 | − | 0.626458i | \(-0.784504\pi\) |
0.626458 | + | 0.779455i | \(0.284504\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 36.7149 | + | 7.30305i | 1.32226 | + | 0.263013i | ||||
\(772\) | 0.575613 | + | 0.114497i | 0.0207168 | + | 0.00412082i | ||||
\(773\) | 3.89373 | − | 9.40030i | 0.140048 | − | 0.338105i | −0.838257 | − | 0.545275i | \(-0.816425\pi\) |
0.978305 | + | 0.207170i | \(0.0664252\pi\) | |||||||
\(774\) | −0.961046 | − | 2.32017i | −0.0345441 | − | 0.0833968i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.72004 | + | 8.64723i | −0.0617459 | + | 0.310417i | ||||
\(777\) | −2.16700 | + | 0.431042i | −0.0777405 | + | 0.0154636i | ||||
\(778\) | 30.9292 | 1.10887 | ||||||||
\(779\) | −0.595617 | + | 0.118476i | −0.0213402 | + | 0.00424483i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 15.4821i | − | 0.553994i | ||||||
\(782\) | 1.73304 | + | 2.01926i | 0.0619734 | + | 0.0722085i | ||||
\(783\) | 22.6744 | + | 22.6744i | 0.810316 | + | 0.810316i | ||||
\(784\) | 2.01508 | − | 4.86483i | 0.0719672 | − | 0.173744i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −20.6885 | − | 20.6885i | −0.737936 | − | 0.737936i | ||||
\(787\) | 7.71384 | + | 38.7801i | 0.274969 | + | 1.38236i | 0.833336 | + | 0.552768i | \(0.186428\pi\) |
−0.558367 | + | 0.829594i | \(0.688572\pi\) | |||||||
\(788\) | 9.89692 | + | 14.8118i | 0.352563 | + | 0.527648i | ||||
\(789\) | −11.4516 | + | 7.65174i | −0.407689 | + | 0.272409i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.74560 | + | 4.03676i | −0.346514 | + | 0.143531i | ||||
\(792\) | −0.216663 | + | 1.08924i | −0.00769880 | + | 0.0387045i | ||||
\(793\) | 7.57614 | − | 5.06222i | 0.269037 | − | 0.179765i | ||||
\(794\) | −3.98598 | + | 5.96544i | −0.141457 | + | 0.211706i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.699239 | + | 3.51531i | 0.0247839 | + | 0.124597i | ||||
\(797\) | 16.6329 | + | 40.1553i | 0.589166 | + | 1.42237i | 0.884301 | + | 0.466917i | \(0.154635\pi\) |
−0.295135 | + | 0.955455i | \(0.595365\pi\) | |||||||
\(798\) | −0.831894 | + | 0.831894i | −0.0294487 | + | 0.0294487i | ||||
\(799\) | 5.51797 | − | 19.7473i | 0.195212 | − | 0.698608i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.89268 | − | 4.09768i | −0.349541 | − | 0.144785i | ||||
\(802\) | 4.14042 | − | 6.19658i | 0.146203 | − | 0.218809i | ||||
\(803\) | 14.0360i | 0.495320i | ||||||||
\(804\) | −9.26744 | − | 6.19231i | −0.326837 | − | 0.218386i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.20160 | + | 6.28815i | 0.147995 | + | 0.221490i | ||||
\(807\) | −4.76954 | − | 1.97561i | −0.167896 | − | 0.0695447i | ||||
\(808\) | 12.2231 | + | 5.06297i | 0.430007 | + | 0.178115i | ||||
\(809\) | −25.9551 | − | 38.8446i | −0.912534 | − | 1.36570i | −0.930667 | − | 0.365868i | \(-0.880772\pi\) |
0.0181324 | − | 0.999836i | \(-0.494228\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.7865 | − | 8.54365i | −0.448994 | − | 0.300008i | 0.310440 | − | 0.950593i | \(-0.399524\pi\) |
−0.759433 | + | 0.650585i | \(0.774524\pi\) | |||||||
\(812\) | − | 19.9433i | − | 0.699872i | ||||||
\(813\) | −16.7648 | + | 25.0904i | −0.587969 | + | 0.879957i | ||||
\(814\) | −0.559342 | − | 0.231687i | −0.0196049 | − | 0.00812062i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4.66597 | + | 4.00460i | −0.163342 | + | 0.140189i | ||||
\(817\) | 0.515466 | − | 0.515466i | 0.0180339 | − | 0.0180339i | ||||
\(818\) | −6.94870 | − | 16.7757i | −0.242956 | − | 0.586547i | ||||
\(819\) | 0.364417 | + | 1.83205i | 0.0127338 | + | 0.0640169i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.91045 | − | 13.3354i | 0.310977 | − | 0.465410i | −0.642753 | − | 0.766073i | \(-0.722208\pi\) |
0.953730 | + | 0.300663i | \(0.0972080\pi\) | |||||||
\(822\) | −8.79634 | + | 5.87753i | −0.306808 | + | 0.205002i | ||||
\(823\) | −2.73864 | + | 13.7681i | −0.0954631 | + | 0.479925i | 0.903246 | + | 0.429124i | \(0.141178\pi\) |
−0.998709 | + | 0.0508015i | \(0.983822\pi\) | |||||||
\(824\) | 16.7680 | − | 6.94551i | 0.584139 | − | 0.241958i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.61653 | + | 5.75738i | −0.299807 | + | 0.200325i | ||||
\(827\) | −18.4325 | − | 27.5862i | −0.640962 | − | 0.959267i | −0.999667 | − | 0.0258161i | \(-0.991782\pi\) |
0.358705 | − | 0.933451i | \(-0.383218\pi\) | |||||||
\(828\) | −0.0977039 | − | 0.491190i | −0.00339544 | − | 0.0170700i | ||||
\(829\) | −19.3397 | − | 19.3397i | −0.671696 | − | 0.671696i | 0.286411 | − | 0.958107i | \(-0.407538\pi\) |
−0.958107 | + | 0.286411i | \(0.907538\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11.4397 | + | 27.6178i | −0.396837 | + | 0.958050i | ||||
\(832\) | 0.486008 | + | 0.486008i | 0.0168493 | + | 0.0168493i | ||||
\(833\) | 17.0822 | + | 13.3999i | 0.591865 | + | 0.464281i | ||||
\(834\) | − | 15.6856i | − | 0.543149i | ||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.316180 | + | 0.0628921i | −0.0109353 | + | 0.00217517i | ||||
\(837\) | 61.9607 | 2.14168 | ||||||||
\(838\) | 5.30674 | − | 1.05558i | 0.183318 | − | 0.0364643i | ||||
\(839\) | −2.67790 | + | 13.4627i | −0.0924512 | + | 0.464784i | 0.906630 | + | 0.421927i | \(0.138646\pi\) |
−0.999081 | + | 0.0428571i | \(0.986354\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.31132 | − | 3.16579i | −0.0452178 | − | 0.109165i | ||||
\(842\) | 6.80990 | − | 16.4405i | 0.234685 | − | 0.566579i | ||||
\(843\) | −31.9708 | − | 6.35938i | −1.10113 | − | 0.219029i | ||||
\(844\) | 4.52362 | + | 0.899804i | 0.155709 | + | 0.0309725i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.72867 | + | 2.72867i | −0.0938138 | + | 0.0938138i | ||||
\(847\) | 26.0675 | + | 17.4178i | 0.895691 | + | 0.598482i | ||||
\(848\) | −2.60552 | + | 1.07924i | −0.0894741 | + | 0.0370614i | ||||
\(849\) | −29.9208 | −1.02688 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.273016 | 0.00935887 | ||||||||
\(852\) | −14.9047 | + | 6.17372i | −0.510626 | + | 0.211508i | ||||
\(853\) | −24.6422 | − | 16.4654i | −0.843734 | − | 0.563765i | 0.0568820 | − | 0.998381i | \(-0.481884\pi\) |
−0.900616 | + | 0.434616i | \(0.856884\pi\) | |||||||
\(854\) | −32.8302 | + | 32.8302i | −1.12343 | + | 1.12343i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 14.2388 | + | 2.83228i | 0.486674 | + | 0.0968055i | ||||
\(857\) | 2.81677 | + | 0.560290i | 0.0962190 | + | 0.0191391i | 0.242965 | − | 0.970035i | \(-0.421880\pi\) |
−0.146746 | + | 0.989174i | \(0.546880\pi\) | |||||||
\(858\) | 0.561381 | − | 1.35529i | 0.0191652 | − | 0.0462689i | ||||
\(859\) | 14.7311 | + | 35.5640i | 0.502618 | + | 1.21343i | 0.948053 | + | 0.318112i | \(0.103049\pi\) |
−0.445435 | + | 0.895314i | \(0.646951\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.74709 | + | 13.8106i | −0.0936206 | + | 0.470663i | ||||
\(862\) | −10.0155 | + | 1.99220i | −0.341129 | + | 0.0678547i | ||||
\(863\) | −12.3538 | −0.420530 | −0.210265 | − | 0.977644i | \(-0.567433\pi\) | ||||
−0.210265 | + | 0.977644i | \(0.567433\pi\) | |||||||
\(864\) | 5.52298 | − | 1.09859i | 0.187895 | − | 0.0373747i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 34.8551i | 1.18442i | ||||||||
\(867\) | −10.7248 | − | 22.9721i | −0.364233 | − | 0.780173i | ||||
\(868\) | −27.2488 | − | 27.2488i | −0.924885 | − | 0.924885i | ||||
\(869\) | −1.00307 | + | 2.42163i | −0.0340268 | + | 0.0821480i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.63236 | − | 3.63236i | −0.123078 | − | 0.123078i | ||||
\(872\) | 2.52344 | + | 12.6862i | 0.0854545 | + | 0.429609i | ||||
\(873\) | 3.80102 | + | 5.68863i | 0.128645 | + | 0.192531i | ||||
\(874\) | 0.120874 | − | 0.0807655i | 0.00408863 | − | 0.00273193i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 13.5125 | − | 5.59706i | 0.456545 | − | 0.189107i | ||||
\(877\) | 0.843295 | − | 4.23953i | 0.0284760 | − | 0.143159i | −0.963932 | − | 0.266149i | \(-0.914249\pi\) |
0.992408 | + | 0.122991i | \(0.0392485\pi\) | |||||||
\(878\) | −2.23789 | + | 1.49531i | −0.0755253 | + | 0.0504644i | ||||
\(879\) | 13.2412 | − | 19.8168i | 0.446613 | − | 0.668404i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.73703 | − | 28.8420i | −0.193285 | − | 0.971711i | −0.948631 | − | 0.316385i | \(-0.897531\pi\) |
0.755346 | − | 0.655327i | \(-0.227469\pi\) | |||||||
\(882\) | −1.56369 | − | 3.77508i | −0.0526522 | − | 0.127114i | ||||
\(883\) | −34.6701 | + | 34.6701i | −1.16674 | + | 1.16674i | −0.183773 | + | 0.982969i | \(0.558831\pi\) |
−0.982969 | + | 0.183773i | \(0.941169\pi\) | |||||||
\(884\) | −2.46922 | + | 1.39065i | −0.0830487 | + | 0.0467727i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 28.1361 | + | 11.6544i | 0.945251 | + | 0.391536i | ||||
\(887\) | 4.91559 | − | 7.35669i | 0.165049 | − | 0.247014i | −0.739721 | − | 0.672914i | \(-0.765043\pi\) |
0.904770 | + | 0.425900i | \(0.140043\pi\) | |||||||
\(888\) | 0.630868i | 0.0211706i | ||||||||
\(889\) | 36.3274 | + | 24.2732i | 1.21838 | + | 0.814097i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.82623 | − | 7.22296i | −0.161685 | − | 0.241978i | ||||
\(892\) | 9.20723 | + | 3.81376i | 0.308281 | + | 0.127694i | ||||
\(893\) | −1.03489 | − | 0.428664i | −0.0346312 | − | 0.0143447i | ||||
\(894\) | 4.38950 | + | 6.56936i | 0.146807 | + | 0.219712i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.91200 | − | 1.94574i | −0.0972832 | − | 0.0650026i | ||||
\(897\) | 0.661522i | 0.0220876i | ||||||||
\(898\) | 14.6651 | − | 21.9479i | 0.489380 | − | 0.732410i | ||||
\(899\) | −57.8873 | − | 23.9777i | −1.93065 | − | 0.799702i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.39454 | − | 11.5441i | −0.0464589 | − | 0.384588i | ||||
\(902\) | −2.72835 | + | 2.72835i | −0.0908441 | + | 0.0908441i | ||||
\(903\) | −6.46843 | − | 15.6162i | −0.215256 | − | 0.519674i | ||||
\(904\) | 0.587603 | + | 2.95408i | 0.0195434 | + | 0.0982512i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 8.69273 | − | 13.0096i | 0.288796 | − | 0.432214i | ||||
\(907\) | 7.60237 | − | 5.07974i | 0.252433 | − | 0.168670i | −0.422916 | − | 0.906169i | \(-0.638993\pi\) |
0.675348 | + | 0.737499i | \(0.263993\pi\) | |||||||
\(908\) | −3.11178 | + | 15.6440i | −0.103268 | + | 0.519163i | ||||
\(909\) | 9.48505 | − | 3.92884i | 0.314599 | − | 0.130311i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.4797 | − | 17.0250i | 0.844181 | − | 0.564064i | −0.0565701 | − | 0.998399i | \(-0.518016\pi\) |
0.900752 | + | 0.434335i | \(0.143016\pi\) | |||||||
\(912\) | 0.186628 | + | 0.279308i | 0.00617986 | + | 0.00924882i | ||||
\(913\) | −0.713971 | − | 3.58938i | −0.0236290 | − | 0.118791i | ||||
\(914\) | 18.1284 | + | 18.1284i | 0.599634 | + | 0.599634i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.9342 | + | 26.3976i | −0.361277 | + | 0.872200i | ||||
\(917\) | 48.5856 | + | 48.5856i | 1.60444 | + | 1.60444i | ||||
\(918\) | −1.76588 | + | 23.1507i | −0.0582828 | + | 0.764087i | ||||
\(919\) | 43.0164i | 1.41898i | 0.704716 | + | 0.709490i | \(0.251074\pi\) | ||||
−0.704716 | + | 0.709490i | \(0.748926\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.84691 | − | 0.566286i | 0.0938089 | − | 0.0186597i | ||||
\(922\) | −13.3685 | −0.440270 | ||||||||
\(923\) | −7.29243 | + | 1.45055i | −0.240033 | + | 0.0477456i | ||||
\(924\) | −1.45828 | + | 7.33126i | −0.0479738 | + | 0.241181i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 12.5834 | + | 30.3791i | 0.413517 | + | 0.998319i | ||||
\(927\) | 5.38968 | − | 13.0118i | 0.177020 | − | 0.427365i | ||||
\(928\) | −5.58502 | − | 1.11093i | −0.183337 | − | 0.0364681i | ||||
\(929\) | −41.3633 | − | 8.22767i | −1.35709 | − | 0.269941i | −0.537677 | − | 0.843151i | \(-0.680698\pi\) |
−0.819408 | + | 0.573210i | \(0.805698\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.838701 | − | 0.838701i | 0.0274873 | − | 0.0274873i | ||||
\(932\) | −19.7880 | − | 13.2219i | −0.648176 | − | 0.433098i | ||||
\(933\) | 28.9724 | − | 12.0008i | 0.948514 | − | 0.392887i | ||||
\(934\) | −4.78801 | −0.156668 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.533356 | 0.0174333 | ||||||||
\(937\) | −39.8003 | + | 16.4858i | −1.30022 | + | 0.538569i | −0.922015 | − | 0.387153i | \(-0.873458\pi\) |
−0.378205 | + | 0.925722i | \(0.623458\pi\) | |||||||
\(938\) | 21.7639 | + | 14.5422i | 0.710617 | + | 0.474819i | ||||
\(939\) | 29.9474 | − | 29.9474i | 0.977295 | − | 0.977295i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.9565 | + | 3.37287i | 0.552768 | + | 0.109952i | 0.463568 | − | 0.886061i | \(-0.346569\pi\) |
0.0891997 | + | 0.996014i | \(0.471569\pi\) | |||||||
\(942\) | −21.9841 | − | 4.37291i | −0.716280 | − | 0.142477i | ||||
\(943\) | 0.665857 | − | 1.60752i | 0.0216833 | − | 0.0523481i | ||||
\(944\) | 1.13235 | + | 2.73373i | 0.0368548 | + | 0.0889754i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.903593 | − | 4.54267i | 0.0293783 | − | 0.147695i | ||||
\(947\) | −8.23276 | + | 1.63760i | −0.267529 | + | 0.0532148i | −0.327032 | − | 0.945013i | \(-0.606048\pi\) |
0.0595030 | + | 0.998228i | \(0.481048\pi\) | |||||||
\(948\) | 2.73129 | 0.0887083 | ||||||||
\(949\) | 6.61128 | − | 1.31506i | 0.214611 | − | 0.0426888i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 41.2465i | 1.33751i | ||||||||
\(952\) | 10.9577 | − | 9.40452i | 0.355141 | − | 0.304802i | ||||
\(953\) | −17.1743 | − | 17.1743i | −0.556330 | − | 0.556330i | 0.371930 | − | 0.928261i | \(-0.378696\pi\) |
−0.928261 | + | 0.371930i | \(0.878696\pi\) | |||||||
\(954\) | −0.837487 | + | 2.02187i | −0.0271146 | + | 0.0654605i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −15.7069 | − | 15.7069i | −0.507997 | − | 0.507997i | ||||
\(957\) | 2.37108 | + | 11.9202i | 0.0766460 | + | 0.385326i | ||||
\(958\) | −18.2911 | − | 27.3745i | −0.590958 | − | 0.884431i | ||||
\(959\) | 20.6576 | − | 13.8030i | 0.667068 | − | 0.445721i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −83.2134 | + | 34.4681i | −2.68430 | + | 1.11187i | ||||
\(962\) | −0.0567238 | + | 0.285170i | −0.00182885 | + | 0.00919424i | ||||
\(963\) | 9.36712 | − | 6.25891i | 0.301851 | − | 0.201690i | ||||
\(964\) | −4.84747 | + | 7.25475i | −0.156126 | + | 0.233660i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.657607 | − | 3.30601i | −0.0211582 | − | 0.106369i | ||||
\(967\) | −0.445933 | − | 1.07658i | −0.0143402 | − | 0.0346204i | 0.916547 | − | 0.399926i | \(-0.130964\pi\) |
−0.930887 | + | 0.365306i | \(0.880964\pi\) | |||||||
\(968\) | 6.32985 | − | 6.32985i | 0.203449 | − | 0.203449i | ||||
\(969\) | −1.31621 | + | 0.431173i | −0.0422829 | + | 0.0138513i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.7627 | − | 7.35756i | −0.570033 | − | 0.236115i | 0.0790013 | − | 0.996875i | \(-0.474827\pi\) |
−0.649034 | + | 0.760759i | \(0.724827\pi\) | |||||||
\(972\) | 4.35651 | − | 6.51997i | 0.139735 | − | 0.209128i | ||||
\(973\) | 36.8366i | 1.18093i | ||||||||
\(974\) | −25.2701 | − | 16.8849i | −0.809706 | − | 0.541029i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.36516 | + | 11.0227i | 0.235753 | + | 0.352829i | ||||
\(977\) | 23.2223 | + | 9.61901i | 0.742949 | + | 0.307739i | 0.721861 | − | 0.692038i | \(-0.243287\pi\) |
0.0210877 | + | 0.999778i | \(0.493287\pi\) | |||||||
\(978\) | 20.6384 | + | 8.54871i | 0.659943 | + | 0.273357i | ||||
\(979\) | −10.9716 | − | 16.4202i | −0.350654 | − | 0.524791i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.34569 | + | 5.57641i | 0.266457 | + | 0.178041i | ||||
\(982\) | − | 16.3302i | − | 0.521116i | ||||||
\(983\) | −19.1109 | + | 28.6015i | −0.609543 | + | 0.912245i | −0.999965 | − | 0.00839065i | \(-0.997329\pi\) |
0.390422 | + | 0.920636i | \(0.372329\pi\) | |||||||
\(984\) | 3.71456 | + | 1.53862i | 0.118416 | + | 0.0490494i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 10.6087 | − | 20.9454i | 0.337850 | − | 0.667036i | ||||
\(987\) | −18.3657 | + | 18.3657i | −0.584585 | + | 0.584585i | ||||
\(988\) | 0.0592472 | + | 0.143035i | 0.00188490 | + | 0.00455056i | ||||
\(989\) | 0.407473 | + | 2.04851i | 0.0129569 | + | 0.0651387i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.9127 | − | 25.3117i | 0.537250 | − | 0.804052i | −0.459191 | − | 0.888337i | \(-0.651861\pi\) |
0.996442 | + | 0.0842855i | \(0.0268608\pi\) | |||||||
\(992\) | −9.14879 | + | 6.11303i | −0.290474 | + | 0.194089i | ||||
\(993\) | −10.0096 | + | 50.3218i | −0.317646 | + | 1.59691i | ||||
\(994\) | 35.0026 | − | 14.4985i | 1.11021 | − | 0.459866i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −3.17080 | + | 2.11866i | −0.100471 | + | 0.0671323i | ||||
\(997\) | −30.7399 | − | 46.0056i | −0.973543 | − | 1.45701i | −0.887548 | − | 0.460715i | \(-0.847593\pi\) |
−0.0859950 | − | 0.996296i | \(-0.527407\pi\) | |||||||
\(998\) | −4.87821 | − | 24.5244i | −0.154417 | − | 0.776307i | ||||
\(999\) | 1.68444 | + | 1.68444i | 0.0532933 | + | 0.0532933i |
(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 | 850.2.v.b.193.2 | yes | 24 | |
5.2 | odd | 4 | 850.2.s.a.57.2 | ✓ | 24 | ||
5.3 | odd | 4 | 850.2.s.b.57.2 | yes | 24 | ||
5.4 | even | 2 | 850.2.v.a.193.2 | yes | 24 | ||
17.3 | odd | 16 | 850.2.s.a.343.2 | yes | 24 | ||
85.3 | even | 16 | 850.2.v.a.207.2 | yes | 24 | ||
85.37 | even | 16 | inner | 850.2.v.b.207.2 | yes | 24 | |
85.54 | odd | 16 | 850.2.s.b.343.2 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
850.2.s.a.57.2 | ✓ | 24 | 5.2 | odd | 4 | ||
850.2.s.a.343.2 | yes | 24 | 17.3 | odd | 16 | ||
850.2.s.b.57.2 | yes | 24 | 5.3 | odd | 4 | ||
850.2.s.b.343.2 | yes | 24 | 85.54 | odd | 16 | ||
850.2.v.a.193.2 | yes | 24 | 5.4 | even | 2 | ||
850.2.v.a.207.2 | yes | 24 | 85.3 | even | 16 | ||
850.2.v.b.193.2 | yes | 24 | 1.1 | even | 1 | trivial | |
850.2.v.b.207.2 | yes | 24 | 85.37 | even | 16 | inner |