Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(5,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 5, 15]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.5");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.ck (of order \(18\), degree \(6\), 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: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(144\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 5.4 | ||
Character | \(\chi\) | \(=\) | 756.5 |
Dual form | 756.2.ck.a.605.4 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.63242 | + | 0.578955i | −0.942481 | + | 0.334260i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.649280 | − | 3.68225i | 0.290367 | − | 1.64675i | −0.395092 | − | 0.918642i | \(-0.629287\pi\) |
0.685459 | − | 0.728111i | \(-0.259602\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.647047 | − | 2.56541i | 0.244561 | − | 0.969634i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.32962 | − | 1.89020i | 0.776541 | − | 0.630067i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.889725 | − | 0.156882i | 0.268262 | − | 0.0473018i | −0.0378990 | − | 0.999282i | \(-0.512067\pi\) |
0.306161 | + | 0.951980i | \(0.400955\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.769375 | + | 0.916906i | −0.213386 | + | 0.254304i | −0.862111 | − | 0.506719i | \(-0.830858\pi\) |
0.648725 | + | 0.761023i | \(0.275303\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.07196 | + | 6.38690i | 0.276778 | + | 1.64909i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.46688 | −1.81098 | −0.905492 | − | 0.424362i | \(-0.860498\pi\) | ||||
−0.905492 | + | 0.424362i | \(0.860498\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.689746i | 0.158239i | 0.996865 | + | 0.0791193i | \(0.0252108\pi\) | ||||
−0.996865 | + | 0.0791193i | \(0.974789\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.429002 | + | 4.56245i | 0.0936159 | + | 0.995608i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.84180 | − | 3.38672i | 0.592555 | − | 0.706180i | −0.383540 | − | 0.923524i | \(-0.625295\pi\) |
0.976095 | + | 0.217344i | \(0.0697395\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −8.43895 | − | 3.07153i | −1.68779 | − | 0.614305i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.70859 | + | 4.43436i | −0.521269 | + | 0.853392i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.230745 | − | 0.274991i | −0.0428482 | − | 0.0510645i | 0.744195 | − | 0.667963i | \(-0.232833\pi\) |
−0.787043 | + | 0.616898i | \(0.788389\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.43265 | + | 9.43113i | 0.616522 | + | 1.69388i | 0.715341 | + | 0.698776i | \(0.246271\pi\) |
−0.0988186 | + | 0.995105i | \(0.531506\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.36158 | + | 0.771209i | −0.237021 | + | 0.134250i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.02637 | − | 4.04826i | −1.52574 | − | 0.684281i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.77757 | − | 8.27499i | −0.785427 | − | 1.36040i | −0.928743 | − | 0.370723i | \(-0.879110\pi\) |
0.143316 | − | 0.989677i | \(-0.454223\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.725101 | − | 1.94221i | 0.116109 | − | 0.311003i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.79118 | − | 4.85938i | −0.904430 | − | 0.758907i | 0.0666210 | − | 0.997778i | \(-0.478778\pi\) |
−0.971051 | + | 0.238871i | \(0.923223\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.12751 | + | 1.50229i | 0.629440 | + | 0.229097i | 0.636988 | − | 0.770874i | \(-0.280180\pi\) |
−0.00754750 | + | 0.999972i | \(0.502402\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.44762 | − | 9.80553i | −0.812083 | − | 1.46172i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.35416 | − | 1.58478i | −0.635119 | − | 0.231165i | 0.00433856 | − | 0.999991i | \(-0.498619\pi\) |
−0.639458 | + | 0.768826i | \(0.720841\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.16266 | − | 3.31988i | −0.880380 | − | 0.474269i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.1891 | − | 4.32299i | 1.70682 | − | 0.605339i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.6009 | − | 6.69781i | 1.59351 | − | 0.920014i | 0.600814 | − | 0.799389i | \(-0.294843\pi\) |
0.992698 | − | 0.120625i | \(-0.0384900\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3.37805i | − | 0.455496i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.399332 | − | 1.12596i | −0.0528928 | − | 0.149137i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.0113213 | + | 0.00949971i | 0.00147391 | + | 0.00123676i | 0.643524 | − | 0.765426i | \(-0.277472\pi\) |
−0.642050 | + | 0.766662i | \(0.721916\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.34236 | + | 3.68810i | −0.171871 | + | 0.472213i | −0.995483 | − | 0.0949418i | \(-0.969733\pi\) |
0.823612 | + | 0.567154i | \(0.191956\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.34177 | − | 7.19949i | −0.421023 | − | 0.907050i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.87674 | + | 3.42836i | 0.356815 | + | 0.425236i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.323090 | + | 1.83233i | −0.0394717 | + | 0.223855i | −0.998162 | − | 0.0605954i | \(-0.980700\pi\) |
0.958691 | + | 0.284451i | \(0.0918112\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.67826 | + | 7.17384i | −0.322425 | + | 0.863629i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.69050 | − | 5.59481i | −1.15005 | − | 0.663982i | −0.201151 | − | 0.979560i | \(-0.564468\pi\) |
−0.948899 | + | 0.315578i | \(0.897801\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.63739 | − | 5.56415i | −1.12797 | − | 0.651234i | −0.184547 | − | 0.982824i | \(-0.559082\pi\) |
−0.943424 | + | 0.331589i | \(0.892415\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 15.5542 | + | 0.128266i | 1.79605 | + | 0.0148108i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.173225 | − | 2.38402i | 0.0197409 | − | 0.271684i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.78156 | + | 10.1037i | 0.200441 | + | 1.13676i | 0.904455 | + | 0.426570i | \(0.140278\pi\) |
−0.704014 | + | 0.710186i | \(0.748611\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.85428 | − | 8.80691i | 0.206031 | − | 0.978545i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.58220 | − | 3.84492i | 0.502962 | − | 0.422035i | −0.355683 | − | 0.934607i | \(-0.615752\pi\) |
0.858644 | + | 0.512572i | \(0.171307\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.84810 | + | 27.4949i | −0.525850 | + | 2.98224i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.535881 | + | 0.315311i | 0.0574525 | + | 0.0338049i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.9206 | 1.47558 | 0.737788 | − | 0.675032i | \(-0.235870\pi\) | ||||
0.737788 | + | 0.675032i | \(0.235870\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.85442 | + | 2.56704i | 0.194396 | + | 0.269099i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −11.0637 | − | 13.4083i | −1.14726 | − | 1.39037i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.53982 | + | 0.447839i | 0.260580 | + | 0.0459473i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.53264 | − | 4.21088i | 0.155616 | − | 0.427550i | −0.837245 | − | 0.546827i | \(-0.815835\pi\) |
0.992861 | + | 0.119277i | \(0.0380576\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.77618 | − | 2.04723i | 0.178513 | − | 0.205755i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.46818 | − | 2.91015i | 0.345097 | − | 0.289571i | −0.453721 | − | 0.891144i | \(-0.649904\pi\) |
0.798818 | + | 0.601573i | \(0.205459\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.5700 | − | 2.04010i | −1.14002 | − | 0.201017i | −0.428406 | − | 0.903586i | \(-0.640925\pi\) |
−0.711615 | + | 0.702570i | \(0.752036\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 17.0786 | + | 1.38262i | 1.66670 | + | 0.134930i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.33302 | − | 3.07902i | −0.515563 | − | 0.297660i | 0.219555 | − | 0.975600i | \(-0.429540\pi\) |
−0.735117 | + | 0.677940i | \(0.762873\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.87972 | + | 4.98782i | 0.275827 | + | 0.477746i | 0.970343 | − | 0.241730i | \(-0.0777150\pi\) |
−0.694516 | + | 0.719477i | \(0.744382\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.5899 | + | 10.7423i | 1.19498 | + | 1.01961i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.26420 | + | 3.47337i | 0.118926 | + | 0.326747i | 0.984845 | − | 0.173438i | \(-0.0554875\pi\) |
−0.865919 | + | 0.500185i | \(0.833265\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.6256 | − | 12.6631i | −0.990846 | − | 1.18084i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.0592181 | + | 3.59032i | −0.00547471 | + | 0.331925i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.83142 | + | 19.1556i | −0.442896 | + | 1.75599i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.56962 | + | 3.48306i | −0.869966 | + | 0.316642i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 12.2670 | + | 4.57974i | 1.10608 | + | 0.412941i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.44173 | + | 12.8895i | −0.665609 | + | 1.15287i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.29860 | + | 12.6416i | 0.647646 | + | 1.12176i | 0.983683 | + | 0.179908i | \(0.0575799\pi\) |
−0.336037 | + | 0.941849i | \(0.609087\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.60762 | − | 0.0627351i | −0.669813 | − | 0.00552352i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.05501 | − | 1.72436i | −0.179547 | − | 0.150658i | 0.548585 | − | 0.836095i | \(-0.315167\pi\) |
−0.728132 | + | 0.685437i | \(0.759611\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.76948 | + | 0.446298i | 0.153434 | + | 0.0386989i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 14.5698 | + | 12.8529i | 1.25397 | + | 1.10620i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.607400 | − | 1.66882i | 0.0518937 | − | 0.142577i | −0.911038 | − | 0.412323i | \(-0.864718\pi\) |
0.962931 | + | 0.269746i | \(0.0869398\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.70465 | + | 1.35854i | 0.653500 | + | 0.115230i | 0.490561 | − | 0.871407i | \(-0.336792\pi\) |
0.162938 | + | 0.986636i | \(0.447903\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.02536 | + | 0.0661799i | 0.675857 | + | 0.00557335i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.540686 | + | 0.936495i | −0.0452144 | + | 0.0783137i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.16240 | + | 0.671114i | −0.0965324 | + | 0.0557330i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 11.9821 | + | 1.85155i | 0.988271 | + | 0.152713i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.08102 | + | 13.9600i | 0.416254 | + | 1.14365i | 0.953808 | + | 0.300418i | \(0.0971262\pi\) |
−0.537554 | + | 0.843229i | \(0.680652\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.80728 | − | 15.9209i | −0.228453 | − | 1.29562i | −0.855972 | − | 0.517022i | \(-0.827040\pi\) |
0.627518 | − | 0.778602i | \(-0.284071\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −17.3950 | + | 14.1139i | −1.40630 | + | 1.14104i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 36.9565 | − | 6.51644i | 2.96842 | − | 0.523413i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.0313116 | − | 0.0373157i | 0.00249894 | − | 0.00297812i | −0.764794 | − | 0.644275i | \(-0.777159\pi\) |
0.767292 | + | 0.641297i | \(0.221603\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −15.0599 | + | 17.6501i | −1.19433 | + | 1.39974i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.84955 | − | 9.48174i | −0.539820 | − | 0.747266i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.22231 | + | 3.84915i | −0.174064 | + | 0.301488i | −0.939837 | − | 0.341623i | \(-0.889023\pi\) |
0.765773 | + | 0.643111i | \(0.222357\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.95574 | + | 5.51441i | 0.152254 | + | 0.429297i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.33767 | − | 1.21481i | 0.258277 | − | 0.0940050i | −0.209637 | − | 0.977779i | \(-0.567228\pi\) |
0.467913 | + | 0.883774i | \(0.345006\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.00865 | + | 11.3916i | 0.154511 | + | 0.876278i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.30376 | + | 1.60685i | 0.0997009 | + | 0.122879i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.4798 | − | 12.1500i | 1.10088 | − | 0.923749i | 0.103397 | − | 0.994640i | \(-0.467029\pi\) |
0.997484 | + | 0.0708908i | \(0.0225842\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.3401 | + | 19.6619i | −1.00842 | + | 1.48630i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.0239811 | − | 0.00895304i | −0.00180253 | − | 0.000672952i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 26.7211i | − | 1.99723i | −0.0526473 | − | 0.998613i | \(-0.516766\pi\) | ||
0.0526473 | − | 0.998613i | \(-0.483234\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.39653 | − | 3.69304i | 0.475450 | − | 0.274501i | −0.243068 | − | 0.970009i | \(-0.578154\pi\) |
0.718519 | + | 0.695508i | \(0.244821\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.0560563 | − | 6.79771i | 0.00414380 | − | 0.502501i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −33.5726 | + | 12.2194i | −2.46831 | + | 0.898390i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.64347 | + | 1.17142i | −0.485819 | + | 0.0856629i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.62336 | + | 9.81789i | 0.699996 | + | 0.714146i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.42440 | + | 0.251161i | −0.103066 | + | 0.0181733i | −0.224943 | − | 0.974372i | \(-0.572220\pi\) |
0.121877 | + | 0.992545i | \(0.461109\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.3927 | − | 5.96644i | 1.17997 | − | 0.429474i | 0.323779 | − | 0.946133i | \(-0.395047\pi\) |
0.856191 | + | 0.516659i | \(0.172825\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.68093 | − | 3.93104i | −0.478431 | − | 0.281508i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.9252 | − | 8.03969i | 0.992126 | − | 0.572804i | 0.0862168 | − | 0.996276i | \(-0.472522\pi\) |
0.905909 | + | 0.423472i | \(0.139189\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 3.28881i | − | 0.233138i | −0.993183 | − | 0.116569i | \(-0.962810\pi\) | ||
0.993183 | − | 0.116569i | \(-0.0371896\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.533418 | − | 3.17820i | −0.0376244 | − | 0.224173i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.854767 | + | 0.414023i | −0.0599929 | + | 0.0290587i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −21.6535 | + | 18.1695i | −1.51235 | + | 1.26901i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.218730 | − | 13.2613i | 0.0152028 | − | 0.921727i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.108209 | + | 0.613684i | 0.00748498 | + | 0.0424494i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.2958 | − | 8.47897i | 1.60375 | − | 0.583717i | 0.623558 | − | 0.781777i | \(-0.285686\pi\) |
0.980190 | + | 0.198060i | \(0.0634642\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 19.0581 | + | 3.52275i | 1.30584 | + | 0.241375i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.21173 | − | 14.2231i | 0.560036 | − | 0.970010i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 26.4158 | − | 2.70378i | 1.79322 | − | 0.183544i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 18.9537 | + | 3.50344i | 1.28077 | + | 0.236741i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.74484 | − | 6.84643i | 0.386439 | − | 0.460541i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.8216 | − | 2.78978i | 1.05949 | − | 0.186817i | 0.383362 | − | 0.923598i | \(-0.374766\pi\) |
0.676132 | + | 0.736781i | \(0.263655\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −25.4654 | + | 8.79581i | −1.69769 | + | 0.586387i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.48157 | − | 8.40237i | −0.0983349 | − | 0.557685i | −0.993674 | − | 0.112301i | \(-0.964178\pi\) |
0.895339 | − | 0.445385i | \(-0.146933\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.302173 | + | 0.830212i | 0.0199681 | + | 0.0548620i | 0.949276 | − | 0.314443i | \(-0.101818\pi\) |
−0.929308 | + | 0.369305i | \(0.879596\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.09746 | + | 3.99202i | 0.0722077 | + | 0.262656i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.90471 | − | 4.56379i | 0.517855 | − | 0.298984i | −0.218202 | − | 0.975904i | \(-0.570019\pi\) |
0.736057 | + | 0.676920i | \(0.236686\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.66265 | + | 15.0041i | −0.565089 | + | 0.978762i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.75785 | − | 15.4621i | −0.568883 | − | 1.00437i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.4613 | − | 2.90258i | −1.06480 | − | 0.187752i | −0.386312 | − | 0.922368i | \(-0.626251\pi\) |
−0.678483 | + | 0.734616i | \(0.737362\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.58860 | − | 23.5970i | 0.553241 | − | 1.52002i | −0.276019 | − | 0.961152i | \(-0.589015\pi\) |
0.829259 | − | 0.558864i | \(-0.188763\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.07183 | + | 15.4502i | 0.132908 | + | 0.991128i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −16.2259 | + | 20.5369i | −1.03664 | + | 1.31206i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.632433 | − | 0.530674i | −0.0402407 | − | 0.0337660i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.25406 | + | 8.92944i | −0.332963 | + | 0.565880i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.73608 | − | 15.1313i | −0.551417 | − | 0.955082i | −0.998173 | − | 0.0604258i | \(-0.980754\pi\) |
0.446756 | − | 0.894656i | \(-0.352579\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.99710 | − | 3.45908i | 0.125557 | − | 0.217470i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.00417 | − | 47.6903i | −0.501241 | − | 2.98648i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −21.3751 | + | 7.77990i | −1.33334 | + | 0.485297i | −0.907709 | − | 0.419599i | \(-0.862171\pi\) |
−0.425632 | + | 0.904896i | \(0.639948\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −24.3201 | + | 6.90212i | −1.51117 | + | 0.428877i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.05734 | − | 0.204471i | −0.0654475 | − | 0.0126564i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.78344 | − | 2.12542i | −0.109972 | − | 0.131059i | 0.708251 | − | 0.705961i | \(-0.249485\pi\) |
−0.818222 | + | 0.574902i | \(0.805040\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −17.1307 | − | 47.0663i | −1.05233 | − | 2.89126i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −22.7243 | + | 8.05937i | −1.39070 | + | 0.493226i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.69974 | + | 9.87224i | 0.347519 | + | 0.601921i | 0.985808 | − | 0.167876i | \(-0.0536908\pi\) |
−0.638289 | + | 0.769797i | \(0.720357\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.39054 | + | 1.95753i | 0.205961 | + | 0.118912i | 0.599433 | − | 0.800425i | \(-0.295393\pi\) |
−0.393472 | + | 0.919337i | \(0.628726\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.51340 | − | 3.11688i | −0.273164 | − | 0.188642i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.99021 | − | 1.40889i | −0.481828 | − | 0.0849592i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.15531 | − | 3.48672i | 0.249669 | − | 0.209497i | −0.509361 | − | 0.860553i | \(-0.670118\pi\) |
0.759030 | + | 0.651056i | \(0.225674\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 25.8235 | + | 15.4826i | 1.54601 | + | 0.926918i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.74746 | + | 18.5385i | −0.402520 | + | 1.10591i | 0.558517 | + | 0.829493i | \(0.311370\pi\) |
−0.961037 | + | 0.276421i | \(0.910852\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.3551 | + | 2.70751i | 0.912764 | + | 0.160945i | 0.610258 | − | 0.792203i | \(-0.291066\pi\) |
0.302506 | + | 0.953147i | \(0.402177\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.40534 | + | 0.739378i | −0.260950 | + | 0.0437970i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −16.2135 | + | 11.7125i | −0.957050 | + | 0.691368i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 38.7543 | 2.27967 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.0640022 | + | 7.76128i | −0.00375188 | + | 0.454974i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.36781 | − | 19.0998i | 0.196749 | − | 1.11582i | −0.713156 | − | 0.701005i | \(-0.752735\pi\) |
0.909905 | − | 0.414816i | \(-0.136154\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.0423310 | − | 0.0355200i | 0.00246461 | − | 0.00206805i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.71423 | + | 4.37029i | −0.0994697 | + | 0.253590i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.918896 | + | 5.21132i | 0.0531411 | + | 0.301378i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.52469 | − | 9.61672i | 0.376077 | − | 0.554298i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.97670 | + | 6.75852i | −0.228455 | + | 0.388267i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.7089 | + | 7.33751i | 0.727712 | + | 0.420145i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.6946 | + | 9.06129i | 0.895739 | + | 0.517155i | 0.875815 | − | 0.482646i | \(-0.160324\pi\) |
0.0199238 | + | 0.999802i | \(0.493658\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 20.0682 | − | 3.36818i | 1.14164 | − | 0.191609i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.95939 | + | 22.4548i | −0.224516 | + | 1.27330i | 0.639091 | + | 0.769131i | \(0.279311\pi\) |
−0.863608 | + | 0.504165i | \(0.831800\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.4418 | − | 19.5945i | −0.929344 | − | 1.10755i | −0.993971 | − | 0.109639i | \(-0.965030\pi\) |
0.0646276 | − | 0.997909i | \(-0.479414\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −28.6801 | + | 7.63074i | −1.61594 | + | 0.429944i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.90887 | − | 16.2345i | 0.331875 | − | 0.911819i | −0.655749 | − | 0.754979i | \(-0.727647\pi\) |
0.987624 | − | 0.156840i | \(-0.0501307\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.248441 | − | 0.208466i | −0.0139100 | − | 0.0116719i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.4884 | + | 1.93869i | 0.585404 | + | 0.108207i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 5.15025i | − | 0.286568i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.30902 | − | 5.37457i | 0.516372 | − | 0.298127i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.58865 | − | 6.47501i | −0.419653 | − | 0.358069i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.88297 | + | 10.1448i | −0.379470 | + | 0.559300i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.3643 | − | 8.50391i | −1.28422 | − | 0.467417i | −0.392393 | − | 0.919797i | \(-0.628353\pi\) |
−0.891825 | + | 0.452380i | \(0.850575\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −26.7713 | − | 10.2470i | −1.46706 | − | 0.561534i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.53734 | + | 2.37940i | 0.357173 | + | 0.130000i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.16317 | − | 4.33242i | −0.281256 | − | 0.236002i | 0.491236 | − | 0.871027i | \(-0.336545\pi\) |
−0.772492 | + | 0.635025i | \(0.780990\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.07465 | − | 4.93810i | −0.221304 | − | 0.268201i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.53369 | + | 7.85259i | 0.245513 | + | 0.425241i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.5044 | + | 13.6616i | −0.675173 | + | 0.737659i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 24.6769 | + | 14.5199i | 1.32856 | + | 0.781723i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.44947 | + | 25.9622i | 0.507274 | + | 1.39372i | 0.884038 | + | 0.467415i | \(0.154815\pi\) |
−0.376764 | + | 0.926309i | \(0.622963\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.8032 | + | 21.2170i | 0.952981 | + | 1.13572i | 0.990650 | + | 0.136429i | \(0.0435624\pi\) |
−0.0376687 | + | 0.999290i | \(0.511993\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.98196 | − | 5.89521i | −0.105789 | − | 0.314663i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.2918 | − | 4.83782i | −0.707451 | − | 0.257491i | −0.0368622 | − | 0.999320i | \(-0.511736\pi\) |
−0.670589 | + | 0.741829i | \(0.733958\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −26.8933 | + | 32.0502i | −1.42735 | + | 1.70105i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.20331 | − | 34.0673i | −0.169537 | − | 1.80303i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 14.6085i | − | 0.771006i | −0.922707 | − | 0.385503i | \(-0.874028\pi\) | ||
0.922707 | − | 0.385503i | \(-0.125972\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.5242 | 0.974961 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 13.6052 | − | 11.2262i | 0.714085 | − | 0.589223i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −26.7460 | + | 31.8746i | −1.39995 | + | 1.66839i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.66648 | + | 0.470173i | −0.139189 | + | 0.0245428i | −0.242809 | − | 0.970074i | \(-0.578069\pi\) |
0.103619 | + | 0.994617i | \(0.466958\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −22.6765 | − | 0.374022i | −1.18049 | − | 0.0194708i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.67627 | − | 34.0950i | −0.502367 | − | 1.77012i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.01731 | + | 28.4546i | −0.259786 | + | 1.47332i | 0.523695 | + | 0.851906i | \(0.324553\pi\) |
−0.783481 | + | 0.621415i | \(0.786558\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.68566 | − | 25.3495i | 0.241966 | − | 1.30904i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.429670 | 0.0221291 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.86950 | 0.198763 | 0.0993815 | − | 0.995049i | \(-0.468314\pi\) | ||||
0.0993815 | + | 0.995049i | \(0.468314\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.2333 | − | 16.4108i | −0.985352 | − | 0.840752i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.64342 | + | 20.6629i | −0.186170 | + | 1.05582i | 0.738273 | + | 0.674502i | \(0.235642\pi\) |
−0.924443 | + | 0.381321i | \(0.875469\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.66609 | − | 2.18576i | −0.441665 | − | 0.111396i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.4552 | − | 4.30206i | 0.633133 | − | 0.218686i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.0482 | + | 2.47708i | −0.712274 | + | 0.125593i | −0.518033 | − | 0.855361i | \(-0.673336\pi\) |
−0.194241 | + | 0.980954i | \(0.562224\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.2194 | + | 25.2882i | −1.07311 | + | 1.27888i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.35298 | + | 1.62513i | 0.219579 | + | 0.0819769i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 38.3611 | 1.93016 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 28.9198i | − | 1.45144i | −0.687989 | − | 0.725721i | \(-0.741506\pi\) | ||
0.687989 | − | 0.725721i | \(-0.258494\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.14693 | + | 0.295903i | −0.157544 | + | 0.0148137i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.75159 | − | 11.6215i | 0.486971 | − | 0.580350i | −0.465473 | − | 0.885062i | \(-0.654116\pi\) |
0.952444 | + | 0.304712i | \(0.0985603\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.2885 | − | 4.10866i | −0.562318 | − | 0.204667i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −31.2253 | − | 12.5461i | −1.55160 | − | 0.623420i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.54892 | − | 6.61295i | −0.275050 | − | 0.327792i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.75940 | + | 21.3188i | 0.383678 | + | 1.05415i | 0.969795 | + | 0.243920i | \(0.0784335\pi\) |
−0.586117 | + | 0.810226i | \(0.699344\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.0253648 | + | 3.07588i | −0.00125115 | + | 0.151722i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.0316961 | − | 0.0228971i | 0.00155966 | − | 0.00112669i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.1828 | − | 19.3693i | −0.548944 | − | 0.950799i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −13.3638 | + | 2.24293i | −0.654427 | + | 0.109837i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 21.2332 | + | 17.8168i | 1.03731 | + | 0.870407i | 0.991703 | − | 0.128552i | \(-0.0410329\pi\) |
0.0456084 | + | 0.998959i | \(0.485477\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.8260 | − | 3.94035i | −0.527628 | − | 0.192041i | 0.0644509 | − | 0.997921i | \(-0.479470\pi\) |
−0.592079 | + | 0.805880i | \(0.701693\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −13.1391 | + | 4.53829i | −0.638845 | + | 0.220659i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 63.0126 | + | 22.9347i | 3.05656 | + | 1.11250i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.59292 | + | 5.83007i | 0.415840 | + | 0.282137i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.340441 | − | 1.84179i | 0.0164366 | − | 0.0889225i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.198915 | − | 0.114844i | 0.00958139 | − | 0.00553182i | −0.495202 | − | 0.868778i | \(-0.664906\pi\) |
0.504783 | + | 0.863246i | \(0.331572\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 27.7350i | − | 1.33286i | −0.745568 | − | 0.666429i | \(-0.767822\pi\) | ||
0.745568 | − | 0.666429i | \(-0.232178\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.50899 | − | 1.76852i | 0.0723506 | − | 0.0847942i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.33598 | + | 1.96012i | 0.111745 | + | 0.0937652i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.1419 | − | 38.8545i | 0.674956 | − | 1.85443i | 0.184841 | − | 0.982768i | \(-0.440823\pi\) |
0.490115 | − | 0.871658i | \(-0.336955\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −20.6319 | + | 3.91460i | −0.982472 | + | 0.186410i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.3456 | + | 13.5212i | 0.539045 | + | 0.642409i | 0.964973 | − | 0.262348i | \(-0.0844968\pi\) |
−0.425928 | + | 0.904757i | \(0.640052\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.03834 | − | 51.2590i | 0.428459 | − | 2.42991i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −16.3766 | − | 19.8470i | −0.774586 | − | 0.938729i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.02166 | − | 1.16721i | −0.0954080 | − | 0.0550838i | 0.451537 | − | 0.892252i | \(-0.350876\pi\) |
−0.546945 | + | 0.837169i | \(0.684209\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.91491 | − | 3.41497i | −0.278522 | − | 0.160805i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.8002 | + | 24.3644i | 0.648388 | + | 1.14474i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.6565 | − | 5.16170i | 0.499586 | − | 0.241984i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.544911 | + | 3.09034i | 0.0254899 | + | 0.144560i | 0.994897 | − | 0.100900i | \(-0.0321721\pi\) |
−0.969407 | + | 0.245460i | \(0.921061\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 20.2247 | − | 33.1108i | 0.944010 | − | 1.54548i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.62681 | − | 8.07785i | 0.448365 | − | 0.376223i | −0.390464 | − | 0.920618i | \(-0.627685\pi\) |
0.838829 | + | 0.544395i | \(0.183241\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.81661 | − | 15.9738i | 0.130899 | − | 0.742364i | −0.846729 | − | 0.532024i | \(-0.821432\pi\) |
0.977628 | − | 0.210340i | \(-0.0674573\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −56.5561 | + | 32.0338i | −2.62272 | + | 1.48553i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.1387 | −0.469162 | −0.234581 | − | 0.972097i | \(-0.575372\pi\) | ||||
−0.234581 | + | 0.972097i | \(0.575372\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.49163 | + | 2.01446i | 0.207404 | + | 0.0930193i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.0295097 | + | 0.0790432i | −0.00135974 | + | 0.00364212i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.90803 | + | 0.689092i | 0.179692 | + | 0.0316845i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.11857 | − | 5.82073i | 0.0972068 | − | 0.267074i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 14.3656 | − | 37.5315i | 0.657756 | − | 1.71845i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.3092 | − | 16.2023i | 0.882259 | − | 0.740303i | −0.0843835 | − | 0.996433i | \(-0.526892\pi\) |
0.966642 | + | 0.256130i | \(0.0824476\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.2631 | + | 1.98599i | 0.513555 | + | 0.0905535i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 16.6709 | + | 11.5126i | 0.758551 | + | 0.523843i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.5104 | − | 8.37760i | −0.658884 | − | 0.380407i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.27727 | − | 7.40844i | −0.193821 | − | 0.335709i | 0.752692 | − | 0.658373i | \(-0.228755\pi\) |
−0.946514 | + | 0.322664i | \(0.895422\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.39927 | − | 7.57006i | 0.0632770 | − | 0.342330i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.2025 | + | 30.7785i | 0.505560 | + | 1.38902i | 0.885774 | + | 0.464117i | \(0.153628\pi\) |
−0.380213 | + | 0.924899i | \(0.624149\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.72294 | + | 2.05333i | 0.0775975 | + | 0.0924771i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.38519 | − | 7.86958i | −0.286993 | − | 0.353711i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −20.6232 | + | 21.2400i | −0.925076 | + | 0.952744i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.7319 | − | 4.63403i | 0.569958 | − | 0.207448i | −0.0409339 | − | 0.999162i | \(-0.513033\pi\) |
0.610892 | + | 0.791714i | \(0.290811\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.74517 | + | 3.91545i | −0.211999 | + | 0.174929i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19.3212 | + | 33.4653i | −0.861490 | + | 1.49215i | 0.00899970 | + | 0.999960i | \(0.497135\pi\) |
−0.870490 | + | 0.492186i | \(0.836198\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.46408 | − | 14.6602i | −0.376647 | − | 0.652371i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.87420 | − | 17.4330i | −0.438528 | − | 0.774228i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.0630183 | − | 0.0528786i | −0.00279324 | − | 0.00234380i | 0.641390 | − | 0.767215i | \(-0.278358\pi\) |
−0.644183 | + | 0.764871i | \(0.722803\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −20.5102 | + | 21.1236i | −0.907316 | + | 0.934453i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.05858 | − | 1.86824i | −0.135040 | − | 0.0824849i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −15.0243 | + | 41.2789i | −0.662049 | + | 1.81897i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.12263 | − | 0.726931i | −0.181313 | − | 0.0319704i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.6029 | + | 28.2172i | −0.728788 | + | 1.23860i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.02550 | + | 1.77622i | −0.0449281 | + | 0.0778177i | −0.887615 | − | 0.460586i | \(-0.847639\pi\) |
0.842687 | + | 0.538404i | \(0.180973\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.666771 | − | 0.384961i | 0.0291559 | − | 0.0168332i | −0.485351 | − | 0.874319i | \(-0.661308\pi\) |
0.514507 | + | 0.857486i | \(0.327975\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 10.3934 | − | 39.8200i | 0.453603 | − | 1.73789i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −25.6312 | − | 70.4211i | −1.11651 | − | 3.06759i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.599836 | + | 3.40184i | 0.0260798 | + | 0.147906i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.0443308 | 0.000731184i | 0.00192379 | 3.17307e-5i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.91118 | − | 1.57128i | 0.385986 | − | 0.0680598i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.8004 | + | 17.6384i | −0.639875 | + | 0.762574i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.4703 | + | 43.6201i | 0.667592 | + | 1.88235i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.00390 | − | 1.98697i | −0.258606 | − | 0.0855847i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.6715 | + | 20.2156i | −0.501796 | + | 0.869136i | 0.498202 | + | 0.867061i | \(0.333994\pi\) |
−0.999998 | + | 0.00207506i | \(0.999339\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.30375 | + | 9.73191i | −0.356348 | + | 0.417636i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 20.2361 | − | 7.36535i | 0.866821 | − | 0.315497i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.13973 | − | 29.1488i | −0.219759 | − | 1.24631i | −0.872455 | − | 0.488695i | \(-0.837473\pi\) |
0.652696 | − | 0.757620i | \(-0.273638\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.84406 | + | 11.1292i | 0.164060 | + | 0.474983i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.189674 | − | 0.159155i | 0.00808038 | − | 0.00678025i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 27.0729 | + | 1.96715i | 1.15126 | + | 0.0836515i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 47.7302 | − | 39.3843i | 2.02604 | − | 1.67177i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 24.7683i | − | 1.04947i | −0.851266 | − | 0.524734i | \(-0.824165\pi\) | ||
0.851266 | − | 0.524734i | \(-0.175835\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.55307 | + | 2.62872i | −0.192574 | + | 0.111183i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.1668 | − | 5.75853i | 0.429241 | − | 0.243125i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17.2769 | + | 6.28829i | −0.728136 | + | 0.265020i | −0.679376 | − | 0.733791i | \(-0.737749\pi\) |
−0.0487606 | + | 0.998810i | \(0.515527\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.6107 | − | 2.39993i | 0.572605 | − | 0.100966i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −21.3935 | − | 10.4555i | −0.898444 | − | 0.439089i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.9229 | + | 2.98396i | −0.709444 | + | 0.125094i | −0.516714 | − | 0.856158i | \(-0.672845\pi\) |
−0.192729 | + | 0.981252i | \(0.561734\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.968221 | + | 0.352404i | −0.0405188 | + | 0.0147476i | −0.362200 | − | 0.932100i | \(-0.617974\pi\) |
0.321681 | + | 0.946848i | \(0.395752\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.17982 | − | 1.23467i | 0.0910633 | − | 0.0515789i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −34.3842 | + | 19.8517i | −1.43392 | + | 0.827873i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 39.7208i | − | 1.65360i | −0.562498 | − | 0.826798i | \(-0.690160\pi\) | ||
0.562498 | − | 0.826798i | \(-0.309840\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −23.3055 | + | 19.2304i | −0.968543 | + | 0.799187i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.89891 | − | 14.2431i | −0.286215 | − | 0.590902i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.27087 | − | 7.77919i | 0.383960 | − | 0.322181i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 13.1820 | + | 2.54918i | 0.545009 | + | 0.105396i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.61600 | + | 9.16478i | 0.0666994 | + | 0.378271i | 0.999825 | + | 0.0187199i | \(0.00595907\pi\) |
−0.933125 | + | 0.359551i | \(0.882930\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.50509 | + | 2.36766i | −0.268037 | + | 0.0975577i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.0771 | + | 21.1862i | −0.743594 | + | 0.871485i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.72573 | + | 9.91725i | −0.235127 | + | 0.407253i | −0.959310 | − | 0.282356i | \(-0.908884\pi\) |
0.724182 | + | 0.689609i | \(0.242217\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 67.3989 | + | 30.2279i | 2.76308 | + | 1.23922i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.90407 | + | 5.36874i | 0.0779286 | + | 0.219728i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.34805 | + | 3.99005i | −0.136798 | + | 0.163029i | −0.830094 | − | 0.557624i | \(-0.811713\pi\) |
0.693296 | + | 0.720653i | \(0.256158\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.98265 | − | 1.05490i | 0.244037 | − | 0.0430304i | −0.0502914 | − | 0.998735i | \(-0.516015\pi\) |
0.294329 | + | 0.955704i | \(0.404904\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.71080 | + | 4.87935i | 0.110392 | + | 0.198703i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.61213 | + | 37.4992i | 0.268821 | + | 1.52456i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.0760370 | − | 0.208910i | −0.00308625 | − | 0.00847940i | 0.938140 | − | 0.346256i | \(-0.112547\pi\) |
−0.941226 | + | 0.337777i | \(0.890325\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.15564 | − | 1.17073i | 0.0468290 | − | 0.0474405i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.80308 | − | 2.77306i | 0.194312 | − | 0.112186i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.4222 | + | 24.9801i | −0.582509 | + | 1.00894i | 0.412672 | + | 0.910880i | \(0.364596\pi\) |
−0.995181 | + | 0.0980556i | \(0.968738\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 24.8285 | − | 42.1967i | 1.00118 | − | 1.70154i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.68410 | + | 1.70757i | 0.389867 | + | 0.0687441i | 0.365146 | − | 0.930950i | \(-0.381019\pi\) |
0.0247213 | + | 0.999694i | \(0.492130\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.486578 | − | 1.33686i | 0.0195572 | − | 0.0537330i | −0.929530 | − | 0.368747i | \(-0.879787\pi\) |
0.949087 | + | 0.315014i | \(0.102009\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.32066 | + | 21.7748i | 0.293768 | + | 0.873792i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.00725 | − | 35.7119i | 0.360868 | − | 1.43077i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.23300 | + | 6.90830i | 0.329320 | + | 0.276332i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.531939 | − | 0.939145i | −0.0212436 | − | 0.0375059i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 35.6735 | + | 61.7884i | 1.42240 | + | 2.46366i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.6519 | − | 23.6458i | 0.543473 | − | 0.941323i | −0.455228 | − | 0.890375i | \(-0.650442\pi\) |
0.998701 | − | 0.0509480i | \(-0.0162243\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −33.1197 | + | 27.3285i | −1.31639 | + | 1.08621i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 51.2882 | − | 18.6674i | 2.03531 | − | 0.740793i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.78542 | − | 3.09635i | 0.308469 | − | 0.122682i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −33.1505 | + | 5.28319i | −1.31141 | + | 0.209000i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.18677 | + | 2.60610i | 0.0863724 | + | 0.102935i | 0.807500 | − | 0.589868i | \(-0.200820\pi\) |
−0.721127 | + | 0.692803i | \(0.756376\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.422932 | − | 1.16200i | −0.0166788 | − | 0.0458247i | 0.931074 | − | 0.364831i | \(-0.118873\pi\) |
−0.947753 | + | 0.319006i | \(0.896651\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.17048 | + | 27.9724i | −0.203588 | + | 1.10141i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.766333 | − | 1.32733i | −0.0301277 | − | 0.0521827i | 0.850568 | − | 0.525864i | \(-0.176258\pi\) |
−0.880696 | + | 0.473682i | \(0.842925\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.0115632 | + | 0.00667601i | 0.000453895 | + | 0.000262056i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −41.5565 | + | 19.7073i | −1.62873 | + | 0.772389i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −29.9964 | − | 5.28917i | −1.17385 | − | 0.206981i | −0.447485 | − | 0.894291i | \(-0.647680\pi\) |
−0.726364 | + | 0.687310i | \(0.758791\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.68380 | + | 6.44747i | −0.300231 | + | 0.251924i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −32.9688 | + | 5.25423i | −1.28624 | + | 0.204987i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.70108 | + | 23.9060i | −0.338946 | + | 0.931246i | 0.646748 | + | 0.762703i | \(0.276128\pi\) |
−0.985694 | + | 0.168543i | \(0.946094\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.7559 | + | 5.42310i | 1.19627 | + | 0.210934i | 0.736084 | − | 0.676890i | \(-0.236673\pi\) |
0.460183 | + | 0.887824i | \(0.347784\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.41424 | + | 14.5023i | −0.210272 | + | 0.563222i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.79227 | − | 6.22591i | 0.108280 | − | 0.241430i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.58705 | −0.0614507 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −24.2125 | + | 13.7141i | −0.936108 | + | 0.530218i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.615731 | + | 3.49198i | −0.0237700 | + | 0.134807i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.3263 | − | 17.8949i | 0.822068 | − | 0.689797i | −0.131388 | − | 0.991331i | \(-0.541943\pi\) |
0.953455 | + | 0.301534i | \(0.0974988\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 36.4779 | − | 29.1018i | 1.40404 | − | 1.12013i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.13907 | + | 17.8025i | 0.120644 | + | 0.684207i | 0.983800 | + | 0.179270i | \(0.0573734\pi\) |
−0.863156 | + | 0.504938i | \(0.831515\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.81096 | − | 6.65648i | −0.376510 | − | 0.255452i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.28314 | + | 12.8585i | 0.279091 | + | 0.492738i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.54357 | − | 4.35528i | −0.288647 | − | 0.166650i | 0.348685 | − | 0.937240i | \(-0.386628\pi\) |
−0.637331 | + | 0.770590i | \(0.719962\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.75064 | − | 3.32013i | −0.219721 | − | 0.126856i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.973930 | − | 1.18032i | −0.0371577 | − | 0.0450318i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.78422 | + | 15.7901i | −0.106070 | + | 0.601555i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.1894 | + | 33.5948i | 1.07238 | + | 1.27801i | 0.958678 | + | 0.284493i | \(0.0918252\pi\) |
0.113698 | + | 0.993515i | \(0.463730\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.10272 | − | 5.88130i | −0.155850 | − | 0.223412i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.0049 | − | 27.4884i | 0.379509 | − | 1.04269i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 43.2421 | + | 36.2844i | 1.63791 | + | 1.37437i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.2616 | + | 12.0265i | −0.388130 | + | 0.454884i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 24.2340i | − | 0.915305i | −0.889131 | − | 0.457652i | \(-0.848690\pi\) | ||
0.889131 | − | 0.457652i | \(-0.151310\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.70765 | − | 3.29531i | 0.215268 | − | 0.124285i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.45440 | − | 29.5084i | 0.205425 | − | 1.11135i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.22165 | − | 10.7803i | −0.196380 | − | 0.405435i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.630968 | − | 0.229653i | −0.0236965 | − | 0.00862481i | 0.330145 | − | 0.943930i | \(-0.392902\pi\) |
−0.353841 | + | 0.935306i | \(0.615125\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 23.2484 | + | 20.1703i | 0.871882 | + | 0.756446i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 41.6955 | + | 15.1759i | 1.56151 | + | 0.568343i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.09735 | + | 2.59899i | 0.115834 | + | 0.0971967i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 28.5524 | − | 4.79213i | 1.06631 | − | 0.178965i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.38852 | − | 16.2614i | −0.350133 | − | 0.606448i | 0.636140 | − | 0.771574i | \(-0.280530\pi\) |
−0.986272 | + | 0.165126i | \(0.947197\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.7200 | + | 28.3616i | −0.473717 | + | 1.05624i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.358656 | + | 43.4927i | −0.0133386 | + | 1.61751i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.10260 | + | 3.02937i | 0.0409496 | + | 0.112508i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.400021 | − | 0.476727i | −0.0148360 | − | 0.0176808i | 0.758575 | − | 0.651585i | \(-0.225896\pi\) |
−0.773411 | + | 0.633904i | \(0.781451\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −12.3270 | − | 24.0217i | −0.456557 | − | 0.889694i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −30.8197 | − | 11.2174i | −1.13991 | − | 0.414892i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.4542 | − | 27.9516i | 0.866301 | − | 1.03242i | −0.132846 | − | 0.991137i | \(-0.542412\pi\) |
0.999148 | − | 0.0412808i | \(-0.0131438\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 14.5976 | − | 42.9191i | 0.538442 | − | 1.58309i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.68096i | 0.0619189i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 42.8175 | 1.57507 | 0.787533 | − | 0.616272i | \(-0.211358\pi\) | ||||
0.787533 | + | 0.616272i | \(0.211358\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.33963 | + | 0.500135i | 0.0492127 | + | 0.0183729i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.05809 | + | 9.60326i | −0.295623 | + | 0.352309i | −0.893327 | − | 0.449407i | \(-0.851635\pi\) |
0.597704 | + | 0.801717i | \(0.296080\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 54.7032 | − | 9.64565i | 2.00417 | − | 0.353389i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.40712 | − | 17.6185i | 0.124660 | − | 0.644627i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.3497 | + | 11.6891i | −0.414708 | + | 0.427111i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.85692 | + | 50.2301i | −0.323193 | + | 1.83292i | 0.198884 | + | 0.980023i | \(0.436268\pi\) |
−0.522077 | + | 0.852898i | \(0.674843\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 23.0214 | + | 19.6430i | 0.838945 | + | 0.715830i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −60.4475 | −2.19991 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −46.4934 | −1.68983 | −0.844916 | − | 0.534899i | \(-0.820350\pi\) | ||||
−0.844916 | + | 0.534899i | \(0.820350\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.25746 | + | 6.80291i | −0.0456431 | + | 0.246930i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.42847 | − | 25.1151i | 0.160532 | − | 0.910423i | −0.793020 | − | 0.609195i | \(-0.791493\pi\) |
0.953552 | − | 0.301227i | \(-0.0973963\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.6591 | − | 4.16031i | 0.530695 | − | 0.150613i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 40.6767 | + | 73.2167i | 1.47067 | + | 2.64716i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.0174207 | + | 0.00307174i | −0.000629025 | + | 0.000110914i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.0032 | + | 20.2637i | −0.613153 | + | 0.730727i | −0.979877 | − | 0.199603i | \(-0.936035\pi\) |
0.366724 | + | 0.930330i | \(0.380479\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 30.3890 | − | 25.0753i | 1.09443 | − | 0.903065i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −35.6277 | −1.28144 | −0.640719 | − | 0.767776i | \(-0.721364\pi\) | ||||
−0.640719 | + | 0.767776i | \(0.721364\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 90.1323i | − | 3.23765i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 35.7047 | − | 25.3474i | 1.28090 | − | 0.909333i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.35174 | − | 3.99444i | 0.120088 | − | 0.143116i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.49960 | − | 3.45757i | −0.339922 | − | 0.123722i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.84440 | − | 0.278366i | 0.0659135 | − | 0.00994800i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.117076 | − | 0.139526i | −0.00417862 | − | 0.00497988i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.831887 | + | 2.28559i | 0.0296536 | + | 0.0814725i | 0.953636 | − | 0.300962i | \(-0.0973079\pi\) |
−0.923982 | + | 0.382435i | \(0.875086\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.14186 | + | 2.43706i | 0.147454 | + | 0.0867617i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.72863 | − | 0.995769i | 0.345910 | − | 0.0354055i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.34886 | − | 4.06835i | −0.0834105 | − | 0.144471i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 55.2139 | + | 66.9143i | 1.95824 | + | 2.37321i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28.5314 | + | 23.9407i | 1.01063 | + | 0.848022i | 0.988422 | − | 0.151731i | \(-0.0484849\pi\) |
0.0222113 | + | 0.999753i | \(0.492929\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 32.5120 | + | 11.8334i | 1.15019 | + | 0.418636i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 32.4296 | − | 26.3126i | 1.14585 | − | 0.929712i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.44754 | − | 3.43862i | −0.333396 | − | 0.121346i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −39.3614 | + | 19.0655i | −1.38731 | + | 0.671970i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −15.0200 | − | 12.8158i | −0.528728 | − | 0.451138i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24.4889 | − | 14.1387i | 0.860983 | − | 0.497089i | −0.00335854 | − | 0.999994i | \(-0.501069\pi\) |
0.864341 | + | 0.502906i | \(0.167736\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.7458i | 1.11475i | 0.830262 | + | 0.557373i | \(0.188191\pi\) | ||||
−0.830262 | + | 0.557373i | \(0.811809\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.66813 | − | 1.23255i | −0.233861 | − | 0.0432274i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.7306 | + | 10.6823i | 0.445934 | + | 0.374183i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.03620 | + | 2.84694i | −0.0362521 | + | 0.0996018i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.17232 | + | 2.47502i | 0.320507 | + | 0.0864843i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.21706 | + | 6.21745i | 0.182077 | + | 0.216990i | 0.849361 | − | 0.527813i | \(-0.176988\pi\) |
−0.667284 | + | 0.744803i | \(0.732543\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.81536 | + | 15.9667i | −0.0981374 | + | 0.556565i | 0.895603 | + | 0.444854i | \(0.146744\pi\) |
−0.993741 | + | 0.111711i | \(0.964367\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 13.8591 | − | 2.32606i | 0.482512 | − | 0.0809831i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.0434 | + | 9.26264i | 0.557882 | + | 0.322093i | 0.752295 | − | 0.658826i | \(-0.228947\pi\) |
−0.194413 | + | 0.980920i | \(0.562280\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.8609 | + | 20.7043i | 1.24550 | + | 0.719091i | 0.970209 | − | 0.242269i | \(-0.0778917\pi\) |
0.275293 | + | 0.961360i | \(0.411225\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.76458 | + | 8.09755i | −0.165282 | + | 0.280901i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 46.0159 | + | 24.7892i | 1.59436 | + | 0.858893i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.30616 | − | 13.0789i | −0.0798080 | − | 0.452614i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −51.1187 | − | 10.3235i | −1.76692 | − | 0.356832i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.1062 | + | 8.48015i | −0.348906 | + | 0.292767i | −0.800351 | − | 0.599532i | \(-0.795353\pi\) |
0.451444 | + | 0.892299i | \(0.350909\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.01342 | − | 28.4325i | 0.172877 | − | 0.980432i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.281771 | − | 34.1692i | 0.00970471 | − | 1.17685i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 43.2510 | 1.48788 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.74348 | + | 26.8037i | 0.0942671 | + | 0.920986i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −26.6335 | + | 4.47008i | −0.914060 | + | 0.153413i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −41.6020 | − | 7.33555i | −1.42610 | − | 0.251459i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.0480517 | + | 0.132021i | −0.00164526 | + | 0.00452031i | −0.940513 | − | 0.339759i | \(-0.889654\pi\) |
0.938867 | + | 0.344279i | \(0.111877\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.76333 | − | 3.75747i | 0.231301 | − | 0.128503i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.9549 | − | 9.19226i | 0.374213 | − | 0.314002i | −0.436213 | − | 0.899844i | \(-0.643680\pi\) |
0.810425 | + | 0.585842i | \(0.199236\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −46.2811 | − | 8.16061i | −1.57909 | − | 0.278436i | −0.685757 | − | 0.727831i | \(-0.740529\pi\) |
−0.893334 | + | 0.449394i | \(0.851640\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 19.6862 | − | 28.5067i | 0.670905 | − | 0.971504i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21.8142 | − | 12.5945i | −0.742566 | − | 0.428720i | 0.0804358 | − | 0.996760i | \(-0.474369\pi\) |
−0.823001 | + | 0.568039i | \(0.807702\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −35.3380 | − | 61.2072i | −1.20153 | − | 2.08111i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −63.2635 | + | 22.4370i | −2.14854 | + | 0.762001i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.17019 | + | 8.71002i | 0.107541 | + | 0.295467i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.43150 | − | 1.70600i | −0.0485045 | − | 0.0578055i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.38895 | − | 12.7068i | −0.148543 | − | 0.430059i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 28.2516 | + | 27.4312i | 0.955079 | + | 0.927343i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31.1326 | − | 11.3313i | 1.05127 | − | 0.382632i | 0.242129 | − | 0.970244i | \(-0.422154\pi\) |
0.809143 | + | 0.587612i | \(0.199932\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.56022 | + | 33.1288i | 0.187542 | + | 1.11741i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.5928 | − | 27.0075i | 0.525334 | − | 0.909906i | −0.474230 | − | 0.880401i | \(-0.657274\pi\) |
0.999565 | − | 0.0295048i | \(-0.00939304\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.90147 | − | 11.9537i | −0.232253 | − | 0.402274i | 0.726218 | − | 0.687465i | \(-0.241276\pi\) |
−0.958471 | + | 0.285191i | \(0.907943\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.0485378 | + | 0.0824914i | −0.00163158 | + | 0.00277292i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −26.9343 | − | 22.6006i | −0.904366 | − | 0.758853i | 0.0666726 | − | 0.997775i | \(-0.478762\pi\) |
−0.971039 | + | 0.238921i | \(0.923206\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 37.1533 | − | 10.5442i | 1.24608 | − | 0.353643i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.268151 | − | 8.12663i | 0.00898341 | − | 0.272252i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.09310 | − | 3.00327i | 0.0365792 | − | 0.100500i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −98.3937 | − | 17.3495i | −3.28894 | − | 0.579929i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.51715 | − | 7.97509i | −0.150823 | − | 0.266280i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.80141 | − | 3.12013i | 0.0600804 | − | 0.104062i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −86.6229 | + | 50.0117i | −2.88583 | + | 1.66613i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.08342 | + | 19.4761i | −0.169166 | + | 0.648123i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.44556 | − | 25.9515i | −0.313981 | − | 0.862655i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.33531 | − | 30.2580i | −0.177156 | − | 1.00470i | −0.935626 | − | 0.352993i | \(-0.885164\pi\) |
0.758470 | − | 0.651708i | \(-0.225947\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.57879 | − | 13.3351i | 0.0855329 | − | 0.442298i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.1059 | − | 4.25052i | 0.798664 | − | 0.140826i | 0.240601 | − | 0.970624i | \(-0.422656\pi\) |
0.558064 | + | 0.829798i | \(0.311545\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.47370 | − | 4.13979i | 0.114963 | − | 0.137007i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −24.9945 | − | 4.62003i | −0.826292 | − | 0.152734i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.75338 | + | 4.15621i | −0.189993 | + | 0.137250i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24.4426 | + | 42.3359i | −0.806288 | + | 1.39653i | 0.109130 | + | 0.994028i | \(0.465194\pi\) |
−0.915418 | + | 0.402505i | \(0.868140\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −30.8664 | − | 5.70540i | −1.01708 | − | 0.187999i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.5855 | − | 4.58076i | 0.414258 | − | 0.150778i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.9008 | + | 84.5066i | 0.489935 | + | 2.77856i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −30.8098 | + | 17.1169i | −1.01193 | + | 0.562192i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21.3175 | + | 17.8875i | −0.699404 | + | 0.586870i | −0.921604 | − | 0.388131i | \(-0.873121\pi\) |
0.222200 | + | 0.975001i | \(0.428676\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.28988 | − | 4.25067i | 0.0750476 | − | 0.139310i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.53692 | − | 38.9481i | −0.214009 | − | 1.27510i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 25.2235i | 0.824897i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29.1474 | + | 16.8282i | −0.952202 | + | 0.549754i | −0.893764 | − | 0.448537i | \(-0.851945\pi\) |
−0.0584380 | + | 0.998291i | \(0.518612\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 38.1843 | + | 22.4676i | 1.24610 | + | 0.733202i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.8407 | − | 7.22141i | 0.646787 | − | 0.235411i | 0.00226561 | − | 0.999997i | \(-0.499279\pi\) |
0.644522 | + | 0.764586i | \(0.277057\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −32.9147 | + | 5.80375i | −1.07185 | + | 0.188996i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 42.4002 | − | 29.0611i | 1.37928 | − | 0.945357i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14.9956 | + | 2.64414i | −0.487293 | + | 0.0859228i | −0.411896 | − | 0.911231i | \(-0.635133\pi\) |
−0.0753965 | + | 0.997154i | \(0.524022\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.5166 | − | 4.55566i | 0.406305 | − | 0.147883i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.246752 | + | 29.9225i | −0.00800147 | + | 0.970305i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −24.0655 | + | 13.8942i | −0.779559 | + | 0.450078i | −0.836274 | − | 0.548312i | \(-0.815271\pi\) |
0.0567152 | + | 0.998390i | \(0.481937\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.40808i | 0.175001i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.526253 | + | 0.196470i | 0.0170114 | + | 0.00635097i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.88819 | − | 2.63803i | −0.125556 | − | 0.0851866i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −53.4158 | + | 44.8211i | −1.72309 | + | 1.44584i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −18.2439 | + | 2.90752i | −0.587901 | + | 0.0936936i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −11.3265 | − | 64.2358i | −0.364613 | − | 2.06782i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.6090 | − | 7.13710i | 0.630584 | − | 0.229514i | −0.00690149 | − | 0.999976i | \(-0.502197\pi\) |
0.637485 | + | 0.770462i | \(0.279975\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.98176 | + | 8.40740i | 0.0957881 | + | 0.270085i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.5782 | − | 23.5181i | 0.435745 | − | 0.754733i | −0.561611 | − | 0.827402i | \(-0.689818\pi\) |
0.997356 | + | 0.0726684i | \(0.0231515\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.47047 | − | 18.8865i | 0.271551 | − | 0.605475i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −12.0846 | + | 14.1631i | −0.387018 | + | 0.453581i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11.8599 | + | 14.1341i | −0.379433 | + | 0.452190i | −0.921635 | − | 0.388058i | \(-0.873146\pi\) |
0.542202 | + | 0.840248i | \(0.317591\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.3855 | − | 2.18389i | 0.395841 | − | 0.0697975i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.1366 | + | 6.17649i | 0.515203 | + | 0.197200i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.35199 | + | 36.0239i | 0.202597 | + | 1.14899i | 0.901176 | + | 0.433453i | \(0.142705\pi\) |
−0.698579 | + | 0.715533i | \(0.746184\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.5628 | − | 56.4959i | −0.655186 | − | 1.80011i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.36256 | − | 20.5455i | 0.170692 | − | 0.653971i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.8174 | − | 9.70953i | 0.534762 | − | 0.308745i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.18639 | + | 2.05490i | −0.0376871 | + | 0.0652759i | −0.884254 | − | 0.467007i | \(-0.845332\pi\) |
0.846567 | + | 0.532283i | \(0.178666\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 43.0639 | + | 0.355120i | 1.36659 | + | 0.0112694i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.1102 | − | 2.13536i | −0.383920 | − | 0.0676955i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.75213 | − | 13.0564i | 0.150502 | − | 0.413500i | −0.841415 | − | 0.540389i | \(-0.818277\pi\) |
0.991917 | + | 0.126889i | \(0.0404993\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 49.6348 | + | 1.22814i | 1.57037 | + | 0.0388566i |
(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 | 756.2.ck.a.5.4 | yes | 144 | |
7.3 | odd | 6 | 756.2.ca.a.437.5 | yes | 144 | ||
27.11 | odd | 18 | 756.2.ca.a.173.5 | ✓ | 144 | ||
189.38 | even | 18 | inner | 756.2.ck.a.605.4 | yes | 144 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.2.ca.a.173.5 | ✓ | 144 | 27.11 | odd | 18 | ||
756.2.ca.a.437.5 | yes | 144 | 7.3 | odd | 6 | ||
756.2.ck.a.5.4 | yes | 144 | 1.1 | even | 1 | trivial | |
756.2.ck.a.605.4 | yes | 144 | 189.38 | even | 18 | inner |