Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [361,2,Mod(28,361)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(361, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("361.28");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 361 = 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 361.e (of order \(9\), degree \(6\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.88259951297\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{9})\) |
Coefficient field: | 12.0.6053445140625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4x^{9} + 17x^{6} + 4x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 28.2 | ||
Root | \(0.473442 - 0.397265i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 361.28 |
Dual form | 361.2.e.i.245.2 |
$q$-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 \(\left(\mathbb{Z}/361\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{4}{9}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.107320 | + | 0.608645i | 0.0758870 | + | 0.430377i | 0.998954 | + | 0.0457364i | \(0.0145634\pi\) |
−0.923067 | + | 0.384640i | \(0.874325\pi\) | |||||||
\(3\) | −2.00553 | + | 1.68284i | −1.15789 | + | 0.971588i | −0.999874 | − | 0.0158480i | \(-0.994955\pi\) |
−0.158019 | + | 0.987436i | \(0.550511\pi\) | |||||||
\(4\) | 1.52045 | − | 0.553400i | 0.760227 | − | 0.276700i | ||||
\(5\) | 1.16152 | + | 0.422760i | 0.519449 | + | 0.189064i | 0.588421 | − | 0.808555i | \(-0.299750\pi\) |
−0.0689720 | + | 0.997619i | \(0.521972\pi\) | |||||||
\(6\) | −1.23949 | − | 1.04005i | −0.506018 | − | 0.424600i | ||||
\(7\) | −1.50000 | + | 2.59808i | −0.566947 | + | 0.981981i | 0.429919 | + | 0.902867i | \(0.358542\pi\) |
−0.996866 | + | 0.0791130i | \(0.974791\pi\) | |||||||
\(8\) | 1.11803 | + | 1.93649i | 0.395285 | + | 0.684653i | ||||
\(9\) | 0.669258 | − | 3.79555i | 0.223086 | − | 1.26518i | ||||
\(10\) | −0.132655 | + | 0.752326i | −0.0419493 | + | 0.237906i | ||||
\(11\) | −0.309017 | − | 0.535233i | −0.0931721 | − | 0.161379i | 0.815672 | − | 0.578514i | \(-0.196367\pi\) |
−0.908844 | + | 0.417136i | \(0.863034\pi\) | |||||||
\(12\) | −2.11803 | + | 3.66854i | −0.611424 | + | 1.05902i | ||||
\(13\) | 0.766044 | + | 0.642788i | 0.212463 | + | 0.178277i | 0.742808 | − | 0.669504i | \(-0.233493\pi\) |
−0.530346 | + | 0.847781i | \(0.677938\pi\) | |||||||
\(14\) | −1.74229 | − | 0.634140i | −0.465646 | − | 0.169481i | ||||
\(15\) | −3.04091 | + | 1.10680i | −0.785159 | + | 0.285775i | ||||
\(16\) | 1.42032 | − | 1.19179i | 0.355081 | − | 0.297948i | ||||
\(17\) | 0.909234 | + | 5.15652i | 0.220522 | + | 1.25064i | 0.871064 | + | 0.491170i | \(0.163431\pi\) |
−0.650542 | + | 0.759470i | \(0.725458\pi\) | |||||||
\(18\) | 2.38197 | 0.561435 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 2.00000 | 0.447214 | ||||||||
\(21\) | −1.36385 | − | 7.73478i | −0.297617 | − | 1.68787i | ||||
\(22\) | 0.292603 | − | 0.245523i | 0.0623832 | − | 0.0523457i | ||||
\(23\) | −7.15861 | + | 2.60552i | −1.49267 | + | 0.543289i | −0.954152 | − | 0.299323i | \(-0.903239\pi\) |
−0.538522 | + | 0.842612i | \(0.681017\pi\) | |||||||
\(24\) | −5.50106 | − | 2.00222i | −1.12290 | − | 0.408702i | ||||
\(25\) | −2.65981 | − | 2.23185i | −0.531962 | − | 0.446369i | ||||
\(26\) | −0.309017 | + | 0.535233i | −0.0606032 | + | 0.104968i | ||||
\(27\) | 1.11803 | + | 1.93649i | 0.215166 | + | 0.372678i | ||||
\(28\) | −0.842906 | + | 4.78036i | −0.159294 | + | 0.903403i | ||||
\(29\) | 0.239976 | − | 1.36097i | 0.0445624 | − | 0.252726i | −0.954386 | − | 0.298576i | \(-0.903488\pi\) |
0.998948 | + | 0.0458498i | \(0.0145996\pi\) | |||||||
\(30\) | −1.00000 | − | 1.73205i | −0.182574 | − | 0.316228i | ||||
\(31\) | −1.07295 | + | 1.85840i | −0.192707 | + | 0.333779i | −0.946147 | − | 0.323739i | \(-0.895060\pi\) |
0.753439 | + | 0.657518i | \(0.228393\pi\) | |||||||
\(32\) | 4.30366 | + | 3.61120i | 0.760787 | + | 0.638376i | ||||
\(33\) | 1.52045 | + | 0.553400i | 0.264677 | + | 0.0963346i | ||||
\(34\) | −3.04091 | + | 1.10680i | −0.521512 | + | 0.189815i | ||||
\(35\) | −2.84065 | + | 2.38359i | −0.480157 | + | 0.402900i | ||||
\(36\) | −1.08288 | − | 6.14133i | −0.180480 | − | 1.02355i | ||||
\(37\) | −2.14590 | −0.352783 | −0.176392 | − | 0.984320i | \(-0.556443\pi\) | ||||
−0.176392 | + | 0.984320i | \(0.556443\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.61803 | −0.419221 | ||||||||
\(40\) | 0.479952 | + | 2.72194i | 0.0758870 | + | 0.430377i | ||||
\(41\) | 2.29813 | − | 1.92836i | 0.358908 | − | 0.301160i | −0.445447 | − | 0.895308i | \(-0.646955\pi\) |
0.804355 | + | 0.594149i | \(0.202511\pi\) | |||||||
\(42\) | 4.56136 | − | 1.66020i | 0.703834 | − | 0.256175i | ||||
\(43\) | 6.44075 | + | 2.34424i | 0.982205 | + | 0.357493i | 0.782697 | − | 0.622403i | \(-0.213843\pi\) |
0.199508 | + | 0.979896i | \(0.436066\pi\) | |||||||
\(44\) | −0.766044 | − | 0.642788i | −0.115486 | − | 0.0969039i | ||||
\(45\) | 2.38197 | − | 4.12569i | 0.355083 | − | 0.615021i | ||||
\(46\) | −2.35410 | − | 4.07742i | −0.347093 | − | 0.601183i | ||||
\(47\) | 0.520945 | − | 2.95442i | 0.0759876 | − | 0.430947i | −0.922952 | − | 0.384914i | \(-0.874231\pi\) |
0.998940 | − | 0.0460327i | \(-0.0146579\pi\) | |||||||
\(48\) | −0.842906 | + | 4.78036i | −0.121663 | + | 0.689985i | ||||
\(49\) | −1.00000 | − | 1.73205i | −0.142857 | − | 0.247436i | ||||
\(50\) | 1.07295 | − | 1.85840i | 0.151738 | − | 0.262818i | ||||
\(51\) | −10.5011 | − | 8.81146i | −1.47045 | − | 1.23385i | ||||
\(52\) | 1.52045 | + | 0.553400i | 0.210849 | + | 0.0767428i | ||||
\(53\) | 8.76380 | − | 3.18976i | 1.20380 | − | 0.438147i | 0.339251 | − | 0.940696i | \(-0.389826\pi\) |
0.864549 | + | 0.502548i | \(0.167604\pi\) | |||||||
\(54\) | −1.05865 | + | 0.888311i | −0.144064 | + | 0.120884i | ||||
\(55\) | −0.132655 | − | 0.752326i | −0.0178873 | − | 0.101444i | ||||
\(56\) | −6.70820 | −0.896421 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.854102 | 0.112149 | ||||||||
\(59\) | 2.66137 | + | 15.0934i | 0.346481 | + | 1.96499i | 0.240671 | + | 0.970607i | \(0.422632\pi\) |
0.105810 | + | 0.994386i | \(0.466256\pi\) | |||||||
\(60\) | −4.01106 | + | 3.36568i | −0.517826 | + | 0.434507i | ||||
\(61\) | 5.41632 | − | 1.97138i | 0.693489 | − | 0.252409i | 0.0288608 | − | 0.999583i | \(-0.490812\pi\) |
0.664628 | + | 0.747174i | \(0.268590\pi\) | |||||||
\(62\) | −1.24626 | − | 0.453600i | −0.158275 | − | 0.0576073i | ||||
\(63\) | 8.85724 | + | 7.43211i | 1.11591 | + | 0.936357i | ||||
\(64\) | 0.118034 | − | 0.204441i | 0.0147542 | − | 0.0255551i | ||||
\(65\) | 0.618034 | + | 1.07047i | 0.0766577 | + | 0.132775i | ||||
\(66\) | −0.173648 | + | 0.984808i | −0.0213746 | + | 0.121221i | ||||
\(67\) | 1.21554 | − | 6.89365i | 0.148502 | − | 0.842194i | −0.815987 | − | 0.578070i | \(-0.803806\pi\) |
0.964489 | − | 0.264124i | \(-0.0850828\pi\) | |||||||
\(68\) | 4.23607 | + | 7.33708i | 0.513699 | + | 0.889752i | ||||
\(69\) | 9.97214 | − | 17.2722i | 1.20050 | − | 2.07933i | ||||
\(70\) | −1.75562 | − | 1.47314i | −0.209836 | − | 0.176074i | ||||
\(71\) | 1.38336 | + | 0.503500i | 0.164174 | + | 0.0597545i | 0.422800 | − | 0.906223i | \(-0.361047\pi\) |
−0.258626 | + | 0.965978i | \(0.583270\pi\) | |||||||
\(72\) | 8.09830 | − | 2.94754i | 0.954394 | − | 0.347371i | ||||
\(73\) | 8.20296 | − | 6.88310i | 0.960084 | − | 0.805606i | −0.0208829 | − | 0.999782i | \(-0.506648\pi\) |
0.980967 | + | 0.194176i | \(0.0622033\pi\) | |||||||
\(74\) | −0.230299 | − | 1.30609i | −0.0267717 | − | 0.151830i | ||||
\(75\) | 9.09017 | 1.04964 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.85410 | 0.211295 | ||||||||
\(78\) | −0.280969 | − | 1.59345i | −0.0318134 | − | 0.180423i | ||||
\(79\) | 10.2776 | − | 8.62390i | 1.15632 | − | 0.970265i | 0.156468 | − | 0.987683i | \(-0.449989\pi\) |
0.999848 | + | 0.0174184i | \(0.00554472\pi\) | |||||||
\(80\) | 2.15358 | − | 0.783840i | 0.240778 | − | 0.0876360i | ||||
\(81\) | 5.36396 | + | 1.95232i | 0.595995 | + | 0.216925i | ||||
\(82\) | 1.42032 | + | 1.19179i | 0.156849 | + | 0.131612i | ||||
\(83\) | 0.236068 | − | 0.408882i | 0.0259118 | − | 0.0448806i | −0.852779 | − | 0.522272i | \(-0.825084\pi\) |
0.878691 | + | 0.477392i | \(0.158418\pi\) | |||||||
\(84\) | −6.35410 | − | 11.0056i | −0.693289 | − | 1.20081i | ||||
\(85\) | −1.12387 | + | 6.37381i | −0.121901 | + | 0.691337i | ||||
\(86\) | −0.735585 | + | 4.17171i | −0.0793202 | + | 0.449847i | ||||
\(87\) | 1.80902 | + | 3.13331i | 0.193947 | + | 0.335926i | ||||
\(88\) | 0.690983 | − | 1.19682i | 0.0736590 | − | 0.127581i | ||||
\(89\) | 9.37337 | + | 7.86519i | 0.993575 | + | 0.833709i | 0.986081 | − | 0.166263i | \(-0.0531701\pi\) |
0.00749401 | + | 0.999972i | \(0.497615\pi\) | |||||||
\(90\) | 2.76671 | + | 1.00700i | 0.291637 | + | 0.106147i | ||||
\(91\) | −2.81908 | + | 1.02606i | −0.295520 | + | 0.107560i | ||||
\(92\) | −9.44245 | + | 7.92315i | −0.984443 | + | 0.826046i | ||||
\(93\) | −0.975561 | − | 5.53268i | −0.101161 | − | 0.573713i | ||||
\(94\) | 1.85410 | 0.191236 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −14.7082 | −1.50115 | ||||||||
\(97\) | −1.24087 | − | 7.03734i | −0.125991 | − | 0.714533i | −0.980714 | − | 0.195448i | \(-0.937384\pi\) |
0.854723 | − | 0.519085i | \(-0.173727\pi\) | |||||||
\(98\) | 0.946883 | − | 0.794529i | 0.0956496 | − | 0.0802596i | ||||
\(99\) | −2.23832 | + | 0.814680i | −0.224959 | + | 0.0818785i | ||||
\(100\) | −5.27923 | − | 1.92148i | −0.527923 | − | 0.192148i | ||||
\(101\) | 10.0967 | + | 8.47216i | 1.00466 | + | 0.843011i | 0.987623 | − | 0.156843i | \(-0.0501318\pi\) |
0.0170383 | + | 0.999855i | \(0.494576\pi\) | |||||||
\(102\) | 4.23607 | − | 7.33708i | 0.419433 | − | 0.726480i | ||||
\(103\) | −0.663119 | − | 1.14856i | −0.0653391 | − | 0.113171i | 0.831505 | − | 0.555517i | \(-0.187480\pi\) |
−0.896844 | + | 0.442346i | \(0.854146\pi\) | |||||||
\(104\) | −0.388289 | + | 2.20210i | −0.0380749 | + | 0.215933i | ||||
\(105\) | 1.68581 | − | 9.56071i | 0.164518 | − | 0.933030i | ||||
\(106\) | 2.88197 | + | 4.99171i | 0.279921 | + | 0.484838i | ||||
\(107\) | −5.20820 | + | 9.02087i | −0.503496 | + | 0.872081i | 0.496496 | + | 0.868039i | \(0.334620\pi\) |
−0.999992 | + | 0.00404164i | \(0.998714\pi\) | |||||||
\(108\) | 2.77157 | + | 2.32563i | 0.266695 | + | 0.223784i | ||||
\(109\) | −15.7006 | − | 5.71454i | −1.50384 | − | 0.547354i | −0.546790 | − | 0.837270i | \(-0.684150\pi\) |
−0.957052 | + | 0.289916i | \(0.906373\pi\) | |||||||
\(110\) | 0.443663 | − | 0.161480i | 0.0423016 | − | 0.0153965i | ||||
\(111\) | 4.30366 | − | 3.61120i | 0.408486 | − | 0.342760i | ||||
\(112\) | 0.965884 | + | 5.47780i | 0.0912675 | + | 0.517604i | ||||
\(113\) | −11.2361 | −1.05700 | −0.528500 | − | 0.848933i | \(-0.677245\pi\) | ||||
−0.528500 | + | 0.848933i | \(0.677245\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.41641 | −0.878085 | ||||||||
\(116\) | −0.388289 | − | 2.20210i | −0.0360517 | − | 0.204460i | ||||
\(117\) | 2.95241 | − | 2.47737i | 0.272951 | − | 0.229033i | ||||
\(118\) | −8.90090 | + | 3.23966i | −0.819394 | + | 0.298235i | ||||
\(119\) | −14.7609 | − | 5.37252i | −1.35313 | − | 0.492498i | ||||
\(120\) | −5.54315 | − | 4.65125i | −0.506018 | − | 0.424600i | ||||
\(121\) | 5.30902 | − | 9.19549i | 0.482638 | − | 0.835953i | ||||
\(122\) | 1.78115 | + | 3.08505i | 0.161258 | + | 0.279307i | ||||
\(123\) | −1.36385 | + | 7.73478i | −0.122974 | + | 0.697422i | ||||
\(124\) | −0.602930 | + | 3.41939i | −0.0541447 | + | 0.307070i | ||||
\(125\) | −5.23607 | − | 9.06914i | −0.468328 | − | 0.811168i | ||||
\(126\) | −3.57295 | + | 6.18853i | −0.318304 | + | 0.551318i | ||||
\(127\) | −7.84128 | − | 6.57962i | −0.695801 | − | 0.583847i | 0.224774 | − | 0.974411i | \(-0.427836\pi\) |
−0.920576 | + | 0.390564i | \(0.872280\pi\) | |||||||
\(128\) | 10.6955 | + | 3.89286i | 0.945362 | + | 0.344084i | ||||
\(129\) | −16.8621 | + | 6.13730i | −1.48463 | + | 0.540359i | ||||
\(130\) | −0.585206 | + | 0.491046i | −0.0513260 | + | 0.0430676i | ||||
\(131\) | 0.678935 | + | 3.85043i | 0.0593188 | + | 0.336414i | 0.999996 | − | 0.00288963i | \(-0.000919800\pi\) |
−0.940677 | + | 0.339303i | \(0.889809\pi\) | |||||||
\(132\) | 2.61803 | 0.227871 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 4.32624 | 0.373730 | ||||||||
\(135\) | 0.479952 | + | 2.72194i | 0.0413077 | + | 0.234267i | ||||
\(136\) | −8.96900 | + | 7.52589i | −0.769086 | + | 0.645340i | ||||
\(137\) | 1.38336 | − | 0.503500i | 0.118188 | − | 0.0430169i | −0.282249 | − | 0.959341i | \(-0.591080\pi\) |
0.400437 | + | 0.916324i | \(0.368858\pi\) | |||||||
\(138\) | 11.5829 | + | 4.21582i | 0.986000 | + | 0.358875i | ||||
\(139\) | −7.50599 | − | 6.29827i | −0.636650 | − | 0.534213i | 0.266338 | − | 0.963880i | \(-0.414186\pi\) |
−0.902987 | + | 0.429667i | \(0.858631\pi\) | |||||||
\(140\) | −3.00000 | + | 5.19615i | −0.253546 | + | 0.439155i | ||||
\(141\) | 3.92705 | + | 6.80185i | 0.330717 | + | 0.572819i | ||||
\(142\) | −0.157990 | + | 0.896008i | −0.0132583 | + | 0.0751913i | ||||
\(143\) | 0.107320 | − | 0.608645i | 0.00897459 | − | 0.0508974i | ||||
\(144\) | −3.57295 | − | 6.18853i | −0.297746 | − | 0.515711i | ||||
\(145\) | 0.854102 | − | 1.47935i | 0.0709293 | − | 0.122853i | ||||
\(146\) | 5.06971 | + | 4.25399i | 0.419572 | + | 0.352063i | ||||
\(147\) | 4.92029 | + | 1.79084i | 0.405819 | + | 0.147706i | ||||
\(148\) | −3.26274 | + | 1.18754i | −0.268196 | + | 0.0976152i | ||||
\(149\) | −10.0277 | + | 8.41420i | −0.821497 | + | 0.689318i | −0.953322 | − | 0.301955i | \(-0.902361\pi\) |
0.131825 | + | 0.991273i | \(0.457916\pi\) | |||||||
\(150\) | 0.975561 | + | 5.53268i | 0.0796543 | + | 0.451742i | ||||
\(151\) | 9.90983 | 0.806451 | 0.403225 | − | 0.915101i | \(-0.367889\pi\) | ||||
0.403225 | + | 0.915101i | \(0.367889\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 20.1803 | 1.63148 | ||||||||
\(154\) | 0.198983 | + | 1.12849i | 0.0160345 | + | 0.0909363i | ||||
\(155\) | −2.03191 | + | 1.70498i | −0.163207 | + | 0.136947i | ||||
\(156\) | −3.98060 | + | 1.44882i | −0.318703 | + | 0.115998i | ||||
\(157\) | 10.4737 | + | 3.81212i | 0.835894 | + | 0.304240i | 0.724275 | − | 0.689511i | \(-0.242174\pi\) |
0.111618 | + | 0.993751i | \(0.464397\pi\) | |||||||
\(158\) | 6.35188 | + | 5.32986i | 0.505329 | + | 0.424021i | ||||
\(159\) | −12.2082 | + | 21.1452i | −0.968174 | + | 1.67693i | ||||
\(160\) | 3.47214 | + | 6.01392i | 0.274496 | + | 0.475442i | ||||
\(161\) | 3.96857 | − | 22.5069i | 0.312767 | − | 1.77379i | ||||
\(162\) | −0.612607 | + | 3.47427i | −0.0481310 | + | 0.272964i | ||||
\(163\) | −3.11803 | − | 5.40059i | −0.244223 | − | 0.423007i | 0.717690 | − | 0.696363i | \(-0.245200\pi\) |
−0.961913 | + | 0.273356i | \(0.911866\pi\) | |||||||
\(164\) | 2.42705 | − | 4.20378i | 0.189521 | − | 0.328260i | ||||
\(165\) | 1.53209 | + | 1.28558i | 0.119273 | + | 0.100082i | ||||
\(166\) | 0.274199 | + | 0.0998001i | 0.0212819 | + | 0.00774599i | ||||
\(167\) | 14.8133 | − | 5.39158i | 1.14628 | − | 0.417213i | 0.302105 | − | 0.953275i | \(-0.402311\pi\) |
0.844179 | + | 0.536062i | \(0.180089\pi\) | |||||||
\(168\) | 13.4535 | − | 11.2888i | 1.03796 | − | 0.870952i | ||||
\(169\) | −2.08378 | − | 11.8177i | −0.160291 | − | 0.909053i | ||||
\(170\) | −4.00000 | −0.306786 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 11.0902 | 0.845618 | ||||||||
\(173\) | −1.47117 | − | 8.34343i | −0.111851 | − | 0.634339i | −0.988261 | − | 0.152773i | \(-0.951180\pi\) |
0.876410 | − | 0.481565i | \(-0.159932\pi\) | |||||||
\(174\) | −1.71293 | + | 1.43732i | −0.129857 | + | 0.108963i | ||||
\(175\) | 9.78822 | − | 3.56262i | 0.739920 | − | 0.269309i | ||||
\(176\) | −1.07679 | − | 0.391920i | −0.0811662 | − | 0.0295421i | ||||
\(177\) | −30.7372 | − | 25.7916i | −2.31035 | − | 1.93862i | ||||
\(178\) | −3.78115 | + | 6.54915i | −0.283409 | + | 0.490879i | ||||
\(179\) | 3.88197 | + | 6.72376i | 0.290152 | + | 0.502558i | 0.973845 | − | 0.227212i | \(-0.0729609\pi\) |
−0.683694 | + | 0.729769i | \(0.739628\pi\) | |||||||
\(180\) | 1.33852 | − | 7.59110i | 0.0997671 | − | 0.565807i | ||||
\(181\) | −2.08378 | + | 11.8177i | −0.154886 | + | 0.878402i | 0.804004 | + | 0.594624i | \(0.202699\pi\) |
−0.958890 | + | 0.283778i | \(0.908412\pi\) | |||||||
\(182\) | −0.927051 | − | 1.60570i | −0.0687176 | − | 0.119022i | ||||
\(183\) | −7.54508 | + | 13.0685i | −0.557749 | + | 0.966049i | ||||
\(184\) | −13.0491 | − | 10.9495i | −0.961995 | − | 0.807210i | ||||
\(185\) | −2.49251 | − | 0.907200i | −0.183253 | − | 0.0666987i | ||||
\(186\) | 3.26274 | − | 1.18754i | 0.239236 | − | 0.0870747i | ||||
\(187\) | 2.47897 | − | 2.08010i | 0.181280 | − | 0.152112i | ||||
\(188\) | −0.842906 | − | 4.78036i | −0.0614752 | − | 0.348643i | ||||
\(189\) | −6.70820 | −0.487950 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.76393 | 0.706493 | 0.353247 | − | 0.935530i | \(-0.385078\pi\) | ||||
0.353247 | + | 0.935530i | \(0.385078\pi\) | |||||||
\(192\) | 0.107320 | + | 0.608645i | 0.00774519 | + | 0.0439251i | ||||
\(193\) | −17.5763 | + | 14.7483i | −1.26517 | + | 1.06161i | −0.270061 | + | 0.962843i | \(0.587044\pi\) |
−0.995111 | + | 0.0987622i | \(0.968512\pi\) | |||||||
\(194\) | 4.15007 | − | 1.51050i | 0.297957 | − | 0.108448i | ||||
\(195\) | −3.04091 | − | 1.10680i | −0.217764 | − | 0.0792596i | ||||
\(196\) | −2.47897 | − | 2.08010i | −0.177069 | − | 0.148579i | ||||
\(197\) | −1.50000 | + | 2.59808i | −0.106871 | + | 0.185105i | −0.914501 | − | 0.404584i | \(-0.867416\pi\) |
0.807630 | + | 0.589689i | \(0.200750\pi\) | |||||||
\(198\) | −0.736068 | − | 1.27491i | −0.0523101 | − | 0.0906037i | ||||
\(199\) | 2.32973 | − | 13.2126i | 0.165151 | − | 0.936615i | −0.783759 | − | 0.621066i | \(-0.786700\pi\) |
0.948909 | − | 0.315550i | \(-0.102189\pi\) | |||||||
\(200\) | 1.34819 | − | 7.64598i | 0.0953316 | − | 0.540652i | ||||
\(201\) | 9.16312 | + | 15.8710i | 0.646317 | + | 1.11945i | ||||
\(202\) | −4.07295 | + | 7.05455i | −0.286572 | + | 0.496357i | ||||
\(203\) | 3.17594 | + | 2.66493i | 0.222907 | + | 0.187042i | ||||
\(204\) | −20.8427 | − | 7.58612i | −1.45928 | − | 0.531135i | ||||
\(205\) | 3.48457 | − | 1.26828i | 0.243373 | − | 0.0885805i | ||||
\(206\) | 0.627896 | − | 0.526867i | 0.0437476 | − | 0.0367086i | ||||
\(207\) | 5.09843 | + | 28.9146i | 0.354365 | + | 2.00971i | ||||
\(208\) | 1.85410 | 0.128559 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 6.00000 | 0.414039 | ||||||||
\(211\) | −0.495610 | − | 2.81074i | −0.0341192 | − | 0.193499i | 0.962984 | − | 0.269558i | \(-0.0868776\pi\) |
−0.997103 | + | 0.0760584i | \(0.975766\pi\) | |||||||
\(212\) | 11.5597 | − | 9.69977i | 0.793926 | − | 0.666183i | ||||
\(213\) | −3.62167 | + | 1.31818i | −0.248153 | + | 0.0903202i | ||||
\(214\) | −6.04945 | − | 2.20182i | −0.413532 | − | 0.150513i | ||||
\(215\) | 6.49003 | + | 5.44578i | 0.442617 | + | 0.371399i | ||||
\(216\) | −2.50000 | + | 4.33013i | −0.170103 | + | 0.294628i | ||||
\(217\) | −3.21885 | − | 5.57521i | −0.218510 | − | 0.378470i | ||||
\(218\) | 1.79313 | − | 10.1694i | 0.121446 | − | 0.688756i | ||||
\(219\) | −4.86813 | + | 27.6085i | −0.328958 | + | 1.86561i | ||||
\(220\) | −0.618034 | − | 1.07047i | −0.0416678 | − | 0.0721708i | ||||
\(221\) | −2.61803 | + | 4.53457i | −0.176108 | + | 0.305028i | ||||
\(222\) | 2.65981 | + | 2.23185i | 0.178515 | + | 0.149792i | ||||
\(223\) | 18.4673 | + | 6.72154i | 1.23666 | + | 0.450108i | 0.875874 | − | 0.482540i | \(-0.160286\pi\) |
0.360787 | + | 0.932648i | \(0.382508\pi\) | |||||||
\(224\) | −15.8377 | + | 5.76444i | −1.05820 | + | 0.385153i | ||||
\(225\) | −10.2512 | + | 8.60176i | −0.683412 | + | 0.573451i | ||||
\(226\) | −1.20586 | − | 6.83877i | −0.0802126 | − | 0.454908i | ||||
\(227\) | 10.4164 | 0.691361 | 0.345681 | − | 0.938352i | \(-0.387648\pi\) | ||||
0.345681 | + | 0.938352i | \(0.387648\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.3820 | −0.752141 | −0.376071 | − | 0.926591i | \(-0.622725\pi\) | ||||
−0.376071 | + | 0.926591i | \(0.622725\pi\) | |||||||
\(230\) | −1.01057 | − | 5.73125i | −0.0666352 | − | 0.377907i | ||||
\(231\) | −3.71846 | + | 3.12016i | −0.244657 | + | 0.205291i | ||||
\(232\) | 2.90381 | − | 1.05690i | 0.190644 | − | 0.0693889i | ||||
\(233\) | −12.6597 | − | 4.60774i | −0.829362 | − | 0.301863i | −0.107765 | − | 0.994176i | \(-0.534369\pi\) |
−0.721597 | + | 0.692313i | \(0.756592\pi\) | |||||||
\(234\) | 1.82469 | + | 1.53110i | 0.119284 | + | 0.100091i | ||||
\(235\) | 1.85410 | − | 3.21140i | 0.120948 | − | 0.209489i | ||||
\(236\) | 12.3992 | + | 21.4760i | 0.807118 | + | 1.39797i | ||||
\(237\) | −6.09932 | + | 34.5910i | −0.396194 | + | 2.24693i | ||||
\(238\) | 1.68581 | − | 9.56071i | 0.109275 | − | 0.619729i | ||||
\(239\) | −7.66312 | − | 13.2729i | −0.495686 | − | 0.858553i | 0.504302 | − | 0.863528i | \(-0.331750\pi\) |
−0.999988 | + | 0.00497428i | \(0.998417\pi\) | |||||||
\(240\) | −3.00000 | + | 5.19615i | −0.193649 | + | 0.335410i | ||||
\(241\) | 14.6930 | + | 12.3289i | 0.946459 | + | 0.794173i | 0.978698 | − | 0.205307i | \(-0.0658193\pi\) |
−0.0322388 | + | 0.999480i | \(0.510264\pi\) | |||||||
\(242\) | 6.16655 | + | 2.24444i | 0.396401 | + | 0.144278i | ||||
\(243\) | −20.3467 | + | 7.40558i | −1.30524 | + | 0.475068i | ||||
\(244\) | 7.14431 | − | 5.99479i | 0.457368 | − | 0.383777i | ||||
\(245\) | −0.429282 | − | 2.43458i | −0.0274258 | − | 0.155540i | ||||
\(246\) | −4.85410 | −0.309486 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −4.79837 | −0.304697 | ||||||||
\(249\) | 0.214641 | + | 1.21729i | 0.0136023 | + | 0.0771426i | ||||
\(250\) | 4.95794 | − | 4.16021i | 0.313568 | − | 0.263115i | ||||
\(251\) | −18.1931 | + | 6.62174i | −1.14834 | + | 0.417961i | −0.844918 | − | 0.534896i | \(-0.820351\pi\) |
−0.303420 | + | 0.952857i | \(0.598128\pi\) | |||||||
\(252\) | 17.5800 | + | 6.39858i | 1.10743 | + | 0.403073i | ||||
\(253\) | 3.60669 | + | 3.02638i | 0.226751 | + | 0.190267i | ||||
\(254\) | 3.16312 | − | 5.47868i | 0.198472 | − | 0.343763i | ||||
\(255\) | −8.47214 | − | 14.6742i | −0.530546 | − | 0.918932i | ||||
\(256\) | −1.13953 | + | 6.46261i | −0.0712208 | + | 0.403913i | ||||
\(257\) | 4.23019 | − | 23.9906i | 0.263872 | − | 1.49649i | −0.508357 | − | 0.861147i | \(-0.669747\pi\) |
0.772228 | − | 0.635345i | \(-0.219142\pi\) | |||||||
\(258\) | −5.54508 | − | 9.60437i | −0.345222 | − | 0.597942i | ||||
\(259\) | 3.21885 | − | 5.57521i | 0.200009 | − | 0.346426i | ||||
\(260\) | 1.53209 | + | 1.28558i | 0.0950161 | + | 0.0797280i | ||||
\(261\) | −5.00503 | − | 1.82168i | −0.309803 | − | 0.112759i | ||||
\(262\) | −2.27068 | + | 0.826460i | −0.140283 | + | 0.0510589i | ||||
\(263\) | 2.25544 | − | 1.89254i | 0.139077 | − | 0.116699i | −0.570595 | − | 0.821231i | \(-0.693288\pi\) |
0.709672 | + | 0.704532i | \(0.248843\pi\) | |||||||
\(264\) | 0.628265 | + | 3.56307i | 0.0386670 | + | 0.219292i | ||||
\(265\) | 11.5279 | 0.708151 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −32.0344 | −1.96048 | ||||||||
\(268\) | −1.96678 | − | 11.1542i | −0.120140 | − | 0.681349i | ||||
\(269\) | −11.2408 | + | 9.43211i | −0.685361 | + | 0.575086i | −0.917567 | − | 0.397580i | \(-0.869850\pi\) |
0.232206 | + | 0.972667i | \(0.425406\pi\) | |||||||
\(270\) | −1.60519 | + | 0.584240i | −0.0976885 | + | 0.0355557i | ||||
\(271\) | −7.38044 | − | 2.68626i | −0.448330 | − | 0.163179i | 0.107981 | − | 0.994153i | \(-0.465561\pi\) |
−0.556311 | + | 0.830974i | \(0.687784\pi\) | |||||||
\(272\) | 7.43692 | + | 6.24031i | 0.450929 | + | 0.378375i | ||||
\(273\) | 3.92705 | − | 6.80185i | 0.237676 | − | 0.411667i | ||||
\(274\) | 0.454915 | + | 0.787936i | 0.0274824 | + | 0.0476010i | ||||
\(275\) | −0.372631 | + | 2.11330i | −0.0224705 | + | 0.127437i | ||||
\(276\) | 5.60372 | − | 31.7802i | 0.337304 | − | 1.91295i | ||||
\(277\) | 7.70820 | + | 13.3510i | 0.463141 | + | 0.802184i | 0.999115 | − | 0.0420503i | \(-0.0133890\pi\) |
−0.535974 | + | 0.844234i | \(0.680056\pi\) | |||||||
\(278\) | 3.02786 | − | 5.24441i | 0.181599 | − | 0.314539i | ||||
\(279\) | 6.33558 | + | 5.31618i | 0.379301 | + | 0.318271i | ||||
\(280\) | −7.79174 | − | 2.83596i | −0.465646 | − | 0.169481i | ||||
\(281\) | 7.99357 | − | 2.90942i | 0.476856 | − | 0.173562i | −0.0923994 | − | 0.995722i | \(-0.529454\pi\) |
0.569256 | + | 0.822161i | \(0.307231\pi\) | |||||||
\(282\) | −3.71846 | + | 3.12016i | −0.221431 | + | 0.185803i | ||||
\(283\) | −0.526925 | − | 2.98834i | −0.0313225 | − | 0.177638i | 0.965133 | − | 0.261760i | \(-0.0843028\pi\) |
−0.996456 | + | 0.0841213i | \(0.973192\pi\) | |||||||
\(284\) | 2.38197 | 0.141344 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.381966 | 0.0225861 | ||||||||
\(287\) | 1.56283 | + | 8.86327i | 0.0922512 | + | 0.523182i | ||||
\(288\) | 16.5868 | − | 13.9179i | 0.977384 | − | 0.820123i | ||||
\(289\) | −9.78822 | + | 3.56262i | −0.575778 | + | 0.209566i | ||||
\(290\) | 0.992060 | + | 0.361080i | 0.0582558 | + | 0.0212034i | ||||
\(291\) | 14.3313 | + | 12.0254i | 0.840117 | + | 0.704942i | ||||
\(292\) | 8.66312 | − | 15.0050i | 0.506971 | − | 0.878099i | ||||
\(293\) | −8.42705 | − | 14.5961i | −0.492314 | − | 0.852712i | 0.507647 | − | 0.861565i | \(-0.330515\pi\) |
−0.999961 | + | 0.00885289i | \(0.997182\pi\) | |||||||
\(294\) | −0.561937 | + | 3.18690i | −0.0327728 | + | 0.185864i | ||||
\(295\) | −3.28964 | + | 18.6565i | −0.191530 | + | 1.08622i | ||||
\(296\) | −2.39919 | − | 4.15551i | −0.139450 | − | 0.241534i | ||||
\(297\) | 0.690983 | − | 1.19682i | 0.0400949 | − | 0.0694464i | ||||
\(298\) | −6.19743 | − | 5.20026i | −0.359007 | − | 0.301243i | ||||
\(299\) | −7.15861 | − | 2.60552i | −0.413993 | − | 0.150681i | ||||
\(300\) | 13.8212 | − | 5.03050i | 0.797967 | − | 0.290436i | ||||
\(301\) | −15.7516 | + | 13.2172i | −0.907909 | + | 0.761826i | ||||
\(302\) | 1.06353 | + | 6.03157i | 0.0611991 | + | 0.347078i | ||||
\(303\) | −34.5066 | −1.98235 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.12461 | 0.407954 | ||||||||
\(306\) | 2.16576 | + | 12.2827i | 0.123808 | + | 0.702153i | ||||
\(307\) | 1.28218 | − | 1.07587i | 0.0731777 | − | 0.0614033i | −0.605465 | − | 0.795872i | \(-0.707013\pi\) |
0.678643 | + | 0.734468i | \(0.262568\pi\) | |||||||
\(308\) | 2.81908 | − | 1.02606i | 0.160632 | − | 0.0584652i | ||||
\(309\) | 3.26274 | + | 1.18754i | 0.185611 | + | 0.0675568i | ||||
\(310\) | −1.25579 | − | 1.05373i | −0.0713242 | − | 0.0598481i | ||||
\(311\) | 9.32624 | − | 16.1535i | 0.528842 | − | 0.915982i | −0.470592 | − | 0.882351i | \(-0.655960\pi\) |
0.999434 | − | 0.0336310i | \(-0.0107071\pi\) | |||||||
\(312\) | −2.92705 | − | 5.06980i | −0.165712 | − | 0.287021i | ||||
\(313\) | 0.751243 | − | 4.26051i | 0.0424628 | − | 0.240818i | −0.956188 | − | 0.292755i | \(-0.905428\pi\) |
0.998650 | + | 0.0519361i | \(0.0165392\pi\) | |||||||
\(314\) | −1.19618 | + | 6.78389i | −0.0675045 | + | 0.382837i | ||||
\(315\) | 7.14590 | + | 12.3771i | 0.402626 | + | 0.697368i | ||||
\(316\) | 10.8541 | − | 18.7999i | 0.610591 | − | 1.05757i | ||||
\(317\) | −13.7888 | − | 11.5702i | −0.774456 | − | 0.649846i | 0.167390 | − | 0.985891i | \(-0.446466\pi\) |
−0.941846 | + | 0.336045i | \(0.890911\pi\) | |||||||
\(318\) | −14.1801 | − | 5.16114i | −0.795182 | − | 0.289422i | ||||
\(319\) | −0.802593 | + | 0.292120i | −0.0449366 | + | 0.0163556i | ||||
\(320\) | 0.223529 | − | 0.187563i | 0.0124956 | − | 0.0104851i | ||||
\(321\) | −4.73547 | − | 26.8562i | −0.264308 | − | 1.49897i | ||||
\(322\) | 14.1246 | 0.787134 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 9.23607 | 0.513115 | ||||||||
\(325\) | −0.602930 | − | 3.41939i | −0.0334445 | − | 0.189673i | ||||
\(326\) | 2.95241 | − | 2.47737i | 0.163519 | − | 0.137209i | ||||
\(327\) | 41.1046 | − | 14.9609i | 2.27309 | − | 0.827338i | ||||
\(328\) | 6.30365 | + | 2.29434i | 0.348061 | + | 0.126684i | ||||
\(329\) | 6.89440 | + | 5.78509i | 0.380101 | + | 0.318942i | ||||
\(330\) | −0.618034 | + | 1.07047i | −0.0340217 | + | 0.0589272i | ||||
\(331\) | −3.47214 | − | 6.01392i | −0.190846 | − | 0.330555i | 0.754685 | − | 0.656087i | \(-0.227790\pi\) |
−0.945531 | + | 0.325533i | \(0.894456\pi\) | |||||||
\(332\) | 0.132655 | − | 0.752326i | 0.00728041 | − | 0.0412893i | ||||
\(333\) | −1.43616 | + | 8.14486i | −0.0787010 | + | 0.446336i | ||||
\(334\) | 4.87132 | + | 8.43738i | 0.266547 | + | 0.461673i | ||||
\(335\) | 4.32624 | − | 7.49326i | 0.236368 | − | 0.409401i | ||||
\(336\) | −11.1554 | − | 9.36047i | −0.608576 | − | 0.510655i | ||||
\(337\) | 21.7300 | + | 7.90908i | 1.18371 | + | 0.430835i | 0.857511 | − | 0.514466i | \(-0.172010\pi\) |
0.326199 | + | 0.945301i | \(0.394232\pi\) | |||||||
\(338\) | 6.96914 | − | 2.53656i | 0.379071 | − | 0.137971i | ||||
\(339\) | 22.5343 | − | 18.9085i | 1.22389 | − | 1.02697i | ||||
\(340\) | 1.81847 | + | 10.3130i | 0.0986202 | + | 0.559303i | ||||
\(341\) | 1.32624 | 0.0718198 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.0000 | −0.809924 | ||||||||
\(344\) | 2.66137 | + | 15.0934i | 0.143492 | + | 0.813781i | ||||
\(345\) | 18.8849 | − | 15.8463i | 1.01673 | − | 0.853136i | ||||
\(346\) | 4.92029 | − | 1.79084i | 0.264517 | − | 0.0962762i | ||||
\(347\) | −1.33099 | − | 0.484440i | −0.0714512 | − | 0.0260061i | 0.306047 | − | 0.952016i | \(-0.400993\pi\) |
−0.377498 | + | 0.926010i | \(0.623216\pi\) | |||||||
\(348\) | 4.48450 | + | 3.76294i | 0.240395 | + | 0.201715i | ||||
\(349\) | −12.9894 | + | 22.4982i | −0.695304 | + | 1.20430i | 0.274774 | + | 0.961509i | \(0.411397\pi\) |
−0.970078 | + | 0.242793i | \(0.921936\pi\) | |||||||
\(350\) | 3.21885 | + | 5.57521i | 0.172055 | + | 0.298007i | ||||
\(351\) | −0.388289 | + | 2.20210i | −0.0207253 | + | 0.117539i | ||||
\(352\) | 0.602930 | − | 3.41939i | 0.0321363 | − | 0.182254i | ||||
\(353\) | 15.7254 | + | 27.2372i | 0.836980 | + | 1.44969i | 0.892408 | + | 0.451229i | \(0.149014\pi\) |
−0.0554283 | + | 0.998463i | \(0.517652\pi\) | |||||||
\(354\) | 12.3992 | − | 21.4760i | 0.659009 | − | 1.14144i | ||||
\(355\) | 1.39394 | + | 1.16965i | 0.0739827 | + | 0.0620788i | ||||
\(356\) | 18.6044 | + | 6.77144i | 0.986030 | + | 0.358886i | ||||
\(357\) | 38.6445 | − | 14.0654i | 2.04528 | − | 0.744422i | ||||
\(358\) | −3.67577 | + | 3.08434i | −0.194270 | + | 0.163012i | ||||
\(359\) | −3.82624 | − | 21.6997i | −0.201941 | − | 1.14527i | −0.902181 | − | 0.431358i | \(-0.858035\pi\) |
0.700240 | − | 0.713908i | \(-0.253076\pi\) | |||||||
\(360\) | 10.6525 | 0.561435 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −7.41641 | −0.389798 | ||||||||
\(363\) | 4.82714 | + | 27.3761i | 0.253359 | + | 1.43687i | ||||
\(364\) | −3.71846 | + | 3.12016i | −0.194900 | + | 0.163541i | ||||
\(365\) | 12.4378 | − | 4.52700i | 0.651026 | − | 0.236954i | ||||
\(366\) | −8.76380 | − | 3.18976i | −0.458091 | − | 0.166731i | ||||
\(367\) | 1.48940 | + | 1.24975i | 0.0777460 | + | 0.0652366i | 0.680832 | − | 0.732439i | \(-0.261618\pi\) |
−0.603086 | + | 0.797676i | \(0.706063\pi\) | |||||||
\(368\) | −7.06231 | + | 12.2323i | −0.368148 | + | 0.637651i | ||||
\(369\) | −5.78115 | − | 10.0133i | −0.300955 | − | 0.521269i | ||||
\(370\) | 0.284665 | − | 1.61442i | 0.0147990 | − | 0.0839295i | ||||
\(371\) | −4.85845 | + | 27.5537i | −0.252238 | + | 1.43051i | ||||
\(372\) | −4.54508 | − | 7.87232i | −0.235652 | − | 0.408161i | ||||
\(373\) | 1.73607 | − | 3.00696i | 0.0898902 | − | 0.155694i | −0.817574 | − | 0.575823i | \(-0.804682\pi\) |
0.907465 | + | 0.420129i | \(0.138015\pi\) | |||||||
\(374\) | 1.53209 | + | 1.28558i | 0.0792224 | + | 0.0664755i | ||||
\(375\) | 25.7630 | + | 9.37696i | 1.33040 | + | 0.484224i | ||||
\(376\) | 6.30365 | − | 2.29434i | 0.325086 | − | 0.118322i | ||||
\(377\) | 1.05865 | − | 0.888311i | 0.0545231 | − | 0.0457503i | ||||
\(378\) | −0.719928 | − | 4.08291i | −0.0370291 | − | 0.210002i | ||||
\(379\) | −25.1246 | −1.29056 | −0.645282 | − | 0.763944i | \(-0.723260\pi\) | ||||
−0.645282 | + | 0.763944i | \(0.723260\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 26.7984 | 1.37292 | ||||||||
\(382\) | 1.04787 | + | 5.94277i | 0.0536137 | + | 0.304058i | ||||
\(383\) | −2.00553 | + | 1.68284i | −0.102478 | + | 0.0859891i | −0.692587 | − | 0.721334i | \(-0.743529\pi\) |
0.590109 | + | 0.807323i | \(0.299085\pi\) | |||||||
\(384\) | −28.0013 | + | 10.1916i | −1.42894 | + | 0.520090i | ||||
\(385\) | 2.15358 | + | 0.783840i | 0.109757 | + | 0.0399482i | ||||
\(386\) | −10.8628 | − | 9.11495i | −0.552900 | − | 0.463939i | ||||
\(387\) | 13.2082 | − | 22.8773i | 0.671411 | − | 1.16292i | ||||
\(388\) | −5.78115 | − | 10.0133i | −0.293494 | − | 0.508346i | ||||
\(389\) | −4.21453 | + | 23.9018i | −0.213685 | + | 1.21187i | 0.669488 | + | 0.742822i | \(0.266513\pi\) |
−0.883174 | + | 0.469046i | \(0.844598\pi\) | |||||||
\(390\) | 0.347296 | − | 1.96962i | 0.0175860 | − | 0.0997354i | ||||
\(391\) | −19.9443 | − | 34.5445i | −1.00863 | − | 1.74699i | ||||
\(392\) | 2.23607 | − | 3.87298i | 0.112938 | − | 0.195615i | ||||
\(393\) | −7.84128 | − | 6.57962i | −0.395540 | − | 0.331898i | ||||
\(394\) | −1.74229 | − | 0.634140i | −0.0877751 | − | 0.0319475i | ||||
\(395\) | 15.5835 | − | 5.67192i | 0.784090 | − | 0.285385i | ||||
\(396\) | −2.95241 | + | 2.47737i | −0.148364 | + | 0.124492i | ||||
\(397\) | −0.438959 | − | 2.48946i | −0.0220307 | − | 0.124942i | 0.971809 | − | 0.235770i | \(-0.0757611\pi\) |
−0.993840 | + | 0.110827i | \(0.964650\pi\) | |||||||
\(398\) | 8.29180 | 0.415630 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.43769 | −0.321885 | ||||||||
\(401\) | 0.0193542 | + | 0.109763i | 0.000966501 | + | 0.00548130i | 0.985287 | − | 0.170907i | \(-0.0546697\pi\) |
−0.984321 | + | 0.176388i | \(0.943559\pi\) | |||||||
\(402\) | −8.67640 | + | 7.28037i | −0.432740 | + | 0.363112i | ||||
\(403\) | −2.01648 | + | 0.733940i | −0.100448 | + | 0.0365602i | ||||
\(404\) | 20.0401 | + | 7.29400i | 0.997033 | + | 0.362890i | ||||
\(405\) | 5.40500 | + | 4.53533i | 0.268577 | + | 0.225363i | ||||
\(406\) | −1.28115 | + | 2.21902i | −0.0635826 | + | 0.110128i | ||||
\(407\) | 0.663119 | + | 1.14856i | 0.0328696 | + | 0.0569318i | ||||
\(408\) | 5.32275 | − | 30.1868i | 0.263515 | − | 1.49447i | ||||
\(409\) | 3.76959 | − | 21.3784i | 0.186394 | − | 1.05709i | −0.737757 | − | 0.675067i | \(-0.764115\pi\) |
0.924151 | − | 0.382028i | \(-0.124774\pi\) | |||||||
\(410\) | 1.14590 | + | 1.98475i | 0.0565919 | + | 0.0980200i | ||||
\(411\) | −1.92705 | + | 3.33775i | −0.0950544 | + | 0.164639i | ||||
\(412\) | −1.64385 | − | 1.37936i | −0.0809868 | − | 0.0679560i | ||||
\(413\) | −43.2059 | − | 15.7256i | −2.12602 | − | 0.773808i | ||||
\(414\) | −17.0516 | + | 6.20626i | −0.838039 | + | 0.305021i | ||||
\(415\) | 0.447058 | − | 0.375126i | 0.0219452 | − | 0.0184142i | ||||
\(416\) | 0.975561 | + | 5.53268i | 0.0478308 | + | 0.271262i | ||||
\(417\) | 25.6525 | 1.25621 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.94427 | 0.436956 | 0.218478 | − | 0.975842i | \(-0.429891\pi\) | ||||
0.218478 | + | 0.975842i | \(0.429891\pi\) | |||||||
\(420\) | −2.72770 | − | 15.4696i | −0.133098 | − | 0.754837i | ||||
\(421\) | 14.1932 | − | 11.9095i | 0.691733 | − | 0.580433i | −0.227676 | − | 0.973737i | \(-0.573113\pi\) |
0.919408 | + | 0.393304i | \(0.128668\pi\) | |||||||
\(422\) | 1.65755 | − | 0.603300i | 0.0806885 | − | 0.0293682i | ||||
\(423\) | −10.8650 | − | 3.95454i | −0.528275 | − | 0.192276i | ||||
\(424\) | 15.9752 | + | 13.4048i | 0.775823 | + | 0.650993i | ||||
\(425\) | 9.09017 | − | 15.7446i | 0.440938 | − | 0.763727i | ||||
\(426\) | −1.19098 | − | 2.06284i | −0.0577033 | − | 0.0999451i | ||||
\(427\) | −3.00269 | + | 17.0291i | −0.145310 | + | 0.824096i | ||||
\(428\) | −2.92668 | + | 16.5981i | −0.141467 | + | 0.802297i | ||||
\(429\) | 0.809017 | + | 1.40126i | 0.0390597 | + | 0.0676534i | ||||
\(430\) | −2.61803 | + | 4.53457i | −0.126253 | + | 0.218676i | ||||
\(431\) | 2.79796 | + | 2.34777i | 0.134773 | + | 0.113088i | 0.707682 | − | 0.706531i | \(-0.249741\pi\) |
−0.572909 | + | 0.819619i | \(0.694185\pi\) | |||||||
\(432\) | 3.89587 | + | 1.41798i | 0.187440 | + | 0.0682226i | ||||
\(433\) | −22.1413 | + | 8.05878i | −1.06404 | + | 0.387280i | −0.813946 | − | 0.580940i | \(-0.802685\pi\) |
−0.250098 | + | 0.968221i | \(0.580463\pi\) | |||||||
\(434\) | 3.04787 | − | 2.55747i | 0.146303 | − | 0.122762i | ||||
\(435\) | 0.776578 | + | 4.40419i | 0.0372341 | + | 0.211165i | ||||
\(436\) | −27.0344 | −1.29471 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −17.3262 | −0.827880 | ||||||||
\(439\) | −2.53470 | − | 14.3750i | −0.120975 | − | 0.686081i | −0.983618 | − | 0.180268i | \(-0.942304\pi\) |
0.862643 | − | 0.505813i | \(-0.168807\pi\) | |||||||
\(440\) | 1.30856 | − | 1.09801i | 0.0623832 | − | 0.0523457i | ||||
\(441\) | −7.24334 | + | 2.63636i | −0.344921 | + | 0.125541i | ||||
\(442\) | −3.04091 | − | 1.10680i | −0.144641 | − | 0.0526451i | ||||
\(443\) | −26.3645 | − | 22.1224i | −1.25262 | − | 1.05107i | −0.996428 | − | 0.0844415i | \(-0.973089\pi\) |
−0.256187 | − | 0.966627i | \(-0.582466\pi\) | |||||||
\(444\) | 4.54508 | − | 7.87232i | 0.215700 | − | 0.373604i | ||||
\(445\) | 7.56231 | + | 13.0983i | 0.358488 | + | 0.620919i | ||||
\(446\) | −2.10911 | + | 11.9614i | −0.0998694 | + | 0.566388i | ||||
\(447\) | 5.95101 | − | 33.7499i | 0.281473 | − | 1.59631i | ||||
\(448\) | 0.354102 | + | 0.613323i | 0.0167297 | + | 0.0289768i | ||||
\(449\) | −16.4443 | + | 28.4823i | −0.776053 | + | 1.34416i | 0.158147 | + | 0.987416i | \(0.449448\pi\) |
−0.934201 | + | 0.356748i | \(0.883885\pi\) | |||||||
\(450\) | −6.33558 | − | 5.31618i | −0.298662 | − | 0.250607i | ||||
\(451\) | −1.74229 | − | 0.634140i | −0.0820410 | − | 0.0298605i | ||||
\(452\) | −17.0839 | + | 6.21804i | −0.803561 | + | 0.292472i | ||||
\(453\) | −19.8745 | + | 16.6767i | −0.933784 | + | 0.783538i | ||||
\(454\) | 1.11789 | + | 6.33989i | 0.0524654 | + | 0.297546i | ||||
\(455\) | −3.70820 | −0.173843 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.29180 | 0.294318 | 0.147159 | − | 0.989113i | \(-0.452987\pi\) | ||||
0.147159 | + | 0.989113i | \(0.452987\pi\) | |||||||
\(458\) | −1.22152 | − | 6.92757i | −0.0570778 | − | 0.323704i | ||||
\(459\) | −8.96900 | + | 7.52589i | −0.418637 | + | 0.351278i | ||||
\(460\) | −14.3172 | + | 5.21104i | −0.667544 | + | 0.242966i | ||||
\(461\) | −2.87145 | − | 1.04512i | −0.133737 | − | 0.0486761i | 0.274285 | − | 0.961648i | \(-0.411559\pi\) |
−0.408021 | + | 0.912972i | \(0.633781\pi\) | |||||||
\(462\) | −2.29813 | − | 1.92836i | −0.106919 | − | 0.0897156i | ||||
\(463\) | 2.63525 | − | 4.56440i | 0.122471 | − | 0.212125i | −0.798271 | − | 0.602299i | \(-0.794252\pi\) |
0.920741 | + | 0.390173i | \(0.127585\pi\) | |||||||
\(464\) | −1.28115 | − | 2.21902i | −0.0594760 | − | 0.103016i | ||||
\(465\) | 1.20586 | − | 6.83877i | 0.0559204 | − | 0.317140i | ||||
\(466\) | 1.44584 | − | 8.19974i | 0.0669771 | − | 0.379846i | ||||
\(467\) | −0.972136 | − | 1.68379i | −0.0449851 | − | 0.0779165i | 0.842656 | − | 0.538452i | \(-0.180991\pi\) |
−0.887641 | + | 0.460536i | \(0.847657\pi\) | |||||||
\(468\) | 3.11803 | − | 5.40059i | 0.144131 | − | 0.249643i | ||||
\(469\) | 16.0869 | + | 13.4985i | 0.742826 | + | 0.623305i | ||||
\(470\) | 2.15358 | + | 0.783840i | 0.0993374 | + | 0.0361559i | ||||
\(471\) | −27.4206 | + | 9.98026i | −1.26347 | + | 0.459866i | ||||
\(472\) | −26.2527 | + | 22.0287i | −1.20838 | + | 1.01395i | ||||
\(473\) | −0.735585 | − | 4.17171i | −0.0338223 | − | 0.191816i | ||||
\(474\) | −21.7082 | −0.997091 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −25.4164 | −1.16496 | ||||||||
\(477\) | −6.24166 | − | 35.3982i | −0.285786 | − | 1.62077i | ||||
\(478\) | 7.25608 | − | 6.08857i | 0.331885 | − | 0.278485i | ||||
\(479\) | −11.1916 | + | 4.07340i | −0.511356 | + | 0.186118i | −0.584795 | − | 0.811181i | \(-0.698825\pi\) |
0.0734385 | + | 0.997300i | \(0.476603\pi\) | |||||||
\(480\) | −17.0839 | − | 6.21804i | −0.779771 | − | 0.283814i | ||||
\(481\) | −1.64385 | − | 1.37936i | −0.0749533 | − | 0.0628933i | ||||
\(482\) | −5.92705 | + | 10.2660i | −0.269970 | + | 0.467601i | ||||
\(483\) | 29.9164 | + | 51.8167i | 1.36124 | + | 2.35774i | ||||
\(484\) | 2.98333 | − | 16.9193i | 0.135606 | − | 0.769061i | ||||
\(485\) | 1.53380 | − | 8.69863i | 0.0696464 | − | 0.394984i | ||||
\(486\) | −6.69098 | − | 11.5891i | −0.303509 | − | 0.525693i | ||||
\(487\) | −9.09017 | + | 15.7446i | −0.411915 | + | 0.713458i | −0.995099 | − | 0.0988824i | \(-0.968473\pi\) |
0.583184 | + | 0.812340i | \(0.301807\pi\) | |||||||
\(488\) | 9.87320 | + | 8.28460i | 0.446939 | + | 0.375026i | ||||
\(489\) | 15.3416 | + | 5.58390i | 0.693773 | + | 0.252513i | ||||
\(490\) | 1.43572 | − | 0.522560i | 0.0648593 | − | 0.0236069i | ||||
\(491\) | 23.1459 | − | 19.4217i | 1.04456 | − | 0.876488i | 0.0520474 | − | 0.998645i | \(-0.483425\pi\) |
0.992511 | + | 0.122156i | \(0.0389809\pi\) | |||||||
\(492\) | 2.20676 | + | 12.5151i | 0.0994883 | + | 0.564226i | ||||
\(493\) | 7.23607 | 0.325896 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.94427 | −0.132335 | ||||||||
\(496\) | 0.690896 | + | 3.91827i | 0.0310222 | + | 0.175935i | ||||
\(497\) | −3.38316 | + | 2.83881i | −0.151756 | + | 0.127338i | ||||
\(498\) | −0.717861 | + | 0.261280i | −0.0321681 | + | 0.0117082i | ||||
\(499\) | 14.2125 | + | 5.17292i | 0.636238 | + | 0.231572i | 0.639944 | − | 0.768421i | \(-0.278957\pi\) |
−0.00370599 | + | 0.999993i | \(0.501180\pi\) | |||||||
\(500\) | −12.9801 | − | 10.8916i | −0.580486 | − | 0.487086i | ||||
\(501\) | −20.6353 | + | 35.7413i | −0.921915 | + | 1.59680i | ||||
\(502\) | −5.98278 | − | 10.3625i | −0.267024 | − | 0.462500i | ||||
\(503\) | −3.09664 | + | 17.5619i | −0.138072 | + | 0.783046i | 0.834599 | + | 0.550858i | \(0.185700\pi\) |
−0.972671 | + | 0.232188i | \(0.925412\pi\) | |||||||
\(504\) | −4.48952 | + | 25.4613i | −0.199979 | + | 1.13414i | ||||
\(505\) | 8.14590 | + | 14.1091i | 0.362488 | + | 0.627847i | ||||
\(506\) | −1.45492 | + | 2.51999i | −0.0646789 | + | 0.112027i | ||||
\(507\) | 24.0664 | + | 20.1941i | 1.06882 | + | 0.896850i | ||||
\(508\) | −15.5635 | − | 5.66464i | −0.690518 | − | 0.251328i | ||||
\(509\) | −25.4041 | + | 9.24632i | −1.12602 | + | 0.409836i | −0.836844 | − | 0.547441i | \(-0.815602\pi\) |
−0.289171 | + | 0.957277i | \(0.593380\pi\) | |||||||
\(510\) | 8.02212 | − | 6.73136i | 0.355226 | − | 0.298070i | ||||
\(511\) | 5.57838 | + | 31.6366i | 0.246773 | + | 1.39952i | ||||
\(512\) | 18.7082 | 0.826794 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 15.0557 | 0.664080 | ||||||||
\(515\) | −0.284665 | − | 1.61442i | −0.0125438 | − | 0.0711396i | ||||
\(516\) | −22.2417 | + | 18.6630i | −0.979135 | + | 0.821592i | ||||
\(517\) | −1.74229 | + | 0.634140i | −0.0766256 | + | 0.0278895i | ||||
\(518\) | 3.73877 | + | 1.36080i | 0.164272 | + | 0.0597901i | ||||
\(519\) | 16.9911 | + | 14.2572i | 0.745828 | + | 0.625824i | ||||
\(520\) | −1.38197 | + | 2.39364i | −0.0606032 | + | 0.104968i | ||||
\(521\) | −13.6353 | − | 23.6170i | −0.597371 | − | 1.03468i | −0.993208 | − | 0.116356i | \(-0.962879\pi\) |
0.395836 | − | 0.918321i | \(-0.370455\pi\) | |||||||
\(522\) | 0.571614 | − | 3.24179i | 0.0250189 | − | 0.141889i | ||||
\(523\) | −3.89257 | + | 22.0759i | −0.170210 | + | 0.965310i | 0.773318 | + | 0.634018i | \(0.218595\pi\) |
−0.943528 | + | 0.331292i | \(0.892516\pi\) | |||||||
\(524\) | 3.16312 | + | 5.47868i | 0.138181 | + | 0.239337i | ||||
\(525\) | −13.6353 | + | 23.6170i | −0.595091 | + | 1.03073i | ||||
\(526\) | 1.39394 | + | 1.16965i | 0.0607787 | + | 0.0509994i | ||||
\(527\) | −10.5585 | − | 3.84296i | −0.459933 | − | 0.167402i | ||||
\(528\) | 2.81908 | − | 1.02606i | 0.122685 | − | 0.0446535i | ||||
\(529\) | 26.8379 | − | 22.5197i | 1.16687 | − | 0.979118i | ||||
\(530\) | 1.23718 | + | 7.01637i | 0.0537395 | + | 0.304772i | ||||
\(531\) | 59.0689 | 2.56337 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.00000 | 0.129944 | ||||||||
\(534\) | −3.43795 | − | 19.4976i | −0.148775 | − | 0.843743i | ||||
\(535\) | −9.86312 | + | 8.27614i | −0.426420 | + | 0.357809i | ||||
\(536\) | 14.7085 | − | 5.35346i | 0.635311 | − | 0.231234i | ||||
\(537\) | −19.1004 | − | 6.95198i | −0.824244 | − | 0.300000i | ||||
\(538\) | −6.94717 | − | 5.82937i | −0.299514 | − | 0.251322i | ||||
\(539\) | −0.618034 | + | 1.07047i | −0.0266206 | + | 0.0461082i | ||||
\(540\) | 2.23607 | + | 3.87298i | 0.0962250 | + | 0.166667i | ||||
\(541\) | 4.13853 | − | 23.4707i | 0.177929 | − | 1.00909i | −0.756779 | − | 0.653670i | \(-0.773228\pi\) |
0.934708 | − | 0.355416i | \(-0.115661\pi\) | |||||||
\(542\) | 0.842906 | − | 4.78036i | 0.0362059 | − | 0.205334i | ||||
\(543\) | −15.7082 | − | 27.2074i | −0.674104 | − | 1.16758i | ||||
\(544\) | −14.7082 | + | 25.4754i | −0.630609 | + | 1.09225i | ||||
\(545\) | −15.8207 | − | 13.2752i | −0.677685 | − | 0.568645i | ||||
\(546\) | 4.56136 | + | 1.66020i | 0.195208 | + | 0.0710500i | ||||
\(547\) | 35.6359 | − | 12.9704i | 1.52368 | − | 0.554575i | 0.561618 | − | 0.827396i | \(-0.310179\pi\) |
0.962065 | + | 0.272821i | \(0.0879567\pi\) | |||||||
\(548\) | 1.82469 | − | 1.53110i | 0.0779470 | − | 0.0654053i | ||||
\(549\) | −3.85756 | − | 21.8773i | −0.164636 | − | 0.933700i | ||||
\(550\) | −1.32624 | −0.0565510 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 44.5967 | 1.89816 | ||||||||
\(553\) | 6.98920 | + | 39.6377i | 0.297211 | + | 1.68557i | ||||
\(554\) | −7.29877 | + | 6.12439i | −0.310095 | + | 0.260201i | ||||
\(555\) | 6.52548 | − | 2.37508i | 0.276991 | − | 0.100817i | ||||
\(556\) | −14.8980 | − | 5.42242i | −0.631815 | − | 0.229962i | ||||
\(557\) | −17.7572 | − | 14.9000i | −0.752395 | − | 0.631335i | 0.183740 | − | 0.982975i | \(-0.441180\pi\) |
−0.936135 | + | 0.351640i | \(0.885624\pi\) | |||||||
\(558\) | −2.55573 | + | 4.42665i | −0.108193 | + | 0.187395i | ||||
\(559\) | 3.42705 | + | 5.93583i | 0.144949 | + | 0.251059i | ||||
\(560\) | −1.19390 | + | 6.77094i | −0.0504514 | + | 0.286124i | ||||
\(561\) | −1.47117 | + | 8.34343i | −0.0621129 | + | 0.352260i | ||||
\(562\) | 2.62868 | + | 4.55300i | 0.110884 | + | 0.192057i | ||||
\(563\) | 10.4164 | − | 18.0417i | 0.438999 | − | 0.760369i | −0.558613 | − | 0.829428i | \(-0.688666\pi\) |
0.997613 | + | 0.0690592i | \(0.0219997\pi\) | |||||||
\(564\) | 9.73505 | + | 8.16868i | 0.409920 | + | 0.343963i | ||||
\(565\) | −13.0510 | − | 4.75016i | −0.549058 | − | 0.199841i | ||||
\(566\) | 1.76229 | − | 0.641421i | 0.0740745 | − | 0.0269609i | ||||
\(567\) | −13.1182 | + | 11.0075i | −0.550913 | + | 0.462271i | ||||
\(568\) | 0.571614 | + | 3.24179i | 0.0239844 | + | 0.136022i | ||||
\(569\) | −28.0902 | −1.17760 | −0.588801 | − | 0.808278i | \(-0.700400\pi\) | ||||
−0.588801 | + | 0.808278i | \(0.700400\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.3262 | 0.934324 | 0.467162 | − | 0.884172i | \(-0.345276\pi\) | ||||
0.467162 | + | 0.884172i | \(0.345276\pi\) | |||||||
\(572\) | −0.173648 | − | 0.984808i | −0.00726060 | − | 0.0411769i | ||||
\(573\) | −19.5819 | + | 16.4311i | −0.818044 | + | 0.686420i | ||||
\(574\) | −5.22686 | + | 1.90242i | −0.218165 | + | 0.0794055i | ||||
\(575\) | 24.8557 | + | 9.04672i | 1.03655 | + | 0.377274i | ||||
\(576\) | −0.696970 | − | 0.584827i | −0.0290404 | − | 0.0243678i | ||||
\(577\) | −14.0623 | + | 24.3566i | −0.585421 | + | 1.01398i | 0.409401 | + | 0.912354i | \(0.365738\pi\) |
−0.994823 | + | 0.101625i | \(0.967596\pi\) | |||||||
\(578\) | −3.21885 | − | 5.57521i | −0.133886 | − | 0.231898i | ||||
\(579\) | 10.4309 | − | 59.1563i | 0.433491 | − | 2.45845i | ||||
\(580\) | 0.479952 | − | 2.72194i | 0.0199289 | − | 0.113022i | ||||
\(581\) | 0.708204 | + | 1.22665i | 0.0293812 | + | 0.0508898i | ||||
\(582\) | −5.78115 | + | 10.0133i | −0.239636 | + | 0.415063i | ||||
\(583\) | −4.41543 | − | 3.70498i | −0.182868 | − | 0.153445i | ||||
\(584\) | 22.5003 | + | 8.18942i | 0.931067 | + | 0.338881i | ||||
\(585\) | 4.47663 | − | 1.62936i | 0.185086 | − | 0.0673658i | ||||
\(586\) | 7.97943 | − | 6.69554i | 0.329627 | − | 0.276590i | ||||
\(587\) | 6.62027 | + | 37.5454i | 0.273248 | + | 1.54967i | 0.744473 | + | 0.667652i | \(0.232701\pi\) |
−0.471225 | + | 0.882013i | \(0.656188\pi\) | |||||||
\(588\) | 8.47214 | 0.349385 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −11.7082 | −0.482019 | ||||||||
\(591\) | −1.36385 | − | 7.73478i | −0.0561013 | − | 0.318166i | ||||
\(592\) | −3.04787 | + | 2.55747i | −0.125267 | + | 0.105111i | ||||
\(593\) | 11.9418 | − | 4.34646i | 0.490391 | − | 0.178488i | −0.0849760 | − | 0.996383i | \(-0.527081\pi\) |
0.575367 | + | 0.817895i | \(0.304859\pi\) | |||||||
\(594\) | 0.802593 | + | 0.292120i | 0.0329308 | + | 0.0119858i | ||||
\(595\) | −14.8738 | − | 12.4806i | −0.609768 | − | 0.511656i | ||||
\(596\) | −10.5902 | + | 18.3427i | −0.433790 | + | 0.751347i | ||||
\(597\) | 17.5623 | + | 30.4188i | 0.718777 | + | 1.24496i | ||||
\(598\) | 0.817571 | − | 4.63668i | 0.0334330 | − | 0.189608i | ||||
\(599\) | −0.274988 | + | 1.55953i | −0.0112357 | + | 0.0637208i | −0.989910 | − | 0.141697i | \(-0.954744\pi\) |
0.978674 | + | 0.205418i | \(0.0658553\pi\) | |||||||
\(600\) | 10.1631 | + | 17.6030i | 0.414908 | + | 0.718641i | ||||
\(601\) | 16.8541 | − | 29.1922i | 0.687493 | − | 1.19077i | −0.285153 | − | 0.958482i | \(-0.592044\pi\) |
0.972646 | − | 0.232291i | \(-0.0746222\pi\) | |||||||
\(602\) | −9.73505 | − | 8.16868i | −0.396771 | − | 0.332930i | ||||
\(603\) | −25.3517 | − | 9.22726i | −1.03240 | − | 0.375763i | ||||
\(604\) | 15.0674 | − | 5.48410i | 0.613086 | − | 0.223145i | ||||
\(605\) | 10.0540 | − | 8.43634i | 0.408755 | − | 0.342986i | ||||
\(606\) | −3.70326 | − | 21.0022i | −0.150435 | − | 0.853158i | ||||
\(607\) | −27.2705 | −1.10688 | −0.553438 | − | 0.832890i | \(-0.686684\pi\) | ||||
−0.553438 | + | 0.832890i | \(0.686684\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.8541 | −0.439830 | ||||||||
\(610\) | 0.764617 | + | 4.33636i | 0.0309584 | + | 0.175574i | ||||
\(611\) | 2.29813 | − | 1.92836i | 0.0929725 | − | 0.0780132i | ||||
\(612\) | 30.6833 | − | 11.1678i | 1.24030 | − | 0.451432i | ||||
\(613\) | 1.93175 | + | 0.703100i | 0.0780227 | + | 0.0283980i | 0.380737 | − | 0.924684i | \(-0.375670\pi\) |
−0.302714 | + | 0.953081i | \(0.597893\pi\) | |||||||
\(614\) | 0.792428 | + | 0.664926i | 0.0319798 | + | 0.0268342i | ||||
\(615\) | −4.85410 | + | 8.40755i | −0.195736 | + | 0.339025i | ||||
\(616\) | 2.07295 | + | 3.59045i | 0.0835215 | + | 0.144663i | ||||
\(617\) | 4.05056 | − | 22.9719i | 0.163069 | − | 0.924812i | −0.787963 | − | 0.615722i | \(-0.788864\pi\) |
0.951033 | − | 0.309090i | \(-0.100024\pi\) | |||||||
\(618\) | −0.372631 | + | 2.11330i | −0.0149894 | + | 0.0850093i | ||||
\(619\) | 15.0623 | + | 26.0887i | 0.605405 | + | 1.04859i | 0.991987 | + | 0.126338i | \(0.0403222\pi\) |
−0.386582 | + | 0.922255i | \(0.626344\pi\) | |||||||
\(620\) | −2.14590 | + | 3.71680i | −0.0861813 | + | 0.149270i | ||||
\(621\) | −13.0491 | − | 10.9495i | −0.523644 | − | 0.439389i | ||||
\(622\) | 10.8326 | + | 3.94276i | 0.434350 | + | 0.158090i | ||||
\(623\) | −34.4944 | + | 12.5549i | −1.38199 | + | 0.503003i | ||||
\(624\) | −3.71846 | + | 3.12016i | −0.148857 | + | 0.124906i | ||||
\(625\) | 0.766901 | + | 4.34931i | 0.0306760 | + | 0.173973i | ||||
\(626\) | 2.67376 | 0.106865 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 18.0344 | 0.719653 | ||||||||
\(629\) | −1.95112 | − | 11.0654i | −0.0777964 | − | 0.441205i | ||||
\(630\) | −6.76633 | + | 5.67762i | −0.269577 | + | 0.226202i | ||||
\(631\) | 14.4343 | − | 5.25366i | 0.574621 | − | 0.209145i | −0.0383309 | − | 0.999265i | \(-0.512204\pi\) |
0.612952 | + | 0.790120i | \(0.289982\pi\) | |||||||
\(632\) | 28.1908 | + | 10.2606i | 1.12137 | + | 0.408145i | ||||
\(633\) | 5.72399 | + | 4.80300i | 0.227508 | + | 0.190902i | ||||
\(634\) | 5.56231 | − | 9.63420i | 0.220907 | − | 0.382623i | ||||
\(635\) | −6.32624 | − | 10.9574i | −0.251049 | − | 0.434830i | ||||
\(636\) | −6.86025 | + | 38.9064i | −0.272026 | + | 1.54274i | ||||
\(637\) | 0.347296 | − | 1.96962i | 0.0137604 | − | 0.0780390i | ||||
\(638\) | −0.263932 | − | 0.457144i | −0.0104492 | − | 0.0180985i | ||||
\(639\) | 2.83688 | − | 4.91362i | 0.112225 | − | 0.194380i | ||||
\(640\) | 10.7774 | + | 9.04330i | 0.426014 | + | 0.357468i | ||||
\(641\) | −1.40336 | − | 0.510780i | −0.0554293 | − | 0.0201746i | 0.314157 | − | 0.949371i | \(-0.398278\pi\) |
−0.369586 | + | 0.929197i | \(0.620500\pi\) | |||||||
\(642\) | 15.8377 | − | 5.76444i | 0.625063 | − | 0.227504i | ||||
\(643\) | −28.8862 | + | 24.2384i | −1.13916 | + | 0.955868i | −0.999411 | − | 0.0343192i | \(-0.989074\pi\) |
−0.139748 | + | 0.990187i | \(0.544629\pi\) | |||||||
\(644\) | −6.42129 | − | 36.4169i | −0.253034 | − | 1.43503i | ||||
\(645\) | −22.1803 | −0.873350 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.47214 | −0.0578756 | −0.0289378 | − | 0.999581i | \(-0.509212\pi\) | ||||
−0.0289378 | + | 0.999581i | \(0.509212\pi\) | |||||||
\(648\) | 2.21643 | + | 12.5700i | 0.0870697 | + | 0.493797i | ||||
\(649\) | 7.25608 | − | 6.08857i | 0.284826 | − | 0.238997i | ||||
\(650\) | 2.01648 | − | 0.733940i | 0.0790930 | − | 0.0287875i | ||||
\(651\) | 15.8377 | + | 5.76444i | 0.620727 | + | 0.225926i | ||||
\(652\) | −7.72952 | − | 6.48584i | −0.302711 | − | 0.254005i | ||||
\(653\) | 1.71885 | − | 2.97713i | 0.0672637 | − | 0.116504i | −0.830432 | − | 0.557120i | \(-0.811906\pi\) |
0.897696 | + | 0.440616i | \(0.145240\pi\) | |||||||
\(654\) | 13.5172 | + | 23.4125i | 0.528565 | + | 0.915502i | ||||
\(655\) | −0.839210 | + | 4.75939i | −0.0327906 | + | 0.185965i | ||||
\(656\) | 0.965884 | − | 5.47780i | 0.0377114 | − | 0.213872i | ||||
\(657\) | −20.6353 | − | 35.7413i | −0.805058 | − | 1.39440i | ||||
\(658\) | −2.78115 | + | 4.81710i | −0.108421 | + | 0.187790i | ||||
\(659\) | −35.0673 | − | 29.4249i | −1.36603 | − | 1.14623i | −0.974069 | − | 0.226250i | \(-0.927353\pi\) |
−0.391958 | − | 0.919983i | \(-0.628202\pi\) | |||||||
\(660\) | 3.04091 | + | 1.10680i | 0.118367 | + | 0.0430821i | ||||
\(661\) | −20.1248 | + | 7.32484i | −0.782766 | + | 0.284903i | −0.702325 | − | 0.711856i | \(-0.747855\pi\) |
−0.0804402 | + | 0.996759i | \(0.525633\pi\) | |||||||
\(662\) | 3.28771 | − | 2.75871i | 0.127780 | − | 0.107220i | ||||
\(663\) | −2.38040 | − | 13.4999i | −0.0924473 | − | 0.524294i | ||||
\(664\) | 1.05573 | 0.0409702 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.11146 | −0.198065 | ||||||||
\(667\) | 1.82814 | + | 10.3679i | 0.0707860 | + | 0.401448i | ||||
\(668\) | 19.5392 | − | 16.3953i | 0.755993 | − | 0.634354i | ||||
\(669\) | −48.3480 | + | 17.5972i | −1.86924 | + | 0.680348i | ||||
\(670\) | 5.02503 | + | 1.82896i | 0.194134 | + | 0.0706589i | ||||
\(671\) | −2.72888 | − | 2.28981i | −0.105347 | − | 0.0883970i | ||||
\(672\) | 22.0623 | − | 38.2130i | 0.851072 | − | 1.47410i | ||||
\(673\) | −3.06231 | − | 5.30407i | −0.118043 | − | 0.204457i | 0.800949 | − | 0.598733i | \(-0.204329\pi\) |
−0.918992 | + | 0.394276i | \(0.870995\pi\) | |||||||
\(674\) | −2.48174 | + | 14.0747i | −0.0955932 | + | 0.542136i | ||||
\(675\) | 1.34819 | − | 7.64598i | 0.0518920 | − | 0.294294i | ||||
\(676\) | −9.70820 | − | 16.8151i | −0.373392 | − | 0.646735i | ||||
\(677\) | 5.87132 | − | 10.1694i | 0.225653 | − | 0.390843i | −0.730862 | − | 0.682525i | \(-0.760882\pi\) |
0.956515 | + | 0.291682i | \(0.0942150\pi\) | |||||||
\(678\) | 13.9269 | + | 11.6861i | 0.534861 | + | 0.448802i | ||||
\(679\) | 20.1448 | + | 7.33212i | 0.773088 | + | 0.281381i | ||||
\(680\) | −13.5994 | + | 4.94976i | −0.521512 | + | 0.189815i | ||||
\(681\) | −20.8904 | + | 17.5291i | −0.800523 | + | 0.671718i | ||||
\(682\) | 0.142332 | + | 0.807208i | 0.00545019 | + | 0.0309096i | ||||
\(683\) | 21.6525 | 0.828509 | 0.414254 | − | 0.910161i | \(-0.364042\pi\) | ||||
0.414254 | + | 0.910161i | \(0.364042\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.81966 | 0.0695256 | ||||||||
\(686\) | −1.60981 | − | 9.12967i | −0.0614627 | − | 0.348572i | ||||
\(687\) | 22.8269 | − | 19.1540i | 0.870900 | − | 0.730772i | ||||
\(688\) | 11.9418 | − | 4.34646i | 0.455277 | − | 0.165707i | ||||
\(689\) | 8.76380 | + | 3.18976i | 0.333874 | + | 0.121520i | ||||
\(690\) | 11.6715 | + | 9.79356i | 0.444327 | + | 0.372834i | ||||
\(691\) | 8.40983 | − | 14.5663i | 0.319925 | − | 0.554126i | −0.660547 | − | 0.750785i | \(-0.729676\pi\) |
0.980472 | + | 0.196658i | \(0.0630089\pi\) | |||||||
\(692\) | −6.85410 | − | 11.8717i | −0.260554 | − | 0.451293i | ||||
\(693\) | 1.24087 | − | 7.03734i | 0.0471368 | − | 0.267326i | ||||
\(694\) | 0.152010 | − | 0.862089i | 0.00577020 | − | 0.0327245i | ||||
\(695\) | −6.05573 | − | 10.4888i | −0.229707 | − | 0.397864i | ||||
\(696\) | −4.04508 | + | 7.00629i | −0.153329 | + | 0.265573i | ||||
\(697\) | 12.0332 | + | 10.0970i | 0.455789 | + | 0.382453i | ||||
\(698\) | −15.0874 | − | 5.49138i | −0.571068 | − | 0.207852i | ||||
\(699\) | 33.1434 | − | 12.0632i | 1.25360 | − | 0.456273i | ||||
\(700\) | 12.9110 | − | 10.8336i | 0.487990 | − | 0.409472i | ||||
\(701\) | 6.70824 | + | 38.0443i | 0.253367 | + | 1.43691i | 0.800231 | + | 0.599692i | \(0.204710\pi\) |
−0.546864 | + | 0.837221i | \(0.684179\pi\) | |||||||
\(702\) | −1.38197 | −0.0521589 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −0.145898 | −0.00549874 | ||||||||
\(705\) | 1.68581 | + | 9.56071i | 0.0634914 | + | 0.360077i | ||||
\(706\) | −14.8901 | + | 12.4943i | −0.560398 | + | 0.470230i | ||||
\(707\) | −37.1564 | + | 13.5238i | −1.39741 | + | 0.508616i | ||||
\(708\) | −61.0077 | − | 22.2050i | −2.29281 | − | 0.834514i | ||||
\(709\) | 33.2589 | + | 27.9075i | 1.24906 | + | 1.04809i | 0.996759 | + | 0.0804414i | \(0.0256330\pi\) |
0.252305 | + | 0.967648i | \(0.418811\pi\) | |||||||
\(710\) | −0.562306 | + | 0.973942i | −0.0211030 | + | 0.0365514i | ||||
\(711\) | −25.8541 | − | 44.7806i | −0.969605 | − | 1.67940i | ||||
\(712\) | −4.75113 | + | 26.9450i | −0.178056 | + | 1.00981i | ||||
\(713\) | 2.83872 | − | 16.0992i | 0.106311 | − | 0.602919i | ||||
\(714\) | 12.7082 | + | 22.0113i | 0.475593 | + | 0.823751i | ||||
\(715\) | 0.381966 | − | 0.661585i | 0.0142847 | − | 0.0247419i | ||||
\(716\) | 9.62328 | + | 8.07489i | 0.359639 | + | 0.301773i | ||||
\(717\) | 37.7048 | + | 13.7234i | 1.40811 | + | 0.512511i | ||||
\(718\) | 12.7968 | − | 4.65764i | 0.477571 | − | 0.173822i | ||||
\(719\) | 13.7624 | − | 11.5480i | 0.513252 | − | 0.430669i | −0.349020 | − | 0.937115i | \(-0.613486\pi\) |
0.862272 | + | 0.506446i | \(0.169041\pi\) | |||||||
\(720\) | −1.53380 | − | 8.69863i | −0.0571614 | − | 0.324179i | ||||
\(721\) | 3.97871 | 0.148175 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −50.2148 | −1.86751 | ||||||||
\(724\) | 3.37162 | + | 19.1214i | 0.125305 | + | 0.710642i | ||||
\(725\) | −3.67577 | + | 3.08434i | −0.136515 | + | 0.114549i | ||||
\(726\) | −16.1442 | + | 5.87602i | −0.599169 | + | 0.218080i | ||||
\(727\) | −39.5318 | − | 14.3884i | −1.46615 | − | 0.533636i | −0.519101 | − | 0.854713i | \(-0.673733\pi\) |
−0.947053 | + | 0.321077i | \(0.895955\pi\) | |||||||
\(728\) | −5.13878 | − | 4.31195i | −0.190456 | − | 0.159812i | ||||
\(729\) | 19.7812 | − | 34.2620i | 0.732635 | − | 1.26896i | ||||
\(730\) | 4.09017 | + | 7.08438i | 0.151384 | + | 0.262205i | ||||
\(731\) | −6.23198 | + | 35.3433i | −0.230498 | + | 1.30722i | ||||
\(732\) | −4.23986 | + | 24.0455i | −0.156710 | + | 0.888746i | ||||
\(733\) | −20.4787 | − | 35.4702i | −0.756399 | − | 1.31012i | −0.944676 | − | 0.328005i | \(-0.893624\pi\) |
0.188277 | − | 0.982116i | \(-0.439710\pi\) | |||||||
\(734\) | −0.600813 | + | 1.04064i | −0.0221764 | + | 0.0384107i | ||||
\(735\) | 4.95794 | + | 4.16021i | 0.182877 | + | 0.153452i | ||||
\(736\) | −40.2173 | − | 14.6379i | −1.48243 | − | 0.539560i | ||||
\(737\) | −4.06533 | + | 1.47966i | −0.149748 | + | 0.0545040i | ||||
\(738\) | 5.47408 | − | 4.59329i | 0.201504 | − | 0.169082i | ||||
\(739\) | −4.34120 | − | 24.6202i | −0.159694 | − | 0.905668i | −0.954368 | − | 0.298633i | \(-0.903470\pi\) |
0.794674 | − | 0.607036i | \(-0.207642\pi\) | |||||||
\(740\) | −4.29180 | −0.157770 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −17.2918 | −0.634802 | ||||||||
\(743\) | −7.18221 | − | 40.7323i | −0.263490 | − | 1.49432i | −0.773302 | − | 0.634038i | \(-0.781396\pi\) |
0.509812 | − | 0.860286i | \(-0.329715\pi\) | |||||||
\(744\) | 9.62328 | − | 8.07489i | 0.352807 | − | 0.296040i | ||||
\(745\) | −15.2045 | + | 5.53400i | −0.557051 | + | 0.202750i | ||||
\(746\) | 2.01648 | + | 0.733940i | 0.0738287 | + | 0.0268715i | ||||
\(747\) | −1.39394 | − | 1.16965i | −0.0510016 | − | 0.0427954i | ||||
\(748\) | 2.61803 | − | 4.53457i | 0.0957248 | − | 0.165800i | ||||
\(749\) | −15.6246 | − | 27.0626i | −0.570911 | − | 0.988847i | ||||
\(750\) | −2.94234 | + | 16.6869i | −0.107439 | + | 0.609318i | ||||
\(751\) | 4.14222 | − | 23.4917i | 0.151152 | − | 0.857224i | −0.811068 | − | 0.584952i | \(-0.801114\pi\) |
0.962220 | − | 0.272273i | \(-0.0877754\pi\) | |||||||
\(752\) | −2.78115 | − | 4.81710i | −0.101418 | − | 0.175661i | ||||
\(753\) | 25.3435 | − | 43.8962i | 0.923567 | − | 1.59966i | ||||
\(754\) | 0.654280 | + | 0.549006i | 0.0238275 | + | 0.0199936i | ||||
\(755\) | 11.5105 | + | 4.18948i | 0.418910 | + | 0.152471i | ||||
\(756\) | −10.1995 | + | 3.71232i | −0.370953 | + | 0.135016i | ||||
\(757\) | −12.0596 | + | 10.1192i | −0.438312 | + | 0.367788i | −0.835077 | − | 0.550132i | \(-0.814577\pi\) |
0.396765 | + | 0.917920i | \(0.370133\pi\) | |||||||
\(758\) | −2.69639 | − | 15.2920i | −0.0979371 | − | 0.555429i | ||||
\(759\) | −12.3262 | −0.447414 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.8885 | −1.11971 | −0.559854 | − | 0.828591i | \(-0.689143\pi\) | ||||
−0.559854 | + | 0.828591i | \(0.689143\pi\) | |||||||
\(762\) | 2.87601 | + | 16.3107i | 0.104187 | + | 0.590874i | ||||
\(763\) | 38.3977 | − | 32.2195i | 1.39009 | − | 1.16642i | ||||
\(764\) | 14.8456 | − | 5.40336i | 0.537096 | − | 0.195487i | ||||
\(765\) | 23.4399 | + | 8.53144i | 0.847473 | + | 0.308455i | ||||
\(766\) | −1.23949 | − | 1.04005i | −0.0447844 | − | 0.0375786i | ||||
\(767\) | −7.66312 | + | 13.2729i | −0.276699 | + | 0.479257i | ||||
\(768\) | −8.59017 | − | 14.8786i | −0.309971 | − | 0.536886i | ||||
\(769\) | −7.22918 | + | 40.9987i | −0.260691 | + | 1.47845i | 0.520340 | + | 0.853959i | \(0.325805\pi\) |
−0.781031 | + | 0.624492i | \(0.785306\pi\) | |||||||
\(770\) | −0.245957 | + | 1.39489i | −0.00886366 | + | 0.0502683i | ||||
\(771\) | 31.8885 | + | 55.2326i | 1.14844 | + | 1.98915i | ||||
\(772\) | −18.5623 | + | 32.1509i | −0.668072 | + | 1.15713i | ||||
\(773\) | −22.1563 | − | 18.5913i | −0.796906 | − | 0.668684i | 0.150538 | − | 0.988604i | \(-0.451899\pi\) |
−0.947444 | + | 0.319920i | \(0.896344\pi\) | |||||||
\(774\) | 15.3416 | + | 5.58390i | 0.551444 | + | 0.200709i | ||||
\(775\) | 7.00151 | − | 2.54834i | 0.251502 | − | 0.0915391i | ||||
\(776\) | 12.2404 | − | 10.2709i | 0.439405 | − | 0.368705i | ||||
\(777\) | 2.92668 | + | 16.5981i | 0.104994 | + | 0.595452i | ||||
\(778\) | −15.0000 | −0.537776 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −5.23607 | −0.187481 | ||||||||
\(781\) | −0.157990 | − | 0.896008i | −0.00565334 | − | 0.0320617i | ||||
\(782\) | 18.8849 | − | 15.8463i | 0.675322 | − | 0.566663i | ||||
\(783\) | 2.90381 | − | 1.05690i | 0.103774 | − | 0.0377705i | ||||
\(784\) | −3.48457 | − | 1.26828i | −0.124449 | − | 0.0452957i | ||||
\(785\) | 10.5539 | + | 8.85574i | 0.376683 | + | 0.316075i | ||||
\(786\) | 3.16312 | − | 5.47868i | 0.112825 | − | 0.195418i | ||||
\(787\) | 19.0000 | + | 32.9090i | 0.677277 | + | 1.17308i | 0.975798 | + | 0.218675i | \(0.0701734\pi\) |
−0.298521 | + | 0.954403i | \(0.596493\pi\) | |||||||
\(788\) | −0.842906 | + | 4.78036i | −0.0300273 | + | 0.170293i | ||||
\(789\) | −1.33852 | + | 7.59110i | −0.0476524 | + | 0.270250i | ||||
\(790\) | 5.12461 | + | 8.87609i | 0.182326 | + | 0.315797i | ||||
\(791\) | 16.8541 | − | 29.1922i | 0.599263 | − | 1.03795i | ||||
\(792\) | −4.08013 | − | 3.42364i | −0.144981 | − | 0.121654i | ||||
\(793\) | 5.41632 | + | 1.97138i | 0.192339 | + | 0.0700058i | ||||
\(794\) | 1.46809 | − | 0.534340i | 0.0521005 | − | 0.0189630i | ||||
\(795\) | −23.1195 | + | 19.3995i | −0.819964 | + | 0.688031i | ||||
\(796\) | −3.76959 | − | 21.3784i | −0.133610 | − | 0.757738i | ||||
\(797\) | 33.7082 | 1.19401 | 0.597003 | − | 0.802239i | \(-0.296358\pi\) | ||||
0.597003 | + | 0.802239i | \(0.296358\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.7082 | 0.555716 | ||||||||
\(800\) | −3.38728 | − | 19.2102i | −0.119758 | − | 0.679184i | ||||
\(801\) | 36.1259 | − | 30.3133i | 1.27645 | − | 1.07107i | ||||
\(802\) | −0.0647295 | + | 0.0235596i | −0.00228568 | + | 0.000831919i | ||||
\(803\) | −6.21892 | − | 2.26350i | −0.219461 | − | 0.0798772i | ||||
\(804\) | 22.7151 | + | 19.0602i | 0.801100 | + | 0.672203i | ||||
\(805\) | 14.1246 | − | 24.4645i | 0.497827 | − | 0.862262i | ||||
\(806\) | −0.663119 | − | 1.14856i | −0.0233574 | − | 0.0404562i | ||||
\(807\) | 6.67094 | − | 37.8328i | 0.234828 | − | 1.33178i | ||||
\(808\) | −5.11778 | + | 29.0244i | −0.180043 | + | 1.02107i | ||||
\(809\) | 0.100813 | + | 0.174613i | 0.00354440 | + | 0.00613908i | 0.867792 | − | 0.496927i | \(-0.165538\pi\) |
−0.864248 | + | 0.503066i | \(0.832205\pi\) | |||||||
\(810\) | −2.18034 | + | 3.77646i | −0.0766093 | + | 0.132691i | ||||
\(811\) | 18.3688 | + | 15.4132i | 0.645014 | + | 0.541231i | 0.905554 | − | 0.424232i | \(-0.139456\pi\) |
−0.260539 | + | 0.965463i | \(0.583900\pi\) | |||||||
\(812\) | 6.30365 | + | 2.29434i | 0.221215 | + | 0.0805156i | ||||
\(813\) | 19.3222 | − | 7.03272i | 0.677661 | − | 0.246648i | ||||
\(814\) | −0.627896 | + | 0.526867i | −0.0220077 | + | 0.0184667i | ||||
\(815\) | −1.33852 | − | 7.59110i | −0.0468862 | − | 0.265905i | ||||
\(816\) | −25.4164 | −0.889752 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 13.4164 | 0.469094 | ||||||||
\(819\) | 2.00777 | + | 11.3866i | 0.0701573 | + | 0.397882i | ||||
\(820\) | 4.59627 | − | 3.85673i | 0.160509 | − | 0.134683i | ||||
\(821\) | 49.8484 | − | 18.1433i | 1.73972 | − | 0.633207i | 0.740478 | − | 0.672080i | \(-0.234599\pi\) |
0.999244 | + | 0.0388731i | \(0.0123768\pi\) | |||||||
\(822\) | −2.23832 | − | 0.814680i | −0.0780702 | − | 0.0284152i | ||||
\(823\) | 18.0762 | + | 15.1677i | 0.630095 | + | 0.528713i | 0.900959 | − | 0.433905i | \(-0.142865\pi\) |
−0.270863 | + | 0.962618i | \(0.587309\pi\) | |||||||
\(824\) | 1.48278 | − | 2.56825i | 0.0516551 | − | 0.0894692i | ||||
\(825\) | −2.80902 | − | 4.86536i | −0.0977974 | − | 0.169390i | ||||
\(826\) | 4.93446 | − | 27.9847i | 0.171692 | − | 0.973712i | ||||
\(827\) | 2.88200 | − | 16.3446i | 0.100217 | − | 0.568358i | −0.892807 | − | 0.450440i | \(-0.851267\pi\) |
0.993023 | − | 0.117917i | \(-0.0376218\pi\) | |||||||
\(828\) | 23.7533 | + | 41.1419i | 0.825484 | + | 1.42978i | ||||
\(829\) | 10.1631 | − | 17.6030i | 0.352980 | − | 0.611379i | −0.633790 | − | 0.773505i | \(-0.718502\pi\) |
0.986770 | + | 0.162126i | \(0.0518351\pi\) | |||||||
\(830\) | 0.276297 | + | 0.231840i | 0.00959040 | + | 0.00804730i | ||||
\(831\) | −37.9266 | − | 13.8042i | −1.31566 | − | 0.478861i | ||||
\(832\) | 0.221831 | − | 0.0807400i | 0.00769062 | − | 0.00279916i | ||||
\(833\) | 8.02212 | − | 6.73136i | 0.277950 | − | 0.233228i | ||||
\(834\) | 2.75304 | + | 15.6132i | 0.0953298 | + | 0.540642i | ||||
\(835\) | 19.4853 | 0.674316 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.79837 | −0.165856 | ||||||||
\(838\) | 0.959904 | + | 5.44388i | 0.0331593 | + | 0.188056i | ||||
\(839\) | −30.4873 | + | 25.5819i | −1.05254 | + | 0.883185i | −0.993358 | − | 0.115062i | \(-0.963293\pi\) |
−0.0591810 | + | 0.998247i | \(0.518849\pi\) | |||||||
\(840\) | 20.3990 | − | 7.42464i | 0.703834 | − | 0.256175i | ||||
\(841\) | 25.4564 | + | 9.26538i | 0.877808 | + | 0.319496i | ||||
\(842\) | 8.77186 | + | 7.36046i | 0.302298 | + | 0.253658i | ||||
\(843\) | −11.1353 | + | 19.2868i | −0.383519 | + | 0.664274i | ||||
\(844\) | −2.30902 | − | 3.99933i | −0.0794796 | − | 0.137663i | ||||
\(845\) | 2.57569 | − | 14.6075i | 0.0886065 | − | 0.502512i | ||||
\(846\) | 1.24087 | − | 7.03734i | 0.0426621 | − | 0.241949i | ||||
\(847\) | 15.9271 | + | 27.5865i | 0.547260 | + | 0.947882i | ||||
\(848\) | 8.64590 | − | 14.9751i | 0.296901 | − | 0.514248i | ||||
\(849\) | 6.08567 | + | 5.10648i | 0.208859 | + | 0.175254i | ||||
\(850\) | 10.5585 | + | 3.84296i | 0.362152 | + | 0.131812i | ||||
\(851\) | 15.3616 | − | 5.59118i | 0.526591 | − | 0.191663i | ||||
\(852\) | −4.77711 | + | 4.00847i | −0.163661 | + | 0.137328i | ||||
\(853\) | 3.00269 | + | 17.0291i | 0.102810 | + | 0.583065i | 0.992072 | + | 0.125668i | \(0.0401073\pi\) |
−0.889262 | + | 0.457398i | \(0.848782\pi\) | |||||||
\(854\) | −10.6869 | −0.365699 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −23.2918 | −0.796097 | ||||||||
\(857\) | 1.45551 | + | 8.25463i | 0.0497194 | + | 0.281973i | 0.999523 | − | 0.0308732i | \(-0.00982880\pi\) |
−0.949804 | + | 0.312846i | \(0.898718\pi\) | |||||||
\(858\) | −0.766044 | + | 0.642788i | −0.0261523 | + | 0.0219444i | ||||
\(859\) | −17.4229 | + | 6.34140i | −0.594460 | + | 0.216366i | −0.621690 | − | 0.783263i | \(-0.713554\pi\) |
0.0272298 | + | 0.999629i | \(0.491331\pi\) | |||||||
\(860\) | 12.8815 | + | 4.68848i | 0.439255 | + | 0.159876i | ||||
\(861\) | −18.0498 | − | 15.1456i | −0.615135 | − | 0.516159i | ||||
\(862\) | −1.12868 | + | 1.95493i | −0.0384429 | + | 0.0665850i | ||||
\(863\) | −22.4721 | − | 38.9229i | −0.764960 | − | 1.32495i | −0.940268 | − | 0.340436i | \(-0.889425\pi\) |
0.175307 | − | 0.984514i | \(-0.443908\pi\) | |||||||
\(864\) | −2.18142 | + | 12.3715i | −0.0742135 | + | 0.420885i | ||||
\(865\) | 1.81847 | − | 10.3130i | 0.0618297 | − | 0.350654i | ||||
\(866\) | −7.28115 | − | 12.6113i | −0.247424 | − | 0.428550i | ||||
\(867\) | 13.6353 | − | 23.6170i | 0.463078 | − | 0.802074i | ||||
\(868\) | −7.97943 | − | 6.69554i | −0.270840 | − | 0.227261i | ||||
\(869\) | −7.79174 | − | 2.83596i | −0.264317 | − | 0.0962034i | ||||
\(870\) | −2.59725 | + | 0.945320i | −0.0880549 | + | 0.0320494i | ||||
\(871\) | 5.36231 | − | 4.49951i | 0.181695 | − | 0.152460i | ||||
\(872\) | −6.48761 | − | 36.7931i | −0.219698 | − | 1.24597i | ||||
\(873\) | −27.5410 | −0.932122 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 31.4164 | 1.06207 | ||||||||
\(876\) | 7.87680 | + | 44.6715i | 0.266132 | + | 1.50931i | ||||
\(877\) | −26.1837 | + | 21.9707i | −0.884159 | + | 0.741898i | −0.967030 | − | 0.254663i | \(-0.918036\pi\) |
0.0828706 | + | 0.996560i | \(0.473591\pi\) | |||||||
\(878\) | 8.47724 | − | 3.08546i | 0.286093 | − | 0.104129i | ||||
\(879\) | 41.4636 | + | 15.0915i | 1.39853 | + | 0.509024i | ||||
\(880\) | −1.08503 | − | 0.910449i | −0.0365764 | − | 0.0306912i | ||||
\(881\) | 11.7254 | − | 20.3090i | 0.395040 | − | 0.684229i | −0.598067 | − | 0.801446i | \(-0.704064\pi\) |
0.993106 | + | 0.117218i | \(0.0373975\pi\) | |||||||
\(882\) | −2.38197 | − | 4.12569i | −0.0802050 | − | 0.138919i | ||||
\(883\) | 2.41770 | − | 13.7115i | 0.0813621 | − | 0.461428i | −0.916720 | − | 0.399529i | \(-0.869174\pi\) |
0.998082 | − | 0.0618981i | \(-0.0197154\pi\) | |||||||
\(884\) | −1.47117 | + | 8.34343i | −0.0494808 | + | 0.280620i | ||||
\(885\) | −24.7984 | − | 42.9520i | −0.833588 | − | 1.44382i | ||||
\(886\) | 10.6353 | − | 18.4208i | 0.357298 | − | 0.618859i | ||||
\(887\) | −44.9304 | − | 37.7011i | −1.50862 | − | 1.26588i | −0.866396 | − | 0.499358i | \(-0.833569\pi\) |
−0.642219 | − | 0.766521i | \(-0.721986\pi\) | |||||||
\(888\) | 11.8047 | + | 4.29656i | 0.396140 | + | 0.144183i | ||||
\(889\) | 28.8563 | − | 10.5028i | 0.967808 | − | 0.352253i | ||||
\(890\) | −7.16062 | + | 6.00847i | −0.240024 | + | 0.201404i | ||||
\(891\) | −0.612607 | − | 3.47427i | −0.0205231 | − | 0.116392i | ||||
\(892\) | 31.7984 | 1.06469 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 21.1803 | 0.708377 | ||||||||
\(895\) | 1.66646 | + | 9.45095i | 0.0557035 | + | 0.315910i | ||||
\(896\) | −26.1573 | + | 21.9486i | −0.873853 | + | 0.733250i | ||||
\(897\) | 18.7415 | − | 6.82134i | 0.625760 | − | 0.227758i | ||||
\(898\) | −19.1004 | − | 6.95198i | −0.637389 | − | 0.231991i | ||||
\(899\) | 2.27175 | + | 1.90622i | 0.0757671 | + | 0.0635761i | ||||
\(900\) | −10.8262 | + | 18.7516i | −0.360875 | + | 0.625053i | ||||
\(901\) | 24.4164 | + | 42.2905i | 0.813428 | + | 1.40890i | ||||
\(902\) | 0.198983 | − | 1.12849i | 0.00662541 | − | 0.0375746i | ||||
\(903\) | 9.34797 | − | 53.0150i | 0.311081 | − | 1.76423i | ||||
\(904\) | −12.5623 | − | 21.7586i | −0.417816 | − | 0.723679i | ||||
\(905\) | −7.41641 | + | 12.8456i | −0.246530 | + | 0.427002i | ||||
\(906\) | −12.2831 | − | 10.3067i | −0.408079 | − | 0.342419i | ||||
\(907\) | −16.4708 | − | 5.99488i | −0.546904 | − | 0.199057i | 0.0537663 | − | 0.998554i | \(-0.482877\pi\) |
−0.600670 | + | 0.799497i | \(0.705100\pi\) | |||||||
\(908\) | 15.8377 | − | 5.76444i | 0.525592 | − | 0.191300i | ||||
\(909\) | 38.9138 | − | 32.6526i | 1.29069 | − | 1.08302i | ||||
\(910\) | −0.397966 | − | 2.25698i | −0.0131925 | − | 0.0748181i | ||||
\(911\) | −5.61803 | −0.186134 | −0.0930669 | − | 0.995660i | \(-0.529667\pi\) | ||||
−0.0930669 | + | 0.995660i | \(0.529667\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.291796 | −0.00965704 | ||||||||
\(914\) | 0.675239 | + | 3.82947i | 0.0223349 | + | 0.126668i | ||||
\(915\) | −14.2886 | + | 11.9896i | −0.472367 | + | 0.396363i | ||||
\(916\) | −17.3058 | + | 6.29878i | −0.571798 | + | 0.208118i | ||||
\(917\) | −11.0221 | − | 4.01172i | −0.363982 | − | 0.132479i | ||||
\(918\) | −5.54315 | − | 4.65125i | −0.182951 | − | 0.153514i | ||||
\(919\) | −18.3541 | + | 31.7902i | −0.605446 | + | 1.04866i | 0.386535 | + | 0.922275i | \(0.373672\pi\) |
−0.991981 | + | 0.126388i | \(0.959661\pi\) | |||||||
\(920\) | −10.5279 | − | 18.2348i | −0.347093 | − | 0.601183i | ||||
\(921\) | −0.760920 | + | 4.31539i | −0.0250732 | + | 0.142197i | ||||
\(922\) | 0.327942 | − | 1.85985i | 0.0108002 | − | 0.0612510i | ||||
\(923\) | 0.736068 | + | 1.27491i | 0.0242280 | + | 0.0419641i | ||||
\(924\) | −3.92705 | + | 6.80185i | −0.129190 | + | 0.223764i | ||||
\(925\) | 5.70768 | + | 4.78931i | 0.187667 | + | 0.157472i | ||||
\(926\) | 3.06091 | + | 1.11408i | 0.100588 | + | 0.0366110i | ||||
\(927\) | −4.80320 | + | 1.74822i | −0.157758 | + | 0.0574191i | ||||
\(928\) | 5.94752 | − | 4.99056i | 0.195237 | − | 0.163823i | ||||
\(929\) | 3.23299 | + | 18.3352i | 0.106071 | + | 0.601558i | 0.990787 | + | 0.135428i | \(0.0432409\pi\) |
−0.884716 | + | 0.466130i | \(0.845648\pi\) | |||||||
\(930\) | 4.29180 | 0.140734 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −21.7984 | −0.714029 | ||||||||
\(933\) | 8.47973 | + | 48.0909i | 0.277614 | + | 1.57443i | ||||
\(934\) | 0.920499 | − | 0.772390i | 0.0301196 | − | 0.0252734i | ||||
\(935\) | 3.75877 | − | 1.36808i | 0.122925 | − | 0.0447410i | ||||
\(936\) | 8.09830 | + | 2.94754i | 0.264701 | + | 0.0963434i | ||||
\(937\) | 15.6562 | + | 13.1371i | 0.511465 | + | 0.429170i | 0.861644 | − | 0.507512i | \(-0.169435\pi\) |
−0.350179 | + | 0.936683i | \(0.613879\pi\) | |||||||
\(938\) | −6.48936 | + | 11.2399i | −0.211885 | + | 0.366996i | ||||
\(939\) | 5.66312 | + | 9.80881i | 0.184809 | + | 0.320098i | ||||
\(940\) | 1.04189 | − | 5.90885i | 0.0339827 | − | 0.192725i | ||||
\(941\) | −8.62804 | + | 48.9321i | −0.281266 | + | 1.59514i | 0.437059 | + | 0.899433i | \(0.356020\pi\) |
−0.718326 | + | 0.695707i | \(0.755091\pi\) | |||||||
\(942\) | −9.01722 | − | 15.6183i | −0.293797 | − | 0.508871i | ||||
\(943\) | −11.4271 | + | 19.7922i | −0.372116 | + | 0.644524i | ||||
\(944\) | 21.7682 | + | 18.2657i | 0.708496 | + | 0.594498i | ||||
\(945\) | −7.79174 | − | 2.83596i | −0.253465 | − | 0.0922538i | ||||
\(946\) | 2.46015 | − | 0.895420i | 0.0799863 | − | 0.0291126i | ||||
\(947\) | −1.03226 | + | 0.866172i | −0.0335441 | + | 0.0281468i | −0.659406 | − | 0.751787i | \(-0.729192\pi\) |
0.625862 | + | 0.779934i | \(0.284748\pi\) | |||||||
\(948\) | 9.86891 | + | 55.9694i | 0.320527 | + | 1.81780i | ||||
\(949\) | 10.7082 | 0.347603 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 47.1246 | 1.52812 | ||||||||
\(952\) | −6.09932 | − | 34.5910i | −0.197680 | − | 1.12110i | ||||
\(953\) | −23.5238 | + | 19.7389i | −0.762012 | + | 0.639404i | −0.938650 | − | 0.344872i | \(-0.887922\pi\) |
0.176638 | + | 0.984276i | \(0.443478\pi\) | |||||||
\(954\) | 20.8751 | − | 7.59790i | 0.675855 | − | 0.245991i | ||||
\(955\) | 11.3410 | + | 4.12780i | 0.366987 | + | 0.133573i | ||||
\(956\) | −18.9967 | − | 15.9401i | −0.614396 | − | 0.515539i | ||||
\(957\) | 1.11803 | − | 1.93649i | 0.0361409 | − | 0.0625979i | ||||
\(958\) | −3.68034 | − | 6.37454i | −0.118906 | − | 0.205952i | ||||
\(959\) | −0.766901 | + | 4.34931i | −0.0247645 | + | 0.140447i | ||||
\(960\) | −0.132655 | + | 0.752326i | −0.00428143 | + | 0.0242812i | ||||
\(961\) | 13.1976 | + | 22.8588i | 0.425728 | + | 0.737382i | ||||
\(962\) | 0.663119 | − | 1.14856i | 0.0213798 | − | 0.0370309i | ||||
\(963\) | 30.7535 | + | 25.8053i | 0.991019 | + | 0.831564i | ||||
\(964\) | 29.1628 | + | 10.6144i | 0.939272 | + | 0.341867i | ||||
\(965\) | −26.6503 | + | 9.69992i | −0.857904 | + | 0.312252i | ||||
\(966\) | −28.3273 | + | 23.7695i | −0.911417 | + | 0.764770i | ||||
\(967\) | −10.5128 | − | 59.6213i | −0.338070 | − | 1.91729i | −0.394524 | − | 0.918885i | \(-0.629091\pi\) |
0.0564543 | − | 0.998405i | \(-0.482020\pi\) | |||||||
\(968\) | 23.7426 | 0.763118 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.45898 | 0.175277 | ||||||||
\(971\) | 2.51904 | + | 14.2862i | 0.0808399 | + | 0.458466i | 0.998177 | + | 0.0603544i | \(0.0192231\pi\) |
−0.917337 | + | 0.398111i | \(0.869666\pi\) | |||||||
\(972\) | −26.8379 | + | 22.5197i | −0.860827 | + | 0.722320i | ||||
\(973\) | 27.6224 | − | 10.0537i | 0.885533 | − | 0.322308i | ||||
\(974\) | −10.5585 | − | 3.84296i | −0.338315 | − | 0.123136i | ||||
\(975\) | 6.96347 | + | 5.84305i | 0.223010 | + | 0.187127i | ||||
\(976\) | 5.34346 | − | 9.25514i | 0.171040 | − | 0.296250i | ||||
\(977\) | 27.6803 | + | 47.9438i | 0.885573 | + | 1.53386i | 0.845056 | + | 0.534678i | \(0.179567\pi\) |
0.0405165 | + | 0.999179i | \(0.487100\pi\) | |||||||
\(978\) | −1.75214 | + | 9.93688i | −0.0560272 | + | 0.317746i | ||||
\(979\) | 1.31318 | − | 7.44742i | 0.0419694 | − | 0.238020i | ||||
\(980\) | −2.00000 | − | 3.46410i | −0.0638877 | − | 0.110657i | ||||
\(981\) | −32.1976 | + | 55.7678i | −1.02799 | + | 1.78053i | ||||
\(982\) | 14.3049 | + | 12.0033i | 0.456489 | + | 0.383040i | ||||
\(983\) | 28.5497 | + | 10.3912i | 0.910594 | + | 0.331429i | 0.754490 | − | 0.656311i | \(-0.227884\pi\) |
0.156104 | + | 0.987741i | \(0.450106\pi\) | |||||||
\(984\) | −16.5032 | + | 6.00666i | −0.526102 | + | 0.191485i | ||||
\(985\) | −2.84065 | + | 2.38359i | −0.0905106 | + | 0.0759474i | ||||
\(986\) | 0.776578 | + | 4.40419i | 0.0247313 | + | 0.140258i | ||||
\(987\) | −23.5623 | −0.749996 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −52.2148 | −1.66033 | ||||||||
\(990\) | −0.315981 | − | 1.79202i | −0.0100425 | − | 0.0569540i | ||||
\(991\) | 37.1155 | − | 31.1436i | 1.17901 | − | 0.989309i | 0.179028 | − | 0.983844i | \(-0.442705\pi\) |
0.999985 | − | 0.00546523i | \(-0.00173964\pi\) | |||||||
\(992\) | −11.3287 | + | 4.12330i | −0.359686 | + | 0.130915i | ||||
\(993\) | 17.0839 | + | 6.21804i | 0.542142 | + | 0.197324i | ||||
\(994\) | −2.09091 | − | 1.75448i | −0.0663197 | − | 0.0556488i | ||||
\(995\) | 8.29180 | − | 14.3618i | 0.262868 | − | 0.455300i | ||||
\(996\) | 1.00000 | + | 1.73205i | 0.0316862 | + | 0.0548821i | ||||
\(997\) | 4.56552 | − | 25.8924i | 0.144592 | − | 0.820019i | −0.823103 | − | 0.567893i | \(-0.807759\pi\) |
0.967694 | − | 0.252127i | \(-0.0811300\pi\) | |||||||
\(998\) | −1.62318 | + | 9.20551i | −0.0513809 | + | 0.291395i | ||||
\(999\) | −2.39919 | − | 4.15551i | −0.0759069 | − | 0.131475i |
(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 | 361.2.e.i.28.2 | 12 | ||
19.2 | odd | 18 | 361.2.e.j.245.1 | 12 | |||
19.3 | odd | 18 | 361.2.e.j.62.2 | 12 | |||
19.4 | even | 9 | 361.2.c.g.68.1 | 4 | |||
19.5 | even | 9 | inner | 361.2.e.i.54.2 | 12 | ||
19.6 | even | 9 | 361.2.a.c.1.2 | ✓ | 2 | ||
19.7 | even | 3 | inner | 361.2.e.i.99.1 | 12 | ||
19.8 | odd | 6 | 361.2.e.j.234.1 | 12 | |||
19.9 | even | 9 | 361.2.c.g.292.1 | 4 | |||
19.10 | odd | 18 | 361.2.c.d.292.2 | 4 | |||
19.11 | even | 3 | inner | 361.2.e.i.234.2 | 12 | ||
19.12 | odd | 6 | 361.2.e.j.99.2 | 12 | |||
19.13 | odd | 18 | 361.2.a.f.1.1 | yes | 2 | ||
19.14 | odd | 18 | 361.2.e.j.54.1 | 12 | |||
19.15 | odd | 18 | 361.2.c.d.68.2 | 4 | |||
19.16 | even | 9 | inner | 361.2.e.i.62.1 | 12 | ||
19.17 | even | 9 | inner | 361.2.e.i.245.2 | 12 | ||
19.18 | odd | 2 | 361.2.e.j.28.1 | 12 | |||
57.32 | even | 18 | 3249.2.a.i.1.2 | 2 | |||
57.44 | odd | 18 | 3249.2.a.o.1.1 | 2 | |||
76.51 | even | 18 | 5776.2.a.s.1.1 | 2 | |||
76.63 | odd | 18 | 5776.2.a.bg.1.2 | 2 | |||
95.44 | even | 18 | 9025.2.a.s.1.1 | 2 | |||
95.89 | odd | 18 | 9025.2.a.n.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
361.2.a.c.1.2 | ✓ | 2 | 19.6 | even | 9 | ||
361.2.a.f.1.1 | yes | 2 | 19.13 | odd | 18 | ||
361.2.c.d.68.2 | 4 | 19.15 | odd | 18 | |||
361.2.c.d.292.2 | 4 | 19.10 | odd | 18 | |||
361.2.c.g.68.1 | 4 | 19.4 | even | 9 | |||
361.2.c.g.292.1 | 4 | 19.9 | even | 9 | |||
361.2.e.i.28.2 | 12 | 1.1 | even | 1 | trivial | ||
361.2.e.i.54.2 | 12 | 19.5 | even | 9 | inner | ||
361.2.e.i.62.1 | 12 | 19.16 | even | 9 | inner | ||
361.2.e.i.99.1 | 12 | 19.7 | even | 3 | inner | ||
361.2.e.i.234.2 | 12 | 19.11 | even | 3 | inner | ||
361.2.e.i.245.2 | 12 | 19.17 | even | 9 | inner | ||
361.2.e.j.28.1 | 12 | 19.18 | odd | 2 | |||
361.2.e.j.54.1 | 12 | 19.14 | odd | 18 | |||
361.2.e.j.62.2 | 12 | 19.3 | odd | 18 | |||
361.2.e.j.99.2 | 12 | 19.12 | odd | 6 | |||
361.2.e.j.234.1 | 12 | 19.8 | odd | 6 | |||
361.2.e.j.245.1 | 12 | 19.2 | odd | 18 | |||
3249.2.a.i.1.2 | 2 | 57.32 | even | 18 | |||
3249.2.a.o.1.1 | 2 | 57.44 | odd | 18 | |||
5776.2.a.s.1.1 | 2 | 76.51 | even | 18 | |||
5776.2.a.bg.1.2 | 2 | 76.63 | odd | 18 | |||
9025.2.a.n.1.2 | 2 | 95.89 | odd | 18 | |||
9025.2.a.s.1.1 | 2 | 95.44 | even | 18 |