Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [361,2,Mod(68,361)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(361, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("361.68");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 361 = 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 361.c (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.88259951297\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 2x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 292.1 | ||
Root | \(-0.309017 - 0.535233i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 361.292 |
Dual form | 361.2.c.g.68.1 |
$q$-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 \(\left(\mathbb{Z}/361\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.309017 | − | 0.535233i | −0.218508 | − | 0.378467i | 0.735844 | − | 0.677151i | \(-0.236786\pi\) |
−0.954352 | + | 0.298684i | \(0.903452\pi\) | |||||||
\(3\) | 1.30902 | + | 2.26728i | 0.755761 | + | 1.30902i | 0.944995 | + | 0.327085i | \(0.106066\pi\) |
−0.189234 | + | 0.981932i | \(0.560600\pi\) | |||||||
\(4\) | 0.809017 | − | 1.40126i | 0.404508 | − | 0.700629i | ||||
\(5\) | 0.618034 | + | 1.07047i | 0.276393 | + | 0.478727i | 0.970486 | − | 0.241159i | \(-0.0775275\pi\) |
−0.694092 | + | 0.719886i | \(0.744194\pi\) | |||||||
\(6\) | 0.809017 | − | 1.40126i | 0.330280 | − | 0.572061i | ||||
\(7\) | 3.00000 | 1.13389 | 0.566947 | − | 0.823754i | \(-0.308125\pi\) | ||||
0.566947 | + | 0.823754i | \(0.308125\pi\) | |||||||
\(8\) | −2.23607 | −0.790569 | ||||||||
\(9\) | −1.92705 | + | 3.33775i | −0.642350 | + | 1.11258i | ||||
\(10\) | 0.381966 | − | 0.661585i | 0.120788 | − | 0.209211i | ||||
\(11\) | 0.618034 | 0.186344 | 0.0931721 | − | 0.995650i | \(-0.470299\pi\) | ||||
0.0931721 | + | 0.995650i | \(0.470299\pi\) | |||||||
\(12\) | 4.23607 | 1.22285 | ||||||||
\(13\) | −0.500000 | + | 0.866025i | −0.138675 | + | 0.240192i | −0.926995 | − | 0.375073i | \(-0.877618\pi\) |
0.788320 | + | 0.615265i | \(0.210951\pi\) | |||||||
\(14\) | −0.927051 | − | 1.60570i | −0.247765 | − | 0.429141i | ||||
\(15\) | −1.61803 | + | 2.80252i | −0.417775 | + | 0.723607i | ||||
\(16\) | −0.927051 | − | 1.60570i | −0.231763 | − | 0.401425i | ||||
\(17\) | −2.61803 | − | 4.53457i | −0.634967 | − | 1.09979i | −0.986522 | − | 0.163627i | \(-0.947681\pi\) |
0.351556 | − | 0.936167i | \(-0.385653\pi\) | |||||||
\(18\) | 2.38197 | 0.561435 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 2.00000 | 0.447214 | ||||||||
\(21\) | 3.92705 | + | 6.80185i | 0.856953 | + | 1.48429i | ||||
\(22\) | −0.190983 | − | 0.330792i | −0.0407177 | − | 0.0705251i | ||||
\(23\) | −3.80902 | + | 6.59741i | −0.794235 | + | 1.37566i | 0.129089 | + | 0.991633i | \(0.458795\pi\) |
−0.923324 | + | 0.384022i | \(0.874539\pi\) | |||||||
\(24\) | −2.92705 | − | 5.06980i | −0.597482 | − | 1.03487i | ||||
\(25\) | 1.73607 | − | 3.00696i | 0.347214 | − | 0.601392i | ||||
\(26\) | 0.618034 | 0.121206 | ||||||||
\(27\) | −2.23607 | −0.430331 | ||||||||
\(28\) | 2.42705 | − | 4.20378i | 0.458670 | − | 0.794439i | ||||
\(29\) | −0.690983 | + | 1.19682i | −0.128312 | + | 0.222243i | −0.923023 | − | 0.384745i | \(-0.874289\pi\) |
0.794711 | + | 0.606989i | \(0.207623\pi\) | |||||||
\(30\) | 2.00000 | 0.365148 | ||||||||
\(31\) | 2.14590 | 0.385415 | 0.192707 | − | 0.981256i | \(-0.438273\pi\) | ||||
0.192707 | + | 0.981256i | \(0.438273\pi\) | |||||||
\(32\) | −2.80902 | + | 4.86536i | −0.496569 | + | 0.860082i | ||||
\(33\) | 0.809017 | + | 1.40126i | 0.140832 | + | 0.243928i | ||||
\(34\) | −1.61803 | + | 2.80252i | −0.277491 | + | 0.480628i | ||||
\(35\) | 1.85410 | + | 3.21140i | 0.313400 | + | 0.542825i | ||||
\(36\) | 3.11803 | + | 5.40059i | 0.519672 | + | 0.900099i | ||||
\(37\) | −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 | ||||||||
\(40\) | −1.38197 | − | 2.39364i | −0.218508 | − | 0.378467i | ||||
\(41\) | −1.50000 | − | 2.59808i | −0.234261 | − | 0.405751i | 0.724797 | − | 0.688963i | \(-0.241934\pi\) |
−0.959058 | + | 0.283211i | \(0.908600\pi\) | |||||||
\(42\) | 2.42705 | − | 4.20378i | 0.374502 | − | 0.648657i | ||||
\(43\) | 3.42705 | + | 5.93583i | 0.522620 | + | 0.905205i | 0.999654 | + | 0.0263198i | \(0.00837881\pi\) |
−0.477033 | + | 0.878885i | \(0.658288\pi\) | |||||||
\(44\) | 0.500000 | − | 0.866025i | 0.0753778 | − | 0.130558i | ||||
\(45\) | −4.76393 | −0.710165 | ||||||||
\(46\) | 4.70820 | 0.694187 | ||||||||
\(47\) | −1.50000 | + | 2.59808i | −0.218797 | + | 0.378968i | −0.954441 | − | 0.298401i | \(-0.903547\pi\) |
0.735643 | + | 0.677369i | \(0.236880\pi\) | |||||||
\(48\) | 2.42705 | − | 4.20378i | 0.350315 | − | 0.606763i | ||||
\(49\) | 2.00000 | 0.285714 | ||||||||
\(50\) | −2.14590 | −0.303476 | ||||||||
\(51\) | 6.85410 | − | 11.8717i | 0.959766 | − | 1.66236i | ||||
\(52\) | 0.809017 | + | 1.40126i | 0.112190 | + | 0.194320i | ||||
\(53\) | 4.66312 | − | 8.07676i | 0.640529 | − | 1.10943i | −0.344786 | − | 0.938681i | \(-0.612049\pi\) |
0.985315 | − | 0.170747i | \(-0.0546181\pi\) | |||||||
\(54\) | 0.690983 | + | 1.19682i | 0.0940309 | + | 0.162866i | ||||
\(55\) | 0.381966 | + | 0.661585i | 0.0515043 | + | 0.0892080i | ||||
\(56\) | −6.70820 | −0.896421 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.854102 | 0.112149 | ||||||||
\(59\) | −7.66312 | − | 13.2729i | −0.997653 | − | 1.72799i | −0.558124 | − | 0.829757i | \(-0.688479\pi\) |
−0.439529 | − | 0.898228i | \(-0.644855\pi\) | |||||||
\(60\) | 2.61803 | + | 4.53457i | 0.337987 | + | 0.585410i | ||||
\(61\) | 2.88197 | − | 4.99171i | 0.368998 | − | 0.639123i | −0.620411 | − | 0.784277i | \(-0.713034\pi\) |
0.989409 | + | 0.145154i | \(0.0463676\pi\) | |||||||
\(62\) | −0.663119 | − | 1.14856i | −0.0842162 | − | 0.145867i | ||||
\(63\) | −5.78115 | + | 10.0133i | −0.728357 | + | 1.26155i | ||||
\(64\) | −0.236068 | −0.0295085 | ||||||||
\(65\) | −1.23607 | −0.153315 | ||||||||
\(66\) | 0.500000 | − | 0.866025i | 0.0615457 | − | 0.106600i | ||||
\(67\) | −3.50000 | + | 6.06218i | −0.427593 | + | 0.740613i | −0.996659 | − | 0.0816792i | \(-0.973972\pi\) |
0.569066 | + | 0.822292i | \(0.307305\pi\) | |||||||
\(68\) | −8.47214 | −1.02740 | ||||||||
\(69\) | −19.9443 | −2.40101 | ||||||||
\(70\) | 1.14590 | − | 1.98475i | 0.136961 | − | 0.237223i | ||||
\(71\) | 0.736068 | + | 1.27491i | 0.0873552 | + | 0.151304i | 0.906392 | − | 0.422437i | \(-0.138825\pi\) |
−0.819037 | + | 0.573740i | \(0.805492\pi\) | |||||||
\(72\) | 4.30902 | − | 7.46344i | 0.507823 | − | 0.879574i | ||||
\(73\) | −5.35410 | − | 9.27358i | −0.626650 | − | 1.08539i | −0.988219 | − | 0.153045i | \(-0.951092\pi\) |
0.361569 | − | 0.932345i | \(-0.382241\pi\) | |||||||
\(74\) | 0.663119 | + | 1.14856i | 0.0770860 | + | 0.133517i | ||||
\(75\) | 9.09017 | 1.04964 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.85410 | 0.211295 | ||||||||
\(78\) | 0.809017 | + | 1.40126i | 0.0916031 | + | 0.158661i | ||||
\(79\) | −6.70820 | − | 11.6190i | −0.754732 | − | 1.30723i | −0.945507 | − | 0.325600i | \(-0.894434\pi\) |
0.190776 | − | 0.981634i | \(-0.438900\pi\) | |||||||
\(80\) | 1.14590 | − | 1.98475i | 0.128115 | − | 0.221902i | ||||
\(81\) | 2.85410 | + | 4.94345i | 0.317122 | + | 0.549272i | ||||
\(82\) | −0.927051 | + | 1.60570i | −0.102376 | + | 0.177320i | ||||
\(83\) | −0.472136 | −0.0518237 | −0.0259118 | − | 0.999664i | \(-0.508249\pi\) | ||||
−0.0259118 | + | 0.999664i | \(0.508249\pi\) | |||||||
\(84\) | 12.7082 | 1.38658 | ||||||||
\(85\) | 3.23607 | − | 5.60503i | 0.351001 | − | 0.607951i | ||||
\(86\) | 2.11803 | − | 3.66854i | 0.228393 | − | 0.395589i | ||||
\(87\) | −3.61803 | −0.387894 | ||||||||
\(88\) | −1.38197 | −0.147318 | ||||||||
\(89\) | −6.11803 | + | 10.5967i | −0.648510 | + | 1.12325i | 0.334968 | + | 0.942229i | \(0.391274\pi\) |
−0.983479 | + | 0.181023i | \(0.942059\pi\) | |||||||
\(90\) | 1.47214 | + | 2.54981i | 0.155177 | + | 0.268774i | ||||
\(91\) | −1.50000 | + | 2.59808i | −0.157243 | + | 0.272352i | ||||
\(92\) | 6.16312 | + | 10.6748i | 0.642550 | + | 1.11293i | ||||
\(93\) | 2.80902 | + | 4.86536i | 0.291281 | + | 0.504514i | ||||
\(94\) | 1.85410 | 0.191236 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −14.7082 | −1.50115 | ||||||||
\(97\) | 3.57295 | + | 6.18853i | 0.362778 | + | 0.628350i | 0.988417 | − | 0.151763i | \(-0.0484950\pi\) |
−0.625639 | + | 0.780113i | \(0.715162\pi\) | |||||||
\(98\) | −0.618034 | − | 1.07047i | −0.0624309 | − | 0.108133i | ||||
\(99\) | −1.19098 | + | 2.06284i | −0.119698 | + | 0.207324i | ||||
\(100\) | −2.80902 | − | 4.86536i | −0.280902 | − | 0.486536i | ||||
\(101\) | −6.59017 | + | 11.4145i | −0.655746 | + | 1.13579i | 0.325960 | + | 0.945384i | \(0.394313\pi\) |
−0.981706 | + | 0.190402i | \(0.939021\pi\) | |||||||
\(102\) | −8.47214 | −0.838866 | ||||||||
\(103\) | 1.32624 | 0.130678 | 0.0653391 | − | 0.997863i | \(-0.479187\pi\) | ||||
0.0653391 | + | 0.997863i | \(0.479187\pi\) | |||||||
\(104\) | 1.11803 | − | 1.93649i | 0.109632 | − | 0.189889i | ||||
\(105\) | −4.85410 | + | 8.40755i | −0.473712 | + | 0.820493i | ||||
\(106\) | −5.76393 | −0.559843 | ||||||||
\(107\) | 10.4164 | 1.00699 | 0.503496 | − | 0.863998i | \(-0.332047\pi\) | ||||
0.503496 | + | 0.863998i | \(0.332047\pi\) | |||||||
\(108\) | −1.80902 | + | 3.13331i | −0.174073 | + | 0.301503i | ||||
\(109\) | −8.35410 | − | 14.4697i | −0.800178 | − | 1.38595i | −0.919499 | − | 0.393093i | \(-0.871405\pi\) |
0.119321 | − | 0.992856i | \(-0.461928\pi\) | |||||||
\(110\) | 0.236068 | − | 0.408882i | 0.0225082 | − | 0.0389853i | ||||
\(111\) | −2.80902 | − | 4.86536i | −0.266620 | − | 0.461800i | ||||
\(112\) | −2.78115 | − | 4.81710i | −0.262794 | − | 0.455173i | ||||
\(113\) | −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 | ||||||||
\(116\) | 1.11803 | + | 1.93649i | 0.103807 | + | 0.179799i | ||||
\(117\) | −1.92705 | − | 3.33775i | −0.178156 | − | 0.308575i | ||||
\(118\) | −4.73607 | + | 8.20311i | −0.435990 | + | 0.755158i | ||||
\(119\) | −7.85410 | − | 13.6037i | −0.719984 | − | 1.24705i | ||||
\(120\) | 3.61803 | − | 6.26662i | 0.330280 | − | 0.572061i | ||||
\(121\) | −10.6180 | −0.965276 | ||||||||
\(122\) | −3.56231 | −0.322516 | ||||||||
\(123\) | 3.92705 | − | 6.80185i | 0.354090 | − | 0.613302i | ||||
\(124\) | 1.73607 | − | 3.00696i | 0.155904 | − | 0.270033i | ||||
\(125\) | 10.4721 | 0.936656 | ||||||||
\(126\) | 7.14590 | 0.636607 | ||||||||
\(127\) | 5.11803 | − | 8.86469i | 0.454152 | − | 0.786614i | −0.544487 | − | 0.838769i | \(-0.683276\pi\) |
0.998639 | + | 0.0521549i | \(0.0166089\pi\) | |||||||
\(128\) | 5.69098 | + | 9.85707i | 0.503017 | + | 0.871250i | ||||
\(129\) | −8.97214 | + | 15.5402i | −0.789953 | + | 1.36824i | ||||
\(130\) | 0.381966 | + | 0.661585i | 0.0335006 | + | 0.0580248i | ||||
\(131\) | −1.95492 | − | 3.38601i | −0.170802 | − | 0.295837i | 0.767899 | − | 0.640571i | \(-0.221302\pi\) |
−0.938700 | + | 0.344734i | \(0.887969\pi\) | |||||||
\(132\) | 2.61803 | 0.227871 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 4.32624 | 0.373730 | ||||||||
\(135\) | −1.38197 | − | 2.39364i | −0.118941 | − | 0.206011i | ||||
\(136\) | 5.85410 | + | 10.1396i | 0.501985 | + | 0.869464i | ||||
\(137\) | 0.736068 | − | 1.27491i | 0.0628865 | − | 0.108923i | −0.832868 | − | 0.553472i | \(-0.813303\pi\) |
0.895755 | + | 0.444549i | \(0.146636\pi\) | |||||||
\(138\) | 6.16312 | + | 10.6748i | 0.524640 | + | 0.908702i | ||||
\(139\) | 4.89919 | − | 8.48564i | 0.415544 | − | 0.719743i | −0.579942 | − | 0.814658i | \(-0.696925\pi\) |
0.995485 | + | 0.0949153i | \(0.0302580\pi\) | |||||||
\(140\) | 6.00000 | 0.507093 | ||||||||
\(141\) | −7.85410 | −0.661435 | ||||||||
\(142\) | 0.454915 | − | 0.787936i | 0.0381756 | − | 0.0661221i | ||||
\(143\) | −0.309017 | + | 0.535233i | −0.0258413 | + | 0.0447584i | ||||
\(144\) | 7.14590 | 0.595492 | ||||||||
\(145\) | −1.70820 | −0.141859 | ||||||||
\(146\) | −3.30902 | + | 5.73139i | −0.273856 | + | 0.474333i | ||||
\(147\) | 2.61803 | + | 4.53457i | 0.215932 | + | 0.374005i | ||||
\(148\) | −1.73607 | + | 3.00696i | −0.142704 | + | 0.247170i | ||||
\(149\) | 6.54508 | + | 11.3364i | 0.536194 | + | 0.928716i | 0.999105 | + | 0.0423105i | \(0.0134719\pi\) |
−0.462910 | + | 0.886405i | \(0.653195\pi\) | |||||||
\(150\) | −2.80902 | − | 4.86536i | −0.229355 | − | 0.397255i | ||||
\(151\) | 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 | ||||||||
\(154\) | −0.572949 | − | 0.992377i | −0.0461695 | − | 0.0799680i | ||||
\(155\) | 1.32624 | + | 2.29711i | 0.106526 | + | 0.184508i | ||||
\(156\) | −2.11803 | + | 3.66854i | −0.169578 | + | 0.293718i | ||||
\(157\) | 5.57295 | + | 9.65263i | 0.444770 | + | 0.770364i | 0.998036 | − | 0.0626406i | \(-0.0199522\pi\) |
−0.553266 | + | 0.833004i | \(0.686619\pi\) | |||||||
\(158\) | −4.14590 | + | 7.18091i | −0.329830 | + | 0.571282i | ||||
\(159\) | 24.4164 | 1.93635 | ||||||||
\(160\) | −6.94427 | −0.548993 | ||||||||
\(161\) | −11.4271 | + | 19.7922i | −0.900578 | + | 1.55985i | ||||
\(162\) | 1.76393 | − | 3.05522i | 0.138588 | − | 0.240041i | ||||
\(163\) | 6.23607 | 0.488447 | 0.244223 | − | 0.969719i | \(-0.421467\pi\) | ||||
0.244223 | + | 0.969719i | \(0.421467\pi\) | |||||||
\(164\) | −4.85410 | −0.379042 | ||||||||
\(165\) | −1.00000 | + | 1.73205i | −0.0778499 | + | 0.134840i | ||||
\(166\) | 0.145898 | + | 0.252703i | 0.0113239 | + | 0.0196135i | ||||
\(167\) | 7.88197 | − | 13.6520i | 0.609925 | − | 1.05642i | −0.381327 | − | 0.924440i | \(-0.624533\pi\) |
0.991252 | − | 0.131981i | \(-0.0421337\pi\) | |||||||
\(168\) | −8.78115 | − | 15.2094i | −0.677481 | − | 1.17343i | ||||
\(169\) | 6.00000 | + | 10.3923i | 0.461538 | + | 0.799408i | ||||
\(170\) | −4.00000 | −0.306786 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 11.0902 | 0.845618 | ||||||||
\(173\) | 4.23607 | + | 7.33708i | 0.322062 | + | 0.557828i | 0.980913 | − | 0.194445i | \(-0.0622906\pi\) |
−0.658851 | + | 0.752273i | \(0.728957\pi\) | |||||||
\(174\) | 1.11803 | + | 1.93649i | 0.0847579 | + | 0.146805i | ||||
\(175\) | 5.20820 | − | 9.02087i | 0.393703 | − | 0.681914i | ||||
\(176\) | −0.572949 | − | 0.992377i | −0.0431877 | − | 0.0748032i | ||||
\(177\) | 20.0623 | − | 34.7489i | 1.50798 | − | 2.61189i | ||||
\(178\) | 7.56231 | 0.566819 | ||||||||
\(179\) | −7.76393 | −0.580304 | −0.290152 | − | 0.956981i | \(-0.593706\pi\) | ||||
−0.290152 | + | 0.956981i | \(0.593706\pi\) | |||||||
\(180\) | −3.85410 | + | 6.67550i | −0.287268 | + | 0.497562i | ||||
\(181\) | 6.00000 | − | 10.3923i | 0.445976 | − | 0.772454i | −0.552143 | − | 0.833749i | \(-0.686190\pi\) |
0.998120 | + | 0.0612954i | \(0.0195232\pi\) | |||||||
\(182\) | 1.85410 | 0.137435 | ||||||||
\(183\) | 15.0902 | 1.11550 | ||||||||
\(184\) | 8.51722 | − | 14.7523i | 0.627898 | − | 1.08755i | ||||
\(185\) | −1.32624 | − | 2.29711i | −0.0975070 | − | 0.168887i | ||||
\(186\) | 1.73607 | − | 3.00696i | 0.127295 | − | 0.220481i | ||||
\(187\) | −1.61803 | − | 2.80252i | −0.118322 | − | 0.204940i | ||||
\(188\) | 2.42705 | + | 4.20378i | 0.177011 | + | 0.306592i | ||||
\(189\) | −6.70820 | −0.487950 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.76393 | 0.706493 | 0.353247 | − | 0.935530i | \(-0.385078\pi\) | ||||
0.353247 | + | 0.935530i | \(0.385078\pi\) | |||||||
\(192\) | −0.309017 | − | 0.535233i | −0.0223014 | − | 0.0386271i | ||||
\(193\) | 11.4721 | + | 19.8703i | 0.825782 | + | 1.43030i | 0.901320 | + | 0.433154i | \(0.142599\pi\) |
−0.0755374 | + | 0.997143i | \(0.524067\pi\) | |||||||
\(194\) | 2.20820 | − | 3.82472i | 0.158540 | − | 0.274599i | ||||
\(195\) | −1.61803 | − | 2.80252i | −0.115870 | − | 0.200692i | ||||
\(196\) | 1.61803 | − | 2.80252i | 0.115574 | − | 0.200180i | ||||
\(197\) | 3.00000 | 0.213741 | 0.106871 | − | 0.994273i | \(-0.465917\pi\) | ||||
0.106871 | + | 0.994273i | \(0.465917\pi\) | |||||||
\(198\) | 1.47214 | 0.104620 | ||||||||
\(199\) | −6.70820 | + | 11.6190i | −0.475532 | + | 0.823646i | −0.999607 | − | 0.0280265i | \(-0.991078\pi\) |
0.524075 | + | 0.851672i | \(0.324411\pi\) | |||||||
\(200\) | −3.88197 | + | 6.72376i | −0.274496 | + | 0.475442i | ||||
\(201\) | −18.3262 | −1.29263 | ||||||||
\(202\) | 8.14590 | 0.573143 | ||||||||
\(203\) | −2.07295 | + | 3.59045i | −0.145492 | + | 0.252000i | ||||
\(204\) | −11.0902 | − | 19.2087i | −0.776467 | − | 1.34488i | ||||
\(205\) | 1.85410 | − | 3.21140i | 0.129496 | − | 0.224294i | ||||
\(206\) | −0.409830 | − | 0.709846i | −0.0285542 | − | 0.0494573i | ||||
\(207\) | −14.6803 | − | 25.4271i | −1.02035 | − | 1.76731i | ||||
\(208\) | 1.85410 | 0.128559 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 6.00000 | 0.414039 | ||||||||
\(211\) | 1.42705 | + | 2.47172i | 0.0982422 | + | 0.170161i | 0.910957 | − | 0.412501i | \(-0.135345\pi\) |
−0.812715 | + | 0.582662i | \(0.802011\pi\) | |||||||
\(212\) | −7.54508 | − | 13.0685i | −0.518199 | − | 0.897546i | ||||
\(213\) | −1.92705 | + | 3.33775i | −0.132039 | + | 0.228699i | ||||
\(214\) | −3.21885 | − | 5.57521i | −0.220036 | − | 0.381113i | ||||
\(215\) | −4.23607 | + | 7.33708i | −0.288897 | + | 0.500385i | ||||
\(216\) | 5.00000 | 0.340207 | ||||||||
\(217\) | 6.43769 | 0.437019 | ||||||||
\(218\) | −5.16312 | + | 8.94278i | −0.349691 | + | 0.605682i | ||||
\(219\) | 14.0172 | − | 24.2785i | 0.947196 | − | 1.64059i | ||||
\(220\) | 1.23607 | 0.0833357 | ||||||||
\(221\) | 5.23607 | 0.352216 | ||||||||
\(222\) | −1.73607 | + | 3.00696i | −0.116517 | + | 0.201814i | ||||
\(223\) | 9.82624 | + | 17.0195i | 0.658014 | + | 1.13971i | 0.981129 | + | 0.193353i | \(0.0619364\pi\) |
−0.323116 | + | 0.946359i | \(0.604730\pi\) | |||||||
\(224\) | −8.42705 | + | 14.5961i | −0.563056 | + | 0.975242i | ||||
\(225\) | 6.69098 | + | 11.5891i | 0.446066 | + | 0.772608i | ||||
\(226\) | 3.47214 | + | 6.01392i | 0.230963 | + | 0.400040i | ||||
\(227\) | 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 | \(0.622725\pi\) | |||||||
\(230\) | 2.90983 | + | 5.03997i | 0.191869 | + | 0.332326i | ||||
\(231\) | 2.42705 | + | 4.20378i | 0.159688 | + | 0.276588i | ||||
\(232\) | 1.54508 | − | 2.67617i | 0.101440 | − | 0.175699i | ||||
\(233\) | −6.73607 | − | 11.6672i | −0.441294 | − | 0.764344i | 0.556491 | − | 0.830853i | \(-0.312147\pi\) |
−0.997786 | + | 0.0665089i | \(0.978814\pi\) | |||||||
\(234\) | −1.19098 | + | 2.06284i | −0.0778570 | + | 0.134852i | ||||
\(235\) | −3.70820 | −0.241897 | ||||||||
\(236\) | −24.7984 | −1.61424 | ||||||||
\(237\) | 17.5623 | − | 30.4188i | 1.14079 | − | 1.97591i | ||||
\(238\) | −4.85410 | + | 8.40755i | −0.314645 | + | 0.544981i | ||||
\(239\) | 15.3262 | 0.991372 | 0.495686 | − | 0.868502i | \(-0.334917\pi\) | ||||
0.495686 | + | 0.868502i | \(0.334917\pi\) | |||||||
\(240\) | 6.00000 | 0.387298 | ||||||||
\(241\) | −9.59017 | + | 16.6107i | −0.617757 | + | 1.06999i | 0.372137 | + | 0.928178i | \(0.378625\pi\) |
−0.989894 | + | 0.141809i | \(0.954708\pi\) | |||||||
\(242\) | 3.28115 | + | 5.68312i | 0.210921 | + | 0.365325i | ||||
\(243\) | −10.8262 | + | 18.7516i | −0.694503 | + | 1.20292i | ||||
\(244\) | −4.66312 | − | 8.07676i | −0.298526 | − | 0.517062i | ||||
\(245\) | 1.23607 | + | 2.14093i | 0.0789695 | + | 0.136779i | ||||
\(246\) | −4.85410 | −0.309486 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −4.79837 | −0.304697 | ||||||||
\(249\) | −0.618034 | − | 1.07047i | −0.0391663 | − | 0.0678380i | ||||
\(250\) | −3.23607 | − | 5.60503i | −0.204667 | − | 0.354493i | ||||
\(251\) | −9.68034 | + | 16.7668i | −0.611018 | + | 1.05831i | 0.380052 | + | 0.924965i | \(0.375906\pi\) |
−0.991069 | + | 0.133348i | \(0.957427\pi\) | |||||||
\(252\) | 9.35410 | + | 16.2018i | 0.589253 | + | 1.02062i | ||||
\(253\) | −2.35410 | + | 4.07742i | −0.148001 | + | 0.256345i | ||||
\(254\) | −6.32624 | −0.396943 | ||||||||
\(255\) | 16.9443 | 1.06109 | ||||||||
\(256\) | 3.28115 | − | 5.68312i | 0.205072 | − | 0.355195i | ||||
\(257\) | −12.1803 | + | 21.0970i | −0.759789 | + | 1.31599i | 0.183169 | + | 0.983081i | \(0.441364\pi\) |
−0.942958 | + | 0.332911i | \(0.891969\pi\) | |||||||
\(258\) | 11.0902 | 0.690444 | ||||||||
\(259\) | −6.43769 | −0.400019 | ||||||||
\(260\) | −1.00000 | + | 1.73205i | −0.0620174 | + | 0.107417i | ||||
\(261\) | −2.66312 | − | 4.61266i | −0.164843 | − | 0.285516i | ||||
\(262\) | −1.20820 | + | 2.09267i | −0.0746431 | + | 0.129286i | ||||
\(263\) | −1.47214 | − | 2.54981i | −0.0907758 | − | 0.157228i | 0.817062 | − | 0.576550i | \(-0.195601\pi\) |
−0.907838 | + | 0.419322i | \(0.862268\pi\) | |||||||
\(264\) | −1.80902 | − | 3.13331i | −0.111337 | − | 0.192842i | ||||
\(265\) | 11.5279 | 0.708151 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −32.0344 | −1.96048 | ||||||||
\(268\) | 5.66312 | + | 9.80881i | 0.345930 | + | 0.599168i | ||||
\(269\) | 7.33688 | + | 12.7079i | 0.447338 | + | 0.774811i | 0.998212 | − | 0.0597769i | \(-0.0190389\pi\) |
−0.550874 | + | 0.834588i | \(0.685706\pi\) | |||||||
\(270\) | −0.854102 | + | 1.47935i | −0.0519790 | + | 0.0900303i | ||||
\(271\) | −3.92705 | − | 6.80185i | −0.238551 | − | 0.413183i | 0.721747 | − | 0.692156i | \(-0.243339\pi\) |
−0.960299 | + | 0.278973i | \(0.910006\pi\) | |||||||
\(272\) | −4.85410 | + | 8.40755i | −0.294323 | + | 0.509783i | ||||
\(273\) | −7.85410 | −0.475352 | ||||||||
\(274\) | −0.909830 | −0.0549648 | ||||||||
\(275\) | 1.07295 | − | 1.85840i | 0.0647013 | − | 0.112066i | ||||
\(276\) | −16.1353 | + | 27.9471i | −0.971228 | + | 1.68222i | ||||
\(277\) | −15.4164 | −0.926282 | −0.463141 | − | 0.886285i | \(-0.653278\pi\) | ||||
−0.463141 | + | 0.886285i | \(0.653278\pi\) | |||||||
\(278\) | −6.05573 | −0.363198 | ||||||||
\(279\) | −4.13525 | + | 7.16247i | −0.247571 | + | 0.428806i | ||||
\(280\) | −4.14590 | − | 7.18091i | −0.247765 | − | 0.429141i | ||||
\(281\) | 4.25329 | − | 7.36691i | 0.253730 | − | 0.439473i | −0.710820 | − | 0.703374i | \(-0.751676\pi\) |
0.964550 | + | 0.263901i | \(0.0850092\pi\) | |||||||
\(282\) | 2.42705 | + | 4.20378i | 0.144529 | + | 0.250331i | ||||
\(283\) | 1.51722 | + | 2.62790i | 0.0901894 | + | 0.156213i | 0.907591 | − | 0.419856i | \(-0.137919\pi\) |
−0.817401 | + | 0.576069i | \(0.804586\pi\) | |||||||
\(284\) | 2.38197 | 0.141344 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.381966 | 0.0225861 | ||||||||
\(287\) | −4.50000 | − | 7.79423i | −0.265627 | − | 0.460079i | ||||
\(288\) | −10.8262 | − | 18.7516i | −0.637942 | − | 1.10495i | ||||
\(289\) | −5.20820 | + | 9.02087i | −0.306365 | + | 0.530640i | ||||
\(290\) | 0.527864 | + | 0.914287i | 0.0309972 | + | 0.0536888i | ||||
\(291\) | −9.35410 | + | 16.2018i | −0.548347 | + | 0.949765i | ||||
\(292\) | −17.3262 | −1.01394 | ||||||||
\(293\) | 16.8541 | 0.984627 | 0.492314 | − | 0.870418i | \(-0.336151\pi\) | ||||
0.492314 | + | 0.870418i | \(0.336151\pi\) | |||||||
\(294\) | 1.61803 | − | 2.80252i | 0.0943657 | − | 0.163446i | ||||
\(295\) | 9.47214 | − | 16.4062i | 0.551489 | − | 0.955207i | ||||
\(296\) | 4.79837 | 0.278900 | ||||||||
\(297\) | −1.38197 | −0.0801898 | ||||||||
\(298\) | 4.04508 | − | 7.00629i | 0.234325 | − | 0.405864i | ||||
\(299\) | −3.80902 | − | 6.59741i | −0.220281 | − | 0.381538i | ||||
\(300\) | 7.35410 | − | 12.7377i | 0.424589 | − | 0.735410i | ||||
\(301\) | 10.2812 | + | 17.8075i | 0.592596 | + | 1.02641i | ||||
\(302\) | −3.06231 | − | 5.30407i | −0.176216 | − | 0.305215i | ||||
\(303\) | −34.5066 | −1.98235 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.12461 | 0.407954 | ||||||||
\(306\) | −6.23607 | − | 10.8012i | −0.356492 | − | 0.617463i | ||||
\(307\) | −0.836881 | − | 1.44952i | −0.0477633 | − | 0.0827285i | 0.841155 | − | 0.540794i | \(-0.181876\pi\) |
−0.888919 | + | 0.458065i | \(0.848543\pi\) | |||||||
\(308\) | 1.50000 | − | 2.59808i | 0.0854704 | − | 0.148039i | ||||
\(309\) | 1.73607 | + | 3.00696i | 0.0987615 | + | 0.171060i | ||||
\(310\) | 0.819660 | − | 1.41969i | 0.0465536 | − | 0.0806331i | ||||
\(311\) | −18.6525 | −1.05768 | −0.528842 | − | 0.848720i | \(-0.677374\pi\) | ||||
−0.528842 | + | 0.848720i | \(0.677374\pi\) | |||||||
\(312\) | 5.85410 | 0.331423 | ||||||||
\(313\) | −2.16312 | + | 3.74663i | −0.122267 | + | 0.211772i | −0.920661 | − | 0.390363i | \(-0.872350\pi\) |
0.798395 | + | 0.602135i | \(0.205683\pi\) | |||||||
\(314\) | 3.44427 | − | 5.96565i | 0.194372 | − | 0.336661i | ||||
\(315\) | −14.2918 | −0.805251 | ||||||||
\(316\) | −21.7082 | −1.22118 | ||||||||
\(317\) | 9.00000 | − | 15.5885i | 0.505490 | − | 0.875535i | −0.494489 | − | 0.869184i | \(-0.664645\pi\) |
0.999980 | − | 0.00635137i | \(-0.00202172\pi\) | |||||||
\(318\) | −7.54508 | − | 13.0685i | −0.423107 | − | 0.732843i | ||||
\(319\) | −0.427051 | + | 0.739674i | −0.0239103 | + | 0.0414138i | ||||
\(320\) | −0.145898 | − | 0.252703i | −0.00815595 | − | 0.0141265i | ||||
\(321\) | 13.6353 | + | 23.6170i | 0.761046 | + | 1.31817i | ||||
\(322\) | 14.1246 | 0.787134 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 9.23607 | 0.513115 | ||||||||
\(325\) | 1.73607 | + | 3.00696i | 0.0962997 | + | 0.166796i | ||||
\(326\) | −1.92705 | − | 3.33775i | −0.106729 | − | 0.184861i | ||||
\(327\) | 21.8713 | − | 37.8822i | 1.20949 | − | 2.09489i | ||||
\(328\) | 3.35410 | + | 5.80948i | 0.185199 | + | 0.320775i | ||||
\(329\) | −4.50000 | + | 7.79423i | −0.248093 | + | 0.429710i | ||||
\(330\) | 1.23607 | 0.0680433 | ||||||||
\(331\) | 6.94427 | 0.381692 | 0.190846 | − | 0.981620i | \(-0.438877\pi\) | ||||
0.190846 | + | 0.981620i | \(0.438877\pi\) | |||||||
\(332\) | −0.381966 | + | 0.661585i | −0.0209631 | + | 0.0363092i | ||||
\(333\) | 4.13525 | − | 7.16247i | 0.226611 | − | 0.392501i | ||||
\(334\) | −9.74265 | −0.533094 | ||||||||
\(335\) | −8.65248 | −0.472735 | ||||||||
\(336\) | 7.28115 | − | 12.6113i | 0.397219 | − | 0.688004i | ||||
\(337\) | 11.5623 | + | 20.0265i | 0.629839 | + | 1.09091i | 0.987584 | + | 0.157094i | \(0.0502124\pi\) |
−0.357745 | + | 0.933819i | \(0.616454\pi\) | |||||||
\(338\) | 3.70820 | − | 6.42280i | 0.201700 | − | 0.349354i | ||||
\(339\) | −14.7082 | − | 25.4754i | −0.798840 | − | 1.38363i | ||||
\(340\) | −5.23607 | − | 9.06914i | −0.283966 | − | 0.491843i | ||||
\(341\) | 1.32624 | 0.0718198 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.0000 | −0.809924 | ||||||||
\(344\) | −7.66312 | − | 13.2729i | −0.413168 | − | 0.715627i | ||||
\(345\) | −12.3262 | − | 21.3497i | −0.663622 | − | 1.14943i | ||||
\(346\) | 2.61803 | − | 4.53457i | 0.140746 | − | 0.243780i | ||||
\(347\) | −0.708204 | − | 1.22665i | −0.0380184 | − | 0.0658498i | 0.846390 | − | 0.532563i | \(-0.178771\pi\) |
−0.884408 | + | 0.466714i | \(0.845438\pi\) | |||||||
\(348\) | −2.92705 | + | 5.06980i | −0.156906 | + | 0.271770i | ||||
\(349\) | 25.9787 | 1.39061 | 0.695304 | − | 0.718715i | \(-0.255270\pi\) | ||||
0.695304 | + | 0.718715i | \(0.255270\pi\) | |||||||
\(350\) | −6.43769 | −0.344109 | ||||||||
\(351\) | 1.11803 | − | 1.93649i | 0.0596762 | − | 0.103362i | ||||
\(352\) | −1.73607 | + | 3.00696i | −0.0925327 | + | 0.160271i | ||||
\(353\) | −31.4508 | −1.67396 | −0.836980 | − | 0.547234i | \(-0.815681\pi\) | ||||
−0.836980 | + | 0.547234i | \(0.815681\pi\) | |||||||
\(354\) | −24.7984 | −1.31802 | ||||||||
\(355\) | −0.909830 | + | 1.57587i | −0.0482888 | + | 0.0836386i | ||||
\(356\) | 9.89919 | + | 17.1459i | 0.524656 | + | 0.908731i | ||||
\(357\) | 20.5623 | − | 35.6150i | 1.08827 | − | 1.88494i | ||||
\(358\) | 2.39919 | + | 4.15551i | 0.126801 | + | 0.219626i | ||||
\(359\) | 11.0172 | + | 19.0824i | 0.581467 | + | 1.00713i | 0.995306 | + | 0.0967798i | \(0.0308543\pi\) |
−0.413839 | + | 0.910350i | \(0.635812\pi\) | |||||||
\(360\) | 10.6525 | 0.561435 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −7.41641 | −0.389798 | ||||||||
\(363\) | −13.8992 | − | 24.0741i | −0.729518 | − | 1.26356i | ||||
\(364\) | 2.42705 | + | 4.20378i | 0.127212 | + | 0.220338i | ||||
\(365\) | 6.61803 | − | 11.4628i | 0.346404 | − | 0.599989i | ||||
\(366\) | −4.66312 | − | 8.07676i | −0.243745 | − | 0.422179i | ||||
\(367\) | −0.972136 | + | 1.68379i | −0.0507451 | + | 0.0878931i | −0.890282 | − | 0.455409i | \(-0.849493\pi\) |
0.839537 | + | 0.543302i | \(0.182826\pi\) | |||||||
\(368\) | 14.1246 | 0.736296 | ||||||||
\(369\) | 11.5623 | 0.601910 | ||||||||
\(370\) | −0.819660 | + | 1.41969i | −0.0426121 | + | 0.0738063i | ||||
\(371\) | 13.9894 | − | 24.2303i | 0.726291 | − | 1.25797i | ||||
\(372\) | 9.09017 | 0.471303 | ||||||||
\(373\) | −3.47214 | −0.179780 | −0.0898902 | − | 0.995952i | \(-0.528652\pi\) | ||||
−0.0898902 | + | 0.995952i | \(0.528652\pi\) | |||||||
\(374\) | −1.00000 | + | 1.73205i | −0.0517088 | + | 0.0895622i | ||||
\(375\) | 13.7082 | + | 23.7433i | 0.707889 | + | 1.22610i | ||||
\(376\) | 3.35410 | − | 5.80948i | 0.172975 | − | 0.299601i | ||||
\(377\) | −0.690983 | − | 1.19682i | −0.0355874 | − | 0.0616392i | ||||
\(378\) | 2.07295 | + | 3.59045i | 0.106621 | + | 0.184673i | ||||
\(379\) | −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 | ||||||||
\(382\) | −3.01722 | − | 5.22598i | −0.154374 | − | 0.267384i | ||||
\(383\) | 1.30902 | + | 2.26728i | 0.0668876 | + | 0.115853i | 0.897530 | − | 0.440954i | \(-0.145360\pi\) |
−0.830642 | + | 0.556807i | \(0.812026\pi\) | |||||||
\(384\) | −14.8992 | + | 25.8061i | −0.760321 | + | 1.31691i | ||||
\(385\) | 1.14590 | + | 1.98475i | 0.0584004 | + | 0.101152i | ||||
\(386\) | 7.09017 | − | 12.2805i | 0.360880 | − | 0.625063i | ||||
\(387\) | −26.4164 | −1.34282 | ||||||||
\(388\) | 11.5623 | 0.586987 | ||||||||
\(389\) | 12.1353 | − | 21.0189i | 0.615282 | − | 1.06570i | −0.375053 | − | 0.927003i | \(-0.622376\pi\) |
0.990335 | − | 0.138696i | \(-0.0442911\pi\) | |||||||
\(390\) | −1.00000 | + | 1.73205i | −0.0506370 | + | 0.0877058i | ||||
\(391\) | 39.8885 | 2.01725 | ||||||||
\(392\) | −4.47214 | −0.225877 | ||||||||
\(393\) | 5.11803 | − | 8.86469i | 0.258171 | − | 0.447165i | ||||
\(394\) | −0.927051 | − | 1.60570i | −0.0467042 | − | 0.0808940i | ||||
\(395\) | 8.29180 | − | 14.3618i | 0.417206 | − | 0.722621i | ||||
\(396\) | 1.92705 | + | 3.33775i | 0.0968380 | + | 0.167728i | ||||
\(397\) | 1.26393 | + | 2.18919i | 0.0634349 | + | 0.109873i | 0.895999 | − | 0.444057i | \(-0.146461\pi\) |
−0.832564 | + | 0.553929i | \(0.813128\pi\) | |||||||
\(398\) | 8.29180 | 0.415630 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.43769 | −0.321885 | ||||||||
\(401\) | −0.0557281 | − | 0.0965239i | −0.00278293 | − | 0.00482017i | 0.864631 | − | 0.502408i | \(-0.167553\pi\) |
−0.867414 | + | 0.497588i | \(0.834219\pi\) | |||||||
\(402\) | 5.66312 | + | 9.80881i | 0.282451 | + | 0.489219i | ||||
\(403\) | −1.07295 | + | 1.85840i | −0.0534474 | + | 0.0925736i | ||||
\(404\) | 10.6631 | + | 18.4691i | 0.530510 | + | 0.918870i | ||||
\(405\) | −3.52786 | + | 6.11044i | −0.175301 | + | 0.303630i | ||||
\(406\) | 2.56231 | 0.127165 | ||||||||
\(407\) | −1.32624 | −0.0657392 | ||||||||
\(408\) | −15.3262 | + | 26.5458i | −0.758762 | + | 1.31421i | ||||
\(409\) | −10.8541 | + | 18.7999i | −0.536701 | + | 0.929593i | 0.462378 | + | 0.886683i | \(0.346996\pi\) |
−0.999079 | + | 0.0429102i | \(0.986337\pi\) | |||||||
\(410\) | −2.29180 | −0.113184 | ||||||||
\(411\) | 3.85410 | 0.190109 | ||||||||
\(412\) | 1.07295 | − | 1.85840i | 0.0528604 | − | 0.0915569i | ||||
\(413\) | −22.9894 | − | 39.8187i | −1.13123 | − | 1.95935i | ||||
\(414\) | −9.07295 | + | 15.7148i | −0.445911 | + | 0.772341i | ||||
\(415\) | −0.291796 | − | 0.505406i | −0.0143237 | − | 0.0248094i | ||||
\(416\) | −2.80902 | − | 4.86536i | −0.137723 | − | 0.238544i | ||||
\(417\) | 25.6525 | 1.25621 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.94427 | 0.436956 | 0.218478 | − | 0.975842i | \(-0.429891\pi\) | ||||
0.218478 | + | 0.975842i | \(0.429891\pi\) | |||||||
\(420\) | 7.85410 | + | 13.6037i | 0.383241 | + | 0.663793i | ||||
\(421\) | −9.26393 | − | 16.0456i | −0.451496 | − | 0.782015i | 0.546983 | − | 0.837144i | \(-0.315776\pi\) |
−0.998479 | + | 0.0551291i | \(0.982443\pi\) | |||||||
\(422\) | 0.881966 | − | 1.52761i | 0.0429334 | − | 0.0743629i | ||||
\(423\) | −5.78115 | − | 10.0133i | −0.281089 | − | 0.486861i | ||||
\(424\) | −10.4271 | + | 18.0602i | −0.506382 | + | 0.877080i | ||||
\(425\) | −18.1803 | −0.881876 | ||||||||
\(426\) | 2.38197 | 0.115407 | ||||||||
\(427\) | 8.64590 | − | 14.9751i | 0.418404 | − | 0.724698i | ||||
\(428\) | 8.42705 | − | 14.5961i | 0.407337 | − | 0.705528i | ||||
\(429\) | −1.61803 | −0.0781194 | ||||||||
\(430\) | 5.23607 | 0.252506 | ||||||||
\(431\) | −1.82624 | + | 3.16314i | −0.0879668 | + | 0.152363i | −0.906652 | − | 0.421880i | \(-0.861370\pi\) |
0.818685 | + | 0.574243i | \(0.194704\pi\) | |||||||
\(432\) | 2.07295 | + | 3.59045i | 0.0997348 | + | 0.172746i | ||||
\(433\) | −11.7812 | + | 20.4056i | −0.566166 | + | 0.980628i | 0.430774 | + | 0.902460i | \(0.358241\pi\) |
−0.996940 | + | 0.0781686i | \(0.975093\pi\) | |||||||
\(434\) | −1.98936 | − | 3.44567i | −0.0954922 | − | 0.165397i | ||||
\(435\) | −2.23607 | − | 3.87298i | −0.107211 | − | 0.185695i | ||||
\(436\) | −27.0344 | −1.29471 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −17.3262 | −0.827880 | ||||||||
\(439\) | 7.29837 | + | 12.6412i | 0.348332 | + | 0.603329i | 0.985953 | − | 0.167021i | \(-0.0534147\pi\) |
−0.637621 | + | 0.770350i | \(0.720081\pi\) | |||||||
\(440\) | −0.854102 | − | 1.47935i | −0.0407177 | − | 0.0705251i | ||||
\(441\) | −3.85410 | + | 6.67550i | −0.183529 | + | 0.317881i | ||||
\(442\) | −1.61803 | − | 2.80252i | −0.0769620 | − | 0.133302i | ||||
\(443\) | 17.2082 | − | 29.8055i | 0.817586 | − | 1.41610i | −0.0898693 | − | 0.995954i | \(-0.528645\pi\) |
0.907456 | − | 0.420148i | \(-0.138022\pi\) | |||||||
\(444\) | −9.09017 | −0.431400 | ||||||||
\(445\) | −15.1246 | −0.716975 | ||||||||
\(446\) | 6.07295 | − | 10.5187i | 0.287562 | − | 0.498073i | ||||
\(447\) | −17.1353 | + | 29.6791i | −0.810470 | + | 1.40377i | ||||
\(448\) | −0.708204 | −0.0334595 | ||||||||
\(449\) | 32.8885 | 1.55211 | 0.776053 | − | 0.630667i | \(-0.217219\pi\) | ||||
0.776053 | + | 0.630667i | \(0.217219\pi\) | |||||||
\(450\) | 4.13525 | − | 7.16247i | 0.194938 | − | 0.337642i | ||||
\(451\) | −0.927051 | − | 1.60570i | −0.0436531 | − | 0.0756094i | ||||
\(452\) | −9.09017 | + | 15.7446i | −0.427566 | + | 0.740565i | ||||
\(453\) | 12.9721 | + | 22.4684i | 0.609484 | + | 1.05566i | ||||
\(454\) | −3.21885 | − | 5.57521i | −0.151068 | − | 0.261657i | ||||
\(455\) | −3.70820 | −0.173843 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.29180 | 0.294318 | 0.147159 | − | 0.989113i | \(-0.452987\pi\) | ||||
0.147159 | + | 0.989113i | \(0.452987\pi\) | |||||||
\(458\) | 3.51722 | + | 6.09201i | 0.164349 | + | 0.284661i | ||||
\(459\) | 5.85410 | + | 10.1396i | 0.273246 | + | 0.473276i | ||||
\(460\) | −7.61803 | + | 13.1948i | −0.355193 | + | 0.615212i | ||||
\(461\) | −1.52786 | − | 2.64634i | −0.0711597 | − | 0.123252i | 0.828250 | − | 0.560359i | \(-0.189337\pi\) |
−0.899410 | + | 0.437106i | \(0.856003\pi\) | |||||||
\(462\) | 1.50000 | − | 2.59808i | 0.0697863 | − | 0.120873i | ||||
\(463\) | −5.27051 | −0.244941 | −0.122471 | − | 0.992472i | \(-0.539082\pi\) | ||||
−0.122471 | + | 0.992472i | \(0.539082\pi\) | |||||||
\(464\) | 2.56231 | 0.118952 | ||||||||
\(465\) | −3.47214 | + | 6.01392i | −0.161016 | + | 0.278889i | ||||
\(466\) | −4.16312 | + | 7.21073i | −0.192853 | + | 0.334031i | ||||
\(467\) | 1.94427 | 0.0899702 | 0.0449851 | − | 0.998988i | \(-0.485676\pi\) | ||||
0.0449851 | + | 0.998988i | \(0.485676\pi\) | |||||||
\(468\) | −6.23607 | −0.288262 | ||||||||
\(469\) | −10.5000 | + | 18.1865i | −0.484845 | + | 0.839776i | ||||
\(470\) | 1.14590 | + | 1.98475i | 0.0528563 | + | 0.0915499i | ||||
\(471\) | −14.5902 | + | 25.2709i | −0.672280 | + | 1.16442i | ||||
\(472\) | 17.1353 | + | 29.6791i | 0.788714 | + | 1.36609i | ||||
\(473\) | 2.11803 | + | 3.66854i | 0.0973873 | + | 0.168680i | ||||
\(474\) | −21.7082 | −0.997091 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −25.4164 | −1.16496 | ||||||||
\(477\) | 17.9721 | + | 31.1287i | 0.822888 | + | 1.42528i | ||||
\(478\) | −4.73607 | − | 8.20311i | −0.216623 | − | 0.375202i | ||||
\(479\) | −5.95492 | + | 10.3142i | −0.272087 | + | 0.471269i | −0.969396 | − | 0.245502i | \(-0.921047\pi\) |
0.697309 | + | 0.716771i | \(0.254381\pi\) | |||||||
\(480\) | −9.09017 | − | 15.7446i | −0.414908 | − | 0.718641i | ||||
\(481\) | 1.07295 | − | 1.85840i | 0.0489223 | − | 0.0847358i | ||||
\(482\) | 11.8541 | 0.539940 | ||||||||
\(483\) | −59.8328 | −2.72249 | ||||||||
\(484\) | −8.59017 | + | 14.8786i | −0.390462 | + | 0.676300i | ||||
\(485\) | −4.41641 | + | 7.64944i | −0.200539 | + | 0.347343i | ||||
\(486\) | 13.3820 | 0.607018 | ||||||||
\(487\) | 18.1803 | 0.823830 | 0.411915 | − | 0.911222i | \(-0.364860\pi\) | ||||
0.411915 | + | 0.911222i | \(0.364860\pi\) | |||||||
\(488\) | −6.44427 | + | 11.1618i | −0.291718 | + | 0.505271i | ||||
\(489\) | 8.16312 | + | 14.1389i | 0.369149 | + | 0.639385i | ||||
\(490\) | 0.763932 | − | 1.32317i | 0.0345109 | − | 0.0597747i | ||||
\(491\) | −15.1074 | − | 26.1668i | −0.681787 | − | 1.18089i | −0.974435 | − | 0.224669i | \(-0.927870\pi\) |
0.292648 | − | 0.956220i | \(-0.405464\pi\) | |||||||
\(492\) | −6.35410 | − | 11.0056i | −0.286465 | − | 0.496172i | ||||
\(493\) | 7.23607 | 0.325896 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.94427 | −0.132335 | ||||||||
\(496\) | −1.98936 | − | 3.44567i | −0.0893248 | − | 0.154715i | ||||
\(497\) | 2.20820 | + | 3.82472i | 0.0990515 | + | 0.171562i | ||||
\(498\) | −0.381966 | + | 0.661585i | −0.0171163 | + | 0.0296463i | ||||
\(499\) | 7.56231 | + | 13.0983i | 0.338535 | + | 0.586360i | 0.984157 | − | 0.177297i | \(-0.0567352\pi\) |
−0.645622 | + | 0.763657i | \(0.723402\pi\) | |||||||
\(500\) | 8.47214 | − | 14.6742i | 0.378885 | − | 0.656249i | ||||
\(501\) | 41.2705 | 1.84383 | ||||||||
\(502\) | 11.9656 | 0.534049 | ||||||||
\(503\) | 8.91641 | − | 15.4437i | 0.397563 | − | 0.688599i | −0.595862 | − | 0.803087i | \(-0.703189\pi\) |
0.993425 | + | 0.114488i | \(0.0365227\pi\) | |||||||
\(504\) | 12.9271 | − | 22.3903i | 0.575817 | − | 0.997344i | ||||
\(505\) | −16.2918 | −0.724975 | ||||||||
\(506\) | 2.90983 | 0.129358 | ||||||||
\(507\) | −15.7082 | + | 27.2074i | −0.697626 | + | 1.20832i | ||||
\(508\) | −8.28115 | − | 14.3434i | −0.367417 | − | 0.636384i | ||||
\(509\) | −13.5172 | + | 23.4125i | −0.599140 | + | 1.03774i | 0.393808 | + | 0.919193i | \(0.371157\pi\) |
−0.992948 | + | 0.118549i | \(0.962176\pi\) | |||||||
\(510\) | −5.23607 | − | 9.06914i | −0.231857 | − | 0.401588i | ||||
\(511\) | −16.0623 | − | 27.8207i | −0.710555 | − | 1.23072i | ||||
\(512\) | 18.7082 | 0.826794 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 15.0557 | 0.664080 | ||||||||
\(515\) | 0.819660 | + | 1.41969i | 0.0361185 | + | 0.0625591i | ||||
\(516\) | 14.5172 | + | 25.1446i | 0.639085 | + | 1.10693i | ||||
\(517\) | −0.927051 | + | 1.60570i | −0.0407717 | + | 0.0706186i | ||||
\(518\) | 1.98936 | + | 3.44567i | 0.0874073 | + | 0.151394i | ||||
\(519\) | −11.0902 | + | 19.2087i | −0.486804 | + | 0.843170i | ||||
\(520\) | 2.76393 | 0.121206 | ||||||||
\(521\) | 27.2705 | 1.19474 | 0.597371 | − | 0.801965i | \(-0.296212\pi\) | ||||
0.597371 | + | 0.801965i | \(0.296212\pi\) | |||||||
\(522\) | −1.64590 | + | 2.85078i | −0.0720390 | + | 0.124775i | ||||
\(523\) | 11.2082 | − | 19.4132i | 0.490101 | − | 0.848879i | −0.509835 | − | 0.860272i | \(-0.670293\pi\) |
0.999935 | + | 0.0113934i | \(0.00362672\pi\) | |||||||
\(524\) | −6.32624 | −0.276363 | ||||||||
\(525\) | 27.2705 | 1.19018 | ||||||||
\(526\) | −0.909830 | + | 1.57587i | −0.0396705 | + | 0.0687113i | ||||
\(527\) | −5.61803 | − | 9.73072i | −0.244725 | − | 0.423877i | ||||
\(528\) | 1.50000 | − | 2.59808i | 0.0652791 | − | 0.113067i | ||||
\(529\) | −17.5172 | − | 30.3407i | −0.761618 | − | 1.31916i | ||||
\(530\) | −3.56231 | − | 6.17009i | −0.154737 | − | 0.268012i | ||||
\(531\) | 59.0689 | 2.56337 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.00000 | 0.129944 | ||||||||
\(534\) | 9.89919 | + | 17.1459i | 0.428380 | + | 0.741975i | ||||
\(535\) | 6.43769 | + | 11.1504i | 0.278326 | + | 0.482074i | ||||
\(536\) | 7.82624 | − | 13.5554i | 0.338042 | − | 0.585506i | ||||
\(537\) | −10.1631 | − | 17.6030i | −0.438571 | − | 0.759627i | ||||
\(538\) | 4.53444 | − | 7.85388i | 0.195494 | − | 0.338605i | ||||
\(539\) | 1.23607 | 0.0532412 | ||||||||
\(540\) | −4.47214 | −0.192450 | ||||||||
\(541\) | −11.9164 | + | 20.6398i | −0.512326 | + | 0.887375i | 0.487571 | + | 0.873083i | \(0.337883\pi\) |
−0.999898 | + | 0.0142923i | \(0.995450\pi\) | |||||||
\(542\) | −2.42705 | + | 4.20378i | −0.104251 | + | 0.180568i | ||||
\(543\) | 31.4164 | 1.34821 | ||||||||
\(544\) | 29.4164 | 1.26122 | ||||||||
\(545\) | 10.3262 | − | 17.8856i | 0.442327 | − | 0.766134i | ||||
\(546\) | 2.42705 | + | 4.20378i | 0.103868 | + | 0.179905i | ||||
\(547\) | 18.9615 | − | 32.8423i | 0.810735 | − | 1.40423i | −0.101615 | − | 0.994824i | \(-0.532401\pi\) |
0.912350 | − | 0.409410i | \(-0.134266\pi\) | |||||||
\(548\) | −1.19098 | − | 2.06284i | −0.0508763 | − | 0.0881203i | ||||
\(549\) | 11.1074 | + | 19.2386i | 0.474052 | + | 0.821082i | ||||
\(550\) | −1.32624 | −0.0565510 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 44.5967 | 1.89816 | ||||||||
\(553\) | −20.1246 | − | 34.8569i | −0.855786 | − | 1.48226i | ||||
\(554\) | 4.76393 | + | 8.25137i | 0.202400 | + | 0.350567i | ||||
\(555\) | 3.47214 | − | 6.01392i | 0.147384 | − | 0.255277i | ||||
\(556\) | −7.92705 | − | 13.7301i | −0.336182 | − | 0.582284i | ||||
\(557\) | 11.5902 | − | 20.0748i | 0.491091 | − | 0.850595i | −0.508856 | − | 0.860852i | \(-0.669931\pi\) |
0.999947 | + | 0.0102566i | \(0.00326482\pi\) | |||||||
\(558\) | 5.11146 | 0.216385 | ||||||||
\(559\) | −6.85410 | −0.289898 | ||||||||
\(560\) | 3.43769 | − | 5.95426i | 0.145269 | − | 0.251613i | ||||
\(561\) | 4.23607 | − | 7.33708i | 0.178847 | − | 0.309772i | ||||
\(562\) | −5.25735 | −0.221768 | ||||||||
\(563\) | −20.8328 | −0.877999 | −0.438999 | − | 0.898487i | \(-0.644667\pi\) | ||||
−0.438999 | + | 0.898487i | \(0.644667\pi\) | |||||||
\(564\) | −6.35410 | + | 11.0056i | −0.267556 | + | 0.463421i | ||||
\(565\) | −6.94427 | − | 12.0278i | −0.292148 | − | 0.506015i | ||||
\(566\) | 0.937694 | − | 1.62413i | 0.0394142 | − | 0.0682674i | ||||
\(567\) | 8.56231 | + | 14.8303i | 0.359583 | + | 0.622816i | ||||
\(568\) | −1.64590 | − | 2.85078i | −0.0690603 | − | 0.119616i | ||||
\(569\) | −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 | \(0.345276\pi\) | |||||||
\(572\) | 0.500000 | + | 0.866025i | 0.0209061 | + | 0.0362103i | ||||
\(573\) | 12.7812 | + | 22.1376i | 0.533940 | + | 0.924812i | ||||
\(574\) | −2.78115 | + | 4.81710i | −0.116083 | + | 0.201062i | ||||
\(575\) | 13.2254 | + | 22.9071i | 0.551538 | + | 0.955292i | ||||
\(576\) | 0.454915 | − | 0.787936i | 0.0189548 | − | 0.0328307i | ||||
\(577\) | 28.1246 | 1.17084 | 0.585421 | − | 0.810729i | \(-0.300929\pi\) | ||||
0.585421 | + | 0.810729i | \(0.300929\pi\) | |||||||
\(578\) | 6.43769 | 0.267773 | ||||||||
\(579\) | −30.0344 | + | 52.0212i | −1.24819 | + | 2.16193i | ||||
\(580\) | −1.38197 | + | 2.39364i | −0.0573830 | + | 0.0993903i | ||||
\(581\) | −1.41641 | −0.0587625 | ||||||||
\(582\) | 11.5623 | 0.479273 | ||||||||
\(583\) | 2.88197 | − | 4.99171i | 0.119359 | − | 0.206736i | ||||
\(584\) | 11.9721 | + | 20.7363i | 0.495411 | + | 0.858076i | ||||
\(585\) | 2.38197 | − | 4.12569i | 0.0984822 | − | 0.170576i | ||||
\(586\) | −5.20820 | − | 9.02087i | −0.215149 | − | 0.372649i | ||||
\(587\) | −19.0623 | − | 33.0169i | −0.786786 | − | 1.36275i | −0.927927 | − | 0.372763i | \(-0.878410\pi\) |
0.141141 | − | 0.989990i | \(-0.454923\pi\) | |||||||
\(588\) | 8.47214 | 0.349385 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −11.7082 | −0.482019 | ||||||||
\(591\) | 3.92705 | + | 6.80185i | 0.161537 | + | 0.279791i | ||||
\(592\) | 1.98936 | + | 3.44567i | 0.0817621 | + | 0.141616i | ||||
\(593\) | 6.35410 | − | 11.0056i | 0.260932 | − | 0.451947i | −0.705558 | − | 0.708652i | \(-0.749304\pi\) |
0.966490 | + | 0.256705i | \(0.0826369\pi\) | |||||||
\(594\) | 0.427051 | + | 0.739674i | 0.0175221 | + | 0.0303492i | ||||
\(595\) | 9.70820 | − | 16.8151i | 0.397998 | − | 0.689352i | ||||
\(596\) | 21.1803 | 0.867581 | ||||||||
\(597\) | −35.1246 | −1.43755 | ||||||||
\(598\) | −2.35410 | + | 4.07742i | −0.0962664 | + | 0.166738i | ||||
\(599\) | 0.791796 | − | 1.37143i | 0.0323519 | − | 0.0560352i | −0.849396 | − | 0.527756i | \(-0.823034\pi\) |
0.881748 | + | 0.471721i | \(0.156367\pi\) | |||||||
\(600\) | −20.3262 | −0.829815 | ||||||||
\(601\) | −33.7082 | −1.37499 | −0.687493 | − | 0.726191i | \(-0.741289\pi\) | ||||
−0.687493 | + | 0.726191i | \(0.741289\pi\) | |||||||
\(602\) | 6.35410 | − | 11.0056i | 0.258974 | − | 0.448556i | ||||
\(603\) | −13.4894 | − | 23.3643i | −0.549329 | − | 0.951466i | ||||
\(604\) | 8.01722 | − | 13.8862i | 0.326216 | − | 0.565023i | ||||
\(605\) | −6.56231 | − | 11.3662i | −0.266796 | − | 0.462104i | ||||
\(606\) | 10.6631 | + | 18.4691i | 0.433160 | + | 0.750254i | ||||
\(607\) | −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 | ||||||||
\(610\) | −2.20163 | − | 3.81333i | −0.0891412 | − | 0.154397i | ||||
\(611\) | −1.50000 | − | 2.59808i | −0.0606835 | − | 0.105107i | ||||
\(612\) | 16.3262 | − | 28.2779i | 0.659949 | − | 1.14307i | ||||
\(613\) | 1.02786 | + | 1.78031i | 0.0415150 | + | 0.0719062i | 0.886036 | − | 0.463616i | \(-0.153448\pi\) |
−0.844521 | + | 0.535522i | \(0.820115\pi\) | |||||||
\(614\) | −0.517221 | + | 0.895853i | −0.0208733 | + | 0.0361537i | ||||
\(615\) | 9.70820 | 0.391473 | ||||||||
\(616\) | −4.14590 | −0.167043 | ||||||||
\(617\) | −11.6631 | + | 20.2011i | −0.469539 | + | 0.813266i | −0.999394 | − | 0.0348226i | \(-0.988913\pi\) |
0.529854 | + | 0.848089i | \(0.322247\pi\) | |||||||
\(618\) | 1.07295 | − | 1.85840i | 0.0431603 | − | 0.0747559i | ||||
\(619\) | −30.1246 | −1.21081 | −0.605405 | − | 0.795917i | \(-0.706989\pi\) | ||||
−0.605405 | + | 0.795917i | \(0.706989\pi\) | |||||||
\(620\) | 4.29180 | 0.172363 | ||||||||
\(621\) | 8.51722 | − | 14.7523i | 0.341784 | − | 0.591988i | ||||
\(622\) | 5.76393 | + | 9.98342i | 0.231113 | + | 0.400299i | ||||
\(623\) | −18.3541 | + | 31.7902i | −0.735342 | + | 1.27365i | ||||
\(624\) | 2.42705 | + | 4.20378i | 0.0971598 | + | 0.168286i | ||||
\(625\) | −2.20820 | − | 3.82472i | −0.0883282 | − | 0.152989i | ||||
\(626\) | 2.67376 | 0.106865 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 18.0344 | 0.719653 | ||||||||
\(629\) | 5.61803 | + | 9.73072i | 0.224006 | + | 0.387989i | ||||
\(630\) | 4.41641 | + | 7.64944i | 0.175954 | + | 0.304761i | ||||
\(631\) | 7.68034 | − | 13.3027i | 0.305750 | − | 0.529574i | −0.671678 | − | 0.740843i | \(-0.734426\pi\) |
0.977428 | + | 0.211269i | \(0.0677597\pi\) | |||||||
\(632\) | 15.0000 | + | 25.9808i | 0.596668 | + | 1.03346i | ||||
\(633\) | −3.73607 | + | 6.47106i | −0.148495 | + | 0.257202i | ||||
\(634\) | −11.1246 | −0.441815 | ||||||||
\(635\) | 12.6525 | 0.502098 | ||||||||
\(636\) | 19.7533 | − | 34.2137i | 0.783269 | − | 1.35666i | ||||
\(637\) | −1.00000 | + | 1.73205i | −0.0396214 | + | 0.0686264i | ||||
\(638\) | 0.527864 | 0.0208983 | ||||||||
\(639\) | −5.67376 | −0.224451 | ||||||||
\(640\) | −7.03444 | + | 12.1840i | −0.278061 | + | 0.481615i | ||||
\(641\) | −0.746711 | − | 1.29334i | −0.0294933 | − | 0.0510839i | 0.850902 | − | 0.525324i | \(-0.176056\pi\) |
−0.880395 | + | 0.474241i | \(0.842723\pi\) | |||||||
\(642\) | 8.42705 | − | 14.5961i | 0.332589 | − | 0.576061i | ||||
\(643\) | 18.8541 | + | 32.6563i | 0.743533 | + | 1.28784i | 0.950877 | + | 0.309569i | \(0.100185\pi\) |
−0.207344 | + | 0.978268i | \(0.566482\pi\) | |||||||
\(644\) | 18.4894 | + | 32.0245i | 0.728583 | + | 1.26194i | ||||
\(645\) | −22.1803 | −0.873350 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.47214 | −0.0578756 | −0.0289378 | − | 0.999581i | \(-0.509212\pi\) | ||||
−0.0289378 | + | 0.999581i | \(0.509212\pi\) | |||||||
\(648\) | −6.38197 | − | 11.0539i | −0.250707 | − | 0.434238i | ||||
\(649\) | −4.73607 | − | 8.20311i | −0.185907 | − | 0.322000i | ||||
\(650\) | 1.07295 | − | 1.85840i | 0.0420845 | − | 0.0728925i | ||||
\(651\) | 8.42705 | + | 14.5961i | 0.330282 | + | 0.572065i | ||||
\(652\) | 5.04508 | − | 8.73834i | 0.197581 | − | 0.342220i | ||||
\(653\) | −3.43769 | −0.134527 | −0.0672637 | − | 0.997735i | \(-0.521427\pi\) | ||||
−0.0672637 | + | 0.997735i | \(0.521427\pi\) | |||||||
\(654\) | −27.0344 | −1.05713 | ||||||||
\(655\) | 2.41641 | − | 4.18534i | 0.0944169 | − | 0.163535i | ||||
\(656\) | −2.78115 | + | 4.81710i | −0.108586 | + | 0.188076i | ||||
\(657\) | 41.2705 | 1.61012 | ||||||||
\(658\) | 5.56231 | 0.216841 | ||||||||
\(659\) | 22.8885 | − | 39.6441i | 0.891611 | − | 1.54432i | 0.0536675 | − | 0.998559i | \(-0.482909\pi\) |
0.837944 | − | 0.545757i | \(-0.183758\pi\) | |||||||
\(660\) | 1.61803 | + | 2.80252i | 0.0629819 | + | 0.109088i | ||||
\(661\) | −10.7082 | + | 18.5472i | −0.416501 | + | 0.721401i | −0.995585 | − | 0.0938673i | \(-0.970077\pi\) |
0.579084 | + | 0.815268i | \(0.303410\pi\) | |||||||
\(662\) | −2.14590 | − | 3.71680i | −0.0834027 | − | 0.144458i | ||||
\(663\) | 6.85410 | + | 11.8717i | 0.266191 | + | 0.461057i | ||||
\(664\) | 1.05573 | 0.0409702 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.11146 | −0.198065 | ||||||||
\(667\) | −5.26393 | − | 9.11740i | −0.203820 | − | 0.353027i | ||||
\(668\) | −12.7533 | − | 22.0893i | −0.493440 | − | 0.854662i | ||||
\(669\) | −25.7254 | + | 44.5577i | −0.994602 | + | 1.72270i | ||||
\(670\) | 2.67376 | + | 4.63109i | 0.103296 | + | 0.178915i | ||||
\(671\) | 1.78115 | − | 3.08505i | 0.0687606 | − | 0.119097i | ||||
\(672\) | −44.1246 | −1.70214 | ||||||||
\(673\) | 6.12461 | 0.236086 | 0.118043 | − | 0.993008i | \(-0.462338\pi\) | ||||
0.118043 | + | 0.993008i | \(0.462338\pi\) | |||||||
\(674\) | 7.14590 | − | 12.3771i | 0.275250 | − | 0.476746i | ||||
\(675\) | −3.88197 | + | 6.72376i | −0.149417 | + | 0.258798i | ||||
\(676\) | 19.4164 | 0.746785 | ||||||||
\(677\) | −11.7426 | −0.451307 | −0.225653 | − | 0.974208i | \(-0.572452\pi\) | ||||
−0.225653 | + | 0.974208i | \(0.572452\pi\) | |||||||
\(678\) | −9.09017 | + | 15.7446i | −0.349106 | + | 0.604669i | ||||
\(679\) | 10.7188 | + | 18.5656i | 0.411352 | + | 0.712482i | ||||
\(680\) | −7.23607 | + | 12.5332i | −0.277491 | + | 0.480628i | ||||
\(681\) | 13.6353 | + | 23.6170i | 0.522504 | + | 0.905004i | ||||
\(682\) | −0.409830 | − | 0.709846i | −0.0156932 | − | 0.0271814i | ||||
\(683\) | 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 | ||||||||
\(686\) | 4.63525 | + | 8.02850i | 0.176975 | + | 0.306529i | ||||
\(687\) | −14.8992 | − | 25.8061i | −0.568439 | − | 0.984566i | ||||
\(688\) | 6.35410 | − | 11.0056i | 0.242248 | − | 0.419586i | ||||
\(689\) | 4.66312 | + | 8.07676i | 0.177651 | + | 0.307700i | ||||
\(690\) | −7.61803 | + | 13.1948i | −0.290014 | + | 0.502318i | ||||
\(691\) | −16.8197 | −0.639850 | −0.319925 | − | 0.947443i | \(-0.603658\pi\) | ||||
−0.319925 | + | 0.947443i | \(0.603658\pi\) | |||||||
\(692\) | 13.7082 | 0.521108 | ||||||||
\(693\) | −3.57295 | + | 6.18853i | −0.135725 | + | 0.235083i | ||||
\(694\) | −0.437694 | + | 0.758108i | −0.0166146 | + | 0.0287774i | ||||
\(695\) | 12.1115 | 0.459414 | ||||||||
\(696\) | 8.09017 | 0.306657 | ||||||||
\(697\) | −7.85410 | + | 13.6037i | −0.297495 | + | 0.515277i | ||||
\(698\) | −8.02786 | − | 13.9047i | −0.303859 | − | 0.526299i | ||||
\(699\) | 17.6353 | − | 30.5452i | 0.667027 | − | 1.15532i | ||||
\(700\) | −8.42705 | − | 14.5961i | −0.318513 | − | 0.551680i | ||||
\(701\) | −19.3156 | − | 33.4556i | −0.729540 | − | 1.26360i | −0.957078 | − | 0.289831i | \(-0.906401\pi\) |
0.227538 | − | 0.973769i | \(-0.426932\pi\) | |||||||
\(702\) | −1.38197 | −0.0521589 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −0.145898 | −0.00549874 | ||||||||
\(705\) | −4.85410 | − | 8.40755i | −0.182816 | − | 0.316647i | ||||
\(706\) | 9.71885 | + | 16.8335i | 0.365774 | + | 0.633539i | ||||
\(707\) | −19.7705 | + | 34.2435i | −0.743547 | + | 1.28786i | ||||
\(708\) | −32.4615 | − | 56.2250i | −1.21998 | − | 2.11306i | ||||
\(709\) | −21.7082 | + | 37.5997i | −0.815269 | + | 1.41209i | 0.0938661 | + | 0.995585i | \(0.470077\pi\) |
−0.909135 | + | 0.416502i | \(0.863256\pi\) | |||||||
\(710\) | 1.12461 | 0.0422059 | ||||||||
\(711\) | 51.7082 | 1.93921 | ||||||||
\(712\) | 13.6803 | − | 23.6950i | 0.512692 | − | 0.888009i | ||||
\(713\) | −8.17376 | + | 14.1574i | −0.306110 | + | 0.530198i | ||||
\(714\) | −25.4164 | −0.951185 | ||||||||
\(715\) | −0.763932 | −0.0285694 | ||||||||
\(716\) | −6.28115 | + | 10.8793i | −0.234738 | + | 0.406578i | ||||
\(717\) | 20.0623 | + | 34.7489i | 0.749241 | + | 1.29772i | ||||
\(718\) | 6.80902 | − | 11.7936i | 0.254110 | − | 0.440132i | ||||
\(719\) | −8.98278 | − | 15.5586i | −0.335001 | − | 0.580239i | 0.648484 | − | 0.761228i | \(-0.275403\pi\) |
−0.983485 | + | 0.180989i | \(0.942070\pi\) | |||||||
\(720\) | 4.41641 | + | 7.64944i | 0.164590 | + | 0.285078i | ||||
\(721\) | 3.97871 | 0.148175 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −50.2148 | −1.86751 | ||||||||
\(724\) | −9.70820 | − | 16.8151i | −0.360803 | − | 0.624928i | ||||
\(725\) | 2.39919 | + | 4.15551i | 0.0891036 | + | 0.154332i | ||||
\(726\) | −8.59017 | + | 14.8786i | −0.318811 | + | 0.552197i | ||||
\(727\) | −21.0344 | − | 36.4327i | −0.780124 | − | 1.35121i | −0.931869 | − | 0.362795i | \(-0.881822\pi\) |
0.151745 | − | 0.988420i | \(-0.451511\pi\) | |||||||
\(728\) | 3.35410 | − | 5.80948i | 0.124311 | − | 0.215313i | ||||
\(729\) | −39.5623 | −1.46527 | ||||||||
\(730\) | −8.18034 | −0.302768 | ||||||||
\(731\) | 17.9443 | − | 31.0804i | 0.663693 | − | 1.14955i | ||||
\(732\) | 12.2082 | − | 21.1452i | 0.451228 | − | 0.781550i | ||||
\(733\) | 40.9574 | 1.51280 | 0.756399 | − | 0.654111i | \(-0.226957\pi\) | ||||
0.756399 | + | 0.654111i | \(0.226957\pi\) | |||||||
\(734\) | 1.20163 | 0.0443528 | ||||||||
\(735\) | −3.23607 | + | 5.60503i | −0.119364 | + | 0.206745i | ||||
\(736\) | −21.3992 | − | 37.0645i | −0.788784 | − | 1.36621i | ||||
\(737\) | −2.16312 | + | 3.74663i | −0.0796795 | + | 0.138009i | ||||
\(738\) | −3.57295 | − | 6.18853i | −0.131522 | − | 0.227803i | ||||
\(739\) | 12.5000 | + | 21.6506i | 0.459820 | + | 0.796431i | 0.998951 | − | 0.0457903i | \(-0.0145806\pi\) |
−0.539131 | + | 0.842222i | \(0.681247\pi\) | |||||||
\(740\) | −4.29180 | −0.157770 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −17.2918 | −0.634802 | ||||||||
\(743\) | 20.6803 | + | 35.8194i | 0.758688 | + | 1.31409i | 0.943520 | + | 0.331316i | \(0.107493\pi\) |
−0.184832 | + | 0.982770i | \(0.559174\pi\) | |||||||
\(744\) | −6.28115 | − | 10.8793i | −0.230278 | − | 0.398854i | ||||
\(745\) | −8.09017 | + | 14.0126i | −0.296401 | + | 0.513381i | ||||
\(746\) | 1.07295 | + | 1.85840i | 0.0392835 | + | 0.0680409i | ||||
\(747\) | 0.909830 | − | 1.57587i | 0.0332889 | − | 0.0576581i | ||||
\(748\) | −5.23607 | −0.191450 | ||||||||
\(749\) | 31.2492 | 1.14182 | ||||||||
\(750\) | 8.47214 | − | 14.6742i | 0.309359 | − | 0.535825i | ||||
\(751\) | −11.9271 | + | 20.6583i | −0.435224 | + | 0.753831i | −0.997314 | − | 0.0732458i | \(-0.976664\pi\) |
0.562090 | + | 0.827076i | \(0.309998\pi\) | |||||||
\(752\) | 5.56231 | 0.202836 | ||||||||
\(753\) | −50.6869 | −1.84713 | ||||||||
\(754\) | −0.427051 | + | 0.739674i | −0.0155523 | + | 0.0269373i | ||||
\(755\) | 6.12461 | + | 10.6081i | 0.222897 | + | 0.386070i | ||||
\(756\) | −5.42705 | + | 9.39993i | −0.197380 | + | 0.341872i | ||||
\(757\) | 7.87132 | + | 13.6335i | 0.286088 | + | 0.495519i | 0.972872 | − | 0.231342i | \(-0.0743117\pi\) |
−0.686784 | + | 0.726861i | \(0.740978\pi\) | |||||||
\(758\) | 7.76393 | + | 13.4475i | 0.281999 | + | 0.488436i | ||||
\(759\) | −12.3262 | −0.447414 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.8885 | −1.11971 | −0.559854 | − | 0.828591i | \(-0.689143\pi\) | ||||
−0.559854 | + | 0.828591i | \(0.689143\pi\) | |||||||
\(762\) | −8.28115 | − | 14.3434i | −0.299995 | − | 0.519606i | ||||
\(763\) | −25.0623 | − | 43.4092i | −0.907316 | − | 1.57152i | ||||
\(764\) | 7.89919 | − | 13.6818i | 0.285783 | − | 0.494990i | ||||
\(765\) | 12.4721 | + | 21.6024i | 0.450931 | + | 0.781035i | ||||
\(766\) | 0.809017 | − | 1.40126i | 0.0292310 | − | 0.0506295i | ||||
\(767\) | 15.3262 | 0.553398 | ||||||||
\(768\) | 17.1803 | 0.619942 | ||||||||
\(769\) | 20.8156 | − | 36.0537i | 0.750630 | − | 1.30013i | −0.196888 | − | 0.980426i | \(-0.563084\pi\) |
0.947518 | − | 0.319703i | \(-0.103583\pi\) | |||||||
\(770\) | 0.708204 | − | 1.22665i | 0.0255219 | − | 0.0442052i | ||||
\(771\) | −63.7771 | −2.29688 | ||||||||
\(772\) | 37.1246 | 1.33614 | ||||||||
\(773\) | 14.4615 | − | 25.0480i | 0.520144 | − | 0.900915i | −0.479582 | − | 0.877497i | \(-0.659212\pi\) |
0.999726 | − | 0.0234183i | \(-0.00745497\pi\) | |||||||
\(774\) | 8.16312 | + | 14.1389i | 0.293417 | + | 0.508214i | ||||
\(775\) | 3.72542 | − | 6.45263i | 0.133821 | − | 0.231785i | ||||
\(776\) | −7.98936 | − | 13.8380i | −0.286801 | − | 0.496754i | ||||
\(777\) | −8.42705 | − | 14.5961i | −0.302319 | − | 0.523631i | ||||
\(778\) | −15.0000 | −0.537776 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −5.23607 | −0.187481 | ||||||||
\(781\) | 0.454915 | + | 0.787936i | 0.0162781 | + | 0.0281946i | ||||
\(782\) | −12.3262 | − | 21.3497i | −0.440785 | − | 0.763463i | ||||
\(783\) | 1.54508 | − | 2.67617i | 0.0552168 | − | 0.0956384i | ||||
\(784\) | −1.85410 | − | 3.21140i | −0.0662179 | − | 0.114693i | ||||
\(785\) | −6.88854 | + | 11.9313i | −0.245863 | + | 0.425847i | ||||
\(786\) | −6.32624 | −0.225649 | ||||||||
\(787\) | −38.0000 | −1.35455 | −0.677277 | − | 0.735728i | \(-0.736840\pi\) | ||||
−0.677277 | + | 0.735728i | \(0.736840\pi\) | |||||||
\(788\) | 2.42705 | − | 4.20378i | 0.0864601 | − | 0.149753i | ||||
\(789\) | 3.85410 | − | 6.67550i | 0.137210 | − | 0.237654i | ||||
\(790\) | −10.2492 | −0.364651 | ||||||||
\(791\) | −33.7082 | −1.19853 | ||||||||
\(792\) | 2.66312 | − | 4.61266i | 0.0946298 | − | 0.163904i | ||||
\(793\) | 2.88197 | + | 4.99171i | 0.102342 | + | 0.177261i | ||||
\(794\) | 0.781153 | − | 1.35300i | 0.0277221 | − | 0.0480161i | ||||
\(795\) | 15.0902 | + | 26.1369i | 0.535193 | + | 0.926982i | ||||
\(796\) | 10.8541 | + | 18.7999i | 0.384713 | + | 0.666343i | ||||
\(797\) | 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 | ||||||||
\(800\) | 9.75329 | + | 16.8932i | 0.344831 | + | 0.597265i | ||||
\(801\) | −23.5795 | − | 40.8409i | −0.833142 | − | 1.44304i | ||||
\(802\) | −0.0344419 | + | 0.0596550i | −0.00121618 | + | 0.00210649i | ||||
\(803\) | −3.30902 | − | 5.73139i | −0.116773 | − | 0.202256i | ||||
\(804\) | −14.8262 | + | 25.6798i | −0.522881 | + | 0.905657i | ||||
\(805\) | −28.2492 | −0.995654 | ||||||||
\(806\) | 1.32624 | 0.0467147 | ||||||||
\(807\) | −19.2082 | + | 33.2696i | −0.676161 | + | 1.17114i | ||||
\(808\) | 14.7361 | − | 25.5236i | 0.518413 | − | 0.897918i | ||||
\(809\) | −0.201626 | −0.00708880 | −0.00354440 | − | 0.999994i | \(-0.501128\pi\) | ||||
−0.00354440 | + | 0.999994i | \(0.501128\pi\) | |||||||
\(810\) | 4.36068 | 0.153219 | ||||||||
\(811\) | −11.9894 | + | 20.7662i | −0.421003 | + | 0.729199i | −0.996038 | − | 0.0889300i | \(-0.971655\pi\) |
0.575035 | + | 0.818129i | \(0.304989\pi\) | |||||||
\(812\) | 3.35410 | + | 5.80948i | 0.117706 | + | 0.203873i | ||||
\(813\) | 10.2812 | − | 17.8075i | 0.360576 | − | 0.624536i | ||||
\(814\) | 0.409830 | + | 0.709846i | 0.0143645 | + | 0.0248801i | ||||
\(815\) | 3.85410 | + | 6.67550i | 0.135003 | + | 0.233833i | ||||
\(816\) | −25.4164 | −0.889752 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 13.4164 | 0.469094 | ||||||||
\(819\) | −5.78115 | − | 10.0133i | −0.202010 | − | 0.349891i | ||||
\(820\) | −3.00000 | − | 5.19615i | −0.104765 | − | 0.181458i | ||||
\(821\) | 26.5238 | − | 45.9406i | 0.925687 | − | 1.60334i | 0.135234 | − | 0.990814i | \(-0.456821\pi\) |
0.790453 | − | 0.612523i | \(-0.209845\pi\) | |||||||
\(822\) | −1.19098 | − | 2.06284i | −0.0415403 | − | 0.0719499i | ||||
\(823\) | −11.7984 | + | 20.4354i | −0.411265 | + | 0.712333i | −0.995028 | − | 0.0995915i | \(-0.968246\pi\) |
0.583763 | + | 0.811924i | \(0.301580\pi\) | |||||||
\(824\) | −2.96556 | −0.103310 | ||||||||
\(825\) | 5.61803 | 0.195595 | ||||||||
\(826\) | −14.2082 | + | 24.6093i | −0.494367 | + | 0.856268i | ||||
\(827\) | −8.29837 | + | 14.3732i | −0.288563 | + | 0.499805i | −0.973467 | − | 0.228828i | \(-0.926511\pi\) |
0.684904 | + | 0.728633i | \(0.259844\pi\) | |||||||
\(828\) | −47.5066 | −1.65097 | ||||||||
\(829\) | −20.3262 | −0.705959 | −0.352980 | − | 0.935631i | \(-0.614832\pi\) | ||||
−0.352980 | + | 0.935631i | \(0.614832\pi\) | |||||||
\(830\) | −0.180340 | + | 0.312358i | −0.00625969 | + | 0.0108421i | ||||
\(831\) | −20.1803 | − | 34.9534i | −0.700048 | − | 1.21252i | ||||
\(832\) | 0.118034 | − | 0.204441i | 0.00409209 | − | 0.00708771i | ||||
\(833\) | −5.23607 | − | 9.06914i | −0.181419 | − | 0.314227i | ||||
\(834\) | −7.92705 | − | 13.7301i | −0.274491 | − | 0.475433i | ||||
\(835\) | 19.4853 | 0.674316 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.79837 | −0.165856 | ||||||||
\(838\) | −2.76393 | − | 4.78727i | −0.0954784 | − | 0.165374i | ||||
\(839\) | 19.8992 | + | 34.4664i | 0.686996 | + | 1.18991i | 0.972805 | + | 0.231626i | \(0.0744045\pi\) |
−0.285809 | + | 0.958287i | \(0.592262\pi\) | |||||||
\(840\) | 10.8541 | − | 18.7999i | 0.374502 | − | 0.648657i | ||||
\(841\) | 13.5451 | + | 23.4608i | 0.467072 | + | 0.808992i | ||||
\(842\) | −5.72542 | + | 9.91673i | −0.197311 | + | 0.341753i | ||||
\(843\) | 22.2705 | 0.767037 | ||||||||
\(844\) | 4.61803 | 0.158959 | ||||||||
\(845\) | −7.41641 | + | 12.8456i | −0.255132 | + | 0.441902i | ||||
\(846\) | −3.57295 | + | 6.18853i | −0.122841 | + | 0.212766i | ||||
\(847\) | −31.8541 | −1.09452 | ||||||||
\(848\) | −17.2918 | −0.593803 | ||||||||
\(849\) | −3.97214 | + | 6.87994i | −0.136323 | + | 0.236119i | ||||
\(850\) | 5.61803 | + | 9.73072i | 0.192697 | + | 0.333761i | ||||
\(851\) | 8.17376 | − | 14.1574i | 0.280193 | − | 0.485308i | ||||
\(852\) | 3.11803 | + | 5.40059i | 0.106822 | + | 0.185021i | ||||
\(853\) | −8.64590 | − | 14.9751i | −0.296030 | − | 0.512739i | 0.679194 | − | 0.733959i | \(-0.262329\pi\) |
−0.975224 | + | 0.221220i | \(0.928996\pi\) | |||||||
\(854\) | −10.6869 | −0.365699 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −23.2918 | −0.796097 | ||||||||
\(857\) | −4.19098 | − | 7.25900i | −0.143161 | − | 0.247963i | 0.785524 | − | 0.618831i | \(-0.212393\pi\) |
−0.928685 | + | 0.370868i | \(0.879060\pi\) | |||||||
\(858\) | 0.500000 | + | 0.866025i | 0.0170697 | + | 0.0295656i | ||||
\(859\) | −9.27051 | + | 16.0570i | −0.316306 | + | 0.547858i | −0.979714 | − | 0.200400i | \(-0.935776\pi\) |
0.663408 | + | 0.748257i | \(0.269109\pi\) | |||||||
\(860\) | 6.85410 | + | 11.8717i | 0.233723 | + | 0.404820i | ||||
\(861\) | 11.7812 | − | 20.4056i | 0.401501 | − | 0.695419i | ||||
\(862\) | 2.25735 | 0.0768858 | ||||||||
\(863\) | 44.9443 | 1.52992 | 0.764960 | − | 0.644077i | \(-0.222759\pi\) | ||||
0.764960 | + | 0.644077i | \(0.222759\pi\) | |||||||
\(864\) | 6.28115 | − | 10.8793i | 0.213689 | − | 0.370120i | ||||
\(865\) | −5.23607 | + | 9.06914i | −0.178032 | + | 0.308360i | ||||
\(866\) | 14.5623 | 0.494847 | ||||||||
\(867\) | −27.2705 | −0.926155 | ||||||||
\(868\) | 5.20820 | − | 9.02087i | 0.176778 | − | 0.306188i | ||||
\(869\) | −4.14590 | − | 7.18091i | −0.140640 | − | 0.243596i | ||||
\(870\) | −1.38197 | + | 2.39364i | −0.0468530 | + | 0.0811518i | ||||
\(871\) | −3.50000 | − | 6.06218i | −0.118593 | − | 0.205409i | ||||
\(872\) | 18.6803 | + | 32.3553i | 0.632596 | + | 1.09569i | ||||
\(873\) | −27.5410 | −0.932122 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 31.4164 | 1.06207 | ||||||||
\(876\) | −22.6803 | − | 39.2835i | −0.766298 | − | 1.32727i | ||||
\(877\) | 17.0902 | + | 29.6010i | 0.577094 | + | 0.999556i | 0.995811 | + | 0.0914392i | \(0.0291467\pi\) |
−0.418717 | + | 0.908117i | \(0.637520\pi\) | |||||||
\(878\) | 4.51064 | − | 7.81266i | 0.152227 | − | 0.263665i | ||||
\(879\) | 22.0623 | + | 38.2130i | 0.744143 | + | 1.28889i | ||||
\(880\) | 0.708204 | − | 1.22665i | 0.0238735 | − | 0.0413502i | ||||
\(881\) | −23.4508 | −0.790079 | −0.395040 | − | 0.918664i | \(-0.629269\pi\) | ||||
−0.395040 | + | 0.918664i | \(0.629269\pi\) | |||||||
\(882\) | 4.76393 | 0.160410 | ||||||||
\(883\) | −6.96149 | + | 12.0577i | −0.234273 | + | 0.405773i | −0.959061 | − | 0.283199i | \(-0.908604\pi\) |
0.724788 | + | 0.688972i | \(0.241938\pi\) | |||||||
\(884\) | 4.23607 | − | 7.33708i | 0.142474 | − | 0.246773i | ||||
\(885\) | 49.5967 | 1.66718 | ||||||||
\(886\) | −21.2705 | −0.714597 | ||||||||
\(887\) | 29.3262 | − | 50.7945i | 0.984679 | − | 1.70551i | 0.341323 | − | 0.939946i | \(-0.389125\pi\) |
0.643356 | − | 0.765568i | \(-0.277542\pi\) | |||||||
\(888\) | 6.28115 | + | 10.8793i | 0.210782 | + | 0.365085i | ||||
\(889\) | 15.3541 | − | 26.5941i | 0.514960 | − | 0.891937i | ||||
\(890\) | 4.67376 | + | 8.09519i | 0.156665 | + | 0.271351i | ||||
\(891\) | 1.76393 | + | 3.05522i | 0.0590939 | + | 0.102354i | ||||
\(892\) | 31.7984 | 1.06469 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 21.1803 | 0.708377 | ||||||||
\(895\) | −4.79837 | − | 8.31103i | −0.160392 | − | 0.277807i | ||||
\(896\) | 17.0729 | + | 29.5712i | 0.570367 | + | 0.987905i | ||||
\(897\) | 9.97214 | − | 17.2722i | 0.332960 | − | 0.576704i | ||||
\(898\) | −10.1631 | − | 17.6030i | −0.339148 | − | 0.587421i | ||||
\(899\) | −1.48278 | + | 2.56825i | −0.0494535 | + | 0.0856559i | ||||
\(900\) | 21.6525 | 0.721749 | ||||||||
\(901\) | −48.8328 | −1.62686 | ||||||||
\(902\) | −0.572949 | + | 0.992377i | −0.0190771 | + | 0.0330425i | ||||
\(903\) | −26.9164 | + | 46.6206i | −0.895722 | + | 1.55144i | ||||
\(904\) | 25.1246 | 0.835632 | ||||||||
\(905\) | 14.8328 | 0.493059 | ||||||||
\(906\) | 8.01722 | − | 13.8862i | 0.266354 | − | 0.461339i | ||||
\(907\) | −8.76393 | − | 15.1796i | −0.291002 | − | 0.504030i | 0.683045 | − | 0.730376i | \(-0.260655\pi\) |
−0.974047 | + | 0.226347i | \(0.927322\pi\) | |||||||
\(908\) | 8.42705 | − | 14.5961i | 0.279662 | − | 0.484388i | ||||
\(909\) | −25.3992 | − | 43.9927i | −0.842438 | − | 1.45915i | ||||
\(910\) | 1.14590 | + | 1.98475i | 0.0379861 | + | 0.0657939i | ||||
\(911\) | −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 | ||||||||
\(914\) | −1.94427 | − | 3.36758i | −0.0643108 | − | 0.111390i | ||||
\(915\) | 9.32624 | + | 16.1535i | 0.308316 | + | 0.534019i | ||||
\(916\) | −9.20820 | + | 15.9491i | −0.304248 | + | 0.526972i | ||||
\(917\) | −5.86475 | − | 10.1580i | −0.193671 | − | 0.335448i | ||||
\(918\) | 3.61803 | − | 6.26662i | 0.119413 | − | 0.206829i | ||||
\(919\) | 36.7082 | 1.21089 | 0.605446 | − | 0.795886i | \(-0.292995\pi\) | ||||
0.605446 | + | 0.795886i | \(0.292995\pi\) | |||||||
\(920\) | 21.0557 | 0.694187 | ||||||||
\(921\) | 2.19098 | − | 3.79489i | 0.0721953 | − | 0.125046i | ||||
\(922\) | −0.944272 | + | 1.63553i | −0.0310979 | + | 0.0538632i | ||||
\(923\) | −1.47214 | −0.0484559 | ||||||||
\(924\) | 7.85410 | 0.258381 | ||||||||
\(925\) | −3.72542 | + | 6.45263i | −0.122491 | + | 0.212161i | ||||
\(926\) | 1.62868 | + | 2.82095i | 0.0535217 | + | 0.0927022i | ||||
\(927\) | −2.55573 | + | 4.42665i | −0.0839411 | + | 0.145390i | ||||
\(928\) | −3.88197 | − | 6.72376i | −0.127432 | − | 0.220718i | ||||
\(929\) | −9.30902 | − | 16.1237i | −0.305419 | − | 0.529001i | 0.671936 | − | 0.740610i | \(-0.265463\pi\) |
−0.977355 | + | 0.211608i | \(0.932130\pi\) | |||||||
\(930\) | 4.29180 | 0.140734 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −21.7984 | −0.714029 | ||||||||
\(933\) | −24.4164 | − | 42.2905i | −0.799357 | − | 1.38453i | ||||
\(934\) | −0.600813 | − | 1.04064i | −0.0196592 | − | 0.0340507i | ||||
\(935\) | 2.00000 | − | 3.46410i | 0.0654070 | − | 0.113288i | ||||
\(936\) | 4.30902 | + | 7.46344i | 0.140845 | + | 0.243950i | ||||
\(937\) | −10.2188 | + | 17.6996i | −0.333835 | + | 0.578219i | −0.983260 | − | 0.182206i | \(-0.941676\pi\) |
0.649425 | + | 0.760425i | \(0.275010\pi\) | |||||||
\(938\) | 12.9787 | 0.423770 | ||||||||
\(939\) | −11.3262 | −0.369618 | ||||||||
\(940\) | −3.00000 | + | 5.19615i | −0.0978492 | + | 0.169480i | ||||
\(941\) | 24.8435 | − | 43.0301i | 0.809874 | − | 1.40274i | −0.103078 | − | 0.994673i | \(-0.532869\pi\) |
0.912951 | − | 0.408069i | \(-0.133798\pi\) | |||||||
\(942\) | 18.0344 | 0.587594 | ||||||||
\(943\) | 22.8541 | 0.744232 | ||||||||
\(944\) | −14.2082 | + | 24.6093i | −0.462438 | + | 0.800966i | ||||
\(945\) | −4.14590 | − | 7.18091i | −0.134866 | − | 0.233595i | ||||
\(946\) | 1.30902 | − | 2.26728i | 0.0425598 | − | 0.0737158i | ||||
\(947\) | 0.673762 | + | 1.16699i | 0.0218943 | + | 0.0379221i | 0.876765 | − | 0.480919i | \(-0.159697\pi\) |
−0.854871 | + | 0.518841i | \(0.826364\pi\) | |||||||
\(948\) | −28.4164 | − | 49.2187i | −0.922922 | − | 1.59855i | ||||
\(949\) | 10.7082 | 0.347603 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 47.1246 | 1.52812 | ||||||||
\(952\) | 17.5623 | + | 30.4188i | 0.569198 | + | 0.985879i | ||||
\(953\) | 15.3541 | + | 26.5941i | 0.497368 | + | 0.861467i | 0.999995 | − | 0.00303634i | \(-0.000966498\pi\) |
−0.502627 | + | 0.864503i | \(0.667633\pi\) | |||||||
\(954\) | 11.1074 | − | 19.2386i | 0.359615 | − | 0.622872i | ||||
\(955\) | 6.03444 | + | 10.4520i | 0.195270 | + | 0.338217i | ||||
\(956\) | 12.3992 | − | 21.4760i | 0.401018 | − | 0.694584i | ||||
\(957\) | −2.23607 | −0.0722818 | ||||||||
\(958\) | 7.36068 | 0.237813 | ||||||||
\(959\) | 2.20820 | − | 3.82472i | 0.0713066 | − | 0.123507i | ||||
\(960\) | 0.381966 | − | 0.661585i | 0.0123279 | − | 0.0213525i | ||||
\(961\) | −26.3951 | −0.851456 | ||||||||
\(962\) | −1.32624 | −0.0427596 | ||||||||
\(963\) | −20.0729 | + | 34.7674i | −0.646842 | + | 1.12036i | ||||
\(964\) | 15.5172 | + | 26.8766i | 0.499776 | + | 0.865637i | ||||
\(965\) | −14.1803 | + | 24.5611i | −0.456481 | + | 0.790649i | ||||
\(966\) | 18.4894 | + | 32.0245i | 0.594885 | + | 1.03037i | ||||
\(967\) | 30.2705 | + | 52.4301i | 0.973434 | + | 1.68604i | 0.685009 | + | 0.728535i | \(0.259798\pi\) |
0.288425 | + | 0.957503i | \(0.406868\pi\) | |||||||
\(968\) | 23.7426 | 0.763118 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.45898 | 0.175277 | ||||||||
\(971\) | −7.25329 | − | 12.5631i | −0.232769 | − | 0.403168i | 0.725853 | − | 0.687850i | \(-0.241445\pi\) |
−0.958622 | + | 0.284682i | \(0.908112\pi\) | |||||||
\(972\) | 17.5172 | + | 30.3407i | 0.561865 | + | 0.973179i | ||||
\(973\) | 14.6976 | − | 25.4569i | 0.471182 | − | 0.816111i | ||||
\(974\) | −5.61803 | − | 9.73072i | −0.180013 | − | 0.311792i | ||||
\(975\) | −4.54508 | + | 7.87232i | −0.145559 | + | 0.252116i | ||||
\(976\) | −10.6869 | −0.342080 | ||||||||
\(977\) | −55.3607 | −1.77115 | −0.885573 | − | 0.464501i | \(-0.846234\pi\) | ||||
−0.885573 | + | 0.464501i | \(0.846234\pi\) | |||||||
\(978\) | 5.04508 | − | 8.73834i | 0.161324 | − | 0.279421i | ||||
\(979\) | −3.78115 | + | 6.54915i | −0.120846 | + | 0.209312i | ||||
\(980\) | 4.00000 | 0.127775 | ||||||||
\(981\) | 64.3951 | 2.05598 | ||||||||
\(982\) | −9.33688 | + | 16.1720i | −0.297952 | + | 0.516068i | ||||
\(983\) | 15.1910 | + | 26.3116i | 0.484517 | + | 0.839208i | 0.999842 | − | 0.0177868i | \(-0.00566200\pi\) |
−0.515325 | + | 0.856995i | \(0.672329\pi\) | |||||||
\(984\) | −8.78115 | + | 15.2094i | −0.279933 | + | 0.484858i | ||||
\(985\) | 1.85410 | + | 3.21140i | 0.0590766 | + | 0.102324i | ||||
\(986\) | −2.23607 | − | 3.87298i | −0.0712109 | − | 0.123341i | ||||
\(987\) | −23.5623 | −0.749996 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −52.2148 | −1.66033 | ||||||||
\(990\) | 0.909830 | + | 1.57587i | 0.0289163 | + | 0.0500845i | ||||
\(991\) | −24.2254 | − | 41.9597i | −0.769546 | − | 1.33289i | −0.937809 | − | 0.347151i | \(-0.887149\pi\) |
0.168263 | − | 0.985742i | \(-0.446184\pi\) | |||||||
\(992\) | −6.02786 | + | 10.4406i | −0.191385 | + | 0.331488i | ||||
\(993\) | 9.09017 | + | 15.7446i | 0.288468 | + | 0.499641i | ||||
\(994\) | 1.36475 | − | 2.36381i | 0.0432871 | − | 0.0749754i | ||||
\(995\) | −16.5836 | −0.525735 | ||||||||
\(996\) | −2.00000 | −0.0633724 | ||||||||
\(997\) | −13.1459 | + | 22.7694i | −0.416335 | + | 0.721113i | −0.995568 | − | 0.0940492i | \(-0.970019\pi\) |
0.579233 | + | 0.815162i | \(0.303352\pi\) | |||||||
\(998\) | 4.67376 | − | 8.09519i | 0.147945 | − | 0.256249i | ||||
\(999\) | 4.79837 | 0.151814 |
(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.c.g.292.1 | 4 | ||
19.2 | odd | 18 | 361.2.e.j.28.1 | 12 | |||
19.3 | odd | 18 | 361.2.e.j.234.1 | 12 | |||
19.4 | even | 9 | 361.2.e.i.245.2 | 12 | |||
19.5 | even | 9 | 361.2.e.i.99.1 | 12 | |||
19.6 | even | 9 | 361.2.e.i.62.1 | 12 | |||
19.7 | even | 3 | 361.2.a.c.1.2 | ✓ | 2 | ||
19.8 | odd | 6 | 361.2.c.d.68.2 | 4 | |||
19.9 | even | 9 | 361.2.e.i.54.2 | 12 | |||
19.10 | odd | 18 | 361.2.e.j.54.1 | 12 | |||
19.11 | even | 3 | inner | 361.2.c.g.68.1 | 4 | ||
19.12 | odd | 6 | 361.2.a.f.1.1 | yes | 2 | ||
19.13 | odd | 18 | 361.2.e.j.62.2 | 12 | |||
19.14 | odd | 18 | 361.2.e.j.99.2 | 12 | |||
19.15 | odd | 18 | 361.2.e.j.245.1 | 12 | |||
19.16 | even | 9 | 361.2.e.i.234.2 | 12 | |||
19.17 | even | 9 | 361.2.e.i.28.2 | 12 | |||
19.18 | odd | 2 | 361.2.c.d.292.2 | 4 | |||
57.26 | odd | 6 | 3249.2.a.o.1.1 | 2 | |||
57.50 | even | 6 | 3249.2.a.i.1.2 | 2 | |||
76.7 | odd | 6 | 5776.2.a.bg.1.2 | 2 | |||
76.31 | even | 6 | 5776.2.a.s.1.1 | 2 | |||
95.64 | even | 6 | 9025.2.a.s.1.1 | 2 | |||
95.69 | odd | 6 | 9025.2.a.n.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
361.2.a.c.1.2 | ✓ | 2 | 19.7 | even | 3 | ||
361.2.a.f.1.1 | yes | 2 | 19.12 | odd | 6 | ||
361.2.c.d.68.2 | 4 | 19.8 | odd | 6 | |||
361.2.c.d.292.2 | 4 | 19.18 | odd | 2 | |||
361.2.c.g.68.1 | 4 | 19.11 | even | 3 | inner | ||
361.2.c.g.292.1 | 4 | 1.1 | even | 1 | trivial | ||
361.2.e.i.28.2 | 12 | 19.17 | even | 9 | |||
361.2.e.i.54.2 | 12 | 19.9 | even | 9 | |||
361.2.e.i.62.1 | 12 | 19.6 | even | 9 | |||
361.2.e.i.99.1 | 12 | 19.5 | even | 9 | |||
361.2.e.i.234.2 | 12 | 19.16 | even | 9 | |||
361.2.e.i.245.2 | 12 | 19.4 | even | 9 | |||
361.2.e.j.28.1 | 12 | 19.2 | odd | 18 | |||
361.2.e.j.54.1 | 12 | 19.10 | odd | 18 | |||
361.2.e.j.62.2 | 12 | 19.13 | odd | 18 | |||
361.2.e.j.99.2 | 12 | 19.14 | odd | 18 | |||
361.2.e.j.234.1 | 12 | 19.3 | odd | 18 | |||
361.2.e.j.245.1 | 12 | 19.15 | odd | 18 | |||
3249.2.a.i.1.2 | 2 | 57.50 | even | 6 | |||
3249.2.a.o.1.1 | 2 | 57.26 | odd | 6 | |||
5776.2.a.s.1.1 | 2 | 76.31 | even | 6 | |||
5776.2.a.bg.1.2 | 2 | 76.7 | odd | 6 | |||
9025.2.a.n.1.2 | 2 | 95.69 | odd | 6 | |||
9025.2.a.s.1.1 | 2 | 95.64 | even | 6 |