Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1274,2,Mod(459,1274)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1274, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1274.459");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1274 = 2 \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1274.o (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.1729412175\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 39 x^{10} - 140 x^{9} + 460 x^{8} - 1066 x^{7} + 2127 x^{6} - 3172 x^{5} + 3842 x^{4} - 3394 x^{3} + 2141 x^{2} - 832 x + 169 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 182) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 569.3 | ||
Root | \(0.500000 - 2.47866i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1274.569 |
Dual form | 1274.2.o.e.459.6 |
$q$-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 \(\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(885\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 1.67234 | − | 2.89658i | 0.965528 | − | 1.67234i | 0.257339 | − | 0.966321i | \(-0.417154\pi\) |
0.708189 | − | 0.706023i | \(-0.249512\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.35408 | − | 0.781779i | −0.605563 | − | 0.349622i | 0.165664 | − | 0.986182i | \(-0.447023\pi\) |
−0.771227 | + | 0.636560i | \(0.780357\pi\) | |||||||
\(6\) | −2.89658 | − | 1.67234i | −1.18253 | − | 0.682732i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −4.09347 | − | 7.09010i | −1.36449 | − | 2.36337i | ||||
\(10\) | −0.781779 | + | 1.35408i | −0.247220 | + | 0.428198i | ||||
\(11\) | 2.48215 | + | 1.43307i | 0.748396 | + | 0.432087i | 0.825114 | − | 0.564966i | \(-0.191111\pi\) |
−0.0767180 | + | 0.997053i | \(0.524444\pi\) | |||||||
\(12\) | −1.67234 | + | 2.89658i | −0.482764 | + | 0.836172i | ||||
\(13\) | −2.99598 | + | 2.00602i | −0.830935 | + | 0.556370i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.52898 | + | 2.61481i | −1.16938 | + | 0.675140i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.22961 | −0.540760 | −0.270380 | − | 0.962754i | \(-0.587149\pi\) | ||||
−0.270380 | + | 0.962754i | \(0.587149\pi\) | |||||||
\(18\) | −7.09010 | + | 4.09347i | −1.67115 | + | 0.964840i | ||||
\(19\) | −6.26657 | + | 3.61801i | −1.43765 | + | 0.830028i | −0.997686 | − | 0.0679872i | \(-0.978342\pi\) |
−0.439964 | + | 0.898015i | \(0.645009\pi\) | |||||||
\(20\) | 1.35408 | + | 0.781779i | 0.302782 | + | 0.174811i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.43307 | − | 2.48215i | 0.305531 | − | 0.529196i | ||||
\(23\) | 1.66735 | 0.347667 | 0.173833 | − | 0.984775i | \(-0.444385\pi\) | ||||
0.173833 | + | 0.984775i | \(0.444385\pi\) | |||||||
\(24\) | 2.89658 | + | 1.67234i | 0.591263 | + | 0.341366i | ||||
\(25\) | −1.27764 | − | 2.21294i | −0.255529 | − | 0.442589i | ||||
\(26\) | 2.00602 | + | 2.99598i | 0.393413 | + | 0.587560i | ||||
\(27\) | −17.3487 | −3.33876 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.41379 | − | 4.18080i | −0.448229 | − | 0.776356i | 0.550042 | − | 0.835137i | \(-0.314612\pi\) |
−0.998271 | + | 0.0587816i | \(0.981278\pi\) | |||||||
\(30\) | 2.61481 | + | 4.52898i | 0.477396 | + | 0.826874i | ||||
\(31\) | −0.517851 | + | 0.298982i | −0.0930088 | + | 0.0536987i | −0.545783 | − | 0.837927i | \(-0.683768\pi\) |
0.452774 | + | 0.891625i | \(0.350434\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 8.30201 | − | 4.79317i | 1.44519 | − | 0.834384i | ||||
\(34\) | 2.22961i | 0.382375i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.09347 | + | 7.09010i | 0.682245 | + | 1.18168i | ||||
\(37\) | 0.0385636i | 0.00633982i | 0.999995 | + | 0.00316991i | \(0.00100902\pi\) | ||||
−0.999995 | + | 0.00316991i | \(0.998991\pi\) | |||||||
\(38\) | 3.61801 | + | 6.26657i | 0.586918 | + | 1.01657i | ||||
\(39\) | 0.800299 | + | 12.0329i | 0.128150 | + | 1.92680i | ||||
\(40\) | 0.781779 | − | 1.35408i | 0.123610 | − | 0.214099i | ||||
\(41\) | 6.88896 | − | 3.97734i | 1.07588 | − | 0.621157i | 0.146095 | − | 0.989271i | \(-0.453330\pi\) |
0.929781 | + | 0.368114i | \(0.119996\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.04571 | − | 8.73942i | 0.769463 | − | 1.33275i | −0.168391 | − | 0.985720i | \(-0.553857\pi\) |
0.937854 | − | 0.347029i | \(-0.112809\pi\) | |||||||
\(44\) | −2.48215 | − | 1.43307i | −0.374198 | − | 0.216043i | ||||
\(45\) | 12.8007i | 1.90822i | ||||||||
\(46\) | − | 1.66735i | − | 0.245838i | ||||||
\(47\) | −6.08501 | − | 3.51318i | −0.887590 | − | 0.512450i | −0.0144363 | − | 0.999896i | \(-0.504595\pi\) |
−0.873153 | + | 0.487446i | \(0.837929\pi\) | |||||||
\(48\) | 1.67234 | − | 2.89658i | 0.241382 | − | 0.418086i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.21294 | + | 1.27764i | −0.312958 | + | 0.180686i | ||||
\(51\) | −3.72868 | + | 6.45826i | −0.522119 | + | 0.904337i | ||||
\(52\) | 2.99598 | − | 2.00602i | 0.415467 | − | 0.278185i | ||||
\(53\) | 2.99202 | + | 5.18233i | 0.410985 | + | 0.711848i | 0.994998 | − | 0.0998972i | \(-0.0318514\pi\) |
−0.584012 | + | 0.811745i | \(0.698518\pi\) | |||||||
\(54\) | 17.3487i | 2.36086i | ||||||||
\(55\) | −2.24069 | − | 3.88098i | −0.302134 | − | 0.523312i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 24.2022i | 3.20566i | ||||||||
\(58\) | −4.18080 | + | 2.41379i | −0.548966 | + | 0.316946i | ||||
\(59\) | 0.896206i | 0.116676i | 0.998297 | + | 0.0583381i | \(0.0185801\pi\) | ||||
−0.998297 | + | 0.0583381i | \(0.981420\pi\) | |||||||
\(60\) | 4.52898 | − | 2.61481i | 0.584688 | − | 0.337570i | ||||
\(61\) | −7.12846 | − | 12.3469i | −0.912706 | − | 1.58085i | −0.810225 | − | 0.586119i | \(-0.800655\pi\) |
−0.102481 | − | 0.994735i | \(-0.532678\pi\) | |||||||
\(62\) | 0.298982 | + | 0.517851i | 0.0379707 | + | 0.0657672i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 5.62506 | − | 0.374120i | 0.697703 | − | 0.0464038i | ||||
\(66\) | −4.79317 | − | 8.30201i | −0.589998 | − | 1.02191i | ||||
\(67\) | 1.42103 | + | 0.820432i | 0.173606 | + | 0.100232i | 0.584285 | − | 0.811548i | \(-0.301375\pi\) |
−0.410679 | + | 0.911780i | \(0.634708\pi\) | |||||||
\(68\) | 2.22961 | 0.270380 | ||||||||
\(69\) | 2.78838 | − | 4.82962i | 0.335682 | − | 0.581418i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.98724 | − | 1.14733i | −0.235841 | − | 0.136163i | 0.377422 | − | 0.926041i | \(-0.376810\pi\) |
−0.613264 | + | 0.789878i | \(0.710144\pi\) | |||||||
\(72\) | 7.09010 | − | 4.09347i | 0.835576 | − | 0.482420i | ||||
\(73\) | 9.72351 | − | 5.61387i | 1.13805 | − | 0.657054i | 0.192104 | − | 0.981375i | \(-0.438469\pi\) |
0.945947 | + | 0.324321i | \(0.105136\pi\) | |||||||
\(74\) | 0.0385636 | 0.00448293 | ||||||||
\(75\) | −8.54664 | −0.986881 | ||||||||
\(76\) | 6.26657 | − | 3.61801i | 0.718825 | − | 0.415014i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 12.0329 | − | 0.800299i | 1.36245 | − | 0.0906160i | ||||
\(79\) | −2.13049 | + | 3.69011i | −0.239699 | + | 0.415170i | −0.960628 | − | 0.277839i | \(-0.910382\pi\) |
0.720929 | + | 0.693009i | \(0.243715\pi\) | |||||||
\(80\) | −1.35408 | − | 0.781779i | −0.151391 | − | 0.0874055i | ||||
\(81\) | −16.7326 | + | 28.9816i | −1.85917 | + | 3.22018i | ||||
\(82\) | −3.97734 | − | 6.88896i | −0.439224 | − | 0.760759i | ||||
\(83\) | − | 4.94829i | − | 0.543145i | −0.962418 | − | 0.271572i | \(-0.912456\pi\) | ||
0.962418 | − | 0.271572i | \(-0.0875437\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.01907 | + | 1.74306i | 0.327465 | + | 0.189062i | ||||
\(86\) | −8.73942 | − | 5.04571i | −0.942396 | − | 0.544092i | ||||
\(87\) | −16.1467 | −1.73111 | ||||||||
\(88\) | −1.43307 | + | 2.48215i | −0.152766 | + | 0.264598i | ||||
\(89\) | − | 2.42120i | − | 0.256647i | −0.991732 | − | 0.128323i | \(-0.959040\pi\) | ||
0.991732 | − | 0.128323i | \(-0.0409595\pi\) | |||||||
\(90\) | 12.8007 | 1.34932 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.66735 | −0.173833 | ||||||||
\(93\) | 2.00000i | 0.207390i | ||||||||
\(94\) | −3.51318 | + | 6.08501i | −0.362357 | + | 0.627621i | ||||
\(95\) | 11.3139 | 1.16078 | ||||||||
\(96\) | −2.89658 | − | 1.67234i | −0.295631 | − | 0.170683i | ||||
\(97\) | 4.23338 | + | 2.44414i | 0.429835 | + | 0.248165i | 0.699276 | − | 0.714852i | \(-0.253506\pi\) |
−0.269442 | + | 0.963017i | \(0.586839\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 23.4649i | − | 2.35831i | ||||||
\(100\) | 1.27764 | + | 2.21294i | 0.127764 | + | 0.221294i | ||||
\(101\) | −3.68373 | + | 6.38042i | −0.366545 | + | 0.634875i | −0.989023 | − | 0.147763i | \(-0.952793\pi\) |
0.622478 | + | 0.782638i | \(0.286126\pi\) | |||||||
\(102\) | 6.45826 | + | 3.72868i | 0.639463 | + | 0.369194i | ||||
\(103\) | −2.89263 | + | 5.01017i | −0.285019 | + | 0.493667i | −0.972614 | − | 0.232427i | \(-0.925333\pi\) |
0.687595 | + | 0.726094i | \(0.258667\pi\) | |||||||
\(104\) | −2.00602 | − | 2.99598i | −0.196706 | − | 0.293780i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.18233 | − | 2.99202i | 0.503352 | − | 0.290611i | ||||
\(107\) | −1.02896 | −0.0994729 | −0.0497365 | − | 0.998762i | \(-0.515838\pi\) | ||||
−0.0497365 | + | 0.998762i | \(0.515838\pi\) | |||||||
\(108\) | 17.3487 | 1.66938 | ||||||||
\(109\) | 12.2573 | − | 7.07674i | 1.17403 | − | 0.677829i | 0.219407 | − | 0.975633i | \(-0.429588\pi\) |
0.954627 | + | 0.297805i | \(0.0962545\pi\) | |||||||
\(110\) | −3.88098 | + | 2.24069i | −0.370037 | + | 0.213641i | ||||
\(111\) | 0.111703 | + | 0.0644917i | 0.0106024 | + | 0.00612128i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.77051 | − | 11.7269i | 0.636916 | − | 1.10317i | −0.349189 | − | 0.937052i | \(-0.613543\pi\) |
0.986106 | − | 0.166119i | \(-0.0531237\pi\) | |||||||
\(114\) | 24.2022 | 2.26675 | ||||||||
\(115\) | −2.25773 | − | 1.30350i | −0.210534 | − | 0.121552i | ||||
\(116\) | 2.41379 | + | 4.18080i | 0.224115 | + | 0.388178i | ||||
\(117\) | 26.4868 | + | 13.0302i | 2.44871 | + | 1.20464i | ||||
\(118\) | 0.896206 | 0.0825025 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.61481 | − | 4.52898i | −0.238698 | − | 0.413437i | ||||
\(121\) | −1.39263 | − | 2.41210i | −0.126602 | − | 0.219282i | ||||
\(122\) | −12.3469 | + | 7.12846i | −1.11783 | + | 0.645381i | ||||
\(123\) | − | 26.6060i | − | 2.39898i | ||||||
\(124\) | 0.517851 | − | 0.298982i | 0.0465044 | − | 0.0268493i | ||||
\(125\) | 11.8131i | 1.05660i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.92583 | + | 8.53178i | 0.437096 | + | 0.757073i | 0.997464 | − | 0.0711707i | \(-0.0226735\pi\) |
−0.560368 | + | 0.828244i | \(0.689340\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −16.8763 | − | 29.2306i | −1.48588 | − | 2.57361i | ||||
\(130\) | −0.374120 | − | 5.62506i | −0.0328125 | − | 0.493350i | ||||
\(131\) | 7.39614 | − | 12.8105i | 0.646204 | − | 1.11926i | −0.337818 | − | 0.941211i | \(-0.609689\pi\) |
0.984022 | − | 0.178047i | \(-0.0569778\pi\) | |||||||
\(132\) | −8.30201 | + | 4.79317i | −0.722597 | + | 0.417192i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.820432 | − | 1.42103i | 0.0708746 | − | 0.122758i | ||||
\(135\) | 23.4915 | + | 13.5628i | 2.02183 | + | 1.16730i | ||||
\(136\) | − | 2.22961i | − | 0.191188i | ||||||
\(137\) | − | 0.458997i | − | 0.0392148i | −0.999808 | − | 0.0196074i | \(-0.993758\pi\) | ||
0.999808 | − | 0.0196074i | \(-0.00624163\pi\) | |||||||
\(138\) | −4.82962 | − | 2.78838i | −0.411125 | − | 0.237363i | ||||
\(139\) | 7.65731 | − | 13.2628i | 0.649485 | − | 1.12494i | −0.333762 | − | 0.942658i | \(-0.608318\pi\) |
0.983246 | − | 0.182283i | \(-0.0583486\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −20.3525 | + | 11.7505i | −1.71399 | + | 0.989570i | ||||
\(142\) | −1.14733 | + | 1.98724i | −0.0962819 | + | 0.166765i | ||||
\(143\) | −10.3112 | + | 0.685794i | −0.862268 | + | 0.0573490i | ||||
\(144\) | −4.09347 | − | 7.09010i | −0.341122 | − | 0.590841i | ||||
\(145\) | 7.54819i | 0.626843i | ||||||||
\(146\) | −5.61387 | − | 9.72351i | −0.464607 | − | 0.804723i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 0.0385636i | − | 0.00316991i | ||||||
\(149\) | −8.86563 | + | 5.11858i | −0.726301 | + | 0.419330i | −0.817067 | − | 0.576542i | \(-0.804402\pi\) |
0.0907665 | + | 0.995872i | \(0.471068\pi\) | |||||||
\(150\) | 8.54664i | 0.697830i | ||||||||
\(151\) | 13.1731 | − | 7.60551i | 1.07201 | − | 0.618927i | 0.143283 | − | 0.989682i | \(-0.454234\pi\) |
0.928731 | + | 0.370754i | \(0.120901\pi\) | |||||||
\(152\) | −3.61801 | − | 6.26657i | −0.293459 | − | 0.508286i | ||||
\(153\) | 9.12684 | + | 15.8082i | 0.737862 | + | 1.27801i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.934950 | 0.0750970 | ||||||||
\(156\) | −0.800299 | − | 12.0329i | −0.0640752 | − | 0.963400i | ||||
\(157\) | −1.13709 | − | 1.96950i | −0.0907500 | − | 0.157184i | 0.817077 | − | 0.576529i | \(-0.195593\pi\) |
−0.907827 | + | 0.419345i | \(0.862260\pi\) | |||||||
\(158\) | 3.69011 | + | 2.13049i | 0.293570 | + | 0.169493i | ||||
\(159\) | 20.0147 | 1.58727 | ||||||||
\(160\) | −0.781779 | + | 1.35408i | −0.0618050 | + | 0.107049i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 28.9816 | + | 16.7326i | 2.27701 | + | 1.31463i | ||||
\(163\) | −0.00848066 | + | 0.00489631i | −0.000664256 | + | 0.000383509i | −0.500332 | − | 0.865834i | \(-0.666789\pi\) |
0.499668 | + | 0.866217i | \(0.333455\pi\) | |||||||
\(164\) | −6.88896 | + | 3.97734i | −0.537938 | + | 0.310578i | ||||
\(165\) | −14.9888 | −1.16688 | ||||||||
\(166\) | −4.94829 | −0.384061 | ||||||||
\(167\) | −21.6080 | + | 12.4754i | −1.67208 | + | 0.965376i | −0.705608 | + | 0.708603i | \(0.749326\pi\) |
−0.966472 | + | 0.256773i | \(0.917341\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.95177 | − | 12.0200i | 0.380906 | − | 0.924614i | ||||
\(170\) | 1.74306 | − | 3.01907i | 0.133687 | − | 0.231552i | ||||
\(171\) | 51.3040 | + | 29.6204i | 3.92332 | + | 2.26513i | ||||
\(172\) | −5.04571 | + | 8.73942i | −0.384731 | + | 0.666374i | ||||
\(173\) | 1.60275 | + | 2.77604i | 0.121855 | + | 0.211058i | 0.920499 | − | 0.390745i | \(-0.127782\pi\) |
−0.798644 | + | 0.601803i | \(0.794449\pi\) | |||||||
\(174\) | 16.1467i | 1.22408i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.48215 | + | 1.43307i | 0.187099 | + | 0.108022i | ||||
\(177\) | 2.59594 | + | 1.49877i | 0.195123 | + | 0.112654i | ||||
\(178\) | −2.42120 | −0.181477 | ||||||||
\(179\) | −7.89998 | + | 13.6832i | −0.590472 | + | 1.02273i | 0.403697 | + | 0.914893i | \(0.367725\pi\) |
−0.994169 | + | 0.107835i | \(0.965608\pi\) | |||||||
\(180\) | − | 12.8007i | − | 0.954111i | ||||||
\(181\) | −9.11907 | −0.677815 | −0.338908 | − | 0.940820i | \(-0.610057\pi\) | ||||
−0.338908 | + | 0.940820i | \(0.610057\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −47.6850 | −3.52497 | ||||||||
\(184\) | 1.66735i | 0.122919i | ||||||||
\(185\) | 0.0301482 | − | 0.0522183i | 0.00221654 | − | 0.00383916i | ||||
\(186\) | 2.00000 | 0.146647 | ||||||||
\(187\) | −5.53423 | − | 3.19519i | −0.404703 | − | 0.233655i | ||||
\(188\) | 6.08501 | + | 3.51318i | 0.443795 | + | 0.256225i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 11.3139i | − | 0.820799i | ||||||
\(191\) | 1.63068 | + | 2.82443i | 0.117992 | + | 0.204368i | 0.918972 | − | 0.394323i | \(-0.129021\pi\) |
−0.800980 | + | 0.598691i | \(0.795688\pi\) | |||||||
\(192\) | −1.67234 | + | 2.89658i | −0.120691 | + | 0.209043i | ||||
\(193\) | −19.1158 | − | 11.0365i | −1.37599 | − | 0.794426i | −0.384313 | − | 0.923203i | \(-0.625562\pi\) |
−0.991674 | + | 0.128777i | \(0.958895\pi\) | |||||||
\(194\) | 2.44414 | − | 4.23338i | 0.175479 | − | 0.303939i | ||||
\(195\) | 8.32336 | − | 16.9191i | 0.596048 | − | 1.21160i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.56660 | + | 2.63653i | −0.325357 | + | 0.187845i | −0.653778 | − | 0.756687i | \(-0.726817\pi\) |
0.328421 | + | 0.944531i | \(0.393484\pi\) | |||||||
\(198\) | −23.4649 | −1.66758 | ||||||||
\(199\) | 8.86762 | 0.628609 | 0.314304 | − | 0.949322i | \(-0.398229\pi\) | ||||
0.314304 | + | 0.949322i | \(0.398229\pi\) | |||||||
\(200\) | 2.21294 | − | 1.27764i | 0.156479 | − | 0.0903431i | ||||
\(201\) | 4.75290 | − | 2.74409i | 0.335244 | − | 0.193553i | ||||
\(202\) | 6.38042 | + | 3.68373i | 0.448924 | + | 0.259187i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 3.72868 | − | 6.45826i | 0.261060 | − | 0.452169i | ||||
\(205\) | −12.4376 | −0.868681 | ||||||||
\(206\) | 5.01017 | + | 2.89263i | 0.349075 | + | 0.201539i | ||||
\(207\) | −6.82525 | − | 11.8217i | −0.474388 | − | 0.821663i | ||||
\(208\) | −2.99598 | + | 2.00602i | −0.207734 | + | 0.139092i | ||||
\(209\) | −20.7394 | −1.43458 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.28453 | − | 5.68898i | −0.226117 | − | 0.391646i | 0.730537 | − | 0.682873i | \(-0.239270\pi\) |
−0.956654 | + | 0.291227i | \(0.905936\pi\) | |||||||
\(212\) | −2.99202 | − | 5.18233i | −0.205493 | − | 0.355924i | ||||
\(213\) | −6.64668 | + | 3.83746i | −0.455423 | + | 0.262939i | ||||
\(214\) | 1.02896i | 0.0703380i | ||||||||
\(215\) | −13.6646 | + | 7.88925i | −0.931917 | + | 0.538043i | ||||
\(216\) | − | 17.3487i | − | 1.18043i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −7.07674 | − | 12.2573i | −0.479297 | − | 0.830167i | ||||
\(219\) | − | 37.5533i | − | 2.53762i | ||||||
\(220\) | 2.24069 | + | 3.88098i | 0.151067 | + | 0.261656i | ||||
\(221\) | 6.67987 | − | 4.47264i | 0.449337 | − | 0.300863i | ||||
\(222\) | 0.0644917 | − | 0.111703i | 0.00432840 | − | 0.00749700i | ||||
\(223\) | 14.6463 | − | 8.45606i | 0.980790 | − | 0.566260i | 0.0782817 | − | 0.996931i | \(-0.475057\pi\) |
0.902509 | + | 0.430672i | \(0.141723\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −10.4600 | + | 18.1172i | −0.697333 | + | 1.20782i | ||||
\(226\) | −11.7269 | − | 6.77051i | −0.780060 | − | 0.450368i | ||||
\(227\) | − | 16.1322i | − | 1.07073i | −0.844620 | − | 0.535367i | \(-0.820173\pi\) | ||
0.844620 | − | 0.535367i | \(-0.179827\pi\) | |||||||
\(228\) | − | 24.2022i | − | 1.60283i | ||||||
\(229\) | 5.98583 | + | 3.45592i | 0.395555 | + | 0.228374i | 0.684564 | − | 0.728953i | \(-0.259993\pi\) |
−0.289009 | + | 0.957326i | \(0.593326\pi\) | |||||||
\(230\) | −1.30350 | + | 2.25773i | −0.0859502 | + | 0.148870i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.18080 | − | 2.41379i | 0.274483 | − | 0.158473i | ||||
\(233\) | −3.73702 | + | 6.47272i | −0.244821 | + | 0.424042i | −0.962081 | − | 0.272763i | \(-0.912062\pi\) |
0.717261 | + | 0.696805i | \(0.245396\pi\) | |||||||
\(234\) | 13.0302 | − | 26.4868i | 0.851810 | − | 1.73150i | ||||
\(235\) | 5.49306 | + | 9.51426i | 0.358328 | + | 0.620642i | ||||
\(236\) | − | 0.896206i | − | 0.0583381i | ||||||
\(237\) | 7.12582 | + | 12.3423i | 0.462872 | + | 0.801717i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.8696i | 1.28526i | 0.766179 | + | 0.642628i | \(0.222156\pi\) | ||||
−0.766179 | + | 0.642628i | \(0.777844\pi\) | |||||||
\(240\) | −4.52898 | + | 2.61481i | −0.292344 | + | 0.168785i | ||||
\(241\) | − | 10.6445i | − | 0.685674i | −0.939395 | − | 0.342837i | \(-0.888612\pi\) | ||
0.939395 | − | 0.342837i | \(-0.111388\pi\) | |||||||
\(242\) | −2.41210 | + | 1.39263i | −0.155055 | + | 0.0895213i | ||||
\(243\) | 29.9422 | + | 51.8613i | 1.92079 | + | 3.32691i | ||||
\(244\) | 7.12846 | + | 12.3469i | 0.456353 | + | 0.790427i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −26.6060 | −1.69633 | ||||||||
\(247\) | 11.5167 | − | 23.4103i | 0.732792 | − | 1.48956i | ||||
\(248\) | −0.298982 | − | 0.517851i | −0.0189853 | − | 0.0328836i | ||||
\(249\) | −14.3331 | − | 8.27524i | −0.908325 | − | 0.524422i | ||||
\(250\) | 11.8131 | 0.747128 | ||||||||
\(251\) | −7.95696 | + | 13.7819i | −0.502239 | + | 0.869904i | 0.497757 | + | 0.867316i | \(0.334157\pi\) |
−0.999997 | + | 0.00258749i | \(0.999176\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.13861 | + | 2.38943i | 0.260192 | + | 0.150222i | ||||
\(254\) | 8.53178 | − | 4.92583i | 0.535332 | − | 0.309074i | ||||
\(255\) | 10.0979 | − | 5.83000i | 0.632352 | − | 0.365089i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −31.1018 | −1.94008 | −0.970039 | − | 0.242950i | \(-0.921885\pi\) | ||||
−0.970039 | + | 0.242950i | \(0.921885\pi\) | |||||||
\(258\) | −29.2306 | + | 16.8763i | −1.81982 | + | 1.05067i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −5.62506 | + | 0.374120i | −0.348851 | + | 0.0232019i | ||||
\(261\) | −19.7615 | + | 34.2280i | −1.22321 | + | 2.11866i | ||||
\(262\) | −12.8105 | − | 7.39614i | −0.791435 | − | 0.456935i | ||||
\(263\) | 14.1873 | − | 24.5732i | 0.874829 | − | 1.51525i | 0.0178837 | − | 0.999840i | \(-0.494307\pi\) |
0.856945 | − | 0.515408i | \(-0.172360\pi\) | |||||||
\(264\) | 4.79317 | + | 8.30201i | 0.294999 | + | 0.510954i | ||||
\(265\) | − | 9.35639i | − | 0.574758i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.01321 | − | 4.04908i | −0.429202 | − | 0.247800i | ||||
\(268\) | −1.42103 | − | 0.820432i | −0.0868032 | − | 0.0501159i | ||||
\(269\) | 21.4017 | 1.30488 | 0.652441 | − | 0.757840i | \(-0.273745\pi\) | ||||
0.652441 | + | 0.757840i | \(0.273745\pi\) | |||||||
\(270\) | 13.5628 | − | 23.4915i | 0.825408 | − | 1.42965i | ||||
\(271\) | − | 5.74656i | − | 0.349079i | −0.984650 | − | 0.174539i | \(-0.944156\pi\) | ||
0.984650 | − | 0.174539i | \(-0.0558436\pi\) | |||||||
\(272\) | −2.22961 | −0.135190 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.458997 | −0.0277290 | ||||||||
\(275\) | − | 7.32381i | − | 0.441642i | ||||||
\(276\) | −2.78838 | + | 4.82962i | −0.167841 | + | 0.290709i | ||||
\(277\) | −26.6020 | −1.59836 | −0.799180 | − | 0.601092i | \(-0.794733\pi\) | ||||
−0.799180 | + | 0.601092i | \(0.794733\pi\) | |||||||
\(278\) | −13.2628 | − | 7.65731i | −0.795453 | − | 0.459255i | ||||
\(279\) | 4.23962 | + | 2.44774i | 0.253819 | + | 0.146543i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.69143i | 0.399177i | 0.979880 | + | 0.199589i | \(0.0639606\pi\) | ||||
−0.979880 | + | 0.199589i | \(0.936039\pi\) | |||||||
\(282\) | 11.7505 | + | 20.3525i | 0.699732 | + | 1.21197i | ||||
\(283\) | −9.96692 | + | 17.2632i | −0.592472 | + | 1.02619i | 0.401426 | + | 0.915891i | \(0.368515\pi\) |
−0.993898 | + | 0.110300i | \(0.964819\pi\) | |||||||
\(284\) | 1.98724 | + | 1.14733i | 0.117921 | + | 0.0680816i | ||||
\(285\) | 18.9208 | − | 32.7717i | 1.12077 | − | 1.94123i | ||||
\(286\) | 0.685794 | + | 10.3112i | 0.0405519 | + | 0.609716i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −7.09010 | + | 4.09347i | −0.417788 | + | 0.241210i | ||||
\(289\) | −12.0288 | −0.707578 | ||||||||
\(290\) | 7.54819 | 0.443245 | ||||||||
\(291\) | 14.1593 | − | 8.17490i | 0.830035 | − | 0.479221i | ||||
\(292\) | −9.72351 | + | 5.61387i | −0.569025 | + | 0.328527i | ||||
\(293\) | 7.67375 | + | 4.43044i | 0.448305 | + | 0.258829i | 0.707114 | − | 0.707099i | \(-0.249997\pi\) |
−0.258809 | + | 0.965929i | \(0.583330\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.700635 | − | 1.21354i | 0.0407926 | − | 0.0706548i | ||||
\(296\) | −0.0385636 | −0.00224147 | ||||||||
\(297\) | −43.0620 | − | 24.8619i | −2.49871 | − | 1.44263i | ||||
\(298\) | 5.11858 | + | 8.86563i | 0.296511 | + | 0.513572i | ||||
\(299\) | −4.99535 | + | 3.34474i | −0.288888 | + | 0.193431i | ||||
\(300\) | 8.54664 | 0.493441 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −7.60551 | − | 13.1731i | −0.437648 | − | 0.758028i | ||||
\(303\) | 12.3209 | + | 21.3405i | 0.707820 | + | 1.22598i | ||||
\(304\) | −6.26657 | + | 3.61801i | −0.359413 | + | 0.207507i | ||||
\(305\) | 22.2915i | 1.27641i | ||||||||
\(306\) | 15.8082 | − | 9.12684i | 0.903692 | − | 0.521747i | ||||
\(307\) | 8.34636i | 0.476352i | 0.971222 | + | 0.238176i | \(0.0765495\pi\) | ||||
−0.971222 | + | 0.238176i | \(0.923450\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.67493 | + | 16.7575i | 0.550387 | + | 0.953299i | ||||
\(310\) | − | 0.934950i | − | 0.0531016i | ||||||
\(311\) | −3.34448 | − | 5.79281i | −0.189648 | − | 0.328480i | 0.755485 | − | 0.655166i | \(-0.227401\pi\) |
−0.945133 | + | 0.326686i | \(0.894068\pi\) | |||||||
\(312\) | −12.0329 | + | 0.800299i | −0.681226 | + | 0.0453080i | ||||
\(313\) | −10.6894 | + | 18.5145i | −0.604199 | + | 1.04650i | 0.387978 | + | 0.921669i | \(0.373174\pi\) |
−0.992177 | + | 0.124835i | \(0.960160\pi\) | |||||||
\(314\) | −1.96950 | + | 1.13709i | −0.111146 | + | 0.0641699i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.13049 | − | 3.69011i | 0.119849 | − | 0.207585i | ||||
\(317\) | 27.4336 | + | 15.8388i | 1.54083 | + | 0.889596i | 0.998787 | + | 0.0492433i | \(0.0156810\pi\) |
0.542039 | + | 0.840353i | \(0.317652\pi\) | |||||||
\(318\) | − | 20.0147i | − | 1.12237i | ||||||
\(319\) | − | 13.8365i | − | 0.774695i | ||||||
\(320\) | 1.35408 | + | 0.781779i | 0.0756954 | + | 0.0437028i | ||||
\(321\) | −1.72077 | + | 2.98046i | −0.0960439 | + | 0.166353i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.9720 | − | 8.06675i | 0.777424 | − | 0.448846i | ||||
\(324\) | 16.7326 | − | 28.9816i | 0.929587 | − | 1.61009i | ||||
\(325\) | 8.26700 | + | 4.06695i | 0.458571 | + | 0.225594i | ||||
\(326\) | 0.00489631 | + | 0.00848066i | 0.000271182 | + | 0.000469700i | ||||
\(327\) | − | 47.3390i | − | 2.61785i | ||||||
\(328\) | 3.97734 | + | 6.88896i | 0.219612 | + | 0.380379i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 14.9888i | 0.825106i | ||||||||
\(331\) | 21.3644 | − | 12.3347i | 1.17429 | − | 0.677979i | 0.219606 | − | 0.975589i | \(-0.429523\pi\) |
0.954688 | + | 0.297609i | \(0.0961893\pi\) | |||||||
\(332\) | 4.94829i | 0.271572i | ||||||||
\(333\) | 0.273420 | − | 0.157859i | 0.0149833 | − | 0.00865062i | ||||
\(334\) | 12.4754 | + | 21.6080i | 0.682624 | + | 1.18234i | ||||
\(335\) | −1.28279 | − | 2.22186i | −0.0700865 | − | 0.121393i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.0871 | 1.53000 | 0.765002 | − | 0.644028i | \(-0.222738\pi\) | ||||
0.765002 | + | 0.644028i | \(0.222738\pi\) | |||||||
\(338\) | −12.0200 | − | 4.95177i | −0.653801 | − | 0.269341i | ||||
\(339\) | −22.6453 | − | 39.2227i | −1.22992 | − | 2.13029i | ||||
\(340\) | −3.01907 | − | 1.74306i | −0.163732 | − | 0.0945309i | ||||
\(341\) | −1.71385 | −0.0928099 | ||||||||
\(342\) | 29.6204 | − | 51.3040i | 1.60169 | − | 2.77420i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 8.73942 | + | 5.04571i | 0.471198 | + | 0.272046i | ||||
\(345\) | −7.55139 | + | 4.35980i | −0.406553 | + | 0.234724i | ||||
\(346\) | 2.77604 | − | 1.60275i | 0.149241 | − | 0.0861643i | ||||
\(347\) | −10.1080 | −0.542623 | −0.271312 | − | 0.962492i | \(-0.587457\pi\) | ||||
−0.271312 | + | 0.962492i | \(0.587457\pi\) | |||||||
\(348\) | 16.1467 | 0.865556 | ||||||||
\(349\) | 15.0596 | − | 8.69465i | 0.806121 | − | 0.465414i | −0.0394863 | − | 0.999220i | \(-0.512572\pi\) |
0.845607 | + | 0.533806i | \(0.179239\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 51.9763 | − | 34.8018i | 2.77429 | − | 1.85758i | ||||
\(352\) | 1.43307 | − | 2.48215i | 0.0763828 | − | 0.132299i | ||||
\(353\) | 2.88091 | + | 1.66329i | 0.153335 | + | 0.0885282i | 0.574704 | − | 0.818361i | \(-0.305117\pi\) |
−0.421369 | + | 0.906889i | \(0.638450\pi\) | |||||||
\(354\) | 1.49877 | − | 2.59594i | 0.0796585 | − | 0.137973i | ||||
\(355\) | 1.79392 | + | 3.10716i | 0.0952113 | + | 0.164911i | ||||
\(356\) | 2.42120i | 0.128323i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 13.6832 | + | 7.89998i | 0.723177 | + | 0.417527i | ||||
\(359\) | −6.94911 | − | 4.01207i | −0.366760 | − | 0.211749i | 0.305282 | − | 0.952262i | \(-0.401249\pi\) |
−0.672042 | + | 0.740513i | \(0.734583\pi\) | |||||||
\(360\) | −12.8007 | −0.674659 | ||||||||
\(361\) | 16.6800 | − | 28.8905i | 0.877893 | − | 1.52055i | ||||
\(362\) | 9.11907i | 0.479288i | ||||||||
\(363\) | −9.31579 | −0.488952 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −17.5552 | −0.918882 | ||||||||
\(366\) | 47.6850i | 2.49253i | ||||||||
\(367\) | 0.519540 | − | 0.899869i | 0.0271198 | − | 0.0469728i | −0.852147 | − | 0.523302i | \(-0.824700\pi\) |
0.879267 | + | 0.476330i | \(0.158033\pi\) | |||||||
\(368\) | 1.66735 | 0.0869167 | ||||||||
\(369\) | −56.3995 | − | 32.5623i | −2.93604 | − | 1.69512i | ||||
\(370\) | −0.0522183 | − | 0.0301482i | −0.00271470 | − | 0.00156733i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 2.00000i | − | 0.103695i | ||||||
\(373\) | −13.6562 | − | 23.6532i | −0.707092 | − | 1.22472i | −0.965931 | − | 0.258798i | \(-0.916673\pi\) |
0.258840 | − | 0.965920i | \(-0.416660\pi\) | |||||||
\(374\) | −3.19519 | + | 5.53423i | −0.165219 | + | 0.286168i | ||||
\(375\) | 34.2177 | + | 19.7556i | 1.76700 | + | 1.02018i | ||||
\(376\) | 3.51318 | − | 6.08501i | 0.181178 | − | 0.313810i | ||||
\(377\) | 15.6184 | + | 7.68349i | 0.804390 | + | 0.395720i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.91535 | + | 1.10583i | −0.0983850 | + | 0.0568026i | −0.548385 | − | 0.836226i | \(-0.684757\pi\) |
0.450000 | + | 0.893028i | \(0.351424\pi\) | |||||||
\(380\) | −11.3139 | −0.580392 | ||||||||
\(381\) | 32.9507 | 1.68812 | ||||||||
\(382\) | 2.82443 | − | 1.63068i | 0.144510 | − | 0.0834331i | ||||
\(383\) | 19.3458 | − | 11.1693i | 0.988522 | − | 0.570724i | 0.0836900 | − | 0.996492i | \(-0.473329\pi\) |
0.904832 | + | 0.425768i | \(0.139996\pi\) | |||||||
\(384\) | 2.89658 | + | 1.67234i | 0.147816 | + | 0.0853414i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −11.0365 | + | 19.1158i | −0.561744 | + | 0.972969i | ||||
\(387\) | −82.6178 | −4.19970 | ||||||||
\(388\) | −4.23338 | − | 2.44414i | −0.214917 | − | 0.124083i | ||||
\(389\) | 6.13022 | + | 10.6178i | 0.310814 | + | 0.538346i | 0.978539 | − | 0.206062i | \(-0.0660649\pi\) |
−0.667725 | + | 0.744408i | \(0.732732\pi\) | |||||||
\(390\) | −16.9191 | − | 8.32336i | −0.856733 | − | 0.421470i | ||||
\(391\) | −3.71755 | −0.188004 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −24.7378 | − | 42.8471i | −1.24786 | − | 2.16135i | ||||
\(394\) | 2.63653 | + | 4.56660i | 0.132826 | + | 0.230062i | ||||
\(395\) | 5.76971 | − | 3.33114i | 0.290305 | − | 0.167608i | ||||
\(396\) | 23.4649i | 1.17916i | ||||||||
\(397\) | 2.54193 | − | 1.46759i | 0.127576 | − | 0.0736561i | −0.434854 | − | 0.900501i | \(-0.643200\pi\) |
0.562430 | + | 0.826845i | \(0.309867\pi\) | |||||||
\(398\) | − | 8.86762i | − | 0.444493i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.27764 | − | 2.21294i | −0.0638822 | − | 0.110647i | ||||
\(401\) | 21.8502i | 1.09115i | 0.838062 | + | 0.545575i | \(0.183689\pi\) | ||||
−0.838062 | + | 0.545575i | \(0.816311\pi\) | |||||||
\(402\) | −2.74409 | − | 4.75290i | −0.136863 | − | 0.237053i | ||||
\(403\) | 0.951708 | − | 1.93456i | 0.0474080 | − | 0.0963674i | ||||
\(404\) | 3.68373 | − | 6.38042i | 0.183273 | − | 0.317438i | ||||
\(405\) | 45.3145 | − | 26.1623i | 2.25169 | − | 1.30002i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.0552644 | + | 0.0957207i | −0.00273935 | + | 0.00474470i | ||||
\(408\) | −6.45826 | − | 3.72868i | −0.319731 | − | 0.184597i | ||||
\(409\) | − | 7.38191i | − | 0.365012i | −0.983205 | − | 0.182506i | \(-0.941579\pi\) | ||
0.983205 | − | 0.182506i | \(-0.0584208\pi\) | |||||||
\(410\) | 12.4376i | 0.614250i | ||||||||
\(411\) | −1.32952 | − | 0.767601i | −0.0655806 | − | 0.0378630i | ||||
\(412\) | 2.89263 | − | 5.01017i | 0.142509 | − | 0.246834i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −11.8217 | + | 6.82525i | −0.581004 | + | 0.335443i | ||||
\(415\) | −3.86846 | + | 6.70038i | −0.189895 | + | 0.328909i | ||||
\(416\) | 2.00602 | + | 2.99598i | 0.0983532 | + | 0.146890i | ||||
\(417\) | −25.6113 | − | 44.3601i | −1.25419 | − | 2.17232i | ||||
\(418\) | 20.7394i | 1.01440i | ||||||||
\(419\) | −4.29137 | − | 7.43287i | −0.209647 | − | 0.363119i | 0.741956 | − | 0.670448i | \(-0.233898\pi\) |
−0.951603 | + | 0.307329i | \(0.900565\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 7.49525i | − | 0.365296i | −0.983178 | − | 0.182648i | \(-0.941533\pi\) | ||
0.983178 | − | 0.182648i | \(-0.0584669\pi\) | |||||||
\(422\) | −5.68898 | + | 3.28453i | −0.276935 | + | 0.159889i | ||||
\(423\) | 57.5244i | 2.79693i | ||||||||
\(424\) | −5.18233 | + | 2.99202i | −0.251676 | + | 0.145305i | ||||
\(425\) | 2.84865 | + | 4.93401i | 0.138180 | + | 0.239334i | ||||
\(426\) | 3.83746 | + | 6.64668i | 0.185926 | + | 0.322033i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.02896 | 0.0497365 | ||||||||
\(429\) | −15.2575 | + | 31.0142i | −0.736637 | + | 1.49738i | ||||
\(430\) | 7.88925 | + | 13.6646i | 0.380454 | + | 0.658965i | ||||
\(431\) | 14.2713 | + | 8.23956i | 0.687426 | + | 0.396886i | 0.802647 | − | 0.596454i | \(-0.203424\pi\) |
−0.115221 | + | 0.993340i | \(0.536758\pi\) | |||||||
\(432\) | −17.3487 | −0.834689 | ||||||||
\(433\) | 12.7805 | − | 22.1365i | 0.614192 | − | 1.06381i | −0.376333 | − | 0.926484i | \(-0.622815\pi\) |
0.990526 | − | 0.137328i | \(-0.0438515\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 21.8640 | + | 12.6232i | 1.04830 | + | 0.605235i | ||||
\(436\) | −12.2573 | + | 7.07674i | −0.587017 | + | 0.338914i | ||||
\(437\) | −10.4486 | + | 6.03249i | −0.499823 | + | 0.288573i | ||||
\(438\) | −37.5533 | −1.79437 | ||||||||
\(439\) | 9.20839 | 0.439493 | 0.219746 | − | 0.975557i | \(-0.429477\pi\) | ||||
0.219746 | + | 0.975557i | \(0.429477\pi\) | |||||||
\(440\) | 3.88098 | − | 2.24069i | 0.185019 | − | 0.106821i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.47264 | − | 6.67987i | −0.212742 | − | 0.317729i | ||||
\(443\) | 3.10379 | − | 5.37593i | 0.147466 | − | 0.255418i | −0.782824 | − | 0.622243i | \(-0.786222\pi\) |
0.930290 | + | 0.366825i | \(0.119555\pi\) | |||||||
\(444\) | −0.111703 | − | 0.0644917i | −0.00530118 | − | 0.00306064i | ||||
\(445\) | −1.89284 | + | 3.27850i | −0.0897294 | + | 0.155416i | ||||
\(446\) | −8.45606 | − | 14.6463i | −0.400406 | − | 0.693523i | ||||
\(447\) | 34.2401i | 1.61950i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.51968 | + | 2.60944i | 0.213297 | + | 0.123147i | 0.602843 | − | 0.797860i | \(-0.294035\pi\) |
−0.389546 | + | 0.921007i | \(0.627368\pi\) | |||||||
\(450\) | 18.1172 | + | 10.4600i | 0.854055 | + | 0.493089i | ||||
\(451\) | 22.7992 | 1.07357 | ||||||||
\(452\) | −6.77051 | + | 11.7269i | −0.318458 | + | 0.551586i | ||||
\(453\) | − | 50.8761i | − | 2.39037i | ||||||
\(454\) | −16.1322 | −0.757123 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −24.2022 | −1.13337 | ||||||||
\(457\) | − | 33.9332i | − | 1.58733i | −0.608357 | − | 0.793664i | \(-0.708171\pi\) | ||
0.608357 | − | 0.793664i | \(-0.291829\pi\) | |||||||
\(458\) | 3.45592 | − | 5.98583i | 0.161484 | − | 0.279699i | ||||
\(459\) | 38.6808 | 1.80547 | ||||||||
\(460\) | 2.25773 | + | 1.30350i | 0.105267 | + | 0.0607760i | ||||
\(461\) | −0.731583 | − | 0.422380i | −0.0340732 | − | 0.0196722i | 0.482867 | − | 0.875694i | \(-0.339596\pi\) |
−0.516940 | + | 0.856022i | \(0.672929\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.50221i | 0.302183i | 0.988520 | + | 0.151092i | \(0.0482789\pi\) | ||||
−0.988520 | + | 0.151092i | \(0.951721\pi\) | |||||||
\(464\) | −2.41379 | − | 4.18080i | −0.112057 | − | 0.194089i | ||||
\(465\) | 1.56356 | − | 2.70816i | 0.0725082 | − | 0.125588i | ||||
\(466\) | 6.47272 | + | 3.73702i | 0.299843 | + | 0.173114i | ||||
\(467\) | 4.76379 | − | 8.25113i | 0.220442 | − | 0.381817i | −0.734500 | − | 0.678608i | \(-0.762583\pi\) |
0.954942 | + | 0.296792i | \(0.0959167\pi\) | |||||||
\(468\) | −26.4868 | − | 13.0302i | −1.22435 | − | 0.602321i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 9.51426 | − | 5.49306i | 0.438860 | − | 0.253376i | ||||
\(471\) | −7.60645 | −0.350487 | ||||||||
\(472\) | −0.896206 | −0.0412512 | ||||||||
\(473\) | 25.0484 | − | 14.4617i | 1.15173 | − | 0.664949i | ||||
\(474\) | 12.3423 | − | 7.12582i | 0.566900 | − | 0.327300i | ||||
\(475\) | 16.0129 | + | 9.24505i | 0.734722 | + | 0.424192i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 24.4955 | − | 42.4274i | 1.12157 | − | 1.94262i | ||||
\(478\) | 19.8696 | 0.908813 | ||||||||
\(479\) | −2.46123 | − | 1.42099i | −0.112457 | − | 0.0649268i | 0.442717 | − | 0.896662i | \(-0.354015\pi\) |
−0.555173 | + | 0.831735i | \(0.687348\pi\) | |||||||
\(480\) | 2.61481 | + | 4.52898i | 0.119349 | + | 0.206719i | ||||
\(481\) | −0.0773594 | − | 0.115536i | −0.00352729 | − | 0.00526798i | ||||
\(482\) | −10.6445 | −0.484844 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.39263 | + | 2.41210i | 0.0633011 | + | 0.109641i | ||||
\(485\) | −3.82156 | − | 6.61913i | −0.173528 | − | 0.300559i | ||||
\(486\) | 51.8613 | − | 29.9422i | 2.35248 | − | 1.35820i | ||||
\(487\) | 5.26374i | 0.238523i | 0.992863 | + | 0.119261i | \(0.0380526\pi\) | ||||
−0.992863 | + | 0.119261i | \(0.961947\pi\) | |||||||
\(488\) | 12.3469 | − | 7.12846i | 0.558916 | − | 0.322690i | ||||
\(489\) | 0.0327533i | 0.00148115i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.4457 | + | 19.8245i | 0.516536 | + | 0.894666i | 0.999816 | + | 0.0192004i | \(0.00611205\pi\) |
−0.483280 | + | 0.875466i | \(0.660555\pi\) | |||||||
\(492\) | 26.6060i | 1.19949i | ||||||||
\(493\) | 5.38181 | + | 9.32157i | 0.242384 | + | 0.419822i | ||||
\(494\) | −23.4103 | − | 11.5167i | −1.05328 | − | 0.518162i | ||||
\(495\) | −18.3444 | + | 31.7734i | −0.824517 | + | 1.42811i | ||||
\(496\) | −0.517851 | + | 0.298982i | −0.0232522 | + | 0.0134247i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −8.27524 | + | 14.3331i | −0.370822 | + | 0.642283i | ||||
\(499\) | 5.88791 | + | 3.39938i | 0.263579 | + | 0.152177i | 0.625966 | − | 0.779850i | \(-0.284705\pi\) |
−0.362387 | + | 0.932028i | \(0.618038\pi\) | |||||||
\(500\) | − | 11.8131i | − | 0.528299i | ||||||
\(501\) | 83.4527i | 3.72839i | ||||||||
\(502\) | 13.7819 | + | 7.95696i | 0.615115 | + | 0.355137i | ||||
\(503\) | 5.40300 | − | 9.35827i | 0.240908 | − | 0.417265i | −0.720065 | − | 0.693906i | \(-0.755888\pi\) |
0.960973 | + | 0.276642i | \(0.0892215\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.97615 | − | 5.75973i | 0.443933 | − | 0.256305i | ||||
\(506\) | 2.38943 | − | 4.13861i | 0.106223 | − | 0.183984i | ||||
\(507\) | −26.5358 | − | 34.4448i | −1.17850 | − | 1.52975i | ||||
\(508\) | −4.92583 | − | 8.53178i | −0.218548 | − | 0.378537i | ||||
\(509\) | 27.3194i | 1.21091i | 0.795879 | + | 0.605455i | \(0.207009\pi\) | ||||
−0.795879 | + | 0.605455i | \(0.792991\pi\) | |||||||
\(510\) | −5.83000 | − | 10.0979i | −0.258157 | − | 0.447141i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 108.717 | − | 62.7677i | 4.79996 | − | 2.77126i | ||||
\(514\) | 31.1018i | 1.37184i | ||||||||
\(515\) | 7.83369 | − | 4.52279i | 0.345194 | − | 0.199298i | ||||
\(516\) | 16.8763 | + | 29.2306i | 0.742938 | + | 1.28681i | ||||
\(517\) | −10.0693 | − | 17.4405i | −0.442846 | − | 0.767031i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.7214 | 0.470616 | ||||||||
\(520\) | 0.374120 | + | 5.62506i | 0.0164062 | + | 0.246675i | ||||
\(521\) | −1.81790 | − | 3.14870i | −0.0796437 | − | 0.137947i | 0.823453 | − | 0.567385i | \(-0.192045\pi\) |
−0.903096 | + | 0.429438i | \(0.858712\pi\) | |||||||
\(522\) | 34.2280 | + | 19.7615i | 1.49812 | + | 0.864938i | ||||
\(523\) | 7.18446 | 0.314155 | 0.157077 | − | 0.987586i | \(-0.449793\pi\) | ||||
0.157077 | + | 0.987586i | \(0.449793\pi\) | |||||||
\(524\) | −7.39614 | + | 12.8105i | −0.323102 | + | 0.559629i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24.5732 | − | 14.1873i | −1.07144 | − | 0.618597i | ||||
\(527\) | 1.15461 | − | 0.666613i | 0.0502955 | − | 0.0290381i | ||||
\(528\) | 8.30201 | − | 4.79317i | 0.361299 | − | 0.208596i | ||||
\(529\) | −20.2199 | −0.879128 | ||||||||
\(530\) | −9.35639 | −0.406415 | ||||||||
\(531\) | 6.35419 | − | 3.66859i | 0.275748 | − | 0.159203i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.6606 | + | 25.7354i | −0.548389 | + | 1.11473i | ||||
\(534\) | −4.04908 | + | 7.01321i | −0.175221 | + | 0.303491i | ||||
\(535\) | 1.39329 | + | 0.804416i | 0.0602371 | + | 0.0347779i | ||||
\(536\) | −0.820432 | + | 1.42103i | −0.0354373 | + | 0.0613792i | ||||
\(537\) | 26.4230 | + | 45.7659i | 1.14023 | + | 1.97494i | ||||
\(538\) | − | 21.4017i | − | 0.922691i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −23.4915 | − | 13.5628i | −1.01091 | − | 0.583651i | ||||
\(541\) | 0.385436 | + | 0.222531i | 0.0165712 | + | 0.00956737i | 0.508263 | − | 0.861202i | \(-0.330288\pi\) |
−0.491692 | + | 0.870769i | \(0.663621\pi\) | |||||||
\(542\) | −5.74656 | −0.246836 | ||||||||
\(543\) | −15.2502 | + | 26.4142i | −0.654450 | + | 1.13354i | ||||
\(544\) | 2.22961i | 0.0955938i | ||||||||
\(545\) | −22.1298 | −0.947935 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.67129 | −0.242487 | −0.121243 | − | 0.992623i | \(-0.538688\pi\) | ||||
−0.121243 | + | 0.992623i | \(0.538688\pi\) | |||||||
\(548\) | 0.458997i | 0.0196074i | ||||||||
\(549\) | −58.3603 | + | 101.083i | −2.49076 | + | 4.31412i | ||||
\(550\) | −7.32381 | −0.312288 | ||||||||
\(551\) | 30.2524 | + | 17.4662i | 1.28879 | + | 0.744085i | ||||
\(552\) | 4.82962 | + | 2.78838i | 0.205562 | + | 0.118682i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 26.6020i | 1.13021i | ||||||||
\(555\) | −0.100836 | − | 0.174654i | −0.00428027 | − | 0.00741364i | ||||
\(556\) | −7.65731 | + | 13.2628i | −0.324742 | + | 0.562470i | ||||
\(557\) | −22.9561 | − | 13.2537i | −0.972683 | − | 0.561579i | −0.0726298 | − | 0.997359i | \(-0.523139\pi\) |
−0.900053 | + | 0.435780i | \(0.856472\pi\) | |||||||
\(558\) | 2.44774 | − | 4.23962i | 0.103621 | − | 0.179477i | ||||
\(559\) | 2.41462 | + | 36.3049i | 0.102128 | + | 1.53553i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.5103 | + | 10.6869i | −0.781504 | + | 0.451202i | ||||
\(562\) | 6.69143 | 0.282261 | ||||||||
\(563\) | −11.5376 | −0.486252 | −0.243126 | − | 0.969995i | \(-0.578173\pi\) | ||||
−0.243126 | + | 0.969995i | \(0.578173\pi\) | |||||||
\(564\) | 20.3525 | − | 11.7505i | 0.856993 | − | 0.494785i | ||||
\(565\) | −18.3356 | + | 10.5861i | −0.771386 | + | 0.445360i | ||||
\(566\) | 17.2632 | + | 9.96692i | 0.725627 | + | 0.418941i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.14733 | − | 1.98724i | 0.0481409 | − | 0.0833826i | ||||
\(569\) | 32.1581 | 1.34814 | 0.674069 | − | 0.738668i | \(-0.264545\pi\) | ||||
0.674069 | + | 0.738668i | \(0.264545\pi\) | |||||||
\(570\) | −32.7717 | − | 18.9208i | −1.37266 | − | 0.792504i | ||||
\(571\) | 5.77702 | + | 10.0061i | 0.241761 | + | 0.418742i | 0.961216 | − | 0.275797i | \(-0.0889418\pi\) |
−0.719455 | + | 0.694539i | \(0.755608\pi\) | |||||||
\(572\) | 10.3112 | − | 0.685794i | 0.431134 | − | 0.0286745i | ||||
\(573\) | 10.9083 | 0.455699 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.13028 | − | 3.68976i | −0.0888389 | − | 0.153873i | ||||
\(576\) | 4.09347 | + | 7.09010i | 0.170561 | + | 0.295421i | ||||
\(577\) | −7.91591 | + | 4.57025i | −0.329543 | + | 0.190262i | −0.655638 | − | 0.755075i | \(-0.727600\pi\) |
0.326095 | + | 0.945337i | \(0.394267\pi\) | |||||||
\(578\) | 12.0288i | 0.500333i | ||||||||
\(579\) | −63.9364 | + | 36.9137i | −2.65711 | + | 1.53408i | ||||
\(580\) | − | 7.54819i | − | 0.313422i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −8.17490 | − | 14.1593i | −0.338860 | − | 0.586923i | ||||
\(583\) | 17.1511i | 0.710325i | ||||||||
\(584\) | 5.61387 | + | 9.72351i | 0.232304 | + | 0.402362i | ||||
\(585\) | −25.6785 | − | 38.3508i | −1.06168 | − | 1.58561i | ||||
\(586\) | 4.43044 | − | 7.67375i | 0.183020 | − | 0.317000i | ||||
\(587\) | −37.0629 | + | 21.3983i | −1.52975 | + | 0.883201i | −0.530378 | + | 0.847761i | \(0.677950\pi\) |
−0.999372 | + | 0.0354398i | \(0.988717\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.16344 | − | 3.74718i | 0.0891428 | − | 0.154400i | ||||
\(590\) | −1.21354 | − | 0.700635i | −0.0499605 | − | 0.0288447i | ||||
\(591\) | 17.6367i | 0.725478i | ||||||||
\(592\) | 0.0385636i | 0.00158496i | ||||||||
\(593\) | −12.3356 | − | 7.12195i | −0.506561 | − | 0.292463i | 0.224858 | − | 0.974392i | \(-0.427808\pi\) |
−0.731419 | + | 0.681928i | \(0.761142\pi\) | |||||||
\(594\) | −24.8619 | + | 43.0620i | −1.02009 | + | 1.76686i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.86563 | − | 5.11858i | 0.363150 | − | 0.209665i | ||||
\(597\) | 14.8297 | − | 25.6858i | 0.606939 | − | 1.05125i | ||||
\(598\) | 3.34474 | + | 4.99535i | 0.136777 | + | 0.204275i | ||||
\(599\) | −1.87367 | − | 3.24530i | −0.0765563 | − | 0.132599i | 0.825206 | − | 0.564832i | \(-0.191059\pi\) |
−0.901762 | + | 0.432233i | \(0.857726\pi\) | |||||||
\(600\) | − | 8.54664i | − | 0.348915i | ||||||
\(601\) | 5.33462 | + | 9.23984i | 0.217604 | + | 0.376901i | 0.954075 | − | 0.299568i | \(-0.0968426\pi\) |
−0.736471 | + | 0.676469i | \(0.763509\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 13.4337i | − | 0.547061i | ||||||
\(604\) | −13.1731 | + | 7.60551i | −0.536007 | + | 0.309464i | ||||
\(605\) | 4.35490i | 0.177052i | ||||||||
\(606\) | 21.3405 | − | 12.3209i | 0.866898 | − | 0.500504i | ||||
\(607\) | 4.82628 | + | 8.35936i | 0.195893 | + | 0.339296i | 0.947193 | − | 0.320665i | \(-0.103906\pi\) |
−0.751300 | + | 0.659961i | \(0.770573\pi\) | |||||||
\(608\) | 3.61801 | + | 6.26657i | 0.146730 | + | 0.254143i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 22.2915 | 0.902558 | ||||||||
\(611\) | 25.2781 | − | 1.68123i | 1.02264 | − | 0.0680153i | ||||
\(612\) | −9.12684 | − | 15.8082i | −0.368931 | − | 0.639007i | ||||
\(613\) | 3.45968 | + | 1.99745i | 0.139735 | + | 0.0806761i | 0.568238 | − | 0.822864i | \(-0.307625\pi\) |
−0.428503 | + | 0.903541i | \(0.640959\pi\) | |||||||
\(614\) | 8.34636 | 0.336832 | ||||||||
\(615\) | −20.8000 | + | 36.0266i | −0.838736 | + | 1.45273i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.80199 | + | 1.61773i | 0.112804 | + | 0.0651273i | 0.555340 | − | 0.831623i | \(-0.312588\pi\) |
−0.442537 | + | 0.896750i | \(0.645921\pi\) | |||||||
\(618\) | 16.7575 | − | 9.67493i | 0.674084 | − | 0.389183i | ||||
\(619\) | 34.0070 | − | 19.6340i | 1.36686 | − | 0.789156i | 0.376333 | − | 0.926485i | \(-0.377185\pi\) |
0.990526 | + | 0.137329i | \(0.0438517\pi\) | |||||||
\(620\) | −0.934950 | −0.0375485 | ||||||||
\(621\) | −28.9263 | −1.16077 | ||||||||
\(622\) | −5.79281 | + | 3.34448i | −0.232270 | + | 0.134101i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0.800299 | + | 12.0329i | 0.0320376 | + | 0.481700i | ||||
\(625\) | 2.84703 | − | 4.93120i | 0.113881 | − | 0.197248i | ||||
\(626\) | 18.5145 | + | 10.6894i | 0.739990 | + | 0.427233i | ||||
\(627\) | −34.6834 | + | 60.0735i | −1.38512 | + | 2.39910i | ||||
\(628\) | 1.13709 | + | 1.96950i | 0.0453750 | + | 0.0785918i | ||||
\(629\) | − | 0.0859819i | − | 0.00342832i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.4983 | + | 14.7215i | 1.01507 | + | 0.586052i | 0.912673 | − | 0.408691i | \(-0.134015\pi\) |
0.102400 | + | 0.994743i | \(0.467348\pi\) | |||||||
\(632\) | −3.69011 | − | 2.13049i | −0.146785 | − | 0.0847463i | ||||
\(633\) | −21.9715 | −0.873288 | ||||||||
\(634\) | 15.8388 | − | 27.4336i | 0.629040 | − | 1.08953i | ||||
\(635\) | − | 15.4036i | − | 0.611274i | ||||||
\(636\) | −20.0147 | −0.793636 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −13.8365 | −0.547792 | ||||||||
\(639\) | 18.7863i | 0.743173i | ||||||||
\(640\) | 0.781779 | − | 1.35408i | 0.0309025 | − | 0.0535247i | ||||
\(641\) | −4.09119 | −0.161592 | −0.0807961 | − | 0.996731i | \(-0.525746\pi\) | ||||
−0.0807961 | + | 0.996731i | \(0.525746\pi\) | |||||||
\(642\) | 2.98046 | + | 1.72077i | 0.117629 | + | 0.0679133i | ||||
\(643\) | −19.2672 | − | 11.1239i | −0.759825 | − | 0.438685i | 0.0694080 | − | 0.997588i | \(-0.477889\pi\) |
−0.829233 | + | 0.558903i | \(0.811222\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 52.7742i | 2.07798i | ||||||||
\(646\) | −8.06675 | − | 13.9720i | −0.317382 | − | 0.549722i | ||||
\(647\) | 24.9292 | − | 43.1786i | 0.980066 | − | 1.69752i | 0.317980 | − | 0.948097i | \(-0.396996\pi\) |
0.662086 | − | 0.749427i | \(-0.269671\pi\) | |||||||
\(648\) | −28.9816 | − | 16.7326i | −1.13851 | − | 0.657317i | ||||
\(649\) | −1.28433 | + | 2.22452i | −0.0504142 | + | 0.0873200i | ||||
\(650\) | 4.06695 | − | 8.26700i | 0.159519 | − | 0.324259i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.00848066 | − | 0.00489631i | 0.000332128 | − | 0.000191754i | ||||
\(653\) | 7.40353 | 0.289723 | 0.144861 | − | 0.989452i | \(-0.453726\pi\) | ||||
0.144861 | + | 0.989452i | \(0.453726\pi\) | |||||||
\(654\) | −47.3390 | −1.85110 | ||||||||
\(655\) | −20.0299 | + | 11.5643i | −0.782635 | + | 0.451854i | ||||
\(656\) | 6.88896 | − | 3.97734i | 0.268969 | − | 0.155289i | ||||
\(657\) | −79.6058 | − | 45.9604i | −3.10572 | − | 1.79309i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.0410 | + | 26.0518i | −0.585914 | + | 1.01483i | 0.408847 | + | 0.912603i | \(0.365931\pi\) |
−0.994761 | + | 0.102230i | \(0.967402\pi\) | |||||||
\(660\) | 14.9888 | 0.583438 | ||||||||
\(661\) | 23.0639 | + | 13.3160i | 0.897082 | + | 0.517931i | 0.876252 | − | 0.481852i | \(-0.160036\pi\) |
0.0208300 | + | 0.999783i | \(0.493369\pi\) | |||||||
\(662\) | −12.3347 | − | 21.3644i | −0.479404 | − | 0.830351i | ||||
\(663\) | −1.78436 | − | 26.8286i | −0.0692986 | − | 1.04194i | ||||
\(664\) | 4.94829 | 0.192031 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.157859 | − | 0.273420i | −0.00611691 | − | 0.0105948i | ||||
\(667\) | −4.02463 | − | 6.97087i | −0.155834 | − | 0.269913i | ||||
\(668\) | 21.6080 | − | 12.4754i | 0.836040 | − | 0.482688i | ||||
\(669\) | − | 56.5657i | − | 2.18696i | ||||||
\(670\) | −2.22186 | + | 1.28279i | −0.0858380 | + | 0.0495586i | ||||
\(671\) | − | 40.8623i | − | 1.57747i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.84652 | − | 3.19827i | −0.0711783 | − | 0.123284i | 0.828240 | − | 0.560374i | \(-0.189343\pi\) |
−0.899418 | + | 0.437090i | \(0.856009\pi\) | |||||||
\(674\) | − | 28.0871i | − | 1.08188i | ||||||
\(675\) | 22.1654 | + | 38.3917i | 0.853148 | + | 1.47770i | ||||
\(676\) | −4.95177 | + | 12.0200i | −0.190453 | + | 0.462307i | ||||
\(677\) | −17.8266 | + | 30.8767i | −0.685134 | + | 1.18669i | 0.288261 | + | 0.957552i | \(0.406923\pi\) |
−0.973395 | + | 0.229134i | \(0.926410\pi\) | |||||||
\(678\) | −39.2227 | + | 22.6453i | −1.50634 | + | 0.869686i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.74306 | + | 3.01907i | −0.0668434 | + | 0.115776i | ||||
\(681\) | −46.7283 | − | 26.9786i | −1.79063 | − | 1.03382i | ||||
\(682\) | 1.71385i | 0.0656265i | ||||||||
\(683\) | 30.2653i | 1.15807i | 0.815304 | + | 0.579034i | \(0.196570\pi\) | ||||
−0.815304 | + | 0.579034i | \(0.803430\pi\) | |||||||
\(684\) | −51.3040 | − | 29.6204i | −1.96166 | − | 1.13256i | ||||
\(685\) | −0.358834 | + | 0.621519i | −0.0137104 | + | 0.0237470i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.0207 | − | 11.5590i | 0.763838 | − | 0.441002i | ||||
\(688\) | 5.04571 | − | 8.73942i | 0.192366 | − | 0.333187i | ||||
\(689\) | −19.3599 | − | 9.52410i | −0.737553 | − | 0.362839i | ||||
\(690\) | 4.35980 | + | 7.55139i | 0.165975 | + | 0.287477i | ||||
\(691\) | − | 3.50309i | − | 0.133264i | −0.997778 | − | 0.0666320i | \(-0.978775\pi\) | ||
0.997778 | − | 0.0666320i | \(-0.0212253\pi\) | |||||||
\(692\) | −1.60275 | − | 2.77604i | −0.0609273 | − | 0.105529i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10.1080i | 0.383693i | ||||||||
\(695\) | −20.7372 | + | 11.9726i | −0.786608 | + | 0.454148i | ||||
\(696\) | − | 16.1467i | − | 0.612040i | ||||||
\(697\) | −15.3597 | + | 8.86793i | −0.581791 | + | 0.335897i | ||||
\(698\) | −8.69465 | − | 15.0596i | −0.329097 | − | 0.570013i | ||||
\(699\) | 12.4992 | + | 21.6492i | 0.472762 | + | 0.818849i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −45.2243 | −1.70810 | −0.854048 | − | 0.520194i | \(-0.825860\pi\) | ||||
−0.854048 | + | 0.520194i | \(0.825860\pi\) | |||||||
\(702\) | −34.8018 | − | 51.9763i | −1.31351 | − | 1.96172i | ||||
\(703\) | −0.139524 | − | 0.241662i | −0.00526223 | − | 0.00911445i | ||||
\(704\) | −2.48215 | − | 1.43307i | −0.0935495 | − | 0.0540108i | ||||
\(705\) | 36.7451 | 1.38390 | ||||||||
\(706\) | 1.66329 | − | 2.88091i | 0.0625989 | − | 0.108424i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.59594 | − | 1.49877i | −0.0975613 | − | 0.0563270i | ||||
\(709\) | −2.59657 | + | 1.49913i | −0.0975161 | + | 0.0563009i | −0.547965 | − | 0.836501i | \(-0.684597\pi\) |
0.450449 | + | 0.892802i | \(0.351264\pi\) | |||||||
\(710\) | 3.10716 | − | 1.79392i | 0.116610 | − | 0.0673245i | ||||
\(711\) | 34.8843 | 1.30827 | ||||||||
\(712\) | 2.42120 | 0.0907383 | ||||||||
\(713\) | −0.863440 | + | 0.498507i | −0.0323361 | + | 0.0186692i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.4984 | + | 7.13248i | 0.542208 | + | 0.266740i | ||||
\(716\) | 7.89998 | − | 13.6832i | 0.295236 | − | 0.511364i | ||||
\(717\) | 57.5539 | + | 33.2287i | 2.14939 | + | 1.24095i | ||||
\(718\) | −4.01207 | + | 6.94911i | −0.149729 | + | 0.259339i | ||||
\(719\) | 10.0397 | + | 17.3892i | 0.374417 | + | 0.648509i | 0.990240 | − | 0.139376i | \(-0.0445096\pi\) |
−0.615823 | + | 0.787885i | \(0.711176\pi\) | |||||||
\(720\) | 12.8007i | 0.477056i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −28.8905 | − | 16.6800i | −1.07519 | − | 0.620764i | ||||
\(723\) | −30.8327 | − | 17.8013i | −1.14668 | − | 0.662037i | ||||
\(724\) | 9.11907 | 0.338908 | ||||||||
\(725\) | −6.16792 | + | 10.6832i | −0.229071 | + | 0.396762i | ||||
\(726\) | 9.31579i | 0.345741i | ||||||||
\(727\) | 32.5895 | 1.20868 | 0.604338 | − | 0.796728i | \(-0.293438\pi\) | ||||
0.604338 | + | 0.796728i | \(0.293438\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 99.8990 | 3.69996 | ||||||||
\(730\) | 17.5552i | 0.649748i | ||||||||
\(731\) | −11.2500 | + | 19.4855i | −0.416095 | + | 0.720698i | ||||
\(732\) | 47.6850 | 1.76249 | ||||||||
\(733\) | 16.0380 | + | 9.25952i | 0.592376 | + | 0.342008i | 0.766036 | − | 0.642797i | \(-0.222226\pi\) |
−0.173661 | + | 0.984806i | \(0.555560\pi\) | |||||||
\(734\) | −0.899869 | − | 0.519540i | −0.0332148 | − | 0.0191766i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 1.66735i | − | 0.0614594i | ||||||
\(737\) | 2.35147 | + | 4.07287i | 0.0866176 | + | 0.150026i | ||||
\(738\) | −32.5623 | + | 56.3995i | −1.19863 | + | 2.07609i | ||||
\(739\) | −13.7968 | − | 7.96559i | −0.507524 | − | 0.293019i | 0.224291 | − | 0.974522i | \(-0.427993\pi\) |
−0.731815 | + | 0.681503i | \(0.761327\pi\) | |||||||
\(740\) | −0.0301482 | + | 0.0522183i | −0.00110827 | + | 0.00191958i | ||||
\(741\) | −48.5501 | − | 72.5093i | −1.78353 | − | 2.66370i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.5962 | − | 6.11773i | 0.388738 | − | 0.224438i | −0.292875 | − | 0.956151i | \(-0.594612\pi\) |
0.681613 | + | 0.731713i | \(0.261279\pi\) | |||||||
\(744\) | −2.00000 | −0.0733236 | ||||||||
\(745\) | 16.0064 | 0.586428 | ||||||||
\(746\) | −23.6532 | + | 13.6562i | −0.866007 | + | 0.499989i | ||||
\(747\) | −35.0838 | + | 20.2556i | −1.28365 | + | 0.741115i | ||||
\(748\) | 5.53423 | + | 3.19519i | 0.202351 | + | 0.116828i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 19.7556 | − | 34.2177i | 0.721373 | − | 1.24945i | ||||
\(751\) | 20.8213 | 0.759782 | 0.379891 | − | 0.925031i | \(-0.375962\pi\) | ||||
0.379891 | + | 0.925031i | \(0.375962\pi\) | |||||||
\(752\) | −6.08501 | − | 3.51318i | −0.221897 | − | 0.128113i | ||||
\(753\) | 26.6136 | + | 46.0960i | 0.969852 | + | 1.67983i | ||||
\(754\) | 7.68349 | − | 15.6184i | 0.279816 | − | 0.568790i | ||||
\(755\) | −23.7833 | −0.865563 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.5575 | − | 23.4823i | −0.492757 | − | 0.853480i | 0.507208 | − | 0.861824i | \(-0.330678\pi\) |
−0.999965 | + | 0.00834344i | \(0.997344\pi\) | |||||||
\(758\) | 1.10583 | + | 1.91535i | 0.0401655 | + | 0.0695687i | ||||
\(759\) | 13.8424 | − | 7.99190i | 0.502446 | − | 0.290087i | ||||
\(760\) | 11.3139i | 0.410399i | ||||||||
\(761\) | 41.8920 | − | 24.1864i | 1.51858 | − | 0.876755i | 0.518824 | − | 0.854881i | \(-0.326370\pi\) |
0.999761 | − | 0.0218739i | \(-0.00696324\pi\) | |||||||
\(762\) | − | 32.9507i | − | 1.19368i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −1.63068 | − | 2.82443i | −0.0589961 | − | 0.102184i | ||||
\(765\) | − | 28.5407i | − | 1.03189i | ||||||
\(766\) | −11.1693 | − | 19.3458i | −0.403563 | − | 0.698991i | ||||
\(767\) | −1.79781 | − | 2.68501i | −0.0649151 | − | 0.0969503i | ||||
\(768\) | 1.67234 | − | 2.89658i | 0.0603455 | − | 0.104521i | ||||
\(769\) | 15.0214 | − | 8.67264i | 0.541687 | − | 0.312743i | −0.204075 | − | 0.978955i | \(-0.565419\pi\) |
0.745762 | + | 0.666212i | \(0.232085\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −52.0129 | + | 90.0890i | −1.87320 | + | 3.24448i | ||||
\(772\) | 19.1158 | + | 11.0365i | 0.687993 | + | 0.397213i | ||||
\(773\) | − | 14.0480i | − | 0.505270i | −0.967562 | − | 0.252635i | \(-0.918703\pi\) | ||
0.967562 | − | 0.252635i | \(-0.0812971\pi\) | |||||||
\(774\) | 82.6178i | 2.96963i | ||||||||
\(775\) | 1.32326 | + | 0.763984i | 0.0475329 | + | 0.0274431i | ||||
\(776\) | −2.44414 | + | 4.23338i | −0.0877396 | + | 0.151970i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.6178 | − | 6.13022i | 0.380668 | − | 0.219779i | ||||
\(779\) | −28.7801 | + | 49.8487i | −1.03116 | + | 1.78601i | ||||
\(780\) | −8.32336 | + | 16.9191i | −0.298024 | + | 0.605802i | ||||
\(781\) | −3.28841 | − | 5.69569i | −0.117669 | − | 0.203808i | ||||
\(782\) | 3.71755i | 0.132939i | ||||||||
\(783\) | 41.8760 | + | 72.5314i | 1.49653 | + | 2.59206i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.55582i | 0.126913i | ||||||||
\(786\) | −42.8471 | + | 24.7378i | −1.52831 | + | 0.882368i | ||||
\(787\) | − | 7.75577i | − | 0.276463i | −0.990400 | − | 0.138232i | \(-0.955858\pi\) | ||
0.990400 | − | 0.138232i | \(-0.0441419\pi\) | |||||||
\(788\) | 4.56660 | − | 2.63653i | 0.162678 | − | 0.0939224i | ||||
\(789\) | −47.4522 | − | 82.1896i | −1.68934 | − | 2.92603i | ||||
\(790\) | −3.33114 | − | 5.76971i | −0.118517 | − | 0.205277i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 23.4649 | 0.833789 | ||||||||
\(793\) | 46.1248 | + | 22.6911i | 1.63794 | + | 0.805784i | ||||
\(794\) | −1.46759 | − | 2.54193i | −0.0520827 | − | 0.0902099i | ||||
\(795\) | −27.1016 | − | 15.6471i | −0.961193 | − | 0.554945i | ||||
\(796\) | −8.86762 | −0.314304 | ||||||||
\(797\) | 16.9246 | − | 29.3143i | 0.599500 | − | 1.03836i | −0.393395 | − | 0.919370i | \(-0.628699\pi\) |
0.992895 | − | 0.118995i | \(-0.0379673\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.5672 | + | 7.83303i | 0.479973 | + | 0.277113i | ||||
\(800\) | −2.21294 | + | 1.27764i | −0.0782394 | + | 0.0451715i | ||||
\(801\) | −17.1665 | + | 9.91111i | −0.606550 | + | 0.350192i | ||||
\(802\) | 21.8502 | 0.771559 | ||||||||
\(803\) | 32.1803 | 1.13562 | ||||||||
\(804\) | −4.75290 | + | 2.74409i | −0.167622 | + | 0.0967766i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.93456 | − | 0.951708i | −0.0681420 | − | 0.0335225i | ||||
\(807\) | 35.7909 | − | 61.9917i | 1.25990 | − | 2.18221i | ||||
\(808\) | −6.38042 | − | 3.68373i | −0.224462 | − | 0.129593i | ||||
\(809\) | 16.4170 | − | 28.4351i | 0.577191 | − | 0.999723i | −0.418609 | − | 0.908166i | \(-0.637482\pi\) |
0.995800 | − | 0.0915570i | \(-0.0291844\pi\) | |||||||
\(810\) | −26.1623 | − | 45.3145i | −0.919250 | − | 1.59219i | ||||
\(811\) | 12.2083i | 0.428690i | 0.976758 | + | 0.214345i | \(0.0687617\pi\) | ||||
−0.976758 | + | 0.214345i | \(0.931238\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.6454 | − | 9.61023i | −0.583780 | − | 0.337045i | ||||
\(814\) | 0.0957207 | + | 0.0552644i | 0.00335501 | + | 0.00193701i | ||||
\(815\) | 0.0153113 | 0.000536332 | ||||||||
\(816\) | −3.72868 | + | 6.45826i | −0.130530 | + | 0.226084i | ||||
\(817\) | 73.0216i | 2.55470i | ||||||||
\(818\) | −7.38191 | −0.258102 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 12.4376 | 0.434340 | ||||||||
\(821\) | 47.4868i | 1.65730i | 0.559767 | + | 0.828650i | \(0.310891\pi\) | ||||
−0.559767 | + | 0.828650i | \(0.689109\pi\) | |||||||
\(822\) | −0.767601 | + | 1.32952i | −0.0267732 | + | 0.0463725i | ||||
\(823\) | −22.0459 | −0.768471 | −0.384235 | − | 0.923235i | \(-0.625535\pi\) | ||||
−0.384235 | + | 0.923235i | \(0.625535\pi\) | |||||||
\(824\) | −5.01017 | − | 2.89263i | −0.174538 | − | 0.100769i | ||||
\(825\) | −21.2140 | − | 12.2479i | −0.738578 | − | 0.426418i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 45.9092i | − | 1.59642i | −0.602380 | − | 0.798209i | \(-0.705781\pi\) | ||
0.602380 | − | 0.798209i | \(-0.294219\pi\) | |||||||
\(828\) | 6.82525 | + | 11.8217i | 0.237194 | + | 0.410832i | ||||
\(829\) | −13.3883 | + | 23.1893i | −0.464996 | + | 0.805396i | −0.999201 | − | 0.0399584i | \(-0.987277\pi\) |
0.534206 | + | 0.845355i | \(0.320611\pi\) | |||||||
\(830\) | 6.70038 | + | 3.86846i | 0.232573 | + | 0.134276i | ||||
\(831\) | −44.4877 | + | 77.0550i | −1.54326 | + | 2.67301i | ||||
\(832\) | 2.99598 | − | 2.00602i | 0.103867 | − | 0.0695462i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −44.3601 | + | 25.6113i | −1.53606 | + | 0.886847i | ||||
\(835\) | 39.0120 | 1.35007 | ||||||||
\(836\) | 20.7394 | 0.717288 | ||||||||
\(837\) | 8.98404 | − | 5.18694i | 0.310534 | − | 0.179287i | ||||
\(838\) | −7.43287 | + | 4.29137i | −0.256764 | + | 0.148243i | ||||
\(839\) | 24.5960 | + | 14.2005i | 0.849147 | + | 0.490255i | 0.860363 | − | 0.509682i | \(-0.170237\pi\) |
−0.0112158 | + | 0.999937i | \(0.503570\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.84726 | − | 4.93160i | 0.0981814 | − | 0.170055i | ||||
\(842\) | −7.49525 | −0.258304 | ||||||||
\(843\) | 19.3823 | + | 11.1904i | 0.667562 | + | 0.385417i | ||||
\(844\) | 3.28453 | + | 5.68898i | 0.113058 | + | 0.195823i | ||||
\(845\) | −16.1021 | + | 12.4048i | −0.553928 | + | 0.426739i | ||||
\(846\) | 57.5244 | 1.97773 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 2.99202 | + | 5.18233i | 0.102746 | + | 0.177962i | ||||
\(849\) | 33.3362 | + | 57.7400i | 1.14410 | + | 1.98163i | ||||
\(850\) | 4.93401 | − | 2.84865i | 0.169235 | − | 0.0977079i | ||||
\(851\) | 0.0642991i | 0.00220415i | ||||||||
\(852\) | 6.64668 | − | 3.83746i | 0.227712 | − | 0.131469i | ||||
\(853\) | 21.3316i | 0.730379i | 0.930933 | + | 0.365189i | \(0.118996\pi\) | ||||
−0.930933 | + | 0.365189i | \(0.881004\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −46.3132 | − | 80.2168i | −1.58388 | − | 2.74336i | ||||
\(856\) | − | 1.02896i | − | 0.0351690i | ||||||
\(857\) | −20.5412 | − | 35.5784i | −0.701673 | − | 1.21533i | −0.967879 | − | 0.251417i | \(-0.919103\pi\) |
0.266206 | − | 0.963916i | \(-0.414230\pi\) | |||||||
\(858\) | 31.0142 | + | 15.2575i | 1.05881 | + | 0.520881i | ||||
\(859\) | 14.4309 | − | 24.9951i | 0.492376 | − | 0.852820i | −0.507586 | − | 0.861601i | \(-0.669462\pi\) |
0.999961 | + | 0.00878126i | \(0.00279520\pi\) | |||||||
\(860\) | 13.6646 | − | 7.88925i | 0.465958 | − | 0.269021i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8.23956 | − | 14.2713i | 0.280641 | − | 0.486084i | ||||
\(863\) | 19.6875 | + | 11.3666i | 0.670171 | + | 0.386923i | 0.796141 | − | 0.605111i | \(-0.206871\pi\) |
−0.125970 | + | 0.992034i | \(0.540204\pi\) | |||||||
\(864\) | 17.3487i | 0.590214i | ||||||||
\(865\) | − | 5.01198i | − | 0.170412i | ||||||
\(866\) | −22.1365 | − | 12.7805i | −0.752229 | − | 0.434300i | ||||
\(867\) | −20.1163 | + | 34.8425i | −0.683187 | + | 1.18331i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.5764 | + | 6.10627i | −0.358779 | + | 0.207141i | ||||
\(870\) | 12.6232 | − | 21.8640i | 0.427966 | − | 0.741258i | ||||
\(871\) | −5.90318 | + | 0.392617i | −0.200022 | + | 0.0133033i | ||||
\(872\) | 7.07674 | + | 12.2573i | 0.239649 | + | 0.415084i | ||||
\(873\) | − | 40.0201i | − | 1.35448i | ||||||
\(874\) | 6.03249 | + | 10.4486i | 0.204052 | + | 0.353428i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 37.5533i | 1.26881i | ||||||||
\(877\) | −25.4765 | + | 14.7089i | −0.860282 | + | 0.496684i | −0.864107 | − | 0.503309i | \(-0.832116\pi\) |
0.00382498 | + | 0.999993i | \(0.498782\pi\) | |||||||
\(878\) | − | 9.20839i | − | 0.310768i | ||||||
\(879\) | 25.6663 | − | 14.8184i | 0.865703 | − | 0.499814i | ||||
\(880\) | −2.24069 | − | 3.88098i | −0.0755335 | − | 0.130828i | ||||
\(881\) | −2.11104 | − | 3.65644i | −0.0711229 | − | 0.123188i | 0.828271 | − | 0.560328i | \(-0.189325\pi\) |
−0.899394 | + | 0.437140i | \(0.855992\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37.1982 | 1.25182 | 0.625910 | − | 0.779895i | \(-0.284728\pi\) | ||||
0.625910 | + | 0.779895i | \(0.284728\pi\) | |||||||
\(884\) | −6.67987 | + | 4.47264i | −0.224668 | + | 0.150431i | ||||
\(885\) | −2.34341 | − | 4.05890i | −0.0787727 | − | 0.136438i | ||||
\(886\) | −5.37593 | − | 3.10379i | −0.180608 | − | 0.104274i | ||||
\(887\) | 56.1894 | 1.88665 | 0.943327 | − | 0.331865i | \(-0.107678\pi\) | ||||
0.943327 | + | 0.331865i | \(0.107678\pi\) | |||||||
\(888\) | −0.0644917 | + | 0.111703i | −0.00216420 | + | 0.00374850i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 3.27850 | + | 1.89284i | 0.109896 | + | 0.0634482i | ||||
\(891\) | −83.0654 | + | 47.9578i | −2.78280 | + | 1.60665i | ||||
\(892\) | −14.6463 | + | 8.45606i | −0.490395 | + | 0.283130i | ||||
\(893\) | 50.8429 | 1.70139 | ||||||||
\(894\) | 34.2401 | 1.14516 | ||||||||
\(895\) | 21.3944 | − | 12.3521i | 0.715136 | − | 0.412884i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.33438 | + | 20.0630i | 0.0445536 | + | 0.669884i | ||||
\(898\) | 2.60944 | − | 4.51968i | 0.0870781 | − | 0.150824i | ||||
\(899\) | 2.49997 | + | 1.44336i | 0.0833785 | + | 0.0481386i | ||||
\(900\) | 10.4600 | − | 18.1172i | 0.348666 | − | 0.603908i | ||||
\(901\) | −6.67104 | − | 11.5546i | −0.222245 | − | 0.384939i | ||||
\(902\) | − | 22.7992i | − | 0.759132i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.7269 | + | 6.77051i | 0.390030 | + | 0.225184i | ||||
\(905\) | 12.3480 | + | 7.12910i | 0.410460 | + | 0.236979i | ||||
\(906\) | −50.8761 | −1.69025 | ||||||||
\(907\) | −0.326806 | + | 0.566045i | −0.0108514 | + | 0.0187952i | −0.871400 | − | 0.490573i | \(-0.836788\pi\) |
0.860549 | + | 0.509368i | \(0.170121\pi\) | |||||||
\(908\) | 16.1322i | 0.535367i | ||||||||
\(909\) | 60.3170 | 2.00059 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.7806 | 1.31799 | 0.658995 | − | 0.752147i | \(-0.270982\pi\) | ||||
0.658995 | + | 0.752147i | \(0.270982\pi\) | |||||||
\(912\) | 24.2022i | 0.801415i | ||||||||
\(913\) | 7.09124 | − | 12.2824i | 0.234686 | − | 0.406487i | ||||
\(914\) | −33.9332 | −1.12241 | ||||||||
\(915\) | 64.5693 | + | 37.2791i | 2.13460 | + | 1.23241i | ||||
\(916\) | −5.98583 | − | 3.45592i | −0.197777 | − | 0.114187i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 38.6808i | − | 1.27666i | ||||||
\(919\) | −17.3028 | − | 29.9693i | −0.570767 | − | 0.988597i | −0.996487 | − | 0.0837423i | \(-0.973313\pi\) |
0.425721 | − | 0.904855i | \(-0.360021\pi\) | |||||||
\(920\) | 1.30350 | − | 2.25773i | 0.0429751 | − | 0.0744351i | ||||
\(921\) | 24.1759 | + | 13.9580i | 0.796624 | + | 0.459931i | ||||
\(922\) | −0.422380 | + | 0.731583i | −0.0139103 | + | 0.0240934i | ||||
\(923\) | 8.25528 | − | 0.549054i | 0.271726 | − | 0.0180723i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.0853392 | − | 0.0492706i | 0.00280593 | − | 0.00162001i | ||||
\(926\) | 6.50221 | 0.213676 | ||||||||
\(927\) | 47.3635 | 1.55562 | ||||||||
\(928\) | −4.18080 | + | 2.41379i | −0.137242 | + | 0.0792365i | ||||
\(929\) | 16.6889 | − | 9.63536i | 0.547546 | − | 0.316126i | −0.200586 | − | 0.979676i | \(-0.564285\pi\) |
0.748132 | + | 0.663550i | \(0.230951\pi\) | |||||||
\(930\) | −2.70816 | − | 1.56356i | −0.0888041 | − | 0.0512711i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 3.73702 | − | 6.47272i | 0.122410 | − | 0.212021i | ||||
\(933\) | −22.3725 | −0.732442 | ||||||||
\(934\) | −8.25113 | − | 4.76379i | −0.269985 | − | 0.155876i | ||||
\(935\) | 4.99586 | + | 8.65308i | 0.163382 | + | 0.282986i | ||||
\(936\) | −13.0302 | + | 26.4868i | −0.425905 | + | 0.865748i | ||||
\(937\) | 50.9507 | 1.66449 | 0.832244 | − | 0.554410i | \(-0.187056\pi\) | ||||
0.832244 | + | 0.554410i | \(0.187056\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 35.7526 | + | 61.9254i | 1.16674 | + | 2.02086i | ||||
\(940\) | −5.49306 | − | 9.51426i | −0.179164 | − | 0.310321i | ||||
\(941\) | −21.0456 | + | 12.1507i | −0.686068 | + | 0.396102i | −0.802138 | − | 0.597139i | \(-0.796304\pi\) |
0.116069 | + | 0.993241i | \(0.462971\pi\) | |||||||
\(942\) | 7.60645i | 0.247831i | ||||||||
\(943\) | 11.4863 | − | 6.63163i | 0.374046 | − | 0.215956i | ||||
\(944\) | 0.896206i | 0.0291690i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −14.4617 | − | 25.0484i | −0.470190 | − | 0.814393i | ||||
\(947\) | 25.6665i | 0.834049i | 0.908895 | + | 0.417024i | \(0.136927\pi\) | ||||
−0.908895 | + | 0.417024i | \(0.863073\pi\) | |||||||
\(948\) | −7.12582 | − | 12.3423i | −0.231436 | − | 0.400859i | ||||
\(949\) | −17.8699 | + | 36.3246i | −0.580081 | + | 1.17915i | ||||
\(950\) | 9.24505 | − | 16.0129i | 0.299949 | − | 0.519527i | ||||
\(951\) | 91.7569 | − | 52.9759i | 2.97542 | − | 1.71786i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.40492 | − | 4.16544i | 0.0779029 | − | 0.134932i | −0.824442 | − | 0.565946i | \(-0.808511\pi\) |
0.902345 | + | 0.431015i | \(0.141844\pi\) | |||||||
\(954\) | −42.4274 | − | 24.4955i | −1.37364 | − | 0.793070i | ||||
\(955\) | − | 5.09934i | − | 0.165011i | ||||||
\(956\) | − | 19.8696i | − | 0.642628i | ||||||
\(957\) | −40.0786 | − | 23.1394i | −1.29556 | − | 0.747990i | ||||
\(958\) | −1.42099 | + | 2.46123i | −0.0459102 | + | 0.0795188i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 4.52898 | − | 2.61481i | 0.146172 | − | 0.0843925i | ||||
\(961\) | −15.3212 | + | 26.5371i | −0.494233 | + | 0.856037i | ||||
\(962\) | −0.115536 | + | 0.0773594i | −0.00372502 | + | 0.00249417i | ||||
\(963\) | 4.21200 | + | 7.29540i | 0.135730 | + | 0.235091i | ||||
\(964\) | 10.6445i | 0.342837i | ||||||||
\(965\) | 17.2562 | + | 29.8887i | 0.555498 | + | 0.962150i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 58.2044i | − | 1.87173i | −0.352362 | − | 0.935864i | \(-0.614622\pi\) | ||
0.352362 | − | 0.935864i | \(-0.385378\pi\) | |||||||
\(968\) | 2.41210 | − | 1.39263i | 0.0775277 | − | 0.0447607i | ||||
\(969\) | − | 53.9615i | − | 1.73349i | ||||||
\(970\) | −6.61913 | + | 3.82156i | −0.212528 | + | 0.122703i | ||||
\(971\) | −18.0669 | − | 31.2927i | −0.579793 | − | 1.00423i | −0.995503 | − | 0.0947336i | \(-0.969800\pi\) |
0.415710 | − | 0.909497i | \(-0.363533\pi\) | |||||||
\(972\) | −29.9422 | − | 51.8613i | −0.960395 | − | 1.66345i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 5.26374 | 0.168661 | ||||||||
\(975\) | 25.6055 | − | 17.1447i | 0.820034 | − | 0.549071i | ||||
\(976\) | −7.12846 | − | 12.3469i | −0.228177 | − | 0.395213i | ||||
\(977\) | −14.4794 | − | 8.35970i | −0.463238 | − | 0.267451i | 0.250167 | − | 0.968203i | \(-0.419515\pi\) |
−0.713405 | + | 0.700752i | \(0.752848\pi\) | |||||||
\(978\) | 0.0327533 | 0.00104733 | ||||||||
\(979\) | 3.46975 | − | 6.00978i | 0.110894 | − | 0.192073i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −100.349 | − | 57.9368i | −3.20391 | − | 1.84978i | ||||
\(982\) | 19.8245 | − | 11.4457i | 0.632625 | − | 0.365246i | ||||
\(983\) | −40.2497 | + | 23.2382i | −1.28377 | + | 0.741183i | −0.977535 | − | 0.210774i | \(-0.932402\pi\) |
−0.306232 | + | 0.951957i | \(0.599068\pi\) | |||||||
\(984\) | 26.6060 | 0.848167 | ||||||||
\(985\) | 8.24472 | 0.262699 | ||||||||
\(986\) | 9.32157 | − | 5.38181i | 0.296859 | − | 0.171392i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −11.5167 | + | 23.4103i | −0.366396 | + | 0.744782i | ||||
\(989\) | 8.41296 | − | 14.5717i | 0.267517 | − | 0.463352i | ||||
\(990\) | 31.7734 | + | 18.3444i | 1.00982 | + | 0.583022i | ||||
\(991\) | −17.6755 | + | 30.6148i | −0.561480 | + | 0.972512i | 0.435887 | + | 0.900001i | \(0.356435\pi\) |
−0.997368 | + | 0.0725110i | \(0.976899\pi\) | |||||||
\(992\) | 0.298982 | + | 0.517851i | 0.00949267 | + | 0.0164418i | ||||
\(993\) | − | 82.5118i | − | 2.61843i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.0075 | − | 6.93251i | −0.380662 | − | 0.219775i | ||||
\(996\) | 14.3331 | + | 8.27524i | 0.454163 | + | 0.262211i | ||||
\(997\) | −1.48780 | −0.0471190 | −0.0235595 | − | 0.999722i | \(-0.507500\pi\) | ||||
−0.0235595 | + | 0.999722i | \(0.507500\pi\) | |||||||
\(998\) | 3.39938 | − | 5.88791i | 0.107606 | − | 0.186378i | ||||
\(999\) | − | 0.669028i | − | 0.0211671i |
(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 | 1274.2.o.e.569.3 | 12 | ||
7.2 | even | 3 | 1274.2.m.c.491.3 | 12 | |||
7.3 | odd | 6 | 1274.2.v.e.361.6 | 12 | |||
7.4 | even | 3 | 1274.2.v.d.361.4 | 12 | |||
7.5 | odd | 6 | 182.2.m.b.127.1 | yes | 12 | ||
7.6 | odd | 2 | 1274.2.o.d.569.1 | 12 | |||
13.4 | even | 6 | 1274.2.v.d.667.4 | 12 | |||
21.5 | even | 6 | 1638.2.bj.g.127.6 | 12 | |||
28.19 | even | 6 | 1456.2.cc.d.673.6 | 12 | |||
91.4 | even | 6 | inner | 1274.2.o.e.459.6 | 12 | ||
91.17 | odd | 6 | 1274.2.o.d.459.4 | 12 | |||
91.30 | even | 6 | 1274.2.m.c.589.3 | 12 | |||
91.54 | even | 12 | 2366.2.a.bf.1.6 | 6 | |||
91.68 | odd | 6 | 2366.2.d.r.337.6 | 12 | |||
91.69 | odd | 6 | 1274.2.v.e.667.6 | 12 | |||
91.75 | odd | 6 | 2366.2.d.r.337.12 | 12 | |||
91.82 | odd | 6 | 182.2.m.b.43.1 | ✓ | 12 | ||
91.89 | even | 12 | 2366.2.a.bh.1.6 | 6 | |||
273.173 | even | 6 | 1638.2.bj.g.1135.4 | 12 | |||
364.355 | even | 6 | 1456.2.cc.d.225.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
182.2.m.b.43.1 | ✓ | 12 | 91.82 | odd | 6 | ||
182.2.m.b.127.1 | yes | 12 | 7.5 | odd | 6 | ||
1274.2.m.c.491.3 | 12 | 7.2 | even | 3 | |||
1274.2.m.c.589.3 | 12 | 91.30 | even | 6 | |||
1274.2.o.d.459.4 | 12 | 91.17 | odd | 6 | |||
1274.2.o.d.569.1 | 12 | 7.6 | odd | 2 | |||
1274.2.o.e.459.6 | 12 | 91.4 | even | 6 | inner | ||
1274.2.o.e.569.3 | 12 | 1.1 | even | 1 | trivial | ||
1274.2.v.d.361.4 | 12 | 7.4 | even | 3 | |||
1274.2.v.d.667.4 | 12 | 13.4 | even | 6 | |||
1274.2.v.e.361.6 | 12 | 7.3 | odd | 6 | |||
1274.2.v.e.667.6 | 12 | 91.69 | odd | 6 | |||
1456.2.cc.d.225.6 | 12 | 364.355 | even | 6 | |||
1456.2.cc.d.673.6 | 12 | 28.19 | even | 6 | |||
1638.2.bj.g.127.6 | 12 | 21.5 | even | 6 | |||
1638.2.bj.g.1135.4 | 12 | 273.173 | even | 6 | |||
2366.2.a.bf.1.6 | 6 | 91.54 | even | 12 | |||
2366.2.a.bh.1.6 | 6 | 91.89 | even | 12 | |||
2366.2.d.r.337.6 | 12 | 91.68 | odd | 6 | |||
2366.2.d.r.337.12 | 12 | 91.75 | odd | 6 |