Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [130,2,Mod(47,130)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(130, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("130.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 130 = 2 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 130.j (of order \(4\), degree \(2\), 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: | \(1.03805522628\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 83.1 | ||
Root | \(1.65831 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 130.83 |
Dual form | 130.2.j.d.47.1 |
$q$-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 \(\left(\mathbb{Z}/130\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(41\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | −1.15831 | − | 1.15831i | −0.668752 | − | 0.668752i | 0.288675 | − | 0.957427i | \(-0.406785\pi\) |
−0.957427 | + | 0.288675i | \(0.906785\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.65831 | − | 1.50000i | 0.741620 | − | 0.670820i | ||||
\(6\) | 1.15831 | − | 1.15831i | 0.472879 | − | 0.472879i | ||||
\(7\) | 3.00000 | 1.13389 | 0.566947 | − | 0.823754i | \(-0.308125\pi\) | ||||
0.566947 | + | 0.823754i | \(0.308125\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | − | 0.316625i | − | 0.105542i | ||||||
\(10\) | 1.50000 | + | 1.65831i | 0.474342 | + | 0.524404i | ||||
\(11\) | 3.31662 | + | 3.31662i | 1.00000 | + | 1.00000i | 1.00000 | \(0\) | ||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 1.15831 | + | 1.15831i | 0.334376 | + | 0.334376i | ||||
\(13\) | −3.00000 | − | 2.00000i | −0.832050 | − | 0.554700i | ||||
\(14\) | 3.00000i | 0.801784i | ||||||||
\(15\) | −3.65831 | − | 0.183375i | −0.944572 | − | 0.0473473i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.15831 | − | 3.15831i | −0.766003 | − | 0.766003i | 0.211397 | − | 0.977400i | \(-0.432199\pi\) |
−0.977400 | + | 0.211397i | \(0.932199\pi\) | |||||||
\(18\) | 0.316625 | 0.0746292 | ||||||||
\(19\) | 2.00000 | + | 2.00000i | 0.458831 | + | 0.458831i | 0.898272 | − | 0.439440i | \(-0.144823\pi\) |
−0.439440 | + | 0.898272i | \(0.644823\pi\) | |||||||
\(20\) | −1.65831 | + | 1.50000i | −0.370810 | + | 0.335410i | ||||
\(21\) | −3.47494 | − | 3.47494i | −0.758293 | − | 0.758293i | ||||
\(22\) | −3.31662 | + | 3.31662i | −0.707107 | + | 0.707107i | ||||
\(23\) | −3.31662 | + | 3.31662i | −0.691564 | + | 0.691564i | −0.962576 | − | 0.271012i | \(-0.912642\pi\) |
0.271012 | + | 0.962576i | \(0.412642\pi\) | |||||||
\(24\) | −1.15831 | + | 1.15831i | −0.236440 | + | 0.236440i | ||||
\(25\) | 0.500000 | − | 4.97494i | 0.100000 | − | 0.994987i | ||||
\(26\) | 2.00000 | − | 3.00000i | 0.392232 | − | 0.588348i | ||||
\(27\) | −3.84169 | + | 3.84169i | −0.739333 | + | 0.739333i | ||||
\(28\) | −3.00000 | −0.566947 | ||||||||
\(29\) | 6.31662i | 1.17297i | 0.809961 | + | 0.586484i | \(0.199488\pi\) | ||||
−0.809961 | + | 0.586484i | \(0.800512\pi\) | |||||||
\(30\) | 0.183375 | − | 3.65831i | 0.0334796 | − | 0.667913i | ||||
\(31\) | 1.00000 | − | 1.00000i | 0.179605 | − | 0.179605i | −0.611578 | − | 0.791184i | \(-0.709465\pi\) |
0.791184 | + | 0.611578i | \(0.209465\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | − | 7.68338i | − | 1.33750i | ||||||
\(34\) | 3.15831 | − | 3.15831i | 0.541646 | − | 0.541646i | ||||
\(35\) | 4.97494 | − | 4.50000i | 0.840918 | − | 0.760639i | ||||
\(36\) | 0.316625i | 0.0527708i | ||||||||
\(37\) | 3.00000 | 0.493197 | 0.246598 | − | 0.969118i | \(-0.420687\pi\) | ||||
0.246598 | + | 0.969118i | \(0.420687\pi\) | |||||||
\(38\) | −2.00000 | + | 2.00000i | −0.324443 | + | 0.324443i | ||||
\(39\) | 1.15831 | + | 5.79156i | 0.185478 | + | 0.927392i | ||||
\(40\) | −1.50000 | − | 1.65831i | −0.237171 | − | 0.262202i | ||||
\(41\) | −6.31662 | + | 6.31662i | −0.986491 | + | 0.986491i | −0.999910 | − | 0.0134189i | \(-0.995729\pi\) |
0.0134189 | + | 0.999910i | \(0.495729\pi\) | |||||||
\(42\) | 3.47494 | − | 3.47494i | 0.536194 | − | 0.536194i | ||||
\(43\) | 2.47494 | − | 2.47494i | 0.377424 | − | 0.377424i | −0.492748 | − | 0.870172i | \(-0.664007\pi\) |
0.870172 | + | 0.492748i | \(0.164007\pi\) | |||||||
\(44\) | −3.31662 | − | 3.31662i | −0.500000 | − | 0.500000i | ||||
\(45\) | −0.474937 | − | 0.525063i | −0.0707995 | − | 0.0782717i | ||||
\(46\) | −3.31662 | − | 3.31662i | −0.489010 | − | 0.489010i | ||||
\(47\) | −9.31662 | −1.35897 | −0.679485 | − | 0.733690i | \(-0.737797\pi\) | ||||
−0.679485 | + | 0.733690i | \(0.737797\pi\) | |||||||
\(48\) | −1.15831 | − | 1.15831i | −0.167188 | − | 0.167188i | ||||
\(49\) | 2.00000 | 0.285714 | ||||||||
\(50\) | 4.97494 | + | 0.500000i | 0.703562 | + | 0.0707107i | ||||
\(51\) | 7.31662i | 1.02453i | ||||||||
\(52\) | 3.00000 | + | 2.00000i | 0.416025 | + | 0.277350i | ||||
\(53\) | 9.63325 | + | 9.63325i | 1.32323 | + | 1.32323i | 0.911147 | + | 0.412082i | \(0.135198\pi\) |
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | −3.84169 | − | 3.84169i | −0.522787 | − | 0.522787i | ||||
\(55\) | 10.4749 | + | 0.525063i | 1.41244 | + | 0.0707995i | ||||
\(56\) | − | 3.00000i | − | 0.400892i | ||||||
\(57\) | − | 4.63325i | − | 0.613689i | ||||||
\(58\) | −6.31662 | −0.829413 | ||||||||
\(59\) | 0.316625 | − | 0.316625i | 0.0412210 | − | 0.0412210i | −0.686196 | − | 0.727417i | \(-0.740721\pi\) |
0.727417 | + | 0.686196i | \(0.240721\pi\) | |||||||
\(60\) | 3.65831 | + | 0.183375i | 0.472286 | + | 0.0236736i | ||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | 1.00000 | + | 1.00000i | 0.127000 | + | 0.127000i | ||||
\(63\) | − | 0.949874i | − | 0.119673i | ||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −7.97494 | + | 1.18338i | −0.989169 | + | 0.146780i | ||||
\(66\) | 7.68338 | 0.945758 | ||||||||
\(67\) | 4.94987i | 0.604723i | 0.953193 | + | 0.302362i | \(0.0977750\pi\) | ||||
−0.953193 | + | 0.302362i | \(0.902225\pi\) | |||||||
\(68\) | 3.15831 | + | 3.15831i | 0.383002 | + | 0.383002i | ||||
\(69\) | 7.68338 | 0.924970 | ||||||||
\(70\) | 4.50000 | + | 4.97494i | 0.537853 | + | 0.594619i | ||||
\(71\) | −2.84169 | + | 2.84169i | −0.337246 | + | 0.337246i | −0.855330 | − | 0.518084i | \(-0.826646\pi\) |
0.518084 | + | 0.855330i | \(0.326646\pi\) | |||||||
\(72\) | −0.316625 | −0.0373146 | ||||||||
\(73\) | − | 4.00000i | − | 0.468165i | −0.972217 | − | 0.234082i | \(-0.924791\pi\) | ||
0.972217 | − | 0.234082i | \(-0.0752085\pi\) | |||||||
\(74\) | 3.00000i | 0.348743i | ||||||||
\(75\) | −6.34169 | + | 5.18338i | −0.732275 | + | 0.598525i | ||||
\(76\) | −2.00000 | − | 2.00000i | −0.229416 | − | 0.229416i | ||||
\(77\) | 9.94987 | + | 9.94987i | 1.13389 | + | 1.13389i | ||||
\(78\) | −5.79156 | + | 1.15831i | −0.655765 | + | 0.131153i | ||||
\(79\) | − | 12.9499i | − | 1.45697i | −0.685059 | − | 0.728487i | \(-0.740224\pi\) | ||
0.685059 | − | 0.728487i | \(-0.259776\pi\) | |||||||
\(80\) | 1.65831 | − | 1.50000i | 0.185405 | − | 0.167705i | ||||
\(81\) | 7.94987 | 0.883319 | ||||||||
\(82\) | −6.31662 | − | 6.31662i | −0.697555 | − | 0.697555i | ||||
\(83\) | 6.31662 | 0.693340 | 0.346670 | − | 0.937987i | \(-0.387312\pi\) | ||||
0.346670 | + | 0.937987i | \(0.387312\pi\) | |||||||
\(84\) | 3.47494 | + | 3.47494i | 0.379147 | + | 0.379147i | ||||
\(85\) | −9.97494 | − | 0.500000i | −1.08193 | − | 0.0542326i | ||||
\(86\) | 2.47494 | + | 2.47494i | 0.266879 | + | 0.266879i | ||||
\(87\) | 7.31662 | − | 7.31662i | 0.784425 | − | 0.784425i | ||||
\(88\) | 3.31662 | − | 3.31662i | 0.353553 | − | 0.353553i | ||||
\(89\) | 0.316625 | − | 0.316625i | 0.0335622 | − | 0.0335622i | −0.690127 | − | 0.723689i | \(-0.742445\pi\) |
0.723689 | + | 0.690127i | \(0.242445\pi\) | |||||||
\(90\) | 0.525063 | − | 0.474937i | 0.0553465 | − | 0.0500628i | ||||
\(91\) | −9.00000 | − | 6.00000i | −0.943456 | − | 0.628971i | ||||
\(92\) | 3.31662 | − | 3.31662i | 0.345782 | − | 0.345782i | ||||
\(93\) | −2.31662 | −0.240223 | ||||||||
\(94\) | − | 9.31662i | − | 0.960936i | ||||||
\(95\) | 6.31662 | + | 0.316625i | 0.648072 | + | 0.0324850i | ||||
\(96\) | 1.15831 | − | 1.15831i | 0.118220 | − | 0.118220i | ||||
\(97\) | − | 8.94987i | − | 0.908722i | −0.890818 | − | 0.454361i | \(-0.849868\pi\) | ||
0.890818 | − | 0.454361i | \(-0.150132\pi\) | |||||||
\(98\) | 2.00000i | 0.202031i | ||||||||
\(99\) | 1.05013 | − | 1.05013i | 0.105542 | − | 0.105542i | ||||
\(100\) | −0.500000 | + | 4.97494i | −0.0500000 | + | 0.497494i | ||||
\(101\) | − | 19.2665i | − | 1.91709i | −0.284944 | − | 0.958544i | \(-0.591975\pi\) | ||
0.284944 | − | 0.958544i | \(-0.408025\pi\) | |||||||
\(102\) | −7.31662 | −0.724454 | ||||||||
\(103\) | −7.94987 | + | 7.94987i | −0.783324 | + | 0.783324i | −0.980390 | − | 0.197066i | \(-0.936859\pi\) |
0.197066 | + | 0.980390i | \(0.436859\pi\) | |||||||
\(104\) | −2.00000 | + | 3.00000i | −0.196116 | + | 0.294174i | ||||
\(105\) | −10.9749 | − | 0.550126i | −1.07104 | − | 0.0536868i | ||||
\(106\) | −9.63325 | + | 9.63325i | −0.935664 | + | 0.935664i | ||||
\(107\) | −9.63325 | + | 9.63325i | −0.931281 | + | 0.931281i | −0.997786 | − | 0.0665047i | \(-0.978815\pi\) |
0.0665047 | + | 0.997786i | \(0.478815\pi\) | |||||||
\(108\) | 3.84169 | − | 3.84169i | 0.369667 | − | 0.369667i | ||||
\(109\) | −1.47494 | − | 1.47494i | −0.141273 | − | 0.141273i | 0.632933 | − | 0.774206i | \(-0.281851\pi\) |
−0.774206 | + | 0.632933i | \(0.781851\pi\) | |||||||
\(110\) | −0.525063 | + | 10.4749i | −0.0500628 | + | 0.998746i | ||||
\(111\) | −3.47494 | − | 3.47494i | −0.329826 | − | 0.329826i | ||||
\(112\) | 3.00000 | 0.283473 | ||||||||
\(113\) | 2.68338 | + | 2.68338i | 0.252431 | + | 0.252431i | 0.821967 | − | 0.569536i | \(-0.192877\pi\) |
−0.569536 | + | 0.821967i | \(0.692877\pi\) | |||||||
\(114\) | 4.63325 | 0.433944 | ||||||||
\(115\) | −0.525063 | + | 10.4749i | −0.0489624 | + | 0.976793i | ||||
\(116\) | − | 6.31662i | − | 0.586484i | ||||||
\(117\) | −0.633250 | + | 0.949874i | −0.0585439 | + | 0.0878159i | ||||
\(118\) | 0.316625 | + | 0.316625i | 0.0291477 | + | 0.0291477i | ||||
\(119\) | −9.47494 | − | 9.47494i | −0.868566 | − | 0.868566i | ||||
\(120\) | −0.183375 | + | 3.65831i | −0.0167398 | + | 0.333957i | ||||
\(121\) | 11.0000i | 1.00000i | ||||||||
\(122\) | 2.00000i | 0.181071i | ||||||||
\(123\) | 14.6332 | 1.31944 | ||||||||
\(124\) | −1.00000 | + | 1.00000i | −0.0898027 | + | 0.0898027i | ||||
\(125\) | −6.63325 | − | 9.00000i | −0.593296 | − | 0.804984i | ||||
\(126\) | 0.949874 | 0.0846215 | ||||||||
\(127\) | −7.00000 | − | 7.00000i | −0.621150 | − | 0.621150i | 0.324676 | − | 0.945825i | \(-0.394745\pi\) |
−0.945825 | + | 0.324676i | \(0.894745\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −5.73350 | −0.504807 | ||||||||
\(130\) | −1.18338 | − | 7.97494i | −0.103789 | − | 0.699448i | ||||
\(131\) | −3.00000 | −0.262111 | −0.131056 | − | 0.991375i | \(-0.541837\pi\) | ||||
−0.131056 | + | 0.991375i | \(0.541837\pi\) | |||||||
\(132\) | 7.68338i | 0.668752i | ||||||||
\(133\) | 6.00000 | + | 6.00000i | 0.520266 | + | 0.520266i | ||||
\(134\) | −4.94987 | −0.427604 | ||||||||
\(135\) | −0.608187 | + | 12.1332i | −0.0523444 | + | 1.04426i | ||||
\(136\) | −3.15831 | + | 3.15831i | −0.270823 | + | 0.270823i | ||||
\(137\) | 5.68338 | 0.485564 | 0.242782 | − | 0.970081i | \(-0.421940\pi\) | ||||
0.242782 | + | 0.970081i | \(0.421940\pi\) | |||||||
\(138\) | 7.68338i | 0.654052i | ||||||||
\(139\) | 15.9499i | 1.35285i | 0.736511 | + | 0.676425i | \(0.236472\pi\) | ||||
−0.736511 | + | 0.676425i | \(0.763528\pi\) | |||||||
\(140\) | −4.97494 | + | 4.50000i | −0.420459 | + | 0.380319i | ||||
\(141\) | 10.7916 | + | 10.7916i | 0.908813 | + | 0.908813i | ||||
\(142\) | −2.84169 | − | 2.84169i | −0.238469 | − | 0.238469i | ||||
\(143\) | −3.31662 | − | 16.5831i | −0.277350 | − | 1.38675i | ||||
\(144\) | − | 0.316625i | − | 0.0263854i | ||||||
\(145\) | 9.47494 | + | 10.4749i | 0.786851 | + | 0.869896i | ||||
\(146\) | 4.00000 | 0.331042 | ||||||||
\(147\) | −2.31662 | − | 2.31662i | −0.191072 | − | 0.191072i | ||||
\(148\) | −3.00000 | −0.246598 | ||||||||
\(149\) | −15.3166 | − | 15.3166i | −1.25479 | − | 1.25479i | −0.953549 | − | 0.301238i | \(-0.902600\pi\) |
−0.301238 | − | 0.953549i | \(-0.597400\pi\) | |||||||
\(150\) | −5.18338 | − | 6.34169i | −0.423221 | − | 0.517797i | ||||
\(151\) | 4.47494 | + | 4.47494i | 0.364165 | + | 0.364165i | 0.865344 | − | 0.501179i | \(-0.167100\pi\) |
−0.501179 | + | 0.865344i | \(0.667100\pi\) | |||||||
\(152\) | 2.00000 | − | 2.00000i | 0.162221 | − | 0.162221i | ||||
\(153\) | −1.00000 | + | 1.00000i | −0.0808452 | + | 0.0808452i | ||||
\(154\) | −9.94987 | + | 9.94987i | −0.801784 | + | 0.801784i | ||||
\(155\) | 0.158312 | − | 3.15831i | 0.0127160 | − | 0.253682i | ||||
\(156\) | −1.15831 | − | 5.79156i | −0.0927392 | − | 0.463696i | ||||
\(157\) | 10.0000 | − | 10.0000i | 0.798087 | − | 0.798087i | −0.184707 | − | 0.982794i | \(-0.559134\pi\) |
0.982794 | + | 0.184707i | \(0.0591335\pi\) | |||||||
\(158\) | 12.9499 | 1.03024 | ||||||||
\(159\) | − | 22.3166i | − | 1.76982i | ||||||
\(160\) | 1.50000 | + | 1.65831i | 0.118585 | + | 0.131101i | ||||
\(161\) | −9.94987 | + | 9.94987i | −0.784160 | + | 0.784160i | ||||
\(162\) | 7.94987i | 0.624601i | ||||||||
\(163\) | 2.94987i | 0.231052i | 0.993304 | + | 0.115526i | \(0.0368554\pi\) | ||||
−0.993304 | + | 0.115526i | \(0.963145\pi\) | |||||||
\(164\) | 6.31662 | − | 6.31662i | 0.493246 | − | 0.493246i | ||||
\(165\) | −11.5251 | − | 12.7414i | −0.897225 | − | 0.991919i | ||||
\(166\) | 6.31662i | 0.490265i | ||||||||
\(167\) | 12.6332 | 0.977590 | 0.488795 | − | 0.872399i | \(-0.337437\pi\) | ||||
0.488795 | + | 0.872399i | \(0.337437\pi\) | |||||||
\(168\) | −3.47494 | + | 3.47494i | −0.268097 | + | 0.268097i | ||||
\(169\) | 5.00000 | + | 12.0000i | 0.384615 | + | 0.923077i | ||||
\(170\) | 0.500000 | − | 9.97494i | 0.0383482 | − | 0.765043i | ||||
\(171\) | 0.633250 | − | 0.633250i | 0.0484258 | − | 0.0484258i | ||||
\(172\) | −2.47494 | + | 2.47494i | −0.188712 | + | 0.188712i | ||||
\(173\) | −3.31662 | + | 3.31662i | −0.252158 | + | 0.252158i | −0.821855 | − | 0.569697i | \(-0.807061\pi\) |
0.569697 | + | 0.821855i | \(0.307061\pi\) | |||||||
\(174\) | 7.31662 | + | 7.31662i | 0.554672 | + | 0.554672i | ||||
\(175\) | 1.50000 | − | 14.9248i | 0.113389 | − | 1.12821i | ||||
\(176\) | 3.31662 | + | 3.31662i | 0.250000 | + | 0.250000i | ||||
\(177\) | −0.733501 | −0.0551333 | ||||||||
\(178\) | 0.316625 | + | 0.316625i | 0.0237320 | + | 0.0237320i | ||||
\(179\) | 15.0000 | 1.12115 | 0.560576 | − | 0.828103i | \(-0.310580\pi\) | ||||
0.560576 | + | 0.828103i | \(0.310580\pi\) | |||||||
\(180\) | 0.474937 | + | 0.525063i | 0.0353997 | + | 0.0391359i | ||||
\(181\) | − | 6.94987i | − | 0.516580i | −0.966067 | − | 0.258290i | \(-0.916841\pi\) | ||
0.966067 | − | 0.258290i | \(-0.0831590\pi\) | |||||||
\(182\) | 6.00000 | − | 9.00000i | 0.444750 | − | 0.667124i | ||||
\(183\) | −2.31662 | − | 2.31662i | −0.171250 | − | 0.171250i | ||||
\(184\) | 3.31662 | + | 3.31662i | 0.244505 | + | 0.244505i | ||||
\(185\) | 4.97494 | − | 4.50000i | 0.365765 | − | 0.330847i | ||||
\(186\) | − | 2.31662i | − | 0.169863i | ||||||
\(187\) | − | 20.9499i | − | 1.53201i | ||||||
\(188\) | 9.31662 | 0.679485 | ||||||||
\(189\) | −11.5251 | + | 11.5251i | −0.838325 | + | 0.838325i | ||||
\(190\) | −0.316625 | + | 6.31662i | −0.0229704 | + | 0.458256i | ||||
\(191\) | 5.05013 | 0.365414 | 0.182707 | − | 0.983167i | \(-0.441514\pi\) | ||||
0.182707 | + | 0.983167i | \(0.441514\pi\) | |||||||
\(192\) | 1.15831 | + | 1.15831i | 0.0835940 | + | 0.0835940i | ||||
\(193\) | − | 10.9499i | − | 0.788189i | −0.919070 | − | 0.394095i | \(-0.871058\pi\) | ||
0.919070 | − | 0.394095i | \(-0.128942\pi\) | |||||||
\(194\) | 8.94987 | 0.642564 | ||||||||
\(195\) | 10.6082 | + | 7.86675i | 0.759668 | + | 0.563350i | ||||
\(196\) | −2.00000 | −0.142857 | ||||||||
\(197\) | − | 3.94987i | − | 0.281417i | −0.990051 | − | 0.140708i | \(-0.955062\pi\) | ||
0.990051 | − | 0.140708i | \(-0.0449380\pi\) | |||||||
\(198\) | 1.05013 | + | 1.05013i | 0.0746292 | + | 0.0746292i | ||||
\(199\) | 16.9499 | 1.20154 | 0.600772 | − | 0.799420i | \(-0.294860\pi\) | ||||
0.600772 | + | 0.799420i | \(0.294860\pi\) | |||||||
\(200\) | −4.97494 | − | 0.500000i | −0.351781 | − | 0.0353553i | ||||
\(201\) | 5.73350 | − | 5.73350i | 0.404410 | − | 0.404410i | ||||
\(202\) | 19.2665 | 1.35559 | ||||||||
\(203\) | 18.9499i | 1.33002i | ||||||||
\(204\) | − | 7.31662i | − | 0.512266i | ||||||
\(205\) | −1.00000 | + | 19.9499i | −0.0698430 | + | 1.39336i | ||||
\(206\) | −7.94987 | − | 7.94987i | −0.553894 | − | 0.553894i | ||||
\(207\) | 1.05013 | + | 1.05013i | 0.0729888 | + | 0.0729888i | ||||
\(208\) | −3.00000 | − | 2.00000i | −0.208013 | − | 0.138675i | ||||
\(209\) | 13.2665i | 0.917663i | ||||||||
\(210\) | 0.550126 | − | 10.9749i | 0.0379623 | − | 0.757343i | ||||
\(211\) | −19.9499 | −1.37341 | −0.686703 | − | 0.726938i | \(-0.740943\pi\) | ||||
−0.686703 | + | 0.726938i | \(0.740943\pi\) | |||||||
\(212\) | −9.63325 | − | 9.63325i | −0.661614 | − | 0.661614i | ||||
\(213\) | 6.58312 | 0.451068 | ||||||||
\(214\) | −9.63325 | − | 9.63325i | −0.658515 | − | 0.658515i | ||||
\(215\) | 0.391813 | − | 7.81662i | 0.0267214 | − | 0.533089i | ||||
\(216\) | 3.84169 | + | 3.84169i | 0.261394 | + | 0.261394i | ||||
\(217\) | 3.00000 | − | 3.00000i | 0.203653 | − | 0.203653i | ||||
\(218\) | 1.47494 | − | 1.47494i | 0.0998954 | − | 0.0998954i | ||||
\(219\) | −4.63325 | + | 4.63325i | −0.313086 | + | 0.313086i | ||||
\(220\) | −10.4749 | − | 0.525063i | −0.706220 | − | 0.0353997i | ||||
\(221\) | 3.15831 | + | 15.7916i | 0.212451 | + | 1.06226i | ||||
\(222\) | 3.47494 | − | 3.47494i | 0.233223 | − | 0.233223i | ||||
\(223\) | 15.9499 | 1.06808 | 0.534041 | − | 0.845458i | \(-0.320673\pi\) | ||||
0.534041 | + | 0.845458i | \(0.320673\pi\) | |||||||
\(224\) | 3.00000i | 0.200446i | ||||||||
\(225\) | −1.57519 | − | 0.158312i | −0.105013 | − | 0.0105542i | ||||
\(226\) | −2.68338 | + | 2.68338i | −0.178495 | + | 0.178495i | ||||
\(227\) | 18.0000i | 1.19470i | 0.801980 | + | 0.597351i | \(0.203780\pi\) | ||||
−0.801980 | + | 0.597351i | \(0.796220\pi\) | |||||||
\(228\) | 4.63325i | 0.306844i | ||||||||
\(229\) | −3.52506 | + | 3.52506i | −0.232943 | + | 0.232943i | −0.813920 | − | 0.580977i | \(-0.802671\pi\) |
0.580977 | + | 0.813920i | \(0.302671\pi\) | |||||||
\(230\) | −10.4749 | − | 0.525063i | −0.690697 | − | 0.0346216i | ||||
\(231\) | − | 23.0501i | − | 1.51659i | ||||||
\(232\) | 6.31662 | 0.414707 | ||||||||
\(233\) | −6.79156 | + | 6.79156i | −0.444930 | + | 0.444930i | −0.893665 | − | 0.448735i | \(-0.851875\pi\) |
0.448735 | + | 0.893665i | \(0.351875\pi\) | |||||||
\(234\) | −0.949874 | − | 0.633250i | −0.0620952 | − | 0.0413968i | ||||
\(235\) | −15.4499 | + | 13.9749i | −1.00784 | + | 0.911624i | ||||
\(236\) | −0.316625 | + | 0.316625i | −0.0206105 | + | 0.0206105i | ||||
\(237\) | −15.0000 | + | 15.0000i | −0.974355 | + | 0.974355i | ||||
\(238\) | 9.47494 | − | 9.47494i | 0.614169 | − | 0.614169i | ||||
\(239\) | −11.8417 | − | 11.8417i | −0.765975 | − | 0.765975i | 0.211420 | − | 0.977395i | \(-0.432191\pi\) |
−0.977395 | + | 0.211420i | \(0.932191\pi\) | |||||||
\(240\) | −3.65831 | − | 0.183375i | −0.236143 | − | 0.0118368i | ||||
\(241\) | 16.0000 | + | 16.0000i | 1.03065 | + | 1.03065i | 0.999515 | + | 0.0311354i | \(0.00991232\pi\) |
0.0311354 | + | 0.999515i | \(0.490088\pi\) | |||||||
\(242\) | −11.0000 | −0.707107 | ||||||||
\(243\) | 2.31662 | + | 2.31662i | 0.148612 | + | 0.148612i | ||||
\(244\) | −2.00000 | −0.128037 | ||||||||
\(245\) | 3.31662 | − | 3.00000i | 0.211891 | − | 0.191663i | ||||
\(246\) | 14.6332i | 0.932982i | ||||||||
\(247\) | −2.00000 | − | 10.0000i | −0.127257 | − | 0.636285i | ||||
\(248\) | −1.00000 | − | 1.00000i | −0.0635001 | − | 0.0635001i | ||||
\(249\) | −7.31662 | − | 7.31662i | −0.463672 | − | 0.463672i | ||||
\(250\) | 9.00000 | − | 6.63325i | 0.569210 | − | 0.419524i | ||||
\(251\) | − | 19.2665i | − | 1.21609i | −0.793902 | − | 0.608045i | \(-0.791954\pi\) | ||
0.793902 | − | 0.608045i | \(-0.208046\pi\) | |||||||
\(252\) | 0.949874i | 0.0598365i | ||||||||
\(253\) | −22.0000 | −1.38313 | ||||||||
\(254\) | 7.00000 | − | 7.00000i | 0.439219 | − | 0.439219i | ||||
\(255\) | 10.9749 | + | 12.1332i | 0.687277 | + | 0.759814i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 11.8417 | + | 11.8417i | 0.738664 | + | 0.738664i | 0.972319 | − | 0.233655i | \(-0.0750687\pi\) |
−0.233655 | + | 0.972319i | \(0.575069\pi\) | |||||||
\(258\) | − | 5.73350i | − | 0.356952i | ||||||
\(259\) | 9.00000 | 0.559233 | ||||||||
\(260\) | 7.97494 | − | 1.18338i | 0.494585 | − | 0.0733898i | ||||
\(261\) | 2.00000 | 0.123797 | ||||||||
\(262\) | − | 3.00000i | − | 0.185341i | ||||||
\(263\) | −12.3166 | − | 12.3166i | −0.759476 | − | 0.759476i | 0.216751 | − | 0.976227i | \(-0.430454\pi\) |
−0.976227 | + | 0.216751i | \(0.930454\pi\) | |||||||
\(264\) | −7.68338 | −0.472879 | ||||||||
\(265\) | 30.4248 | + | 1.52506i | 1.86898 | + | 0.0936839i | ||||
\(266\) | −6.00000 | + | 6.00000i | −0.367884 | + | 0.367884i | ||||
\(267\) | −0.733501 | −0.0448895 | ||||||||
\(268\) | − | 4.94987i | − | 0.302362i | ||||||
\(269\) | 13.2665i | 0.808873i | 0.914566 | + | 0.404436i | \(0.132532\pi\) | ||||
−0.914566 | + | 0.404436i | \(0.867468\pi\) | |||||||
\(270\) | −12.1332 | − | 0.608187i | −0.738406 | − | 0.0370131i | ||||
\(271\) | −10.5251 | − | 10.5251i | −0.639352 | − | 0.639352i | 0.311044 | − | 0.950396i | \(-0.399321\pi\) |
−0.950396 | + | 0.311044i | \(0.899321\pi\) | |||||||
\(272\) | −3.15831 | − | 3.15831i | −0.191501 | − | 0.191501i | ||||
\(273\) | 3.47494 | + | 17.3747i | 0.210313 | + | 1.05156i | ||||
\(274\) | 5.68338i | 0.343345i | ||||||||
\(275\) | 18.1583 | − | 14.8417i | 1.09499 | − | 0.894987i | ||||
\(276\) | −7.68338 | −0.462485 | ||||||||
\(277\) | 21.8997 | + | 21.8997i | 1.31583 | + | 1.31583i | 0.917045 | + | 0.398783i | \(0.130567\pi\) |
0.398783 | + | 0.917045i | \(0.369433\pi\) | |||||||
\(278\) | −15.9499 | −0.956610 | ||||||||
\(279\) | −0.316625 | − | 0.316625i | −0.0189558 | − | 0.0189558i | ||||
\(280\) | −4.50000 | − | 4.97494i | −0.268926 | − | 0.297309i | ||||
\(281\) | −11.6834 | − | 11.6834i | −0.696972 | − | 0.696972i | 0.266784 | − | 0.963756i | \(-0.414039\pi\) |
−0.963756 | + | 0.266784i | \(0.914039\pi\) | |||||||
\(282\) | −10.7916 | + | 10.7916i | −0.642628 | + | 0.642628i | ||||
\(283\) | −7.94987 | + | 7.94987i | −0.472571 | + | 0.472571i | −0.902746 | − | 0.430175i | \(-0.858452\pi\) |
0.430175 | + | 0.902746i | \(0.358452\pi\) | |||||||
\(284\) | 2.84169 | − | 2.84169i | 0.168623 | − | 0.168623i | ||||
\(285\) | −6.94987 | − | 7.68338i | −0.411675 | − | 0.455124i | ||||
\(286\) | 16.5831 | − | 3.31662i | 0.980581 | − | 0.196116i | ||||
\(287\) | −18.9499 | + | 18.9499i | −1.11858 | + | 1.11858i | ||||
\(288\) | 0.316625 | 0.0186573 | ||||||||
\(289\) | 2.94987i | 0.173522i | ||||||||
\(290\) | −10.4749 | + | 9.47494i | −0.615109 | + | 0.556387i | ||||
\(291\) | −10.3668 | + | 10.3668i | −0.607710 | + | 0.607710i | ||||
\(292\) | 4.00000i | 0.234082i | ||||||||
\(293\) | − | 22.8997i | − | 1.33782i | −0.743344 | − | 0.668909i | \(-0.766762\pi\) | ||
0.743344 | − | 0.668909i | \(-0.233238\pi\) | |||||||
\(294\) | 2.31662 | − | 2.31662i | 0.135108 | − | 0.135108i | ||||
\(295\) | 0.0501256 | − | 1.00000i | 0.00291843 | − | 0.0582223i | ||||
\(296\) | − | 3.00000i | − | 0.174371i | ||||||
\(297\) | −25.4829 | −1.47867 | ||||||||
\(298\) | 15.3166 | − | 15.3166i | 0.887268 | − | 0.887268i | ||||
\(299\) | 16.5831 | − | 3.31662i | 0.959027 | − | 0.191805i | ||||
\(300\) | 6.34169 | − | 5.18338i | 0.366138 | − | 0.299262i | ||||
\(301\) | 7.42481 | − | 7.42481i | 0.427959 | − | 0.427959i | ||||
\(302\) | −4.47494 | + | 4.47494i | −0.257504 | + | 0.257504i | ||||
\(303\) | −22.3166 | + | 22.3166i | −1.28206 | + | 1.28206i | ||||
\(304\) | 2.00000 | + | 2.00000i | 0.114708 | + | 0.114708i | ||||
\(305\) | 3.31662 | − | 3.00000i | 0.189909 | − | 0.171780i | ||||
\(306\) | −1.00000 | − | 1.00000i | −0.0571662 | − | 0.0571662i | ||||
\(307\) | −25.8997 | −1.47818 | −0.739088 | − | 0.673608i | \(-0.764743\pi\) | ||||
−0.739088 | + | 0.673608i | \(0.764743\pi\) | |||||||
\(308\) | −9.94987 | − | 9.94987i | −0.566947 | − | 0.566947i | ||||
\(309\) | 18.4169 | 1.04770 | ||||||||
\(310\) | 3.15831 | + | 0.158312i | 0.179380 | + | 0.00899154i | ||||
\(311\) | − | 19.2665i | − | 1.09250i | −0.837621 | − | 0.546251i | \(-0.816054\pi\) | ||
0.837621 | − | 0.546251i | \(-0.183946\pi\) | |||||||
\(312\) | 5.79156 | − | 1.15831i | 0.327883 | − | 0.0655765i | ||||
\(313\) | −15.4248 | − | 15.4248i | −0.871862 | − | 0.871862i | 0.120813 | − | 0.992675i | \(-0.461450\pi\) |
−0.992675 | + | 0.120813i | \(0.961450\pi\) | |||||||
\(314\) | 10.0000 | + | 10.0000i | 0.564333 | + | 0.564333i | ||||
\(315\) | −1.42481 | − | 1.57519i | −0.0802790 | − | 0.0887518i | ||||
\(316\) | 12.9499i | 0.728487i | ||||||||
\(317\) | − | 12.0000i | − | 0.673987i | −0.941507 | − | 0.336994i | \(-0.890590\pi\) | ||
0.941507 | − | 0.336994i | \(-0.109410\pi\) | |||||||
\(318\) | 22.3166 | 1.25145 | ||||||||
\(319\) | −20.9499 | + | 20.9499i | −1.17297 | + | 1.17297i | ||||
\(320\) | −1.65831 | + | 1.50000i | −0.0927025 | + | 0.0838525i | ||||
\(321\) | 22.3166 | 1.24559 | ||||||||
\(322\) | −9.94987 | − | 9.94987i | −0.554485 | − | 0.554485i | ||||
\(323\) | − | 12.6332i | − | 0.702933i | ||||||
\(324\) | −7.94987 | −0.441660 | ||||||||
\(325\) | −11.4499 | + | 13.9248i | −0.635125 | + | 0.772410i | ||||
\(326\) | −2.94987 | −0.163378 | ||||||||
\(327\) | 3.41688i | 0.188954i | ||||||||
\(328\) | 6.31662 | + | 6.31662i | 0.348777 | + | 0.348777i | ||||
\(329\) | −27.9499 | −1.54093 | ||||||||
\(330\) | 12.7414 | − | 11.5251i | 0.701393 | − | 0.634434i | ||||
\(331\) | 1.00000 | − | 1.00000i | 0.0549650 | − | 0.0549650i | −0.679090 | − | 0.734055i | \(-0.737625\pi\) |
0.734055 | + | 0.679090i | \(0.237625\pi\) | |||||||
\(332\) | −6.31662 | −0.346670 | ||||||||
\(333\) | − | 0.949874i | − | 0.0520528i | ||||||
\(334\) | 12.6332i | 0.691261i | ||||||||
\(335\) | 7.42481 | + | 8.20844i | 0.405661 | + | 0.448475i | ||||
\(336\) | −3.47494 | − | 3.47494i | −0.189573 | − | 0.189573i | ||||
\(337\) | −3.52506 | − | 3.52506i | −0.192022 | − | 0.192022i | 0.604547 | − | 0.796569i | \(-0.293354\pi\) |
−0.796569 | + | 0.604547i | \(0.793354\pi\) | |||||||
\(338\) | −12.0000 | + | 5.00000i | −0.652714 | + | 0.271964i | ||||
\(339\) | − | 6.21637i | − | 0.337627i | ||||||
\(340\) | 9.97494 | + | 0.500000i | 0.540967 | + | 0.0271163i | ||||
\(341\) | 6.63325 | 0.359211 | ||||||||
\(342\) | 0.633250 | + | 0.633250i | 0.0342422 | + | 0.0342422i | ||||
\(343\) | −15.0000 | −0.809924 | ||||||||
\(344\) | −2.47494 | − | 2.47494i | −0.133440 | − | 0.133440i | ||||
\(345\) | 12.7414 | − | 11.5251i | 0.685976 | − | 0.620489i | ||||
\(346\) | −3.31662 | − | 3.31662i | −0.178303 | − | 0.178303i | ||||
\(347\) | 0.791562 | − | 0.791562i | 0.0424933 | − | 0.0424933i | −0.685541 | − | 0.728034i | \(-0.740434\pi\) |
0.728034 | + | 0.685541i | \(0.240434\pi\) | |||||||
\(348\) | −7.31662 | + | 7.31662i | −0.392212 | + | 0.392212i | ||||
\(349\) | 18.4248 | − | 18.4248i | 0.986258 | − | 0.986258i | −0.0136493 | − | 0.999907i | \(-0.504345\pi\) |
0.999907 | + | 0.0136493i | \(0.00434484\pi\) | |||||||
\(350\) | 14.9248 | + | 1.50000i | 0.797765 | + | 0.0801784i | ||||
\(351\) | 19.2084 | − | 3.84169i | 1.02527 | − | 0.205054i | ||||
\(352\) | −3.31662 | + | 3.31662i | −0.176777 | + | 0.176777i | ||||
\(353\) | −7.58312 | −0.403609 | −0.201804 | − | 0.979426i | \(-0.564681\pi\) | ||||
−0.201804 | + | 0.979426i | \(0.564681\pi\) | |||||||
\(354\) | − | 0.733501i | − | 0.0389851i | ||||||
\(355\) | −0.449874 | + | 8.97494i | −0.0238769 | + | 0.476340i | ||||
\(356\) | −0.316625 | + | 0.316625i | −0.0167811 | + | 0.0167811i | ||||
\(357\) | 21.9499i | 1.16171i | ||||||||
\(358\) | 15.0000i | 0.792775i | ||||||||
\(359\) | 22.2665 | − | 22.2665i | 1.17518 | − | 1.17518i | 0.194224 | − | 0.980957i | \(-0.437781\pi\) |
0.980957 | − | 0.194224i | \(-0.0622187\pi\) | |||||||
\(360\) | −0.525063 | + | 0.474937i | −0.0276732 | + | 0.0250314i | ||||
\(361\) | − | 11.0000i | − | 0.578947i | ||||||
\(362\) | 6.94987 | 0.365277 | ||||||||
\(363\) | 12.7414 | − | 12.7414i | 0.668752 | − | 0.668752i | ||||
\(364\) | 9.00000 | + | 6.00000i | 0.471728 | + | 0.314485i | ||||
\(365\) | −6.00000 | − | 6.63325i | −0.314054 | − | 0.347200i | ||||
\(366\) | 2.31662 | − | 2.31662i | 0.121092 | − | 0.121092i | ||||
\(367\) | 1.94987 | − | 1.94987i | 0.101783 | − | 0.101783i | −0.654382 | − | 0.756164i | \(-0.727071\pi\) |
0.756164 | + | 0.654382i | \(0.227071\pi\) | |||||||
\(368\) | −3.31662 | + | 3.31662i | −0.172891 | + | 0.172891i | ||||
\(369\) | 2.00000 | + | 2.00000i | 0.104116 | + | 0.104116i | ||||
\(370\) | 4.50000 | + | 4.97494i | 0.233944 | + | 0.258635i | ||||
\(371\) | 28.8997 | + | 28.8997i | 1.50040 | + | 1.50040i | ||||
\(372\) | 2.31662 | 0.120111 | ||||||||
\(373\) | −20.0000 | − | 20.0000i | −1.03556 | − | 1.03556i | −0.999344 | − | 0.0362168i | \(-0.988469\pi\) |
−0.0362168 | − | 0.999344i | \(-0.511531\pi\) | |||||||
\(374\) | 20.9499 | 1.08329 | ||||||||
\(375\) | −2.74144 | + | 18.1082i | −0.141567 | + | 0.935103i | ||||
\(376\) | 9.31662i | 0.480468i | ||||||||
\(377\) | 12.6332 | − | 18.9499i | 0.650645 | − | 0.975968i | ||||
\(378\) | −11.5251 | − | 11.5251i | −0.592785 | − | 0.592785i | ||||
\(379\) | −13.0000 | − | 13.0000i | −0.667765 | − | 0.667765i | 0.289433 | − | 0.957198i | \(-0.406533\pi\) |
−0.957198 | + | 0.289433i | \(0.906533\pi\) | |||||||
\(380\) | −6.31662 | − | 0.316625i | −0.324036 | − | 0.0162425i | ||||
\(381\) | 16.2164i | 0.830790i | ||||||||
\(382\) | 5.05013i | 0.258387i | ||||||||
\(383\) | 14.3668 | 0.734107 | 0.367053 | − | 0.930200i | \(-0.380367\pi\) | ||||
0.367053 | + | 0.930200i | \(0.380367\pi\) | |||||||
\(384\) | −1.15831 | + | 1.15831i | −0.0591099 | + | 0.0591099i | ||||
\(385\) | 31.4248 | + | 1.57519i | 1.60156 | + | 0.0802790i | ||||
\(386\) | 10.9499 | 0.557334 | ||||||||
\(387\) | −0.783626 | − | 0.783626i | −0.0398340 | − | 0.0398340i | ||||
\(388\) | 8.94987i | 0.454361i | ||||||||
\(389\) | −13.8997 | −0.704745 | −0.352373 | − | 0.935860i | \(-0.614625\pi\) | ||||
−0.352373 | + | 0.935860i | \(0.614625\pi\) | |||||||
\(390\) | −7.86675 | + | 10.6082i | −0.398348 | + | 0.537166i | ||||
\(391\) | 20.9499 | 1.05948 | ||||||||
\(392\) | − | 2.00000i | − | 0.101015i | ||||||
\(393\) | 3.47494 | + | 3.47494i | 0.175287 | + | 0.175287i | ||||
\(394\) | 3.94987 | 0.198992 | ||||||||
\(395\) | −19.4248 | − | 21.4749i | −0.977368 | − | 1.08052i | ||||
\(396\) | −1.05013 | + | 1.05013i | −0.0527708 | + | 0.0527708i | ||||
\(397\) | 18.0000 | 0.903394 | 0.451697 | − | 0.892171i | \(-0.350819\pi\) | ||||
0.451697 | + | 0.892171i | \(0.350819\pi\) | |||||||
\(398\) | 16.9499i | 0.849620i | ||||||||
\(399\) | − | 13.8997i | − | 0.695858i | ||||||
\(400\) | 0.500000 | − | 4.97494i | 0.0250000 | − | 0.248747i | ||||
\(401\) | −10.5831 | − | 10.5831i | −0.528496 | − | 0.528496i | 0.391628 | − | 0.920124i | \(-0.371912\pi\) |
−0.920124 | + | 0.391628i | \(0.871912\pi\) | |||||||
\(402\) | 5.73350 | + | 5.73350i | 0.285961 | + | 0.285961i | ||||
\(403\) | −5.00000 | + | 1.00000i | −0.249068 | + | 0.0498135i | ||||
\(404\) | 19.2665i | 0.958544i | ||||||||
\(405\) | 13.1834 | − | 11.9248i | 0.655087 | − | 0.592549i | ||||
\(406\) | −18.9499 | −0.940466 | ||||||||
\(407\) | 9.94987 | + | 9.94987i | 0.493197 | + | 0.493197i | ||||
\(408\) | 7.31662 | 0.362227 | ||||||||
\(409\) | 23.9499 | + | 23.9499i | 1.18425 | + | 1.18425i | 0.978634 | + | 0.205611i | \(0.0659183\pi\) |
0.205611 | + | 0.978634i | \(0.434082\pi\) | |||||||
\(410\) | −19.9499 | − | 1.00000i | −0.985254 | − | 0.0493865i | ||||
\(411\) | −6.58312 | − | 6.58312i | −0.324722 | − | 0.324722i | ||||
\(412\) | 7.94987 | − | 7.94987i | 0.391662 | − | 0.391662i | ||||
\(413\) | 0.949874 | − | 0.949874i | 0.0467403 | − | 0.0467403i | ||||
\(414\) | −1.05013 | + | 1.05013i | −0.0516109 | + | 0.0516109i | ||||
\(415\) | 10.4749 | − | 9.47494i | 0.514194 | − | 0.465106i | ||||
\(416\) | 2.00000 | − | 3.00000i | 0.0980581 | − | 0.147087i | ||||
\(417\) | 18.4749 | − | 18.4749i | 0.904722 | − | 0.904722i | ||||
\(418\) | −13.2665 | −0.648886 | ||||||||
\(419\) | − | 8.68338i | − | 0.424211i | −0.977247 | − | 0.212105i | \(-0.931968\pi\) | ||
0.977247 | − | 0.212105i | \(-0.0680320\pi\) | |||||||
\(420\) | 10.9749 | + | 0.550126i | 0.535522 | + | 0.0268434i | ||||
\(421\) | −2.47494 | + | 2.47494i | −0.120621 | + | 0.120621i | −0.764841 | − | 0.644220i | \(-0.777182\pi\) |
0.644220 | + | 0.764841i | \(0.277182\pi\) | |||||||
\(422\) | − | 19.9499i | − | 0.971145i | ||||||
\(423\) | 2.94987i | 0.143428i | ||||||||
\(424\) | 9.63325 | − | 9.63325i | 0.467832 | − | 0.467832i | ||||
\(425\) | −17.2916 | + | 14.1332i | −0.838764 | + | 0.685563i | ||||
\(426\) | 6.58312i | 0.318953i | ||||||||
\(427\) | 6.00000 | 0.290360 | ||||||||
\(428\) | 9.63325 | − | 9.63325i | 0.465641 | − | 0.465641i | ||||
\(429\) | −15.3668 | + | 23.0501i | −0.741914 | + | 1.11287i | ||||
\(430\) | 7.81662 | + | 0.391813i | 0.376951 | + | 0.0188949i | ||||
\(431\) | 12.1583 | − | 12.1583i | 0.585645 | − | 0.585645i | −0.350804 | − | 0.936449i | \(-0.614092\pi\) |
0.936449 | + | 0.350804i | \(0.114092\pi\) | |||||||
\(432\) | −3.84169 | + | 3.84169i | −0.184833 | + | 0.184833i | ||||
\(433\) | −12.5251 | + | 12.5251i | −0.601916 | + | 0.601916i | −0.940821 | − | 0.338905i | \(-0.889944\pi\) |
0.338905 | + | 0.940821i | \(0.389944\pi\) | |||||||
\(434\) | 3.00000 | + | 3.00000i | 0.144005 | + | 0.144005i | ||||
\(435\) | 1.15831 | − | 23.1082i | 0.0555368 | − | 1.10795i | ||||
\(436\) | 1.47494 | + | 1.47494i | 0.0706367 | + | 0.0706367i | ||||
\(437\) | −13.2665 | −0.634623 | ||||||||
\(438\) | −4.63325 | − | 4.63325i | −0.221385 | − | 0.221385i | ||||
\(439\) | −33.8997 | −1.61795 | −0.808973 | − | 0.587845i | \(-0.799976\pi\) | ||||
−0.808973 | + | 0.587845i | \(0.799976\pi\) | |||||||
\(440\) | 0.525063 | − | 10.4749i | 0.0250314 | − | 0.499373i | ||||
\(441\) | − | 0.633250i | − | 0.0301547i | ||||||
\(442\) | −15.7916 | + | 3.15831i | −0.751128 | + | 0.150226i | ||||
\(443\) | 20.0581 | + | 20.0581i | 0.952987 | + | 0.952987i | 0.998943 | − | 0.0459562i | \(-0.0146335\pi\) |
−0.0459562 | + | 0.998943i | \(0.514633\pi\) | |||||||
\(444\) | 3.47494 | + | 3.47494i | 0.164913 | + | 0.164913i | ||||
\(445\) | 0.0501256 | − | 1.00000i | 0.00237618 | − | 0.0474045i | ||||
\(446\) | 15.9499i | 0.755248i | ||||||||
\(447\) | 35.4829i | 1.67828i | ||||||||
\(448\) | −3.00000 | −0.141737 | ||||||||
\(449\) | −21.6332 | + | 21.6332i | −1.02094 | + | 1.02094i | −0.0211601 | + | 0.999776i | \(0.506736\pi\) |
−0.999776 | + | 0.0211601i | \(0.993264\pi\) | |||||||
\(450\) | 0.158312 | − | 1.57519i | 0.00746292 | − | 0.0742551i | ||||
\(451\) | −41.8997 | −1.97298 | ||||||||
\(452\) | −2.68338 | − | 2.68338i | −0.126215 | − | 0.126215i | ||||
\(453\) | − | 10.3668i | − | 0.487072i | ||||||
\(454\) | −18.0000 | −0.844782 | ||||||||
\(455\) | −23.9248 | + | 3.55013i | −1.12161 | + | 0.166432i | ||||
\(456\) | −4.63325 | −0.216972 | ||||||||
\(457\) | − | 2.00000i | − | 0.0935561i | −0.998905 | − | 0.0467780i | \(-0.985105\pi\) | ||
0.998905 | − | 0.0467780i | \(-0.0148953\pi\) | |||||||
\(458\) | −3.52506 | − | 3.52506i | −0.164715 | − | 0.164715i | ||||
\(459\) | 24.2665 | 1.13266 | ||||||||
\(460\) | 0.525063 | − | 10.4749i | 0.0244812 | − | 0.488396i | ||||
\(461\) | 4.10819 | − | 4.10819i | 0.191337 | − | 0.191337i | −0.604936 | − | 0.796274i | \(-0.706801\pi\) |
0.796274 | + | 0.604936i | \(0.206801\pi\) | |||||||
\(462\) | 23.0501 | 1.07239 | ||||||||
\(463\) | 9.89975i | 0.460080i | 0.973181 | + | 0.230040i | \(0.0738858\pi\) | ||||
−0.973181 | + | 0.230040i | \(0.926114\pi\) | |||||||
\(464\) | 6.31662i | 0.293242i | ||||||||
\(465\) | −3.84169 | + | 3.47494i | −0.178154 | + | 0.161146i | ||||
\(466\) | −6.79156 | − | 6.79156i | −0.314613 | − | 0.314613i | ||||
\(467\) | 8.36675 | + | 8.36675i | 0.387167 | + | 0.387167i | 0.873676 | − | 0.486509i | \(-0.161730\pi\) |
−0.486509 | + | 0.873676i | \(0.661730\pi\) | |||||||
\(468\) | 0.633250 | − | 0.949874i | 0.0292720 | − | 0.0439080i | ||||
\(469\) | 14.8496i | 0.685692i | ||||||||
\(470\) | −13.9749 | − | 15.4499i | −0.644616 | − | 0.712650i | ||||
\(471\) | −23.1662 | −1.06744 | ||||||||
\(472\) | −0.316625 | − | 0.316625i | −0.0145738 | − | 0.0145738i | ||||
\(473\) | 16.4169 | 0.754849 | ||||||||
\(474\) | −15.0000 | − | 15.0000i | −0.688973 | − | 0.688973i | ||||
\(475\) | 10.9499 | − | 8.94987i | 0.502415 | − | 0.410648i | ||||
\(476\) | 9.47494 | + | 9.47494i | 0.434283 | + | 0.434283i | ||||
\(477\) | 3.05013 | − | 3.05013i | 0.139656 | − | 0.139656i | ||||
\(478\) | 11.8417 | − | 11.8417i | 0.541626 | − | 0.541626i | ||||
\(479\) | −3.15831 | + | 3.15831i | −0.144307 | + | 0.144307i | −0.775569 | − | 0.631262i | \(-0.782537\pi\) |
0.631262 | + | 0.775569i | \(0.282537\pi\) | |||||||
\(480\) | 0.183375 | − | 3.65831i | 0.00836989 | − | 0.166978i | ||||
\(481\) | −9.00000 | − | 6.00000i | −0.410365 | − | 0.273576i | ||||
\(482\) | −16.0000 | + | 16.0000i | −0.728780 | + | 0.728780i | ||||
\(483\) | 23.0501 | 1.04882 | ||||||||
\(484\) | − | 11.0000i | − | 0.500000i | ||||||
\(485\) | −13.4248 | − | 14.8417i | −0.609589 | − | 0.673926i | ||||
\(486\) | −2.31662 | + | 2.31662i | −0.105084 | + | 0.105084i | ||||
\(487\) | − | 2.00000i | − | 0.0906287i | −0.998973 | − | 0.0453143i | \(-0.985571\pi\) | ||
0.998973 | − | 0.0453143i | \(-0.0144289\pi\) | |||||||
\(488\) | − | 2.00000i | − | 0.0905357i | ||||||
\(489\) | 3.41688 | − | 3.41688i | 0.154516 | − | 0.154516i | ||||
\(490\) | 3.00000 | + | 3.31662i | 0.135526 | + | 0.149830i | ||||
\(491\) | 32.6834i | 1.47498i | 0.675358 | + | 0.737490i | \(0.263989\pi\) | ||||
−0.675358 | + | 0.737490i | \(0.736011\pi\) | |||||||
\(492\) | −14.6332 | −0.659718 | ||||||||
\(493\) | 19.9499 | − | 19.9499i | 0.898497 | − | 0.898497i | ||||
\(494\) | 10.0000 | − | 2.00000i | 0.449921 | − | 0.0899843i | ||||
\(495\) | 0.166248 | − | 3.31662i | 0.00747229 | − | 0.149071i | ||||
\(496\) | 1.00000 | − | 1.00000i | 0.0449013 | − | 0.0449013i | ||||
\(497\) | −8.52506 | + | 8.52506i | −0.382401 | + | 0.382401i | ||||
\(498\) | 7.31662 | − | 7.31662i | 0.327866 | − | 0.327866i | ||||
\(499\) | 8.94987 | + | 8.94987i | 0.400651 | + | 0.400651i | 0.878463 | − | 0.477811i | \(-0.158570\pi\) |
−0.477811 | + | 0.878463i | \(0.658570\pi\) | |||||||
\(500\) | 6.63325 | + | 9.00000i | 0.296648 | + | 0.402492i | ||||
\(501\) | −14.6332 | − | 14.6332i | −0.653765 | − | 0.653765i | ||||
\(502\) | 19.2665 | 0.859906 | ||||||||
\(503\) | 1.58312 | + | 1.58312i | 0.0705880 | + | 0.0705880i | 0.741519 | − | 0.670931i | \(-0.234106\pi\) |
−0.670931 | + | 0.741519i | \(0.734106\pi\) | |||||||
\(504\) | −0.949874 | −0.0423108 | ||||||||
\(505\) | −28.8997 | − | 31.9499i | −1.28602 | − | 1.42175i | ||||
\(506\) | − | 22.0000i | − | 0.978019i | ||||||
\(507\) | 8.10819 | − | 19.6913i | 0.360097 | − | 0.874522i | ||||
\(508\) | 7.00000 | + | 7.00000i | 0.310575 | + | 0.310575i | ||||
\(509\) | −15.3166 | − | 15.3166i | −0.678897 | − | 0.678897i | 0.280853 | − | 0.959751i | \(-0.409383\pi\) |
−0.959751 | + | 0.280853i | \(0.909383\pi\) | |||||||
\(510\) | −12.1332 | + | 10.9749i | −0.537269 | + | 0.485978i | ||||
\(511\) | − | 12.0000i | − | 0.530849i | ||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −15.3668 | −0.678459 | ||||||||
\(514\) | −11.8417 | + | 11.8417i | −0.522314 | + | 0.522314i | ||||
\(515\) | −1.25856 | + | 25.1082i | −0.0554589 | + | 1.10640i | ||||
\(516\) | 5.73350 | 0.252403 | ||||||||
\(517\) | −30.8997 | − | 30.8997i | −1.35897 | − | 1.35897i | ||||
\(518\) | 9.00000i | 0.395437i | ||||||||
\(519\) | 7.68338 | 0.337263 | ||||||||
\(520\) | 1.18338 | + | 7.97494i | 0.0518944 | + | 0.349724i | ||||
\(521\) | 10.8997 | 0.477527 | 0.238763 | − | 0.971078i | \(-0.423258\pi\) | ||||
0.238763 | + | 0.971078i | \(0.423258\pi\) | |||||||
\(522\) | 2.00000i | 0.0875376i | ||||||||
\(523\) | −5.00000 | − | 5.00000i | −0.218635 | − | 0.218635i | 0.589288 | − | 0.807923i | \(-0.299408\pi\) |
−0.807923 | + | 0.589288i | \(0.799408\pi\) | |||||||
\(524\) | 3.00000 | 0.131056 | ||||||||
\(525\) | −19.0251 | + | 15.5501i | −0.830322 | + | 0.678663i | ||||
\(526\) | 12.3166 | − | 12.3166i | 0.537030 | − | 0.537030i | ||||
\(527\) | −6.31662 | −0.275156 | ||||||||
\(528\) | − | 7.68338i | − | 0.334376i | ||||||
\(529\) | 1.00000i | 0.0434783i | ||||||||
\(530\) | −1.52506 | + | 30.4248i | −0.0662445 | + | 1.32157i | ||||
\(531\) | −0.100251 | − | 0.100251i | −0.00435053 | − | 0.00435053i | ||||
\(532\) | −6.00000 | − | 6.00000i | −0.260133 | − | 0.260133i | ||||
\(533\) | 31.5831 | − | 6.31662i | 1.36802 | − | 0.273603i | ||||
\(534\) | − | 0.733501i | − | 0.0317417i | ||||||
\(535\) | −1.52506 | + | 30.4248i | −0.0659342 | + | 1.31538i | ||||
\(536\) | 4.94987 | 0.213802 | ||||||||
\(537\) | −17.3747 | − | 17.3747i | −0.749773 | − | 0.749773i | ||||
\(538\) | −13.2665 | −0.571959 | ||||||||
\(539\) | 6.63325 | + | 6.63325i | 0.285714 | + | 0.285714i | ||||
\(540\) | 0.608187 | − | 12.1332i | 0.0261722 | − | 0.522132i | ||||
\(541\) | 4.47494 | + | 4.47494i | 0.192393 | + | 0.192393i | 0.796729 | − | 0.604337i | \(-0.206562\pi\) |
−0.604337 | + | 0.796729i | \(0.706562\pi\) | |||||||
\(542\) | 10.5251 | − | 10.5251i | 0.452090 | − | 0.452090i | ||||
\(543\) | −8.05013 | + | 8.05013i | −0.345464 | + | 0.345464i | ||||
\(544\) | 3.15831 | − | 3.15831i | 0.135412 | − | 0.135412i | ||||
\(545\) | −4.65831 | − | 0.233501i | −0.199540 | − | 0.0100021i | ||||
\(546\) | −17.3747 | + | 3.47494i | −0.743568 | + | 0.148714i | ||||
\(547\) | 21.5251 | − | 21.5251i | 0.920345 | − | 0.920345i | −0.0767083 | − | 0.997054i | \(-0.524441\pi\) |
0.997054 | + | 0.0767083i | \(0.0244410\pi\) | |||||||
\(548\) | −5.68338 | −0.242782 | ||||||||
\(549\) | − | 0.633250i | − | 0.0270264i | ||||||
\(550\) | 14.8417 | + | 18.1583i | 0.632852 | + | 0.774273i | ||||
\(551\) | −12.6332 | + | 12.6332i | −0.538195 | + | 0.538195i | ||||
\(552\) | − | 7.68338i | − | 0.327026i | ||||||
\(553\) | − | 38.8496i | − | 1.65205i | ||||||
\(554\) | −21.8997 | + | 21.8997i | −0.930431 | + | 0.930431i | ||||
\(555\) | −10.9749 | − | 0.550126i | −0.465860 | − | 0.0233515i | ||||
\(556\) | − | 15.9499i | − | 0.676425i | ||||||
\(557\) | 4.58312 | 0.194193 | 0.0970966 | − | 0.995275i | \(-0.469044\pi\) | ||||
0.0970966 | + | 0.995275i | \(0.469044\pi\) | |||||||
\(558\) | 0.316625 | − | 0.316625i | 0.0134038 | − | 0.0134038i | ||||
\(559\) | −12.3747 | + | 2.47494i | −0.523393 | + | 0.104679i | ||||
\(560\) | 4.97494 | − | 4.50000i | 0.210229 | − | 0.190160i | ||||
\(561\) | −24.2665 | + | 24.2665i | −1.02453 | + | 1.02453i | ||||
\(562\) | 11.6834 | − | 11.6834i | 0.492833 | − | 0.492833i | ||||
\(563\) | −6.79156 | + | 6.79156i | −0.286230 | + | 0.286230i | −0.835588 | − | 0.549357i | \(-0.814873\pi\) |
0.549357 | + | 0.835588i | \(0.314873\pi\) | |||||||
\(564\) | −10.7916 | − | 10.7916i | −0.454407 | − | 0.454407i | ||||
\(565\) | 8.47494 | + | 0.424812i | 0.356543 | + | 0.0178720i | ||||
\(566\) | −7.94987 | − | 7.94987i | −0.334158 | − | 0.334158i | ||||
\(567\) | 23.8496 | 1.00159 | ||||||||
\(568\) | 2.84169 | + | 2.84169i | 0.119235 | + | 0.119235i | ||||
\(569\) | 42.7995 | 1.79425 | 0.897124 | − | 0.441779i | \(-0.145652\pi\) | ||||
0.897124 | + | 0.441779i | \(0.145652\pi\) | |||||||
\(570\) | 7.68338 | − | 6.94987i | 0.321821 | − | 0.291098i | ||||
\(571\) | 28.8997i | 1.20942i | 0.796447 | + | 0.604708i | \(0.206710\pi\) | ||||
−0.796447 | + | 0.604708i | \(0.793290\pi\) | |||||||
\(572\) | 3.31662 | + | 16.5831i | 0.138675 | + | 0.693375i | ||||
\(573\) | −5.84962 | − | 5.84962i | −0.244372 | − | 0.244372i | ||||
\(574\) | −18.9499 | − | 18.9499i | −0.790952 | − | 0.790952i | ||||
\(575\) | 14.8417 | + | 18.1583i | 0.618941 | + | 0.757254i | ||||
\(576\) | 0.316625i | 0.0131927i | ||||||||
\(577\) | 41.8997i | 1.74431i | 0.489230 | + | 0.872155i | \(0.337278\pi\) | ||||
−0.489230 | + | 0.872155i | \(0.662722\pi\) | |||||||
\(578\) | −2.94987 | −0.122699 | ||||||||
\(579\) | −12.6834 | + | 12.6834i | −0.527103 | + | 0.527103i | ||||
\(580\) | −9.47494 | − | 10.4749i | −0.393425 | − | 0.434948i | ||||
\(581\) | 18.9499 | 0.786173 | ||||||||
\(582\) | −10.3668 | − | 10.3668i | −0.429716 | − | 0.429716i | ||||
\(583\) | 63.8997i | 2.64646i | ||||||||
\(584\) | −4.00000 | −0.165521 | ||||||||
\(585\) | 0.374686 | + | 2.52506i | 0.0154914 | + | 0.104398i | ||||
\(586\) | 22.8997 | 0.945980 | ||||||||
\(587\) | 24.9499i | 1.02979i | 0.857253 | + | 0.514896i | \(0.172169\pi\) | ||||
−0.857253 | + | 0.514896i | \(0.827831\pi\) | |||||||
\(588\) | 2.31662 | + | 2.31662i | 0.0955360 | + | 0.0955360i | ||||
\(589\) | 4.00000 | 0.164817 | ||||||||
\(590\) | 1.00000 | + | 0.0501256i | 0.0411693 | + | 0.00206364i | ||||
\(591\) | −4.57519 | + | 4.57519i | −0.188198 | + | 0.188198i | ||||
\(592\) | 3.00000 | 0.123299 | ||||||||
\(593\) | 12.9499i | 0.531788i | 0.964002 | + | 0.265894i | \(0.0856671\pi\) | ||||
−0.964002 | + | 0.265894i | \(0.914333\pi\) | |||||||
\(594\) | − | 25.4829i | − | 1.04557i | ||||||
\(595\) | −29.9248 | − | 1.50000i | −1.22680 | − | 0.0614940i | ||||
\(596\) | 15.3166 | + | 15.3166i | 0.627393 | + | 0.627393i | ||||
\(597\) | −19.6332 | − | 19.6332i | −0.803535 | − | 0.803535i | ||||
\(598\) | 3.31662 | + | 16.5831i | 0.135627 | + | 0.678134i | ||||
\(599\) | 13.2665i | 0.542054i | 0.962572 | + | 0.271027i | \(0.0873633\pi\) | ||||
−0.962572 | + | 0.271027i | \(0.912637\pi\) | |||||||
\(600\) | 5.18338 | + | 6.34169i | 0.211610 | + | 0.258898i | ||||
\(601\) | −6.05013 | −0.246790 | −0.123395 | − | 0.992358i | \(-0.539378\pi\) | ||||
−0.123395 | + | 0.992358i | \(0.539378\pi\) | |||||||
\(602\) | 7.42481 | + | 7.42481i | 0.302613 | + | 0.302613i | ||||
\(603\) | 1.56725 | 0.0638235 | ||||||||
\(604\) | −4.47494 | − | 4.47494i | −0.182083 | − | 0.182083i | ||||
\(605\) | 16.5000 | + | 18.2414i | 0.670820 | + | 0.741620i | ||||
\(606\) | −22.3166 | − | 22.3166i | −0.906551 | − | 0.906551i | ||||
\(607\) | 3.05013 | − | 3.05013i | 0.123801 | − | 0.123801i | −0.642492 | − | 0.766293i | \(-0.722099\pi\) |
0.766293 | + | 0.642492i | \(0.222099\pi\) | |||||||
\(608\) | −2.00000 | + | 2.00000i | −0.0811107 | + | 0.0811107i | ||||
\(609\) | 21.9499 | − | 21.9499i | 0.889454 | − | 0.889454i | ||||
\(610\) | 3.00000 | + | 3.31662i | 0.121466 | + | 0.134286i | ||||
\(611\) | 27.9499 | + | 18.6332i | 1.13073 | + | 0.753821i | ||||
\(612\) | 1.00000 | − | 1.00000i | 0.0404226 | − | 0.0404226i | ||||
\(613\) | 24.0000 | 0.969351 | 0.484675 | − | 0.874694i | \(-0.338938\pi\) | ||||
0.484675 | + | 0.874694i | \(0.338938\pi\) | |||||||
\(614\) | − | 25.8997i | − | 1.04523i | ||||||
\(615\) | 24.2665 | − | 21.9499i | 0.978520 | − | 0.885104i | ||||
\(616\) | 9.94987 | − | 9.94987i | 0.400892 | − | 0.400892i | ||||
\(617\) | − | 12.0000i | − | 0.483102i | −0.970388 | − | 0.241551i | \(-0.922344\pi\) | ||
0.970388 | − | 0.241551i | \(-0.0776561\pi\) | |||||||
\(618\) | 18.4169i | 0.740835i | ||||||||
\(619\) | 21.8997 | − | 21.8997i | 0.880225 | − | 0.880225i | −0.113332 | − | 0.993557i | \(-0.536152\pi\) |
0.993557 | + | 0.113332i | \(0.0361524\pi\) | |||||||
\(620\) | −0.158312 | + | 3.15831i | −0.00635798 | + | 0.126841i | ||||
\(621\) | − | 25.4829i | − | 1.02259i | ||||||
\(622\) | 19.2665 | 0.772516 | ||||||||
\(623\) | 0.949874 | − | 0.949874i | 0.0380559 | − | 0.0380559i | ||||
\(624\) | 1.15831 | + | 5.79156i | 0.0463696 | + | 0.231848i | ||||
\(625\) | −24.5000 | − | 4.97494i | −0.980000 | − | 0.198997i | ||||
\(626\) | 15.4248 | − | 15.4248i | 0.616499 | − | 0.616499i | ||||
\(627\) | 15.3668 | − | 15.3668i | 0.613689 | − | 0.613689i | ||||
\(628\) | −10.0000 | + | 10.0000i | −0.399043 | + | 0.399043i | ||||
\(629\) | −9.47494 | − | 9.47494i | −0.377790 | − | 0.377790i | ||||
\(630\) | 1.57519 | − | 1.42481i | 0.0627570 | − | 0.0567659i | ||||
\(631\) | 4.47494 | + | 4.47494i | 0.178144 | + | 0.178144i | 0.790546 | − | 0.612402i | \(-0.209797\pi\) |
−0.612402 | + | 0.790546i | \(0.709797\pi\) | |||||||
\(632\) | −12.9499 | −0.515118 | ||||||||
\(633\) | 23.1082 | + | 23.1082i | 0.918468 | + | 0.918468i | ||||
\(634\) | 12.0000 | 0.476581 | ||||||||
\(635\) | −22.1082 | − | 1.10819i | −0.877337 | − | 0.0439771i | ||||
\(636\) | 22.3166i | 0.884912i | ||||||||
\(637\) | −6.00000 | − | 4.00000i | −0.237729 | − | 0.158486i | ||||
\(638\) | −20.9499 | − | 20.9499i | −0.829413 | − | 0.829413i | ||||
\(639\) | 0.899749 | + | 0.899749i | 0.0355935 | + | 0.0355935i | ||||
\(640\) | −1.50000 | − | 1.65831i | −0.0592927 | − | 0.0655506i | ||||
\(641\) | − | 5.36675i | − | 0.211974i | −0.994368 | − | 0.105987i | \(-0.966200\pi\) | ||
0.994368 | − | 0.105987i | \(-0.0338002\pi\) | |||||||
\(642\) | 22.3166i | 0.880767i | ||||||||
\(643\) | −12.9499 | −0.510693 | −0.255347 | − | 0.966850i | \(-0.582190\pi\) | ||||
−0.255347 | + | 0.966850i | \(0.582190\pi\) | |||||||
\(644\) | 9.94987 | − | 9.94987i | 0.392080 | − | 0.392080i | ||||
\(645\) | −9.50794 | + | 8.60025i | −0.374375 | + | 0.338635i | ||||
\(646\) | 12.6332 | 0.497049 | ||||||||
\(647\) | −6.63325 | − | 6.63325i | −0.260780 | − | 0.260780i | 0.564591 | − | 0.825371i | \(-0.309034\pi\) |
−0.825371 | + | 0.564591i | \(0.809034\pi\) | |||||||
\(648\) | − | 7.94987i | − | 0.312301i | ||||||
\(649\) | 2.10025 | 0.0824421 | ||||||||
\(650\) | −13.9248 | − | 11.4499i | −0.546176 | − | 0.449101i | ||||
\(651\) | −6.94987 | −0.272387 | ||||||||
\(652\) | − | 2.94987i | − | 0.115526i | ||||||
\(653\) | 31.5831 | + | 31.5831i | 1.23594 | + | 1.23594i | 0.961645 | + | 0.274299i | \(0.0884457\pi\) |
0.274299 | + | 0.961645i | \(0.411554\pi\) | |||||||
\(654\) | −3.41688 | −0.133610 | ||||||||
\(655\) | −4.97494 | + | 4.50000i | −0.194387 | + | 0.175830i | ||||
\(656\) | −6.31662 | + | 6.31662i | −0.246623 | + | 0.246623i | ||||
\(657\) | −1.26650 | −0.0494108 | ||||||||
\(658\) | − | 27.9499i | − | 1.08960i | ||||||
\(659\) | − | 0.633250i | − | 0.0246679i | −0.999924 | − | 0.0123340i | \(-0.996074\pi\) | ||
0.999924 | − | 0.0123340i | \(-0.00392612\pi\) | |||||||
\(660\) | 11.5251 | + | 12.7414i | 0.448612 | + | 0.495960i | ||||
\(661\) | −12.8997 | − | 12.8997i | −0.501742 | − | 0.501742i | 0.410237 | − | 0.911979i | \(-0.365446\pi\) |
−0.911979 | + | 0.410237i | \(0.865446\pi\) | |||||||
\(662\) | 1.00000 | + | 1.00000i | 0.0388661 | + | 0.0388661i | ||||
\(663\) | 14.6332 | − | 21.9499i | 0.568308 | − | 0.852462i | ||||
\(664\) | − | 6.31662i | − | 0.245133i | ||||||
\(665\) | 18.9499 | + | 0.949874i | 0.734845 | + | 0.0368345i | ||||
\(666\) | 0.949874 | 0.0368069 | ||||||||
\(667\) | −20.9499 | − | 20.9499i | −0.811182 | − | 0.811182i | ||||
\(668\) | −12.6332 | −0.488795 | ||||||||
\(669\) | −18.4749 | − | 18.4749i | −0.714282 | − | 0.714282i | ||||
\(670\) | −8.20844 | + | 7.42481i | −0.317120 | + | 0.286845i | ||||
\(671\) | 6.63325 | + | 6.63325i | 0.256074 | + | 0.256074i | ||||
\(672\) | 3.47494 | − | 3.47494i | 0.134049 | − | 0.134049i | ||||
\(673\) | −11.4248 | + | 11.4248i | −0.440394 | + | 0.440394i | −0.892144 | − | 0.451750i | \(-0.850800\pi\) |
0.451750 | + | 0.892144i | \(0.350800\pi\) | |||||||
\(674\) | 3.52506 | − | 3.52506i | 0.135780 | − | 0.135780i | ||||
\(675\) | 17.1913 | + | 21.0330i | 0.661694 | + | 0.809560i | ||||
\(676\) | −5.00000 | − | 12.0000i | −0.192308 | − | 0.461538i | ||||
\(677\) | −2.68338 | + | 2.68338i | −0.103130 | + | 0.103130i | −0.756789 | − | 0.653659i | \(-0.773233\pi\) |
0.653659 | + | 0.756789i | \(0.273233\pi\) | |||||||
\(678\) | 6.21637 | 0.238738 | ||||||||
\(679\) | − | 26.8496i | − | 1.03039i | ||||||
\(680\) | −0.500000 | + | 9.97494i | −0.0191741 | + | 0.382521i | ||||
\(681\) | 20.8496 | − | 20.8496i | 0.798959 | − | 0.798959i | ||||
\(682\) | 6.63325i | 0.254000i | ||||||||
\(683\) | − | 30.9499i | − | 1.18426i | −0.805841 | − | 0.592132i | \(-0.798286\pi\) | ||
0.805841 | − | 0.592132i | \(-0.201714\pi\) | |||||||
\(684\) | −0.633250 | + | 0.633250i | −0.0242129 | + | 0.0242129i | ||||
\(685\) | 9.42481 | − | 8.52506i | 0.360104 | − | 0.325726i | ||||
\(686\) | − | 15.0000i | − | 0.572703i | ||||||
\(687\) | 8.16625 | 0.311562 | ||||||||
\(688\) | 2.47494 | − | 2.47494i | 0.0943561 | − | 0.0943561i | ||||
\(689\) | −9.63325 | − | 48.1662i | −0.366998 | − | 1.83499i | ||||
\(690\) | 11.5251 | + | 12.7414i | 0.438752 | + | 0.485058i | ||||
\(691\) | −14.0000 | + | 14.0000i | −0.532585 | + | 0.532585i | −0.921341 | − | 0.388756i | \(-0.872905\pi\) |
0.388756 | + | 0.921341i | \(0.372905\pi\) | |||||||
\(692\) | 3.31662 | − | 3.31662i | 0.126079 | − | 0.126079i | ||||
\(693\) | 3.15038 | − | 3.15038i | 0.119673 | − | 0.119673i | ||||
\(694\) | 0.791562 | + | 0.791562i | 0.0300473 | + | 0.0300473i | ||||
\(695\) | 23.9248 | + | 26.4499i | 0.907520 | + | 1.00330i | ||||
\(696\) | −7.31662 | − | 7.31662i | −0.277336 | − | 0.277336i | ||||
\(697\) | 39.8997 | 1.51131 | ||||||||
\(698\) | 18.4248 | + | 18.4248i | 0.697389 | + | 0.697389i | ||||
\(699\) | 15.7335 | 0.595096 | ||||||||
\(700\) | −1.50000 | + | 14.9248i | −0.0566947 | + | 0.564105i | ||||
\(701\) | 45.4829i | 1.71786i | 0.512089 | + | 0.858932i | \(0.328872\pi\) | ||||
−0.512089 | + | 0.858932i | \(0.671128\pi\) | |||||||
\(702\) | 3.84169 | + | 19.2084i | 0.144995 | + | 0.724976i | ||||
\(703\) | 6.00000 | + | 6.00000i | 0.226294 | + | 0.226294i | ||||
\(704\) | −3.31662 | − | 3.31662i | −0.125000 | − | 0.125000i | ||||
\(705\) | 34.0831 | + | 1.70844i | 1.28364 | + | 0.0643435i | ||||
\(706\) | − | 7.58312i | − | 0.285395i | ||||||
\(707\) | − | 57.7995i | − | 2.17377i | ||||||
\(708\) | 0.733501 | 0.0275666 | ||||||||
\(709\) | 29.9499 | − | 29.9499i | 1.12479 | − | 1.12479i | 0.133780 | − | 0.991011i | \(-0.457288\pi\) |
0.991011 | − | 0.133780i | \(-0.0427116\pi\) | |||||||
\(710\) | −8.97494 | − | 0.449874i | −0.336823 | − | 0.0168835i | ||||
\(711\) | −4.10025 | −0.153771 | ||||||||
\(712\) | −0.316625 | − | 0.316625i | −0.0118660 | − | 0.0118660i | ||||
\(713\) | 6.63325i | 0.248417i | ||||||||
\(714\) | −21.9499 | −0.821453 | ||||||||
\(715\) | −30.3747 | − | 22.5251i | −1.13595 | − | 0.842390i | ||||
\(716\) | −15.0000 | −0.560576 | ||||||||
\(717\) | 27.4327i | 1.02449i | ||||||||
\(718\) | 22.2665 | + | 22.2665i | 0.830978 | + | 0.830978i | ||||
\(719\) | −6.94987 | −0.259187 | −0.129593 | − | 0.991567i | \(-0.541367\pi\) | ||||
−0.129593 | + | 0.991567i | \(0.541367\pi\) | |||||||
\(720\) | −0.474937 | − | 0.525063i | −0.0176999 | − | 0.0195679i | ||||
\(721\) | −23.8496 | + | 23.8496i | −0.888206 | + | 0.888206i | ||||
\(722\) | 11.0000 | 0.409378 | ||||||||
\(723\) | − | 37.0660i | − | 1.37850i | ||||||
\(724\) | 6.94987i | 0.258290i | ||||||||
\(725\) | 31.4248 | + | 3.15831i | 1.16709 | + | 0.117297i | ||||
\(726\) | 12.7414 | + | 12.7414i | 0.472879 | + | 0.472879i | ||||
\(727\) | −13.9499 | − | 13.9499i | −0.517372 | − | 0.517372i | 0.399403 | − | 0.916775i | \(-0.369217\pi\) |
−0.916775 | + | 0.399403i | \(0.869217\pi\) | |||||||
\(728\) | −6.00000 | + | 9.00000i | −0.222375 | + | 0.333562i | ||||
\(729\) | − | 29.2164i | − | 1.08209i | ||||||
\(730\) | 6.63325 | − | 6.00000i | 0.245508 | − | 0.222070i | ||||
\(731\) | −15.6332 | −0.578217 | ||||||||
\(732\) | 2.31662 | + | 2.31662i | 0.0856249 | + | 0.0856249i | ||||
\(733\) | 36.7995 | 1.35922 | 0.679610 | − | 0.733573i | \(-0.262149\pi\) | ||||
0.679610 | + | 0.733573i | \(0.262149\pi\) | |||||||
\(734\) | 1.94987 | + | 1.94987i | 0.0719712 | + | 0.0719712i | ||||
\(735\) | −7.31662 | − | 0.366750i | −0.269878 | − | 0.0135278i | ||||
\(736\) | −3.31662 | − | 3.31662i | −0.122252 | − | 0.122252i | ||||
\(737\) | −16.4169 | + | 16.4169i | −0.604723 | + | 0.604723i | ||||
\(738\) | −2.00000 | + | 2.00000i | −0.0736210 | + | 0.0736210i | ||||
\(739\) | −35.8997 | + | 35.8997i | −1.32059 | + | 1.32059i | −0.407299 | + | 0.913295i | \(0.633529\pi\) |
−0.913295 | + | 0.407299i | \(0.866471\pi\) | |||||||
\(740\) | −4.97494 | + | 4.50000i | −0.182882 | + | 0.165423i | ||||
\(741\) | −9.26650 | + | 13.8997i | −0.340413 | + | 0.510620i | ||||
\(742\) | −28.8997 | + | 28.8997i | −1.06094 | + | 1.06094i | ||||
\(743\) | −15.6332 | −0.573528 | −0.286764 | − | 0.958001i | \(-0.592580\pi\) | ||||
−0.286764 | + | 0.958001i | \(0.592580\pi\) | |||||||
\(744\) | 2.31662i | 0.0849316i | ||||||||
\(745\) | −48.3747 | − | 2.42481i | −1.77231 | − | 0.0888382i | ||||
\(746\) | 20.0000 | − | 20.0000i | 0.732252 | − | 0.732252i | ||||
\(747\) | − | 2.00000i | − | 0.0731762i | ||||||
\(748\) | 20.9499i | 0.766003i | ||||||||
\(749\) | −28.8997 | + | 28.8997i | −1.05597 | + | 1.05597i | ||||
\(750\) | −18.1082 | − | 2.74144i | −0.661217 | − | 0.100103i | ||||
\(751\) | 13.8997i | 0.507209i | 0.967308 | + | 0.253605i | \(0.0816162\pi\) | ||||
−0.967308 | + | 0.253605i | \(0.918384\pi\) | |||||||
\(752\) | −9.31662 | −0.339742 | ||||||||
\(753\) | −22.3166 | + | 22.3166i | −0.813263 | + | 0.813263i | ||||
\(754\) | 18.9499 | + | 12.6332i | 0.690114 | + | 0.460076i | ||||
\(755\) | 14.1332 | + | 0.708438i | 0.514362 | + | 0.0257827i | ||||
\(756\) | 11.5251 | − | 11.5251i | 0.419162 | − | 0.419162i | ||||
\(757\) | −5.00000 | + | 5.00000i | −0.181728 | + | 0.181728i | −0.792108 | − | 0.610380i | \(-0.791017\pi\) |
0.610380 | + | 0.792108i | \(0.291017\pi\) | |||||||
\(758\) | 13.0000 | − | 13.0000i | 0.472181 | − | 0.472181i | ||||
\(759\) | 25.4829 | + | 25.4829i | 0.924970 | + | 0.924970i | ||||
\(760\) | 0.316625 | − | 6.31662i | 0.0114852 | − | 0.229128i | ||||
\(761\) | −25.5831 | − | 25.5831i | −0.927388 | − | 0.927388i | 0.0701490 | − | 0.997537i | \(-0.477653\pi\) |
−0.997537 | + | 0.0701490i | \(0.977653\pi\) | |||||||
\(762\) | −16.2164 | −0.587457 | ||||||||
\(763\) | −4.42481 | − | 4.42481i | −0.160189 | − | 0.160189i | ||||
\(764\) | −5.05013 | −0.182707 | ||||||||
\(765\) | −0.158312 | + | 3.15831i | −0.00572380 | + | 0.114189i | ||||
\(766\) | 14.3668i | 0.519092i | ||||||||
\(767\) | −1.58312 | + | 0.316625i | −0.0571633 | + | 0.0114327i | ||||
\(768\) | −1.15831 | − | 1.15831i | −0.0417970 | − | 0.0417970i | ||||
\(769\) | −4.94987 | − | 4.94987i | −0.178497 | − | 0.178497i | 0.612203 | − | 0.790700i | \(-0.290283\pi\) |
−0.790700 | + | 0.612203i | \(0.790283\pi\) | |||||||
\(770\) | −1.57519 | + | 31.4248i | −0.0567659 | + | 1.13247i | ||||
\(771\) | − | 27.4327i | − | 0.987966i | ||||||
\(772\) | 10.9499i | 0.394095i | ||||||||
\(773\) | −22.5831 | −0.812259 | −0.406129 | − | 0.913816i | \(-0.633122\pi\) | ||||
−0.406129 | + | 0.913816i | \(0.633122\pi\) | |||||||
\(774\) | 0.783626 | − | 0.783626i | 0.0281669 | − | 0.0281669i | ||||
\(775\) | −4.47494 | − | 5.47494i | −0.160744 | − | 0.196666i | ||||
\(776\) | −8.94987 | −0.321282 | ||||||||
\(777\) | −10.4248 | − | 10.4248i | −0.373988 | − | 0.373988i | ||||
\(778\) | − | 13.8997i | − | 0.498330i | ||||||
\(779\) | −25.2665 | −0.905266 | ||||||||
\(780\) | −10.6082 | − | 7.86675i | −0.379834 | − | 0.281675i | ||||
\(781\) | −18.8496 | −0.674493 | ||||||||
\(782\) | 20.9499i | 0.749166i | ||||||||
\(783\) | −24.2665 | − | 24.2665i | −0.867214 | − | 0.867214i | ||||
\(784\) | 2.00000 | 0.0714286 | ||||||||
\(785\) | 1.58312 | − | 31.5831i | 0.0565041 | − | 1.12725i | ||||
\(786\) | −3.47494 | + | 3.47494i | −0.123947 | + | 0.123947i | ||||
\(787\) | −25.8997 | −0.923226 | −0.461613 | − | 0.887081i | \(-0.652729\pi\) | ||||
−0.461613 | + | 0.887081i | \(0.652729\pi\) | |||||||
\(788\) | 3.94987i | 0.140708i | ||||||||
\(789\) | 28.5330i | 1.01580i | ||||||||
\(790\) | 21.4749 | − | 19.4248i | 0.764044 | − | 0.691104i | ||||
\(791\) | 8.05013 | + | 8.05013i | 0.286230 | + | 0.286230i | ||||
\(792\) | −1.05013 | − | 1.05013i | −0.0373146 | − | 0.0373146i | ||||
\(793\) | −6.00000 | − | 4.00000i | −0.213066 | − | 0.142044i | ||||
\(794\) | 18.0000i | 0.638796i | ||||||||
\(795\) | −33.4749 | − | 37.0079i | −1.18723 | − | 1.31254i | ||||
\(796\) | −16.9499 | −0.600772 | ||||||||
\(797\) | 7.26650 | + | 7.26650i | 0.257393 | + | 0.257393i | 0.823993 | − | 0.566600i | \(-0.191742\pi\) |
−0.566600 | + | 0.823993i | \(0.691742\pi\) | |||||||
\(798\) | 13.8997 | 0.492046 | ||||||||
\(799\) | 29.4248 | + | 29.4248i | 1.04098 | + | 1.04098i | ||||
\(800\) | 4.97494 | + | 0.500000i | 0.175891 | + | 0.0176777i | ||||
\(801\) | −0.100251 | − | 0.100251i | −0.00354220 | − | 0.00354220i | ||||
\(802\) | 10.5831 | − | 10.5831i | 0.373703 | − | 0.373703i | ||||
\(803\) | 13.2665 | − | 13.2665i | 0.468165 | − | 0.468165i | ||||
\(804\) | −5.73350 | + | 5.73350i | −0.202205 | + | 0.202205i | ||||
\(805\) | −1.57519 | + | 31.4248i | −0.0555181 | + | 1.10758i | ||||
\(806\) | −1.00000 | − | 5.00000i | −0.0352235 | − | 0.176117i | ||||
\(807\) | 15.3668 | − | 15.3668i | 0.540935 | − | 0.540935i | ||||
\(808\) | −19.2665 | −0.677793 | ||||||||
\(809\) | 14.3668i | 0.505108i | 0.967583 | + | 0.252554i | \(0.0812705\pi\) | ||||
−0.967583 | + | 0.252554i | \(0.918729\pi\) | |||||||
\(810\) | 11.9248 | + | 13.1834i | 0.418995 | + | 0.463217i | ||||
\(811\) | 22.9499 | − | 22.9499i | 0.805879 | − | 0.805879i | −0.178128 | − | 0.984007i | \(-0.557004\pi\) |
0.984007 | + | 0.178128i | \(0.0570042\pi\) | |||||||
\(812\) | − | 18.9499i | − | 0.665010i | ||||||
\(813\) | 24.3826i | 0.855136i | ||||||||
\(814\) | −9.94987 | + | 9.94987i | −0.348743 | + | 0.348743i | ||||
\(815\) | 4.42481 | + | 4.89181i | 0.154994 | + | 0.171353i | ||||
\(816\) | 7.31662i | 0.256133i | ||||||||
\(817\) | 9.89975 | 0.346348 | ||||||||
\(818\) | −23.9499 | + | 23.9499i | −0.837388 | + | 0.837388i | ||||
\(819\) | −1.89975 | + | 2.84962i | −0.0663826 | + | 0.0995739i | ||||
\(820\) | 1.00000 | − | 19.9499i | 0.0349215 | − | 0.696680i | ||||
\(821\) | −24.7916 | + | 24.7916i | −0.865231 | + | 0.865231i | −0.991940 | − | 0.126709i | \(-0.959559\pi\) |
0.126709 | + | 0.991940i | \(0.459559\pi\) | |||||||
\(822\) | 6.58312 | − | 6.58312i | 0.229613 | − | 0.229613i | ||||
\(823\) | 27.8997 | − | 27.8997i | 0.972524 | − | 0.972524i | −0.0271084 | − | 0.999632i | \(-0.508630\pi\) |
0.999632 | + | 0.0271084i | \(0.00862993\pi\) | |||||||
\(824\) | 7.94987 | + | 7.94987i | 0.276947 | + | 0.276947i | ||||
\(825\) | −38.2243 | − | 3.84169i | −1.33080 | − | 0.133750i | ||||
\(826\) | 0.949874 | + | 0.949874i | 0.0330504 | + | 0.0330504i | ||||
\(827\) | −31.2665 | −1.08724 | −0.543621 | − | 0.839331i | \(-0.682947\pi\) | ||||
−0.543621 | + | 0.839331i | \(0.682947\pi\) | |||||||
\(828\) | −1.05013 | − | 1.05013i | −0.0364944 | − | 0.0364944i | ||||
\(829\) | 30.8496 | 1.07145 | 0.535726 | − | 0.844392i | \(-0.320038\pi\) | ||||
0.535726 | + | 0.844392i | \(0.320038\pi\) | |||||||
\(830\) | 9.47494 | + | 10.4749i | 0.328880 | + | 0.363590i | ||||
\(831\) | − | 50.7335i | − | 1.75993i | ||||||
\(832\) | 3.00000 | + | 2.00000i | 0.104006 | + | 0.0693375i | ||||
\(833\) | −6.31662 | − | 6.31662i | −0.218858 | − | 0.218858i | ||||
\(834\) | 18.4749 | + | 18.4749i | 0.639735 | + | 0.639735i | ||||
\(835\) | 20.9499 | − | 18.9499i | 0.725000 | − | 0.655787i | ||||
\(836\) | − | 13.2665i | − | 0.458831i | ||||||
\(837\) | 7.68338i | 0.265576i | ||||||||
\(838\) | 8.68338 | 0.299962 | ||||||||
\(839\) | −21.6332 | + | 21.6332i | −0.746863 | + | 0.746863i | −0.973889 | − | 0.227026i | \(-0.927100\pi\) |
0.227026 | + | 0.973889i | \(0.427100\pi\) | |||||||
\(840\) | −0.550126 | + | 10.9749i | −0.0189811 | + | 0.378671i | ||||
\(841\) | −10.8997 | −0.375853 | ||||||||
\(842\) | −2.47494 | − | 2.47494i | −0.0852920 | − | 0.0852920i | ||||
\(843\) | 27.0660i | 0.932202i | ||||||||
\(844\) | 19.9499 | 0.686703 | ||||||||
\(845\) | 26.2916 | + | 12.3997i | 0.904457 | + | 0.426564i | ||||
\(846\) | −2.94987 | −0.101419 | ||||||||
\(847\) | 33.0000i | 1.13389i | ||||||||
\(848\) | 9.63325 | + | 9.63325i | 0.330807 | + | 0.330807i | ||||
\(849\) | 18.4169 | 0.632066 | ||||||||
\(850\) | −14.1332 | − | 17.2916i | −0.484766 | − | 0.593096i | ||||
\(851\) | −9.94987 | + | 9.94987i | −0.341077 | + | 0.341077i | ||||
\(852\) | −6.58312 | −0.225534 | ||||||||
\(853\) | 4.05013i | 0.138674i | 0.997593 | + | 0.0693368i | \(0.0220883\pi\) | ||||
−0.997593 | + | 0.0693368i | \(0.977912\pi\) | |||||||
\(854\) | 6.00000i | 0.205316i | ||||||||
\(855\) | 0.100251 | − | 2.00000i | 0.00342852 | − | 0.0683986i | ||||
\(856\) | 9.63325 | + | 9.63325i | 0.329258 | + | 0.329258i | ||||
\(857\) | 15.3166 | + | 15.3166i | 0.523206 | + | 0.523206i | 0.918538 | − | 0.395332i | \(-0.129371\pi\) |
−0.395332 | + | 0.918538i | \(0.629371\pi\) | |||||||
\(858\) | −23.0501 | − | 15.3668i | −0.786918 | − | 0.524612i | ||||
\(859\) | − | 19.8997i | − | 0.678971i | −0.940611 | − | 0.339485i | \(-0.889747\pi\) | ||
0.940611 | − | 0.339485i | \(-0.110253\pi\) | |||||||
\(860\) | −0.391813 | + | 7.81662i | −0.0133607 | + | 0.266545i | ||||
\(861\) | 43.8997 | 1.49610 | ||||||||
\(862\) | 12.1583 | + | 12.1583i | 0.414114 | + | 0.414114i | ||||
\(863\) | −22.5831 | −0.768738 | −0.384369 | − | 0.923179i | \(-0.625581\pi\) | ||||
−0.384369 | + | 0.923179i | \(0.625581\pi\) | |||||||
\(864\) | −3.84169 | − | 3.84169i | −0.130697 | − | 0.130697i | ||||
\(865\) | −0.525063 | + | 10.4749i | −0.0178527 | + | 0.356159i | ||||
\(866\) | −12.5251 | − | 12.5251i | −0.425619 | − | 0.425619i | ||||
\(867\) | 3.41688 | − | 3.41688i | 0.116043 | − | 0.116043i | ||||
\(868\) | −3.00000 | + | 3.00000i | −0.101827 | + | 0.101827i | ||||
\(869\) | 42.9499 | − | 42.9499i | 1.45697 | − | 1.45697i | ||||
\(870\) | 23.1082 | + | 1.15831i | 0.783441 | + | 0.0392705i | ||||
\(871\) | 9.89975 | − | 14.8496i | 0.335440 | − | 0.503160i | ||||
\(872\) | −1.47494 | + | 1.47494i | −0.0499477 | + | 0.0499477i | ||||
\(873\) | −2.83375 | −0.0959080 | ||||||||
\(874\) | − | 13.2665i | − | 0.448746i | ||||||
\(875\) | −19.8997 | − | 27.0000i | −0.672734 | − | 0.912767i | ||||
\(876\) | 4.63325 | − | 4.63325i | 0.156543 | − | 0.156543i | ||||
\(877\) | 6.05013i | 0.204298i | 0.994769 | + | 0.102149i | \(0.0325719\pi\) | ||||
−0.994769 | + | 0.102149i | \(0.967428\pi\) | |||||||
\(878\) | − | 33.8997i | − | 1.14406i | ||||||
\(879\) | −26.5251 | + | 26.5251i | −0.894668 | + | 0.894668i | ||||
\(880\) | 10.4749 | + | 0.525063i | 0.353110 | + | 0.0176999i | ||||
\(881\) | 16.5831i | 0.558700i | 0.960189 | + | 0.279350i | \(0.0901189\pi\) | ||||
−0.960189 | + | 0.279350i | \(0.909881\pi\) | |||||||
\(882\) | 0.633250 | 0.0213226 | ||||||||
\(883\) | 24.4248 | − | 24.4248i | 0.821960 | − | 0.821960i | −0.164429 | − | 0.986389i | \(-0.552578\pi\) |
0.986389 | + | 0.164429i | \(0.0525780\pi\) | |||||||
\(884\) | −3.15831 | − | 15.7916i | −0.106226 | − | 0.531128i | ||||
\(885\) | −1.21637 | + | 1.10025i | −0.0408879 | + | 0.0369845i | ||||
\(886\) | −20.0581 | + | 20.0581i | −0.673864 | + | 0.673864i | ||||
\(887\) | 5.36675 | − | 5.36675i | 0.180198 | − | 0.180198i | −0.611244 | − | 0.791442i | \(-0.709331\pi\) |
0.791442 | + | 0.611244i | \(0.209331\pi\) | |||||||
\(888\) | −3.47494 | + | 3.47494i | −0.116611 | + | 0.116611i | ||||
\(889\) | −21.0000 | − | 21.0000i | −0.704317 | − | 0.704317i | ||||
\(890\) | 1.00000 | + | 0.0501256i | 0.0335201 | + | 0.00168021i | ||||
\(891\) | 26.3668 | + | 26.3668i | 0.883319 | + | 0.883319i | ||||
\(892\) | −15.9499 | −0.534041 | ||||||||
\(893\) | −18.6332 | − | 18.6332i | −0.623538 | − | 0.623538i | ||||
\(894\) | −35.4829 | −1.18672 | ||||||||
\(895\) | 24.8747 | − | 22.5000i | 0.831469 | − | 0.752092i | ||||
\(896\) | − | 3.00000i | − | 0.100223i | ||||||
\(897\) | −23.0501 | − | 15.3668i | −0.769621 | − | 0.513081i | ||||
\(898\) | −21.6332 | − | 21.6332i | −0.721911 | − | 0.721911i | ||||
\(899\) | 6.31662 | + | 6.31662i | 0.210671 | + | 0.210671i | ||||
\(900\) | 1.57519 | + | 0.158312i | 0.0525063 | + | 0.00527708i | ||||
\(901\) | − | 60.8496i | − | 2.02719i | ||||||
\(902\) | − | 41.8997i | − | 1.39511i | ||||||
\(903\) | −17.2005 | −0.572397 | ||||||||
\(904\) | 2.68338 | − | 2.68338i | 0.0892477 | − | 0.0892477i | ||||
\(905\) | −10.4248 | − | 11.5251i | −0.346532 | − | 0.383106i | ||||
\(906\) | 10.3668 | 0.344412 | ||||||||
\(907\) | 32.3246 | + | 32.3246i | 1.07332 | + | 1.07332i | 0.997090 | + | 0.0762291i | \(0.0242880\pi\) |
0.0762291 | + | 0.997090i | \(0.475712\pi\) | |||||||
\(908\) | − | 18.0000i | − | 0.597351i | ||||||
\(909\) | −6.10025 | −0.202333 | ||||||||
\(910\) | −3.55013 | − | 23.9248i | −0.117686 | − | 0.793100i | ||||
\(911\) | −11.0501 | −0.366107 | −0.183053 | − | 0.983103i | \(-0.558598\pi\) | ||||
−0.183053 | + | 0.983103i | \(0.558598\pi\) | |||||||
\(912\) | − | 4.63325i | − | 0.153422i | ||||||
\(913\) | 20.9499 | + | 20.9499i | 0.693340 | + | 0.693340i | ||||
\(914\) | 2.00000 | 0.0661541 | ||||||||
\(915\) | −7.31662 | − | 0.366750i | −0.241880 | − | 0.0121244i | ||||
\(916\) | 3.52506 | − | 3.52506i | 0.116471 | − | 0.116471i | ||||
\(917\) | −9.00000 | −0.297206 | ||||||||
\(918\) | 24.2665i | 0.800914i | ||||||||
\(919\) | 10.1003i | 0.333177i | 0.986027 | + | 0.166588i | \(0.0532751\pi\) | ||||
−0.986027 | + | 0.166588i | \(0.946725\pi\) | |||||||
\(920\) | 10.4749 | + | 0.525063i | 0.345348 | + | 0.0173108i | ||||
\(921\) | 30.0000 | + | 30.0000i | 0.988534 | + | 0.988534i | ||||
\(922\) | 4.10819 | + | 4.10819i | 0.135296 | + | 0.135296i | ||||
\(923\) | 14.2084 | − | 2.84169i | 0.467676 | − | 0.0935353i | ||||
\(924\) | 23.0501i | 0.758293i | ||||||||
\(925\) | 1.50000 | − | 14.9248i | 0.0493197 | − | 0.490725i | ||||
\(926\) | −9.89975 | −0.325326 | ||||||||
\(927\) | 2.51713 | + | 2.51713i | 0.0826733 | + | 0.0826733i | ||||
\(928\) | −6.31662 | −0.207353 | ||||||||
\(929\) | 13.5831 | + | 13.5831i | 0.445648 | + | 0.445648i | 0.893905 | − | 0.448257i | \(-0.147955\pi\) |
−0.448257 | + | 0.893905i | \(0.647955\pi\) | |||||||
\(930\) | −3.47494 | − | 3.84169i | −0.113948 | − | 0.125974i | ||||
\(931\) | 4.00000 | + | 4.00000i | 0.131095 | + | 0.131095i | ||||
\(932\) | 6.79156 | − | 6.79156i | 0.222465 | − | 0.222465i | ||||
\(933\) | −22.3166 | + | 22.3166i | −0.730613 | + | 0.730613i | ||||
\(934\) | −8.36675 | + | 8.36675i | −0.273768 | + | 0.273768i | ||||
\(935\) | −31.4248 | − | 34.7414i | −1.02770 | − | 1.13617i | ||||
\(936\) | 0.949874 | + | 0.633250i | 0.0310476 | + | 0.0206984i | ||||
\(937\) | 1.94987 | − | 1.94987i | 0.0636996 | − | 0.0636996i | −0.674539 | − | 0.738239i | \(-0.735658\pi\) |
0.738239 | + | 0.674539i | \(0.235658\pi\) | |||||||
\(938\) | −14.8496 | −0.484857 | ||||||||
\(939\) | 35.7335i | 1.16612i | ||||||||
\(940\) | 15.4499 | − | 13.9749i | 0.503919 | − | 0.455812i | ||||
\(941\) | −1.74144 | + | 1.74144i | −0.0567692 | + | 0.0567692i | −0.734921 | − | 0.678152i | \(-0.762781\pi\) |
0.678152 | + | 0.734921i | \(0.262781\pi\) | |||||||
\(942\) | − | 23.1662i | − | 0.754797i | ||||||
\(943\) | − | 41.8997i | − | 1.36444i | ||||||
\(944\) | 0.316625 | − | 0.316625i | 0.0103053 | − | 0.0103053i | ||||
\(945\) | −1.82456 | + | 36.3997i | −0.0593530 | + | 1.18408i | ||||
\(946\) | 16.4169i | 0.533759i | ||||||||
\(947\) | 5.68338 | 0.184685 | 0.0923424 | − | 0.995727i | \(-0.470565\pi\) | ||||
0.0923424 | + | 0.995727i | \(0.470565\pi\) | |||||||
\(948\) | 15.0000 | − | 15.0000i | 0.487177 | − | 0.487177i | ||||
\(949\) | −8.00000 | + | 12.0000i | −0.259691 | + | 0.389536i | ||||
\(950\) | 8.94987 | + | 10.9499i | 0.290372 | + | 0.355261i | ||||
\(951\) | −13.8997 | + | 13.8997i | −0.450730 | + | 0.450730i | ||||
\(952\) | −9.47494 | + | 9.47494i | −0.307084 | + | 0.307084i | ||||
\(953\) | 21.0079 | − | 21.0079i | 0.680514 | − | 0.680514i | −0.279602 | − | 0.960116i | \(-0.590203\pi\) |
0.960116 | + | 0.279602i | \(0.0902026\pi\) | |||||||
\(954\) | 3.05013 | + | 3.05013i | 0.0987515 | + | 0.0987515i | ||||
\(955\) | 8.37469 | − | 7.57519i | 0.270998 | − | 0.245127i | ||||
\(956\) | 11.8417 | + | 11.8417i | 0.382988 | + | 0.382988i | ||||
\(957\) | 48.5330 | 1.56885 | ||||||||
\(958\) | −3.15831 | − | 3.15831i | −0.102040 | − | 0.102040i | ||||
\(959\) | 17.0501 | 0.550577 | ||||||||
\(960\) | 3.65831 | + | 0.183375i | 0.118072 | + | 0.00591841i | ||||
\(961\) | 29.0000i | 0.935484i | ||||||||
\(962\) | 6.00000 | − | 9.00000i | 0.193448 | − | 0.290172i | ||||
\(963\) | 3.05013 | + | 3.05013i | 0.0982889 | + | 0.0982889i | ||||
\(964\) | −16.0000 | − | 16.0000i | −0.515325 | − | 0.515325i | ||||
\(965\) | −16.4248 | − | 18.1583i | −0.528733 | − | 0.584537i | ||||
\(966\) | 23.0501i | 0.741626i | ||||||||
\(967\) | 36.0501i | 1.15929i | 0.814868 | + | 0.579647i | \(0.196810\pi\) | ||||
−0.814868 | + | 0.579647i | \(0.803190\pi\) | |||||||
\(968\) | 11.0000 | 0.353553 | ||||||||
\(969\) | −14.6332 | + | 14.6332i | −0.470088 | + | 0.470088i | ||||
\(970\) | 14.8417 | − | 13.4248i | 0.476538 | − | 0.431045i | ||||
\(971\) | 20.0501 | 0.643439 | 0.321720 | − | 0.946835i | \(-0.395739\pi\) | ||||
0.321720 | + | 0.946835i | \(0.395739\pi\) | |||||||
\(972\) | −2.31662 | − | 2.31662i | −0.0743058 | − | 0.0743058i | ||||
\(973\) | 47.8496i | 1.53399i | ||||||||
\(974\) | 2.00000 | 0.0640841 | ||||||||
\(975\) | 29.3918 | − | 2.86675i | 0.941291 | − | 0.0918095i | ||||
\(976\) | 2.00000 | 0.0640184 | ||||||||
\(977\) | − | 35.0501i | − | 1.12135i | −0.828035 | − | 0.560676i | \(-0.810541\pi\) | ||
0.828035 | − | 0.560676i | \(-0.189459\pi\) | |||||||
\(978\) | 3.41688 | + | 3.41688i | 0.109260 | + | 0.109260i | ||||
\(979\) | 2.10025 | 0.0671243 | ||||||||
\(980\) | −3.31662 | + | 3.00000i | −0.105946 | + | 0.0958315i | ||||
\(981\) | −0.467002 | + | 0.467002i | −0.0149102 | + | 0.0149102i | ||||
\(982\) | −32.6834 | −1.04297 | ||||||||
\(983\) | − | 2.05013i | − | 0.0653889i | −0.999465 | − | 0.0326944i | \(-0.989591\pi\) | ||
0.999465 | − | 0.0326944i | \(-0.0104088\pi\) | |||||||
\(984\) | − | 14.6332i | − | 0.466491i | ||||||
\(985\) | −5.92481 | − | 6.55013i | −0.188780 | − | 0.208704i | ||||
\(986\) | 19.9499 | + | 19.9499i | 0.635333 | + | 0.635333i | ||||
\(987\) | 32.3747 | + | 32.3747i | 1.03050 | + | 1.03050i | ||||
\(988\) | 2.00000 | + | 10.0000i | 0.0636285 | + | 0.318142i | ||||
\(989\) | 16.4169i | 0.522026i | ||||||||
\(990\) | 3.31662 | + | 0.166248i | 0.105409 | + | 0.00528371i | ||||
\(991\) | 59.7995 | 1.89959 | 0.949797 | − | 0.312867i | \(-0.101290\pi\) | ||||
0.949797 | + | 0.312867i | \(0.101290\pi\) | |||||||
\(992\) | 1.00000 | + | 1.00000i | 0.0317500 | + | 0.0317500i | ||||
\(993\) | −2.31662 | −0.0735159 | ||||||||
\(994\) | −8.52506 | − | 8.52506i | −0.270399 | − | 0.270399i | ||||
\(995\) | 28.1082 | − | 25.4248i | 0.891089 | − | 0.806021i | ||||
\(996\) | 7.31662 | + | 7.31662i | 0.231836 | + | 0.231836i | ||||
\(997\) | 8.89975 | − | 8.89975i | 0.281858 | − | 0.281858i | −0.551992 | − | 0.833850i | \(-0.686132\pi\) |
0.833850 | + | 0.551992i | \(0.186132\pi\) | |||||||
\(998\) | −8.94987 | + | 8.94987i | −0.283303 | + | 0.283303i | ||||
\(999\) | −11.5251 | + | 11.5251i | −0.364637 | + | 0.364637i |
(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 | 130.2.j.d.83.1 | yes | 4 | |
3.2 | odd | 2 | 1170.2.w.e.343.1 | 4 | |||
4.3 | odd | 2 | 1040.2.cd.i.993.2 | 4 | |||
5.2 | odd | 4 | 130.2.g.d.57.1 | ✓ | 4 | ||
5.3 | odd | 4 | 650.2.g.g.57.2 | 4 | |||
5.4 | even | 2 | 650.2.j.f.343.2 | 4 | |||
13.8 | odd | 4 | 130.2.g.d.73.1 | yes | 4 | ||
15.2 | even | 4 | 1170.2.m.e.577.2 | 4 | |||
20.7 | even | 4 | 1040.2.bg.k.577.2 | 4 | |||
39.8 | even | 4 | 1170.2.m.e.73.1 | 4 | |||
52.47 | even | 4 | 1040.2.bg.k.593.2 | 4 | |||
65.8 | even | 4 | 650.2.j.f.307.2 | 4 | |||
65.34 | odd | 4 | 650.2.g.g.593.2 | 4 | |||
65.47 | even | 4 | inner | 130.2.j.d.47.1 | yes | 4 | |
195.47 | odd | 4 | 1170.2.w.e.307.1 | 4 | |||
260.47 | odd | 4 | 1040.2.cd.i.177.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
130.2.g.d.57.1 | ✓ | 4 | 5.2 | odd | 4 | ||
130.2.g.d.73.1 | yes | 4 | 13.8 | odd | 4 | ||
130.2.j.d.47.1 | yes | 4 | 65.47 | even | 4 | inner | |
130.2.j.d.83.1 | yes | 4 | 1.1 | even | 1 | trivial | |
650.2.g.g.57.2 | 4 | 5.3 | odd | 4 | |||
650.2.g.g.593.2 | 4 | 65.34 | odd | 4 | |||
650.2.j.f.307.2 | 4 | 65.8 | even | 4 | |||
650.2.j.f.343.2 | 4 | 5.4 | even | 2 | |||
1040.2.bg.k.577.2 | 4 | 20.7 | even | 4 | |||
1040.2.bg.k.593.2 | 4 | 52.47 | even | 4 | |||
1040.2.cd.i.177.2 | 4 | 260.47 | odd | 4 | |||
1040.2.cd.i.993.2 | 4 | 4.3 | odd | 2 | |||
1170.2.m.e.73.1 | 4 | 39.8 | even | 4 | |||
1170.2.m.e.577.2 | 4 | 15.2 | even | 4 | |||
1170.2.w.e.307.1 | 4 | 195.47 | odd | 4 | |||
1170.2.w.e.343.1 | 4 | 3.2 | odd | 2 |