Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1734,2,Mod(829,1734)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1734, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1734.829");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1734 = 2 \cdot 3 \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1734.f (of order \(4\), 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: | \(13.8460597105\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | 12.0.722204136308736.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 18x^{8} + 69x^{4} + 1 \) |
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 | 829.5 | ||
Root | \(-1.08335 + 1.08335i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1734.829 |
Dual form | 1734.2.f.n.1483.5 |
$q$-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 \(\left(\mathbb{Z}/1734\mathbb{Z}\right)^\times\).
\(n\) | \(1157\) | \(1159\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(3\) | 0.707107 | + | 0.707107i | 0.408248 | + | 0.408248i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.65979 | − | 1.65979i | −0.742280 | − | 0.742280i | 0.230736 | − | 0.973016i | \(-0.425887\pi\) |
−0.973016 | + | 0.230736i | \(0.925887\pi\) | |||||||
\(6\) | −0.707107 | + | 0.707107i | −0.288675 | + | 0.288675i | ||||
\(7\) | −2.87381 | + | 2.87381i | −1.08620 | + | 1.08620i | −0.0902809 | + | 0.995916i | \(0.528776\pi\) |
−0.995916 | + | 0.0902809i | \(0.971224\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 1.65979 | − | 1.65979i | 0.524871 | − | 0.524871i | ||||
\(11\) | 2.00641 | − | 2.00641i | 0.604956 | − | 0.604956i | −0.336667 | − | 0.941624i | \(-0.609300\pi\) |
0.941624 | + | 0.336667i | \(0.109300\pi\) | |||||||
\(12\) | −0.707107 | − | 0.707107i | −0.204124 | − | 0.204124i | ||||
\(13\) | −2.69459 | −0.747346 | −0.373673 | − | 0.927561i | \(-0.621902\pi\) | ||||
−0.373673 | + | 0.927561i | \(0.621902\pi\) | |||||||
\(14\) | −2.87381 | − | 2.87381i | −0.768057 | − | 0.768057i | ||||
\(15\) | − | 2.34730i | − | 0.606069i | ||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 6.45336i | 1.48050i | 0.672330 | + | 0.740252i | \(0.265294\pi\) | ||||
−0.672330 | + | 0.740252i | \(0.734706\pi\) | |||||||
\(20\) | 1.65979 | + | 1.65979i | 0.371140 | + | 0.371140i | ||||
\(21\) | −4.06418 | −0.886876 | ||||||||
\(22\) | 2.00641 | + | 2.00641i | 0.427769 | + | 0.427769i | ||||
\(23\) | 4.24264 | − | 4.24264i | 0.884652 | − | 0.884652i | −0.109351 | − | 0.994003i | \(-0.534877\pi\) |
0.994003 | + | 0.109351i | \(0.0348774\pi\) | |||||||
\(24\) | 0.707107 | − | 0.707107i | 0.144338 | − | 0.144338i | ||||
\(25\) | 0.509800i | 0.101960i | ||||||||
\(26\) | − | 2.69459i | − | 0.528453i | ||||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | 2.87381 | − | 2.87381i | 0.543099 | − | 0.543099i | ||||
\(29\) | −6.15348 | − | 6.15348i | −1.14267 | − | 1.14267i | −0.987959 | − | 0.154713i | \(-0.950555\pi\) |
−0.154713 | − | 0.987959i | \(-0.549445\pi\) | |||||||
\(30\) | 2.34730 | 0.428556 | ||||||||
\(31\) | 0.405864 | + | 0.405864i | 0.0728953 | + | 0.0728953i | 0.742614 | − | 0.669719i | \(-0.233586\pi\) |
−0.669719 | + | 0.742614i | \(0.733586\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 2.83750 | 0.493945 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9.53983 | 1.61253 | ||||||||
\(36\) | − | 1.00000i | − | 0.166667i | ||||||
\(37\) | −5.57704 | − | 5.57704i | −0.916860 | − | 0.916860i | 0.0799399 | − | 0.996800i | \(-0.474527\pi\) |
−0.996800 | + | 0.0799399i | \(0.974527\pi\) | |||||||
\(38\) | −6.45336 | −1.04687 | ||||||||
\(39\) | −1.90536 | − | 1.90536i | −0.305103 | − | 0.305103i | ||||
\(40\) | −1.65979 | + | 1.65979i | −0.262436 | + | 0.262436i | ||||
\(41\) | 2.42804 | − | 2.42804i | 0.379196 | − | 0.379196i | −0.491616 | − | 0.870812i | \(-0.663594\pi\) |
0.870812 | + | 0.491616i | \(0.163594\pi\) | |||||||
\(42\) | − | 4.06418i | − | 0.627116i | ||||||
\(43\) | − | 11.6459i | − | 1.77598i | −0.459860 | − | 0.887991i | \(-0.652101\pi\) | ||
0.459860 | − | 0.887991i | \(-0.347899\pi\) | |||||||
\(44\) | −2.00641 | + | 2.00641i | −0.302478 | + | 0.302478i | ||||
\(45\) | 1.65979 | − | 1.65979i | 0.247427 | − | 0.247427i | ||||
\(46\) | 4.24264 | + | 4.24264i | 0.625543 | + | 0.625543i | ||||
\(47\) | 10.5817 | 1.54350 | 0.771751 | − | 0.635925i | \(-0.219381\pi\) | ||||
0.771751 | + | 0.635925i | \(0.219381\pi\) | |||||||
\(48\) | 0.707107 | + | 0.707107i | 0.102062 | + | 0.102062i | ||||
\(49\) | − | 9.51754i | − | 1.35965i | ||||||
\(50\) | −0.509800 | −0.0720966 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.69459 | 0.373673 | ||||||||
\(53\) | 3.29086i | 0.452034i | 0.974123 | + | 0.226017i | \(0.0725705\pi\) | ||||
−0.974123 | + | 0.226017i | \(0.927429\pi\) | |||||||
\(54\) | −0.707107 | − | 0.707107i | −0.0962250 | − | 0.0962250i | ||||
\(55\) | −6.66044 | −0.898094 | ||||||||
\(56\) | 2.87381 | + | 2.87381i | 0.384029 | + | 0.384029i | ||||
\(57\) | −4.56322 | + | 4.56322i | −0.604413 | + | 0.604413i | ||||
\(58\) | 6.15348 | − | 6.15348i | 0.807991 | − | 0.807991i | ||||
\(59\) | 4.34730i | 0.565970i | 0.959124 | + | 0.282985i | \(0.0913246\pi\) | ||||
−0.959124 | + | 0.282985i | \(0.908675\pi\) | |||||||
\(60\) | 2.34730i | 0.303035i | ||||||||
\(61\) | 9.23777 | − | 9.23777i | 1.18278 | − | 1.18278i | 0.203753 | − | 0.979022i | \(-0.434686\pi\) |
0.979022 | − | 0.203753i | \(-0.0653138\pi\) | |||||||
\(62\) | −0.405864 | + | 0.405864i | −0.0515447 | + | 0.0515447i | ||||
\(63\) | −2.87381 | − | 2.87381i | −0.362066 | − | 0.362066i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 4.47246 | + | 4.47246i | 0.554740 | + | 0.554740i | ||||
\(66\) | 2.83750i | 0.349272i | ||||||||
\(67\) | 12.2121 | 1.49195 | 0.745975 | − | 0.665974i | \(-0.231984\pi\) | ||||
0.745975 | + | 0.665974i | \(0.231984\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.00000 | 0.722315 | ||||||||
\(70\) | 9.53983i | 1.14023i | ||||||||
\(71\) | −8.20337 | − | 8.20337i | −0.973561 | − | 0.973561i | 0.0260983 | − | 0.999659i | \(-0.491692\pi\) |
−0.999659 | + | 0.0260983i | \(0.991692\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 1.67008 | + | 1.67008i | 0.195468 | + | 0.195468i | 0.798054 | − | 0.602586i | \(-0.205863\pi\) |
−0.602586 | + | 0.798054i | \(0.705863\pi\) | |||||||
\(74\) | 5.57704 | − | 5.57704i | 0.648318 | − | 0.648318i | ||||
\(75\) | −0.360483 | + | 0.360483i | −0.0416250 | + | 0.0416250i | ||||
\(76\) | − | 6.45336i | − | 0.740252i | ||||||
\(77\) | 11.5321i | 1.31420i | ||||||||
\(78\) | 1.90536 | − | 1.90536i | 0.215740 | − | 0.215740i | ||||
\(79\) | −5.21466 | + | 5.21466i | −0.586695 | + | 0.586695i | −0.936735 | − | 0.350040i | \(-0.886168\pi\) |
0.350040 | + | 0.936735i | \(0.386168\pi\) | |||||||
\(80\) | −1.65979 | − | 1.65979i | −0.185570 | − | 0.185570i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 2.42804 | + | 2.42804i | 0.268132 | + | 0.268132i | ||||
\(83\) | − | 3.21213i | − | 0.352577i | −0.984338 | − | 0.176289i | \(-0.943591\pi\) | ||
0.984338 | − | 0.176289i | \(-0.0564092\pi\) | |||||||
\(84\) | 4.06418 | 0.443438 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 11.6459 | 1.25581 | ||||||||
\(87\) | − | 8.70233i | − | 0.932988i | ||||||
\(88\) | −2.00641 | − | 2.00641i | −0.213884 | − | 0.213884i | ||||
\(89\) | 6.34049 | 0.672091 | 0.336045 | − | 0.941846i | \(-0.390910\pi\) | ||||
0.336045 | + | 0.941846i | \(0.390910\pi\) | |||||||
\(90\) | 1.65979 | + | 1.65979i | 0.174957 | + | 0.174957i | ||||
\(91\) | 7.74374 | − | 7.74374i | 0.811765 | − | 0.811765i | ||||
\(92\) | −4.24264 | + | 4.24264i | −0.442326 | + | 0.442326i | ||||
\(93\) | 0.573978i | 0.0595187i | ||||||||
\(94\) | 10.5817i | 1.09142i | ||||||||
\(95\) | 10.7112 | − | 10.7112i | 1.09895 | − | 1.09895i | ||||
\(96\) | −0.707107 | + | 0.707107i | −0.0721688 | + | 0.0721688i | ||||
\(97\) | −5.73733 | − | 5.73733i | −0.582537 | − | 0.582537i | 0.353062 | − | 0.935600i | \(-0.385140\pi\) |
−0.935600 | + | 0.353062i | \(0.885140\pi\) | |||||||
\(98\) | 9.51754 | 0.961417 | ||||||||
\(99\) | 2.00641 | + | 2.00641i | 0.201652 | + | 0.201652i | ||||
\(100\) | − | 0.509800i | − | 0.0509800i | ||||||
\(101\) | −9.17024 | −0.912473 | −0.456237 | − | 0.889858i | \(-0.650803\pi\) | ||||
−0.456237 | + | 0.889858i | \(0.650803\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.35235 | −0.724448 | −0.362224 | − | 0.932091i | \(-0.617983\pi\) | ||||
−0.362224 | + | 0.932091i | \(0.617983\pi\) | |||||||
\(104\) | 2.69459i | 0.264227i | ||||||||
\(105\) | 6.74568 | + | 6.74568i | 0.658311 | + | 0.658311i | ||||
\(106\) | −3.29086 | −0.319637 | ||||||||
\(107\) | 3.55487 | + | 3.55487i | 0.343662 | + | 0.343662i | 0.857742 | − | 0.514080i | \(-0.171867\pi\) |
−0.514080 | + | 0.857742i | \(0.671867\pi\) | |||||||
\(108\) | 0.707107 | − | 0.707107i | 0.0680414 | − | 0.0680414i | ||||
\(109\) | 6.40934 | − | 6.40934i | 0.613904 | − | 0.613904i | −0.330057 | − | 0.943961i | \(-0.607068\pi\) |
0.943961 | + | 0.330057i | \(0.107068\pi\) | |||||||
\(110\) | − | 6.66044i | − | 0.635048i | ||||||
\(111\) | − | 7.88713i | − | 0.748613i | ||||||
\(112\) | −2.87381 | + | 2.87381i | −0.271549 | + | 0.271549i | ||||
\(113\) | 7.88280 | − | 7.88280i | 0.741551 | − | 0.741551i | −0.231325 | − | 0.972876i | \(-0.574306\pi\) |
0.972876 | + | 0.231325i | \(0.0743062\pi\) | |||||||
\(114\) | −4.56322 | − | 4.56322i | −0.427384 | − | 0.427384i | ||||
\(115\) | −14.0838 | −1.31332 | ||||||||
\(116\) | 6.15348 | + | 6.15348i | 0.571336 | + | 0.571336i | ||||
\(117\) | − | 2.69459i | − | 0.249115i | ||||||
\(118\) | −4.34730 | −0.400201 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.34730 | −0.214278 | ||||||||
\(121\) | 2.94862i | 0.268056i | ||||||||
\(122\) | 9.23777 | + | 9.23777i | 0.836348 | + | 0.836348i | ||||
\(123\) | 3.43376 | 0.309612 | ||||||||
\(124\) | −0.405864 | − | 0.405864i | −0.0364476 | − | 0.0364476i | ||||
\(125\) | −7.45279 | + | 7.45279i | −0.666597 | + | 0.666597i | ||||
\(126\) | 2.87381 | − | 2.87381i | 0.256019 | − | 0.256019i | ||||
\(127\) | − | 1.93582i | − | 0.171776i | −0.996305 | − | 0.0858882i | \(-0.972627\pi\) | ||
0.996305 | − | 0.0858882i | \(-0.0273728\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 8.23489 | − | 8.23489i | 0.725042 | − | 0.725042i | ||||
\(130\) | −4.47246 | + | 4.47246i | −0.392260 | + | 0.392260i | ||||
\(131\) | −11.8297 | − | 11.8297i | −1.03356 | − | 1.03356i | −0.999417 | − | 0.0341459i | \(-0.989129\pi\) |
−0.0341459 | − | 0.999417i | \(-0.510871\pi\) | |||||||
\(132\) | −2.83750 | −0.246972 | ||||||||
\(133\) | −18.5457 | − | 18.5457i | −1.60812 | − | 1.60812i | ||||
\(134\) | 12.2121i | 1.05497i | ||||||||
\(135\) | 2.34730 | 0.202023 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.45336 | 0.380476 | 0.190238 | − | 0.981738i | \(-0.439074\pi\) | ||||
0.190238 | + | 0.981738i | \(0.439074\pi\) | |||||||
\(138\) | 6.00000i | 0.510754i | ||||||||
\(139\) | −9.00795 | − | 9.00795i | −0.764045 | − | 0.764045i | 0.213006 | − | 0.977051i | \(-0.431675\pi\) |
−0.977051 | + | 0.213006i | \(0.931675\pi\) | |||||||
\(140\) | −9.53983 | −0.806263 | ||||||||
\(141\) | 7.48241 | + | 7.48241i | 0.630132 | + | 0.630132i | ||||
\(142\) | 8.20337 | − | 8.20337i | 0.688412 | − | 0.688412i | ||||
\(143\) | −5.40647 | + | 5.40647i | −0.452111 | + | 0.452111i | ||||
\(144\) | 1.00000i | 0.0833333i | ||||||||
\(145\) | 20.4270i | 1.69637i | ||||||||
\(146\) | −1.67008 | + | 1.67008i | −0.138216 | + | 0.138216i | ||||
\(147\) | 6.72992 | − | 6.72992i | 0.555074 | − | 0.555074i | ||||
\(148\) | 5.57704 | + | 5.57704i | 0.458430 | + | 0.458430i | ||||
\(149\) | −19.2909 | −1.58037 | −0.790184 | − | 0.612869i | \(-0.790015\pi\) | ||||
−0.790184 | + | 0.612869i | \(0.790015\pi\) | |||||||
\(150\) | −0.360483 | − | 0.360483i | −0.0294333 | − | 0.0294333i | ||||
\(151\) | − | 13.0787i | − | 1.06433i | −0.846640 | − | 0.532166i | \(-0.821378\pi\) | ||
0.846640 | − | 0.532166i | \(-0.178622\pi\) | |||||||
\(152\) | 6.45336 | 0.523437 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −11.5321 | −0.929282 | ||||||||
\(155\) | − | 1.34730i | − | 0.108217i | ||||||
\(156\) | 1.90536 | + | 1.90536i | 0.152551 | + | 0.152551i | ||||
\(157\) | −10.1284 | −0.808331 | −0.404165 | − | 0.914686i | \(-0.632438\pi\) | ||||
−0.404165 | + | 0.914686i | \(0.632438\pi\) | |||||||
\(158\) | −5.21466 | − | 5.21466i | −0.414856 | − | 0.414856i | ||||
\(159\) | −2.32699 | + | 2.32699i | −0.184542 | + | 0.184542i | ||||
\(160\) | 1.65979 | − | 1.65979i | 0.131218 | − | 0.131218i | ||||
\(161\) | 24.3851i | 1.92181i | ||||||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | −0.150001 | + | 0.150001i | −0.0117490 | + | 0.0117490i | −0.712957 | − | 0.701208i | \(-0.752644\pi\) |
0.701208 | + | 0.712957i | \(0.252644\pi\) | |||||||
\(164\) | −2.42804 | + | 2.42804i | −0.189598 | + | 0.189598i | ||||
\(165\) | −4.70965 | − | 4.70965i | −0.366645 | − | 0.366645i | ||||
\(166\) | 3.21213 | 0.249310 | ||||||||
\(167\) | 6.00895 | + | 6.00895i | 0.464987 | + | 0.464987i | 0.900286 | − | 0.435299i | \(-0.143357\pi\) |
−0.435299 | + | 0.900286i | \(0.643357\pi\) | |||||||
\(168\) | 4.06418i | 0.313558i | ||||||||
\(169\) | −5.73917 | −0.441475 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.45336 | −0.493501 | ||||||||
\(172\) | 11.6459i | 0.887991i | ||||||||
\(173\) | 0.160288 | + | 0.160288i | 0.0121865 | + | 0.0121865i | 0.713174 | − | 0.700987i | \(-0.247257\pi\) |
−0.700987 | + | 0.713174i | \(0.747257\pi\) | |||||||
\(174\) | 8.70233 | 0.659722 | ||||||||
\(175\) | −1.46507 | − | 1.46507i | −0.110749 | − | 0.110749i | ||||
\(176\) | 2.00641 | − | 2.00641i | 0.151239 | − | 0.151239i | ||||
\(177\) | −3.07400 | + | 3.07400i | −0.231056 | + | 0.231056i | ||||
\(178\) | 6.34049i | 0.475240i | ||||||||
\(179\) | 11.6946i | 0.874095i | 0.899438 | + | 0.437047i | \(0.143976\pi\) | ||||
−0.899438 | + | 0.437047i | \(0.856024\pi\) | |||||||
\(180\) | −1.65979 | + | 1.65979i | −0.123713 | + | 0.123713i | ||||
\(181\) | 1.76631 | − | 1.76631i | 0.131289 | − | 0.131289i | −0.638409 | − | 0.769698i | \(-0.720407\pi\) |
0.769698 | + | 0.638409i | \(0.220407\pi\) | |||||||
\(182\) | 7.74374 | + | 7.74374i | 0.574004 | + | 0.574004i | ||||
\(183\) | 13.0642 | 0.965732 | ||||||||
\(184\) | −4.24264 | − | 4.24264i | −0.312772 | − | 0.312772i | ||||
\(185\) | 18.5134i | 1.36113i | ||||||||
\(186\) | −0.573978 | −0.0420861 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −10.5817 | −0.771751 | ||||||||
\(189\) | − | 4.06418i | − | 0.295625i | ||||||
\(190\) | 10.7112 | + | 10.7112i | 0.777074 | + | 0.777074i | ||||
\(191\) | 2.73917 | 0.198199 | 0.0990997 | − | 0.995078i | \(-0.468404\pi\) | ||||
0.0990997 | + | 0.995078i | \(0.468404\pi\) | |||||||
\(192\) | −0.707107 | − | 0.707107i | −0.0510310 | − | 0.0510310i | ||||
\(193\) | 9.37201 | − | 9.37201i | 0.674612 | − | 0.674612i | −0.284164 | − | 0.958776i | \(-0.591716\pi\) |
0.958776 | + | 0.284164i | \(0.0917159\pi\) | |||||||
\(194\) | 5.73733 | − | 5.73733i | 0.411916 | − | 0.411916i | ||||
\(195\) | 6.32501i | 0.452943i | ||||||||
\(196\) | 9.51754i | 0.679824i | ||||||||
\(197\) | −16.2744 | + | 16.2744i | −1.15950 | + | 1.15950i | −0.174921 | + | 0.984583i | \(0.555967\pi\) |
−0.984583 | + | 0.174921i | \(0.944033\pi\) | |||||||
\(198\) | −2.00641 | + | 2.00641i | −0.142590 | + | 0.142590i | ||||
\(199\) | 12.8139 | + | 12.8139i | 0.908351 | + | 0.908351i | 0.996139 | − | 0.0877880i | \(-0.0279798\pi\) |
−0.0877880 | + | 0.996139i | \(0.527980\pi\) | |||||||
\(200\) | 0.509800 | 0.0360483 | ||||||||
\(201\) | 8.63528 | + | 8.63528i | 0.609086 | + | 0.609086i | ||||
\(202\) | − | 9.17024i | − | 0.645216i | ||||||
\(203\) | 35.3678 | 2.48234 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.06006 | −0.562939 | ||||||||
\(206\) | − | 7.35235i | − | 0.512262i | ||||||
\(207\) | 4.24264 | + | 4.24264i | 0.294884 | + | 0.294884i | ||||
\(208\) | −2.69459 | −0.186836 | ||||||||
\(209\) | 12.9481 | + | 12.9481i | 0.895640 | + | 0.895640i | ||||
\(210\) | −6.74568 | + | 6.74568i | −0.465496 | + | 0.465496i | ||||
\(211\) | −11.0041 | + | 11.0041i | −0.757552 | + | 0.757552i | −0.975876 | − | 0.218324i | \(-0.929941\pi\) |
0.218324 | + | 0.975876i | \(0.429941\pi\) | |||||||
\(212\) | − | 3.29086i | − | 0.226017i | ||||||
\(213\) | − | 11.6013i | − | 0.794909i | ||||||
\(214\) | −3.55487 | + | 3.55487i | −0.243006 | + | 0.243006i | ||||
\(215\) | −19.3297 | + | 19.3297i | −1.31828 | + | 1.31828i | ||||
\(216\) | 0.707107 | + | 0.707107i | 0.0481125 | + | 0.0481125i | ||||
\(217\) | −2.33275 | −0.158357 | ||||||||
\(218\) | 6.40934 | + | 6.40934i | 0.434095 | + | 0.434095i | ||||
\(219\) | 2.36184i | 0.159599i | ||||||||
\(220\) | 6.66044 | 0.449047 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 7.88713 | 0.529349 | ||||||||
\(223\) | − | 13.3063i | − | 0.891058i | −0.895267 | − | 0.445529i | \(-0.853016\pi\) | ||
0.895267 | − | 0.445529i | \(-0.146984\pi\) | |||||||
\(224\) | −2.87381 | − | 2.87381i | −0.192014 | − | 0.192014i | ||||
\(225\) | −0.509800 | −0.0339867 | ||||||||
\(226\) | 7.88280 | + | 7.88280i | 0.524356 | + | 0.524356i | ||||
\(227\) | −2.61247 | + | 2.61247i | −0.173396 | + | 0.173396i | −0.788470 | − | 0.615074i | \(-0.789126\pi\) |
0.615074 | + | 0.788470i | \(0.289126\pi\) | |||||||
\(228\) | 4.56322 | − | 4.56322i | 0.302206 | − | 0.302206i | ||||
\(229\) | 8.85204i | 0.584960i | 0.956272 | + | 0.292480i | \(0.0944804\pi\) | ||||
−0.956272 | + | 0.292480i | \(0.905520\pi\) | |||||||
\(230\) | − | 14.0838i | − | 0.928657i | ||||||
\(231\) | −8.15442 | + | 8.15442i | −0.536521 | + | 0.536521i | ||||
\(232\) | −6.15348 | + | 6.15348i | −0.403996 | + | 0.403996i | ||||
\(233\) | 4.16283 | + | 4.16283i | 0.272716 | + | 0.272716i | 0.830193 | − | 0.557477i | \(-0.188230\pi\) |
−0.557477 | + | 0.830193i | \(0.688230\pi\) | |||||||
\(234\) | 2.69459 | 0.176151 | ||||||||
\(235\) | −17.5634 | − | 17.5634i | −1.14571 | − | 1.14571i | ||||
\(236\) | − | 4.34730i | − | 0.282985i | ||||||
\(237\) | −7.37464 | −0.479034 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.6108 | 1.07446 | 0.537232 | − | 0.843434i | \(-0.319470\pi\) | ||||
0.537232 | + | 0.843434i | \(0.319470\pi\) | |||||||
\(240\) | − | 2.34730i | − | 0.151517i | ||||||
\(241\) | −6.02091 | − | 6.02091i | −0.387841 | − | 0.387841i | 0.486076 | − | 0.873917i | \(-0.338428\pi\) |
−0.873917 | + | 0.486076i | \(0.838428\pi\) | |||||||
\(242\) | −2.94862 | −0.189544 | ||||||||
\(243\) | −0.707107 | − | 0.707107i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | −9.23777 | + | 9.23777i | −0.591388 | + | 0.591388i | ||||
\(245\) | −15.7971 | + | 15.7971i | −1.00924 | + | 1.00924i | ||||
\(246\) | 3.43376i | 0.218929i | ||||||||
\(247\) | − | 17.3892i | − | 1.10645i | ||||||
\(248\) | 0.405864 | − | 0.405864i | 0.0257724 | − | 0.0257724i | ||||
\(249\) | 2.27132 | − | 2.27132i | 0.143939 | − | 0.143939i | ||||
\(250\) | −7.45279 | − | 7.45279i | −0.471356 | − | 0.471356i | ||||
\(251\) | 6.89899 | 0.435460 | 0.217730 | − | 0.976009i | \(-0.430135\pi\) | ||||
0.217730 | + | 0.976009i | \(0.430135\pi\) | |||||||
\(252\) | 2.87381 | + | 2.87381i | 0.181033 | + | 0.181033i | ||||
\(253\) | − | 17.0250i | − | 1.07035i | ||||||
\(254\) | 1.93582 | 0.121464 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 22.5526i | − | 1.40679i | −0.710797 | − | 0.703397i | \(-0.751666\pi\) | ||
0.710797 | − | 0.703397i | \(-0.248334\pi\) | |||||||
\(258\) | 8.23489 | + | 8.23489i | 0.512682 | + | 0.512682i | ||||
\(259\) | 32.0547 | 1.99178 | ||||||||
\(260\) | −4.47246 | − | 4.47246i | −0.277370 | − | 0.277370i | ||||
\(261\) | 6.15348 | − | 6.15348i | 0.380891 | − | 0.380891i | ||||
\(262\) | 11.8297 | − | 11.8297i | 0.730839 | − | 0.730839i | ||||
\(263\) | − | 16.9513i | − | 1.04526i | −0.852559 | − | 0.522631i | \(-0.824951\pi\) | ||
0.852559 | − | 0.522631i | \(-0.175049\pi\) | |||||||
\(264\) | − | 2.83750i | − | 0.174636i | ||||||
\(265\) | 5.46213 | − | 5.46213i | 0.335536 | − | 0.335536i | ||||
\(266\) | 18.5457 | − | 18.5457i | 1.13711 | − | 1.13711i | ||||
\(267\) | 4.48340 | + | 4.48340i | 0.274380 | + | 0.274380i | ||||
\(268\) | −12.2121 | −0.745975 | ||||||||
\(269\) | 7.64269 | + | 7.64269i | 0.465983 | + | 0.465983i | 0.900610 | − | 0.434627i | \(-0.143120\pi\) |
−0.434627 | + | 0.900610i | \(0.643120\pi\) | |||||||
\(270\) | 2.34730i | 0.142852i | ||||||||
\(271\) | −21.3131 | −1.29468 | −0.647341 | − | 0.762201i | \(-0.724119\pi\) | ||||
−0.647341 | + | 0.762201i | \(0.724119\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.9513 | 0.662803 | ||||||||
\(274\) | 4.45336i | 0.269038i | ||||||||
\(275\) | 1.02287 | + | 1.02287i | 0.0616814 | + | 0.0616814i | ||||
\(276\) | −6.00000 | −0.361158 | ||||||||
\(277\) | −15.6581 | − | 15.6581i | −0.940801 | − | 0.940801i | 0.0575416 | − | 0.998343i | \(-0.481674\pi\) |
−0.998343 | + | 0.0575416i | \(0.981674\pi\) | |||||||
\(278\) | 9.00795 | − | 9.00795i | 0.540261 | − | 0.540261i | ||||
\(279\) | −0.405864 | + | 0.405864i | −0.0242984 | + | 0.0242984i | ||||
\(280\) | − | 9.53983i | − | 0.570114i | ||||||
\(281\) | − | 10.0155i | − | 0.597474i | −0.954336 | − | 0.298737i | \(-0.903435\pi\) | ||
0.954336 | − | 0.298737i | \(-0.0965653\pi\) | |||||||
\(282\) | −7.48241 | + | 7.48241i | −0.445571 | + | 0.445571i | ||||
\(283\) | −7.13031 | + | 7.13031i | −0.423853 | + | 0.423853i | −0.886528 | − | 0.462675i | \(-0.846890\pi\) |
0.462675 | + | 0.886528i | \(0.346890\pi\) | |||||||
\(284\) | 8.20337 | + | 8.20337i | 0.486781 | + | 0.486781i | ||||
\(285\) | 15.1480 | 0.897287 | ||||||||
\(286\) | −5.40647 | − | 5.40647i | −0.319691 | − | 0.319691i | ||||
\(287\) | 13.9554i | 0.823763i | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −20.4270 | −1.19951 | ||||||||
\(291\) | − | 8.11381i | − | 0.475640i | ||||||
\(292\) | −1.67008 | − | 1.67008i | −0.0977338 | − | 0.0977338i | ||||
\(293\) | 14.5594 | 0.850571 | 0.425285 | − | 0.905059i | \(-0.360174\pi\) | ||||
0.425285 | + | 0.905059i | \(0.360174\pi\) | |||||||
\(294\) | 6.72992 | + | 6.72992i | 0.392497 | + | 0.392497i | ||||
\(295\) | 7.21560 | − | 7.21560i | 0.420108 | − | 0.420108i | ||||
\(296\) | −5.57704 | + | 5.57704i | −0.324159 | + | 0.324159i | ||||
\(297\) | 2.83750i | 0.164648i | ||||||||
\(298\) | − | 19.2909i | − | 1.11749i | ||||||
\(299\) | −11.4322 | + | 11.4322i | −0.661141 | + | 0.661141i | ||||
\(300\) | 0.360483 | − | 0.360483i | 0.0208125 | − | 0.0208125i | ||||
\(301\) | 33.4681 | + | 33.4681i | 1.92907 | + | 1.92907i | ||||
\(302\) | 13.0787 | 0.752596 | ||||||||
\(303\) | −6.48434 | − | 6.48434i | −0.372516 | − | 0.372516i | ||||
\(304\) | 6.45336i | 0.370126i | ||||||||
\(305\) | −30.6655 | −1.75590 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.6459 | −1.12125 | −0.560625 | − | 0.828070i | \(-0.689439\pi\) | ||||
−0.560625 | + | 0.828070i | \(0.689439\pi\) | |||||||
\(308\) | − | 11.5321i | − | 0.657102i | ||||||
\(309\) | −5.19890 | − | 5.19890i | −0.295755 | − | 0.295755i | ||||
\(310\) | 1.34730 | 0.0765213 | ||||||||
\(311\) | −10.0810 | − | 10.0810i | −0.571642 | − | 0.571642i | 0.360945 | − | 0.932587i | \(-0.382454\pi\) |
−0.932587 | + | 0.360945i | \(0.882454\pi\) | |||||||
\(312\) | −1.90536 | + | 1.90536i | −0.107870 | + | 0.107870i | ||||
\(313\) | −14.8740 | + | 14.8740i | −0.840731 | + | 0.840731i | −0.988954 | − | 0.148223i | \(-0.952645\pi\) |
0.148223 | + | 0.988954i | \(0.452645\pi\) | |||||||
\(314\) | − | 10.1284i | − | 0.571576i | ||||||
\(315\) | 9.53983i | 0.537509i | ||||||||
\(316\) | 5.21466 | − | 5.21466i | 0.293347 | − | 0.293347i | ||||
\(317\) | −4.04726 | + | 4.04726i | −0.227317 | + | 0.227317i | −0.811571 | − | 0.584254i | \(-0.801387\pi\) |
0.584254 | + | 0.811571i | \(0.301387\pi\) | |||||||
\(318\) | −2.32699 | − | 2.32699i | −0.130491 | − | 0.130491i | ||||
\(319\) | −24.6928 | −1.38253 | ||||||||
\(320\) | 1.65979 | + | 1.65979i | 0.0927850 | + | 0.0927850i | ||||
\(321\) | 5.02734i | 0.280599i | ||||||||
\(322\) | −24.3851 | −1.35893 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | − | 1.37370i | − | 0.0761994i | ||||||
\(326\) | −0.150001 | − | 0.150001i | −0.00830780 | − | 0.00830780i | ||||
\(327\) | 9.06418 | 0.501250 | ||||||||
\(328\) | −2.42804 | − | 2.42804i | −0.134066 | − | 0.134066i | ||||
\(329\) | −30.4098 | + | 30.4098i | −1.67655 | + | 1.67655i | ||||
\(330\) | 4.70965 | − | 4.70965i | 0.259257 | − | 0.259257i | ||||
\(331\) | 3.14796i | 0.173027i | 0.996251 | + | 0.0865137i | \(0.0275726\pi\) | ||||
−0.996251 | + | 0.0865137i | \(0.972427\pi\) | |||||||
\(332\) | 3.21213i | 0.176289i | ||||||||
\(333\) | 5.57704 | − | 5.57704i | 0.305620 | − | 0.305620i | ||||
\(334\) | −6.00895 | + | 6.00895i | −0.328795 | + | 0.328795i | ||||
\(335\) | −20.2696 | − | 20.2696i | −1.10744 | − | 1.10744i | ||||
\(336\) | −4.06418 | −0.221719 | ||||||||
\(337\) | 22.5834 | + | 22.5834i | 1.23019 | + | 1.23019i | 0.963889 | + | 0.266305i | \(0.0858028\pi\) |
0.266305 | + | 0.963889i | \(0.414197\pi\) | |||||||
\(338\) | − | 5.73917i | − | 0.312170i | ||||||
\(339\) | 11.1480 | 0.605474 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.62866 | 0.0881969 | ||||||||
\(342\) | − | 6.45336i | − | 0.348958i | ||||||
\(343\) | 7.23493 | + | 7.23493i | 0.390649 | + | 0.390649i | ||||
\(344\) | −11.6459 | −0.627905 | ||||||||
\(345\) | −9.95874 | − | 9.95874i | −0.536160 | − | 0.536160i | ||||
\(346\) | −0.160288 | + | 0.160288i | −0.00861714 | + | 0.00861714i | ||||
\(347\) | 25.5418 | − | 25.5418i | 1.37116 | − | 1.37116i | 0.512421 | − | 0.858735i | \(-0.328749\pi\) |
0.858735 | − | 0.512421i | \(-0.171251\pi\) | |||||||
\(348\) | 8.70233i | 0.466494i | ||||||||
\(349\) | 12.7493i | 0.682453i | 0.939981 | + | 0.341227i | \(0.110842\pi\) | ||||
−0.939981 | + | 0.341227i | \(0.889158\pi\) | |||||||
\(350\) | 1.46507 | − | 1.46507i | 0.0783112 | − | 0.0783112i | ||||
\(351\) | 1.90536 | − | 1.90536i | 0.101701 | − | 0.101701i | ||||
\(352\) | 2.00641 | + | 2.00641i | 0.106942 | + | 0.106942i | ||||
\(353\) | 7.09327 | 0.377537 | 0.188768 | − | 0.982022i | \(-0.439550\pi\) | ||||
0.188768 | + | 0.982022i | \(0.439550\pi\) | |||||||
\(354\) | −3.07400 | − | 3.07400i | −0.163381 | − | 0.163381i | ||||
\(355\) | 27.2317i | 1.44531i | ||||||||
\(356\) | −6.34049 | −0.336045 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11.6946 | −0.618078 | ||||||||
\(359\) | − | 10.6655i | − | 0.562903i | −0.959575 | − | 0.281452i | \(-0.909184\pi\) | ||
0.959575 | − | 0.281452i | \(-0.0908159\pi\) | |||||||
\(360\) | −1.65979 | − | 1.65979i | −0.0874786 | − | 0.0874786i | ||||
\(361\) | −22.6459 | −1.19189 | ||||||||
\(362\) | 1.76631 | + | 1.76631i | 0.0928352 | + | 0.0928352i | ||||
\(363\) | −2.08499 | + | 2.08499i | −0.109433 | + | 0.109433i | ||||
\(364\) | −7.74374 | + | 7.74374i | −0.405882 | + | 0.405882i | ||||
\(365\) | − | 5.54395i | − | 0.290184i | ||||||
\(366\) | 13.0642i | 0.682876i | ||||||||
\(367\) | 17.1473 | − | 17.1473i | 0.895080 | − | 0.895080i | −0.0999156 | − | 0.994996i | \(-0.531857\pi\) |
0.994996 | + | 0.0999156i | \(0.0318573\pi\) | |||||||
\(368\) | 4.24264 | − | 4.24264i | 0.221163 | − | 0.221163i | ||||
\(369\) | 2.42804 | + | 2.42804i | 0.126399 | + | 0.126399i | ||||
\(370\) | −18.5134 | −0.962467 | ||||||||
\(371\) | −9.45730 | − | 9.45730i | −0.490998 | − | 0.490998i | ||||
\(372\) | − | 0.573978i | − | 0.0297594i | ||||||
\(373\) | −22.7547 | −1.17819 | −0.589096 | − | 0.808063i | \(-0.700516\pi\) | ||||
−0.589096 | + | 0.808063i | \(0.700516\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.5398 | −0.544274 | ||||||||
\(376\) | − | 10.5817i | − | 0.545710i | ||||||
\(377\) | 16.5811 | + | 16.5811i | 0.853971 | + | 0.853971i | ||||
\(378\) | 4.06418 | 0.209039 | ||||||||
\(379\) | −14.0308 | − | 14.0308i | −0.720714 | − | 0.720714i | 0.248037 | − | 0.968751i | \(-0.420215\pi\) |
−0.968751 | + | 0.248037i | \(0.920215\pi\) | |||||||
\(380\) | −10.7112 | + | 10.7112i | −0.549474 | + | 0.549474i | ||||
\(381\) | 1.36883 | − | 1.36883i | 0.0701274 | − | 0.0701274i | ||||
\(382\) | 2.73917i | 0.140148i | ||||||||
\(383\) | − | 15.7196i | − | 0.803232i | −0.915808 | − | 0.401616i | \(-0.868449\pi\) | ||
0.915808 | − | 0.401616i | \(-0.131551\pi\) | |||||||
\(384\) | 0.707107 | − | 0.707107i | 0.0360844 | − | 0.0360844i | ||||
\(385\) | 19.1408 | − | 19.1408i | 0.975507 | − | 0.975507i | ||||
\(386\) | 9.37201 | + | 9.37201i | 0.477023 | + | 0.477023i | ||||
\(387\) | 11.6459 | 0.591994 | ||||||||
\(388\) | 5.73733 | + | 5.73733i | 0.291269 | + | 0.291269i | ||||
\(389\) | − | 32.4766i | − | 1.64663i | −0.567586 | − | 0.823314i | \(-0.692123\pi\) | ||
0.567586 | − | 0.823314i | \(-0.307877\pi\) | |||||||
\(390\) | −6.32501 | −0.320279 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −9.51754 | −0.480708 | ||||||||
\(393\) | − | 16.7297i | − | 0.843900i | ||||||
\(394\) | −16.2744 | − | 16.2744i | −0.819893 | − | 0.819893i | ||||
\(395\) | 17.3105 | 0.870984 | ||||||||
\(396\) | −2.00641 | − | 2.00641i | −0.100826 | − | 0.100826i | ||||
\(397\) | 1.30288 | − | 1.30288i | 0.0653896 | − | 0.0653896i | −0.673656 | − | 0.739045i | \(-0.735277\pi\) |
0.739045 | + | 0.673656i | \(0.235277\pi\) | |||||||
\(398\) | −12.8139 | + | 12.8139i | −0.642301 | + | 0.642301i | ||||
\(399\) | − | 26.2276i | − | 1.31302i | ||||||
\(400\) | 0.509800i | 0.0254900i | ||||||||
\(401\) | −7.54165 | + | 7.54165i | −0.376612 | + | 0.376612i | −0.869878 | − | 0.493266i | \(-0.835803\pi\) |
0.493266 | + | 0.869878i | \(0.335803\pi\) | |||||||
\(402\) | −8.63528 | + | 8.63528i | −0.430689 | + | 0.430689i | ||||
\(403\) | −1.09364 | − | 1.09364i | −0.0544780 | − | 0.0544780i | ||||
\(404\) | 9.17024 | 0.456237 | ||||||||
\(405\) | 1.65979 | + | 1.65979i | 0.0824756 | + | 0.0824756i | ||||
\(406\) | 35.3678i | 1.75528i | ||||||||
\(407\) | −22.3797 | −1.10932 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.33544 | −0.263820 | −0.131910 | − | 0.991262i | \(-0.542111\pi\) | ||||
−0.131910 | + | 0.991262i | \(0.542111\pi\) | |||||||
\(410\) | − | 8.06006i | − | 0.398058i | ||||||
\(411\) | 3.14900 | + | 3.14900i | 0.155329 | + | 0.155329i | ||||
\(412\) | 7.35235 | 0.362224 | ||||||||
\(413\) | −12.4933 | − | 12.4933i | −0.614755 | − | 0.614755i | ||||
\(414\) | −4.24264 | + | 4.24264i | −0.208514 | + | 0.208514i | ||||
\(415\) | −5.33146 | + | 5.33146i | −0.261711 | + | 0.261711i | ||||
\(416\) | − | 2.69459i | − | 0.132113i | ||||||
\(417\) | − | 12.7392i | − | 0.623840i | ||||||
\(418\) | −12.9481 | + | 12.9481i | −0.633313 | + | 0.633313i | ||||
\(419\) | −17.3977 | + | 17.3977i | −0.849931 | + | 0.849931i | −0.990124 | − | 0.140193i | \(-0.955228\pi\) |
0.140193 | + | 0.990124i | \(0.455228\pi\) | |||||||
\(420\) | −6.74568 | − | 6.74568i | −0.329155 | − | 0.329155i | ||||
\(421\) | 2.89662 | 0.141173 | 0.0705863 | − | 0.997506i | \(-0.477513\pi\) | ||||
0.0705863 | + | 0.997506i | \(0.477513\pi\) | |||||||
\(422\) | −11.0041 | − | 11.0041i | −0.535670 | − | 0.535670i | ||||
\(423\) | 10.5817i | 0.514501i | ||||||||
\(424\) | 3.29086 | 0.159818 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 11.6013 | 0.562086 | ||||||||
\(427\) | 53.0951i | 2.56945i | ||||||||
\(428\) | −3.55487 | − | 3.55487i | −0.171831 | − | 0.171831i | ||||
\(429\) | −7.64590 | −0.369147 | ||||||||
\(430\) | −19.3297 | − | 19.3297i | −0.932162 | − | 0.932162i | ||||
\(431\) | −5.77914 | + | 5.77914i | −0.278371 | + | 0.278371i | −0.832459 | − | 0.554087i | \(-0.813067\pi\) |
0.554087 | + | 0.832459i | \(0.313067\pi\) | |||||||
\(432\) | −0.707107 | + | 0.707107i | −0.0340207 | + | 0.0340207i | ||||
\(433\) | − | 21.7365i | − | 1.04459i | −0.852765 | − | 0.522294i | \(-0.825076\pi\) | ||
0.852765 | − | 0.522294i | \(-0.174924\pi\) | |||||||
\(434\) | − | 2.33275i | − | 0.111976i | ||||||
\(435\) | −14.4440 | + | 14.4440i | −0.692539 | + | 0.692539i | ||||
\(436\) | −6.40934 | + | 6.40934i | −0.306952 | + | 0.306952i | ||||
\(437\) | 27.3793 | + | 27.3793i | 1.30973 | + | 1.30973i | ||||
\(438\) | −2.36184 | −0.112853 | ||||||||
\(439\) | 7.96261 | + | 7.96261i | 0.380035 | + | 0.380035i | 0.871115 | − | 0.491080i | \(-0.163398\pi\) |
−0.491080 | + | 0.871115i | \(0.663398\pi\) | |||||||
\(440\) | 6.66044i | 0.317524i | ||||||||
\(441\) | 9.51754 | 0.453216 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.4730 | −1.06772 | −0.533861 | − | 0.845572i | \(-0.679260\pi\) | ||||
−0.533861 | + | 0.845572i | \(0.679260\pi\) | |||||||
\(444\) | 7.88713i | 0.374306i | ||||||||
\(445\) | −10.5239 | − | 10.5239i | −0.498880 | − | 0.498880i | ||||
\(446\) | 13.3063 | 0.630074 | ||||||||
\(447\) | −13.6407 | − | 13.6407i | −0.645183 | − | 0.645183i | ||||
\(448\) | 2.87381 | − | 2.87381i | 0.135775 | − | 0.135775i | ||||
\(449\) | 6.58706 | − | 6.58706i | 0.310863 | − | 0.310863i | −0.534381 | − | 0.845244i | \(-0.679455\pi\) |
0.845244 | + | 0.534381i | \(0.179455\pi\) | |||||||
\(450\) | − | 0.509800i | − | 0.0240322i | ||||||
\(451\) | − | 9.74329i | − | 0.458794i | ||||||
\(452\) | −7.88280 | + | 7.88280i | −0.370775 | + | 0.370775i | ||||
\(453\) | 9.24806 | − | 9.24806i | 0.434512 | − | 0.434512i | ||||
\(454\) | −2.61247 | − | 2.61247i | −0.122609 | − | 0.122609i | ||||
\(455\) | −25.7060 | −1.20511 | ||||||||
\(456\) | 4.56322 | + | 4.56322i | 0.213692 | + | 0.213692i | ||||
\(457\) | − | 21.4124i | − | 1.00163i | −0.865554 | − | 0.500815i | \(-0.833034\pi\) | ||
0.865554 | − | 0.500815i | \(-0.166966\pi\) | |||||||
\(458\) | −8.85204 | −0.413629 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 14.0838 | 0.656660 | ||||||||
\(461\) | 20.6287i | 0.960772i | 0.877057 | + | 0.480386i | \(0.159504\pi\) | ||||
−0.877057 | + | 0.480386i | \(0.840496\pi\) | |||||||
\(462\) | −8.15442 | − | 8.15442i | −0.379378 | − | 0.379378i | ||||
\(463\) | 25.6973 | 1.19425 | 0.597127 | − | 0.802147i | \(-0.296309\pi\) | ||||
0.597127 | + | 0.802147i | \(0.296309\pi\) | |||||||
\(464\) | −6.15348 | − | 6.15348i | −0.285668 | − | 0.285668i | ||||
\(465\) | 0.952682 | − | 0.952682i | 0.0441796 | − | 0.0441796i | ||||
\(466\) | −4.16283 | + | 4.16283i | −0.192839 | + | 0.192839i | ||||
\(467\) | − | 3.15570i | − | 0.146028i | −0.997331 | − | 0.0730141i | \(-0.976738\pi\) | ||
0.997331 | − | 0.0730141i | \(-0.0232618\pi\) | |||||||
\(468\) | 2.69459i | 0.124558i | ||||||||
\(469\) | −35.0953 | + | 35.0953i | −1.62055 | + | 1.62055i | ||||
\(470\) | 17.5634 | − | 17.5634i | 0.810140 | − | 0.810140i | ||||
\(471\) | −7.16183 | − | 7.16183i | −0.330000 | − | 0.330000i | ||||
\(472\) | 4.34730 | 0.200101 | ||||||||
\(473\) | −23.3665 | − | 23.3665i | −1.07439 | − | 1.07439i | ||||
\(474\) | − | 7.37464i | − | 0.338728i | ||||||
\(475\) | −3.28993 | −0.150952 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.29086 | −0.150678 | ||||||||
\(478\) | 16.6108i | 0.759761i | ||||||||
\(479\) | 1.36212 | + | 1.36212i | 0.0622368 | + | 0.0622368i | 0.737540 | − | 0.675303i | \(-0.235987\pi\) |
−0.675303 | + | 0.737540i | \(0.735987\pi\) | |||||||
\(480\) | 2.34730 | 0.107139 | ||||||||
\(481\) | 15.0279 | + | 15.0279i | 0.685211 | + | 0.685211i | ||||
\(482\) | 6.02091 | − | 6.02091i | 0.274245 | − | 0.274245i | ||||
\(483\) | −17.2428 | + | 17.2428i | −0.784577 | + | 0.784577i | ||||
\(484\) | − | 2.94862i | − | 0.134028i | ||||||
\(485\) | 19.0455i | 0.864812i | ||||||||
\(486\) | 0.707107 | − | 0.707107i | 0.0320750 | − | 0.0320750i | ||||
\(487\) | −5.62052 | + | 5.62052i | −0.254690 | + | 0.254690i | −0.822890 | − | 0.568200i | \(-0.807640\pi\) |
0.568200 | + | 0.822890i | \(0.307640\pi\) | |||||||
\(488\) | −9.23777 | − | 9.23777i | −0.418174 | − | 0.418174i | ||||
\(489\) | −0.212134 | −0.00959302 | ||||||||
\(490\) | −15.7971 | − | 15.7971i | −0.713641 | − | 0.713641i | ||||
\(491\) | − | 5.25402i | − | 0.237111i | −0.992947 | − | 0.118555i | \(-0.962174\pi\) | ||
0.992947 | − | 0.118555i | \(-0.0378263\pi\) | |||||||
\(492\) | −3.43376 | −0.154806 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 17.3892 | 0.782376 | ||||||||
\(495\) | − | 6.66044i | − | 0.299365i | ||||||
\(496\) | 0.405864 | + | 0.405864i | 0.0182238 | + | 0.0182238i | ||||
\(497\) | 47.1498 | 2.11496 | ||||||||
\(498\) | 2.27132 | + | 2.27132i | 0.101780 | + | 0.101780i | ||||
\(499\) | −17.5911 | + | 17.5911i | −0.787488 | + | 0.787488i | −0.981082 | − | 0.193594i | \(-0.937986\pi\) |
0.193594 | + | 0.981082i | \(0.437986\pi\) | |||||||
\(500\) | 7.45279 | − | 7.45279i | 0.333299 | − | 0.333299i | ||||
\(501\) | 8.49794i | 0.379660i | ||||||||
\(502\) | 6.89899i | 0.307917i | ||||||||
\(503\) | 7.73279 | − | 7.73279i | 0.344788 | − | 0.344788i | −0.513376 | − | 0.858164i | \(-0.671605\pi\) |
0.858164 | + | 0.513376i | \(0.171605\pi\) | |||||||
\(504\) | −2.87381 | + | 2.87381i | −0.128010 | + | 0.128010i | ||||
\(505\) | 15.2207 | + | 15.2207i | 0.677311 | + | 0.677311i | ||||
\(506\) | 17.0250 | 0.756853 | ||||||||
\(507\) | −4.05821 | − | 4.05821i | −0.180231 | − | 0.180231i | ||||
\(508\) | 1.93582i | 0.0858882i | ||||||||
\(509\) | 38.4219 | 1.70302 | 0.851510 | − | 0.524338i | \(-0.175687\pi\) | ||||
0.851510 | + | 0.524338i | \(0.175687\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.59896 | −0.424633 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −4.56322 | − | 4.56322i | −0.201471 | − | 0.201471i | ||||
\(514\) | 22.5526 | 0.994754 | ||||||||
\(515\) | 12.2033 | + | 12.2033i | 0.537744 | + | 0.537744i | ||||
\(516\) | −8.23489 | + | 8.23489i | −0.362521 | + | 0.362521i | ||||
\(517\) | 21.2313 | − | 21.2313i | 0.933751 | − | 0.933751i | ||||
\(518\) | 32.0547i | 1.40840i | ||||||||
\(519\) | 0.226682i | 0.00995022i | ||||||||
\(520\) | 4.47246 | − | 4.47246i | 0.196130 | − | 0.196130i | ||||
\(521\) | 22.0745 | − | 22.0745i | 0.967103 | − | 0.967103i | −0.0323725 | − | 0.999476i | \(-0.510306\pi\) |
0.999476 | + | 0.0323725i | \(0.0103063\pi\) | |||||||
\(522\) | 6.15348 | + | 6.15348i | 0.269330 | + | 0.269330i | ||||
\(523\) | 17.5567 | 0.767703 | 0.383851 | − | 0.923395i | \(-0.374598\pi\) | ||||
0.383851 | + | 0.923395i | \(0.374598\pi\) | |||||||
\(524\) | 11.8297 | + | 11.8297i | 0.516781 | + | 0.516781i | ||||
\(525\) | − | 2.07192i | − | 0.0904259i | ||||||
\(526\) | 16.9513 | 0.739112 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 2.83750 | 0.123486 | ||||||||
\(529\) | − | 13.0000i | − | 0.565217i | ||||||
\(530\) | 5.46213 | + | 5.46213i | 0.237260 | + | 0.237260i | ||||
\(531\) | −4.34730 | −0.188657 | ||||||||
\(532\) | 18.5457 | + | 18.5457i | 0.804059 | + | 0.804059i | ||||
\(533\) | −6.54257 | + | 6.54257i | −0.283390 | + | 0.283390i | ||||
\(534\) | −4.48340 | + | 4.48340i | −0.194016 | + | 0.194016i | ||||
\(535\) | − | 11.8007i | − | 0.510187i | ||||||
\(536\) | − | 12.2121i | − | 0.527484i | ||||||
\(537\) | −8.26933 | + | 8.26933i | −0.356848 | + | 0.356848i | ||||
\(538\) | −7.64269 | + | 7.64269i | −0.329500 | + | 0.329500i | ||||
\(539\) | −19.0961 | − | 19.0961i | −0.822528 | − | 0.822528i | ||||
\(540\) | −2.34730 | −0.101012 | ||||||||
\(541\) | −7.55127 | − | 7.55127i | −0.324655 | − | 0.324655i | 0.525895 | − | 0.850550i | \(-0.323730\pi\) |
−0.850550 | + | 0.525895i | \(0.823730\pi\) | |||||||
\(542\) | − | 21.3131i | − | 0.915478i | ||||||
\(543\) | 2.49794 | 0.107197 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −21.2763 | −0.911377 | ||||||||
\(546\) | 10.9513i | 0.468673i | ||||||||
\(547\) | 5.34723 | + | 5.34723i | 0.228631 | + | 0.228631i | 0.812121 | − | 0.583490i | \(-0.198313\pi\) |
−0.583490 | + | 0.812121i | \(0.698313\pi\) | |||||||
\(548\) | −4.45336 | −0.190238 | ||||||||
\(549\) | 9.23777 | + | 9.23777i | 0.394258 | + | 0.394258i | ||||
\(550\) | −1.02287 | + | 1.02287i | −0.0436153 | + | 0.0436153i | ||||
\(551\) | 39.7106 | − | 39.7106i | 1.69173 | − | 1.69173i | ||||
\(552\) | − | 6.00000i | − | 0.255377i | ||||||
\(553\) | − | 29.9718i | − | 1.27453i | ||||||
\(554\) | 15.6581 | − | 15.6581i | 0.665247 | − | 0.665247i | ||||
\(555\) | −13.0910 | + | 13.0910i | −0.555681 | + | 0.555681i | ||||
\(556\) | 9.00795 | + | 9.00795i | 0.382022 | + | 0.382022i | ||||
\(557\) | 13.9222 | 0.589903 | 0.294951 | − | 0.955512i | \(-0.404697\pi\) | ||||
0.294951 | + | 0.955512i | \(0.404697\pi\) | |||||||
\(558\) | −0.405864 | − | 0.405864i | −0.0171816 | − | 0.0171816i | ||||
\(559\) | 31.3809i | 1.32727i | ||||||||
\(560\) | 9.53983 | 0.403131 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10.0155 | 0.422478 | ||||||||
\(563\) | 2.71595i | 0.114464i | 0.998361 | + | 0.0572318i | \(0.0182274\pi\) | ||||
−0.998361 | + | 0.0572318i | \(0.981773\pi\) | |||||||
\(564\) | −7.48241 | − | 7.48241i | −0.315066 | − | 0.315066i | ||||
\(565\) | −26.1676 | −1.10088 | ||||||||
\(566\) | −7.13031 | − | 7.13031i | −0.299709 | − | 0.299709i | ||||
\(567\) | 2.87381 | − | 2.87381i | 0.120689 | − | 0.120689i | ||||
\(568\) | −8.20337 | + | 8.20337i | −0.344206 | + | 0.344206i | ||||
\(569\) | 29.8735i | 1.25236i | 0.779677 | + | 0.626181i | \(0.215383\pi\) | ||||
−0.779677 | + | 0.626181i | \(0.784617\pi\) | |||||||
\(570\) | 15.1480i | 0.634478i | ||||||||
\(571\) | −23.3703 | + | 23.3703i | −0.978016 | + | 0.978016i | −0.999763 | − | 0.0217478i | \(-0.993077\pi\) |
0.0217478 | + | 0.999763i | \(0.493077\pi\) | |||||||
\(572\) | 5.40647 | − | 5.40647i | 0.226056 | − | 0.226056i | ||||
\(573\) | 1.93689 | + | 1.93689i | 0.0809146 | + | 0.0809146i | ||||
\(574\) | −13.9554 | −0.582488 | ||||||||
\(575\) | 2.16290 | + | 2.16290i | 0.0901991 | + | 0.0901991i | ||||
\(576\) | − | 1.00000i | − | 0.0416667i | ||||||
\(577\) | 8.96080 | 0.373043 | 0.186521 | − | 0.982451i | \(-0.440279\pi\) | ||||
0.186521 | + | 0.982451i | \(0.440279\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.2540 | 0.550818 | ||||||||
\(580\) | − | 20.4270i | − | 0.848183i | ||||||
\(581\) | 9.23105 | + | 9.23105i | 0.382969 | + | 0.382969i | ||||
\(582\) | 8.11381 | 0.336328 | ||||||||
\(583\) | 6.60282 | + | 6.60282i | 0.273461 | + | 0.273461i | ||||
\(584\) | 1.67008 | − | 1.67008i | 0.0691082 | − | 0.0691082i | ||||
\(585\) | −4.47246 | + | 4.47246i | −0.184913 | + | 0.184913i | ||||
\(586\) | 14.5594i | 0.601445i | ||||||||
\(587\) | − | 12.3919i | − | 0.511467i | −0.966747 | − | 0.255734i | \(-0.917683\pi\) | ||
0.966747 | − | 0.255734i | \(-0.0823170\pi\) | |||||||
\(588\) | −6.72992 | + | 6.72992i | −0.277537 | + | 0.277537i | ||||
\(589\) | −2.61919 | + | 2.61919i | −0.107922 | + | 0.107922i | ||||
\(590\) | 7.21560 | + | 7.21560i | 0.297061 | + | 0.297061i | ||||
\(591\) | −23.0155 | −0.946730 | ||||||||
\(592\) | −5.57704 | − | 5.57704i | −0.229215 | − | 0.229215i | ||||
\(593\) | 46.4005i | 1.90544i | 0.303846 | + | 0.952721i | \(0.401729\pi\) | ||||
−0.303846 | + | 0.952721i | \(0.598271\pi\) | |||||||
\(594\) | −2.83750 | −0.116424 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 19.2909 | 0.790184 | ||||||||
\(597\) | 18.1215i | 0.741666i | ||||||||
\(598\) | −11.4322 | − | 11.4322i | −0.467497 | − | 0.467497i | ||||
\(599\) | −19.4492 | −0.794675 | −0.397337 | − | 0.917673i | \(-0.630066\pi\) | ||||
−0.397337 | + | 0.917673i | \(0.630066\pi\) | |||||||
\(600\) | 0.360483 | + | 0.360483i | 0.0147167 | + | 0.0147167i | ||||
\(601\) | −22.4623 | + | 22.4623i | −0.916257 | + | 0.916257i | −0.996755 | − | 0.0804978i | \(-0.974349\pi\) |
0.0804978 | + | 0.996755i | \(0.474349\pi\) | |||||||
\(602\) | −33.4681 | + | 33.4681i | −1.36406 | + | 1.36406i | ||||
\(603\) | 12.2121i | 0.497317i | ||||||||
\(604\) | 13.0787i | 0.532166i | ||||||||
\(605\) | 4.89408 | − | 4.89408i | 0.198973 | − | 0.198973i | ||||
\(606\) | 6.48434 | − | 6.48434i | 0.263408 | − | 0.263408i | ||||
\(607\) | −6.52235 | − | 6.52235i | −0.264734 | − | 0.264734i | 0.562240 | − | 0.826974i | \(-0.309940\pi\) |
−0.826974 | + | 0.562240i | \(0.809940\pi\) | |||||||
\(608\) | −6.45336 | −0.261718 | ||||||||
\(609\) | 25.0088 | + | 25.0088i | 1.01341 | + | 1.01341i | ||||
\(610\) | − | 30.6655i | − | 1.24161i | ||||||
\(611\) | −28.5134 | −1.15353 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.1634 | 0.693225 | 0.346612 | − | 0.938008i | \(-0.387332\pi\) | ||||
0.346612 | + | 0.938008i | \(0.387332\pi\) | |||||||
\(614\) | − | 19.6459i | − | 0.792844i | ||||||
\(615\) | −5.69932 | − | 5.69932i | −0.229819 | − | 0.229819i | ||||
\(616\) | 11.5321 | 0.464641 | ||||||||
\(617\) | 11.5788 | + | 11.5788i | 0.466147 | + | 0.466147i | 0.900664 | − | 0.434517i | \(-0.143081\pi\) |
−0.434517 | + | 0.900664i | \(0.643081\pi\) | |||||||
\(618\) | 5.19890 | − | 5.19890i | 0.209130 | − | 0.209130i | ||||
\(619\) | −21.3742 | + | 21.3742i | −0.859100 | + | 0.859100i | −0.991232 | − | 0.132132i | \(-0.957818\pi\) |
0.132132 | + | 0.991232i | \(0.457818\pi\) | |||||||
\(620\) | 1.34730i | 0.0541087i | ||||||||
\(621\) | 6.00000i | 0.240772i | ||||||||
\(622\) | 10.0810 | − | 10.0810i | 0.404212 | − | 0.404212i | ||||
\(623\) | −18.2213 | + | 18.2213i | −0.730023 | + | 0.730023i | ||||
\(624\) | −1.90536 | − | 1.90536i | −0.0762756 | − | 0.0762756i | ||||
\(625\) | 27.2891 | 1.09156 | ||||||||
\(626\) | −14.8740 | − | 14.8740i | −0.594487 | − | 0.594487i | ||||
\(627\) | 18.3114i | 0.731287i | ||||||||
\(628\) | 10.1284 | 0.404165 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −9.53983 | −0.380076 | ||||||||
\(631\) | − | 15.1848i | − | 0.604497i | −0.953229 | − | 0.302249i | \(-0.902263\pi\) | ||
0.953229 | − | 0.302249i | \(-0.0977372\pi\) | |||||||
\(632\) | 5.21466 | + | 5.21466i | 0.207428 | + | 0.207428i | ||||
\(633\) | −15.5621 | −0.618539 | ||||||||
\(634\) | −4.04726 | − | 4.04726i | −0.160737 | − | 0.160737i | ||||
\(635\) | −3.21306 | + | 3.21306i | −0.127506 | + | 0.127506i | ||||
\(636\) | 2.32699 | − | 2.32699i | 0.0922711 | − | 0.0922711i | ||||
\(637\) | 25.6459i | 1.01613i | ||||||||
\(638\) | − | 24.6928i | − | 0.977599i | ||||||
\(639\) | 8.20337 | − | 8.20337i | 0.324520 | − | 0.324520i | ||||
\(640\) | −1.65979 | + | 1.65979i | −0.0656089 | + | 0.0656089i | ||||
\(641\) | −5.92914 | − | 5.92914i | −0.234187 | − | 0.234187i | 0.580251 | − | 0.814438i | \(-0.302954\pi\) |
−0.814438 | + | 0.580251i | \(0.802954\pi\) | |||||||
\(642\) | −5.02734 | −0.198413 | ||||||||
\(643\) | −3.84225 | − | 3.84225i | −0.151524 | − | 0.151524i | 0.627275 | − | 0.778798i | \(-0.284170\pi\) |
−0.778798 | + | 0.627275i | \(0.784170\pi\) | |||||||
\(644\) | − | 24.3851i | − | 0.960906i | ||||||
\(645\) | −27.3364 | −1.07637 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.0797 | 0.514214 | 0.257107 | − | 0.966383i | \(-0.417231\pi\) | ||||
0.257107 | + | 0.966383i | \(0.417231\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | 8.72247 | + | 8.72247i | 0.342387 | + | 0.342387i | ||||
\(650\) | 1.37370 | 0.0538811 | ||||||||
\(651\) | −1.64950 | − | 1.64950i | −0.0646491 | − | 0.0646491i | ||||
\(652\) | 0.150001 | − | 0.150001i | 0.00587450 | − | 0.00587450i | ||||
\(653\) | 20.8721 | − | 20.8721i | 0.816787 | − | 0.816787i | −0.168854 | − | 0.985641i | \(-0.554007\pi\) |
0.985641 | + | 0.168854i | \(0.0540068\pi\) | |||||||
\(654\) | 9.06418i | 0.354437i | ||||||||
\(655\) | 39.2695i | 1.53439i | ||||||||
\(656\) | 2.42804 | − | 2.42804i | 0.0947989 | − | 0.0947989i | ||||
\(657\) | −1.67008 | + | 1.67008i | −0.0651559 | + | 0.0651559i | ||||
\(658\) | −30.4098 | − | 30.4098i | −1.18550 | − | 1.18550i | ||||
\(659\) | −21.5084 | −0.837847 | −0.418924 | − | 0.908022i | \(-0.637592\pi\) | ||||
−0.418924 | + | 0.908022i | \(0.637592\pi\) | |||||||
\(660\) | 4.70965 | + | 4.70965i | 0.183323 | + | 0.183323i | ||||
\(661\) | − | 35.2080i | − | 1.36943i | −0.728809 | − | 0.684717i | \(-0.759926\pi\) | ||
0.728809 | − | 0.684717i | \(-0.240074\pi\) | |||||||
\(662\) | −3.14796 | −0.122349 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.21213 | −0.124655 | ||||||||
\(665\) | 61.5640i | 2.38735i | ||||||||
\(666\) | 5.57704 | + | 5.57704i | 0.216106 | + | 0.216106i | ||||
\(667\) | −52.2140 | −2.02173 | ||||||||
\(668\) | −6.00895 | − | 6.00895i | −0.232493 | − | 0.232493i | ||||
\(669\) | 9.40900 | − | 9.40900i | 0.363773 | − | 0.363773i | ||||
\(670\) | 20.2696 | − | 20.2696i | 0.783082 | − | 0.783082i | ||||
\(671\) | − | 37.0696i | − | 1.43105i | ||||||
\(672\) | − | 4.06418i | − | 0.156779i | ||||||
\(673\) | 1.37307 | − | 1.37307i | 0.0529278 | − | 0.0529278i | −0.680147 | − | 0.733075i | \(-0.738084\pi\) |
0.733075 | + | 0.680147i | \(0.238084\pi\) | |||||||
\(674\) | −22.5834 | + | 22.5834i | −0.869878 | + | 0.869878i | ||||
\(675\) | −0.360483 | − | 0.360483i | −0.0138750 | − | 0.0138750i | ||||
\(676\) | 5.73917 | 0.220737 | ||||||||
\(677\) | −1.02388 | − | 1.02388i | −0.0393509 | − | 0.0393509i | 0.687158 | − | 0.726508i | \(-0.258858\pi\) |
−0.726508 | + | 0.687158i | \(0.758858\pi\) | |||||||
\(678\) | 11.1480i | 0.428135i | ||||||||
\(679\) | 32.9760 | 1.26550 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.69459 | −0.141577 | ||||||||
\(682\) | 1.62866i | 0.0623646i | ||||||||
\(683\) | −12.4135 | − | 12.4135i | −0.474989 | − | 0.474989i | 0.428536 | − | 0.903525i | \(-0.359029\pi\) |
−0.903525 | + | 0.428536i | \(0.859029\pi\) | |||||||
\(684\) | 6.45336 | 0.246751 | ||||||||
\(685\) | −7.39164 | − | 7.39164i | −0.282420 | − | 0.282420i | ||||
\(686\) | −7.23493 | + | 7.23493i | −0.276231 | + | 0.276231i | ||||
\(687\) | −6.25934 | + | 6.25934i | −0.238809 | + | 0.238809i | ||||
\(688\) | − | 11.6459i | − | 0.443996i | ||||||
\(689\) | − | 8.86753i | − | 0.337826i | ||||||
\(690\) | 9.95874 | − | 9.95874i | 0.379123 | − | 0.379123i | ||||
\(691\) | 12.6166 | − | 12.6166i | 0.479958 | − | 0.479958i | −0.425160 | − | 0.905118i | \(-0.639782\pi\) |
0.905118 | + | 0.425160i | \(0.139782\pi\) | |||||||
\(692\) | −0.160288 | − | 0.160288i | −0.00609324 | − | 0.00609324i | ||||
\(693\) | −11.5321 | −0.438068 | ||||||||
\(694\) | 25.5418 | + | 25.5418i | 0.969553 | + | 0.969553i | ||||
\(695\) | 29.9026i | 1.13427i | ||||||||
\(696\) | −8.70233 | −0.329861 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −12.7493 | −0.482567 | ||||||||
\(699\) | 5.88713i | 0.222672i | ||||||||
\(700\) | 1.46507 | + | 1.46507i | 0.0553744 | + | 0.0553744i | ||||
\(701\) | −43.0051 | −1.62428 | −0.812139 | − | 0.583464i | \(-0.801697\pi\) | ||||
−0.812139 | + | 0.583464i | \(0.801697\pi\) | |||||||
\(702\) | 1.90536 | + | 1.90536i | 0.0719134 | + | 0.0719134i | ||||
\(703\) | 35.9907 | − | 35.9907i | 1.35741 | − | 1.35741i | ||||
\(704\) | −2.00641 | + | 2.00641i | −0.0756195 | + | 0.0756195i | ||||
\(705\) | − | 24.8384i | − | 0.935469i | ||||||
\(706\) | 7.09327i | 0.266959i | ||||||||
\(707\) | 26.3535 | − | 26.3535i | 0.991126 | − | 0.991126i | ||||
\(708\) | 3.07400 | − | 3.07400i | 0.115528 | − | 0.115528i | ||||
\(709\) | −7.70507 | − | 7.70507i | −0.289370 | − | 0.289370i | 0.547461 | − | 0.836831i | \(-0.315594\pi\) |
−0.836831 | + | 0.547461i | \(0.815594\pi\) | |||||||
\(710\) | −27.2317 | −1.02199 | ||||||||
\(711\) | −5.21466 | − | 5.21466i | −0.195565 | − | 0.195565i | ||||
\(712\) | − | 6.34049i | − | 0.237620i | ||||||
\(713\) | 3.44387 | 0.128974 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 17.9472 | 0.671187 | ||||||||
\(716\) | − | 11.6946i | − | 0.437047i | ||||||
\(717\) | 11.7456 | + | 11.7456i | 0.438648 | + | 0.438648i | ||||
\(718\) | 10.6655 | 0.398033 | ||||||||
\(719\) | −6.93201 | − | 6.93201i | −0.258520 | − | 0.258520i | 0.565932 | − | 0.824452i | \(-0.308517\pi\) |
−0.824452 | + | 0.565932i | \(0.808517\pi\) | |||||||
\(720\) | 1.65979 | − | 1.65979i | 0.0618567 | − | 0.0618567i | ||||
\(721\) | 21.1292 | − | 21.1292i | 0.786894 | − | 0.786894i | ||||
\(722\) | − | 22.6459i | − | 0.842793i | ||||||
\(723\) | − | 8.51485i | − | 0.316671i | ||||||
\(724\) | −1.76631 | + | 1.76631i | −0.0656444 | + | 0.0656444i | ||||
\(725\) | 3.13704 | − | 3.13704i | 0.116507 | − | 0.116507i | ||||
\(726\) | −2.08499 | − | 2.08499i | −0.0773811 | − | 0.0773811i | ||||
\(727\) | 0.598631 | 0.0222020 | 0.0111010 | − | 0.999938i | \(-0.496466\pi\) | ||||
0.0111010 | + | 0.999938i | \(0.496466\pi\) | |||||||
\(728\) | −7.74374 | − | 7.74374i | −0.287002 | − | 0.287002i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 5.54395 | 0.205191 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −13.0642 | −0.482866 | ||||||||
\(733\) | − | 44.4944i | − | 1.64344i | −0.569892 | − | 0.821720i | \(-0.693015\pi\) | ||
0.569892 | − | 0.821720i | \(-0.306985\pi\) | |||||||
\(734\) | 17.1473 | + | 17.1473i | 0.632917 | + | 0.632917i | ||||
\(735\) | −22.3405 | −0.824041 | ||||||||
\(736\) | 4.24264 | + | 4.24264i | 0.156386 | + | 0.156386i | ||||
\(737\) | 24.5026 | − | 24.5026i | 0.902564 | − | 0.902564i | ||||
\(738\) | −2.42804 | + | 2.42804i | −0.0893773 | + | 0.0893773i | ||||
\(739\) | − | 21.0060i | − | 0.772718i | −0.922349 | − | 0.386359i | \(-0.873733\pi\) | ||
0.922349 | − | 0.386359i | \(-0.126267\pi\) | |||||||
\(740\) | − | 18.5134i | − | 0.680567i | ||||||
\(741\) | 12.2960 | − | 12.2960i | 0.451705 | − | 0.451705i | ||||
\(742\) | 9.45730 | − | 9.45730i | 0.347188 | − | 0.347188i | ||||
\(743\) | −17.0202 | − | 17.0202i | −0.624410 | − | 0.624410i | 0.322246 | − | 0.946656i | \(-0.395562\pi\) |
−0.946656 | + | 0.322246i | \(0.895562\pi\) | |||||||
\(744\) | 0.573978 | 0.0210431 | ||||||||
\(745\) | 32.0188 | + | 32.0188i | 1.17308 | + | 1.17308i | ||||
\(746\) | − | 22.7547i | − | 0.833107i | ||||||
\(747\) | 3.21213 | 0.117526 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −20.4320 | −0.746569 | ||||||||
\(750\) | − | 10.5398i | − | 0.384860i | ||||||
\(751\) | 1.05016 | + | 1.05016i | 0.0383208 | + | 0.0383208i | 0.726008 | − | 0.687687i | \(-0.241374\pi\) |
−0.687687 | + | 0.726008i | \(0.741374\pi\) | |||||||
\(752\) | 10.5817 | 0.385876 | ||||||||
\(753\) | 4.87832 | + | 4.87832i | 0.177776 | + | 0.177776i | ||||
\(754\) | −16.5811 | + | 16.5811i | −0.603849 | + | 0.603849i | ||||
\(755\) | −21.7079 | + | 21.7079i | −0.790032 | + | 0.790032i | ||||
\(756\) | 4.06418i | 0.147813i | ||||||||
\(757\) | 36.5134i | 1.32710i | 0.748131 | + | 0.663551i | \(0.230952\pi\) | ||||
−0.748131 | + | 0.663551i | \(0.769048\pi\) | |||||||
\(758\) | 14.0308 | − | 14.0308i | 0.509622 | − | 0.509622i | ||||
\(759\) | 12.0385 | − | 12.0385i | 0.436969 | − | 0.436969i | ||||
\(760\) | −10.7112 | − | 10.7112i | −0.388537 | − | 0.388537i | ||||
\(761\) | 7.06418 | 0.256076 | 0.128038 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128038 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(762\) | 1.36883 | + | 1.36883i | 0.0495876 | + | 0.0495876i | ||||
\(763\) | 36.8384i | 1.33364i | ||||||||
\(764\) | −2.73917 | −0.0990997 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.7196 | 0.567971 | ||||||||
\(767\) | − | 11.7142i | − | 0.422975i | ||||||
\(768\) | 0.707107 | + | 0.707107i | 0.0255155 | + | 0.0255155i | ||||
\(769\) | −9.04189 | −0.326059 | −0.163029 | − | 0.986621i | \(-0.552127\pi\) | ||||
−0.163029 | + | 0.986621i | \(0.552127\pi\) | |||||||
\(770\) | 19.1408 | + | 19.1408i | 0.689788 | + | 0.689788i | ||||
\(771\) | 15.9471 | − | 15.9471i | 0.574321 | − | 0.574321i | ||||
\(772\) | −9.37201 | + | 9.37201i | −0.337306 | + | 0.337306i | ||||
\(773\) | 3.06324i | 0.110177i | 0.998481 | + | 0.0550886i | \(0.0175441\pi\) | ||||
−0.998481 | + | 0.0550886i | \(0.982456\pi\) | |||||||
\(774\) | 11.6459i | 0.418603i | ||||||||
\(775\) | −0.206909 | + | 0.206909i | −0.00743240 | + | 0.00743240i | ||||
\(776\) | −5.73733 | + | 5.73733i | −0.205958 | + | 0.205958i | ||||
\(777\) | 22.6661 | + | 22.6661i | 0.813141 | + | 0.813141i | ||||
\(778\) | 32.4766 | 1.16434 | ||||||||
\(779\) | 15.6690 | + | 15.6690i | 0.561400 | + | 0.561400i | ||||
\(780\) | − | 6.32501i | − | 0.226472i | ||||||
\(781\) | −32.9187 | −1.17792 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.70233 | 0.310996 | ||||||||
\(784\) | − | 9.51754i | − | 0.339912i | ||||||
\(785\) | 16.8109 | + | 16.8109i | 0.600008 | + | 0.600008i | ||||
\(786\) | 16.7297 | 0.596728 | ||||||||
\(787\) | 12.9023 | + | 12.9023i | 0.459917 | + | 0.459917i | 0.898628 | − | 0.438711i | \(-0.144565\pi\) |
−0.438711 | + | 0.898628i | \(0.644565\pi\) | |||||||
\(788\) | 16.2744 | − | 16.2744i | 0.579752 | − | 0.579752i | ||||
\(789\) | 11.9864 | − | 11.9864i | 0.426726 | − | 0.426726i | ||||
\(790\) | 17.3105i | 0.615879i | ||||||||
\(791\) | 45.3073i | 1.61094i | ||||||||
\(792\) | 2.00641 | − | 2.00641i | 0.0712948 | − | 0.0712948i | ||||
\(793\) | −24.8920 | + | 24.8920i | −0.883942 | + | 0.883942i | ||||
\(794\) | 1.30288 | + | 1.30288i | 0.0462374 | + | 0.0462374i | ||||
\(795\) | 7.72462 | 0.273964 | ||||||||
\(796\) | −12.8139 | − | 12.8139i | −0.454176 | − | 0.454176i | ||||
\(797\) | − | 45.2222i | − | 1.60185i | −0.598762 | − | 0.800927i | \(-0.704341\pi\) | ||
0.598762 | − | 0.800927i | \(-0.295659\pi\) | |||||||
\(798\) | 26.2276 | 0.928448 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.509800 | −0.0180242 | ||||||||
\(801\) | 6.34049i | 0.224030i | ||||||||
\(802\) | −7.54165 | − | 7.54165i | −0.266305 | − | 0.266305i | ||||
\(803\) | 6.70172 | 0.236499 | ||||||||
\(804\) | −8.63528 | − | 8.63528i | −0.304543 | − | 0.304543i | ||||
\(805\) | 40.4741 | − | 40.4741i | 1.42652 | − | 1.42652i | ||||
\(806\) | 1.09364 | − | 1.09364i | 0.0385217 | − | 0.0385217i | ||||
\(807\) | 10.8084i | 0.380474i | ||||||||
\(808\) | 9.17024i | 0.322608i | ||||||||
\(809\) | 10.5999 | − | 10.5999i | 0.372672 | − | 0.372672i | −0.495777 | − | 0.868450i | \(-0.665117\pi\) |
0.868450 | + | 0.495777i | \(0.165117\pi\) | |||||||
\(810\) | −1.65979 | + | 1.65979i | −0.0583190 | + | 0.0583190i | ||||
\(811\) | −14.2438 | − | 14.2438i | −0.500169 | − | 0.500169i | 0.411321 | − | 0.911490i | \(-0.365067\pi\) |
−0.911490 | + | 0.411321i | \(0.865067\pi\) | |||||||
\(812\) | −35.3678 | −1.24117 | ||||||||
\(813\) | −15.0707 | − | 15.0707i | −0.528552 | − | 0.528552i | ||||
\(814\) | − | 22.3797i | − | 0.784408i | ||||||
\(815\) | 0.497941 | 0.0174421 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 75.1552 | 2.62935 | ||||||||
\(818\) | − | 5.33544i | − | 0.186549i | ||||||
\(819\) | 7.74374 | + | 7.74374i | 0.270588 | + | 0.270588i | ||||
\(820\) | 8.06006 | 0.281469 | ||||||||
\(821\) | 30.4027 | + | 30.4027i | 1.06106 | + | 1.06106i | 0.998010 | + | 0.0630505i | \(0.0200829\pi\) |
0.0630505 | + | 0.998010i | \(0.479917\pi\) | |||||||
\(822\) | −3.14900 | + | 3.14900i | −0.109834 | + | 0.109834i | ||||
\(823\) | 10.6140 | − | 10.6140i | 0.369980 | − | 0.369980i | −0.497490 | − | 0.867470i | \(-0.665745\pi\) |
0.867470 | + | 0.497490i | \(0.165745\pi\) | |||||||
\(824\) | 7.35235i | 0.256131i | ||||||||
\(825\) | 1.44656i | 0.0503626i | ||||||||
\(826\) | 12.4933 | − | 12.4933i | 0.434697 | − | 0.434697i | ||||
\(827\) | −5.18861 | + | 5.18861i | −0.180426 | + | 0.180426i | −0.791541 | − | 0.611116i | \(-0.790721\pi\) |
0.611116 | + | 0.791541i | \(0.290721\pi\) | |||||||
\(828\) | −4.24264 | − | 4.24264i | −0.147442 | − | 0.147442i | ||||
\(829\) | 14.0310 | 0.487315 | 0.243658 | − | 0.969861i | \(-0.421653\pi\) | ||||
0.243658 | + | 0.969861i | \(0.421653\pi\) | |||||||
\(830\) | −5.33146 | − | 5.33146i | −0.185058 | − | 0.185058i | ||||
\(831\) | − | 22.1438i | − | 0.768161i | ||||||
\(832\) | 2.69459 | 0.0934182 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 12.7392 | 0.441121 | ||||||||
\(835\) | − | 19.9472i | − | 0.690301i | ||||||
\(836\) | −12.9481 | − | 12.9481i | −0.447820 | − | 0.447820i | ||||
\(837\) | −0.573978 | −0.0198396 | ||||||||
\(838\) | −17.3977 | − | 17.3977i | −0.600992 | − | 0.600992i | ||||
\(839\) | 22.3674 | − | 22.3674i | 0.772208 | − | 0.772208i | −0.206284 | − | 0.978492i | \(-0.566137\pi\) |
0.978492 | + | 0.206284i | \(0.0661370\pi\) | |||||||
\(840\) | 6.74568 | − | 6.74568i | 0.232748 | − | 0.232748i | ||||
\(841\) | 46.7306i | 1.61140i | ||||||||
\(842\) | 2.89662i | 0.0998242i | ||||||||
\(843\) | 7.08201 | − | 7.08201i | 0.243918 | − | 0.243918i | ||||
\(844\) | 11.0041 | − | 11.0041i | 0.378776 | − | 0.378776i | ||||
\(845\) | 9.52581 | + | 9.52581i | 0.327698 | + | 0.327698i | ||||
\(846\) | −10.5817 | −0.363807 | ||||||||
\(847\) | −8.47375 | − | 8.47375i | −0.291162 | − | 0.291162i | ||||
\(848\) | 3.29086i | 0.113009i | ||||||||
\(849\) | −10.0838 | −0.346074 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −47.3228 | −1.62220 | ||||||||
\(852\) | 11.6013i | 0.397455i | ||||||||
\(853\) | 23.8820 | + | 23.8820i | 0.817704 | + | 0.817704i | 0.985775 | − | 0.168071i | \(-0.0537537\pi\) |
−0.168071 | + | 0.985775i | \(0.553754\pi\) | |||||||
\(854\) | −53.0951 | −1.81688 | ||||||||
\(855\) | 10.7112 | + | 10.7112i | 0.366316 | + | 0.366316i | ||||
\(856\) | 3.55487 | − | 3.55487i | 0.121503 | − | 0.121503i | ||||
\(857\) | 6.76858 | − | 6.76858i | 0.231210 | − | 0.231210i | −0.581987 | − | 0.813198i | \(-0.697725\pi\) |
0.813198 | + | 0.581987i | \(0.197725\pi\) | |||||||
\(858\) | − | 7.64590i | − | 0.261027i | ||||||
\(859\) | − | 45.6870i | − | 1.55882i | −0.626515 | − | 0.779410i | \(-0.715519\pi\) | ||
0.626515 | − | 0.779410i | \(-0.284481\pi\) | |||||||
\(860\) | 19.3297 | − | 19.3297i | 0.659138 | − | 0.659138i | ||||
\(861\) | −9.86797 | + | 9.86797i | −0.336300 | + | 0.336300i | ||||
\(862\) | −5.77914 | − | 5.77914i | −0.196838 | − | 0.196838i | ||||
\(863\) | 38.6674 | 1.31625 | 0.658126 | − | 0.752908i | \(-0.271349\pi\) | ||||
0.658126 | + | 0.752908i | \(0.271349\pi\) | |||||||
\(864\) | −0.707107 | − | 0.707107i | −0.0240563 | − | 0.0240563i | ||||
\(865\) | − | 0.532089i | − | 0.0180916i | ||||||
\(866\) | 21.7365 | 0.738636 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.33275 | 0.0791786 | ||||||||
\(869\) | 20.9255i | 0.709849i | ||||||||
\(870\) | −14.4440 | − | 14.4440i | −0.489699 | − | 0.489699i | ||||
\(871\) | −32.9067 | −1.11500 | ||||||||
\(872\) | −6.40934 | − | 6.40934i | −0.217048 | − | 0.217048i | ||||
\(873\) | 5.73733 | − | 5.73733i | 0.194179 | − | 0.194179i | ||||
\(874\) | −27.3793 | + | 27.3793i | −0.926119 | + | 0.926119i | ||||
\(875\) | − | 42.8357i | − | 1.44811i | ||||||
\(876\) | − | 2.36184i | − | 0.0797993i | ||||||
\(877\) | 6.78201 | − | 6.78201i | 0.229012 | − | 0.229012i | −0.583268 | − | 0.812280i | \(-0.698226\pi\) |
0.812280 | + | 0.583268i | \(0.198226\pi\) | |||||||
\(878\) | −7.96261 | + | 7.96261i | −0.268725 | + | 0.268725i | ||||
\(879\) | 10.2951 | + | 10.2951i | 0.347244 | + | 0.347244i | ||||
\(880\) | −6.66044 | −0.224524 | ||||||||
\(881\) | 32.1652 | + | 32.1652i | 1.08367 | + | 1.08367i | 0.996164 | + | 0.0875090i | \(0.0278907\pi\) |
0.0875090 | + | 0.996164i | \(0.472109\pi\) | |||||||
\(882\) | 9.51754i | 0.320472i | ||||||||
\(883\) | 47.3911 | 1.59484 | 0.797418 | − | 0.603427i | \(-0.206199\pi\) | ||||
0.797418 | + | 0.603427i | \(0.206199\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.2044 | 0.343017 | ||||||||
\(886\) | − | 22.4730i | − | 0.754994i | ||||||
\(887\) | −0.784008 | − | 0.784008i | −0.0263244 | − | 0.0263244i | 0.693822 | − | 0.720146i | \(-0.255925\pi\) |
−0.720146 | + | 0.693822i | \(0.755925\pi\) | |||||||
\(888\) | −7.88713 | −0.264675 | ||||||||
\(889\) | 5.56318 | + | 5.56318i | 0.186583 | + | 0.186583i | ||||
\(890\) | 10.5239 | − | 10.5239i | 0.352761 | − | 0.352761i | ||||
\(891\) | −2.00641 | + | 2.00641i | −0.0672174 | + | 0.0672174i | ||||
\(892\) | 13.3063i | 0.445529i | ||||||||
\(893\) | 68.2877i | 2.28516i | ||||||||
\(894\) | 13.6407 | − | 13.6407i | 0.456213 | − | 0.456213i | ||||
\(895\) | 19.4106 | − | 19.4106i | 0.648823 | − | 0.648823i | ||||
\(896\) | 2.87381 | + | 2.87381i | 0.0960072 | + | 0.0960072i | ||||
\(897\) | −16.1676 | −0.539819 | ||||||||
\(898\) | 6.58706 | + | 6.58706i | 0.219813 | + | 0.219813i | ||||
\(899\) | − | 4.99495i | − | 0.166591i | ||||||
\(900\) | 0.509800 | 0.0169933 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 9.74329 | 0.324416 | ||||||||
\(903\) | 47.3310i | 1.57508i | ||||||||
\(904\) | −7.88280 | − | 7.88280i | −0.262178 | − | 0.262178i | ||||
\(905\) | −5.86341 | −0.194906 | ||||||||
\(906\) | 9.24806 | + | 9.24806i | 0.307246 | + | 0.307246i | ||||
\(907\) | 2.57672 | − | 2.57672i | 0.0855585 | − | 0.0855585i | −0.663032 | − | 0.748591i | \(-0.730731\pi\) |
0.748591 | + | 0.663032i | \(0.230731\pi\) | |||||||
\(908\) | 2.61247 | − | 2.61247i | 0.0866979 | − | 0.0866979i | ||||
\(909\) | − | 9.17024i | − | 0.304158i | ||||||
\(910\) | − | 25.7060i | − | 0.852144i | ||||||
\(911\) | 3.85902 | − | 3.85902i | 0.127855 | − | 0.127855i | −0.640284 | − | 0.768139i | \(-0.721183\pi\) |
0.768139 | + | 0.640284i | \(0.221183\pi\) | |||||||
\(912\) | −4.56322 | + | 4.56322i | −0.151103 | + | 0.151103i | ||||
\(913\) | −6.44487 | − | 6.44487i | −0.213294 | − | 0.213294i | ||||
\(914\) | 21.4124 | 0.708259 | ||||||||
\(915\) | −21.6838 | − | 21.6838i | −0.716844 | − | 0.716844i | ||||
\(916\) | − | 8.85204i | − | 0.292480i | ||||||
\(917\) | 67.9924 | 2.24531 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −44.0060 | −1.45162 | −0.725812 | − | 0.687893i | \(-0.758536\pi\) | ||||
−0.725812 | + | 0.687893i | \(0.758536\pi\) | |||||||
\(920\) | 14.0838i | 0.464328i | ||||||||
\(921\) | −13.8917 | − | 13.8917i | −0.457749 | − | 0.457749i | ||||
\(922\) | −20.6287 | −0.679369 | ||||||||
\(923\) | 22.1047 | + | 22.1047i | 0.727587 | + | 0.727587i | ||||
\(924\) | 8.15442 | − | 8.15442i | 0.268261 | − | 0.268261i | ||||
\(925\) | 2.84318 | − | 2.84318i | 0.0934831 | − | 0.0934831i | ||||
\(926\) | 25.6973i | 0.844465i | ||||||||
\(927\) | − | 7.35235i | − | 0.241483i | ||||||
\(928\) | 6.15348 | − | 6.15348i | 0.201998 | − | 0.201998i | ||||
\(929\) | 33.4088 | − | 33.4088i | 1.09611 | − | 1.09611i | 0.101247 | − | 0.994861i | \(-0.467717\pi\) |
0.994861 | − | 0.101247i | \(-0.0322831\pi\) | |||||||
\(930\) | 0.952682 | + | 0.952682i | 0.0312397 | + | 0.0312397i | ||||
\(931\) | 61.4201 | 2.01296 | ||||||||
\(932\) | −4.16283 | − | 4.16283i | −0.136358 | − | 0.136358i | ||||
\(933\) | − | 14.2567i | − | 0.466744i | ||||||
\(934\) | 3.15570 | 0.103258 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.69459 | −0.0880755 | ||||||||
\(937\) | 42.9445i | 1.40294i | 0.712701 | + | 0.701468i | \(0.247472\pi\) | ||||
−0.712701 | + | 0.701468i | \(0.752528\pi\) | |||||||
\(938\) | −35.0953 | − | 35.0953i | −1.14590 | − | 1.14590i | ||||
\(939\) | −21.0351 | −0.686454 | ||||||||
\(940\) | 17.5634 | + | 17.5634i | 0.572856 | + | 0.572856i | ||||
\(941\) | −40.0518 | + | 40.0518i | −1.30565 | + | 1.30565i | −0.381129 | + | 0.924522i | \(0.624465\pi\) |
−0.924522 | + | 0.381129i | \(0.875535\pi\) | |||||||
\(942\) | 7.16183 | − | 7.16183i | 0.233345 | − | 0.233345i | ||||
\(943\) | − | 20.6026i | − | 0.670912i | ||||||
\(944\) | 4.34730i | 0.141492i | ||||||||
\(945\) | −6.74568 | + | 6.74568i | −0.219437 | + | 0.219437i | ||||
\(946\) | 23.3665 | − | 23.3665i | 0.759710 | − | 0.759710i | ||||
\(947\) | 39.6411 | + | 39.6411i | 1.28816 | + | 1.28816i | 0.935902 | + | 0.352261i | \(0.114587\pi\) |
0.352261 | + | 0.935902i | \(0.385413\pi\) | |||||||
\(948\) | 7.37464 | 0.239517 | ||||||||
\(949\) | −4.50017 | − | 4.50017i | −0.146082 | − | 0.146082i | ||||
\(950\) | − | 3.28993i | − | 0.106739i | ||||||
\(951\) | −5.72369 | −0.185603 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 41.5586 | 1.34622 | 0.673108 | − | 0.739544i | \(-0.264959\pi\) | ||||
0.673108 | + | 0.739544i | \(0.264959\pi\) | |||||||
\(954\) | − | 3.29086i | − | 0.106546i | ||||||
\(955\) | −4.54644 | − | 4.54644i | −0.147120 | − | 0.147120i | ||||
\(956\) | −16.6108 | −0.537232 | ||||||||
\(957\) | −17.4605 | − | 17.4605i | −0.564417 | − | 0.564417i | ||||
\(958\) | −1.36212 | + | 1.36212i | −0.0440081 | + | 0.0440081i | ||||
\(959\) | −12.7981 | + | 12.7981i | −0.413273 | + | 0.413273i | ||||
\(960\) | 2.34730i | 0.0757587i | ||||||||
\(961\) | − | 30.6705i | − | 0.989373i | ||||||
\(962\) | −15.0279 | + | 15.0279i | −0.484517 | + | 0.484517i | ||||
\(963\) | −3.55487 | + | 3.55487i | −0.114554 | + | 0.114554i | ||||
\(964\) | 6.02091 | + | 6.02091i | 0.193920 | + | 0.193920i | ||||
\(965\) | −31.1111 | −1.00150 | ||||||||
\(966\) | −17.2428 | − | 17.2428i | −0.554779 | − | 0.554779i | ||||
\(967\) | 25.3040i | 0.813721i | 0.913490 | + | 0.406861i | \(0.133376\pi\) | ||||
−0.913490 | + | 0.406861i | \(0.866624\pi\) | |||||||
\(968\) | 2.94862 | 0.0947721 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −19.0455 | −0.611515 | ||||||||
\(971\) | − | 20.2558i | − | 0.650039i | −0.945707 | − | 0.325019i | \(-0.894629\pi\) | ||
0.945707 | − | 0.325019i | \(-0.105371\pi\) | |||||||
\(972\) | 0.707107 | + | 0.707107i | 0.0226805 | + | 0.0226805i | ||||
\(973\) | 51.7743 | 1.65981 | ||||||||
\(974\) | −5.62052 | − | 5.62052i | −0.180093 | − | 0.180093i | ||||
\(975\) | 0.971355 | − | 0.971355i | 0.0311083 | − | 0.0311083i | ||||
\(976\) | 9.23777 | − | 9.23777i | 0.295694 | − | 0.295694i | ||||
\(977\) | 1.17705i | 0.0376572i | 0.999823 | + | 0.0188286i | \(0.00599369\pi\) | ||||
−0.999823 | + | 0.0188286i | \(0.994006\pi\) | |||||||
\(978\) | − | 0.212134i | − | 0.00678329i | ||||||
\(979\) | 12.7216 | − | 12.7216i | 0.406585 | − | 0.406585i | ||||
\(980\) | 15.7971 | − | 15.7971i | 0.504620 | − | 0.504620i | ||||
\(981\) | 6.40934 | + | 6.40934i | 0.204635 | + | 0.204635i | ||||
\(982\) | 5.25402 | 0.167663 | ||||||||
\(983\) | −24.1543 | − | 24.1543i | −0.770402 | − | 0.770402i | 0.207775 | − | 0.978177i | \(-0.433378\pi\) |
−0.978177 | + | 0.207775i | \(0.933378\pi\) | |||||||
\(984\) | − | 3.43376i | − | 0.109464i | ||||||
\(985\) | 54.0242 | 1.72135 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −43.0060 | −1.36890 | ||||||||
\(988\) | 17.3892i | 0.553224i | ||||||||
\(989\) | −49.4094 | − | 49.4094i | −1.57113 | − | 1.57113i | ||||
\(990\) | 6.66044 | 0.211683 | ||||||||
\(991\) | 11.3591 | + | 11.3591i | 0.360833 | + | 0.360833i | 0.864120 | − | 0.503286i | \(-0.167876\pi\) |
−0.503286 | + | 0.864120i | \(0.667876\pi\) | |||||||
\(992\) | −0.405864 | + | 0.405864i | −0.0128862 | + | 0.0128862i | ||||
\(993\) | −2.22594 | + | 2.22594i | −0.0706381 | + | 0.0706381i | ||||
\(994\) | 47.1498i | 1.49550i | ||||||||
\(995\) | − | 42.5366i | − | 1.34850i | ||||||
\(996\) | −2.27132 | + | 2.27132i | −0.0719696 | + | 0.0719696i | ||||
\(997\) | 13.2783 | − | 13.2783i | 0.420528 | − | 0.420528i | −0.464857 | − | 0.885386i | \(-0.653894\pi\) |
0.885386 | + | 0.464857i | \(0.153894\pi\) | |||||||
\(998\) | −17.5911 | − | 17.5911i | −0.556838 | − | 0.556838i | ||||
\(999\) | 7.88713 | 0.249538 |
(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 | 1734.2.f.n.829.5 | 12 | ||
17.2 | even | 8 | 1734.2.a.q.1.2 | yes | 3 | ||
17.4 | even | 4 | inner | 1734.2.f.n.1483.5 | 12 | ||
17.8 | even | 8 | 1734.2.b.j.577.2 | 6 | |||
17.9 | even | 8 | 1734.2.b.j.577.5 | 6 | |||
17.13 | even | 4 | inner | 1734.2.f.n.1483.2 | 12 | ||
17.15 | even | 8 | 1734.2.a.p.1.2 | ✓ | 3 | ||
17.16 | even | 2 | inner | 1734.2.f.n.829.2 | 12 | ||
51.2 | odd | 8 | 5202.2.a.bm.1.2 | 3 | |||
51.32 | odd | 8 | 5202.2.a.bp.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1734.2.a.p.1.2 | ✓ | 3 | 17.15 | even | 8 | ||
1734.2.a.q.1.2 | yes | 3 | 17.2 | even | 8 | ||
1734.2.b.j.577.2 | 6 | 17.8 | even | 8 | |||
1734.2.b.j.577.5 | 6 | 17.9 | even | 8 | |||
1734.2.f.n.829.2 | 12 | 17.16 | even | 2 | inner | ||
1734.2.f.n.829.5 | 12 | 1.1 | even | 1 | trivial | ||
1734.2.f.n.1483.2 | 12 | 17.13 | even | 4 | inner | ||
1734.2.f.n.1483.5 | 12 | 17.4 | even | 4 | inner | ||
5202.2.a.bm.1.2 | 3 | 51.2 | odd | 8 | |||
5202.2.a.bp.1.2 | 3 | 51.32 | odd | 8 |