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: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 47.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 130.47 |
Dual form | 130.2.j.a.83.1 |
$q$-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 \(\left(\mathbb{Z}/130\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(41\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||
\(3\) | −2.00000 | + | 2.00000i | −1.15470 | + | 1.15470i | −0.169102 | + | 0.985599i | \(0.554087\pi\) |
−0.985599 | + | 0.169102i | \(0.945913\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.00000 | − | 2.00000i | −0.447214 | − | 0.894427i | ||||
\(6\) | 2.00000 | + | 2.00000i | 0.816497 | + | 0.816497i | ||||
\(7\) | −4.00000 | −1.51186 | −0.755929 | − | 0.654654i | \(-0.772814\pi\) | ||||
−0.755929 | + | 0.654654i | \(0.772814\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | − | 5.00000i | − | 1.66667i | ||||||
\(10\) | −2.00000 | + | 1.00000i | −0.632456 | + | 0.316228i | ||||
\(11\) | −2.00000 | + | 2.00000i | −0.603023 | + | 0.603023i | −0.941113 | − | 0.338091i | \(-0.890219\pi\) |
0.338091 | + | 0.941113i | \(0.390219\pi\) | |||||||
\(12\) | 2.00000 | − | 2.00000i | 0.577350 | − | 0.577350i | ||||
\(13\) | −3.00000 | + | 2.00000i | −0.832050 | + | 0.554700i | ||||
\(14\) | 4.00000i | 1.06904i | ||||||||
\(15\) | 6.00000 | + | 2.00000i | 1.54919 | + | 0.516398i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.00000 | − | 3.00000i | 0.727607 | − | 0.727607i | −0.242536 | − | 0.970143i | \(-0.577979\pi\) |
0.970143 | + | 0.242536i | \(0.0779791\pi\) | |||||||
\(18\) | −5.00000 | −1.17851 | ||||||||
\(19\) | 2.00000 | − | 2.00000i | 0.458831 | − | 0.458831i | −0.439440 | − | 0.898272i | \(-0.644823\pi\) |
0.898272 | + | 0.439440i | \(0.144823\pi\) | |||||||
\(20\) | 1.00000 | + | 2.00000i | 0.223607 | + | 0.447214i | ||||
\(21\) | 8.00000 | − | 8.00000i | 1.74574 | − | 1.74574i | ||||
\(22\) | 2.00000 | + | 2.00000i | 0.426401 | + | 0.426401i | ||||
\(23\) | 2.00000 | + | 2.00000i | 0.417029 | + | 0.417029i | 0.884178 | − | 0.467150i | \(-0.154719\pi\) |
−0.467150 | + | 0.884178i | \(0.654719\pi\) | |||||||
\(24\) | −2.00000 | − | 2.00000i | −0.408248 | − | 0.408248i | ||||
\(25\) | −3.00000 | + | 4.00000i | −0.600000 | + | 0.800000i | ||||
\(26\) | 2.00000 | + | 3.00000i | 0.392232 | + | 0.588348i | ||||
\(27\) | 4.00000 | + | 4.00000i | 0.769800 | + | 0.769800i | ||||
\(28\) | 4.00000 | 0.755929 | ||||||||
\(29\) | 6.00000i | 1.11417i | 0.830455 | + | 0.557086i | \(0.188081\pi\) | ||||
−0.830455 | + | 0.557086i | \(0.811919\pi\) | |||||||
\(30\) | 2.00000 | − | 6.00000i | 0.365148 | − | 1.09545i | ||||
\(31\) | −6.00000 | − | 6.00000i | −1.07763 | − | 1.07763i | −0.996721 | − | 0.0809104i | \(-0.974217\pi\) |
−0.0809104 | − | 0.996721i | \(-0.525783\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | − | 8.00000i | − | 1.39262i | ||||||
\(34\) | −3.00000 | − | 3.00000i | −0.514496 | − | 0.514496i | ||||
\(35\) | 4.00000 | + | 8.00000i | 0.676123 | + | 1.35225i | ||||
\(36\) | 5.00000i | 0.833333i | ||||||||
\(37\) | −4.00000 | −0.657596 | −0.328798 | − | 0.944400i | \(-0.606644\pi\) | ||||
−0.328798 | + | 0.944400i | \(0.606644\pi\) | |||||||
\(38\) | −2.00000 | − | 2.00000i | −0.324443 | − | 0.324443i | ||||
\(39\) | 2.00000 | − | 10.0000i | 0.320256 | − | 1.60128i | ||||
\(40\) | 2.00000 | − | 1.00000i | 0.316228 | − | 0.158114i | ||||
\(41\) | −1.00000 | − | 1.00000i | −0.156174 | − | 0.156174i | 0.624695 | − | 0.780869i | \(-0.285223\pi\) |
−0.780869 | + | 0.624695i | \(0.785223\pi\) | |||||||
\(42\) | −8.00000 | − | 8.00000i | −1.23443 | − | 1.23443i | ||||
\(43\) | −2.00000 | − | 2.00000i | −0.304997 | − | 0.304997i | 0.537968 | − | 0.842965i | \(-0.319192\pi\) |
−0.842965 | + | 0.537968i | \(0.819192\pi\) | |||||||
\(44\) | 2.00000 | − | 2.00000i | 0.301511 | − | 0.301511i | ||||
\(45\) | −10.0000 | + | 5.00000i | −1.49071 | + | 0.745356i | ||||
\(46\) | 2.00000 | − | 2.00000i | 0.294884 | − | 0.294884i | ||||
\(47\) | −4.00000 | −0.583460 | −0.291730 | − | 0.956501i | \(-0.594231\pi\) | ||||
−0.291730 | + | 0.956501i | \(0.594231\pi\) | |||||||
\(48\) | −2.00000 | + | 2.00000i | −0.288675 | + | 0.288675i | ||||
\(49\) | 9.00000 | 1.28571 | ||||||||
\(50\) | 4.00000 | + | 3.00000i | 0.565685 | + | 0.424264i | ||||
\(51\) | 12.0000i | 1.68034i | ||||||||
\(52\) | 3.00000 | − | 2.00000i | 0.416025 | − | 0.277350i | ||||
\(53\) | −1.00000 | + | 1.00000i | −0.137361 | + | 0.137361i | −0.772444 | − | 0.635083i | \(-0.780966\pi\) |
0.635083 | + | 0.772444i | \(0.280966\pi\) | |||||||
\(54\) | 4.00000 | − | 4.00000i | 0.544331 | − | 0.544331i | ||||
\(55\) | 6.00000 | + | 2.00000i | 0.809040 | + | 0.269680i | ||||
\(56\) | − | 4.00000i | − | 0.534522i | ||||||
\(57\) | 8.00000i | 1.05963i | ||||||||
\(58\) | 6.00000 | 0.787839 | ||||||||
\(59\) | 2.00000 | + | 2.00000i | 0.260378 | + | 0.260378i | 0.825208 | − | 0.564830i | \(-0.191058\pi\) |
−0.564830 | + | 0.825208i | \(0.691058\pi\) | |||||||
\(60\) | −6.00000 | − | 2.00000i | −0.774597 | − | 0.258199i | ||||
\(61\) | −12.0000 | −1.53644 | −0.768221 | − | 0.640184i | \(-0.778858\pi\) | ||||
−0.768221 | + | 0.640184i | \(0.778858\pi\) | |||||||
\(62\) | −6.00000 | + | 6.00000i | −0.762001 | + | 0.762001i | ||||
\(63\) | 20.0000i | 2.51976i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 7.00000 | + | 4.00000i | 0.868243 | + | 0.496139i | ||||
\(66\) | −8.00000 | −0.984732 | ||||||||
\(67\) | 4.00000i | 0.488678i | 0.969690 | + | 0.244339i | \(0.0785709\pi\) | ||||
−0.969690 | + | 0.244339i | \(0.921429\pi\) | |||||||
\(68\) | −3.00000 | + | 3.00000i | −0.363803 | + | 0.363803i | ||||
\(69\) | −8.00000 | −0.963087 | ||||||||
\(70\) | 8.00000 | − | 4.00000i | 0.956183 | − | 0.478091i | ||||
\(71\) | −2.00000 | − | 2.00000i | −0.237356 | − | 0.237356i | 0.578398 | − | 0.815755i | \(-0.303678\pi\) |
−0.815755 | + | 0.578398i | \(0.803678\pi\) | |||||||
\(72\) | 5.00000 | 0.589256 | ||||||||
\(73\) | − | 10.0000i | − | 1.17041i | −0.810885 | − | 0.585206i | \(-0.801014\pi\) | ||
0.810885 | − | 0.585206i | \(-0.198986\pi\) | |||||||
\(74\) | 4.00000i | 0.464991i | ||||||||
\(75\) | −2.00000 | − | 14.0000i | −0.230940 | − | 1.61658i | ||||
\(76\) | −2.00000 | + | 2.00000i | −0.229416 | + | 0.229416i | ||||
\(77\) | 8.00000 | − | 8.00000i | 0.911685 | − | 0.911685i | ||||
\(78\) | −10.0000 | − | 2.00000i | −1.13228 | − | 0.226455i | ||||
\(79\) | 4.00000i | 0.450035i | 0.974355 | + | 0.225018i | \(0.0722440\pi\) | ||||
−0.974355 | + | 0.225018i | \(0.927756\pi\) | |||||||
\(80\) | −1.00000 | − | 2.00000i | −0.111803 | − | 0.223607i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −1.00000 | + | 1.00000i | −0.110432 | + | 0.110432i | ||||
\(83\) | 8.00000 | 0.878114 | 0.439057 | − | 0.898459i | \(-0.355313\pi\) | ||||
0.439057 | + | 0.898459i | \(0.355313\pi\) | |||||||
\(84\) | −8.00000 | + | 8.00000i | −0.872872 | + | 0.872872i | ||||
\(85\) | −9.00000 | − | 3.00000i | −0.976187 | − | 0.325396i | ||||
\(86\) | −2.00000 | + | 2.00000i | −0.215666 | + | 0.215666i | ||||
\(87\) | −12.0000 | − | 12.0000i | −1.28654 | − | 1.28654i | ||||
\(88\) | −2.00000 | − | 2.00000i | −0.213201 | − | 0.213201i | ||||
\(89\) | −5.00000 | − | 5.00000i | −0.529999 | − | 0.529999i | 0.390573 | − | 0.920572i | \(-0.372277\pi\) |
−0.920572 | + | 0.390573i | \(0.872277\pi\) | |||||||
\(90\) | 5.00000 | + | 10.0000i | 0.527046 | + | 1.05409i | ||||
\(91\) | 12.0000 | − | 8.00000i | 1.25794 | − | 0.838628i | ||||
\(92\) | −2.00000 | − | 2.00000i | −0.208514 | − | 0.208514i | ||||
\(93\) | 24.0000 | 2.48868 | ||||||||
\(94\) | 4.00000i | 0.412568i | ||||||||
\(95\) | −6.00000 | − | 2.00000i | −0.615587 | − | 0.205196i | ||||
\(96\) | 2.00000 | + | 2.00000i | 0.204124 | + | 0.204124i | ||||
\(97\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(98\) | − | 9.00000i | − | 0.909137i | ||||||
\(99\) | 10.0000 | + | 10.0000i | 1.00504 | + | 1.00504i | ||||
\(100\) | 3.00000 | − | 4.00000i | 0.300000 | − | 0.400000i | ||||
\(101\) | 12.0000i | 1.19404i | 0.802225 | + | 0.597022i | \(0.203650\pi\) | ||||
−0.802225 | + | 0.597022i | \(0.796350\pi\) | |||||||
\(102\) | 12.0000 | 1.18818 | ||||||||
\(103\) | −6.00000 | − | 6.00000i | −0.591198 | − | 0.591198i | 0.346757 | − | 0.937955i | \(-0.387283\pi\) |
−0.937955 | + | 0.346757i | \(0.887283\pi\) | |||||||
\(104\) | −2.00000 | − | 3.00000i | −0.196116 | − | 0.294174i | ||||
\(105\) | −24.0000 | − | 8.00000i | −2.34216 | − | 0.780720i | ||||
\(106\) | 1.00000 | + | 1.00000i | 0.0971286 | + | 0.0971286i | ||||
\(107\) | −6.00000 | − | 6.00000i | −0.580042 | − | 0.580042i | 0.354873 | − | 0.934915i | \(-0.384524\pi\) |
−0.934915 | + | 0.354873i | \(0.884524\pi\) | |||||||
\(108\) | −4.00000 | − | 4.00000i | −0.384900 | − | 0.384900i | ||||
\(109\) | −11.0000 | + | 11.0000i | −1.05361 | + | 1.05361i | −0.0551297 | + | 0.998479i | \(0.517557\pi\) |
−0.998479 | + | 0.0551297i | \(0.982443\pi\) | |||||||
\(110\) | 2.00000 | − | 6.00000i | 0.190693 | − | 0.572078i | ||||
\(111\) | 8.00000 | − | 8.00000i | 0.759326 | − | 0.759326i | ||||
\(112\) | −4.00000 | −0.377964 | ||||||||
\(113\) | 1.00000 | − | 1.00000i | 0.0940721 | − | 0.0940721i | −0.658505 | − | 0.752577i | \(-0.728811\pi\) |
0.752577 | + | 0.658505i | \(0.228811\pi\) | |||||||
\(114\) | 8.00000 | 0.749269 | ||||||||
\(115\) | 2.00000 | − | 6.00000i | 0.186501 | − | 0.559503i | ||||
\(116\) | − | 6.00000i | − | 0.557086i | ||||||
\(117\) | 10.0000 | + | 15.0000i | 0.924500 | + | 1.38675i | ||||
\(118\) | 2.00000 | − | 2.00000i | 0.184115 | − | 0.184115i | ||||
\(119\) | −12.0000 | + | 12.0000i | −1.10004 | + | 1.10004i | ||||
\(120\) | −2.00000 | + | 6.00000i | −0.182574 | + | 0.547723i | ||||
\(121\) | 3.00000i | 0.272727i | ||||||||
\(122\) | 12.0000i | 1.08643i | ||||||||
\(123\) | 4.00000 | 0.360668 | ||||||||
\(124\) | 6.00000 | + | 6.00000i | 0.538816 | + | 0.538816i | ||||
\(125\) | 11.0000 | + | 2.00000i | 0.983870 | + | 0.178885i | ||||
\(126\) | 20.0000 | 1.78174 | ||||||||
\(127\) | 14.0000 | − | 14.0000i | 1.24230 | − | 1.24230i | 0.283254 | − | 0.959045i | \(-0.408586\pi\) |
0.959045 | − | 0.283254i | \(-0.0914140\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 8.00000 | 0.704361 | ||||||||
\(130\) | 4.00000 | − | 7.00000i | 0.350823 | − | 0.613941i | ||||
\(131\) | 4.00000 | 0.349482 | 0.174741 | − | 0.984614i | \(-0.444091\pi\) | ||||
0.174741 | + | 0.984614i | \(0.444091\pi\) | |||||||
\(132\) | 8.00000i | 0.696311i | ||||||||
\(133\) | −8.00000 | + | 8.00000i | −0.693688 | + | 0.693688i | ||||
\(134\) | 4.00000 | 0.345547 | ||||||||
\(135\) | 4.00000 | − | 12.0000i | 0.344265 | − | 1.03280i | ||||
\(136\) | 3.00000 | + | 3.00000i | 0.257248 | + | 0.257248i | ||||
\(137\) | 18.0000 | 1.53784 | 0.768922 | − | 0.639343i | \(-0.220793\pi\) | ||||
0.768922 | + | 0.639343i | \(0.220793\pi\) | |||||||
\(138\) | 8.00000i | 0.681005i | ||||||||
\(139\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(140\) | −4.00000 | − | 8.00000i | −0.338062 | − | 0.676123i | ||||
\(141\) | 8.00000 | − | 8.00000i | 0.673722 | − | 0.673722i | ||||
\(142\) | −2.00000 | + | 2.00000i | −0.167836 | + | 0.167836i | ||||
\(143\) | 2.00000 | − | 10.0000i | 0.167248 | − | 0.836242i | ||||
\(144\) | − | 5.00000i | − | 0.416667i | ||||||
\(145\) | 12.0000 | − | 6.00000i | 0.996546 | − | 0.498273i | ||||
\(146\) | −10.0000 | −0.827606 | ||||||||
\(147\) | −18.0000 | + | 18.0000i | −1.48461 | + | 1.48461i | ||||
\(148\) | 4.00000 | 0.328798 | ||||||||
\(149\) | 11.0000 | − | 11.0000i | 0.901155 | − | 0.901155i | −0.0943810 | − | 0.995536i | \(-0.530087\pi\) |
0.995536 | + | 0.0943810i | \(0.0300872\pi\) | |||||||
\(150\) | −14.0000 | + | 2.00000i | −1.14310 | + | 0.163299i | ||||
\(151\) | −14.0000 | + | 14.0000i | −1.13930 | + | 1.13930i | −0.150729 | + | 0.988575i | \(0.548162\pi\) |
−0.988575 | + | 0.150729i | \(0.951838\pi\) | |||||||
\(152\) | 2.00000 | + | 2.00000i | 0.162221 | + | 0.162221i | ||||
\(153\) | −15.0000 | − | 15.0000i | −1.21268 | − | 1.21268i | ||||
\(154\) | −8.00000 | − | 8.00000i | −0.644658 | − | 0.644658i | ||||
\(155\) | −6.00000 | + | 18.0000i | −0.481932 | + | 1.44579i | ||||
\(156\) | −2.00000 | + | 10.0000i | −0.160128 | + | 0.800641i | ||||
\(157\) | 3.00000 | + | 3.00000i | 0.239426 | + | 0.239426i | 0.816612 | − | 0.577186i | \(-0.195849\pi\) |
−0.577186 | + | 0.816612i | \(0.695849\pi\) | |||||||
\(158\) | 4.00000 | 0.318223 | ||||||||
\(159\) | − | 4.00000i | − | 0.317221i | ||||||
\(160\) | −2.00000 | + | 1.00000i | −0.158114 | + | 0.0790569i | ||||
\(161\) | −8.00000 | − | 8.00000i | −0.630488 | − | 0.630488i | ||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 20.0000i | 1.56652i | 0.621694 | + | 0.783260i | \(0.286445\pi\) | ||||
−0.621694 | + | 0.783260i | \(0.713555\pi\) | |||||||
\(164\) | 1.00000 | + | 1.00000i | 0.0780869 | + | 0.0780869i | ||||
\(165\) | −16.0000 | + | 8.00000i | −1.24560 | + | 0.622799i | ||||
\(166\) | − | 8.00000i | − | 0.620920i | ||||||
\(167\) | −12.0000 | −0.928588 | −0.464294 | − | 0.885681i | \(-0.653692\pi\) | ||||
−0.464294 | + | 0.885681i | \(0.653692\pi\) | |||||||
\(168\) | 8.00000 | + | 8.00000i | 0.617213 | + | 0.617213i | ||||
\(169\) | 5.00000 | − | 12.0000i | 0.384615 | − | 0.923077i | ||||
\(170\) | −3.00000 | + | 9.00000i | −0.230089 | + | 0.690268i | ||||
\(171\) | −10.0000 | − | 10.0000i | −0.764719 | − | 0.764719i | ||||
\(172\) | 2.00000 | + | 2.00000i | 0.152499 | + | 0.152499i | ||||
\(173\) | 9.00000 | + | 9.00000i | 0.684257 | + | 0.684257i | 0.960957 | − | 0.276699i | \(-0.0892406\pi\) |
−0.276699 | + | 0.960957i | \(0.589241\pi\) | |||||||
\(174\) | −12.0000 | + | 12.0000i | −0.909718 | + | 0.909718i | ||||
\(175\) | 12.0000 | − | 16.0000i | 0.907115 | − | 1.20949i | ||||
\(176\) | −2.00000 | + | 2.00000i | −0.150756 | + | 0.150756i | ||||
\(177\) | −8.00000 | −0.601317 | ||||||||
\(178\) | −5.00000 | + | 5.00000i | −0.374766 | + | 0.374766i | ||||
\(179\) | −20.0000 | −1.49487 | −0.747435 | − | 0.664335i | \(-0.768715\pi\) | ||||
−0.747435 | + | 0.664335i | \(0.768715\pi\) | |||||||
\(180\) | 10.0000 | − | 5.00000i | 0.745356 | − | 0.372678i | ||||
\(181\) | − | 2.00000i | − | 0.148659i | −0.997234 | − | 0.0743294i | \(-0.976318\pi\) | ||
0.997234 | − | 0.0743294i | \(-0.0236816\pi\) | |||||||
\(182\) | −8.00000 | − | 12.0000i | −0.592999 | − | 0.889499i | ||||
\(183\) | 24.0000 | − | 24.0000i | 1.77413 | − | 1.77413i | ||||
\(184\) | −2.00000 | + | 2.00000i | −0.147442 | + | 0.147442i | ||||
\(185\) | 4.00000 | + | 8.00000i | 0.294086 | + | 0.588172i | ||||
\(186\) | − | 24.0000i | − | 1.75977i | ||||||
\(187\) | 12.0000i | 0.877527i | ||||||||
\(188\) | 4.00000 | 0.291730 | ||||||||
\(189\) | −16.0000 | − | 16.0000i | −1.16383 | − | 1.16383i | ||||
\(190\) | −2.00000 | + | 6.00000i | −0.145095 | + | 0.435286i | ||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 2.00000 | − | 2.00000i | 0.144338 | − | 0.144338i | ||||
\(193\) | 16.0000i | 1.15171i | 0.817554 | + | 0.575853i | \(0.195330\pi\) | ||||
−0.817554 | + | 0.575853i | \(0.804670\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −22.0000 | + | 6.00000i | −1.57545 | + | 0.429669i | ||||
\(196\) | −9.00000 | −0.642857 | ||||||||
\(197\) | − | 12.0000i | − | 0.854965i | −0.904024 | − | 0.427482i | \(-0.859401\pi\) | ||
0.904024 | − | 0.427482i | \(-0.140599\pi\) | |||||||
\(198\) | 10.0000 | − | 10.0000i | 0.710669 | − | 0.710669i | ||||
\(199\) | 8.00000 | 0.567105 | 0.283552 | − | 0.958957i | \(-0.408487\pi\) | ||||
0.283552 | + | 0.958957i | \(0.408487\pi\) | |||||||
\(200\) | −4.00000 | − | 3.00000i | −0.282843 | − | 0.212132i | ||||
\(201\) | −8.00000 | − | 8.00000i | −0.564276 | − | 0.564276i | ||||
\(202\) | 12.0000 | 0.844317 | ||||||||
\(203\) | − | 24.0000i | − | 1.68447i | ||||||
\(204\) | − | 12.0000i | − | 0.840168i | ||||||
\(205\) | −1.00000 | + | 3.00000i | −0.0698430 | + | 0.209529i | ||||
\(206\) | −6.00000 | + | 6.00000i | −0.418040 | + | 0.418040i | ||||
\(207\) | 10.0000 | − | 10.0000i | 0.695048 | − | 0.695048i | ||||
\(208\) | −3.00000 | + | 2.00000i | −0.208013 | + | 0.138675i | ||||
\(209\) | 8.00000i | 0.553372i | ||||||||
\(210\) | −8.00000 | + | 24.0000i | −0.552052 | + | 1.65616i | ||||
\(211\) | −4.00000 | −0.275371 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | 1.00000 | − | 1.00000i | 0.0686803 | − | 0.0686803i | ||||
\(213\) | 8.00000 | 0.548151 | ||||||||
\(214\) | −6.00000 | + | 6.00000i | −0.410152 | + | 0.410152i | ||||
\(215\) | −2.00000 | + | 6.00000i | −0.136399 | + | 0.409197i | ||||
\(216\) | −4.00000 | + | 4.00000i | −0.272166 | + | 0.272166i | ||||
\(217\) | 24.0000 | + | 24.0000i | 1.62923 | + | 1.62923i | ||||
\(218\) | 11.0000 | + | 11.0000i | 0.745014 | + | 0.745014i | ||||
\(219\) | 20.0000 | + | 20.0000i | 1.35147 | + | 1.35147i | ||||
\(220\) | −6.00000 | − | 2.00000i | −0.404520 | − | 0.134840i | ||||
\(221\) | −3.00000 | + | 15.0000i | −0.201802 | + | 1.00901i | ||||
\(222\) | −8.00000 | − | 8.00000i | −0.536925 | − | 0.536925i | ||||
\(223\) | −28.0000 | −1.87502 | −0.937509 | − | 0.347960i | \(-0.886874\pi\) | ||||
−0.937509 | + | 0.347960i | \(0.886874\pi\) | |||||||
\(224\) | 4.00000i | 0.267261i | ||||||||
\(225\) | 20.0000 | + | 15.0000i | 1.33333 | + | 1.00000i | ||||
\(226\) | −1.00000 | − | 1.00000i | −0.0665190 | − | 0.0665190i | ||||
\(227\) | − | 4.00000i | − | 0.265489i | −0.991150 | − | 0.132745i | \(-0.957621\pi\) | ||
0.991150 | − | 0.132745i | \(-0.0423790\pi\) | |||||||
\(228\) | − | 8.00000i | − | 0.529813i | ||||||
\(229\) | −1.00000 | − | 1.00000i | −0.0660819 | − | 0.0660819i | 0.673293 | − | 0.739375i | \(-0.264879\pi\) |
−0.739375 | + | 0.673293i | \(0.764879\pi\) | |||||||
\(230\) | −6.00000 | − | 2.00000i | −0.395628 | − | 0.131876i | ||||
\(231\) | 32.0000i | 2.10545i | ||||||||
\(232\) | −6.00000 | −0.393919 | ||||||||
\(233\) | −11.0000 | − | 11.0000i | −0.720634 | − | 0.720634i | 0.248100 | − | 0.968734i | \(-0.420194\pi\) |
−0.968734 | + | 0.248100i | \(0.920194\pi\) | |||||||
\(234\) | 15.0000 | − | 10.0000i | 0.980581 | − | 0.653720i | ||||
\(235\) | 4.00000 | + | 8.00000i | 0.260931 | + | 0.521862i | ||||
\(236\) | −2.00000 | − | 2.00000i | −0.130189 | − | 0.130189i | ||||
\(237\) | −8.00000 | − | 8.00000i | −0.519656 | − | 0.519656i | ||||
\(238\) | 12.0000 | + | 12.0000i | 0.777844 | + | 0.777844i | ||||
\(239\) | 10.0000 | − | 10.0000i | 0.646846 | − | 0.646846i | −0.305383 | − | 0.952230i | \(-0.598785\pi\) |
0.952230 | + | 0.305383i | \(0.0987846\pi\) | |||||||
\(240\) | 6.00000 | + | 2.00000i | 0.387298 | + | 0.129099i | ||||
\(241\) | −5.00000 | + | 5.00000i | −0.322078 | + | 0.322078i | −0.849564 | − | 0.527486i | \(-0.823135\pi\) |
0.527486 | + | 0.849564i | \(0.323135\pi\) | |||||||
\(242\) | 3.00000 | 0.192847 | ||||||||
\(243\) | −10.0000 | + | 10.0000i | −0.641500 | + | 0.641500i | ||||
\(244\) | 12.0000 | 0.768221 | ||||||||
\(245\) | −9.00000 | − | 18.0000i | −0.574989 | − | 1.14998i | ||||
\(246\) | − | 4.00000i | − | 0.255031i | ||||||
\(247\) | −2.00000 | + | 10.0000i | −0.127257 | + | 0.636285i | ||||
\(248\) | 6.00000 | − | 6.00000i | 0.381000 | − | 0.381000i | ||||
\(249\) | −16.0000 | + | 16.0000i | −1.01396 | + | 1.01396i | ||||
\(250\) | 2.00000 | − | 11.0000i | 0.126491 | − | 0.695701i | ||||
\(251\) | − | 16.0000i | − | 1.00991i | −0.863145 | − | 0.504956i | \(-0.831509\pi\) | ||
0.863145 | − | 0.504956i | \(-0.168491\pi\) | |||||||
\(252\) | − | 20.0000i | − | 1.25988i | ||||||
\(253\) | −8.00000 | −0.502956 | ||||||||
\(254\) | −14.0000 | − | 14.0000i | −0.878438 | − | 0.878438i | ||||
\(255\) | 24.0000 | − | 12.0000i | 1.50294 | − | 0.751469i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −17.0000 | + | 17.0000i | −1.06043 | + | 1.06043i | −0.0623783 | + | 0.998053i | \(0.519869\pi\) |
−0.998053 | + | 0.0623783i | \(0.980131\pi\) | |||||||
\(258\) | − | 8.00000i | − | 0.498058i | ||||||
\(259\) | 16.0000 | 0.994192 | ||||||||
\(260\) | −7.00000 | − | 4.00000i | −0.434122 | − | 0.248069i | ||||
\(261\) | 30.0000 | 1.85695 | ||||||||
\(262\) | − | 4.00000i | − | 0.247121i | ||||||
\(263\) | 14.0000 | − | 14.0000i | 0.863277 | − | 0.863277i | −0.128440 | − | 0.991717i | \(-0.540997\pi\) |
0.991717 | + | 0.128440i | \(0.0409971\pi\) | |||||||
\(264\) | 8.00000 | 0.492366 | ||||||||
\(265\) | 3.00000 | + | 1.00000i | 0.184289 | + | 0.0614295i | ||||
\(266\) | 8.00000 | + | 8.00000i | 0.490511 | + | 0.490511i | ||||
\(267\) | 20.0000 | 1.22398 | ||||||||
\(268\) | − | 4.00000i | − | 0.244339i | ||||||
\(269\) | − | 20.0000i | − | 1.21942i | −0.792624 | − | 0.609711i | \(-0.791286\pi\) | ||
0.792624 | − | 0.609711i | \(-0.208714\pi\) | |||||||
\(270\) | −12.0000 | − | 4.00000i | −0.730297 | − | 0.243432i | ||||
\(271\) | 6.00000 | − | 6.00000i | 0.364474 | − | 0.364474i | −0.500983 | − | 0.865457i | \(-0.667028\pi\) |
0.865457 | + | 0.500983i | \(0.167028\pi\) | |||||||
\(272\) | 3.00000 | − | 3.00000i | 0.181902 | − | 0.181902i | ||||
\(273\) | −8.00000 | + | 40.0000i | −0.484182 | + | 2.42091i | ||||
\(274\) | − | 18.0000i | − | 1.08742i | ||||||
\(275\) | −2.00000 | − | 14.0000i | −0.120605 | − | 0.844232i | ||||
\(276\) | 8.00000 | 0.481543 | ||||||||
\(277\) | −3.00000 | + | 3.00000i | −0.180253 | + | 0.180253i | −0.791466 | − | 0.611213i | \(-0.790682\pi\) |
0.611213 | + | 0.791466i | \(0.290682\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −30.0000 | + | 30.0000i | −1.79605 | + | 1.79605i | ||||
\(280\) | −8.00000 | + | 4.00000i | −0.478091 | + | 0.239046i | ||||
\(281\) | 11.0000 | − | 11.0000i | 0.656205 | − | 0.656205i | −0.298275 | − | 0.954480i | \(-0.596411\pi\) |
0.954480 | + | 0.298275i | \(0.0964112\pi\) | |||||||
\(282\) | −8.00000 | − | 8.00000i | −0.476393 | − | 0.476393i | ||||
\(283\) | −6.00000 | − | 6.00000i | −0.356663 | − | 0.356663i | 0.505918 | − | 0.862581i | \(-0.331154\pi\) |
−0.862581 | + | 0.505918i | \(0.831154\pi\) | |||||||
\(284\) | 2.00000 | + | 2.00000i | 0.118678 | + | 0.118678i | ||||
\(285\) | 16.0000 | − | 8.00000i | 0.947758 | − | 0.473879i | ||||
\(286\) | −10.0000 | − | 2.00000i | −0.591312 | − | 0.118262i | ||||
\(287\) | 4.00000 | + | 4.00000i | 0.236113 | + | 0.236113i | ||||
\(288\) | −5.00000 | −0.294628 | ||||||||
\(289\) | − | 1.00000i | − | 0.0588235i | ||||||
\(290\) | −6.00000 | − | 12.0000i | −0.352332 | − | 0.704664i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 10.0000i | 0.585206i | ||||||||
\(293\) | 26.0000i | 1.51894i | 0.650545 | + | 0.759468i | \(0.274541\pi\) | ||||
−0.650545 | + | 0.759468i | \(0.725459\pi\) | |||||||
\(294\) | 18.0000 | + | 18.0000i | 1.04978 | + | 1.04978i | ||||
\(295\) | 2.00000 | − | 6.00000i | 0.116445 | − | 0.349334i | ||||
\(296\) | − | 4.00000i | − | 0.232495i | ||||||
\(297\) | −16.0000 | −0.928414 | ||||||||
\(298\) | −11.0000 | − | 11.0000i | −0.637213 | − | 0.637213i | ||||
\(299\) | −10.0000 | − | 2.00000i | −0.578315 | − | 0.115663i | ||||
\(300\) | 2.00000 | + | 14.0000i | 0.115470 | + | 0.808290i | ||||
\(301\) | 8.00000 | + | 8.00000i | 0.461112 | + | 0.461112i | ||||
\(302\) | 14.0000 | + | 14.0000i | 0.805609 | + | 0.805609i | ||||
\(303\) | −24.0000 | − | 24.0000i | −1.37876 | − | 1.37876i | ||||
\(304\) | 2.00000 | − | 2.00000i | 0.114708 | − | 0.114708i | ||||
\(305\) | 12.0000 | + | 24.0000i | 0.687118 | + | 1.37424i | ||||
\(306\) | −15.0000 | + | 15.0000i | −0.857493 | + | 0.857493i | ||||
\(307\) | −8.00000 | −0.456584 | −0.228292 | − | 0.973593i | \(-0.573314\pi\) | ||||
−0.228292 | + | 0.973593i | \(0.573314\pi\) | |||||||
\(308\) | −8.00000 | + | 8.00000i | −0.455842 | + | 0.455842i | ||||
\(309\) | 24.0000 | 1.36531 | ||||||||
\(310\) | 18.0000 | + | 6.00000i | 1.02233 | + | 0.340777i | ||||
\(311\) | 12.0000i | 0.680458i | 0.940343 | + | 0.340229i | \(0.110505\pi\) | ||||
−0.940343 | + | 0.340229i | \(0.889495\pi\) | |||||||
\(312\) | 10.0000 | + | 2.00000i | 0.566139 | + | 0.113228i | ||||
\(313\) | −9.00000 | + | 9.00000i | −0.508710 | + | 0.508710i | −0.914130 | − | 0.405420i | \(-0.867125\pi\) |
0.405420 | + | 0.914130i | \(0.367125\pi\) | |||||||
\(314\) | 3.00000 | − | 3.00000i | 0.169300 | − | 0.169300i | ||||
\(315\) | 40.0000 | − | 20.0000i | 2.25374 | − | 1.12687i | ||||
\(316\) | − | 4.00000i | − | 0.225018i | ||||||
\(317\) | − | 30.0000i | − | 1.68497i | −0.538721 | − | 0.842484i | \(-0.681092\pi\) | ||
0.538721 | − | 0.842484i | \(-0.318908\pi\) | |||||||
\(318\) | −4.00000 | −0.224309 | ||||||||
\(319\) | −12.0000 | − | 12.0000i | −0.671871 | − | 0.671871i | ||||
\(320\) | 1.00000 | + | 2.00000i | 0.0559017 | + | 0.111803i | ||||
\(321\) | 24.0000 | 1.33955 | ||||||||
\(322\) | −8.00000 | + | 8.00000i | −0.445823 | + | 0.445823i | ||||
\(323\) | − | 12.0000i | − | 0.667698i | ||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 1.00000 | − | 18.0000i | 0.0554700 | − | 0.998460i | ||||
\(326\) | 20.0000 | 1.10770 | ||||||||
\(327\) | − | 44.0000i | − | 2.43321i | ||||||
\(328\) | 1.00000 | − | 1.00000i | 0.0552158 | − | 0.0552158i | ||||
\(329\) | 16.0000 | 0.882109 | ||||||||
\(330\) | 8.00000 | + | 16.0000i | 0.440386 | + | 0.880771i | ||||
\(331\) | −6.00000 | − | 6.00000i | −0.329790 | − | 0.329790i | 0.522717 | − | 0.852506i | \(-0.324919\pi\) |
−0.852506 | + | 0.522717i | \(0.824919\pi\) | |||||||
\(332\) | −8.00000 | −0.439057 | ||||||||
\(333\) | 20.0000i | 1.09599i | ||||||||
\(334\) | 12.0000i | 0.656611i | ||||||||
\(335\) | 8.00000 | − | 4.00000i | 0.437087 | − | 0.218543i | ||||
\(336\) | 8.00000 | − | 8.00000i | 0.436436 | − | 0.436436i | ||||
\(337\) | −15.0000 | + | 15.0000i | −0.817102 | + | 0.817102i | −0.985687 | − | 0.168585i | \(-0.946080\pi\) |
0.168585 | + | 0.985687i | \(0.446080\pi\) | |||||||
\(338\) | −12.0000 | − | 5.00000i | −0.652714 | − | 0.271964i | ||||
\(339\) | 4.00000i | 0.217250i | ||||||||
\(340\) | 9.00000 | + | 3.00000i | 0.488094 | + | 0.162698i | ||||
\(341\) | 24.0000 | 1.29967 | ||||||||
\(342\) | −10.0000 | + | 10.0000i | −0.540738 | + | 0.540738i | ||||
\(343\) | −8.00000 | −0.431959 | ||||||||
\(344\) | 2.00000 | − | 2.00000i | 0.107833 | − | 0.107833i | ||||
\(345\) | 8.00000 | + | 16.0000i | 0.430706 | + | 0.861411i | ||||
\(346\) | 9.00000 | − | 9.00000i | 0.483843 | − | 0.483843i | ||||
\(347\) | −2.00000 | − | 2.00000i | −0.107366 | − | 0.107366i | 0.651383 | − | 0.758749i | \(-0.274189\pi\) |
−0.758749 | + | 0.651383i | \(0.774189\pi\) | |||||||
\(348\) | 12.0000 | + | 12.0000i | 0.643268 | + | 0.643268i | ||||
\(349\) | −23.0000 | − | 23.0000i | −1.23116 | − | 1.23116i | −0.963518 | − | 0.267644i | \(-0.913755\pi\) |
−0.267644 | − | 0.963518i | \(-0.586245\pi\) | |||||||
\(350\) | −16.0000 | − | 12.0000i | −0.855236 | − | 0.641427i | ||||
\(351\) | −20.0000 | − | 4.00000i | −1.06752 | − | 0.213504i | ||||
\(352\) | 2.00000 | + | 2.00000i | 0.106600 | + | 0.106600i | ||||
\(353\) | −16.0000 | −0.851594 | −0.425797 | − | 0.904819i | \(-0.640006\pi\) | ||||
−0.425797 | + | 0.904819i | \(0.640006\pi\) | |||||||
\(354\) | 8.00000i | 0.425195i | ||||||||
\(355\) | −2.00000 | + | 6.00000i | −0.106149 | + | 0.318447i | ||||
\(356\) | 5.00000 | + | 5.00000i | 0.264999 | + | 0.264999i | ||||
\(357\) | − | 48.0000i | − | 2.54043i | ||||||
\(358\) | 20.0000i | 1.05703i | ||||||||
\(359\) | 22.0000 | + | 22.0000i | 1.16112 | + | 1.16112i | 0.984232 | + | 0.176884i | \(0.0566017\pi\) |
0.176884 | + | 0.984232i | \(0.443398\pi\) | |||||||
\(360\) | −5.00000 | − | 10.0000i | −0.263523 | − | 0.527046i | ||||
\(361\) | 11.0000i | 0.578947i | ||||||||
\(362\) | −2.00000 | −0.105118 | ||||||||
\(363\) | −6.00000 | − | 6.00000i | −0.314918 | − | 0.314918i | ||||
\(364\) | −12.0000 | + | 8.00000i | −0.628971 | + | 0.419314i | ||||
\(365\) | −20.0000 | + | 10.0000i | −1.04685 | + | 0.523424i | ||||
\(366\) | −24.0000 | − | 24.0000i | −1.25450 | − | 1.25450i | ||||
\(367\) | −14.0000 | − | 14.0000i | −0.730794 | − | 0.730794i | 0.239983 | − | 0.970777i | \(-0.422858\pi\) |
−0.970777 | + | 0.239983i | \(0.922858\pi\) | |||||||
\(368\) | 2.00000 | + | 2.00000i | 0.104257 | + | 0.104257i | ||||
\(369\) | −5.00000 | + | 5.00000i | −0.260290 | + | 0.260290i | ||||
\(370\) | 8.00000 | − | 4.00000i | 0.415900 | − | 0.207950i | ||||
\(371\) | 4.00000 | − | 4.00000i | 0.207670 | − | 0.207670i | ||||
\(372\) | −24.0000 | −1.24434 | ||||||||
\(373\) | 15.0000 | − | 15.0000i | 0.776671 | − | 0.776671i | −0.202593 | − | 0.979263i | \(-0.564937\pi\) |
0.979263 | + | 0.202593i | \(0.0649367\pi\) | |||||||
\(374\) | 12.0000 | 0.620505 | ||||||||
\(375\) | −26.0000 | + | 18.0000i | −1.34263 | + | 0.929516i | ||||
\(376\) | − | 4.00000i | − | 0.206284i | ||||||
\(377\) | −12.0000 | − | 18.0000i | −0.618031 | − | 0.927047i | ||||
\(378\) | −16.0000 | + | 16.0000i | −0.822951 | + | 0.822951i | ||||
\(379\) | −6.00000 | + | 6.00000i | −0.308199 | + | 0.308199i | −0.844211 | − | 0.536011i | \(-0.819930\pi\) |
0.536011 | + | 0.844211i | \(0.319930\pi\) | |||||||
\(380\) | 6.00000 | + | 2.00000i | 0.307794 | + | 0.102598i | ||||
\(381\) | 56.0000i | 2.86897i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.00000 | 0.204390 | 0.102195 | − | 0.994764i | \(-0.467413\pi\) | ||||
0.102195 | + | 0.994764i | \(0.467413\pi\) | |||||||
\(384\) | −2.00000 | − | 2.00000i | −0.102062 | − | 0.102062i | ||||
\(385\) | −24.0000 | − | 8.00000i | −1.22315 | − | 0.407718i | ||||
\(386\) | 16.0000 | 0.814379 | ||||||||
\(387\) | −10.0000 | + | 10.0000i | −0.508329 | + | 0.508329i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −38.0000 | −1.92668 | −0.963338 | − | 0.268290i | \(-0.913542\pi\) | ||||
−0.963338 | + | 0.268290i | \(0.913542\pi\) | |||||||
\(390\) | 6.00000 | + | 22.0000i | 0.303822 | + | 1.11401i | ||||
\(391\) | 12.0000 | 0.606866 | ||||||||
\(392\) | 9.00000i | 0.454569i | ||||||||
\(393\) | −8.00000 | + | 8.00000i | −0.403547 | + | 0.403547i | ||||
\(394\) | −12.0000 | −0.604551 | ||||||||
\(395\) | 8.00000 | − | 4.00000i | 0.402524 | − | 0.201262i | ||||
\(396\) | −10.0000 | − | 10.0000i | −0.502519 | − | 0.502519i | ||||
\(397\) | 4.00000 | 0.200754 | 0.100377 | − | 0.994949i | \(-0.467995\pi\) | ||||
0.100377 | + | 0.994949i | \(0.467995\pi\) | |||||||
\(398\) | − | 8.00000i | − | 0.401004i | ||||||
\(399\) | − | 32.0000i | − | 1.60200i | ||||||
\(400\) | −3.00000 | + | 4.00000i | −0.150000 | + | 0.200000i | ||||
\(401\) | −5.00000 | + | 5.00000i | −0.249688 | + | 0.249688i | −0.820843 | − | 0.571154i | \(-0.806496\pi\) |
0.571154 | + | 0.820843i | \(0.306496\pi\) | |||||||
\(402\) | −8.00000 | + | 8.00000i | −0.399004 | + | 0.399004i | ||||
\(403\) | 30.0000 | + | 6.00000i | 1.49441 | + | 0.298881i | ||||
\(404\) | − | 12.0000i | − | 0.597022i | ||||||
\(405\) | 1.00000 | + | 2.00000i | 0.0496904 | + | 0.0993808i | ||||
\(406\) | −24.0000 | −1.19110 | ||||||||
\(407\) | 8.00000 | − | 8.00000i | 0.396545 | − | 0.396545i | ||||
\(408\) | −12.0000 | −0.594089 | ||||||||
\(409\) | 15.0000 | − | 15.0000i | 0.741702 | − | 0.741702i | −0.231203 | − | 0.972905i | \(-0.574266\pi\) |
0.972905 | + | 0.231203i | \(0.0742662\pi\) | |||||||
\(410\) | 3.00000 | + | 1.00000i | 0.148159 | + | 0.0493865i | ||||
\(411\) | −36.0000 | + | 36.0000i | −1.77575 | + | 1.77575i | ||||
\(412\) | 6.00000 | + | 6.00000i | 0.295599 | + | 0.295599i | ||||
\(413\) | −8.00000 | − | 8.00000i | −0.393654 | − | 0.393654i | ||||
\(414\) | −10.0000 | − | 10.0000i | −0.491473 | − | 0.491473i | ||||
\(415\) | −8.00000 | − | 16.0000i | −0.392705 | − | 0.785409i | ||||
\(416\) | 2.00000 | + | 3.00000i | 0.0980581 | + | 0.147087i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 8.00000 | 0.391293 | ||||||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | 24.0000 | + | 8.00000i | 1.17108 | + | 0.390360i | ||||
\(421\) | −19.0000 | − | 19.0000i | −0.926003 | − | 0.926003i | 0.0714415 | − | 0.997445i | \(-0.477240\pi\) |
−0.997445 | + | 0.0714415i | \(0.977240\pi\) | |||||||
\(422\) | 4.00000i | 0.194717i | ||||||||
\(423\) | 20.0000i | 0.972433i | ||||||||
\(424\) | −1.00000 | − | 1.00000i | −0.0485643 | − | 0.0485643i | ||||
\(425\) | 3.00000 | + | 21.0000i | 0.145521 | + | 1.01865i | ||||
\(426\) | − | 8.00000i | − | 0.387601i | ||||||
\(427\) | 48.0000 | 2.32288 | ||||||||
\(428\) | 6.00000 | + | 6.00000i | 0.290021 | + | 0.290021i | ||||
\(429\) | 16.0000 | + | 24.0000i | 0.772487 | + | 1.15873i | ||||
\(430\) | 6.00000 | + | 2.00000i | 0.289346 | + | 0.0964486i | ||||
\(431\) | 6.00000 | + | 6.00000i | 0.289010 | + | 0.289010i | 0.836689 | − | 0.547679i | \(-0.184488\pi\) |
−0.547679 | + | 0.836689i | \(0.684488\pi\) | |||||||
\(432\) | 4.00000 | + | 4.00000i | 0.192450 | + | 0.192450i | ||||
\(433\) | −3.00000 | − | 3.00000i | −0.144171 | − | 0.144171i | 0.631337 | − | 0.775508i | \(-0.282506\pi\) |
−0.775508 | + | 0.631337i | \(0.782506\pi\) | |||||||
\(434\) | 24.0000 | − | 24.0000i | 1.15204 | − | 1.15204i | ||||
\(435\) | −12.0000 | + | 36.0000i | −0.575356 | + | 1.72607i | ||||
\(436\) | 11.0000 | − | 11.0000i | 0.526804 | − | 0.526804i | ||||
\(437\) | 8.00000 | 0.382692 | ||||||||
\(438\) | 20.0000 | − | 20.0000i | 0.955637 | − | 0.955637i | ||||
\(439\) | 40.0000 | 1.90910 | 0.954548 | − | 0.298057i | \(-0.0963387\pi\) | ||||
0.954548 | + | 0.298057i | \(0.0963387\pi\) | |||||||
\(440\) | −2.00000 | + | 6.00000i | −0.0953463 | + | 0.286039i | ||||
\(441\) | − | 45.0000i | − | 2.14286i | ||||||
\(442\) | 15.0000 | + | 3.00000i | 0.713477 | + | 0.142695i | ||||
\(443\) | −18.0000 | + | 18.0000i | −0.855206 | + | 0.855206i | −0.990769 | − | 0.135563i | \(-0.956716\pi\) |
0.135563 | + | 0.990769i | \(0.456716\pi\) | |||||||
\(444\) | −8.00000 | + | 8.00000i | −0.379663 | + | 0.379663i | ||||
\(445\) | −5.00000 | + | 15.0000i | −0.237023 | + | 0.711068i | ||||
\(446\) | 28.0000i | 1.32584i | ||||||||
\(447\) | 44.0000i | 2.08113i | ||||||||
\(448\) | 4.00000 | 0.188982 | ||||||||
\(449\) | −11.0000 | − | 11.0000i | −0.519122 | − | 0.519122i | 0.398184 | − | 0.917306i | \(-0.369641\pi\) |
−0.917306 | + | 0.398184i | \(0.869641\pi\) | |||||||
\(450\) | 15.0000 | − | 20.0000i | 0.707107 | − | 0.942809i | ||||
\(451\) | 4.00000 | 0.188353 | ||||||||
\(452\) | −1.00000 | + | 1.00000i | −0.0470360 | + | 0.0470360i | ||||
\(453\) | − | 56.0000i | − | 2.63111i | ||||||
\(454\) | −4.00000 | −0.187729 | ||||||||
\(455\) | −28.0000 | − | 16.0000i | −1.31266 | − | 0.750092i | ||||
\(456\) | −8.00000 | −0.374634 | ||||||||
\(457\) | 16.0000i | 0.748448i | 0.927338 | + | 0.374224i | \(0.122091\pi\) | ||||
−0.927338 | + | 0.374224i | \(0.877909\pi\) | |||||||
\(458\) | −1.00000 | + | 1.00000i | −0.0467269 | + | 0.0467269i | ||||
\(459\) | 24.0000 | 1.12022 | ||||||||
\(460\) | −2.00000 | + | 6.00000i | −0.0932505 | + | 0.279751i | ||||
\(461\) | −11.0000 | − | 11.0000i | −0.512321 | − | 0.512321i | 0.402916 | − | 0.915237i | \(-0.367997\pi\) |
−0.915237 | + | 0.402916i | \(0.867997\pi\) | |||||||
\(462\) | 32.0000 | 1.48877 | ||||||||
\(463\) | 8.00000i | 0.371792i | 0.982569 | + | 0.185896i | \(0.0595187\pi\) | ||||
−0.982569 | + | 0.185896i | \(0.940481\pi\) | |||||||
\(464\) | 6.00000i | 0.278543i | ||||||||
\(465\) | −24.0000 | − | 48.0000i | −1.11297 | − | 2.22595i | ||||
\(466\) | −11.0000 | + | 11.0000i | −0.509565 | + | 0.509565i | ||||
\(467\) | −2.00000 | + | 2.00000i | −0.0925490 | + | 0.0925490i | −0.751865 | − | 0.659317i | \(-0.770846\pi\) |
0.659317 | + | 0.751865i | \(0.270846\pi\) | |||||||
\(468\) | −10.0000 | − | 15.0000i | −0.462250 | − | 0.693375i | ||||
\(469\) | − | 16.0000i | − | 0.738811i | ||||||
\(470\) | 8.00000 | − | 4.00000i | 0.369012 | − | 0.184506i | ||||
\(471\) | −12.0000 | −0.552931 | ||||||||
\(472\) | −2.00000 | + | 2.00000i | −0.0920575 | + | 0.0920575i | ||||
\(473\) | 8.00000 | 0.367840 | ||||||||
\(474\) | −8.00000 | + | 8.00000i | −0.367452 | + | 0.367452i | ||||
\(475\) | 2.00000 | + | 14.0000i | 0.0917663 | + | 0.642364i | ||||
\(476\) | 12.0000 | − | 12.0000i | 0.550019 | − | 0.550019i | ||||
\(477\) | 5.00000 | + | 5.00000i | 0.228934 | + | 0.228934i | ||||
\(478\) | −10.0000 | − | 10.0000i | −0.457389 | − | 0.457389i | ||||
\(479\) | 10.0000 | + | 10.0000i | 0.456912 | + | 0.456912i | 0.897640 | − | 0.440729i | \(-0.145280\pi\) |
−0.440729 | + | 0.897640i | \(0.645280\pi\) | |||||||
\(480\) | 2.00000 | − | 6.00000i | 0.0912871 | − | 0.273861i | ||||
\(481\) | 12.0000 | − | 8.00000i | 0.547153 | − | 0.364769i | ||||
\(482\) | 5.00000 | + | 5.00000i | 0.227744 | + | 0.227744i | ||||
\(483\) | 32.0000 | 1.45605 | ||||||||
\(484\) | − | 3.00000i | − | 0.136364i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 10.0000 | + | 10.0000i | 0.453609 | + | 0.453609i | ||||
\(487\) | 16.0000i | 0.725029i | 0.931978 | + | 0.362515i | \(0.118082\pi\) | ||||
−0.931978 | + | 0.362515i | \(0.881918\pi\) | |||||||
\(488\) | − | 12.0000i | − | 0.543214i | ||||||
\(489\) | −40.0000 | − | 40.0000i | −1.80886 | − | 1.80886i | ||||
\(490\) | −18.0000 | + | 9.00000i | −0.813157 | + | 0.406579i | ||||
\(491\) | − | 24.0000i | − | 1.08310i | −0.840667 | − | 0.541552i | \(-0.817837\pi\) | ||
0.840667 | − | 0.541552i | \(-0.182163\pi\) | |||||||
\(492\) | −4.00000 | −0.180334 | ||||||||
\(493\) | 18.0000 | + | 18.0000i | 0.810679 | + | 0.810679i | ||||
\(494\) | 10.0000 | + | 2.00000i | 0.449921 | + | 0.0899843i | ||||
\(495\) | 10.0000 | − | 30.0000i | 0.449467 | − | 1.34840i | ||||
\(496\) | −6.00000 | − | 6.00000i | −0.269408 | − | 0.269408i | ||||
\(497\) | 8.00000 | + | 8.00000i | 0.358849 | + | 0.358849i | ||||
\(498\) | 16.0000 | + | 16.0000i | 0.716977 | + | 0.716977i | ||||
\(499\) | 14.0000 | − | 14.0000i | 0.626726 | − | 0.626726i | −0.320517 | − | 0.947243i | \(-0.603857\pi\) |
0.947243 | + | 0.320517i | \(0.103857\pi\) | |||||||
\(500\) | −11.0000 | − | 2.00000i | −0.491935 | − | 0.0894427i | ||||
\(501\) | 24.0000 | − | 24.0000i | 1.07224 | − | 1.07224i | ||||
\(502\) | −16.0000 | −0.714115 | ||||||||
\(503\) | −18.0000 | + | 18.0000i | −0.802580 | + | 0.802580i | −0.983498 | − | 0.180918i | \(-0.942093\pi\) |
0.180918 | + | 0.983498i | \(0.442093\pi\) | |||||||
\(504\) | −20.0000 | −0.890871 | ||||||||
\(505\) | 24.0000 | − | 12.0000i | 1.06799 | − | 0.533993i | ||||
\(506\) | 8.00000i | 0.355643i | ||||||||
\(507\) | 14.0000 | + | 34.0000i | 0.621762 | + | 1.50999i | ||||
\(508\) | −14.0000 | + | 14.0000i | −0.621150 | + | 0.621150i | ||||
\(509\) | −3.00000 | + | 3.00000i | −0.132973 | + | 0.132973i | −0.770460 | − | 0.637488i | \(-0.779974\pi\) |
0.637488 | + | 0.770460i | \(0.279974\pi\) | |||||||
\(510\) | −12.0000 | − | 24.0000i | −0.531369 | − | 1.06274i | ||||
\(511\) | 40.0000i | 1.76950i | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 16.0000 | 0.706417 | ||||||||
\(514\) | 17.0000 | + | 17.0000i | 0.749838 | + | 0.749838i | ||||
\(515\) | −6.00000 | + | 18.0000i | −0.264392 | + | 0.793175i | ||||
\(516\) | −8.00000 | −0.352180 | ||||||||
\(517\) | 8.00000 | − | 8.00000i | 0.351840 | − | 0.351840i | ||||
\(518\) | − | 16.0000i | − | 0.703000i | ||||||
\(519\) | −36.0000 | −1.58022 | ||||||||
\(520\) | −4.00000 | + | 7.00000i | −0.175412 | + | 0.306970i | ||||
\(521\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(522\) | − | 30.0000i | − | 1.31306i | ||||||
\(523\) | 30.0000 | − | 30.0000i | 1.31181 | − | 1.31181i | 0.391727 | − | 0.920082i | \(-0.371878\pi\) |
0.920082 | − | 0.391727i | \(-0.128122\pi\) | |||||||
\(524\) | −4.00000 | −0.174741 | ||||||||
\(525\) | 8.00000 | + | 56.0000i | 0.349149 | + | 2.44404i | ||||
\(526\) | −14.0000 | − | 14.0000i | −0.610429 | − | 0.610429i | ||||
\(527\) | −36.0000 | −1.56818 | ||||||||
\(528\) | − | 8.00000i | − | 0.348155i | ||||||
\(529\) | − | 15.0000i | − | 0.652174i | ||||||
\(530\) | 1.00000 | − | 3.00000i | 0.0434372 | − | 0.130312i | ||||
\(531\) | 10.0000 | − | 10.0000i | 0.433963 | − | 0.433963i | ||||
\(532\) | 8.00000 | − | 8.00000i | 0.346844 | − | 0.346844i | ||||
\(533\) | 5.00000 | + | 1.00000i | 0.216574 | + | 0.0433148i | ||||
\(534\) | − | 20.0000i | − | 0.865485i | ||||||
\(535\) | −6.00000 | + | 18.0000i | −0.259403 | + | 0.778208i | ||||
\(536\) | −4.00000 | −0.172774 | ||||||||
\(537\) | 40.0000 | − | 40.0000i | 1.72613 | − | 1.72613i | ||||
\(538\) | −20.0000 | −0.862261 | ||||||||
\(539\) | −18.0000 | + | 18.0000i | −0.775315 | + | 0.775315i | ||||
\(540\) | −4.00000 | + | 12.0000i | −0.172133 | + | 0.516398i | ||||
\(541\) | 7.00000 | − | 7.00000i | 0.300954 | − | 0.300954i | −0.540433 | − | 0.841387i | \(-0.681740\pi\) |
0.841387 | + | 0.540433i | \(0.181740\pi\) | |||||||
\(542\) | −6.00000 | − | 6.00000i | −0.257722 | − | 0.257722i | ||||
\(543\) | 4.00000 | + | 4.00000i | 0.171656 | + | 0.171656i | ||||
\(544\) | −3.00000 | − | 3.00000i | −0.128624 | − | 0.128624i | ||||
\(545\) | 33.0000 | + | 11.0000i | 1.41356 | + | 0.471188i | ||||
\(546\) | 40.0000 | + | 8.00000i | 1.71184 | + | 0.342368i | ||||
\(547\) | −30.0000 | − | 30.0000i | −1.28271 | − | 1.28271i | −0.939121 | − | 0.343586i | \(-0.888358\pi\) |
−0.343586 | − | 0.939121i | \(-0.611642\pi\) | |||||||
\(548\) | −18.0000 | −0.768922 | ||||||||
\(549\) | 60.0000i | 2.56074i | ||||||||
\(550\) | −14.0000 | + | 2.00000i | −0.596962 | + | 0.0852803i | ||||
\(551\) | 12.0000 | + | 12.0000i | 0.511217 | + | 0.511217i | ||||
\(552\) | − | 8.00000i | − | 0.340503i | ||||||
\(553\) | − | 16.0000i | − | 0.680389i | ||||||
\(554\) | 3.00000 | + | 3.00000i | 0.127458 | + | 0.127458i | ||||
\(555\) | −24.0000 | − | 8.00000i | −1.01874 | − | 0.339581i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.0000 | 0.847427 | 0.423714 | − | 0.905796i | \(-0.360726\pi\) | ||||
0.423714 | + | 0.905796i | \(0.360726\pi\) | |||||||
\(558\) | 30.0000 | + | 30.0000i | 1.27000 | + | 1.27000i | ||||
\(559\) | 10.0000 | + | 2.00000i | 0.422955 | + | 0.0845910i | ||||
\(560\) | 4.00000 | + | 8.00000i | 0.169031 | + | 0.338062i | ||||
\(561\) | −24.0000 | − | 24.0000i | −1.01328 | − | 1.01328i | ||||
\(562\) | −11.0000 | − | 11.0000i | −0.464007 | − | 0.464007i | ||||
\(563\) | 10.0000 | + | 10.0000i | 0.421450 | + | 0.421450i | 0.885703 | − | 0.464253i | \(-0.153677\pi\) |
−0.464253 | + | 0.885703i | \(0.653677\pi\) | |||||||
\(564\) | −8.00000 | + | 8.00000i | −0.336861 | + | 0.336861i | ||||
\(565\) | −3.00000 | − | 1.00000i | −0.126211 | − | 0.0420703i | ||||
\(566\) | −6.00000 | + | 6.00000i | −0.252199 | + | 0.252199i | ||||
\(567\) | 4.00000 | 0.167984 | ||||||||
\(568\) | 2.00000 | − | 2.00000i | 0.0839181 | − | 0.0839181i | ||||
\(569\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(570\) | −8.00000 | − | 16.0000i | −0.335083 | − | 0.670166i | ||||
\(571\) | − | 32.0000i | − | 1.33916i | −0.742741 | − | 0.669579i | \(-0.766474\pi\) | ||
0.742741 | − | 0.669579i | \(-0.233526\pi\) | |||||||
\(572\) | −2.00000 | + | 10.0000i | −0.0836242 | + | 0.418121i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.00000 | − | 4.00000i | 0.166957 | − | 0.166957i | ||||
\(575\) | −14.0000 | + | 2.00000i | −0.583840 | + | 0.0834058i | ||||
\(576\) | 5.00000i | 0.208333i | ||||||||
\(577\) | 18.0000i | 0.749350i | 0.927156 | + | 0.374675i | \(0.122246\pi\) | ||||
−0.927156 | + | 0.374675i | \(0.877754\pi\) | |||||||
\(578\) | −1.00000 | −0.0415945 | ||||||||
\(579\) | −32.0000 | − | 32.0000i | −1.32987 | − | 1.32987i | ||||
\(580\) | −12.0000 | + | 6.00000i | −0.498273 | + | 0.249136i | ||||
\(581\) | −32.0000 | −1.32758 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 4.00000i | − | 0.165663i | ||||||
\(584\) | 10.0000 | 0.413803 | ||||||||
\(585\) | 20.0000 | − | 35.0000i | 0.826898 | − | 1.44707i | ||||
\(586\) | 26.0000 | 1.07405 | ||||||||
\(587\) | 12.0000i | 0.495293i | 0.968850 | + | 0.247647i | \(0.0796572\pi\) | ||||
−0.968850 | + | 0.247647i | \(0.920343\pi\) | |||||||
\(588\) | 18.0000 | − | 18.0000i | 0.742307 | − | 0.742307i | ||||
\(589\) | −24.0000 | −0.988903 | ||||||||
\(590\) | −6.00000 | − | 2.00000i | −0.247016 | − | 0.0823387i | ||||
\(591\) | 24.0000 | + | 24.0000i | 0.987228 | + | 0.987228i | ||||
\(592\) | −4.00000 | −0.164399 | ||||||||
\(593\) | 24.0000i | 0.985562i | 0.870153 | + | 0.492781i | \(0.164020\pi\) | ||||
−0.870153 | + | 0.492781i | \(0.835980\pi\) | |||||||
\(594\) | 16.0000i | 0.656488i | ||||||||
\(595\) | 36.0000 | + | 12.0000i | 1.47586 | + | 0.491952i | ||||
\(596\) | −11.0000 | + | 11.0000i | −0.450578 | + | 0.450578i | ||||
\(597\) | −16.0000 | + | 16.0000i | −0.654836 | + | 0.654836i | ||||
\(598\) | −2.00000 | + | 10.0000i | −0.0817861 | + | 0.408930i | ||||
\(599\) | 36.0000i | 1.47092i | 0.677568 | + | 0.735460i | \(0.263034\pi\) | ||||
−0.677568 | + | 0.735460i | \(0.736966\pi\) | |||||||
\(600\) | 14.0000 | − | 2.00000i | 0.571548 | − | 0.0816497i | ||||
\(601\) | −22.0000 | −0.897399 | −0.448699 | − | 0.893683i | \(-0.648113\pi\) | ||||
−0.448699 | + | 0.893683i | \(0.648113\pi\) | |||||||
\(602\) | 8.00000 | − | 8.00000i | 0.326056 | − | 0.326056i | ||||
\(603\) | 20.0000 | 0.814463 | ||||||||
\(604\) | 14.0000 | − | 14.0000i | 0.569652 | − | 0.569652i | ||||
\(605\) | 6.00000 | − | 3.00000i | 0.243935 | − | 0.121967i | ||||
\(606\) | −24.0000 | + | 24.0000i | −0.974933 | + | 0.974933i | ||||
\(607\) | 26.0000 | + | 26.0000i | 1.05531 | + | 1.05531i | 0.998378 | + | 0.0569292i | \(0.0181309\pi\) |
0.0569292 | + | 0.998378i | \(0.481869\pi\) | |||||||
\(608\) | −2.00000 | − | 2.00000i | −0.0811107 | − | 0.0811107i | ||||
\(609\) | 48.0000 | + | 48.0000i | 1.94506 | + | 1.94506i | ||||
\(610\) | 24.0000 | − | 12.0000i | 0.971732 | − | 0.485866i | ||||
\(611\) | 12.0000 | − | 8.00000i | 0.485468 | − | 0.323645i | ||||
\(612\) | 15.0000 | + | 15.0000i | 0.606339 | + | 0.606339i | ||||
\(613\) | −18.0000 | −0.727013 | −0.363507 | − | 0.931592i | \(-0.618421\pi\) | ||||
−0.363507 | + | 0.931592i | \(0.618421\pi\) | |||||||
\(614\) | 8.00000i | 0.322854i | ||||||||
\(615\) | −4.00000 | − | 8.00000i | −0.161296 | − | 0.322591i | ||||
\(616\) | 8.00000 | + | 8.00000i | 0.322329 | + | 0.322329i | ||||
\(617\) | 40.0000i | 1.61034i | 0.593045 | + | 0.805170i | \(0.297926\pi\) | ||||
−0.593045 | + | 0.805170i | \(0.702074\pi\) | |||||||
\(618\) | − | 24.0000i | − | 0.965422i | ||||||
\(619\) | 18.0000 | + | 18.0000i | 0.723481 | + | 0.723481i | 0.969313 | − | 0.245831i | \(-0.0790610\pi\) |
−0.245831 | + | 0.969313i | \(0.579061\pi\) | |||||||
\(620\) | 6.00000 | − | 18.0000i | 0.240966 | − | 0.722897i | ||||
\(621\) | 16.0000i | 0.642058i | ||||||||
\(622\) | 12.0000 | 0.481156 | ||||||||
\(623\) | 20.0000 | + | 20.0000i | 0.801283 | + | 0.801283i | ||||
\(624\) | 2.00000 | − | 10.0000i | 0.0800641 | − | 0.400320i | ||||
\(625\) | −7.00000 | − | 24.0000i | −0.280000 | − | 0.960000i | ||||
\(626\) | 9.00000 | + | 9.00000i | 0.359712 | + | 0.359712i | ||||
\(627\) | −16.0000 | − | 16.0000i | −0.638978 | − | 0.638978i | ||||
\(628\) | −3.00000 | − | 3.00000i | −0.119713 | − | 0.119713i | ||||
\(629\) | −12.0000 | + | 12.0000i | −0.478471 | + | 0.478471i | ||||
\(630\) | −20.0000 | − | 40.0000i | −0.796819 | − | 1.59364i | ||||
\(631\) | 14.0000 | − | 14.0000i | 0.557331 | − | 0.557331i | −0.371216 | − | 0.928547i | \(-0.621059\pi\) |
0.928547 | + | 0.371216i | \(0.121059\pi\) | |||||||
\(632\) | −4.00000 | −0.159111 | ||||||||
\(633\) | 8.00000 | − | 8.00000i | 0.317971 | − | 0.317971i | ||||
\(634\) | −30.0000 | −1.19145 | ||||||||
\(635\) | −42.0000 | − | 14.0000i | −1.66672 | − | 0.555573i | ||||
\(636\) | 4.00000i | 0.158610i | ||||||||
\(637\) | −27.0000 | + | 18.0000i | −1.06978 | + | 0.713186i | ||||
\(638\) | −12.0000 | + | 12.0000i | −0.475085 | + | 0.475085i | ||||
\(639\) | −10.0000 | + | 10.0000i | −0.395594 | + | 0.395594i | ||||
\(640\) | 2.00000 | − | 1.00000i | 0.0790569 | − | 0.0395285i | ||||
\(641\) | − | 40.0000i | − | 1.57991i | −0.613168 | − | 0.789953i | \(-0.710105\pi\) | ||
0.613168 | − | 0.789953i | \(-0.289895\pi\) | |||||||
\(642\) | − | 24.0000i | − | 0.947204i | ||||||
\(643\) | −32.0000 | −1.26196 | −0.630978 | − | 0.775800i | \(-0.717346\pi\) | ||||
−0.630978 | + | 0.775800i | \(0.717346\pi\) | |||||||
\(644\) | 8.00000 | + | 8.00000i | 0.315244 | + | 0.315244i | ||||
\(645\) | −8.00000 | − | 16.0000i | −0.315000 | − | 0.629999i | ||||
\(646\) | −12.0000 | −0.472134 | ||||||||
\(647\) | −10.0000 | + | 10.0000i | −0.393141 | + | 0.393141i | −0.875805 | − | 0.482665i | \(-0.839669\pi\) |
0.482665 | + | 0.875805i | \(0.339669\pi\) | |||||||
\(648\) | − | 1.00000i | − | 0.0392837i | ||||||
\(649\) | −8.00000 | −0.314027 | ||||||||
\(650\) | −18.0000 | − | 1.00000i | −0.706018 | − | 0.0392232i | ||||
\(651\) | −96.0000 | −3.76254 | ||||||||
\(652\) | − | 20.0000i | − | 0.783260i | ||||||
\(653\) | 5.00000 | − | 5.00000i | 0.195665 | − | 0.195665i | −0.602474 | − | 0.798139i | \(-0.705818\pi\) |
0.798139 | + | 0.602474i | \(0.205818\pi\) | |||||||
\(654\) | −44.0000 | −1.72054 | ||||||||
\(655\) | −4.00000 | − | 8.00000i | −0.156293 | − | 0.312586i | ||||
\(656\) | −1.00000 | − | 1.00000i | −0.0390434 | − | 0.0390434i | ||||
\(657\) | −50.0000 | −1.95069 | ||||||||
\(658\) | − | 16.0000i | − | 0.623745i | ||||||
\(659\) | 32.0000i | 1.24654i | 0.782006 | + | 0.623272i | \(0.214197\pi\) | ||||
−0.782006 | + | 0.623272i | \(0.785803\pi\) | |||||||
\(660\) | 16.0000 | − | 8.00000i | 0.622799 | − | 0.311400i | ||||
\(661\) | −23.0000 | + | 23.0000i | −0.894596 | + | 0.894596i | −0.994952 | − | 0.100355i | \(-0.968002\pi\) |
0.100355 | + | 0.994952i | \(0.468002\pi\) | |||||||
\(662\) | −6.00000 | + | 6.00000i | −0.233197 | + | 0.233197i | ||||
\(663\) | −24.0000 | − | 36.0000i | −0.932083 | − | 1.39812i | ||||
\(664\) | 8.00000i | 0.310460i | ||||||||
\(665\) | 24.0000 | + | 8.00000i | 0.930680 | + | 0.310227i | ||||
\(666\) | 20.0000 | 0.774984 | ||||||||
\(667\) | −12.0000 | + | 12.0000i | −0.464642 | + | 0.464642i | ||||
\(668\) | 12.0000 | 0.464294 | ||||||||
\(669\) | 56.0000 | − | 56.0000i | 2.16509 | − | 2.16509i | ||||
\(670\) | −4.00000 | − | 8.00000i | −0.154533 | − | 0.309067i | ||||
\(671\) | 24.0000 | − | 24.0000i | 0.926510 | − | 0.926510i | ||||
\(672\) | −8.00000 | − | 8.00000i | −0.308607 | − | 0.308607i | ||||
\(673\) | −5.00000 | − | 5.00000i | −0.192736 | − | 0.192736i | 0.604141 | − | 0.796877i | \(-0.293516\pi\) |
−0.796877 | + | 0.604141i | \(0.793516\pi\) | |||||||
\(674\) | 15.0000 | + | 15.0000i | 0.577778 | + | 0.577778i | ||||
\(675\) | −28.0000 | + | 4.00000i | −1.07772 | + | 0.153960i | ||||
\(676\) | −5.00000 | + | 12.0000i | −0.192308 | + | 0.461538i | ||||
\(677\) | 27.0000 | + | 27.0000i | 1.03769 | + | 1.03769i | 0.999261 | + | 0.0384331i | \(0.0122367\pi\) |
0.0384331 | + | 0.999261i | \(0.487763\pi\) | |||||||
\(678\) | 4.00000 | 0.153619 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 3.00000 | − | 9.00000i | 0.115045 | − | 0.345134i | ||||
\(681\) | 8.00000 | + | 8.00000i | 0.306561 | + | 0.306561i | ||||
\(682\) | − | 24.0000i | − | 0.919007i | ||||||
\(683\) | 36.0000i | 1.37750i | 0.724998 | + | 0.688751i | \(0.241841\pi\) | ||||
−0.724998 | + | 0.688751i | \(0.758159\pi\) | |||||||
\(684\) | 10.0000 | + | 10.0000i | 0.382360 | + | 0.382360i | ||||
\(685\) | −18.0000 | − | 36.0000i | −0.687745 | − | 1.37549i | ||||
\(686\) | 8.00000i | 0.305441i | ||||||||
\(687\) | 4.00000 | 0.152610 | ||||||||
\(688\) | −2.00000 | − | 2.00000i | −0.0762493 | − | 0.0762493i | ||||
\(689\) | 1.00000 | − | 5.00000i | 0.0380970 | − | 0.190485i | ||||
\(690\) | 16.0000 | − | 8.00000i | 0.609110 | − | 0.304555i | ||||
\(691\) | 14.0000 | + | 14.0000i | 0.532585 | + | 0.532585i | 0.921341 | − | 0.388756i | \(-0.127095\pi\) |
−0.388756 | + | 0.921341i | \(0.627095\pi\) | |||||||
\(692\) | −9.00000 | − | 9.00000i | −0.342129 | − | 0.342129i | ||||
\(693\) | −40.0000 | − | 40.0000i | −1.51947 | − | 1.51947i | ||||
\(694\) | −2.00000 | + | 2.00000i | −0.0759190 | + | 0.0759190i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 12.0000 | − | 12.0000i | 0.454859 | − | 0.454859i | ||||
\(697\) | −6.00000 | −0.227266 | ||||||||
\(698\) | −23.0000 | + | 23.0000i | −0.870563 | + | 0.870563i | ||||
\(699\) | 44.0000 | 1.66423 | ||||||||
\(700\) | −12.0000 | + | 16.0000i | −0.453557 | + | 0.604743i | ||||
\(701\) | 20.0000i | 0.755390i | 0.925930 | + | 0.377695i | \(0.123283\pi\) | ||||
−0.925930 | + | 0.377695i | \(0.876717\pi\) | |||||||
\(702\) | −4.00000 | + | 20.0000i | −0.150970 | + | 0.754851i | ||||
\(703\) | −8.00000 | + | 8.00000i | −0.301726 | + | 0.301726i | ||||
\(704\) | 2.00000 | − | 2.00000i | 0.0753778 | − | 0.0753778i | ||||
\(705\) | −24.0000 | − | 8.00000i | −0.903892 | − | 0.301297i | ||||
\(706\) | 16.0000i | 0.602168i | ||||||||
\(707\) | − | 48.0000i | − | 1.80523i | ||||||
\(708\) | 8.00000 | 0.300658 | ||||||||
\(709\) | 7.00000 | + | 7.00000i | 0.262891 | + | 0.262891i | 0.826227 | − | 0.563337i | \(-0.190483\pi\) |
−0.563337 | + | 0.826227i | \(0.690483\pi\) | |||||||
\(710\) | 6.00000 | + | 2.00000i | 0.225176 | + | 0.0750587i | ||||
\(711\) | 20.0000 | 0.750059 | ||||||||
\(712\) | 5.00000 | − | 5.00000i | 0.187383 | − | 0.187383i | ||||
\(713\) | − | 24.0000i | − | 0.898807i | ||||||
\(714\) | −48.0000 | −1.79635 | ||||||||
\(715\) | −22.0000 | + | 6.00000i | −0.822753 | + | 0.224387i | ||||
\(716\) | 20.0000 | 0.747435 | ||||||||
\(717\) | 40.0000i | 1.49383i | ||||||||
\(718\) | 22.0000 | − | 22.0000i | 0.821033 | − | 0.821033i | ||||
\(719\) | 16.0000 | 0.596699 | 0.298350 | − | 0.954457i | \(-0.403564\pi\) | ||||
0.298350 | + | 0.954457i | \(0.403564\pi\) | |||||||
\(720\) | −10.0000 | + | 5.00000i | −0.372678 | + | 0.186339i | ||||
\(721\) | 24.0000 | + | 24.0000i | 0.893807 | + | 0.893807i | ||||
\(722\) | 11.0000 | 0.409378 | ||||||||
\(723\) | − | 20.0000i | − | 0.743808i | ||||||
\(724\) | 2.00000i | 0.0743294i | ||||||||
\(725\) | −24.0000 | − | 18.0000i | −0.891338 | − | 0.668503i | ||||
\(726\) | −6.00000 | + | 6.00000i | −0.222681 | + | 0.222681i | ||||
\(727\) | 30.0000 | − | 30.0000i | 1.11264 | − | 1.11264i | 0.119846 | − | 0.992793i | \(-0.461760\pi\) |
0.992793 | − | 0.119846i | \(-0.0382401\pi\) | |||||||
\(728\) | 8.00000 | + | 12.0000i | 0.296500 | + | 0.444750i | ||||
\(729\) | − | 43.0000i | − | 1.59259i | ||||||
\(730\) | 10.0000 | + | 20.0000i | 0.370117 | + | 0.740233i | ||||
\(731\) | −12.0000 | −0.443836 | ||||||||
\(732\) | −24.0000 | + | 24.0000i | −0.887066 | + | 0.887066i | ||||
\(733\) | −6.00000 | −0.221615 | −0.110808 | − | 0.993842i | \(-0.535344\pi\) | ||||
−0.110808 | + | 0.993842i | \(0.535344\pi\) | |||||||
\(734\) | −14.0000 | + | 14.0000i | −0.516749 | + | 0.516749i | ||||
\(735\) | 54.0000 | + | 18.0000i | 1.99182 | + | 0.663940i | ||||
\(736\) | 2.00000 | − | 2.00000i | 0.0737210 | − | 0.0737210i | ||||
\(737\) | −8.00000 | − | 8.00000i | −0.294684 | − | 0.294684i | ||||
\(738\) | 5.00000 | + | 5.00000i | 0.184053 | + | 0.184053i | ||||
\(739\) | −18.0000 | − | 18.0000i | −0.662141 | − | 0.662141i | 0.293744 | − | 0.955884i | \(-0.405099\pi\) |
−0.955884 | + | 0.293744i | \(0.905099\pi\) | |||||||
\(740\) | −4.00000 | − | 8.00000i | −0.147043 | − | 0.294086i | ||||
\(741\) | −16.0000 | − | 24.0000i | −0.587775 | − | 0.881662i | ||||
\(742\) | −4.00000 | − | 4.00000i | −0.146845 | − | 0.146845i | ||||
\(743\) | 44.0000 | 1.61420 | 0.807102 | − | 0.590412i | \(-0.201035\pi\) | ||||
0.807102 | + | 0.590412i | \(0.201035\pi\) | |||||||
\(744\) | 24.0000i | 0.879883i | ||||||||
\(745\) | −33.0000 | − | 11.0000i | −1.20903 | − | 0.403009i | ||||
\(746\) | −15.0000 | − | 15.0000i | −0.549189 | − | 0.549189i | ||||
\(747\) | − | 40.0000i | − | 1.46352i | ||||||
\(748\) | − | 12.0000i | − | 0.438763i | ||||||
\(749\) | 24.0000 | + | 24.0000i | 0.876941 | + | 0.876941i | ||||
\(750\) | 18.0000 | + | 26.0000i | 0.657267 | + | 0.949386i | ||||
\(751\) | 4.00000i | 0.145962i | 0.997333 | + | 0.0729810i | \(0.0232513\pi\) | ||||
−0.997333 | + | 0.0729810i | \(0.976749\pi\) | |||||||
\(752\) | −4.00000 | −0.145865 | ||||||||
\(753\) | 32.0000 | + | 32.0000i | 1.16614 | + | 1.16614i | ||||
\(754\) | −18.0000 | + | 12.0000i | −0.655521 | + | 0.437014i | ||||
\(755\) | 42.0000 | + | 14.0000i | 1.52854 | + | 0.509512i | ||||
\(756\) | 16.0000 | + | 16.0000i | 0.581914 | + | 0.581914i | ||||
\(757\) | 9.00000 | + | 9.00000i | 0.327111 | + | 0.327111i | 0.851487 | − | 0.524376i | \(-0.175701\pi\) |
−0.524376 | + | 0.851487i | \(0.675701\pi\) | |||||||
\(758\) | 6.00000 | + | 6.00000i | 0.217930 | + | 0.217930i | ||||
\(759\) | 16.0000 | − | 16.0000i | 0.580763 | − | 0.580763i | ||||
\(760\) | 2.00000 | − | 6.00000i | 0.0725476 | − | 0.217643i | ||||
\(761\) | 1.00000 | − | 1.00000i | 0.0362500 | − | 0.0362500i | −0.688749 | − | 0.724999i | \(-0.741840\pi\) |
0.724999 | + | 0.688749i | \(0.241840\pi\) | |||||||
\(762\) | 56.0000 | 2.02867 | ||||||||
\(763\) | 44.0000 | − | 44.0000i | 1.59291 | − | 1.59291i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −15.0000 | + | 45.0000i | −0.542326 | + | 1.62698i | ||||
\(766\) | − | 4.00000i | − | 0.144526i | ||||||
\(767\) | −10.0000 | − | 2.00000i | −0.361079 | − | 0.0722158i | ||||
\(768\) | −2.00000 | + | 2.00000i | −0.0721688 | + | 0.0721688i | ||||
\(769\) | −3.00000 | + | 3.00000i | −0.108183 | + | 0.108183i | −0.759126 | − | 0.650943i | \(-0.774373\pi\) |
0.650943 | + | 0.759126i | \(0.274373\pi\) | |||||||
\(770\) | −8.00000 | + | 24.0000i | −0.288300 | + | 0.864900i | ||||
\(771\) | − | 68.0000i | − | 2.44896i | ||||||
\(772\) | − | 16.0000i | − | 0.575853i | ||||||
\(773\) | 4.00000 | 0.143870 | 0.0719350 | − | 0.997409i | \(-0.477083\pi\) | ||||
0.0719350 | + | 0.997409i | \(0.477083\pi\) | |||||||
\(774\) | 10.0000 | + | 10.0000i | 0.359443 | + | 0.359443i | ||||
\(775\) | 42.0000 | − | 6.00000i | 1.50868 | − | 0.215526i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −32.0000 | + | 32.0000i | −1.14799 | + | 1.14799i | ||||
\(778\) | 38.0000i | 1.36237i | ||||||||
\(779\) | −4.00000 | −0.143315 | ||||||||
\(780\) | 22.0000 | − | 6.00000i | 0.787726 | − | 0.214834i | ||||
\(781\) | 8.00000 | 0.286263 | ||||||||
\(782\) | − | 12.0000i | − | 0.429119i | ||||||
\(783\) | −24.0000 | + | 24.0000i | −0.857690 | + | 0.857690i | ||||
\(784\) | 9.00000 | 0.321429 | ||||||||
\(785\) | 3.00000 | − | 9.00000i | 0.107075 | − | 0.321224i | ||||
\(786\) | 8.00000 | + | 8.00000i | 0.285351 | + | 0.285351i | ||||
\(787\) | −8.00000 | −0.285169 | −0.142585 | − | 0.989783i | \(-0.545541\pi\) | ||||
−0.142585 | + | 0.989783i | \(0.545541\pi\) | |||||||
\(788\) | 12.0000i | 0.427482i | ||||||||
\(789\) | 56.0000i | 1.99365i | ||||||||
\(790\) | −4.00000 | − | 8.00000i | −0.142314 | − | 0.284627i | ||||
\(791\) | −4.00000 | + | 4.00000i | −0.142224 | + | 0.142224i | ||||
\(792\) | −10.0000 | + | 10.0000i | −0.355335 | + | 0.355335i | ||||
\(793\) | 36.0000 | − | 24.0000i | 1.27840 | − | 0.852265i | ||||
\(794\) | − | 4.00000i | − | 0.141955i | ||||||
\(795\) | −8.00000 | + | 4.00000i | −0.283731 | + | 0.141865i | ||||
\(796\) | −8.00000 | −0.283552 | ||||||||
\(797\) | 35.0000 | − | 35.0000i | 1.23976 | − | 1.23976i | 0.279666 | − | 0.960097i | \(-0.409776\pi\) |
0.960097 | − | 0.279666i | \(-0.0902238\pi\) | |||||||
\(798\) | −32.0000 | −1.13279 | ||||||||
\(799\) | −12.0000 | + | 12.0000i | −0.424529 | + | 0.424529i | ||||
\(800\) | 4.00000 | + | 3.00000i | 0.141421 | + | 0.106066i | ||||
\(801\) | −25.0000 | + | 25.0000i | −0.883332 | + | 0.883332i | ||||
\(802\) | 5.00000 | + | 5.00000i | 0.176556 | + | 0.176556i | ||||
\(803\) | 20.0000 | + | 20.0000i | 0.705785 | + | 0.705785i | ||||
\(804\) | 8.00000 | + | 8.00000i | 0.282138 | + | 0.282138i | ||||
\(805\) | −8.00000 | + | 24.0000i | −0.281963 | + | 0.845889i | ||||
\(806\) | 6.00000 | − | 30.0000i | 0.211341 | − | 1.05670i | ||||
\(807\) | 40.0000 | + | 40.0000i | 1.40807 | + | 1.40807i | ||||
\(808\) | −12.0000 | −0.422159 | ||||||||
\(809\) | − | 18.0000i | − | 0.632846i | −0.948618 | − | 0.316423i | \(-0.897518\pi\) | ||
0.948618 | − | 0.316423i | \(-0.102482\pi\) | |||||||
\(810\) | 2.00000 | − | 1.00000i | 0.0702728 | − | 0.0351364i | ||||
\(811\) | 14.0000 | + | 14.0000i | 0.491606 | + | 0.491606i | 0.908812 | − | 0.417206i | \(-0.136991\pi\) |
−0.417206 | + | 0.908812i | \(0.636991\pi\) | |||||||
\(812\) | 24.0000i | 0.842235i | ||||||||
\(813\) | 24.0000i | 0.841717i | ||||||||
\(814\) | −8.00000 | − | 8.00000i | −0.280400 | − | 0.280400i | ||||
\(815\) | 40.0000 | − | 20.0000i | 1.40114 | − | 0.700569i | ||||
\(816\) | 12.0000i | 0.420084i | ||||||||
\(817\) | −8.00000 | −0.279885 | ||||||||
\(818\) | −15.0000 | − | 15.0000i | −0.524463 | − | 0.524463i | ||||
\(819\) | −40.0000 | − | 60.0000i | −1.39771 | − | 2.09657i | ||||
\(820\) | 1.00000 | − | 3.00000i | 0.0349215 | − | 0.104765i | ||||
\(821\) | −29.0000 | − | 29.0000i | −1.01211 | − | 1.01211i | −0.999926 | − | 0.0121812i | \(-0.996123\pi\) |
−0.0121812 | − | 0.999926i | \(-0.503877\pi\) | |||||||
\(822\) | 36.0000 | + | 36.0000i | 1.25564 | + | 1.25564i | ||||
\(823\) | −18.0000 | − | 18.0000i | −0.627441 | − | 0.627441i | 0.319983 | − | 0.947423i | \(-0.396323\pi\) |
−0.947423 | + | 0.319983i | \(0.896323\pi\) | |||||||
\(824\) | 6.00000 | − | 6.00000i | 0.209020 | − | 0.209020i | ||||
\(825\) | 32.0000 | + | 24.0000i | 1.11410 | + | 0.835573i | ||||
\(826\) | −8.00000 | + | 8.00000i | −0.278356 | + | 0.278356i | ||||
\(827\) | −24.0000 | −0.834562 | −0.417281 | − | 0.908778i | \(-0.637017\pi\) | ||||
−0.417281 | + | 0.908778i | \(0.637017\pi\) | |||||||
\(828\) | −10.0000 | + | 10.0000i | −0.347524 | + | 0.347524i | ||||
\(829\) | 4.00000 | 0.138926 | 0.0694629 | − | 0.997585i | \(-0.477871\pi\) | ||||
0.0694629 | + | 0.997585i | \(0.477871\pi\) | |||||||
\(830\) | −16.0000 | + | 8.00000i | −0.555368 | + | 0.277684i | ||||
\(831\) | − | 12.0000i | − | 0.416275i | ||||||
\(832\) | 3.00000 | − | 2.00000i | 0.104006 | − | 0.0693375i | ||||
\(833\) | 27.0000 | − | 27.0000i | 0.935495 | − | 0.935495i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.0000 | + | 24.0000i | 0.415277 | + | 0.830554i | ||||
\(836\) | − | 8.00000i | − | 0.276686i | ||||||
\(837\) | − | 48.0000i | − | 1.65912i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.0000 | − | 18.0000i | −0.621429 | − | 0.621429i | 0.324468 | − | 0.945897i | \(-0.394815\pi\) |
−0.945897 | + | 0.324468i | \(0.894815\pi\) | |||||||
\(840\) | 8.00000 | − | 24.0000i | 0.276026 | − | 0.828079i | ||||
\(841\) | −7.00000 | −0.241379 | ||||||||
\(842\) | −19.0000 | + | 19.0000i | −0.654783 | + | 0.654783i | ||||
\(843\) | 44.0000i | 1.51544i | ||||||||
\(844\) | 4.00000 | 0.137686 | ||||||||
\(845\) | −29.0000 | + | 2.00000i | −0.997630 | + | 0.0688021i | ||||
\(846\) | 20.0000 | 0.687614 | ||||||||
\(847\) | − | 12.0000i | − | 0.412325i | ||||||
\(848\) | −1.00000 | + | 1.00000i | −0.0343401 | + | 0.0343401i | ||||
\(849\) | 24.0000 | 0.823678 | ||||||||
\(850\) | 21.0000 | − | 3.00000i | 0.720294 | − | 0.102899i | ||||
\(851\) | −8.00000 | − | 8.00000i | −0.274236 | − | 0.274236i | ||||
\(852\) | −8.00000 | −0.274075 | ||||||||
\(853\) | 22.0000i | 0.753266i | 0.926363 | + | 0.376633i | \(0.122918\pi\) | ||||
−0.926363 | + | 0.376633i | \(0.877082\pi\) | |||||||
\(854\) | − | 48.0000i | − | 1.64253i | ||||||
\(855\) | −10.0000 | + | 30.0000i | −0.341993 | + | 1.02598i | ||||
\(856\) | 6.00000 | − | 6.00000i | 0.205076 | − | 0.205076i | ||||
\(857\) | 31.0000 | − | 31.0000i | 1.05894 | − | 1.05894i | 0.0607892 | − | 0.998151i | \(-0.480638\pi\) |
0.998151 | − | 0.0607892i | \(-0.0193617\pi\) | |||||||
\(858\) | 24.0000 | − | 16.0000i | 0.819346 | − | 0.546231i | ||||
\(859\) | − | 40.0000i | − | 1.36478i | −0.730987 | − | 0.682391i | \(-0.760940\pi\) | ||
0.730987 | − | 0.682391i | \(-0.239060\pi\) | |||||||
\(860\) | 2.00000 | − | 6.00000i | 0.0681994 | − | 0.204598i | ||||
\(861\) | −16.0000 | −0.545279 | ||||||||
\(862\) | 6.00000 | − | 6.00000i | 0.204361 | − | 0.204361i | ||||
\(863\) | −52.0000 | −1.77010 | −0.885050 | − | 0.465495i | \(-0.845876\pi\) | ||||
−0.885050 | + | 0.465495i | \(0.845876\pi\) | |||||||
\(864\) | 4.00000 | − | 4.00000i | 0.136083 | − | 0.136083i | ||||
\(865\) | 9.00000 | − | 27.0000i | 0.306009 | − | 0.918028i | ||||
\(866\) | −3.00000 | + | 3.00000i | −0.101944 | + | 0.101944i | ||||
\(867\) | 2.00000 | + | 2.00000i | 0.0679236 | + | 0.0679236i | ||||
\(868\) | −24.0000 | − | 24.0000i | −0.814613 | − | 0.814613i | ||||
\(869\) | −8.00000 | − | 8.00000i | −0.271381 | − | 0.271381i | ||||
\(870\) | 36.0000 | + | 12.0000i | 1.22051 | + | 0.406838i | ||||
\(871\) | −8.00000 | − | 12.0000i | −0.271070 | − | 0.406604i | ||||
\(872\) | −11.0000 | − | 11.0000i | −0.372507 | − | 0.372507i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 8.00000i | − | 0.270604i | ||||||
\(875\) | −44.0000 | − | 8.00000i | −1.48747 | − | 0.270449i | ||||
\(876\) | −20.0000 | − | 20.0000i | −0.675737 | − | 0.675737i | ||||
\(877\) | 20.0000i | 0.675352i | 0.941262 | + | 0.337676i | \(0.109641\pi\) | ||||
−0.941262 | + | 0.337676i | \(0.890359\pi\) | |||||||
\(878\) | − | 40.0000i | − | 1.34993i | ||||||
\(879\) | −52.0000 | − | 52.0000i | −1.75392 | − | 1.75392i | ||||
\(880\) | 6.00000 | + | 2.00000i | 0.202260 | + | 0.0674200i | ||||
\(881\) | 38.0000i | 1.28025i | 0.768270 | + | 0.640126i | \(0.221118\pi\) | ||||
−0.768270 | + | 0.640126i | \(0.778882\pi\) | |||||||
\(882\) | −45.0000 | −1.51523 | ||||||||
\(883\) | 18.0000 | + | 18.0000i | 0.605748 | + | 0.605748i | 0.941832 | − | 0.336084i | \(-0.109103\pi\) |
−0.336084 | + | 0.941832i | \(0.609103\pi\) | |||||||
\(884\) | 3.00000 | − | 15.0000i | 0.100901 | − | 0.504505i | ||||
\(885\) | 8.00000 | + | 16.0000i | 0.268917 | + | 0.537834i | ||||
\(886\) | 18.0000 | + | 18.0000i | 0.604722 | + | 0.604722i | ||||
\(887\) | 2.00000 | + | 2.00000i | 0.0671534 | + | 0.0671534i | 0.739886 | − | 0.672732i | \(-0.234879\pi\) |
−0.672732 | + | 0.739886i | \(0.734879\pi\) | |||||||
\(888\) | 8.00000 | + | 8.00000i | 0.268462 | + | 0.268462i | ||||
\(889\) | −56.0000 | + | 56.0000i | −1.87818 | + | 1.87818i | ||||
\(890\) | 15.0000 | + | 5.00000i | 0.502801 | + | 0.167600i | ||||
\(891\) | 2.00000 | − | 2.00000i | 0.0670025 | − | 0.0670025i | ||||
\(892\) | 28.0000 | 0.937509 | ||||||||
\(893\) | −8.00000 | + | 8.00000i | −0.267710 | + | 0.267710i | ||||
\(894\) | 44.0000 | 1.47158 | ||||||||
\(895\) | 20.0000 | + | 40.0000i | 0.668526 | + | 1.33705i | ||||
\(896\) | − | 4.00000i | − | 0.133631i | ||||||
\(897\) | 24.0000 | − | 16.0000i | 0.801337 | − | 0.534224i | ||||
\(898\) | −11.0000 | + | 11.0000i | −0.367075 | + | 0.367075i | ||||
\(899\) | 36.0000 | − | 36.0000i | 1.20067 | − | 1.20067i | ||||
\(900\) | −20.0000 | − | 15.0000i | −0.666667 | − | 0.500000i | ||||
\(901\) | 6.00000i | 0.199889i | ||||||||
\(902\) | − | 4.00000i | − | 0.133185i | ||||||
\(903\) | −32.0000 | −1.06489 | ||||||||
\(904\) | 1.00000 | + | 1.00000i | 0.0332595 | + | 0.0332595i | ||||
\(905\) | −4.00000 | + | 2.00000i | −0.132964 | + | 0.0664822i | ||||
\(906\) | −56.0000 | −1.86048 | ||||||||
\(907\) | −6.00000 | + | 6.00000i | −0.199227 | + | 0.199227i | −0.799668 | − | 0.600442i | \(-0.794991\pi\) |
0.600442 | + | 0.799668i | \(0.294991\pi\) | |||||||
\(908\) | 4.00000i | 0.132745i | ||||||||
\(909\) | 60.0000 | 1.99007 | ||||||||
\(910\) | −16.0000 | + | 28.0000i | −0.530395 | + | 0.928191i | ||||
\(911\) | 8.00000 | 0.265052 | 0.132526 | − | 0.991180i | \(-0.457691\pi\) | ||||
0.132526 | + | 0.991180i | \(0.457691\pi\) | |||||||
\(912\) | 8.00000i | 0.264906i | ||||||||
\(913\) | −16.0000 | + | 16.0000i | −0.529523 | + | 0.529523i | ||||
\(914\) | 16.0000 | 0.529233 | ||||||||
\(915\) | −72.0000 | − | 24.0000i | −2.38025 | − | 0.793416i | ||||
\(916\) | 1.00000 | + | 1.00000i | 0.0330409 | + | 0.0330409i | ||||
\(917\) | −16.0000 | −0.528367 | ||||||||
\(918\) | − | 24.0000i | − | 0.792118i | ||||||
\(919\) | 28.0000i | 0.923635i | 0.886975 | + | 0.461817i | \(0.152802\pi\) | ||||
−0.886975 | + | 0.461817i | \(0.847198\pi\) | |||||||
\(920\) | 6.00000 | + | 2.00000i | 0.197814 | + | 0.0659380i | ||||
\(921\) | 16.0000 | − | 16.0000i | 0.527218 | − | 0.527218i | ||||
\(922\) | −11.0000 | + | 11.0000i | −0.362266 | + | 0.362266i | ||||
\(923\) | 10.0000 | + | 2.00000i | 0.329154 | + | 0.0658308i | ||||
\(924\) | − | 32.0000i | − | 1.05272i | ||||||
\(925\) | 12.0000 | − | 16.0000i | 0.394558 | − | 0.526077i | ||||
\(926\) | 8.00000 | 0.262896 | ||||||||
\(927\) | −30.0000 | + | 30.0000i | −0.985329 | + | 0.985329i | ||||
\(928\) | 6.00000 | 0.196960 | ||||||||
\(929\) | −27.0000 | + | 27.0000i | −0.885841 | + | 0.885841i | −0.994121 | − | 0.108279i | \(-0.965466\pi\) |
0.108279 | + | 0.994121i | \(0.465466\pi\) | |||||||
\(930\) | −48.0000 | + | 24.0000i | −1.57398 | + | 0.786991i | ||||
\(931\) | 18.0000 | − | 18.0000i | 0.589926 | − | 0.589926i | ||||
\(932\) | 11.0000 | + | 11.0000i | 0.360317 | + | 0.360317i | ||||
\(933\) | −24.0000 | − | 24.0000i | −0.785725 | − | 0.785725i | ||||
\(934\) | 2.00000 | + | 2.00000i | 0.0654420 | + | 0.0654420i | ||||
\(935\) | 24.0000 | − | 12.0000i | 0.784884 | − | 0.392442i | ||||
\(936\) | −15.0000 | + | 10.0000i | −0.490290 | + | 0.326860i | ||||
\(937\) | −35.0000 | − | 35.0000i | −1.14340 | − | 1.14340i | −0.987824 | − | 0.155576i | \(-0.950277\pi\) |
−0.155576 | − | 0.987824i | \(-0.549723\pi\) | |||||||
\(938\) | −16.0000 | −0.522419 | ||||||||
\(939\) | − | 36.0000i | − | 1.17482i | ||||||
\(940\) | −4.00000 | − | 8.00000i | −0.130466 | − | 0.260931i | ||||
\(941\) | −25.0000 | − | 25.0000i | −0.814977 | − | 0.814977i | 0.170399 | − | 0.985375i | \(-0.445494\pi\) |
−0.985375 | + | 0.170399i | \(0.945494\pi\) | |||||||
\(942\) | 12.0000i | 0.390981i | ||||||||
\(943\) | − | 4.00000i | − | 0.130258i | ||||||
\(944\) | 2.00000 | + | 2.00000i | 0.0650945 | + | 0.0650945i | ||||
\(945\) | −16.0000 | + | 48.0000i | −0.520480 | + | 1.56144i | ||||
\(946\) | − | 8.00000i | − | 0.260102i | ||||||
\(947\) | 32.0000 | 1.03986 | 0.519930 | − | 0.854209i | \(-0.325958\pi\) | ||||
0.519930 | + | 0.854209i | \(0.325958\pi\) | |||||||
\(948\) | 8.00000 | + | 8.00000i | 0.259828 | + | 0.259828i | ||||
\(949\) | 20.0000 | + | 30.0000i | 0.649227 | + | 0.973841i | ||||
\(950\) | 14.0000 | − | 2.00000i | 0.454220 | − | 0.0648886i | ||||
\(951\) | 60.0000 | + | 60.0000i | 1.94563 | + | 1.94563i | ||||
\(952\) | −12.0000 | − | 12.0000i | −0.388922 | − | 0.388922i | ||||
\(953\) | 23.0000 | + | 23.0000i | 0.745043 | + | 0.745043i | 0.973544 | − | 0.228501i | \(-0.0733823\pi\) |
−0.228501 | + | 0.973544i | \(0.573382\pi\) | |||||||
\(954\) | 5.00000 | − | 5.00000i | 0.161881 | − | 0.161881i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −10.0000 | + | 10.0000i | −0.323423 | + | 0.323423i | ||||
\(957\) | 48.0000 | 1.55162 | ||||||||
\(958\) | 10.0000 | − | 10.0000i | 0.323085 | − | 0.323085i | ||||
\(959\) | −72.0000 | −2.32500 | ||||||||
\(960\) | −6.00000 | − | 2.00000i | −0.193649 | − | 0.0645497i | ||||
\(961\) | 41.0000i | 1.32258i | ||||||||
\(962\) | −8.00000 | − | 12.0000i | −0.257930 | − | 0.386896i | ||||
\(963\) | −30.0000 | + | 30.0000i | −0.966736 | + | 0.966736i | ||||
\(964\) | 5.00000 | − | 5.00000i | 0.161039 | − | 0.161039i | ||||
\(965\) | 32.0000 | − | 16.0000i | 1.03012 | − | 0.515058i | ||||
\(966\) | − | 32.0000i | − | 1.02958i | ||||||
\(967\) | − | 24.0000i | − | 0.771788i | −0.922543 | − | 0.385894i | \(-0.873893\pi\) | ||
0.922543 | − | 0.385894i | \(-0.126107\pi\) | |||||||
\(968\) | −3.00000 | −0.0964237 | ||||||||
\(969\) | 24.0000 | + | 24.0000i | 0.770991 | + | 0.770991i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36.0000 | 1.15529 | 0.577647 | − | 0.816286i | \(-0.303971\pi\) | ||||
0.577647 | + | 0.816286i | \(0.303971\pi\) | |||||||
\(972\) | 10.0000 | − | 10.0000i | 0.320750 | − | 0.320750i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 16.0000 | 0.512673 | ||||||||
\(975\) | 34.0000 | + | 38.0000i | 1.08887 | + | 1.21697i | ||||
\(976\) | −12.0000 | −0.384111 | ||||||||
\(977\) | 2.00000i | 0.0639857i | 0.999488 | + | 0.0319928i | \(0.0101854\pi\) | ||||
−0.999488 | + | 0.0319928i | \(0.989815\pi\) | |||||||
\(978\) | −40.0000 | + | 40.0000i | −1.27906 | + | 1.27906i | ||||
\(979\) | 20.0000 | 0.639203 | ||||||||
\(980\) | 9.00000 | + | 18.0000i | 0.287494 | + | 0.574989i | ||||
\(981\) | 55.0000 | + | 55.0000i | 1.75601 | + | 1.75601i | ||||
\(982\) | −24.0000 | −0.765871 | ||||||||
\(983\) | − | 24.0000i | − | 0.765481i | −0.923856 | − | 0.382741i | \(-0.874980\pi\) | ||
0.923856 | − | 0.382741i | \(-0.125020\pi\) | |||||||
\(984\) | 4.00000i | 0.127515i | ||||||||
\(985\) | −24.0000 | + | 12.0000i | −0.764704 | + | 0.382352i | ||||
\(986\) | 18.0000 | − | 18.0000i | 0.573237 | − | 0.573237i | ||||
\(987\) | −32.0000 | + | 32.0000i | −1.01857 | + | 1.01857i | ||||
\(988\) | 2.00000 | − | 10.0000i | 0.0636285 | − | 0.318142i | ||||
\(989\) | − | 8.00000i | − | 0.254385i | ||||||
\(990\) | −30.0000 | − | 10.0000i | −0.953463 | − | 0.317821i | ||||
\(991\) | −32.0000 | −1.01651 | −0.508257 | − | 0.861206i | \(-0.669710\pi\) | ||||
−0.508257 | + | 0.861206i | \(0.669710\pi\) | |||||||
\(992\) | −6.00000 | + | 6.00000i | −0.190500 | + | 0.190500i | ||||
\(993\) | 24.0000 | 0.761617 | ||||||||
\(994\) | 8.00000 | − | 8.00000i | 0.253745 | − | 0.253745i | ||||
\(995\) | −8.00000 | − | 16.0000i | −0.253617 | − | 0.507234i | ||||
\(996\) | 16.0000 | − | 16.0000i | 0.506979 | − | 0.506979i | ||||
\(997\) | −37.0000 | − | 37.0000i | −1.17180 | − | 1.17180i | −0.981780 | − | 0.190022i | \(-0.939144\pi\) |
−0.190022 | − | 0.981780i | \(-0.560856\pi\) | |||||||
\(998\) | −14.0000 | − | 14.0000i | −0.443162 | − | 0.443162i | ||||
\(999\) | −16.0000 | − | 16.0000i | −0.506218 | − | 0.506218i |
(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.a.47.1 | yes | 2 | |
3.2 | odd | 2 | 1170.2.w.b.307.1 | 2 | |||
4.3 | odd | 2 | 1040.2.cd.g.177.1 | 2 | |||
5.2 | odd | 4 | 650.2.g.e.593.1 | 2 | |||
5.3 | odd | 4 | 130.2.g.a.73.1 | yes | 2 | ||
5.4 | even | 2 | 650.2.j.e.307.1 | 2 | |||
13.5 | odd | 4 | 130.2.g.a.57.1 | ✓ | 2 | ||
15.8 | even | 4 | 1170.2.m.c.73.1 | 2 | |||
20.3 | even | 4 | 1040.2.bg.g.593.1 | 2 | |||
39.5 | even | 4 | 1170.2.m.c.577.1 | 2 | |||
52.31 | even | 4 | 1040.2.bg.g.577.1 | 2 | |||
65.18 | even | 4 | inner | 130.2.j.a.83.1 | yes | 2 | |
65.44 | odd | 4 | 650.2.g.e.57.1 | 2 | |||
65.57 | even | 4 | 650.2.j.e.343.1 | 2 | |||
195.83 | odd | 4 | 1170.2.w.b.343.1 | 2 | |||
260.83 | odd | 4 | 1040.2.cd.g.993.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
130.2.g.a.57.1 | ✓ | 2 | 13.5 | odd | 4 | ||
130.2.g.a.73.1 | yes | 2 | 5.3 | odd | 4 | ||
130.2.j.a.47.1 | yes | 2 | 1.1 | even | 1 | trivial | |
130.2.j.a.83.1 | yes | 2 | 65.18 | even | 4 | inner | |
650.2.g.e.57.1 | 2 | 65.44 | odd | 4 | |||
650.2.g.e.593.1 | 2 | 5.2 | odd | 4 | |||
650.2.j.e.307.1 | 2 | 5.4 | even | 2 | |||
650.2.j.e.343.1 | 2 | 65.57 | even | 4 | |||
1040.2.bg.g.577.1 | 2 | 52.31 | even | 4 | |||
1040.2.bg.g.593.1 | 2 | 20.3 | even | 4 | |||
1040.2.cd.g.177.1 | 2 | 4.3 | odd | 2 | |||
1040.2.cd.g.993.1 | 2 | 260.83 | odd | 4 | |||
1170.2.m.c.73.1 | 2 | 15.8 | even | 4 | |||
1170.2.m.c.577.1 | 2 | 39.5 | even | 4 | |||
1170.2.w.b.307.1 | 2 | 3.2 | odd | 2 | |||
1170.2.w.b.343.1 | 2 | 195.83 | odd | 4 |