Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(265,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.265");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.o (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: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.7442857984.4 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 26x^{6} + 205x^{4} + 540x^{2} + 324 \) |
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 | 265.3 | ||
Root | \(-1.91681i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.265 |
Dual form | 546.2.o.a.307.3 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −2.56510 | − | 2.56510i | −1.14715 | − | 1.14715i | −0.987111 | − | 0.160035i | \(-0.948839\pi\) |
−0.160035 | − | 0.987111i | \(-0.551161\pi\) | |||||||
\(6\) | 0.707107 | + | 0.707107i | 0.288675 | + | 0.288675i | ||||
\(7\) | −0.648285 | + | 2.56510i | −0.245029 | + | 0.969516i | ||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −3.62760 | −1.14715 | ||||||||
\(11\) | −1.64828 | − | 1.64828i | −0.496977 | − | 0.496977i | 0.413519 | − | 0.910496i | \(-0.364300\pi\) |
−0.910496 | + | 0.413519i | \(0.864300\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 2.00000 | − | 3.00000i | 0.554700 | − | 0.832050i | ||||
\(14\) | 1.35539 | + | 2.27220i | 0.362244 | + | 0.607272i | ||||
\(15\) | 2.56510 | − | 2.56510i | 0.662305 | − | 0.662305i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −7.15945 | −1.73642 | −0.868211 | − | 0.496195i | \(-0.834730\pi\) | ||||
−0.868211 | + | 0.496195i | \(0.834730\pi\) | |||||||
\(18\) | −0.707107 | + | 0.707107i | −0.166667 | + | 0.166667i | ||||
\(19\) | −2.86167 | − | 2.86167i | −0.656512 | − | 0.656512i | 0.298041 | − | 0.954553i | \(-0.403667\pi\) |
−0.954553 | + | 0.298041i | \(0.903667\pi\) | |||||||
\(20\) | −2.56510 | + | 2.56510i | −0.573573 | + | 0.573573i | ||||
\(21\) | −2.56510 | − | 0.648285i | −0.559750 | − | 0.141467i | ||||
\(22\) | −2.33103 | −0.496977 | ||||||||
\(23\) | − | 4.45602i | − | 0.929145i | −0.885535 | − | 0.464573i | \(-0.846208\pi\) | ||
0.885535 | − | 0.464573i | \(-0.153792\pi\) | |||||||
\(24\) | 0.707107 | − | 0.707107i | 0.144338 | − | 0.144338i | ||||
\(25\) | 8.15945i | 1.63189i | ||||||||
\(26\) | −0.707107 | − | 3.53553i | −0.138675 | − | 0.693375i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 2.56510 | + | 0.648285i | 0.484758 | + | 0.122514i | ||||
\(29\) | −9.75259 | −1.81101 | −0.905506 | − | 0.424335i | \(-0.860508\pi\) | ||||
−0.905506 | + | 0.424335i | \(0.860508\pi\) | |||||||
\(30\) | − | 3.62760i | − | 0.662305i | ||||||
\(31\) | 3.91681 | + | 3.91681i | 0.703480 | + | 0.703480i | 0.965156 | − | 0.261676i | \(-0.0842750\pi\) |
−0.261676 | + | 0.965156i | \(0.584275\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 1.64828 | − | 1.64828i | 0.286930 | − | 0.286930i | ||||
\(34\) | −5.06250 | + | 5.06250i | −0.868211 | + | 0.868211i | ||||
\(35\) | 8.24264 | − | 4.91681i | 1.39326 | − | 0.831093i | ||||
\(36\) | 1.00000i | 0.166667i | ||||||||
\(37\) | 2.48191 | + | 2.48191i | 0.408024 | + | 0.408024i | 0.881049 | − | 0.473025i | \(-0.156838\pi\) |
−0.473025 | + | 0.881049i | \(0.656838\pi\) | |||||||
\(38\) | −4.04701 | −0.656512 | ||||||||
\(39\) | 3.00000 | + | 2.00000i | 0.480384 | + | 0.320256i | ||||
\(40\) | 3.62760i | 0.573573i | ||||||||
\(41\) | 7.53921 | + | 7.53921i | 1.17743 | + | 1.17743i | 0.980398 | + | 0.197029i | \(0.0631294\pi\) |
0.197029 | + | 0.980398i | \(0.436871\pi\) | |||||||
\(42\) | −2.27220 | + | 1.35539i | −0.350609 | + | 0.209141i | ||||
\(43\) | − | 8.62240i | − | 1.31490i | −0.753497 | − | 0.657452i | \(-0.771634\pi\) | ||
0.753497 | − | 0.657452i | \(-0.228366\pi\) | |||||||
\(44\) | −1.64828 | + | 1.64828i | −0.248488 | + | 0.248488i | ||||
\(45\) | 2.56510 | + | 2.56510i | 0.382382 | + | 0.382382i | ||||
\(46\) | −3.15088 | − | 3.15088i | −0.464573 | − | 0.464573i | ||||
\(47\) | −0.703431 | + | 0.703431i | −0.102606 | + | 0.102606i | −0.756546 | − | 0.653940i | \(-0.773115\pi\) |
0.653940 | + | 0.756546i | \(0.273115\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | −6.15945 | − | 3.32583i | −0.879922 | − | 0.475118i | ||||
\(50\) | 5.76961 | + | 5.76961i | 0.815945 | + | 0.815945i | ||||
\(51\) | − | 7.15945i | − | 1.00252i | ||||||
\(52\) | −3.00000 | − | 2.00000i | −0.416025 | − | 0.277350i | ||||
\(53\) | 2.42677 | 0.333342 | 0.166671 | − | 0.986013i | \(-0.446698\pi\) | ||||
0.166671 | + | 0.986013i | \(0.446698\pi\) | |||||||
\(54\) | −0.707107 | − | 0.707107i | −0.0962250 | − | 0.0962250i | ||||
\(55\) | 8.45602i | 1.14021i | ||||||||
\(56\) | 2.27220 | − | 1.35539i | 0.303636 | − | 0.181122i | ||||
\(57\) | 2.86167 | − | 2.86167i | 0.379037 | − | 0.379037i | ||||
\(58\) | −6.89612 | + | 6.89612i | −0.905506 | + | 0.905506i | ||||
\(59\) | 10.4560 | − | 10.4560i | 1.36126 | − | 1.36126i | 0.488942 | − | 0.872316i | \(-0.337383\pi\) |
0.872316 | − | 0.488942i | \(-0.162617\pi\) | |||||||
\(60\) | −2.56510 | − | 2.56510i | −0.331153 | − | 0.331153i | ||||
\(61\) | − | 7.15945i | − | 0.916674i | −0.888778 | − | 0.458337i | \(-0.848445\pi\) | ||
0.888778 | − | 0.458337i | \(-0.151555\pi\) | |||||||
\(62\) | 5.53921 | 0.703480 | ||||||||
\(63\) | 0.648285 | − | 2.56510i | 0.0816762 | − | 0.323172i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −12.8255 | + | 2.56510i | −1.59081 | + | 0.318161i | ||||
\(66\) | − | 2.33103i | − | 0.286930i | ||||||
\(67\) | −4.53921 | + | 4.53921i | −0.554553 | + | 0.554553i | −0.927751 | − | 0.373199i | \(-0.878261\pi\) |
0.373199 | + | 0.927751i | \(0.378261\pi\) | |||||||
\(68\) | 7.15945i | 0.868211i | ||||||||
\(69\) | 4.45602 | 0.536442 | ||||||||
\(70\) | 2.35172 | − | 9.30514i | 0.281084 | − | 1.11218i | ||||
\(71\) | −0.456023 | + | 0.456023i | −0.0541200 | + | 0.0541200i | −0.733649 | − | 0.679529i | \(-0.762184\pi\) |
0.679529 | + | 0.733649i | \(0.262184\pi\) | |||||||
\(72\) | 0.707107 | + | 0.707107i | 0.0833333 | + | 0.0833333i | ||||
\(73\) | 2.48191 | − | 2.48191i | 0.290486 | − | 0.290486i | −0.546786 | − | 0.837272i | \(-0.684149\pi\) |
0.837272 | + | 0.546786i | \(0.184149\pi\) | |||||||
\(74\) | 3.50995 | 0.408024 | ||||||||
\(75\) | −8.15945 | −0.942173 | ||||||||
\(76\) | −2.86167 | + | 2.86167i | −0.328256 | + | 0.328256i | ||||
\(77\) | 5.29657 | − | 3.15945i | 0.603600 | − | 0.360053i | ||||
\(78\) | 3.53553 | − | 0.707107i | 0.400320 | − | 0.0800641i | ||||
\(79\) | 12.0422 | 1.35486 | 0.677429 | − | 0.735588i | \(-0.263094\pi\) | ||||
0.677429 | + | 0.735588i | \(0.263094\pi\) | |||||||
\(80\) | 2.56510 | + | 2.56510i | 0.286787 | + | 0.286787i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 10.6621 | 1.17743 | ||||||||
\(83\) | 2.70343 | + | 2.70343i | 0.296740 | + | 0.296740i | 0.839736 | − | 0.542996i | \(-0.182710\pi\) |
−0.542996 | + | 0.839736i | \(0.682710\pi\) | |||||||
\(84\) | −0.648285 | + | 2.56510i | −0.0707337 | + | 0.279875i | ||||
\(85\) | 18.3647 | + | 18.3647i | 1.99193 | + | 1.99193i | ||||
\(86\) | −6.09696 | − | 6.09696i | −0.657452 | − | 0.657452i | ||||
\(87\) | − | 9.75259i | − | 1.04559i | ||||||
\(88\) | 2.33103i | 0.248488i | ||||||||
\(89\) | 4.75044 | − | 4.75044i | 0.503546 | − | 0.503546i | −0.408992 | − | 0.912538i | \(-0.634120\pi\) |
0.912538 | + | 0.408992i | \(0.134120\pi\) | |||||||
\(90\) | 3.62760 | 0.382382 | ||||||||
\(91\) | 6.39872 | + | 7.07505i | 0.670769 | + | 0.741667i | ||||
\(92\) | −4.45602 | −0.464573 | ||||||||
\(93\) | −3.91681 | + | 3.91681i | −0.406155 | + | 0.406155i | ||||
\(94\) | 0.994801i | 0.102606i | ||||||||
\(95\) | 14.6809i | 1.50623i | ||||||||
\(96\) | −0.707107 | − | 0.707107i | −0.0721688 | − | 0.0721688i | ||||
\(97\) | −4.49220 | − | 4.49220i | −0.456114 | − | 0.456114i | 0.441264 | − | 0.897378i | \(-0.354530\pi\) |
−0.897378 | + | 0.441264i | \(0.854530\pi\) | |||||||
\(98\) | −6.70711 | + | 2.00368i | −0.677520 | + | 0.202402i | ||||
\(99\) | 1.64828 | + | 1.64828i | 0.165659 | + | 0.165659i | ||||
\(100\) | 8.15945 | 0.815945 | ||||||||
\(101\) | 3.55696 | 0.353931 | 0.176965 | − | 0.984217i | \(-0.443372\pi\) | ||||
0.176965 | + | 0.984217i | \(0.443372\pi\) | |||||||
\(102\) | −5.06250 | − | 5.06250i | −0.501262 | − | 0.501262i | ||||
\(103\) | −9.80437 | −0.966053 | −0.483027 | − | 0.875606i | \(-0.660463\pi\) | ||||
−0.483027 | + | 0.875606i | \(0.660463\pi\) | |||||||
\(104\) | −3.53553 | + | 0.707107i | −0.346688 | + | 0.0693375i | ||||
\(105\) | 4.91681 | + | 8.24264i | 0.479832 | + | 0.804399i | ||||
\(106\) | 1.71598 | − | 1.71598i | 0.166671 | − | 0.166671i | ||||
\(107\) | −0.332748 | −0.0321679 | −0.0160840 | − | 0.999871i | \(-0.505120\pi\) | ||||
−0.0160840 | + | 0.999871i | \(0.505120\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −12.9672 | + | 12.9672i | −1.24203 | + | 1.24203i | −0.282875 | + | 0.959157i | \(0.591288\pi\) |
−0.959157 | + | 0.282875i | \(0.908712\pi\) | |||||||
\(110\) | 5.97931 | + | 5.97931i | 0.570105 | + | 0.570105i | ||||
\(111\) | −2.48191 | + | 2.48191i | −0.235573 | + | 0.235573i | ||||
\(112\) | 0.648285 | − | 2.56510i | 0.0612572 | − | 0.242379i | ||||
\(113\) | −12.6872 | −1.19351 | −0.596754 | − | 0.802425i | \(-0.703543\pi\) | ||||
−0.596754 | + | 0.802425i | \(0.703543\pi\) | |||||||
\(114\) | − | 4.04701i | − | 0.379037i | ||||||
\(115\) | −11.4301 | + | 11.4301i | −1.06587 | + | 1.06587i | ||||
\(116\) | 9.75259i | 0.905506i | ||||||||
\(117\) | −2.00000 | + | 3.00000i | −0.184900 | + | 0.277350i | ||||
\(118\) | − | 14.7870i | − | 1.36126i | ||||||
\(119\) | 4.64136 | − | 18.3647i | 0.425473 | − | 1.68349i | ||||
\(120\) | −3.62760 | −0.331153 | ||||||||
\(121\) | − | 5.56631i | − | 0.506029i | ||||||
\(122\) | −5.06250 | − | 5.06250i | −0.458337 | − | 0.458337i | ||||
\(123\) | −7.53921 | + | 7.53921i | −0.679788 | + | 0.679788i | ||||
\(124\) | 3.91681 | − | 3.91681i | 0.351740 | − | 0.351740i | ||||
\(125\) | 8.10431 | − | 8.10431i | 0.724871 | − | 0.724871i | ||||
\(126\) | −1.35539 | − | 2.27220i | −0.120748 | − | 0.202424i | ||||
\(127\) | 5.94822i | 0.527820i | 0.964547 | + | 0.263910i | \(0.0850121\pi\) | ||||
−0.964547 | + | 0.263910i | \(0.914988\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 8.62240 | 0.759160 | ||||||||
\(130\) | −7.25519 | + | 10.8828i | −0.636322 | + | 0.954484i | ||||
\(131\) | − | 0.0292581i | − | 0.00255629i | −0.999999 | − | 0.00127815i | \(-0.999593\pi\) | ||
0.999999 | − | 0.00127815i | \(-0.000406847\pi\) | |||||||
\(132\) | −1.64828 | − | 1.64828i | −0.143465 | − | 0.143465i | ||||
\(133\) | 9.19563 | − | 5.48528i | 0.797362 | − | 0.475634i | ||||
\(134\) | 6.41941i | 0.554553i | ||||||||
\(135\) | −2.56510 | + | 2.56510i | −0.220768 | + | 0.220768i | ||||
\(136\) | 5.06250 | + | 5.06250i | 0.434106 | + | 0.434106i | ||||
\(137\) | 4.56510 | + | 4.56510i | 0.390023 | + | 0.390023i | 0.874695 | − | 0.484673i | \(-0.161061\pi\) |
−0.484673 | + | 0.874695i | \(0.661061\pi\) | |||||||
\(138\) | 3.15088 | − | 3.15088i | 0.268221 | − | 0.268221i | ||||
\(139\) | − | 12.6872i | − | 1.07611i | −0.842910 | − | 0.538055i | \(-0.819159\pi\) | ||
0.842910 | − | 0.538055i | \(-0.180841\pi\) | |||||||
\(140\) | −4.91681 | − | 8.24264i | −0.415547 | − | 0.696630i | ||||
\(141\) | −0.703431 | − | 0.703431i | −0.0592395 | − | 0.0592395i | ||||
\(142\) | 0.644914i | 0.0541200i | ||||||||
\(143\) | −8.24142 | + | 1.64828i | −0.689182 | + | 0.137836i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 25.0164 | + | 25.0164i | 2.07750 | + | 2.07750i | ||||
\(146\) | − | 3.50995i | − | 0.290486i | ||||||
\(147\) | 3.32583 | − | 6.15945i | 0.274310 | − | 0.508023i | ||||
\(148\) | 2.48191 | − | 2.48191i | 0.204012 | − | 0.204012i | ||||
\(149\) | 13.4021 | − | 13.4021i | 1.09794 | − | 1.09794i | 0.103291 | − | 0.994651i | \(-0.467063\pi\) |
0.994651 | − | 0.103291i | \(-0.0329374\pi\) | |||||||
\(150\) | −5.76961 | + | 5.76961i | −0.471086 | + | 0.471086i | ||||
\(151\) | 3.02804 | + | 3.02804i | 0.246418 | + | 0.246418i | 0.819499 | − | 0.573081i | \(-0.194252\pi\) |
−0.573081 | + | 0.819499i | \(0.694252\pi\) | |||||||
\(152\) | 4.04701i | 0.328256i | ||||||||
\(153\) | 7.15945 | 0.578808 | ||||||||
\(154\) | 1.51117 | − | 5.97931i | 0.121773 | − | 0.481827i | ||||
\(155\) | − | 20.0940i | − | 1.61399i | ||||||
\(156\) | 2.00000 | − | 3.00000i | 0.160128 | − | 0.240192i | ||||
\(157\) | 11.4198i | 0.911403i | 0.890133 | + | 0.455701i | \(0.150612\pi\) | ||||
−0.890133 | + | 0.455701i | \(0.849388\pi\) | |||||||
\(158\) | 8.51515 | − | 8.51515i | 0.677429 | − | 0.677429i | ||||
\(159\) | 2.42677i | 0.192455i | ||||||||
\(160\) | 3.62760 | 0.286787 | ||||||||
\(161\) | 11.4301 | + | 2.88877i | 0.900821 | + | 0.227667i | ||||
\(162\) | 0.707107 | − | 0.707107i | 0.0555556 | − | 0.0555556i | ||||
\(163\) | −9.07627 | − | 9.07627i | −0.710908 | − | 0.710908i | 0.255817 | − | 0.966725i | \(-0.417656\pi\) |
−0.966725 | + | 0.255817i | \(0.917656\pi\) | |||||||
\(164\) | 7.53921 | − | 7.53921i | 0.588713 | − | 0.588713i | ||||
\(165\) | −8.45602 | −0.658301 | ||||||||
\(166\) | 3.82323 | 0.296740 | ||||||||
\(167\) | 3.31554 | − | 3.31554i | 0.256564 | − | 0.256564i | −0.567091 | − | 0.823655i | \(-0.691931\pi\) |
0.823655 | + | 0.567091i | \(0.191931\pi\) | |||||||
\(168\) | 1.35539 | + | 2.27220i | 0.104571 | + | 0.175304i | ||||
\(169\) | −5.00000 | − | 12.0000i | −0.384615 | − | 0.923077i | ||||
\(170\) | 25.9716 | 1.99193 | ||||||||
\(171\) | 2.86167 | + | 2.86167i | 0.218837 | + | 0.218837i | ||||
\(172\) | −8.62240 | −0.657452 | ||||||||
\(173\) | −6.05852 | −0.460620 | −0.230310 | − | 0.973117i | \(-0.573974\pi\) | ||||
−0.230310 | + | 0.973117i | \(0.573974\pi\) | |||||||
\(174\) | −6.89612 | − | 6.89612i | −0.522794 | − | 0.522794i | ||||
\(175\) | −20.9298 | − | 5.28965i | −1.58214 | − | 0.399860i | ||||
\(176\) | 1.64828 | + | 1.64828i | 0.124244 | + | 0.124244i | ||||
\(177\) | 10.4560 | + | 10.4560i | 0.785923 | + | 0.785923i | ||||
\(178\) | − | 6.71814i | − | 0.503546i | ||||||
\(179\) | − | 13.5570i | − | 1.01329i | −0.862153 | − | 0.506647i | \(-0.830885\pi\) | ||
0.862153 | − | 0.506647i | \(-0.169115\pi\) | |||||||
\(180\) | 2.56510 | − | 2.56510i | 0.191191 | − | 0.191191i | ||||
\(181\) | −14.5793 | −1.08367 | −0.541835 | − | 0.840485i | \(-0.682270\pi\) | ||||
−0.541835 | + | 0.840485i | \(0.682270\pi\) | |||||||
\(182\) | 9.52740 | + | 0.478235i | 0.706218 | + | 0.0354491i | ||||
\(183\) | 7.15945 | 0.529242 | ||||||||
\(184\) | −3.15088 | + | 3.15088i | −0.232286 | + | 0.232286i | ||||
\(185\) | − | 12.7327i | − | 0.936126i | ||||||
\(186\) | 5.53921i | 0.406155i | ||||||||
\(187\) | 11.8008 | + | 11.8008i | 0.862961 | + | 0.862961i | ||||
\(188\) | 0.703431 | + | 0.703431i | 0.0513029 | + | 0.0513029i | ||||
\(189\) | 2.56510 | + | 0.648285i | 0.186583 | + | 0.0471558i | ||||
\(190\) | 10.3810 | + | 10.3810i | 0.753115 | + | 0.753115i | ||||
\(191\) | −26.3837 | −1.90906 | −0.954528 | − | 0.298123i | \(-0.903640\pi\) | ||||
−0.954528 | + | 0.298123i | \(0.903640\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 2.86288 | + | 2.86288i | 0.206075 | + | 0.206075i | 0.802597 | − | 0.596522i | \(-0.203451\pi\) |
−0.596522 | + | 0.802597i | \(0.703451\pi\) | |||||||
\(194\) | −6.35293 | −0.456114 | ||||||||
\(195\) | −2.56510 | − | 12.8255i | −0.183690 | − | 0.918452i | ||||
\(196\) | −3.32583 | + | 6.15945i | −0.237559 | + | 0.439961i | ||||
\(197\) | −6.21338 | + | 6.21338i | −0.442685 | + | 0.442685i | −0.892913 | − | 0.450228i | \(-0.851343\pi\) |
0.450228 | + | 0.892913i | \(0.351343\pi\) | |||||||
\(198\) | 2.33103 | 0.165659 | ||||||||
\(199\) | −1.63799 | −0.116114 | −0.0580572 | − | 0.998313i | \(-0.518491\pi\) | ||||
−0.0580572 | + | 0.998313i | \(0.518491\pi\) | |||||||
\(200\) | 5.76961 | − | 5.76961i | 0.407973 | − | 0.407973i | ||||
\(201\) | −4.53921 | − | 4.53921i | −0.320171 | − | 0.320171i | ||||
\(202\) | 2.51515 | − | 2.51515i | 0.176965 | − | 0.176965i | ||||
\(203\) | 6.32246 | − | 25.0164i | 0.443749 | − | 1.75580i | ||||
\(204\) | −7.15945 | −0.501262 | ||||||||
\(205\) | − | 38.6776i | − | 2.70136i | ||||||
\(206\) | −6.93274 | + | 6.93274i | −0.483027 | + | 0.483027i | ||||
\(207\) | 4.45602i | 0.309715i | ||||||||
\(208\) | −2.00000 | + | 3.00000i | −0.138675 | + | 0.208013i | ||||
\(209\) | 9.43369i | 0.652542i | ||||||||
\(210\) | 9.30514 | + | 2.35172i | 0.642116 | + | 0.162284i | ||||
\(211\) | 0.622397 | 0.0428476 | 0.0214238 | − | 0.999770i | \(-0.493180\pi\) | ||||
0.0214238 | + | 0.999770i | \(0.493180\pi\) | |||||||
\(212\) | − | 2.42677i | − | 0.166671i | ||||||
\(213\) | −0.456023 | − | 0.456023i | −0.0312462 | − | 0.0312462i | ||||
\(214\) | −0.235288 | + | 0.235288i | −0.0160840 | + | 0.0160840i | ||||
\(215\) | −22.1173 | + | 22.1173i | −1.50839 | + | 1.50839i | ||||
\(216\) | −0.707107 | + | 0.707107i | −0.0481125 | + | 0.0481125i | ||||
\(217\) | −12.5862 | + | 7.50780i | −0.854408 | + | 0.509663i | ||||
\(218\) | 18.3384i | 1.24203i | ||||||||
\(219\) | 2.48191 | + | 2.48191i | 0.167712 | + | 0.167712i | ||||
\(220\) | 8.45602 | 0.570105 | ||||||||
\(221\) | −14.3189 | + | 21.4784i | −0.963194 | + | 1.44479i | ||||
\(222\) | 3.50995i | 0.235573i | ||||||||
\(223\) | −15.5615 | − | 15.5615i | −1.04208 | − | 1.04208i | −0.999075 | − | 0.0430034i | \(-0.986307\pi\) |
−0.0430034 | − | 0.999075i | \(-0.513693\pi\) | |||||||
\(224\) | −1.35539 | − | 2.27220i | −0.0905609 | − | 0.151818i | ||||
\(225\) | − | 8.15945i | − | 0.543964i | ||||||
\(226\) | −8.97117 | + | 8.97117i | −0.596754 | + | 0.596754i | ||||
\(227\) | 1.15945 | + | 1.15945i | 0.0769556 | + | 0.0769556i | 0.744537 | − | 0.667581i | \(-0.232670\pi\) |
−0.667581 | + | 0.744537i | \(0.732670\pi\) | |||||||
\(228\) | −2.86167 | − | 2.86167i | −0.189519 | − | 0.189519i | ||||
\(229\) | 4.15945 | − | 4.15945i | 0.274864 | − | 0.274864i | −0.556190 | − | 0.831055i | \(-0.687737\pi\) |
0.831055 | + | 0.556190i | \(0.187737\pi\) | |||||||
\(230\) | 16.1647i | 1.06587i | ||||||||
\(231\) | 3.15945 | + | 5.29657i | 0.207877 | + | 0.348489i | ||||
\(232\) | 6.89612 | + | 6.89612i | 0.452753 | + | 0.452753i | ||||
\(233\) | 10.7974i | 0.707364i | 0.935366 | + | 0.353682i | \(0.115071\pi\) | ||||
−0.935366 | + | 0.353682i | \(0.884929\pi\) | |||||||
\(234\) | 0.707107 | + | 3.53553i | 0.0462250 | + | 0.231125i | ||||
\(235\) | 3.60874 | 0.235408 | ||||||||
\(236\) | −10.4560 | − | 10.4560i | −0.680629 | − | 0.680629i | ||||
\(237\) | 12.0422i | 0.782228i | ||||||||
\(238\) | −9.70386 | − | 16.2677i | −0.629008 | − | 1.05448i | ||||
\(239\) | 16.1501 | − | 16.1501i | 1.04466 | − | 1.04466i | 0.0457083 | − | 0.998955i | \(-0.485446\pi\) |
0.998955 | − | 0.0457083i | \(-0.0145545\pi\) | |||||||
\(240\) | −2.56510 | + | 2.56510i | −0.165576 | + | 0.165576i | ||||
\(241\) | 3.45602 | − | 3.45602i | 0.222622 | − | 0.222622i | −0.586980 | − | 0.809602i | \(-0.699683\pi\) |
0.809602 | + | 0.586980i | \(0.199683\pi\) | |||||||
\(242\) | −3.93598 | − | 3.93598i | −0.253014 | − | 0.253014i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −7.15945 | −0.458337 | ||||||||
\(245\) | 7.26853 | + | 24.3307i | 0.464369 | + | 1.55443i | ||||
\(246\) | 10.6621i | 0.679788i | ||||||||
\(247\) | −14.3083 | + | 2.86167i | −0.910418 | + | 0.182084i | ||||
\(248\) | − | 5.53921i | − | 0.351740i | ||||||
\(249\) | −2.70343 | + | 2.70343i | −0.171323 | + | 0.171323i | ||||
\(250\) | − | 11.4612i | − | 0.724871i | ||||||
\(251\) | −5.64230 | −0.356139 | −0.178069 | − | 0.984018i | \(-0.556985\pi\) | ||||
−0.178069 | + | 0.984018i | \(0.556985\pi\) | |||||||
\(252\) | −2.56510 | − | 0.648285i | −0.161586 | − | 0.0408381i | ||||
\(253\) | −7.34480 | + | 7.34480i | −0.461763 | + | 0.461763i | ||||
\(254\) | 4.20603 | + | 4.20603i | 0.263910 | + | 0.263910i | ||||
\(255\) | −18.3647 | + | 18.3647i | −1.15004 | + | 1.15004i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 25.0199 | 1.56070 | 0.780349 | − | 0.625344i | \(-0.215041\pi\) | ||||
0.780349 | + | 0.625344i | \(0.215041\pi\) | |||||||
\(258\) | 6.09696 | − | 6.09696i | 0.379580 | − | 0.379580i | ||||
\(259\) | −7.97533 | + | 4.75736i | −0.495563 | + | 0.295608i | ||||
\(260\) | 2.56510 | + | 12.8255i | 0.159081 | + | 0.795403i | ||||
\(261\) | 9.75259 | 0.603670 | ||||||||
\(262\) | −0.0206886 | − | 0.0206886i | −0.00127815 | − | 0.00127815i | ||||
\(263\) | −12.1525 | −0.749357 | −0.374679 | − | 0.927155i | \(-0.622247\pi\) | ||||
−0.374679 | + | 0.927155i | \(0.622247\pi\) | |||||||
\(264\) | −2.33103 | −0.143465 | ||||||||
\(265\) | −6.22489 | − | 6.22489i | −0.382392 | − | 0.382392i | ||||
\(266\) | 2.62361 | − | 10.3810i | 0.160864 | − | 0.636498i | ||||
\(267\) | 4.75044 | + | 4.75044i | 0.290722 | + | 0.290722i | ||||
\(268\) | 4.53921 | + | 4.53921i | 0.277276 | + | 0.277276i | ||||
\(269\) | 19.9482i | 1.21626i | 0.793836 | + | 0.608132i | \(0.208081\pi\) | ||||
−0.793836 | + | 0.608132i | \(0.791919\pi\) | |||||||
\(270\) | 3.62760i | 0.220768i | ||||||||
\(271\) | −8.31432 | + | 8.31432i | −0.505059 | + | 0.505059i | −0.913006 | − | 0.407947i | \(-0.866245\pi\) |
0.407947 | + | 0.913006i | \(0.366245\pi\) | |||||||
\(272\) | 7.15945 | 0.434106 | ||||||||
\(273\) | −7.07505 | + | 6.39872i | −0.428201 | + | 0.387268i | ||||
\(274\) | 6.45602 | 0.390023 | ||||||||
\(275\) | 13.4491 | − | 13.4491i | 0.811011 | − | 0.811011i | ||||
\(276\) | − | 4.45602i | − | 0.268221i | ||||||
\(277\) | − | 5.55696i | − | 0.333885i | −0.985967 | − | 0.166943i | \(-0.946611\pi\) | ||
0.985967 | − | 0.166943i | \(-0.0533895\pi\) | |||||||
\(278\) | −8.97117 | − | 8.97117i | −0.538055 | − | 0.538055i | ||||
\(279\) | −3.91681 | − | 3.91681i | −0.234493 | − | 0.234493i | ||||
\(280\) | −9.30514 | − | 2.35172i | −0.556088 | − | 0.140542i | ||||
\(281\) | −11.4807 | − | 11.4807i | −0.684881 | − | 0.684881i | 0.276215 | − | 0.961096i | \(-0.410920\pi\) |
−0.961096 | + | 0.276215i | \(0.910920\pi\) | |||||||
\(282\) | −0.994801 | −0.0592395 | ||||||||
\(283\) | 6.44735 | 0.383255 | 0.191627 | − | 0.981468i | \(-0.438623\pi\) | ||||
0.191627 | + | 0.981468i | \(0.438623\pi\) | |||||||
\(284\) | 0.456023 | + | 0.456023i | 0.0270600 | + | 0.0270600i | ||||
\(285\) | −14.6809 | −0.869622 | ||||||||
\(286\) | −4.66205 | + | 6.99308i | −0.275673 | + | 0.413509i | ||||
\(287\) | −24.2264 | + | 14.4513i | −1.43004 | + | 0.853031i | ||||
\(288\) | 0.707107 | − | 0.707107i | 0.0416667 | − | 0.0416667i | ||||
\(289\) | 34.2578 | 2.01516 | ||||||||
\(290\) | 35.3785 | 2.07750 | ||||||||
\(291\) | 4.49220 | − | 4.49220i | 0.263338 | − | 0.263338i | ||||
\(292\) | −2.48191 | − | 2.48191i | −0.145243 | − | 0.145243i | ||||
\(293\) | −22.1703 | + | 22.1703i | −1.29520 | + | 1.29520i | −0.363677 | + | 0.931525i | \(0.618479\pi\) |
−0.931525 | + | 0.363677i | \(0.881521\pi\) | |||||||
\(294\) | −2.00368 | − | 6.70711i | −0.116857 | − | 0.391166i | ||||
\(295\) | −53.6414 | −3.12313 | ||||||||
\(296\) | − | 3.50995i | − | 0.204012i | ||||||
\(297\) | −1.64828 | + | 1.64828i | −0.0956432 | + | 0.0956432i | ||||
\(298\) | − | 18.9534i | − | 1.09794i | ||||||
\(299\) | −13.3681 | − | 8.91205i | −0.773095 | − | 0.515397i | ||||
\(300\) | 8.15945i | 0.471086i | ||||||||
\(301\) | 22.1173 | + | 5.58977i | 1.27482 | + | 0.322189i | ||||
\(302\) | 4.28230 | 0.246418 | ||||||||
\(303\) | 3.55696i | 0.204342i | ||||||||
\(304\) | 2.86167 | + | 2.86167i | 0.164128 | + | 0.164128i | ||||
\(305\) | −18.3647 | + | 18.3647i | −1.05156 | + | 1.05156i | ||||
\(306\) | 5.06250 | − | 5.06250i | 0.289404 | − | 0.289404i | ||||
\(307\) | 5.54613 | − | 5.54613i | 0.316534 | − | 0.316534i | −0.530900 | − | 0.847434i | \(-0.678146\pi\) |
0.847434 | + | 0.530900i | \(0.178146\pi\) | |||||||
\(308\) | −3.15945 | − | 5.29657i | −0.180027 | − | 0.301800i | ||||
\(309\) | − | 9.80437i | − | 0.557751i | ||||||
\(310\) | −14.2086 | − | 14.2086i | −0.806995 | − | 0.806995i | ||||
\(311\) | −15.6648 | −0.888270 | −0.444135 | − | 0.895960i | \(-0.646489\pi\) | ||||
−0.444135 | + | 0.895960i | \(0.646489\pi\) | |||||||
\(312\) | −0.707107 | − | 3.53553i | −0.0400320 | − | 0.200160i | ||||
\(313\) | − | 2.58640i | − | 0.146192i | −0.997325 | − | 0.0730959i | \(-0.976712\pi\) | ||
0.997325 | − | 0.0730959i | \(-0.0232879\pi\) | |||||||
\(314\) | 8.07505 | + | 8.07505i | 0.455701 | + | 0.455701i | ||||
\(315\) | −8.24264 | + | 4.91681i | −0.464420 | + | 0.277031i | ||||
\(316\) | − | 12.0422i | − | 0.677429i | ||||||
\(317\) | 5.33059 | − | 5.33059i | 0.299396 | − | 0.299396i | −0.541381 | − | 0.840777i | \(-0.682098\pi\) |
0.840777 | + | 0.541381i | \(0.182098\pi\) | |||||||
\(318\) | 1.71598 | + | 1.71598i | 0.0962275 | + | 0.0962275i | ||||
\(319\) | 16.0750 | + | 16.0750i | 0.900030 | + | 0.900030i | ||||
\(320\) | 2.56510 | − | 2.56510i | 0.143393 | − | 0.143393i | ||||
\(321\) | − | 0.332748i | − | 0.0185722i | ||||||
\(322\) | 10.1250 | − | 6.03966i | 0.564244 | − | 0.336577i | ||||
\(323\) | 20.4880 | + | 20.4880i | 1.13998 | + | 1.13998i | ||||
\(324\) | − | 1.00000i | − | 0.0555556i | ||||||
\(325\) | 24.4784 | + | 16.3189i | 1.35782 | + | 0.905210i | ||||
\(326\) | −12.8358 | −0.710908 | ||||||||
\(327\) | −12.9672 | − | 12.9672i | −0.717087 | − | 0.717087i | ||||
\(328\) | − | 10.6621i | − | 0.588713i | ||||||
\(329\) | −1.34834 | − | 2.26039i | −0.0743367 | − | 0.124619i | ||||
\(330\) | −5.97931 | + | 5.97931i | −0.329150 | + | 0.329150i | ||||
\(331\) | 17.3927 | − | 17.3927i | 0.955991 | − | 0.955991i | −0.0430801 | − | 0.999072i | \(-0.513717\pi\) |
0.999072 | + | 0.0430801i | \(0.0137171\pi\) | |||||||
\(332\) | 2.70343 | − | 2.70343i | 0.148370 | − | 0.148370i | ||||
\(333\) | −2.48191 | − | 2.48191i | −0.136008 | − | 0.136008i | ||||
\(334\) | − | 4.68888i | − | 0.256564i | ||||||
\(335\) | 23.2870 | 1.27231 | ||||||||
\(336\) | 2.56510 | + | 0.648285i | 0.139938 | + | 0.0353668i | ||||
\(337\) | − | 9.75259i | − | 0.531258i | −0.964075 | − | 0.265629i | \(-0.914420\pi\) | ||
0.964075 | − | 0.265629i | \(-0.0855795\pi\) | |||||||
\(338\) | −12.0208 | − | 4.94975i | −0.653846 | − | 0.269231i | ||||
\(339\) | − | 12.6872i | − | 0.689072i | ||||||
\(340\) | 18.3647 | − | 18.3647i | 0.995966 | − | 0.995966i | ||||
\(341\) | − | 12.9120i | − | 0.699227i | ||||||
\(342\) | 4.04701 | 0.218837 | ||||||||
\(343\) | 12.5242 | − | 13.6435i | 0.676241 | − | 0.736681i | ||||
\(344\) | −6.09696 | + | 6.09696i | −0.328726 | + | 0.328726i | ||||
\(345\) | −11.4301 | − | 11.4301i | −0.615378 | − | 0.615378i | ||||
\(346\) | −4.28402 | + | 4.28402i | −0.230310 | + | 0.230310i | ||||
\(347\) | 2.38696 | 0.128139 | 0.0640693 | − | 0.997945i | \(-0.479592\pi\) | ||||
0.0640693 | + | 0.997945i | \(0.479592\pi\) | |||||||
\(348\) | −9.75259 | −0.522794 | ||||||||
\(349\) | 1.27667 | − | 1.27667i | 0.0683383 | − | 0.0683383i | −0.672112 | − | 0.740450i | \(-0.734612\pi\) |
0.740450 | + | 0.672112i | \(0.234612\pi\) | |||||||
\(350\) | −18.5399 | + | 11.0593i | −0.991002 | + | 0.591142i | ||||
\(351\) | −3.00000 | − | 2.00000i | −0.160128 | − | 0.106752i | ||||
\(352\) | 2.33103 | 0.124244 | ||||||||
\(353\) | −16.3074 | − | 16.3074i | −0.867955 | − | 0.867955i | 0.124291 | − | 0.992246i | \(-0.460335\pi\) |
−0.992246 | + | 0.124291i | \(0.960335\pi\) | |||||||
\(354\) | 14.7870 | 0.785923 | ||||||||
\(355\) | 2.33949 | 0.124167 | ||||||||
\(356\) | −4.75044 | − | 4.75044i | −0.251773 | − | 0.251773i | ||||
\(357\) | 18.3647 | + | 4.64136i | 0.971963 | + | 0.245647i | ||||
\(358\) | −9.58622 | − | 9.58622i | −0.506647 | − | 0.506647i | ||||
\(359\) | 16.0130 | + | 16.0130i | 0.845133 | + | 0.845133i | 0.989521 | − | 0.144388i | \(-0.0461214\pi\) |
−0.144388 | + | 0.989521i | \(0.546121\pi\) | |||||||
\(360\) | − | 3.62760i | − | 0.191191i | ||||||
\(361\) | − | 2.62172i | − | 0.137985i | ||||||
\(362\) | −10.3091 | + | 10.3091i | −0.541835 | + | 0.541835i | ||||
\(363\) | 5.56631 | 0.292156 | ||||||||
\(364\) | 7.07505 | − | 6.39872i | 0.370833 | − | 0.335384i | ||||
\(365\) | −12.7327 | −0.666459 | ||||||||
\(366\) | 5.06250 | − | 5.06250i | 0.264621 | − | 0.264621i | ||||
\(367\) | − | 2.42677i | − | 0.126676i | −0.997992 | − | 0.0633381i | \(-0.979825\pi\) | ||
0.997992 | − | 0.0633381i | \(-0.0201746\pi\) | |||||||
\(368\) | 4.45602i | 0.232286i | ||||||||
\(369\) | −7.53921 | − | 7.53921i | −0.392476 | − | 0.392476i | ||||
\(370\) | −9.00337 | − | 9.00337i | −0.468063 | − | 0.468063i | ||||
\(371\) | −1.57323 | + | 6.22489i | −0.0816783 | + | 0.323180i | ||||
\(372\) | 3.91681 | + | 3.91681i | 0.203077 | + | 0.203077i | ||||
\(373\) | −11.8759 | −0.614909 | −0.307455 | − | 0.951563i | \(-0.599477\pi\) | ||||
−0.307455 | + | 0.951563i | \(0.599477\pi\) | |||||||
\(374\) | 16.6889 | 0.862961 | ||||||||
\(375\) | 8.10431 | + | 8.10431i | 0.418505 | + | 0.418505i | ||||
\(376\) | 0.994801 | 0.0513029 | ||||||||
\(377\) | −19.5052 | + | 29.2578i | −1.00457 | + | 1.50685i | ||||
\(378\) | 2.27220 | − | 1.35539i | 0.116870 | − | 0.0697138i | ||||
\(379\) | 14.4021 | − | 14.4021i | 0.739786 | − | 0.739786i | −0.232751 | − | 0.972536i | \(-0.574773\pi\) |
0.972536 | + | 0.232751i | \(0.0747726\pi\) | |||||||
\(380\) | 14.6809 | 0.753115 | ||||||||
\(381\) | −5.94822 | −0.304737 | ||||||||
\(382\) | −18.6561 | + | 18.6561i | −0.954528 | + | 0.954528i | ||||
\(383\) | 18.6121 | + | 18.6121i | 0.951034 | + | 0.951034i | 0.998856 | − | 0.0478217i | \(-0.0152279\pi\) |
−0.0478217 | + | 0.998856i | \(0.515228\pi\) | |||||||
\(384\) | −0.707107 | + | 0.707107i | −0.0360844 | + | 0.0360844i | ||||
\(385\) | −21.6905 | − | 5.48191i | −1.10545 | − | 0.279384i | ||||
\(386\) | 4.04873 | 0.206075 | ||||||||
\(387\) | 8.62240i | 0.438301i | ||||||||
\(388\) | −4.49220 | + | 4.49220i | −0.228057 | + | 0.228057i | ||||
\(389\) | 0.107858i | 0.00546860i | 0.999996 | + | 0.00273430i | \(0.000870356\pi\) | ||||
−0.999996 | + | 0.00273430i | \(0.999130\pi\) | |||||||
\(390\) | −10.8828 | − | 7.25519i | −0.551071 | − | 0.367381i | ||||
\(391\) | 31.9027i | 1.61339i | ||||||||
\(392\) | 2.00368 | + | 6.70711i | 0.101201 | + | 0.338760i | ||||
\(393\) | 0.0292581 | 0.00147588 | ||||||||
\(394\) | 8.78705i | 0.442685i | ||||||||
\(395\) | −30.8895 | − | 30.8895i | −1.55422 | − | 1.55422i | ||||
\(396\) | 1.64828 | − | 1.64828i | 0.0828294 | − | 0.0828294i | ||||
\(397\) | 18.9320 | − | 18.9320i | 0.950167 | − | 0.950167i | −0.0486486 | − | 0.998816i | \(-0.515491\pi\) |
0.998816 | + | 0.0486486i | \(0.0154914\pi\) | |||||||
\(398\) | −1.15824 | + | 1.15824i | −0.0580572 | + | 0.0580572i | ||||
\(399\) | 5.48528 | + | 9.19563i | 0.274608 | + | 0.460357i | ||||
\(400\) | − | 8.15945i | − | 0.407973i | ||||||
\(401\) | 1.33059 | + | 1.33059i | 0.0664467 | + | 0.0664467i | 0.739549 | − | 0.673103i | \(-0.235039\pi\) |
−0.673103 | + | 0.739549i | \(0.735039\pi\) | |||||||
\(402\) | −6.41941 | −0.320171 | ||||||||
\(403\) | 19.5841 | − | 3.91681i | 0.975552 | − | 0.195110i | ||||
\(404\) | − | 3.55696i | − | 0.176965i | ||||||
\(405\) | −2.56510 | − | 2.56510i | −0.127461 | − | 0.127461i | ||||
\(406\) | −13.2186 | − | 22.1599i | −0.656027 | − | 1.09978i | ||||
\(407\) | − | 8.18179i | − | 0.405556i | ||||||
\(408\) | −5.06250 | + | 5.06250i | −0.250631 | + | 0.250631i | ||||
\(409\) | −21.6543 | − | 21.6543i | −1.07074 | − | 1.07074i | −0.997300 | − | 0.0734389i | \(-0.976603\pi\) |
−0.0734389 | − | 0.997300i | \(-0.523397\pi\) | |||||||
\(410\) | −27.3492 | − | 27.3492i | −1.35068 | − | 1.35068i | ||||
\(411\) | −4.56510 | + | 4.56510i | −0.225180 | + | 0.225180i | ||||
\(412\) | 9.80437i | 0.483027i | ||||||||
\(413\) | 20.0422 | + | 33.5992i | 0.986214 | + | 1.65331i | ||||
\(414\) | 3.15088 | + | 3.15088i | 0.154858 | + | 0.154858i | ||||
\(415\) | − | 13.8691i | − | 0.680809i | ||||||
\(416\) | 0.707107 | + | 3.53553i | 0.0346688 | + | 0.173344i | ||||
\(417\) | 12.6872 | 0.621293 | ||||||||
\(418\) | 6.67062 | + | 6.67062i | 0.326271 | + | 0.326271i | ||||
\(419\) | − | 3.41741i | − | 0.166951i | −0.996510 | − | 0.0834757i | \(-0.973398\pi\) | ||
0.996510 | − | 0.0834757i | \(-0.0266021\pi\) | |||||||
\(420\) | 8.24264 | − | 4.91681i | 0.402200 | − | 0.239916i | ||||
\(421\) | −1.36201 | + | 1.36201i | −0.0663801 | + | 0.0663801i | −0.739517 | − | 0.673137i | \(-0.764946\pi\) |
0.673137 | + | 0.739517i | \(0.264946\pi\) | |||||||
\(422\) | 0.440101 | − | 0.440101i | 0.0214238 | − | 0.0214238i | ||||
\(423\) | 0.703431 | − | 0.703431i | 0.0342020 | − | 0.0342020i | ||||
\(424\) | −1.71598 | − | 1.71598i | −0.0833355 | − | 0.0833355i | ||||
\(425\) | − | 58.4172i | − | 2.83365i | ||||||
\(426\) | −0.644914 | −0.0312462 | ||||||||
\(427\) | 18.3647 | + | 4.64136i | 0.888730 | + | 0.224611i | ||||
\(428\) | 0.332748i | 0.0160840i | ||||||||
\(429\) | −1.64828 | − | 8.24142i | −0.0795799 | − | 0.397900i | ||||
\(430\) | 31.2786i | 1.50839i | ||||||||
\(431\) | 11.1302 | − | 11.1302i | 0.536123 | − | 0.536123i | −0.386265 | − | 0.922388i | \(-0.626235\pi\) |
0.922388 | + | 0.386265i | \(0.126235\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | −19.7843 | −0.950772 | −0.475386 | − | 0.879777i | \(-0.657692\pi\) | ||||
−0.475386 | + | 0.879777i | \(0.657692\pi\) | |||||||
\(434\) | −3.59099 | + | 14.2086i | −0.172373 | + | 0.682035i | ||||
\(435\) | −25.0164 | + | 25.0164i | −1.19944 | + | 1.19944i | ||||
\(436\) | 12.9672 | + | 12.9672i | 0.621016 | + | 0.621016i | ||||
\(437\) | −12.7517 | + | 12.7517i | −0.609994 | + | 0.609994i | ||||
\(438\) | 3.50995 | 0.167712 | ||||||||
\(439\) | 26.7749 | 1.27790 | 0.638949 | − | 0.769249i | \(-0.279370\pi\) | ||||
0.638949 | + | 0.769249i | \(0.279370\pi\) | |||||||
\(440\) | 5.97931 | − | 5.97931i | 0.285052 | − | 0.285052i | ||||
\(441\) | 6.15945 | + | 3.32583i | 0.293307 | + | 0.158373i | ||||
\(442\) | 5.06250 | + | 25.3125i | 0.240798 | + | 1.20399i | ||||
\(443\) | 28.3587 | 1.34736 | 0.673682 | − | 0.739022i | \(-0.264712\pi\) | ||||
0.673682 | + | 0.739022i | \(0.264712\pi\) | |||||||
\(444\) | 2.48191 | + | 2.48191i | 0.117786 | + | 0.117786i | ||||
\(445\) | −24.3707 | −1.15528 | ||||||||
\(446\) | −22.0074 | −1.04208 | ||||||||
\(447\) | 13.4021 | + | 13.4021i | 0.633897 | + | 0.633897i | ||||
\(448\) | −2.56510 | − | 0.648285i | −0.121189 | − | 0.0306286i | ||||
\(449\) | 2.28843 | + | 2.28843i | 0.107998 | + | 0.107998i | 0.759041 | − | 0.651043i | \(-0.225668\pi\) |
−0.651043 | + | 0.759041i | \(0.725668\pi\) | |||||||
\(450\) | −5.76961 | − | 5.76961i | −0.271982 | − | 0.271982i | ||||
\(451\) | − | 24.8535i | − | 1.17031i | ||||||
\(452\) | 12.6872i | 0.596754i | ||||||||
\(453\) | −3.02804 | + | 3.02804i | −0.142270 | + | 0.142270i | ||||
\(454\) | 1.63972 | 0.0769556 | ||||||||
\(455\) | 1.73484 | − | 34.5615i | 0.0813307 | − | 1.62027i | ||||
\(456\) | −4.04701 | −0.189519 | ||||||||
\(457\) | −5.68091 | + | 5.68091i | −0.265742 | + | 0.265742i | −0.827382 | − | 0.561640i | \(-0.810171\pi\) |
0.561640 | + | 0.827382i | \(0.310171\pi\) | |||||||
\(458\) | − | 5.88236i | − | 0.274864i | ||||||
\(459\) | 7.15945i | 0.334175i | ||||||||
\(460\) | 11.4301 | + | 11.4301i | 0.532933 | + | 0.532933i | ||||
\(461\) | −15.6953 | − | 15.6953i | −0.731003 | − | 0.731003i | 0.239816 | − | 0.970818i | \(-0.422913\pi\) |
−0.970818 | + | 0.239816i | \(0.922913\pi\) | |||||||
\(462\) | 5.97931 | + | 1.51117i | 0.278183 | + | 0.0703059i | ||||
\(463\) | −11.2324 | − | 11.2324i | −0.522012 | − | 0.522012i | 0.396167 | − | 0.918179i | \(-0.370340\pi\) |
−0.918179 | + | 0.396167i | \(0.870340\pi\) | |||||||
\(464\) | 9.75259 | 0.452753 | ||||||||
\(465\) | 20.0940 | 0.931838 | ||||||||
\(466\) | 7.63495 | + | 7.63495i | 0.353682 | + | 0.353682i | ||||
\(467\) | 2.81997 | 0.130492 | 0.0652462 | − | 0.997869i | \(-0.479217\pi\) | ||||
0.0652462 | + | 0.997869i | \(0.479217\pi\) | |||||||
\(468\) | 3.00000 | + | 2.00000i | 0.138675 | + | 0.0924500i | ||||
\(469\) | −8.70082 | − | 14.5862i | −0.401766 | − | 0.673529i | ||||
\(470\) | 2.55176 | − | 2.55176i | 0.117704 | − | 0.117704i | ||||
\(471\) | −11.4198 | −0.526199 | ||||||||
\(472\) | −14.7870 | −0.680629 | ||||||||
\(473\) | −14.2122 | + | 14.2122i | −0.653476 | + | 0.653476i | ||||
\(474\) | 8.51515 | + | 8.51515i | 0.391114 | + | 0.391114i | ||||
\(475\) | 23.3496 | − | 23.3496i | 1.07136 | − | 1.07136i | ||||
\(476\) | −18.3647 | − | 4.64136i | −0.841745 | − | 0.212737i | ||||
\(477\) | −2.42677 | −0.111114 | ||||||||
\(478\) | − | 22.8397i | − | 1.04466i | ||||||
\(479\) | −23.0456 | + | 23.0456i | −1.05298 | + | 1.05298i | −0.0544653 | + | 0.998516i | \(0.517345\pi\) |
−0.998516 | + | 0.0544653i | \(0.982655\pi\) | |||||||
\(480\) | 3.62760i | 0.165576i | ||||||||
\(481\) | 12.4096 | − | 2.48191i | 0.565827 | − | 0.113165i | ||||
\(482\) | − | 4.88755i | − | 0.222622i | ||||||
\(483\) | −2.88877 | + | 11.4301i | −0.131444 | + | 0.520089i | ||||
\(484\) | −5.56631 | −0.253014 | ||||||||
\(485\) | 23.0459i | 1.04646i | ||||||||
\(486\) | 0.707107 | + | 0.707107i | 0.0320750 | + | 0.0320750i | ||||
\(487\) | 26.3503 | − | 26.3503i | 1.19405 | − | 1.19405i | 0.218126 | − | 0.975921i | \(-0.430005\pi\) |
0.975921 | − | 0.218126i | \(-0.0699945\pi\) | |||||||
\(488\) | −5.06250 | + | 5.06250i | −0.229169 | + | 0.229169i | ||||
\(489\) | 9.07627 | − | 9.07627i | 0.410443 | − | 0.410443i | ||||
\(490\) | 22.3440 | + | 12.0648i | 1.00940 | + | 0.545030i | ||||
\(491\) | − | 11.7819i | − | 0.531707i | −0.964013 | − | 0.265854i | \(-0.914346\pi\) | ||
0.964013 | − | 0.265854i | \(-0.0856538\pi\) | |||||||
\(492\) | 7.53921 | + | 7.53921i | 0.339894 | + | 0.339894i | ||||
\(493\) | 69.8232 | 3.14468 | ||||||||
\(494\) | −8.09402 | + | 12.1410i | −0.364167 | + | 0.546251i | ||||
\(495\) | − | 8.45602i | − | 0.380070i | ||||||
\(496\) | −3.91681 | − | 3.91681i | −0.175870 | − | 0.175870i | ||||
\(497\) | −0.874111 | − | 1.46538i | −0.0392093 | − | 0.0657312i | ||||
\(498\) | 3.82323i | 0.171323i | ||||||||
\(499\) | −25.6014 | + | 25.6014i | −1.14607 | + | 1.14607i | −0.158756 | + | 0.987318i | \(0.550748\pi\) |
−0.987318 | + | 0.158756i | \(0.949252\pi\) | |||||||
\(500\) | −8.10431 | − | 8.10431i | −0.362436 | − | 0.362436i | ||||
\(501\) | 3.31554 | + | 3.31554i | 0.148127 | + | 0.148127i | ||||
\(502\) | −3.98971 | + | 3.98971i | −0.178069 | + | 0.178069i | ||||
\(503\) | 12.0000i | 0.535054i | 0.963550 | + | 0.267527i | \(0.0862064\pi\) | ||||
−0.963550 | + | 0.267527i | \(0.913794\pi\) | |||||||
\(504\) | −2.27220 | + | 1.35539i | −0.101212 | + | 0.0603739i | ||||
\(505\) | −9.12395 | − | 9.12395i | −0.406011 | − | 0.406011i | ||||
\(506\) | 10.3871i | 0.461763i | ||||||||
\(507\) | 12.0000 | − | 5.00000i | 0.532939 | − | 0.222058i | ||||
\(508\) | 5.94822 | 0.263910 | ||||||||
\(509\) | −24.4927 | − | 24.4927i | −1.08562 | − | 1.08562i | −0.995973 | − | 0.0896482i | \(-0.971426\pi\) |
−0.0896482 | − | 0.995973i | \(-0.528574\pi\) | |||||||
\(510\) | 25.9716i | 1.15004i | ||||||||
\(511\) | 4.75736 | + | 7.97533i | 0.210453 | + | 0.352808i | ||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | −2.86167 | + | 2.86167i | −0.126346 | + | 0.126346i | ||||
\(514\) | 17.6917 | − | 17.6917i | 0.780349 | − | 0.780349i | ||||
\(515\) | 25.1492 | + | 25.1492i | 1.10820 | + | 1.10820i | ||||
\(516\) | − | 8.62240i | − | 0.379580i | ||||||
\(517\) | 2.31891 | 0.101985 | ||||||||
\(518\) | −2.27545 | + | 9.00337i | −0.0999775 | + | 0.395585i | ||||
\(519\) | − | 6.05852i | − | 0.265939i | ||||||
\(520\) | 10.8828 | + | 7.25519i | 0.477242 | + | 0.318161i | ||||
\(521\) | − | 24.7188i | − | 1.08295i | −0.840716 | − | 0.541476i | \(-0.817866\pi\) | ||
0.840716 | − | 0.541476i | \(-0.182134\pi\) | |||||||
\(522\) | 6.89612 | − | 6.89612i | 0.301835 | − | 0.301835i | ||||
\(523\) | 8.22489i | 0.359649i | 0.983699 | + | 0.179825i | \(0.0575530\pi\) | ||||
−0.983699 | + | 0.179825i | \(0.942447\pi\) | |||||||
\(524\) | −0.0292581 | −0.00127815 | ||||||||
\(525\) | 5.28965 | − | 20.9298i | 0.230859 | − | 0.913451i | ||||
\(526\) | −8.59314 | + | 8.59314i | −0.374679 | + | 0.374679i | ||||
\(527\) | −28.0422 | − | 28.0422i | −1.22154 | − | 1.22154i | ||||
\(528\) | −1.64828 | + | 1.64828i | −0.0717324 | + | 0.0717324i | ||||
\(529\) | 3.14386 | 0.136689 | ||||||||
\(530\) | −8.80332 | −0.382392 | ||||||||
\(531\) | −10.4560 | + | 10.4560i | −0.453753 | + | 0.453753i | ||||
\(532\) | −5.48528 | − | 9.19563i | −0.237817 | − | 0.398681i | ||||
\(533\) | 37.6961 | − | 7.53921i | 1.63280 | − | 0.326559i | ||||
\(534\) | 6.71814 | 0.290722 | ||||||||
\(535\) | 0.853530 | + | 0.853530i | 0.0369013 | + | 0.0369013i | ||||
\(536\) | 6.41941 | 0.277276 | ||||||||
\(537\) | 13.5570 | 0.585026 | ||||||||
\(538\) | 14.1055 | + | 14.1055i | 0.608132 | + | 0.608132i | ||||
\(539\) | 4.67062 | + | 15.6344i | 0.201178 | + | 0.673423i | ||||
\(540\) | 2.56510 | + | 2.56510i | 0.110384 | + | 0.110384i | ||||
\(541\) | 15.1691 | + | 15.1691i | 0.652169 | + | 0.652169i | 0.953515 | − | 0.301346i | \(-0.0974358\pi\) |
−0.301346 | + | 0.953515i | \(0.597436\pi\) | |||||||
\(542\) | 11.7582i | 0.505059i | ||||||||
\(543\) | − | 14.5793i | − | 0.625658i | ||||||
\(544\) | 5.06250 | − | 5.06250i | 0.217053 | − | 0.217053i | ||||
\(545\) | 66.5242 | 2.84959 | ||||||||
\(546\) | −0.478235 | + | 9.52740i | −0.0204666 | + | 0.407735i | ||||
\(547\) | −15.2261 | −0.651020 | −0.325510 | − | 0.945539i | \(-0.605536\pi\) | ||||
−0.325510 | + | 0.945539i | \(0.605536\pi\) | |||||||
\(548\) | 4.56510 | − | 4.56510i | 0.195011 | − | 0.195011i | ||||
\(549\) | 7.15945i | 0.305558i | ||||||||
\(550\) | − | 19.0199i | − | 0.811011i | ||||||
\(551\) | 27.9087 | + | 27.9087i | 1.18895 | + | 1.18895i | ||||
\(552\) | −3.15088 | − | 3.15088i | −0.134111 | − | 0.134111i | ||||
\(553\) | −7.80680 | + | 30.8895i | −0.331979 | + | 1.31356i | ||||
\(554\) | −3.92936 | − | 3.92936i | −0.166943 | − | 0.166943i | ||||
\(555\) | 12.7327 | 0.540473 | ||||||||
\(556\) | −12.6872 | −0.538055 | ||||||||
\(557\) | 24.0893 | + | 24.0893i | 1.02069 | + | 1.02069i | 0.999781 | + | 0.0209130i | \(0.00665731\pi\) |
0.0209130 | + | 0.999781i | \(0.493343\pi\) | |||||||
\(558\) | −5.53921 | −0.234493 | ||||||||
\(559\) | −25.8672 | − | 17.2448i | −1.09407 | − | 0.729377i | ||||
\(560\) | −8.24264 | + | 4.91681i | −0.348315 | + | 0.207773i | ||||
\(561\) | −11.8008 | + | 11.8008i | −0.498231 | + | 0.498231i | ||||
\(562\) | −16.2362 | −0.684881 | ||||||||
\(563\) | 31.8346 | 1.34167 | 0.670835 | − | 0.741607i | \(-0.265936\pi\) | ||||
0.670835 | + | 0.741607i | \(0.265936\pi\) | |||||||
\(564\) | −0.703431 | + | 0.703431i | −0.0296198 | + | 0.0296198i | ||||
\(565\) | 32.5438 | + | 32.5438i | 1.36913 | + | 1.36913i | ||||
\(566\) | 4.55896 | − | 4.55896i | 0.191627 | − | 0.191627i | ||||
\(567\) | −0.648285 | + | 2.56510i | −0.0272254 | + | 0.107724i | ||||
\(568\) | 0.644914 | 0.0270600 | ||||||||
\(569\) | − | 15.2218i | − | 0.638130i | −0.947733 | − | 0.319065i | \(-0.896631\pi\) | ||
0.947733 | − | 0.319065i | \(-0.103369\pi\) | |||||||
\(570\) | −10.3810 | + | 10.3810i | −0.434811 | + | 0.434811i | ||||
\(571\) | − | 2.53462i | − | 0.106071i | −0.998593 | − | 0.0530353i | \(-0.983110\pi\) | ||
0.998593 | − | 0.0530353i | \(-0.0168896\pi\) | |||||||
\(572\) | 1.64828 | + | 8.24142i | 0.0689182 | + | 0.344591i | ||||
\(573\) | − | 26.3837i | − | 1.10219i | ||||||
\(574\) | −6.91205 | + | 27.3492i | −0.288503 | + | 1.14153i | ||||
\(575\) | 36.3587 | 1.51626 | ||||||||
\(576\) | − | 1.00000i | − | 0.0416667i | ||||||
\(577\) | 14.6380 | + | 14.6380i | 0.609388 | + | 0.609388i | 0.942786 | − | 0.333398i | \(-0.108195\pi\) |
−0.333398 | + | 0.942786i | \(0.608195\pi\) | |||||||
\(578\) | 24.2239 | − | 24.2239i | 1.00758 | − | 1.00758i | ||||
\(579\) | −2.86288 | + | 2.86288i | −0.118977 | + | 0.118977i | ||||
\(580\) | 25.0164 | − | 25.0164i | 1.03875 | − | 1.03875i | ||||
\(581\) | −8.68716 | + | 5.18197i | −0.360404 | + | 0.214984i | ||||
\(582\) | − | 6.35293i | − | 0.263338i | ||||||
\(583\) | −4.00000 | − | 4.00000i | −0.165663 | − | 0.165663i | ||||
\(584\) | −3.50995 | −0.145243 | ||||||||
\(585\) | 12.8255 | − | 2.56510i | 0.530269 | − | 0.106054i | ||||
\(586\) | 31.3535i | 1.29520i | ||||||||
\(587\) | 21.2017 | + | 21.2017i | 0.875088 | + | 0.875088i | 0.993021 | − | 0.117934i | \(-0.0376271\pi\) |
−0.117934 | + | 0.993021i | \(0.537627\pi\) | |||||||
\(588\) | −6.15945 | − | 3.32583i | −0.254012 | − | 0.137155i | ||||
\(589\) | − | 22.4172i | − | 0.923686i | ||||||
\(590\) | −37.9302 | + | 37.9302i | −1.56156 | + | 1.56156i | ||||
\(591\) | −6.21338 | − | 6.21338i | −0.255584 | − | 0.255584i | ||||
\(592\) | −2.48191 | − | 2.48191i | −0.102006 | − | 0.102006i | ||||
\(593\) | −13.9952 | + | 13.9952i | −0.574715 | + | 0.574715i | −0.933442 | − | 0.358727i | \(-0.883211\pi\) |
0.358727 | + | 0.933442i | \(0.383211\pi\) | |||||||
\(594\) | 2.33103i | 0.0956432i | ||||||||
\(595\) | −59.0128 | + | 35.2017i | −2.41929 | + | 1.44313i | ||||
\(596\) | −13.4021 | − | 13.4021i | −0.548971 | − | 0.548971i | ||||
\(597\) | − | 1.63799i | − | 0.0670386i | ||||||
\(598\) | −15.7544 | + | 3.15088i | −0.644246 | + | 0.128849i | ||||
\(599\) | 26.4603 | 1.08114 | 0.540570 | − | 0.841299i | \(-0.318209\pi\) | ||||
0.540570 | + | 0.841299i | \(0.318209\pi\) | |||||||
\(600\) | 5.76961 | + | 5.76961i | 0.235543 | + | 0.235543i | ||||
\(601\) | 8.65166i | 0.352908i | 0.984309 | + | 0.176454i | \(0.0564627\pi\) | ||||
−0.984309 | + | 0.176454i | \(0.943537\pi\) | |||||||
\(602\) | 19.5919 | − | 11.6867i | 0.798504 | − | 0.476315i | ||||
\(603\) | 4.53921 | − | 4.53921i | 0.184851 | − | 0.184851i | ||||
\(604\) | 3.02804 | − | 3.02804i | 0.123209 | − | 0.123209i | ||||
\(605\) | −14.2781 | + | 14.2781i | −0.580489 | + | 0.580489i | ||||
\(606\) | 2.51515 | + | 2.51515i | 0.102171 | + | 0.102171i | ||||
\(607\) | − | 2.46556i | − | 0.100074i | −0.998747 | − | 0.0500369i | \(-0.984066\pi\) | ||
0.998747 | − | 0.0500369i | \(-0.0159339\pi\) | |||||||
\(608\) | 4.04701 | 0.164128 | ||||||||
\(609\) | 25.0164 | + | 6.32246i | 1.01371 | + | 0.256199i | ||||
\(610\) | 25.9716i | 1.05156i | ||||||||
\(611\) | 0.703431 | + | 3.51715i | 0.0284578 | + | 0.142289i | ||||
\(612\) | − | 7.15945i | − | 0.289404i | ||||||
\(613\) | −6.36488 | + | 6.36488i | −0.257075 | + | 0.257075i | −0.823863 | − | 0.566788i | \(-0.808186\pi\) |
0.566788 | + | 0.823863i | \(0.308186\pi\) | |||||||
\(614\) | − | 7.84341i | − | 0.316534i | ||||||
\(615\) | 38.6776 | 1.55963 | ||||||||
\(616\) | −5.97931 | − | 1.51117i | −0.240913 | − | 0.0608867i | ||||
\(617\) | −21.1065 | + | 21.1065i | −0.849714 | + | 0.849714i | −0.990097 | − | 0.140383i | \(-0.955167\pi\) |
0.140383 | + | 0.990097i | \(0.455167\pi\) | |||||||
\(618\) | −6.93274 | − | 6.93274i | −0.278876 | − | 0.278876i | ||||
\(619\) | 20.3108 | − | 20.3108i | 0.816359 | − | 0.816359i | −0.169220 | − | 0.985578i | \(-0.554125\pi\) |
0.985578 | + | 0.169220i | \(0.0541247\pi\) | |||||||
\(620\) | −20.0940 | −0.806995 | ||||||||
\(621\) | −4.45602 | −0.178814 | ||||||||
\(622\) | −11.0767 | + | 11.0767i | −0.444135 | + | 0.444135i | ||||
\(623\) | 9.10570 | + | 15.2650i | 0.364812 | + | 0.611578i | ||||
\(624\) | −3.00000 | − | 2.00000i | −0.120096 | − | 0.0800641i | ||||
\(625\) | −0.779417 | −0.0311767 | ||||||||
\(626\) | −1.82886 | − | 1.82886i | −0.0730959 | − | 0.0730959i | ||||
\(627\) | −9.43369 | −0.376745 | ||||||||
\(628\) | 11.4198 | 0.455701 | ||||||||
\(629\) | −17.7691 | − | 17.7691i | −0.708501 | − | 0.708501i | ||||
\(630\) | −2.35172 | + | 9.30514i | −0.0936946 | + | 0.370726i | ||||
\(631\) | −10.3788 | − | 10.3788i | −0.413174 | − | 0.413174i | 0.469669 | − | 0.882843i | \(-0.344373\pi\) |
−0.882843 | + | 0.469669i | \(0.844373\pi\) | |||||||
\(632\) | −8.51515 | − | 8.51515i | −0.338715 | − | 0.338715i | ||||
\(633\) | 0.622397i | 0.0247381i | ||||||||
\(634\) | − | 7.53860i | − | 0.299396i | ||||||
\(635\) | 15.2578 | − | 15.2578i | 0.605486 | − | 0.605486i | ||||
\(636\) | 2.42677 | 0.0962275 | ||||||||
\(637\) | −22.2964 | + | 11.8267i | −0.883415 | + | 0.468591i | ||||
\(638\) | 22.7336 | 0.900030 | ||||||||
\(639\) | 0.456023 | − | 0.456023i | 0.0180400 | − | 0.0180400i | ||||
\(640\) | − | 3.62760i | − | 0.143393i | ||||||
\(641\) | − | 0.168808i | − | 0.00666750i | −0.999994 | − | 0.00333375i | \(-0.998939\pi\) | ||
0.999994 | − | 0.00333375i | \(-0.00106117\pi\) | |||||||
\(642\) | −0.235288 | − | 0.235288i | −0.00928608 | − | 0.00928608i | ||||
\(643\) | −23.4995 | − | 23.4995i | −0.926729 | − | 0.926729i | 0.0707640 | − | 0.997493i | \(-0.477456\pi\) |
−0.997493 | + | 0.0707640i | \(0.977456\pi\) | |||||||
\(644\) | 2.88877 | − | 11.4301i | 0.113834 | − | 0.450410i | ||||
\(645\) | −22.1173 | − | 22.1173i | −0.870868 | − | 0.870868i | ||||
\(646\) | 28.9744 | 1.13998 | ||||||||
\(647\) | −7.68783 | −0.302240 | −0.151120 | − | 0.988515i | \(-0.548288\pi\) | ||||
−0.151120 | + | 0.988515i | \(0.548288\pi\) | |||||||
\(648\) | −0.707107 | − | 0.707107i | −0.0277778 | − | 0.0277778i | ||||
\(649\) | −34.4690 | −1.35303 | ||||||||
\(650\) | 28.8480 | − | 5.76961i | 1.13151 | − | 0.226303i | ||||
\(651\) | −7.50780 | − | 12.5862i | −0.294254 | − | 0.493293i | ||||
\(652\) | −9.07627 | + | 9.07627i | −0.355454 | + | 0.355454i | ||||
\(653\) | 15.9545 | 0.624347 | 0.312173 | − | 0.950025i | \(-0.398943\pi\) | ||||
0.312173 | + | 0.950025i | \(0.398943\pi\) | |||||||
\(654\) | −18.3384 | −0.717087 | ||||||||
\(655\) | −0.0750499 | + | 0.0750499i | −0.00293244 | + | 0.00293244i | ||||
\(656\) | −7.53921 | − | 7.53921i | −0.294357 | − | 0.294357i | ||||
\(657\) | −2.48191 | + | 2.48191i | −0.0968286 | + | 0.0968286i | ||||
\(658\) | −2.55176 | − | 0.644914i | −0.0994780 | − | 0.0251414i | ||||
\(659\) | −24.5438 | −0.956091 | −0.478045 | − | 0.878335i | \(-0.658655\pi\) | ||||
−0.478045 | + | 0.878335i | \(0.658655\pi\) | |||||||
\(660\) | 8.45602i | 0.329150i | ||||||||
\(661\) | −3.34817 | + | 3.34817i | −0.130229 | + | 0.130229i | −0.769217 | − | 0.638988i | \(-0.779353\pi\) |
0.638988 | + | 0.769217i | \(0.279353\pi\) | |||||||
\(662\) | − | 24.5970i | − | 0.955991i | ||||||
\(663\) | −21.4784 | − | 14.3189i | −0.834150 | − | 0.556100i | ||||
\(664\) | − | 3.82323i | − | 0.148370i | ||||||
\(665\) | −37.6580 | − | 9.51741i | −1.46031 | − | 0.369069i | ||||
\(666\) | −3.50995 | −0.136008 | ||||||||
\(667\) | 43.4578i | 1.68269i | ||||||||
\(668\) | −3.31554 | − | 3.31554i | −0.128282 | − | 0.128282i | ||||
\(669\) | 15.5615 | − | 15.5615i | 0.601644 | − | 0.601644i | ||||
\(670\) | 16.4664 | − | 16.4664i | 0.636153 | − | 0.636153i | ||||
\(671\) | −11.8008 | + | 11.8008i | −0.455566 | + | 0.455566i | ||||
\(672\) | 2.27220 | − | 1.35539i | 0.0876522 | − | 0.0522854i | ||||
\(673\) | 11.5369i | 0.444714i | 0.974965 | + | 0.222357i | \(0.0713750\pi\) | ||||
−0.974965 | + | 0.222357i | \(0.928625\pi\) | |||||||
\(674\) | −6.89612 | − | 6.89612i | −0.265629 | − | 0.265629i | ||||
\(675\) | 8.15945 | 0.314058 | ||||||||
\(676\) | −12.0000 | + | 5.00000i | −0.461538 | + | 0.192308i | ||||
\(677\) | 12.8958i | 0.495625i | 0.968808 | + | 0.247812i | \(0.0797117\pi\) | ||||
−0.968808 | + | 0.247812i | \(0.920288\pi\) | |||||||
\(678\) | −8.97117 | − | 8.97117i | −0.344536 | − | 0.344536i | ||||
\(679\) | 14.4352 | − | 8.61071i | 0.553971 | − | 0.330449i | ||||
\(680\) | − | 25.9716i | − | 0.995966i | ||||||
\(681\) | −1.15945 | + | 1.15945i | −0.0444304 | + | 0.0444304i | ||||
\(682\) | −9.13020 | − | 9.13020i | −0.349613 | − | 0.349613i | ||||
\(683\) | 14.7785 | + | 14.7785i | 0.565483 | + | 0.565483i | 0.930860 | − | 0.365377i | \(-0.119060\pi\) |
−0.365377 | + | 0.930860i | \(0.619060\pi\) | |||||||
\(684\) | 2.86167 | − | 2.86167i | 0.109419 | − | 0.109419i | ||||
\(685\) | − | 23.4198i | − | 0.894826i | ||||||
\(686\) | −0.791511 | − | 18.5033i | −0.0302200 | − | 0.706461i | ||||
\(687\) | 4.15945 | + | 4.15945i | 0.158693 | + | 0.158693i | ||||
\(688\) | 8.62240i | 0.328726i | ||||||||
\(689\) | 4.85353 | − | 7.28030i | 0.184905 | − | 0.277357i | ||||
\(690\) | −16.1647 | −0.615378 | ||||||||
\(691\) | 13.4220 | + | 13.4220i | 0.510597 | + | 0.510597i | 0.914709 | − | 0.404112i | \(-0.132420\pi\) |
−0.404112 | + | 0.914709i | \(0.632420\pi\) | |||||||
\(692\) | 6.05852i | 0.230310i | ||||||||
\(693\) | −5.29657 | + | 3.15945i | −0.201200 | + | 0.120018i | ||||
\(694\) | 1.68783 | − | 1.68783i | 0.0640693 | − | 0.0640693i | ||||
\(695\) | −32.5438 | + | 32.5438i | −1.23446 | + | 1.23446i | ||||
\(696\) | −6.89612 | + | 6.89612i | −0.261397 | + | 0.261397i | ||||
\(697\) | −53.9766 | − | 53.9766i | −2.04451 | − | 2.04451i | ||||
\(698\) | − | 1.80548i | − | 0.0683383i | ||||||
\(699\) | −10.7974 | −0.408397 | ||||||||
\(700\) | −5.28965 | + | 20.9298i | −0.199930 | + | 0.791072i | ||||
\(701\) | 19.5009i | 0.736538i | 0.929719 | + | 0.368269i | \(0.120049\pi\) | ||||
−0.929719 | + | 0.368269i | \(0.879951\pi\) | |||||||
\(702\) | −3.53553 | + | 0.707107i | −0.133440 | + | 0.0266880i | ||||
\(703\) | − | 14.2048i | − | 0.535744i | ||||||
\(704\) | 1.64828 | − | 1.64828i | 0.0621221 | − | 0.0621221i | ||||
\(705\) | 3.60874i | 0.135913i | ||||||||
\(706\) | −23.0621 | −0.867955 | ||||||||
\(707\) | −2.30592 | + | 9.12395i | −0.0867232 | + | 0.343142i | ||||
\(708\) | 10.4560 | − | 10.4560i | 0.392961 | − | 0.392961i | ||||
\(709\) | 36.2084 | + | 36.2084i | 1.35984 | + | 1.35984i | 0.874112 | + | 0.485724i | \(0.161444\pi\) |
0.485724 | + | 0.874112i | \(0.338556\pi\) | |||||||
\(710\) | 1.65427 | − | 1.65427i | 0.0620836 | − | 0.0620836i | ||||
\(711\) | −12.0422 | −0.451619 | ||||||||
\(712\) | −6.71814 | −0.251773 | ||||||||
\(713\) | 17.4534 | − | 17.4534i | 0.653635 | − | 0.653635i | ||||
\(714\) | 16.2677 | − | 9.70386i | 0.608805 | − | 0.363158i | ||||
\(715\) | 25.3681 | + | 16.9120i | 0.948712 | + | 0.632475i | ||||
\(716\) | −13.5570 | −0.506647 | ||||||||
\(717\) | 16.1501 | + | 16.1501i | 0.603137 | + | 0.603137i | ||||
\(718\) | 22.6458 | 0.845133 | ||||||||
\(719\) | 31.8404 | 1.18745 | 0.593723 | − | 0.804670i | \(-0.297658\pi\) | ||||
0.593723 | + | 0.804670i | \(0.297658\pi\) | |||||||
\(720\) | −2.56510 | − | 2.56510i | −0.0955956 | − | 0.0955956i | ||||
\(721\) | 6.35602 | − | 25.1492i | 0.236711 | − | 0.936604i | ||||
\(722\) | −1.85384 | − | 1.85384i | −0.0689926 | − | 0.0689926i | ||||
\(723\) | 3.45602 | + | 3.45602i | 0.128531 | + | 0.128531i | ||||
\(724\) | 14.5793i | 0.541835i | ||||||||
\(725\) | − | 79.5758i | − | 2.95537i | ||||||
\(726\) | 3.93598 | − | 3.93598i | 0.146078 | − | 0.146078i | ||||
\(727\) | 0.263681 | 0.00977940 | 0.00488970 | − | 0.999988i | \(-0.498444\pi\) | ||||
0.00488970 | + | 0.999988i | \(0.498444\pi\) | |||||||
\(728\) | 0.478235 | − | 9.52740i | 0.0177246 | − | 0.353109i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −9.00337 | + | 9.00337i | −0.333230 | + | 0.333230i | ||||
\(731\) | 61.7317i | 2.28323i | ||||||||
\(732\) | − | 7.15945i | − | 0.264621i | ||||||
\(733\) | 14.4266 | + | 14.4266i | 0.532858 | + | 0.532858i | 0.921422 | − | 0.388564i | \(-0.127029\pi\) |
−0.388564 | + | 0.921422i | \(0.627029\pi\) | |||||||
\(734\) | −1.71598 | − | 1.71598i | −0.0633381 | − | 0.0633381i | ||||
\(735\) | −24.3307 | + | 7.26853i | −0.897450 | + | 0.268104i | ||||
\(736\) | 3.15088 | + | 3.15088i | 0.116143 | + | 0.116143i | ||||
\(737\) | 14.9638 | 0.551199 | ||||||||
\(738\) | −10.6621 | −0.392476 | ||||||||
\(739\) | 6.59099 | + | 6.59099i | 0.242453 | + | 0.242453i | 0.817864 | − | 0.575411i | \(-0.195158\pi\) |
−0.575411 | + | 0.817864i | \(0.695158\pi\) | |||||||
\(740\) | −12.7327 | −0.468063 | ||||||||
\(741\) | −2.86167 | − | 14.3083i | −0.105126 | − | 0.525630i | ||||
\(742\) | 3.28922 | + | 5.51411i | 0.120751 | + | 0.202429i | ||||
\(743\) | 18.2311 | − | 18.2311i | 0.668835 | − | 0.668835i | −0.288611 | − | 0.957446i | \(-0.593193\pi\) |
0.957446 | + | 0.288611i | \(0.0931934\pi\) | |||||||
\(744\) | 5.53921 | 0.203077 | ||||||||
\(745\) | −68.7554 | −2.51900 | ||||||||
\(746\) | −8.39751 | + | 8.39751i | −0.307455 | + | 0.307455i | ||||
\(747\) | −2.70343 | − | 2.70343i | −0.0989133 | − | 0.0989133i | ||||
\(748\) | 11.8008 | − | 11.8008i | 0.431481 | − | 0.431481i | ||||
\(749\) | 0.215715 | − | 0.853530i | 0.00788206 | − | 0.0311873i | ||||
\(750\) | 11.4612 | 0.418505 | ||||||||
\(751\) | − | 17.5282i | − | 0.639613i | −0.947483 | − | 0.319807i | \(-0.896382\pi\) | ||
0.947483 | − | 0.319807i | \(-0.103618\pi\) | |||||||
\(752\) | 0.703431 | − | 0.703431i | 0.0256515 | − | 0.0256515i | ||||
\(753\) | − | 5.64230i | − | 0.205617i | ||||||
\(754\) | 6.89612 | + | 34.4806i | 0.251142 | + | 1.25571i | ||||
\(755\) | − | 15.5344i | − | 0.565356i | ||||||
\(756\) | 0.648285 | − | 2.56510i | 0.0235779 | − | 0.0932917i | ||||
\(757\) | 31.7843 | 1.15522 | 0.577610 | − | 0.816313i | \(-0.303986\pi\) | ||||
0.577610 | + | 0.816313i | \(0.303986\pi\) | |||||||
\(758\) | − | 20.3676i | − | 0.739786i | ||||||
\(759\) | −7.34480 | − | 7.34480i | −0.266599 | − | 0.266599i | ||||
\(760\) | 10.3810 | − | 10.3810i | 0.376557 | − | 0.376557i | ||||
\(761\) | −1.82886 | + | 1.82886i | −0.0662961 | + | 0.0662961i | −0.739477 | − | 0.673181i | \(-0.764927\pi\) |
0.673181 | + | 0.739477i | \(0.264927\pi\) | |||||||
\(762\) | −4.20603 | + | 4.20603i | −0.152368 | + | 0.152368i | ||||
\(763\) | −24.8557 | − | 41.6685i | −0.899836 | − | 1.50850i | ||||
\(764\) | 26.3837i | 0.954528i | ||||||||
\(765\) | −18.3647 | − | 18.3647i | −0.663977 | − | 0.663977i | ||||
\(766\) | 26.3215 | 0.951034 | ||||||||
\(767\) | −10.4560 | − | 52.2801i | −0.377545 | − | 1.88773i | ||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | 1.20162 | + | 1.20162i | 0.0433314 | + | 0.0433314i | 0.728440 | − | 0.685109i | \(-0.240245\pi\) |
−0.685109 | + | 0.728440i | \(0.740245\pi\) | |||||||
\(770\) | −19.2138 | + | 11.4612i | −0.692418 | + | 0.413034i | ||||
\(771\) | 25.0199i | 0.901070i | ||||||||
\(772\) | 2.86288 | − | 2.86288i | 0.103037 | − | 0.103037i | ||||
\(773\) | 2.61687 | + | 2.61687i | 0.0941224 | + | 0.0941224i | 0.752600 | − | 0.658478i | \(-0.228799\pi\) |
−0.658478 | + | 0.752600i | \(0.728799\pi\) | |||||||
\(774\) | 6.09696 | + | 6.09696i | 0.219151 | + | 0.219151i | ||||
\(775\) | −31.9591 | + | 31.9591i | −1.14800 | + | 1.14800i | ||||
\(776\) | 6.35293i | 0.228057i | ||||||||
\(777\) | −4.75736 | − | 7.97533i | −0.170669 | − | 0.286113i | ||||
\(778\) | 0.0762669 | + | 0.0762669i | 0.00273430 | + | 0.00273430i | ||||
\(779\) | − | 43.1494i | − | 1.54599i | ||||||
\(780\) | −12.8255 | + | 2.56510i | −0.459226 | + | 0.0918452i | ||||
\(781\) | 1.50331 | 0.0537927 | ||||||||
\(782\) | 22.5586 | + | 22.5586i | 0.806694 | + | 0.806694i | ||||
\(783\) | 9.75259i | 0.348529i | ||||||||
\(784\) | 6.15945 | + | 3.32583i | 0.219980 | + | 0.118780i | ||||
\(785\) | 29.2930 | − | 29.2930i | 1.04551 | − | 1.04551i | ||||
\(786\) | 0.0206886 | − | 0.0206886i | 0.000737938 | − | 0.000737938i | ||||
\(787\) | 23.2324 | − | 23.2324i | 0.828144 | − | 0.828144i | −0.159116 | − | 0.987260i | \(-0.550864\pi\) |
0.987260 | + | 0.159116i | \(0.0508644\pi\) | |||||||
\(788\) | 6.21338 | + | 6.21338i | 0.221343 | + | 0.221343i | ||||
\(789\) | − | 12.1525i | − | 0.432642i | ||||||
\(790\) | −43.6844 | −1.55422 | ||||||||
\(791\) | 8.22489 | − | 32.5438i | 0.292443 | − | 1.15712i | ||||
\(792\) | − | 2.33103i | − | 0.0828294i | ||||||
\(793\) | −21.4784 | − | 14.3189i | −0.762719 | − | 0.508479i | ||||
\(794\) | − | 26.7738i | − | 0.950167i | ||||||
\(795\) | 6.22489 | − | 6.22489i | 0.220774 | − | 0.220774i | ||||
\(796\) | 1.63799i | 0.0580572i | ||||||||
\(797\) | −33.6371 | −1.19149 | −0.595744 | − | 0.803174i | \(-0.703143\pi\) | ||||
−0.595744 | + | 0.803174i | \(0.703143\pi\) | |||||||
\(798\) | 10.3810 | + | 2.62361i | 0.367482 | + | 0.0928749i | ||||
\(799\) | 5.03618 | − | 5.03618i | 0.178167 | − | 0.178167i | ||||
\(800\) | −5.76961 | − | 5.76961i | −0.203986 | − | 0.203986i | ||||
\(801\) | −4.75044 | + | 4.75044i | −0.167849 | + | 0.167849i | ||||
\(802\) | 1.88174 | 0.0664467 | ||||||||
\(803\) | −8.18179 | −0.288729 | ||||||||
\(804\) | −4.53921 | + | 4.53921i | −0.160086 | + | 0.160086i | ||||
\(805\) | −21.9094 | − | 36.7294i | −0.772206 | − | 1.29454i | ||||
\(806\) | 11.0784 | − | 16.6176i | 0.390221 | − | 0.585331i | ||||
\(807\) | −19.9482 | −0.702211 | ||||||||
\(808\) | −2.51515 | − | 2.51515i | −0.0884827 | − | 0.0884827i | ||||
\(809\) | −20.3165 | −0.714289 | −0.357145 | − | 0.934049i | \(-0.616250\pi\) | ||||
−0.357145 | + | 0.934049i | \(0.616250\pi\) | |||||||
\(810\) | −3.62760 | −0.127461 | ||||||||
\(811\) | 11.7152 | + | 11.7152i | 0.411376 | + | 0.411376i | 0.882218 | − | 0.470842i | \(-0.156050\pi\) |
−0.470842 | + | 0.882218i | \(0.656050\pi\) | |||||||
\(812\) | −25.0164 | − | 6.32246i | −0.877902 | − | 0.221875i | ||||
\(813\) | −8.31432 | − | 8.31432i | −0.291596 | − | 0.291596i | ||||
\(814\) | −5.78540 | − | 5.78540i | −0.202778 | − | 0.202778i | ||||
\(815\) | 46.5630i | 1.63103i | ||||||||
\(816\) | 7.15945i | 0.250631i | ||||||||
\(817\) | −24.6744 | + | 24.6744i | −0.863249 | + | 0.863249i | ||||
\(818\) | −30.6239 | −1.07074 | ||||||||
\(819\) | −6.39872 | − | 7.07505i | −0.223590 | − | 0.247222i | ||||
\(820\) | −38.6776 | −1.35068 | ||||||||
\(821\) | 3.79529 | − | 3.79529i | 0.132457 | − | 0.132457i | −0.637770 | − | 0.770227i | \(-0.720143\pi\) |
0.770227 | + | 0.637770i | \(0.220143\pi\) | |||||||
\(822\) | 6.45602i | 0.225180i | ||||||||
\(823\) | 42.2235i | 1.47182i | 0.677079 | + | 0.735910i | \(0.263245\pi\) | ||||
−0.677079 | + | 0.735910i | \(0.736755\pi\) | |||||||
\(824\) | 6.93274 | + | 6.93274i | 0.241513 | + | 0.241513i | ||||
\(825\) | 13.4491 | + | 13.4491i | 0.468238 | + | 0.468238i | ||||
\(826\) | 37.9302 | + | 9.58622i | 1.31976 | + | 0.333547i | ||||
\(827\) | 8.55602 | + | 8.55602i | 0.297522 | + | 0.297522i | 0.840043 | − | 0.542520i | \(-0.182530\pi\) |
−0.542520 | + | 0.840043i | \(0.682530\pi\) | |||||||
\(828\) | 4.45602 | 0.154858 | ||||||||
\(829\) | −40.5026 | −1.40671 | −0.703356 | − | 0.710838i | \(-0.748316\pi\) | ||||
−0.703356 | + | 0.710838i | \(0.748316\pi\) | |||||||
\(830\) | −9.80695 | − | 9.80695i | −0.340404 | − | 0.340404i | ||||
\(831\) | 5.55696 | 0.192769 | ||||||||
\(832\) | 3.00000 | + | 2.00000i | 0.104006 | + | 0.0693375i | ||||
\(833\) | 44.0983 | + | 23.8111i | 1.52792 | + | 0.825006i | ||||
\(834\) | 8.97117 | − | 8.97117i | 0.310646 | − | 0.310646i | ||||
\(835\) | −17.0094 | −0.588633 | ||||||||
\(836\) | 9.43369 | 0.326271 | ||||||||
\(837\) | 3.91681 | − | 3.91681i | 0.135385 | − | 0.135385i | ||||
\(838\) | −2.41647 | − | 2.41647i | −0.0834757 | − | 0.0834757i | ||||
\(839\) | −13.3882 | + | 13.3882i | −0.462210 | + | 0.462210i | −0.899379 | − | 0.437169i | \(-0.855981\pi\) |
0.437169 | + | 0.899379i | \(0.355981\pi\) | |||||||
\(840\) | 2.35172 | − | 9.30514i | 0.0811419 | − | 0.321058i | ||||
\(841\) | 66.1131 | 2.27976 | ||||||||
\(842\) | 1.92617i | 0.0663801i | ||||||||
\(843\) | 11.4807 | − | 11.4807i | 0.395416 | − | 0.395416i | ||||
\(844\) | − | 0.622397i | − | 0.0214238i | ||||||
\(845\) | −17.9557 | + | 43.6067i | −0.617694 | + | 1.50011i | ||||
\(846\) | − | 0.994801i | − | 0.0342020i | ||||||
\(847\) | 14.2781 | + | 3.60856i | 0.490603 | + | 0.123991i | ||||
\(848\) | −2.42677 | −0.0833355 | ||||||||
\(849\) | 6.44735i | 0.221272i | ||||||||
\(850\) | −41.3072 | − | 41.3072i | −1.41683 | − | 1.41683i | ||||
\(851\) | 11.0595 | − | 11.0595i | 0.379113 | − | 0.379113i | ||||
\(852\) | −0.456023 | + | 0.456023i | −0.0156231 | + | 0.0156231i | ||||
\(853\) | −3.51211 | + | 3.51211i | −0.120252 | + | 0.120252i | −0.764672 | − | 0.644420i | \(-0.777099\pi\) |
0.644420 | + | 0.764672i | \(0.277099\pi\) | |||||||
\(854\) | 16.2677 | − | 9.70386i | 0.556671 | − | 0.332059i | ||||
\(855\) | − | 14.6809i | − | 0.502077i | ||||||
\(856\) | 0.235288 | + | 0.235288i | 0.00804198 | + | 0.00804198i | ||||
\(857\) | 24.3679 | 0.832391 | 0.416196 | − | 0.909275i | \(-0.363363\pi\) | ||||
0.416196 | + | 0.909275i | \(0.363363\pi\) | |||||||
\(858\) | −6.99308 | − | 4.66205i | −0.238740 | − | 0.159160i | ||||
\(859\) | − | 2.26749i | − | 0.0773658i | −0.999252 | − | 0.0386829i | \(-0.987684\pi\) | ||
0.999252 | − | 0.0386829i | \(-0.0123162\pi\) | |||||||
\(860\) | 22.1173 | + | 22.1173i | 0.754193 | + | 0.754193i | ||||
\(861\) | −14.4513 | − | 24.2264i | −0.492498 | − | 0.825632i | ||||
\(862\) | − | 15.7405i | − | 0.536123i | ||||||
\(863\) | −24.0154 | + | 24.0154i | −0.817494 | + | 0.817494i | −0.985744 | − | 0.168250i | \(-0.946188\pi\) |
0.168250 | + | 0.985744i | \(0.446188\pi\) | |||||||
\(864\) | 0.707107 | + | 0.707107i | 0.0240563 | + | 0.0240563i | ||||
\(865\) | 15.5407 | + | 15.5407i | 0.528399 | + | 0.528399i | ||||
\(866\) | −13.9896 | + | 13.9896i | −0.475386 | + | 0.475386i | ||||
\(867\) | 34.2578i | 1.16346i | ||||||||
\(868\) | 7.50780 | + | 12.5862i | 0.254831 | + | 0.427204i | ||||
\(869\) | −19.8490 | − | 19.8490i | −0.673333 | − | 0.673333i | ||||
\(870\) | 35.3785i | 1.19944i | ||||||||
\(871\) | 4.53921 | + | 22.6961i | 0.153805 | + | 0.769026i | ||||
\(872\) | 18.3384 | 0.621016 | ||||||||
\(873\) | 4.49220 | + | 4.49220i | 0.152038 | + | 0.152038i | ||||
\(874\) | 18.0336i | 0.609994i | ||||||||
\(875\) | 15.5344 | + | 26.0422i | 0.525160 | + | 0.880388i | ||||
\(876\) | 2.48191 | − | 2.48191i | 0.0838560 | − | 0.0838560i | ||||
\(877\) | −38.9474 | + | 38.9474i | −1.31516 | + | 1.31516i | −0.397601 | + | 0.917559i | \(0.630157\pi\) |
−0.917559 | + | 0.397601i | \(0.869843\pi\) | |||||||
\(878\) | 18.9327 | − | 18.9327i | 0.638949 | − | 0.638949i | ||||
\(879\) | −22.1703 | − | 22.1703i | −0.747785 | − | 0.747785i | ||||
\(880\) | − | 8.45602i | − | 0.285052i | ||||||
\(881\) | −19.7569 | −0.665627 | −0.332813 | − | 0.942993i | \(-0.607998\pi\) | ||||
−0.332813 | + | 0.942993i | \(0.607998\pi\) | |||||||
\(882\) | 6.70711 | − | 2.00368i | 0.225840 | − | 0.0674673i | ||||
\(883\) | − | 19.9027i | − | 0.669779i | −0.942257 | − | 0.334889i | \(-0.891301\pi\) | ||
0.942257 | − | 0.334889i | \(-0.108699\pi\) | |||||||
\(884\) | 21.4784 | + | 14.3189i | 0.722395 | + | 0.481597i | ||||
\(885\) | − | 53.6414i | − | 1.80314i | ||||||
\(886\) | 20.0526 | − | 20.0526i | 0.673682 | − | 0.673682i | ||||
\(887\) | 1.87156i | 0.0628409i | 0.999506 | + | 0.0314204i | \(0.0100031\pi\) | ||||
−0.999506 | + | 0.0314204i | \(0.989997\pi\) | |||||||
\(888\) | 3.50995 | 0.117786 | ||||||||
\(889\) | −15.2578 | − | 3.85614i | −0.511729 | − | 0.129331i | ||||
\(890\) | −17.2327 | + | 17.2327i | −0.577641 | + | 0.577641i | ||||
\(891\) | −1.64828 | − | 1.64828i | −0.0552196 | − | 0.0552196i | ||||
\(892\) | −15.5615 | + | 15.5615i | −0.521039 | + | 0.521039i | ||||
\(893\) | 4.02597 | 0.134724 | ||||||||
\(894\) | 18.9534 | 0.633897 | ||||||||
\(895\) | −34.7749 | + | 34.7749i | −1.16240 | + | 1.16240i | ||||
\(896\) | −2.27220 | + | 1.35539i | −0.0759090 | + | 0.0452805i | ||||
\(897\) | 8.91205 | − | 13.3681i | 0.297565 | − | 0.446347i | ||||
\(898\) | 3.23633 | 0.107998 | ||||||||
\(899\) | −38.1991 | − | 38.1991i | −1.27401 | − | 1.27401i | ||||
\(900\) | −8.15945 | −0.271982 | ||||||||
\(901\) | −17.3743 | −0.578822 | ||||||||
\(902\) | −17.5741 | − | 17.5741i | −0.585154 | − | 0.585154i | ||||
\(903\) | −5.58977 | + | 22.1173i | −0.186016 | + | 0.736017i | ||||
\(904\) | 8.97117 | + | 8.97117i | 0.298377 | + | 0.298377i | ||||
\(905\) | 37.3973 | + | 37.3973i | 1.24313 | + | 1.24313i | ||||
\(906\) | 4.28230i | 0.142270i | ||||||||
\(907\) | − | 35.5637i | − | 1.18087i | −0.807084 | − | 0.590437i | \(-0.798956\pi\) | ||
0.807084 | − | 0.590437i | \(-0.201044\pi\) | |||||||
\(908\) | 1.15945 | − | 1.15945i | 0.0384778 | − | 0.0384778i | ||||
\(909\) | −3.55696 | −0.117977 | ||||||||
\(910\) | −23.2120 | − | 25.6654i | −0.769470 | − | 0.850801i | ||||
\(911\) | −19.6150 | −0.649873 | −0.324937 | − | 0.945736i | \(-0.605343\pi\) | ||||
−0.324937 | + | 0.945736i | \(0.605343\pi\) | |||||||
\(912\) | −2.86167 | + | 2.86167i | −0.0947593 | + | 0.0947593i | ||||
\(913\) | − | 8.91205i | − | 0.294946i | ||||||
\(914\) | 8.03402i | 0.265742i | ||||||||
\(915\) | −18.3647 | − | 18.3647i | −0.607118 | − | 0.607118i | ||||
\(916\) | −4.15945 | − | 4.15945i | −0.137432 | − | 0.137432i | ||||
\(917\) | 0.0750499 | + | 0.0189676i | 0.00247837 | + | 0.000626365i | ||||
\(918\) | 5.06250 | + | 5.06250i | 0.167087 | + | 0.167087i | ||||
\(919\) | −34.3682 | −1.13370 | −0.566852 | − | 0.823820i | \(-0.691839\pi\) | ||||
−0.566852 | + | 0.823820i | \(0.691839\pi\) | |||||||
\(920\) | 16.1647 | 0.532933 | ||||||||
\(921\) | 5.54613 | + | 5.54613i | 0.182751 | + | 0.182751i | ||||
\(922\) | −22.1965 | −0.731003 | ||||||||
\(923\) | 0.456023 | + | 2.28012i | 0.0150102 | + | 0.0750509i | ||||
\(924\) | 5.29657 | − | 3.15945i | 0.174244 | − | 0.103938i | ||||
\(925\) | −20.2510 | + | 20.2510i | −0.665850 | + | 0.665850i | ||||
\(926\) | −15.8849 | −0.522012 | ||||||||
\(927\) | 9.80437 | 0.322018 | ||||||||
\(928\) | 6.89612 | − | 6.89612i | 0.226376 | − | 0.226376i | ||||
\(929\) | −21.5546 | − | 21.5546i | −0.707184 | − | 0.707184i | 0.258758 | − | 0.965942i | \(-0.416687\pi\) |
−0.965942 | + | 0.258758i | \(0.916687\pi\) | |||||||
\(930\) | 14.2086 | − | 14.2086i | 0.465919 | − | 0.465919i | ||||
\(931\) | 8.10890 | + | 27.1437i | 0.265758 | + | 0.889599i | ||||
\(932\) | 10.7974 | 0.353682 | ||||||||
\(933\) | − | 15.6648i | − | 0.512843i | ||||||
\(934\) | 1.99402 | − | 1.99402i | 0.0652462 | − | 0.0652462i | ||||
\(935\) | − | 60.5405i | − | 1.97989i | ||||||
\(936\) | 3.53553 | − | 0.707107i | 0.115563 | − | 0.0231125i | ||||
\(937\) | 15.9071i | 0.519661i | 0.965654 | + | 0.259831i | \(0.0836667\pi\) | ||||
−0.965654 | + | 0.259831i | \(0.916333\pi\) | |||||||
\(938\) | −16.4664 | − | 4.16161i | −0.537648 | − | 0.135881i | ||||
\(939\) | 2.58640 | 0.0844039 | ||||||||
\(940\) | − | 3.60874i | − | 0.117704i | ||||||
\(941\) | −10.1348 | − | 10.1348i | −0.330384 | − | 0.330384i | 0.522348 | − | 0.852732i | \(-0.325056\pi\) |
−0.852732 | + | 0.522348i | \(0.825056\pi\) | |||||||
\(942\) | −8.07505 | + | 8.07505i | −0.263099 | + | 0.263099i | ||||
\(943\) | 33.5949 | − | 33.5949i | 1.09400 | − | 1.09400i | ||||
\(944\) | −10.4560 | + | 10.4560i | −0.340315 | + | 0.340315i | ||||
\(945\) | −4.91681 | − | 8.24264i | −0.159944 | − | 0.268133i | ||||
\(946\) | 20.0990i | 0.653476i | ||||||||
\(947\) | 8.77848 | + | 8.77848i | 0.285262 | + | 0.285262i | 0.835203 | − | 0.549941i | \(-0.185350\pi\) |
−0.549941 | + | 0.835203i | \(0.685350\pi\) | |||||||
\(948\) | 12.0422 | 0.391114 | ||||||||
\(949\) | −2.48191 | − | 12.4096i | −0.0805662 | − | 0.402831i | ||||
\(950\) | − | 33.0214i | − | 1.07136i | ||||||
\(951\) | 5.33059 | + | 5.33059i | 0.172856 | + | 0.172856i | ||||
\(952\) | −16.2677 | + | 9.70386i | −0.527241 | + | 0.314504i | ||||
\(953\) | − | 41.5076i | − | 1.34456i | −0.740295 | − | 0.672282i | \(-0.765314\pi\) | ||
0.740295 | − | 0.672282i | \(-0.234686\pi\) | |||||||
\(954\) | −1.71598 | + | 1.71598i | −0.0555570 | + | 0.0555570i | ||||
\(955\) | 67.6767 | + | 67.6767i | 2.18997 | + | 2.18997i | ||||
\(956\) | −16.1501 | − | 16.1501i | −0.522332 | − | 0.522332i | ||||
\(957\) | −16.0750 | + | 16.0750i | −0.519633 | + | 0.519633i | ||||
\(958\) | 32.5914i | 1.05298i | ||||||||
\(959\) | −14.6694 | + | 8.75044i | −0.473700 | + | 0.282566i | ||||
\(960\) | 2.56510 | + | 2.56510i | 0.0827882 | + | 0.0827882i | ||||
\(961\) | − | 0.317151i | − | 0.0102307i | ||||||
\(962\) | 7.01990 | − | 10.5299i | 0.226331 | − | 0.339496i | ||||
\(963\) | 0.332748 | 0.0107226 | ||||||||
\(964\) | −3.45602 | − | 3.45602i | −0.111311 | − | 0.111311i | ||||
\(965\) | − | 14.6872i | − | 0.472796i | ||||||
\(966\) | 6.03966 | + | 10.1250i | 0.194323 | + | 0.325766i | ||||
\(967\) | −14.2124 | + | 14.2124i | −0.457041 | + | 0.457041i | −0.897683 | − | 0.440642i | \(-0.854751\pi\) |
0.440642 | + | 0.897683i | \(0.354751\pi\) | |||||||
\(968\) | −3.93598 | + | 3.93598i | −0.126507 | + | 0.126507i | ||||
\(969\) | −20.4880 | + | 20.4880i | −0.658169 | + | 0.658169i | ||||
\(970\) | 16.2959 | + | 16.2959i | 0.523230 | + | 0.523230i | ||||
\(971\) | − | 48.8259i | − | 1.56690i | −0.621457 | − | 0.783448i | \(-0.713459\pi\) | ||
0.621457 | − | 0.783448i | \(-0.286541\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 32.5438 | + | 8.22489i | 1.04331 | + | 0.263678i | ||||
\(974\) | − | 37.2650i | − | 1.19405i | ||||||
\(975\) | −16.3189 | + | 24.4784i | −0.522623 | + | 0.783935i | ||||
\(976\) | 7.15945i | 0.229169i | ||||||||
\(977\) | −28.0635 | + | 28.0635i | −0.897832 | + | 0.897832i | −0.995244 | − | 0.0974119i | \(-0.968944\pi\) |
0.0974119 | + | 0.995244i | \(0.468944\pi\) | |||||||
\(978\) | − | 12.8358i | − | 0.410443i | ||||||
\(979\) | −15.6602 | −0.500501 | ||||||||
\(980\) | 24.3307 | − | 7.26853i | 0.777215 | − | 0.232185i | ||||
\(981\) | 12.9672 | − | 12.9672i | 0.414011 | − | 0.414011i | ||||
\(982\) | −8.33103 | − | 8.33103i | −0.265854 | − | 0.265854i | ||||
\(983\) | 24.2698 | − | 24.2698i | 0.774087 | − | 0.774087i | −0.204731 | − | 0.978818i | \(-0.565632\pi\) |
0.978818 | + | 0.204731i | \(0.0656320\pi\) | |||||||
\(984\) | 10.6621 | 0.339894 | ||||||||
\(985\) | 31.8759 | 1.01565 | ||||||||
\(986\) | 49.3725 | − | 49.3725i | 1.57234 | − | 1.57234i | ||||
\(987\) | 2.26039 | − | 1.34834i | 0.0719490 | − | 0.0429183i | ||||
\(988\) | 2.86167 | + | 14.3083i | 0.0910418 | + | 0.455209i | ||||
\(989\) | −38.4216 | −1.22174 | ||||||||
\(990\) | −5.97931 | − | 5.97931i | −0.190035 | − | 0.190035i | ||||
\(991\) | 46.7432 | 1.48485 | 0.742424 | − | 0.669930i | \(-0.233676\pi\) | ||||
0.742424 | + | 0.669930i | \(0.233676\pi\) | |||||||
\(992\) | −5.53921 | −0.175870 | ||||||||
\(993\) | 17.3927 | + | 17.3927i | 0.551942 | + | 0.551942i | ||||
\(994\) | −1.65427 | − | 0.418088i | −0.0524702 | − | 0.0132609i | ||||
\(995\) | 4.20162 | + | 4.20162i | 0.133200 | + | 0.133200i | ||||
\(996\) | 2.70343 | + | 2.70343i | 0.0856615 | + | 0.0856615i | ||||
\(997\) | 30.1568i | 0.955077i | 0.878611 | + | 0.477538i | \(0.158471\pi\) | ||||
−0.878611 | + | 0.477538i | \(0.841529\pi\) | |||||||
\(998\) | 36.2058i | 1.14607i | ||||||||
\(999\) | 2.48191 | − | 2.48191i | 0.0785242 | − | 0.0785242i |
(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 | 546.2.o.a.265.3 | ✓ | 8 | |
3.2 | odd | 2 | 1638.2.x.d.811.2 | 8 | |||
7.6 | odd | 2 | 546.2.o.d.265.4 | yes | 8 | ||
13.8 | odd | 4 | 546.2.o.d.307.4 | yes | 8 | ||
21.20 | even | 2 | 1638.2.x.b.811.1 | 8 | |||
39.8 | even | 4 | 1638.2.x.b.307.1 | 8 | |||
91.34 | even | 4 | inner | 546.2.o.a.307.3 | yes | 8 | |
273.125 | odd | 4 | 1638.2.x.d.307.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.o.a.265.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
546.2.o.a.307.3 | yes | 8 | 91.34 | even | 4 | inner | |
546.2.o.d.265.4 | yes | 8 | 7.6 | odd | 2 | ||
546.2.o.d.307.4 | yes | 8 | 13.8 | odd | 4 | ||
1638.2.x.b.307.1 | 8 | 39.8 | even | 4 | |||
1638.2.x.b.811.1 | 8 | 21.20 | even | 2 | |||
1638.2.x.d.307.2 | 8 | 273.125 | odd | 4 | |||
1638.2.x.d.811.2 | 8 | 3.2 | odd | 2 |