Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(121,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.i (of order \(3\), 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: | \(5.03057532734\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 12.0.91830304992969.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2x^{11} + x^{10} + 4x^{9} - 7x^{8} + x^{7} + 7x^{6} + 2x^{5} - 28x^{4} + 32x^{3} + 16x^{2} - 64x + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 121.2 | ||
Root | \(0.683706 - 1.23796i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.121 |
Dual form | 630.2.i.f.151.2 |
$q$-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 \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.554872 | − | 1.64077i | −0.320356 | − | 0.947297i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | 0.554872 | + | 1.64077i | 0.226526 | + | 0.669840i | ||||
\(7\) | 2.32383 | + | 1.26483i | 0.878326 | + | 0.478062i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.38423 | + | 1.82083i | −0.794744 | + | 0.606944i | ||||
\(10\) | 0.500000 | + | 0.866025i | 0.158114 | + | 0.273861i | ||||
\(11\) | −1.25470 | + | 2.17320i | −0.378306 | + | 0.655245i | −0.990816 | − | 0.135218i | \(-0.956827\pi\) |
0.612510 | + | 0.790463i | \(0.290160\pi\) | |||||||
\(12\) | −0.554872 | − | 1.64077i | −0.160178 | − | 0.473649i | ||||
\(13\) | −2.97905 | + | 5.15987i | −0.826240 | + | 1.43109i | 0.0747277 | + | 0.997204i | \(0.476191\pi\) |
−0.900968 | + | 0.433886i | \(0.857142\pi\) | |||||||
\(14\) | −2.32383 | − | 1.26483i | −0.621070 | − | 0.338041i | ||||
\(15\) | −1.14351 | + | 1.30092i | −0.295253 | + | 0.335895i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.65781 | − | 4.60347i | −0.644615 | − | 1.11651i | −0.984390 | − | 0.175999i | \(-0.943684\pi\) |
0.339776 | − | 0.940507i | \(-0.389649\pi\) | |||||||
\(18\) | 2.38423 | − | 1.82083i | 0.561969 | − | 0.429174i | ||||
\(19\) | −2.97905 | + | 5.15987i | −0.683441 | + | 1.18375i | 0.290483 | + | 0.956880i | \(0.406184\pi\) |
−0.973924 | + | 0.226875i | \(0.927149\pi\) | |||||||
\(20\) | −0.500000 | − | 0.866025i | −0.111803 | − | 0.193649i | ||||
\(21\) | 0.785868 | − | 4.51469i | 0.171491 | − | 0.985186i | ||||
\(22\) | 1.25470 | − | 2.17320i | 0.267503 | − | 0.463328i | ||||
\(23\) | −0.678764 | − | 1.17565i | −0.141532 | − | 0.245141i | 0.786542 | − | 0.617537i | \(-0.211869\pi\) |
−0.928074 | + | 0.372397i | \(0.878536\pi\) | |||||||
\(24\) | 0.554872 | + | 1.64077i | 0.113263 | + | 0.334920i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 2.97905 | − | 5.15987i | 0.584240 | − | 1.01193i | ||||
\(27\) | 4.31051 | + | 2.90164i | 0.829558 | + | 0.558421i | ||||
\(28\) | 2.32383 | + | 1.26483i | 0.439163 | + | 0.239031i | ||||
\(29\) | 3.10212 | + | 5.37303i | 0.576049 | + | 0.997747i | 0.995927 | + | 0.0901657i | \(0.0287397\pi\) |
−0.419878 | + | 0.907581i | \(0.637927\pi\) | |||||||
\(30\) | 1.14351 | − | 1.30092i | 0.208775 | − | 0.237514i | ||||
\(31\) | −6.16523 | −1.10731 | −0.553654 | − | 0.832747i | \(-0.686767\pi\) | ||||
−0.553654 | + | 0.832747i | \(0.686767\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 4.26192 | + | 0.852819i | 0.741904 | + | 0.148457i | ||||
\(34\) | 2.65781 | + | 4.60347i | 0.455811 | + | 0.789489i | ||||
\(35\) | −0.0665372 | − | 2.64491i | −0.0112468 | − | 0.447072i | ||||
\(36\) | −2.38423 | + | 1.82083i | −0.397372 | + | 0.303472i | ||||
\(37\) | 2.58315 | − | 4.47415i | 0.424668 | − | 0.735546i | −0.571722 | − | 0.820448i | \(-0.693724\pi\) |
0.996389 | + | 0.0849016i | \(0.0270576\pi\) | |||||||
\(38\) | 2.97905 | − | 5.15987i | 0.483266 | − | 0.837041i | ||||
\(39\) | 10.1191 | + | 2.02486i | 1.62036 | + | 0.324237i | ||||
\(40\) | 0.500000 | + | 0.866025i | 0.0790569 | + | 0.136931i | ||||
\(41\) | −4.43192 | + | 7.67631i | −0.692149 | + | 1.19884i | 0.278983 | + | 0.960296i | \(0.410003\pi\) |
−0.971132 | + | 0.238542i | \(0.923331\pi\) | |||||||
\(42\) | −0.785868 | + | 4.51469i | −0.121262 | + | 0.696632i | ||||
\(43\) | 0.977900 | + | 1.69377i | 0.149128 | + | 0.258298i | 0.930906 | − | 0.365260i | \(-0.119020\pi\) |
−0.781777 | + | 0.623558i | \(0.785687\pi\) | |||||||
\(44\) | −1.25470 | + | 2.17320i | −0.189153 | + | 0.327623i | ||||
\(45\) | 2.76900 | + | 1.15439i | 0.412779 | + | 0.172086i | ||||
\(46\) | 0.678764 | + | 1.17565i | 0.100078 | + | 0.173341i | ||||
\(47\) | −2.04420 | −0.298177 | −0.149089 | − | 0.988824i | \(-0.547634\pi\) | ||||
−0.149089 | + | 0.988824i | \(0.547634\pi\) | |||||||
\(48\) | −0.554872 | − | 1.64077i | −0.0800889 | − | 0.236824i | ||||
\(49\) | 3.80039 | + | 5.87852i | 0.542913 | + | 0.839789i | ||||
\(50\) | 0.500000 | − | 0.866025i | 0.0707107 | − | 0.122474i | ||||
\(51\) | −6.07847 | + | 6.91519i | −0.851157 | + | 0.968321i | ||||
\(52\) | −2.97905 | + | 5.15987i | −0.413120 | + | 0.715545i | ||||
\(53\) | −0.179671 | − | 0.311199i | −0.0246796 | − | 0.0427464i | 0.853422 | − | 0.521221i | \(-0.174523\pi\) |
−0.878101 | + | 0.478475i | \(0.841190\pi\) | |||||||
\(54\) | −4.31051 | − | 2.90164i | −0.586586 | − | 0.394863i | ||||
\(55\) | 2.50940 | 0.338367 | ||||||||
\(56\) | −2.32383 | − | 1.26483i | −0.310535 | − | 0.169021i | ||||
\(57\) | 10.1191 | + | 2.02486i | 1.34031 | + | 0.268199i | ||||
\(58\) | −3.10212 | − | 5.37303i | −0.407328 | − | 0.705513i | ||||
\(59\) | −2.86874 | −0.373478 | −0.186739 | − | 0.982410i | \(-0.559792\pi\) | ||||
−0.186739 | + | 0.982410i | \(0.559792\pi\) | |||||||
\(60\) | −1.14351 | + | 1.30092i | −0.147626 | + | 0.167948i | ||||
\(61\) | 3.82899 | 0.490252 | 0.245126 | − | 0.969491i | \(-0.421171\pi\) | ||||
0.245126 | + | 0.969491i | \(0.421171\pi\) | |||||||
\(62\) | 6.16523 | 0.782985 | ||||||||
\(63\) | −7.84361 | + | 1.21565i | −0.988202 | + | 0.153157i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.95810 | 0.739012 | ||||||||
\(66\) | −4.26192 | − | 0.852819i | −0.524606 | − | 0.104975i | ||||
\(67\) | 12.9461 | 1.58161 | 0.790806 | − | 0.612066i | \(-0.209661\pi\) | ||||
0.790806 | + | 0.612066i | \(0.209661\pi\) | |||||||
\(68\) | −2.65781 | − | 4.60347i | −0.322307 | − | 0.558253i | ||||
\(69\) | −1.55235 | + | 1.76603i | −0.186880 | + | 0.212605i | ||||
\(70\) | 0.0665372 | + | 2.64491i | 0.00795272 | + | 0.316128i | ||||
\(71\) | 3.52556 | 0.418407 | 0.209203 | − | 0.977872i | \(-0.432913\pi\) | ||||
0.209203 | + | 0.977872i | \(0.432913\pi\) | |||||||
\(72\) | 2.38423 | − | 1.82083i | 0.280985 | − | 0.214587i | ||||
\(73\) | 5.60063 | + | 9.70058i | 0.655504 | + | 1.13537i | 0.981767 | + | 0.190088i | \(0.0608772\pi\) |
−0.326263 | + | 0.945279i | \(0.605789\pi\) | |||||||
\(74\) | −2.58315 | + | 4.47415i | −0.300285 | + | 0.520110i | ||||
\(75\) | 1.69838 | + | 0.339850i | 0.196112 | + | 0.0392425i | ||||
\(76\) | −2.97905 | + | 5.15987i | −0.341721 | + | 0.591877i | ||||
\(77\) | −5.66445 | + | 3.46317i | −0.645524 | + | 0.394665i | ||||
\(78\) | −10.1191 | − | 2.02486i | −1.14577 | − | 0.229270i | ||||
\(79\) | −14.7994 | −1.66506 | −0.832530 | − | 0.553980i | \(-0.813108\pi\) | ||||
−0.832530 | + | 0.553980i | \(0.813108\pi\) | |||||||
\(80\) | −0.500000 | − | 0.866025i | −0.0559017 | − | 0.0968246i | ||||
\(81\) | 2.36914 | − | 8.68258i | 0.263237 | − | 0.964731i | ||||
\(82\) | 4.43192 | − | 7.67631i | 0.489423 | − | 0.847706i | ||||
\(83\) | −2.54006 | − | 4.39951i | −0.278808 | − | 0.482909i | 0.692281 | − | 0.721628i | \(-0.256606\pi\) |
−0.971089 | + | 0.238719i | \(0.923273\pi\) | |||||||
\(84\) | 0.785868 | − | 4.51469i | 0.0857453 | − | 0.492593i | ||||
\(85\) | −2.65781 | + | 4.60347i | −0.288280 | + | 0.499316i | ||||
\(86\) | −0.977900 | − | 1.69377i | −0.105450 | − | 0.182644i | ||||
\(87\) | 7.09461 | − | 8.07120i | 0.760622 | − | 0.865324i | ||||
\(88\) | 1.25470 | − | 2.17320i | 0.133751 | − | 0.231664i | ||||
\(89\) | −0.367362 | + | 0.636290i | −0.0389403 | + | 0.0674466i | −0.884839 | − | 0.465897i | \(-0.845732\pi\) |
0.845898 | + | 0.533344i | \(0.179065\pi\) | |||||||
\(90\) | −2.76900 | − | 1.15439i | −0.291879 | − | 0.121683i | ||||
\(91\) | −13.4492 | + | 8.22266i | −1.40986 | + | 0.861969i | ||||
\(92\) | −0.678764 | − | 1.17565i | −0.0707660 | − | 0.122570i | ||||
\(93\) | 3.42092 | + | 10.1157i | 0.354733 | + | 1.04895i | ||||
\(94\) | 2.04420 | 0.210843 | ||||||||
\(95\) | 5.95810 | 0.611288 | ||||||||
\(96\) | 0.554872 | + | 1.64077i | 0.0566314 | + | 0.167460i | ||||
\(97\) | −6.19076 | − | 10.7227i | −0.628576 | − | 1.08873i | −0.987838 | − | 0.155489i | \(-0.950305\pi\) |
0.359261 | − | 0.933237i | \(-0.383029\pi\) | |||||||
\(98\) | −3.80039 | − | 5.87852i | −0.383897 | − | 0.593821i | ||||
\(99\) | −0.965543 | − | 7.46602i | −0.0970407 | − | 0.750363i | ||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | −4.02012 | + | 6.96305i | −0.400017 | + | 0.692849i | −0.993727 | − | 0.111829i | \(-0.964329\pi\) |
0.593711 | + | 0.804679i | \(0.297662\pi\) | |||||||
\(102\) | 6.07847 | − | 6.91519i | 0.601859 | − | 0.684706i | ||||
\(103\) | −5.60483 | − | 9.70785i | −0.552260 | − | 0.956543i | −0.998111 | − | 0.0614356i | \(-0.980432\pi\) |
0.445851 | − | 0.895107i | \(-0.352901\pi\) | |||||||
\(104\) | 2.97905 | − | 5.15987i | 0.292120 | − | 0.505967i | ||||
\(105\) | −4.30277 | + | 1.57676i | −0.419907 | + | 0.153876i | ||||
\(106\) | 0.179671 | + | 0.311199i | 0.0174511 | + | 0.0302263i | ||||
\(107\) | 3.76525 | − | 6.52160i | 0.364000 | − | 0.630467i | −0.624615 | − | 0.780933i | \(-0.714744\pi\) |
0.988615 | + | 0.150466i | \(0.0480774\pi\) | |||||||
\(108\) | 4.31051 | + | 2.90164i | 0.414779 | + | 0.279211i | ||||
\(109\) | 5.59671 | + | 9.69378i | 0.536067 | + | 0.928496i | 0.999111 | + | 0.0421601i | \(0.0134240\pi\) |
−0.463044 | + | 0.886335i | \(0.653243\pi\) | |||||||
\(110\) | −2.50940 | −0.239262 | ||||||||
\(111\) | −8.77436 | − | 1.75577i | −0.832826 | − | 0.166650i | ||||
\(112\) | 2.32383 | + | 1.26483i | 0.219581 | + | 0.119516i | ||||
\(113\) | −5.83876 | + | 10.1130i | −0.549264 | + | 0.951354i | 0.449061 | + | 0.893501i | \(0.351759\pi\) |
−0.998325 | + | 0.0578524i | \(0.981575\pi\) | |||||||
\(114\) | −10.1191 | − | 2.02486i | −0.947744 | − | 0.189646i | ||||
\(115\) | −0.678764 | + | 1.17565i | −0.0632950 | + | 0.109630i | ||||
\(116\) | 3.10212 | + | 5.37303i | 0.288025 | + | 0.498873i | ||||
\(117\) | −2.29250 | − | 17.7267i | −0.211942 | − | 1.63883i | ||||
\(118\) | 2.86874 | 0.264089 | ||||||||
\(119\) | −0.353687 | − | 14.0594i | −0.0324225 | − | 1.28882i | ||||
\(120\) | 1.14351 | − | 1.30092i | 0.104388 | − | 0.118757i | ||||
\(121\) | 2.35146 | + | 4.07285i | 0.213769 | + | 0.370259i | ||||
\(122\) | −3.82899 | −0.346661 | ||||||||
\(123\) | 15.0542 | + | 3.01237i | 1.35739 | + | 0.271617i | ||||
\(124\) | −6.16523 | −0.553654 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 7.84361 | − | 1.21565i | 0.698764 | − | 0.108299i | ||||
\(127\) | −1.08717 | −0.0964710 | −0.0482355 | − | 0.998836i | \(-0.515360\pi\) | ||||
−0.0482355 | + | 0.998836i | \(0.515360\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 2.23648 | − | 2.54433i | 0.196911 | − | 0.224016i | ||||
\(130\) | −5.95810 | −0.522560 | ||||||||
\(131\) | −4.30124 | − | 7.44996i | −0.375801 | − | 0.650906i | 0.614646 | − | 0.788803i | \(-0.289299\pi\) |
−0.990447 | + | 0.137897i | \(0.955966\pi\) | |||||||
\(132\) | 4.26192 | + | 0.852819i | 0.370952 | + | 0.0742283i | ||||
\(133\) | −13.4492 | + | 8.22266i | −1.16619 | + | 0.712995i | ||||
\(134\) | −12.9461 | −1.11837 | ||||||||
\(135\) | 0.357641 | − | 5.18383i | 0.0307809 | − | 0.446153i | ||||
\(136\) | 2.65781 | + | 4.60347i | 0.227906 | + | 0.394744i | ||||
\(137\) | 1.02295 | − | 1.77180i | 0.0873966 | − | 0.151375i | −0.819013 | − | 0.573774i | \(-0.805479\pi\) |
0.906410 | + | 0.422399i | \(0.138812\pi\) | |||||||
\(138\) | 1.55235 | − | 1.76603i | 0.132144 | − | 0.150335i | ||||
\(139\) | 5.44268 | − | 9.42700i | 0.461642 | − | 0.799588i | −0.537401 | − | 0.843327i | \(-0.680594\pi\) |
0.999043 | + | 0.0437392i | \(0.0139270\pi\) | |||||||
\(140\) | −0.0665372 | − | 2.64491i | −0.00562342 | − | 0.223536i | ||||
\(141\) | 1.13427 | + | 3.35406i | 0.0955228 | + | 0.282463i | ||||
\(142\) | −3.52556 | −0.295858 | ||||||||
\(143\) | −7.47562 | − | 12.9482i | −0.625143 | − | 1.08278i | ||||
\(144\) | −2.38423 | + | 1.82083i | −0.198686 | + | 0.151736i | ||||
\(145\) | 3.10212 | − | 5.37303i | 0.257617 | − | 0.446206i | ||||
\(146\) | −5.60063 | − | 9.70058i | −0.463512 | − | 0.802825i | ||||
\(147\) | 7.53656 | − | 9.49738i | 0.621605 | − | 0.783331i | ||||
\(148\) | 2.58315 | − | 4.47415i | 0.212334 | − | 0.367773i | ||||
\(149\) | 0.250077 | + | 0.433146i | 0.0204871 | + | 0.0354847i | 0.876087 | − | 0.482153i | \(-0.160145\pi\) |
−0.855600 | + | 0.517637i | \(0.826812\pi\) | |||||||
\(150\) | −1.69838 | − | 0.339850i | −0.138672 | − | 0.0277486i | ||||
\(151\) | 8.28820 | − | 14.3556i | 0.674484 | − | 1.16824i | −0.302135 | − | 0.953265i | \(-0.597699\pi\) |
0.976619 | − | 0.214976i | \(-0.0689672\pi\) | |||||||
\(152\) | 2.97905 | − | 5.15987i | 0.241633 | − | 0.418521i | ||||
\(153\) | 14.7190 | + | 6.13631i | 1.18996 | + | 0.496091i | ||||
\(154\) | 5.66445 | − | 3.46317i | 0.456454 | − | 0.279070i | ||||
\(155\) | 3.08262 | + | 5.33925i | 0.247602 | + | 0.428859i | ||||
\(156\) | 10.1191 | + | 2.02486i | 0.810179 | + | 0.162119i | ||||
\(157\) | −1.10586 | −0.0882570 | −0.0441285 | − | 0.999026i | \(-0.514051\pi\) | ||||
−0.0441285 | + | 0.999026i | \(0.514051\pi\) | |||||||
\(158\) | 14.7994 | 1.17738 | ||||||||
\(159\) | −0.410910 | + | 0.467473i | −0.0325873 | + | 0.0370730i | ||||
\(160\) | 0.500000 | + | 0.866025i | 0.0395285 | + | 0.0684653i | ||||
\(161\) | −0.0903261 | − | 3.59054i | −0.00711870 | − | 0.282975i | ||||
\(162\) | −2.36914 | + | 8.68258i | −0.186137 | + | 0.682168i | ||||
\(163\) | −3.44888 | + | 5.97364i | −0.270137 | + | 0.467892i | −0.968897 | − | 0.247465i | \(-0.920402\pi\) |
0.698759 | + | 0.715357i | \(0.253736\pi\) | |||||||
\(164\) | −4.43192 | + | 7.67631i | −0.346075 | + | 0.599419i | ||||
\(165\) | −1.39240 | − | 4.11734i | −0.108398 | − | 0.320534i | ||||
\(166\) | 2.54006 | + | 4.39951i | 0.197147 | + | 0.341468i | ||||
\(167\) | −6.61206 | + | 11.4524i | −0.511657 | + | 0.886215i | 0.488252 | + | 0.872703i | \(0.337635\pi\) |
−0.999909 | + | 0.0135125i | \(0.995699\pi\) | |||||||
\(168\) | −0.785868 | + | 4.51469i | −0.0606311 | + | 0.348316i | ||||
\(169\) | −11.2495 | − | 19.4847i | −0.865345 | − | 1.49882i | ||||
\(170\) | 2.65781 | − | 4.60347i | 0.203845 | − | 0.353070i | ||||
\(171\) | −2.29250 | − | 17.7267i | −0.175312 | − | 1.35559i | ||||
\(172\) | 0.977900 | + | 1.69377i | 0.0745642 | + | 0.129149i | ||||
\(173\) | −15.2751 | −1.16135 | −0.580673 | − | 0.814137i | \(-0.697210\pi\) | ||||
−0.580673 | + | 0.814137i | \(0.697210\pi\) | |||||||
\(174\) | −7.09461 | + | 8.07120i | −0.537841 | + | 0.611876i | ||||
\(175\) | −2.25729 | + | 1.38008i | −0.170635 | + | 0.104324i | ||||
\(176\) | −1.25470 | + | 2.17320i | −0.0945765 | + | 0.163811i | ||||
\(177\) | 1.59178 | + | 4.70693i | 0.119646 | + | 0.353795i | ||||
\(178\) | 0.367362 | − | 0.636290i | 0.0275350 | − | 0.0476919i | ||||
\(179\) | −0.232599 | − | 0.402873i | −0.0173853 | − | 0.0301121i | 0.857202 | − | 0.514981i | \(-0.172201\pi\) |
−0.874587 | + | 0.484868i | \(0.838868\pi\) | |||||||
\(180\) | 2.76900 | + | 1.15439i | 0.206389 | + | 0.0860432i | ||||
\(181\) | 26.1282 | 1.94209 | 0.971046 | − | 0.238892i | \(-0.0767841\pi\) | ||||
0.971046 | + | 0.238892i | \(0.0767841\pi\) | |||||||
\(182\) | 13.4492 | − | 8.22266i | 0.996920 | − | 0.609504i | ||||
\(183\) | −2.12460 | − | 6.28248i | −0.157055 | − | 0.464415i | ||||
\(184\) | 0.678764 | + | 1.17565i | 0.0500391 | + | 0.0866703i | ||||
\(185\) | −5.16631 | −0.379834 | ||||||||
\(186\) | −3.42092 | − | 10.1157i | −0.250834 | − | 0.741720i | ||||
\(187\) | 13.3390 | 0.975446 | ||||||||
\(188\) | −2.04420 | −0.149089 | ||||||||
\(189\) | 6.34680 | + | 12.1950i | 0.461662 | + | 0.887056i | ||||
\(190\) | −5.95810 | −0.432246 | ||||||||
\(191\) | −20.6483 | −1.49406 | −0.747029 | − | 0.664791i | \(-0.768521\pi\) | ||||
−0.747029 | + | 0.664791i | \(0.768521\pi\) | |||||||
\(192\) | −0.554872 | − | 1.64077i | −0.0400445 | − | 0.118412i | ||||
\(193\) | −15.7801 | −1.13587 | −0.567937 | − | 0.823072i | \(-0.692258\pi\) | ||||
−0.567937 | + | 0.823072i | \(0.692258\pi\) | |||||||
\(194\) | 6.19076 | + | 10.7227i | 0.444470 | + | 0.769845i | ||||
\(195\) | −3.30599 | − | 9.77586i | −0.236747 | − | 0.700064i | ||||
\(196\) | 3.80039 | + | 5.87852i | 0.271456 | + | 0.419895i | ||||
\(197\) | 11.1659 | 0.795536 | 0.397768 | − | 0.917486i | \(-0.369785\pi\) | ||||
0.397768 | + | 0.917486i | \(0.369785\pi\) | |||||||
\(198\) | 0.965543 | + | 7.46602i | 0.0686182 | + | 0.530587i | ||||
\(199\) | −12.9803 | − | 22.4825i | −0.920148 | − | 1.59374i | −0.799183 | − | 0.601087i | \(-0.794734\pi\) |
−0.120965 | − | 0.992657i | \(-0.538599\pi\) | |||||||
\(200\) | 0.500000 | − | 0.866025i | 0.0353553 | − | 0.0612372i | ||||
\(201\) | −7.18341 | − | 21.2415i | −0.506679 | − | 1.49826i | ||||
\(202\) | 4.02012 | − | 6.96305i | 0.282855 | − | 0.489918i | ||||
\(203\) | 0.412813 | + | 16.4097i | 0.0289738 | + | 1.15173i | ||||
\(204\) | −6.07847 | + | 6.91519i | −0.425578 | + | 0.484160i | ||||
\(205\) | 8.86383 | 0.619077 | ||||||||
\(206\) | 5.60483 | + | 9.70785i | 0.390507 | + | 0.676378i | ||||
\(207\) | 3.75900 | + | 1.56712i | 0.261269 | + | 0.108922i | ||||
\(208\) | −2.97905 | + | 5.15987i | −0.206560 | + | 0.357772i | ||||
\(209\) | −7.47562 | − | 12.9482i | −0.517100 | − | 0.895643i | ||||
\(210\) | 4.30277 | − | 1.57676i | 0.296919 | − | 0.108807i | ||||
\(211\) | −2.97056 | + | 5.14516i | −0.204502 | + | 0.354207i | −0.949974 | − | 0.312329i | \(-0.898891\pi\) |
0.745472 | + | 0.666537i | \(0.232224\pi\) | |||||||
\(212\) | −0.179671 | − | 0.311199i | −0.0123398 | − | 0.0213732i | ||||
\(213\) | −1.95623 | − | 5.78462i | −0.134039 | − | 0.396356i | ||||
\(214\) | −3.76525 | + | 6.52160i | −0.257387 | + | 0.445807i | ||||
\(215\) | 0.977900 | − | 1.69377i | 0.0666922 | − | 0.115514i | ||||
\(216\) | −4.31051 | − | 2.90164i | −0.293293 | − | 0.197432i | ||||
\(217\) | −14.3270 | − | 7.79800i | −0.972577 | − | 0.529362i | ||||
\(218\) | −5.59671 | − | 9.69378i | −0.379057 | − | 0.656546i | ||||
\(219\) | 12.8088 | − | 14.5719i | 0.865535 | − | 0.984679i | ||||
\(220\) | 2.50940 | 0.169184 | ||||||||
\(221\) | 31.6711 | 2.13043 | ||||||||
\(222\) | 8.77436 | + | 1.75577i | 0.588897 | + | 0.117839i | ||||
\(223\) | −8.23601 | − | 14.2652i | −0.551524 | − | 0.955267i | −0.998165 | − | 0.0605541i | \(-0.980713\pi\) |
0.446641 | − | 0.894713i | \(-0.352620\pi\) | |||||||
\(224\) | −2.32383 | − | 1.26483i | −0.155268 | − | 0.0845103i | ||||
\(225\) | −0.384771 | − | 2.97522i | −0.0256514 | − | 0.198348i | ||||
\(226\) | 5.83876 | − | 10.1130i | 0.388388 | − | 0.672709i | ||||
\(227\) | −8.90835 | + | 15.4297i | −0.591268 | + | 1.02411i | 0.402794 | + | 0.915291i | \(0.368039\pi\) |
−0.994062 | + | 0.108816i | \(0.965294\pi\) | |||||||
\(228\) | 10.1191 | + | 2.02486i | 0.670156 | + | 0.134100i | ||||
\(229\) | 11.5572 | + | 20.0177i | 0.763723 | + | 1.32281i | 0.940919 | + | 0.338631i | \(0.109964\pi\) |
−0.177197 | + | 0.984175i | \(0.556703\pi\) | |||||||
\(230\) | 0.678764 | − | 1.17565i | 0.0447564 | − | 0.0775203i | ||||
\(231\) | 8.82530 | + | 7.37243i | 0.580662 | + | 0.485070i | ||||
\(232\) | −3.10212 | − | 5.37303i | −0.203664 | − | 0.352757i | ||||
\(233\) | 4.94916 | − | 8.57219i | 0.324230 | − | 0.561583i | −0.657126 | − | 0.753781i | \(-0.728228\pi\) |
0.981356 | + | 0.192198i | \(0.0615614\pi\) | |||||||
\(234\) | 2.29250 | + | 17.7267i | 0.149866 | + | 1.15883i | ||||
\(235\) | 1.02210 | + | 1.77033i | 0.0666745 | + | 0.115484i | ||||
\(236\) | −2.86874 | −0.186739 | ||||||||
\(237\) | 8.21177 | + | 24.2823i | 0.533412 | + | 1.57731i | ||||
\(238\) | 0.353687 | + | 14.0594i | 0.0229261 | + | 0.911335i | ||||
\(239\) | −12.6933 | + | 21.9855i | −0.821064 | + | 1.42212i | 0.0838266 | + | 0.996480i | \(0.473286\pi\) |
−0.904891 | + | 0.425644i | \(0.860048\pi\) | |||||||
\(240\) | −1.14351 | + | 1.30092i | −0.0738132 | + | 0.0839738i | ||||
\(241\) | −14.3326 | + | 24.8249i | −0.923247 | + | 1.59911i | −0.128890 | + | 0.991659i | \(0.541141\pi\) |
−0.794357 | + | 0.607451i | \(0.792192\pi\) | |||||||
\(242\) | −2.35146 | − | 4.07285i | −0.151158 | − | 0.261813i | ||||
\(243\) | −15.5607 | + | 0.930524i | −0.998217 | + | 0.0596931i | ||||
\(244\) | 3.82899 | 0.245126 | ||||||||
\(245\) | 3.19076 | − | 6.23049i | 0.203850 | − | 0.398052i | ||||
\(246\) | −15.0542 | − | 3.01237i | −0.959819 | − | 0.192062i | ||||
\(247\) | −17.7495 | − | 30.7430i | −1.12937 | − | 1.95613i | ||||
\(248\) | 6.16523 | 0.391493 | ||||||||
\(249\) | −5.80917 | + | 6.60881i | −0.368141 | + | 0.418817i | ||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 27.3920 | 1.72897 | 0.864484 | − | 0.502660i | \(-0.167645\pi\) | ||||
0.864484 | + | 0.502660i | \(0.167645\pi\) | |||||||
\(252\) | −7.84361 | + | 1.21565i | −0.494101 | + | 0.0765787i | ||||
\(253\) | 3.40658 | 0.214170 | ||||||||
\(254\) | 1.08717 | 0.0682153 | ||||||||
\(255\) | 9.02797 | + | 1.80652i | 0.565353 | + | 0.113128i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 12.9546 | + | 22.4380i | 0.808085 | + | 1.39964i | 0.914189 | + | 0.405289i | \(0.132829\pi\) |
−0.106104 | + | 0.994355i | \(0.533838\pi\) | |||||||
\(258\) | −2.23648 | + | 2.54433i | −0.139237 | + | 0.158403i | ||||
\(259\) | 11.6619 | − | 7.12992i | 0.724634 | − | 0.443031i | ||||
\(260\) | 5.95810 | 0.369506 | ||||||||
\(261\) | −17.1796 | − | 7.16211i | −1.06339 | − | 0.443324i | ||||
\(262\) | 4.30124 | + | 7.44996i | 0.265731 | + | 0.460260i | ||||
\(263\) | −14.5434 | + | 25.1899i | −0.896784 | + | 1.55327i | −0.0652021 | + | 0.997872i | \(0.520769\pi\) |
−0.831582 | + | 0.555403i | \(0.812564\pi\) | |||||||
\(264\) | −4.26192 | − | 0.852819i | −0.262303 | − | 0.0524874i | ||||
\(265\) | −0.179671 | + | 0.311199i | −0.0110371 | + | 0.0191168i | ||||
\(266\) | 13.4492 | − | 8.22266i | 0.824623 | − | 0.504164i | ||||
\(267\) | 1.24784 | + | 0.249696i | 0.0763667 | + | 0.0152811i | ||||
\(268\) | 12.9461 | 0.790806 | ||||||||
\(269\) | −4.69888 | − | 8.13870i | −0.286496 | − | 0.496225i | 0.686475 | − | 0.727153i | \(-0.259157\pi\) |
−0.972971 | + | 0.230928i | \(0.925824\pi\) | |||||||
\(270\) | −0.357641 | + | 5.18383i | −0.0217654 | + | 0.315478i | ||||
\(271\) | −0.571895 | + | 0.990552i | −0.0347402 | + | 0.0601717i | −0.882873 | − | 0.469612i | \(-0.844394\pi\) |
0.848133 | + | 0.529784i | \(0.177727\pi\) | |||||||
\(272\) | −2.65781 | − | 4.60347i | −0.161154 | − | 0.279126i | ||||
\(273\) | 20.9541 | + | 17.5045i | 1.26820 | + | 1.05942i | ||||
\(274\) | −1.02295 | + | 1.77180i | −0.0617987 | + | 0.107038i | ||||
\(275\) | −1.25470 | − | 2.17320i | −0.0756612 | − | 0.131049i | ||||
\(276\) | −1.55235 | + | 1.76603i | −0.0934402 | + | 0.106303i | ||||
\(277\) | 3.56388 | − | 6.17281i | 0.214133 | − | 0.370888i | −0.738871 | − | 0.673847i | \(-0.764641\pi\) |
0.953004 | + | 0.302958i | \(0.0979742\pi\) | |||||||
\(278\) | −5.44268 | + | 9.42700i | −0.326430 | + | 0.565394i | ||||
\(279\) | 14.6993 | − | 11.2259i | 0.880027 | − | 0.672074i | ||||
\(280\) | 0.0665372 | + | 2.64491i | 0.00397636 | + | 0.158064i | ||||
\(281\) | 9.36628 | + | 16.2229i | 0.558746 | + | 0.967776i | 0.997602 | + | 0.0692183i | \(0.0220505\pi\) |
−0.438856 | + | 0.898557i | \(0.644616\pi\) | |||||||
\(282\) | −1.13427 | − | 3.35406i | −0.0675448 | − | 0.199731i | ||||
\(283\) | −31.6080 | −1.87890 | −0.939450 | − | 0.342686i | \(-0.888663\pi\) | ||||
−0.939450 | + | 0.342686i | \(0.888663\pi\) | |||||||
\(284\) | 3.52556 | 0.209203 | ||||||||
\(285\) | −3.30599 | − | 9.77586i | −0.195830 | − | 0.579072i | ||||
\(286\) | 7.47562 | + | 12.9482i | 0.442043 | + | 0.765641i | ||||
\(287\) | −20.0083 | + | 12.2328i | −1.18105 | + | 0.722080i | ||||
\(288\) | 2.38423 | − | 1.82083i | 0.140492 | − | 0.107294i | ||||
\(289\) | −5.62796 | + | 9.74791i | −0.331056 | + | 0.573407i | ||||
\(290\) | −3.10212 | + | 5.37303i | −0.182163 | + | 0.315515i | ||||
\(291\) | −14.1584 | + | 16.1073i | −0.829979 | + | 0.944228i | ||||
\(292\) | 5.60063 | + | 9.70058i | 0.327752 | + | 0.567683i | ||||
\(293\) | −2.92595 | + | 5.06790i | −0.170936 | + | 0.296070i | −0.938747 | − | 0.344606i | \(-0.888012\pi\) |
0.767811 | + | 0.640676i | \(0.221346\pi\) | |||||||
\(294\) | −7.53656 | + | 9.49738i | −0.439541 | + | 0.553899i | ||||
\(295\) | 1.43437 | + | 2.48440i | 0.0835122 | + | 0.144647i | ||||
\(296\) | −2.58315 | + | 4.47415i | −0.150143 | + | 0.260055i | ||||
\(297\) | −11.7142 | + | 5.72692i | −0.679729 | + | 0.332310i | ||||
\(298\) | −0.250077 | − | 0.433146i | −0.0144866 | − | 0.0250915i | ||||
\(299\) | 8.08829 | 0.467758 | ||||||||
\(300\) | 1.69838 | + | 0.339850i | 0.0980561 | + | 0.0196212i | ||||
\(301\) | 0.130134 | + | 5.17292i | 0.00750077 | + | 0.298162i | ||||
\(302\) | −8.28820 | + | 14.3556i | −0.476932 | + | 0.826071i | ||||
\(303\) | 13.6554 | + | 2.73247i | 0.784482 | + | 0.156977i | ||||
\(304\) | −2.97905 | + | 5.15987i | −0.170860 | + | 0.295939i | ||||
\(305\) | −1.91450 | − | 3.31600i | −0.109624 | − | 0.189874i | ||||
\(306\) | −14.7190 | − | 6.13631i | −0.841429 | − | 0.350790i | ||||
\(307\) | 18.0889 | 1.03239 | 0.516193 | − | 0.856472i | \(-0.327349\pi\) | ||||
0.516193 | + | 0.856472i | \(0.327349\pi\) | |||||||
\(308\) | −5.66445 | + | 3.46317i | −0.322762 | + | 0.197332i | ||||
\(309\) | −12.8184 | + | 14.5828i | −0.729211 | + | 0.829589i | ||||
\(310\) | −3.08262 | − | 5.33925i | −0.175081 | − | 0.303249i | ||||
\(311\) | 28.7843 | 1.63221 | 0.816105 | − | 0.577904i | \(-0.196129\pi\) | ||||
0.816105 | + | 0.577904i | \(0.196129\pi\) | |||||||
\(312\) | −10.1191 | − | 2.02486i | −0.572883 | − | 0.114635i | ||||
\(313\) | −0.185134 | −0.0104644 | −0.00523219 | − | 0.999986i | \(-0.501665\pi\) | ||||
−0.00523219 | + | 0.999986i | \(0.501665\pi\) | |||||||
\(314\) | 1.10586 | 0.0624071 | ||||||||
\(315\) | 4.97459 | + | 6.18494i | 0.280286 | + | 0.348482i | ||||
\(316\) | −14.7994 | −0.832530 | ||||||||
\(317\) | 5.86194 | 0.329239 | 0.164620 | − | 0.986357i | \(-0.447360\pi\) | ||||
0.164620 | + | 0.986357i | \(0.447360\pi\) | |||||||
\(318\) | 0.410910 | − | 0.467473i | 0.0230427 | − | 0.0262146i | ||||
\(319\) | −15.5689 | −0.871691 | ||||||||
\(320\) | −0.500000 | − | 0.866025i | −0.0279508 | − | 0.0484123i | ||||
\(321\) | −12.7897 | − | 2.55924i | −0.713849 | − | 0.142843i | ||||
\(322\) | 0.0903261 | + | 3.59054i | 0.00503368 | + | 0.200093i | ||||
\(323\) | 31.6711 | 1.76223 | ||||||||
\(324\) | 2.36914 | − | 8.68258i | 0.131619 | − | 0.482366i | ||||
\(325\) | −2.97905 | − | 5.15987i | −0.165248 | − | 0.286218i | ||||
\(326\) | 3.44888 | − | 5.97364i | 0.191016 | − | 0.330849i | ||||
\(327\) | 12.7998 | − | 14.5617i | 0.707829 | − | 0.805264i | ||||
\(328\) | 4.43192 | − | 7.67631i | 0.244712 | − | 0.423853i | ||||
\(329\) | −4.75038 | − | 2.58557i | −0.261897 | − | 0.142547i | ||||
\(330\) | 1.39240 | + | 4.11734i | 0.0766489 | + | 0.226652i | ||||
\(331\) | −1.74896 | −0.0961314 | −0.0480657 | − | 0.998844i | \(-0.515306\pi\) | ||||
−0.0480657 | + | 0.998844i | \(0.515306\pi\) | |||||||
\(332\) | −2.54006 | − | 4.39951i | −0.139404 | − | 0.241455i | ||||
\(333\) | 1.98784 | + | 15.3709i | 0.108933 | + | 0.842321i | ||||
\(334\) | 6.61206 | − | 11.4524i | 0.361796 | − | 0.626649i | ||||
\(335\) | −6.47303 | − | 11.2116i | −0.353659 | − | 0.612556i | ||||
\(336\) | 0.785868 | − | 4.51469i | 0.0428726 | − | 0.246296i | ||||
\(337\) | 8.99813 | − | 15.5852i | 0.490160 | − | 0.848981i | −0.509776 | − | 0.860307i | \(-0.670272\pi\) |
0.999936 | + | 0.0113258i | \(0.00360518\pi\) | |||||||
\(338\) | 11.2495 | + | 19.4847i | 0.611892 | + | 1.05983i | ||||
\(339\) | 19.8329 | + | 3.96860i | 1.07717 | + | 0.215545i | ||||
\(340\) | −2.65781 | + | 4.60347i | −0.144140 | + | 0.249658i | ||||
\(341\) | 7.73551 | − | 13.3983i | 0.418901 | − | 0.725558i | ||||
\(342\) | 2.29250 | + | 17.7267i | 0.123964 | + | 0.958549i | ||||
\(343\) | 1.39610 | + | 18.4676i | 0.0753825 | + | 0.997155i | ||||
\(344\) | −0.977900 | − | 1.69377i | −0.0527248 | − | 0.0913221i | ||||
\(345\) | 2.30560 | + | 0.461356i | 0.124129 | + | 0.0248386i | ||||
\(346\) | 15.2751 | 0.821195 | ||||||||
\(347\) | −4.14672 | −0.222608 | −0.111304 | − | 0.993786i | \(-0.535503\pi\) | ||||
−0.111304 | + | 0.993786i | \(0.535503\pi\) | |||||||
\(348\) | 7.09461 | − | 8.07120i | 0.380311 | − | 0.432662i | ||||
\(349\) | −11.4215 | − | 19.7827i | −0.611381 | − | 1.05894i | −0.991008 | − | 0.133804i | \(-0.957281\pi\) |
0.379627 | − | 0.925140i | \(-0.376052\pi\) | |||||||
\(350\) | 2.25729 | − | 1.38008i | 0.120657 | − | 0.0737684i | ||||
\(351\) | −27.8133 | + | 13.5975i | −1.48456 | + | 0.725781i | ||||
\(352\) | 1.25470 | − | 2.17320i | 0.0668757 | − | 0.115832i | ||||
\(353\) | 11.7572 | − | 20.3640i | 0.625771 | − | 1.08387i | −0.362621 | − | 0.931937i | \(-0.618118\pi\) |
0.988391 | − | 0.151930i | \(-0.0485487\pi\) | |||||||
\(354\) | −1.59178 | − | 4.70693i | −0.0846024 | − | 0.250171i | ||||
\(355\) | −1.76278 | − | 3.05322i | −0.0935586 | − | 0.162048i | ||||
\(356\) | −0.367362 | + | 0.636290i | −0.0194702 | + | 0.0337233i | ||||
\(357\) | −22.8719 | + | 8.38148i | −1.21051 | + | 0.443595i | ||||
\(358\) | 0.232599 | + | 0.402873i | 0.0122932 | + | 0.0212925i | ||||
\(359\) | −6.12241 | + | 10.6043i | −0.323128 | + | 0.559675i | −0.981132 | − | 0.193340i | \(-0.938068\pi\) |
0.658003 | + | 0.753015i | \(0.271401\pi\) | |||||||
\(360\) | −2.76900 | − | 1.15439i | −0.145939 | − | 0.0608417i | ||||
\(361\) | −8.24949 | − | 14.2885i | −0.434184 | − | 0.752028i | ||||
\(362\) | −26.1282 | −1.37327 | ||||||||
\(363\) | 5.37784 | − | 6.11811i | 0.282263 | − | 0.321118i | ||||
\(364\) | −13.4492 | + | 8.22266i | −0.704929 | + | 0.430984i | ||||
\(365\) | 5.60063 | − | 9.70058i | 0.293150 | − | 0.507751i | ||||
\(366\) | 2.12460 | + | 6.28248i | 0.111055 | + | 0.328391i | ||||
\(367\) | 5.78768 | − | 10.0246i | 0.302114 | − | 0.523277i | −0.674500 | − | 0.738275i | \(-0.735641\pi\) |
0.976615 | + | 0.214997i | \(0.0689742\pi\) | |||||||
\(368\) | −0.678764 | − | 1.17565i | −0.0353830 | − | 0.0612852i | ||||
\(369\) | −3.41055 | − | 26.3719i | −0.177546 | − | 1.37287i | ||||
\(370\) | 5.16631 | 0.268583 | ||||||||
\(371\) | −0.0239096 | − | 0.950427i | −0.00124132 | − | 0.0493437i | ||||
\(372\) | 3.42092 | + | 10.1157i | 0.177366 | + | 0.524475i | ||||
\(373\) | 7.15324 | + | 12.3898i | 0.370381 | + | 0.641518i | 0.989624 | − | 0.143681i | \(-0.0458939\pi\) |
−0.619243 | + | 0.785199i | \(0.712561\pi\) | |||||||
\(374\) | −13.3390 | −0.689745 | ||||||||
\(375\) | −0.554872 | − | 1.64077i | −0.0286535 | − | 0.0847288i | ||||
\(376\) | 2.04420 | 0.105422 | ||||||||
\(377\) | −36.9655 | −1.90382 | ||||||||
\(378\) | −6.34680 | − | 12.1950i | −0.326444 | − | 0.627243i | ||||
\(379\) | −5.19451 | −0.266824 | −0.133412 | − | 0.991061i | \(-0.542593\pi\) | ||||
−0.133412 | + | 0.991061i | \(0.542593\pi\) | |||||||
\(380\) | 5.95810 | 0.305644 | ||||||||
\(381\) | 0.603243 | + | 1.78380i | 0.0309050 | + | 0.0913868i | ||||
\(382\) | 20.6483 | 1.05646 | ||||||||
\(383\) | −5.92200 | − | 10.2572i | −0.302600 | − | 0.524119i | 0.674124 | − | 0.738618i | \(-0.264521\pi\) |
−0.976724 | + | 0.214499i | \(0.931188\pi\) | |||||||
\(384\) | 0.554872 | + | 1.64077i | 0.0283157 | + | 0.0837300i | ||||
\(385\) | 5.83142 | + | 3.17397i | 0.297197 | + | 0.161761i | ||||
\(386\) | 15.7801 | 0.803184 | ||||||||
\(387\) | −5.41562 | − | 2.25776i | −0.275291 | − | 0.114768i | ||||
\(388\) | −6.19076 | − | 10.7227i | −0.314288 | − | 0.544363i | ||||
\(389\) | −17.6616 | + | 30.5908i | −0.895480 | + | 1.55102i | −0.0622714 | + | 0.998059i | \(0.519834\pi\) |
−0.833209 | + | 0.552958i | \(0.813499\pi\) | |||||||
\(390\) | 3.30599 | + | 9.77586i | 0.167405 | + | 0.495020i | ||||
\(391\) | −3.60806 | + | 6.24934i | −0.182467 | + | 0.316043i | ||||
\(392\) | −3.80039 | − | 5.87852i | −0.191949 | − | 0.296910i | ||||
\(393\) | −9.83702 | + | 11.1911i | −0.496212 | + | 0.564517i | ||||
\(394\) | −11.1659 | −0.562529 | ||||||||
\(395\) | 7.39969 | + | 12.8166i | 0.372319 | + | 0.644875i | ||||
\(396\) | −0.965543 | − | 7.46602i | −0.0485204 | − | 0.375182i | ||||
\(397\) | −5.44065 | + | 9.42348i | −0.273058 | + | 0.472951i | −0.969643 | − | 0.244523i | \(-0.921369\pi\) |
0.696585 | + | 0.717474i | \(0.254702\pi\) | |||||||
\(398\) | 12.9803 | + | 22.4825i | 0.650643 | + | 1.12695i | ||||
\(399\) | 20.9541 | + | 17.5045i | 1.04901 | + | 0.876319i | ||||
\(400\) | −0.500000 | + | 0.866025i | −0.0250000 | + | 0.0433013i | ||||
\(401\) | −14.3646 | − | 24.8801i | −0.717332 | − | 1.24246i | −0.962053 | − | 0.272862i | \(-0.912030\pi\) |
0.244722 | − | 0.969593i | \(-0.421303\pi\) | |||||||
\(402\) | 7.18341 | + | 21.2415i | 0.358276 | + | 1.05943i | ||||
\(403\) | 18.3665 | − | 31.8118i | 0.914902 | − | 1.58466i | ||||
\(404\) | −4.02012 | + | 6.96305i | −0.200008 | + | 0.346425i | ||||
\(405\) | −8.70390 | + | 2.28956i | −0.432500 | + | 0.113769i | ||||
\(406\) | −0.412813 | − | 16.4097i | −0.0204876 | − | 0.814399i | ||||
\(407\) | 6.48216 | + | 11.2274i | 0.321309 | + | 0.556523i | ||||
\(408\) | 6.07847 | − | 6.91519i | 0.300929 | − | 0.342353i | ||||
\(409\) | 2.79310 | 0.138110 | 0.0690550 | − | 0.997613i | \(-0.478002\pi\) | ||||
0.0690550 | + | 0.997613i | \(0.478002\pi\) | |||||||
\(410\) | −8.86383 | −0.437754 | ||||||||
\(411\) | −3.47472 | − | 0.695299i | −0.171395 | − | 0.0342966i | ||||
\(412\) | −5.60483 | − | 9.70785i | −0.276130 | − | 0.478271i | ||||
\(413\) | −6.66647 | − | 3.62848i | −0.328035 | − | 0.178546i | ||||
\(414\) | −3.75900 | − | 1.56712i | −0.184745 | − | 0.0770196i | ||||
\(415\) | −2.54006 | + | 4.39951i | −0.124687 | + | 0.215964i | ||||
\(416\) | 2.97905 | − | 5.15987i | 0.146060 | − | 0.252983i | ||||
\(417\) | −18.4875 | − | 3.69939i | −0.905337 | − | 0.181160i | ||||
\(418\) | 7.47562 | + | 12.9482i | 0.365645 | + | 0.633315i | ||||
\(419\) | 14.8923 | − | 25.7942i | 0.727535 | − | 1.26013i | −0.230387 | − | 0.973099i | \(-0.573999\pi\) |
0.957922 | − | 0.287028i | \(-0.0926674\pi\) | |||||||
\(420\) | −4.30277 | + | 1.57676i | −0.209954 | + | 0.0769381i | ||||
\(421\) | 10.7947 | + | 18.6969i | 0.526101 | + | 0.911233i | 0.999538 | + | 0.0304053i | \(0.00967978\pi\) |
−0.473437 | + | 0.880828i | \(0.656987\pi\) | |||||||
\(422\) | 2.97056 | − | 5.14516i | 0.144605 | − | 0.250462i | ||||
\(423\) | 4.87385 | − | 3.72215i | 0.236975 | − | 0.180977i | ||||
\(424\) | 0.179671 | + | 0.311199i | 0.00872557 | + | 0.0151131i | ||||
\(425\) | 5.31563 | 0.257846 | ||||||||
\(426\) | 1.95623 | + | 5.78462i | 0.0947799 | + | 0.280266i | ||||
\(427\) | 8.89793 | + | 4.84304i | 0.430601 | + | 0.234371i | ||||
\(428\) | 3.76525 | − | 6.52160i | 0.182000 | − | 0.315233i | ||||
\(429\) | −17.0969 | + | 19.4503i | −0.825446 | + | 0.939071i | ||||
\(430\) | −0.977900 | + | 1.69377i | −0.0471585 | + | 0.0816810i | ||||
\(431\) | 17.4006 | + | 30.1387i | 0.838157 | + | 1.45173i | 0.891434 | + | 0.453151i | \(0.149700\pi\) |
−0.0532769 | + | 0.998580i | \(0.516967\pi\) | |||||||
\(432\) | 4.31051 | + | 2.90164i | 0.207389 | + | 0.139605i | ||||
\(433\) | −16.7114 | −0.803098 | −0.401549 | − | 0.915838i | \(-0.631528\pi\) | ||||
−0.401549 | + | 0.915838i | \(0.631528\pi\) | |||||||
\(434\) | 14.3270 | + | 7.79800i | 0.687716 | + | 0.374316i | ||||
\(435\) | −10.5372 | − | 2.10851i | −0.505219 | − | 0.101095i | ||||
\(436\) | 5.59671 | + | 9.69378i | 0.268034 | + | 0.464248i | ||||
\(437\) | 8.08829 | 0.386915 | ||||||||
\(438\) | −12.8088 | + | 14.5719i | −0.612026 | + | 0.696273i | ||||
\(439\) | 30.6286 | 1.46182 | 0.730911 | − | 0.682473i | \(-0.239095\pi\) | ||||
0.730911 | + | 0.682473i | \(0.239095\pi\) | |||||||
\(440\) | −2.50940 | −0.119631 | ||||||||
\(441\) | −19.7648 | − | 7.09590i | −0.941182 | − | 0.337900i | ||||
\(442\) | −31.6711 | −1.50644 | ||||||||
\(443\) | 27.0075 | 1.28316 | 0.641582 | − | 0.767055i | \(-0.278278\pi\) | ||||
0.641582 | + | 0.767055i | \(0.278278\pi\) | |||||||
\(444\) | −8.77436 | − | 1.75577i | −0.416413 | − | 0.0833251i | ||||
\(445\) | 0.734724 | 0.0348293 | ||||||||
\(446\) | 8.23601 | + | 14.2652i | 0.389986 | + | 0.675476i | ||||
\(447\) | 0.571930 | − | 0.650658i | 0.0270514 | − | 0.0307751i | ||||
\(448\) | 2.32383 | + | 1.26483i | 0.109791 | + | 0.0597578i | ||||
\(449\) | 40.6860 | 1.92009 | 0.960045 | − | 0.279845i | \(-0.0902831\pi\) | ||||
0.960045 | + | 0.279845i | \(0.0902831\pi\) | |||||||
\(450\) | 0.384771 | + | 2.97522i | 0.0181383 | + | 0.140253i | ||||
\(451\) | −11.1214 | − | 19.2629i | −0.523688 | − | 0.907055i | ||||
\(452\) | −5.83876 | + | 10.1130i | −0.274632 | + | 0.475677i | ||||
\(453\) | −28.1531 | − | 5.63349i | −1.32275 | − | 0.264684i | ||||
\(454\) | 8.90835 | − | 15.4297i | 0.418090 | − | 0.724153i | ||||
\(455\) | 13.8456 | + | 7.53601i | 0.649093 | + | 0.353294i | ||||
\(456\) | −10.1191 | − | 2.02486i | −0.473872 | − | 0.0948228i | ||||
\(457\) | 35.4495 | 1.65826 | 0.829129 | − | 0.559057i | \(-0.188837\pi\) | ||||
0.829129 | + | 0.559057i | \(0.188837\pi\) | |||||||
\(458\) | −11.5572 | − | 20.0177i | −0.540033 | − | 0.935365i | ||||
\(459\) | 1.90109 | − | 27.5553i | 0.0887352 | − | 1.28617i | ||||
\(460\) | −0.678764 | + | 1.17565i | −0.0316475 | + | 0.0548151i | ||||
\(461\) | 11.9946 | + | 20.7753i | 0.558645 | + | 0.967601i | 0.997610 | + | 0.0690971i | \(0.0220118\pi\) |
−0.438965 | + | 0.898504i | \(0.644655\pi\) | |||||||
\(462\) | −8.82530 | − | 7.37243i | −0.410590 | − | 0.342996i | ||||
\(463\) | 6.53066 | − | 11.3114i | 0.303506 | − | 0.525687i | −0.673422 | − | 0.739258i | \(-0.735176\pi\) |
0.976927 | + | 0.213571i | \(0.0685096\pi\) | |||||||
\(464\) | 3.10212 | + | 5.37303i | 0.144012 | + | 0.249437i | ||||
\(465\) | 7.05000 | − | 8.02045i | 0.326936 | − | 0.371940i | ||||
\(466\) | −4.94916 | + | 8.57219i | −0.229265 | + | 0.397099i | ||||
\(467\) | −11.0880 | + | 19.2050i | −0.513092 | + | 0.888701i | 0.486793 | + | 0.873517i | \(0.338167\pi\) |
−0.999885 | + | 0.0151836i | \(0.995167\pi\) | |||||||
\(468\) | −2.29250 | − | 17.7267i | −0.105971 | − | 0.819416i | ||||
\(469\) | 30.0845 | + | 16.3746i | 1.38917 | + | 0.756110i | ||||
\(470\) | −1.02210 | − | 1.77033i | −0.0471460 | − | 0.0816592i | ||||
\(471\) | 0.613609 | + | 1.81445i | 0.0282736 | + | 0.0836056i | ||||
\(472\) | 2.86874 | 0.132044 | ||||||||
\(473\) | −4.90788 | −0.225665 | ||||||||
\(474\) | −8.21177 | − | 24.2823i | −0.377179 | − | 1.11532i | ||||
\(475\) | −2.97905 | − | 5.15987i | −0.136688 | − | 0.236751i | ||||
\(476\) | −0.353687 | − | 14.0594i | −0.0162112 | − | 0.644411i | ||||
\(477\) | 0.995017 | + | 0.414820i | 0.0455587 | + | 0.0189933i | ||||
\(478\) | 12.6933 | − | 21.9855i | 0.580580 | − | 1.00559i | ||||
\(479\) | 16.2605 | − | 28.1639i | 0.742959 | − | 1.28684i | −0.208183 | − | 0.978090i | \(-0.566755\pi\) |
0.951142 | − | 0.308753i | \(-0.0999116\pi\) | |||||||
\(480\) | 1.14351 | − | 1.30092i | 0.0521938 | − | 0.0593785i | ||||
\(481\) | 15.3907 | + | 26.6575i | 0.701755 | + | 1.21548i | ||||
\(482\) | 14.3326 | − | 24.8249i | 0.652834 | − | 1.13074i | ||||
\(483\) | −5.84113 | + | 2.14050i | −0.265781 | + | 0.0973960i | ||||
\(484\) | 2.35146 | + | 4.07285i | 0.106885 | + | 0.185130i | ||||
\(485\) | −6.19076 | + | 10.7227i | −0.281108 | + | 0.486893i | ||||
\(486\) | 15.5607 | − | 0.930524i | 0.705846 | − | 0.0422094i | ||||
\(487\) | −9.99511 | − | 17.3120i | −0.452922 | − | 0.784483i | 0.545644 | − | 0.838017i | \(-0.316285\pi\) |
−0.998566 | + | 0.0535335i | \(0.982952\pi\) | |||||||
\(488\) | −3.82899 | −0.173330 | ||||||||
\(489\) | 11.7150 | + | 2.34421i | 0.529773 | + | 0.106009i | ||||
\(490\) | −3.19076 | + | 6.23049i | −0.144144 | + | 0.281465i | ||||
\(491\) | 15.5637 | − | 26.9570i | 0.702378 | − | 1.21655i | −0.265251 | − | 0.964179i | \(-0.585455\pi\) |
0.967629 | − | 0.252375i | \(-0.0812117\pi\) | |||||||
\(492\) | 15.0542 | + | 3.01237i | 0.678695 | + | 0.135808i | ||||
\(493\) | 16.4897 | − | 28.5610i | 0.742660 | − | 1.28632i | ||||
\(494\) | 17.7495 | + | 30.7430i | 0.798587 | + | 1.38319i | ||||
\(495\) | −5.98299 | + | 4.56919i | −0.268915 | + | 0.205370i | ||||
\(496\) | −6.16523 | −0.276827 | ||||||||
\(497\) | 8.19280 | + | 4.45925i | 0.367497 | + | 0.200025i | ||||
\(498\) | 5.80917 | − | 6.60881i | 0.260315 | − | 0.296148i | ||||
\(499\) | −7.40897 | − | 12.8327i | −0.331671 | − | 0.574471i | 0.651169 | − | 0.758933i | \(-0.274279\pi\) |
−0.982840 | + | 0.184462i | \(0.940946\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 22.4596 | + | 4.49422i | 1.00342 | + | 0.200787i | ||||
\(502\) | −27.3920 | −1.22257 | ||||||||
\(503\) | −2.45622 | −0.109518 | −0.0547588 | − | 0.998500i | \(-0.517439\pi\) | ||||
−0.0547588 | + | 0.998500i | \(0.517439\pi\) | |||||||
\(504\) | 7.84361 | − | 1.21565i | 0.349382 | − | 0.0541493i | ||||
\(505\) | 8.04024 | 0.357786 | ||||||||
\(506\) | −3.40658 | −0.151441 | ||||||||
\(507\) | −25.7278 | + | 29.2693i | −1.14261 | + | 1.29990i | ||||
\(508\) | −1.08717 | −0.0482355 | ||||||||
\(509\) | 6.67596 | + | 11.5631i | 0.295907 | + | 0.512526i | 0.975195 | − | 0.221345i | \(-0.0710448\pi\) |
−0.679289 | + | 0.733871i | \(0.737712\pi\) | |||||||
\(510\) | −9.02797 | − | 1.80652i | −0.399765 | − | 0.0799939i | ||||
\(511\) | 0.745301 | + | 29.6264i | 0.0329702 | + | 1.31059i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −27.8133 | + | 13.5975i | −1.22799 | + | 0.600345i | ||||
\(514\) | −12.9546 | − | 22.4380i | −0.571402 | − | 0.989698i | ||||
\(515\) | −5.60483 | + | 9.70785i | −0.246978 | + | 0.427779i | ||||
\(516\) | 2.23648 | − | 2.54433i | 0.0984554 | − | 0.112008i | ||||
\(517\) | 2.56486 | − | 4.44246i | 0.112802 | − | 0.195379i | ||||
\(518\) | −11.6619 | + | 7.12992i | −0.512393 | + | 0.313271i | ||||
\(519\) | 8.47574 | + | 25.0629i | 0.372044 | + | 1.10014i | ||||
\(520\) | −5.95810 | −0.261280 | ||||||||
\(521\) | −17.5850 | − | 30.4582i | −0.770415 | − | 1.33440i | −0.937336 | − | 0.348427i | \(-0.886716\pi\) |
0.166921 | − | 0.985970i | \(-0.446617\pi\) | |||||||
\(522\) | 17.1796 | + | 7.16211i | 0.751929 | + | 0.313477i | ||||
\(523\) | 5.78531 | − | 10.0204i | 0.252974 | − | 0.438164i | −0.711369 | − | 0.702818i | \(-0.751925\pi\) |
0.964343 | + | 0.264655i | \(0.0852580\pi\) | |||||||
\(524\) | −4.30124 | − | 7.44996i | −0.187900 | − | 0.325453i | ||||
\(525\) | 3.51690 | + | 2.93793i | 0.153490 | + | 0.128222i | ||||
\(526\) | 14.5434 | − | 25.1899i | 0.634122 | − | 1.09833i | ||||
\(527\) | 16.3860 | + | 28.3815i | 0.713787 | + | 1.23632i | ||||
\(528\) | 4.26192 | + | 0.852819i | 0.185476 | + | 0.0371142i | ||||
\(529\) | 10.5786 | − | 18.3226i | 0.459937 | − | 0.796635i | ||||
\(530\) | 0.179671 | − | 0.311199i | 0.00780439 | − | 0.0135176i | ||||
\(531\) | 6.83974 | − | 5.22349i | 0.296820 | − | 0.226680i | ||||
\(532\) | −13.4492 | + | 8.22266i | −0.583096 | + | 0.356497i | ||||
\(533\) | −26.4058 | − | 45.7362i | −1.14376 | − | 1.98106i | ||||
\(534\) | −1.24784 | − | 0.249696i | −0.0539994 | − | 0.0108054i | ||||
\(535\) | −7.53050 | −0.325572 | ||||||||
\(536\) | −12.9461 | −0.559185 | ||||||||
\(537\) | −0.531958 | + | 0.605184i | −0.0229557 | + | 0.0261156i | ||||
\(538\) | 4.69888 | + | 8.13870i | 0.202583 | + | 0.350884i | ||||
\(539\) | −17.5436 | + | 0.883234i | −0.755655 | + | 0.0380436i | ||||
\(540\) | 0.357641 | − | 5.18383i | 0.0153904 | − | 0.223077i | ||||
\(541\) | −2.16363 | + | 3.74752i | −0.0930218 | + | 0.161119i | −0.908781 | − | 0.417273i | \(-0.862986\pi\) |
0.815759 | + | 0.578391i | \(0.196319\pi\) | |||||||
\(542\) | 0.571895 | − | 0.990552i | 0.0245650 | − | 0.0425478i | ||||
\(543\) | −14.4978 | − | 42.8703i | −0.622160 | − | 1.83974i | ||||
\(544\) | 2.65781 | + | 4.60347i | 0.113953 | + | 0.197372i | ||||
\(545\) | 5.59671 | − | 9.69378i | 0.239737 | − | 0.415236i | ||||
\(546\) | −20.9541 | − | 17.5045i | −0.896751 | − | 0.749122i | ||||
\(547\) | −0.544266 | − | 0.942697i | −0.0232711 | − | 0.0403068i | 0.854155 | − | 0.520018i | \(-0.174075\pi\) |
−0.877426 | + | 0.479711i | \(0.840741\pi\) | |||||||
\(548\) | 1.02295 | − | 1.77180i | 0.0436983 | − | 0.0756876i | ||||
\(549\) | −9.12921 | + | 6.97195i | −0.389625 | + | 0.297556i | ||||
\(550\) | 1.25470 | + | 2.17320i | 0.0535005 | + | 0.0926657i | ||||
\(551\) | −36.9655 | −1.57478 | ||||||||
\(552\) | 1.55235 | − | 1.76603i | 0.0660722 | − | 0.0751673i | ||||
\(553\) | −34.3913 | − | 18.7188i | −1.46247 | − | 0.796003i | ||||
\(554\) | −3.56388 | + | 6.17281i | −0.151415 | + | 0.262258i | ||||
\(555\) | 2.86664 | + | 8.47670i | 0.121682 | + | 0.359816i | ||||
\(556\) | 5.44268 | − | 9.42700i | 0.230821 | − | 0.399794i | ||||
\(557\) | −9.25764 | − | 16.0347i | −0.392259 | − | 0.679412i | 0.600488 | − | 0.799633i | \(-0.294973\pi\) |
−0.992747 | + | 0.120221i | \(0.961640\pi\) | |||||||
\(558\) | −14.6993 | + | 11.2259i | −0.622273 | + | 0.475228i | ||||
\(559\) | −11.6529 | −0.492863 | ||||||||
\(560\) | −0.0665372 | − | 2.64491i | −0.00281171 | − | 0.111768i | ||||
\(561\) | −7.40146 | − | 21.8862i | −0.312490 | − | 0.924038i | ||||
\(562\) | −9.36628 | − | 16.2229i | −0.395093 | − | 0.684321i | ||||
\(563\) | 12.4134 | 0.523163 | 0.261581 | − | 0.965181i | \(-0.415756\pi\) | ||||
0.261581 | + | 0.965181i | \(0.415756\pi\) | |||||||
\(564\) | 1.13427 | + | 3.35406i | 0.0477614 | + | 0.141231i | ||||
\(565\) | 11.6775 | 0.491277 | ||||||||
\(566\) | 31.6080 | 1.32858 | ||||||||
\(567\) | 16.4875 | − | 17.1803i | 0.692410 | − | 0.721504i | ||||
\(568\) | −3.52556 | −0.147929 | ||||||||
\(569\) | 9.25085 | 0.387816 | 0.193908 | − | 0.981020i | \(-0.437884\pi\) | ||||
0.193908 | + | 0.981020i | \(0.437884\pi\) | |||||||
\(570\) | 3.30599 | + | 9.77586i | 0.138473 | + | 0.409466i | ||||
\(571\) | −12.1307 | −0.507652 | −0.253826 | − | 0.967250i | \(-0.581689\pi\) | ||||
−0.253826 | + | 0.967250i | \(0.581689\pi\) | |||||||
\(572\) | −7.47562 | − | 12.9482i | −0.312572 | − | 0.541390i | ||||
\(573\) | 11.4572 | + | 33.8791i | 0.478630 | + | 1.41532i | ||||
\(574\) | 20.0083 | − | 12.2328i | 0.835130 | − | 0.510587i | ||||
\(575\) | 1.35753 | 0.0566128 | ||||||||
\(576\) | −2.38423 | + | 1.82083i | −0.0993431 | + | 0.0758680i | ||||
\(577\) | 3.58092 | + | 6.20234i | 0.149076 | + | 0.258207i | 0.930886 | − | 0.365310i | \(-0.119037\pi\) |
−0.781810 | + | 0.623516i | \(0.785704\pi\) | |||||||
\(578\) | 5.62796 | − | 9.74791i | 0.234092 | − | 0.405460i | ||||
\(579\) | 8.75592 | + | 25.8914i | 0.363884 | + | 1.07601i | ||||
\(580\) | 3.10212 | − | 5.37303i | 0.128809 | − | 0.223103i | ||||
\(581\) | −0.338017 | − | 13.4365i | −0.0140233 | − | 0.557439i | ||||
\(582\) | 14.1584 | − | 16.1073i | 0.586884 | − | 0.667670i | ||||
\(583\) | 0.901730 | 0.0373458 | ||||||||
\(584\) | −5.60063 | − | 9.70058i | −0.231756 | − | 0.401413i | ||||
\(585\) | −14.2055 | + | 10.8487i | −0.587325 | + | 0.448539i | ||||
\(586\) | 2.92595 | − | 5.06790i | 0.120870 | − | 0.209353i | ||||
\(587\) | −14.4975 | − | 25.1104i | −0.598375 | − | 1.03642i | −0.993061 | − | 0.117600i | \(-0.962480\pi\) |
0.394686 | − | 0.918816i | \(-0.370853\pi\) | |||||||
\(588\) | 7.53656 | − | 9.49738i | 0.310802 | − | 0.391665i | ||||
\(589\) | 18.3665 | − | 31.8118i | 0.756780 | − | 1.31078i | ||||
\(590\) | −1.43437 | − | 2.48440i | −0.0590521 | − | 0.102281i | ||||
\(591\) | −6.19564 | − | 18.3206i | −0.254854 | − | 0.753609i | ||||
\(592\) | 2.58315 | − | 4.47415i | 0.106167 | − | 0.183887i | ||||
\(593\) | 15.1709 | − | 26.2768i | 0.622994 | − | 1.07906i | −0.365931 | − | 0.930642i | \(-0.619249\pi\) |
0.988925 | − | 0.148416i | \(-0.0474174\pi\) | |||||||
\(594\) | 11.7142 | − | 5.72692i | 0.480641 | − | 0.234978i | ||||
\(595\) | −11.9989 | + | 7.33600i | −0.491909 | + | 0.300746i | ||||
\(596\) | 0.250077 | + | 0.433146i | 0.0102435 | + | 0.0177423i | ||||
\(597\) | −29.6862 | + | 33.7726i | −1.21497 | + | 1.38222i | ||||
\(598\) | −8.08829 | −0.330755 | ||||||||
\(599\) | −14.9439 | −0.610593 | −0.305297 | − | 0.952257i | \(-0.598756\pi\) | ||||
−0.305297 | + | 0.952257i | \(0.598756\pi\) | |||||||
\(600\) | −1.69838 | − | 0.339850i | −0.0693362 | − | 0.0138743i | ||||
\(601\) | 4.85451 | + | 8.40827i | 0.198020 | + | 0.342980i | 0.947886 | − | 0.318609i | \(-0.103216\pi\) |
−0.749866 | + | 0.661589i | \(0.769882\pi\) | |||||||
\(602\) | −0.130134 | − | 5.17292i | −0.00530385 | − | 0.210833i | ||||
\(603\) | −30.8664 | + | 23.5726i | −1.25698 | + | 0.959951i | ||||
\(604\) | 8.28820 | − | 14.3556i | 0.337242 | − | 0.584120i | ||||
\(605\) | 2.35146 | − | 4.07285i | 0.0956005 | − | 0.165585i | ||||
\(606\) | −13.6554 | − | 2.73247i | −0.554712 | − | 0.110999i | ||||
\(607\) | 7.93110 | + | 13.7371i | 0.321913 | + | 0.557570i | 0.980883 | − | 0.194599i | \(-0.0623407\pi\) |
−0.658969 | + | 0.752170i | \(0.729007\pi\) | |||||||
\(608\) | 2.97905 | − | 5.15987i | 0.120816 | − | 0.209260i | ||||
\(609\) | 26.6954 | − | 9.78261i | 1.08175 | − | 0.396411i | ||||
\(610\) | 1.91450 | + | 3.31600i | 0.0775157 | + | 0.134261i | ||||
\(611\) | 6.08978 | − | 10.5478i | 0.246366 | − | 0.426718i | ||||
\(612\) | 14.7190 | + | 6.13631i | 0.594980 | + | 0.248046i | ||||
\(613\) | 17.2918 | + | 29.9503i | 0.698409 | + | 1.20968i | 0.969018 | + | 0.246991i | \(0.0794417\pi\) |
−0.270609 | + | 0.962689i | \(0.587225\pi\) | |||||||
\(614\) | −18.0889 | −0.730007 | ||||||||
\(615\) | −4.91830 | − | 14.5435i | −0.198325 | − | 0.586450i | ||||
\(616\) | 5.66445 | − | 3.46317i | 0.228227 | − | 0.139535i | ||||
\(617\) | −5.89064 | + | 10.2029i | −0.237148 | + | 0.410753i | −0.959895 | − | 0.280360i | \(-0.909546\pi\) |
0.722747 | + | 0.691113i | \(0.242879\pi\) | |||||||
\(618\) | 12.8184 | − | 14.5828i | 0.515630 | − | 0.586608i | ||||
\(619\) | −17.4140 | + | 30.1620i | −0.699928 | + | 1.21231i | 0.268562 | + | 0.963262i | \(0.413451\pi\) |
−0.968491 | + | 0.249049i | \(0.919882\pi\) | |||||||
\(620\) | 3.08262 | + | 5.33925i | 0.123801 | + | 0.214429i | ||||
\(621\) | 0.485508 | − | 7.03719i | 0.0194828 | − | 0.282393i | ||||
\(622\) | −28.7843 | −1.15415 | ||||||||
\(623\) | −1.65849 | + | 1.01398i | −0.0664460 | + | 0.0406242i | ||||
\(624\) | 10.1191 | + | 2.02486i | 0.405090 | + | 0.0810593i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0.185134 | 0.00739944 | ||||||||
\(627\) | −17.0969 | + | 19.4503i | −0.682784 | + | 0.776772i | ||||
\(628\) | −1.10586 | −0.0441285 | ||||||||
\(629\) | −27.4622 | −1.09499 | ||||||||
\(630\) | −4.97459 | − | 6.18494i | −0.198192 | − | 0.246414i | ||||
\(631\) | −21.5511 | −0.857934 | −0.428967 | − | 0.903320i | \(-0.641122\pi\) | ||||
−0.428967 | + | 0.903320i | \(0.641122\pi\) | |||||||
\(632\) | 14.7994 | 0.588688 | ||||||||
\(633\) | 10.0903 | + | 2.01909i | 0.401053 | + | 0.0802516i | ||||
\(634\) | −5.86194 | −0.232807 | ||||||||
\(635\) | 0.543587 | + | 0.941520i | 0.0215716 | + | 0.0373631i | ||||
\(636\) | −0.410910 | + | 0.467473i | −0.0162936 | + | 0.0185365i | ||||
\(637\) | −41.6540 | + | 2.09708i | −1.65039 | + | 0.0830892i | ||||
\(638\) | 15.5689 | 0.616379 | ||||||||
\(639\) | −8.40575 | + | 6.41945i | −0.332526 | + | 0.253950i | ||||
\(640\) | 0.500000 | + | 0.866025i | 0.0197642 | + | 0.0342327i | ||||
\(641\) | 11.2726 | − | 19.5247i | 0.445241 | − | 0.771180i | −0.552828 | − | 0.833295i | \(-0.686451\pi\) |
0.998069 | + | 0.0621154i | \(0.0197847\pi\) | |||||||
\(642\) | 12.7897 | + | 2.55924i | 0.504768 | + | 0.101005i | ||||
\(643\) | 4.05308 | − | 7.02014i | 0.159838 | − | 0.276847i | −0.774972 | − | 0.631995i | \(-0.782236\pi\) |
0.934810 | + | 0.355148i | \(0.115570\pi\) | |||||||
\(644\) | −0.0903261 | − | 3.59054i | −0.00355935 | − | 0.141487i | ||||
\(645\) | −3.32170 | − | 0.664678i | −0.130792 | − | 0.0261717i | ||||
\(646\) | −31.6711 | −1.24608 | ||||||||
\(647\) | 13.3586 | + | 23.1378i | 0.525180 | + | 0.909639i | 0.999570 | + | 0.0293242i | \(0.00933553\pi\) |
−0.474389 | + | 0.880315i | \(0.657331\pi\) | |||||||
\(648\) | −2.36914 | + | 8.68258i | −0.0930685 | + | 0.341084i | ||||
\(649\) | 3.59940 | − | 6.23435i | 0.141289 | − | 0.244720i | ||||
\(650\) | 2.97905 | + | 5.15987i | 0.116848 | + | 0.202387i | ||||
\(651\) | −4.84506 | + | 27.8341i | −0.189893 | + | 1.09090i | ||||
\(652\) | −3.44888 | + | 5.97364i | −0.135069 | + | 0.233946i | ||||
\(653\) | −3.03938 | − | 5.26436i | −0.118940 | − | 0.206010i | 0.800408 | − | 0.599456i | \(-0.204616\pi\) |
−0.919348 | + | 0.393446i | \(0.871283\pi\) | |||||||
\(654\) | −12.7998 | + | 14.5617i | −0.500511 | + | 0.569408i | ||||
\(655\) | −4.30124 | + | 7.44996i | −0.168063 | + | 0.291094i | ||||
\(656\) | −4.43192 | + | 7.67631i | −0.173037 | + | 0.299709i | ||||
\(657\) | −31.0163 | − | 12.9306i | −1.21006 | − | 0.504472i | ||||
\(658\) | 4.75038 | + | 2.58557i | 0.185189 | + | 0.100796i | ||||
\(659\) | −3.02425 | − | 5.23816i | −0.117808 | − | 0.204050i | 0.801091 | − | 0.598543i | \(-0.204253\pi\) |
−0.918899 | + | 0.394493i | \(0.870920\pi\) | |||||||
\(660\) | −1.39240 | − | 4.11734i | −0.0541989 | − | 0.160267i | ||||
\(661\) | 9.99425 | 0.388731 | 0.194366 | − | 0.980929i | \(-0.437735\pi\) | ||||
0.194366 | + | 0.980929i | \(0.437735\pi\) | |||||||
\(662\) | 1.74896 | 0.0679752 | ||||||||
\(663\) | −17.5734 | − | 51.9648i | −0.682494 | − | 2.01815i | ||||
\(664\) | 2.54006 | + | 4.39951i | 0.0985734 | + | 0.170734i | ||||
\(665\) | 13.8456 | + | 7.53601i | 0.536910 | + | 0.292234i | ||||
\(666\) | −1.98784 | − | 15.3709i | −0.0770274 | − | 0.595611i | ||||
\(667\) | 4.21121 | − | 7.29404i | 0.163059 | − | 0.282426i | ||||
\(668\) | −6.61206 | + | 11.4524i | −0.255828 | + | 0.443108i | ||||
\(669\) | −18.8359 | + | 21.4287i | −0.728238 | + | 0.828482i | ||||
\(670\) | 6.47303 | + | 11.2116i | 0.250075 | + | 0.433142i | ||||
\(671\) | −4.80423 | + | 8.32117i | −0.185465 | + | 0.321235i | ||||
\(672\) | −0.785868 | + | 4.51469i | −0.0303155 | + | 0.174158i | ||||
\(673\) | 2.40233 | + | 4.16096i | 0.0926031 | + | 0.160393i | 0.908606 | − | 0.417655i | \(-0.137148\pi\) |
−0.816003 | + | 0.578048i | \(0.803815\pi\) | |||||||
\(674\) | −8.99813 | + | 15.5852i | −0.346595 | + | 0.600320i | ||||
\(675\) | −4.66815 | + | 2.28219i | −0.179677 | + | 0.0878415i | ||||
\(676\) | −11.2495 | − | 19.4847i | −0.432673 | − | 0.749411i | ||||
\(677\) | −48.9810 | −1.88249 | −0.941247 | − | 0.337719i | \(-0.890345\pi\) | ||||
−0.941247 | + | 0.337719i | \(0.890345\pi\) | |||||||
\(678\) | −19.8329 | − | 3.96860i | −0.761677 | − | 0.152413i | ||||
\(679\) | −0.823832 | − | 32.7480i | −0.0316158 | − | 1.25675i | ||||
\(680\) | 2.65781 | − | 4.60347i | 0.101923 | − | 0.176535i | ||||
\(681\) | 30.2596 | + | 6.05501i | 1.15955 | + | 0.232028i | ||||
\(682\) | −7.73551 | + | 13.3983i | −0.296208 | + | 0.513047i | ||||
\(683\) | 8.41351 | + | 14.5726i | 0.321934 | + | 0.557606i | 0.980887 | − | 0.194578i | \(-0.0623338\pi\) |
−0.658953 | + | 0.752184i | \(0.729000\pi\) | |||||||
\(684\) | −2.29250 | − | 17.7267i | −0.0876561 | − | 0.677797i | ||||
\(685\) | −2.04590 | −0.0781699 | ||||||||
\(686\) | −1.39610 | − | 18.4676i | −0.0533035 | − | 0.705095i | ||||
\(687\) | 26.4316 | − | 30.0700i | 1.00843 | − | 1.14724i | ||||
\(688\) | 0.977900 | + | 1.69377i | 0.0372821 | + | 0.0645745i | ||||
\(689\) | 2.14099 | 0.0815653 | ||||||||
\(690\) | −2.30560 | − | 0.461356i | −0.0877727 | − | 0.0175635i | ||||
\(691\) | 13.1129 | 0.498840 | 0.249420 | − | 0.968395i | \(-0.419760\pi\) | ||||
0.249420 | + | 0.968395i | \(0.419760\pi\) | |||||||
\(692\) | −15.2751 | −0.580673 | ||||||||
\(693\) | 7.19952 | − | 18.5710i | 0.273487 | − | 0.705455i | ||||
\(694\) | 4.14672 | 0.157407 | ||||||||
\(695\) | −10.8854 | −0.412905 | ||||||||
\(696\) | −7.09461 | + | 8.07120i | −0.268920 | + | 0.305938i | ||||
\(697\) | 47.1169 | 1.78468 | ||||||||
\(698\) | 11.4215 | + | 19.7827i | 0.432312 | + | 0.748786i | ||||
\(699\) | −16.8111 | − | 3.36394i | −0.635855 | − | 0.127236i | ||||
\(700\) | −2.25729 | + | 1.38008i | −0.0853177 | + | 0.0521621i | ||||
\(701\) | 20.8396 | 0.787099 | 0.393550 | − | 0.919303i | \(-0.371247\pi\) | ||||
0.393550 | + | 0.919303i | \(0.371247\pi\) | |||||||
\(702\) | 27.8133 | − | 13.5975i | 1.04975 | − | 0.513205i | ||||
\(703\) | 15.3907 | + | 26.6575i | 0.580471 | + | 1.00540i | ||||
\(704\) | −1.25470 | + | 2.17320i | −0.0472882 | + | 0.0819056i | ||||
\(705\) | 2.33756 | − | 2.65934i | 0.0880377 | − | 0.100156i | ||||
\(706\) | −11.7572 | + | 20.3640i | −0.442487 | + | 0.766409i | ||||
\(707\) | −18.1492 | + | 11.0962i | −0.682570 | + | 0.417314i | ||||
\(708\) | 1.59178 | + | 4.70693i | 0.0598229 | + | 0.176897i | ||||
\(709\) | −12.8592 | −0.482938 | −0.241469 | − | 0.970408i | \(-0.577629\pi\) | ||||
−0.241469 | + | 0.970408i | \(0.577629\pi\) | |||||||
\(710\) | 1.76278 | + | 3.05322i | 0.0661559 | + | 0.114585i | ||||
\(711\) | 35.2852 | − | 26.9472i | 1.32330 | − | 1.01060i | ||||
\(712\) | 0.367362 | − | 0.636290i | 0.0137675 | − | 0.0238460i | ||||
\(713\) | 4.18474 | + | 7.24817i | 0.156720 | + | 0.271446i | ||||
\(714\) | 22.8719 | − | 8.38148i | 0.855960 | − | 0.313669i | ||||
\(715\) | −7.47562 | + | 12.9482i | −0.279573 | + | 0.484234i | ||||
\(716\) | −0.232599 | − | 0.402873i | −0.00869263 | − | 0.0150561i | ||||
\(717\) | 43.1163 | + | 8.62766i | 1.61021 | + | 0.322206i | ||||
\(718\) | 6.12241 | − | 10.6043i | 0.228486 | − | 0.395750i | ||||
\(719\) | 9.29950 | − | 16.1072i | 0.346813 | − | 0.600698i | −0.638869 | − | 0.769316i | \(-0.720597\pi\) |
0.985681 | + | 0.168618i | \(0.0539306\pi\) | |||||||
\(720\) | 2.76900 | + | 1.15439i | 0.103195 | + | 0.0430216i | ||||
\(721\) | −0.745860 | − | 29.6486i | −0.0277773 | − | 1.10417i | ||||
\(722\) | 8.24949 | + | 14.2885i | 0.307014 | + | 0.531764i | ||||
\(723\) | 48.6846 | + | 9.74190i | 1.81060 | + | 0.362305i | ||||
\(724\) | 26.1282 | 0.971046 | ||||||||
\(725\) | −6.20424 | −0.230420 | ||||||||
\(726\) | −5.37784 | + | 6.11811i | −0.199590 | + | 0.227064i | ||||
\(727\) | −7.48277 | − | 12.9605i | −0.277520 | − | 0.480680i | 0.693247 | − | 0.720700i | \(-0.256179\pi\) |
−0.970768 | + | 0.240020i | \(0.922846\pi\) | |||||||
\(728\) | 13.4492 | − | 8.22266i | 0.498460 | − | 0.304752i | ||||
\(729\) | 10.1610 | + | 25.0151i | 0.376332 | + | 0.926485i | ||||
\(730\) | −5.60063 | + | 9.70058i | −0.207289 | + | 0.359034i | ||||
\(731\) | 5.19815 | − | 9.00347i | 0.192261 | − | 0.333005i | ||||
\(732\) | −2.12460 | − | 6.28248i | −0.0785275 | − | 0.232207i | ||||
\(733\) | 12.4231 | + | 21.5174i | 0.458857 | + | 0.794764i | 0.998901 | − | 0.0468727i | \(-0.0149255\pi\) |
−0.540043 | + | 0.841637i | \(0.681592\pi\) | |||||||
\(734\) | −5.78768 | + | 10.0246i | −0.213627 | + | 0.370013i | ||||
\(735\) | −11.9933 | − | 1.77816i | −0.442378 | − | 0.0655884i | ||||
\(736\) | 0.678764 | + | 1.17565i | 0.0250196 | + | 0.0433352i | ||||
\(737\) | −16.2434 | + | 28.1344i | −0.598334 | + | 1.03634i | ||||
\(738\) | 3.41055 | + | 26.3719i | 0.125544 | + | 0.970762i | ||||
\(739\) | 2.77974 | + | 4.81466i | 0.102254 | + | 0.177110i | 0.912613 | − | 0.408824i | \(-0.134061\pi\) |
−0.810359 | + | 0.585934i | \(0.800728\pi\) | |||||||
\(740\) | −5.16631 | −0.189917 | ||||||||
\(741\) | −40.5934 | + | 46.1812i | −1.49124 | + | 1.69651i | ||||
\(742\) | 0.0239096 | + | 0.950427i | 0.000877748 | + | 0.0348913i | ||||
\(743\) | −13.6878 | + | 23.7080i | −0.502157 | + | 0.869762i | 0.497840 | + | 0.867269i | \(0.334127\pi\) |
−0.999997 | + | 0.00249280i | \(0.999207\pi\) | |||||||
\(744\) | −3.42092 | − | 10.1157i | −0.125417 | − | 0.370860i | ||||
\(745\) | 0.250077 | − | 0.433146i | 0.00916210 | − | 0.0158692i | ||||
\(746\) | −7.15324 | − | 12.3898i | −0.261899 | − | 0.453622i | ||||
\(747\) | 14.0669 | + | 5.86444i | 0.514680 | + | 0.214569i | ||||
\(748\) | 13.3390 | 0.487723 | ||||||||
\(749\) | 16.9985 | − | 10.3927i | 0.621113 | − | 0.379741i | ||||
\(750\) | 0.554872 | + | 1.64077i | 0.0202611 | + | 0.0599123i | ||||
\(751\) | 20.0674 | + | 34.7578i | 0.732271 | + | 1.26833i | 0.955910 | + | 0.293659i | \(0.0948731\pi\) |
−0.223639 | + | 0.974672i | \(0.571794\pi\) | |||||||
\(752\) | −2.04420 | −0.0745443 | ||||||||
\(753\) | −15.1991 | − | 44.9439i | −0.553885 | − | 1.63785i | ||||
\(754\) | 36.9655 | 1.34620 | ||||||||
\(755\) | −16.5764 | −0.603277 | ||||||||
\(756\) | 6.34680 | + | 12.1950i | 0.230831 | + | 0.443528i | ||||
\(757\) | −2.26550 | −0.0823410 | −0.0411705 | − | 0.999152i | \(-0.513109\pi\) | ||||
−0.0411705 | + | 0.999152i | \(0.513109\pi\) | |||||||
\(758\) | 5.19451 | 0.188673 | ||||||||
\(759\) | −1.89022 | − | 5.58940i | −0.0686105 | − | 0.202882i | ||||
\(760\) | −5.95810 | −0.216123 | ||||||||
\(761\) | 5.36510 | + | 9.29263i | 0.194485 | + | 0.336858i | 0.946732 | − | 0.322024i | \(-0.104363\pi\) |
−0.752247 | + | 0.658882i | \(0.771030\pi\) | |||||||
\(762\) | −0.603243 | − | 1.78380i | −0.0218532 | − | 0.0646202i | ||||
\(763\) | 0.744779 | + | 29.6056i | 0.0269628 | + | 1.07180i | ||||
\(764\) | −20.6483 | −0.747029 | ||||||||
\(765\) | −2.04530 | − | 15.8152i | −0.0739479 | − | 0.571799i | ||||
\(766\) | 5.92200 | + | 10.2572i | 0.213971 | + | 0.370608i | ||||
\(767\) | 8.54612 | − | 14.8023i | 0.308583 | − | 0.534481i | ||||
\(768\) | −0.554872 | − | 1.64077i | −0.0200222 | − | 0.0592061i | ||||
\(769\) | 3.58422 | − | 6.20804i | 0.129250 | − | 0.223868i | −0.794136 | − | 0.607740i | \(-0.792076\pi\) |
0.923386 | + | 0.383872i | \(0.125410\pi\) | |||||||
\(770\) | −5.83142 | − | 3.17397i | −0.210150 | − | 0.114382i | ||||
\(771\) | 29.6274 | − | 33.7057i | 1.06700 | − | 1.21388i | ||||
\(772\) | −15.7801 | −0.567937 | ||||||||
\(773\) | 12.1491 | + | 21.0428i | 0.436972 | + | 0.756859i | 0.997454 | − | 0.0713082i | \(-0.0227174\pi\) |
−0.560482 | + | 0.828167i | \(0.689384\pi\) | |||||||
\(774\) | 5.41562 | + | 2.25776i | 0.194660 | + | 0.0811534i | ||||
\(775\) | 3.08262 | − | 5.33925i | 0.110731 | − | 0.191791i | ||||
\(776\) | 6.19076 | + | 10.7227i | 0.222235 | + | 0.384923i | ||||
\(777\) | −18.1694 | − | 15.1782i | −0.651823 | − | 0.544516i | ||||
\(778\) | 17.6616 | − | 30.5908i | 0.633200 | − | 1.09673i | ||||
\(779\) | −26.4058 | − | 45.7362i | −0.946087 | − | 1.63867i | ||||
\(780\) | −3.30599 | − | 9.77586i | −0.118373 | − | 0.350032i | ||||
\(781\) | −4.42351 | + | 7.66175i | −0.158286 | + | 0.274159i | ||||
\(782\) | 3.60806 | − | 6.24934i | 0.129024 | − | 0.223476i | ||||
\(783\) | −2.21889 | + | 32.1617i | −0.0792968 | + | 1.14937i | ||||
\(784\) | 3.80039 | + | 5.87852i | 0.135728 | + | 0.209947i | ||||
\(785\) | 0.552928 | + | 0.957700i | 0.0197349 | + | 0.0341818i | ||||
\(786\) | 9.83702 | − | 11.1911i | 0.350875 | − | 0.399174i | ||||
\(787\) | −39.8058 | −1.41892 | −0.709462 | − | 0.704744i | \(-0.751062\pi\) | ||||
−0.709462 | + | 0.704744i | \(0.751062\pi\) | |||||||
\(788\) | 11.1659 | 0.397768 | ||||||||
\(789\) | 49.4005 | + | 9.88514i | 1.75870 | + | 0.351920i | ||||
\(790\) | −7.39969 | − | 12.8166i | −0.263269 | − | 0.455996i | ||||
\(791\) | −26.3596 | + | 16.1159i | −0.937239 | + | 0.573016i | ||||
\(792\) | 0.965543 | + | 7.46602i | 0.0343091 | + | 0.265293i | ||||
\(793\) | −11.4068 | + | 19.7571i | −0.405066 | + | 0.701595i | ||||
\(794\) | 5.44065 | − | 9.42348i | 0.193081 | − | 0.334427i | ||||
\(795\) | 0.610299 | + | 0.122122i | 0.0216451 | + | 0.00433122i | ||||
\(796\) | −12.9803 | − | 22.4825i | −0.460074 | − | 0.796872i | ||||
\(797\) | −21.8579 | + | 37.8591i | −0.774248 | + | 1.34104i | 0.160968 | + | 0.986960i | \(0.448538\pi\) |
−0.935216 | + | 0.354077i | \(0.884795\pi\) | |||||||
\(798\) | −20.9541 | − | 17.5045i | −0.741765 | − | 0.619651i | ||||
\(799\) | 5.43311 | + | 9.41042i | 0.192209 | + | 0.332917i | ||||
\(800\) | 0.500000 | − | 0.866025i | 0.0176777 | − | 0.0306186i | ||||
\(801\) | −0.282700 | − | 2.18597i | −0.00998873 | − | 0.0772374i | ||||
\(802\) | 14.3646 | + | 24.8801i | 0.507230 | + | 0.878548i | ||||
\(803\) | −28.1084 | −0.991925 | ||||||||
\(804\) | −7.18341 | − | 21.2415i | −0.253339 | − | 0.749129i | ||||
\(805\) | −3.06434 | + | 1.87350i | −0.108004 | + | 0.0660321i | ||||
\(806\) | −18.3665 | + | 31.8118i | −0.646934 | + | 1.12052i | ||||
\(807\) | −10.7464 | + | 12.2257i | −0.378292 | + | 0.430365i | ||||
\(808\) | 4.02012 | − | 6.96305i | 0.141427 | − | 0.244959i | ||||
\(809\) | −8.14162 | − | 14.1017i | −0.286244 | − | 0.495789i | 0.686666 | − | 0.726973i | \(-0.259073\pi\) |
−0.972910 | + | 0.231184i | \(0.925740\pi\) | |||||||
\(810\) | 8.70390 | − | 2.28956i | 0.305824 | − | 0.0804469i | ||||
\(811\) | −5.38713 | −0.189168 | −0.0945839 | − | 0.995517i | \(-0.530152\pi\) | ||||
−0.0945839 | + | 0.995517i | \(0.530152\pi\) | |||||||
\(812\) | 0.412813 | + | 16.4097i | 0.0144869 | + | 0.575867i | ||||
\(813\) | 1.94259 | + | 0.388717i | 0.0681297 | + | 0.0136329i | ||||
\(814\) | −6.48216 | − | 11.2274i | −0.227200 | − | 0.393521i | ||||
\(815\) | 6.89777 | 0.241618 | ||||||||
\(816\) | −6.07847 | + | 6.91519i | −0.212789 | + | 0.242080i | ||||
\(817\) | −11.6529 | −0.407682 | ||||||||
\(818\) | −2.79310 | −0.0976585 | ||||||||
\(819\) | 17.0939 | − | 44.0935i | 0.597310 | − | 1.54075i | ||||
\(820\) | 8.86383 | 0.309539 | ||||||||
\(821\) | 22.8971 | 0.799115 | 0.399557 | − | 0.916708i | \(-0.369164\pi\) | ||||
0.399557 | + | 0.916708i | \(0.369164\pi\) | |||||||
\(822\) | 3.47472 | + | 0.695299i | 0.121195 | + | 0.0242514i | ||||
\(823\) | −0.900425 | −0.0313869 | −0.0156934 | − | 0.999877i | \(-0.504996\pi\) | ||||
−0.0156934 | + | 0.999877i | \(0.504996\pi\) | |||||||
\(824\) | 5.60483 | + | 9.70785i | 0.195254 | + | 0.338189i | ||||
\(825\) | −2.86952 | + | 3.26452i | −0.0999039 | + | 0.113656i | ||||
\(826\) | 6.66647 | + | 3.62848i | 0.231956 | + | 0.126251i | ||||
\(827\) | 41.9173 | 1.45761 | 0.728803 | − | 0.684723i | \(-0.240077\pi\) | ||||
0.728803 | + | 0.684723i | \(0.240077\pi\) | |||||||
\(828\) | 3.75900 | + | 1.56712i | 0.130634 | + | 0.0544611i | ||||
\(829\) | 9.65386 | + | 16.7210i | 0.335293 | + | 0.580744i | 0.983541 | − | 0.180685i | \(-0.0578315\pi\) |
−0.648248 | + | 0.761429i | \(0.724498\pi\) | |||||||
\(830\) | 2.54006 | − | 4.39951i | 0.0881667 | − | 0.152709i | ||||
\(831\) | −12.1056 | − | 2.42237i | −0.419940 | − | 0.0840309i | ||||
\(832\) | −2.97905 | + | 5.15987i | −0.103280 | + | 0.178886i | ||||
\(833\) | 16.9609 | − | 33.1190i | 0.587660 | − | 1.14751i | ||||
\(834\) | 18.4875 | + | 3.69939i | 0.640170 | + | 0.128099i | ||||
\(835\) | 13.2241 | 0.457640 | ||||||||
\(836\) | −7.47562 | − | 12.9482i | −0.258550 | − | 0.447822i | ||||
\(837\) | −26.5753 | − | 17.8893i | −0.918576 | − | 0.618344i | ||||
\(838\) | −14.8923 | + | 25.7942i | −0.514445 | + | 0.891045i | ||||
\(839\) | 26.7782 | + | 46.3812i | 0.924486 | + | 1.60126i | 0.792386 | + | 0.610020i | \(0.208838\pi\) |
0.132099 | + | 0.991236i | \(0.457828\pi\) | |||||||
\(840\) | 4.30277 | − | 1.57676i | 0.148460 | − | 0.0544035i | ||||
\(841\) | −4.74630 | + | 8.22083i | −0.163665 | + | 0.283477i | ||||
\(842\) | −10.7947 | − | 18.6969i | −0.372009 | − | 0.644339i | ||||
\(843\) | 21.4209 | − | 24.3695i | 0.737774 | − | 0.839331i | ||||
\(844\) | −2.97056 | + | 5.14516i | −0.102251 | + | 0.177104i | ||||
\(845\) | −11.2495 | + | 19.4847i | −0.386994 | + | 0.670294i | ||||
\(846\) | −4.87385 | + | 3.72215i | −0.167566 | + | 0.127970i | ||||
\(847\) | 0.312919 | + | 12.4388i | 0.0107520 | + | 0.427403i | ||||
\(848\) | −0.179671 | − | 0.311199i | −0.00616991 | − | 0.0106866i | ||||
\(849\) | 17.5384 | + | 51.8614i | 0.601916 | + | 1.77988i | ||||
\(850\) | −5.31563 | −0.182325 | ||||||||
\(851\) | −7.01340 | −0.240416 | ||||||||
\(852\) | −1.95623 | − | 5.78462i | −0.0670195 | − | 0.198178i | ||||
\(853\) | 15.3011 | + | 26.5022i | 0.523899 | + | 0.907419i | 0.999613 | + | 0.0278194i | \(0.00885633\pi\) |
−0.475714 | + | 0.879600i | \(0.657810\pi\) | |||||||
\(854\) | −8.89793 | − | 4.84304i | −0.304481 | − | 0.165725i | ||||
\(855\) | −14.2055 | + | 10.8487i | −0.485818 | + | 0.371018i | ||||
\(856\) | −3.76525 | + | 6.52160i | −0.128694 | + | 0.222904i | ||||
\(857\) | 15.7006 | − | 27.1943i | 0.536323 | − | 0.928938i | −0.462776 | − | 0.886476i | \(-0.653146\pi\) |
0.999098 | − | 0.0424624i | \(-0.0135203\pi\) | |||||||
\(858\) | 17.0969 | − | 19.4503i | 0.583679 | − | 0.664024i | ||||
\(859\) | 16.9692 | + | 29.3915i | 0.578982 | + | 1.00283i | 0.995596 | + | 0.0937429i | \(0.0298832\pi\) |
−0.416614 | + | 0.909083i | \(0.636783\pi\) | |||||||
\(860\) | 0.977900 | − | 1.69377i | 0.0333461 | − | 0.0577572i | ||||
\(861\) | 31.1732 | + | 26.0413i | 1.06238 | + | 0.887485i | ||||
\(862\) | −17.4006 | − | 30.1387i | −0.592667 | − | 1.02653i | ||||
\(863\) | −1.42043 | + | 2.46026i | −0.0483521 | + | 0.0837483i | −0.889189 | − | 0.457541i | \(-0.848730\pi\) |
0.840836 | + | 0.541289i | \(0.182064\pi\) | |||||||
\(864\) | −4.31051 | − | 2.90164i | −0.146646 | − | 0.0987158i | ||||
\(865\) | 7.63756 | + | 13.2286i | 0.259685 | + | 0.449787i | ||||
\(866\) | 16.7114 | 0.567876 | ||||||||
\(867\) | 19.1169 | + | 3.82532i | 0.649242 | + | 0.129915i | ||||
\(868\) | −14.3270 | − | 7.79800i | −0.486289 | − | 0.264681i | ||||
\(869\) | 18.5688 | − | 32.1620i | 0.629902 | − | 1.09102i | ||||
\(870\) | 10.5372 | + | 2.10851i | 0.357244 | + | 0.0714852i | ||||
\(871\) | −38.5670 | + | 66.7999i | −1.30679 | + | 2.26343i | ||||
\(872\) | −5.59671 | − | 9.69378i | −0.189528 | − | 0.328273i | ||||
\(873\) | 34.2845 | + | 14.2931i | 1.16035 | + | 0.483748i | ||||
\(874\) | −8.08829 | −0.273590 | ||||||||
\(875\) | 2.32383 | + | 1.26483i | 0.0785599 | + | 0.0427592i | ||||
\(876\) | 12.8088 | − | 14.5719i | 0.432768 | − | 0.492339i | ||||
\(877\) | −1.85738 | − | 3.21708i | −0.0627193 | − | 0.108633i | 0.832961 | − | 0.553332i | \(-0.186644\pi\) |
−0.895680 | + | 0.444699i | \(0.853311\pi\) | |||||||
\(878\) | −30.6286 | −1.03366 | ||||||||
\(879\) | 9.93877 | + | 1.98877i | 0.335226 | + | 0.0670795i | ||||
\(880\) | 2.50940 | 0.0845918 | ||||||||
\(881\) | −13.9925 | −0.471420 | −0.235710 | − | 0.971823i | \(-0.575742\pi\) | ||||
−0.235710 | + | 0.971823i | \(0.575742\pi\) | |||||||
\(882\) | 19.7648 | + | 7.09590i | 0.665516 | + | 0.238931i | ||||
\(883\) | 5.02808 | 0.169208 | 0.0846041 | − | 0.996415i | \(-0.473037\pi\) | ||||
0.0846041 | + | 0.996415i | \(0.473037\pi\) | |||||||
\(884\) | 31.6711 | 1.06521 | ||||||||
\(885\) | 3.28043 | − | 3.73199i | 0.110270 | − | 0.125450i | ||||
\(886\) | −27.0075 | −0.907334 | ||||||||
\(887\) | −1.17692 | − | 2.03849i | −0.0395171 | − | 0.0684457i | 0.845590 | − | 0.533832i | \(-0.179249\pi\) |
−0.885108 | + | 0.465387i | \(0.845915\pi\) | |||||||
\(888\) | 8.77436 | + | 1.75577i | 0.294448 | + | 0.0589197i | ||||
\(889\) | −2.52641 | − | 1.37509i | −0.0847330 | − | 0.0461192i | ||||
\(890\) | −0.734724 | −0.0246280 | ||||||||
\(891\) | 15.8965 | + | 16.0426i | 0.532551 | + | 0.537449i | ||||
\(892\) | −8.23601 | − | 14.2652i | −0.275762 | − | 0.477634i | ||||
\(893\) | 6.08978 | − | 10.5478i | 0.203787 | − | 0.352969i | ||||
\(894\) | −0.571930 | + | 0.650658i | −0.0191282 | + | 0.0217613i | ||||
\(895\) | −0.232599 | + | 0.402873i | −0.00777492 | + | 0.0134666i | ||||
\(896\) | −2.32383 | − | 1.26483i | −0.0776338 | − | 0.0422551i | ||||
\(897\) | −4.48797 | − | 13.2710i | −0.149849 | − | 0.443106i | ||||
\(898\) | −40.6860 | −1.35771 | ||||||||
\(899\) | −19.1253 | − | 33.1260i | −0.637864 | − | 1.10481i | ||||
\(900\) | −0.384771 | − | 2.97522i | −0.0128257 | − | 0.0991741i | ||||
\(901\) | −0.955062 | + | 1.65422i | −0.0318177 | + | 0.0551099i | ||||
\(902\) | 11.1214 | + | 19.2629i | 0.370304 | + | 0.641385i | ||||
\(903\) | 8.41535 | − | 3.08383i | 0.280045 | − | 0.102623i | ||||
\(904\) | 5.83876 | − | 10.1130i | 0.194194 | − | 0.336354i | ||||
\(905\) | −13.0641 | − | 22.6277i | −0.434265 | − | 0.752169i | ||||
\(906\) | 28.1531 | + | 5.63349i | 0.935323 | + | 0.187160i | ||||
\(907\) | −5.42043 | + | 9.38845i | −0.179982 | + | 0.311739i | −0.941874 | − | 0.335966i | \(-0.890937\pi\) |
0.761892 | + | 0.647704i | \(0.224271\pi\) | |||||||
\(908\) | −8.90835 | + | 15.4297i | −0.295634 | + | 0.512053i | ||||
\(909\) | −3.09365 | − | 23.9215i | −0.102610 | − | 0.793426i | ||||
\(910\) | −13.8456 | − | 7.53601i | −0.458978 | − | 0.249816i | ||||
\(911\) | 10.8536 | + | 18.7990i | 0.359597 | + | 0.622839i | 0.987893 | − | 0.155134i | \(-0.0495810\pi\) |
−0.628297 | + | 0.777974i | \(0.716248\pi\) | |||||||
\(912\) | 10.1191 | + | 2.02486i | 0.335078 | + | 0.0670498i | ||||
\(913\) | 12.7480 | 0.421899 | ||||||||
\(914\) | −35.4495 | −1.17257 | ||||||||
\(915\) | −4.37849 | + | 4.98120i | −0.144748 | + | 0.164673i | ||||
\(916\) | 11.5572 | + | 20.0177i | 0.381861 | + | 0.661403i | ||||
\(917\) | −0.572385 | − | 22.7528i | −0.0189018 | − | 0.751364i | ||||
\(918\) | −1.90109 | + | 27.5553i | −0.0627453 | + | 0.909461i | ||||
\(919\) | −2.25667 | + | 3.90867i | −0.0744407 | + | 0.128935i | −0.900843 | − | 0.434145i | \(-0.857050\pi\) |
0.826402 | + | 0.563080i | \(0.190384\pi\) | |||||||
\(920\) | 0.678764 | − | 1.17565i | 0.0223782 | − | 0.0387601i | ||||
\(921\) | −10.0370 | − | 29.6796i | −0.330731 | − | 0.977977i | ||||
\(922\) | −11.9946 | − | 20.7753i | −0.395022 | − | 0.684197i | ||||
\(923\) | −10.5028 | + | 18.1914i | −0.345704 | + | 0.598778i | ||||
\(924\) | 8.82530 | + | 7.37243i | 0.290331 | + | 0.242535i | ||||
\(925\) | 2.58315 | + | 4.47415i | 0.0849335 | + | 0.147109i | ||||
\(926\) | −6.53066 | + | 11.3114i | −0.214611 | + | 0.371717i | ||||
\(927\) | 31.0396 | + | 12.9403i | 1.01947 | + | 0.425016i | ||||
\(928\) | −3.10212 | − | 5.37303i | −0.101832 | − | 0.176378i | ||||
\(929\) | 49.8155 | 1.63439 | 0.817196 | − | 0.576359i | \(-0.195527\pi\) | ||||
0.817196 | + | 0.576359i | \(0.195527\pi\) | |||||||
\(930\) | −7.05000 | + | 8.02045i | −0.231179 | + | 0.263001i | ||||
\(931\) | −41.6540 | + | 2.09708i | −1.36515 | + | 0.0687289i | ||||
\(932\) | 4.94916 | − | 8.57219i | 0.162115 | − | 0.280792i | ||||
\(933\) | −15.9716 | − | 47.2284i | −0.522888 | − | 1.54619i | ||||
\(934\) | 11.0880 | − | 19.2050i | 0.362811 | − | 0.628406i | ||||
\(935\) | −6.66952 | − | 11.5519i | −0.218116 | − | 0.377789i | ||||
\(936\) | 2.29250 | + | 17.7267i | 0.0749328 | + | 0.579415i | ||||
\(937\) | 21.8677 | 0.714387 | 0.357194 | − | 0.934030i | \(-0.383734\pi\) | ||||
0.357194 | + | 0.934030i | \(0.383734\pi\) | |||||||
\(938\) | −30.0845 | − | 16.3746i | −0.982292 | − | 0.534650i | ||||
\(939\) | 0.102726 | + | 0.303762i | 0.00335233 | + | 0.00991289i | ||||
\(940\) | 1.02210 | + | 1.77033i | 0.0333372 | + | 0.0577418i | ||||
\(941\) | 1.42852 | 0.0465685 | 0.0232842 | − | 0.999729i | \(-0.492588\pi\) | ||||
0.0232842 | + | 0.999729i | \(0.492588\pi\) | |||||||
\(942\) | −0.613609 | − | 1.81445i | −0.0199925 | − | 0.0591181i | ||||
\(943\) | 12.0329 | 0.391845 | ||||||||
\(944\) | −2.86874 | −0.0933695 | ||||||||
\(945\) | 7.38778 | − | 11.5940i | 0.240325 | − | 0.377153i | ||||
\(946\) | 4.90788 | 0.159569 | ||||||||
\(947\) | 7.84837 | 0.255038 | 0.127519 | − | 0.991836i | \(-0.459299\pi\) | ||||
0.127519 | + | 0.991836i | \(0.459299\pi\) | |||||||
\(948\) | 8.21177 | + | 24.2823i | 0.266706 | + | 0.788654i | ||||
\(949\) | −66.7383 | −2.16642 | ||||||||
\(950\) | 2.97905 | + | 5.15987i | 0.0966532 | + | 0.167408i | ||||
\(951\) | −3.25263 | − | 9.61807i | −0.105474 | − | 0.311887i | ||||
\(952\) | 0.353687 | + | 14.0594i | 0.0114631 | + | 0.455667i | ||||
\(953\) | −20.2969 | −0.657480 | −0.328740 | − | 0.944420i | \(-0.606624\pi\) | ||||
−0.328740 | + | 0.944420i | \(0.606624\pi\) | |||||||
\(954\) | −0.995017 | − | 0.414820i | −0.0322149 | − | 0.0134303i | ||||
\(955\) | 10.3242 | + | 17.8820i | 0.334082 | + | 0.578647i | ||||
\(956\) | −12.6933 | + | 21.9855i | −0.410532 | + | 0.711062i | ||||
\(957\) | 8.63876 | + | 25.5450i | 0.279251 | + | 0.825751i | ||||
\(958\) | −16.2605 | + | 28.1639i | −0.525351 | + | 0.909935i | ||||
\(959\) | 4.61820 | − | 2.82351i | 0.149130 | − | 0.0911758i | ||||
\(960\) | −1.14351 | + | 1.30092i | −0.0369066 | + | 0.0419869i | ||||
\(961\) | 7.01007 | 0.226131 | ||||||||
\(962\) | −15.3907 | − | 26.6575i | −0.496216 | − | 0.859471i | ||||
\(963\) | 2.89752 | + | 22.4049i | 0.0933711 | + | 0.721988i | ||||
\(964\) | −14.3326 | + | 24.8249i | −0.461623 | + | 0.799555i | ||||
\(965\) | 7.89003 | + | 13.6659i | 0.253989 | + | 0.439922i | ||||
\(966\) | 5.84113 | − | 2.14050i | 0.187935 | − | 0.0688694i | ||||
\(967\) | 4.14865 | − | 7.18567i | 0.133411 | − | 0.231075i | −0.791578 | − | 0.611068i | \(-0.790740\pi\) |
0.924990 | + | 0.379993i | \(0.124073\pi\) | |||||||
\(968\) | −2.35146 | − | 4.07285i | −0.0755788 | − | 0.130906i | ||||
\(969\) | −17.5734 | − | 51.9648i | −0.564539 | − | 1.66935i | ||||
\(970\) | 6.19076 | − | 10.7227i | 0.198773 | − | 0.344285i | ||||
\(971\) | −23.9345 | + | 41.4558i | −0.768096 | + | 1.33038i | 0.170498 | + | 0.985358i | \(0.445462\pi\) |
−0.938594 | + | 0.345023i | \(0.887871\pi\) | |||||||
\(972\) | −15.5607 | + | 0.930524i | −0.499108 | + | 0.0298466i | ||||
\(973\) | 24.5715 | − | 15.0227i | 0.787725 | − | 0.481605i | ||||
\(974\) | 9.99511 | + | 17.3120i | 0.320264 | + | 0.554713i | ||||
\(975\) | −6.81315 | + | 7.75100i | −0.218195 | + | 0.248231i | ||||
\(976\) | 3.82899 | 0.122563 | ||||||||
\(977\) | −13.1524 | −0.420783 | −0.210391 | − | 0.977617i | \(-0.567474\pi\) | ||||
−0.210391 | + | 0.977617i | \(0.567474\pi\) | |||||||
\(978\) | −11.7150 | − | 2.34421i | −0.374606 | − | 0.0749594i | ||||
\(979\) | −0.921858 | − | 1.59670i | −0.0294627 | − | 0.0510309i | ||||
\(980\) | 3.19076 | − | 6.23049i | 0.101925 | − | 0.199026i | ||||
\(981\) | −30.9946 | − | 12.9216i | −0.989581 | − | 0.412554i | ||||
\(982\) | −15.5637 | + | 26.9570i | −0.496656 | + | 0.860234i | ||||
\(983\) | −26.9090 | + | 46.6077i | −0.858262 | + | 1.48655i | 0.0153228 | + | 0.999883i | \(0.495122\pi\) |
−0.873585 | + | 0.486671i | \(0.838211\pi\) | |||||||
\(984\) | −15.0542 | − | 3.01237i | −0.479910 | − | 0.0960310i | ||||
\(985\) | −5.58294 | − | 9.66993i | −0.177887 | − | 0.308110i | ||||
\(986\) | −16.4897 | + | 28.5610i | −0.525140 | + | 0.909569i | ||||
\(987\) | −1.60647 | + | 9.22893i | −0.0511346 | + | 0.293760i | ||||
\(988\) | −17.7495 | − | 30.7430i | −0.564687 | − | 0.978066i | ||||
\(989\) | 1.32753 | − | 2.29934i | 0.0422129 | − | 0.0731148i | ||||
\(990\) | 5.98299 | − | 4.56919i | 0.190152 | − | 0.145219i | ||||
\(991\) | 12.4080 | + | 21.4913i | 0.394153 | + | 0.682693i | 0.992993 | − | 0.118176i | \(-0.0377046\pi\) |
−0.598839 | + | 0.800869i | \(0.704371\pi\) | |||||||
\(992\) | 6.16523 | 0.195746 | ||||||||
\(993\) | 0.970448 | + | 2.86963i | 0.0307963 | + | 0.0910650i | ||||
\(994\) | −8.19280 | − | 4.45925i | −0.259860 | − | 0.141439i | ||||
\(995\) | −12.9803 | + | 22.4825i | −0.411503 | + | 0.712744i | ||||
\(996\) | −5.80917 | + | 6.60881i | −0.184070 | + | 0.209408i | ||||
\(997\) | −21.8366 | + | 37.8220i | −0.691571 | + | 1.19784i | 0.279752 | + | 0.960072i | \(0.409748\pi\) |
−0.971323 | + | 0.237764i | \(0.923586\pi\) | |||||||
\(998\) | 7.40897 | + | 12.8327i | 0.234527 | + | 0.406212i | ||||
\(999\) | 24.1171 | − | 11.7905i | 0.763031 | − | 0.373034i |
(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 | 630.2.i.f.121.2 | ✓ | 12 | |
3.2 | odd | 2 | 1890.2.i.h.1171.6 | 12 | |||
7.4 | even | 3 | 630.2.l.h.571.2 | yes | 12 | ||
9.2 | odd | 6 | 1890.2.l.f.1801.3 | 12 | |||
9.7 | even | 3 | 630.2.l.h.331.2 | yes | 12 | ||
21.11 | odd | 6 | 1890.2.l.f.361.3 | 12 | |||
63.11 | odd | 6 | 1890.2.i.h.991.6 | 12 | |||
63.25 | even | 3 | inner | 630.2.i.f.151.2 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.i.f.121.2 | ✓ | 12 | 1.1 | even | 1 | trivial | |
630.2.i.f.151.2 | yes | 12 | 63.25 | even | 3 | inner | |
630.2.l.h.331.2 | yes | 12 | 9.7 | even | 3 | ||
630.2.l.h.571.2 | yes | 12 | 7.4 | even | 3 | ||
1890.2.i.h.991.6 | 12 | 63.11 | odd | 6 | |||
1890.2.i.h.1171.6 | 12 | 3.2 | odd | 2 | |||
1890.2.l.f.361.3 | 12 | 21.11 | odd | 6 | |||
1890.2.l.f.1801.3 | 12 | 9.2 | odd | 6 |