Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(109,630)]
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([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.109");
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.u (of order \(6\), 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: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 70) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 109.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.109 |
Dual form | 630.2.u.a.289.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | −0.133975 | − | 2.23205i | −0.0599153 | − | 0.998203i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.73205 | − | 2.00000i | −0.654654 | − | 0.755929i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.23205 | + | 1.86603i | 0.389609 | + | 0.590089i | ||||
\(11\) | 1.50000 | − | 2.59808i | 0.452267 | − | 0.783349i | −0.546259 | − | 0.837616i | \(-0.683949\pi\) |
0.998526 | + | 0.0542666i | \(0.0172821\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.00000i | 1.38675i | 0.720577 | + | 0.693375i | \(0.243877\pi\) | ||||
−0.720577 | + | 0.693375i | \(0.756123\pi\) | |||||||
\(14\) | 2.50000 | + | 0.866025i | 0.668153 | + | 0.231455i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.73205 | − | 1.00000i | −0.420084 | − | 0.242536i | 0.275029 | − | 0.961436i | \(-0.411312\pi\) |
−0.695113 | + | 0.718900i | \(0.744646\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.50000 | − | 4.33013i | −0.573539 | − | 0.993399i | −0.996199 | − | 0.0871106i | \(-0.972237\pi\) |
0.422659 | − | 0.906289i | \(-0.361097\pi\) | |||||||
\(20\) | −2.00000 | − | 1.00000i | −0.447214 | − | 0.223607i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.00000i | 0.639602i | ||||||||
\(23\) | −6.06218 | + | 3.50000i | −1.26405 | + | 0.729800i | −0.973856 | − | 0.227167i | \(-0.927054\pi\) |
−0.290196 | + | 0.956967i | \(0.593720\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.96410 | + | 0.598076i | −0.992820 | + | 0.119615i | ||||
\(26\) | −2.50000 | − | 4.33013i | −0.490290 | − | 0.849208i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.59808 | + | 0.500000i | −0.490990 | + | 0.0944911i | ||||
\(29\) | −4.00000 | −0.742781 | −0.371391 | − | 0.928477i | \(-0.621119\pi\) | ||||
−0.371391 | + | 0.928477i | \(0.621119\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.00000 | − | 1.73205i | 0.179605 | − | 0.311086i | −0.762140 | − | 0.647412i | \(-0.775851\pi\) |
0.941745 | + | 0.336327i | \(0.109185\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | −4.23205 | + | 4.13397i | −0.715347 | + | 0.698769i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.866025 | − | 0.500000i | 0.142374 | − | 0.0821995i | −0.427121 | − | 0.904194i | \(-0.640472\pi\) |
0.569495 | + | 0.821995i | \(0.307139\pi\) | |||||||
\(38\) | 4.33013 | + | 2.50000i | 0.702439 | + | 0.405554i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.23205 | − | 0.133975i | 0.352918 | − | 0.0211832i | ||||
\(41\) | −3.00000 | −0.468521 | −0.234261 | − | 0.972174i | \(-0.575267\pi\) | ||||
−0.234261 | + | 0.972174i | \(0.575267\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.00000i | − | 0.304997i | −0.988304 | − | 0.152499i | \(-0.951268\pi\) | ||
0.988304 | − | 0.152499i | \(-0.0487319\pi\) | |||||||
\(44\) | −1.50000 | − | 2.59808i | −0.226134 | − | 0.391675i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.50000 | − | 6.06218i | 0.516047 | − | 0.893819i | ||||
\(47\) | 6.06218 | − | 3.50000i | 0.884260 | − | 0.510527i | 0.0121990 | − | 0.999926i | \(-0.496117\pi\) |
0.872060 | + | 0.489398i | \(0.162783\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | + | 6.92820i | −0.142857 | + | 0.989743i | ||||
\(50\) | 4.00000 | − | 3.00000i | 0.565685 | − | 0.424264i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.33013 | + | 2.50000i | 0.600481 | + | 0.346688i | ||||
\(53\) | −7.79423 | − | 4.50000i | −1.07062 | − | 0.618123i | −0.142269 | − | 0.989828i | \(-0.545440\pi\) |
−0.928351 | + | 0.371706i | \(0.878773\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.00000 | − | 3.00000i | −0.809040 | − | 0.404520i | ||||
\(56\) | 2.00000 | − | 1.73205i | 0.267261 | − | 0.231455i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.46410 | − | 2.00000i | 0.454859 | − | 0.262613i | ||||
\(59\) | 2.00000 | − | 3.46410i | 0.260378 | − | 0.450988i | −0.705965 | − | 0.708247i | \(-0.749486\pi\) |
0.966342 | + | 0.257260i | \(0.0828195\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.00000 | − | 5.19615i | −0.384111 | − | 0.665299i | 0.607535 | − | 0.794293i | \(-0.292159\pi\) |
−0.991645 | + | 0.128994i | \(0.958825\pi\) | |||||||
\(62\) | 2.00000i | 0.254000i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 11.1603 | − | 0.669873i | 1.38426 | − | 0.0830875i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.73205 | − | 1.00000i | −0.211604 | − | 0.122169i | 0.390453 | − | 0.920623i | \(-0.372318\pi\) |
−0.602056 | + | 0.798454i | \(0.705652\pi\) | |||||||
\(68\) | −1.73205 | + | 1.00000i | −0.210042 | + | 0.121268i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.59808 | − | 5.69615i | 0.191007 | − | 0.680820i | ||||
\(71\) | 6.00000 | 0.712069 | 0.356034 | − | 0.934473i | \(-0.384129\pi\) | ||||
0.356034 | + | 0.934473i | \(0.384129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.8564 | − | 8.00000i | −1.62177 | − | 0.936329i | −0.986447 | − | 0.164083i | \(-0.947534\pi\) |
−0.635323 | − | 0.772246i | \(-0.719133\pi\) | |||||||
\(74\) | −0.500000 | + | 0.866025i | −0.0581238 | + | 0.100673i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.00000 | −0.573539 | ||||||||
\(77\) | −7.79423 | + | 1.50000i | −0.888235 | + | 0.170941i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.00000 | + | 12.1244i | 0.787562 | + | 1.36410i | 0.927457 | + | 0.373930i | \(0.121990\pi\) |
−0.139895 | + | 0.990166i | \(0.544677\pi\) | |||||||
\(80\) | −1.86603 | + | 1.23205i | −0.208628 | + | 0.137747i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.59808 | − | 1.50000i | 0.286910 | − | 0.165647i | ||||
\(83\) | − | 6.00000i | − | 0.658586i | −0.944228 | − | 0.329293i | \(-0.893190\pi\) | ||
0.944228 | − | 0.329293i | \(-0.106810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.00000 | + | 4.00000i | −0.216930 | + | 0.433861i | ||||
\(86\) | 1.00000 | + | 1.73205i | 0.107833 | + | 0.186772i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.59808 | + | 1.50000i | 0.276956 | + | 0.159901i | ||||
\(89\) | −1.00000 | − | 1.73205i | −0.106000 | − | 0.183597i | 0.808146 | − | 0.588982i | \(-0.200471\pi\) |
−0.914146 | + | 0.405385i | \(0.867138\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.0000 | − | 8.66025i | 1.04828 | − | 0.907841i | ||||
\(92\) | 7.00000i | 0.729800i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.50000 | + | 6.06218i | −0.360997 | + | 0.625266i | ||||
\(95\) | −9.33013 | + | 6.16025i | −0.957251 | + | 0.632029i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 12.0000i | − | 1.21842i | −0.793011 | − | 0.609208i | \(-0.791488\pi\) | ||
0.793011 | − | 0.609208i | \(-0.208512\pi\) | |||||||
\(98\) | −2.59808 | − | 6.50000i | −0.262445 | − | 0.656599i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.96410 | + | 4.59808i | −0.196410 | + | 0.459808i | ||||
\(101\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.92820 | − | 4.00000i | 0.682656 | − | 0.394132i | −0.118199 | − | 0.992990i | \(-0.537712\pi\) |
0.800855 | + | 0.598858i | \(0.204379\pi\) | |||||||
\(104\) | −5.00000 | −0.490290 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.00000 | 0.874157 | ||||||||
\(107\) | 13.8564 | − | 8.00000i | 1.33955 | − | 0.773389i | 0.352809 | − | 0.935695i | \(-0.385227\pi\) |
0.986740 | + | 0.162306i | \(0.0518932\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.00000 | − | 1.73205i | 0.0957826 | − | 0.165900i | −0.814152 | − | 0.580651i | \(-0.802798\pi\) |
0.909935 | + | 0.414751i | \(0.136131\pi\) | |||||||
\(110\) | 6.69615 | − | 0.401924i | 0.638453 | − | 0.0383219i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.866025 | + | 2.50000i | −0.0818317 | + | 0.236228i | ||||
\(113\) | 14.0000i | 1.31701i | 0.752577 | + | 0.658505i | \(0.228811\pi\) | ||||
−0.752577 | + | 0.658505i | \(0.771189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.62436 | + | 13.0622i | 0.804225 | + | 1.21805i | ||||
\(116\) | −2.00000 | + | 3.46410i | −0.185695 | + | 0.321634i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.00000i | 0.368230i | ||||||||
\(119\) | 1.00000 | + | 5.19615i | 0.0916698 | + | 0.476331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | + | 1.73205i | 0.0909091 | + | 0.157459i | ||||
\(122\) | 5.19615 | + | 3.00000i | 0.470438 | + | 0.271607i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.00000 | − | 1.73205i | −0.0898027 | − | 0.155543i | ||||
\(125\) | 2.00000 | + | 11.0000i | 0.178885 | + | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.00000i | 0.621150i | 0.950549 | + | 0.310575i | \(0.100522\pi\) | ||||
−0.950549 | + | 0.310575i | \(0.899478\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −9.33013 | + | 6.16025i | −0.818306 | + | 0.540290i | ||||
\(131\) | −0.500000 | − | 0.866025i | −0.0436852 | − | 0.0756650i | 0.843356 | − | 0.537355i | \(-0.180577\pi\) |
−0.887041 | + | 0.461690i | \(0.847243\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.33013 | + | 12.5000i | −0.375470 | + | 1.08389i | ||||
\(134\) | 2.00000 | 0.172774 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.00000 | − | 1.73205i | 0.0857493 | − | 0.148522i | ||||
\(137\) | −6.92820 | − | 4.00000i | −0.591916 | − | 0.341743i | 0.173939 | − | 0.984757i | \(-0.444351\pi\) |
−0.765855 | + | 0.643013i | \(0.777684\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.0000 | −1.35710 | −0.678551 | − | 0.734553i | \(-0.737392\pi\) | ||||
−0.678551 | + | 0.734553i | \(0.737392\pi\) | |||||||
\(140\) | 1.46410 | + | 5.73205i | 0.123739 | + | 0.484447i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.19615 | + | 3.00000i | −0.436051 | + | 0.251754i | ||||
\(143\) | 12.9904 | + | 7.50000i | 1.08631 | + | 0.627182i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.535898 | + | 8.92820i | 0.0445039 | + | 0.741447i | ||||
\(146\) | 16.0000 | 1.32417 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 1.00000i | − | 0.0821995i | ||||||
\(149\) | 9.00000 | + | 15.5885i | 0.737309 | + | 1.27706i | 0.953703 | + | 0.300750i | \(0.0972370\pi\) |
−0.216394 | + | 0.976306i | \(0.569430\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.00000 | − | 5.19615i | 0.244137 | − | 0.422857i | −0.717752 | − | 0.696299i | \(-0.754829\pi\) |
0.961888 | + | 0.273442i | \(0.0881622\pi\) | |||||||
\(152\) | 4.33013 | − | 2.50000i | 0.351220 | − | 0.202777i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.00000 | − | 5.19615i | 0.483494 | − | 0.418718i | ||||
\(155\) | −4.00000 | − | 2.00000i | −0.321288 | − | 0.160644i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.79423 | + | 4.50000i | 0.622047 | + | 0.359139i | 0.777666 | − | 0.628678i | \(-0.216404\pi\) |
−0.155618 | + | 0.987817i | \(0.549737\pi\) | |||||||
\(158\) | −12.1244 | − | 7.00000i | −0.964562 | − | 0.556890i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.00000 | − | 2.00000i | 0.0790569 | − | 0.158114i | ||||
\(161\) | 17.5000 | + | 6.06218i | 1.37919 | + | 0.477767i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.3923 | − | 6.00000i | 0.813988 | − | 0.469956i | −0.0343508 | − | 0.999410i | \(-0.510936\pi\) |
0.848339 | + | 0.529454i | \(0.177603\pi\) | |||||||
\(164\) | −1.50000 | + | 2.59808i | −0.117130 | + | 0.202876i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.00000 | + | 5.19615i | 0.232845 | + | 0.403300i | ||||
\(167\) | − | 15.0000i | − | 1.16073i | −0.814355 | − | 0.580367i | \(-0.802909\pi\) | ||
0.814355 | − | 0.580367i | \(-0.197091\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | −0.267949 | − | 4.46410i | −0.0205508 | − | 0.342381i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.73205 | − | 1.00000i | −0.132068 | − | 0.0762493i | ||||
\(173\) | 7.79423 | − | 4.50000i | 0.592584 | − | 0.342129i | −0.173534 | − | 0.984828i | \(-0.555519\pi\) |
0.766119 | + | 0.642699i | \(0.222185\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.79423 | + | 8.89230i | 0.740374 | + | 0.672195i | ||||
\(176\) | −3.00000 | −0.226134 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.73205 | + | 1.00000i | 0.129823 | + | 0.0749532i | ||||
\(179\) | −6.50000 | + | 11.2583i | −0.485833 | + | 0.841487i | −0.999867 | − | 0.0162823i | \(-0.994817\pi\) |
0.514035 | + | 0.857769i | \(0.328150\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 26.0000 | 1.93256 | 0.966282 | − | 0.257485i | \(-0.0828937\pi\) | ||||
0.966282 | + | 0.257485i | \(0.0828937\pi\) | |||||||
\(182\) | −4.33013 | + | 12.5000i | −0.320970 | + | 0.926562i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.50000 | − | 6.06218i | −0.258023 | − | 0.446910i | ||||
\(185\) | −1.23205 | − | 1.86603i | −0.0905822 | − | 0.137193i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.19615 | + | 3.00000i | −0.379980 | + | 0.219382i | ||||
\(188\) | − | 7.00000i | − | 0.510527i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.00000 | − | 10.0000i | 0.362738 | − | 0.725476i | ||||
\(191\) | −10.0000 | − | 17.3205i | −0.723575 | − | 1.25327i | −0.959558 | − | 0.281511i | \(-0.909164\pi\) |
0.235983 | − | 0.971757i | \(-0.424169\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.66025 | − | 5.00000i | −0.623379 | − | 0.359908i | 0.154805 | − | 0.987945i | \(-0.450525\pi\) |
−0.778183 | + | 0.628037i | \(0.783859\pi\) | |||||||
\(194\) | 6.00000 | + | 10.3923i | 0.430775 | + | 0.746124i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.50000 | + | 4.33013i | 0.392857 | + | 0.309295i | ||||
\(197\) | 5.00000i | 0.356235i | 0.984009 | + | 0.178118i | \(0.0570008\pi\) | ||||
−0.984009 | + | 0.178118i | \(0.942999\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.00000 | − | 15.5885i | 0.637993 | − | 1.10504i | −0.347879 | − | 0.937539i | \(-0.613098\pi\) |
0.985873 | − | 0.167497i | \(-0.0535685\pi\) | |||||||
\(200\) | −0.598076 | − | 4.96410i | −0.0422904 | − | 0.351015i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.92820 | + | 8.00000i | 0.486265 | + | 0.561490i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.401924 | + | 6.69615i | 0.0280716 | + | 0.467680i | ||||
\(206\) | −4.00000 | + | 6.92820i | −0.278693 | + | 0.482711i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.33013 | − | 2.50000i | 0.300240 | − | 0.173344i | ||||
\(209\) | −15.0000 | −1.03757 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.00000 | −0.619586 | −0.309793 | − | 0.950804i | \(-0.600260\pi\) | ||||
−0.309793 | + | 0.950804i | \(0.600260\pi\) | |||||||
\(212\) | −7.79423 | + | 4.50000i | −0.535310 | + | 0.309061i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8.00000 | + | 13.8564i | −0.546869 | + | 0.947204i | ||||
\(215\) | −4.46410 | + | 0.267949i | −0.304449 | + | 0.0182740i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.19615 | + | 1.00000i | −0.352738 | + | 0.0678844i | ||||
\(218\) | 2.00000i | 0.135457i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −5.59808 | + | 3.69615i | −0.377422 | + | 0.249195i | ||||
\(221\) | 5.00000 | − | 8.66025i | 0.336336 | − | 0.582552i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.00000i | 0.535720i | 0.963458 | + | 0.267860i | \(0.0863164\pi\) | ||||
−0.963458 | + | 0.267860i | \(0.913684\pi\) | |||||||
\(224\) | −0.500000 | − | 2.59808i | −0.0334077 | − | 0.173591i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.00000 | − | 12.1244i | −0.465633 | − | 0.806500i | ||||
\(227\) | −5.19615 | − | 3.00000i | −0.344881 | − | 0.199117i | 0.317547 | − | 0.948242i | \(-0.397141\pi\) |
−0.662428 | + | 0.749125i | \(0.730474\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.00000 | + | 13.8564i | 0.528655 | + | 0.915657i | 0.999442 | + | 0.0334101i | \(0.0106368\pi\) |
−0.470787 | + | 0.882247i | \(0.656030\pi\) | |||||||
\(230\) | −14.0000 | − | 7.00000i | −0.923133 | − | 0.461566i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 4.00000i | − | 0.262613i | ||||||
\(233\) | −6.92820 | + | 4.00000i | −0.453882 | + | 0.262049i | −0.709468 | − | 0.704737i | \(-0.751065\pi\) |
0.255586 | + | 0.966786i | \(0.417731\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.62436 | − | 13.0622i | −0.562591 | − | 0.852083i | ||||
\(236\) | −2.00000 | − | 3.46410i | −0.130189 | − | 0.225494i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.46410 | − | 4.00000i | −0.224544 | − | 0.259281i | ||||
\(239\) | 20.0000 | 1.29369 | 0.646846 | − | 0.762620i | \(-0.276088\pi\) | ||||
0.646846 | + | 0.762620i | \(0.276088\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.50000 | − | 7.79423i | 0.289870 | − | 0.502070i | −0.683908 | − | 0.729568i | \(-0.739721\pi\) |
0.973779 | + | 0.227498i | \(0.0730544\pi\) | |||||||
\(242\) | −1.73205 | − | 1.00000i | −0.111340 | − | 0.0642824i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.00000 | −0.384111 | ||||||||
\(245\) | 15.5981 | + | 1.30385i | 0.996525 | + | 0.0832998i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 21.6506 | − | 12.5000i | 1.37760 | − | 0.795356i | ||||
\(248\) | 1.73205 | + | 1.00000i | 0.109985 | + | 0.0635001i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −7.23205 | − | 8.52628i | −0.457395 | − | 0.539249i | ||||
\(251\) | −5.00000 | −0.315597 | −0.157799 | − | 0.987471i | \(-0.550440\pi\) | ||||
−0.157799 | + | 0.987471i | \(0.550440\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.0000i | 1.32026i | ||||||||
\(254\) | −3.50000 | − | 6.06218i | −0.219610 | − | 0.380375i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 5.19615 | − | 3.00000i | 0.324127 | − | 0.187135i | −0.329104 | − | 0.944294i | \(-0.606747\pi\) |
0.653231 | + | 0.757159i | \(0.273413\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.50000 | − | 0.866025i | −0.155342 | − | 0.0538122i | ||||
\(260\) | 5.00000 | − | 10.0000i | 0.310087 | − | 0.620174i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.866025 | + | 0.500000i | 0.0535032 | + | 0.0308901i | ||||
\(263\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.00000 | + | 18.0000i | −0.552866 | + | 1.10573i | ||||
\(266\) | −2.50000 | − | 12.9904i | −0.153285 | − | 0.796491i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.73205 | + | 1.00000i | −0.105802 | + | 0.0610847i | ||||
\(269\) | 5.00000 | − | 8.66025i | 0.304855 | − | 0.528025i | −0.672374 | − | 0.740212i | \(-0.734725\pi\) |
0.977229 | + | 0.212187i | \(0.0680585\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.0000 | − | 20.7846i | −0.728948 | − | 1.26258i | −0.957328 | − | 0.289003i | \(-0.906676\pi\) |
0.228380 | − | 0.973572i | \(-0.426657\pi\) | |||||||
\(272\) | 2.00000i | 0.121268i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.00000 | 0.483298 | ||||||||
\(275\) | −5.89230 | + | 13.7942i | −0.355319 | + | 0.831823i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.73205 | + | 1.00000i | 0.104069 | + | 0.0600842i | 0.551131 | − | 0.834419i | \(-0.314196\pi\) |
−0.447062 | + | 0.894503i | \(0.647530\pi\) | |||||||
\(278\) | 13.8564 | − | 8.00000i | 0.831052 | − | 0.479808i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.13397 | − | 4.23205i | −0.247052 | − | 0.252913i | ||||
\(281\) | −9.00000 | −0.536895 | −0.268447 | − | 0.963294i | \(-0.586511\pi\) | ||||
−0.268447 | + | 0.963294i | \(0.586511\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.1244 | + | 7.00000i | 0.720718 | + | 0.416107i | 0.815017 | − | 0.579437i | \(-0.196728\pi\) |
−0.0942988 | + | 0.995544i | \(0.530061\pi\) | |||||||
\(284\) | 3.00000 | − | 5.19615i | 0.178017 | − | 0.308335i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −15.0000 | −0.886969 | ||||||||
\(287\) | 5.19615 | + | 6.00000i | 0.306719 | + | 0.354169i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.50000 | − | 11.2583i | −0.382353 | − | 0.662255i | ||||
\(290\) | −4.92820 | − | 7.46410i | −0.289394 | − | 0.438307i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −13.8564 | + | 8.00000i | −0.810885 | + | 0.468165i | ||||
\(293\) | − | 9.00000i | − | 0.525786i | −0.964825 | − | 0.262893i | \(-0.915323\pi\) | ||
0.964825 | − | 0.262893i | \(-0.0846766\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.00000 | − | 4.00000i | −0.465778 | − | 0.232889i | ||||
\(296\) | 0.500000 | + | 0.866025i | 0.0290619 | + | 0.0503367i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −15.5885 | − | 9.00000i | −0.903015 | − | 0.521356i | ||||
\(299\) | −17.5000 | − | 30.3109i | −1.01205 | − | 1.75292i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.00000 | + | 3.46410i | −0.230556 | + | 0.199667i | ||||
\(302\) | 6.00000i | 0.345261i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.50000 | + | 4.33013i | −0.143385 | + | 0.248350i | ||||
\(305\) | −11.1962 | + | 7.39230i | −0.641090 | + | 0.423282i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 22.0000i | − | 1.25561i | −0.778372 | − | 0.627803i | \(-0.783954\pi\) | ||
0.778372 | − | 0.627803i | \(-0.216046\pi\) | |||||||
\(308\) | −2.59808 | + | 7.50000i | −0.148039 | + | 0.427352i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.46410 | − | 0.267949i | 0.253544 | − | 0.0152185i | ||||
\(311\) | 3.00000 | − | 5.19615i | 0.170114 | − | 0.294647i | −0.768345 | − | 0.640036i | \(-0.778920\pi\) |
0.938460 | + | 0.345389i | \(0.112253\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.0526 | − | 11.0000i | 1.07691 | − | 0.621757i | 0.146852 | − | 0.989158i | \(-0.453086\pi\) |
0.930062 | + | 0.367402i | \(0.119753\pi\) | |||||||
\(314\) | −9.00000 | −0.507899 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.0000 | 0.787562 | ||||||||
\(317\) | 1.73205 | − | 1.00000i | 0.0972817 | − | 0.0561656i | −0.450570 | − | 0.892741i | \(-0.648779\pi\) |
0.547852 | + | 0.836576i | \(0.315446\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.00000 | + | 10.3923i | −0.335936 | + | 0.581857i | ||||
\(320\) | 0.133975 | + | 2.23205i | 0.00748941 | + | 0.124775i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −18.1865 | + | 3.50000i | −1.01350 | + | 0.195047i | ||||
\(323\) | 10.0000i | 0.556415i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.99038 | − | 24.8205i | −0.165876 | − | 1.37679i | ||||
\(326\) | −6.00000 | + | 10.3923i | −0.332309 | + | 0.575577i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 3.00000i | − | 0.165647i | ||||||
\(329\) | −17.5000 | − | 6.06218i | −0.964806 | − | 0.334219i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.50000 | − | 4.33013i | −0.137412 | − | 0.238005i | 0.789104 | − | 0.614260i | \(-0.210545\pi\) |
−0.926516 | + | 0.376254i | \(0.877212\pi\) | |||||||
\(332\) | −5.19615 | − | 3.00000i | −0.285176 | − | 0.164646i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7.50000 | + | 12.9904i | 0.410382 | + | 0.710802i | ||||
\(335\) | −2.00000 | + | 4.00000i | −0.109272 | + | 0.218543i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.0000i | 0.544735i | 0.962193 | + | 0.272367i | \(0.0878066\pi\) | ||||
−0.962193 | + | 0.272367i | \(0.912193\pi\) | |||||||
\(338\) | 10.3923 | − | 6.00000i | 0.565267 | − | 0.326357i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.46410 | + | 3.73205i | 0.133635 | + | 0.202399i | ||||
\(341\) | −3.00000 | − | 5.19615i | −0.162459 | − | 0.281387i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.5885 | − | 10.0000i | 0.841698 | − | 0.539949i | ||||
\(344\) | 2.00000 | 0.107833 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.50000 | + | 7.79423i | −0.241921 | + | 0.419020i | ||||
\(347\) | −10.3923 | − | 6.00000i | −0.557888 | − | 0.322097i | 0.194409 | − | 0.980921i | \(-0.437721\pi\) |
−0.752297 | + | 0.658824i | \(0.771054\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.0000 | 0.642345 | 0.321173 | − | 0.947021i | \(-0.395923\pi\) | ||||
0.321173 | + | 0.947021i | \(0.395923\pi\) | |||||||
\(350\) | −12.9282 | − | 2.80385i | −0.691042 | − | 0.149872i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.59808 | − | 1.50000i | 0.138478 | − | 0.0799503i | ||||
\(353\) | −20.7846 | − | 12.0000i | −1.10625 | − | 0.638696i | −0.168397 | − | 0.985719i | \(-0.553859\pi\) |
−0.937856 | + | 0.347024i | \(0.887192\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.803848 | − | 13.3923i | −0.0426638 | − | 0.710790i | ||||
\(356\) | −2.00000 | −0.106000 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 13.0000i | − | 0.687071i | ||||||
\(359\) | −8.00000 | − | 13.8564i | −0.422224 | − | 0.731313i | 0.573933 | − | 0.818902i | \(-0.305417\pi\) |
−0.996157 | + | 0.0875892i | \(0.972084\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | + | 5.19615i | −0.157895 | + | 0.273482i | ||||
\(362\) | −22.5167 | + | 13.0000i | −1.18345 | + | 0.683265i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.50000 | − | 12.9904i | −0.131036 | − | 0.680881i | ||||
\(365\) | −16.0000 | + | 32.0000i | −0.837478 | + | 1.67496i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.2583 | − | 6.50000i | −0.587680 | − | 0.339297i | 0.176500 | − | 0.984301i | \(-0.443523\pi\) |
−0.764180 | + | 0.645003i | \(0.776856\pi\) | |||||||
\(368\) | 6.06218 | + | 3.50000i | 0.316013 | + | 0.182450i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.00000 | + | 1.00000i | 0.103975 | + | 0.0519875i | ||||
\(371\) | 4.50000 | + | 23.3827i | 0.233628 | + | 1.21397i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.5167 | + | 13.0000i | −1.16587 | + | 0.673114i | −0.952703 | − | 0.303902i | \(-0.901711\pi\) |
−0.213165 | + | 0.977016i | \(0.568377\pi\) | |||||||
\(374\) | 3.00000 | − | 5.19615i | 0.155126 | − | 0.268687i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.50000 | + | 6.06218i | 0.180499 | + | 0.312633i | ||||
\(377\) | − | 20.0000i | − | 1.03005i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.0000 | 1.48963 | 0.744815 | − | 0.667271i | \(-0.232538\pi\) | ||||
0.744815 | + | 0.667271i | \(0.232538\pi\) | |||||||
\(380\) | 0.669873 | + | 11.1603i | 0.0343638 | + | 0.572509i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 17.3205 | + | 10.0000i | 0.886194 | + | 0.511645i | ||||
\(383\) | 18.1865 | − | 10.5000i | 0.929288 | − | 0.536525i | 0.0427020 | − | 0.999088i | \(-0.486403\pi\) |
0.886586 | + | 0.462563i | \(0.153070\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.39230 | + | 17.1962i | 0.223853 | + | 0.876397i | ||||
\(386\) | 10.0000 | 0.508987 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −10.3923 | − | 6.00000i | −0.527589 | − | 0.304604i | ||||
\(389\) | 3.00000 | − | 5.19615i | 0.152106 | − | 0.263455i | −0.779895 | − | 0.625910i | \(-0.784728\pi\) |
0.932002 | + | 0.362454i | \(0.118061\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.0000 | 0.708010 | ||||||||
\(392\) | −6.92820 | − | 1.00000i | −0.349927 | − | 0.0505076i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.50000 | − | 4.33013i | −0.125948 | − | 0.218149i | ||||
\(395\) | 26.1244 | − | 17.2487i | 1.31446 | − | 0.867877i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.1244 | + | 7.00000i | −0.608504 | + | 0.351320i | −0.772380 | − | 0.635161i | \(-0.780934\pi\) |
0.163876 | + | 0.986481i | \(0.447600\pi\) | |||||||
\(398\) | 18.0000i | 0.902258i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.00000 | + | 4.00000i | 0.150000 | + | 0.200000i | ||||
\(401\) | −7.50000 | − | 12.9904i | −0.374532 | − | 0.648709i | 0.615725 | − | 0.787961i | \(-0.288863\pi\) |
−0.990257 | + | 0.139253i | \(0.955530\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.66025 | + | 5.00000i | 0.431398 | + | 0.249068i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10.0000 | − | 3.46410i | −0.496292 | − | 0.171920i | ||||
\(407\) | − | 3.00000i | − | 0.148704i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.00000 | + | 12.1244i | −0.346128 | + | 0.599511i | −0.985558 | − | 0.169338i | \(-0.945837\pi\) |
0.639430 | + | 0.768849i | \(0.279170\pi\) | |||||||
\(410\) | −3.69615 | − | 5.59808i | −0.182540 | − | 0.276469i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 8.00000i | − | 0.394132i | ||||||
\(413\) | −10.3923 | + | 2.00000i | −0.511372 | + | 0.0984136i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.3923 | + | 0.803848i | −0.657402 | + | 0.0394593i | ||||
\(416\) | −2.50000 | + | 4.33013i | −0.122573 | + | 0.212302i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 12.9904 | − | 7.50000i | 0.635380 | − | 0.366837i | ||||
\(419\) | 35.0000 | 1.70986 | 0.854931 | − | 0.518742i | \(-0.173599\pi\) | ||||
0.854931 | + | 0.518742i | \(0.173599\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.0000 | −0.974740 | −0.487370 | − | 0.873195i | \(-0.662044\pi\) | ||||
−0.487370 | + | 0.873195i | \(0.662044\pi\) | |||||||
\(422\) | 7.79423 | − | 4.50000i | 0.379417 | − | 0.219057i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.50000 | − | 7.79423i | 0.218539 | − | 0.378521i | ||||
\(425\) | 9.19615 | + | 3.92820i | 0.446079 | + | 0.190546i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.19615 | + | 15.0000i | −0.251459 | + | 0.725901i | ||||
\(428\) | − | 16.0000i | − | 0.773389i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.73205 | − | 2.46410i | 0.179975 | − | 0.118830i | ||||
\(431\) | 1.00000 | − | 1.73205i | 0.0481683 | − | 0.0834300i | −0.840936 | − | 0.541135i | \(-0.817995\pi\) |
0.889104 | + | 0.457705i | \(0.151328\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 28.0000i | − | 1.34559i | −0.739827 | − | 0.672797i | \(-0.765093\pi\) | ||
0.739827 | − | 0.672797i | \(-0.234907\pi\) | |||||||
\(434\) | 4.00000 | − | 3.46410i | 0.192006 | − | 0.166282i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.00000 | − | 1.73205i | −0.0478913 | − | 0.0829502i | ||||
\(437\) | 30.3109 | + | 17.5000i | 1.44997 | + | 0.837139i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.0000 | − | 24.2487i | −0.668184 | − | 1.15733i | −0.978412 | − | 0.206666i | \(-0.933739\pi\) |
0.310228 | − | 0.950662i | \(-0.399595\pi\) | |||||||
\(440\) | 3.00000 | − | 6.00000i | 0.143019 | − | 0.286039i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 10.0000i | 0.475651i | ||||||||
\(443\) | 25.9808 | − | 15.0000i | 1.23438 | − | 0.712672i | 0.266443 | − | 0.963851i | \(-0.414152\pi\) |
0.967941 | + | 0.251179i | \(0.0808184\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.73205 | + | 2.46410i | −0.176916 | + | 0.116810i | ||||
\(446\) | −4.00000 | − | 6.92820i | −0.189405 | − | 0.328060i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.73205 | + | 2.00000i | 0.0818317 | + | 0.0944911i | ||||
\(449\) | 5.00000 | 0.235965 | 0.117982 | − | 0.993016i | \(-0.462357\pi\) | ||||
0.117982 | + | 0.993016i | \(0.462357\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.50000 | + | 7.79423i | −0.211897 | + | 0.367016i | ||||
\(452\) | 12.1244 | + | 7.00000i | 0.570282 | + | 0.329252i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.00000 | 0.281594 | ||||||||
\(455\) | −20.6699 | − | 21.1603i | −0.969019 | − | 0.992008i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.66025 | + | 5.00000i | −0.405110 | + | 0.233890i | −0.688686 | − | 0.725059i | \(-0.741812\pi\) |
0.283577 | + | 0.958950i | \(0.408479\pi\) | |||||||
\(458\) | −13.8564 | − | 8.00000i | −0.647467 | − | 0.373815i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 15.6244 | − | 0.937822i | 0.728489 | − | 0.0437262i | ||||
\(461\) | 32.0000 | 1.49039 | 0.745194 | − | 0.666847i | \(-0.232357\pi\) | ||||
0.745194 | + | 0.666847i | \(0.232357\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.0000i | 0.790057i | 0.918669 | + | 0.395029i | \(0.129265\pi\) | ||||
−0.918669 | + | 0.395029i | \(0.870735\pi\) | |||||||
\(464\) | 2.00000 | + | 3.46410i | 0.0928477 | + | 0.160817i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.00000 | − | 6.92820i | 0.185296 | − | 0.320943i | ||||
\(467\) | −29.4449 | + | 17.0000i | −1.36255 | + | 0.786666i | −0.989962 | − | 0.141332i | \(-0.954861\pi\) |
−0.372584 | + | 0.927999i | \(0.621528\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.00000 | + | 5.19615i | 0.0461757 | + | 0.239936i | ||||
\(470\) | 14.0000 | + | 7.00000i | 0.645772 | + | 0.322886i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.46410 | + | 2.00000i | 0.159448 | + | 0.0920575i | ||||
\(473\) | −5.19615 | − | 3.00000i | −0.238919 | − | 0.137940i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.0000 | + | 20.0000i | 0.688247 | + | 0.917663i | ||||
\(476\) | 5.00000 | + | 1.73205i | 0.229175 | + | 0.0793884i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −17.3205 | + | 10.0000i | −0.792222 | + | 0.457389i | ||||
\(479\) | −18.0000 | + | 31.1769i | −0.822441 | + | 1.42451i | 0.0814184 | + | 0.996680i | \(0.474055\pi\) |
−0.903859 | + | 0.427830i | \(0.859278\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.50000 | + | 4.33013i | 0.113990 | + | 0.197437i | ||||
\(482\) | 9.00000i | 0.409939i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.00000 | 0.0909091 | ||||||||
\(485\) | −26.7846 | + | 1.60770i | −1.21623 | + | 0.0730017i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.7128 | + | 16.0000i | 1.25579 | + | 0.725029i | 0.972253 | − | 0.233933i | \(-0.0751596\pi\) |
0.283535 | + | 0.958962i | \(0.408493\pi\) | |||||||
\(488\) | 5.19615 | − | 3.00000i | 0.235219 | − | 0.135804i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −14.1603 | + | 6.66987i | −0.639695 | + | 0.301314i | ||||
\(491\) | −24.0000 | −1.08310 | −0.541552 | − | 0.840667i | \(-0.682163\pi\) | ||||
−0.541552 | + | 0.840667i | \(0.682163\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.92820 | + | 4.00000i | 0.312031 | + | 0.180151i | ||||
\(494\) | −12.5000 | + | 21.6506i | −0.562402 | + | 0.974108i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.00000 | −0.0898027 | ||||||||
\(497\) | −10.3923 | − | 12.0000i | −0.466159 | − | 0.538274i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.00000 | + | 3.46410i | 0.0895323 | + | 0.155074i | 0.907314 | − | 0.420455i | \(-0.138129\pi\) |
−0.817781 | + | 0.575529i | \(0.804796\pi\) | |||||||
\(500\) | 10.5263 | + | 3.76795i | 0.470750 | + | 0.168508i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.33013 | − | 2.50000i | 0.193263 | − | 0.111580i | ||||
\(503\) | 40.0000i | 1.78351i | 0.452517 | + | 0.891756i | \(0.350526\pi\) | ||||
−0.452517 | + | 0.891756i | \(0.649474\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −10.5000 | − | 18.1865i | −0.466782 | − | 0.808490i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.06218 | + | 3.50000i | 0.268966 | + | 0.155287i | ||||
\(509\) | 17.0000 | + | 29.4449i | 0.753512 | + | 1.30512i | 0.946111 | + | 0.323843i | \(0.104975\pi\) |
−0.192599 | + | 0.981278i | \(0.561692\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.00000 | + | 41.5692i | 0.353899 | + | 1.83891i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.00000 | + | 5.19615i | −0.132324 | + | 0.229192i | ||||
\(515\) | −9.85641 | − | 14.9282i | −0.434325 | − | 0.657815i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 21.0000i | − | 0.923579i | ||||||
\(518\) | 2.59808 | − | 0.500000i | 0.114153 | − | 0.0219687i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.669873 | + | 11.1603i | 0.0293759 | + | 0.489410i | ||||
\(521\) | −13.5000 | + | 23.3827i | −0.591446 | + | 1.02441i | 0.402592 | + | 0.915379i | \(0.368109\pi\) |
−0.994038 | + | 0.109035i | \(0.965224\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.8564 | + | 8.00000i | −0.605898 | + | 0.349816i | −0.771358 | − | 0.636401i | \(-0.780422\pi\) |
0.165460 | + | 0.986216i | \(0.447089\pi\) | |||||||
\(524\) | −1.00000 | −0.0436852 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.46410 | + | 2.00000i | −0.150899 | + | 0.0871214i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.0000 | − | 22.5167i | 0.565217 | − | 0.978985i | ||||
\(530\) | −1.20577 | − | 20.0885i | −0.0523754 | − | 0.872587i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.66025 | + | 10.0000i | 0.375470 | + | 0.433555i | ||||
\(533\) | − | 15.0000i | − | 0.649722i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19.7128 | − | 29.8564i | −0.852259 | − | 1.29081i | ||||
\(536\) | 1.00000 | − | 1.73205i | 0.0431934 | − | 0.0748132i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 10.0000i | 0.431131i | ||||||||
\(539\) | 16.5000 | + | 12.9904i | 0.710705 | + | 0.559535i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.00000 | + | 13.8564i | 0.343947 | + | 0.595733i | 0.985162 | − | 0.171628i | \(-0.0549027\pi\) |
−0.641215 | + | 0.767361i | \(0.721569\pi\) | |||||||
\(542\) | 20.7846 | + | 12.0000i | 0.892775 | + | 0.515444i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.00000 | − | 1.73205i | −0.0428746 | − | 0.0742611i | ||||
\(545\) | −4.00000 | − | 2.00000i | −0.171341 | − | 0.0856706i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 26.0000i | − | 1.11168i | −0.831289 | − | 0.555840i | \(-0.812397\pi\) | ||
0.831289 | − | 0.555840i | \(-0.187603\pi\) | |||||||
\(548\) | −6.92820 | + | 4.00000i | −0.295958 | + | 0.170872i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.79423 | − | 14.8923i | −0.0765062 | − | 0.635010i | ||||
\(551\) | 10.0000 | + | 17.3205i | 0.426014 | + | 0.737878i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.1244 | − | 35.0000i | 0.515580 | − | 1.48835i | ||||
\(554\) | −2.00000 | −0.0849719 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.00000 | + | 13.8564i | −0.339276 | + | 0.587643i | ||||
\(557\) | 19.9186 | + | 11.5000i | 0.843978 | + | 0.487271i | 0.858614 | − | 0.512622i | \(-0.171326\pi\) |
−0.0146368 | + | 0.999893i | \(0.504659\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.0000 | 0.422955 | ||||||||
\(560\) | 5.69615 | + | 1.59808i | 0.240706 | + | 0.0675310i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.79423 | − | 4.50000i | 0.328780 | − | 0.189821i | ||||
\(563\) | −1.73205 | − | 1.00000i | −0.0729972 | − | 0.0421450i | 0.463057 | − | 0.886328i | \(-0.346752\pi\) |
−0.536054 | + | 0.844183i | \(0.680086\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 31.2487 | − | 1.87564i | 1.31464 | − | 0.0789090i | ||||
\(566\) | −14.0000 | −0.588464 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.00000i | 0.251754i | ||||||||
\(569\) | 7.50000 | + | 12.9904i | 0.314416 | + | 0.544585i | 0.979313 | − | 0.202350i | \(-0.0648579\pi\) |
−0.664897 | + | 0.746935i | \(0.731525\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.0000 | + | 27.7128i | −0.669579 | + | 1.15975i | 0.308443 | + | 0.951243i | \(0.400192\pi\) |
−0.978022 | + | 0.208502i | \(0.933141\pi\) | |||||||
\(572\) | 12.9904 | − | 7.50000i | 0.543155 | − | 0.313591i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −7.50000 | − | 2.59808i | −0.313044 | − | 0.108442i | ||||
\(575\) | 28.0000 | − | 21.0000i | 1.16768 | − | 0.875761i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.46410 | + | 2.00000i | 0.144212 | + | 0.0832611i | 0.570370 | − | 0.821388i | \(-0.306800\pi\) |
−0.426158 | + | 0.904649i | \(0.640133\pi\) | |||||||
\(578\) | 11.2583 | + | 6.50000i | 0.468285 | + | 0.270364i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 8.00000 | + | 4.00000i | 0.332182 | + | 0.166091i | ||||
\(581\) | −12.0000 | + | 10.3923i | −0.497844 | + | 0.431145i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23.3827 | + | 13.5000i | −0.968412 | + | 0.559113i | ||||
\(584\) | 8.00000 | − | 13.8564i | 0.331042 | − | 0.573382i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.50000 | + | 7.79423i | 0.185893 | + | 0.321977i | ||||
\(587\) | − | 34.0000i | − | 1.40333i | −0.712507 | − | 0.701665i | \(-0.752440\pi\) | ||
0.712507 | − | 0.701665i | \(-0.247560\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.0000 | −0.412043 | ||||||||
\(590\) | 8.92820 | − | 0.535898i | 0.367568 | − | 0.0220626i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.866025 | − | 0.500000i | −0.0355934 | − | 0.0205499i | ||||
\(593\) | −5.19615 | + | 3.00000i | −0.213380 | + | 0.123195i | −0.602881 | − | 0.797831i | \(-0.705981\pi\) |
0.389501 | + | 0.921026i | \(0.372647\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.4641 | − | 2.92820i | 0.469982 | − | 0.120045i | ||||
\(596\) | 18.0000 | 0.737309 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 30.3109 | + | 17.5000i | 1.23950 | + | 0.715628i | ||||
\(599\) | 6.00000 | − | 10.3923i | 0.245153 | − | 0.424618i | −0.717021 | − | 0.697051i | \(-0.754495\pi\) |
0.962175 | + | 0.272433i | \(0.0878284\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.0000 | −0.897399 | −0.448699 | − | 0.893683i | \(-0.648113\pi\) | ||||
−0.448699 | + | 0.893683i | \(0.648113\pi\) | |||||||
\(602\) | 1.73205 | − | 5.00000i | 0.0705931 | − | 0.203785i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.00000 | − | 5.19615i | −0.122068 | − | 0.211428i | ||||
\(605\) | 3.73205 | − | 2.46410i | 0.151729 | − | 0.100180i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.2583 | + | 6.50000i | −0.456962 | + | 0.263827i | −0.710766 | − | 0.703429i | \(-0.751651\pi\) |
0.253804 | + | 0.967256i | \(0.418318\pi\) | |||||||
\(608\) | − | 5.00000i | − | 0.202777i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.00000 | − | 12.0000i | 0.242933 | − | 0.485866i | ||||
\(611\) | 17.5000 | + | 30.3109i | 0.707974 | + | 1.22625i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.9904 | − | 7.50000i | −0.524677 | − | 0.302922i | 0.214169 | − | 0.976797i | \(-0.431296\pi\) |
−0.738846 | + | 0.673874i | \(0.764629\pi\) | |||||||
\(614\) | 11.0000 | + | 19.0526i | 0.443924 | + | 0.768899i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.50000 | − | 7.79423i | −0.0604367 | − | 0.314038i | ||||
\(617\) | − | 14.0000i | − | 0.563619i | −0.959470 | − | 0.281809i | \(-0.909065\pi\) | ||
0.959470 | − | 0.281809i | \(-0.0909346\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.50000 | − | 16.4545i | 0.381837 | − | 0.661361i | −0.609488 | − | 0.792796i | \(-0.708625\pi\) |
0.991325 | + | 0.131434i | \(0.0419582\pi\) | |||||||
\(620\) | −3.73205 | + | 2.46410i | −0.149883 | + | 0.0989607i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.00000i | 0.240578i | ||||||||
\(623\) | −1.73205 | + | 5.00000i | −0.0693932 | + | 0.200321i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.2846 | − | 5.93782i | 0.971384 | − | 0.237513i | ||||
\(626\) | −11.0000 | + | 19.0526i | −0.439648 | + | 0.761493i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.79423 | − | 4.50000i | 0.311024 | − | 0.179570i | ||||
\(629\) | −2.00000 | −0.0797452 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.0000 | −0.716569 | −0.358284 | − | 0.933613i | \(-0.616638\pi\) | ||||
−0.358284 | + | 0.933613i | \(0.616638\pi\) | |||||||
\(632\) | −12.1244 | + | 7.00000i | −0.482281 | + | 0.278445i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.00000 | + | 1.73205i | −0.0397151 | + | 0.0687885i | ||||
\(635\) | 15.6244 | − | 0.937822i | 0.620034 | − | 0.0372163i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −34.6410 | − | 5.00000i | −1.37253 | − | 0.198107i | ||||
\(638\) | − | 12.0000i | − | 0.475085i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.23205 | − | 1.86603i | −0.0487011 | − | 0.0737611i | ||||
\(641\) | −2.50000 | + | 4.33013i | −0.0987441 | + | 0.171030i | −0.911165 | − | 0.412042i | \(-0.864816\pi\) |
0.812421 | + | 0.583071i | \(0.198149\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.0000i | 0.552106i | 0.961142 | + | 0.276053i | \(0.0890266\pi\) | ||||
−0.961142 | + | 0.276053i | \(0.910973\pi\) | |||||||
\(644\) | 14.0000 | − | 12.1244i | 0.551677 | − | 0.477767i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.00000 | − | 8.66025i | −0.196722 | − | 0.340733i | ||||
\(647\) | −23.3827 | − | 13.5000i | −0.919268 | − | 0.530740i | −0.0358667 | − | 0.999357i | \(-0.511419\pi\) |
−0.883402 | + | 0.468617i | \(0.844753\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.00000 | − | 10.3923i | −0.235521 | − | 0.407934i | ||||
\(650\) | 15.0000 | + | 20.0000i | 0.588348 | + | 0.784465i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 12.0000i | − | 0.469956i | ||||||
\(653\) | 2.59808 | − | 1.50000i | 0.101671 | − | 0.0586995i | −0.448303 | − | 0.893882i | \(-0.647971\pi\) |
0.549973 | + | 0.835182i | \(0.314638\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.86603 | + | 1.23205i | −0.0729116 | + | 0.0481402i | ||||
\(656\) | 1.50000 | + | 2.59808i | 0.0585652 | + | 0.101438i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 18.1865 | − | 3.50000i | 0.708985 | − | 0.136444i | ||||
\(659\) | −36.0000 | −1.40236 | −0.701180 | − | 0.712984i | \(-0.747343\pi\) | ||||
−0.701180 | + | 0.712984i | \(0.747343\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.00000 | + | 13.8564i | −0.311164 | + | 0.538952i | −0.978615 | − | 0.205702i | \(-0.934052\pi\) |
0.667451 | + | 0.744654i | \(0.267385\pi\) | |||||||
\(662\) | 4.33013 | + | 2.50000i | 0.168295 | + | 0.0971653i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.00000 | 0.232845 | ||||||||
\(665\) | 28.4808 | + | 7.99038i | 1.10444 | + | 0.309854i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 24.2487 | − | 14.0000i | 0.938914 | − | 0.542082i | ||||
\(668\) | −12.9904 | − | 7.50000i | −0.502613 | − | 0.290184i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −0.267949 | − | 4.46410i | −0.0103518 | − | 0.172463i | ||||
\(671\) | −18.0000 | −0.694882 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 32.0000i | − | 1.23351i | −0.787155 | − | 0.616755i | \(-0.788447\pi\) | ||
0.787155 | − | 0.616755i | \(-0.211553\pi\) | |||||||
\(674\) | −5.00000 | − | 8.66025i | −0.192593 | − | 0.333581i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.00000 | + | 10.3923i | −0.230769 | + | 0.399704i | ||||
\(677\) | 14.7224 | − | 8.50000i | 0.565829 | − | 0.326682i | −0.189653 | − | 0.981851i | \(-0.560736\pi\) |
0.755482 | + | 0.655170i | \(0.227403\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −24.0000 | + | 20.7846i | −0.921035 | + | 0.797640i | ||||
\(680\) | −4.00000 | − | 2.00000i | −0.153393 | − | 0.0766965i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5.19615 | + | 3.00000i | 0.198971 | + | 0.114876i | ||||
\(683\) | 38.1051 | + | 22.0000i | 1.45805 | + | 0.841807i | 0.998916 | − | 0.0465592i | \(-0.0148256\pi\) |
0.459136 | + | 0.888366i | \(0.348159\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.00000 | + | 16.0000i | −0.305664 | + | 0.611329i | ||||
\(686\) | −8.50000 | + | 16.4545i | −0.324532 | + | 0.628235i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.73205 | + | 1.00000i | −0.0660338 | + | 0.0381246i | ||||
\(689\) | 22.5000 | − | 38.9711i | 0.857182 | − | 1.48468i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.0000 | + | 38.1051i | 0.836919 | + | 1.44959i | 0.892458 | + | 0.451130i | \(0.148979\pi\) |
−0.0555386 | + | 0.998457i | \(0.517688\pi\) | |||||||
\(692\) | − | 9.00000i | − | 0.342129i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12.0000 | 0.455514 | ||||||||
\(695\) | 2.14359 | + | 35.7128i | 0.0813111 | + | 1.35466i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.19615 | + | 3.00000i | 0.196818 | + | 0.113633i | ||||
\(698\) | −10.3923 | + | 6.00000i | −0.393355 | + | 0.227103i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 12.5981 | − | 4.03590i | 0.476163 | − | 0.152543i | ||||
\(701\) | −26.0000 | −0.982006 | −0.491003 | − | 0.871158i | \(-0.663370\pi\) | ||||
−0.491003 | + | 0.871158i | \(0.663370\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.33013 | − | 2.50000i | −0.163314 | − | 0.0942893i | ||||
\(704\) | −1.50000 | + | 2.59808i | −0.0565334 | + | 0.0979187i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 24.0000 | 0.903252 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.00000 | + | 10.3923i | 0.225335 | + | 0.390291i | 0.956420 | − | 0.291995i | \(-0.0943191\pi\) |
−0.731085 | + | 0.682286i | \(0.760986\pi\) | |||||||
\(710\) | 7.39230 | + | 11.1962i | 0.277428 | + | 0.420184i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.73205 | − | 1.00000i | 0.0649113 | − | 0.0374766i | ||||
\(713\) | 14.0000i | 0.524304i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.0000 | − | 30.0000i | 0.560968 | − | 1.12194i | ||||
\(716\) | 6.50000 | + | 11.2583i | 0.242916 | + | 0.420744i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 13.8564 | + | 8.00000i | 0.517116 | + | 0.298557i | ||||
\(719\) | −13.0000 | − | 22.5167i | −0.484818 | − | 0.839730i | 0.515030 | − | 0.857172i | \(-0.327781\pi\) |
−0.999848 | + | 0.0174426i | \(0.994448\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.0000 | − | 6.92820i | −0.744839 | − | 0.258020i | ||||
\(722\) | − | 6.00000i | − | 0.223297i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 13.0000 | − | 22.5167i | 0.483141 | − | 0.836825i | ||||
\(725\) | 19.8564 | − | 2.39230i | 0.737448 | − | 0.0888480i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 29.0000i | − | 1.07555i | −0.843088 | − | 0.537775i | \(-0.819265\pi\) | ||
0.843088 | − | 0.537775i | \(-0.180735\pi\) | |||||||
\(728\) | 8.66025 | + | 10.0000i | 0.320970 | + | 0.370625i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.14359 | − | 35.7128i | −0.0793380 | − | 1.32179i | ||||
\(731\) | −2.00000 | + | 3.46410i | −0.0739727 | + | 0.128124i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35.5070 | + | 20.5000i | −1.31148 | + | 0.757185i | −0.982342 | − | 0.187096i | \(-0.940092\pi\) |
−0.329141 | + | 0.944281i | \(0.606759\pi\) | |||||||
\(734\) | 13.0000 | 0.479839 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.00000 | −0.258023 | ||||||||
\(737\) | −5.19615 | + | 3.00000i | −0.191403 | + | 0.110506i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.5000 | + | 25.1147i | −0.533391 | + | 0.923861i | 0.465848 | + | 0.884865i | \(0.345749\pi\) |
−0.999239 | + | 0.0389959i | \(0.987584\pi\) | |||||||
\(740\) | −2.23205 | + | 0.133975i | −0.0820518 | + | 0.00492500i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −15.5885 | − | 18.0000i | −0.572270 | − | 0.660801i | ||||
\(743\) | − | 21.0000i | − | 0.770415i | −0.922830 | − | 0.385208i | \(-0.874130\pi\) | ||
0.922830 | − | 0.385208i | \(-0.125870\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 33.5885 | − | 22.1769i | 1.23059 | − | 0.812499i | ||||
\(746\) | 13.0000 | − | 22.5167i | 0.475964 | − | 0.824394i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 6.00000i | 0.219382i | ||||||||
\(749\) | −40.0000 | − | 13.8564i | −1.46157 | − | 0.506302i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.0000 | − | 24.2487i | −0.510867 | − | 0.884848i | −0.999921 | − | 0.0125942i | \(-0.995991\pi\) |
0.489053 | − | 0.872254i | \(-0.337342\pi\) | |||||||
\(752\) | −6.06218 | − | 3.50000i | −0.221065 | − | 0.127632i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 10.0000 | + | 17.3205i | 0.364179 | + | 0.630776i | ||||
\(755\) | −12.0000 | − | 6.00000i | −0.436725 | − | 0.218362i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.0000i | 1.52652i | 0.646094 | + | 0.763258i | \(0.276401\pi\) | ||||
−0.646094 | + | 0.763258i | \(0.723599\pi\) | |||||||
\(758\) | −25.1147 | + | 14.5000i | −0.912208 | + | 0.526664i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.16025 | − | 9.33013i | −0.223456 | − | 0.338439i | ||||
\(761\) | 0.500000 | + | 0.866025i | 0.0181250 | + | 0.0313934i | 0.874946 | − | 0.484221i | \(-0.160897\pi\) |
−0.856821 | + | 0.515615i | \(0.827564\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.19615 | + | 1.00000i | −0.188113 | + | 0.0362024i | ||||
\(764\) | −20.0000 | −0.723575 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.5000 | + | 18.1865i | −0.379380 | + | 0.657106i | ||||
\(767\) | 17.3205 | + | 10.0000i | 0.625407 | + | 0.361079i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.0000 | 1.04577 | 0.522883 | − | 0.852404i | \(-0.324856\pi\) | ||||
0.522883 | + | 0.852404i | \(0.324856\pi\) | |||||||
\(770\) | −12.4019 | − | 12.6962i | −0.446934 | − | 0.457538i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8.66025 | + | 5.00000i | −0.311689 | + | 0.179954i | ||||
\(773\) | −38.9711 | − | 22.5000i | −1.40169 | − | 0.809269i | −0.407128 | − | 0.913371i | \(-0.633470\pi\) |
−0.994567 | + | 0.104102i | \(0.966803\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.92820 | + | 9.19615i | −0.141105 | + | 0.330336i | ||||
\(776\) | 12.0000 | 0.430775 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.00000i | 0.215110i | ||||||||
\(779\) | 7.50000 | + | 12.9904i | 0.268715 | + | 0.465429i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.00000 | − | 15.5885i | 0.322045 | − | 0.557799i | ||||
\(782\) | −12.1244 | + | 7.00000i | −0.433566 | + | 0.250319i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.50000 | − | 2.59808i | 0.232143 | − | 0.0927884i | ||||
\(785\) | 9.00000 | − | 18.0000i | 0.321224 | − | 0.642448i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.5885 | − | 9.00000i | −0.555668 | − | 0.320815i | 0.195737 | − | 0.980656i | \(-0.437290\pi\) |
−0.751405 | + | 0.659841i | \(0.770624\pi\) | |||||||
\(788\) | 4.33013 | + | 2.50000i | 0.154254 | + | 0.0890588i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −14.0000 | + | 28.0000i | −0.498098 | + | 0.996195i | ||||
\(791\) | 28.0000 | − | 24.2487i | 0.995565 | − | 0.862185i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25.9808 | − | 15.0000i | 0.922604 | − | 0.532666i | ||||
\(794\) | 7.00000 | − | 12.1244i | 0.248421 | − | 0.430277i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.00000 | − | 15.5885i | −0.318997 | − | 0.552518i | ||||
\(797\) | 2.00000i | 0.0708436i | 0.999372 | + | 0.0354218i | \(0.0112775\pi\) | ||||
−0.999372 | + | 0.0354218i | \(0.988723\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.0000 | −0.495284 | ||||||||
\(800\) | −4.59808 | − | 1.96410i | −0.162567 | − | 0.0694415i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 12.9904 | + | 7.50000i | 0.458706 | + | 0.264834i | ||||
\(803\) | −41.5692 | + | 24.0000i | −1.46695 | + | 0.846942i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.1865 | − | 39.8731i | 0.394273 | − | 1.40534i | ||||
\(806\) | −10.0000 | −0.352235 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.50000 | − | 4.33013i | 0.0878953 | − | 0.152239i | −0.818726 | − | 0.574184i | \(-0.805319\pi\) |
0.906621 | + | 0.421945i | \(0.138653\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33.0000 | −1.15879 | −0.579393 | − | 0.815048i | \(-0.696710\pi\) | ||||
−0.579393 | + | 0.815048i | \(0.696710\pi\) | |||||||
\(812\) | 10.3923 | − | 2.00000i | 0.364698 | − | 0.0701862i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.50000 | + | 2.59808i | 0.0525750 | + | 0.0910625i | ||||
\(815\) | −14.7846 | − | 22.3923i | −0.517882 | − | 0.784368i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.66025 | + | 5.00000i | −0.302984 | + | 0.174928i | ||||
\(818\) | − | 14.0000i | − | 0.489499i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.00000 | + | 3.00000i | 0.209529 | + | 0.104765i | ||||
\(821\) | −9.00000 | − | 15.5885i | −0.314102 | − | 0.544041i | 0.665144 | − | 0.746715i | \(-0.268370\pi\) |
−0.979246 | + | 0.202674i | \(0.935037\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.7846 | − | 12.0000i | −0.724506 | − | 0.418294i | 0.0919029 | − | 0.995768i | \(-0.470705\pi\) |
−0.816409 | + | 0.577474i | \(0.804038\pi\) | |||||||
\(824\) | 4.00000 | + | 6.92820i | 0.139347 | + | 0.241355i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.00000 | − | 6.92820i | 0.278356 | − | 0.241063i | ||||
\(827\) | 22.0000i | 0.765015i | 0.923952 | + | 0.382507i | \(0.124939\pi\) | ||||
−0.923952 | + | 0.382507i | \(0.875061\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.0000 | + | 22.5167i | −0.451509 | + | 0.782036i | −0.998480 | − | 0.0551154i | \(-0.982447\pi\) |
0.546971 | + | 0.837151i | \(0.315781\pi\) | |||||||
\(830\) | 11.1962 | − | 7.39230i | 0.388624 | − | 0.256591i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 5.00000i | − | 0.173344i | ||||||
\(833\) | 8.66025 | − | 11.0000i | 0.300060 | − | 0.381127i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −33.4808 | + | 2.00962i | −1.15865 | + | 0.0695457i | ||||
\(836\) | −7.50000 | + | 12.9904i | −0.259393 | + | 0.449282i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −30.3109 | + | 17.5000i | −1.04707 | + | 0.604527i | ||||
\(839\) | −34.0000 | −1.17381 | −0.586905 | − | 0.809656i | \(-0.699654\pi\) | ||||
−0.586905 | + | 0.809656i | \(0.699654\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0000 | −0.448276 | ||||||||
\(842\) | 17.3205 | − | 10.0000i | 0.596904 | − | 0.344623i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.50000 | + | 7.79423i | −0.154896 | + | 0.268288i | ||||
\(845\) | 1.60770 | + | 26.7846i | 0.0553064 | + | 0.921419i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.73205 | − | 5.00000i | 0.0595140 | − | 0.171802i | ||||
\(848\) | 9.00000i | 0.309061i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −9.92820 | + | 1.19615i | −0.340535 | + | 0.0410277i | ||||
\(851\) | −3.50000 | + | 6.06218i | −0.119978 | + | 0.207809i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 43.0000i | 1.47229i | 0.676823 | + | 0.736146i | \(0.263356\pi\) | ||||
−0.676823 | + | 0.736146i | \(0.736644\pi\) | |||||||
\(854\) | −3.00000 | − | 15.5885i | −0.102658 | − | 0.533426i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.00000 | + | 13.8564i | 0.273434 | + | 0.473602i | ||||
\(857\) | 6.92820 | + | 4.00000i | 0.236663 | + | 0.136637i | 0.613642 | − | 0.789584i | \(-0.289704\pi\) |
−0.376979 | + | 0.926222i | \(0.623037\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.00000 | − | 10.3923i | −0.204717 | − | 0.354581i | 0.745325 | − | 0.666701i | \(-0.232294\pi\) |
−0.950043 | + | 0.312120i | \(0.898961\pi\) | |||||||
\(860\) | −2.00000 | + | 4.00000i | −0.0681994 | + | 0.136399i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.00000i | 0.0681203i | ||||||||
\(863\) | −9.52628 | + | 5.50000i | −0.324278 | + | 0.187222i | −0.653298 | − | 0.757101i | \(-0.726615\pi\) |
0.329020 | + | 0.944323i | \(0.393282\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.0885 | − | 16.7942i | −0.377019 | − | 0.571021i | ||||
\(866\) | 14.0000 | + | 24.2487i | 0.475739 | + | 0.824005i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.73205 | + | 5.00000i | −0.0587896 | + | 0.169711i | ||||
\(869\) | 42.0000 | 1.42475 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.00000 | − | 8.66025i | 0.169419 | − | 0.293442i | ||||
\(872\) | 1.73205 | + | 1.00000i | 0.0586546 | + | 0.0338643i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −35.0000 | −1.18389 | ||||||||
\(875\) | 18.5359 | − | 23.0526i | 0.626628 | − | 0.779319i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.8468 | − | 15.5000i | 0.906552 | − | 0.523398i | 0.0272316 | − | 0.999629i | \(-0.491331\pi\) |
0.879320 | + | 0.476231i | \(0.157998\pi\) | |||||||
\(878\) | 24.2487 | + | 14.0000i | 0.818354 | + | 0.472477i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.401924 | + | 6.69615i | 0.0135488 | + | 0.225727i | ||||
\(881\) | 15.0000 | 0.505363 | 0.252681 | − | 0.967550i | \(-0.418688\pi\) | ||||
0.252681 | + | 0.967550i | \(0.418688\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 16.0000i | − | 0.538443i | −0.963078 | − | 0.269221i | \(-0.913234\pi\) | ||
0.963078 | − | 0.269221i | \(-0.0867663\pi\) | |||||||
\(884\) | −5.00000 | − | 8.66025i | −0.168168 | − | 0.291276i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.0000 | + | 25.9808i | −0.503935 | + | 0.872841i | ||||
\(887\) | −31.1769 | + | 18.0000i | −1.04682 | + | 0.604381i | −0.921757 | − | 0.387768i | \(-0.873246\pi\) |
−0.125061 | + | 0.992149i | \(0.539913\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.0000 | − | 12.1244i | 0.469545 | − | 0.406638i | ||||
\(890\) | 2.00000 | − | 4.00000i | 0.0670402 | − | 0.134080i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.92820 | + | 4.00000i | 0.231973 | + | 0.133930i | ||||
\(893\) | −30.3109 | − | 17.5000i | −1.01432 | − | 0.585615i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 26.0000 | + | 13.0000i | 0.869084 | + | 0.434542i | ||||
\(896\) | −2.50000 | − | 0.866025i | −0.0835191 | − | 0.0289319i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.33013 | + | 2.50000i | −0.144498 | + | 0.0834261i | ||||
\(899\) | −4.00000 | + | 6.92820i | −0.133407 | + | 0.231069i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.00000 | + | 15.5885i | 0.299833 | + | 0.519327i | ||||
\(902\) | − | 9.00000i | − | 0.299667i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14.0000 | −0.465633 | ||||||||
\(905\) | −3.48334 | − | 58.0333i | −0.115790 | − | 1.92909i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 34.6410 | + | 20.0000i | 1.15024 | + | 0.664089i | 0.948945 | − | 0.315442i | \(-0.102153\pi\) |
0.201291 | + | 0.979531i | \(0.435486\pi\) | |||||||
\(908\) | −5.19615 | + | 3.00000i | −0.172440 | + | 0.0995585i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 28.4808 | + | 7.99038i | 0.944128 | + | 0.264879i | ||||
\(911\) | −2.00000 | −0.0662630 | −0.0331315 | − | 0.999451i | \(-0.510548\pi\) | ||||
−0.0331315 | + | 0.999451i | \(0.510548\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.5885 | − | 9.00000i | −0.515903 | − | 0.297857i | ||||
\(914\) | 5.00000 | − | 8.66025i | 0.165385 | − | 0.286456i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 16.0000 | 0.528655 | ||||||||
\(917\) | −0.866025 | + | 2.50000i | −0.0285987 | + | 0.0825573i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.0000 | + | 17.3205i | 0.329870 | + | 0.571351i | 0.982486 | − | 0.186338i | \(-0.0596619\pi\) |
−0.652616 | + | 0.757689i | \(0.726329\pi\) | |||||||
\(920\) | −13.0622 | + | 8.62436i | −0.430647 | + | 0.284337i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −27.7128 | + | 16.0000i | −0.912673 | + | 0.526932i | ||||
\(923\) | 30.0000i | 0.987462i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.00000 | + | 3.00000i | −0.131519 | + | 0.0986394i | ||||
\(926\) | −8.50000 | − | 14.7224i | −0.279327 | − | 0.483809i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.46410 | − | 2.00000i | −0.113715 | − | 0.0656532i | ||||
\(929\) | −10.5000 | − | 18.1865i | −0.344494 | − | 0.596681i | 0.640768 | − | 0.767735i | \(-0.278616\pi\) |
−0.985262 | + | 0.171054i | \(0.945283\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 32.5000 | − | 12.9904i | 1.06514 | − | 0.425743i | ||||
\(932\) | 8.00000i | 0.262049i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 17.0000 | − | 29.4449i | 0.556257 | − | 0.963465i | ||||
\(935\) | 7.39230 | + | 11.1962i | 0.241754 | + | 0.366153i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 26.0000i | − | 0.849383i | −0.905338 | − | 0.424691i | \(-0.860383\pi\) | ||
0.905338 | − | 0.424691i | \(-0.139617\pi\) | |||||||
\(938\) | −3.46410 | − | 4.00000i | −0.113107 | − | 0.130605i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −15.6244 | + | 0.937822i | −0.509610 | + | 0.0305884i | ||||
\(941\) | −14.0000 | + | 24.2487i | −0.456387 | + | 0.790485i | −0.998767 | − | 0.0496480i | \(-0.984190\pi\) |
0.542380 | + | 0.840133i | \(0.317523\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.1865 | − | 10.5000i | 0.592235 | − | 0.341927i | ||||
\(944\) | −4.00000 | −0.130189 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.00000 | 0.195077 | ||||||||
\(947\) | 10.3923 | − | 6.00000i | 0.337705 | − | 0.194974i | −0.321552 | − | 0.946892i | \(-0.604204\pi\) |
0.659256 | + | 0.751918i | \(0.270871\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 40.0000 | − | 69.2820i | 1.29845 | − | 2.24899i | ||||
\(950\) | −22.9904 | − | 9.82051i | −0.745906 | − | 0.318619i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.19615 | + | 1.00000i | −0.168408 | + | 0.0324102i | ||||
\(953\) | − | 24.0000i | − | 0.777436i | −0.921357 | − | 0.388718i | \(-0.872918\pi\) | ||
0.921357 | − | 0.388718i | \(-0.127082\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −37.3205 | + | 24.6410i | −1.20766 | + | 0.797365i | ||||
\(956\) | 10.0000 | − | 17.3205i | 0.323423 | − | 0.560185i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 36.0000i | − | 1.16311i | ||||||
\(959\) | 4.00000 | + | 20.7846i | 0.129167 | + | 0.671170i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.5000 | + | 23.3827i | 0.435484 | + | 0.754280i | ||||
\(962\) | −4.33013 | − | 2.50000i | −0.139609 | − | 0.0806032i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.50000 | − | 7.79423i | −0.144935 | − | 0.251035i | ||||
\(965\) | −10.0000 | + | 20.0000i | −0.321911 | + | 0.643823i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.0000i | 1.02905i | 0.857475 | + | 0.514525i | \(0.172032\pi\) | ||||
−0.857475 | + | 0.514525i | \(0.827968\pi\) | |||||||
\(968\) | −1.73205 | + | 1.00000i | −0.0556702 | + | 0.0321412i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 22.3923 | − | 14.7846i | 0.718974 | − | 0.474705i | ||||
\(971\) | −16.5000 | − | 28.5788i | −0.529510 | − | 0.917139i | −0.999408 | − | 0.0344175i | \(-0.989042\pi\) |
0.469897 | − | 0.882721i | \(-0.344291\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 27.7128 | + | 32.0000i | 0.888432 | + | 1.02587i | ||||
\(974\) | −32.0000 | −1.02535 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.00000 | + | 5.19615i | −0.0960277 | + | 0.166325i | ||||
\(977\) | 46.7654 | + | 27.0000i | 1.49616 | + | 0.863807i | 0.999990 | − | 0.00442082i | \(-0.00140720\pi\) |
0.496167 | + | 0.868227i | \(0.334741\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.00000 | −0.191761 | ||||||||
\(980\) | 8.92820 | − | 12.8564i | 0.285201 | − | 0.410683i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 20.7846 | − | 12.0000i | 0.663264 | − | 0.382935i | ||||
\(983\) | 25.1147 | + | 14.5000i | 0.801036 | + | 0.462478i | 0.843833 | − | 0.536606i | \(-0.180294\pi\) |
−0.0427975 | + | 0.999084i | \(0.513627\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.1603 | − | 0.669873i | 0.355595 | − | 0.0213439i | ||||
\(986\) | −8.00000 | −0.254772 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 25.0000i | − | 0.795356i | ||||||
\(989\) | 7.00000 | + | 12.1244i | 0.222587 | + | 0.385532i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.00000 | − | 6.92820i | 0.127064 | − | 0.220082i | −0.795474 | − | 0.605988i | \(-0.792778\pi\) |
0.922538 | + | 0.385906i | \(0.126111\pi\) | |||||||
\(992\) | 1.73205 | − | 1.00000i | 0.0549927 | − | 0.0317500i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 15.0000 | + | 5.19615i | 0.475771 | + | 0.164812i | ||||
\(995\) | −36.0000 | − | 18.0000i | −1.14128 | − | 0.570638i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.9090 | + | 19.0000i | 1.04224 | + | 0.601736i | 0.920466 | − | 0.390822i | \(-0.127809\pi\) |
0.121771 | + | 0.992558i | \(0.461143\pi\) | |||||||
\(998\) | −3.46410 | − | 2.00000i | −0.109654 | − | 0.0633089i | ||||
\(999\) | 0 | 0 |
(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.u.a.109.1 | 4 | ||
3.2 | odd | 2 | 70.2.i.b.39.2 | yes | 4 | ||
5.4 | even | 2 | inner | 630.2.u.a.109.2 | 4 | ||
7.2 | even | 3 | inner | 630.2.u.a.289.2 | 4 | ||
12.11 | even | 2 | 560.2.bw.d.529.1 | 4 | |||
15.2 | even | 4 | 350.2.e.j.151.1 | 2 | |||
15.8 | even | 4 | 350.2.e.c.151.1 | 2 | |||
15.14 | odd | 2 | 70.2.i.b.39.1 | yes | 4 | ||
21.2 | odd | 6 | 70.2.i.b.9.1 | ✓ | 4 | ||
21.5 | even | 6 | 490.2.i.a.79.1 | 4 | |||
21.11 | odd | 6 | 490.2.c.a.99.2 | 2 | |||
21.17 | even | 6 | 490.2.c.d.99.2 | 2 | |||
21.20 | even | 2 | 490.2.i.a.459.2 | 4 | |||
35.9 | even | 6 | inner | 630.2.u.a.289.1 | 4 | ||
60.59 | even | 2 | 560.2.bw.d.529.2 | 4 | |||
84.23 | even | 6 | 560.2.bw.d.289.2 | 4 | |||
105.2 | even | 12 | 350.2.e.j.51.1 | 2 | |||
105.17 | odd | 12 | 2450.2.a.j.1.1 | 1 | |||
105.23 | even | 12 | 350.2.e.c.51.1 | 2 | |||
105.32 | even | 12 | 2450.2.a.k.1.1 | 1 | |||
105.38 | odd | 12 | 2450.2.a.bb.1.1 | 1 | |||
105.44 | odd | 6 | 70.2.i.b.9.2 | yes | 4 | ||
105.53 | even | 12 | 2450.2.a.ba.1.1 | 1 | |||
105.59 | even | 6 | 490.2.c.d.99.1 | 2 | |||
105.74 | odd | 6 | 490.2.c.a.99.1 | 2 | |||
105.89 | even | 6 | 490.2.i.a.79.2 | 4 | |||
105.104 | even | 2 | 490.2.i.a.459.1 | 4 | |||
420.359 | even | 6 | 560.2.bw.d.289.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.2.i.b.9.1 | ✓ | 4 | 21.2 | odd | 6 | ||
70.2.i.b.9.2 | yes | 4 | 105.44 | odd | 6 | ||
70.2.i.b.39.1 | yes | 4 | 15.14 | odd | 2 | ||
70.2.i.b.39.2 | yes | 4 | 3.2 | odd | 2 | ||
350.2.e.c.51.1 | 2 | 105.23 | even | 12 | |||
350.2.e.c.151.1 | 2 | 15.8 | even | 4 | |||
350.2.e.j.51.1 | 2 | 105.2 | even | 12 | |||
350.2.e.j.151.1 | 2 | 15.2 | even | 4 | |||
490.2.c.a.99.1 | 2 | 105.74 | odd | 6 | |||
490.2.c.a.99.2 | 2 | 21.11 | odd | 6 | |||
490.2.c.d.99.1 | 2 | 105.59 | even | 6 | |||
490.2.c.d.99.2 | 2 | 21.17 | even | 6 | |||
490.2.i.a.79.1 | 4 | 21.5 | even | 6 | |||
490.2.i.a.79.2 | 4 | 105.89 | even | 6 | |||
490.2.i.a.459.1 | 4 | 105.104 | even | 2 | |||
490.2.i.a.459.2 | 4 | 21.20 | even | 2 | |||
560.2.bw.d.289.1 | 4 | 420.359 | even | 6 | |||
560.2.bw.d.289.2 | 4 | 84.23 | even | 6 | |||
560.2.bw.d.529.1 | 4 | 12.11 | even | 2 | |||
560.2.bw.d.529.2 | 4 | 60.59 | even | 2 | |||
630.2.u.a.109.1 | 4 | 1.1 | even | 1 | trivial | ||
630.2.u.a.109.2 | 4 | 5.4 | even | 2 | inner | ||
630.2.u.a.289.1 | 4 | 35.9 | even | 6 | inner | ||
630.2.u.a.289.2 | 4 | 7.2 | even | 3 | inner | ||
2450.2.a.j.1.1 | 1 | 105.17 | odd | 12 | |||
2450.2.a.k.1.1 | 1 | 105.32 | even | 12 | |||
2450.2.a.ba.1.1 | 1 | 105.53 | even | 12 | |||
2450.2.a.bb.1.1 | 1 | 105.38 | odd | 12 |