Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [70,2,Mod(9,70)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(70, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("70.9");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 70 = 2 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 70.i (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: | \(0.558952814149\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 9.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 70.9 |
Dual form | 70.2.i.b.39.1 |
$q$-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 \(\left(\mathbb{Z}/70\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(57\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 1.86603 | − | 1.23205i | 0.834512 | − | 0.550990i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.73205 | − | 2.00000i | 0.654654 | − | 0.755929i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −1.50000 | + | 2.59808i | −0.500000 | + | 0.866025i | ||||
\(10\) | −2.23205 | + | 0.133975i | −0.705836 | + | 0.0423665i | ||||
\(11\) | −1.50000 | − | 2.59808i | −0.452267 | − | 0.783349i | 0.546259 | − | 0.837616i | \(-0.316051\pi\) |
−0.998526 | + | 0.0542666i | \(0.982718\pi\) | |||||||
\(12\) | 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 | −0.695113 | − | 0.718900i | \(-0.744646\pi\) |
0.275029 | + | 0.961436i | \(0.411312\pi\) | |||||||
\(18\) | 2.59808 | − | 1.50000i | 0.612372 | − | 0.353553i | ||||
\(19\) | −2.50000 | + | 4.33013i | −0.573539 | + | 0.993399i | 0.422659 | + | 0.906289i | \(0.361097\pi\) |
−0.996199 | + | 0.0871106i | \(0.972237\pi\) | |||||||
\(20\) | 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 | −0.290196 | − | 0.956967i | \(-0.593720\pi\) |
−0.973856 | + | 0.227167i | \(0.927054\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.96410 | − | 4.59808i | 0.392820 | − | 0.919615i | ||||
\(26\) | 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 | \(-0.378881\pi\) | ||||
0.371391 | + | 0.928477i | \(0.378881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.00000 | + | 1.73205i | 0.179605 | + | 0.311086i | 0.941745 | − | 0.336327i | \(-0.109185\pi\) |
−0.762140 | + | 0.647412i | \(0.775851\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | 0.767949 | − | 5.86603i | 0.129807 | − | 0.991539i | ||||
\(36\) | −3.00000 | −0.500000 | ||||||||
\(37\) | −0.866025 | − | 0.500000i | −0.142374 | − | 0.0821995i | 0.427121 | − | 0.904194i | \(-0.359528\pi\) |
−0.569495 | + | 0.821995i | \(0.692861\pi\) | |||||||
\(38\) | 4.33013 | − | 2.50000i | 0.702439 | − | 0.405554i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.23205 | − | 1.86603i | −0.194804 | − | 0.295045i | ||||
\(41\) | 3.00000 | 0.468521 | 0.234261 | − | 0.972174i | \(-0.424733\pi\) | ||||
0.234261 | + | 0.972174i | \(0.424733\pi\) | |||||||
\(42\) | 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 | ||||
\(45\) | 0.401924 | + | 6.69615i | 0.0599153 | + | 0.998203i | ||||
\(46\) | 3.50000 | + | 6.06218i | 0.516047 | + | 0.893819i | ||||
\(47\) | 6.06218 | + | 3.50000i | 0.884260 | + | 0.510527i | 0.872060 | − | 0.489398i | \(-0.162783\pi\) |
0.0121990 | + | 0.999926i | \(0.496117\pi\) | |||||||
\(48\) | 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 | −0.928351 | − | 0.371706i | \(-0.878773\pi\) |
−0.142269 | + | 0.989828i | \(0.545440\pi\) | |||||||
\(54\) | 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 | \(-0.250514\pi\) |
−0.966342 | + | 0.257260i | \(0.917180\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.00000 | + | 5.19615i | −0.384111 | + | 0.665299i | −0.991645 | − | 0.128994i | \(-0.958825\pi\) |
0.607535 | + | 0.794293i | \(0.292159\pi\) | |||||||
\(62\) | − | 2.00000i | − | 0.254000i | ||||||
\(63\) | 2.59808 | + | 7.50000i | 0.327327 | + | 0.944911i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 6.16025 | + | 9.33013i | 0.764085 | + | 1.15726i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.73205 | − | 1.00000i | 0.211604 | − | 0.122169i | −0.390453 | − | 0.920623i | \(-0.627682\pi\) |
0.602056 | + | 0.798454i | \(0.294348\pi\) | |||||||
\(68\) | −1.73205 | − | 1.00000i | −0.210042 | − | 0.121268i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.59808 | + | 4.69615i | −0.430052 | + | 0.561298i | ||||
\(71\) | −6.00000 | −0.712069 | −0.356034 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356034 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(72\) | 2.59808 | + | 1.50000i | 0.306186 | + | 0.176777i | ||||
\(73\) | 13.8564 | − | 8.00000i | 1.62177 | − | 0.936329i | 0.635323 | − | 0.772246i | \(-0.280867\pi\) |
0.986447 | − | 0.164083i | \(-0.0524664\pi\) | |||||||
\(74\) | 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 | −0.139895 | − | 0.990166i | \(-0.544677\pi\) |
0.927457 | − | 0.373930i | \(-0.121990\pi\) | |||||||
\(80\) | 0.133975 | + | 2.23205i | 0.0149788 | + | 0.249551i | ||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | −2.59808 | − | 1.50000i | −0.286910 | − | 0.165647i | ||||
\(83\) | 6.00000i | 0.658586i | 0.944228 | + | 0.329293i | \(0.106810\pi\) | ||||
−0.944228 | + | 0.329293i | \(0.893190\pi\) | |||||||
\(84\) | 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 | \(-0.799529\pi\) |
0.914146 | + | 0.405385i | \(0.132862\pi\) | |||||||
\(90\) | 3.00000 | − | 6.00000i | 0.316228 | − | 0.632456i | ||||
\(91\) | 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 | ||||
\(95\) | 0.669873 | + | 11.1603i | 0.0687275 | + | 1.14502i | ||||
\(96\) | 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 | ||||
\(99\) | 9.00000 | 0.904534 | ||||||||
\(100\) | 4.96410 | − | 0.598076i | 0.496410 | − | 0.0598076i | ||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.92820 | − | 4.00000i | −0.682656 | − | 0.394132i | 0.118199 | − | 0.992990i | \(-0.462288\pi\) |
−0.800855 | + | 0.598858i | \(0.795621\pi\) | |||||||
\(104\) | 5.00000 | 0.490290 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.00000 | 0.874157 | ||||||||
\(107\) | 13.8564 | + | 8.00000i | 1.33955 | + | 0.773389i | 0.986740 | − | 0.162306i | \(-0.0518932\pi\) |
0.352809 | + | 0.935695i | \(0.385227\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.00000 | + | 1.73205i | 0.0957826 | + | 0.165900i | 0.909935 | − | 0.414751i | \(-0.136131\pi\) |
−0.814152 | + | 0.580651i | \(0.802798\pi\) | |||||||
\(110\) | 3.69615 | + | 5.59808i | 0.352414 | + | 0.533756i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.866025 | + | 2.50000i | 0.0818317 | + | 0.236228i | ||||
\(113\) | − | 14.0000i | − | 1.31701i | −0.752577 | − | 0.658505i | \(-0.771189\pi\) | ||
0.752577 | − | 0.658505i | \(-0.228811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.6244 | + | 0.937822i | −1.45698 | + | 0.0874524i | ||||
\(116\) | 2.00000 | + | 3.46410i | 0.185695 | + | 0.321634i | ||||
\(117\) | −12.9904 | − | 7.50000i | −1.20096 | − | 0.693375i | ||||
\(118\) | 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 | ||||
\(126\) | 1.50000 | − | 7.79423i | 0.133631 | − | 0.694365i | ||||
\(127\) | 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 | ||||||||
\(130\) | −0.669873 | − | 11.1603i | −0.0587517 | − | 0.978819i | ||||
\(131\) | 0.500000 | − | 0.866025i | 0.0436852 | − | 0.0756650i | −0.843356 | − | 0.537355i | \(-0.819423\pi\) |
0.887041 | + | 0.461690i | \(0.152757\pi\) | |||||||
\(132\) | 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 | −0.765855 | − | 0.643013i | \(-0.777684\pi\) |
0.173939 | + | 0.984757i | \(0.444351\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.0000 | −1.35710 | −0.678551 | − | 0.734553i | \(-0.737392\pi\) | ||||
−0.678551 | + | 0.734553i | \(0.737392\pi\) | |||||||
\(140\) | 5.46410 | − | 2.26795i | 0.461801 | − | 0.191677i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.19615 | + | 3.00000i | 0.436051 | + | 0.251754i | ||||
\(143\) | 12.9904 | − | 7.50000i | 1.08631 | − | 0.627182i | ||||
\(144\) | −1.50000 | − | 2.59808i | −0.125000 | − | 0.216506i | ||||
\(145\) | 7.46410 | − | 4.92820i | 0.619860 | − | 0.409265i | ||||
\(146\) | −16.0000 | −1.32417 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 1.00000i | − | 0.0821995i | ||||||
\(149\) | −9.00000 | + | 15.5885i | −0.737309 | + | 1.27706i | 0.216394 | + | 0.976306i | \(0.430570\pi\) |
−0.953703 | + | 0.300750i | \(0.902763\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.00000 | + | 5.19615i | 0.244137 | + | 0.422857i | 0.961888 | − | 0.273442i | \(-0.0881622\pi\) |
−0.717752 | + | 0.696299i | \(0.754829\pi\) | |||||||
\(152\) | 4.33013 | + | 2.50000i | 0.351220 | + | 0.202777i | ||||
\(153\) | − | 6.00000i | − | 0.485071i | ||||||
\(154\) | 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 | \(-0.783596\pi\) |
0.155618 | + | 0.987817i | \(0.450263\pi\) | |||||||
\(158\) | −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 | ||||
\(162\) | 9.00000i | 0.707107i | ||||||||
\(163\) | −10.3923 | − | 6.00000i | −0.813988 | − | 0.469956i | 0.0343508 | − | 0.999410i | \(-0.489064\pi\) |
−0.848339 | + | 0.529454i | \(0.822397\pi\) | |||||||
\(164\) | 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 | \(0.197091\pi\) | ||||
−0.814355 | + | 0.580367i | \(0.802909\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 3.73205 | − | 2.46410i | 0.286235 | − | 0.188988i | ||||
\(171\) | −7.50000 | − | 12.9904i | −0.573539 | − | 0.993399i | ||||
\(172\) | 1.73205 | − | 1.00000i | 0.132068 | − | 0.0762493i | ||||
\(173\) | 7.79423 | + | 4.50000i | 0.592584 | + | 0.342129i | 0.766119 | − | 0.642699i | \(-0.222185\pi\) |
−0.173534 | + | 0.984828i | \(0.555519\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.79423 | − | 11.8923i | −0.438003 | − | 0.898974i | ||||
\(176\) | 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 | \(-0.00518305\pi\) |
−0.514035 | + | 0.857769i | \(0.671850\pi\) | |||||||
\(180\) | −5.59808 | + | 3.69615i | −0.417256 | + | 0.275495i | ||||
\(181\) | 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 | ||||
\(185\) | −2.23205 | + | 0.133975i | −0.164104 | + | 0.00985001i | ||||
\(186\) | 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 | −0.235983 | − | 0.971757i | \(-0.575831\pi\) |
0.959558 | − | 0.281511i | \(-0.0908356\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.66025 | − | 5.00000i | 0.623379 | − | 0.359908i | −0.154805 | − | 0.987945i | \(-0.549475\pi\) |
0.778183 | + | 0.628037i | \(0.216141\pi\) | |||||||
\(194\) | −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 | \(-0.942999\pi\) | ||
0.984009 | − | 0.178118i | \(-0.0570008\pi\) | |||||||
\(198\) | −7.79423 | − | 4.50000i | −0.553912 | − | 0.319801i | ||||
\(199\) | 9.00000 | + | 15.5885i | 0.637993 | + | 1.10504i | 0.985873 | + | 0.167497i | \(0.0535685\pi\) |
−0.347879 | + | 0.937539i | \(0.613098\pi\) | |||||||
\(200\) | −4.59808 | − | 1.96410i | −0.325133 | − | 0.138883i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.92820 | − | 8.00000i | 0.486265 | − | 0.561490i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.59808 | − | 3.69615i | 0.390987 | − | 0.258150i | ||||
\(206\) | 4.00000 | + | 6.92820i | 0.278693 | + | 0.482711i | ||||
\(207\) | 18.1865 | − | 10.5000i | 1.26405 | − | 0.729800i | ||||
\(208\) | −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 | ||||
\(215\) | −2.46410 | − | 3.73205i | −0.168050 | − | 0.254524i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.19615 | + | 1.00000i | 0.352738 | + | 0.0678844i | ||||
\(218\) | − | 2.00000i | − | 0.135457i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.401924 | − | 6.69615i | −0.0270977 | − | 0.451455i | ||||
\(221\) | −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 | ||||
\(225\) | 9.00000 | + | 12.0000i | 0.600000 | + | 0.800000i | ||||
\(226\) | −7.00000 | + | 12.1244i | −0.465633 | + | 0.806500i | ||||
\(227\) | −5.19615 | + | 3.00000i | −0.344881 | + | 0.199117i | −0.662428 | − | 0.749125i | \(-0.730474\pi\) |
0.317547 | + | 0.948242i | \(0.397141\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.00000 | − | 13.8564i | 0.528655 | − | 0.915657i | −0.470787 | − | 0.882247i | \(-0.656030\pi\) |
0.999442 | − | 0.0334101i | \(-0.0106368\pi\) | |||||||
\(230\) | 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 | 0.255586 | − | 0.966786i | \(-0.417731\pi\) |
−0.709468 | + | 0.704737i | \(0.751065\pi\) | |||||||
\(234\) | 7.50000 | + | 12.9904i | 0.490290 | + | 0.849208i | ||||
\(235\) | 15.6244 | − | 0.937822i | 1.01922 | − | 0.0611768i | ||||
\(236\) | 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 | \(-0.723912\pi\) | ||||
−0.646846 | + | 0.762620i | \(0.723912\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.50000 | + | 7.79423i | 0.289870 | + | 0.502070i | 0.973779 | − | 0.227498i | \(-0.0730544\pi\) |
−0.683908 | + | 0.729568i | \(0.739721\pi\) | |||||||
\(242\) | −1.73205 | + | 1.00000i | −0.111340 | + | 0.0642824i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.00000 | −0.384111 | ||||||||
\(245\) | −10.4019 | − | 11.6962i | −0.664555 | − | 0.747240i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −21.6506 | − | 12.5000i | −1.37760 | − | 0.795356i | ||||
\(248\) | 1.73205 | − | 1.00000i | 0.109985 | − | 0.0635001i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3.76795 | + | 10.5263i | −0.238306 | + | 0.665740i | ||||
\(251\) | 5.00000 | 0.315597 | 0.157799 | − | 0.987471i | \(-0.449560\pi\) | ||||
0.157799 | + | 0.987471i | \(0.449560\pi\) | |||||||
\(252\) | −5.19615 | + | 6.00000i | −0.327327 | + | 0.377964i | ||||
\(253\) | 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 | 0.653231 | − | 0.757159i | \(-0.273413\pi\) |
−0.329104 | + | 0.944294i | \(0.606747\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.50000 | + | 0.866025i | −0.155342 | + | 0.0538122i | ||||
\(260\) | −5.00000 | + | 10.0000i | −0.310087 | + | 0.620174i | ||||
\(261\) | −6.00000 | + | 10.3923i | −0.371391 | + | 0.643268i | ||||
\(262\) | −0.866025 | + | 0.500000i | −0.0535032 | + | 0.0308901i | ||||
\(263\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(264\) | 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 | \(-0.265275\pi\) |
−0.977229 | + | 0.212187i | \(0.931941\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.0000 | + | 20.7846i | −0.728948 | + | 1.26258i | 0.228380 | + | 0.973572i | \(0.426657\pi\) |
−0.957328 | + | 0.289003i | \(0.906676\pi\) | |||||||
\(272\) | − | 2.00000i | − | 0.121268i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.00000 | 0.483298 | ||||||||
\(275\) | −14.8923 | + | 1.79423i | −0.898040 | + | 0.108196i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.73205 | + | 1.00000i | −0.104069 | + | 0.0600842i | −0.551131 | − | 0.834419i | \(-0.685804\pi\) |
0.447062 | + | 0.894503i | \(0.352470\pi\) | |||||||
\(278\) | 13.8564 | + | 8.00000i | 0.831052 | + | 0.479808i | ||||
\(279\) | −6.00000 | −0.359211 | ||||||||
\(280\) | −5.86603 | − | 0.767949i | −0.350562 | − | 0.0458937i | ||||
\(281\) | 9.00000 | 0.536895 | 0.268447 | − | 0.963294i | \(-0.413489\pi\) | ||||
0.268447 | + | 0.963294i | \(0.413489\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.1244 | + | 7.00000i | −0.720718 | + | 0.416107i | −0.815017 | − | 0.579437i | \(-0.803272\pi\) |
0.0942988 | + | 0.995544i | \(0.469939\pi\) | |||||||
\(284\) | −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 | ||||
\(288\) | 3.00000i | 0.176777i | ||||||||
\(289\) | −6.50000 | + | 11.2583i | −0.382353 | + | 0.662255i | ||||
\(290\) | −8.92820 | + | 0.535898i | −0.524282 | + | 0.0314690i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 13.8564 | + | 8.00000i | 0.810885 | + | 0.468165i | ||||
\(293\) | 9.00000i | 0.525786i | 0.964825 | + | 0.262893i | \(0.0846766\pi\) | ||||
−0.964825 | + | 0.262893i | \(0.915323\pi\) | |||||||
\(294\) | 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 | ||||
\(305\) | 0.803848 | + | 13.3923i | 0.0460282 | + | 0.766841i | ||||
\(306\) | −3.00000 | + | 5.19615i | −0.171499 | + | 0.297044i | ||||
\(307\) | − | 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 | ||||||||
\(310\) | −2.46410 | − | 3.73205i | −0.139952 | − | 0.211966i | ||||
\(311\) | −3.00000 | − | 5.19615i | −0.170114 | − | 0.294647i | 0.768345 | − | 0.640036i | \(-0.221080\pi\) |
−0.938460 | + | 0.345389i | \(0.887747\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.0526 | − | 11.0000i | −1.07691 | − | 0.621757i | −0.146852 | − | 0.989158i | \(-0.546914\pi\) |
−0.930062 | + | 0.367402i | \(0.880247\pi\) | |||||||
\(314\) | 9.00000 | 0.507899 | ||||||||
\(315\) | 14.0885 | + | 10.7942i | 0.793795 | + | 0.608186i | ||||
\(316\) | 14.0000 | 0.787562 | ||||||||
\(317\) | 1.73205 | + | 1.00000i | 0.0972817 | + | 0.0561656i | 0.547852 | − | 0.836576i | \(-0.315446\pi\) |
−0.450570 | + | 0.892741i | \(0.648779\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.00000 | − | 10.3923i | −0.335936 | − | 0.581857i | ||||
\(320\) | −1.86603 | + | 1.23205i | −0.104314 | + | 0.0688737i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 18.1865 | + | 3.50000i | 1.01350 | + | 0.195047i | ||||
\(323\) | − | 10.0000i | − | 0.556415i | ||||||
\(324\) | 4.50000 | − | 7.79423i | 0.250000 | − | 0.433013i | ||||
\(325\) | 22.9904 | + | 9.82051i | 1.27528 | + | 0.544744i | ||||
\(326\) | 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 | −0.926516 | − | 0.376254i | \(-0.877212\pi\) |
0.789104 | + | 0.614260i | \(0.210545\pi\) | |||||||
\(332\) | −5.19615 | + | 3.00000i | −0.285176 | + | 0.164646i | ||||
\(333\) | 2.59808 | − | 1.50000i | 0.142374 | − | 0.0821995i | ||||
\(334\) | 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 | ||||||||
\(340\) | −4.46410 | + | 0.267949i | −0.242100 | + | 0.0145316i | ||||
\(341\) | 3.00000 | − | 5.19615i | 0.162459 | − | 0.281387i | ||||
\(342\) | 15.0000i | 0.811107i | ||||||||
\(343\) | −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 | −0.752297 | − | 0.658824i | \(-0.771054\pi\) |
0.194409 | + | 0.980921i | \(0.437721\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.0000 | 0.642345 | 0.321173 | − | 0.947021i | \(-0.395923\pi\) | ||||
0.321173 | + | 0.947021i | \(0.395923\pi\) | |||||||
\(350\) | −0.928203 | + | 13.1962i | −0.0496145 | + | 0.705364i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.59808 | − | 1.50000i | −0.138478 | − | 0.0799503i | ||||
\(353\) | −20.7846 | + | 12.0000i | −1.10625 | + | 0.638696i | −0.937856 | − | 0.347024i | \(-0.887192\pi\) |
−0.168397 | + | 0.985719i | \(0.553859\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.1962 | + | 7.39230i | −0.594230 | + | 0.392343i | ||||
\(356\) | 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 | \(-0.694583\pi\) |
0.996157 | + | 0.0875892i | \(0.0279163\pi\) | |||||||
\(360\) | 6.69615 | − | 0.401924i | 0.352918 | − | 0.0211832i | ||||
\(361\) | −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 | \(-0.556477\pi\) |
0.764180 | + | 0.645003i | \(0.223144\pi\) | |||||||
\(368\) | 6.06218 | − | 3.50000i | 0.316013 | − | 0.182450i | ||||
\(369\) | −4.50000 | + | 7.79423i | −0.234261 | + | 0.405751i | ||||
\(370\) | 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 | \(-0.0982894\pi\) |
0.213165 | + | 0.977016i | \(0.431623\pi\) | |||||||
\(374\) | −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 | \(0.232538\pi\) | |||||||
\(380\) | −9.33013 | + | 6.16025i | −0.478625 | + | 0.316014i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −17.3205 | + | 10.0000i | −0.886194 | + | 0.511645i | ||||
\(383\) | 18.1865 | + | 10.5000i | 0.929288 | + | 0.536525i | 0.886586 | − | 0.462563i | \(-0.153070\pi\) |
0.0427020 | + | 0.999088i | \(0.486403\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.3923 | + | 6.80385i | −0.835429 | + | 0.346756i | ||||
\(386\) | −10.0000 | −0.508987 | ||||||||
\(387\) | 5.19615 | + | 3.00000i | 0.264135 | + | 0.152499i | ||||
\(388\) | 10.3923 | − | 6.00000i | 0.527589 | − | 0.304604i | ||||
\(389\) | −3.00000 | − | 5.19615i | −0.152106 | − | 0.263455i | 0.779895 | − | 0.625910i | \(-0.215272\pi\) |
−0.932002 | + | 0.362454i | \(0.881939\pi\) | |||||||
\(390\) | 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 | ||||
\(395\) | −1.87564 | − | 31.2487i | −0.0943739 | − | 1.57229i | ||||
\(396\) | 4.50000 | + | 7.79423i | 0.226134 | + | 0.391675i | ||||
\(397\) | 12.1244 | + | 7.00000i | 0.608504 | + | 0.351320i | 0.772380 | − | 0.635161i | \(-0.219066\pi\) |
−0.163876 | + | 0.986481i | \(0.552400\pi\) | |||||||
\(398\) | − | 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 | \(-0.711137\pi\) |
0.990257 | + | 0.139253i | \(0.0444700\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.66025 | + | 5.00000i | −0.431398 | + | 0.249068i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −18.0000 | − | 9.00000i | −0.894427 | − | 0.447214i | ||||
\(406\) | −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 | 0.639430 | − | 0.768849i | \(-0.279170\pi\) |
−0.985558 | + | 0.169338i | \(0.945837\pi\) | |||||||
\(410\) | −6.69615 | + | 0.401924i | −0.330699 | + | 0.0198496i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 8.00000i | − | 0.394132i | ||||||
\(413\) | −10.3923 | − | 2.00000i | −0.511372 | − | 0.0984136i | ||||
\(414\) | −21.0000 | −1.03209 | ||||||||
\(415\) | 7.39230 | + | 11.1962i | 0.362874 | + | 0.549598i | ||||
\(416\) | 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 | \(-0.826401\pi\) | ||||
−0.854931 | + | 0.518742i | \(0.826401\pi\) | |||||||
\(420\) | 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 | ||||
\(423\) | −18.1865 | + | 10.5000i | −0.884260 | + | 0.510527i | ||||
\(424\) | 4.50000 | + | 7.79423i | 0.218539 | + | 0.378521i | ||||
\(425\) | 1.19615 | + | 9.92820i | 0.0580219 | + | 0.481589i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.19615 | + | 15.0000i | 0.251459 | + | 0.725901i | ||||
\(428\) | 16.0000i | 0.773389i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.267949 | + | 4.46410i | 0.0129217 | + | 0.215278i | ||||
\(431\) | −1.00000 | − | 1.73205i | −0.0481683 | − | 0.0834300i | 0.840936 | − | 0.541135i | \(-0.182005\pi\) |
−0.889104 | + | 0.457705i | \(0.848672\pi\) | |||||||
\(432\) | 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 | 0.310228 | + | 0.950662i | \(0.399595\pi\) |
−0.978412 | + | 0.206666i | \(0.933739\pi\) | |||||||
\(440\) | −3.00000 | + | 6.00000i | −0.143019 | + | 0.286039i | ||||
\(441\) | 19.5000 | + | 7.79423i | 0.928571 | + | 0.371154i | ||||
\(442\) | 10.0000i | 0.475651i | ||||||||
\(443\) | 25.9808 | + | 15.0000i | 1.23438 | + | 0.712672i | 0.967941 | − | 0.251179i | \(-0.0808184\pi\) |
0.266443 | + | 0.963851i | \(0.414152\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.267949 | − | 4.46410i | −0.0127020 | − | 0.211619i | ||||
\(446\) | 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 | \(-0.537643\pi\) | ||||
−0.117982 | + | 0.993016i | \(0.537643\pi\) | |||||||
\(450\) | −1.79423 | − | 14.8923i | −0.0845807 | − | 0.702030i | ||||
\(451\) | −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 | ||||||||
\(455\) | 29.3301 | + | 3.83975i | 1.37502 | + | 0.180010i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.66025 | + | 5.00000i | 0.405110 | + | 0.233890i | 0.688686 | − | 0.725059i | \(-0.258188\pi\) |
−0.283577 | + | 0.958950i | \(0.591521\pi\) | |||||||
\(458\) | −13.8564 | + | 8.00000i | −0.647467 | + | 0.373815i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −8.62436 | − | 13.0622i | −0.402113 | − | 0.609027i | ||||
\(461\) | −32.0000 | −1.49039 | −0.745194 | − | 0.666847i | \(-0.767643\pi\) | ||||
−0.745194 | + | 0.666847i | \(0.767643\pi\) | |||||||
\(462\) | 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 | −0.372584 | − | 0.927999i | \(-0.621528\pi\) |
−0.989962 | + | 0.141332i | \(0.954861\pi\) | |||||||
\(468\) | − | 15.0000i | − | 0.693375i | ||||||
\(469\) | 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 | ||||
\(477\) | − | 27.0000i | − | 1.23625i | ||||||
\(478\) | 17.3205 | + | 10.0000i | 0.792222 | + | 0.457389i | ||||
\(479\) | 18.0000 | + | 31.1769i | 0.822441 | + | 1.42451i | 0.903859 | + | 0.427830i | \(0.140722\pi\) |
−0.0814184 | + | 0.996680i | \(0.525945\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.50000 | − | 4.33013i | 0.113990 | − | 0.197437i | ||||
\(482\) | − | 9.00000i | − | 0.409939i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.00000 | 0.0909091 | ||||||||
\(485\) | −14.7846 | − | 22.3923i | −0.671335 | − | 1.01678i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −27.7128 | + | 16.0000i | −1.25579 | + | 0.725029i | −0.972253 | − | 0.233933i | \(-0.924840\pi\) |
−0.283535 | + | 0.958962i | \(0.591507\pi\) | |||||||
\(488\) | 5.19615 | + | 3.00000i | 0.235219 | + | 0.135804i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.16025 | + | 15.3301i | 0.142766 | + | 0.692545i | ||||
\(491\) | 24.0000 | 1.08310 | 0.541552 | − | 0.840667i | \(-0.317837\pi\) | ||||
0.541552 | + | 0.840667i | \(0.317837\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.92820 | + | 4.00000i | −0.312031 | + | 0.180151i | ||||
\(494\) | 12.5000 | + | 21.6506i | 0.562402 | + | 0.974108i | ||||
\(495\) | 16.7942 | − | 11.0885i | 0.754844 | − | 0.498389i | ||||
\(496\) | −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 | −0.817781 | − | 0.575529i | \(-0.804796\pi\) |
0.907314 | + | 0.420455i | \(0.138129\pi\) | |||||||
\(500\) | 8.52628 | − | 7.23205i | 0.381307 | − | 0.323427i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.33013 | − | 2.50000i | −0.193263 | − | 0.111580i | ||||
\(503\) | − | 40.0000i | − | 1.78351i | −0.452517 | − | 0.891756i | \(-0.649474\pi\) | ||
0.452517 | − | 0.891756i | \(-0.350526\pi\) | |||||||
\(504\) | 7.50000 | − | 2.59808i | 0.334077 | − | 0.115728i | ||||
\(505\) | 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 | 0.192599 | + | 0.981278i | \(0.438308\pi\) |
−0.946111 | + | 0.323843i | \(0.895025\pi\) | |||||||
\(510\) | 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 | ||||
\(515\) | −17.8564 | + | 1.07180i | −0.786847 | + | 0.0472290i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 21.0000i | − | 0.923579i | ||||||
\(518\) | 2.59808 | + | 0.500000i | 0.114153 | + | 0.0219687i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.33013 | − | 6.16025i | 0.409153 | − | 0.270145i | ||||
\(521\) | 13.5000 | + | 23.3827i | 0.591446 | + | 1.02441i | 0.994038 | + | 0.109035i | \(0.0347759\pi\) |
−0.402592 | + | 0.915379i | \(0.631891\pi\) | |||||||
\(522\) | 10.3923 | − | 6.00000i | 0.454859 | − | 0.262613i | ||||
\(523\) | 13.8564 | + | 8.00000i | 0.605898 | + | 0.349816i | 0.771358 | − | 0.636401i | \(-0.219578\pi\) |
−0.165460 | + | 0.986216i | \(0.552911\pi\) | |||||||
\(524\) | 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 | ||||
\(530\) | 16.7942 | − | 11.0885i | 0.729495 | − | 0.481652i | ||||
\(531\) | 12.0000 | 0.520756 | ||||||||
\(532\) | −8.66025 | + | 10.0000i | −0.375470 | + | 0.433555i | ||||
\(533\) | 15.0000i | 0.649722i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 35.7128 | − | 2.14359i | 1.54400 | − | 0.0926756i | ||||
\(536\) | −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 | −0.641215 | − | 0.767361i | \(-0.721569\pi\) |
0.985162 | + | 0.171628i | \(0.0549027\pi\) | |||||||
\(542\) | 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 | ||||
\(549\) | −9.00000 | − | 15.5885i | −0.384111 | − | 0.665299i | ||||
\(550\) | 13.7942 | + | 5.89230i | 0.588188 | + | 0.251249i | ||||
\(551\) | −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 | −0.0146368 | − | 0.999893i | \(-0.504659\pi\) |
0.858614 | + | 0.512622i | \(0.171326\pi\) | |||||||
\(558\) | 5.19615 | + | 3.00000i | 0.219971 | + | 0.127000i | ||||
\(559\) | 10.0000 | 0.422955 | ||||||||
\(560\) | 4.69615 | + | 3.59808i | 0.198449 | + | 0.152046i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.79423 | − | 4.50000i | −0.328780 | − | 0.189821i | ||||
\(563\) | −1.73205 | + | 1.00000i | −0.0729972 | + | 0.0421450i | −0.536054 | − | 0.844183i | \(-0.680086\pi\) |
0.463057 | + | 0.886328i | \(0.346752\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −17.2487 | − | 26.1244i | −0.725659 | − | 1.09906i | ||||
\(566\) | 14.0000 | 0.588464 | ||||||||
\(567\) | −23.3827 | − | 4.50000i | −0.981981 | − | 0.188982i | ||||
\(568\) | 6.00000i | 0.251754i | ||||||||
\(569\) | −7.50000 | + | 12.9904i | −0.314416 | + | 0.544585i | −0.979313 | − | 0.202350i | \(-0.935142\pi\) |
0.664897 | + | 0.746935i | \(0.268475\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.0000 | − | 27.7128i | −0.669579 | − | 1.15975i | −0.978022 | − | 0.208502i | \(-0.933141\pi\) |
0.308443 | − | 0.951243i | \(-0.400192\pi\) | |||||||
\(572\) | 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 | ||||
\(576\) | 1.50000 | − | 2.59808i | 0.0625000 | − | 0.108253i | ||||
\(577\) | −3.46410 | + | 2.00000i | −0.144212 | + | 0.0832611i | −0.570370 | − | 0.821388i | \(-0.693200\pi\) |
0.426158 | + | 0.904649i | \(0.359867\pi\) | |||||||
\(578\) | 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 | ||||
\(585\) | −33.4808 | + | 2.00962i | −1.38426 | + | 0.0830875i | ||||
\(586\) | 4.50000 | − | 7.79423i | 0.185893 | − | 0.321977i | ||||
\(587\) | 34.0000i | 1.40333i | 0.712507 | + | 0.701665i | \(0.247560\pi\) | ||||
−0.712507 | + | 0.701665i | \(0.752440\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.0000 | −0.412043 | ||||||||
\(590\) | 4.92820 | + | 7.46410i | 0.202891 | + | 0.307292i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.866025 | − | 0.500000i | 0.0355934 | − | 0.0205499i | ||||
\(593\) | −5.19615 | − | 3.00000i | −0.213380 | − | 0.123195i | 0.389501 | − | 0.921026i | \(-0.372647\pi\) |
−0.602881 | + | 0.797831i | \(0.705981\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.53590 | + | 10.9282i | 0.185954 | + | 0.448013i | ||||
\(596\) | −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 | \(-0.245505\pi\) |
−0.962175 | + | 0.272433i | \(0.912172\pi\) | |||||||
\(600\) | 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 | ||||
\(603\) | 6.00000i | 0.244339i | ||||||||
\(604\) | −3.00000 | + | 5.19615i | −0.122068 | + | 0.211428i | ||||
\(605\) | −0.267949 | − | 4.46410i | −0.0108937 | − | 0.181492i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.2583 | + | 6.50000i | 0.456962 | + | 0.263827i | 0.710766 | − | 0.703429i | \(-0.248349\pi\) |
−0.253804 | + | 0.967256i | \(0.581682\pi\) | |||||||
\(608\) | 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 | ||||
\(612\) | 5.19615 | − | 3.00000i | 0.210042 | − | 0.121268i | ||||
\(613\) | 12.9904 | − | 7.50000i | 0.524677 | − | 0.302922i | −0.214169 | − | 0.976797i | \(-0.568704\pi\) |
0.738846 | + | 0.673874i | \(0.235371\pi\) | |||||||
\(614\) | −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 | \(0.0909346\pi\) | ||||
−0.959470 | + | 0.281809i | \(0.909065\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.50000 | + | 16.4545i | 0.381837 | + | 0.661361i | 0.991325 | − | 0.131434i | \(-0.0419582\pi\) |
−0.609488 | + | 0.792796i | \(0.708625\pi\) | |||||||
\(620\) | 0.267949 | + | 4.46410i | 0.0107611 | + | 0.179283i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.00000i | 0.240578i | ||||||||
\(623\) | −1.73205 | − | 5.00000i | −0.0693932 | − | 0.200321i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.2846 | − | 18.0622i | −0.691384 | − | 0.722487i | ||||
\(626\) | 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 | ||||||||
\(630\) | −6.80385 | − | 16.3923i | −0.271072 | − | 0.653085i | ||||
\(631\) | −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 | ||||
\(635\) | 8.62436 | + | 13.0622i | 0.342247 | + | 0.518357i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 34.6410 | − | 5.00000i | 1.37253 | − | 0.198107i | ||||
\(638\) | 12.0000i | 0.475085i | ||||||||
\(639\) | 9.00000 | − | 15.5885i | 0.356034 | − | 0.616670i | ||||
\(640\) | 2.23205 | − | 0.133975i | 0.0882296 | − | 0.00529581i | ||||
\(641\) | 2.50000 | + | 4.33013i | 0.0987441 | + | 0.171030i | 0.911165 | − | 0.412042i | \(-0.135184\pi\) |
−0.812421 | + | 0.583071i | \(0.801851\pi\) | |||||||
\(642\) | 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 | −0.883402 | − | 0.468617i | \(-0.844753\pi\) |
−0.0358667 | + | 0.999357i | \(0.511419\pi\) | |||||||
\(648\) | −7.79423 | + | 4.50000i | −0.306186 | + | 0.176777i | ||||
\(649\) | −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 | 0.549973 | − | 0.835182i | \(-0.314638\pi\) |
−0.448303 | + | 0.893882i | \(0.647971\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.133975 | − | 2.23205i | −0.00523482 | − | 0.0872134i | ||||
\(656\) | −1.50000 | + | 2.59808i | −0.0585652 | + | 0.101438i | ||||
\(657\) | 48.0000i | 1.87266i | ||||||||
\(658\) | −18.1865 | − | 3.50000i | −0.708985 | − | 0.136444i | ||||
\(659\) | 36.0000 | 1.40236 | 0.701180 | − | 0.712984i | \(-0.252657\pi\) | ||||
0.701180 | + | 0.712984i | \(0.252657\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.00000 | − | 13.8564i | −0.311164 | − | 0.538952i | 0.667451 | − | 0.744654i | \(-0.267385\pi\) |
−0.978615 | + | 0.205702i | \(0.934052\pi\) | |||||||
\(662\) | 4.33013 | − | 2.50000i | 0.168295 | − | 0.0971653i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.00000 | 0.232845 | ||||||||
\(665\) | 23.4808 | + | 17.9904i | 0.910545 | + | 0.697637i | ||||
\(666\) | −3.00000 | −0.116248 | ||||||||
\(667\) | −24.2487 | − | 14.0000i | −0.938914 | − | 0.542082i | ||||
\(668\) | −12.9904 | + | 7.50000i | −0.502613 | + | 0.290184i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.73205 | + | 2.46410i | −0.144182 | + | 0.0951966i | ||||
\(671\) | 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 | 0.755482 | − | 0.655170i | \(-0.227403\pi\) |
−0.189653 | + | 0.981851i | \(0.560736\pi\) | |||||||
\(678\) | 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 | 0.459136 | − | 0.888366i | \(-0.348159\pi\) |
0.998916 | + | 0.0465592i | \(0.0148256\pi\) | |||||||
\(684\) | 7.50000 | − | 12.9904i | 0.286770 | − | 0.496700i | ||||
\(685\) | −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 | −0.0555386 | − | 0.998457i | \(-0.517688\pi\) |
0.892458 | − | 0.451130i | \(-0.148979\pi\) | |||||||
\(692\) | 9.00000i | 0.342129i | ||||||||
\(693\) | 15.5885 | − | 18.0000i | 0.592157 | − | 0.683763i | ||||
\(694\) | 12.0000 | 0.455514 | ||||||||
\(695\) | −29.8564 | + | 19.7128i | −1.13252 | + | 0.747750i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.19615 | + | 3.00000i | −0.196818 | + | 0.113633i | ||||
\(698\) | −10.3923 | − | 6.00000i | −0.393355 | − | 0.227103i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 7.40192 | − | 10.9641i | 0.279766 | − | 0.414404i | ||||
\(701\) | 26.0000 | 0.982006 | 0.491003 | − | 0.871158i | \(-0.336630\pi\) | ||||
0.491003 | + | 0.871158i | \(0.336630\pi\) | |||||||
\(702\) | 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 | −0.731085 | − | 0.682286i | \(-0.760986\pi\) |
0.956420 | + | 0.291995i | \(0.0943191\pi\) | |||||||
\(710\) | 13.3923 | − | 0.803848i | 0.502604 | − | 0.0301679i | ||||
\(711\) | 21.0000 | + | 36.3731i | 0.787562 | + | 1.36410i | ||||
\(712\) | −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 | \(-0.672219\pi\) |
0.999848 | + | 0.0174426i | \(0.00555244\pi\) | |||||||
\(720\) | −6.00000 | − | 3.00000i | −0.223607 | − | 0.111803i | ||||
\(721\) | −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 | ||||
\(725\) | 7.85641 | − | 18.3923i | 0.291780 | − | 0.683073i | ||||
\(726\) | 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 | ||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | −29.8564 | + | 19.7128i | −1.10504 | + | 0.729604i | ||||
\(731\) | 2.00000 | + | 3.46410i | 0.0739727 | + | 0.128124i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.5070 | + | 20.5000i | 1.31148 | + | 0.757185i | 0.982342 | − | 0.187096i | \(-0.0599076\pi\) |
0.329141 | + | 0.944281i | \(0.393241\pi\) | |||||||
\(734\) | −13.0000 | −0.479839 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.00000 | −0.258023 | ||||||||
\(737\) | −5.19615 | − | 3.00000i | −0.191403 | − | 0.110506i | ||||
\(738\) | 7.79423 | − | 4.50000i | 0.286910 | − | 0.165647i | ||||
\(739\) | −14.5000 | − | 25.1147i | −0.533391 | − | 0.923861i | −0.999239 | − | 0.0389959i | \(-0.987584\pi\) |
0.465848 | − | 0.884865i | \(-0.345749\pi\) | |||||||
\(740\) | −1.23205 | − | 1.86603i | −0.0452911 | − | 0.0685965i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 15.5885 | − | 18.0000i | 0.572270 | − | 0.660801i | ||||
\(743\) | 21.0000i | 0.770415i | 0.922830 | + | 0.385208i | \(0.125870\pi\) | ||||
−0.922830 | + | 0.385208i | \(0.874130\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.41154 | + | 40.1769i | 0.0883521 | + | 1.47197i | ||||
\(746\) | −13.0000 | − | 22.5167i | −0.475964 | − | 0.824394i | ||||
\(747\) | −15.5885 | − | 9.00000i | −0.570352 | − | 0.329293i | ||||
\(748\) | 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 | 0.489053 | + | 0.872254i | \(0.337342\pi\) |
−0.999921 | + | 0.0125942i | \(0.995991\pi\) | |||||||
\(752\) | −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 | ||||||||
\(760\) | 11.1603 | − | 0.669873i | 0.404825 | − | 0.0242988i | ||||
\(761\) | −0.500000 | + | 0.866025i | −0.0181250 | + | 0.0313934i | −0.874946 | − | 0.484221i | \(-0.839103\pi\) |
0.856821 | + | 0.515615i | \(0.172436\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.19615 | + | 1.00000i | 0.188113 | + | 0.0362024i | ||||
\(764\) | 20.0000 | 0.723575 | ||||||||
\(765\) | −7.39230 | − | 11.1962i | −0.267269 | − | 0.404798i | ||||
\(766\) | −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 | \(0.324856\pi\) | |||||||
\(770\) | 17.5981 | + | 2.30385i | 0.634191 | + | 0.0830249i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 8.66025 | + | 5.00000i | 0.311689 | + | 0.179954i | ||||
\(773\) | −38.9711 | + | 22.5000i | −1.40169 | + | 0.809269i | −0.994567 | − | 0.104102i | \(-0.966803\pi\) |
−0.407128 | + | 0.913371i | \(0.633470\pi\) | |||||||
\(774\) | −3.00000 | − | 5.19615i | −0.107833 | − | 0.186772i | ||||
\(775\) | 9.92820 | − | 1.19615i | 0.356632 | − | 0.0429671i | ||||
\(776\) | −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 | \(-0.562710\pi\) |
0.751405 | + | 0.659841i | \(0.229376\pi\) | |||||||
\(788\) | 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 | ||||
\(792\) | − | 9.00000i | − | 0.319801i | ||||||
\(793\) | −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 | \(-0.988723\pi\) | ||
0.999372 | − | 0.0354218i | \(-0.0112775\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.0000 | −0.495284 | ||||||||
\(800\) | −0.598076 | − | 4.96410i | −0.0211452 | − | 0.175507i | ||||
\(801\) | 3.00000 | + | 5.19615i | 0.106000 | + | 0.183597i | ||||
\(802\) | −12.9904 | + | 7.50000i | −0.458706 | + | 0.264834i | ||||
\(803\) | −41.5692 | − | 24.0000i | −1.46695 | − | 0.846942i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −25.1865 | + | 32.8731i | −0.887709 | + | 1.15862i | ||||
\(806\) | 10.0000 | 0.352235 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.50000 | − | 4.33013i | −0.0878953 | − | 0.152239i | 0.818726 | − | 0.574184i | \(-0.194681\pi\) |
−0.906621 | + | 0.421945i | \(0.861347\pi\) | |||||||
\(810\) | 11.0885 | + | 16.7942i | 0.389609 | + | 0.590089i | ||||
\(811\) | −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 | ||||
\(815\) | −26.7846 | + | 1.60770i | −0.938224 | + | 0.0563151i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.66025 | + | 5.00000i | 0.302984 | + | 0.174928i | ||||
\(818\) | 14.0000i | 0.489499i | ||||||||
\(819\) | −37.5000 | + | 12.9904i | −1.31036 | + | 0.453921i | ||||
\(820\) | 6.00000 | + | 3.00000i | 0.209529 | + | 0.104765i | ||||
\(821\) | 9.00000 | − | 15.5885i | 0.314102 | − | 0.544041i | −0.665144 | − | 0.746715i | \(-0.731630\pi\) |
0.979246 | + | 0.202674i | \(0.0649632\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.7846 | − | 12.0000i | 0.724506 | − | 0.418294i | −0.0919029 | − | 0.995768i | \(-0.529295\pi\) |
0.816409 | + | 0.577474i | \(0.195962\pi\) | |||||||
\(824\) | −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 | \(-0.875061\pi\) | ||
0.923952 | − | 0.382507i | \(-0.124939\pi\) | |||||||
\(828\) | 18.1865 | + | 10.5000i | 0.632026 | + | 0.364900i | ||||
\(829\) | −13.0000 | − | 22.5167i | −0.451509 | − | 0.782036i | 0.546971 | − | 0.837151i | \(-0.315781\pi\) |
−0.998480 | + | 0.0551154i | \(0.982447\pi\) | |||||||
\(830\) | −0.803848 | − | 13.3923i | −0.0279020 | − | 0.464854i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 5.00000i | − | 0.173344i | ||||||
\(833\) | 8.66025 | + | 11.0000i | 0.300060 | + | 0.381127i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.4808 | + | 27.9904i | 0.639553 | + | 0.968647i | ||||
\(836\) | 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 | \(-0.300346\pi\) | ||||
0.586905 | + | 0.809656i | \(0.300346\pi\) | |||||||
\(840\) | 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 | ||||
\(845\) | −22.3923 | + | 14.7846i | −0.770319 | + | 0.508606i | ||||
\(846\) | 21.0000 | 0.721995 | ||||||||
\(847\) | −1.73205 | − | 5.00000i | −0.0595140 | − | 0.171802i | ||||
\(848\) | − | 9.00000i | − | 0.309061i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.92820 | − | 9.19615i | 0.134736 | − | 0.315425i | ||||
\(851\) | 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 | ||||
\(855\) | −30.0000 | − | 15.0000i | −1.02598 | − | 0.512989i | ||||
\(856\) | 8.00000 | − | 13.8564i | 0.273434 | − | 0.473602i | ||||
\(857\) | 6.92820 | − | 4.00000i | 0.236663 | − | 0.136637i | −0.376979 | − | 0.926222i | \(-0.623037\pi\) |
0.613642 | + | 0.789584i | \(0.289704\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.00000 | + | 10.3923i | −0.204717 | + | 0.354581i | −0.950043 | − | 0.312120i | \(-0.898961\pi\) |
0.745325 | + | 0.666701i | \(0.232294\pi\) | |||||||
\(860\) | 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 | 0.329020 | − | 0.944323i | \(-0.393282\pi\) |
−0.653298 | + | 0.757101i | \(0.726615\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20.0885 | − | 1.20577i | 0.683028 | − | 0.0409975i | ||||
\(866\) | −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 | ||||
\(873\) | 31.1769 | + | 18.0000i | 1.05518 | + | 0.609208i | ||||
\(874\) | −35.0000 | −1.18389 | ||||||||
\(875\) | −25.4641 | − | 15.0526i | −0.860844 | − | 0.508869i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.8468 | − | 15.5000i | −0.906552 | − | 0.523398i | −0.0272316 | − | 0.999629i | \(-0.508669\pi\) |
−0.879320 | + | 0.476231i | \(0.842002\pi\) | |||||||
\(878\) | 24.2487 | − | 14.0000i | 0.818354 | − | 0.472477i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 5.59808 | − | 3.69615i | 0.188711 | − | 0.124597i | ||||
\(881\) | −15.0000 | −0.505363 | −0.252681 | − | 0.967550i | \(-0.581312\pi\) | ||||
−0.252681 | + | 0.967550i | \(0.581312\pi\) | |||||||
\(882\) | −12.9904 | − | 16.5000i | −0.437409 | − | 0.555584i | ||||
\(883\) | − | 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 | −0.125061 | − | 0.992149i | \(-0.539913\pi\) |
−0.921757 | + | 0.387768i | \(0.873246\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.0000 | + | 12.1244i | 0.469545 | + | 0.406638i | ||||
\(890\) | −2.00000 | + | 4.00000i | −0.0670402 | + | 0.134080i | ||||
\(891\) | −13.5000 | + | 23.3827i | −0.452267 | + | 0.783349i | ||||
\(892\) | −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 | ||||
\(900\) | −5.89230 | + | 13.7942i | −0.196410 | + | 0.459808i | ||||
\(901\) | 9.00000 | − | 15.5885i | 0.299833 | − | 0.519327i | ||||
\(902\) | 9.00000i | 0.299667i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14.0000 | −0.465633 | ||||||||
\(905\) | 48.5167 | − | 32.0333i | 1.61275 | − | 1.06482i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34.6410 | + | 20.0000i | −1.15024 | + | 0.664089i | −0.948945 | − | 0.315442i | \(-0.897847\pi\) |
−0.201291 | + | 0.979531i | \(0.564514\pi\) | |||||||
\(908\) | −5.19615 | − | 3.00000i | −0.172440 | − | 0.0995585i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −23.4808 | − | 17.9904i | −0.778380 | − | 0.596375i | ||||
\(911\) | 2.00000 | 0.0662630 | 0.0331315 | − | 0.999451i | \(-0.489452\pi\) | ||||
0.0331315 | + | 0.999451i | \(0.489452\pi\) | |||||||
\(912\) | 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 | −0.652616 | − | 0.757689i | \(-0.726329\pi\) |
0.982486 | + | 0.186338i | \(0.0596619\pi\) | |||||||
\(920\) | 0.937822 | + | 15.6244i | 0.0309191 | + | 0.515120i | ||||
\(921\) | 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 | ||||
\(927\) | 20.7846 | − | 12.0000i | 0.682656 | − | 0.394132i | ||||
\(928\) | 3.46410 | − | 2.00000i | 0.113715 | − | 0.0656532i | ||||
\(929\) | 10.5000 | − | 18.1865i | 0.344494 | − | 0.596681i | −0.640768 | − | 0.767735i | \(-0.721384\pi\) |
0.985262 | + | 0.171054i | \(0.0547172\pi\) | |||||||
\(930\) | 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 | ||||
\(935\) | 13.3923 | − | 0.803848i | 0.437975 | − | 0.0262886i | ||||
\(936\) | −7.50000 | + | 12.9904i | −0.245145 | + | 0.424604i | ||||
\(937\) | − | 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 | ||||||||
\(940\) | 8.62436 | + | 13.0622i | 0.281295 | + | 0.426041i | ||||
\(941\) | 14.0000 | + | 24.2487i | 0.456387 | + | 0.790485i | 0.998767 | − | 0.0496480i | \(-0.0158099\pi\) |
−0.542380 | + | 0.840133i | \(0.682477\pi\) | |||||||
\(942\) | 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 | 0.659256 | − | 0.751918i | \(-0.270871\pi\) |
−0.321552 | + | 0.946892i | \(0.604204\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 40.0000 | + | 69.2820i | 1.29845 | + | 2.24899i | ||||
\(950\) | −2.99038 | − | 24.8205i | −0.0970208 | − | 0.805284i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.19615 | + | 1.00000i | 0.168408 | + | 0.0324102i | ||||
\(953\) | 24.0000i | 0.777436i | 0.921357 | + | 0.388718i | \(0.127082\pi\) | ||||
−0.921357 | + | 0.388718i | \(0.872918\pi\) | |||||||
\(954\) | −13.5000 | + | 23.3827i | −0.437079 | + | 0.757042i | ||||
\(955\) | −2.67949 | − | 44.6410i | −0.0867063 | − | 1.44455i | ||||
\(956\) | −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 | ||||
\(963\) | −41.5692 | + | 24.0000i | −1.33955 | + | 0.773389i | ||||
\(964\) | −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 | ||||||||
\(970\) | 1.60770 | + | 26.7846i | 0.0516200 | + | 0.860002i | ||||
\(971\) | 16.5000 | − | 28.5788i | 0.529510 | − | 0.917139i | −0.469897 | − | 0.882721i | \(-0.655709\pi\) |
0.999408 | − | 0.0344175i | \(-0.0109576\pi\) | |||||||
\(972\) | 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 | 0.496167 | − | 0.868227i | \(-0.334741\pi\) |
0.999990 | + | 0.00442082i | \(0.00140720\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.00000 | −0.191761 | ||||||||
\(980\) | 4.92820 | − | 14.8564i | 0.157426 | − | 0.474570i | ||||
\(981\) | −6.00000 | −0.191565 | ||||||||
\(982\) | −20.7846 | − | 12.0000i | −0.663264 | − | 0.382935i | ||||
\(983\) | 25.1147 | − | 14.5000i | 0.801036 | − | 0.462478i | −0.0427975 | − | 0.999084i | \(-0.513627\pi\) |
0.843833 | + | 0.536606i | \(0.180294\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.16025 | − | 9.33013i | −0.196282 | − | 0.297283i | ||||
\(986\) | 8.00000 | 0.254772 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 25.0000i | − | 0.795356i | ||||||
\(989\) | −7.00000 | + | 12.1244i | −0.222587 | + | 0.385532i | ||||
\(990\) | −20.0885 | + | 1.20577i | −0.638453 | + | 0.0383219i | ||||
\(991\) | 4.00000 | + | 6.92820i | 0.127064 | + | 0.220082i | 0.922538 | − | 0.385906i | \(-0.126111\pi\) |
−0.795474 | + | 0.605988i | \(0.792778\pi\) | |||||||
\(992\) | 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 | \(-0.872191\pi\) |
−0.121771 | + | 0.992558i | \(0.538857\pi\) | |||||||
\(998\) | −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 | 70.2.i.b.9.1 | ✓ | 4 | |
3.2 | odd | 2 | 630.2.u.a.289.2 | 4 | |||
4.3 | odd | 2 | 560.2.bw.d.289.2 | 4 | |||
5.2 | odd | 4 | 350.2.e.j.51.1 | 2 | |||
5.3 | odd | 4 | 350.2.e.c.51.1 | 2 | |||
5.4 | even | 2 | inner | 70.2.i.b.9.2 | yes | 4 | |
7.2 | even | 3 | 490.2.c.a.99.2 | 2 | |||
7.3 | odd | 6 | 490.2.i.a.459.2 | 4 | |||
7.4 | even | 3 | inner | 70.2.i.b.39.2 | yes | 4 | |
7.5 | odd | 6 | 490.2.c.d.99.2 | 2 | |||
7.6 | odd | 2 | 490.2.i.a.79.1 | 4 | |||
15.14 | odd | 2 | 630.2.u.a.289.1 | 4 | |||
20.19 | odd | 2 | 560.2.bw.d.289.1 | 4 | |||
21.11 | odd | 6 | 630.2.u.a.109.1 | 4 | |||
28.11 | odd | 6 | 560.2.bw.d.529.1 | 4 | |||
35.2 | odd | 12 | 2450.2.a.k.1.1 | 1 | |||
35.4 | even | 6 | inner | 70.2.i.b.39.1 | yes | 4 | |
35.9 | even | 6 | 490.2.c.a.99.1 | 2 | |||
35.12 | even | 12 | 2450.2.a.j.1.1 | 1 | |||
35.18 | odd | 12 | 350.2.e.c.151.1 | 2 | |||
35.19 | odd | 6 | 490.2.c.d.99.1 | 2 | |||
35.23 | odd | 12 | 2450.2.a.ba.1.1 | 1 | |||
35.24 | odd | 6 | 490.2.i.a.459.1 | 4 | |||
35.32 | odd | 12 | 350.2.e.j.151.1 | 2 | |||
35.33 | even | 12 | 2450.2.a.bb.1.1 | 1 | |||
35.34 | odd | 2 | 490.2.i.a.79.2 | 4 | |||
105.74 | odd | 6 | 630.2.u.a.109.2 | 4 | |||
140.39 | odd | 6 | 560.2.bw.d.529.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.2.i.b.9.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
70.2.i.b.9.2 | yes | 4 | 5.4 | even | 2 | inner | |
70.2.i.b.39.1 | yes | 4 | 35.4 | even | 6 | inner | |
70.2.i.b.39.2 | yes | 4 | 7.4 | even | 3 | inner | |
350.2.e.c.51.1 | 2 | 5.3 | odd | 4 | |||
350.2.e.c.151.1 | 2 | 35.18 | odd | 12 | |||
350.2.e.j.51.1 | 2 | 5.2 | odd | 4 | |||
350.2.e.j.151.1 | 2 | 35.32 | odd | 12 | |||
490.2.c.a.99.1 | 2 | 35.9 | even | 6 | |||
490.2.c.a.99.2 | 2 | 7.2 | even | 3 | |||
490.2.c.d.99.1 | 2 | 35.19 | odd | 6 | |||
490.2.c.d.99.2 | 2 | 7.5 | odd | 6 | |||
490.2.i.a.79.1 | 4 | 7.6 | odd | 2 | |||
490.2.i.a.79.2 | 4 | 35.34 | odd | 2 | |||
490.2.i.a.459.1 | 4 | 35.24 | odd | 6 | |||
490.2.i.a.459.2 | 4 | 7.3 | odd | 6 | |||
560.2.bw.d.289.1 | 4 | 20.19 | odd | 2 | |||
560.2.bw.d.289.2 | 4 | 4.3 | odd | 2 | |||
560.2.bw.d.529.1 | 4 | 28.11 | odd | 6 | |||
560.2.bw.d.529.2 | 4 | 140.39 | odd | 6 | |||
630.2.u.a.109.1 | 4 | 21.11 | odd | 6 | |||
630.2.u.a.109.2 | 4 | 105.74 | odd | 6 | |||
630.2.u.a.289.1 | 4 | 15.14 | odd | 2 | |||
630.2.u.a.289.2 | 4 | 3.2 | odd | 2 | |||
2450.2.a.j.1.1 | 1 | 35.12 | even | 12 | |||
2450.2.a.k.1.1 | 1 | 35.2 | odd | 12 | |||
2450.2.a.ba.1.1 | 1 | 35.23 | odd | 12 | |||
2450.2.a.bb.1.1 | 1 | 35.33 | even | 12 |