Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,2,Mod(59,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.59");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.t (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: | \(1.67685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.3317760000.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 59.1 | ||
Root | \(-1.01575 + 1.40294i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.59 |
Dual form | 210.2.t.e.89.1 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | −1.72286 | − | 0.178197i | −0.994694 | − | 0.102882i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 2.20711 | + | 0.358719i | 0.987048 | + | 0.160424i | ||||
\(6\) | 0.707107 | + | 1.58114i | 0.288675 | + | 0.645497i | ||||
\(7\) | −1.41421 | + | 2.23607i | −0.534522 | + | 0.845154i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.93649 | + | 0.614017i | 0.978831 | + | 0.204672i | ||||
\(10\) | −0.792893 | − | 2.09077i | −0.250735 | − | 0.661160i | ||||
\(11\) | 0.184829 | + | 0.106711i | 0.0557279 | + | 0.0321745i | 0.527605 | − | 0.849490i | \(-0.323090\pi\) |
−0.471877 | + | 0.881664i | \(0.656423\pi\) | |||||||
\(12\) | 1.01575 | − | 1.40294i | 0.293223 | − | 0.404994i | ||||
\(13\) | 6.70141 | 1.85864 | 0.929318 | − | 0.369279i | \(-0.120395\pi\) | ||||
0.929318 | + | 0.369279i | \(0.120395\pi\) | |||||||
\(14\) | 2.64360 | + | 0.106711i | 0.706531 | + | 0.0285197i | ||||
\(15\) | −3.73861 | − | 1.01132i | −0.965306 | − | 0.261123i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −2.73861 | − | 1.58114i | −0.664211 | − | 0.383482i | 0.129668 | − | 0.991557i | \(-0.458609\pi\) |
−0.793880 | + | 0.608075i | \(0.791942\pi\) | |||||||
\(18\) | −0.936492 | − | 2.85008i | −0.220733 | − | 0.671771i | ||||
\(19\) | 4.23861 | − | 2.44716i | 0.972404 | − | 0.561418i | 0.0724360 | − | 0.997373i | \(-0.476923\pi\) |
0.899968 | + | 0.435955i | \(0.143589\pi\) | |||||||
\(20\) | −1.41421 | + | 1.73205i | −0.316228 | + | 0.387298i | ||||
\(21\) | 2.83495 | − | 3.60042i | 0.618637 | − | 0.785677i | ||||
\(22\) | − | 0.213422i | − | 0.0455017i | ||||||
\(23\) | 3.23861 | + | 5.60944i | 0.675297 | + | 1.16965i | 0.976382 | + | 0.216052i | \(0.0693181\pi\) |
−0.301084 | + | 0.953597i | \(0.597349\pi\) | |||||||
\(24\) | −1.72286 | − | 0.178197i | −0.351677 | − | 0.0363743i | ||||
\(25\) | 4.74264 | + | 1.58346i | 0.948528 | + | 0.316693i | ||||
\(26\) | −3.35071 | − | 5.80359i | −0.657127 | − | 1.13818i | ||||
\(27\) | −4.94975 | − | 1.58114i | −0.952579 | − | 0.304290i | ||||
\(28\) | −1.22938 | − | 2.34278i | −0.232332 | − | 0.442744i | ||||
\(29\) | 2.02265i | 0.375596i | 0.982208 | + | 0.187798i | \(0.0601350\pi\) | ||||
−0.982208 | + | 0.187798i | \(0.939865\pi\) | |||||||
\(30\) | 0.993475 | + | 3.74340i | 0.181383 | + | 0.683447i | ||||
\(31\) | −0.261387 | − | 0.150912i | −0.0469465 | − | 0.0271046i | 0.476343 | − | 0.879260i | \(-0.341962\pi\) |
−0.523290 | + | 0.852155i | \(0.675295\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −0.299418 | − | 0.216784i | −0.0521220 | − | 0.0377372i | ||||
\(34\) | 3.16228i | 0.542326i | ||||||||
\(35\) | −3.92344 | + | 4.42793i | −0.663183 | + | 0.748458i | ||||
\(36\) | −2.00000 | + | 2.23607i | −0.333333 | + | 0.372678i | ||||
\(37\) | −6.17913 | + | 3.56752i | −1.01584 | + | 0.586497i | −0.912897 | − | 0.408190i | \(-0.866160\pi\) |
−0.102946 | + | 0.994687i | \(0.532827\pi\) | |||||||
\(38\) | −4.23861 | − | 2.44716i | −0.687594 | − | 0.396982i | ||||
\(39\) | −11.5456 | − | 1.19417i | −1.84877 | − | 0.191220i | ||||
\(40\) | 2.20711 | + | 0.358719i | 0.348974 | + | 0.0567185i | ||||
\(41\) | −6.70141 | −1.04658 | −0.523292 | − | 0.852153i | \(-0.675296\pi\) | ||||
−0.523292 | + | 0.852153i | \(0.675296\pi\) | |||||||
\(42\) | −4.53553 | − | 0.654929i | −0.699848 | − | 0.101058i | ||||
\(43\) | 2.02265i | 0.308451i | 0.988036 | + | 0.154225i | \(0.0492882\pi\) | ||||
−0.988036 | + | 0.154225i | \(0.950712\pi\) | |||||||
\(44\) | −0.184829 | + | 0.106711i | −0.0278640 | + | 0.0160873i | ||||
\(45\) | 6.26089 | + | 2.40858i | 0.933319 | + | 0.359050i | ||||
\(46\) | 3.23861 | − | 5.60944i | 0.477507 | − | 0.827067i | ||||
\(47\) | 6.71584 | − | 3.87739i | 0.979606 | − | 0.565576i | 0.0774546 | − | 0.996996i | \(-0.475321\pi\) |
0.902151 | + | 0.431420i | \(0.141987\pi\) | |||||||
\(48\) | 0.707107 | + | 1.58114i | 0.102062 | + | 0.228218i | ||||
\(49\) | −3.00000 | − | 6.32456i | −0.428571 | − | 0.903508i | ||||
\(50\) | −1.00000 | − | 4.89898i | −0.141421 | − | 0.692820i | ||||
\(51\) | 4.43649 | + | 3.21209i | 0.621233 | + | 0.449783i | ||||
\(52\) | −3.35071 | + | 5.80359i | −0.464659 | + | 0.804813i | ||||
\(53\) | −2.50000 | + | 4.33013i | −0.343401 | + | 0.594789i | −0.985062 | − | 0.172200i | \(-0.944912\pi\) |
0.641661 | + | 0.766989i | \(0.278246\pi\) | |||||||
\(54\) | 1.10557 | + | 5.07718i | 0.150449 | + | 0.690916i | ||||
\(55\) | 0.369657 | + | 0.301824i | 0.0498446 | + | 0.0406979i | ||||
\(56\) | −1.41421 | + | 2.23607i | −0.188982 | + | 0.298807i | ||||
\(57\) | −7.73861 | + | 3.46081i | −1.02500 | + | 0.458396i | ||||
\(58\) | 1.75166 | − | 1.01132i | 0.230005 | − | 0.132793i | ||||
\(59\) | −2.45877 | + | 4.25871i | −0.320105 | + | 0.554437i | −0.980509 | − | 0.196472i | \(-0.937051\pi\) |
0.660405 | + | 0.750910i | \(0.270385\pi\) | |||||||
\(60\) | 2.74514 | − | 2.73207i | 0.354396 | − | 0.352709i | ||||
\(61\) | 3.00000 | − | 1.73205i | 0.384111 | − | 0.221766i | −0.295495 | − | 0.955344i | \(-0.595484\pi\) |
0.679605 | + | 0.733578i | \(0.262151\pi\) | |||||||
\(62\) | 0.301824i | 0.0383317i | ||||||||
\(63\) | −5.52581 | + | 5.69784i | −0.696187 | + | 0.717861i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 14.7907 | + | 2.40393i | 1.83456 | + | 0.298170i | ||||
\(66\) | −0.0380311 | + | 0.367696i | −0.00468131 | + | 0.0452602i | ||||
\(67\) | −4.61230 | − | 2.66291i | −0.563482 | − | 0.325326i | 0.191060 | − | 0.981578i | \(-0.438808\pi\) |
−0.754542 | + | 0.656252i | \(0.772141\pi\) | |||||||
\(68\) | 2.73861 | − | 1.58114i | 0.332106 | − | 0.191741i | ||||
\(69\) | −4.58009 | − | 10.2414i | −0.551378 | − | 1.23292i | ||||
\(70\) | 5.79642 | + | 1.18383i | 0.692805 | + | 0.141495i | ||||
\(71\) | − | 2.02265i | − | 0.240044i | −0.992771 | − | 0.120022i | \(-0.961703\pi\) | ||
0.992771 | − | 0.120022i | \(-0.0382965\pi\) | |||||||
\(72\) | 2.93649 | + | 0.614017i | 0.346069 | + | 0.0723626i | ||||
\(73\) | 5.99430 | − | 10.3824i | 0.701580 | − | 1.21517i | −0.266331 | − | 0.963882i | \(-0.585812\pi\) |
0.967912 | − | 0.251291i | \(-0.0808551\pi\) | |||||||
\(74\) | 6.17913 | + | 3.56752i | 0.718310 | + | 0.414716i | ||||
\(75\) | −7.88874 | − | 3.57321i | −0.910913 | − | 0.412599i | ||||
\(76\) | 4.89433i | 0.561418i | ||||||||
\(77\) | −0.500000 | + | 0.262377i | −0.0569803 | + | 0.0299007i | ||||
\(78\) | 4.73861 | + | 10.5959i | 0.536542 | + | 1.19974i | ||||
\(79\) | −0.261387 | − | 0.452736i | −0.0294084 | − | 0.0509368i | 0.850947 | − | 0.525252i | \(-0.176029\pi\) |
−0.880355 | + | 0.474315i | \(0.842696\pi\) | |||||||
\(80\) | −0.792893 | − | 2.09077i | −0.0886482 | − | 0.233755i | ||||
\(81\) | 8.24597 | + | 3.60611i | 0.916219 | + | 0.400679i | ||||
\(82\) | 3.35071 | + | 5.80359i | 0.370023 | + | 0.640899i | ||||
\(83\) | − | 16.7169i | − | 1.83491i | −0.397835 | − | 0.917457i | \(-0.630238\pi\) | ||
0.397835 | − | 0.917457i | \(-0.369762\pi\) | |||||||
\(84\) | 1.70058 | + | 4.25535i | 0.185549 | + | 0.464297i | ||||
\(85\) | −5.47723 | − | 4.47214i | −0.594089 | − | 0.485071i | ||||
\(86\) | 1.75166 | − | 1.01132i | 0.188887 | − | 0.109054i | ||||
\(87\) | 0.360429 | − | 3.48474i | 0.0386421 | − | 0.373603i | ||||
\(88\) | 0.184829 | + | 0.106711i | 0.0197028 | + | 0.0113754i | ||||
\(89\) | −5.28720 | − | 9.15769i | −0.560442 | − | 0.970714i | −0.997458 | − | 0.0712599i | \(-0.977298\pi\) |
0.437016 | − | 0.899454i | \(-0.356035\pi\) | |||||||
\(90\) | −1.04456 | − | 6.62638i | −0.110106 | − | 0.698482i | ||||
\(91\) | −9.47723 | + | 14.9848i | −0.993483 | + | 1.57083i | ||||
\(92\) | −6.47723 | −0.675297 | ||||||||
\(93\) | 0.423441 | + | 0.306579i | 0.0439088 | + | 0.0317907i | ||||
\(94\) | −6.71584 | − | 3.87739i | −0.692686 | − | 0.399922i | ||||
\(95\) | 10.2329 | − | 3.88068i | 1.04988 | − | 0.398149i | ||||
\(96\) | 1.01575 | − | 1.40294i | 0.103670 | − | 0.143187i | ||||
\(97\) | −3.50333 | −0.355709 | −0.177854 | − | 0.984057i | \(-0.556916\pi\) | ||||
−0.177854 | + | 0.984057i | \(0.556916\pi\) | |||||||
\(98\) | −3.97723 | + | 5.76035i | −0.401760 | + | 0.581884i | ||||
\(99\) | 0.477226 | + | 0.426844i | 0.0479630 | + | 0.0428994i | ||||
\(100\) | −3.74264 | + | 3.31552i | −0.374264 | + | 0.331552i | ||||
\(101\) | −5.65685 | + | 9.79796i | −0.562878 | + | 0.974933i | 0.434366 | + | 0.900737i | \(0.356973\pi\) |
−0.997244 | + | 0.0741967i | \(0.976361\pi\) | |||||||
\(102\) | 0.563508 | − | 5.44816i | 0.0557956 | − | 0.539448i | ||||
\(103\) | −5.28720 | − | 9.15769i | −0.520963 | − | 0.902334i | −0.999703 | − | 0.0243776i | \(-0.992240\pi\) |
0.478740 | − | 0.877957i | \(-0.341094\pi\) | |||||||
\(104\) | 6.70141 | 0.657127 | ||||||||
\(105\) | 7.54858 | − | 6.92957i | 0.736666 | − | 0.676256i | ||||
\(106\) | 5.00000 | 0.485643 | ||||||||
\(107\) | −2.73861 | − | 4.74342i | −0.264752 | − | 0.458563i | 0.702747 | − | 0.711440i | \(-0.251957\pi\) |
−0.967499 | + | 0.252877i | \(0.918623\pi\) | |||||||
\(108\) | 3.84418 | − | 3.49604i | 0.369906 | − | 0.336406i | ||||
\(109\) | −6.21584 | + | 10.7661i | −0.595369 | + | 1.03121i | 0.398125 | + | 0.917331i | \(0.369661\pi\) |
−0.993495 | + | 0.113879i | \(0.963672\pi\) | |||||||
\(110\) | 0.0765585 | − | 0.471045i | 0.00729957 | − | 0.0449123i | ||||
\(111\) | 11.2815 | − | 5.04524i | 1.07079 | − | 0.478873i | ||||
\(112\) | 2.64360 | + | 0.106711i | 0.249797 | + | 0.0100832i | ||||
\(113\) | 6.52277 | 0.613611 | 0.306806 | − | 0.951772i | \(-0.400740\pi\) | ||||
0.306806 | + | 0.951772i | \(0.400740\pi\) | |||||||
\(114\) | 6.86646 | + | 4.97143i | 0.643103 | + | 0.465617i | ||||
\(115\) | 5.13575 | + | 13.5424i | 0.478911 | + | 1.26283i | ||||
\(116\) | −1.75166 | − | 1.01132i | −0.162638 | − | 0.0938990i | ||||
\(117\) | 19.6786 | + | 4.11478i | 1.81929 | + | 0.380411i | ||||
\(118\) | 4.91754 | 0.452696 | ||||||||
\(119\) | 7.40852 | − | 3.88766i | 0.679138 | − | 0.356381i | ||||
\(120\) | −3.73861 | − | 1.01132i | −0.341287 | − | 0.0923207i | ||||
\(121\) | −5.47723 | − | 9.48683i | −0.497930 | − | 0.862439i | ||||
\(122\) | −3.00000 | − | 1.73205i | −0.271607 | − | 0.156813i | ||||
\(123\) | 11.5456 | + | 1.19417i | 1.04103 | + | 0.107675i | ||||
\(124\) | 0.261387 | − | 0.150912i | 0.0234733 | − | 0.0135523i | ||||
\(125\) | 9.89949 | + | 5.19615i | 0.885438 | + | 0.464758i | ||||
\(126\) | 7.69738 | + | 1.93657i | 0.685737 | + | 0.172523i | ||||
\(127\) | − | 13.6298i | − | 1.20945i | −0.796434 | − | 0.604726i | \(-0.793283\pi\) | ||
0.796434 | − | 0.604726i | \(-0.206717\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0.360429 | − | 3.48474i | 0.0317340 | − | 0.306814i | ||||
\(130\) | −5.31350 | − | 14.0111i | −0.466025 | − | 1.22886i | ||||
\(131\) | 3.01326 | + | 5.21911i | 0.263269 | + | 0.455996i | 0.967109 | − | 0.254363i | \(-0.0818659\pi\) |
−0.703839 | + | 0.710359i | \(0.748533\pi\) | |||||||
\(132\) | 0.337449 | − | 0.150912i | 0.0293712 | − | 0.0131352i | ||||
\(133\) | −0.522278 | + | 12.9386i | −0.0452873 | + | 1.12192i | ||||
\(134\) | 5.32582i | 0.460081i | ||||||||
\(135\) | −10.3574 | − | 5.26531i | −0.891426 | − | 0.453166i | ||||
\(136\) | −2.73861 | − | 1.58114i | −0.234834 | − | 0.135582i | ||||
\(137\) | −3.73861 | + | 6.47547i | −0.319411 | + | 0.553237i | −0.980365 | − | 0.197190i | \(-0.936818\pi\) |
0.660954 | + | 0.750426i | \(0.270152\pi\) | |||||||
\(138\) | −6.57926 | + | 9.08717i | −0.560064 | + | 0.773551i | ||||
\(139\) | 7.53185i | 0.638843i | 0.947613 | + | 0.319422i | \(0.103489\pi\) | ||||
−0.947613 | + | 0.319422i | \(0.896511\pi\) | |||||||
\(140\) | −1.87298 | − | 5.61177i | −0.158296 | − | 0.474281i | ||||
\(141\) | −12.2614 | + | 5.48346i | −1.03260 | + | 0.461791i | ||||
\(142\) | −1.75166 | + | 1.01132i | −0.146996 | + | 0.0848683i | ||||
\(143\) | 1.23861 | + | 0.715113i | 0.103578 | + | 0.0598008i | ||||
\(144\) | −0.936492 | − | 2.85008i | −0.0780410 | − | 0.237507i | ||||
\(145\) | −0.725563 | + | 4.46420i | −0.0602547 | + | 0.370731i | ||||
\(146\) | −11.9886 | −0.992184 | ||||||||
\(147\) | 4.04156 | + | 11.4309i | 0.333342 | + | 0.942806i | ||||
\(148\) | − | 7.13505i | − | 0.586497i | ||||||
\(149\) | 2.12132 | − | 1.22474i | 0.173785 | − | 0.100335i | −0.410584 | − | 0.911823i | \(-0.634675\pi\) |
0.584370 | + | 0.811488i | \(0.301342\pi\) | |||||||
\(150\) | 0.849876 | + | 8.61845i | 0.0693921 | + | 0.703694i | ||||
\(151\) | 1.00000 | − | 1.73205i | 0.0813788 | − | 0.140952i | −0.822464 | − | 0.568818i | \(-0.807401\pi\) |
0.903842 | + | 0.427865i | \(0.140734\pi\) | |||||||
\(152\) | 4.23861 | − | 2.44716i | 0.343797 | − | 0.198491i | ||||
\(153\) | −7.07107 | − | 6.32456i | −0.571662 | − | 0.511310i | ||||
\(154\) | 0.477226 | + | 0.301824i | 0.0384559 | + | 0.0243217i | ||||
\(155\) | −0.522774 | − | 0.426844i | −0.0419903 | − | 0.0342849i | ||||
\(156\) | 6.80698 | − | 9.40169i | 0.544994 | − | 0.752738i | ||||
\(157\) | 4.39526 | − | 7.61282i | 0.350780 | − | 0.607569i | −0.635606 | − | 0.772013i | \(-0.719250\pi\) |
0.986386 | + | 0.164445i | \(0.0525831\pi\) | |||||||
\(158\) | −0.261387 | + | 0.452736i | −0.0207949 | + | 0.0360177i | ||||
\(159\) | 5.07877 | − | 7.01471i | 0.402772 | − | 0.556303i | ||||
\(160\) | −1.41421 | + | 1.73205i | −0.111803 | + | 0.136931i | ||||
\(161\) | −17.1232 | − | 0.691190i | −1.34950 | − | 0.0544734i | ||||
\(162\) | −1.00000 | − | 8.94427i | −0.0785674 | − | 0.702728i | ||||
\(163\) | −12.7279 | + | 7.34847i | −0.996928 | + | 0.575577i | −0.907338 | − | 0.420402i | \(-0.861889\pi\) |
−0.0895899 | + | 0.995979i | \(0.528556\pi\) | |||||||
\(164\) | 3.35071 | − | 5.80359i | 0.261646 | − | 0.453184i | ||||
\(165\) | −0.583084 | − | 0.585872i | −0.0453930 | − | 0.0456101i | ||||
\(166\) | −14.4772 | + | 8.35843i | −1.12365 | + | 0.648740i | ||||
\(167\) | 14.6830i | 1.13620i | 0.822958 | + | 0.568102i | \(0.192322\pi\) | ||||
−0.822958 | + | 0.568102i | \(0.807678\pi\) | |||||||
\(168\) | 2.83495 | − | 3.60042i | 0.218721 | − | 0.277779i | ||||
\(169\) | 31.9089 | 2.45453 | ||||||||
\(170\) | −1.13437 | + | 6.97948i | −0.0870023 | + | 0.535302i | ||||
\(171\) | 13.9493 | − | 4.58350i | 1.06673 | − | 0.350509i | ||||
\(172\) | −1.75166 | − | 1.01132i | −0.133563 | − | 0.0771127i | ||||
\(173\) | −9.97723 | + | 5.76035i | −0.758554 | + | 0.437952i | −0.828776 | − | 0.559580i | \(-0.810963\pi\) |
0.0702221 | + | 0.997531i | \(0.477629\pi\) | |||||||
\(174\) | −3.19808 | + | 1.43023i | −0.242446 | + | 0.108425i | ||||
\(175\) | −10.2478 | + | 8.36551i | −0.774664 | + | 0.632373i | ||||
\(176\) | − | 0.213422i | − | 0.0160873i | ||||||
\(177\) | 4.99501 | − | 6.89902i | 0.375448 | − | 0.518562i | ||||
\(178\) | −5.28720 | + | 9.15769i | −0.396292 | + | 0.686398i | ||||
\(179\) | −12.9128 | − | 7.45518i | −0.965144 | − | 0.557226i | −0.0673918 | − | 0.997727i | \(-0.521468\pi\) |
−0.897752 | + | 0.440500i | \(0.854801\pi\) | |||||||
\(180\) | −5.21633 | + | 4.21780i | −0.388803 | + | 0.314376i | ||||
\(181\) | − | 3.16228i | − | 0.235050i | −0.993070 | − | 0.117525i | \(-0.962504\pi\) | ||
0.993070 | − | 0.117525i | \(-0.0374961\pi\) | |||||||
\(182\) | 17.7158 | + | 0.715113i | 1.31319 | + | 0.0530077i | ||||
\(183\) | −5.47723 | + | 2.44949i | −0.404888 | + | 0.181071i | ||||
\(184\) | 3.23861 | + | 5.60944i | 0.238754 | + | 0.413534i | ||||
\(185\) | −14.9177 | + | 5.65733i | −1.09677 | + | 0.415935i | ||||
\(186\) | 0.0537841 | − | 0.520000i | 0.00394364 | − | 0.0381283i | ||||
\(187\) | −0.337449 | − | 0.584480i | −0.0246767 | − | 0.0427414i | ||||
\(188\) | 7.75478i | 0.565576i | ||||||||
\(189\) | 10.5355 | − | 8.83190i | 0.766347 | − | 0.642426i | ||||
\(190\) | −8.47723 | − | 6.92163i | −0.615003 | − | 0.502148i | ||||
\(191\) | −1.38201 | + | 0.797901i | −0.0999984 | + | 0.0577341i | −0.549165 | − | 0.835714i | \(-0.685054\pi\) |
0.449167 | + | 0.893448i | \(0.351721\pi\) | |||||||
\(192\) | −1.72286 | − | 0.178197i | −0.124337 | − | 0.0128603i | ||||
\(193\) | −6.36396 | − | 3.67423i | −0.458088 | − | 0.264477i | 0.253152 | − | 0.967427i | \(-0.418533\pi\) |
−0.711240 | + | 0.702949i | \(0.751866\pi\) | |||||||
\(194\) | 1.75166 | + | 3.03397i | 0.125762 | + | 0.217826i | ||||
\(195\) | −25.0540 | − | 6.77729i | −1.79415 | − | 0.485332i | ||||
\(196\) | 6.97723 | + | 0.564201i | 0.498373 | + | 0.0403001i | ||||
\(197\) | 9.00000 | 0.641223 | 0.320612 | − | 0.947211i | \(-0.396112\pi\) | ||||
0.320612 | + | 0.947211i | \(0.396112\pi\) | |||||||
\(198\) | 0.131045 | − | 0.626711i | 0.00931293 | − | 0.0445384i | ||||
\(199\) | −19.4317 | − | 11.2189i | −1.37748 | − | 0.795286i | −0.385620 | − | 0.922658i | \(-0.626012\pi\) |
−0.991855 | + | 0.127372i | \(0.959346\pi\) | |||||||
\(200\) | 4.74264 | + | 1.58346i | 0.335355 | + | 0.111968i | ||||
\(201\) | 7.47182 | + | 5.40972i | 0.527022 | + | 0.381572i | ||||
\(202\) | 11.3137 | 0.796030 | ||||||||
\(203\) | −4.52277 | − | 2.86045i | −0.317437 | − | 0.200764i | ||||
\(204\) | −5.00000 | + | 2.23607i | −0.350070 | + | 0.156556i | ||||
\(205\) | −14.7907 | − | 2.40393i | −1.03303 | − | 0.167898i | ||||
\(206\) | −5.28720 | + | 9.15769i | −0.368376 | + | 0.638047i | ||||
\(207\) | 6.06587 | + | 18.4606i | 0.421607 | + | 1.28310i | ||||
\(208\) | −3.35071 | − | 5.80359i | −0.232330 | − | 0.402407i | ||||
\(209\) | 1.04456 | 0.0722535 | ||||||||
\(210\) | −9.77547 | − | 3.07248i | −0.674572 | − | 0.212021i | ||||
\(211\) | 13.5228 | 0.930946 | 0.465473 | − | 0.885062i | \(-0.345884\pi\) | ||||
0.465473 | + | 0.885062i | \(0.345884\pi\) | |||||||
\(212\) | −2.50000 | − | 4.33013i | −0.171701 | − | 0.297394i | ||||
\(213\) | −0.360429 | + | 3.48474i | −0.0246962 | + | 0.238770i | ||||
\(214\) | −2.73861 | + | 4.74342i | −0.187208 | + | 0.324253i | ||||
\(215\) | −0.725563 | + | 4.46420i | −0.0494830 | + | 0.304456i | ||||
\(216\) | −4.94975 | − | 1.58114i | −0.336788 | − | 0.107583i | ||||
\(217\) | 0.707107 | − | 0.371058i | 0.0480015 | − | 0.0251890i | ||||
\(218\) | 12.4317 | 0.841979 | ||||||||
\(219\) | −12.1775 | + | 16.8193i | −0.822877 | + | 1.13654i | ||||
\(220\) | −0.446216 | + | 0.169221i | −0.0300839 | + | 0.0114089i | ||||
\(221\) | −18.3526 | − | 10.5959i | −1.23453 | − | 0.712755i | ||||
\(222\) | −10.0101 | − | 7.24745i | −0.671831 | − | 0.486417i | ||||
\(223\) | 6.39617 | 0.428319 | 0.214160 | − | 0.976799i | \(-0.431299\pi\) | ||||
0.214160 | + | 0.976799i | \(0.431299\pi\) | |||||||
\(224\) | −1.22938 | − | 2.34278i | −0.0821417 | − | 0.156533i | ||||
\(225\) | 12.9545 | + | 7.56189i | 0.863630 | + | 0.504126i | ||||
\(226\) | −3.26139 | − | 5.64889i | −0.216944 | − | 0.375758i | ||||
\(227\) | 9.00000 | + | 5.19615i | 0.597351 | + | 0.344881i | 0.767999 | − | 0.640451i | \(-0.221253\pi\) |
−0.170648 | + | 0.985332i | \(0.554586\pi\) | |||||||
\(228\) | 0.872155 | − | 8.43224i | 0.0577598 | − | 0.558439i | ||||
\(229\) | −6.26139 | + | 3.61501i | −0.413764 | + | 0.238887i | −0.692406 | − | 0.721508i | \(-0.743449\pi\) |
0.278642 | + | 0.960395i | \(0.410116\pi\) | |||||||
\(230\) | 9.16018 | − | 11.2189i | 0.604004 | − | 0.739751i | ||||
\(231\) | 0.908185 | − | 0.362941i | 0.0597542 | − | 0.0238798i | ||||
\(232\) | 2.02265i | 0.132793i | ||||||||
\(233\) | 2.00000 | + | 3.46410i | 0.131024 | + | 0.226941i | 0.924072 | − | 0.382219i | \(-0.124840\pi\) |
−0.793047 | + | 0.609160i | \(0.791507\pi\) | |||||||
\(234\) | −6.27582 | − | 19.0996i | −0.410263 | − | 1.24858i | ||||
\(235\) | 16.2135 | − | 6.14871i | 1.05765 | − | 0.401098i | ||||
\(236\) | −2.45877 | − | 4.25871i | −0.160052 | − | 0.277219i | ||||
\(237\) | 0.369657 | + | 0.826579i | 0.0240118 | + | 0.0536921i | ||||
\(238\) | −7.07107 | − | 4.47214i | −0.458349 | − | 0.289886i | ||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0.993475 | + | 3.74340i | 0.0641285 | + | 0.241635i | ||||
\(241\) | 3.45445 | + | 1.99443i | 0.222521 | + | 0.128472i | 0.607117 | − | 0.794613i | \(-0.292326\pi\) |
−0.384596 | + | 0.923085i | \(0.625659\pi\) | |||||||
\(242\) | −5.47723 | + | 9.48683i | −0.352089 | + | 0.609837i | ||||
\(243\) | −13.5640 | − | 7.68223i | −0.870134 | − | 0.492815i | ||||
\(244\) | 3.46410i | 0.221766i | ||||||||
\(245\) | −4.35258 | − | 15.0351i | −0.278076 | − | 0.960559i | ||||
\(246\) | −4.73861 | − | 10.5959i | −0.302123 | − | 0.675567i | ||||
\(247\) | 28.4047 | − | 16.3995i | 1.80735 | − | 1.04347i | ||||
\(248\) | −0.261387 | − | 0.150912i | −0.0165981 | − | 0.00958292i | ||||
\(249\) | −2.97889 | + | 28.8008i | −0.188780 | + | 1.82518i | ||||
\(250\) | −0.449747 | − | 11.1713i | −0.0284445 | − | 0.706534i | ||||
\(251\) | 16.6009 | 1.04784 | 0.523920 | − | 0.851768i | \(-0.324469\pi\) | ||||
0.523920 | + | 0.851768i | \(0.324469\pi\) | |||||||
\(252\) | −2.17157 | − | 7.63441i | −0.136796 | − | 0.480923i | ||||
\(253\) | 1.38238i | 0.0869095i | ||||||||
\(254\) | −11.8038 | + | 6.81491i | −0.740635 | + | 0.427606i | ||||
\(255\) | 8.63957 | + | 8.68089i | 0.541031 | + | 0.543618i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −20.4772 | + | 11.8225i | −1.27733 | + | 0.737469i | −0.976357 | − | 0.216162i | \(-0.930646\pi\) |
−0.300977 | + | 0.953631i | \(0.597313\pi\) | |||||||
\(258\) | −3.19808 | + | 1.43023i | −0.199104 | + | 0.0890420i | ||||
\(259\) | 0.761387 | − | 18.8622i | 0.0473103 | − | 1.17204i | ||||
\(260\) | −9.47723 | + | 11.6072i | −0.587753 | + | 0.719847i | ||||
\(261\) | −1.24194 | + | 5.93948i | −0.0768741 | + | 0.367645i | ||||
\(262\) | 3.01326 | − | 5.21911i | 0.186160 | − | 0.322438i | ||||
\(263\) | 1.00000 | − | 1.73205i | 0.0616626 | − | 0.106803i | −0.833546 | − | 0.552450i | \(-0.813693\pi\) |
0.895209 | + | 0.445647i | \(0.147026\pi\) | |||||||
\(264\) | −0.299418 | − | 0.216784i | −0.0184279 | − | 0.0133421i | ||||
\(265\) | −7.07107 | + | 8.66025i | −0.434372 | + | 0.531995i | ||||
\(266\) | 11.4663 | − | 6.01701i | 0.703046 | − | 0.368927i | ||||
\(267\) | 7.47723 | + | 16.7196i | 0.457599 | + | 1.02322i | ||||
\(268\) | 4.61230 | − | 2.66291i | 0.281741 | − | 0.162663i | ||||
\(269\) | 14.4474 | − | 25.0236i | 0.880872 | − | 1.52572i | 0.0304992 | − | 0.999535i | \(-0.490290\pi\) |
0.850373 | − | 0.526180i | \(-0.176376\pi\) | |||||||
\(270\) | 0.618823 | + | 11.6025i | 0.0376604 | + | 0.706103i | ||||
\(271\) | 5.47723 | − | 3.16228i | 0.332718 | − | 0.192095i | −0.324329 | − | 0.945944i | \(-0.605139\pi\) |
0.657047 | + | 0.753850i | \(0.271805\pi\) | |||||||
\(272\) | 3.16228i | 0.191741i | ||||||||
\(273\) | 18.9982 | − | 24.1279i | 1.14982 | − | 1.46029i | ||||
\(274\) | 7.47723 | 0.451716 | ||||||||
\(275\) | 0.707603 | + | 0.798761i | 0.0426701 | + | 0.0481671i | ||||
\(276\) | 11.1594 | + | 1.15422i | 0.671714 | + | 0.0694760i | ||||
\(277\) | 8.48528 | + | 4.89898i | 0.509831 | + | 0.294351i | 0.732764 | − | 0.680483i | \(-0.238230\pi\) |
−0.222933 | + | 0.974834i | \(0.571563\pi\) | |||||||
\(278\) | 6.52277 | − | 3.76593i | 0.391210 | − | 0.225865i | ||||
\(279\) | −0.674899 | − | 0.603648i | −0.0404051 | − | 0.0361395i | ||||
\(280\) | −3.92344 | + | 4.42793i | −0.234470 | + | 0.264620i | ||||
\(281\) | − | 11.6072i | − | 0.692427i | −0.938156 | − | 0.346213i | \(-0.887467\pi\) | ||
0.938156 | − | 0.346213i | \(-0.112533\pi\) | |||||||
\(282\) | 10.8795 | + | 7.87694i | 0.647865 | + | 0.469065i | ||||
\(283\) | −12.3583 | + | 21.4051i | −0.734623 | + | 1.27240i | 0.220266 | + | 0.975440i | \(0.429307\pi\) |
−0.954889 | + | 0.296964i | \(0.904026\pi\) | |||||||
\(284\) | 1.75166 | + | 1.01132i | 0.103942 | + | 0.0600110i | ||||
\(285\) | −18.3214 | + | 4.86239i | −1.08527 | + | 0.288023i | ||||
\(286\) | − | 1.43023i | − | 0.0845711i | ||||||
\(287\) | 9.47723 | − | 14.9848i | 0.559423 | − | 0.884525i | ||||
\(288\) | −2.00000 | + | 2.23607i | −0.117851 | + | 0.131762i | ||||
\(289\) | −3.50000 | − | 6.06218i | −0.205882 | − | 0.356599i | ||||
\(290\) | 4.22889 | − | 1.60374i | 0.248329 | − | 0.0941750i | ||||
\(291\) | 6.03574 | + | 0.624282i | 0.353821 | + | 0.0365961i | ||||
\(292\) | 5.99430 | + | 10.3824i | 0.350790 | + | 0.607586i | ||||
\(293\) | − | 4.59250i | − | 0.268297i | −0.990961 | − | 0.134148i | \(-0.957170\pi\) | ||
0.990961 | − | 0.134148i | \(-0.0428299\pi\) | |||||||
\(294\) | 7.87868 | − | 9.21555i | 0.459494 | − | 0.537462i | ||||
\(295\) | −6.95445 | + | 8.51743i | −0.404904 | + | 0.495904i | ||||
\(296\) | −6.17913 | + | 3.56752i | −0.359155 | + | 0.207358i | ||||
\(297\) | −0.746131 | − | 0.820432i | −0.0432949 | − | 0.0476063i | ||||
\(298\) | −2.12132 | − | 1.22474i | −0.122885 | − | 0.0709476i | ||||
\(299\) | 21.7033 | + | 37.5912i | 1.25513 | + | 2.17395i | ||||
\(300\) | 7.03886 | − | 5.04524i | 0.406389 | − | 0.291287i | ||||
\(301\) | −4.52277 | − | 2.86045i | −0.260688 | − | 0.164874i | ||||
\(302\) | −2.00000 | −0.115087 | ||||||||
\(303\) | 11.4919 | − | 15.8725i | 0.660194 | − | 0.911850i | ||||
\(304\) | −4.23861 | − | 2.44716i | −0.243101 | − | 0.140354i | ||||
\(305\) | 7.24264 | − | 2.74666i | 0.414712 | − | 0.157273i | ||||
\(306\) | −1.94169 | + | 9.28600i | −0.110999 | + | 0.530845i | ||||
\(307\) | 3.50333 | 0.199945 | 0.0999727 | − | 0.994990i | \(-0.468124\pi\) | ||||
0.0999727 | + | 0.994990i | \(0.468124\pi\) | |||||||
\(308\) | 0.0227744 | − | 0.564201i | 0.00129769 | − | 0.0321484i | ||||
\(309\) | 7.47723 | + | 16.7196i | 0.425365 | + | 0.951144i | ||||
\(310\) | −0.108270 | + | 0.666158i | −0.00614933 | + | 0.0378352i | ||||
\(311\) | 14.4474 | − | 25.0236i | 0.819236 | − | 1.41896i | −0.0870106 | − | 0.996207i | \(-0.527731\pi\) |
0.906246 | − | 0.422750i | \(-0.138935\pi\) | |||||||
\(312\) | −11.5456 | − | 1.19417i | −0.653640 | − | 0.0676066i | ||||
\(313\) | 11.6190 | + | 20.1246i | 0.656742 | + | 1.13751i | 0.981454 | + | 0.191697i | \(0.0613992\pi\) |
−0.324712 | + | 0.945813i | \(0.605267\pi\) | |||||||
\(314\) | −8.79052 | −0.496078 | ||||||||
\(315\) | −14.2400 | + | 10.5935i | −0.802332 | + | 0.596878i | ||||
\(316\) | 0.522774 | 0.0294084 | ||||||||
\(317\) | −16.9545 | − | 29.3660i | −0.952257 | − | 1.64936i | −0.740524 | − | 0.672030i | \(-0.765423\pi\) |
−0.211733 | − | 0.977328i | \(-0.567911\pi\) | |||||||
\(318\) | −8.61430 | − | 0.890985i | −0.483066 | − | 0.0499640i | ||||
\(319\) | −0.215838 | + | 0.373843i | −0.0120846 | + | 0.0209312i | ||||
\(320\) | 2.20711 | + | 0.358719i | 0.123381 | + | 0.0200530i | ||||
\(321\) | 3.87298 | + | 8.66025i | 0.216169 | + | 0.483368i | ||||
\(322\) | 7.96300 | + | 15.1747i | 0.443761 | + | 0.845653i | ||||
\(323\) | −15.4772 | −0.861176 | ||||||||
\(324\) | −7.24597 | + | 5.33816i | −0.402554 | + | 0.296565i | ||||
\(325\) | 31.7824 | + | 10.6114i | 1.76297 | + | 0.588617i | ||||
\(326\) | 12.7279 | + | 7.34847i | 0.704934 | + | 0.406994i | ||||
\(327\) | 12.6275 | − | 17.4409i | 0.698303 | − | 0.964485i | ||||
\(328\) | −6.70141 | −0.370023 | ||||||||
\(329\) | −0.827520 | + | 20.5005i | −0.0456226 | + | 1.13023i | ||||
\(330\) | −0.215838 | + | 0.797901i | −0.0118815 | + | 0.0439230i | ||||
\(331\) | 5.71584 | + | 9.90012i | 0.314171 | + | 0.544160i | 0.979261 | − | 0.202603i | \(-0.0649402\pi\) |
−0.665090 | + | 0.746763i | \(0.731607\pi\) | |||||||
\(332\) | 14.4772 | + | 8.35843i | 0.794541 | + | 0.458728i | ||||
\(333\) | −20.3355 | + | 6.68191i | −1.11438 | + | 0.366167i | ||||
\(334\) | 12.7158 | − | 7.34149i | 0.695780 | − | 0.401709i | ||||
\(335\) | −9.22460 | − | 7.53185i | −0.503994 | − | 0.411509i | ||||
\(336\) | −4.53553 | − | 0.654929i | −0.247434 | − | 0.0357293i | ||||
\(337\) | − | 17.1464i | − | 0.934025i | −0.884251 | − | 0.467013i | \(-0.845330\pi\) | ||
0.884251 | − | 0.467013i | \(-0.154670\pi\) | |||||||
\(338\) | −15.9545 | − | 27.6339i | −0.867808 | − | 1.50309i | ||||
\(339\) | −11.2378 | − | 1.16234i | −0.610355 | − | 0.0631296i | ||||
\(340\) | 6.61160 | − | 2.50735i | 0.358564 | − | 0.135980i | ||||
\(341\) | −0.0322079 | − | 0.0557857i | −0.00174416 | − | 0.00302097i | ||||
\(342\) | −10.9441 | − | 9.78866i | −0.591787 | − | 0.529310i | ||||
\(343\) | 18.3848 | + | 2.23607i | 0.992685 | + | 0.120736i | ||||
\(344\) | 2.02265i | 0.109054i | ||||||||
\(345\) | −6.43496 | − | 24.2468i | −0.346447 | − | 1.30540i | ||||
\(346\) | 9.97723 | + | 5.76035i | 0.536379 | + | 0.309679i | ||||
\(347\) | 3.26139 | − | 5.64889i | 0.175080 | − | 0.303248i | −0.765109 | − | 0.643901i | \(-0.777315\pi\) |
0.940189 | + | 0.340653i | \(0.110648\pi\) | |||||||
\(348\) | 2.83766 | + | 2.05451i | 0.152114 | + | 0.110133i | ||||
\(349\) | 32.5282i | 1.74120i | 0.491994 | + | 0.870599i | \(0.336268\pi\) | ||||
−0.491994 | + | 0.870599i | \(0.663732\pi\) | |||||||
\(350\) | 12.3687 | + | 4.69214i | 0.661133 | + | 0.250805i | ||||
\(351\) | −33.1703 | − | 10.5959i | −1.77050 | − | 0.565565i | ||||
\(352\) | −0.184829 | + | 0.106711i | −0.00985140 | + | 0.00568771i | ||||
\(353\) | 11.4772 | + | 6.62638i | 0.610871 | + | 0.352687i | 0.773306 | − | 0.634033i | \(-0.218602\pi\) |
−0.162435 | + | 0.986719i | \(0.551935\pi\) | |||||||
\(354\) | −8.47223 | − | 0.876291i | −0.450294 | − | 0.0465743i | ||||
\(355\) | 0.725563 | − | 4.46420i | 0.0385089 | − | 0.236935i | ||||
\(356\) | 10.5744 | 0.560442 | ||||||||
\(357\) | −13.4566 | + | 5.37771i | −0.712199 | + | 0.284619i | ||||
\(358\) | 14.9104i | 0.788037i | ||||||||
\(359\) | 5.62465 | − | 3.24739i | 0.296857 | − | 0.171391i | −0.344173 | − | 0.938906i | \(-0.611841\pi\) |
0.641030 | + | 0.767516i | \(0.278507\pi\) | |||||||
\(360\) | 6.26089 | + | 2.40858i | 0.329978 | + | 0.126943i | ||||
\(361\) | 2.47723 | − | 4.29068i | 0.130380 | − | 0.225825i | ||||
\(362\) | −2.73861 | + | 1.58114i | −0.143938 | + | 0.0831028i | ||||
\(363\) | 7.74597 | + | 17.3205i | 0.406558 | + | 0.909091i | ||||
\(364\) | −8.23861 | − | 15.6999i | −0.431821 | − | 0.822900i | ||||
\(365\) | 16.9545 | − | 20.7649i | 0.887437 | − | 1.08688i | ||||
\(366\) | 4.85993 | + | 3.51867i | 0.254033 | + | 0.183924i | ||||
\(367\) | −4.05781 | + | 7.02834i | −0.211816 | + | 0.366876i | −0.952283 | − | 0.305217i | \(-0.901271\pi\) |
0.740467 | + | 0.672093i | \(0.234604\pi\) | |||||||
\(368\) | 3.23861 | − | 5.60944i | 0.168824 | − | 0.292412i | ||||
\(369\) | −19.6786 | − | 4.11478i | −1.02443 | − | 0.214207i | ||||
\(370\) | 12.3583 | + | 10.0905i | 0.642476 | + | 0.524579i | ||||
\(371\) | −6.14692 | − | 11.7139i | −0.319132 | − | 0.608155i | ||||
\(372\) | −0.477226 | + | 0.213422i | −0.0247430 | + | 0.0110654i | ||||
\(373\) | −3.13367 | + | 1.80922i | −0.162255 | + | 0.0936781i | −0.578929 | − | 0.815378i | \(-0.696529\pi\) |
0.416674 | + | 0.909056i | \(0.363196\pi\) | |||||||
\(374\) | −0.337449 | + | 0.584480i | −0.0174491 | + | 0.0302227i | ||||
\(375\) | −16.1295 | − | 10.7163i | −0.832924 | − | 0.553387i | ||||
\(376\) | 6.71584 | − | 3.87739i | 0.346343 | − | 0.199961i | ||||
\(377\) | 13.5546i | 0.698097i | ||||||||
\(378\) | −12.9164 | − | 4.70809i | −0.664349 | − | 0.242158i | ||||
\(379\) | −9.52277 | −0.489152 | −0.244576 | − | 0.969630i | \(-0.578649\pi\) | ||||
−0.244576 | + | 0.969630i | \(0.578649\pi\) | |||||||
\(380\) | −1.75569 | + | 10.8023i | −0.0900650 | + | 0.554147i | ||||
\(381\) | −2.42879 | + | 23.4823i | −0.124431 | + | 1.20303i | ||||
\(382\) | 1.38201 | + | 0.797901i | 0.0707096 | + | 0.0408242i | ||||
\(383\) | −0.715838 | + | 0.413289i | −0.0365776 | + | 0.0211181i | −0.518177 | − | 0.855273i | \(-0.673389\pi\) |
0.481600 | + | 0.876391i | \(0.340056\pi\) | |||||||
\(384\) | 0.707107 | + | 1.58114i | 0.0360844 | + | 0.0806872i | ||||
\(385\) | −1.19767 | + | 0.399735i | −0.0610391 | + | 0.0203724i | ||||
\(386\) | 7.34847i | 0.374027i | ||||||||
\(387\) | −1.24194 | + | 5.93948i | −0.0631313 | + | 0.301921i | ||||
\(388\) | 1.75166 | − | 3.03397i | 0.0889272 | − | 0.154026i | ||||
\(389\) | −6.36396 | − | 3.67423i | −0.322666 | − | 0.186291i | 0.329914 | − | 0.944011i | \(-0.392980\pi\) |
−0.652580 | + | 0.757720i | \(0.726313\pi\) | |||||||
\(390\) | 6.65768 | + | 25.0860i | 0.337125 | + | 1.27028i | ||||
\(391\) | − | 20.4828i | − | 1.03586i | ||||||
\(392\) | −3.00000 | − | 6.32456i | −0.151523 | − | 0.319438i | ||||
\(393\) | −4.26139 | − | 9.52875i | −0.214959 | − | 0.480662i | ||||
\(394\) | −4.50000 | − | 7.79423i | −0.226707 | − | 0.392668i | ||||
\(395\) | −0.414504 | − | 1.09300i | −0.0208560 | − | 0.0549949i | ||||
\(396\) | −0.608270 | + | 0.199868i | −0.0305667 | + | 0.0100437i | ||||
\(397\) | −15.1867 | − | 26.3041i | −0.762198 | − | 1.32017i | −0.941715 | − | 0.336411i | \(-0.890787\pi\) |
0.179517 | − | 0.983755i | \(-0.442547\pi\) | |||||||
\(398\) | 22.4378i | 1.12470i | ||||||||
\(399\) | 3.20544 | − | 22.1984i | 0.160473 | − | 1.11131i | ||||
\(400\) | −1.00000 | − | 4.89898i | −0.0500000 | − | 0.244949i | ||||
\(401\) | −26.2834 | + | 15.1747i | −1.31253 | + | 0.757789i | −0.982514 | − | 0.186187i | \(-0.940387\pi\) |
−0.330014 | + | 0.943976i | \(0.607054\pi\) | |||||||
\(402\) | 0.949046 | − | 9.17565i | 0.0473341 | − | 0.457640i | ||||
\(403\) | −1.75166 | − | 1.01132i | −0.0872565 | − | 0.0503776i | ||||
\(404\) | −5.65685 | − | 9.79796i | −0.281439 | − | 0.487467i | ||||
\(405\) | 16.9061 | + | 10.9171i | 0.840073 | + | 0.542473i | ||||
\(406\) | −0.215838 | + | 5.34706i | −0.0107119 | + | 0.265370i | ||||
\(407\) | −1.52277 | −0.0754811 | ||||||||
\(408\) | 4.43649 | + | 3.21209i | 0.219639 | + | 0.159022i | ||||
\(409\) | −19.4317 | − | 11.2189i | −0.960835 | − | 0.554738i | −0.0644048 | − | 0.997924i | \(-0.520515\pi\) |
−0.896430 | + | 0.443186i | \(0.853848\pi\) | |||||||
\(410\) | 5.31350 | + | 14.0111i | 0.262415 | + | 0.691959i | ||||
\(411\) | 7.59501 | − | 10.4901i | 0.374634 | − | 0.517439i | ||||
\(412\) | 10.5744 | 0.520963 | ||||||||
\(413\) | −6.04555 | − | 11.5207i | −0.297482 | − | 0.566897i | ||||
\(414\) | 12.9545 | − | 14.4835i | 0.636677 | − | 0.711826i | ||||
\(415\) | 5.99666 | − | 36.8959i | 0.294365 | − | 1.81115i | ||||
\(416\) | −3.35071 | + | 5.80359i | −0.164282 | + | 0.284544i | ||||
\(417\) | 1.34215 | − | 12.9763i | 0.0657255 | − | 0.635453i | ||||
\(418\) | −0.522278 | − | 0.904612i | −0.0255455 | − | 0.0442460i | ||||
\(419\) | −16.6009 | −0.811007 | −0.405504 | − | 0.914093i | \(-0.632904\pi\) | ||||
−0.405504 | + | 0.914093i | \(0.632904\pi\) | |||||||
\(420\) | 2.22689 | + | 10.0020i | 0.108661 | + | 0.488050i | ||||
\(421\) | −2.95445 | −0.143991 | −0.0719956 | − | 0.997405i | \(-0.522937\pi\) | ||||
−0.0719956 | + | 0.997405i | \(0.522937\pi\) | |||||||
\(422\) | −6.76139 | − | 11.7111i | −0.329139 | − | 0.570086i | ||||
\(423\) | 22.1018 | − | 7.26229i | 1.07463 | − | 0.353105i | ||||
\(424\) | −2.50000 | + | 4.33013i | −0.121411 | + | 0.210290i | ||||
\(425\) | −10.4846 | − | 11.8353i | −0.508577 | − | 0.574095i | ||||
\(426\) | 3.19808 | − | 1.43023i | 0.154948 | − | 0.0692947i | ||||
\(427\) | −0.369657 | + | 9.15769i | −0.0178890 | + | 0.443172i | ||||
\(428\) | 5.47723 | 0.264752 | ||||||||
\(429\) | −2.00653 | − | 1.45276i | −0.0968759 | − | 0.0701398i | ||||
\(430\) | 4.22889 | − | 1.60374i | 0.203935 | − | 0.0773393i | ||||
\(431\) | 32.0928 | + | 18.5288i | 1.54586 | + | 0.892501i | 0.998451 | + | 0.0556344i | \(0.0177181\pi\) |
0.547406 | + | 0.836867i | \(0.315615\pi\) | |||||||
\(432\) | 1.10557 | + | 5.07718i | 0.0531916 | + | 0.244276i | ||||
\(433\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(434\) | −0.674899 | − | 0.426844i | −0.0323962 | − | 0.0204891i | ||||
\(435\) | 2.04555 | − | 7.56189i | 0.0980766 | − | 0.362565i | ||||
\(436\) | −6.21584 | − | 10.7661i | −0.297685 | − | 0.515605i | ||||
\(437\) | 27.4545 | + | 15.8508i | 1.31332 | + | 0.758248i | ||||
\(438\) | 20.6547 | + | 2.13633i | 0.986919 | + | 0.102078i | ||||
\(439\) | 19.6931 | − | 11.3698i | 0.939899 | − | 0.542651i | 0.0499701 | − | 0.998751i | \(-0.484087\pi\) |
0.889929 | + | 0.456100i | \(0.150754\pi\) | |||||||
\(440\) | 0.369657 | + | 0.301824i | 0.0176227 | + | 0.0143889i | ||||
\(441\) | −4.92609 | − | 20.4141i | −0.234576 | − | 0.972098i | ||||
\(442\) | 21.1917i | 1.00799i | ||||||||
\(443\) | 18.4772 | + | 32.0035i | 0.877879 | + | 1.52053i | 0.853663 | + | 0.520825i | \(0.174376\pi\) |
0.0242161 | + | 0.999707i | \(0.492291\pi\) | |||||||
\(444\) | −1.27144 | + | 12.2927i | −0.0603401 | + | 0.583385i | ||||
\(445\) | −8.38437 | − | 22.1086i | −0.397457 | − | 1.04805i | ||||
\(446\) | −3.19808 | − | 5.53924i | −0.151434 | − | 0.262291i | ||||
\(447\) | −3.87298 | + | 1.73205i | −0.183186 | + | 0.0819232i | ||||
\(448\) | −1.41421 | + | 2.23607i | −0.0668153 | + | 0.105644i | ||||
\(449\) | 3.51660i | 0.165959i | 0.996551 | + | 0.0829793i | \(0.0264435\pi\) | ||||
−0.996551 | + | 0.0829793i | \(0.973556\pi\) | |||||||
\(450\) | 0.0715641 | − | 14.9998i | 0.00337357 | − | 0.707099i | ||||
\(451\) | −1.23861 | − | 0.715113i | −0.0583240 | − | 0.0336734i | ||||
\(452\) | −3.26139 | + | 5.64889i | −0.153403 | + | 0.265701i | ||||
\(453\) | −2.03151 | + | 2.80588i | −0.0954485 | + | 0.131832i | ||||
\(454\) | − | 10.3923i | − | 0.487735i | ||||||
\(455\) | −26.2926 | + | 29.6734i | −1.23262 | + | 1.39111i | ||||
\(456\) | −7.73861 | + | 3.46081i | −0.362394 | + | 0.162067i | ||||
\(457\) | −32.8322 | + | 18.9557i | −1.53582 | + | 0.886708i | −0.536747 | + | 0.843743i | \(0.680347\pi\) |
−0.999077 | + | 0.0429646i | \(0.986320\pi\) | |||||||
\(458\) | 6.26139 | + | 3.61501i | 0.292575 | + | 0.168918i | ||||
\(459\) | 11.0554 | + | 12.1564i | 0.516024 | + | 0.567411i | ||||
\(460\) | −14.2959 | − | 2.32351i | −0.666551 | − | 0.108334i | ||||
\(461\) | −16.2957 | −0.758965 | −0.379482 | − | 0.925199i | \(-0.623898\pi\) | ||||
−0.379482 | + | 0.925199i | \(0.623898\pi\) | |||||||
\(462\) | −0.768409 | − | 0.605041i | −0.0357496 | − | 0.0281490i | ||||
\(463\) | − | 17.6751i | − | 0.821433i | −0.911763 | − | 0.410716i | \(-0.865279\pi\) | ||
0.911763 | − | 0.410716i | \(-0.134721\pi\) | |||||||
\(464\) | 1.75166 | − | 1.01132i | 0.0813189 | − | 0.0469495i | ||||
\(465\) | 0.824605 | + | 0.828548i | 0.0382401 | + | 0.0384230i | ||||
\(466\) | 2.00000 | − | 3.46410i | 0.0926482 | − | 0.160471i | ||||
\(467\) | −29.7386 | + | 17.1696i | −1.37614 | + | 0.794514i | −0.991692 | − | 0.128633i | \(-0.958941\pi\) |
−0.384447 | + | 0.923147i | \(0.625608\pi\) | |||||||
\(468\) | −13.4028 | + | 14.9848i | −0.619546 | + | 0.692673i | ||||
\(469\) | 12.4772 | − | 6.54749i | 0.576145 | − | 0.302335i | ||||
\(470\) | −13.4317 | − | 10.9669i | −0.619557 | − | 0.505866i | ||||
\(471\) | −8.92900 | + | 12.3326i | −0.411427 | + | 0.568256i | ||||
\(472\) | −2.45877 | + | 4.25871i | −0.113174 | + | 0.196023i | ||||
\(473\) | −0.215838 | + | 0.373843i | −0.00992426 | + | 0.0171893i | ||||
\(474\) | 0.531010 | − | 0.733422i | 0.0243901 | − | 0.0336872i | ||||
\(475\) | 23.9772 | − | 4.89433i | 1.10015 | − | 0.224567i | ||||
\(476\) | −0.337449 | + | 8.35979i | −0.0154670 | + | 0.383170i | ||||
\(477\) | −10.0000 | + | 11.1803i | −0.457869 | + | 0.511913i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.68906 | − | 9.85374i | 0.259940 | − | 0.450229i | −0.706286 | − | 0.707927i | \(-0.749631\pi\) |
0.966226 | + | 0.257698i | \(0.0829639\pi\) | |||||||
\(480\) | 2.74514 | − | 2.73207i | 0.125298 | − | 0.124701i | ||||
\(481\) | −41.4089 | + | 23.9074i | −1.88808 | + | 1.09009i | ||||
\(482\) | − | 3.98886i | − | 0.181687i | ||||||
\(483\) | 29.3777 | + | 4.24212i | 1.33673 | + | 0.193023i | ||||
\(484\) | 10.9545 | 0.497930 | ||||||||
\(485\) | −7.73221 | − | 1.25671i | −0.351102 | − | 0.0570643i | ||||
\(486\) | 0.129018 | + | 15.5879i | 0.00585235 | + | 0.707083i | ||||
\(487\) | −31.7232 | − | 18.3154i | −1.43751 | − | 0.829949i | −0.439838 | − | 0.898077i | \(-0.644964\pi\) |
−0.997677 | + | 0.0681277i | \(0.978297\pi\) | |||||||
\(488\) | 3.00000 | − | 1.73205i | 0.135804 | − | 0.0784063i | ||||
\(489\) | 23.2379 | − | 10.3923i | 1.05085 | − | 0.469956i | ||||
\(490\) | −10.8445 | + | 11.2870i | −0.489905 | + | 0.509895i | ||||
\(491\) | 4.04529i | 0.182561i | 0.995825 | + | 0.0912807i | \(0.0290961\pi\) | ||||
−0.995825 | + | 0.0912807i | \(0.970904\pi\) | |||||||
\(492\) | −6.80698 | + | 9.40169i | −0.306882 | + | 0.423861i | ||||
\(493\) | 3.19808 | − | 5.53924i | 0.144034 | − | 0.249475i | ||||
\(494\) | −28.4047 | − | 16.3995i | −1.27799 | − | 0.737846i | ||||
\(495\) | 0.900171 | + | 1.11328i | 0.0404597 | + | 0.0500382i | ||||
\(496\) | 0.301824i | 0.0135523i | ||||||||
\(497\) | 4.52277 | + | 2.86045i | 0.202874 | + | 0.128309i | ||||
\(498\) | 26.4317 | − | 11.8206i | 1.18443 | − | 0.529694i | ||||
\(499\) | 20.9545 | + | 36.2942i | 0.938050 | + | 1.62475i | 0.769103 | + | 0.639125i | \(0.220703\pi\) |
0.168947 | + | 0.985625i | \(0.445963\pi\) | |||||||
\(500\) | −9.44975 | + | 5.97514i | −0.422606 | + | 0.267216i | ||||
\(501\) | 2.61646 | − | 25.2967i | 0.116895 | − | 1.13017i | ||||
\(502\) | −8.30045 | − | 14.3768i | −0.370467 | − | 0.641668i | ||||
\(503\) | − | 22.4378i | − | 1.00045i | −0.865895 | − | 0.500225i | \(-0.833251\pi\) | ||
0.865895 | − | 0.500225i | \(-0.166749\pi\) | |||||||
\(504\) | −5.52581 | + | 5.69784i | −0.246139 | + | 0.253802i | ||||
\(505\) | −16.0000 | + | 19.5959i | −0.711991 | + | 0.872007i | ||||
\(506\) | 1.19718 | − | 0.691190i | 0.0532210 | − | 0.0307272i | ||||
\(507\) | −54.9746 | − | 5.68607i | −2.44151 | − | 0.252527i | ||||
\(508\) | 11.8038 | + | 6.81491i | 0.523708 | + | 0.302363i | ||||
\(509\) | 4.61230 | + | 7.98873i | 0.204437 | + | 0.354094i | 0.949953 | − | 0.312393i | \(-0.101130\pi\) |
−0.745517 | + | 0.666487i | \(0.767797\pi\) | |||||||
\(510\) | 3.19808 | − | 11.8225i | 0.141614 | − | 0.523511i | ||||
\(511\) | 14.7386 | + | 28.0867i | 0.651998 | + | 1.24248i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −24.8494 | + | 5.41101i | −1.09713 | + | 0.238902i | ||||
\(514\) | 20.4772 | + | 11.8225i | 0.903212 | + | 0.521470i | ||||
\(515\) | −8.38437 | − | 22.1086i | −0.369459 | − | 0.974223i | ||||
\(516\) | 2.83766 | + | 2.05451i | 0.124921 | + | 0.0904447i | ||||
\(517\) | 1.65504 | 0.0727885 | ||||||||
\(518\) | −16.7158 | + | 8.77172i | −0.734452 | + | 0.385407i | ||||
\(519\) | 18.2158 | − | 8.14637i | 0.799587 | − | 0.357586i | ||||
\(520\) | 14.7907 | + | 2.40393i | 0.648616 | + | 0.105419i | ||||
\(521\) | −9.31280 | + | 16.1302i | −0.408001 | + | 0.706679i | −0.994666 | − | 0.103151i | \(-0.967107\pi\) |
0.586664 | + | 0.809830i | \(0.300441\pi\) | |||||||
\(522\) | 5.76471 | − | 1.89419i | 0.252315 | − | 0.0829065i | ||||
\(523\) | −7.03886 | − | 12.1917i | −0.307788 | − | 0.533104i | 0.670090 | − | 0.742280i | \(-0.266255\pi\) |
−0.977878 | + | 0.209175i | \(0.932922\pi\) | |||||||
\(524\) | −6.02651 | −0.263269 | ||||||||
\(525\) | 19.1463 | − | 12.5865i | 0.835613 | − | 0.549318i | ||||
\(526\) | −2.00000 | −0.0872041 | ||||||||
\(527\) | 0.477226 | + | 0.826579i | 0.0207883 | + | 0.0360063i | ||||
\(528\) | −0.0380311 | + | 0.367696i | −0.00165509 | + | 0.0160019i | ||||
\(529\) | −9.47723 | + | 16.4150i | −0.412053 | + | 0.713697i | ||||
\(530\) | 11.0355 | + | 1.79360i | 0.479353 | + | 0.0779089i | ||||
\(531\) | −9.83508 | + | 10.9960i | −0.426806 | + | 0.477184i | ||||
\(532\) | −10.9441 | − | 6.92163i | −0.474485 | − | 0.300091i | ||||
\(533\) | −44.9089 | −1.94522 | ||||||||
\(534\) | 10.7410 | − | 14.8353i | 0.464807 | − | 0.641984i | ||||
\(535\) | −4.34286 | − | 11.4516i | −0.187758 | − | 0.495097i | ||||
\(536\) | −4.61230 | − | 2.66291i | −0.199221 | − | 0.115020i | ||||
\(537\) | 20.9184 | + | 15.1452i | 0.902694 | + | 0.653565i | ||||
\(538\) | −28.8948 | −1.24574 | ||||||||
\(539\) | 0.120413 | − | 1.48909i | 0.00518655 | − | 0.0641397i | ||||
\(540\) | 9.73861 | − | 6.33715i | 0.419083 | − | 0.272707i | ||||
\(541\) | −9.73861 | − | 16.8678i | −0.418696 | − | 0.725202i | 0.577113 | − | 0.816664i | \(-0.304179\pi\) |
−0.995809 | + | 0.0914622i | \(0.970846\pi\) | |||||||
\(542\) | −5.47723 | − | 3.16228i | −0.235267 | − | 0.135831i | ||||
\(543\) | −0.563508 | + | 5.44816i | −0.0241825 | + | 0.233803i | ||||
\(544\) | 2.73861 | − | 1.58114i | 0.117417 | − | 0.0677908i | ||||
\(545\) | −17.5810 | + | 21.5323i | −0.753089 | + | 0.922342i | ||||
\(546\) | −30.3945 | − | 4.38895i | −1.30076 | − | 0.187830i | ||||
\(547\) | 23.2144i | 0.992575i | 0.868158 | + | 0.496287i | \(0.165304\pi\) | ||||
−0.868158 | + | 0.496287i | \(0.834696\pi\) | |||||||
\(548\) | −3.73861 | − | 6.47547i | −0.159706 | − | 0.276618i | ||||
\(549\) | 9.87298 | − | 3.24410i | 0.421369 | − | 0.138455i | ||||
\(550\) | 0.337946 | − | 1.01218i | 0.0144101 | − | 0.0431596i | ||||
\(551\) | 4.94975 | + | 8.57321i | 0.210866 | + | 0.365231i | ||||
\(552\) | −4.58009 | − | 10.2414i | −0.194942 | − | 0.435903i | ||||
\(553\) | 1.38201 | + | 0.0557857i | 0.0587689 | + | 0.00237225i | ||||
\(554\) | − | 9.79796i | − | 0.416275i | ||||||
\(555\) | 26.7093 | − | 7.08849i | 1.13375 | − | 0.300890i | ||||
\(556\) | −6.52277 | − | 3.76593i | −0.276627 | − | 0.159711i | ||||
\(557\) | 18.9317 | − | 32.7906i | 0.802161 | − | 1.38938i | −0.116030 | − | 0.993246i | \(-0.537017\pi\) |
0.918191 | − | 0.396138i | \(-0.129650\pi\) | |||||||
\(558\) | −0.185325 | + | 0.886304i | −0.00784543 | + | 0.0375202i | ||||
\(559\) | 13.5546i | 0.573298i | ||||||||
\(560\) | 5.79642 | + | 1.18383i | 0.244944 | + | 0.0500261i | ||||
\(561\) | 0.477226 | + | 1.06711i | 0.0201485 | + | 0.0450534i | ||||
\(562\) | −10.0521 | + | 5.80359i | −0.424023 | + | 0.244810i | ||||
\(563\) | 9.00000 | + | 5.19615i | 0.379305 | + | 0.218992i | 0.677516 | − | 0.735508i | \(-0.263057\pi\) |
−0.298211 | + | 0.954500i | \(0.596390\pi\) | |||||||
\(564\) | 1.38188 | − | 13.3604i | 0.0581876 | − | 0.562574i | ||||
\(565\) | 14.3965 | + | 2.33985i | 0.605664 | + | 0.0984381i | ||||
\(566\) | 24.7165 | 1.03891 | ||||||||
\(567\) | −19.7251 | + | 13.3387i | −0.828375 | + | 0.560174i | ||||
\(568\) | − | 2.02265i | − | 0.0848683i | ||||||
\(569\) | 10.4218 | − | 6.01701i | 0.436903 | − | 0.252246i | −0.265380 | − | 0.964144i | \(-0.585497\pi\) |
0.702283 | + | 0.711898i | \(0.252164\pi\) | |||||||
\(570\) | 13.3717 | + | 13.4356i | 0.560077 | + | 0.562756i | ||||
\(571\) | 3.47723 | − | 6.02273i | 0.145517 | − | 0.252043i | −0.784048 | − | 0.620700i | \(-0.786849\pi\) |
0.929566 | + | 0.368656i | \(0.120182\pi\) | |||||||
\(572\) | −1.23861 | + | 0.715113i | −0.0517890 | + | 0.0299004i | ||||
\(573\) | 2.52319 | − | 1.12840i | 0.105408 | − | 0.0471397i | ||||
\(574\) | −17.7158 | − | 0.715113i | −0.739445 | − | 0.0298483i | ||||
\(575\) | 6.47723 | + | 31.7318i | 0.270119 | + | 1.32331i | ||||
\(576\) | 2.93649 | + | 0.614017i | 0.122354 | + | 0.0255840i | ||||
\(577\) | −7.40852 | + | 12.8319i | −0.308421 | + | 0.534200i | −0.978017 | − | 0.208525i | \(-0.933134\pi\) |
0.669596 | + | 0.742725i | \(0.266467\pi\) | |||||||
\(578\) | −3.50000 | + | 6.06218i | −0.145581 | + | 0.252153i | ||||
\(579\) | 10.3095 | + | 7.46423i | 0.428447 | + | 0.310203i | ||||
\(580\) | −3.50333 | − | 2.86045i | −0.145468 | − | 0.118774i | ||||
\(581\) | 37.3800 | + | 23.6412i | 1.55079 | + | 0.980803i | ||||
\(582\) | −2.47723 | − | 5.53924i | −0.102684 | − | 0.229609i | ||||
\(583\) | −0.924143 | + | 0.533554i | −0.0382741 | + | 0.0220976i | ||||
\(584\) | 5.99430 | − | 10.3824i | 0.248046 | − | 0.429628i | ||||
\(585\) | 41.9568 | + | 16.1409i | 1.73470 | + | 0.667343i | ||||
\(586\) | −3.97723 | + | 2.29625i | −0.164298 | + | 0.0948573i | ||||
\(587\) | − | 27.4110i | − | 1.13137i | −0.824621 | − | 0.565686i | \(-0.808611\pi\) | ||
0.824621 | − | 0.565686i | \(-0.191389\pi\) | |||||||
\(588\) | −11.9202 | − | 2.21536i | −0.491583 | − | 0.0913599i | ||||
\(589\) | −1.47723 | −0.0608680 | ||||||||
\(590\) | 10.8535 | + | 1.76402i | 0.446833 | + | 0.0726234i | ||||
\(591\) | −15.5057 | − | 1.60377i | −0.637821 | − | 0.0659704i | ||||
\(592\) | 6.17913 | + | 3.56752i | 0.253961 | + | 0.146624i | ||||
\(593\) | 31.4317 | − | 18.1471i | 1.29074 | − | 0.745212i | 0.311958 | − | 0.950096i | \(-0.399015\pi\) |
0.978786 | + | 0.204884i | \(0.0656818\pi\) | |||||||
\(594\) | −0.337449 | + | 1.05638i | −0.0138457 | + | 0.0433440i | ||||
\(595\) | 17.7460 | − | 5.92289i | 0.727514 | − | 0.242815i | ||||
\(596\) | 2.44949i | 0.100335i | ||||||||
\(597\) | 31.4789 | + | 22.7912i | 1.28834 | + | 0.932783i | ||||
\(598\) | 21.7033 | − | 37.5912i | 0.887513 | − | 1.53722i | ||||
\(599\) | 4.98196 | + | 2.87633i | 0.203557 | + | 0.117524i | 0.598314 | − | 0.801262i | \(-0.295838\pi\) |
−0.394756 | + | 0.918786i | \(0.629171\pi\) | |||||||
\(600\) | −7.88874 | − | 3.57321i | −0.322056 | − | 0.145876i | ||||
\(601\) | − | 16.7169i | − | 0.681895i | −0.940082 | − | 0.340947i | \(-0.889252\pi\) | ||
0.940082 | − | 0.340947i | \(-0.110748\pi\) | |||||||
\(602\) | −0.215838 | + | 5.34706i | −0.00879691 | + | 0.217930i | ||||
\(603\) | −11.9089 | − | 10.6516i | −0.484968 | − | 0.433769i | ||||
\(604\) | 1.00000 | + | 1.73205i | 0.0406894 | + | 0.0704761i | ||||
\(605\) | −8.68571 | − | 22.9032i | −0.353124 | − | 0.931149i | ||||
\(606\) | −19.4919 | − | 2.01607i | −0.791806 | − | 0.0818972i | ||||
\(607\) | 13.2180 | + | 22.8942i | 0.536502 | + | 0.929248i | 0.999089 | + | 0.0426745i | \(0.0135879\pi\) |
−0.462587 | + | 0.886574i | \(0.653079\pi\) | |||||||
\(608\) | 4.89433i | 0.198491i | ||||||||
\(609\) | 7.28238 | + | 5.73411i | 0.295097 | + | 0.232358i | ||||
\(610\) | −6.00000 | − | 4.89898i | −0.242933 | − | 0.198354i | ||||
\(611\) | 45.0056 | − | 25.9840i | 1.82073 | − | 1.05120i | ||||
\(612\) | 9.01276 | − | 2.96145i | 0.364319 | − | 0.119709i | ||||
\(613\) | 22.0407 | + | 12.7252i | 0.890216 | + | 0.513967i | 0.874013 | − | 0.485902i | \(-0.161509\pi\) |
0.0162031 | + | 0.999869i | \(0.494842\pi\) | |||||||
\(614\) | −1.75166 | − | 3.03397i | −0.0706914 | − | 0.122441i | ||||
\(615\) | 25.0540 | + | 6.77729i | 1.01027 | + | 0.273287i | ||||
\(616\) | −0.500000 | + | 0.262377i | −0.0201456 | + | 0.0105715i | ||||
\(617\) | 25.4772 | 1.02567 | 0.512837 | − | 0.858486i | \(-0.328594\pi\) | ||||
0.512837 | + | 0.858486i | \(0.328594\pi\) | |||||||
\(618\) | 10.7410 | − | 14.8353i | 0.432065 | − | 0.596762i | ||||
\(619\) | −23.1475 | − | 13.3642i | −0.930377 | − | 0.537154i | −0.0434463 | − | 0.999056i | \(-0.513834\pi\) |
−0.886931 | + | 0.461902i | \(0.847167\pi\) | |||||||
\(620\) | 0.631045 | − | 0.239314i | 0.0253434 | − | 0.00961109i | ||||
\(621\) | −7.16101 | − | 32.8860i | −0.287361 | − | 1.31967i | ||||
\(622\) | −28.8948 | −1.15857 | ||||||||
\(623\) | 27.9545 | + | 1.12840i | 1.11997 | + | 0.0452085i | ||||
\(624\) | 4.73861 | + | 10.5959i | 0.189696 | + | 0.424174i | ||||
\(625\) | 19.9853 | + | 15.0196i | 0.799411 | + | 0.600784i | ||||
\(626\) | 11.6190 | − | 20.1246i | 0.464387 | − | 0.804341i | ||||
\(627\) | −1.79962 | − | 0.186137i | −0.0718701 | − | 0.00743359i | ||||
\(628\) | 4.39526 | + | 7.61282i | 0.175390 | + | 0.303784i | ||||
\(629\) | 22.5630 | 0.899646 | ||||||||
\(630\) | 16.2943 | + | 7.03542i | 0.649179 | + | 0.280298i | ||||
\(631\) | −7.47723 | −0.297664 | −0.148832 | − | 0.988863i | \(-0.547551\pi\) | ||||
−0.148832 | + | 0.988863i | \(0.547551\pi\) | |||||||
\(632\) | −0.261387 | − | 0.452736i | −0.0103974 | − | 0.0180089i | ||||
\(633\) | −23.2978 | − | 2.40972i | −0.926006 | − | 0.0957777i | ||||
\(634\) | −16.9545 | + | 29.3660i | −0.673347 | + | 1.16627i | ||||
\(635\) | 4.88929 | − | 30.0825i | 0.194025 | − | 1.19379i | ||||
\(636\) | 3.53553 | + | 7.90569i | 0.140193 | + | 0.313481i | ||||
\(637\) | −20.1042 | − | 42.3834i | −0.796559 | − | 1.67929i | ||||
\(638\) | 0.431677 | 0.0170902 | ||||||||
\(639\) | 1.24194 | − | 5.93948i | 0.0491303 | − | 0.234962i | ||||
\(640\) | −0.792893 | − | 2.09077i | −0.0313419 | − | 0.0826450i | ||||
\(641\) | 5.43982 | + | 3.14068i | 0.214860 | + | 0.124049i | 0.603568 | − | 0.797312i | \(-0.293745\pi\) |
−0.388708 | + | 0.921361i | \(0.627079\pi\) | |||||||
\(642\) | 5.56351 | − | 7.68423i | 0.219574 | − | 0.303272i | ||||
\(643\) | −20.4095 | −0.804871 | −0.402436 | − | 0.915448i | \(-0.631836\pi\) | ||||
−0.402436 | + | 0.915448i | \(0.631836\pi\) | |||||||
\(644\) | 9.16018 | − | 14.4835i | 0.360962 | − | 0.570731i | ||||
\(645\) | 2.04555 | − | 7.56189i | 0.0805434 | − | 0.297749i | ||||
\(646\) | 7.73861 | + | 13.4037i | 0.304472 | + | 0.527360i | ||||
\(647\) | −20.6703 | − | 11.9340i | −0.812633 | − | 0.469174i | 0.0352364 | − | 0.999379i | \(-0.488782\pi\) |
−0.847869 | + | 0.530205i | \(0.822115\pi\) | |||||||
\(648\) | 8.24597 | + | 3.60611i | 0.323932 | + | 0.141661i | ||||
\(649\) | −0.908902 | + | 0.524755i | −0.0356775 | + | 0.0205984i | ||||
\(650\) | −6.70141 | − | 32.8301i | −0.262851 | − | 1.28770i | ||||
\(651\) | −1.28437 | + | 0.513276i | −0.0503383 | + | 0.0201169i | ||||
\(652\) | − | 14.6969i | − | 0.575577i | ||||||
\(653\) | 12.9317 | + | 22.3983i | 0.506056 | + | 0.876514i | 0.999975 | + | 0.00700659i | \(0.00223029\pi\) |
−0.493920 | + | 0.869507i | \(0.664436\pi\) | |||||||
\(654\) | −21.4180 | − | 2.21529i | −0.837511 | − | 0.0866246i | ||||
\(655\) | 4.77838 | + | 12.6001i | 0.186707 | + | 0.492325i | ||||
\(656\) | 3.35071 | + | 5.80359i | 0.130823 | + | 0.226592i | ||||
\(657\) | 23.9772 | − | 26.8073i | 0.935440 | − | 1.04585i | ||||
\(658\) | 18.1677 | − | 9.53361i | 0.708252 | − | 0.371659i | ||||
\(659\) | 34.2929i | 1.33586i | 0.744224 | + | 0.667930i | \(0.232819\pi\) | ||||
−0.744224 | + | 0.667930i | \(0.767181\pi\) | |||||||
\(660\) | 0.798922 | − | 0.212029i | 0.0310980 | − | 0.00825322i | ||||
\(661\) | 11.4772 | + | 6.62638i | 0.446412 | + | 0.257736i | 0.706314 | − | 0.707899i | \(-0.250357\pi\) |
−0.259901 | + | 0.965635i | \(0.583690\pi\) | |||||||
\(662\) | 5.71584 | − | 9.90012i | 0.222152 | − | 0.384779i | ||||
\(663\) | 29.7308 | + | 21.5256i | 1.15465 | + | 0.835983i | ||||
\(664\) | − | 16.7169i | − | 0.648740i | ||||||
\(665\) | −5.79407 | + | 28.3696i | −0.224684 | + | 1.10013i | ||||
\(666\) | 15.9545 | + | 14.2701i | 0.618222 | + | 0.552955i | ||||
\(667\) | −11.3459 | + | 6.55057i | −0.439316 | + | 0.253639i | ||||
\(668\) | −12.7158 | − | 7.34149i | −0.491991 | − | 0.284051i | ||||
\(669\) | −11.0197 | − | 1.13978i | −0.426046 | − | 0.0440664i | ||||
\(670\) | −1.91048 | + | 11.7547i | −0.0738081 | + | 0.454122i | ||||
\(671\) | 0.739315 | 0.0285409 | ||||||||
\(672\) | 1.70058 | + | 4.25535i | 0.0656014 | + | 0.164154i | ||||
\(673\) | − | 48.4514i | − | 1.86766i | −0.357713 | − | 0.933832i | \(-0.616443\pi\) | ||
0.357713 | − | 0.933832i | \(-0.383557\pi\) | |||||||
\(674\) | −14.8492 | + | 8.57321i | −0.571971 | + | 0.330228i | ||||
\(675\) | −20.9712 | − | 15.3365i | −0.807182 | − | 0.590303i | ||||
\(676\) | −15.9545 | + | 27.6339i | −0.613633 | + | 1.06284i | ||||
\(677\) | −28.5000 | + | 16.4545i | −1.09534 | + | 0.632397i | −0.934994 | − | 0.354663i | \(-0.884596\pi\) |
−0.160350 | + | 0.987060i | \(0.551262\pi\) | |||||||
\(678\) | 4.61230 | + | 10.3134i | 0.177134 | + | 0.396084i | ||||
\(679\) | 4.95445 | − | 7.83368i | 0.190134 | − | 0.300629i | ||||
\(680\) | −5.47723 | − | 4.47214i | −0.210042 | − | 0.171499i | ||||
\(681\) | −14.5798 | − | 10.5560i | −0.558699 | − | 0.404507i | ||||
\(682\) | −0.0322079 | + | 0.0557857i | −0.00123330 | + | 0.00213615i | ||||
\(683\) | −1.47723 | + | 2.55863i | −0.0565245 | + | 0.0979032i | −0.892903 | − | 0.450249i | \(-0.851335\pi\) |
0.836379 | + | 0.548152i | \(0.184669\pi\) | |||||||
\(684\) | −3.00520 | + | 14.3722i | −0.114907 | + | 0.549533i | ||||
\(685\) | −10.5744 | + | 12.9509i | −0.404027 | + | 0.494830i | ||||
\(686\) | −7.25590 | − | 17.0397i | −0.277031 | − | 0.650579i | ||||
\(687\) | 11.4317 | − | 5.11240i | 0.436146 | − | 0.195050i | ||||
\(688\) | 1.75166 | − | 1.01132i | 0.0667815 | − | 0.0385563i | ||||
\(689\) | −16.7535 | + | 29.0180i | −0.638259 | + | 1.10550i | ||||
\(690\) | −17.7809 | + | 17.6962i | −0.676906 | + | 0.673685i | ||||
\(691\) | 3.00000 | − | 1.73205i | 0.114125 | − | 0.0658903i | −0.441851 | − | 0.897089i | \(-0.645678\pi\) |
0.555976 | + | 0.831198i | \(0.312345\pi\) | |||||||
\(692\) | − | 11.5207i | − | 0.437952i | ||||||
\(693\) | −1.62935 | + | 0.463461i | −0.0618939 | + | 0.0176054i | ||||
\(694\) | −6.52277 | −0.247601 | ||||||||
\(695\) | −2.70182 | + | 16.6236i | −0.102486 | + | 0.630569i | ||||
\(696\) | 0.360429 | − | 3.48474i | 0.0136620 | − | 0.132089i | ||||
\(697\) | 18.3526 | + | 10.5959i | 0.695153 | + | 0.401347i | ||||
\(698\) | 28.1703 | − | 16.2641i | 1.06626 | − | 0.615606i | ||||
\(699\) | −2.82843 | − | 6.32456i | −0.106981 | − | 0.239217i | ||||
\(700\) | −2.12082 | − | 13.0576i | −0.0801596 | − | 0.493533i | ||||
\(701\) | − | 7.03320i | − | 0.265640i | −0.991140 | − | 0.132820i | \(-0.957597\pi\) | ||
0.991140 | − | 0.132820i | \(-0.0424033\pi\) | |||||||
\(702\) | 7.40886 | + | 34.0242i | 0.279629 | + | 1.28416i | ||||
\(703\) | −17.4606 | + | 30.2427i | −0.658540 | + | 1.14063i | ||||
\(704\) | 0.184829 | + | 0.106711i | 0.00696599 | + | 0.00402182i | ||||
\(705\) | −29.0292 | + | 7.70418i | −1.09330 | + | 0.290156i | ||||
\(706\) | − | 13.2528i | − | 0.498774i | ||||||
\(707\) | −13.9089 | − | 26.5055i | −0.523098 | − | 0.996843i | ||||
\(708\) | 3.47723 | + | 7.77531i | 0.130682 | + | 0.292214i | ||||
\(709\) | −5.21584 | − | 9.03410i | −0.195885 | − | 0.339283i | 0.751305 | − | 0.659955i | \(-0.229425\pi\) |
−0.947190 | + | 0.320672i | \(0.896091\pi\) | |||||||
\(710\) | −4.22889 | + | 1.60374i | −0.158707 | + | 0.0601874i | ||||
\(711\) | −0.489574 | − | 1.48995i | −0.0183605 | − | 0.0558775i | ||||
\(712\) | −5.28720 | − | 9.15769i | −0.198146 | − | 0.343199i | ||||
\(713\) | − | 1.95498i | − | 0.0732146i | ||||||
\(714\) | 11.3855 | + | 8.96491i | 0.426093 | + | 0.335503i | ||||
\(715\) | 2.47723 | + | 2.02265i | 0.0926430 | + | 0.0756427i | ||||
\(716\) | 12.9128 | − | 7.45518i | 0.482572 | − | 0.278613i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.62465 | − | 3.24739i | −0.209910 | − | 0.121192i | ||||
\(719\) | −23.6398 | − | 40.9453i | −0.881614 | − | 1.52700i | −0.849545 | − | 0.527515i | \(-0.823124\pi\) |
−0.0320690 | − | 0.999486i | \(-0.510210\pi\) | |||||||
\(720\) | −1.04456 | − | 6.62638i | −0.0389283 | − | 0.246951i | ||||
\(721\) | 27.9545 | + | 1.12840i | 1.04108 | + | 0.0420239i | ||||
\(722\) | −4.95445 | −0.184386 | ||||||||
\(723\) | −5.59613 | − | 4.05169i | −0.208122 | − | 0.150684i | ||||
\(724\) | 2.73861 | + | 1.58114i | 0.101780 | + | 0.0587626i | ||||
\(725\) | −3.20279 | + | 9.59268i | −0.118949 | + | 0.356263i | ||||
\(726\) | 11.1270 | − | 15.3685i | 0.412962 | − | 0.570377i | ||||
\(727\) | −23.6076 | −0.875556 | −0.437778 | − | 0.899083i | \(-0.644234\pi\) | ||||
−0.437778 | + | 0.899083i | \(0.644234\pi\) | |||||||
\(728\) | −9.47723 | + | 14.9848i | −0.351249 | + | 0.555374i | ||||
\(729\) | 22.0000 | + | 15.6525i | 0.814815 | + | 0.579721i | ||||
\(730\) | −26.4601 | − | 4.30055i | −0.979334 | − | 0.159170i | ||||
\(731\) | 3.19808 | − | 5.53924i | 0.118285 | − | 0.204876i | ||||
\(732\) | 0.617292 | − | 5.96816i | 0.0228158 | − | 0.220590i | ||||
\(733\) | 18.1677 | + | 31.4674i | 0.671041 | + | 1.16228i | 0.977609 | + | 0.210428i | \(0.0674858\pi\) |
−0.306569 | + | 0.951849i | \(0.599181\pi\) | |||||||
\(734\) | 8.11562 | 0.299553 | ||||||||
\(735\) | 4.81967 | + | 26.6790i | 0.177776 | + | 0.984071i | ||||
\(736\) | −6.47723 | −0.238754 | ||||||||
\(737\) | −0.568323 | − | 0.984365i | −0.0209345 | − | 0.0362595i | ||||
\(738\) | 6.27582 | + | 19.0996i | 0.231016 | + | 0.703066i | ||||
\(739\) | 2.23861 | − | 3.87739i | 0.0823487 | − | 0.142632i | −0.821910 | − | 0.569618i | \(-0.807091\pi\) |
0.904258 | + | 0.426986i | \(0.140425\pi\) | |||||||
\(740\) | 2.55948 | − | 15.7478i | 0.0940884 | − | 0.578901i | ||||
\(741\) | −51.8596 | + | 23.1923i | −1.90511 | + | 0.851991i | ||||
\(742\) | −7.07107 | + | 11.1803i | −0.259587 | + | 0.410443i | ||||
\(743\) | −19.4317 | −0.712879 | −0.356440 | − | 0.934318i | \(-0.616009\pi\) | ||||
−0.356440 | + | 0.934318i | \(0.616009\pi\) | |||||||
\(744\) | 0.423441 | + | 0.306579i | 0.0155241 | + | 0.0112397i | ||||
\(745\) | 5.12132 | − | 1.94218i | 0.187631 | − | 0.0711561i | ||||
\(746\) | 3.13367 | + | 1.80922i | 0.114732 | + | 0.0662404i | ||||
\(747\) | 10.2644 | − | 49.0889i | 0.375556 | − | 1.79607i | ||||
\(748\) | 0.674899 | 0.0246767 | ||||||||
\(749\) | 14.4796 | + | 0.584480i | 0.529073 | + | 0.0213564i | ||||
\(750\) | −1.21584 | + | 19.3267i | −0.0443961 | + | 0.705712i | ||||
\(751\) | 16.0000 | + | 27.7128i | 0.583848 | + | 1.01125i | 0.995018 | + | 0.0996961i | \(0.0317870\pi\) |
−0.411170 | + | 0.911559i | \(0.634880\pi\) | |||||||
\(752\) | −6.71584 | − | 3.87739i | −0.244901 | − | 0.141394i | ||||
\(753\) | −28.6010 | − | 2.95823i | −1.04228 | − | 0.107804i | ||||
\(754\) | 11.7386 | − | 6.77729i | 0.427495 | − | 0.246814i | ||||
\(755\) | 2.82843 | − | 3.46410i | 0.102937 | − | 0.126072i | ||||
\(756\) | 2.38089 | + | 13.5400i | 0.0865920 | + | 0.492445i | ||||
\(757\) | 30.2476i | 1.09937i | 0.835373 | + | 0.549683i | \(0.185252\pi\) | ||||
−0.835373 | + | 0.549683i | \(0.814748\pi\) | |||||||
\(758\) | 4.76139 | + | 8.24696i | 0.172941 | + | 0.299543i | ||||
\(759\) | 0.246336 | − | 2.38165i | 0.00894143 | − | 0.0864484i | ||||
\(760\) | 10.2329 | − | 3.88068i | 0.371187 | − | 0.140767i | ||||
\(761\) | 4.76492 | + | 8.25308i | 0.172728 | + | 0.299174i | 0.939373 | − | 0.342898i | \(-0.111408\pi\) |
−0.766645 | + | 0.642072i | \(0.778075\pi\) | |||||||
\(762\) | 21.5507 | − | 9.63774i | 0.780698 | − | 0.349139i | ||||
\(763\) | −15.2833 | − | 29.1247i | −0.553293 | − | 1.05438i | ||||
\(764\) | − | 1.59580i | − | 0.0577341i | ||||||
\(765\) | −13.3379 | − | 16.4955i | −0.482231 | − | 0.596396i | ||||
\(766\) | 0.715838 | + | 0.413289i | 0.0258643 | + | 0.0149328i | ||||
\(767\) | −16.4772 | + | 28.5394i | −0.594958 | + | 1.03050i | ||||
\(768\) | 1.01575 | − | 1.40294i | 0.0366528 | − | 0.0506243i | ||||
\(769\) | − | 28.8412i | − | 1.04004i | −0.854154 | − | 0.520020i | \(-0.825924\pi\) | ||
0.854154 | − | 0.520020i | \(-0.174076\pi\) | |||||||
\(770\) | 0.945018 | + | 0.837348i | 0.0340561 | + | 0.0301759i | ||||
\(771\) | 37.3861 | − | 16.7196i | 1.34643 | − | 0.602141i | ||||
\(772\) | 6.36396 | − | 3.67423i | 0.229044 | − | 0.132239i | ||||
\(773\) | −24.9772 | − | 14.4206i | −0.898368 | − | 0.518673i | −0.0216979 | − | 0.999765i | \(-0.506907\pi\) |
−0.876670 | + | 0.481091i | \(0.840241\pi\) | |||||||
\(774\) | 5.76471 | − | 1.89419i | 0.207208 | − | 0.0680853i | ||||
\(775\) | −1.00070 | − | 1.12962i | −0.0359463 | − | 0.0405771i | ||||
\(776\) | −3.50333 | −0.125762 | ||||||||
\(777\) | −4.67295 | + | 32.3612i | −0.167641 | + | 1.16095i | ||||
\(778\) | 7.34847i | 0.263455i | ||||||||
\(779\) | −28.4047 | + | 16.3995i | −1.01770 | + | 0.587571i | ||||
\(780\) | 18.3963 | − | 18.3087i | 0.658693 | − | 0.655558i | ||||
\(781\) | 0.215838 | − | 0.373843i | 0.00772330 | − | 0.0133772i | ||||
\(782\) | −17.7386 | + | 10.2414i | −0.634331 | + | 0.366231i | ||||
\(783\) | 3.19808 | − | 10.0116i | 0.114290 | − | 0.357785i | ||||
\(784\) | −3.97723 | + | 5.76035i | −0.142044 | + | 0.205727i | ||||
\(785\) | 12.4317 | − | 15.2256i | 0.443706 | − | 0.543426i | ||||
\(786\) | −6.12145 | + | 8.45485i | −0.218345 | + | 0.301574i | ||||
\(787\) | 17.3402 | − | 30.0341i | 0.618112 | − | 1.07060i | −0.371718 | − | 0.928346i | \(-0.621231\pi\) |
0.989830 | − | 0.142256i | \(-0.0454356\pi\) | |||||||
\(788\) | −4.50000 | + | 7.79423i | −0.160306 | + | 0.277658i | ||||
\(789\) | −2.03151 | + | 2.80588i | −0.0723235 | + | 0.0998921i | ||||
\(790\) | −0.739315 | + | 0.905472i | −0.0263036 | + | 0.0322152i | ||||
\(791\) | −9.22460 | + | 14.5854i | −0.327989 | + | 0.518596i | ||||
\(792\) | 0.477226 | + | 0.426844i | 0.0169575 | + | 0.0151672i | ||||
\(793\) | 20.1042 | − | 11.6072i | 0.713922 | − | 0.412183i | ||||
\(794\) | −15.1867 | + | 26.3041i | −0.538956 | + | 0.933498i | ||||
\(795\) | 13.7257 | − | 13.6604i | 0.486800 | − | 0.484483i | ||||
\(796\) | 19.4317 | − | 11.2189i | 0.688738 | − | 0.397643i | ||||
\(797\) | 28.9201i | 1.02440i | 0.858865 | + | 0.512201i | \(0.171170\pi\) | ||||
−0.858865 | + | 0.512201i | \(0.828830\pi\) | |||||||
\(798\) | −20.8271 | + | 8.32321i | −0.737271 | + | 0.294638i | ||||
\(799\) | −24.5228 | −0.867553 | ||||||||
\(800\) | −3.74264 | + | 3.31552i | −0.132322 | + | 0.117221i | ||||
\(801\) | −9.90283 | − | 30.1379i | −0.349899 | − | 1.06487i | ||||
\(802\) | 26.2834 | + | 15.1747i | 0.928098 | + | 0.535838i | ||||
\(803\) | 2.21584 | − | 1.27931i | 0.0781952 | − | 0.0451460i | ||||
\(804\) | −8.42087 | + | 3.76593i | −0.296981 | + | 0.132814i | ||||
\(805\) | −37.5448 | − | 7.66795i | −1.32328 | − | 0.270260i | ||||
\(806\) | 2.02265i | 0.0712447i | ||||||||
\(807\) | −29.3499 | + | 40.5377i | −1.03317 | + | 1.42699i | ||||
\(808\) | −5.65685 | + | 9.79796i | −0.199007 | + | 0.344691i | ||||
\(809\) | −34.7686 | − | 20.0737i | −1.22240 | − | 0.705753i | −0.256971 | − | 0.966419i | \(-0.582725\pi\) |
−0.965429 | + | 0.260666i | \(0.916058\pi\) | |||||||
\(810\) | 1.00138 | − | 20.0997i | 0.0351848 | − | 0.706231i | ||||
\(811\) | − | 6.70527i | − | 0.235454i | −0.993046 | − | 0.117727i | \(-0.962439\pi\) | ||
0.993046 | − | 0.117727i | \(-0.0375608\pi\) | |||||||
\(812\) | 4.73861 | − | 2.48661i | 0.166293 | − | 0.0872629i | ||||
\(813\) | −10.0000 | + | 4.47214i | −0.350715 | + | 0.156845i | ||||
\(814\) | 0.761387 | + | 1.31876i | 0.0266866 | + | 0.0462226i | ||||
\(815\) | −30.7279 | + | 11.6531i | −1.07635 | + | 0.408190i | ||||
\(816\) | 0.563508 | − | 5.44816i | 0.0197267 | − | 0.190724i | ||||
\(817\) | 4.94975 | + | 8.57321i | 0.173170 | + | 0.299939i | ||||
\(818\) | 22.4378i | 0.784518i | ||||||||
\(819\) | −37.0307 | + | 38.1836i | −1.29396 | + | 1.33424i | ||||
\(820\) | 9.47723 | − | 11.6072i | 0.330959 | − | 0.405340i | ||||
\(821\) | 44.0814 | − | 25.4504i | 1.53845 | − | 0.888226i | 0.539523 | − | 0.841971i | \(-0.318604\pi\) |
0.998930 | − | 0.0462557i | \(-0.0147289\pi\) | |||||||
\(822\) | −12.8822 | − | 1.33242i | −0.449319 | − | 0.0464734i | ||||
\(823\) | −28.2199 | − | 16.2927i | −0.983682 | − | 0.567929i | −0.0803025 | − | 0.996771i | \(-0.525589\pi\) |
−0.903380 | + | 0.428841i | \(0.858922\pi\) | |||||||
\(824\) | −5.28720 | − | 9.15769i | −0.184188 | − | 0.319023i | ||||
\(825\) | −1.07676 | − | 1.50225i | −0.0374881 | − | 0.0523015i | ||||
\(826\) | −6.95445 | + | 10.9960i | −0.241976 | + | 0.382598i | ||||
\(827\) | 39.9089 | 1.38777 | 0.693884 | − | 0.720087i | \(-0.255898\pi\) | ||||
0.693884 | + | 0.720087i | \(0.255898\pi\) | |||||||
\(828\) | −19.0203 | − | 3.97713i | −0.661002 | − | 0.138215i | ||||
\(829\) | −16.3069 | − | 9.41481i | −0.566363 | − | 0.326990i | 0.189332 | − | 0.981913i | \(-0.439368\pi\) |
−0.755696 | + | 0.654923i | \(0.772701\pi\) | |||||||
\(830\) | −34.9511 | + | 13.2547i | −1.21317 | + | 0.460077i | ||||
\(831\) | −13.7460 | − | 9.95231i | −0.476842 | − | 0.345242i | ||||
\(832\) | 6.70141 | 0.232330 | ||||||||
\(833\) | −1.78416 | + | 22.0639i | −0.0618175 | + | 0.764470i | ||||
\(834\) | −11.9089 | + | 5.32582i | −0.412372 | + | 0.184418i | ||||
\(835\) | −5.26707 | + | 32.4069i | −0.182275 | + | 1.12149i | ||||
\(836\) | −0.522278 | + | 0.904612i | −0.0180634 | + | 0.0312867i | ||||
\(837\) | 1.05519 | + | 1.16027i | 0.0364726 | + | 0.0401046i | ||||
\(838\) | 8.30045 | + | 14.3768i | 0.286734 | + | 0.496639i | ||||
\(839\) | −37.3156 | −1.28828 | −0.644139 | − | 0.764908i | \(-0.722784\pi\) | ||||
−0.644139 | + | 0.764908i | \(0.722784\pi\) | |||||||
\(840\) | 7.54858 | − | 6.92957i | 0.260451 | − | 0.239093i | ||||
\(841\) | 24.9089 | 0.858928 | ||||||||
\(842\) | 1.47723 | + | 2.55863i | 0.0509086 | + | 0.0881762i | ||||
\(843\) | −2.06837 | + | 19.9975i | −0.0712383 | + | 0.688752i | ||||
\(844\) | −6.76139 | + | 11.7111i | −0.232737 | + | 0.403112i | ||||
\(845\) | 70.4264 | + | 11.4463i | 2.42274 | + | 0.393766i | ||||
\(846\) | −17.3402 | − | 15.5096i | −0.596169 | − | 0.533230i | ||||
\(847\) | 28.9592 | + | 1.16896i | 0.995049 | + | 0.0401659i | ||||
\(848\) | 5.00000 | 0.171701 | ||||||||
\(849\) | 25.1059 | − | 34.6759i | 0.861632 | − | 1.19007i | ||||
\(850\) | −5.00735 | + | 14.9975i | −0.171751 | + | 0.514412i | ||||
\(851\) | −40.0236 | − | 23.1077i | −1.37199 | − | 0.792120i | ||||
\(852\) | −2.83766 | − | 2.05451i | −0.0972165 | − | 0.0703863i | ||||
\(853\) | 53.9165 | 1.84607 | 0.923033 | − | 0.384720i | \(-0.125702\pi\) | ||||
0.923033 | + | 0.384720i | \(0.125702\pi\) | |||||||
\(854\) | 8.11562 | − | 4.25871i | 0.277711 | − | 0.145730i | ||||
\(855\) | 32.4317 | − | 5.11240i | 1.10914 | − | 0.174840i | ||||
\(856\) | −2.73861 | − | 4.74342i | −0.0936039 | − | 0.162127i | ||||
\(857\) | 34.9545 | + | 20.1810i | 1.19402 | + | 0.689369i | 0.959216 | − | 0.282674i | \(-0.0912214\pi\) |
0.234805 | + | 0.972042i | \(0.424555\pi\) | |||||||
\(858\) | −0.254862 | + | 2.46408i | −0.00870085 | + | 0.0841223i | ||||
\(859\) | −15.5228 | + | 8.96208i | −0.529630 | + | 0.305782i | −0.740866 | − | 0.671653i | \(-0.765585\pi\) |
0.211236 | + | 0.977435i | \(0.432251\pi\) | |||||||
\(860\) | −3.50333 | − | 2.86045i | −0.119462 | − | 0.0975407i | ||||
\(861\) | −18.9982 | + | 24.1279i | −0.647456 | + | 0.822277i | ||||
\(862\) | − | 37.0576i | − | 1.26219i | ||||||
\(863\) | 7.76139 | + | 13.4431i | 0.264201 | + | 0.457609i | 0.967354 | − | 0.253429i | \(-0.0815585\pi\) |
−0.703153 | + | 0.711038i | \(0.748225\pi\) | |||||||
\(864\) | 3.84418 | − | 3.49604i | 0.130782 | − | 0.118938i | ||||
\(865\) | −24.0872 | + | 9.13469i | −0.818988 | + | 0.310589i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.94975 | + | 11.0680i | 0.168102 | + | 0.375888i | ||||
\(868\) | −0.0322079 | + | 0.797901i | −0.00109321 | + | 0.0270825i | ||||
\(869\) | − | 0.111571i | − | 0.00378480i | ||||||
\(870\) | −7.57156 | + | 2.00945i | −0.256700 | + | 0.0681267i | ||||
\(871\) | −30.9089 | − | 17.8453i | −1.04731 | − | 0.604664i | ||||
\(872\) | −6.21584 | + | 10.7661i | −0.210495 | + | 0.364588i | ||||
\(873\) | −10.2875 | − | 2.15110i | −0.348179 | − | 0.0728037i | ||||
\(874\) | − | 31.7017i | − | 1.07232i | ||||||
\(875\) | −25.6190 | + | 14.7875i | −0.866079 | + | 0.499908i | ||||
\(876\) | −8.47723 | − | 18.9557i | −0.286419 | − | 0.640452i | ||||
\(877\) | 36.6169 | − | 21.1408i | 1.23647 | − | 0.713874i | 0.268096 | − | 0.963392i | \(-0.413606\pi\) |
0.968370 | + | 0.249518i | \(0.0802723\pi\) | |||||||
\(878\) | −19.6931 | − | 11.3698i | −0.664609 | − | 0.383712i | ||||
\(879\) | −0.818370 | + | 7.91224i | −0.0276029 | + | 0.266873i | ||||
\(880\) | 0.0765585 | − | 0.471045i | 0.00258079 | − | 0.0158789i | ||||
\(881\) | 26.5004 | 0.892821 | 0.446411 | − | 0.894828i | \(-0.352702\pi\) | ||||
0.446411 | + | 0.894828i | \(0.352702\pi\) | |||||||
\(882\) | −15.2160 | + | 14.4731i | −0.512351 | + | 0.487336i | ||||
\(883\) | 29.2823i | 0.985428i | 0.870191 | + | 0.492714i | \(0.163995\pi\) | ||||
−0.870191 | + | 0.492714i | \(0.836005\pi\) | |||||||
\(884\) | 18.3526 | − | 10.5959i | 0.617264 | − | 0.356377i | ||||
\(885\) | 13.4993 | − | 13.4351i | 0.453775 | − | 0.451615i | ||||
\(886\) | 18.4772 | − | 32.0035i | 0.620755 | − | 1.07518i | ||||
\(887\) | 3.00000 | − | 1.73205i | 0.100730 | − | 0.0581566i | −0.448789 | − | 0.893638i | \(-0.648144\pi\) |
0.549519 | + | 0.835481i | \(0.314811\pi\) | |||||||
\(888\) | 11.2815 | − | 5.04524i | 0.378582 | − | 0.169307i | ||||
\(889\) | 30.4772 | + | 19.2755i | 1.02217 | + | 0.646479i | ||||
\(890\) | −14.9545 | + | 18.3154i | −0.501274 | + | 0.613933i | ||||
\(891\) | 1.13928 | + | 1.54645i | 0.0381673 | + | 0.0518079i | ||||
\(892\) | −3.19808 | + | 5.53924i | −0.107080 | + | 0.185468i | ||||
\(893\) | 18.9772 | − | 32.8695i | 0.635049 | − | 1.09994i | ||||
\(894\) | 3.43649 | + | 2.48808i | 0.114933 | + | 0.0832137i | ||||
\(895\) | −25.8255 | − | 21.0864i | −0.863251 | − | 0.704842i | ||||
\(896\) | 2.64360 | + | 0.106711i | 0.0883164 | + | 0.00356496i | ||||
\(897\) | −30.6931 | − | 68.6318i | −1.02481 | − | 2.29155i | ||||
\(898\) | 3.04546 | − | 1.75830i | 0.101628 | − | 0.0586752i | ||||
\(899\) | 0.305242 | − | 0.528694i | 0.0101804 | − | 0.0176329i | ||||
\(900\) | −13.0260 | + | 7.43794i | −0.434201 | + | 0.247931i | ||||
\(901\) | 13.6931 | − | 7.90569i | 0.456182 | − | 0.263377i | ||||
\(902\) | 1.43023i | 0.0476213i | ||||||||
\(903\) | 7.28238 | + | 5.73411i | 0.242342 | + | 0.190819i | ||||
\(904\) | 6.52277 | 0.216944 | ||||||||
\(905\) | 1.13437 | − | 6.97948i | 0.0377078 | − | 0.232006i | ||||
\(906\) | 3.44572 | + | 0.356394i | 0.114476 | + | 0.0118404i | ||||
\(907\) | 8.48528 | + | 4.89898i | 0.281749 | + | 0.162668i | 0.634215 | − | 0.773157i | \(-0.281323\pi\) |
−0.352466 | + | 0.935825i | \(0.614657\pi\) | |||||||
\(908\) | −9.00000 | + | 5.19615i | −0.298675 | + | 0.172440i | ||||
\(909\) | −22.6274 | + | 25.2982i | −0.750504 | + | 0.839089i | ||||
\(910\) | 38.8442 | + | 7.93335i | 1.28767 | + | 0.262988i | ||||
\(911\) | 15.1238i | 0.501073i | 0.968107 | + | 0.250537i | \(0.0806071\pi\) | ||||
−0.968107 | + | 0.250537i | \(0.919393\pi\) | |||||||
\(912\) | 6.86646 | + | 4.97143i | 0.227371 | + | 0.164620i | ||||
\(913\) | 1.78387 | − | 3.08976i | 0.0590375 | − | 0.102256i | ||||
\(914\) | 32.8322 | + | 18.9557i | 1.08599 | + | 0.626997i | ||||
\(915\) | −12.9675 | + | 3.44150i | −0.428692 | + | 0.113772i | ||||
\(916\) | − | 7.23003i | − | 0.238887i | ||||||
\(917\) | −15.9317 | − | 0.643094i | −0.526110 | − | 0.0212368i | ||||
\(918\) | 5.00000 | − | 15.6525i | 0.165025 | − | 0.516609i | ||||
\(919\) | 16.2158 | + | 28.0867i | 0.534911 | + | 0.926493i | 0.999168 | + | 0.0407925i | \(0.0129883\pi\) |
−0.464256 | + | 0.885701i | \(0.653678\pi\) | |||||||
\(920\) | 5.13575 | + | 13.5424i | 0.169321 | + | 0.446479i | ||||
\(921\) | −6.03574 | − | 0.624282i | −0.198884 | − | 0.0205708i | ||||
\(922\) | 8.14783 | + | 14.1125i | 0.268335 | + | 0.464769i | ||||
\(923\) | − | 13.5546i | − | 0.446155i | ||||||
\(924\) | −0.139776 | + | 0.967982i | −0.00459830 | + | 0.0318443i | ||||
\(925\) | −34.9545 | + | 7.13505i | −1.14930 | + | 0.234599i | ||||
\(926\) | −15.3071 | + | 8.83756i | −0.503023 | + | 0.290420i | ||||
\(927\) | −9.90283 | − | 30.1379i | −0.325252 | − | 0.989859i | ||||
\(928\) | −1.75166 | − | 1.01132i | −0.0575012 | − | 0.0331983i | ||||
\(929\) | −11.8360 | − | 20.5005i | −0.388326 | − | 0.672601i | 0.603898 | − | 0.797061i | \(-0.293613\pi\) |
−0.992225 | + | 0.124461i | \(0.960280\pi\) | |||||||
\(930\) | 0.305242 | − | 1.12840i | 0.0100093 | − | 0.0370018i | ||||
\(931\) | −28.1931 | − | 19.4658i | −0.923990 | − | 0.637967i | ||||
\(932\) | −4.00000 | −0.131024 | ||||||||
\(933\) | −29.3499 | + | 40.5377i | −0.960874 | + | 1.32714i | ||||
\(934\) | 29.7386 | + | 17.1696i | 0.973077 | + | 0.561806i | ||||
\(935\) | −0.535123 | − | 1.41106i | −0.0175004 | − | 0.0461465i | ||||
\(936\) | 19.6786 | + | 4.11478i | 0.643216 | + | 0.134496i | ||||
\(937\) | 22.6918 | 0.741310 | 0.370655 | − | 0.928771i | \(-0.379133\pi\) | ||||
0.370655 | + | 0.928771i | \(0.379133\pi\) | |||||||
\(938\) | −11.9089 | − | 7.53185i | −0.388839 | − | 0.245924i | ||||
\(939\) | −16.4317 | − | 36.7423i | −0.536228 | − | 1.19904i | ||||
\(940\) | −2.78179 | + | 17.1156i | −0.0907320 | + | 0.558250i | ||||
\(941\) | 2.49098 | − | 4.31450i | 0.0812036 | − | 0.140649i | −0.822564 | − | 0.568673i | \(-0.807457\pi\) |
0.903767 | + | 0.428024i | \(0.140790\pi\) | |||||||
\(942\) | 15.1448 | + | 1.56644i | 0.493445 | + | 0.0510375i | ||||
\(943\) | −21.7033 | − | 37.5912i | −0.706756 | − | 1.22414i | ||||
\(944\) | 4.91754 | 0.160052 | ||||||||
\(945\) | 26.4212 | − | 15.7137i | 0.859482 | − | 0.511165i | ||||
\(946\) | 0.431677 | 0.0140350 | ||||||||
\(947\) | 16.4317 | + | 28.4605i | 0.533958 | + | 0.924842i | 0.999213 | + | 0.0396654i | \(0.0126292\pi\) |
−0.465255 | + | 0.885177i | \(0.654037\pi\) | |||||||
\(948\) | −0.900667 | − | 0.0931568i | −0.0292523 | − | 0.00302559i | ||||
\(949\) | 40.1703 | − | 69.5770i | 1.30398 | − | 2.25856i | ||||
\(950\) | −16.2272 | − | 18.3177i | −0.526481 | − | 0.594305i | ||||
\(951\) | 23.9772 | + | 53.6147i | 0.777514 | + | 1.73858i | ||||
\(952\) | 7.40852 | − | 3.88766i | 0.240111 | − | 0.126000i | ||||
\(953\) | 25.0455 | 0.811305 | 0.405652 | − | 0.914027i | \(-0.367044\pi\) | ||||
0.405652 | + | 0.914027i | \(0.367044\pi\) | |||||||
\(954\) | 14.6825 | + | 3.07008i | 0.475362 | + | 0.0993976i | ||||
\(955\) | −3.33646 | + | 1.26530i | −0.107965 | + | 0.0409442i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.438477 | − | 0.605617i | 0.0141739 | − | 0.0195768i | ||||
\(958\) | −11.3781 | −0.367611 | ||||||||
\(959\) | −9.19239 | − | 17.5175i | −0.296838 | − | 0.565669i | ||||
\(960\) | −3.73861 | − | 1.01132i | −0.120663 | − | 0.0326403i | ||||
\(961\) | −15.4545 | − | 26.7679i | −0.498531 | − | 0.863480i | ||||
\(962\) | 41.4089 | + | 23.9074i | 1.33508 | + | 0.770807i | ||||
\(963\) | −5.12938 | − | 15.6106i | −0.165292 | − | 0.503043i | ||||
\(964\) | −3.45445 | + | 1.99443i | −0.111260 | + | 0.0642362i | ||||
\(965\) | −12.7279 | − | 10.3923i | −0.409726 | − | 0.334540i | ||||
\(966\) | −11.0151 | − | 27.5629i | −0.354403 | − | 0.886821i | ||||
\(967\) | 46.4287i | 1.49305i | 0.665359 | + | 0.746524i | \(0.268279\pi\) | ||||
−0.665359 | + | 0.746524i | \(0.731721\pi\) | |||||||
\(968\) | −5.47723 | − | 9.48683i | −0.176045 | − | 0.304918i | ||||
\(969\) | 26.6651 | + | 2.75799i | 0.856606 | + | 0.0885996i | ||||
\(970\) | 2.77776 | + | 7.32465i | 0.0891886 | + | 0.235180i | ||||
\(971\) | −0.490070 | − | 0.848827i | −0.0157271 | − | 0.0272401i | 0.858055 | − | 0.513558i | \(-0.171673\pi\) |
−0.873782 | + | 0.486318i | \(0.838340\pi\) | |||||||
\(972\) | 13.4350 | − | 7.90569i | 0.430929 | − | 0.253575i | ||||
\(973\) | −16.8417 | − | 10.6516i | −0.539921 | − | 0.341476i | ||||
\(974\) | 36.6308i | 1.17373i | ||||||||
\(975\) | −52.8657 | − | 23.9456i | −1.69306 | − | 0.766872i | ||||
\(976\) | −3.00000 | − | 1.73205i | −0.0960277 | − | 0.0554416i | ||||
\(977\) | 19.9545 | − | 34.5621i | 0.638399 | − | 1.10574i | −0.347385 | − | 0.937723i | \(-0.612930\pi\) |
0.985784 | − | 0.168018i | \(-0.0537365\pi\) | |||||||
\(978\) | −20.6190 | − | 14.9285i | −0.659321 | − | 0.477359i | ||||
\(979\) | − | 2.25681i | − | 0.0721278i | ||||||
\(980\) | 15.1971 | + | 3.74812i | 0.485453 | + | 0.119729i | ||||
\(981\) | −24.8634 | + | 27.7981i | −0.793826 | + | 0.887524i | ||||
\(982\) | 3.50333 | − | 2.02265i | 0.111796 | − | 0.0645452i | ||||
\(983\) | −29.2842 | − | 16.9072i | −0.934020 | − | 0.539257i | −0.0459391 | − | 0.998944i | \(-0.514628\pi\) |
−0.888081 | + | 0.459688i | \(0.847961\pi\) | |||||||
\(984\) | 11.5456 | + | 1.19417i | 0.368060 | + | 0.0380688i | ||||
\(985\) | 19.8640 | + | 3.22848i | 0.632918 | + | 0.102868i | ||||
\(986\) | −6.39617 | −0.203696 | ||||||||
\(987\) | 5.07883 | − | 35.1721i | 0.161661 | − | 1.11954i | ||||
\(988\) | 32.7989i | 1.04347i | ||||||||
\(989\) | −11.3459 | + | 6.55057i | −0.360779 | + | 0.208296i | ||||
\(990\) | 0.514043 | − | 1.33621i | 0.0163374 | − | 0.0424676i | ||||
\(991\) | −10.7386 | + | 18.5998i | −0.341123 | + | 0.590843i | −0.984642 | − | 0.174588i | \(-0.944141\pi\) |
0.643518 | + | 0.765431i | \(0.277474\pi\) | |||||||
\(992\) | 0.261387 | − | 0.150912i | 0.00829905 | − | 0.00479146i | ||||
\(993\) | −8.08342 | − | 18.0751i | −0.256519 | − | 0.573595i | ||||
\(994\) | 0.215838 | − | 5.34706i | 0.00684598 | − | 0.169599i | ||||
\(995\) | −38.8634 | − | 31.7318i | −1.23205 | − | 1.00597i | ||||
\(996\) | −23.4528 | − | 16.9802i | −0.743130 | − | 0.538038i | ||||
\(997\) | 7.74597 | − | 13.4164i | 0.245317 | − | 0.424902i | −0.716904 | − | 0.697172i | \(-0.754441\pi\) |
0.962221 | + | 0.272270i | \(0.0877745\pi\) | |||||||
\(998\) | 20.9545 | − | 36.2942i | 0.663302 | − | 1.14887i | ||||
\(999\) | 36.2259 | − | 7.88828i | 1.14614 | − | 0.249574i |
(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 | 210.2.t.e.59.1 | ✓ | 8 | |
3.2 | odd | 2 | 210.2.t.f.59.3 | yes | 8 | ||
5.2 | odd | 4 | 1050.2.s.i.101.6 | 16 | |||
5.3 | odd | 4 | 1050.2.s.i.101.3 | 16 | |||
5.4 | even | 2 | 210.2.t.f.59.4 | yes | 8 | ||
7.3 | odd | 6 | 1470.2.d.f.1469.1 | 8 | |||
7.4 | even | 3 | 1470.2.d.f.1469.8 | 8 | |||
7.5 | odd | 6 | inner | 210.2.t.e.89.2 | yes | 8 | |
15.2 | even | 4 | 1050.2.s.i.101.4 | 16 | |||
15.8 | even | 4 | 1050.2.s.i.101.5 | 16 | |||
15.14 | odd | 2 | inner | 210.2.t.e.59.2 | yes | 8 | |
21.5 | even | 6 | 210.2.t.f.89.4 | yes | 8 | ||
21.11 | odd | 6 | 1470.2.d.e.1469.5 | 8 | |||
21.17 | even | 6 | 1470.2.d.e.1469.4 | 8 | |||
35.4 | even | 6 | 1470.2.d.e.1469.1 | 8 | |||
35.12 | even | 12 | 1050.2.s.i.551.4 | 16 | |||
35.19 | odd | 6 | 210.2.t.f.89.3 | yes | 8 | ||
35.24 | odd | 6 | 1470.2.d.e.1469.8 | 8 | |||
35.33 | even | 12 | 1050.2.s.i.551.5 | 16 | |||
105.47 | odd | 12 | 1050.2.s.i.551.6 | 16 | |||
105.59 | even | 6 | 1470.2.d.f.1469.5 | 8 | |||
105.68 | odd | 12 | 1050.2.s.i.551.3 | 16 | |||
105.74 | odd | 6 | 1470.2.d.f.1469.4 | 8 | |||
105.89 | even | 6 | inner | 210.2.t.e.89.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.t.e.59.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
210.2.t.e.59.2 | yes | 8 | 15.14 | odd | 2 | inner | |
210.2.t.e.89.1 | yes | 8 | 105.89 | even | 6 | inner | |
210.2.t.e.89.2 | yes | 8 | 7.5 | odd | 6 | inner | |
210.2.t.f.59.3 | yes | 8 | 3.2 | odd | 2 | ||
210.2.t.f.59.4 | yes | 8 | 5.4 | even | 2 | ||
210.2.t.f.89.3 | yes | 8 | 35.19 | odd | 6 | ||
210.2.t.f.89.4 | yes | 8 | 21.5 | even | 6 | ||
1050.2.s.i.101.3 | 16 | 5.3 | odd | 4 | |||
1050.2.s.i.101.4 | 16 | 15.2 | even | 4 | |||
1050.2.s.i.101.5 | 16 | 15.8 | even | 4 | |||
1050.2.s.i.101.6 | 16 | 5.2 | odd | 4 | |||
1050.2.s.i.551.3 | 16 | 105.68 | odd | 12 | |||
1050.2.s.i.551.4 | 16 | 35.12 | even | 12 | |||
1050.2.s.i.551.5 | 16 | 35.33 | even | 12 | |||
1050.2.s.i.551.6 | 16 | 105.47 | odd | 12 | |||
1470.2.d.e.1469.1 | 8 | 35.4 | even | 6 | |||
1470.2.d.e.1469.4 | 8 | 21.17 | even | 6 | |||
1470.2.d.e.1469.5 | 8 | 21.11 | odd | 6 | |||
1470.2.d.e.1469.8 | 8 | 35.24 | odd | 6 | |||
1470.2.d.f.1469.1 | 8 | 7.3 | odd | 6 | |||
1470.2.d.f.1469.4 | 8 | 105.74 | odd | 6 | |||
1470.2.d.f.1469.5 | 8 | 105.59 | even | 6 | |||
1470.2.d.f.1469.8 | 8 | 7.4 | even | 3 |