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 | 59.4 | ||
Root | \(1.01575 - 1.40294i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.59 |
Dual form | 210.2.t.f.89.4 |
$q$-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 | ||||
\(5\) | −0.792893 | + | 2.09077i | −0.354593 | + | 0.935021i | ||||
\(6\) | 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 | ||||
\(10\) | −2.20711 | + | 0.358719i | −0.697948 | + | 0.113437i | ||||
\(11\) | 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 | \(-0.879605\pi\) | ||||
−0.929318 | + | 0.369279i | \(0.879605\pi\) | |||||||
\(14\) | 2.64360 | + | 0.106711i | 0.706531 | + | 0.0285197i | ||||
\(15\) | −1.73861 | + | 3.46081i | −0.448908 | + | 0.893578i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 2.73861 | + | 1.58114i | 0.664211 | + | 0.383482i | 0.793880 | − | 0.608075i | \(-0.208058\pi\) |
−0.129668 | + | 0.991557i | \(0.541391\pi\) | |||||||
\(18\) | 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 | \(-0.930682\pi\) |
0.301084 | − | 0.953597i | \(-0.402651\pi\) | |||||||
\(24\) | −1.72286 | − | 0.178197i | −0.351677 | − | 0.0363743i | ||||
\(25\) | −3.74264 | − | 3.31552i | −0.748528 | − | 0.663103i | ||||
\(26\) | −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 | \(0.939865\pi\) | |||||||
\(30\) | −3.86646 | + | 0.224724i | −0.705915 | + | 0.0410287i | ||||
\(31\) | −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 | ||||||||
\(35\) | 3.55378 | + | 4.72976i | 0.600699 | + | 0.799475i | ||||
\(36\) | −2.00000 | + | 2.23607i | −0.333333 | + | 0.372678i | ||||
\(37\) | 6.17913 | − | 3.56752i | 1.01584 | − | 0.586497i | 0.102946 | − | 0.994687i | \(-0.467173\pi\) |
0.912897 | + | 0.408190i | \(0.133840\pi\) | |||||||
\(38\) | 4.23861 | + | 2.44716i | 0.687594 | + | 0.396982i | ||||
\(39\) | −11.5456 | − | 1.19417i | −1.84877 | − | 0.191220i | ||||
\(40\) | 0.792893 | − | 2.09077i | 0.125367 | − | 0.330580i | ||||
\(41\) | −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 | \(-0.950712\pi\) | ||
0.988036 | − | 0.154225i | \(-0.0492882\pi\) | |||||||
\(44\) | −0.184829 | + | 0.106711i | −0.0278640 | + | 0.0160873i | ||||
\(45\) | −3.61209 | + | 5.65268i | −0.538459 | + | 0.842652i | ||||
\(46\) | 3.23861 | − | 5.60944i | 0.477507 | − | 0.827067i | ||||
\(47\) | −6.71584 | + | 3.87739i | −0.979606 | + | 0.565576i | −0.902151 | − | 0.431420i | \(-0.858013\pi\) |
−0.0774546 | + | 0.996996i | \(0.524679\pi\) | |||||||
\(48\) | −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 | −0.641661 | − | 0.766989i | \(-0.721754\pi\) |
0.985062 | + | 0.172200i | \(0.0550875\pi\) | |||||||
\(54\) | 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 | \(0.270385\pi\) | |||||||
\(60\) | −2.12785 | − | 3.23609i | −0.274704 | − | 0.417777i | ||||
\(61\) | 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 | ||||||||
\(65\) | 5.31350 | − | 14.0111i | 0.659059 | − | 1.73786i | ||||
\(66\) | −0.0380311 | + | 0.367696i | −0.00468131 | + | 0.0452602i | ||||
\(67\) | 4.61230 | + | 2.66291i | 0.563482 | + | 0.325326i | 0.754542 | − | 0.656252i | \(-0.227859\pi\) |
−0.191060 | + | 0.981578i | \(0.561192\pi\) | |||||||
\(68\) | −2.73861 | + | 1.58114i | −0.332106 | + | 0.191741i | ||||
\(69\) | −4.58009 | − | 10.2414i | −0.551378 | − | 1.23292i | ||||
\(70\) | −2.31920 | + | 5.44255i | −0.277197 | + | 0.650509i | ||||
\(71\) | − | 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 | \(0.414188\pi\) |
−0.967912 | + | 0.251291i | \(0.919145\pi\) | |||||||
\(74\) | 6.17913 | + | 3.56752i | 0.718310 | + | 0.414716i | ||||
\(75\) | −5.85723 | − | 6.37909i | −0.676335 | − | 0.736594i | ||||
\(76\) | 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 | \(0.842696\pi\) | |||||||
\(80\) | 2.20711 | − | 0.358719i | 0.246762 | − | 0.0401061i | ||||
\(81\) | 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 | \(0.369762\pi\) | ||||
−0.397835 | + | 0.917457i | \(0.630238\pi\) | |||||||
\(84\) | 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 | \(-0.356035\pi\) | |||||||
\(90\) | −6.70141 | − | 0.301824i | −0.706391 | − | 0.0318150i | ||||
\(91\) | −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 | ||||
\(95\) | 1.75569 | + | 10.8023i | 0.180130 | + | 1.10829i | ||||
\(96\) | 1.01575 | − | 1.40294i | 0.103670 | − | 0.143187i | ||||
\(97\) | 3.50333 | 0.355709 | 0.177854 | − | 0.984057i | \(-0.443084\pi\) | ||||
0.177854 | + | 0.984057i | \(0.443084\pi\) | |||||||
\(98\) | 3.97723 | − | 5.76035i | 0.401760 | − | 0.581884i | ||||
\(99\) | 0.477226 | + | 0.426844i | 0.0479630 | + | 0.0428994i | ||||
\(100\) | 4.74264 | − | 1.58346i | 0.474264 | − | 0.158346i | ||||
\(101\) | −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 | \(0.00776038\pi\) |
−0.478740 | + | 0.877957i | \(0.658906\pi\) | |||||||
\(104\) | 6.70141 | 0.657127 | ||||||||
\(105\) | 5.27984 | + | 8.78198i | 0.515260 | + | 0.857034i | ||||
\(106\) | 5.00000 | 0.485643 | ||||||||
\(107\) | 2.73861 | + | 4.74342i | 0.264752 | + | 0.458563i | 0.967499 | − | 0.252877i | \(-0.0813767\pi\) |
−0.702747 | + | 0.711440i | \(0.748043\pi\) | |||||||
\(108\) | −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 | \(0.963672\pi\) | |||||||
\(110\) | −0.446216 | − | 0.169221i | −0.0425450 | − | 0.0161346i | ||||
\(111\) | 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 | \(-0.599260\pi\) | ||||
−0.306806 | + | 0.951772i | \(0.599260\pi\) | |||||||
\(114\) | 6.86646 | + | 4.97143i | 0.643103 | + | 0.465617i | ||||
\(115\) | 14.2959 | − | 2.32351i | 1.33310 | − | 0.216668i | ||||
\(116\) | −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 | ||||
\(120\) | 1.73861 | − | 3.46081i | 0.158713 | − | 0.315928i | ||||
\(121\) | −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 | \(0.206717\pi\) | ||||
−0.796434 | + | 0.604726i | \(0.793283\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 0.360429 | − | 3.48474i | 0.0317340 | − | 0.306814i | ||||
\(130\) | 14.7907 | − | 2.40393i | 1.29723 | − | 0.210838i | ||||
\(131\) | 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 | ||||||||
\(135\) | −7.23042 | + | 9.09511i | −0.622295 | + | 0.782782i | ||||
\(136\) | −2.73861 | − | 1.58114i | −0.234834 | − | 0.135582i | ||||
\(137\) | 3.73861 | − | 6.47547i | 0.319411 | − | 0.553237i | −0.660954 | − | 0.750426i | \(-0.729848\pi\) |
0.980365 | + | 0.197190i | \(0.0631815\pi\) | |||||||
\(138\) | 6.57926 | − | 9.08717i | 0.560064 | − | 0.773551i | ||||
\(139\) | 7.53185i | 0.638843i | 0.947613 | + | 0.319422i | \(0.103489\pi\) | ||||
−0.947613 | + | 0.319422i | \(0.896511\pi\) | |||||||
\(140\) | −5.87298 | + | 0.712788i | −0.496358 | + | 0.0602416i | ||||
\(141\) | −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 | ||||
\(145\) | −4.22889 | − | 1.60374i | −0.351190 | − | 0.133184i | ||||
\(146\) | −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 | \(0.301342\pi\) | |||||||
\(150\) | 2.59584 | − | 8.26206i | 0.211950 | − | 0.674594i | ||||
\(151\) | 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 | −0.986386 | − | 0.164445i | \(-0.947417\pi\) |
0.635606 | + | 0.772013i | \(0.280750\pi\) | |||||||
\(158\) | 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 | 0.0895899 | − | 0.995979i | \(-0.471444\pi\) |
0.907338 | + | 0.420402i | \(0.138111\pi\) | |||||||
\(164\) | 3.35071 | − | 5.80359i | 0.261646 | − | 0.453184i | ||||
\(165\) | −0.690652 | + | 0.454129i | −0.0537672 | + | 0.0353539i | ||||
\(166\) | −14.4772 | + | 8.35843i | −1.12365 | + | 0.648740i | ||||
\(167\) | − | 14.6830i | − | 1.13620i | −0.822958 | − | 0.568102i | \(-0.807678\pi\) | ||
0.822958 | − | 0.568102i | \(-0.192322\pi\) | |||||||
\(168\) | −2.83495 | + | 3.60042i | −0.218721 | + | 0.277779i | ||||
\(169\) | 31.9089 | 2.45453 | ||||||||
\(170\) | −6.61160 | − | 2.50735i | −0.507086 | − | 0.192305i | ||||
\(171\) | 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 | −0.0702221 | − | 0.997531i | \(-0.522371\pi\) |
0.828776 | + | 0.559580i | \(0.189037\pi\) | |||||||
\(174\) | −3.19808 | + | 1.43023i | −0.242446 | + | 0.108425i | ||||
\(175\) | −12.7066 | + | 3.67995i | −0.960529 | + | 0.278178i | ||||
\(176\) | − | 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 | \(0.854801\pi\) | |||||||
\(180\) | −3.08932 | − | 5.95450i | −0.230264 | − | 0.443823i | ||||
\(181\) | − | 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 | ||||
\(185\) | 2.55948 | + | 15.7478i | 0.188177 | + | 1.15780i | ||||
\(186\) | 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 | 0.711240 | − | 0.702949i | \(-0.248134\pi\) |
−0.253152 | + | 0.967427i | \(0.581467\pi\) | |||||||
\(194\) | 1.75166 | + | 3.03397i | 0.125762 | + | 0.217826i | ||||
\(195\) | 11.6512 | − | 23.1923i | 0.834357 | − | 1.66084i | ||||
\(196\) | 6.97723 | + | 0.564201i | 0.498373 | + | 0.0403001i | ||||
\(197\) | −9.00000 | −0.641223 | −0.320612 | − | 0.947211i | \(-0.603888\pi\) | ||||
−0.320612 | + | 0.947211i | \(0.603888\pi\) | |||||||
\(198\) | −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 | \(0.959346\pi\) | |||||||
\(200\) | 3.74264 | + | 3.31552i | 0.264645 | + | 0.234442i | ||||
\(201\) | 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 | ||||
\(205\) | 5.31350 | − | 14.0111i | 0.371111 | − | 0.978578i | ||||
\(206\) | −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 | ||||||||
\(210\) | −4.96550 | + | 8.96347i | −0.342652 | + | 0.618538i | ||||
\(211\) | 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 | ||||
\(215\) | 4.22889 | + | 1.60374i | 0.288408 | + | 0.109374i | ||||
\(216\) | −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 | ||||
\(220\) | −0.0765585 | − | 0.471045i | −0.00516158 | − | 0.0317578i | ||||
\(221\) | −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 | \(-0.568701\pi\) | ||||
−0.214160 | + | 0.976799i | \(0.568701\pi\) | |||||||
\(224\) | −1.22938 | − | 2.34278i | −0.0821417 | − | 0.156533i | ||||
\(225\) | −8.95445 | − | 12.0340i | −0.596963 | − | 0.802268i | ||||
\(226\) | −3.26139 | − | 5.64889i | −0.216944 | − | 0.375758i | ||||
\(227\) | −9.00000 | − | 5.19615i | −0.597351 | − | 0.344881i | 0.170648 | − | 0.985332i | \(-0.445414\pi\) |
−0.767999 | + | 0.640451i | \(0.778747\pi\) | |||||||
\(228\) | −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 | 0.793047 | − | 0.609160i | \(-0.208493\pi\) |
−0.924072 | + | 0.382219i | \(0.875160\pi\) | |||||||
\(234\) | −6.27582 | − | 19.0996i | −0.410263 | − | 1.24858i | ||||
\(235\) | −2.78179 | − | 17.1156i | −0.181464 | − | 1.11650i | ||||
\(236\) | −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 | \(\pi\) | |||||||||
\(240\) | 3.86646 | − | 0.224724i | 0.249579 | − | 0.0145058i | ||||
\(241\) | 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 | ||||||||
\(245\) | 15.6019 | − | 1.25761i | 0.996767 | − | 0.0803460i | ||||
\(246\) | −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 | ||||
\(250\) | 9.44975 | + | 5.97514i | 0.597655 | + | 0.377901i | ||||
\(251\) | 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 | ||||
\(255\) | −10.2334 | + | 6.72884i | −0.640841 | + | 0.421376i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 20.4772 | − | 11.8225i | 1.27733 | − | 0.737469i | 0.300977 | − | 0.953631i | \(-0.402687\pi\) |
0.976357 | + | 0.216162i | \(0.0693540\pi\) | |||||||
\(258\) | 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 | −0.895209 | − | 0.445647i | \(-0.852974\pi\) |
0.833546 | + | 0.552450i | \(0.186307\pi\) | |||||||
\(264\) | −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 | \(-0.176376\pi\) | |||||||
\(270\) | −11.4918 | − | 1.71417i | −0.699369 | − | 0.104321i | ||||
\(271\) | 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 | ||||||||
\(275\) | −0.337946 | − | 1.01218i | −0.0203789 | − | 0.0610369i | ||||
\(276\) | 11.1594 | + | 1.15422i | 0.671714 | + | 0.0694760i | ||||
\(277\) | −8.48528 | − | 4.89898i | −0.509831 | − | 0.294351i | 0.222933 | − | 0.974834i | \(-0.428437\pi\) |
−0.732764 | + | 0.680483i | \(0.761770\pi\) | |||||||
\(278\) | −6.52277 | + | 3.76593i | −0.391210 | + | 0.225865i | ||||
\(279\) | −0.674899 | − | 0.603648i | −0.0404051 | − | 0.0361395i | ||||
\(280\) | −3.55378 | − | 4.72976i | −0.212379 | − | 0.282657i | ||||
\(281\) | − | 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 | \(-0.570693\pi\) |
0.954889 | − | 0.296964i | \(-0.0959741\pi\) | |||||||
\(284\) | 1.75166 | + | 1.01132i | 0.103942 | + | 0.0600110i | ||||
\(285\) | 1.09987 | + | 18.9237i | 0.0651507 | + | 1.12094i | ||||
\(286\) | − | 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 | ||||
\(290\) | −0.725563 | − | 4.46420i | −0.0426065 | − | 0.262147i | ||||
\(291\) | 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 | \(0.0428299\pi\) | ||||
−0.990961 | + | 0.134148i | \(0.957170\pi\) | |||||||
\(294\) | 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 | ||||
\(300\) | 8.45307 | − | 1.88296i | 0.488038 | − | 0.108713i | ||||
\(301\) | −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 | ||||
\(305\) | 1.24264 | + | 7.64564i | 0.0711534 | + | 0.437788i | ||||
\(306\) | −1.94169 | + | 9.28600i | −0.110999 | + | 0.530845i | ||||
\(307\) | −3.50333 | −0.199945 | −0.0999727 | − | 0.994990i | \(-0.531876\pi\) | ||||
−0.0999727 | + | 0.994990i | \(0.531876\pi\) | |||||||
\(308\) | −0.0227744 | + | 0.564201i | −0.00129769 | + | 0.0321484i | ||||
\(309\) | 7.47723 | + | 16.7196i | 0.425365 | + | 0.951144i | ||||
\(310\) | 0.631045 | + | 0.239314i | 0.0358409 | + | 0.0135921i | ||||
\(311\) | 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 | \(-0.938601\pi\) |
0.324712 | − | 0.945813i | \(-0.394733\pi\) | |||||||
\(314\) | −8.79052 | −0.496078 | ||||||||
\(315\) | 7.53151 | + | 16.0710i | 0.424352 | + | 0.905497i | ||||
\(316\) | 0.522774 | 0.0294084 | ||||||||
\(317\) | 16.9545 | + | 29.3660i | 0.952257 | + | 1.64936i | 0.740524 | + | 0.672030i | \(0.234577\pi\) |
0.211733 | + | 0.977328i | \(0.432089\pi\) | |||||||
\(318\) | 8.61430 | + | 0.890985i | 0.483066 | + | 0.0499640i | ||||
\(319\) | −0.215838 | + | 0.373843i | −0.0120846 | + | 0.0209312i | ||||
\(320\) | −0.792893 | + | 2.09077i | −0.0443241 | + | 0.116878i | ||||
\(321\) | 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 | ||||
\(325\) | 25.0810 | + | 22.2186i | 1.39124 | + | 1.23247i | ||||
\(326\) | 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 | ||||
\(330\) | −0.738613 | − | 0.371058i | −0.0406593 | − | 0.0204261i | ||||
\(331\) | 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 | \(0.154670\pi\) | ||||
−0.884251 | + | 0.467013i | \(0.845330\pi\) | |||||||
\(338\) | 15.9545 | + | 27.6339i | 0.867808 | + | 1.50309i | ||||
\(339\) | −11.2378 | − | 1.16234i | −0.610355 | − | 0.0631296i | ||||
\(340\) | −1.13437 | − | 6.97948i | −0.0615199 | − | 0.378516i | ||||
\(341\) | −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 | ||||||||
\(345\) | 25.0439 | − | 1.45559i | 1.34832 | − | 0.0783661i | ||||
\(346\) | 9.97723 | + | 5.76035i | 0.536379 | + | 0.309679i | ||||
\(347\) | −3.26139 | + | 5.64889i | −0.175080 | + | 0.303248i | −0.940189 | − | 0.340653i | \(-0.889352\pi\) |
0.765109 | + | 0.643901i | \(0.222685\pi\) | |||||||
\(348\) | −2.83766 | − | 2.05451i | −0.152114 | − | 0.110133i | ||||
\(349\) | 32.5282i | 1.74120i | 0.491994 | + | 0.870599i | \(0.336268\pi\) | ||||
−0.491994 | + | 0.870599i | \(0.663732\pi\) | |||||||
\(350\) | −9.54024 | − | 9.16427i | −0.509947 | − | 0.489851i | ||||
\(351\) | −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 | 0.162435 | − | 0.986719i | \(-0.448065\pi\) |
−0.773306 | + | 0.634033i | \(0.781398\pi\) | |||||||
\(354\) | −8.47223 | − | 0.876291i | −0.450294 | − | 0.0465743i | ||||
\(355\) | 4.22889 | + | 1.60374i | 0.224446 | + | 0.0851178i | ||||
\(356\) | 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 | \(0.278507\pi\) | |||||||
\(360\) | 3.61209 | − | 5.65268i | 0.190374 | − | 0.297922i | ||||
\(361\) | 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 | −0.740467 | − | 0.672093i | \(-0.765396\pi\) |
0.952283 | + | 0.305217i | \(0.0987289\pi\) | |||||||
\(368\) | −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 | −0.416674 | − | 0.909056i | \(-0.636804\pi\) |
0.578929 | + | 0.815378i | \(0.303471\pi\) | |||||||
\(374\) | −0.337449 | + | 0.584480i | −0.0174491 | + | 0.0302227i | ||||
\(375\) | 17.9814 | − | 7.18818i | 0.928554 | − | 0.371196i | ||||
\(376\) | 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 | \(0.578649\pi\) | |||||||
\(380\) | −10.2329 | − | 3.88068i | −0.524938 | − | 0.199075i | ||||
\(381\) | −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 | −0.481600 | − | 0.876391i | \(-0.659944\pi\) |
0.518177 | + | 0.855273i | \(0.326611\pi\) | |||||||
\(384\) | 0.707107 | + | 1.58114i | 0.0360844 | + | 0.0806872i | ||||
\(385\) | 0.152124 | + | 1.25342i | 0.00775298 | + | 0.0638803i | ||||
\(386\) | 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 | \(0.726313\pi\) | |||||||
\(390\) | 25.9107 | − | 1.50596i | 1.31204 | − | 0.0762575i | ||||
\(391\) | − | 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 | ||||
\(395\) | 1.15382 | − | 0.187529i | 0.0580549 | − | 0.00943563i | ||||
\(396\) | −0.608270 | + | 0.199868i | −0.0305667 | + | 0.0100437i | ||||
\(397\) | 15.1867 | + | 26.3041i | 0.762198 | + | 1.32017i | 0.941715 | + | 0.336411i | \(0.109213\pi\) |
−0.179517 | + | 0.983755i | \(0.557453\pi\) | |||||||
\(398\) | − | 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 | ||||
\(405\) | −14.0777 | + | 14.3812i | −0.699528 | + | 0.714606i | ||||
\(406\) | −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 | \(0.853848\pi\) | |||||||
\(410\) | 14.7907 | − | 2.40393i | 0.730462 | − | 0.118721i | ||||
\(411\) | 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 | ||||
\(415\) | −34.9511 | − | 13.2547i | −1.71568 | − | 0.650647i | ||||
\(416\) | −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 | \(0.632904\pi\) | |||||||
\(420\) | −10.2453 | + | 0.181486i | −0.499922 | + | 0.00885560i | ||||
\(421\) | −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 | ||||
\(425\) | −5.00735 | − | 14.9975i | −0.242892 | − | 0.727488i | ||||
\(426\) | 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 | ||||
\(430\) | 0.725563 | + | 4.46420i | 0.0349897 | + | 0.215283i | ||||
\(431\) | 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 | ||||
\(435\) | −7.00000 | − | 3.51660i | −0.335624 | − | 0.168608i | ||||
\(436\) | −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 | \(-0.825624\pi\) |
−0.0242161 | − | 0.999707i | \(-0.507709\pi\) | |||||||
\(444\) | −1.27144 | + | 12.2927i | −0.0603401 | + | 0.583385i | ||||
\(445\) | 23.3388 | − | 3.79324i | 1.10637 | − | 0.179817i | ||||
\(446\) | −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 | \(0.973556\pi\) | |||||||
\(450\) | 5.94455 | − | 13.7718i | 0.280229 | − | 0.649209i | ||||
\(451\) | −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 | ||||||
\(455\) | −23.8154 | − | 31.6961i | −1.11648 | − | 1.48593i | ||||
\(456\) | −7.73861 | + | 3.46081i | −0.362394 | + | 0.162067i | ||||
\(457\) | 32.8322 | − | 18.9557i | 1.53582 | − | 0.886708i | 0.536747 | − | 0.843743i | \(-0.319653\pi\) |
0.999077 | − | 0.0429646i | \(-0.0136803\pi\) | |||||||
\(458\) | −6.26139 | − | 3.61501i | −0.292575 | − | 0.168918i | ||||
\(459\) | 11.0554 | + | 12.1564i | 0.516024 | + | 0.567411i | ||||
\(460\) | −5.13575 | + | 13.5424i | −0.239455 | + | 0.631417i | ||||
\(461\) | −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 | \(0.134721\pi\) | ||||
−0.911763 | + | 0.410716i | \(0.865279\pi\) | |||||||
\(464\) | 1.75166 | − | 1.01132i | 0.0813189 | − | 0.0469495i | ||||
\(465\) | 0.976729 | − | 0.642235i | 0.0452947 | − | 0.0297829i | ||||
\(466\) | 2.00000 | − | 3.46410i | 0.0926482 | − | 0.160471i | ||||
\(467\) | 29.7386 | − | 17.1696i | 1.37614 | − | 0.794514i | 0.384447 | − | 0.923147i | \(-0.374392\pi\) |
0.991692 | + | 0.128633i | \(0.0410589\pi\) | |||||||
\(468\) | 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 | \(0.0829639\pi\) | |||||||
\(480\) | 2.12785 | + | 3.23609i | 0.0971224 | + | 0.147707i | ||||
\(481\) | −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 | ||||||||
\(485\) | −2.77776 | + | 7.32465i | −0.126132 | + | 0.332595i | ||||
\(486\) | 0.129018 | + | 15.5879i | 0.00585235 | + | 0.707083i | ||||
\(487\) | 31.7232 | + | 18.3154i | 1.43751 | + | 0.829949i | 0.997677 | − | 0.0681277i | \(-0.0217025\pi\) |
0.439838 | + | 0.898077i | \(0.355036\pi\) | |||||||
\(488\) | −3.00000 | + | 1.73205i | −0.135804 | + | 0.0784063i | ||||
\(489\) | 23.2379 | − | 10.3923i | 1.05085 | − | 0.469956i | ||||
\(490\) | 8.89006 | + | 12.8828i | 0.401612 | + | 0.581986i | ||||
\(491\) | 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 | ||||
\(495\) | −1.27082 | + | 0.659328i | −0.0571191 | + | 0.0296346i | ||||
\(496\) | 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 | \(0.445963\pi\) | |||||||
\(500\) | −0.449747 | + | 11.1713i | −0.0201133 | + | 0.499595i | ||||
\(501\) | 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 | \(0.166749\pi\) | ||||
−0.865895 | + | 0.500225i | \(0.833251\pi\) | |||||||
\(504\) | −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 | \(0.767797\pi\) | |||||||
\(510\) | −10.9441 | − | 5.49798i | −0.484611 | − | 0.243454i | ||||
\(511\) | 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 | ||||
\(515\) | −23.3388 | + | 3.79324i | −1.02843 | + | 0.167150i | ||||
\(516\) | 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 | ||||
\(520\) | −5.31350 | + | 14.0111i | −0.233013 | + | 0.614428i | ||||
\(521\) | −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 | 0.977878 | − | 0.209175i | \(-0.0670780\pi\) |
−0.670090 | + | 0.742280i | \(0.733745\pi\) | |||||||
\(524\) | −6.02651 | −0.263269 | ||||||||
\(525\) | −22.5475 | + | 4.07576i | −0.984052 | + | 0.177881i | ||||
\(526\) | −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 | ||||
\(530\) | −3.96447 | + | 10.4539i | −0.172205 | + | 0.454086i | ||||
\(531\) | −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 | ||||
\(535\) | −12.0888 | + | 1.96479i | −0.522645 | + | 0.0849452i | ||||
\(536\) | −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 | ||||
\(540\) | −4.26139 | − | 10.8093i | −0.183381 | − | 0.465157i | ||||
\(541\) | −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 | \(-0.834696\pi\) | ||
0.868158 | − | 0.496287i | \(-0.165304\pi\) | |||||||
\(548\) | 3.73861 | + | 6.47547i | 0.159706 | + | 0.276618i | ||||
\(549\) | 9.87298 | − | 3.24410i | 0.421369 | − | 0.138455i | ||||
\(550\) | 0.707603 | − | 0.798761i | 0.0301723 | − | 0.0340593i | ||||
\(551\) | 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 | ||||||
\(555\) | 1.60341 | + | 27.5874i | 0.0680611 | + | 1.17102i | ||||
\(556\) | −6.52277 | − | 3.76593i | −0.276627 | − | 0.159711i | ||||
\(557\) | −18.9317 | + | 32.7906i | −0.802161 | + | 1.38938i | 0.116030 | + | 0.993246i | \(0.462983\pi\) |
−0.918191 | + | 0.396138i | \(0.870350\pi\) | |||||||
\(558\) | 0.185325 | − | 0.886304i | 0.00784543 | − | 0.0375202i | ||||
\(559\) | 13.5546i | 0.573298i | ||||||||
\(560\) | 2.31920 | − | 5.44255i | 0.0980041 | − | 0.229990i | ||||
\(561\) | 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 | 0.298211 | − | 0.954500i | \(-0.403610\pi\) |
−0.677516 | + | 0.735508i | \(0.736943\pi\) | |||||||
\(564\) | 1.38188 | − | 13.3604i | 0.0581876 | − | 0.562574i | ||||
\(565\) | 5.17186 | − | 13.6376i | 0.217582 | − | 0.573739i | ||||
\(566\) | 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 | \(0.252164\pi\) | |||||||
\(570\) | −15.8385 | + | 10.4144i | −0.663401 | + | 0.436210i | ||||
\(571\) | 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 | −0.669596 | − | 0.742725i | \(-0.733533\pi\) |
0.978017 | + | 0.208525i | \(0.0668663\pi\) | |||||||
\(578\) | 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 | ||||
\(585\) | 24.2061 | − | 37.8809i | 1.00080 | − | 1.56618i | ||||
\(586\) | −3.97723 | + | 2.29625i | −0.164298 | + | 0.0948573i | ||||
\(587\) | 27.4110i | 1.13137i | 0.824621 | + | 0.565686i | \(0.191389\pi\) | ||||
−0.824621 | + | 0.565686i | \(0.808611\pi\) | |||||||
\(588\) | 11.9202 | + | 2.21536i | 0.491583 | + | 0.0913599i | ||||
\(589\) | −1.47723 | −0.0608680 | ||||||||
\(590\) | 3.89908 | − | 10.2814i | 0.160523 | − | 0.423280i | ||||
\(591\) | −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 | −0.978786 | − | 0.204884i | \(-0.934318\pi\) |
−0.311958 | + | 0.950096i | \(0.600985\pi\) | |||||||
\(594\) | −0.337449 | + | 1.05638i | −0.0138457 | + | 0.0433440i | ||||
\(595\) | 2.25403 | + | 18.5720i | 0.0924064 | + | 0.761378i | ||||
\(596\) | 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 | \(0.629171\pi\) | |||||||
\(600\) | 5.85723 | + | 6.37909i | 0.239120 | + | 0.260425i | ||||
\(601\) | − | 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 | ||||
\(605\) | 24.1776 | − | 3.92957i | 0.982961 | − | 0.159760i | ||||
\(606\) | −19.4919 | − | 2.01607i | −0.791806 | − | 0.0818972i | ||||
\(607\) | −13.2180 | − | 22.8942i | −0.536502 | − | 0.929248i | −0.999089 | − | 0.0426745i | \(-0.986412\pi\) |
0.462587 | − | 0.886574i | \(-0.346921\pi\) | |||||||
\(608\) | − | 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 | −0.0162031 | − | 0.999869i | \(-0.505158\pi\) |
−0.874013 | + | 0.485902i | \(0.838491\pi\) | |||||||
\(614\) | −1.75166 | − | 3.03397i | −0.0706914 | − | 0.122441i | ||||
\(615\) | 11.6512 | − | 23.1923i | 0.469820 | − | 0.935205i | ||||
\(616\) | −0.500000 | + | 0.262377i | −0.0201456 | + | 0.0105715i | ||||
\(617\) | −25.4772 | −1.02567 | −0.512837 | − | 0.858486i | \(-0.671406\pi\) | ||||
−0.512837 | + | 0.858486i | \(0.671406\pi\) | |||||||
\(618\) | −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 | \(0.847167\pi\) | |||||||
\(620\) | 0.108270 | + | 0.666158i | 0.00434823 | + | 0.0267535i | ||||
\(621\) | −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 | ||||
\(625\) | 3.01472 | + | 24.8176i | 0.120589 | + | 0.992703i | ||||
\(626\) | 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 | ||||||||
\(630\) | −10.1521 | + | 14.5580i | −0.404470 | + | 0.580003i | ||||
\(631\) | −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 | ||||
\(635\) | −28.4968 | − | 10.8070i | −1.13086 | − | 0.428863i | ||||
\(636\) | 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 | ||||
\(640\) | −2.20711 | + | 0.358719i | −0.0872436 | + | 0.0141796i | ||||
\(641\) | 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 | \(-0.368164\pi\) | ||||
0.402436 | + | 0.915448i | \(0.368164\pi\) | |||||||
\(644\) | 9.16018 | − | 14.4835i | 0.360962 | − | 0.570731i | ||||
\(645\) | 7.00000 | + | 3.51660i | 0.275625 | + | 0.138466i | ||||
\(646\) | 7.73861 | + | 13.4037i | 0.304472 | + | 0.527360i | ||||
\(647\) | 20.6703 | + | 11.9340i | 0.812633 | + | 0.469174i | 0.847869 | − | 0.530205i | \(-0.177885\pi\) |
−0.0352364 | + | 0.999379i | \(0.511218\pi\) | |||||||
\(648\) | −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 | \(-0.997770\pi\) |
0.493920 | − | 0.869507i | \(-0.335564\pi\) | |||||||
\(654\) | −21.4180 | − | 2.21529i | −0.837511 | − | 0.0866246i | ||||
\(655\) | −13.3012 | + | 2.16183i | −0.519719 | + | 0.0844696i | ||||
\(656\) | 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 | \(0.767181\pi\) | |||||||
\(660\) | −0.0479609 | − | 0.825186i | −0.00186688 | − | 0.0321203i | ||||
\(661\) | 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 | ||||||
\(665\) | 26.6376 | + | 11.3509i | 1.03296 | + | 0.440170i | ||||
\(666\) | 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 | ||||
\(670\) | −11.1351 | − | 4.22281i | −0.430185 | − | 0.163141i | ||||
\(671\) | 0.739315 | 0.0285409 | ||||||||
\(672\) | −1.70058 | − | 4.25535i | −0.0656014 | − | 0.164154i | ||||
\(673\) | 48.4514i | 1.86766i | 0.357713 | + | 0.933832i | \(0.383557\pi\) | ||||
−0.357713 | + | 0.933832i | \(0.616443\pi\) | |||||||
\(674\) | −14.8492 | + | 8.57321i | −0.571971 | + | 0.330228i | ||||
\(675\) | −13.2828 | − | 22.3286i | −0.511257 | − | 0.859428i | ||||
\(676\) | −15.9545 | + | 27.6339i | −0.613633 | + | 1.06284i | ||||
\(677\) | 28.5000 | − | 16.4545i | 1.09534 | − | 0.632397i | 0.160350 | − | 0.987060i | \(-0.448738\pi\) |
0.934994 | + | 0.354663i | \(0.115404\pi\) | |||||||
\(678\) | −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 | −0.836379 | − | 0.548152i | \(-0.815331\pi\) |
0.892903 | + | 0.450249i | \(0.148665\pi\) | |||||||
\(684\) | −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 | ||||
\(690\) | 13.7825 | + | 20.9609i | 0.524692 | + | 0.797967i | ||||
\(691\) | 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 | ||||||||
\(695\) | −15.7474 | − | 5.97195i | −0.597332 | − | 0.226529i | ||||
\(696\) | 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 | ||||
\(700\) | 3.16637 | − | 12.8442i | 0.119678 | − | 0.485466i | ||||
\(701\) | − | 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 | ||||
\(705\) | −1.74268 | − | 29.9835i | −0.0656332 | − | 1.12925i | ||||
\(706\) | − | 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 | \(0.896091\pi\) | |||||||
\(710\) | 0.725563 | + | 4.46420i | 0.0272299 | + | 0.167538i | ||||
\(711\) | −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 | \(-0.510210\pi\) | |||||||
\(720\) | 6.70141 | + | 0.301824i | 0.249747 | + | 0.0112483i | ||||
\(721\) | 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 | ||||
\(725\) | 6.70611 | − | 7.57004i | 0.249059 | − | 0.281144i | ||||
\(726\) | 11.1270 | − | 15.3685i | 0.412962 | − | 0.570377i | ||||
\(727\) | 23.6076 | 0.875556 | 0.437778 | − | 0.899083i | \(-0.355766\pi\) | ||||
0.437778 | + | 0.899083i | \(0.355766\pi\) | |||||||
\(728\) | 9.47723 | − | 14.9848i | 0.351249 | − | 0.555374i | ||||
\(729\) | 22.0000 | + | 15.6525i | 0.814815 | + | 0.579721i | ||||
\(730\) | 9.50569 | − | 25.0654i | 0.351821 | − | 0.927713i | ||||
\(731\) | 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 | \(-0.932514\pi\) |
0.306569 | − | 0.951849i | \(-0.400819\pi\) | |||||||
\(734\) | 8.11562 | 0.299553 | ||||||||
\(735\) | 27.1039 | + | 0.613514i | 0.999744 | + | 0.0226298i | ||||
\(736\) | −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 | \(0.140425\pi\) | |||||||
\(740\) | −14.9177 | − | 5.65733i | −0.548387 | − | 0.207968i | ||||
\(741\) | −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 | \(-0.383991\pi\) | ||||
0.356440 | + | 0.934318i | \(0.383991\pi\) | |||||||
\(744\) | 0.423441 | + | 0.306579i | 0.0155241 | + | 0.0112397i | ||||
\(745\) | 0.878680 | + | 5.40629i | 0.0321923 | + | 0.198071i | ||||
\(746\) | 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 | ||||
\(750\) | 15.2158 | + | 11.9782i | 0.555604 | + | 0.437384i | ||||
\(751\) | 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 | \(-0.814748\pi\) | ||
0.835373 | − | 0.549683i | \(-0.185252\pi\) | |||||||
\(758\) | −4.76139 | − | 8.24696i | −0.172941 | − | 0.299543i | ||||
\(759\) | 0.246336 | − | 2.38165i | 0.00894143 | − | 0.0864484i | ||||
\(760\) | −1.75569 | − | 10.8023i | −0.0636856 | − | 0.391841i | ||||
\(761\) | 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 | ||||||
\(765\) | −18.8298 | + | 9.76928i | −0.680793 | + | 0.353209i | ||||
\(766\) | 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 | \(-0.174076\pi\) | |||||||
\(770\) | −1.00943 | + | 0.758455i | −0.0363775 | + | 0.0273328i | ||||
\(771\) | 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 | 0.876670 | − | 0.481091i | \(-0.159759\pi\) |
0.0216979 | + | 0.999765i | \(0.493093\pi\) | |||||||
\(774\) | 5.76471 | − | 1.89419i | 0.207208 | − | 0.0680853i | ||||
\(775\) | 0.477927 | + | 1.43144i | 0.0171677 | + | 0.0514189i | ||||
\(776\) | −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 | ||||
\(780\) | 14.2596 | + | 21.6864i | 0.510574 | + | 0.776496i | ||||
\(781\) | 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 | \(0.378769\pi\) |
−0.989830 | + | 0.142256i | \(0.954564\pi\) | |||||||
\(788\) | 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 | ||||
\(795\) | 10.6392 | + | 16.1804i | 0.377335 | + | 0.573861i | ||||
\(796\) | 19.4317 | − | 11.2189i | 0.688738 | − | 0.397643i | ||||
\(797\) | − | 28.9201i | − | 1.02440i | −0.858865 | − | 0.512201i | \(-0.828830\pi\) | ||
0.858865 | − | 0.512201i | \(-0.171170\pi\) | |||||||
\(798\) | 20.8271 | − | 8.32321i | 0.737271 | − | 0.294638i | ||||
\(799\) | −24.5228 | −0.867553 | ||||||||
\(800\) | −4.74264 | + | 1.58346i | −0.167678 | + | 0.0559839i | ||||
\(801\) | −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 | ||||
\(805\) | 15.0220 | − | 35.2526i | 0.529455 | − | 1.24249i | ||||
\(806\) | 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 | \(0.916058\pi\) | |||||||
\(810\) | −19.4933 | − | 5.00108i | −0.684925 | − | 0.175720i | ||||
\(811\) | − | 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 | ||||
\(815\) | 5.27208 | + | 32.4377i | 0.184673 | + | 1.13624i | ||||
\(816\) | 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 | 0.903380 | − | 0.428841i | \(-0.141078\pi\) |
0.0803025 | + | 0.996771i | \(0.474411\pi\) | |||||||
\(824\) | −5.28720 | − | 9.15769i | −0.184188 | − | 0.319023i | ||||
\(825\) | −0.401865 | − | 1.80407i | −0.0139912 | − | 0.0628097i | ||||
\(826\) | −6.95445 | + | 10.9960i | −0.241976 | + | 0.382598i | ||||
\(827\) | −39.9089 | −1.38777 | −0.693884 | − | 0.720087i | \(-0.744102\pi\) | ||||
−0.693884 | + | 0.720087i | \(0.744102\pi\) | |||||||
\(828\) | 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 | \(0.772701\pi\) | |||||||
\(830\) | −5.99666 | − | 36.8959i | −0.208147 | − | 1.28068i | ||||
\(831\) | −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 | ||||
\(835\) | 30.6987 | + | 11.6420i | 1.06237 | + | 0.402889i | ||||
\(836\) | −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 | \(0.722784\pi\) | |||||||
\(840\) | −5.27984 | − | 8.78198i | −0.182172 | − | 0.303007i | ||||
\(841\) | 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 | ||||
\(845\) | −25.3004 | + | 66.7142i | −0.870359 | + | 2.29504i | ||||
\(846\) | −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 | ||||
\(850\) | 10.4846 | − | 11.8353i | 0.359618 | − | 0.405946i | ||||
\(851\) | −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 | \(-0.874298\pi\) | ||||
−0.923033 | + | 0.384720i | \(0.874298\pi\) | |||||||
\(854\) | 8.11562 | − | 4.25871i | 0.277711 | − | 0.145730i | ||||
\(855\) | −1.47723 | + | 32.7989i | −0.0505200 | + | 1.12170i | ||||
\(856\) | −2.73861 | − | 4.74342i | −0.0936039 | − | 0.162127i | ||||
\(857\) | −34.9545 | − | 20.1810i | −1.19402 | − | 0.689369i | −0.234805 | − | 0.972042i | \(-0.575445\pi\) |
−0.959216 | + | 0.282674i | \(0.908779\pi\) | |||||||
\(858\) | 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 | 0.703153 | − | 0.711038i | \(-0.251775\pi\) |
−0.967354 | + | 0.253429i | \(0.918441\pi\) | |||||||
\(864\) | 3.84418 | − | 3.49604i | 0.130782 | − | 0.118938i | ||||
\(865\) | 4.13270 | + | 25.4274i | 0.140516 | + | 0.864559i | ||||
\(866\) | 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 | ||||||
\(870\) | −0.454536 | − | 7.82048i | −0.0154102 | − | 0.265139i | ||||
\(871\) | −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 | ||||||
\(875\) | 2.38105 | − | 29.4844i | 0.0804942 | − | 0.996755i | ||||
\(876\) | −8.47723 | − | 18.9557i | −0.286419 | − | 0.640452i | ||||
\(877\) | −36.6169 | + | 21.1408i | −1.23647 | + | 0.713874i | −0.968370 | − | 0.249518i | \(-0.919728\pi\) |
−0.268096 | + | 0.963392i | \(0.586394\pi\) | |||||||
\(878\) | 19.6931 | + | 11.3698i | 0.664609 | + | 0.383712i | ||||
\(879\) | −0.818370 | + | 7.91224i | −0.0276029 | + | 0.266873i | ||||
\(880\) | 0.446216 | + | 0.169221i | 0.0150419 | + | 0.00570443i | ||||
\(881\) | 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 | \(-0.836005\pi\) | ||
0.870191 | − | 0.492714i | \(-0.163995\pi\) | |||||||
\(884\) | 18.3526 | − | 10.5959i | 0.617264 | − | 0.356377i | ||||
\(885\) | −10.4638 | − | 15.9136i | −0.351736 | − | 0.534930i | ||||
\(886\) | 18.4772 | − | 32.0035i | 0.620755 | − | 1.07518i | ||||
\(887\) | −3.00000 | + | 1.73205i | −0.100730 | + | 0.0581566i | −0.549519 | − | 0.835481i | \(-0.685189\pi\) |
0.448789 | + | 0.893638i | \(0.351856\pi\) | |||||||
\(888\) | −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 | ||||
\(900\) | 14.8990 | − | 1.73777i | 0.496633 | − | 0.0579256i | ||||
\(901\) | 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 | ||||||||
\(905\) | 6.61160 | + | 2.50735i | 0.219777 | + | 0.0833471i | ||||
\(906\) | 3.44572 | + | 0.356394i | 0.114476 | + | 0.0118404i | ||||
\(907\) | −8.48528 | − | 4.89898i | −0.281749 | − | 0.162668i | 0.352466 | − | 0.935825i | \(-0.385343\pi\) |
−0.634215 | + | 0.773157i | \(0.718677\pi\) | |||||||
\(908\) | 9.00000 | − | 5.19615i | 0.298675 | − | 0.172440i | ||||
\(909\) | −22.6274 | + | 25.2982i | −0.750504 | + | 0.839089i | ||||
\(910\) | 15.5419 | − | 36.4727i | 0.515209 | − | 1.20906i | ||||
\(911\) | 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 | ||||
\(915\) | 0.778465 | + | 13.3938i | 0.0257353 | + | 0.442786i | ||||
\(916\) | − | 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 | \(0.653678\pi\) | |||||||
\(920\) | −14.2959 | + | 2.32351i | −0.471323 | + | 0.0766038i | ||||
\(921\) | −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 | \(0.960280\pi\) | |||||||
\(930\) | 1.04456 | + | 0.524755i | 0.0342523 | + | 0.0172074i | ||||
\(931\) | −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 | ||||
\(935\) | −1.48957 | + | 0.242099i | −0.0487143 | + | 0.00791750i | ||||
\(936\) | 19.6786 | + | 4.11478i | 0.643216 | + | 0.134496i | ||||
\(937\) | −22.6918 | −0.741310 | −0.370655 | − | 0.928771i | \(-0.620867\pi\) | ||||
−0.370655 | + | 0.928771i | \(0.620867\pi\) | |||||||
\(938\) | 11.9089 | + | 7.53185i | 0.388839 | + | 0.245924i | ||||
\(939\) | −16.4317 | − | 36.7423i | −0.536228 | − | 1.19904i | ||||
\(940\) | 16.2135 | + | 6.14871i | 0.528825 | + | 0.200549i | ||||
\(941\) | 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 | ||||||||
\(945\) | 10.1119 | + | 29.0301i | 0.328941 | + | 0.944350i | ||||
\(946\) | 0.431677 | 0.0140350 | ||||||||
\(947\) | −16.4317 | − | 28.4605i | −0.533958 | − | 0.924842i | −0.999213 | − | 0.0396654i | \(-0.987371\pi\) |
0.465255 | − | 0.885177i | \(-0.345963\pi\) | |||||||
\(948\) | 0.900667 | + | 0.0931568i | 0.0292523 | + | 0.00302559i | ||||
\(949\) | 40.1703 | − | 69.5770i | 1.30398 | − | 2.25856i | ||||
\(950\) | −7.74999 | − | 23.2120i | −0.251443 | − | 0.753098i | ||||
\(951\) | 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 | \(-0.632956\pi\) | ||||
−0.405652 | + | 0.914027i | \(0.632956\pi\) | |||||||
\(954\) | 14.6825 | + | 3.07008i | 0.475362 | + | 0.0993976i | ||||
\(955\) | −0.572445 | − | 3.52211i | −0.0185239 | − | 0.113973i | ||||
\(956\) | 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 | ||||
\(960\) | −1.73861 | + | 3.46081i | −0.0561135 | + | 0.111697i | ||||
\(961\) | −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 | \(-0.731721\pi\) | ||
0.665359 | − | 0.746524i | \(-0.268279\pi\) | |||||||
\(968\) | 5.47723 | + | 9.48683i | 0.176045 | + | 0.304918i | ||||
\(969\) | 26.6651 | + | 2.75799i | 0.856606 | + | 0.0885996i | ||||
\(970\) | −7.73221 | + | 1.25671i | −0.248266 | + | 0.0403506i | ||||
\(971\) | −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 | ||||||||
\(975\) | 39.2517 | + | 42.7489i | 1.25706 | + | 1.36906i | ||||
\(976\) | −3.00000 | − | 1.73205i | −0.0960277 | − | 0.0554416i | ||||
\(977\) | −19.9545 | + | 34.5621i | −0.638399 | + | 1.10574i | 0.347385 | + | 0.937723i | \(0.387070\pi\) |
−0.985784 | + | 0.168018i | \(0.946263\pi\) | |||||||
\(978\) | 20.6190 | + | 14.9285i | 0.659321 | + | 0.477359i | ||||
\(979\) | − | 2.25681i | − | 0.0721278i | ||||||
\(980\) | −6.71181 | + | 14.1404i | −0.214401 | + | 0.451699i | ||||
\(981\) | −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 | 0.888081 | − | 0.459688i | \(-0.152039\pi\) |
0.0459391 | + | 0.998944i | \(0.485372\pi\) | |||||||
\(984\) | 11.5456 | + | 1.19417i | 0.368060 | + | 0.0380688i | ||||
\(985\) | 7.13604 | − | 18.8169i | 0.227373 | − | 0.599557i | ||||
\(986\) | −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 | ||||
\(990\) | −1.20640 | − | 0.770899i | −0.0383421 | − | 0.0245008i | ||||
\(991\) | −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 | −0.962221 | − | 0.272270i | \(-0.912225\pi\) |
0.716904 | + | 0.697172i | \(0.245559\pi\) | |||||||
\(998\) | −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.f.59.4 | yes | 8 | |
3.2 | odd | 2 | 210.2.t.e.59.2 | yes | 8 | ||
5.2 | odd | 4 | 1050.2.s.i.101.3 | 16 | |||
5.3 | odd | 4 | 1050.2.s.i.101.6 | 16 | |||
5.4 | even | 2 | 210.2.t.e.59.1 | ✓ | 8 | ||
7.3 | odd | 6 | 1470.2.d.e.1469.8 | 8 | |||
7.4 | even | 3 | 1470.2.d.e.1469.1 | 8 | |||
7.5 | odd | 6 | inner | 210.2.t.f.89.3 | yes | 8 | |
15.2 | even | 4 | 1050.2.s.i.101.5 | 16 | |||
15.8 | even | 4 | 1050.2.s.i.101.4 | 16 | |||
15.14 | odd | 2 | inner | 210.2.t.f.59.3 | yes | 8 | |
21.5 | even | 6 | 210.2.t.e.89.1 | yes | 8 | ||
21.11 | odd | 6 | 1470.2.d.f.1469.4 | 8 | |||
21.17 | even | 6 | 1470.2.d.f.1469.5 | 8 | |||
35.4 | even | 6 | 1470.2.d.f.1469.8 | 8 | |||
35.12 | even | 12 | 1050.2.s.i.551.5 | 16 | |||
35.19 | odd | 6 | 210.2.t.e.89.2 | yes | 8 | ||
35.24 | odd | 6 | 1470.2.d.f.1469.1 | 8 | |||
35.33 | even | 12 | 1050.2.s.i.551.4 | 16 | |||
105.47 | odd | 12 | 1050.2.s.i.551.3 | 16 | |||
105.59 | even | 6 | 1470.2.d.e.1469.4 | 8 | |||
105.68 | odd | 12 | 1050.2.s.i.551.6 | 16 | |||
105.74 | odd | 6 | 1470.2.d.e.1469.5 | 8 | |||
105.89 | even | 6 | inner | 210.2.t.f.89.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.t.e.59.1 | ✓ | 8 | 5.4 | even | 2 | ||
210.2.t.e.59.2 | yes | 8 | 3.2 | odd | 2 | ||
210.2.t.e.89.1 | yes | 8 | 21.5 | even | 6 | ||
210.2.t.e.89.2 | yes | 8 | 35.19 | odd | 6 | ||
210.2.t.f.59.3 | yes | 8 | 15.14 | odd | 2 | inner | |
210.2.t.f.59.4 | yes | 8 | 1.1 | even | 1 | trivial | |
210.2.t.f.89.3 | yes | 8 | 7.5 | odd | 6 | inner | |
210.2.t.f.89.4 | yes | 8 | 105.89 | even | 6 | inner | |
1050.2.s.i.101.3 | 16 | 5.2 | odd | 4 | |||
1050.2.s.i.101.4 | 16 | 15.8 | even | 4 | |||
1050.2.s.i.101.5 | 16 | 15.2 | even | 4 | |||
1050.2.s.i.101.6 | 16 | 5.3 | odd | 4 | |||
1050.2.s.i.551.3 | 16 | 105.47 | odd | 12 | |||
1050.2.s.i.551.4 | 16 | 35.33 | even | 12 | |||
1050.2.s.i.551.5 | 16 | 35.12 | even | 12 | |||
1050.2.s.i.551.6 | 16 | 105.68 | odd | 12 | |||
1470.2.d.e.1469.1 | 8 | 7.4 | even | 3 | |||
1470.2.d.e.1469.4 | 8 | 105.59 | even | 6 | |||
1470.2.d.e.1469.5 | 8 | 105.74 | odd | 6 | |||
1470.2.d.e.1469.8 | 8 | 7.3 | odd | 6 | |||
1470.2.d.f.1469.1 | 8 | 35.24 | odd | 6 | |||
1470.2.d.f.1469.4 | 8 | 21.11 | odd | 6 | |||
1470.2.d.f.1469.5 | 8 | 21.17 | even | 6 | |||
1470.2.d.f.1469.8 | 8 | 35.4 | even | 6 |