Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(49,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 5, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.bx (of order \(10\), degree \(4\), not 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: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{14} + 15x^{12} - 59x^{10} + 104x^{8} - 59x^{6} + 15x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 724.4 | ||
Root | \(0.280526 + 0.386111i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.724 |
Dual form | 825.2.bx.f.49.4 |
$q$-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 \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(e\left(\frac{3}{5}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.40496 | + | 0.456498i | 0.993455 | + | 0.322793i | 0.760247 | − | 0.649634i | \(-0.225078\pi\) |
0.233208 | + | 0.972427i | \(0.425078\pi\) | |||||||
\(3\) | −0.587785 | − | 0.809017i | −0.339358 | − | 0.467086i | ||||
\(4\) | 0.147481 | + | 0.107152i | 0.0737407 | + | 0.0535758i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.456498 | − | 1.40496i | −0.186365 | − | 0.573572i | ||||
\(7\) | 1.34895 | − | 1.85666i | 0.509853 | − | 0.701753i | −0.474041 | − | 0.880503i | \(-0.657205\pi\) |
0.983895 | + | 0.178750i | \(0.0572052\pi\) | |||||||
\(8\) | −1.57833 | − | 2.17239i | −0.558025 | − | 0.768055i | ||||
\(9\) | −0.309017 | + | 0.951057i | −0.103006 | + | 0.317019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.12020 | − | 1.12443i | −0.940776 | − | 0.339029i | ||||
\(12\) | − | 0.182297i | − | 0.0526246i | ||||||
\(13\) | −2.03600 | − | 0.661536i | −0.564684 | − | 0.183477i | 0.0127437 | − | 0.999919i | \(-0.495943\pi\) |
−0.577428 | + | 0.816442i | \(0.695943\pi\) | |||||||
\(14\) | 2.74278 | − | 1.99274i | 0.733038 | − | 0.532583i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.33846 | − | 4.11937i | −0.334616 | − | 1.02984i | ||||
\(17\) | 0.517799 | − | 0.168243i | 0.125585 | − | 0.0408049i | −0.245550 | − | 0.969384i | \(-0.578969\pi\) |
0.371135 | + | 0.928579i | \(0.378969\pi\) | |||||||
\(18\) | −0.868312 | + | 1.19513i | −0.204663 | + | 0.281694i | ||||
\(19\) | −1.76552 | + | 1.28272i | −0.405037 | + | 0.294277i | −0.771590 | − | 0.636121i | \(-0.780538\pi\) |
0.366553 | + | 0.930397i | \(0.380538\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.29496 | −0.500802 | ||||||||
\(22\) | −3.87045 | − | 3.00415i | −0.825183 | − | 0.640486i | ||||
\(23\) | 2.03908i | 0.425177i | 0.977142 | + | 0.212589i | \(0.0681894\pi\) | ||||
−0.977142 | + | 0.212589i | \(0.931811\pi\) | |||||||
\(24\) | −0.829779 | + | 2.55380i | −0.169378 | + | 0.521291i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.55850 | − | 1.85886i | −0.501763 | − | 0.364552i | ||||
\(27\) | 0.951057 | − | 0.309017i | 0.183031 | − | 0.0594703i | ||||
\(28\) | 0.397889 | − | 0.129282i | 0.0751939 | − | 0.0244320i | ||||
\(29\) | −8.04603 | − | 5.84578i | −1.49411 | − | 1.08553i | −0.972655 | − | 0.232256i | \(-0.925389\pi\) |
−0.521455 | − | 0.853279i | \(-0.674611\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.09249 | − | 6.44002i | 0.375822 | − | 1.15666i | −0.567101 | − | 0.823649i | \(-0.691935\pi\) |
0.942922 | − | 0.333012i | \(-0.108065\pi\) | |||||||
\(32\) | − | 1.02811i | − | 0.181746i | ||||||
\(33\) | 0.924324 | + | 3.18522i | 0.160904 | + | 0.554476i | ||||
\(34\) | 0.804288 | 0.137934 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.147481 | + | 0.107152i | −0.0245802 | + | 0.0178586i | ||||
\(37\) | 5.18403 | − | 7.13520i | 0.852249 | − | 1.17302i | −0.131114 | − | 0.991367i | \(-0.541855\pi\) |
0.983363 | − | 0.181652i | \(-0.0581445\pi\) | |||||||
\(38\) | −3.06604 | + | 0.996215i | −0.497377 | + | 0.161607i | ||||
\(39\) | 0.661536 | + | 2.03600i | 0.105930 | + | 0.326020i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.47470 | − | 1.07143i | 0.230309 | − | 0.167329i | −0.466646 | − | 0.884444i | \(-0.654538\pi\) |
0.696955 | + | 0.717115i | \(0.254538\pi\) | |||||||
\(42\) | −3.22433 | − | 1.04765i | −0.497524 | − | 0.161655i | ||||
\(43\) | − | 0.620713i | − | 0.0946578i | −0.998879 | − | 0.0473289i | \(-0.984929\pi\) | ||
0.998879 | − | 0.0473289i | \(-0.0150709\pi\) | |||||||
\(44\) | −0.339687 | − | 0.500167i | −0.0512098 | − | 0.0754030i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.930836 | + | 2.86482i | −0.137244 | + | 0.422394i | ||||
\(47\) | −0.222188 | − | 0.305816i | −0.0324095 | − | 0.0446078i | 0.792505 | − | 0.609866i | \(-0.208777\pi\) |
−0.824914 | + | 0.565258i | \(0.808777\pi\) | |||||||
\(48\) | −2.54591 | + | 3.50415i | −0.367471 | + | 0.505780i | ||||
\(49\) | 0.535571 | + | 1.64832i | 0.0765102 | + | 0.235474i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.440466 | − | 0.320017i | −0.0616776 | − | 0.0448114i | ||||
\(52\) | −0.229387 | − | 0.315724i | −0.0318103 | − | 0.0437831i | ||||
\(53\) | 11.0257 | + | 3.58246i | 1.51449 | + | 0.492089i | 0.944206 | − | 0.329355i | \(-0.106831\pi\) |
0.570288 | + | 0.821445i | \(0.306831\pi\) | |||||||
\(54\) | 1.47726 | 0.201030 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −6.16248 | −0.823496 | ||||||||
\(57\) | 2.07549 | + | 0.674367i | 0.274905 | + | 0.0893221i | ||||
\(58\) | −8.63574 | − | 11.8861i | −1.13393 | − | 1.56072i | ||||
\(59\) | −6.53518 | − | 4.74808i | −0.850807 | − | 0.618148i | 0.0745611 | − | 0.997216i | \(-0.476244\pi\) |
−0.925369 | + | 0.379069i | \(0.876244\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.69647 | + | 8.29887i | 0.345247 | + | 1.06256i | 0.961451 | + | 0.274975i | \(0.0886697\pi\) |
−0.616204 | + | 0.787587i | \(0.711330\pi\) | |||||||
\(62\) | 5.87971 | − | 8.09273i | 0.746724 | − | 1.02778i | ||||
\(63\) | 1.34895 | + | 1.85666i | 0.169951 | + | 0.233918i | ||||
\(64\) | −2.20760 | + | 6.79429i | −0.275950 | + | 0.849286i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.155412 | + | 4.89705i | −0.0191299 | + | 0.602785i | ||||
\(67\) | 9.75802i | 1.19213i | 0.802936 | + | 0.596066i | \(0.203270\pi\) | ||||
−0.802936 | + | 0.596066i | \(0.796730\pi\) | |||||||
\(68\) | 0.0943932 | + | 0.0306702i | 0.0114469 | + | 0.00371931i | ||||
\(69\) | 1.64965 | − | 1.19854i | 0.198594 | − | 0.144287i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.63426 | − | 14.2628i | −0.549985 | − | 1.69268i | −0.708833 | − | 0.705376i | \(-0.750778\pi\) |
0.158848 | − | 0.987303i | \(-0.449222\pi\) | |||||||
\(72\) | 2.55380 | − | 0.829779i | 0.300968 | − | 0.0977903i | ||||
\(73\) | 4.61907 | − | 6.35761i | 0.540622 | − | 0.744102i | −0.448081 | − | 0.893993i | \(-0.647892\pi\) |
0.988702 | + | 0.149891i | \(0.0478924\pi\) | |||||||
\(74\) | 10.5405 | − | 7.65815i | 1.22531 | − | 0.890242i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.397826 | −0.0456338 | ||||||||
\(77\) | −6.29667 | + | 4.27637i | −0.717572 | + | 0.487337i | ||||
\(78\) | 3.16248i | 0.358080i | ||||||||
\(79\) | 2.85054 | − | 8.77306i | 0.320711 | − | 0.987046i | −0.652629 | − | 0.757678i | \(-0.726334\pi\) |
0.973340 | − | 0.229369i | \(-0.0736661\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | − | 0.587785i | −0.0898908 | − | 0.0653095i | ||||
\(82\) | 2.56099 | − | 0.832118i | 0.282815 | − | 0.0918920i | ||||
\(83\) | 8.98969 | − | 2.92093i | 0.986747 | − | 0.320613i | 0.229189 | − | 0.973382i | \(-0.426393\pi\) |
0.757557 | + | 0.652769i | \(0.226393\pi\) | |||||||
\(84\) | −0.338464 | − | 0.245909i | −0.0369295 | − | 0.0268309i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.283354 | − | 0.872075i | 0.0305549 | − | 0.0940383i | ||||
\(87\) | 9.94544i | 1.06626i | ||||||||
\(88\) | 2.48201 | + | 8.55302i | 0.264583 | + | 0.911754i | ||||
\(89\) | −0.583290 | −0.0618287 | −0.0309143 | − | 0.999522i | \(-0.509842\pi\) | ||||
−0.0309143 | + | 0.999522i | \(0.509842\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.97470 | + | 2.88779i | −0.416662 | + | 0.302722i | ||||
\(92\) | −0.218490 | + | 0.300726i | −0.0227792 | + | 0.0313529i | ||||
\(93\) | −6.44002 | + | 2.09249i | −0.667798 | + | 0.216981i | ||||
\(94\) | −0.172561 | − | 0.531087i | −0.0177983 | − | 0.0547774i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.831757 | + | 0.604307i | −0.0848908 | + | 0.0616768i | ||||
\(97\) | 5.11479 | + | 1.66190i | 0.519328 | + | 0.168740i | 0.556940 | − | 0.830552i | \(-0.311975\pi\) |
−0.0376122 | + | 0.999292i | \(0.511975\pi\) | |||||||
\(98\) | 2.56031i | 0.258630i | ||||||||
\(99\) | 2.03359 | − | 2.62002i | 0.204384 | − | 0.263322i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.03482 | + | 18.5733i | −0.600487 | + | 1.84811i | −0.0752256 | + | 0.997167i | \(0.523968\pi\) |
−0.525261 | + | 0.850941i | \(0.676032\pi\) | |||||||
\(102\) | −0.472749 | − | 0.650683i | −0.0468091 | − | 0.0644272i | ||||
\(103\) | 7.64487 | − | 10.5223i | 0.753271 | − | 1.03679i | −0.244473 | − | 0.969656i | \(-0.578615\pi\) |
0.997744 | − | 0.0671325i | \(-0.0213850\pi\) | |||||||
\(104\) | 1.77637 | + | 5.46710i | 0.174187 | + | 0.536093i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.8552 | + | 10.0664i | 1.34574 | + | 0.977737i | ||||
\(107\) | 1.16002 | + | 1.59663i | 0.112144 | + | 0.154352i | 0.861399 | − | 0.507928i | \(-0.169589\pi\) |
−0.749256 | + | 0.662281i | \(0.769589\pi\) | |||||||
\(108\) | 0.173375 | + | 0.0563329i | 0.0166830 | + | 0.00542064i | ||||
\(109\) | −10.6212 | −1.01733 | −0.508663 | − | 0.860966i | \(-0.669860\pi\) | ||||
−0.508663 | + | 0.860966i | \(0.669860\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.81959 | −0.837119 | ||||||||
\(112\) | −9.45380 | − | 3.07173i | −0.893300 | − | 0.290251i | ||||
\(113\) | 9.93096 | + | 13.6688i | 0.934226 | + | 1.28585i | 0.958188 | + | 0.286139i | \(0.0923719\pi\) |
−0.0239621 | + | 0.999713i | \(0.507628\pi\) | |||||||
\(114\) | 2.60813 | + | 1.89491i | 0.244273 | + | 0.177475i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.560255 | − | 1.72429i | −0.0520184 | − | 0.160096i | ||||
\(117\) | 1.25832 | − | 1.73192i | 0.116331 | − | 0.160116i | ||||
\(118\) | −7.01415 | − | 9.65415i | −0.645705 | − | 0.888737i | ||||
\(119\) | 0.386111 | − | 1.18833i | 0.0353948 | − | 0.108934i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.47131 | + | 7.01690i | 0.770119 | + | 0.637900i | ||||
\(122\) | 12.8905i | 1.16705i | ||||||||
\(123\) | −1.73361 | − | 0.563285i | −0.156314 | − | 0.0507897i | ||||
\(124\) | 0.998661 | − | 0.725569i | 0.0896824 | − | 0.0651581i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.04765 | + | 3.22433i | 0.0933318 | + | 0.287246i | ||||
\(127\) | 3.93022 | − | 1.27701i | 0.348751 | − | 0.113316i | −0.129403 | − | 0.991592i | \(-0.541306\pi\) |
0.478154 | + | 0.878276i | \(0.341306\pi\) | |||||||
\(128\) | −7.41178 | + | 10.2014i | −0.655115 | + | 0.901689i | ||||
\(129\) | −0.502167 | + | 0.364846i | −0.0442133 | + | 0.0321229i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.436527 | −0.0381395 | −0.0190698 | − | 0.999818i | \(-0.506070\pi\) | ||||
−0.0190698 | + | 0.999818i | \(0.506070\pi\) | |||||||
\(132\) | −0.204981 | + | 0.568804i | −0.0178413 | + | 0.0495080i | ||||
\(133\) | 5.00829i | 0.434274i | ||||||||
\(134\) | −4.45452 | + | 13.7096i | −0.384812 | + | 1.18433i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.18275 | − | 0.859317i | −0.101420 | − | 0.0736858i | ||||
\(137\) | −7.48281 | + | 2.43131i | −0.639300 | + | 0.207721i | −0.610690 | − | 0.791870i | \(-0.709108\pi\) |
−0.0286095 | + | 0.999591i | \(0.509108\pi\) | |||||||
\(138\) | 2.86482 | − | 0.930836i | 0.243869 | − | 0.0792380i | ||||
\(139\) | 14.2736 | + | 10.3704i | 1.21067 | + | 0.879604i | 0.995292 | − | 0.0969265i | \(-0.0309012\pi\) |
0.215379 | + | 0.976530i | \(0.430901\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.116811 | + | 0.359508i | −0.00983728 | + | 0.0302760i | ||||
\(142\) | − | 22.1541i | − | 1.85913i | ||||||
\(143\) | 5.60887 | + | 4.35346i | 0.469037 | + | 0.364055i | ||||
\(144\) | 4.33136 | 0.360947 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 9.39184 | − | 6.82357i | 0.777274 | − | 0.564723i | ||||
\(147\) | 1.01872 | − | 1.40214i | 0.0840224 | − | 0.115647i | ||||
\(148\) | 1.52910 | − | 0.496833i | 0.125691 | − | 0.0408394i | ||||
\(149\) | 3.38687 | + | 10.4237i | 0.277463 | + | 0.853943i | 0.988557 | + | 0.150846i | \(0.0481999\pi\) |
−0.711094 | + | 0.703097i | \(0.751800\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.2065 | − | 11.7747i | 1.31887 | − | 0.958214i | 0.318923 | − | 0.947781i | \(-0.396679\pi\) |
0.999946 | − | 0.0104337i | \(-0.00332120\pi\) | |||||||
\(152\) | 5.57314 | + | 1.81082i | 0.452041 | + | 0.146877i | ||||
\(153\) | 0.544446i | 0.0440158i | ||||||||
\(154\) | −10.7987 | + | 3.13370i | −0.870185 | + | 0.252520i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.120596 | + | 0.371156i | −0.00965541 | + | 0.0297163i | ||||
\(157\) | 5.38098 | + | 7.40629i | 0.429449 | + | 0.591086i | 0.967827 | − | 0.251618i | \(-0.0809625\pi\) |
−0.538377 | + | 0.842704i | \(0.680963\pi\) | |||||||
\(158\) | 8.00978 | − | 11.0245i | 0.637224 | − | 0.877063i | ||||
\(159\) | −3.58246 | − | 11.0257i | −0.284108 | − | 0.874394i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.78588 | + | 2.75060i | 0.298369 | + | 0.216778i | ||||
\(162\) | −0.868312 | − | 1.19513i | −0.0682210 | − | 0.0938982i | ||||
\(163\) | −10.7775 | − | 3.50181i | −0.844155 | − | 0.274283i | −0.145159 | − | 0.989408i | \(-0.546369\pi\) |
−0.698996 | + | 0.715126i | \(0.746369\pi\) | |||||||
\(164\) | 0.332296 | 0.0259480 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 13.9635 | 1.08378 | ||||||||
\(167\) | −14.3611 | − | 4.66619i | −1.11129 | − | 0.361081i | −0.304854 | − | 0.952399i | \(-0.598608\pi\) |
−0.806438 | + | 0.591318i | \(0.798608\pi\) | |||||||
\(168\) | 3.62221 | + | 4.98555i | 0.279460 | + | 0.384644i | ||||
\(169\) | −6.80957 | − | 4.94744i | −0.523813 | − | 0.380572i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.674367 | − | 2.07549i | −0.0515701 | − | 0.158717i | ||||
\(172\) | 0.0665103 | − | 0.0915436i | 0.00507136 | − | 0.00698013i | ||||
\(173\) | −10.7354 | − | 14.7760i | −0.816195 | − | 1.12340i | −0.990338 | − | 0.138676i | \(-0.955715\pi\) |
0.174143 | − | 0.984720i | \(-0.444285\pi\) | |||||||
\(174\) | −4.54008 | + | 13.9729i | −0.344182 | + | 1.05928i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.455671 | + | 14.3583i | −0.0343475 | + | 1.08230i | ||||
\(177\) | 8.07792i | 0.607174i | ||||||||
\(178\) | −0.819498 | − | 0.266271i | −0.0614240 | − | 0.0199579i | ||||
\(179\) | −0.425073 | + | 0.308833i | −0.0317714 | + | 0.0230833i | −0.603558 | − | 0.797319i | \(-0.706251\pi\) |
0.571786 | + | 0.820403i | \(0.306251\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.47289 | − | 16.8438i | −0.406797 | − | 1.25199i | −0.919386 | − | 0.393358i | \(-0.871313\pi\) |
0.512589 | − | 0.858634i | \(-0.328687\pi\) | |||||||
\(182\) | −6.90255 | + | 2.24278i | −0.511651 | + | 0.166246i | ||||
\(183\) | 5.12899 | − | 7.05944i | 0.379146 | − | 0.521849i | ||||
\(184\) | 4.42967 | − | 3.21834i | 0.326560 | − | 0.237259i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −10.0032 | −0.733468 | ||||||||
\(187\) | −1.80481 | − | 0.0572771i | −0.131981 | − | 0.00418852i | ||||
\(188\) | − | 0.0689100i | − | 0.00502578i | ||||||
\(189\) | 0.709183 | − | 2.18264i | 0.0515854 | − | 0.158764i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.3908 | + | 9.72899i | 0.968925 | + | 0.703965i | 0.955206 | − | 0.295941i | \(-0.0956331\pi\) |
0.0137185 | + | 0.999906i | \(0.495633\pi\) | |||||||
\(192\) | 6.79429 | − | 2.20760i | 0.490336 | − | 0.159320i | ||||
\(193\) | 23.3040 | − | 7.57191i | 1.67746 | − | 0.545038i | 0.693040 | − | 0.720899i | \(-0.256271\pi\) |
0.984415 | + | 0.175860i | \(0.0562707\pi\) | |||||||
\(194\) | 6.42741 | + | 4.66979i | 0.461461 | + | 0.335271i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.0976331 | + | 0.300484i | −0.00697379 | + | 0.0214631i | ||||
\(197\) | 7.50877i | 0.534978i | 0.963561 | + | 0.267489i | \(0.0861938\pi\) | ||||
−0.963561 | + | 0.267489i | \(0.913806\pi\) | |||||||
\(198\) | 4.05315 | − | 2.75268i | 0.288045 | − | 0.195625i | ||||
\(199\) | 20.0956 | 1.42454 | 0.712270 | − | 0.701906i | \(-0.247667\pi\) | ||||
0.712270 | + | 0.701906i | \(0.247667\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.89440 | − | 5.73562i | 0.556828 | − | 0.404559i | ||||
\(202\) | −16.9573 | + | 23.3398i | −1.19311 | + | 1.64218i | ||||
\(203\) | −21.7073 | + | 7.05313i | −1.52355 | + | 0.495033i | ||||
\(204\) | −0.0306702 | − | 0.0943932i | −0.00214734 | − | 0.00660885i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 15.5441 | − | 11.2935i | 1.08301 | − | 0.786852i | ||||
\(207\) | −1.93928 | − | 0.630110i | −0.134789 | − | 0.0437956i | ||||
\(208\) | 9.27247i | 0.642930i | ||||||||
\(209\) | 6.95110 | − | 2.01715i | 0.480817 | − | 0.139529i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.67444 | − | 5.15339i | 0.115273 | − | 0.354774i | −0.876731 | − | 0.480981i | \(-0.840280\pi\) |
0.992004 | + | 0.126207i | \(0.0402804\pi\) | |||||||
\(212\) | 1.24222 | + | 1.70977i | 0.0853159 | + | 0.117427i | ||||
\(213\) | −8.81488 | + | 12.1326i | −0.603985 | + | 0.831315i | ||||
\(214\) | 0.900921 | + | 2.77275i | 0.0615857 | + | 0.189541i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.17239 | − | 1.57833i | −0.147812 | − | 0.107392i | ||||
\(217\) | −9.13429 | − | 12.5723i | −0.620076 | − | 0.853462i | ||||
\(218\) | −14.9223 | − | 4.84856i | −1.01067 | − | 0.328386i | ||||
\(219\) | −7.85844 | −0.531024 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.16554 | −0.0784024 | ||||||||
\(222\) | −12.3912 | − | 4.02613i | −0.831640 | − | 0.270216i | ||||
\(223\) | −9.23259 | − | 12.7076i | −0.618260 | − | 0.850961i | 0.378965 | − | 0.925411i | \(-0.376280\pi\) |
−0.997225 | + | 0.0744495i | \(0.976280\pi\) | |||||||
\(224\) | −1.90885 | − | 1.38686i | −0.127541 | − | 0.0926636i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.71280 | + | 23.7375i | 0.513048 | + | 1.57900i | ||||
\(227\) | 0.864876 | − | 1.19040i | 0.0574038 | − | 0.0790096i | −0.779350 | − | 0.626589i | \(-0.784451\pi\) |
0.836754 | + | 0.547579i | \(0.184451\pi\) | |||||||
\(228\) | 0.233837 | + | 0.321848i | 0.0154862 | + | 0.0213149i | ||||
\(229\) | 4.93656 | − | 15.1932i | 0.326217 | − | 1.00399i | −0.644671 | − | 0.764460i | \(-0.723006\pi\) |
0.970888 | − | 0.239533i | \(-0.0769945\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.16075 | + | 2.58053i | 0.471142 | + | 0.169786i | ||||
\(232\) | 26.7057i | 1.75331i | ||||||||
\(233\) | −24.3833 | − | 7.92263i | −1.59741 | − | 0.519029i | −0.630942 | − | 0.775830i | \(-0.717331\pi\) |
−0.966464 | + | 0.256802i | \(0.917331\pi\) | |||||||
\(234\) | 2.55850 | − | 1.85886i | 0.167254 | − | 0.121517i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.455053 | − | 1.40051i | −0.0296214 | − | 0.0911653i | ||||
\(237\) | −8.77306 | + | 2.85054i | −0.569872 | + | 0.185162i | ||||
\(238\) | 1.08494 | − | 1.49329i | 0.0703262 | − | 0.0967958i | ||||
\(239\) | −3.38336 | + | 2.45816i | −0.218851 | + | 0.159005i | −0.691809 | − | 0.722080i | \(-0.743186\pi\) |
0.472958 | + | 0.881085i | \(0.343186\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.29180 | −0.212043 | −0.106022 | − | 0.994364i | \(-0.533811\pi\) | ||||
−0.106022 | + | 0.994364i | \(0.533811\pi\) | |||||||
\(242\) | 8.69862 | + | 13.7256i | 0.559169 | + | 0.882314i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −0.491558 | + | 1.51286i | −0.0314688 | + | 0.0968510i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.17851 | − | 1.58278i | −0.138897 | − | 0.100914i | ||||
\(247\) | 4.44315 | − | 1.44367i | 0.282711 | − | 0.0918583i | ||||
\(248\) | −17.2929 | + | 5.61879i | −1.09810 | + | 0.356794i | ||||
\(249\) | −7.64709 | − | 5.55593i | −0.484614 | − | 0.352093i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.89382 | + | 8.90626i | −0.182656 | + | 0.562158i | −0.999900 | − | 0.0141339i | \(-0.995501\pi\) |
0.817244 | + | 0.576292i | \(0.195501\pi\) | |||||||
\(252\) | 0.418365i | 0.0263545i | ||||||||
\(253\) | 2.29280 | − | 6.36233i | 0.144147 | − | 0.399996i | ||||
\(254\) | 6.10475 | 0.383046 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.51104 | + | 2.55092i | −0.219440 | + | 0.159433i | ||||
\(257\) | 7.38928 | − | 10.1705i | 0.460930 | − | 0.634416i | −0.513771 | − | 0.857927i | \(-0.671752\pi\) |
0.974701 | + | 0.223511i | \(0.0717519\pi\) | |||||||
\(258\) | −0.872075 | + | 0.283354i | −0.0542930 | + | 0.0176409i | ||||
\(259\) | −6.25470 | − | 19.2500i | −0.388648 | − | 1.19614i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.04603 | − | 5.84578i | 0.498037 | − | 0.361845i | ||||
\(262\) | −0.613302 | − | 0.199274i | −0.0378899 | − | 0.0123112i | ||||
\(263\) | 4.82946i | 0.297797i | 0.988852 | + | 0.148899i | \(0.0475728\pi\) | ||||
−0.988852 | + | 0.148899i | \(0.952427\pi\) | |||||||
\(264\) | 5.46064 | − | 7.03533i | 0.336079 | − | 0.432994i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.28628 | + | 7.03644i | −0.140181 | + | 0.431432i | ||||
\(267\) | 0.342849 | + | 0.471892i | 0.0209820 | + | 0.0288793i | ||||
\(268\) | −1.04559 | + | 1.43913i | −0.0638694 | + | 0.0879087i | ||||
\(269\) | 1.61594 | + | 4.97335i | 0.0985255 | + | 0.303230i | 0.988156 | − | 0.153450i | \(-0.0490383\pi\) |
−0.889631 | + | 0.456680i | \(0.849038\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.5383 | − | 17.8281i | −1.49060 | − | 1.08298i | −0.973944 | − | 0.226789i | \(-0.927177\pi\) |
−0.516654 | − | 0.856194i | \(-0.672823\pi\) | |||||||
\(272\) | −1.38611 | − | 1.90782i | −0.0840453 | − | 0.115678i | ||||
\(273\) | 4.67254 | + | 1.51820i | 0.282795 | + | 0.0918856i | ||||
\(274\) | −11.6229 | −0.702167 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.371718 | 0.0223748 | ||||||||
\(277\) | −15.1878 | − | 4.93483i | −0.912549 | − | 0.296505i | −0.185142 | − | 0.982712i | \(-0.559275\pi\) |
−0.727407 | + | 0.686206i | \(0.759275\pi\) | |||||||
\(278\) | 15.3197 | + | 21.0858i | 0.918817 | + | 1.26464i | ||||
\(279\) | 5.47820 | + | 3.98015i | 0.327972 | + | 0.238285i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.429741 | − | 1.32261i | −0.0256362 | − | 0.0789000i | 0.937420 | − | 0.348201i | \(-0.113207\pi\) |
−0.963056 | + | 0.269301i | \(0.913207\pi\) | |||||||
\(282\) | −0.328230 | + | 0.451769i | −0.0195458 | + | 0.0269025i | ||||
\(283\) | −3.45296 | − | 4.75259i | −0.205257 | − | 0.282512i | 0.693961 | − | 0.720013i | \(-0.255864\pi\) |
−0.899218 | + | 0.437500i | \(0.855864\pi\) | |||||||
\(284\) | 0.844811 | − | 2.60006i | 0.0501303 | − | 0.154285i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.89287 | + | 8.67687i | 0.348453 | + | 0.513074i | ||||
\(287\) | − | 4.18332i | − | 0.246934i | ||||||
\(288\) | 0.977789 | + | 0.317703i | 0.0576168 | + | 0.0187208i | ||||
\(289\) | −13.5135 | + | 9.81812i | −0.794911 | + | 0.577536i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.66190 | − | 5.11479i | −0.0974221 | − | 0.299834i | ||||
\(292\) | 1.36246 | − | 0.442688i | 0.0797317 | − | 0.0259064i | ||||
\(293\) | 11.7407 | − | 16.1597i | 0.685900 | − | 0.944060i | −0.314086 | − | 0.949395i | \(-0.601698\pi\) |
0.999986 | + | 0.00533421i | \(0.00169794\pi\) | |||||||
\(294\) | 2.07133 | − | 1.50491i | 0.120802 | − | 0.0877681i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −23.6825 | −1.37652 | ||||||||
\(297\) | −3.31496 | − | 0.105203i | −0.192353 | − | 0.00610448i | ||||
\(298\) | 16.1910i | 0.937917i | ||||||||
\(299\) | 1.34892 | − | 4.15156i | 0.0780102 | − | 0.240091i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.15245 | − | 0.837307i | −0.0664264 | − | 0.0482616i | ||||
\(302\) | 28.1446 | − | 9.14475i | 1.61954 | − | 0.526221i | ||||
\(303\) | 18.5733 | − | 6.03482i | 1.06701 | − | 0.346691i | ||||
\(304\) | 7.64709 | + | 5.55593i | 0.438590 | + | 0.318655i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.248539 | + | 0.764923i | −0.0142080 | + | 0.0437278i | ||||
\(307\) | − | 19.4372i | − | 1.10934i | −0.832070 | − | 0.554671i | \(-0.812844\pi\) | ||
0.832070 | − | 0.554671i | \(-0.187156\pi\) | |||||||
\(308\) | −1.38686 | − | 0.0440131i | −0.0790238 | − | 0.00250788i | ||||
\(309\) | −13.0062 | −0.739898 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.87175 | + | 3.53954i | −0.276252 | + | 0.200709i | −0.717281 | − | 0.696784i | \(-0.754614\pi\) |
0.441029 | + | 0.897493i | \(0.354614\pi\) | |||||||
\(312\) | 3.37885 | − | 4.65059i | 0.191290 | − | 0.263288i | ||||
\(313\) | 4.85831 | − | 1.57856i | 0.274608 | − | 0.0892256i | −0.168476 | − | 0.985706i | \(-0.553884\pi\) |
0.443084 | + | 0.896480i | \(0.353884\pi\) | |||||||
\(314\) | 4.17910 | + | 12.8619i | 0.235840 | + | 0.725841i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.36045 | − | 0.988424i | 0.0765312 | − | 0.0556032i | ||||
\(317\) | −13.0093 | − | 4.22699i | −0.730677 | − | 0.237411i | −0.0800306 | − | 0.996792i | \(-0.525502\pi\) |
−0.650646 | + | 0.759381i | \(0.725502\pi\) | |||||||
\(318\) | − | 17.1260i | − | 0.960379i | ||||||
\(319\) | 18.5320 | + | 27.2872i | 1.03760 | + | 1.52779i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.609860 | − | 1.87695i | 0.0340390 | − | 0.104761i | ||||
\(322\) | 4.06336 | + | 5.59273i | 0.226442 | + | 0.311671i | ||||
\(323\) | −0.698373 | + | 0.961227i | −0.0388585 | + | 0.0534841i | ||||
\(324\) | −0.0563329 | − | 0.173375i | −0.00312961 | − | 0.00963194i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −13.5433 | − | 9.83978i | −0.750094 | − | 0.544975i | ||||
\(327\) | 6.24299 | + | 8.59273i | 0.345238 | + | 0.475179i | ||||
\(328\) | −4.65513 | − | 1.51254i | −0.257036 | − | 0.0835162i | ||||
\(329\) | −0.867517 | −0.0478278 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.4695 | 0.630418 | 0.315209 | − | 0.949022i | \(-0.397925\pi\) | ||||
0.315209 | + | 0.949022i | \(0.397925\pi\) | |||||||
\(332\) | 1.63879 | + | 0.532477i | 0.0899405 | + | 0.0292234i | ||||
\(333\) | 5.18403 | + | 7.13520i | 0.284083 | + | 0.391007i | ||||
\(334\) | −18.0466 | − | 13.1116i | −0.987465 | − | 0.717435i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.07173 | + | 9.45380i | 0.167576 | + | 0.515747i | ||||
\(337\) | −2.21245 | + | 3.04517i | −0.120520 | + | 0.165881i | −0.865014 | − | 0.501748i | \(-0.832691\pi\) |
0.744494 | + | 0.667629i | \(0.232691\pi\) | |||||||
\(338\) | −7.30865 | − | 10.0595i | −0.397538 | − | 0.547165i | ||||
\(339\) | 5.22101 | − | 16.0686i | 0.283567 | − | 0.872728i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13.7703 | + | 17.7413i | −0.745706 | + | 0.960744i | ||||
\(342\) | − | 3.22382i | − | 0.174324i | ||||||
\(343\) | 19.0613 | + | 6.19339i | 1.02921 | + | 0.334412i | ||||
\(344\) | −1.34843 | + | 0.979691i | −0.0727024 | + | 0.0528214i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.33754 | − | 25.6603i | −0.448229 | − | 1.37951i | ||||
\(347\) | −0.376600 | + | 0.122365i | −0.0202169 | + | 0.00656888i | −0.319108 | − | 0.947718i | \(-0.603383\pi\) |
0.298891 | + | 0.954287i | \(0.403383\pi\) | |||||||
\(348\) | −1.06567 | + | 1.46677i | −0.0571259 | + | 0.0786270i | ||||
\(349\) | −10.6554 | + | 7.74158i | −0.570369 | + | 0.414398i | −0.835239 | − | 0.549887i | \(-0.814671\pi\) |
0.264870 | + | 0.964284i | \(0.414671\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.14077 | −0.114266 | ||||||||
\(352\) | −1.15604 | + | 3.20790i | −0.0616170 | + | 0.170982i | ||||
\(353\) | 11.3853i | 0.605977i | 0.952994 | + | 0.302989i | \(0.0979844\pi\) | ||||
−0.952994 | + | 0.302989i | \(0.902016\pi\) | |||||||
\(354\) | −3.68756 | + | 11.3491i | −0.195992 | + | 0.603200i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.0860245 | − | 0.0625005i | −0.00455929 | − | 0.00331252i | ||||
\(357\) | −1.18833 | + | 0.386111i | −0.0628930 | + | 0.0204352i | ||||
\(358\) | −0.738191 | + | 0.239853i | −0.0390146 | + | 0.0126766i | ||||
\(359\) | −11.6241 | − | 8.44543i | −0.613499 | − | 0.445733i | 0.237146 | − | 0.971474i | \(-0.423788\pi\) |
−0.850645 | + | 0.525741i | \(0.823788\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.39965 | + | 13.5407i | −0.231561 | + | 0.712671i | ||||
\(362\) | − | 26.1632i | − | 1.37511i | ||||||
\(363\) | 0.697484 | − | 10.9779i | 0.0366084 | − | 0.576188i | ||||
\(364\) | −0.895625 | −0.0469435 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 10.4286 | − | 7.57685i | 0.545113 | − | 0.396048i | ||||
\(367\) | 15.4376 | − | 21.2480i | 0.805836 | − | 1.10914i | −0.186117 | − | 0.982528i | \(-0.559590\pi\) |
0.991953 | − | 0.126610i | \(-0.0404097\pi\) | |||||||
\(368\) | 8.39972 | − | 2.72923i | 0.437865 | − | 0.142271i | ||||
\(369\) | 0.563285 | + | 1.73361i | 0.0293234 | + | 0.0902482i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 21.5245 | − | 15.6384i | 1.11750 | − | 0.811908i | ||||
\(372\) | −1.17400 | − | 0.381454i | −0.0608689 | − | 0.0197775i | ||||
\(373\) | 21.8951i | 1.13368i | 0.823827 | + | 0.566842i | \(0.191835\pi\) | ||||
−0.823827 | + | 0.566842i | \(0.808165\pi\) | |||||||
\(374\) | −2.50954 | − | 0.904367i | −0.129765 | − | 0.0467637i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.313664 | + | 0.965358i | −0.0161760 | + | 0.0497845i | ||||
\(377\) | 12.5145 | + | 17.2247i | 0.644529 | + | 0.887119i | ||||
\(378\) | 1.99274 | − | 2.74278i | 0.102496 | − | 0.141073i | ||||
\(379\) | −7.89836 | − | 24.3087i | −0.405711 | − | 1.24865i | −0.920300 | − | 0.391214i | \(-0.872055\pi\) |
0.514588 | − | 0.857437i | \(-0.327945\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.34325 | − | 2.42901i | −0.171280 | − | 0.124442i | ||||
\(382\) | 14.3722 | + | 19.7817i | 0.735348 | + | 1.01212i | ||||
\(383\) | 18.1195 | + | 5.88737i | 0.925862 | + | 0.300831i | 0.732869 | − | 0.680370i | \(-0.238181\pi\) |
0.192992 | + | 0.981200i | \(0.438181\pi\) | |||||||
\(384\) | 12.6097 | 0.643485 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 36.1976 | 1.84241 | ||||||||
\(387\) | 0.590333 | + | 0.191811i | 0.0300083 | + | 0.00975029i | ||||
\(388\) | 0.576262 | + | 0.793157i | 0.0292553 | + | 0.0402664i | ||||
\(389\) | 13.2618 | + | 9.63528i | 0.672401 | + | 0.488528i | 0.870828 | − | 0.491587i | \(-0.163583\pi\) |
−0.198427 | + | 0.980116i | \(0.563583\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.343061 | + | 1.05583i | 0.0173493 | + | 0.0533957i | ||||
\(392\) | 2.73548 | − | 3.76506i | 0.138163 | − | 0.190164i | ||||
\(393\) | 0.256584 | + | 0.353158i | 0.0129430 | + | 0.0178145i | ||||
\(394\) | −3.42774 | + | 10.5495i | −0.172687 | + | 0.531476i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.580656 | − | 0.168502i | 0.0291791 | − | 0.00846752i | ||||
\(397\) | − | 30.9826i | − | 1.55497i | −0.628901 | − | 0.777485i | \(-0.716495\pi\) | ||
0.628901 | − | 0.777485i | \(-0.283505\pi\) | |||||||
\(398\) | 28.2335 | + | 9.17361i | 1.41522 | + | 0.459832i | ||||
\(399\) | 4.05179 | − | 2.94380i | 0.202843 | − | 0.147374i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.96723 | − | 6.05453i | −0.0982390 | − | 0.302349i | 0.889845 | − | 0.456262i | \(-0.150812\pi\) |
−0.988084 | + | 0.153914i | \(0.950812\pi\) | |||||||
\(402\) | 13.7096 | − | 4.45452i | 0.683773 | − | 0.222171i | ||||
\(403\) | −8.52060 | + | 11.7276i | −0.424441 | + | 0.584193i | ||||
\(404\) | −2.88018 | + | 2.09257i | −0.143294 | + | 0.104109i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −33.7176 | −1.67338 | ||||||||
\(407\) | −24.1982 | + | 16.4342i | −1.19946 | + | 0.814612i | ||||
\(408\) | 1.46196i | 0.0723776i | ||||||||
\(409\) | 1.93715 | − | 5.96193i | 0.0957858 | − | 0.294798i | −0.891672 | − | 0.452682i | \(-0.850467\pi\) |
0.987458 | + | 0.157884i | \(0.0504672\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.36526 | + | 4.62463i | 0.313975 | + | 0.228116i | ||||
\(412\) | 2.25495 | − | 0.732678i | 0.111093 | − | 0.0360965i | ||||
\(413\) | −17.6312 | + | 5.72872i | −0.867574 | + | 0.281892i | ||||
\(414\) | −2.43696 | − | 1.77055i | −0.119770 | − | 0.0870180i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.680130 | + | 2.09323i | −0.0333461 | + | 0.102629i | ||||
\(417\) | − | 17.6431i | − | 0.863988i | ||||||
\(418\) | 10.6868 | + | 0.339154i | 0.522710 | + | 0.0165886i | ||||
\(419\) | −3.90332 | −0.190689 | −0.0953447 | − | 0.995444i | \(-0.530395\pi\) | ||||
−0.0953447 | + | 0.995444i | \(0.530395\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.0539 | + | 10.2107i | −0.684944 | + | 0.497641i | −0.874994 | − | 0.484134i | \(-0.839135\pi\) |
0.190050 | + | 0.981774i | \(0.439135\pi\) | |||||||
\(422\) | 4.70503 | − | 6.47592i | 0.229037 | − | 0.315243i | ||||
\(423\) | 0.359508 | − | 0.116811i | 0.0174799 | − | 0.00567956i | ||||
\(424\) | −9.61970 | − | 29.6064i | −0.467174 | − | 1.43781i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −17.9231 | + | 13.0219i | −0.868375 | + | 0.630911i | ||||
\(427\) | 19.0456 | + | 6.18829i | 0.921682 | + | 0.299473i | ||||
\(428\) | 0.359772i | 0.0173902i | ||||||||
\(429\) | 0.225215 | − | 7.09657i | 0.0108735 | − | 0.342626i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.17440 | + | 6.69212i | −0.104737 | + | 0.322348i | −0.989669 | − | 0.143373i | \(-0.954205\pi\) |
0.884931 | + | 0.465721i | \(0.154205\pi\) | |||||||
\(432\) | −2.54591 | − | 3.50415i | −0.122490 | − | 0.168593i | ||||
\(433\) | 1.61776 | − | 2.22665i | 0.0777445 | − | 0.107006i | −0.768374 | − | 0.640002i | \(-0.778934\pi\) |
0.846118 | + | 0.532995i | \(0.178934\pi\) | |||||||
\(434\) | −7.09407 | − | 21.8333i | −0.340526 | − | 1.04803i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.56643 | − | 1.13808i | −0.0750184 | − | 0.0545041i | ||||
\(437\) | −2.61557 | − | 3.60002i | −0.125120 | − | 0.172212i | ||||
\(438\) | −11.0408 | − | 3.58736i | −0.527548 | − | 0.171411i | ||||
\(439\) | 2.73703 | 0.130631 | 0.0653157 | − | 0.997865i | \(-0.479195\pi\) | ||||
0.0653157 | + | 0.997865i | \(0.479195\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.73315 | −0.0825307 | ||||||||
\(442\) | −1.63753 | − | 0.532065i | −0.0778893 | − | 0.0253078i | ||||
\(443\) | −6.52688 | − | 8.98348i | −0.310102 | − | 0.426818i | 0.625311 | − | 0.780375i | \(-0.284972\pi\) |
−0.935413 | + | 0.353557i | \(0.884972\pi\) | |||||||
\(444\) | −1.30073 | − | 0.945033i | −0.0617297 | − | 0.0448493i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7.17041 | − | 22.0683i | −0.339529 | − | 1.04496i | ||||
\(447\) | 6.44220 | − | 8.86693i | 0.304706 | − | 0.419392i | ||||
\(448\) | 9.63679 | + | 13.2639i | 0.455295 | + | 0.626660i | ||||
\(449\) | −4.58174 | + | 14.1012i | −0.216226 | + | 0.665475i | 0.782838 | + | 0.622225i | \(0.213771\pi\) |
−0.999064 | + | 0.0432498i | \(0.986229\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.80610 | + | 1.68488i | −0.273399 | + | 0.0793380i | ||||
\(452\) | 3.08001i | 0.144872i | ||||||||
\(453\) | −19.0519 | − | 6.19034i | −0.895137 | − | 0.290848i | ||||
\(454\) | 1.75853 | − | 1.27765i | 0.0825319 | − | 0.0599629i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.81082 | − | 5.57314i | −0.0847996 | − | 0.260986i | ||||
\(457\) | 27.7542 | − | 9.01788i | 1.29829 | − | 0.421838i | 0.423301 | − | 0.905989i | \(-0.360871\pi\) |
0.874985 | + | 0.484151i | \(0.160871\pi\) | |||||||
\(458\) | 13.8713 | − | 19.0922i | 0.648165 | − | 0.892122i | ||||
\(459\) | 0.440466 | − | 0.320017i | 0.0205592 | − | 0.0149371i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −31.1798 | −1.45219 | −0.726094 | − | 0.687595i | \(-0.758666\pi\) | ||||
−0.726094 | + | 0.687595i | \(0.758666\pi\) | |||||||
\(462\) | 8.88254 | + | 6.89440i | 0.413253 | + | 0.320757i | ||||
\(463\) | 41.1642i | 1.91306i | 0.291631 | + | 0.956531i | \(0.405802\pi\) | ||||
−0.291631 | + | 0.956531i | \(0.594198\pi\) | |||||||
\(464\) | −13.3116 | + | 40.9689i | −0.617976 | + | 1.90194i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −30.6409 | − | 22.2619i | −1.41941 | − | 1.03126i | ||||
\(467\) | 36.8788 | − | 11.9826i | 1.70655 | − | 0.554490i | 0.716794 | − | 0.697285i | \(-0.245609\pi\) |
0.989752 | + | 0.142795i | \(0.0456090\pi\) | |||||||
\(468\) | 0.371156 | − | 0.120596i | 0.0171567 | − | 0.00557455i | ||||
\(469\) | 18.1174 | + | 13.1630i | 0.836582 | + | 0.607812i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.82895 | − | 8.70662i | 0.130351 | − | 0.401180i | ||||
\(472\) | 21.6910i | 0.998409i | ||||||||
\(473\) | −0.697949 | + | 1.93675i | −0.0320917 | + | 0.0890518i | ||||
\(474\) | −13.6270 | −0.625911 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.184276 | − | 0.133884i | 0.00844626 | − | 0.00613656i | ||||
\(477\) | −6.81425 | + | 9.37901i | −0.312003 | + | 0.429435i | ||||
\(478\) | −5.87562 | + | 1.90911i | −0.268745 | + | 0.0873205i | ||||
\(479\) | −5.15675 | − | 15.8708i | −0.235618 | − | 0.725158i | −0.997039 | − | 0.0768997i | \(-0.975498\pi\) |
0.761421 | − | 0.648258i | \(-0.224502\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.2748 | + | 11.0978i | −0.696473 | + | 0.506017i | ||||
\(482\) | −4.62483 | − | 1.50270i | −0.210655 | − | 0.0684461i | ||||
\(483\) | − | 4.67961i | − | 0.212930i | ||||||
\(484\) | 0.497489 | + | 1.94258i | 0.0226131 | + | 0.0882989i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.456498 | + | 1.40496i | −0.0207072 | + | 0.0637302i | ||||
\(487\) | 1.47648 | + | 2.03220i | 0.0669056 | + | 0.0920877i | 0.841158 | − | 0.540789i | \(-0.181874\pi\) |
−0.774253 | + | 0.632876i | \(0.781874\pi\) | |||||||
\(488\) | 13.7725 | − | 18.9562i | 0.623450 | − | 0.858105i | ||||
\(489\) | 3.50181 | + | 10.7775i | 0.158357 | + | 0.487373i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.11508 | + | 4.44286i | 0.275970 | + | 0.200504i | 0.717158 | − | 0.696911i | \(-0.245443\pi\) |
−0.441188 | + | 0.897415i | \(0.645443\pi\) | |||||||
\(492\) | −0.195319 | − | 0.268833i | −0.00880565 | − | 0.0121199i | ||||
\(493\) | −5.14974 | − | 1.67325i | −0.231932 | − | 0.0753594i | ||||
\(494\) | 6.90147 | 0.310512 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −29.3295 | −1.31693 | ||||||||
\(497\) | −32.7325 | − | 10.6354i | −1.46825 | − | 0.477065i | ||||
\(498\) | −8.20756 | − | 11.2967i | −0.367789 | − | 0.506219i | ||||
\(499\) | 13.5886 | + | 9.87269i | 0.608309 | + | 0.441962i | 0.848818 | − | 0.528685i | \(-0.177315\pi\) |
−0.240510 | + | 0.970647i | \(0.577315\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.66619 | + | 14.3611i | 0.208470 | + | 0.641605i | ||||
\(502\) | −8.13139 | + | 11.1919i | −0.362922 | + | 0.499519i | ||||
\(503\) | −4.48632 | − | 6.17489i | −0.200035 | − | 0.275325i | 0.697201 | − | 0.716876i | \(-0.254428\pi\) |
−0.897236 | + | 0.441551i | \(0.854428\pi\) | |||||||
\(504\) | 1.90431 | − | 5.86087i | 0.0848248 | − | 0.261064i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6.12569 | − | 7.89215i | 0.272320 | − | 0.350849i | ||||
\(507\) | 8.41709i | 0.373816i | ||||||||
\(508\) | 0.716469 | + | 0.232795i | 0.0317882 | + | 0.0103286i | ||||
\(509\) | 26.6198 | − | 19.3404i | 1.17990 | − | 0.857249i | 0.187741 | − | 0.982219i | \(-0.439883\pi\) |
0.992161 | + | 0.124970i | \(0.0398834\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.57307 | − | 17.1521i | −0.246538 | − | 0.758766i | ||||
\(512\) | 17.8877 | − | 5.81206i | 0.790531 | − | 0.256859i | ||||
\(513\) | −1.28272 | + | 1.76552i | −0.0566336 | + | 0.0779494i | ||||
\(514\) | 15.0244 | − | 10.9159i | 0.662699 | − | 0.481479i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.113154 | −0.00498133 | ||||||||
\(517\) | 0.349403 | + | 1.20404i | 0.0153667 | + | 0.0529537i | ||||
\(518\) | − | 29.9007i | − | 1.31376i | ||||||
\(519\) | −5.64392 | + | 17.3702i | −0.247741 | + | 0.762467i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.645559 | − | 0.469026i | −0.0282824 | − | 0.0205484i | 0.573554 | − | 0.819168i | \(-0.305564\pi\) |
−0.601837 | + | 0.798619i | \(0.705564\pi\) | |||||||
\(522\) | 13.9729 | − | 4.54008i | 0.611578 | − | 0.198714i | ||||
\(523\) | −4.09443 | + | 1.33036i | −0.179037 | + | 0.0581727i | −0.397164 | − | 0.917748i | \(-0.630005\pi\) |
0.218127 | + | 0.975920i | \(0.430005\pi\) | |||||||
\(524\) | −0.0643796 | − | 0.0467745i | −0.00281244 | − | 0.00204336i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.20464 | + | 6.78519i | −0.0961270 | + | 0.295848i | ||||
\(527\) | − | 3.68668i | − | 0.160594i | ||||||
\(528\) | 11.8839 | − | 8.07094i | 0.517181 | − | 0.351242i | ||||
\(529\) | 18.8422 | 0.819224 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.53518 | − | 4.74808i | 0.283602 | − | 0.206049i | ||||
\(532\) | −0.536646 | + | 0.738630i | −0.0232666 | + | 0.0320237i | ||||
\(533\) | −3.71127 | + | 1.20586i | −0.160753 | + | 0.0522318i | ||||
\(534\) | 0.266271 | + | 0.819498i | 0.0115227 | + | 0.0354632i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 21.1982 | − | 15.4014i | 0.915623 | − | 0.665239i | ||||
\(537\) | 0.499703 | + | 0.162363i | 0.0215638 | + | 0.00700649i | ||||
\(538\) | 7.72502i | 0.333049i | ||||||||
\(539\) | 0.182331 | − | 5.74530i | 0.00785357 | − | 0.247468i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.01720 | + | 21.5967i | −0.301693 | + | 0.928516i | 0.679198 | + | 0.733955i | \(0.262328\pi\) |
−0.980891 | + | 0.194560i | \(0.937672\pi\) | |||||||
\(542\) | −26.3368 | − | 36.2495i | −1.13126 | − | 1.55705i | ||||
\(543\) | −10.4101 | + | 14.3282i | −0.446738 | + | 0.614883i | ||||
\(544\) | −0.172972 | − | 0.532353i | −0.00741611 | − | 0.0228245i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 5.87166 | + | 4.26601i | 0.251284 | + | 0.182568i | ||||
\(547\) | 18.9003 | + | 26.0140i | 0.808117 | + | 1.11228i | 0.991611 | + | 0.129257i | \(0.0412592\pi\) |
−0.183494 | + | 0.983021i | \(0.558741\pi\) | |||||||
\(548\) | −1.36409 | − | 0.443221i | −0.0582712 | − | 0.0189335i | ||||
\(549\) | −8.72595 | −0.372415 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.7039 | 0.924617 | ||||||||
\(552\) | −5.20739 | − | 1.69198i | −0.221641 | − | 0.0720156i | ||||
\(553\) | −12.4434 | − | 17.1269i | −0.529147 | − | 0.728309i | ||||
\(554\) | −19.0855 | − | 13.8665i | −0.810867 | − | 0.589129i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.993889 | + | 3.05888i | 0.0421503 | + | 0.129725i | ||||
\(557\) | −22.1684 | + | 30.5122i | −0.939306 | + | 1.29284i | 0.0168116 | + | 0.999859i | \(0.494648\pi\) |
−0.956117 | + | 0.292985i | \(0.905352\pi\) | |||||||
\(558\) | 5.87971 | + | 8.09273i | 0.248908 | + | 0.342593i | ||||
\(559\) | −0.410623 | + | 1.26377i | −0.0173675 | + | 0.0534517i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.01450 | + | 1.49379i | 0.0428324 | + | 0.0630679i | ||||
\(562\) | − | 2.05438i | − | 0.0866588i | ||||||
\(563\) | 20.9109 | + | 6.79438i | 0.881291 | + | 0.286349i | 0.714493 | − | 0.699642i | \(-0.246657\pi\) |
0.166798 | + | 0.985991i | \(0.446657\pi\) | |||||||
\(564\) | −0.0557493 | + | 0.0405043i | −0.00234747 | + | 0.00170554i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.68171 | − | 8.25347i | −0.112721 | − | 0.346919i | ||||
\(567\) | −2.18264 | + | 0.709183i | −0.0916622 | + | 0.0297829i | ||||
\(568\) | −23.6699 | + | 32.5788i | −0.993166 | + | 1.36698i | ||||
\(569\) | −16.5690 | + | 12.0381i | −0.694609 | + | 0.504663i | −0.878172 | − | 0.478345i | \(-0.841237\pi\) |
0.183563 | + | 0.983008i | \(0.441237\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.4373 | 0.729728 | 0.364864 | − | 0.931061i | \(-0.381116\pi\) | ||||
0.364864 | + | 0.931061i | \(0.381116\pi\) | |||||||
\(572\) | 0.360724 | + | 1.24305i | 0.0150826 | + | 0.0519747i | ||||
\(573\) | − | 16.5519i | − | 0.691467i | ||||||
\(574\) | 1.90968 | − | 5.87739i | 0.0797085 | − | 0.245317i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −5.77957 | − | 4.19910i | −0.240815 | − | 0.174963i | ||||
\(577\) | −31.6082 | + | 10.2701i | −1.31587 | + | 0.427551i | −0.881074 | − | 0.472978i | \(-0.843179\pi\) |
−0.434794 | + | 0.900530i | \(0.643179\pi\) | |||||||
\(578\) | −23.4678 | + | 7.62516i | −0.976133 | + | 0.317165i | ||||
\(579\) | −19.8235 | − | 14.4026i | −0.823838 | − | 0.598553i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.70342 | − | 20.6310i | 0.278105 | − | 0.855918i | ||||
\(582\) | − | 7.94472i | − | 0.329319i | ||||||
\(583\) | −30.3741 | − | 23.5756i | −1.25797 | − | 0.976403i | ||||
\(584\) | −21.1016 | −0.873192 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 23.8721 | − | 17.3441i | 0.986147 | − | 0.716478i | ||||
\(587\) | 25.1545 | − | 34.6222i | 1.03824 | − | 1.42901i | 0.139657 | − | 0.990200i | \(-0.455400\pi\) |
0.898580 | − | 0.438811i | \(-0.144600\pi\) | |||||||
\(588\) | 0.300484 | − | 0.0976331i | 0.0123917 | − | 0.00402632i | ||||
\(589\) | 4.56643 | + | 14.0540i | 0.188156 | + | 0.579086i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.07472 | − | 4.41354i | 0.249881 | − | 0.181549i | ||||
\(592\) | −36.3312 | − | 11.8047i | −1.49320 | − | 0.485171i | ||||
\(593\) | − | 42.6570i | − | 1.75171i | −0.482570 | − | 0.875857i | \(-0.660297\pi\) | ||
0.482570 | − | 0.875857i | \(-0.339703\pi\) | |||||||
\(594\) | −4.60935 | − | 1.66108i | −0.189124 | − | 0.0681548i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.617416 | + | 1.90021i | −0.0252903 | + | 0.0778357i | ||||
\(597\) | −11.8119 | − | 16.2577i | −0.483429 | − | 0.665383i | ||||
\(598\) | 3.79036 | − | 5.21698i | 0.154999 | − | 0.213338i | ||||
\(599\) | −8.75148 | − | 26.9343i | −0.357576 | − | 1.10051i | −0.954501 | − | 0.298208i | \(-0.903611\pi\) |
0.596925 | − | 0.802297i | \(-0.296389\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.19268 | + | 4.49925i | 0.252605 | + | 0.183528i | 0.706880 | − | 0.707333i | \(-0.250102\pi\) |
−0.454276 | + | 0.890861i | \(0.650102\pi\) | |||||||
\(602\) | −1.23692 | − | 1.70248i | −0.0504131 | − | 0.0693877i | ||||
\(603\) | −9.28043 | − | 3.01539i | −0.377928 | − | 0.122796i | ||||
\(604\) | 3.65184 | 0.148591 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 28.8495 | 1.17193 | ||||||||
\(607\) | −11.0309 | − | 3.58415i | −0.447730 | − | 0.145476i | 0.0764693 | − | 0.997072i | \(-0.475635\pi\) |
−0.524199 | + | 0.851596i | \(0.675635\pi\) | |||||||
\(608\) | 1.31878 | + | 1.81514i | 0.0534835 | + | 0.0736137i | ||||
\(609\) | 18.4653 | + | 13.4159i | 0.748253 | + | 0.543638i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.250066 | + | 0.769625i | 0.0101166 | + | 0.0311357i | ||||
\(612\) | −0.0583382 | + | 0.0802957i | −0.00235818 | + | 0.00324576i | ||||
\(613\) | 18.8725 | + | 25.9757i | 0.762251 | + | 1.04915i | 0.997023 | + | 0.0770985i | \(0.0245656\pi\) |
−0.234772 | + | 0.972050i | \(0.575434\pi\) | |||||||
\(614\) | 8.87307 | − | 27.3085i | 0.358088 | − | 1.10208i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 19.2282 | + | 6.92929i | 0.774725 | + | 0.279189i | ||||
\(617\) | 18.7392i | 0.754414i | 0.926129 | + | 0.377207i | \(0.123115\pi\) | ||||
−0.926129 | + | 0.377207i | \(0.876885\pi\) | |||||||
\(618\) | −18.2732 | − | 5.93732i | −0.735056 | − | 0.238834i | ||||
\(619\) | −31.6002 | + | 22.9589i | −1.27012 | + | 0.922796i | −0.999207 | − | 0.0398085i | \(-0.987325\pi\) |
−0.270912 | + | 0.962604i | \(0.587325\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.630110 | + | 1.93928i | 0.0252854 | + | 0.0778205i | ||||
\(622\) | −8.46040 | + | 2.74895i | −0.339231 | + | 0.110223i | ||||
\(623\) | −0.786827 | + | 1.08297i | −0.0315236 | + | 0.0433884i | ||||
\(624\) | 7.50158 | − | 5.45022i | 0.300304 | − | 0.218183i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 7.54633 | 0.301612 | ||||||||
\(627\) | −5.71766 | − | 4.43790i | −0.228341 | − | 0.177233i | ||||
\(628\) | 1.66887i | 0.0665952i | ||||||||
\(629\) | 1.48383 | − | 4.56677i | 0.0591644 | − | 0.182089i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −36.4512 | − | 26.4833i | −1.45110 | − | 1.05428i | −0.985573 | − | 0.169249i | \(-0.945866\pi\) |
−0.465524 | − | 0.885035i | \(-0.654134\pi\) | |||||||
\(632\) | −23.5576 | + | 7.65433i | −0.937071 | + | 0.304473i | ||||
\(633\) | −5.15339 | + | 1.67444i | −0.204829 | + | 0.0665530i | ||||
\(634\) | −16.3479 | − | 11.8775i | −0.649260 | − | 0.471715i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.653073 | − | 2.00995i | 0.0258960 | − | 0.0796997i | ||||
\(637\) | − | 3.71027i | − | 0.147006i | ||||||
\(638\) | 13.5802 | + | 46.7972i | 0.537644 | + | 1.85272i | ||||
\(639\) | 14.9968 | 0.593263 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.9477 | + | 15.2194i | −0.827384 | + | 0.601130i | −0.918818 | − | 0.394682i | \(-0.870855\pi\) |
0.0914341 | + | 0.995811i | \(0.470855\pi\) | |||||||
\(642\) | 1.71365 | − | 2.35864i | 0.0676325 | − | 0.0930882i | ||||
\(643\) | −29.1386 | + | 9.46770i | −1.14911 | + | 0.373370i | −0.820809 | − | 0.571202i | \(-0.806477\pi\) |
−0.328304 | + | 0.944572i | \(0.606477\pi\) | |||||||
\(644\) | 0.263616 | + | 0.811326i | 0.0103879 | + | 0.0319707i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.41998 | + | 1.03168i | −0.0558685 | + | 0.0405908i | ||||
\(647\) | 14.3689 | + | 4.66875i | 0.564901 | + | 0.183547i | 0.577525 | − | 0.816373i | \(-0.304019\pi\) |
−0.0126243 | + | 0.999920i | \(0.504019\pi\) | |||||||
\(648\) | 2.68522i | 0.105485i | ||||||||
\(649\) | 15.0522 | + | 22.1633i | 0.590849 | + | 0.869987i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.80218 | + | 14.7796i | −0.188212 | + | 0.579258i | ||||
\(652\) | −1.21425 | − | 1.67127i | −0.0475537 | − | 0.0654521i | ||||
\(653\) | −3.07722 | + | 4.23543i | −0.120421 | + | 0.165745i | −0.864972 | − | 0.501821i | \(-0.832664\pi\) |
0.744551 | + | 0.667566i | \(0.232664\pi\) | |||||||
\(654\) | 4.84856 | + | 14.9223i | 0.189594 | + | 0.583510i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6.38745 | − | 4.64075i | −0.249388 | − | 0.181191i | ||||
\(657\) | 4.61907 | + | 6.35761i | 0.180207 | + | 0.248034i | ||||
\(658\) | −1.21882 | − | 0.396020i | −0.0475147 | − | 0.0154385i | ||||
\(659\) | −14.9207 | −0.581229 | −0.290615 | − | 0.956840i | \(-0.593860\pi\) | ||||
−0.290615 | + | 0.956840i | \(0.593860\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 45.7403 | 1.77909 | 0.889545 | − | 0.456847i | \(-0.151021\pi\) | ||||
0.889545 | + | 0.456847i | \(0.151021\pi\) | |||||||
\(662\) | 16.1141 | + | 5.23579i | 0.626292 | + | 0.203495i | ||||
\(663\) | 0.685085 | + | 0.942938i | 0.0266065 | + | 0.0366207i | ||||
\(664\) | −20.5341 | − | 14.9189i | −0.796878 | − | 0.578966i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.02613 | + | 12.3912i | 0.156009 | + | 0.480147i | ||||
\(667\) | 11.9200 | − | 16.4065i | 0.461544 | − | 0.635261i | ||||
\(668\) | −1.61800 | − | 2.22699i | −0.0626023 | − | 0.0861647i | ||||
\(669\) | −4.85386 | + | 14.9386i | −0.187661 | + | 0.577561i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.917993 | − | 28.9261i | 0.0354387 | − | 1.11668i | ||||
\(672\) | 2.35947i | 0.0910185i | ||||||||
\(673\) | 20.0755 | + | 6.52294i | 0.773855 | + | 0.251441i | 0.669214 | − | 0.743069i | \(-0.266631\pi\) |
0.104641 | + | 0.994510i | \(0.466631\pi\) | |||||||
\(674\) | −4.49852 | + | 3.26836i | −0.173276 | + | 0.125893i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.474159 | − | 1.45931i | −0.0182369 | − | 0.0561273i | ||||
\(677\) | −41.9125 | + | 13.6182i | −1.61083 | + | 0.523390i | −0.969753 | − | 0.244087i | \(-0.921512\pi\) |
−0.641077 | + | 0.767477i | \(0.721512\pi\) | |||||||
\(678\) | 14.6706 | − | 20.1924i | 0.563421 | − | 0.775483i | ||||
\(679\) | 9.98516 | − | 7.25464i | 0.383195 | − | 0.278408i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.47141 | −0.0563847 | ||||||||
\(682\) | −27.4456 | + | 18.6396i | −1.05095 | + | 0.713748i | ||||
\(683\) | − | 42.5318i | − | 1.62743i | −0.581261 | − | 0.813717i | \(-0.697440\pi\) | ||
0.581261 | − | 0.813717i | \(-0.302560\pi\) | |||||||
\(684\) | 0.122935 | − | 0.378355i | 0.00470054 | − | 0.0144668i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 23.9531 | + | 17.4029i | 0.914532 | + | 0.664446i | ||||
\(687\) | −15.1932 | + | 4.93656i | −0.579656 | + | 0.188342i | ||||
\(688\) | −2.55694 | + | 0.830802i | −0.0974826 | + | 0.0316740i | ||||
\(689\) | −20.0783 | − | 14.5878i | −0.764924 | − | 0.555750i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.77552 | + | 5.46449i | −0.0675439 | + | 0.207879i | −0.979132 | − | 0.203227i | \(-0.934857\pi\) |
0.911588 | + | 0.411105i | \(0.134857\pi\) | |||||||
\(692\) | − | 3.32949i | − | 0.126568i | ||||||
\(693\) | −2.12129 | − | 7.30996i | −0.0805811 | − | 0.277682i | ||||
\(694\) | −0.584966 | −0.0222050 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 21.6054 | − | 15.6972i | 0.818949 | − | 0.595001i | ||||
\(697\) | 0.583336 | − | 0.802893i | 0.0220954 | − | 0.0304117i | ||||
\(698\) | −18.5044 | + | 6.01244i | −0.700401 | + | 0.227574i | ||||
\(699\) | 7.92263 | + | 24.3833i | 0.299661 | + | 0.922263i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.983718 | − | 0.714713i | 0.0371545 | − | 0.0269943i | −0.569053 | − | 0.822301i | \(-0.692690\pi\) |
0.606208 | + | 0.795307i | \(0.292690\pi\) | |||||||
\(702\) | −3.00770 | − | 0.977260i | −0.113518 | − | 0.0368843i | ||||
\(703\) | 19.2470i | 0.725913i | ||||||||
\(704\) | 14.5279 | − | 18.7173i | 0.547540 | − | 0.705433i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.19736 | + | 15.9958i | −0.195605 | + | 0.602011i | ||||
\(707\) | 26.3437 | + | 36.2589i | 0.990755 | + | 1.36366i | ||||
\(708\) | −0.865562 | + | 1.19134i | −0.0325298 | + | 0.0447734i | ||||
\(709\) | 8.16115 | + | 25.1174i | 0.306498 | + | 0.943305i | 0.979114 | + | 0.203313i | \(0.0651709\pi\) |
−0.672615 | + | 0.739992i | \(0.734829\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.46281 | + | 5.42205i | 0.279877 | + | 0.203343i | ||||
\(712\) | 0.920626 | + | 1.26713i | 0.0345019 | + | 0.0474878i | ||||
\(713\) | 13.1317 | + | 4.26675i | 0.491786 | + | 0.159791i | ||||
\(714\) | −1.84581 | −0.0690777 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.0957823 | −0.00357955 | ||||||||
\(717\) | 3.97738 | + | 1.29233i | 0.148538 | + | 0.0482629i | ||||
\(718\) | −12.4761 | − | 17.1719i | −0.465604 | − | 0.640849i | ||||
\(719\) | 40.0007 | + | 29.0622i | 1.49177 | + | 1.08384i | 0.973518 | + | 0.228611i | \(0.0734183\pi\) |
0.518255 | + | 0.855226i | \(0.326582\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.22379 | − | 28.3879i | −0.343512 | − | 1.05722i | ||||
\(722\) | −12.3627 | + | 17.0157i | −0.460090 | + | 0.633260i | ||||
\(723\) | 1.93487 | + | 2.66312i | 0.0719586 | + | 0.0990425i | ||||
\(724\) | 0.997692 | − | 3.07058i | 0.0370789 | − | 0.114117i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 5.99131 | − | 15.1050i | 0.222359 | − | 0.560600i | ||||
\(727\) | 39.2447i | 1.45551i | 0.685839 | + | 0.727753i | \(0.259435\pi\) | ||||
−0.685839 | + | 0.727753i | \(0.740565\pi\) | |||||||
\(728\) | 12.5468 | + | 4.07670i | 0.465015 | + | 0.151093i | ||||
\(729\) | 0.809017 | − | 0.587785i | 0.0299636 | − | 0.0217698i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.104431 | − | 0.321404i | −0.00386250 | − | 0.0118876i | ||||
\(732\) | 1.51286 | − | 0.491558i | 0.0559169 | − | 0.0181685i | ||||
\(733\) | 3.05601 | − | 4.20624i | 0.112876 | − | 0.155361i | −0.748841 | − | 0.662750i | \(-0.769389\pi\) |
0.861717 | + | 0.507389i | \(0.169389\pi\) | |||||||
\(734\) | 31.3888 | − | 22.8053i | 1.15858 | − | 0.841760i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.09639 | 0.0772740 | ||||||||
\(737\) | 10.9722 | − | 30.4470i | 0.404167 | − | 1.12153i | ||||
\(738\) | 2.69279i | 0.0991229i | ||||||||
\(739\) | −8.96428 | + | 27.5892i | −0.329757 | + | 1.01489i | 0.639491 | + | 0.768799i | \(0.279145\pi\) |
−0.969248 | + | 0.246088i | \(0.920855\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.77957 | − | 2.74602i | −0.138846 | − | 0.100877i | ||||
\(742\) | 37.3799 | − | 12.1455i | 1.37226 | − | 0.445874i | ||||
\(743\) | −8.09042 | + | 2.62874i | −0.296809 | + | 0.0964390i | −0.453636 | − | 0.891187i | \(-0.649873\pi\) |
0.156827 | + | 0.987626i | \(0.449873\pi\) | |||||||
\(744\) | 14.7102 | + | 10.6876i | 0.539301 | + | 0.391825i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −9.99506 | + | 30.7616i | −0.365945 | + | 1.12626i | ||||
\(747\) | 9.45232i | 0.345842i | ||||||||
\(748\) | −0.260039 | − | 0.201836i | −0.00950798 | − | 0.00737985i | ||||
\(749\) | 4.52922 | 0.165494 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.4006 | − | 20.6343i | 1.03635 | − | 0.752955i | 0.0667831 | − | 0.997768i | \(-0.478726\pi\) |
0.969570 | + | 0.244813i | \(0.0787264\pi\) | |||||||
\(752\) | −0.962377 | + | 1.32460i | −0.0350943 | + | 0.0483032i | ||||
\(753\) | 8.90626 | − | 2.89382i | 0.324562 | − | 0.105457i | ||||
\(754\) | 9.71928 | + | 29.9129i | 0.353955 | + | 1.08936i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.338464 | − | 0.245909i | 0.0123098 | − | 0.00894362i | ||||
\(757\) | 6.83159 | + | 2.21972i | 0.248298 | + | 0.0806771i | 0.430522 | − | 0.902580i | \(-0.358329\pi\) |
−0.182224 | + | 0.983257i | \(0.558329\pi\) | |||||||
\(758\) | − | 37.7582i | − | 1.37144i | ||||||
\(759\) | −6.49491 | + | 1.88477i | −0.235750 | + | 0.0684128i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.4072 | + | 41.2631i | −0.486011 | + | 1.49579i | 0.344501 | + | 0.938786i | \(0.388048\pi\) |
−0.830512 | + | 0.557001i | \(0.811952\pi\) | |||||||
\(762\) | −3.58828 | − | 4.93885i | −0.129990 | − | 0.178916i | ||||
\(763\) | −14.3274 | + | 19.7200i | −0.518687 | + | 0.713912i | ||||
\(764\) | 0.932419 | + | 2.86969i | 0.0337337 | + | 0.103822i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 22.7695 | + | 16.5430i | 0.822696 | + | 0.597724i | ||||
\(767\) | 10.1646 | + | 13.9903i | 0.367021 | + | 0.505162i | ||||
\(768\) | 4.12748 | + | 1.34110i | 0.148937 | + | 0.0483927i | ||||
\(769\) | 19.6548 | 0.708771 | 0.354385 | − | 0.935099i | \(-0.384690\pi\) | ||||
0.354385 | + | 0.935099i | \(0.384690\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.5714 | −0.452747 | ||||||||
\(772\) | 4.24824 | + | 1.38034i | 0.152898 | + | 0.0496795i | ||||
\(773\) | 14.3631 | + | 19.7691i | 0.516604 | + | 0.711044i | 0.985015 | − | 0.172466i | \(-0.0551735\pi\) |
−0.468412 | + | 0.883510i | \(0.655174\pi\) | |||||||
\(774\) | 0.741831 | + | 0.538972i | 0.0266646 | + | 0.0193729i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4.46256 | − | 13.7343i | −0.160196 | − | 0.493034i | ||||
\(777\) | −11.8971 | + | 16.3750i | −0.426808 | + | 0.587450i | ||||
\(778\) | 14.2338 | + | 19.5912i | 0.510307 | + | 0.702377i | ||||
\(779\) | −1.22925 | + | 3.78326i | −0.0440426 | + | 0.135549i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.57770 | + | 49.7136i | −0.0564545 | + | 1.77889i | ||||
\(782\) | 1.64001i | 0.0586465i | ||||||||
\(783\) | −9.45867 | − | 3.07331i | −0.338025 | − | 0.109831i | ||||
\(784\) | 6.07319 | − | 4.41243i | 0.216900 | − | 0.157587i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.199274 | + | 0.613302i | 0.00710786 | + | 0.0218758i | ||||
\(787\) | −32.4721 | + | 10.5508i | −1.15750 | + | 0.376096i | −0.823965 | − | 0.566640i | \(-0.808243\pi\) |
−0.333539 | + | 0.942736i | \(0.608243\pi\) | |||||||
\(788\) | −0.804576 | + | 1.10740i | −0.0286618 | + | 0.0394496i | ||||
\(789\) | 3.90712 | − | 2.83869i | 0.139097 | − | 0.101060i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 38.7747 | 1.37867 | ||||||||
\(792\) | −8.90139 | − | 0.282492i | −0.316297 | − | 0.0100379i | ||||
\(793\) | − | 18.6803i | − | 0.663357i | ||||||
\(794\) | 14.1435 | − | 43.5292i | 0.501934 | − | 1.54479i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.96373 | + | 2.15327i | 0.105047 | + | 0.0763208i | ||||
\(797\) | −2.89410 | + | 0.940349i | −0.102514 | + | 0.0333089i | −0.359825 | − | 0.933020i | \(-0.617164\pi\) |
0.257311 | + | 0.966329i | \(0.417164\pi\) | |||||||
\(798\) | 7.03644 | − | 2.28628i | 0.249087 | − | 0.0809333i | ||||
\(799\) | −0.166500 | − | 0.120969i | −0.00589035 | − | 0.00427959i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.180247 | − | 0.554742i | 0.00636870 | − | 0.0196008i | ||||
\(802\) | − | 9.40439i | − | 0.332081i | ||||||
\(803\) | −21.5611 | + | 14.6432i | −0.760876 | + | 0.516747i | ||||
\(804\) | 1.77886 | 0.0627355 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −17.3247 | + | 12.5871i | −0.610237 | + | 0.443363i | ||||
\(807\) | 3.07370 | − | 4.23058i | 0.108199 | − | 0.148924i | ||||
\(808\) | 49.8733 | − | 16.2048i | 1.75454 | − | 0.570083i | ||||
\(809\) | 3.43043 | + | 10.5578i | 0.120607 | + | 0.371191i | 0.993075 | − | 0.117480i | \(-0.0374816\pi\) |
−0.872468 | + | 0.488672i | \(0.837482\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33.4336 | + | 24.2909i | −1.17401 | + | 0.852969i | −0.991484 | − | 0.130231i | \(-0.958428\pi\) |
−0.182528 | + | 0.983201i | \(0.558428\pi\) | |||||||
\(812\) | −3.95718 | − | 1.28577i | −0.138870 | − | 0.0451215i | ||||
\(813\) | 30.3311i | 1.06376i | ||||||||
\(814\) | −41.4997 | + | 12.0429i | −1.45456 | + | 0.422102i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.728721 | + | 2.24277i | −0.0255103 | + | 0.0785128i | ||||
\(817\) | 0.796202 | + | 1.09588i | 0.0278556 | + | 0.0383399i | ||||
\(818\) | 5.44322 | − | 7.49195i | 0.190318 | − | 0.261950i | ||||
\(819\) | −1.51820 | − | 4.67254i | −0.0530502 | − | 0.163272i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.61681 | − | 4.80739i | −0.230928 | − | 0.167779i | 0.466304 | − | 0.884625i | \(-0.345585\pi\) |
−0.697232 | + | 0.716845i | \(0.745585\pi\) | |||||||
\(822\) | 6.83178 | + | 9.40314i | 0.238286 | + | 0.327972i | ||||
\(823\) | 12.5514 | + | 4.07819i | 0.437513 | + | 0.142157i | 0.519488 | − | 0.854478i | \(-0.326123\pi\) |
−0.0819748 | + | 0.996634i | \(0.526123\pi\) | |||||||
\(824\) | −34.9246 | −1.21665 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −27.3862 | −0.952889 | ||||||||
\(827\) | 29.2326 | + | 9.49825i | 1.01652 | + | 0.330287i | 0.769447 | − | 0.638711i | \(-0.220532\pi\) |
0.247071 | + | 0.968997i | \(0.420532\pi\) | |||||||
\(828\) | −0.218490 | − | 0.300726i | −0.00759306 | − | 0.0104510i | ||||
\(829\) | 2.98357 | + | 2.16769i | 0.103624 | + | 0.0752871i | 0.638390 | − | 0.769713i | \(-0.279601\pi\) |
−0.534767 | + | 0.845000i | \(0.679601\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.93483 | + | 15.1878i | 0.171187 | + | 0.526861i | ||||
\(832\) | 8.98933 | − | 12.3728i | 0.311649 | − | 0.428948i | ||||
\(833\) | 0.554636 | + | 0.763391i | 0.0192170 | + | 0.0264499i | ||||
\(834\) | 8.05407 | − | 24.7879i | 0.278889 | − | 0.858334i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.24130 | + | 0.447329i | 0.0429312 | + | 0.0154712i | ||||
\(837\) | − | 6.77143i | − | 0.234055i | ||||||
\(838\) | −5.48399 | − | 1.78186i | −0.189441 | − | 0.0615533i | ||||
\(839\) | 35.2341 | − | 25.5991i | 1.21642 | − | 0.883778i | 0.220618 | − | 0.975360i | \(-0.429192\pi\) |
0.995798 | + | 0.0915823i | \(0.0291924\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.6039 | + | 66.4900i | 0.744963 | + | 2.29276i | ||||
\(842\) | −24.4063 | + | 7.93008i | −0.841096 | + | 0.273289i | ||||
\(843\) | −0.817415 | + | 1.12508i | −0.0281533 | + | 0.0387497i | ||||
\(844\) | 0.799143 | − | 0.580611i | 0.0275076 | − | 0.0199855i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.558418 | 0.0191988 | ||||||||
\(847\) | 24.4554 | − | 6.26295i | 0.840296 | − | 0.215198i | ||||
\(848\) | − | 50.2139i | − | 1.72435i | ||||||
\(849\) | −1.81533 | + | 5.58701i | −0.0623019 | + | 0.191746i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.5492 | + | 10.5706i | 0.498741 | + | 0.362357i | ||||
\(852\) | −2.60006 | + | 0.844811i | −0.0890766 | + | 0.0289428i | ||||
\(853\) | 28.8583 | − | 9.37662i | 0.988088 | − | 0.321049i | 0.229992 | − | 0.973192i | \(-0.426130\pi\) |
0.758096 | + | 0.652143i | \(0.226130\pi\) | |||||||
\(854\) | 23.9333 | + | 17.3886i | 0.818982 | + | 0.595025i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.63761 | − | 5.04004i | 0.0559723 | − | 0.172265i | ||||
\(857\) | − | 12.5402i | − | 0.428365i | −0.976794 | − | 0.214182i | \(-0.931291\pi\) | ||
0.976794 | − | 0.214182i | \(-0.0687087\pi\) | |||||||
\(858\) | 3.55599 | − | 9.86757i | 0.121400 | − | 0.336873i | ||||
\(859\) | 8.67783 | 0.296084 | 0.148042 | − | 0.988981i | \(-0.452703\pi\) | ||||
0.148042 | + | 0.988981i | \(0.452703\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.38438 | + | 2.45889i | −0.115339 | + | 0.0837989i | ||||
\(862\) | −6.10988 | + | 8.40953i | −0.208103 | + | 0.286430i | ||||
\(863\) | 36.5128 | − | 11.8637i | 1.24291 | − | 0.403846i | 0.387535 | − | 0.921855i | \(-0.373327\pi\) |
0.855375 | + | 0.518009i | \(0.173327\pi\) | |||||||
\(864\) | −0.317703 | − | 0.977789i | −0.0108085 | − | 0.0332651i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 3.28935 | − | 2.38985i | 0.111777 | − | 0.0812104i | ||||
\(867\) | 15.8860 | + | 5.16169i | 0.539518 | + | 0.175300i | ||||
\(868\) | − | 2.83293i | − | 0.0961559i | ||||||
\(869\) | −18.7590 | + | 24.1685i | −0.636354 | + | 0.819859i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.45528 | − | 19.8673i | 0.218729 | − | 0.673178i | ||||
\(872\) | 16.7638 | + | 23.0734i | 0.567693 | + | 0.781363i | ||||
\(873\) | −3.16111 | + | 4.35090i | −0.106988 | + | 0.147256i | ||||
\(874\) | −2.03136 | − | 6.25188i | −0.0687118 | − | 0.211473i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.15897 | − | 0.842044i | −0.0391581 | − | 0.0284500i | ||||
\(877\) | 18.3917 | + | 25.3140i | 0.621043 | + | 0.854792i | 0.997428 | − | 0.0716708i | \(-0.0228331\pi\) |
−0.376385 | + | 0.926463i | \(0.622833\pi\) | |||||||
\(878\) | 3.84542 | + | 1.24945i | 0.129777 | + | 0.0421669i | ||||
\(879\) | −19.9745 | −0.673723 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 49.2703 | 1.65996 | 0.829979 | − | 0.557795i | \(-0.188353\pi\) | ||||
0.829979 | + | 0.557795i | \(0.188353\pi\) | |||||||
\(882\) | −2.43500 | − | 0.791178i | −0.0819906 | − | 0.0266404i | ||||
\(883\) | −16.5674 | − | 22.8031i | −0.557537 | − | 0.767385i | 0.433473 | − | 0.901166i | \(-0.357288\pi\) |
−0.991011 | + | 0.133782i | \(0.957288\pi\) | |||||||
\(884\) | −0.171895 | − | 0.124889i | −0.00578145 | − | 0.00420047i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.06905 | − | 15.6009i | −0.170298 | − | 0.524123i | ||||
\(887\) | 14.9852 | − | 20.6253i | 0.503153 | − | 0.692531i | −0.479593 | − | 0.877491i | \(-0.659216\pi\) |
0.982746 | + | 0.184960i | \(0.0592155\pi\) | |||||||
\(888\) | 13.9202 | + | 19.1596i | 0.467133 | + | 0.642953i | ||||
\(889\) | 2.93068 | − | 9.01972i | 0.0982920 | − | 0.302512i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.86337 | + | 2.74369i | 0.0624253 | + | 0.0919171i | ||||
\(892\) | − | 2.86342i | − | 0.0958743i | ||||||
\(893\) | 0.784553 | + | 0.254917i | 0.0262541 | + | 0.00853047i | ||||
\(894\) | 13.0988 | − | 9.51681i | 0.438088 | − | 0.318290i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 8.94256 | + | 27.5224i | 0.298750 | + | 0.919458i | ||||
\(897\) | −4.15156 | + | 1.34892i | −0.138616 | + | 0.0450392i | ||||
\(898\) | −12.8743 | + | 17.7200i | −0.429621 | + | 0.591323i | ||||
\(899\) | −54.4831 | + | 39.5843i | −1.81711 | + | 1.32021i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.31181 | 0.210277 | ||||||||
\(902\) | −8.92648 | − | 0.283289i | −0.297219 | − | 0.00943248i | ||||
\(903\) | 1.42451i | 0.0474048i | ||||||||
\(904\) | 14.0196 | − | 43.1478i | 0.466284 | − | 1.43507i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −23.9413 | − | 17.3943i | −0.795395 | − | 0.577888i | ||||
\(907\) | 2.35913 | − | 0.766528i | 0.0783337 | − | 0.0254522i | −0.269588 | − | 0.962976i | \(-0.586888\pi\) |
0.347922 | + | 0.937524i | \(0.386888\pi\) | |||||||
\(908\) | 0.255106 | − | 0.0828891i | 0.00846600 | − | 0.00275077i | ||||
\(909\) | −15.7994 | − | 11.4789i | −0.524031 | − | 0.380731i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.839165 | − | 2.58268i | 0.0278028 | − | 0.0855681i | −0.936192 | − | 0.351488i | \(-0.885676\pi\) |
0.963995 | + | 0.265920i | \(0.0856757\pi\) | |||||||
\(912\) | − | 9.45232i | − | 0.312998i | ||||||
\(913\) | −31.3340 | − | 0.994409i | −1.03700 | − | 0.0329101i | ||||
\(914\) | 43.1101 | 1.42595 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.35602 | − | 1.71175i | 0.0778453 | − | 0.0565579i | ||||
\(917\) | −0.588851 | + | 0.810484i | −0.0194456 | + | 0.0267645i | ||||
\(918\) | 0.764923 | − | 0.248539i | 0.0252462 | − | 0.00820300i | ||||
\(919\) | −1.00091 | − | 3.08047i | −0.0330169 | − | 0.101615i | 0.933190 | − | 0.359383i | \(-0.117013\pi\) |
−0.966207 | + | 0.257768i | \(0.917013\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.7251 | + | 11.4249i | −0.518158 | + | 0.376464i | ||||
\(922\) | −43.8063 | − | 14.2335i | −1.44268 | − | 0.468757i | ||||
\(923\) | 32.1047i | 1.05674i | ||||||||
\(924\) | 0.779570 | + | 1.14786i | 0.0256460 | + | 0.0377620i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −18.7914 | + | 57.8339i | −0.617523 | + | 1.90054i | ||||
\(927\) | 7.64487 | + | 10.5223i | 0.251090 | + | 0.345596i | ||||
\(928\) | −6.01010 | + | 8.27219i | −0.197291 | + | 0.271548i | ||||
\(929\) | −2.21938 | − | 6.83056i | −0.0728156 | − | 0.224103i | 0.908025 | − | 0.418916i | \(-0.137590\pi\) |
−0.980840 | + | 0.194813i | \(0.937590\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.05989 | − | 2.22314i | −0.100284 | − | 0.0728606i | ||||
\(932\) | −2.74717 | − | 3.78115i | −0.0899865 | − | 0.123856i | ||||
\(933\) | 5.72709 | + | 1.86084i | 0.187496 | + | 0.0609213i | ||||
\(934\) | 57.2832 | 1.87436 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.74845 | −0.187894 | ||||||||
\(937\) | −19.3185 | − | 6.27696i | −0.631108 | − | 0.205059i | −0.0240421 | − | 0.999711i | \(-0.507654\pi\) |
−0.607066 | + | 0.794652i | \(0.707654\pi\) | |||||||
\(938\) | 19.4452 | + | 26.7641i | 0.634909 | + | 0.873877i | ||||
\(939\) | −4.13273 | − | 3.00260i | −0.134866 | − | 0.0979862i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.85663 | − | 24.1802i | −0.256119 | − | 0.788253i | −0.993607 | − | 0.112893i | \(-0.963988\pi\) |
0.737488 | − | 0.675360i | \(-0.236012\pi\) | |||||||
\(942\) | 7.94911 | − | 10.9410i | 0.258996 | − | 0.356478i | ||||
\(943\) | 2.18473 | + | 3.00702i | 0.0711446 | + | 0.0979222i | ||||
\(944\) | −10.8120 | + | 33.2760i | −0.351901 | + | 1.08304i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.86471 | + | 2.40244i | −0.0606270 | + | 0.0781099i | ||||
\(947\) | 4.55536i | 0.148029i | 0.997257 | + | 0.0740147i | \(0.0235812\pi\) | ||||
−0.997257 | + | 0.0740147i | \(0.976419\pi\) | |||||||
\(948\) | −1.59930 | − | 0.519645i | −0.0519430 | − | 0.0168773i | ||||
\(949\) | −13.6102 | + | 9.88839i | −0.441806 | + | 0.320991i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.22699 | + | 13.0093i | 0.137069 | + | 0.421856i | ||||
\(952\) | −3.19092 | + | 1.03679i | −0.103418 | + | 0.0336027i | ||||
\(953\) | −24.4433 | + | 33.6433i | −0.791797 | + | 1.08981i | 0.202085 | + | 0.979368i | \(0.435228\pi\) |
−0.993882 | + | 0.110447i | \(0.964772\pi\) | |||||||
\(954\) | −13.8552 | + | 10.0664i | −0.448580 | + | 0.325912i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.762378 | −0.0246571 | ||||||||
\(957\) | 11.1830 | − | 31.0318i | 0.361494 | − | 1.00311i | ||||
\(958\) | − | 24.6519i | − | 0.796467i | ||||||
\(959\) | −5.57977 | + | 17.1728i | −0.180180 | + | 0.554538i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.0158 | − | 8.72996i | −0.387605 | − | 0.281612i | ||||
\(962\) | −26.5267 | + | 8.61903i | −0.855254 | + | 0.277889i | ||||
\(963\) | −1.87695 | + | 0.609860i | −0.0604840 | + | 0.0196525i | ||||
\(964\) | −0.485479 | − | 0.352721i | −0.0156362 | − | 0.0113604i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.13623 | − | 6.57465i | 0.0687322 | − | 0.211536i | ||||
\(967\) | 16.2161i | 0.521476i | 0.965410 | + | 0.260738i | \(0.0839658\pi\) | ||||
−0.965410 | + | 0.260738i | \(0.916034\pi\) | |||||||
\(968\) | 1.87290 | − | 29.4780i | 0.0601972 | − | 0.947458i | ||||
\(969\) | 1.18814 | 0.0381686 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.8979 | − | 7.91778i | 0.349730 | − | 0.254094i | −0.399026 | − | 0.916940i | \(-0.630652\pi\) |
0.748756 | + | 0.662846i | \(0.230652\pi\) | |||||||
\(972\) | −0.107152 | + | 0.147481i | −0.00343689 | + | 0.00473047i | ||||
\(973\) | 38.5086 | − | 12.5122i | 1.23453 | − | 0.401123i | ||||
\(974\) | 1.14669 | + | 3.52916i | 0.0367425 | + | 0.113082i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 30.5770 | − | 22.2155i | 0.978746 | − | 0.711101i | ||||
\(977\) | 13.8284 | + | 4.49311i | 0.442409 | + | 0.143747i | 0.521747 | − | 0.853100i | \(-0.325281\pi\) |
−0.0793377 | + | 0.996848i | \(0.525281\pi\) | |||||||
\(978\) | 16.7404i | 0.535300i | ||||||||
\(979\) | 1.81998 | + | 0.655870i | 0.0581669 | + | 0.0209617i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.28213 | − | 10.1014i | 0.104790 | − | 0.322512i | ||||
\(982\) | 6.56326 | + | 9.03356i | 0.209442 | + | 0.288272i | ||||
\(983\) | −14.4559 | + | 19.8968i | −0.461072 | + | 0.634611i | −0.974731 | − | 0.223384i | \(-0.928290\pi\) |
0.513659 | + | 0.857994i | \(0.328290\pi\) | |||||||
\(984\) | 1.51254 | + | 4.65513i | 0.0482181 | + | 0.148400i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −6.47132 | − | 4.70169i | −0.206089 | − | 0.149732i | ||||
\(987\) | 0.509914 | + | 0.701836i | 0.0162307 | + | 0.0223397i | ||||
\(988\) | 0.809973 | + | 0.263176i | 0.0257687 | + | 0.00837275i | ||||
\(989\) | 1.26568 | 0.0402463 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.43775 | 0.140970 | 0.0704848 | − | 0.997513i | \(-0.477545\pi\) | ||||
0.0704848 | + | 0.997513i | \(0.477545\pi\) | |||||||
\(992\) | −6.62103 | − | 2.15130i | −0.210218 | − | 0.0683040i | ||||
\(993\) | −6.74158 | − | 9.27899i | −0.213938 | − | 0.294460i | ||||
\(994\) | −41.1328 | − | 29.8847i | −1.30465 | − | 0.947885i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.532477 | − | 1.63879i | −0.0168722 | − | 0.0519272i | ||||
\(997\) | −0.00615442 | + | 0.00847083i | −0.000194912 | + | 0.000268274i | −0.809114 | − | 0.587651i | \(-0.800053\pi\) |
0.808920 | + | 0.587919i | \(0.200053\pi\) | |||||||
\(998\) | 14.5845 | + | 20.0739i | 0.461665 | + | 0.635427i | ||||
\(999\) | 2.72540 | − | 8.38793i | 0.0862280 | − | 0.265382i |
(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 | 825.2.bx.f.724.4 | 16 | ||
5.2 | odd | 4 | 165.2.m.d.31.1 | yes | 8 | ||
5.3 | odd | 4 | 825.2.n.g.526.2 | 8 | |||
5.4 | even | 2 | inner | 825.2.bx.f.724.1 | 16 | ||
11.5 | even | 5 | inner | 825.2.bx.f.49.1 | 16 | ||
15.2 | even | 4 | 495.2.n.a.361.2 | 8 | |||
55.7 | even | 20 | 1815.2.a.w.1.3 | 4 | |||
55.18 | even | 20 | 9075.2.a.cm.1.2 | 4 | |||
55.27 | odd | 20 | 165.2.m.d.16.1 | ✓ | 8 | ||
55.37 | odd | 20 | 1815.2.a.p.1.2 | 4 | |||
55.38 | odd | 20 | 825.2.n.g.676.2 | 8 | |||
55.48 | odd | 20 | 9075.2.a.di.1.3 | 4 | |||
55.49 | even | 10 | inner | 825.2.bx.f.49.4 | 16 | ||
165.62 | odd | 20 | 5445.2.a.bf.1.2 | 4 | |||
165.92 | even | 20 | 5445.2.a.bt.1.3 | 4 | |||
165.137 | even | 20 | 495.2.n.a.181.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.m.d.16.1 | ✓ | 8 | 55.27 | odd | 20 | ||
165.2.m.d.31.1 | yes | 8 | 5.2 | odd | 4 | ||
495.2.n.a.181.2 | 8 | 165.137 | even | 20 | |||
495.2.n.a.361.2 | 8 | 15.2 | even | 4 | |||
825.2.n.g.526.2 | 8 | 5.3 | odd | 4 | |||
825.2.n.g.676.2 | 8 | 55.38 | odd | 20 | |||
825.2.bx.f.49.1 | 16 | 11.5 | even | 5 | inner | ||
825.2.bx.f.49.4 | 16 | 55.49 | even | 10 | inner | ||
825.2.bx.f.724.1 | 16 | 5.4 | even | 2 | inner | ||
825.2.bx.f.724.4 | 16 | 1.1 | even | 1 | trivial | ||
1815.2.a.p.1.2 | 4 | 55.37 | odd | 20 | |||
1815.2.a.w.1.3 | 4 | 55.7 | even | 20 | |||
5445.2.a.bf.1.2 | 4 | 165.62 | odd | 20 | |||
5445.2.a.bt.1.3 | 4 | 165.92 | even | 20 | |||
9075.2.a.cm.1.2 | 4 | 55.18 | even | 20 | |||
9075.2.a.di.1.3 | 4 | 55.48 | odd | 20 |