Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(67,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.67");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.g (of order \(3\), degree \(2\), 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: | \(3.52140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 67.11 | ||
Character | \(\chi\) | \(=\) | 441.67 |
Dual form | 441.2.g.h.79.11 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.35757 | − | 2.35137i | 0.959944 | − | 1.66267i | 0.237320 | − | 0.971432i | \(-0.423731\pi\) |
0.722624 | − | 0.691241i | \(-0.242936\pi\) | |||||||
\(3\) | −1.69116 | − | 0.374116i | −0.976394 | − | 0.215996i | ||||
\(4\) | −2.68597 | − | 4.65224i | −1.34299 | − | 2.32612i | ||||
\(5\) | −1.58639 | −0.709457 | −0.354728 | − | 0.934969i | \(-0.615427\pi\) | ||||
−0.354728 | + | 0.934969i | \(0.615427\pi\) | |||||||
\(6\) | −3.17555 | + | 3.46867i | −1.29641 | + | 1.41608i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −9.15528 | −3.23688 | ||||||||
\(9\) | 2.72007 | + | 1.26538i | 0.906691 | + | 0.421795i | ||||
\(10\) | −2.15363 | + | 3.73020i | −0.681039 | + | 1.17959i | ||||
\(11\) | −1.34875 | −0.406664 | −0.203332 | − | 0.979110i | \(-0.565177\pi\) | ||||
−0.203332 | + | 0.979110i | \(0.565177\pi\) | |||||||
\(12\) | 2.80194 | + | 8.87257i | 0.808851 | + | 2.56129i | ||||
\(13\) | 1.58916 | − | 2.75251i | 0.440754 | − | 0.763409i | −0.556991 | − | 0.830518i | \(-0.688044\pi\) |
0.997746 | + | 0.0671096i | \(0.0213777\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.68285 | + | 0.593495i | 0.692709 | + | 0.153240i | ||||
\(16\) | −7.05696 | + | 12.2230i | −1.76424 | + | 3.05575i | ||||
\(17\) | −1.40027 | + | 2.42534i | −0.339615 | + | 0.588230i | −0.984360 | − | 0.176167i | \(-0.943630\pi\) |
0.644745 | + | 0.764397i | \(0.276963\pi\) | |||||||
\(18\) | 6.66807 | − | 4.67807i | 1.57168 | − | 1.10263i | ||||
\(19\) | −0.312846 | − | 0.541866i | −0.0717719 | − | 0.124313i | 0.827906 | − | 0.560867i | \(-0.189532\pi\) |
−0.899678 | + | 0.436554i | \(0.856199\pi\) | |||||||
\(20\) | 4.26101 | + | 7.38028i | 0.952791 | + | 1.65028i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.83102 | + | 3.17142i | −0.390375 | + | 0.676149i | ||||
\(23\) | −0.284867 | −0.0593989 | −0.0296995 | − | 0.999559i | \(-0.509455\pi\) | ||||
−0.0296995 | + | 0.999559i | \(0.509455\pi\) | |||||||
\(24\) | 15.4831 | + | 3.42514i | 3.16047 | + | 0.699153i | ||||
\(25\) | −2.48336 | −0.496671 | ||||||||
\(26\) | −4.31479 | − | 7.47343i | −0.846199 | − | 1.46566i | ||||
\(27\) | −4.12669 | − | 3.15760i | −0.794182 | − | 0.607679i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.27396 | + | 3.93861i | 0.422264 | + | 0.731382i | 0.996161 | − | 0.0875454i | \(-0.0279023\pi\) |
−0.573897 | + | 0.818928i | \(0.694569\pi\) | |||||||
\(30\) | 5.03768 | − | 5.50268i | 0.919750 | − | 1.00465i | ||||
\(31\) | −3.71502 | − | 6.43461i | −0.667238 | − | 1.15569i | −0.978673 | − | 0.205423i | \(-0.934143\pi\) |
0.311435 | − | 0.950267i | \(-0.399190\pi\) | |||||||
\(32\) | 10.0053 | + | 17.3297i | 1.76870 | + | 3.06348i | ||||
\(33\) | 2.28096 | + | 0.504590i | 0.397064 | + | 0.0878378i | ||||
\(34\) | 3.80191 | + | 6.58511i | 0.652023 | + | 1.12934i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.41918 | − | 16.0532i | −0.236529 | − | 2.67554i | ||||
\(37\) | −4.01126 | − | 6.94770i | −0.659447 | − | 1.14220i | −0.980759 | − | 0.195222i | \(-0.937457\pi\) |
0.321312 | − | 0.946973i | \(-0.395876\pi\) | |||||||
\(38\) | −1.69884 | −0.275588 | ||||||||
\(39\) | −3.71729 | + | 4.06041i | −0.595243 | + | 0.650187i | ||||
\(40\) | 14.5239 | 2.29643 | ||||||||
\(41\) | 5.01329 | − | 8.68327i | 0.782944 | − | 1.35610i | −0.147275 | − | 0.989096i | \(-0.547050\pi\) |
0.930219 | − | 0.367004i | \(-0.119616\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.12937 | − | 5.42022i | −0.477224 | − | 0.826576i | 0.522435 | − | 0.852679i | \(-0.325024\pi\) |
−0.999659 | + | 0.0261027i | \(0.991690\pi\) | |||||||
\(44\) | 3.62271 | + | 6.27472i | 0.546144 | + | 0.945950i | ||||
\(45\) | −4.31511 | − | 2.00740i | −0.643258 | − | 0.299245i | ||||
\(46\) | −0.386726 | + | 0.669829i | −0.0570197 | + | 0.0987609i | ||||
\(47\) | −5.57383 | + | 9.65415i | −0.813026 | + | 1.40820i | 0.0977106 | + | 0.995215i | \(0.468848\pi\) |
−0.910737 | + | 0.412988i | \(0.864485\pi\) | |||||||
\(48\) | 16.5073 | − | 18.0310i | 2.38262 | − | 2.60255i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −3.37132 | + | 5.83930i | −0.476777 | + | 0.825802i | ||||
\(51\) | 3.27544 | − | 3.57778i | 0.458653 | − | 0.500989i | ||||
\(52\) | −17.0738 | −2.36771 | ||||||||
\(53\) | −1.39349 | + | 2.41359i | −0.191410 | + | 0.331532i | −0.945718 | − | 0.324989i | \(-0.894639\pi\) |
0.754308 | + | 0.656521i | \(0.227973\pi\) | |||||||
\(54\) | −13.0269 | + | 5.41675i | −1.77274 | + | 0.737127i | ||||
\(55\) | 2.13965 | 0.288510 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.326354 | + | 1.03343i | 0.0432266 | + | 0.136881i | ||||
\(58\) | 12.3482 | 1.62140 | ||||||||
\(59\) | −2.28734 | − | 3.96180i | −0.297787 | − | 0.515782i | 0.677842 | − | 0.735207i | \(-0.262915\pi\) |
−0.975629 | + | 0.219425i | \(0.929582\pi\) | |||||||
\(60\) | −4.44498 | − | 14.0754i | −0.573845 | − | 1.81712i | ||||
\(61\) | 0.192507 | − | 0.333432i | 0.0246480 | − | 0.0426916i | −0.853438 | − | 0.521194i | \(-0.825487\pi\) |
0.878086 | + | 0.478502i | \(0.158820\pi\) | |||||||
\(62\) | −20.1736 | −2.56205 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 26.1036 | 3.26295 | ||||||||
\(65\) | −2.52104 | + | 4.36656i | −0.312696 | + | 0.541605i | ||||
\(66\) | 4.28304 | − | 4.67838i | 0.527205 | − | 0.575869i | ||||
\(67\) | 1.26958 | + | 2.19898i | 0.155104 | + | 0.268648i | 0.933097 | − | 0.359625i | \(-0.117095\pi\) |
−0.777993 | + | 0.628273i | \(0.783762\pi\) | |||||||
\(68\) | 15.0443 | 1.82439 | ||||||||
\(69\) | 0.481757 | + | 0.106573i | 0.0579968 | + | 0.0128299i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.45208 | −0.172330 | −0.0861651 | − | 0.996281i | \(-0.527461\pi\) | ||||
−0.0861651 | + | 0.996281i | \(0.527461\pi\) | |||||||
\(72\) | −24.9030 | − | 11.5849i | −2.93485 | − | 1.36530i | ||||
\(73\) | 0.234067 | − | 0.405416i | 0.0273955 | − | 0.0474503i | −0.852003 | − | 0.523538i | \(-0.824612\pi\) |
0.879398 | + | 0.476087i | \(0.157945\pi\) | |||||||
\(74\) | −21.7822 | −2.53213 | ||||||||
\(75\) | 4.19977 | + | 0.929064i | 0.484947 | + | 0.107279i | ||||
\(76\) | −1.68059 | + | 2.91087i | −0.192777 | + | 0.333900i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.50108 | + | 14.2530i | 0.509647 | + | 1.61384i | ||||
\(79\) | 7.85620 | − | 13.6073i | 0.883892 | − | 1.53095i | 0.0369135 | − | 0.999318i | \(-0.488247\pi\) |
0.846978 | − | 0.531627i | \(-0.178419\pi\) | |||||||
\(80\) | 11.1951 | − | 19.3905i | 1.25165 | − | 2.16792i | ||||
\(81\) | 5.79761 | + | 6.88387i | 0.644179 | + | 0.764875i | ||||
\(82\) | −13.6117 | − | 23.5762i | −1.50317 | − | 2.60356i | ||||
\(83\) | −6.99338 | − | 12.1129i | −0.767623 | − | 1.32956i | −0.938848 | − | 0.344331i | \(-0.888106\pi\) |
0.171225 | − | 0.985232i | \(-0.445228\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.22138 | − | 3.84754i | 0.240942 | − | 0.417324i | ||||
\(86\) | −16.9933 | −1.83243 | ||||||||
\(87\) | −2.37214 | − | 7.51157i | −0.254320 | − | 0.805325i | ||||
\(88\) | 12.3482 | 1.31632 | ||||||||
\(89\) | 1.29353 | + | 2.24046i | 0.137114 | + | 0.237488i | 0.926403 | − | 0.376534i | \(-0.122884\pi\) |
−0.789289 | + | 0.614022i | \(0.789551\pi\) | |||||||
\(90\) | −10.5782 | + | 7.42126i | −1.11504 | + | 0.782269i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.765146 | + | 1.32527i | 0.0797719 | + | 0.138169i | ||||
\(93\) | 3.87543 | + | 12.2718i | 0.401863 | + | 1.27253i | ||||
\(94\) | 15.1337 | + | 26.2123i | 1.56092 | + | 2.70359i | ||||
\(95\) | 0.496297 | + | 0.859612i | 0.0509190 | + | 0.0881944i | ||||
\(96\) | −10.4373 | − | 33.0505i | −1.06525 | − | 3.37320i | ||||
\(97\) | 7.22962 | + | 12.5221i | 0.734057 | + | 1.27142i | 0.955136 | + | 0.296168i | \(0.0957089\pi\) |
−0.221079 | + | 0.975256i | \(0.570958\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.66871 | − | 1.70669i | −0.368719 | − | 0.171529i | ||||
\(100\) | 6.67023 | + | 11.5532i | 0.667023 | + | 1.15532i | ||||
\(101\) | 9.83776 | 0.978894 | 0.489447 | − | 0.872033i | \(-0.337199\pi\) | ||||
0.489447 | + | 0.872033i | \(0.337199\pi\) | |||||||
\(102\) | −3.96607 | − | 12.5589i | −0.392699 | − | 1.24351i | ||||
\(103\) | 11.0579 | 1.08957 | 0.544786 | − | 0.838575i | \(-0.316611\pi\) | ||||
0.544786 | + | 0.838575i | \(0.316611\pi\) | |||||||
\(104\) | −14.5492 | + | 25.2000i | −1.42667 | + | 2.47106i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.78350 | + | 6.55322i | 0.367486 | + | 0.636505i | ||||
\(107\) | 0.962153 | + | 1.66650i | 0.0930149 | + | 0.161106i | 0.908778 | − | 0.417279i | \(-0.137016\pi\) |
−0.815764 | + | 0.578386i | \(0.803683\pi\) | |||||||
\(108\) | −3.60571 | + | 27.6796i | −0.346960 | + | 2.66347i | ||||
\(109\) | 9.30341 | − | 16.1140i | 0.891105 | − | 1.54344i | 0.0525523 | − | 0.998618i | \(-0.483264\pi\) |
0.838553 | − | 0.544821i | \(-0.183402\pi\) | |||||||
\(110\) | 2.90472 | − | 5.03112i | 0.276954 | − | 0.479698i | ||||
\(111\) | 4.18445 | + | 13.2504i | 0.397170 | + | 1.25767i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.59338 | − | 2.75982i | 0.149893 | − | 0.259622i | −0.781295 | − | 0.624162i | \(-0.785440\pi\) |
0.931188 | + | 0.364540i | \(0.118774\pi\) | |||||||
\(114\) | 2.87302 | + | 0.635563i | 0.269083 | + | 0.0595259i | ||||
\(115\) | 0.451911 | 0.0421410 | ||||||||
\(116\) | 12.2156 | − | 21.1580i | 1.13419 | − | 1.96447i | ||||
\(117\) | 7.80562 | − | 5.47613i | 0.721630 | − | 0.506268i | ||||
\(118\) | −12.4209 | −1.14344 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −24.5623 | − | 5.43361i | −2.24222 | − | 0.496019i | ||||
\(121\) | −9.18087 | −0.834624 | ||||||||
\(122\) | −0.522682 | − | 0.905312i | −0.0473214 | − | 0.0819631i | ||||
\(123\) | −11.7268 | + | 12.8093i | −1.05737 | + | 1.15497i | ||||
\(124\) | −19.9569 | + | 34.5664i | −1.79218 | + | 3.10415i | ||||
\(125\) | 11.8715 | 1.06182 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.37387 | −0.743061 | −0.371530 | − | 0.928421i | \(-0.621167\pi\) | ||||
−0.371530 | + | 0.928421i | \(0.621167\pi\) | |||||||
\(128\) | 15.4267 | − | 26.7199i | 1.36354 | − | 2.36173i | ||||
\(129\) | 3.26448 | + | 10.3372i | 0.287422 | + | 0.910143i | ||||
\(130\) | 6.84495 | + | 11.8558i | 0.600341 | + | 1.03982i | ||||
\(131\) | −11.9726 | −1.04605 | −0.523024 | − | 0.852318i | \(-0.675196\pi\) | ||||
−0.523024 | + | 0.852318i | \(0.675196\pi\) | |||||||
\(132\) | −3.77913 | − | 11.9669i | −0.328931 | − | 1.04158i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 6.89415 | 0.595564 | ||||||||
\(135\) | 6.54656 | + | 5.00919i | 0.563438 | + | 0.431122i | ||||
\(136\) | 12.8199 | − | 22.2046i | 1.09929 | − | 1.90403i | ||||
\(137\) | 16.5505 | 1.41401 | 0.707003 | − | 0.707211i | \(-0.250047\pi\) | ||||
0.707003 | + | 0.707211i | \(0.250047\pi\) | |||||||
\(138\) | 0.904611 | − | 0.988111i | 0.0770056 | − | 0.0841136i | ||||
\(139\) | 3.95119 | − | 6.84367i | 0.335136 | − | 0.580472i | −0.648375 | − | 0.761321i | \(-0.724551\pi\) |
0.983511 | + | 0.180849i | \(0.0578845\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.0380 | − | 14.2415i | 1.09800 | − | 1.19935i | ||||
\(142\) | −1.97130 | + | 3.41438i | −0.165427 | + | 0.286529i | ||||
\(143\) | −2.14339 | + | 3.71245i | −0.179239 | + | 0.310451i | ||||
\(144\) | −34.6622 | + | 24.3177i | −2.88852 | + | 2.02648i | ||||
\(145\) | −3.60739 | − | 6.24819i | −0.299578 | − | 0.518884i | ||||
\(146\) | −0.635523 | − | 1.10076i | −0.0525962 | − | 0.0910994i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −21.5483 | + | 37.3227i | −1.77126 | + | 3.06791i | ||||
\(149\) | −13.6685 | −1.11977 | −0.559885 | − | 0.828570i | \(-0.689155\pi\) | ||||
−0.559885 | + | 0.828570i | \(0.689155\pi\) | |||||||
\(150\) | 7.88604 | − | 8.61395i | 0.643892 | − | 0.703326i | ||||
\(151\) | 3.89963 | 0.317348 | 0.158674 | − | 0.987331i | \(-0.449278\pi\) | ||||
0.158674 | + | 0.987331i | \(0.449278\pi\) | |||||||
\(152\) | 2.86420 | + | 4.96093i | 0.232317 | + | 0.402385i | ||||
\(153\) | −6.87781 | + | 4.82522i | −0.556038 | + | 0.390096i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.89349 | + | 10.2078i | 0.473376 | + | 0.819912i | ||||
\(156\) | 28.8746 | + | 6.38758i | 2.31182 | + | 0.511415i | ||||
\(157\) | 0.147176 | + | 0.254917i | 0.0117459 | + | 0.0203446i | 0.871839 | − | 0.489793i | \(-0.162928\pi\) |
−0.860093 | + | 0.510138i | \(0.829594\pi\) | |||||||
\(158\) | −21.3306 | − | 36.9457i | −1.69697 | − | 2.93925i | ||||
\(159\) | 3.25958 | − | 3.56045i | 0.258502 | − | 0.282362i | ||||
\(160\) | −15.8723 | − | 27.4917i | −1.25482 | − | 2.17341i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 24.0572 | − | 4.28703i | 1.89011 | − | 0.336821i | ||||
\(163\) | −5.35455 | − | 9.27436i | −0.419401 | − | 0.726424i | 0.576478 | − | 0.817112i | \(-0.304427\pi\) |
−0.995879 | + | 0.0906886i | \(0.971093\pi\) | |||||||
\(164\) | −53.8622 | −4.20593 | ||||||||
\(165\) | −3.61850 | − | 0.800478i | −0.281700 | − | 0.0623171i | ||||
\(166\) | −37.9759 | −2.94750 | ||||||||
\(167\) | 1.59872 | − | 2.76907i | 0.123713 | − | 0.214277i | −0.797516 | − | 0.603298i | \(-0.793853\pi\) |
0.921229 | + | 0.389020i | \(0.127186\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.44913 | + | 2.50997i | 0.111472 | + | 0.193074i | ||||
\(170\) | −6.03133 | − | 10.4466i | −0.462582 | − | 0.801215i | ||||
\(171\) | −0.165297 | − | 1.86979i | −0.0126406 | − | 0.142986i | ||||
\(172\) | −16.8108 | + | 29.1171i | −1.28181 | + | 2.22016i | ||||
\(173\) | 5.71875 | − | 9.90517i | 0.434789 | − | 0.753076i | −0.562490 | − | 0.826804i | \(-0.690156\pi\) |
0.997278 | + | 0.0737284i | \(0.0234898\pi\) | |||||||
\(174\) | −20.8828 | − | 4.61966i | −1.58312 | − | 0.350216i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 9.51809 | − | 16.4858i | 0.717453 | − | 1.24266i | ||||
\(177\) | 2.38610 | + | 7.55578i | 0.179351 | + | 0.567927i | ||||
\(178\) | 7.02421 | 0.526487 | ||||||||
\(179\) | −0.549275 | + | 0.951372i | −0.0410547 | + | 0.0711089i | −0.885823 | − | 0.464024i | \(-0.846405\pi\) |
0.844768 | + | 0.535133i | \(0.179738\pi\) | |||||||
\(180\) | 2.25137 | + | 25.4667i | 0.167807 | + | 1.89818i | ||||
\(181\) | 3.19013 | 0.237120 | 0.118560 | − | 0.992947i | \(-0.462172\pi\) | ||||
0.118560 | + | 0.992947i | \(0.462172\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.450303 | + | 0.491868i | −0.0332874 | + | 0.0363599i | ||||
\(184\) | 2.60804 | 0.192267 | ||||||||
\(185\) | 6.36343 | + | 11.0218i | 0.467849 | + | 0.810338i | ||||
\(186\) | 34.1168 | + | 7.54725i | 2.50157 | + | 0.553392i | ||||
\(187\) | 1.88861 | − | 3.27118i | 0.138109 | − | 0.239212i | ||||
\(188\) | 59.8846 | 4.36753 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.69503 | 0.195518 | ||||||||
\(191\) | −1.93407 | + | 3.34992i | −0.139945 | + | 0.242391i | −0.927475 | − | 0.373884i | \(-0.878026\pi\) |
0.787531 | + | 0.616275i | \(0.211359\pi\) | |||||||
\(192\) | −44.1454 | − | 9.76576i | −3.18592 | − | 0.704783i | ||||
\(193\) | 2.06793 | + | 3.58175i | 0.148853 | + | 0.257820i | 0.930804 | − | 0.365520i | \(-0.119109\pi\) |
−0.781951 | + | 0.623340i | \(0.785775\pi\) | |||||||
\(194\) | 39.2588 | 2.81862 | ||||||||
\(195\) | 5.89709 | − | 6.44141i | 0.422299 | − | 0.461279i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.889267 | −0.0633576 | −0.0316788 | − | 0.999498i | \(-0.510085\pi\) | ||||
−0.0316788 | + | 0.999498i | \(0.510085\pi\) | |||||||
\(198\) | −8.99358 | + | 6.30956i | −0.639146 | + | 0.448401i | ||||
\(199\) | −3.16193 | + | 5.47663i | −0.224143 | + | 0.388228i | −0.956062 | − | 0.293164i | \(-0.905292\pi\) |
0.731919 | + | 0.681392i | \(0.238625\pi\) | |||||||
\(200\) | 22.7358 | 1.60767 | ||||||||
\(201\) | −1.32440 | − | 4.19380i | −0.0934157 | − | 0.295808i | ||||
\(202\) | 13.3554 | − | 23.1323i | 0.939684 | − | 1.62758i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −25.4424 | − | 5.62833i | −1.78133 | − | 0.394062i | ||||
\(205\) | −7.95305 | + | 13.7751i | −0.555465 | + | 0.962093i | ||||
\(206\) | 15.0119 | − | 26.0014i | 1.04593 | − | 1.81160i | ||||
\(207\) | −0.774860 | − | 0.360466i | −0.0538565 | − | 0.0250541i | ||||
\(208\) | 22.4293 | + | 38.8487i | 1.55519 | + | 2.69367i | ||||
\(209\) | 0.421952 | + | 0.730843i | 0.0291870 | + | 0.0505535i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.71291 | − | 9.89505i | 0.393293 | − | 0.681204i | −0.599589 | − | 0.800308i | \(-0.704669\pi\) |
0.992882 | + | 0.119105i | \(0.0380025\pi\) | |||||||
\(212\) | 14.9715 | 1.02825 | ||||||||
\(213\) | 2.45571 | + | 0.543247i | 0.168262 | + | 0.0372226i | ||||
\(214\) | 5.22475 | 0.357156 | ||||||||
\(215\) | 4.96441 | + | 8.59860i | 0.338570 | + | 0.586420i | ||||
\(216\) | 37.7810 | + | 28.9087i | 2.57067 | + | 1.96699i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −25.2600 | − | 43.7516i | −1.71082 | − | 2.96323i | ||||
\(219\) | −0.547518 | + | 0.598057i | −0.0369979 | + | 0.0404129i | ||||
\(220\) | −5.74705 | − | 9.95417i | −0.387466 | − | 0.671110i | ||||
\(221\) | 4.45051 | + | 7.70850i | 0.299373 | + | 0.518530i | ||||
\(222\) | 36.8373 | + | 8.14907i | 2.47236 | + | 0.546930i | ||||
\(223\) | 8.35953 | + | 14.4791i | 0.559796 | + | 0.969595i | 0.997513 | + | 0.0704822i | \(0.0224538\pi\) |
−0.437717 | + | 0.899113i | \(0.644213\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.75492 | − | 3.14240i | −0.450328 | − | 0.209493i | ||||
\(226\) | −4.32625 | − | 7.49328i | −0.287778 | − | 0.498446i | ||||
\(227\) | 17.0700 | 1.13298 | 0.566489 | − | 0.824070i | \(-0.308302\pi\) | ||||
0.566489 | + | 0.824070i | \(0.308302\pi\) | |||||||
\(228\) | 3.93117 | − | 4.29403i | 0.260348 | − | 0.284379i | ||||
\(229\) | 19.7894 | 1.30772 | 0.653861 | − | 0.756615i | \(-0.273148\pi\) | ||||
0.653861 | + | 0.756615i | \(0.273148\pi\) | |||||||
\(230\) | 0.613500 | − | 1.06261i | 0.0404530 | − | 0.0700666i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −20.8187 | − | 36.0591i | −1.36682 | − | 2.36740i | ||||
\(233\) | −2.96579 | − | 5.13691i | −0.194296 | − | 0.336530i | 0.752374 | − | 0.658736i | \(-0.228909\pi\) |
−0.946669 | + | 0.322207i | \(0.895575\pi\) | |||||||
\(234\) | −2.27978 | − | 25.7881i | −0.149034 | − | 1.68582i | ||||
\(235\) | 8.84228 | − | 15.3153i | 0.576807 | − | 0.999058i | ||||
\(236\) | −12.2875 | + | 21.2826i | −0.799847 | + | 1.38538i | ||||
\(237\) | −18.3769 | + | 20.0731i | −1.19371 | + | 1.30389i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.0277 | + | 17.3685i | −0.648637 | + | 1.12347i | 0.334812 | + | 0.942285i | \(0.391327\pi\) |
−0.983449 | + | 0.181187i | \(0.942006\pi\) | |||||||
\(240\) | −26.1871 | + | 28.6042i | −1.69037 | + | 1.84640i | ||||
\(241\) | 29.2887 | 1.88665 | 0.943326 | − | 0.331869i | \(-0.107679\pi\) | ||||
0.943326 | + | 0.331869i | \(0.107679\pi\) | |||||||
\(242\) | −12.4636 | + | 21.5877i | −0.801193 | + | 1.38771i | ||||
\(243\) | −7.22934 | − | 13.8107i | −0.463763 | − | 0.885960i | ||||
\(244\) | −2.06827 | −0.132408 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 14.1995 | + | 44.9637i | 0.905324 | + | 2.86678i | ||||
\(247\) | −1.98865 | −0.126535 | ||||||||
\(248\) | 34.0121 | + | 58.9107i | 2.15977 | + | 3.74083i | ||||
\(249\) | 7.29533 | + | 23.1012i | 0.462323 | + | 1.46398i | ||||
\(250\) | 16.1164 | − | 27.9144i | 1.01929 | − | 1.76546i | ||||
\(251\) | −22.7856 | −1.43821 | −0.719106 | − | 0.694901i | \(-0.755448\pi\) | ||||
−0.719106 | + | 0.694901i | \(0.755448\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.384215 | 0.0241554 | ||||||||
\(254\) | −11.3681 | + | 19.6901i | −0.713297 | + | 1.23547i | ||||
\(255\) | −5.19614 | + | 5.67576i | −0.325395 | + | 0.355430i | ||||
\(256\) | −15.7821 | − | 27.3354i | −0.986381 | − | 1.70846i | ||||
\(257\) | −24.2889 | −1.51510 | −0.757550 | − | 0.652778i | \(-0.773604\pi\) | ||||
−0.757550 | + | 0.652778i | \(0.773604\pi\) | |||||||
\(258\) | 28.7385 | + | 6.35747i | 1.78918 | + | 0.395798i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 27.0857 | 1.67979 | ||||||||
\(261\) | 1.20148 | + | 13.5908i | 0.0743699 | + | 0.841247i | ||||
\(262\) | −16.2536 | + | 28.1520i | −1.00415 | + | 1.73924i | ||||
\(263\) | −8.61155 | −0.531011 | −0.265506 | − | 0.964109i | \(-0.585539\pi\) | ||||
−0.265506 | + | 0.964109i | \(0.585539\pi\) | |||||||
\(264\) | −20.8828 | − | 4.61966i | −1.28525 | − | 0.284321i | ||||
\(265\) | 2.21062 | − | 3.82890i | 0.135797 | − | 0.235208i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.34938 | − | 4.27291i | −0.0825807 | − | 0.261498i | ||||
\(268\) | 6.82011 | − | 11.8128i | 0.416605 | − | 0.721581i | ||||
\(269\) | 7.61561 | − | 13.1906i | 0.464332 | − | 0.804247i | −0.534839 | − | 0.844954i | \(-0.679628\pi\) |
0.999171 | + | 0.0407073i | \(0.0129611\pi\) | |||||||
\(270\) | 20.6659 | − | 8.59310i | 1.25768 | − | 0.522959i | ||||
\(271\) | 2.33910 | + | 4.05144i | 0.142090 | + | 0.246108i | 0.928284 | − | 0.371873i | \(-0.121284\pi\) |
−0.786193 | + | 0.617981i | \(0.787951\pi\) | |||||||
\(272\) | −19.7633 | − | 34.2310i | −1.19832 | − | 2.07556i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 22.4684 | − | 38.9164i | 1.35737 | − | 2.35103i | ||||
\(275\) | 3.34943 | 0.201978 | ||||||||
\(276\) | −0.798182 | − | 2.52750i | −0.0480449 | − | 0.152138i | ||||
\(277\) | −16.3907 | −0.984824 | −0.492412 | − | 0.870362i | \(-0.663885\pi\) | ||||
−0.492412 | + | 0.870362i | \(0.663885\pi\) | |||||||
\(278\) | −10.7280 | − | 18.5815i | −0.643423 | − | 1.11444i | ||||
\(279\) | −1.96289 | − | 22.2035i | −0.117515 | − | 1.32929i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.75702 | + | 3.04325i | 0.104815 | + | 0.181545i | 0.913663 | − | 0.406473i | \(-0.133242\pi\) |
−0.808848 | + | 0.588018i | \(0.799908\pi\) | |||||||
\(282\) | −15.7871 | − | 49.9911i | −0.940108 | − | 2.97692i | ||||
\(283\) | −13.0354 | − | 22.5780i | −0.774874 | − | 1.34212i | −0.934865 | − | 0.355002i | \(-0.884480\pi\) |
0.159992 | − | 0.987118i | \(-0.448853\pi\) | |||||||
\(284\) | 3.90025 | + | 6.75543i | 0.231437 | + | 0.400861i | ||||
\(285\) | −0.517726 | − | 1.63942i | −0.0306674 | − | 0.0971108i | ||||
\(286\) | 5.81958 | + | 10.0798i | 0.344119 | + | 0.596031i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 5.28645 | + | 59.7985i | 0.311507 | + | 3.52366i | ||||
\(289\) | 4.57850 | + | 7.93019i | 0.269323 | + | 0.466482i | ||||
\(290\) | −19.5891 | −1.15031 | ||||||||
\(291\) | −7.54177 | − | 23.8816i | −0.442107 | − | 1.39996i | ||||
\(292\) | −2.51479 | −0.147167 | ||||||||
\(293\) | −9.44192 | + | 16.3539i | −0.551603 | + | 0.955404i | 0.446556 | + | 0.894756i | \(0.352650\pi\) |
−0.998159 | + | 0.0606487i | \(0.980683\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.62863 | + | 6.28497i | 0.211267 | + | 0.365925i | ||||
\(296\) | 36.7242 | + | 63.6082i | 2.13455 | + | 3.69715i | ||||
\(297\) | 5.56589 | + | 4.25881i | 0.322965 | + | 0.247121i | ||||
\(298\) | −18.5559 | + | 32.1398i | −1.07492 | + | 1.86181i | ||||
\(299\) | −0.452700 | + | 0.784099i | −0.0261803 | + | 0.0453456i | ||||
\(300\) | −6.95823 | − | 22.0338i | −0.401733 | − | 1.27212i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 5.29401 | − | 9.16950i | 0.304636 | − | 0.527645i | ||||
\(303\) | −16.6373 | − | 3.68046i | −0.955786 | − | 0.211437i | ||||
\(304\) | 8.83097 | 0.506491 | ||||||||
\(305\) | −0.305392 | + | 0.528954i | −0.0174867 | + | 0.0302878i | ||||
\(306\) | 2.00880 | + | 22.7229i | 0.114836 | + | 1.29898i | ||||
\(307\) | −21.6407 | −1.23510 | −0.617551 | − | 0.786531i | \(-0.711875\pi\) | ||||
−0.617551 | + | 0.786531i | \(0.711875\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.7008 | − | 4.13696i | −1.06385 | − | 0.235343i | ||||
\(310\) | 32.0032 | 1.81766 | ||||||||
\(311\) | −2.24724 | − | 3.89234i | −0.127429 | − | 0.220714i | 0.795251 | − | 0.606281i | \(-0.207339\pi\) |
−0.922680 | + | 0.385567i | \(0.874006\pi\) | |||||||
\(312\) | 34.0329 | − | 37.1742i | 1.92673 | − | 2.10458i | ||||
\(313\) | −4.30102 | + | 7.44958i | −0.243108 | + | 0.421075i | −0.961598 | − | 0.274462i | \(-0.911500\pi\) |
0.718490 | + | 0.695537i | \(0.244834\pi\) | |||||||
\(314\) | 0.799206 | 0.0451018 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −84.4062 | −4.74822 | ||||||||
\(317\) | 4.03128 | − | 6.98237i | 0.226419 | − | 0.392169i | −0.730325 | − | 0.683100i | \(-0.760631\pi\) |
0.956744 | + | 0.290930i | \(0.0939648\pi\) | |||||||
\(318\) | −3.94686 | − | 12.4980i | −0.221329 | − | 0.700856i | ||||
\(319\) | −3.06701 | − | 5.31221i | −0.171719 | − | 0.297427i | ||||
\(320\) | −41.4105 | −2.31492 | ||||||||
\(321\) | −1.00370 | − | 3.17828i | −0.0560208 | − | 0.177394i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.75228 | 0.0974992 | ||||||||
\(324\) | 16.4532 | − | 45.4618i | 0.914068 | − | 2.52565i | ||||
\(325\) | −3.94646 | + | 6.83546i | −0.218910 | + | 0.379163i | ||||
\(326\) | −29.0766 | −1.61041 | ||||||||
\(327\) | −21.7621 | + | 23.7708i | −1.20345 | + | 1.31453i | ||||
\(328\) | −45.8981 | + | 79.4978i | −2.53430 | + | 4.38953i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −6.79458 | + | 7.42175i | −0.374029 | + | 0.408554i | ||||
\(331\) | 11.4513 | − | 19.8342i | 0.629419 | − | 1.09019i | −0.358249 | − | 0.933626i | \(-0.616626\pi\) |
0.987668 | − | 0.156560i | \(-0.0500405\pi\) | |||||||
\(332\) | −37.5681 | + | 65.0698i | −2.06182 | + | 3.57117i | ||||
\(333\) | −2.11941 | − | 23.9740i | −0.116143 | − | 1.31377i | ||||
\(334\) | −4.34075 | − | 7.51840i | −0.237515 | − | 0.411388i | ||||
\(335\) | −2.01405 | − | 3.48844i | −0.110039 | − | 0.190594i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.81891 | + | 11.8107i | −0.371450 | + | 0.643369i | −0.989789 | − | 0.142542i | \(-0.954472\pi\) |
0.618339 | + | 0.785911i | \(0.287806\pi\) | |||||||
\(338\) | 7.86916 | 0.428026 | ||||||||
\(339\) | −3.72717 | + | 4.07120i | −0.202432 | + | 0.221117i | ||||
\(340\) | −23.8662 | −1.29433 | ||||||||
\(341\) | 5.01065 | + | 8.67869i | 0.271342 | + | 0.469978i | ||||
\(342\) | −4.62097 | − | 2.14968i | −0.249873 | − | 0.116242i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 28.6502 | + | 49.6237i | 1.54472 | + | 2.67553i | ||||
\(345\) | −0.764256 | − | 0.169067i | −0.0411462 | − | 0.00910228i | ||||
\(346\) | −15.5272 | − | 26.8938i | −0.834746 | − | 1.44582i | ||||
\(347\) | 1.41282 | + | 2.44707i | 0.0758440 | + | 0.131366i | 0.901453 | − | 0.432877i | \(-0.142502\pi\) |
−0.825609 | + | 0.564243i | \(0.809168\pi\) | |||||||
\(348\) | −28.5741 | + | 31.2116i | −1.53173 | + | 1.67312i | ||||
\(349\) | −1.81202 | − | 3.13851i | −0.0969951 | − | 0.168000i | 0.813444 | − | 0.581643i | \(-0.197590\pi\) |
−0.910440 | + | 0.413642i | \(0.864256\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.2493 | + | 6.34083i | −0.813947 | + | 0.338448i | ||||
\(352\) | −13.4947 | − | 23.3734i | −0.719268 | − | 1.24581i | ||||
\(353\) | −2.75401 | −0.146581 | −0.0732907 | − | 0.997311i | \(-0.523350\pi\) | ||||
−0.0732907 | + | 0.997311i | \(0.523350\pi\) | |||||||
\(354\) | 21.0058 | + | 4.64685i | 1.11644 | + | 0.246977i | ||||
\(355\) | 2.30357 | 0.122261 | ||||||||
\(356\) | 6.94877 | − | 12.0356i | 0.368284 | − | 0.637887i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.49135 | + | 2.58310i | 0.0788205 | + | 0.136521i | ||||
\(359\) | 8.40076 | + | 14.5505i | 0.443375 | + | 0.767948i | 0.997937 | − | 0.0641941i | \(-0.0204477\pi\) |
−0.554562 | + | 0.832142i | \(0.687114\pi\) | |||||||
\(360\) | 39.5060 | + | 18.3783i | 2.08215 | + | 0.968620i | ||||
\(361\) | 9.30425 | − | 16.1154i | 0.489698 | − | 0.848181i | ||||
\(362\) | 4.33081 | − | 7.50119i | 0.227622 | − | 0.394254i | ||||
\(363\) | 15.5264 | + | 3.43471i | 0.814922 | + | 0.180276i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.371322 | + | 0.643149i | −0.0194359 | + | 0.0336640i | ||||
\(366\) | 0.545250 | + | 1.72657i | 0.0285007 | + | 0.0902495i | ||||
\(367\) | −23.9339 | −1.24934 | −0.624670 | − | 0.780889i | \(-0.714767\pi\) | ||||
−0.624670 | + | 0.780889i | \(0.714767\pi\) | |||||||
\(368\) | 2.01030 | − | 3.48193i | 0.104794 | − | 0.181508i | ||||
\(369\) | 24.6242 | − | 17.2754i | 1.28188 | − | 0.899322i | ||||
\(370\) | 34.5551 | 1.79644 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 46.6822 | − | 50.9912i | 2.42036 | − | 2.64377i | ||||
\(373\) | −19.1606 | −0.992098 | −0.496049 | − | 0.868295i | \(-0.665216\pi\) | ||||
−0.496049 | + | 0.868295i | \(0.665216\pi\) | |||||||
\(374\) | −5.12784 | − | 8.88168i | −0.265154 | − | 0.459261i | ||||
\(375\) | −20.0767 | − | 4.44134i | −1.03676 | − | 0.229350i | ||||
\(376\) | 51.0299 | − | 88.3865i | 2.63167 | − | 4.55818i | ||||
\(377\) | 14.4548 | 0.744458 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.0770 | 0.517622 | 0.258811 | − | 0.965928i | \(-0.416669\pi\) | ||||
0.258811 | + | 0.965928i | \(0.416669\pi\) | |||||||
\(380\) | 2.66608 | − | 4.61779i | 0.136767 | − | 0.236888i | ||||
\(381\) | 14.1616 | + | 3.13280i | 0.725520 | + | 0.160498i | ||||
\(382\) | 5.25127 | + | 9.09546i | 0.268678 | + | 0.465364i | ||||
\(383\) | −20.1435 | −1.02929 | −0.514643 | − | 0.857405i | \(-0.672075\pi\) | ||||
−0.514643 | + | 0.857405i | \(0.672075\pi\) | |||||||
\(384\) | −36.0855 | + | 39.4164i | −1.84148 | + | 2.01146i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 11.2294 | 0.571561 | ||||||||
\(387\) | −1.65345 | − | 18.7033i | −0.0840496 | − | 0.950740i | ||||
\(388\) | 38.8372 | − | 67.2679i | 1.97166 | − | 3.41501i | ||||
\(389\) | 13.3947 | 0.679139 | 0.339570 | − | 0.940581i | \(-0.389719\pi\) | ||||
0.339570 | + | 0.940581i | \(0.389719\pi\) | |||||||
\(390\) | −7.14049 | − | 22.6109i | −0.361573 | − | 1.14495i | ||||
\(391\) | 0.398891 | − | 0.690899i | 0.0201728 | − | 0.0349402i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 20.2476 | + | 4.47913i | 1.02136 | + | 0.225942i | ||||
\(394\) | −1.20724 | + | 2.09100i | −0.0608198 | + | 0.105343i | ||||
\(395\) | −12.4630 | + | 21.5866i | −0.627083 | + | 1.08614i | ||||
\(396\) | 1.91412 | + | 21.6518i | 0.0961880 | + | 1.08805i | ||||
\(397\) | 9.00664 | + | 15.6000i | 0.452031 | + | 0.782940i | 0.998512 | − | 0.0545313i | \(-0.0173665\pi\) |
−0.546482 | + | 0.837471i | \(0.684033\pi\) | |||||||
\(398\) | 8.58506 | + | 14.8698i | 0.430330 | + | 0.745354i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 17.5249 | − | 30.3541i | 0.876247 | − | 1.51770i | ||||
\(401\) | 28.8675 | 1.44157 | 0.720787 | − | 0.693157i | \(-0.243781\pi\) | ||||
0.720787 | + | 0.693157i | \(0.243781\pi\) | |||||||
\(402\) | −11.6591 | − | 2.57921i | −0.581505 | − | 0.128639i | ||||
\(403\) | −23.6151 | −1.17635 | ||||||||
\(404\) | −26.4240 | − | 45.7676i | −1.31464 | − | 2.27703i | ||||
\(405\) | −9.19729 | − | 10.9205i | −0.457017 | − | 0.542646i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.41019 | + | 9.37073i | 0.268173 | + | 0.464490i | ||||
\(408\) | −29.9876 | + | 32.7556i | −1.48461 | + | 1.62164i | ||||
\(409\) | 5.42937 | + | 9.40395i | 0.268465 | + | 0.464995i | 0.968466 | − | 0.249147i | \(-0.0801502\pi\) |
−0.700000 | + | 0.714142i | \(0.746817\pi\) | |||||||
\(410\) | 21.5936 | + | 37.4012i | 1.06643 | + | 1.84711i | ||||
\(411\) | −27.9896 | − | 6.19181i | −1.38063 | − | 0.305419i | ||||
\(412\) | −29.7014 | − | 51.4443i | −1.46328 | − | 2.53448i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.89951 | + | 1.33263i | −0.0933561 | + | 0.0654951i | ||||
\(415\) | 11.0943 | + | 19.2158i | 0.544595 | + | 0.943267i | ||||
\(416\) | 63.6001 | 3.11825 | ||||||||
\(417\) | −9.24244 | + | 10.0956i | −0.452604 | + | 0.494382i | ||||
\(418\) | 2.29131 | 0.112072 | ||||||||
\(419\) | −0.247572 | + | 0.428807i | −0.0120947 | + | 0.0209486i | −0.872009 | − | 0.489489i | \(-0.837183\pi\) |
0.859915 | + | 0.510438i | \(0.170517\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.50320 | + | 16.4600i | 0.463158 | + | 0.802212i | 0.999116 | − | 0.0420318i | \(-0.0133831\pi\) |
−0.535959 | + | 0.844244i | \(0.680050\pi\) | |||||||
\(422\) | −15.5113 | − | 26.8664i | −0.755079 | − | 1.30784i | ||||
\(423\) | −27.3774 | + | 19.2070i | −1.33114 | + | 0.933875i | ||||
\(424\) | 12.7578 | − | 22.0971i | 0.619572 | − | 1.07313i | ||||
\(425\) | 3.47737 | − | 6.02298i | 0.168677 | − | 0.292157i | ||||
\(426\) | 4.61116 | − | 5.03679i | 0.223411 | − | 0.244033i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 5.16864 | − | 8.95234i | 0.249835 | − | 0.432728i | ||||
\(429\) | 5.01371 | − | 5.47649i | 0.242064 | − | 0.264408i | ||||
\(430\) | 26.9580 | 1.30003 | ||||||||
\(431\) | 8.46073 | − | 14.6544i | 0.407539 | − | 0.705878i | −0.587074 | − | 0.809533i | \(-0.699720\pi\) |
0.994613 | + | 0.103655i | \(0.0330538\pi\) | |||||||
\(432\) | 67.7172 | − | 28.1576i | 3.25805 | − | 1.35473i | ||||
\(433\) | −33.4740 | −1.60866 | −0.804330 | − | 0.594183i | \(-0.797476\pi\) | ||||
−0.804330 | + | 0.594183i | \(0.797476\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.76315 | + | 11.9163i | 0.180429 | + | 0.571343i | ||||
\(436\) | −99.9548 | −4.78697 | ||||||||
\(437\) | 0.0891197 | + | 0.154360i | 0.00426317 | + | 0.00738403i | ||||
\(438\) | 0.662962 | + | 2.09932i | 0.0316776 | + | 0.100309i | ||||
\(439\) | −10.4657 | + | 18.1272i | −0.499502 | + | 0.865163i | −1.00000 | 0.000574559i | \(-0.999817\pi\) | |
0.500498 | + | 0.865738i | \(0.333150\pi\) | |||||||
\(440\) | −19.5891 | −0.933874 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 24.1674 | 1.14953 | ||||||||
\(443\) | 15.4290 | − | 26.7238i | 0.733054 | − | 1.26969i | −0.222517 | − | 0.974929i | \(-0.571427\pi\) |
0.955572 | − | 0.294759i | \(-0.0952393\pi\) | |||||||
\(444\) | 50.4047 | − | 55.0572i | 2.39210 | − | 2.61290i | ||||
\(445\) | −2.05205 | − | 3.55425i | −0.0972763 | − | 0.168487i | ||||
\(446\) | 45.3945 | 2.14949 | ||||||||
\(447\) | 23.1157 | + | 5.11362i | 1.09334 | + | 0.241866i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −33.2789 | −1.57053 | −0.785263 | − | 0.619162i | \(-0.787472\pi\) | ||||
−0.785263 | + | 0.619162i | \(0.787472\pi\) | |||||||
\(450\) | −16.5592 | + | 11.6173i | −0.780608 | + | 0.547646i | ||||
\(451\) | −6.76168 | + | 11.7116i | −0.318395 | + | 0.551477i | ||||
\(452\) | −17.1191 | −0.805217 | ||||||||
\(453\) | −6.59492 | − | 1.45892i | −0.309857 | − | 0.0685458i | ||||
\(454\) | 23.1737 | − | 40.1380i | 1.08760 | − | 1.88377i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.98786 | − | 9.46130i | −0.139919 | − | 0.443066i | ||||
\(457\) | −11.8952 | + | 20.6031i | −0.556434 | + | 0.963772i | 0.441356 | + | 0.897332i | \(0.354498\pi\) |
−0.997790 | + | 0.0664402i | \(0.978836\pi\) | |||||||
\(458\) | 26.8654 | − | 46.5323i | 1.25534 | − | 2.17431i | ||||
\(459\) | 13.4367 | − | 5.58714i | 0.627172 | − | 0.260785i | ||||
\(460\) | −1.21382 | − | 2.10240i | −0.0565947 | − | 0.0980249i | ||||
\(461\) | 8.53122 | + | 14.7765i | 0.397339 | + | 0.688211i | 0.993397 | − | 0.114731i | \(-0.0366005\pi\) |
−0.596058 | + | 0.802941i | \(0.703267\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.1243 | − | 31.3922i | 0.842306 | − | 1.45892i | −0.0456338 | − | 0.998958i | \(-0.514531\pi\) |
0.887940 | − | 0.459959i | \(-0.152136\pi\) | |||||||
\(464\) | −64.1889 | −2.97990 | ||||||||
\(465\) | −6.14795 | − | 19.4680i | −0.285104 | − | 0.902805i | ||||
\(466\) | −16.1051 | −0.746052 | ||||||||
\(467\) | 4.09580 | + | 7.09413i | 0.189531 | + | 0.328277i | 0.945094 | − | 0.326799i | \(-0.105970\pi\) |
−0.755563 | + | 0.655076i | \(0.772637\pi\) | |||||||
\(468\) | −46.4420 | − | 21.6049i | −2.14678 | − | 0.998686i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −24.0080 | − | 41.5830i | −1.10740 | − | 1.91808i | ||||
\(471\) | −0.153531 | − | 0.486167i | −0.00707432 | − | 0.0224014i | ||||
\(472\) | 20.9413 | + | 36.2714i | 0.963900 | + | 1.66952i | ||||
\(473\) | 4.22074 | + | 7.31054i | 0.194070 | + | 0.336139i | ||||
\(474\) | 22.2516 | + | 70.4615i | 1.02205 | + | 3.23640i | ||||
\(475\) | 0.776909 | + | 1.34565i | 0.0356470 | + | 0.0617425i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.84451 | + | 4.80185i | −0.313389 | + | 0.219862i | ||||
\(478\) | 27.2265 | + | 47.1577i | 1.24531 | + | 2.15694i | ||||
\(479\) | −25.5549 | −1.16763 | −0.583817 | − | 0.811885i | \(-0.698441\pi\) | ||||
−0.583817 | + | 0.811885i | \(0.698441\pi\) | |||||||
\(480\) | 16.5576 | + | 52.4310i | 0.755749 | + | 2.39314i | ||||
\(481\) | −25.4982 | −1.16262 | ||||||||
\(482\) | 39.7614 | − | 68.8687i | 1.81108 | − | 3.13688i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 24.6596 | + | 42.7116i | 1.12089 | + | 1.94144i | ||||
\(485\) | −11.4690 | − | 19.8649i | −0.520782 | − | 0.902020i | ||||
\(486\) | −42.2885 | − | 1.75011i | −1.91825 | − | 0.0793868i | ||||
\(487\) | 3.46140 | − | 5.99533i | 0.156851 | − | 0.271674i | −0.776880 | − | 0.629648i | \(-0.783199\pi\) |
0.933732 | + | 0.357974i | \(0.116532\pi\) | |||||||
\(488\) | −1.76246 | + | 3.05266i | −0.0797826 | + | 0.138188i | ||||
\(489\) | 5.58574 | + | 17.6877i | 0.252596 | + | 0.799865i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.7262 | − | 32.4348i | 0.845103 | − | 1.46376i | −0.0404294 | − | 0.999182i | \(-0.512873\pi\) |
0.885532 | − | 0.464578i | \(-0.153794\pi\) | |||||||
\(492\) | 91.0899 | + | 20.1507i | 4.10665 | + | 0.908465i | ||||
\(493\) | −12.7366 | −0.573628 | ||||||||
\(494\) | −2.69973 | + | 4.67607i | −0.121467 | + | 0.210386i | ||||
\(495\) | 5.82001 | + | 2.70748i | 0.261590 | + | 0.121692i | ||||
\(496\) | 104.867 | 4.70867 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 64.2235 | + | 14.2074i | 2.87793 | + | 0.636649i | ||||
\(499\) | 25.6250 | 1.14713 | 0.573566 | − | 0.819159i | \(-0.305560\pi\) | ||||
0.573566 | + | 0.819159i | \(0.305560\pi\) | |||||||
\(500\) | −31.8867 | − | 55.2293i | −1.42601 | − | 2.46993i | ||||
\(501\) | −3.73966 | + | 4.08485i | −0.167076 | + | 0.182497i | ||||
\(502\) | −30.9329 | + | 53.5774i | −1.38060 | + | 2.39127i | ||||
\(503\) | −5.79692 | −0.258472 | −0.129236 | − | 0.991614i | \(-0.541252\pi\) | ||||
−0.129236 | + | 0.991614i | \(0.541252\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.6066 | −0.694483 | ||||||||
\(506\) | 0.521598 | − | 0.903434i | 0.0231878 | − | 0.0401625i | ||||
\(507\) | −1.51170 | − | 4.78691i | −0.0671369 | − | 0.212594i | ||||
\(508\) | 22.4920 | + | 38.9573i | 0.997921 | + | 1.72845i | ||||
\(509\) | 25.1395 | 1.11429 | 0.557144 | − | 0.830416i | \(-0.311897\pi\) | ||||
0.557144 | + | 0.830416i | \(0.311897\pi\) | |||||||
\(510\) | 6.29174 | + | 19.9233i | 0.278603 | + | 0.882218i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −23.9940 | −1.06039 | ||||||||
\(513\) | −0.419972 | + | 3.22396i | −0.0185422 | + | 0.142341i | ||||
\(514\) | −32.9738 | + | 57.1123i | −1.45441 | + | 2.51911i | ||||
\(515\) | −17.5423 | −0.773004 | ||||||||
\(516\) | 39.3230 | − | 42.9527i | 1.73110 | − | 1.89089i | ||||
\(517\) | 7.51771 | − | 13.0211i | 0.330629 | − | 0.572665i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13.3770 | + | 14.6118i | −0.587186 | + | 0.641386i | ||||
\(520\) | 23.0808 | − | 39.9771i | 1.01216 | − | 1.75311i | ||||
\(521\) | −3.64828 | + | 6.31900i | −0.159834 | + | 0.276841i | −0.934809 | − | 0.355152i | \(-0.884429\pi\) |
0.774975 | + | 0.631992i | \(0.217763\pi\) | |||||||
\(522\) | 33.5880 | + | 15.6252i | 1.47011 | + | 0.683897i | ||||
\(523\) | −8.38637 | − | 14.5256i | −0.366710 | − | 0.635161i | 0.622339 | − | 0.782748i | \(-0.286183\pi\) |
−0.989049 | + | 0.147587i | \(0.952849\pi\) | |||||||
\(524\) | 32.1580 | + | 55.6993i | 1.40483 | + | 2.43324i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.6908 | + | 20.2490i | −0.509741 | + | 0.882898i | ||||
\(527\) | 20.8081 | 0.906416 | ||||||||
\(528\) | −22.2643 | + | 24.3193i | −0.968927 | + | 1.05836i | ||||
\(529\) | −22.9189 | −0.996472 | ||||||||
\(530\) | −6.00212 | − | 10.3960i | −0.260716 | − | 0.451573i | ||||
\(531\) | −1.20855 | − | 13.6707i | −0.0524468 | − | 0.593260i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −15.9339 | − | 27.5982i | −0.690172 | − | 1.19541i | ||||
\(534\) | −11.8791 | − | 2.62787i | −0.514058 | − | 0.113719i | ||||
\(535\) | −1.52635 | − | 2.64372i | −0.0659900 | − | 0.114298i | ||||
\(536\) | −11.6234 | − | 20.1322i | −0.502053 | − | 0.869581i | ||||
\(537\) | 1.28484 | − | 1.40343i | 0.0554449 | − | 0.0605627i | ||||
\(538\) | −20.6774 | − | 35.8143i | −0.891466 | − | 1.54406i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 5.72007 | − | 43.9107i | 0.246153 | − | 1.88962i | ||||
\(541\) | 2.64908 | + | 4.58834i | 0.113893 | + | 0.197268i | 0.917337 | − | 0.398112i | \(-0.130335\pi\) |
−0.803444 | + | 0.595381i | \(0.797001\pi\) | |||||||
\(542\) | 12.7019 | 0.545595 | ||||||||
\(543\) | −5.39503 | − | 1.19348i | −0.231523 | − | 0.0512171i | ||||
\(544\) | −56.0404 | −2.40271 | ||||||||
\(545\) | −14.7589 | + | 25.5631i | −0.632200 | + | 1.09500i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.4325 | + | 28.4619i | 0.702603 | + | 1.21694i | 0.967550 | + | 0.252681i | \(0.0813123\pi\) |
−0.264947 | + | 0.964263i | \(0.585354\pi\) | |||||||
\(548\) | −44.4542 | − | 76.9970i | −1.89899 | − | 3.28915i | ||||
\(549\) | 0.945552 | − | 0.663364i | 0.0403552 | − | 0.0283117i | ||||
\(550\) | 4.54708 | − | 7.87577i | 0.193888 | − | 0.335824i | ||||
\(551\) | 1.42280 | − | 2.46436i | 0.0606133 | − | 0.104985i | ||||
\(552\) | −4.41062 | − | 0.975709i | −0.187729 | − | 0.0415290i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −22.2515 | + | 38.5408i | −0.945376 | + | 1.63744i | ||||
\(555\) | −6.63818 | − | 21.0203i | −0.281775 | − | 0.892263i | ||||
\(556\) | −42.4512 | −1.80033 | ||||||||
\(557\) | 9.40798 | − | 16.2951i | 0.398629 | − | 0.690446i | −0.594928 | − | 0.803779i | \(-0.702819\pi\) |
0.993557 | + | 0.113333i | \(0.0361527\pi\) | |||||||
\(558\) | −54.8736 | − | 25.5273i | −2.32298 | − | 1.08066i | ||||
\(559\) | −19.8923 | −0.841354 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.41776 | + | 4.82554i | −0.186518 | + | 0.203734i | ||||
\(562\) | 9.54108 | 0.402466 | ||||||||
\(563\) | −13.8325 | − | 23.9586i | −0.582970 | − | 1.00973i | −0.995125 | − | 0.0986197i | \(-0.968557\pi\) |
0.412155 | − | 0.911114i | \(-0.364776\pi\) | |||||||
\(564\) | −101.275 | − | 22.4038i | −4.26443 | − | 0.943370i | ||||
\(565\) | −2.52773 | + | 4.37816i | −0.106343 | + | 0.184191i | ||||
\(566\) | −70.7856 | −2.97534 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 13.2942 | 0.557812 | ||||||||
\(569\) | 20.0916 | − | 34.7996i | 0.842282 | − | 1.45888i | −0.0456782 | − | 0.998956i | \(-0.514545\pi\) |
0.887961 | − | 0.459920i | \(-0.152122\pi\) | |||||||
\(570\) | −4.55773 | − | 1.00825i | −0.190902 | − | 0.0422311i | ||||
\(571\) | 3.40565 | + | 5.89875i | 0.142522 | + | 0.246855i | 0.928446 | − | 0.371468i | \(-0.121146\pi\) |
−0.785924 | + | 0.618323i | \(0.787812\pi\) | |||||||
\(572\) | 23.0283 | 0.962862 | ||||||||
\(573\) | 4.52409 | − | 4.94169i | 0.188997 | − | 0.206442i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.707427 | 0.0295017 | ||||||||
\(576\) | 71.0036 | + | 33.0310i | 2.95849 | + | 1.37629i | ||||
\(577\) | 18.2111 | − | 31.5425i | 0.758138 | − | 1.31313i | −0.185661 | − | 0.982614i | \(-0.559443\pi\) |
0.943799 | − | 0.330519i | \(-0.107224\pi\) | |||||||
\(578\) | 24.8625 | 1.03414 | ||||||||
\(579\) | −2.15721 | − | 6.83098i | −0.0896507 | − | 0.283886i | ||||
\(580\) | −19.3787 | + | 33.5649i | −0.804658 | + | 1.39371i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −66.3930 | − | 14.6873i | −2.75208 | − | 0.608810i | ||||
\(583\) | 1.87947 | − | 3.25534i | 0.0778397 | − | 0.134822i | ||||
\(584\) | −2.14295 | + | 3.71170i | −0.0886759 | + | 0.153591i | ||||
\(585\) | −12.3828 | + | 8.68729i | −0.511965 | + | 0.359175i | ||||
\(586\) | 25.6361 | + | 44.4030i | 1.05902 | + | 1.83427i | ||||
\(587\) | 5.57943 | + | 9.66385i | 0.230288 | + | 0.398870i | 0.957893 | − | 0.287126i | \(-0.0927000\pi\) |
−0.727605 | + | 0.685996i | \(0.759367\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.32446 | + | 4.02609i | −0.0957779 | + | 0.165892i | ||||
\(590\) | 19.7044 | 0.811218 | ||||||||
\(591\) | 1.50390 | + | 0.332689i | 0.0618620 | + | 0.0136850i | ||||
\(592\) | 113.229 | 4.65369 | ||||||||
\(593\) | −9.90427 | − | 17.1547i | −0.406720 | − | 0.704459i | 0.587800 | − | 0.809006i | \(-0.299994\pi\) |
−0.994520 | + | 0.104547i | \(0.966661\pi\) | |||||||
\(594\) | 17.5701 | − | 7.30586i | 0.720911 | − | 0.299763i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 36.7133 | + | 63.5893i | 1.50384 | + | 2.60472i | ||||
\(597\) | 7.39624 | − | 8.07895i | 0.302708 | − | 0.330649i | ||||
\(598\) | 1.22914 | + | 2.12893i | 0.0502633 | + | 0.0870586i | ||||
\(599\) | 9.06600 | + | 15.7028i | 0.370427 | + | 0.641598i | 0.989631 | − | 0.143632i | \(-0.0458781\pi\) |
−0.619204 | + | 0.785230i | \(0.712545\pi\) | |||||||
\(600\) | −38.4500 | − | 8.50584i | −1.56972 | − | 0.347249i | ||||
\(601\) | −12.3285 | − | 21.3536i | −0.502889 | − | 0.871030i | −0.999994 | − | 0.00333942i | \(-0.998937\pi\) |
0.497105 | − | 0.867690i | \(-0.334396\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.670802 | + | 7.58788i | 0.0273172 | + | 0.309003i | ||||
\(604\) | −10.4743 | − | 18.1420i | −0.426194 | − | 0.738189i | ||||
\(605\) | 14.5645 | 0.592130 | ||||||||
\(606\) | −31.2404 | + | 34.1240i | −1.26905 | + | 1.38619i | ||||
\(607\) | 17.2775 | 0.701273 | 0.350637 | − | 0.936512i | \(-0.385965\pi\) | ||||
0.350637 | + | 0.936512i | \(0.385965\pi\) | |||||||
\(608\) | 6.26024 | − | 10.8431i | 0.253886 | − | 0.439744i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.829179 | + | 1.43618i | 0.0335725 | + | 0.0581492i | ||||
\(611\) | 17.7154 | + | 30.6840i | 0.716689 | + | 1.24134i | ||||
\(612\) | 40.9217 | + | 19.0368i | 1.65416 | + | 0.769519i | ||||
\(613\) | −9.77828 | + | 16.9365i | −0.394941 | + | 0.684058i | −0.993094 | − | 0.117324i | \(-0.962568\pi\) |
0.598153 | + | 0.801382i | \(0.295902\pi\) | |||||||
\(614\) | −29.3787 | + | 50.8855i | −1.18563 | + | 2.05357i | ||||
\(615\) | 18.6034 | − | 20.3206i | 0.750161 | − | 0.819404i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.8723 | − | 18.8314i | 0.437702 | − | 0.758122i | −0.559810 | − | 0.828621i | \(-0.689126\pi\) |
0.997512 | + | 0.0704988i | \(0.0224591\pi\) | |||||||
\(618\) | −35.1151 | + | 38.3564i | −1.41254 | + | 1.54292i | ||||
\(619\) | 33.8048 | 1.35873 | 0.679366 | − | 0.733800i | \(-0.262255\pi\) | ||||
0.679366 | + | 0.733800i | \(0.262255\pi\) | |||||||
\(620\) | 31.6595 | − | 54.8359i | 1.27148 | − | 2.20226i | ||||
\(621\) | 1.17556 | + | 0.899495i | 0.0471736 | + | 0.0360955i | ||||
\(622\) | −12.2031 | −0.489300 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −23.3977 | − | 74.0906i | −0.936658 | − | 2.96600i | ||||
\(625\) | −6.41615 | −0.256646 | ||||||||
\(626\) | 11.6778 | + | 20.2266i | 0.466740 | + | 0.808418i | ||||
\(627\) | −0.440171 | − | 1.39383i | −0.0175787 | − | 0.0556644i | ||||
\(628\) | 0.790623 | − | 1.36940i | 0.0315493 | − | 0.0546450i | ||||
\(629\) | 22.4674 | 0.895832 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.6410 | −0.941134 | −0.470567 | − | 0.882364i | \(-0.655951\pi\) | ||||
−0.470567 | + | 0.882364i | \(0.655951\pi\) | |||||||
\(632\) | −71.9258 | + | 124.579i | −2.86105 | + | 4.95549i | ||||
\(633\) | −13.3634 | + | 14.5969i | −0.531146 | + | 0.580173i | ||||
\(634\) | −10.9454 | − | 18.9581i | −0.434699 | − | 0.752921i | ||||
\(635\) | 13.2843 | 0.527169 | ||||||||
\(636\) | −25.3192 | − | 5.60107i | −1.00397 | − | 0.222097i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −16.6547 | −0.659365 | ||||||||
\(639\) | −3.94977 | − | 1.83744i | −0.156250 | − | 0.0726879i | ||||
\(640\) | −24.4729 | + | 42.3883i | −0.967375 | + | 1.67554i | ||||
\(641\) | 15.9180 | 0.628724 | 0.314362 | − | 0.949303i | \(-0.398209\pi\) | ||||
0.314362 | + | 0.949303i | \(0.398209\pi\) | |||||||
\(642\) | −8.83591 | − | 1.95466i | −0.348725 | − | 0.0771444i | ||||
\(643\) | −13.2527 | + | 22.9544i | −0.522636 | + | 0.905231i | 0.477017 | + | 0.878894i | \(0.341718\pi\) |
−0.999653 | + | 0.0263376i | \(0.991616\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.17875 | − | 16.3989i | −0.203913 | − | 0.645707i | ||||
\(646\) | 2.37883 | − | 4.12026i | 0.0935938 | − | 0.162109i | ||||
\(647\) | −0.00801958 | + | 0.0138903i | −0.000315282 | + | 0.000546085i | −0.866183 | − | 0.499727i | \(-0.833434\pi\) |
0.865868 | + | 0.500273i | \(0.166767\pi\) | |||||||
\(648\) | −53.0787 | − | 63.0238i | −2.08513 | − | 2.47581i | ||||
\(649\) | 3.08506 | + | 5.34348i | 0.121099 | + | 0.209750i | ||||
\(650\) | 10.7152 | + | 18.5592i | 0.420283 | + | 0.727951i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −28.7644 | + | 49.8214i | −1.12650 | + | 1.95115i | ||||
\(653\) | −33.2879 | −1.30266 | −0.651328 | − | 0.758796i | \(-0.725788\pi\) | ||||
−0.651328 | + | 0.758796i | \(0.725788\pi\) | |||||||
\(654\) | 26.3506 | + | 83.4413i | 1.03039 | + | 3.26281i | ||||
\(655\) | 18.9932 | 0.742126 | ||||||||
\(656\) | 70.7571 | + | 122.555i | 2.76260 | + | 4.78497i | ||||
\(657\) | 1.14969 | − | 0.806577i | 0.0448535 | − | 0.0314676i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.4156 | + | 33.6288i | 0.756324 | + | 1.30999i | 0.944713 | + | 0.327897i | \(0.106340\pi\) |
−0.188389 | + | 0.982094i | \(0.560327\pi\) | |||||||
\(660\) | 5.99518 | + | 18.9842i | 0.233362 | + | 0.738959i | ||||
\(661\) | −2.65322 | − | 4.59551i | −0.103198 | − | 0.178745i | 0.809802 | − | 0.586703i | \(-0.199574\pi\) |
−0.913001 | + | 0.407958i | \(0.866241\pi\) | |||||||
\(662\) | −31.0917 | − | 53.8525i | −1.20842 | − | 2.09304i | ||||
\(663\) | −4.64266 | − | 14.7013i | −0.180306 | − | 0.570953i | ||||
\(664\) | 64.0264 | + | 110.897i | 2.48471 | + | 4.30364i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −59.2492 | − | 27.5628i | −2.29586 | − | 1.06804i | ||||
\(667\) | −0.647777 | − | 1.12198i | −0.0250820 | − | 0.0434433i | ||||
\(668\) | −17.1765 | −0.664579 | ||||||||
\(669\) | −8.72047 | − | 27.6140i | −0.337153 | − | 1.06762i | ||||
\(670\) | −10.9368 | −0.422527 | ||||||||
\(671\) | −0.259644 | + | 0.449717i | −0.0100235 | + | 0.0173611i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.03565 | − | 5.25789i | −0.117016 | − | 0.202677i | 0.801568 | − | 0.597903i | \(-0.203999\pi\) |
−0.918584 | + | 0.395227i | \(0.870666\pi\) | |||||||
\(674\) | 18.5142 | + | 32.0676i | 0.713142 | + | 1.23520i | ||||
\(675\) | 10.2481 | + | 7.84144i | 0.394448 | + | 0.301817i | ||||
\(676\) | 7.78465 | − | 13.4834i | 0.299410 | − | 0.518593i | ||||
\(677\) | 17.3925 | − | 30.1247i | 0.668449 | − | 1.15779i | −0.309889 | − | 0.950773i | \(-0.600292\pi\) |
0.978338 | − | 0.207014i | \(-0.0663747\pi\) | |||||||
\(678\) | 4.51304 | + | 14.2909i | 0.173322 | + | 0.548838i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −20.3373 | + | 35.2253i | −0.779901 | + | 1.35083i | ||||
\(681\) | −28.8682 | − | 6.38617i | −1.10623 | − | 0.244719i | ||||
\(682\) | 27.2091 | 1.04189 | ||||||||
\(683\) | −9.71206 | + | 16.8218i | −0.371622 | + | 0.643667i | −0.989815 | − | 0.142358i | \(-0.954531\pi\) |
0.618194 | + | 0.786026i | \(0.287865\pi\) | |||||||
\(684\) | −8.25471 | + | 5.79120i | −0.315627 | + | 0.221432i | ||||
\(685\) | −26.2556 | −1.00318 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −33.4672 | − | 7.40354i | −1.27685 | − | 0.282463i | ||||
\(688\) | 88.3352 | 3.36775 | ||||||||
\(689\) | 4.42895 | + | 7.67117i | 0.168730 | + | 0.292248i | ||||
\(690\) | −1.43507 | + | 1.56753i | −0.0546322 | + | 0.0596749i | ||||
\(691\) | 3.31837 | − | 5.74759i | 0.126237 | − | 0.218649i | −0.795979 | − | 0.605324i | \(-0.793043\pi\) |
0.922216 | + | 0.386676i | \(0.126377\pi\) | |||||||
\(692\) | −61.4416 | −2.33566 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.67197 | 0.291224 | ||||||||
\(695\) | −6.26814 | + | 10.8567i | −0.237764 | + | 0.411820i | ||||
\(696\) | 21.7176 | + | 68.7705i | 0.823204 | + | 2.60674i | ||||
\(697\) | 14.0399 | + | 24.3178i | 0.531799 | + | 0.921103i | ||||
\(698\) | −9.83974 | −0.372440 | ||||||||
\(699\) | 3.09385 | + | 9.79690i | 0.117020 | + | 0.370553i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.9153 | −0.525574 | −0.262787 | − | 0.964854i | \(-0.584642\pi\) | ||||
−0.262787 | + | 0.964854i | \(0.584642\pi\) | |||||||
\(702\) | −5.79226 | + | 44.4649i | −0.218615 | + | 1.67822i | ||||
\(703\) | −2.50982 | + | 4.34713i | −0.0946595 | + | 0.163955i | ||||
\(704\) | −35.2072 | −1.32692 | ||||||||
\(705\) | −20.6834 | + | 22.5926i | −0.778983 | + | 0.850887i | ||||
\(706\) | −3.73876 | + | 6.47571i | −0.140710 | + | 0.243717i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 28.7423 | − | 31.3954i | 1.08020 | − | 1.17991i | ||||
\(709\) | −17.0778 | + | 29.5796i | −0.641370 | + | 1.11089i | 0.343757 | + | 0.939059i | \(0.388300\pi\) |
−0.985127 | + | 0.171827i | \(0.945033\pi\) | |||||||
\(710\) | 3.12725 | − | 5.41655i | 0.117364 | − | 0.203280i | ||||
\(711\) | 38.5880 | − | 27.0719i | 1.44716 | − | 1.01527i | ||||
\(712\) | −11.8426 | − | 20.5120i | −0.443821 | − | 0.768721i | ||||
\(713\) | 1.05829 | + | 1.83301i | 0.0396332 | + | 0.0686467i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.40025 | − | 5.88941i | 0.127162 | − | 0.220251i | ||||
\(716\) | 5.90135 | 0.220544 | ||||||||
\(717\) | 23.4563 | − | 25.6214i | 0.875991 | − | 0.956849i | ||||
\(718\) | 45.6183 | 1.70246 | ||||||||
\(719\) | 22.1450 | + | 38.3563i | 0.825870 | + | 1.43045i | 0.901253 | + | 0.433294i | \(0.142649\pi\) |
−0.0753825 | + | 0.997155i | \(0.524018\pi\) | |||||||
\(720\) | 54.9879 | − | 38.5775i | 2.04928 | − | 1.43770i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −25.2623 | − | 43.7556i | −0.940165 | − | 1.62841i | ||||
\(723\) | −49.5320 | − | 10.9574i | −1.84212 | − | 0.407509i | ||||
\(724\) | −8.56860 | − | 14.8413i | −0.318450 | − | 0.551571i | ||||
\(725\) | −5.64705 | − | 9.78099i | −0.209726 | − | 0.363257i | ||||
\(726\) | 29.1543 | − | 31.8454i | 1.08202 | − | 1.18189i | ||||
\(727\) | 14.1247 | + | 24.4647i | 0.523857 | + | 0.907346i | 0.999614 | + | 0.0277700i | \(0.00884060\pi\) |
−0.475758 | + | 0.879576i | \(0.657826\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.05919 | + | 26.0608i | 0.261451 | + | 0.965217i | ||||
\(730\) | 1.00819 | + | 1.74623i | 0.0373147 | + | 0.0646310i | ||||
\(731\) | 17.5278 | 0.648290 | ||||||||
\(732\) | 3.49779 | + | 0.773775i | 0.129282 | + | 0.0285995i | ||||
\(733\) | −25.0169 | −0.924020 | −0.462010 | − | 0.886875i | \(-0.652872\pi\) | ||||
−0.462010 | + | 0.886875i | \(0.652872\pi\) | |||||||
\(734\) | −32.4919 | + | 56.2776i | −1.19930 | + | 2.07724i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.85018 | − | 4.93666i | −0.105059 | − | 0.181968i | ||||
\(737\) | −1.71235 | − | 2.96587i | −0.0630752 | − | 0.109249i | ||||
\(738\) | −7.19198 | − | 81.3532i | −0.264740 | − | 2.99465i | ||||
\(739\) | −16.0115 | + | 27.7327i | −0.588992 | + | 1.02016i | 0.405373 | + | 0.914151i | \(0.367142\pi\) |
−0.994365 | + | 0.106013i | \(0.966192\pi\) | |||||||
\(740\) | 34.1840 | − | 59.2084i | 1.25663 | − | 2.17655i | ||||
\(741\) | 3.36314 | + | 0.743987i | 0.123548 | + | 0.0273311i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.4031 | − | 33.6072i | 0.711833 | − | 1.23293i | −0.252336 | − | 0.967640i | \(-0.581199\pi\) |
0.964169 | − | 0.265290i | \(-0.0854678\pi\) | |||||||
\(744\) | −35.4806 | − | 112.352i | −1.30078 | − | 4.11903i | ||||
\(745\) | 21.6837 | 0.794428 | ||||||||
\(746\) | −26.0118 | + | 45.0537i | −0.952359 | + | 1.64953i | ||||
\(747\) | −3.69506 | − | 41.7973i | −0.135195 | − | 1.52928i | ||||
\(748\) | −20.2911 | −0.741915 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −37.6987 | + | 41.1785i | −1.37656 | + | 1.50363i | ||||
\(751\) | 21.6991 | 0.791811 | 0.395905 | − | 0.918291i | \(-0.370431\pi\) | ||||
0.395905 | + | 0.918291i | \(0.370431\pi\) | |||||||
\(752\) | −78.6685 | − | 136.258i | −2.86874 | − | 4.96881i | ||||
\(753\) | 38.5341 | + | 8.52444i | 1.40426 | + | 0.310648i | ||||
\(754\) | 19.6233 | − | 33.9885i | 0.714638 | − | 1.23779i | ||||
\(755\) | −6.18635 | −0.225144 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.5242 | 1.21846 | 0.609229 | − | 0.792995i | \(-0.291479\pi\) | ||||
0.609229 | + | 0.792995i | \(0.291479\pi\) | |||||||
\(758\) | 13.6802 | − | 23.6949i | 0.496889 | − | 0.860637i | ||||
\(759\) | −0.649771 | − | 0.143741i | −0.0235852 | − | 0.00521747i | ||||
\(760\) | −4.54374 | − | 7.86999i | −0.164819 | − | 0.285475i | ||||
\(761\) | −13.3210 | −0.482884 | −0.241442 | − | 0.970415i | \(-0.577620\pi\) | ||||
−0.241442 | + | 0.970415i | \(0.577620\pi\) | |||||||
\(762\) | 26.5917 | − | 29.0462i | 0.963315 | − | 1.05223i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 20.7795 | 0.751775 | ||||||||
\(765\) | 10.9109 | − | 7.65469i | 0.394485 | − | 0.276756i | ||||
\(766\) | −27.3462 | + | 47.3649i | −0.988057 | + | 1.71137i | ||||
\(767\) | −14.5398 | −0.525003 | ||||||||
\(768\) | 16.4635 | + | 52.1330i | 0.594075 | + | 1.88119i | ||||
\(769\) | 27.3568 | − | 47.3833i | 0.986510 | − | 1.70869i | 0.351488 | − | 0.936192i | \(-0.385676\pi\) |
0.635022 | − | 0.772494i | \(-0.280991\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 41.0765 | + | 9.08686i | 1.47933 | + | 0.327255i | ||||
\(772\) | 11.1088 | − | 19.2410i | 0.399814 | − | 0.692498i | ||||
\(773\) | −1.18021 | + | 2.04418i | −0.0424491 | + | 0.0735240i | −0.886469 | − | 0.462787i | \(-0.846849\pi\) |
0.844020 | + | 0.536311i | \(0.180183\pi\) | |||||||
\(774\) | −46.2230 | − | 21.5030i | −1.66145 | − | 0.772911i | ||||
\(775\) | 9.22573 | + | 15.9794i | 0.331398 | + | 0.573998i | ||||
\(776\) | −66.1892 | − | 114.643i | −2.37606 | − | 4.11545i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 18.1842 | − | 31.4960i | 0.651936 | − | 1.12919i | ||||
\(779\) | −6.27356 | −0.224774 | ||||||||
\(780\) | −45.8064 | − | 10.1332i | −1.64013 | − | 0.362827i | ||||
\(781\) | 1.95850 | 0.0700805 | ||||||||
\(782\) | −1.08304 | − | 1.87588i | −0.0387295 | − | 0.0670814i | ||||
\(783\) | 3.05261 | − | 23.4337i | 0.109092 | − | 0.837452i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.233479 | − | 0.404398i | −0.00833323 | − | 0.0144336i | ||||
\(786\) | 38.0196 | − | 41.5290i | 1.35611 | − | 1.48129i | ||||
\(787\) | 0.833971 | + | 1.44448i | 0.0297278 | + | 0.0514901i | 0.880507 | − | 0.474034i | \(-0.157203\pi\) |
−0.850779 | + | 0.525524i | \(0.823869\pi\) | |||||||
\(788\) | 2.38855 | + | 4.13708i | 0.0850884 | + | 0.147377i | ||||
\(789\) | 14.5636 | + | 3.22172i | 0.518476 | + | 0.114696i | ||||
\(790\) | 33.8388 | + | 58.6105i | 1.20393 | + | 2.08527i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 33.5880 | + | 15.6252i | 1.19350 | + | 0.555218i | ||||
\(793\) | −0.611849 | − | 1.05975i | −0.0217274 | − | 0.0376330i | ||||
\(794\) | 48.9085 | 1.73570 | ||||||||
\(795\) | −5.17098 | + | 5.64828i | −0.183396 | + | 0.200324i | ||||
\(796\) | 33.9715 | 1.20409 | ||||||||
\(797\) | −14.3148 | + | 24.7939i | −0.507055 | + | 0.878244i | 0.492912 | + | 0.870079i | \(0.335932\pi\) |
−0.999967 | + | 0.00816511i | \(0.997401\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.6097 | − | 27.0368i | −0.552232 | − | 0.956493i | ||||
\(800\) | −24.8467 | − | 43.0358i | −0.878464 | − | 1.52154i | ||||
\(801\) | 0.683457 | + | 7.73102i | 0.0241487 | + | 0.273162i | ||||
\(802\) | 39.1895 | − | 67.8783i | 1.38383 | − | 2.39687i | ||||
\(803\) | −0.315698 | + | 0.546805i | −0.0111408 | + | 0.0192963i | ||||
\(804\) | −15.9533 | + | 17.4258i | −0.562629 | + | 0.614562i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −32.0591 | + | 55.5279i | −1.12923 | + | 1.95589i | ||||
\(807\) | −17.8141 | + | 19.4584i | −0.627085 | + | 0.684968i | ||||
\(808\) | −90.0675 | −3.16856 | ||||||||
\(809\) | 1.42846 | − | 2.47416i | 0.0502219 | − | 0.0869868i | −0.839822 | − | 0.542862i | \(-0.817340\pi\) |
0.890043 | + | 0.455876i | \(0.150674\pi\) | |||||||
\(810\) | −38.1642 | + | 6.80091i | −1.34095 | + | 0.238960i | ||||
\(811\) | 26.2917 | 0.923225 | 0.461613 | − | 0.887082i | \(-0.347271\pi\) | ||||
0.461613 | + | 0.887082i | \(0.347271\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.44010 | − | 7.72675i | −0.0855779 | − | 0.270989i | ||||
\(814\) | 29.3788 | 1.02973 | ||||||||
\(815\) | 8.49443 | + | 14.7128i | 0.297547 | + | 0.515366i | ||||
\(816\) | 20.6166 | + | 65.2840i | 0.721724 | + | 2.28540i | ||||
\(817\) | −1.95802 | + | 3.39139i | −0.0685025 | + | 0.118650i | ||||
\(818\) | 29.4829 | 1.03085 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 85.4467 | 2.98393 | ||||||||
\(821\) | 1.32925 | − | 2.30232i | 0.0463910 | − | 0.0803517i | −0.841897 | − | 0.539638i | \(-0.818561\pi\) |
0.888289 | + | 0.459286i | \(0.151895\pi\) | |||||||
\(822\) | −52.5570 | + | 57.4083i | −1.83314 | + | 2.00234i | ||||
\(823\) | 6.10769 | + | 10.5788i | 0.212901 | + | 0.368755i | 0.952621 | − | 0.304160i | \(-0.0983756\pi\) |
−0.739721 | + | 0.672914i | \(0.765042\pi\) | |||||||
\(824\) | −101.239 | −3.52681 | ||||||||
\(825\) | −5.66444 | − | 1.25308i | −0.197211 | − | 0.0436265i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.15812 | 0.318459 | 0.159230 | − | 0.987242i | \(-0.449099\pi\) | ||||
0.159230 | + | 0.987242i | \(0.449099\pi\) | |||||||
\(828\) | 0.404277 | + | 4.57304i | 0.0140496 | + | 0.158924i | ||||
\(829\) | −9.17156 | + | 15.8856i | −0.318541 | + | 0.551730i | −0.980184 | − | 0.198089i | \(-0.936526\pi\) |
0.661642 | + | 0.749819i | \(0.269860\pi\) | |||||||
\(830\) | 60.2447 | 2.09113 | ||||||||
\(831\) | 27.7194 | + | 6.13204i | 0.961576 | + | 0.212718i | ||||
\(832\) | 41.4828 | − | 71.8503i | 1.43816 | − | 2.49096i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 11.1912 | + | 35.4378i | 0.387520 | + | 1.22711i | ||||
\(835\) | −2.53620 | + | 4.39284i | −0.0877690 | + | 0.152020i | ||||
\(836\) | 2.26670 | − | 3.92605i | 0.0783956 | − | 0.135785i | ||||
\(837\) | −4.98713 | + | 38.2842i | −0.172380 | + | 1.32330i | ||||
\(838\) | 0.672190 | + | 1.16427i | 0.0232204 | + | 0.0402190i | ||||
\(839\) | −9.47055 | − | 16.4035i | −0.326960 | − | 0.566311i | 0.654947 | − | 0.755675i | \(-0.272691\pi\) |
−0.981907 | + | 0.189364i | \(0.939357\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.15821 | − | 7.20224i | 0.143387 | − | 0.248353i | ||||
\(842\) | 51.6049 | 1.77842 | ||||||||
\(843\) | −1.83288 | − | 5.80396i | −0.0631278 | − | 0.199899i | ||||
\(844\) | −61.3789 | −2.11275 | ||||||||
\(845\) | −2.29889 | − | 3.98179i | −0.0790842 | − | 0.136978i | ||||
\(846\) | 7.99612 | + | 90.4493i | 0.274912 | + | 3.10971i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −19.6676 | − | 34.0652i | −0.675387 | − | 1.16980i | ||||
\(849\) | 13.5982 | + | 43.0598i | 0.466690 | + | 1.47781i | ||||
\(850\) | −9.44151 | − | 16.3532i | −0.323841 | − | 0.560909i | ||||
\(851\) | 1.14268 | + | 1.97917i | 0.0391704 | + | 0.0678452i | ||||
\(852\) | −4.06865 | − | 12.8837i | −0.139390 | − | 0.441388i | ||||
\(853\) | −9.97922 | − | 17.2845i | −0.341682 | − | 0.591811i | 0.643063 | − | 0.765813i | \(-0.277663\pi\) |
−0.984745 | + | 0.174002i | \(0.944330\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.262227 | + | 2.96622i | 0.00896796 | + | 0.101442i | ||||
\(856\) | −8.80878 | − | 15.2573i | −0.301078 | − | 0.521482i | ||||
\(857\) | −16.4000 | −0.560214 | −0.280107 | − | 0.959969i | \(-0.590370\pi\) | ||||
−0.280107 | + | 0.959969i | \(0.590370\pi\) | |||||||
\(858\) | −6.07084 | − | 19.2238i | −0.207255 | − | 0.656290i | ||||
\(859\) | 33.7151 | 1.15034 | 0.575172 | − | 0.818033i | \(-0.304935\pi\) | ||||
0.575172 | + | 0.818033i | \(0.304935\pi\) | |||||||
\(860\) | 26.6685 | − | 46.1912i | 0.909389 | − | 1.57511i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −22.9720 | − | 39.7887i | −0.782429 | − | 1.35521i | ||||
\(863\) | 14.3415 | + | 24.8403i | 0.488191 | + | 0.845572i | 0.999908 | − | 0.0135822i | \(-0.00432348\pi\) |
−0.511716 | + | 0.859154i | \(0.670990\pi\) | |||||||
\(864\) | 13.4313 | − | 103.107i | 0.456943 | − | 3.50777i | ||||
\(865\) | −9.07219 | + | 15.7135i | −0.308464 | + | 0.534275i | ||||
\(866\) | −45.4432 | + | 78.7100i | −1.54422 | + | 2.67467i | ||||
\(867\) | −4.77618 | − | 15.1241i | −0.162208 | − | 0.513643i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.5961 | + | 18.3529i | −0.359447 | + | 0.622581i | ||||
\(870\) | 33.1284 | + | 7.32860i | 1.12316 | + | 0.248463i | ||||
\(871\) | 8.07027 | 0.273451 | ||||||||
\(872\) | −85.1753 | + | 147.528i | −2.88440 | + | 4.99593i | ||||
\(873\) | 3.81989 | + | 43.2092i | 0.129284 | + | 1.46241i | ||||
\(874\) | 0.483944 | 0.0163696 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.25292 | + | 0.940823i | 0.143693 | + | 0.0317875i | ||||
\(877\) | −29.5243 | −0.996964 | −0.498482 | − | 0.866900i | \(-0.666109\pi\) | ||||
−0.498482 | + | 0.866900i | \(0.666109\pi\) | |||||||
\(878\) | 28.4159 | + | 49.2177i | 0.958989 | + | 1.66102i | ||||
\(879\) | 22.0861 | − | 24.1247i | 0.744945 | − | 0.813707i | ||||
\(880\) | −15.0994 | + | 26.1530i | −0.509001 | + | 0.881616i | ||||
\(881\) | 57.5032 | 1.93733 | 0.968666 | − | 0.248366i | \(-0.0798934\pi\) | ||||
0.968666 | + | 0.248366i | \(0.0798934\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.8715 | 0.668730 | 0.334365 | − | 0.942444i | \(-0.391478\pi\) | ||||
0.334365 | + | 0.942444i | \(0.391478\pi\) | |||||||
\(884\) | 23.9079 | − | 41.4097i | 0.804109 | − | 1.39276i | ||||
\(885\) | −3.78530 | − | 11.9864i | −0.127241 | − | 0.402920i | ||||
\(886\) | −41.8918 | − | 72.5587i | −1.40738 | − | 2.43766i | ||||
\(887\) | 37.0951 | 1.24553 | 0.622766 | − | 0.782408i | \(-0.286009\pi\) | ||||
0.622766 | + | 0.782408i | \(0.286009\pi\) | |||||||
\(888\) | −38.3098 | − | 121.311i | −1.28559 | − | 4.07093i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −11.1432 | −0.373519 | ||||||||
\(891\) | −7.81954 | − | 9.28464i | −0.261964 | − | 0.311047i | ||||
\(892\) | 44.9070 | − | 77.7812i | 1.50360 | − | 2.60431i | ||||
\(893\) | 6.97501 | 0.233410 | ||||||||
\(894\) | 43.4052 | − | 47.4117i | 1.45169 | − | 1.58568i | ||||
\(895\) | 0.871366 | − | 1.50925i | 0.0291266 | − | 0.0504487i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.05893 | − | 1.15668i | 0.0353568 | − | 0.0386204i | ||||
\(898\) | −45.1783 | + | 78.2511i | −1.50762 | + | 2.61127i | ||||
\(899\) | 16.8956 | − | 29.2641i | 0.563501 | − | 0.976012i | ||||
\(900\) | 3.52432 | + | 39.8659i | 0.117477 | + | 1.32886i | ||||
\(901\) | −3.90251 | − | 6.75935i | −0.130012 | − | 0.225187i | ||||
\(902\) | 18.3589 | + | 31.7985i | 0.611284 | + | 1.05877i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14.5879 | + | 25.2669i | −0.485185 | + | 0.840366i | ||||
\(905\) | −5.06080 | −0.168227 | ||||||||
\(906\) | −12.3835 | + | 13.5266i | −0.411414 | + | 0.449390i | ||||
\(907\) | 24.4088 | 0.810479 | 0.405240 | − | 0.914210i | \(-0.367188\pi\) | ||||
0.405240 | + | 0.914210i | \(0.367188\pi\) | |||||||
\(908\) | −45.8496 | − | 79.4139i | −1.52157 | − | 2.63544i | ||||
\(909\) | 26.7594 | + | 12.4485i | 0.887555 | + | 0.412892i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.5493 | − | 21.7360i | −0.415776 | − | 0.720146i | 0.579733 | − | 0.814806i | \(-0.303157\pi\) |
−0.995510 | + | 0.0946604i | \(0.969823\pi\) | |||||||
\(912\) | −14.9346 | − | 3.30381i | −0.494535 | − | 0.109400i | ||||
\(913\) | 9.43234 | + | 16.3373i | 0.312165 | + | 0.540685i | ||||
\(914\) | 32.2971 | + | 55.9401i | 1.06829 | + | 1.85034i | ||||
\(915\) | 0.714358 | − | 0.780296i | 0.0236159 | − | 0.0257958i | ||||
\(916\) | −53.1538 | − | 92.0652i | −1.75625 | − | 3.04192i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 5.10378 | − | 39.1796i | 0.168450 | − | 1.29312i | ||||
\(919\) | 14.2988 | + | 24.7662i | 0.471674 | + | 0.816963i | 0.999475 | − | 0.0324050i | \(-0.0103167\pi\) |
−0.527801 | + | 0.849368i | \(0.676983\pi\) | |||||||
\(920\) | −4.13738 | −0.136405 | ||||||||
\(921\) | 36.5980 | + | 8.09615i | 1.20595 | + | 0.266777i | ||||
\(922\) | 46.3268 | 1.52569 | ||||||||
\(923\) | −2.30759 | + | 3.99686i | −0.0759553 | + | 0.131558i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.96139 | + | 17.2536i | 0.327528 | + | 0.567296i | ||||
\(926\) | −49.2098 | − | 85.2339i | −1.61713 | − | 2.80096i | ||||
\(927\) | 30.0784 | + | 13.9925i | 0.987906 | + | 0.459576i | ||||
\(928\) | −45.5033 | + | 78.8140i | −1.49372 | + | 2.58720i | ||||
\(929\) | 22.7285 | − | 39.3669i | 0.745698 | − | 1.29159i | −0.204170 | − | 0.978935i | \(-0.565450\pi\) |
0.949868 | − | 0.312651i | \(-0.101217\pi\) | |||||||
\(930\) | −54.1227 | − | 11.9729i | −1.77475 | − | 0.392607i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −15.9321 | + | 27.5952i | −0.521873 | + | 0.903910i | ||||
\(933\) | 2.34427 | + | 7.42331i | 0.0767479 | + | 0.243028i | ||||
\(934\) | 22.2413 | 0.727757 | ||||||||
\(935\) | −2.99609 | + | 5.18937i | −0.0979825 | + | 0.169711i | ||||
\(936\) | −71.4626 | + | 50.1355i | −2.33583 | + | 1.63873i | ||||
\(937\) | 27.0083 | 0.882322 | 0.441161 | − | 0.897428i | \(-0.354567\pi\) | ||||
0.441161 | + | 0.897428i | \(0.354567\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.0607 | − | 10.9894i | 0.328320 | − | 0.358625i | ||||
\(940\) | −95.0005 | −3.09857 | ||||||||
\(941\) | −6.35657 | − | 11.0099i | −0.207218 | − | 0.358912i | 0.743619 | − | 0.668604i | \(-0.233108\pi\) |
−0.950837 | + | 0.309691i | \(0.899774\pi\) | |||||||
\(942\) | −1.35159 | − | 0.298996i | −0.0440371 | − | 0.00974181i | ||||
\(943\) | −1.42812 | + | 2.47358i | −0.0465060 | + | 0.0805508i | ||||
\(944\) | 64.5667 | 2.10147 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 22.9197 | 0.745185 | ||||||||
\(947\) | −23.7724 | + | 41.1749i | −0.772498 | + | 1.33801i | 0.163692 | + | 0.986511i | \(0.447660\pi\) |
−0.936190 | + | 0.351494i | \(0.885674\pi\) | |||||||
\(948\) | 142.745 | + | 31.5777i | 4.63613 | + | 1.02560i | ||||
\(949\) | −0.743940 | − | 1.28854i | −0.0241493 | − | 0.0418279i | ||||
\(950\) | 4.21882 | 0.136877 | ||||||||
\(951\) | −9.42977 | + | 10.3002i | −0.305781 | + | 0.334006i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38.2355 | 1.23857 | 0.619285 | − | 0.785166i | \(-0.287423\pi\) | ||||
0.619285 | + | 0.785166i | \(0.287423\pi\) | |||||||
\(954\) | 1.99907 | + | 22.6128i | 0.0647224 | + | 0.732118i | ||||
\(955\) | 3.06820 | − | 5.31428i | 0.0992847 | − | 0.171966i | ||||
\(956\) | 107.736 | 3.48444 | ||||||||
\(957\) | 3.19943 | + | 10.1312i | 0.103423 | + | 0.327497i | ||||
\(958\) | −34.6925 | + | 60.0891i | −1.12086 | + | 1.94139i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 70.0320 | + | 15.4923i | 2.26027 | + | 0.500013i | ||||
\(961\) | −12.1028 | + | 20.9627i | −0.390413 | + | 0.676215i | ||||
\(962\) | −34.6154 | + | 59.9557i | −1.11605 | + | 1.93305i | ||||
\(963\) | 0.508369 | + | 5.75049i | 0.0163820 | + | 0.185307i | ||||
\(964\) | −78.6687 | − | 136.258i | −2.53375 | − | 4.38858i | ||||
\(965\) | −3.28054 | − | 5.68207i | −0.105604 | − | 0.182912i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.4093 | + | 35.3499i | −0.656317 | + | 1.13678i | 0.325244 | + | 0.945630i | \(0.394553\pi\) |
−0.981562 | + | 0.191145i | \(0.938780\pi\) | |||||||
\(968\) | 84.0534 | 2.70158 | ||||||||
\(969\) | −2.96339 | − | 0.655554i | −0.0951977 | − | 0.0210594i | ||||
\(970\) | −62.2799 | −1.99969 | ||||||||
\(971\) | −22.4735 | − | 38.9253i | −0.721210 | − | 1.24917i | −0.960515 | − | 0.278228i | \(-0.910253\pi\) |
0.239305 | − | 0.970944i | \(-0.423080\pi\) | |||||||
\(972\) | −44.8331 | + | 70.7279i | −1.43802 | + | 2.26860i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −9.39817 | − | 16.2781i | −0.301137 | − | 0.521584i | ||||
\(975\) | 9.23136 | − | 10.0835i | 0.295640 | − | 0.322929i | ||||
\(976\) | 2.71703 | + | 4.70603i | 0.0869699 | + | 0.150636i | ||||
\(977\) | −26.7552 | − | 46.3414i | −0.855974 | − | 1.48259i | −0.875738 | − | 0.482787i | \(-0.839625\pi\) |
0.0197635 | − | 0.999805i | \(-0.493709\pi\) | |||||||
\(978\) | 49.1734 | + | 10.8780i | 1.57239 | + | 0.347841i | ||||
\(979\) | −1.74465 | − | 3.02182i | −0.0557593 | − | 0.0965779i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 45.6963 | − | 32.0588i | 1.45897 | − | 1.02356i | ||||
\(982\) | −50.8442 | − | 88.0647i | −1.62250 | − | 2.81026i | ||||
\(983\) | 11.6056 | 0.370160 | 0.185080 | − | 0.982723i | \(-0.440746\pi\) | ||||
0.185080 | + | 0.982723i | \(0.440746\pi\) | |||||||
\(984\) | 107.363 | − | 117.273i | 3.42259 | − | 3.73852i | ||||
\(985\) | 1.41073 | 0.0449495 | ||||||||
\(986\) | −17.2908 | + | 29.9485i | −0.550651 | + | 0.953756i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.34147 | + | 9.25170i | 0.169935 | + | 0.294336i | ||||
\(989\) | 0.891454 | + | 1.54404i | 0.0283466 | + | 0.0490977i | ||||
\(990\) | 14.2673 | − | 10.0094i | 0.453446 | − | 0.318121i | ||||
\(991\) | −13.0046 | + | 22.5246i | −0.413104 | + | 0.715517i | −0.995227 | − | 0.0975835i | \(-0.968889\pi\) |
0.582123 | + | 0.813100i | \(0.302222\pi\) | |||||||
\(992\) | 74.3398 | − | 128.760i | 2.36029 | − | 4.08814i | ||||
\(993\) | −26.7863 | + | 29.2588i | −0.850037 | + | 0.928500i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.01607 | − | 8.68808i | 0.159020 | − | 0.275431i | ||||
\(996\) | 87.8774 | − | 95.9889i | 2.78450 | − | 3.04153i | ||||
\(997\) | −46.8998 | −1.48533 | −0.742666 | − | 0.669662i | \(-0.766439\pi\) | ||||
−0.742666 | + | 0.669662i | \(0.766439\pi\) | |||||||
\(998\) | 34.7876 | − | 60.2539i | 1.10118 | − | 1.90731i | ||||
\(999\) | −5.38480 | + | 41.3370i | −0.170368 | + | 1.30784i |
(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 | 441.2.g.h.67.11 | 24 | ||
3.2 | odd | 2 | 1323.2.g.h.361.1 | 24 | |||
7.2 | even | 3 | 441.2.h.h.373.2 | 24 | |||
7.3 | odd | 6 | 441.2.f.h.148.11 | ✓ | 24 | ||
7.4 | even | 3 | 441.2.f.h.148.12 | yes | 24 | ||
7.5 | odd | 6 | 441.2.h.h.373.1 | 24 | |||
7.6 | odd | 2 | inner | 441.2.g.h.67.12 | 24 | ||
9.2 | odd | 6 | 1323.2.h.h.802.12 | 24 | |||
9.7 | even | 3 | 441.2.h.h.214.2 | 24 | |||
21.2 | odd | 6 | 1323.2.h.h.226.12 | 24 | |||
21.5 | even | 6 | 1323.2.h.h.226.11 | 24 | |||
21.11 | odd | 6 | 1323.2.f.h.442.2 | 24 | |||
21.17 | even | 6 | 1323.2.f.h.442.1 | 24 | |||
21.20 | even | 2 | 1323.2.g.h.361.2 | 24 | |||
63.2 | odd | 6 | 1323.2.g.h.667.1 | 24 | |||
63.4 | even | 3 | 3969.2.a.bh.1.1 | 12 | |||
63.11 | odd | 6 | 1323.2.f.h.883.2 | 24 | |||
63.16 | even | 3 | inner | 441.2.g.h.79.11 | 24 | ||
63.20 | even | 6 | 1323.2.h.h.802.11 | 24 | |||
63.25 | even | 3 | 441.2.f.h.295.12 | yes | 24 | ||
63.31 | odd | 6 | 3969.2.a.bh.1.2 | 12 | |||
63.32 | odd | 6 | 3969.2.a.bi.1.12 | 12 | |||
63.34 | odd | 6 | 441.2.h.h.214.1 | 24 | |||
63.38 | even | 6 | 1323.2.f.h.883.1 | 24 | |||
63.47 | even | 6 | 1323.2.g.h.667.2 | 24 | |||
63.52 | odd | 6 | 441.2.f.h.295.11 | yes | 24 | ||
63.59 | even | 6 | 3969.2.a.bi.1.11 | 12 | |||
63.61 | odd | 6 | inner | 441.2.g.h.79.12 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.h.148.11 | ✓ | 24 | 7.3 | odd | 6 | ||
441.2.f.h.148.12 | yes | 24 | 7.4 | even | 3 | ||
441.2.f.h.295.11 | yes | 24 | 63.52 | odd | 6 | ||
441.2.f.h.295.12 | yes | 24 | 63.25 | even | 3 | ||
441.2.g.h.67.11 | 24 | 1.1 | even | 1 | trivial | ||
441.2.g.h.67.12 | 24 | 7.6 | odd | 2 | inner | ||
441.2.g.h.79.11 | 24 | 63.16 | even | 3 | inner | ||
441.2.g.h.79.12 | 24 | 63.61 | odd | 6 | inner | ||
441.2.h.h.214.1 | 24 | 63.34 | odd | 6 | |||
441.2.h.h.214.2 | 24 | 9.7 | even | 3 | |||
441.2.h.h.373.1 | 24 | 7.5 | odd | 6 | |||
441.2.h.h.373.2 | 24 | 7.2 | even | 3 | |||
1323.2.f.h.442.1 | 24 | 21.17 | even | 6 | |||
1323.2.f.h.442.2 | 24 | 21.11 | odd | 6 | |||
1323.2.f.h.883.1 | 24 | 63.38 | even | 6 | |||
1323.2.f.h.883.2 | 24 | 63.11 | odd | 6 | |||
1323.2.g.h.361.1 | 24 | 3.2 | odd | 2 | |||
1323.2.g.h.361.2 | 24 | 21.20 | even | 2 | |||
1323.2.g.h.667.1 | 24 | 63.2 | odd | 6 | |||
1323.2.g.h.667.2 | 24 | 63.47 | even | 6 | |||
1323.2.h.h.226.11 | 24 | 21.5 | even | 6 | |||
1323.2.h.h.226.12 | 24 | 21.2 | odd | 6 | |||
1323.2.h.h.802.11 | 24 | 63.20 | even | 6 | |||
1323.2.h.h.802.12 | 24 | 9.2 | odd | 6 | |||
3969.2.a.bh.1.1 | 12 | 63.4 | even | 3 | |||
3969.2.a.bh.1.2 | 12 | 63.31 | odd | 6 | |||
3969.2.a.bi.1.11 | 12 | 63.59 | even | 6 | |||
3969.2.a.bi.1.12 | 12 | 63.32 | odd | 6 |