Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8027,2,Mod(1,8027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8027, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8027 = 23 \cdot 349 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8027.a (trivial) |
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: | yes |
Analytic conductor: | \(64.0959177025\) |
Analytic rank: | \(0\) |
Dimension: | \(169\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 8027.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.48779 | −1.75914 | −0.879568 | − | 0.475773i | \(-0.842168\pi\) | ||||
−0.879568 | + | 0.475773i | \(0.842168\pi\) | |||||||
\(3\) | −1.56706 | −0.904742 | −0.452371 | − | 0.891830i | \(-0.649422\pi\) | ||||
−0.452371 | + | 0.891830i | \(0.649422\pi\) | |||||||
\(4\) | 4.18912 | 2.09456 | ||||||||
\(5\) | −0.470974 | −0.210626 | −0.105313 | − | 0.994439i | \(-0.533584\pi\) | ||||
−0.105313 | + | 0.994439i | \(0.533584\pi\) | |||||||
\(6\) | 3.89852 | 1.59156 | ||||||||
\(7\) | −0.335999 | −0.126996 | −0.0634979 | − | 0.997982i | \(-0.520226\pi\) | ||||
−0.0634979 | + | 0.997982i | \(0.520226\pi\) | |||||||
\(8\) | −5.44607 | −1.92548 | ||||||||
\(9\) | −0.544327 | −0.181442 | ||||||||
\(10\) | 1.17169 | 0.370519 | ||||||||
\(11\) | 5.06537 | 1.52727 | 0.763633 | − | 0.645651i | \(-0.223414\pi\) | ||||
0.763633 | + | 0.645651i | \(0.223414\pi\) | |||||||
\(12\) | −6.56459 | −1.89503 | ||||||||
\(13\) | −0.350034 | −0.0970819 | −0.0485410 | − | 0.998821i | \(-0.515457\pi\) | ||||
−0.0485410 | + | 0.998821i | \(0.515457\pi\) | |||||||
\(14\) | 0.835897 | 0.223403 | ||||||||
\(15\) | 0.738043 | 0.190562 | ||||||||
\(16\) | 5.17047 | 1.29262 | ||||||||
\(17\) | −3.11361 | −0.755160 | −0.377580 | − | 0.925977i | \(-0.623244\pi\) | ||||
−0.377580 | + | 0.925977i | \(0.623244\pi\) | |||||||
\(18\) | 1.35417 | 0.319182 | ||||||||
\(19\) | 2.58200 | 0.592352 | 0.296176 | − | 0.955133i | \(-0.404288\pi\) | ||||
0.296176 | + | 0.955133i | \(0.404288\pi\) | |||||||
\(20\) | −1.97296 | −0.441168 | ||||||||
\(21\) | 0.526530 | 0.114898 | ||||||||
\(22\) | −12.6016 | −2.68667 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 8.53432 | 1.74206 | ||||||||
\(25\) | −4.77818 | −0.955637 | ||||||||
\(26\) | 0.870812 | 0.170780 | ||||||||
\(27\) | 5.55417 | 1.06890 | ||||||||
\(28\) | −1.40754 | −0.266000 | ||||||||
\(29\) | −9.91707 | −1.84155 | −0.920777 | − | 0.390090i | \(-0.872444\pi\) | ||||
−0.920777 | + | 0.390090i | \(0.872444\pi\) | |||||||
\(30\) | −1.83610 | −0.335224 | ||||||||
\(31\) | −8.29672 | −1.49013 | −0.745067 | − | 0.666989i | \(-0.767583\pi\) | ||||
−0.745067 | + | 0.666989i | \(0.767583\pi\) | |||||||
\(32\) | −1.97092 | −0.348413 | ||||||||
\(33\) | −7.93773 | −1.38178 | ||||||||
\(34\) | 7.74601 | 1.32843 | ||||||||
\(35\) | 0.158247 | 0.0267486 | ||||||||
\(36\) | −2.28025 | −0.380042 | ||||||||
\(37\) | 5.32250 | 0.875013 | 0.437507 | − | 0.899215i | \(-0.355862\pi\) | ||||
0.437507 | + | 0.899215i | \(0.355862\pi\) | |||||||
\(38\) | −6.42349 | −1.04203 | ||||||||
\(39\) | 0.548524 | 0.0878341 | ||||||||
\(40\) | 2.56496 | 0.405555 | ||||||||
\(41\) | −8.80884 | −1.37571 | −0.687855 | − | 0.725848i | \(-0.741448\pi\) | ||||
−0.687855 | + | 0.725848i | \(0.741448\pi\) | |||||||
\(42\) | −1.30990 | −0.202122 | ||||||||
\(43\) | −4.09651 | −0.624712 | −0.312356 | − | 0.949965i | \(-0.601118\pi\) | ||||
−0.312356 | + | 0.949965i | \(0.601118\pi\) | |||||||
\(44\) | 21.2194 | 3.19895 | ||||||||
\(45\) | 0.256364 | 0.0382164 | ||||||||
\(46\) | 2.48779 | 0.366805 | ||||||||
\(47\) | 8.33840 | 1.21628 | 0.608140 | − | 0.793830i | \(-0.291916\pi\) | ||||
0.608140 | + | 0.793830i | \(0.291916\pi\) | |||||||
\(48\) | −8.10243 | −1.16949 | ||||||||
\(49\) | −6.88710 | −0.983872 | ||||||||
\(50\) | 11.8871 | 1.68109 | ||||||||
\(51\) | 4.87920 | 0.683225 | ||||||||
\(52\) | −1.46633 | −0.203344 | ||||||||
\(53\) | 1.16674 | 0.160265 | 0.0801323 | − | 0.996784i | \(-0.474466\pi\) | ||||
0.0801323 | + | 0.996784i | \(0.474466\pi\) | |||||||
\(54\) | −13.8176 | −1.88034 | ||||||||
\(55\) | −2.38565 | −0.321681 | ||||||||
\(56\) | 1.82988 | 0.244528 | ||||||||
\(57\) | −4.04615 | −0.535926 | ||||||||
\(58\) | 24.6716 | 3.23954 | ||||||||
\(59\) | 0.831949 | 0.108311 | 0.0541553 | − | 0.998533i | \(-0.482753\pi\) | ||||
0.0541553 | + | 0.998533i | \(0.482753\pi\) | |||||||
\(60\) | 3.09175 | 0.399143 | ||||||||
\(61\) | 9.02470 | 1.15549 | 0.577747 | − | 0.816216i | \(-0.303932\pi\) | ||||
0.577747 | + | 0.816216i | \(0.303932\pi\) | |||||||
\(62\) | 20.6405 | 2.62135 | ||||||||
\(63\) | 0.182893 | 0.0230424 | ||||||||
\(64\) | −5.43770 | −0.679712 | ||||||||
\(65\) | 0.164857 | 0.0204480 | ||||||||
\(66\) | 19.7474 | 2.43074 | ||||||||
\(67\) | 5.05580 | 0.617664 | 0.308832 | − | 0.951117i | \(-0.400062\pi\) | ||||
0.308832 | + | 0.951117i | \(0.400062\pi\) | |||||||
\(68\) | −13.0433 | −1.58173 | ||||||||
\(69\) | 1.56706 | 0.188652 | ||||||||
\(70\) | −0.393685 | −0.0470544 | ||||||||
\(71\) | 14.0398 | 1.66622 | 0.833110 | − | 0.553108i | \(-0.186558\pi\) | ||||
0.833110 | + | 0.553108i | \(0.186558\pi\) | |||||||
\(72\) | 2.96445 | 0.349363 | ||||||||
\(73\) | −4.31779 | −0.505359 | −0.252679 | − | 0.967550i | \(-0.581312\pi\) | ||||
−0.252679 | + | 0.967550i | \(0.581312\pi\) | |||||||
\(74\) | −13.2413 | −1.53927 | ||||||||
\(75\) | 7.48769 | 0.864604 | ||||||||
\(76\) | 10.8163 | 1.24072 | ||||||||
\(77\) | −1.70196 | −0.193956 | ||||||||
\(78\) | −1.36461 | −0.154512 | ||||||||
\(79\) | −6.82411 | −0.767772 | −0.383886 | − | 0.923380i | \(-0.625414\pi\) | ||||
−0.383886 | + | 0.923380i | \(0.625414\pi\) | |||||||
\(80\) | −2.43516 | −0.272259 | ||||||||
\(81\) | −7.07073 | −0.785636 | ||||||||
\(82\) | 21.9146 | 2.42006 | ||||||||
\(83\) | −16.5666 | −1.81842 | −0.909209 | − | 0.416339i | \(-0.863313\pi\) | ||||
−0.909209 | + | 0.416339i | \(0.863313\pi\) | |||||||
\(84\) | 2.20570 | 0.240661 | ||||||||
\(85\) | 1.46643 | 0.159056 | ||||||||
\(86\) | 10.1913 | 1.09895 | ||||||||
\(87\) | 15.5406 | 1.66613 | ||||||||
\(88\) | −27.5864 | −2.94072 | ||||||||
\(89\) | −5.90829 | −0.626278 | −0.313139 | − | 0.949707i | \(-0.601381\pi\) | ||||
−0.313139 | + | 0.949707i | \(0.601381\pi\) | |||||||
\(90\) | −0.637780 | −0.0672279 | ||||||||
\(91\) | 0.117611 | 0.0123290 | ||||||||
\(92\) | −4.18912 | −0.436746 | ||||||||
\(93\) | 13.0014 | 1.34819 | ||||||||
\(94\) | −20.7442 | −2.13960 | ||||||||
\(95\) | −1.21606 | −0.124765 | ||||||||
\(96\) | 3.08855 | 0.315224 | ||||||||
\(97\) | 16.2984 | 1.65486 | 0.827428 | − | 0.561572i | \(-0.189803\pi\) | ||||
0.827428 | + | 0.561572i | \(0.189803\pi\) | |||||||
\(98\) | 17.1337 | 1.73076 | ||||||||
\(99\) | −2.75722 | −0.277111 | ||||||||
\(100\) | −20.0164 | −2.00164 | ||||||||
\(101\) | −16.8293 | −1.67458 | −0.837289 | − | 0.546761i | \(-0.815861\pi\) | ||||
−0.837289 | + | 0.546761i | \(0.815861\pi\) | |||||||
\(102\) | −12.1385 | −1.20189 | ||||||||
\(103\) | 18.4116 | 1.81415 | 0.907075 | − | 0.420970i | \(-0.138310\pi\) | ||||
0.907075 | + | 0.420970i | \(0.138310\pi\) | |||||||
\(104\) | 1.90631 | 0.186929 | ||||||||
\(105\) | −0.247982 | −0.0242006 | ||||||||
\(106\) | −2.90262 | −0.281927 | ||||||||
\(107\) | −6.11460 | −0.591121 | −0.295561 | − | 0.955324i | \(-0.595506\pi\) | ||||
−0.295561 | + | 0.955324i | \(0.595506\pi\) | |||||||
\(108\) | 23.2671 | 2.23887 | ||||||||
\(109\) | −18.9266 | −1.81284 | −0.906420 | − | 0.422377i | \(-0.861196\pi\) | ||||
−0.906420 | + | 0.422377i | \(0.861196\pi\) | |||||||
\(110\) | 5.93501 | 0.565881 | ||||||||
\(111\) | −8.34067 | −0.791661 | ||||||||
\(112\) | −1.73727 | −0.164157 | ||||||||
\(113\) | 4.06224 | 0.382144 | 0.191072 | − | 0.981576i | \(-0.438804\pi\) | ||||
0.191072 | + | 0.981576i | \(0.438804\pi\) | |||||||
\(114\) | 10.0660 | 0.942766 | ||||||||
\(115\) | 0.470974 | 0.0439185 | ||||||||
\(116\) | −41.5438 | −3.85724 | ||||||||
\(117\) | 0.190533 | 0.0176148 | ||||||||
\(118\) | −2.06972 | −0.190533 | ||||||||
\(119\) | 1.04617 | 0.0959021 | ||||||||
\(120\) | −4.01944 | −0.366923 | ||||||||
\(121\) | 14.6579 | 1.33254 | ||||||||
\(122\) | −22.4516 | −2.03267 | ||||||||
\(123\) | 13.8040 | 1.24466 | ||||||||
\(124\) | −34.7559 | −3.12118 | ||||||||
\(125\) | 4.60527 | 0.411908 | ||||||||
\(126\) | −0.455001 | −0.0405347 | ||||||||
\(127\) | −13.9328 | −1.23634 | −0.618168 | − | 0.786046i | \(-0.712125\pi\) | ||||
−0.618168 | + | 0.786046i | \(0.712125\pi\) | |||||||
\(128\) | 17.4697 | 1.54412 | ||||||||
\(129\) | 6.41947 | 0.565203 | ||||||||
\(130\) | −0.410129 | −0.0359707 | ||||||||
\(131\) | 7.04555 | 0.615573 | 0.307786 | − | 0.951456i | \(-0.400412\pi\) | ||||
0.307786 | + | 0.951456i | \(0.400412\pi\) | |||||||
\(132\) | −33.2521 | −2.89422 | ||||||||
\(133\) | −0.867551 | −0.0752262 | ||||||||
\(134\) | −12.5778 | −1.08655 | ||||||||
\(135\) | −2.61587 | −0.225138 | ||||||||
\(136\) | 16.9569 | 1.45404 | ||||||||
\(137\) | 2.36941 | 0.202432 | 0.101216 | − | 0.994864i | \(-0.467727\pi\) | ||||
0.101216 | + | 0.994864i | \(0.467727\pi\) | |||||||
\(138\) | −3.89852 | −0.331864 | ||||||||
\(139\) | 19.2979 | 1.63683 | 0.818415 | − | 0.574627i | \(-0.194853\pi\) | ||||
0.818415 | + | 0.574627i | \(0.194853\pi\) | |||||||
\(140\) | 0.662914 | 0.0560265 | ||||||||
\(141\) | −13.0668 | −1.10042 | ||||||||
\(142\) | −34.9282 | −2.93111 | ||||||||
\(143\) | −1.77305 | −0.148270 | ||||||||
\(144\) | −2.81443 | −0.234536 | ||||||||
\(145\) | 4.67068 | 0.387879 | ||||||||
\(146\) | 10.7418 | 0.888995 | ||||||||
\(147\) | 10.7925 | 0.890150 | ||||||||
\(148\) | 22.2966 | 1.83277 | ||||||||
\(149\) | −13.6893 | −1.12147 | −0.560736 | − | 0.827995i | \(-0.689482\pi\) | ||||
−0.560736 | + | 0.827995i | \(0.689482\pi\) | |||||||
\(150\) | −18.6278 | −1.52096 | ||||||||
\(151\) | 14.1903 | 1.15479 | 0.577395 | − | 0.816465i | \(-0.304069\pi\) | ||||
0.577395 | + | 0.816465i | \(0.304069\pi\) | |||||||
\(152\) | −14.0618 | −1.14056 | ||||||||
\(153\) | 1.69482 | 0.137018 | ||||||||
\(154\) | 4.23412 | 0.341195 | ||||||||
\(155\) | 3.90754 | 0.313861 | ||||||||
\(156\) | 2.29783 | 0.183974 | ||||||||
\(157\) | 19.8711 | 1.58589 | 0.792944 | − | 0.609295i | \(-0.208547\pi\) | ||||
0.792944 | + | 0.609295i | \(0.208547\pi\) | |||||||
\(158\) | 16.9770 | 1.35062 | ||||||||
\(159\) | −1.82836 | −0.144998 | ||||||||
\(160\) | 0.928252 | 0.0733848 | ||||||||
\(161\) | 0.335999 | 0.0264804 | ||||||||
\(162\) | 17.5905 | 1.38204 | ||||||||
\(163\) | 14.4801 | 1.13417 | 0.567085 | − | 0.823659i | \(-0.308071\pi\) | ||||
0.567085 | + | 0.823659i | \(0.308071\pi\) | |||||||
\(164\) | −36.9013 | −2.88151 | ||||||||
\(165\) | 3.73846 | 0.291039 | ||||||||
\(166\) | 41.2142 | 3.19885 | ||||||||
\(167\) | −8.90133 | −0.688805 | −0.344403 | − | 0.938822i | \(-0.611919\pi\) | ||||
−0.344403 | + | 0.938822i | \(0.611919\pi\) | |||||||
\(168\) | −2.86752 | −0.221234 | ||||||||
\(169\) | −12.8775 | −0.990575 | ||||||||
\(170\) | −3.64817 | −0.279801 | ||||||||
\(171\) | −1.40545 | −0.107478 | ||||||||
\(172\) | −17.1608 | −1.30850 | ||||||||
\(173\) | 15.4942 | 1.17800 | 0.589001 | − | 0.808132i | \(-0.299521\pi\) | ||||
0.589001 | + | 0.808132i | \(0.299521\pi\) | |||||||
\(174\) | −38.6619 | −2.93095 | ||||||||
\(175\) | 1.60547 | 0.121362 | ||||||||
\(176\) | 26.1903 | 1.97417 | ||||||||
\(177\) | −1.30371 | −0.0979931 | ||||||||
\(178\) | 14.6986 | 1.10171 | ||||||||
\(179\) | −0.645088 | −0.0482161 | −0.0241081 | − | 0.999709i | \(-0.507675\pi\) | ||||
−0.0241081 | + | 0.999709i | \(0.507675\pi\) | |||||||
\(180\) | 1.07394 | 0.0800466 | ||||||||
\(181\) | −0.656289 | −0.0487816 | −0.0243908 | − | 0.999703i | \(-0.507765\pi\) | ||||
−0.0243908 | + | 0.999703i | \(0.507765\pi\) | |||||||
\(182\) | −0.292592 | −0.0216884 | ||||||||
\(183\) | −14.1422 | −1.04542 | ||||||||
\(184\) | 5.44607 | 0.401490 | ||||||||
\(185\) | −2.50676 | −0.184300 | ||||||||
\(186\) | −32.3449 | −2.37164 | ||||||||
\(187\) | −15.7716 | −1.15333 | ||||||||
\(188\) | 34.9305 | 2.54757 | ||||||||
\(189\) | −1.86620 | −0.135746 | ||||||||
\(190\) | 3.02529 | 0.219478 | ||||||||
\(191\) | 8.97318 | 0.649276 | 0.324638 | − | 0.945838i | \(-0.394757\pi\) | ||||
0.324638 | + | 0.945838i | \(0.394757\pi\) | |||||||
\(192\) | 8.52119 | 0.614964 | ||||||||
\(193\) | −5.87251 | −0.422713 | −0.211356 | − | 0.977409i | \(-0.567788\pi\) | ||||
−0.211356 | + | 0.977409i | \(0.567788\pi\) | |||||||
\(194\) | −40.5471 | −2.91112 | ||||||||
\(195\) | −0.258340 | −0.0185001 | ||||||||
\(196\) | −28.8509 | −2.06078 | ||||||||
\(197\) | −19.5731 | −1.39453 | −0.697263 | − | 0.716816i | \(-0.745599\pi\) | ||||
−0.697263 | + | 0.716816i | \(0.745599\pi\) | |||||||
\(198\) | 6.85938 | 0.487475 | ||||||||
\(199\) | 25.5399 | 1.81048 | 0.905238 | − | 0.424905i | \(-0.139693\pi\) | ||||
0.905238 | + | 0.424905i | \(0.139693\pi\) | |||||||
\(200\) | 26.0223 | 1.84006 | ||||||||
\(201\) | −7.92273 | −0.558826 | ||||||||
\(202\) | 41.8678 | 2.94581 | ||||||||
\(203\) | 3.33213 | 0.233869 | ||||||||
\(204\) | 20.4396 | 1.43106 | ||||||||
\(205\) | 4.14873 | 0.289760 | ||||||||
\(206\) | −45.8043 | −3.19133 | ||||||||
\(207\) | 0.544327 | 0.0378333 | ||||||||
\(208\) | −1.80984 | −0.125490 | ||||||||
\(209\) | 13.0788 | 0.904679 | ||||||||
\(210\) | 0.616928 | 0.0425721 | ||||||||
\(211\) | −9.28151 | −0.638965 | −0.319483 | − | 0.947592i | \(-0.603509\pi\) | ||||
−0.319483 | + | 0.947592i | \(0.603509\pi\) | |||||||
\(212\) | 4.88763 | 0.335684 | ||||||||
\(213\) | −22.0012 | −1.50750 | ||||||||
\(214\) | 15.2119 | 1.03986 | ||||||||
\(215\) | 1.92935 | 0.131580 | ||||||||
\(216\) | −30.2484 | −2.05814 | ||||||||
\(217\) | 2.78769 | 0.189241 | ||||||||
\(218\) | 47.0855 | 3.18903 | ||||||||
\(219\) | 6.76623 | 0.457219 | ||||||||
\(220\) | −9.99378 | −0.673781 | ||||||||
\(221\) | 1.08987 | 0.0733124 | ||||||||
\(222\) | 20.7499 | 1.39264 | ||||||||
\(223\) | 16.8445 | 1.12799 | 0.563994 | − | 0.825779i | \(-0.309264\pi\) | ||||
0.563994 | + | 0.825779i | \(0.309264\pi\) | |||||||
\(224\) | 0.662228 | 0.0442470 | ||||||||
\(225\) | 2.60089 | 0.173393 | ||||||||
\(226\) | −10.1060 | −0.672242 | ||||||||
\(227\) | 1.37966 | 0.0915713 | 0.0457857 | − | 0.998951i | \(-0.485421\pi\) | ||||
0.0457857 | + | 0.998951i | \(0.485421\pi\) | |||||||
\(228\) | −16.9498 | −1.12253 | ||||||||
\(229\) | −19.7876 | −1.30760 | −0.653802 | − | 0.756665i | \(-0.726827\pi\) | ||||
−0.653802 | + | 0.756665i | \(0.726827\pi\) | |||||||
\(230\) | −1.17169 | −0.0772586 | ||||||||
\(231\) | 2.66707 | 0.175480 | ||||||||
\(232\) | 54.0091 | 3.54587 | ||||||||
\(233\) | −17.7548 | −1.16316 | −0.581578 | − | 0.813490i | \(-0.697565\pi\) | ||||
−0.581578 | + | 0.813490i | \(0.697565\pi\) | |||||||
\(234\) | −0.474007 | −0.0309868 | ||||||||
\(235\) | −3.92716 | −0.256180 | ||||||||
\(236\) | 3.48513 | 0.226863 | ||||||||
\(237\) | 10.6938 | 0.694636 | ||||||||
\(238\) | −2.60265 | −0.168705 | ||||||||
\(239\) | −8.75121 | −0.566069 | −0.283034 | − | 0.959110i | \(-0.591341\pi\) | ||||
−0.283034 | + | 0.959110i | \(0.591341\pi\) | |||||||
\(240\) | 3.81603 | 0.246324 | ||||||||
\(241\) | −9.47928 | −0.610614 | −0.305307 | − | 0.952254i | \(-0.598759\pi\) | ||||
−0.305307 | + | 0.952254i | \(0.598759\pi\) | |||||||
\(242\) | −36.4659 | −2.34412 | ||||||||
\(243\) | −5.58226 | −0.358102 | ||||||||
\(244\) | 37.8055 | 2.42025 | ||||||||
\(245\) | 3.24364 | 0.207229 | ||||||||
\(246\) | −34.3414 | −2.18953 | ||||||||
\(247\) | −0.903788 | −0.0575067 | ||||||||
\(248\) | 45.1845 | 2.86922 | ||||||||
\(249\) | 25.9608 | 1.64520 | ||||||||
\(250\) | −11.4570 | −0.724601 | ||||||||
\(251\) | −7.74307 | −0.488738 | −0.244369 | − | 0.969682i | \(-0.578581\pi\) | ||||
−0.244369 | + | 0.969682i | \(0.578581\pi\) | |||||||
\(252\) | 0.766162 | 0.0482637 | ||||||||
\(253\) | −5.06537 | −0.318457 | ||||||||
\(254\) | 34.6619 | 2.17488 | ||||||||
\(255\) | −2.29798 | −0.143905 | ||||||||
\(256\) | −32.5857 | −2.03660 | ||||||||
\(257\) | −20.1148 | −1.25472 | −0.627362 | − | 0.778728i | \(-0.715865\pi\) | ||||
−0.627362 | + | 0.778728i | \(0.715865\pi\) | |||||||
\(258\) | −15.9703 | −0.994269 | ||||||||
\(259\) | −1.78836 | −0.111123 | ||||||||
\(260\) | 0.690604 | 0.0428294 | ||||||||
\(261\) | 5.39813 | 0.334136 | ||||||||
\(262\) | −17.5279 | −1.08288 | ||||||||
\(263\) | 9.84468 | 0.607049 | 0.303524 | − | 0.952824i | \(-0.401837\pi\) | ||||
0.303524 | + | 0.952824i | \(0.401837\pi\) | |||||||
\(264\) | 43.2294 | 2.66059 | ||||||||
\(265\) | −0.549506 | −0.0337559 | ||||||||
\(266\) | 2.15829 | 0.132333 | ||||||||
\(267\) | 9.25864 | 0.566619 | ||||||||
\(268\) | 21.1793 | 1.29373 | ||||||||
\(269\) | −22.3874 | −1.36498 | −0.682492 | − | 0.730893i | \(-0.739104\pi\) | ||||
−0.682492 | + | 0.730893i | \(0.739104\pi\) | |||||||
\(270\) | 6.50774 | 0.396048 | ||||||||
\(271\) | 8.77313 | 0.532930 | 0.266465 | − | 0.963845i | \(-0.414144\pi\) | ||||
0.266465 | + | 0.963845i | \(0.414144\pi\) | |||||||
\(272\) | −16.0988 | −0.976134 | ||||||||
\(273\) | −0.184303 | −0.0111546 | ||||||||
\(274\) | −5.89460 | −0.356106 | ||||||||
\(275\) | −24.2033 | −1.45951 | ||||||||
\(276\) | 6.56459 | 0.395142 | ||||||||
\(277\) | −8.98312 | −0.539743 | −0.269872 | − | 0.962896i | \(-0.586981\pi\) | ||||
−0.269872 | + | 0.962896i | \(0.586981\pi\) | |||||||
\(278\) | −48.0093 | −2.87941 | ||||||||
\(279\) | 4.51613 | 0.270374 | ||||||||
\(280\) | −0.861823 | −0.0515038 | ||||||||
\(281\) | 6.10871 | 0.364415 | 0.182207 | − | 0.983260i | \(-0.441676\pi\) | ||||
0.182207 | + | 0.983260i | \(0.441676\pi\) | |||||||
\(282\) | 32.5074 | 1.93579 | ||||||||
\(283\) | −6.13832 | −0.364885 | −0.182443 | − | 0.983216i | \(-0.558400\pi\) | ||||
−0.182443 | + | 0.983216i | \(0.558400\pi\) | |||||||
\(284\) | 58.8144 | 3.48999 | ||||||||
\(285\) | 1.90563 | 0.112880 | ||||||||
\(286\) | 4.41098 | 0.260827 | ||||||||
\(287\) | 2.95976 | 0.174709 | ||||||||
\(288\) | 1.07283 | 0.0632169 | ||||||||
\(289\) | −7.30546 | −0.429733 | ||||||||
\(290\) | −11.6197 | −0.682331 | ||||||||
\(291\) | −25.5406 | −1.49722 | ||||||||
\(292\) | −18.0877 | −1.05850 | ||||||||
\(293\) | −0.664082 | −0.0387961 | −0.0193980 | − | 0.999812i | \(-0.506175\pi\) | ||||
−0.0193980 | + | 0.999812i | \(0.506175\pi\) | |||||||
\(294\) | −26.8495 | −1.56590 | ||||||||
\(295\) | −0.391826 | −0.0228130 | ||||||||
\(296\) | −28.9867 | −1.68482 | ||||||||
\(297\) | 28.1339 | 1.63249 | ||||||||
\(298\) | 34.0562 | 1.97282 | ||||||||
\(299\) | 0.350034 | 0.0202430 | ||||||||
\(300\) | 31.3668 | 1.81097 | ||||||||
\(301\) | 1.37642 | 0.0793357 | ||||||||
\(302\) | −35.3026 | −2.03143 | ||||||||
\(303\) | 26.3725 | 1.51506 | ||||||||
\(304\) | 13.3502 | 0.765685 | ||||||||
\(305\) | −4.25039 | −0.243377 | ||||||||
\(306\) | −4.21636 | −0.241033 | ||||||||
\(307\) | 19.5257 | 1.11439 | 0.557195 | − | 0.830382i | \(-0.311878\pi\) | ||||
0.557195 | + | 0.830382i | \(0.311878\pi\) | |||||||
\(308\) | −7.12971 | −0.406253 | ||||||||
\(309\) | −28.8521 | −1.64134 | ||||||||
\(310\) | −9.72114 | −0.552124 | ||||||||
\(311\) | −0.522895 | −0.0296507 | −0.0148253 | − | 0.999890i | \(-0.504719\pi\) | ||||
−0.0148253 | + | 0.999890i | \(0.504719\pi\) | |||||||
\(312\) | −2.98730 | −0.169123 | ||||||||
\(313\) | 21.3409 | 1.20626 | 0.603128 | − | 0.797644i | \(-0.293921\pi\) | ||||
0.603128 | + | 0.797644i | \(0.293921\pi\) | |||||||
\(314\) | −49.4352 | −2.78979 | ||||||||
\(315\) | −0.0861380 | −0.00485333 | ||||||||
\(316\) | −28.5870 | −1.60814 | ||||||||
\(317\) | −0.420362 | −0.0236099 | −0.0118049 | − | 0.999930i | \(-0.503758\pi\) | ||||
−0.0118049 | + | 0.999930i | \(0.503758\pi\) | |||||||
\(318\) | 4.54857 | 0.255071 | ||||||||
\(319\) | −50.2336 | −2.81254 | ||||||||
\(320\) | 2.56101 | 0.143165 | ||||||||
\(321\) | 9.58194 | 0.534812 | ||||||||
\(322\) | −0.835897 | −0.0465827 | ||||||||
\(323\) | −8.03934 | −0.447321 | ||||||||
\(324\) | −29.6201 | −1.64556 | ||||||||
\(325\) | 1.67253 | 0.0927751 | ||||||||
\(326\) | −36.0236 | −1.99516 | ||||||||
\(327\) | 29.6591 | 1.64015 | ||||||||
\(328\) | 47.9736 | 2.64890 | ||||||||
\(329\) | −2.80169 | −0.154462 | ||||||||
\(330\) | −9.30052 | −0.511977 | ||||||||
\(331\) | 26.2070 | 1.44047 | 0.720234 | − | 0.693731i | \(-0.244034\pi\) | ||||
0.720234 | + | 0.693731i | \(0.244034\pi\) | |||||||
\(332\) | −69.3994 | −3.80879 | ||||||||
\(333\) | −2.89718 | −0.158765 | ||||||||
\(334\) | 22.1447 | 1.21170 | ||||||||
\(335\) | −2.38115 | −0.130096 | ||||||||
\(336\) | 2.72241 | 0.148520 | ||||||||
\(337\) | 9.00093 | 0.490312 | 0.245156 | − | 0.969484i | \(-0.421161\pi\) | ||||
0.245156 | + | 0.969484i | \(0.421161\pi\) | |||||||
\(338\) | 32.0365 | 1.74256 | ||||||||
\(339\) | −6.36577 | −0.345741 | ||||||||
\(340\) | 6.14303 | 0.333153 | ||||||||
\(341\) | −42.0259 | −2.27583 | ||||||||
\(342\) | 3.49648 | 0.189068 | ||||||||
\(343\) | 4.66606 | 0.251943 | ||||||||
\(344\) | 22.3099 | 1.20287 | ||||||||
\(345\) | −0.738043 | −0.0397349 | ||||||||
\(346\) | −38.5464 | −2.07226 | ||||||||
\(347\) | 7.33953 | 0.394007 | 0.197003 | − | 0.980403i | \(-0.436879\pi\) | ||||
0.197003 | + | 0.980403i | \(0.436879\pi\) | |||||||
\(348\) | 65.1015 | 3.48981 | ||||||||
\(349\) | 1.00000 | 0.0535288 | ||||||||
\(350\) | −3.99407 | −0.213492 | ||||||||
\(351\) | −1.94415 | −0.103771 | ||||||||
\(352\) | −9.98344 | −0.532119 | ||||||||
\(353\) | −6.87289 | −0.365807 | −0.182904 | − | 0.983131i | \(-0.558550\pi\) | ||||
−0.182904 | + | 0.983131i | \(0.558550\pi\) | |||||||
\(354\) | 3.24337 | 0.172383 | ||||||||
\(355\) | −6.61238 | −0.350949 | ||||||||
\(356\) | −24.7505 | −1.31178 | ||||||||
\(357\) | −1.63941 | −0.0867667 | ||||||||
\(358\) | 1.60485 | 0.0848188 | ||||||||
\(359\) | −13.2408 | −0.698822 | −0.349411 | − | 0.936970i | \(-0.613618\pi\) | ||||
−0.349411 | + | 0.936970i | \(0.613618\pi\) | |||||||
\(360\) | −1.39618 | −0.0735849 | ||||||||
\(361\) | −12.3333 | −0.649119 | ||||||||
\(362\) | 1.63271 | 0.0858134 | ||||||||
\(363\) | −22.9698 | −1.20560 | ||||||||
\(364\) | 0.492687 | 0.0258238 | ||||||||
\(365\) | 2.03356 | 0.106442 | ||||||||
\(366\) | 35.1830 | 1.83904 | ||||||||
\(367\) | 22.2551 | 1.16171 | 0.580855 | − | 0.814007i | \(-0.302719\pi\) | ||||
0.580855 | + | 0.814007i | \(0.302719\pi\) | |||||||
\(368\) | −5.17047 | −0.269530 | ||||||||
\(369\) | 4.79489 | 0.249612 | ||||||||
\(370\) | 6.23629 | 0.324209 | ||||||||
\(371\) | −0.392025 | −0.0203529 | ||||||||
\(372\) | 54.4646 | 2.82386 | ||||||||
\(373\) | −19.0422 | −0.985966 | −0.492983 | − | 0.870039i | \(-0.664094\pi\) | ||||
−0.492983 | + | 0.870039i | \(0.664094\pi\) | |||||||
\(374\) | 39.2364 | 2.02886 | ||||||||
\(375\) | −7.21672 | −0.372670 | ||||||||
\(376\) | −45.4115 | −2.34192 | ||||||||
\(377\) | 3.47131 | 0.178782 | ||||||||
\(378\) | 4.64271 | 0.238795 | ||||||||
\(379\) | −7.15989 | −0.367779 | −0.183889 | − | 0.982947i | \(-0.558869\pi\) | ||||
−0.183889 | + | 0.982947i | \(0.558869\pi\) | |||||||
\(380\) | −5.09420 | −0.261327 | ||||||||
\(381\) | 21.8335 | 1.11856 | ||||||||
\(382\) | −22.3234 | −1.14217 | ||||||||
\(383\) | −13.1827 | −0.673603 | −0.336801 | − | 0.941576i | \(-0.609345\pi\) | ||||
−0.336801 | + | 0.941576i | \(0.609345\pi\) | |||||||
\(384\) | −27.3761 | −1.39703 | ||||||||
\(385\) | 0.801578 | 0.0408522 | ||||||||
\(386\) | 14.6096 | 0.743609 | ||||||||
\(387\) | 2.22984 | 0.113349 | ||||||||
\(388\) | 68.2761 | 3.46619 | ||||||||
\(389\) | 19.4173 | 0.984496 | 0.492248 | − | 0.870455i | \(-0.336175\pi\) | ||||
0.492248 | + | 0.870455i | \(0.336175\pi\) | |||||||
\(390\) | 0.642697 | 0.0325442 | ||||||||
\(391\) | 3.11361 | 0.157462 | ||||||||
\(392\) | 37.5077 | 1.89442 | ||||||||
\(393\) | −11.0408 | −0.556934 | ||||||||
\(394\) | 48.6938 | 2.45316 | ||||||||
\(395\) | 3.21398 | 0.161713 | ||||||||
\(396\) | −11.5503 | −0.580425 | ||||||||
\(397\) | −12.5470 | −0.629714 | −0.314857 | − | 0.949139i | \(-0.601957\pi\) | ||||
−0.314857 | + | 0.949139i | \(0.601957\pi\) | |||||||
\(398\) | −63.5380 | −3.18487 | ||||||||
\(399\) | 1.35950 | 0.0680603 | ||||||||
\(400\) | −24.7055 | −1.23527 | ||||||||
\(401\) | −14.7606 | −0.737108 | −0.368554 | − | 0.929606i | \(-0.620147\pi\) | ||||
−0.368554 | + | 0.929606i | \(0.620147\pi\) | |||||||
\(402\) | 19.7101 | 0.983051 | ||||||||
\(403\) | 2.90413 | 0.144665 | ||||||||
\(404\) | −70.4999 | −3.50750 | ||||||||
\(405\) | 3.33013 | 0.165475 | ||||||||
\(406\) | −8.28964 | −0.411408 | ||||||||
\(407\) | 26.9604 | 1.33638 | ||||||||
\(408\) | −26.5725 | −1.31553 | ||||||||
\(409\) | 24.8020 | 1.22638 | 0.613191 | − | 0.789935i | \(-0.289886\pi\) | ||||
0.613191 | + | 0.789935i | \(0.289886\pi\) | |||||||
\(410\) | −10.3212 | −0.509727 | ||||||||
\(411\) | −3.71300 | −0.183149 | ||||||||
\(412\) | 77.1284 | 3.79984 | ||||||||
\(413\) | −0.279534 | −0.0137550 | ||||||||
\(414\) | −1.35417 | −0.0665540 | ||||||||
\(415\) | 7.80242 | 0.383006 | ||||||||
\(416\) | 0.689889 | 0.0338246 | ||||||||
\(417\) | −30.2410 | −1.48091 | ||||||||
\(418\) | −32.5373 | −1.59145 | ||||||||
\(419\) | 7.75564 | 0.378888 | 0.189444 | − | 0.981892i | \(-0.439331\pi\) | ||||
0.189444 | + | 0.981892i | \(0.439331\pi\) | |||||||
\(420\) | −1.03883 | −0.0506895 | ||||||||
\(421\) | −22.3424 | −1.08890 | −0.544450 | − | 0.838793i | \(-0.683262\pi\) | ||||
−0.544450 | + | 0.838793i | \(0.683262\pi\) | |||||||
\(422\) | 23.0905 | 1.12403 | ||||||||
\(423\) | −4.53882 | −0.220685 | ||||||||
\(424\) | −6.35417 | −0.308586 | ||||||||
\(425\) | 14.8774 | 0.721659 | ||||||||
\(426\) | 54.7345 | 2.65189 | ||||||||
\(427\) | −3.03229 | −0.146743 | ||||||||
\(428\) | −25.6148 | −1.23814 | ||||||||
\(429\) | 2.77847 | 0.134146 | ||||||||
\(430\) | −4.79982 | −0.231468 | ||||||||
\(431\) | −11.6119 | −0.559325 | −0.279663 | − | 0.960098i | \(-0.590223\pi\) | ||||
−0.279663 | + | 0.960098i | \(0.590223\pi\) | |||||||
\(432\) | 28.7177 | 1.38168 | ||||||||
\(433\) | −5.55487 | −0.266950 | −0.133475 | − | 0.991052i | \(-0.542614\pi\) | ||||
−0.133475 | + | 0.991052i | \(0.542614\pi\) | |||||||
\(434\) | −6.93520 | −0.332900 | ||||||||
\(435\) | −7.31922 | −0.350930 | ||||||||
\(436\) | −79.2858 | −3.79710 | ||||||||
\(437\) | −2.58200 | −0.123514 | ||||||||
\(438\) | −16.8330 | −0.804311 | ||||||||
\(439\) | −10.5959 | −0.505716 | −0.252858 | − | 0.967503i | \(-0.581371\pi\) | ||||
−0.252858 | + | 0.967503i | \(0.581371\pi\) | |||||||
\(440\) | 12.9924 | 0.619391 | ||||||||
\(441\) | 3.74884 | 0.178516 | ||||||||
\(442\) | −2.71137 | −0.128966 | ||||||||
\(443\) | 31.3152 | 1.48783 | 0.743916 | − | 0.668273i | \(-0.232966\pi\) | ||||
0.743916 | + | 0.668273i | \(0.232966\pi\) | |||||||
\(444\) | −34.9400 | −1.65818 | ||||||||
\(445\) | 2.78265 | 0.131910 | ||||||||
\(446\) | −41.9055 | −1.98428 | ||||||||
\(447\) | 21.4520 | 1.01464 | ||||||||
\(448\) | 1.82706 | 0.0863206 | ||||||||
\(449\) | 25.1815 | 1.18839 | 0.594195 | − | 0.804321i | \(-0.297471\pi\) | ||||
0.594195 | + | 0.804321i | \(0.297471\pi\) | |||||||
\(450\) | −6.47049 | −0.305022 | ||||||||
\(451\) | −44.6200 | −2.10107 | ||||||||
\(452\) | 17.0172 | 0.800422 | ||||||||
\(453\) | −22.2370 | −1.04479 | ||||||||
\(454\) | −3.43231 | −0.161086 | ||||||||
\(455\) | −0.0553917 | −0.00259680 | ||||||||
\(456\) | 22.0356 | 1.03191 | ||||||||
\(457\) | 4.20332 | 0.196623 | 0.0983114 | − | 0.995156i | \(-0.468656\pi\) | ||||
0.0983114 | + | 0.995156i | \(0.468656\pi\) | |||||||
\(458\) | 49.2276 | 2.30025 | ||||||||
\(459\) | −17.2935 | −0.807191 | ||||||||
\(460\) | 1.97296 | 0.0919899 | ||||||||
\(461\) | −31.5623 | −1.47001 | −0.735003 | − | 0.678064i | \(-0.762819\pi\) | ||||
−0.735003 | + | 0.678064i | \(0.762819\pi\) | |||||||
\(462\) | −6.63512 | −0.308694 | ||||||||
\(463\) | −9.68047 | −0.449890 | −0.224945 | − | 0.974372i | \(-0.572220\pi\) | ||||
−0.224945 | + | 0.974372i | \(0.572220\pi\) | |||||||
\(464\) | −51.2759 | −2.38042 | ||||||||
\(465\) | −6.12334 | −0.283963 | ||||||||
\(466\) | 44.1703 | 2.04615 | ||||||||
\(467\) | −10.4946 | −0.485631 | −0.242815 | − | 0.970073i | \(-0.578071\pi\) | ||||
−0.242815 | + | 0.970073i | \(0.578071\pi\) | |||||||
\(468\) | 0.798165 | 0.0368952 | ||||||||
\(469\) | −1.69874 | −0.0784407 | ||||||||
\(470\) | 9.76998 | 0.450655 | ||||||||
\(471\) | −31.1392 | −1.43482 | ||||||||
\(472\) | −4.53086 | −0.208550 | ||||||||
\(473\) | −20.7503 | −0.954101 | ||||||||
\(474\) | −26.6039 | −1.22196 | ||||||||
\(475\) | −12.3373 | −0.566073 | ||||||||
\(476\) | 4.38252 | 0.200873 | ||||||||
\(477\) | −0.635090 | −0.0290788 | ||||||||
\(478\) | 21.7712 | 0.995792 | ||||||||
\(479\) | −9.34130 | −0.426815 | −0.213407 | − | 0.976963i | \(-0.568456\pi\) | ||||
−0.213407 | + | 0.976963i | \(0.568456\pi\) | |||||||
\(480\) | −1.45463 | −0.0663943 | ||||||||
\(481\) | −1.86305 | −0.0849480 | ||||||||
\(482\) | 23.5825 | 1.07415 | ||||||||
\(483\) | −0.526530 | −0.0239580 | ||||||||
\(484\) | 61.4038 | 2.79108 | ||||||||
\(485\) | −7.67613 | −0.348555 | ||||||||
\(486\) | 13.8875 | 0.629951 | ||||||||
\(487\) | 0.228229 | 0.0103420 | 0.00517102 | − | 0.999987i | \(-0.498354\pi\) | ||||
0.00517102 | + | 0.999987i | \(0.498354\pi\) | |||||||
\(488\) | −49.1492 | −2.22488 | ||||||||
\(489\) | −22.6912 | −1.02613 | ||||||||
\(490\) | −8.06952 | −0.364544 | ||||||||
\(491\) | −11.1342 | −0.502480 | −0.251240 | − | 0.967925i | \(-0.580838\pi\) | ||||
−0.251240 | + | 0.967925i | \(0.580838\pi\) | |||||||
\(492\) | 57.8265 | 2.60702 | ||||||||
\(493\) | 30.8778 | 1.39067 | ||||||||
\(494\) | 2.24844 | 0.101162 | ||||||||
\(495\) | 1.29858 | 0.0583666 | ||||||||
\(496\) | −42.8980 | −1.92618 | ||||||||
\(497\) | −4.71737 | −0.211603 | ||||||||
\(498\) | −64.5851 | −2.89413 | ||||||||
\(499\) | 5.02082 | 0.224763 | 0.112381 | − | 0.993665i | \(-0.464152\pi\) | ||||
0.112381 | + | 0.993665i | \(0.464152\pi\) | |||||||
\(500\) | 19.2920 | 0.862765 | ||||||||
\(501\) | 13.9489 | 0.623191 | ||||||||
\(502\) | 19.2632 | 0.859757 | ||||||||
\(503\) | 5.18423 | 0.231153 | 0.115577 | − | 0.993299i | \(-0.463128\pi\) | ||||
0.115577 | + | 0.993299i | \(0.463128\pi\) | |||||||
\(504\) | −0.996051 | −0.0443676 | ||||||||
\(505\) | 7.92615 | 0.352709 | ||||||||
\(506\) | 12.6016 | 0.560209 | ||||||||
\(507\) | 20.1798 | 0.896215 | ||||||||
\(508\) | −58.3661 | −2.58958 | ||||||||
\(509\) | 2.54684 | 0.112887 | 0.0564434 | − | 0.998406i | \(-0.482024\pi\) | ||||
0.0564434 | + | 0.998406i | \(0.482024\pi\) | |||||||
\(510\) | 5.71689 | 0.253148 | ||||||||
\(511\) | 1.45077 | 0.0641784 | ||||||||
\(512\) | 46.1269 | 2.03854 | ||||||||
\(513\) | 14.3409 | 0.633165 | ||||||||
\(514\) | 50.0414 | 2.20723 | ||||||||
\(515\) | −8.67138 | −0.382107 | ||||||||
\(516\) | 26.8919 | 1.18385 | ||||||||
\(517\) | 42.2370 | 1.85758 | ||||||||
\(518\) | 4.44906 | 0.195480 | ||||||||
\(519\) | −24.2803 | −1.06579 | ||||||||
\(520\) | −0.897822 | −0.0393721 | ||||||||
\(521\) | 12.6274 | 0.553217 | 0.276608 | − | 0.960983i | \(-0.410790\pi\) | ||||
0.276608 | + | 0.960983i | \(0.410790\pi\) | |||||||
\(522\) | −13.4294 | −0.587790 | ||||||||
\(523\) | −25.0533 | −1.09550 | −0.547751 | − | 0.836641i | \(-0.684516\pi\) | ||||
−0.547751 | + | 0.836641i | \(0.684516\pi\) | |||||||
\(524\) | 29.5146 | 1.28935 | ||||||||
\(525\) | −2.51586 | −0.109801 | ||||||||
\(526\) | −24.4915 | −1.06788 | ||||||||
\(527\) | 25.8327 | 1.12529 | ||||||||
\(528\) | −41.0418 | −1.78611 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 1.36706 | 0.0593812 | ||||||||
\(531\) | −0.452853 | −0.0196521 | ||||||||
\(532\) | −3.63427 | −0.157566 | ||||||||
\(533\) | 3.08339 | 0.133557 | ||||||||
\(534\) | −23.0336 | −0.996761 | ||||||||
\(535\) | 2.87982 | 0.124505 | ||||||||
\(536\) | −27.5342 | −1.18930 | ||||||||
\(537\) | 1.01089 | 0.0436232 | ||||||||
\(538\) | 55.6952 | 2.40119 | ||||||||
\(539\) | −34.8857 | −1.50263 | ||||||||
\(540\) | −10.9582 | −0.471565 | ||||||||
\(541\) | 2.55159 | 0.109701 | 0.0548506 | − | 0.998495i | \(-0.482532\pi\) | ||||
0.0548506 | + | 0.998495i | \(0.482532\pi\) | |||||||
\(542\) | −21.8257 | −0.937496 | ||||||||
\(543\) | 1.02844 | 0.0441347 | ||||||||
\(544\) | 6.13667 | 0.263108 | ||||||||
\(545\) | 8.91393 | 0.381831 | ||||||||
\(546\) | 0.458509 | 0.0196224 | ||||||||
\(547\) | 2.55567 | 0.109273 | 0.0546364 | − | 0.998506i | \(-0.482600\pi\) | ||||
0.0546364 | + | 0.998506i | \(0.482600\pi\) | |||||||
\(548\) | 9.92574 | 0.424006 | ||||||||
\(549\) | −4.91239 | −0.209656 | ||||||||
\(550\) | 60.2127 | 2.56748 | ||||||||
\(551\) | −25.6059 | −1.09085 | ||||||||
\(552\) | −8.53432 | −0.363245 | ||||||||
\(553\) | 2.29290 | 0.0975038 | ||||||||
\(554\) | 22.3481 | 0.949481 | ||||||||
\(555\) | 3.92823 | 0.166744 | ||||||||
\(556\) | 80.8414 | 3.42844 | ||||||||
\(557\) | 15.6981 | 0.665151 | 0.332575 | − | 0.943077i | \(-0.392082\pi\) | ||||
0.332575 | + | 0.943077i | \(0.392082\pi\) | |||||||
\(558\) | −11.2352 | −0.475624 | ||||||||
\(559\) | 1.43392 | 0.0606482 | ||||||||
\(560\) | 0.818210 | 0.0345757 | ||||||||
\(561\) | 24.7149 | 1.04347 | ||||||||
\(562\) | −15.1972 | −0.641055 | ||||||||
\(563\) | 37.3544 | 1.57430 | 0.787150 | − | 0.616761i | \(-0.211556\pi\) | ||||
0.787150 | + | 0.616761i | \(0.211556\pi\) | |||||||
\(564\) | −54.7382 | −2.30489 | ||||||||
\(565\) | −1.91321 | −0.0804893 | ||||||||
\(566\) | 15.2709 | 0.641883 | ||||||||
\(567\) | 2.37576 | 0.0997725 | ||||||||
\(568\) | −76.4619 | −3.20827 | ||||||||
\(569\) | −27.1803 | −1.13946 | −0.569728 | − | 0.821833i | \(-0.692951\pi\) | ||||
−0.569728 | + | 0.821833i | \(0.692951\pi\) | |||||||
\(570\) | −4.74081 | −0.198571 | ||||||||
\(571\) | 40.4782 | 1.69396 | 0.846980 | − | 0.531624i | \(-0.178418\pi\) | ||||
0.846980 | + | 0.531624i | \(0.178418\pi\) | |||||||
\(572\) | −7.42751 | −0.310560 | ||||||||
\(573\) | −14.0615 | −0.587427 | ||||||||
\(574\) | −7.36328 | −0.307337 | ||||||||
\(575\) | 4.77818 | 0.199264 | ||||||||
\(576\) | 2.95989 | 0.123329 | ||||||||
\(577\) | 10.7852 | 0.448992 | 0.224496 | − | 0.974475i | \(-0.427926\pi\) | ||||
0.224496 | + | 0.974475i | \(0.427926\pi\) | |||||||
\(578\) | 18.1745 | 0.755959 | ||||||||
\(579\) | 9.20257 | 0.382446 | ||||||||
\(580\) | 19.5660 | 0.812434 | ||||||||
\(581\) | 5.56636 | 0.230931 | ||||||||
\(582\) | 63.5398 | 2.63381 | ||||||||
\(583\) | 5.90999 | 0.244767 | ||||||||
\(584\) | 23.5150 | 0.973057 | ||||||||
\(585\) | −0.0897360 | −0.00371013 | ||||||||
\(586\) | 1.65210 | 0.0682476 | ||||||||
\(587\) | 5.48151 | 0.226246 | 0.113123 | − | 0.993581i | \(-0.463915\pi\) | ||||
0.113123 | + | 0.993581i | \(0.463915\pi\) | |||||||
\(588\) | 45.2110 | 1.86447 | ||||||||
\(589\) | −21.4222 | −0.882685 | ||||||||
\(590\) | 0.974783 | 0.0401312 | ||||||||
\(591\) | 30.6722 | 1.26169 | ||||||||
\(592\) | 27.5198 | 1.13106 | ||||||||
\(593\) | 25.9759 | 1.06670 | 0.533352 | − | 0.845894i | \(-0.320932\pi\) | ||||
0.533352 | + | 0.845894i | \(0.320932\pi\) | |||||||
\(594\) | −69.9913 | −2.87178 | ||||||||
\(595\) | −0.492718 | −0.0201995 | ||||||||
\(596\) | −57.3461 | −2.34899 | ||||||||
\(597\) | −40.0225 | −1.63801 | ||||||||
\(598\) | −0.870812 | −0.0356102 | ||||||||
\(599\) | 11.3592 | 0.464123 | 0.232061 | − | 0.972701i | \(-0.425453\pi\) | ||||
0.232061 | + | 0.972701i | \(0.425453\pi\) | |||||||
\(600\) | −40.7785 | −1.66478 | ||||||||
\(601\) | 36.5995 | 1.49293 | 0.746463 | − | 0.665427i | \(-0.231750\pi\) | ||||
0.746463 | + | 0.665427i | \(0.231750\pi\) | |||||||
\(602\) | −3.42426 | −0.139562 | ||||||||
\(603\) | −2.75201 | −0.112070 | ||||||||
\(604\) | 59.4449 | 2.41878 | ||||||||
\(605\) | −6.90350 | −0.280667 | ||||||||
\(606\) | −65.6093 | −2.66520 | ||||||||
\(607\) | −28.9238 | −1.17398 | −0.586991 | − | 0.809593i | \(-0.699688\pi\) | ||||
−0.586991 | + | 0.809593i | \(0.699688\pi\) | |||||||
\(608\) | −5.08893 | −0.206383 | ||||||||
\(609\) | −5.22164 | −0.211591 | ||||||||
\(610\) | 10.5741 | 0.428133 | ||||||||
\(611\) | −2.91872 | −0.118079 | ||||||||
\(612\) | 7.09980 | 0.286992 | ||||||||
\(613\) | 19.8061 | 0.799961 | 0.399980 | − | 0.916524i | \(-0.369017\pi\) | ||||
0.399980 | + | 0.916524i | \(0.369017\pi\) | |||||||
\(614\) | −48.5759 | −1.96036 | ||||||||
\(615\) | −6.50131 | −0.262158 | ||||||||
\(616\) | 9.26899 | 0.373458 | ||||||||
\(617\) | −1.36172 | −0.0548207 | −0.0274104 | − | 0.999624i | \(-0.508726\pi\) | ||||
−0.0274104 | + | 0.999624i | \(0.508726\pi\) | |||||||
\(618\) | 71.7780 | 2.88733 | ||||||||
\(619\) | 14.1234 | 0.567668 | 0.283834 | − | 0.958873i | \(-0.408394\pi\) | ||||
0.283834 | + | 0.958873i | \(0.408394\pi\) | |||||||
\(620\) | 16.3691 | 0.657400 | ||||||||
\(621\) | −5.55417 | −0.222881 | ||||||||
\(622\) | 1.30086 | 0.0521596 | ||||||||
\(623\) | 1.98518 | 0.0795346 | ||||||||
\(624\) | 2.83613 | 0.113536 | ||||||||
\(625\) | 21.7220 | 0.868878 | ||||||||
\(626\) | −53.0916 | −2.12197 | ||||||||
\(627\) | −20.4952 | −0.818501 | ||||||||
\(628\) | 83.2424 | 3.32173 | ||||||||
\(629\) | −16.5722 | −0.660775 | ||||||||
\(630\) | 0.214294 | 0.00853766 | ||||||||
\(631\) | 32.0582 | 1.27622 | 0.638109 | − | 0.769946i | \(-0.279717\pi\) | ||||
0.638109 | + | 0.769946i | \(0.279717\pi\) | |||||||
\(632\) | 37.1646 | 1.47833 | ||||||||
\(633\) | 14.5447 | 0.578099 | ||||||||
\(634\) | 1.04577 | 0.0415330 | ||||||||
\(635\) | 6.56198 | 0.260404 | ||||||||
\(636\) | −7.65920 | −0.303707 | ||||||||
\(637\) | 2.41072 | 0.0955162 | ||||||||
\(638\) | 124.971 | 4.94764 | ||||||||
\(639\) | −7.64225 | −0.302323 | ||||||||
\(640\) | −8.22777 | −0.325231 | ||||||||
\(641\) | −1.51282 | −0.0597527 | −0.0298764 | − | 0.999554i | \(-0.509511\pi\) | ||||
−0.0298764 | + | 0.999554i | \(0.509511\pi\) | |||||||
\(642\) | −23.8379 | −0.940807 | ||||||||
\(643\) | −44.9863 | −1.77409 | −0.887043 | − | 0.461687i | \(-0.847244\pi\) | ||||
−0.887043 | + | 0.461687i | \(0.847244\pi\) | |||||||
\(644\) | 1.40754 | 0.0554649 | ||||||||
\(645\) | −3.02340 | −0.119046 | ||||||||
\(646\) | 20.0002 | 0.786898 | ||||||||
\(647\) | −2.30366 | −0.0905661 | −0.0452831 | − | 0.998974i | \(-0.514419\pi\) | ||||
−0.0452831 | + | 0.998974i | \(0.514419\pi\) | |||||||
\(648\) | 38.5077 | 1.51273 | ||||||||
\(649\) | 4.21413 | 0.165419 | ||||||||
\(650\) | −4.16090 | −0.163204 | ||||||||
\(651\) | −4.36848 | −0.171214 | ||||||||
\(652\) | 60.6589 | 2.37559 | ||||||||
\(653\) | −3.63855 | −0.142387 | −0.0711937 | − | 0.997463i | \(-0.522681\pi\) | ||||
−0.0711937 | + | 0.997463i | \(0.522681\pi\) | |||||||
\(654\) | −73.7857 | −2.88525 | ||||||||
\(655\) | −3.31827 | −0.129655 | ||||||||
\(656\) | −45.5459 | −1.77827 | ||||||||
\(657\) | 2.35029 | 0.0916935 | ||||||||
\(658\) | 6.97004 | 0.271720 | ||||||||
\(659\) | 20.3199 | 0.791550 | 0.395775 | − | 0.918347i | \(-0.370476\pi\) | ||||
0.395775 | + | 0.918347i | \(0.370476\pi\) | |||||||
\(660\) | 15.6608 | 0.609598 | ||||||||
\(661\) | 8.06801 | 0.313809 | 0.156905 | − | 0.987614i | \(-0.449848\pi\) | ||||
0.156905 | + | 0.987614i | \(0.449848\pi\) | |||||||
\(662\) | −65.1977 | −2.53398 | ||||||||
\(663\) | −1.70789 | −0.0663288 | ||||||||
\(664\) | 90.2228 | 3.50132 | ||||||||
\(665\) | 0.408594 | 0.0158446 | ||||||||
\(666\) | 7.20759 | 0.279288 | ||||||||
\(667\) | 9.91707 | 0.383990 | ||||||||
\(668\) | −37.2887 | −1.44274 | ||||||||
\(669\) | −26.3962 | −1.02054 | ||||||||
\(670\) | 5.92380 | 0.228856 | ||||||||
\(671\) | 45.7134 | 1.76475 | ||||||||
\(672\) | −1.03775 | −0.0400321 | ||||||||
\(673\) | 13.5378 | 0.521844 | 0.260922 | − | 0.965360i | \(-0.415973\pi\) | ||||
0.260922 | + | 0.965360i | \(0.415973\pi\) | |||||||
\(674\) | −22.3925 | −0.862525 | ||||||||
\(675\) | −26.5388 | −1.02148 | ||||||||
\(676\) | −53.9453 | −2.07482 | ||||||||
\(677\) | −23.3595 | −0.897777 | −0.448889 | − | 0.893588i | \(-0.648180\pi\) | ||||
−0.448889 | + | 0.893588i | \(0.648180\pi\) | |||||||
\(678\) | 15.8367 | 0.608206 | ||||||||
\(679\) | −5.47626 | −0.210160 | ||||||||
\(680\) | −7.98626 | −0.306259 | ||||||||
\(681\) | −2.16201 | −0.0828484 | ||||||||
\(682\) | 104.552 | 4.00350 | ||||||||
\(683\) | 9.00578 | 0.344597 | 0.172298 | − | 0.985045i | \(-0.444881\pi\) | ||||
0.172298 | + | 0.985045i | \(0.444881\pi\) | |||||||
\(684\) | −5.88761 | −0.225119 | ||||||||
\(685\) | −1.11593 | −0.0426375 | ||||||||
\(686\) | −11.6082 | −0.443203 | ||||||||
\(687\) | 31.0084 | 1.18304 | ||||||||
\(688\) | −21.1809 | −0.807514 | ||||||||
\(689\) | −0.408400 | −0.0155588 | ||||||||
\(690\) | 1.83610 | 0.0698991 | ||||||||
\(691\) | −19.5090 | −0.742156 | −0.371078 | − | 0.928602i | \(-0.621012\pi\) | ||||
−0.371078 | + | 0.928602i | \(0.621012\pi\) | |||||||
\(692\) | 64.9070 | 2.46739 | ||||||||
\(693\) | 0.926422 | 0.0351919 | ||||||||
\(694\) | −18.2592 | −0.693112 | ||||||||
\(695\) | −9.08882 | −0.344759 | ||||||||
\(696\) | −84.6354 | −3.20810 | ||||||||
\(697\) | 27.4273 | 1.03888 | ||||||||
\(698\) | −2.48779 | −0.0941644 | ||||||||
\(699\) | 27.8228 | 1.05236 | ||||||||
\(700\) | 6.72549 | 0.254199 | ||||||||
\(701\) | 25.5272 | 0.964150 | 0.482075 | − | 0.876130i | \(-0.339883\pi\) | ||||
0.482075 | + | 0.876130i | \(0.339883\pi\) | |||||||
\(702\) | 4.83664 | 0.182547 | ||||||||
\(703\) | 13.7427 | 0.518316 | ||||||||
\(704\) | −27.5439 | −1.03810 | ||||||||
\(705\) | 6.15410 | 0.231777 | ||||||||
\(706\) | 17.0983 | 0.643504 | ||||||||
\(707\) | 5.65463 | 0.212664 | ||||||||
\(708\) | −5.46141 | −0.205252 | ||||||||
\(709\) | −33.2523 | −1.24882 | −0.624408 | − | 0.781098i | \(-0.714660\pi\) | ||||
−0.624408 | + | 0.781098i | \(0.714660\pi\) | |||||||
\(710\) | 16.4502 | 0.617366 | ||||||||
\(711\) | 3.71455 | 0.139306 | ||||||||
\(712\) | 32.1770 | 1.20588 | ||||||||
\(713\) | 8.29672 | 0.310715 | ||||||||
\(714\) | 4.07851 | 0.152634 | ||||||||
\(715\) | 0.835060 | 0.0312295 | ||||||||
\(716\) | −2.70235 | −0.100992 | ||||||||
\(717\) | 13.7137 | 0.512146 | ||||||||
\(718\) | 32.9403 | 1.22932 | ||||||||
\(719\) | −28.6719 | −1.06928 | −0.534642 | − | 0.845079i | \(-0.679553\pi\) | ||||
−0.534642 | + | 0.845079i | \(0.679553\pi\) | |||||||
\(720\) | 1.32552 | 0.0493993 | ||||||||
\(721\) | −6.18628 | −0.230389 | ||||||||
\(722\) | 30.6826 | 1.14189 | ||||||||
\(723\) | 14.8546 | 0.552448 | ||||||||
\(724\) | −2.74927 | −0.102176 | ||||||||
\(725\) | 47.3856 | 1.75986 | ||||||||
\(726\) | 57.1442 | 2.12082 | ||||||||
\(727\) | −42.9821 | −1.59412 | −0.797058 | − | 0.603902i | \(-0.793612\pi\) | ||||
−0.797058 | + | 0.603902i | \(0.793612\pi\) | |||||||
\(728\) | −0.640519 | −0.0237392 | ||||||||
\(729\) | 29.9599 | 1.10963 | ||||||||
\(730\) | −5.05909 | −0.187245 | ||||||||
\(731\) | 12.7549 | 0.471758 | ||||||||
\(732\) | −59.2435 | −2.18970 | ||||||||
\(733\) | −25.1275 | −0.928106 | −0.464053 | − | 0.885807i | \(-0.653605\pi\) | ||||
−0.464053 | + | 0.885807i | \(0.653605\pi\) | |||||||
\(734\) | −55.3662 | −2.04360 | ||||||||
\(735\) | −5.08298 | −0.187489 | ||||||||
\(736\) | 1.97092 | 0.0726491 | ||||||||
\(737\) | 25.6095 | 0.943337 | ||||||||
\(738\) | −11.9287 | −0.439102 | ||||||||
\(739\) | −2.84812 | −0.104770 | −0.0523849 | − | 0.998627i | \(-0.516682\pi\) | ||||
−0.0523849 | + | 0.998627i | \(0.516682\pi\) | |||||||
\(740\) | −10.5011 | −0.386028 | ||||||||
\(741\) | 1.41629 | 0.0520287 | ||||||||
\(742\) | 0.975278 | 0.0358036 | ||||||||
\(743\) | 8.99408 | 0.329961 | 0.164980 | − | 0.986297i | \(-0.447244\pi\) | ||||
0.164980 | + | 0.986297i | \(0.447244\pi\) | |||||||
\(744\) | −70.8068 | −2.59590 | ||||||||
\(745\) | 6.44730 | 0.236211 | ||||||||
\(746\) | 47.3730 | 1.73445 | ||||||||
\(747\) | 9.01764 | 0.329938 | ||||||||
\(748\) | −66.0689 | −2.41572 | ||||||||
\(749\) | 2.05450 | 0.0750699 | ||||||||
\(750\) | 17.9537 | 0.655577 | ||||||||
\(751\) | 18.9189 | 0.690362 | 0.345181 | − | 0.938536i | \(-0.387818\pi\) | ||||
0.345181 | + | 0.938536i | \(0.387818\pi\) | |||||||
\(752\) | 43.1135 | 1.57219 | ||||||||
\(753\) | 12.1338 | 0.442182 | ||||||||
\(754\) | −8.63590 | −0.314501 | ||||||||
\(755\) | −6.68326 | −0.243229 | ||||||||
\(756\) | −7.81772 | −0.284328 | ||||||||
\(757\) | 23.9906 | 0.871953 | 0.435976 | − | 0.899958i | \(-0.356403\pi\) | ||||
0.435976 | + | 0.899958i | \(0.356403\pi\) | |||||||
\(758\) | 17.8123 | 0.646973 | ||||||||
\(759\) | 7.93773 | 0.288121 | ||||||||
\(760\) | 6.62273 | 0.240232 | ||||||||
\(761\) | 31.3449 | 1.13625 | 0.568125 | − | 0.822942i | \(-0.307669\pi\) | ||||
0.568125 | + | 0.822942i | \(0.307669\pi\) | |||||||
\(762\) | −54.3173 | −1.96771 | ||||||||
\(763\) | 6.35932 | 0.230223 | ||||||||
\(764\) | 37.5897 | 1.35995 | ||||||||
\(765\) | −0.798215 | −0.0288595 | ||||||||
\(766\) | 32.7957 | 1.18496 | ||||||||
\(767\) | −0.291210 | −0.0105150 | ||||||||
\(768\) | 51.0636 | 1.84260 | ||||||||
\(769\) | 46.2211 | 1.66678 | 0.833388 | − | 0.552688i | \(-0.186398\pi\) | ||||
0.833388 | + | 0.552688i | \(0.186398\pi\) | |||||||
\(770\) | −1.99416 | −0.0718645 | ||||||||
\(771\) | 31.5210 | 1.13520 | ||||||||
\(772\) | −24.6007 | −0.885397 | ||||||||
\(773\) | −10.6969 | −0.384741 | −0.192370 | − | 0.981322i | \(-0.561617\pi\) | ||||
−0.192370 | + | 0.981322i | \(0.561617\pi\) | |||||||
\(774\) | −5.54738 | −0.199397 | ||||||||
\(775\) | 39.6433 | 1.42403 | ||||||||
\(776\) | −88.7625 | −3.18639 | ||||||||
\(777\) | 2.80246 | 0.100538 | ||||||||
\(778\) | −48.3062 | −1.73186 | ||||||||
\(779\) | −22.7445 | −0.814905 | ||||||||
\(780\) | −1.08222 | −0.0387496 | ||||||||
\(781\) | 71.1168 | 2.54476 | ||||||||
\(782\) | −7.74601 | −0.276997 | ||||||||
\(783\) | −55.0811 | −1.96844 | ||||||||
\(784\) | −35.6096 | −1.27177 | ||||||||
\(785\) | −9.35877 | −0.334029 | ||||||||
\(786\) | 27.4672 | 0.979723 | ||||||||
\(787\) | −16.4830 | −0.587557 | −0.293778 | − | 0.955874i | \(-0.594913\pi\) | ||||
−0.293778 | + | 0.955874i | \(0.594913\pi\) | |||||||
\(788\) | −81.9940 | −2.92092 | ||||||||
\(789\) | −15.4272 | −0.549222 | ||||||||
\(790\) | −7.99571 | −0.284475 | ||||||||
\(791\) | −1.36491 | −0.0485306 | ||||||||
\(792\) | 15.0160 | 0.533570 | ||||||||
\(793\) | −3.15895 | −0.112178 | ||||||||
\(794\) | 31.2142 | 1.10775 | ||||||||
\(795\) | 0.861108 | 0.0305403 | ||||||||
\(796\) | 106.990 | 3.79215 | ||||||||
\(797\) | 20.2229 | 0.716332 | 0.358166 | − | 0.933658i | \(-0.383402\pi\) | ||||
0.358166 | + | 0.933658i | \(0.383402\pi\) | |||||||
\(798\) | −3.38216 | −0.119727 | ||||||||
\(799\) | −25.9625 | −0.918486 | ||||||||
\(800\) | 9.41743 | 0.332956 | ||||||||
\(801\) | 3.21604 | 0.113633 | ||||||||
\(802\) | 36.7213 | 1.29667 | ||||||||
\(803\) | −21.8712 | −0.771817 | ||||||||
\(804\) | −33.1892 | −1.17049 | ||||||||
\(805\) | −0.158247 | −0.00557746 | ||||||||
\(806\) | −7.22488 | −0.254486 | ||||||||
\(807\) | 35.0824 | 1.23496 | ||||||||
\(808\) | 91.6536 | 3.22436 | ||||||||
\(809\) | 30.4746 | 1.07143 | 0.535715 | − | 0.844399i | \(-0.320042\pi\) | ||||
0.535715 | + | 0.844399i | \(0.320042\pi\) | |||||||
\(810\) | −8.28467 | −0.291093 | ||||||||
\(811\) | −36.2133 | −1.27162 | −0.635811 | − | 0.771845i | \(-0.719334\pi\) | ||||
−0.635811 | + | 0.771845i | \(0.719334\pi\) | |||||||
\(812\) | 13.9587 | 0.489853 | ||||||||
\(813\) | −13.7480 | −0.482164 | ||||||||
\(814\) | −67.0719 | −2.35087 | ||||||||
\(815\) | −6.81976 | −0.238886 | ||||||||
\(816\) | 25.2278 | 0.883149 | ||||||||
\(817\) | −10.5772 | −0.370049 | ||||||||
\(818\) | −61.7023 | −2.15737 | ||||||||
\(819\) | −0.0640189 | −0.00223700 | ||||||||
\(820\) | 17.3795 | 0.606919 | ||||||||
\(821\) | 24.4959 | 0.854912 | 0.427456 | − | 0.904036i | \(-0.359410\pi\) | ||||
0.427456 | + | 0.904036i | \(0.359410\pi\) | |||||||
\(822\) | 9.23719 | 0.322184 | ||||||||
\(823\) | 19.6961 | 0.686562 | 0.343281 | − | 0.939233i | \(-0.388462\pi\) | ||||
0.343281 | + | 0.939233i | \(0.388462\pi\) | |||||||
\(824\) | −100.271 | −3.49310 | ||||||||
\(825\) | 37.9279 | 1.32048 | ||||||||
\(826\) | 0.695424 | 0.0241969 | ||||||||
\(827\) | 2.02743 | 0.0705006 | 0.0352503 | − | 0.999379i | \(-0.488777\pi\) | ||||
0.0352503 | + | 0.999379i | \(0.488777\pi\) | |||||||
\(828\) | 2.28025 | 0.0792442 | ||||||||
\(829\) | 20.9975 | 0.729273 | 0.364637 | − | 0.931150i | \(-0.381193\pi\) | ||||
0.364637 | + | 0.931150i | \(0.381193\pi\) | |||||||
\(830\) | −19.4108 | −0.673759 | ||||||||
\(831\) | 14.0771 | 0.488328 | ||||||||
\(832\) | 1.90338 | 0.0659878 | ||||||||
\(833\) | 21.4437 | 0.742981 | ||||||||
\(834\) | 75.2334 | 2.60512 | ||||||||
\(835\) | 4.19229 | 0.145080 | ||||||||
\(836\) | 54.7886 | 1.89490 | ||||||||
\(837\) | −46.0814 | −1.59281 | ||||||||
\(838\) | −19.2944 | −0.666515 | ||||||||
\(839\) | 15.7053 | 0.542209 | 0.271104 | − | 0.962550i | \(-0.412611\pi\) | ||||
0.271104 | + | 0.962550i | \(0.412611\pi\) | |||||||
\(840\) | 1.35053 | 0.0465976 | ||||||||
\(841\) | 69.3482 | 2.39132 | ||||||||
\(842\) | 55.5832 | 1.91552 | ||||||||
\(843\) | −9.57270 | −0.329701 | ||||||||
\(844\) | −38.8813 | −1.33835 | ||||||||
\(845\) | 6.06495 | 0.208641 | ||||||||
\(846\) | 11.2916 | 0.388214 | ||||||||
\(847\) | −4.92505 | −0.169227 | ||||||||
\(848\) | 6.03262 | 0.207161 | ||||||||
\(849\) | 9.61911 | 0.330127 | ||||||||
\(850\) | −37.0119 | −1.26950 | ||||||||
\(851\) | −5.32250 | −0.182453 | ||||||||
\(852\) | −92.1657 | −3.15754 | ||||||||
\(853\) | −5.75815 | −0.197155 | −0.0985776 | − | 0.995129i | \(-0.531429\pi\) | ||||
−0.0985776 | + | 0.995129i | \(0.531429\pi\) | |||||||
\(854\) | 7.54371 | 0.258141 | ||||||||
\(855\) | 0.661932 | 0.0226376 | ||||||||
\(856\) | 33.3006 | 1.13819 | ||||||||
\(857\) | 13.2855 | 0.453822 | 0.226911 | − | 0.973915i | \(-0.427137\pi\) | ||||
0.226911 | + | 0.973915i | \(0.427137\pi\) | |||||||
\(858\) | −6.91227 | −0.235981 | ||||||||
\(859\) | 53.0647 | 1.81054 | 0.905272 | − | 0.424832i | \(-0.139667\pi\) | ||||
0.905272 | + | 0.424832i | \(0.139667\pi\) | |||||||
\(860\) | 8.08226 | 0.275603 | ||||||||
\(861\) | −4.63812 | −0.158067 | ||||||||
\(862\) | 28.8880 | 0.983929 | ||||||||
\(863\) | 20.3099 | 0.691355 | 0.345678 | − | 0.938353i | \(-0.387649\pi\) | ||||
0.345678 | + | 0.938353i | \(0.387649\pi\) | |||||||
\(864\) | −10.9468 | −0.372419 | ||||||||
\(865\) | −7.29735 | −0.248118 | ||||||||
\(866\) | 13.8194 | 0.469601 | ||||||||
\(867\) | 11.4481 | 0.388797 | ||||||||
\(868\) | 11.6780 | 0.396376 | ||||||||
\(869\) | −34.5666 | −1.17259 | ||||||||
\(870\) | 18.2087 | 0.617333 | ||||||||
\(871\) | −1.76970 | −0.0599640 | ||||||||
\(872\) | 103.076 | 3.49058 | ||||||||
\(873\) | −8.87168 | −0.300261 | ||||||||
\(874\) | 6.42349 | 0.217278 | ||||||||
\(875\) | −1.54737 | −0.0523105 | ||||||||
\(876\) | 28.3445 | 0.957673 | ||||||||
\(877\) | 54.6432 | 1.84517 | 0.922586 | − | 0.385792i | \(-0.126072\pi\) | ||||
0.922586 | + | 0.385792i | \(0.126072\pi\) | |||||||
\(878\) | 26.3605 | 0.889624 | ||||||||
\(879\) | 1.04066 | 0.0351004 | ||||||||
\(880\) | −12.3350 | −0.415811 | ||||||||
\(881\) | −44.3072 | −1.49275 | −0.746374 | − | 0.665527i | \(-0.768207\pi\) | ||||
−0.746374 | + | 0.665527i | \(0.768207\pi\) | |||||||
\(882\) | −9.32633 | −0.314034 | ||||||||
\(883\) | 13.2858 | 0.447101 | 0.223551 | − | 0.974692i | \(-0.428235\pi\) | ||||
0.223551 | + | 0.974692i | \(0.428235\pi\) | |||||||
\(884\) | 4.56558 | 0.153557 | ||||||||
\(885\) | 0.614015 | 0.0206399 | ||||||||
\(886\) | −77.9059 | −2.61730 | ||||||||
\(887\) | −0.473815 | −0.0159092 | −0.00795458 | − | 0.999968i | \(-0.502532\pi\) | ||||
−0.00795458 | + | 0.999968i | \(0.502532\pi\) | |||||||
\(888\) | 45.4239 | 1.52433 | ||||||||
\(889\) | 4.68141 | 0.157009 | ||||||||
\(890\) | −6.92266 | −0.232048 | ||||||||
\(891\) | −35.8158 | −1.19988 | ||||||||
\(892\) | 70.5634 | 2.36264 | ||||||||
\(893\) | 21.5298 | 0.720466 | ||||||||
\(894\) | −53.3680 | −1.78489 | ||||||||
\(895\) | 0.303819 | 0.0101556 | ||||||||
\(896\) | −5.86981 | −0.196097 | ||||||||
\(897\) | −0.548524 | −0.0183147 | ||||||||
\(898\) | −62.6465 | −2.09054 | ||||||||
\(899\) | 82.2791 | 2.74416 | ||||||||
\(900\) | 10.8955 | 0.363182 | ||||||||
\(901\) | −3.63278 | −0.121025 | ||||||||
\(902\) | 111.005 | 3.69608 | ||||||||
\(903\) | −2.15694 | −0.0717784 | ||||||||
\(904\) | −22.1233 | −0.735809 | ||||||||
\(905\) | 0.309095 | 0.0102747 | ||||||||
\(906\) | 55.3212 | 1.83792 | ||||||||
\(907\) | 47.3641 | 1.57270 | 0.786350 | − | 0.617781i | \(-0.211968\pi\) | ||||
0.786350 | + | 0.617781i | \(0.211968\pi\) | |||||||
\(908\) | 5.77956 | 0.191802 | ||||||||
\(909\) | 9.16064 | 0.303839 | ||||||||
\(910\) | 0.137803 | 0.00456813 | ||||||||
\(911\) | 17.7875 | 0.589325 | 0.294662 | − | 0.955601i | \(-0.404793\pi\) | ||||
0.294662 | + | 0.955601i | \(0.404793\pi\) | |||||||
\(912\) | −20.9205 | −0.692747 | ||||||||
\(913\) | −83.9158 | −2.77721 | ||||||||
\(914\) | −10.4570 | −0.345886 | ||||||||
\(915\) | 6.66062 | 0.220193 | ||||||||
\(916\) | −82.8928 | −2.73885 | ||||||||
\(917\) | −2.36730 | −0.0781751 | ||||||||
\(918\) | 43.0226 | 1.41996 | ||||||||
\(919\) | −18.3646 | −0.605793 | −0.302897 | − | 0.953023i | \(-0.597954\pi\) | ||||
−0.302897 | + | 0.953023i | \(0.597954\pi\) | |||||||
\(920\) | −2.56496 | −0.0845641 | ||||||||
\(921\) | −30.5979 | −1.00823 | ||||||||
\(922\) | 78.5206 | 2.58594 | ||||||||
\(923\) | −4.91441 | −0.161760 | ||||||||
\(924\) | 11.1727 | 0.367554 | ||||||||
\(925\) | −25.4319 | −0.836195 | ||||||||
\(926\) | 24.0830 | 0.791417 | ||||||||
\(927\) | −10.0219 | −0.329163 | ||||||||
\(928\) | 19.5458 | 0.641621 | ||||||||
\(929\) | −41.5224 | −1.36231 | −0.681153 | − | 0.732141i | \(-0.738521\pi\) | ||||
−0.681153 | + | 0.732141i | \(0.738521\pi\) | |||||||
\(930\) | 15.2336 | 0.499529 | ||||||||
\(931\) | −17.7825 | −0.582799 | ||||||||
\(932\) | −74.3770 | −2.43630 | ||||||||
\(933\) | 0.819408 | 0.0268262 | ||||||||
\(934\) | 26.1083 | 0.854291 | ||||||||
\(935\) | 7.42798 | 0.242921 | ||||||||
\(936\) | −1.03766 | −0.0339169 | ||||||||
\(937\) | 48.9662 | 1.59966 | 0.799828 | − | 0.600229i | \(-0.204924\pi\) | ||||
0.799828 | + | 0.600229i | \(0.204924\pi\) | |||||||
\(938\) | 4.22612 | 0.137988 | ||||||||
\(939\) | −33.4424 | −1.09135 | ||||||||
\(940\) | −16.4514 | −0.536584 | ||||||||
\(941\) | 27.8976 | 0.909437 | 0.454719 | − | 0.890635i | \(-0.349740\pi\) | ||||
0.454719 | + | 0.890635i | \(0.349740\pi\) | |||||||
\(942\) | 77.4679 | 2.52404 | ||||||||
\(943\) | 8.80884 | 0.286855 | ||||||||
\(944\) | 4.30157 | 0.140004 | ||||||||
\(945\) | 0.878929 | 0.0285916 | ||||||||
\(946\) | 51.6225 | 1.67839 | ||||||||
\(947\) | 21.8444 | 0.709847 | 0.354924 | − | 0.934895i | \(-0.384507\pi\) | ||||
0.354924 | + | 0.934895i | \(0.384507\pi\) | |||||||
\(948\) | 44.7975 | 1.45496 | ||||||||
\(949\) | 1.51137 | 0.0490612 | ||||||||
\(950\) | 30.6926 | 0.995800 | ||||||||
\(951\) | 0.658732 | 0.0213608 | ||||||||
\(952\) | −5.69751 | −0.184657 | ||||||||
\(953\) | 13.3513 | 0.432491 | 0.216246 | − | 0.976339i | \(-0.430619\pi\) | ||||
0.216246 | + | 0.976339i | \(0.430619\pi\) | |||||||
\(954\) | 1.57997 | 0.0511536 | ||||||||
\(955\) | −4.22613 | −0.136754 | ||||||||
\(956\) | −36.6599 | −1.18566 | ||||||||
\(957\) | 78.7190 | 2.54462 | ||||||||
\(958\) | 23.2392 | 0.750825 | ||||||||
\(959\) | −0.796120 | −0.0257080 | ||||||||
\(960\) | −4.01326 | −0.129527 | ||||||||
\(961\) | 37.8356 | 1.22050 | ||||||||
\(962\) | 4.63490 | 0.149435 | ||||||||
\(963\) | 3.32834 | 0.107254 | ||||||||
\(964\) | −39.7098 | −1.27897 | ||||||||
\(965\) | 2.76580 | 0.0890342 | ||||||||
\(966\) | 1.30990 | 0.0421453 | ||||||||
\(967\) | 18.0686 | 0.581046 | 0.290523 | − | 0.956868i | \(-0.406171\pi\) | ||||
0.290523 | + | 0.956868i | \(0.406171\pi\) | |||||||
\(968\) | −79.8282 | −2.56578 | ||||||||
\(969\) | 12.5981 | 0.404710 | ||||||||
\(970\) | 19.0966 | 0.613156 | ||||||||
\(971\) | −14.7636 | −0.473788 | −0.236894 | − | 0.971536i | \(-0.576129\pi\) | ||||
−0.236894 | + | 0.971536i | \(0.576129\pi\) | |||||||
\(972\) | −23.3848 | −0.750066 | ||||||||
\(973\) | −6.48409 | −0.207871 | ||||||||
\(974\) | −0.567786 | −0.0181931 | ||||||||
\(975\) | −2.62095 | −0.0839375 | ||||||||
\(976\) | 46.6619 | 1.49361 | ||||||||
\(977\) | 44.1532 | 1.41259 | 0.706293 | − | 0.707920i | \(-0.250366\pi\) | ||||
0.706293 | + | 0.707920i | \(0.250366\pi\) | |||||||
\(978\) | 56.4510 | 1.80511 | ||||||||
\(979\) | −29.9277 | −0.956492 | ||||||||
\(980\) | 13.5880 | 0.434053 | ||||||||
\(981\) | 10.3023 | 0.328926 | ||||||||
\(982\) | 27.6997 | 0.883931 | ||||||||
\(983\) | −50.2940 | −1.60413 | −0.802064 | − | 0.597238i | \(-0.796265\pi\) | ||||
−0.802064 | + | 0.597238i | \(0.796265\pi\) | |||||||
\(984\) | −75.1775 | −2.39657 | ||||||||
\(985\) | 9.21841 | 0.293723 | ||||||||
\(986\) | −76.8177 | −2.44637 | ||||||||
\(987\) | 4.39042 | 0.139749 | ||||||||
\(988\) | −3.78608 | −0.120451 | ||||||||
\(989\) | 4.09651 | 0.130261 | ||||||||
\(990\) | −3.23059 | −0.102675 | ||||||||
\(991\) | 34.2725 | 1.08870 | 0.544351 | − | 0.838857i | \(-0.316776\pi\) | ||||
0.544351 | + | 0.838857i | \(0.316776\pi\) | |||||||
\(992\) | 16.3522 | 0.519182 | ||||||||
\(993\) | −41.0679 | −1.30325 | ||||||||
\(994\) | 11.7358 | 0.372238 | ||||||||
\(995\) | −12.0286 | −0.381333 | ||||||||
\(996\) | 108.753 | 3.44597 | ||||||||
\(997\) | −12.4521 | −0.394361 | −0.197181 | − | 0.980367i | \(-0.563179\pi\) | ||||
−0.197181 | + | 0.980367i | \(0.563179\pi\) | |||||||
\(998\) | −12.4908 | −0.395389 | ||||||||
\(999\) | 29.5621 | 0.935302 |
(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 | 8027.2.a.e.1.13 | ✓ | 169 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8027.2.a.e.1.13 | ✓ | 169 | 1.1 | even | 1 | trivial |